LMFDB - Embedded newform 5054.2.a.v.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.17557$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.175571 q^{3} +1.00000 q^{4} -0.284079 q^{5} -0.175571 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.96917 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.175571 q^{3} +1.00000 q^{4} -0.284079 q^{5} -0.175571 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.96917 q^{9} +0.284079 q^{10} +4.80423 q^{11} +0.175571 q^{12} +0.108509 q^{13} -1.00000 q^{14} -0.0498759 q^{15} +1.00000 q^{16} +2.45965 q^{17} +2.96917 q^{18} -0.284079 q^{20} +0.175571 q^{21} -4.80423 q^{22} -2.80423 q^{23} -0.175571 q^{24} -4.91930 q^{25} -0.108509 q^{26} -1.04801 q^{27} +1.00000 q^{28} -0.648859 q^{29} +0.0498759 q^{30} -8.08831 q^{31} -1.00000 q^{32} +0.843480 q^{33} -2.45965 q^{34} -0.284079 q^{35} -2.96917 q^{36} +2.39144 q^{37} +0.0190509 q^{39} +0.284079 q^{40} -11.0201 q^{41} -0.175571 q^{42} +3.04988 q^{43} +4.80423 q^{44} +0.843480 q^{45} +2.80423 q^{46} -2.73497 q^{47} +0.175571 q^{48} +1.00000 q^{49} +4.91930 q^{50} +0.431842 q^{51} +0.108509 q^{52} -6.93835 q^{53} +1.04801 q^{54} -1.36478 q^{55} -1.00000 q^{56} +0.648859 q^{58} +6.20930 q^{59} -0.0498759 q^{60} -5.42412 q^{61} +8.08831 q^{62} -2.96917 q^{63} +1.00000 q^{64} -0.0308250 q^{65} -0.843480 q^{66} -10.1921 q^{67} +2.45965 q^{68} -0.492339 q^{69} +0.284079 q^{70} -1.90025 q^{71} +2.96917 q^{72} +13.6341 q^{73} -2.39144 q^{74} -0.863684 q^{75} +4.80423 q^{77} -0.0190509 q^{78} +5.32251 q^{79} -0.284079 q^{80} +8.72353 q^{81} +11.0201 q^{82} -10.8576 q^{83} +0.175571 q^{84} -0.698735 q^{85} -3.04988 q^{86} -0.113921 q^{87} -4.80423 q^{88} +4.83203 q^{89} -0.843480 q^{90} +0.108509 q^{91} -2.80423 q^{92} -1.42007 q^{93} +2.73497 q^{94} -0.175571 q^{96} +7.50702 q^{97} -1.00000 q^{98} -14.2646 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 4 q^{11} - 4 q^{12} + 2 q^{13} - 4 q^{14} - 2 q^{15} + 4 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{20} - 4 q^{21} - 4 q^{22} + 4 q^{23} + 4 q^{24} - 4 q^{25} - 2 q^{26} - 10 q^{27} + 4 q^{28} - 12 q^{29} + 2 q^{30} - 14 q^{31} - 4 q^{32} - 4 q^{33} - 2 q^{34} + 2 q^{35} + 2 q^{36} - 24 q^{37} - 12 q^{39} - 2 q^{40} + 4 q^{42} + 14 q^{43} + 4 q^{44} - 4 q^{45} - 4 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 4 q^{50} + 8 q^{51} + 2 q^{52} + 10 q^{54} - 18 q^{55} - 4 q^{56} + 12 q^{58} - 2 q^{59} - 2 q^{60} + 2 q^{61} + 14 q^{62} + 2 q^{63} + 4 q^{64} - 14 q^{65} + 4 q^{66} - 22 q^{67} + 2 q^{68} - 4 q^{69} - 2 q^{70} - 4 q^{71} - 2 q^{72} + 10 q^{73} + 24 q^{74} - 16 q^{75} + 4 q^{77} + 12 q^{78} - 2 q^{79} + 2 q^{80} + 4 q^{81} - 4 q^{84} - 14 q^{85} - 14 q^{86} + 32 q^{87} - 4 q^{88} - 10 q^{89} + 4 q^{90} + 2 q^{91} + 4 q^{92} + 14 q^{93} + 2 q^{94} + 4 q^{96} + 22 q^{97} - 4 q^{98} + 2 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 + 4 * q^11 - 4 * q^12 + 2 * q^13 - 4 * q^14 - 2 * q^15 + 4 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^20 - 4 * q^21 - 4 * q^22 + 4 * q^23 + 4 * q^24 - 4 * q^25 - 2 * q^26 - 10 * q^27 + 4 * q^28 - 12 * q^29 + 2 * q^30 - 14 * q^31 - 4 * q^32 - 4 * q^33 - 2 * q^34 + 2 * q^35 + 2 * q^36 - 24 * q^37 - 12 * q^39 - 2 * q^40 + 4 * q^42 + 14 * q^43 + 4 * q^44 - 4 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 4 * q^50 + 8 * q^51 + 2 * q^52 + 10 * q^54 - 18 * q^55 - 4 * q^56 + 12 * q^58 - 2 * q^59 - 2 * q^60 + 2 * q^61 + 14 * q^62 + 2 * q^63 + 4 * q^64 - 14 * q^65 + 4 * q^66 - 22 * q^67 + 2 * q^68 - 4 * q^69 - 2 * q^70 - 4 * q^71 - 2 * q^72 + 10 * q^73 + 24 * q^74 - 16 * q^75 + 4 * q^77 + 12 * q^78 - 2 * q^79 + 2 * q^80 + 4 * q^81 - 4 * q^84 - 14 * q^85 - 14 * q^86 + 32 * q^87 - 4 * q^88 - 10 * q^89 + 4 * q^90 + 2 * q^91 + 4 * q^92 + 14 * q^93 + 2 * q^94 + 4 * q^96 + 22 * q^97 - 4 * q^98 + 2 * 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
$3$	0.175571	0.101366	0.0506828	−	0.998715i	$-0.483860\pi$
$3$	0.175571	0.101366	0.0506828	+	0.998715i	$0.483860\pi$
$4$	1.00000	0.500000
$5$	−0.284079	−0.127044	−0.0635220	−	0.997980i	$-0.520233\pi$
$5$	−0.284079	−0.127044	−0.0635220	+	0.997980i	$0.520233\pi$
$6$	−0.175571	−0.0716764
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.96917	−0.989725
$10$	0.284079	0.0898337
$11$	4.80423	1.44853	0.724264	−	0.689522i	$-0.242180\pi$
$11$	4.80423	1.44853	0.724264	+	0.689522i	$0.242180\pi$
$12$	0.175571	0.0506828
$13$	0.108509	0.0300949	0.0150474	−	0.999887i	$-0.495210\pi$
$13$	0.108509	0.0300949	0.0150474	+	0.999887i	$0.495210\pi$
$14$	−1.00000	−0.267261
$15$	−0.0498759	−0.0128779
$16$	1.00000	0.250000
$17$	2.45965	0.596553	0.298276	−	0.954480i	$-0.403588\pi$
$17$	2.45965	0.596553	0.298276	+	0.954480i	$0.403588\pi$
$18$	2.96917	0.699841
$19$	0	0
$19$	0	0
$20$	−0.284079	−0.0635220
$21$	0.175571	0.0383126
$22$	−4.80423	−1.02426
$23$	−2.80423	−0.584722	−0.292361	−	0.956308i	$-0.594441\pi$
$23$	−2.80423	−0.584722	−0.292361	+	0.956308i	$0.594441\pi$
$24$	−0.175571	−0.0358382
$25$	−4.91930	−0.983860
$26$	−0.108509	−0.0212803
$27$	−1.04801	−0.201690
$28$	1.00000	0.188982
$29$	−0.648859	−0.120490	−0.0602450	−	0.998184i	$-0.519188\pi$
$29$	−0.648859	−0.120490	−0.0602450	+	0.998184i	$0.519188\pi$
$30$	0.0498759	0.00910605
$31$	−8.08831	−1.45270	−0.726351	−	0.687324i	$-0.758785\pi$
$31$	−8.08831	−1.45270	−0.726351	+	0.687324i	$0.758785\pi$
$32$	−1.00000	−0.176777
$33$	0.843480	0.146831
$34$	−2.45965	−0.421826
$35$	−0.284079	−0.0480181
$36$	−2.96917	−0.494862
$37$	2.39144	0.393150	0.196575	−	0.980489i	$-0.437018\pi$
$37$	2.39144	0.393150	0.196575	+	0.980489i	$0.437018\pi$
$38$	0	0
$39$	0.0190509	0.00305059
$40$	0.284079	0.0449168
$41$	−11.0201	−1.72105	−0.860525	−	0.509409i	$-0.829864\pi$
$41$	−11.0201	−1.72105	−0.860525	+	0.509409i	$0.829864\pi$
$42$	−0.175571	−0.0270911
$43$	3.04988	0.465102	0.232551	−	0.972584i	$-0.425293\pi$
$43$	3.04988	0.465102	0.232551	+	0.972584i	$0.425293\pi$
$44$	4.80423	0.724264
$45$	0.843480	0.125739
$46$	2.80423	0.413461
