LMFDB - Embedded newform 4018.2.a.bs.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 17x^{8} + 36x^{7} + 75x^{6} - 174x^{5} - 69x^{4} + 260x^{3} - 104x^{2} - 24x + 14 $ x^10 - 2x^9 - 17x^8 + 36x^7 + 75x^6 - 174x^5 - 69x^4 + 260x^3 - 104x^2 - 24*x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-1.85317$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.08180 q^{3} +1.00000 q^{4} +2.32009 q^{5} -3.08180 q^{6} -1.00000 q^{8} +6.49750 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.08180 q^{3} +1.00000 q^{4} +2.32009 q^{5} -3.08180 q^{6} -1.00000 q^{8} +6.49750 q^{9} -2.32009 q^{10} +4.60635 q^{11} +3.08180 q^{12} +6.25200 q^{13} +7.15005 q^{15} +1.00000 q^{16} +4.31586 q^{17} -6.49750 q^{18} -8.07305 q^{19} +2.32009 q^{20} -4.60635 q^{22} -2.30051 q^{23} -3.08180 q^{24} +0.382815 q^{25} -6.25200 q^{26} +10.7786 q^{27} -7.84231 q^{29} -7.15005 q^{30} +4.09893 q^{31} -1.00000 q^{32} +14.1959 q^{33} -4.31586 q^{34} +6.49750 q^{36} -1.22300 q^{37} +8.07305 q^{38} +19.2674 q^{39} -2.32009 q^{40} +1.00000 q^{41} +5.81088 q^{43} +4.60635 q^{44} +15.0748 q^{45} +2.30051 q^{46} -10.5878 q^{47} +3.08180 q^{48} -0.382815 q^{50} +13.3006 q^{51} +6.25200 q^{52} +7.51063 q^{53} -10.7786 q^{54} +10.6872 q^{55} -24.8795 q^{57} +7.84231 q^{58} -2.94182 q^{59} +7.15005 q^{60} -6.03373 q^{61} -4.09893 q^{62} +1.00000 q^{64} +14.5052 q^{65} -14.1959 q^{66} -5.05068 q^{67} +4.31586 q^{68} -7.08972 q^{69} -10.2436 q^{71} -6.49750 q^{72} -11.6420 q^{73} +1.22300 q^{74} +1.17976 q^{75} -8.07305 q^{76} -19.2674 q^{78} +0.348408 q^{79} +2.32009 q^{80} +13.7250 q^{81} -1.00000 q^{82} -2.13073 q^{83} +10.0132 q^{85} -5.81088 q^{86} -24.1684 q^{87} -4.60635 q^{88} -13.2642 q^{89} -15.0748 q^{90} -2.30051 q^{92} +12.6321 q^{93} +10.5878 q^{94} -18.7302 q^{95} -3.08180 q^{96} -12.6840 q^{97} +29.9298 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 20 q^{17} - 10 q^{18} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 16 q^{27} - 4 q^{29} - 4 q^{30} - 4 q^{31} - 10 q^{32} + 36 q^{33} - 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} - 4 q^{40} + 10 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 4 q^{46} + 24 q^{47} + 4 q^{48} - 6 q^{50} + 20 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{54} + 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} + 4 q^{62} + 10 q^{64} - 12 q^{65} - 36 q^{66} + 8 q^{67} + 20 q^{68} + 4 q^{71} - 10 q^{72} - 24 q^{73} + 16 q^{74} + 48 q^{75} - 20 q^{78} + 24 q^{79} + 4 q^{80} - 18 q^{81} - 10 q^{82} + 48 q^{83} + 8 q^{85} + 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 24 q^{94} - 4 q^{95} - 4 q^{96} + 4 q^{97} + 32 q^{99}+O(q^{100}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 20 * q^17 - 10 * q^18 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 16 * q^27 - 4 * q^29 - 4 * q^30 - 4 * q^31 - 10 * q^32 + 36 * q^33 - 20 * q^34 + 10 * q^36 - 16 * q^37 + 20 * q^39 - 4 * q^40 + 10 * q^41 - 8 * q^43 + 4 * q^44 + 4 * q^45 - 4 * q^46 + 24 * q^47 + 4 * q^48 - 6 * q^50 + 20 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^54 + 20 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^60 + 4 * q^62 + 10 * q^64 - 12 * q^65 - 36 * q^66 + 8 * q^67 + 20 * q^68 + 4 * q^71 - 10 * q^72 - 24 * q^73 + 16 * q^74 + 48 * q^75 - 20 * q^78 + 24 * q^79 + 4 * q^80 - 18 * q^81 - 10 * q^82 + 48 * q^83 + 8 * q^85 + 8 * q^86 + 4 * q^87 - 4 * q^88 + 20 * q^89 - 4 * q^90 + 4 * q^92 + 4 * q^93 - 24 * q^94 - 4 * q^95 - 4 * q^96 + 4 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	3.08180	1.77928	0.889639	−	0.456664i	$-0.150956\pi$
$3$	3.08180	1.77928	0.889639	+	0.456664i	$0.150956\pi$
$4$	1.00000	0.500000
$5$	2.32009	1.03758	0.518788	−	0.854903i	$-0.326383\pi$
$5$	2.32009	1.03758	0.518788	+	0.854903i	$0.326383\pi$
$6$	−3.08180	−1.25814
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	6.49750	2.16583
$10$	−2.32009	−0.733677
$11$	4.60635	1.38887	0.694434	−	0.719556i	$-0.255655\pi$
$11$	4.60635	1.38887	0.694434	+	0.719556i	$0.255655\pi$
$12$	3.08180	0.889639
$13$	6.25200	1.73399	0.866997	−	0.498314i	$-0.166047\pi$
$13$	6.25200	1.73399	0.866997	+	0.498314i	$0.166047\pi$
$14$	0	0
$15$	7.15005	1.84614
$16$	1.00000	0.250000
$17$	4.31586	1.04675	0.523375	−	0.852102i	$-0.324673\pi$
$17$	4.31586	1.04675	0.523375	+	0.852102i	$0.324673\pi$
$18$	−6.49750	−1.53148
$19$	−8.07305	−1.85208	−0.926042	−	0.377420i	$-0.876811\pi$
$19$	−8.07305	−1.85208	−0.926042	+	0.377420i	$0.876811\pi$
$20$	2.32009	0.518788
$21$	0	0
$22$	−4.60635	−0.982078
$23$	−2.30051	−0.479690	−0.239845	−	0.970811i	$-0.577097\pi$
$23$	−2.30051	−0.479690	−0.239845	+	0.970811i	$0.577097\pi$
$24$	−3.08180	−0.629070
$25$	0.382815	0.0765629
$26$	−6.25200	−1.22612
$27$	10.7786	2.07434
$28$	0	0
$29$	−7.84231	−1.45628	−0.728140	−	0.685429i	$-0.759615\pi$
$29$	−7.84231	−1.45628	−0.728140	+	0.685429i	$0.759615\pi$
$30$	−7.15005	−1.30542
$31$	4.09893	0.736189	0.368094	−	0.929788i	$-0.380010\pi$
$31$	4.09893	0.736189	0.368094	+	0.929788i	$0.380010\pi$
$32$	−1.00000	−0.176777
$33$	14.1959	2.47118
$34$	−4.31586	−0.740164
$35$	0	0
$36$	6.49750	1.08292
$37$	−1.22300	−0.201059	−0.100530	−	0.994934i	$-0.532054\pi$
$37$	−1.22300	−0.201059	−0.100530	+	0.994934i	$0.532054\pi$
$38$	8.07305	1.30962
$39$	19.2674	3.08526
$40$	−2.32009	−0.366838
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	5.81088	0.886150	0.443075	−	0.896484i	$-0.353887\pi$
$43$	5.81088	0.886150	0.443075	+	0.896484i	$0.353887\pi$
$44$	4.60635	0.694434
$45$	15.0748	2.24722
$46$	2.30051	0.339192
$47$	−10.5878	−1.54439	−0.772196	−	0.635384i	$-0.780842\pi$
