LMFDB - Embedded newform 4598.2.a.bk.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, 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("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
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			1.2
Root			$-0.363328$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.36333 q^{3} +1.00000 q^{4} +0.363328 q^{5} +1.36333 q^{6} -2.14134 q^{7} -1.00000 q^{8} -1.14134 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.36333 q^{3} +1.00000 q^{4} +0.363328 q^{5} +1.36333 q^{6} -2.14134 q^{7} -1.00000 q^{8} -1.14134 q^{9} -0.363328 q^{10} -1.36333 q^{12} +3.14134 q^{13} +2.14134 q^{14} -0.495336 q^{15} +1.00000 q^{16} -1.14134 q^{17} +1.14134 q^{18} +1.00000 q^{19} +0.363328 q^{20} +2.91934 q^{21} -2.14134 q^{23} +1.36333 q^{24} -4.86799 q^{25} -3.14134 q^{26} +5.64600 q^{27} -2.14134 q^{28} +1.77801 q^{29} +0.495336 q^{30} +7.00933 q^{31} -1.00000 q^{32} +1.14134 q^{34} -0.778008 q^{35} -1.14134 q^{36} -9.77801 q^{37} -1.00000 q^{38} -4.28267 q^{39} -0.363328 q^{40} +7.91934 q^{41} -2.91934 q^{42} +4.28267 q^{43} -0.414680 q^{45} +2.14134 q^{46} -7.59465 q^{47} -1.36333 q^{48} -2.41468 q^{49} +4.86799 q^{50} +1.55602 q^{51} +3.14134 q^{52} +10.7873 q^{53} -5.64600 q^{54} +2.14134 q^{56} -1.36333 q^{57} -1.77801 q^{58} -1.08066 q^{59} -0.495336 q^{60} +8.51399 q^{61} -7.00933 q^{62} +2.44398 q^{63} +1.00000 q^{64} +1.14134 q^{65} +8.56534 q^{67} -1.14134 q^{68} +2.91934 q^{69} +0.778008 q^{70} +3.50466 q^{71} +1.14134 q^{72} -11.7360 q^{73} +9.77801 q^{74} +6.63667 q^{75} +1.00000 q^{76} +4.28267 q^{78} -0.778008 q^{79} +0.363328 q^{80} -4.27334 q^{81} -7.91934 q^{82} +0.778008 q^{83} +2.91934 q^{84} -0.414680 q^{85} -4.28267 q^{86} -2.42401 q^{87} -8.20202 q^{89} +0.414680 q^{90} -6.72666 q^{91} -2.14134 q^{92} -9.55602 q^{93} +7.59465 q^{94} +0.363328 q^{95} +1.36333 q^{96} -1.86799 q^{97} +2.41468 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - q^{5} + 2 q^{6} + 2 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - q^5 + 2 * q^6 + 2 * q^7 - 3 * q^8 + 5 * q^9	$ 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - q^{5} + 2 q^{6} + 2 q^{7} - 3 q^{8} + 5 q^{9} + q^{10} - 2 q^{12} + q^{13} - 2 q^{14} - 12 q^{15} + 3 q^{16} + 5 q^{17} - 5 q^{18} + 3 q^{19} - q^{20} - 6 q^{21} + 2 q^{23} + 2 q^{24} - 2 q^{25} - q^{26} - 2 q^{27} + 2 q^{28} - q^{29} + 12 q^{30} - 3 q^{32} - 5 q^{34} + 4 q^{35} + 5 q^{36} - 23 q^{37} - 3 q^{38} + 4 q^{39} + q^{40} + 9 q^{41} + 6 q^{42} - 4 q^{43} + 3 q^{45} - 2 q^{46} - 6 q^{47} - 2 q^{48} - 3 q^{49} + 2 q^{50} - 8 q^{51} + q^{52} + 5 q^{53} + 2 q^{54} - 2 q^{56} - 2 q^{57} + q^{58} - 18 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{63} + 3 q^{64} - 5 q^{65} - 8 q^{67} + 5 q^{68} - 6 q^{69} - 4 q^{70} - 5 q^{72} - 10 q^{73} + 23 q^{74} + 22 q^{75} + 3 q^{76} - 4 q^{78} + 4 q^{79} - q^{80} - 17 q^{81} - 9 q^{82} - 4 q^{83} - 6 q^{84} + 3 q^{85} + 4 q^{86} + 18 q^{87} + 7 q^{89} - 3 q^{90} - 16 q^{91} + 2 q^{92} - 16 q^{93} + 6 q^{94} - q^{95} + 2 q^{96} + 7 q^{97} + 3 q^{98}+O(q^{100}) $ 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - q^5 + 2 * q^6 + 2 * q^7 - 3 * q^8 + 5 * q^9 + q^10 - 2 * q^12 + q^13 - 2 * q^14 - 12 * q^15 + 3 * q^16 + 5 * q^17 - 5 * q^18 + 3 * q^19 - q^20 - 6 * q^21 + 2 * q^23 + 2 * q^24 - 2 * q^25 - q^26 - 2 * q^27 + 2 * q^28 - q^29 + 12 * q^30 - 3 * q^32 - 5 * q^34 + 4 * q^35 + 5 * q^36 - 23 * q^37 - 3 * q^38 + 4 * q^39 + q^40 + 9 * q^41 + 6 * q^42 - 4 * q^43 + 3 * q^45 - 2 * q^46 - 6 * q^47 - 2 * q^48 - 3 * q^49 + 2 * q^50 - 8 * q^51 + q^52 + 5 * q^53 + 2 * q^54 - 2 * q^56 - 2 * q^57 + q^58 - 18 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^63 + 3 * q^64 - 5 * q^65 - 8 * q^67 + 5 * q^68 - 6 * q^69 - 4 * q^70 - 5 * q^72 - 10 * q^73 + 23 * q^74 + 22 * q^75 + 3 * q^76 - 4 * q^78 + 4 * q^79 - q^80 - 17 * q^81 - 9 * q^82 - 4 * q^83 - 6 * q^84 + 3 * q^85 + 4 * q^86 + 18 * q^87 + 7 * q^89 - 3 * q^90 - 16 * q^91 + 2 * q^92 - 16 * q^93 + 6 * q^94 - q^95 + 2 * q^96 + 7 * q^97 + 3 * q^98

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
$3$	−1.36333	−0.787118	−0.393559	−	0.919299i	$-0.628756\pi$
$3$	−1.36333	−0.787118	−0.393559	+	0.919299i	$0.628756\pi$
$4$	1.00000	0.500000
$5$	0.363328	0.162485	0.0812427	−	0.996694i	$-0.474111\pi$
$5$	0.363328	0.162485	0.0812427	+	0.996694i	$0.474111\pi$
$6$	1.36333	0.556576
$7$	−2.14134	−0.809349	−0.404674	−	0.914461i	$-0.632615\pi$
$7$	−2.14134	−0.809349	−0.404674	+	0.914461i	$0.632615\pi$
$8$	−1.00000	−0.353553
$9$	−1.14134	−0.380445
$10$	−0.363328	−0.114894
$11$	0	0
$11$	0	0
$12$	−1.36333	−0.393559
$13$	3.14134	0.871250	0.435625	−	0.900128i	$-0.356527\pi$
$13$	3.14134	0.871250	0.435625	+	0.900128i	$0.356527\pi$
$14$	2.14134	0.572296
$15$	−0.495336	−0.127895
$16$	1.00000	0.250000
$17$	−1.14134	−0.276815	−0.138407	−	0.990375i	$-0.544198\pi$
$17$	−1.14134	−0.276815	−0.138407	+	0.990375i	$0.544198\pi$
$18$	1.14134	0.269016
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.363328	0.0812427
$21$	2.91934	0.637053
$22$	0	0
$23$	−2.14134	−0.446499	−0.223250	−	0.974761i	$-0.571667\pi$
$23$	−2.14134	−0.446499	−0.223250	+	0.974761i	$0.571667\pi$
$24$	1.36333	0.278288
$25$	−4.86799	−0.973599
$26$	−3.14134	−0.616067
$27$	5.64600	1.08657
$28$	−2.14134	−0.404674
$29$	1.77801	0.330168	0.165084	−	0.986280i	$-0.447211\pi$
$29$	1.77801	0.330168	0.165084	+	0.986280i	$0.447211\pi$
$30$	0.495336	0.0904355
$31$	7.00933	1.25891	0.629456	−	0.777036i	$-0.283278\pi$
$31$	7.00933	1.25891	0.629456	+	0.777036i	$0.283278\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	1.14134	0.195738
$35$	−0.778008	−0.131507
$36$	−1.14134	−0.190223
$37$	−9.77801	−1.60749	−0.803747	−	0.594971i	$-0.797164\pi$
$37$	−9.77801	−1.60749	−0.803747	+	0.594971i	$0.797164\pi$
$38$	−1.00000	−0.162221
$39$	−4.28267	−0.685776
$40$	−0.363328	−0.0574472
$41$	7.91934	1.23679	0.618397	−	0.785866i	$-0.287782\pi$
