LMFDB - Embedded newform 5610.2.a.bw.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -7.12311 q^{13} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +3.12311 q^{19} -1.00000 q^{20} -1.00000 q^{22} -0.876894 q^{23} +1.00000 q^{24} +1.00000 q^{25} -7.12311 q^{26} +1.00000 q^{27} -0.876894 q^{29} -1.00000 q^{30} +1.12311 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{36} -7.12311 q^{37} +3.12311 q^{38} -7.12311 q^{39} -1.00000 q^{40} -5.12311 q^{41} -1.00000 q^{44} -1.00000 q^{45} -0.876894 q^{46} -1.12311 q^{47} +1.00000 q^{48} -7.00000 q^{49} +1.00000 q^{50} -1.00000 q^{51} -7.12311 q^{52} +4.00000 q^{53} +1.00000 q^{54} +1.00000 q^{55} +3.12311 q^{57} -0.876894 q^{58} -6.24621 q^{59} -1.00000 q^{60} +8.24621 q^{61} +1.12311 q^{62} +1.00000 q^{64} +7.12311 q^{65} -1.00000 q^{66} -15.1231 q^{67} -1.00000 q^{68} -0.876894 q^{69} -8.00000 q^{71} +1.00000 q^{72} +0.246211 q^{73} -7.12311 q^{74} +1.00000 q^{75} +3.12311 q^{76} -7.12311 q^{78} +3.12311 q^{79} -1.00000 q^{80} +1.00000 q^{81} -5.12311 q^{82} -10.2462 q^{83} +1.00000 q^{85} -0.876894 q^{87} -1.00000 q^{88} -4.24621 q^{89} -1.00000 q^{90} -0.876894 q^{92} +1.12311 q^{93} -1.12311 q^{94} -3.12311 q^{95} +1.00000 q^{96} +2.87689 q^{97} -7.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{15} + 2 q^{16} - 2 q^{17} + 2 q^{18} - 2 q^{19} - 2 q^{20} - 2 q^{22} - 10 q^{23} + 2 q^{24} + 2 q^{25} - 6 q^{26} + 2 q^{27} - 10 q^{29} - 2 q^{30} - 6 q^{31} + 2 q^{32} - 2 q^{33} - 2 q^{34} + 2 q^{36} - 6 q^{37} - 2 q^{38} - 6 q^{39} - 2 q^{40} - 2 q^{41} - 2 q^{44} - 2 q^{45} - 10 q^{46} + 6 q^{47} + 2 q^{48} - 14 q^{49} + 2 q^{50} - 2 q^{51} - 6 q^{52} + 8 q^{53} + 2 q^{54} + 2 q^{55} - 2 q^{57} - 10 q^{58} + 4 q^{59} - 2 q^{60} - 6 q^{62} + 2 q^{64} + 6 q^{65} - 2 q^{66} - 22 q^{67} - 2 q^{68} - 10 q^{69} - 16 q^{71} + 2 q^{72} - 16 q^{73} - 6 q^{74} + 2 q^{75} - 2 q^{76} - 6 q^{78} - 2 q^{79} - 2 q^{80} + 2 q^{81} - 2 q^{82} - 4 q^{83} + 2 q^{85} - 10 q^{87} - 2 q^{88} + 8 q^{89} - 2 q^{90} - 10 q^{92} - 6 q^{93} + 6 q^{94} + 2 q^{95} + 2 q^{96} + 14 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 6 * q^13 - 2 * q^15 + 2 * q^16 - 2 * q^17 + 2 * q^18 - 2 * q^19 - 2 * q^20 - 2 * q^22 - 10 * q^23 + 2 * q^24 + 2 * q^25 - 6 * q^26 + 2 * q^27 - 10 * q^29 - 2 * q^30 - 6 * q^31 + 2 * q^32 - 2 * q^33 - 2 * q^34 + 2 * q^36 - 6 * q^37 - 2 * q^38 - 6 * q^39 - 2 * q^40 - 2 * q^41 - 2 * q^44 - 2 * q^45 - 10 * q^46 + 6 * q^47 + 2 * q^48 - 14 * q^49 + 2 * q^50 - 2 * q^51 - 6 * q^52 + 8 * q^53 + 2 * q^54 + 2 * q^55 - 2 * q^57 - 10 * q^58 + 4 * q^59 - 2 * q^60 - 6 * q^62 + 2 * q^64 + 6 * q^65 - 2 * q^66 - 22 * q^67 - 2 * q^68 - 10 * q^69 - 16 * q^71 + 2 * q^72 - 16 * q^73 - 6 * q^74 + 2 * q^75 - 2 * q^76 - 6 * q^78 - 2 * q^79 - 2 * q^80 + 2 * q^81 - 2 * q^82 - 4 * q^83 + 2 * q^85 - 10 * q^87 - 2 * q^88 + 8 * q^89 - 2 * q^90 - 10 * q^92 - 6 * q^93 + 6 * q^94 + 2 * q^95 + 2 * q^96 + 14 * q^97 - 14 * q^98 - 2 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	−7.12311	−1.97559	−0.987797	−	0.155747i	$-0.950222\pi$
$13$	−7.12311	−1.97559	−0.987797	+	0.155747i	$0.950222\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	3.12311	0.716490	0.358245	−	0.933628i	$-0.383375\pi$
$19$	3.12311	0.716490	0.358245	+	0.933628i	$0.383375\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−1.00000	−0.213201
$23$	−0.876894	−0.182845	−0.0914226	−	0.995812i	$-0.529141\pi$
$23$	−0.876894	−0.182845	−0.0914226	+	0.995812i	$0.529141\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−7.12311	−1.39696
$27$	1.00000	0.192450
$28$	0	0
$29$	−0.876894	−0.162835	−0.0814176	−	0.996680i	$-0.525945\pi$
$29$	−0.876894	−0.162835	−0.0814176	+	0.996680i	$0.525945\pi$
$30$	−1.00000	−0.182574
$31$	1.12311	0.201716	0.100858	−	0.994901i	$-0.467841\pi$
$31$	1.12311	0.201716	0.100858	+	0.994901i	$0.467841\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	−7.12311	−1.17103	−0.585516	−	0.810661i	$-0.699108\pi$
$37$	−7.12311	−1.17103	−0.585516	+	0.810661i	$0.699108\pi$
$38$	3.12311	0.506635
$39$	−7.12311	−1.14061
$40$	−1.00000	−0.158114
$41$	−5.12311	−0.800095	−0.400047	−	0.916494i	$-0.631006\pi$
$41$	−5.12311	−0.800095	−0.400047	+	0.916494i	$0.631006\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	−0.876894	−0.129291
$47$	−1.12311	−0.163822	−0.0819109	−	0.996640i	$-0.526102\pi$
$47$	−1.12311	−0.163822	−0.0819109	+	0.996640i	$0.526102\pi$
$48$	1.00000	0.144338
$49$	−7.00000	−1.00000
$50$	1.00000	0.141421
$51$	−1.00000	−0.140028
$52$	−7.12311	−0.987797
$53$	4.00000	0.549442	0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000	0.549442	0.274721	+	0.961524i	$0.411414\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	0	0
$57$	3.12311	0.413665
$58$	−0.876894	−0.115142
$59$	−6.24621	−0.813187	−0.406594	−	0.913609i	$-0.633284\pi$
$59$	−6.24621	−0.813187	−0.406594	+	0.913609i	$0.633284\pi$
$60$	−1.00000	−0.129099
$61$	8.24621	1.05582	0.527910	−	0.849301i	$-0.322976\pi$
$61$	8.24621	1.05582	0.527910	+	0.849301i	$0.322976\pi$
$62$	1.12311	0.142635
$63$	0	0
$64$	1.00000	0.125000
$65$	7.12311	0.883513
$66$	−1.00000	−0.123091
$67$	−15.1231	−1.84758	−0.923791	−	0.382898i	$-0.874926\pi$
$67$	−15.1231	−1.84758	−0.923791	+	0.382898i	$0.874926\pi$
$68$	−1.00000	−0.121268
$69$	−0.876894	−0.105566
$70$	0	0
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	1.00000	0.117851
$73$	0.246211	0.0288168	0.0144084	−	0.999896i	$-0.495413\pi$
