LMFDB - Embedded newform 5610.2.a.by.1.3

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:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.87939$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +3.75877 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +3.75877 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} +4.36959 q^{13} -3.75877 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.36959 q^{19} -1.00000 q^{20} +3.75877 q^{21} -1.00000 q^{22} +1.75877 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.36959 q^{26} +1.00000 q^{27} +3.75877 q^{28} +9.51754 q^{29} +1.00000 q^{30} +1.38919 q^{31} -1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} -3.75877 q^{35} +1.00000 q^{36} +2.00000 q^{37} -4.36959 q^{38} +4.36959 q^{39} +1.00000 q^{40} -5.38919 q^{41} -3.75877 q^{42} +0.241230 q^{43} +1.00000 q^{44} -1.00000 q^{45} -1.75877 q^{46} +1.00000 q^{48} +7.12836 q^{49} -1.00000 q^{50} +1.00000 q^{51} +4.36959 q^{52} -5.88713 q^{53} -1.00000 q^{54} -1.00000 q^{55} -3.75877 q^{56} +4.36959 q^{57} -9.51754 q^{58} -7.75877 q^{59} -1.00000 q^{60} -8.12836 q^{61} -1.38919 q^{62} +3.75877 q^{63} +1.00000 q^{64} -4.36959 q^{65} -1.00000 q^{66} -1.51754 q^{67} +1.00000 q^{68} +1.75877 q^{69} +3.75877 q^{70} +7.75877 q^{71} -1.00000 q^{72} +8.53714 q^{73} -2.00000 q^{74} +1.00000 q^{75} +4.36959 q^{76} +3.75877 q^{77} -4.36959 q^{78} +4.36959 q^{79} -1.00000 q^{80} +1.00000 q^{81} +5.38919 q^{82} +3.75877 q^{84} -1.00000 q^{85} -0.241230 q^{86} +9.51754 q^{87} -1.00000 q^{88} -14.2567 q^{89} +1.00000 q^{90} +16.4243 q^{91} +1.75877 q^{92} +1.38919 q^{93} -4.36959 q^{95} -1.00000 q^{96} -11.0351 q^{97} -7.12836 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 6 q^{13} - 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} - 3 q^{22} - 6 q^{23} - 3 q^{24} + 3 q^{25} - 6 q^{26} + 3 q^{27} + 6 q^{29} + 3 q^{30} - 3 q^{32} + 3 q^{33} - 3 q^{34} + 3 q^{36} + 6 q^{37} - 6 q^{38} + 6 q^{39} + 3 q^{40} - 12 q^{41} + 12 q^{43} + 3 q^{44} - 3 q^{45} + 6 q^{46} + 3 q^{48} + 3 q^{49} - 3 q^{50} + 3 q^{51} + 6 q^{52} + 12 q^{53} - 3 q^{54} - 3 q^{55} + 6 q^{57} - 6 q^{58} - 12 q^{59} - 3 q^{60} - 6 q^{61} + 3 q^{64} - 6 q^{65} - 3 q^{66} + 18 q^{67} + 3 q^{68} - 6 q^{69} + 12 q^{71} - 3 q^{72} + 6 q^{73} - 6 q^{74} + 3 q^{75} + 6 q^{76} - 6 q^{78} + 6 q^{79} - 3 q^{80} + 3 q^{81} + 12 q^{82} - 3 q^{85} - 12 q^{86} + 6 q^{87} - 3 q^{88} - 6 q^{89} + 3 q^{90} - 6 q^{92} - 6 q^{95} - 3 q^{96} + 12 q^{97} - 3 q^{98} + 3 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 6 * q^13 - 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 - 3 * q^22 - 6 * q^23 - 3 * q^24 + 3 * q^25 - 6 * q^26 + 3 * q^27 + 6 * q^29 + 3 * q^30 - 3 * q^32 + 3 * q^33 - 3 * q^34 + 3 * q^36 + 6 * q^37 - 6 * q^38 + 6 * q^39 + 3 * q^40 - 12 * q^41 + 12 * q^43 + 3 * q^44 - 3 * q^45 + 6 * q^46 + 3 * q^48 + 3 * q^49 - 3 * q^50 + 3 * q^51 + 6 * q^52 + 12 * q^53 - 3 * q^54 - 3 * q^55 + 6 * q^57 - 6 * q^58 - 12 * q^59 - 3 * q^60 - 6 * q^61 + 3 * q^64 - 6 * q^65 - 3 * q^66 + 18 * q^67 + 3 * q^68 - 6 * q^69 + 12 * q^71 - 3 * q^72 + 6 * q^73 - 6 * q^74 + 3 * q^75 + 6 * q^76 - 6 * q^78 + 6 * q^79 - 3 * q^80 + 3 * q^81 + 12 * q^82 - 3 * q^85 - 12 * q^86 + 6 * q^87 - 3 * q^88 - 6 * q^89 + 3 * q^90 - 6 * q^92 - 6 * q^95 - 3 * q^96 + 12 * q^97 - 3 * q^98 + 3 * 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
$7$	3.75877	1.42068	0.710341	−	0.703858i	$-0.248541\pi$
$7$	3.75877	1.42068	0.710341	+	0.703858i	$0.248541\pi$
$8$	−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
$13$	4.36959	1.21190	0.605952	−	0.795501i	$-0.292792\pi$
$13$	4.36959	1.21190	0.605952	+	0.795501i	$0.292792\pi$
$14$	−3.75877	−1.00457
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	4.36959	1.00245	0.501226	−	0.865317i	$-0.332883\pi$
$19$	4.36959	1.00245	0.501226	+	0.865317i	$0.332883\pi$
$20$	−1.00000	−0.223607
$21$	3.75877	0.820231
$22$	−1.00000	−0.213201
$23$	1.75877	0.366729	0.183364	−	0.983045i	$-0.441301\pi$
$23$	1.75877	0.366729	0.183364	+	0.983045i	$0.441301\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−4.36959	−0.856946
$27$	1.00000	0.192450
$28$	3.75877	0.710341
$29$	9.51754	1.76736	0.883681	−	0.468089i	$-0.155057\pi$
$29$	9.51754	1.76736	0.883681	+	0.468089i	$0.155057\pi$
$30$	1.00000	0.182574
$31$	1.38919	0.249505	0.124753	−	0.992188i	$-0.460186\pi$
$31$	1.38919	0.249505	0.124753	+	0.992188i	$0.460186\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	−1.00000	−0.171499
$35$	−3.75877	−0.635348
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−4.36959	−0.708840
$39$	4.36959	0.699694
$40$	1.00000	0.158114
$41$	−5.38919	−0.841649	−0.420825	−	0.907142i	$-0.638259\pi$
$41$	−5.38919	−0.841649	−0.420825	+	0.907142i	$0.638259\pi$
$42$	−3.75877	−0.579991
$43$	0.241230	0.0367872	0.0183936	−	0.999831i	$-0.494145\pi$
$43$	0.241230	0.0367872	0.0183936	+	0.999831i	$0.494145\pi$
$44$	1.00000	0.150756
$45$	−1.00000	−0.149071
$46$	−1.75877	−0.259317
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000	0.144338
$49$	7.12836	1.01834
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	4.36959	0.605952
$53$	−5.88713	−0.808659	−0.404329	−	0.914613i	$-0.632495\pi$
$53$	−5.88713	−0.808659	−0.404329	+	0.914613i	$0.632495\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	−3.75877	−0.502287
$57$	4.36959	0.578766
$58$	−9.51754	−1.24971
$59$	−7.75877	−1.01011	−0.505053	−	0.863088i	$-0.668527\pi$
$59$	−7.75877	−1.01011	−0.505053	+	0.863088i	$0.668527\pi$
$60$	−1.00000	−0.129099
$61$	−8.12836	−1.04073	−0.520365	−	0.853944i	$-0.674204\pi$
$61$	−8.12836	−1.04073	−0.520365	+	0.853944i	$0.674204\pi$
$62$	−1.38919	−0.176427
$63$	3.75877	0.473561
$64$	1.00000	0.125000
$65$	−4.36959	−0.541980
