LMFDB - Embedded newform 2310.2.a.x.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2310,2,Mod(1,2310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2310, 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("2310.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2310.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:	$18.4454428669$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.37228$ of defining polynomial
Character	$\chi$	$=$	2310.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} +6.74456 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -6.74456 q^{17} -1.00000 q^{18} +1.00000 q^{20} +1.00000 q^{21} +1.00000 q^{22} +4.74456 q^{23} +1.00000 q^{24} +1.00000 q^{25} -6.74456 q^{26} -1.00000 q^{27} -1.00000 q^{28} +2.00000 q^{29} +1.00000 q^{30} -1.00000 q^{32} +1.00000 q^{33} +6.74456 q^{34} -1.00000 q^{35} +1.00000 q^{36} -2.74456 q^{37} -6.74456 q^{39} -1.00000 q^{40} +6.00000 q^{41} -1.00000 q^{42} +4.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} -4.74456 q^{46} -4.00000 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +6.74456 q^{51} +6.74456 q^{52} -6.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} +1.00000 q^{56} -2.00000 q^{58} +4.00000 q^{59} -1.00000 q^{60} +6.00000 q^{61} -1.00000 q^{63} +1.00000 q^{64} +6.74456 q^{65} -1.00000 q^{66} -12.7446 q^{67} -6.74456 q^{68} -4.74456 q^{69} +1.00000 q^{70} -1.00000 q^{72} +6.00000 q^{73} +2.74456 q^{74} -1.00000 q^{75} +1.00000 q^{77} +6.74456 q^{78} +12.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -4.00000 q^{83} +1.00000 q^{84} -6.74456 q^{85} -4.00000 q^{86} -2.00000 q^{87} +1.00000 q^{88} +6.74456 q^{89} -1.00000 q^{90} -6.74456 q^{91} +4.74456 q^{92} +4.00000 q^{94} +1.00000 q^{96} +15.4891 q^{97} -1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{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} + 2 q^{13} + 2 q^{14} - 2 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} + 2 q^{20} + 2 q^{21} + 2 q^{22} - 2 q^{23} + 2 q^{24} + 2 q^{25} - 2 q^{26} - 2 q^{27} - 2 q^{28} + 4 q^{29} + 2 q^{30} - 2 q^{32} + 2 q^{33} + 2 q^{34} - 2 q^{35} + 2 q^{36} + 6 q^{37} - 2 q^{39} - 2 q^{40} + 12 q^{41} - 2 q^{42} + 8 q^{43} - 2 q^{44} + 2 q^{45} + 2 q^{46} - 8 q^{47} - 2 q^{48} + 2 q^{49} - 2 q^{50} + 2 q^{51} + 2 q^{52} - 12 q^{53} + 2 q^{54} - 2 q^{55} + 2 q^{56} - 4 q^{58} + 8 q^{59} - 2 q^{60} + 12 q^{61} - 2 q^{63} + 2 q^{64} + 2 q^{65} - 2 q^{66} - 14 q^{67} - 2 q^{68} + 2 q^{69} + 2 q^{70} - 2 q^{72} + 12 q^{73} - 6 q^{74} - 2 q^{75} + 2 q^{77} + 2 q^{78} + 24 q^{79} + 2 q^{80} + 2 q^{81} - 12 q^{82} - 8 q^{83} + 2 q^{84} - 2 q^{85} - 8 q^{86} - 4 q^{87} + 2 q^{88} + 2 q^{89} - 2 q^{90} - 2 q^{91} - 2 q^{92} + 8 q^{94} + 2 q^{96} + 8 q^{97} - 2 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 + 2 * q^13 + 2 * q^14 - 2 * q^15 + 2 * q^16 - 2 * q^17 - 2 * q^18 + 2 * q^20 + 2 * q^21 + 2 * q^22 - 2 * q^23 + 2 * q^24 + 2 * q^25 - 2 * q^26 - 2 * q^27 - 2 * q^28 + 4 * q^29 + 2 * q^30 - 2 * q^32 + 2 * q^33 + 2 * q^34 - 2 * q^35 + 2 * q^36 + 6 * q^37 - 2 * q^39 - 2 * q^40 + 12 * q^41 - 2 * q^42 + 8 * q^43 - 2 * q^44 + 2 * q^45 + 2 * q^46 - 8 * q^47 - 2 * q^48 + 2 * q^49 - 2 * q^50 + 2 * q^51 + 2 * q^52 - 12 * q^53 + 2 * q^54 - 2 * q^55 + 2 * q^56 - 4 * q^58 + 8 * q^59 - 2 * q^60 + 12 * q^61 - 2 * q^63 + 2 * q^64 + 2 * q^65 - 2 * q^66 - 14 * q^67 - 2 * q^68 + 2 * q^69 + 2 * q^70 - 2 * q^72 + 12 * q^73 - 6 * q^74 - 2 * q^75 + 2 * q^77 + 2 * q^78 + 24 * q^79 + 2 * q^80 + 2 * q^81 - 12 * q^82 - 8 * q^83 + 2 * q^84 - 2 * q^85 - 8 * q^86 - 4 * q^87 + 2 * q^88 + 2 * q^89 - 2 * q^90 - 2 * q^91 - 2 * q^92 + 8 * q^94 + 2 * q^96 + 8 * q^97 - 2 * 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
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−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
$13$	6.74456	1.87061	0.935303	−	0.353849i	$-0.115127\pi$
$13$	6.74456	1.87061	0.935303	+	0.353849i	$0.115127\pi$
$14$	1.00000	0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−6.74456	−1.63580	−0.817898	−	0.575363i	$-0.804861\pi$
$17$	−6.74456	−1.63580	−0.817898	+	0.575363i	$0.804861\pi$
$18$	−1.00000	−0.235702
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	1.00000	0.223607
$21$	1.00000	0.218218
$22$	1.00000	0.213201
$23$	4.74456	0.989310	0.494655	−	0.869090i	$-0.335294\pi$
$23$	4.74456	0.989310	0.494655	+	0.869090i	$0.335294\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−6.74456	−1.32272
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	1.00000	0.182574
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	6.74456	1.15668
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	−2.74456	−0.451203	−0.225602	−	0.974220i	$-0.572435\pi$
$37$	−2.74456	−0.451203	−0.225602	+	0.974220i	$0.572435\pi$
$38$	0	0
$39$	−6.74456	−1.07999
$40$	−1.00000	−0.158114
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	−1.00000	−0.154303
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−1.00000	−0.150756
$45$	1.00000	0.149071
$46$	−4.74456	−0.699548
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	6.74456	0.944428
$52$	6.74456	0.935303
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	1.00000	0.136083
$55$	−1.00000	−0.134840
$56$	1.00000	0.133631
$57$	0	0
$58$	−2.00000	−0.262613
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	−1.00000	−0.129099
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	0	0
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	6.74456	0.836560
