LMFDB - Embedded newform 4235.2.a.t.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 3x^{2} + x + 1 $ x^4 - x^3 - 3*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.09529$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.39026 q^{2} -1.47726 q^{3} +3.71333 q^{4} +1.00000 q^{5} -3.53103 q^{6} -1.00000 q^{7} +4.09529 q^{8} -0.817703 q^{9} +O(q^{10})$	\(q+2.39026 q^{2} -1.47726 q^{3} +3.71333 q^{4} +1.00000 q^{5} -3.53103 q^{6} -1.00000 q^{7} +4.09529 q^{8} -0.817703 q^{9} +2.39026 q^{10} -5.48555 q^{12} -3.86752 q^{13} -2.39026 q^{14} -1.47726 q^{15} +2.36215 q^{16} +1.52274 q^{17} -1.95452 q^{18} +0.845811 q^{19} +3.71333 q^{20} +1.47726 q^{21} -0.986585 q^{23} -6.04981 q^{24} +1.00000 q^{25} -9.24436 q^{26} +5.63974 q^{27} -3.71333 q^{28} -6.53103 q^{29} -3.53103 q^{30} -8.51366 q^{31} -2.54445 q^{32} +3.63974 q^{34} -1.00000 q^{35} -3.03640 q^{36} -9.47214 q^{37} +2.02171 q^{38} +5.71333 q^{39} +4.09529 q^{40} +3.32063 q^{41} +3.53103 q^{42} -3.28155 q^{43} -0.817703 q^{45} -2.35819 q^{46} +13.3895 q^{47} -3.48951 q^{48} +1.00000 q^{49} +2.39026 q^{50} -2.24948 q^{51} -14.3614 q^{52} -3.11945 q^{53} +13.4804 q^{54} -4.09529 q^{56} -1.24948 q^{57} -15.6108 q^{58} -6.36648 q^{59} -5.48555 q^{60} +0.460678 q^{61} -20.3498 q^{62} +0.817703 q^{63} -10.8062 q^{64} -3.86752 q^{65} -10.1146 q^{67} +5.65443 q^{68} +1.45744 q^{69} -2.39026 q^{70} -5.75881 q^{71} -3.34873 q^{72} +5.37722 q^{73} -22.6408 q^{74} -1.47726 q^{75} +3.14077 q^{76} +13.6563 q^{78} +5.72825 q^{79} +2.36215 q^{80} -5.87825 q^{81} +7.93715 q^{82} -12.2392 q^{83} +5.48555 q^{84} +1.52274 q^{85} -7.84374 q^{86} +9.64803 q^{87} -8.86318 q^{89} -1.95452 q^{90} +3.86752 q^{91} -3.66351 q^{92} +12.5769 q^{93} +32.0043 q^{94} +0.845811 q^{95} +3.75881 q^{96} +6.35435 q^{97} +2.39026 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 3 q^{3} + 3 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} + 9 q^{8} - 3 q^{9}+O(q^{10}) $ 4 * q - q^2 - 3 * q^3 + 3 * q^4 + 4 * q^5 - 2 * q^6 - 4 * q^7 + 9 * q^8 - 3 * q^9	$ 4 q - q^{2} - 3 q^{3} + 3 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} + 9 q^{8} - 3 q^{9} - q^{10} - 4 q^{12} - 2 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 9 q^{17} - 2 q^{18} + 5 q^{19} + 3 q^{20} + 3 q^{21} - 4 q^{23} - 11 q^{24} + 4 q^{25} - 13 q^{26} + 3 q^{27} - 3 q^{28} - 14 q^{29} - 2 q^{30} - 18 q^{31} + 2 q^{32} - 5 q^{34} - 4 q^{35} + q^{36} - 20 q^{37} - 7 q^{38} + 11 q^{39} + 9 q^{40} - q^{41} + 2 q^{42} - 10 q^{43} - 3 q^{45} + 7 q^{46} + 9 q^{47} + 4 q^{49} - q^{50} - 11 q^{52} - 3 q^{53} + 21 q^{54} - 9 q^{56} + 4 q^{57} - 7 q^{58} + 6 q^{59} - 4 q^{60} + 29 q^{61} - 3 q^{62} + 3 q^{63} - 11 q^{64} - 2 q^{65} - 5 q^{67} + 5 q^{68} - 14 q^{69} + q^{70} - 17 q^{71} - q^{72} - 12 q^{73} - 5 q^{74} - 3 q^{75} + 11 q^{76} + 5 q^{78} + 2 q^{79} - 3 q^{80} - 8 q^{81} + 22 q^{82} - 10 q^{83} + 4 q^{84} + 9 q^{85} + 3 q^{86} + 4 q^{87} - 41 q^{89} - 2 q^{90} + 2 q^{91} - 16 q^{92} + 21 q^{93} + 32 q^{94} + 5 q^{95} + 9 q^{96} - 4 q^{97} - q^{98}+O(q^{100}) $ 4 * q - q^2 - 3 * q^3 + 3 * q^4 + 4 * q^5 - 2 * q^6 - 4 * q^7 + 9 * q^8 - 3 * q^9 - q^10 - 4 * q^12 - 2 * q^13 + q^14 - 3 * q^15 - 3 * q^16 + 9 * q^17 - 2 * q^18 + 5 * q^19 + 3 * q^20 + 3 * q^21 - 4 * q^23 - 11 * q^24 + 4 * q^25 - 13 * q^26 + 3 * q^27 - 3 * q^28 - 14 * q^29 - 2 * q^30 - 18 * q^31 + 2 * q^32 - 5 * q^34 - 4 * q^35 + q^36 - 20 * q^37 - 7 * q^38 + 11 * q^39 + 9 * q^40 - q^41 + 2 * q^42 - 10 * q^43 - 3 * q^45 + 7 * q^46 + 9 * q^47 + 4 * q^49 - q^50 - 11 * q^52 - 3 * q^53 + 21 * q^54 - 9 * q^56 + 4 * q^57 - 7 * q^58 + 6 * q^59 - 4 * q^60 + 29 * q^61 - 3 * q^62 + 3 * q^63 - 11 * q^64 - 2 * q^65 - 5 * q^67 + 5 * q^68 - 14 * q^69 + q^70 - 17 * q^71 - q^72 - 12 * q^73 - 5 * q^74 - 3 * q^75 + 11 * q^76 + 5 * q^78 + 2 * q^79 - 3 * q^80 - 8 * q^81 + 22 * q^82 - 10 * q^83 + 4 * q^84 + 9 * q^85 + 3 * q^86 + 4 * q^87 - 41 * q^89 - 2 * q^90 + 2 * q^91 - 16 * q^92 + 21 * q^93 + 32 * q^94 + 5 * q^95 + 9 * q^96 - 4 * q^97 - q^98

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 $

$2$	2.39026	1.69017	0.845083	−	0.534634i	$-0.179551\pi$
$2$	2.39026	1.69017	0.845083	+	0.534634i	$0.179551\pi$
$3$	−1.47726	−0.852896	−0.426448	−	0.904512i	$-0.640235\pi$
$3$	−1.47726	−0.852896	−0.426448	+	0.904512i	$0.640235\pi$
$4$	3.71333	1.85666
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.53103	−1.44154
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	4.09529	1.44791
$9$	−0.817703	−0.272568
$10$	2.39026	0.755866
$11$	0	0
$11$	0	0
$12$	−5.48555	−1.58354
$13$	−3.86752	−1.07266	−0.536328	−	0.844010i	$-0.680189\pi$
$13$	−3.86752	−1.07266	−0.536328	+	0.844010i	$0.680189\pi$
$14$	−2.39026	−0.638823
$15$	−1.47726	−0.381427
$16$	2.36215	0.590537
$17$	1.52274	0.369319	0.184659	−	0.982803i	$-0.440882\pi$
$17$	1.52274	0.369319	0.184659	+	0.982803i	$0.440882\pi$
$18$	−1.95452	−0.460685
$19$	0.845811	0.194042	0.0970212	−	0.995282i	$-0.469069\pi$
$19$	0.845811	0.194042	0.0970212	+	0.995282i	$0.469069\pi$
$20$	3.71333	0.830325
$21$	1.47726	0.322365
$22$	0	0
$23$	−0.986585	−0.205717	−0.102859	−	0.994696i	$-0.532799\pi$
$23$	−0.986585	−0.205717	−0.102859	+	0.994696i	$0.532799\pi$
$24$	−6.04981	−1.23491
$25$	1.00000	0.200000
$26$	−9.24436	−1.81297
$27$	5.63974	1.08537
$28$	−3.71333	−0.701753
$29$	−6.53103	−1.21278	−0.606391	−	0.795167i	$-0.707383\pi$
$29$	−6.53103	−1.21278	−0.606391	+	0.795167i	$0.707383\pi$
$30$	−3.53103	−0.644675
$31$	−8.51366	−1.52910	−0.764549	−	0.644565i	$-0.777038\pi$
$31$	−8.51366	−1.52910	−0.764549	+	0.644565i	$0.777038\pi$
$32$	−2.54445	−0.449799
$33$	0	0
$34$	3.63974	0.624210
$35$	−1.00000	−0.169031
$36$	−3.03640	−0.506067
$37$	−9.47214	−1.55721	−0.778605	−	0.627515i	$-0.784072\pi$
$37$	−9.47214	−1.55721	−0.778605	+	0.627515i	$0.784072\pi$
$38$	2.02171	0.327964
$39$	5.71333	0.914865
$40$	4.09529	0.647523
$41$	3.32063	0.518595	0.259297	−	0.965798i	$-0.416509\pi$
