LMFDB - Embedded newform 4034.2.a.d.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, 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("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.50477 q^{3} +1.00000 q^{4} +2.73541 q^{5} -1.50477 q^{6} -4.93109 q^{7} +1.00000 q^{8} -0.735674 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.50477 q^{3} +1.00000 q^{4} +2.73541 q^{5} -1.50477 q^{6} -4.93109 q^{7} +1.00000 q^{8} -0.735674 q^{9} +2.73541 q^{10} -4.98556 q^{11} -1.50477 q^{12} +0.102554 q^{13} -4.93109 q^{14} -4.11616 q^{15} +1.00000 q^{16} +7.96188 q^{17} -0.735674 q^{18} -4.05252 q^{19} +2.73541 q^{20} +7.42015 q^{21} -4.98556 q^{22} +0.735432 q^{23} -1.50477 q^{24} +2.48249 q^{25} +0.102554 q^{26} +5.62132 q^{27} -4.93109 q^{28} -7.78081 q^{29} -4.11616 q^{30} +9.44412 q^{31} +1.00000 q^{32} +7.50211 q^{33} +7.96188 q^{34} -13.4886 q^{35} -0.735674 q^{36} +5.24006 q^{37} -4.05252 q^{38} -0.154320 q^{39} +2.73541 q^{40} -4.82502 q^{41} +7.42015 q^{42} +0.575677 q^{43} -4.98556 q^{44} -2.01237 q^{45} +0.735432 q^{46} -3.55433 q^{47} -1.50477 q^{48} +17.3157 q^{49} +2.48249 q^{50} -11.9808 q^{51} +0.102554 q^{52} +9.20953 q^{53} +5.62132 q^{54} -13.6376 q^{55} -4.93109 q^{56} +6.09810 q^{57} -7.78081 q^{58} -11.4877 q^{59} -4.11616 q^{60} +8.23271 q^{61} +9.44412 q^{62} +3.62768 q^{63} +1.00000 q^{64} +0.280527 q^{65} +7.50211 q^{66} +13.2654 q^{67} +7.96188 q^{68} -1.10665 q^{69} -13.4886 q^{70} +16.2062 q^{71} -0.735674 q^{72} +8.65535 q^{73} +5.24006 q^{74} -3.73557 q^{75} -4.05252 q^{76} +24.5843 q^{77} -0.154320 q^{78} -2.06054 q^{79} +2.73541 q^{80} -6.25176 q^{81} -4.82502 q^{82} +10.5262 q^{83} +7.42015 q^{84} +21.7790 q^{85} +0.575677 q^{86} +11.7083 q^{87} -4.98556 q^{88} -4.62592 q^{89} -2.01237 q^{90} -0.505703 q^{91} +0.735432 q^{92} -14.2112 q^{93} -3.55433 q^{94} -11.0853 q^{95} -1.50477 q^{96} -15.4073 q^{97} +17.3157 q^{98} +3.66775 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) $ 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * 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
$3$	−1.50477	−0.868778	−0.434389	−	0.900725i	$-0.643036\pi$
$3$	−1.50477	−0.868778	−0.434389	+	0.900725i	$0.643036\pi$
$4$	1.00000	0.500000
$5$	2.73541	1.22331	0.611657	−	0.791123i	$-0.290503\pi$
$5$	2.73541	1.22331	0.611657	+	0.791123i	$0.290503\pi$
$6$	−1.50477	−0.614319
$7$	−4.93109	−1.86378	−0.931889	−	0.362743i	$-0.881840\pi$
$7$	−4.93109	−1.86378	−0.931889	+	0.362743i	$0.881840\pi$
$8$	1.00000	0.353553
$9$	−0.735674	−0.245225
$10$	2.73541	0.865014
$11$	−4.98556	−1.50320	−0.751601	−	0.659618i	$-0.770718\pi$
$11$	−4.98556	−1.50320	−0.751601	+	0.659618i	$0.770718\pi$
$12$	−1.50477	−0.434389
$13$	0.102554	0.0284433	0.0142217	−	0.999899i	$-0.495473\pi$
$13$	0.102554	0.0284433	0.0142217	+	0.999899i	$0.495473\pi$
$14$	−4.93109	−1.31789
$15$	−4.11616	−1.06279
$16$	1.00000	0.250000
$17$	7.96188	1.93104	0.965520	−	0.260330i	$-0.0838313\pi$
$17$	7.96188	1.93104	0.965520	+	0.260330i	$0.0838313\pi$
$18$	−0.735674	−0.173400
$19$	−4.05252	−0.929712	−0.464856	−	0.885386i	$-0.653894\pi$
$19$	−4.05252	−0.929712	−0.464856	+	0.885386i	$0.653894\pi$
$20$	2.73541	0.611657
$21$	7.42015	1.61921
$22$	−4.98556	−1.06292
$23$	0.735432	0.153348	0.0766741	−	0.997056i	$-0.475570\pi$
$23$	0.735432	0.153348	0.0766741	+	0.997056i	$0.475570\pi$
$24$	−1.50477	−0.307159
$25$	2.48249	0.496499
$26$	0.102554	0.0201125
$27$	5.62132	1.08182
$28$	−4.93109	−0.931889
$29$	−7.78081	−1.44486	−0.722430	−	0.691444i	$-0.756975\pi$
$29$	−7.78081	−1.44486	−0.722430	+	0.691444i	$0.756975\pi$
$30$	−4.11616	−0.751505
$31$	9.44412	1.69621	0.848107	−	0.529825i	$-0.177743\pi$
$31$	9.44412	1.69621	0.848107	+	0.529825i	$0.177743\pi$
$32$	1.00000	0.176777
$33$	7.50211	1.30595
$34$	7.96188	1.36545
$35$	−13.4886	−2.27999
$36$	−0.735674	−0.122612
$37$	5.24006	0.861461	0.430730	−	0.902481i	$-0.358256\pi$
$37$	5.24006	0.861461	0.430730	+	0.902481i	$0.358256\pi$
$38$	−4.05252	−0.657406
$39$	−0.154320	−0.0247109
$40$	2.73541	0.432507
$41$	−4.82502	−0.753541	−0.376771	−	0.926307i	$-0.622966\pi$
$41$	−4.82502	−0.753541	−0.376771	+	0.926307i	$0.622966\pi$
$42$	7.42015	1.14495
$43$	0.575677	0.0877899	0.0438949	−	0.999036i	$-0.486023\pi$
$43$	0.575677	0.0877899	0.0438949	+	0.999036i	$0.486023\pi$
$44$	−4.98556	−0.751601
$45$	−2.01237	−0.299987
$46$	0.735432	0.108433
$47$	−3.55433	−0.518452	−0.259226	−	0.965817i	$-0.583468\pi$
$47$	−3.55433	−0.518452	−0.259226	+	0.965817i	$0.583468\pi$
$48$	−1.50477	−0.217195
$49$	17.3157	2.47367
$50$	2.48249	0.351077
$51$	−11.9808	−1.67764
$52$	0.102554	0.0142217
$53$	9.20953	1.26503	0.632513	−	0.774550i	$-0.282024\pi$
$53$	9.20953	1.26503	0.632513	+	0.774550i	$0.282024\pi$
$54$	5.62132	0.764965
$55$	−13.6376	−1.83889
$56$	−4.93109	−0.658945
$57$	6.09810	0.807714
$58$	−7.78081	−1.02167
$59$	−11.4877	−1.49558	−0.747788	−	0.663937i	$-0.768884\pi$
$59$	−11.4877	−1.49558	−0.747788	+	0.663937i	$0.768884\pi$
$60$	−4.11616	−0.531394
$61$	8.23271	1.05409	0.527045	−	0.849837i	$-0.323300\pi$
$61$	8.23271	1.05409	0.527045	+	0.849837i	$0.323300\pi$
$62$	9.44412	1.19940
$63$	3.62768	0.457045
$64$	1.00000	0.125000
$65$	0.280527	0.0347951
$66$	7.50211	0.923446
$67$	13.2654	1.62063	0.810313	−	0.585997i	$-0.199297\pi$
$67$	13.2654	1.62063	0.810313	+	0.585997i	$0.199297\pi$
$68$	7.96188	0.965520
$69$	−1.10665	−0.133225
$70$	−13.4886	−1.61219
$71$	16.2062	1.92332	0.961662	−	0.274237i	$-0.0884254\pi$
$71$	16.2062	1.92332	0.961662	+	0.274237i	$0.0884254\pi$
$72$	−0.735674	−0.0867000
