LMFDB - Embedded newform 4598.2.a.bt.1.4

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:	$4$
Coefficient field:	4.4.7488.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 2x + 1 $ x^4 - 2x^3 - 4x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.698857$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.43091 q^{3} +1.00000 q^{4} -0.301143 q^{5} +1.43091 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.952503 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.43091 q^{3} +1.00000 q^{4} -0.301143 q^{5} +1.43091 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.952503 q^{9} -0.301143 q^{10} +1.43091 q^{12} -1.39771 q^{13} -1.00000 q^{14} -0.430908 q^{15} +1.00000 q^{16} -3.90931 q^{17} -0.952503 q^{18} +1.00000 q^{19} -0.301143 q^{20} -1.43091 q^{21} -3.57498 q^{23} +1.43091 q^{24} -4.90931 q^{25} -1.39771 q^{26} -5.65567 q^{27} -1.00000 q^{28} -0.635480 q^{29} -0.430908 q^{30} -8.90089 q^{31} +1.00000 q^{32} -3.90931 q^{34} +0.301143 q^{35} -0.952503 q^{36} -0.187258 q^{37} +1.00000 q^{38} -2.00000 q^{39} -0.301143 q^{40} +8.02908 q^{41} -1.43091 q^{42} -0.641364 q^{43} +0.286840 q^{45} -3.57498 q^{46} -7.55068 q^{47} +1.43091 q^{48} -6.00000 q^{49} -4.90931 q^{50} -5.59387 q^{51} -1.39771 q^{52} -0.919309 q^{53} -5.65567 q^{54} -1.00000 q^{56} +1.43091 q^{57} -0.635480 q^{58} +0.502705 q^{59} -0.430908 q^{60} -1.41072 q^{61} -8.90089 q^{62} +0.952503 q^{63} +1.00000 q^{64} +0.420912 q^{65} +8.14454 q^{67} -3.90931 q^{68} -5.11546 q^{69} +0.301143 q^{70} +7.20634 q^{71} -0.952503 q^{72} +4.86612 q^{73} -0.187258 q^{74} -7.02477 q^{75} +1.00000 q^{76} -2.00000 q^{78} +5.73363 q^{79} -0.301143 q^{80} -5.23523 q^{81} +8.02908 q^{82} -14.9152 q^{83} -1.43091 q^{84} +1.17726 q^{85} -0.641364 q^{86} -0.909313 q^{87} +3.76955 q^{89} +0.286840 q^{90} +1.39771 q^{91} -3.57498 q^{92} -12.7364 q^{93} -7.55068 q^{94} -0.301143 q^{95} +1.43091 q^{96} -1.58641 q^{97} -6.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	$ 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} - 2 q^{12} - 4 q^{13} - 4 q^{14} + 6 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{19} - 2 q^{20} + 2 q^{21} - 8 q^{23} - 2 q^{24} - 8 q^{25} - 4 q^{26} - 14 q^{27} - 4 q^{28} + 2 q^{29} + 6 q^{30} + 4 q^{32} - 4 q^{34} + 2 q^{35} - 10 q^{37} + 4 q^{38} - 8 q^{39} - 2 q^{40} - 2 q^{41} + 2 q^{42} + 16 q^{43} - 8 q^{45} - 8 q^{46} - 2 q^{48} - 24 q^{49} - 8 q^{50} - 4 q^{52} - 6 q^{53} - 14 q^{54} - 4 q^{56} - 2 q^{57} + 2 q^{58} + 22 q^{59} + 6 q^{60} - 2 q^{61} + 4 q^{64} - 20 q^{65} - 20 q^{67} - 4 q^{68} - 2 q^{69} + 2 q^{70} - 10 q^{71} - 10 q^{74} + 2 q^{75} + 4 q^{76} - 8 q^{78} + 6 q^{79} - 2 q^{80} + 20 q^{81} - 2 q^{82} - 34 q^{83} + 2 q^{84} + 16 q^{86} + 8 q^{87} - 2 q^{89} - 8 q^{90} + 4 q^{91} - 8 q^{92} - 40 q^{93} - 2 q^{95} - 2 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 - 2 * q^12 - 4 * q^13 - 4 * q^14 + 6 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^19 - 2 * q^20 + 2 * q^21 - 8 * q^23 - 2 * q^24 - 8 * q^25 - 4 * q^26 - 14 * q^27 - 4 * q^28 + 2 * q^29 + 6 * q^30 + 4 * q^32 - 4 * q^34 + 2 * q^35 - 10 * q^37 + 4 * q^38 - 8 * q^39 - 2 * q^40 - 2 * q^41 + 2 * q^42 + 16 * q^43 - 8 * q^45 - 8 * q^46 - 2 * q^48 - 24 * q^49 - 8 * q^50 - 4 * q^52 - 6 * q^53 - 14 * q^54 - 4 * q^56 - 2 * q^57 + 2 * q^58 + 22 * q^59 + 6 * q^60 - 2 * q^61 + 4 * q^64 - 20 * q^65 - 20 * q^67 - 4 * q^68 - 2 * q^69 + 2 * q^70 - 10 * q^71 - 10 * q^74 + 2 * q^75 + 4 * q^76 - 8 * q^78 + 6 * q^79 - 2 * q^80 + 20 * q^81 - 2 * q^82 - 34 * q^83 + 2 * q^84 + 16 * q^86 + 8 * q^87 - 2 * q^89 - 8 * q^90 + 4 * q^91 - 8 * q^92 - 40 * q^93 - 2 * q^95 - 2 * q^96 - 8 * q^97 - 24 * 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
$3$	1.43091	0.826135	0.413068	−	0.910700i	$-0.364457\pi$
$3$	1.43091	0.826135	0.413068	+	0.910700i	$0.364457\pi$
$4$	1.00000	0.500000
$5$	−0.301143	−0.134675	−0.0673376	−	0.997730i	$-0.521450\pi$
$5$	−0.301143	−0.134675	−0.0673376	+	0.997730i	$0.521450\pi$
$6$	1.43091	0.584166
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000	0.353553
$9$	−0.952503	−0.317501
$10$	−0.301143	−0.0952298
$11$	0	0
$11$	0	0
$12$	1.43091	0.413068
$13$	−1.39771	−0.387656	−0.193828	−	0.981036i	$-0.562090\pi$
$13$	−1.39771	−0.387656	−0.193828	+	0.981036i	$0.562090\pi$
$14$	−1.00000	−0.267261
$15$	−0.430908	−0.111260
$16$	1.00000	0.250000
$17$	−3.90931	−0.948148	−0.474074	−	0.880485i	$-0.657217\pi$
$17$	−3.90931	−0.948148	−0.474074	+	0.880485i	$0.657217\pi$
$18$	−0.952503	−0.224507
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.301143	−0.0673376
$21$	−1.43091	−0.312250
$22$	0	0
$23$	−3.57498	−0.745434	−0.372717	−	0.927945i	$-0.621574\pi$
$23$	−3.57498	−0.745434	−0.372717	+	0.927945i	$0.621574\pi$
$24$	1.43091	0.292083
$25$	−4.90931	−0.981863
$26$	−1.39771	−0.274114
$27$	−5.65567	−1.08843
$28$	−1.00000	−0.188982
$29$	−0.635480	−0.118006	−0.0590028	−	0.998258i	$-0.518792\pi$
$29$	−0.635480	−0.118006	−0.0590028	+	0.998258i	$0.518792\pi$
$30$	−0.430908	−0.0786726
$31$	−8.90089	−1.59865	−0.799324	−	0.600901i	$-0.794809\pi$
$31$	−8.90089	−1.59865	−0.799324	+	0.600901i	$0.794809\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−3.90931	−0.670442
$35$	0.301143	0.0509025
$36$	−0.952503	−0.158750
$37$	−0.187258	−0.0307851	−0.0153925	−	0.999882i	$-0.504900\pi$
$37$	−0.187258	−0.0307851	−0.0153925	+	0.999882i	$0.504900\pi$
$38$	1.00000	0.162221
$39$	−2.00000	−0.320256
$40$	−0.301143	−0.0476149
$41$	8.02908	1.25393	0.626966	−	0.779047i	$-0.284297\pi$
$41$	8.02908	1.25393	0.626966	+	0.779047i	$0.284297\pi$
$42$	−1.43091	−0.220794
$43$	−0.641364	−0.0978071	−0.0489035	−	0.998804i	$-0.515573\pi$
$43$	−0.641364	−0.0978071	−0.0489035	+	0.998804i	$0.515573\pi$
$44$	0	0
$45$	0.286840	0.0427595
$46$	−3.57498	−0.527101
$47$	−7.55068	−1.10138	−0.550690	−	0.834710i	$-0.685635\pi$
