LMFDB - Embedded newform 2299.2.a.n.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2299,2,Mod(1,2299)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2299, 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("2299.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2299 = 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2299.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$18.3576074247$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.246832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 $ x^5 - 2x^4 - 5x^3 + 6x^2 + 7x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 209)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.71250$ of defining polynomial
Character	$\chi$	$=$	2299.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.779856 q^{2} -2.98063 q^{3} -1.39182 q^{4} -3.49235 q^{5} -2.32446 q^{6} -1.06736 q^{7} -2.64513 q^{8} +5.88418 q^{9} -2.72353 q^{10} +4.14852 q^{12} +0.0563258 q^{13} -0.832387 q^{14} +10.4094 q^{15} +0.720827 q^{16} +4.53628 q^{17} +4.58881 q^{18} +1.00000 q^{19} +4.86074 q^{20} +3.18141 q^{21} -1.07949 q^{23} +7.88418 q^{24} +7.19651 q^{25} +0.0439260 q^{26} -8.59667 q^{27} +1.48558 q^{28} -0.299905 q^{29} +8.11784 q^{30} +9.18548 q^{31} +5.85241 q^{32} +3.53764 q^{34} +3.72760 q^{35} -8.18974 q^{36} +4.50448 q^{37} +0.779856 q^{38} -0.167887 q^{39} +9.23774 q^{40} -12.0009 q^{41} +2.48104 q^{42} -10.7260 q^{43} -20.5496 q^{45} -0.841844 q^{46} +2.89630 q^{47} -2.14852 q^{48} -5.86074 q^{49} +5.61224 q^{50} -13.5210 q^{51} -0.0783957 q^{52} -12.3213 q^{53} -6.70416 q^{54} +2.82331 q^{56} -2.98063 q^{57} -0.233882 q^{58} -1.14582 q^{59} -14.4881 q^{60} +8.09599 q^{61} +7.16335 q^{62} -6.28054 q^{63} +3.12238 q^{64} -0.196709 q^{65} +11.2733 q^{67} -6.31370 q^{68} +3.21755 q^{69} +2.90699 q^{70} +13.4948 q^{71} -15.5644 q^{72} +11.1470 q^{73} +3.51284 q^{74} -21.4502 q^{75} -1.39182 q^{76} -0.130927 q^{78} -11.4250 q^{79} -2.51738 q^{80} +7.97100 q^{81} -9.35899 q^{82} +13.9802 q^{83} -4.42797 q^{84} -15.8423 q^{85} -8.36475 q^{86} +0.893906 q^{87} -0.183185 q^{89} -16.0257 q^{90} -0.0601200 q^{91} +1.50246 q^{92} -27.3785 q^{93} +2.25870 q^{94} -3.49235 q^{95} -17.4439 q^{96} +5.66263 q^{97} -4.57053 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + q^{3} + 6 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} - 6 q^{8} + 4 q^{9} - 12 q^{10} + 6 q^{12} - 4 q^{13} - 14 q^{14} + 3 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} + 5 q^{19} - 8 q^{20} - 10 q^{21}+ \cdots + 10 q^{98}+O(q^{100}) $ 5 * q - 2 * q^2 + q^3 + 6 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 - 6 * q^8 + 4 * q^9 - 12 * q^10 + 6 * q^12 - 4 * q^13 - 14 * q^14 + 3 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 + 5 * q^19 - 8 * q^20 - 10 * q^21 + 3 * q^23 + 14 * q^24 + 6 * q^25 - 6 * q^26 - 11 * q^27 + 10 * q^28 - 10 * q^29 - 6 * q^30 + 11 * q^31 - 