LMFDB - Embedded newform 2366.2.a.ba.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(1,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2366.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.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:	$18.8926051182$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.80194 q^{3} +1.00000 q^{4} +0.554958 q^{5} -2.80194 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.85086 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.80194 q^{3} +1.00000 q^{4} +0.554958 q^{5} -2.80194 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.85086 q^{9} +0.554958 q^{10} -5.24698 q^{11} -2.80194 q^{12} +1.00000 q^{14} -1.55496 q^{15} +1.00000 q^{16} +7.23490 q^{17} +4.85086 q^{18} -5.80194 q^{19} +0.554958 q^{20} -2.80194 q^{21} -5.24698 q^{22} -5.15883 q^{23} -2.80194 q^{24} -4.69202 q^{25} -5.18598 q^{27} +1.00000 q^{28} +5.43296 q^{29} -1.55496 q^{30} +5.54288 q^{31} +1.00000 q^{32} +14.7017 q^{33} +7.23490 q^{34} +0.554958 q^{35} +4.85086 q^{36} -0.335126 q^{37} -5.80194 q^{38} +0.554958 q^{40} -3.11529 q^{41} -2.80194 q^{42} -6.91185 q^{43} -5.24698 q^{44} +2.69202 q^{45} -5.15883 q^{46} -5.56465 q^{47} -2.80194 q^{48} +1.00000 q^{49} -4.69202 q^{50} -20.2717 q^{51} -7.78986 q^{53} -5.18598 q^{54} -2.91185 q^{55} +1.00000 q^{56} +16.2567 q^{57} +5.43296 q^{58} -7.24698 q^{59} -1.55496 q^{60} +8.45473 q^{61} +5.54288 q^{62} +4.85086 q^{63} +1.00000 q^{64} +14.7017 q^{66} -2.59419 q^{67} +7.23490 q^{68} +14.4547 q^{69} +0.554958 q^{70} +9.18060 q^{71} +4.85086 q^{72} -4.29590 q^{73} -0.335126 q^{74} +13.1468 q^{75} -5.80194 q^{76} -5.24698 q^{77} -4.00969 q^{79} +0.554958 q^{80} -0.0217703 q^{81} -3.11529 q^{82} +8.36658 q^{83} -2.80194 q^{84} +4.01507 q^{85} -6.91185 q^{86} -15.2228 q^{87} -5.24698 q^{88} +2.11529 q^{89} +2.69202 q^{90} -5.15883 q^{92} -15.5308 q^{93} -5.56465 q^{94} -3.21983 q^{95} -2.80194 q^{96} -15.9269 q^{97} +1.00000 q^{98} -25.4523 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 3 * q^8 + q^9	$ 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 3 q^{8} + q^{9} + 2 q^{10} - 11 q^{11} - 4 q^{12} + 3 q^{14} - 5 q^{15} + 3 q^{16} - 2 q^{17} + q^{18} - 13 q^{19} + 2 q^{20} - 4 q^{21} - 11 q^{22} - 7 q^{23} - 4 q^{24} - 9 q^{25} - q^{27} + 3 q^{28} - 3 q^{29} - 5 q^{30} - 2 q^{31} + 3 q^{32} + 17 q^{33} - 2 q^{34} + 2 q^{35} + q^{36} - 13 q^{38} + 2 q^{40} - 7 q^{41} - 4 q^{42} - 17 q^{43} - 11 q^{44} + 3 q^{45} - 7 q^{46} + 5 q^{47} - 4 q^{48} + 3 q^{49} - 9 q^{50} - 9 q^{51} - q^{54} - 5 q^{55} + 3 q^{56} + 22 q^{57} - 3 q^{58} - 17 q^{59} - 5 q^{60} + 3 q^{61} - 2 q^{62} + q^{63} + 3 q^{64} + 17 q^{66} - 21 q^{67} - 2 q^{68} + 21 q^{69} + 2 q^{70} + 16 q^{71} + q^{72} + q^{73} + 12 q^{75} - 13 q^{76} - 11 q^{77} + 10 q^{79} + 2 q^{80} + 3 q^{81} - 7 q^{82} - q^{83} - 4 q^{84} - 13 q^{85} - 17 q^{86} - 3 q^{87} - 11 q^{88} + 4 q^{89} + 3 q^{90} - 7 q^{92} - 9 q^{93} + 5 q^{94} - 11 q^{95} - 4 q^{96} - 19 q^{97} + 3 q^{98} - 13 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 3 * q^8 + q^9 + 2 * q^10 - 11 * q^11 - 4 * q^12 + 3 * q^14 - 5 * q^15 + 3 * q^16 - 2 * q^17 + q^18 - 13 * q^19 + 2 * q^20 - 4 * q^21 - 11 * q^22 - 7 * q^23 - 4 * q^24 - 9 * q^25 - q^27 + 3 * q^28 - 3 * q^29 - 5 * q^30 - 2 * q^31 + 3 * q^32 + 17 * q^33 - 2 * q^34 + 2 * q^35 + q^36 - 13 * q^38 + 2 * q^40 - 7 * q^41 - 4 * q^42 - 17 * q^43 - 11 * q^44 + 3 * q^45 - 7 * q^46 + 5 * q^47 - 4 * q^48 + 3 * q^49 - 9 * q^50 - 9 * q^51 - q^54 - 5 * q^55 + 3 * q^56 + 22 * q^57 - 3 * q^58 - 17 * q^59 - 5 * q^60 + 3 * q^61 - 2 * q^62 + q^63 + 3 * q^64 + 17 * q^66 - 21 * q^67 - 2 * q^68 + 21 * q^69 + 2 * q^70 + 16 * q^71 + q^72 + q^73 + 12 * q^75 - 13 * q^76 - 11 * q^77 + 10 * q^79 + 2 * q^80 + 3 * q^81 - 7 * q^82 - q^83 - 4 * q^84 - 13 * q^85 - 17 * q^86 - 3 * q^87 - 11 * q^88 + 4 * q^89 + 3 * q^90 - 7 * q^92 - 9 * q^93 + 5 * q^94 - 11 * q^95 - 4 * q^96 - 19 * q^97 + 3 * q^98 - 13 * 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
$3$	−2.80194	−1.61770	−0.808850	−	0.588015i	$-0.799909\pi$
$3$	−2.80194	−1.61770	−0.808850	+	0.588015i	$0.799909\pi$
$4$	1.00000	0.500000
$5$	0.554958	0.248185	0.124092	−	0.992271i	$-0.460398\pi$
$5$	0.554958	0.248185	0.124092	+	0.992271i	$0.460398\pi$
$6$	−2.80194	−1.14389
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	4.85086	1.61695
$10$	0.554958	0.175493
$11$	−5.24698	−1.58202	−0.791012	−	0.611801i	$-0.790445\pi$
$11$	−5.24698	−1.58202	−0.791012	+	0.611801i	$0.790445\pi$
$12$	−2.80194	−0.808850
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−1.55496	−0.401488
$16$	1.00000	0.250000
$17$	7.23490	1.75472	0.877360	−	0.479832i	$-0.159302\pi$
$17$	7.23490	1.75472	0.877360	+	0.479832i	$0.159302\pi$
$18$	4.85086	1.14336
$19$	−5.80194	−1.33106	−0.665528	−	0.746373i	$-0.731794\pi$
$19$	−5.80194	−1.33106	−0.665528	+	0.746373i	$0.731794\pi$
$20$	0.554958	0.124092
$21$	−2.80194	−0.611433
$22$	−5.24698	−1.11866
$23$	−5.15883	−1.07569	−0.537846	−	0.843043i	$-0.680762\pi$
$23$	−5.15883	−1.07569	−0.537846	+	0.843043i	$0.680762\pi$
$24$	−2.80194	−0.571943
$25$	−4.69202	−0.938404
$26$	0	0
$27$	−5.18598	−0.998042
$28$	1.00000	0.188982
$29$	5.43296	1.00888	0.504438	−	0.863448i	$-0.331700\pi$
$29$	5.43296	1.00888	0.504438	+	0.863448i	$0.331700\pi$
$30$	−1.55496	−0.283895
$31$	5.54288	0.995530	0.497765	−	0.867312i	$-0.334154\pi$
$31$	5.54288	0.995530	0.497765	+	0.867312i	$0.334154\pi$
$32$	1.00000	0.176777
$33$	14.7017	2.55924
$34$	7.23490	1.24077
$35$	0.554958	0.0938050
$36$	4.85086	0.808476
$37$	−0.335126	−0.0550943	−0.0275472	−	0.999621i	$-0.508770\pi$
$37$	−0.335126	−0.0550943	−0.0275472	+	0.999621i	$0.508770\pi$
$38$	−5.80194	−0.941199
$39$	0	0
$40$	0.554958	0.0877466
$41$	−3.11529	−0.486527	−0.243264	−	0.969960i	$-0.578218\pi$
$41$	−3.11529	−0.486527	−0.243264	+	0.969960i	$0.578218\pi$
$42$	−2.80194	−0.432348
$43$	−6.91185	−1.05405	−0.527024	−	0.849850i	$-0.676692\pi$
