LMFDB - Embedded newform 1849.2.a.m.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{44})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 11x^{8} + 44x^{6} - 77x^{4} + 55x^{2} - 11 $ x^10 - 11x^8 + 44x^6 - 77x^4 + 55x^2 - 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$1.97964$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.97964 q^{2} +0.160379 q^{3} +1.91899 q^{4} -3.06092 q^{5} +0.317493 q^{6} +2.43240 q^{7} -0.160379 q^{8} -2.97428 q^{9} +O(q^{10})$	\(q+1.97964 q^{2} +0.160379 q^{3} +1.91899 q^{4} -3.06092 q^{5} +0.317493 q^{6} +2.43240 q^{7} -0.160379 q^{8} -2.97428 q^{9} -6.05954 q^{10} -2.02509 q^{11} +0.307765 q^{12} +2.03223 q^{13} +4.81529 q^{14} -0.490908 q^{15} -4.15546 q^{16} +5.09398 q^{17} -5.88801 q^{18} -1.84640 q^{19} -5.87387 q^{20} +0.390106 q^{21} -4.00896 q^{22} -8.84936 q^{23} -0.0257214 q^{24} +4.36926 q^{25} +4.02310 q^{26} -0.958148 q^{27} +4.66775 q^{28} -8.85560 q^{29} -0.971822 q^{30} -7.31555 q^{31} -7.90558 q^{32} -0.324782 q^{33} +10.0843 q^{34} -7.44540 q^{35} -5.70760 q^{36} +6.31728 q^{37} -3.65520 q^{38} +0.325927 q^{39} +0.490908 q^{40} +5.04241 q^{41} +0.772270 q^{42} -3.88612 q^{44} +9.10404 q^{45} -17.5186 q^{46} -10.0338 q^{47} -0.666449 q^{48} -1.08342 q^{49} +8.64957 q^{50} +0.816967 q^{51} +3.89983 q^{52} -3.73269 q^{53} -1.89679 q^{54} +6.19865 q^{55} -0.390106 q^{56} -0.296123 q^{57} -17.5309 q^{58} +0.708914 q^{59} -0.942045 q^{60} +5.56173 q^{61} -14.4822 q^{62} -7.23464 q^{63} -7.33929 q^{64} -6.22051 q^{65} -0.642952 q^{66} +4.74471 q^{67} +9.77528 q^{68} -1.41925 q^{69} -14.7392 q^{70} -1.53205 q^{71} +0.477012 q^{72} +0.861116 q^{73} +12.5059 q^{74} +0.700737 q^{75} -3.54321 q^{76} -4.92584 q^{77} +0.645220 q^{78} -12.2106 q^{79} +12.7196 q^{80} +8.76917 q^{81} +9.98218 q^{82} -6.37482 q^{83} +0.748608 q^{84} -15.5923 q^{85} -1.42025 q^{87} +0.324782 q^{88} +0.792034 q^{89} +18.0228 q^{90} +4.94321 q^{91} -16.9818 q^{92} -1.17326 q^{93} -19.8634 q^{94} +5.65168 q^{95} -1.26789 q^{96} +14.4708 q^{97} -2.14479 q^{98} +6.02319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9}+O(q^{10}) $ 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9	$ 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9} - 22 q^{10} - 10 q^{11} - 14 q^{13} - 22 q^{14} - 22 q^{15} - 26 q^{16} - 16 q^{17} - 44 q^{21} - 18 q^{23} - 44 q^{24} - 6 q^{25} - 2 q^{31} - 28 q^{36} - 22 q^{38} + 22 q^{40} - 2 q^{44} - 18 q^{47} + 18 q^{49} + 28 q^{52} + 2 q^{53} + 44 q^{56} - 22 q^{57} - 22 q^{58} + 14 q^{59} + 8 q^{64} - 22 q^{66} + 26 q^{67} + 32 q^{68} + 44 q^{74} - 44 q^{78} - 56 q^{79} + 2 q^{81} - 38 q^{83} - 22 q^{87} - 22 q^{90} - 74 q^{92} + 22 q^{96} + 34 q^{97} - 36 q^{99}+O(q^{100}) $ 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9 - 22 * q^10 - 10 * q^11 - 14 * q^13 - 22 * q^14 - 22 * q^15 - 26 * q^16 - 16 * q^17 - 44 * q^21 - 18 * q^23 - 44 * q^24 - 6 * q^25 - 2 * q^31 - 28 * q^36 - 22 * q^38 + 22 * q^40 - 2 * q^44 - 18 * q^47 + 18 * q^49 + 28 * q^52 + 2 * q^53 + 44 * q^56 - 22 * q^57 - 22 * q^58 + 14 * q^59 + 8 * q^64 - 22 * q^66 + 26 * q^67 + 32 * q^68 + 44 * q^74 - 44 * q^78 - 56 * q^79 + 2 * q^81 - 38 * q^83 - 22 * q^87 - 22 * q^90 - 74 * q^92 + 22 * q^96 + 34 * q^97 - 36 * 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 $

$2$	1.97964	1.39982	0.699909	−	0.714232i	$-0.253224\pi$
$2$	1.97964	1.39982	0.699909	+	0.714232i	$0.253224\pi$
$3$	0.160379	0.0925948	0.0462974	−	0.998928i	$-0.485258\pi$
$3$	0.160379	0.0925948	0.0462974	+	0.998928i	$0.485258\pi$
$4$	1.91899	0.959493
$5$	−3.06092	−1.36889	−0.684444	−	0.729066i	$-0.739955\pi$
$5$	−3.06092	−1.36889	−0.684444	+	0.729066i	$0.739955\pi$
$6$	0.317493	0.129616
$7$	2.43240	0.919361	0.459681	−	0.888084i	$-0.347964\pi$
$7$	2.43240	0.919361	0.459681	+	0.888084i	$0.347964\pi$
$8$	−0.160379	−0.0567025
$9$	−2.97428	−0.991426
$10$	−6.05954	−1.91619
$11$	−2.02509	−0.610588	−0.305294	−	0.952258i	$-0.598755\pi$
$11$	−2.02509	−0.610588	−0.305294	+	0.952258i	$0.598755\pi$
$12$	0.307765	0.0888441
$13$	2.03223	0.563640	0.281820	−	0.959467i	$-0.409062\pi$
$13$	2.03223	0.563640	0.281820	+	0.959467i	$0.409062\pi$
$14$	4.81529	1.28694
$15$	−0.490908	−0.126752
$16$	−4.15546	−1.03887
$17$	5.09398	1.23547	0.617736	−	0.786385i	$-0.288050\pi$
$17$	5.09398	1.23547	0.617736	+	0.786385i	$0.288050\pi$
$18$	−5.88801	−1.38782
$19$	−1.84640	−0.423592	−0.211796	−	0.977314i	$-0.567931\pi$
$19$	−1.84640	−0.423592	−0.211796	+	0.977314i	$0.567931\pi$
$20$	−5.87387	−1.31344
$21$	0.390106	0.0851281
$22$	−4.00896	−0.854713
$23$	−8.84936	−1.84522	−0.922609	−	0.385736i	$-0.873948\pi$
$23$	−8.84936	−1.84522	−0.922609	+	0.385736i	$0.873948\pi$
$24$	−0.0257214	−0.00525036
$25$	4.36926	0.873852
$26$	4.02310	0.788994
$27$	−0.958148	−0.184396
$28$	4.66775	0.882121
$29$	−8.85560	−1.64444	−0.822222	−	0.569167i	$-0.807266\pi$
$29$	−8.85560	−1.64444	−0.822222	+	0.569167i	$0.807266\pi$
$30$	−0.971822	−0.177430
$31$	−7.31555	−1.31391	−0.656956	−	0.753929i	$-0.728156\pi$
$31$	−7.31555	−1.31391	−0.656956	+	0.753929i	$0.728156\pi$
$32$	−7.90558	−1.39752
$33$	−0.324782	−0.0565373
$34$	10.0843	1.72944
$35$	−7.44540	−1.25850
$36$	−5.70760	−0.951266
$37$	6.31728	1.03855	0.519277	−	0.854606i	$-0.326201\pi$
$37$	6.31728	1.03855	0.519277	+	0.854606i	$0.326201\pi$
$38$	−3.65520	−0.592952
$39$	0.325927	0.0521902
$40$	0.490908	0.0776193
$41$	5.04241	0.787492	0.393746	−	0.919219i	$-0.371179\pi$
$41$	5.04241	0.787492	0.393746	+	0.919219i	$0.371179\pi$
$42$	0.772270	0.119164
$43$	0	0
$43$	0	0
$44$	−3.88612	−0.585855
$45$	9.10404	1.35715
$46$	−17.5186	−2.58297
$47$	−10.0338	−1.46358	−0.731791	−	0.681529i	$-0.761315\pi$
$47$	−10.0338	−1.46358	−0.731791	+	0.681529i	$0.761315\pi$
$48$	−0.666449	−0.0961936
$49$	−1.08342	−0.154774
$50$	8.64957	1.22323
$51$	0.816967	0.114398
$52$	3.89983	0.540809
