LMFDB - Embedded newform 8670.2.a.ci.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8670,2,Mod(1,8670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8670, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8670.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8670.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:	$69.2302985525$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.30652992.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 15x^{4} + 63x^{2} - 73 $ x^6 - 15x^4 + 63x^2 - 73
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.07495$ of defining polynomial
Character	$\chi$	$=$	8670.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +3.79557 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +3.79557 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +0.804438 q^{11} +1.00000 q^{12} -4.25395 q^{13} +3.79557 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} +5.71109 q^{19} +1.00000 q^{20} +3.79557 q^{21} +0.804438 q^{22} -7.82485 q^{23} +1.00000 q^{24} +1.00000 q^{25} -4.25395 q^{26} +1.00000 q^{27} +3.79557 q^{28} +2.57900 q^{29} +1.00000 q^{30} -0.592208 q^{31} +1.00000 q^{32} +0.804438 q^{33} +3.79557 q^{35} +1.00000 q^{36} -5.34021 q^{37} +5.71109 q^{38} -4.25395 q^{39} +1.00000 q^{40} +5.58847 q^{41} +3.79557 q^{42} +5.19054 q^{43} +0.804438 q^{44} +1.00000 q^{45} -7.82485 q^{46} +4.71607 q^{47} +1.00000 q^{48} +7.40635 q^{49} +1.00000 q^{50} -4.25395 q^{52} +5.34790 q^{53} +1.00000 q^{54} +0.804438 q^{55} +3.79557 q^{56} +5.71109 q^{57} +2.57900 q^{58} -5.49903 q^{59} +1.00000 q^{60} -1.84636 q^{61} -0.592208 q^{62} +3.79557 q^{63} +1.00000 q^{64} -4.25395 q^{65} +0.804438 q^{66} +11.9252 q^{67} -7.82485 q^{69} +3.79557 q^{70} +9.31407 q^{71} +1.00000 q^{72} +6.32700 q^{73} -5.34021 q^{74} +1.00000 q^{75} +5.71109 q^{76} +3.05330 q^{77} -4.25395 q^{78} +14.1634 q^{79} +1.00000 q^{80} +1.00000 q^{81} +5.58847 q^{82} -0.704063 q^{83} +3.79557 q^{84} +5.19054 q^{86} +2.57900 q^{87} +0.804438 q^{88} -9.89756 q^{89} +1.00000 q^{90} -16.1462 q^{91} -7.82485 q^{92} -0.592208 q^{93} +4.71607 q^{94} +5.71109 q^{95} +1.00000 q^{96} +19.3656 q^{97} +7.40635 q^{98} +0.804438 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 6 q^{10} + 6 q^{11} + 6 q^{12} + 6 q^{13} + 6 q^{14} + 6 q^{15} + 6 q^{16} + 6 q^{18} + 6 q^{19} + 6 q^{20} + 6 q^{21} + 6 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{25} + 6 q^{26} + 6 q^{27} + 6 q^{28} + 12 q^{29} + 6 q^{30} + 6 q^{31} + 6 q^{32} + 6 q^{33} + 6 q^{35} + 6 q^{36} + 6 q^{37} + 6 q^{38} + 6 q^{39} + 6 q^{40} + 12 q^{41} + 6 q^{42} + 18 q^{43} + 6 q^{44} + 6 q^{45} + 6 q^{46} - 6 q^{47} + 6 q^{48} + 18 q^{49} + 6 q^{50} + 6 q^{52} - 6 q^{53} + 6 q^{54} + 6 q^{55} + 6 q^{56} + 6 q^{57} + 12 q^{58} - 30 q^{59} + 6 q^{60} - 24 q^{61} + 6 q^{62} + 6 q^{63} + 6 q^{64} + 6 q^{65} + 6 q^{66} + 6 q^{69} + 6 q^{70} + 24 q^{71} + 6 q^{72} + 6 q^{73} + 6 q^{74} + 6 q^{75} + 6 q^{76} + 6 q^{78} + 6 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} + 18 q^{83} + 6 q^{84} + 18 q^{86} + 12 q^{87} + 6 q^{88} - 12 q^{89} + 6 q^{90} + 6 q^{91} + 6 q^{92} + 6 q^{93} - 6 q^{94} + 6 q^{95} + 6 q^{96} + 18 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 6 * q^10 + 6 * q^11 + 6 * q^12 + 6 * q^13 + 6 * q^14 + 6 * q^15 + 6 * q^16 + 6 * q^18 + 6 * q^19 + 6 * q^20 + 6 * q^21 + 6 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^25 + 6 * q^26 + 6 * q^27 + 6 * q^28 + 12 * q^29 + 6 * q^30 + 6 * q^31 + 6 * q^32 + 6 * q^33 + 6 * q^35 + 6 * q^36 + 6 * q^37 + 6 * q^38 + 6 * q^39 + 6 * q^40 + 12 * q^41 + 6 * q^42 + 18 * q^43 + 6 * q^44 + 6 * q^45 + 6 * q^46 - 6 * q^47 + 6 * q^48 + 18 * q^49 + 6 * q^50 + 6 * q^52 - 6 * q^53 + 6 * q^54 + 6 * q^55 + 6 * q^56 + 6 * q^57 + 12 * q^58 - 30 * q^59 + 6 * q^60 - 24 * q^61 + 6 * q^62 + 6 * q^63 + 6 * q^64 + 6 * q^65 + 6 * q^66 + 6 * q^69 + 6 * q^70 + 24 * q^71 + 6 * q^72 + 6 * q^73 + 6 * q^74 + 6 * q^75 + 6 * q^76 + 6 * q^78 + 6 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 + 18 * q^83 + 6 * q^84 + 18 * q^86 + 12 * q^87 + 6 * q^88 - 12 * q^89 + 6 * q^90 + 6 * q^91 + 6 * q^92 + 6 * q^93 - 6 * q^94 + 6 * q^95 + 6 * q^96 + 18 * q^97 + 18 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	3.79557	1.43459	0.717295	−	0.696769i	$-0.245380\pi$
$7$	3.79557	1.43459	0.717295	+	0.696769i	$0.245380\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	0.804438	0.242547	0.121274	−	0.992619i	$-0.461302\pi$
$11$	0.804438	0.242547	0.121274	+	0.992619i	$0.461302\pi$
$12$	1.00000	0.288675
$13$	−4.25395	−1.17983	−0.589917	−	0.807464i	$-0.700840\pi$
$13$	−4.25395	−1.17983	−0.589917	+	0.807464i	$0.700840\pi$
$14$	3.79557	1.01441
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	1.00000	0.235702
$19$	5.71109	1.31021	0.655107	−	0.755536i	$-0.272623\pi$
$19$	5.71109	1.31021	0.655107	+	0.755536i	$0.272623\pi$
$20$	1.00000	0.223607
$21$	3.79557	0.828261
$22$	0.804438	0.171507
$23$	−7.82485	−1.63159	−0.815797	−	0.578338i	$-0.803701\pi$
$23$	−7.82485	−1.63159	−0.815797	+	0.578338i	$0.803701\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−4.25395	−0.834269
$27$	1.00000	0.192450
$28$	3.79557	0.717295
$29$	2.57900	0.478908	0.239454	−	0.970908i	$-0.423032\pi$
$29$	2.57900	0.478908	0.239454	+	0.970908i	$0.423032\pi$
$30$	1.00000	0.182574
$31$	−0.592208	−0.106364	−0.0531819	−	0.998585i	$-0.516936\pi$
$31$	−0.592208	−0.106364	−0.0531819	+	0.998585i	$0.516936\pi$
$32$	1.00000	0.176777
$33$	0.804438	0.140035
$34$	0	0
$35$	3.79557	0.641568
$36$	1.00000	0.166667
$37$	−5.34021	−0.877925	−0.438962	−	0.898505i	$-0.644654\pi$
$37$	−5.34021	−0.877925	−0.438962	+	0.898505i	$0.644654\pi$
$38$	5.71109	0.926462
$39$	−4.25395	−0.681177
$40$	1.00000	0.158114
$41$	5.58847	0.872772	0.436386	−	0.899760i	$-0.356258\pi$
$41$	5.58847	0.872772	0.436386	+	0.899760i	$0.356258\pi$
$42$	3.79557	0.585669
$43$	5.19054	0.791550	0.395775	−	0.918347i	$-0.370476\pi$