$41$	3.32063	0.518595	0.259297	+	0.965798i	$0.416509\pi$
$42$	3.53103	0.544850
$43$	−3.28155	−0.500431	−0.250216	−	0.968190i	$-0.580502\pi$
$43$	−3.28155	−0.500431	−0.250216	+	0.968190i	$0.580502\pi$
$44$	0	0
$45$	−0.817703	−0.121896
$46$	−2.35819	−0.347696
$47$	13.3895	1.95305	0.976527	−	0.215394i	$-0.0691036\pi$
$47$	13.3895	1.95305	0.976527	+	0.215394i	$0.0691036\pi$
$48$	−3.48951	−0.503667
$49$	1.00000	0.142857
$50$	2.39026	0.338033
$51$	−2.24948	−0.314991
$52$	−14.3614	−1.99156
$53$	−3.11945	−0.428489	−0.214244	−	0.976780i	$-0.568729\pi$
$53$	−3.11945	−0.428489	−0.214244	+	0.976780i	$0.568729\pi$
$54$	13.4804	1.83445
$55$	0	0
$56$	−4.09529	−0.547257
$57$	−1.24948	−0.165498
$58$	−15.6108	−2.04980
$59$	−6.36648	−0.828845	−0.414423	−	0.910085i	$-0.636016\pi$
$59$	−6.36648	−0.828845	−0.414423	+	0.910085i	$0.636016\pi$
$60$	−5.48555	−0.708182
$61$	0.460678	0.0589838	0.0294919	−	0.999565i	$-0.490611\pi$
$61$	0.460678	0.0589838	0.0294919	+	0.999565i	$0.490611\pi$
$62$	−20.3498	−2.58443
$63$	0.817703	0.103021
$64$	−10.8062	−1.35077
$65$	−3.86752	−0.479706
$66$	0	0
$67$	−10.1146	−1.23569	−0.617845	−	0.786300i	$-0.711994\pi$
$67$	−10.1146	−1.23569	−0.617845	+	0.786300i	$0.711994\pi$
$68$	5.65443	0.685701
$69$	1.45744	0.175455
$70$	−2.39026	−0.285690
$71$	−5.75881	−0.683445	−0.341722	−	0.939801i	$-0.611010\pi$
$71$	−5.75881	−0.683445	−0.341722	+	0.939801i	$0.611010\pi$
$72$	−3.34873	−0.394652
$73$	5.37722	0.629356	0.314678	−	0.949199i	$-0.398103\pi$
$73$	5.37722	0.629356	0.314678	+	0.949199i	$0.398103\pi$
$74$	−22.6408	−2.63194
$75$	−1.47726	−0.170579
$76$	3.14077	0.360271
$77$	0	0
$78$	13.6563	1.54627
$79$	5.72825	0.644479	0.322239	−	0.946658i	$-0.395564\pi$
$79$	5.72825	0.644479	0.322239	+	0.946658i	$0.395564\pi$
$80$	2.36215	0.264096
$81$	−5.87825	−0.653139
$82$	7.93715	0.876511
$83$	−12.2392	−1.34343	−0.671715	−	0.740809i	$-0.734442\pi$
$83$	−12.2392	−1.34343	−0.671715	+	0.740809i	$0.734442\pi$
$84$	5.48555	0.598523
$85$	1.52274	0.165164
$86$	−7.84374	−0.845813
$87$	9.64803	1.03438
$88$	0	0
$89$	−8.86318	−0.939496	−0.469748	−	0.882801i	$-0.655655\pi$
$89$	−8.86318	−0.939496	−0.469748	+	0.882801i	$0.655655\pi$
$90$	−1.95452	−0.206024
$91$	3.86752	0.405426
$92$	−3.66351	−0.381948
$93$	12.5769	1.30416
$94$	32.0043	3.30099
$95$	0.845811	0.0867784
$96$	3.75881	0.383632
$97$	6.35435	0.645186	0.322593	−	0.946538i	$-0.395445\pi$
$97$	6.35435	0.645186	0.322593	+	0.946538i	$0.395445\pi$
$98$	2.39026	0.241452
$99$	0	0
$100$	3.71333	0.371333
$101$	7.50062	0.746340	0.373170	−	0.927763i	$-0.378271\pi$
$101$	7.50062	0.746340	0.373170	+	0.927763i	$0.378271\pi$
$102$	−5.37684	−0.532387
$103$	−6.39342	−0.629963	−0.314981	−	0.949098i	$-0.601998\pi$
$103$	−6.39342	−0.629963	−0.314981	+	0.949098i	$0.601998\pi$
$104$	−15.8386	−1.55310
$105$	1.47726	0.144166
$106$	−7.45628	−0.724218
$107$	−14.2961	−1.38205	−0.691026	−	0.722830i	$-0.742841\pi$
$107$	−14.2961	−1.38205	−0.691026	+	0.722830i	$0.742841\pi$
$108$	20.9422	2.01516
$109$	15.6231	1.49642	0.748210	−	0.663462i	$-0.230913\pi$
$109$	15.6231	1.49642	0.748210	+	0.663462i	$0.230913\pi$
$110$	0	0
$111$	13.9928	1.32814
$112$	−2.36215	−0.223202
$113$	−14.3839	−1.35312	−0.676560	−	0.736388i	$-0.736530\pi$
$113$	−14.3839	−1.35312	−0.676560	+	0.736388i	$0.736530\pi$
$114$	−2.98659	−0.279719
$115$	−0.986585	−0.0919995
$116$	−24.2519	−2.25173
$117$	3.16248	0.292371
$118$	−15.2175	−1.40089
$119$	−1.52274	−0.139589
$120$	−6.04981	−0.552270
$121$	0	0
$122$	1.10114	0.0996925
$123$	−4.90543	−0.442307
$124$	−31.6140	−2.83902
$125$	1.00000	0.0894427
$126$	1.95452	0.174122
$127$	6.31082	0.559995	0.279998	−	0.960001i	$-0.409666\pi$
$127$	6.31082	0.559995	0.279998	+	0.960001i	$0.409666\pi$
$128$	−20.7406	−1.83323
$129$	4.84770	0.426816
$130$	−9.24436	−0.810784
$131$	−11.9054	−1.04018	−0.520091	−	0.854111i	$-0.674102\pi$
$131$	−11.9054	−1.04018	−0.520091	+	0.854111i	$0.674102\pi$
$132$	0	0
$133$	−0.845811	−0.0733411
$134$	−24.1764	−2.08852
$135$	5.63974	0.485392
$136$	6.23607	0.534738
$137$	21.7361	1.85704	0.928522	−	0.371279i	$-0.121080\pi$
$137$	21.7361	1.85704	0.928522	+	0.371279i	$0.121080\pi$
$138$	3.48366	0.296549
$139$	7.47330	0.633877	0.316939	−	0.948446i	$-0.397345\pi$
$139$	7.47330	0.633877	0.316939	+	0.948446i	$0.397345\pi$
$140$	−3.71333	−0.313833
$141$	−19.7797	−1.66575
$142$	−13.7650	−1.15514
$143$	0	0
$144$	−1.93154	−0.160961
$145$	−6.53103	−0.542373
$146$	12.8529	1.06372
$147$	−1.47726	−0.121842
$148$	−35.1731	−2.89121
$149$	−9.53804	−0.781387	−0.390693	−	0.920521i	$-0.627765\pi$
$149$	−9.53804	−0.781387	−0.390693	+	0.920521i	$0.627765\pi$
$150$	−3.53103	−0.288307
$151$	−10.9015	−0.887149	−0.443575	−	0.896237i	$-0.646290\pi$
$151$	−10.9015	−0.887149	−0.443575	+	0.896237i	$0.646290\pi$
$152$	3.46385	0.280955
$153$	−1.24515	−0.100664
$154$	0	0
$155$	−8.51366	−0.683834
$156$	21.2155	1.69860
$157$	0.0605504	0.00483244	0.00241622	−	0.999997i	$-0.499231\pi$
$157$	0.0605504	0.00483244	0.00241622	+	0.999997i	$0.499231\pi$
$158$	13.6920	1.08928
$159$	4.60823	0.365457
$160$	−2.54445	−0.201156
$161$	0.986585	0.0777538
$162$	−14.0505	−1.10391
$163$	12.7752	1.00063	0.500314	−	0.865844i	$-0.333218\pi$
$163$	12.7752	1.00063	0.500314	+	0.865844i	$0.333218\pi$
$164$	12.3306	0.962856
$165$	0	0
$166$	−29.2549	−2.27062
$167$	20.0928	1.55483	0.777416	−	0.628987i	$-0.216530\pi$
$167$	20.0928	1.55483	0.777416	+	0.628987i	$0.216530\pi$
$168$	6.04981	0.466753
$169$	1.95769	0.150591
$170$	3.63974	0.279155
$171$	−0.691622	−0.0528897
$172$	−12.1855	−0.929133
$173$	−7.37684	−0.560851	−0.280425	−	0.959876i	$-0.590476\pi$
$173$	−7.37684	−0.560851	−0.280425	+	0.959876i	$0.590476\pi$
$174$	23.0613	1.74827
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	9.40495	0.706919
$178$	−21.1853	−1.58790
$179$	9.74856	0.728642	0.364321	−	0.931274i	$-0.381301\pi$
$179$	9.74856	0.728642	0.364321	+	0.931274i	$0.381301\pi$
