LMFDB - Embedded newform 4235.2.a.bp.1.18

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:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 28 x^{16} + 54 x^{15} + 317 x^{14} - 580 x^{13} - 1874 x^{12} + 3158 x^{11} + \cdots - 176 $ x^18 - 2x^17 - 28x^16 + 54x^15 + 317x^14 - 580x^13 - 1874x^12 + 3158x^11 + 6290x^10 - 9228x^9 - 12411x^8 + 14224x^7 + 14618x^6 - 10744x^5 - 9817x^4 + 3146x^3 + 3048x^2 - 16*x - 176
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			1.18
Root			$2.77774$ 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)

$f(q)$	$=$	$q+2.77774 q^{2} -1.15501 q^{3} +5.71583 q^{4} +1.00000 q^{5} -3.20831 q^{6} +1.00000 q^{7} +10.3216 q^{8} -1.66596 q^{9} +O(q^{10})$	\(q+2.77774 q^{2} -1.15501 q^{3} +5.71583 q^{4} +1.00000 q^{5} -3.20831 q^{6} +1.00000 q^{7} +10.3216 q^{8} -1.66596 q^{9} +2.77774 q^{10} -6.60184 q^{12} +4.48271 q^{13} +2.77774 q^{14} -1.15501 q^{15} +17.2391 q^{16} +3.65680 q^{17} -4.62759 q^{18} +1.28546 q^{19} +5.71583 q^{20} -1.15501 q^{21} -6.46047 q^{23} -11.9216 q^{24} +1.00000 q^{25} +12.4518 q^{26} +5.38922 q^{27} +5.71583 q^{28} -1.21204 q^{29} -3.20831 q^{30} -7.51569 q^{31} +27.2424 q^{32} +10.1576 q^{34} +1.00000 q^{35} -9.52232 q^{36} -6.29940 q^{37} +3.57067 q^{38} -5.17757 q^{39} +10.3216 q^{40} +8.93325 q^{41} -3.20831 q^{42} +2.40712 q^{43} -1.66596 q^{45} -17.9455 q^{46} +0.468011 q^{47} -19.9113 q^{48} +1.00000 q^{49} +2.77774 q^{50} -4.22364 q^{51} +25.6224 q^{52} +2.47206 q^{53} +14.9698 q^{54} +10.3216 q^{56} -1.48472 q^{57} -3.36673 q^{58} -12.1993 q^{59} -6.60184 q^{60} -1.04789 q^{61} -20.8766 q^{62} -1.66596 q^{63} +41.1942 q^{64} +4.48271 q^{65} +6.47842 q^{67} +20.9017 q^{68} +7.46190 q^{69} +2.77774 q^{70} -9.27952 q^{71} -17.1953 q^{72} +2.57523 q^{73} -17.4981 q^{74} -1.15501 q^{75} +7.34748 q^{76} -14.3819 q^{78} -11.5599 q^{79} +17.2391 q^{80} -1.22673 q^{81} +24.8142 q^{82} +10.1307 q^{83} -6.60184 q^{84} +3.65680 q^{85} +6.68635 q^{86} +1.39992 q^{87} +15.0783 q^{89} -4.62759 q^{90} +4.48271 q^{91} -36.9270 q^{92} +8.68069 q^{93} +1.30001 q^{94} +1.28546 q^{95} -31.4652 q^{96} -3.45073 q^{97} +2.77774 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9}+O(q^{10}) $ 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9} + 2 q^{10} + 15 q^{12} + 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} - 5 q^{17} + 2 q^{18} + 15 q^{19} + 24 q^{20} + 5 q^{21} + 4 q^{23} + 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} + 24 q^{28} - 6 q^{29} - q^{30} + 22 q^{31} - 6 q^{32} + 44 q^{34} + 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} - 38 q^{39} + 6 q^{40} + 7 q^{41} - q^{42} + 10 q^{43} + 37 q^{45} - 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} + 2 q^{50} - 11 q^{51} + 18 q^{52} + 23 q^{53} + 13 q^{54} + 6 q^{56} - 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} + 17 q^{61} + 57 q^{62} + 37 q^{63} + 64 q^{64} + 8 q^{65} + 29 q^{67} - 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} - 77 q^{72} + 3 q^{73} - 48 q^{74} + 5 q^{75} + 47 q^{76} + 10 q^{78} - 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} + 9 q^{83} + 15 q^{84} - 5 q^{85} + 25 q^{86} + 23 q^{87} + 59 q^{89} + 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} - 19 q^{94} + 15 q^{95} + 14 q^{96} + 30 q^{97} + 2 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9 + 2 * q^10 + 15 * q^12 + 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 - 5 * q^17 + 2 * q^18 + 15 * q^19 + 24 * q^20 + 5 * q^21 + 4 * q^23 + 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 + 24 * q^28 - 6 * q^29 - q^30 + 22 * q^31 - 6 * q^32 + 44 * q^34 + 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 - 38 * q^39 + 6 * q^40 + 7 * q^41 - q^42 + 10 * q^43 + 37 * q^45 - 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 + 2 * q^50 - 11 * q^51 + 18 * q^52 + 23 * q^53 + 13 * q^54 + 6 * q^56 - 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 + 17 * q^61 + 57 * q^62 + 37 * q^63 + 64 * q^64 + 8 * q^65 + 29 * q^67 - 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 - 77 * q^72 + 3 * q^73 - 48 * q^74 + 5 * q^75 + 47 * q^76 + 10 * q^78 - 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 + 9 * q^83 + 15 * q^84 - 5 * q^85 + 25 * q^86 + 23 * q^87 + 59 * q^89 + 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 - 19 * q^94 + 15 * q^95 + 14 * q^96 + 30 * q^97 + 2 * 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 $

$2$	2.77774	1.96416	0.982079	−	0.188470i	$-0.0603528\pi$
$2$	2.77774	1.96416	0.982079	+	0.188470i	$0.0603528\pi$
$3$	−1.15501	−0.666844	−0.333422	−	0.942778i	$-0.608203\pi$
$3$	−1.15501	−0.666844	−0.333422	+	0.942778i	$0.608203\pi$
$4$	5.71583	2.85792
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.20831	−1.30979
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	10.3216	3.64924
$9$	−1.66596	−0.555319
$10$	2.77774	0.878398
$11$	0	0
$11$	0	0
$12$	−6.60184	−1.90579
$13$	4.48271	1.24328	0.621640	−	0.783303i	$-0.286467\pi$
$13$	4.48271	1.24328	0.621640	+	0.783303i	$0.286467\pi$
$14$	2.77774	0.742382
$15$	−1.15501	−0.298222
$16$	17.2391	4.30977
$17$	3.65680	0.886905	0.443452	−	0.896298i	$-0.353754\pi$
$17$	3.65680	0.886905	0.443452	+	0.896298i	$0.353754\pi$
$18$	−4.62759	−1.09073
$19$	1.28546	0.294905	0.147452	−	0.989069i	$-0.452893\pi$
$19$	1.28546	0.294905	0.147452	+	0.989069i	$0.452893\pi$
$20$	5.71583	1.27810
$21$	−1.15501	−0.252043
$22$	0	0
$23$	−6.46047	−1.34710	−0.673551	−	0.739141i	$-0.735232\pi$
$23$	−6.46047	−1.34710	−0.673551	+	0.739141i	$0.735232\pi$
$24$	−11.9216	−2.43348
$25$	1.00000	0.200000
$26$	12.4518	2.44200
$27$	5.38922	1.03716
$28$	5.71583	1.08019
$29$	−1.21204	−0.225070	−0.112535	−	0.993648i	$-0.535897\pi$
$29$	−1.21204	−0.225070	−0.112535	+	0.993648i	$0.535897\pi$
$30$	−3.20831	−0.585755
$31$	−7.51569	−1.34986	−0.674929	−	0.737882i	$-0.735826\pi$
$31$	−7.51569	−1.34986	−0.674929	+	0.737882i	$0.735826\pi$
$32$	27.2424	4.81583
