LMFDB - Embedded newform 4598.2.a.by.1.7

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:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 16x^{6} - 4x^{5} + 75x^{4} + 32x^{3} - 90x^{2} - 28x - 2 $ x^8 - 16x^6 - 4x^5 + 75x^4 + 32x^3 - 90x^2 - 28x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.182716$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +3.30349 q^{3} +1.00000 q^{4} +1.88260 q^{5} -3.30349 q^{6} -2.41197 q^{7} -1.00000 q^{8} +7.91304 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.30349 q^{3} +1.00000 q^{4} +1.88260 q^{5} -3.30349 q^{6} -2.41197 q^{7} -1.00000 q^{8} +7.91304 q^{9} -1.88260 q^{10} +3.30349 q^{12} +3.16592 q^{13} +2.41197 q^{14} +6.21916 q^{15} +1.00000 q^{16} +0.0684367 q^{17} -7.91304 q^{18} +1.00000 q^{19} +1.88260 q^{20} -7.96793 q^{21} -7.39138 q^{23} -3.30349 q^{24} -1.45580 q^{25} -3.16592 q^{26} +16.2302 q^{27} -2.41197 q^{28} +7.11637 q^{29} -6.21916 q^{30} -5.53983 q^{31} -1.00000 q^{32} -0.0684367 q^{34} -4.54079 q^{35} +7.91304 q^{36} +8.71254 q^{37} -1.00000 q^{38} +10.4586 q^{39} -1.88260 q^{40} -2.36137 q^{41} +7.96793 q^{42} +1.76442 q^{43} +14.8971 q^{45} +7.39138 q^{46} +9.11437 q^{47} +3.30349 q^{48} -1.18238 q^{49} +1.45580 q^{50} +0.226080 q^{51} +3.16592 q^{52} +8.63343 q^{53} -16.2302 q^{54} +2.41197 q^{56} +3.30349 q^{57} -7.11637 q^{58} +5.32542 q^{59} +6.21916 q^{60} +14.3424 q^{61} +5.53983 q^{62} -19.0860 q^{63} +1.00000 q^{64} +5.96017 q^{65} +11.3594 q^{67} +0.0684367 q^{68} -24.4173 q^{69} +4.54079 q^{70} -13.1580 q^{71} -7.91304 q^{72} -5.34443 q^{73} -8.71254 q^{74} -4.80922 q^{75} +1.00000 q^{76} -10.4586 q^{78} +3.95165 q^{79} +1.88260 q^{80} +29.8770 q^{81} +2.36137 q^{82} +5.25612 q^{83} -7.96793 q^{84} +0.128839 q^{85} -1.76442 q^{86} +23.5089 q^{87} +6.41191 q^{89} -14.8971 q^{90} -7.63611 q^{91} -7.39138 q^{92} -18.3008 q^{93} -9.11437 q^{94} +1.88260 q^{95} -3.30349 q^{96} -2.67951 q^{97} +1.18238 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 22 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 22 * q^9	$ 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 22 q^{9} + 8 q^{12} + 12 q^{13} + 4 q^{14} + 4 q^{15} + 8 q^{16} + 4 q^{17} - 22 q^{18} + 8 q^{19} + 20 q^{21} + 14 q^{23} - 8 q^{24} + 36 q^{25} - 12 q^{26} + 32 q^{27} - 4 q^{28} + 2 q^{29} - 4 q^{30} - 8 q^{32} - 4 q^{34} - 36 q^{35} + 22 q^{36} + 24 q^{37} - 8 q^{38} - 16 q^{39} - 8 q^{41} - 20 q^{42} - 8 q^{43} + 16 q^{45} - 14 q^{46} - 16 q^{47} + 8 q^{48} + 34 q^{49} - 36 q^{50} - 18 q^{51} + 12 q^{52} + 36 q^{53} - 32 q^{54} + 4 q^{56} + 8 q^{57} - 2 q^{58} - 24 q^{59} + 4 q^{60} - 12 q^{61} - 24 q^{63} + 8 q^{64} - 16 q^{65} + 16 q^{67} + 4 q^{68} + 4 q^{69} + 36 q^{70} + 4 q^{71} - 22 q^{72} + 20 q^{73} - 24 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{78} + 12 q^{79} + 40 q^{81} + 8 q^{82} - 20 q^{83} + 20 q^{84} - 12 q^{85} + 8 q^{86} + 36 q^{87} + 8 q^{89} - 16 q^{90} - 24 q^{91} + 14 q^{92} + 12 q^{93} + 16 q^{94} - 8 q^{96} + 4 q^{97} - 34 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 22 * q^9 + 8 * q^12 + 12 * q^13 + 4 * q^14 + 4 * q^15 + 8 * q^16 + 4 * q^17 - 22 * q^18 + 8 * q^19 + 20 * q^21 + 14 * q^23 - 8 * q^24 + 36 * q^25 - 12 * q^26 + 32 * q^27 - 4 * q^28 + 2 * q^29 - 4 * q^30 - 8 * q^32 - 4 * q^34 - 36 * q^35 + 22 * q^36 + 24 * q^37 - 8 * q^38 - 16 * q^39 - 8 * q^41 - 20 * q^42 - 8 * q^43 + 16 * q^45 - 14 * q^46 - 16 * q^47 + 8 * q^48 + 34 * q^49 - 36 * q^50 - 18 * q^51 + 12 * q^52 + 36 * q^53 - 32 * q^54 + 4 * q^56 + 8 * q^57 - 2 * q^58 - 24 * q^59 + 4 * q^60 - 12 * q^61 - 24 * q^63 + 8 * q^64 - 16 * q^65 + 16 * q^67 + 4 * q^68 + 4 * q^69 + 36 * q^70 + 4 * q^71 - 22 * q^72 + 20 * q^73 - 24 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^78 + 12 * q^79 + 40 * q^81 + 8 * q^82 - 20 * q^83 + 20 * q^84 - 12 * q^85 + 8 * q^86 + 36 * q^87 + 8 * q^89 - 16 * q^90 - 24 * q^91 + 14 * q^92 + 12 * q^93 + 16 * q^94 - 8 * q^96 + 4 * q^97 - 34 * 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
$3$	3.30349	1.90727	0.953635	−	0.300966i	$-0.0973089\pi$
$3$	3.30349	1.90727	0.953635	+	0.300966i	$0.0973089\pi$
$4$	1.00000	0.500000
$5$	1.88260	0.841926	0.420963	−	0.907078i	$-0.361692\pi$
$5$	1.88260	0.841926	0.420963	+	0.907078i	$0.361692\pi$
$6$	−3.30349	−1.34864
$7$	−2.41197	−0.911640	−0.455820	−	0.890072i	$-0.650654\pi$
$7$	−2.41197	−0.911640	−0.455820	+	0.890072i	$0.650654\pi$
$8$	−1.00000	−0.353553
$9$	7.91304	2.63768
$10$	−1.88260	−0.595332
$11$	0	0
$11$	0	0
$12$	3.30349	0.953635
$13$	3.16592	0.878068	0.439034	−	0.898470i	$-0.355321\pi$
$13$	3.16592	0.878068	0.439034	+	0.898470i	$0.355321\pi$
$14$	2.41197	0.644627
$15$	6.21916	1.60578
$16$	1.00000	0.250000
$17$	0.0684367	0.0165983	0.00829916	−	0.999966i	$-0.497358\pi$
$17$	0.0684367	0.0165983	0.00829916	+	0.999966i	$0.497358\pi$
$18$	−7.91304	−1.86512
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.88260	0.420963
$21$	−7.96793	−1.73874
$22$	0	0
$23$	−7.39138	−1.54121	−0.770605	−	0.637313i	$-0.780046\pi$
$23$	−7.39138	−1.54121	−0.770605	+	0.637313i	$0.780046\pi$
$24$	−3.30349	−0.674322
$25$	−1.45580	−0.291160
$26$	−3.16592	−0.620888
$27$	16.2302	3.12350
$28$	−2.41197	−0.455820
$29$	7.11637	1.32148	0.660738	−	0.750616i	$-0.270243\pi$
$29$	7.11637	1.32148	0.660738	+	0.750616i	$0.270243\pi$
$30$	−6.21916	−1.13546
$31$	−5.53983	−0.994982	−0.497491	−	0.867469i	$-0.665745\pi$
$31$	−5.53983	−0.994982	−0.497491	+	0.867469i	$0.665745\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−0.0684367	−0.0117368
$35$	−4.54079	−0.767534
$36$	7.91304	1.31884
$37$	8.71254	1.43233	0.716166	−	0.697930i	$-0.245895\pi$
$37$	8.71254	1.43233	0.716166	+	0.697930i	$0.245895\pi$
$38$	−1.00000	−0.162221
$39$	10.4586	1.67471
$40$	−1.88260	−0.297666
$41$	−2.36137	−0.368783	−0.184392	−	0.982853i	$-0.559031\pi$
$41$	−2.36137	−0.368783	−0.184392	+	0.982853i	$0.559031\pi$
