LMFDB - Embedded newform 5054.2.a.bm.1.10

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:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 24 x^{10} + 68 x^{9} + 213 x^{8} - 555 x^{7} - 814 x^{6} + 1911 x^{5} + 1005 x^{4} + \cdots + 1 $ x^12 - 3x^11 - 24x^10 + 68x^9 + 213x^8 - 555x^7 - 814x^6 + 1911x^5 + 1005x^4 - 2326x^3 + 570x^2 + 105*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.93688$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.93688 q^{3} +1.00000 q^{4} -0.167883 q^{5} +2.93688 q^{6} +1.00000 q^{7} +1.00000 q^{8} +5.62525 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.93688 q^{3} +1.00000 q^{4} -0.167883 q^{5} +2.93688 q^{6} +1.00000 q^{7} +1.00000 q^{8} +5.62525 q^{9} -0.167883 q^{10} +5.85382 q^{11} +2.93688 q^{12} +1.66176 q^{13} +1.00000 q^{14} -0.493051 q^{15} +1.00000 q^{16} -1.41436 q^{17} +5.62525 q^{18} -0.167883 q^{20} +2.93688 q^{21} +5.85382 q^{22} +8.26954 q^{23} +2.93688 q^{24} -4.97182 q^{25} +1.66176 q^{26} +7.71005 q^{27} +1.00000 q^{28} -6.89591 q^{29} -0.493051 q^{30} -8.06786 q^{31} +1.00000 q^{32} +17.1919 q^{33} -1.41436 q^{34} -0.167883 q^{35} +5.62525 q^{36} -6.18176 q^{37} +4.88037 q^{39} -0.167883 q^{40} -4.84436 q^{41} +2.93688 q^{42} +1.16579 q^{43} +5.85382 q^{44} -0.944382 q^{45} +8.26954 q^{46} +0.154029 q^{47} +2.93688 q^{48} +1.00000 q^{49} -4.97182 q^{50} -4.15379 q^{51} +1.66176 q^{52} -1.53808 q^{53} +7.71005 q^{54} -0.982754 q^{55} +1.00000 q^{56} -6.89591 q^{58} -5.20856 q^{59} -0.493051 q^{60} +12.3790 q^{61} -8.06786 q^{62} +5.62525 q^{63} +1.00000 q^{64} -0.278980 q^{65} +17.1919 q^{66} -2.21973 q^{67} -1.41436 q^{68} +24.2866 q^{69} -0.167883 q^{70} -8.24515 q^{71} +5.62525 q^{72} -10.6280 q^{73} -6.18176 q^{74} -14.6016 q^{75} +5.85382 q^{77} +4.88037 q^{78} +5.69649 q^{79} -0.167883 q^{80} +5.76771 q^{81} -4.84436 q^{82} -9.93514 q^{83} +2.93688 q^{84} +0.237446 q^{85} +1.16579 q^{86} -20.2524 q^{87} +5.85382 q^{88} +10.0204 q^{89} -0.944382 q^{90} +1.66176 q^{91} +8.26954 q^{92} -23.6943 q^{93} +0.154029 q^{94} +2.93688 q^{96} -12.2202 q^{97} +1.00000 q^{98} +32.9292 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} + 12 q^{8} + 21 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 + 12 * q^8 + 21 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} + 12 q^{8} + 21 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 6 q^{13} + 12 q^{14} - 6 q^{15} + 12 q^{16} + 3 q^{17} + 21 q^{18} + 3 q^{20} + 3 q^{21} + 3 q^{22} + 12 q^{23} + 3 q^{24} + 33 q^{25} - 6 q^{26} + 21 q^{27} + 12 q^{28} + 6 q^{29} - 6 q^{30} + 3 q^{31} + 12 q^{32} - 6 q^{33} + 3 q^{34} + 3 q^{35} + 21 q^{36} + 27 q^{37} + 27 q^{39} + 3 q^{40} - 27 q^{41} + 3 q^{42} + 30 q^{43} + 3 q^{44} + 30 q^{45} + 12 q^{46} + 21 q^{47} + 3 q^{48} + 12 q^{49} + 33 q^{50} + 3 q^{51} - 6 q^{52} + 6 q^{53} + 21 q^{54} + 48 q^{55} + 12 q^{56} + 6 q^{58} - 27 q^{59} - 6 q^{60} + 18 q^{61} + 3 q^{62} + 21 q^{63} + 12 q^{64} - 9 q^{65} - 6 q^{66} + 9 q^{67} + 3 q^{68} + 18 q^{69} + 3 q^{70} + 27 q^{71} + 21 q^{72} - 9 q^{73} + 27 q^{74} + 33 q^{75} + 3 q^{77} + 27 q^{78} - 12 q^{79} + 3 q^{80} + 24 q^{81} - 27 q^{82} + 9 q^{83} + 3 q^{84} + 78 q^{85} + 30 q^{86} - 45 q^{87} + 3 q^{88} - 24 q^{89} + 30 q^{90} - 6 q^{91} + 12 q^{92} + 3 q^{93} + 21 q^{94} + 3 q^{96} - 18 q^{97} + 12 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 + 12 * q^8 + 21 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 6 * q^13 + 12 * q^14 - 6 * q^15 + 12 * q^16 + 3 * q^17 + 21 * q^18 + 3 * q^20 + 3 * q^21 + 3 * q^22 + 12 * q^23 + 3 * q^24 + 33 * q^25 - 6 * q^26 + 21 * q^27 + 12 * q^28 + 6 * q^29 - 6 * q^30 + 3 * q^31 + 12 * q^32 - 6 * q^33 + 3 * q^34 + 3 * q^35 + 21 * q^36 + 27 * q^37 + 27 * q^39 + 3 * q^40 - 27 * q^41 + 3 * q^42 + 30 * q^43 + 3 * q^44 + 30 * q^45 + 12 * q^46 + 21 * q^47 + 3 * q^48 + 12 * q^49 + 33 * q^50 + 3 * q^51 - 6 * q^52 + 6 * q^53 + 21 * q^54 + 48 * q^55 + 12 * q^56 + 6 * q^58 - 27 * q^59 - 6 * q^60 + 18 * q^61 + 3 * q^62 + 21 * q^63 + 12 * q^64 - 9 * q^65 - 6 * q^66 + 9 * q^67 + 3 * q^68 + 18 * q^69 + 3 * q^70 + 27 * q^71 + 21 * q^72 - 9 * q^73 + 27 * q^74 + 33 * q^75 + 3 * q^77 + 27 * q^78 - 12 * q^79 + 3 * q^80 + 24 * q^81 - 27 * q^82 + 9 * q^83 + 3 * q^84 + 78 * q^85 + 30 * q^86 - 45 * q^87 + 3 * q^88 - 24 * q^89 + 30 * q^90 - 6 * q^91 + 12 * q^92 + 3 * q^93 + 21 * q^94 + 3 * q^96 - 18 * q^97 + 12 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.93688	1.69561	0.847804	−	0.530310i	$-0.177925\pi$
$3$	2.93688	1.69561	0.847804	+	0.530310i	$0.177925\pi$
$4$	1.00000	0.500000
$5$	−0.167883	−0.0750794	−0.0375397	−	0.999295i	$-0.511952\pi$
$5$	−0.167883	−0.0750794	−0.0375397	+	0.999295i	$0.511952\pi$
$6$	2.93688	1.19898
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	5.62525	1.87508
$10$	−0.167883	−0.0530892
$11$	5.85382	1.76499	0.882496	−	0.470320i	$-0.155862\pi$
$11$	5.85382	1.76499	0.882496	+	0.470320i	$0.155862\pi$
$12$	2.93688	0.847804
$13$	1.66176	0.460888	0.230444	−	0.973086i	$-0.425982\pi$
$13$	1.66176	0.460888	0.230444	+	0.973086i	$0.425982\pi$
$14$	1.00000	0.267261
$15$	−0.493051	−0.127305
$16$	1.00000	0.250000
$17$	−1.41436	−0.343032	−0.171516	−	0.985181i	$-0.554867\pi$
$17$	−1.41436	−0.343032	−0.171516	+	0.985181i	$0.554867\pi$
$18$	5.62525	1.32588
$19$	0	0
$19$	0	0
$20$	−0.167883	−0.0375397
$21$	2.93688	0.640879
$22$	5.85382	1.24804
$23$	8.26954	1.72432	0.862159	−	0.506637i	$-0.169112\pi$
$23$	8.26954	1.72432	0.862159	+	0.506637i	$0.169112\pi$
$24$	2.93688	0.599488
$25$	−4.97182	−0.994363
$26$	1.66176	0.325897
$27$	7.71005	1.48380
$28$	1.00000	0.188982
$29$	−6.89591	−1.28054	−0.640269	−	0.768151i	$-0.721177\pi$
$29$	−6.89591	−1.28054	−0.640269	+	0.768151i	$0.721177\pi$
$30$	−0.493051	−0.0900184
$31$	−8.06786	−1.44903	−0.724515	−	0.689259i	$-0.757936\pi$
$31$	−8.06786	−1.44903	−0.724515	+	0.689259i	$0.757936\pi$
$32$	1.00000	0.176777
$33$	17.1919	2.99273
$34$	−1.41436	−0.242560
$35$	−0.167883	−0.0283774
$36$	5.62525	0.937542
$37$	−6.18176	−1.01628	−0.508138	−	0.861276i	$-0.669666\pi$