$66$	−1.00000	−0.123091
$67$	−1.51754	−0.185397	−0.0926986	−	0.995694i	$-0.529549\pi$
$67$	−1.51754	−0.185397	−0.0926986	+	0.995694i	$0.529549\pi$
$68$	1.00000	0.121268
$69$	1.75877	0.211731
$70$	3.75877	0.449259
$71$	7.75877	0.920797	0.460398	−	0.887712i	$-0.347707\pi$
$71$	7.75877	0.920797	0.460398	+	0.887712i	$0.347707\pi$
$72$	−1.00000	−0.117851
$73$	8.53714	0.999197	0.499598	−	0.866257i	$-0.333481\pi$
$73$	8.53714	0.999197	0.499598	+	0.866257i	$0.333481\pi$
$74$	−2.00000	−0.232495
$75$	1.00000	0.115470
$76$	4.36959	0.501226
$77$	3.75877	0.428352
$78$	−4.36959	−0.494758
$79$	4.36959	0.491617	0.245808	−	0.969318i	$-0.420947\pi$
$79$	4.36959	0.491617	0.245808	+	0.969318i	$0.420947\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	5.38919	0.595136
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	3.75877	0.410115
$85$	−1.00000	−0.108465
$86$	−0.241230	−0.0260124
$87$	9.51754	1.02039
$88$	−1.00000	−0.106600
$89$	−14.2567	−1.51121	−0.755604	−	0.655028i	$-0.772657\pi$
$89$	−14.2567	−1.51121	−0.755604	+	0.655028i	$0.772657\pi$
$90$	1.00000	0.105409
$91$	16.4243	1.72173
$92$	1.75877	0.183364
$93$	1.38919	0.144052
$94$	0	0
$95$	−4.36959	−0.448310
$96$	−1.00000	−0.102062
$97$	−11.0351	−1.12044	−0.560221	−	0.828343i	$-0.689284\pi$
$97$	−11.0351	−1.12044	−0.560221	+	0.828343i	$0.689284\pi$
$98$	−7.12836	−0.720073
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	−1.87164	−0.186236	−0.0931178	−	0.995655i	$-0.529683\pi$
$101$	−1.87164	−0.186236	−0.0931178	+	0.995655i	$0.529683\pi$
$102$	−1.00000	−0.0990148
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	−4.36959	−0.428473
$105$	−3.75877	−0.366818
$106$	5.88713	0.571808
$107$	−17.1634	−1.65925	−0.829626	−	0.558319i	$-0.811446\pi$
$107$	−17.1634	−1.65925	−0.829626	+	0.558319i	$0.811446\pi$
$108$	1.00000	0.0962250
$109$	10.9067	1.04467	0.522337	−	0.852739i	$-0.325060\pi$
$109$	10.9067	1.04467	0.522337	+	0.852739i	$0.325060\pi$
$110$	1.00000	0.0953463
$111$	2.00000	0.189832
$112$	3.75877	0.355170
$113$	7.75877	0.729884	0.364942	−	0.931030i	$-0.381089\pi$
$113$	7.75877	0.729884	0.364942	+	0.931030i	$0.381089\pi$
$114$	−4.36959	−0.409249
$115$	−1.75877	−0.164006
$116$	9.51754	0.883681
$117$	4.36959	0.403968
$118$	7.75877	0.714253
$119$	3.75877	0.344566
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	8.12836	0.735907
$123$	−5.38919	−0.485926
$124$	1.38919	0.124753
$125$	−1.00000	−0.0894427
$126$	−3.75877	−0.334858
$127$	16.9067	1.50023	0.750115	−	0.661308i	$-0.229998\pi$
$127$	16.9067	1.50023	0.750115	+	0.661308i	$0.229998\pi$
$128$	−1.00000	−0.0883883
$129$	0.241230	0.0212391
$130$	4.36959	0.383238
$131$	7.03508	0.614658	0.307329	−	0.951603i	$-0.400565\pi$
$131$	7.03508	0.614658	0.307329	+	0.951603i	$0.400565\pi$
$132$	1.00000	0.0870388
$133$	16.4243	1.42416
$134$	1.51754	0.131096
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	−14.9067	−1.27357	−0.636784	−	0.771042i	$-0.719736\pi$
$137$	−14.9067	−1.27357	−0.636784	+	0.771042i	$0.719736\pi$
$138$	−1.75877	−0.149716
$139$	−12.9067	−1.09473	−0.547367	−	0.836893i	$-0.684370\pi$
$139$	−12.9067	−1.09473	−0.547367	+	0.836893i	$0.684370\pi$
$140$	−3.75877	−0.317674
$141$	0	0
$142$	−7.75877	−0.651102
$143$	4.36959	0.365403
$144$	1.00000	0.0833333
$145$	−9.51754	−0.790389
$146$	−8.53714	−0.706539
$147$	7.12836	0.587937
$148$	2.00000	0.164399
$149$	5.38919	0.441499	0.220750	−	0.975331i	$-0.429150\pi$
$149$	5.38919	0.441499	0.220750	+	0.975331i	$0.429150\pi$
$150$	−1.00000	−0.0816497
$151$	−0.906726	−0.0737883	−0.0368942	−	0.999319i	$-0.511746\pi$
$151$	−0.906726	−0.0737883	−0.0368942	+	0.999319i	$0.511746\pi$
$152$	−4.36959	−0.354420
$153$	1.00000	0.0808452
$154$	−3.75877	−0.302890
$155$	−1.38919	−0.111582
$156$	4.36959	0.349847
$157$	−12.2567	−0.978192	−0.489096	−	0.872230i	$-0.662673\pi$
$157$	−12.2567	−0.978192	−0.489096	+	0.872230i	$0.662673\pi$
$158$	−4.36959	−0.347626
$159$	−5.88713	−0.466879
$160$	1.00000	0.0790569
$161$	6.61081	0.521005
$162$	−1.00000	−0.0785674
$163$	−9.16344	−0.717736	−0.358868	−	0.933388i	$-0.616837\pi$
$163$	−9.16344	−0.717736	−0.358868	+	0.933388i	$0.616837\pi$
$164$	−5.38919	−0.420825
$165$	−1.00000	−0.0778499
$166$	0	0
$167$	6.61081	0.511560	0.255780	−	0.966735i	$-0.417668\pi$
$167$	6.61081	0.511560	0.255780	+	0.966735i	$0.417668\pi$
$168$	−3.75877	−0.289995
$169$	6.09327	0.468713
$170$	1.00000	0.0766965
$171$	4.36959	0.334151
$172$	0.241230	0.0183936
$173$	−11.3892	−0.865904	−0.432952	−	0.901417i	$-0.642528\pi$
$173$	−11.3892	−0.865904	−0.432952	+	0.901417i	$0.642528\pi$
$174$	−9.51754	−0.721523
$175$	3.75877	0.284136
$176$	1.00000	0.0753778
$177$	−7.75877	−0.583185
$178$	14.2567	1.06859
$179$	−3.01960	−0.225696	−0.112848	−	0.993612i	$-0.535997\pi$
$179$	−3.01960	−0.225696	−0.112848	+	0.993612i	$0.535997\pi$
$180$	−1.00000	−0.0745356
$181$	15.6459	1.16295	0.581475	−	0.813564i	$-0.302476\pi$
$181$	15.6459	1.16295	0.581475	+	0.813564i	$0.302476\pi$
$182$	−16.4243	−1.21745
$183$	−8.12836	−0.600865
$184$	−1.75877	−0.129658
$185$	−2.00000	−0.147043
$186$	−1.38919	−0.101860
$187$	1.00000	0.0731272
$188$	0	0
$189$	3.75877	0.273410
$190$	4.36959	0.317003
$191$	−17.1634	−1.24190	−0.620951	−	0.783849i	$-0.713254\pi$
$191$	−17.1634	−1.24190	−0.620951	+	0.783849i	$0.713254\pi$
$192$	1.00000	0.0721688
$193$	−6.98040	−0.502460	−0.251230	−	0.967927i	$-0.580835\pi$
$193$	−6.98040	−0.502460	−0.251230	+	0.967927i	$0.580835\pi$
$194$	11.0351	0.792273
$195$	−4.36959	−0.312912
$196$	7.12836	0.509168
$197$	9.51754	0.678097	0.339048	−	0.940769i	$-0.389895\pi$
$197$	9.51754	0.678097	0.339048	+	0.940769i	$0.389895\pi$
$198$	−1.00000	−0.0710669
$199$	−16.4243	−1.16429	−0.582143	−	0.813087i	$-0.697786\pi$