$47$	−2.73497	−0.398937	−0.199468	−	0.979904i	$-0.563921\pi$
$47$	−2.73497	−0.398937	−0.199468	+	0.979904i	$0.563921\pi$
$48$	0.175571	0.0253414
$49$	1.00000	0.142857
$50$	4.91930	0.695694
$51$	0.431842	0.0604700
$52$	0.108509	0.0150474
$53$	−6.93835	−0.953056	−0.476528	−	0.879159i	$-0.658105\pi$
$53$	−6.93835	−0.953056	−0.476528	+	0.879159i	$0.658105\pi$
$54$	1.04801	0.142616
$55$	−1.36478	−0.184027
$56$	−1.00000	−0.133631
$57$	0	0
$58$	0.648859	0.0851994
$59$	6.20930	0.808382	0.404191	−	0.914675i	$-0.367553\pi$
$59$	6.20930	0.808382	0.404191	+	0.914675i	$0.367553\pi$
$60$	−0.0498759	−0.00643895
$61$	−5.42412	−0.694488	−0.347244	−	0.937775i	$-0.612882\pi$
$61$	−5.42412	−0.694488	−0.347244	+	0.937775i	$0.612882\pi$
$62$	8.08831	1.02722
$63$	−2.96917	−0.374081
$64$	1.00000	0.125000
$65$	−0.0308250	−0.00382337
$66$	−0.843480	−0.103825
$67$	−10.1921	−1.24516	−0.622582	−	0.782554i	$-0.713916\pi$
$67$	−10.1921	−1.24516	−0.622582	+	0.782554i	$0.713916\pi$
$68$	2.45965	0.298276
$69$	−0.492339	−0.0592707
$70$	0.284079	0.0339539
$71$	−1.90025	−0.225518	−0.112759	−	0.993622i	$-0.535969\pi$
$71$	−1.90025	−0.225518	−0.112759	+	0.993622i	$0.535969\pi$
$72$	2.96917	0.349921
$73$	13.6341	1.59575	0.797873	−	0.602825i	$-0.205958\pi$
$73$	13.6341	1.59575	0.797873	+	0.602825i	$0.205958\pi$
$74$	−2.39144	−0.277999
$75$	−0.863684	−0.0997296
$76$	0	0
$77$	4.80423	0.547492
$78$	−0.0190509	−0.00215709
$79$	5.32251	0.598829	0.299414	−	0.954123i	$-0.403209\pi$
$79$	5.32251	0.598829	0.299414	+	0.954123i	$0.403209\pi$
$80$	−0.284079	−0.0317610
$81$	8.72353	0.969281
$82$	11.0201	1.21697
$83$	−10.8576	−1.19178	−0.595891	−	0.803065i	$-0.703201\pi$
$83$	−10.8576	−1.19178	−0.595891	+	0.803065i	$0.703201\pi$
$84$	0.175571	0.0191563
$85$	−0.698735	−0.0757884
$86$	−3.04988	−0.328877
$87$	−0.113921	−0.0122136
$88$	−4.80423	−0.512132
$89$	4.83203	0.512195	0.256097	−	0.966651i	$-0.417563\pi$
$89$	4.83203	0.512195	0.256097	+	0.966651i	$0.417563\pi$
$90$	−0.843480	−0.0889106
$91$	0.108509	0.0113748
$92$	−2.80423	−0.292361
$93$	−1.42007	−0.147254
$94$	2.73497	0.282091
$95$	0	0
$96$	−0.175571	−0.0179191
$97$	7.50702	0.762222	0.381111	−	0.924529i	$-0.375542\pi$
$97$	7.50702	0.762222	0.381111	+	0.924529i	$0.375542\pi$
$98$	−1.00000	−0.101015
$99$	−14.2646	−1.43365
$100$	−4.91930	−0.491930
$101$	18.7283	1.86353	0.931767	−	0.363056i	$-0.118266\pi$
$101$	18.7283	1.86353	0.931767	+	0.363056i	$0.118266\pi$
$102$	−0.431842	−0.0427587
$103$	7.02009	0.691710	0.345855	−	0.938288i	$-0.387589\pi$
$103$	7.02009	0.691710	0.345855	+	0.938288i	$0.387589\pi$
$104$	−0.108509	−0.0106401
$105$	−0.0498759	−0.00486739
$106$	6.93835	0.673912
$107$	−9.64063	−0.931995	−0.465998	−	0.884786i	$-0.654304\pi$
$107$	−9.64063	−0.931995	−0.465998	+	0.884786i	$0.654304\pi$
$108$	−1.04801	−0.100845
$109$	−9.75435	−0.934297	−0.467149	−	0.884179i	$-0.654719\pi$
$109$	−9.75435	−0.934297	−0.467149	+	0.884179i	$0.654719\pi$
$110$	1.36478	0.130127
$111$	0.419865	0.0398519
$112$	1.00000	0.0944911
$113$	−10.3013	−0.969062	−0.484531	−	0.874774i	$-0.661010\pi$
$113$	−10.3013	−0.969062	−0.484531	+	0.874774i	$0.661010\pi$
$114$	0	0
$115$	0.796622	0.0742854
$116$	−0.648859	−0.0602450
$117$	−0.322181	−0.0297856
$118$	−6.20930	−0.571612
$119$	2.45965	0.225476
$120$	0.0498759	0.00455303
$121$	12.0806	1.09824
$122$	5.42412	0.491077
$123$	−1.93480	−0.174455
$124$	−8.08831	−0.726351
$125$	2.81787	0.252038
$126$	2.96917	0.264515
$127$	−0.598983	−0.0531512	−0.0265756	−	0.999647i	$-0.508460\pi$
$127$	−0.598983	−0.0531512	−0.0265756	+	0.999647i	$0.508460\pi$
$128$	−1.00000	−0.0883883
$129$	0.535468	0.0471454
$130$	0.0308250	0.00270353
$131$	−18.7016	−1.63397	−0.816985	−	0.576659i	$-0.804356\pi$
$131$	−18.7016	−1.63397	−0.816985	+	0.576659i	$0.804356\pi$
$132$	0.843480	0.0734155
$133$	0	0
$134$	10.1921	0.880465
$135$	0.297718	0.0256235
$136$	−2.45965	−0.210913
$137$	−8.65478	−0.739428	−0.369714	−	0.929146i	$-0.620544\pi$
$137$	−8.65478	−0.739428	−0.369714	+	0.929146i	$0.620544\pi$
$138$	0.492339	0.0419107
$139$	−0.203491	−0.0172599	−0.00862994	−	0.999963i	$-0.502747\pi$
$139$	−0.203491	−0.0172599	−0.00862994	+	0.999963i	$0.502747\pi$
$140$	−0.284079	−0.0240091
$141$	−0.480180	−0.0404385
$142$	1.90025	0.159465
$143$	0.521300	0.0435933
$144$	−2.96917	−0.247431
$145$	0.184327	0.0153075
$146$	−13.6341	−1.12836
$147$	0.175571	0.0144808
$148$	2.39144	0.196575
$149$	17.5754	1.43984	0.719918	−	0.694059i	$-0.244179\pi$
$149$	17.5754	1.43984	0.719918	+	0.694059i	$0.244179\pi$
$150$	0.863684	0.0705195
$151$	4.16129	0.338641	0.169320	−	0.985561i	$-0.445843\pi$
$151$	4.16129	0.338641	0.169320	+	0.985561i	$0.445843\pi$
$152$	0	0
$153$	−7.30313	−0.590423
$154$	−4.80423	−0.387136
$155$	2.29772	0.184557
$156$	0.0190509	0.00152529
$157$	−16.1220	−1.28668	−0.643339	−	0.765581i	$-0.722451\pi$
$157$	−16.1220	−1.28668	−0.643339	+	0.765581i	$0.722451\pi$
$158$	−5.32251	−0.423436
$159$	−1.21817	−0.0966071
$160$	0.284079	0.0224584
$161$	−2.80423	−0.221004
$162$	−8.72353	−0.685385
$163$	5.97876	0.468292	0.234146	−	0.972201i	$-0.424771\pi$
$163$	5.97876	0.468292	0.234146	+	0.972201i	$0.424771\pi$
$164$	−11.0201	−0.860525
$165$	−0.239615	−0.0186540
$166$	10.8576	0.842717
$167$	−18.5659	−1.43667	−0.718334	−	0.695698i	$-0.755095\pi$
$167$	−18.5659	−1.43667	−0.718334	+	0.695698i	$0.755095\pi$
$168$	−0.175571	−0.0135456
$169$	−12.9882	−0.999094
$170$	0.698735	0.0535905
$171$	0	0
$172$	3.04988	0.232551
$173$	2.80975	0.213621	0.106811	−	0.994279i	$-0.465936\pi$
$173$	2.80975	0.213621	0.106811	+	0.994279i	$0.465936\pi$
$174$	0.113921	0.00863629
$175$	−4.91930	−0.371864
$176$	4.80423	0.362132
$177$	1.09017	0.0819422
$178$	−4.83203	−0.362176
$179$	−8.25867	−0.617282	−0.308641	−	0.951179i	$-0.599874\pi$
$179$	−8.25867	−0.617282	−0.308641	+	0.951179i	$0.599874\pi$
$180$	0.843480	0.0628693
$181$	−20.1204	−1.49554	−0.747768	−	0.663960i	$-0.768874\pi$
$181$	−20.1204	−1.49554	−0.747768	+	0.663960i	$0.768874\pi$
$182$	−0.108509	−0.00804319
$183$	−0.952316	−0.0703972
$184$	2.80423	0.206730