$66$	−1.00000	−0.123091
$67$	−12.7446	−1.55700	−0.778498	−	0.627647i	$-0.784018\pi$
$67$	−12.7446	−1.55700	−0.778498	+	0.627647i	$0.784018\pi$
$68$	−6.74456	−0.817898
$69$	−4.74456	−0.571178
$70$	1.00000	0.119523
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	−1.00000	−0.117851
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	2.74456	0.319049
$75$	−1.00000	−0.115470
$76$	0	0
$77$	1.00000	0.113961
$78$	6.74456	0.763671
$79$	12.0000	1.35011	0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000	1.35011	0.675053	+	0.737769i	$0.264121\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	1.00000	0.109109
$85$	−6.74456	−0.731551
$86$	−4.00000	−0.431331
$87$	−2.00000	−0.214423
$88$	1.00000	0.106600
$89$	6.74456	0.714922	0.357461	−	0.933928i	$-0.383642\pi$
$89$	6.74456	0.714922	0.357461	+	0.933928i	$0.383642\pi$
$90$	−1.00000	−0.105409
$91$	−6.74456	−0.707022
$92$	4.74456	0.494655
$93$	0	0
$94$	4.00000	0.412568
$95$	0	0
$96$	1.00000	0.102062
$97$	15.4891	1.57268	0.786341	−	0.617792i	$-0.211973\pi$
$97$	15.4891	1.57268	0.786341	+	0.617792i	$0.211973\pi$
$98$	−1.00000	−0.101015
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	−6.74456	−0.667811
$103$	−13.4891	−1.32912	−0.664562	−	0.747234i	$-0.731382\pi$
$103$	−13.4891	−1.32912	−0.664562	+	0.747234i	$0.731382\pi$
$104$	−6.74456	−0.661359
$105$	1.00000	0.0975900
$106$	6.00000	0.582772
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	−1.00000	−0.0962250
$109$	14.7446	1.41227	0.706136	−	0.708076i	$-0.250436\pi$
$109$	14.7446	1.41227	0.706136	+	0.708076i	$0.250436\pi$
$110$	1.00000	0.0953463
$111$	2.74456	0.260502
$112$	−1.00000	−0.0944911
$113$	−10.7446	−1.01076	−0.505382	−	0.862896i	$-0.668648\pi$
$113$	−10.7446	−1.01076	−0.505382	+	0.862896i	$0.668648\pi$
$114$	0	0
$115$	4.74456	0.442433
$116$	2.00000	0.185695
$117$	6.74456	0.623535
$118$	−4.00000	−0.368230
$119$	6.74456	0.618273
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−6.00000	−0.543214
$123$	−6.00000	−0.541002
$124$	0	0
$125$	1.00000	0.0894427
$126$	1.00000	0.0890871
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	−4.00000	−0.352180
$130$	−6.74456	−0.591537
$131$	9.48913	0.829069	0.414534	−	0.910034i	$-0.363944\pi$
$131$	9.48913	0.829069	0.414534	+	0.910034i	$0.363944\pi$
$132$	1.00000	0.0870388
$133$	0	0
$134$	12.7446	1.10096
$135$	−1.00000	−0.0860663
$136$	6.74456	0.578341
$137$	16.2337	1.38694	0.693469	−	0.720487i	$-0.256082\pi$
$137$	16.2337	1.38694	0.693469	+	0.720487i	$0.256082\pi$
$138$	4.74456	0.403884
$139$	−1.48913	−0.126306	−0.0631530	−	0.998004i	$-0.520116\pi$
$139$	−1.48913	−0.126306	−0.0631530	+	0.998004i	$0.520116\pi$
$140$	−1.00000	−0.0845154
$141$	4.00000	0.336861
$142$	0	0
$143$	−6.74456	−0.564009
$144$	1.00000	0.0833333
$145$	2.00000	0.166091
$146$	−6.00000	−0.496564
$147$	−1.00000	−0.0824786
$148$	−2.74456	−0.225602
$149$	−7.48913	−0.613533	−0.306767	−	0.951785i	$-0.599247\pi$
$149$	−7.48913	−0.613533	−0.306767	+	0.951785i	$0.599247\pi$
$150$	1.00000	0.0816497
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	0	0
$153$	−6.74456	−0.545266
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	−6.74456	−0.539997
$157$	6.00000	0.478852	0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000	0.478852	0.239426	+	0.970915i	$0.423041\pi$
$158$	−12.0000	−0.954669
$159$	6.00000	0.475831
$160$	−1.00000	−0.0790569
$161$	−4.74456	−0.373924
$162$	−1.00000	−0.0785674
$163$	3.25544	0.254986	0.127493	−	0.991840i	$-0.459307\pi$
$163$	3.25544	0.254986	0.127493	+	0.991840i	$0.459307\pi$
$164$	6.00000	0.468521
$165$	1.00000	0.0778499
$166$	4.00000	0.310460
$167$	−14.2337	−1.10144	−0.550718	−	0.834691i	$-0.685646\pi$
$167$	−14.2337	−1.10144	−0.550718	+	0.834691i	$0.685646\pi$
$168$	−1.00000	−0.0771517
$169$	32.4891	2.49916
$170$	6.74456	0.517284
$171$	0	0
$172$	4.00000	0.304997
$173$	0.510875	0.0388411	0.0194205	−	0.999811i	$-0.493818\pi$
$173$	0.510875	0.0388411	0.0194205	+	0.999811i	$0.493818\pi$
$174$	2.00000	0.151620
$175$	−1.00000	−0.0755929
$176$	−1.00000	−0.0753778
$177$	−4.00000	−0.300658
$178$	−6.74456	−0.505526
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	1.00000	0.0745356
$181$	1.25544	0.0933159	0.0466580	−	0.998911i	$-0.485143\pi$
$181$	1.25544	0.0933159	0.0466580	+	0.998911i	$0.485143\pi$
$182$	6.74456	0.499940
$183$	−6.00000	−0.443533
$184$	−4.74456	−0.349774
$185$	−2.74456	−0.201784
$186$	0	0
$187$	6.74456	0.493211
$188$	−4.00000	−0.291730
$189$	1.00000	0.0727393
$190$	0	0
$191$	17.4891	1.26547	0.632734	−	0.774369i	$-0.281933\pi$
$191$	17.4891	1.26547	0.632734	+	0.774369i	$0.281933\pi$
$192$	−1.00000	−0.0721688
$193$	24.9783	1.79797	0.898987	−	0.437975i	$-0.144304\pi$
$193$	24.9783	1.79797	0.898987	+	0.437975i	$0.144304\pi$
$194$	−15.4891	−1.11205
$195$	−6.74456	−0.482988
$196$	1.00000	0.0714286
$197$	0.510875	0.0363983	0.0181992	−	0.999834i	$-0.494207\pi$
$197$	0.510875	0.0363983	0.0181992	+	0.999834i	$0.494207\pi$
$198$	1.00000	0.0710669
$199$	−18.9783	−1.34533	−0.672666	−	0.739946i	$-0.734851\pi$
$199$	−18.9783	−1.34533	−0.672666	+	0.739946i	$0.734851\pi$
$200$	−1.00000	−0.0707107
$201$	12.7446	0.898932
$202$	−6.00000	−0.422159
$203$	−2.00000	−0.140372
$204$	6.74456	0.472214
$205$	6.00000	0.419058
$206$	13.4891	0.939832
$207$	4.74456	0.329770
$208$	6.74456	0.467651
$209$	0	0
$210$	−1.00000	−0.0690066
$211$	24.7446	1.70349	0.851743	−	0.523960i	$-0.175546\pi$