$47$	−7.55068	−1.10138	−0.550690	+	0.834710i	$0.685635\pi$
$48$	1.43091	0.206534
$49$	−6.00000	−0.857143
$50$	−4.90931	−0.694282
$51$	−5.59387	−0.783298
$52$	−1.39771	−0.193828
$53$	−0.919309	−0.126277	−0.0631384	−	0.998005i	$-0.520111\pi$
$53$	−0.919309	−0.126277	−0.0631384	+	0.998005i	$0.520111\pi$
$54$	−5.65567	−0.769639
$55$	0	0
$56$	−1.00000	−0.133631
$57$	1.43091	0.189528
$58$	−0.635480	−0.0834426
$59$	0.502705	0.0654466	0.0327233	−	0.999464i	$-0.489582\pi$
$59$	0.502705	0.0654466	0.0327233	+	0.999464i	$0.489582\pi$
$60$	−0.430908	−0.0556300
$61$	−1.41072	−0.180624	−0.0903121	−	0.995914i	$-0.528786\pi$
$61$	−1.41072	−0.180624	−0.0903121	+	0.995914i	$0.528786\pi$
$62$	−8.90089	−1.13041
$63$	0.952503	0.120004
$64$	1.00000	0.125000
$65$	0.420912	0.0522077
$66$	0	0
$67$	8.14454	0.995014	0.497507	−	0.867460i	$-0.334249\pi$
$67$	8.14454	0.995014	0.497507	+	0.867460i	$0.334249\pi$
$68$	−3.90931	−0.474074
$69$	−5.11546	−0.615829
$70$	0.301143	0.0359935
$71$	7.20634	0.855236	0.427618	−	0.903960i	$-0.359353\pi$
$71$	7.20634	0.855236	0.427618	+	0.903960i	$0.359353\pi$
$72$	−0.952503	−0.112254
$73$	4.86612	0.569537	0.284768	−	0.958596i	$-0.408083\pi$
$73$	4.86612	0.569537	0.284768	+	0.958596i	$0.408083\pi$
$74$	−0.187258	−0.0217683
$75$	−7.02477	−0.811151
$76$	1.00000	0.114708
$77$	0	0
$78$	−2.00000	−0.226455
$79$	5.73363	0.645083	0.322542	−	0.946555i	$-0.395463\pi$
$79$	5.73363	0.645083	0.322542	+	0.946555i	$0.395463\pi$
$80$	−0.301143	−0.0336688
$81$	−5.23523	−0.581692
$82$	8.02908	0.886664
$83$	−14.9152	−1.63716	−0.818578	−	0.574396i	$-0.805237\pi$
$83$	−14.9152	−1.63716	−0.818578	+	0.574396i	$0.805237\pi$
$84$	−1.43091	−0.156125
$85$	1.17726	0.127692
$86$	−0.641364	−0.0691600
$87$	−0.909313	−0.0974886
$88$	0	0
$89$	3.76955	0.399572	0.199786	−	0.979840i	$-0.435975\pi$
$89$	3.76955	0.399572	0.199786	+	0.979840i	$0.435975\pi$
$90$	0.286840	0.0302355
$91$	1.39771	0.146520
$92$	−3.57498	−0.372717
$93$	−12.7364	−1.32070
$94$	−7.55068	−0.778793
$95$	−0.301143	−0.0308966
$96$	1.43091	0.146041
$97$	−1.58641	−0.161075	−0.0805376	−	0.996752i	$-0.525664\pi$
$97$	−1.58641	−0.161075	−0.0805376	+	0.996752i	$0.525664\pi$
$98$	−6.00000	−0.606092
$99$	0	0
$100$	−4.90931	−0.490931
$101$	6.84751	0.681353	0.340676	−	0.940181i	$-0.389344\pi$
$101$	6.84751	0.681353	0.340676	+	0.940181i	$0.389344\pi$
$102$	−5.59387	−0.553875
$103$	5.20634	0.512996	0.256498	−	0.966545i	$-0.417431\pi$
$103$	5.20634	0.512996	0.256498	+	0.966545i	$0.417431\pi$
$104$	−1.39771	−0.137057
$105$	0.430908	0.0420523
$106$	−0.919309	−0.0892912
$107$	−7.67997	−0.742450	−0.371225	−	0.928543i	$-0.621062\pi$
$107$	−7.67997	−0.742450	−0.371225	+	0.928543i	$0.621062\pi$
$108$	−5.65567	−0.544217
$109$	11.1198	1.06508	0.532540	−	0.846405i	$-0.321237\pi$
$109$	11.1198	1.06508	0.532540	+	0.846405i	$0.321237\pi$
$110$	0	0
$111$	−0.267949	−0.0254326
$112$	−1.00000	−0.0944911
$113$	−7.33180	−0.689718	−0.344859	−	0.938655i	$-0.612073\pi$
$113$	−7.33180	−0.689718	−0.344859	+	0.938655i	$0.612073\pi$
$114$	1.43091	0.134017
$115$	1.07658	0.100392
$116$	−0.635480	−0.0590028
$117$	1.33133	0.123081
$118$	0.502705	0.0462777
$119$	3.90931	0.358366
$120$	−0.430908	−0.0393363
$121$	0	0
$122$	−1.41072	−0.127721
$123$	11.4889	1.03592
$124$	−8.90089	−0.799324
$125$	2.98412	0.266908
$126$	0.952503	0.0848557
$127$	4.07816	0.361878	0.180939	−	0.983494i	$-0.442086\pi$
$127$	4.07816	0.361878	0.180939	+	0.983494i	$0.442086\pi$
$128$	1.00000	0.0883883
$129$	−0.917732	−0.0808018
$130$	0.420912	0.0369164
$131$	6.73636	0.588558	0.294279	−	0.955720i	$-0.404920\pi$
$131$	6.73636	0.588558	0.294279	+	0.955720i	$0.404920\pi$
$132$	0	0
$133$	−1.00000	−0.0867110
$134$	8.14454	0.703581
$135$	1.70316	0.146585
$136$	−3.90931	−0.335221
$137$	−21.0107	−1.79506	−0.897531	−	0.440951i	$-0.854641\pi$
$137$	−21.0107	−1.79506	−0.897531	+	0.440951i	$0.854641\pi$
$138$	−5.11546	−0.435457
$139$	1.30272	0.110495	0.0552476	−	0.998473i	$-0.482405\pi$
$139$	1.30272	0.110495	0.0552476	+	0.998473i	$0.482405\pi$
$140$	0.301143	0.0254512
$141$	−10.8043	−0.909888
$142$	7.20634	0.604743
$143$	0	0
$144$	−0.952503	−0.0793752
$145$	0.191370	0.0158924
$146$	4.86612	0.402723
$147$	−8.58545	−0.708116
$148$	−0.187258	−0.0153925
$149$	−15.9514	−1.30679	−0.653395	−	0.757017i	$-0.726656\pi$
$149$	−15.9514	−1.30679	−0.653395	+	0.757017i	$0.726656\pi$
$150$	−7.02477	−0.573570
$151$	0.910890	0.0741271	0.0370636	−	0.999313i	$-0.488200\pi$
$151$	0.910890	0.0741271	0.0370636	+	0.999313i	$0.488200\pi$
$152$	1.00000	0.0811107
$153$	3.72363	0.301038
$154$	0	0
$155$	2.68044	0.215298
$156$	−2.00000	−0.160128
$157$	14.4848	1.15601	0.578005	−	0.816033i	$-0.303831\pi$
$157$	14.4848	1.15601	0.578005	+	0.816033i	$0.303831\pi$
$158$	5.73363	0.456143
$159$	−1.31545	−0.104322
$160$	−0.301143	−0.0238074
$161$	3.57498	0.281748
$162$	−5.23523	−0.411319
$163$	−14.7364	−1.15424	−0.577120	−	0.816659i	$-0.695824\pi$
$163$	−14.7364	−1.15424	−0.577120	+	0.816659i	$0.695824\pi$
$164$	8.02908	0.626966
$165$	0	0
$166$	−14.9152	−1.15764
$167$	16.4978	1.27664	0.638318	−	0.769773i	$-0.279631\pi$
$167$	16.4978	1.27664	0.638318	+	0.769773i	$0.279631\pi$
$168$	−1.43091	−0.110397
$169$	−11.0464	−0.849723
$170$	1.17726	0.0902919
$171$	−0.952503	−0.0728397
$172$	−0.641364	−0.0489035
$173$	−5.07638	−0.385950	−0.192975	−	0.981204i	$-0.561814\pi$
$173$	−5.07638	−0.385950	−0.192975	+	0.981204i	$0.561814\pi$
$174$	−0.909313	−0.0689348
$175$	4.90931	0.371109
$176$	0	0
$177$	0.719324	0.0540677
$178$	3.76955	0.282540
$179$	4.26111	0.318490	0.159245	−	0.987239i	$-0.449094\pi$
$179$	4.26111	0.318490	0.159245	+	0.987239i	$0.449094\pi$
$180$	0.286840	0.0213798
$181$	−11.2827	−0.838639	−0.419319	−	0.907839i	$-0.637731\pi$
$181$	−11.2827	−0.838639	−0.419319	+	0.907839i	$0.637731\pi$
$182$	1.39771	0.103605
$183$	−2.01861	−0.149220
