LMFDB - Embedded newform 5610.2.a.bs.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{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.30278$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.60555 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.60555 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -6.60555 q^{13} -4.60555 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -6.60555 q^{19} -1.00000 q^{20} +4.60555 q^{21} +1.00000 q^{22} +2.60555 q^{23} -1.00000 q^{24} +1.00000 q^{25} +6.60555 q^{26} +1.00000 q^{27} +4.60555 q^{28} +6.00000 q^{29} +1.00000 q^{30} -9.21110 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -4.60555 q^{35} +1.00000 q^{36} +7.21110 q^{37} +6.60555 q^{38} -6.60555 q^{39} +1.00000 q^{40} -5.21110 q^{41} -4.60555 q^{42} -12.6056 q^{43} -1.00000 q^{44} -1.00000 q^{45} -2.60555 q^{46} +12.0000 q^{47} +1.00000 q^{48} +14.2111 q^{49} -1.00000 q^{50} +1.00000 q^{51} -6.60555 q^{52} -8.60555 q^{53} -1.00000 q^{54} +1.00000 q^{55} -4.60555 q^{56} -6.60555 q^{57} -6.00000 q^{58} -3.39445 q^{59} -1.00000 q^{60} +2.00000 q^{61} +9.21110 q^{62} +4.60555 q^{63} +1.00000 q^{64} +6.60555 q^{65} +1.00000 q^{66} -10.0000 q^{67} +1.00000 q^{68} +2.60555 q^{69} +4.60555 q^{70} -8.60555 q^{71} -1.00000 q^{72} -1.39445 q^{73} -7.21110 q^{74} +1.00000 q^{75} -6.60555 q^{76} -4.60555 q^{77} +6.60555 q^{78} -6.60555 q^{79} -1.00000 q^{80} +1.00000 q^{81} +5.21110 q^{82} +4.60555 q^{84} -1.00000 q^{85} +12.6056 q^{86} +6.00000 q^{87} +1.00000 q^{88} +6.00000 q^{89} +1.00000 q^{90} -30.4222 q^{91} +2.60555 q^{92} -9.21110 q^{93} -12.0000 q^{94} +6.60555 q^{95} -1.00000 q^{96} +1.21110 q^{97} -14.2111 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} - 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^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} - 6 q^{19} - 2 q^{20} + 2 q^{21} + 2 q^{22} - 2 q^{23} - 2 q^{24} + 2 q^{25} + 6 q^{26} + 2 q^{27} + 2 q^{28} + 12 q^{29} + 2 q^{30} - 4 q^{31} - 2 q^{32} - 2 q^{33} - 2 q^{34} - 2 q^{35} + 2 q^{36} + 6 q^{38} - 6 q^{39} + 2 q^{40} + 4 q^{41} - 2 q^{42} - 18 q^{43} - 2 q^{44} - 2 q^{45} + 2 q^{46} + 24 q^{47} + 2 q^{48} + 14 q^{49} - 2 q^{50} + 2 q^{51} - 6 q^{52} - 10 q^{53} - 2 q^{54} + 2 q^{55} - 2 q^{56} - 6 q^{57} - 12 q^{58} - 14 q^{59} - 2 q^{60} + 4 q^{61} + 4 q^{62} + 2 q^{63} + 2 q^{64} + 6 q^{65} + 2 q^{66} - 20 q^{67} + 2 q^{68} - 2 q^{69} + 2 q^{70} - 10 q^{71} - 2 q^{72} - 10 q^{73} + 2 q^{75} - 6 q^{76} - 2 q^{77} + 6 q^{78} - 6 q^{79} - 2 q^{80} + 2 q^{81} - 4 q^{82} + 2 q^{84} - 2 q^{85} + 18 q^{86} + 12 q^{87} + 2 q^{88} + 12 q^{89} + 2 q^{90} - 32 q^{91} - 2 q^{92} - 4 q^{93} - 24 q^{94} + 6 q^{95} - 2 q^{96} - 12 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 + 2 * q^12 - 6 * q^13 - 2 * q^14 - 2 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 - 6 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 - 2 * q^23 - 2 * q^24 + 2 * q^25 + 6 * q^26 + 2 * q^27 + 2 * q^28 + 12 * q^29 + 2 * q^30 - 4 * q^31 - 2 * q^32 - 2 * q^33 - 2 * q^34 - 2 * q^35 + 2 * q^36 + 6 * q^38 - 6 * q^39 + 2 * q^40 + 4 * q^41 - 2 * q^42 - 18 * q^43 - 2 * q^44 - 2 * q^45 + 2 * q^46 + 24 * q^47 + 2 * q^48 + 14 * q^49 - 2 * q^50 + 2 * q^51 - 6 * q^52 - 10 * q^53 - 2 * q^54 + 2 * q^55 - 2 * q^56 - 6 * q^57 - 12 * q^58 - 14 * q^59 - 2 * q^60 + 4 * q^61 + 4 * q^62 + 2 * q^63 + 2 * q^64 + 6 * q^65 + 2 * q^66 - 20 * q^67 + 2 * q^68 - 2 * q^69 + 2 * q^70 - 10 * q^71 - 2 * q^72 - 10 * q^73 + 2 * q^75 - 6 * q^76 - 2 * q^77 + 6 * q^78 - 6 * q^79 - 2 * q^80 + 2 * q^81 - 4 * q^82 + 2 * q^84 - 2 * q^85 + 18 * q^86 + 12 * q^87 + 2 * q^88 + 12 * q^89 + 2 * q^90 - 32 * q^91 - 2 * q^92 - 4 * q^93 - 24 * q^94 + 6 * q^95 - 2 * q^96 - 12 * 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
$7$	4.60555	1.74073	0.870367	−	0.492403i	$-0.163881\pi$
$7$	4.60555	1.74073	0.870367	+	0.492403i	$0.163881\pi$
$8$	−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
$13$	−6.60555	−1.83205	−0.916025	−	0.401121i	$-0.868621\pi$
$13$	−6.60555	−1.83205	−0.916025	+	0.401121i	$0.868621\pi$
$14$	−4.60555	−1.23089
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−6.60555	−1.51542	−0.757709	−	0.652593i	$-0.773681\pi$
$19$	−6.60555	−1.51542	−0.757709	+	0.652593i	$0.773681\pi$
$20$	−1.00000	−0.223607
$21$	4.60555	1.00501
$22$	1.00000	0.213201
$23$	2.60555	0.543295	0.271647	−	0.962397i	$-0.412432\pi$
$23$	2.60555	0.543295	0.271647	+	0.962397i	$0.412432\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	6.60555	1.29546
$27$	1.00000	0.192450
$28$	4.60555	0.870367
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	1.00000	0.182574
$31$	−9.21110	−1.65436	−0.827181	−	0.561935i	$-0.810057\pi$
$31$	−9.21110	−1.65436	−0.827181	+	0.561935i	$0.810057\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	−4.60555	−0.778480
$36$	1.00000	0.166667
$37$	7.21110	1.18550	0.592749	−	0.805387i	$-0.298043\pi$
$37$	7.21110	1.18550	0.592749	+	0.805387i	$0.298043\pi$
$38$	6.60555	1.07156
$39$	−6.60555	−1.05773
$40$	1.00000	0.158114
$41$	−5.21110	−0.813837	−0.406919	−	0.913464i	$-0.633397\pi$
$41$	−5.21110	−0.813837	−0.406919	+	0.913464i	$0.633397\pi$
$42$	−4.60555	−0.710652
$43$	−12.6056	−1.92233	−0.961164	−	0.275977i	$-0.910999\pi$
$43$	−12.6056	−1.92233	−0.961164	+	0.275977i	$0.910999\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	−2.60555	−0.384168
$47$	12.0000	1.75038	0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000	1.75038	0.875190	+	0.483779i	$0.160736\pi$
$48$	1.00000	0.144338
$49$	14.2111	2.03016
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	−6.60555	−0.916025
$53$	−8.60555	−1.18206	−0.591032	−	0.806648i	$-0.701279\pi$