$73$	8.65535	1.01303	0.506516	−	0.862230i	$-0.330933\pi$
$73$	8.65535	1.01303	0.506516	+	0.862230i	$0.330933\pi$
$74$	5.24006	0.609145
$75$	−3.73557	−0.431347
$76$	−4.05252	−0.464856
$77$	24.5843	2.80164
$78$	−0.154320	−0.0174733
$79$	−2.06054	−0.231829	−0.115915	−	0.993259i	$-0.536980\pi$
$79$	−2.06054	−0.231829	−0.115915	+	0.993259i	$0.536980\pi$
$80$	2.73541	0.305829
$81$	−6.25176	−0.694640
$82$	−4.82502	−0.532834
$83$	10.5262	1.15540	0.577698	−	0.816250i	$-0.303951\pi$
$83$	10.5262	1.15540	0.577698	+	0.816250i	$0.303951\pi$
$84$	7.42015	0.809605
$85$	21.7790	2.36227
$86$	0.575677	0.0620768
$87$	11.7083	1.25526
$88$	−4.98556	−0.531462
$89$	−4.62592	−0.490346	−0.245173	−	0.969479i	$-0.578845\pi$
$89$	−4.62592	−0.490346	−0.245173	+	0.969479i	$0.578845\pi$
$90$	−2.01237	−0.212123
$91$	−0.505703	−0.0530120
$92$	0.735432	0.0766741
$93$	−14.2112	−1.47363
$94$	−3.55433	−0.366601
$95$	−11.0853	−1.13733
$96$	−1.50477	−0.153580
$97$	−15.4073	−1.56438	−0.782188	−	0.623042i	$-0.785897\pi$
$97$	−15.4073	−1.56438	−0.782188	+	0.623042i	$0.785897\pi$
$98$	17.3157	1.74915
$99$	3.66775	0.368622
$100$	2.48249	0.248249
$101$	13.1657	1.31004	0.655020	−	0.755612i	$-0.272660\pi$
$101$	13.1657	1.31004	0.655020	+	0.755612i	$0.272660\pi$
$102$	−11.9808	−1.18627
$103$	9.66992	0.952806	0.476403	−	0.879227i	$-0.341940\pi$
$103$	9.66992	0.952806	0.476403	+	0.879227i	$0.341940\pi$
$104$	0.102554	0.0100562
$105$	20.2972	1.98080
$106$	9.20953	0.894508
$107$	13.9644	1.34999	0.674996	−	0.737821i	$-0.264145\pi$
$107$	13.9644	1.34999	0.674996	+	0.737821i	$0.264145\pi$
$108$	5.62132	0.540912
$109$	−2.88816	−0.276635	−0.138318	−	0.990388i	$-0.544169\pi$
$109$	−2.88816	−0.276635	−0.138318	+	0.990388i	$0.544169\pi$
$110$	−13.6376	−1.30029
$111$	−7.88507	−0.748418
$112$	−4.93109	−0.465945
$113$	1.34838	0.126845	0.0634226	−	0.997987i	$-0.479798\pi$
$113$	1.34838	0.126845	0.0634226	+	0.997987i	$0.479798\pi$
$114$	6.09810	0.571140
$115$	2.01171	0.187593
$116$	−7.78081	−0.722430
$117$	−0.0754462	−0.00697500
$118$	−11.4877	−1.05753
$119$	−39.2608	−3.59903
$120$	−4.11616	−0.375753
$121$	13.8558	1.25962
$122$	8.23271	0.745355
$123$	7.26053	0.654660
$124$	9.44412	0.848107
$125$	−6.88643	−0.615941
$126$	3.62768	0.323179
$127$	−2.30339	−0.204393	−0.102196	−	0.994764i	$-0.532587\pi$
$127$	−2.30339	−0.204393	−0.102196	+	0.994764i	$0.532587\pi$
$128$	1.00000	0.0883883
$129$	−0.866260	−0.0762699
$130$	0.280527	0.0246039
$131$	−8.01865	−0.700593	−0.350296	−	0.936639i	$-0.613919\pi$
$131$	−8.01865	−0.700593	−0.350296	+	0.936639i	$0.613919\pi$
$132$	7.50211	0.652975
$133$	19.9834	1.73278
$134$	13.2654	1.14596
$135$	15.3766	1.32341
$136$	7.96188	0.682726
$137$	−6.74363	−0.576147	−0.288073	−	0.957608i	$-0.593015\pi$
$137$	−6.74363	−0.576147	−0.288073	+	0.957608i	$0.593015\pi$
$138$	−1.10665	−0.0942046
$139$	−21.5373	−1.82677	−0.913384	−	0.407100i	$-0.866540\pi$
$139$	−21.5373	−1.82677	−0.913384	+	0.407100i	$0.866540\pi$
$140$	−13.4886	−1.13999
$141$	5.34844	0.450420
$142$	16.2062	1.36000
$143$	−0.511288	−0.0427561
$144$	−0.735674	−0.0613062
$145$	−21.2837	−1.76752
$146$	8.65535	0.716322
$147$	−26.0561	−2.14907
$148$	5.24006	0.430730
$149$	−0.540345	−0.0442668	−0.0221334	−	0.999755i	$-0.507046\pi$
$149$	−0.540345	−0.0442668	−0.0221334	+	0.999755i	$0.507046\pi$
$150$	−3.73557	−0.305008
$151$	3.41149	0.277623	0.138811	−	0.990319i	$-0.455672\pi$
$151$	3.41149	0.277623	0.138811	+	0.990319i	$0.455672\pi$
$152$	−4.05252	−0.328703
$153$	−5.85735	−0.473539
$154$	24.5843	1.98106
$155$	25.8336	2.07500
$156$	−0.154320	−0.0123555
$157$	1.29208	0.103120	0.0515598	−	0.998670i	$-0.483581\pi$
$157$	1.29208	0.103120	0.0515598	+	0.998670i	$0.483581\pi$
$158$	−2.06054	−0.163928
$159$	−13.8582	−1.09903
$160$	2.73541	0.216254
$161$	−3.62648	−0.285807
$162$	−6.25176	−0.491185
$163$	−0.961834	−0.0753367	−0.0376683	−	0.999290i	$-0.511993\pi$
$163$	−0.961834	−0.0753367	−0.0376683	+	0.999290i	$0.511993\pi$
$164$	−4.82502	−0.376771
$165$	20.5214	1.59759
$166$	10.5262	0.816989
$167$	−14.0151	−1.08452	−0.542261	−	0.840210i	$-0.682432\pi$
$167$	−14.0151	−1.08452	−0.542261	+	0.840210i	$0.682432\pi$
$168$	7.42015	0.572477
$169$	−12.9895	−0.999191
$170$	21.7790	1.67038
$171$	2.98134	0.227988
$172$	0.575677	0.0438949
$173$	12.1712	0.925357	0.462679	−	0.886526i	$-0.346888\pi$
$173$	12.1712	0.925357	0.462679	+	0.886526i	$0.346888\pi$
$174$	11.7083	0.887605
$175$	−12.2414	−0.925363
$176$	−4.98556	−0.375801
$177$	17.2864	1.29932
$178$	−4.62592	−0.346727
$179$	5.98057	0.447009	0.223504	−	0.974703i	$-0.428250\pi$
$179$	5.98057	0.447009	0.223504	+	0.974703i	$0.428250\pi$
$180$	−2.01237	−0.149993
$181$	3.15793	0.234727	0.117364	−	0.993089i	$-0.462556\pi$
$181$	3.15793	0.234727	0.117364	+	0.993089i	$0.462556\pi$
$182$	−0.505703	−0.0374852
$183$	−12.3883	−0.915771
$184$	0.735432	0.0542167
$185$	14.3337	1.05384
$186$	−14.2112	−1.04202
$187$	−39.6944	−2.90274
$188$	−3.55433	−0.259226
$189$	−27.7193	−2.01628
$190$	−11.0853	−0.804214
$191$	−2.11301	−0.152892	−0.0764461	−	0.997074i	$-0.524357\pi$
$191$	−2.11301	−0.152892	−0.0764461	+	0.997074i	$0.524357\pi$
$192$	−1.50477	−0.108597
$193$	−4.86178	−0.349959	−0.174979	−	0.984572i	$-0.555986\pi$
$193$	−4.86178	−0.349959	−0.174979	+	0.984572i	$0.555986\pi$
$194$	−15.4073	−1.10618
$195$	−0.422128	−0.0302292
$196$	17.3157	1.23684
$197$	10.7814	0.768144	0.384072	−	0.923303i	$-0.374521\pi$
$197$	10.7814	0.768144	0.384072	+	0.923303i	$0.374521\pi$
$198$	3.66775	0.260655
$199$	8.11711	0.575407	0.287703	−	0.957720i	$-0.407108\pi$
$199$	8.11711	0.575407	0.287703	+	0.957720i	$0.407108\pi$