$42$	7.96793	1.22948
$43$	1.76442	0.269072	0.134536	−	0.990909i	$-0.457046\pi$
$43$	1.76442	0.269072	0.134536	+	0.990909i	$0.457046\pi$
$44$	0	0
$45$	14.8971	2.22073
$46$	7.39138	1.08980
$47$	9.11437	1.32947	0.664734	−	0.747080i	$-0.268545\pi$
$47$	9.11437	1.32947	0.664734	+	0.747080i	$0.268545\pi$
$48$	3.30349	0.476818
$49$	−1.18238	−0.168912
$50$	1.45580	0.205881
$51$	0.226080	0.0316575
$52$	3.16592	0.439034
$53$	8.63343	1.18589	0.592947	−	0.805242i	$-0.297964\pi$
$53$	8.63343	1.18589	0.592947	+	0.805242i	$0.297964\pi$
$54$	−16.2302	−2.20865
$55$	0	0
$56$	2.41197	0.322314
$57$	3.30349	0.437558
$58$	−7.11637	−0.934425
$59$	5.32542	0.693311	0.346655	−	0.937993i	$-0.387317\pi$
$59$	5.32542	0.693311	0.346655	+	0.937993i	$0.387317\pi$
$60$	6.21916	0.802891
$61$	14.3424	1.83636	0.918179	−	0.396165i	$-0.129659\pi$
$61$	14.3424	1.83636	0.918179	+	0.396165i	$0.129659\pi$
$62$	5.53983	0.703559
$63$	−19.0860	−2.40461
$64$	1.00000	0.125000
$65$	5.96017	0.739269
$66$	0	0
$67$	11.3594	1.38777	0.693883	−	0.720088i	$-0.255898\pi$
$67$	11.3594	1.38777	0.693883	+	0.720088i	$0.255898\pi$
$68$	0.0684367	0.00829916
$69$	−24.4173	−2.93950
$70$	4.54079	0.542729
$71$	−13.1580	−1.56156	−0.780782	−	0.624803i	$-0.785179\pi$
$71$	−13.1580	−1.56156	−0.780782	+	0.624803i	$0.785179\pi$
$72$	−7.91304	−0.932560
$73$	−5.34443	−0.625519	−0.312759	−	0.949832i	$-0.601253\pi$
$73$	−5.34443	−0.625519	−0.312759	+	0.949832i	$0.601253\pi$
$74$	−8.71254	−1.01281
$75$	−4.80922	−0.555320
$76$	1.00000	0.114708
$77$	0	0
$78$	−10.4586	−1.18420
$79$	3.95165	0.444595	0.222298	−	0.974979i	$-0.428644\pi$
$79$	3.95165	0.444595	0.222298	+	0.974979i	$0.428644\pi$
$80$	1.88260	0.210482
$81$	29.8770	3.31967
$82$	2.36137	0.260769
$83$	5.25612	0.576934	0.288467	−	0.957490i	$-0.406854\pi$
$83$	5.25612	0.576934	0.288467	+	0.957490i	$0.406854\pi$
$84$	−7.96793	−0.869372
$85$	0.128839	0.0139746
$86$	−1.76442	−0.190262
$87$	23.5089	2.52041
$88$	0	0
$89$	6.41191	0.679661	0.339831	−	0.940487i	$-0.389630\pi$
$89$	6.41191	0.679661	0.339831	+	0.940487i	$0.389630\pi$
$90$	−14.8971	−1.57029
$91$	−7.63611	−0.800482
$92$	−7.39138	−0.770605
$93$	−18.3008	−1.89770
$94$	−9.11437	−0.940075
$95$	1.88260	0.193151
$96$	−3.30349	−0.337161
$97$	−2.67951	−0.272063	−0.136032	−	0.990704i	$-0.543435\pi$
$97$	−2.67951	−0.272063	−0.136032	+	0.990704i	$0.543435\pi$
$98$	1.18238	0.119439
$99$	0	0
$100$	−1.45580	−0.145580
$101$	11.8482	1.17894	0.589471	−	0.807789i	$-0.299336\pi$
$101$	11.8482	1.17894	0.589471	+	0.807789i	$0.299336\pi$
$102$	−0.226080	−0.0223852
$103$	−11.8327	−1.16591	−0.582957	−	0.812503i	$-0.698104\pi$
$103$	−11.8327	−1.16591	−0.582957	+	0.812503i	$0.698104\pi$
$104$	−3.16592	−0.310444
$105$	−15.0005	−1.46389
$106$	−8.63343	−0.838553
$107$	−8.26216	−0.798733	−0.399367	−	0.916791i	$-0.630770\pi$
$107$	−8.26216	−0.798733	−0.399367	+	0.916791i	$0.630770\pi$
$108$	16.2302	1.56175
$109$	−4.92876	−0.472090	−0.236045	−	0.971742i	$-0.575851\pi$
$109$	−4.92876	−0.472090	−0.236045	+	0.971742i	$0.575851\pi$
$110$	0	0
$111$	28.7818	2.73184
$112$	−2.41197	−0.227910
$113$	−19.1454	−1.80105	−0.900524	−	0.434807i	$-0.856817\pi$
$113$	−19.1454	−1.80105	−0.900524	+	0.434807i	$0.856817\pi$
$114$	−3.30349	−0.309400
$115$	−13.9151	−1.29759
$116$	7.11637	0.660738
$117$	25.0520	2.31606
$118$	−5.32542	−0.490245
$119$	−0.165067	−0.0151317
$120$	−6.21916	−0.567729
$121$	0	0
$122$	−14.3424	−1.29850
$123$	−7.80074	−0.703369
$124$	−5.53983	−0.497491
$125$	−12.1537	−1.08706
$126$	19.0860	1.70032
$127$	1.25227	0.111121	0.0555606	−	0.998455i	$-0.482305\pi$
$127$	1.25227	0.111121	0.0555606	+	0.998455i	$0.482305\pi$
$128$	−1.00000	−0.0883883
$129$	5.82874	0.513192
$130$	−5.96017	−0.522742
$131$	−13.7739	−1.20343	−0.601714	−	0.798711i	$-0.705515\pi$
$131$	−13.7739	−1.20343	−0.601714	+	0.798711i	$0.705515\pi$
$132$	0	0
$133$	−2.41197	−0.209145
$134$	−11.3594	−0.981299
$135$	30.5550	2.62975
$136$	−0.0684367	−0.00586839
$137$	1.83597	0.156858	0.0784289	−	0.996920i	$-0.475010\pi$
$137$	1.83597	0.156858	0.0784289	+	0.996920i	$0.475010\pi$
$138$	24.4173	2.07854
$139$	15.9172	1.35008	0.675039	−	0.737782i	$-0.264127\pi$
$139$	15.9172	1.35008	0.675039	+	0.737782i	$0.264127\pi$
$140$	−4.54079	−0.383767
$141$	30.1092	2.53565
$142$	13.1580	1.10419
$143$	0	0
$144$	7.91304	0.659420
$145$	13.3973	1.11259
$146$	5.34443	0.442308
$147$	−3.90598	−0.322160
$148$	8.71254	0.716166
$149$	3.08074	0.252384	0.126192	−	0.992006i	$-0.459724\pi$
$149$	3.08074	0.252384	0.126192	+	0.992006i	$0.459724\pi$
$150$	4.80922	0.392671
$151$	−17.4026	−1.41620	−0.708101	−	0.706112i	$-0.750448\pi$
$151$	−17.4026	−1.41620	−0.708101	+	0.706112i	$0.750448\pi$
$152$	−1.00000	−0.0811107
$153$	0.541542	0.0437811
$154$	0	0
$155$	−10.4293	−0.837702
$156$	10.4586	0.837356
$157$	8.92808	0.712538	0.356269	−	0.934383i	$-0.384049\pi$
$157$	8.92808	0.712538	0.356269	+	0.934383i	$0.384049\pi$
$158$	−3.95165	−0.314376
$159$	28.5205	2.26182
$160$	−1.88260	−0.148833
$161$	17.8278	1.40503
$162$	−29.8770	−2.34736
$163$	−3.61306	−0.282997	−0.141498	−	0.989938i	$-0.545192\pi$
$163$	−3.61306	−0.282997	−0.141498	+	0.989938i	$0.545192\pi$
$164$	−2.36137	−0.184392
$165$	0	0
$166$	−5.25612	−0.407954
$167$	24.7026	1.91154	0.955771	−	0.294112i	$-0.0950238\pi$
$167$	24.7026	1.91154	0.955771	+	0.294112i	$0.0950238\pi$
$168$	7.96793	0.614739
$169$	−2.97696	−0.228997
$170$	−0.128839	−0.00988151
$171$	7.91304	0.605125
$172$	1.76442	0.134536
$173$	−14.2517	−1.08354	−0.541770	−	0.840527i	$-0.682246\pi$
$173$	−14.2517	−1.08354	−0.541770	+	0.840527i	$0.682246\pi$
$174$	−23.5089	−1.78220
$175$	3.51135	0.265433
$176$	0	0
$177$	17.5925	1.32233
$178$	−6.41191	−0.480593
$179$	−12.3954	−0.926475	−0.463237	−	0.886234i	$-0.653312\pi$
$179$	−12.3954	−0.926475	−0.463237	+	0.886234i	$0.653312\pi$
$180$	14.8971	1.11037