$211$	24.7446	1.70349	0.851743	+	0.523960i	$0.175546\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	4.00000	0.273434
$215$	4.00000	0.272798
$216$	1.00000	0.0680414
$217$	0	0
$218$	−14.7446	−0.998628
$219$	−6.00000	−0.405442
$220$	−1.00000	−0.0674200
$221$	−45.4891	−3.05993
$222$	−2.74456	−0.184203
$223$	21.4891	1.43902	0.719509	−	0.694483i	$-0.244367\pi$
$223$	21.4891	1.43902	0.719509	+	0.694483i	$0.244367\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	10.7446	0.714718
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	0	0
$229$	26.7446	1.76733	0.883665	−	0.468119i	$-0.155068\pi$
$229$	26.7446	1.76733	0.883665	+	0.468119i	$0.155068\pi$
$230$	−4.74456	−0.312847
$231$	−1.00000	−0.0657952
$232$	−2.00000	−0.131306
$233$	22.0000	1.44127	0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000	1.44127	0.720634	+	0.693316i	$0.243851\pi$
$234$	−6.74456	−0.440906
$235$	−4.00000	−0.260931
$236$	4.00000	0.260378
$237$	−12.0000	−0.779484
$238$	−6.74456	−0.437185
$239$	18.2337	1.17944	0.589720	−	0.807608i	$-0.299238\pi$
$239$	18.2337	1.17944	0.589720	+	0.807608i	$0.299238\pi$
$240$	−1.00000	−0.0645497
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	6.00000	0.384111
$245$	1.00000	0.0638877
$246$	6.00000	0.382546
$247$	0	0
$248$	0	0
$249$	4.00000	0.253490
$250$	−1.00000	−0.0632456
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	−1.00000	−0.0629941
$253$	−4.74456	−0.298288
$254$	−8.00000	−0.501965
$255$	6.74456	0.422361
$256$	1.00000	0.0625000
$257$	23.4891	1.46521	0.732606	−	0.680653i	$-0.238304\pi$
$257$	23.4891	1.46521	0.732606	+	0.680653i	$0.238304\pi$
$258$	4.00000	0.249029
$259$	2.74456	0.170539
$260$	6.74456	0.418280
$261$	2.00000	0.123797
$262$	−9.48913	−0.586240
$263$	−25.4891	−1.57173	−0.785863	−	0.618400i	$-0.787781\pi$
$263$	−25.4891	−1.57173	−0.785863	+	0.618400i	$0.787781\pi$
$264$	−1.00000	−0.0615457
$265$	−6.00000	−0.368577
$266$	0	0
$267$	−6.74456	−0.412761
$268$	−12.7446	−0.778498
$269$	23.4891	1.43216	0.716079	−	0.698020i	$-0.245935\pi$
$269$	23.4891	1.43216	0.716079	+	0.698020i	$0.245935\pi$
$270$	1.00000	0.0608581
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	−6.74456	−0.408949
$273$	6.74456	0.408200
$274$	−16.2337	−0.980713
$275$	−1.00000	−0.0603023
$276$	−4.74456	−0.285589
$277$	19.4891	1.17099	0.585494	−	0.810677i	$-0.300901\pi$
$277$	19.4891	1.17099	0.585494	+	0.810677i	$0.300901\pi$
$278$	1.48913	0.0893118
$279$	0	0
$280$	1.00000	0.0597614
$281$	−20.2337	−1.20704	−0.603520	−	0.797348i	$-0.706236\pi$
$281$	−20.2337	−1.20704	−0.603520	+	0.797348i	$0.706236\pi$
$282$	−4.00000	−0.238197
$283$	10.2337	0.608330	0.304165	−	0.952619i	$-0.401623\pi$
$283$	10.2337	0.608330	0.304165	+	0.952619i	$0.401623\pi$
$284$	0	0
$285$	0	0
$286$	6.74456	0.398814
$287$	−6.00000	−0.354169
$288$	−1.00000	−0.0589256
$289$	28.4891	1.67583
$290$	−2.00000	−0.117444
$291$	−15.4891	−0.907989
$292$	6.00000	0.351123
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	1.00000	0.0583212
$295$	4.00000	0.232889
$296$	2.74456	0.159524
$297$	1.00000	0.0580259
$298$	7.48913	0.433833
$299$	32.0000	1.85061
$300$	−1.00000	−0.0577350
$301$	−4.00000	−0.230556
$302$	4.00000	0.230174
$303$	−6.00000	−0.344691
$304$	0	0
$305$	6.00000	0.343559
$306$	6.74456	0.385561
$307$	18.2337	1.04065	0.520326	−	0.853968i	$-0.325811\pi$
$307$	18.2337	1.04065	0.520326	+	0.853968i	$0.325811\pi$
$308$	1.00000	0.0569803
$309$	13.4891	0.767370
$310$	0	0
$311$	4.74456	0.269039	0.134520	−	0.990911i	$-0.457051\pi$
$311$	4.74456	0.269039	0.134520	+	0.990911i	$0.457051\pi$
$312$	6.74456	0.381836
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	−6.00000	−0.338600
$315$	−1.00000	−0.0563436
$316$	12.0000	0.675053
$317$	−16.9783	−0.953594	−0.476797	−	0.879014i	$-0.658202\pi$
$317$	−16.9783	−0.953594	−0.476797	+	0.879014i	$0.658202\pi$
$318$	−6.00000	−0.336463
$319$	−2.00000	−0.111979
$320$	1.00000	0.0559017
$321$	4.00000	0.223258
$322$	4.74456	0.264404
$323$	0	0
$324$	1.00000	0.0555556
$325$	6.74456	0.374121
$326$	−3.25544	−0.180302
$327$	−14.7446	−0.815376
$328$	−6.00000	−0.331295
$329$	4.00000	0.220527
$330$	−1.00000	−0.0550482
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	−4.00000	−0.219529
$333$	−2.74456	−0.150401
$334$	14.2337	0.778833
$335$	−12.7446	−0.696310
$336$	1.00000	0.0545545
$337$	15.4891	0.843746	0.421873	−	0.906655i	$-0.361373\pi$
$337$	15.4891	0.843746	0.421873	+	0.906655i	$0.361373\pi$
$338$	−32.4891	−1.76718
$339$	10.7446	0.583565
$340$	−6.74456	−0.365775
$341$	0	0
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−4.00000	−0.215666
$345$	−4.74456	−0.255439
$346$	−0.510875	−0.0274648
$347$	−20.0000	−1.07366	−0.536828	−	0.843692i	$-0.680378\pi$
$347$	−20.0000	−1.07366	−0.536828	+	0.843692i	$0.680378\pi$
$348$	−2.00000	−0.107211
$349$	−20.9783	−1.12294	−0.561470	−	0.827497i	$-0.689764\pi$
$349$	−20.9783	−1.12294	−0.561470	+	0.827497i	$0.689764\pi$
$350$	1.00000	0.0534522
$351$	−6.74456	−0.359998
$352$	1.00000	0.0533002
$353$	−8.51087	−0.452988	−0.226494	−	0.974013i	$-0.572726\pi$
$353$	−8.51087	−0.452988	−0.226494	+	0.974013i	$0.572726\pi$
$354$	4.00000	0.212598
$355$	0	0
$356$	6.74456	0.357461
$357$	−6.74456	−0.356960
$358$	4.00000	0.211407
$359$	−7.25544	−0.382927	−0.191464	−	0.981500i	$-0.561323\pi$
$359$	−7.25544	−0.382927	−0.191464	+	0.981500i	$0.561323\pi$
$360$	−1.00000	−0.0527046
$361$	−19.0000	−1.00000
$362$	−1.25544	−0.0659843
$363$	−1.00000	−0.0524864
$364$	−6.74456	−0.353511
$365$	6.00000	0.314054
$366$	6.00000	0.313625