$41$	7.91934	1.23679	0.618397	+	0.785866i	$0.287782\pi$
$42$	−2.91934	−0.450465
$43$	4.28267	0.653101	0.326551	−	0.945180i	$-0.394114\pi$
$43$	4.28267	0.653101	0.326551	+	0.945180i	$0.394114\pi$
$44$	0	0
$45$	−0.414680	−0.0618168
$46$	2.14134	0.315723
$47$	−7.59465	−1.10779	−0.553897	−	0.832585i	$-0.686860\pi$
$47$	−7.59465	−1.10779	−0.553897	+	0.832585i	$0.686860\pi$
$48$	−1.36333	−0.196779
$49$	−2.41468	−0.344954
$50$	4.86799	0.688438
$51$	1.55602	0.217886
$52$	3.14134	0.435625
$53$	10.7873	1.48175	0.740877	−	0.671640i	$-0.234410\pi$
$53$	10.7873	1.48175	0.740877	+	0.671640i	$0.234410\pi$
$54$	−5.64600	−0.768323
$55$	0	0
$56$	2.14134	0.286148
$57$	−1.36333	−0.180577
$58$	−1.77801	−0.233464
$59$	−1.08066	−0.140689	−0.0703447	−	0.997523i	$-0.522410\pi$
$59$	−1.08066	−0.140689	−0.0703447	+	0.997523i	$0.522410\pi$
$60$	−0.495336	−0.0639476
$61$	8.51399	1.09011	0.545053	−	0.838402i	$-0.316510\pi$
$61$	8.51399	1.09011	0.545053	+	0.838402i	$0.316510\pi$
$62$	−7.00933	−0.890186
$63$	2.44398	0.307913
$64$	1.00000	0.125000
$65$	1.14134	0.141565
$66$	0	0
$67$	8.56534	1.04642	0.523212	−	0.852203i	$-0.324734\pi$
$67$	8.56534	1.04642	0.523212	+	0.852203i	$0.324734\pi$
$68$	−1.14134	−0.138407
$69$	2.91934	0.351448
$70$	0.778008	0.0929897
$71$	3.50466	0.415927	0.207964	−	0.978137i	$-0.433316\pi$
$71$	3.50466	0.415927	0.207964	+	0.978137i	$0.433316\pi$
$72$	1.14134	0.134508
$73$	−11.7360	−1.37359	−0.686797	−	0.726850i	$-0.740984\pi$
$73$	−11.7360	−1.37359	−0.686797	+	0.726850i	$0.740984\pi$
$74$	9.77801	1.13667
$75$	6.63667	0.766337
$76$	1.00000	0.114708
$77$	0	0
$78$	4.28267	0.484917
$79$	−0.778008	−0.0875327	−0.0437664	−	0.999042i	$-0.513936\pi$
$79$	−0.778008	−0.0875327	−0.0437664	+	0.999042i	$0.513936\pi$
$80$	0.363328	0.0406213
$81$	−4.27334	−0.474816
$82$	−7.91934	−0.874545
$83$	0.778008	0.0853975	0.0426987	−	0.999088i	$-0.486404\pi$
$83$	0.778008	0.0853975	0.0426987	+	0.999088i	$0.486404\pi$
$84$	2.91934	0.318527
$85$	−0.414680	−0.0449783
$86$	−4.28267	−0.461812
$87$	−2.42401	−0.259881
$88$	0	0
$89$	−8.20202	−0.869412	−0.434706	−	0.900572i	$-0.643148\pi$
$89$	−8.20202	−0.869412	−0.434706	+	0.900572i	$0.643148\pi$
$90$	0.414680	0.0437111
$91$	−6.72666	−0.705145
$92$	−2.14134	−0.223250
$93$	−9.55602	−0.990913
$94$	7.59465	0.783328
$95$	0.363328	0.0372767
$96$	1.36333	0.139144
$97$	−1.86799	−0.189666	−0.0948330	−	0.995493i	$-0.530232\pi$
$97$	−1.86799	−0.189666	−0.0948330	+	0.995493i	$0.530232\pi$
$98$	2.41468	0.243919
$99$	0	0
$100$	−4.86799	−0.486799
$101$	10.0700	1.00200	0.501002	−	0.865446i	$-0.332965\pi$
$101$	10.0700	1.00200	0.501002	+	0.865446i	$0.332965\pi$
$102$	−1.55602	−0.154069
$103$	−17.3434	−1.70889	−0.854446	−	0.519541i	$-0.826103\pi$
$103$	−17.3434	−1.70889	−0.854446	+	0.519541i	$0.826103\pi$
$104$	−3.14134	−0.308033
$105$	1.06068	0.103512
$106$	−10.7873	−1.04776
$107$	13.6460	1.31921	0.659604	−	0.751613i	$-0.270724\pi$
$107$	13.6460	1.31921	0.659604	+	0.751613i	$0.270724\pi$
$108$	5.64600	0.543287
$109$	−5.33402	−0.510907	−0.255453	−	0.966821i	$-0.582225\pi$
$109$	−5.33402	−0.510907	−0.255453	+	0.966821i	$0.582225\pi$
$110$	0	0
$111$	13.3306	1.26529
$112$	−2.14134	−0.202337
$113$	−14.3633	−1.35119	−0.675594	−	0.737274i	$-0.736113\pi$
$113$	−14.3633	−1.35119	−0.675594	+	0.737274i	$0.736113\pi$
$114$	1.36333	0.127687
$115$	−0.778008	−0.0725496
$116$	1.77801	0.165084
$117$	−3.58532	−0.331463
$118$	1.08066	0.0994824
$119$	2.44398	0.224040
$120$	0.495336	0.0452178
$121$	0	0
$122$	−8.51399	−0.770821
$123$	−10.7967	−0.973503
$124$	7.00933	0.629456
$125$	−3.58532	−0.320681
$126$	−2.44398	−0.217727
$127$	2.44398	0.216869	0.108434	−	0.994104i	$-0.465416\pi$
$127$	2.44398	0.216869	0.108434	+	0.994104i	$0.465416\pi$
$128$	−1.00000	−0.0883883
$129$	−5.83869	−0.514068
$130$	−1.14134	−0.100102
$131$	0.707999	0.0618582	0.0309291	−	0.999522i	$-0.490153\pi$
$131$	0.707999	0.0618582	0.0309291	+	0.999522i	$0.490153\pi$
$132$	0	0
$133$	−2.14134	−0.185677
$134$	−8.56534	−0.739933
$135$	2.05135	0.176552
$136$	1.14134	0.0978688
$137$	6.28267	0.536765	0.268382	−	0.963312i	$-0.413511\pi$
$137$	6.28267	0.536765	0.268382	+	0.963312i	$0.413511\pi$
$138$	−2.91934	−0.248511
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	−0.778008	−0.0657537
$141$	10.3540	0.871964
$142$	−3.50466	−0.294105
$143$	0	0
$144$	−1.14134	−0.0951113
$145$	0.646000	0.0536474
$146$	11.7360	0.971277
$147$	3.29200	0.271520
$148$	−9.77801	−0.803747
$149$	−11.1600	−0.914262	−0.457131	−	0.889399i	$-0.651123\pi$
$149$	−11.1600	−0.914262	−0.457131	+	0.889399i	$0.651123\pi$
$150$	−6.63667	−0.541882
$151$	13.8060	1.12352	0.561758	−	0.827302i	$-0.310125\pi$
$151$	13.8060	1.12352	0.561758	+	0.827302i	$0.310125\pi$
$152$	−1.00000	−0.0811107
$153$	1.30265	0.105313
$154$	0	0
$155$	2.54669	0.204555
$156$	−4.28267	−0.342888
$157$	15.8060	1.26146	0.630728	−	0.776004i	$-0.282756\pi$
$157$	15.8060	1.26146	0.630728	+	0.776004i	$0.282756\pi$
$158$	0.778008	0.0618950
$159$	−14.7067	−1.16632
$160$	−0.363328	−0.0287236
$161$	4.58532	0.361374
$162$	4.27334	0.335746
$163$	−3.71733	−0.291164	−0.145582	−	0.989346i	$-0.546505\pi$
$163$	−3.71733	−0.291164	−0.145582	+	0.989346i	$0.546505\pi$
$164$	7.91934	0.618397
$165$	0	0
$166$	−0.778008	−0.0603851
$167$	−5.27334	−0.408064	−0.204032	−	0.978964i	$-0.565405\pi$
$167$	−5.27334	−0.408064	−0.204032	+	0.978964i	$0.565405\pi$
$168$	−2.91934	−0.225232
$169$	−3.13201	−0.240924
$170$	0.414680	0.0318045
$171$	−1.14134	−0.0872802
$172$	4.28267	0.326551
$173$	−11.4660	−0.871746	−0.435873	−	0.900008i	$-0.643560\pi$
$173$	−11.4660	−0.871746	−0.435873	+	0.900008i	$0.643560\pi$
$174$	2.42401	0.183764
$175$	10.4240	0.787981
$176$	0	0
$177$	1.47329	0.110739
$178$	8.20202	0.614767
$179$	−0.900687	−0.0673205	−0.0336602	−	0.999433i	$-0.510716\pi$
$179$	−0.900687	−0.0673205	−0.0336602	+	0.999433i	$0.510716\pi$
$180$	−0.414680	−0.0309084