$53$	−8.60555	−1.18206	−0.591032	+	0.806648i	$0.701279\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	−4.60555	−0.615443
$57$	−6.60555	−0.874927
$58$	−6.00000	−0.787839
$59$	−3.39445	−0.441920	−0.220960	−	0.975283i	$-0.570919\pi$
$59$	−3.39445	−0.441920	−0.220960	+	0.975283i	$0.570919\pi$
$60$	−1.00000	−0.129099
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	9.21110	1.16981
$63$	4.60555	0.580245
$64$	1.00000	0.125000
$65$	6.60555	0.819318
$66$	1.00000	0.123091
$67$	−10.0000	−1.22169	−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000	−1.22169	−0.610847	+	0.791748i	$0.709171\pi$
$68$	1.00000	0.121268
$69$	2.60555	0.313672
$70$	4.60555	0.550469
$71$	−8.60555	−1.02129	−0.510646	−	0.859791i	$-0.670594\pi$
$71$	−8.60555	−1.02129	−0.510646	+	0.859791i	$0.670594\pi$
$72$	−1.00000	−0.117851
$73$	−1.39445	−0.163208	−0.0816039	−	0.996665i	$-0.526004\pi$
$73$	−1.39445	−0.163208	−0.0816039	+	0.996665i	$0.526004\pi$
$74$	−7.21110	−0.838274
$75$	1.00000	0.115470
$76$	−6.60555	−0.757709
$77$	−4.60555	−0.524851
$78$	6.60555	0.747931
$79$	−6.60555	−0.743183	−0.371591	−	0.928396i	$-0.621188\pi$
$79$	−6.60555	−0.743183	−0.371591	+	0.928396i	$0.621188\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	5.21110	0.575470
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	4.60555	0.502507
$85$	−1.00000	−0.108465
$86$	12.6056	1.35929
$87$	6.00000	0.643268
$88$	1.00000	0.106600
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	1.00000	0.105409
$91$	−30.4222	−3.18911
$92$	2.60555	0.271647
$93$	−9.21110	−0.955147
$94$	−12.0000	−1.23771
$95$	6.60555	0.677715
$96$	−1.00000	−0.102062
$97$	1.21110	0.122969	0.0614844	−	0.998108i	$-0.480417\pi$
$97$	1.21110	0.122969	0.0614844	+	0.998108i	$0.480417\pi$
$98$	−14.2111	−1.43554
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−12.0000	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$102$	−1.00000	−0.0990148
$103$	−14.4222	−1.42106	−0.710531	−	0.703666i	$-0.751545\pi$
$103$	−14.4222	−1.42106	−0.710531	+	0.703666i	$0.751545\pi$
$104$	6.60555	0.647728
$105$	−4.60555	−0.449456
$106$	8.60555	0.835845
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	1.00000	0.0962250
$109$	−20.4222	−1.95609	−0.978046	−	0.208388i	$-0.933178\pi$
$109$	−20.4222	−1.95609	−0.978046	+	0.208388i	$0.933178\pi$
$110$	−1.00000	−0.0953463
$111$	7.21110	0.684448
$112$	4.60555	0.435184
$113$	−1.81665	−0.170896	−0.0854482	−	0.996343i	$-0.527232\pi$
$113$	−1.81665	−0.170896	−0.0854482	+	0.996343i	$0.527232\pi$
$114$	6.60555	0.618667
$115$	−2.60555	−0.242969
$116$	6.00000	0.557086
$117$	−6.60555	−0.610683
$118$	3.39445	0.312484
$119$	4.60555	0.422190
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	−5.21110	−0.469869
$124$	−9.21110	−0.827181
$125$	−1.00000	−0.0894427
$126$	−4.60555	−0.410295
$127$	1.21110	0.107468	0.0537340	−	0.998555i	$-0.482888\pi$
$127$	1.21110	0.107468	0.0537340	+	0.998555i	$0.482888\pi$
$128$	−1.00000	−0.0883883
$129$	−12.6056	−1.10986
$130$	−6.60555	−0.579345
$131$	10.4222	0.910592	0.455296	−	0.890340i	$-0.349533\pi$
$131$	10.4222	0.910592	0.455296	+	0.890340i	$0.349533\pi$
$132$	−1.00000	−0.0870388
$133$	−30.4222	−2.63794
$134$	10.0000	0.863868
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	−2.60555	−0.221799
$139$	18.4222	1.56255	0.781276	−	0.624186i	$-0.214569\pi$
$139$	18.4222	1.56255	0.781276	+	0.624186i	$0.214569\pi$
$140$	−4.60555	−0.389240
$141$	12.0000	1.01058
$142$	8.60555	0.722162
$143$	6.60555	0.552384
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	1.39445	0.115405
$147$	14.2111	1.17211
$148$	7.21110	0.592749
$149$	−6.78890	−0.556168	−0.278084	−	0.960557i	$-0.589699\pi$
$149$	−6.78890	−0.556168	−0.278084	+	0.960557i	$0.589699\pi$
$150$	−1.00000	−0.0816497
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	6.60555	0.535781
$153$	1.00000	0.0808452
$154$	4.60555	0.371126
$155$	9.21110	0.739854
$156$	−6.60555	−0.528867
$157$	1.21110	0.0966565	0.0483283	−	0.998832i	$-0.484611\pi$
$157$	1.21110	0.0966565	0.0483283	+	0.998832i	$0.484611\pi$
$158$	6.60555	0.525509
$159$	−8.60555	−0.682465
$160$	1.00000	0.0790569
$161$	12.0000	0.945732
$162$	−1.00000	−0.0785674
$163$	−9.21110	−0.721469	−0.360735	−	0.932669i	$-0.617474\pi$
$163$	−9.21110	−0.721469	−0.360735	+	0.932669i	$0.617474\pi$
$164$	−5.21110	−0.406919
$165$	1.00000	0.0778499
$166$	0	0
$167$	−6.78890	−0.525341	−0.262670	−	0.964886i	$-0.584603\pi$
$167$	−6.78890	−0.525341	−0.262670	+	0.964886i	$0.584603\pi$
$168$	−4.60555	−0.355326
$169$	30.6333	2.35641
$170$	1.00000	0.0766965
$171$	−6.60555	−0.505139
$172$	−12.6056	−0.961164
$173$	16.4222	1.24856	0.624279	−	0.781202i	$-0.285393\pi$
$173$	16.4222	1.24856	0.624279	+	0.781202i	$0.285393\pi$
$174$	−6.00000	−0.454859
$175$	4.60555	0.348147
$176$	−1.00000	−0.0753778
$177$	−3.39445	−0.255142
$178$	−6.00000	−0.449719
$179$	13.8167	1.03271	0.516353	−	0.856376i	$-0.327289\pi$
$179$	13.8167	1.03271	0.516353	+	0.856376i	$0.327289\pi$
$180$	−1.00000	−0.0745356
$181$	−8.42221	−0.626018	−0.313009	−	0.949750i	$-0.601337\pi$
$181$	−8.42221	−0.626018	−0.313009	+	0.949750i	$0.601337\pi$
$182$	30.4222	2.25504
$183$	2.00000	0.147844
$184$	−2.60555	−0.192084
$185$	−7.21110	−0.530171
$186$	9.21110	0.675391
$187$	−1.00000	−0.0731272
$188$	12.0000	0.875190
$189$	4.60555	0.335005
$190$	−6.60555	−0.479217
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	1.00000	0.0721688
$193$	5.39445	0.388301	0.194150	−	0.980972i	$-0.437805\pi$
$193$	5.39445	0.388301	0.194150	+	0.980972i	$0.437805\pi$
$194$	−1.21110	−0.0869521
$195$	6.60555	0.473033
$196$	14.2111	1.01508
$197$	−0.788897	−0.0562066	−0.0281033	−	0.999605i	$-0.508947\pi$
$197$	−0.788897	−0.0562066	−0.0281033	+	0.999605i	$0.508947\pi$
$198$	1.00000	0.0710669
$199$	−9.21110	−0.652958	−0.326479	−	0.945204i	$-0.605862\pi$