$180$	−3.03640	−0.226320
$181$	−5.28644	−0.392938	−0.196469	−	0.980510i	$-0.562947\pi$
$181$	−5.28644	−0.392938	−0.196469	+	0.980510i	$0.562947\pi$
$182$	9.24436	0.685237
$183$	−0.680542	−0.0503071
$184$	−4.04036	−0.297859
$185$	−9.47214	−0.696405
$186$	30.0620	2.20425
$187$	0	0
$188$	49.7195	3.62617
$189$	−5.63974	−0.410231
$190$	2.02171	0.146670
$191$	−12.1562	−0.879591	−0.439795	−	0.898098i	$-0.644949\pi$
$191$	−12.1562	−0.879591	−0.439795	+	0.898098i	$0.644949\pi$
$192$	15.9635	1.15207
$193$	−5.23772	−0.377020	−0.188510	−	0.982071i	$-0.560366\pi$
$193$	−5.23772	−0.377020	−0.188510	+	0.982071i	$0.560366\pi$
$194$	15.1885	1.09047
$195$	5.71333	0.409140
$196$	3.71333	0.265238
$197$	3.51610	0.250512	0.125256	−	0.992124i	$-0.460025\pi$
$197$	3.51610	0.250512	0.125256	+	0.992124i	$0.460025\pi$
$198$	0	0
$199$	7.63650	0.541337	0.270669	−	0.962673i	$-0.412755\pi$
$199$	7.63650	0.541337	0.270669	+	0.962673i	$0.412755\pi$
$200$	4.09529	0.289581
$201$	14.9418	1.05392
$202$	17.9284	1.26144
$203$	6.53103	0.458389
$204$	−8.35307	−0.584832
$205$	3.32063	0.231923
$206$	−15.2819	−1.06474
$207$	0.806733	0.0560719
$208$	−9.13565	−0.633443
$209$	0	0
$210$	3.53103	0.243664
$211$	−21.3804	−1.47189	−0.735943	−	0.677043i	$-0.763261\pi$
$211$	−21.3804	−1.47189	−0.735943	+	0.677043i	$0.763261\pi$
$212$	−11.5835	−0.795560
$213$	8.50726	0.582908
$214$	−34.1713	−2.33590
$215$	−3.28155	−0.223800
$216$	23.0964	1.57151
$217$	8.51366	0.577945
$218$	37.3432	2.52920
$219$	−7.94355	−0.536775
$220$	0	0
$221$	−5.88922	−0.396152
$222$	33.4464	2.24478
$223$	24.4245	1.63559	0.817793	−	0.575512i	$-0.195197\pi$
$223$	24.4245	1.63559	0.817793	+	0.575512i	$0.195197\pi$
$224$	2.54445	0.170008
$225$	−0.817703	−0.0545135
$226$	−34.3811	−2.28700
$227$	−23.8564	−1.58340	−0.791701	−	0.610908i	$-0.790804\pi$
$227$	−23.8564	−1.58340	−0.791701	+	0.610908i	$0.790804\pi$
$228$	−4.63974	−0.307274
$229$	0.960365	0.0634627	0.0317314	−	0.999496i	$-0.489898\pi$
$229$	0.960365	0.0634627	0.0317314	+	0.999496i	$0.489898\pi$
$230$	−2.35819	−0.155495
$231$	0	0
$232$	−26.7465	−1.75599
$233$	25.4926	1.67007	0.835037	−	0.550194i	$-0.185446\pi$
$233$	25.4926	1.67007	0.835037	+	0.550194i	$0.185446\pi$
$234$	7.55914	0.494156
$235$	13.3895	0.873433
$236$	−23.6408	−1.53889
$237$	−8.46212	−0.549674
$238$	−3.63974	−0.235929
$239$	23.4802	1.51881	0.759405	−	0.650618i	$-0.225490\pi$
$239$	23.4802	1.51881	0.759405	+	0.650618i	$0.225490\pi$
$240$	−3.48951	−0.225247
$241$	13.0860	0.842942	0.421471	−	0.906842i	$-0.361514\pi$
$241$	13.0860	0.842942	0.421471	+	0.906842i	$0.361514\pi$
$242$	0	0
$243$	−8.23551	−0.528308
$244$	1.71065	0.109513
$245$	1.00000	0.0638877
$246$	−11.7252	−0.747573
$247$	−3.27119	−0.208141
$248$	−34.8659	−2.21399
$249$	18.0805	1.14581
$250$	2.39026	0.151173
$251$	−12.3910	−0.782116	−0.391058	−	0.920366i	$-0.627891\pi$
$251$	−12.3910	−0.782116	−0.391058	+	0.920366i	$0.627891\pi$
$252$	3.03640	0.191275
$253$	0	0
$254$	15.0845	0.946485
$255$	−2.24948	−0.140868
$256$	−27.9631	−1.74769
$257$	18.4017	1.14787	0.573934	−	0.818902i	$-0.305417\pi$
$257$	18.4017	1.14787	0.573934	+	0.818902i	$0.305417\pi$
$258$	11.5872	0.721391
$259$	9.47214	0.588570
$260$	−14.3614	−0.890654
$261$	5.34044	0.330565
$262$	−28.4570	−1.75808
$263$	9.82776	0.606006	0.303003	−	0.952990i	$-0.402011\pi$
$263$	9.82776	0.606006	0.303003	+	0.952990i	$0.402011\pi$
$264$	0	0
$265$	−3.11945	−0.191626
$266$	−2.02171	−0.123959
$267$	13.0932	0.801292
$268$	−37.5587	−2.29426
$269$	−8.96605	−0.546669	−0.273335	−	0.961919i	$-0.588127\pi$
$269$	−8.96605	−0.546669	−0.273335	+	0.961919i	$0.588127\pi$
$270$	13.4804	0.820393
$271$	7.71601	0.468714	0.234357	−	0.972151i	$-0.424702\pi$
$271$	7.71601	0.468714	0.234357	+	0.972151i	$0.424702\pi$
$272$	3.59694	0.218096
$273$	−5.71333	−0.345786
$274$	51.9549	3.13871
$275$	0	0
$276$	5.41196	0.325762
$277$	−2.92897	−0.175985	−0.0879923	−	0.996121i	$-0.528045\pi$
$277$	−2.92897	−0.175985	−0.0879923	+	0.996121i	$0.528045\pi$
$278$	17.8631	1.07136
$279$	6.96164	0.416783
$280$	−4.09529	−0.244741
$281$	−28.7936	−1.71768	−0.858842	−	0.512241i	$-0.828816\pi$
$281$	−28.7936	−1.71768	−0.858842	+	0.512241i	$0.828816\pi$
$282$	−47.2786	−2.81540
$283$	28.9336	1.71992	0.859962	−	0.510358i	$-0.170487\pi$
$283$	28.9336	1.71992	0.859962	+	0.510358i	$0.170487\pi$
$284$	−21.3843	−1.26893
$285$	−1.24948	−0.0740130
$286$	0	0
$287$	−3.32063	−0.196010
$288$	2.08060	0.122601
$289$	−14.6813	−0.863604
$290$	−15.6108	−0.916700
$291$	−9.38702	−0.550277
$292$	19.9674	1.16850
$293$	−19.3723	−1.13174	−0.565872	−	0.824493i	$-0.691460\pi$
$293$	−19.3723	−1.13174	−0.565872	+	0.824493i	$0.691460\pi$
$294$	−3.53103	−0.205934
$295$	−6.36648	−0.370671
$296$	−38.7912	−2.25469
$297$	0	0
$298$	−22.7984	−1.32067
$299$	3.81563	0.220664
$300$	−5.48555	−0.316708
$301$	3.28155	0.189145
$302$	−26.0573	−1.49943
$303$	−11.0804	−0.636550
$304$	1.99793	0.114589
$305$	0.460678	0.0263784
$306$	−2.97623	−0.170140
$307$	17.2849	0.986504	0.493252	−	0.869886i	$-0.335808\pi$
$307$	17.2849	0.986504	0.493252	+	0.869886i	$0.335808\pi$
$308$	0	0
$309$	9.44475	0.537293
$310$	−20.3498	−1.15579
$311$	19.8110	1.12338	0.561689	−	0.827348i	$-0.310152\pi$
$311$	19.8110	1.12338	0.561689	+	0.827348i	$0.310152\pi$
$312$	23.3978	1.32464
$313$	−30.4405	−1.72060	−0.860299	−	0.509790i	$-0.829723\pi$
$313$	−30.4405	−1.72060	−0.860299	+	0.509790i	$0.829723\pi$
$314$	0.144731	0.00816764
$315$	0.817703	0.0460723
$316$	21.2709	1.19658
$317$	−4.35235	−0.244452	−0.122226	−	0.992502i	$-0.539003\pi$
$317$	−4.35235	−0.244452	−0.122226	+	0.992502i	$0.539003\pi$
$318$	11.0149	0.617683
$319$	0	0
$320$	−10.8062	−0.604084
$321$	21.1190	1.17875
$322$	2.35819	0.131417
$323$	1.28795	0.0716635
$324$	−21.8279	−1.21266
$325$	−3.86752	−0.214531
$326$	30.5359	1.69123
$327$	−23.0794	−1.27629
$328$	13.5989	0.750876
$329$	−13.3895	−0.738185
$330$	0	0
$331$	7.44787	0.409372	0.204686	−	0.978828i	$-0.434383\pi$