$185$	−0.679357	−0.0499473
$186$	1.42007	0.104124
$187$	11.8167	0.864124
$188$	−2.73497	−0.199468
$189$	−1.04801	−0.0762316
$190$	0	0
$191$	25.9039	1.87434	0.937169	−	0.348876i	$-0.113437\pi$
$191$	25.9039	1.87434	0.937169	+	0.348876i	$0.113437\pi$
$192$	0.175571	0.0126707
$193$	−23.0403	−1.65848	−0.829238	−	0.558895i	$-0.811225\pi$
$193$	−23.0403	−1.65848	−0.829238	+	0.558895i	$0.811225\pi$
$194$	−7.50702	−0.538972
$195$	−0.00541196	−0.000387559 0
$196$	1.00000	0.0714286
$197$	3.74122	0.266551	0.133275	−	0.991079i	$-0.457450\pi$
$197$	3.74122	0.266551	0.133275	+	0.991079i	$0.457450\pi$
$198$	14.2646	1.01374
$199$	−20.0010	−1.41784	−0.708918	−	0.705291i	$-0.750816\pi$
$199$	−20.0010	−1.41784	−0.708918	+	0.705291i	$0.750816\pi$
$200$	4.91930	0.347847
$201$	−1.78943	−0.126217
$202$	−18.7283	−1.31772
$203$	−0.648859	−0.0455410
$204$	0.431842	0.0302350
$205$	3.13058	0.218649
$206$	−7.02009	−0.489113
$207$	8.32624	0.578714
$208$	0.108509	0.00752371
$209$	0	0
$210$	0.0498759	0.00344176
$211$	−18.0211	−1.24063	−0.620313	−	0.784354i	$-0.712994\pi$
$211$	−18.0211	−1.24063	−0.620313	+	0.784354i	$0.712994\pi$
$212$	−6.93835	−0.476528
$213$	−0.333628	−0.0228598
$214$	9.64063	0.659020
$215$	−0.866406	−0.0590884
$216$	1.04801	0.0713081
$217$	−8.08831	−0.549070
$218$	9.75435	0.660648
$219$	2.39374	0.161754
$220$	−1.36478	−0.0920134
$221$	0.266893	0.0179532
$222$	−0.419865	−0.0281795
$223$	−22.2949	−1.49298	−0.746489	−	0.665398i	$-0.768262\pi$
$223$	−22.2949	−1.49298	−0.746489	+	0.665398i	$0.768262\pi$
$224$	−1.00000	−0.0668153
$225$	14.6063	0.973751
$226$	10.3013	0.685230
$227$	19.1879	1.27355	0.636774	−	0.771050i	$-0.280268\pi$
$227$	19.1879	1.27355	0.636774	+	0.771050i	$0.280268\pi$
$228$	0	0
$229$	3.18317	0.210350	0.105175	−	0.994454i	$-0.466460\pi$
$229$	3.18317	0.210350	0.105175	+	0.994454i	$0.466460\pi$
$230$	−0.796622	−0.0525277
$231$	0.843480	0.0554969
$232$	0.648859	0.0425997
$233$	−5.86002	−0.383903	−0.191951	−	0.981404i	$-0.561482\pi$
$233$	−5.86002	−0.383903	−0.191951	+	0.981404i	$0.561482\pi$
$234$	0.322181	0.0210616
$235$	0.776948	0.0506825
$236$	6.20930	0.404191
$237$	0.934475	0.0607007
$238$	−2.45965	−0.159435
$239$	5.53141	0.357797	0.178899	−	0.983868i	$-0.442747\pi$
$239$	5.53141	0.357797	0.178899	+	0.983868i	$0.442747\pi$
$240$	−0.0498759	−0.00321948
$241$	15.0872	0.971849	0.485924	−	0.874001i	$-0.338483\pi$
$241$	15.0872	0.971849	0.485924	+	0.874001i	$0.338483\pi$
$242$	−12.0806	−0.776570
$243$	4.67563	0.299942
$244$	−5.42412	−0.347244
$245$	−0.284079	−0.0181491
$246$	1.93480	0.123359
$247$	0	0
$248$	8.08831	0.513608
$249$	−1.90628	−0.120806
$250$	−2.81787	−0.178217
$251$	−7.04402	−0.444615	−0.222307	−	0.974977i	$-0.571359\pi$
$251$	−7.04402	−0.444615	−0.222307	+	0.974977i	$0.571359\pi$
$252$	−2.96917	−0.187040
$253$	−13.4721	−0.846986
$254$	0.598983	0.0375835
$255$	−0.122677	−0.00768235
$256$	1.00000	0.0625000
$257$	14.3030	0.892198	0.446099	−	0.894984i	$-0.352813\pi$
$257$	14.3030	0.892198	0.446099	+	0.894984i	$0.352813\pi$
$258$	−0.535468	−0.0333368
$259$	2.39144	0.148597
$260$	−0.0308250	−0.00191169
$261$	1.92658	0.119252
$262$	18.7016	1.15539
$263$	24.4127	1.50535	0.752675	−	0.658392i	$-0.228763\pi$
$263$	24.4127	1.50535	0.752675	+	0.658392i	$0.228763\pi$
$264$	−0.843480	−0.0519126
$265$	1.97104	0.121080
$266$	0	0
$267$	0.848363	0.0519189
$268$	−10.1921	−0.622582
$269$	−15.4262	−0.940552	−0.470276	−	0.882519i	$-0.655846\pi$
$269$	−15.4262	−0.940552	−0.470276	+	0.882519i	$0.655846\pi$
$270$	−0.297718	−0.0181185
$271$	4.79059	0.291007	0.145504	−	0.989358i	$-0.453520\pi$
$271$	4.79059	0.291007	0.145504	+	0.989358i	$0.453520\pi$
$272$	2.45965	0.149138
$273$	0.0190509	0.00115301
$274$	8.65478	0.522854
$275$	−23.6334	−1.42515
$276$	−0.492339	−0.0296353
$277$	−4.99781	−0.300289	−0.150145	−	0.988664i	$-0.547974\pi$
$277$	−4.99781	−0.300289	−0.150145	+	0.988664i	$0.547974\pi$
$278$	0.203491	0.0122046
$279$	24.0156	1.43778
$280$	0.284079	0.0169770
$281$	−7.89677	−0.471082	−0.235541	−	0.971864i	$-0.575686\pi$
$281$	−7.89677	−0.471082	−0.235541	+	0.971864i	$0.575686\pi$
$282$	0.480180	0.0285943
$283$	−15.6688	−0.931416	−0.465708	−	0.884939i	$-0.654200\pi$
$283$	−15.6688	−0.931416	−0.465708	+	0.884939i	$0.654200\pi$
$284$	−1.90025	−0.112759
$285$	0	0
$286$	−0.521300	−0.0308251
$287$	−11.0201	−0.650495
$288$	2.96917	0.174960
$289$	−10.9501	−0.644125
$290$	−0.184327	−0.0108241
$291$	1.31801	0.0772632
$292$	13.6341	0.797873
$293$	23.1286	1.35119	0.675594	−	0.737274i	$-0.263887\pi$
$293$	23.1286	1.35119	0.675594	+	0.737274i	$0.263887\pi$
$294$	−0.175571	−0.0102395
$295$	−1.76393	−0.102700
$296$	−2.39144	−0.138999
$297$	−5.03488	−0.292153
$298$	−17.5754	−1.01812
$299$	−0.304282	−0.0175971
$300$	−0.863684	−0.0498648
$301$	3.04988	0.175792
$302$	−4.16129	−0.239455
$303$	3.28814	0.188898
$304$	0	0
$305$	1.54088	0.0882305
$306$	7.30313	0.417492
$307$	−16.1341	−0.920823	−0.460412	−	0.887706i	$-0.652298\pi$
$307$	−16.1341	−0.920823	−0.460412	+	0.887706i	$0.652298\pi$
$308$	4.80423	0.273746
$309$	1.23252	0.0701157
$310$	−2.29772	−0.130502
$311$	2.91158	0.165101	0.0825503	−	0.996587i	$-0.473693\pi$
$311$	2.91158	0.165101	0.0825503	+	0.996587i	$0.473693\pi$
$312$	−0.0190509	−0.00107854
$313$	3.99164	0.225621	0.112810	−	0.993617i	$-0.464015\pi$
$313$	3.99164	0.225621	0.112810	+	0.993617i	$0.464015\pi$
$314$	16.1220	0.909819
$315$	0.843480	0.0475247
$316$	5.32251	0.299414
$317$	2.17442	0.122127	0.0610637	−	0.998134i	$-0.480551\pi$
$317$	2.17442	0.122127	0.0610637	+	0.998134i	$0.480551\pi$
$318$	1.21817	0.0683116
$319$	−3.11727	−0.174533
$320$	−0.284079	−0.0158805
$321$	−1.69261	−0.0944723
$322$	2.80423	0.156273
$323$	0	0
$324$	8.72353	0.484640
$325$	−0.533786	−0.0296091
$326$	−5.97876	−0.331133
$327$	−1.71258	−0.0947057
$328$	11.0201	0.608483
$329$	−2.73497	−0.150784
$330$	0.239615	0.0131904
$331$	−20.3145	−1.11658	−0.558292	−	0.829645i	$-0.688543\pi$
$331$	−20.3145	−1.11658	−0.558292	+	0.829645i	$0.688543\pi$
$332$	−10.8576	−0.595891