$73$	0.246211	0.0288168	0.0144084	+	0.999896i	$0.495413\pi$
$74$	−7.12311	−0.828044
$75$	1.00000	0.115470
$76$	3.12311	0.358245
$77$	0	0
$78$	−7.12311	−0.806533
$79$	3.12311	0.351377	0.175688	−	0.984446i	$-0.443785\pi$
$79$	3.12311	0.351377	0.175688	+	0.984446i	$0.443785\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−5.12311	−0.565752
$83$	−10.2462	−1.12467	−0.562334	−	0.826910i	$-0.690096\pi$
$83$	−10.2462	−1.12467	−0.562334	+	0.826910i	$0.690096\pi$
$84$	0	0
$85$	1.00000	0.108465
$86$	0	0
$87$	−0.876894	−0.0940129
$88$	−1.00000	−0.106600
$89$	−4.24621	−0.450097	−0.225049	−	0.974348i	$-0.572254\pi$
$89$	−4.24621	−0.450097	−0.225049	+	0.974348i	$0.572254\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	−0.876894	−0.0914226
$93$	1.12311	0.116461
$94$	−1.12311	−0.115840
$95$	−3.12311	−0.320424
$96$	1.00000	0.102062
$97$	2.87689	0.292104	0.146052	−	0.989277i	$-0.453343\pi$
$97$	2.87689	0.292104	0.146052	+	0.989277i	$0.453343\pi$
$98$	−7.00000	−0.707107
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	15.3693	1.52930	0.764652	−	0.644443i	$-0.222911\pi$
$101$	15.3693	1.52930	0.764652	+	0.644443i	$0.222911\pi$
$102$	−1.00000	−0.0990148
$103$	−14.2462	−1.40372	−0.701860	−	0.712314i	$-0.747647\pi$
$103$	−14.2462	−1.40372	−0.701860	+	0.712314i	$0.747647\pi$
$104$	−7.12311	−0.698478
$105$	0	0
$106$	4.00000	0.388514
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	1.00000	0.0962250
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	1.00000	0.0953463
$111$	−7.12311	−0.676095
$112$	0	0
$113$	−15.3693	−1.44582	−0.722912	−	0.690940i	$-0.757197\pi$
$113$	−15.3693	−1.44582	−0.722912	+	0.690940i	$0.757197\pi$
$114$	3.12311	0.292506
$115$	0.876894	0.0817708
$116$	−0.876894	−0.0814176
$117$	−7.12311	−0.658531
$118$	−6.24621	−0.575010
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	8.24621	0.746577
$123$	−5.12311	−0.461935
$124$	1.12311	0.100858
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−15.3693	−1.36381	−0.681903	−	0.731442i	$-0.738847\pi$
$127$	−15.3693	−1.36381	−0.681903	+	0.731442i	$0.738847\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	7.12311	0.624738
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	−1.00000	−0.0870388
$133$	0	0
$134$	−15.1231	−1.30644
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	12.2462	1.04626	0.523132	−	0.852252i	$-0.324763\pi$
$137$	12.2462	1.04626	0.523132	+	0.852252i	$0.324763\pi$
$138$	−0.876894	−0.0746462
$139$	−2.24621	−0.190521	−0.0952606	−	0.995452i	$-0.530368\pi$
$139$	−2.24621	−0.190521	−0.0952606	+	0.995452i	$0.530368\pi$
$140$	0	0
$141$	−1.12311	−0.0945826
$142$	−8.00000	−0.671345
$143$	7.12311	0.595664
$144$	1.00000	0.0833333
$145$	0.876894	0.0728221
$146$	0.246211	0.0203766
$147$	−7.00000	−0.577350
$148$	−7.12311	−0.585516
$149$	−19.3693	−1.58680	−0.793398	−	0.608703i	$-0.791690\pi$
$149$	−19.3693	−1.58680	−0.793398	+	0.608703i	$0.791690\pi$
$150$	1.00000	0.0816497
$151$	−15.3693	−1.25074	−0.625369	−	0.780329i	$-0.715051\pi$
$151$	−15.3693	−1.25074	−0.625369	+	0.780329i	$0.715051\pi$
$152$	3.12311	0.253317
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	−1.12311	−0.0902100
$156$	−7.12311	−0.570305
$157$	17.6155	1.40587	0.702936	−	0.711253i	$-0.251872\pi$
$157$	17.6155	1.40587	0.702936	+	0.711253i	$0.251872\pi$
$158$	3.12311	0.248461
$159$	4.00000	0.317221
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	−24.4924	−1.91839	−0.959197	−	0.282738i	$-0.908757\pi$
$163$	−24.4924	−1.91839	−0.959197	+	0.282738i	$0.908757\pi$
$164$	−5.12311	−0.400047
$165$	1.00000	0.0778499
$166$	−10.2462	−0.795260
$167$	−14.8769	−1.15121	−0.575604	−	0.817728i	$-0.695233\pi$
$167$	−14.8769	−1.15121	−0.575604	+	0.817728i	$0.695233\pi$
$168$	0	0
$169$	37.7386	2.90297
$170$	1.00000	0.0766965
$171$	3.12311	0.238830
$172$	0	0
$173$	−23.1231	−1.75802	−0.879009	−	0.476806i	$-0.841794\pi$
$173$	−23.1231	−1.75802	−0.879009	+	0.476806i	$0.841794\pi$
$174$	−0.876894	−0.0664772
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	−6.24621	−0.469494
$178$	−4.24621	−0.318267
$179$	16.4924	1.23270	0.616351	−	0.787472i	$-0.288610\pi$
$179$	16.4924	1.23270	0.616351	+	0.787472i	$0.288610\pi$
$180$	−1.00000	−0.0745356
$181$	23.6155	1.75533	0.877664	−	0.479276i	$-0.159101\pi$
$181$	23.6155	1.75533	0.877664	+	0.479276i	$0.159101\pi$
$182$	0	0
$183$	8.24621	0.609577
$184$	−0.876894	−0.0646455
$185$	7.12311	0.523701
$186$	1.12311	0.0823501
$187$	1.00000	0.0731272
$188$	−1.12311	−0.0819109
$189$	0	0
$190$	−3.12311	−0.226574
$191$	21.1231	1.52841	0.764207	−	0.644971i	$-0.223131\pi$
$191$	21.1231	1.52841	0.764207	+	0.644971i	$0.223131\pi$
$192$	1.00000	0.0721688
$193$	10.4924	0.755261	0.377631	−	0.925956i	$-0.376739\pi$
$193$	10.4924	0.755261	0.377631	+	0.925956i	$0.376739\pi$
$194$	2.87689	0.206549
$195$	7.12311	0.510096
$196$	−7.00000	−0.500000
$197$	−23.6155	−1.68254	−0.841268	−	0.540618i	$-0.818191\pi$
$197$	−23.6155	−1.68254	−0.841268	+	0.540618i	$0.818191\pi$
$198$	−1.00000	−0.0710669
$199$	−6.87689	−0.487490	−0.243745	−	0.969839i	$-0.578376\pi$
$199$	−6.87689	−0.487490	−0.243745	+	0.969839i	$0.578376\pi$
$200$	1.00000	0.0707107
$201$	−15.1231	−1.06670
$202$	15.3693	1.08138
$203$	0	0
$204$	−1.00000	−0.0700140
$205$	5.12311	0.357813
$206$	−14.2462	−0.992581
$207$	−0.876894	−0.0609484
$208$	−7.12311	−0.493899
$209$	−3.12311	−0.216030