$47$	−10.5878	−1.54439	−0.772196	+	0.635384i	$0.780842\pi$
$48$	3.08180	0.444820
$49$	0	0
$50$	−0.382815	−0.0541382
$51$	13.3006	1.86246
$52$	6.25200	0.866997
$53$	7.51063	1.03166	0.515832	−	0.856690i	$-0.327483\pi$
$53$	7.51063	1.03166	0.515832	+	0.856690i	$0.327483\pi$
$54$	−10.7786	−1.46678
$55$	10.6872	1.44106
$56$	0	0
$57$	−24.8795	−3.29538
$58$	7.84231	1.02975
$59$	−2.94182	−0.382992	−0.191496	−	0.981493i	$-0.561334\pi$
$59$	−2.94182	−0.382992	−0.191496	+	0.981493i	$0.561334\pi$
$60$	7.15005	0.923068
$61$	−6.03373	−0.772540	−0.386270	−	0.922386i	$-0.626237\pi$
$61$	−6.03373	−0.772540	−0.386270	+	0.922386i	$0.626237\pi$
$62$	−4.09893	−0.520564
$63$	0	0
$64$	1.00000	0.125000
$65$	14.5052	1.79915
$66$	−14.1959	−1.74739
$67$	−5.05068	−0.617039	−0.308519	−	0.951218i	$-0.599834\pi$
$67$	−5.05068	−0.617039	−0.308519	+	0.951218i	$0.599834\pi$
$68$	4.31586	0.523375
$69$	−7.08972	−0.853502
$70$	0	0
$71$	−10.2436	−1.21570	−0.607848	−	0.794054i	$-0.707967\pi$
$71$	−10.2436	−1.21570	−0.607848	+	0.794054i	$0.707967\pi$
$72$	−6.49750	−0.765738
$73$	−11.6420	−1.36259	−0.681294	−	0.732010i	$-0.738583\pi$
$73$	−11.6420	−1.36259	−0.681294	+	0.732010i	$0.738583\pi$
$74$	1.22300	0.142170
$75$	1.17976	0.136227
$76$	−8.07305	−0.926042
$77$	0	0
$78$	−19.2674	−2.18161
$79$	0.348408	0.0391990	0.0195995	−	0.999808i	$-0.493761\pi$
$79$	0.348408	0.0391990	0.0195995	+	0.999808i	$0.493761\pi$
$80$	2.32009	0.259394
$81$	13.7250	1.52500
$82$	−1.00000	−0.110432
$83$	−2.13073	−0.233878	−0.116939	−	0.993139i	$-0.537308\pi$
$83$	−2.13073	−0.233878	−0.116939	+	0.993139i	$0.537308\pi$
$84$	0	0
$85$	10.0132	1.08608
$86$	−5.81088	−0.626603
$87$	−24.1684	−2.59113
$88$	−4.60635	−0.491039
$89$	−13.2642	−1.40600	−0.703001	−	0.711189i	$-0.748157\pi$
$89$	−13.2642	−1.40600	−0.703001	+	0.711189i	$0.748157\pi$
$90$	−15.0748	−1.58902
$91$	0	0
$92$	−2.30051	−0.239845
$93$	12.6321	1.30989
$94$	10.5878	1.09205
$95$	−18.7302	−1.92168
$96$	−3.08180	−0.314535
$97$	−12.6840	−1.28787	−0.643933	−	0.765082i	$-0.722698\pi$
$97$	−12.6840	−1.28787	−0.643933	+	0.765082i	$0.722698\pi$
$98$	0	0
$99$	29.9298	3.00806
$100$	0.382815	0.0382815
$101$	2.73959	0.272600	0.136300	−	0.990668i	$-0.456479\pi$
$101$	2.73959	0.272600	0.136300	+	0.990668i	$0.456479\pi$
$102$	−13.3006	−1.31696
$103$	7.69871	0.758577	0.379288	−	0.925279i	$-0.376169\pi$
$103$	7.69871	0.758577	0.379288	+	0.925279i	$0.376169\pi$
$104$	−6.25200	−0.613059
$105$	0	0
$106$	−7.51063	−0.729497
$107$	13.7046	1.32487	0.662436	−	0.749118i	$-0.269523\pi$
$107$	13.7046	1.32487	0.662436	+	0.749118i	$0.269523\pi$
$108$	10.7786	1.03717
$109$	0.303339	0.0290546	0.0145273	−	0.999894i	$-0.495376\pi$
$109$	0.303339	0.0290546	0.0145273	+	0.999894i	$0.495376\pi$
$110$	−10.6872	−1.01898
$111$	−3.76903	−0.357741
$112$	0	0
$113$	−19.0826	−1.79514	−0.897568	−	0.440876i	$-0.854668\pi$
$113$	−19.0826	−1.79514	−0.897568	+	0.440876i	$0.854668\pi$
$114$	24.8795	2.33018
$115$	−5.33739	−0.497714
$116$	−7.84231	−0.728140
$117$	40.6224	3.75554
$118$	2.94182	0.270816
$119$	0	0
$120$	−7.15005	−0.652708
$121$	10.2185	0.928954
$122$	6.03373	0.546268
$123$	3.08180	0.277877
$124$	4.09893	0.368094
$125$	−10.7123	−0.958136
$126$	0	0
$127$	2.39881	0.212860	0.106430	−	0.994320i	$-0.466058\pi$
$127$	2.39881	0.212860	0.106430	+	0.994320i	$0.466058\pi$
$128$	−1.00000	−0.0883883
$129$	17.9080	1.57671
$130$	−14.5052	−1.27219
$131$	12.0856	1.05592	0.527960	−	0.849269i	$-0.322957\pi$
$131$	12.0856	1.05592	0.527960	+	0.849269i	$0.322957\pi$
$132$	14.1959	1.23559
$133$	0	0
$134$	5.05068	0.436312
$135$	25.0073	2.15229
$136$	−4.31586	−0.370082
$137$	−17.0527	−1.45691	−0.728456	−	0.685092i	$-0.759762\pi$
$137$	−17.0527	−1.45691	−0.728456	+	0.685092i	$0.759762\pi$
$138$	7.08972	0.603517
$139$	−7.38876	−0.626706	−0.313353	−	0.949637i	$-0.601452\pi$
$139$	−7.38876	−0.626706	−0.313353	+	0.949637i	$0.601452\pi$
$140$	0	0
$141$	−32.6296	−2.74791
$142$	10.2436	0.859626
$143$	28.7989	2.40829
$144$	6.49750	0.541458
$145$	−18.1948	−1.51100
$146$	11.6420	0.963496
$147$	0	0
$148$	−1.22300	−0.100530
$149$	10.1256	0.829518	0.414759	−	0.909931i	$-0.363866\pi$
$149$	10.1256	0.829518	0.414759	+	0.909931i	$0.363866\pi$
$150$	−1.17976	−0.0963269
$151$	21.5795	1.75612	0.878058	−	0.478554i	$-0.158839\pi$
$151$	21.5795	1.75612	0.878058	+	0.478554i	$0.158839\pi$
$152$	8.07305	0.654811
$153$	28.0423	2.26709
$154$	0	0
$155$	9.50987	0.763851
$156$	19.2674	1.54263
$157$	−24.3034	−1.93963	−0.969813	−	0.243852i	$-0.921589\pi$
$157$	−24.3034	−1.93963	−0.969813	+	0.243852i	$0.921589\pi$
$158$	−0.348408	−0.0277179
$159$	23.1463	1.83562
$160$	−2.32009	−0.183419
$161$	0	0
$162$	−13.7250	−1.07834
$163$	−15.2496	−1.19444	−0.597221	−	0.802076i	$-0.703729\pi$
$163$	−15.2496	−1.19444	−0.597221	+	0.802076i	$0.703729\pi$
$164$	1.00000	0.0780869
$165$	32.9357	2.56404
$166$	2.13073	0.165377
$167$	15.5795	1.20558	0.602788	−	0.797901i	$-0.294056\pi$
$167$	15.5795	1.20558	0.602788	+	0.797901i	$0.294056\pi$
$168$	0	0
$169$	26.0875	2.00673
$170$	−10.0132	−0.767976
$171$	−52.4546	−4.01131
$172$	5.81088	0.443075
$173$	−15.0234	−1.14221	−0.571105	−	0.820877i	$-0.693485\pi$
$173$	−15.0234	−1.14221	−0.571105	+	0.820877i	$0.693485\pi$
$174$	24.1684	1.83220
$175$	0	0
$176$	4.60635	0.347217
$177$	−9.06609	−0.681449
$178$	13.2642	0.994193
$179$	−9.17502	−0.685773	−0.342886	−	0.939377i	$-0.611405\pi$
$179$	−9.17502	−0.685773	−0.342886	+	0.939377i	$0.611405\pi$
$180$	15.0748	1.12361
$181$	6.41339	0.476703	0.238352	−	0.971179i	$-0.423393\pi$
$181$	6.41339	0.476703	0.238352	+	0.971179i	$0.423393\pi$
$182$	0	0
$183$	−18.5948	−1.37456
$184$	2.30051	0.169596
