LMFDB - Embedded newform 507.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(1,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, 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("507.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.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:	$4.04841538248$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
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			1.2
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	507.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.35690 q^{2} -1.00000 q^{3} +3.55496 q^{4} -3.69202 q^{5} +2.35690 q^{6} +0.801938 q^{7} -3.66487 q^{8} +1.00000 q^{9} +8.70171 q^{10} +2.85086 q^{11} -3.55496 q^{12} -1.89008 q^{14} +3.69202 q^{15} +1.52781 q^{16} +2.93900 q^{17} -2.35690 q^{18} +2.44504 q^{19} -13.1250 q^{20} -0.801938 q^{21} -6.71917 q^{22} -7.78986 q^{23} +3.66487 q^{24} +8.63102 q^{25} -1.00000 q^{27} +2.85086 q^{28} +3.85086 q^{29} -8.70171 q^{30} -2.34481 q^{31} +3.72886 q^{32} -2.85086 q^{33} -6.92692 q^{34} -2.96077 q^{35} +3.55496 q^{36} -7.44504 q^{37} -5.76271 q^{38} +13.5308 q^{40} +0.850855 q^{41} +1.89008 q^{42} -1.61596 q^{43} +10.1347 q^{44} -3.69202 q^{45} +18.3599 q^{46} -2.44504 q^{47} -1.52781 q^{48} -6.35690 q^{49} -20.3424 q^{50} -2.93900 q^{51} -9.96077 q^{53} +2.35690 q^{54} -10.5254 q^{55} -2.93900 q^{56} -2.44504 q^{57} -9.07606 q^{58} +5.38404 q^{59} +13.1250 q^{60} -13.2567 q^{61} +5.52648 q^{62} +0.801938 q^{63} -11.8442 q^{64} +6.71917 q^{66} -14.3937 q^{67} +10.4480 q^{68} +7.78986 q^{69} +6.97823 q^{70} -8.12498 q^{71} -3.66487 q^{72} +11.8877 q^{73} +17.5472 q^{74} -8.63102 q^{75} +8.69202 q^{76} +2.28621 q^{77} +5.40581 q^{79} -5.64071 q^{80} +1.00000 q^{81} -2.00538 q^{82} -7.04892 q^{83} -2.85086 q^{84} -10.8509 q^{85} +3.80864 q^{86} -3.85086 q^{87} -10.4480 q^{88} -1.13169 q^{89} +8.70171 q^{90} -27.6926 q^{92} +2.34481 q^{93} +5.76271 q^{94} -9.02715 q^{95} -3.72886 q^{96} +5.94438 q^{97} +14.9825 q^{98} +2.85086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 6 q^{5} + 3 q^{6} - 2 q^{7} - 12 q^{8} + 3 q^{9} - q^{10} - 5 q^{11} - 11 q^{12} - 5 q^{14} + 6 q^{15} + 11 q^{16} - q^{17} - 3 q^{18} + 7 q^{19} - 15 q^{20} + 2 q^{21}+ \cdots - 5 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 6 * q^5 + 3 * q^6 - 2 * q^7 - 12 * q^8 + 3 * q^9 - q^10 - 5 * q^11 - 11 * q^12 - 5 * q^14 + 6 * q^15 + 11 * q^16 - q^17 - 3 * q^18 + 7 * q^19 - 15 * q^20 + 2 * q^21 - 9 * q^22 + 12 * q^24 + 11 * q^25 - 3 * q^27 - 5 * q^28 - 2 * q^29 + q^30 + 16 * q^31 - 22 * q^32 + 5 * q^33 + 8 * q^34 + 4 * q^35 + 11 * q^36 - 22 * q^37 + 3 * q^40 - 11 * q^41 + 5 * q^42 - 15 * q^43 - 16 * q^44 - 6 * q^45 + 7 * q^46 - 7 * q^47 - 11 * q^48 - 15 * q^49 + 3 * q^50 + q^51 - 17 * q^53 + 3 * q^54 + 3 * q^55 + q^56 - 7 * q^57 - 12 * q^58 + 6 * q^59 + 15 * q^60 - 13 * q^61 - 2 * q^62 - 2 * q^63 + 9 * q^66 - 11 * q^67 - 13 * q^68 + 24 * q^70 - 12 * q^72 - 6 * q^73 + 15 * q^74 - 11 * q^75 + 21 * q^76 + 15 * q^77 + 3 * q^79 + 20 * q^80 + 3 * q^81 - 3 * q^82 - 12 * q^83 + 5 * q^84 - 19 * q^85 + 29 * q^86 + 2 * q^87 + 13 * q^88 - q^89 - q^90 + 7 * q^92 - 16 * q^93 - 21 * q^95 + 22 * q^96 + 5 * q^97 + 29 * q^98 - 5 * q^99

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 $

$2$	−2.35690	−1.66658	−0.833289	−	0.552838i	$-0.813545\pi$
$2$	−2.35690	−1.66658	−0.833289	+	0.552838i	$0.813545\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.55496	1.77748
$5$	−3.69202	−1.65112	−0.825561	−	0.564313i	$-0.809141\pi$
$5$	−3.69202	−1.65112	−0.825561	+	0.564313i	$0.809141\pi$
$6$	2.35690	0.962199
$7$	0.801938	0.303104	0.151552	−	0.988449i	$-0.451573\pi$
$7$	0.801938	0.303104	0.151552	+	0.988449i	$0.451573\pi$
$8$	−3.66487	−1.29573
$9$	1.00000	0.333333
$10$	8.70171	2.75172
$11$	2.85086	0.859565	0.429783	−	0.902932i	$-0.358590\pi$
$11$	2.85086	0.859565	0.429783	+	0.902932i	$0.358590\pi$
$12$	−3.55496	−1.02623
$13$	0	0
$13$	0	0
$14$	−1.89008	−0.505146
$15$	3.69202	0.953276
$16$	1.52781	0.381953
$17$	2.93900	0.712812	0.356406	−	0.934331i	$-0.384002\pi$
$17$	2.93900	0.712812	0.356406	+	0.934331i	$0.384002\pi$
$18$	−2.35690	−0.555526
$19$	2.44504	0.560931	0.280466	−	0.959864i	$-0.409511\pi$
$19$	2.44504	0.560931	0.280466	+	0.959864i	$0.409511\pi$
$20$	−13.1250	−2.93484
$21$	−0.801938	−0.174997
$22$	−6.71917	−1.43253
$23$	−7.78986	−1.62430	−0.812149	−	0.583451i	$-0.801702\pi$
$23$	−7.78986	−1.62430	−0.812149	+	0.583451i	$0.801702\pi$
$24$	3.66487	0.748089
$25$	8.63102	1.72620
$26$	0	0
$27$	−1.00000	−0.192450
$28$	2.85086	0.538761
$29$	3.85086	0.715086	0.357543	−	0.933897i	$-0.383615\pi$
$29$	3.85086	0.715086	0.357543	+	0.933897i	$0.383615\pi$
$30$	−8.70171	−1.58871
$31$	−2.34481	−0.421141	−0.210571	−	0.977579i	$-0.567532\pi$
$31$	−2.34481	−0.421141	−0.210571	+	0.977579i	$0.567532\pi$
$32$	3.72886	0.659175
$33$	−2.85086	−0.496270
$34$	−6.92692	−1.18796
$35$	−2.96077	−0.500462
$36$	3.55496	0.592493
$37$	−7.44504	−1.22396	−0.611979	−	0.790874i	$-0.709626\pi$
$37$	−7.44504	−1.22396	−0.611979	+	0.790874i	$0.709626\pi$
$38$	−5.76271	−0.934835
$39$	0	0
$40$	13.5308	2.13941
$41$	0.850855	0.132881	0.0664406	−	0.997790i	$-0.478836\pi$
$41$	0.850855	0.132881	0.0664406	+	0.997790i	$0.478836\pi$
$42$	1.89008	0.291646
$43$	−1.61596	−0.246431	−0.123216	−	0.992380i	$-0.539321\pi$
$43$	−1.61596	−0.246431	−0.123216	+	0.992380i	$0.539321\pi$
$44$	10.1347	1.52786
$45$	−3.69202	−0.550374
$46$	18.3599	2.70702
$47$	−2.44504	−0.356646	−0.178323	−	0.983972i	$-0.557067\pi$
$47$	−2.44504	−0.356646	−0.178323	+	0.983972i	$0.557067\pi$
$48$	−1.52781	−0.220521
$49$	−6.35690	−0.908128
$50$	−20.3424	−2.87685
$51$	−2.93900	−0.411542
$52$	0	0
$53$	−9.96077	−1.36822	−0.684109	−	0.729380i	$-0.739809\pi$
$53$	−9.96077	−1.36822	−0.684109	+	0.729380i	$0.739809\pi$