$181$	−16.6974	−1.24110	−0.620552	−	0.784165i	$-0.713091\pi$
$181$	−16.6974	−1.24110	−0.620552	+	0.784165i	$0.713091\pi$
$182$	6.72666	0.498613
$183$	−11.6074	−0.858041
$184$	2.14134	0.157861
$185$	−3.55263	−0.261194
$186$	9.55602	0.700681
$187$	0	0
$188$	−7.59465	−0.553897
$189$	−12.0900	−0.879417
$190$	−0.363328	−0.0263586
$191$	−3.87732	−0.280553	−0.140277	−	0.990112i	$-0.544799\pi$
$191$	−3.87732	−0.280553	−0.140277	+	0.990112i	$0.544799\pi$
$192$	−1.36333	−0.0983897
$193$	−5.32131	−0.383036	−0.191518	−	0.981489i	$-0.561341\pi$
$193$	−5.32131	−0.383036	−0.191518	+	0.981489i	$0.561341\pi$
$194$	1.86799	0.134114
$195$	−1.55602	−0.111429
$196$	−2.41468	−0.172477
$197$	14.3306	1.02102	0.510508	−	0.859873i	$-0.329457\pi$
$197$	14.3306	1.02102	0.510508	+	0.859873i	$0.329457\pi$
$198$	0	0
$199$	5.83869	0.413894	0.206947	−	0.978352i	$-0.433647\pi$
$199$	5.83869	0.413894	0.206947	+	0.978352i	$0.433647\pi$
$200$	4.86799	0.344219
$201$	−11.6774	−0.823659
$202$	−10.0700	−0.708523
$203$	−3.80731	−0.267221
$204$	1.55602	0.108943
$205$	2.87732	0.200961
$206$	17.3434	1.20837
$207$	2.44398	0.169869
$208$	3.14134	0.217812
$209$	0	0
$210$	−1.06068	−0.0731939
$211$	−9.74870	−0.671128	−0.335564	−	0.942017i	$-0.608927\pi$
$211$	−9.74870	−0.671128	−0.335564	+	0.942017i	$0.608927\pi$
$212$	10.7873	0.740877
$213$	−4.77801	−0.327384
$214$	−13.6460	−0.932821
$215$	1.55602	0.106119
$216$	−5.64600	−0.384162
$217$	−15.0093	−1.01890
$218$	5.33402	0.361266
$219$	16.0000	1.08118
$220$	0	0
$221$	−3.58532	−0.241175
$222$	−13.3306	−0.894694
$223$	−18.6167	−1.24667	−0.623333	−	0.781956i	$-0.714222\pi$
$223$	−18.6167	−1.24667	−0.623333	+	0.781956i	$0.714222\pi$
$224$	2.14134	0.143074
$225$	5.55602	0.370401
$226$	14.3633	0.955434
$227$	17.9160	1.18912	0.594562	−	0.804050i	$-0.297326\pi$
$227$	17.9160	1.18912	0.594562	+	0.804050i	$0.297326\pi$
$228$	−1.36333	−0.0902886
$229$	−8.31198	−0.549271	−0.274635	−	0.961548i	$-0.588557\pi$
$229$	−8.31198	−0.549271	−0.274635	+	0.961548i	$0.588557\pi$
$230$	0.778008	0.0513003
$231$	0	0
$232$	−1.77801	−0.116732
$233$	−7.28267	−0.477104	−0.238552	−	0.971130i	$-0.576673\pi$
$233$	−7.28267	−0.477104	−0.238552	+	0.971130i	$0.576673\pi$
$234$	3.58532	0.234380
$235$	−2.75935	−0.180000
$236$	−1.08066	−0.0703447
$237$	1.06068	0.0688986
$238$	−2.44398	−0.158420
$239$	−11.1693	−0.722483	−0.361242	−	0.932472i	$-0.617647\pi$
$239$	−11.1693	−0.722483	−0.361242	+	0.932472i	$0.617647\pi$
$240$	−0.495336	−0.0319738
$241$	−6.39263	−0.411786	−0.205893	−	0.978575i	$-0.566010\pi$
$241$	−6.39263	−0.411786	−0.205893	+	0.978575i	$0.566010\pi$
$242$	0	0
$243$	−11.1120	−0.712837
$244$	8.51399	0.545053
$245$	−0.877321	−0.0560500
$246$	10.7967	0.688370
$247$	3.14134	0.199878
$248$	−7.00933	−0.445093
$249$	−1.06068	−0.0672179
$250$	3.58532	0.226756
$251$	8.17997	0.516315	0.258158	−	0.966103i	$-0.416885\pi$
$251$	8.17997	0.516315	0.258158	+	0.966103i	$0.416885\pi$
$252$	2.44398	0.153957
$253$	0	0
$254$	−2.44398	−0.153349
$255$	0.565344	0.0354032
$256$	1.00000	0.0625000
$257$	−28.8773	−1.80132	−0.900659	−	0.434527i	$-0.856916\pi$
$257$	−28.8773	−1.80132	−0.900659	+	0.434527i	$0.856916\pi$
$258$	5.83869	0.363501
$259$	20.9380	1.30102
$260$	1.14134	0.0707827
$261$	−2.02930	−0.125611
$262$	−0.707999	−0.0437403
$263$	−0.385375	−0.0237632	−0.0118816	−	0.999929i	$-0.503782\pi$
$263$	−0.385375	−0.0237632	−0.0118816	+	0.999929i	$0.503782\pi$
$264$	0	0
$265$	3.91934	0.240763
$266$	2.14134	0.131294
$267$	11.1820	0.684330
$268$	8.56534	0.523212
$269$	13.5140	0.823963	0.411981	−	0.911192i	$-0.364837\pi$
$269$	13.5140	0.823963	0.411981	+	0.911192i	$0.364837\pi$
$270$	−2.05135	−0.124841
$271$	9.73599	0.591419	0.295709	−	0.955278i	$-0.404444\pi$
$271$	9.73599	0.591419	0.295709	+	0.955278i	$0.404444\pi$
$272$	−1.14134	−0.0692037
$273$	9.17064	0.555032
$274$	−6.28267	−0.379550
$275$	0	0
$276$	2.91934	0.175724
$277$	6.74870	0.405490	0.202745	−	0.979232i	$-0.435014\pi$
$277$	6.74870	0.405490	0.202745	+	0.979232i	$0.435014\pi$
$278$	4.00000	0.239904
$279$	−8.00000	−0.478947
$280$	0.778008	0.0464949
$281$	7.06068	0.421205	0.210602	−	0.977572i	$-0.432457\pi$
$281$	7.06068	0.421205	0.210602	+	0.977572i	$0.432457\pi$
$282$	−10.3540	−0.616572
$283$	8.46264	0.503052	0.251526	−	0.967851i	$-0.419068\pi$
$283$	8.46264	0.503052	0.251526	+	0.967851i	$0.419068\pi$
$284$	3.50466	0.207964
$285$	−0.495336	−0.0293412
$286$	0	0
$287$	−16.9580	−1.00100
$288$	1.14134	0.0672539
$289$	−15.6974	−0.923374
$290$	−0.646000	−0.0379345
$291$	2.54669	0.149289
$292$	−11.7360	−0.686797
$293$	−21.7967	−1.27337	−0.636687	−	0.771122i	$-0.719696\pi$
$293$	−21.7967	−1.27337	−0.636687	+	0.771122i	$0.719696\pi$
$294$	−3.29200	−0.191993
$295$	−0.392633	−0.0228600
$296$	9.77801	0.568335
$297$	0	0
$298$	11.1600	0.646481
$299$	−6.72666	−0.389013
$300$	6.63667	0.383168
$301$	−9.17064	−0.528587
$302$	−13.8060	−0.794446
$303$	−13.7287	−0.788695
$304$	1.00000	0.0573539
$305$	3.09337	0.177126
$306$	−1.30265	−0.0744674
$307$	16.5526	0.944708	0.472354	−	0.881409i	$-0.343404\pi$
$307$	16.5526	0.944708	0.472354	+	0.881409i	$0.343404\pi$
$308$	0	0
$309$	23.6447	1.34510
$310$	−2.54669	−0.144642
$311$	−20.8480	−1.18218	−0.591091	−	0.806605i	$-0.701303\pi$
$311$	−20.8480	−1.18218	−0.591091	+	0.806605i	$0.701303\pi$
$312$	4.28267	0.242459
$313$	−2.98134	−0.168515	−0.0842577	−	0.996444i	$-0.526852\pi$
$313$	−2.98134	−0.168515	−0.0842577	+	0.996444i	$0.526852\pi$
$314$	−15.8060	−0.891984
$315$	0.887968	0.0500314
$316$	−0.778008	−0.0437664
$317$	−11.9160	−0.669267	−0.334633	−	0.942348i	$-0.608612\pi$
$317$	−11.9160	−0.669267	−0.334633	+	0.942348i	$0.608612\pi$
$318$	14.7067	0.824710
$319$	0	0
$320$	0.363328	0.0203107
$321$	−18.6040	−1.03837
$322$	−4.58532	−0.255530
$323$	−1.14134	−0.0635056
$324$	−4.27334	−0.237408
$325$	−15.2920	−0.848248
$326$	3.71733	0.205884
$327$	7.27203	0.402144
$328$	−7.91934	−0.437273