$181$	9.78871	0.727589	0.363795	−	0.931479i	$-0.381481\pi$
$181$	9.78871	0.727589	0.363795	+	0.931479i	$0.381481\pi$
$182$	7.63611	0.566026
$183$	47.3800	3.50243
$184$	7.39138	0.544900
$185$	16.4023	1.20592
$186$	18.3008	1.34188
$187$	0	0
$188$	9.11437	0.664734
$189$	−39.1467	−2.84751
$190$	−1.88260	−0.136579
$191$	4.26597	0.308674	0.154337	−	0.988018i	$-0.450676\pi$
$191$	4.26597	0.308674	0.154337	+	0.988018i	$0.450676\pi$
$192$	3.30349	0.238409
$193$	10.3339	0.743854	0.371927	−	0.928262i	$-0.378697\pi$
$193$	10.3339	0.743854	0.371927	+	0.928262i	$0.378697\pi$
$194$	2.67951	0.192378
$195$	19.6894	1.40998
$196$	−1.18238	−0.0844558
$197$	−12.8943	−0.918683	−0.459342	−	0.888260i	$-0.651915\pi$
$197$	−12.8943	−0.918683	−0.459342	+	0.888260i	$0.651915\pi$
$198$	0	0
$199$	13.1491	0.932117	0.466059	−	0.884754i	$-0.345674\pi$
$199$	13.1491	0.932117	0.466059	+	0.884754i	$0.345674\pi$
$200$	1.45580	0.102941
$201$	37.5255	2.64684
$202$	−11.8482	−0.833638
$203$	−17.1645	−1.20471
$204$	0.226080	0.0158287
$205$	−4.44552	−0.310488
$206$	11.8327	0.824426
$207$	−58.4883	−4.06522
$208$	3.16592	0.219517
$209$	0	0
$210$	15.0005	1.03513
$211$	−26.5013	−1.82442	−0.912212	−	0.409719i	$-0.865627\pi$
$211$	−26.5013	−1.82442	−0.912212	+	0.409719i	$0.865627\pi$
$212$	8.63343	0.592947
$213$	−43.4672	−2.97833
$214$	8.26216	0.564790
$215$	3.32171	0.226539
$216$	−16.2302	−1.10432
$217$	13.3619	0.907066
$218$	4.92876	0.333818
$219$	−17.6553	−1.19303
$220$	0	0
$221$	0.216665	0.0145745
$222$	−28.7818	−1.93171
$223$	−29.7656	−1.99325	−0.996625	−	0.0820854i	$-0.973842\pi$
$223$	−29.7656	−1.99325	−0.996625	+	0.0820854i	$0.973842\pi$
$224$	2.41197	0.161157
$225$	−11.5198	−0.767986
$226$	19.1454	1.27353
$227$	−24.0754	−1.59794	−0.798969	−	0.601372i	$-0.794621\pi$
$227$	−24.0754	−1.59794	−0.798969	+	0.601372i	$0.794621\pi$
$228$	3.30349	0.218779
$229$	7.85068	0.518787	0.259394	−	0.965772i	$-0.416477\pi$
$229$	7.85068	0.518787	0.259394	+	0.965772i	$0.416477\pi$
$230$	13.9151	0.917531
$231$	0	0
$232$	−7.11637	−0.467213
$233$	22.1903	1.45374	0.726869	−	0.686776i	$-0.240975\pi$
$233$	22.1903	1.45374	0.726869	+	0.686776i	$0.240975\pi$
$234$	−25.0520	−1.63770
$235$	17.1588	1.11931
$236$	5.32542	0.346655
$237$	13.0542	0.847963
$238$	0.165067	0.0106997
$239$	2.33473	0.151021	0.0755107	−	0.997145i	$-0.475941\pi$
$239$	2.33473	0.151021	0.0755107	+	0.997145i	$0.475941\pi$
$240$	6.21916	0.401445
$241$	−28.6284	−1.84412	−0.922060	−	0.387046i	$-0.873495\pi$
$241$	−28.6284	−1.84412	−0.922060	+	0.387046i	$0.873495\pi$
$242$	0	0
$243$	50.0080	3.20801
$244$	14.3424	0.918179
$245$	−2.22596	−0.142211
$246$	7.80074	0.497357
$247$	3.16592	0.201443
$248$	5.53983	0.351779
$249$	17.3635	1.10037
$250$	12.1537	0.768669
$251$	5.69434	0.359424	0.179712	−	0.983719i	$-0.442483\pi$
$251$	5.69434	0.359424	0.179712	+	0.983719i	$0.442483\pi$
$252$	−19.0860	−1.20231
$253$	0	0
$254$	−1.25227	−0.0785746
$255$	0.425619	0.0266533
$256$	1.00000	0.0625000
$257$	−14.4196	−0.899473	−0.449737	−	0.893161i	$-0.648482\pi$
$257$	−14.4196	−0.899473	−0.449737	+	0.893161i	$0.648482\pi$
$258$	−5.82874	−0.362882
$259$	−21.0144	−1.30577
$260$	5.96017	0.369634
$261$	56.3121	3.48563
$262$	13.7739	0.850953
$263$	6.25442	0.385664	0.192832	−	0.981232i	$-0.438233\pi$
$263$	6.25442	0.385664	0.192832	+	0.981232i	$0.438233\pi$
$264$	0	0
$265$	16.2533	0.998435
$266$	2.41197	0.147888
$267$	21.1817	1.29630
$268$	11.3594	0.693883
$269$	16.9603	1.03409	0.517043	−	0.855960i	$-0.327033\pi$
$269$	16.9603	1.03409	0.517043	+	0.855960i	$0.327033\pi$
$270$	−30.5550	−1.85952
$271$	−10.9294	−0.663912	−0.331956	−	0.943295i	$-0.607709\pi$
$271$	−10.9294	−0.663912	−0.331956	+	0.943295i	$0.607709\pi$
$272$	0.0684367	0.00414958
$273$	−25.2258	−1.52674
$274$	−1.83597	−0.110915
$275$	0	0
$276$	−24.4173	−1.46975
$277$	−17.4179	−1.04654	−0.523271	−	0.852166i	$-0.675289\pi$
$277$	−17.4179	−1.04654	−0.523271	+	0.852166i	$0.675289\pi$
$278$	−15.9172	−0.954649
$279$	−43.8368	−2.62444
$280$	4.54079	0.271364
$281$	−11.8423	−0.706451	−0.353225	−	0.935538i	$-0.614915\pi$
$281$	−11.8423	−0.706451	−0.353225	+	0.935538i	$0.614915\pi$
$282$	−30.1092	−1.79298
$283$	−3.87917	−0.230593	−0.115296	−	0.993331i	$-0.536782\pi$
$283$	−3.87917	−0.230593	−0.115296	+	0.993331i	$0.536782\pi$
$284$	−13.1580	−0.780782
$285$	6.21916	0.368391
$286$	0	0
$287$	5.69555	0.336198
$288$	−7.91304	−0.466280
$289$	−16.9953	−0.999724
$290$	−13.3973	−0.786717
$291$	−8.85174	−0.518898
$292$	−5.34443	−0.312759
$293$	0.882661	0.0515656	0.0257828	−	0.999668i	$-0.491792\pi$
$293$	0.882661	0.0515656	0.0257828	+	0.999668i	$0.491792\pi$
$294$	3.90598	0.227802
$295$	10.0257	0.583717
$296$	−8.71254	−0.506406
$297$	0	0
$298$	−3.08074	−0.178462
$299$	−23.4005	−1.35329
$300$	−4.80922	−0.277660
$301$	−4.25574	−0.245297
$302$	17.4026	1.00141
$303$	39.1405	2.24856
$304$	1.00000	0.0573539
$305$	27.0011	1.54608
$306$	−0.541542	−0.0309579
$307$	−21.8100	−1.24476	−0.622380	−	0.782715i	$-0.713834\pi$
$307$	−21.8100	−1.24476	−0.622380	+	0.782715i	$0.713834\pi$
$308$	0	0
$309$	−39.0893	−2.22371
$310$	10.4293	0.592345
$311$	7.08973	0.402022	0.201011	−	0.979589i	$-0.435577\pi$
$311$	7.08973	0.402022	0.201011	+	0.979589i	$0.435577\pi$
$312$	−10.4586	−0.592100
$313$	7.51385	0.424708	0.212354	−	0.977193i	$-0.431887\pi$
$313$	7.51385	0.424708	0.212354	+	0.977193i	$0.431887\pi$
$314$	−8.92808	−0.503841
$315$	−35.9315	−2.02451
$316$	3.95165	0.222298
$317$	15.4744	0.869131	0.434566	−	0.900640i	$-0.356902\pi$
$317$	15.4744	0.869131	0.434566	+	0.900640i	$0.356902\pi$
$318$	−28.5205	−1.59935
$319$	0	0
$320$	1.88260	0.105241
$321$	−27.2940	−1.52340
$322$	−17.8278	−0.993506
$323$	0.0684367	0.00380792
$324$	29.8770	1.65984
$325$	−4.60894	−0.255658
$326$	3.61306	0.200109
$327$	−16.2821	−0.900402
$328$	2.36137	0.130385
$329$	−21.9836	−1.21200
$330$	0	0