$331$	7.44787	0.409372	0.204686	+	0.978828i	$0.434383\pi$
$332$	−45.4483	−2.49430
$333$	7.74539	0.424445
$334$	48.0271	2.62792
$335$	−10.1146	−0.552617
$336$	3.48951	0.190368
$337$	−23.4024	−1.27481	−0.637405	−	0.770529i	$-0.719992\pi$
$337$	−23.4024	−1.27481	−0.637405	+	0.770529i	$0.719992\pi$
$338$	4.67937	0.254524
$339$	21.2487	1.15407
$340$	5.65443	0.306655
$341$	0	0
$342$	−1.65315	−0.0893924
$343$	−1.00000	−0.0539949
$344$	−13.4389	−0.724577
$345$	1.45744	0.0784661
$346$	−17.6325	−0.947932
$347$	23.3915	1.25572	0.627860	−	0.778326i	$-0.283931\pi$
$347$	23.3915	1.25572	0.627860	+	0.778326i	$0.283931\pi$
$348$	35.8263	1.92049
$349$	2.05005	0.109737	0.0548683	−	0.998494i	$-0.482526\pi$
$349$	2.05005	0.109737	0.0548683	+	0.998494i	$0.482526\pi$
$350$	−2.39026	−0.127765
$351$	−21.8118	−1.16423
$352$	0	0
$353$	−19.3842	−1.03172	−0.515858	−	0.856674i	$-0.672527\pi$
$353$	−19.3842	−1.03172	−0.515858	+	0.856674i	$0.672527\pi$
$354$	22.4802	1.19481
$355$	−5.75881	−0.305646
$356$	−32.9119	−1.74433
$357$	2.24948	0.119055
$358$	23.3016	1.23153
$359$	−8.65127	−0.456596	−0.228298	−	0.973591i	$-0.573316\pi$
$359$	−8.65127	−0.456596	−0.228298	+	0.973591i	$0.573316\pi$
$360$	−3.34873	−0.176494
$361$	−18.2846	−0.962348
$362$	−12.6359	−0.664131
$363$	0	0
$364$	14.3614	0.752740
$365$	5.37722	0.281457
$366$	−1.62667	−0.0850274
$367$	−10.9340	−0.570749	−0.285375	−	0.958416i	$-0.592118\pi$
$367$	−10.9340	−0.570749	−0.285375	+	0.958416i	$0.592118\pi$
$368$	−2.33046	−0.121484
$369$	−2.71529	−0.141352
$370$	−22.6408	−1.17704
$371$	3.11945	0.161954
$372$	46.7021	2.42139
$373$	29.2848	1.51631	0.758154	−	0.652076i	$-0.226102\pi$
$373$	29.2848	1.51631	0.758154	+	0.652076i	$0.226102\pi$
$374$	0	0
$375$	−1.47726	−0.0762854
$376$	54.8338	2.82784
$377$	25.2589	1.30090
$378$	−13.4804	−0.693358
$379$	32.6200	1.67558	0.837788	−	0.545995i	$-0.183848\pi$
$379$	32.6200	1.67558	0.837788	+	0.545995i	$0.183848\pi$
$380$	3.14077	0.161118
$381$	−9.32273	−0.477618
$382$	−29.0564	−1.48666
$383$	−18.9524	−0.968423	−0.484212	−	0.874951i	$-0.660894\pi$
$383$	−18.9524	−0.968423	−0.484212	+	0.874951i	$0.660894\pi$
$384$	30.6393	1.56356
$385$	0	0
$386$	−12.5195	−0.637226
$387$	2.68333	0.136401
$388$	23.5958	1.19789
$389$	−38.8427	−1.96941	−0.984703	−	0.174244i	$-0.944252\pi$
$389$	−38.8427	−1.96941	−0.984703	+	0.174244i	$0.944252\pi$
$390$	13.6563	0.691515
$391$	−1.50231	−0.0759752
$392$	4.09529	0.206844
$393$	17.5874	0.887168
$394$	8.40439	0.423407
$395$	5.72825	0.288220
$396$	0	0
$397$	−7.29557	−0.366154	−0.183077	−	0.983099i	$-0.558606\pi$
$397$	−7.29557	−0.366154	−0.183077	+	0.983099i	$0.558606\pi$
$398$	18.2532	0.914951
$399$	1.24948	0.0625524
$400$	2.36215	0.118107
$401$	−37.6289	−1.87910	−0.939550	−	0.342413i	$-0.888756\pi$
$401$	−37.6289	−1.87910	−0.939550	+	0.342413i	$0.888756\pi$
$402$	35.7148	1.78129
$403$	32.9267	1.64020
$404$	27.8523	1.38570
$405$	−5.87825	−0.292093
$406$	15.6108	0.774753
$407$	0	0
$408$	−9.21229	−0.456077
$409$	19.3030	0.954470	0.477235	−	0.878776i	$-0.341639\pi$
$409$	19.3030	0.954470	0.477235	+	0.878776i	$0.341639\pi$
$410$	7.93715	0.391988
$411$	−32.1099	−1.58387
$412$	−23.7409	−1.16963
$413$	6.36648	0.313274
$414$	1.92830	0.0947708
$415$	−12.2392	−0.600800
$416$	9.84069	0.482479
$417$	−11.0400	−0.540632
$418$	0	0
$419$	18.1588	0.887114	0.443557	−	0.896246i	$-0.353716\pi$
$419$	18.1588	0.887114	0.443557	+	0.896246i	$0.353716\pi$
$420$	5.48555	0.267667
$421$	−19.5678	−0.953677	−0.476838	−	0.878991i	$-0.658217\pi$
$421$	−19.5678	−0.953677	−0.476838	+	0.878991i	$0.658217\pi$
$422$	−51.1046	−2.48773
$423$	−10.9486	−0.532339
$424$	−12.7750	−0.620411
$425$	1.52274	0.0738637
$426$	20.3345	0.985211
$427$	−0.460678	−0.0222938
$428$	−53.0860	−2.56601
$429$	0	0
$430$	−7.84374	−0.378259
$431$	30.3340	1.46114	0.730569	−	0.682839i	$-0.239255\pi$
$431$	30.3340	1.46114	0.730569	+	0.682839i	$0.239255\pi$
$432$	13.3219	0.640950
$433$	−8.27209	−0.397531	−0.198766	−	0.980047i	$-0.563693\pi$
$433$	−8.27209	−0.397531	−0.198766	+	0.980047i	$0.563693\pi$
$434$	20.3498	0.976823
$435$	9.64803	0.462588
$436$	58.0137	2.77835
$437$	−0.834465	−0.0399179
$438$	−18.9871	−0.907240
$439$	2.08907	0.0997059	0.0498530	−	0.998757i	$-0.484125\pi$
$439$	2.08907	0.0997059	0.0498530	+	0.998757i	$0.484125\pi$
$440$	0	0
$441$	−0.817703	−0.0389382
$442$	−14.0768	−0.669563
$443$	16.4383	0.781009	0.390505	−	0.920601i	$-0.372301\pi$
$443$	16.4383	0.781009	0.390505	+	0.920601i	$0.372301\pi$
$444$	51.9599	2.46591
$445$	−8.86318	−0.420155
$446$	58.3809	2.76441
$447$	14.0902	0.666442
$448$	10.8062	0.510544
$449$	−8.90100	−0.420064	−0.210032	−	0.977694i	$-0.567357\pi$
$449$	−8.90100	−0.420064	−0.210032	+	0.977694i	$0.567357\pi$
$450$	−1.95452	−0.0921370
$451$	0	0
$452$	−53.4120	−2.51229
$453$	16.1043	0.756646
$454$	−57.0228	−2.67621
$455$	3.86752	0.181312
$456$	−5.11700	−0.239625
$457$	−6.60555	−0.308995	−0.154497	−	0.987993i	$-0.549376\pi$
$457$	−6.60555	−0.308995	−0.154497	+	0.987993i	$0.549376\pi$
$458$	2.29552	0.107263
$459$	8.58786	0.400847
$460$	−3.66351	−0.170812
$461$	−19.8327	−0.923701	−0.461851	−	0.886958i	$-0.652814\pi$
$461$	−19.8327	−0.923701	−0.461851	+	0.886958i	$0.652814\pi$
$462$	0	0
$463$	10.7257	0.498465	0.249233	−	0.968444i	$-0.419822\pi$
$463$	10.7257	0.498465	0.249233	+	0.968444i	$0.419822\pi$
$464$	−15.4273	−0.716193
$465$	12.5769	0.583239
$466$	60.9338	2.82270
$467$	19.1742	0.887278	0.443639	−	0.896206i	$-0.353687\pi$
$467$	19.1742	0.887278	0.443639	+	0.896206i	$0.353687\pi$
$468$	11.7433	0.542835
$469$	10.1146	0.467047
$470$	32.0043	1.47625
$471$	−0.0894486	−0.00412157
$472$	−26.0726	−1.20009
$473$	0	0
$474$	−20.2266	−0.929040
$475$	0.845811	0.0388085
$476$	−5.65443	−0.259171
$477$	2.55078	0.116792
$478$	56.1238	2.56704
$479$	1.71905	0.0785455	0.0392727	−	0.999229i	$-0.487496\pi$
$479$	1.71905	0.0785455	0.0392727	+	0.999229i	$0.487496\pi$