$329$	16.2627	0.896591
$330$	0	0
$331$	0.0127181	0.000699049 0	0.000349525	−	1.00000i	$-0.499889\pi$
$331$	0.0127181	0.000699049 0	0.000349525		1.00000i	$0.499889\pi$
$332$	0.778008	0.0426987
$333$	11.1600	0.611564
$334$	5.27334	0.288545
$335$	3.11203	0.170028
$336$	2.91934	0.159263
$337$	−28.1180	−1.53168	−0.765842	−	0.643029i	$-0.777677\pi$
$337$	−28.1180	−1.53168	−0.765842	+	0.643029i	$0.777677\pi$
$338$	3.13201	0.170359
$339$	19.5819	1.06354
$340$	−0.414680	−0.0224892
$341$	0	0
$342$	1.14134	0.0617164
$343$	20.1600	1.08854
$344$	−4.28267	−0.230906
$345$	1.06068	0.0571051
$346$	11.4660	0.616418
$347$	−5.66598	−0.304166	−0.152083	−	0.988368i	$-0.548598\pi$
$347$	−5.66598	−0.304166	−0.152083	+	0.988368i	$0.548598\pi$
$348$	−2.42401	−0.129940
$349$	−24.3306	−1.30239	−0.651194	−	0.758911i	$-0.725732\pi$
$349$	−24.3306	−1.30239	−0.651194	+	0.758911i	$0.725732\pi$
$350$	−10.4240	−0.557187
$351$	17.7360	0.946677
$352$	0	0
$353$	2.11203	0.112412	0.0562060	−	0.998419i	$-0.482100\pi$
$353$	2.11203	0.112412	0.0562060	+	0.998419i	$0.482100\pi$
$354$	−1.47329	−0.0783044
$355$	1.27334	0.0675821
$356$	−8.20202	−0.434706
$357$	−3.33195	−0.176346
$358$	0.900687	0.0476028
$359$	34.6613	1.82935	0.914676	−	0.404188i	$-0.132446\pi$
$359$	34.6613	1.82935	0.914676	+	0.404188i	$0.132446\pi$
$360$	0.414680	0.0218555
$361$	1.00000	0.0526316
$362$	16.6974	0.877593
$363$	0	0
$364$	−6.72666	−0.352573
$365$	−4.26401	−0.223189
$366$	11.6074	0.606727
$367$	−36.3400	−1.89693	−0.948465	−	0.316881i	$-0.897364\pi$
$367$	−36.3400	−1.89693	−0.948465	+	0.316881i	$0.897364\pi$
$368$	−2.14134	−0.111625
$369$	−9.03863	−0.470532
$370$	3.55263	0.184692
$371$	−23.0993	−1.19926
$372$	−9.55602	−0.495456
$373$	−30.1273	−1.55993	−0.779966	−	0.625822i	$-0.784764\pi$
$373$	−30.1273	−1.55993	−0.779966	+	0.625822i	$0.784764\pi$
$374$	0	0
$375$	4.88797	0.252414
$376$	7.59465	0.391664
$377$	5.58532	0.287659
$378$	12.0900	0.621842
$379$	3.06200	0.157284	0.0786422	−	0.996903i	$-0.474942\pi$
$379$	3.06200	0.157284	0.0786422	+	0.996903i	$0.474942\pi$
$380$	0.363328	0.0186383
$381$	−3.33195	−0.170701
$382$	3.87732	0.198381
$383$	33.1307	1.69290	0.846450	−	0.532469i	$-0.178736\pi$
$383$	33.1307	1.69290	0.846450	+	0.532469i	$0.178736\pi$
$384$	1.36333	0.0695721
$385$	0	0
$386$	5.32131	0.270847
$387$	−4.88797	−0.248469
$388$	−1.86799	−0.0948330
$389$	−3.81664	−0.193511	−0.0967557	−	0.995308i	$-0.530847\pi$
$389$	−3.81664	−0.193511	−0.0967557	+	0.995308i	$0.530847\pi$
$390$	1.55602	0.0787919
$391$	2.44398	0.123598
$392$	2.41468	0.121960
$393$	−0.965235	−0.0486897
$394$	−14.3306	−0.721967
$395$	−0.282672	−0.0142228
$396$	0	0
$397$	−25.0573	−1.25759	−0.628795	−	0.777571i	$-0.716451\pi$
$397$	−25.0573	−1.25759	−0.628795	+	0.777571i	$0.716451\pi$
$398$	−5.83869	−0.292667
$399$	2.91934	0.146150
$400$	−4.86799	−0.243400
$401$	−31.9567	−1.59584	−0.797920	−	0.602764i	$-0.794066\pi$
$401$	−31.9567	−1.59584	−0.797920	+	0.602764i	$0.794066\pi$
$402$	11.6774	0.582415
$403$	22.0187	1.09683
$404$	10.0700	0.501002
$405$	−1.55263	−0.0771506
$406$	3.80731	0.188954
$407$	0	0
$408$	−1.55602	−0.0770343
$409$	−27.8280	−1.37601	−0.688004	−	0.725707i	$-0.741513\pi$
$409$	−27.8280	−1.37601	−0.688004	+	0.725707i	$0.741513\pi$
$410$	−2.87732	−0.142101
$411$	−8.56534	−0.422497
$412$	−17.3434	−0.854446
$413$	2.31405	0.113867
$414$	−2.44398	−0.120115
$415$	0.282672	0.0138758
$416$	−3.14134	−0.154017
$417$	5.45331	0.267050
$418$	0	0
$419$	−5.24065	−0.256022	−0.128011	−	0.991773i	$-0.540859\pi$
$419$	−5.24065	−0.256022	−0.128011	+	0.991773i	$0.540859\pi$
$420$	1.06068	0.0517559
$421$	−15.3340	−0.747335	−0.373667	−	0.927563i	$-0.621900\pi$
$421$	−15.3340	−0.747335	−0.373667	+	0.927563i	$0.621900\pi$
$422$	9.74870	0.474559
$423$	8.66805	0.421455
$424$	−10.7873	−0.523879
$425$	5.55602	0.269506
$426$	4.77801	0.231495
$427$	−18.2313	−0.882275
$428$	13.6460	0.659604
$429$	0	0
$430$	−1.55602	−0.0750377
$431$	−18.8994	−0.910351	−0.455175	−	0.890402i	$-0.650423\pi$
$431$	−18.8994	−0.910351	−0.455175	+	0.890402i	$0.650423\pi$
$432$	5.64600	0.271643
$433$	−11.1787	−0.537212	−0.268606	−	0.963250i	$-0.586563\pi$
$433$	−11.1787	−0.537212	−0.268606	+	0.963250i	$0.586563\pi$
$434$	15.0093	0.720471
$435$	−0.880711	−0.0422268
$436$	−5.33402	−0.255453
$437$	−2.14134	−0.102434
$438$	−16.0000	−0.764510
$439$	−23.4720	−1.12026	−0.560128	−	0.828406i	$-0.689248\pi$
$439$	−23.4720	−1.12026	−0.560128	+	0.828406i	$0.689248\pi$
$440$	0	0
$441$	2.75596	0.131236
$442$	3.58532	0.170536
$443$	−29.8387	−1.41768	−0.708839	−	0.705370i	$-0.750781\pi$
$443$	−29.8387	−1.41768	−0.708839	+	0.705370i	$0.750781\pi$
$444$	13.3306	0.632644
$445$	−2.98002	−0.141267
$446$	18.6167	0.881526
$447$	15.2147	0.719632
$448$	−2.14134	−0.101169
$449$	−10.6133	−0.500873	−0.250436	−	0.968133i	$-0.580574\pi$
$449$	−10.6133	−0.500873	−0.250436	+	0.968133i	$0.580574\pi$
$450$	−5.55602	−0.261913
$451$	0	0
$452$	−14.3633	−0.675594
$453$	−18.8221	−0.884339
$454$	−17.9160	−0.840837
$455$	−2.44398	−0.114576
$456$	1.36333	0.0638437
$457$	7.82936	0.366242	0.183121	−	0.983090i	$-0.441380\pi$
$457$	7.82936	0.366242	0.183121	+	0.983090i	$0.441380\pi$
$458$	8.31198	0.388393
$459$	−6.44398	−0.300779
$460$	−0.778008	−0.0362748
$461$	2.54330	0.118453	0.0592266	−	0.998245i	$-0.481137\pi$
$461$	2.54330	0.118453	0.0592266	+	0.998245i	$0.481137\pi$
$462$	0	0
$463$	−31.6519	−1.47099	−0.735495	−	0.677530i	$-0.763050\pi$
$463$	−31.6519	−1.47099	−0.735495	+	0.677530i	$0.763050\pi$
$464$	1.77801	0.0825419
$465$	−3.47197	−0.161009
$466$	7.28267	0.337363
$467$	−7.85735	−0.363595	−0.181797	−	0.983336i	$-0.558191\pi$
$467$	−7.85735	−0.363595	−0.181797	+	0.983336i	$0.558191\pi$
$468$	−3.58532	−0.165731
$469$	−18.3413	−0.846922
$470$	2.75935	0.127279
$471$	−21.5488	−0.992914
$472$	1.08066	0.0497412
$473$	0	0
$474$	−1.06068	−0.0487187
$475$	−4.86799	−0.223359
$476$	2.44398	0.112020