$185$	−2.83746	−0.208614
$186$	−12.6321	−0.926229
$187$	19.8804	1.45380
$188$	−10.5878	−0.772196
$189$	0	0
$190$	18.7302	1.35883
$191$	−1.14267	−0.0826804	−0.0413402	−	0.999145i	$-0.513163\pi$
$191$	−1.14267	−0.0826804	−0.0413402	+	0.999145i	$0.513163\pi$
$192$	3.08180	0.222410
$193$	−7.79550	−0.561132	−0.280566	−	0.959835i	$-0.590522\pi$
$193$	−7.79550	−0.561132	−0.280566	+	0.959835i	$0.590522\pi$
$194$	12.6840	0.910658
$195$	44.7022	3.20119
$196$	0	0
$197$	−1.95008	−0.138938	−0.0694688	−	0.997584i	$-0.522130\pi$
$197$	−1.95008	−0.138938	−0.0694688	+	0.997584i	$0.522130\pi$
$198$	−29.9298	−2.12702
$199$	15.1870	1.07657	0.538287	−	0.842761i	$-0.319072\pi$
$199$	15.1870	1.07657	0.538287	+	0.842761i	$0.319072\pi$
$200$	−0.382815	−0.0270691
$201$	−15.5652	−1.09788
$202$	−2.73959	−0.192757
$203$	0	0
$204$	13.3006	0.931230
$205$	2.32009	0.162042
$206$	−7.69871	−0.536395
$207$	−14.9476	−1.03893
$208$	6.25200	0.433498
$209$	−37.1873	−2.57230
$210$	0	0
$211$	10.4146	0.716974	0.358487	−	0.933535i	$-0.383293\pi$
$211$	10.4146	0.716974	0.358487	+	0.933535i	$0.383293\pi$
$212$	7.51063	0.515832
$213$	−31.5688	−2.16306
$214$	−13.7046	−0.936826
$215$	13.4818	0.919448
$216$	−10.7786	−0.733391
$217$	0	0
$218$	−0.303339	−0.0205447
$219$	−35.8782	−2.42443
$220$	10.6872	0.720528
$221$	26.9828	1.81506
$222$	3.76903	0.252961
$223$	−10.8892	−0.729198	−0.364599	−	0.931165i	$-0.618794\pi$
$223$	−10.8892	−0.729198	−0.364599	+	0.931165i	$0.618794\pi$
$224$	0	0
$225$	2.48734	0.165823
$226$	19.0826	1.26935
$227$	19.7323	1.30968	0.654839	−	0.755768i	$-0.272736\pi$
$227$	19.7323	1.30968	0.654839	+	0.755768i	$0.272736\pi$
$228$	−24.8795	−1.64769
$229$	0.803338	0.0530861	0.0265430	−	0.999648i	$-0.491550\pi$
$229$	0.803338	0.0530861	0.0265430	+	0.999648i	$0.491550\pi$
$230$	5.33739	0.351937
$231$	0	0
$232$	7.84231	0.514873
$233$	−9.00657	−0.590040	−0.295020	−	0.955491i	$-0.595326\pi$
$233$	−9.00657	−0.590040	−0.295020	+	0.955491i	$0.595326\pi$
$234$	−40.6224	−2.65557
$235$	−24.5647	−1.60242
$236$	−2.94182	−0.191496
$237$	1.07373	0.0697460
$238$	0	0
$239$	2.96336	0.191684	0.0958418	−	0.995397i	$-0.469446\pi$
$239$	2.96336	0.191684	0.0958418	+	0.995397i	$0.469446\pi$
$240$	7.15005	0.461534
$241$	9.27361	0.597366	0.298683	−	0.954352i	$-0.403453\pi$
$241$	9.27361	0.597366	0.298683	+	0.954352i	$0.403453\pi$
$242$	−10.2185	−0.656870
$243$	9.96195	0.639060
$244$	−6.03373	−0.386270
$245$	0	0
$246$	−3.08180	−0.196488
$247$	−50.4727	−3.21150
$248$	−4.09893	−0.260282
$249$	−6.56648	−0.416134
$250$	10.7123	0.677504
$251$	10.7084	0.675907	0.337953	−	0.941163i	$-0.390265\pi$
$251$	10.7084	0.675907	0.337953	+	0.941163i	$0.390265\pi$
$252$	0	0
$253$	−10.5970	−0.666225
$254$	−2.39881	−0.150515
$255$	30.8587	1.93244
$256$	1.00000	0.0625000
$257$	12.9276	0.806403	0.403202	−	0.915111i	$-0.367897\pi$
$257$	12.9276	0.806403	0.403202	+	0.915111i	$0.367897\pi$
$258$	−17.9080	−1.11490
$259$	0	0
$260$	14.5052	0.899575
$261$	−50.9554	−3.15406
$262$	−12.0856	−0.746649
$263$	26.0488	1.60624	0.803120	−	0.595817i	$-0.203172\pi$
$263$	26.0488	1.60624	0.803120	+	0.595817i	$0.203172\pi$
$264$	−14.1959	−0.873695
$265$	17.4253	1.07043
$266$	0	0
$267$	−40.8776	−2.50167
$268$	−5.05068	−0.308519
$269$	5.73844	0.349879	0.174939	−	0.984579i	$-0.444027\pi$
$269$	5.73844	0.349879	0.174939	+	0.984579i	$0.444027\pi$
$270$	−25.0073	−1.52190
$271$	31.2392	1.89765	0.948824	−	0.315805i	$-0.102274\pi$
$271$	31.2392	1.89765	0.948824	+	0.315805i	$0.102274\pi$
$272$	4.31586	0.261688
$273$	0	0
$274$	17.0527	1.03019
$275$	1.76338	0.106336
$276$	−7.08972	−0.426751
$277$	2.70580	0.162576	0.0812878	−	0.996691i	$-0.474097\pi$
$277$	2.70580	0.162576	0.0812878	+	0.996691i	$0.474097\pi$
$278$	7.38876	0.443148
$279$	26.6328	1.59446
$280$	0	0
$281$	3.42049	0.204050	0.102025	−	0.994782i	$-0.467468\pi$
$281$	3.42049	0.204050	0.102025	+	0.994782i	$0.467468\pi$
$282$	32.6296	1.94306
$283$	−17.8719	−1.06238	−0.531189	−	0.847254i	$-0.678254\pi$
$283$	−17.8719	−1.06238	−0.531189	+	0.847254i	$0.678254\pi$
$284$	−10.2436	−0.607848
$285$	−57.7227	−3.41920
$286$	−28.7989	−1.70292
$287$	0	0
$288$	−6.49750	−0.382869
$289$	1.62667	0.0956864
$290$	18.1948	1.06844
$291$	−39.0896	−2.29147
$292$	−11.6420	−0.681294
$293$	13.1855	0.770308	0.385154	−	0.922852i	$-0.374148\pi$
$293$	13.1855	0.770308	0.385154	+	0.922852i	$0.374148\pi$
$294$	0	0
$295$	−6.82528	−0.397383
$296$	1.22300	0.0710852
$297$	49.6501	2.88099
$298$	−10.1256	−0.586558
$299$	−14.3828	−0.831779
$300$	1.17976	0.0681134
$301$	0	0
$302$	−21.5795	−1.24176
$303$	8.44288	0.485031
$304$	−8.07305	−0.463021
$305$	−13.9988	−0.801568
$306$	−28.0423	−1.60307
$307$	7.10752	0.405648	0.202824	−	0.979215i	$-0.434988\pi$
$307$	7.10752	0.405648	0.202824	+	0.979215i	$0.434988\pi$
$308$	0	0
$309$	23.7259	1.34972
$310$	−9.50987	−0.540124
$311$	10.2528	0.581383	0.290692	−	0.956817i	$-0.406115\pi$
$311$	10.2528	0.581383	0.290692	+	0.956817i	$0.406115\pi$
$312$	−19.2674	−1.09080
$313$	20.1061	1.13646	0.568232	−	0.822868i	$-0.307628\pi$
$313$	20.1061	1.13646	0.568232	+	0.822868i	$0.307628\pi$
$314$	24.3034	1.37152
$315$	0	0
$316$	0.348408	0.0195995
$317$	−7.29271	−0.409600	−0.204800	−	0.978804i	$-0.565654\pi$
$317$	−7.29271	−0.409600	−0.204800	+	0.978804i	$0.565654\pi$
$318$	−23.1463	−1.29798
$319$	−36.1244	−2.02258
$320$	2.32009	0.129697
$321$	42.2348	2.35732
$322$	0	0
$323$	−34.8422	−1.93867
$324$	13.7250	0.762501
$325$	2.39336	0.132760
$326$	15.2496	0.844599
$327$	0.934830	0.0516962
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	−32.9357	−1.81305
$331$	18.9946	1.04404	0.522019	−	0.852934i	$-0.325179\pi$