$43$	5.19054	0.791550	0.395775	+	0.918347i	$0.370476\pi$
$44$	0.804438	0.121274
$45$	1.00000	0.149071
$46$	−7.82485	−1.15371
$47$	4.71607	0.687910	0.343955	−	0.938986i	$-0.388233\pi$
$47$	4.71607	0.687910	0.343955	+	0.938986i	$0.388233\pi$
$48$	1.00000	0.144338
$49$	7.40635	1.05805
$50$	1.00000	0.141421
$51$	0	0
$52$	−4.25395	−0.589917
$53$	5.34790	0.734590	0.367295	−	0.930104i	$-0.380284\pi$
$53$	5.34790	0.734590	0.367295	+	0.930104i	$0.380284\pi$
$54$	1.00000	0.136083
$55$	0.804438	0.108470
$56$	3.79557	0.507204
$57$	5.71109	0.756453
$58$	2.57900	0.338639
$59$	−5.49903	−0.715913	−0.357956	−	0.933738i	$-0.616526\pi$
$59$	−5.49903	−0.715913	−0.357956	+	0.933738i	$0.616526\pi$
$60$	1.00000	0.129099
$61$	−1.84636	−0.236403	−0.118201	−	0.992990i	$-0.537713\pi$
$61$	−1.84636	−0.236403	−0.118201	+	0.992990i	$0.537713\pi$
$62$	−0.592208	−0.0752105
$63$	3.79557	0.478197
$64$	1.00000	0.125000
$65$	−4.25395	−0.527638
$66$	0.804438	0.0990194
$67$	11.9252	1.45689	0.728445	−	0.685104i	$-0.240243\pi$
$67$	11.9252	1.45689	0.728445	+	0.685104i	$0.240243\pi$
$68$	0	0
$69$	−7.82485	−0.942001
$70$	3.79557	0.453657
$71$	9.31407	1.10538	0.552688	−	0.833388i	$-0.313602\pi$
$71$	9.31407	1.10538	0.552688	+	0.833388i	$0.313602\pi$
$72$	1.00000	0.117851
$73$	6.32700	0.740519	0.370260	−	0.928928i	$-0.379269\pi$
$73$	6.32700	0.740519	0.370260	+	0.928928i	$0.379269\pi$
$74$	−5.34021	−0.620787
$75$	1.00000	0.115470
$76$	5.71109	0.655107
$77$	3.05330	0.347956
$78$	−4.25395	−0.481665
$79$	14.1634	1.59351	0.796753	−	0.604305i	$-0.206549\pi$
$79$	14.1634	1.59351	0.796753	+	0.604305i	$0.206549\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	5.58847	0.617143
$83$	−0.704063	−0.0772810	−0.0386405	−	0.999253i	$-0.512303\pi$
$83$	−0.704063	−0.0772810	−0.0386405	+	0.999253i	$0.512303\pi$
$84$	3.79557	0.414131
$85$	0	0
$86$	5.19054	0.559711
$87$	2.57900	0.276498
$88$	0.804438	0.0857533
$89$	−9.89756	−1.04914	−0.524569	−	0.851368i	$-0.675774\pi$
$89$	−9.89756	−1.04914	−0.524569	+	0.851368i	$0.675774\pi$
$90$	1.00000	0.105409
$91$	−16.1462	−1.69258
$92$	−7.82485	−0.815797
$93$	−0.592208	−0.0614091
$94$	4.71607	0.486426
$95$	5.71109	0.585946
$96$	1.00000	0.102062
$97$	19.3656	1.96628	0.983139	−	0.182857i	$-0.0585346\pi$
$97$	19.3656	1.96628	0.983139	+	0.182857i	$0.0585346\pi$
$98$	7.40635	0.748154
$99$	0.804438	0.0808490
$100$	1.00000	0.100000
$101$	9.91353	0.986433	0.493216	−	0.869907i	$-0.335821\pi$
$101$	9.91353	0.986433	0.493216	+	0.869907i	$0.335821\pi$
$102$	0	0
$103$	−18.0553	−1.77904	−0.889522	−	0.456893i	$-0.848962\pi$
$103$	−18.0553	−1.77904	−0.889522	+	0.456893i	$0.848962\pi$
$104$	−4.25395	−0.417134
$105$	3.79557	0.370410
$106$	5.34790	0.519434
$107$	3.97765	0.384534	0.192267	−	0.981343i	$-0.438416\pi$
$107$	3.97765	0.384534	0.192267	+	0.981343i	$0.438416\pi$
$108$	1.00000	0.0962250
$109$	−1.24047	−0.118816	−0.0594079	−	0.998234i	$-0.518921\pi$
$109$	−1.24047	−0.118816	−0.0594079	+	0.998234i	$0.518921\pi$
$110$	0.804438	0.0767001
$111$	−5.34021	−0.506870
$112$	3.79557	0.358648
$113$	−0.827278	−0.0778237	−0.0389119	−	0.999243i	$-0.512389\pi$
$113$	−0.827278	−0.0778237	−0.0389119	+	0.999243i	$0.512389\pi$
$114$	5.71109	0.534893
$115$	−7.82485	−0.729671
$116$	2.57900	0.239454
$117$	−4.25395	−0.393278
$118$	−5.49903	−0.506227
$119$	0	0
$120$	1.00000	0.0912871
$121$	−10.3529	−0.941171
$122$	−1.84636	−0.167162
$123$	5.58847	0.503895
$124$	−0.592208	−0.0531819
$125$	1.00000	0.0894427
$126$	3.79557	0.338136
$127$	−4.72447	−0.419229	−0.209615	−	0.977784i	$-0.567221\pi$
$127$	−4.72447	−0.419229	−0.209615	+	0.977784i	$0.567221\pi$
$128$	1.00000	0.0883883
$129$	5.19054	0.457002
$130$	−4.25395	−0.373096
$131$	−18.5325	−1.61920	−0.809598	−	0.586985i	$-0.800315\pi$
$131$	−18.5325	−1.61920	−0.809598	+	0.586985i	$0.800315\pi$
$132$	0.804438	0.0700173
$133$	21.6768	1.87962
$134$	11.9252	1.03018
$135$	1.00000	0.0860663
$136$	0	0
$137$	12.8407	1.09706	0.548530	−	0.836131i	$-0.315188\pi$
$137$	12.8407	1.09706	0.548530	+	0.836131i	$0.315188\pi$
$138$	−7.82485	−0.666095
$139$	3.86445	0.327778	0.163889	−	0.986479i	$-0.447596\pi$
$139$	3.86445	0.327778	0.163889	+	0.986479i	$0.447596\pi$
$140$	3.79557	0.320784
$141$	4.71607	0.397165
$142$	9.31407	0.781619
$143$	−3.42204	−0.286165
$144$	1.00000	0.0833333
$145$	2.57900	0.214174
$146$	6.32700	0.523626
$147$	7.40635	0.610865
$148$	−5.34021	−0.438962
$149$	−13.8509	−1.13471	−0.567353	−	0.823475i	$-0.692033\pi$
$149$	−13.8509	−1.13471	−0.567353	+	0.823475i	$0.692033\pi$
$150$	1.00000	0.0816497
$151$	−13.3519	−1.08656	−0.543281	−	0.839551i	$-0.682818\pi$
$151$	−13.3519	−1.08656	−0.543281	+	0.839551i	$0.682818\pi$
$152$	5.71109	0.463231
$153$	0	0
$154$	3.05330	0.246042
$155$	−0.592208	−0.0475673
$156$	−4.25395	−0.340589
$157$	13.7161	1.09467	0.547333	−	0.836915i	$-0.315643\pi$
$157$	13.7161	1.09467	0.547333	+	0.836915i	$0.315643\pi$
$158$	14.1634	1.12678
$159$	5.34790	0.424116
$160$	1.00000	0.0790569
$161$	−29.6998	−2.34067
$162$	1.00000	0.0785674
$163$	−6.35803	−0.497999	−0.249000	−	0.968504i	$-0.580102\pi$
$163$	−6.35803	−0.497999	−0.249000	+	0.968504i	$0.580102\pi$
$164$	5.58847	0.436386
$165$	0.804438	0.0626254
$166$	−0.704063	−0.0546459
$167$	10.1107	0.782391	0.391195	−	0.920308i	$-0.372062\pi$
$167$	10.1107	0.782391	0.391195	+	0.920308i	$0.372062\pi$
$168$	3.79557	0.292835
$169$	5.09610	0.392008
$170$	0	0
$171$	5.71109	0.436738
$172$	5.19054	0.395775
$173$	−17.4312	−1.32527	−0.662634	−	0.748943i	$-0.730562\pi$
$173$	−17.4312	−1.32527	−0.662634	+	0.748943i	$0.730562\pi$
$174$	2.57900	0.195513
$175$	3.79557	0.286918
$176$	0.804438	0.0606368
$177$	−5.49903	−0.413332
$178$	−9.89756	−0.741853
$179$	−24.7564	−1.85038	−0.925189	−	0.379507i	$-0.876094\pi$
$179$	−24.7564	−1.85038	−0.925189	+	0.379507i	$0.876094\pi$
$180$	1.00000	0.0745356
$181$	19.2155	1.42827	0.714137	−	0.700005i	$-0.246819\pi$