$200$	2.48249	0.175539
$201$	−19.9613	−1.40796
$202$	13.1657	0.926338
$203$	38.3679	2.69290
$204$	−11.9808	−0.838822
$205$	−13.1984	−0.921818
$206$	9.66992	0.673736
$207$	−0.541038	−0.0376047
$208$	0.102554	0.00711083
$209$	20.2041	1.39755
$210$	20.2972	1.40064
$211$	15.6956	1.08053	0.540266	−	0.841495i	$-0.318324\pi$
$211$	15.6956	1.08053	0.540266	+	0.841495i	$0.318324\pi$
$212$	9.20953	0.632513
$213$	−24.3866	−1.67094
$214$	13.9644	0.954589
$215$	1.57471	0.107395
$216$	5.62132	0.382483
$217$	−46.5698	−3.16137
$218$	−2.88816	−0.195611
$219$	−13.0243	−0.880100
$220$	−13.6376	−0.919445
$221$	0.816521	0.0549252
$222$	−7.88507	−0.529212
$223$	−17.1093	−1.14572	−0.572861	−	0.819653i	$-0.694166\pi$
$223$	−17.1093	−1.14572	−0.572861	+	0.819653i	$0.694166\pi$
$224$	−4.93109	−0.329473
$225$	−1.82631	−0.121754
$226$	1.34838	0.0896931
$227$	4.10041	0.272154	0.136077	−	0.990698i	$-0.456551\pi$
$227$	4.10041	0.272154	0.136077	+	0.990698i	$0.456551\pi$
$228$	6.09810	0.403857
$229$	4.10530	0.271286	0.135643	−	0.990758i	$-0.456690\pi$
$229$	4.10530	0.271286	0.135643	+	0.990758i	$0.456690\pi$
$230$	2.01171	0.132648
$231$	−36.9936	−2.43400
$232$	−7.78081	−0.510835
$233$	20.4431	1.33927	0.669635	−	0.742690i	$-0.266450\pi$
$233$	20.4431	1.33927	0.669635	+	0.742690i	$0.266450\pi$
$234$	−0.0754462	−0.00493207
$235$	−9.72257	−0.634230
$236$	−11.4877	−0.747788
$237$	3.10064	0.201408
$238$	−39.2608	−2.54490
$239$	26.9553	1.74359	0.871797	−	0.489866i	$-0.162954\pi$
$239$	26.9553	1.74359	0.871797	+	0.489866i	$0.162954\pi$
$240$	−4.11616	−0.265697
$241$	6.50847	0.419248	0.209624	−	0.977782i	$-0.432776\pi$
$241$	6.50847	0.419248	0.209624	+	0.977782i	$0.432776\pi$
$242$	13.8558	0.890684
$243$	−7.45652	−0.478336
$244$	8.23271	0.527045
$245$	47.3656	3.02608
$246$	7.26053	0.462915
$247$	−0.415602	−0.0264441
$248$	9.44412	0.599702
$249$	−15.8394	−1.00378
$250$	−6.88643	−0.435536
$251$	21.5456	1.35994	0.679972	−	0.733238i	$-0.261992\pi$
$251$	21.5456	1.35994	0.679972	+	0.733238i	$0.261992\pi$
$252$	3.62768	0.228522
$253$	−3.66654	−0.230513
$254$	−2.30339	−0.144527
$255$	−32.7724	−2.05229
$256$	1.00000	0.0625000
$257$	20.1535	1.25714	0.628571	−	0.777752i	$-0.283640\pi$
$257$	20.1535	1.25714	0.628571	+	0.777752i	$0.283640\pi$
$258$	−0.866260	−0.0539310
$259$	−25.8392	−1.60557
$260$	0.280527	0.0173976
$261$	5.72414	0.354315
$262$	−8.01865	−0.495394
$263$	−7.18797	−0.443229	−0.221615	−	0.975134i	$-0.571133\pi$
$263$	−7.18797	−0.443229	−0.221615	+	0.975134i	$0.571133\pi$
$264$	7.50211	0.461723
$265$	25.1919	1.54752
$266$	19.9834	1.22526
$267$	6.96093	0.426002
$268$	13.2654	0.810313
$269$	25.8220	1.57439	0.787197	−	0.616701i	$-0.211531\pi$
$269$	25.8220	1.57439	0.787197	+	0.616701i	$0.211531\pi$
$270$	15.3766	0.935793
$271$	4.19859	0.255046	0.127523	−	0.991836i	$-0.459297\pi$
$271$	4.19859	0.255046	0.127523	+	0.991836i	$0.459297\pi$
$272$	7.96188	0.482760
$273$	0.760965	0.0460557
$274$	−6.74363	−0.407397
$275$	−12.3766	−0.746338
$276$	−1.10665	−0.0666127
$277$	20.2506	1.21674	0.608370	−	0.793654i	$-0.291824\pi$
$277$	20.2506	1.21674	0.608370	+	0.793654i	$0.291824\pi$
$278$	−21.5373	−1.29172
$279$	−6.94779	−0.415953
$280$	−13.4886	−0.806097
$281$	−24.6153	−1.46843	−0.734213	−	0.678919i	$-0.762449\pi$
$281$	−24.6153	−1.46843	−0.734213	+	0.678919i	$0.762449\pi$
$282$	5.34844	0.318495
$283$	−5.39550	−0.320729	−0.160365	−	0.987058i	$-0.551267\pi$
$283$	−5.39550	−0.320729	−0.160365	+	0.987058i	$0.551267\pi$
$284$	16.2062	0.961662
$285$	16.6808	0.988088
$286$	−0.511288	−0.0302331
$287$	23.7926	1.40443
$288$	−0.735674	−0.0433500
$289$	46.3915	2.72891
$290$	−21.2837	−1.24982
$291$	23.1844	1.35910
$292$	8.65535	0.506516
$293$	−1.49306	−0.0872253	−0.0436126	−	0.999049i	$-0.513887\pi$
$293$	−1.49306	−0.0872253	−0.0436126	+	0.999049i	$0.513887\pi$
$294$	−26.0561	−1.51962
$295$	−31.4237	−1.82956
$296$	5.24006	0.304572
$297$	−28.0254	−1.62620
$298$	−0.540345	−0.0313014
$299$	0.0754213	0.00436173
$300$	−3.73557	−0.215674
$301$	−2.83872	−0.163621
$302$	3.41149	0.196309
$303$	−19.8114	−1.13813
$304$	−4.05252	−0.232428
$305$	22.5199	1.28948
$306$	−5.85735	−0.334842
$307$	14.6934	0.838596	0.419298	−	0.907849i	$-0.362276\pi$
$307$	14.6934	0.838596	0.419298	+	0.907849i	$0.362276\pi$
$308$	24.5843	1.40082
$309$	−14.5510	−0.827777
$310$	25.8336	1.46725
$311$	5.10960	0.289739	0.144870	−	0.989451i	$-0.453724\pi$
$311$	5.10960	0.289739	0.144870	+	0.989451i	$0.453724\pi$
$312$	−0.154320	−0.00873663
$313$	1.66623	0.0941808	0.0470904	−	0.998891i	$-0.485005\pi$
$313$	1.66623	0.0941808	0.0470904	+	0.998891i	$0.485005\pi$
$314$	1.29208	0.0729166
$315$	9.92320	0.559109
$316$	−2.06054	−0.115915
$317$	−15.9013	−0.893106	−0.446553	−	0.894757i	$-0.647349\pi$
$317$	−15.9013	−0.893106	−0.446553	+	0.894757i	$0.647349\pi$
$318$	−13.8582	−0.777129
$319$	38.7917	2.17192
$320$	2.73541	0.152914
$321$	−21.0132	−1.17284
$322$	−3.62648	−0.202096
$323$	−32.2657	−1.79531
$324$	−6.25176	−0.347320
$325$	0.254589	0.0141221
$326$	−0.961834	−0.0532711
$327$	4.34600	0.240335
$328$	−4.82502	−0.266417
$329$	17.5267	0.966281
$330$	20.5214	1.12966
$331$	−25.5467	−1.40417	−0.702086	−	0.712092i	$-0.747748\pi$
$331$	−25.5467	−1.40417	−0.702086	+	0.712092i	$0.747748\pi$
$332$	10.5262	0.577698
$333$	−3.85498	−0.211251
$334$	−14.0151	−0.766873
$335$	36.2864	1.98254
$336$	7.42015	0.404802
$337$	27.2088	1.48216	0.741078	−	0.671419i	$-0.234315\pi$
$337$	27.2088	1.48216	0.741078	+	0.671419i	$0.234315\pi$
$338$	−12.9895	−0.706535
$339$	−2.02900	−0.110200