$54$	2.35690	0.320733
$55$	−10.5254	−1.41925
$56$	−2.93900	−0.392741
$57$	−2.44504	−0.323854
$58$	−9.07606	−1.19175
$59$	5.38404	0.700943	0.350471	−	0.936573i	$-0.386021\pi$
$59$	5.38404	0.700943	0.350471	+	0.936573i	$0.386021\pi$
$60$	13.1250	1.69443
$61$	−13.2567	−1.69734	−0.848671	−	0.528921i	$-0.822597\pi$
$61$	−13.2567	−1.69734	−0.848671	+	0.528921i	$0.822597\pi$
$62$	5.52648	0.701864
$63$	0.801938	0.101035
$64$	−11.8442	−1.48052
$65$	0	0
$66$	6.71917	0.827072
$67$	−14.3937	−1.75847	−0.879237	−	0.476384i	$-0.841947\pi$
$67$	−14.3937	−1.75847	−0.879237	+	0.476384i	$0.841947\pi$
$68$	10.4480	1.26701
$69$	7.78986	0.937788
$70$	6.97823	0.834058
$71$	−8.12498	−0.964258	−0.482129	−	0.876100i	$-0.660136\pi$
$71$	−8.12498	−0.964258	−0.482129	+	0.876100i	$0.660136\pi$
$72$	−3.66487	−0.431910
$73$	11.8877	1.39135	0.695674	−	0.718357i	$-0.255106\pi$
$73$	11.8877	1.39135	0.695674	+	0.718357i	$0.255106\pi$
$74$	17.5472	2.03982
$75$	−8.63102	−0.996625
$76$	8.69202	0.997043
$77$	2.28621	0.260538
$78$	0	0
$79$	5.40581	0.608202	0.304101	−	0.952640i	$-0.401644\pi$
$79$	5.40581	0.608202	0.304101	+	0.952640i	$0.401644\pi$
$80$	−5.64071	−0.630651
$81$	1.00000	0.111111
$82$	−2.00538	−0.221457
$83$	−7.04892	−0.773719	−0.386860	−	0.922139i	$-0.626440\pi$
$83$	−7.04892	−0.773719	−0.386860	+	0.922139i	$0.626440\pi$
$84$	−2.85086	−0.311054
$85$	−10.8509	−1.17694
$86$	3.80864	0.410696
$87$	−3.85086	−0.412855
$88$	−10.4480	−1.11376
$89$	−1.13169	−0.119959	−0.0599793	−	0.998200i	$-0.519103\pi$
$89$	−1.13169	−0.119959	−0.0599793	+	0.998200i	$0.519103\pi$
$90$	8.70171	0.917241
$91$	0	0
$92$	−27.6926	−2.88715
$93$	2.34481	0.243146
$94$	5.76271	0.594378
$95$	−9.02715	−0.926166
$96$	−3.72886	−0.380575
$97$	5.94438	0.603560	0.301780	−	0.953378i	$-0.402419\pi$
$97$	5.94438	0.603560	0.301780	+	0.953378i	$0.402419\pi$
$98$	14.9825	1.51347
$99$	2.85086	0.286522
$100$	30.6829	3.06829
$101$	4.62565	0.460269	0.230134	−	0.973159i	$-0.426083\pi$
$101$	4.62565	0.460269	0.230134	+	0.973159i	$0.426083\pi$
$102$	6.92692	0.685867
$103$	1.20775	0.119003	0.0595016	−	0.998228i	$-0.481049\pi$
$103$	1.20775	0.119003	0.0595016	+	0.998228i	$0.481049\pi$
$104$	0	0
$105$	2.96077	0.288942
$106$	23.4765	2.28024
$107$	−9.52111	−0.920440	−0.460220	−	0.887805i	$-0.652229\pi$
$107$	−9.52111	−0.920440	−0.460220	+	0.887805i	$0.652229\pi$
$108$	−3.55496	−0.342076
$109$	1.78448	0.170922	0.0854611	−	0.996342i	$-0.472764\pi$
$109$	1.78448	0.170922	0.0854611	+	0.996342i	$0.472764\pi$
$110$	24.8073	2.36528
$111$	7.44504	0.706652
$112$	1.22521	0.115771
$113$	4.95108	0.465759	0.232879	−	0.972506i	$-0.425185\pi$
$113$	4.95108	0.465759	0.232879	+	0.972506i	$0.425185\pi$
$114$	5.76271	0.539727
$115$	28.7603	2.68191
$116$	13.6896	1.27105
$117$	0	0
$118$	−12.6896	−1.16817
$119$	2.35690	0.216056
$120$	−13.5308	−1.23519
$121$	−2.87263	−0.261148
$122$	31.2446	2.82875
$123$	−0.850855	−0.0767190
$124$	−8.33572	−0.748569
$125$	−13.4058	−1.19905
$126$	−1.89008	−0.168382
$127$	5.67025	0.503153	0.251577	−	0.967837i	$-0.419051\pi$
$127$	5.67025	0.503153	0.251577	+	0.967837i	$0.419051\pi$
$128$	20.4577	1.80822
$129$	1.61596	0.142277
$130$	0	0
$131$	18.2228	1.59213	0.796067	−	0.605208i	$-0.206910\pi$
$131$	18.2228	1.59213	0.796067	+	0.605208i	$0.206910\pi$
$132$	−10.1347	−0.882110
$133$	1.96077	0.170020
$134$	33.9245	2.93063
$135$	3.69202	0.317759
$136$	−10.7711	−0.923612
$137$	−9.45042	−0.807404	−0.403702	−	0.914891i	$-0.632277\pi$
$137$	−9.45042	−0.807404	−0.403702	+	0.914891i	$0.632277\pi$
$138$	−18.3599	−1.56290
$139$	4.01507	0.340553	0.170277	−	0.985396i	$-0.445534\pi$
$139$	4.01507	0.340553	0.170277	+	0.985396i	$0.445534\pi$
$140$	−10.5254	−0.889560
$141$	2.44504	0.205910
$142$	19.1497	1.60701
$143$	0	0
$144$	1.52781	0.127318
$145$	−14.2174	−1.18069
$146$	−28.0180	−2.31879
$147$	6.35690	0.524308
$148$	−26.4668	−2.17556
$149$	−19.4058	−1.58979	−0.794893	−	0.606750i	$-0.792473\pi$
$149$	−19.4058	−1.58979	−0.794893	+	0.606750i	$0.792473\pi$
$150$	20.3424	1.66095
$151$	12.3623	1.00603	0.503014	−	0.864278i	$-0.332225\pi$
$151$	12.3623	1.00603	0.503014	+	0.864278i	$0.332225\pi$
$152$	−8.96077	−0.726815
$153$	2.93900	0.237604
$154$	−5.38835	−0.434206
$155$	8.65710	0.695355
$156$	0	0
$157$	−18.6775	−1.49063	−0.745315	−	0.666712i	$-0.767701\pi$
$157$	−18.6775	−1.49063	−0.745315	+	0.666712i	$0.767701\pi$
$158$	−12.7409	−1.01361
$159$	9.96077	0.789941
$160$	−13.7670	−1.08838
$161$	−6.24698	−0.492331
$162$	−2.35690	−0.185175
$163$	−12.3394	−0.966499	−0.483250	−	0.875483i	$-0.660544\pi$
$163$	−12.3394	−0.966499	−0.483250	+	0.875483i	$0.660544\pi$
$164$	3.02475	0.236194
$165$	10.5254	0.819403
$166$	16.6136	1.28946
$167$	−11.4940	−0.889429	−0.444715	−	0.895672i	$-0.646695\pi$
$167$	−11.4940	−0.889429	−0.444715	+	0.895672i	$0.646695\pi$
$168$	2.93900	0.226749
$169$	0	0
$170$	25.5743	1.96146
$171$	2.44504	0.186977
$172$	−5.74466	−0.438026
$173$	12.1142	0.921028	0.460514	−	0.887653i	$-0.347665\pi$
$173$	12.1142	0.921028	0.460514	+	0.887653i	$0.347665\pi$
$174$	9.07606	0.688055
$175$	6.92154	0.523219
$176$	4.35557	0.328313
$177$	−5.38404	−0.404689
$178$	2.66727	0.199920
$179$	−0.538565	−0.0402542	−0.0201271	−	0.999797i	$-0.506407\pi$
$179$	−0.538565	−0.0402542	−0.0201271	+	0.999797i	$0.506407\pi$
$180$	−13.1250	−0.978278
$181$	−23.2838	−1.73067	−0.865336	−	0.501192i	$-0.832895\pi$
$181$	−23.2838	−1.73067	−0.865336	+	0.501192i	$0.832895\pi$
$182$	0	0
$183$	13.2567	0.979961
$184$	28.5488	2.10465
$185$	27.4873	2.02090
$186$	−5.52648	−0.405221
$187$	8.37867	0.612709
$188$	−8.69202	−0.633931
$189$	−0.801938	−0.0583324
$190$	21.2760	1.54353
$191$	16.7657	1.21312	0.606561	−	0.795037i	$-0.292548\pi$
$191$	16.7657	1.21312	0.606561	+	0.795037i	$0.292548\pi$
$192$	11.8442	0.854778
$193$	−25.7439	−1.85309	−0.926544	−	0.376186i	$-0.877235\pi$