$37$	−6.18176	−1.01628	−0.508138	+	0.861276i	$0.669666\pi$
$38$	0	0
$39$	4.88037	0.781485
$40$	−0.167883	−0.0265446
$41$	−4.84436	−0.756561	−0.378281	−	0.925691i	$-0.623485\pi$
$41$	−4.84436	−0.756561	−0.378281	+	0.925691i	$0.623485\pi$
$42$	2.93688	0.453170
$43$	1.16579	0.177782	0.0888908	−	0.996041i	$-0.471668\pi$
$43$	1.16579	0.177782	0.0888908	+	0.996041i	$0.471668\pi$
$44$	5.85382	0.882496
$45$	−0.944382	−0.140780
$46$	8.26954	1.21928
$47$	0.154029	0.0224675	0.0112337	−	0.999937i	$-0.496424\pi$
$47$	0.154029	0.0224675	0.0112337	+	0.999937i	$0.496424\pi$
$48$	2.93688	0.423902
$49$	1.00000	0.142857
$50$	−4.97182	−0.703121
$51$	−4.15379	−0.581647
$52$	1.66176	0.230444
$53$	−1.53808	−0.211272	−0.105636	−	0.994405i	$-0.533688\pi$
$53$	−1.53808	−0.211272	−0.105636	+	0.994405i	$0.533688\pi$
$54$	7.71005	1.04920
$55$	−0.982754	−0.132515
$56$	1.00000	0.133631
$57$	0	0
$58$	−6.89591	−0.905477
$59$	−5.20856	−0.678097	−0.339049	−	0.940769i	$-0.610105\pi$
$59$	−5.20856	−0.678097	−0.339049	+	0.940769i	$0.610105\pi$
$60$	−0.493051	−0.0636526
$61$	12.3790	1.58497	0.792485	−	0.609891i	$-0.208787\pi$
$61$	12.3790	1.58497	0.792485	+	0.609891i	$0.208787\pi$
$62$	−8.06786	−1.02462
$63$	5.62525	0.708715
$64$	1.00000	0.125000
$65$	−0.278980	−0.0346032
$66$	17.1919	2.11618
$67$	−2.21973	−0.271184	−0.135592	−	0.990765i	$-0.543294\pi$
$67$	−2.21973	−0.271184	−0.135592	+	0.990765i	$0.543294\pi$
$68$	−1.41436	−0.171516
$69$	24.2866	2.92377
$70$	−0.167883	−0.0200658
$71$	−8.24515	−0.978519	−0.489259	−	0.872138i	$-0.662733\pi$
$71$	−8.24515	−0.978519	−0.489259	+	0.872138i	$0.662733\pi$
$72$	5.62525	0.662942
$73$	−10.6280	−1.24391	−0.621956	−	0.783052i	$-0.713662\pi$
$73$	−10.6280	−1.24391	−0.621956	+	0.783052i	$0.713662\pi$
$74$	−6.18176	−0.718615
$75$	−14.6016	−1.68605
$76$	0	0
$77$	5.85382	0.667104
$78$	4.88037	0.552594
$79$	5.69649	0.640905	0.320453	−	0.947265i	$-0.396165\pi$
$79$	5.69649	0.640905	0.320453	+	0.947265i	$0.396165\pi$
$80$	−0.167883	−0.0187699
$81$	5.76771	0.640856
$82$	−4.84436	−0.534970
$83$	−9.93514	−1.09052	−0.545262	−	0.838266i	$-0.683570\pi$
$83$	−9.93514	−1.09052	−0.545262	+	0.838266i	$0.683570\pi$
$84$	2.93688	0.320440
$85$	0.237446	0.0257546
$86$	1.16579	0.125711
$87$	−20.2524	−2.17129
$88$	5.85382	0.624019
$89$	10.0204	1.06216	0.531081	−	0.847321i	$-0.321786\pi$
$89$	10.0204	1.06216	0.531081	+	0.847321i	$0.321786\pi$
$90$	−0.944382	−0.0995467
$91$	1.66176	0.174199
$92$	8.26954	0.862159
$93$	−23.6943	−2.45699
$94$	0.154029	0.0158869
$95$	0	0
$96$	2.93688	0.299744
$97$	−12.2202	−1.24077	−0.620384	−	0.784298i	$-0.713023\pi$
$97$	−12.2202	−1.24077	−0.620384	+	0.784298i	$0.713023\pi$
$98$	1.00000	0.101015
$99$	32.9292	3.30951
$100$	−4.97182	−0.497182
$101$	0.331346	0.0329701	0.0164851	−	0.999864i	$-0.494752\pi$
$101$	0.331346	0.0329701	0.0164851	+	0.999864i	$0.494752\pi$
$102$	−4.15379	−0.411287
$103$	0.895065	0.0881934	0.0440967	−	0.999027i	$-0.485959\pi$
$103$	0.895065	0.0881934	0.0440967	+	0.999027i	$0.485959\pi$
$104$	1.66176	0.162949
$105$	−0.493051	−0.0481168
$106$	−1.53808	−0.149392
$107$	10.1687	0.983045	0.491522	−	0.870865i	$-0.336441\pi$
$107$	10.1687	0.983045	0.491522	+	0.870865i	$0.336441\pi$
$108$	7.71005	0.741900
$109$	6.05462	0.579927	0.289964	−	0.957038i	$-0.406357\pi$
$109$	6.05462	0.579927	0.289964	+	0.957038i	$0.406357\pi$
$110$	−0.982754	−0.0937019
$111$	−18.1551	−1.72320
$112$	1.00000	0.0944911
$113$	3.80616	0.358053	0.179027	−	0.983844i	$-0.442705\pi$
$113$	3.80616	0.358053	0.179027	+	0.983844i	$0.442705\pi$
$114$	0	0
$115$	−1.38831	−0.129461
$116$	−6.89591	−0.640269
$117$	9.34780	0.864204
$118$	−5.20856	−0.479487
$119$	−1.41436	−0.129654
$120$	−0.493051	−0.0450092
$121$	23.2672	2.11520
$122$	12.3790	1.12074
$123$	−14.2273	−1.28283
$124$	−8.06786	−0.724515
$125$	1.67410	0.149736
$126$	5.62525	0.501137
$127$	6.28735	0.557912	0.278956	−	0.960304i	$-0.410012\pi$
$127$	6.28735	0.557912	0.278956	+	0.960304i	$0.410012\pi$
$128$	1.00000	0.0883883
$129$	3.42379	0.301448
$130$	−0.278980	−0.0244682
$131$	−18.9747	−1.65782	−0.828912	−	0.559380i	$-0.811039\pi$
$131$	−18.9747	−1.65782	−0.828912	+	0.559380i	$0.811039\pi$
$132$	17.1919	1.49637
$133$	0	0
$134$	−2.21973	−0.191756
$135$	−1.29438	−0.111403
$136$	−1.41436	−0.121280
$137$	10.2547	0.876119	0.438060	−	0.898946i	$-0.355666\pi$
$137$	10.2547	0.876119	0.438060	+	0.898946i	$0.355666\pi$
$138$	24.2866	2.06742
$139$	−17.3342	−1.47027	−0.735134	−	0.677921i	$-0.762881\pi$
$139$	−17.3342	−1.47027	−0.735134	+	0.677921i	$0.762881\pi$
$140$	−0.167883	−0.0141887
$141$	0.452366	0.0380961
$142$	−8.24515	−0.691917
$143$	9.72761	0.813464
$144$	5.62525	0.468771
$145$	1.15770	0.0961421
$146$	−10.6280	−0.879579
$147$	2.93688	0.242230
$148$	−6.18176	−0.508138
$149$	22.4619	1.84015	0.920074	−	0.391745i	$-0.128129\pi$
$149$	22.4619	1.84015	0.920074	+	0.391745i	$0.128129\pi$
$150$	−14.6016	−1.19222
$151$	−11.9005	−0.968452	−0.484226	−	0.874943i	$-0.660899\pi$
$151$	−11.9005	−0.968452	−0.484226	+	0.874943i	$0.660899\pi$
$152$	0	0
$153$	−7.95611	−0.643214
$154$	5.85382	0.471714
$155$	1.35445	0.108792
$156$	4.88037	0.390743
$157$	−0.147652	−0.0117839	−0.00589195	−	0.999983i	$-0.501875\pi$
$157$	−0.147652	−0.0117839	−0.00589195	+	0.999983i	$0.501875\pi$
$158$	5.69649	0.453189
$159$	−4.51715	−0.358234
$160$	−0.167883	−0.0132723
$161$	8.26954	0.651731
$162$	5.76771	0.453154
$163$	−20.2248	−1.58413	−0.792063	−	0.610440i	$-0.790993\pi$
$163$	−20.2248	−1.58413	−0.792063	+	0.610440i	$0.790993\pi$
$164$	−4.84436	−0.378281
$165$	−2.88623	−0.224693
$166$	−9.93514	−0.771117
$167$	14.6174	1.13113	0.565565	−	0.824703i	$-0.308658\pi$
$167$	14.6174	1.13113	0.565565	+	0.824703i	$0.308658\pi$
$168$	2.93688	0.226585
$169$	−10.2386	−0.787582
$170$	0.237446	0.0182113
$171$	0	0
$172$	1.16579	0.0888908
$173$	−16.5277	−1.25658	−0.628289	−	0.777980i	$-0.716245\pi$
$173$	−16.5277	−1.25658	−0.628289	+	0.777980i	$0.716245\pi$
$174$	−20.2524	−1.53533
$175$	−4.97182	−0.375834
$176$	5.85382	0.441248
$177$	−15.2969	−1.14979
$178$	10.0204	0.751062