$331$	10.4405	0.573864	0.286932	−	0.957951i	$-0.407365\pi$
$331$	10.4405	0.573864	0.286932	+	0.957951i	$0.407365\pi$
$332$	5.25612	0.288467
$333$	68.9426	3.77803
$334$	−24.7026	−1.35166
$335$	21.3852	1.16840
$336$	−7.96793	−0.434686
$337$	26.5055	1.44385	0.721924	−	0.691972i	$-0.243258\pi$
$337$	26.5055	1.44385	0.721924	+	0.691972i	$0.243258\pi$
$338$	2.97696	0.161925
$339$	−63.2466	−3.43508
$340$	0.128839	0.00698729
$341$	0	0
$342$	−7.91304	−0.427888
$343$	19.7357	1.06563
$344$	−1.76442	−0.0951312
$345$	−45.9682	−2.47485
$346$	14.2517	0.766179
$347$	−23.8096	−1.27817	−0.639084	−	0.769137i	$-0.720686\pi$
$347$	−23.8096	−1.27817	−0.639084	+	0.769137i	$0.720686\pi$
$348$	23.5089	1.26021
$349$	21.0247	1.12543	0.562714	−	0.826652i	$-0.309757\pi$
$349$	21.0247	1.12543	0.562714	+	0.826652i	$0.309757\pi$
$350$	−3.51135	−0.187690
$351$	51.3834	2.74264
$352$	0	0
$353$	18.4736	0.983253	0.491626	−	0.870806i	$-0.336403\pi$
$353$	18.4736	0.983253	0.491626	+	0.870806i	$0.336403\pi$
$354$	−17.5925	−0.935029
$355$	−24.7713	−1.31472
$356$	6.41191	0.339831
$357$	−0.545298	−0.0288603
$358$	12.3954	0.655117
$359$	−34.8001	−1.83668	−0.918341	−	0.395791i	$-0.870471\pi$
$359$	−34.8001	−1.83668	−0.918341	+	0.395791i	$0.870471\pi$
$360$	−14.8971	−0.785147
$361$	1.00000	0.0526316
$362$	−9.78871	−0.514483
$363$	0	0
$364$	−7.63611	−0.400241
$365$	−10.0615	−0.526641
$366$	−47.3800	−2.47659
$367$	−10.0520	−0.524713	−0.262356	−	0.964971i	$-0.584500\pi$
$367$	−10.0520	−0.524713	−0.262356	+	0.964971i	$0.584500\pi$
$368$	−7.39138	−0.385302
$369$	−18.6856	−0.972732
$370$	−16.4023	−0.852713
$371$	−20.8236	−1.08111
$372$	−18.3008	−0.948850
$373$	20.6591	1.06969	0.534843	−	0.844951i	$-0.320371\pi$
$373$	20.6591	1.06969	0.534843	+	0.844951i	$0.320371\pi$
$374$	0	0
$375$	−40.1497	−2.07332
$376$	−9.11437	−0.470038
$377$	22.5299	1.16035
$378$	39.1467	2.01349
$379$	11.5387	0.592704	0.296352	−	0.955079i	$-0.404230\pi$
$379$	11.5387	0.592704	0.296352	+	0.955079i	$0.404230\pi$
$380$	1.88260	0.0965756
$381$	4.13687	0.211938
$382$	−4.26597	−0.218266
$383$	5.30452	0.271048	0.135524	−	0.990774i	$-0.456728\pi$
$383$	5.30452	0.271048	0.135524	+	0.990774i	$0.456728\pi$
$384$	−3.30349	−0.168580
$385$	0	0
$386$	−10.3339	−0.525984
$387$	13.9619	0.709725
$388$	−2.67951	−0.136032
$389$	−22.9500	−1.16361	−0.581805	−	0.813328i	$-0.697653\pi$
$389$	−22.9500	−1.16361	−0.581805	+	0.813328i	$0.697653\pi$
$390$	−19.6894	−0.997010
$391$	−0.505842	−0.0255815
$392$	1.18238	0.0597193
$393$	−45.5018	−2.29526
$394$	12.8943	0.649607
$395$	7.43939	0.374316
$396$	0	0
$397$	0.483759	0.0242792	0.0121396	−	0.999926i	$-0.496136\pi$
$397$	0.483759	0.0242792	0.0121396	+	0.999926i	$0.496136\pi$
$398$	−13.1491	−0.659106
$399$	−7.96793	−0.398895
$400$	−1.45580	−0.0727900
$401$	−36.1672	−1.80610	−0.903051	−	0.429532i	$-0.858678\pi$
$401$	−36.1672	−1.80610	−0.903051	+	0.429532i	$0.858678\pi$
$402$	−37.5255	−1.87160
$403$	−17.5386	−0.873662
$404$	11.8482	0.589471
$405$	56.2467	2.79492
$406$	17.1645	0.851860
$407$	0	0
$408$	−0.226080	−0.0111926
$409$	−12.0788	−0.597256	−0.298628	−	0.954370i	$-0.596529\pi$
$409$	−12.0788	−0.597256	−0.298628	+	0.954370i	$0.596529\pi$
$410$	4.44552	0.219548
$411$	6.06512	0.299170
$412$	−11.8327	−0.582957
$413$	−12.8448	−0.632050
$414$	58.4883	2.87454
$415$	9.89520	0.485736
$416$	−3.16592	−0.155222
$417$	52.5822	2.57496
$418$	0	0
$419$	−14.4844	−0.707611	−0.353806	−	0.935319i	$-0.615113\pi$
$419$	−14.4844	−0.707611	−0.353806	+	0.935319i	$0.615113\pi$
$420$	−15.0005	−0.731947
$421$	8.74595	0.426252	0.213126	−	0.977025i	$-0.431636\pi$
$421$	8.74595	0.426252	0.213126	+	0.977025i	$0.431636\pi$
$422$	26.5013	1.29006
$423$	72.1223	3.50671
$424$	−8.63343	−0.419277
$425$	−0.0996300	−0.00483277
$426$	43.4672	2.10599
$427$	−34.5935	−1.67410
$428$	−8.26216	−0.399367
$429$	0	0
$430$	−3.32171	−0.160187
$431$	−18.0983	−0.871763	−0.435881	−	0.900004i	$-0.643563\pi$
$431$	−18.0983	−0.871763	−0.435881	+	0.900004i	$0.643563\pi$
$432$	16.2302	0.780874
$433$	19.3031	0.927648	0.463824	−	0.885927i	$-0.346477\pi$
$433$	19.3031	0.927648	0.463824	+	0.885927i	$0.346477\pi$
$434$	−13.3619	−0.641392
$435$	44.2579	2.12200
$436$	−4.92876	−0.236045
$437$	−7.39138	−0.353578
$438$	17.6553	0.843602
$439$	0.543248	0.0259278	0.0129639	−	0.999916i	$-0.495873\pi$
$439$	0.543248	0.0259278	0.0129639	+	0.999916i	$0.495873\pi$
$440$	0	0
$441$	−9.35623	−0.445535
$442$	−0.216665	−0.0103057
$443$	−24.5763	−1.16765	−0.583827	−	0.811878i	$-0.698445\pi$
$443$	−24.5763	−1.16765	−0.583827	+	0.811878i	$0.698445\pi$
$444$	28.7818	1.36592
$445$	12.0711	0.572225
$446$	29.7656	1.40944
$447$	10.1772	0.481365
$448$	−2.41197	−0.113955
$449$	30.2173	1.42604	0.713022	−	0.701141i	$-0.247326\pi$
$449$	30.2173	1.42604	0.713022	+	0.701141i	$0.247326\pi$
$450$	11.5198	0.543048
$451$	0	0
$452$	−19.1454	−0.900524
$453$	−57.4892	−2.70108
$454$	24.0754	1.12991
$455$	−14.3758	−0.673947
$456$	−3.30349	−0.154700
$457$	−34.7631	−1.62615	−0.813073	−	0.582161i	$-0.802207\pi$
$457$	−34.7631	−1.62615	−0.813073	+	0.582161i	$0.802207\pi$
$458$	−7.85068	−0.366838
$459$	1.11074	0.0518448
$460$	−13.9151	−0.648793
$461$	−10.2206	−0.476019	−0.238010	−	0.971263i	$-0.576495\pi$
$461$	−10.2206	−0.476019	−0.238010	+	0.971263i	$0.576495\pi$
$462$	0	0
$463$	−5.73645	−0.266596	−0.133298	−	0.991076i	$-0.542557\pi$
$463$	−5.73645	−0.266596	−0.133298	+	0.991076i	$0.542557\pi$
$464$	7.11637	0.330369
$465$	−34.4531	−1.59772
$466$	−22.1903	−1.02795
$467$	−25.2965	−1.17058	−0.585292	−	0.810823i	$-0.699020\pi$
$467$	−25.2965	−1.17058	−0.585292	+	0.810823i	$0.699020\pi$
$468$	25.0520	1.15803
$469$	−27.3985	−1.26514
$470$	−17.1588	−0.791474
$471$	29.4938	1.35900
$472$	−5.32542	−0.245122
$473$	0	0
$474$	−13.0542	−0.599600
$475$	−1.45580	−0.0667966
$476$	−0.165067	−0.00756585
$477$	68.3167	3.12801
$478$	−2.33473	−0.106788