$480$	3.75881	0.171565
$481$	36.6336	1.67035
$482$	31.2789	1.42471
$483$	−1.45744	−0.0663159
$484$	0	0
$485$	6.35435	0.288536
$486$	−19.6850	−0.892929
$487$	−16.1309	−0.730961	−0.365480	−	0.930819i	$-0.619095\pi$
$487$	−16.1309	−0.730961	−0.365480	+	0.930819i	$0.619095\pi$
$488$	1.88661	0.0854030
$489$	−18.8722	−0.853432
$490$	2.39026	0.107981
$491$	18.0369	0.813993	0.406997	−	0.913430i	$-0.366576\pi$
$491$	18.0369	0.813993	0.406997	+	0.913430i	$0.366576\pi$
$492$	−18.2155	−0.821216
$493$	−9.94506	−0.447903
$494$	−7.81898	−0.351793
$495$	0	0
$496$	−20.1105	−0.902989
$497$	5.75881	0.258318
$498$	43.2171	1.93661
$499$	−7.37055	−0.329951	−0.164976	−	0.986298i	$-0.552755\pi$
$499$	−7.37055	−0.329951	−0.164976	+	0.986298i	$0.552755\pi$
$500$	3.71333	0.166065
$501$	−29.6824	−1.32611
$502$	−29.6178	−1.32191
$503$	36.0046	1.60537	0.802684	−	0.596405i	$-0.203405\pi$
$503$	36.0046	1.60537	0.802684	+	0.596405i	$0.203405\pi$
$504$	3.34873	0.149164
$505$	7.50062	0.333773
$506$	0	0
$507$	−2.89201	−0.128439
$508$	23.4342	1.03972
$509$	−34.1032	−1.51160	−0.755798	−	0.654805i	$-0.772751\pi$
$509$	−34.1032	−1.51160	−0.755798	+	0.654805i	$0.772751\pi$
$510$	−5.37684	−0.238091
$511$	−5.37722	−0.237874
$512$	−25.3577	−1.12066
$513$	4.77015	0.210607
$514$	43.9848	1.94009
$515$	−6.39342	−0.281728
$516$	18.0011	0.792454
$517$	0	0
$518$	22.6408	0.994781
$519$	10.8975	0.478348
$520$	−15.8386	−0.694569
$521$	34.5998	1.51584	0.757922	−	0.652345i	$-0.226215\pi$
$521$	34.5998	1.51584	0.757922	+	0.652345i	$0.226215\pi$
$522$	12.7650	0.558710
$523$	42.6808	1.86630	0.933150	−	0.359487i	$-0.117048\pi$
$523$	42.6808	1.86630	0.933150	+	0.359487i	$0.117048\pi$
$524$	−44.2088	−1.93127
$525$	1.47726	0.0644729
$526$	23.4909	1.02425
$527$	−12.9641	−0.564725
$528$	0	0
$529$	−22.0266	−0.957680
$530$	−7.45628	−0.323880
$531$	5.20589	0.225916
$532$	−3.14077	−0.136170
$533$	−12.8426	−0.556274
$534$	31.2962	1.35432
$535$	−14.2961	−0.618073
$536$	−41.4221	−1.78916
$537$	−14.4012	−0.621456
$538$	−21.4312	−0.923963
$539$	0	0
$540$	20.9422	0.901209
$541$	−14.1591	−0.608746	−0.304373	−	0.952553i	$-0.598447\pi$
$541$	−14.1591	−0.608746	−0.304373	+	0.952553i	$0.598447\pi$
$542$	18.4432	0.792205
$543$	7.80944	0.335135
$544$	−3.87453	−0.166119
$545$	15.6231	0.669220
$546$	−13.6563	−0.584437
$547$	39.6414	1.69495	0.847473	−	0.530839i	$-0.178123\pi$
$547$	39.6414	1.69495	0.847473	+	0.530839i	$0.178123\pi$
$548$	80.7134	3.44791
$549$	−0.376698	−0.0160771
$550$	0	0
$551$	−5.52402	−0.235331
$552$	5.96866	0.254043
$553$	−5.72825	−0.243590
$554$	−7.00099	−0.297443
$555$	13.9928	0.593962
$556$	27.7508	1.17690
$557$	21.8819	0.927166	0.463583	−	0.886053i	$-0.346564\pi$
$557$	21.8819	0.927166	0.463583	+	0.886053i	$0.346564\pi$
$558$	16.6401	0.704432
$559$	12.6914	0.536791
$560$	−2.36215	−0.0998190
$561$	0	0
$562$	−68.8242	−2.90317
$563$	−13.7561	−0.579750	−0.289875	−	0.957064i	$-0.593614\pi$
$563$	−13.7561	−0.579750	−0.289875	+	0.957064i	$0.593614\pi$
$564$	−73.4486	−3.09274
$565$	−14.3839	−0.605133
$566$	69.1588	2.90696
$567$	5.87825	0.246863
$568$	−23.5840	−0.989563
$569$	14.7504	0.618368	0.309184	−	0.951002i	$-0.399944\pi$
$569$	14.7504	0.618368	0.309184	+	0.951002i	$0.399944\pi$
$570$	−2.98659	−0.125094
$571$	−32.3734	−1.35478	−0.677392	−	0.735622i	$-0.736890\pi$
$571$	−32.3734	−1.35478	−0.677392	+	0.735622i	$0.736890\pi$
$572$	0	0
$573$	17.9579	0.750200
$574$	−7.93715	−0.331290
$575$	−0.986585	−0.0411434
$576$	8.83624	0.368177
$577$	5.96700	0.248409	0.124205	−	0.992257i	$-0.460362\pi$
$577$	5.96700	0.248409	0.124205	+	0.992257i	$0.460362\pi$
$578$	−35.0920	−1.45963
$579$	7.73748	0.321559
$580$	−24.2519	−1.00700
$581$	12.2392	0.507769
$582$	−22.4374	−0.930060
$583$	0	0
$584$	22.0213	0.911248
$585$	3.16248	0.130752
$586$	−46.3048	−1.91284
$587$	−38.2756	−1.57980	−0.789901	−	0.613234i	$-0.789868\pi$
$587$	−38.2756	−1.57980	−0.789901	+	0.613234i	$0.789868\pi$
$588$	−5.48555	−0.226220
$589$	−7.20095	−0.296710
$590$	−15.2175	−0.626496
$591$	−5.19420	−0.213661
$592$	−22.3746	−0.919590
$593$	46.1732	1.89611	0.948053	−	0.318112i	$-0.103049\pi$
$593$	46.1732	1.89611	0.948053	+	0.318112i	$0.103049\pi$
$594$	0	0
$595$	−1.52274	−0.0624263
$596$	−35.4179	−1.45077
$597$	−11.2811	−0.461705
$598$	9.12035	0.372959
$599$	32.9133	1.34480	0.672400	−	0.740188i	$-0.265264\pi$
$599$	32.9133	1.34480	0.672400	+	0.740188i	$0.265264\pi$
$600$	−6.04981	−0.246983
$601$	−3.14315	−0.128212	−0.0641059	−	0.997943i	$-0.520420\pi$
$601$	−3.14315	−0.128212	−0.0641059	+	0.997943i	$0.520420\pi$
$602$	7.84374	0.319687
$603$	8.27070	0.336809
$604$	−40.4807	−1.64714
$605$	0	0
$606$	−26.4849	−1.07588
$607$	−10.1576	−0.412284	−0.206142	−	0.978522i	$-0.566091\pi$
$607$	−10.1576	−0.412284	−0.206142	+	0.978522i	$0.566091\pi$
$608$	−2.15212	−0.0872800
$609$	−9.64803	−0.390958
$610$	1.10114	0.0445838
$611$	−51.7840	−2.09496
$612$	−4.62365	−0.186900
$613$	−9.15687	−0.369842	−0.184921	−	0.982753i	$-0.559203\pi$
$613$	−9.15687	−0.369842	−0.184921	+	0.982753i	$0.559203\pi$
$614$	41.3155	1.66736
$615$	−4.90543	−0.197806
$616$	0	0
$617$	37.1224	1.49449	0.747245	−	0.664548i	$-0.231376\pi$
$617$	37.1224	1.49449	0.747245	+	0.664548i	$0.231376\pi$
$618$	22.5754	0.908115
$619$	3.40635	0.136913	0.0684564	−	0.997654i	$-0.478193\pi$
$619$	3.40635	0.136913	0.0684564	+	0.997654i	$0.478193\pi$
$620$	−31.6140	−1.26965
$621$	−5.56408	−0.223279
$622$	47.3534	1.89870
$623$	8.86318	0.355096
$624$	13.4957	0.540262
$625$	1.00000	0.0400000
$626$	−72.7606	−2.90810
$627$	0	0
$628$	0.224843	0.00897222
$629$	−14.4236	−0.575107
$630$	1.95452	0.0778699
$631$	−9.72698	−0.387225	−0.193612	−	0.981078i	$-0.562020\pi$
$631$	−9.72698	−0.387225	−0.193612	+	0.981078i	$0.562020\pi$
$632$	23.4589	0.933144
$633$	31.5844	1.25537
$634$	−10.4032	−0.413165
$635$	6.31082	0.250437
$636$	17.1119	0.678530
$637$	−3.86752	−0.153237
$638$	0	0
$639$	4.70899	0.186285