$193$	−25.7439	−1.85309	−0.926544	+	0.376186i	$0.877235\pi$
$194$	−14.0103	−1.00588
$195$	0	0
$196$	−22.5985	−1.61418
$197$	−21.4209	−1.52617	−0.763087	−	0.646296i	$-0.776317\pi$
$197$	−21.4209	−1.52617	−0.763087	+	0.646296i	$0.776317\pi$
$198$	−6.71917	−0.477511
$199$	3.52781	0.250080	0.125040	−	0.992152i	$-0.460094\pi$
$199$	3.52781	0.250080	0.125040	+	0.992152i	$0.460094\pi$
$200$	−31.6316	−2.23669
$201$	14.3937	1.01526
$202$	−10.9022	−0.767074
$203$	3.08815	0.216745
$204$	−10.4480	−0.731508
$205$	−3.14138	−0.219403
$206$	−2.84654	−0.198328
$207$	−7.78986	−0.541432
$208$	0	0
$209$	6.97046	0.482157
$210$	−6.97823	−0.481544
$211$	1.21552	0.0836799	0.0418399	−	0.999124i	$-0.486678\pi$
$211$	1.21552	0.0836799	0.0418399	+	0.999124i	$0.486678\pi$
$212$	−35.4101	−2.43198
$213$	8.12498	0.556715
$214$	22.4403	1.53398
$215$	5.96615	0.406888
$216$	3.66487	0.249363
$217$	−1.88040	−0.127650
$218$	−4.20583	−0.284855
$219$	−11.8877	−0.803296
$220$	−37.4174	−2.52268
$221$	0	0
$222$	−17.5472	−1.17769
$223$	17.3884	1.16441	0.582205	−	0.813042i	$-0.302190\pi$
$223$	17.3884	1.16441	0.582205	+	0.813042i	$0.302190\pi$
$224$	2.99031	0.199799
$225$	8.63102	0.575402
$226$	−11.6692	−0.776223
$227$	−17.4155	−1.15591	−0.577954	−	0.816070i	$-0.696149\pi$
$227$	−17.4155	−1.15591	−0.577954	+	0.816070i	$0.696149\pi$
$228$	−8.69202	−0.575643
$229$	−18.7603	−1.23972	−0.619858	−	0.784714i	$-0.712810\pi$
$229$	−18.7603	−1.23972	−0.619858	+	0.784714i	$0.712810\pi$
$230$	−67.7851	−4.46962
$231$	−2.28621	−0.150421
$232$	−14.1129	−0.926557
$233$	3.95108	0.258844	0.129422	−	0.991590i	$-0.458688\pi$
$233$	3.95108	0.258844	0.129422	+	0.991590i	$0.458688\pi$
$234$	0	0
$235$	9.02715	0.588866
$236$	19.1400	1.24591
$237$	−5.40581	−0.351145
$238$	−5.55496	−0.360074
$239$	−0.818331	−0.0529334	−0.0264667	−	0.999650i	$-0.508426\pi$
$239$	−0.818331	−0.0529334	−0.0264667	+	0.999650i	$0.508426\pi$
$240$	5.64071	0.364106
$241$	−6.03252	−0.388589	−0.194295	−	0.980943i	$-0.562242\pi$
$241$	−6.03252	−0.388589	−0.194295	+	0.980943i	$0.562242\pi$
$242$	6.77048	0.435223
$243$	−1.00000	−0.0641500
$244$	−47.1269	−3.01699
$245$	23.4698	1.49943
$246$	2.00538	0.127858
$247$	0	0
$248$	8.59345	0.545685
$249$	7.04892	0.446707
$250$	31.5961	1.99831
$251$	−26.8799	−1.69665	−0.848323	−	0.529479i	$-0.822387\pi$
$251$	−26.8799	−1.69665	−0.848323	+	0.529479i	$0.822387\pi$
$252$	2.85086	0.179587
$253$	−22.2078	−1.39619
$254$	−13.3642	−0.838544
$255$	10.8509	0.679507
$256$	−24.5284	−1.53303
$257$	−9.05323	−0.564725	−0.282362	−	0.959308i	$-0.591118\pi$
$257$	−9.05323	−0.564725	−0.282362	+	0.959308i	$0.591118\pi$
$258$	−3.80864	−0.237116
$259$	−5.97046	−0.370986
$260$	0	0
$261$	3.85086	0.238362
$262$	−42.9493	−2.65342
$263$	23.1511	1.42756	0.713778	−	0.700372i	$-0.246983\pi$
$263$	23.1511	1.42756	0.713778	+	0.700372i	$0.246983\pi$
$264$	10.4480	0.643032
$265$	36.7754	2.25909
$266$	−4.62133	−0.283352
$267$	1.13169	0.0692581
$268$	−51.1691	−3.12565
$269$	−2.42088	−0.147604	−0.0738018	−	0.997273i	$-0.523513\pi$
$269$	−2.42088	−0.147604	−0.0738018	+	0.997273i	$0.523513\pi$
$270$	−8.70171	−0.529569
$271$	21.4450	1.30269	0.651347	−	0.758780i	$-0.274204\pi$
$271$	21.4450	1.30269	0.651347	+	0.758780i	$0.274204\pi$
$272$	4.49024	0.272261
$273$	0	0
$274$	22.2737	1.34560
$275$	24.6058	1.48379
$276$	27.6926	1.66690
$277$	−14.8073	−0.889685	−0.444843	−	0.895609i	$-0.646740\pi$
$277$	−14.8073	−0.889685	−0.444843	+	0.895609i	$0.646740\pi$
$278$	−9.46309	−0.567558
$279$	−2.34481	−0.140380
$280$	10.8509	0.648463
$281$	−14.5036	−0.865215	−0.432608	−	0.901582i	$-0.642406\pi$
$281$	−14.5036	−0.865215	−0.432608	+	0.901582i	$0.642406\pi$
$282$	−5.76271	−0.343164
$283$	25.6722	1.52605	0.763026	−	0.646368i	$-0.223713\pi$
$283$	25.6722	1.52605	0.763026	+	0.646368i	$0.223713\pi$
$284$	−28.8840	−1.71395
$285$	9.02715	0.534722
$286$	0	0
$287$	0.682333	0.0402768
$288$	3.72886	0.219725
$289$	−8.36227	−0.491898
$290$	33.5090	1.96772
$291$	−5.94438	−0.348466
$292$	42.2602	2.47309
$293$	26.5230	1.54949	0.774746	−	0.632273i	$-0.217878\pi$
$293$	26.5230	1.54949	0.774746	+	0.632273i	$0.217878\pi$
$294$	−14.9825	−0.873800
$295$	−19.8780	−1.15734
$296$	27.2851	1.58592
$297$	−2.85086	−0.165423
$298$	45.7375	2.64950
$299$	0	0
$300$	−30.6829	−1.77148
$301$	−1.29590	−0.0746943
$302$	−29.1366	−1.67662
$303$	−4.62565	−0.265736
$304$	3.73556	0.214249
$305$	48.9439	2.80252
$306$	−6.92692	−0.395986
$307$	8.24698	0.470680	0.235340	−	0.971913i	$-0.424380\pi$
$307$	8.24698	0.470680	0.235340	+	0.971913i	$0.424380\pi$
$308$	8.12737	0.463100
$309$	−1.20775	−0.0687066
$310$	−20.4039	−1.15886
$311$	−14.4179	−0.817564	−0.408782	−	0.912632i	$-0.634046\pi$
$311$	−14.4179	−0.817564	−0.408782	+	0.912632i	$0.634046\pi$
$312$	0	0
$313$	14.2338	0.804544	0.402272	−	0.915520i	$-0.368221\pi$
$313$	14.2338	0.804544	0.402272	+	0.915520i	$0.368221\pi$
$314$	44.0210	2.48425
$315$	−2.96077	−0.166821
$316$	19.2174	1.08107
$317$	6.84415	0.384406	0.192203	−	0.981355i	$-0.438437\pi$
$317$	6.84415	0.384406	0.192203	+	0.981355i	$0.438437\pi$
$318$	−23.4765	−1.31650
$319$	10.9782	0.614663
$320$	43.7289	2.44452
$321$	9.52111	0.531416
$322$	14.7235	0.820507
$323$	7.18598	0.399839
$324$	3.55496	0.197498
$325$	0	0
$326$	29.0828	1.61075
$327$	−1.78448	−0.0986819
$328$	−3.11828	−0.172178
$329$	−1.96077	−0.108101
$330$	−24.8073	−1.36560
$331$	−9.44265	−0.519015	−0.259507	−	0.965741i	$-0.583560\pi$
$331$	−9.44265	−0.519015	−0.259507	+	0.965741i	$0.583560\pi$
$332$	−25.0586	−1.37527
$333$	−7.44504	−0.407986
$334$	27.0901	1.48230
$335$	53.1420	2.90346
$336$	−1.22521	−0.0668406
$337$	2.64310	0.143979	0.0719895	−	0.997405i	$-0.477065\pi$
$337$	2.64310	0.143979	0.0719895	+	0.997405i	$0.477065\pi$
$338$	0	0
$339$	−4.95108	−0.268906
$340$	−38.5743	−2.09199