$331$	18.9946	1.04404	0.522019	+	0.852934i	$0.325179\pi$
$332$	−2.13073	−0.116939
$333$	−7.94642	−0.435461
$334$	−15.5795	−0.852471
$335$	−11.7180	−0.640225
$336$	0	0
$337$	−23.6954	−1.29077	−0.645385	−	0.763858i	$-0.723303\pi$
$337$	−23.6954	−1.29077	−0.645385	+	0.763858i	$0.723303\pi$
$338$	−26.0875	−1.41897
$339$	−58.8086	−3.19405
$340$	10.0132	0.543041
$341$	18.8811	1.02247
$342$	52.4546	2.83642
$343$	0	0
$344$	−5.81088	−0.313301
$345$	−16.4488	−0.885572
$346$	15.0234	0.807664
$347$	21.7778	1.16910	0.584548	−	0.811359i	$-0.301272\pi$
$347$	21.7778	1.16910	0.584548	+	0.811359i	$0.301272\pi$
$348$	−24.1684	−1.29556
$349$	−20.9549	−1.12169	−0.560846	−	0.827920i	$-0.689524\pi$
$349$	−20.9549	−1.12169	−0.560846	+	0.827920i	$0.689524\pi$
$350$	0	0
$351$	67.3879	3.59690
$352$	−4.60635	−0.245519
$353$	31.9532	1.70070	0.850348	−	0.526220i	$-0.176391\pi$
$353$	31.9532	1.70070	0.850348	+	0.526220i	$0.176391\pi$
$354$	9.06609	0.481858
$355$	−23.7661	−1.26138
$356$	−13.2642	−0.703001
$357$	0	0
$358$	9.17502	0.484915
$359$	−2.03141	−0.107214	−0.0536069	−	0.998562i	$-0.517072\pi$
$359$	−2.03141	−0.107214	−0.0536069	+	0.998562i	$0.517072\pi$
$360$	−15.0748	−0.794511
$361$	46.1741	2.43022
$362$	−6.41339	−0.337080
$363$	31.4914	1.65287
$364$	0	0
$365$	−27.0104	−1.41379
$366$	18.5948	0.971963
$367$	10.6947	0.558256	0.279128	−	0.960254i	$-0.409955\pi$
$367$	10.6947	0.558256	0.279128	+	0.960254i	$0.409955\pi$
$368$	−2.30051	−0.119922
$369$	6.49750	0.338246
$370$	2.83746	0.147513
$371$	0	0
$372$	12.6321	0.654943
$373$	20.2377	1.04787	0.523935	−	0.851758i	$-0.324463\pi$
$373$	20.2377	1.04787	0.523935	+	0.851758i	$0.324463\pi$
$374$	−19.8804	−1.02799
$375$	−33.0131	−1.70479
$376$	10.5878	0.546025
$377$	−49.0301	−2.52518
$378$	0	0
$379$	−4.65967	−0.239351	−0.119676	−	0.992813i	$-0.538185\pi$
$379$	−4.65967	−0.239351	−0.119676	+	0.992813i	$0.538185\pi$
$380$	−18.7302	−0.960839
$381$	7.39267	0.378738
$382$	1.14267	0.0584639
$383$	22.2743	1.13816	0.569081	−	0.822281i	$-0.307299\pi$
$383$	22.2743	1.13816	0.569081	+	0.822281i	$0.307299\pi$
$384$	−3.08180	−0.157268
$385$	0	0
$386$	7.79550	0.396781
$387$	37.7562	1.91925
$388$	−12.6840	−0.643933
$389$	−18.0875	−0.917072	−0.458536	−	0.888676i	$-0.651626\pi$
$389$	−18.0875	−0.917072	−0.458536	+	0.888676i	$0.651626\pi$
$390$	−44.7022	−2.26358
$391$	−9.92869	−0.502115
$392$	0	0
$393$	37.2453	1.87878
$394$	1.95008	0.0982437
$395$	0.808339	0.0406719
$396$	29.9298	1.50403
$397$	−4.18190	−0.209883	−0.104942	−	0.994478i	$-0.533466\pi$
$397$	−4.18190	−0.209883	−0.104942	+	0.994478i	$0.533466\pi$
$398$	−15.1870	−0.761253
$399$	0	0
$400$	0.382815	0.0191407
$401$	16.9057	0.844229	0.422114	−	0.906543i	$-0.361288\pi$
$401$	16.9057	0.844229	0.422114	+	0.906543i	$0.361288\pi$
$402$	15.5652	0.776322
$403$	25.6265	1.27655
$404$	2.73959	0.136300
$405$	31.8433	1.58230
$406$	0	0
$407$	−5.63356	−0.279245
$408$	−13.3006	−0.658479
$409$	12.1534	0.600947	0.300473	−	0.953790i	$-0.402855\pi$
$409$	12.1534	0.600947	0.300473	+	0.953790i	$0.402855\pi$
$410$	−2.32009	−0.114581
$411$	−52.5531	−2.59225
$412$	7.69871	0.379288
$413$	0	0
$414$	14.9476	0.734633
$415$	−4.94348	−0.242666
$416$	−6.25200	−0.306530
$417$	−22.7707	−1.11509
$418$	37.1873	1.81889
$419$	21.8309	1.06651	0.533254	−	0.845955i	$-0.320969\pi$
$419$	21.8309	1.06651	0.533254	+	0.845955i	$0.320969\pi$
$420$	0	0
$421$	−27.4543	−1.33804	−0.669019	−	0.743245i	$-0.733286\pi$
$421$	−27.4543	−1.33804	−0.669019	+	0.743245i	$0.733286\pi$
$422$	−10.4146	−0.506977
$423$	−68.7944	−3.34490
$424$	−7.51063	−0.364749
$425$	1.65218	0.0801423
$426$	31.5688	1.52951
$427$	0	0
$428$	13.7046	0.662436
$429$	88.7526	4.28502
$430$	−13.4818	−0.650148
$431$	−5.71269	−0.275171	−0.137585	−	0.990490i	$-0.543934\pi$
$431$	−5.71269	−0.275171	−0.137585	+	0.990490i	$0.543934\pi$
$432$	10.7786	0.518586
$433$	−32.6769	−1.57035	−0.785175	−	0.619274i	$-0.787427\pi$
$433$	−32.6769	−1.57035	−0.785175	+	0.619274i	$0.787427\pi$
$434$	0	0
$435$	−56.0729	−2.68849
$436$	0.303339	0.0145273
$437$	18.5721	0.888426
$438$	35.8782	1.71433
$439$	−0.822211	−0.0392420	−0.0196210	−	0.999807i	$-0.506246\pi$
$439$	−0.822211	−0.0392420	−0.0196210	+	0.999807i	$0.506246\pi$
$440$	−10.6872	−0.509490
$441$	0	0
$442$	−26.9828	−1.28344
$443$	31.4921	1.49623	0.748117	−	0.663567i	$-0.230958\pi$
$443$	31.4921	1.49623	0.748117	+	0.663567i	$0.230958\pi$
$444$	−3.76903	−0.178870
$445$	−30.7741	−1.45883
$446$	10.8892	0.515621
$447$	31.2050	1.47594
$448$	0	0
$449$	4.63010	0.218508	0.109254	−	0.994014i	$-0.465154\pi$
$449$	4.63010	0.218508	0.109254	+	0.994014i	$0.465154\pi$
$450$	−2.48734	−0.117254
$451$	4.60635	0.216905
$452$	−19.0826	−0.897568
$453$	66.5038	3.12462
$454$	−19.7323	−0.926082
$455$	0	0
$456$	24.8795	1.16509
$457$	5.20774	0.243608	0.121804	−	0.992554i	$-0.461132\pi$
$457$	5.20774	0.243608	0.121804	+	0.992554i	$0.461132\pi$
$458$	−0.803338	−0.0375375
$459$	46.5190	2.17132
$460$	−5.33739	−0.248857
$461$	17.7047	0.824592	0.412296	−	0.911050i	$-0.364727\pi$
$461$	17.7047	0.824592	0.412296	+	0.911050i	$0.364727\pi$
$462$	0	0
$463$	0.868568	0.0403658	0.0201829	−	0.999796i	$-0.493575\pi$
$463$	0.868568	0.0403658	0.0201829	+	0.999796i	$0.493575\pi$
$464$	−7.84231	−0.364070
$465$	29.3075	1.35910
$466$	9.00657	0.417221
$467$	10.1656	0.470407	0.235203	−	0.971946i	$-0.424424\pi$
$467$	10.1656	0.470407	0.235203	+	0.971946i	$0.424424\pi$
$468$	40.6224	1.87777
$469$	0	0
$470$	24.5647	1.13308
$471$	−74.8984	−3.45113
$472$	2.94182	0.135408
$473$	26.7669	1.23075
$474$	−1.07373	−0.0493179
$475$	−3.09048	−0.141801
$476$	0	0
$477$	48.8003	2.23441