$33$	0	0
$34$	10.1576	1.74202
$35$	1.00000	0.169031
$36$	−9.52232	−1.58705
$37$	−6.29940	−1.03561	−0.517807	−	0.855497i	$-0.673252\pi$
$37$	−6.29940	−1.03561	−0.517807	+	0.855497i	$0.673252\pi$
$38$	3.57067	0.579240
$39$	−5.17757	−0.829074
$40$	10.3216	1.63199
$41$	8.93325	1.39514	0.697569	−	0.716517i	$-0.254265\pi$
$41$	8.93325	1.39514	0.697569	+	0.716517i	$0.254265\pi$
$42$	−3.20831	−0.495053
$43$	2.40712	0.367082	0.183541	−	0.983012i	$-0.441244\pi$
$43$	2.40712	0.367082	0.183541	+	0.983012i	$0.441244\pi$
$44$	0	0
$45$	−1.66596	−0.248346
$46$	−17.9455	−2.64592
$47$	0.468011	0.0682664	0.0341332	−	0.999417i	$-0.489133\pi$
$47$	0.468011	0.0682664	0.0341332	+	0.999417i	$0.489133\pi$
$48$	−19.9113	−2.87395
$49$	1.00000	0.142857
$50$	2.77774	0.392832
$51$	−4.22364	−0.591428
$52$	25.6224	3.55319
$53$	2.47206	0.339563	0.169782	−	0.985482i	$-0.445694\pi$
$53$	2.47206	0.339563	0.169782	+	0.985482i	$0.445694\pi$
$54$	14.9698	2.03714
$55$	0	0
$56$	10.3216	1.37928
$57$	−1.48472	−0.196656
$58$	−3.36673	−0.442074
$59$	−12.1993	−1.58822	−0.794110	−	0.607774i	$-0.792063\pi$
$59$	−12.1993	−1.58822	−0.794110	+	0.607774i	$0.792063\pi$
$60$	−6.60184	−0.852293
$61$	−1.04789	−0.134168	−0.0670840	−	0.997747i	$-0.521370\pi$
$61$	−1.04789	−0.134168	−0.0670840	+	0.997747i	$0.521370\pi$
$62$	−20.8766	−2.65134
$63$	−1.66596	−0.209891
$64$	41.1942	5.14928
$65$	4.48271	0.556012
$66$	0	0
$67$	6.47842	0.791465	0.395732	−	0.918366i	$-0.370491\pi$
$67$	6.47842	0.791465	0.395732	+	0.918366i	$0.370491\pi$
$68$	20.9017	2.53470
$69$	7.46190	0.898307
$70$	2.77774	0.332003
$71$	−9.27952	−1.10128	−0.550638	−	0.834744i	$-0.685616\pi$
$71$	−9.27952	−1.10128	−0.550638	+	0.834744i	$0.685616\pi$
$72$	−17.1953	−2.02649
$73$	2.57523	0.301408	0.150704	−	0.988579i	$-0.451846\pi$
$73$	2.57523	0.301408	0.150704	+	0.988579i	$0.451846\pi$
$74$	−17.4981	−2.03411
$75$	−1.15501	−0.133369
$76$	7.34748	0.842813
$77$	0	0
$78$	−14.3819	−1.62843
$79$	−11.5599	−1.30059	−0.650297	−	0.759680i	$-0.725356\pi$
$79$	−11.5599	−1.30059	−0.650297	+	0.759680i	$0.725356\pi$
$80$	17.2391	1.92739
$81$	−1.22673	−0.136303
$82$	24.8142	2.74027
$83$	10.1307	1.11198	0.555992	−	0.831188i	$-0.312339\pi$
$83$	10.1307	1.11198	0.555992	+	0.831188i	$0.312339\pi$
$84$	−6.60184	−0.720319
$85$	3.65680	0.396636
$86$	6.68635	0.721007
$87$	1.39992	0.150087
$88$	0	0
$89$	15.0783	1.59830	0.799150	−	0.601132i	$-0.205283\pi$
$89$	15.0783	1.59830	0.799150	+	0.601132i	$0.205283\pi$
$90$	−4.62759	−0.487791
$91$	4.48271	0.469916
$92$	−36.9270	−3.84990
$93$	8.68069	0.900146
$94$	1.30001	0.134086
$95$	1.28546	0.131885
$96$	−31.4652	−3.21141
$97$	−3.45073	−0.350369	−0.175184	−	0.984536i	$-0.556052\pi$
$97$	−3.45073	−0.350369	−0.175184	+	0.984536i	$0.556052\pi$
$98$	2.77774	0.280594
$99$	0	0
$100$	5.71583	0.571583
$101$	5.19003	0.516427	0.258213	−	0.966088i	$-0.416866\pi$
$101$	5.19003	0.516427	0.258213	+	0.966088i	$0.416866\pi$
$102$	−11.7322	−1.16166
$103$	12.8387	1.26503	0.632517	−	0.774547i	$-0.282022\pi$
$103$	12.8387	1.26503	0.632517	+	0.774547i	$0.282022\pi$
$104$	46.2688	4.53703
$105$	−1.15501	−0.112717
$106$	6.86673	0.666956
$107$	−2.42799	−0.234723	−0.117361	−	0.993089i	$-0.537444\pi$
$107$	−2.42799	−0.234723	−0.117361	+	0.993089i	$0.537444\pi$
$108$	30.8039	2.96410
$109$	−13.0822	−1.25305	−0.626525	−	0.779401i	$-0.715524\pi$
$109$	−13.0822	−1.25305	−0.626525	+	0.779401i	$0.715524\pi$
$110$	0	0
$111$	7.27586	0.690594
$112$	17.2391	1.62894
$113$	9.19356	0.864858	0.432429	−	0.901668i	$-0.357657\pi$
$113$	9.19356	0.864858	0.432429	+	0.901668i	$0.357657\pi$
$114$	−4.12416	−0.386263
$115$	−6.46047	−0.602442
$116$	−6.92783	−0.643233
$117$	−7.46799	−0.690416
$118$	−33.8866	−3.11951
$119$	3.65680	0.335219
$120$	−11.9216	−1.08828
$121$	0	0
$122$	−2.91075	−0.263527
$123$	−10.3180	−0.930341
$124$	−42.9585	−3.85778
$125$	1.00000	0.0894427
$126$	−4.62759	−0.412258
$127$	−7.73310	−0.686202	−0.343101	−	0.939299i	$-0.611477\pi$
$127$	−7.73310	−0.686202	−0.343101	+	0.939299i	$0.611477\pi$
$128$	59.9419	5.29816
$129$	−2.78024	−0.244787
$130$	12.4518	1.09209
$131$	−6.47417	−0.565651	−0.282825	−	0.959171i	$-0.591272\pi$
$131$	−6.47417	−0.565651	−0.282825	+	0.959171i	$0.591272\pi$
$132$	0	0
$133$	1.28546	0.111464
$134$	17.9954	1.55456
$135$	5.38922	0.463830
$136$	37.7441	3.23653
$137$	−18.6570	−1.59397	−0.796987	−	0.603997i	$-0.793574\pi$
$137$	−18.6570	−1.59397	−0.796987	+	0.603997i	$0.793574\pi$
$138$	20.7272	1.76442
$139$	−2.23616	−0.189668	−0.0948342	−	0.995493i	$-0.530232\pi$
$139$	−2.23616	−0.189668	−0.0948342	+	0.995493i	$0.530232\pi$
$140$	5.71583	0.483076
$141$	−0.540556	−0.0455231
$142$	−25.7761	−2.16308
$143$	0	0
$144$	−28.7195	−2.39330
$145$	−1.21204	−0.100655
$146$	7.15333	0.592014
$147$	−1.15501	−0.0952635
$148$	−36.0063	−2.95970
$149$	12.0490	0.987093	0.493546	−	0.869720i	$-0.335700\pi$
$149$	12.0490	0.987093	0.493546	+	0.869720i	$0.335700\pi$
$150$	−3.20831	−0.261958
$151$	16.5031	1.34300	0.671502	−	0.741003i	$-0.265650\pi$
$151$	16.5031	1.34300	0.671502	+	0.741003i	$0.265650\pi$
$152$	13.2680	1.07618
$153$	−6.09207	−0.492515
$154$	0	0
$155$	−7.51569	−0.603675
$156$	−29.5941	−2.36942
$157$	−14.4338	−1.15195	−0.575973	−	0.817469i	$-0.695377\pi$
$157$	−14.4338	−1.15195	−0.575973	+	0.817469i	$0.695377\pi$
$158$	−32.1105	−2.55457
$159$	−2.85525	−0.226436
$160$	27.2424	2.15370
$161$	−6.46047	−0.509157
$162$	−3.40752	−0.267720
$163$	6.14472	0.481291	0.240646	−	0.970613i	$-0.422641\pi$
$163$	6.14472	0.481291	0.240646	+	0.970613i	$0.422641\pi$
$164$	51.0609	3.98719
$165$	0	0
$166$	28.1403	2.18411
$167$	−4.78841	−0.370538	−0.185269	−	0.982688i	$-0.559316\pi$
$167$	−4.78841	−0.370538	−0.185269	+	0.982688i	$0.559316\pi$
$168$	−11.9216	−0.919768
$169$	7.09468	0.545745
$170$	10.1576	0.779056
$171$	−2.14152	−0.163766
$172$	13.7587	1.04909
$173$	6.41031	0.487367	0.243683	−	0.969855i	$-0.421644\pi$
$173$	6.41031	0.487367	0.243683	+	0.969855i	$0.421644\pi$