$477$	−12.3120	−0.563727
$478$	11.1693	0.510873
$479$	−13.9614	−0.637911	−0.318956	−	0.947770i	$-0.603332\pi$
$479$	−13.9614	−0.637911	−0.318956	+	0.947770i	$0.603332\pi$
$480$	0.495336	0.0226089
$481$	−30.7160	−1.40053
$482$	6.39263	0.291176
$483$	−6.25130	−0.284444
$484$	0	0
$485$	−0.678694	−0.0308179
$486$	11.1120	0.504052
$487$	1.83869	0.0833189	0.0416595	−	0.999132i	$-0.486736\pi$
$487$	1.83869	0.0833189	0.0416595	+	0.999132i	$0.486736\pi$
$488$	−8.51399	−0.385410
$489$	5.06794	0.229180
$490$	0.877321	0.0396333
$491$	−27.5747	−1.24443	−0.622214	−	0.782847i	$-0.713767\pi$
$491$	−27.5747	−1.24443	−0.622214	+	0.782847i	$0.713767\pi$
$492$	−10.7967	−0.486751
$493$	−2.02930	−0.0913953
$494$	−3.14134	−0.141335
$495$	0	0
$496$	7.00933	0.314728
$497$	−7.50466	−0.336630
$498$	1.06068	0.0475302
$499$	26.4113	1.18233	0.591166	−	0.806550i	$-0.298668\pi$
$499$	26.4113	1.18233	0.591166	+	0.806550i	$0.298668\pi$
$500$	−3.58532	−0.160340
$501$	7.18930	0.321194
$502$	−8.17997	−0.365090
$503$	−12.5853	−0.561152	−0.280576	−	0.959832i	$-0.590525\pi$
$503$	−12.5853	−0.561152	−0.280576	+	0.959832i	$0.590525\pi$
$504$	−2.44398	−0.108864
$505$	3.65872	0.162811
$506$	0	0
$507$	4.26995	0.189635
$508$	2.44398	0.108434
$509$	28.8166	1.27728	0.638638	−	0.769508i	$-0.279498\pi$
$509$	28.8166	1.27728	0.638638	+	0.769508i	$0.279498\pi$
$510$	−0.565344	−0.0250339
$511$	25.1307	1.11172
$512$	−1.00000	−0.0441942
$513$	5.64600	0.249277
$514$	28.8773	1.27372
$515$	−6.30133	−0.277670
$516$	−5.83869	−0.257034
$517$	0	0
$518$	−20.9380	−0.919963
$519$	15.6320	0.686167
$520$	−1.14134	−0.0500509
$521$	32.5840	1.42753	0.713766	−	0.700385i	$-0.246988\pi$
$521$	32.5840	1.42753	0.713766	+	0.700385i	$0.246988\pi$
$522$	2.02930	0.0888202
$523$	−43.3820	−1.89696	−0.948481	−	0.316834i	$-0.897380\pi$
$523$	−43.3820	−1.89696	−0.948481	+	0.316834i	$0.897380\pi$
$524$	0.707999	0.0309291
$525$	−14.2113	−0.620234
$526$	0.385375	0.0168032
$527$	−8.00000	−0.348485
$528$	0	0
$529$	−18.4147	−0.800638
$530$	−3.91934	−0.170245
$531$	1.23339	0.0535246
$532$	−2.14134	−0.0928387
$533$	24.8773	1.07756
$534$	−11.1820	−0.483894
$535$	4.95798	0.214352
$536$	−8.56534	−0.369967
$537$	1.22793	0.0529892
$538$	−13.5140	−0.582630
$539$	0	0
$540$	2.05135	0.0882761
$541$	28.6867	1.23334	0.616669	−	0.787223i	$-0.288482\pi$
$541$	28.6867	1.23334	0.616669	+	0.787223i	$0.288482\pi$
$542$	−9.73599	−0.418196
$543$	22.7640	0.976896
$544$	1.14134	0.0489344
$545$	−1.93800	−0.0830149
$546$	−9.17064	−0.392467
$547$	3.09931	0.132517	0.0662585	−	0.997802i	$-0.478894\pi$
$547$	3.09931	0.132517	0.0662585	+	0.997802i	$0.478894\pi$
$548$	6.28267	0.268382
$549$	−9.71733	−0.414725
$550$	0	0
$551$	1.77801	0.0757457
$552$	−2.91934	−0.124256
$553$	1.66598	0.0708445
$554$	−6.74870	−0.286725
$555$	4.84340	0.205591
$556$	−4.00000	−0.169638
$557$	−23.9160	−1.01335	−0.506676	−	0.862137i	$-0.669126\pi$
$557$	−23.9160	−1.01335	−0.506676	+	0.862137i	$0.669126\pi$
$558$	8.00000	0.338667
$559$	13.4533	0.569015
$560$	−0.778008	−0.0328768
$561$	0	0
$562$	−7.06068	−0.297837
$563$	−35.7674	−1.50741	−0.753707	−	0.657210i	$-0.771736\pi$
$563$	−35.7674	−1.50741	−0.753707	+	0.657210i	$0.771736\pi$
$564$	10.3540	0.435982
$565$	−5.21860	−0.219548
$566$	−8.46264	−0.355711
$567$	9.15066	0.384292
$568$	−3.50466	−0.147052
$569$	9.71733	0.407372	0.203686	−	0.979036i	$-0.434708\pi$
$569$	9.71733	0.407372	0.203686	+	0.979036i	$0.434708\pi$
$570$	0.495336	0.0207473
$571$	37.6260	1.57460	0.787300	−	0.616570i	$-0.211478\pi$
$571$	37.6260	1.57460	0.787300	+	0.616570i	$0.211478\pi$
$572$	0	0
$573$	5.28606	0.220828
$574$	16.9580	0.707812
$575$	10.4240	0.434711
$576$	−1.14134	−0.0475557
$577$	9.60398	0.399819	0.199909	−	0.979814i	$-0.435935\pi$
$577$	9.60398	0.399819	0.199909	+	0.979814i	$0.435935\pi$
$578$	15.6974	0.652924
$579$	7.25469	0.301494
$580$	0.646000	0.0268237
$581$	−1.66598	−0.0691163
$582$	−2.54669	−0.105564
$583$	0	0
$584$	11.7360	0.485639
$585$	−1.30265	−0.0538579
$586$	21.7967	0.900412
$587$	40.8153	1.68463	0.842314	−	0.538987i	$-0.181193\pi$
$587$	40.8153	1.68463	0.842314	+	0.538987i	$0.181193\pi$
$588$	3.29200	0.135760
$589$	7.00933	0.288814
$590$	0.392633	0.0161644
$591$	−19.5374	−0.803660
$592$	−9.77801	−0.401874
$593$	−47.8853	−1.96641	−0.983207	−	0.182491i	$-0.941584\pi$
$593$	−47.8853	−1.96641	−0.983207	+	0.182491i	$0.941584\pi$
$594$	0	0
$595$	0.887968	0.0364032
$596$	−11.1600	−0.457131
$597$	−7.96005	−0.325783
$598$	6.72666	0.275073
$599$	24.9253	1.01842	0.509210	−	0.860642i	$-0.329938\pi$
$599$	24.9253	1.01842	0.509210	+	0.860642i	$0.329938\pi$
$600$	−6.63667	−0.270941
$601$	−8.29332	−0.338292	−0.169146	−	0.985591i	$-0.554101\pi$
$601$	−8.29332	−0.338292	−0.169146	+	0.985591i	$0.554101\pi$
$602$	9.17064	0.373767
$603$	−9.77594	−0.398107
$604$	13.8060	0.561758
$605$	0	0
$606$	13.7287	0.557691
$607$	−5.13795	−0.208543	−0.104271	−	0.994549i	$-0.533251\pi$
$607$	−5.13795	−0.208543	−0.104271	+	0.994549i	$0.533251\pi$
$608$	−1.00000	−0.0405554
$609$	5.19062	0.210334
$610$	−3.09337	−0.125247
$611$	−23.8573	−0.965165
$612$	1.30265	0.0526564
$613$	−1.63667	−0.0661045	−0.0330523	−	0.999454i	$-0.510523\pi$
$613$	−1.63667	−0.0661045	−0.0330523	+	0.999454i	$0.510523\pi$
$614$	−16.5526	−0.668010
$615$	−3.92273	−0.158180
$616$	0	0
$617$	−16.8973	−0.680260	−0.340130	−	0.940379i	$-0.610471\pi$
$617$	−16.8973	−0.680260	−0.340130	+	0.940379i	$0.610471\pi$
$618$	−23.6447	−0.951129
$619$	−28.8480	−1.15950	−0.579750	−	0.814795i	$-0.696850\pi$
$619$	−28.8480	−1.15950	−0.579750	+	0.814795i	$0.696850\pi$
$620$	2.54669	0.102277
$621$	−12.0900	−0.485154
$622$	20.8480	0.835929
$623$	17.5633	0.703658
$624$	−4.28267	−0.171444
$625$	23.0373	0.921493
$626$	2.98134	0.119158
$627$	0	0
$628$	15.8060	0.630728
$629$	11.1600	0.444978
$630$	−0.887968	−0.0353775
$631$	−2.24404	−0.0893338	−0.0446669	−	0.999002i	$-0.514223\pi$