$181$	19.2155	1.42827	0.714137	+	0.700005i	$0.246819\pi$
$182$	−16.1462	−1.19683
$183$	−1.84636	−0.136487
$184$	−7.82485	−0.576856
$185$	−5.34021	−0.392620
$186$	−0.592208	−0.0434228
$187$	0	0
$188$	4.71607	0.343955
$189$	3.79557	0.276087
$190$	5.71109	0.414326
$191$	−8.93913	−0.646813	−0.323406	−	0.946260i	$-0.604828\pi$
$191$	−8.93913	−0.646813	−0.323406	+	0.946260i	$0.604828\pi$
$192$	1.00000	0.0721688
$193$	−13.4719	−0.969732	−0.484866	−	0.874589i	$-0.661132\pi$
$193$	−13.4719	−0.969732	−0.484866	+	0.874589i	$0.661132\pi$
$194$	19.3656	1.39037
$195$	−4.25395	−0.304632
$196$	7.40635	0.529025
$197$	12.0135	0.855924	0.427962	−	0.903797i	$-0.359232\pi$
$197$	12.0135	0.855924	0.427962	+	0.903797i	$0.359232\pi$
$198$	0.804438	0.0571689
$199$	11.9693	0.848483	0.424241	−	0.905549i	$-0.360541\pi$
$199$	11.9693	0.848483	0.424241	+	0.905549i	$0.360541\pi$
$200$	1.00000	0.0707107
$201$	11.9252	0.841136
$202$	9.91353	0.697513
$203$	9.78876	0.687036
$204$	0	0
$205$	5.58847	0.390316
$206$	−18.0553	−1.25797
$207$	−7.82485	−0.543865
$208$	−4.25395	−0.294958
$209$	4.59422	0.317789
$210$	3.79557	0.261919
$211$	0.382123	0.0263064	0.0131532	−	0.999913i	$-0.495813\pi$
$211$	0.382123	0.0263064	0.0131532	+	0.999913i	$0.495813\pi$
$212$	5.34790	0.367295
$213$	9.31407	0.638190
$214$	3.97765	0.271907
$215$	5.19054	0.353992
$216$	1.00000	0.0680414
$217$	−2.24777	−0.152588
$218$	−1.24047	−0.0840155
$219$	6.32700	0.427539
$220$	0.804438	0.0542352
$221$	0	0
$222$	−5.34021	−0.358411
$223$	14.8901	0.997118	0.498559	−	0.866856i	$-0.333863\pi$
$223$	14.8901	0.997118	0.498559	+	0.866856i	$0.333863\pi$
$224$	3.79557	0.253602
$225$	1.00000	0.0666667
$226$	−0.827278	−0.0550297
$227$	8.48302	0.563038	0.281519	−	0.959556i	$-0.409162\pi$
$227$	8.48302	0.563038	0.281519	+	0.959556i	$0.409162\pi$
$228$	5.71109	0.378226
$229$	−23.0649	−1.52417	−0.762087	−	0.647474i	$-0.775825\pi$
$229$	−23.0649	−1.52417	−0.762087	+	0.647474i	$0.775825\pi$
$230$	−7.82485	−0.515955
$231$	3.05330	0.200892
$232$	2.57900	0.169319
$233$	−21.8136	−1.42906	−0.714528	−	0.699607i	$-0.753358\pi$
$233$	−21.8136	−1.42906	−0.714528	+	0.699607i	$0.753358\pi$
$234$	−4.25395	−0.278090
$235$	4.71607	0.307643
$236$	−5.49903	−0.357956
$237$	14.1634	0.920011
$238$	0	0
$239$	23.9606	1.54988	0.774941	−	0.632033i	$-0.217779\pi$
$239$	23.9606	1.54988	0.774941	+	0.632033i	$0.217779\pi$
$240$	1.00000	0.0645497
$241$	−28.1240	−1.81163	−0.905814	−	0.423676i	$-0.860740\pi$
$241$	−28.1240	−1.81163	−0.905814	+	0.423676i	$0.860740\pi$
$242$	−10.3529	−0.665508
$243$	1.00000	0.0641500
$244$	−1.84636	−0.118201
$245$	7.40635	0.473174
$246$	5.58847	0.356308
$247$	−24.2947	−1.54584
$248$	−0.592208	−0.0376053
$249$	−0.704063	−0.0446182
$250$	1.00000	0.0632456
$251$	−17.5259	−1.10622	−0.553112	−	0.833107i	$-0.686560\pi$
$251$	−17.5259	−1.10622	−0.553112	+	0.833107i	$0.686560\pi$
$252$	3.79557	0.239098
$253$	−6.29460	−0.395738
$254$	−4.72447	−0.296440
$255$	0	0
$256$	1.00000	0.0625000
$257$	−15.5691	−0.971177	−0.485588	−	0.874188i	$-0.661395\pi$
$257$	−15.5691	−0.971177	−0.485588	+	0.874188i	$0.661395\pi$
$258$	5.19054	0.323149
$259$	−20.2691	−1.25946
$260$	−4.25395	−0.263819
$261$	2.57900	0.159636
$262$	−18.5325	−1.14494
$263$	−5.12041	−0.315738	−0.157869	−	0.987460i	$-0.550462\pi$
$263$	−5.12041	−0.315738	−0.157869	+	0.987460i	$0.550462\pi$
$264$	0.804438	0.0495097
$265$	5.34790	0.328519
$266$	21.6768	1.32909
$267$	−9.89756	−0.605721
$268$	11.9252	0.728445
$269$	0.377571	0.0230209	0.0115105	−	0.999934i	$-0.496336\pi$
$269$	0.377571	0.0230209	0.0115105	+	0.999934i	$0.496336\pi$
$270$	1.00000	0.0608581
$271$	−16.5926	−1.00793	−0.503964	−	0.863725i	$-0.668126\pi$
$271$	−16.5926	−1.00793	−0.503964	+	0.863725i	$0.668126\pi$
$272$	0	0
$273$	−16.1462	−0.977211
$274$	12.8407	0.775738
$275$	0.804438	0.0485094
$276$	−7.82485	−0.471001
$277$	30.5882	1.83787	0.918934	−	0.394412i	$-0.129052\pi$
$277$	30.5882	1.83787	0.918934	+	0.394412i	$0.129052\pi$
$278$	3.86445	0.231774
$279$	−0.592208	−0.0354546
$280$	3.79557	0.226829
$281$	−24.0015	−1.43181	−0.715904	−	0.698198i	$-0.753985\pi$
$281$	−24.0015	−1.43181	−0.715904	+	0.698198i	$0.753985\pi$
$282$	4.71607	0.280838
$283$	13.0199	0.773955	0.386977	−	0.922089i	$-0.373519\pi$
$283$	13.0199	0.773955	0.386977	+	0.922089i	$0.373519\pi$
$284$	9.31407	0.552688
$285$	5.71109	0.338296
$286$	−3.42204	−0.202349
$287$	21.2114	1.25207
$288$	1.00000	0.0589256
$289$	0	0
$290$	2.57900	0.151444
$291$	19.3656	1.13523
$292$	6.32700	0.370260
$293$	32.0249	1.87091	0.935456	−	0.353443i	$-0.114989\pi$
$293$	32.0249	1.87091	0.935456	+	0.353443i	$0.114989\pi$
$294$	7.40635	0.431947
$295$	−5.49903	−0.320166
$296$	−5.34021	−0.310393
$297$	0.804438	0.0466782
$298$	−13.8509	−0.802359
$299$	33.2865	1.92501
$300$	1.00000	0.0577350
$301$	19.7011	1.13555
$302$	−13.3519	−0.768315
$303$	9.91353	0.569517
$304$	5.71109	0.327554
$305$	−1.84636	−0.105723
$306$	0	0
$307$	−2.93201	−0.167338	−0.0836692	−	0.996494i	$-0.526664\pi$
$307$	−2.93201	−0.167338	−0.0836692	+	0.996494i	$0.526664\pi$
$308$	3.05330	0.173978
$309$	−18.0553	−1.02713
$310$	−0.592208	−0.0336352
$311$	2.93740	0.166565	0.0832824	−	0.996526i	$-0.473460\pi$
$311$	2.93740	0.166565	0.0832824	+	0.996526i	$0.473460\pi$
$312$	−4.25395	−0.240833
$313$	4.74511	0.268210	0.134105	−	0.990967i	$-0.457184\pi$
$313$	4.74511	0.268210	0.134105	+	0.990967i	$0.457184\pi$
$314$	13.7161	0.774046
$315$	3.79557	0.213856
$316$	14.1634	0.796753
$317$	13.5880	0.763178	0.381589	−	0.924332i	$-0.375377\pi$
$317$	13.5880	0.763178	0.381589	+	0.924332i	$0.375377\pi$
$318$	5.34790	0.299895
$319$	2.07464	0.116158
$320$	1.00000	0.0559017
$321$	3.97765	0.222011
$322$	−29.6998	−1.65510
$323$	0	0
$324$	1.00000	0.0555556
$325$	−4.25395	−0.235967
$326$	−6.35803	−0.352139
$327$	−1.24047	−0.0685983
$328$	5.58847	0.308572
$329$	17.9002	0.986869
$330$	0.804438	0.0442828