$199$	−9.21110	−0.652958	−0.326479	+	0.945204i	$0.605862\pi$
$200$	−1.00000	−0.0707107
$201$	−10.0000	−0.705346
$202$	12.0000	0.844317
$203$	27.6333	1.93948
$204$	1.00000	0.0700140
$205$	5.21110	0.363959
$206$	14.4222	1.00484
$207$	2.60555	0.181098
$208$	−6.60555	−0.458013
$209$	6.60555	0.456916
$210$	4.60555	0.317813
$211$	−10.7889	−0.742738	−0.371369	−	0.928485i	$-0.621112\pi$
$211$	−10.7889	−0.742738	−0.371369	+	0.928485i	$0.621112\pi$
$212$	−8.60555	−0.591032
$213$	−8.60555	−0.589643
$214$	0	0
$215$	12.6056	0.859691
$216$	−1.00000	−0.0680414
$217$	−42.4222	−2.87981
$218$	20.4222	1.38317
$219$	−1.39445	−0.0942281
$220$	1.00000	0.0674200
$221$	−6.60555	−0.444337
$222$	−7.21110	−0.483978
$223$	23.6333	1.58260	0.791302	−	0.611426i	$-0.209404\pi$
$223$	23.6333	1.58260	0.791302	+	0.611426i	$0.209404\pi$
$224$	−4.60555	−0.307721
$225$	1.00000	0.0666667
$226$	1.81665	0.120842
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	−6.60555	−0.437463
$229$	−15.2111	−1.00518	−0.502589	−	0.864525i	$-0.667619\pi$
$229$	−15.2111	−1.00518	−0.502589	+	0.864525i	$0.667619\pi$
$230$	2.60555	0.171805
$231$	−4.60555	−0.303023
$232$	−6.00000	−0.393919
$233$	−0.788897	−0.0516824	−0.0258412	−	0.999666i	$-0.508226\pi$
$233$	−0.788897	−0.0516824	−0.0258412	+	0.999666i	$0.508226\pi$
$234$	6.60555	0.431818
$235$	−12.0000	−0.782794
$236$	−3.39445	−0.220960
$237$	−6.60555	−0.429077
$238$	−4.60555	−0.298534
$239$	−27.6333	−1.78745	−0.893725	−	0.448615i	$-0.851917\pi$
$239$	−27.6333	−1.78745	−0.893725	+	0.448615i	$0.851917\pi$
$240$	−1.00000	−0.0645497
$241$	27.0278	1.74101	0.870505	−	0.492159i	$-0.163792\pi$
$241$	27.0278	1.74101	0.870505	+	0.492159i	$0.163792\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	−14.2111	−0.907914
$246$	5.21110	0.332248
$247$	43.6333	2.77632
$248$	9.21110	0.584906
$249$	0	0
$250$	1.00000	0.0632456
$251$	15.3944	0.971689	0.485844	−	0.874045i	$-0.338512\pi$
$251$	15.3944	0.971689	0.485844	+	0.874045i	$0.338512\pi$
$252$	4.60555	0.290122
$253$	−2.60555	−0.163810
$254$	−1.21110	−0.0759913
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	−21.6333	−1.34945	−0.674724	−	0.738070i	$-0.735737\pi$
$257$	−21.6333	−1.34945	−0.674724	+	0.738070i	$0.735737\pi$
$258$	12.6056	0.784787
$259$	33.2111	2.06364
$260$	6.60555	0.409659
$261$	6.00000	0.371391
$262$	−10.4222	−0.643886
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	1.00000	0.0615457
$265$	8.60555	0.528635
$266$	30.4222	1.86531
$267$	6.00000	0.367194
$268$	−10.0000	−0.610847
$269$	−21.6333	−1.31901	−0.659503	−	0.751702i	$-0.729233\pi$
$269$	−21.6333	−1.31901	−0.659503	+	0.751702i	$0.729233\pi$
$270$	1.00000	0.0608581
$271$	13.2111	0.802517	0.401259	−	0.915965i	$-0.368573\pi$
$271$	13.2111	0.802517	0.401259	+	0.915965i	$0.368573\pi$
$272$	1.00000	0.0606339
$273$	−30.4222	−1.84124
$274$	−6.00000	−0.362473
$275$	−1.00000	−0.0603023
$276$	2.60555	0.156836
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	−18.4222	−1.10489
$279$	−9.21110	−0.551454
$280$	4.60555	0.275234
$281$	11.2111	0.668798	0.334399	−	0.942432i	$-0.391467\pi$
$281$	11.2111	0.668798	0.334399	+	0.942432i	$0.391467\pi$
$282$	−12.0000	−0.714590
$283$	1.21110	0.0719926	0.0359963	−	0.999352i	$-0.488540\pi$
$283$	1.21110	0.0719926	0.0359963	+	0.999352i	$0.488540\pi$
$284$	−8.60555	−0.510646
$285$	6.60555	0.391279
$286$	−6.60555	−0.390594
$287$	−24.0000	−1.41668
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	6.00000	0.352332
$291$	1.21110	0.0709961
$292$	−1.39445	−0.0816039
$293$	−30.0000	−1.75262	−0.876309	−	0.481749i	$-0.840002\pi$
$293$	−30.0000	−1.75262	−0.876309	+	0.481749i	$0.840002\pi$
$294$	−14.2111	−0.828808
$295$	3.39445	0.197632
$296$	−7.21110	−0.419137
$297$	−1.00000	−0.0580259
$298$	6.78890	0.393270
$299$	−17.2111	−0.995344
$300$	1.00000	0.0577350
$301$	−58.0555	−3.34626
$302$	16.0000	0.920697
$303$	−12.0000	−0.689382
$304$	−6.60555	−0.378854
$305$	−2.00000	−0.114520
$306$	−1.00000	−0.0571662
$307$	3.02776	0.172803	0.0864016	−	0.996260i	$-0.472463\pi$
$307$	3.02776	0.172803	0.0864016	+	0.996260i	$0.472463\pi$
$308$	−4.60555	−0.262426
$309$	−14.4222	−0.820451
$310$	−9.21110	−0.523155
$311$	24.2389	1.37446	0.687230	−	0.726440i	$-0.258827\pi$
$311$	24.2389	1.37446	0.687230	+	0.726440i	$0.258827\pi$
$312$	6.60555	0.373966
$313$	−33.2111	−1.87720	−0.938601	−	0.345004i	$-0.887878\pi$
$313$	−33.2111	−1.87720	−0.938601	+	0.345004i	$0.887878\pi$
$314$	−1.21110	−0.0683465
$315$	−4.60555	−0.259493
$316$	−6.60555	−0.371591
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	8.60555	0.482575
$319$	−6.00000	−0.335936
$320$	−1.00000	−0.0559017
$321$	0	0
$322$	−12.0000	−0.668734
$323$	−6.60555	−0.367543
$324$	1.00000	0.0555556
$325$	−6.60555	−0.366410
$326$	9.21110	0.510156
$327$	−20.4222	−1.12935
$328$	5.21110	0.287735
$329$	55.2666	3.04695
$330$	−1.00000	−0.0550482
$331$	−26.4222	−1.45230	−0.726148	−	0.687539i	$-0.758691\pi$
$331$	−26.4222	−1.45230	−0.726148	+	0.687539i	$0.758691\pi$
$332$	0	0
$333$	7.21110	0.395166
$334$	6.78890	0.371472
$335$	10.0000	0.546358
$336$	4.60555	0.251253
$337$	−11.8167	−0.643694	−0.321847	−	0.946792i	$-0.604304\pi$
$337$	−11.8167	−0.643694	−0.321847	+	0.946792i	$0.604304\pi$
$338$	−30.6333	−1.66623
$339$	−1.81665	−0.0986671
$340$	−1.00000	−0.0542326
$341$	9.21110	0.498809
$342$	6.60555	0.357187
$343$	33.2111	1.79323
$344$	12.6056	0.679646
$345$	−2.60555	−0.140278
$346$	−16.4222	−0.882863
$347$	−32.8444	−1.76318	−0.881590	−	0.472016i	$-0.843527\pi$
$347$	−32.8444	−1.76318	−0.881590	+	0.472016i	$0.843527\pi$
$348$	6.00000	0.321634
$349$	20.2389	1.08336	0.541681	−	0.840584i	$-0.317788\pi$
$349$	20.2389	1.08336	0.541681	+	0.840584i	$0.317788\pi$
$350$	−4.60555	−0.246177