$340$	21.7790	1.18113
$341$	−47.0842	−2.54975
$342$	2.98134	0.161212
$343$	−50.8677	−2.74660
$344$	0.575677	0.0310384
$345$	−3.02716	−0.162977
$346$	12.1712	0.654327
$347$	−16.3312	−0.876706	−0.438353	−	0.898803i	$-0.644438\pi$
$347$	−16.3312	−0.876706	−0.438353	+	0.898803i	$0.644438\pi$
$348$	11.7083	0.627631
$349$	7.22320	0.386649	0.193325	−	0.981135i	$-0.438073\pi$
$349$	7.22320	0.386649	0.193325	+	0.981135i	$0.438073\pi$
$350$	−12.2414	−0.654331
$351$	0.576488	0.0307707
$352$	−4.98556	−0.265731
$353$	−16.4445	−0.875251	−0.437626	−	0.899157i	$-0.644180\pi$
$353$	−16.4445	−0.875251	−0.437626	+	0.899157i	$0.644180\pi$
$354$	17.2864	0.918761
$355$	44.3307	2.35283
$356$	−4.62592	−0.245173
$357$	59.0784	3.12676
$358$	5.98057	0.316083
$359$	−7.24471	−0.382361	−0.191181	−	0.981555i	$-0.561232\pi$
$359$	−7.24471	−0.382361	−0.191181	+	0.981555i	$0.561232\pi$
$360$	−2.01237	−0.106061
$361$	−2.57706	−0.135635
$362$	3.15793	0.165977
$363$	−20.8497	−1.09433
$364$	−0.505703	−0.0265060
$365$	23.6760	1.23926
$366$	−12.3883	−0.647548
$367$	7.33536	0.382903	0.191451	−	0.981502i	$-0.438681\pi$
$367$	7.33536	0.382903	0.191451	+	0.981502i	$0.438681\pi$
$368$	0.735432	0.0383370
$369$	3.54964	0.184787
$370$	14.3337	0.745176
$371$	−45.4130	−2.35773
$372$	−14.2112	−0.736817
$373$	−1.46386	−0.0757959	−0.0378979	−	0.999282i	$-0.512066\pi$
$373$	−1.46386	−0.0757959	−0.0378979	+	0.999282i	$0.512066\pi$
$374$	−39.6944	−2.05255
$375$	10.3625	0.535116
$376$	−3.55433	−0.183301
$377$	−0.797952	−0.0410966
$378$	−27.7193	−1.42573
$379$	7.07306	0.363319	0.181659	−	0.983362i	$-0.441853\pi$
$379$	7.07306	0.363319	0.181659	+	0.983362i	$0.441853\pi$
$380$	−11.0853	−0.568665
$381$	3.46606	0.177572
$382$	−2.11301	−0.108111
$383$	−34.5437	−1.76510	−0.882551	−	0.470217i	$-0.844176\pi$
$383$	−34.5437	−1.76510	−0.882551	+	0.470217i	$0.844176\pi$
$384$	−1.50477	−0.0767899
$385$	67.2481	3.42728
$386$	−4.86178	−0.247458
$387$	−0.423510	−0.0215282
$388$	−15.4073	−0.782188
$389$	20.9113	1.06024	0.530122	−	0.847921i	$-0.322146\pi$
$389$	20.9113	1.06024	0.530122	+	0.847921i	$0.322146\pi$
$390$	−0.422128	−0.0213753
$391$	5.85542	0.296121
$392$	17.3157	0.874575
$393$	12.0662	0.608660
$394$	10.7814	0.543160
$395$	−5.63644	−0.283600
$396$	3.66775	0.184311
$397$	−38.8730	−1.95098	−0.975491	−	0.220040i	$-0.929381\pi$
$397$	−38.8730	−1.95098	−0.975491	+	0.220040i	$0.929381\pi$
$398$	8.11711	0.406874
$399$	−30.0703	−1.50540
$400$	2.48249	0.124125
$401$	−22.7453	−1.13585	−0.567923	−	0.823082i	$-0.692253\pi$
$401$	−22.7453	−1.13585	−0.567923	+	0.823082i	$0.692253\pi$
$402$	−19.9613	−0.995581
$403$	0.968530	0.0482459
$404$	13.1657	0.655020
$405$	−17.1012	−0.849763
$406$	38.3679	1.90417
$407$	−26.1246	−1.29495
$408$	−11.9808	−0.593137
$409$	−37.7598	−1.86710	−0.933550	−	0.358447i	$-0.883306\pi$
$409$	−37.7598	−1.86710	−0.933550	+	0.358447i	$0.883306\pi$
$410$	−13.1984	−0.651824
$411$	10.1476	0.500544
$412$	9.66992	0.476403
$413$	56.6471	2.78742
$414$	−0.541038	−0.0265906
$415$	28.7934	1.41341
$416$	0.102554	0.00502811
$417$	32.4086	1.58706
$418$	20.2041	0.988214
$419$	−11.5818	−0.565806	−0.282903	−	0.959149i	$-0.591297\pi$
$419$	−11.5818	−0.565806	−0.282903	+	0.959149i	$0.591297\pi$
$420$	20.2972	0.990402
$421$	13.4217	0.654134	0.327067	−	0.945001i	$-0.393940\pi$
$421$	13.4217	0.654134	0.327067	+	0.945001i	$0.393940\pi$
$422$	15.6956	0.764051
$423$	2.61483	0.127137
$424$	9.20953	0.447254
$425$	19.7653	0.958758
$426$	−24.3866	−1.18153
$427$	−40.5963	−1.96459
$428$	13.9644	0.674996
$429$	0.769370	0.0371455
$430$	1.57471	0.0759395
$431$	13.7025	0.660025	0.330013	−	0.943977i	$-0.392947\pi$
$431$	13.7025	0.660025	0.330013	+	0.943977i	$0.392947\pi$
$432$	5.62132	0.270456
$433$	23.9057	1.14884	0.574418	−	0.818562i	$-0.305228\pi$
$433$	23.9057	1.14884	0.574418	+	0.818562i	$0.305228\pi$
$434$	−46.5698	−2.23542
$435$	32.0271	1.53558
$436$	−2.88816	−0.138318
$437$	−2.98035	−0.142570
$438$	−13.0243	−0.622325
$439$	30.6347	1.46211	0.731057	−	0.682316i	$-0.239027\pi$
$439$	30.6347	1.46211	0.731057	+	0.682316i	$0.239027\pi$
$440$	−13.6376	−0.650146
$441$	−12.7387	−0.606605
$442$	0.816521	0.0388380
$443$	20.7587	0.986274	0.493137	−	0.869952i	$-0.335850\pi$
$443$	20.7587	0.986274	0.493137	+	0.869952i	$0.335850\pi$
$444$	−7.88507	−0.374209
$445$	−12.6538	−0.599848
$446$	−17.1093	−0.810148
$447$	0.813094	0.0384580
$448$	−4.93109	−0.232972
$449$	27.3002	1.28838	0.644188	−	0.764867i	$-0.277195\pi$
$449$	27.3002	1.28838	0.644188	+	0.764867i	$0.277195\pi$
$450$	−1.82631	−0.0860929
$451$	24.0554	1.13273
$452$	1.34838	0.0634226
$453$	−5.13350	−0.241193
$454$	4.10041	0.192442
$455$	−1.38331	−0.0648504
$456$	6.09810	0.285570
$457$	−34.3961	−1.60898	−0.804490	−	0.593966i	$-0.797561\pi$
$457$	−34.3961	−1.60898	−0.804490	+	0.593966i	$0.797561\pi$
$458$	4.10530	0.191828
$459$	44.7563	2.08904
$460$	2.01171	0.0937965
$461$	−36.7782	−1.71293	−0.856466	−	0.516203i	$-0.827345\pi$
$461$	−36.7782	−1.71293	−0.856466	+	0.516203i	$0.827345\pi$
$462$	−36.9936	−1.72110
$463$	−22.0291	−1.02378	−0.511890	−	0.859051i	$-0.671054\pi$
$463$	−22.0291	−1.02378	−0.511890	+	0.859051i	$0.671054\pi$
$464$	−7.78081	−0.361215
$465$	−38.8735	−1.80272
$466$	20.4431	0.947007
$467$	−23.7451	−1.09879	−0.549395	−	0.835563i	$-0.685142\pi$
$467$	−23.7451	−1.09879	−0.549395	+	0.835563i	$0.685142\pi$
$468$	−0.0754462	−0.00348750
$469$	−65.4129	−3.02049
$470$	−9.72257	−0.448469
$471$	−1.94429	−0.0895880
$472$	−11.4877	−0.528766
$473$	−2.87007	−0.131966
$474$	3.10064	0.142417
$475$	−10.0604	−0.461601
$476$	−39.2608	−1.79952