$333$	−7.10059	−0.389110
$334$	18.5659	1.01588
$335$	2.89537	0.158191
$336$	0.175571	0.00957816
$337$	14.0176	0.763586	0.381793	−	0.924248i	$-0.375307\pi$
$337$	14.0176	0.763586	0.381793	+	0.924248i	$0.375307\pi$
$338$	12.9882	0.706466
$339$	−1.80860	−0.0982296
$340$	−0.698735	−0.0378942
$341$	−38.8580	−2.10428
$342$	0	0
$343$	1.00000	0.0539949
$344$	−3.04988	−0.164438
$345$	0.139863	0.00752999
$346$	−2.80975	−0.151053
$347$	−21.6486	−1.16216	−0.581080	−	0.813847i	$-0.697370\pi$
$347$	−21.6486	−1.16216	−0.581080	+	0.813847i	$0.697370\pi$
$348$	−0.113921	−0.00610678
$349$	−6.63522	−0.355175	−0.177588	−	0.984105i	$-0.556829\pi$
$349$	−6.63522	−0.355175	−0.177588	+	0.984105i	$0.556829\pi$
$350$	4.91930	0.262948
$351$	−0.113718	−0.00606983
$352$	−4.80423	−0.256066
$353$	15.8777	0.845087	0.422543	−	0.906343i	$-0.361137\pi$
$353$	15.8777	0.845087	0.422543	+	0.906343i	$0.361137\pi$
$354$	−1.09017	−0.0579419
$355$	0.539821	0.0286507
$356$	4.83203	0.256097
$357$	0.431842	0.0228555
$358$	8.25867	0.436484
$359$	−9.76974	−0.515627	−0.257814	−	0.966195i	$-0.583002\pi$
$359$	−9.76974	−0.515627	−0.257814	+	0.966195i	$0.583002\pi$
$360$	−0.843480	−0.0444553
$361$	0	0
$362$	20.1204	1.05750
$363$	2.12099	0.111323
$364$	0.108509	0.00568739
$365$	−3.87315	−0.202730
$366$	0.952316	0.0497784
$367$	−23.7355	−1.23898	−0.619492	−	0.785003i	$-0.712661\pi$
$367$	−23.7355	−1.23898	−0.619492	+	0.785003i	$0.712661\pi$
$368$	−2.80423	−0.146180
$369$	32.7206	1.70337
$370$	0.679357	0.0353181
$371$	−6.93835	−0.360221
$372$	−1.42007	−0.0736271
$373$	18.1516	0.939854	0.469927	−	0.882705i	$-0.344280\pi$
$373$	18.1516	0.939854	0.469927	+	0.882705i	$0.344280\pi$
$374$	−11.8167	−0.611028
$375$	0.494734	0.0255480
$376$	2.73497	0.141045
$377$	−0.0704067	−0.00362613
$378$	1.04801	0.0539039
$379$	−33.9940	−1.74616	−0.873078	−	0.487580i	$-0.837880\pi$
$379$	−33.9940	−1.74616	−0.873078	+	0.487580i	$0.837880\pi$
$380$	0	0
$381$	−0.105164	−0.00538770
$382$	−25.9039	−1.32536
$383$	25.4241	1.29911	0.649556	−	0.760314i	$-0.274955\pi$
$383$	25.4241	1.29911	0.649556	+	0.760314i	$0.274955\pi$
$384$	−0.175571	−0.00895954
$385$	−1.36478	−0.0695556
$386$	23.0403	1.17272
$387$	−9.05562	−0.460323
$388$	7.50702	0.381111
$389$	−3.36072	−0.170395	−0.0851977	−	0.996364i	$-0.527152\pi$
$389$	−3.36072	−0.170395	−0.0851977	+	0.996364i	$0.527152\pi$
$390$	0.00541196	0.000274045 0
$391$	−6.89741	−0.348817
$392$	−1.00000	−0.0505076
$393$	−3.28346	−0.165628
$394$	−3.74122	−0.188480
$395$	−1.51201	−0.0760776
$396$	−14.2646	−0.716823
$397$	−22.6804	−1.13830	−0.569148	−	0.822235i	$-0.692727\pi$
$397$	−22.6804	−1.13830	−0.569148	+	0.822235i	$0.692727\pi$
$398$	20.0010	1.00256
$399$	0	0
$400$	−4.91930	−0.245965
$401$	−17.8636	−0.892064	−0.446032	−	0.895017i	$-0.647163\pi$
$401$	−17.8636	−0.892064	−0.446032	+	0.895017i	$0.647163\pi$
$402$	1.78943	0.0892489
$403$	−0.877650	−0.0437189
$404$	18.7283	0.931767
$405$	−2.47817	−0.123141
$406$	0.648859	0.0322023
$407$	11.4890	0.569488
$408$	−0.431842	−0.0213794
$409$	9.22731	0.456261	0.228131	−	0.973631i	$-0.426739\pi$
$409$	9.22731	0.456261	0.228131	+	0.973631i	$0.426739\pi$
$410$	−3.13058	−0.154608
$411$	−1.51952	−0.0749526
$412$	7.02009	0.345855
$413$	6.20930	0.305540
$414$	−8.32624	−0.409212
$415$	3.08443	0.151409
$416$	−0.108509	−0.00532007
$417$	−0.0357270	−0.00174956
$418$	0	0
$419$	−27.8528	−1.36070	−0.680348	−	0.732889i	$-0.738172\pi$
$419$	−27.8528	−1.36070	−0.680348	+	0.732889i	$0.738172\pi$
$420$	−0.0498759	−0.00243369
$421$	12.9917	0.633175	0.316587	−	0.948563i	$-0.397463\pi$
$421$	12.9917	0.633175	0.316587	+	0.948563i	$0.397463\pi$
$422$	18.0211	0.877255
$423$	8.12061	0.394838
$424$	6.93835	0.336956
$425$	−12.0998	−0.586924
$426$	0.333628	0.0161643
$427$	−5.42412	−0.262492
$428$	−9.64063	−0.465998
$429$	0.0915248	0.00441886
$430$	0.866406	0.0417818
$431$	23.1802	1.11655	0.558276	−	0.829655i	$-0.311463\pi$
$431$	23.1802	1.11655	0.558276	+	0.829655i	$0.311463\pi$
$432$	−1.04801	−0.0504225
$433$	7.65904	0.368070	0.184035	−	0.982920i	$-0.441084\pi$
$433$	7.65904	0.368070	0.184035	+	0.982920i	$0.441084\pi$
$434$	8.08831	0.388251
$435$	0.0323624	0.00155166
$436$	−9.75435	−0.467149
$437$	0	0
$438$	−2.39374	−0.114377
$439$	24.0587	1.14826	0.574130	−	0.818764i	$-0.305340\pi$
$439$	24.0587	1.14826	0.574130	+	0.818764i	$0.305340\pi$
$440$	1.36478	0.0650633
$441$	−2.96917	−0.141389
$442$	−0.266893	−0.0126948
$443$	3.56951	0.169593	0.0847963	−	0.996398i	$-0.472976\pi$
$443$	3.56951	0.169593	0.0847963	+	0.996398i	$0.472976\pi$
$444$	0.419865	0.0199259
$445$	−1.37268	−0.0650712
$446$	22.2949	1.05569
$447$	3.08573	0.145950
$448$	1.00000	0.0472456
$449$	−3.19566	−0.150813	−0.0754063	−	0.997153i	$-0.524025\pi$
$449$	−3.19566	−0.150813	−0.0754063	+	0.997153i	$0.524025\pi$
$450$	−14.6063	−0.688546
$451$	−52.9430	−2.49299
$452$	−10.3013	−0.484531
$453$	0.730600	0.0343266
$454$	−19.1879	−0.900535
$455$	−0.0308250	−0.00144510
$456$	0	0
$457$	−15.0461	−0.703827	−0.351914	−	0.936033i	$-0.614469\pi$
$457$	−15.0461	−0.703827	−0.351914	+	0.936033i	$0.614469\pi$
$458$	−3.18317	−0.148740
$459$	−2.57774	−0.120319
$460$	0.796622	0.0371427
$461$	−8.35487	−0.389125	−0.194563	−	0.980890i	$-0.562329\pi$
$461$	−8.35487	−0.389125	−0.194563	+	0.980890i	$0.562329\pi$
$462$	−0.843480	−0.0392423
$463$	−30.7307	−1.42818	−0.714088	−	0.700056i	$-0.753158\pi$
$463$	−30.7307	−1.42818	−0.714088	+	0.700056i	$0.753158\pi$
$464$	−0.648859	−0.0301225
$465$	0.403412	0.0187078
$466$	5.86002	0.271460
$467$	−9.49158	−0.439218	−0.219609	−	0.975588i	$-0.570478\pi$
$467$	−9.49158	−0.439218	−0.219609	+	0.975588i	$0.570478\pi$
$468$	−0.322181	−0.0148928
$469$	−10.1921	−0.470628
$470$	−0.776948	−0.0358379
$471$	−2.83055	−0.130425
$472$	−6.20930	−0.285806
$473$	14.6523	0.673713
$474$	−0.934475	−0.0429219
$475$	0	0
$476$	2.45965	0.112738
$477$	20.6012	0.943263
$478$	−5.53141	−0.253001
$479$	1.39516	0.0637467	0.0318734	−	0.999492i	$-0.489853\pi$
$479$	1.39516	0.0637467	0.0318734	+	0.999492i	$0.489853\pi$