$184$	−3.57498	−0.263551
$185$	0.0563915	0.00414598
$186$	−12.7364	−0.933875
$187$	0	0
$188$	−7.55068	−0.550690
$189$	5.65567	0.411389
$190$	−0.301143	−0.0218472
$191$	−0.495719	−0.0358690	−0.0179345	−	0.999839i	$-0.505709\pi$
$191$	−0.495719	−0.0358690	−0.0179345	+	0.999839i	$0.505709\pi$
$192$	1.43091	0.103267
$193$	−19.3018	−1.38937	−0.694687	−	0.719312i	$-0.744457\pi$
$193$	−19.3018	−1.38937	−0.694687	+	0.719312i	$0.744457\pi$
$194$	−1.58641	−0.113897
$195$	0.602286	0.0431306
$196$	−6.00000	−0.428571
$197$	−22.9591	−1.63577	−0.817883	−	0.575385i	$-0.804852\pi$
$197$	−22.9591	−1.63577	−0.817883	+	0.575385i	$0.804852\pi$
$198$	0	0
$199$	−24.5611	−1.74109	−0.870547	−	0.492086i	$-0.836235\pi$
$199$	−24.5611	−1.74109	−0.870547	+	0.492086i	$0.836235\pi$
$200$	−4.90931	−0.347141
$201$	11.6541	0.822016
$202$	6.84751	0.481789
$203$	0.635480	0.0446019
$204$	−5.59387	−0.391649
$205$	−2.41790	−0.168874
$206$	5.20634	0.362743
$207$	3.40517	0.236676
$208$	−1.39771	−0.0969140
$209$	0	0
$210$	0.430908	0.0297355
$211$	13.0321	0.897166	0.448583	−	0.893741i	$-0.351929\pi$
$211$	13.0321	0.897166	0.448583	+	0.893741i	$0.351929\pi$
$212$	−0.919309	−0.0631384
$213$	10.3116	0.706540
$214$	−7.67997	−0.524992
$215$	0.193142	0.0131722
$216$	−5.65567	−0.384819
$217$	8.90089	0.604232
$218$	11.1198	0.753126
$219$	6.96297	0.470514
$220$	0	0
$221$	5.46410	0.367555
$222$	−0.267949	−0.0179836
$223$	−7.01450	−0.469726	−0.234863	−	0.972029i	$-0.575464\pi$
$223$	−7.01450	−0.469726	−0.234863	+	0.972029i	$0.575464\pi$
$224$	−1.00000	−0.0668153
$225$	4.67613	0.311742
$226$	−7.33180	−0.487704
$227$	2.63089	0.174618	0.0873092	−	0.996181i	$-0.472173\pi$
$227$	2.63089	0.174618	0.0873092	+	0.996181i	$0.472173\pi$
$228$	1.43091	0.0947642
$229$	−4.43961	−0.293377	−0.146689	−	0.989183i	$-0.546862\pi$
$229$	−4.43961	−0.293377	−0.146689	+	0.989183i	$0.546862\pi$
$230$	1.07658	0.0709875
$231$	0	0
$232$	−0.635480	−0.0417213
$233$	15.4482	1.01205	0.506023	−	0.862520i	$-0.331115\pi$
$233$	15.4482	1.01205	0.506023	+	0.862520i	$0.331115\pi$
$234$	1.33133	0.0870315
$235$	2.27383	0.148329
$236$	0.502705	0.0327233
$237$	8.20429	0.532926
$238$	3.90931	0.253403
$239$	13.1489	0.850528	0.425264	−	0.905069i	$-0.360181\pi$
$239$	13.1489	0.850528	0.425264	+	0.905069i	$0.360181\pi$
$240$	−0.430908	−0.0278150
$241$	16.1545	1.04061	0.520303	−	0.853982i	$-0.325819\pi$
$241$	16.1545	1.04061	0.520303	+	0.853982i	$0.325819\pi$
$242$	0	0
$243$	9.47587	0.607877
$244$	−1.41072	−0.0903121
$245$	1.80686	0.115436
$246$	11.4889	0.732504
$247$	−1.39771	−0.0889344
$248$	−8.90089	−0.565207
$249$	−21.3423	−1.35251
$250$	2.98412	0.188732
$251$	4.74683	0.299617	0.149809	−	0.988715i	$-0.452134\pi$
$251$	4.74683	0.299617	0.149809	+	0.988715i	$0.452134\pi$
$252$	0.952503	0.0600020
$253$	0	0
$254$	4.07816	0.255886
$255$	1.68455	0.105491
$256$	1.00000	0.0625000
$257$	20.6804	1.29001	0.645005	−	0.764178i	$-0.276855\pi$
$257$	20.6804	1.29001	0.645005	+	0.764178i	$0.276855\pi$
$258$	−0.917732	−0.0571355
$259$	0.187258	0.0116357
$260$	0.420912	0.0261038
$261$	0.605296	0.0374669
$262$	6.73636	0.416174
$263$	16.2184	1.00007	0.500034	−	0.866006i	$-0.333321\pi$
$263$	16.2184	1.00007	0.500034	+	0.866006i	$0.333321\pi$
$264$	0	0
$265$	0.276843	0.0170064
$266$	−1.00000	−0.0613139
$267$	5.39388	0.330100
$268$	8.14454	0.497507
$269$	−1.93074	−0.117719	−0.0588596	−	0.998266i	$-0.518746\pi$
$269$	−1.93074	−0.117719	−0.0588596	+	0.998266i	$0.518746\pi$
$270$	1.70316	0.103651
$271$	4.51475	0.274252	0.137126	−	0.990554i	$-0.456214\pi$
$271$	4.51475	0.274252	0.137126	+	0.990554i	$0.456214\pi$
$272$	−3.90931	−0.237037
$273$	2.00000	0.121046
$274$	−21.0107	−1.26930
$275$	0	0
$276$	−5.11546	−0.307915
$277$	12.6071	0.757485	0.378743	−	0.925502i	$-0.376357\pi$
$277$	12.6071	0.757485	0.378743	+	0.925502i	$0.376357\pi$
$278$	1.30272	0.0781319
$279$	8.47813	0.507572
$280$	0.301143	0.0179967
$281$	−13.3200	−0.794607	−0.397303	−	0.917687i	$-0.630054\pi$
$281$	−13.3200	−0.794607	−0.397303	+	0.917687i	$0.630054\pi$
$282$	−10.8043	−0.643388
$283$	−24.5772	−1.46096	−0.730482	−	0.682932i	$-0.760705\pi$
$283$	−24.5772	−1.46096	−0.730482	+	0.682932i	$0.760705\pi$
$284$	7.20634	0.427618
$285$	−0.430908	−0.0255248
$286$	0	0
$287$	−8.02908	−0.473942
$288$	−0.952503	−0.0561268
$289$	−1.71727	−0.101016
$290$	0.191370	0.0112376
$291$	−2.27000	−0.133070
$292$	4.86612	0.284768
$293$	6.95839	0.406513	0.203257	−	0.979125i	$-0.434847\pi$
$293$	6.95839	0.406513	0.203257	+	0.979125i	$0.434847\pi$
$294$	−8.58545	−0.500713
$295$	−0.151386	−0.00881403
$296$	−0.187258	−0.0108842
$297$	0	0
$298$	−15.9514	−0.924040
$299$	4.99679	0.288972
$300$	−7.02477	−0.405576
$301$	0.641364	0.0369676
$302$	0.910890	0.0524158
$303$	9.79816	0.562890
$304$	1.00000	0.0573539
$305$	0.424829	0.0243256
$306$	3.72363	0.212866
$307$	−11.0608	−0.631276	−0.315638	−	0.948880i	$-0.602218\pi$
$307$	−11.0608	−0.631276	−0.315638	+	0.948880i	$0.602218\pi$
$308$	0	0
$309$	7.44980	0.423804
$310$	2.68044	0.152239
$311$	25.7857	1.46217	0.731087	−	0.682284i	$-0.239013\pi$
$311$	25.7857	1.46217	0.731087	+	0.682284i	$0.239013\pi$
$312$	−2.00000	−0.113228
$313$	−17.3016	−0.977945	−0.488973	−	0.872299i	$-0.662628\pi$
$313$	−17.3016	−0.977945	−0.488973	+	0.872299i	$0.662628\pi$
$314$	14.4848	0.817423
$315$	−0.286840	−0.0161616
$316$	5.73363	0.322542
$317$	−11.8272	−0.664284	−0.332142	−	0.943229i	$-0.607771\pi$
$317$	−11.8272	−0.664284	−0.332142	+	0.943229i	$0.607771\pi$
$318$	−1.31545	−0.0737666
$319$	0	0
$320$	−0.301143	−0.0168344
$321$	−10.9893	−0.613364
$322$	3.57498	0.199226
$323$	−3.90931	−0.217520
$324$	−5.23523	−0.290846
$325$	6.86182	0.380625
$326$	−14.7364	−0.816171
$327$	15.9114	0.879900
$328$	8.02908	0.443332
$329$	7.55068	0.416282
$330$	0	0
$331$	−21.1398	−1.16195	−0.580973	−	0.813923i	$-0.697328\pi$