$640$	−20.7406	−0.819846
$641$	−17.6052	−0.695362	−0.347681	−	0.937613i	$-0.613031\pi$
$641$	−17.6052	−0.695362	−0.347681	+	0.937613i	$0.613031\pi$
$642$	50.4798	1.99228
$643$	38.1880	1.50599	0.752993	−	0.658028i	$-0.228609\pi$
$643$	38.1880	1.50599	0.752993	+	0.658028i	$0.228609\pi$
$644$	3.66351	0.144363
$645$	4.84770	0.190878
$646$	3.07853	0.121123
$647$	−18.8704	−0.741871	−0.370936	−	0.928659i	$-0.620963\pi$
$647$	−18.8704	−0.741871	−0.370936	+	0.928659i	$0.620963\pi$
$648$	−24.0732	−0.945684
$649$	0	0
$650$	−9.24436	−0.362594
$651$	−12.5769	−0.492927
$652$	47.4383	1.85783
$653$	16.3664	0.640469	0.320234	−	0.947338i	$-0.396238\pi$
$653$	16.3664	0.640469	0.320234	+	0.947338i	$0.396238\pi$
$654$	−55.1656	−2.15715
$655$	−11.9054	−0.465184
$656$	7.84381	0.306249
$657$	−4.39697	−0.171542
$658$	−32.0043	−1.24766
$659$	5.42317	0.211257	0.105628	−	0.994406i	$-0.466315\pi$
$659$	5.42317	0.211257	0.105628	+	0.994406i	$0.466315\pi$
$660$	0	0
$661$	−17.4333	−0.678077	−0.339039	−	0.940772i	$-0.610102\pi$
$661$	−17.4333	−0.678077	−0.339039	+	0.940772i	$0.610102\pi$
$662$	17.8023	0.691907
$663$	8.69991	0.337877
$664$	−50.1233	−1.94516
$665$	−0.845811	−0.0327991
$666$	18.5135	0.717383
$667$	6.44342	0.249490
$668$	74.6113	2.88680
$669$	−36.0814	−1.39499
$670$	−24.1764	−0.934015
$671$	0	0
$672$	−3.75881	−0.144999
$673$	2.45665	0.0946970	0.0473485	−	0.998878i	$-0.484923\pi$
$673$	2.45665	0.0946970	0.0473485	+	0.998878i	$0.484923\pi$
$674$	−55.9377	−2.15464
$675$	5.63974	0.217074
$676$	7.26953	0.279597
$677$	−22.0757	−0.848438	−0.424219	−	0.905560i	$-0.639451\pi$
$677$	−22.0757	−0.848438	−0.424219	+	0.905560i	$0.639451\pi$
$678$	50.7898	1.95057
$679$	−6.35435	−0.243857
$680$	6.23607	0.239142
$681$	35.2421	1.35048
$682$	0	0
$683$	0.861150	0.0329510	0.0164755	−	0.999864i	$-0.494755\pi$
$683$	0.861150	0.0329510	0.0164755	+	0.999864i	$0.494755\pi$
$684$	−2.56822	−0.0981983
$685$	21.7361	0.830495
$686$	−2.39026	−0.0912604
$687$	−1.41871	−0.0541271
$688$	−7.75150	−0.295523
$689$	12.0645	0.459621
$690$	3.48366	0.132621
$691$	24.0177	0.913676	0.456838	−	0.889550i	$-0.348982\pi$
$691$	24.0177	0.913676	0.456838	+	0.889550i	$0.348982\pi$
$692$	−27.3926	−1.04131
$693$	0	0
$694$	55.9116	2.12238
$695$	7.47330	0.283479
$696$	39.5115	1.49768
$697$	5.05645	0.191527
$698$	4.90014	0.185473
$699$	−37.6591	−1.42440
$700$	−3.71333	−0.140351
$701$	−11.3451	−0.428498	−0.214249	−	0.976779i	$-0.568730\pi$
$701$	−11.3451	−0.428498	−0.214249	+	0.976779i	$0.568730\pi$
$702$	−52.1358	−1.96774
$703$	−8.01164	−0.302165
$704$	0	0
$705$	−19.7797	−0.744947
$706$	−46.3332	−1.74377
$707$	−7.50062	−0.282090
$708$	34.9237	1.31251
$709$	−43.9243	−1.64961	−0.824807	−	0.565415i	$-0.808716\pi$
$709$	−43.9243	−1.64961	−0.824807	+	0.565415i	$0.808716\pi$
$710$	−13.7650	−0.516592
$711$	−4.68401	−0.175664
$712$	−36.2973	−1.36030
$713$	8.39945	0.314562
$714$	5.37684	0.201223
$715$	0	0
$716$	36.1996	1.35284
$717$	−34.6864	−1.29539
$718$	−20.6787	−0.771724
$719$	−9.78062	−0.364756	−0.182378	−	0.983229i	$-0.558379\pi$
$719$	−9.78062	−0.364756	−0.182378	+	0.983229i	$0.558379\pi$
$720$	−1.93154	−0.0719841
$721$	6.39342	0.238104
$722$	−43.7049	−1.62653
$723$	−19.3314	−0.718942
$724$	−19.6303	−0.729554
$725$	−6.53103	−0.242556
$726$	0	0
$727$	1.08785	0.0403460	0.0201730	−	0.999797i	$-0.493578\pi$
$727$	1.08785	0.0403460	0.0201730	+	0.999797i	$0.493578\pi$
$728$	15.8386	0.587018
$729$	29.8008	1.10373
$730$	12.8529	0.475708
$731$	−4.99694	−0.184819
$732$	−2.52707	−0.0934033
$733$	8.41380	0.310771	0.155385	−	0.987854i	$-0.450338\pi$
$733$	8.41380	0.310771	0.155385	+	0.987854i	$0.450338\pi$
$734$	−26.1350	−0.964661
$735$	−1.47726	−0.0544896
$736$	2.51031	0.0925313
$737$	0	0
$738$	−6.49023	−0.238909
$739$	2.66939	0.0981952	0.0490976	−	0.998794i	$-0.484365\pi$
$739$	2.66939	0.0981952	0.0490976	+	0.998794i	$0.484365\pi$
$740$	−35.1731	−1.29299
$741$	4.83240	0.177523
$742$	7.45628	0.273728
$743$	−17.4031	−0.638459	−0.319230	−	0.947677i	$-0.603424\pi$
$743$	−17.4031	−0.638459	−0.319230	+	0.947677i	$0.603424\pi$
$744$	51.5061	1.88830
$745$	−9.53804	−0.349447
$746$	69.9981	2.56281
$747$	10.0081	0.366176
$748$	0	0
$749$	14.2961	0.522367
$750$	−3.53103	−0.128935
$751$	23.3141	0.850745	0.425372	−	0.905018i	$-0.360143\pi$
$751$	23.3141	0.850745	0.425372	+	0.905018i	$0.360143\pi$
$752$	31.6279	1.15335
$753$	18.3048	0.667064
$754$	60.3752	2.19873
$755$	−10.9015	−0.396745
$756$	−20.9422	−0.761661
$757$	13.0116	0.472914	0.236457	−	0.971642i	$-0.424014\pi$
$757$	13.0116	0.472914	0.236457	+	0.971642i	$0.424014\pi$
$758$	77.9702	2.83200
$759$	0	0
$760$	3.46385	0.125647
$761$	−13.7576	−0.498712	−0.249356	−	0.968412i	$-0.580219\pi$
$761$	−13.7576	−0.498712	−0.249356	+	0.968412i	$0.580219\pi$
$762$	−22.2837	−0.807254
$763$	−15.6231	−0.565594
$764$	−45.1399	−1.63310
$765$	−1.24515	−0.0450185
$766$	−45.3011	−1.63680
$767$	24.6225	0.889066
$768$	41.3088	1.49060
$769$	32.1927	1.16090	0.580450	−	0.814296i	$-0.302877\pi$
$769$	32.1927	1.16090	0.580450	+	0.814296i	$0.302877\pi$
$770$	0	0
$771$	−27.1841	−0.979012
$772$	−19.4494	−0.699999
$773$	9.47616	0.340834	0.170417	−	0.985372i	$-0.445489\pi$
$773$	9.47616	0.340834	0.170417	+	0.985372i	$0.445489\pi$
$774$	6.41385	0.230541
$775$	−8.51366	−0.305820
$776$	26.0229	0.934168
$777$	−13.9928	−0.501989
$778$	−92.8441	−3.32862
$779$	2.80862	0.100629
$780$	21.2155	0.759635
$781$	0	0
$782$	−3.59091	−0.128411
$783$	−36.8333	−1.31632
$784$	2.36215	0.0843625
$785$	0.0605504	0.00216113
$786$	42.0384	1.49946
$787$	−36.2272	−1.29136	−0.645680	−	0.763608i	$-0.723426\pi$
$787$	−36.2272	−1.29136	−0.645680	+	0.763608i	$0.723426\pi$
$788$	13.0564	0.465117
$789$	−14.5182	−0.516860
$790$	13.6920	0.487139
$791$	14.3839	0.511431
$792$	0	0
$793$	−1.78168	−0.0632693
$794$	−17.4383	−0.618862
$795$	4.60823	0.163437
$796$	28.3568	1.00508
$797$	9.94954	0.352431	0.176215	−	0.984352i	$-0.443614\pi$