$341$	−6.68473	−0.361998
$342$	−5.76271	−0.311612
$343$	−10.7114	−0.578361
$344$	5.92228	0.319308
$345$	−28.7603	−1.54840
$346$	−28.5520	−1.53496
$347$	−10.1588	−0.545355	−0.272677	−	0.962106i	$-0.587909\pi$
$347$	−10.1588	−0.545355	−0.272677	+	0.962106i	$0.587909\pi$
$348$	−13.6896	−0.733841
$349$	−10.4397	−0.558822	−0.279411	−	0.960172i	$-0.590139\pi$
$349$	−10.4397	−0.558822	−0.279411	+	0.960172i	$0.590139\pi$
$350$	−16.3134	−0.871986
$351$	0	0
$352$	10.6304	0.566604
$353$	−18.2911	−0.973538	−0.486769	−	0.873531i	$-0.661825\pi$
$353$	−18.2911	−0.973538	−0.486769	+	0.873531i	$0.661825\pi$
$354$	12.6896	0.674446
$355$	29.9976	1.59211
$356$	−4.02310	−0.213224
$357$	−2.35690	−0.124740
$358$	1.26934	0.0670867
$359$	15.2731	0.806081	0.403041	−	0.915182i	$-0.367953\pi$
$359$	15.2731	0.806081	0.403041	+	0.915182i	$0.367953\pi$
$360$	13.5308	0.713136
$361$	−13.0218	−0.685356
$362$	54.8775	2.88430
$363$	2.87263	0.150774
$364$	0	0
$365$	−43.8896	−2.29729
$366$	−31.2446	−1.63318
$367$	−22.2717	−1.16258	−0.581288	−	0.813698i	$-0.697451\pi$
$367$	−22.2717	−1.16258	−0.581288	+	0.813698i	$0.697451\pi$
$368$	−11.9014	−0.620405
$369$	0.850855	0.0442937
$370$	−64.7846	−3.36799
$371$	−7.98792	−0.414712
$372$	8.33572	0.432187
$373$	4.12631	0.213652	0.106826	−	0.994278i	$-0.465931\pi$
$373$	4.12631	0.213652	0.106826	+	0.994278i	$0.465931\pi$
$374$	−19.7476	−1.02113
$375$	13.4058	0.692273
$376$	8.96077	0.462116
$377$	0	0
$378$	1.89008	0.0972154
$379$	10.7071	0.549986	0.274993	−	0.961446i	$-0.411324\pi$
$379$	10.7071	0.549986	0.274993	+	0.961446i	$0.411324\pi$
$380$	−32.0911	−1.64624
$381$	−5.67025	−0.290496
$382$	−39.5150	−2.02176
$383$	−6.52648	−0.333488	−0.166744	−	0.986000i	$-0.553325\pi$
$383$	−6.52648	−0.333488	−0.166744	+	0.986000i	$0.553325\pi$
$384$	−20.4577	−1.04398
$385$	−8.44073	−0.430179
$386$	60.6757	3.08831
$387$	−1.61596	−0.0821437
$388$	21.1320	1.07282
$389$	−11.7922	−0.597891	−0.298945	−	0.954270i	$-0.596635\pi$
$389$	−11.7922	−0.597891	−0.298945	+	0.954270i	$0.596635\pi$
$390$	0	0
$391$	−22.8944	−1.15782
$392$	23.2972	1.17669
$393$	−18.2228	−0.919219
$394$	50.4868	2.54349
$395$	−19.9584	−1.00422
$396$	10.1347	0.509286
$397$	12.5429	0.629509	0.314754	−	0.949173i	$-0.398078\pi$
$397$	12.5429	0.629509	0.314754	+	0.949173i	$0.398078\pi$
$398$	−8.31468	−0.416777
$399$	−1.96077	−0.0981613
$400$	13.1866	0.659329
$401$	−17.8702	−0.892397	−0.446198	−	0.894934i	$-0.647222\pi$
$401$	−17.8702	−0.892397	−0.446198	+	0.894934i	$0.647222\pi$
$402$	−33.9245	−1.69200
$403$	0	0
$404$	16.4440	0.818118
$405$	−3.69202	−0.183458
$406$	−7.27844	−0.361223
$407$	−21.2247	−1.05207
$408$	10.7711	0.533247
$409$	27.9119	1.38015	0.690076	−	0.723737i	$-0.257577\pi$
$409$	27.9119	1.38015	0.690076	+	0.723737i	$0.257577\pi$
$410$	7.40389	0.365652
$411$	9.45042	0.466155
$412$	4.29350	0.211526
$413$	4.31767	0.212459
$414$	18.3599	0.902339
$415$	26.0248	1.27750
$416$	0	0
$417$	−4.01507	−0.196619
$418$	−16.4286	−0.803551
$419$	−16.4034	−0.801360	−0.400680	−	0.916218i	$-0.631226\pi$
$419$	−16.4034	−0.801360	−0.400680	+	0.916218i	$0.631226\pi$
$420$	10.5254	0.513588
$421$	3.03684	0.148006	0.0740032	−	0.997258i	$-0.476423\pi$
$421$	3.03684	0.148006	0.0740032	+	0.997258i	$0.476423\pi$
$422$	−2.86486	−0.139459
$423$	−2.44504	−0.118882
$424$	36.5050	1.77284
$425$	25.3666	1.23046
$426$	−19.1497	−0.927808
$427$	−10.6310	−0.514471
$428$	−33.8471	−1.63606
$429$	0	0
$430$	−14.0616	−0.678110
$431$	3.33811	0.160791	0.0803955	−	0.996763i	$-0.474382\pi$
$431$	3.33811	0.160791	0.0803955	+	0.996763i	$0.474382\pi$
$432$	−1.52781	−0.0735068
$433$	11.9028	0.572010	0.286005	−	0.958228i	$-0.407673\pi$
$433$	11.9028	0.572010	0.286005	+	0.958228i	$0.407673\pi$
$434$	4.43190	0.212738
$435$	14.2174	0.681674
$436$	6.34375	0.303810
$437$	−19.0465	−0.911119
$438$	28.0180	1.33875
$439$	3.71810	0.177455	0.0887277	−	0.996056i	$-0.471720\pi$
$439$	3.71810	0.177455	0.0887277	+	0.996056i	$0.471720\pi$
$440$	38.5743	1.83896
$441$	−6.35690	−0.302709
$442$	0	0
$443$	1.45712	0.0692300	0.0346150	−	0.999401i	$-0.488979\pi$
$443$	1.45712	0.0692300	0.0346150	+	0.999401i	$0.488979\pi$
$444$	26.4668	1.25606
$445$	4.17821	0.198066
$446$	−40.9825	−1.94058
$447$	19.4058	0.917863
$448$	−9.49827	−0.448751
$449$	12.1274	0.572326	0.286163	−	0.958181i	$-0.407620\pi$
$449$	12.1274	0.572326	0.286163	+	0.958181i	$0.407620\pi$
$450$	−20.3424	−0.958951
$451$	2.42566	0.114220
$452$	17.6009	0.827876
$453$	−12.3623	−0.580830
$454$	41.0465	1.92641
$455$	0	0
$456$	8.96077	0.419627
$457$	3.44803	0.161292	0.0806459	−	0.996743i	$-0.474302\pi$
$457$	3.44803	0.161292	0.0806459	+	0.996743i	$0.474302\pi$
$458$	44.2161	2.06608
$459$	−2.93900	−0.137181
$460$	102.242	4.76704
$461$	6.75600	0.314658	0.157329	−	0.987546i	$-0.449712\pi$
$461$	6.75600	0.314658	0.157329	+	0.987546i	$0.449712\pi$
$462$	5.38835	0.250689
$463$	7.45175	0.346312	0.173156	−	0.984894i	$-0.444604\pi$
$463$	7.45175	0.346312	0.173156	+	0.984894i	$0.444604\pi$
$464$	5.88338	0.273129
$465$	−8.65710	−0.401464
$466$	−9.31229	−0.431384
$467$	32.6098	1.50900	0.754502	−	0.656298i	$-0.227879\pi$
$467$	32.6098	1.50900	0.754502	+	0.656298i	$0.227879\pi$
$468$	0	0
$469$	−11.5429	−0.533001
$470$	−21.2760	−0.981391
$471$	18.6775	0.860616
$472$	−19.7318	−0.908232
$473$	−4.60686	−0.211824
$474$	12.7409	0.585211
$475$	21.1032	0.968282
$476$	8.37867	0.384036
$477$	−9.96077	−0.456072
$478$	1.92872	0.0882177
$479$	−2.82908	−0.129264	−0.0646321	−	0.997909i	$-0.520587\pi$
$479$	−2.82908	−0.129264	−0.0646321	+	0.997909i	$0.520587\pi$
$480$	13.7670	0.628376
$481$	0	0
$482$	14.2180	0.647614
$483$	6.24698	0.284247
$484$	−10.2121	−0.464185
$485$	−21.9468	−0.996552
$486$	2.35690	0.106911
$487$	41.2935	1.87119	0.935594	−	0.353079i	$-0.114865\pi$
$487$	41.2935	1.87119	0.935594	+	0.353079i	$0.114865\pi$