14 * q^32 - 4 * q^34 + 8 * q^35 - 26 * q^36 + q^37 - 2 * q^38 - 2 * q^39 + 16 * q^40 - 2 * q^41 - 16 * q^42 - 20 * q^43 - 28 * q^45 + 4 * q^46 - 20 * q^47 + 4 * q^48 + 3 * q^49 + 32 * q^50 - 24 * q^51 - 6 * q^52 - 14 * q^53 - 16 * q^54 - 38 * q^56 + q^57 - 6 * q^58 + 3 * q^59 - 40 * q^60 + 10 * q^61 + 6 * q^62 - 24 * q^63 + 9 * q^67 - 24 * q^68 - 5 * q^69 + 50 * q^70 + 23 * q^71 + 12 * q^72 - 8 * q^74 - 18 * q^75 + 6 * q^76 - 22 * q^78 - 44 * q^79 - 18 * q^80 + q^81 - 30 * q^82 + 14 * q^83 - 14 * q^84 + 12 * q^85 + 52 * q^86 - 28 * q^87 - 27 * q^89 - 26 * q^90 + 24 * q^91 + 58 * q^92 - 27 * q^93 + 8 * q^94 - 5 * q^95 - 50 * q^96 + 15 * q^97 + 10 * q^98

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 $

$2$	0.779856	0.551441	0.275721	−	0.961238i	$-0.411084\pi$
$2$	0.779856	0.551441	0.275721	+	0.961238i	$0.411084\pi$
$3$	−2.98063	−1.72087	−0.860435	−	0.509561i	$-0.829808\pi$
$3$	−2.98063	−1.72087	−0.860435	+	0.509561i	$0.829808\pi$
$4$	−1.39182	−0.695912
$5$	−3.49235	−1.56183	−0.780913	−	0.624639i	$-0.785246\pi$
$5$	−3.49235	−1.56183	−0.780913	+	0.624639i	$0.785246\pi$
$6$	−2.32446	−0.948959
$7$	−1.06736	−0.403424	−0.201712	−	0.979445i	$-0.564651\pi$
$7$	−1.06736	−0.403424	−0.201712	+	0.979445i	$0.564651\pi$
$8$	−2.64513	−0.935196
$9$	5.88418	1.96139
$10$	−2.72353	−0.861256
$11$	0	0
$11$	0	0
$12$	4.14852	1.19757
$13$	0.0563258	0.0156220	0.00781098	−	0.999969i	$-0.497514\pi$
$13$	0.0563258	0.0156220	0.00781098	+	0.999969i	$0.497514\pi$
$14$	−0.832387	−0.222465
$15$	10.4094	2.68770
$16$	0.720827	0.180207
$17$	4.53628	1.10021	0.550104	−	0.835096i	$-0.314588\pi$
$17$	4.53628	1.10021	0.550104	+	0.835096i	$0.314588\pi$
$18$	4.58881	1.08159
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	4.86074	1.08689
$21$	3.18141	0.694241
$22$	0	0
$23$	−1.07949	−0.225088	−0.112544	−	0.993647i	$-0.535900\pi$
$23$	−1.07949	−0.225088	−0.112544	+	0.993647i	$0.535900\pi$
$24$	7.88418	1.60935
$25$	7.19651	1.43930
$26$	0.0439260	0.00861460
$27$	−8.59667	−1.65443
$28$	1.48558	0.280748
$29$	−0.299905	−0.0556909	−0.0278455	−	0.999612i	$-0.508865\pi$
$29$	−0.299905	−0.0556909	−0.0278455	+	0.999612i	$0.508865\pi$
$30$	8.11784	1.48211
$31$	9.18548	1.64976	0.824880	−	0.565307i	$-0.191242\pi$
$31$	9.18548	1.64976	0.824880	+	0.565307i	$0.191242\pi$
$32$	5.85241	1.03457
$33$	0	0
$34$	3.53764	0.606701
$35$	3.72760	0.630079
$36$	−8.18974	−1.36496
$37$	4.50448	0.740531	0.370266	−	0.928926i	$-0.379267\pi$
$37$	4.50448	0.740531	0.370266	+	0.928926i	$0.379267\pi$
$38$	0.779856	0.126509
$39$	−0.167887	−0.0268834
$40$	9.23774	1.46061
$41$	−12.0009	−1.87423	−0.937115	−	0.349020i	$-0.886514\pi$
$41$	−12.0009	−1.87423	−0.937115	+	0.349020i	$0.886514\pi$
$42$	2.48104	0.382833
$43$	−10.7260	−1.63570	−0.817851	−	0.575430i	$-0.804835\pi$
$43$	−10.7260	−1.63570	−0.817851	+	0.575430i	$0.804835\pi$
$44$	0	0
$45$	−20.5496	−3.06335
$46$	−0.841844	−0.124123