$331$	−27.3064	−1.50090	−0.750448	−	0.660930i	$-0.770162\pi$
$331$	−27.3064	−1.50090	−0.750448	+	0.660930i	$0.770162\pi$
$332$	−0.704063	−0.0386405
$333$	−5.34021	−0.292642
$334$	10.1107	0.553234
$335$	11.9252	0.651541
$336$	3.79557	0.207065
$337$	−11.9000	−0.648235	−0.324118	−	0.946017i	$-0.605067\pi$
$337$	−11.9000	−0.648235	−0.324118	+	0.946017i	$0.605067\pi$
$338$	5.09610	0.277192
$339$	−0.827278	−0.0449316
$340$	0	0
$341$	−0.476395	−0.0257982
$342$	5.71109	0.308821
$343$	1.54231	0.0832771
$344$	5.19054	0.279855
$345$	−7.82485	−0.421276
$346$	−17.4312	−0.937107
$347$	−34.0894	−1.83001	−0.915006	−	0.403439i	$-0.867815\pi$
$347$	−34.0894	−1.83001	−0.915006	+	0.403439i	$0.867815\pi$
$348$	2.57900	0.138249
$349$	−20.1799	−1.08020	−0.540102	−	0.841599i	$-0.681614\pi$
$349$	−20.1799	−1.08020	−0.540102	+	0.841599i	$0.681614\pi$
$350$	3.79557	0.202882
$351$	−4.25395	−0.227059
$352$	0.804438	0.0428767
$353$	−5.24453	−0.279138	−0.139569	−	0.990212i	$-0.544572\pi$
$353$	−5.24453	−0.279138	−0.139569	+	0.990212i	$0.544572\pi$
$354$	−5.49903	−0.292270
$355$	9.31407	0.494340
$356$	−9.89756	−0.524569
$357$	0	0
$358$	−24.7564	−1.30841
$359$	6.58973	0.347793	0.173896	−	0.984764i	$-0.444364\pi$
$359$	6.58973	0.347793	0.173896	+	0.984764i	$0.444364\pi$
$360$	1.00000	0.0527046
$361$	13.6166	0.716662
$362$	19.2155	1.00994
$363$	−10.3529	−0.543385
$364$	−16.1462	−0.846289
$365$	6.32700	0.331170
$366$	−1.84636	−0.0965110
$367$	−29.0677	−1.51732	−0.758662	−	0.651484i	$-0.774147\pi$
$367$	−29.0677	−1.51732	−0.758662	+	0.651484i	$0.774147\pi$
$368$	−7.82485	−0.407898
$369$	5.58847	0.290924
$370$	−5.34021	−0.277624
$371$	20.2983	1.05384
$372$	−0.592208	−0.0307046
$373$	23.1502	1.19867	0.599337	−	0.800497i	$-0.295431\pi$
$373$	23.1502	1.19867	0.599337	+	0.800497i	$0.295431\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	4.71607	0.243213
$377$	−10.9709	−0.565032
$378$	3.79557	0.195223
$379$	−27.8603	−1.43109	−0.715544	−	0.698568i	$-0.753821\pi$
$379$	−27.8603	−1.43109	−0.715544	+	0.698568i	$0.753821\pi$
$380$	5.71109	0.292973
$381$	−4.72447	−0.242042
$382$	−8.93913	−0.457366
$383$	−37.7469	−1.92878	−0.964389	−	0.264490i	$-0.914796\pi$
$383$	−37.7469	−1.92878	−0.964389	+	0.264490i	$0.914796\pi$
$384$	1.00000	0.0510310
$385$	3.05330	0.155611
$386$	−13.4719	−0.685704
$387$	5.19054	0.263850
$388$	19.3656	0.983139
$389$	8.76118	0.444210	0.222105	−	0.975023i	$-0.428707\pi$
$389$	8.76118	0.444210	0.222105	+	0.975023i	$0.428707\pi$
$390$	−4.25395	−0.215407
$391$	0	0
$392$	7.40635	0.374077
$393$	−18.5325	−0.934843
$394$	12.0135	0.605230
$395$	14.1634	0.712637
$396$	0.804438	0.0404245
$397$	2.52190	0.126570	0.0632852	−	0.997995i	$-0.479842\pi$
$397$	2.52190	0.126570	0.0632852	+	0.997995i	$0.479842\pi$
$398$	11.9693	0.599968
$399$	21.6768	1.08520
$400$	1.00000	0.0500000
$401$	−23.7926	−1.18815	−0.594073	−	0.804411i	$-0.702481\pi$
$401$	−23.7926	−1.18815	−0.594073	+	0.804411i	$0.702481\pi$
$402$	11.9252	0.594773
$403$	2.51922	0.125492
$404$	9.91353	0.493216
$405$	1.00000	0.0496904
$406$	9.78876	0.485808
$407$	−4.29587	−0.212938
$408$	0	0
$409$	17.3508	0.857943	0.428971	−	0.903318i	$-0.358876\pi$
$409$	17.3508	0.857943	0.428971	+	0.903318i	$0.358876\pi$
$410$	5.58847	0.275995
$411$	12.8407	0.633387
$412$	−18.0553	−0.889522
$413$	−20.8720	−1.02704
$414$	−7.82485	−0.384570
$415$	−0.704063	−0.0345611
$416$	−4.25395	−0.208567
$417$	3.86445	0.189243
$418$	4.59422	0.224711
$419$	−7.00037	−0.341990	−0.170995	−	0.985272i	$-0.554698\pi$
$419$	−7.00037	−0.341990	−0.170995	+	0.985272i	$0.554698\pi$
$420$	3.79557	0.185205
$421$	28.8204	1.40462	0.702310	−	0.711871i	$-0.252152\pi$
$421$	28.8204	1.40462	0.702310	+	0.711871i	$0.252152\pi$
$422$	0.382123	0.0186014
$423$	4.71607	0.229303
$424$	5.34790	0.259717
$425$	0	0
$426$	9.31407	0.451268
$427$	−7.00800	−0.339141
$428$	3.97765	0.192267
$429$	−3.42204	−0.165218
$430$	5.19054	0.250310
$431$	32.9500	1.58715	0.793573	−	0.608475i	$-0.208218\pi$
$431$	32.9500	1.58715	0.793573	+	0.608475i	$0.208218\pi$
$432$	1.00000	0.0481125
$433$	6.71647	0.322773	0.161386	−	0.986891i	$-0.448403\pi$
$433$	6.71647	0.322773	0.161386	+	0.986891i	$0.448403\pi$
$434$	−2.24777	−0.107896
$435$	2.57900	0.123653
$436$	−1.24047	−0.0594079
$437$	−44.6884	−2.13774
$438$	6.32700	0.302316
$439$	−8.88195	−0.423912	−0.211956	−	0.977279i	$-0.567983\pi$
$439$	−8.88195	−0.423912	−0.211956	+	0.977279i	$0.567983\pi$
$440$	0.804438	0.0383501
$441$	7.40635	0.352683
$442$	0	0
$443$	−28.4920	−1.35370	−0.676848	−	0.736123i	$-0.736655\pi$
$443$	−28.4920	−1.35370	−0.676848	+	0.736123i	$0.736655\pi$
$444$	−5.34021	−0.253435
$445$	−9.89756	−0.469189
$446$	14.8901	0.705069
$447$	−13.8509	−0.655123
$448$	3.79557	0.179324
$449$	−24.3579	−1.14952	−0.574760	−	0.818322i	$-0.694905\pi$
$449$	−24.3579	−1.14952	−0.574760	+	0.818322i	$0.694905\pi$
$450$	1.00000	0.0471405
$451$	4.49557	0.211688
$452$	−0.827278	−0.0389119
$453$	−13.3519	−0.627327
$454$	8.48302	0.398128
$455$	−16.1462	−0.756944
$456$	5.71109	0.267446
$457$	37.6880	1.76297	0.881486	−	0.472211i	$-0.156544\pi$
$457$	37.6880	1.76297	0.881486	+	0.472211i	$0.156544\pi$
$458$	−23.0649	−1.07775
$459$	0	0
$460$	−7.82485	−0.364835
$461$	−14.6240	−0.681106	−0.340553	−	0.940225i	$-0.610614\pi$
$461$	−14.6240	−0.681106	−0.340553	+	0.940225i	$0.610614\pi$
$462$	3.05330	0.142052
$463$	18.8544	0.876239	0.438119	−	0.898917i	$-0.355645\pi$
$463$	18.8544	0.876239	0.438119	+	0.898917i	$0.355645\pi$
$464$	2.57900	0.119727
$465$	−0.592208	−0.0274630
$466$	−21.8136	−1.01050
$467$	−35.0767	−1.62316	−0.811579	−	0.584243i	$-0.801392\pi$
$467$	−35.0767	−1.62316	−0.811579	+	0.584243i	$0.801392\pi$
$468$	−4.25395	−0.196639
$469$	45.2628	2.09004
$470$	4.71607	0.217536
$471$	13.7161	0.632006
$472$	−5.49903	−0.253113
$473$	4.17547	0.191988
$474$	14.1634	0.650546
$475$	5.71109	0.262043
$476$	0	0
$477$	5.34790	0.244863
$478$	23.9606	1.09593