$43$	−6.91185	−1.05405	−0.527024	+	0.849850i	$0.676692\pi$
$44$	−5.24698	−0.791012
$45$	2.69202	0.401303
$46$	−5.15883	−0.760629
$47$	−5.56465	−0.811687	−0.405844	−	0.913943i	$-0.633022\pi$
$47$	−5.56465	−0.811687	−0.405844	+	0.913943i	$0.633022\pi$
$48$	−2.80194	−0.404425
$49$	1.00000	0.142857
$50$	−4.69202	−0.663552
$51$	−20.2717	−2.83861
$52$	0	0
$53$	−7.78986	−1.07002	−0.535010	−	0.844846i	$-0.679692\pi$
$53$	−7.78986	−1.07002	−0.535010	+	0.844846i	$0.679692\pi$
$54$	−5.18598	−0.705723
$55$	−2.91185	−0.392634
$56$	1.00000	0.133631
$57$	16.2567	2.15325
$58$	5.43296	0.713383
$59$	−7.24698	−0.943476	−0.471738	−	0.881739i	$-0.656373\pi$
$59$	−7.24698	−0.943476	−0.471738	+	0.881739i	$0.656373\pi$
$60$	−1.55496	−0.200744
$61$	8.45473	1.08252	0.541259	−	0.840856i	$-0.317948\pi$
$61$	8.45473	1.08252	0.541259	+	0.840856i	$0.317948\pi$
$62$	5.54288	0.703946
$63$	4.85086	0.611150
$64$	1.00000	0.125000
$65$	0	0
$66$	14.7017	1.80966
$67$	−2.59419	−0.316930	−0.158465	−	0.987365i	$-0.550655\pi$
$67$	−2.59419	−0.316930	−0.158465	+	0.987365i	$0.550655\pi$
$68$	7.23490	0.877360
$69$	14.4547	1.74015
$70$	0.554958	0.0663302
$71$	9.18060	1.08954	0.544769	−	0.838586i	$-0.316617\pi$
$71$	9.18060	1.08954	0.544769	+	0.838586i	$0.316617\pi$
$72$	4.85086	0.571679
$73$	−4.29590	−0.502797	−0.251398	−	0.967884i	$-0.580890\pi$
$73$	−4.29590	−0.502797	−0.251398	+	0.967884i	$0.580890\pi$
$74$	−0.335126	−0.0389576
$75$	13.1468	1.51806
$76$	−5.80194	−0.665528
$77$	−5.24698	−0.597949
$78$	0	0
$79$	−4.00969	−0.451125	−0.225563	−	0.974229i	$-0.572422\pi$
$79$	−4.00969	−0.451125	−0.225563	+	0.974229i	$0.572422\pi$
$80$	0.554958	0.0620462
$81$	−0.0217703	−0.00241892
$82$	−3.11529	−0.344027
$83$	8.36658	0.918352	0.459176	−	0.888345i	$-0.348145\pi$
$83$	8.36658	0.918352	0.459176	+	0.888345i	$0.348145\pi$
$84$	−2.80194	−0.305716
$85$	4.01507	0.435495
$86$	−6.91185	−0.745324
$87$	−15.2228	−1.63206
$88$	−5.24698	−0.559330
$89$	2.11529	0.224221	0.112110	−	0.993696i	$-0.464239\pi$
$89$	2.11529	0.224221	0.112110	+	0.993696i	$0.464239\pi$
$90$	2.69202	0.283764
$91$	0	0
$92$	−5.15883	−0.537846
$93$	−15.5308	−1.61047
$94$	−5.56465	−0.573949
$95$	−3.21983	−0.330348
$96$	−2.80194	−0.285972
$97$	−15.9269	−1.61713	−0.808567	−	0.588404i	$-0.799756\pi$
$97$	−15.9269	−1.61713	−0.808567	+	0.588404i	$0.799756\pi$
$98$	1.00000	0.101015
$99$	−25.4523	−2.55806
$100$	−4.69202	−0.469202
$101$	−11.7385	−1.16803	−0.584014	−	0.811743i	$-0.698519\pi$
$101$	−11.7385	−1.16803	−0.584014	+	0.811743i	$0.698519\pi$
$102$	−20.2717	−2.00720
$103$	15.6799	1.54499	0.772495	−	0.635021i	$-0.219008\pi$
$103$	15.6799	1.54499	0.772495	+	0.635021i	$0.219008\pi$
$104$	0	0
$105$	−1.55496	−0.151748
$106$	−7.78986	−0.756618
$107$	−10.3569	−1.00124	−0.500619	−	0.865667i	$-0.666894\pi$
$107$	−10.3569	−1.00124	−0.500619	+	0.865667i	$0.666894\pi$
$108$	−5.18598	−0.499021
$109$	−17.6528	−1.69083	−0.845415	−	0.534109i	$-0.820647\pi$
$109$	−17.6528	−1.69083	−0.845415	+	0.534109i	$0.820647\pi$
$110$	−2.91185	−0.277634
$111$	0.939001	0.0891260
$112$	1.00000	0.0944911
$113$	−19.2010	−1.80628	−0.903141	−	0.429344i	$-0.858745\pi$
$113$	−19.2010	−1.80628	−0.903141	+	0.429344i	$0.858745\pi$
$114$	16.2567	1.52258
$115$	−2.86294	−0.266970
$116$	5.43296	0.504438
$117$	0	0
$118$	−7.24698	−0.667139
$119$	7.23490	0.663222
$120$	−1.55496	−0.141948
$121$	16.5308	1.50280
$122$	8.45473	0.765455
$123$	8.72886	0.787055
$124$	5.54288	0.497765
$125$	−5.37867	−0.481083
$126$	4.85086	0.432149
$127$	−5.70410	−0.506157	−0.253079	−	0.967446i	$-0.581443\pi$
$127$	−5.70410	−0.506157	−0.253079	+	0.967446i	$0.581443\pi$
$128$	1.00000	0.0883883
$129$	19.3666	1.70513
$130$	0	0
$131$	−15.4306	−1.34817	−0.674087	−	0.738652i	$-0.735463\pi$
$131$	−15.4306	−1.34817	−0.674087	+	0.738652i	$0.735463\pi$
$132$	14.7017	1.27962
$133$	−5.80194	−0.503092
$134$	−2.59419	−0.224104
$135$	−2.87800	−0.247699
$136$	7.23490	0.620387
$137$	−15.8116	−1.35088	−0.675439	−	0.737416i	$-0.736046\pi$
$137$	−15.8116	−1.35088	−0.675439	+	0.737416i	$0.736046\pi$
$138$	14.4547	1.23047
$139$	−1.78017	−0.150992	−0.0754959	−	0.997146i	$-0.524054\pi$
$139$	−1.78017	−0.150992	−0.0754959	+	0.997146i	$0.524054\pi$
$140$	0.554958	0.0469025
$141$	15.5918	1.31307
$142$	9.18060	0.770419
$143$	0	0
$144$	4.85086	0.404238
$145$	3.01507	0.250388
$146$	−4.29590	−0.355531
$147$	−2.80194	−0.231100
$148$	−0.335126	−0.0275472
$149$	−6.94869	−0.569259	−0.284629	−	0.958638i	$-0.591871\pi$
$149$	−6.94869	−0.569259	−0.284629	+	0.958638i	$0.591871\pi$
$150$	13.1468	1.07343
$151$	−22.8823	−1.86214	−0.931068	−	0.364845i	$-0.881122\pi$
$151$	−22.8823	−1.86214	−0.931068	+	0.364845i	$0.881122\pi$
$152$	−5.80194	−0.470599
$153$	35.0954	2.83730
$154$	−5.24698	−0.422814
$155$	3.07606	0.247075
$156$	0	0
$157$	0.401501	0.0320433	0.0160216	−	0.999872i	$-0.494900\pi$
$157$	0.401501	0.0320433	0.0160216	+	0.999872i	$0.494900\pi$
$158$	−4.00969	−0.318994
$159$	21.8267	1.73097
$160$	0.554958	0.0438733
$161$	−5.15883	−0.406573
$162$	−0.0217703	−0.00171043
$163$	−2.01746	−0.158020	−0.0790098	−	0.996874i	$-0.525176\pi$
$163$	−2.01746	−0.158020	−0.0790098	+	0.996874i	$0.525176\pi$
$164$	−3.11529	−0.243264
$165$	8.15883	0.635164
$166$	8.36658	0.649373
$167$	−6.18060	−0.478269	−0.239135	−	0.970986i	$-0.576864\pi$
$167$	−6.18060	−0.478269	−0.239135	+	0.970986i	$0.576864\pi$
$168$	−2.80194	−0.216174
$169$	0	0
$170$	4.01507	0.307941
$171$	−28.1444	−2.15225
$172$	−6.91185	−0.527024
$173$	25.3763	1.92932	0.964661	−	0.263494i	$-0.0848748\pi$
$173$	25.3763	1.92932	0.964661	+	0.263494i	$0.0848748\pi$
$174$	−15.2228	−1.15404
$175$	−4.69202	−0.354683
$176$	−5.24698	−0.395506
$177$	20.3056	1.52626
$178$	2.11529	0.158548
$179$	2.83446	0.211858	0.105929	−	0.994374i	$-0.466218\pi$
$179$	2.83446	0.211858	0.105929	+	0.994374i	$0.466218\pi$
$180$	2.69202	0.200651
$181$	−9.57971	−0.712054	−0.356027	−	0.934476i	$-0.615869\pi$