$199$	−16.4243	−1.16429	−0.582143	+	0.813087i	$0.697786\pi$
$200$	−1.00000	−0.0707107
$201$	−1.51754	−0.107039
$202$	1.87164	0.131688
$203$	35.7743	2.51086
$204$	1.00000	0.0700140
$205$	5.38919	0.376397
$206$	4.00000	0.278693
$207$	1.75877	0.122243
$208$	4.36959	0.302976
$209$	4.36959	0.302251
$210$	3.75877	0.259380
$211$	12.1676	0.837649	0.418825	−	0.908067i	$-0.362442\pi$
$211$	12.1676	0.837649	0.418825	+	0.908067i	$0.362442\pi$
$212$	−5.88713	−0.404329
$213$	7.75877	0.531622
$214$	17.1634	1.17327
$215$	−0.241230	−0.0164517
$216$	−1.00000	−0.0680414
$217$	5.22163	0.354467
$218$	−10.9067	−0.738697
$219$	8.53714	0.576887
$220$	−1.00000	−0.0674200
$221$	4.36959	0.293930
$222$	−2.00000	−0.134231
$223$	−0.906726	−0.0607189	−0.0303594	−	0.999539i	$-0.509665\pi$
$223$	−0.906726	−0.0607189	−0.0303594	+	0.999539i	$0.509665\pi$
$224$	−3.75877	−0.251143
$225$	1.00000	0.0666667
$226$	−7.75877	−0.516106
$227$	−3.51754	−0.233467	−0.116734	−	0.993163i	$-0.537242\pi$
$227$	−3.51754	−0.233467	−0.116734	+	0.993163i	$0.537242\pi$
$228$	4.36959	0.289383
$229$	17.5175	1.15759	0.578796	−	0.815472i	$-0.303523\pi$
$229$	17.5175	1.15759	0.578796	+	0.815472i	$0.303523\pi$
$230$	1.75877	0.115970
$231$	3.75877	0.247309
$232$	−9.51754	−0.624857
$233$	10.7392	0.703546	0.351773	−	0.936085i	$-0.385579\pi$
$233$	10.7392	0.703546	0.351773	+	0.936085i	$0.385579\pi$
$234$	−4.36959	−0.285649
$235$	0	0
$236$	−7.75877	−0.505053
$237$	4.36959	0.283835
$238$	−3.75877	−0.243645
$239$	−3.09327	−0.200087	−0.100044	−	0.994983i	$-0.531898\pi$
$239$	−3.09327	−0.200087	−0.100044	+	0.994983i	$0.531898\pi$
$240$	−1.00000	−0.0645497
$241$	5.63041	0.362687	0.181343	−	0.983420i	$-0.441955\pi$
$241$	5.63041	0.362687	0.181343	+	0.983420i	$0.441955\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	−8.12836	−0.520365
$245$	−7.12836	−0.455414
$246$	5.38919	0.343602
$247$	19.0933	1.21488
$248$	−1.38919	−0.0882134
$249$	0	0
$250$	1.00000	0.0632456
$251$	−0.497941	−0.0314297	−0.0157149	−	0.999877i	$-0.505002\pi$
$251$	−0.497941	−0.0314297	−0.0157149	+	0.999877i	$0.505002\pi$
$252$	3.75877	0.236780
$253$	1.75877	0.110573
$254$	−16.9067	−1.06082
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	11.3892	0.710438	0.355219	−	0.934783i	$-0.384406\pi$
$257$	11.3892	0.710438	0.355219	+	0.934783i	$0.384406\pi$
$258$	−0.241230	−0.0150183
$259$	7.51754	0.467117
$260$	−4.36959	−0.270990
$261$	9.51754	0.589121
$262$	−7.03508	−0.434629
$263$	−4.16756	−0.256983	−0.128491	−	0.991711i	$-0.541013\pi$
$263$	−4.16756	−0.256983	−0.128491	+	0.991711i	$0.541013\pi$
$264$	−1.00000	−0.0615457
$265$	5.88713	0.361643
$266$	−16.4243	−1.00704
$267$	−14.2567	−0.872497
$268$	−1.51754	−0.0926986
$269$	−2.48246	−0.151358	−0.0756791	−	0.997132i	$-0.524112\pi$
$269$	−2.48246	−0.151358	−0.0756791	+	0.997132i	$0.524112\pi$
$270$	1.00000	0.0608581
$271$	−17.6459	−1.07191	−0.535956	−	0.844246i	$-0.680049\pi$
$271$	−17.6459	−1.07191	−0.535956	+	0.844246i	$0.680049\pi$
$272$	1.00000	0.0606339
$273$	16.4243	0.994042
$274$	14.9067	0.900548
$275$	1.00000	0.0603023
$276$	1.75877	0.105866
$277$	−9.77425	−0.587278	−0.293639	−	0.955916i	$-0.594866\pi$
$277$	−9.77425	−0.587278	−0.293639	+	0.955916i	$0.594866\pi$
$278$	12.9067	0.774094
$279$	1.38919	0.0831684
$280$	3.75877	0.224630
$281$	2.48246	0.148091	0.0740455	−	0.997255i	$-0.476409\pi$
$281$	2.48246	0.148091	0.0740455	+	0.997255i	$0.476409\pi$
$282$	0	0
$283$	−23.0351	−1.36929	−0.684647	−	0.728875i	$-0.740044\pi$
$283$	−23.0351	−1.36929	−0.684647	+	0.728875i	$0.740044\pi$
$284$	7.75877	0.460398
$285$	−4.36959	−0.258832
$286$	−4.36959	−0.258379
$287$	−20.2567	−1.19572
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	9.51754	0.558889
$291$	−11.0351	−0.646888
$292$	8.53714	0.499598
$293$	−26.2567	−1.53393	−0.766967	−	0.641687i	$-0.778235\pi$
$293$	−26.2567	−1.53393	−0.766967	+	0.641687i	$0.778235\pi$
$294$	−7.12836	−0.415734
$295$	7.75877	0.451733
$296$	−2.00000	−0.116248
$297$	1.00000	0.0580259
$298$	−5.38919	−0.312187
$299$	7.68510	0.444441
$300$	1.00000	0.0577350
$301$	0.906726	0.0522628
$302$	0.906726	0.0521762
$303$	−1.87164	−0.107523
$304$	4.36959	0.250613
$305$	8.12836	0.465428
$306$	−1.00000	−0.0571662
$307$	13.2371	0.755482	0.377741	−	0.925911i	$-0.376701\pi$
$307$	13.2371	0.755482	0.377741	+	0.925911i	$0.376701\pi$
$308$	3.75877	0.214176
$309$	−4.00000	−0.227552
$310$	1.38919	0.0789004
$311$	−1.79797	−0.101954	−0.0509768	−	0.998700i	$-0.516233\pi$
$311$	−1.79797	−0.101954	−0.0509768	+	0.998700i	$0.516233\pi$
$312$	−4.36959	−0.247379
$313$	6.77837	0.383136	0.191568	−	0.981479i	$-0.438643\pi$
$313$	6.77837	0.383136	0.191568	+	0.981479i	$0.438643\pi$
$314$	12.2567	0.691686
$315$	−3.75877	−0.211783
$316$	4.36959	0.245808
$317$	33.2918	1.86985	0.934927	−	0.354841i	$-0.115465\pi$
$317$	33.2918	1.86985	0.934927	+	0.354841i	$0.115465\pi$
$318$	5.88713	0.330134
$319$	9.51754	0.532880
$320$	−1.00000	−0.0559017
$321$	−17.1634	−0.957970
$322$	−6.61081	−0.368406
$323$	4.36959	0.243130
$324$	1.00000	0.0555556
$325$	4.36959	0.242381
$326$	9.16344	0.507516
$327$	10.9067	0.603143
$328$	5.38919	0.297568
$329$	0	0
$330$	1.00000	0.0550482
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	0	0
$333$	2.00000	0.109599
$334$	−6.61081	−0.361728
$335$	1.51754	0.0829121
$336$	3.75877	0.205058
$337$	1.50206	0.0818224	0.0409112	−	0.999163i	$-0.486974\pi$
$337$	1.50206	0.0818224	0.0409112	+	0.999163i	$0.486974\pi$
$338$	−6.09327	−0.331430
$339$	7.75877	0.421399
$340$	−1.00000	−0.0542326
$341$	1.38919	0.0752286
$342$	−4.36959	−0.236280
$343$	0.482459	0.0260503
$344$	−0.241230	−0.0130062
$345$	−1.75877	−0.0946890
$346$	11.3892	0.612286
$347$	34.5526	1.85488	0.927441	−	0.373970i	$-0.122004\pi$
$347$	34.5526	1.85488	0.927441	+	0.373970i	$0.122004\pi$