$631$	−2.24404	−0.0893338	−0.0446669	+	0.999002i	$0.514223\pi$
$632$	0.778008	0.0309475
$633$	13.2907	0.528257
$634$	11.9160	0.473243
$635$	0.887968	0.0352380
$636$	−14.7067	−0.583158
$637$	−7.58532	−0.300541
$638$	0	0
$639$	−4.00000	−0.158238
$640$	−0.363328	−0.0143618
$641$	43.2300	1.70748	0.853741	−	0.520698i	$-0.174328\pi$
$641$	43.2300	1.70748	0.853741	+	0.520698i	$0.174328\pi$
$642$	18.6040	0.734240
$643$	9.69867	0.382478	0.191239	−	0.981543i	$-0.438749\pi$
$643$	9.69867	0.382478	0.191239	+	0.981543i	$0.438749\pi$
$644$	4.58532	0.180687
$645$	−2.12136	−0.0835285
$646$	1.14134	0.0449053
$647$	3.59465	0.141320	0.0706601	−	0.997500i	$-0.477489\pi$
$647$	3.59465	0.141320	0.0706601	+	0.997500i	$0.477489\pi$
$648$	4.27334	0.167873
$649$	0	0
$650$	15.2920	0.599802
$651$	20.4626	0.801994
$652$	−3.71733	−0.145582
$653$	18.8226	0.736584	0.368292	−	0.929710i	$-0.379943\pi$
$653$	18.8226	0.736584	0.368292	+	0.929710i	$0.379943\pi$
$654$	−7.27203	−0.284359
$655$	0.257236	0.0100510
$656$	7.91934	0.309198
$657$	13.3947	0.522577
$658$	−16.2627	−0.633986
$659$	−46.6613	−1.81766	−0.908832	−	0.417161i	$-0.863025\pi$
$659$	−46.6613	−1.81766	−0.908832	+	0.417161i	$0.863025\pi$
$660$	0	0
$661$	−25.4554	−0.990100	−0.495050	−	0.868865i	$-0.664850\pi$
$661$	−25.4554	−0.990100	−0.495050	+	0.868865i	$0.664850\pi$
$662$	−0.0127181	−0.000494303 0
$663$	4.88797	0.189833
$664$	−0.778008	−0.0301926
$665$	−0.778008	−0.0301699
$666$	−11.1600	−0.432441
$667$	−3.80731	−0.147420
$668$	−5.27334	−0.204032
$669$	25.3807	0.981273
$670$	−3.11203	−0.120228
$671$	0	0
$672$	−2.91934	−0.112616
$673$	2.03269	0.0783546	0.0391773	−	0.999232i	$-0.487526\pi$
$673$	2.03269	0.0783546	0.0391773	+	0.999232i	$0.487526\pi$
$674$	28.1180	1.08306
$675$	−27.4847	−1.05789
$676$	−3.13201	−0.120462
$677$	−15.1727	−0.583135	−0.291567	−	0.956550i	$-0.594177\pi$
$677$	−15.1727	−0.583135	−0.291567	+	0.956550i	$0.594177\pi$
$678$	−19.5819	−0.752040
$679$	4.00000	0.153506
$680$	0.414680	0.0159022
$681$	−24.4253	−0.935981
$682$	0	0
$683$	14.2241	0.544269	0.272134	−	0.962259i	$-0.412270\pi$
$683$	14.2241	0.544269	0.272134	+	0.962259i	$0.412270\pi$
$684$	−1.14134	−0.0436401
$685$	2.28267	0.0872164
$686$	−20.1600	−0.769712
$687$	11.3320	0.432341
$688$	4.28267	0.163275
$689$	33.8867	1.29098
$690$	−1.06068	−0.0403794
$691$	13.1379	0.499791	0.249896	−	0.968273i	$-0.419604\pi$
$691$	13.1379	0.499791	0.249896	+	0.968273i	$0.419604\pi$
$692$	−11.4660	−0.435873
$693$	0	0
$694$	5.66598	0.215078
$695$	−1.45331	−0.0551273
$696$	2.42401	0.0918818
$697$	−9.03863	−0.342363
$698$	24.3306	0.920928
$699$	9.92867	0.375537
$700$	10.4240	0.393990
$701$	25.2373	0.953198	0.476599	−	0.879121i	$-0.341869\pi$
$701$	25.2373	0.953198	0.476599	+	0.879121i	$0.341869\pi$
$702$	−17.7360	−0.669402
$703$	−9.77801	−0.368785
$704$	0	0
$705$	3.76190	0.141681
$706$	−2.11203	−0.0794874
$707$	−21.5633	−0.810970
$708$	1.47329	0.0553696
$709$	23.3760	0.877906	0.438953	−	0.898510i	$-0.355349\pi$
$709$	23.3760	0.877906	0.438953	+	0.898510i	$0.355349\pi$
$710$	−1.27334	−0.0477877
$711$	0.887968	0.0333014
$712$	8.20202	0.307384
$713$	−15.0093	−0.562104
$714$	3.33195	0.124695
$715$	0	0
$716$	−0.900687	−0.0336602
$717$	15.2275	0.568680
$718$	−34.6613	−1.29355
$719$	31.6774	1.18137	0.590683	−	0.806903i	$-0.298858\pi$
$719$	31.6774	1.18137	0.590683	+	0.806903i	$0.298858\pi$
$720$	−0.414680	−0.0154542
$721$	37.1379	1.38309
$722$	−1.00000	−0.0372161
$723$	8.71526	0.324124
$724$	−16.6974	−0.620552
$725$	−8.65533	−0.321451
$726$	0	0
$727$	−36.5199	−1.35445	−0.677225	−	0.735776i	$-0.736817\pi$
$727$	−36.5199	−1.35445	−0.677225	+	0.735776i	$0.736817\pi$
$728$	6.72666	0.249306
$729$	27.9694	1.03590
$730$	4.26401	0.157818
$731$	−4.88797	−0.180788
$732$	−11.6074	−0.429021
$733$	−36.1880	−1.33663	−0.668317	−	0.743877i	$-0.732985\pi$
$733$	−36.1880	−1.33663	−0.668317	+	0.743877i	$0.732985\pi$
$734$	36.3400	1.34133
$735$	1.19608	0.0441180
$736$	2.14134	0.0789307
$737$	0	0
$738$	9.03863	0.332717
$739$	15.1447	0.557108	0.278554	−	0.960421i	$-0.410145\pi$
$739$	15.1447	0.557108	0.278554	+	0.960421i	$0.410145\pi$
$740$	−3.55263	−0.130597
$741$	−4.28267	−0.157328
$742$	23.0993	0.848002
$743$	3.85735	0.141512	0.0707561	−	0.997494i	$-0.477459\pi$
$743$	3.85735	0.141512	0.0707561	+	0.997494i	$0.477459\pi$
$744$	9.55602	0.350341
$745$	−4.05474	−0.148554
$746$	30.1273	1.10304
$747$	−0.887968	−0.0324891
$748$	0	0
$749$	−29.2207	−1.06770
$750$	−4.88797	−0.178483
$751$	15.9346	0.581462	0.290731	−	0.956805i	$-0.406101\pi$
$751$	15.9346	0.581462	0.290731	+	0.956805i	$0.406101\pi$
$752$	−7.59465	−0.276948
$753$	−11.1520	−0.406401
$754$	−5.58532	−0.203405
$755$	5.01611	0.182555
$756$	−12.0900	−0.439708
$757$	25.7767	0.936870	0.468435	−	0.883498i	$-0.344818\pi$
$757$	25.7767	0.936870	0.468435	+	0.883498i	$0.344818\pi$
$758$	−3.06200	−0.111217
$759$	0	0
$760$	−0.363328	−0.0131793
$761$	24.5747	0.890831	0.445416	−	0.895324i	$-0.353056\pi$
$761$	24.5747	0.890831	0.445416	+	0.895324i	$0.353056\pi$
$762$	3.33195	0.120704
$763$	11.4219	0.413502
$764$	−3.87732	−0.140277
$765$	0.473289	0.0171118
$766$	−33.1307	−1.19706
$767$	−3.39470	−0.122576
$768$	−1.36333	−0.0491949
$769$	−51.3200	−1.85065	−0.925323	−	0.379180i	$-0.876206\pi$
$769$	−51.3200	−1.85065	−0.925323	+	0.379180i	$0.876206\pi$
$770$	0	0
$771$	39.3693	1.41785
$772$	−5.32131	−0.191518
$773$	27.0153	0.971672	0.485836	−	0.874050i	$-0.338515\pi$
$773$	27.0153	0.971672	0.485836	+	0.874050i	$0.338515\pi$
$774$	4.88797	0.175694
$775$	−34.1214	−1.22568
$776$	1.86799	0.0670570
$777$	−28.5454	−1.02406
$778$	3.81664	0.136833
$779$	7.91934	0.283740
$780$	−1.55602	−0.0557143
$781$	0	0
$782$	−2.44398	−0.0873967
$783$	10.0386	0.358751
$784$	−2.41468	−0.0862386
$785$	5.74276	0.204968
$786$	0.965235	0.0344288
$787$	22.8794	0.815562	0.407781	−	0.913080i	$-0.366303\pi$
$787$	22.8794	0.815562	0.407781	+	0.913080i	$0.366303\pi$
$788$	14.3306	0.510508