$351$	−6.60555	−0.352578
$352$	1.00000	0.0533002
$353$	−11.2111	−0.596707	−0.298353	−	0.954455i	$-0.596437\pi$
$353$	−11.2111	−0.596707	−0.298353	+	0.954455i	$0.596437\pi$
$354$	3.39445	0.180413
$355$	8.60555	0.456735
$356$	6.00000	0.317999
$357$	4.60555	0.243752
$358$	−13.8167	−0.730233
$359$	−29.2111	−1.54170	−0.770852	−	0.637015i	$-0.780169\pi$
$359$	−29.2111	−1.54170	−0.770852	+	0.637015i	$0.780169\pi$
$360$	1.00000	0.0527046
$361$	24.6333	1.29649
$362$	8.42221	0.442661
$363$	1.00000	0.0524864
$364$	−30.4222	−1.59456
$365$	1.39445	0.0729888
$366$	−2.00000	−0.104542
$367$	−22.0000	−1.14839	−0.574195	−	0.818718i	$-0.694685\pi$
$367$	−22.0000	−1.14839	−0.574195	+	0.818718i	$0.694685\pi$
$368$	2.60555	0.135824
$369$	−5.21110	−0.271279
$370$	7.21110	0.374887
$371$	−39.6333	−2.05766
$372$	−9.21110	−0.477573
$373$	−5.02776	−0.260327	−0.130164	−	0.991493i	$-0.541550\pi$
$373$	−5.02776	−0.260327	−0.130164	+	0.991493i	$0.541550\pi$
$374$	1.00000	0.0517088
$375$	−1.00000	−0.0516398
$376$	−12.0000	−0.618853
$377$	−39.6333	−2.04122
$378$	−4.60555	−0.236884
$379$	−5.57779	−0.286512	−0.143256	−	0.989686i	$-0.545757\pi$
$379$	−5.57779	−0.286512	−0.143256	+	0.989686i	$0.545757\pi$
$380$	6.60555	0.338858
$381$	1.21110	0.0620467
$382$	−12.0000	−0.613973
$383$	1.57779	0.0806216	0.0403108	−	0.999187i	$-0.487165\pi$
$383$	1.57779	0.0806216	0.0403108	+	0.999187i	$0.487165\pi$
$384$	−1.00000	−0.0510310
$385$	4.60555	0.234721
$386$	−5.39445	−0.274570
$387$	−12.6056	−0.640776
$388$	1.21110	0.0614844
$389$	−13.0278	−0.660533	−0.330267	−	0.943888i	$-0.607139\pi$
$389$	−13.0278	−0.660533	−0.330267	+	0.943888i	$0.607139\pi$
$390$	−6.60555	−0.334485
$391$	2.60555	0.131768
$392$	−14.2111	−0.717769
$393$	10.4222	0.525731
$394$	0.788897	0.0397441
$395$	6.60555	0.332361
$396$	−1.00000	−0.0502519
$397$	−4.78890	−0.240348	−0.120174	−	0.992753i	$-0.538345\pi$
$397$	−4.78890	−0.240348	−0.120174	+	0.992753i	$0.538345\pi$
$398$	9.21110	0.461711
$399$	−30.4222	−1.52302
$400$	1.00000	0.0500000
$401$	4.18335	0.208906	0.104453	−	0.994530i	$-0.466691\pi$
$401$	4.18335	0.208906	0.104453	+	0.994530i	$0.466691\pi$
$402$	10.0000	0.498755
$403$	60.8444	3.03088
$404$	−12.0000	−0.597022
$405$	−1.00000	−0.0496904
$406$	−27.6333	−1.37142
$407$	−7.21110	−0.357441
$408$	−1.00000	−0.0495074
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	−5.21110	−0.257358
$411$	6.00000	0.295958
$412$	−14.4222	−0.710531
$413$	−15.6333	−0.769265
$414$	−2.60555	−0.128056
$415$	0	0
$416$	6.60555	0.323864
$417$	18.4222	0.902139
$418$	−6.60555	−0.323088
$419$	18.7889	0.917898	0.458949	−	0.888463i	$-0.348226\pi$
$419$	18.7889	0.917898	0.458949	+	0.888463i	$0.348226\pi$
$420$	−4.60555	−0.224728
$421$	34.8444	1.69821	0.849106	−	0.528222i	$-0.177141\pi$
$421$	34.8444	1.69821	0.849106	+	0.528222i	$0.177141\pi$
$422$	10.7889	0.525195
$423$	12.0000	0.583460
$424$	8.60555	0.417923
$425$	1.00000	0.0485071
$426$	8.60555	0.416940
$427$	9.21110	0.445756
$428$	0	0
$429$	6.60555	0.318919
$430$	−12.6056	−0.607894
$431$	−4.42221	−0.213010	−0.106505	−	0.994312i	$-0.533966\pi$
$431$	−4.42221	−0.213010	−0.106505	+	0.994312i	$0.533966\pi$
$432$	1.00000	0.0481125
$433$	−8.42221	−0.404745	−0.202373	−	0.979309i	$-0.564865\pi$
$433$	−8.42221	−0.404745	−0.202373	+	0.979309i	$0.564865\pi$
$434$	42.4222	2.03633
$435$	−6.00000	−0.287678
$436$	−20.4222	−0.978046
$437$	−17.2111	−0.823319
$438$	1.39445	0.0666293
$439$	−6.60555	−0.315266	−0.157633	−	0.987498i	$-0.550386\pi$
$439$	−6.60555	−0.315266	−0.157633	+	0.987498i	$0.550386\pi$
$440$	−1.00000	−0.0476731
$441$	14.2111	0.676719
$442$	6.60555	0.314194
$443$	19.8167	0.941518	0.470759	−	0.882262i	$-0.343980\pi$
$443$	19.8167	0.941518	0.470759	+	0.882262i	$0.343980\pi$
$444$	7.21110	0.342224
$445$	−6.00000	−0.284427
$446$	−23.6333	−1.11907
$447$	−6.78890	−0.321104
$448$	4.60555	0.217592
$449$	−35.4500	−1.67299	−0.836494	−	0.547977i	$-0.815398\pi$
$449$	−35.4500	−1.67299	−0.836494	+	0.547977i	$0.815398\pi$
$450$	−1.00000	−0.0471405
$451$	5.21110	0.245381
$452$	−1.81665	−0.0854482
$453$	−16.0000	−0.751746
$454$	12.0000	0.563188
$455$	30.4222	1.42621
$456$	6.60555	0.309333
$457$	34.8444	1.62995	0.814976	−	0.579494i	$-0.196750\pi$
$457$	34.8444	1.62995	0.814976	+	0.579494i	$0.196750\pi$
$458$	15.2111	0.710768
$459$	1.00000	0.0466760
$460$	−2.60555	−0.121484
$461$	18.7889	0.875086	0.437543	−	0.899197i	$-0.355849\pi$
$461$	18.7889	0.875086	0.437543	+	0.899197i	$0.355849\pi$
$462$	4.60555	0.214270
$463$	−10.7889	−0.501403	−0.250701	−	0.968064i	$-0.580661\pi$
$463$	−10.7889	−0.501403	−0.250701	+	0.968064i	$0.580661\pi$
$464$	6.00000	0.278543
$465$	9.21110	0.427155
$466$	0.788897	0.0365450
$467$	18.2389	0.843994	0.421997	−	0.906597i	$-0.361329\pi$
$467$	18.2389	0.843994	0.421997	+	0.906597i	$0.361329\pi$
$468$	−6.60555	−0.305342
$469$	−46.0555	−2.12665
$470$	12.0000	0.553519
$471$	1.21110	0.0558047
$472$	3.39445	0.156242
$473$	12.6056	0.579604
$474$	6.60555	0.303403
$475$	−6.60555	−0.303083
$476$	4.60555	0.211095
$477$	−8.60555	−0.394021
$478$	27.6333	1.26392
$479$	12.7889	0.584340	0.292170	−	0.956366i	$-0.405623\pi$
$479$	12.7889	0.584340	0.292170	+	0.956366i	$0.405623\pi$
$480$	1.00000	0.0456435
$481$	−47.6333	−2.17189
$482$	−27.0278	−1.23108
$483$	12.0000	0.546019
$484$	1.00000	0.0454545
$485$	−1.21110	−0.0549933
$486$	−1.00000	−0.0453609
$487$	0.422205	0.0191319	0.00956597	−	0.999954i	$-0.496955\pi$
$487$	0.422205	0.0191319	0.00956597	+	0.999954i	$0.496955\pi$
$488$	−2.00000	−0.0905357
$489$	−9.21110	−0.416540
$490$	14.2111	0.641992
$491$	4.42221	0.199571	0.0997857	−	0.995009i	$-0.468184\pi$
$491$	4.42221	0.199571	0.0997857	+	0.995009i	$0.468184\pi$
$492$	−5.21110	−0.234935
$493$	6.00000	0.270226