$179$	11.8788	0.887861	0.443931	−	0.896061i	$-0.353584\pi$
$179$	11.8788	0.887861	0.443931	+	0.896061i	$0.353584\pi$
$180$	−0.944382	−0.0703901
$181$	14.3711	1.06820	0.534098	−	0.845423i	$-0.320651\pi$
$181$	14.3711	1.06820	0.534098	+	0.845423i	$0.320651\pi$
$182$	1.66176	0.123178
$183$	36.3557	2.68749
$184$	8.26954	0.609639
$185$	1.03781	0.0763013
$186$	−23.6943	−1.73735
$187$	−8.27938	−0.605448
$188$	0.154029	0.0112337
$189$	7.71005	0.560823
$190$	0	0
$191$	9.38259	0.678900	0.339450	−	0.940624i	$-0.389759\pi$
$191$	9.38259	0.678900	0.339450	+	0.940624i	$0.389759\pi$
$192$	2.93688	0.211951
$193$	−25.0448	−1.80276	−0.901382	−	0.433025i	$-0.857446\pi$
$193$	−25.0448	−1.80276	−0.901382	+	0.433025i	$0.857446\pi$
$194$	−12.2202	−0.877356
$195$	−0.819330	−0.0586735
$196$	1.00000	0.0714286
$197$	−0.596816	−0.0425214	−0.0212607	−	0.999774i	$-0.506768\pi$
$197$	−0.596816	−0.0425214	−0.0212607	+	0.999774i	$0.506768\pi$
$198$	32.9292	2.34018
$199$	23.0163	1.63158	0.815792	−	0.578345i	$-0.196301\pi$
$199$	23.0163	1.63158	0.815792	+	0.578345i	$0.196301\pi$
$200$	−4.97182	−0.351560
$201$	−6.51908	−0.459821
$202$	0.331346	0.0233134
$203$	−6.89591	−0.483998
$204$	−4.15379	−0.290824
$205$	0.813283	0.0568022
$206$	0.895065	0.0623621
$207$	46.5183	3.23324
$208$	1.66176	0.115222
$209$	0	0
$210$	−0.493051	−0.0340237
$211$	13.3969	0.922283	0.461142	−	0.887327i	$-0.347440\pi$
$211$	13.3969	0.922283	0.461142	+	0.887327i	$0.347440\pi$
$212$	−1.53808	−0.105636
$213$	−24.2150	−1.65918
$214$	10.1687	0.695117
$215$	−0.195716	−0.0133477
$216$	7.71005	0.524602
$217$	−8.06786	−0.547682
$218$	6.05462	0.410070
$219$	−31.2131	−2.10919
$220$	−0.982754	−0.0662573
$221$	−2.35032	−0.158099
$222$	−18.1551	−1.21849
$223$	−7.31711	−0.489990	−0.244995	−	0.969524i	$-0.578786\pi$
$223$	−7.31711	−0.489990	−0.244995	+	0.969524i	$0.578786\pi$
$224$	1.00000	0.0668153
$225$	−27.9677	−1.86451
$226$	3.80616	0.253182
$227$	9.49511	0.630213	0.315106	−	0.949056i	$-0.397960\pi$
$227$	9.49511	0.630213	0.315106	+	0.949056i	$0.397960\pi$
$228$	0	0
$229$	12.1411	0.802307	0.401153	−	0.916011i	$-0.368609\pi$
$229$	12.1411	0.802307	0.401153	+	0.916011i	$0.368609\pi$
$230$	−1.38831	−0.0915426
$231$	17.1919	1.13115
$232$	−6.89591	−0.452739
$233$	−2.05744	−0.134788	−0.0673938	−	0.997726i	$-0.521468\pi$
$233$	−2.05744	−0.134788	−0.0673938	+	0.997726i	$0.521468\pi$
$234$	9.34780	0.611085
$235$	−0.0258589	−0.00168685
$236$	−5.20856	−0.339049
$237$	16.7299	1.08672
$238$	−1.41436	−0.0916791
$239$	−6.66574	−0.431171	−0.215586	−	0.976485i	$-0.569166\pi$
$239$	−6.66574	−0.431171	−0.215586	+	0.976485i	$0.569166\pi$
$240$	−0.493051	−0.0318263
$241$	−9.30578	−0.599438	−0.299719	−	0.954027i	$-0.596893\pi$
$241$	−9.30578	−0.599438	−0.299719	+	0.954027i	$0.596893\pi$
$242$	23.2672	1.49567
$243$	−6.19108	−0.397158
$244$	12.3790	0.792485
$245$	−0.167883	−0.0107256
$246$	−14.2273	−0.907098
$247$	0	0
$248$	−8.06786	−0.512310
$249$	−29.1783	−1.84910
$250$	1.67410	0.105879
$251$	−10.4927	−0.662296	−0.331148	−	0.943579i	$-0.607436\pi$
$251$	−10.4927	−0.662296	−0.331148	+	0.943579i	$0.607436\pi$
$252$	5.62525	0.354358
$253$	48.4084	3.04341
$254$	6.28735	0.394503
$255$	0.697350	0.0436697
$256$	1.00000	0.0625000
$257$	23.7324	1.48039	0.740194	−	0.672394i	$-0.234734\pi$
$257$	23.7324	1.48039	0.740194	+	0.672394i	$0.234734\pi$
$258$	3.42379	0.213156
$259$	−6.18176	−0.384116
$260$	−0.278980	−0.0173016
$261$	−38.7912	−2.40112
$262$	−18.9747	−1.17226
$263$	10.3381	0.637474	0.318737	−	0.947843i	$-0.396741\pi$
$263$	10.3381	0.637474	0.318737	+	0.947843i	$0.396741\pi$
$264$	17.1919	1.05809
$265$	0.258217	0.0158621
$266$	0	0
$267$	29.4288	1.80101
$268$	−2.21973	−0.135592
$269$	20.6722	1.26040	0.630202	−	0.776431i	$-0.282972\pi$
$269$	20.6722	1.26040	0.630202	+	0.776431i	$0.282972\pi$
$270$	−1.29438	−0.0787737
$271$	5.33469	0.324059	0.162030	−	0.986786i	$-0.448196\pi$
$271$	5.33469	0.324059	0.162030	+	0.986786i	$0.448196\pi$
$272$	−1.41436	−0.0857580
$273$	4.88037	0.295374
$274$	10.2547	0.619510
$275$	−29.1041	−1.75504
$276$	24.2866	1.46188
$277$	23.0145	1.38280	0.691402	−	0.722470i	$-0.256993\pi$
$277$	23.0145	1.38280	0.691402	+	0.722470i	$0.256993\pi$
$278$	−17.3342	−1.03964
$279$	−45.3838	−2.71705
$280$	−0.167883	−0.0100329
$281$	3.40916	0.203374	0.101687	−	0.994816i	$-0.467576\pi$
$281$	3.40916	0.203374	0.101687	+	0.994816i	$0.467576\pi$
$282$	0.452366	0.0269380
$283$	4.21235	0.250398	0.125199	−	0.992132i	$-0.460043\pi$
$283$	4.21235	0.250398	0.125199	+	0.992132i	$0.460043\pi$
$284$	−8.24515	−0.489259
$285$	0	0
$286$	9.72761	0.575206
$287$	−4.84436	−0.285953
$288$	5.62525	0.331471
$289$	−14.9996	−0.882329
$290$	1.15770	0.0679827
$291$	−35.8891	−2.10386
$292$	−10.6280	−0.621956
$293$	−16.6053	−0.970090	−0.485045	−	0.874489i	$-0.661197\pi$
$293$	−16.6053	−0.970090	−0.485045	+	0.874489i	$0.661197\pi$
$294$	2.93688	0.171282
$295$	0.874428	0.0509112
$296$	−6.18176	−0.359307
$297$	45.1332	2.61889
$298$	22.4619	1.30118
$299$	13.7420	0.794718
$300$	−14.6016	−0.843025
$301$	1.16579	0.0671951
$302$	−11.9005	−0.684799
$303$	0.973122	0.0559044
$304$	0	0
$305$	−2.07822	−0.118999
$306$	−7.95611	−0.454821
$307$	−13.7816	−0.786560	−0.393280	−	0.919419i	$-0.628660\pi$
$307$	−13.7816	−0.786560	−0.393280	+	0.919419i	$0.628660\pi$
$308$	5.85382	0.333552
$309$	2.62870	0.149541
$310$	1.35445	0.0769278
$311$	−4.09294	−0.232089	−0.116045	−	0.993244i	$-0.537022\pi$
$311$	−4.09294	−0.232089	−0.116045	+	0.993244i	$0.537022\pi$
$312$	4.88037	0.276297
$313$	7.23396	0.408887	0.204444	−	0.978878i	$-0.434461\pi$
$313$	7.23396	0.408887	0.204444	+	0.978878i	$0.434461\pi$
$314$	−0.147652	−0.00833248
$315$	−0.944382	−0.0532099
$316$	5.69649	0.320453
$317$	31.7010	1.78050	0.890252	−	0.455468i	$-0.150528\pi$
$317$	31.7010	1.78050	0.890252	+	0.455468i	$0.150528\pi$
$318$	−4.51715	−0.253309
$319$	−40.3674	−2.26014
$320$	−0.167883	−0.00938493
$321$	29.8642	1.66686
$322$	8.26954	0.460843
$323$	0	0
$324$	5.76771	0.320428
$325$	−8.26194	−0.458290
$326$	−20.2248	−1.12015
$327$	17.7817	0.983329
$328$	−4.84436	−0.267485