$797$	9.94954	0.352431	0.176215	+	0.984352i	$0.443614\pi$
$798$	2.98659	0.105724
$799$	20.3887	0.721300
$800$	−2.54445	−0.0899597
$801$	7.24745	0.256076
$802$	−89.9428	−3.17599
$803$	0	0
$804$	55.4839	1.95677
$805$	0.986585	0.0347726
$806$	78.7033	2.77221
$807$	13.2452	0.466252
$808$	30.7172	1.08063
$809$	−13.0220	−0.457829	−0.228915	−	0.973446i	$-0.573518\pi$
$809$	−13.0220	−0.457829	−0.228915	+	0.973446i	$0.573518\pi$
$810$	−14.0505	−0.493685
$811$	31.3696	1.10153	0.550767	−	0.834659i	$-0.314335\pi$
$811$	31.3696	1.10153	0.550767	+	0.834659i	$0.314335\pi$
$812$	24.2519	0.851073
$813$	−11.3985	−0.399765
$814$	0	0
$815$	12.7752	0.447494
$816$	−5.31361	−0.186014
$817$	−2.77557	−0.0971049
$818$	46.1390	1.61321
$819$	−3.16248	−0.110506
$820$	12.3306	0.430602
$821$	−10.7598	−0.375518	−0.187759	−	0.982215i	$-0.560122\pi$
$821$	−10.7598	−0.375518	−0.187759	+	0.982215i	$0.560122\pi$
$822$	−76.7510	−2.67700
$823$	−47.3989	−1.65222	−0.826111	−	0.563507i	$-0.809452\pi$
$823$	−47.3989	−1.65222	−0.826111	+	0.563507i	$0.809452\pi$
$824$	−26.1829	−0.912126
$825$	0	0
$826$	15.2175	0.529486
$827$	45.9382	1.59743	0.798715	−	0.601710i	$-0.205514\pi$
$827$	45.9382	1.59743	0.798715	+	0.601710i	$0.205514\pi$
$828$	2.99567	0.104107
$829$	−52.6054	−1.82706	−0.913531	−	0.406769i	$-0.866655\pi$
$829$	−52.6054	−1.82706	−0.913531	+	0.406769i	$0.866655\pi$
$830$	−29.2549	−1.01545
$831$	4.32685	0.150097
$832$	41.7931	1.44891
$833$	1.52274	0.0527598
$834$	−26.3885	−0.913758
$835$	20.0928	0.695342
$836$	0	0
$837$	−48.0148	−1.65964
$838$	43.4041	1.49937
$839$	−29.8644	−1.03103	−0.515516	−	0.856880i	$-0.672400\pi$
$839$	−29.8644	−1.03103	−0.515516	+	0.856880i	$0.672400\pi$
$840$	6.04981	0.208738
$841$	13.6544	0.470840
$842$	−46.7721	−1.61187
$843$	42.5357	1.46501
$844$	−79.3924	−2.73280
$845$	1.95769	0.0673465
$846$	−26.1700	−0.899742
$847$	0	0
$848$	−7.36859	−0.253039
$849$	−42.7425	−1.46692
$850$	3.63974	0.124842
$851$	9.34507	0.320345
$852$	31.5902	1.08226
$853$	52.6812	1.80377	0.901885	−	0.431976i	$-0.142184\pi$
$853$	52.6812	1.80377	0.901885	+	0.431976i	$0.142184\pi$
$854$	−1.10114	−0.0376802
$855$	−0.691622	−0.0236530
$856$	−58.5466	−2.00108
$857$	0.0751683	0.00256770	0.00128385	−	0.999999i	$-0.499591\pi$
$857$	0.0751683	0.00256770	0.00128385	+	0.999999i	$0.499591\pi$
$858$	0	0
$859$	32.9785	1.12521	0.562606	−	0.826725i	$-0.309799\pi$
$859$	32.9785	1.12521	0.562606	+	0.826725i	$0.309799\pi$
$860$	−12.1855	−0.415521
$861$	4.90543	0.167177
$862$	72.5061	2.46957
$863$	−51.0876	−1.73904	−0.869521	−	0.493895i	$-0.835573\pi$
$863$	−51.0876	−1.73904	−0.869521	+	0.493895i	$0.835573\pi$
$864$	−14.3500	−0.488197
$865$	−7.37684	−0.250820
$866$	−19.7724	−0.671894
$867$	21.6880	0.736565
$868$	31.6140	1.07305
$869$	0	0
$870$	23.0613	0.781850
$871$	39.1182	1.32547
$872$	63.9811	2.16667
$873$	−5.19597	−0.175857
$874$	−1.99458	−0.0674678
$875$	−1.00000	−0.0338062
$876$	−29.4970	−0.996612
$877$	−21.6175	−0.729970	−0.364985	−	0.931013i	$-0.618926\pi$
$877$	−21.6175	−0.729970	−0.364985	+	0.931013i	$0.618926\pi$
$878$	4.99342	0.168520
$879$	28.6180	0.965260
$880$	0	0
$881$	12.2075	0.411280	0.205640	−	0.978628i	$-0.434072\pi$
$881$	12.2075	0.411280	0.205640	+	0.978628i	$0.434072\pi$
$882$	−1.95452	−0.0658121
$883$	2.37183	0.0798184	0.0399092	−	0.999203i	$-0.487293\pi$
$883$	2.37183	0.0798184	0.0399092	+	0.999203i	$0.487293\pi$
$884$	−21.8686	−0.735521
$885$	9.40495	0.316144
$886$	39.2919	1.32004
$887$	10.1657	0.341332	0.170666	−	0.985329i	$-0.445408\pi$
$887$	10.1657	0.341332	0.170666	+	0.985329i	$0.445408\pi$
$888$	57.3047	1.92302
$889$	−6.31082	−0.211658
$890$	−21.1853	−0.710132
$891$	0	0
$892$	90.6962	3.03674
$893$	11.3250	0.378975
$894$	33.6791	1.12640
$895$	9.74856	0.325858
$896$	20.7406	0.692896
$897$	−5.63668	−0.188203
$898$	−21.2757	−0.709979
$899$	55.6030	1.85446
$900$	−3.03640	−0.101213
$901$	−4.75010	−0.158249
$902$	0	0
$903$	−4.84770	−0.161321
$904$	−58.9061	−1.95919
$905$	−5.28644	−0.175727
$906$	38.4934	1.27886
$907$	−33.6746	−1.11815	−0.559074	−	0.829118i	$-0.688843\pi$
$907$	−33.6746	−1.11815	−0.559074	+	0.829118i	$0.688843\pi$
$908$	−88.5865	−2.93985
$909$	−6.13328	−0.203428
$910$	9.24436	0.306448
$911$	46.7678	1.54949	0.774744	−	0.632276i	$-0.217879\pi$
$911$	46.7678	1.54949	0.774744	+	0.632276i	$0.217879\pi$
$912$	−2.95146	−0.0977328
$913$	0	0
$914$	−15.7890	−0.522253
$915$	−0.680542	−0.0224980
$916$	3.56615	0.117829
$917$	11.9054	0.393152
$918$	20.5272	0.677498
$919$	5.52188	0.182150	0.0910750	−	0.995844i	$-0.470970\pi$
$919$	5.52188	0.182150	0.0910750	+	0.995844i	$0.470970\pi$
$920$	−4.04036	−0.133207
$921$	−25.5344	−0.841386
$922$	−47.4053	−1.56121
$923$	22.2723	0.733101
$924$	0	0
$925$	−9.47214	−0.311442
$926$	25.6372	0.842490
$927$	5.22792	0.171707
$928$	16.6179	0.545508
$929$	−4.61181	−0.151309	−0.0756543	−	0.997134i	$-0.524105\pi$
$929$	−4.61181	−0.151309	−0.0756543	+	0.997134i	$0.524105\pi$
$930$	30.0620	0.985772
$931$	0.845811	0.0277203
$932$	94.6622	3.10077
$933$	−29.2660	−0.958126
$934$	45.8314	1.49965
$935$	0	0
$936$	12.9513	0.423326
$937$	0.800908	0.0261645	0.0130823	−	0.999914i	$-0.495836\pi$
$937$	0.800908	0.0261645	0.0130823	+	0.999914i	$0.495836\pi$
$938$	24.1764	0.789387
$939$	44.9685	1.46749
$940$	49.7195	1.62167
$941$	−0.562752	−0.0183452	−0.00917259	−	0.999958i	$-0.502920\pi$
$941$	−0.562752	−0.0183452	−0.00917259	+	0.999958i	$0.502920\pi$
$942$	−0.213805	−0.00696615
$943$	−3.27608	−0.106684
$944$	−15.0386	−0.489464
$945$	−5.63974	−0.183461
$946$	0	0
$947$	43.8097	1.42362	0.711812	−	0.702370i	$-0.247875\pi$
$947$	43.8097	1.42362	0.711812	+	0.702370i	$0.247875\pi$
$948$	−31.4226	−1.02056
$949$	−20.7965	−0.675082
$950$	2.02171	0.0655928
$951$	6.42955	0.208492
$952$	−6.23607	−0.202112
$953$	26.7501	0.866522	0.433261	−	0.901268i	$-0.357363\pi$
$953$	26.7501	0.866522	0.433261	+	0.901268i	$0.357363\pi$
$954$	6.09702	0.197398
$955$	−12.1562	−0.393365