$479$	6.51483	0.297670	0.148835	−	0.988862i	$-0.452448\pi$
$479$	6.51483	0.297670	0.148835	+	0.988862i	$0.452448\pi$
$480$	−6.21916	−0.283865
$481$	27.5832	1.25769
$482$	28.6284	1.30399
$483$	58.8940	2.67977
$484$	0	0
$485$	−5.04446	−0.229057
$486$	−50.0080	−2.26841
$487$	−26.5992	−1.20532	−0.602662	−	0.797997i	$-0.705893\pi$
$487$	−26.5992	−1.20532	−0.602662	+	0.797997i	$0.705893\pi$
$488$	−14.3424	−0.649251
$489$	−11.9357	−0.539751
$490$	2.22596	0.100559
$491$	16.5430	0.746576	0.373288	−	0.927715i	$-0.378230\pi$
$491$	16.5430	0.746576	0.373288	+	0.927715i	$0.378230\pi$
$492$	−7.80074	−0.351685
$493$	0.487021	0.0219343
$494$	−3.16592	−0.142441
$495$	0	0
$496$	−5.53983	−0.248746
$497$	31.7367	1.42359
$498$	−17.3635	−0.778079
$499$	8.60654	0.385282	0.192641	−	0.981269i	$-0.438295\pi$
$499$	8.60654	0.385282	0.192641	+	0.981269i	$0.438295\pi$
$500$	−12.1537	−0.543531
$501$	81.6047	3.64583
$502$	−5.69434	−0.254151
$503$	10.3371	0.460906	0.230453	−	0.973083i	$-0.425979\pi$
$503$	10.3371	0.460906	0.230453	+	0.973083i	$0.425979\pi$
$504$	19.0860	0.850160
$505$	22.3055	0.992583
$506$	0	0
$507$	−9.83434	−0.436758
$508$	1.25227	0.0555606
$509$	−35.1873	−1.55965	−0.779825	−	0.625997i	$-0.784692\pi$
$509$	−35.1873	−1.55965	−0.779825	+	0.625997i	$0.784692\pi$
$510$	−0.425619	−0.0188467
$511$	12.8906	0.570248
$512$	−1.00000	−0.0441942
$513$	16.2302	0.716579
$514$	14.4196	0.636023
$515$	−22.2764	−0.981614
$516$	5.82874	0.256596
$517$	0	0
$518$	21.0144	0.923320
$519$	−47.0805	−2.06660
$520$	−5.96017	−0.261371
$521$	9.17004	0.401747	0.200873	−	0.979617i	$-0.435622\pi$
$521$	9.17004	0.401747	0.200873	+	0.979617i	$0.435622\pi$
$522$	−56.3121	−2.46471
$523$	40.4012	1.76662	0.883311	−	0.468788i	$-0.155309\pi$
$523$	40.4012	1.76662	0.883311	+	0.468788i	$0.155309\pi$
$524$	−13.7739	−0.601714
$525$	11.5997	0.506253
$526$	−6.25442	−0.272706
$527$	−0.379127	−0.0165150
$528$	0	0
$529$	31.6325	1.37533
$530$	−16.2533	−0.706000
$531$	42.1402	1.82873
$532$	−2.41197	−0.104572
$533$	−7.47589	−0.323817
$534$	−21.1817	−0.916620
$535$	−15.5544	−0.672475
$536$	−11.3594	−0.490649
$537$	−40.9480	−1.76704
$538$	−16.9603	−0.731209
$539$	0	0
$540$	30.5550	1.31488
$541$	22.9546	0.986895	0.493447	−	0.869776i	$-0.335737\pi$
$541$	22.9546	0.986895	0.493447	+	0.869776i	$0.335737\pi$
$542$	10.9294	0.469456
$543$	32.3369	1.38771
$544$	−0.0684367	−0.00293420
$545$	−9.27891	−0.397465
$546$	25.2258	1.07957
$547$	22.0926	0.944611	0.472306	−	0.881435i	$-0.343422\pi$
$547$	22.0926	0.944611	0.472306	+	0.881435i	$0.343422\pi$
$548$	1.83597	0.0784289
$549$	113.492	4.84373
$550$	0	0
$551$	7.11637	0.303168
$552$	24.4173	1.03927
$553$	−9.53127	−0.405311
$554$	17.4179	0.740017
$555$	54.1847	2.30001
$556$	15.9172	0.675039
$557$	1.14809	0.0486463	0.0243232	−	0.999704i	$-0.492257\pi$
$557$	1.14809	0.0486463	0.0243232	+	0.999704i	$0.492257\pi$
$558$	43.8368	1.85576
$559$	5.58601	0.236263
$560$	−4.54079	−0.191884
$561$	0	0
$562$	11.8423	0.499536
$563$	40.9190	1.72453	0.862265	−	0.506458i	$-0.169046\pi$
$563$	40.9190	1.72453	0.862265	+	0.506458i	$0.169046\pi$
$564$	30.1092	1.26783
$565$	−36.0432	−1.51635
$566$	3.87917	0.163054
$567$	−72.0626	−3.02635
$568$	13.1580	0.552097
$569$	−7.10111	−0.297694	−0.148847	−	0.988860i	$-0.547556\pi$
$569$	−7.10111	−0.297694	−0.148847	+	0.988860i	$0.547556\pi$
$570$	−6.21916	−0.260492
$571$	−21.1001	−0.883012	−0.441506	−	0.897258i	$-0.645556\pi$
$571$	−21.1001	−0.883012	−0.441506	+	0.897258i	$0.645556\pi$
$572$	0	0
$573$	14.0926	0.588725
$574$	−5.69555	−0.237728
$575$	10.7604	0.448738
$576$	7.91304	0.329710
$577$	−24.3512	−1.01375	−0.506877	−	0.862018i	$-0.669200\pi$
$577$	−24.3512	−1.01375	−0.506877	+	0.862018i	$0.669200\pi$
$578$	16.9953	0.706912
$579$	34.1381	1.41873
$580$	13.3973	0.556293
$581$	−12.6776	−0.525957
$582$	8.85174	0.366916
$583$	0	0
$584$	5.34443	0.221154
$585$	47.1631	1.94995
$586$	−0.882661	−0.0364624
$587$	10.9498	0.451946	0.225973	−	0.974134i	$-0.427444\pi$
$587$	10.9498	0.451946	0.225973	+	0.974134i	$0.427444\pi$
$588$	−3.90598	−0.161080
$589$	−5.53983	−0.228265
$590$	−10.0257	−0.412750
$591$	−42.5963	−1.75218
$592$	8.71254	0.358083
$593$	−34.8544	−1.43130	−0.715649	−	0.698461i	$-0.753869\pi$
$593$	−34.8544	−1.43130	−0.715649	+	0.698461i	$0.753869\pi$
$594$	0	0
$595$	−0.310757	−0.0127398
$596$	3.08074	0.126192
$597$	43.4380	1.77780
$598$	23.4005	0.956918
$599$	12.0037	0.490460	0.245230	−	0.969465i	$-0.421137\pi$
$599$	12.0037	0.490460	0.245230	+	0.969465i	$0.421137\pi$
$600$	4.80922	0.196335
$601$	15.7288	0.641591	0.320795	−	0.947148i	$-0.396050\pi$
$601$	15.7288	0.641591	0.320795	+	0.947148i	$0.396050\pi$
$602$	4.25574	0.173451
$603$	89.8870	3.66048
$604$	−17.4026	−0.708101
$605$	0	0
$606$	−39.1405	−1.58997
$607$	25.9881	1.05482	0.527412	−	0.849610i	$-0.323163\pi$
$607$	25.9881	1.05482	0.527412	+	0.849610i	$0.323163\pi$
$608$	−1.00000	−0.0405554
$609$	−56.7027	−2.29771
$610$	−27.0011	−1.09324
$611$	28.8554	1.16736
$612$	0.541542	0.0218905
$613$	−38.5286	−1.55616	−0.778078	−	0.628168i	$-0.783805\pi$
$613$	−38.5286	−1.55616	−0.778078	+	0.628168i	$0.783805\pi$
$614$	21.8100	0.880178
$615$	−14.6857	−0.592185
$616$	0	0
$617$	1.01409	0.0408255	0.0204128	−	0.999792i	$-0.493502\pi$
$617$	1.01409	0.0408255	0.0204128	+	0.999792i	$0.493502\pi$
$618$	39.0893	1.57240
$619$	23.3860	0.939964	0.469982	−	0.882676i	$-0.344260\pi$
$619$	23.3860	0.939964	0.469982	+	0.882676i	$0.344260\pi$
$620$	−10.4293	−0.418851
$621$	−119.963	−4.81396
$622$	−7.08973	−0.284272
$623$	−15.4654	−0.619606
$624$	10.4586	0.418678
$625$	−15.6017	−0.624066
$626$	−7.51385	−0.300314
$627$	0	0
$628$	8.92808	0.356269
$629$	0.596257	0.0237743
$630$	35.9315	1.43154
$631$	11.2632	0.448382	0.224191	−	0.974545i	$-0.428026\pi$
$631$	11.2632	0.448382	0.224191	+	0.974545i	$0.428026\pi$
$632$	−3.95165	−0.157188
$633$	−87.5467	−3.47967