$479$	7.53020	0.344064	0.172032	−	0.985091i	$-0.444967\pi$
$479$	7.53020	0.344064	0.172032	+	0.985091i	$0.444967\pi$
$480$	1.00000	0.0456435
$481$	22.7170	1.03581
$482$	−28.1240	−1.28101
$483$	−29.6998	−1.35139
$484$	−10.3529	−0.470585
$485$	19.3656	0.879347
$486$	1.00000	0.0453609
$487$	−39.6386	−1.79620	−0.898098	−	0.439796i	$-0.855051\pi$
$487$	−39.6386	−1.79620	−0.898098	+	0.439796i	$0.855051\pi$
$488$	−1.84636	−0.0835810
$489$	−6.35803	−0.287520
$490$	7.40635	0.334585
$491$	−29.3103	−1.32275	−0.661377	−	0.750054i	$-0.730028\pi$
$491$	−29.3103	−1.32275	−0.661377	+	0.750054i	$0.730028\pi$
$492$	5.58847	0.251948
$493$	0	0
$494$	−24.2947	−1.09307
$495$	0.804438	0.0361568
$496$	−0.592208	−0.0265909
$497$	35.3522	1.58576
$498$	−0.704063	−0.0315498
$499$	−4.91144	−0.219866	−0.109933	−	0.993939i	$-0.535064\pi$
$499$	−4.91144	−0.219866	−0.109933	+	0.993939i	$0.535064\pi$
$500$	1.00000	0.0447214
$501$	10.1107	0.451713
$502$	−17.5259	−0.782218
$503$	35.3982	1.57833	0.789164	−	0.614182i	$-0.210514\pi$
$503$	35.3982	1.57833	0.789164	+	0.614182i	$0.210514\pi$
$504$	3.79557	0.169068
$505$	9.91353	0.441146
$506$	−6.29460	−0.279829
$507$	5.09610	0.226326
$508$	−4.72447	−0.209615
$509$	−15.3206	−0.679072	−0.339536	−	0.940593i	$-0.610270\pi$
$509$	−15.3206	−0.679072	−0.339536	+	0.940593i	$0.610270\pi$
$510$	0	0
$511$	24.0146	1.06234
$512$	1.00000	0.0441942
$513$	5.71109	0.252151
$514$	−15.5691	−0.686726
$515$	−18.0553	−0.795613
$516$	5.19054	0.228501
$517$	3.79379	0.166851
$518$	−20.2691	−0.890575
$519$	−17.4312	−0.765144
$520$	−4.25395	−0.186548
$521$	16.5634	0.725655	0.362828	−	0.931856i	$-0.381811\pi$
$521$	16.5634	0.725655	0.362828	+	0.931856i	$0.381811\pi$
$522$	2.57900	0.112880
$523$	−36.5004	−1.59605	−0.798026	−	0.602623i	$-0.794122\pi$
$523$	−36.5004	−1.59605	−0.798026	+	0.602623i	$0.794122\pi$
$524$	−18.5325	−0.809598
$525$	3.79557	0.165652
$526$	−5.12041	−0.223260
$527$	0	0
$528$	0.804438	0.0350087
$529$	38.2283	1.66210
$530$	5.34790	0.232298
$531$	−5.49903	−0.238638
$532$	21.6768	0.939811
$533$	−23.7731	−1.02973
$534$	−9.89756	−0.428309
$535$	3.97765	0.171969
$536$	11.9252	0.515089
$537$	−24.7564	−1.06832
$538$	0.377571	0.0162782
$539$	5.95794	0.256627
$540$	1.00000	0.0430331
$541$	28.3436	1.21859	0.609293	−	0.792945i	$-0.291453\pi$
$541$	28.3436	1.21859	0.609293	+	0.792945i	$0.291453\pi$
$542$	−16.5926	−0.712713
$543$	19.2155	0.824615
$544$	0	0
$545$	−1.24047	−0.0531360
$546$	−16.1462	−0.690992
$547$	19.8797	0.849995	0.424997	−	0.905195i	$-0.360275\pi$
$547$	19.8797	0.849995	0.424997	+	0.905195i	$0.360275\pi$
$548$	12.8407	0.548530
$549$	−1.84636	−0.0788009
$550$	0.804438	0.0343013
$551$	14.7289	0.627472
$552$	−7.82485	−0.333048
$553$	53.7581	2.28603
$554$	30.5882	1.29957
$555$	−5.34021	−0.226679
$556$	3.86445	0.163889
$557$	−16.9621	−0.718705	−0.359353	−	0.933202i	$-0.617002\pi$
$557$	−16.9621	−0.718705	−0.359353	+	0.933202i	$0.617002\pi$
$558$	−0.592208	−0.0250702
$559$	−22.0803	−0.933898
$560$	3.79557	0.160392
$561$	0	0
$562$	−24.0015	−1.01244
$563$	−31.9656	−1.34719	−0.673595	−	0.739100i	$-0.735251\pi$
$563$	−31.9656	−1.34719	−0.673595	+	0.739100i	$0.735251\pi$
$564$	4.71607	0.198583
$565$	−0.827278	−0.0348038
$566$	13.0199	0.547269
$567$	3.79557	0.159399
$568$	9.31407	0.390810
$569$	−13.0649	−0.547707	−0.273854	−	0.961771i	$-0.588298\pi$
$569$	−13.0649	−0.547707	−0.273854	+	0.961771i	$0.588298\pi$
$570$	5.71109	0.239211
$571$	−16.7640	−0.701550	−0.350775	−	0.936460i	$-0.614082\pi$
$571$	−16.7640	−0.701550	−0.350775	+	0.936460i	$0.614082\pi$
$572$	−3.42204	−0.143083
$573$	−8.93913	−0.373438
$574$	21.2114	0.885347
$575$	−7.82485	−0.326319
$576$	1.00000	0.0416667
$577$	−8.29810	−0.345455	−0.172727	−	0.984970i	$-0.555258\pi$
$577$	−8.29810	−0.345455	−0.172727	+	0.984970i	$0.555258\pi$
$578$	0	0
$579$	−13.4719	−0.559875
$580$	2.57900	0.107087
$581$	−2.67232	−0.110867
$582$	19.3656	0.802730
$583$	4.30205	0.178173
$584$	6.32700	0.261813
$585$	−4.25395	−0.175879
$586$	32.0249	1.32293
$587$	18.7596	0.774292	0.387146	−	0.922018i	$-0.373461\pi$
$587$	18.7596	0.774292	0.387146	+	0.922018i	$0.373461\pi$
$588$	7.40635	0.305433
$589$	−3.38216	−0.139359
$590$	−5.49903	−0.226391
$591$	12.0135	0.494168
$592$	−5.34021	−0.219481
$593$	10.7160	0.440051	0.220026	−	0.975494i	$-0.429386\pi$
$593$	10.7160	0.440051	0.220026	+	0.975494i	$0.429386\pi$
$594$	0.804438	0.0330065
$595$	0	0
$596$	−13.8509	−0.567353
$597$	11.9693	0.489872
$598$	33.2865	1.36119
$599$	35.6978	1.45857	0.729286	−	0.684209i	$-0.239852\pi$
$599$	35.6978	1.45857	0.729286	+	0.684209i	$0.239852\pi$
$600$	1.00000	0.0408248
$601$	−7.94023	−0.323889	−0.161944	−	0.986800i	$-0.551776\pi$
$601$	−7.94023	−0.323889	−0.161944	+	0.986800i	$0.551776\pi$
$602$	19.7011	0.802956
$603$	11.9252	0.485630
$604$	−13.3519	−0.543281
$605$	−10.3529	−0.420904
$606$	9.91353	0.402709
$607$	19.2504	0.781351	0.390676	−	0.920528i	$-0.372241\pi$
$607$	19.2504	0.781351	0.390676	+	0.920528i	$0.372241\pi$
$608$	5.71109	0.231615
$609$	9.78876	0.396661
$610$	−1.84636	−0.0747571
$611$	−20.0620	−0.811620
$612$	0	0
$613$	−17.3339	−0.700108	−0.350054	−	0.936730i	$-0.613837\pi$
$613$	−17.3339	−0.700108	−0.350054	+	0.936730i	$0.613837\pi$
$614$	−2.93201	−0.118326
$615$	5.58847	0.225349
$616$	3.05330	0.123021
$617$	−23.2266	−0.935066	−0.467533	−	0.883976i	$-0.654857\pi$
$617$	−23.2266	−0.935066	−0.467533	+	0.883976i	$0.654857\pi$
$618$	−18.0553	−0.726292
$619$	9.59412	0.385620	0.192810	−	0.981236i	$-0.438240\pi$
$619$	9.59412	0.385620	0.192810	+	0.981236i	$0.438240\pi$
$620$	−0.592208	−0.0237837
$621$	−7.82485	−0.314000
$622$	2.93740	0.117779
$623$	−37.5669	−1.50508
$624$	−4.25395	−0.170294
$625$	1.00000	0.0400000
$626$	4.74511	0.189653
$627$	4.59422	0.183475
$628$	13.7161	0.547333
$629$	0	0
$630$	3.79557	0.151219
$631$	−14.1066	−0.561574	−0.280787	−	0.959770i	$-0.590595\pi$
$631$	−14.1066	−0.561574	−0.280787	+	0.959770i	$0.590595\pi$