$477$	−6.77521	−0.310216
$478$	26.9553	1.23291
$479$	6.52391	0.298085	0.149043	−	0.988831i	$-0.452381\pi$
$479$	6.52391	0.298085	0.149043	+	0.988831i	$0.452381\pi$
$480$	−4.11616	−0.187876
$481$	0.537388	0.0245028
$482$	6.50847	0.296453
$483$	5.45702	0.248303
$484$	13.8558	0.629809
$485$	−42.1454	−1.91372
$486$	−7.45652	−0.338234
$487$	−23.9603	−1.08574	−0.542872	−	0.839816i	$-0.682663\pi$
$487$	−23.9603	−1.08574	−0.542872	+	0.839816i	$0.682663\pi$
$488$	8.23271	0.372677
$489$	1.44734	0.0654509
$490$	47.3656	2.13976
$491$	25.1927	1.13693	0.568465	−	0.822707i	$-0.307537\pi$
$491$	25.1927	1.13693	0.568465	+	0.822707i	$0.307537\pi$
$492$	7.26053	0.327330
$493$	−61.9499	−2.79008
$494$	−0.415602	−0.0186988
$495$	10.0328	0.450941
$496$	9.44412	0.424053
$497$	−79.9144	−3.58465
$498$	−15.8394	−0.709782
$499$	21.7355	0.973016	0.486508	−	0.873676i	$-0.338270\pi$
$499$	21.7355	0.973016	0.486508	+	0.873676i	$0.338270\pi$
$500$	−6.88643	−0.307970
$501$	21.0895	0.942209
$502$	21.5456	0.961625
$503$	−4.83712	−0.215676	−0.107838	−	0.994168i	$-0.534393\pi$
$503$	−4.83712	−0.215676	−0.107838	+	0.994168i	$0.534393\pi$
$504$	3.62768	0.161590
$505$	36.0137	1.60259
$506$	−3.66654	−0.162997
$507$	19.5462	0.868075
$508$	−2.30339	−0.102196
$509$	−20.6042	−0.913265	−0.456632	−	0.889655i	$-0.650945\pi$
$509$	−20.6042	−0.913265	−0.456632	+	0.889655i	$0.650945\pi$
$510$	−32.7724	−1.45119
$511$	−42.6804	−1.88807
$512$	1.00000	0.0441942
$513$	−22.7805	−1.00579
$514$	20.1535	0.888934
$515$	26.4512	1.16558
$516$	−0.866260	−0.0381350
$517$	17.7203	0.779339
$518$	−25.8392	−1.13531
$519$	−18.3148	−0.803930
$520$	0.280527	0.0123019
$521$	11.0010	0.481962	0.240981	−	0.970530i	$-0.422531\pi$
$521$	11.0010	0.481962	0.240981	+	0.970530i	$0.422531\pi$
$522$	5.72414	0.250539
$523$	30.7617	1.34512	0.672559	−	0.740044i	$-0.265195\pi$
$523$	30.7617	1.34512	0.672559	+	0.740044i	$0.265195\pi$
$524$	−8.01865	−0.350296
$525$	18.4205	0.803935
$526$	−7.18797	−0.313410
$527$	75.1929	3.27546
$528$	7.50211	0.326487
$529$	−22.4591	−0.976484
$530$	25.1919	1.09426
$531$	8.45123	0.366752
$532$	19.9834	0.866389
$533$	−0.494824	−0.0214332
$534$	6.96093	0.301229
$535$	38.1985	1.65147
$536$	13.2654	0.572978
$537$	−8.99936	−0.388351
$538$	25.8220	1.11326
$539$	−86.3284	−3.71843
$540$	15.3766	0.661705
$541$	39.1575	1.68351	0.841757	−	0.539857i	$-0.181522\pi$
$541$	39.1575	1.68351	0.841757	+	0.539857i	$0.181522\pi$
$542$	4.19859	0.180345
$543$	−4.75195	−0.203926
$544$	7.96188	0.341363
$545$	−7.90030	−0.338412
$546$	0.760965	0.0325663
$547$	9.21363	0.393946	0.196973	−	0.980409i	$-0.436889\pi$
$547$	9.21363	0.393946	0.196973	+	0.980409i	$0.436889\pi$
$548$	−6.74363	−0.288073
$549$	−6.05659	−0.258489
$550$	−12.3766	−0.527740
$551$	31.5319	1.34330
$552$	−1.10665	−0.0471023
$553$	10.1607	0.432078
$554$	20.2506	0.860365
$555$	−21.5689	−0.915551
$556$	−21.5373	−0.913384
$557$	−23.9606	−1.01524	−0.507622	−	0.861580i	$-0.669476\pi$
$557$	−23.9606	−1.01524	−0.507622	+	0.861580i	$0.669476\pi$
$558$	−6.94779	−0.294123
$559$	0.0590378	0.00249703
$560$	−13.4886	−0.569997
$561$	59.7309	2.52184
$562$	−24.6153	−1.03833
$563$	−12.1851	−0.513542	−0.256771	−	0.966472i	$-0.582659\pi$
$563$	−12.1851	−0.513542	−0.256771	+	0.966472i	$0.582659\pi$
$564$	5.34844	0.225210
$565$	3.68839	0.155172
$566$	−5.39550	−0.226790
$567$	30.8280	1.29466
$568$	16.2062	0.679998
$569$	−12.3570	−0.518032	−0.259016	−	0.965873i	$-0.583398\pi$
$569$	−12.3570	−0.518032	−0.259016	+	0.965873i	$0.583398\pi$
$570$	16.6808	0.698684
$571$	−21.6717	−0.906934	−0.453467	−	0.891273i	$-0.649813\pi$
$571$	−21.6717	−0.906934	−0.453467	+	0.891273i	$0.649813\pi$
$572$	−0.511288	−0.0213780
$573$	3.17959	0.132829
$574$	23.7926	0.993085
$575$	1.82570	0.0761371
$576$	−0.735674	−0.0306531
$577$	27.4282	1.14185	0.570925	−	0.821002i	$-0.306585\pi$
$577$	27.4282	1.14185	0.570925	+	0.821002i	$0.306585\pi$
$578$	46.3915	1.92963
$579$	7.31585	0.304037
$580$	−21.2837	−0.883759
$581$	−51.9055	−2.15340
$582$	23.1844	0.961026
$583$	−45.9146	−1.90159
$584$	8.65535	0.358161
$585$	−0.206377	−0.00853262
$586$	−1.49306	−0.0616776
$587$	24.8615	1.02614	0.513072	−	0.858346i	$-0.328507\pi$
$587$	24.8615	1.02614	0.513072	+	0.858346i	$0.328507\pi$
$588$	−26.0561	−1.07454
$589$	−38.2725	−1.57699
$590$	−31.4237	−1.29369
$591$	−16.2235	−0.667347
$592$	5.24006	0.215365
$593$	3.92197	0.161056	0.0805280	−	0.996752i	$-0.474339\pi$
$593$	3.92197	0.161056	0.0805280	+	0.996752i	$0.474339\pi$
$594$	−28.0254	−1.14990
$595$	−107.395	−4.40275
$596$	−0.540345	−0.0221334
$597$	−12.2144	−0.499901
$598$	0.0754213	0.00308421
$599$	29.8645	1.22023	0.610115	−	0.792313i	$-0.291123\pi$
$599$	29.8645	1.22023	0.610115	+	0.792313i	$0.291123\pi$
$600$	−3.73557	−0.152504
$601$	9.15211	0.373322	0.186661	−	0.982424i	$-0.440233\pi$
$601$	9.15211	0.373322	0.186661	+	0.982424i	$0.440233\pi$
$602$	−2.83872	−0.115697
$603$	−9.75901	−0.397418
$604$	3.41149	0.138811
$605$	37.9013	1.54091
$606$	−19.8114	−0.804782
$607$	33.3457	1.35346	0.676730	−	0.736231i	$-0.263396\pi$
$607$	33.3457	1.35346	0.676730	+	0.736231i	$0.263396\pi$
$608$	−4.05252	−0.164351
$609$	−57.7348	−2.33953
$610$	22.5199	0.911803
$611$	−0.364510	−0.0147465
$612$	−5.85735	−0.236769
$613$	5.23266	0.211345	0.105673	−	0.994401i	$-0.466300\pi$
$613$	5.23266	0.211345	0.105673	+	0.994401i	$0.466300\pi$
$614$	14.6934	0.592977
$615$	19.8606	0.800855
$616$	24.5843	0.990528
$617$	21.3102	0.857916	0.428958	−	0.903324i	$-0.358881\pi$
$617$	21.3102	0.857916	0.428958	+	0.903324i	$0.358881\pi$
