LMFDB - Embedded newform 5610.2.a.bw.1.2

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			1.2
Root			$-1.56155$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +1.12311 q^{13} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -5.12311 q^{19} -1.00000 q^{20} -1.00000 q^{22} -9.12311 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.12311 q^{26} +1.00000 q^{27} -9.12311 q^{29} -1.00000 q^{30} -7.12311 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{36} +1.12311 q^{37} -5.12311 q^{38} +1.12311 q^{39} -1.00000 q^{40} +3.12311 q^{41} -1.00000 q^{44} -1.00000 q^{45} -9.12311 q^{46} +7.12311 q^{47} +1.00000 q^{48} -7.00000 q^{49} +1.00000 q^{50} -1.00000 q^{51} +1.12311 q^{52} +4.00000 q^{53} +1.00000 q^{54} +1.00000 q^{55} -5.12311 q^{57} -9.12311 q^{58} +10.2462 q^{59} -1.00000 q^{60} -8.24621 q^{61} -7.12311 q^{62} +1.00000 q^{64} -1.12311 q^{65} -1.00000 q^{66} -6.87689 q^{67} -1.00000 q^{68} -9.12311 q^{69} -8.00000 q^{71} +1.00000 q^{72} -16.2462 q^{73} +1.12311 q^{74} +1.00000 q^{75} -5.12311 q^{76} +1.12311 q^{78} -5.12311 q^{79} -1.00000 q^{80} +1.00000 q^{81} +3.12311 q^{82} +6.24621 q^{83} +1.00000 q^{85} -9.12311 q^{87} -1.00000 q^{88} +12.2462 q^{89} -1.00000 q^{90} -9.12311 q^{92} -7.12311 q^{93} +7.12311 q^{94} +5.12311 q^{95} +1.00000 q^{96} +11.1231 q^{97} -7.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$13$	1.12311	0.311493	0.155747	−	0.987797i	$-0.450222\pi$
$13$	1.12311	0.311493	0.155747	+	0.987797i	$0.450222\pi$
$14$	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
$19$	−5.12311	−1.17532	−0.587661	−	0.809108i	$-0.699951\pi$
$19$	−5.12311	−1.17532	−0.587661	+	0.809108i	$0.699951\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−1.00000	−0.213201
$23$	−9.12311	−1.90230	−0.951150	−	0.308731i	$-0.900096\pi$
$23$	−9.12311	−1.90230	−0.951150	+	0.308731i	$0.900096\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	1.12311	0.220259
$27$	1.00000	0.192450
$28$	0	0
$29$	−9.12311	−1.69412	−0.847059	−	0.531499i	$-0.821629\pi$
$29$	−9.12311	−1.69412	−0.847059	+	0.531499i	$0.821629\pi$
$30$	−1.00000	−0.182574
$31$	−7.12311	−1.27935	−0.639674	−	0.768647i	$-0.720931\pi$
$31$	−7.12311	−1.27935	−0.639674	+	0.768647i	$0.720931\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	1.12311	0.184637	0.0923187	−	0.995730i	$-0.470572\pi$
$37$	1.12311	0.184637	0.0923187	+	0.995730i	$0.470572\pi$
$38$	−5.12311	−0.831077
$39$	1.12311	0.179841
$40$	−1.00000	−0.158114
$41$	3.12311	0.487747	0.243874	−	0.969807i	$-0.421582\pi$
$41$	3.12311	0.487747	0.243874	+	0.969807i	$0.421582\pi$
$42$	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
$46$	−9.12311	−1.34513
$47$	7.12311	1.03901	0.519506	−	0.854467i	$-0.326116\pi$
$47$	7.12311	1.03901	0.519506	+	0.854467i	$0.326116\pi$
$48$	1.00000	0.144338
$49$	−7.00000	−1.00000
$50$	1.00000	0.141421
$51$	−1.00000	−0.140028
$52$	1.12311	0.155747
$53$	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
$57$	−5.12311	−0.678572
$58$	−9.12311	−1.19792
$59$	10.2462	1.33394	0.666972	−	0.745083i	$-0.267590\pi$
$59$	10.2462	1.33394	0.666972	+	0.745083i	$0.267590\pi$
$60$	−1.00000	−0.129099
$61$	−8.24621	−1.05582	−0.527910	−	0.849301i	$-0.677024\pi$
$61$	−8.24621	−1.05582	−0.527910	+	0.849301i	$0.677024\pi$
$62$	−7.12311	−0.904635
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.12311	−0.139304
$66$	−1.00000	−0.123091
$67$	−6.87689	−0.840146	−0.420073	−	0.907490i	$-0.637996\pi$
$67$	−6.87689	−0.840146	−0.420073	+	0.907490i	$0.637996\pi$
$68$	−1.00000	−0.121268
$69$	−9.12311	−1.09829
$70$	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
$73$	−16.2462	−1.90148	−0.950738	−	0.309997i	$-0.899672\pi$
$73$	−16.2462	−1.90148	−0.950738	+	0.309997i	$0.899672\pi$
$74$	1.12311	0.130558
$75$	1.00000	0.115470
$76$	−5.12311	−0.587661
$77$	0	0
$78$	1.12311	0.127167
$79$	−5.12311	−0.576394	−0.288197	−	0.957571i	$-0.593056\pi$
$79$	−5.12311	−0.576394	−0.288197	+	0.957571i	$0.593056\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	3.12311	0.344889
$83$	6.24621	0.685611	0.342805	−	0.939406i	$-0.388623\pi$
$83$	6.24621	0.685611	0.342805	+	0.939406i	$0.388623\pi$
$84$	0	0
$85$	1.00000	0.108465
$86$	0	0
$87$	−9.12311	−0.978100
$88$	−1.00000	−0.106600
$89$	12.2462	1.29810	0.649048	−	0.760748i	$-0.275167\pi$
$89$	12.2462	1.29810	0.649048	+	0.760748i	$0.275167\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	−9.12311	−0.951150
$93$	−7.12311	−0.738632
$94$	7.12311	0.734692
$95$	5.12311	0.525620
$96$	1.00000	0.102062
$97$	11.1231	1.12938	0.564690	−	0.825303i	$-0.308996\pi$
$97$	11.1231	1.12938	0.564690	+	0.825303i	$0.308996\pi$
$98$	−7.00000	−0.707107
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−9.36932	−0.932282	−0.466141	−	0.884710i	$-0.654356\pi$
$101$	−9.36932	−0.932282	−0.466141	+	0.884710i	$0.654356\pi$
$102$	−1.00000	−0.0990148