$494$	−43.6333	−1.96316
$495$	1.00000	0.0449467
$496$	−9.21110	−0.413591
$497$	−39.6333	−1.77780
$498$	0	0
$499$	9.57779	0.428761	0.214380	−	0.976750i	$-0.431227\pi$
$499$	9.57779	0.428761	0.214380	+	0.976750i	$0.431227\pi$
$500$	−1.00000	−0.0447214
$501$	−6.78890	−0.303306
$502$	−15.3944	−0.687088
$503$	10.4222	0.464703	0.232352	−	0.972632i	$-0.425358\pi$
$503$	10.4222	0.464703	0.232352	+	0.972632i	$0.425358\pi$
$504$	−4.60555	−0.205148
$505$	12.0000	0.533993
$506$	2.60555	0.115831
$507$	30.6333	1.36047
$508$	1.21110	0.0537340
$509$	42.2389	1.87220	0.936102	−	0.351728i	$-0.114406\pi$
$509$	42.2389	1.87220	0.936102	+	0.351728i	$0.114406\pi$
$510$	1.00000	0.0442807
$511$	−6.42221	−0.284102
$512$	−1.00000	−0.0441942
$513$	−6.60555	−0.291642
$514$	21.6333	0.954204
$515$	14.4222	0.635518
$516$	−12.6056	−0.554928
$517$	−12.0000	−0.527759
$518$	−33.2111	−1.45921
$519$	16.4222	0.720855
$520$	−6.60555	−0.289673
$521$	1.02776	0.0450268	0.0225134	−	0.999747i	$-0.492833\pi$
$521$	1.02776	0.0450268	0.0225134	+	0.999747i	$0.492833\pi$
$522$	−6.00000	−0.262613
$523$	25.4500	1.11285	0.556425	−	0.830898i	$-0.312173\pi$
$523$	25.4500	1.11285	0.556425	+	0.830898i	$0.312173\pi$
$524$	10.4222	0.455296
$525$	4.60555	0.201003
$526$	−12.0000	−0.523225
$527$	−9.21110	−0.401242
$528$	−1.00000	−0.0435194
$529$	−16.2111	−0.704831
$530$	−8.60555	−0.373801
$531$	−3.39445	−0.147307
$532$	−30.4222	−1.31897
$533$	34.4222	1.49099
$534$	−6.00000	−0.259645
$535$	0	0
$536$	10.0000	0.431934
$537$	13.8167	0.596233
$538$	21.6333	0.932678
$539$	−14.2111	−0.612116
$540$	−1.00000	−0.0430331
$541$	−42.8444	−1.84203	−0.921013	−	0.389533i	$-0.872636\pi$
$541$	−42.8444	−1.84203	−0.921013	+	0.389533i	$0.872636\pi$
$542$	−13.2111	−0.567465
$543$	−8.42221	−0.361431
$544$	−1.00000	−0.0428746
$545$	20.4222	0.874791
$546$	30.4222	1.30195
$547$	14.7889	0.632328	0.316164	−	0.948705i	$-0.397605\pi$
$547$	14.7889	0.632328	0.316164	+	0.948705i	$0.397605\pi$
$548$	6.00000	0.256307
$549$	2.00000	0.0853579
$550$	1.00000	0.0426401
$551$	−39.6333	−1.68844
$552$	−2.60555	−0.110900
$553$	−30.4222	−1.29368
$554$	−2.00000	−0.0849719
$555$	−7.21110	−0.306094
$556$	18.4222	0.781276
$557$	6.00000	0.254228	0.127114	−	0.991888i	$-0.459429\pi$
$557$	6.00000	0.254228	0.127114	+	0.991888i	$0.459429\pi$
$558$	9.21110	0.389937
$559$	83.2666	3.52180
$560$	−4.60555	−0.194620
$561$	−1.00000	−0.0422200
$562$	−11.2111	−0.472912
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	12.0000	0.505291
$565$	1.81665	0.0764272
$566$	−1.21110	−0.0509064
$567$	4.60555	0.193415
$568$	8.60555	0.361081
$569$	−2.36669	−0.0992169	−0.0496085	−	0.998769i	$-0.515797\pi$
$569$	−2.36669	−0.0992169	−0.0496085	+	0.998769i	$0.515797\pi$
$570$	−6.60555	−0.276676
$571$	−26.4222	−1.10573	−0.552867	−	0.833269i	$-0.686466\pi$
$571$	−26.4222	−1.10573	−0.552867	+	0.833269i	$0.686466\pi$
$572$	6.60555	0.276192
$573$	12.0000	0.501307
$574$	24.0000	1.00174
$575$	2.60555	0.108659
$576$	1.00000	0.0416667
$577$	−32.4222	−1.34975	−0.674877	−	0.737930i	$-0.735803\pi$
$577$	−32.4222	−1.34975	−0.674877	+	0.737930i	$0.735803\pi$
$578$	−1.00000	−0.0415945
$579$	5.39445	0.224186
$580$	−6.00000	−0.249136
$581$	0	0
$582$	−1.21110	−0.0502018
$583$	8.60555	0.356406
$584$	1.39445	0.0577027
$585$	6.60555	0.273106
$586$	30.0000	1.23929
$587$	−38.6056	−1.59342	−0.796711	−	0.604361i	$-0.793429\pi$
$587$	−38.6056	−1.59342	−0.796711	+	0.604361i	$0.793429\pi$
$588$	14.2111	0.586056
$589$	60.8444	2.50705
$590$	−3.39445	−0.139747
$591$	−0.788897	−0.0324509
$592$	7.21110	0.296374
$593$	−24.7889	−1.01796	−0.508979	−	0.860779i	$-0.669977\pi$
$593$	−24.7889	−1.01796	−0.508979	+	0.860779i	$0.669977\pi$
$594$	1.00000	0.0410305
$595$	−4.60555	−0.188809
$596$	−6.78890	−0.278084
$597$	−9.21110	−0.376985
$598$	17.2111	0.703814
$599$	1.57779	0.0644670	0.0322335	−	0.999480i	$-0.489738\pi$
$599$	1.57779	0.0644670	0.0322335	+	0.999480i	$0.489738\pi$
$600$	−1.00000	−0.0408248
$601$	−14.1833	−0.578551	−0.289275	−	0.957246i	$-0.593414\pi$
$601$	−14.1833	−0.578551	−0.289275	+	0.957246i	$0.593414\pi$
$602$	58.0555	2.36617
$603$	−10.0000	−0.407231
$604$	−16.0000	−0.651031
$605$	−1.00000	−0.0406558
$606$	12.0000	0.487467
$607$	−16.2389	−0.659115	−0.329557	−	0.944136i	$-0.606900\pi$
$607$	−16.2389	−0.659115	−0.329557	+	0.944136i	$0.606900\pi$
$608$	6.60555	0.267890
$609$	27.6333	1.11976
$610$	2.00000	0.0809776
$611$	−79.2666	−3.20678
$612$	1.00000	0.0404226
$613$	29.3944	1.18723	0.593615	−	0.804749i	$-0.297700\pi$
$613$	29.3944	1.18723	0.593615	+	0.804749i	$0.297700\pi$
$614$	−3.02776	−0.122190
$615$	5.21110	0.210132
$616$	4.60555	0.185563
$617$	−22.1833	−0.893068	−0.446534	−	0.894767i	$-0.647342\pi$
$617$	−22.1833	−0.893068	−0.446534	+	0.894767i	$0.647342\pi$
$618$	14.4222	0.580146
$619$	16.8444	0.677034	0.338517	−	0.940960i	$-0.390075\pi$
$619$	16.8444	0.677034	0.338517	+	0.940960i	$0.390075\pi$
$620$	9.21110	0.369927
$621$	2.60555	0.104557
$622$	−24.2389	−0.971890
$623$	27.6333	1.10711
$624$	−6.60555	−0.264434
$625$	1.00000	0.0400000
$626$	33.2111	1.32738
$627$	6.60555	0.263800
$628$	1.21110	0.0483283
$629$	7.21110	0.287525
$630$	4.60555	0.183490
$631$	−4.00000	−0.159237	−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000	−0.159237	−0.0796187	+	0.996825i	$0.525370\pi$
$632$	6.60555	0.262755
$633$	−10.7889	−0.428820
$634$	−6.00000	−0.238290
$635$	−1.21110	−0.0480611
$636$	−8.60555	−0.341232
$637$	−93.8722	−3.71935
$638$	6.00000	0.237542
$639$	−8.60555	−0.340430
$640$	1.00000	0.0395285
$641$	−30.2389	−1.19436	−0.597182	−	0.802106i	$-0.703713\pi$
$641$	−30.2389	−1.19436	−0.597182	+	0.802106i	$0.703713\pi$
$642$	0	0
$643$	−16.0000	−0.630978	−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000	−0.630978	−0.315489	+	0.948929i	$0.602169\pi$