$181$	−9.57971	−0.712054	−0.356027	+	0.934476i	$0.615869\pi$
$182$	0	0
$183$	−23.6896	−1.75119
$184$	−5.15883	−0.380314
$185$	−0.185981	−0.0136736
$186$	−15.5308	−1.13877
$187$	−37.9614	−2.77601
$188$	−5.56465	−0.405844
$189$	−5.18598	−0.377225
$190$	−3.21983	−0.233591
$191$	19.5851	1.41713	0.708564	−	0.705647i	$-0.249343\pi$
$191$	19.5851	1.41713	0.708564	+	0.705647i	$0.249343\pi$
$192$	−2.80194	−0.202212
$193$	−6.16123	−0.443495	−0.221747	−	0.975104i	$-0.571176\pi$
$193$	−6.16123	−0.443495	−0.221747	+	0.975104i	$0.571176\pi$
$194$	−15.9269	−1.14349
$195$	0	0
$196$	1.00000	0.0714286
$197$	−6.03252	−0.429800	−0.214900	−	0.976636i	$-0.568942\pi$
$197$	−6.03252	−0.429800	−0.214900	+	0.976636i	$0.568942\pi$
$198$	−25.4523	−1.80882
$199$	12.2513	0.868471	0.434236	−	0.900799i	$-0.357019\pi$
$199$	12.2513	0.868471	0.434236	+	0.900799i	$0.357019\pi$
$200$	−4.69202	−0.331776
$201$	7.26875	0.512698
$202$	−11.7385	−0.825921
$203$	5.43296	0.381319
$204$	−20.2717	−1.41931
$205$	−1.72886	−0.120749
$206$	15.6799	1.09247
$207$	−25.0248	−1.73934
$208$	0	0
$209$	30.4426	2.10576
$210$	−1.55496	−0.107302
$211$	−18.7168	−1.28852	−0.644258	−	0.764808i	$-0.722834\pi$
$211$	−18.7168	−1.28852	−0.644258	+	0.764808i	$0.722834\pi$
$212$	−7.78986	−0.535010
$213$	−25.7235	−1.76254
$214$	−10.3569	−0.707983
$215$	−3.83579	−0.261599
$216$	−5.18598	−0.352861
$217$	5.54288	0.376275
$218$	−17.6528	−1.19560
$219$	12.0368	0.813374
$220$	−2.91185	−0.196317
$221$	0	0
$222$	0.939001	0.0630216
$223$	23.7114	1.58783	0.793916	−	0.608027i	$-0.208039\pi$
$223$	23.7114	1.58783	0.793916	+	0.608027i	$0.208039\pi$
$224$	1.00000	0.0668153
$225$	−22.7603	−1.51735
$226$	−19.2010	−1.27723
$227$	1.60925	0.106810	0.0534049	−	0.998573i	$-0.482993\pi$
$227$	1.60925	0.106810	0.0534049	+	0.998573i	$0.482993\pi$
$228$	16.2567	1.07662
$229$	−7.41657	−0.490101	−0.245050	−	0.969510i	$-0.578804\pi$
$229$	−7.41657	−0.490101	−0.245050	+	0.969510i	$0.578804\pi$
$230$	−2.86294	−0.188776
$231$	14.7017	0.967302
$232$	5.43296	0.356691
$233$	22.9922	1.50627	0.753136	−	0.657865i	$-0.228540\pi$
$233$	22.9922	1.50627	0.753136	+	0.657865i	$0.228540\pi$
$234$	0	0
$235$	−3.08815	−0.201448
$236$	−7.24698	−0.471738
$237$	11.2349	0.729785
$238$	7.23490	0.468969
$239$	29.4359	1.90405	0.952026	−	0.306016i	$-0.0989960\pi$
$239$	29.4359	1.90405	0.952026	+	0.306016i	$0.0989960\pi$
$240$	−1.55496	−0.100372
$241$	−16.3080	−1.05049	−0.525245	−	0.850951i	$-0.676026\pi$
$241$	−16.3080	−1.05049	−0.525245	+	0.850951i	$0.676026\pi$
$242$	16.5308	1.06264
$243$	15.6189	1.00196
$244$	8.45473	0.541259
$245$	0.554958	0.0354550
$246$	8.72886	0.556532
$247$	0	0
$248$	5.54288	0.351973
$249$	−23.4426	−1.48562
$250$	−5.37867	−0.340177
$251$	3.03684	0.191683	0.0958417	−	0.995397i	$-0.469446\pi$
$251$	3.03684	0.191683	0.0958417	+	0.995397i	$0.469446\pi$
$252$	4.85086	0.305575
$253$	27.0683	1.70177
$254$	−5.70410	−0.357907
$255$	−11.2500	−0.704500
$256$	1.00000	0.0625000
$257$	9.93900	0.619978	0.309989	−	0.950740i	$-0.399675\pi$
$257$	9.93900	0.619978	0.309989	+	0.950740i	$0.399675\pi$
$258$	19.3666	1.20571
$259$	−0.335126	−0.0208237
$260$	0	0
$261$	26.3545	1.63130
$262$	−15.4306	−0.953304
$263$	8.59850	0.530206	0.265103	−	0.964220i	$-0.414594\pi$
$263$	8.59850	0.530206	0.265103	+	0.964220i	$0.414594\pi$
$264$	14.7017	0.904828
$265$	−4.32304	−0.265562
$266$	−5.80194	−0.355740
$267$	−5.92692	−0.362722
$268$	−2.59419	−0.158465
$269$	−17.1051	−1.04292	−0.521459	−	0.853276i	$-0.674612\pi$
$269$	−17.1051	−1.04292	−0.521459	+	0.853276i	$0.674612\pi$
$270$	−2.87800	−0.175150
$271$	−18.3220	−1.11298	−0.556490	−	0.830854i	$-0.687852\pi$
$271$	−18.3220	−1.11298	−0.556490	+	0.830854i	$0.687852\pi$
$272$	7.23490	0.438680
$273$	0	0
$274$	−15.8116	−0.955215
$275$	24.6189	1.48458
$276$	14.4547	0.870073
$277$	−14.3884	−0.864512	−0.432256	−	0.901751i	$-0.642282\pi$
$277$	−14.3884	−0.864512	−0.432256	+	0.901751i	$0.642282\pi$
$278$	−1.78017	−0.106767
$279$	26.8877	1.60972
$280$	0.554958	0.0331651
$281$	−1.14914	−0.0685522	−0.0342761	−	0.999412i	$-0.510913\pi$
$281$	−1.14914	−0.0685522	−0.0342761	+	0.999412i	$0.510913\pi$
$282$	15.5918	0.928478
$283$	3.21552	0.191143	0.0955714	−	0.995423i	$-0.469532\pi$
$283$	3.21552	0.191143	0.0955714	+	0.995423i	$0.469532\pi$
$284$	9.18060	0.544769
$285$	9.02177	0.534404
$286$	0	0
$287$	−3.11529	−0.183890
$288$	4.85086	0.285839
$289$	35.3437	2.07904
$290$	3.01507	0.177051
$291$	44.6262	2.61604
$292$	−4.29590	−0.251398
$293$	23.5646	1.37666	0.688331	−	0.725397i	$-0.258344\pi$
$293$	23.5646	1.37666	0.688331	+	0.725397i	$0.258344\pi$
$294$	−2.80194	−0.163412
$295$	−4.02177	−0.234157
$296$	−0.335126	−0.0194788
$297$	27.2107	1.57893
$298$	−6.94869	−0.402527
$299$	0	0
$300$	13.1468	0.759028
$301$	−6.91185	−0.398393
$302$	−22.8823	−1.31673
$303$	32.8907	1.88952
$304$	−5.80194	−0.332764
$305$	4.69202	0.268664
$306$	35.0954	2.00627
$307$	10.7463	0.613325	0.306662	−	0.951818i	$-0.400788\pi$
$307$	10.7463	0.613325	0.306662	+	0.951818i	$0.400788\pi$
$308$	−5.24698	−0.298974
$309$	−43.9342	−2.49933
$310$	3.07606	0.174709
$311$	9.05429	0.513422	0.256711	−	0.966488i	$-0.417361\pi$
$311$	9.05429	0.513422	0.256711	+	0.966488i	$0.417361\pi$
$312$	0	0
$313$	11.1424	0.629808	0.314904	−	0.949124i	$-0.398028\pi$
$313$	11.1424	0.629808	0.314904	+	0.949124i	$0.398028\pi$
$314$	0.401501	0.0226580
$315$	2.69202	0.151678
$316$	−4.00969	−0.225563
$317$	26.0887	1.46529	0.732645	−	0.680611i	$-0.238286\pi$
$317$	26.0887	1.46529	0.732645	+	0.680611i	$0.238286\pi$
$318$	21.8267	1.22398
$319$	−28.5066	−1.59606
$320$	0.554958	0.0310231
$321$	29.0194	1.61970
$322$	−5.15883	−0.287491
$323$	−41.9764	−2.33563
$324$	−0.0217703	−0.00120946
$325$	0	0
$326$	−2.01746	−0.111737
$327$	49.4620	2.73526
$328$	−3.11529	−0.172013
$329$	−5.56465	−0.306789
$330$	8.15883	0.449129
$331$	−20.9782	−1.15307	−0.576534	−	0.817073i	$-0.695595\pi$
$331$	−20.9782	−1.15307	−0.576534	+	0.817073i	$0.695595\pi$