$480$	0.0498759	0.00227651
$481$	0.259491	0.0118318
$482$	−15.0872	−0.687201
$483$	−0.492339	−0.0224022
$484$	12.0806	0.549118
$485$	−2.13259	−0.0968358
$486$	−4.67563	−0.212091
$487$	−42.7878	−1.93890	−0.969450	−	0.245291i	$-0.921117\pi$
$487$	−42.7878	−1.93890	−0.969450	+	0.245291i	$0.921117\pi$
$488$	5.42412	0.245539
$489$	1.04969	0.0474688
$490$	0.284079	0.0128334
$491$	15.3548	0.692951	0.346475	−	0.938059i	$-0.387378\pi$
$491$	15.3548	0.692951	0.346475	+	0.938059i	$0.387378\pi$
$492$	−1.93480	−0.0872276
$493$	−1.59597	−0.0718787
$494$	0	0
$495$	4.05227	0.182136
$496$	−8.08831	−0.363176
$497$	−1.90025	−0.0852378
$498$	1.90628	0.0854226
$499$	−5.85765	−0.262224	−0.131112	−	0.991368i	$-0.541855\pi$
$499$	−5.85765	−0.262224	−0.131112	+	0.991368i	$0.541855\pi$
$500$	2.81787	0.126019
$501$	−3.25962	−0.145629
$502$	7.04402	0.314390
$503$	31.6392	1.41072	0.705362	−	0.708847i	$-0.250785\pi$
$503$	31.6392	1.41072	0.705362	+	0.708847i	$0.250785\pi$
$504$	2.96917	0.132258
$505$	−5.32032	−0.236751
$506$	13.4721	0.598909
$507$	−2.28035	−0.101274
$508$	−0.598983	−0.0265756
$509$	−31.2645	−1.38578	−0.692888	−	0.721045i	$-0.743662\pi$
$509$	−31.2645	−1.38578	−0.692888	+	0.721045i	$0.743662\pi$
$510$	0.122677	0.00543224
$511$	13.6341	0.603136
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−14.3030	−0.630879
$515$	−1.99426	−0.0878776
$516$	0.535468	0.0235727
$517$	−13.1394	−0.577871
$518$	−2.39144	−0.105074
$519$	0.493309	0.0216539
$520$	0.0308250	0.00135177
$521$	3.50830	0.153702	0.0768508	−	0.997043i	$-0.475513\pi$
$521$	3.50830	0.153702	0.0768508	+	0.997043i	$0.475513\pi$
$522$	−1.92658	−0.0843239
$523$	3.19901	0.139883	0.0699414	−	0.997551i	$-0.477719\pi$
$523$	3.19901	0.139883	0.0699414	+	0.997551i	$0.477719\pi$
$524$	−18.7016	−0.816985
$525$	−0.863684	−0.0376943
$526$	−24.4127	−1.06444
$527$	−19.8944	−0.866614
$528$	0.843480	0.0367078
$529$	−15.1363	−0.658101
$530$	−1.97104	−0.0856165
$531$	−18.4365	−0.800076
$532$	0	0
$533$	−1.19577	−0.0517947
$534$	−0.848363	−0.0367122
$535$	2.73870	0.118404
$536$	10.1921	0.440232
$537$	−1.44998	−0.0625712
$538$	15.4262	0.665071
$539$	4.80423	0.206933
$540$	0.297718	0.0128117
$541$	−35.6121	−1.53108	−0.765541	−	0.643387i	$-0.777529\pi$
$541$	−35.6121	−1.53108	−0.765541	+	0.643387i	$0.777529\pi$
$542$	−4.79059	−0.205773
$543$	−3.53254	−0.151596
$544$	−2.45965	−0.105457
$545$	2.77101	0.118697
$546$	−0.0190509	−0.000815303 0
$547$	29.9001	1.27844	0.639219	−	0.769025i	$-0.279258\pi$
$547$	29.9001	1.27844	0.639219	+	0.769025i	$0.279258\pi$
$548$	−8.65478	−0.369714
$549$	16.1052	0.687352
$550$	23.6334	1.00773
$551$	0	0
$552$	0.492339	0.0209554
$553$	5.32251	0.226336
$554$	4.99781	0.212337
$555$	−0.119275	−0.00506294
$556$	−0.203491	−0.00862994
$557$	−29.1443	−1.23488	−0.617442	−	0.786616i	$-0.711831\pi$
$557$	−29.1443	−1.23488	−0.617442	+	0.786616i	$0.711831\pi$
$558$	−24.0156	−1.01666
$559$	0.330938	0.0139972
$560$	−0.284079	−0.0120045
$561$	2.07467	0.0875925
$562$	7.89677	0.333105
$563$	44.6485	1.88171	0.940855	−	0.338808i	$-0.110024\pi$
$563$	44.6485	1.88171	0.940855	+	0.338808i	$0.110024\pi$
$564$	−0.480180	−0.0202192
$565$	2.92637	0.123113
$566$	15.6688	0.658610
$567$	8.72353	0.366354
$568$	1.90025	0.0797326
$569$	−4.43989	−0.186130	−0.0930649	−	0.995660i	$-0.529666\pi$
$569$	−4.43989	−0.186130	−0.0930649	+	0.995660i	$0.529666\pi$
$570$	0	0
$571$	−1.32269	−0.0553529	−0.0276764	−	0.999617i	$-0.508811\pi$
$571$	−1.32269	−0.0553529	−0.0276764	+	0.999617i	$0.508811\pi$
$572$	0.521300	0.0217966
$573$	4.54795	0.189994
$574$	11.0201	0.459970
$575$	13.7948	0.575284
$576$	−2.96917	−0.123716
$577$	38.5912	1.60657	0.803287	−	0.595592i	$-0.203083\pi$
$577$	38.5912	1.60657	0.803287	+	0.595592i	$0.203083\pi$
$578$	10.9501	0.455465
$579$	−4.04520	−0.168113
$580$	0.184327	0.00765377
$581$	−10.8576	−0.450451
$582$	−1.31801	−0.0546333
$583$	−33.3334	−1.38053
$584$	−13.6341	−0.564182
$585$	0.0915248	0.00378409
$586$	−23.1286	−0.955434
$587$	6.66831	0.275230	0.137615	−	0.990486i	$-0.456056\pi$
$587$	6.66831	0.275230	0.137615	+	0.990486i	$0.456056\pi$
$588$	0.175571	0.00724041
$589$	0	0
$590$	1.76393	0.0726199
$591$	0.656848	0.0270191
$592$	2.39144	0.0982874
$593$	12.4340	0.510604	0.255302	−	0.966861i	$-0.417825\pi$
$593$	12.4340	0.510604	0.255302	+	0.966861i	$0.417825\pi$
$594$	5.03488	0.206584
$595$	−0.698735	−0.0286453
$596$	17.5754	0.719918
$597$	−3.51159	−0.143720
$598$	0.304282	0.0124430
$599$	7.99408	0.326629	0.163315	−	0.986574i	$-0.447781\pi$
$599$	7.99408	0.326629	0.163315	+	0.986574i	$0.447781\pi$
$600$	0.863684	0.0352597
$601$	−36.7762	−1.50013	−0.750066	−	0.661363i	$-0.769978\pi$
$601$	−36.7762	−1.50013	−0.750066	+	0.661363i	$0.769978\pi$
$602$	−3.04988	−0.124304
$603$	30.2622	1.23237
$604$	4.16129	0.169320
$605$	−3.43184	−0.139524
$606$	−3.28814	−0.133571
$607$	−40.5835	−1.64723	−0.823617	−	0.567147i	$-0.808047\pi$
$607$	−40.5835	−1.64723	−0.823617	+	0.567147i	$0.808047\pi$
$608$	0	0
$609$	−0.113921	−0.00461629
$610$	−1.54088	−0.0623884
$611$	−0.296768	−0.0120059
$612$	−7.30313	−0.295212
$613$	−44.0308	−1.77839	−0.889193	−	0.457532i	$-0.848734\pi$
$613$	−44.0308	−1.77839	−0.889193	+	0.457532i	$0.848734\pi$
$614$	16.1341	0.651120
$615$	0.549637	0.0221635
$616$	−4.80423	−0.193568
$617$	−30.8099	−1.24036	−0.620179	−	0.784460i	$-0.712940\pi$
$617$	−30.8099	−1.24036	−0.620179	+	0.784460i	$0.712940\pi$
$618$	−1.23252	−0.0495793
$619$	−15.6095	−0.627398	−0.313699	−	0.949522i	$-0.601568\pi$
$619$	−15.6095	−0.627398	−0.313699	+	0.949522i	$0.601568\pi$
$620$	2.29772	0.0922786
$621$	2.93886	0.117932
$622$	−2.91158	−0.116744
$623$	4.83203	0.193591
$624$	0.0190509	0.000762646 0
$625$	23.7960	0.951840
$626$	−3.99164	−0.159538
$627$	0	0
$628$	−16.1220	−0.643339
$629$	5.88209	0.234534
$630$	−0.843480	−0.0336051
$631$	45.4637	1.80988	0.904940	−	0.425538i	$-0.139915\pi$
$631$	45.4637	1.80988	0.904940	+	0.425538i	$0.139915\pi$
$632$	−5.32251	−0.211718
$633$	−3.16398	−0.125757
$634$	−2.17442	−0.0863572