$331$	−21.1398	−1.16195	−0.580973	+	0.813923i	$0.697328\pi$
$332$	−14.9152	−0.818578
$333$	0.178364	0.00977428
$334$	16.4978	0.902718
$335$	−2.45267	−0.134004
$336$	−1.43091	−0.0780624
$337$	−3.64725	−0.198678	−0.0993391	−	0.995054i	$-0.531673\pi$
$337$	−3.64725	−0.198678	−0.0993391	+	0.995054i	$0.531673\pi$
$338$	−11.0464	−0.600845
$339$	−10.4911	−0.569800
$340$	1.17726	0.0638460
$341$	0	0
$342$	−0.952503	−0.0515055
$343$	13.0000	0.701934
$344$	−0.641364	−0.0345800
$345$	1.54049	0.0829369
$346$	−5.07638	−0.272908
$347$	−5.70933	−0.306493	−0.153246	−	0.988188i	$-0.548973\pi$
$347$	−5.70933	−0.306493	−0.153246	+	0.988188i	$0.548973\pi$
$348$	−0.909313	−0.0487443
$349$	−7.82910	−0.419082	−0.209541	−	0.977800i	$-0.567197\pi$
$349$	−7.82910	−0.419082	−0.209541	+	0.977800i	$0.567197\pi$
$350$	4.90931	0.262414
$351$	7.90501	0.421938
$352$	0	0
$353$	3.13708	0.166970	0.0834850	−	0.996509i	$-0.473395\pi$
$353$	3.13708	0.166970	0.0834850	+	0.996509i	$0.473395\pi$
$354$	0.719324	0.0382316
$355$	−2.17014	−0.115179
$356$	3.76955	0.199786
$357$	5.59387	0.296059
$358$	4.26111	0.225206
$359$	9.10566	0.480578	0.240289	−	0.970701i	$-0.422758\pi$
$359$	9.10566	0.480578	0.240289	+	0.970701i	$0.422758\pi$
$360$	0.286840	0.0151178
$361$	1.00000	0.0526316
$362$	−11.2827	−0.593007
$363$	0	0
$364$	1.39771	0.0732601
$365$	−1.46540	−0.0767025
$366$	−2.01861	−0.105514
$367$	1.30291	0.0680116	0.0340058	−	0.999422i	$-0.489174\pi$
$367$	1.30291	0.0680116	0.0340058	+	0.999422i	$0.489174\pi$
$368$	−3.57498	−0.186359
$369$	−7.64772	−0.398125
$370$	0.0563915	0.00293165
$371$	0.919309	0.0477281
$372$	−12.7364	−0.660349
$373$	0.845461	0.0437763	0.0218882	−	0.999760i	$-0.493032\pi$
$373$	0.845461	0.0437763	0.0218882	+	0.999760i	$0.493032\pi$
$374$	0	0
$375$	4.27000	0.220502
$376$	−7.55068	−0.389396
$377$	0.888219	0.0457456
$378$	5.65567	0.290896
$379$	−16.4689	−0.845950	−0.422975	−	0.906141i	$-0.639014\pi$
$379$	−16.4689	−0.845950	−0.422975	+	0.906141i	$0.639014\pi$
$380$	−0.301143	−0.0154483
$381$	5.83546	0.298960
$382$	−0.495719	−0.0253632
$383$	14.8014	0.756319	0.378159	−	0.925741i	$-0.376557\pi$
$383$	14.8014	0.756319	0.378159	+	0.925741i	$0.376557\pi$
$384$	1.43091	0.0730207
$385$	0	0
$386$	−19.3018	−0.982436
$387$	0.610901	0.0310538
$388$	−1.58641	−0.0805376
$389$	−3.91931	−0.198717	−0.0993584	−	0.995052i	$-0.531679\pi$
$389$	−3.91931	−0.198717	−0.0993584	+	0.995052i	$0.531679\pi$
$390$	0.602286	0.0304979
$391$	13.9757	0.706782
$392$	−6.00000	−0.303046
$393$	9.63911	0.486229
$394$	−22.9591	−1.15666
$395$	−1.72664	−0.0868768
$396$	0	0
$397$	12.9082	0.647845	0.323922	−	0.946084i	$-0.394998\pi$
$397$	12.9082	0.647845	0.323922	+	0.946084i	$0.394998\pi$
$398$	−24.5611	−1.23114
$399$	−1.43091	−0.0716350
$400$	−4.90931	−0.245466
$401$	−2.53413	−0.126548	−0.0632741	−	0.997996i	$-0.520154\pi$
$401$	−2.53413	−0.126548	−0.0632741	+	0.997996i	$0.520154\pi$
$402$	11.6541	0.581253
$403$	12.4409	0.619726
$404$	6.84751	0.340676
$405$	1.57655	0.0783395
$406$	0.635480	0.0315383
$407$	0	0
$408$	−5.59387	−0.276938
$409$	28.3472	1.40168	0.700841	−	0.713318i	$-0.252808\pi$
$409$	28.3472	1.40168	0.700841	+	0.713318i	$0.252808\pi$
$410$	−2.41790	−0.119412
$411$	−30.0643	−1.48296
$412$	5.20634	0.256498
$413$	−0.502705	−0.0247365
$414$	3.40517	0.167355
$415$	4.49161	0.220484
$416$	−1.39771	−0.0685286
$417$	1.86407	0.0912840
$418$	0	0
$419$	−1.82561	−0.0891870	−0.0445935	−	0.999005i	$-0.514199\pi$
$419$	−1.82561	−0.0891870	−0.0445935	+	0.999005i	$0.514199\pi$
$420$	0.430908	0.0210261
$421$	24.0238	1.17085	0.585425	−	0.810727i	$-0.300928\pi$
$421$	24.0238	1.17085	0.585425	+	0.810727i	$0.300928\pi$
$422$	13.0321	0.634392
$423$	7.19204	0.349689
$424$	−0.919309	−0.0446456
$425$	19.1920	0.930951
$426$	10.3116	0.499599
$427$	1.41072	0.0682695
$428$	−7.67997	−0.371225
$429$	0	0
$430$	0.193142	0.00931414
$431$	21.4490	1.03316	0.516582	−	0.856238i	$-0.327204\pi$
$431$	21.4490	1.03316	0.516582	+	0.856238i	$0.327204\pi$
$432$	−5.65567	−0.272108
$433$	−7.85455	−0.377466	−0.188733	−	0.982028i	$-0.560438\pi$
$433$	−7.85455	−0.377466	−0.188733	+	0.982028i	$0.560438\pi$
$434$	8.90089	0.427257
$435$	0.273833	0.0131293
$436$	11.1198	0.532540
$437$	−3.57498	−0.171014
$438$	6.96297	0.332704
$439$	0.650885	0.0310650	0.0155325	−	0.999879i	$-0.495056\pi$
$439$	0.650885	0.0310650	0.0155325	+	0.999879i	$0.495056\pi$
$440$	0	0
$441$	5.71502	0.272144
$442$	5.46410	0.259901
$443$	4.53815	0.215614	0.107807	−	0.994172i	$-0.465617\pi$
$443$	4.53815	0.215614	0.107807	+	0.994172i	$0.465617\pi$
$444$	−0.267949	−0.0127163
$445$	−1.13517	−0.0538124
$446$	−7.01450	−0.332146
$447$	−22.8250	−1.07958
$448$	−1.00000	−0.0472456
$449$	37.3091	1.76073	0.880363	−	0.474300i	$-0.157299\pi$
$449$	37.3091	1.76073	0.880363	+	0.474300i	$0.157299\pi$
$450$	4.67613	0.220435
$451$	0	0
$452$	−7.33180	−0.344859
$453$	1.30340	0.0612390
$454$	2.63089	0.123474
$455$	−0.420912	−0.0197326
$456$	1.43091	0.0670084
$457$	21.3693	0.999614	0.499807	−	0.866137i	$-0.333404\pi$
$457$	21.3693	0.999614	0.499807	+	0.866137i	$0.333404\pi$
$458$	−4.43961	−0.207449
$459$	22.1098	1.03200
$460$	1.07658	0.0501958
$461$	−9.44157	−0.439738	−0.219869	−	0.975529i	$-0.570563\pi$
$461$	−9.44157	−0.439738	−0.219869	+	0.975529i	$0.570563\pi$
$462$	0	0
$463$	−15.4976	−0.720233	−0.360117	−	0.932907i	$-0.617263\pi$
$463$	−15.4976	−0.720233	−0.360117	+	0.932907i	$0.617263\pi$
$464$	−0.635480	−0.0295014
$465$	3.83546	0.177865
$466$	15.4482	0.715625
$467$	−5.81733	−0.269194	−0.134597	−	0.990900i	$-0.542974\pi$
$467$	−5.81733	−0.269194	−0.134597	+	0.990900i	$0.542974\pi$
$468$	1.33133	0.0615406
$469$	−8.14454	−0.376080
$470$	2.27383	0.104884
$471$	20.7264	0.955020
$472$	0.502705	0.0231389
$473$	0	0
$474$	8.20429	0.376836
$475$	−4.90931	−0.225255
$476$	3.90931	0.179183
$477$	0.875644	0.0400930
$478$	13.1489	0.601414