$332$	8.36658	0.459176
$333$	−1.62565	−0.0890848
$334$	−6.18060	−0.338188
$335$	−1.43967	−0.0786573
$336$	−2.80194	−0.152858
$337$	29.6926	1.61746	0.808730	−	0.588180i	$-0.200155\pi$
$337$	29.6926	1.61746	0.808730	+	0.588180i	$0.200155\pi$
$338$	0	0
$339$	53.8001	2.92202
$340$	4.01507	0.217747
$341$	−29.0834	−1.57495
$342$	−28.1444	−1.52187
$343$	1.00000	0.0539949
$344$	−6.91185	−0.372662
$345$	8.02177	0.431878
$346$	25.3763	1.36424
$347$	−14.3013	−0.767733	−0.383866	−	0.923389i	$-0.625408\pi$
$347$	−14.3013	−0.767733	−0.383866	+	0.923389i	$0.625408\pi$
$348$	−15.2228	−0.816029
$349$	3.02608	0.161982	0.0809912	−	0.996715i	$-0.474191\pi$
$349$	3.02608	0.161982	0.0809912	+	0.996715i	$0.474191\pi$
$350$	−4.69202	−0.250799
$351$	0	0
$352$	−5.24698	−0.279665
$353$	−22.6209	−1.20399	−0.601993	−	0.798501i	$-0.705627\pi$
$353$	−22.6209	−1.20399	−0.601993	+	0.798501i	$0.705627\pi$
$354$	20.3056	1.07923
$355$	5.09485	0.270407
$356$	2.11529	0.112110
$357$	−20.2717	−1.07289
$358$	2.83446	0.149806
$359$	16.9162	0.892801	0.446401	−	0.894833i	$-0.352706\pi$
$359$	16.9162	0.892801	0.446401	+	0.894833i	$0.352706\pi$
$360$	2.69202	0.141882
$361$	14.6625	0.771710
$362$	−9.57971	−0.503499
$363$	−46.3183	−2.43108
$364$	0	0
$365$	−2.38404	−0.124787
$366$	−23.6896	−1.23828
$367$	−9.02044	−0.470863	−0.235432	−	0.971891i	$-0.575650\pi$
$367$	−9.02044	−0.470863	−0.235432	+	0.971891i	$0.575650\pi$
$368$	−5.15883	−0.268923
$369$	−15.1118	−0.786691
$370$	−0.185981	−0.00966868
$371$	−7.78986	−0.404429
$372$	−15.5308	−0.805234
$373$	12.3254	0.638187	0.319093	−	0.947723i	$-0.396622\pi$
$373$	12.3254	0.638187	0.319093	+	0.947723i	$0.396622\pi$
$374$	−37.9614	−1.96294
$375$	15.0707	0.778247
$376$	−5.56465	−0.286975
$377$	0	0
$378$	−5.18598	−0.266738
$379$	7.61894	0.391359	0.195679	−	0.980668i	$-0.437309\pi$
$379$	7.61894	0.391359	0.195679	+	0.980668i	$0.437309\pi$
$380$	−3.21983	−0.165174
$381$	15.9825	0.818810
$382$	19.5851	1.00206
$383$	13.0610	0.667386	0.333693	−	0.942682i	$-0.391705\pi$
$383$	13.0610	0.667386	0.333693	+	0.942682i	$0.391705\pi$
$384$	−2.80194	−0.142986
$385$	−2.91185	−0.148402
$386$	−6.16123	−0.313598
$387$	−33.5284	−1.70434
$388$	−15.9269	−0.808567
$389$	16.0127	0.811875	0.405937	−	0.913901i	$-0.366945\pi$
$389$	16.0127	0.811875	0.405937	+	0.913901i	$0.366945\pi$
$390$	0	0
$391$	−37.3236	−1.88754
$392$	1.00000	0.0505076
$393$	43.2355	2.18094
$394$	−6.03252	−0.303914
$395$	−2.22521	−0.111962
$396$	−25.4523	−1.27903
$397$	−20.0170	−1.00462	−0.502312	−	0.864687i	$-0.667517\pi$
$397$	−20.0170	−1.00462	−0.502312	+	0.864687i	$0.667517\pi$
$398$	12.2513	0.614102
$399$	16.2567	0.813851
$400$	−4.69202	−0.234601
$401$	−25.5773	−1.27727	−0.638635	−	0.769510i	$-0.720501\pi$
$401$	−25.5773	−1.27727	−0.638635	+	0.769510i	$0.720501\pi$
$402$	7.26875	0.362532
$403$	0	0
$404$	−11.7385	−0.584014
$405$	−0.0120816	−0.000600339 0
$406$	5.43296	0.269633
$407$	1.75840	0.0871605
$408$	−20.2717	−1.00360
$409$	22.7332	1.12408	0.562041	−	0.827109i	$-0.310016\pi$
$409$	22.7332	1.12408	0.562041	+	0.827109i	$0.310016\pi$
$410$	−1.72886	−0.0853822
$411$	44.3032	2.18532
$412$	15.6799	0.772495
$413$	−7.24698	−0.356601
$414$	−25.0248	−1.22990
$415$	4.64310	0.227921
$416$	0	0
$417$	4.98792	0.244259
$418$	30.4426	1.48900
$419$	24.3183	1.18802	0.594012	−	0.804456i	$-0.297543\pi$
$419$	24.3183	1.18802	0.594012	+	0.804456i	$0.297543\pi$
$420$	−1.55496	−0.0758742
$421$	17.7313	0.864168	0.432084	−	0.901833i	$-0.357778\pi$
$421$	17.7313	0.864168	0.432084	+	0.901833i	$0.357778\pi$
$422$	−18.7168	−0.911118
$423$	−26.9933	−1.31246
$424$	−7.78986	−0.378309
$425$	−33.9463	−1.64664
$426$	−25.7235	−1.24631
$427$	8.45473	0.409153
$428$	−10.3569	−0.500619
$429$	0	0
$430$	−3.83579	−0.184978
$431$	20.8116	1.00246	0.501230	−	0.865314i	$-0.332881\pi$
$431$	20.8116	1.00246	0.501230	+	0.865314i	$0.332881\pi$
$432$	−5.18598	−0.249511
$433$	8.53989	0.410401	0.205201	−	0.978720i	$-0.434215\pi$
$433$	8.53989	0.410401	0.205201	+	0.978720i	$0.434215\pi$
$434$	5.54288	0.266067
$435$	−8.44803	−0.405052
$436$	−17.6528	−0.845415
$437$	29.9312	1.43180
$438$	12.0368	0.575142
$439$	−35.1129	−1.67585	−0.837924	−	0.545787i	$-0.816231\pi$
$439$	−35.1129	−1.67585	−0.837924	+	0.545787i	$0.816231\pi$
$440$	−2.91185	−0.138817
$441$	4.85086	0.230993
$442$	0	0
$443$	20.7918	0.987847	0.493924	−	0.869505i	$-0.335562\pi$
$443$	20.7918	0.987847	0.493924	+	0.869505i	$0.335562\pi$
$444$	0.939001	0.0445630
$445$	1.17390	0.0556482
$446$	23.7114	1.12277
$447$	19.4698	0.920890
$448$	1.00000	0.0472456
$449$	−0.977165	−0.0461153	−0.0230576	−	0.999734i	$-0.507340\pi$
$449$	−0.977165	−0.0461153	−0.0230576	+	0.999734i	$0.507340\pi$
$450$	−22.7603	−1.07293
$451$	16.3459	0.769697
$452$	−19.2010	−0.903141
$453$	64.1148	3.01238
$454$	1.60925	0.0755260
$455$	0	0
$456$	16.2567	0.761288
$457$	−31.9409	−1.49413	−0.747067	−	0.664749i	$-0.768538\pi$
$457$	−31.9409	−1.49413	−0.747067	+	0.664749i	$0.768538\pi$
$458$	−7.41657	−0.346553
$459$	−37.5200	−1.75129
$460$	−2.86294	−0.133485
$461$	−10.1414	−0.472331	−0.236165	−	0.971713i	$-0.575891\pi$
$461$	−10.1414	−0.472331	−0.236165	+	0.971713i	$0.575891\pi$
$462$	14.7017	0.683985
$463$	25.8049	1.19926	0.599628	−	0.800279i	$-0.295315\pi$
$463$	25.8049	1.19926	0.599628	+	0.800279i	$0.295315\pi$
$464$	5.43296	0.252219
$465$	−8.61894	−0.399694
$466$	22.9922	1.06509
$467$	−25.2784	−1.16975	−0.584873	−	0.811125i	$-0.698856\pi$
$467$	−25.2784	−1.16975	−0.584873	+	0.811125i	$0.698856\pi$
$468$	0	0
$469$	−2.59419	−0.119788
$470$	−3.08815	−0.142446
$471$	−1.12498	−0.0518364
$472$	−7.24698	−0.333569
$473$	36.2664	1.66753
$474$	11.2349	0.516036
$475$	27.2228	1.24907
$476$	7.23490	0.331611
$477$	−37.7875	−1.73017
$478$	29.4359	1.34637
$479$	8.63879	0.394716	0.197358	−	0.980331i	$-0.436764\pi$
$479$	8.63879	0.394716	0.197358	+	0.980331i	$0.436764\pi$
$480$	−1.55496	−0.0709738
$481$	0	0
$482$	−16.3080	−0.742808