$635$	0.170159	0.00675254
$636$	−1.21817	−0.0483036
$637$	0.108509	0.00429926
$638$	3.11727	0.123414
$639$	5.64217	0.223201
$640$	0.284079	0.0112292
$641$	3.11643	0.123092	0.0615458	−	0.998104i	$-0.480397\pi$
$641$	3.11643	0.123092	0.0615458	+	0.998104i	$0.480397\pi$
$642$	1.69261	0.0668020
$643$	16.6596	0.656989	0.328495	−	0.944506i	$-0.393459\pi$
$643$	16.6596	0.656989	0.328495	+	0.944506i	$0.393459\pi$
$644$	−2.80423	−0.110502
$645$	−0.152115	−0.00598953
$646$	0	0
$647$	2.34238	0.0920886	0.0460443	−	0.998939i	$-0.485338\pi$
$647$	2.34238	0.0920886	0.0460443	+	0.998939i	$0.485338\pi$
$648$	−8.72353	−0.342692
$649$	29.8309	1.17096
$650$	0.533786	0.0209368
$651$	−1.42007	−0.0556568
$652$	5.97876	0.234146
$653$	33.1400	1.29687	0.648434	−	0.761271i	$-0.275424\pi$
$653$	33.1400	1.29687	0.648434	+	0.761271i	$0.275424\pi$
$654$	1.71258	0.0669670
$655$	5.31274	0.207586
$656$	−11.0201	−0.430262
$657$	−40.4819	−1.57935
$658$	2.73497	0.106620
$659$	21.3532	0.831803	0.415902	−	0.909410i	$-0.363466\pi$
$659$	21.3532	0.831803	0.415902	+	0.909410i	$0.363466\pi$
$660$	−0.239615	−0.00932701
$661$	−27.0147	−1.05075	−0.525375	−	0.850871i	$-0.676075\pi$
$661$	−27.0147	−1.05075	−0.525375	+	0.850871i	$0.676075\pi$
$662$	20.3145	0.789544
$663$	0.0468585	0.00181983
$664$	10.8576	0.421359
$665$	0	0
$666$	7.10059	0.275142
$667$	1.81955	0.0704532
$668$	−18.5659	−0.718334
$669$	−3.91433	−0.151337
$670$	−2.89537	−0.111858
$671$	−26.0587	−1.00599
$672$	−0.175571	−0.00677278
$673$	−5.44362	−0.209836	−0.104918	−	0.994481i	$-0.533458\pi$
$673$	−5.44362	−0.209836	−0.104918	+	0.994481i	$0.533458\pi$
$674$	−14.0176	−0.539937
$675$	5.15548	0.198435
$676$	−12.9882	−0.499547
$677$	38.5217	1.48051	0.740255	−	0.672326i	$-0.234705\pi$
$677$	38.5217	1.48051	0.740255	+	0.672326i	$0.234705\pi$
$678$	1.80860	0.0694588
$679$	7.50702	0.288093
$680$	0.698735	0.0267953
$681$	3.36884	0.129094
$682$	38.8580	1.48795
$683$	49.5622	1.89644	0.948222	−	0.317607i	$-0.102879\pi$
$683$	49.5622	1.89644	0.948222	+	0.317607i	$0.102879\pi$
$684$	0	0
$685$	2.45864	0.0939399
$686$	−1.00000	−0.0381802
$687$	0.558872	0.0213223
$688$	3.04988	0.116275
$689$	−0.752870	−0.0286821
$690$	−0.139863	−0.00532450
$691$	−35.3552	−1.34497	−0.672487	−	0.740109i	$-0.734774\pi$
$691$	−35.3552	−1.34497	−0.672487	+	0.740109i	$0.734774\pi$
$692$	2.80975	0.106811
$693$	−14.2646	−0.541867
$694$	21.6486	0.821771
$695$	0.0578075	0.00219276
$696$	0.113921	0.00431815
$697$	−27.1056	−1.02670
$698$	6.63522	0.251147
$699$	−1.02885	−0.0389146
$700$	−4.91930	−0.185932
$701$	−41.5824	−1.57055	−0.785273	−	0.619150i	$-0.787477\pi$
$701$	−41.5824	−1.57055	−0.785273	+	0.619150i	$0.787477\pi$
$702$	0.113718	0.00429201
$703$	0	0
$704$	4.80423	0.181066
$705$	0.136409	0.00513747
$706$	−15.8777	−0.597567
$707$	18.7283	0.704350
$708$	1.09017	0.0409711
$709$	−33.6927	−1.26535	−0.632677	−	0.774416i	$-0.718044\pi$
$709$	−33.6927	−1.26535	−0.632677	+	0.774416i	$0.718044\pi$
$710$	−0.539821	−0.0202591
$711$	−15.8035	−0.592676
$712$	−4.83203	−0.181088
$713$	22.6814	0.849426
$714$	−0.431842	−0.0161613
$715$	−0.148090	−0.00553826
$716$	−8.25867	−0.308641
$717$	0.971153	0.0362684
$718$	9.76974	0.364604
$719$	−11.9555	−0.445864	−0.222932	−	0.974834i	$-0.571563\pi$
$719$	−11.9555	−0.445864	−0.222932	+	0.974834i	$0.571563\pi$
$720$	0.843480	0.0314347
$721$	7.02009	0.261442
$722$	0	0
$723$	2.64886	0.0985121
$724$	−20.1204	−0.747768
$725$	3.19193	0.118545
$726$	−2.12099	−0.0787175
$727$	−20.7431	−0.769318	−0.384659	−	0.923059i	$-0.625681\pi$
$727$	−20.7431	−0.769318	−0.384659	+	0.923059i	$0.625681\pi$
$728$	−0.108509	−0.00402159
$729$	−25.3497	−0.938877
$730$	3.87315	0.143352
$731$	7.50163	0.277458
$732$	−0.952316	−0.0351986
$733$	40.1962	1.48468	0.742340	−	0.670024i	$-0.233716\pi$
$733$	40.1962	1.48468	0.742340	+	0.670024i	$0.233716\pi$
$734$	23.7355	0.876093
$735$	−0.0498759	−0.00183970
$736$	2.80423	0.103365
$737$	−48.9652	−1.80366
$738$	−32.7206	−1.20446
$739$	25.0697	0.922202	0.461101	−	0.887348i	$-0.347455\pi$
$739$	25.0697	0.922202	0.461101	+	0.887348i	$0.347455\pi$
$740$	−0.679357	−0.0249736
$741$	0	0
$742$	6.93835	0.254715
$743$	28.4675	1.04437	0.522185	−	0.852832i	$-0.325117\pi$
$743$	28.4675	1.04437	0.522185	+	0.852832i	$0.325117\pi$
$744$	1.42007	0.0520622
$745$	−4.99281	−0.182923
$746$	−18.1516	−0.664577
$747$	32.2383	1.17954
$748$	11.8167	0.432062
$749$	−9.64063	−0.352261
$750$	−0.494734	−0.0180651
$751$	3.18253	0.116132	0.0580661	−	0.998313i	$-0.481507\pi$
$751$	3.18253	0.116132	0.0580661	+	0.998313i	$0.481507\pi$
$752$	−2.73497	−0.0997342
$753$	−1.23672	−0.0450687
$754$	0.0704067	0.00256406
$755$	−1.18213	−0.0430223
$756$	−1.04801	−0.0381158
$757$	−15.5851	−0.566451	−0.283226	−	0.959053i	$-0.591405\pi$
$757$	−15.5851	−0.566451	−0.283226	+	0.959053i	$0.591405\pi$
$758$	33.9940	1.23472
$759$	−2.36531	−0.0858553
$760$	0	0
$761$	−48.6885	−1.76496	−0.882479	−	0.470352i	$-0.844127\pi$
$761$	−48.6885	−1.76496	−0.882479	+	0.470352i	$0.844127\pi$
$762$	0.105164	0.00380968
$763$	−9.75435	−0.353131
$764$	25.9039	0.937169
$765$	2.07467	0.0750097
$766$	−25.4241	−0.918611
$767$	0.673762	0.0243281
$768$	0.175571	0.00633535
$769$	41.2096	1.48606	0.743028	−	0.669261i	$-0.233389\pi$
$769$	41.2096	1.48606	0.743028	+	0.669261i	$0.233389\pi$
$770$	1.36478	0.0491833
$771$	2.51119	0.0904382
$772$	−23.0403	−0.829238
$773$	−5.39040	−0.193879	−0.0969395	−	0.995290i	$-0.530905\pi$
$773$	−5.39040	−0.193879	−0.0969395	+	0.995290i	$0.530905\pi$
$774$	9.05562	0.325497
$775$	39.7888	1.42926
$776$	−7.50702	−0.269486
$777$	0.419865	0.0150626
$778$	3.36072	0.120488
$779$	0	0
$780$	−0.00541196	−0.000193779 0
$781$	−9.12922	−0.326669
$782$	6.89741	0.246651
$783$	0.680011	0.0243016
$784$	1.00000	0.0357143
$785$	4.57993	0.163465
$786$	3.28346	0.117117
$787$	−45.4603	−1.62049	−0.810243	−	0.586094i	$-0.800665\pi$
$787$	−45.4603	−1.62049	−0.810243	+	0.586094i	$0.800665\pi$
$788$	3.74122	0.133275
$789$	4.28615	0.152591
$790$	1.51201	0.0537950