$53$	−3.73269	−0.512724	−0.256362	−	0.966581i	$-0.582524\pi$
$53$	−3.73269	−0.512724	−0.256362	+	0.966581i	$0.582524\pi$
$54$	−1.89679	−0.258121
$55$	6.19865	0.835826
$56$	−0.390106	−0.0521301
$57$	−0.296123	−0.0392224
$58$	−17.5309	−2.30192
$59$	0.708914	0.0922927	0.0461463	−	0.998935i	$-0.485306\pi$
$59$	0.708914	0.0922927	0.0461463	+	0.998935i	$0.485306\pi$
$60$	−0.942045	−0.121617
$61$	5.56173	0.712106	0.356053	−	0.934466i	$-0.384122\pi$
$61$	5.56173	0.712106	0.356053	+	0.934466i	$0.384122\pi$
$62$	−14.4822	−1.83924
$63$	−7.23464	−0.911479
$64$	−7.33929	−0.917412
$65$	−6.22051	−0.771560
$66$	−0.642952	−0.0791420
$67$	4.74471	0.579658	0.289829	−	0.957078i	$-0.406402\pi$
$67$	4.74471	0.579658	0.289829	+	0.957078i	$0.406402\pi$
$68$	9.77528	1.18543
$69$	−1.41925	−0.170858
$70$	−14.7392	−1.76167
$71$	−1.53205	−0.181821	−0.0909106	−	0.995859i	$-0.528978\pi$
$71$	−1.53205	−0.181821	−0.0909106	+	0.995859i	$0.528978\pi$
$72$	0.477012	0.0562163
$73$	0.861116	0.100786	0.0503930	−	0.998729i	$-0.483953\pi$
$73$	0.861116	0.100786	0.0503930	+	0.998729i	$0.483953\pi$
$74$	12.5059	1.45379
$75$	0.700737	0.0809141
$76$	−3.54321	−0.406434
$77$	−4.92584	−0.561351
$78$	0.645220	0.0730568
$79$	−12.2106	−1.37380	−0.686899	−	0.726753i	$-0.741028\pi$
$79$	−12.2106	−1.37380	−0.686899	+	0.726753i	$0.741028\pi$
$80$	12.7196	1.42209
$81$	8.76917	0.974352
$82$	9.98218	1.10235
$83$	−6.37482	−0.699727	−0.349864	−	0.936801i	$-0.613772\pi$
$83$	−6.37482	−0.699727	−0.349864	+	0.936801i	$0.613772\pi$
$84$	0.748608	0.0816798
$85$	−15.5923	−1.69122
$86$	0	0
$87$	−1.42025	−0.152267
$88$	0.324782	0.0346219
$89$	0.792034	0.0839554	0.0419777	−	0.999119i	$-0.486634\pi$
$89$	0.792034	0.0839554	0.0419777	+	0.999119i	$0.486634\pi$
$90$	18.0228	1.89976
$91$	4.94321	0.518189
$92$	−16.9818	−1.77047
$93$	−1.17326	−0.121661
$94$	−19.8634	−2.04875
$95$	5.65168	0.579850
$96$	−1.26789	−0.129403
$97$	14.4708	1.46929	0.734645	−	0.678451i	$-0.237349\pi$
$97$	14.4708	1.46929	0.734645	+	0.678451i	$0.237349\pi$
$98$	−2.14479	−0.216656
$99$	6.02319	0.605353
$100$	8.38455	0.838455
$101$	−2.27103	−0.225976	−0.112988	−	0.993596i	$-0.536042\pi$
$101$	−2.27103	−0.225976	−0.112988	+	0.993596i	$0.536042\pi$
$102$	1.61730	0.160137
$103$	1.28242	0.126360	0.0631802	−	0.998002i	$-0.479876\pi$
$103$	1.28242	0.126360	0.0631802	+	0.998002i	$0.479876\pi$
$104$	−0.325927	−0.0319598
$105$	−1.19408	−0.116531
$106$	−7.38939	−0.717721
$107$	10.3610	1.00164	0.500820	−	0.865552i	$-0.333032\pi$
$107$	10.3610	1.00164	0.500820	+	0.865552i	$0.333032\pi$
$108$	−1.83867	−0.176926
$109$	2.98156	0.285582	0.142791	−	0.989753i	$-0.454392\pi$
$109$	2.98156	0.285582	0.142791	+	0.989753i	$0.454392\pi$
$110$	12.2711	1.17001
$111$	1.01316	0.0961647
$112$	−10.1078	−0.955094
$113$	2.06254	0.194027	0.0970136	−	0.995283i	$-0.469071\pi$
$113$	2.06254	0.194027	0.0970136	+	0.995283i	$0.469071\pi$
$114$	−0.586217	−0.0549043
$115$	27.0872	2.52590
$116$	−16.9938	−1.57783
$117$	−6.04443	−0.558808
$118$	1.40340	0.129193
$119$	12.3906	1.13585
$120$	0.0787312	0.00718715
$121$	−6.89900	−0.627182
$122$	11.0102	0.996820
$123$	0.808696	0.0729177
$124$	−14.0384	−1.26069
$125$	1.93065	0.172683
$126$	−14.3220	−1.27591
$127$	4.64052	0.411780	0.205890	−	0.978575i	$-0.433991\pi$
$127$	4.64052	0.411780	0.205890	+	0.978575i	$0.433991\pi$
$128$	1.28198	0.113312
$129$	0	0
$130$	−12.3144	−1.08004
$131$	10.8939	0.951803	0.475902	−	0.879499i	$-0.342122\pi$
$131$	10.8939	0.951803	0.475902	+	0.879499i	$0.342122\pi$
$132$	−0.623252	−0.0542471
$133$	−4.49118	−0.389434
$134$	9.39283	0.811417
$135$	2.93282	0.252417
$136$	−0.816967	−0.0700544
$137$	11.0927	0.947709	0.473855	−	0.880603i	$-0.342862\pi$
$137$	11.0927	0.947709	0.473855	+	0.880603i	$0.342862\pi$
$138$	−2.80961	−0.239170
$139$	−1.77723	−0.150742	−0.0753712	−	0.997156i	$-0.524014\pi$
$139$	−1.77723	−0.150742	−0.0753712	+	0.997156i	$0.524014\pi$
$140$	−14.2876	−1.20752
$141$	−1.60921	−0.135520
$142$	−3.03292	−0.254517
$143$	−4.11546	−0.344152
$144$	12.3595	1.02996
$145$	27.1063	2.25106
$146$	1.70470	0.141082
$147$	−0.173758	−0.0143313
$148$	12.1228	0.996485
$149$	19.3388	1.58430	0.792148	−	0.610330i	$-0.208963\pi$
$149$	19.3388	1.58430	0.792148	+	0.610330i	$0.208963\pi$
$150$	1.38721	0.113265
$151$	10.3178	0.839647	0.419823	−	0.907606i	$-0.362092\pi$
$151$	10.3178	0.839647	0.419823	+	0.907606i	$0.362092\pi$
$152$	0.296123	0.0240187
$153$	−15.1509	−1.22488
$154$	−9.75140	−0.785790
$155$	22.3923	1.79860
$156$	0.625450	0.0500761
$157$	7.46859	0.596058	0.298029	−	0.954557i	$-0.403671\pi$
$157$	7.46859	0.596058	0.298029	+	0.954557i	$0.403671\pi$
$158$	−24.1726	−1.92307
$159$	−0.598645	−0.0474756
$160$	24.1984	1.91305
$161$	−21.5252	−1.69642
$162$	17.3598	1.36392
$163$	−8.48183	−0.664348	−0.332174	−	0.943218i	$-0.607782\pi$
$163$	−8.48183	−0.664348	−0.332174	+	0.943218i	$0.607782\pi$
$164$	9.67632	0.755593
$165$	0.994133	0.0773932
$166$	−12.6199	−0.979491
$167$	−12.8155	−0.991696	−0.495848	−	0.868409i	$-0.665143\pi$
$167$	−12.8155	−0.991696	−0.495848	+	0.868409i	$0.665143\pi$
$168$	−0.0625648	−0.00482698
$169$	−8.87003	−0.682310
$170$	−30.8672	−2.36740
$171$	5.49169	0.419960
$172$	0	0
$173$	−20.3235	−1.54517	−0.772583	−	0.634913i	$-0.781036\pi$
$173$	−20.3235	−1.54517	−0.772583	+	0.634913i	$0.781036\pi$
$174$	−2.81159	−0.213146
$175$	10.6278	0.803386
$176$	8.41520	0.634319
$177$	0.113695	0.00854582
$178$	1.56794	0.117522
$179$	−14.3540	−1.07287	−0.536433	−	0.843943i	$-0.680229\pi$
$179$	−14.3540	−1.07287	−0.536433	+	0.843943i	$0.680229\pi$
$180$	17.4705	1.30218
$181$	−9.14104	−0.679448	−0.339724	−	0.940525i	$-0.610334\pi$
$181$	−9.14104	−0.679448	−0.339724	+	0.940525i	$0.610334\pi$
$182$	9.78579	0.725371
$183$	0.891984	0.0659373
$184$	1.41925	0.104629
$185$	−19.3367	−1.42166
$186$	−2.32264	−0.170304
$187$	−10.3158	−0.754365
$188$	−19.2548	−1.40430