$644$	12.0000	0.472866
$645$	12.6056	0.496343
$646$	6.60555	0.259892
$647$	6.78890	0.266899	0.133450	−	0.991056i	$-0.457395\pi$
$647$	6.78890	0.266899	0.133450	+	0.991056i	$0.457395\pi$
$648$	−1.00000	−0.0392837
$649$	3.39445	0.133244
$650$	6.60555	0.259091
$651$	−42.4222	−1.66266
$652$	−9.21110	−0.360735
$653$	42.0000	1.64359	0.821794	−	0.569785i	$-0.192974\pi$
$653$	42.0000	1.64359	0.821794	+	0.569785i	$0.192974\pi$
$654$	20.4222	0.798571
$655$	−10.4222	−0.407229
$656$	−5.21110	−0.203459
$657$	−1.39445	−0.0544026
$658$	−55.2666	−2.15452
$659$	−30.0000	−1.16863	−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000	−1.16863	−0.584317	+	0.811525i	$0.698638\pi$
$660$	1.00000	0.0389249
$661$	31.2111	1.21397	0.606986	−	0.794713i	$-0.292379\pi$
$661$	31.2111	1.21397	0.606986	+	0.794713i	$0.292379\pi$
$662$	26.4222	1.02693
$663$	−6.60555	−0.256538
$664$	0	0
$665$	30.4222	1.17972
$666$	−7.21110	−0.279425
$667$	15.6333	0.605324
$668$	−6.78890	−0.262670
$669$	23.6333	0.913716
$670$	−10.0000	−0.386334
$671$	−2.00000	−0.0772091
$672$	−4.60555	−0.177663
$673$	−18.6056	−0.717191	−0.358596	−	0.933493i	$-0.616744\pi$
$673$	−18.6056	−0.717191	−0.358596	+	0.933493i	$0.616744\pi$
$674$	11.8167	0.455160
$675$	1.00000	0.0384900
$676$	30.6333	1.17820
$677$	9.63331	0.370238	0.185119	−	0.982716i	$-0.440733\pi$
$677$	9.63331	0.370238	0.185119	+	0.982716i	$0.440733\pi$
$678$	1.81665	0.0697682
$679$	5.57779	0.214056
$680$	1.00000	0.0383482
$681$	−12.0000	−0.459841
$682$	−9.21110	−0.352711
$683$	−22.4222	−0.857962	−0.428981	−	0.903314i	$-0.641127\pi$
$683$	−22.4222	−0.857962	−0.428981	+	0.903314i	$0.641127\pi$
$684$	−6.60555	−0.252570
$685$	−6.00000	−0.229248
$686$	−33.2111	−1.26801
$687$	−15.2111	−0.580340
$688$	−12.6056	−0.480582
$689$	56.8444	2.16560
$690$	2.60555	0.0991916
$691$	32.0000	1.21734	0.608669	−	0.793424i	$-0.291704\pi$
$691$	32.0000	1.21734	0.608669	+	0.793424i	$0.291704\pi$
$692$	16.4222	0.624279
$693$	−4.60555	−0.174950
$694$	32.8444	1.24676
$695$	−18.4222	−0.698794
$696$	−6.00000	−0.227429
$697$	−5.21110	−0.197385
$698$	−20.2389	−0.766052
$699$	−0.788897	−0.0298388
$700$	4.60555	0.174073
$701$	−39.6333	−1.49693	−0.748465	−	0.663175i	$-0.769209\pi$
$701$	−39.6333	−1.49693	−0.748465	+	0.663175i	$0.769209\pi$
$702$	6.60555	0.249310
$703$	−47.6333	−1.79652
$704$	−1.00000	−0.0376889
$705$	−12.0000	−0.451946
$706$	11.2111	0.421935
$707$	−55.2666	−2.07851
$708$	−3.39445	−0.127571
$709$	31.2111	1.17216	0.586079	−	0.810254i	$-0.300671\pi$
$709$	31.2111	1.17216	0.586079	+	0.810254i	$0.300671\pi$
$710$	−8.60555	−0.322961
$711$	−6.60555	−0.247728
$712$	−6.00000	−0.224860
$713$	−24.0000	−0.898807
$714$	−4.60555	−0.172358
$715$	−6.60555	−0.247034
$716$	13.8167	0.516353
$717$	−27.6333	−1.03198
$718$	29.2111	1.09015
$719$	41.4500	1.54582	0.772911	−	0.634514i	$-0.218800\pi$
$719$	41.4500	1.54582	0.772911	+	0.634514i	$0.218800\pi$
$720$	−1.00000	−0.0372678
$721$	−66.4222	−2.47369
$722$	−24.6333	−0.916757
$723$	27.0278	1.00517
$724$	−8.42221	−0.313009
$725$	6.00000	0.222834
$726$	−1.00000	−0.0371135
$727$	40.8444	1.51484	0.757418	−	0.652931i	$-0.226461\pi$
$727$	40.8444	1.51484	0.757418	+	0.652931i	$0.226461\pi$
$728$	30.4222	1.12752
$729$	1.00000	0.0370370
$730$	−1.39445	−0.0516109
$731$	−12.6056	−0.466233
$732$	2.00000	0.0739221
$733$	−18.6056	−0.687212	−0.343606	−	0.939114i	$-0.611648\pi$
$733$	−18.6056	−0.687212	−0.343606	+	0.939114i	$0.611648\pi$
$734$	22.0000	0.812035
$735$	−14.2111	−0.524184
$736$	−2.60555	−0.0960419
$737$	10.0000	0.368355
$738$	5.21110	0.191823
$739$	−29.0278	−1.06780	−0.533902	−	0.845547i	$-0.679275\pi$
$739$	−29.0278	−1.06780	−0.533902	+	0.845547i	$0.679275\pi$
$740$	−7.21110	−0.265085
$741$	43.6333	1.60291
$742$	39.6333	1.45498
$743$	−43.2666	−1.58730	−0.793649	−	0.608376i	$-0.791821\pi$
$743$	−43.2666	−1.58730	−0.793649	+	0.608376i	$0.791821\pi$
$744$	9.21110	0.337695
$745$	6.78890	0.248726
$746$	5.02776	0.184079
$747$	0	0
$748$	−1.00000	−0.0365636
$749$	0	0
$750$	1.00000	0.0365148
$751$	42.4222	1.54801	0.774004	−	0.633181i	$-0.218251\pi$
$751$	42.4222	1.54801	0.774004	+	0.633181i	$0.218251\pi$
$752$	12.0000	0.437595
$753$	15.3944	0.561005
$754$	39.6333	1.44336
$755$	16.0000	0.582300
$756$	4.60555	0.167502
$757$	−38.4222	−1.39648	−0.698239	−	0.715864i	$-0.746033\pi$
$757$	−38.4222	−1.39648	−0.698239	+	0.715864i	$0.746033\pi$
$758$	5.57779	0.202595
$759$	−2.60555	−0.0945755
$760$	−6.60555	−0.239609
$761$	54.4777	1.97482	0.987408	−	0.158195i	$-0.0505675\pi$
$761$	54.4777	1.97482	0.987408	+	0.158195i	$0.0505675\pi$
$762$	−1.21110	−0.0438736
$763$	−94.0555	−3.40504
$764$	12.0000	0.434145
$765$	−1.00000	−0.0361551
$766$	−1.57779	−0.0570080
$767$	22.4222	0.809619
$768$	1.00000	0.0360844
$769$	43.2111	1.55823	0.779116	−	0.626880i	$-0.215668\pi$
$769$	43.2111	1.55823	0.779116	+	0.626880i	$0.215668\pi$
$770$	−4.60555	−0.165973
$771$	−21.6333	−0.779105
$772$	5.39445	0.194150
$773$	55.0278	1.97921	0.989605	−	0.143809i	$-0.0459352\pi$
$773$	55.0278	1.97921	0.989605	+	0.143809i	$0.0459352\pi$
$774$	12.6056	0.453097
$775$	−9.21110	−0.330873
$776$	−1.21110	−0.0434760
$777$	33.2111	1.19144
$778$	13.0278	0.467068
$779$	34.4222	1.23330
$780$	6.60555	0.236517
$781$	8.60555	0.307931
$782$	−2.60555	−0.0931743
$783$	6.00000	0.214423
$784$	14.2111	0.507539
$785$	−1.21110	−0.0432261
$786$	−10.4222	−0.371748
$787$	−50.4222	−1.79736	−0.898679	−	0.438607i	$-0.855472\pi$
$787$	−50.4222	−1.79736	−0.898679	+	0.438607i	$0.855472\pi$
$788$	−0.788897	−0.0281033
$789$	12.0000	0.427211
$790$	−6.60555	−0.235015
$791$	−8.36669	−0.297485
$792$	1.00000	0.0355335
$793$	−13.2111	−0.469140
$794$	4.78890	0.169952
$795$	8.60555	0.305207