$478$	−2.96336	−0.135541
$479$	−11.5948	−0.529779	−0.264890	−	0.964279i	$-0.585335\pi$
$479$	−11.5948	−0.529779	−0.264890	+	0.964279i	$0.585335\pi$
$480$	−7.15005	−0.326354
$481$	−7.64618	−0.348636
$482$	−9.27361	−0.422401
$483$	0	0
$484$	10.2185	0.464477
$485$	−29.4280	−1.33626
$486$	−9.96195	−0.451883
$487$	−26.9925	−1.22315	−0.611573	−	0.791188i	$-0.709463\pi$
$487$	−26.9925	−1.22315	−0.611573	+	0.791188i	$0.709463\pi$
$488$	6.03373	0.273134
$489$	−46.9963	−2.12525
$490$	0	0
$491$	−12.0422	−0.543455	−0.271728	−	0.962374i	$-0.587595\pi$
$491$	−12.0422	−0.543455	−0.271728	+	0.962374i	$0.587595\pi$
$492$	3.08180	0.138938
$493$	−33.8463	−1.52436
$494$	50.4727	2.27088
$495$	69.4398	3.12109
$496$	4.09893	0.184047
$497$	0	0
$498$	6.56648	0.294251
$499$	5.88313	0.263365	0.131683	−	0.991292i	$-0.457962\pi$
$499$	5.88313	0.263365	0.131683	+	0.991292i	$0.457962\pi$
$500$	−10.7123	−0.479068
$501$	48.0129	2.14506
$502$	−10.7084	−0.477938
$503$	35.6288	1.58861	0.794304	−	0.607520i	$-0.207836\pi$
$503$	35.6288	1.58861	0.794304	+	0.607520i	$0.207836\pi$
$504$	0	0
$505$	6.35610	0.282843
$506$	10.5970	0.471093
$507$	80.3966	3.57054
$508$	2.39881	0.106430
$509$	33.5113	1.48536	0.742682	−	0.669645i	$-0.233554\pi$
$509$	33.5113	1.48536	0.742682	+	0.669645i	$0.233554\pi$
$510$	−30.8587	−1.36644
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−87.0162	−3.84186
$514$	−12.9276	−0.570213
$515$	17.8617	0.787081
$516$	17.9080	0.788354
$517$	−48.7713	−2.14496
$518$	0	0
$519$	−46.2992	−2.03231
$520$	−14.5052	−0.636095
$521$	27.2136	1.19225	0.596124	−	0.802892i	$-0.296707\pi$
$521$	27.2136	1.19225	0.596124	+	0.802892i	$0.296707\pi$
$522$	50.9554	2.23026
$523$	−6.32749	−0.276682	−0.138341	−	0.990385i	$-0.544177\pi$
$523$	−6.32749	−0.276682	−0.138341	+	0.990385i	$0.544177\pi$
$524$	12.0856	0.527960
$525$	0	0
$526$	−26.0488	−1.13578
$527$	17.6904	0.770606
$528$	14.1959	0.617796
$529$	−17.7077	−0.769898
$530$	−17.4253	−0.756908
$531$	−19.1145	−0.829497
$532$	0	0
$533$	6.25200	0.270804
$534$	40.8776	1.76895
$535$	31.7959	1.37466
$536$	5.05068	0.218156
$537$	−28.2756	−1.22018
$538$	−5.73844	−0.247402
$539$	0	0
$540$	25.0073	1.07614
$541$	−26.8943	−1.15628	−0.578138	−	0.815939i	$-0.696220\pi$
$541$	−26.8943	−1.15628	−0.578138	+	0.815939i	$0.696220\pi$
$542$	−31.2392	−1.34184
$543$	19.7648	0.848188
$544$	−4.31586	−0.185041
$545$	0.703773	0.0301463
$546$	0	0
$547$	10.1670	0.434709	0.217355	−	0.976093i	$-0.430257\pi$
$547$	10.1670	0.434709	0.217355	+	0.976093i	$0.430257\pi$
$548$	−17.0527	−0.728456
$549$	−39.2042	−1.67319
$550$	−1.76338	−0.0751908
$551$	63.3113	2.69715
$552$	7.08972	0.301758
$553$	0	0
$554$	−2.70580	−0.114958
$555$	−8.74449	−0.371183
$556$	−7.38876	−0.313353
$557$	−6.78889	−0.287654	−0.143827	−	0.989603i	$-0.545941\pi$
$557$	−6.78889	−0.287654	−0.143827	+	0.989603i	$0.545941\pi$
$558$	−26.6328	−1.12745
$559$	36.3296	1.53658
$560$	0	0
$561$	61.2674	2.58671
$562$	−3.42049	−0.144285
$563$	−29.5299	−1.24454	−0.622269	−	0.782804i	$-0.713789\pi$
$563$	−29.5299	−1.24454	−0.622269	+	0.782804i	$0.713789\pi$
$564$	−32.6296	−1.37395
$565$	−44.2732	−1.86259
$566$	17.8719	0.751214
$567$	0	0
$568$	10.2436	0.429813
$569$	−20.2993	−0.850992	−0.425496	−	0.904960i	$-0.639900\pi$
$569$	−20.2993	−0.850992	−0.425496	+	0.904960i	$0.639900\pi$
$570$	57.7227	2.41774
$571$	5.62158	0.235256	0.117628	−	0.993058i	$-0.462471\pi$
$571$	5.62158	0.235256	0.117628	+	0.993058i	$0.462471\pi$
$572$	28.7989	1.20414
$573$	−3.52147	−0.147111
$574$	0	0
$575$	−0.880669	−0.0367264
$576$	6.49750	0.270729
$577$	2.63835	0.109836	0.0549180	−	0.998491i	$-0.482510\pi$
$577$	2.63835	0.109836	0.0549180	+	0.998491i	$0.482510\pi$
$578$	−1.62667	−0.0676605
$579$	−24.0242	−0.998411
$580$	−18.1948	−0.755500
$581$	0	0
$582$	39.0896	1.62032
$583$	34.5966	1.43285
$584$	11.6420	0.481748
$585$	94.2476	3.89666
$586$	−13.1855	−0.544690
$587$	26.6650	1.10058	0.550292	−	0.834972i	$-0.314516\pi$
$587$	26.6650	1.10058	0.550292	+	0.834972i	$0.314516\pi$
$588$	0	0
$589$	−33.0908	−1.36348
$590$	6.82528	0.280992
$591$	−6.00977	−0.247209
$592$	−1.22300	−0.0502649
$593$	−29.5685	−1.21423	−0.607117	−	0.794612i	$-0.707674\pi$
$593$	−29.5685	−1.21423	−0.607117	+	0.794612i	$0.707674\pi$
$594$	−49.6501	−2.03717
$595$	0	0
$596$	10.1256	0.414759
$597$	46.8032	1.91553
$598$	14.3828	0.588156
$599$	−28.7427	−1.17439	−0.587197	−	0.809444i	$-0.699768\pi$
$599$	−28.7427	−1.17439	−0.587197	+	0.809444i	$0.699768\pi$
$600$	−1.17976	−0.0481635
$601$	−0.534655	−0.0218090	−0.0109045	−	0.999941i	$-0.503471\pi$
$601$	−0.534655	−0.0218090	−0.0109045	+	0.999941i	$0.503471\pi$
$602$	0	0
$603$	−32.8168	−1.33640
$604$	21.5795	0.878058
$605$	23.7078	0.963860
$606$	−8.44288	−0.342968
$607$	−26.4569	−1.07385	−0.536927	−	0.843629i	$-0.680415\pi$
$607$	−26.4569	−1.07385	−0.536927	+	0.843629i	$0.680415\pi$
$608$	8.07305	0.327405
$609$	0	0
$610$	13.9988	0.566794
$611$	−66.1951	−2.67797
$612$	28.0423	1.13354
$613$	−2.64418	−0.106797	−0.0533987	−	0.998573i	$-0.517005\pi$
$613$	−2.64418	−0.106797	−0.0533987	+	0.998573i	$0.517005\pi$
$614$	−7.10752	−0.286836
$615$	7.15005	0.288318
$616$	0	0
$617$	32.2337	1.29768	0.648841	−	0.760924i	$-0.275254\pi$
$617$	32.2337	1.29768	0.648841	+	0.760924i	$0.275254\pi$
$618$	−23.7259	−0.954396
$619$	2.16967	0.0872064	0.0436032	−	0.999049i	$-0.486116\pi$
$619$	2.16967	0.0872064	0.0436032	+	0.999049i	$0.486116\pi$
$620$	9.50987	0.381926
$621$	−24.7963	−0.995041
$622$	−10.2528	−0.411100
$623$	0	0
$624$	19.2674	0.771315
$625$	−26.7675	−1.07070
$626$	−20.1061	−0.803601
$627$	−114.604	−4.57684
$628$	−24.3034	−0.969813