$329$	0.154029	0.00849192
$330$	−2.88623	−0.158882
$331$	1.66753	0.0916557	0.0458278	−	0.998949i	$-0.485407\pi$
$331$	1.66753	0.0916557	0.0458278	+	0.998949i	$0.485407\pi$
$332$	−9.93514	−0.545262
$333$	−34.7740	−1.90560
$334$	14.6174	0.799830
$335$	0.372655	0.0203603
$336$	2.93688	0.160220
$337$	23.1063	1.25868	0.629340	−	0.777130i	$-0.283325\pi$
$337$	23.1063	1.25868	0.629340	+	0.777130i	$0.283325\pi$
$338$	−10.2386	−0.556905
$339$	11.1782	0.607118
$340$	0.237446	0.0128773
$341$	−47.2278	−2.55753
$342$	0	0
$343$	1.00000	0.0539949
$344$	1.16579	0.0628553
$345$	−4.07730	−0.219515
$346$	−16.5277	−0.888535
$347$	35.3703	1.89878	0.949388	−	0.314106i	$-0.101705\pi$
$347$	35.3703	1.89878	0.949388	+	0.314106i	$0.101705\pi$
$348$	−20.2524	−1.08565
$349$	32.6789	1.74926	0.874632	−	0.484788i	$-0.161103\pi$
$349$	32.6789	1.74926	0.874632	+	0.484788i	$0.161103\pi$
$350$	−4.97182	−0.265755
$351$	12.8122	0.683865
$352$	5.85382	0.312009
$353$	16.5338	0.880006	0.440003	−	0.897996i	$-0.354977\pi$
$353$	16.5338	0.880006	0.440003	+	0.897996i	$0.354977\pi$
$354$	−15.2969	−0.813022
$355$	1.38422	0.0734666
$356$	10.0204	0.531081
$357$	−4.15379	−0.219842
$358$	11.8788	0.627813
$359$	−6.82256	−0.360081	−0.180040	−	0.983659i	$-0.557623\pi$
$359$	−6.82256	−0.360081	−0.180040	+	0.983659i	$0.557623\pi$
$360$	−0.944382	−0.0497733
$361$	0	0
$362$	14.3711	0.755328
$363$	68.3328	3.58654
$364$	1.66176	0.0870997
$365$	1.78426	0.0933922
$366$	36.3557	1.90034
$367$	10.3686	0.541235	0.270617	−	0.962687i	$-0.412772\pi$
$367$	10.3686	0.541235	0.270617	+	0.962687i	$0.412772\pi$
$368$	8.26954	0.431080
$369$	−27.2507	−1.41862
$370$	1.03781	0.0539532
$371$	−1.53808	−0.0798531
$372$	−23.6943	−1.22849
$373$	−9.75909	−0.505306	−0.252653	−	0.967557i	$-0.581303\pi$
$373$	−9.75909	−0.505306	−0.252653	+	0.967557i	$0.581303\pi$
$374$	−8.27938	−0.428117
$375$	4.91661	0.253893
$376$	0.154029	0.00794346
$377$	−11.4593	−0.590185
$378$	7.71005	0.396562
$379$	18.9676	0.974302	0.487151	−	0.873318i	$-0.338036\pi$
$379$	18.9676	0.974302	0.487151	+	0.873318i	$0.338036\pi$
$380$	0	0
$381$	18.4652	0.945999
$382$	9.38259	0.480055
$383$	7.57482	0.387055	0.193528	−	0.981095i	$-0.438007\pi$
$383$	7.57482	0.387055	0.193528	+	0.981095i	$0.438007\pi$
$384$	2.93688	0.149872
$385$	−0.982754	−0.0500858
$386$	−25.0448	−1.27475
$387$	6.55787	0.333355
$388$	−12.2202	−0.620384
$389$	−19.4484	−0.986073	−0.493037	−	0.870009i	$-0.664113\pi$
$389$	−19.4484	−0.986073	−0.493037	+	0.870009i	$0.664113\pi$
$390$	−0.819330	−0.0414884
$391$	−11.6961	−0.591496
$392$	1.00000	0.0505076
$393$	−55.7262	−2.81102
$394$	−0.596816	−0.0300672
$395$	−0.956342	−0.0481188
$396$	32.9292	1.65475
$397$	−12.6930	−0.637045	−0.318523	−	0.947915i	$-0.603187\pi$
$397$	−12.6930	−0.637045	−0.318523	+	0.947915i	$0.603187\pi$
$398$	23.0163	1.15370
$399$	0	0
$400$	−4.97182	−0.248591
$401$	−18.9738	−0.947508	−0.473754	−	0.880657i	$-0.657101\pi$
$401$	−18.9738	−0.947508	−0.473754	+	0.880657i	$0.657101\pi$
$402$	−6.51908	−0.325142
$403$	−13.4068	−0.667841
$404$	0.331346	0.0164851
$405$	−0.968298	−0.0481151
$406$	−6.89591	−0.342238
$407$	−36.1869	−1.79372
$408$	−4.15379	−0.205643
$409$	−10.1298	−0.500887	−0.250443	−	0.968131i	$-0.580576\pi$
$409$	−10.1298	−0.500887	−0.250443	+	0.968131i	$0.580576\pi$
$410$	0.813283	0.0401652
$411$	30.1168	1.48555
$412$	0.895065	0.0440967
$413$	−5.20856	−0.256297
$414$	46.5183	2.28625
$415$	1.66794	0.0818759
$416$	1.66176	0.0814743
$417$	−50.9085	−2.49300
$418$	0	0
$419$	−26.3112	−1.28539	−0.642694	−	0.766123i	$-0.722183\pi$
$419$	−26.3112	−1.28539	−0.642694	+	0.766123i	$0.722183\pi$
$420$	−0.493051	−0.0240584
$421$	−26.5413	−1.29354	−0.646772	−	0.762683i	$-0.723882\pi$
$421$	−26.5413	−1.29354	−0.646772	+	0.762683i	$0.723882\pi$
$422$	13.3969	0.652153
$423$	0.866454	0.0421284
$424$	−1.53808	−0.0746958
$425$	7.03192	0.341098
$426$	−24.2150	−1.17322
$427$	12.3790	0.599063
$428$	10.1687	0.491522
$429$	28.5688	1.37932
$430$	−0.195716	−0.00943827
$431$	−25.5907	−1.23266	−0.616331	−	0.787487i	$-0.711382\pi$
$431$	−25.5907	−1.23266	−0.616331	+	0.787487i	$0.711382\pi$
$432$	7.71005	0.370950
$433$	8.94247	0.429748	0.214874	−	0.976642i	$-0.431066\pi$
$433$	8.94247	0.429748	0.214874	+	0.976642i	$0.431066\pi$
$434$	−8.06786	−0.387270
$435$	3.40004	0.163019
$436$	6.05462	0.289964
$437$	0	0
$438$	−31.2131	−1.49142
$439$	−12.4057	−0.592090	−0.296045	−	0.955174i	$-0.595668\pi$
$439$	−12.4057	−0.592090	−0.296045	+	0.955174i	$0.595668\pi$
$440$	−0.982754	−0.0468510
$441$	5.62525	0.267869
$442$	−2.35032	−0.111793
$443$	−17.6686	−0.839463	−0.419731	−	0.907648i	$-0.637876\pi$
$443$	−17.6686	−0.839463	−0.419731	+	0.907648i	$0.637876\pi$
$444$	−18.1551	−0.861602
$445$	−1.68225	−0.0797465
$446$	−7.31711	−0.346475
$447$	65.9678	3.12017
$448$	1.00000	0.0472456
$449$	−14.1170	−0.666220	−0.333110	−	0.942888i	$-0.608098\pi$
$449$	−14.1170	−0.666220	−0.333110	+	0.942888i	$0.608098\pi$
$450$	−27.9677	−1.31841
$451$	−28.3580	−1.33532
$452$	3.80616	0.179027
$453$	−34.9504	−1.64211
$454$	9.49511	0.445628
$455$	−0.278980	−0.0130788
$456$	0	0
$457$	−22.6332	−1.05874	−0.529369	−	0.848392i	$-0.677571\pi$
$457$	−22.6332	−1.05874	−0.529369	+	0.848392i	$0.677571\pi$
$458$	12.1411	0.567317
$459$	−10.9048	−0.508990
$460$	−1.38831	−0.0647304
$461$	−28.3983	−1.32264	−0.661319	−	0.750104i	$-0.730003\pi$
$461$	−28.3983	−1.32264	−0.661319	+	0.750104i	$0.730003\pi$
$462$	17.1919	0.799842
$463$	2.08478	0.0968878	0.0484439	−	0.998826i	$-0.484574\pi$
$463$	2.08478	0.0968878	0.0484439	+	0.998826i	$0.484574\pi$
$464$	−6.89591	−0.320135
$465$	3.97787	0.184469
$466$	−2.05744	−0.0953092
$467$	−26.3159	−1.21776	−0.608878	−	0.793264i	$-0.708380\pi$
$467$	−26.3159	−1.21776	−0.608878	+	0.793264i	$0.708380\pi$
$468$	9.34780	0.432102
$469$	−2.21973	−0.102498
$470$	−0.0258589	−0.00119278
$471$	−0.433636	−0.0199809
$472$	−5.20856	−0.239744
$473$	6.82433	0.313783
$474$	16.7299	0.768430
$475$	0	0
$476$	−1.41436	−0.0648269
$477$	−8.65209	−0.396152
$478$	−6.66574	−0.304884
$479$	−4.82538	−0.220477	−0.110239	−	0.993905i	$-0.535161\pi$