$367$	−21.4891	−1.12172	−0.560862	−	0.827910i	$-0.689530\pi$
$367$	−21.4891	−1.12172	−0.560862	+	0.827910i	$0.689530\pi$
$368$	4.74456	0.247327
$369$	6.00000	0.312348
$370$	2.74456	0.142683
$371$	6.00000	0.311504
$372$	0	0
$373$	−24.9783	−1.29332	−0.646662	−	0.762776i	$-0.723836\pi$
$373$	−24.9783	−1.29332	−0.646662	+	0.762776i	$0.723836\pi$
$374$	−6.74456	−0.348753
$375$	−1.00000	−0.0516398
$376$	4.00000	0.206284
$377$	13.4891	0.694725
$378$	−1.00000	−0.0514344
$379$	−14.9783	−0.769381	−0.384691	−	0.923046i	$-0.625692\pi$
$379$	−14.9783	−0.769381	−0.384691	+	0.923046i	$0.625692\pi$
$380$	0	0
$381$	−8.00000	−0.409852
$382$	−17.4891	−0.894821
$383$	20.0000	1.02195	0.510976	−	0.859595i	$-0.329284\pi$
$383$	20.0000	1.02195	0.510976	+	0.859595i	$0.329284\pi$
$384$	1.00000	0.0510310
$385$	1.00000	0.0509647
$386$	−24.9783	−1.27136
$387$	4.00000	0.203331
$388$	15.4891	0.786341
$389$	−27.4891	−1.39375	−0.696877	−	0.717191i	$-0.745428\pi$
$389$	−27.4891	−1.39375	−0.696877	+	0.717191i	$0.745428\pi$
$390$	6.74456	0.341524
$391$	−32.0000	−1.61831
$392$	−1.00000	−0.0505076
$393$	−9.48913	−0.478663
$394$	−0.510875	−0.0257375
$395$	12.0000	0.603786
$396$	−1.00000	−0.0502519
$397$	−38.4674	−1.93062	−0.965311	−	0.261102i	$-0.915914\pi$
$397$	−38.4674	−1.93062	−0.965311	+	0.261102i	$0.915914\pi$
$398$	18.9783	0.951294
$399$	0	0
$400$	1.00000	0.0500000
$401$	−32.9783	−1.64686	−0.823428	−	0.567421i	$-0.807941\pi$
$401$	−32.9783	−1.64686	−0.823428	+	0.567421i	$0.807941\pi$
$402$	−12.7446	−0.635641
$403$	0	0
$404$	6.00000	0.298511
$405$	1.00000	0.0496904
$406$	2.00000	0.0992583
$407$	2.74456	0.136043
$408$	−6.74456	−0.333906
$409$	23.4891	1.16146	0.580731	−	0.814095i	$-0.302767\pi$
$409$	23.4891	1.16146	0.580731	+	0.814095i	$0.302767\pi$
$410$	−6.00000	−0.296319
$411$	−16.2337	−0.800749
$412$	−13.4891	−0.664562
$413$	−4.00000	−0.196827
$414$	−4.74456	−0.233183
$415$	−4.00000	−0.196352
$416$	−6.74456	−0.330679
$417$	1.48913	0.0729228
$418$	0	0
$419$	−2.51087	−0.122664	−0.0613321	−	0.998117i	$-0.519535\pi$
$419$	−2.51087	−0.122664	−0.0613321	+	0.998117i	$0.519535\pi$
$420$	1.00000	0.0487950
$421$	−28.9783	−1.41231	−0.706157	−	0.708056i	$-0.749573\pi$
$421$	−28.9783	−1.41231	−0.706157	+	0.708056i	$0.749573\pi$
$422$	−24.7446	−1.20455
$423$	−4.00000	−0.194487
$424$	6.00000	0.291386
$425$	−6.74456	−0.327159
$426$	0	0
$427$	−6.00000	−0.290360
$428$	−4.00000	−0.193347
$429$	6.74456	0.325631
$430$	−4.00000	−0.192897
$431$	−24.7446	−1.19190	−0.595952	−	0.803020i	$-0.703225\pi$
$431$	−24.7446	−1.19190	−0.595952	+	0.803020i	$0.703225\pi$
$432$	−1.00000	−0.0481125
$433$	−27.4891	−1.32104	−0.660522	−	0.750807i	$-0.729665\pi$
$433$	−27.4891	−1.32104	−0.660522	+	0.750807i	$0.729665\pi$
$434$	0	0
$435$	−2.00000	−0.0958927
$436$	14.7446	0.706136
$437$	0	0
$438$	6.00000	0.286691
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	1.00000	0.0476731
$441$	1.00000	0.0476190
$442$	45.4891	2.16370
$443$	34.9783	1.66187	0.830933	−	0.556372i	$-0.187807\pi$
$443$	34.9783	1.66187	0.830933	+	0.556372i	$0.187807\pi$
$444$	2.74456	0.130251
$445$	6.74456	0.319723
$446$	−21.4891	−1.01754
$447$	7.48913	0.354223
$448$	−1.00000	−0.0472456
$449$	−14.0000	−0.660701	−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000	−0.660701	−0.330350	+	0.943858i	$0.607167\pi$
$450$	−1.00000	−0.0471405
$451$	−6.00000	−0.282529
$452$	−10.7446	−0.505382
$453$	4.00000	0.187936
$454$	−4.00000	−0.187729
$455$	−6.74456	−0.316190
$456$	0	0
$457$	−28.9783	−1.35555	−0.677773	−	0.735271i	$-0.737055\pi$
$457$	−28.9783	−1.35555	−0.677773	+	0.735271i	$0.737055\pi$
$458$	−26.7446	−1.24969
$459$	6.74456	0.314809
$460$	4.74456	0.221216
$461$	−0.510875	−0.0237938	−0.0118969	−	0.999929i	$-0.503787\pi$
$461$	−0.510875	−0.0237938	−0.0118969	+	0.999929i	$0.503787\pi$
$462$	1.00000	0.0465242
$463$	−14.5109	−0.674378	−0.337189	−	0.941437i	$-0.609476\pi$
$463$	−14.5109	−0.674378	−0.337189	+	0.941437i	$0.609476\pi$
$464$	2.00000	0.0928477
$465$	0	0
$466$	−22.0000	−1.01913
$467$	4.00000	0.185098	0.0925490	−	0.995708i	$-0.470499\pi$
$467$	4.00000	0.185098	0.0925490	+	0.995708i	$0.470499\pi$
$468$	6.74456	0.311768
$469$	12.7446	0.588489
$470$	4.00000	0.184506
$471$	−6.00000	−0.276465
$472$	−4.00000	−0.184115
$473$	−4.00000	−0.183920
$474$	12.0000	0.551178
$475$	0	0
$476$	6.74456	0.309137
$477$	−6.00000	−0.274721
$478$	−18.2337	−0.833989
$479$	−8.00000	−0.365529	−0.182765	−	0.983157i	$-0.558505\pi$
$479$	−8.00000	−0.365529	−0.182765	+	0.983157i	$0.558505\pi$
$480$	1.00000	0.0456435
$481$	−18.5109	−0.844023
$482$	−14.0000	−0.637683
$483$	4.74456	0.215885
$484$	1.00000	0.0454545
$485$	15.4891	0.703325
$486$	1.00000	0.0453609
$487$	−33.4891	−1.51754	−0.758769	−	0.651360i	$-0.774199\pi$
$487$	−33.4891	−1.51754	−0.758769	+	0.651360i	$0.774199\pi$
$488$	−6.00000	−0.271607
$489$	−3.25544	−0.147216
$490$	−1.00000	−0.0451754
$491$	22.9783	1.03699	0.518497	−	0.855079i	$-0.326492\pi$
$491$	22.9783	1.03699	0.518497	+	0.855079i	$0.326492\pi$
$492$	−6.00000	−0.270501
$493$	−13.4891	−0.607520
$494$	0	0
$495$	−1.00000	−0.0449467
$496$	0	0
$497$	0	0
$498$	−4.00000	−0.179244
$499$	−2.51087	−0.112402	−0.0562011	−	0.998419i	$-0.517899\pi$
$499$	−2.51087	−0.112402	−0.0562011	+	0.998419i	$0.517899\pi$
$500$	1.00000	0.0447214
$501$	14.2337	0.635914
$502$	4.00000	0.178529
$503$	28.7446	1.28166	0.640828	−	0.767684i	$-0.278591\pi$
$503$	28.7446	1.28166	0.640828	+	0.767684i	$0.278591\pi$
$504$	1.00000	0.0445435