$103$	2.24621	0.221326	0.110663	−	0.993858i	$-0.464703\pi$
$103$	2.24621	0.221326	0.110663	+	0.993858i	$0.464703\pi$
$104$	1.12311	0.110130
$105$	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
$111$	1.12311	0.106600
$112$	0	0
$113$	9.36932	0.881391	0.440696	−	0.897657i	$-0.354732\pi$
$113$	9.36932	0.881391	0.440696	+	0.897657i	$0.354732\pi$
$114$	−5.12311	−0.479823
$115$	9.12311	0.850734
$116$	−9.12311	−0.847059
$117$	1.12311	0.103831
$118$	10.2462	0.943240
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−8.24621	−0.746577
$123$	3.12311	0.281601
$124$	−7.12311	−0.639674
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	9.36932	0.831392	0.415696	−	0.909504i	$-0.363538\pi$
$127$	9.36932	0.831392	0.415696	+	0.909504i	$0.363538\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−1.12311	−0.0985029
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	−1.00000	−0.0870388
$133$	0	0
$134$	−6.87689	−0.594073
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	−4.24621	−0.362778	−0.181389	−	0.983411i	$-0.558059\pi$
$137$	−4.24621	−0.362778	−0.181389	+	0.983411i	$0.558059\pi$
$138$	−9.12311	−0.776610
$139$	14.2462	1.20835	0.604174	−	0.796852i	$-0.293503\pi$
$139$	14.2462	1.20835	0.604174	+	0.796852i	$0.293503\pi$
$140$	0	0
$141$	7.12311	0.599874
$142$	−8.00000	−0.671345
$143$	−1.12311	−0.0939188
$144$	1.00000	0.0833333
$145$	9.12311	0.757633
$146$	−16.2462	−1.34455
$147$	−7.00000	−0.577350
$148$	1.12311	0.0923187
$149$	5.36932	0.439872	0.219936	−	0.975514i	$-0.429415\pi$
$149$	5.36932	0.439872	0.219936	+	0.975514i	$0.429415\pi$
$150$	1.00000	0.0816497
$151$	9.36932	0.762464	0.381232	−	0.924479i	$-0.375500\pi$
$151$	9.36932	0.762464	0.381232	+	0.924479i	$0.375500\pi$
$152$	−5.12311	−0.415539
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	7.12311	0.572142
$156$	1.12311	0.0899204
$157$	−23.6155	−1.88472	−0.942362	−	0.334595i	$-0.891401\pi$
$157$	−23.6155	−1.88472	−0.942362	+	0.334595i	$0.891401\pi$
$158$	−5.12311	−0.407572
$159$	4.00000	0.317221
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	8.49242	0.665178	0.332589	−	0.943072i	$-0.392078\pi$
$163$	8.49242	0.665178	0.332589	+	0.943072i	$0.392078\pi$
$164$	3.12311	0.243874
$165$	1.00000	0.0778499
$166$	6.24621	0.484800
$167$	−23.1231	−1.78932	−0.894660	−	0.446748i	$-0.852582\pi$
$167$	−23.1231	−1.78932	−0.894660	+	0.446748i	$0.852582\pi$
$168$	0	0
$169$	−11.7386	−0.902972
$170$	1.00000	0.0766965
$171$	−5.12311	−0.391774
$172$	0	0
$173$	−14.8769	−1.13107	−0.565535	−	0.824725i	$-0.691330\pi$
$173$	−14.8769	−1.13107	−0.565535	+	0.824725i	$0.691330\pi$
$174$	−9.12311	−0.691621
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	10.2462	0.770152
$178$	12.2462	0.917892
$179$	−16.4924	−1.23270	−0.616351	−	0.787472i	$-0.711390\pi$
$179$	−16.4924	−1.23270	−0.616351	+	0.787472i	$0.711390\pi$
$180$	−1.00000	−0.0745356
$181$	−17.6155	−1.30935	−0.654676	−	0.755910i	$-0.727195\pi$
$181$	−17.6155	−1.30935	−0.654676	+	0.755910i	$0.727195\pi$
$182$	0	0
$183$	−8.24621	−0.609577
$184$	−9.12311	−0.672564
$185$	−1.12311	−0.0825724
$186$	−7.12311	−0.522291
$187$	1.00000	0.0731272
$188$	7.12311	0.519506
$189$	0	0
$190$	5.12311	0.371669
$191$	12.8769	0.931739	0.465870	−	0.884853i	$-0.345742\pi$
$191$	12.8769	0.931739	0.465870	+	0.884853i	$0.345742\pi$
$192$	1.00000	0.0721688
$193$	−22.4924	−1.61904	−0.809520	−	0.587092i	$-0.800273\pi$
$193$	−22.4924	−1.61904	−0.809520	+	0.587092i	$0.800273\pi$
$194$	11.1231	0.798592
$195$	−1.12311	−0.0804273
$196$	−7.00000	−0.500000
$197$	17.6155	1.25505	0.627527	−	0.778595i	$-0.284067\pi$
$197$	17.6155	1.25505	0.627527	+	0.778595i	$0.284067\pi$
$198$	−1.00000	−0.0710669
$199$	−15.1231	−1.07205	−0.536024	−	0.844203i	$-0.680074\pi$
$199$	−15.1231	−1.07205	−0.536024	+	0.844203i	$0.680074\pi$
$200$	1.00000	0.0707107
$201$	−6.87689	−0.485059
$202$	−9.36932	−0.659223
$203$	0	0
$204$	−1.00000	−0.0700140
$205$	−3.12311	−0.218127
$206$	2.24621	0.156501
$207$	−9.12311	−0.634100
$208$	1.12311	0.0778734
$209$	5.12311	0.354373
$210$	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
$219$	−16.2462	−1.09782
$220$	1.00000	0.0674200
$221$	−1.12311	−0.0755483
$222$	1.12311	0.0753779
$223$	9.75379	0.653162	0.326581	−	0.945169i	$-0.394103\pi$
$223$	9.75379	0.653162	0.326581	+	0.945169i	$0.394103\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	9.36932	0.623238
$227$	−18.2462	−1.21104	−0.605522	−	0.795829i	$-0.707036\pi$
$227$	−18.2462	−1.21104	−0.605522	+	0.795829i	$0.707036\pi$
$228$	−5.12311	−0.339286
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	9.12311	0.601560
$231$	0	0
$232$	−9.12311	−0.598961
$233$	−10.4924	−0.687381	−0.343691	−	0.939083i	$-0.611677\pi$
$233$	−10.4924	−0.687381	−0.343691	+	0.939083i	$0.611677\pi$
$234$	1.12311	0.0734197
$235$	−7.12311	−0.464660
$236$	10.2462	0.666972
$237$	−5.12311	−0.332781
$238$	0	0