$632$	14.1634	0.563389
$633$	0.382123	0.0151880
$634$	13.5880	0.539648
$635$	−4.72447	−0.187485
$636$	5.34790	0.212058
$637$	−31.5062	−1.24832
$638$	2.07464	0.0821359
$639$	9.31407	0.368459
$640$	1.00000	0.0395285
$641$	23.2318	0.917601	0.458800	−	0.888539i	$-0.348279\pi$
$641$	23.2318	0.917601	0.458800	+	0.888539i	$0.348279\pi$
$642$	3.97765	0.156985
$643$	42.0185	1.65705	0.828524	−	0.559953i	$-0.189181\pi$
$643$	42.0185	1.65705	0.828524	+	0.559953i	$0.189181\pi$
$644$	−29.6998	−1.17033
$645$	5.19054	0.204377
$646$	0	0
$647$	−20.1032	−0.790337	−0.395168	−	0.918609i	$-0.629314\pi$
$647$	−20.1032	−0.790337	−0.395168	+	0.918609i	$0.629314\pi$
$648$	1.00000	0.0392837
$649$	−4.42363	−0.173643
$650$	−4.25395	−0.166854
$651$	−2.24777	−0.0880969
$652$	−6.35803	−0.249000
$653$	20.2575	0.792737	0.396369	−	0.918091i	$-0.370270\pi$
$653$	20.2575	0.792737	0.396369	+	0.918091i	$0.370270\pi$
$654$	−1.24047	−0.0485063
$655$	−18.5325	−0.724126
$656$	5.58847	0.218193
$657$	6.32700	0.246840
$658$	17.9002	0.697822
$659$	−16.7239	−0.651471	−0.325735	−	0.945461i	$-0.605612\pi$
$659$	−16.7239	−0.651471	−0.325735	+	0.945461i	$0.605612\pi$
$660$	0.804438	0.0313127
$661$	−3.05867	−0.118968	−0.0594841	−	0.998229i	$-0.518946\pi$
$661$	−3.05867	−0.118968	−0.0594841	+	0.998229i	$0.518946\pi$
$662$	−27.3064	−1.06129
$663$	0	0
$664$	−0.704063	−0.0273230
$665$	21.6768	0.840592
$666$	−5.34021	−0.206929
$667$	−20.1803	−0.781383
$668$	10.1107	0.391195
$669$	14.8901	0.575686
$670$	11.9252	0.460709
$671$	−1.48529	−0.0573388
$672$	3.79557	0.146417
$673$	−2.76524	−0.106592	−0.0532960	−	0.998579i	$-0.516973\pi$
$673$	−2.76524	−0.106592	−0.0532960	+	0.998579i	$0.516973\pi$
$674$	−11.9000	−0.458372
$675$	1.00000	0.0384900
$676$	5.09610	0.196004
$677$	39.7706	1.52851	0.764254	−	0.644915i	$-0.223107\pi$
$677$	39.7706	1.52851	0.764254	+	0.644915i	$0.223107\pi$
$678$	−0.827278	−0.0317714
$679$	73.5035	2.82080
$680$	0	0
$681$	8.48302	0.325070
$682$	−0.476395	−0.0182421
$683$	48.6187	1.86034	0.930171	−	0.367126i	$-0.119658\pi$
$683$	48.6187	1.86034	0.930171	+	0.367126i	$0.119658\pi$
$684$	5.71109	0.218369
$685$	12.8407	0.490620
$686$	1.54231	0.0588858
$687$	−23.0649	−0.879983
$688$	5.19054	0.197888
$689$	−22.7497	−0.866695
$690$	−7.82485	−0.297887
$691$	38.5877	1.46794	0.733972	−	0.679180i	$-0.237664\pi$
$691$	38.5877	1.46794	0.733972	+	0.679180i	$0.237664\pi$
$692$	−17.4312	−0.662634
$693$	3.05330	0.115985
$694$	−34.0894	−1.29401
$695$	3.86445	0.146587
$696$	2.57900	0.0977566
$697$	0	0
$698$	−20.1799	−0.763820
$699$	−21.8136	−0.825066
$700$	3.79557	0.143459
$701$	−13.9766	−0.527890	−0.263945	−	0.964538i	$-0.585024\pi$
$701$	−13.9766	−0.527890	−0.263945	+	0.964538i	$0.585024\pi$
$702$	−4.25395	−0.160555
$703$	−30.4984	−1.15027
$704$	0.804438	0.0303184
$705$	4.71607	0.177618
$706$	−5.24453	−0.197380
$707$	37.6275	1.41513
$708$	−5.49903	−0.206666
$709$	−13.6183	−0.511445	−0.255723	−	0.966750i	$-0.582313\pi$
$709$	−13.6183	−0.511445	−0.255723	+	0.966750i	$0.582313\pi$
$710$	9.31407	0.349551
$711$	14.1634	0.531168
$712$	−9.89756	−0.370927
$713$	4.63394	0.173542
$714$	0	0
$715$	−3.42204	−0.127977
$716$	−24.7564	−0.925189
$717$	23.9606	0.894825
$718$	6.58973	0.245927
$719$	−3.83987	−0.143203	−0.0716014	−	0.997433i	$-0.522811\pi$
$719$	−3.83987	−0.143203	−0.0716014	+	0.997433i	$0.522811\pi$
$720$	1.00000	0.0372678
$721$	−68.5302	−2.55220
$722$	13.6166	0.506757
$723$	−28.1240	−1.04594
$724$	19.2155	0.714137
$725$	2.57900	0.0957815
$726$	−10.3529	−0.384231
$727$	−7.41245	−0.274913	−0.137456	−	0.990508i	$-0.543893\pi$
$727$	−7.41245	−0.274913	−0.137456	+	0.990508i	$0.543893\pi$
$728$	−16.1462	−0.598417
$729$	1.00000	0.0370370
$730$	6.32700	0.234173
$731$	0	0
$732$	−1.84636	−0.0682436
$733$	28.3396	1.04675	0.523373	−	0.852103i	$-0.324673\pi$
$733$	28.3396	1.04675	0.523373	+	0.852103i	$0.324673\pi$
$734$	−29.0677	−1.07291
$735$	7.40635	0.273187
$736$	−7.82485	−0.288428
$737$	9.59305	0.353365
$738$	5.58847	0.205714
$739$	28.6102	1.05245	0.526223	−	0.850347i	$-0.323608\pi$
$739$	28.6102	1.05245	0.526223	+	0.850347i	$0.323608\pi$
$740$	−5.34021	−0.196310
$741$	−24.2947	−0.892489
$742$	20.2983	0.745175
$743$	46.4586	1.70440	0.852200	−	0.523215i	$-0.175268\pi$
$743$	46.4586	1.70440	0.852200	+	0.523215i	$0.175268\pi$
$744$	−0.592208	−0.0217114
$745$	−13.8509	−0.507456
$746$	23.1502	0.847590
$747$	−0.704063	−0.0257603
$748$	0	0
$749$	15.0975	0.551649
$750$	1.00000	0.0365148
$751$	15.0085	0.547667	0.273834	−	0.961777i	$-0.411708\pi$
$751$	15.0085	0.547667	0.273834	+	0.961777i	$0.411708\pi$
$752$	4.71607	0.171978
$753$	−17.5259	−0.638678
$754$	−10.9709	−0.399538
$755$	−13.3519	−0.485925
$756$	3.79557	0.138044
$757$	−26.9753	−0.980433	−0.490217	−	0.871601i	$-0.663082\pi$
$757$	−26.9753	−0.980433	−0.490217	+	0.871601i	$0.663082\pi$
$758$	−27.8603	−1.01193
$759$	−6.29460	−0.228480
$760$	5.71109	0.207163
$761$	9.84336	0.356822	0.178411	−	0.983956i	$-0.442904\pi$
$761$	9.84336	0.356822	0.178411	+	0.983956i	$0.442904\pi$
$762$	−4.72447	−0.171150
$763$	−4.70830	−0.170452
$764$	−8.93913	−0.323406
$765$	0	0
$766$	−37.7469	−1.36385
$767$	23.3926	0.844658
$768$	1.00000	0.0360844
$769$	40.1556	1.44805	0.724024	−	0.689775i	$-0.242291\pi$
$769$	40.1556	1.44805	0.724024	+	0.689775i	$0.242291\pi$
$770$	3.05330	0.110033
$771$	−15.5691	−0.560709
$772$	−13.4719	−0.484866
$773$	−10.9309	−0.393157	−0.196579	−	0.980488i	$-0.562983\pi$
$773$	−10.9309	−0.393157	−0.196579	+	0.980488i	$0.562983\pi$
$774$	5.19054	0.186570
$775$	−0.592208	−0.0212727
$776$	19.3656	0.695185
$777$	−20.2691	−0.727151
$778$	8.76118	0.314104
$779$	31.9163	1.14352
$780$	−4.25395	−0.152316
$781$	7.49259	0.268106
$782$	0	0
$783$	2.57900	0.0921658
$784$	7.40635	0.264512
$785$	13.7161	0.489550
$786$	−18.5325	−0.661034
$787$	−43.3000	−1.54348	−0.771740	−	0.635938i	$-0.780613\pi$
$787$	−43.3000	−1.54348	−0.771740	+	0.635938i	$0.780613\pi$