$174$	3.88861	0.294794
$175$	1.00000	0.0755929
$176$	0	0
$177$	14.0903	1.05910
$178$	41.8837	3.13931
$179$	−16.8368	−1.25844	−0.629221	−	0.777226i	$-0.716626\pi$
$179$	−16.8368	−1.25844	−0.629221	+	0.777226i	$0.716626\pi$
$180$	−9.52232	−0.709752
$181$	18.1064	1.34584	0.672920	−	0.739715i	$-0.265040\pi$
$181$	18.1064	1.34584	0.672920	+	0.739715i	$0.265040\pi$
$182$	12.4518	0.922988
$183$	1.21032	0.0894692
$184$	−66.6825	−4.91590
$185$	−6.29940	−0.463141
$186$	24.1127	1.76803
$187$	0	0
$188$	2.67507	0.195100
$189$	5.38922	0.392008
$190$	3.57067	0.259044
$191$	−1.71869	−0.124360	−0.0621800	−	0.998065i	$-0.519805\pi$
$191$	−1.71869	−0.124360	−0.0621800	+	0.998065i	$0.519805\pi$
$192$	−47.5797	−3.43377
$193$	−6.81024	−0.490212	−0.245106	−	0.969496i	$-0.578823\pi$
$193$	−6.81024	−0.490212	−0.245106	+	0.969496i	$0.578823\pi$
$194$	−9.58523	−0.688179
$195$	−5.17757	−0.370773
$196$	5.71583	0.408274
$197$	4.38112	0.312142	0.156071	−	0.987746i	$-0.450117\pi$
$197$	4.38112	0.312142	0.156071	+	0.987746i	$0.450117\pi$
$198$	0	0
$199$	−13.7523	−0.974874	−0.487437	−	0.873158i	$-0.662068\pi$
$199$	−13.7523	−0.974874	−0.487437	+	0.873158i	$0.662068\pi$
$200$	10.3216	0.729848
$201$	−7.48263	−0.527784
$202$	14.4165	1.01434
$203$	−1.21204	−0.0850686
$204$	−24.1416	−1.69025
$205$	8.93325	0.623925
$206$	35.6625	2.48473
$207$	10.7629	0.748071
$208$	77.2778	5.35825
$209$	0	0
$210$	−3.20831	−0.221395
$211$	−22.5775	−1.55430	−0.777150	−	0.629315i	$-0.783336\pi$
$211$	−22.5775	−1.55430	−0.777150	+	0.629315i	$0.783336\pi$
$212$	14.1299	0.970443
$213$	10.7179	0.734380
$214$	−6.74432	−0.461032
$215$	2.40712	0.164164
$216$	55.6254	3.78483
$217$	−7.51569	−0.510199
$218$	−36.3390	−2.46119
$219$	−2.97442	−0.200993
$220$	0	0
$221$	16.3924	1.10267
$222$	20.2104	1.35644
$223$	16.0835	1.07703	0.538517	−	0.842615i	$-0.318985\pi$
$223$	16.0835	1.07703	0.538517	+	0.842615i	$0.318985\pi$
$224$	27.2424	1.82021
$225$	−1.66596	−0.111064
$226$	25.5373	1.69872
$227$	−14.0741	−0.934128	−0.467064	−	0.884223i	$-0.654688\pi$
$227$	−14.0741	−0.934128	−0.467064	+	0.884223i	$0.654688\pi$
$228$	−8.48640	−0.562025
$229$	−21.3486	−1.41076	−0.705379	−	0.708830i	$-0.749223\pi$
$229$	−21.3486	−1.41076	−0.705379	+	0.708830i	$0.749223\pi$
$230$	−17.9455	−1.18329
$231$	0	0
$232$	−12.5102	−0.821336
$233$	−16.4117	−1.07517	−0.537584	−	0.843210i	$-0.680663\pi$
$233$	−16.4117	−1.07517	−0.537584	+	0.843210i	$0.680663\pi$
$234$	−20.7441	−1.35609
$235$	0.468011	0.0305297
$236$	−69.7294	−4.53900
$237$	13.3518	0.867294
$238$	10.1576	0.658422
$239$	11.4374	0.739822	0.369911	−	0.929067i	$-0.379388\pi$
$239$	11.4374	0.739822	0.369911	+	0.929067i	$0.379388\pi$
$240$	−19.9113	−1.28527
$241$	−3.22706	−0.207873	−0.103937	−	0.994584i	$-0.533144\pi$
$241$	−3.22706	−0.207873	−0.103937	+	0.994584i	$0.533144\pi$
$242$	0	0
$243$	−14.7508	−0.946263
$244$	−5.98954	−0.383441
$245$	1.00000	0.0638877
$246$	−28.6606	−1.82734
$247$	5.76234	0.366649
$248$	−77.5741	−4.92596
$249$	−11.7010	−0.741520
$250$	2.77774	0.175680
$251$	−18.0848	−1.14150	−0.570751	−	0.821123i	$-0.693348\pi$
$251$	−18.0848	−1.14150	−0.570751	+	0.821123i	$0.693348\pi$
$252$	−9.52232	−0.599850
$253$	0	0
$254$	−21.4805	−1.34781
$255$	−4.22364	−0.264494
$256$	84.1145	5.25716
$257$	−19.2571	−1.20123	−0.600613	−	0.799540i	$-0.705077\pi$
$257$	−19.2571	−1.20123	−0.600613	+	0.799540i	$0.705077\pi$
$258$	−7.72279	−0.480800
$259$	−6.29940	−0.391426
$260$	25.6224	1.58903
$261$	2.01921	0.124986
$262$	−17.9835	−1.11103
$263$	2.77990	0.171416	0.0857079	−	0.996320i	$-0.472685\pi$
$263$	2.77990	0.171416	0.0857079	+	0.996320i	$0.472685\pi$
$264$	0	0
$265$	2.47206	0.151857
$266$	3.57067	0.218932
$267$	−17.4156	−1.06582
$268$	37.0296	2.26194
$269$	−5.63799	−0.343754	−0.171877	−	0.985118i	$-0.554983\pi$
$269$	−5.63799	−0.343754	−0.171877	+	0.985118i	$0.554983\pi$
$270$	14.9698	0.911035
$271$	22.4787	1.36549	0.682743	−	0.730658i	$-0.260787\pi$
$271$	22.4787	1.36549	0.682743	+	0.730658i	$0.260787\pi$
$272$	63.0399	3.82236
$273$	−5.17757	−0.313361
$274$	−51.8242	−3.13082
$275$	0	0
$276$	42.6510	2.56729
$277$	3.31132	0.198958	0.0994791	−	0.995040i	$-0.468282\pi$
$277$	3.31132	0.198958	0.0994791	+	0.995040i	$0.468282\pi$
$278$	−6.21146	−0.372539
$279$	12.5208	0.749601
$280$	10.3216	0.616834
$281$	−19.8458	−1.18390	−0.591951	−	0.805974i	$-0.701642\pi$
$281$	−19.8458	−1.18390	−0.591951	+	0.805974i	$0.701642\pi$
$282$	−1.50152	−0.0894145
$283$	−6.09795	−0.362485	−0.181243	−	0.983438i	$-0.558012\pi$
$283$	−6.09795	−0.362485	−0.181243	+	0.983438i	$0.558012\pi$
$284$	−53.0402	−3.14736
$285$	−1.48472	−0.0879471
$286$	0	0
$287$	8.93325	0.527313
$288$	−45.3847	−2.67432
$289$	−3.62779	−0.213400
$290$	−3.36673	−0.197701
$291$	3.98562	0.233641
$292$	14.7196	0.861400
$293$	−12.8040	−0.748020	−0.374010	−	0.927425i	$-0.622017\pi$
$293$	−12.8040	−0.748020	−0.374010	+	0.927425i	$0.622017\pi$
$294$	−3.20831	−0.187113
$295$	−12.1993	−0.710273
$296$	−65.0199	−3.77921
$297$	0	0
$298$	33.4690	1.93881
$299$	−28.9604	−1.67482
$300$	−6.60184	−0.381157
$301$	2.40712	0.138744
$302$	45.8413	2.63787
$303$	−5.99452	−0.344376
$304$	22.1602	1.27097
$305$	−1.04789	−0.0600017
$306$	−16.9222	−0.967377
$307$	20.7766	1.18578	0.592892	−	0.805282i	$-0.297986\pi$
$307$	20.7766	1.18578	0.592892	+	0.805282i	$0.297986\pi$
$308$	0	0
$309$	−14.8288	−0.843580
$310$	−20.8766	−1.18571
$311$	2.71750	0.154095	0.0770476	−	0.997027i	$-0.475451\pi$
$311$	2.71750	0.154095	0.0770476	+	0.997027i	$0.475451\pi$
$312$	−53.4408	−3.02549
$313$	17.4305	0.985232	0.492616	−	0.870247i	$-0.336041\pi$
$313$	17.4305	0.985232	0.492616	+	0.870247i	$0.336041\pi$
$314$	−40.0934	−2.26260
$315$	−1.66596	−0.0938660
$316$	−66.0747	−3.71699
$317$	−23.6291	−1.32714	−0.663570	−	0.748114i	$-0.730960\pi$
$317$	−23.6291	−1.32714	−0.663570	+	0.748114i	$0.730960\pi$
$318$	−7.93113	−0.444756
$319$	0	0
$320$	41.1942	2.30283
$321$	2.80435	0.156523
$322$	−17.9455	−1.00006