$239$	26.2462	1.69773	0.848863	−	0.528613i	$-0.177288\pi$
$239$	26.2462	1.69773	0.848863	+	0.528613i	$0.177288\pi$
$240$	−1.00000	−0.0645497
$241$	15.6155	1.00588	0.502942	−	0.864320i	$-0.332251\pi$
$241$	15.6155	1.00588	0.502942	+	0.864320i	$0.332251\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−8.24621	−0.527910
$245$	7.00000	0.447214
$246$	3.12311	0.199122
$247$	−5.75379	−0.366105
$248$	−7.12311	−0.452318
$249$	6.24621	0.395838
$250$	−1.00000	−0.0632456
$251$	−26.7386	−1.68773	−0.843864	−	0.536557i	$-0.819724\pi$
$251$	−26.7386	−1.68773	−0.843864	+	0.536557i	$0.819724\pi$
$252$	0	0
$253$	9.12311	0.573565
$254$	9.36932	0.587883
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	−10.4924	−0.654499	−0.327250	−	0.944938i	$-0.606122\pi$
$257$	−10.4924	−0.654499	−0.327250	+	0.944938i	$0.606122\pi$
$258$	0	0
$259$	0	0
$260$	−1.12311	−0.0696521
$261$	−9.12311	−0.564706
$262$	0	0
$263$	30.2462	1.86506	0.932531	−	0.361091i	$-0.117596\pi$
$263$	30.2462	1.86506	0.932531	+	0.361091i	$0.117596\pi$
$264$	−1.00000	−0.0615457
$265$	−4.00000	−0.245718
$266$	0	0
$267$	12.2462	0.749456
$268$	−6.87689	−0.420073
$269$	7.75379	0.472757	0.236378	−	0.971661i	$-0.424040\pi$
$269$	7.75379	0.472757	0.236378	+	0.971661i	$0.424040\pi$
$270$	−1.00000	−0.0608581
$271$	−2.63068	−0.159803	−0.0799013	−	0.996803i	$-0.525461\pi$
$271$	−2.63068	−0.159803	−0.0799013	+	0.996803i	$0.525461\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	−4.24621	−0.256523
$275$	−1.00000	−0.0603023
$276$	−9.12311	−0.549146
$277$	−12.2462	−0.735804	−0.367902	−	0.929865i	$-0.619924\pi$
$277$	−12.2462	−0.735804	−0.367902	+	0.929865i	$0.619924\pi$
$278$	14.2462	0.854431
$279$	−7.12311	−0.426449
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	7.12311	0.424175
$283$	8.49242	0.504822	0.252411	−	0.967620i	$-0.418776\pi$
$283$	8.49242	0.504822	0.252411	+	0.967620i	$0.418776\pi$
$284$	−8.00000	−0.474713
$285$	5.12311	0.303467
$286$	−1.12311	−0.0664106
$287$	0	0
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	9.12311	0.535727
$291$	11.1231	0.652048
$292$	−16.2462	−0.950738
$293$	−14.4924	−0.846656	−0.423328	−	0.905976i	$-0.639138\pi$
$293$	−14.4924	−0.846656	−0.423328	+	0.905976i	$0.639138\pi$
$294$	−7.00000	−0.408248
$295$	−10.2462	−0.596557
$296$	1.12311	0.0652792
$297$	−1.00000	−0.0580259
$298$	5.36932	0.311036
$299$	−10.2462	−0.592554
$300$	1.00000	0.0577350
$301$	0	0
$302$	9.36932	0.539144
$303$	−9.36932	−0.538253
$304$	−5.12311	−0.293830
$305$	8.24621	0.472177
$306$	−1.00000	−0.0571662
$307$	−16.4924	−0.941272	−0.470636	−	0.882327i	$-0.655976\pi$
$307$	−16.4924	−0.941272	−0.470636	+	0.882327i	$0.655976\pi$
$308$	0	0
$309$	2.24621	0.127782
$310$	7.12311	0.404565
$311$	−4.00000	−0.226819	−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000	−0.226819	−0.113410	+	0.993548i	$0.536177\pi$
$312$	1.12311	0.0635833
$313$	3.12311	0.176528	0.0882642	−	0.996097i	$-0.471868\pi$
$313$	3.12311	0.176528	0.0882642	+	0.996097i	$0.471868\pi$
$314$	−23.6155	−1.33270
$315$	0	0
$316$	−5.12311	−0.288197
$317$	28.2462	1.58647	0.793233	−	0.608919i	$-0.208396\pi$
$317$	28.2462	1.58647	0.793233	+	0.608919i	$0.208396\pi$
$318$	4.00000	0.224309
$319$	9.12311	0.510796
$320$	−1.00000	−0.0559017
$321$	12.0000	0.669775
$322$	0	0
$323$	5.12311	0.285057
$324$	1.00000	0.0555556
$325$	1.12311	0.0622987
$326$	8.49242	0.470352
$327$	−6.00000	−0.331801
$328$	3.12311	0.172445
$329$	0	0
$330$	1.00000	0.0550482
$331$	−30.2462	−1.66248	−0.831241	−	0.555912i	$-0.812369\pi$
$331$	−30.2462	−1.66248	−0.831241	+	0.555912i	$0.812369\pi$
$332$	6.24621	0.342805
$333$	1.12311	0.0615458
$334$	−23.1231	−1.26524
$335$	6.87689	0.375725
$336$	0	0
$337$	10.4924	0.571559	0.285779	−	0.958295i	$-0.407748\pi$
$337$	10.4924	0.571559	0.285779	+	0.958295i	$0.407748\pi$
$338$	−11.7386	−0.638498
$339$	9.36932	0.508871
$340$	1.00000	0.0542326
$341$	7.12311	0.385738
$342$	−5.12311	−0.277026
$343$	0	0
$344$	0	0
$345$	9.12311	0.491171
$346$	−14.8769	−0.799787
$347$	20.0000	1.07366	0.536828	−	0.843692i	$-0.319622\pi$
$347$	20.0000	1.07366	0.536828	+	0.843692i	$0.319622\pi$
$348$	−9.12311	−0.489050
$349$	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
$351$	1.12311	0.0599469
$352$	−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	$0.256765\pi$
$354$	10.2462	0.544580
$355$	8.00000	0.424596
$356$	12.2462	0.649048
$357$	0	0
$358$	−16.4924	−0.871652
$359$	−22.2462	−1.17411	−0.587055	−	0.809547i	$-0.699713\pi$
$359$	−22.2462	−1.17411	−0.587055	+	0.809547i	$0.699713\pi$
$360$	−1.00000	−0.0527046
$361$	7.24621	0.381380
$362$	−17.6155	−0.925852
$363$	1.00000	0.0524864
$364$	0	0
$365$	16.2462	0.850366
$366$	−8.24621	−0.431036
$367$	−14.4924	−0.756498	−0.378249	−	0.925704i	$-0.623474\pi$
$367$	−14.4924	−0.756498	−0.378249	+	0.925704i	$0.623474\pi$
$368$	−9.12311	−0.475575
$369$	3.12311	0.162582