$505$	6.00000	0.266996
$506$	4.74456	0.210922
$507$	−32.4891	−1.44289
$508$	8.00000	0.354943
$509$	39.4891	1.75032	0.875162	−	0.483829i	$-0.160754\pi$
$509$	39.4891	1.75032	0.875162	+	0.483829i	$0.160754\pi$
$510$	−6.74456	−0.298654
$511$	−6.00000	−0.265424
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−23.4891	−1.03606
$515$	−13.4891	−0.594402
$516$	−4.00000	−0.176090
$517$	4.00000	0.175920
$518$	−2.74456	−0.120589
$519$	−0.510875	−0.0224249
$520$	−6.74456	−0.295769
$521$	25.7228	1.12694	0.563468	−	0.826138i	$-0.309467\pi$
$521$	25.7228	1.12694	0.563468	+	0.826138i	$0.309467\pi$
$522$	−2.00000	−0.0875376
$523$	16.7446	0.732189	0.366094	−	0.930578i	$-0.380695\pi$
$523$	16.7446	0.732189	0.366094	+	0.930578i	$0.380695\pi$
$524$	9.48913	0.414534
$525$	1.00000	0.0436436
$526$	25.4891	1.11138
$527$	0	0
$528$	1.00000	0.0435194
$529$	−0.489125	−0.0212663
$530$	6.00000	0.260623
$531$	4.00000	0.173585
$532$	0	0
$533$	40.4674	1.75284
$534$	6.74456	0.291866
$535$	−4.00000	−0.172935
$536$	12.7446	0.550481
$537$	4.00000	0.172613
$538$	−23.4891	−1.01269
$539$	−1.00000	−0.0430730
$540$	−1.00000	−0.0430331
$541$	16.2337	0.697941	0.348970	−	0.937134i	$-0.386531\pi$
$541$	16.2337	0.697941	0.348970	+	0.937134i	$0.386531\pi$
$542$	−8.00000	−0.343629
$543$	−1.25544	−0.0538760
$544$	6.74456	0.289171
$545$	14.7446	0.631588
$546$	−6.74456	−0.288641
$547$	32.4674	1.38820	0.694102	−	0.719876i	$-0.255801\pi$
$547$	32.4674	1.38820	0.694102	+	0.719876i	$0.255801\pi$
$548$	16.2337	0.693469
$549$	6.00000	0.256074
$550$	1.00000	0.0426401
$551$	0	0
$552$	4.74456	0.201942
$553$	−12.0000	−0.510292
$554$	−19.4891	−0.828014
$555$	2.74456	0.116500
$556$	−1.48913	−0.0631530
$557$	11.4891	0.486810	0.243405	−	0.969925i	$-0.421736\pi$
$557$	11.4891	0.486810	0.243405	+	0.969925i	$0.421736\pi$
$558$	0	0
$559$	26.9783	1.14106
$560$	−1.00000	−0.0422577
$561$	−6.74456	−0.284756
$562$	20.2337	0.853507
$563$	5.48913	0.231339	0.115670	−	0.993288i	$-0.463099\pi$
$563$	5.48913	0.231339	0.115670	+	0.993288i	$0.463099\pi$
$564$	4.00000	0.168430
$565$	−10.7446	−0.452027
$566$	−10.2337	−0.430154
$567$	−1.00000	−0.0419961
$568$	0	0
$569$	−26.7446	−1.12119	−0.560595	−	0.828090i	$-0.689428\pi$
$569$	−26.7446	−1.12119	−0.560595	+	0.828090i	$0.689428\pi$
$570$	0	0
$571$	−40.7446	−1.70511	−0.852553	−	0.522640i	$-0.824947\pi$
$571$	−40.7446	−1.70511	−0.852553	+	0.522640i	$0.824947\pi$
$572$	−6.74456	−0.282004
$573$	−17.4891	−0.730619
$574$	6.00000	0.250435
$575$	4.74456	0.197862
$576$	1.00000	0.0416667
$577$	−10.0000	−0.416305	−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000	−0.416305	−0.208153	+	0.978096i	$0.566745\pi$
$578$	−28.4891	−1.18499
$579$	−24.9783	−1.03806
$580$	2.00000	0.0830455
$581$	4.00000	0.165948
$582$	15.4891	0.642045
$583$	6.00000	0.248495
$584$	−6.00000	−0.248282
$585$	6.74456	0.278853
$586$	6.00000	0.247858
$587$	28.0000	1.15568	0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000	1.15568	0.577842	+	0.816149i	$0.303895\pi$
$588$	−1.00000	−0.0412393
$589$	0	0
$590$	−4.00000	−0.164677
$591$	−0.510875	−0.0210146
$592$	−2.74456	−0.112801
$593$	−0.233688	−0.00959641	−0.00479821	−	0.999988i	$-0.501527\pi$
$593$	−0.233688	−0.00959641	−0.00479821	+	0.999988i	$0.501527\pi$
$594$	−1.00000	−0.0410305
$595$	6.74456	0.276500
$596$	−7.48913	−0.306767
$597$	18.9783	0.776728
$598$	−32.0000	−1.30858
$599$	−44.4674	−1.81689	−0.908444	−	0.418007i	$-0.862729\pi$
$599$	−44.4674	−1.81689	−0.908444	+	0.418007i	$0.862729\pi$
$600$	1.00000	0.0408248
$601$	−30.4674	−1.24279	−0.621395	−	0.783497i	$-0.713434\pi$
$601$	−30.4674	−1.24279	−0.621395	+	0.783497i	$0.713434\pi$
$602$	4.00000	0.163028
$603$	−12.7446	−0.518999
$604$	−4.00000	−0.162758
$605$	1.00000	0.0406558
$606$	6.00000	0.243733
$607$	−34.9783	−1.41972	−0.709862	−	0.704341i	$-0.751243\pi$
$607$	−34.9783	−1.41972	−0.709862	+	0.704341i	$0.751243\pi$
$608$	0	0
$609$	2.00000	0.0810441
$610$	−6.00000	−0.242933
$611$	−26.9783	−1.09142
$612$	−6.74456	−0.272633
$613$	−31.4891	−1.27183	−0.635917	−	0.771758i	$-0.719378\pi$
$613$	−31.4891	−1.27183	−0.635917	+	0.771758i	$0.719378\pi$
$614$	−18.2337	−0.735852
$615$	−6.00000	−0.241943
$616$	−1.00000	−0.0402911
$617$	−7.76631	−0.312660	−0.156330	−	0.987705i	$-0.549966\pi$
$617$	−7.76631	−0.312660	−0.156330	+	0.987705i	$0.549966\pi$
$618$	−13.4891	−0.542612
$619$	−2.23369	−0.0897795	−0.0448897	−	0.998992i	$-0.514294\pi$
$619$	−2.23369	−0.0897795	−0.0448897	+	0.998992i	$0.514294\pi$
$620$	0	0
$621$	−4.74456	−0.190393
$622$	−4.74456	−0.190240
$623$	−6.74456	−0.270215
$624$	−6.74456	−0.269999
$625$	1.00000	0.0400000
$626$	−6.00000	−0.239808
$627$	0	0
$628$	6.00000	0.239426
$629$	18.5109	0.738077
$630$	1.00000	0.0398410
$631$	26.9783	1.07399	0.536994	−	0.843586i	$-0.319560\pi$
$631$	26.9783	1.07399	0.536994	+	0.843586i	$0.319560\pi$
$632$	−12.0000	−0.477334
$633$	−24.7446	−0.983508
$634$	16.9783	0.674292
$635$	8.00000	0.317470
$636$	6.00000	0.237915
$637$	6.74456	0.267229
$638$	2.00000	0.0791808
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	−48.9783	−1.93452	−0.967262	−	0.253779i	$-0.918326\pi$
$641$	−48.9783	−1.93452	−0.967262	+	0.253779i	$0.918326\pi$
$642$	−4.00000	−0.157867
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	−4.74456	−0.186962
$645$	−4.00000	−0.157500
$646$	0	0
$647$	20.0000	0.786281	0.393141	−	0.919478i	$-0.371389\pi$
$647$	20.0000	0.786281	0.393141	+	0.919478i	$0.371389\pi$
$648$	−1.00000	−0.0392837
$649$	−4.00000	−0.157014