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	4.00000	0.274721
$213$	−8.00000	−0.548151
$214$	12.0000	0.820303
$215$	0	0
$216$	1.00000	0.0680414
$217$	0	0
$218$	−6.00000	−0.406371
$219$	0.246211	0.0166374
$220$	1.00000	0.0674200
$221$	7.12311	0.479152
$222$	−7.12311	−0.478072
$223$	26.2462	1.75758	0.878788	−	0.477212i	$-0.158353\pi$
$223$	26.2462	1.75758	0.878788	+	0.477212i	$0.158353\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−15.3693	−1.02235
$227$	−1.75379	−0.116403	−0.0582015	−	0.998305i	$-0.518537\pi$
$227$	−1.75379	−0.116403	−0.0582015	+	0.998305i	$0.518537\pi$
$228$	3.12311	0.206833
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	0.876894	0.0578207
$231$	0	0
$232$	−0.876894	−0.0575709
$233$	22.4924	1.47353	0.736764	−	0.676150i	$-0.236353\pi$
$233$	22.4924	1.47353	0.736764	+	0.676150i	$0.236353\pi$
$234$	−7.12311	−0.465652
$235$	1.12311	0.0732633
$236$	−6.24621	−0.406594
$237$	3.12311	0.202868
$238$	0	0
$239$	9.75379	0.630920	0.315460	−	0.948939i	$-0.397841\pi$
$239$	9.75379	0.630920	0.315460	+	0.948939i	$0.397841\pi$
$240$	−1.00000	−0.0645497
$241$	−25.6155	−1.65004	−0.825021	−	0.565103i	$-0.808837\pi$
$241$	−25.6155	−1.65004	−0.825021	+	0.565103i	$0.808837\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	8.24621	0.527910
$245$	7.00000	0.447214
$246$	−5.12311	−0.326637
$247$	−22.2462	−1.41549
$248$	1.12311	0.0713173
$249$	−10.2462	−0.649327
$250$	−1.00000	−0.0632456
$251$	22.7386	1.43525	0.717625	−	0.696430i	$-0.245229\pi$
$251$	22.7386	1.43525	0.717625	+	0.696430i	$0.245229\pi$
$252$	0	0
$253$	0.876894	0.0551299
$254$	−15.3693	−0.964357
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	22.4924	1.40304	0.701519	−	0.712650i	$-0.252505\pi$
$257$	22.4924	1.40304	0.701519	+	0.712650i	$0.252505\pi$
$258$	0	0
$259$	0	0
$260$	7.12311	0.441756
$261$	−0.876894	−0.0542784
$262$	0	0
$263$	13.7538	0.848095	0.424047	−	0.905640i	$-0.360609\pi$
$263$	13.7538	0.848095	0.424047	+	0.905640i	$0.360609\pi$
$264$	−1.00000	−0.0615457
$265$	−4.00000	−0.245718
$266$	0	0
$267$	−4.24621	−0.259864
$268$	−15.1231	−0.923791
$269$	24.2462	1.47832	0.739159	−	0.673531i	$-0.235223\pi$
$269$	24.2462	1.47832	0.739159	+	0.673531i	$0.235223\pi$
$270$	−1.00000	−0.0608581
$271$	−27.3693	−1.66257	−0.831284	−	0.555848i	$-0.812394\pi$
$271$	−27.3693	−1.66257	−0.831284	+	0.555848i	$0.812394\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	12.2462	0.739821
$275$	−1.00000	−0.0603023
$276$	−0.876894	−0.0527828
$277$	4.24621	0.255130	0.127565	−	0.991830i	$-0.459284\pi$
$277$	4.24621	0.255130	0.127565	+	0.991830i	$0.459284\pi$
$278$	−2.24621	−0.134719
$279$	1.12311	0.0672386
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	−1.12311	−0.0668800
$283$	−24.4924	−1.45592	−0.727962	−	0.685618i	$-0.759532\pi$
$283$	−24.4924	−1.45592	−0.727962	+	0.685618i	$0.759532\pi$
$284$	−8.00000	−0.474713
$285$	−3.12311	−0.184997
$286$	7.12311	0.421198
$287$	0	0
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	0.876894	0.0514930
$291$	2.87689	0.168647
$292$	0.246211	0.0144084
$293$	18.4924	1.08034	0.540169	−	0.841556i	$-0.318360\pi$
$293$	18.4924	1.08034	0.540169	+	0.841556i	$0.318360\pi$
$294$	−7.00000	−0.408248
$295$	6.24621	0.363668
$296$	−7.12311	−0.414022
$297$	−1.00000	−0.0580259
$298$	−19.3693	−1.12203
$299$	6.24621	0.361228
$300$	1.00000	0.0577350
$301$	0	0
$302$	−15.3693	−0.884405
$303$	15.3693	0.882944
$304$	3.12311	0.179122
$305$	−8.24621	−0.472177
$306$	−1.00000	−0.0571662
$307$	16.4924	0.941272	0.470636	−	0.882327i	$-0.344024\pi$
$307$	16.4924	0.941272	0.470636	+	0.882327i	$0.344024\pi$
$308$	0	0
$309$	−14.2462	−0.810439
$310$	−1.12311	−0.0637881
$311$	−4.00000	−0.226819	−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000	−0.226819	−0.113410	+	0.993548i	$0.536177\pi$
$312$	−7.12311	−0.403266
$313$	−5.12311	−0.289575	−0.144788	−	0.989463i	$-0.546250\pi$
$313$	−5.12311	−0.289575	−0.144788	+	0.989463i	$0.546250\pi$
$314$	17.6155	0.994102
$315$	0	0
$316$	3.12311	0.175688
$317$	11.7538	0.660159	0.330079	−	0.943953i	$-0.392925\pi$
$317$	11.7538	0.660159	0.330079	+	0.943953i	$0.392925\pi$
$318$	4.00000	0.224309
$319$	0.876894	0.0490967
$320$	−1.00000	−0.0559017
$321$	12.0000	0.669775
$322$	0	0
$323$	−3.12311	−0.173774
$324$	1.00000	0.0555556
$325$	−7.12311	−0.395119
$326$	−24.4924	−1.35651
$327$	−6.00000	−0.331801
$328$	−5.12311	−0.282876
$329$	0	0
$330$	1.00000	0.0550482
$331$	−13.7538	−0.755977	−0.377988	−	0.925810i	$-0.623384\pi$
$331$	−13.7538	−0.755977	−0.377988	+	0.925810i	$0.623384\pi$
$332$	−10.2462	−0.562334
$333$	−7.12311	−0.390344
$334$	−14.8769	−0.814027
$335$	15.1231	0.826264
$336$	0	0
$337$	−22.4924	−1.22524	−0.612620	−	0.790377i	$-0.709884\pi$
$337$	−22.4924	−1.22524	−0.612620	+	0.790377i	$0.709884\pi$
$338$	37.7386	2.05271
$339$	−15.3693	−0.834747
$340$	1.00000	0.0542326
$341$	−1.12311	−0.0608196
$342$	3.12311	0.168878
$343$	0	0
$344$	0	0
$345$	0.876894	0.0472104
$346$	−23.1231	−1.24311
$347$	20.0000	1.07366	0.536828	−	0.843692i	$-0.319622\pi$
$347$	20.0000	1.07366	0.536828	+	0.843692i	$0.319622\pi$
$348$	−0.876894	−0.0470065
$349$	4.00000	0.214115	0.107058	−	0.994253i	$-0.465857\pi$
$349$	4.00000	0.214115	0.107058	+	0.994253i	$0.465857\pi$
$350$	0	0
$351$	−7.12311	−0.380203
$352$	−1.00000	−0.0533002
$353$	26.0000	1.38384	0.691920	−	0.721974i	$-0.256765\pi$
$353$	26.0000	1.38384	0.691920	+	0.721974i	$0.256765\pi$
$354$	−6.24621	−0.331982