$370$	−1.12311	−0.0583875
$371$	0	0
$372$	−7.12311	−0.369316
$373$	−37.6155	−1.94766	−0.973829	−	0.227281i	$-0.927016\pi$
$373$	−37.6155	−1.94766	−0.973829	+	0.227281i	$0.927016\pi$
$374$	1.00000	0.0517088
$375$	−1.00000	−0.0516398
$376$	7.12311	0.367346
$377$	−10.2462	−0.527707
$378$	0	0
$379$	28.0000	1.43826	0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000	1.43826	0.719132	+	0.694874i	$0.244540\pi$
$380$	5.12311	0.262810
$381$	9.36932	0.480005
$382$	12.8769	0.658839
$383$	5.36932	0.274359	0.137180	−	0.990546i	$-0.456196\pi$
$383$	5.36932	0.274359	0.137180	+	0.990546i	$0.456196\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−22.4924	−1.14483
$387$	0	0
$388$	11.1231	0.564690
$389$	33.6155	1.70437	0.852187	−	0.523237i	$-0.175276\pi$
$389$	33.6155	1.70437	0.852187	+	0.523237i	$0.175276\pi$
$390$	−1.12311	−0.0568707
$391$	9.12311	0.461375
$392$	−7.00000	−0.353553
$393$	0	0
$394$	17.6155	0.887457
$395$	5.12311	0.257771
$396$	−1.00000	−0.0502519
$397$	35.8617	1.79985	0.899925	−	0.436046i	$-0.143621\pi$
$397$	35.8617	1.79985	0.899925	+	0.436046i	$0.143621\pi$
$398$	−15.1231	−0.758053
$399$	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	$0.648376\pi$
$402$	−6.87689	−0.342988
$403$	−8.00000	−0.398508
$404$	−9.36932	−0.466141
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−1.12311	−0.0556703
$408$	−1.00000	−0.0495074
$409$	−22.4924	−1.11218	−0.556089	−	0.831123i	$-0.687699\pi$
$409$	−22.4924	−1.11218	−0.556089	+	0.831123i	$0.687699\pi$
$410$	−3.12311	−0.154239
$411$	−4.24621	−0.209450
$412$	2.24621	0.110663
$413$	0	0
$414$	−9.12311	−0.448376
$415$	−6.24621	−0.306614
$416$	1.12311	0.0550648
$417$	14.2462	0.697640
$418$	5.12311	0.250579
$419$	−16.4924	−0.805708	−0.402854	−	0.915264i	$-0.631982\pi$
$419$	−16.4924	−0.805708	−0.402854	+	0.915264i	$0.631982\pi$
$420$	0	0
$421$	8.73863	0.425895	0.212947	−	0.977064i	$-0.431694\pi$
$421$	8.73863	0.425895	0.212947	+	0.977064i	$0.431694\pi$
$422$	20.0000	0.973585
$423$	7.12311	0.346337
$424$	4.00000	0.194257
$425$	−1.00000	−0.0485071
$426$	−8.00000	−0.387601
$427$	0	0
$428$	12.0000	0.580042
$429$	−1.12311	−0.0542241
$430$	0	0
$431$	34.9848	1.68516	0.842580	−	0.538571i	$-0.181036\pi$
$431$	34.9848	1.68516	0.842580	+	0.538571i	$0.181036\pi$
$432$	1.00000	0.0481125
$433$	2.49242	0.119778	0.0598891	−	0.998205i	$-0.480925\pi$
$433$	2.49242	0.119778	0.0598891	+	0.998205i	$0.480925\pi$
$434$	0	0
$435$	9.12311	0.437419
$436$	−6.00000	−0.287348
$437$	46.7386	2.23581
$438$	−16.2462	−0.776274
$439$	37.6155	1.79529	0.897646	−	0.440718i	$-0.145276\pi$
$439$	37.6155	1.79529	0.897646	+	0.440718i	$0.145276\pi$
$440$	1.00000	0.0476731
$441$	−7.00000	−0.333333
$442$	−1.12311	−0.0534207
$443$	−17.1231	−0.813543	−0.406772	−	0.913530i	$-0.633346\pi$
$443$	−17.1231	−0.813543	−0.406772	+	0.913530i	$0.633346\pi$
$444$	1.12311	0.0533002
$445$	−12.2462	−0.580526
$446$	9.75379	0.461855
$447$	5.36932	0.253960
$448$	0	0
$449$	−32.7386	−1.54503	−0.772516	−	0.634996i	$-0.781002\pi$
$449$	−32.7386	−1.54503	−0.772516	+	0.634996i	$0.781002\pi$
$450$	1.00000	0.0471405
$451$	−3.12311	−0.147061
$452$	9.36932	0.440696
$453$	9.36932	0.440209
$454$	−18.2462	−0.856337
$455$	0	0
$456$	−5.12311	−0.239911
$457$	18.4924	0.865039	0.432520	−	0.901625i	$-0.357625\pi$
$457$	18.4924	0.865039	0.432520	+	0.901625i	$0.357625\pi$
$458$	−6.00000	−0.280362
$459$	−1.00000	−0.0466760
$460$	9.12311	0.425367
$461$	−3.12311	−0.145458	−0.0727288	−	0.997352i	$-0.523171\pi$
$461$	−3.12311	−0.145458	−0.0727288	+	0.997352i	$0.523171\pi$
$462$	0	0
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	−9.12311	−0.423530
$465$	7.12311	0.330326
$466$	−10.4924	−0.486052
$467$	39.3693	1.82179	0.910897	−	0.412633i	$-0.135391\pi$
$467$	39.3693	1.82179	0.910897	+	0.412633i	$0.135391\pi$
$468$	1.12311	0.0519156
$469$	0	0
$470$	−7.12311	−0.328564
$471$	−23.6155	−1.08815
$472$	10.2462	0.471620
$473$	0	0
$474$	−5.12311	−0.235312
$475$	−5.12311	−0.235064
$476$	0	0
$477$	4.00000	0.183147
$478$	26.2462	1.20047
$479$	−12.2462	−0.559544	−0.279772	−	0.960067i	$-0.590259\pi$
$479$	−12.2462	−0.559544	−0.279772	+	0.960067i	$0.590259\pi$
$480$	−1.00000	−0.0456435
$481$	1.26137	0.0575134
$482$	15.6155	0.711268
$483$	0	0
$484$	1.00000	0.0454545
$485$	−11.1231	−0.505074
$486$	1.00000	0.0453609
$487$	−42.4924	−1.92552	−0.962758	−	0.270366i	$-0.912855\pi$
$487$	−42.4924	−1.92552	−0.962758	+	0.270366i	$0.912855\pi$
$488$	−8.24621	−0.373288
$489$	8.49242	0.384041
$490$	7.00000	0.316228
$491$	−29.6155	−1.33653	−0.668265	−	0.743923i	$-0.732963\pi$
$491$	−29.6155	−1.33653	−0.668265	+	0.743923i	$0.732963\pi$
$492$	3.12311	0.140800
$493$	9.12311	0.410884
$494$	−5.75379	−0.258875
$495$	1.00000	0.0449467
$496$	−7.12311	−0.319837
$497$	0	0
$498$	6.24621	0.279899
$499$	34.2462	1.53307	0.766535	−	0.642202i	$-0.221979\pi$
$499$	34.2462	1.53307	0.766535	+	0.642202i	$0.221979\pi$