$189$	−2.33060	−0.169526
$190$	11.1883	0.811685
$191$	10.3453	0.748561	0.374280	−	0.927316i	$-0.377890\pi$
$191$	10.3453	0.748561	0.374280	+	0.927316i	$0.377890\pi$
$192$	−1.17707	−0.0849475
$193$	5.03046	0.362100	0.181050	−	0.983474i	$-0.442050\pi$
$193$	5.03046	0.362100	0.181050	+	0.983474i	$0.442050\pi$
$194$	28.6471	2.05674
$195$	−0.997639	−0.0714424
$196$	−2.07907	−0.148505
$197$	−20.2866	−1.44536	−0.722681	−	0.691182i	$-0.757090\pi$
$197$	−20.2866	−1.44536	−0.722681	+	0.691182i	$0.757090\pi$
$198$	11.9238	0.847385
$199$	23.5648	1.67046	0.835231	−	0.549900i	$-0.185334\pi$
$199$	23.5648	1.67046	0.835231	+	0.549900i	$0.185334\pi$
$200$	−0.700737	−0.0495496
$201$	0.760951	0.0536733
$202$	−4.49583	−0.316326
$203$	−21.5404	−1.51184
$204$	1.56775	0.109764
$205$	−15.4344	−1.07799
$206$	2.53873	0.176882
$207$	26.3205	1.82940
$208$	−8.44488	−0.585547
$209$	3.73912	0.258640
$210$	−2.36386	−0.163122
$211$	−4.63863	−0.319336	−0.159668	−	0.987171i	$-0.551042\pi$
$211$	−4.63863	−0.319336	−0.159668	+	0.987171i	$0.551042\pi$
$212$	−7.16298	−0.491956
$213$	−0.245709	−0.0168357
$214$	20.5112	1.40211
$215$	0	0
$216$	0.153667	0.0104557
$217$	−17.7944	−1.20796
$218$	5.90242	0.399763
$219$	0.138105	0.00933226
$220$	11.8951	0.801969
$221$	10.3522	0.696362
$222$	2.00569	0.134613
$223$	−26.1849	−1.75347	−0.876737	−	0.480971i	$-0.840284\pi$
$223$	−26.1849	−1.75347	−0.876737	+	0.480971i	$0.840284\pi$
$224$	−19.2295	−1.28483
$225$	−12.9954	−0.866360
$226$	4.08309	0.271603
$227$	−9.43793	−0.626417	−0.313209	−	0.949684i	$-0.601404\pi$
$227$	−9.43793	−0.626417	−0.313209	+	0.949684i	$0.601404\pi$
$228$	−0.568256	−0.0376336
$229$	−3.44029	−0.227341	−0.113670	−	0.993519i	$-0.536261\pi$
$229$	−3.44029	−0.227341	−0.113670	+	0.993519i	$0.536261\pi$
$230$	53.6230	3.53580
$231$	−0.790000	−0.0519782
$232$	1.42025	0.0932441
$233$	6.25626	0.409861	0.204931	−	0.978777i	$-0.434303\pi$
$233$	6.25626	0.409861	0.204931	+	0.978777i	$0.434303\pi$
$234$	−11.9658	−0.782230
$235$	30.7128	2.00348
$236$	1.36040	0.0885542
$237$	−1.95832	−0.127206
$238$	24.5290	1.58998
$239$	−22.6864	−1.46746	−0.733729	−	0.679442i	$-0.762222\pi$
$239$	−22.6864	−1.46746	−0.733729	+	0.679442i	$0.762222\pi$
$240$	2.03995	0.131678
$241$	−17.7965	−1.14637	−0.573186	−	0.819425i	$-0.694293\pi$
$241$	−17.7965	−1.14637	−0.573186	+	0.819425i	$0.694293\pi$
$242$	−13.6576	−0.877941
$243$	4.28083	0.274616
$244$	10.6729	0.683261
$245$	3.31627	0.211869
$246$	1.60093	0.102072
$247$	−3.75231	−0.238754
$248$	1.17326	0.0745021
$249$	−1.02239	−0.0647911
$250$	3.82200	0.241724
$251$	9.19690	0.580503	0.290252	−	0.956950i	$-0.406261\pi$
$251$	9.19690	0.580503	0.290252	+	0.956950i	$0.406261\pi$
$252$	−13.8832	−0.874558
$253$	17.9208	1.12667
$254$	9.18658	0.576417
$255$	−2.50068	−0.156598
$256$	17.2164	1.07603
$257$	−3.32596	−0.207468	−0.103734	−	0.994605i	$-0.533079\pi$
$257$	−3.32596	−0.207468	−0.103734	+	0.994605i	$0.533079\pi$
$258$	0	0
$259$	15.3662	0.954806
$260$	−11.9371	−0.740306
$261$	26.3390	1.63034
$262$	21.5660	1.33235
$263$	−0.0848812	−0.00523400	−0.00261700	−	0.999997i	$-0.500833\pi$
$263$	−0.0848812	−0.00523400	−0.00261700	+	0.999997i	$0.500833\pi$
$264$	0.0520882	0.00320581
$265$	11.4255	0.701862
$266$	−8.89092	−0.545137
$267$	0.127026	0.00777384
$268$	9.10503	0.556178
$269$	−17.9644	−1.09531	−0.547655	−	0.836704i	$-0.684480\pi$
$269$	−17.9644	−1.09531	−0.547655	+	0.836704i	$0.684480\pi$
$270$	5.80593	0.353338
$271$	4.74062	0.287972	0.143986	−	0.989580i	$-0.454008\pi$
$271$	4.74062	0.287972	0.143986	+	0.989580i	$0.454008\pi$
$272$	−21.1679	−1.28349
$273$	0.792786	0.0479816
$274$	21.9595	1.32662
$275$	−8.84815	−0.533564
$276$	−2.72352	−0.163937
$277$	17.3912	1.04494	0.522469	−	0.852658i	$-0.325011\pi$
$277$	17.3912	1.04494	0.522469	+	0.852658i	$0.325011\pi$
$278$	−3.51827	−0.211012
$279$	21.7585	1.30265
$280$	1.19408	0.0713602
$281$	−0.978435	−0.0583685	−0.0291843	−	0.999574i	$-0.509291\pi$
$281$	−0.978435	−0.0583685	−0.0291843	+	0.999574i	$0.509291\pi$
$282$	−3.18567	−0.189704
$283$	27.9616	1.66215	0.831074	−	0.556162i	$-0.187727\pi$
$283$	27.9616	1.66215	0.831074	+	0.556162i	$0.187727\pi$
$284$	−2.93999	−0.174456
$285$	0.906410	0.0536911
$286$	−8.14714	−0.481751
$287$	12.2652	0.723990
$288$	23.5134	1.38554
$289$	8.94866	0.526392
$290$	53.6608	3.15107
$291$	2.32082	0.136049
$292$	1.65247	0.0967034
$293$	−13.0308	−0.761266	−0.380633	−	0.924726i	$-0.624294\pi$
$293$	−13.0308	−0.761266	−0.380633	+	0.924726i	$0.624294\pi$
$294$	−0.343979	−0.0200612
$295$	−2.16993	−0.126338
$296$	−1.01316	−0.0588886
$297$	1.94034	0.112590
$298$	38.2839	2.21773
$299$	−17.9840	−1.04004
$300$	1.34470	0.0776365
$301$	0	0
$302$	20.4255	1.17535
$303$	−0.364225	−0.0209242
$304$	7.67263	0.440056
$305$	−17.0240	−0.974793
$306$	−29.9934	−1.71461
$307$	−7.97567	−0.455195	−0.227598	−	0.973755i	$-0.573087\pi$
$307$	−7.97567	−0.455195	−0.227598	+	0.973755i	$0.573087\pi$
$308$	−9.45261	−0.538613
$309$	0.205673	0.0117003
$310$	44.3288	2.51771
$311$	15.1874	0.861198	0.430599	−	0.902543i	$-0.358302\pi$
$311$	15.1874	0.861198	0.430599	+	0.902543i	$0.358302\pi$
$312$	−0.0522719	−0.00295931
$313$	−5.63654	−0.318596	−0.159298	−	0.987231i	$-0.550923\pi$
$313$	−5.63654	−0.318596	−0.159298	+	0.987231i	$0.550923\pi$
$314$	14.7851	0.834374
$315$	22.1447	1.24771
$316$	−23.4319	−1.31815
$317$	−2.56040	−0.143806	−0.0719031	−	0.997412i	$-0.522907\pi$
$317$	−2.56040	−0.143806	−0.0719031	+	0.997412i	$0.522907\pi$
$318$	−1.18510	−0.0664573
$319$	17.9334	1.00408
$320$	22.4650	1.25583
$321$	1.66169	0.0927466
$322$	−42.6122	−2.37469
$323$	−9.40551	−0.523336
$324$	16.8279	0.934884
$325$	8.87936	0.492538
$326$	−16.7910	−0.929967
$327$	0.478179	0.0264434
$328$	−0.808696	−0.0446528
$329$	−24.4063	−1.34556
$330$	1.96803	0.108336
$331$	16.6273	0.913916	0.456958	−	0.889488i	$-0.348939\pi$