$650$	−6.74456	−0.264544
$651$	0	0
$652$	3.25544	0.127493
$653$	11.4891	0.449604	0.224802	−	0.974404i	$-0.427826\pi$
$653$	11.4891	0.449604	0.224802	+	0.974404i	$0.427826\pi$
$654$	14.7446	0.576558
$655$	9.48913	0.370771
$656$	6.00000	0.234261
$657$	6.00000	0.234082
$658$	−4.00000	−0.155936
$659$	−38.9783	−1.51838	−0.759189	−	0.650871i	$-0.774404\pi$
$659$	−38.9783	−1.51838	−0.759189	+	0.650871i	$0.774404\pi$
$660$	1.00000	0.0389249
$661$	−11.7663	−0.457656	−0.228828	−	0.973467i	$-0.573489\pi$
$661$	−11.7663	−0.457656	−0.228828	+	0.973467i	$0.573489\pi$
$662$	20.0000	0.777322
$663$	45.4891	1.76665
$664$	4.00000	0.155230
$665$	0	0
$666$	2.74456	0.106350
$667$	9.48913	0.367420
$668$	−14.2337	−0.550718
$669$	−21.4891	−0.830818
$670$	12.7446	0.492365
$671$	−6.00000	−0.231627
$672$	−1.00000	−0.0385758
$673$	31.4891	1.21382	0.606908	−	0.794772i	$-0.292410\pi$
$673$	31.4891	1.21382	0.606908	+	0.794772i	$0.292410\pi$
$674$	−15.4891	−0.596619
$675$	−1.00000	−0.0384900
$676$	32.4891	1.24958
$677$	22.4674	0.863491	0.431746	−	0.901995i	$-0.357898\pi$
$677$	22.4674	0.863491	0.431746	+	0.901995i	$0.357898\pi$
$678$	−10.7446	−0.412642
$679$	−15.4891	−0.594418
$680$	6.74456	0.258642
$681$	−4.00000	−0.153280
$682$	0	0
$683$	−34.9783	−1.33841	−0.669203	−	0.743080i	$-0.733364\pi$
$683$	−34.9783	−1.33841	−0.669203	+	0.743080i	$0.733364\pi$
$684$	0	0
$685$	16.2337	0.620257
$686$	1.00000	0.0381802
$687$	−26.7446	−1.02037
$688$	4.00000	0.152499
$689$	−40.4674	−1.54168
$690$	4.74456	0.180622
$691$	−18.2337	−0.693642	−0.346821	−	0.937931i	$-0.612739\pi$
$691$	−18.2337	−0.693642	−0.346821	+	0.937931i	$0.612739\pi$
$692$	0.510875	0.0194205
$693$	1.00000	0.0379869
$694$	20.0000	0.759190
$695$	−1.48913	−0.0564857
$696$	2.00000	0.0758098
$697$	−40.4674	−1.53281
$698$	20.9783	0.794038
$699$	−22.0000	−0.832116
$700$	−1.00000	−0.0377964
$701$	26.0000	0.982006	0.491003	−	0.871158i	$-0.336630\pi$
$701$	26.0000	0.982006	0.491003	+	0.871158i	$0.336630\pi$
$702$	6.74456	0.254557
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	4.00000	0.150649
$706$	8.51087	0.320311
$707$	−6.00000	−0.225653
$708$	−4.00000	−0.150329
$709$	16.9783	0.637632	0.318816	−	0.947817i	$-0.396715\pi$
$709$	16.9783	0.637632	0.318816	+	0.947817i	$0.396715\pi$
$710$	0	0
$711$	12.0000	0.450035
$712$	−6.74456	−0.252763
$713$	0	0
$714$	6.74456	0.252409
$715$	−6.74456	−0.252232
$716$	−4.00000	−0.149487
$717$	−18.2337	−0.680950
$718$	7.25544	0.270771
$719$	−23.7228	−0.884712	−0.442356	−	0.896840i	$-0.645857\pi$
$719$	−23.7228	−0.884712	−0.442356	+	0.896840i	$0.645857\pi$
$720$	1.00000	0.0372678
$721$	13.4891	0.502361
$722$	19.0000	0.707107
$723$	−14.0000	−0.520666
$724$	1.25544	0.0466580
$725$	2.00000	0.0742781
$726$	1.00000	0.0371135
$727$	−10.5109	−0.389827	−0.194913	−	0.980820i	$-0.562443\pi$
$727$	−10.5109	−0.389827	−0.194913	+	0.980820i	$0.562443\pi$
$728$	6.74456	0.249970
$729$	1.00000	0.0370370
$730$	−6.00000	−0.222070
$731$	−26.9783	−0.997827
$732$	−6.00000	−0.221766
$733$	−1.25544	−0.0463706	−0.0231853	−	0.999731i	$-0.507381\pi$
$733$	−1.25544	−0.0463706	−0.0231853	+	0.999731i	$0.507381\pi$
$734$	21.4891	0.793178
$735$	−1.00000	−0.0368856
$736$	−4.74456	−0.174887
$737$	12.7446	0.469452
$738$	−6.00000	−0.220863
$739$	31.2554	1.14975	0.574875	−	0.818241i	$-0.305051\pi$
$739$	31.2554	1.14975	0.574875	+	0.818241i	$0.305051\pi$
$740$	−2.74456	−0.100892
$741$	0	0
$742$	−6.00000	−0.220267
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	0	0
$745$	−7.48913	−0.274380
$746$	24.9783	0.914519
$747$	−4.00000	−0.146352
$748$	6.74456	0.246606
$749$	4.00000	0.146157
$750$	1.00000	0.0365148
$751$	−5.02175	−0.183246	−0.0916231	−	0.995794i	$-0.529206\pi$
$751$	−5.02175	−0.183246	−0.0916231	+	0.995794i	$0.529206\pi$
$752$	−4.00000	−0.145865
$753$	4.00000	0.145768
$754$	−13.4891	−0.491245
$755$	−4.00000	−0.145575
$756$	1.00000	0.0363696
$757$	−5.72281	−0.207999	−0.104000	−	0.994577i	$-0.533164\pi$
$757$	−5.72281	−0.207999	−0.104000	+	0.994577i	$0.533164\pi$
$758$	14.9783	0.544035
$759$	4.74456	0.172217
$760$	0	0
$761$	51.9565	1.88342	0.941711	−	0.336423i	$-0.109217\pi$
$761$	51.9565	1.88342	0.941711	+	0.336423i	$0.109217\pi$
$762$	8.00000	0.289809
$763$	−14.7446	−0.533789
$764$	17.4891	0.632734
$765$	−6.74456	−0.243850
$766$	−20.0000	−0.722629
$767$	26.9783	0.974128
$768$	−1.00000	−0.0360844
$769$	31.4891	1.13553	0.567763	−	0.823192i	$-0.307809\pi$
$769$	31.4891	1.13553	0.567763	+	0.823192i	$0.307809\pi$
$770$	−1.00000	−0.0360375
$771$	−23.4891	−0.845940
$772$	24.9783	0.898987
$773$	−14.4674	−0.520355	−0.260178	−	0.965561i	$-0.583781\pi$
$773$	−14.4674	−0.520355	−0.260178	+	0.965561i	$0.583781\pi$
$774$	−4.00000	−0.143777
$775$	0	0
$776$	−15.4891	−0.556027
$777$	−2.74456	−0.0984606
$778$	27.4891	0.985533
$779$	0	0
$780$	−6.74456	−0.241494
$781$	0	0
$782$	32.0000	1.14432
$783$	−2.00000	−0.0714742
$784$	1.00000	0.0357143
$785$	6.00000	0.214149
$786$	9.48913	0.338466
$787$	−5.76631	−0.205547	−0.102773	−	0.994705i	$-0.532772\pi$
$787$	−5.76631	−0.205547	−0.102773	+	0.994705i	$0.532772\pi$
$788$	0.510875	0.0181992
$789$	25.4891	0.907437
$790$	−12.0000	−0.426941
$791$	10.7446	0.382033
$792$	1.00000	0.0355335
$793$	40.4674	1.43704
$794$	38.4674	1.36516
$795$	6.00000	0.212798
$796$	−18.9783	−0.672666
$797$	47.4891	1.68215	0.841076	−	0.540918i	$-0.181923\pi$
$797$	47.4891	1.68215	0.841076	+	0.540918i	$0.181923\pi$
$798$	0	0
$799$	26.9783	0.954422
$800$	−1.00000	−0.0353553