$483$	14.4547	0.657713
$484$	16.5308	0.751400
$485$	−8.83877	−0.401348
$486$	15.6189	0.708490
$487$	−20.4142	−0.925055	−0.462527	−	0.886605i	$-0.653057\pi$
$487$	−20.4142	−0.925055	−0.462527	+	0.886605i	$0.653057\pi$
$488$	8.45473	0.382728
$489$	5.65279	0.255628
$490$	0.554958	0.0250705
$491$	7.18359	0.324191	0.162095	−	0.986775i	$-0.448175\pi$
$491$	7.18359	0.324191	0.162095	+	0.986775i	$0.448175\pi$
$492$	8.72886	0.393527
$493$	39.3069	1.77029
$494$	0	0
$495$	−14.1250	−0.634871
$496$	5.54288	0.248883
$497$	9.18060	0.411806
$498$	−23.4426	−1.05049
$499$	−13.9892	−0.626245	−0.313122	−	0.949713i	$-0.601375\pi$
$499$	−13.9892	−0.626245	−0.313122	+	0.949713i	$0.601375\pi$
$500$	−5.37867	−0.240541
$501$	17.3177	0.773696
$502$	3.03684	0.135541
$503$	1.18492	0.0528328	0.0264164	−	0.999651i	$-0.491590\pi$
$503$	1.18492	0.0528328	0.0264164	+	0.999651i	$0.491590\pi$
$504$	4.85086	0.216074
$505$	−6.51440	−0.289887
$506$	27.0683	1.20333
$507$	0	0
$508$	−5.70410	−0.253079
$509$	0.214456	0.00950558	0.00475279	−	0.999989i	$-0.498487\pi$
$509$	0.214456	0.00950558	0.00475279	+	0.999989i	$0.498487\pi$
$510$	−11.2500	−0.498157
$511$	−4.29590	−0.190039
$512$	1.00000	0.0441942
$513$	30.0887	1.32845
$514$	9.93900	0.438391
$515$	8.70171	0.383443
$516$	19.3666	0.852566
$517$	29.1976	1.28411
$518$	−0.335126	−0.0147246
$519$	−71.1027	−3.12106
$520$	0	0
$521$	10.1793	0.445962	0.222981	−	0.974823i	$-0.428421\pi$
$521$	10.1793	0.445962	0.222981	+	0.974823i	$0.428421\pi$
$522$	26.3545	1.15351
$523$	−4.21850	−0.184462	−0.0922312	−	0.995738i	$-0.529400\pi$
$523$	−4.21850	−0.184462	−0.0922312	+	0.995738i	$0.529400\pi$
$524$	−15.4306	−0.674087
$525$	13.1468	0.573771
$526$	8.59850	0.374912
$527$	40.1021	1.74688
$528$	14.7017	0.639810
$529$	3.61356	0.157111
$530$	−4.32304	−0.187781
$531$	−35.1540	−1.52556
$532$	−5.80194	−0.251546
$533$	0	0
$534$	−5.92692	−0.256483
$535$	−5.74764	−0.248492
$536$	−2.59419	−0.112052
$537$	−7.94198	−0.342722
$538$	−17.1051	−0.737455
$539$	−5.24698	−0.226003
$540$	−2.87800	−0.123849
$541$	10.5743	0.454626	0.227313	−	0.973822i	$-0.427006\pi$
$541$	10.5743	0.454626	0.227313	+	0.973822i	$0.427006\pi$
$542$	−18.3220	−0.786996
$543$	26.8418	1.15189
$544$	7.23490	0.310194
$545$	−9.79656	−0.419639
$546$	0	0
$547$	−10.8804	−0.465212	−0.232606	−	0.972571i	$-0.574725\pi$
$547$	−10.8804	−0.465212	−0.232606	+	0.972571i	$0.574725\pi$
$548$	−15.8116	−0.675439
$549$	41.0127	1.75038
$550$	24.6189	1.04976
$551$	−31.5217	−1.34287
$552$	14.4547	0.615234
$553$	−4.00969	−0.170509
$554$	−14.3884	−0.611303
$555$	0.521106	0.0221197
$556$	−1.78017	−0.0754959
$557$	0.967476	0.0409933	0.0204966	−	0.999790i	$-0.493475\pi$
$557$	0.967476	0.0409933	0.0204966	+	0.999790i	$0.493475\pi$
$558$	26.8877	1.13825
$559$	0	0
$560$	0.554958	0.0234513
$561$	106.365	4.49075
$562$	−1.14914	−0.0484738
$563$	−36.3153	−1.53051	−0.765253	−	0.643729i	$-0.777386\pi$
$563$	−36.3153	−1.53051	−0.765253	+	0.643729i	$0.777386\pi$
$564$	15.5918	0.656533
$565$	−10.6558	−0.448292
$566$	3.21552	0.135158
$567$	−0.0217703	−0.000914265 0
$568$	9.18060	0.385210
$569$	−38.8219	−1.62750	−0.813749	−	0.581216i	$-0.802577\pi$
$569$	−38.8219	−1.62750	−0.813749	+	0.581216i	$0.802577\pi$
$570$	9.02177	0.377880
$571$	18.5730	0.777256	0.388628	−	0.921395i	$-0.372949\pi$
$571$	18.5730	0.777256	0.388628	+	0.921395i	$0.372949\pi$
$572$	0	0
$573$	−54.8762	−2.29249
$574$	−3.11529	−0.130030
$575$	24.2054	1.00943
$576$	4.85086	0.202119
$577$	−30.5066	−1.27001	−0.635004	−	0.772509i	$-0.719001\pi$
$577$	−30.5066	−1.27001	−0.635004	+	0.772509i	$0.719001\pi$
$578$	35.3437	1.47011
$579$	17.2634	0.717441
$580$	3.01507	0.125194
$581$	8.36658	0.347104
$582$	44.6262	1.84982
$583$	40.8732	1.69280
$584$	−4.29590	−0.177765
$585$	0	0
$586$	23.5646	0.973447
$587$	−0.956459	−0.0394773	−0.0197387	−	0.999805i	$-0.506283\pi$
$587$	−0.956459	−0.0394773	−0.0197387	+	0.999805i	$0.506283\pi$
$588$	−2.80194	−0.115550
$589$	−32.1594	−1.32511
$590$	−4.02177	−0.165574
$591$	16.9028	0.695286
$592$	−0.335126	−0.0137736
$593$	−15.0543	−0.618206	−0.309103	−	0.951029i	$-0.600029\pi$
$593$	−15.0543	−0.618206	−0.309103	+	0.951029i	$0.600029\pi$
$594$	27.2107	1.11647
$595$	4.01507	0.164602
$596$	−6.94869	−0.284629
$597$	−34.3274	−1.40493
$598$	0	0
$599$	7.76164	0.317132	0.158566	−	0.987348i	$-0.449313\pi$
$599$	7.76164	0.317132	0.158566	+	0.987348i	$0.449313\pi$
$600$	13.1468	0.536714
$601$	−15.2218	−0.620908	−0.310454	−	0.950588i	$-0.600481\pi$
$601$	−15.2218	−0.620908	−0.310454	+	0.950588i	$0.600481\pi$
$602$	−6.91185	−0.281706
$603$	−12.5840	−0.512461
$604$	−22.8823	−0.931068
$605$	9.17390	0.372972
$606$	32.8907	1.33609
$607$	6.94677	0.281961	0.140980	−	0.990012i	$-0.454975\pi$
$607$	6.94677	0.281961	0.140980	+	0.990012i	$0.454975\pi$
$608$	−5.80194	−0.235300
$609$	−15.2228	−0.616860
$610$	4.69202	0.189974
$611$	0	0
$612$	35.0954	1.41865
$613$	24.7754	1.00067	0.500334	−	0.865832i	$-0.333211\pi$
$613$	24.7754	1.00067	0.500334	+	0.865832i	$0.333211\pi$
$614$	10.7463	0.433686
$615$	4.84415	0.195335
$616$	−5.24698	−0.211407
$617$	0.919624	0.0370227	0.0185113	−	0.999829i	$-0.494107\pi$
$617$	0.919624	0.0370227	0.0185113	+	0.999829i	$0.494107\pi$
$618$	−43.9342	−1.76729
$619$	−31.9715	−1.28504	−0.642522	−	0.766267i	$-0.722112\pi$
$619$	−31.9715	−1.28504	−0.642522	+	0.766267i	$0.722112\pi$
$620$	3.07606	0.123538
$621$	26.7536	1.07359
$622$	9.05429	0.363044
$623$	2.11529	0.0847474
$624$	0	0
$625$	20.4752	0.819007
$626$	11.1424	0.445341
$627$	−85.2984	−3.40649
$628$	0.401501	0.0160216
$629$	−2.42460	−0.0966751
$630$	2.69202	0.107253
$631$	−41.1275	−1.63726	−0.818630	−	0.574322i	$-0.805266\pi$
$631$	−41.1275	−1.63726	−0.818630	+	0.574322i	$0.805266\pi$
$632$	−4.00969	−0.159497
$633$	52.4432	2.08443
$634$	26.0887	1.03612
$635$	−3.16554	−0.125621
$636$	21.8267	0.865485
$637$	0	0
$638$	−28.5066	−1.12859
$639$	44.5338	1.76173
$640$	0.554958	0.0219366