$788$	12.0135	0.427962
$789$	−5.12041	−0.182291
$790$	14.1634	0.503911
$791$	−3.13999	−0.111645
$792$	0.804438	0.0285844
$793$	7.85435	0.278916
$794$	2.52190	0.0894988
$795$	5.34790	0.189670
$796$	11.9693	0.424241
$797$	−11.0647	−0.391931	−0.195966	−	0.980611i	$-0.562784\pi$
$797$	−11.0647	−0.391931	−0.195966	+	0.980611i	$0.562784\pi$
$798$	21.6768	0.767352
$799$	0	0
$800$	1.00000	0.0353553
$801$	−9.89756	−0.349713
$802$	−23.7926	−0.840147
$803$	5.08968	0.179611
$804$	11.9252	0.420568
$805$	−29.6998	−1.04678
$806$	2.51922	0.0887359
$807$	0.377571	0.0132911
$808$	9.91353	0.348757
$809$	5.95723	0.209445	0.104723	−	0.994501i	$-0.466605\pi$
$809$	5.95723	0.209445	0.104723	+	0.994501i	$0.466605\pi$
$810$	1.00000	0.0351364
$811$	15.8844	0.557777	0.278888	−	0.960324i	$-0.410034\pi$
$811$	15.8844	0.557777	0.278888	+	0.960324i	$0.410034\pi$
$812$	9.78876	0.343518
$813$	−16.5926	−0.581927
$814$	−4.29587	−0.150570
$815$	−6.35803	−0.222712
$816$	0	0
$817$	29.6437	1.03710
$818$	17.3508	0.606657
$819$	−16.1462	−0.564193
$820$	5.58847	0.195158
$821$	0.497544	0.0173644	0.00868220	−	0.999962i	$-0.497236\pi$
$821$	0.497544	0.0173644	0.00868220	+	0.999962i	$0.497236\pi$
$822$	12.8407	0.447872
$823$	−6.50865	−0.226877	−0.113439	−	0.993545i	$-0.536187\pi$
$823$	−6.50865	−0.226877	−0.113439	+	0.993545i	$0.536187\pi$
$824$	−18.0553	−0.628987
$825$	0.804438	0.0280069
$826$	−20.8720	−0.726228
$827$	1.07915	0.0375256	0.0187628	−	0.999824i	$-0.494027\pi$
$827$	1.07915	0.0375256	0.0187628	+	0.999824i	$0.494027\pi$
$828$	−7.82485	−0.271932
$829$	14.2905	0.496330	0.248165	−	0.968718i	$-0.420172\pi$
$829$	14.2905	0.496330	0.248165	+	0.968718i	$0.420172\pi$
$830$	−0.704063	−0.0244384
$831$	30.5882	1.06109
$832$	−4.25395	−0.147479
$833$	0	0
$834$	3.86445	0.133815
$835$	10.1107	0.349896
$836$	4.59422	0.158894
$837$	−0.592208	−0.0204697
$838$	−7.00037	−0.241824
$839$	20.2086	0.697677	0.348838	−	0.937183i	$-0.386576\pi$
$839$	20.2086	0.697677	0.348838	+	0.937183i	$0.386576\pi$
$840$	3.79557	0.130960
$841$	−22.3488	−0.770647
$842$	28.8204	0.993217
$843$	−24.0015	−0.826655
$844$	0.382123	0.0131532
$845$	5.09610	0.175311
$846$	4.71607	0.162142
$847$	−39.2951	−1.35019
$848$	5.34790	0.183648
$849$	13.0199	0.446843
$850$	0	0
$851$	41.7863	1.43242
$852$	9.31407	0.319095
$853$	8.47280	0.290103	0.145051	−	0.989424i	$-0.453665\pi$
$853$	8.47280	0.290103	0.145051	+	0.989424i	$0.453665\pi$
$854$	−7.00800	−0.239809
$855$	5.71109	0.195315
$856$	3.97765	0.135953
$857$	−6.97217	−0.238165	−0.119082	−	0.992884i	$-0.537995\pi$
$857$	−6.97217	−0.238165	−0.119082	+	0.992884i	$0.537995\pi$
$858$	−3.42204	−0.116826
$859$	42.1491	1.43811	0.719055	−	0.694953i	$-0.244575\pi$
$859$	42.1491	1.43811	0.719055	+	0.694953i	$0.244575\pi$
$860$	5.19054	0.176996
$861$	21.2114	0.722883
$862$	32.9500	1.12228
$863$	−45.0658	−1.53406	−0.767028	−	0.641613i	$-0.778265\pi$
$863$	−45.0658	−1.53406	−0.767028	+	0.641613i	$0.778265\pi$
$864$	1.00000	0.0340207
$865$	−17.4312	−0.592678
$866$	6.71647	0.228235
$867$	0	0
$868$	−2.24777	−0.0762942
$869$	11.3936	0.386500
$870$	2.57900	0.0874362
$871$	−50.7291	−1.71889
$872$	−1.24047	−0.0420077
$873$	19.3656	0.655426
$874$	−44.6884	−1.51161
$875$	3.79557	0.128314
$876$	6.32700	0.213769
$877$	−14.2826	−0.482288	−0.241144	−	0.970489i	$-0.577523\pi$
$877$	−14.2826	−0.482288	−0.241144	+	0.970489i	$0.577523\pi$
$878$	−8.88195	−0.299751
$879$	32.0249	1.08017
$880$	0.804438	0.0271176
$881$	−32.7496	−1.10336	−0.551681	−	0.834055i	$-0.686013\pi$
$881$	−32.7496	−1.10336	−0.551681	+	0.834055i	$0.686013\pi$
$882$	7.40635	0.249385
$883$	24.8579	0.836536	0.418268	−	0.908324i	$-0.362637\pi$
$883$	24.8579	0.836536	0.418268	+	0.908324i	$0.362637\pi$
$884$	0	0
$885$	−5.49903	−0.184848
$886$	−28.4920	−0.957208
$887$	−30.3024	−1.01745	−0.508727	−	0.860928i	$-0.669884\pi$
$887$	−30.3024	−1.01745	−0.508727	+	0.860928i	$0.669884\pi$
$888$	−5.34021	−0.179206
$889$	−17.9321	−0.601422
$890$	−9.89756	−0.331767
$891$	0.804438	0.0269497
$892$	14.8901	0.498559
$893$	26.9339	0.901310
$894$	−13.8509	−0.463242
$895$	−24.7564	−0.827514
$896$	3.79557	0.126801
$897$	33.2865	1.11140
$898$	−24.3579	−0.812833
$899$	−1.52730	−0.0509384
$900$	1.00000	0.0333333
$901$	0	0
$902$	4.49557	0.149686
$903$	19.7011	0.655610
$904$	−0.827278	−0.0275148
$905$	19.2155	0.638744
$906$	−13.3519	−0.443587
$907$	45.5256	1.51165	0.755826	−	0.654773i	$-0.227236\pi$
$907$	45.5256	1.51165	0.755826	+	0.654773i	$0.227236\pi$
$908$	8.48302	0.281519
$909$	9.91353	0.328811
$910$	−16.1462	−0.535240
$911$	41.5951	1.37811	0.689053	−	0.724711i	$-0.258027\pi$
$911$	41.5951	1.37811	0.689053	+	0.724711i	$0.258027\pi$
$912$	5.71109	0.189113
$913$	−0.566375	−0.0187443
$914$	37.6880	1.24661
$915$	−1.84636	−0.0610389
$916$	−23.0649	−0.762087
$917$	−70.3415	−2.32288
$918$	0	0
$919$	20.6236	0.680308	0.340154	−	0.940370i	$-0.389521\pi$
$919$	20.6236	0.680308	0.340154	+	0.940370i	$0.389521\pi$
$920$	−7.82485	−0.257978
$921$	−2.93201	−0.0966129
$922$	−14.6240	−0.481615
$923$	−39.6216	−1.30416
$924$	3.05330	0.100446
$925$	−5.34021	−0.175585
$926$	18.8544	0.619594
$927$	−18.0553	−0.593015
$928$	2.57900	0.0846597
$929$	−47.5141	−1.55889	−0.779443	−	0.626473i	$-0.784498\pi$
$929$	−47.5141	−1.55889	−0.779443	+	0.626473i	$0.784498\pi$
$930$	−0.592208	−0.0194193
$931$	42.2983	1.38627
$932$	−21.8136	−0.714528
$933$	2.93740	0.0961662
$934$	−35.0767	−1.14775
$935$	0	0
$936$	−4.25395	−0.139045
$937$	−33.8771	−1.10672	−0.553358	−	0.832943i	$-0.686654\pi$
$937$	−33.8771	−1.10672	−0.553358	+	0.832943i	$0.686654\pi$
$938$	45.2628	1.47788
$939$	4.74511	0.154851
$940$	4.71607	0.153821
$941$	−9.52831	−0.310614	−0.155307	−	0.987866i	$-0.549637\pi$
$941$	−9.52831	−0.310614	−0.155307	+	0.987866i	$0.549637\pi$
$942$	13.7161	0.446896
$943$	−43.7289	−1.42401
$944$	−5.49903	−0.178978
$945$	3.79557	0.123470
$946$	4.17547	0.135756