$488$	48.5840	2.19930
$489$	12.3394	0.558009
$490$	−55.3159	−2.49892
$491$	−34.6698	−1.56463	−0.782313	−	0.622886i	$-0.785960\pi$
$491$	−34.6698	−1.56463	−0.782313	+	0.622886i	$0.785960\pi$
$492$	−3.02475	−0.136366
$493$	11.3177	0.509722
$494$	0	0
$495$	−10.5254	−0.473082
$496$	−3.58243	−0.160856
$497$	−6.51573	−0.292270
$498$	−16.6136	−0.744472
$499$	−17.9409	−0.803146	−0.401573	−	0.915827i	$-0.631536\pi$
$499$	−17.9409	−0.803146	−0.401573	+	0.915827i	$0.631536\pi$
$500$	−47.6571	−2.13129
$501$	11.4940	0.513512
$502$	63.3532	2.82759
$503$	−26.1812	−1.16736	−0.583681	−	0.811983i	$-0.698388\pi$
$503$	−26.1812	−1.16736	−0.583681	+	0.811983i	$0.698388\pi$
$504$	−2.93900	−0.130914
$505$	−17.0780	−0.759960
$506$	52.3414	2.32686
$507$	0	0
$508$	20.1575	0.894345
$509$	5.50604	0.244051	0.122025	−	0.992527i	$-0.461061\pi$
$509$	5.50604	0.244051	0.122025	+	0.992527i	$0.461061\pi$
$510$	−25.5743	−1.13245
$511$	9.53319	0.421723
$512$	16.8955	0.746681
$513$	−2.44504	−0.107951
$514$	21.3375	0.941158
$515$	−4.45904	−0.196489
$516$	5.74466	0.252895
$517$	−6.97046	−0.306560
$518$	14.0718	0.618277
$519$	−12.1142	−0.531756
$520$	0	0
$521$	−26.7211	−1.17067	−0.585336	−	0.810791i	$-0.699037\pi$
$521$	−26.7211	−1.17067	−0.585336	+	0.810791i	$0.699037\pi$
$522$	−9.07606	−0.397249
$523$	36.5230	1.59704	0.798520	−	0.601968i	$-0.205617\pi$
$523$	36.5230	1.59704	0.798520	+	0.601968i	$0.205617\pi$
$524$	64.7813	2.82999
$525$	−6.92154	−0.302081
$526$	−54.5646	−2.37913
$527$	−6.89141	−0.300195
$528$	−4.35557	−0.189552
$529$	37.6819	1.63834
$530$	−86.6757	−3.76495
$531$	5.38404	0.233648
$532$	6.97046	0.302208
$533$	0	0
$534$	−2.66727	−0.115424
$535$	35.1521	1.51976
$536$	52.7512	2.27851
$537$	0.538565	0.0232408
$538$	5.70576	0.245993
$539$	−18.1226	−0.780595
$540$	13.1250	0.564809
$541$	−18.4655	−0.793893	−0.396947	−	0.917842i	$-0.629930\pi$
$541$	−18.4655	−0.793893	−0.396947	+	0.917842i	$0.629930\pi$
$542$	−50.5437	−2.17104
$543$	23.2838	0.999204
$544$	10.9591	0.469868
$545$	−6.58834	−0.282213
$546$	0	0
$547$	39.8471	1.70374	0.851870	−	0.523753i	$-0.175468\pi$
$547$	39.8471	1.70374	0.851870	+	0.523753i	$0.175468\pi$
$548$	−33.5958	−1.43514
$549$	−13.2567	−0.565781
$550$	−57.9933	−2.47284
$551$	9.41550	0.401114
$552$	−28.5488	−1.21512
$553$	4.33513	0.184348
$554$	34.8993	1.48273
$555$	−27.4873	−1.16677
$556$	14.2734	0.605327
$557$	−9.20477	−0.390018	−0.195009	−	0.980801i	$-0.562474\pi$
$557$	−9.20477	−0.390018	−0.195009	+	0.980801i	$0.562474\pi$
$558$	5.52648	0.233955
$559$	0	0
$560$	−4.52350	−0.191153
$561$	−8.37867	−0.353748
$562$	34.1836	1.44195
$563$	−0.975246	−0.0411017	−0.0205509	−	0.999789i	$-0.506542\pi$
$563$	−0.975246	−0.0411017	−0.0205509	+	0.999789i	$0.506542\pi$
$564$	8.69202	0.366000
$565$	−18.2795	−0.769024
$566$	−60.5066	−2.54328
$567$	0.801938	0.0336782
$568$	29.7770	1.24942
$569$	−16.8944	−0.708250	−0.354125	−	0.935198i	$-0.615221\pi$
$569$	−16.8944	−0.708250	−0.354125	+	0.935198i	$0.615221\pi$
$570$	−21.2760	−0.891155
$571$	−44.3226	−1.85484	−0.927421	−	0.374019i	$-0.877979\pi$
$571$	−44.3226	−1.85484	−0.927421	+	0.374019i	$0.877979\pi$
$572$	0	0
$573$	−16.7657	−0.700397
$574$	−1.60819	−0.0671244
$575$	−67.2344	−2.80387
$576$	−11.8442	−0.493506
$577$	−3.56704	−0.148498	−0.0742489	−	0.997240i	$-0.523656\pi$
$577$	−3.56704	−0.148498	−0.0742489	+	0.997240i	$0.523656\pi$
$578$	19.7090	0.819787
$579$	25.7439	1.06988
$580$	−50.5424	−2.09866
$581$	−5.65279	−0.234517
$582$	14.0103	0.580745
$583$	−28.3967	−1.17607
$584$	−43.5669	−1.80281
$585$	0	0
$586$	−62.5120	−2.58235
$587$	16.1172	0.665229	0.332614	−	0.943063i	$-0.392069\pi$
$587$	16.1172	0.665229	0.332614	+	0.943063i	$0.392069\pi$
$588$	22.5985	0.931946
$589$	−5.73317	−0.236231
$590$	46.8504	1.92880
$591$	21.4209	0.881137
$592$	−11.3746	−0.467494
$593$	42.8611	1.76010	0.880048	−	0.474885i	$-0.157510\pi$
$593$	42.8611	1.76010	0.880048	+	0.474885i	$0.157510\pi$
$594$	6.71917	0.275691
$595$	−8.70171	−0.356735
$596$	−68.9869	−2.82581
$597$	−3.52781	−0.144384
$598$	0	0
$599$	40.9420	1.67284	0.836422	−	0.548086i	$-0.184643\pi$
$599$	40.9420	1.67284	0.836422	+	0.548086i	$0.184643\pi$
$600$	31.6316	1.29136
$601$	1.18705	0.0484206	0.0242103	−	0.999707i	$-0.492293\pi$
$601$	1.18705	0.0484206	0.0242103	+	0.999707i	$0.492293\pi$
$602$	3.05429	0.124484
$603$	−14.3937	−0.586158
$604$	43.9474	1.78819
$605$	10.6058	0.431187
$606$	10.9022	0.442870
$607$	19.9922	0.811460	0.405730	−	0.913993i	$-0.367017\pi$
$607$	19.9922	0.811460	0.405730	+	0.913993i	$0.367017\pi$
$608$	9.11721	0.369752
$609$	−3.08815	−0.125138
$610$	−115.356	−4.67062
$611$	0	0
$612$	10.4480	0.422336
$613$	33.3618	1.34747	0.673735	−	0.738973i	$-0.264689\pi$
$613$	33.3618	1.34747	0.673735	+	0.738973i	$0.264689\pi$
$614$	−19.4373	−0.784424
$615$	3.14138	0.126672
$616$	−8.37867	−0.337586
$617$	−11.6233	−0.467935	−0.233967	−	0.972244i	$-0.575171\pi$
$617$	−11.6233	−0.467935	−0.233967	+	0.972244i	$0.575171\pi$
$618$	2.84654	0.114505
$619$	16.5381	0.664722	0.332361	−	0.943152i	$-0.392155\pi$
$619$	16.5381	0.664722	0.332361	+	0.943152i	$0.392155\pi$
$620$	30.7756	1.23598
$621$	7.78986	0.312596
$622$	33.9815	1.36253
$623$	−0.907542	−0.0363599
$624$	0	0
$625$	6.33944	0.253577
$626$	−33.5477	−1.34083
$627$	−6.97046	−0.278373
$628$	−66.3979	−2.64956
$629$	−21.8810	−0.872452
$630$	6.97823	0.278019
$631$	36.4416	1.45072	0.725358	−	0.688372i	$-0.241674\pi$
$631$	36.4416	1.45072	0.725358	+	0.688372i	$0.241674\pi$
$632$	−19.8116	−0.788064
$633$	−1.21552	−0.0483126
$634$	−16.1309	−0.640642
$635$	−20.9347	−0.830768
$636$	35.4101	1.40410
$637$	0	0
$638$	−25.8745	−1.02438
$639$	−8.12498	−0.321419
$640$	−75.5303	−2.98560
$641$	27.2067	1.07460	0.537300	−	0.843391i	$-0.319444\pi$
$641$	27.2067	1.07460	0.537300	+	0.843391i	$0.319444\pi$