$796$	−9.21110	−0.326479
$797$	48.2389	1.70871	0.854354	−	0.519691i	$-0.173953\pi$
$797$	48.2389	1.70871	0.854354	+	0.519691i	$0.173953\pi$
$798$	30.4222	1.07693
$799$	12.0000	0.424529
$800$	−1.00000	−0.0353553
$801$	6.00000	0.212000
$802$	−4.18335	−0.147719
$803$	1.39445	0.0492090
$804$	−10.0000	−0.352673
$805$	−12.0000	−0.422944
$806$	−60.8444	−2.14315
$807$	−21.6333	−0.761528
$808$	12.0000	0.422159
$809$	44.8444	1.57665	0.788323	−	0.615262i	$-0.210950\pi$
$809$	44.8444	1.57665	0.788323	+	0.615262i	$0.210950\pi$
$810$	1.00000	0.0351364
$811$	13.2111	0.463905	0.231952	−	0.972727i	$-0.425489\pi$
$811$	13.2111	0.463905	0.231952	+	0.972727i	$0.425489\pi$
$812$	27.6333	0.969739
$813$	13.2111	0.463334
$814$	7.21110	0.252749
$815$	9.21110	0.322651
$816$	1.00000	0.0350070
$817$	83.2666	2.91313
$818$	−14.0000	−0.489499
$819$	−30.4222	−1.06304
$820$	5.21110	0.181980
$821$	−38.8444	−1.35568	−0.677840	−	0.735210i	$-0.737084\pi$
$821$	−38.8444	−1.35568	−0.677840	+	0.735210i	$0.737084\pi$
$822$	−6.00000	−0.209274
$823$	−37.6333	−1.31181	−0.655907	−	0.754841i	$-0.727714\pi$
$823$	−37.6333	−1.31181	−0.655907	+	0.754841i	$0.727714\pi$
$824$	14.4222	0.502421
$825$	−1.00000	−0.0348155
$826$	15.6333	0.543952
$827$	−44.8444	−1.55939	−0.779696	−	0.626158i	$-0.784627\pi$
$827$	−44.8444	−1.55939	−0.779696	+	0.626158i	$0.784627\pi$
$828$	2.60555	0.0905492
$829$	26.0000	0.903017	0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000	0.903017	0.451509	+	0.892267i	$0.350886\pi$
$830$	0	0
$831$	2.00000	0.0693792
$832$	−6.60555	−0.229006
$833$	14.2111	0.492386
$834$	−18.4222	−0.637909
$835$	6.78890	0.234939
$836$	6.60555	0.228458
$837$	−9.21110	−0.318382
$838$	−18.7889	−0.649052
$839$	−10.1833	−0.351568	−0.175784	−	0.984429i	$-0.556246\pi$
$839$	−10.1833	−0.351568	−0.175784	+	0.984429i	$0.556246\pi$
$840$	4.60555	0.158907
$841$	7.00000	0.241379
$842$	−34.8444	−1.20082
$843$	11.2111	0.386131
$844$	−10.7889	−0.371369
$845$	−30.6333	−1.05382
$846$	−12.0000	−0.412568
$847$	4.60555	0.158249
$848$	−8.60555	−0.295516
$849$	1.21110	0.0415649
$850$	−1.00000	−0.0342997
$851$	18.7889	0.644075
$852$	−8.60555	−0.294821
$853$	−51.2111	−1.75343	−0.876717	−	0.481006i	$-0.840272\pi$
$853$	−51.2111	−1.75343	−0.876717	+	0.481006i	$0.840272\pi$
$854$	−9.21110	−0.315197
$855$	6.60555	0.225905
$856$	0	0
$857$	−30.0000	−1.02478	−0.512390	−	0.858753i	$-0.671240\pi$
$857$	−30.0000	−1.02478	−0.512390	+	0.858753i	$0.671240\pi$
$858$	−6.60555	−0.225510
$859$	−16.0000	−0.545913	−0.272956	−	0.962026i	$-0.588002\pi$
$859$	−16.0000	−0.545913	−0.272956	+	0.962026i	$0.588002\pi$
$860$	12.6056	0.429846
$861$	−24.0000	−0.817918
$862$	4.42221	0.150621
$863$	−27.6333	−0.940649	−0.470324	−	0.882494i	$-0.655863\pi$
$863$	−27.6333	−0.940649	−0.470324	+	0.882494i	$0.655863\pi$
$864$	−1.00000	−0.0340207
$865$	−16.4222	−0.558372
$866$	8.42221	0.286198
$867$	1.00000	0.0339618
$868$	−42.4222	−1.43990
$869$	6.60555	0.224078
$870$	6.00000	0.203419
$871$	66.0555	2.23821
$872$	20.4222	0.691583
$873$	1.21110	0.0409896
$874$	17.2111	0.582174
$875$	−4.60555	−0.155696
$876$	−1.39445	−0.0471141
$877$	−24.0555	−0.812297	−0.406148	−	0.913807i	$-0.633128\pi$
$877$	−24.0555	−0.812297	−0.406148	+	0.913807i	$0.633128\pi$
$878$	6.60555	0.222927
$879$	−30.0000	−1.01187
$880$	1.00000	0.0337100
$881$	51.0833	1.72104	0.860520	−	0.509417i	$-0.170139\pi$
$881$	51.0833	1.72104	0.860520	+	0.509417i	$0.170139\pi$
$882$	−14.2111	−0.478513
$883$	−27.2111	−0.915727	−0.457863	−	0.889023i	$-0.651385\pi$
$883$	−27.2111	−0.915727	−0.457863	+	0.889023i	$0.651385\pi$
$884$	−6.60555	−0.222169
$885$	3.39445	0.114103
$886$	−19.8167	−0.665754
$887$	−26.0555	−0.874858	−0.437429	−	0.899253i	$-0.644111\pi$
$887$	−26.0555	−0.874858	−0.437429	+	0.899253i	$0.644111\pi$
$888$	−7.21110	−0.241989
$889$	5.57779	0.187073
$890$	6.00000	0.201120
$891$	−1.00000	−0.0335013
$892$	23.6333	0.791302
$893$	−79.2666	−2.65256
$894$	6.78890	0.227055
$895$	−13.8167	−0.461840
$896$	−4.60555	−0.153861
$897$	−17.2111	−0.574662
$898$	35.4500	1.18298
$899$	−55.2666	−1.84324
$900$	1.00000	0.0333333
$901$	−8.60555	−0.286692
$902$	−5.21110	−0.173511
$903$	−58.0555	−1.93197
$904$	1.81665	0.0604210
$905$	8.42221	0.279964
$906$	16.0000	0.531564
$907$	32.0000	1.06254	0.531271	−	0.847202i	$-0.321714\pi$
$907$	32.0000	1.06254	0.531271	+	0.847202i	$0.321714\pi$
$908$	−12.0000	−0.398234
$909$	−12.0000	−0.398015
$910$	−30.4222	−1.00849
$911$	22.6611	0.750795	0.375397	−	0.926864i	$-0.377506\pi$
$911$	22.6611	0.750795	0.375397	+	0.926864i	$0.377506\pi$
$912$	−6.60555	−0.218732
$913$	0	0
$914$	−34.8444	−1.15255
$915$	−2.00000	−0.0661180
$916$	−15.2111	−0.502589
$917$	48.0000	1.58510
$918$	−1.00000	−0.0330049
$919$	42.4222	1.39938	0.699690	−	0.714447i	$-0.253322\pi$
$919$	42.4222	1.39938	0.699690	+	0.714447i	$0.253322\pi$
$920$	2.60555	0.0859025
$921$	3.02776	0.0997680
$922$	−18.7889	−0.618779
$923$	56.8444	1.87106
$924$	−4.60555	−0.151512
$925$	7.21110	0.237100
$926$	10.7889	0.354545
$927$	−14.4222	−0.473687
$928$	−6.00000	−0.196960
$929$	7.81665	0.256456	0.128228	−	0.991745i	$-0.459071\pi$
$929$	7.81665	0.256456	0.128228	+	0.991745i	$0.459071\pi$
$930$	−9.21110	−0.302044
$931$	−93.8722	−3.07654
$932$	−0.788897	−0.0258412
$933$	24.2389	0.793545
$934$	−18.2389	−0.596794
$935$	1.00000	0.0327035
$936$	6.60555	0.215909
$937$	53.6333	1.75212	0.876062	−	0.482199i	$-0.160162\pi$
$937$	53.6333	1.75212	0.876062	+	0.482199i	$0.160162\pi$
$938$	46.0555	1.50377
$939$	−33.2111	−1.08380
$940$	−12.0000	−0.391397
$941$	−4.42221	−0.144160	−0.0720799	−	0.997399i	$-0.522964\pi$
$941$	−4.42221	−0.144160	−0.0720799	+	0.997399i	$0.522964\pi$
$942$	−1.21110	−0.0394599
$943$	−13.5778	−0.442154