$331$	16.6273	0.913916	0.456958	+	0.889488i	$0.348939\pi$
$332$	−12.2332	−0.671383
$333$	−18.7893	−1.02965
$334$	−25.3702	−1.38820
$335$	−14.5232	−0.793487
$336$	−1.62107	−0.0884367
$337$	3.11472	0.169670	0.0848349	−	0.996395i	$-0.472964\pi$
$337$	3.11472	0.169670	0.0848349	+	0.996395i	$0.472964\pi$
$338$	−17.5595	−0.955110
$339$	0.330787	0.0179659
$340$	−29.9214	−1.62272
$341$	14.8147	0.802259
$342$	10.8716	0.587868
$343$	−19.6621	−1.06166
$344$	0	0
$345$	4.34422	0.233885
$346$	−40.2333	−2.16295
$347$	−22.0326	−1.18277	−0.591387	−	0.806388i	$-0.701419\pi$
$347$	−22.0326	−1.18277	−0.591387	+	0.806388i	$0.701419\pi$
$348$	−2.72544	−0.146099
$349$	11.4244	0.611534	0.305767	−	0.952106i	$-0.401087\pi$
$349$	11.4244	0.611534	0.305767	+	0.952106i	$0.401087\pi$
$350$	21.0392	1.12459
$351$	−1.94718	−0.103933
$352$	16.0095	0.853310
$353$	−24.9089	−1.32577	−0.662883	−	0.748723i	$-0.730667\pi$
$353$	−24.9089	−1.32577	−0.662883	+	0.748723i	$0.730667\pi$
$354$	0.225075	0.0119626
$355$	4.68950	0.248893
$356$	1.51990	0.0805547
$357$	1.98719	0.105173
$358$	−28.4158	−1.50182
$359$	−12.9413	−0.683017	−0.341509	−	0.939879i	$-0.610938\pi$
$359$	−12.9413	−0.683017	−0.341509	+	0.939879i	$0.610938\pi$
$360$	−1.46010	−0.0769538
$361$	−15.5908	−0.820570
$362$	−18.0960	−0.951105
$363$	−1.10645	−0.0580738
$364$	9.48595	0.497199
$365$	−2.63581	−0.137965
$366$	1.76581	0.0923003
$367$	−19.5175	−1.01881	−0.509403	−	0.860528i	$-0.670134\pi$
$367$	−19.5175	−1.01881	−0.509403	+	0.860528i	$0.670134\pi$
$368$	36.7732	1.91694
$369$	−14.9975	−0.780741
$370$	−38.2798	−1.99007
$371$	−9.07940	−0.471379
$372$	−2.25147	−0.116733
$373$	−14.5674	−0.754271	−0.377136	−	0.926158i	$-0.623091\pi$
$373$	−14.5674	−0.754271	−0.377136	+	0.926158i	$0.623091\pi$
$374$	−20.4216	−1.05597
$375$	0.309636	0.0159895
$376$	1.60921	0.0829888
$377$	−17.9966	−0.926875
$378$	−4.61376	−0.237306
$379$	−22.2547	−1.14315	−0.571573	−	0.820551i	$-0.693667\pi$
$379$	−22.2547	−1.14315	−0.571573	+	0.820551i	$0.693667\pi$
$380$	10.8455	0.556362
$381$	0.744242	0.0381287
$382$	20.4800	1.04785
$383$	−31.0245	−1.58528	−0.792640	−	0.609690i	$-0.791294\pi$
$383$	−31.0245	−1.58528	−0.792640	+	0.609690i	$0.791294\pi$
$384$	0.205602	0.0104921
$385$	15.0776	0.768426
$386$	9.95851	0.506875
$387$	0	0
$388$	27.7693	1.40977
$389$	25.7373	1.30493	0.652466	−	0.757818i	$-0.273734\pi$
$389$	25.7373	1.30493	0.652466	+	0.757818i	$0.273734\pi$
$390$	−1.97497	−0.100006
$391$	−45.0785	−2.27972
$392$	0.173758	0.00877610
$393$	1.74715	0.0881320
$394$	−40.1602	−2.02324
$395$	37.3757	1.88057
$396$	11.5584	0.580832
$397$	33.4005	1.67632	0.838162	−	0.545421i	$-0.183630\pi$
$397$	33.4005	1.67632	0.838162	+	0.545421i	$0.183630\pi$
$398$	46.6498	2.33834
$399$	−0.720290	−0.0360596
$400$	−18.1563	−0.907815
$401$	2.67422	0.133544	0.0667722	−	0.997768i	$-0.478730\pi$
$401$	2.67422	0.133544	0.0667722	+	0.997768i	$0.478730\pi$
$402$	1.50641	0.0751329
$403$	−14.8669	−0.740573
$404$	−4.35808	−0.216822
$405$	−26.8418	−1.33378
$406$	−42.6423	−2.11630
$407$	−12.7931	−0.634129
$408$	−0.131024	−0.00648667
$409$	−30.3672	−1.50156	−0.750780	−	0.660552i	$-0.770322\pi$
$409$	−30.3672	−1.50156	−0.750780	+	0.660552i	$0.770322\pi$
$410$	−30.5547	−1.50899
$411$	1.77903	0.0877530
$412$	2.46094	0.121242
$413$	1.72436	0.0848503
$414$	52.1051	2.56083
$415$	19.5128	0.957848
$416$	−16.0660	−0.787700
$417$	−0.285030	−0.0139580
$418$	7.40212	0.362050
$419$	34.0536	1.66362	0.831812	−	0.555057i	$-0.187303\pi$
$419$	34.0536	1.66362	0.831812	+	0.555057i	$0.187303\pi$
$420$	−2.29143	−0.111810
$421$	−4.90689	−0.239147	−0.119574	−	0.992825i	$-0.538153\pi$
$421$	−4.90689	−0.239147	−0.119574	+	0.992825i	$0.538153\pi$
$422$	−9.18282	−0.447013
$423$	29.8434	1.45103
$424$	0.598645	0.0290728
$425$	22.2569	1.07962
$426$	−0.486416	−0.0235669
$427$	13.5284	0.654683
$428$	19.8827	0.961066
$429$	−0.660033	−0.0318667
$430$	0	0
$431$	16.2775	0.784058	0.392029	−	0.919953i	$-0.371773\pi$
$431$	16.2775	0.784058	0.392029	+	0.919953i	$0.371773\pi$
$432$	3.98155	0.191562
$433$	−17.0243	−0.818138	−0.409069	−	0.912503i	$-0.634146\pi$
$433$	−17.0243	−0.818138	−0.409069	+	0.912503i	$0.634146\pi$
$434$	−35.2265	−1.69092
$435$	4.34728	0.208436
$436$	5.72157	0.274014
$437$	16.3394	0.781620
$438$	0.273398	0.0130635
$439$	38.2536	1.82574	0.912872	−	0.408245i	$-0.133859\pi$
$439$	38.2536	1.82574	0.912872	+	0.408245i	$0.133859\pi$
$440$	−0.994133	−0.0473934
$441$	3.22240	0.153447
$442$	20.4936	0.974781
$443$	−1.49828	−0.0711856	−0.0355928	−	0.999366i	$-0.511332\pi$
$443$	−1.49828	−0.0711856	−0.0355928	+	0.999366i	$0.511332\pi$
$444$	1.94424	0.0922693
$445$	−2.42436	−0.114926
$446$	−51.8368	−2.45455
$447$	3.10153	0.146697
$448$	−17.8521	−0.843433
$449$	25.8063	1.21787	0.608937	−	0.793219i	$-0.291596\pi$
$449$	25.8063	1.21787	0.608937	+	0.793219i	$0.291596\pi$
$450$	−25.7262	−1.21275
$451$	−10.2113	−0.480834
$452$	3.95798	0.186168
$453$	1.65475	0.0777469
$454$	−18.6837	−0.876871
$455$	−15.1308	−0.709342
$456$	0.0474919	0.00222401
$457$	−11.9397	−0.558515	−0.279258	−	0.960216i	$-0.590088\pi$
$457$	−11.9397	−0.558515	−0.279258	+	0.960216i	$0.590088\pi$
$458$	−6.81054	−0.318236
$459$	−4.88079	−0.227816
$460$	51.9800	2.42358
$461$	−15.4926	−0.721564	−0.360782	−	0.932650i	$-0.617490\pi$
$461$	−15.4926	−0.721564	−0.360782	+	0.932650i	$0.617490\pi$
$462$	−1.56392	−0.0727601
$463$	8.33730	0.387467	0.193734	−	0.981054i	$-0.437940\pi$
$463$	8.33730	0.387467	0.193734	+	0.981054i	$0.437940\pi$
$464$	36.7991	1.70836
$465$	3.59126	0.166541
$466$	12.3852	0.573731
$467$	0.257604	0.0119205	0.00596024	−	0.999982i	$-0.498103\pi$
$467$	0.257604	0.0119205	0.00596024	+	0.999982i	$0.498103\pi$
$468$	−11.5992	−0.536172
$469$	11.5410	0.532915
$470$	60.8003	2.80451
$471$	1.19780	0.0551919
$472$	−0.113695	−0.00523323
$473$	0	0
$474$	−3.87677	−0.178066
$475$	−8.06738	−0.370157