$479$	−24.8407	−1.13500	−0.567501	−	0.823373i	$-0.692090\pi$
$479$	−24.8407	−1.13500	−0.567501	+	0.823373i	$0.692090\pi$
$480$	−0.430908	−0.0196682
$481$	0.261733	0.0119340
$482$	16.1545	0.735819
$483$	5.11546	0.232762
$484$	0	0
$485$	0.477735	0.0216928
$486$	9.47587	0.429834
$487$	−10.5918	−0.479961	−0.239980	−	0.970778i	$-0.577141\pi$
$487$	−10.5918	−0.479961	−0.239980	+	0.970778i	$0.577141\pi$
$488$	−1.41072	−0.0638603
$489$	−21.0864	−0.953559
$490$	1.80686	0.0816255
$491$	−38.6077	−1.74234	−0.871170	−	0.490981i	$-0.836638\pi$
$491$	−38.6077	−1.74234	−0.871170	+	0.490981i	$0.836638\pi$
$492$	11.4889	0.517959
$493$	2.48429	0.111887
$494$	−1.39771	−0.0628861
$495$	0	0
$496$	−8.90089	−0.399662
$497$	−7.20634	−0.323249
$498$	−21.3423	−0.956370
$499$	4.54198	0.203327	0.101663	−	0.994819i	$-0.467584\pi$
$499$	4.54198	0.203327	0.101663	+	0.994819i	$0.467584\pi$
$500$	2.98412	0.133454
$501$	23.6068	1.05467
$502$	4.74683	0.211861
$503$	−34.6954	−1.54699	−0.773496	−	0.633801i	$-0.781494\pi$
$503$	−34.6954	−1.54699	−0.773496	+	0.633801i	$0.781494\pi$
$504$	0.952503	0.0424278
$505$	−2.06208	−0.0917614
$506$	0	0
$507$	−15.8064	−0.701986
$508$	4.07816	0.180939
$509$	25.2232	1.11800	0.558999	−	0.829168i	$-0.311186\pi$
$509$	25.2232	1.11800	0.558999	+	0.829168i	$0.311186\pi$
$510$	1.68455	0.0745933
$511$	−4.86612	−0.215265
$512$	1.00000	0.0441942
$513$	−5.65567	−0.249704
$514$	20.6804	0.912175
$515$	−1.56785	−0.0690879
$516$	−0.917732	−0.0404009
$517$	0	0
$518$	0.187258	0.00822765
$519$	−7.26384	−0.318847
$520$	0.420912	0.0184582
$521$	−2.72459	−0.119366	−0.0596832	−	0.998217i	$-0.519009\pi$
$521$	−2.72459	−0.119366	−0.0596832	+	0.998217i	$0.519009\pi$
$522$	0.605296	0.0264931
$523$	22.7787	0.996044	0.498022	−	0.867164i	$-0.334060\pi$
$523$	22.7787	0.996044	0.498022	+	0.867164i	$0.334060\pi$
$524$	6.73636	0.294279
$525$	7.02477	0.306586
$526$	16.2184	0.707155
$527$	34.7964	1.51575
$528$	0	0
$529$	−10.2195	−0.444328
$530$	0.276843	0.0120253
$531$	−0.478828	−0.0207793
$532$	−1.00000	−0.0433555
$533$	−11.2224	−0.486094
$534$	5.39388	0.233416
$535$	2.31277	0.0999897
$536$	8.14454	0.351791
$537$	6.09725	0.263116
$538$	−1.93074	−0.0832401
$539$	0	0
$540$	1.70316	0.0732925
$541$	−12.8536	−0.552619	−0.276310	−	0.961069i	$-0.589111\pi$
$541$	−12.8536	−0.552619	−0.276310	+	0.961069i	$0.589111\pi$
$542$	4.51475	0.193925
$543$	−16.1445	−0.692829
$544$	−3.90931	−0.167610
$545$	−3.34864	−0.143440
$546$	2.00000	0.0855921
$547$	−31.7903	−1.35926	−0.679628	−	0.733557i	$-0.737859\pi$
$547$	−31.7903	−1.35926	−0.679628	+	0.733557i	$0.737859\pi$
$548$	−21.0107	−0.897531
$549$	1.34372	0.0573484
$550$	0	0
$551$	−0.635480	−0.0270723
$552$	−5.11546	−0.217728
$553$	−5.73363	−0.243819
$554$	12.6071	0.535623
$555$	0.0806910	0.00342514
$556$	1.30272	0.0552476
$557$	3.20457	0.135782	0.0678910	−	0.997693i	$-0.478373\pi$
$557$	3.20457	0.135782	0.0678910	+	0.997693i	$0.478373\pi$
$558$	8.47813	0.358908
$559$	0.896443	0.0379155
$560$	0.301143	0.0127256
$561$	0	0
$562$	−13.3200	−0.561872
$563$	0.824315	0.0347407	0.0173704	−	0.999849i	$-0.494471\pi$
$563$	0.824315	0.0347407	0.0173704	+	0.999849i	$0.494471\pi$
$564$	−10.8043	−0.454944
$565$	2.20792	0.0928879
$566$	−24.5772	−1.03306
$567$	5.23523	0.219859
$568$	7.20634	0.302371
$569$	16.0832	0.674244	0.337122	−	0.941461i	$-0.390547\pi$
$569$	16.0832	0.674244	0.337122	+	0.941461i	$0.390547\pi$
$570$	−0.430908	−0.0180487
$571$	26.7916	1.12119	0.560597	−	0.828089i	$-0.310572\pi$
$571$	26.7916	1.12119	0.560597	+	0.828089i	$0.310572\pi$
$572$	0	0
$573$	−0.709328	−0.0296326
$574$	−8.02908	−0.335127
$575$	17.5507	0.731914
$576$	−0.952503	−0.0396876
$577$	19.2616	0.801870	0.400935	−	0.916106i	$-0.368685\pi$
$577$	19.2616	0.801870	0.400935	+	0.916106i	$0.368685\pi$
$578$	−1.71727	−0.0714291
$579$	−27.6191	−1.14781
$580$	0.191370	0.00794622
$581$	14.9152	0.618787
$582$	−2.27000	−0.0940946
$583$	0	0
$584$	4.86612	0.201362
$585$	−0.400920	−0.0165760
$586$	6.95839	0.287448
$587$	−38.6661	−1.59592	−0.797961	−	0.602709i	$-0.794088\pi$
$587$	−38.6661	−1.59592	−0.797961	+	0.602709i	$0.794088\pi$
$588$	−8.58545	−0.354058
$589$	−8.90089	−0.366755
$590$	−0.151386	−0.00623246
$591$	−32.8523	−1.35136
$592$	−0.187258	−0.00769626
$593$	−38.0454	−1.56234	−0.781169	−	0.624319i	$-0.785377\pi$
$593$	−38.0454	−1.56234	−0.781169	+	0.624319i	$0.785377\pi$
$594$	0	0
$595$	−1.17726	−0.0482630
$596$	−15.9514	−0.653395
$597$	−35.1447	−1.43838
$598$	4.99679	0.204334
$599$	31.7240	1.29621	0.648104	−	0.761552i	$-0.275562\pi$
$599$	31.7240	1.29621	0.648104	+	0.761552i	$0.275562\pi$
$600$	−7.02477	−0.286785
$601$	47.9295	1.95508	0.977542	−	0.210739i	$-0.0675870\pi$
$601$	47.9295	1.95508	0.977542	+	0.210739i	$0.0675870\pi$
$602$	0.641364	0.0261400
$603$	−7.75770	−0.315918
$604$	0.910890	0.0370636
$605$	0	0
$606$	9.79816	0.398023
$607$	−35.2950	−1.43258	−0.716289	−	0.697803i	$-0.754161\pi$
$607$	−35.2950	−1.43258	−0.716289	+	0.697803i	$0.754161\pi$
$608$	1.00000	0.0405554
$609$	0.909313	0.0368472
$610$	0.424829	0.0172008
$611$	10.5537	0.426956
$612$	3.72363	0.150519
$613$	16.4588	0.664763	0.332381	−	0.943145i	$-0.392148\pi$
$613$	16.4588	0.664763	0.332381	+	0.943145i	$0.392148\pi$
$614$	−11.0608	−0.446379
$615$	−3.45979	−0.139512
$616$	0	0
$617$	19.0456	0.766748	0.383374	−	0.923593i	$-0.374762\pi$
$617$	19.0456	0.766748	0.383374	+	0.923593i	$0.374762\pi$
$618$	7.44980	0.299675
$619$	−15.5372	−0.624492	−0.312246	−	0.950001i	$-0.601081\pi$
$619$	−15.5372	−0.624492	−0.312246	+	0.950001i	$0.601081\pi$
$620$	2.68044	0.107649
$621$	20.2189	0.811356
$622$	25.7857	1.03391
$623$	−3.76955	−0.151024
$624$	−2.00000	−0.0800641
$625$	23.6479	0.945917
$626$	−17.3016	−0.691512
$627$	0	0
$628$	14.4848	0.578005
$629$	0.732051	0.0291888
$630$	−0.286840	−0.0114280
$631$	−17.1545	−0.682908	−0.341454	−	0.939898i	$-0.610919\pi$