$642$	−22.4403	−0.885646
$643$	5.06962	0.199926	0.0999632	−	0.994991i	$-0.468127\pi$
$643$	5.06962	0.199926	0.0999632	+	0.994991i	$0.468127\pi$
$644$	−22.2078	−0.875108
$645$	−5.96615	−0.234917
$646$	−16.9366	−0.666362
$647$	19.3207	0.759573	0.379787	−	0.925074i	$-0.375997\pi$
$647$	19.3207	0.759573	0.379787	+	0.925074i	$0.375997\pi$
$648$	−3.66487	−0.143970
$649$	15.3491	0.602506
$650$	0	0
$651$	1.88040	0.0736985
$652$	−43.8662	−1.71793
$653$	35.2355	1.37887	0.689436	−	0.724347i	$-0.257859\pi$
$653$	35.2355	1.37887	0.689436	+	0.724347i	$0.257859\pi$
$654$	4.20583	0.164461
$655$	−67.2790	−2.62881
$656$	1.29995	0.0507544
$657$	11.8877	0.463783
$658$	4.62133	0.180158
$659$	−4.36168	−0.169907	−0.0849535	−	0.996385i	$-0.527074\pi$
$659$	−4.36168	−0.169907	−0.0849535	+	0.996385i	$0.527074\pi$
$660$	37.4174	1.45647
$661$	15.4709	0.601747	0.300873	−	0.953664i	$-0.402722\pi$
$661$	15.4709	0.601747	0.300873	+	0.953664i	$0.402722\pi$
$662$	22.2553	0.864978
$663$	0	0
$664$	25.8334	1.00253
$665$	−7.23921	−0.280725
$666$	17.5472	0.679940
$667$	−29.9976	−1.16151
$668$	−40.8605	−1.58094
$669$	−17.3884	−0.672273
$670$	−125.250	−4.83883
$671$	−37.7928	−1.45898
$672$	−2.99031	−0.115354
$673$	−11.7409	−0.452580	−0.226290	−	0.974060i	$-0.572660\pi$
$673$	−11.7409	−0.452580	−0.226290	+	0.974060i	$0.572660\pi$
$674$	−6.22952	−0.239952
$675$	−8.63102	−0.332208
$676$	0	0
$677$	3.44504	0.132404	0.0662019	−	0.997806i	$-0.478912\pi$
$677$	3.44504	0.132404	0.0662019	+	0.997806i	$0.478912\pi$
$678$	11.6692	0.448152
$679$	4.76702	0.182941
$680$	39.7670	1.52500
$681$	17.4155	0.667363
$682$	15.7552	0.603298
$683$	−20.4058	−0.780807	−0.390403	−	0.920644i	$-0.627664\pi$
$683$	−20.4058	−0.780807	−0.390403	+	0.920644i	$0.627664\pi$
$684$	8.69202	0.332348
$685$	34.8911	1.33312
$686$	25.2457	0.963883
$687$	18.7603	0.715751
$688$	−2.46888	−0.0941251
$689$	0	0
$690$	67.7851	2.58053
$691$	−27.8039	−1.05771	−0.528854	−	0.848713i	$-0.677378\pi$
$691$	−27.8039	−1.05771	−0.528854	+	0.848713i	$0.677378\pi$
$692$	43.0656	1.63711
$693$	2.28621	0.0868459
$694$	23.9433	0.908876
$695$	−14.8237	−0.562295
$696$	14.1129	0.534948
$697$	2.50066	0.0947194
$698$	24.6052	0.931321
$699$	−3.95108	−0.149444
$700$	24.6058	0.930012
$701$	11.9715	0.452158	0.226079	−	0.974109i	$-0.427409\pi$
$701$	11.9715	0.452158	0.226079	+	0.974109i	$0.427409\pi$
$702$	0	0
$703$	−18.2034	−0.686556
$704$	−33.7660	−1.27260
$705$	−9.02715	−0.339982
$706$	43.1102	1.62248
$707$	3.70948	0.139509
$708$	−19.1400	−0.719327
$709$	−32.2664	−1.21179	−0.605894	−	0.795545i	$-0.707185\pi$
$709$	−32.2664	−1.21179	−0.605894	+	0.795545i	$0.707185\pi$
$710$	−70.7012	−2.65337
$711$	5.40581	0.202734
$712$	4.14749	0.155434
$713$	18.2658	0.684058
$714$	5.55496	0.207889
$715$	0	0
$716$	−1.91457	−0.0715510
$717$	0.818331	0.0305611
$718$	−35.9970	−1.34340
$719$	12.1086	0.451574	0.225787	−	0.974177i	$-0.427505\pi$
$719$	12.1086	0.451574	0.225787	+	0.974177i	$0.427505\pi$
$720$	−5.64071	−0.210217
$721$	0.968541	0.0360704
$722$	30.6910	1.14220
$723$	6.03252	0.224352
$724$	−82.7730	−3.07623
$725$	33.2368	1.23438
$726$	−6.77048	−0.251276
$727$	−16.6200	−0.616402	−0.308201	−	0.951321i	$-0.599727\pi$
$727$	−16.6200	−0.616402	−0.308201	+	0.951321i	$0.599727\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	103.443	3.82861
$731$	−4.74930	−0.175659
$732$	47.1269	1.74186
$733$	−17.7912	−0.657132	−0.328566	−	0.944481i	$-0.606565\pi$
$733$	−17.7912	−0.657132	−0.328566	+	0.944481i	$0.606565\pi$
$734$	52.4922	1.93752
$735$	−23.4698	−0.865696
$736$	−29.0473	−1.07070
$737$	−41.0344	−1.51152
$738$	−2.00538	−0.0738189
$739$	27.3618	1.00652	0.503260	−	0.864135i	$-0.332134\pi$
$739$	27.3618	1.00652	0.503260	+	0.864135i	$0.332134\pi$
$740$	97.7160	3.59211
$741$	0	0
$742$	18.8267	0.691150
$743$	−8.38596	−0.307651	−0.153826	−	0.988098i	$-0.549159\pi$
$743$	−8.38596	−0.307651	−0.153826	+	0.988098i	$0.549159\pi$
$744$	−8.59345	−0.315051
$745$	71.6467	2.62493
$746$	−9.72528	−0.356068
$747$	−7.04892	−0.257906
$748$	29.7858	1.08908
$749$	−7.63533	−0.278989
$750$	−31.5961	−1.15373
$751$	−38.7778	−1.41502	−0.707511	−	0.706703i	$-0.750182\pi$
$751$	−38.7778	−1.41502	−0.707511	+	0.706703i	$0.750182\pi$
$752$	−3.73556	−0.136222
$753$	26.8799	0.979559
$754$	0	0
$755$	−45.6418	−1.66107
$756$	−2.85086	−0.103685
$757$	12.9729	0.471506	0.235753	−	0.971813i	$-0.424244\pi$
$757$	12.9729	0.471506	0.235753	+	0.971813i	$0.424244\pi$
$758$	−25.2355	−0.916594
$759$	22.2078	0.806090
$760$	33.0834	1.20006
$761$	5.15585	0.186899	0.0934497	−	0.995624i	$-0.470211\pi$
$761$	5.15585	0.186899	0.0934497	+	0.995624i	$0.470211\pi$
$762$	13.3642	0.484134
$763$	1.43104	0.0518072
$764$	59.6013	2.15630
$765$	−10.8509	−0.392313
$766$	15.3822	0.555783
$767$	0	0
$768$	24.5284	0.885092
$769$	35.5013	1.28021	0.640104	−	0.768288i	$-0.278891\pi$
$769$	35.5013	1.28021	0.640104	+	0.768288i	$0.278891\pi$
$770$	19.8939	0.716927
$771$	9.05323	0.326044
$772$	−91.5186	−3.29383
$773$	6.15585	0.221411	0.110705	−	0.993853i	$-0.464689\pi$
$773$	6.15585	0.221411	0.110705	+	0.993853i	$0.464689\pi$
$774$	3.80864	0.136899
$775$	−20.2381	−0.726976
$776$	−21.7854	−0.782050
$777$	5.97046	0.214189
$778$	27.7931	0.996431
$779$	2.08038	0.0745372
$780$	0	0
$781$	−23.1631	−0.828843
$782$	53.9597	1.92960
$783$	−3.85086	−0.137618
$784$	−9.71214	−0.346862
$785$	68.9579	2.46121
$786$	42.9493	1.53195
$787$	−14.2107	−0.506558	−0.253279	−	0.967393i	$-0.581509\pi$
$787$	−14.2107	−0.506558	−0.253279	+	0.967393i	$0.581509\pi$
$788$	−76.1503	−2.71274
$789$	−23.1511	−0.824200
$790$	47.0398	1.67360
$791$	3.97046	0.141173
$792$	−10.4480	−0.371254
$793$	0	0
$794$	−29.5623	−1.04913
$795$	−36.7754	−1.30429
$796$	12.5412	0.444512
$797$	11.9022	0.421596	0.210798	−	0.977530i	$-0.432394\pi$