$618$	−14.5510	−0.585327
$619$	−5.08649	−0.204443	−0.102222	−	0.994762i	$-0.532595\pi$
$619$	−5.08649	−0.204443	−0.102222	+	0.994762i	$0.532595\pi$
$620$	25.8336	1.03750
$621$	4.13410	0.165896
$622$	5.10960	0.204876
$623$	22.8108	0.913897
$624$	−0.154320	−0.00617773
$625$	−31.2497	−1.24999
$626$	1.66623	0.0665959
$627$	−30.4025	−1.21416
$628$	1.29208	0.0515598
$629$	41.7207	1.66351
$630$	9.92320	0.395350
$631$	4.86892	0.193829	0.0969143	−	0.995293i	$-0.469103\pi$
$631$	4.86892	0.193829	0.0969143	+	0.995293i	$0.469103\pi$
$632$	−2.06054	−0.0819640
$633$	−23.6183	−0.938742
$634$	−15.9013	−0.631521
$635$	−6.30072	−0.250037
$636$	−13.8582	−0.549513
$637$	1.77579	0.0703594
$638$	38.7917	1.53578
$639$	−11.9225	−0.471647
$640$	2.73541	0.108127
$641$	−4.65497	−0.183860	−0.0919301	−	0.995765i	$-0.529304\pi$
$641$	−4.65497	−0.183860	−0.0919301	+	0.995765i	$0.529304\pi$
$642$	−21.0132	−0.829326
$643$	27.2027	1.07277	0.536385	−	0.843973i	$-0.319790\pi$
$643$	27.2027	1.07277	0.536385	+	0.843973i	$0.319790\pi$
$644$	−3.62648	−0.142903
$645$	−2.36958	−0.0933021
$646$	−32.2657	−1.26948
$647$	4.73464	0.186138	0.0930690	−	0.995660i	$-0.470332\pi$
$647$	4.73464	0.186138	0.0930690	+	0.995660i	$0.470332\pi$
$648$	−6.25176	−0.245592
$649$	57.2728	2.24815
$650$	0.254589	0.00998581
$651$	70.0768	2.74653
$652$	−0.961834	−0.0376683
$653$	36.3752	1.42347	0.711736	−	0.702447i	$-0.247909\pi$
$653$	36.3752	1.42347	0.711736	+	0.702447i	$0.247909\pi$
$654$	4.34600	0.169942
$655$	−21.9343	−0.857045
$656$	−4.82502	−0.188385
$657$	−6.36752	−0.248421
$658$	17.5267	0.683264
$659$	4.56390	0.177784	0.0888922	−	0.996041i	$-0.471667\pi$
$659$	4.56390	0.177784	0.0888922	+	0.996041i	$0.471667\pi$
$660$	20.5214	0.798793
$661$	36.8544	1.43347	0.716736	−	0.697345i	$-0.245635\pi$
$661$	36.8544	1.43347	0.716736	+	0.697345i	$0.245635\pi$
$662$	−25.5467	−0.992900
$663$	−1.22867	−0.0477178
$664$	10.5262	0.408494
$665$	54.6628	2.11973
$666$	−3.85498	−0.149377
$667$	−5.72225	−0.221567
$668$	−14.0151	−0.542261
$669$	25.7455	0.995378
$670$	36.2864	1.40186
$671$	−41.0447	−1.58451
$672$	7.42015	0.286239
$673$	−37.5732	−1.44834	−0.724170	−	0.689622i	$-0.757777\pi$
$673$	−37.5732	−1.44834	−0.724170	+	0.689622i	$0.757777\pi$
$674$	27.2088	1.04804
$675$	13.9549	0.537124
$676$	−12.9895	−0.499595
$677$	−6.25448	−0.240379	−0.120190	−	0.992751i	$-0.538350\pi$
$677$	−6.25448	−0.240379	−0.120190	+	0.992751i	$0.538350\pi$
$678$	−2.02900	−0.0779234
$679$	75.9750	2.91565
$680$	21.7790	0.835188
$681$	−6.17016	−0.236441
$682$	−47.0842	−1.80295
$683$	25.2672	0.966821	0.483410	−	0.875394i	$-0.339398\pi$
$683$	25.2672	0.966821	0.483410	+	0.875394i	$0.339398\pi$
$684$	2.98134	0.113994
$685$	−18.4466	−0.704809
$686$	−50.8677	−1.94214
$687$	−6.17753	−0.235687
$688$	0.575677	0.0219475
$689$	0.944472	0.0359815
$690$	−3.02716	−0.115242
$691$	19.2786	0.733393	0.366697	−	0.930341i	$-0.380489\pi$
$691$	19.2786	0.733393	0.366697	+	0.930341i	$0.380489\pi$
$692$	12.1712	0.462679
$693$	−18.0860	−0.687030
$694$	−16.3312	−0.619924
$695$	−58.9134	−2.23471
$696$	11.7083	0.443802
$697$	−38.4162	−1.45512
$698$	7.22320	0.273402
$699$	−30.7621	−1.16353
$700$	−12.2414	−0.462682
$701$	−16.6584	−0.629180	−0.314590	−	0.949228i	$-0.601867\pi$
$701$	−16.6584	−0.629180	−0.314590	+	0.949228i	$0.601867\pi$
$702$	0.576488	0.0217581
$703$	−21.2355	−0.800911
$704$	−4.98556	−0.187900
$705$	14.6302	0.551005
$706$	−16.4445	−0.618896
$707$	−64.9215	−2.44162
$708$	17.2864	0.649662
$709$	−8.52198	−0.320050	−0.160025	−	0.987113i	$-0.551157\pi$
$709$	−8.52198	−0.320050	−0.160025	+	0.987113i	$0.551157\pi$
$710$	44.3307	1.66370
$711$	1.51589	0.0568502
$712$	−4.62592	−0.173364
$713$	6.94550	0.260111
$714$	59.0784	2.21095
$715$	−1.39858	−0.0523041
$716$	5.98057	0.223504
$717$	−40.5615	−1.51480
$718$	−7.24471	−0.270370
$719$	35.2173	1.31338	0.656691	−	0.754159i	$-0.271955\pi$
$719$	35.2173	1.31338	0.656691	+	0.754159i	$0.271955\pi$
$720$	−2.01237	−0.0749967
$721$	−47.6833	−1.77582
$722$	−2.57706	−0.0959083
$723$	−9.79374	−0.364233
$724$	3.15793	0.117364
$725$	−19.3158	−0.717371
$726$	−20.8497	−0.773807
$727$	51.1741	1.89794	0.948970	−	0.315365i	$-0.102127\pi$
$727$	51.1741	1.89794	0.948970	+	0.315365i	$0.102127\pi$
$728$	−0.505703	−0.0187426
$729$	29.9756	1.11021
$730$	23.6760	0.876287
$731$	4.58347	0.169526
$732$	−12.3883	−0.457885
$733$	−50.3526	−1.85982	−0.929908	−	0.367793i	$-0.880114\pi$
$733$	−50.3526	−1.85982	−0.929908	+	0.367793i	$0.880114\pi$
$734$	7.33536	0.270753
$735$	−71.2742	−2.62899
$736$	0.735432	0.0271084
$737$	−66.1354	−2.43613
$738$	3.54964	0.130664
$739$	−41.9777	−1.54417	−0.772086	−	0.635518i	$-0.780787\pi$
$739$	−41.9777	−1.54417	−0.772086	+	0.635518i	$0.780787\pi$
$740$	14.3337	0.526919
$741$	0.625384	0.0229741
$742$	−45.4130	−1.66717
$743$	42.0807	1.54379	0.771896	−	0.635749i	$-0.219309\pi$
$743$	42.0807	1.54379	0.771896	+	0.635749i	$0.219309\pi$
$744$	−14.2112	−0.521008
$745$	−1.47807	−0.0541522
$746$	−1.46386	−0.0535958
$747$	−7.74383	−0.283332
$748$	−39.6944	−1.45137
$749$	−68.8599	−2.51609
$750$	10.3625	0.378384
$751$	−3.43268	−0.125260	−0.0626301	−	0.998037i	$-0.519949\pi$
$751$	−3.43268	−0.125260	−0.0626301	+	0.998037i	$0.519949\pi$
$752$	−3.55433	−0.129613
$753$	−32.4211	−1.18149
$754$	−0.797952	−0.0290597
$755$	9.33184	0.339620
$756$	−27.7193	−1.00814
$757$	34.3171	1.24728	0.623638	−	0.781713i	$-0.285654\pi$
$757$	34.3171	1.24728	0.623638	+	0.781713i	$0.285654\pi$
$758$	7.07306	0.256905
$759$	5.51729	0.200265
$760$	−11.0853	−0.402107
$761$	−2.62723	−0.0952370	−0.0476185	−	0.998866i	$-0.515163\pi$