$629$	−5.27829	−0.210459
$630$	0	0
$631$	−26.6839	−1.06227	−0.531135	−	0.847287i	$-0.678234\pi$
$631$	−26.6839	−1.06227	−0.531135	+	0.847287i	$0.678234\pi$
$632$	−0.348408	−0.0138589
$633$	32.0959	1.27570
$634$	7.29271	0.289631
$635$	5.56546	0.220859
$636$	23.1463	0.917810
$637$	0	0
$638$	36.1244	1.43018
$639$	−66.5580	−2.63299
$640$	−2.32009	−0.0917096
$641$	−36.8550	−1.45569	−0.727843	−	0.685744i	$-0.759477\pi$
$641$	−36.8550	−1.45569	−0.727843	+	0.685744i	$0.759477\pi$
$642$	−42.2348	−1.66688
$643$	−50.1526	−1.97782	−0.988912	−	0.148502i	$-0.952555\pi$
$643$	−50.1526	−1.97782	−0.988912	+	0.148502i	$0.952555\pi$
$644$	0	0
$645$	41.5481	1.63595
$646$	34.8422	1.37085
$647$	−6.15319	−0.241907	−0.120953	−	0.992658i	$-0.538595\pi$
$647$	−6.15319	−0.241907	−0.120953	+	0.992658i	$0.538595\pi$
$648$	−13.7250	−0.539169
$649$	−13.5510	−0.531925
$650$	−2.39336	−0.0938752
$651$	0	0
$652$	−15.2496	−0.597221
$653$	−2.58983	−0.101348	−0.0506740	−	0.998715i	$-0.516137\pi$
$653$	−2.58983	−0.101348	−0.0506740	+	0.998715i	$0.516137\pi$
$654$	−0.934830	−0.0365547
$655$	28.0396	1.09560
$656$	1.00000	0.0390434
$657$	−75.6437	−2.95114
$658$	0	0
$659$	−1.80547	−0.0703311	−0.0351655	−	0.999382i	$-0.511196\pi$
$659$	−1.80547	−0.0703311	−0.0351655	+	0.999382i	$0.511196\pi$
$660$	32.9357	1.28202
$661$	33.1190	1.28818	0.644089	−	0.764951i	$-0.277237\pi$
$661$	33.1190	1.28818	0.644089	+	0.764951i	$0.277237\pi$
$662$	−18.9946	−0.738246
$663$	83.1556	3.22950
$664$	2.13073	0.0826883
$665$	0	0
$666$	7.94642	0.307918
$667$	18.0413	0.698562
$668$	15.5795	0.602788
$669$	−33.5585	−1.29745
$670$	11.7180	0.452707
$671$	−27.7935	−1.07296
$672$	0	0
$673$	16.3479	0.630167	0.315084	−	0.949064i	$-0.397967\pi$
$673$	16.3479	0.630167	0.315084	+	0.949064i	$0.397967\pi$
$674$	23.6954	0.912712
$675$	4.12621	0.158818
$676$	26.0875	1.00337
$677$	35.5816	1.36751	0.683757	−	0.729710i	$-0.260345\pi$
$677$	35.5816	1.36751	0.683757	+	0.729710i	$0.260345\pi$
$678$	58.8086	2.25853
$679$	0	0
$680$	−10.0132	−0.383988
$681$	60.8110	2.33028
$682$	−18.8811	−0.722995
$683$	30.2611	1.15791	0.578955	−	0.815359i	$-0.303461\pi$
$683$	30.2611	1.15791	0.578955	+	0.815359i	$0.303461\pi$
$684$	−52.4546	−2.00565
$685$	−39.5638	−1.51166
$686$	0	0
$687$	2.47573	0.0944549
$688$	5.81088	0.221538
$689$	46.9565	1.78890
$690$	16.4488	0.626194
$691$	−27.2121	−1.03520	−0.517599	−	0.855623i	$-0.673174\pi$
$691$	−27.2121	−1.03520	−0.517599	+	0.855623i	$0.673174\pi$
$692$	−15.0234	−0.571105
$693$	0	0
$694$	−21.7778	−0.826675
$695$	−17.1426	−0.650255
$696$	24.1684	0.916102
$697$	4.31586	0.163475
$698$	20.9549	0.793156
$699$	−27.7565	−1.04985
$700$	0	0
$701$	23.0677	0.871253	0.435627	−	0.900127i	$-0.356527\pi$
$701$	23.0677	0.871253	0.435627	+	0.900127i	$0.356527\pi$
$702$	−67.3879	−2.54339
$703$	9.87331	0.372379
$704$	4.60635	0.173608
$705$	−75.7035	−2.85116
$706$	−31.9532	−1.20257
$707$	0	0
$708$	−9.06609	−0.340725
$709$	34.6933	1.30294	0.651468	−	0.758676i	$-0.274154\pi$
$709$	34.6933	1.30294	0.651468	+	0.758676i	$0.274154\pi$
$710$	23.7661	0.891927
$711$	2.26378	0.0848985
$712$	13.2642	0.497096
$713$	−9.42962	−0.353142
$714$	0	0
$715$	66.8161	2.49878
$716$	−9.17502	−0.342886
$717$	9.13248	0.341059
$718$	2.03141	0.0758116
$719$	7.50157	0.279761	0.139881	−	0.990168i	$-0.455328\pi$
$719$	7.50157	0.279761	0.139881	+	0.990168i	$0.455328\pi$
$720$	15.0748	0.561804
$721$	0	0
$722$	−46.1741	−1.71842
$723$	28.5794	1.06288
$724$	6.41339	0.238352
$725$	−3.00215	−0.111497
$726$	−31.4914	−1.16875
$727$	−2.87052	−0.106462	−0.0532309	−	0.998582i	$-0.516952\pi$
$727$	−2.87052	−0.106462	−0.0532309	+	0.998582i	$0.516952\pi$
$728$	0	0
$729$	−10.4743	−0.387936
$730$	27.0104	0.999700
$731$	25.0789	0.927578
$732$	−18.5948	−0.687282
$733$	45.1262	1.66677	0.833387	−	0.552690i	$-0.186399\pi$
$733$	45.1262	1.66677	0.833387	+	0.552690i	$0.186399\pi$
$734$	−10.6947	−0.394747
$735$	0	0
$736$	2.30051	0.0847979
$737$	−23.2652	−0.856986
$738$	−6.49750	−0.239176
$739$	13.0957	0.481734	0.240867	−	0.970558i	$-0.422568\pi$
$739$	13.0957	0.481734	0.240867	+	0.970558i	$0.422568\pi$
$740$	−2.83746	−0.104307
$741$	−155.547	−5.71416
$742$	0	0
$743$	−30.1799	−1.10719	−0.553596	−	0.832785i	$-0.686745\pi$
$743$	−30.1799	−1.10719	−0.553596	+	0.832785i	$0.686745\pi$
$744$	−12.6321	−0.463114
$745$	23.4922	0.860687
$746$	−20.2377	−0.740956
$747$	−13.8444	−0.506540
$748$	19.8804	0.726899
$749$	0	0
$750$	33.0131	1.20547
$751$	−28.8221	−1.05173	−0.525866	−	0.850567i	$-0.676259\pi$
$751$	−28.8221	−1.05173	−0.525866	+	0.850567i	$0.676259\pi$
$752$	−10.5878	−0.386098
$753$	33.0011	1.20263
$754$	49.0301	1.78557
$755$	50.0664	1.82210
$756$	0	0
$757$	30.1979	1.09756	0.548781	−	0.835966i	$-0.315092\pi$
$757$	30.1979	1.09756	0.548781	+	0.835966i	$0.315092\pi$
$758$	4.65967	0.169247
$759$	−32.6577	−1.18540
$760$	18.7302	0.679416
$761$	−34.9310	−1.26625	−0.633124	−	0.774051i	$-0.718228\pi$
$761$	−34.9310	−1.26625	−0.633124	+	0.774051i	$0.718228\pi$
$762$	−7.39267	−0.267808
$763$	0	0
$764$	−1.14267	−0.0413402
$765$	65.0607	2.35227
$766$	−22.2743	−0.804803
$767$	−18.3922	−0.664105
$768$	3.08180	0.111205
$769$	12.9751	0.467894	0.233947	−	0.972249i	$-0.424836\pi$
$769$	12.9751	0.467894	0.233947	+	0.972249i	$0.424836\pi$
$770$	0	0
$771$	39.8404	1.43482
$772$	−7.79550	−0.280566
$773$	30.9598	1.11355	0.556773	−	0.830665i	$-0.312039\pi$
$773$	30.9598	1.11355	0.556773	+	0.830665i	$0.312039\pi$
$774$	−37.7562	−1.35712
$775$	1.56913	0.0563648
$776$	12.6840	0.455329
$777$	0	0
$778$	18.0875	0.648467
$779$	−8.07305	−0.289247
$780$	44.7022	1.60059
$781$	−47.1858	−1.68844
$782$	9.92869	0.355049