$797$	11.9022	0.421596	0.210798	+	0.977530i	$0.432394\pi$
$798$	4.62133	0.163593
$799$	−7.18598	−0.254222
$800$	32.1839	1.13787
$801$	−1.13169	−0.0399862
$802$	42.1183	1.48725
$803$	33.8901	1.19596
$804$	51.1691	1.80460
$805$	23.0640	0.812899
$806$	0	0
$807$	2.42088	0.0852190
$808$	−16.9524	−0.596384
$809$	1.61596	0.0568140	0.0284070	−	0.999596i	$-0.490957\pi$
$809$	1.61596	0.0568140	0.0284070	+	0.999596i	$0.490957\pi$
$810$	8.70171	0.305747
$811$	51.9657	1.82476	0.912381	−	0.409342i	$-0.134242\pi$
$811$	51.9657	1.82476	0.912381	+	0.409342i	$0.134242\pi$
$812$	10.9782	0.385260
$813$	−21.4450	−0.752110
$814$	50.0245	1.75336
$815$	45.5575	1.59581
$816$	−4.49024	−0.157190
$817$	−3.95108	−0.138231
$818$	−65.7853	−2.30013
$819$	0	0
$820$	−11.1675	−0.389985
$821$	−54.8327	−1.91367	−0.956837	−	0.290627i	$-0.906136\pi$
$821$	−54.8327	−1.91367	−0.956837	+	0.290627i	$0.906136\pi$
$822$	−22.2737	−0.776883
$823$	−46.8514	−1.63314	−0.816569	−	0.577247i	$-0.804127\pi$
$823$	−46.8514	−1.63314	−0.816569	+	0.577247i	$0.804127\pi$
$824$	−4.42626	−0.154196
$825$	−24.6058	−0.856664
$826$	−10.1763	−0.354078
$827$	−21.2021	−0.737270	−0.368635	−	0.929574i	$-0.620175\pi$
$827$	−21.2021	−0.737270	−0.368635	+	0.929574i	$0.620175\pi$
$828$	−27.6926	−0.962385
$829$	18.2972	0.635489	0.317744	−	0.948176i	$-0.397075\pi$
$829$	18.2972	0.635489	0.317744	+	0.948176i	$0.397075\pi$
$830$	−61.3376	−2.12906
$831$	14.8073	0.513660
$832$	0	0
$833$	−18.6829	−0.647325
$834$	9.46309	0.327680
$835$	42.4359	1.46856
$836$	24.7797	0.857024
$837$	2.34481	0.0810486
$838$	38.6612	1.33553
$839$	−21.1414	−0.729881	−0.364941	−	0.931031i	$-0.618911\pi$
$839$	−21.1414	−0.729881	−0.364941	+	0.931031i	$0.618911\pi$
$840$	−10.8509	−0.374390
$841$	−14.1709	−0.488652
$842$	−7.15751	−0.246664
$843$	14.5036	0.499532
$844$	4.32113	0.148739
$845$	0	0
$846$	5.76271	0.198126
$847$	−2.30367	−0.0791549
$848$	−15.2182	−0.522594
$849$	−25.6722	−0.881067
$850$	−59.7864	−2.05066
$851$	57.9958	1.98807
$852$	28.8840	0.989549
$853$	7.13036	0.244139	0.122069	−	0.992522i	$-0.461047\pi$
$853$	7.13036	0.244139	0.122069	+	0.992522i	$0.461047\pi$
$854$	25.0562	0.857406
$855$	−9.02715	−0.308722
$856$	34.8937	1.19264
$857$	−44.7741	−1.52945	−0.764726	−	0.644355i	$-0.777126\pi$
$857$	−44.7741	−1.52945	−0.764726	+	0.644355i	$0.777126\pi$
$858$	0	0
$859$	57.3782	1.95772	0.978859	−	0.204535i	$-0.0655681\pi$
$859$	57.3782	1.95772	0.978859	+	0.204535i	$0.0655681\pi$
$860$	21.2094	0.723235
$861$	−0.682333	−0.0232538
$862$	−7.86758	−0.267971
$863$	6.67563	0.227241	0.113621	−	0.993524i	$-0.463755\pi$
$863$	6.67563	0.227241	0.113621	+	0.993524i	$0.463755\pi$
$864$	−3.72886	−0.126858
$865$	−44.7260	−1.52073
$866$	−28.0536	−0.953299
$867$	8.36227	0.283998
$868$	−6.68473	−0.226894
$869$	15.4112	0.522789
$870$	−33.5090	−1.13606
$871$	0	0
$872$	−6.53989	−0.221469
$873$	5.94438	0.201187
$874$	44.8907	1.51845
$875$	−10.7506	−0.363438
$876$	−42.2602	−1.42784
$877$	−25.2983	−0.854263	−0.427131	−	0.904190i	$-0.640476\pi$
$877$	−25.2983	−0.854263	−0.427131	+	0.904190i	$0.640476\pi$
$878$	−8.76318	−0.295743
$879$	−26.5230	−0.894599
$880$	−16.0809	−0.542085
$881$	−35.3787	−1.19194	−0.595969	−	0.803008i	$-0.703232\pi$
$881$	−35.3787	−1.19194	−0.595969	+	0.803008i	$0.703232\pi$
$882$	14.9825	0.504488
$883$	−11.5851	−0.389869	−0.194935	−	0.980816i	$-0.562449\pi$
$883$	−11.5851	−0.389869	−0.194935	+	0.980816i	$0.562449\pi$
$884$	0	0
$885$	19.8780	0.668192
$886$	−3.43429	−0.115377
$887$	−27.2892	−0.916281	−0.458141	−	0.888880i	$-0.651484\pi$
$887$	−27.2892	−0.916281	−0.458141	+	0.888880i	$0.651484\pi$
$888$	−27.2851	−0.915629
$889$	4.54719	0.152508
$890$	−9.84761	−0.330093
$891$	2.85086	0.0955072
$892$	61.8149	2.06972
$893$	−5.97823	−0.200054
$894$	−45.7375	−1.52969
$895$	1.98839	0.0664646
$896$	16.4058	0.548080
$897$	0	0
$898$	−28.5830	−0.953826
$899$	−9.02954	−0.301152
$900$	30.6829	1.02276
$901$	−29.2747	−0.975282
$902$	−5.71704	−0.190357
$903$	1.29590	0.0431247
$904$	−18.1451	−0.603497
$905$	85.9643	2.85755
$906$	29.1366	0.967998
$907$	−30.4219	−1.01014	−0.505072	−	0.863077i	$-0.668534\pi$
$907$	−30.4219	−1.01014	−0.505072	+	0.863077i	$0.668534\pi$
$908$	−61.9114	−2.05460
$909$	4.62565	0.153423
$910$	0	0
$911$	53.5719	1.77492	0.887459	−	0.460887i	$-0.152469\pi$
$911$	53.5719	1.77492	0.887459	+	0.460887i	$0.152469\pi$
$912$	−3.73556	−0.123697
$913$	−20.0954	−0.665062
$914$	−8.12664	−0.268805
$915$	−48.9439	−1.61804
$916$	−66.6921	−2.20357
$917$	14.6136	0.482582
$918$	6.92692	0.228622
$919$	−36.1672	−1.19305	−0.596523	−	0.802596i	$-0.703451\pi$
$919$	−36.1672	−1.19305	−0.596523	+	0.802596i	$0.703451\pi$
$920$	−105.403	−3.47503
$921$	−8.24698	−0.271747
$922$	−15.9232	−0.524403
$923$	0	0
$924$	−8.12737	−0.267371
$925$	−64.2583	−2.11280
$926$	−17.5630	−0.577156
$927$	1.20775	0.0396677
$928$	14.3593	0.471367
$929$	13.3478	0.437927	0.218964	−	0.975733i	$-0.429732\pi$
$929$	13.3478	0.437927	0.218964	+	0.975733i	$0.429732\pi$
$930$	20.4039	0.669070
$931$	−15.5429	−0.509397
$932$	14.0459	0.460090
$933$	14.4179	0.472021
$934$	−76.8580	−2.51487
$935$	−30.9342	−1.01166
$936$	0	0
$937$	38.6872	1.26386	0.631928	−	0.775027i	$-0.282264\pi$
$937$	38.6872	1.26386	0.631928	+	0.775027i	$0.282264\pi$
$938$	27.2054	0.888286
$939$	−14.2338	−0.464504
$940$	32.0911	1.04670
$941$	−35.7275	−1.16468	−0.582342	−	0.812944i	$-0.697864\pi$
$941$	−35.7275	−1.16468	−0.582342	+	0.812944i	$0.697864\pi$
$942$	−44.0210	−1.43428
$943$	−6.62804	−0.215839
$944$	8.22580	0.267727
$945$	2.96077	0.0963139
$946$	10.8579	0.353020
$947$	17.8436	0.579838	0.289919	−	0.957051i	$-0.406372\pi$
$947$	17.8436	0.579838	0.289919	+	0.957051i	$0.406372\pi$
$948$	−19.2174	−0.624153
$949$	0	0
$950$	−49.7381	−1.61372
$951$	−6.84415	−0.221937
$952$	−8.63773	−0.279950