$789$	0.525393	0.0187045
$790$	0.282672	0.0100570
$791$	30.7567	1.09358
$792$	0	0
$793$	26.7453	0.949754
$794$	25.0573	0.889250
$795$	−5.34335	−0.189509
$796$	5.83869	0.206947
$797$	41.6774	1.47629	0.738144	−	0.674643i	$-0.235702\pi$
$797$	41.6774	1.47629	0.738144	+	0.674643i	$0.235702\pi$
$798$	−2.91934	−0.103344
$799$	8.66805	0.306653
$800$	4.86799	0.172110
$801$	9.36126	0.330764
$802$	31.9567	1.12843
$803$	0	0
$804$	−11.6774	−0.411829
$805$	1.66598	0.0587180
$806$	−22.0187	−0.775574
$807$	−18.4240	−0.648556
$808$	−10.0700	−0.354262
$809$	−29.7347	−1.04542	−0.522708	−	0.852512i	$-0.675078\pi$
$809$	−29.7347	−1.04542	−0.522708	+	0.852512i	$0.675078\pi$
$810$	1.55263	0.0545537
$811$	−17.6460	−0.619635	−0.309817	−	0.950796i	$-0.600268\pi$
$811$	−17.6460	−0.619635	−0.309817	+	0.950796i	$0.600268\pi$
$812$	−3.80731	−0.133610
$813$	−13.2733	−0.465516
$814$	0	0
$815$	−1.35061	−0.0473098
$816$	1.55602	0.0544714
$817$	4.28267	0.149832
$818$	27.8280	0.972985
$819$	7.67738	0.268269
$820$	2.87732	0.100480
$821$	36.9766	1.29049	0.645247	−	0.763974i	$-0.276755\pi$
$821$	36.9766	1.29049	0.645247	+	0.763974i	$0.276755\pi$
$822$	8.56534	0.298751
$823$	−38.8094	−1.35281	−0.676405	−	0.736530i	$-0.736463\pi$
$823$	−38.8094	−1.35281	−0.676405	+	0.736530i	$0.736463\pi$
$824$	17.3434	0.604184
$825$	0	0
$826$	−2.31405	−0.0805160
$827$	29.0534	1.01029	0.505143	−	0.863036i	$-0.331440\pi$
$827$	29.0534	1.01029	0.505143	+	0.863036i	$0.331440\pi$
$828$	2.44398	0.0849343
$829$	44.9333	1.56060	0.780299	−	0.625407i	$-0.215067\pi$
$829$	44.9333	1.56060	0.780299	+	0.625407i	$0.215067\pi$
$830$	−0.282672	−0.00981170
$831$	−9.20070	−0.319169
$832$	3.14134	0.108906
$833$	2.75596	0.0954884
$834$	−5.45331	−0.188833
$835$	−1.91595	−0.0663043
$836$	0	0
$837$	39.5747	1.36790
$838$	5.24065	0.181035
$839$	10.5140	0.362983	0.181492	−	0.983392i	$-0.441907\pi$
$839$	10.5140	0.362983	0.181492	+	0.983392i	$0.441907\pi$
$840$	−1.06068	−0.0365969
$841$	−25.8387	−0.890989
$842$	15.3340	0.528445
$843$	−9.62602	−0.331538
$844$	−9.74870	−0.335564
$845$	−1.13795	−0.0391466
$846$	−8.66805	−0.298014
$847$	0	0
$848$	10.7873	0.370439
$849$	−11.5374	−0.395961
$850$	−5.55602	−0.190570
$851$	20.9380	0.717745
$852$	−4.77801	−0.163692
$853$	8.55733	0.292998	0.146499	−	0.989211i	$-0.453200\pi$
$853$	8.55733	0.292998	0.146499	+	0.989211i	$0.453200\pi$
$854$	18.2313	0.623863
$855$	−0.414680	−0.0141817
$856$	−13.6460	−0.466411
$857$	−19.5560	−0.668021	−0.334010	−	0.942569i	$-0.608402\pi$
$857$	−19.5560	−0.668021	−0.334010	+	0.942569i	$0.608402\pi$
$858$	0	0
$859$	31.7873	1.08457	0.542285	−	0.840195i	$-0.317559\pi$
$859$	31.7873	1.08457	0.542285	+	0.840195i	$0.317559\pi$
$860$	1.55602	0.0530597
$861$	23.1193	0.787903
$862$	18.8994	0.643715
$863$	28.8226	0.981132	0.490566	−	0.871404i	$-0.336790\pi$
$863$	28.8226	0.981132	0.490566	+	0.871404i	$0.336790\pi$
$864$	−5.64600	−0.192081
$865$	−4.16593	−0.141646
$866$	11.1787	0.379866
$867$	21.4006	0.726804
$868$	−15.0093	−0.509450
$869$	0	0
$870$	0.880711	0.0298589
$871$	26.9066	0.911696
$872$	5.33402	0.180633
$873$	2.13201	0.0721575
$874$	2.14134	0.0724318
$875$	7.67738	0.259543
$876$	16.0000	0.540590
$877$	11.4613	0.387021	0.193511	−	0.981098i	$-0.438013\pi$
$877$	11.4613	0.387021	0.193511	+	0.981098i	$0.438013\pi$
$878$	23.4720	0.792141
$879$	29.7160	1.00230
$880$	0	0
$881$	−45.7826	−1.54246	−0.771228	−	0.636559i	$-0.780357\pi$
$881$	−45.7826	−1.54246	−0.771228	+	0.636559i	$0.780357\pi$
$882$	−2.75596	−0.0927980
$883$	−39.9673	−1.34501	−0.672503	−	0.740094i	$-0.734781\pi$
$883$	−39.9673	−1.34501	−0.672503	+	0.740094i	$0.734781\pi$
$884$	−3.58532	−0.120587
$885$	0.535287	0.0179935
$886$	29.8387	1.00245
$887$	−37.8833	−1.27200	−0.635998	−	0.771691i	$-0.719411\pi$
$887$	−37.8833	−1.27200	−0.635998	+	0.771691i	$0.719411\pi$
$888$	−13.3306	−0.447347
$889$	−5.23339	−0.175522
$890$	2.98002	0.0998906
$891$	0	0
$892$	−18.6167	−0.623333
$893$	−7.59465	−0.254145
$894$	−15.2147	−0.508857
$895$	−0.327245	−0.0109386
$896$	2.14134	0.0715370
$897$	9.17064	0.306199
$898$	10.6133	0.354171
$899$	12.4626	0.415652
$900$	5.55602	0.185201
$901$	−12.3120	−0.410171
$902$	0	0
$903$	12.5026	0.416060
$904$	14.3633	0.477717
$905$	−6.06662	−0.201661
$906$	18.8221	0.625322
$907$	9.11797	0.302757	0.151379	−	0.988476i	$-0.451629\pi$
$907$	9.11797	0.302757	0.151379	+	0.988476i	$0.451629\pi$
$908$	17.9160	0.594562
$909$	−11.4933	−0.381208
$910$	2.44398	0.0810173
$911$	−13.9087	−0.460816	−0.230408	−	0.973094i	$-0.574006\pi$
$911$	−13.9087	−0.460816	−0.230408	+	0.973094i	$0.574006\pi$
$912$	−1.36333	−0.0451443
$913$	0	0
$914$	−7.82936	−0.258972
$915$	−4.21728	−0.139419
$916$	−8.31198	−0.274635
$917$	−1.51606	−0.0500648
$918$	6.44398	0.212683
$919$	35.1120	1.15824	0.579120	−	0.815243i	$-0.303396\pi$
$919$	35.1120	1.15824	0.579120	+	0.815243i	$0.303396\pi$
$920$	0.778008	0.0256502
$921$	−22.5667	−0.743597
$922$	−2.54330	−0.0837590
$923$	11.0093	0.362376
$924$	0	0
$925$	47.5993	1.56505
$926$	31.6519	1.04015
$927$	19.7946	0.650140
$928$	−1.77801	−0.0583660
$929$	−2.47875	−0.0813251	−0.0406626	−	0.999173i	$-0.512947\pi$
$929$	−2.47875	−0.0813251	−0.0406626	+	0.999173i	$0.512947\pi$
$930$	3.47197	0.113850
$931$	−2.41468	−0.0791379
$932$	−7.28267	−0.238552
$933$	28.4227	0.930517
$934$	7.85735	0.257100
$935$	0	0
$936$	3.58532	0.117190
$937$	6.41600	0.209602	0.104801	−	0.994493i	$-0.466580\pi$
$937$	6.41600	0.209602	0.104801	+	0.994493i	$0.466580\pi$
$938$	18.3413	0.598864
$939$	4.06455	0.132642
$940$	−2.75935	−0.0900001
$941$	−19.2373	−0.627117	−0.313558	−	0.949569i	$-0.601521\pi$
$941$	−19.2373	−0.627117	−0.313558	+	0.949569i	$0.601521\pi$
$942$	21.5488	0.702096
$943$	−16.9580	−0.552228
$944$	−1.08066	−0.0351724
$945$	−4.39263	−0.142892
$946$	0	0
$947$	46.2614	1.50329	0.751646	−	0.659566i	$-0.229260\pi$
$947$	46.2614	1.50329	0.751646	+	0.659566i	$0.229260\pi$