$500$	−1.00000	−0.0447214
$501$	−23.1231	−1.03306
$502$	−26.7386	−1.19340
$503$	−39.1231	−1.74441	−0.872207	−	0.489138i	$-0.837312\pi$
$503$	−39.1231	−1.74441	−0.872207	+	0.489138i	$0.837312\pi$
$504$	0	0
$505$	9.36932	0.416929
$506$	9.12311	0.405572
$507$	−11.7386	−0.521331
$508$	9.36932	0.415696
$509$	38.1080	1.68911	0.844553	−	0.535473i	$-0.179866\pi$
$509$	38.1080	1.68911	0.844553	+	0.535473i	$0.179866\pi$
$510$	1.00000	0.0442807
$511$	0	0
$512$	1.00000	0.0441942
$513$	−5.12311	−0.226191
$514$	−10.4924	−0.462801
$515$	−2.24621	−0.0989799
$516$	0	0
$517$	−7.12311	−0.313274
$518$	0	0
$519$	−14.8769	−0.653023
$520$	−1.12311	−0.0492514
$521$	22.0000	0.963837	0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000	0.963837	0.481919	+	0.876216i	$0.339940\pi$
$522$	−9.12311	−0.399307
$523$	−18.7386	−0.819383	−0.409692	−	0.912224i	$-0.634364\pi$
$523$	−18.7386	−0.819383	−0.409692	+	0.912224i	$0.634364\pi$
$524$	0	0
$525$	0	0
$526$	30.2462	1.31880
$527$	7.12311	0.310287
$528$	−1.00000	−0.0435194
$529$	60.2311	2.61874
$530$	−4.00000	−0.173749
$531$	10.2462	0.444648
$532$	0	0
$533$	3.50758	0.151930
$534$	12.2462	0.529945
$535$	−12.0000	−0.518805
$536$	−6.87689	−0.297037
$537$	−16.4924	−0.711701
$538$	7.75379	0.334290
$539$	7.00000	0.301511
$540$	−1.00000	−0.0430331
$541$	18.4924	0.795051	0.397526	−	0.917591i	$-0.369869\pi$
$541$	18.4924	0.795051	0.397526	+	0.917591i	$0.369869\pi$
$542$	−2.63068	−0.112998
$543$	−17.6155	−0.755955
$544$	−1.00000	−0.0428746
$545$	6.00000	0.257012
$546$	0	0
$547$	−40.4924	−1.73133	−0.865665	−	0.500623i	$-0.833104\pi$
$547$	−40.4924	−1.73133	−0.865665	+	0.500623i	$0.833104\pi$
$548$	−4.24621	−0.181389
$549$	−8.24621	−0.351940
$550$	−1.00000	−0.0426401
$551$	46.7386	1.99113
$552$	−9.12311	−0.388305
$553$	0	0
$554$	−12.2462	−0.520292
$555$	−1.12311	−0.0476732
$556$	14.2462	0.604174
$557$	−34.4924	−1.46149	−0.730745	−	0.682650i	$-0.760827\pi$
$557$	−34.4924	−1.46149	−0.730745	+	0.682650i	$0.760827\pi$
$558$	−7.12311	−0.301545
$559$	0	0
$560$	0	0
$561$	1.00000	0.0422200
$562$	−18.0000	−0.759284
$563$	26.7386	1.12690	0.563450	−	0.826150i	$-0.309474\pi$
$563$	26.7386	1.12690	0.563450	+	0.826150i	$0.309474\pi$
$564$	7.12311	0.299937
$565$	−9.36932	−0.394170
$566$	8.49242	0.356963
$567$	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	$0.247483\pi$
$570$	5.12311	0.214583
$571$	6.24621	0.261396	0.130698	−	0.991422i	$-0.458278\pi$
$571$	6.24621	0.261396	0.130698	+	0.991422i	$0.458278\pi$
$572$	−1.12311	−0.0469594
$573$	12.8769	0.537940
$574$	0	0
$575$	−9.12311	−0.380460
$576$	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
$579$	−22.4924	−0.934753
$580$	9.12311	0.378816
$581$	0	0
$582$	11.1231	0.461068
$583$	−4.00000	−0.165663
$584$	−16.2462	−0.672273
$585$	−1.12311	−0.0464347
$586$	−14.4924	−0.598676
$587$	35.3693	1.45985	0.729924	−	0.683528i	$-0.239555\pi$
$587$	35.3693	1.45985	0.729924	+	0.683528i	$0.239555\pi$
$588$	−7.00000	−0.288675
$589$	36.4924	1.50364
$590$	−10.2462	−0.421830
$591$	17.6155	0.724606
$592$	1.12311	0.0461594
$593$	7.75379	0.318410	0.159205	−	0.987246i	$-0.449107\pi$
$593$	7.75379	0.318410	0.159205	+	0.987246i	$0.449107\pi$
$594$	−1.00000	−0.0410305
$595$	0	0
$596$	5.36932	0.219936
$597$	−15.1231	−0.618948
$598$	−10.2462	−0.418999
$599$	33.3693	1.36343	0.681717	−	0.731616i	$-0.261234\pi$
$599$	33.3693	1.36343	0.681717	+	0.731616i	$0.261234\pi$
$600$	1.00000	0.0408248
$601$	−19.1231	−0.780048	−0.390024	−	0.920805i	$-0.627533\pi$
$601$	−19.1231	−0.780048	−0.390024	+	0.920805i	$0.627533\pi$
$602$	0	0
$603$	−6.87689	−0.280049
$604$	9.36932	0.381232
$605$	−1.00000	−0.0406558
$606$	−9.36932	−0.380602
$607$	36.4924	1.48118	0.740591	−	0.671956i	$-0.234546\pi$
$607$	36.4924	1.48118	0.740591	+	0.671956i	$0.234546\pi$
$608$	−5.12311	−0.207769
$609$	0	0
$610$	8.24621	0.333879
$611$	8.00000	0.323645
$612$	−1.00000	−0.0404226
$613$	−21.6155	−0.873043	−0.436521	−	0.899694i	$-0.643790\pi$
$613$	−21.6155	−0.873043	−0.436521	+	0.899694i	$0.643790\pi$
$614$	−16.4924	−0.665580
$615$	−3.12311	−0.125936
$616$	0	0
$617$	6.63068	0.266941	0.133471	−	0.991053i	$-0.457388\pi$
$617$	6.63068	0.266941	0.133471	+	0.991053i	$0.457388\pi$
$618$	2.24621	0.0903559
$619$	26.2462	1.05492	0.527462	−	0.849579i	$-0.323144\pi$
$619$	26.2462	1.05492	0.527462	+	0.849579i	$0.323144\pi$
$620$	7.12311	0.286071
$621$	−9.12311	−0.366098
$622$	−4.00000	−0.160385
$623$	0	0
$624$	1.12311	0.0449602
$625$	1.00000	0.0400000
$626$	3.12311	0.124824
$627$	5.12311	0.204597
$628$	−23.6155	−0.942362
$629$	−1.12311	−0.0447812
$630$	0	0
$631$	−17.7538	−0.706767	−0.353384	−	0.935479i	$-0.614969\pi$
$631$	−17.7538	−0.706767	−0.353384	+	0.935479i	$0.614969\pi$
$632$	−5.12311	−0.203786
$633$	20.0000	0.794929
$634$	28.2462	1.12180
$635$	−9.36932	−0.371810
$636$	4.00000	0.158610
$637$	−7.86174	−0.311493