$641$	−6.98984	−0.276082	−0.138041	−	0.990427i	$-0.544081\pi$
$641$	−6.98984	−0.276082	−0.138041	+	0.990427i	$0.544081\pi$
$642$	29.0194	1.14530
$643$	−24.3676	−0.960966	−0.480483	−	0.877004i	$-0.659539\pi$
$643$	−24.3676	−0.960966	−0.480483	+	0.877004i	$0.659539\pi$
$644$	−5.15883	−0.203287
$645$	10.7476	0.423188
$646$	−41.9764	−1.65154
$647$	1.12870	0.0443739	0.0221869	−	0.999754i	$-0.492937\pi$
$647$	1.12870	0.0443739	0.0221869	+	0.999754i	$0.492937\pi$
$648$	−0.0217703	−0.000855217 0
$649$	38.0248	1.49260
$650$	0	0
$651$	−15.5308	−0.608700
$652$	−2.01746	−0.0790098
$653$	20.7845	0.813360	0.406680	−	0.913571i	$-0.366686\pi$
$653$	20.7845	0.813360	0.406680	+	0.913571i	$0.366686\pi$
$654$	49.4620	1.93412
$655$	−8.56332	−0.334597
$656$	−3.11529	−0.121632
$657$	−20.8388	−0.812998
$658$	−5.56465	−0.216933
$659$	48.3497	1.88344	0.941719	−	0.336401i	$-0.109210\pi$
$659$	48.3497	1.88344	0.941719	+	0.336401i	$0.109210\pi$
$660$	8.15883	0.317582
$661$	10.4819	0.407698	0.203849	−	0.979002i	$-0.434655\pi$
$661$	10.4819	0.407698	0.203849	+	0.979002i	$0.434655\pi$
$662$	−20.9782	−0.815342
$663$	0	0
$664$	8.36658	0.324686
$665$	−3.21983	−0.124860
$666$	−1.62565	−0.0629925
$667$	−28.0277	−1.08524
$668$	−6.18060	−0.239135
$669$	−66.4379	−2.56864
$670$	−1.43967	−0.0556191
$671$	−44.3618	−1.71257
$672$	−2.80194	−0.108087
$673$	16.5652	0.638543	0.319271	−	0.947663i	$-0.396562\pi$
$673$	16.5652	0.638543	0.319271	+	0.947663i	$0.396562\pi$
$674$	29.6926	1.14372
$675$	24.3327	0.936567
$676$	0	0
$677$	5.80492	0.223101	0.111551	−	0.993759i	$-0.464418\pi$
$677$	5.80492	0.223101	0.111551	+	0.993759i	$0.464418\pi$
$678$	53.8001	2.06618
$679$	−15.9269	−0.611219
$680$	4.01507	0.153971
$681$	−4.50902	−0.172786
$682$	−29.0834	−1.11366
$683$	−19.3491	−0.740374	−0.370187	−	0.928957i	$-0.620706\pi$
$683$	−19.3491	−0.740374	−0.370187	+	0.928957i	$0.620706\pi$
$684$	−28.1444	−1.07613
$685$	−8.77479	−0.335268
$686$	1.00000	0.0381802
$687$	20.7808	0.792835
$688$	−6.91185	−0.263512
$689$	0	0
$690$	8.02177	0.305384
$691$	14.7952	0.562837	0.281419	−	0.959585i	$-0.409195\pi$
$691$	14.7952	0.562837	0.281419	+	0.959585i	$0.409195\pi$
$692$	25.3763	0.964661
$693$	−25.4523	−0.966854
$694$	−14.3013	−0.542869
$695$	−0.987918	−0.0374739
$696$	−15.2228	−0.577019
$697$	−22.5388	−0.853719
$698$	3.02608	0.114539
$699$	−64.4228	−2.43669
$700$	−4.69202	−0.177342
$701$	22.5797	0.852824	0.426412	−	0.904529i	$-0.359777\pi$
$701$	22.5797	0.852824	0.426412	+	0.904529i	$0.359777\pi$
$702$	0	0
$703$	1.94438	0.0733336
$704$	−5.24698	−0.197753
$705$	8.65279	0.325883
$706$	−22.6209	−0.851347
$707$	−11.7385	−0.441473
$708$	20.3056	0.763131
$709$	−19.3588	−0.727036	−0.363518	−	0.931587i	$-0.618424\pi$
$709$	−19.3588	−0.727036	−0.363518	+	0.931587i	$0.618424\pi$
$710$	5.09485	0.191206
$711$	−19.4504	−0.729448
$712$	2.11529	0.0792740
$713$	−28.5948	−1.07088
$714$	−20.2717	−0.758651
$715$	0	0
$716$	2.83446	0.105929
$717$	−82.4777	−3.08019
$718$	16.9162	0.631306
$719$	2.43727	0.0908949	0.0454475	−	0.998967i	$-0.485529\pi$
$719$	2.43727	0.0908949	0.0454475	+	0.998967i	$0.485529\pi$
$720$	2.69202	0.100326
$721$	15.6799	0.583951
$722$	14.6625	0.545681
$723$	45.6939	1.69938
$724$	−9.57971	−0.356027
$725$	−25.4916	−0.946733
$726$	−46.3183	−1.71903
$727$	49.2863	1.82793	0.913964	−	0.405795i	$-0.133005\pi$
$727$	49.2863	1.82793	0.913964	+	0.405795i	$0.133005\pi$
$728$	0	0
$729$	−43.6980	−1.61844
$730$	−2.38404	−0.0882374
$731$	−50.0066	−1.84956
$732$	−23.6896	−0.875594
$733$	34.7657	1.28410	0.642050	−	0.766663i	$-0.278084\pi$
$733$	34.7657	1.28410	0.642050	+	0.766663i	$0.278084\pi$
$734$	−9.02044	−0.332951
$735$	−1.55496	−0.0573555
$736$	−5.15883	−0.190157
$737$	13.6116	0.501391
$738$	−15.1118	−0.556274
$739$	−29.6770	−1.09168	−0.545842	−	0.837888i	$-0.683790\pi$
$739$	−29.6770	−1.09168	−0.545842	+	0.837888i	$0.683790\pi$
$740$	−0.185981	−0.00683679
$741$	0	0
$742$	−7.78986	−0.285975
$743$	−33.9095	−1.24402	−0.622009	−	0.783010i	$-0.713683\pi$
$743$	−33.9095	−1.24402	−0.622009	+	0.783010i	$0.713683\pi$
$744$	−15.5308	−0.569387
$745$	−3.85623	−0.141281
$746$	12.3254	0.451266
$747$	40.5851	1.48493
$748$	−37.9614	−1.38800
$749$	−10.3569	−0.378433
$750$	15.0707	0.550304
$751$	13.8605	0.505778	0.252889	−	0.967495i	$-0.418619\pi$
$751$	13.8605	0.505778	0.252889	+	0.967495i	$0.418619\pi$
$752$	−5.56465	−0.202922
$753$	−8.50902	−0.310086
$754$	0	0
$755$	−12.6987	−0.462154
$756$	−5.18598	−0.188612
$757$	−18.6606	−0.678230	−0.339115	−	0.940745i	$-0.610128\pi$
$757$	−18.6606	−0.678230	−0.339115	+	0.940745i	$0.610128\pi$
$758$	7.61894	0.276732
$759$	−75.8437	−2.75295
$760$	−3.21983	−0.116796
$761$	−7.29291	−0.264368	−0.132184	−	0.991225i	$-0.542199\pi$
$761$	−7.29291	−0.264368	−0.132184	+	0.991225i	$0.542199\pi$
$762$	15.9825	0.578986
$763$	−17.6528	−0.639074
$764$	19.5851	0.708564
$765$	19.4765	0.704174
$766$	13.0610	0.471913
$767$	0	0
$768$	−2.80194	−0.101106
$769$	−9.62266	−0.347002	−0.173501	−	0.984834i	$-0.555508\pi$
$769$	−9.62266	−0.347002	−0.173501	+	0.984834i	$0.555508\pi$
$770$	−2.91185	−0.104936
$771$	−27.8485	−1.00294
$772$	−6.16123	−0.221747
$773$	36.7614	1.32221	0.661107	−	0.750291i	$-0.270087\pi$
$773$	36.7614	1.32221	0.661107	+	0.750291i	$0.270087\pi$
$774$	−33.5284	−1.20515
$775$	−26.0073	−0.934210
$776$	−15.9269	−0.571743
$777$	0.939001	0.0336865
$778$	16.0127	0.574082
$779$	18.0747	0.647595
$780$	0	0
$781$	−48.1704	−1.72367
$782$	−37.3236	−1.33469
$783$	−28.1752	−1.00690
$784$	1.00000	0.0357143
$785$	0.222816	0.00795266
$786$	43.2355	1.54216
$787$	3.62086	0.129070	0.0645349	−	0.997915i	$-0.479444\pi$
$787$	3.62086	0.129070	0.0645349	+	0.997915i	$0.479444\pi$
$788$	−6.03252	−0.214900
$789$	−24.0925	−0.857714
$790$	−2.22521	−0.0791694
$791$	−19.2010	−0.682711
$792$	−25.4523	−0.904409
$793$	0	0
$794$	−20.0170	−0.710376
$795$	12.1129	0.429600
$796$	12.2513	0.434236
$797$	−14.1951	−0.502815	−0.251408	−	0.967881i	$-0.580894\pi$