$476$	23.7774	1.08984
$477$	11.1021	0.508328
$478$	−44.9109	−2.05418
$479$	−11.0980	−0.507079	−0.253540	−	0.967325i	$-0.581595\pi$
$479$	−11.0980	−0.507079	−0.253540	+	0.967325i	$0.581595\pi$
$480$	3.88091	0.177138
$481$	12.8382	0.585371
$482$	−35.2307	−1.60471
$483$	−3.45219	−0.157080
$484$	−13.2391	−0.601777
$485$	−44.2941	−2.01129
$486$	8.47452	0.384412
$487$	−5.84979	−0.265079	−0.132540	−	0.991178i	$-0.542313\pi$
$487$	−5.84979	−0.265079	−0.132540	+	0.991178i	$0.542313\pi$
$488$	−0.891984	−0.0403782
$489$	−1.36031	−0.0615152
$490$	6.56503	0.296578
$491$	−2.87014	−0.129528	−0.0647638	−	0.997901i	$-0.520629\pi$
$491$	−2.87014	−0.129528	−0.0647638	+	0.997901i	$0.520629\pi$
$492$	1.55188	0.0699640
$493$	−45.1103	−2.03166
$494$	−7.42823	−0.334212
$495$	−18.4365	−0.828660
$496$	30.3995	1.36498
$497$	−3.72657	−0.167159
$498$	−2.02396	−0.0906958
$499$	−4.47529	−0.200342	−0.100171	−	0.994970i	$-0.531939\pi$
$499$	−4.47529	−0.200342	−0.100171	+	0.994970i	$0.531939\pi$
$500$	3.70489	0.165688
$501$	−2.05534	−0.0918259
$502$	18.2066	0.812600
$503$	−14.9161	−0.665078	−0.332539	−	0.943090i	$-0.607905\pi$
$503$	−14.9161	−0.665078	−0.332539	+	0.943090i	$0.607905\pi$
$504$	1.16028	0.0516831
$505$	6.95145	0.309336
$506$	35.4767	1.57713
$507$	−1.42257	−0.0631783
$508$	8.90510	0.395100
$509$	−7.36523	−0.326458	−0.163229	−	0.986588i	$-0.552191\pi$
$509$	−7.36523	−0.326458	−0.163229	+	0.986588i	$0.552191\pi$
$510$	−4.95044	−0.219209
$511$	2.09458	0.0926588
$512$	31.5185	1.39293
$513$	1.76912	0.0781086
$514$	−6.58422	−0.290417
$515$	−3.92538	−0.172973
$516$	0	0
$517$	20.3194	0.893646
$518$	30.4195	1.33656
$519$	−3.25946	−0.143074
$520$	0.997639	0.0437494
$521$	−6.72559	−0.294654	−0.147327	−	0.989088i	$-0.547067\pi$
$521$	−6.72559	−0.294654	−0.147327	+	0.989088i	$0.547067\pi$
$522$	52.1419	2.28219
$523$	−5.21329	−0.227961	−0.113981	−	0.993483i	$-0.536360\pi$
$523$	−5.21329	−0.227961	−0.113981	+	0.993483i	$0.536360\pi$
$524$	20.9052	0.913248
$525$	1.70447	0.0743893
$526$	−0.168034	−0.00732665
$527$	−37.2653	−1.62330
$528$	1.34962	0.0587347
$529$	55.3111	2.40483
$530$	22.6184	0.982480
$531$	−2.10851	−0.0915014
$532$	−8.61850	−0.373659
$533$	10.2474	0.443862
$534$	0.251465	0.0108820
$535$	−31.7144	−1.37113
$536$	−0.760951	−0.0328681
$537$	−2.30208	−0.0993419
$538$	−35.5632	−1.53324
$539$	2.19403	0.0945034
$540$	5.62804	0.242192
$541$	30.9453	1.33044	0.665222	−	0.746646i	$-0.268337\pi$
$541$	30.9453	1.33044	0.665222	+	0.746646i	$0.268337\pi$
$542$	9.38474	0.403109
$543$	−1.46603	−0.0629134
$544$	−40.2709	−1.72660
$545$	−9.12633	−0.390929
$546$	1.56943	0.0671656
$547$	−38.6408	−1.65216	−0.826081	−	0.563551i	$-0.809435\pi$
$547$	−38.6408	−1.65216	−0.826081	+	0.563551i	$0.809435\pi$
$548$	21.2866	0.909320
$549$	−16.5421	−0.706001
$550$	−17.5162	−0.746892
$551$	16.3509	0.696573
$552$	0.227618	0.00968806
$553$	−29.7010	−1.26302
$554$	34.4284	1.46272
$555$	−3.10120	−0.131639
$556$	−3.41047	−0.144636
$557$	5.03559	0.213365	0.106682	−	0.994293i	$-0.465977\pi$
$557$	5.03559	0.213365	0.106682	+	0.994293i	$0.465977\pi$
$558$	43.0740	1.82347
$559$	0	0
$560$	30.9391	1.30742
$561$	−1.65443	−0.0698503
$562$	−1.93695	−0.0817054
$563$	35.5657	1.49892	0.749459	−	0.662051i	$-0.230314\pi$
$563$	35.5657	1.49892	0.749459	+	0.662051i	$0.230314\pi$
$564$	−3.08806	−0.130031
$565$	−6.31327	−0.265601
$566$	55.3541	2.32671
$567$	21.3301	0.895782
$568$	0.245709	0.0103097
$569$	2.53126	0.106116	0.0530581	−	0.998591i	$-0.483103\pi$
$569$	2.53126	0.106116	0.0530581	+	0.998591i	$0.483103\pi$
$570$	1.79437	0.0751578
$571$	27.8264	1.16450	0.582250	−	0.813010i	$-0.302173\pi$
$571$	27.8264	1.16450	0.582250	+	0.813010i	$0.302173\pi$
$572$	−7.89751	−0.330211
$573$	1.65917	0.0693128
$574$	24.2807	1.01346
$575$	−38.6651	−1.61245
$576$	21.8291	0.909546
$577$	−16.1258	−0.671325	−0.335662	−	0.941982i	$-0.608960\pi$
$577$	−16.1258	−0.671325	−0.335662	+	0.941982i	$0.608960\pi$
$578$	17.7152	0.736853
$579$	0.806779	0.0335286
$580$	52.0167	2.15987
$581$	−15.5061	−0.643302
$582$	4.59439	0.190443
$583$	7.55904	0.313063
$584$	−0.138105	−0.00571482
$585$	18.5015	0.764945
$586$	−25.7963	−1.06563
$587$	3.74391	0.154528	0.0772638	−	0.997011i	$-0.475382\pi$
$587$	3.74391	0.154528	0.0772638	+	0.997011i	$0.475382\pi$
$588$	−0.333439	−0.0137508
$589$	13.5074	0.556562
$590$	−4.29569	−0.176851
$591$	−3.25354	−0.133833
$592$	−26.2512	−1.07892
$593$	−4.67218	−0.191864	−0.0959318	−	0.995388i	$-0.530583\pi$
$593$	−4.67218	−0.191864	−0.0959318	+	0.995388i	$0.530583\pi$
$594$	3.84118	0.157605
$595$	−37.9267	−1.55484
$596$	37.1109	1.52012
$597$	3.77929	0.154676
$598$	−35.6018	−1.45587
$599$	−24.6917	−1.00888	−0.504439	−	0.863448i	$-0.668301\pi$
$599$	−24.6917	−1.00888	−0.504439	+	0.863448i	$0.668301\pi$
$600$	−0.112383	−0.00458803
$601$	17.8648	0.728720	0.364360	−	0.931258i	$-0.381288\pi$
$601$	17.8648	0.728720	0.364360	+	0.931258i	$0.381288\pi$
$602$	0	0
$603$	−14.1121	−0.574688
$604$	19.7996	0.805635
$605$	21.1173	0.858541
$606$	−0.721036	−0.0292901
$607$	−38.9307	−1.58015	−0.790075	−	0.613010i	$-0.789959\pi$
$607$	−38.9307	−1.58015	−0.790075	+	0.613010i	$0.789959\pi$
$608$	14.5968	0.591979
$609$	−3.45462	−0.139988
$610$	−33.7015	−1.36453
$611$	−20.3911	−0.824934
$612$	−29.0744	−1.17526
$613$	27.6778	1.11789	0.558947	−	0.829203i	$-0.311206\pi$
$613$	27.6778	1.11789	0.558947	+	0.829203i	$0.311206\pi$
$614$	−15.7890	−0.637191
$615$	−2.47536	−0.0998161
$616$	0.790000	0.0318300
$617$	13.2152	0.532026	0.266013	−	0.963969i	$-0.414294\pi$
$617$	13.2152	0.532026	0.266013	+	0.963969i	$0.414294\pi$
$618$	0.407159	0.0163783
$619$	−45.2008	−1.81677	−0.908387	−	0.418131i	$-0.862685\pi$
$619$	−45.2008	−1.81677	−0.908387	+	0.418131i	$0.862685\pi$
$620$	42.9706	1.72574
$621$	8.47900	0.340250
$622$	30.0656	1.20552
$623$	1.92655	0.0771854
$624$	−1.35438	−0.0542186