$479$	−4.82538	−0.220477	−0.110239	+	0.993905i	$0.535161\pi$
$480$	−0.493051	−0.0225046
$481$	−10.2726	−0.468389
$482$	−9.30578	−0.423867
$483$	24.2866	1.10508
$484$	23.2672	1.05760
$485$	2.05155	0.0931562
$486$	−6.19108	−0.280833
$487$	−24.0690	−1.09067	−0.545335	−	0.838218i	$-0.683597\pi$
$487$	−24.0690	−1.09067	−0.545335	+	0.838218i	$0.683597\pi$
$488$	12.3790	0.560372
$489$	−59.3977	−2.68605
$490$	−0.167883	−0.00758417
$491$	16.4774	0.743616	0.371808	−	0.928310i	$-0.378738\pi$
$491$	16.4774	0.743616	0.371808	+	0.928310i	$0.378738\pi$
$492$	−14.2273	−0.641415
$493$	9.75328	0.439265
$494$	0	0
$495$	−5.52824	−0.248476
$496$	−8.06786	−0.362258
$497$	−8.24515	−0.369845
$498$	−29.1783	−1.30751
$499$	−33.9334	−1.51907	−0.759533	−	0.650469i	$-0.774573\pi$
$499$	−33.9334	−1.51907	−0.759533	+	0.650469i	$0.774573\pi$
$500$	1.67410	0.0748678
$501$	42.9296	1.91795
$502$	−10.4927	−0.468314
$503$	−15.5750	−0.694455	−0.347227	−	0.937781i	$-0.612877\pi$
$503$	−15.5750	−0.694455	−0.347227	+	0.937781i	$0.612877\pi$
$504$	5.62525	0.250569
$505$	−0.0556272	−0.00247538
$506$	48.4084	2.15201
$507$	−30.0694	−1.33543
$508$	6.28735	0.278956
$509$	−33.7611	−1.49643	−0.748217	−	0.663454i	$-0.769090\pi$
$509$	−33.7611	−1.49643	−0.748217	+	0.663454i	$0.769090\pi$
$510$	0.697350	0.0308792
$511$	−10.6280	−0.470154
$512$	1.00000	0.0441942
$513$	0	0
$514$	23.7324	1.04679
$515$	−0.150266	−0.00662151
$516$	3.42379	0.150724
$517$	0.901660	0.0396549
$518$	−6.18176	−0.271611
$519$	−48.5399	−2.13066
$520$	−0.278980	−0.0122341
$521$	−4.70124	−0.205965	−0.102982	−	0.994683i	$-0.532839\pi$
$521$	−4.70124	−0.205965	−0.102982	+	0.994683i	$0.532839\pi$
$522$	−38.7912	−1.69785
$523$	−41.8308	−1.82913	−0.914566	−	0.404437i	$-0.867468\pi$
$523$	−41.8308	−1.82913	−0.914566	+	0.404437i	$0.867468\pi$
$524$	−18.9747	−0.828912
$525$	−14.6016	−0.637267
$526$	10.3381	0.450762
$527$	11.4108	0.497064
$528$	17.1919	0.748183
$529$	45.3853	1.97327
$530$	0.258217	0.0112162
$531$	−29.2995	−1.27149
$532$	0	0
$533$	−8.05014	−0.348690
$534$	29.4288	1.27351
$535$	−1.70715	−0.0738064
$536$	−2.21973	−0.0958779
$537$	34.8865	1.50546
$538$	20.6722	0.891240
$539$	5.85382	0.252142
$540$	−1.29438	−0.0557014
$541$	−3.33966	−0.143583	−0.0717916	−	0.997420i	$-0.522872\pi$
$541$	−3.33966	−0.143583	−0.0717916	+	0.997420i	$0.522872\pi$
$542$	5.33469	0.229144
$543$	42.2062	1.81124
$544$	−1.41436	−0.0606400
$545$	−1.01647	−0.0435406
$546$	4.88037	0.208861
$547$	25.1993	1.07744	0.538722	−	0.842484i	$-0.318907\pi$
$547$	25.1993	1.07744	0.538722	+	0.842484i	$0.318907\pi$
$548$	10.2547	0.438060
$549$	69.6351	2.97195
$550$	−29.1041	−1.24100
$551$	0	0
$552$	24.2866	1.03371
$553$	5.69649	0.242239
$554$	23.0145	0.977791
$555$	3.04792	0.129377
$556$	−17.3342	−0.735134
$557$	−20.4468	−0.866359	−0.433180	−	0.901308i	$-0.642608\pi$
$557$	−20.4468	−0.866359	−0.433180	+	0.901308i	$0.642608\pi$
$558$	−45.3838	−1.92125
$559$	1.93726	0.0819374
$560$	−0.167883	−0.00709434
$561$	−24.3155	−1.02660
$562$	3.40916	0.143807
$563$	−6.79170	−0.286236	−0.143118	−	0.989706i	$-0.545713\pi$
$563$	−6.79170	−0.286236	−0.143118	+	0.989706i	$0.545713\pi$
$564$	0.452366	0.0190480
$565$	−0.638988	−0.0268824
$566$	4.21235	0.177058
$567$	5.76771	0.242221
$568$	−8.24515	−0.345959
$569$	23.1581	0.970836	0.485418	−	0.874282i	$-0.338667\pi$
$569$	23.1581	0.970836	0.485418	+	0.874282i	$0.338667\pi$
$570$	0	0
$571$	28.7662	1.20383	0.601914	−	0.798561i	$-0.294405\pi$
$571$	28.7662	1.20383	0.601914	+	0.798561i	$0.294405\pi$
$572$	9.72761	0.406732
$573$	27.5555	1.15115
$574$	−4.84436	−0.202199
$575$	−41.1146	−1.71460
$576$	5.62525	0.234386
$577$	18.3410	0.763547	0.381773	−	0.924256i	$-0.375314\pi$
$577$	18.3410	0.763547	0.381773	+	0.924256i	$0.375314\pi$
$578$	−14.9996	−0.623901
$579$	−73.5535	−3.05678
$580$	1.15770	0.0480710
$581$	−9.93514	−0.412179
$582$	−35.8891	−1.48765
$583$	−9.00364	−0.372893
$584$	−10.6280	−0.439789
$585$	−1.56933	−0.0648839
$586$	−16.6053	−0.685957
$587$	−47.4916	−1.96019	−0.980095	−	0.198529i	$-0.936384\pi$
$587$	−47.4916	−1.96019	−0.980095	+	0.198529i	$0.936384\pi$
$588$	2.93688	0.121115
$589$	0	0
$590$	0.874428	0.0359996
$591$	−1.75278	−0.0720996
$592$	−6.18176	−0.254069
$593$	11.7283	0.481625	0.240812	−	0.970572i	$-0.422586\pi$
$593$	11.7283	0.481625	0.240812	+	0.970572i	$0.422586\pi$
$594$	45.1332	1.85184
$595$	0.237446	0.00973434
$596$	22.4619	0.920074
$597$	67.5961	2.76653
$598$	13.7420	0.561950
$599$	−37.5795	−1.53546	−0.767728	−	0.640775i	$-0.778613\pi$
$599$	−37.5795	−1.53546	−0.767728	+	0.640775i	$0.778613\pi$
$600$	−14.6016	−0.596108
$601$	−1.33987	−0.0546545	−0.0273273	−	0.999627i	$-0.508700\pi$
$601$	−1.33987	−0.0546545	−0.0273273	+	0.999627i	$0.508700\pi$
$602$	1.16579	0.0475141
$603$	−12.4866	−0.508492
$604$	−11.9005	−0.484226
$605$	−3.90615	−0.158808
$606$	0.973122	0.0395304
$607$	−5.32483	−0.216128	−0.108064	−	0.994144i	$-0.534465\pi$
$607$	−5.32483	−0.216128	−0.108064	+	0.994144i	$0.534465\pi$
$608$	0	0
$609$	−20.2524	−0.820671
$610$	−2.07822	−0.0841448
$611$	0.255959	0.0103550
$612$	−7.95611	−0.321607
$613$	15.3686	0.620733	0.310367	−	0.950617i	$-0.399548\pi$
$613$	15.3686	0.620733	0.310367	+	0.950617i	$0.399548\pi$
$614$	−13.7816	−0.556182
$615$	2.38851	0.0963142
$616$	5.85382	0.235857
$617$	27.8968	1.12308	0.561541	−	0.827449i	$-0.310209\pi$
$617$	27.8968	1.12308	0.561541	+	0.827449i	$0.310209\pi$
$618$	2.62870	0.105742
$619$	25.1582	1.01119	0.505597	−	0.862770i	$-0.331272\pi$
$619$	25.1582	1.01119	0.505597	+	0.862770i	$0.331272\pi$
$620$	1.35445	0.0543962
$621$	63.7585	2.55854
$622$	−4.09294	−0.164112
$623$	10.0204	0.401460
$624$	4.88037	0.195371
$625$	24.5780	0.983121
$626$	7.23396	0.289127
$627$	0	0
$628$	−0.147652	−0.00589195
$629$	8.74321	0.348615
$630$	−0.944382	−0.0376251
$631$	6.07571	0.241870	0.120935	−	0.992660i	$-0.461411\pi$
$631$	6.07571	0.241870	0.120935	+	0.992660i	$0.461411\pi$
$632$	5.69649	0.226594
$633$	39.3452	1.56383
$634$	31.7010	1.25901
$635$	−1.05554	−0.0418877
$636$	−4.51715	−0.179117
$637$	1.66176	0.0658412