$797$	−14.1951	−0.502815	−0.251408	+	0.967881i	$0.580894\pi$
$798$	16.2567	0.575480
$799$	−40.2597	−1.42428
$800$	−4.69202	−0.165888
$801$	10.2610	0.362554
$802$	−25.5773	−0.903167
$803$	22.5405	0.795436
$804$	7.26875	0.256349
$805$	−2.86294	−0.100905
$806$	0	0
$807$	47.9275	1.68713
$808$	−11.7385	−0.412961
$809$	16.6243	0.584480	0.292240	−	0.956345i	$-0.405599\pi$
$809$	16.6243	0.584480	0.292240	+	0.956345i	$0.405599\pi$
$810$	−0.0120816	−0.000424504 0
$811$	−15.7178	−0.551928	−0.275964	−	0.961168i	$-0.588997\pi$
$811$	−15.7178	−0.551928	−0.275964	+	0.961168i	$0.588997\pi$
$812$	5.43296	0.190660
$813$	51.3370	1.80047
$814$	1.75840	0.0616318
$815$	−1.11960	−0.0392181
$816$	−20.2717	−0.709653
$817$	40.1021	1.40300
$818$	22.7332	0.794847
$819$	0	0
$820$	−1.72886	−0.0603743
$821$	−2.79954	−0.0977048	−0.0488524	−	0.998806i	$-0.515556\pi$
$821$	−2.79954	−0.0977048	−0.0488524	+	0.998806i	$0.515556\pi$
$822$	44.3032	1.54525
$823$	46.1885	1.61003	0.805015	−	0.593255i	$-0.202157\pi$
$823$	46.1885	1.61003	0.805015	+	0.593255i	$0.202157\pi$
$824$	15.6799	0.546237
$825$	−68.9807	−2.40160
$826$	−7.24698	−0.252155
$827$	14.9769	0.520798	0.260399	−	0.965501i	$-0.416146\pi$
$827$	14.9769	0.520798	0.260399	+	0.965501i	$0.416146\pi$
$828$	−25.0248	−0.869670
$829$	41.7101	1.44865	0.724325	−	0.689458i	$-0.242151\pi$
$829$	41.7101	1.44865	0.724325	+	0.689458i	$0.242151\pi$
$830$	4.64310	0.161164
$831$	40.3153	1.39852
$832$	0	0
$833$	7.23490	0.250674
$834$	4.98792	0.172717
$835$	−3.42998	−0.118699
$836$	30.4426	1.05288
$837$	−28.7453	−0.993581
$838$	24.3183	0.840060
$839$	−29.8944	−1.03207	−0.516035	−	0.856568i	$-0.672592\pi$
$839$	−29.8944	−1.03207	−0.516035	+	0.856568i	$0.672592\pi$
$840$	−1.55496	−0.0536512
$841$	0.517057	0.0178296
$842$	17.7313	0.611059
$843$	3.21983	0.110897
$844$	−18.7168	−0.644258
$845$	0	0
$846$	−26.9933	−0.928049
$847$	16.5308	0.568005
$848$	−7.78986	−0.267505
$849$	−9.00969	−0.309212
$850$	−33.9463	−1.16435
$851$	1.72886	0.0592645
$852$	−25.7235	−0.881272
$853$	−11.5321	−0.394852	−0.197426	−	0.980318i	$-0.563258\pi$
$853$	−11.5321	−0.394852	−0.197426	+	0.980318i	$0.563258\pi$
$854$	8.45473	0.289315
$855$	−15.6189	−0.534157
$856$	−10.3569	−0.353991
$857$	11.6246	0.397088	0.198544	−	0.980092i	$-0.436379\pi$
$857$	11.6246	0.397088	0.198544	+	0.980092i	$0.436379\pi$
$858$	0	0
$859$	−14.2440	−0.485999	−0.242999	−	0.970026i	$-0.578131\pi$
$859$	−14.2440	−0.485999	−0.242999	+	0.970026i	$0.578131\pi$
$860$	−3.83579	−0.130799
$861$	8.72886	0.297479
$862$	20.8116	0.708847
$863$	36.9396	1.25744	0.628719	−	0.777632i	$-0.283580\pi$
$863$	36.9396	1.25744	0.628719	+	0.777632i	$0.283580\pi$
$864$	−5.18598	−0.176431
$865$	14.0828	0.478829
$866$	8.53989	0.290197
$867$	−99.0310	−3.36327
$868$	5.54288	0.188137
$869$	21.0388	0.713691
$870$	−8.44803	−0.286415
$871$	0	0
$872$	−17.6528	−0.597799
$873$	−77.2592	−2.61483
$874$	29.9312	1.01244
$875$	−5.37867	−0.181832
$876$	12.0368	0.406687
$877$	22.0271	0.743804	0.371902	−	0.928272i	$-0.378706\pi$
$877$	22.0271	0.743804	0.371902	+	0.928272i	$0.378706\pi$
$878$	−35.1129	−1.18500
$879$	−66.0267	−2.22702
$880$	−2.91185	−0.0981586
$881$	−31.3454	−1.05605	−0.528027	−	0.849228i	$-0.677068\pi$
$881$	−31.3454	−1.05605	−0.528027	+	0.849228i	$0.677068\pi$
$882$	4.85086	0.163337
$883$	2.15452	0.0725054	0.0362527	−	0.999343i	$-0.488458\pi$
$883$	2.15452	0.0725054	0.0362527	+	0.999343i	$0.488458\pi$
$884$	0	0
$885$	11.2687	0.378795
$886$	20.7918	0.698513
$887$	27.2543	0.915109	0.457555	−	0.889182i	$-0.348725\pi$
$887$	27.2543	0.915109	0.457555	+	0.889182i	$0.348725\pi$
$888$	0.939001	0.0315108
$889$	−5.70410	−0.191309
$890$	1.17390	0.0393492
$891$	0.114228	0.00382679
$892$	23.7114	0.793916
$893$	32.2857	1.08040
$894$	19.4698	0.651167
$895$	1.57301	0.0525798
$896$	1.00000	0.0334077
$897$	0	0
$898$	−0.977165	−0.0326084
$899$	30.1142	1.00437
$900$	−22.7603	−0.758677
$901$	−56.3588	−1.87758
$902$	16.3459	0.544258
$903$	19.3666	0.644480
$904$	−19.2010	−0.638617
$905$	−5.31634	−0.176721
$906$	64.1148	2.13007
$907$	−5.08251	−0.168762	−0.0843809	−	0.996434i	$-0.526891\pi$
$907$	−5.08251	−0.168762	−0.0843809	+	0.996434i	$0.526891\pi$
$908$	1.60925	0.0534049
$909$	−56.9420	−1.88865
$910$	0	0
$911$	−2.79092	−0.0924673	−0.0462337	−	0.998931i	$-0.514722\pi$
$911$	−2.79092	−0.0924673	−0.0462337	+	0.998931i	$0.514722\pi$
$912$	16.2567	0.538312
$913$	−43.8993	−1.45285
$914$	−31.9409	−1.05651
$915$	−13.1468	−0.434618
$916$	−7.41657	−0.245050
$917$	−15.4306	−0.509562
$918$	−37.5200	−1.23835
$919$	−26.0562	−0.859515	−0.429758	−	0.902944i	$-0.641401\pi$
$919$	−26.0562	−0.859515	−0.429758	+	0.902944i	$0.641401\pi$
$920$	−2.86294	−0.0943882
$921$	−30.1105	−0.992175
$922$	−10.1414	−0.333988
$923$	0	0
$924$	14.7017	0.483651
$925$	1.57242	0.0517007
$926$	25.8049	0.848002
$927$	76.0611	2.49817
$928$	5.43296	0.178346
$929$	−22.3515	−0.733330	−0.366665	−	0.930353i	$-0.619500\pi$
$929$	−22.3515	−0.733330	−0.366665	+	0.930353i	$0.619500\pi$
$930$	−8.61894	−0.282626
$931$	−5.80194	−0.190151
$932$	22.9922	0.753136
$933$	−25.3696	−0.830562
$934$	−25.2784	−0.827136
$935$	−21.0670	−0.688963
$936$	0	0
$937$	47.3139	1.54568	0.772840	−	0.634601i	$-0.218836\pi$
$937$	47.3139	1.54568	0.772840	+	0.634601i	$0.218836\pi$
$938$	−2.59419	−0.0847032
$939$	−31.2204	−1.01884
$940$	−3.08815	−0.100724
$941$	−1.45281	−0.0473603	−0.0236802	−	0.999720i	$-0.507538\pi$
$941$	−1.45281	−0.0473603	−0.0236802	+	0.999720i	$0.507538\pi$
$942$	−1.12498	−0.0366539
$943$	16.0713	0.523353
$944$	−7.24698	−0.235869
$945$	−2.87800	−0.0936214
$946$	36.2664	1.17912
$947$	12.7245	0.413492	0.206746	−	0.978395i	$-0.433713\pi$
$947$	12.7245	0.413492	0.206746	+	0.978395i	$0.433713\pi$
$948$	11.2349	0.364893
$949$	0	0
$950$	27.2228	0.883225
$951$	−73.0990	−2.37040
$952$	7.23490	0.234484
$953$	4.66189	0.151013	0.0755067	−	0.997145i	$-0.475943\pi$
$953$	4.66189	0.151013	0.0755067	+	0.997145i	$0.475943\pi$