$631$	−17.1545	−0.682908	−0.341454	+	0.939898i	$0.610919\pi$
$632$	5.73363	0.228071
$633$	18.6477	0.741180
$634$	−11.8272	−0.469720
$635$	−1.22811	−0.0487360
$636$	−1.31545	−0.0521608
$637$	8.38628	0.332277
$638$	0	0
$639$	−6.86406	−0.271538
$640$	−0.301143	−0.0119037
$641$	3.65547	0.144382	0.0721912	−	0.997391i	$-0.477001\pi$
$641$	3.65547	0.144382	0.0721912	+	0.997391i	$0.477001\pi$
$642$	−10.9893	−0.433714
$643$	47.9841	1.89231	0.946154	−	0.323716i	$-0.104932\pi$
$643$	47.9841	1.89231	0.946154	+	0.323716i	$0.104932\pi$
$644$	3.57498	0.140874
$645$	0.276369	0.0108820
$646$	−3.90931	−0.153810
$647$	−44.3431	−1.74331	−0.871654	−	0.490121i	$-0.836953\pi$
$647$	−44.3431	−1.74331	−0.871654	+	0.490121i	$0.836953\pi$
$648$	−5.23523	−0.205659
$649$	0	0
$650$	6.86182	0.269143
$651$	12.7364	0.499177
$652$	−14.7364	−0.577120
$653$	−36.1754	−1.41565	−0.707826	−	0.706386i	$-0.750324\pi$
$653$	−36.1754	−1.41565	−0.707826	+	0.706386i	$0.750324\pi$
$654$	15.9114	0.622184
$655$	−2.02861	−0.0792642
$656$	8.02908	0.313483
$657$	−4.63500	−0.180828
$658$	7.55068	0.294356
$659$	27.7848	1.08234	0.541171	−	0.840912i	$-0.317981\pi$
$659$	27.7848	1.08234	0.541171	+	0.840912i	$0.317981\pi$
$660$	0	0
$661$	−15.1358	−0.588716	−0.294358	−	0.955695i	$-0.595106\pi$
$661$	−15.1358	−0.588716	−0.294358	+	0.955695i	$0.595106\pi$
$662$	−21.1398	−0.821620
$663$	7.81863	0.303650
$664$	−14.9152	−0.578822
$665$	0.301143	0.0116778
$666$	0.178364	0.00691146
$667$	2.27182	0.0879654
$668$	16.4978	0.638318
$669$	−10.0371	−0.388057
$670$	−2.45267	−0.0947550
$671$	0	0
$672$	−1.43091	−0.0551985
$673$	−2.79968	−0.107920	−0.0539598	−	0.998543i	$-0.517184\pi$
$673$	−2.79968	−0.107920	−0.0539598	+	0.998543i	$0.517184\pi$
$674$	−3.64725	−0.140487
$675$	27.7654	1.06869
$676$	−11.0464	−0.424861
$677$	−0.584013	−0.0224455	−0.0112227	−	0.999937i	$-0.503572\pi$
$677$	−0.584013	−0.0224455	−0.0112227	+	0.999937i	$0.503572\pi$
$678$	−10.4911	−0.402909
$679$	1.58641	0.0608807
$680$	1.17726	0.0451459
$681$	3.76457	0.144258
$682$	0	0
$683$	5.43455	0.207947	0.103974	−	0.994580i	$-0.466844\pi$
$683$	5.43455	0.207947	0.103974	+	0.994580i	$0.466844\pi$
$684$	−0.952503	−0.0364199
$685$	6.32721	0.241750
$686$	13.0000	0.496342
$687$	−6.35267	−0.242369
$688$	−0.641364	−0.0244518
$689$	1.28493	0.0489520
$690$	1.54049	0.0586453
$691$	−2.27124	−0.0864020	−0.0432010	−	0.999066i	$-0.513756\pi$
$691$	−2.27124	−0.0864020	−0.0432010	+	0.999066i	$0.513756\pi$
$692$	−5.07638	−0.192975
$693$	0	0
$694$	−5.70933	−0.216723
$695$	−0.392305	−0.0148810
$696$	−0.909313	−0.0344674
$697$	−31.3882	−1.18891
$698$	−7.82910	−0.296336
$699$	22.1050	0.836087
$700$	4.90931	0.185555
$701$	25.4477	0.961145	0.480572	−	0.876955i	$-0.340429\pi$
$701$	25.4477	0.961145	0.480572	+	0.876955i	$0.340429\pi$
$702$	7.90501	0.298355
$703$	−0.187258	−0.00706258
$704$	0	0
$705$	3.25365	0.122539
$706$	3.13708	0.118066
$707$	−6.84751	−0.257527
$708$	0.719324	0.0270338
$709$	−10.9778	−0.412278	−0.206139	−	0.978523i	$-0.566090\pi$
$709$	−10.9778	−0.412278	−0.206139	+	0.978523i	$0.566090\pi$
$710$	−2.17014	−0.0814439
$711$	−5.46130	−0.204815
$712$	3.76955	0.141270
$713$	31.8205	1.19169
$714$	5.59387	0.209345
$715$	0	0
$716$	4.26111	0.159245
$717$	18.8148	0.702651
$718$	9.10566	0.339820
$719$	−32.1855	−1.20032	−0.600158	−	0.799882i	$-0.704896\pi$
$719$	−32.1855	−1.20032	−0.600158	+	0.799882i	$0.704896\pi$
$720$	0.286840	0.0106899
$721$	−5.20634	−0.193894
$722$	1.00000	0.0372161
$723$	23.1157	0.859681
$724$	−11.2827	−0.419319
$725$	3.11977	0.115865
$726$	0	0
$727$	47.1057	1.74705	0.873526	−	0.486778i	$-0.161828\pi$
$727$	47.1057	1.74705	0.873526	+	0.486778i	$0.161828\pi$
$728$	1.39771	0.0518027
$729$	29.2648	1.08388
$730$	−1.46540	−0.0542368
$731$	2.50729	0.0927355
$732$	−2.01861	−0.0746100
$733$	39.3132	1.45207	0.726033	−	0.687660i	$-0.241362\pi$
$733$	39.3132	1.45207	0.726033	+	0.687660i	$0.241362\pi$
$734$	1.30291	0.0480915
$735$	2.58545	0.0953657
$736$	−3.57498	−0.131775
$737$	0	0
$738$	−7.64772	−0.281517
$739$	−29.1248	−1.07137	−0.535687	−	0.844417i	$-0.679947\pi$
$739$	−29.1248	−1.07137	−0.535687	+	0.844417i	$0.679947\pi$
$740$	0.0563915	0.00207299
$741$	−2.00000	−0.0734718
$742$	0.919309	0.0337489
$743$	−16.7650	−0.615047	−0.307523	−	0.951540i	$-0.599500\pi$
$743$	−16.7650	−0.615047	−0.307523	+	0.951540i	$0.599500\pi$
$744$	−12.7364	−0.466938
$745$	4.80365	0.175992
$746$	0.845461	0.0309545
$747$	14.2068	0.519798
$748$	0	0
$749$	7.67997	0.280620
$750$	4.27000	0.155918
$751$	19.0714	0.695927	0.347964	−	0.937508i	$-0.386873\pi$
$751$	19.0714	0.695927	0.347964	+	0.937508i	$0.386873\pi$
$752$	−7.55068	−0.275345
$753$	6.79227	0.247524
$754$	0.888219	0.0323470
$755$	−0.274308	−0.00998309
$756$	5.65567	0.205695
$757$	−51.1070	−1.85752	−0.928759	−	0.370685i	$-0.879123\pi$
$757$	−51.1070	−1.85752	−0.928759	+	0.370685i	$0.879123\pi$
$758$	−16.4689	−0.598177
$759$	0	0
$760$	−0.301143	−0.0109236
$761$	−13.0980	−0.474802	−0.237401	−	0.971412i	$-0.576296\pi$
$761$	−13.0980	−0.474802	−0.237401	+	0.971412i	$0.576296\pi$
$762$	5.83546	0.211397
$763$	−11.1198	−0.402563
$764$	−0.495719	−0.0179345
$765$	−1.12135	−0.0405423
$766$	14.8014	0.534798
$767$	−0.702637	−0.0253708
$768$	1.43091	0.0516334
$769$	−23.8480	−0.859980	−0.429990	−	0.902834i	$-0.641483\pi$
$769$	−23.8480	−0.859980	−0.429990	+	0.902834i	$0.641483\pi$
$770$	0	0
$771$	29.5918	1.06572
$772$	−19.3018	−0.694687
$773$	−15.1475	−0.544817	−0.272408	−	0.962182i	$-0.587820\pi$
$773$	−15.1475	−0.544817	−0.272408	+	0.962182i	$0.587820\pi$
$774$	0.610901	0.0219584
$775$	43.6973	1.56965
$776$	−1.58641	−0.0569487
$777$	0.267949	0.00961262
$778$	−3.91931	−0.140514
$779$	8.02908	0.287672
$780$	0.602286	0.0215653
$781$	0	0
$782$	13.9757	0.499770
$783$	3.59406	0.128441
$784$	−6.00000	−0.214286
$785$	−4.36198	−0.155686