$783$	−84.5291	−3.02082
$784$	0	0
$785$	−56.3861	−2.01251
$786$	−37.2453	−1.32850
$787$	42.0345	1.49837	0.749183	−	0.662363i	$-0.230446\pi$
$787$	42.0345	1.49837	0.749183	+	0.662363i	$0.230446\pi$
$788$	−1.95008	−0.0694688
$789$	80.2774	2.85795
$790$	−0.808339	−0.0287594
$791$	0	0
$792$	−29.9298	−1.06351
$793$	−37.7229	−1.33958
$794$	4.18190	0.148410
$795$	53.7014	1.90459
$796$	15.1870	0.538287
$797$	43.8462	1.55311	0.776556	−	0.630049i	$-0.216965\pi$
$797$	43.8462	1.55311	0.776556	+	0.630049i	$0.216965\pi$
$798$	0	0
$799$	−45.6956	−1.61659
$800$	−0.382815	−0.0135345
$801$	−86.1841	−3.04516
$802$	−16.9057	−0.596960
$803$	−53.6270	−1.89246
$804$	−15.5652	−0.548942
$805$	0	0
$806$	−25.6265	−0.902655
$807$	17.6847	0.622532
$808$	−2.73959	−0.0963785
$809$	−28.1588	−0.990011	−0.495006	−	0.868890i	$-0.664834\pi$
$809$	−28.1588	−0.990011	−0.495006	+	0.868890i	$0.664834\pi$
$810$	−31.8433	−1.11886
$811$	−19.8079	−0.695550	−0.347775	−	0.937578i	$-0.613063\pi$
$811$	−19.8079	−0.695550	−0.347775	+	0.937578i	$0.613063\pi$
$812$	0	0
$813$	96.2731	3.37645
$814$	5.63356	0.197456
$815$	−35.3805	−1.23932
$816$	13.3006	0.465615
$817$	−46.9115	−1.64123
$818$	−12.1534	−0.424934
$819$	0	0
$820$	2.32009	0.0810210
$821$	38.5014	1.34371	0.671855	−	0.740683i	$-0.265498\pi$
$821$	38.5014	1.34371	0.671855	+	0.740683i	$0.265498\pi$
$822$	52.5531	1.83300
$823$	28.3601	0.988571	0.494285	−	0.869300i	$-0.335430\pi$
$823$	28.3601	0.988571	0.494285	+	0.869300i	$0.335430\pi$
$824$	−7.69871	−0.268197
$825$	5.43439	0.189201
$826$	0	0
$827$	−29.1731	−1.01445	−0.507224	−	0.861814i	$-0.669328\pi$
$827$	−29.1731	−1.01445	−0.507224	+	0.861814i	$0.669328\pi$
$828$	−14.9476	−0.519464
$829$	−29.6149	−1.02857	−0.514285	−	0.857620i	$-0.671943\pi$
$829$	−29.6149	−1.02857	−0.514285	+	0.857620i	$0.671943\pi$
$830$	4.94348	0.171591
$831$	8.33873	0.289267
$832$	6.25200	0.216749
$833$	0	0
$834$	22.7707	0.788485
$835$	36.1458	1.25088
$836$	−37.1873	−1.28615
$837$	44.1807	1.52711
$838$	−21.8309	−0.754135
$839$	41.0147	1.41598	0.707992	−	0.706221i	$-0.249601\pi$
$839$	41.0147	1.41598	0.707992	+	0.706221i	$0.249601\pi$
$840$	0	0
$841$	32.5017	1.12075
$842$	27.4543	0.946136
$843$	10.5413	0.363061
$844$	10.4146	0.358487
$845$	60.5254	2.08214
$846$	68.7944	2.36520
$847$	0	0
$848$	7.51063	0.257916
$849$	−55.0778	−1.89027
$850$	−1.65218	−0.0566692
$851$	2.81352	0.0964461
$852$	−31.5688	−1.08153
$853$	40.7787	1.39623	0.698117	−	0.715983i	$-0.254021\pi$
$853$	40.7787	1.39623	0.698117	+	0.715983i	$0.254021\pi$
$854$	0	0
$855$	−121.699	−4.16203
$856$	−13.7046	−0.468413
$857$	54.7090	1.86882	0.934412	−	0.356194i	$-0.115926\pi$
$857$	54.7090	1.86882	0.934412	+	0.356194i	$0.115926\pi$
$858$	−88.7526	−3.02996
$859$	27.2515	0.929808	0.464904	−	0.885361i	$-0.346089\pi$
$859$	27.2515	0.929808	0.464904	+	0.885361i	$0.346089\pi$
$860$	13.4818	0.459724
$861$	0	0
$862$	5.71269	0.194575
$863$	7.09772	0.241609	0.120805	−	0.992676i	$-0.461453\pi$
$863$	7.09772	0.241609	0.120805	+	0.992676i	$0.461453\pi$
$864$	−10.7786	−0.366695
$865$	−34.8557	−1.18513
$866$	32.6769	1.11040
$867$	5.01307	0.170253
$868$	0	0
$869$	1.60489	0.0544423
$870$	56.0729	1.90105
$871$	−31.5769	−1.06994
$872$	−0.303339	−0.0102723
$873$	−82.4143	−2.78930
$874$	−18.5721	−0.628212
$875$	0	0
$876$	−35.8782	−1.21221
$877$	−21.8760	−0.738699	−0.369350	−	0.929290i	$-0.620420\pi$
$877$	−21.8760	−0.738699	−0.369350	+	0.929290i	$0.620420\pi$
$878$	0.822211	0.0277483
$879$	40.6352	1.37059
$880$	10.6872	0.360264
$881$	−7.99974	−0.269518	−0.134759	−	0.990878i	$-0.543026\pi$
$881$	−7.99974	−0.269518	−0.134759	+	0.990878i	$0.543026\pi$
$882$	0	0
$883$	2.80127	0.0942704	0.0471352	−	0.998889i	$-0.484991\pi$
$883$	2.80127	0.0942704	0.0471352	+	0.998889i	$0.484991\pi$
$884$	26.9828	0.907529
$885$	−21.0342	−0.707055
$886$	−31.4921	−1.05800
$887$	−37.8490	−1.27084	−0.635422	−	0.772165i	$-0.719174\pi$
$887$	−37.8490	−1.27084	−0.635422	+	0.772165i	$0.719174\pi$
$888$	3.76903	0.126480
$889$	0	0
$890$	30.7741	1.03155
$891$	63.2223	2.11803
$892$	−10.8892	−0.364599
$893$	85.4760	2.86035
$894$	−31.2050	−1.04365
$895$	−21.2869	−0.711541
$896$	0	0
$897$	−44.3249	−1.47997
$898$	−4.63010	−0.154508
$899$	−32.1450	−1.07210
$900$	2.48734	0.0829113
$901$	32.4149	1.07990
$902$	−4.60635	−0.153375
$903$	0	0
$904$	19.0826	0.634676
$905$	14.8796	0.494616
$906$	−66.5038	−2.20944
$907$	40.8812	1.35744	0.678719	−	0.734398i	$-0.262535\pi$
$907$	40.8812	1.35744	0.678719	+	0.734398i	$0.262535\pi$
$908$	19.7323	0.654839
$909$	17.8005	0.590405
$910$	0	0
$911$	16.6163	0.550522	0.275261	−	0.961369i	$-0.411236\pi$
$911$	16.6163	0.550522	0.275261	+	0.961369i	$0.411236\pi$
$912$	−24.8795	−0.823844
$913$	−9.81489	−0.324825
$914$	−5.20774	−0.172257
$915$	−43.1415	−1.42621
$916$	0.803338	0.0265430
$917$	0	0
$918$	−46.5190	−1.53535
$919$	−37.0592	−1.22247	−0.611234	−	0.791450i	$-0.709327\pi$
$919$	−37.0592	−1.22247	−0.611234	+	0.791450i	$0.709327\pi$
$920$	5.33739	0.175969
$921$	21.9040	0.721760
$922$	−17.7047	−0.583075
$923$	−64.0432	−2.10801
$924$	0	0
$925$	−0.468181	−0.0153937
$926$	−0.868568	−0.0285429
$927$	50.0224	1.64295
$928$	7.84231	0.257436
$929$	−28.1025	−0.922012	−0.461006	−	0.887397i	$-0.652511\pi$
$929$	−28.1025	−0.922012	−0.461006	+	0.887397i	$0.652511\pi$
$930$	−29.3075	−0.961032
$931$	0	0
$932$	−9.00657	−0.295020
$933$	31.5971	1.03444
$934$	−10.1656	−0.332628
$935$	46.1243	1.50843
$936$	−40.6224	−1.32778
$937$	−37.0880	−1.21161	−0.605807	−	0.795612i	$-0.707150\pi$
$937$	−37.0880	−1.21161	−0.605807	+	0.795612i	$0.707150\pi$
$938$	0	0
$939$	61.9630	2.02209
$940$	−24.5647	−0.801212