$355$	8.00000	0.424596
$356$	−4.24621	−0.225049
$357$	0	0
$358$	16.4924	0.871652
$359$	−5.75379	−0.303673	−0.151837	−	0.988406i	$-0.548519\pi$
$359$	−5.75379	−0.303673	−0.151837	+	0.988406i	$0.548519\pi$
$360$	−1.00000	−0.0527046
$361$	−9.24621	−0.486643
$362$	23.6155	1.24120
$363$	1.00000	0.0524864
$364$	0	0
$365$	−0.246211	−0.0128873
$366$	8.24621	0.431036
$367$	18.4924	0.965297	0.482648	−	0.875814i	$-0.339675\pi$
$367$	18.4924	0.965297	0.482648	+	0.875814i	$0.339675\pi$
$368$	−0.876894	−0.0457113
$369$	−5.12311	−0.266698
$370$	7.12311	0.370313
$371$	0	0
$372$	1.12311	0.0582303
$373$	3.61553	0.187205	0.0936025	−	0.995610i	$-0.470162\pi$
$373$	3.61553	0.187205	0.0936025	+	0.995610i	$0.470162\pi$
$374$	1.00000	0.0517088
$375$	−1.00000	−0.0516398
$376$	−1.12311	−0.0579198
$377$	6.24621	0.321696
$378$	0	0
$379$	28.0000	1.43826	0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000	1.43826	0.719132	+	0.694874i	$0.244540\pi$
$380$	−3.12311	−0.160212
$381$	−15.3693	−0.787394
$382$	21.1231	1.08075
$383$	−19.3693	−0.989726	−0.494863	−	0.868971i	$-0.664782\pi$
$383$	−19.3693	−0.989726	−0.494863	+	0.868971i	$0.664782\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	10.4924	0.534050
$387$	0	0
$388$	2.87689	0.146052
$389$	−7.61553	−0.386123	−0.193061	−	0.981187i	$-0.561842\pi$
$389$	−7.61553	−0.386123	−0.193061	+	0.981187i	$0.561842\pi$
$390$	7.12311	0.360692
$391$	0.876894	0.0443465
$392$	−7.00000	−0.353553
$393$	0	0
$394$	−23.6155	−1.18973
$395$	−3.12311	−0.157140
$396$	−1.00000	−0.0502519
$397$	−21.8617	−1.09721	−0.548605	−	0.836082i	$-0.684841\pi$
$397$	−21.8617	−1.09721	−0.548605	+	0.836082i	$0.684841\pi$
$398$	−6.87689	−0.344708
$399$	0	0
$400$	1.00000	0.0500000
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	−15.1231	−0.754272
$403$	−8.00000	−0.398508
$404$	15.3693	0.764652
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	7.12311	0.353079
$408$	−1.00000	−0.0495074
$409$	10.4924	0.518817	0.259408	−	0.965768i	$-0.416472\pi$
$409$	10.4924	0.518817	0.259408	+	0.965768i	$0.416472\pi$
$410$	5.12311	0.253012
$411$	12.2462	0.604061
$412$	−14.2462	−0.701860
$413$	0	0
$414$	−0.876894	−0.0430970
$415$	10.2462	0.502967
$416$	−7.12311	−0.349239
$417$	−2.24621	−0.109997
$418$	−3.12311	−0.152756
$419$	16.4924	0.805708	0.402854	−	0.915264i	$-0.368018\pi$
$419$	16.4924	0.805708	0.402854	+	0.915264i	$0.368018\pi$
$420$	0	0
$421$	−40.7386	−1.98548	−0.992740	−	0.120282i	$-0.961620\pi$
$421$	−40.7386	−1.98548	−0.992740	+	0.120282i	$0.961620\pi$
$422$	20.0000	0.973585
$423$	−1.12311	−0.0546073
$424$	4.00000	0.194257
$425$	−1.00000	−0.0485071
$426$	−8.00000	−0.387601
$427$	0	0
$428$	12.0000	0.580042
$429$	7.12311	0.343907
$430$	0	0
$431$	−30.9848	−1.49249	−0.746244	−	0.665673i	$-0.768145\pi$
$431$	−30.9848	−1.49249	−0.746244	+	0.665673i	$0.768145\pi$
$432$	1.00000	0.0481125
$433$	−30.4924	−1.46537	−0.732686	−	0.680567i	$-0.761734\pi$
$433$	−30.4924	−1.46537	−0.732686	+	0.680567i	$0.761734\pi$
$434$	0	0
$435$	0.876894	0.0420439
$436$	−6.00000	−0.287348
$437$	−2.73863	−0.131007
$438$	0.246211	0.0117644
$439$	−3.61553	−0.172560	−0.0862799	−	0.996271i	$-0.527498\pi$
$439$	−3.61553	−0.172560	−0.0862799	+	0.996271i	$0.527498\pi$
$440$	1.00000	0.0476731
$441$	−7.00000	−0.333333
$442$	7.12311	0.338812
$443$	−8.87689	−0.421754	−0.210877	−	0.977513i	$-0.567632\pi$
$443$	−8.87689	−0.421754	−0.210877	+	0.977513i	$0.567632\pi$
$444$	−7.12311	−0.338048
$445$	4.24621	0.201290
$446$	26.2462	1.24279
$447$	−19.3693	−0.916137
$448$	0	0
$449$	16.7386	0.789945	0.394972	−	0.918693i	$-0.370754\pi$
$449$	16.7386	0.789945	0.394972	+	0.918693i	$0.370754\pi$
$450$	1.00000	0.0471405
$451$	5.12311	0.241238
$452$	−15.3693	−0.722912
$453$	−15.3693	−0.722113
$454$	−1.75379	−0.0823094
$455$	0	0
$456$	3.12311	0.146253
$457$	−14.4924	−0.677927	−0.338963	−	0.940800i	$-0.610076\pi$
$457$	−14.4924	−0.677927	−0.338963	+	0.940800i	$0.610076\pi$
$458$	−6.00000	−0.280362
$459$	−1.00000	−0.0466760
$460$	0.876894	0.0408854
$461$	5.12311	0.238607	0.119303	−	0.992858i	$-0.461934\pi$
$461$	5.12311	0.238607	0.119303	+	0.992858i	$0.461934\pi$
$462$	0	0
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	−0.876894	−0.0407088
$465$	−1.12311	−0.0520828
$466$	22.4924	1.04194
$467$	14.6307	0.677027	0.338514	−	0.940961i	$-0.390076\pi$
$467$	14.6307	0.677027	0.338514	+	0.940961i	$0.390076\pi$
$468$	−7.12311	−0.329266
$469$	0	0
$470$	1.12311	0.0518050
$471$	17.6155	0.811681
$472$	−6.24621	−0.287505
$473$	0	0
$474$	3.12311	0.143449
$475$	3.12311	0.143298
$476$	0	0
$477$	4.00000	0.183147
$478$	9.75379	0.446128
$479$	4.24621	0.194014	0.0970072	−	0.995284i	$-0.469073\pi$
$479$	4.24621	0.194014	0.0970072	+	0.995284i	$0.469073\pi$
$480$	−1.00000	−0.0456435
$481$	50.7386	2.31348
$482$	−25.6155	−1.16676
$483$	0	0
$484$	1.00000	0.0454545
$485$	−2.87689	−0.130633
$486$	1.00000	0.0453609
$487$	−9.50758	−0.430829	−0.215415	−	0.976523i	$-0.569110\pi$
$487$	−9.50758	−0.430829	−0.215415	+	0.976523i	$0.569110\pi$
$488$	8.24621	0.373288
$489$	−24.4924	−1.10759
$490$	7.00000	0.316228
$491$	11.6155	0.524201	0.262101	−	0.965041i	$-0.415585\pi$
$491$	11.6155	0.524201	0.262101	+	0.965041i	$0.415585\pi$
$492$	−5.12311	−0.230967
$493$	0.876894	0.0394933
$494$	−22.2462	−1.00090
$495$	1.00000	0.0449467
$496$	1.12311	0.0504289
$497$	0	0
$498$	−10.2462	−0.459144
$499$	17.7538	0.794769	0.397384	−	0.917652i	$-0.369918\pi$