$786$	9.63911	0.343816
$787$	10.5856	0.377335	0.188668	−	0.982041i	$-0.439583\pi$
$787$	10.5856	0.377335	0.188668	+	0.982041i	$0.439583\pi$
$788$	−22.9591	−0.817883
$789$	23.2070	0.826192
$790$	−1.72664	−0.0614312
$791$	7.33180	0.260689
$792$	0	0
$793$	1.97178	0.0700201
$794$	12.9082	0.458095
$795$	0.396137	0.0140495
$796$	−24.5611	−0.870547
$797$	−31.4937	−1.11556	−0.557781	−	0.829988i	$-0.688347\pi$
$797$	−31.4937	−1.11556	−0.557781	+	0.829988i	$0.688347\pi$
$798$	−1.43091	−0.0506536
$799$	29.5180	1.04427
$800$	−4.90931	−0.173570
$801$	−3.59051	−0.126864
$802$	−2.53413	−0.0894831
$803$	0	0
$804$	11.6541	0.411008
$805$	−1.07658	−0.0379444
$806$	12.4409	0.438212
$807$	−2.76271	−0.0972520
$808$	6.84751	0.240895
$809$	−4.29264	−0.150921	−0.0754606	−	0.997149i	$-0.524043\pi$
$809$	−4.29264	−0.150921	−0.0754606	+	0.997149i	$0.524043\pi$
$810$	1.57655	0.0553944
$811$	−45.3464	−1.59233	−0.796163	−	0.605082i	$-0.793140\pi$
$811$	−45.3464	−1.59233	−0.796163	+	0.605082i	$0.793140\pi$
$812$	0.635480	0.0223010
$813$	6.46019	0.226569
$814$	0	0
$815$	4.43775	0.155448
$816$	−5.59387	−0.195824
$817$	−0.641364	−0.0224385
$818$	28.3472	0.991138
$819$	−1.33133	−0.0465203
$820$	−2.41790	−0.0844368
$821$	26.1744	0.913492	0.456746	−	0.889597i	$-0.349015\pi$
$821$	26.1744	0.913492	0.456746	+	0.889597i	$0.349015\pi$
$822$	−30.0643	−1.04861
$823$	−42.1604	−1.46962	−0.734810	−	0.678273i	$-0.762729\pi$
$823$	−42.1604	−1.46962	−0.734810	+	0.678273i	$0.762729\pi$
$824$	5.20634	0.181372
$825$	0	0
$826$	−0.502705	−0.0174913
$827$	−29.8252	−1.03712	−0.518562	−	0.855040i	$-0.673532\pi$
$827$	−29.8252	−1.03712	−0.518562	+	0.855040i	$0.673532\pi$
$828$	3.40517	0.118338
$829$	−27.5800	−0.957894	−0.478947	−	0.877844i	$-0.658981\pi$
$829$	−27.5800	−0.957894	−0.478947	+	0.877844i	$0.658981\pi$
$830$	4.49161	0.155906
$831$	18.0396	0.625785
$832$	−1.39771	−0.0484570
$833$	23.4559	0.812698
$834$	1.86407	0.0645475
$835$	−4.96819	−0.171931
$836$	0	0
$837$	50.3405	1.74002
$838$	−1.82561	−0.0630647
$839$	−38.6032	−1.33273	−0.666364	−	0.745626i	$-0.732150\pi$
$839$	−38.6032	−1.33273	−0.666364	+	0.745626i	$0.732150\pi$
$840$	0.430908	0.0148677
$841$	−28.5962	−0.986075
$842$	24.0238	0.827915
$843$	−19.0597	−0.656452
$844$	13.0321	0.448583
$845$	3.32654	0.114437
$846$	7.19204	0.247267
$847$	0	0
$848$	−0.919309	−0.0315692
$849$	−35.1677	−1.20695
$850$	19.1920	0.658282
$851$	0.669444	0.0229482
$852$	10.3116	0.353270
$853$	−30.2567	−1.03597	−0.517985	−	0.855390i	$-0.673318\pi$
$853$	−30.2567	−1.03597	−0.517985	+	0.855390i	$0.673318\pi$
$854$	1.41072	0.0482739
$855$	0.286840	0.00980970
$856$	−7.67997	−0.262496
$857$	10.1668	0.347291	0.173645	−	0.984808i	$-0.444445\pi$
$857$	10.1668	0.347291	0.173645	+	0.984808i	$0.444445\pi$
$858$	0	0
$859$	−6.90568	−0.235619	−0.117809	−	0.993036i	$-0.537587\pi$
$859$	−6.90568	−0.235619	−0.117809	+	0.993036i	$0.537587\pi$
$860$	0.193142	0.00658609
$861$	−11.4889	−0.391540
$862$	21.4490	0.730557
$863$	49.7723	1.69427	0.847134	−	0.531379i	$-0.178326\pi$
$863$	49.7723	1.69427	0.847134	+	0.531379i	$0.178326\pi$
$864$	−5.65567	−0.192410
$865$	1.52872	0.0519779
$866$	−7.85455	−0.266908
$867$	−2.45726	−0.0834529
$868$	8.90089	0.302116
$869$	0	0
$870$	0.273833	0.00928381
$871$	−11.3837	−0.385723
$872$	11.1198	0.376563
$873$	1.51106	0.0511415
$874$	−3.57498	−0.120925
$875$	−2.98412	−0.100882
$876$	6.96297	0.235257
$877$	−46.3334	−1.56457	−0.782284	−	0.622922i	$-0.785946\pi$
$877$	−46.3334	−1.56457	−0.782284	+	0.622922i	$0.785946\pi$
$878$	0.650885	0.0219663
$879$	9.95681	0.335835
$880$	0	0
$881$	19.6804	0.663051	0.331525	−	0.943446i	$-0.392437\pi$
$881$	19.6804	0.663051	0.331525	+	0.943446i	$0.392437\pi$
$882$	5.71502	0.192435
$883$	34.0283	1.14514	0.572572	−	0.819854i	$-0.305946\pi$
$883$	34.0283	1.14514	0.572572	+	0.819854i	$0.305946\pi$
$884$	5.46410	0.183778
$885$	−0.216619	−0.00728158
$886$	4.53815	0.152462
$887$	−1.87463	−0.0629438	−0.0314719	−	0.999505i	$-0.510019\pi$
$887$	−1.87463	−0.0629438	−0.0314719	+	0.999505i	$0.510019\pi$
$888$	−0.267949	−0.00899179
$889$	−4.07816	−0.136777
$890$	−1.13517	−0.0380511
$891$	0	0
$892$	−7.01450	−0.234863
$893$	−7.55068	−0.252674
$894$	−22.8250	−0.763382
$895$	−1.28320	−0.0428927
$896$	−1.00000	−0.0334077
$897$	7.14995	0.238730
$898$	37.3091	1.24502
$899$	5.65634	0.188649
$900$	4.67613	0.155871
$901$	3.59387	0.119729
$902$	0	0
$903$	0.917732	0.0305402
$904$	−7.33180	−0.243852
$905$	3.39771	0.112944
$906$	1.30340	0.0433025
$907$	56.5072	1.87629	0.938145	−	0.346242i	$-0.112542\pi$
$907$	56.5072	1.87629	0.938145	+	0.346242i	$0.112542\pi$
$908$	2.63089	0.0873092
$909$	−6.52227	−0.216330
$910$	−0.420912	−0.0139531
$911$	34.8858	1.15582	0.577909	−	0.816101i	$-0.303869\pi$
$911$	34.8858	1.15582	0.577909	+	0.816101i	$0.303869\pi$
$912$	1.43091	0.0473821
$913$	0	0
$914$	21.3693	0.706834
$915$	0.607890	0.0200962
$916$	−4.43961	−0.146689
$917$	−6.73636	−0.222454
$918$	22.1098	0.729731
$919$	−27.5658	−0.909312	−0.454656	−	0.890667i	$-0.650238\pi$
$919$	−27.5658	−0.909312	−0.454656	+	0.890667i	$0.650238\pi$
$920$	1.07658	0.0354938
$921$	−15.8270	−0.521519
$922$	−9.44157	−0.310942
$923$	−10.0724	−0.331537
$924$	0	0
$925$	0.919309	0.0302267
$926$	−15.4976	−0.509282
$927$	−4.95906	−0.162877
$928$	−0.635480	−0.0208606
$929$	−56.1027	−1.84067	−0.920335	−	0.391131i	$-0.872084\pi$
$929$	−56.1027	−1.84067	−0.920335	+	0.391131i	$0.872084\pi$
$930$	3.83546	0.125770
$931$	−6.00000	−0.196642
$932$	15.4482	0.506023
$933$	36.8970	1.20795
$934$	−5.81733	−0.190349
$935$	0	0
$936$	1.33133	0.0435158
$937$	−29.4082	−0.960725	−0.480363	−	0.877070i	$-0.659495\pi$
$937$	−29.4082	−0.960725	−0.480363	+	0.877070i	$0.659495\pi$
$938$	−8.14454	−0.265929
$939$	−24.7570	−0.807915
$940$	2.27383	0.0741643
$941$	50.0127	1.63037	0.815184	−	0.579202i	$-0.196636\pi$