$944$	−3.39445	−0.110480
$945$	−4.60555	−0.149819
$946$	−12.6056	−0.409842
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	−6.60555	−0.214538
$949$	9.21110	0.299005
$950$	6.60555	0.214312
$951$	6.00000	0.194563
$952$	−4.60555	−0.149267
$953$	−33.6333	−1.08949	−0.544745	−	0.838602i	$-0.683373\pi$
$953$	−33.6333	−1.08949	−0.544745	+	0.838602i	$0.683373\pi$
$954$	8.60555	0.278615
$955$	−12.0000	−0.388311
$956$	−27.6333	−0.893725
$957$	−6.00000	−0.193952
$958$	−12.7889	−0.413191
$959$	27.6333	0.892326
$960$	−1.00000	−0.0322749
$961$	53.8444	1.73692
$962$	47.6333	1.53576
$963$	0	0
$964$	27.0278	0.870505
$965$	−5.39445	−0.173653
$966$	−12.0000	−0.386094
$967$	−40.0000	−1.28631	−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000	−1.28631	−0.643157	+	0.765735i	$0.722376\pi$
$968$	−1.00000	−0.0321412
$969$	−6.60555	−0.212201
$970$	1.21110	0.0388862
$971$	−12.2389	−0.392764	−0.196382	−	0.980527i	$-0.562919\pi$
$971$	−12.2389	−0.392764	−0.196382	+	0.980527i	$0.562919\pi$
$972$	1.00000	0.0320750
$973$	84.8444	2.71999
$974$	−0.422205	−0.0135283
$975$	−6.60555	−0.211547
$976$	2.00000	0.0640184
$977$	−35.2111	−1.12650	−0.563251	−	0.826286i	$-0.690450\pi$
$977$	−35.2111	−1.12650	−0.563251	+	0.826286i	$0.690450\pi$
$978$	9.21110	0.294539
$979$	−6.00000	−0.191761
$980$	−14.2111	−0.453957
$981$	−20.4222	−0.652031
$982$	−4.42221	−0.141118
$983$	38.6056	1.23133	0.615663	−	0.788010i	$-0.288888\pi$
$983$	38.6056	1.23133	0.615663	+	0.788010i	$0.288888\pi$
$984$	5.21110	0.166124
$985$	0.788897	0.0251364
$986$	−6.00000	−0.191079
$987$	55.2666	1.75916
$988$	43.6333	1.38816
$989$	−32.8444	−1.04439
$990$	−1.00000	−0.0317821
$991$	51.2666	1.62854	0.814269	−	0.580488i	$-0.197138\pi$
$991$	51.2666	1.62854	0.814269	+	0.580488i	$0.197138\pi$
$992$	9.21110	0.292453
$993$	−26.4222	−0.838483
$994$	39.6333	1.25709
$995$	9.21110	0.292012
$996$	0	0
$997$	8.78890	0.278347	0.139174	−	0.990268i	$-0.455555\pi$
$997$	8.78890	0.278347	0.139174	+	0.990268i	$0.455555\pi$
$998$	−9.57779	−0.303180
$999$	7.21110	0.228149

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bs.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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.60555 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.60555 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -6.60555 q^{13} -4.60555 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -6.60555 q^{19} -1.00000 q^{20} +4.60555 q^{21} +1.00000 q^{22} +2.60555 q^{23} -1.00000 q^{24} +1.00000 q^{25} +6.60555 q^{26} +1.00000 q^{27} +4.60555 q^{28} +6.00000 q^{29} +1.00000 q^{30} -9.21110 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -4.60555 q^{35} +1.00000 q^{36} +7.21110 q^{37} +6.60555 q^{38} -6.60555 q^{39} +1.00000 q^{40} -5.21110 q^{41} -4.60555 q^{42} -12.6056 q^{43} -1.00000 q^{44} -1.00000 q^{45} -2.60555 q^{46} +12.0000 q^{47} +1.00000 q^{48} +14.2111 q^{49} -1.00000 q^{50} +1.00000 q^{51} -6.60555 q^{52} -8.60555 q^{53} -1.00000 q^{54} +1.00000 q^{55} -4.60555 q^{56} -6.60555 q^{57} -6.00000 q^{58} -3.39445 q^{59} -1.00000 q^{60} +2.00000 q^{61} +9.21110 q^{62} +4.60555 q^{63} +1.00000 q^{64} +6.60555 q^{65} +1.00000 q^{66} -10.0000 q^{67} +1.00000 q^{68} +2.60555 q^{69} +4.60555 q^{70} -8.60555 q^{71} -1.00000 q^{72} -1.39445 q^{73} -7.21110 q^{74} +1.00000 q^{75} -6.60555 q^{76} -4.60555 q^{77} +6.60555 q^{78} -6.60555 q^{79} -1.00000 q^{80} +1.00000 q^{81} +5.21110 q^{82} +4.60555 q^{84} -1.00000 q^{85} +12.6056 q^{86} +6.00000 q^{87} +1.00000 q^{88} +6.00000 q^{89} +1.00000 q^{90} -30.4222 q^{91} +2.60555 q^{92} -9.21110 q^{93} -12.0000 q^{94} +6.60555 q^{95} -1.00000 q^{96} +1.21110 q^{97} -14.2111 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} - 6 q^{19} - 2 q^{20} + 2 q^{21} + 2 q^{22} - 2 q^{23} - 2 q^{24} + 2 q^{25} + 6 q^{26} + 2 q^{27} + 2 q^{28} + 12 q^{29} + 2 q^{30} - 4 q^{31} - 2 q^{32} - 2 q^{33} - 2 q^{34} - 2 q^{35} + 2 q^{36} + 6 q^{38} - 6 q^{39} + 2 q^{40} + 4 q^{41} - 2 q^{42} - 18 q^{43} - 2 q^{44} - 2 q^{45} + 2 q^{46} + 24 q^{47} + 2 q^{48} + 14 q^{49} - 2 q^{50} + 2 q^{51} - 6 q^{52} - 10 q^{53} - 2 q^{54} + 2 q^{55} - 2 q^{56} - 6 q^{57} - 12 q^{58} - 14 q^{59} - 2 q^{60} + 4 q^{61} + 4 q^{62} + 2 q^{63} + 2 q^{64} + 6 q^{65} + 2 q^{66} - 20 q^{67} + 2 q^{68} - 2 q^{69} + 2 q^{70} - 10 q^{71} - 2 q^{72} - 10 q^{73} + 2 q^{75} - 6 q^{76} - 2 q^{77} + 6 q^{78} - 6 q^{79} - 2 q^{80} + 2 q^{81} - 4 q^{82} + 2 q^{84} - 2 q^{85} + 18 q^{86} + 12 q^{87} + 2 q^{88} + 12 q^{89} + 2 q^{90} - 32 q^{91} - 2 q^{92} - 4 q^{93} - 24 q^{94} + 6 q^{95} - 2 q^{96} - 12 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 + 2 * q^12 - 6 * q^13 - 2 * q^14 - 2 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 - 6 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 - 2 * q^23 - 2 * q^24 + 2 * q^25 + 6 * q^26 + 2 * q^27 + 2 * q^28 + 12 * q^29 + 2 * q^30 - 4 * q^31 - 2 * q^32 - 2 * q^33 - 2 * q^34 - 2 * q^35 + 2 * q^36 + 6 * q^38 - 6 * q^39 + 2 * q^40 + 4 * q^41 - 2 * q^42 - 18 * q^43 - 2 * q^44 - 2 * q^45 + 2 * q^46 + 24 * q^47 + 2 * q^48 + 14 * q^49 - 2 * q^50 + 2 * q^51 - 6 * q^52 - 10 * q^53 - 2 * q^54 + 2 * q^55 - 2 * q^56 - 6 * q^57 - 12 * q^58 - 14 * q^59 - 2 * q^60 + 4 * q^61 + 4 * q^62 + 2 * q^63 + 2 * q^64 + 6 * q^65 + 2 * q^66 - 20 * q^67 + 2 * q^68 - 2 * q^69 + 2 * q^70 - 10 * q^71 - 2 * q^72 - 10 * q^73 + 2 * q^75 - 6 * q^76 - 2 * q^77 + 6 * q^78 - 6 * q^79 - 2 * q^80 + 2 * q^81 - 4 * q^82 + 2 * q^84 - 2 * q^85 + 18 * q^86 + 12 * q^87 + 2 * q^88 + 12 * q^89 + 2 * q^90 - 32 * q^91 - 2 * q^92 - 4 * q^93 - 24 * q^94 + 6 * q^95 - 2 * q^96 - 12 * q^97 - 14 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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