$638$	−40.3674	−1.59816
$639$	−46.3810	−1.83481
$640$	−0.167883	−0.00663615
$641$	−18.7683	−0.741301	−0.370651	−	0.928772i	$-0.620865\pi$
$641$	−18.7683	−0.741301	−0.370651	+	0.928772i	$0.620865\pi$
$642$	29.8642	1.17865
$643$	17.7478	0.699906	0.349953	−	0.936767i	$-0.386198\pi$
$643$	17.7478	0.699906	0.349953	+	0.936767i	$0.386198\pi$
$644$	8.26954	0.325866
$645$	−0.574795	−0.0226325
$646$	0	0
$647$	48.6137	1.91120	0.955601	−	0.294664i	$-0.0952077\pi$
$647$	48.6137	1.91120	0.955601	+	0.294664i	$0.0952077\pi$
$648$	5.76771	0.226577
$649$	−30.4900	−1.19684
$650$	−8.26194	−0.324060
$651$	−23.6943	−0.928654
$652$	−20.2248	−0.792063
$653$	−35.4440	−1.38703	−0.693515	−	0.720442i	$-0.743939\pi$
$653$	−35.4440	−1.38703	−0.693515	+	0.720442i	$0.743939\pi$
$654$	17.7817	0.695318
$655$	3.18552	0.124468
$656$	−4.84436	−0.189140
$657$	−59.7851	−2.33244
$658$	0.154029	0.00600469
$659$	16.3470	0.636790	0.318395	−	0.947958i	$-0.396856\pi$
$659$	16.3470	0.636790	0.318395	+	0.947958i	$0.396856\pi$
$660$	−2.88623	−0.112346
$661$	23.7150	0.922405	0.461203	−	0.887295i	$-0.347418\pi$
$661$	23.7150	0.922405	0.461203	+	0.887295i	$0.347418\pi$
$662$	1.66753	0.0648104
$663$	−6.90259	−0.268074
$664$	−9.93514	−0.385558
$665$	0	0
$666$	−34.7740	−1.34746
$667$	−57.0260	−2.20806
$668$	14.6174	0.565565
$669$	−21.4895	−0.830831
$670$	0.372655	0.0143969
$671$	72.4645	2.79746
$672$	2.93688	0.113293
$673$	12.9809	0.500377	0.250188	−	0.968197i	$-0.419507\pi$
$673$	12.9809	0.500377	0.250188	+	0.968197i	$0.419507\pi$
$674$	23.1063	0.890022
$675$	−38.3329	−1.47544
$676$	−10.2386	−0.393791
$677$	−17.3842	−0.668129	−0.334064	−	0.942550i	$-0.608420\pi$
$677$	−17.3842	−0.668129	−0.334064	+	0.942550i	$0.608420\pi$
$678$	11.1782	0.429297
$679$	−12.2202	−0.468966
$680$	0.237446	0.00910564
$681$	27.8860	1.06859
$682$	−47.2278	−1.80844
$683$	33.6737	1.28849	0.644243	−	0.764821i	$-0.277172\pi$
$683$	33.6737	1.28849	0.644243	+	0.764821i	$0.277172\pi$
$684$	0	0
$685$	−1.72159	−0.0657785
$686$	1.00000	0.0381802
$687$	35.6570	1.36040
$688$	1.16579	0.0444454
$689$	−2.55591	−0.0973726
$690$	−4.07730	−0.155220
$691$	11.2788	0.429067	0.214533	−	0.976717i	$-0.431177\pi$
$691$	11.2788	0.429067	0.214533	+	0.976717i	$0.431177\pi$
$692$	−16.5277	−0.628289
$693$	32.9292	1.25088
$694$	35.3703	1.34264
$695$	2.91011	0.110387
$696$	−20.2524	−0.767667
$697$	6.85165	0.259525
$698$	32.6789	1.23692
$699$	−6.04246	−0.228547
$700$	−4.97182	−0.187917
$701$	15.0140	0.567071	0.283535	−	0.958962i	$-0.408493\pi$
$701$	15.0140	0.567071	0.283535	+	0.958962i	$0.408493\pi$
$702$	12.8122	0.483566
$703$	0	0
$704$	5.85382	0.220624
$705$	−0.0759443	−0.00286023
$706$	16.5338	0.622259
$707$	0.331346	0.0124615
$708$	−15.2969	−0.574893
$709$	43.3744	1.62896	0.814479	−	0.580192i	$-0.197023\pi$
$709$	43.3744	1.62896	0.814479	+	0.580192i	$0.197023\pi$
$710$	1.38422	0.0519488
$711$	32.0442	1.20175
$712$	10.0204	0.375531
$713$	−66.7175	−2.49859
$714$	−4.15379	−0.155452
$715$	−1.63310	−0.0610744
$716$	11.8788	0.443931
$717$	−19.5765	−0.731097
$718$	−6.82256	−0.254616
$719$	7.68558	0.286624	0.143312	−	0.989678i	$-0.454225\pi$
$719$	7.68558	0.286624	0.143312	+	0.989678i	$0.454225\pi$
$720$	−0.944382	−0.0351951
$721$	0.895065	0.0333340
$722$	0	0
$723$	−27.3299	−1.01641
$724$	14.3711	0.534098
$725$	34.2852	1.27332
$726$	68.3328	2.53607
$727$	12.4987	0.463551	0.231775	−	0.972769i	$-0.425547\pi$
$727$	12.4987	0.463551	0.231775	+	0.972769i	$0.425547\pi$
$728$	1.66176	0.0615888
$729$	−35.4856	−1.31428
$730$	1.78426	0.0660382
$731$	−1.64884	−0.0609847
$732$	36.3557	1.34374
$733$	28.5108	1.05307	0.526534	−	0.850154i	$-0.323491\pi$
$733$	28.5108	1.05307	0.526534	+	0.850154i	$0.323491\pi$
$734$	10.3686	0.382711
$735$	−0.493051	−0.0181865
$736$	8.26954	0.304819
$737$	−12.9939	−0.478637
$738$	−27.2507	−1.00311
$739$	−50.0584	−1.84143	−0.920715	−	0.390237i	$-0.872393\pi$
$739$	−50.0584	−1.84143	−0.920715	+	0.390237i	$0.872393\pi$
$740$	1.03781	0.0381507
$741$	0	0
$742$	−1.53808	−0.0564647
$743$	6.73643	0.247136	0.123568	−	0.992336i	$-0.460566\pi$
$743$	6.73643	0.247136	0.123568	+	0.992336i	$0.460566\pi$
$744$	−23.6943	−0.868676
$745$	−3.77096	−0.138157
$746$	−9.75909	−0.357306
$747$	−55.8877	−2.04482
$748$	−8.27938	−0.302724
$749$	10.1687	0.371556
$750$	4.91661	0.179529
$751$	−38.5477	−1.40662	−0.703312	−	0.710881i	$-0.748296\pi$
$751$	−38.5477	−1.40662	−0.703312	+	0.710881i	$0.748296\pi$
$752$	0.154029	0.00561687
$753$	−30.8159	−1.12299
$754$	−11.4593	−0.417324
$755$	1.99789	0.0727108
$756$	7.71005	0.280412
$757$	−27.8178	−1.01105	−0.505527	−	0.862811i	$-0.668702\pi$
$757$	−27.8178	−1.01105	−0.505527	+	0.862811i	$0.668702\pi$
$758$	18.9676	0.688936
$759$	142.169	5.16042
$760$	0	0
$761$	−0.533458	−0.0193378	−0.00966891	−	0.999953i	$-0.503078\pi$
$761$	−0.533458	−0.0193378	−0.00966891	+	0.999953i	$0.503078\pi$
$762$	18.4652	0.668922
$763$	6.05462	0.219192
$764$	9.38259	0.339450
$765$	1.33569	0.0482921
$766$	7.57482	0.273689
$767$	−8.65536	−0.312527
$768$	2.93688	0.105975
$769$	43.0058	1.55083	0.775414	−	0.631453i	$-0.217541\pi$
$769$	43.0058	1.55083	0.775414	+	0.631453i	$0.217541\pi$
$770$	−0.982754	−0.0354160
$771$	69.6992	2.51016
$772$	−25.0448	−0.901382
$773$	19.1707	0.689523	0.344762	−	0.938690i	$-0.387960\pi$
$773$	19.1707	0.689523	0.344762	+	0.938690i	$0.387960\pi$
$774$	6.55787	0.235718
$775$	40.1119	1.44086
$776$	−12.2202	−0.438678
$777$	−18.1551	−0.651310
$778$	−19.4484	−0.697259
$779$	0	0
$780$	−0.819330	−0.0293367
$781$	−48.2656	−1.72708
$782$	−11.6961	−0.418251
$783$	−53.1678	−1.90006
$784$	1.00000	0.0357143
$785$	0.0247882	0.000884729 0
$786$	−55.7262	−1.98769
$787$	−36.5017	−1.30114	−0.650572	−	0.759444i	$-0.725471\pi$
$787$	−36.5017	−1.30114	−0.650572	+	0.759444i	$0.725471\pi$
$788$	−0.596816	−0.0212607
$789$	30.3617	1.08091
$790$	−0.956342	−0.0340251
$791$	3.80616	0.135331
$792$	32.9292	1.17009
$793$	20.5709	0.730494
$794$	−12.6930	−0.450459
$795$	0.758352	0.0268960
$796$	23.0163	0.815792
$797$	−24.7472	−0.876590	−0.438295	−	0.898831i	$-0.644417\pi$