$499$	17.7538	0.794769	0.397384	+	0.917652i	$0.369918\pi$
$500$	−1.00000	−0.0447214
$501$	−14.8769	−0.664651
$502$	22.7386	1.01487
$503$	−30.8769	−1.37673	−0.688366	−	0.725363i	$-0.741672\pi$
$503$	−30.8769	−1.37673	−0.688366	+	0.725363i	$0.741672\pi$
$504$	0	0
$505$	−15.3693	−0.683926
$506$	0.876894	0.0389827
$507$	37.7386	1.67603
$508$	−15.3693	−0.681903
$509$	−36.1080	−1.60046	−0.800228	−	0.599695i	$-0.795288\pi$
$509$	−36.1080	−1.60046	−0.800228	+	0.599695i	$0.795288\pi$
$510$	1.00000	0.0442807
$511$	0	0
$512$	1.00000	0.0441942
$513$	3.12311	0.137888
$514$	22.4924	0.992098
$515$	14.2462	0.627763
$516$	0	0
$517$	1.12311	0.0493941
$518$	0	0
$519$	−23.1231	−1.01499
$520$	7.12311	0.312369
$521$	22.0000	0.963837	0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000	0.963837	0.481919	+	0.876216i	$0.339940\pi$
$522$	−0.876894	−0.0383806
$523$	30.7386	1.34411	0.672053	−	0.740503i	$-0.265413\pi$
$523$	30.7386	1.34411	0.672053	+	0.740503i	$0.265413\pi$
$524$	0	0
$525$	0	0
$526$	13.7538	0.599694
$527$	−1.12311	−0.0489232
$528$	−1.00000	−0.0435194
$529$	−22.2311	−0.966568
$530$	−4.00000	−0.173749
$531$	−6.24621	−0.271062
$532$	0	0
$533$	36.4924	1.58066
$534$	−4.24621	−0.183752
$535$	−12.0000	−0.518805
$536$	−15.1231	−0.653219
$537$	16.4924	0.711701
$538$	24.2462	1.04533
$539$	7.00000	0.301511
$540$	−1.00000	−0.0430331
$541$	−14.4924	−0.623078	−0.311539	−	0.950233i	$-0.600844\pi$
$541$	−14.4924	−0.623078	−0.311539	+	0.950233i	$0.600844\pi$
$542$	−27.3693	−1.17561
$543$	23.6155	1.01344
$544$	−1.00000	−0.0428746
$545$	6.00000	0.257012
$546$	0	0
$547$	−7.50758	−0.321001	−0.160500	−	0.987036i	$-0.551311\pi$
$547$	−7.50758	−0.321001	−0.160500	+	0.987036i	$0.551311\pi$
$548$	12.2462	0.523132
$549$	8.24621	0.351940
$550$	−1.00000	−0.0426401
$551$	−2.73863	−0.116670
$552$	−0.876894	−0.0373231
$553$	0	0
$554$	4.24621	0.180404
$555$	7.12311	0.302359
$556$	−2.24621	−0.0952606
$557$	−1.50758	−0.0638781	−0.0319391	−	0.999490i	$-0.510168\pi$
$557$	−1.50758	−0.0638781	−0.0319391	+	0.999490i	$0.510168\pi$
$558$	1.12311	0.0475449
$559$	0	0
$560$	0	0
$561$	1.00000	0.0422200
$562$	−18.0000	−0.759284
$563$	−22.7386	−0.958319	−0.479160	−	0.877728i	$-0.659058\pi$
$563$	−22.7386	−0.958319	−0.479160	+	0.877728i	$0.659058\pi$
$564$	−1.12311	−0.0472913
$565$	15.3693	0.646592
$566$	−24.4924	−1.02949
$567$	0	0
$568$	−8.00000	−0.335673
$569$	34.0000	1.42535	0.712677	−	0.701492i	$-0.247483\pi$
$569$	34.0000	1.42535	0.712677	+	0.701492i	$0.247483\pi$
$570$	−3.12311	−0.130812
$571$	−10.2462	−0.428791	−0.214395	−	0.976747i	$-0.568778\pi$
$571$	−10.2462	−0.428791	−0.214395	+	0.976747i	$0.568778\pi$
$572$	7.12311	0.297832
$573$	21.1231	0.882430
$574$	0	0
$575$	−0.876894	−0.0365690
$576$	1.00000	0.0416667
$577$	22.0000	0.915872	0.457936	−	0.888985i	$-0.348589\pi$
$577$	22.0000	0.915872	0.457936	+	0.888985i	$0.348589\pi$
$578$	1.00000	0.0415945
$579$	10.4924	0.436050
$580$	0.876894	0.0364111
$581$	0	0
$582$	2.87689	0.119251
$583$	−4.00000	−0.165663
$584$	0.246211	0.0101883
$585$	7.12311	0.294504
$586$	18.4924	0.763915
$587$	10.6307	0.438775	0.219388	−	0.975638i	$-0.429594\pi$
$587$	10.6307	0.438775	0.219388	+	0.975638i	$0.429594\pi$
$588$	−7.00000	−0.288675
$589$	3.50758	0.144527
$590$	6.24621	0.257152
$591$	−23.6155	−0.971413
$592$	−7.12311	−0.292758
$593$	24.2462	0.995673	0.497836	−	0.867271i	$-0.334128\pi$
$593$	24.2462	0.995673	0.497836	+	0.867271i	$0.334128\pi$
$594$	−1.00000	−0.0410305
$595$	0	0
$596$	−19.3693	−0.793398
$597$	−6.87689	−0.281453
$598$	6.24621	0.255427
$599$	8.63068	0.352640	0.176320	−	0.984333i	$-0.443581\pi$
$599$	8.63068	0.352640	0.176320	+	0.984333i	$0.443581\pi$
$600$	1.00000	0.0408248
$601$	−10.8769	−0.443678	−0.221839	−	0.975083i	$-0.571206\pi$
$601$	−10.8769	−0.443678	−0.221839	+	0.975083i	$0.571206\pi$
$602$	0	0
$603$	−15.1231	−0.615860
$604$	−15.3693	−0.625369
$605$	−1.00000	−0.0406558
$606$	15.3693	0.624336
$607$	3.50758	0.142368	0.0711841	−	0.997463i	$-0.477322\pi$
$607$	3.50758	0.142368	0.0711841	+	0.997463i	$0.477322\pi$
$608$	3.12311	0.126659
$609$	0	0
$610$	−8.24621	−0.333879
$611$	8.00000	0.323645
$612$	−1.00000	−0.0404226
$613$	19.6155	0.792264	0.396132	−	0.918194i	$-0.370352\pi$
$613$	19.6155	0.792264	0.396132	+	0.918194i	$0.370352\pi$
$614$	16.4924	0.665580
$615$	5.12311	0.206584
$616$	0	0
$617$	31.3693	1.26288	0.631441	−	0.775424i	$-0.282464\pi$
$617$	31.3693	1.26288	0.631441	+	0.775424i	$0.282464\pi$
$618$	−14.2462	−0.573067
$619$	9.75379	0.392038	0.196019	−	0.980600i	$-0.437199\pi$
$619$	9.75379	0.392038	0.196019	+	0.980600i	$0.437199\pi$
$620$	−1.12311	−0.0451050
$621$	−0.876894	−0.0351886
$622$	−4.00000	−0.160385
$623$	0	0
$624$	−7.12311	−0.285152
$625$	1.00000	0.0400000
$626$	−5.12311	−0.204760
$627$	−3.12311	−0.124725
$628$	17.6155	0.702936
$629$	7.12311	0.284017
$630$	0	0
$631$	−34.2462	−1.36332	−0.681660	−	0.731669i	$-0.738742\pi$
$631$	−34.2462	−1.36332	−0.681660	+	0.731669i	$0.738742\pi$
$632$	3.12311	0.124230
$633$	20.0000	0.794929
$634$	11.7538	0.466803
$635$	15.3693	0.609913
$636$	4.00000	0.158610
$637$	49.8617	1.97559
$638$	0.876894	0.0347166
$639$	−8.00000	−0.316475
$640$	−1.00000	−0.0395285
$641$	36.7386	1.45109	0.725544	−	0.688175i	$-0.241588\pi$
$641$	36.7386	1.45109	0.725544	+	0.688175i	$0.241588\pi$
$642$	12.0000	0.473602
$643$	40.0000	1.57745	0.788723	−	0.614749i	$-0.210743\pi$