$634$	−15.4744	−0.614569
$635$	2.35753	0.0935559
$636$	28.5205	1.13091
$637$	−3.74333	−0.148316
$638$	0	0
$639$	−104.120	−4.11891
$640$	−1.88260	−0.0744165
$641$	−12.1252	−0.478918	−0.239459	−	0.970906i	$-0.576970\pi$
$641$	−12.1252	−0.478918	−0.239459	+	0.970906i	$0.576970\pi$
$642$	27.2940	1.07721
$643$	9.15192	0.360916	0.180458	−	0.983583i	$-0.442242\pi$
$643$	9.15192	0.360916	0.180458	+	0.983583i	$0.442242\pi$
$644$	17.8278	0.702515
$645$	10.9732	0.432070
$646$	−0.0684367	−0.00269260
$647$	24.1081	0.947788	0.473894	−	0.880582i	$-0.342848\pi$
$647$	24.1081	0.947788	0.473894	+	0.880582i	$0.342848\pi$
$648$	−29.8770	−1.17368
$649$	0	0
$650$	4.60894	0.180778
$651$	44.1409	1.73002
$652$	−3.61306	−0.141498
$653$	−14.8121	−0.579642	−0.289821	−	0.957081i	$-0.593596\pi$
$653$	−14.8121	−0.579642	−0.289821	+	0.957081i	$0.593596\pi$
$654$	16.2821	0.636681
$655$	−25.9308	−1.01320
$656$	−2.36137	−0.0921958
$657$	−42.2907	−1.64992
$658$	21.9836	0.857011
$659$	−21.6275	−0.842489	−0.421244	−	0.906947i	$-0.638407\pi$
$659$	−21.6275	−0.842489	−0.421244	+	0.906947i	$0.638407\pi$
$660$	0	0
$661$	7.88808	0.306811	0.153405	−	0.988163i	$-0.450976\pi$
$661$	7.88808	0.306811	0.153405	+	0.988163i	$0.450976\pi$
$662$	−10.4405	−0.405783
$663$	0.715750	0.0277974
$664$	−5.25612	−0.203977
$665$	−4.54079	−0.176084
$666$	−68.9426	−2.67147
$667$	−52.5998	−2.03667
$668$	24.7026	0.955771
$669$	−98.3302	−3.80167
$670$	−21.3852	−0.826181
$671$	0	0
$672$	7.96793	0.307370
$673$	29.4014	1.13334	0.566669	−	0.823945i	$-0.308232\pi$
$673$	29.4014	1.13334	0.566669	+	0.823945i	$0.308232\pi$
$674$	−26.5055	−1.02095
$675$	−23.6279	−0.909437
$676$	−2.97696	−0.114498
$677$	27.6599	1.06306	0.531528	−	0.847041i	$-0.321618\pi$
$677$	27.6599	1.06306	0.531528	+	0.847041i	$0.321618\pi$
$678$	63.2466	2.42897
$679$	6.46291	0.248024
$680$	−0.128839	−0.00494076
$681$	−79.5327	−3.04770
$682$	0	0
$683$	−43.0143	−1.64589	−0.822947	−	0.568117i	$-0.807672\pi$
$683$	−43.0143	−1.64589	−0.822947	+	0.568117i	$0.807672\pi$
$684$	7.91304	0.302563
$685$	3.45641	0.132063
$686$	−19.7357	−0.753512
$687$	25.9346	0.989468
$688$	1.76442	0.0672679
$689$	27.3328	1.04129
$690$	45.9682	1.74998
$691$	−22.3751	−0.851190	−0.425595	−	0.904914i	$-0.639935\pi$
$691$	−22.3751	−0.851190	−0.425595	+	0.904914i	$0.639935\pi$
$692$	−14.2517	−0.541770
$693$	0	0
$694$	23.8096	0.903801
$695$	29.9658	1.13667
$696$	−23.5089	−0.891101
$697$	−0.161604	−0.00612119
$698$	−21.0247	−0.795798
$699$	73.3055	2.77267
$700$	3.51135	0.132717
$701$	−16.8504	−0.636430	−0.318215	−	0.948019i	$-0.603083\pi$
$701$	−16.8504	−0.636430	−0.318215	+	0.948019i	$0.603083\pi$
$702$	−51.3834	−1.93934
$703$	8.71254	0.328600
$704$	0	0
$705$	56.6838	2.13483
$706$	−18.4736	−0.695265
$707$	−28.5776	−1.07477
$708$	17.5925	0.661165
$709$	1.44052	0.0541000	0.0270500	−	0.999634i	$-0.491389\pi$
$709$	1.44052	0.0541000	0.0270500	+	0.999634i	$0.491389\pi$
$710$	24.7713	0.929649
$711$	31.2695	1.17270
$712$	−6.41191	−0.240296
$713$	40.9470	1.53348
$714$	0.545298	0.0204073
$715$	0	0
$716$	−12.3954	−0.463237
$717$	7.71277	0.288039
$718$	34.8001	1.29873
$719$	−20.5362	−0.765870	−0.382935	−	0.923775i	$-0.625087\pi$
$719$	−20.5362	−0.765870	−0.382935	+	0.923775i	$0.625087\pi$
$720$	14.8971	0.555183
$721$	28.5403	1.06289
$722$	−1.00000	−0.0372161
$723$	−94.5738	−3.51724
$724$	9.78871	0.363795
$725$	−10.3600	−0.384761
$726$	0	0
$727$	14.6689	0.544041	0.272021	−	0.962291i	$-0.412308\pi$
$727$	14.6689	0.544041	0.272021	+	0.962291i	$0.412308\pi$
$728$	7.63611	0.283013
$729$	75.5697	2.79888
$730$	10.0615	0.372391
$731$	0.120751	0.00446614
$732$	47.3800	1.75122
$733$	−49.7416	−1.83725	−0.918623	−	0.395135i	$-0.870698\pi$
$733$	−49.7416	−1.83725	−0.918623	+	0.395135i	$0.870698\pi$
$734$	10.0520	0.371028
$735$	−7.35343	−0.271235
$736$	7.39138	0.272450
$737$	0	0
$738$	18.6856	0.687825
$739$	−42.1810	−1.55165	−0.775826	−	0.630947i	$-0.782667\pi$
$739$	−42.1810	−1.55165	−0.775826	+	0.630947i	$0.782667\pi$
$740$	16.4023	0.602959
$741$	10.4586	0.384205
$742$	20.8236	0.764459
$743$	−4.83219	−0.177276	−0.0886380	−	0.996064i	$-0.528251\pi$
$743$	−4.83219	−0.177276	−0.0886380	+	0.996064i	$0.528251\pi$
$744$	18.3008	0.670938
$745$	5.79982	0.212489
$746$	−20.6591	−0.756383
$747$	41.5919	1.52177
$748$	0	0
$749$	19.9281	0.728158
$750$	40.1497	1.46606
$751$	28.9857	1.05770	0.528851	−	0.848714i	$-0.322623\pi$
$751$	28.9857	1.05770	0.528851	+	0.848714i	$0.322623\pi$
$752$	9.11437	0.332367
$753$	18.8112	0.685518
$754$	−22.5299	−0.820489
$755$	−32.7622	−1.19234
$756$	−39.1467	−1.42375
$757$	32.3975	1.17751	0.588753	−	0.808313i	$-0.299619\pi$
$757$	32.3975	1.17751	0.588753	+	0.808313i	$0.299619\pi$
$758$	−11.5387	−0.419105
$759$	0	0
$760$	−1.88260	−0.0682893
$761$	−20.0438	−0.726587	−0.363293	−	0.931675i	$-0.618348\pi$
$761$	−20.0438	−0.726587	−0.363293	+	0.931675i	$0.618348\pi$
$762$	−4.13687	−0.149863
$763$	11.8880	0.430376
$764$	4.26597	0.154337
$765$	1.01951	0.0368604
$766$	−5.30452	−0.191660
$767$	16.8598	0.608774
$768$	3.30349	0.119204
$769$	−25.6006	−0.923182	−0.461591	−	0.887093i	$-0.652721\pi$
$769$	−25.6006	−0.923182	−0.461591	+	0.887093i	$0.652721\pi$
$770$	0	0
$771$	−47.6351	−1.71554
$772$	10.3339	0.371927
$773$	33.8041	1.21585	0.607925	−	0.793995i	$-0.292002\pi$
$773$	33.8041	1.21585	0.607925	+	0.793995i	$0.292002\pi$
$774$	−13.9619	−0.501851
$775$	8.06487	0.289699
$776$	2.67951	0.0961889
$777$	−69.4209	−2.49046
$778$	22.9500	0.822796
$779$	−2.36137	−0.0846047
$780$	19.6894	0.704992
$781$	0	0
$782$	0.505842	0.0180889
$783$	115.500	4.12763
$784$	−1.18238	−0.0422279
$785$	16.8080	0.599905
$786$	45.5018	1.62300
$787$	−18.3654	−0.654656	−0.327328	−	0.944911i	$-0.606148\pi$
$787$	−18.3654	−0.654656	−0.327328	+	0.944911i	$0.606148\pi$
$788$	−12.8943	−0.459342
$789$	20.6614	0.735566
$790$	−7.43939	−0.264682
$791$	46.1782	1.64191