$956$	87.1899	2.81992
$957$	0	0
$958$	4.10897	0.132755
$959$	−21.7361	−0.701896
$960$	15.9635	0.515221
$961$	41.4824	1.33814
$962$	87.5638	2.82317
$963$	11.6899	0.376703
$964$	48.5925	1.56506
$965$	−5.23772	−0.168608
$966$	−3.48366	−0.112085
$967$	10.8617	0.349290	0.174645	−	0.984631i	$-0.444122\pi$
$967$	10.8617	0.349290	0.174645	+	0.984631i	$0.444122\pi$
$968$	0	0
$969$	−1.90264	−0.0611215
$970$	15.1885	0.487674
$971$	−52.8281	−1.69533	−0.847667	−	0.530529i	$-0.821993\pi$
$971$	−52.8281	−1.69533	−0.847667	+	0.530529i	$0.821993\pi$
$972$	−30.5812	−0.980891
$973$	−7.47330	−0.239583
$974$	−38.5570	−1.23545
$975$	5.71333	0.182973
$976$	1.08819	0.0348321
$977$	−12.9205	−0.413362	−0.206681	−	0.978408i	$-0.566266\pi$
$977$	−12.9205	−0.413362	−0.206681	+	0.978408i	$0.566266\pi$
$978$	−45.1095	−1.44244
$979$	0	0
$980$	3.71333	0.118618
$981$	−12.7750	−0.407876
$982$	43.1128	1.37578
$983$	−33.3756	−1.06452	−0.532259	−	0.846582i	$-0.678657\pi$
$983$	−33.3756	−1.06452	−0.532259	+	0.846582i	$0.678657\pi$
$984$	−20.0892	−0.640419
$985$	3.51610	0.112032
$986$	−23.7713	−0.757031
$987$	19.7797	0.629596
$988$	−12.1470	−0.386447
$989$	3.23753	0.102947
$990$	0	0
$991$	21.2540	0.675157	0.337579	−	0.941297i	$-0.390392\pi$
$991$	21.2540	0.675157	0.337579	+	0.941297i	$0.390392\pi$
$992$	21.6625	0.687786
$993$	−11.0024	−0.349152
$994$	13.7650	0.436600
$995$	7.63650	0.242093
$996$	67.1389	2.12738
$997$	−13.0452	−0.413147	−0.206574	−	0.978431i	$-0.566231\pi$
$997$	−13.0452	−0.413147	−0.206574	+	0.978431i	$0.566231\pi$
$998$	−17.6175	−0.557673
$999$	−53.4204	−1.69015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.t.1.4		4
11.2	odd	10		385.2.n.c.246.2	yes	8
11.6	odd	10		385.2.n.c.36.2	✓	8
11.10	odd	2		4235.2.a.w.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.c.36.2	✓	8	11.6	odd	10
385.2.n.c.246.2	yes	8	11.2	odd	10
4235.2.a.t.1.4		4	1.1	even	1	trivial
4235.2.a.w.1.1		4	11.10	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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+2.39026 q^{2} -1.47726 q^{3} +3.71333 q^{4} +1.00000 q^{5} -3.53103 q^{6} -1.00000 q^{7} +4.09529 q^{8} -0.817703 q^{9} +O(q^{10})\)	\(q+2.39026 q^{2} -1.47726 q^{3} +3.71333 q^{4} +1.00000 q^{5} -3.53103 q^{6} -1.00000 q^{7} +4.09529 q^{8} -0.817703 q^{9} +2.39026 q^{10} -5.48555 q^{12} -3.86752 q^{13} -2.39026 q^{14} -1.47726 q^{15} +2.36215 q^{16} +1.52274 q^{17} -1.95452 q^{18} +0.845811 q^{19} +3.71333 q^{20} +1.47726 q^{21} -0.986585 q^{23} -6.04981 q^{24} +1.00000 q^{25} -9.24436 q^{26} +5.63974 q^{27} -3.71333 q^{28} -6.53103 q^{29} -3.53103 q^{30} -8.51366 q^{31} -2.54445 q^{32} +3.63974 q^{34} -1.00000 q^{35} -3.03640 q^{36} -9.47214 q^{37} +2.02171 q^{38} +5.71333 q^{39} +4.09529 q^{40} +3.32063 q^{41} +3.53103 q^{42} -3.28155 q^{43} -0.817703 q^{45} -2.35819 q^{46} +13.3895 q^{47} -3.48951 q^{48} +1.00000 q^{49} +2.39026 q^{50} -2.24948 q^{51} -14.3614 q^{52} -3.11945 q^{53} +13.4804 q^{54} -4.09529 q^{56} -1.24948 q^{57} -15.6108 q^{58} -6.36648 q^{59} -5.48555 q^{60} +0.460678 q^{61} -20.3498 q^{62} +0.817703 q^{63} -10.8062 q^{64} -3.86752 q^{65} -10.1146 q^{67} +5.65443 q^{68} +1.45744 q^{69} -2.39026 q^{70} -5.75881 q^{71} -3.34873 q^{72} +5.37722 q^{73} -22.6408 q^{74} -1.47726 q^{75} +3.14077 q^{76} +13.6563 q^{78} +5.72825 q^{79} +2.36215 q^{80} -5.87825 q^{81} +7.93715 q^{82} -12.2392 q^{83} +5.48555 q^{84} +1.52274 q^{85} -7.84374 q^{86} +9.64803 q^{87} -8.86318 q^{89} -1.95452 q^{90} +3.86752 q^{91} -3.66351 q^{92} +12.5769 q^{93} +32.0043 q^{94} +0.845811 q^{95} +3.75881 q^{96} +6.35435 q^{97} +2.39026 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 3 q^{3} + 3 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} + 9 q^{8} - 3 q^{9}+O(q^{10}) \) 4 * q - q^2 - 3 * q^3 + 3 * q^4 + 4 * q^5 - 2 * q^6 - 4 * q^7 + 9 * q^8 - 3 * q^9	\( 4 q - q^{2} - 3 q^{3} + 3 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} + 9 q^{8} - 3 q^{9} - q^{10} - 4 q^{12} - 2 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 9 q^{17} - 2 q^{18} + 5 q^{19} + 3 q^{20} + 3 q^{21} - 4 q^{23} - 11 q^{24} + 4 q^{25} - 13 q^{26} + 3 q^{27} - 3 q^{28} - 14 q^{29} - 2 q^{30} - 18 q^{31} + 2 q^{32} - 5 q^{34} - 4 q^{35} + q^{36} - 20 q^{37} - 7 q^{38} + 11 q^{39} + 9 q^{40} - q^{41} + 2 q^{42} - 10 q^{43} - 3 q^{45} + 7 q^{46} + 9 q^{47} + 4 q^{49} - q^{50} - 11 q^{52} - 3 q^{53} + 21 q^{54} - 9 q^{56} + 4 q^{57} - 7 q^{58} + 6 q^{59} - 4 q^{60} + 29 q^{61} - 3 q^{62} + 3 q^{63} - 11 q^{64} - 2 q^{65} - 5 q^{67} + 5 q^{68} - 14 q^{69} + q^{70} - 17 q^{71} - q^{72} - 12 q^{73} - 5 q^{74} - 3 q^{75} + 11 q^{76} + 5 q^{78} + 2 q^{79} - 3 q^{80} - 8 q^{81} + 22 q^{82} - 10 q^{83} + 4 q^{84} + 9 q^{85} + 3 q^{86} + 4 q^{87} - 41 q^{89} - 2 q^{90} + 2 q^{91} - 16 q^{92} + 21 q^{93} + 32 q^{94} + 5 q^{95} + 9 q^{96} - 4 q^{97} - q^{98}+O(q^{100}) \) 4 * q - q^2 - 3 * q^3 + 3 * q^4 + 4 * q^5 - 2 * q^6 - 4 * q^7 + 9 * q^8 - 3 * q^9 - q^10 - 4 * q^12 - 2 * q^13 + q^14 - 3 * q^15 - 3 * q^16 + 9 * q^17 - 2 * q^18 + 5 * q^19 + 3 * q^20 + 3 * q^21 - 4 * q^23 - 11 * q^24 + 4 * q^25 - 13 * q^26 + 3 * q^27 - 3 * q^28 - 14 * q^29 - 2 * q^30 - 18 * q^31 + 2 * q^32 - 5 * q^34 - 4 * q^35 + q^36 - 20 * q^37 - 7 * q^38 + 11 * q^39 + 9 * q^40 - q^41 + 2 * q^42 - 10 * q^43 - 3 * q^45 + 7 * q^46 + 9 * q^47 + 4 * q^49 - q^50 - 11 * q^52 - 3 * q^53 + 21 * q^54 - 9 * q^56 + 4 * q^57 - 7 * q^58 + 6 * q^59 - 4 * q^60 + 29 * q^61 - 3 * q^62 + 3 * q^63 - 11 * q^64 - 2 * q^65 - 5 * q^67 + 5 * q^68 - 14 * q^69 + q^70 - 17 * q^71 - q^72 - 12 * q^73 - 5 * q^74 - 3 * q^75 + 11 * q^76 + 5 * q^78 + 2 * q^79 - 3 * q^80 - 8 * q^81 + 22 * q^82 - 10 * q^83 + 4 * q^84 + 9 * q^85 + 3 * q^86 + 4 * q^87 - 41 * q^89 - 2 * q^90 + 2 * q^91 - 16 * q^92 + 21 * q^93 + 32 * q^94 + 5 * q^95 + 9 * q^96 - 4 * q^97 - q^98

Introduction

L-functions

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