$625$	−27.7559	−1.11023
$626$	−11.1583	−0.445977
$627$	0.599676	0.0239487
$628$	14.3321	0.571914
$629$	32.1801	1.28310
$630$	43.8386	1.74657
$631$	−24.0320	−0.956699	−0.478350	−	0.878169i	$-0.658765\pi$
$631$	−24.0320	−0.956699	−0.478350	+	0.878169i	$0.658765\pi$
$632$	1.95832	0.0778977
$633$	−0.743938	−0.0295689
$634$	−5.06867	−0.201303
$635$	−14.2043	−0.563680
$636$	−1.14879	−0.0455525
$637$	−2.20176	−0.0872371
$638$	35.5017	1.40553
$639$	4.55675	0.180262
$640$	−3.92404	−0.155111
$641$	12.2581	0.484164	0.242082	−	0.970256i	$-0.422170\pi$
$641$	12.2581	0.484164	0.242082	+	0.970256i	$0.422170\pi$
$642$	3.28956	0.129828
$643$	12.8463	0.506609	0.253305	−	0.967387i	$-0.418482\pi$
$643$	12.8463	0.506609	0.253305	+	0.967387i	$0.418482\pi$
$644$	−41.3065	−1.62771
$645$	0	0
$646$	−18.6195	−0.732576
$647$	−36.8522	−1.44881	−0.724404	−	0.689376i	$-0.757885\pi$
$647$	−36.8522	−1.44881	−0.724404	+	0.689376i	$0.757885\pi$
$648$	−1.40639	−0.0552482
$649$	−1.43562	−0.0563528
$650$	17.5780	0.689464
$651$	−2.85384	−0.111851
$652$	−16.2765	−0.637437
$653$	−21.8257	−0.854107	−0.427054	−	0.904226i	$-0.640448\pi$
$653$	−21.8257	−0.854107	−0.427054	+	0.904226i	$0.640448\pi$
$654$	0.946624	0.0370159
$655$	−33.3454	−1.30291
$656$	−20.9536	−0.818099
$657$	−2.56120	−0.0999219
$658$	−48.3157	−1.88354
$659$	44.3752	1.72861	0.864307	−	0.502964i	$-0.167757\pi$
$659$	44.3752	1.72861	0.864307	+	0.502964i	$0.167757\pi$
$660$	1.90773	0.0742582
$661$	42.5847	1.65635	0.828176	−	0.560468i	$-0.189379\pi$
$661$	42.5847	1.65635	0.828176	+	0.560468i	$0.189379\pi$
$662$	32.9160	1.27932
$663$	1.66027	0.0644795
$664$	1.02239	0.0396763
$665$	13.7471	0.533092
$666$	−37.1962	−1.44132
$667$	78.3664	3.03436
$668$	−24.5928	−0.951526
$669$	−4.19951	−0.162363
$670$	−28.7507	−1.11074
$671$	−11.2630	−0.434804
$672$	−3.08401	−0.118968
$673$	18.2839	0.704793	0.352397	−	0.935851i	$-0.385367\pi$
$673$	18.2839	0.704793	0.352397	+	0.935851i	$0.385367\pi$
$674$	6.16604	0.237507
$675$	−4.18640	−0.161135
$676$	−17.0215	−0.654671
$677$	−19.5234	−0.750346	−0.375173	−	0.926955i	$-0.622417\pi$
$677$	−19.5234	−0.750346	−0.375173	+	0.926955i	$0.622417\pi$
$678$	0.654841	0.0251490
$679$	35.1989	1.35081
$680$	2.50068	0.0958965
$681$	−1.51364	−0.0580030
$682$	29.3277	1.12302
$683$	−38.4155	−1.46993	−0.734964	−	0.678106i	$-0.762801\pi$
$683$	−38.4155	−1.46993	−0.734964	+	0.678106i	$0.762801\pi$
$684$	10.5385	0.402949
$685$	−33.9538	−1.29731
$686$	−38.9240	−1.48612
$687$	−0.551750	−0.0210506
$688$	0	0
$689$	−7.58570	−0.288992
$690$	8.60000	0.327396
$691$	5.82885	0.221740	0.110870	−	0.993835i	$-0.464636\pi$
$691$	5.82885	0.221740	0.110870	+	0.993835i	$0.464636\pi$
$692$	−39.0005	−1.48258
$693$	14.6508	0.556538
$694$	−43.6167	−1.65567
$695$	5.43996	0.206349
$696$	0.227778	0.00863392
$697$	25.6860	0.972925
$698$	22.6162	0.856037
$699$	1.00337	0.0379510
$700$	20.3946	0.770843
$701$	−20.4564	−0.772628	−0.386314	−	0.922367i	$-0.626252\pi$
$701$	−20.4564	−0.772628	−0.386314	+	0.922367i	$0.626252\pi$
$702$	−3.85472	−0.145487
$703$	−11.6642	−0.439923
$704$	14.8627	0.560161
$705$	4.92568	0.185512
$706$	−49.3107	−1.85583
$707$	−5.52406	−0.207754
$708$	0.218179	0.00819966
$709$	−49.8166	−1.87090	−0.935451	−	0.353455i	$-0.885007\pi$
$709$	−49.8166	−1.87090	−0.935451	+	0.353455i	$0.885007\pi$
$710$	9.28354	0.348405
$711$	36.3177	1.36202
$712$	−0.127026	−0.00476048
$713$	64.7379	2.42445
$714$	3.93393	0.147224
$715$	12.5971	0.471105
$716$	−27.5451	−1.02941
$717$	−3.63841	−0.135879
$718$	−25.6192	−0.956100
$719$	38.2219	1.42543	0.712717	−	0.701451i	$-0.247464\pi$
$719$	38.2219	1.42543	0.712717	+	0.701451i	$0.247464\pi$
$720$	−37.8315	−1.40990
$721$	3.11936	0.116171
$722$	−30.8643	−1.14865
$723$	−2.85418	−0.106148
$724$	−17.5415	−0.651926
$725$	−38.6924	−1.43700
$726$	−2.19038	−0.0812928
$727$	−42.5500	−1.57809	−0.789047	−	0.614333i	$-0.789425\pi$
$727$	−42.5500	−1.57809	−0.789047	+	0.614333i	$0.789425\pi$
$728$	−0.792786	−0.0293826
$729$	−25.6210	−0.948924
$730$	−5.21796	−0.193125
$731$	0	0
$732$	1.71170	0.0632664
$733$	−24.5238	−0.905806	−0.452903	−	0.891560i	$-0.649612\pi$
$733$	−24.5238	−0.905806	−0.452903	+	0.891560i	$0.649612\pi$
$734$	−38.6377	−1.42614
$735$	0.531860	0.0196179
$736$	69.9593	2.57873
$737$	−9.60847	−0.353932
$738$	−29.6898	−1.09290
$739$	26.7549	0.984194	0.492097	−	0.870540i	$-0.336231\pi$
$739$	26.7549	0.984194	0.492097	+	0.870540i	$0.336231\pi$
$740$	−37.1069	−1.36408
$741$	−0.601791	−0.0221073
$742$	−17.9740	−0.659845
$743$	8.79505	0.322659	0.161330	−	0.986901i	$-0.448422\pi$
$743$	8.79505	0.322659	0.161330	+	0.986901i	$0.448422\pi$
$744$	0.188166	0.00689850
$745$	−59.1946	−2.16872
$746$	−28.8382	−1.05584
$747$	18.9605	0.693728
$748$	−19.7958	−0.723808
$749$	25.2022	0.920869
$750$	0.612968	0.0223824
$751$	−3.07888	−0.112350	−0.0561749	−	0.998421i	$-0.517890\pi$
$751$	−3.07888	−0.112350	−0.0561749	+	0.998421i	$0.517890\pi$
$752$	41.6952	1.52047
$753$	1.47499	0.0537516
$754$	−35.6269	−1.29746
$755$	−31.5819	−1.14938
$756$	−4.47239	−0.162659
$757$	20.4021	0.741527	0.370763	−	0.928727i	$-0.379096\pi$
$757$	20.4021	0.741527	0.370763	+	0.928727i	$0.379096\pi$
$758$	−44.0563	−1.60020
$759$	2.87411	0.104324
$760$	−0.906410	−0.0328789
$761$	−31.2997	−1.13461	−0.567306	−	0.823507i	$-0.692014\pi$
$761$	−31.2997	−1.13461	−0.567306	+	0.823507i	$0.692014\pi$
$762$	1.47333	0.0533733
$763$	7.25235	0.262553
$764$	19.8525	0.718239
$765$	46.3758	1.67672
$766$	−61.4175	−2.21911
$767$	1.44068	0.0520199
$768$	2.76115	0.0996346
$769$	−38.1657	−1.37629	−0.688144	−	0.725574i	$-0.741574\pi$
$769$	−38.1657	−1.37629	−0.688144	+	0.725574i	$0.741574\pi$
$770$	29.8483	1.07566
$771$	−0.533414	−0.0192104
$772$	9.65337	0.347433
$773$	7.04664	0.253450	0.126725	−	0.991938i	$-0.459553\pi$
$773$	7.04664	0.253450	0.126725	+	0.991938i	$0.459553\pi$
$774$	0	0