$323$	4.70067	0.261553
$324$	−7.01176	−0.389542
$325$	4.48271	0.248656
$326$	17.0684	0.945332
$327$	15.1101	0.835590
$328$	92.2055	5.09120
$329$	0.468011	0.0258023
$330$	0	0
$331$	−0.849850	−0.0467120	−0.0233560	−	0.999727i	$-0.507435\pi$
$331$	−0.849850	−0.0467120	−0.0233560	+	0.999727i	$0.507435\pi$
$332$	57.9051	3.17796
$333$	10.4945	0.575096
$334$	−13.3010	−0.727796
$335$	6.47842	0.353954
$336$	−19.9113	−1.08625
$337$	−15.6954	−0.854982	−0.427491	−	0.904020i	$-0.640602\pi$
$337$	−15.6954	−0.854982	−0.427491	+	0.904020i	$0.640602\pi$
$338$	19.7072	1.07193
$339$	−10.6186	−0.576726
$340$	20.9017	1.13355
$341$	0	0
$342$	−5.94858	−0.321663
$343$	1.00000	0.0539949
$344$	24.8454	1.33957
$345$	7.46190	0.401735
$346$	17.8062	0.957265
$347$	20.9538	1.12486	0.562429	−	0.826846i	$-0.309867\pi$
$347$	20.9538	1.12486	0.562429	+	0.826846i	$0.309867\pi$
$348$	8.00170	0.428936
$349$	−12.0223	−0.643541	−0.321770	−	0.946818i	$-0.604278\pi$
$349$	−12.0223	−0.643541	−0.321770	+	0.946818i	$0.604278\pi$
$350$	2.77774	0.148476
$351$	24.1583	1.28947
$352$	0	0
$353$	17.6191	0.937769	0.468884	−	0.883260i	$-0.344656\pi$
$353$	17.6191	0.937769	0.468884	+	0.883260i	$0.344656\pi$
$354$	39.1393	2.08023
$355$	−9.27952	−0.492506
$356$	86.1852	4.56781
$357$	−4.22364	−0.223539
$358$	−46.7683	−2.47178
$359$	−18.9537	−1.00034	−0.500170	−	0.865927i	$-0.666729\pi$
$359$	−18.9537	−1.00034	−0.500170	+	0.865927i	$0.666729\pi$
$360$	−17.1953	−0.906275
$361$	−17.3476	−0.913031
$362$	50.2949	2.64344
$363$	0	0
$364$	25.6224	1.34298
$365$	2.57523	0.134794
$366$	3.36194	0.175732
$367$	21.3716	1.11559	0.557794	−	0.829979i	$-0.311648\pi$
$367$	21.3716	1.11559	0.557794	+	0.829979i	$0.311648\pi$
$368$	−111.373	−5.80570
$369$	−14.8824	−0.774746
$370$	−17.4981	−0.909682
$371$	2.47206	0.128343
$372$	49.6174	2.57254
$373$	−5.41272	−0.280260	−0.140130	−	0.990133i	$-0.544752\pi$
$373$	−5.41272	−0.280260	−0.140130	+	0.990133i	$0.544752\pi$
$374$	0	0
$375$	−1.15501	−0.0596444
$376$	4.83063	0.249121
$377$	−5.43323	−0.279826
$378$	14.9698	0.769965
$379$	2.19843	0.112926	0.0564629	−	0.998405i	$-0.482018\pi$
$379$	2.19843	0.112926	0.0564629	+	0.998405i	$0.482018\pi$
$380$	7.34748	0.376918
$381$	8.93180	0.457590
$382$	−4.77407	−0.244263
$383$	−22.6413	−1.15692	−0.578458	−	0.815712i	$-0.696345\pi$
$383$	−22.6413	−1.15692	−0.578458	+	0.815712i	$0.696345\pi$
$384$	−69.2334	−3.53305
$385$	0	0
$386$	−18.9171	−0.962854
$387$	−4.01015	−0.203848
$388$	−19.7238	−1.00132
$389$	16.0607	0.814310	0.407155	−	0.913359i	$-0.366521\pi$
$389$	16.0607	0.814310	0.407155	+	0.913359i	$0.366521\pi$
$390$	−14.3819	−0.728257
$391$	−23.6247	−1.19475
$392$	10.3216	0.521320
$393$	7.47772	0.377201
$394$	12.1696	0.613097
$395$	−11.5599	−0.581644
$396$	0	0
$397$	26.9841	1.35429	0.677146	−	0.735849i	$-0.263216\pi$
$397$	26.9841	1.35429	0.677146	+	0.735849i	$0.263216\pi$
$398$	−38.2003	−1.91481
$399$	−1.48472	−0.0743288
$400$	17.2391	0.861954
$401$	9.23112	0.460980	0.230490	−	0.973075i	$-0.425967\pi$
$401$	9.23112	0.460980	0.230490	+	0.973075i	$0.425967\pi$
$402$	−20.7848	−1.03665
$403$	−33.6907	−1.67825
$404$	29.6653	1.47590
$405$	−1.22673	−0.0609565
$406$	−3.36673	−0.167088
$407$	0	0
$408$	−43.5948	−2.15826
$409$	16.6243	0.822019	0.411009	−	0.911631i	$-0.365176\pi$
$409$	16.6243	0.822019	0.411009	+	0.911631i	$0.365176\pi$
$410$	24.8142	1.22549
$411$	21.5490	1.06293
$412$	73.3838	3.61536
$413$	−12.1993	−0.600291
$414$	29.8964	1.46933
$415$	10.1307	0.497294
$416$	122.120	5.98742
$417$	2.58278	0.126479
$418$	0	0
$419$	−16.4519	−0.803729	−0.401865	−	0.915699i	$-0.631638\pi$
$419$	−16.4519	−0.803729	−0.401865	+	0.915699i	$0.631638\pi$
$420$	−6.60184	−0.322137
$421$	12.4863	0.608544	0.304272	−	0.952585i	$-0.401587\pi$
$421$	12.4863	0.608544	0.304272	+	0.952585i	$0.401587\pi$
$422$	−62.7145	−3.05289
$423$	−0.779685	−0.0379096
$424$	25.5156	1.23915
$425$	3.65680	0.177381
$426$	29.7716	1.44244
$427$	−1.04789	−0.0507107
$428$	−13.8780	−0.670818
$429$	0	0
$430$	6.68635	0.322444
$431$	−0.590022	−0.0284204	−0.0142102	−	0.999899i	$-0.504523\pi$
$431$	−0.590022	−0.0284204	−0.0142102	+	0.999899i	$0.504523\pi$
$432$	92.9052	4.46990
$433$	−14.8634	−0.714290	−0.357145	−	0.934049i	$-0.616250\pi$
$433$	−14.8634	−0.714290	−0.357145	+	0.934049i	$0.616250\pi$
$434$	−20.8766	−1.00211
$435$	1.39992	0.0671209
$436$	−74.7759	−3.58111
$437$	−8.30468	−0.397267
$438$	−8.26216	−0.394781
$439$	−18.3667	−0.876597	−0.438298	−	0.898830i	$-0.644419\pi$
$439$	−18.3667	−0.876597	−0.438298	+	0.898830i	$0.644419\pi$
$440$	0	0
$441$	−1.66596	−0.0793312
$442$	45.5338	2.16582
$443$	−7.22772	−0.343399	−0.171700	−	0.985149i	$-0.554926\pi$
$443$	−7.22772	−0.343399	−0.171700	+	0.985149i	$0.554926\pi$
$444$	41.5876	1.97366
$445$	15.0783	0.714782
$446$	44.6759	2.11546
$447$	−13.9167	−0.658237
$448$	41.1942	1.94624
$449$	32.3983	1.52897	0.764484	−	0.644642i	$-0.222994\pi$
$449$	32.3983	1.52897	0.764484	+	0.644642i	$0.222994\pi$
$450$	−4.62759	−0.218147
$451$	0	0
$452$	52.5489	2.47169
$453$	−19.0612	−0.895574
$454$	−39.0941	−1.83478
$455$	4.48271	0.210153
$456$	−15.3247	−0.717644
$457$	−5.62053	−0.262917	−0.131459	−	0.991322i	$-0.541966\pi$
$457$	−5.62053	−0.262917	−0.131459	+	0.991322i	$0.541966\pi$
$458$	−59.3009	−2.77095
$459$	19.7073	0.919858
$460$	−36.9270	−1.72173
$461$	−13.3557	−0.622039	−0.311019	−	0.950404i	$-0.600670\pi$
$461$	−13.3557	−0.622039	−0.311019	+	0.950404i	$0.600670\pi$
$462$	0	0
$463$	9.36407	0.435185	0.217593	−	0.976040i	$-0.430180\pi$
$463$	9.36407	0.435185	0.217593	+	0.976040i	$0.430180\pi$
$464$	−20.8945	−0.970002
$465$	8.68069	0.402557
$466$	−45.5875	−2.11180
$467$	−43.1231	−1.99550	−0.997750	−	0.0670399i	$-0.978645\pi$
$467$	−43.1231	−1.99550	−0.997750	+	0.0670399i	$0.978645\pi$
$468$	−42.6858	−1.97315
$469$	6.47842	0.299146
$470$	1.30001	0.0599651
$471$	16.6712	0.768169
$472$	−125.917	−5.79580
$473$	0	0
$474$	37.0879	1.70350
$475$	1.28546	0.0589810