$638$	9.12311	0.361187
$639$	−8.00000	−0.316475
$640$	−1.00000	−0.0395285
$641$	−12.7386	−0.503146	−0.251573	−	0.967838i	$-0.580948\pi$
$641$	−12.7386	−0.503146	−0.251573	+	0.967838i	$0.580948\pi$
$642$	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
$646$	5.12311	0.201566
$647$	6.63068	0.260679	0.130340	−	0.991469i	$-0.458393\pi$
$647$	6.63068	0.260679	0.130340	+	0.991469i	$0.458393\pi$
$648$	1.00000	0.0392837
$649$	−10.2462	−0.402199
$650$	1.12311	0.0440518
$651$	0	0
$652$	8.49242	0.332589
$653$	−28.2462	−1.10536	−0.552680	−	0.833394i	$-0.686395\pi$
$653$	−28.2462	−1.10536	−0.552680	+	0.833394i	$0.686395\pi$
$654$	−6.00000	−0.234619
$655$	0	0
$656$	3.12311	0.121937
$657$	−16.2462	−0.633825
$658$	0	0
$659$	−42.1080	−1.64029	−0.820146	−	0.572154i	$-0.806108\pi$
$659$	−42.1080	−1.64029	−0.820146	+	0.572154i	$0.806108\pi$
$660$	1.00000	0.0389249
$661$	−34.9848	−1.36075	−0.680376	−	0.732863i	$-0.738184\pi$
$661$	−34.9848	−1.36075	−0.680376	+	0.732863i	$0.738184\pi$
$662$	−30.2462	−1.17555
$663$	−1.12311	−0.0436178
$664$	6.24621	0.242400
$665$	0	0
$666$	1.12311	0.0435195
$667$	83.2311	3.22272
$668$	−23.1231	−0.894660
$669$	9.75379	0.377103
$670$	6.87689	0.265678
$671$	8.24621	0.318341
$672$	0	0
$673$	−42.9848	−1.65694	−0.828472	−	0.560030i	$-0.810789\pi$
$673$	−42.9848	−1.65694	−0.828472	+	0.560030i	$0.810789\pi$
$674$	10.4924	0.404153
$675$	1.00000	0.0384900
$676$	−11.7386	−0.451486
$677$	38.1080	1.46461	0.732304	−	0.680978i	$-0.238445\pi$
$677$	38.1080	1.46461	0.732304	+	0.680978i	$0.238445\pi$
$678$	9.36932	0.359826
$679$	0	0
$680$	1.00000	0.0383482
$681$	−18.2462	−0.699196
$682$	7.12311	0.272758
$683$	−32.4924	−1.24329	−0.621644	−	0.783300i	$-0.713535\pi$
$683$	−32.4924	−1.24329	−0.621644	+	0.783300i	$0.713535\pi$
$684$	−5.12311	−0.195887
$685$	4.24621	0.162239
$686$	0	0
$687$	−6.00000	−0.228914
$688$	0	0
$689$	4.49242	0.171148
$690$	9.12311	0.347311
$691$	−16.4924	−0.627401	−0.313701	−	0.949522i	$-0.601569\pi$
$691$	−16.4924	−0.627401	−0.313701	+	0.949522i	$0.601569\pi$
$692$	−14.8769	−0.565535
$693$	0	0
$694$	20.0000	0.759190
$695$	−14.2462	−0.540390
$696$	−9.12311	−0.345810
$697$	−3.12311	−0.118296
$698$	4.00000	0.151402
$699$	−10.4924	−0.396860
$700$	0	0
$701$	1.36932	0.0517184	0.0258592	−	0.999666i	$-0.491768\pi$
$701$	1.36932	0.0517184	0.0258592	+	0.999666i	$0.491768\pi$
$702$	1.12311	0.0423889
$703$	−5.75379	−0.217008
$704$	−1.00000	−0.0376889
$705$	−7.12311	−0.268272
$706$	26.0000	0.978523
$707$	0	0
$708$	10.2462	0.385076
$709$	−19.3693	−0.727430	−0.363715	−	0.931510i	$-0.618492\pi$
$709$	−19.3693	−0.727430	−0.363715	+	0.931510i	$0.618492\pi$
$710$	8.00000	0.300235
$711$	−5.12311	−0.192131
$712$	12.2462	0.458946
$713$	64.9848	2.43370
$714$	0	0
$715$	1.12311	0.0420018
$716$	−16.4924	−0.616351
$717$	26.2462	0.980183
$718$	−22.2462	−0.830221
$719$	30.7386	1.14636	0.573179	−	0.819430i	$-0.305710\pi$
$719$	30.7386	1.14636	0.573179	+	0.819430i	$0.305710\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	7.24621	0.269676
$723$	15.6155	0.580748
$724$	−17.6155	−0.654676
$725$	−9.12311	−0.338824
$726$	1.00000	0.0371135
$727$	−40.4924	−1.50178	−0.750890	−	0.660427i	$-0.770375\pi$
$727$	−40.4924	−1.50178	−0.750890	+	0.660427i	$0.770375\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	16.2462	0.601299
$731$	0	0
$732$	−8.24621	−0.304789
$733$	−33.1231	−1.22343	−0.611715	−	0.791078i	$-0.709520\pi$
$733$	−33.1231	−1.22343	−0.611715	+	0.791078i	$0.709520\pi$
$734$	−14.4924	−0.534925
$735$	7.00000	0.258199
$736$	−9.12311	−0.336282
$737$	6.87689	0.253314
$738$	3.12311	0.114963
$739$	38.8769	1.43011	0.715055	−	0.699068i	$-0.246402\pi$
$739$	38.8769	1.43011	0.715055	+	0.699068i	$0.246402\pi$
$740$	−1.12311	−0.0412862
$741$	−5.75379	−0.211371
$742$	0	0
$743$	−0.384472	−0.0141049	−0.00705245	−	0.999975i	$-0.502245\pi$
$743$	−0.384472	−0.0141049	−0.00705245	+	0.999975i	$0.502245\pi$
$744$	−7.12311	−0.261146
$745$	−5.36932	−0.196717
$746$	−37.6155	−1.37720
$747$	6.24621	0.228537
$748$	1.00000	0.0365636
$749$	0	0
$750$	−1.00000	−0.0365148
$751$	7.12311	0.259926	0.129963	−	0.991519i	$-0.458514\pi$
$751$	7.12311	0.259926	0.129963	+	0.991519i	$0.458514\pi$
$752$	7.12311	0.259753
$753$	−26.7386	−0.974410
$754$	−10.2462	−0.373145
$755$	−9.36932	−0.340984
$756$	0	0
$757$	−7.12311	−0.258894	−0.129447	−	0.991586i	$-0.541320\pi$
$757$	−7.12311	−0.258894	−0.129447	+	0.991586i	$0.541320\pi$
$758$	28.0000	1.01701
$759$	9.12311	0.331148
$760$	5.12311	0.185835
$761$	13.5076	0.489649	0.244825	−	0.969567i	$-0.421270\pi$
$761$	13.5076	0.489649	0.244825	+	0.969567i	$0.421270\pi$
$762$	9.36932	0.339415
$763$	0	0
$764$	12.8769	0.465870
$765$	1.00000	0.0361551
$766$	5.36932	0.194001
$767$	11.5076	0.415515
$768$	1.00000	0.0360844
$769$	−28.2462	−1.01858	−0.509292	−	0.860594i	$-0.670093\pi$
$769$	−28.2462	−1.01858	−0.509292	+	0.860594i	$0.670093\pi$