$948$	1.06068	0.0344493
$949$	−36.8667	−1.19674
$950$	4.86799	0.157939
$951$	16.2454	0.526792
$952$	−2.44398	−0.0792100
$953$	55.4541	1.79633	0.898167	−	0.439655i	$-0.144899\pi$
$953$	55.4541	1.79633	0.898167	+	0.439655i	$0.144899\pi$
$954$	12.3120	0.398615
$955$	−1.40874	−0.0455858
$956$	−11.1693	−0.361242
$957$	0	0
$958$	13.9614	0.451071
$959$	−13.4533	−0.434430
$960$	−0.495336	−0.0159869
$961$	18.1307	0.584861
$962$	30.7160	0.990324
$963$	−15.5747	−0.501887
$964$	−6.39263	−0.205893
$965$	−1.93338	−0.0622377
$966$	6.25130	0.201132
$967$	14.4240	0.463845	0.231922	−	0.972734i	$-0.425498\pi$
$967$	14.4240	0.463845	0.231922	+	0.972734i	$0.425498\pi$
$968$	0	0
$969$	1.55602	0.0499864
$970$	0.678694	0.0217916
$971$	46.3140	1.48629	0.743144	−	0.669131i	$-0.233334\pi$
$971$	46.3140	1.48629	0.743144	+	0.669131i	$0.233334\pi$
$972$	−11.1120	−0.356419
$973$	8.56534	0.274592
$974$	−1.83869	−0.0589154
$975$	20.8480	0.667671
$976$	8.51399	0.272526
$977$	47.8680	1.53143	0.765716	−	0.643178i	$-0.222385\pi$
$977$	47.8680	1.53143	0.765716	+	0.643178i	$0.222385\pi$
$978$	−5.06794	−0.162055
$979$	0	0
$980$	−0.877321	−0.0280250
$981$	6.08791	0.194372
$982$	27.5747	0.879943
$983$	−3.54198	−0.112972	−0.0564858	−	0.998403i	$-0.517990\pi$
$983$	−3.54198	−0.112972	−0.0564858	+	0.998403i	$0.517990\pi$
$984$	10.7967	0.344185
$985$	5.20672	0.165900
$986$	2.02930	0.0646262
$987$	−22.1714	−0.705723
$988$	3.14134	0.0999392
$989$	−9.17064	−0.291609
$990$	0	0
$991$	−10.4113	−0.330726	−0.165363	−	0.986233i	$-0.552879\pi$
$991$	−10.4113	−0.330726	−0.165363	+	0.986233i	$0.552879\pi$
$992$	−7.00933	−0.222546
$993$	−0.0173389	−0.000550234 0
$994$	7.50466	0.238033
$995$	2.12136	0.0672516
$996$	−1.06068	−0.0336089
$997$	10.1834	0.322510	0.161255	−	0.986913i	$-0.448446\pi$
$997$	10.1834	0.322510	0.161255	+	0.986913i	$0.448446\pi$
$998$	−26.4113	−0.836035
$999$	−55.2066	−1.74666

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bk.1.2	✓	3
11.10	odd	2		4598.2.a.bn.1.2	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.bk.1.2	✓	3	1.1	even	1	trivial
4598.2.a.bn.1.2	yes	3	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.36333 q^{3} +1.00000 q^{4} +0.363328 q^{5} +1.36333 q^{6} -2.14134 q^{7} -1.00000 q^{8} -1.14134 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.36333 q^{3} +1.00000 q^{4} +0.363328 q^{5} +1.36333 q^{6} -2.14134 q^{7} -1.00000 q^{8} -1.14134 q^{9} -0.363328 q^{10} -1.36333 q^{12} +3.14134 q^{13} +2.14134 q^{14} -0.495336 q^{15} +1.00000 q^{16} -1.14134 q^{17} +1.14134 q^{18} +1.00000 q^{19} +0.363328 q^{20} +2.91934 q^{21} -2.14134 q^{23} +1.36333 q^{24} -4.86799 q^{25} -3.14134 q^{26} +5.64600 q^{27} -2.14134 q^{28} +1.77801 q^{29} +0.495336 q^{30} +7.00933 q^{31} -1.00000 q^{32} +1.14134 q^{34} -0.778008 q^{35} -1.14134 q^{36} -9.77801 q^{37} -1.00000 q^{38} -4.28267 q^{39} -0.363328 q^{40} +7.91934 q^{41} -2.91934 q^{42} +4.28267 q^{43} -0.414680 q^{45} +2.14134 q^{46} -7.59465 q^{47} -1.36333 q^{48} -2.41468 q^{49} +4.86799 q^{50} +1.55602 q^{51} +3.14134 q^{52} +10.7873 q^{53} -5.64600 q^{54} +2.14134 q^{56} -1.36333 q^{57} -1.77801 q^{58} -1.08066 q^{59} -0.495336 q^{60} +8.51399 q^{61} -7.00933 q^{62} +2.44398 q^{63} +1.00000 q^{64} +1.14134 q^{65} +8.56534 q^{67} -1.14134 q^{68} +2.91934 q^{69} +0.778008 q^{70} +3.50466 q^{71} +1.14134 q^{72} -11.7360 q^{73} +9.77801 q^{74} +6.63667 q^{75} +1.00000 q^{76} +4.28267 q^{78} -0.778008 q^{79} +0.363328 q^{80} -4.27334 q^{81} -7.91934 q^{82} +0.778008 q^{83} +2.91934 q^{84} -0.414680 q^{85} -4.28267 q^{86} -2.42401 q^{87} -8.20202 q^{89} +0.414680 q^{90} -6.72666 q^{91} -2.14134 q^{92} -9.55602 q^{93} +7.59465 q^{94} +0.363328 q^{95} +1.36333 q^{96} -1.86799 q^{97} +2.41468 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - q^{5} + 2 q^{6} + 2 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - q^5 + 2 * q^6 + 2 * q^7 - 3 * q^8 + 5 * q^9	\( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - q^{5} + 2 q^{6} + 2 q^{7} - 3 q^{8} + 5 q^{9} + q^{10} - 2 q^{12} + q^{13} - 2 q^{14} - 12 q^{15} + 3 q^{16} + 5 q^{17} - 5 q^{18} + 3 q^{19} - q^{20} - 6 q^{21} + 2 q^{23} + 2 q^{24} - 2 q^{25} - q^{26} - 2 q^{27} + 2 q^{28} - q^{29} + 12 q^{30} - 3 q^{32} - 5 q^{34} + 4 q^{35} + 5 q^{36} - 23 q^{37} - 3 q^{38} + 4 q^{39} + q^{40} + 9 q^{41} + 6 q^{42} - 4 q^{43} + 3 q^{45} - 2 q^{46} - 6 q^{47} - 2 q^{48} - 3 q^{49} + 2 q^{50} - 8 q^{51} + q^{52} + 5 q^{53} + 2 q^{54} - 2 q^{56} - 2 q^{57} + q^{58} - 18 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{63} + 3 q^{64} - 5 q^{65} - 8 q^{67} + 5 q^{68} - 6 q^{69} - 4 q^{70} - 5 q^{72} - 10 q^{73} + 23 q^{74} + 22 q^{75} + 3 q^{76} - 4 q^{78} + 4 q^{79} - q^{80} - 17 q^{81} - 9 q^{82} - 4 q^{83} - 6 q^{84} + 3 q^{85} + 4 q^{86} + 18 q^{87} + 7 q^{89} - 3 q^{90} - 16 q^{91} + 2 q^{92} - 16 q^{93} + 6 q^{94} - q^{95} + 2 q^{96} + 7 q^{97} + 3 q^{98}+O(q^{100}) \) 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - q^5 + 2 * q^6 + 2 * q^7 - 3 * q^8 + 5 * q^9 + q^10 - 2 * q^12 + q^13 - 2 * q^14 - 12 * q^15 + 3 * q^16 + 5 * q^17 - 5 * q^18 + 3 * q^19 - q^20 - 6 * q^21 + 2 * q^23 + 2 * q^24 - 2 * q^25 - q^26 - 2 * q^27 + 2 * q^28 - q^29 + 12 * q^30 - 3 * q^32 - 5 * q^34 + 4 * q^35 + 5 * q^36 - 23 * q^37 - 3 * q^38 + 4 * q^39 + q^40 + 9 * q^41 + 6 * q^42 - 4 * q^43 + 3 * q^45 - 2 * q^46 - 6 * q^47 - 2 * q^48 - 3 * q^49 + 2 * q^50 - 8 * q^51 + q^52 + 5 * q^53 + 2 * q^54 - 2 * q^56 - 2 * q^57 + q^58 - 18 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^63 + 3 * q^64 - 5 * q^65 - 8 * q^67 + 5 * q^68 - 6 * q^69 - 4 * q^70 - 5 * q^72 - 10 * q^73 + 23 * q^74 + 22 * q^75 + 3 * q^76 - 4 * q^78 + 4 * q^79 - q^80 - 17 * q^81 - 9 * q^82 - 4 * q^83 - 6 * q^84 + 3 * q^85 + 4 * q^86 + 18 * q^87 + 7 * q^89 - 3 * q^90 - 16 * q^91 + 2 * q^92 - 16 * q^93 + 6 * q^94 - q^95 + 2 * q^96 + 7 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more