$941$	50.0127	1.63037	0.815184	+	0.579202i	$0.196636\pi$
$942$	20.7264	0.675301
$943$	−28.7038	−0.934724
$944$	0.502705	0.0163616
$945$	−1.70316	−0.0554039
$946$	0	0
$947$	20.5117	0.666542	0.333271	−	0.942831i	$-0.391848\pi$
$947$	20.5117	0.666542	0.333271	+	0.942831i	$0.391848\pi$
$948$	8.20429	0.266463
$949$	−6.80145	−0.220784
$950$	−4.90931	−0.159279
$951$	−16.9237	−0.548788
$952$	3.90931	0.126702
$953$	12.2473	0.396729	0.198364	−	0.980128i	$-0.436437\pi$
$953$	12.2473	0.396729	0.198364	+	0.980128i	$0.436437\pi$
$954$	0.875644	0.0283500
$955$	0.149282	0.00483066
$956$	13.1489	0.425264
$957$	0	0
$958$	−24.8407	−0.802567
$959$	21.0107	0.678470
$960$	−0.430908	−0.0139075
$961$	48.2259	1.55567
$962$	0.261733	0.00843862
$963$	7.31519	0.235729
$964$	16.1545	0.520303
$965$	5.81261	0.187114
$966$	5.11546	0.164587
$967$	−14.7363	−0.473889	−0.236945	−	0.971523i	$-0.576146\pi$
$967$	−14.7363	−0.473889	−0.236945	+	0.971523i	$0.576146\pi$
$968$	0	0
$969$	−5.59387	−0.179701
$970$	0.477735	0.0153391
$971$	16.1716	0.518970	0.259485	−	0.965747i	$-0.416447\pi$
$971$	16.1716	0.518970	0.259485	+	0.965747i	$0.416447\pi$
$972$	9.47587	0.303939
$973$	−1.30272	−0.0417633
$974$	−10.5918	−0.339384
$975$	9.81863	0.314448
$976$	−1.41072	−0.0451561
$977$	13.4473	0.430216	0.215108	−	0.976590i	$-0.430990\pi$
$977$	13.4473	0.430216	0.215108	+	0.976590i	$0.430990\pi$
$978$	−21.0864	−0.674268
$979$	0	0
$980$	1.80686	0.0577180
$981$	−10.5916	−0.338164
$982$	−38.6077	−1.23202
$983$	22.9399	0.731669	0.365834	−	0.930680i	$-0.380784\pi$
$983$	22.9399	0.731669	0.365834	+	0.930680i	$0.380784\pi$
$984$	11.4889	0.366252
$985$	6.91396	0.220297
$986$	2.48429	0.0791159
$987$	10.8043	0.343905
$988$	−1.39771	−0.0444672
$989$	2.29286	0.0729087
$990$	0	0
$991$	−9.97222	−0.316778	−0.158389	−	0.987377i	$-0.550630\pi$
$991$	−9.97222	−0.316778	−0.158389	+	0.987377i	$0.550630\pi$
$992$	−8.90089	−0.282604
$993$	−30.2490	−0.959925
$994$	−7.20634	−0.228571
$995$	7.39642	0.234482
$996$	−21.3423	−0.676256
$997$	47.9311	1.51799	0.758997	−	0.651094i	$-0.225690\pi$
$997$	47.9311	1.51799	0.758997	+	0.651094i	$0.225690\pi$
$998$	4.54198	0.143774
$999$	1.05907	0.0335075

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bt.1.4	yes	4
11.10	odd	2		4598.2.a.bq.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.bq.1.4	✓	4	11.10	odd	2
4598.2.a.bt.1.4	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.43091 q^{3} +1.00000 q^{4} -0.301143 q^{5} +1.43091 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.952503 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.43091 q^{3} +1.00000 q^{4} -0.301143 q^{5} +1.43091 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.952503 q^{9} -0.301143 q^{10} +1.43091 q^{12} -1.39771 q^{13} -1.00000 q^{14} -0.430908 q^{15} +1.00000 q^{16} -3.90931 q^{17} -0.952503 q^{18} +1.00000 q^{19} -0.301143 q^{20} -1.43091 q^{21} -3.57498 q^{23} +1.43091 q^{24} -4.90931 q^{25} -1.39771 q^{26} -5.65567 q^{27} -1.00000 q^{28} -0.635480 q^{29} -0.430908 q^{30} -8.90089 q^{31} +1.00000 q^{32} -3.90931 q^{34} +0.301143 q^{35} -0.952503 q^{36} -0.187258 q^{37} +1.00000 q^{38} -2.00000 q^{39} -0.301143 q^{40} +8.02908 q^{41} -1.43091 q^{42} -0.641364 q^{43} +0.286840 q^{45} -3.57498 q^{46} -7.55068 q^{47} +1.43091 q^{48} -6.00000 q^{49} -4.90931 q^{50} -5.59387 q^{51} -1.39771 q^{52} -0.919309 q^{53} -5.65567 q^{54} -1.00000 q^{56} +1.43091 q^{57} -0.635480 q^{58} +0.502705 q^{59} -0.430908 q^{60} -1.41072 q^{61} -8.90089 q^{62} +0.952503 q^{63} +1.00000 q^{64} +0.420912 q^{65} +8.14454 q^{67} -3.90931 q^{68} -5.11546 q^{69} +0.301143 q^{70} +7.20634 q^{71} -0.952503 q^{72} +4.86612 q^{73} -0.187258 q^{74} -7.02477 q^{75} +1.00000 q^{76} -2.00000 q^{78} +5.73363 q^{79} -0.301143 q^{80} -5.23523 q^{81} +8.02908 q^{82} -14.9152 q^{83} -1.43091 q^{84} +1.17726 q^{85} -0.641364 q^{86} -0.909313 q^{87} +3.76955 q^{89} +0.286840 q^{90} +1.39771 q^{91} -3.57498 q^{92} -12.7364 q^{93} -7.55068 q^{94} -0.301143 q^{95} +1.43091 q^{96} -1.58641 q^{97} -6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	\( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} - 2 q^{12} - 4 q^{13} - 4 q^{14} + 6 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{19} - 2 q^{20} + 2 q^{21} - 8 q^{23} - 2 q^{24} - 8 q^{25} - 4 q^{26} - 14 q^{27} - 4 q^{28} + 2 q^{29} + 6 q^{30} + 4 q^{32} - 4 q^{34} + 2 q^{35} - 10 q^{37} + 4 q^{38} - 8 q^{39} - 2 q^{40} - 2 q^{41} + 2 q^{42} + 16 q^{43} - 8 q^{45} - 8 q^{46} - 2 q^{48} - 24 q^{49} - 8 q^{50} - 4 q^{52} - 6 q^{53} - 14 q^{54} - 4 q^{56} - 2 q^{57} + 2 q^{58} + 22 q^{59} + 6 q^{60} - 2 q^{61} + 4 q^{64} - 20 q^{65} - 20 q^{67} - 4 q^{68} - 2 q^{69} + 2 q^{70} - 10 q^{71} - 10 q^{74} + 2 q^{75} + 4 q^{76} - 8 q^{78} + 6 q^{79} - 2 q^{80} + 20 q^{81} - 2 q^{82} - 34 q^{83} + 2 q^{84} + 16 q^{86} + 8 q^{87} - 2 q^{89} - 8 q^{90} + 4 q^{91} - 8 q^{92} - 40 q^{93} - 2 q^{95} - 2 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 - 2 * q^12 - 4 * q^13 - 4 * q^14 + 6 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^19 - 2 * q^20 + 2 * q^21 - 8 * q^23 - 2 * q^24 - 8 * q^25 - 4 * q^26 - 14 * q^27 - 4 * q^28 + 2 * q^29 + 6 * q^30 + 4 * q^32 - 4 * q^34 + 2 * q^35 - 10 * q^37 + 4 * q^38 - 8 * q^39 - 2 * q^40 - 2 * q^41 + 2 * q^42 + 16 * q^43 - 8 * q^45 - 8 * q^46 - 2 * q^48 - 24 * q^49 - 8 * q^50 - 4 * q^52 - 6 * q^53 - 14 * q^54 - 4 * q^56 - 2 * q^57 + 2 * q^58 + 22 * q^59 + 6 * q^60 - 2 * q^61 + 4 * q^64 - 20 * q^65 - 20 * q^67 - 4 * q^68 - 2 * q^69 + 2 * q^70 - 10 * q^71 - 10 * q^74 + 2 * q^75 + 4 * q^76 - 8 * q^78 + 6 * q^79 - 2 * q^80 + 20 * q^81 - 2 * q^82 - 34 * q^83 + 2 * q^84 + 16 * q^86 + 8 * q^87 - 2 * q^89 - 8 * q^90 + 4 * q^91 - 8 * q^92 - 40 * q^93 - 2 * q^95 - 2 * q^96 - 8 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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