$476$	20.9017	0.958027
$477$	−4.11834	−0.188566
$478$	31.7700	1.45313
$479$	9.85294	0.450192	0.225096	−	0.974337i	$-0.427730\pi$
$479$	9.85294	0.450192	0.225096	+	0.974337i	$0.427730\pi$
$480$	−31.4652	−1.43619
$481$	−28.2384	−1.28756
$482$	−8.96392	−0.408296
$483$	7.46190	0.339528
$484$	0	0
$485$	−3.45073	−0.156690
$486$	−40.9738	−1.85861
$487$	17.3140	0.784573	0.392286	−	0.919843i	$-0.371684\pi$
$487$	17.3140	0.784573	0.392286	+	0.919843i	$0.371684\pi$
$488$	−10.8159	−0.489611
$489$	−7.09720	−0.320946
$490$	2.77774	0.125485
$491$	−21.1368	−0.953892	−0.476946	−	0.878933i	$-0.658256\pi$
$491$	−21.1368	−0.953892	−0.476946	+	0.878933i	$0.658256\pi$
$492$	−58.9758	−2.65884
$493$	−4.43220	−0.199616
$494$	16.0063	0.720157
$495$	0	0
$496$	−129.564	−5.81758
$497$	−9.27952	−0.416243
$498$	−32.5023	−1.45646
$499$	−31.9991	−1.43247	−0.716237	−	0.697857i	$-0.754137\pi$
$499$	−31.9991	−1.43247	−0.716237	+	0.697857i	$0.754137\pi$
$500$	5.71583	0.255620
$501$	5.53065	0.247091
$502$	−50.2348	−2.24209
$503$	−35.1104	−1.56550	−0.782749	−	0.622338i	$-0.786183\pi$
$503$	−35.1104	−1.56550	−0.782749	+	0.622338i	$0.786183\pi$
$504$	−17.1953	−0.765942
$505$	5.19003	0.230953
$506$	0	0
$507$	−8.19442	−0.363927
$508$	−44.2011	−1.96111
$509$	38.5427	1.70838	0.854188	−	0.519965i	$-0.174055\pi$
$509$	38.5427	1.70838	0.854188	+	0.519965i	$0.174055\pi$
$510$	−11.7322	−0.519509
$511$	2.57523	0.113922
$512$	113.764	5.02772
$513$	6.92763	0.305862
$514$	−53.4913	−2.35940
$515$	12.8387	0.565740
$516$	−15.8914	−0.699580
$517$	0	0
$518$	−17.4981	−0.768822
$519$	−7.40396	−0.324998
$520$	46.2688	2.02902
$521$	27.9605	1.22497	0.612486	−	0.790482i	$-0.290170\pi$
$521$	27.9605	1.22497	0.612486	+	0.790482i	$0.290170\pi$
$522$	5.60883	0.245492
$523$	−11.7430	−0.513487	−0.256743	−	0.966480i	$-0.582650\pi$
$523$	−11.7430	−0.513487	−0.256743	+	0.966480i	$0.582650\pi$
$524$	−37.0053	−1.61658
$525$	−1.15501	−0.0504087
$526$	7.72183	0.336688
$527$	−27.4834	−1.19720
$528$	0	0
$529$	18.7377	0.814683
$530$	6.86673	0.298272
$531$	20.3236	0.881968
$532$	7.34748	0.318554
$533$	40.0451	1.73455
$534$	−48.3760	−2.09343
$535$	−2.42799	−0.104971
$536$	66.8677	2.88825
$537$	19.4467	0.839185
$538$	−15.6609	−0.675188
$539$	0	0
$540$	30.8039	1.32559
$541$	−1.93772	−0.0833089	−0.0416545	−	0.999132i	$-0.513263\pi$
$541$	−1.93772	−0.0833089	−0.0416545	+	0.999132i	$0.513263\pi$
$542$	62.4401	2.68203
$543$	−20.9131	−0.897466
$544$	99.6202	4.27118
$545$	−13.0822	−0.560381
$546$	−14.3819	−0.615490
$547$	37.7431	1.61378	0.806889	−	0.590703i	$-0.201150\pi$
$547$	37.7431	1.61378	0.806889	+	0.590703i	$0.201150\pi$
$548$	−106.640	−4.55544
$549$	1.74573	0.0745060
$550$	0	0
$551$	−1.55803	−0.0663744
$552$	77.0189	3.27814
$553$	−11.5599	−0.491579
$554$	9.19799	0.390785
$555$	7.27586	0.308843
$556$	−12.7815	−0.542057
$557$	41.8875	1.77483	0.887415	−	0.460971i	$-0.152499\pi$
$557$	41.8875	1.77483	0.887415	+	0.460971i	$0.152499\pi$
$558$	34.7795	1.47234
$559$	10.7904	0.456386
$560$	17.2391	0.728484
$561$	0	0
$562$	−55.1264	−2.32537
$563$	−31.0293	−1.30773	−0.653864	−	0.756612i	$-0.726853\pi$
$563$	−31.0293	−1.30773	−0.653864	+	0.756612i	$0.726853\pi$
$564$	−3.08973	−0.130101
$565$	9.19356	0.386776
$566$	−16.9385	−0.711978
$567$	−1.22673	−0.0515176
$568$	−95.7796	−4.01882
$569$	16.2684	0.682008	0.341004	−	0.940062i	$-0.389233\pi$
$569$	16.2684	0.682008	0.341004	+	0.940062i	$0.389233\pi$
$570$	−4.12416	−0.172742
$571$	22.6531	0.948004	0.474002	−	0.880524i	$-0.342809\pi$
$571$	22.6531	0.948004	0.474002	+	0.880524i	$0.342809\pi$
$572$	0	0
$573$	1.98510	0.0829288
$574$	24.8142	1.03573
$575$	−6.46047	−0.269420
$576$	−68.6277	−2.85949
$577$	−37.3118	−1.55331	−0.776656	−	0.629925i	$-0.783085\pi$
$577$	−37.3118	−1.55331	−0.776656	+	0.629925i	$0.783085\pi$
$578$	−10.0771	−0.419151
$579$	7.86589	0.326895
$580$	−6.92783	−0.287662
$581$	10.1307	0.420290
$582$	11.0710	0.458909
$583$	0	0
$584$	26.5806	1.09991
$585$	−7.46799	−0.308764
$586$	−35.5663	−1.46923
$587$	−2.97792	−0.122912	−0.0614560	−	0.998110i	$-0.519574\pi$
$587$	−2.97792	−0.122912	−0.0614560	+	0.998110i	$0.519574\pi$
$588$	−6.60184	−0.272255
$589$	−9.66113	−0.398080
$590$	−33.8866	−1.39509
$591$	−5.06024	−0.208150
$592$	−108.596	−4.46326
$593$	−18.4497	−0.757637	−0.378818	−	0.925471i	$-0.623669\pi$
$593$	−18.4497	−0.757637	−0.378818	+	0.925471i	$0.623669\pi$
$594$	0	0
$595$	3.65680	0.149914
$596$	68.8701	2.82103
$597$	15.8840	0.650089
$598$	−80.4445	−3.28962
$599$	−23.0293	−0.940953	−0.470477	−	0.882413i	$-0.655918\pi$
$599$	−23.0293	−0.940953	−0.470477	+	0.882413i	$0.655918\pi$
$600$	−11.9216	−0.486695
$601$	33.0156	1.34674	0.673368	−	0.739308i	$-0.264847\pi$
$601$	33.0156	1.34674	0.673368	+	0.739308i	$0.264847\pi$
$602$	6.68635	0.272515
$603$	−10.7928	−0.439515
$604$	94.3290	3.83819
$605$	0	0
$606$	−16.6512	−0.676410
$607$	13.8037	0.560275	0.280137	−	0.959960i	$-0.409620\pi$
$607$	13.8037	0.560275	0.280137	+	0.959960i	$0.409620\pi$
$608$	35.0191	1.42021
$609$	1.39992	0.0567275
$610$	−2.91075	−0.117853
$611$	2.09796	0.0848742
$612$	−34.8213	−1.40757
$613$	−9.18783	−0.371093	−0.185546	−	0.982635i	$-0.559406\pi$
$613$	−9.18783	−0.371093	−0.185546	+	0.982635i	$0.559406\pi$
$614$	57.7120	2.32907
$615$	−10.3180	−0.416061
$616$	0	0
$617$	11.1177	0.447581	0.223791	−	0.974637i	$-0.428157\pi$
$617$	11.1177	0.447581	0.223791	+	0.974637i	$0.428157\pi$
$618$	−41.1905	−1.65693
$619$	−30.9979	−1.24591	−0.622956	−	0.782257i	$-0.714068\pi$
$619$	−30.9979	−1.24591	−0.622956	+	0.782257i	$0.714068\pi$
$620$	−42.9585	−1.72525
$621$	−34.8169	−1.39715
$622$	7.54850	0.302667
$623$	15.0783	0.604101
$624$	−89.2565	−3.57312
$625$	1.00000	0.0400000
$626$	48.4175	1.93515
$627$	0	0
$628$	−82.5014	−3.29217
$629$	−23.0357	−0.918492
$630$	−4.62759	−0.184368
$631$	41.9537	1.67015	0.835074	−	0.550137i	$-0.185424\pi$
$631$	41.9537	1.67015	0.835074	+	0.550137i	$0.185424\pi$
$632$	−119.317	−4.74618