$792$	0	0
$793$	45.4069	1.61245
$794$	−0.483759	−0.0171680
$795$	53.6927	1.90429
$796$	13.1491	0.466059
$797$	−32.4974	−1.15112	−0.575559	−	0.817760i	$-0.695215\pi$
$797$	−32.4974	−1.15112	−0.575559	+	0.817760i	$0.695215\pi$
$798$	7.96793	0.282062
$799$	0.623757	0.0220669
$800$	1.45580	0.0514703
$801$	50.7377	1.79273
$802$	36.1672	1.27711
$803$	0	0
$804$	37.5255	1.32342
$805$	33.5627	1.18293
$806$	17.5386	0.617772
$807$	56.0280	1.97228
$808$	−11.8482	−0.416819
$809$	−36.7995	−1.29380	−0.646901	−	0.762574i	$-0.723935\pi$
$809$	−36.7995	−1.29380	−0.646901	+	0.762574i	$0.723935\pi$
$810$	−56.2467	−1.97631
$811$	27.2780	0.957862	0.478931	−	0.877853i	$-0.341024\pi$
$811$	27.2780	0.957862	0.478931	+	0.877853i	$0.341024\pi$
$812$	−17.1645	−0.602356
$813$	−36.1050	−1.26626
$814$	0	0
$815$	−6.80196	−0.238262
$816$	0.226080	0.00791437
$817$	1.76442	0.0617293
$818$	12.0788	0.422324
$819$	−60.4249	−2.11142
$820$	−4.44552	−0.155244
$821$	−1.63228	−0.0569669	−0.0284835	−	0.999594i	$-0.509068\pi$
$821$	−1.63228	−0.0569669	−0.0284835	+	0.999594i	$0.509068\pi$
$822$	−6.06512	−0.211545
$823$	53.4082	1.86169	0.930846	−	0.365412i	$-0.119072\pi$
$823$	53.4082	1.86169	0.930846	+	0.365412i	$0.119072\pi$
$824$	11.8327	0.412213
$825$	0	0
$826$	12.8448	0.446927
$827$	−4.12284	−0.143365	−0.0716825	−	0.997427i	$-0.522837\pi$
$827$	−4.12284	−0.143365	−0.0716825	+	0.997427i	$0.522837\pi$
$828$	−58.4883	−2.03261
$829$	12.8328	0.445702	0.222851	−	0.974853i	$-0.428464\pi$
$829$	12.8328	0.445702	0.222851	+	0.974853i	$0.428464\pi$
$830$	−9.89520	−0.343467
$831$	−57.5400	−1.99604
$832$	3.16592	0.109758
$833$	−0.0809183	−0.00280365
$834$	−52.5822	−1.82077
$835$	46.5052	1.60938
$836$	0	0
$837$	−89.9123	−3.10782
$838$	14.4844	0.500357
$839$	−16.9755	−0.586058	−0.293029	−	0.956104i	$-0.594663\pi$
$839$	−16.9755	−0.586058	−0.293029	+	0.956104i	$0.594663\pi$
$840$	15.0005	0.517565
$841$	21.6427	0.746301
$842$	−8.74595	−0.301405
$843$	−39.1208	−1.34739
$844$	−26.5013	−0.912212
$845$	−5.60443	−0.192798
$846$	−72.1223	−2.47962
$847$	0	0
$848$	8.63343	0.296473
$849$	−12.8148	−0.439803
$850$	0.0996300	0.00341728
$851$	−64.3977	−2.20752
$852$	−43.4672	−1.48916
$853$	18.3348	0.627771	0.313886	−	0.949461i	$-0.398369\pi$
$853$	18.3348	0.627771	0.313886	+	0.949461i	$0.398369\pi$
$854$	34.5935	1.18377
$855$	14.8971	0.509471
$856$	8.26216	0.282395
$857$	−9.14446	−0.312369	−0.156184	−	0.987728i	$-0.549919\pi$
$857$	−9.14446	−0.312369	−0.156184	+	0.987728i	$0.549919\pi$
$858$	0	0
$859$	56.1013	1.91415	0.957076	−	0.289836i	$-0.0936007\pi$
$859$	56.1013	1.91415	0.957076	+	0.289836i	$0.0936007\pi$
$860$	3.32171	0.113269
$861$	18.8152	0.641220
$862$	18.0983	0.616429
$863$	9.49783	0.323310	0.161655	−	0.986847i	$-0.448317\pi$
$863$	9.49783	0.323310	0.161655	+	0.986847i	$0.448317\pi$
$864$	−16.2302	−0.552161
$865$	−26.8304	−0.912261
$866$	−19.3031	−0.655946
$867$	−56.1438	−1.90674
$868$	13.3619	0.453533
$869$	0	0
$870$	−44.2579	−1.50048
$871$	35.9628	1.21855
$872$	4.92876	0.166909
$873$	−21.2031	−0.717616
$874$	7.39138	0.250017
$875$	29.3145	0.991009
$876$	−17.6553	−0.596516
$877$	49.0925	1.65773	0.828867	−	0.559445i	$-0.188986\pi$
$877$	49.0925	1.65773	0.828867	+	0.559445i	$0.188986\pi$
$878$	−0.543248	−0.0183337
$879$	2.91586	0.0983495
$880$	0	0
$881$	−37.3645	−1.25884	−0.629422	−	0.777064i	$-0.716708\pi$
$881$	−37.3645	−1.25884	−0.629422	+	0.777064i	$0.716708\pi$
$882$	9.35623	0.315041
$883$	22.6572	0.762476	0.381238	−	0.924477i	$-0.375498\pi$
$883$	22.6572	0.762476	0.381238	+	0.924477i	$0.375498\pi$
$884$	0.216665	0.00728723
$885$	33.1197	1.11330
$886$	24.5763	0.825656
$887$	31.0484	1.04250	0.521251	−	0.853403i	$-0.325465\pi$
$887$	31.0484	1.04250	0.521251	+	0.853403i	$0.325465\pi$
$888$	−28.7818	−0.965853
$889$	−3.02045	−0.101303
$890$	−12.0711	−0.404624
$891$	0	0
$892$	−29.7656	−0.996625
$893$	9.11437	0.305001
$894$	−10.1772	−0.340376
$895$	−23.3356	−0.780024
$896$	2.41197	0.0805784
$897$	−77.3034	−2.58108
$898$	−30.2173	−1.00837
$899$	−39.4235	−1.31485
$900$	−11.5198	−0.383993
$901$	0.590843	0.0196838
$902$	0	0
$903$	−14.0588	−0.467847
$904$	19.1454	0.636767
$905$	18.4283	0.612577
$906$	57.4892	1.90995
$907$	−11.8840	−0.394603	−0.197301	−	0.980343i	$-0.563218\pi$
$907$	−11.8840	−0.394603	−0.197301	+	0.980343i	$0.563218\pi$
$908$	−24.0754	−0.798969
$909$	93.7554	3.10967
$910$	14.3758	0.476553
$911$	−33.5828	−1.11265	−0.556324	−	0.830966i	$-0.687788\pi$
$911$	−33.5828	−1.11265	−0.556324	+	0.830966i	$0.687788\pi$
$912$	3.30349	0.109389
$913$	0	0
$914$	34.7631	1.14986
$915$	89.1979	2.94879
$916$	7.85068	0.259394
$917$	33.2222	1.09709
$918$	−1.11074	−0.0366598
$919$	3.27575	0.108057	0.0540285	−	0.998539i	$-0.482794\pi$
$919$	3.27575	0.108057	0.0540285	+	0.998539i	$0.482794\pi$
$920$	13.9151	0.458766
$921$	−72.0489	−2.37409
$922$	10.2206	0.336597
$923$	−41.6571	−1.37116
$924$	0	0
$925$	−12.6837	−0.417038
$926$	5.73645	0.188512
$927$	−93.6329	−3.07531
$928$	−7.11637	−0.233606
$929$	−0.192133	−0.00630369	−0.00315185	−	0.999995i	$-0.501003\pi$
$929$	−0.192133	−0.00630369	−0.00315185	+	0.999995i	$0.501003\pi$
$930$	34.4531	1.12976
$931$	−1.18238	−0.0387510
$932$	22.1903	0.726869
$933$	23.4208	0.766764
$934$	25.2965	0.827728
$935$	0	0
$936$	−25.0520	−0.818851
$937$	−8.33878	−0.272416	−0.136208	−	0.990680i	$-0.543492\pi$
$937$	−8.33878	−0.272416	−0.136208	+	0.990680i	$0.543492\pi$
$938$	27.3985	0.894592
$939$	24.8219	0.810032
$940$	17.1588	0.559657
$941$	−32.4537	−1.05796	−0.528980	−	0.848634i	$-0.677425\pi$
$941$	−32.4537	−1.05796	−0.528980	+	0.848634i	$0.677425\pi$
$942$	−29.4938	−0.960960
$943$	17.4538	0.568373
$944$	5.32542	0.173328
$945$	−73.6978	−2.39739
$946$	0	0
$947$	39.7033	1.29018	0.645092	−	0.764105i	$-0.276819\pi$
$947$	39.7033	1.29018	0.645092	+	0.764105i	$0.276819\pi$
$948$	13.0542	0.423982
$949$	−16.9200	−0.549248