$761$	−2.62723	−0.0952370	−0.0476185	+	0.998866i	$0.515163\pi$
$762$	3.46606	0.125562
$763$	14.2418	0.515587
$764$	−2.11301	−0.0764461
$765$	−16.0223	−0.579287
$766$	−34.5437	−1.24812
$767$	−1.17811	−0.0425391
$768$	−1.50477	−0.0542986
$769$	17.3270	0.624828	0.312414	−	0.949946i	$-0.398862\pi$
$769$	17.3270	0.624828	0.312414	+	0.949946i	$0.398862\pi$
$770$	67.2481	2.42345
$771$	−30.3264	−1.09218
$772$	−4.86178	−0.174979
$773$	−6.32441	−0.227473	−0.113737	−	0.993511i	$-0.536282\pi$
$773$	−6.32441	−0.227473	−0.113737	+	0.993511i	$0.536282\pi$
$774$	−0.423510	−0.0152228
$775$	23.4450	0.842167
$776$	−15.4073	−0.553091
$777$	38.8820	1.39489
$778$	20.9113	0.749706
$779$	19.5535	0.700577
$780$	−0.422128	−0.0151146
$781$	−80.7970	−2.89115
$782$	5.85542	0.209389
$783$	−43.7384	−1.56308
$784$	17.3157	0.618418
$785$	3.53439	0.126148
$786$	12.0662	0.430387
$787$	20.0519	0.714772	0.357386	−	0.933957i	$-0.383668\pi$
$787$	20.0519	0.714772	0.357386	+	0.933957i	$0.383668\pi$
$788$	10.7814	0.384072
$789$	10.8162	0.385068
$790$	−5.63644	−0.200535
$791$	−6.64901	−0.236411
$792$	3.66775	0.130328
$793$	0.844296	0.0299818
$794$	−38.8730	−1.37955
$795$	−37.9079	−1.34446
$796$	8.11711	0.287703
$797$	−8.65621	−0.306619	−0.153309	−	0.988178i	$-0.548993\pi$
$797$	−8.65621	−0.306619	−0.153309	+	0.988178i	$0.548993\pi$
$798$	−30.0703	−1.06448
$799$	−28.2992	−1.00115
$800$	2.48249	0.0877694
$801$	3.40317	0.120245
$802$	−22.7453	−0.803164
$803$	−43.1518	−1.52279
$804$	−19.9613	−0.703982
$805$	−9.91994	−0.349632
$806$	0.968530	0.0341150
$807$	−38.8561	−1.36780
$808$	13.1657	0.463169
$809$	−44.8620	−1.57726	−0.788631	−	0.614867i	$-0.789210\pi$
$809$	−44.8620	−1.57726	−0.788631	+	0.614867i	$0.789210\pi$
$810$	−17.1012	−0.600873
$811$	−26.4432	−0.928546	−0.464273	−	0.885692i	$-0.653684\pi$
$811$	−26.4432	−0.928546	−0.464273	+	0.885692i	$0.653684\pi$
$812$	38.3679	1.34645
$813$	−6.31791	−0.221579
$814$	−26.1246	−0.915668
$815$	−2.63102	−0.0921605
$816$	−11.9808	−0.419411
$817$	−2.33294	−0.0816193
$818$	−37.7598	−1.32024
$819$	0.372032	0.0129999
$820$	−13.1984	−0.460909
$821$	9.95956	0.347591	0.173795	−	0.984782i	$-0.444397\pi$
$821$	9.95956	0.347591	0.173795	+	0.984782i	$0.444397\pi$
$822$	10.1476	0.353938
$823$	−11.0022	−0.383513	−0.191756	−	0.981443i	$-0.561418\pi$
$823$	−11.0022	−0.383513	−0.191756	+	0.981443i	$0.561418\pi$
$824$	9.66992	0.336868
$825$	18.6239	0.648402
$826$	56.6471	1.97101
$827$	−52.1893	−1.81480	−0.907399	−	0.420270i	$-0.861935\pi$
$827$	−52.1893	−1.81480	−0.907399	+	0.420270i	$0.861935\pi$
$828$	−0.541038	−0.0188024
$829$	−47.4591	−1.64832	−0.824162	−	0.566354i	$-0.808354\pi$
$829$	−47.4591	−1.64832	−0.824162	+	0.566354i	$0.808354\pi$
$830$	28.7934	0.999434
$831$	−30.4724	−1.05708
$832$	0.102554	0.00355541
$833$	137.865	4.77676
$834$	32.4086	1.12222
$835$	−38.3371	−1.32671
$836$	20.2041	0.698773
$837$	53.0884	1.83500
$838$	−11.5818	−0.400085
$839$	−18.7226	−0.646376	−0.323188	−	0.946335i	$-0.604755\pi$
$839$	−18.7226	−0.646376	−0.323188	+	0.946335i	$0.604755\pi$
$840$	20.2972	0.700320
$841$	31.5410	1.08762
$842$	13.4217	0.462542
$843$	37.0403	1.27574
$844$	15.6956	0.540266
$845$	−35.5316	−1.22232
$846$	2.61483	0.0898997
$847$	−68.3242	−2.34765
$848$	9.20953	0.316256
$849$	8.11898	0.278643
$850$	19.7653	0.677944
$851$	3.85371	0.132103
$852$	−24.3866	−0.835471
$853$	9.10498	0.311748	0.155874	−	0.987777i	$-0.450181\pi$
$853$	9.10498	0.311748	0.155874	+	0.987777i	$0.450181\pi$
$854$	−40.5963	−1.38918
$855$	8.15519	0.278902
$856$	13.9644	0.477294
$857$	56.5667	1.93228	0.966141	−	0.258014i	$-0.0830681\pi$
$857$	56.5667	1.93228	0.966141	+	0.258014i	$0.0830681\pi$
$858$	0.769370	0.0262659
$859$	17.4765	0.596289	0.298145	−	0.954521i	$-0.403632\pi$
$859$	17.4765	0.596289	0.298145	+	0.954521i	$0.403632\pi$
$860$	1.57471	0.0536973
$861$	−35.8024	−1.22014
$862$	13.7025	0.466708
$863$	33.9452	1.15551	0.577754	−	0.816211i	$-0.303929\pi$
$863$	33.9452	1.15551	0.577754	+	0.816211i	$0.303929\pi$
$864$	5.62132	0.191241
$865$	33.2932	1.13200
$866$	23.9057	0.812350
$867$	−69.8085	−2.37082
$868$	−46.5698	−1.58068
$869$	10.2730	0.348486
$870$	32.0271	1.08582
$871$	1.36042	0.0460960
$872$	−2.88816	−0.0978053
$873$	11.3348	0.383624
$874$	−2.98035	−0.100812
$875$	33.9576	1.14798
$876$	−13.0243	−0.440050
$877$	−24.4296	−0.824928	−0.412464	−	0.910974i	$-0.635332\pi$
$877$	−24.4296	−0.824928	−0.412464	+	0.910974i	$0.635332\pi$
$878$	30.6347	1.03387
$879$	2.24670	0.0757794
$880$	−13.6376	−0.459722
$881$	4.28019	0.144203	0.0721016	−	0.997397i	$-0.477029\pi$
$881$	4.28019	0.144203	0.0721016	+	0.997397i	$0.477029\pi$
$882$	−12.7387	−0.428935
$883$	−11.8656	−0.399308	−0.199654	−	0.979866i	$-0.563982\pi$
$883$	−11.8656	−0.399308	−0.199654	+	0.979866i	$0.563982\pi$
$884$	0.816521	0.0274626
$885$	47.2854	1.58948
$886$	20.7587	0.697401
$887$	−19.2943	−0.647839	−0.323919	−	0.946085i	$-0.605001\pi$
$887$	−19.2943	−0.647839	−0.323919	+	0.946085i	$0.605001\pi$
$888$	−7.88507	−0.264606
$889$	11.3582	0.380943
$890$	−12.6538	−0.424157
$891$	31.1685	1.04418
$892$	−17.1093	−0.572861
$893$	14.4040	0.482012
$894$	0.813094	0.0271939
$895$	16.3593	0.546832
$896$	−4.93109	−0.164736
$897$	−0.113492	−0.00378937
$898$	27.3002	0.911019
$899$	−73.4829	−2.45079
$900$	−1.82631	−0.0608768
$901$	73.3251	2.44281
$902$	24.0554	0.800958
$903$	4.27161	0.142150
$904$	1.34838	0.0448466
$905$	8.63825	0.287145
$906$	−5.13350	−0.170549
$907$	−1.32649	−0.0440452	−0.0220226	−	0.999757i	$-0.507011\pi$
$907$	−1.32649	−0.0440452	−0.0220226	+	0.999757i	$0.507011\pi$