$348$	9.51754	0.510194
$349$	1.46286	0.0783050	0.0391525	−	0.999233i	$-0.487534\pi$
$349$	1.46286	0.0783050	0.0391525	+	0.999233i	$0.487534\pi$
$350$	−3.75877	−0.200915
$351$	4.36959	0.233231
$352$	−1.00000	−0.0533002
$353$	27.9026	1.48511	0.742553	−	0.669787i	$-0.233615\pi$
$353$	27.9026	1.48511	0.742553	+	0.669787i	$0.233615\pi$
$354$	7.75877	0.412374
$355$	−7.75877	−0.411793
$356$	−14.2567	−0.755604
$357$	3.75877	0.198935
$358$	3.01960	0.159591
$359$	8.90673	0.470079	0.235040	−	0.971986i	$-0.424478\pi$
$359$	8.90673	0.470079	0.235040	+	0.971986i	$0.424478\pi$
$360$	1.00000	0.0527046
$361$	0.0932736	0.00490914
$362$	−15.6459	−0.822330
$363$	1.00000	0.0524864
$364$	16.4243	0.860866
$365$	−8.53714	−0.446854
$366$	8.12836	0.424876
$367$	0.354103	0.0184841	0.00924203	−	0.999957i	$-0.497058\pi$
$367$	0.354103	0.0184841	0.00924203	+	0.999957i	$0.497058\pi$
$368$	1.75877	0.0916822
$369$	−5.38919	−0.280550
$370$	2.00000	0.103975
$371$	−22.1284	−1.14885
$372$	1.38919	0.0720259
$373$	−7.63041	−0.395088	−0.197544	−	0.980294i	$-0.563297\pi$
$373$	−7.63041	−0.395088	−0.197544	+	0.980294i	$0.563297\pi$
$374$	−1.00000	−0.0517088
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	41.5877	2.14188
$378$	−3.75877	−0.193330
$379$	−19.9418	−1.02434	−0.512171	−	0.858884i	$-0.671159\pi$
$379$	−19.9418	−1.02434	−0.512171	+	0.858884i	$0.671159\pi$
$380$	−4.36959	−0.224155
$381$	16.9067	0.866158
$382$	17.1634	0.878158
$383$	−7.03508	−0.359476	−0.179738	−	0.983715i	$-0.557525\pi$
$383$	−7.03508	−0.359476	−0.179738	+	0.983715i	$0.557525\pi$
$384$	−1.00000	−0.0510310
$385$	−3.75877	−0.191565
$386$	6.98040	0.355293
$387$	0.241230	0.0122624
$388$	−11.0351	−0.560221
$389$	−7.14796	−0.362416	−0.181208	−	0.983445i	$-0.558001\pi$
$389$	−7.14796	−0.362416	−0.181208	+	0.983445i	$0.558001\pi$
$390$	4.36959	0.221263
$391$	1.75877	0.0889448
$392$	−7.12836	−0.360036
$393$	7.03508	0.354873
$394$	−9.51754	−0.479487
$395$	−4.36959	−0.219858
$396$	1.00000	0.0502519
$397$	28.8675	1.44882	0.724410	−	0.689370i	$-0.242112\pi$
$397$	28.8675	1.44882	0.724410	+	0.689370i	$0.242112\pi$
$398$	16.4243	0.823274
$399$	16.4243	0.822242
$400$	1.00000	0.0500000
$401$	22.2412	1.11067	0.555337	−	0.831625i	$-0.312589\pi$
$401$	22.2412	1.11067	0.555337	+	0.831625i	$0.312589\pi$
$402$	1.51754	0.0756881
$403$	6.07016	0.302376
$404$	−1.87164	−0.0931178
$405$	−1.00000	−0.0496904
$406$	−35.7743	−1.77545
$407$	2.00000	0.0991363
$408$	−1.00000	−0.0495074
$409$	−30.2567	−1.49610	−0.748049	−	0.663643i	$-0.769009\pi$
$409$	−30.2567	−1.49610	−0.748049	+	0.663643i	$0.769009\pi$
$410$	−5.38919	−0.266153
$411$	−14.9067	−0.735295
$412$	−4.00000	−0.197066
$413$	−29.1634	−1.43504
$414$	−1.75877	−0.0864389
$415$	0	0
$416$	−4.36959	−0.214237
$417$	−12.9067	−0.632045
$418$	−4.36959	−0.213723
$419$	−14.2959	−0.698401	−0.349200	−	0.937048i	$-0.613547\pi$
$419$	−14.2959	−0.698401	−0.349200	+	0.937048i	$0.613547\pi$
$420$	−3.75877	−0.183409
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−12.1676	−0.592307
$423$	0	0
$424$	5.88713	0.285904
$425$	1.00000	0.0485071
$426$	−7.75877	−0.375914
$427$	−30.5526	−1.47855
$428$	−17.1634	−0.829626
$429$	4.36959	0.210966
$430$	0.241230	0.0116331
$431$	−10.9649	−0.528162	−0.264081	−	0.964501i	$-0.585069\pi$
$431$	−10.9649	−0.528162	−0.264081	+	0.964501i	$0.585069\pi$
$432$	1.00000	0.0481125
$433$	16.8675	0.810602	0.405301	−	0.914183i	$-0.367167\pi$
$433$	16.8675	0.810602	0.405301	+	0.914183i	$0.367167\pi$
$434$	−5.22163	−0.250646
$435$	−9.51754	−0.456331
$436$	10.9067	0.522337
$437$	7.68510	0.367628
$438$	−8.53714	−0.407920
$439$	−15.8871	−0.758251	−0.379126	−	0.925345i	$-0.623775\pi$
$439$	−15.8871	−0.758251	−0.379126	+	0.925345i	$0.623775\pi$
$440$	1.00000	0.0476731
$441$	7.12836	0.339446
$442$	−4.36959	−0.207840
$443$	4.05468	0.192644	0.0963219	−	0.995350i	$-0.469292\pi$
$443$	4.05468	0.192644	0.0963219	+	0.995350i	$0.469292\pi$
$444$	2.00000	0.0949158
$445$	14.2567	0.675833
$446$	0.906726	0.0429347
$447$	5.38919	0.254900
$448$	3.75877	0.177585
$449$	−5.27631	−0.249005	−0.124502	−	0.992219i	$-0.539733\pi$
$449$	−5.27631	−0.249005	−0.124502	+	0.992219i	$0.539733\pi$
$450$	−1.00000	−0.0471405
$451$	−5.38919	−0.253767
$452$	7.75877	0.364942
$453$	−0.906726	−0.0426017
$454$	3.51754	0.165086
$455$	−16.4243	−0.769982
$456$	−4.36959	−0.204625
$457$	18.7392	0.876581	0.438291	−	0.898833i	$-0.355584\pi$
$457$	18.7392	0.876581	0.438291	+	0.898833i	$0.355584\pi$
$458$	−17.5175	−0.818541
$459$	1.00000	0.0466760
$460$	−1.75877	−0.0820031
$461$	−6.61081	−0.307896	−0.153948	−	0.988079i	$-0.549199\pi$
$461$	−6.61081	−0.307896	−0.153948	+	0.988079i	$0.549199\pi$
$462$	−3.75877	−0.174874
$463$	26.3851	1.22622	0.613109	−	0.789998i	$-0.289919\pi$
$463$	26.3851	1.22622	0.613109	+	0.789998i	$0.289919\pi$
$464$	9.51754	0.441841
$465$	−1.38919	−0.0644219
$466$	−10.7392	−0.497482
$467$	40.0547	1.85351	0.926755	−	0.375667i	$-0.122586\pi$
$467$	40.0547	1.85351	0.926755	+	0.375667i	$0.122586\pi$
$468$	4.36959	0.201984
$469$	−5.70409	−0.263390
$470$	0	0
$471$	−12.2567	−0.564759
$472$	7.75877	0.357126
$473$	0.241230	0.0110917
$474$	−4.36959	−0.200702
$475$	4.36959	0.200490
$476$	3.75877	0.172283
$477$	−5.88713	−0.269553
$478$	3.09327	0.141483
$479$	−26.0310	−1.18939	−0.594693	−	0.803953i	$-0.702726\pi$
$479$	−26.0310	−1.18939	−0.594693	+	0.803953i	$0.702726\pi$
$480$	1.00000	0.0456435
$481$	8.73917	0.398472
$482$	−5.63041	−0.256458
$483$	6.61081	0.300802
$484$	1.00000	0.0454545
$485$	11.0351	0.501077
$486$	−1.00000	−0.0453609
$487$	15.6459	0.708983	0.354492	−	0.935059i	$-0.384654\pi$
$487$	15.6459	0.708983	0.354492	+	0.935059i	$0.384654\pi$
$488$	8.12836	0.367953
$489$	−9.16344	−0.414385