$791$	−10.3013	−0.366271
$792$	14.2646	0.506870
$793$	−0.588564	−0.0209005
$794$	22.6804	0.804897
$795$	0.346056	0.0122734
$796$	−20.0010	−0.708918
$797$	42.9905	1.52280	0.761401	−	0.648281i	$-0.224512\pi$
$797$	42.9905	1.52280	0.761401	+	0.648281i	$0.224512\pi$
$798$	0	0
$799$	−6.72707	−0.237987
$800$	4.91930	0.173923
$801$	−14.3472	−0.506932
$802$	17.8636	0.630785
$803$	65.5011	2.31149
$804$	−1.78943	−0.0631085
$805$	0.796622	0.0280772
$806$	0.877650	0.0309139
$807$	−2.70839	−0.0953397
$808$	−18.7283	−0.658859
$809$	−27.1956	−0.956146	−0.478073	−	0.878320i	$-0.658665\pi$
$809$	−27.1956	−0.956146	−0.478073	+	0.878320i	$0.658665\pi$
$810$	2.47817	0.0870740
$811$	50.0891	1.75887	0.879433	−	0.476022i	$-0.157922\pi$
$811$	50.0891	1.75887	0.879433	+	0.476022i	$0.157922\pi$
$812$	−0.648859	−0.0227705
$813$	0.841086	0.0294982
$814$	−11.4890	−0.402689
$815$	−1.69844	−0.0594937
$816$	0.431842	0.0151175
$817$	0	0
$818$	−9.22731	−0.322625
$819$	−0.322181	−0.0112579
$820$	3.13058	0.109324
$821$	50.5311	1.76355	0.881775	−	0.471671i	$-0.156349\pi$
$821$	50.5311	1.76355	0.881775	+	0.471671i	$0.156349\pi$
$822$	1.51952	0.0529995
$823$	−24.7688	−0.863387	−0.431694	−	0.902020i	$-0.642084\pi$
$823$	−24.7688	−0.863387	−0.431694	+	0.902020i	$0.642084\pi$
$824$	−7.02009	−0.244556
$825$	−4.14933	−0.144461
$826$	−6.20930	−0.216049
$827$	−4.88836	−0.169985	−0.0849925	−	0.996382i	$-0.527087\pi$
$827$	−4.88836	−0.169985	−0.0849925	+	0.996382i	$0.527087\pi$
$828$	8.32624	0.289357
$829$	−6.86975	−0.238596	−0.119298	−	0.992858i	$-0.538064\pi$
$829$	−6.86975	−0.238596	−0.119298	+	0.992858i	$0.538064\pi$
$830$	−3.08443	−0.107062
$831$	−0.877468	−0.0304390
$832$	0.108509	0.00376186
$833$	2.45965	0.0852218
$834$	0.0357270	0.00123713
$835$	5.27417	0.182520
$836$	0	0
$837$	8.47663	0.292995
$838$	27.8528	0.962158
$839$	39.6982	1.37053	0.685267	−	0.728292i	$-0.259686\pi$
$839$	39.6982	1.37053	0.685267	+	0.728292i	$0.259686\pi$
$840$	0.0498759	0.00172088
$841$	−28.5790	−0.985482
$842$	−12.9917	−0.447722
$843$	−1.38644	−0.0477515
$844$	−18.0211	−0.620313
$845$	3.68968	0.126929
$846$	−8.12061	−0.279192
$847$	12.0806	0.415094
$848$	−6.93835	−0.238264
$849$	−2.75099	−0.0944136
$850$	12.0998	0.415018
$851$	−6.70612	−0.229883
$852$	−0.333628	−0.0114299
$853$	−27.4487	−0.939827	−0.469913	−	0.882713i	$-0.655715\pi$
$853$	−27.4487	−0.939827	−0.469913	+	0.882713i	$0.655715\pi$
$854$	5.42412	0.185610
$855$	0	0
$856$	9.64063	0.329510
$857$	−36.0523	−1.23152	−0.615761	−	0.787933i	$-0.711151\pi$
$857$	−36.0523	−1.23152	−0.615761	+	0.787933i	$0.711151\pi$
$858$	−0.0915248	−0.00312461
$859$	17.5595	0.599124	0.299562	−	0.954077i	$-0.403160\pi$
$859$	17.5595	0.599124	0.299562	+	0.954077i	$0.403160\pi$
$860$	−0.866406	−0.0295442
$861$	−1.93480	−0.0659379
$862$	−23.1802	−0.789522
$863$	−5.71786	−0.194638	−0.0973190	−	0.995253i	$-0.531027\pi$
$863$	−5.71786	−0.194638	−0.0973190	+	0.995253i	$0.531027\pi$
$864$	1.04801	0.0356541
$865$	−0.798191	−0.0271393
$866$	−7.65904	−0.260265
$867$	−1.92252	−0.0652922
$868$	−8.08831	−0.274535
$869$	25.5705	0.867421
$870$	−0.0323624	−0.00109719
$871$	−1.10593	−0.0374731
$872$	9.75435	0.330324
$873$	−22.2897	−0.754390
$874$	0	0
$875$	2.81787	0.0952612
$876$	2.39374	0.0808770
$877$	−8.42445	−0.284474	−0.142237	−	0.989833i	$-0.545429\pi$
$877$	−8.42445	−0.284474	−0.142237	+	0.989833i	$0.545429\pi$
$878$	−24.0587	−0.811943
$879$	4.06070	0.136964
$880$	−1.36478	−0.0460067
$881$	−32.0089	−1.07841	−0.539204	−	0.842175i	$-0.681275\pi$
$881$	−32.0089	−1.07841	−0.539204	+	0.842175i	$0.681275\pi$
$882$	2.96917	0.0999773
$883$	22.0499	0.742037	0.371019	−	0.928625i	$-0.379009\pi$
$883$	22.0499	0.742037	0.371019	+	0.928625i	$0.379009\pi$
$884$	0.266893	0.00897658
$885$	−0.309694	−0.0104103
$886$	−3.56951	−0.119920
$887$	31.3891	1.05394	0.526972	−	0.849883i	$-0.323327\pi$
$887$	31.3891	1.05394	0.526972	+	0.849883i	$0.323327\pi$
$888$	−0.419865	−0.0140898
$889$	−0.598983	−0.0200892
$890$	1.37268	0.0460123
$891$	41.9098	1.40403
$892$	−22.2949	−0.746489
$893$	0	0
$894$	−3.08573	−0.103202
$895$	2.34611	0.0784219
$896$	−1.00000	−0.0334077
$897$	−0.0534230	−0.00178374
$898$	3.19566	0.106641
$899$	5.24817	0.175036
$900$	14.6063	0.486875
$901$	−17.0659	−0.568548
$902$	52.9430	1.76281
$903$	0.535468	0.0178193
$904$	10.3013	0.342615
$905$	5.71578	0.189999
$906$	−0.730600	−0.0242725
$907$	1.40603	0.0466865	0.0233433	−	0.999728i	$-0.492569\pi$
$907$	1.40603	0.0466865	0.0233433	+	0.999728i	$0.492569\pi$
$908$	19.1879	0.636774
$909$	−55.6076	−1.84439
$910$	0.0308250	0.00102184
$911$	−19.0119	−0.629893	−0.314946	−	0.949109i	$-0.601987\pi$
$911$	−19.0119	−0.629893	−0.314946	+	0.949109i	$0.601987\pi$
$912$	0	0
$913$	−52.1626	−1.72633
$914$	15.0461	0.497681
$915$	0.270533	0.00894355
$916$	3.18317	0.105175
$917$	−18.7016	−0.617583
$918$	2.57774	0.0850781
$919$	31.7783	1.04827	0.524135	−	0.851635i	$-0.324389\pi$
$919$	31.7783	1.04827	0.524135	+	0.851635i	$0.324389\pi$
$920$	−0.796622	−0.0262638
$921$	−2.83268	−0.0933399
$922$	8.35487	0.275153
$923$	−0.206193	−0.00678693
$924$	0.843480	0.0277485
$925$	−11.7642	−0.386804
$926$	30.7307	1.00987
$927$	−20.8439	−0.684603
$928$	0.648859	0.0212998
$929$	−55.0707	−1.80681	−0.903405	−	0.428788i	$-0.858941\pi$
$929$	−55.0707	−1.80681	−0.903405	+	0.428788i	$0.858941\pi$
$930$	−0.403412	−0.0132284
$931$	0	0
$932$	−5.86002	−0.191951
$933$	0.511188	0.0167355
$934$	9.49158	0.310574
$935$	−3.35688	−0.109782
$936$	0.322181	0.0105308
$937$	15.4768	0.505605	0.252802	−	0.967518i	$-0.418648\pi$
$937$	15.4768	0.505605	0.252802	+	0.967518i	$0.418648\pi$
$938$	10.1921	0.332784
$939$	0.700814	0.0228702
$940$	0.776948	0.0253413
$941$	50.4286	1.64392	0.821962	−	0.569542i	$-0.192880\pi$
$941$	50.4286	1.64392	0.821962	+	0.569542i	$0.192880\pi$
$942$	2.83055	0.0922244
$943$	30.9028	1.00633
$944$	6.20930	0.202096
$945$	0.297718	0.00968477
$946$	−14.6523	−0.476387
$947$	−22.1089	−0.718444	−0.359222	−	0.933252i	$-0.616958\pi$
$947$	−22.1089	−0.718444	−0.359222	+	0.933252i	$0.616958\pi$