$947$	−11.3082	−0.367468	−0.183734	−	0.982976i	$-0.558818\pi$
$947$	−11.3082	−0.367468	−0.183734	+	0.982976i	$0.558818\pi$
$948$	14.1634	0.460005
$949$	−26.9147	−0.873690
$950$	5.71109	0.185292
$951$	13.5880	0.440621
$952$	0	0
$953$	14.0973	0.456655	0.228328	−	0.973584i	$-0.426674\pi$
$953$	14.0973	0.456655	0.228328	+	0.973584i	$0.426674\pi$
$954$	5.34790	0.173145
$955$	−8.93913	−0.289264
$956$	23.9606	0.774941
$957$	2.07464	0.0670637
$958$	7.53020	0.243290
$959$	48.7379	1.57383
$960$	1.00000	0.0322749
$961$	−30.6493	−0.988687
$962$	22.7170	0.732425
$963$	3.97765	0.128178
$964$	−28.1240	−0.905814
$965$	−13.4719	−0.433677
$966$	−29.6998	−0.955574
$967$	31.6897	1.01907	0.509536	−	0.860450i	$-0.329817\pi$
$967$	31.6897	1.01907	0.509536	+	0.860450i	$0.329817\pi$
$968$	−10.3529	−0.332754
$969$	0	0
$970$	19.3656	0.621792
$971$	−24.6127	−0.789858	−0.394929	−	0.918712i	$-0.629231\pi$
$971$	−24.6127	−0.789858	−0.394929	+	0.918712i	$0.629231\pi$
$972$	1.00000	0.0320750
$973$	14.6678	0.470227
$974$	−39.6386	−1.27010
$975$	−4.25395	−0.136235
$976$	−1.84636	−0.0591007
$977$	−26.9926	−0.863570	−0.431785	−	0.901976i	$-0.642116\pi$
$977$	−26.9926	−0.863570	−0.431785	+	0.901976i	$0.642116\pi$
$978$	−6.35803	−0.203307
$979$	−7.96197	−0.254466
$980$	7.40635	0.236587
$981$	−1.24047	−0.0396053
$982$	−29.3103	−0.935328
$983$	40.9645	1.30656	0.653282	−	0.757115i	$-0.273392\pi$
$983$	40.9645	1.30656	0.653282	+	0.757115i	$0.273392\pi$
$984$	5.58847	0.178154
$985$	12.0135	0.382781
$986$	0	0
$987$	17.9002	0.569769
$988$	−24.2947	−0.772918
$989$	−40.6152	−1.29149
$990$	0.804438	0.0255667
$991$	−13.4406	−0.426953	−0.213477	−	0.976948i	$-0.568479\pi$
$991$	−13.4406	−0.426953	−0.213477	+	0.976948i	$0.568479\pi$
$992$	−0.592208	−0.0188026
$993$	−27.3064	−0.866542
$994$	35.3522	1.12130
$995$	11.9693	0.379453
$996$	−0.704063	−0.0223091
$997$	−6.16933	−0.195385	−0.0976923	−	0.995217i	$-0.531146\pi$
$997$	−6.16933	−0.195385	−0.0976923	+	0.995217i	$0.531146\pi$
$998$	−4.91144	−0.155469
$999$	−5.34021	−0.168957

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8670.2.a.ci.1.5	yes	6
17.16	even	2		8670.2.a.cf.1.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8670.2.a.cf.1.2	✓	6	17.16	even	2
8670.2.a.ci.1.5	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8670.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +3.79557 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +3.79557 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +0.804438 q^{11} +1.00000 q^{12} -4.25395 q^{13} +3.79557 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} +5.71109 q^{19} +1.00000 q^{20} +3.79557 q^{21} +0.804438 q^{22} -7.82485 q^{23} +1.00000 q^{24} +1.00000 q^{25} -4.25395 q^{26} +1.00000 q^{27} +3.79557 q^{28} +2.57900 q^{29} +1.00000 q^{30} -0.592208 q^{31} +1.00000 q^{32} +0.804438 q^{33} +3.79557 q^{35} +1.00000 q^{36} -5.34021 q^{37} +5.71109 q^{38} -4.25395 q^{39} +1.00000 q^{40} +5.58847 q^{41} +3.79557 q^{42} +5.19054 q^{43} +0.804438 q^{44} +1.00000 q^{45} -7.82485 q^{46} +4.71607 q^{47} +1.00000 q^{48} +7.40635 q^{49} +1.00000 q^{50} -4.25395 q^{52} +5.34790 q^{53} +1.00000 q^{54} +0.804438 q^{55} +3.79557 q^{56} +5.71109 q^{57} +2.57900 q^{58} -5.49903 q^{59} +1.00000 q^{60} -1.84636 q^{61} -0.592208 q^{62} +3.79557 q^{63} +1.00000 q^{64} -4.25395 q^{65} +0.804438 q^{66} +11.9252 q^{67} -7.82485 q^{69} +3.79557 q^{70} +9.31407 q^{71} +1.00000 q^{72} +6.32700 q^{73} -5.34021 q^{74} +1.00000 q^{75} +5.71109 q^{76} +3.05330 q^{77} -4.25395 q^{78} +14.1634 q^{79} +1.00000 q^{80} +1.00000 q^{81} +5.58847 q^{82} -0.704063 q^{83} +3.79557 q^{84} +5.19054 q^{86} +2.57900 q^{87} +0.804438 q^{88} -9.89756 q^{89} +1.00000 q^{90} -16.1462 q^{91} -7.82485 q^{92} -0.592208 q^{93} +4.71607 q^{94} +5.71109 q^{95} +1.00000 q^{96} +19.3656 q^{97} +7.40635 q^{98} +0.804438 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 6 q^{10} + 6 q^{11} + 6 q^{12} + 6 q^{13} + 6 q^{14} + 6 q^{15} + 6 q^{16} + 6 q^{18} + 6 q^{19} + 6 q^{20} + 6 q^{21} + 6 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{25} + 6 q^{26} + 6 q^{27} + 6 q^{28} + 12 q^{29} + 6 q^{30} + 6 q^{31} + 6 q^{32} + 6 q^{33} + 6 q^{35} + 6 q^{36} + 6 q^{37} + 6 q^{38} + 6 q^{39} + 6 q^{40} + 12 q^{41} + 6 q^{42} + 18 q^{43} + 6 q^{44} + 6 q^{45} + 6 q^{46} - 6 q^{47} + 6 q^{48} + 18 q^{49} + 6 q^{50} + 6 q^{52} - 6 q^{53} + 6 q^{54} + 6 q^{55} + 6 q^{56} + 6 q^{57} + 12 q^{58} - 30 q^{59} + 6 q^{60} - 24 q^{61} + 6 q^{62} + 6 q^{63} + 6 q^{64} + 6 q^{65} + 6 q^{66} + 6 q^{69} + 6 q^{70} + 24 q^{71} + 6 q^{72} + 6 q^{73} + 6 q^{74} + 6 q^{75} + 6 q^{76} + 6 q^{78} + 6 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} + 18 q^{83} + 6 q^{84} + 18 q^{86} + 12 q^{87} + 6 q^{88} - 12 q^{89} + 6 q^{90} + 6 q^{91} + 6 q^{92} + 6 q^{93} - 6 q^{94} + 6 q^{95} + 6 q^{96} + 18 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 6 * q^10 + 6 * q^11 + 6 * q^12 + 6 * q^13 + 6 * q^14 + 6 * q^15 + 6 * q^16 + 6 * q^18 + 6 * q^19 + 6 * q^20 + 6 * q^21 + 6 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^25 + 6 * q^26 + 6 * q^27 + 6 * q^28 + 12 * q^29 + 6 * q^30 + 6 * q^31 + 6 * q^32 + 6 * q^33 + 6 * q^35 + 6 * q^36 + 6 * q^37 + 6 * q^38 + 6 * q^39 + 6 * q^40 + 12 * q^41 + 6 * q^42 + 18 * q^43 + 6 * q^44 + 6 * q^45 + 6 * q^46 - 6 * q^47 + 6 * q^48 + 18 * q^49 + 6 * q^50 + 6 * q^52 - 6 * q^53 + 6 * q^54 + 6 * q^55 + 6 * q^56 + 6 * q^57 + 12 * q^58 - 30 * q^59 + 6 * q^60 - 24 * q^61 + 6 * q^62 + 6 * q^63 + 6 * q^64 + 6 * q^65 + 6 * q^66 + 6 * q^69 + 6 * q^70 + 24 * q^71 + 6 * q^72 + 6 * q^73 + 6 * q^74 + 6 * q^75 + 6 * q^76 + 6 * q^78 + 6 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 + 18 * q^83 + 6 * q^84 + 18 * q^86 + 12 * q^87 + 6 * q^88 - 12 * q^89 + 6 * q^90 + 6 * q^91 + 6 * q^92 + 6 * q^93 - 6 * q^94 + 6 * q^95 + 6 * q^96 + 18 * q^97 + 18 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more