$633$	26.0772	1.03648
$634$	−65.6354	−2.60671
$635$	−7.73310	−0.306879
$636$	−16.3201	−0.647135
$637$	4.48271	0.177611
$638$	0	0
$639$	15.4593	0.611559
$640$	59.9419	2.36941
$641$	−18.7682	−0.741301	−0.370651	−	0.928772i	$-0.620865\pi$
$641$	−18.7682	−0.741301	−0.370651	+	0.928772i	$0.620865\pi$
$642$	7.78975	0.307437
$643$	13.0459	0.514479	0.257240	−	0.966348i	$-0.417187\pi$
$643$	13.0459	0.514479	0.257240	+	0.966348i	$0.417187\pi$
$644$	−36.9270	−1.45513
$645$	−2.78024	−0.109472
$646$	13.0572	0.513730
$647$	−24.7499	−0.973020	−0.486510	−	0.873675i	$-0.661730\pi$
$647$	−24.7499	−0.973020	−0.486510	+	0.873675i	$0.661730\pi$
$648$	−12.6618	−0.497402
$649$	0	0
$650$	12.4518	0.488400
$651$	8.68069	0.340223
$652$	35.1222	1.37549
$653$	1.30049	0.0508920	0.0254460	−	0.999676i	$-0.491899\pi$
$653$	1.30049	0.0508920	0.0254460	+	0.999676i	$0.491899\pi$
$654$	41.9719	1.64123
$655$	−6.47417	−0.252967
$656$	154.001	6.01273
$657$	−4.29023	−0.167378
$658$	1.30001	0.0506797
$659$	29.0445	1.13141	0.565707	−	0.824606i	$-0.308603\pi$
$659$	29.0445	1.13141	0.565707	+	0.824606i	$0.308603\pi$
$660$	0	0
$661$	10.0945	0.392632	0.196316	−	0.980541i	$-0.437102\pi$
$661$	10.0945	0.392632	0.196316	+	0.980541i	$0.437102\pi$
$662$	−2.36066	−0.0917497
$663$	−18.9333	−0.735310
$664$	104.565	4.05790
$665$	1.28546	0.0498480
$666$	29.1510	1.12958
$667$	7.83036	0.303193
$668$	−27.3698	−1.05897
$669$	−18.5766	−0.718214
$670$	17.9954	0.695221
$671$	0	0
$672$	−31.4652	−1.21380
$673$	−32.2658	−1.24376	−0.621878	−	0.783114i	$-0.713630\pi$
$673$	−32.2658	−1.24376	−0.621878	+	0.783114i	$0.713630\pi$
$674$	−43.5977	−1.67932
$675$	5.38922	0.207431
$676$	40.5520	1.55969
$677$	−31.1548	−1.19738	−0.598688	−	0.800982i	$-0.704311\pi$
$677$	−31.1548	−1.19738	−0.598688	+	0.800982i	$0.704311\pi$
$678$	−29.4958	−1.13278
$679$	−3.45073	−0.132427
$680$	37.7441	1.44742
$681$	16.2557	0.622918
$682$	0	0
$683$	18.4863	0.707358	0.353679	−	0.935367i	$-0.384930\pi$
$683$	18.4863	0.707358	0.353679	+	0.935367i	$0.384930\pi$
$684$	−12.2406	−0.468030
$685$	−18.6570	−0.712847
$686$	2.77774	0.106055
$687$	24.6579	0.940756
$688$	41.4965	1.58204
$689$	11.0815	0.422172
$690$	20.7272	0.789071
$691$	−17.0730	−0.649487	−0.324743	−	0.945802i	$-0.605278\pi$
$691$	−17.0730	−0.649487	−0.324743	+	0.945802i	$0.605278\pi$
$692$	36.6403	1.39285
$693$	0	0
$694$	58.2041	2.20940
$695$	−2.23616	−0.0848223
$696$	14.4494	0.547704
$697$	32.6671	1.23736
$698$	−33.3949	−1.26402
$699$	18.9557	0.716970
$700$	5.71583	0.216038
$701$	−6.95205	−0.262575	−0.131288	−	0.991344i	$-0.541911\pi$
$701$	−6.95205	−0.262575	−0.131288	+	0.991344i	$0.541911\pi$
$702$	67.1054	2.53273
$703$	−8.09763	−0.305408
$704$	0	0
$705$	−0.540556	−0.0203585
$706$	48.9412	1.84193
$707$	5.19003	0.195191
$708$	80.5381	3.02681
$709$	16.0259	0.601864	0.300932	−	0.953646i	$-0.402702\pi$
$709$	16.0259	0.601864	0.300932	+	0.953646i	$0.402702\pi$
$710$	−25.7761	−0.967359
$711$	19.2583	0.722244
$712$	155.633	5.83258
$713$	48.5549	1.81840
$714$	−11.7322	−0.439065
$715$	0	0
$716$	−96.2364	−3.59652
$717$	−13.2103	−0.493346
$718$	−52.6486	−1.96483
$719$	−21.1638	−0.789275	−0.394637	−	0.918837i	$-0.629130\pi$
$719$	−21.1638	−0.789275	−0.394637	+	0.918837i	$0.629130\pi$
$720$	−28.7195	−1.07031
$721$	12.8387	0.478138
$722$	−48.1871	−1.79334
$723$	3.72728	0.138619
$724$	103.493	3.84630
$725$	−1.21204	−0.0450141
$726$	0	0
$727$	10.0732	0.373593	0.186796	−	0.982399i	$-0.440190\pi$
$727$	10.0732	0.373593	0.186796	+	0.982399i	$0.440190\pi$
$728$	46.2688	1.71484
$729$	20.7174	0.767313
$730$	7.15333	0.264757
$731$	8.80236	0.325567
$732$	6.91797	0.255695
$733$	−1.52717	−0.0564074	−0.0282037	−	0.999602i	$-0.508979\pi$
$733$	−1.52717	−0.0564074	−0.0282037	+	0.999602i	$0.508979\pi$
$734$	59.3647	2.19119
$735$	−1.15501	−0.0426031
$736$	−175.999	−6.48741
$737$	0	0
$738$	−41.3394	−1.52172
$739$	−31.6718	−1.16507	−0.582534	−	0.812807i	$-0.697939\pi$
$739$	−31.6718	−1.16507	−0.582534	+	0.812807i	$0.697939\pi$
$740$	−36.0063	−1.32362
$741$	−6.65556	−0.244498
$742$	6.86673	0.252086
$743$	26.1445	0.959150	0.479575	−	0.877501i	$-0.340791\pi$
$743$	26.1445	0.959150	0.479575	+	0.877501i	$0.340791\pi$
$744$	89.5987	3.28485
$745$	12.0490	0.441441
$746$	−15.0351	−0.550475
$747$	−16.8772	−0.617505
$748$	0	0
$749$	−2.42799	−0.0887168
$750$	−3.20831	−0.117151
$751$	48.6352	1.77472	0.887362	−	0.461074i	$-0.152536\pi$
$751$	48.6352	1.77472	0.887362	+	0.461074i	$0.152536\pi$
$752$	8.06807	0.294212
$753$	20.8881	0.761204
$754$	−15.0921	−0.549622
$755$	16.5031	0.600609
$756$	30.8039	1.12033
$757$	24.2801	0.882476	0.441238	−	0.897390i	$-0.354539\pi$
$757$	24.2801	0.882476	0.441238	+	0.897390i	$0.354539\pi$
$758$	6.10666	0.221804
$759$	0	0
$760$	13.2680	0.481282
$761$	46.5334	1.68683	0.843417	−	0.537260i	$-0.180541\pi$
$761$	46.5334	1.68683	0.843417	+	0.537260i	$0.180541\pi$
$762$	24.8102	0.898779
$763$	−13.0822	−0.473609
$764$	−9.82374	−0.355410
$765$	−6.09207	−0.220259
$766$	−62.8915	−2.27236
$767$	−54.6861	−1.97460
$768$	−97.1529	−3.50570
$769$	18.6950	0.674158	0.337079	−	0.941476i	$-0.390561\pi$
$769$	18.6950	0.674158	0.337079	+	0.941476i	$0.390561\pi$
$770$	0	0
$771$	22.2421	0.801031
$772$	−38.9262	−1.40098
$773$	−52.3469	−1.88279	−0.941393	−	0.337311i	$-0.890483\pi$
$773$	−52.3469	−1.88279	−0.941393	+	0.337311i	$0.890483\pi$
$774$	−11.1392	−0.400389
$775$	−7.51569	−0.269972
$776$	−35.6171	−1.27858
$777$	7.27586	0.261020
$778$	44.6124	1.59943
$779$	11.4833	0.411433
$780$	−29.5941	−1.05964
$781$	0	0
$782$	−65.6232	−2.34668
$783$	−6.53196	−0.233433
$784$	17.2391	0.615681
$785$	−14.4338	−0.515166
$786$	20.7711	0.740882
$787$	−23.1462	−0.825074	−0.412537	−	0.910941i	$-0.635357\pi$
$787$	−23.1462	−0.825074	−0.412537	+	0.910941i	$0.635357\pi$
$788$	25.0418	0.892076
$789$	−3.21080	−0.114308
$790$	−32.1105	−1.14244
$791$	9.19356	0.326886
$792$	0	0
$793$	−4.69736	−0.166808
$794$	74.9547	2.66004
$795$	−2.85525	−0.101265