$490$	7.12836	0.322026
$491$	14.9067	0.672731	0.336366	−	0.941731i	$-0.390802\pi$
$491$	14.9067	0.672731	0.336366	+	0.941731i	$0.390802\pi$
$492$	−5.38919	−0.242963
$493$	9.51754	0.428648
$494$	−19.0933	−0.859047
$495$	−1.00000	−0.0449467
$496$	1.38919	0.0623763
$497$	29.1634	1.30816
$498$	0	0
$499$	4.48246	0.200662	0.100331	−	0.994954i	$-0.468010\pi$
$499$	4.48246	0.200662	0.100331	+	0.994954i	$0.468010\pi$
$500$	−1.00000	−0.0447214
$501$	6.61081	0.295349
$502$	0.497941	0.0222242
$503$	−15.0933	−0.672976	−0.336488	−	0.941688i	$-0.609239\pi$
$503$	−15.0933	−0.672976	−0.336488	+	0.941688i	$0.609239\pi$
$504$	−3.75877	−0.167429
$505$	1.87164	0.0832871
$506$	−1.75877	−0.0781869
$507$	6.09327	0.270612
$508$	16.9067	0.750115
$509$	−27.4047	−1.21469	−0.607345	−	0.794438i	$-0.707766\pi$
$509$	−27.4047	−1.21469	−0.607345	+	0.794438i	$0.707766\pi$
$510$	1.00000	0.0442807
$511$	32.0892	1.41954
$512$	−1.00000	−0.0441942
$513$	4.36959	0.192922
$514$	−11.3892	−0.502355
$515$	4.00000	0.176261
$516$	0.241230	0.0106195
$517$	0	0
$518$	−7.51754	−0.330302
$519$	−11.3892	−0.499930
$520$	4.36959	0.191619
$521$	−24.4587	−1.07156	−0.535778	−	0.844359i	$-0.679982\pi$
$521$	−24.4587	−1.07156	−0.535778	+	0.844359i	$0.679982\pi$
$522$	−9.51754	−0.416571
$523$	8.72369	0.381460	0.190730	−	0.981643i	$-0.438914\pi$
$523$	8.72369	0.381460	0.190730	+	0.981643i	$0.438914\pi$
$524$	7.03508	0.307329
$525$	3.75877	0.164046
$526$	4.16756	0.181714
$527$	1.38919	0.0605139
$528$	1.00000	0.0435194
$529$	−19.9067	−0.865510
$530$	−5.88713	−0.255720
$531$	−7.75877	−0.336702
$532$	16.4243	0.712082
$533$	−23.5485	−1.02000
$534$	14.2567	0.616948
$535$	17.1634	0.742040
$536$	1.51754	0.0655478
$537$	−3.01960	−0.130305
$538$	2.48246	0.107026
$539$	7.12836	0.307040
$540$	−1.00000	−0.0430331
$541$	−37.8634	−1.62788	−0.813938	−	0.580952i	$-0.802680\pi$
$541$	−37.8634	−1.62788	−0.813938	+	0.580952i	$0.802680\pi$
$542$	17.6459	0.757956
$543$	15.6459	0.671430
$544$	−1.00000	−0.0428746
$545$	−10.9067	−0.467193
$546$	−16.4243	−0.702894
$547$	−19.2918	−0.824858	−0.412429	−	0.910990i	$-0.635319\pi$
$547$	−19.2918	−0.824858	−0.412429	+	0.910990i	$0.635319\pi$
$548$	−14.9067	−0.636784
$549$	−8.12836	−0.346910
$550$	−1.00000	−0.0426401
$551$	41.5877	1.77170
$552$	−1.75877	−0.0748582
$553$	16.4243	0.698431
$554$	9.77425	0.415268
$555$	−2.00000	−0.0848953
$556$	−12.9067	−0.547367
$557$	6.00000	0.254228	0.127114	−	0.991888i	$-0.459429\pi$
$557$	6.00000	0.254228	0.127114	+	0.991888i	$0.459429\pi$
$558$	−1.38919	−0.0588089
$559$	1.05407	0.0445825
$560$	−3.75877	−0.158837
$561$	1.00000	0.0422200
$562$	−2.48246	−0.104716
$563$	−3.74329	−0.157761	−0.0788804	−	0.996884i	$-0.525135\pi$
$563$	−3.74329	−0.157761	−0.0788804	+	0.996884i	$0.525135\pi$
$564$	0	0
$565$	−7.75877	−0.326414
$566$	23.0351	0.968237
$567$	3.75877	0.157854
$568$	−7.75877	−0.325551
$569$	−2.90673	−0.121856	−0.0609282	−	0.998142i	$-0.519406\pi$
$569$	−2.90673	−0.121856	−0.0609282	+	0.998142i	$0.519406\pi$
$570$	4.36959	0.183022
$571$	28.9067	1.20971	0.604854	−	0.796336i	$-0.293231\pi$
$571$	28.9067	1.20971	0.604854	+	0.796336i	$0.293231\pi$
$572$	4.36959	0.182702
$573$	−17.1634	−0.717013
$574$	20.2567	0.845499
$575$	1.75877	0.0733458
$576$	1.00000	0.0416667
$577$	34.6810	1.44379	0.721894	−	0.692004i	$-0.243272\pi$
$577$	34.6810	1.44379	0.721894	+	0.692004i	$0.243272\pi$
$578$	−1.00000	−0.0415945
$579$	−6.98040	−0.290096
$580$	−9.51754	−0.395194
$581$	0	0
$582$	11.0351	0.457419
$583$	−5.88713	−0.243820
$584$	−8.53714	−0.353269
$585$	−4.36959	−0.180660
$586$	26.2567	1.08465
$587$	−17.0506	−0.703752	−0.351876	−	0.936047i	$-0.614456\pi$
$587$	−17.0506	−0.703752	−0.351876	+	0.936047i	$0.614456\pi$
$588$	7.12836	0.293968
$589$	6.07016	0.250117
$590$	−7.75877	−0.319424
$591$	9.51754	0.391499
$592$	2.00000	0.0821995
$593$	13.6851	0.561980	0.280990	−	0.959711i	$-0.409337\pi$
$593$	13.6851	0.561980	0.280990	+	0.959711i	$0.409337\pi$
$594$	−1.00000	−0.0410305
$595$	−3.75877	−0.154095
$596$	5.38919	0.220750
$597$	−16.4243	−0.672201
$598$	−7.68510	−0.314267
$599$	17.1634	0.701279	0.350640	−	0.936511i	$-0.385964\pi$
$599$	17.1634	0.701279	0.350640	+	0.936511i	$0.385964\pi$
$600$	−1.00000	−0.0408248
$601$	19.8479	0.809614	0.404807	−	0.914402i	$-0.367339\pi$
$601$	19.8479	0.809614	0.404807	+	0.914402i	$0.367339\pi$
$602$	−0.906726	−0.0369554
$603$	−1.51754	−0.0617990
$604$	−0.906726	−0.0368942
$605$	−1.00000	−0.0406558
$606$	1.87164	0.0760304
$607$	−27.2763	−1.10711	−0.553556	−	0.832812i	$-0.686729\pi$
$607$	−27.2763	−1.10711	−0.553556	+	0.832812i	$0.686729\pi$
$608$	−4.36959	−0.177210
$609$	35.7743	1.44965
$610$	−8.12836	−0.329107
$611$	0	0
$612$	1.00000	0.0404226
$613$	24.7047	0.997813	0.498907	−	0.866656i	$-0.333735\pi$
$613$	24.7047	0.997813	0.498907	+	0.866656i	$0.333735\pi$
$614$	−13.2371	−0.534206
$615$	5.38919	0.217313
$616$	−3.75877	−0.151445
$617$	0.576342	0.0232027	0.0116013	−	0.999933i	$-0.496307\pi$
$617$	0.576342	0.0232027	0.0116013	+	0.999933i	$0.496307\pi$
$618$	4.00000	0.160904
$619$	−21.9608	−0.882679	−0.441340	−	0.897340i	$-0.645497\pi$
$619$	−21.9608	−0.882679	−0.441340	+	0.897340i	$0.645497\pi$
$620$	−1.38919	−0.0557910
$621$	1.75877	0.0705770
$622$	1.79797	0.0720921
$623$	−53.5877	−2.14695
$624$	4.36959	0.174923
$625$	1.00000	0.0400000
$626$	−6.77837	−0.270918
$627$	4.36959	0.174504
$628$	−12.2567	−0.489096
$629$	2.00000	0.0797452
$630$	3.75877	0.149753
$631$	34.8675	1.38805	0.694027	−	0.719949i	$-0.255835\pi$
$631$	34.8675	1.38805	0.694027	+	0.719949i	$0.255835\pi$
$632$	−4.36959	−0.173813
$633$	12.1676	0.483617
$634$	−33.2918	−1.32219
$635$	−16.9067	−0.670923
$636$	−5.88713	−0.233440
$637$	31.1480	1.23413
$638$	−9.51754	−0.376803
$639$	7.75877	0.306932