$643$	40.0000	1.57745	0.788723	+	0.614749i	$0.210743\pi$
$644$	0	0
$645$	0	0
$646$	−3.12311	−0.122877
$647$	31.3693	1.23326	0.616628	−	0.787255i	$-0.288498\pi$
$647$	31.3693	1.23326	0.616628	+	0.787255i	$0.288498\pi$
$648$	1.00000	0.0392837
$649$	6.24621	0.245185
$650$	−7.12311	−0.279391
$651$	0	0
$652$	−24.4924	−0.959197
$653$	−11.7538	−0.459961	−0.229981	−	0.973195i	$-0.573866\pi$
$653$	−11.7538	−0.459961	−0.229981	+	0.973195i	$0.573866\pi$
$654$	−6.00000	−0.234619
$655$	0	0
$656$	−5.12311	−0.200024
$657$	0.246211	0.00960562
$658$	0	0
$659$	32.1080	1.25075	0.625374	−	0.780325i	$-0.284946\pi$
$659$	32.1080	1.25075	0.625374	+	0.780325i	$0.284946\pi$
$660$	1.00000	0.0389249
$661$	30.9848	1.20517	0.602585	−	0.798054i	$-0.294137\pi$
$661$	30.9848	1.20517	0.602585	+	0.798054i	$0.294137\pi$
$662$	−13.7538	−0.534556
$663$	7.12311	0.276638
$664$	−10.2462	−0.397630
$665$	0	0
$666$	−7.12311	−0.276015
$667$	0.768944	0.0297736
$668$	−14.8769	−0.575604
$669$	26.2462	1.01474
$670$	15.1231	0.584257
$671$	−8.24621	−0.318341
$672$	0	0
$673$	22.9848	0.886001	0.443000	−	0.896521i	$-0.353914\pi$
$673$	22.9848	0.886001	0.443000	+	0.896521i	$0.353914\pi$
$674$	−22.4924	−0.866376
$675$	1.00000	0.0384900
$676$	37.7386	1.45149
$677$	−36.1080	−1.38774	−0.693871	−	0.720100i	$-0.744096\pi$
$677$	−36.1080	−1.38774	−0.693871	+	0.720100i	$0.744096\pi$
$678$	−15.3693	−0.590255
$679$	0	0
$680$	1.00000	0.0383482
$681$	−1.75379	−0.0672053
$682$	−1.12311	−0.0430059
$683$	0.492423	0.0188420	0.00942101	−	0.999956i	$-0.497001\pi$
$683$	0.492423	0.0188420	0.00942101	+	0.999956i	$0.497001\pi$
$684$	3.12311	0.119415
$685$	−12.2462	−0.467904
$686$	0	0
$687$	−6.00000	−0.228914
$688$	0	0
$689$	−28.4924	−1.08547
$690$	0.876894	0.0333828
$691$	16.4924	0.627401	0.313701	−	0.949522i	$-0.398431\pi$
$691$	16.4924	0.627401	0.313701	+	0.949522i	$0.398431\pi$
$692$	−23.1231	−0.879009
$693$	0	0
$694$	20.0000	0.759190
$695$	2.24621	0.0852036
$696$	−0.876894	−0.0332386
$697$	5.12311	0.194051
$698$	4.00000	0.151402
$699$	22.4924	0.850742
$700$	0	0
$701$	−23.3693	−0.882647	−0.441323	−	0.897348i	$-0.645491\pi$
$701$	−23.3693	−0.882647	−0.441323	+	0.897348i	$0.645491\pi$
$702$	−7.12311	−0.268844
$703$	−22.2462	−0.839032
$704$	−1.00000	−0.0376889
$705$	1.12311	0.0422986
$706$	26.0000	0.978523
$707$	0	0
$708$	−6.24621	−0.234747
$709$	5.36932	0.201649	0.100824	−	0.994904i	$-0.467852\pi$
$709$	5.36932	0.201649	0.100824	+	0.994904i	$0.467852\pi$
$710$	8.00000	0.300235
$711$	3.12311	0.117126
$712$	−4.24621	−0.159133
$713$	−0.984845	−0.0368827
$714$	0	0
$715$	−7.12311	−0.266389
$716$	16.4924	0.616351
$717$	9.75379	0.364262
$718$	−5.75379	−0.214729
$719$	−18.7386	−0.698833	−0.349417	−	0.936967i	$-0.613620\pi$
$719$	−18.7386	−0.698833	−0.349417	+	0.936967i	$0.613620\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	−9.24621	−0.344108
$723$	−25.6155	−0.952652
$724$	23.6155	0.877664
$725$	−0.876894	−0.0325670
$726$	1.00000	0.0371135
$727$	−7.50758	−0.278441	−0.139220	−	0.990261i	$-0.544460\pi$
$727$	−7.50758	−0.278441	−0.139220	+	0.990261i	$0.544460\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−0.246211	−0.00911269
$731$	0	0
$732$	8.24621	0.304789
$733$	−24.8769	−0.918849	−0.459425	−	0.888217i	$-0.651944\pi$
$733$	−24.8769	−0.918849	−0.459425	+	0.888217i	$0.651944\pi$
$734$	18.4924	0.682568
$735$	7.00000	0.258199
$736$	−0.876894	−0.0323228
$737$	15.1231	0.557067
$738$	−5.12311	−0.188584
$739$	47.1231	1.73345	0.866726	−	0.498785i	$-0.166220\pi$
$739$	47.1231	1.73345	0.866726	+	0.498785i	$0.166220\pi$
$740$	7.12311	0.261851
$741$	−22.2462	−0.817235
$742$	0	0
$743$	−41.6155	−1.52673	−0.763363	−	0.645970i	$-0.776453\pi$
$743$	−41.6155	−1.52673	−0.763363	+	0.645970i	$0.776453\pi$
$744$	1.12311	0.0411750
$745$	19.3693	0.709637
$746$	3.61553	0.132374
$747$	−10.2462	−0.374889
$748$	1.00000	0.0365636
$749$	0	0
$750$	−1.00000	−0.0365148
$751$	−1.12311	−0.0409827	−0.0204914	−	0.999790i	$-0.506523\pi$
$751$	−1.12311	−0.0409827	−0.0204914	+	0.999790i	$0.506523\pi$
$752$	−1.12311	−0.0409554
$753$	22.7386	0.828642
$754$	6.24621	0.227474
$755$	15.3693	0.559347
$756$	0	0
$757$	1.12311	0.0408200	0.0204100	−	0.999792i	$-0.493503\pi$
$757$	1.12311	0.0408200	0.0204100	+	0.999792i	$0.493503\pi$
$758$	28.0000	1.01701
$759$	0.876894	0.0318292
$760$	−3.12311	−0.113287
$761$	46.4924	1.68535	0.842674	−	0.538423i	$-0.180980\pi$
$761$	46.4924	1.68535	0.842674	+	0.538423i	$0.180980\pi$
$762$	−15.3693	−0.556772
$763$	0	0
$764$	21.1231	0.764207
$765$	1.00000	0.0361551
$766$	−19.3693	−0.699842
$767$	44.4924	1.60653
$768$	1.00000	0.0360844
$769$	−11.7538	−0.423852	−0.211926	−	0.977286i	$-0.567974\pi$
$769$	−11.7538	−0.423852	−0.211926	+	0.977286i	$0.567974\pi$
$770$	0	0
$771$	22.4924	0.810045
$772$	10.4924	0.377631
$773$	−12.4924	−0.449321	−0.224661	−	0.974437i	$-0.572127\pi$
$773$	−12.4924	−0.449321	−0.224661	+	0.974437i	$0.572127\pi$
$774$	0	0
$775$	1.12311	0.0403431
$776$	2.87689	0.103274
$777$	0	0
$778$	−7.61553	−0.273030
$779$	−16.0000	−0.573259
$780$	7.12311	0.255048
$781$	8.00000	0.286263
$782$	0.876894	0.0313577
$783$	−0.876894	−0.0313376
$784$	−7.00000	−0.250000
$785$	−17.6155	−0.628725
$786$	0	0
$787$	16.4924	0.587891	0.293946	−	0.955822i	$-0.405032\pi$
$787$	16.4924	0.587891	0.293946	+	0.955822i	$0.405032\pi$
$788$	−23.6155	−0.841268
$789$	13.7538	0.489648
$790$	−3.12311	−0.111115
$791$	0	0
$792$	−1.00000	−0.0355335
$793$	−58.7386	−2.08587