$796$	−78.6058	−2.78611
$797$	11.9648	0.423815	0.211908	−	0.977290i	$-0.432032\pi$
$797$	11.9648	0.423815	0.211908	+	0.977290i	$0.432032\pi$
$798$	−4.12416	−0.145994
$799$	1.71142	0.0605458
$800$	27.2424	0.963166
$801$	−25.1198	−0.887566
$802$	25.6416	0.905438
$803$	0	0
$804$	−42.7694	−1.50836
$805$	−6.46047	−0.227702
$806$	−93.5839	−3.29635
$807$	6.51193	0.229231
$808$	53.5694	1.88457
$809$	−41.8229	−1.47042	−0.735208	−	0.677841i	$-0.762916\pi$
$809$	−41.8229	−1.47042	−0.735208	+	0.677841i	$0.762916\pi$
$810$	−3.40752	−0.119728
$811$	47.5831	1.67087	0.835434	−	0.549591i	$-0.185216\pi$
$811$	47.5831	1.67087	0.835434	+	0.549591i	$0.185216\pi$
$812$	−6.92783	−0.243119
$813$	−25.9631	−0.910567
$814$	0	0
$815$	6.14472	0.215240
$816$	−72.8116	−2.54892
$817$	3.09426	0.108254
$818$	46.1780	1.61457
$819$	−7.46799	−0.260953
$820$	51.0609	1.78313
$821$	−49.8550	−1.73995	−0.869976	−	0.493094i	$-0.835866\pi$
$821$	−49.8550	−1.73995	−0.869976	+	0.493094i	$0.835866\pi$
$822$	59.8574	2.08777
$823$	−7.34630	−0.256076	−0.128038	−	0.991769i	$-0.540868\pi$
$823$	−7.34630	−0.256076	−0.128038	+	0.991769i	$0.540868\pi$
$824$	132.516	4.61641
$825$	0	0
$826$	−33.8866	−1.17907
$827$	−31.3151	−1.08893	−0.544466	−	0.838783i	$-0.683268\pi$
$827$	−31.3151	−1.08893	−0.544466	+	0.838783i	$0.683268\pi$
$828$	61.5187	2.13792
$829$	32.9839	1.14558	0.572789	−	0.819703i	$-0.305862\pi$
$829$	32.9839	1.14558	0.572789	+	0.819703i	$0.305862\pi$
$830$	28.1403	0.976764
$831$	−3.82461	−0.132674
$832$	184.662	6.40199
$833$	3.65680	0.126701
$834$	7.17429	0.248425
$835$	−4.78841	−0.165710
$836$	0	0
$837$	−40.5037	−1.40001
$838$	−45.6992	−1.57865
$839$	20.4414	0.705714	0.352857	−	0.935677i	$-0.385210\pi$
$839$	20.4414	0.705714	0.352857	+	0.935677i	$0.385210\pi$
$840$	−11.9216	−0.411333
$841$	−27.5310	−0.949343
$842$	34.6836	1.19528
$843$	22.9221	0.789478
$844$	−129.049	−4.44206
$845$	7.09468	0.244064
$846$	−2.16576	−0.0744604
$847$	0	0
$848$	42.6160	1.46344
$849$	7.04318	0.241721
$850$	10.1576	0.348404
$851$	40.6971	1.39508
$852$	61.2618	2.09880
$853$	−7.73950	−0.264995	−0.132498	−	0.991183i	$-0.542300\pi$
$853$	−7.73950	−0.264995	−0.132498	+	0.991183i	$0.542300\pi$
$854$	−2.91075	−0.0996039
$855$	−2.14152	−0.0732384
$856$	−25.0608	−0.856559
$857$	−31.7584	−1.08484	−0.542422	−	0.840106i	$-0.682493\pi$
$857$	−31.7584	−1.08484	−0.542422	+	0.840106i	$0.682493\pi$
$858$	0	0
$859$	−20.8053	−0.709867	−0.354933	−	0.934892i	$-0.615496\pi$
$859$	−20.8053	−0.709867	−0.354933	+	0.934892i	$0.615496\pi$
$860$	13.7587	0.469167
$861$	−10.3180	−0.351636
$862$	−1.63893	−0.0558221
$863$	3.96961	0.135127	0.0675636	−	0.997715i	$-0.478477\pi$
$863$	3.96961	0.135127	0.0675636	+	0.997715i	$0.478477\pi$
$864$	146.815	4.99476
$865$	6.41031	0.217957
$866$	−41.2867	−1.40298
$867$	4.19013	0.142304
$868$	−42.9585	−1.45810
$869$	0	0
$870$	3.88861	0.131836
$871$	29.0409	0.984012
$872$	−135.030	−4.57268
$873$	5.74876	0.194566
$874$	−23.0682	−0.780295
$875$	1.00000	0.0338062
$876$	−17.0013	−0.574420
$877$	7.62758	0.257565	0.128783	−	0.991673i	$-0.458893\pi$
$877$	7.62758	0.257565	0.128783	+	0.991673i	$0.458893\pi$
$878$	−51.0180	−1.72177
$879$	14.7888	0.498813
$880$	0	0
$881$	47.7079	1.60732	0.803660	−	0.595089i	$-0.202883\pi$
$881$	47.7079	1.60732	0.803660	+	0.595089i	$0.202883\pi$
$882$	−4.62759	−0.155819
$883$	56.2403	1.89264	0.946318	−	0.323238i	$-0.104772\pi$
$883$	56.2403	1.89264	0.946318	+	0.323238i	$0.104772\pi$
$884$	93.6961	3.15134
$885$	14.0903	0.473642
$886$	−20.0767	−0.674491
$887$	−15.8480	−0.532123	−0.266061	−	0.963956i	$-0.585722\pi$
$887$	−15.8480	−0.532123	−0.266061	+	0.963956i	$0.585722\pi$
$888$	75.0986	2.52014
$889$	−7.73310	−0.259360
$890$	41.8837	1.40394
$891$	0	0
$892$	91.9308	3.07807
$893$	0.601609	0.0201321
$894$	−38.6570	−1.29288
$895$	−16.8368	−0.562792
$896$	59.9419	2.00252
$897$	33.4495	1.11685
$898$	89.9939	3.00314
$899$	9.10933	0.303813
$900$	−9.52232	−0.317411
$901$	9.03983	0.301160
$902$	0	0
$903$	−2.78024	−0.0925207
$904$	94.8924	3.15607
$905$	18.1064	0.601878
$906$	−52.9471	−1.75905
$907$	−49.8742	−1.65605	−0.828023	−	0.560694i	$-0.810535\pi$
$907$	−49.8742	−1.65605	−0.828023	+	0.560694i	$0.810535\pi$
$908$	−80.4450	−2.66966
$909$	−8.64635	−0.286781
$910$	12.4518	0.412773
$911$	−21.2736	−0.704827	−0.352413	−	0.935844i	$-0.614639\pi$
$911$	−21.2736	−0.704827	−0.352413	+	0.935844i	$0.614639\pi$
$912$	−25.5952	−0.847541
$913$	0	0
$914$	−15.6124	−0.516411
$915$	1.21032	0.0400118
$916$	−122.025	−4.03183
$917$	−6.47417	−0.213796
$918$	54.7417	1.80675
$919$	−27.2864	−0.900096	−0.450048	−	0.893004i	$-0.648593\pi$
$919$	−27.2864	−0.900096	−0.450048	+	0.893004i	$0.648593\pi$
$920$	−66.6825	−2.19846
$921$	−23.9972	−0.790734
$922$	−37.0988	−1.22178
$923$	−41.5974	−1.36919
$924$	0	0
$925$	−6.29940	−0.207123
$926$	26.0109	0.854772
$927$	−21.3887	−0.702497
$928$	−33.0190	−1.08390
$929$	−4.03316	−0.132324	−0.0661619	−	0.997809i	$-0.521075\pi$
$929$	−4.03316	−0.132324	−0.0661619	+	0.997809i	$0.521075\pi$
$930$	24.1127	0.790686
$931$	1.28546	0.0421293
$932$	−93.8068	−3.07274
$933$	−3.13873	−0.102758
$934$	−119.785	−3.91948
$935$	0	0
$936$	−77.0817	−2.51950
$937$	−33.0733	−1.08046	−0.540229	−	0.841518i	$-0.681662\pi$
$937$	−33.0733	−1.08046	−0.540229	+	0.841518i	$0.681662\pi$
$938$	17.9954	0.587569
$939$	−20.1324	−0.656996
$940$	2.67507	0.0872512
$941$	32.2377	1.05092	0.525460	−	0.850818i	$-0.323893\pi$
$941$	32.2377	1.05092	0.525460	+	0.850818i	$0.323893\pi$
$942$	46.3083	1.50880
$943$	−57.7130	−1.87939
$944$	−210.306	−6.84486
$945$	5.38922	0.175311
$946$	0	0
$947$	19.6501	0.638544	0.319272	−	0.947663i	$-0.396562\pi$
$947$	19.6501	0.638544	0.319272	+	0.947663i	$0.396562\pi$
$948$	76.3168	2.47866
$949$	11.5440	0.374735
$950$	3.57067	0.115848
$951$	27.2918	0.884996
$952$	37.7441	1.22329
$953$	28.1115	0.910620	0.455310	−	0.890333i	$-0.349528\pi$
$953$	28.1115	0.910620	0.455310	+	0.890333i	$0.349528\pi$