$770$	0	0
$771$	−10.4924	−0.377875
$772$	−22.4924	−0.809520
$773$	20.4924	0.737061	0.368531	−	0.929616i	$-0.379861\pi$
$773$	20.4924	0.737061	0.368531	+	0.929616i	$0.379861\pi$
$774$	0	0
$775$	−7.12311	−0.255870
$776$	11.1231	0.399296
$777$	0	0
$778$	33.6155	1.20518
$779$	−16.0000	−0.573259
$780$	−1.12311	−0.0402136
$781$	8.00000	0.286263
$782$	9.12311	0.326242
$783$	−9.12311	−0.326033
$784$	−7.00000	−0.250000
$785$	23.6155	0.842874
$786$	0	0
$787$	−16.4924	−0.587891	−0.293946	−	0.955822i	$-0.594968\pi$
$787$	−16.4924	−0.587891	−0.293946	+	0.955822i	$0.594968\pi$
$788$	17.6155	0.627527
$789$	30.2462	1.07679
$790$	5.12311	0.182272
$791$	0	0
$792$	−1.00000	−0.0355335
$793$	−9.26137	−0.328881
$794$	35.8617	1.27269
$795$	−4.00000	−0.141865
$796$	−15.1231	−0.536024
$797$	25.7538	0.912246	0.456123	−	0.889917i	$-0.349238\pi$
$797$	25.7538	0.912246	0.456123	+	0.889917i	$0.349238\pi$
$798$	0	0
$799$	−7.12311	−0.251997
$800$	1.00000	0.0353553
$801$	12.2462	0.432699
$802$	−18.0000	−0.635602
$803$	16.2462	0.573316
$804$	−6.87689	−0.242529
$805$	0	0
$806$	−8.00000	−0.281788
$807$	7.75379	0.272946
$808$	−9.36932	−0.329611
$809$	−18.6307	−0.655020	−0.327510	−	0.944848i	$-0.606210\pi$
$809$	−18.6307	−0.655020	−0.327510	+	0.944848i	$0.606210\pi$
$810$	−1.00000	−0.0351364
$811$	44.9848	1.57963	0.789816	−	0.613344i	$-0.210176\pi$
$811$	44.9848	1.57963	0.789816	+	0.613344i	$0.210176\pi$
$812$	0	0
$813$	−2.63068	−0.0922621
$814$	−1.12311	−0.0393648
$815$	−8.49242	−0.297477
$816$	−1.00000	−0.0350070
$817$	0	0
$818$	−22.4924	−0.786429
$819$	0	0
$820$	−3.12311	−0.109064
$821$	−16.6307	−0.580415	−0.290207	−	0.956964i	$-0.593724\pi$
$821$	−16.6307	−0.580415	−0.290207	+	0.956964i	$0.593724\pi$
$822$	−4.24621	−0.148104
$823$	33.2311	1.15836	0.579181	−	0.815199i	$-0.303372\pi$
$823$	33.2311	1.15836	0.579181	+	0.815199i	$0.303372\pi$
$824$	2.24621	0.0782505
$825$	−1.00000	−0.0348155
$826$	0	0
$827$	50.2462	1.74723	0.873616	−	0.486616i	$-0.161769\pi$
$827$	50.2462	1.74723	0.873616	+	0.486616i	$0.161769\pi$
$828$	−9.12311	−0.317050
$829$	−20.2462	−0.703180	−0.351590	−	0.936154i	$-0.614359\pi$
$829$	−20.2462	−0.703180	−0.351590	+	0.936154i	$0.614359\pi$
$830$	−6.24621	−0.216809
$831$	−12.2462	−0.424816
$832$	1.12311	0.0389367
$833$	7.00000	0.242536
$834$	14.2462	0.493306
$835$	23.1231	0.800208
$836$	5.12311	0.177186
$837$	−7.12311	−0.246211
$838$	−16.4924	−0.569721
$839$	−12.9848	−0.448287	−0.224143	−	0.974556i	$-0.571958\pi$
$839$	−12.9848	−0.448287	−0.224143	+	0.974556i	$0.571958\pi$
$840$	0	0
$841$	54.2311	1.87004
$842$	8.73863	0.301153
$843$	−18.0000	−0.619953
$844$	20.0000	0.688428
$845$	11.7386	0.403821
$846$	7.12311	0.244897
$847$	0	0
$848$	4.00000	0.137361
$849$	8.49242	0.291459
$850$	−1.00000	−0.0342997
$851$	−10.2462	−0.351236
$852$	−8.00000	−0.274075
$853$	10.4924	0.359254	0.179627	−	0.983735i	$-0.442511\pi$
$853$	10.4924	0.359254	0.179627	+	0.983735i	$0.442511\pi$
$854$	0	0
$855$	5.12311	0.175207
$856$	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	$0.646466\pi$
$858$	−1.12311	−0.0383422
$859$	−39.2311	−1.33855	−0.669273	−	0.743016i	$-0.733394\pi$
$859$	−39.2311	−1.33855	−0.669273	+	0.743016i	$0.733394\pi$
$860$	0	0
$861$	0	0
$862$	34.9848	1.19159
$863$	19.1231	0.650958	0.325479	−	0.945549i	$-0.394474\pi$
$863$	19.1231	0.650958	0.325479	+	0.945549i	$0.394474\pi$
$864$	1.00000	0.0340207
$865$	14.8769	0.505830
$866$	2.49242	0.0846960
$867$	1.00000	0.0339618
$868$	0	0
$869$	5.12311	0.173789
$870$	9.12311	0.309302
$871$	−7.72348	−0.261700
$872$	−6.00000	−0.203186
$873$	11.1231	0.376460
$874$	46.7386	1.58096
$875$	0	0
$876$	−16.2462	−0.548909
$877$	−12.7386	−0.430153	−0.215077	−	0.976597i	$-0.569000\pi$
$877$	−12.7386	−0.430153	−0.215077	+	0.976597i	$0.569000\pi$
$878$	37.6155	1.26946
$879$	−14.4924	−0.488817
$880$	1.00000	0.0337100
$881$	−4.24621	−0.143058	−0.0715292	−	0.997439i	$-0.522788\pi$
$881$	−4.24621	−0.143058	−0.0715292	+	0.997439i	$0.522788\pi$
$882$	−7.00000	−0.235702
$883$	1.12311	0.0377955	0.0188978	−	0.999821i	$-0.493984\pi$
$883$	1.12311	0.0377955	0.0188978	+	0.999821i	$0.493984\pi$
$884$	−1.12311	−0.0377741
$885$	−10.2462	−0.344423
$886$	−17.1231	−0.575262
$887$	−6.63068	−0.222637	−0.111318	−	0.993785i	$-0.535507\pi$
$887$	−6.63068	−0.222637	−0.111318	+	0.993785i	$0.535507\pi$
$888$	1.12311	0.0376890
$889$	0	0
$890$	−12.2462	−0.410494
$891$	−1.00000	−0.0335013
$892$	9.75379	0.326581
$893$	−36.4924	−1.22117
$894$	5.36932	0.179577
$895$	16.4924	0.551281
$896$	0	0
$897$	−10.2462	−0.342111
$898$	−32.7386	−1.09250
$899$	64.9848	2.16737
$900$	1.00000	0.0333333
$901$	−4.00000	−0.133259
$902$	−3.12311	−0.103988
$903$	0	0
$904$	9.36932	0.311619
$905$	17.6155	0.585560
$906$	9.36932	0.311275
$907$	−5.26137	−0.174701	−0.0873504	−	0.996178i	$-0.527840\pi$
$907$	−5.26137	−0.174701	−0.0873504	+	0.996178i	$0.527840\pi$