$794$	−21.8617	−0.775844
$795$	−4.00000	−0.141865
$796$	−6.87689	−0.243745
$797$	42.2462	1.49644	0.748219	−	0.663452i	$-0.230909\pi$
$797$	42.2462	1.49644	0.748219	+	0.663452i	$0.230909\pi$
$798$	0	0
$799$	1.12311	0.0397326
$800$	1.00000	0.0353553
$801$	−4.24621	−0.150032
$802$	−18.0000	−0.635602
$803$	−0.246211	−0.00868861
$804$	−15.1231	−0.533351
$805$	0	0
$806$	−8.00000	−0.281788
$807$	24.2462	0.853507
$808$	15.3693	0.540691
$809$	−43.3693	−1.52478	−0.762392	−	0.647115i	$-0.775975\pi$
$809$	−43.3693	−1.52478	−0.762392	+	0.647115i	$0.775975\pi$
$810$	−1.00000	−0.0351364
$811$	−20.9848	−0.736878	−0.368439	−	0.929652i	$-0.620108\pi$
$811$	−20.9848	−0.736878	−0.368439	+	0.929652i	$0.620108\pi$
$812$	0	0
$813$	−27.3693	−0.959884
$814$	7.12311	0.249665
$815$	24.4924	0.857932
$816$	−1.00000	−0.0350070
$817$	0	0
$818$	10.4924	0.366859
$819$	0	0
$820$	5.12311	0.178907
$821$	−41.3693	−1.44380	−0.721900	−	0.691998i	$-0.756731\pi$
$821$	−41.3693	−1.44380	−0.721900	+	0.691998i	$0.756731\pi$
$822$	12.2462	0.427136
$823$	−49.2311	−1.71609	−0.858043	−	0.513577i	$-0.828320\pi$
$823$	−49.2311	−1.71609	−0.858043	+	0.513577i	$0.828320\pi$
$824$	−14.2462	−0.496290
$825$	−1.00000	−0.0348155
$826$	0	0
$827$	33.7538	1.17373	0.586867	−	0.809683i	$-0.300361\pi$
$827$	33.7538	1.17373	0.586867	+	0.809683i	$0.300361\pi$
$828$	−0.876894	−0.0304742
$829$	−3.75379	−0.130374	−0.0651872	−	0.997873i	$-0.520764\pi$
$829$	−3.75379	−0.130374	−0.0651872	+	0.997873i	$0.520764\pi$
$830$	10.2462	0.355651
$831$	4.24621	0.147299
$832$	−7.12311	−0.246949
$833$	7.00000	0.242536
$834$	−2.24621	−0.0777799
$835$	14.8769	0.514836
$836$	−3.12311	−0.108015
$837$	1.12311	0.0388202
$838$	16.4924	0.569721
$839$	52.9848	1.82924	0.914620	−	0.404315i	$-0.132490\pi$
$839$	52.9848	1.82924	0.914620	+	0.404315i	$0.132490\pi$
$840$	0	0
$841$	−28.2311	−0.973485
$842$	−40.7386	−1.40395
$843$	−18.0000	−0.619953
$844$	20.0000	0.688428
$845$	−37.7386	−1.29825
$846$	−1.12311	−0.0386132
$847$	0	0
$848$	4.00000	0.137361
$849$	−24.4924	−0.840578
$850$	−1.00000	−0.0342997
$851$	6.24621	0.214117
$852$	−8.00000	−0.274075
$853$	−22.4924	−0.770126	−0.385063	−	0.922890i	$-0.625820\pi$
$853$	−22.4924	−0.770126	−0.385063	+	0.922890i	$0.625820\pi$
$854$	0	0
$855$	−3.12311	−0.106808
$856$	12.0000	0.410152
$857$	−26.0000	−0.888143	−0.444072	−	0.895991i	$-0.646466\pi$
$857$	−26.0000	−0.888143	−0.444072	+	0.895991i	$0.646466\pi$
$858$	7.12311	0.243179
$859$	43.2311	1.47502	0.737512	−	0.675334i	$-0.236000\pi$
$859$	43.2311	1.47502	0.737512	+	0.675334i	$0.236000\pi$
$860$	0	0
$861$	0	0
$862$	−30.9848	−1.05535
$863$	10.8769	0.370254	0.185127	−	0.982715i	$-0.440730\pi$
$863$	10.8769	0.370254	0.185127	+	0.982715i	$0.440730\pi$
$864$	1.00000	0.0340207
$865$	23.1231	0.786209
$866$	−30.4924	−1.03617
$867$	1.00000	0.0339618
$868$	0	0
$869$	−3.12311	−0.105944
$870$	0.876894	0.0297295
$871$	107.723	3.65007
$872$	−6.00000	−0.203186
$873$	2.87689	0.0973681
$874$	−2.73863	−0.0926357
$875$	0	0
$876$	0.246211	0.00831871
$877$	36.7386	1.24058	0.620288	−	0.784374i	$-0.287016\pi$
$877$	36.7386	1.24058	0.620288	+	0.784374i	$0.287016\pi$
$878$	−3.61553	−0.122018
$879$	18.4924	0.623734
$880$	1.00000	0.0337100
$881$	12.2462	0.412585	0.206293	−	0.978490i	$-0.433860\pi$
$881$	12.2462	0.412585	0.206293	+	0.978490i	$0.433860\pi$
$882$	−7.00000	−0.235702
$883$	−7.12311	−0.239712	−0.119856	−	0.992791i	$-0.538243\pi$
$883$	−7.12311	−0.239712	−0.119856	+	0.992791i	$0.538243\pi$
$884$	7.12311	0.239576
$885$	6.24621	0.209964
$886$	−8.87689	−0.298225
$887$	−31.3693	−1.05328	−0.526639	−	0.850089i	$-0.676548\pi$
$887$	−31.3693	−1.05328	−0.526639	+	0.850089i	$0.676548\pi$
$888$	−7.12311	−0.239036
$889$	0	0
$890$	4.24621	0.142333
$891$	−1.00000	−0.0335013
$892$	26.2462	0.878788
$893$	−3.50758	−0.117377
$894$	−19.3693	−0.647807
$895$	−16.4924	−0.551281
$896$	0	0
$897$	6.24621	0.208555
$898$	16.7386	0.558575
$899$	−0.984845	−0.0328464
$900$	1.00000	0.0333333
$901$	−4.00000	−0.133259
$902$	5.12311	0.170581
$903$	0	0
$904$	−15.3693	−0.511176
$905$	−23.6155	−0.785007
$906$	−15.3693	−0.510611
$907$	−54.7386	−1.81757	−0.908783	−	0.417269i	$-0.862987\pi$
$907$	−54.7386	−1.81757	−0.908783	+	0.417269i	$0.862987\pi$
$908$	−1.75379	−0.0582015
$909$	15.3693	0.509768
$910$	0	0
$911$	−24.0000	−0.795155	−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000	−0.795155	−0.397578	+	0.917568i	$0.630149\pi$
$912$	3.12311	0.103416
$913$	10.2462	0.339100
$914$	−14.4924	−0.479367
$915$	−8.24621	−0.272611
$916$	−6.00000	−0.198246
$917$	0	0
$918$	−1.00000	−0.0330049
$919$	−38.1080	−1.25707	−0.628533	−	0.777783i	$-0.716344\pi$
$919$	−38.1080	−1.25707	−0.628533	+	0.777783i	$0.716344\pi$
$920$	0.876894	0.0289104
$921$	16.4924	0.543444
$922$	5.12311	0.168720
$923$	56.9848	1.87568
$924$	0	0
$925$	−7.12311	−0.234206
$926$	−24.0000	−0.788689
$927$	−14.2462	−0.467907
$928$	−0.876894	−0.0287855
$929$	3.75379	0.123158	0.0615789	−	0.998102i	$-0.480386\pi$
$929$	3.75379	0.123158	0.0615789	+	0.998102i	$0.480386\pi$
$930$	−1.12311	−0.0368281
$931$	−21.8617	−0.716490
$932$	22.4924	0.736764
$933$	−4.00000	−0.130954
$934$	14.6307	0.478731
$935$	−1.00000	−0.0327035
$936$	−7.12311	−0.232826
$937$	−10.4924	−0.342773	−0.171386	−	0.985204i	$-0.554825\pi$
$937$	−10.4924	−0.342773	−0.171386	+	0.985204i	$0.554825\pi$
$938$	0	0
$939$	−5.12311	−0.167186
$940$	1.12311	0.0366317