$797$	−24.7472	−0.876590	−0.438295	+	0.898831i	$0.644417\pi$
$798$	0	0
$799$	−0.217852	−0.00770707
$800$	−4.97182	−0.175780
$801$	56.3674	1.99164
$802$	−18.9738	−0.669989
$803$	−62.2143	−2.19549
$804$	−6.51908	−0.229910
$805$	−1.38831	−0.0489316
$806$	−13.4068	−0.472235
$807$	60.7116	2.13715
$808$	0.331346	0.0116567
$809$	−1.07032	−0.0376303	−0.0188151	−	0.999823i	$-0.505989\pi$
$809$	−1.07032	−0.0376303	−0.0188151	+	0.999823i	$0.505989\pi$
$810$	−0.968298	−0.0340225
$811$	19.1387	0.672049	0.336025	−	0.941853i	$-0.390917\pi$
$811$	19.1387	0.672049	0.336025	+	0.941853i	$0.390917\pi$
$812$	−6.89591	−0.241999
$813$	15.6673	0.549477
$814$	−36.1869	−1.26835
$815$	3.39539	0.118935
$816$	−4.15379	−0.145412
$817$	0	0
$818$	−10.1298	−0.354180
$819$	9.34780	0.326638
$820$	0.813283	0.0284011
$821$	11.9598	0.417401	0.208701	−	0.977980i	$-0.433077\pi$
$821$	11.9598	0.417401	0.208701	+	0.977980i	$0.433077\pi$
$822$	30.1168	1.05045
$823$	−1.13531	−0.0395743	−0.0197871	−	0.999804i	$-0.506299\pi$
$823$	−1.13531	−0.0395743	−0.0197871	+	0.999804i	$0.506299\pi$
$824$	0.895065	0.0311811
$825$	−85.4752	−2.97586
$826$	−5.20856	−0.181229
$827$	40.9885	1.42531	0.712654	−	0.701515i	$-0.247493\pi$
$827$	40.9885	1.42531	0.712654	+	0.701515i	$0.247493\pi$
$828$	46.5183	1.61662
$829$	45.8211	1.59143	0.795716	−	0.605670i	$-0.207095\pi$
$829$	45.8211	1.59143	0.795716	+	0.605670i	$0.207095\pi$
$830$	1.66794	0.0578950
$831$	67.5907	2.34469
$832$	1.66176	0.0576110
$833$	−1.41436	−0.0490046
$834$	−50.9085	−1.76282
$835$	−2.45401	−0.0849246
$836$	0	0
$837$	−62.2036	−2.15007
$838$	−26.3112	−0.908907
$839$	52.3712	1.80805	0.904027	−	0.427476i	$-0.140597\pi$
$839$	52.3712	1.80805	0.904027	+	0.427476i	$0.140597\pi$
$840$	−0.493051	−0.0170119
$841$	18.5536	0.639779
$842$	−26.5413	−0.914674
$843$	10.0123	0.344842
$844$	13.3969	0.461142
$845$	1.71888	0.0591312
$846$	0.866454	0.0297893
$847$	23.2672	0.799469
$848$	−1.53808	−0.0528179
$849$	12.3712	0.424577
$850$	7.03192	0.241193
$851$	−51.1203	−1.75238
$852$	−24.2150	−0.829592
$853$	0.305369	0.0104556	0.00522782	−	0.999986i	$-0.498336\pi$
$853$	0.305369	0.0104556	0.00522782	+	0.999986i	$0.498336\pi$
$854$	12.3790	0.423601
$855$	0	0
$856$	10.1687	0.347559
$857$	12.5164	0.427550	0.213775	−	0.976883i	$-0.431424\pi$
$857$	12.5164	0.427550	0.213775	+	0.976883i	$0.431424\pi$
$858$	28.5688	0.975323
$859$	−8.17940	−0.279078	−0.139539	−	0.990217i	$-0.544562\pi$
$859$	−8.17940	−0.279078	−0.139539	+	0.990217i	$0.544562\pi$
$860$	−0.195716	−0.00667387
$861$	−14.2273	−0.484864
$862$	−25.5907	−0.871624
$863$	12.3286	0.419669	0.209835	−	0.977737i	$-0.432707\pi$
$863$	12.3286	0.419669	0.209835	+	0.977737i	$0.432707\pi$
$864$	7.71005	0.262301
$865$	2.77472	0.0943432
$866$	8.94247	0.303878
$867$	−44.0520	−1.49608
$868$	−8.06786	−0.273841
$869$	33.3462	1.13119
$870$	3.40004	0.115272
$871$	−3.68865	−0.124985
$872$	6.05462	0.205035
$873$	−68.7414	−2.32655
$874$	0	0
$875$	1.67410	0.0565947
$876$	−31.2131	−1.05459
$877$	21.7354	0.733951	0.366976	−	0.930231i	$-0.380393\pi$
$877$	21.7354	0.733951	0.366976	+	0.930231i	$0.380393\pi$
$878$	−12.4057	−0.418671
$879$	−48.7676	−1.64489
$880$	−0.982754	−0.0331286
$881$	10.7650	0.362683	0.181341	−	0.983420i	$-0.441956\pi$
$881$	10.7650	0.362683	0.181341	+	0.983420i	$0.441956\pi$
$882$	5.62525	0.189412
$883$	−55.9766	−1.88376	−0.941881	−	0.335947i	$-0.890944\pi$
$883$	−55.9766	−1.88376	−0.941881	+	0.335947i	$0.890944\pi$
$884$	−2.35032	−0.0790497
$885$	2.56809	0.0863253
$886$	−17.6686	−0.593590
$887$	−16.5852	−0.556875	−0.278437	−	0.960454i	$-0.589817\pi$
$887$	−16.5852	−0.556875	−0.278437	+	0.960454i	$0.589817\pi$
$888$	−18.1551	−0.609244
$889$	6.28735	0.210871
$890$	−1.68225	−0.0563893
$891$	33.7631	1.13111
$892$	−7.31711	−0.244995
$893$	0	0
$894$	65.9678	2.20629
$895$	−1.99424	−0.0666601
$896$	1.00000	0.0334077
$897$	40.3585	1.34753
$898$	−14.1170	−0.471089
$899$	55.6353	1.85554
$900$	−27.9677	−0.932257
$901$	2.17539	0.0724729
$902$	−28.3580	−0.944217
$903$	3.42379	0.113936
$904$	3.80616	0.126591
$905$	−2.41266	−0.0801995
$906$	−34.9504	−1.16115
$907$	−34.5946	−1.14870	−0.574348	−	0.818611i	$-0.694744\pi$
$907$	−34.5946	−1.14870	−0.574348	+	0.818611i	$0.694744\pi$
$908$	9.49511	0.315106
$909$	1.86390	0.0618218
$910$	−0.278980	−0.00924810
$911$	22.9274	0.759618	0.379809	−	0.925065i	$-0.375990\pi$
$911$	22.9274	0.759618	0.379809	+	0.925065i	$0.375990\pi$
$912$	0	0
$913$	−58.1585	−1.92477
$914$	−22.6332	−0.748641
$915$	−6.10349	−0.201775
$916$	12.1411	0.401153
$917$	−18.9747	−0.626598
$918$	−10.9048	−0.359911
$919$	4.19535	0.138392	0.0691958	−	0.997603i	$-0.477957\pi$
$919$	4.19535	0.138392	0.0691958	+	0.997603i	$0.477957\pi$
$920$	−1.38831	−0.0457713
$921$	−40.4750	−1.33370
$922$	−28.3983	−0.935247
$923$	−13.7014	−0.450988
$924$	17.1919	0.565573
$925$	30.7346	1.01055
$926$	2.08478	0.0685100
$927$	5.03497	0.165370
$928$	−6.89591	−0.226369
$929$	−18.6427	−0.611647	−0.305823	−	0.952088i	$-0.598932\pi$
$929$	−18.6427	−0.611647	−0.305823	+	0.952088i	$0.598932\pi$
$930$	3.97787	0.130439
$931$	0	0
$932$	−2.05744	−0.0673938
$933$	−12.0205	−0.393532
$934$	−26.3159	−0.861083
$935$	1.38996	0.0454567
$936$	9.34780	0.305542
$937$	34.7710	1.13592	0.567960	−	0.823056i	$-0.307733\pi$
$937$	34.7710	1.13592	0.567960	+	0.823056i	$0.307733\pi$
$938$	−2.21973	−0.0724768
$939$	21.2453	0.693313
$940$	−0.0258589	−0.000843423 0
$941$	−20.8774	−0.680583	−0.340292	−	0.940320i	$-0.610526\pi$
$941$	−20.8774	−0.680583	−0.340292	+	0.940320i	$0.610526\pi$
$942$	−0.433636	−0.0141286
$943$	−40.0606	−1.30455
$944$	−5.20856	−0.169524
$945$	−1.29438	−0.0421063
$946$	6.82433	0.221878
$947$	15.9651	0.518797	0.259399	−	0.965770i	$-0.416476\pi$
$947$	15.9651	0.518797	0.259399	+	0.965770i	$0.416476\pi$
$948$	16.7299	0.543362
$949$	−17.6611	−0.573304
$950$	0	0
$951$	93.1019	3.01904
$952$	−1.41436	−0.0458396
$953$	−33.4673	−1.08411	−0.542056	−	0.840343i	$-0.682354\pi$
$953$	−33.4673	−1.08411	−0.542056	+	0.840343i	$0.682354\pi$
$954$	−8.65209	−0.280122
$955$	−1.57517	−0.0509714