$775$	−31.9635	−1.14816
$776$	−2.32082	−0.0833125
$777$	2.46441	0.0884101
$778$	50.9507	1.82667
$779$	−9.31029	−0.333576
$780$	−1.91446	−0.0685485
$781$	3.10255	0.111018
$782$	−89.2393	−3.19119
$783$	8.48498	0.303228
$784$	4.50212	0.160790
$785$	−22.8608	−0.815937
$786$	3.45873	0.123369
$787$	17.3595	0.618799	0.309399	−	0.950932i	$-0.399872\pi$
$787$	17.3595	0.618799	0.309399	+	0.950932i	$0.399872\pi$
$788$	−38.9297	−1.38681
$789$	−0.0136132	−0.000484641 0
$790$	73.9905	2.63246
$791$	5.01692	0.178381
$792$	−0.965992	−0.0343250
$793$	11.3027	0.401372
$794$	66.1211	2.34655
$795$	1.83241	0.0649888
$796$	45.2204	1.60280
$797$	2.67108	0.0946144	0.0473072	−	0.998880i	$-0.484936\pi$
$797$	2.67108	0.0946144	0.0473072	+	0.998880i	$0.484936\pi$
$798$	−1.42592	−0.0504769
$799$	−51.1121	−1.80822
$800$	−34.5415	−1.22123
$801$	−2.35573	−0.0832356
$802$	5.29401	0.186938
$803$	−1.74384	−0.0615387
$804$	1.46025	0.0514992
$805$	65.8870	2.32221
$806$	−29.4312	−1.03667
$807$	−2.88112	−0.101420
$808$	0.364225	0.0128134
$809$	22.8399	0.803009	0.401504	−	0.915857i	$-0.368487\pi$
$809$	22.8399	0.803009	0.401504	+	0.915857i	$0.368487\pi$
$810$	−53.1371	−1.86705
$811$	−38.1235	−1.33870	−0.669348	−	0.742949i	$-0.733427\pi$
$811$	−38.1235	−1.33870	−0.669348	+	0.742949i	$0.733427\pi$
$812$	−41.3357	−1.45060
$813$	0.760296	0.0266647
$814$	−25.3257	−0.887665
$815$	25.9622	0.909417
$816$	−3.39488	−0.118845
$817$	0	0
$818$	−60.1162	−2.10191
$819$	−14.7025	−0.513746
$820$	−29.6185	−1.03432
$821$	31.0075	1.08217	0.541085	−	0.840968i	$-0.318014\pi$
$821$	31.0075	1.08217	0.541085	+	0.840968i	$0.318014\pi$
$822$	3.52184	0.122838
$823$	−21.1779	−0.738217	−0.369108	−	0.929386i	$-0.620337\pi$
$823$	−21.1779	−0.738217	−0.369108	+	0.929386i	$0.620337\pi$
$824$	−0.205673	−0.00716495
$825$	−1.41906	−0.0494052
$826$	3.41362	0.118775
$827$	−7.37460	−0.256440	−0.128220	−	0.991746i	$-0.540926\pi$
$827$	−7.37460	−0.256440	−0.128220	+	0.991746i	$0.540926\pi$
$828$	50.5086	1.75529
$829$	−0.892898	−0.0310116	−0.0155058	−	0.999880i	$-0.504936\pi$
$829$	−0.892898	−0.0310116	−0.0155058	+	0.999880i	$0.504936\pi$
$830$	38.6285	1.34081
$831$	2.78919	0.0967558
$832$	−14.9152	−0.517090
$833$	−5.51893	−0.191220
$834$	−0.564257	−0.0195386
$835$	39.2274	1.35752
$836$	7.17532	0.248164
$837$	7.00938	0.242280
$838$	67.4139	2.32877
$839$	−21.1769	−0.731109	−0.365554	−	0.930790i	$-0.619121\pi$
$839$	−21.1769	−0.731109	−0.365554	+	0.930790i	$0.619121\pi$
$840$	0.191506	0.00660758
$841$	49.4216	1.70419
$842$	−9.71390	−0.334763
$843$	−0.156920	−0.00540462
$844$	−8.90146	−0.306401
$845$	27.1505	0.934005
$846$	59.0792	2.03118
$847$	−16.7811	−0.576607
$848$	15.5111	0.532652
$849$	4.48446	0.153906
$850$	44.0608	1.51127
$851$	−55.9038	−1.91636
$852$	−0.471512	−0.0161537
$853$	−15.9065	−0.544629	−0.272314	−	0.962208i	$-0.587789\pi$
$853$	−15.9065	−0.544629	−0.272314	+	0.962208i	$0.587789\pi$
$854$	26.7813	0.916438
$855$	−16.8097	−0.574878
$856$	−1.66169	−0.0567955
$857$	−8.76091	−0.299267	−0.149634	−	0.988742i	$-0.547809\pi$
$857$	−8.76091	−0.299267	−0.149634	+	0.988742i	$0.547809\pi$
$858$	−1.30663	−0.0446076
$859$	−24.8045	−0.846318	−0.423159	−	0.906055i	$-0.639079\pi$
$859$	−24.8045	−0.846318	−0.423159	+	0.906055i	$0.639079\pi$
$860$	0	0
$861$	1.96707	0.0670377
$862$	32.2236	1.09754
$863$	19.6833	0.670027	0.335013	−	0.942213i	$-0.391259\pi$
$863$	19.6833	0.670027	0.335013	+	0.942213i	$0.391259\pi$
$864$	7.57472	0.257697
$865$	62.2087	2.11516
$866$	−33.7021	−1.14524
$867$	1.43518	0.0487412
$868$	−34.1471	−1.15903
$869$	24.7275	0.838824
$870$	8.60607	0.291773
$871$	9.64235	0.326719
$872$	−0.478179	−0.0161932
$873$	−43.0403	−1.45669
$874$	32.3462	1.09413
$875$	4.69612	0.158758
$876$	0.265021	0.00895424
$877$	30.3663	1.02540	0.512699	−	0.858568i	$-0.328646\pi$
$877$	30.3663	1.02540	0.512699	+	0.858568i	$0.328646\pi$
$878$	75.7285	2.55571
$879$	−2.08986	−0.0704893
$880$	−25.7583	−0.868312
$881$	−11.3720	−0.383133	−0.191567	−	0.981480i	$-0.561357\pi$
$881$	−11.3720	−0.383133	−0.191567	+	0.981480i	$0.561357\pi$
$882$	6.37919	0.214799
$883$	40.7015	1.36971	0.684857	−	0.728677i	$-0.259865\pi$
$883$	40.7015	1.36971	0.684857	+	0.728677i	$0.259865\pi$
$884$	19.8657	0.668154
$885$	−0.348011	−0.0116983
$886$	−2.96607	−0.0996470
$887$	−38.0952	−1.27911	−0.639555	−	0.768745i	$-0.720881\pi$
$887$	−38.0952	−1.27911	−0.639555	+	0.768745i	$0.720881\pi$
$888$	−0.162489	−0.00545278
$889$	11.2876	0.378575
$890$	−4.79936	−0.160875
$891$	−17.7584	−0.594928
$892$	−50.2485	−1.68245
$893$	18.5264	0.619962
$894$	6.13993	0.205350
$895$	43.9365	1.46863
$896$	3.11829	0.104175
$897$	−2.88425	−0.0963022
$898$	51.0872	1.70480
$899$	64.7836	2.16065
$900$	−24.9380	−0.831266
$901$	−19.0143	−0.633457
$902$	−20.2148	−0.673080
$903$	0	0
$904$	−0.330787	−0.0110018
$905$	27.9800	0.930088
$906$	3.27581	0.108832
$907$	37.8762	1.25766	0.628830	−	0.777543i	$-0.283534\pi$
$907$	37.8762	1.25766	0.628830	+	0.777543i	$0.283534\pi$
$908$	−18.1112	−0.601043
$909$	6.75468	0.224039
$910$	−29.9536	−0.992951
$911$	−47.6125	−1.57747	−0.788736	−	0.614732i	$-0.789264\pi$
$911$	−47.6125	−1.57747	−0.788736	+	0.614732i	$0.789264\pi$
$912$	1.23053	0.0407469
$913$	12.9096	0.427245
$914$	−23.6363	−0.781820
$915$	−2.73029	−0.0902608
$916$	−6.60187	−0.218132
$917$	26.4983	0.875051
$918$	−9.66222	−0.318901
$919$	11.9064	0.392757	0.196378	−	0.980528i	$-0.437082\pi$
$919$	11.9064	0.392757	0.196378	+	0.980528i	$0.437082\pi$
$920$	−4.34422	−0.143225
$921$	−1.27913	−0.0421487
$922$	−30.6699	−1.01006
$923$	−3.11349	−0.102482
$924$	−1.51600	−0.0498727
$925$	27.6018	0.907542
$926$	16.5049	0.542384
$927$	−3.81427	−0.125277
$928$	70.0086	2.29815
$929$	−44.5378	−1.46124	−0.730619	−	0.682785i	$-0.760768\pi$
$929$	−44.5378	−1.46124	−0.730619	+	0.682785i	$0.760768\pi$
$930$	7.10941	0.233127
$931$	2.00042	0.0655612