$801$	6.74456	0.238307
$802$	32.9783	1.16450
$803$	−6.00000	−0.211735
$804$	12.7446	0.449466
$805$	−4.74456	−0.167224
$806$	0	0
$807$	−23.4891	−0.826856
$808$	−6.00000	−0.211079
$809$	8.23369	0.289481	0.144741	−	0.989470i	$-0.453765\pi$
$809$	8.23369	0.289481	0.144741	+	0.989470i	$0.453765\pi$
$810$	−1.00000	−0.0351364
$811$	−16.0000	−0.561836	−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000	−0.561836	−0.280918	+	0.959732i	$0.590639\pi$
$812$	−2.00000	−0.0701862
$813$	−8.00000	−0.280572
$814$	−2.74456	−0.0961969
$815$	3.25544	0.114033
$816$	6.74456	0.236107
$817$	0	0
$818$	−23.4891	−0.821278
$819$	−6.74456	−0.235674
$820$	6.00000	0.209529
$821$	−0.978251	−0.0341412	−0.0170706	−	0.999854i	$-0.505434\pi$
$821$	−0.978251	−0.0341412	−0.0170706	+	0.999854i	$0.505434\pi$
$822$	16.2337	0.566215
$823$	8.00000	0.278862	0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000	0.278862	0.139431	+	0.990232i	$0.455473\pi$
$824$	13.4891	0.469916
$825$	1.00000	0.0348155
$826$	4.00000	0.139178
$827$	1.02175	0.0355297	0.0177649	−	0.999842i	$-0.494345\pi$
$827$	1.02175	0.0355297	0.0177649	+	0.999842i	$0.494345\pi$
$828$	4.74456	0.164885
$829$	28.2337	0.980597	0.490298	−	0.871555i	$-0.336888\pi$
$829$	28.2337	0.980597	0.490298	+	0.871555i	$0.336888\pi$
$830$	4.00000	0.138842
$831$	−19.4891	−0.676070
$832$	6.74456	0.233826
$833$	−6.74456	−0.233685
$834$	−1.48913	−0.0515642
$835$	−14.2337	−0.492577
$836$	0	0
$837$	0	0
$838$	2.51087	0.0867367
$839$	28.7446	0.992373	0.496186	−	0.868216i	$-0.334733\pi$
$839$	28.7446	0.992373	0.496186	+	0.868216i	$0.334733\pi$
$840$	−1.00000	−0.0345033
$841$	−25.0000	−0.862069
$842$	28.9783	0.998656
$843$	20.2337	0.696885
$844$	24.7446	0.851743
$845$	32.4891	1.11766
$846$	4.00000	0.137523
$847$	−1.00000	−0.0343604
$848$	−6.00000	−0.206041
$849$	−10.2337	−0.351219
$850$	6.74456	0.231337
$851$	−13.0217	−0.446380
$852$	0	0
$853$	−44.2337	−1.51453	−0.757266	−	0.653106i	$-0.773466\pi$
$853$	−44.2337	−1.51453	−0.757266	+	0.653106i	$0.773466\pi$
$854$	6.00000	0.205316
$855$	0	0
$856$	4.00000	0.136717
$857$	26.7446	0.913577	0.456788	−	0.889575i	$-0.349000\pi$
$857$	26.7446	0.913577	0.456788	+	0.889575i	$0.349000\pi$
$858$	−6.74456	−0.230256
$859$	58.2337	1.98691	0.993454	−	0.114234i	$-0.0364413\pi$
$859$	58.2337	1.98691	0.993454	+	0.114234i	$0.0364413\pi$
$860$	4.00000	0.136399
$861$	6.00000	0.204479
$862$	24.7446	0.842803
$863$	20.7446	0.706153	0.353077	−	0.935594i	$-0.385136\pi$
$863$	20.7446	0.706153	0.353077	+	0.935594i	$0.385136\pi$
$864$	1.00000	0.0340207
$865$	0.510875	0.0173703
$866$	27.4891	0.934119
$867$	−28.4891	−0.967541
$868$	0	0
$869$	−12.0000	−0.407072
$870$	2.00000	0.0678064
$871$	−85.9565	−2.91252
$872$	−14.7446	−0.499314
$873$	15.4891	0.524227
$874$	0	0
$875$	−1.00000	−0.0338062
$876$	−6.00000	−0.202721
$877$	−4.51087	−0.152321	−0.0761607	−	0.997096i	$-0.524266\pi$
$877$	−4.51087	−0.152321	−0.0761607	+	0.997096i	$0.524266\pi$
$878$	−16.0000	−0.539974
$879$	6.00000	0.202375
$880$	−1.00000	−0.0337100
$881$	−9.25544	−0.311824	−0.155912	−	0.987771i	$-0.549832\pi$
$881$	−9.25544	−0.311824	−0.155912	+	0.987771i	$0.549832\pi$
$882$	−1.00000	−0.0336718
$883$	−58.7011	−1.97545	−0.987724	−	0.156209i	$-0.950073\pi$
$883$	−58.7011	−1.97545	−0.987724	+	0.156209i	$0.950073\pi$
$884$	−45.4891	−1.52996
$885$	−4.00000	−0.134459
$886$	−34.9783	−1.17512
$887$	−23.7228	−0.796534	−0.398267	−	0.917270i	$-0.630388\pi$
$887$	−23.7228	−0.796534	−0.398267	+	0.917270i	$0.630388\pi$
$888$	−2.74456	−0.0921015
$889$	−8.00000	−0.268311
$890$	−6.74456	−0.226078
$891$	−1.00000	−0.0335013
$892$	21.4891	0.719509
$893$	0	0
$894$	−7.48913	−0.250474
$895$	−4.00000	−0.133705
$896$	1.00000	0.0334077
$897$	−32.0000	−1.06845
$898$	14.0000	0.467186
$899$	0	0
$900$	1.00000	0.0333333
$901$	40.4674	1.34816
$902$	6.00000	0.199778
$903$	4.00000	0.133112
$904$	10.7446	0.357359
$905$	1.25544	0.0417321
$906$	−4.00000	−0.132891
$907$	12.7446	0.423176	0.211588	−	0.977359i	$-0.432136\pi$
$907$	12.7446	0.423176	0.211588	+	0.977359i	$0.432136\pi$
$908$	4.00000	0.132745
$909$	6.00000	0.199007
$910$	6.74456	0.223580
$911$	34.9783	1.15888	0.579441	−	0.815014i	$-0.303271\pi$
$911$	34.9783	1.15888	0.579441	+	0.815014i	$0.303271\pi$
$912$	0	0
$913$	4.00000	0.132381
$914$	28.9783	0.958515
$915$	−6.00000	−0.198354
$916$	26.7446	0.883665
$917$	−9.48913	−0.313359
$918$	−6.74456	−0.222604
$919$	−29.4891	−0.972756	−0.486378	−	0.873748i	$-0.661682\pi$
$919$	−29.4891	−0.972756	−0.486378	+	0.873748i	$0.661682\pi$
$920$	−4.74456	−0.156424
$921$	−18.2337	−0.600820
$922$	0.510875	0.0168248
$923$	0	0
$924$	−1.00000	−0.0328976
$925$	−2.74456	−0.0902407
$926$	14.5109	0.476857
$927$	−13.4891	−0.443041
$928$	−2.00000	−0.0656532
$929$	−26.7446	−0.877461	−0.438730	−	0.898619i	$-0.644572\pi$
$929$	−26.7446	−0.877461	−0.438730	+	0.898619i	$0.644572\pi$
$930$	0	0
$931$	0	0
$932$	22.0000	0.720634
$933$	−4.74456	−0.155330
$934$	−4.00000	−0.130884
$935$	6.74456	0.220571
$936$	−6.74456	−0.220453
$937$	−3.48913	−0.113985	−0.0569924	−	0.998375i	$-0.518151\pi$
$937$	−3.48913	−0.113985	−0.0569924	+	0.998375i	$0.518151\pi$
$938$	−12.7446	−0.416125
$939$	−6.00000	−0.195803
$940$	−4.00000	−0.130466
$941$	51.9565	1.69373	0.846867	−	0.531805i	$-0.178486\pi$
$941$	51.9565	1.69373	0.846867	+	0.531805i	$0.178486\pi$
$942$	6.00000	0.195491
$943$	28.4674	0.927025
$944$	4.00000	0.130189
$945$	1.00000	0.0325300
$946$	4.00000	0.130051