$908$	−18.2462	−0.605522
$909$	−9.36932	−0.310761
$910$	0	0
$911$	−24.0000	−0.795155	−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000	−0.795155	−0.397578	+	0.917568i	$0.630149\pi$
$912$	−5.12311	−0.169643
$913$	−6.24621	−0.206719
$914$	18.4924	0.611675
$915$	8.24621	0.272611
$916$	−6.00000	−0.198246
$917$	0	0
$918$	−1.00000	−0.0330049
$919$	36.1080	1.19109	0.595546	−	0.803321i	$-0.296936\pi$
$919$	36.1080	1.19109	0.595546	+	0.803321i	$0.296936\pi$
$920$	9.12311	0.300780
$921$	−16.4924	−0.543444
$922$	−3.12311	−0.102854
$923$	−8.98485	−0.295740
$924$	0	0
$925$	1.12311	0.0369275
$926$	−24.0000	−0.788689
$927$	2.24621	0.0737753
$928$	−9.12311	−0.299481
$929$	20.2462	0.664257	0.332128	−	0.943234i	$-0.392233\pi$
$929$	20.2462	0.664257	0.332128	+	0.943234i	$0.392233\pi$
$930$	7.12311	0.233576
$931$	35.8617	1.17532
$932$	−10.4924	−0.343691
$933$	−4.00000	−0.130954
$934$	39.3693	1.28820
$935$	−1.00000	−0.0327035
$936$	1.12311	0.0367099
$937$	22.4924	0.734795	0.367398	−	0.930064i	$-0.380249\pi$
$937$	22.4924	0.734795	0.367398	+	0.930064i	$0.380249\pi$
$938$	0	0
$939$	3.12311	0.101919
$940$	−7.12311	−0.232330
$941$	−49.6155	−1.61742	−0.808710	−	0.588208i	$-0.799834\pi$
$941$	−49.6155	−1.61742	−0.808710	+	0.588208i	$0.799834\pi$
$942$	−23.6155	−0.769435
$943$	−28.4924	−0.927841
$944$	10.2462	0.333486
$945$	0	0
$946$	0	0
$947$	56.4924	1.83576	0.917879	−	0.396861i	$-0.129901\pi$
$947$	56.4924	1.83576	0.917879	+	0.396861i	$0.129901\pi$
$948$	−5.12311	−0.166391
$949$	−18.2462	−0.592297
$950$	−5.12311	−0.166215
$951$	28.2462	0.915946
$952$	0	0
$953$	−25.5076	−0.826271	−0.413136	−	0.910669i	$-0.635567\pi$
$953$	−25.5076	−0.826271	−0.413136	+	0.910669i	$0.635567\pi$
$954$	4.00000	0.129505
$955$	−12.8769	−0.416687
$956$	26.2462	0.848863
$957$	9.12311	0.294908
$958$	−12.2462	−0.395657
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	19.7386	0.636730
$962$	1.26137	0.0406681
$963$	12.0000	0.386695
$964$	15.6155	0.502942
$965$	22.4924	0.724057
$966$	0	0
$967$	−49.3693	−1.58761	−0.793805	−	0.608172i	$-0.791903\pi$
$967$	−49.3693	−1.58761	−0.793805	+	0.608172i	$0.791903\pi$
$968$	1.00000	0.0321412
$969$	5.12311	0.164578
$970$	−11.1231	−0.357141
$971$	45.4773	1.45943	0.729717	−	0.683749i	$-0.239652\pi$
$971$	45.4773	1.45943	0.729717	+	0.683749i	$0.239652\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−42.4924	−1.36155
$975$	1.12311	0.0359682
$976$	−8.24621	−0.263955
$977$	−21.2311	−0.679242	−0.339621	−	0.940562i	$-0.610299\pi$
$977$	−21.2311	−0.679242	−0.339621	+	0.940562i	$0.610299\pi$
$978$	8.49242	0.271558
$979$	−12.2462	−0.391391
$980$	7.00000	0.223607
$981$	−6.00000	−0.191565
$982$	−29.6155	−0.945069
$983$	−29.1231	−0.928883	−0.464441	−	0.885604i	$-0.653745\pi$
$983$	−29.1231	−0.928883	−0.464441	+	0.885604i	$0.653745\pi$
$984$	3.12311	0.0995610
$985$	−17.6155	−0.561277
$986$	9.12311	0.290539
$987$	0	0
$988$	−5.75379	−0.183052
$989$	0	0
$990$	1.00000	0.0317821
$991$	−11.1231	−0.353337	−0.176669	−	0.984270i	$-0.556532\pi$
$991$	−11.1231	−0.353337	−0.176669	+	0.984270i	$0.556532\pi$
$992$	−7.12311	−0.226159
$993$	−30.2462	−0.959835
$994$	0	0
$995$	15.1231	0.479435
$996$	6.24621	0.197919
$997$	28.7386	0.910162	0.455081	−	0.890450i	$-0.349610\pi$
$997$	28.7386	0.910162	0.455081	+	0.890450i	$0.349610\pi$
$998$	34.2462	1.08404
$999$	1.12311	0.0355335

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.bw.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bw.1.2	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +1.12311 q^{13} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -5.12311 q^{19} -1.00000 q^{20} -1.00000 q^{22} -9.12311 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.12311 q^{26} +1.00000 q^{27} -9.12311 q^{29} -1.00000 q^{30} -7.12311 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{36} +1.12311 q^{37} -5.12311 q^{38} +1.12311 q^{39} -1.00000 q^{40} +3.12311 q^{41} -1.00000 q^{44} -1.00000 q^{45} -9.12311 q^{46} +7.12311 q^{47} +1.00000 q^{48} -7.00000 q^{49} +1.00000 q^{50} -1.00000 q^{51} +1.12311 q^{52} +4.00000 q^{53} +1.00000 q^{54} +1.00000 q^{55} -5.12311 q^{57} -9.12311 q^{58} +10.2462 q^{59} -1.00000 q^{60} -8.24621 q^{61} -7.12311 q^{62} +1.00000 q^{64} -1.12311 q^{65} -1.00000 q^{66} -6.87689 q^{67} -1.00000 q^{68} -9.12311 q^{69} -8.00000 q^{71} +1.00000 q^{72} -16.2462 q^{73} +1.12311 q^{74} +1.00000 q^{75} -5.12311 q^{76} +1.12311 q^{78} -5.12311 q^{79} -1.00000 q^{80} +1.00000 q^{81} +3.12311 q^{82} +6.24621 q^{83} +1.00000 q^{85} -9.12311 q^{87} -1.00000 q^{88} +12.2462 q^{89} -1.00000 q^{90} -9.12311 q^{92} -7.12311 q^{93} +7.12311 q^{94} +5.12311 q^{95} +1.00000 q^{96} +11.1231 q^{97} -7.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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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