$47$	2.89630	0.422469	0.211235	−	0.977435i	$-0.432252\pi$
$47$	2.89630	0.422469	0.211235	+	0.977435i	$0.432252\pi$
$48$	−2.14852	−0.310112
$49$	−5.86074	−0.837249
$50$	5.61224	0.793691
$51$	−13.5210	−1.89332
$52$	−0.0783957	−0.0108715
$53$	−12.3213	−1.69246	−0.846230	−	0.532818i	$-0.821133\pi$
$53$	−12.3213	−1.69246	−0.846230	+	0.532818i	$0.821133\pi$
$54$	−6.70416	−0.912321
$55$	0	0
$56$	2.82331	0.377281
$57$	−2.98063	−0.394795
$58$	−0.233882	−0.0307103
$59$	−1.14582	−0.149173	−0.0745863	−	0.997215i	$-0.523764\pi$
$59$	−1.14582	−0.149173	−0.0745863	+	0.997215i	$0.523764\pi$
$60$	−14.4881	−1.87040
$61$	8.09599	1.03659	0.518293	−	0.855203i	$-0.326568\pi$
$61$	8.09599	1.03659	0.518293	+	0.855203i	$0.326568\pi$
$62$	7.16335	0.909746
$63$	−6.28054	−0.791273
$64$	3.12238	0.390298
$65$	−0.196709	−0.0243988
$66$	0	0
$67$	11.2733	1.37726	0.688628	−	0.725115i	$-0.258213\pi$
$67$	11.2733	1.37726	0.688628	+	0.725115i	$0.258213\pi$
$68$	−6.31370	−0.765649
$69$	3.21755	0.387348
$70$	2.90699	0.347452
$71$	13.4948	1.60154	0.800771	−	0.598970i	$-0.204423\pi$
$71$	13.4948	1.60154	0.800771	+	0.598970i	$0.204423\pi$
$72$	−15.5644	−1.83429
$73$	11.1470	1.30466	0.652330	−	0.757935i	$-0.273792\pi$
$73$	11.1470	1.30466	0.652330	+	0.757935i	$0.273792\pi$
$74$	3.51284	0.408360
$75$	−21.4502	−2.47685
$76$	−1.39182	−0.159653
$77$	0	0
$78$	−0.130927	−0.0148246
$79$	−11.4250	−1.28541	−0.642706	−	0.766113i	$-0.722188\pi$
$79$	−11.4250	−1.28541	−0.642706	+	0.766113i	$0.722188\pi$
$80$	−2.51738	−0.281452
$81$	7.97100	0.885666
$82$	−9.35899	−1.03353
$83$	13.9802	1.53452	0.767261	−	0.641335i	$-0.221619\pi$
$83$	13.9802	1.53452	0.767261	+	0.641335i	$0.221619\pi$
$84$	−4.42797	−0.483131
$85$	−15.8423	−1.71834
$86$	−8.36475	−0.901994
$87$	0.893906	0.0958368
$88$	0	0
$89$	−0.183185	−0.0194176	−0.00970878	−	0.999953i	$-0.503090\pi$
$89$	−0.183185	−0.0194176	−0.00970878	+	0.999953i	$0.503090\pi$
$90$	−16.0257	−1.68926
$91$	−0.0601200	−0.00630228
$92$	1.50246	0.156642
$93$	−27.3785	−2.83902
$94$	2.25870	0.232967
$95$	−3.49235	−0.358308
$96$	−17.4439	−1.78036
$97$	5.66263	0.574953	0.287477	−	0.957788i	$-0.407184\pi$
$97$	5.66263	0.574953	0.287477	+	0.957788i	$0.407184\pi$
$98$	−4.57053	−0.461694
$99$	0	0
$100$	−10.0163	−1.00163
$101$	−8.00759	−0.796785	−0.398392	−	0.917215i	$-0.630432\pi$
$101$	−8.00759	−0.796785	−0.398392	+	0.917215i	$0.630432\pi$
$102$	−10.5444	−1.04405
$103$	6.18725	0.609648	0.304824	−	0.952409i	$-0.401402\pi$
$103$	6.18725	0.609648	0.304824	+	0.952409i	$0.401402\pi$
$104$	−0.148989	−0.0146096
$105$	−11.1106	−1.08428
$106$	−9.60883	−0.933292
$107$	7.29027	0.704777	0.352388	−	0.935854i	$-0.385370\pi$
$107$	7.29027	0.704777	0.352388	+	0.935854i	$0.385370\pi$
$108$	11.9651	1.15134
$109$	−7.79895	−0.747004	−0.373502	−	0.927629i	$-0.621843\pi$
$109$	−7.79895	−0.747004	−0.373502	+	0.927629i	$0.621843\pi$
$110$	0	0
$111$	−13.4262	−1.27436