$941$	−7.24646	−0.236228	−0.118114	−	0.993000i	$-0.537685\pi$
$941$	−7.24646	−0.236228	−0.118114	+	0.993000i	$0.537685\pi$
$942$	74.8984	2.44032
$943$	−2.30051	−0.0749149
$944$	−2.94182	−0.0957480
$945$	0	0
$946$	−26.7669	−0.870269
$947$	−44.7050	−1.45272	−0.726359	−	0.687316i	$-0.758789\pi$
$947$	−44.7050	−1.45272	−0.726359	+	0.687316i	$0.758789\pi$
$948$	1.07373	0.0348730
$949$	−72.7856	−2.36272
$950$	3.09048	0.100268
$951$	−22.4747	−0.728792
$952$	0	0
$953$	13.8763	0.449496	0.224748	−	0.974417i	$-0.427844\pi$
$953$	13.8763	0.449496	0.224748	+	0.974417i	$0.427844\pi$
$954$	−48.8003	−1.57997
$955$	−2.65109	−0.0857872
$956$	2.96336	0.0958418
$957$	−111.328	−3.59873
$958$	11.5948	0.374610
$959$	0	0
$960$	7.15005	0.230767
$961$	−14.1988	−0.458026
$962$	7.64618	0.246523
$963$	89.0456	2.86945
$964$	9.27361	0.298683
$965$	−18.0863	−0.582217
$966$	0	0
$967$	−3.77922	−0.121532	−0.0607658	−	0.998152i	$-0.519354\pi$
$967$	−3.77922	−0.121532	−0.0607658	+	0.998152i	$0.519354\pi$
$968$	−10.2185	−0.328435
$969$	−107.377	−3.44944
$970$	29.4280	0.944877
$971$	−37.2950	−1.19685	−0.598426	−	0.801178i	$-0.704207\pi$
$971$	−37.2950	−1.19685	−0.598426	+	0.801178i	$0.704207\pi$
$972$	9.96195	0.319530
$973$	0	0
$974$	26.9925	0.864896
$975$	7.37586	0.236216
$976$	−6.03373	−0.193135
$977$	−32.0938	−1.02677	−0.513385	−	0.858158i	$-0.671609\pi$
$977$	−32.0938	−1.02677	−0.513385	+	0.858158i	$0.671609\pi$
$978$	46.9963	1.50278
$979$	−61.0995	−1.95275
$980$	0	0
$981$	1.97094	0.0629274
$982$	12.0422	0.384281
$983$	26.0744	0.831644	0.415822	−	0.909446i	$-0.363494\pi$
$983$	26.0744	0.831644	0.415822	+	0.909446i	$0.363494\pi$
$984$	−3.08180	−0.0982442
$985$	−4.52437	−0.144158
$986$	33.8463	1.07789
$987$	0	0
$988$	−50.4727	−1.60575
$989$	−13.3680	−0.425077
$990$	−69.4398	−2.20694
$991$	−13.7567	−0.436996	−0.218498	−	0.975837i	$-0.570116\pi$
$991$	−13.7567	−0.436996	−0.218498	+	0.975837i	$0.570116\pi$
$992$	−4.09893	−0.130141
$993$	58.5376	1.85763
$994$	0	0
$995$	35.2351	1.11703
$996$	−6.56648	−0.208067
$997$	−25.7524	−0.815587	−0.407794	−	0.913074i	$-0.633702\pi$
$997$	−25.7524	−0.815587	−0.407794	+	0.913074i	$0.633702\pi$
$998$	−5.88313	−0.186227
$999$	−13.1822	−0.417066

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bs.1.10	yes	10
7.6	odd	2		4018.2.a.br.1.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.br.1.1	✓	10	7.6	odd	2
4018.2.a.bs.1.10	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.08180 q^{3} +1.00000 q^{4} +2.32009 q^{5} -3.08180 q^{6} -1.00000 q^{8} +6.49750 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.08180 q^{3} +1.00000 q^{4} +2.32009 q^{5} -3.08180 q^{6} -1.00000 q^{8} +6.49750 q^{9} -2.32009 q^{10} +4.60635 q^{11} +3.08180 q^{12} +6.25200 q^{13} +7.15005 q^{15} +1.00000 q^{16} +4.31586 q^{17} -6.49750 q^{18} -8.07305 q^{19} +2.32009 q^{20} -4.60635 q^{22} -2.30051 q^{23} -3.08180 q^{24} +0.382815 q^{25} -6.25200 q^{26} +10.7786 q^{27} -7.84231 q^{29} -7.15005 q^{30} +4.09893 q^{31} -1.00000 q^{32} +14.1959 q^{33} -4.31586 q^{34} +6.49750 q^{36} -1.22300 q^{37} +8.07305 q^{38} +19.2674 q^{39} -2.32009 q^{40} +1.00000 q^{41} +5.81088 q^{43} +4.60635 q^{44} +15.0748 q^{45} +2.30051 q^{46} -10.5878 q^{47} +3.08180 q^{48} -0.382815 q^{50} +13.3006 q^{51} +6.25200 q^{52} +7.51063 q^{53} -10.7786 q^{54} +10.6872 q^{55} -24.8795 q^{57} +7.84231 q^{58} -2.94182 q^{59} +7.15005 q^{60} -6.03373 q^{61} -4.09893 q^{62} +1.00000 q^{64} +14.5052 q^{65} -14.1959 q^{66} -5.05068 q^{67} +4.31586 q^{68} -7.08972 q^{69} -10.2436 q^{71} -6.49750 q^{72} -11.6420 q^{73} +1.22300 q^{74} +1.17976 q^{75} -8.07305 q^{76} -19.2674 q^{78} +0.348408 q^{79} +2.32009 q^{80} +13.7250 q^{81} -1.00000 q^{82} -2.13073 q^{83} +10.0132 q^{85} -5.81088 q^{86} -24.1684 q^{87} -4.60635 q^{88} -13.2642 q^{89} -15.0748 q^{90} -2.30051 q^{92} +12.6321 q^{93} +10.5878 q^{94} -18.7302 q^{95} -3.08180 q^{96} -12.6840 q^{97} +29.9298 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 20 q^{17} - 10 q^{18} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 16 q^{27} - 4 q^{29} - 4 q^{30} - 4 q^{31} - 10 q^{32} + 36 q^{33} - 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} - 4 q^{40} + 10 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 4 q^{46} + 24 q^{47} + 4 q^{48} - 6 q^{50} + 20 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{54} + 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} + 4 q^{62} + 10 q^{64} - 12 q^{65} - 36 q^{66} + 8 q^{67} + 20 q^{68} + 4 q^{71} - 10 q^{72} - 24 q^{73} + 16 q^{74} + 48 q^{75} - 20 q^{78} + 24 q^{79} + 4 q^{80} - 18 q^{81} - 10 q^{82} + 48 q^{83} + 8 q^{85} + 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 24 q^{94} - 4 q^{95} - 4 q^{96} + 4 q^{97} + 32 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 20 * q^17 - 10 * q^18 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 16 * q^27 - 4 * q^29 - 4 * q^30 - 4 * q^31 - 10 * q^32 + 36 * q^33 - 20 * q^34 + 10 * q^36 - 16 * q^37 + 20 * q^39 - 4 * q^40 + 10 * q^41 - 8 * q^43 + 4 * q^44 + 4 * q^45 - 4 * q^46 + 24 * q^47 + 4 * q^48 - 6 * q^50 + 20 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^54 + 20 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^60 + 4 * q^62 + 10 * q^64 - 12 * q^65 - 36 * q^66 + 8 * q^67 + 20 * q^68 + 4 * q^71 - 10 * q^72 - 24 * q^73 + 16 * q^74 + 48 * q^75 - 20 * q^78 + 24 * q^79 + 4 * q^80 - 18 * q^81 - 10 * q^82 + 48 * q^83 + 8 * q^85 + 8 * q^86 + 4 * q^87 - 4 * q^88 + 20 * q^89 - 4 * q^90 + 4 * q^92 + 4 * q^93 - 24 * q^94 - 4 * q^95 - 4 * q^96 + 4 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more