$956$	−6.66574	−0.215586
$957$	−118.554	−3.83231
$958$	−4.82538	−0.155901
$959$	10.2547	0.331142
$960$	−0.493051	−0.0159132
$961$	34.0904	1.09969
$962$	−10.2726	−0.331201
$963$	57.2015	1.84329
$964$	−9.30578	−0.299719
$965$	4.20459	0.135350
$966$	24.2866	0.781410
$967$	−11.6426	−0.374401	−0.187201	−	0.982322i	$-0.559941\pi$
$967$	−11.6426	−0.374401	−0.187201	+	0.982322i	$0.559941\pi$
$968$	23.2672	0.747835
$969$	0	0
$970$	2.05155	0.0658714
$971$	−48.8627	−1.56808	−0.784040	−	0.620711i	$-0.786844\pi$
$971$	−48.8627	−1.56808	−0.784040	+	0.620711i	$0.786844\pi$
$972$	−6.19108	−0.198579
$973$	−17.3342	−0.555709
$974$	−24.0690	−0.771220
$975$	−24.2643	−0.777080
$976$	12.3790	0.396243
$977$	13.7007	0.438325	0.219163	−	0.975688i	$-0.429667\pi$
$977$	13.7007	0.438325	0.219163	+	0.975688i	$0.429667\pi$
$978$	−59.3977	−1.89933
$979$	58.6577	1.87471
$980$	−0.167883	−0.00536282
$981$	34.0588	1.08741
$982$	16.4774	0.525816
$983$	15.7814	0.503347	0.251674	−	0.967812i	$-0.419019\pi$
$983$	15.7814	0.503347	0.251674	+	0.967812i	$0.419019\pi$
$984$	−14.2273	−0.453549
$985$	0.100195	0.00319248
$986$	9.75328	0.310608
$987$	0.452366	0.0143990
$988$	0	0
$989$	9.64056	0.306552
$990$	−5.52824	−0.175699
$991$	2.61470	0.0830588	0.0415294	−	0.999137i	$-0.486777\pi$
$991$	2.61470	0.0830588	0.0415294	+	0.999137i	$0.486777\pi$
$992$	−8.06786	−0.256155
$993$	4.89733	0.155412
$994$	−8.24515	−0.261520
$995$	−3.86404	−0.122498
$996$	−29.1783	−0.924550
$997$	20.7617	0.657529	0.328765	−	0.944412i	$-0.393368\pi$
$997$	20.7617	0.657529	0.328765	+	0.944412i	$0.393368\pi$
$998$	−33.9334	−1.07414
$999$	−47.6617	−1.50795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bm.1.10		12
19.3	odd	18		266.2.u.d.85.1	✓	24
19.13	odd	18		266.2.u.d.169.1	yes	24
19.18	odd	2		5054.2.a.bl.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.d.85.1	✓	24	19.3	odd	18
266.2.u.d.169.1	yes	24	19.13	odd	18
5054.2.a.bl.1.3		12	19.18	odd	2
5054.2.a.bm.1.10		12	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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.93688 q^{3} +1.00000 q^{4} -0.167883 q^{5} +2.93688 q^{6} +1.00000 q^{7} +1.00000 q^{8} +5.62525 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.93688 q^{3} +1.00000 q^{4} -0.167883 q^{5} +2.93688 q^{6} +1.00000 q^{7} +1.00000 q^{8} +5.62525 q^{9} -0.167883 q^{10} +5.85382 q^{11} +2.93688 q^{12} +1.66176 q^{13} +1.00000 q^{14} -0.493051 q^{15} +1.00000 q^{16} -1.41436 q^{17} +5.62525 q^{18} -0.167883 q^{20} +2.93688 q^{21} +5.85382 q^{22} +8.26954 q^{23} +2.93688 q^{24} -4.97182 q^{25} +1.66176 q^{26} +7.71005 q^{27} +1.00000 q^{28} -6.89591 q^{29} -0.493051 q^{30} -8.06786 q^{31} +1.00000 q^{32} +17.1919 q^{33} -1.41436 q^{34} -0.167883 q^{35} +5.62525 q^{36} -6.18176 q^{37} +4.88037 q^{39} -0.167883 q^{40} -4.84436 q^{41} +2.93688 q^{42} +1.16579 q^{43} +5.85382 q^{44} -0.944382 q^{45} +8.26954 q^{46} +0.154029 q^{47} +2.93688 q^{48} +1.00000 q^{49} -4.97182 q^{50} -4.15379 q^{51} +1.66176 q^{52} -1.53808 q^{53} +7.71005 q^{54} -0.982754 q^{55} +1.00000 q^{56} -6.89591 q^{58} -5.20856 q^{59} -0.493051 q^{60} +12.3790 q^{61} -8.06786 q^{62} +5.62525 q^{63} +1.00000 q^{64} -0.278980 q^{65} +17.1919 q^{66} -2.21973 q^{67} -1.41436 q^{68} +24.2866 q^{69} -0.167883 q^{70} -8.24515 q^{71} +5.62525 q^{72} -10.6280 q^{73} -6.18176 q^{74} -14.6016 q^{75} +5.85382 q^{77} +4.88037 q^{78} +5.69649 q^{79} -0.167883 q^{80} +5.76771 q^{81} -4.84436 q^{82} -9.93514 q^{83} +2.93688 q^{84} +0.237446 q^{85} +1.16579 q^{86} -20.2524 q^{87} +5.85382 q^{88} +10.0204 q^{89} -0.944382 q^{90} +1.66176 q^{91} +8.26954 q^{92} -23.6943 q^{93} +0.154029 q^{94} +2.93688 q^{96} -12.2202 q^{97} +1.00000 q^{98} +32.9292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} + 12 q^{8} + 21 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 + 12 * q^8 + 21 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} + 12 q^{8} + 21 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 6 q^{13} + 12 q^{14} - 6 q^{15} + 12 q^{16} + 3 q^{17} + 21 q^{18} + 3 q^{20} + 3 q^{21} + 3 q^{22} + 12 q^{23} + 3 q^{24} + 33 q^{25} - 6 q^{26} + 21 q^{27} + 12 q^{28} + 6 q^{29} - 6 q^{30} + 3 q^{31} + 12 q^{32} - 6 q^{33} + 3 q^{34} + 3 q^{35} + 21 q^{36} + 27 q^{37} + 27 q^{39} + 3 q^{40} - 27 q^{41} + 3 q^{42} + 30 q^{43} + 3 q^{44} + 30 q^{45} + 12 q^{46} + 21 q^{47} + 3 q^{48} + 12 q^{49} + 33 q^{50} + 3 q^{51} - 6 q^{52} + 6 q^{53} + 21 q^{54} + 48 q^{55} + 12 q^{56} + 6 q^{58} - 27 q^{59} - 6 q^{60} + 18 q^{61} + 3 q^{62} + 21 q^{63} + 12 q^{64} - 9 q^{65} - 6 q^{66} + 9 q^{67} + 3 q^{68} + 18 q^{69} + 3 q^{70} + 27 q^{71} + 21 q^{72} - 9 q^{73} + 27 q^{74} + 33 q^{75} + 3 q^{77} + 27 q^{78} - 12 q^{79} + 3 q^{80} + 24 q^{81} - 27 q^{82} + 9 q^{83} + 3 q^{84} + 78 q^{85} + 30 q^{86} - 45 q^{87} + 3 q^{88} - 24 q^{89} + 30 q^{90} - 6 q^{91} + 12 q^{92} + 3 q^{93} + 21 q^{94} + 3 q^{96} - 18 q^{97} + 12 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 + 12 * q^8 + 21 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 6 * q^13 + 12 * q^14 - 6 * q^15 + 12 * q^16 + 3 * q^17 + 21 * q^18 + 3 * q^20 + 3 * q^21 + 3 * q^22 + 12 * q^23 + 3 * q^24 + 33 * q^25 - 6 * q^26 + 21 * q^27 + 12 * q^28 + 6 * q^29 - 6 * q^30 + 3 * q^31 + 12 * q^32 - 6 * q^33 + 3 * q^34 + 3 * q^35 + 21 * q^36 + 27 * q^37 + 27 * q^39 + 3 * q^40 - 27 * q^41 + 3 * q^42 + 30 * q^43 + 3 * q^44 + 30 * q^45 + 12 * q^46 + 21 * q^47 + 3 * q^48 + 12 * q^49 + 33 * q^50 + 3 * q^51 - 6 * q^52 + 6 * q^53 + 21 * q^54 + 48 * q^55 + 12 * q^56 + 6 * q^58 - 27 * q^59 - 6 * q^60 + 18 * q^61 + 3 * q^62 + 21 * q^63 + 12 * q^64 - 9 * q^65 - 6 * q^66 + 9 * q^67 + 3 * q^68 + 18 * q^69 + 3 * q^70 + 27 * q^71 + 21 * q^72 - 9 * q^73 + 27 * q^74 + 33 * q^75 + 3 * q^77 + 27 * q^78 - 12 * q^79 + 3 * q^80 + 24 * q^81 - 27 * q^82 + 9 * q^83 + 3 * q^84 + 78 * q^85 + 30 * q^86 - 45 * q^87 + 3 * q^88 - 24 * q^89 + 30 * q^90 - 6 * q^91 + 12 * q^92 + 3 * q^93 + 21 * q^94 + 3 * q^96 - 18 * q^97 + 12 * q^98 + 48 * q^99

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