$948$	0.934475	0.0303504
$949$	1.47941	0.0480238
$950$	0	0
$951$	0.381764	0.0123795
$952$	−2.45965	−0.0797177
$953$	40.5006	1.31194	0.655971	−	0.754786i	$-0.272259\pi$
$953$	40.5006	1.31194	0.655971	+	0.754786i	$0.272259\pi$
$954$	−20.6012	−0.666988
$955$	−7.35875	−0.238123
$956$	5.53141	0.178899
$957$	−0.547300	−0.0176917
$958$	−1.39516	−0.0450757
$959$	−8.65478	−0.279477
$960$	−0.0498759	−0.00160974
$961$	34.4207	1.11034
$962$	−0.259491	−0.00836633
$963$	28.6247	0.922419
$964$	15.0872	0.485924
$965$	6.54526	0.210700
$966$	0.492339	0.0158408
$967$	31.7198	1.02004	0.510019	−	0.860163i	$-0.329638\pi$
$967$	31.7198	1.02004	0.510019	+	0.860163i	$0.329638\pi$
$968$	−12.0806	−0.388285
$969$	0	0
$970$	2.13259	0.0684732
$971$	29.6126	0.950313	0.475156	−	0.879901i	$-0.342391\pi$
$971$	29.6126	0.950313	0.475156	+	0.879901i	$0.342391\pi$
$972$	4.67563	0.149971
$973$	−0.203491	−0.00652362
$974$	42.7878	1.37101
$975$	−0.0937171	−0.00300135
$976$	−5.42412	−0.173622
$977$	−3.31175	−0.105952	−0.0529762	−	0.998596i	$-0.516871\pi$
$977$	−3.31175	−0.105952	−0.0529762	+	0.998596i	$0.516871\pi$
$978$	−1.04969	−0.0335655
$979$	23.2142	0.741928
$980$	−0.284079	−0.00907457
$981$	28.9624	0.924697
$982$	−15.3548	−0.489990
$983$	−27.2766	−0.869990	−0.434995	−	0.900433i	$-0.643250\pi$
$983$	−27.2766	−0.869990	−0.434995	+	0.900433i	$0.643250\pi$
$984$	1.93480	0.0616793
$985$	−1.06280	−0.0338637
$986$	1.59597	0.0508259
$987$	−0.480180	−0.0152843
$988$	0	0
$989$	−8.55254	−0.271955
$990$	−4.05227	−0.128790
$991$	−15.6855	−0.498267	−0.249134	−	0.968469i	$-0.580146\pi$
$991$	−15.6855	−0.498267	−0.249134	+	0.968469i	$0.580146\pi$
$992$	8.08831	0.256804
$993$	−3.56662	−0.113183
$994$	1.90025	0.0602722
$995$	5.68188	0.180128
$996$	−1.90628	−0.0604029
$997$	17.1657	0.543642	0.271821	−	0.962348i	$-0.412374\pi$
$997$	17.1657	0.543642	0.271821	+	0.962348i	$0.412374\pi$
$998$	5.85765	0.185421
$999$	−2.50625	−0.0792943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.v.1.3	✓	4
19.18	odd	2		5054.2.a.y.1.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.v.1.3	✓	4	1.1	even	1	trivial
5054.2.a.y.1.2	yes	4	19.18	odd	2

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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.175571 q^{3} +1.00000 q^{4} -0.284079 q^{5} -0.175571 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.96917 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.175571 q^{3} +1.00000 q^{4} -0.284079 q^{5} -0.175571 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.96917 q^{9} +0.284079 q^{10} +4.80423 q^{11} +0.175571 q^{12} +0.108509 q^{13} -1.00000 q^{14} -0.0498759 q^{15} +1.00000 q^{16} +2.45965 q^{17} +2.96917 q^{18} -0.284079 q^{20} +0.175571 q^{21} -4.80423 q^{22} -2.80423 q^{23} -0.175571 q^{24} -4.91930 q^{25} -0.108509 q^{26} -1.04801 q^{27} +1.00000 q^{28} -0.648859 q^{29} +0.0498759 q^{30} -8.08831 q^{31} -1.00000 q^{32} +0.843480 q^{33} -2.45965 q^{34} -0.284079 q^{35} -2.96917 q^{36} +2.39144 q^{37} +0.0190509 q^{39} +0.284079 q^{40} -11.0201 q^{41} -0.175571 q^{42} +3.04988 q^{43} +4.80423 q^{44} +0.843480 q^{45} +2.80423 q^{46} -2.73497 q^{47} +0.175571 q^{48} +1.00000 q^{49} +4.91930 q^{50} +0.431842 q^{51} +0.108509 q^{52} -6.93835 q^{53} +1.04801 q^{54} -1.36478 q^{55} -1.00000 q^{56} +0.648859 q^{58} +6.20930 q^{59} -0.0498759 q^{60} -5.42412 q^{61} +8.08831 q^{62} -2.96917 q^{63} +1.00000 q^{64} -0.0308250 q^{65} -0.843480 q^{66} -10.1921 q^{67} +2.45965 q^{68} -0.492339 q^{69} +0.284079 q^{70} -1.90025 q^{71} +2.96917 q^{72} +13.6341 q^{73} -2.39144 q^{74} -0.863684 q^{75} +4.80423 q^{77} -0.0190509 q^{78} +5.32251 q^{79} -0.284079 q^{80} +8.72353 q^{81} +11.0201 q^{82} -10.8576 q^{83} +0.175571 q^{84} -0.698735 q^{85} -3.04988 q^{86} -0.113921 q^{87} -4.80423 q^{88} +4.83203 q^{89} -0.843480 q^{90} +0.108509 q^{91} -2.80423 q^{92} -1.42007 q^{93} +2.73497 q^{94} -0.175571 q^{96} +7.50702 q^{97} -1.00000 q^{98} -14.2646 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 4 q^{11} - 4 q^{12} + 2 q^{13} - 4 q^{14} - 2 q^{15} + 4 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{20} - 4 q^{21} - 4 q^{22} + 4 q^{23} + 4 q^{24} - 4 q^{25} - 2 q^{26} - 10 q^{27} + 4 q^{28} - 12 q^{29} + 2 q^{30} - 14 q^{31} - 4 q^{32} - 4 q^{33} - 2 q^{34} + 2 q^{35} + 2 q^{36} - 24 q^{37} - 12 q^{39} - 2 q^{40} + 4 q^{42} + 14 q^{43} + 4 q^{44} - 4 q^{45} - 4 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 4 q^{50} + 8 q^{51} + 2 q^{52} + 10 q^{54} - 18 q^{55} - 4 q^{56} + 12 q^{58} - 2 q^{59} - 2 q^{60} + 2 q^{61} + 14 q^{62} + 2 q^{63} + 4 q^{64} - 14 q^{65} + 4 q^{66} - 22 q^{67} + 2 q^{68} - 4 q^{69} - 2 q^{70} - 4 q^{71} - 2 q^{72} + 10 q^{73} + 24 q^{74} - 16 q^{75} + 4 q^{77} + 12 q^{78} - 2 q^{79} + 2 q^{80} + 4 q^{81} - 4 q^{84} - 14 q^{85} - 14 q^{86} + 32 q^{87} - 4 q^{88} - 10 q^{89} + 4 q^{90} + 2 q^{91} + 4 q^{92} + 14 q^{93} + 2 q^{94} + 4 q^{96} + 22 q^{97} - 4 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 + 4 * q^11 - 4 * q^12 + 2 * q^13 - 4 * q^14 - 2 * q^15 + 4 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^20 - 4 * q^21 - 4 * q^22 + 4 * q^23 + 4 * q^24 - 4 * q^25 - 2 * q^26 - 10 * q^27 + 4 * q^28 - 12 * q^29 + 2 * q^30 - 14 * q^31 - 4 * q^32 - 4 * q^33 - 2 * q^34 + 2 * q^35 + 2 * q^36 - 24 * q^37 - 12 * q^39 - 2 * q^40 + 4 * q^42 + 14 * q^43 + 4 * q^44 - 4 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 4 * q^50 + 8 * q^51 + 2 * q^52 + 10 * q^54 - 18 * q^55 - 4 * q^56 + 12 * q^58 - 2 * q^59 - 2 * q^60 + 2 * q^61 + 14 * q^62 + 2 * q^63 + 4 * q^64 - 14 * q^65 + 4 * q^66 - 22 * q^67 + 2 * q^68 - 4 * q^69 - 2 * q^70 - 4 * q^71 - 2 * q^72 + 10 * q^73 + 24 * q^74 - 16 * q^75 + 4 * q^77 + 12 * q^78 - 2 * q^79 + 2 * q^80 + 4 * q^81 - 4 * q^84 - 14 * q^85 - 14 * q^86 + 32 * q^87 - 4 * q^88 - 10 * q^89 + 4 * q^90 + 2 * q^91 + 4 * q^92 + 14 * q^93 + 2 * q^94 + 4 * q^96 + 22 * q^97 - 4 * q^98 + 2 * q^99

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