$947$	−41.4891	−1.34822	−0.674108	−	0.738633i	$-0.735472\pi$
$947$	−41.4891	−1.34822	−0.674108	+	0.738633i	$0.735472\pi$
$948$	−12.0000	−0.389742
$949$	40.4674	1.31363
$950$	0	0
$951$	16.9783	0.550557
$952$	−6.74456	−0.218593
$953$	−16.5109	−0.534840	−0.267420	−	0.963580i	$-0.586171\pi$
$953$	−16.5109	−0.534840	−0.267420	+	0.963580i	$0.586171\pi$
$954$	6.00000	0.194257
$955$	17.4891	0.565935
$956$	18.2337	0.589720
$957$	2.00000	0.0646508
$958$	8.00000	0.258468
$959$	−16.2337	−0.524213
$960$	−1.00000	−0.0322749
$961$	−31.0000	−1.00000
$962$	18.5109	0.596815
$963$	−4.00000	−0.128898
$964$	14.0000	0.450910
$965$	24.9783	0.804078
$966$	−4.74456	−0.152654
$967$	−18.9783	−0.610299	−0.305150	−	0.952304i	$-0.598707\pi$
$967$	−18.9783	−0.610299	−0.305150	+	0.952304i	$0.598707\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	−15.4891	−0.497326
$971$	−5.48913	−0.176154	−0.0880772	−	0.996114i	$-0.528072\pi$
$971$	−5.48913	−0.176154	−0.0880772	+	0.996114i	$0.528072\pi$
$972$	−1.00000	−0.0320750
$973$	1.48913	0.0477392
$974$	33.4891	1.07306
$975$	−6.74456	−0.215999
$976$	6.00000	0.192055
$977$	14.7446	0.471720	0.235860	−	0.971787i	$-0.424209\pi$
$977$	14.7446	0.471720	0.235860	+	0.971787i	$0.424209\pi$
$978$	3.25544	0.104097
$979$	−6.74456	−0.215557
$980$	1.00000	0.0319438
$981$	14.7446	0.470758
$982$	−22.9783	−0.733265
$983$	−54.9783	−1.75353	−0.876767	−	0.480916i	$-0.840304\pi$
$983$	−54.9783	−1.75353	−0.876767	+	0.480916i	$0.840304\pi$
$984$	6.00000	0.191273
$985$	0.510875	0.0162778
$986$	13.4891	0.429581
$987$	−4.00000	−0.127321
$988$	0	0
$989$	18.9783	0.603473
$990$	1.00000	0.0317821
$991$	10.9783	0.348736	0.174368	−	0.984681i	$-0.444212\pi$
$991$	10.9783	0.348736	0.174368	+	0.984681i	$0.444212\pi$
$992$	0	0
$993$	20.0000	0.634681
$994$	0	0
$995$	−18.9783	−0.601651
$996$	4.00000	0.126745
$997$	48.2337	1.52758	0.763788	−	0.645467i	$-0.223337\pi$
$997$	48.2337	1.52758	0.763788	+	0.645467i	$0.223337\pi$
$998$	2.51087	0.0794804
$999$	2.74456	0.0868341

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2310.2.a.x.1.2	✓	2
3.2	odd	2		6930.2.a.by.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2310.2.a.x.1.2	✓	2	1.1	even	1	trivial
6930.2.a.by.1.2		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2310.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} +6.74456 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -6.74456 q^{17} -1.00000 q^{18} +1.00000 q^{20} +1.00000 q^{21} +1.00000 q^{22} +4.74456 q^{23} +1.00000 q^{24} +1.00000 q^{25} -6.74456 q^{26} -1.00000 q^{27} -1.00000 q^{28} +2.00000 q^{29} +1.00000 q^{30} -1.00000 q^{32} +1.00000 q^{33} +6.74456 q^{34} -1.00000 q^{35} +1.00000 q^{36} -2.74456 q^{37} -6.74456 q^{39} -1.00000 q^{40} +6.00000 q^{41} -1.00000 q^{42} +4.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} -4.74456 q^{46} -4.00000 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +6.74456 q^{51} +6.74456 q^{52} -6.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} +1.00000 q^{56} -2.00000 q^{58} +4.00000 q^{59} -1.00000 q^{60} +6.00000 q^{61} -1.00000 q^{63} +1.00000 q^{64} +6.74456 q^{65} -1.00000 q^{66} -12.7446 q^{67} -6.74456 q^{68} -4.74456 q^{69} +1.00000 q^{70} -1.00000 q^{72} +6.00000 q^{73} +2.74456 q^{74} -1.00000 q^{75} +1.00000 q^{77} +6.74456 q^{78} +12.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -4.00000 q^{83} +1.00000 q^{84} -6.74456 q^{85} -4.00000 q^{86} -2.00000 q^{87} +1.00000 q^{88} +6.74456 q^{89} -1.00000 q^{90} -6.74456 q^{91} +4.74456 q^{92} +4.00000 q^{94} +1.00000 q^{96} +15.4891 q^{97} -1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} + 2 q^{20} + 2 q^{21} + 2 q^{22} - 2 q^{23} + 2 q^{24} + 2 q^{25} - 2 q^{26} - 2 q^{27} - 2 q^{28} + 4 q^{29} + 2 q^{30} - 2 q^{32} + 2 q^{33} + 2 q^{34} - 2 q^{35} + 2 q^{36} + 6 q^{37} - 2 q^{39} - 2 q^{40} + 12 q^{41} - 2 q^{42} + 8 q^{43} - 2 q^{44} + 2 q^{45} + 2 q^{46} - 8 q^{47} - 2 q^{48} + 2 q^{49} - 2 q^{50} + 2 q^{51} + 2 q^{52} - 12 q^{53} + 2 q^{54} - 2 q^{55} + 2 q^{56} - 4 q^{58} + 8 q^{59} - 2 q^{60} + 12 q^{61} - 2 q^{63} + 2 q^{64} + 2 q^{65} - 2 q^{66} - 14 q^{67} - 2 q^{68} + 2 q^{69} + 2 q^{70} - 2 q^{72} + 12 q^{73} - 6 q^{74} - 2 q^{75} + 2 q^{77} + 2 q^{78} + 24 q^{79} + 2 q^{80} + 2 q^{81} - 12 q^{82} - 8 q^{83} + 2 q^{84} - 2 q^{85} - 8 q^{86} - 4 q^{87} + 2 q^{88} + 2 q^{89} - 2 q^{90} - 2 q^{91} - 2 q^{92} + 8 q^{94} + 2 q^{96} + 8 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 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 + 2 * q^13 + 2 * q^14 - 2 * q^15 + 2 * q^16 - 2 * q^17 - 2 * q^18 + 2 * q^20 + 2 * q^21 + 2 * q^22 - 2 * q^23 + 2 * q^24 + 2 * q^25 - 2 * q^26 - 2 * q^27 - 2 * q^28 + 4 * q^29 + 2 * q^30 - 2 * q^32 + 2 * q^33 + 2 * q^34 - 2 * q^35 + 2 * q^36 + 6 * q^37 - 2 * q^39 - 2 * q^40 + 12 * q^41 - 2 * q^42 + 8 * q^43 - 2 * q^44 + 2 * q^45 + 2 * q^46 - 8 * q^47 - 2 * q^48 + 2 * q^49 - 2 * q^50 + 2 * q^51 + 2 * q^52 - 12 * q^53 + 2 * q^54 - 2 * q^55 + 2 * q^56 - 4 * q^58 + 8 * q^59 - 2 * q^60 + 12 * q^61 - 2 * q^63 + 2 * q^64 + 2 * q^65 - 2 * q^66 - 14 * q^67 - 2 * q^68 + 2 * q^69 + 2 * q^70 - 2 * q^72 + 12 * q^73 - 6 * q^74 - 2 * q^75 + 2 * q^77 + 2 * q^78 + 24 * q^79 + 2 * q^80 + 2 * q^81 - 12 * q^82 - 8 * q^83 + 2 * q^84 - 2 * q^85 - 8 * q^86 - 4 * q^87 + 2 * q^88 + 2 * q^89 - 2 * q^90 - 2 * q^91 - 2 * q^92 + 8 * q^94 + 2 * q^96 + 8 * q^97 - 2 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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