$640$	1.00000	0.0395285
$641$	−18.2722	−0.721708	−0.360854	−	0.932622i	$-0.617515\pi$
$641$	−18.2722	−0.721708	−0.360854	+	0.932622i	$0.617515\pi$
$642$	17.1634	0.677387
$643$	8.00000	0.315489	0.157745	−	0.987480i	$-0.449578\pi$
$643$	8.00000	0.315489	0.157745	+	0.987480i	$0.449578\pi$
$644$	6.61081	0.260503
$645$	−0.241230	−0.00949840
$646$	−4.36959	−0.171919
$647$	41.5877	1.63498	0.817491	−	0.575942i	$-0.195365\pi$
$647$	41.5877	1.63498	0.817491	+	0.575942i	$0.195365\pi$
$648$	−1.00000	−0.0392837
$649$	−7.75877	−0.304558
$650$	−4.36959	−0.171389
$651$	5.22163	0.204652
$652$	−9.16344	−0.358868
$653$	42.8485	1.67679	0.838396	−	0.545061i	$-0.183494\pi$
$653$	42.8485	1.67679	0.838396	+	0.545061i	$0.183494\pi$
$654$	−10.9067	−0.426487
$655$	−7.03508	−0.274883
$656$	−5.38919	−0.210412
$657$	8.53714	0.333066
$658$	0	0
$659$	−26.9067	−1.04814	−0.524069	−	0.851676i	$-0.675586\pi$
$659$	−26.9067	−1.04814	−0.524069	+	0.851676i	$0.675586\pi$
$660$	−1.00000	−0.0389249
$661$	12.5526	0.488240	0.244120	−	0.969745i	$-0.421501\pi$
$661$	12.5526	0.488240	0.244120	+	0.969745i	$0.421501\pi$
$662$	−8.00000	−0.310929
$663$	4.36959	0.169701
$664$	0	0
$665$	−16.4243	−0.636906
$666$	−2.00000	−0.0774984
$667$	16.7392	0.648143
$668$	6.61081	0.255780
$669$	−0.906726	−0.0350561
$670$	−1.51754	−0.0586277
$671$	−8.12836	−0.313792
$672$	−3.75877	−0.144998
$673$	−28.5371	−1.10003	−0.550013	−	0.835156i	$-0.685377\pi$
$673$	−28.5371	−1.10003	−0.550013	+	0.835156i	$0.685377\pi$
$674$	−1.50206	−0.0578572
$675$	1.00000	0.0384900
$676$	6.09327	0.234357
$677$	11.9608	0.459691	0.229845	−	0.973227i	$-0.426178\pi$
$677$	11.9608	0.459691	0.229845	+	0.973227i	$0.426178\pi$
$678$	−7.75877	−0.297974
$679$	−41.4783	−1.59179
$680$	1.00000	0.0383482
$681$	−3.51754	−0.134792
$682$	−1.38919	−0.0531947
$683$	−47.6269	−1.82239	−0.911196	−	0.411972i	$-0.864840\pi$
$683$	−47.6269	−1.82239	−0.911196	+	0.411972i	$0.864840\pi$
$684$	4.36959	0.167075
$685$	14.9067	0.569557
$686$	−0.482459	−0.0184204
$687$	17.5175	0.668336
$688$	0.241230	0.00919679
$689$	−25.7243	−0.980018
$690$	1.75877	0.0669552
$691$	−4.57161	−0.173912	−0.0869562	−	0.996212i	$-0.527714\pi$
$691$	−4.57161	−0.173912	−0.0869562	+	0.996212i	$0.527714\pi$
$692$	−11.3892	−0.432952
$693$	3.75877	0.142784
$694$	−34.5526	−1.31160
$695$	12.9067	0.489580
$696$	−9.51754	−0.360761
$697$	−5.38919	−0.204130
$698$	−1.46286	−0.0553700
$699$	10.7392	0.406193
$700$	3.75877	0.142068
$701$	−44.6810	−1.68758	−0.843789	−	0.536676i	$-0.819680\pi$
$701$	−44.6810	−1.68758	−0.843789	+	0.536676i	$0.819680\pi$
$702$	−4.36959	−0.164919
$703$	8.73917	0.329604
$704$	1.00000	0.0376889
$705$	0	0
$706$	−27.9026	−1.05013
$707$	−7.03508	−0.264581
$708$	−7.75877	−0.291592
$709$	36.4742	1.36982	0.684909	−	0.728629i	$-0.259842\pi$
$709$	36.4742	1.36982	0.684909	+	0.728629i	$0.259842\pi$
$710$	7.75877	0.291181
$711$	4.36959	0.163872
$712$	14.2567	0.534293
$713$	2.44326	0.0915007
$714$	−3.75877	−0.140668
$715$	−4.36959	−0.163413
$716$	−3.01960	−0.112848
$717$	−3.09327	−0.115520
$718$	−8.90673	−0.332396
$719$	44.7547	1.66907	0.834533	−	0.550957i	$-0.185737\pi$
$719$	44.7547	1.66907	0.834533	+	0.550957i	$0.185737\pi$
$720$	−1.00000	−0.0372678
$721$	−15.0351	−0.559936
$722$	−0.0932736	−0.00347128
$723$	5.63041	0.209397
$724$	15.6459	0.581475
$725$	9.51754	0.353473
$726$	−1.00000	−0.0371135
$727$	−25.5567	−0.947847	−0.473924	−	0.880566i	$-0.657163\pi$
$727$	−25.5567	−0.947847	−0.473924	+	0.880566i	$0.657163\pi$
$728$	−16.4243	−0.608724
$729$	1.00000	0.0370370
$730$	8.53714	0.315974
$731$	0.241230	0.00892220
$732$	−8.12836	−0.300433
$733$	−20.4005	−0.753511	−0.376756	−	0.926313i	$-0.622960\pi$
$733$	−20.4005	−0.753511	−0.376756	+	0.926313i	$0.622960\pi$
$734$	−0.354103	−0.0130702
$735$	−7.12836	−0.262933
$736$	−1.75877	−0.0648291
$737$	−1.51754	−0.0558993
$738$	5.38919	0.198379
$739$	24.7047	0.908777	0.454388	−	0.890804i	$-0.349858\pi$
$739$	24.7047	0.908777	0.454388	+	0.890804i	$0.349858\pi$
$740$	−2.00000	−0.0735215
$741$	19.0933	0.701409
$742$	22.1284	0.812357
$743$	10.1284	0.371573	0.185787	−	0.982590i	$-0.440517\pi$
$743$	10.1284	0.371573	0.185787	+	0.982590i	$0.440517\pi$
$744$	−1.38919	−0.0509300
$745$	−5.38919	−0.197444
$746$	7.63041	0.279369
$747$	0	0
$748$	1.00000	0.0365636
$749$	−64.5134	−2.35727
$750$	1.00000	0.0365148
$751$	20.1985	0.737054	0.368527	−	0.929617i	$-0.379862\pi$
$751$	20.1985	0.737054	0.368527	+	0.929617i	$0.379862\pi$
$752$	0	0
$753$	−0.497941	−0.0181460
$754$	−41.5877	−1.51453
$755$	0.906726	0.0329992
$756$	3.75877	0.136705
$757$	33.0743	1.20211	0.601053	−	0.799209i	$-0.294748\pi$
$757$	33.0743	1.20211	0.601053	+	0.799209i	$0.294748\pi$
$758$	19.9418	0.724319
$759$	1.75877	0.0638393
$760$	4.36959	0.158502
$761$	13.1824	0.477863	0.238931	−	0.971036i	$-0.423203\pi$
$761$	13.1824	0.477863	0.238931	+	0.971036i	$0.423203\pi$
$762$	−16.9067	−0.612466
$763$	40.9959	1.48415
$764$	−17.1634	−0.620951
$765$	−1.00000	−0.0361551
$766$	7.03508	0.254188
$767$	−33.9026	−1.22415
$768$	1.00000	0.0360844
$769$	−35.0743	−1.26481	−0.632405	−	0.774638i	$-0.717932\pi$
$769$	−35.0743	−1.26481	−0.632405	+	0.774638i	$0.717932\pi$
$770$	3.75877	0.135457
$771$	11.3892	0.410171
$772$	−6.98040	−0.251230
$773$	21.6304	0.777992	0.388996	−	0.921239i	$-0.372822\pi$
$773$	21.6304	0.777992	0.388996	+	0.921239i	$0.372822\pi$
$774$	−0.241230	−0.00867082
$775$	1.38919	0.0499010
$776$	11.0351	0.396136
$777$	7.51754	0.269690
$778$	7.14796	0.256267
$779$	−23.5485	−0.843713
$780$	−4.36959	−0.156456
$781$	7.75877	0.277631
$782$	−1.75877	−0.0628935
$783$	9.51754	0.340129
$784$	7.12836	0.254584
$785$	12.2567	0.437461
$786$	−7.03508	−0.250933
$787$	−24.0310	−0.856611	−0.428306	−	0.903634i	$-0.640889\pi$