$953$	20.1691	0.653342	0.326671	−	0.945138i	$-0.394073\pi$
$953$	20.1691	0.653342	0.326671	+	0.945138i	$0.394073\pi$
$954$	23.4765	0.760080
$955$	−61.8993	−2.00301
$956$	−2.90913	−0.0940881
$957$	−10.9782	−0.354876
$958$	6.66786	0.215429
$959$	−7.57865	−0.244727
$960$	−43.7289	−1.41134
$961$	−25.5018	−0.822640
$962$	0	0
$963$	−9.52111	−0.306813
$964$	−21.4454	−0.690709
$965$	95.0471	3.05967
$966$	−14.7235	−0.473720
$967$	32.7894	1.05444	0.527218	−	0.849730i	$-0.323235\pi$
$967$	32.7894	1.05444	0.527218	+	0.849730i	$0.323235\pi$
$968$	10.5278	0.338377
$969$	−7.18598	−0.230847
$970$	51.7263	1.66083
$971$	−26.9845	−0.865973	−0.432986	−	0.901401i	$-0.642540\pi$
$971$	−26.9845	−0.865973	−0.432986	+	0.901401i	$0.642540\pi$
$972$	−3.55496	−0.114025
$973$	3.21983	0.103223
$974$	−97.3245	−3.11848
$975$	0	0
$976$	−20.2537	−0.648305
$977$	16.9571	0.542504	0.271252	−	0.962508i	$-0.412562\pi$
$977$	16.9571	0.542504	0.271252	+	0.962508i	$0.412562\pi$
$978$	−29.0828	−0.929964
$979$	−3.22627	−0.103112
$980$	83.4341	2.66521
$981$	1.78448	0.0569740
$982$	81.7131	2.60757
$983$	32.6631	1.04179	0.520895	−	0.853621i	$-0.325598\pi$
$983$	32.6631	1.04179	0.520895	+	0.853621i	$0.325598\pi$
$984$	3.11828	0.0994070
$985$	79.0863	2.51990
$986$	−26.6746	−0.849491
$987$	1.96077	0.0624120
$988$	0	0
$989$	12.5881	0.400277
$990$	24.8073	0.788428
$991$	7.64310	0.242791	0.121396	−	0.992604i	$-0.461263\pi$
$991$	7.64310	0.242791	0.121396	+	0.992604i	$0.461263\pi$
$992$	−8.74348	−0.277606
$993$	9.44265	0.299653
$994$	15.3569	0.487091
$995$	−13.0248	−0.412912
$996$	25.0586	0.794012
$997$	36.1256	1.14411	0.572054	−	0.820216i	$-0.306147\pi$
$997$	36.1256	1.14411	0.572054	+	0.820216i	$0.306147\pi$
$998$	42.2849	1.33850
$999$	7.44504	0.235551

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.a.i.1.2	✓	3
3.2	odd	2		1521.2.a.s.1.2		3
4.3	odd	2		8112.2.a.cg.1.1		3
13.2	odd	12		507.2.j.i.316.2		12
13.3	even	3		507.2.e.l.22.2		6
13.4	even	6		507.2.e.i.484.2		6
13.5	odd	4		507.2.b.f.337.5		6
13.6	odd	12		507.2.j.i.361.5		12
13.7	odd	12		507.2.j.i.361.2		12
13.8	odd	4		507.2.b.f.337.2		6
13.9	even	3		507.2.e.l.484.2		6
13.10	even	6		507.2.e.i.22.2		6
13.11	odd	12		507.2.j.i.316.5		12
13.12	even	2		507.2.a.l.1.2	yes	3
39.5	even	4		1521.2.b.k.1351.2		6
39.8	even	4		1521.2.b.k.1351.5		6
39.38	odd	2		1521.2.a.n.1.2		3
52.51	odd	2		8112.2.a.cp.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.a.i.1.2	✓	3	1.1	even	1	trivial
507.2.a.l.1.2	yes	3	13.12	even	2
507.2.b.f.337.2		6	13.8	odd	4
507.2.b.f.337.5		6	13.5	odd	4
507.2.e.i.22.2		6	13.10	even	6
507.2.e.i.484.2		6	13.4	even	6
507.2.e.l.22.2		6	13.3	even	3
507.2.e.l.484.2		6	13.9	even	3
507.2.j.i.316.2		12	13.2	odd	12
507.2.j.i.316.5		12	13.11	odd	12
507.2.j.i.361.2		12	13.7	odd	12
507.2.j.i.361.5		12	13.6	odd	12
1521.2.a.n.1.2		3	39.38	odd	2
1521.2.a.s.1.2		3	3.2	odd	2
1521.2.b.k.1351.2		6	39.5	even	4
1521.2.b.k.1351.5		6	39.8	even	4
8112.2.a.cg.1.1		3	4.3	odd	2
8112.2.a.cp.1.3		3	52.51	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.a (trivial)

\(f(q)\)	\(=\)	\(q-2.35690 q^{2} -1.00000 q^{3} +3.55496 q^{4} -3.69202 q^{5} +2.35690 q^{6} +0.801938 q^{7} -3.66487 q^{8} +1.00000 q^{9} +8.70171 q^{10} +2.85086 q^{11} -3.55496 q^{12} -1.89008 q^{14} +3.69202 q^{15} +1.52781 q^{16} +2.93900 q^{17} -2.35690 q^{18} +2.44504 q^{19} -13.1250 q^{20} -0.801938 q^{21} -6.71917 q^{22} -7.78986 q^{23} +3.66487 q^{24} +8.63102 q^{25} -1.00000 q^{27} +2.85086 q^{28} +3.85086 q^{29} -8.70171 q^{30} -2.34481 q^{31} +3.72886 q^{32} -2.85086 q^{33} -6.92692 q^{34} -2.96077 q^{35} +3.55496 q^{36} -7.44504 q^{37} -5.76271 q^{38} +13.5308 q^{40} +0.850855 q^{41} +1.89008 q^{42} -1.61596 q^{43} +10.1347 q^{44} -3.69202 q^{45} +18.3599 q^{46} -2.44504 q^{47} -1.52781 q^{48} -6.35690 q^{49} -20.3424 q^{50} -2.93900 q^{51} -9.96077 q^{53} +2.35690 q^{54} -10.5254 q^{55} -2.93900 q^{56} -2.44504 q^{57} -9.07606 q^{58} +5.38404 q^{59} +13.1250 q^{60} -13.2567 q^{61} +5.52648 q^{62} +0.801938 q^{63} -11.8442 q^{64} +6.71917 q^{66} -14.3937 q^{67} +10.4480 q^{68} +7.78986 q^{69} +6.97823 q^{70} -8.12498 q^{71} -3.66487 q^{72} +11.8877 q^{73} +17.5472 q^{74} -8.63102 q^{75} +8.69202 q^{76} +2.28621 q^{77} +5.40581 q^{79} -5.64071 q^{80} +1.00000 q^{81} -2.00538 q^{82} -7.04892 q^{83} -2.85086 q^{84} -10.8509 q^{85} +3.80864 q^{86} -3.85086 q^{87} -10.4480 q^{88} -1.13169 q^{89} +8.70171 q^{90} -27.6926 q^{92} +2.34481 q^{93} +5.76271 q^{94} -9.02715 q^{95} -3.72886 q^{96} +5.94438 q^{97} +14.9825 q^{98} +2.85086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 6 q^{5} + 3 q^{6} - 2 q^{7} - 12 q^{8} + 3 q^{9} - q^{10} - 5 q^{11} - 11 q^{12} - 5 q^{14} + 6 q^{15} + 11 q^{16} - q^{17} - 3 q^{18} + 7 q^{19} - 15 q^{20} + 2 q^{21}+ \cdots - 5 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 6 * q^5 + 3 * q^6 - 2 * q^7 - 12 * q^8 + 3 * q^9 - q^10 - 5 * q^11 - 11 * q^12 - 5 * q^14 + 6 * q^15 + 11 * q^16 - q^17 - 3 * q^18 + 7 * q^19 - 15 * q^20 + 2 * q^21 - 9 * q^22 + 12 * q^24 + 11 * q^25 - 3 * q^27 - 5 * q^28 - 2 * q^29 + q^30 + 16 * q^31 - 22 * q^32 + 5 * q^33 + 8 * q^34 + 4 * q^35 + 11 * q^36 - 22 * q^37 + 3 * q^40 - 11 * q^41 + 5 * q^42 - 15 * q^43 - 16 * q^44 - 6 * q^45 + 7 * q^46 - 7 * q^47 - 11 * q^48 - 15 * q^49 + 3 * q^50 + q^51 - 17 * q^53 + 3 * q^54 + 3 * q^55 + q^56 - 7 * q^57 - 12 * q^58 + 6 * q^59 + 15 * q^60 - 13 * q^61 - 2 * q^62 - 2 * q^63 + 9 * q^66 - 11 * q^67 - 13 * q^68 + 24 * q^70 - 12 * q^72 - 6 * q^73 + 15 * q^74 - 11 * q^75 + 21 * q^76 + 15 * q^77 + 3 * q^79 + 20 * q^80 + 3 * q^81 - 3 * q^82 - 12 * q^83 + 5 * q^84 - 19 * q^85 + 29 * q^86 + 2 * q^87 + 13 * q^88 - q^89 - q^90 + 7 * q^92 - 16 * q^93 - 21 * q^95 + 22 * q^96 + 5 * q^97 + 29 * q^98 - 5 * q^99

Introduction

L-functions

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