$932$	12.0057	0.393259
$933$	2.43574	0.0797425
$934$	0.509963	0.0166865
$935$	31.5758	1.03264
$936$	0.969399	0.0316858
$937$	−42.2239	−1.37939	−0.689697	−	0.724098i	$-0.742256\pi$
$937$	−42.2239	−1.37939	−0.689697	+	0.724098i	$0.742256\pi$
$938$	22.8471	0.745985
$939$	−0.903983	−0.0295004
$940$	58.9373	1.92232
$941$	29.8118	0.971838	0.485919	−	0.874004i	$-0.338485\pi$
$941$	29.8118	0.971838	0.485919	+	0.874004i	$0.338485\pi$
$942$	2.37122	0.0772587
$943$	−44.6221	−1.45310
$944$	−2.94587	−0.0958798
$945$	7.13380	0.232062
$946$	0	0
$947$	−35.0818	−1.14000	−0.570002	−	0.821643i	$-0.693058\pi$
$947$	−35.0818	−1.14000	−0.570002	+	0.821643i	$0.693058\pi$
$948$	−3.75799	−0.122054
$949$	1.74999	0.0568070
$950$	−15.9705	−0.518152
$951$	−0.410634	−0.0133157
$952$	−1.98719	−0.0644053
$953$	43.2193	1.40001	0.700005	−	0.714138i	$-0.253181\pi$
$953$	43.2193	1.40001	0.700005	+	0.714138i	$0.253181\pi$
$954$	21.9781	0.711568
$955$	−31.6662	−1.02470
$956$	−43.5348	−1.40802
$957$	2.87614	0.0929724
$958$	−21.9700	−0.709819
$959$	26.9818	0.871288
$960$	3.60292	0.116284
$961$	22.5173	0.726363
$962$	25.4150	0.819413
$963$	−30.8166	−0.993051
$964$	−34.1512	−1.09994
$965$	−15.3978	−0.495674
$966$	−6.83410	−0.219883
$967$	−32.3393	−1.03996	−0.519982	−	0.854178i	$-0.674061\pi$
$967$	−32.3393	−1.03996	−0.519982	+	0.854178i	$0.674061\pi$
$968$	1.10645	0.0355628
$969$	−1.50844	−0.0484582
$970$	−87.6866	−2.81545
$971$	−38.9301	−1.24933	−0.624663	−	0.780895i	$-0.714764\pi$
$971$	−38.9301	−1.24933	−0.624663	+	0.780895i	$0.714764\pi$
$972$	8.21486	0.263492
$973$	−4.32293	−0.138587
$974$	−11.5805	−0.371063
$975$	1.42406	0.0456065
$976$	−23.1116	−0.739783
$977$	47.9997	1.53565	0.767824	−	0.640661i	$-0.221340\pi$
$977$	47.9997	1.53565	0.767824	+	0.640661i	$0.221340\pi$
$978$	−2.69292	−0.0861101
$979$	−1.60394	−0.0512622
$980$	6.36388	0.203287
$981$	−8.86799	−0.283133
$982$	−5.68185	−0.181315
$983$	50.9185	1.62405	0.812024	−	0.583625i	$-0.198366\pi$
$983$	50.9185	1.62405	0.812024	+	0.583625i	$0.198366\pi$
$984$	−0.129698	−0.00413462
$985$	62.0958	1.97854
$986$	−89.3022	−2.84396
$987$	−3.91425	−0.124592
$988$	−7.20062	−0.229082
$989$	0	0
$990$	−36.4977	−1.15997
$991$	−8.98089	−0.285287	−0.142644	−	0.989774i	$-0.545560\pi$
$991$	−8.98089	−0.285287	−0.142644	+	0.989774i	$0.545560\pi$
$992$	57.8336	1.83622
$993$	2.66666	0.0846239
$994$	−7.37728	−0.233993
$995$	−72.1300	−2.28667
$996$	−1.96194	−0.0621666
$997$	42.4486	1.34436	0.672180	−	0.740388i	$-0.265358\pi$
$997$	42.4486	1.34436	0.672180	+	0.740388i	$0.265358\pi$
$998$	−8.85948	−0.280442
$999$	−6.05289	−0.191505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.m.1.10	yes	10
43.42	odd	2	inner	1849.2.a.m.1.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.m.1.1	✓	10	43.42	odd	2	inner
1849.2.a.m.1.10	yes	10	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+1.97964 q^{2} +0.160379 q^{3} +1.91899 q^{4} -3.06092 q^{5} +0.317493 q^{6} +2.43240 q^{7} -0.160379 q^{8} -2.97428 q^{9} +O(q^{10})\)	\(q+1.97964 q^{2} +0.160379 q^{3} +1.91899 q^{4} -3.06092 q^{5} +0.317493 q^{6} +2.43240 q^{7} -0.160379 q^{8} -2.97428 q^{9} -6.05954 q^{10} -2.02509 q^{11} +0.307765 q^{12} +2.03223 q^{13} +4.81529 q^{14} -0.490908 q^{15} -4.15546 q^{16} +5.09398 q^{17} -5.88801 q^{18} -1.84640 q^{19} -5.87387 q^{20} +0.390106 q^{21} -4.00896 q^{22} -8.84936 q^{23} -0.0257214 q^{24} +4.36926 q^{25} +4.02310 q^{26} -0.958148 q^{27} +4.66775 q^{28} -8.85560 q^{29} -0.971822 q^{30} -7.31555 q^{31} -7.90558 q^{32} -0.324782 q^{33} +10.0843 q^{34} -7.44540 q^{35} -5.70760 q^{36} +6.31728 q^{37} -3.65520 q^{38} +0.325927 q^{39} +0.490908 q^{40} +5.04241 q^{41} +0.772270 q^{42} -3.88612 q^{44} +9.10404 q^{45} -17.5186 q^{46} -10.0338 q^{47} -0.666449 q^{48} -1.08342 q^{49} +8.64957 q^{50} +0.816967 q^{51} +3.89983 q^{52} -3.73269 q^{53} -1.89679 q^{54} +6.19865 q^{55} -0.390106 q^{56} -0.296123 q^{57} -17.5309 q^{58} +0.708914 q^{59} -0.942045 q^{60} +5.56173 q^{61} -14.4822 q^{62} -7.23464 q^{63} -7.33929 q^{64} -6.22051 q^{65} -0.642952 q^{66} +4.74471 q^{67} +9.77528 q^{68} -1.41925 q^{69} -14.7392 q^{70} -1.53205 q^{71} +0.477012 q^{72} +0.861116 q^{73} +12.5059 q^{74} +0.700737 q^{75} -3.54321 q^{76} -4.92584 q^{77} +0.645220 q^{78} -12.2106 q^{79} +12.7196 q^{80} +8.76917 q^{81} +9.98218 q^{82} -6.37482 q^{83} +0.748608 q^{84} -15.5923 q^{85} -1.42025 q^{87} +0.324782 q^{88} +0.792034 q^{89} +18.0228 q^{90} +4.94321 q^{91} -16.9818 q^{92} -1.17326 q^{93} -19.8634 q^{94} +5.65168 q^{95} -1.26789 q^{96} +14.4708 q^{97} -2.14479 q^{98} +6.02319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9}+O(q^{10}) \) 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9	\( 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9} - 22 q^{10} - 10 q^{11} - 14 q^{13} - 22 q^{14} - 22 q^{15} - 26 q^{16} - 16 q^{17} - 44 q^{21} - 18 q^{23} - 44 q^{24} - 6 q^{25} - 2 q^{31} - 28 q^{36} - 22 q^{38} + 22 q^{40} - 2 q^{44} - 18 q^{47} + 18 q^{49} + 28 q^{52} + 2 q^{53} + 44 q^{56} - 22 q^{57} - 22 q^{58} + 14 q^{59} + 8 q^{64} - 22 q^{66} + 26 q^{67} + 32 q^{68} + 44 q^{74} - 44 q^{78} - 56 q^{79} + 2 q^{81} - 38 q^{83} - 22 q^{87} - 22 q^{90} - 74 q^{92} + 22 q^{96} + 34 q^{97} - 36 q^{99}+O(q^{100}) \) 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9 - 22 * q^10 - 10 * q^11 - 14 * q^13 - 22 * q^14 - 22 * q^15 - 26 * q^16 - 16 * q^17 - 44 * q^21 - 18 * q^23 - 44 * q^24 - 6 * q^25 - 2 * q^31 - 28 * q^36 - 22 * q^38 + 22 * q^40 - 2 * q^44 - 18 * q^47 + 18 * q^49 + 28 * q^52 + 2 * q^53 + 44 * q^56 - 22 * q^57 - 22 * q^58 + 14 * q^59 + 8 * q^64 - 22 * q^66 + 26 * q^67 + 32 * q^68 + 44 * q^74 - 44 * q^78 - 56 * q^79 + 2 * q^81 - 38 * q^83 - 22 * q^87 - 22 * q^90 - 74 * q^92 + 22 * q^96 + 34 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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