$787$	−24.0310	−0.856611	−0.428306	+	0.903634i	$0.640889\pi$
$788$	9.51754	0.339048
$789$	−4.16756	−0.148369
$790$	4.36959	0.155463
$791$	29.1634	1.03693
$792$	−1.00000	−0.0355335
$793$	−35.5175	−1.26126
$794$	−28.8675	−1.02447
$795$	5.88713	0.208795
$796$	−16.4243	−0.582143
$797$	53.6614	1.90078	0.950392	−	0.311055i	$-0.100682\pi$
$797$	53.6614	1.90078	0.950392	+	0.311055i	$0.100682\pi$
$798$	−16.4243	−0.581413
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	−14.2567	−0.503736
$802$	−22.2412	−0.785365
$803$	8.53714	0.301269
$804$	−1.51754	−0.0535195
$805$	−6.61081	−0.233001
$806$	−6.07016	−0.213812
$807$	−2.48246	−0.0873867
$808$	1.87164	0.0658442
$809$	−0.571614	−0.0200969	−0.0100484	−	0.999950i	$-0.503199\pi$
$809$	−0.571614	−0.0200969	−0.0100484	+	0.999950i	$0.503199\pi$
$810$	1.00000	0.0351364
$811$	−1.05407	−0.0370135	−0.0185068	−	0.999829i	$-0.505891\pi$
$811$	−1.05407	−0.0370135	−0.0185068	+	0.999829i	$0.505891\pi$
$812$	35.7743	1.25543
$813$	−17.6459	−0.618869
$814$	−2.00000	−0.0701000
$815$	9.16344	0.320981
$816$	1.00000	0.0350070
$817$	1.05407	0.0368773
$818$	30.2567	1.05790
$819$	16.4243	0.573910
$820$	5.38919	0.188199
$821$	26.8283	0.936315	0.468157	−	0.883645i	$-0.344918\pi$
$821$	26.8283	0.936315	0.468157	+	0.883645i	$0.344918\pi$
$822$	14.9067	0.519932
$823$	22.8283	0.795745	0.397873	−	0.917441i	$-0.369749\pi$
$823$	22.8283	0.795745	0.397873	+	0.917441i	$0.369749\pi$
$824$	4.00000	0.139347
$825$	1.00000	0.0348155
$826$	29.1634	1.01473
$827$	−20.9067	−0.726998	−0.363499	−	0.931595i	$-0.618418\pi$
$827$	−20.9067	−0.726998	−0.363499	+	0.931595i	$0.618418\pi$
$828$	1.75877	0.0611215
$829$	−49.2918	−1.71197	−0.855987	−	0.516997i	$-0.827050\pi$
$829$	−49.2918	−1.71197	−0.855987	+	0.516997i	$0.827050\pi$
$830$	0	0
$831$	−9.77425	−0.339065
$832$	4.36959	0.151488
$833$	7.12836	0.246983
$834$	12.9067	0.446923
$835$	−6.61081	−0.228777
$836$	4.36959	0.151125
$837$	1.38919	0.0480173
$838$	14.2959	0.493844
$839$	−11.2763	−0.389302	−0.194651	−	0.980873i	$-0.562357\pi$
$839$	−11.2763	−0.389302	−0.194651	+	0.980873i	$0.562357\pi$
$840$	3.75877	0.129690
$841$	61.5836	2.12357
$842$	10.0000	0.344623
$843$	2.48246	0.0855004
$844$	12.1676	0.418825
$845$	−6.09327	−0.209615
$846$	0	0
$847$	3.75877	0.129153
$848$	−5.88713	−0.202165
$849$	−23.0351	−0.790562
$850$	−1.00000	−0.0342997
$851$	3.51754	0.120580
$852$	7.75877	0.265811
$853$	35.1052	1.20198	0.600990	−	0.799256i	$-0.294773\pi$
$853$	35.1052	1.20198	0.600990	+	0.799256i	$0.294773\pi$
$854$	30.5526	1.04549
$855$	−4.36959	−0.149437
$856$	17.1634	0.586634
$857$	54.7701	1.87091	0.935456	−	0.353443i	$-0.114989\pi$
$857$	54.7701	1.87091	0.935456	+	0.353443i	$0.114989\pi$
$858$	−4.36959	−0.149175
$859$	−28.7701	−0.981624	−0.490812	−	0.871265i	$-0.663300\pi$
$859$	−28.7701	−0.981624	−0.490812	+	0.871265i	$0.663300\pi$
$860$	−0.241230	−0.00822586
$861$	−20.2567	−0.690347
$862$	10.9649	0.373467
$863$	28.3661	0.965592	0.482796	−	0.875733i	$-0.339621\pi$
$863$	28.3661	0.965592	0.482796	+	0.875733i	$0.339621\pi$
$864$	−1.00000	−0.0340207
$865$	11.3892	0.387244
$866$	−16.8675	−0.573182
$867$	1.00000	0.0339618
$868$	5.22163	0.177234
$869$	4.36959	0.148228
$870$	9.51754	0.322675
$871$	−6.63102	−0.224684
$872$	−10.9067	−0.369348
$873$	−11.0351	−0.373481
$874$	−7.68510	−0.259952
$875$	−3.75877	−0.127070
$876$	8.53714	0.288443
$877$	−20.7784	−0.701636	−0.350818	−	0.936444i	$-0.614096\pi$
$877$	−20.7784	−0.701636	−0.350818	+	0.936444i	$0.614096\pi$
$878$	15.8871	0.536165
$879$	−26.2567	−0.885617
$880$	−1.00000	−0.0337100
$881$	−37.4546	−1.26188	−0.630939	−	0.775832i	$-0.717330\pi$
$881$	−37.4546	−1.26188	−0.630939	+	0.775832i	$0.717330\pi$
$882$	−7.12836	−0.240024
$883$	−1.66489	−0.0560279	−0.0280140	−	0.999608i	$-0.508918\pi$
$883$	−1.66489	−0.0560279	−0.0280140	+	0.999608i	$0.508918\pi$
$884$	4.36959	0.146965
$885$	7.75877	0.260808
$886$	−4.05468	−0.136220
$887$	12.4243	0.417166	0.208583	−	0.978005i	$-0.433115\pi$
$887$	12.4243	0.417166	0.208583	+	0.978005i	$0.433115\pi$
$888$	−2.00000	−0.0671156
$889$	63.5485	2.13135
$890$	−14.2567	−0.477886
$891$	1.00000	0.0335013
$892$	−0.906726	−0.0303594
$893$	0	0
$894$	−5.38919	−0.180241
$895$	3.01960	0.100934
$896$	−3.75877	−0.125572
$897$	7.68510	0.256598
$898$	5.27631	0.176073
$899$	13.2216	0.440966
$900$	1.00000	0.0333333
$901$	−5.88713	−0.196129
$902$	5.38919	0.179440
$903$	0.906726	0.0301740
$904$	−7.75877	−0.258053
$905$	−15.6459	−0.520087
$906$	0.906726	0.0301240
$907$	−1.47834	−0.0490875	−0.0245437	−	0.999699i	$-0.507813\pi$
$907$	−1.47834	−0.0490875	−0.0245437	+	0.999699i	$0.507813\pi$
$908$	−3.51754	−0.116734
$909$	−1.87164	−0.0620785
$910$	16.4243	0.544459
$911$	−3.01960	−0.100044	−0.0500219	−	0.998748i	$-0.515929\pi$
$911$	−3.01960	−0.100044	−0.0500219	+	0.998748i	$0.515929\pi$
$912$	4.36959	0.144691
$913$	0	0
$914$	−18.7392	−0.619837
$915$	8.12836	0.268715
$916$	17.5175	0.578796
$917$	26.4433	0.873233
$918$	−1.00000	−0.0330049
$919$	−38.1284	−1.25774	−0.628869	−	0.777511i	$-0.716482\pi$
$919$	−38.1284	−1.25774	−0.628869	+	0.777511i	$0.716482\pi$
$920$	1.75877	0.0579849
$921$	13.2371	0.436178
$922$	6.61081	0.217716
$923$	33.9026	1.11592
$924$	3.75877	0.123654
$925$	2.00000	0.0657596
$926$	−26.3851	−0.867067
$927$	−4.00000	−0.131377
$928$	−9.51754	−0.312429
$929$	−40.8248	−1.33942	−0.669709	−	0.742623i	$-0.733581\pi$
$929$	−40.8248	−1.33942	−0.669709	+	0.742623i	$0.733581\pi$
$930$	1.38919	0.0455532
$931$	31.1480	1.02083
$932$	10.7392	0.351773
$933$	−1.79797	−0.0588629
$934$	−40.0547	−1.31063
$935$	−1.00000	−0.0327035
$936$	−4.36959	−0.142824
$937$	−34.7701	−1.13589	−0.567945	−	0.823066i	$-0.692262\pi$
$937$	−34.7701	−1.13589	−0.567945	+	0.823066i	$0.692262\pi$