$954$	−37.7875	−1.22341
$955$	10.8689	0.351709
$956$	29.4359	0.952026
$957$	79.8738	2.58195
$958$	8.63879	0.279107
$959$	−15.8116	−0.510584
$960$	−1.55496	−0.0501861
$961$	−0.276520	−0.00891999
$962$	0	0
$963$	−50.2398	−1.61895
$964$	−16.3080	−0.525245
$965$	−3.41922	−0.110069
$966$	14.4547	0.465073
$967$	3.48752	0.112151	0.0560755	−	0.998427i	$-0.482141\pi$
$967$	3.48752	0.112151	0.0560755	+	0.998427i	$0.482141\pi$
$968$	16.5308	0.531320
$969$	117.615	3.77835
$970$	−8.83877	−0.283796
$971$	−44.5230	−1.42881	−0.714406	−	0.699731i	$-0.753303\pi$
$971$	−44.5230	−1.42881	−0.714406	+	0.699731i	$0.753303\pi$
$972$	15.6189	0.500978
$973$	−1.78017	−0.0570695
$974$	−20.4142	−0.654112
$975$	0	0
$976$	8.45473	0.270629
$977$	30.2271	0.967052	0.483526	−	0.875330i	$-0.339356\pi$
$977$	30.2271	0.967052	0.483526	+	0.875330i	$0.339356\pi$
$978$	5.65279	0.180756
$979$	−11.0989	−0.354722
$980$	0.554958	0.0177275
$981$	−85.6311	−2.73399
$982$	7.18359	0.229237
$983$	23.4862	0.749093	0.374547	−	0.927208i	$-0.377798\pi$
$983$	23.4862	0.749093	0.374547	+	0.927208i	$0.377798\pi$
$984$	8.72886	0.278266
$985$	−3.34780	−0.106670
$986$	39.3069	1.25179
$987$	15.5918	0.496292
$988$	0	0
$989$	35.6571	1.13383
$990$	−14.1250	−0.448921
$991$	−59.7773	−1.89889	−0.949444	−	0.313936i	$-0.898352\pi$
$991$	−59.7773	−1.89889	−0.949444	+	0.313936i	$0.898352\pi$
$992$	5.54288	0.175987
$993$	58.7797	1.86532
$994$	9.18060	0.291191
$995$	6.79895	0.215541
$996$	−23.4426	−0.742809
$997$	−5.27737	−0.167136	−0.0835680	−	0.996502i	$-0.526632\pi$
$997$	−5.27737	−0.167136	−0.0835680	+	0.996502i	$0.526632\pi$
$998$	−13.9892	−0.442822
$999$	1.73795	0.0549865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.ba.1.1	yes	3
13.5	odd	4		2366.2.d.n.337.1		6
13.8	odd	4		2366.2.d.n.337.4		6
13.12	even	2		2366.2.a.v.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2366.2.a.v.1.1	✓	3	13.12	even	2
2366.2.a.ba.1.1	yes	3	1.1	even	1	trivial
2366.2.d.n.337.1		6	13.5	odd	4
2366.2.d.n.337.4		6	13.8	odd	4

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:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.80194 q^{3} +1.00000 q^{4} +0.554958 q^{5} -2.80194 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.85086 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.80194 q^{3} +1.00000 q^{4} +0.554958 q^{5} -2.80194 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.85086 q^{9} +0.554958 q^{10} -5.24698 q^{11} -2.80194 q^{12} +1.00000 q^{14} -1.55496 q^{15} +1.00000 q^{16} +7.23490 q^{17} +4.85086 q^{18} -5.80194 q^{19} +0.554958 q^{20} -2.80194 q^{21} -5.24698 q^{22} -5.15883 q^{23} -2.80194 q^{24} -4.69202 q^{25} -5.18598 q^{27} +1.00000 q^{28} +5.43296 q^{29} -1.55496 q^{30} +5.54288 q^{31} +1.00000 q^{32} +14.7017 q^{33} +7.23490 q^{34} +0.554958 q^{35} +4.85086 q^{36} -0.335126 q^{37} -5.80194 q^{38} +0.554958 q^{40} -3.11529 q^{41} -2.80194 q^{42} -6.91185 q^{43} -5.24698 q^{44} +2.69202 q^{45} -5.15883 q^{46} -5.56465 q^{47} -2.80194 q^{48} +1.00000 q^{49} -4.69202 q^{50} -20.2717 q^{51} -7.78986 q^{53} -5.18598 q^{54} -2.91185 q^{55} +1.00000 q^{56} +16.2567 q^{57} +5.43296 q^{58} -7.24698 q^{59} -1.55496 q^{60} +8.45473 q^{61} +5.54288 q^{62} +4.85086 q^{63} +1.00000 q^{64} +14.7017 q^{66} -2.59419 q^{67} +7.23490 q^{68} +14.4547 q^{69} +0.554958 q^{70} +9.18060 q^{71} +4.85086 q^{72} -4.29590 q^{73} -0.335126 q^{74} +13.1468 q^{75} -5.80194 q^{76} -5.24698 q^{77} -4.00969 q^{79} +0.554958 q^{80} -0.0217703 q^{81} -3.11529 q^{82} +8.36658 q^{83} -2.80194 q^{84} +4.01507 q^{85} -6.91185 q^{86} -15.2228 q^{87} -5.24698 q^{88} +2.11529 q^{89} +2.69202 q^{90} -5.15883 q^{92} -15.5308 q^{93} -5.56465 q^{94} -3.21983 q^{95} -2.80194 q^{96} -15.9269 q^{97} +1.00000 q^{98} -25.4523 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 3 * q^8 + q^9	\( 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} + 2 q^{5} - 4 q^{6} + 3 q^{7} + 3 q^{8} + q^{9} + 2 q^{10} - 11 q^{11} - 4 q^{12} + 3 q^{14} - 5 q^{15} + 3 q^{16} - 2 q^{17} + q^{18} - 13 q^{19} + 2 q^{20} - 4 q^{21} - 11 q^{22} - 7 q^{23} - 4 q^{24} - 9 q^{25} - q^{27} + 3 q^{28} - 3 q^{29} - 5 q^{30} - 2 q^{31} + 3 q^{32} + 17 q^{33} - 2 q^{34} + 2 q^{35} + q^{36} - 13 q^{38} + 2 q^{40} - 7 q^{41} - 4 q^{42} - 17 q^{43} - 11 q^{44} + 3 q^{45} - 7 q^{46} + 5 q^{47} - 4 q^{48} + 3 q^{49} - 9 q^{50} - 9 q^{51} - q^{54} - 5 q^{55} + 3 q^{56} + 22 q^{57} - 3 q^{58} - 17 q^{59} - 5 q^{60} + 3 q^{61} - 2 q^{62} + q^{63} + 3 q^{64} + 17 q^{66} - 21 q^{67} - 2 q^{68} + 21 q^{69} + 2 q^{70} + 16 q^{71} + q^{72} + q^{73} + 12 q^{75} - 13 q^{76} - 11 q^{77} + 10 q^{79} + 2 q^{80} + 3 q^{81} - 7 q^{82} - q^{83} - 4 q^{84} - 13 q^{85} - 17 q^{86} - 3 q^{87} - 11 q^{88} + 4 q^{89} + 3 q^{90} - 7 q^{92} - 9 q^{93} + 5 q^{94} - 11 q^{95} - 4 q^{96} - 19 q^{97} + 3 q^{98} - 13 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 + 2 * q^5 - 4 * q^6 + 3 * q^7 + 3 * q^8 + q^9 + 2 * q^10 - 11 * q^11 - 4 * q^12 + 3 * q^14 - 5 * q^15 + 3 * q^16 - 2 * q^17 + q^18 - 13 * q^19 + 2 * q^20 - 4 * q^21 - 11 * q^22 - 7 * q^23 - 4 * q^24 - 9 * q^25 - q^27 + 3 * q^28 - 3 * q^29 - 5 * q^30 - 2 * q^31 + 3 * q^32 + 17 * q^33 - 2 * q^34 + 2 * q^35 + q^36 - 13 * q^38 + 2 * q^40 - 7 * q^41 - 4 * q^42 - 17 * q^43 - 11 * q^44 + 3 * q^45 - 7 * q^46 + 5 * q^47 - 4 * q^48 + 3 * q^49 - 9 * q^50 - 9 * q^51 - q^54 - 5 * q^55 + 3 * q^56 + 22 * q^57 - 3 * q^58 - 17 * q^59 - 5 * q^60 + 3 * q^61 - 2 * q^62 + q^63 + 3 * q^64 + 17 * q^66 - 21 * q^67 - 2 * q^68 + 21 * q^69 + 2 * q^70 + 16 * q^71 + q^72 + q^73 + 12 * q^75 - 13 * q^76 - 11 * q^77 + 10 * q^79 + 2 * q^80 + 3 * q^81 - 7 * q^82 - q^83 - 4 * q^84 - 13 * q^85 - 17 * q^86 - 3 * q^87 - 11 * q^88 + 4 * q^89 + 3 * q^90 - 7 * q^92 - 9 * q^93 + 5 * q^94 - 11 * q^95 - 4 * q^96 - 19 * q^97 + 3 * q^98 - 13 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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