$954$	−11.4397	−0.370373
$955$	−1.71869	−0.0556155
$956$	65.3741	2.11435
$957$	0	0
$958$	27.3689	0.884249
$959$	−18.6570	−0.602465
$960$	−47.5797	−1.53563
$961$	25.4857	0.822118
$962$	−78.4388	−2.52897
$963$	4.04492	0.130346
$964$	−18.4453	−0.594084
$965$	−6.81024	−0.219229
$966$	20.7272	0.666887
$967$	10.1349	0.325916	0.162958	−	0.986633i	$-0.447896\pi$
$967$	10.1349	0.325916	0.162958	+	0.986633i	$0.447896\pi$
$968$	0	0
$969$	−5.42932	−0.174415
$970$	−9.58523	−0.307763
$971$	−20.0004	−0.641843	−0.320921	−	0.947106i	$-0.603993\pi$
$971$	−20.0004	−0.641843	−0.320921	+	0.947106i	$0.603993\pi$
$972$	−84.3130	−2.70434
$973$	−2.23616	−0.0716879
$974$	48.0938	1.54103
$975$	−5.17757	−0.165815
$976$	−18.0646	−0.578233
$977$	−6.52831	−0.208859	−0.104430	−	0.994532i	$-0.533302\pi$
$977$	−6.52831	−0.208859	−0.104430	+	0.994532i	$0.533302\pi$
$978$	−19.7142	−0.630389
$979$	0	0
$980$	5.71583	0.182586
$981$	21.7944	0.695842
$982$	−58.7126	−1.87360
$983$	−21.9801	−0.701057	−0.350528	−	0.936552i	$-0.613998\pi$
$983$	−21.9801	−0.701057	−0.350528	+	0.936552i	$0.613998\pi$
$984$	−106.498	−3.39504
$985$	4.38112	0.139594
$986$	−12.3115	−0.392078
$987$	−0.540556	−0.0172061
$988$	32.9366	1.04785
$989$	−15.5511	−0.494497
$990$	0	0
$991$	11.2873	0.358552	0.179276	−	0.983799i	$-0.442625\pi$
$991$	11.2873	0.358552	0.179276	+	0.983799i	$0.442625\pi$
$992$	−204.746	−6.50069
$993$	0.981584	0.0311496
$994$	−25.7761	−0.817567
$995$	−13.7523	−0.435977
$996$	−66.8809	−2.11920
$997$	−7.70229	−0.243934	−0.121967	−	0.992534i	$-0.538920\pi$
$997$	−7.70229	−0.243934	−0.121967	+	0.992534i	$0.538920\pi$
$998$	−88.8850	−2.81361
$999$	−33.9488	−1.07409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bp.1.18		18
11.7	odd	10		385.2.n.f.71.1	✓	36
11.8	odd	10		385.2.n.f.141.1	yes	36
11.10	odd	2		4235.2.a.bo.1.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.71.1	✓	36	11.7	odd	10
385.2.n.f.141.1	yes	36	11.8	odd	10
4235.2.a.bo.1.1		18	11.10	odd	2
4235.2.a.bp.1.18		18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+2.77774 q^{2} -1.15501 q^{3} +5.71583 q^{4} +1.00000 q^{5} -3.20831 q^{6} +1.00000 q^{7} +10.3216 q^{8} -1.66596 q^{9} +O(q^{10})\)	\(q+2.77774 q^{2} -1.15501 q^{3} +5.71583 q^{4} +1.00000 q^{5} -3.20831 q^{6} +1.00000 q^{7} +10.3216 q^{8} -1.66596 q^{9} +2.77774 q^{10} -6.60184 q^{12} +4.48271 q^{13} +2.77774 q^{14} -1.15501 q^{15} +17.2391 q^{16} +3.65680 q^{17} -4.62759 q^{18} +1.28546 q^{19} +5.71583 q^{20} -1.15501 q^{21} -6.46047 q^{23} -11.9216 q^{24} +1.00000 q^{25} +12.4518 q^{26} +5.38922 q^{27} +5.71583 q^{28} -1.21204 q^{29} -3.20831 q^{30} -7.51569 q^{31} +27.2424 q^{32} +10.1576 q^{34} +1.00000 q^{35} -9.52232 q^{36} -6.29940 q^{37} +3.57067 q^{38} -5.17757 q^{39} +10.3216 q^{40} +8.93325 q^{41} -3.20831 q^{42} +2.40712 q^{43} -1.66596 q^{45} -17.9455 q^{46} +0.468011 q^{47} -19.9113 q^{48} +1.00000 q^{49} +2.77774 q^{50} -4.22364 q^{51} +25.6224 q^{52} +2.47206 q^{53} +14.9698 q^{54} +10.3216 q^{56} -1.48472 q^{57} -3.36673 q^{58} -12.1993 q^{59} -6.60184 q^{60} -1.04789 q^{61} -20.8766 q^{62} -1.66596 q^{63} +41.1942 q^{64} +4.48271 q^{65} +6.47842 q^{67} +20.9017 q^{68} +7.46190 q^{69} +2.77774 q^{70} -9.27952 q^{71} -17.1953 q^{72} +2.57523 q^{73} -17.4981 q^{74} -1.15501 q^{75} +7.34748 q^{76} -14.3819 q^{78} -11.5599 q^{79} +17.2391 q^{80} -1.22673 q^{81} +24.8142 q^{82} +10.1307 q^{83} -6.60184 q^{84} +3.65680 q^{85} +6.68635 q^{86} +1.39992 q^{87} +15.0783 q^{89} -4.62759 q^{90} +4.48271 q^{91} -36.9270 q^{92} +8.68069 q^{93} +1.30001 q^{94} +1.28546 q^{95} -31.4652 q^{96} -3.45073 q^{97} +2.77774 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9}+O(q^{10}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9} + 2 q^{10} + 15 q^{12} + 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} - 5 q^{17} + 2 q^{18} + 15 q^{19} + 24 q^{20} + 5 q^{21} + 4 q^{23} + 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} + 24 q^{28} - 6 q^{29} - q^{30} + 22 q^{31} - 6 q^{32} + 44 q^{34} + 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} - 38 q^{39} + 6 q^{40} + 7 q^{41} - q^{42} + 10 q^{43} + 37 q^{45} - 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} + 2 q^{50} - 11 q^{51} + 18 q^{52} + 23 q^{53} + 13 q^{54} + 6 q^{56} - 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} + 17 q^{61} + 57 q^{62} + 37 q^{63} + 64 q^{64} + 8 q^{65} + 29 q^{67} - 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} - 77 q^{72} + 3 q^{73} - 48 q^{74} + 5 q^{75} + 47 q^{76} + 10 q^{78} - 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} + 9 q^{83} + 15 q^{84} - 5 q^{85} + 25 q^{86} + 23 q^{87} + 59 q^{89} + 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} - 19 q^{94} + 15 q^{95} + 14 q^{96} + 30 q^{97} + 2 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9 + 2 * q^10 + 15 * q^12 + 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 - 5 * q^17 + 2 * q^18 + 15 * q^19 + 24 * q^20 + 5 * q^21 + 4 * q^23 + 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 + 24 * q^28 - 6 * q^29 - q^30 + 22 * q^31 - 6 * q^32 + 44 * q^34 + 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 - 38 * q^39 + 6 * q^40 + 7 * q^41 - q^42 + 10 * q^43 + 37 * q^45 - 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 + 2 * q^50 - 11 * q^51 + 18 * q^52 + 23 * q^53 + 13 * q^54 + 6 * q^56 - 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 + 17 * q^61 + 57 * q^62 + 37 * q^63 + 64 * q^64 + 8 * q^65 + 29 * q^67 - 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 - 77 * q^72 + 3 * q^73 - 48 * q^74 + 5 * q^75 + 47 * q^76 + 10 * q^78 - 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 + 9 * q^83 + 15 * q^84 - 5 * q^85 + 25 * q^86 + 23 * q^87 + 59 * q^89 + 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 - 19 * q^94 + 15 * q^95 + 14 * q^96 + 30 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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