$941$	−8.38447	−0.273326	−0.136663	−	0.990618i	$-0.543638\pi$
$941$	−8.38447	−0.273326	−0.136663	+	0.990618i	$0.543638\pi$
$942$	17.6155	0.573945
$943$	4.49242	0.146293
$944$	−6.24621	−0.203297
$945$	0	0
$946$	0	0
$947$	23.5076	0.763894	0.381947	−	0.924184i	$-0.375254\pi$
$947$	23.5076	0.763894	0.381947	+	0.924184i	$0.375254\pi$
$948$	3.12311	0.101434
$949$	−1.75379	−0.0569304
$950$	3.12311	0.101327
$951$	11.7538	0.381143
$952$	0	0
$953$	−58.4924	−1.89476	−0.947378	−	0.320118i	$-0.896277\pi$
$953$	−58.4924	−1.89476	−0.947378	+	0.320118i	$0.896277\pi$
$954$	4.00000	0.129505
$955$	−21.1231	−0.683528
$956$	9.75379	0.315460
$957$	0.876894	0.0283460
$958$	4.24621	0.137189
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	−29.7386	−0.959311
$962$	50.7386	1.63588
$963$	12.0000	0.386695
$964$	−25.6155	−0.825021
$965$	−10.4924	−0.337763
$966$	0	0
$967$	−24.6307	−0.792069	−0.396035	−	0.918236i	$-0.629614\pi$
$967$	−24.6307	−0.792069	−0.396035	+	0.918236i	$0.629614\pi$
$968$	1.00000	0.0321412
$969$	−3.12311	−0.100329
$970$	−2.87689	−0.0923715
$971$	−53.4773	−1.71617	−0.858084	−	0.513510i	$-0.828345\pi$
$971$	−53.4773	−1.71617	−0.858084	+	0.513510i	$0.828345\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−9.50758	−0.304642
$975$	−7.12311	−0.228122
$976$	8.24621	0.263955
$977$	61.2311	1.95896	0.979478	−	0.201553i	$-0.0645990\pi$
$977$	61.2311	1.95896	0.979478	+	0.201553i	$0.0645990\pi$
$978$	−24.4924	−0.783181
$979$	4.24621	0.135710
$980$	7.00000	0.223607
$981$	−6.00000	−0.191565
$982$	11.6155	0.370666
$983$	−20.8769	−0.665870	−0.332935	−	0.942950i	$-0.608039\pi$
$983$	−20.8769	−0.665870	−0.332935	+	0.942950i	$0.608039\pi$
$984$	−5.12311	−0.163319
$985$	23.6155	0.752453
$986$	0.876894	0.0279260
$987$	0	0
$988$	−22.2462	−0.707746
$989$	0	0
$990$	1.00000	0.0317821
$991$	−2.87689	−0.0913876	−0.0456938	−	0.998955i	$-0.514550\pi$
$991$	−2.87689	−0.0913876	−0.0456938	+	0.998955i	$0.514550\pi$
$992$	1.12311	0.0356586
$993$	−13.7538	−0.436463
$994$	0	0
$995$	6.87689	0.218012
$996$	−10.2462	−0.324664
$997$	−20.7386	−0.656799	−0.328400	−	0.944539i	$-0.606509\pi$
$997$	−20.7386	−0.656799	−0.328400	+	0.944539i	$0.606509\pi$
$998$	17.7538	0.561986
$999$	−7.12311	−0.225365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.bw.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bw.1.1	✓	2	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:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -7.12311 q^{13} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +3.12311 q^{19} -1.00000 q^{20} -1.00000 q^{22} -0.876894 q^{23} +1.00000 q^{24} +1.00000 q^{25} -7.12311 q^{26} +1.00000 q^{27} -0.876894 q^{29} -1.00000 q^{30} +1.12311 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{36} -7.12311 q^{37} +3.12311 q^{38} -7.12311 q^{39} -1.00000 q^{40} -5.12311 q^{41} -1.00000 q^{44} -1.00000 q^{45} -0.876894 q^{46} -1.12311 q^{47} +1.00000 q^{48} -7.00000 q^{49} +1.00000 q^{50} -1.00000 q^{51} -7.12311 q^{52} +4.00000 q^{53} +1.00000 q^{54} +1.00000 q^{55} +3.12311 q^{57} -0.876894 q^{58} -6.24621 q^{59} -1.00000 q^{60} +8.24621 q^{61} +1.12311 q^{62} +1.00000 q^{64} +7.12311 q^{65} -1.00000 q^{66} -15.1231 q^{67} -1.00000 q^{68} -0.876894 q^{69} -8.00000 q^{71} +1.00000 q^{72} +0.246211 q^{73} -7.12311 q^{74} +1.00000 q^{75} +3.12311 q^{76} -7.12311 q^{78} +3.12311 q^{79} -1.00000 q^{80} +1.00000 q^{81} -5.12311 q^{82} -10.2462 q^{83} +1.00000 q^{85} -0.876894 q^{87} -1.00000 q^{88} -4.24621 q^{89} -1.00000 q^{90} -0.876894 q^{92} +1.12311 q^{93} -1.12311 q^{94} -3.12311 q^{95} +1.00000 q^{96} +2.87689 q^{97} -7.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{15} + 2 q^{16} - 2 q^{17} + 2 q^{18} - 2 q^{19} - 2 q^{20} - 2 q^{22} - 10 q^{23} + 2 q^{24} + 2 q^{25} - 6 q^{26} + 2 q^{27} - 10 q^{29} - 2 q^{30} - 6 q^{31} + 2 q^{32} - 2 q^{33} - 2 q^{34} + 2 q^{36} - 6 q^{37} - 2 q^{38} - 6 q^{39} - 2 q^{40} - 2 q^{41} - 2 q^{44} - 2 q^{45} - 10 q^{46} + 6 q^{47} + 2 q^{48} - 14 q^{49} + 2 q^{50} - 2 q^{51} - 6 q^{52} + 8 q^{53} + 2 q^{54} + 2 q^{55} - 2 q^{57} - 10 q^{58} + 4 q^{59} - 2 q^{60} - 6 q^{62} + 2 q^{64} + 6 q^{65} - 2 q^{66} - 22 q^{67} - 2 q^{68} - 10 q^{69} - 16 q^{71} + 2 q^{72} - 16 q^{73} - 6 q^{74} + 2 q^{75} - 2 q^{76} - 6 q^{78} - 2 q^{79} - 2 q^{80} + 2 q^{81} - 2 q^{82} - 4 q^{83} + 2 q^{85} - 10 q^{87} - 2 q^{88} + 8 q^{89} - 2 q^{90} - 10 q^{92} - 6 q^{93} + 6 q^{94} + 2 q^{95} + 2 q^{96} + 14 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 6 * q^13 - 2 * q^15 + 2 * q^16 - 2 * q^17 + 2 * q^18 - 2 * q^19 - 2 * q^20 - 2 * q^22 - 10 * q^23 + 2 * q^24 + 2 * q^25 - 6 * q^26 + 2 * q^27 - 10 * q^29 - 2 * q^30 - 6 * q^31 + 2 * q^32 - 2 * q^33 - 2 * q^34 + 2 * q^36 - 6 * q^37 - 2 * q^38 - 6 * q^39 - 2 * q^40 - 2 * q^41 - 2 * q^44 - 2 * q^45 - 10 * q^46 + 6 * q^47 + 2 * q^48 - 14 * q^49 + 2 * q^50 - 2 * q^51 - 6 * q^52 + 8 * q^53 + 2 * q^54 + 2 * q^55 - 2 * q^57 - 10 * q^58 + 4 * q^59 - 2 * q^60 - 6 * q^62 + 2 * q^64 + 6 * q^65 - 2 * q^66 - 22 * q^67 - 2 * q^68 - 10 * q^69 - 16 * q^71 + 2 * q^72 - 16 * q^73 - 6 * q^74 + 2 * q^75 - 2 * q^76 - 6 * q^78 - 2 * q^79 - 2 * q^80 + 2 * q^81 - 2 * q^82 - 4 * q^83 + 2 * q^85 - 10 * q^87 - 2 * q^88 + 8 * q^89 - 2 * q^90 - 10 * q^92 - 6 * q^93 + 6 * q^94 + 2 * q^95 + 2 * q^96 + 14 * q^97 - 14 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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