$908$	4.10041	0.136077
$909$	−9.68569	−0.321254
$910$	−1.38331	−0.0458562
$911$	−11.7523	−0.389372	−0.194686	−	0.980866i	$-0.562369\pi$
$911$	−11.7523	−0.389372	−0.194686	+	0.980866i	$0.562369\pi$
$912$	6.09810	0.201928
$913$	−52.4788	−1.73679
$914$	−34.3961	−1.13772
$915$	−33.8872	−1.12028
$916$	4.10530	0.135643
$917$	39.5407	1.30575
$918$	44.7563	1.47718
$919$	−10.0337	−0.330980	−0.165490	−	0.986211i	$-0.552921\pi$
$919$	−10.0337	−0.330980	−0.165490	+	0.986211i	$0.552921\pi$
$920$	2.01171	0.0663241
$921$	−22.1101	−0.728554
$922$	−36.7782	−1.21123
$923$	1.66201	0.0547057
$924$	−36.9936	−1.21700
$925$	13.0084	0.427714
$926$	−22.0291	−0.723922
$927$	−7.11391	−0.233652
$928$	−7.78081	−0.255418
$929$	15.1084	0.495690	0.247845	−	0.968800i	$-0.420278\pi$
$929$	15.1084	0.495690	0.247845	+	0.968800i	$0.420278\pi$
$930$	−38.8735	−1.27471
$931$	−70.1722	−2.29980
$932$	20.4431	0.669635
$933$	−7.68877	−0.251719
$934$	−23.7451	−0.776962
$935$	−108.581	−3.55097
$936$	−0.0754462	−0.00246604
$937$	−39.0853	−1.27686	−0.638430	−	0.769680i	$-0.720416\pi$
$937$	−39.0853	−1.27686	−0.638430	+	0.769680i	$0.720416\pi$
$938$	−65.4129	−2.13581
$939$	−2.50729	−0.0818222
$940$	−9.72257	−0.317115
$941$	−47.9201	−1.56215	−0.781075	−	0.624437i	$-0.785328\pi$
$941$	−47.9201	−1.56215	−0.781075	+	0.624437i	$0.785328\pi$
$942$	−1.94429	−0.0633483
$943$	−3.54847	−0.115554
$944$	−11.4877	−0.373894
$945$	−75.8237	−2.46654
$946$	−2.87007	−0.0933140
$947$	−29.6186	−0.962476	−0.481238	−	0.876590i	$-0.659813\pi$
$947$	−29.6186	−0.962476	−0.481238	+	0.876590i	$0.659813\pi$
$948$	3.10064	0.100704
$949$	0.887639	0.0288140
$950$	−10.0604	−0.326401
$951$	23.9278	0.775911
$952$	−39.2608	−1.27245
$953$	−37.8402	−1.22577	−0.612883	−	0.790174i	$-0.709990\pi$
$953$	−37.8402	−1.22577	−0.612883	+	0.790174i	$0.709990\pi$
$954$	−6.77521	−0.219355
$955$	−5.77996	−0.187035
$956$	26.9553	0.871797
$957$	−58.3725	−1.88691
$958$	6.52391	0.210778
$959$	33.2535	1.07381
$960$	−4.11616	−0.132849
$961$	58.1913	1.87714
$962$	0.537388	0.0173261
$963$	−10.2733	−0.331051
$964$	6.50847	0.209624
$965$	−13.2990	−0.428110
$966$	5.45702	0.175577
$967$	−38.9251	−1.25175	−0.625874	−	0.779924i	$-0.715258\pi$
$967$	−38.9251	−1.25175	−0.625874	+	0.779924i	$0.715258\pi$
$968$	13.8558	0.445342
$969$	48.5524	1.55973
$970$	−42.1454	−1.35321
$971$	−14.4657	−0.464228	−0.232114	−	0.972689i	$-0.574564\pi$
$971$	−14.4657	−0.464228	−0.232114	+	0.972689i	$0.574564\pi$
$972$	−7.45652	−0.239168
$973$	106.202	3.40469
$974$	−23.9603	−0.767737
$975$	−0.383097	−0.0122689
$976$	8.23271	0.263523
$977$	−49.6445	−1.58827	−0.794134	−	0.607743i	$-0.792075\pi$
$977$	−49.6445	−1.58827	−0.794134	+	0.607743i	$0.792075\pi$
$978$	1.44734	0.0462807
$979$	23.0628	0.737090
$980$	47.3656	1.51304
$981$	2.12474	0.0678378
$982$	25.1927	0.803931
$983$	6.82300	0.217620	0.108810	−	0.994063i	$-0.465296\pi$
$983$	6.82300	0.217620	0.108810	+	0.994063i	$0.465296\pi$
$984$	7.26053	0.231457
$985$	29.4917	0.939682
$986$	−61.9499	−1.97289
$987$	−26.3737	−0.839483
$988$	−0.415602	−0.0132221
$989$	0.423371	0.0134624
$990$	10.0328	0.318864
$991$	31.4288	0.998368	0.499184	−	0.866496i	$-0.333633\pi$
$991$	31.4288	0.998368	0.499184	+	0.866496i	$0.333633\pi$
$992$	9.44412	0.299851
$993$	38.4418	1.21991
$994$	−79.9144	−2.53473
$995$	22.2037	0.703903
$996$	−15.8394	−0.501892
$997$	−23.5005	−0.744269	−0.372134	−	0.928179i	$-0.621374\pi$
$997$	−23.5005	−0.744269	−0.372134	+	0.928179i	$0.621374\pi$
$998$	21.7355	0.688026
$999$	29.4561	0.931949

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.13	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.13	✓	52	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.50477 q^{3} +1.00000 q^{4} +2.73541 q^{5} -1.50477 q^{6} -4.93109 q^{7} +1.00000 q^{8} -0.735674 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.50477 q^{3} +1.00000 q^{4} +2.73541 q^{5} -1.50477 q^{6} -4.93109 q^{7} +1.00000 q^{8} -0.735674 q^{9} +2.73541 q^{10} -4.98556 q^{11} -1.50477 q^{12} +0.102554 q^{13} -4.93109 q^{14} -4.11616 q^{15} +1.00000 q^{16} +7.96188 q^{17} -0.735674 q^{18} -4.05252 q^{19} +2.73541 q^{20} +7.42015 q^{21} -4.98556 q^{22} +0.735432 q^{23} -1.50477 q^{24} +2.48249 q^{25} +0.102554 q^{26} +5.62132 q^{27} -4.93109 q^{28} -7.78081 q^{29} -4.11616 q^{30} +9.44412 q^{31} +1.00000 q^{32} +7.50211 q^{33} +7.96188 q^{34} -13.4886 q^{35} -0.735674 q^{36} +5.24006 q^{37} -4.05252 q^{38} -0.154320 q^{39} +2.73541 q^{40} -4.82502 q^{41} +7.42015 q^{42} +0.575677 q^{43} -4.98556 q^{44} -2.01237 q^{45} +0.735432 q^{46} -3.55433 q^{47} -1.50477 q^{48} +17.3157 q^{49} +2.48249 q^{50} -11.9808 q^{51} +0.102554 q^{52} +9.20953 q^{53} +5.62132 q^{54} -13.6376 q^{55} -4.93109 q^{56} +6.09810 q^{57} -7.78081 q^{58} -11.4877 q^{59} -4.11616 q^{60} +8.23271 q^{61} +9.44412 q^{62} +3.62768 q^{63} +1.00000 q^{64} +0.280527 q^{65} +7.50211 q^{66} +13.2654 q^{67} +7.96188 q^{68} -1.10665 q^{69} -13.4886 q^{70} +16.2062 q^{71} -0.735674 q^{72} +8.65535 q^{73} +5.24006 q^{74} -3.73557 q^{75} -4.05252 q^{76} +24.5843 q^{77} -0.154320 q^{78} -2.06054 q^{79} +2.73541 q^{80} -6.25176 q^{81} -4.82502 q^{82} +10.5262 q^{83} +7.42015 q^{84} +21.7790 q^{85} +0.575677 q^{86} +11.7083 q^{87} -4.98556 q^{88} -4.62592 q^{89} -2.01237 q^{90} -0.505703 q^{91} +0.735432 q^{92} -14.2112 q^{93} -3.55433 q^{94} -11.0853 q^{95} -1.50477 q^{96} -15.4073 q^{97} +17.3157 q^{98} +3.66775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

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