$938$	5.70409	0.186245
$939$	6.77837	0.221204
$940$	0	0
$941$	6.57161	0.214228	0.107114	−	0.994247i	$-0.465839\pi$
$941$	6.57161	0.214228	0.107114	+	0.994247i	$0.465839\pi$
$942$	12.2567	0.399345
$943$	−9.47834	−0.308657
$944$	−7.75877	−0.252526
$945$	−3.75877	−0.122273
$946$	−0.241230	−0.00784305
$947$	−21.4783	−0.697952	−0.348976	−	0.937132i	$-0.613471\pi$
$947$	−21.4783	−0.697952	−0.348976	+	0.937132i	$0.613471\pi$
$948$	4.36959	0.141918
$949$	37.3038	1.21093
$950$	−4.36959	−0.141768
$951$	33.2918	1.07956
$952$	−3.75877	−0.121822
$953$	−26.9067	−0.871594	−0.435797	−	0.900045i	$-0.643534\pi$
$953$	−26.9067	−0.871594	−0.435797	+	0.900045i	$0.643534\pi$
$954$	5.88713	0.190603
$955$	17.1634	0.555396
$956$	−3.09327	−0.100044
$957$	9.51754	0.307658
$958$	26.0310	0.841022
$959$	−56.0310	−1.80933
$960$	−1.00000	−0.0322749
$961$	−29.0702	−0.937747
$962$	−8.73917	−0.281762
$963$	−17.1634	−0.553084
$964$	5.63041	0.181343
$965$	6.98040	0.224707
$966$	−6.61081	−0.212699
$967$	13.3108	0.428046	0.214023	−	0.976829i	$-0.431343\pi$
$967$	13.3108	0.428046	0.214023	+	0.976829i	$0.431343\pi$
$968$	−1.00000	−0.0321412
$969$	4.36959	0.140371
$970$	−11.0351	−0.354315
$971$	29.0898	0.933535	0.466767	−	0.884380i	$-0.345418\pi$
$971$	29.0898	0.933535	0.466767	+	0.884380i	$0.345418\pi$
$972$	1.00000	0.0320750
$973$	−48.5134	−1.55527
$974$	−15.6459	−0.501327
$975$	4.36959	0.139939
$976$	−8.12836	−0.260182
$977$	−26.6810	−0.853600	−0.426800	−	0.904346i	$-0.640359\pi$
$977$	−26.6810	−0.853600	−0.426800	+	0.904346i	$0.640359\pi$
$978$	9.16344	0.293014
$979$	−14.2567	−0.455646
$980$	−7.12836	−0.227707
$981$	10.9067	0.348225
$982$	−14.9067	−0.475693
$983$	6.72369	0.214452	0.107226	−	0.994235i	$-0.465803\pi$
$983$	6.72369	0.214452	0.107226	+	0.994235i	$0.465803\pi$
$984$	5.38919	0.171801
$985$	−9.51754	−0.303254
$986$	−9.51754	−0.303100
$987$	0	0
$988$	19.0933	0.607438
$989$	0.424267	0.0134909
$990$	1.00000	0.0317821
$991$	49.1634	1.56173	0.780864	−	0.624701i	$-0.214779\pi$
$991$	49.1634	1.56173	0.780864	+	0.624701i	$0.214779\pi$
$992$	−1.38919	−0.0441067
$993$	8.00000	0.253872
$994$	−29.1634	−0.925008
$995$	16.4243	0.520684
$996$	0	0
$997$	−15.8135	−0.500817	−0.250409	−	0.968140i	$-0.580565\pi$
$997$	−15.8135	−0.500817	−0.250409	+	0.968140i	$0.580565\pi$
$998$	−4.48246	−0.141890
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.by.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.by.1.3	✓	3	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +3.75877 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +3.75877 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} +4.36959 q^{13} -3.75877 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.36959 q^{19} -1.00000 q^{20} +3.75877 q^{21} -1.00000 q^{22} +1.75877 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.36959 q^{26} +1.00000 q^{27} +3.75877 q^{28} +9.51754 q^{29} +1.00000 q^{30} +1.38919 q^{31} -1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} -3.75877 q^{35} +1.00000 q^{36} +2.00000 q^{37} -4.36959 q^{38} +4.36959 q^{39} +1.00000 q^{40} -5.38919 q^{41} -3.75877 q^{42} +0.241230 q^{43} +1.00000 q^{44} -1.00000 q^{45} -1.75877 q^{46} +1.00000 q^{48} +7.12836 q^{49} -1.00000 q^{50} +1.00000 q^{51} +4.36959 q^{52} -5.88713 q^{53} -1.00000 q^{54} -1.00000 q^{55} -3.75877 q^{56} +4.36959 q^{57} -9.51754 q^{58} -7.75877 q^{59} -1.00000 q^{60} -8.12836 q^{61} -1.38919 q^{62} +3.75877 q^{63} +1.00000 q^{64} -4.36959 q^{65} -1.00000 q^{66} -1.51754 q^{67} +1.00000 q^{68} +1.75877 q^{69} +3.75877 q^{70} +7.75877 q^{71} -1.00000 q^{72} +8.53714 q^{73} -2.00000 q^{74} +1.00000 q^{75} +4.36959 q^{76} +3.75877 q^{77} -4.36959 q^{78} +4.36959 q^{79} -1.00000 q^{80} +1.00000 q^{81} +5.38919 q^{82} +3.75877 q^{84} -1.00000 q^{85} -0.241230 q^{86} +9.51754 q^{87} -1.00000 q^{88} -14.2567 q^{89} +1.00000 q^{90} +16.4243 q^{91} +1.75877 q^{92} +1.38919 q^{93} -4.36959 q^{95} -1.00000 q^{96} -11.0351 q^{97} -7.12836 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 6 q^{13} - 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} - 3 q^{22} - 6 q^{23} - 3 q^{24} + 3 q^{25} - 6 q^{26} + 3 q^{27} + 6 q^{29} + 3 q^{30} - 3 q^{32} + 3 q^{33} - 3 q^{34} + 3 q^{36} + 6 q^{37} - 6 q^{38} + 6 q^{39} + 3 q^{40} - 12 q^{41} + 12 q^{43} + 3 q^{44} - 3 q^{45} + 6 q^{46} + 3 q^{48} + 3 q^{49} - 3 q^{50} + 3 q^{51} + 6 q^{52} + 12 q^{53} - 3 q^{54} - 3 q^{55} + 6 q^{57} - 6 q^{58} - 12 q^{59} - 3 q^{60} - 6 q^{61} + 3 q^{64} - 6 q^{65} - 3 q^{66} + 18 q^{67} + 3 q^{68} - 6 q^{69} + 12 q^{71} - 3 q^{72} + 6 q^{73} - 6 q^{74} + 3 q^{75} + 6 q^{76} - 6 q^{78} + 6 q^{79} - 3 q^{80} + 3 q^{81} + 12 q^{82} - 3 q^{85} - 12 q^{86} + 6 q^{87} - 3 q^{88} - 6 q^{89} + 3 q^{90} - 6 q^{92} - 6 q^{95} - 3 q^{96} + 12 q^{97} - 3 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 6 * q^13 - 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 - 3 * q^22 - 6 * q^23 - 3 * q^24 + 3 * q^25 - 6 * q^26 + 3 * q^27 + 6 * q^29 + 3 * q^30 - 3 * q^32 + 3 * q^33 - 3 * q^34 + 3 * q^36 + 6 * q^37 - 6 * q^38 + 6 * q^39 + 3 * q^40 - 12 * q^41 + 12 * q^43 + 3 * q^44 - 3 * q^45 + 6 * q^46 + 3 * q^48 + 3 * q^49 - 3 * q^50 + 3 * q^51 + 6 * q^52 + 12 * q^53 - 3 * q^54 - 3 * q^55 + 6 * q^57 - 6 * q^58 - 12 * q^59 - 3 * q^60 - 6 * q^61 + 3 * q^64 - 6 * q^65 - 3 * q^66 + 18 * q^67 + 3 * q^68 - 6 * q^69 + 12 * q^71 - 3 * q^72 + 6 * q^73 - 6 * q^74 + 3 * q^75 + 6 * q^76 - 6 * q^78 + 6 * q^79 - 3 * q^80 + 3 * q^81 + 12 * q^82 - 3 * q^85 - 12 * q^86 + 6 * q^87 - 3 * q^88 - 6 * q^89 + 3 * q^90 - 6 * q^92 - 6 * q^95 - 3 * q^96 + 12 * q^97 - 3 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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