$950$	1.45580	0.0472324
$951$	51.1196	1.65767
$952$	0.165067	0.00534987
$953$	−28.2036	−0.913604	−0.456802	−	0.889568i	$-0.651005\pi$
$953$	−28.2036	−0.913604	−0.456802	+	0.889568i	$0.651005\pi$
$954$	−68.3167	−2.21183
$955$	8.03113	0.259881
$956$	2.33473	0.0755107
$957$	0	0
$958$	−6.51483	−0.210485
$959$	−4.42832	−0.142998
$960$	6.21916	0.200723
$961$	−0.310330	−0.0100106
$962$	−27.5832	−0.889318
$963$	−65.3788	−2.10680
$964$	−28.6284	−0.922060
$965$	19.4547	0.626270
$966$	−58.8940	−1.89488
$967$	50.9270	1.63770	0.818851	−	0.574006i	$-0.194611\pi$
$967$	50.9270	1.63770	0.818851	+	0.574006i	$0.194611\pi$
$968$	0	0
$969$	0.226080	0.00726273
$970$	5.04446	0.161968
$971$	−25.2762	−0.811151	−0.405576	−	0.914062i	$-0.632929\pi$
$971$	−25.2762	−0.811151	−0.405576	+	0.914062i	$0.632929\pi$
$972$	50.0080	1.60401
$973$	−38.3918	−1.23079
$974$	26.5992	0.852293
$975$	−15.2256	−0.487609
$976$	14.3424	0.459090
$977$	−51.5477	−1.64916	−0.824579	−	0.565747i	$-0.808588\pi$
$977$	−51.5477	−1.64916	−0.824579	+	0.565747i	$0.808588\pi$
$978$	11.9357	0.381662
$979$	0	0
$980$	−2.22596	−0.0711056
$981$	−39.0015	−1.24522
$982$	−16.5430	−0.527909
$983$	−8.63287	−0.275346	−0.137673	−	0.990478i	$-0.543962\pi$
$983$	−8.63287	−0.275346	−0.137673	+	0.990478i	$0.543962\pi$
$984$	7.80074	0.248679
$985$	−24.2749	−0.773464
$986$	−0.487021	−0.0155099
$987$	−72.6226	−2.31160
$988$	3.16592	0.100721
$989$	−13.0415	−0.414696
$990$	0	0
$991$	−23.8596	−0.757925	−0.378962	−	0.925412i	$-0.623719\pi$
$991$	−23.8596	−0.757925	−0.378962	+	0.925412i	$0.623719\pi$
$992$	5.53983	0.175890
$993$	34.4902	1.09451
$994$	−31.7367	−1.00663
$995$	24.7546	0.784774
$996$	17.3635	0.550185
$997$	15.9135	0.503987	0.251993	−	0.967729i	$-0.418914\pi$
$997$	15.9135	0.503987	0.251993	+	0.967729i	$0.418914\pi$
$998$	−8.60654	−0.272435
$999$	141.406	4.47388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.by.1.7	✓	8
11.10	odd	2		4598.2.a.cb.1.7	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.by.1.7	✓	8	1.1	even	1	trivial
4598.2.a.cb.1.7	yes	8	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.30349 q^{3} +1.00000 q^{4} +1.88260 q^{5} -3.30349 q^{6} -2.41197 q^{7} -1.00000 q^{8} +7.91304 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.30349 q^{3} +1.00000 q^{4} +1.88260 q^{5} -3.30349 q^{6} -2.41197 q^{7} -1.00000 q^{8} +7.91304 q^{9} -1.88260 q^{10} +3.30349 q^{12} +3.16592 q^{13} +2.41197 q^{14} +6.21916 q^{15} +1.00000 q^{16} +0.0684367 q^{17} -7.91304 q^{18} +1.00000 q^{19} +1.88260 q^{20} -7.96793 q^{21} -7.39138 q^{23} -3.30349 q^{24} -1.45580 q^{25} -3.16592 q^{26} +16.2302 q^{27} -2.41197 q^{28} +7.11637 q^{29} -6.21916 q^{30} -5.53983 q^{31} -1.00000 q^{32} -0.0684367 q^{34} -4.54079 q^{35} +7.91304 q^{36} +8.71254 q^{37} -1.00000 q^{38} +10.4586 q^{39} -1.88260 q^{40} -2.36137 q^{41} +7.96793 q^{42} +1.76442 q^{43} +14.8971 q^{45} +7.39138 q^{46} +9.11437 q^{47} +3.30349 q^{48} -1.18238 q^{49} +1.45580 q^{50} +0.226080 q^{51} +3.16592 q^{52} +8.63343 q^{53} -16.2302 q^{54} +2.41197 q^{56} +3.30349 q^{57} -7.11637 q^{58} +5.32542 q^{59} +6.21916 q^{60} +14.3424 q^{61} +5.53983 q^{62} -19.0860 q^{63} +1.00000 q^{64} +5.96017 q^{65} +11.3594 q^{67} +0.0684367 q^{68} -24.4173 q^{69} +4.54079 q^{70} -13.1580 q^{71} -7.91304 q^{72} -5.34443 q^{73} -8.71254 q^{74} -4.80922 q^{75} +1.00000 q^{76} -10.4586 q^{78} +3.95165 q^{79} +1.88260 q^{80} +29.8770 q^{81} +2.36137 q^{82} +5.25612 q^{83} -7.96793 q^{84} +0.128839 q^{85} -1.76442 q^{86} +23.5089 q^{87} +6.41191 q^{89} -14.8971 q^{90} -7.63611 q^{91} -7.39138 q^{92} -18.3008 q^{93} -9.11437 q^{94} +1.88260 q^{95} -3.30349 q^{96} -2.67951 q^{97} +1.18238 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 22 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 22 * q^9	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{6} - 4 q^{7} - 8 q^{8} + 22 q^{9} + 8 q^{12} + 12 q^{13} + 4 q^{14} + 4 q^{15} + 8 q^{16} + 4 q^{17} - 22 q^{18} + 8 q^{19} + 20 q^{21} + 14 q^{23} - 8 q^{24} + 36 q^{25} - 12 q^{26} + 32 q^{27} - 4 q^{28} + 2 q^{29} - 4 q^{30} - 8 q^{32} - 4 q^{34} - 36 q^{35} + 22 q^{36} + 24 q^{37} - 8 q^{38} - 16 q^{39} - 8 q^{41} - 20 q^{42} - 8 q^{43} + 16 q^{45} - 14 q^{46} - 16 q^{47} + 8 q^{48} + 34 q^{49} - 36 q^{50} - 18 q^{51} + 12 q^{52} + 36 q^{53} - 32 q^{54} + 4 q^{56} + 8 q^{57} - 2 q^{58} - 24 q^{59} + 4 q^{60} - 12 q^{61} - 24 q^{63} + 8 q^{64} - 16 q^{65} + 16 q^{67} + 4 q^{68} + 4 q^{69} + 36 q^{70} + 4 q^{71} - 22 q^{72} + 20 q^{73} - 24 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{78} + 12 q^{79} + 40 q^{81} + 8 q^{82} - 20 q^{83} + 20 q^{84} - 12 q^{85} + 8 q^{86} + 36 q^{87} + 8 q^{89} - 16 q^{90} - 24 q^{91} + 14 q^{92} + 12 q^{93} + 16 q^{94} - 8 q^{96} + 4 q^{97} - 34 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^6 - 4 * q^7 - 8 * q^8 + 22 * q^9 + 8 * q^12 + 12 * q^13 + 4 * q^14 + 4 * q^15 + 8 * q^16 + 4 * q^17 - 22 * q^18 + 8 * q^19 + 20 * q^21 + 14 * q^23 - 8 * q^24 + 36 * q^25 - 12 * q^26 + 32 * q^27 - 4 * q^28 + 2 * q^29 - 4 * q^30 - 8 * q^32 - 4 * q^34 - 36 * q^35 + 22 * q^36 + 24 * q^37 - 8 * q^38 - 16 * q^39 - 8 * q^41 - 20 * q^42 - 8 * q^43 + 16 * q^45 - 14 * q^46 - 16 * q^47 + 8 * q^48 + 34 * q^49 - 36 * q^50 - 18 * q^51 + 12 * q^52 + 36 * q^53 - 32 * q^54 + 4 * q^56 + 8 * q^57 - 2 * q^58 - 24 * q^59 + 4 * q^60 - 12 * q^61 - 24 * q^63 + 8 * q^64 - 16 * q^65 + 16 * q^67 + 4 * q^68 + 4 * q^69 + 36 * q^70 + 4 * q^71 - 22 * q^72 + 20 * q^73 - 24 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^78 + 12 * q^79 + 40 * q^81 + 8 * q^82 - 20 * q^83 + 20 * q^84 - 12 * q^85 + 8 * q^86 + 36 * q^87 + 8 * q^89 - 16 * q^90 - 24 * q^91 + 14 * q^92 + 12 * q^93 + 16 * q^94 - 8 * q^96 + 4 * q^97 - 34 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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