$112$	−0.769382	−0.0726998
$113$	−0.430558	−0.0405035	−0.0202517	−	0.999795i	$-0.506447\pi$
$113$	−0.430558	−0.0405035	−0.0202517	+	0.999795i	$0.506447\pi$
$114$	−2.32446	−0.217706
$115$	3.76995	0.351549
$116$	0.417415	0.0387560
$117$	0.331431	0.0306408
$118$	−0.893572	−0.0822600
$119$	−4.84184	−0.443851
$120$	−27.5343	−2.51353
$121$	0	0
$122$	6.31370	0.571616
$123$	35.7704	3.22531
$124$	−12.7846	−1.14809
$125$	−7.67100	−0.686115
$126$	−4.89791	−0.436341
$127$	3.13888	0.278531	0.139265	−	0.990255i	$-0.455526\pi$
$127$	3.13888	0.278531	0.139265	+	0.990255i	$0.455526\pi$
$128$	−9.26981	−0.819343
$129$	31.9703	2.81483
$130$	−0.153405	−0.0134545
$131$	−12.4315	−1.08615	−0.543075	−	0.839684i	$-0.682740\pi$
$131$	−12.4315	−1.08615	−0.543075	+	0.839684i	$0.682740\pi$
$132$	0	0
$133$	−1.06736	−0.0925519
$134$	8.79157	0.759476
$135$	30.0226	2.58393
$136$	−11.9991	−1.02891
$137$	13.8301	1.18159	0.590794	−	0.806822i	$-0.298814\pi$
$137$	13.8301	1.18159	0.590794	+	0.806822i	$0.298814\pi$
$138$	2.50923	0.213600
$139$	−15.9968	−1.35683	−0.678417	−	0.734677i	$-0.737334\pi$
$139$	−15.9968	−1.35683	−0.678417	+	0.734677i	$0.737334\pi$
$140$	−5.18816	−0.438480
$141$	−8.63281	−0.727014
$142$	10.5240	0.883157
$143$	0	0
$144$	4.24147	0.353456
$145$	1.04737	0.0869796
$146$	8.69307	0.719443
$147$	17.4687	1.44080
$148$	−6.26944	−0.515345
$149$	−11.3620	−0.930812	−0.465406	−	0.885097i	$-0.654092\pi$
$149$	−11.3620	−0.930812	−0.465406	+	0.885097i	$0.654092\pi$
$150$	−16.7280	−1.36584
$151$	−4.66341	−0.379503	−0.189751	−	0.981832i	$-0.560768\pi$
$151$	−4.66341	−0.379503	−0.189751	+	0.981832i	$0.560768\pi$
$152$	−2.64513	−0.214549
$153$	26.6923	2.15794
$154$	0	0
$155$	−32.0789	−2.57664
$156$	0.233669	0.0187085
$157$	−9.05206	−0.722433	−0.361217	−	0.932482i	$-0.617639\pi$
$157$	−9.05206	−0.722433	−0.361217	+	0.932482i	$0.617639\pi$
$158$	−8.90984	−0.708829
$159$	36.7253	2.91250
$160$	−20.4387	−1.61582
$161$	1.15220	0.0908062
$162$	6.21623	0.488393
$163$	2.36761	0.185446	0.0927229	−	0.995692i	$-0.470443\pi$
$163$	2.36761	0.185446	0.0927229	+	0.995692i	$0.470443\pi$
$164$	16.7032	1.30430
$165$	0	0
$166$	10.9025	0.846199
$167$	9.27361	0.717613	0.358807	−	0.933412i	$-0.383184\pi$
$167$	9.27361	0.717613	0.358807	+	0.933412i	$0.383184\pi$
$168$	−8.41526	−0.649251
$169$	−12.9968	−0.999756
$170$	−12.3547	−0.947561
$171$	5.88418	0.449974
$172$	14.9287	1.13831
$173$	−10.7172	−0.814812	−0.407406	−	0.913247i	$-0.633567\pi$
$173$	−10.7172	−0.814812	−0.407406	+	0.913247i	$0.633567\pi$
$174$	0.697118	0.0528484
$175$	−7.68128	−0.580650
$176$	0	0
$177$	3.41526	0.256707
$178$	−0.142858	−0.0107076
$179$	−22.9070	−1.71215	−0.856073	−	0.516854i	$-0.827103\pi$
$179$	−22.9070	−1.71215	−0.856073	+	0.516854i	$0.827103\pi$
$180$	28.6015	2.13183
$181$	5.90522	0.438931	0.219466	−	0.975620i	$-0.429569\pi$
$181$	5.90522	0.438931	0.219466	+	0.975620i	$0.429569\pi$
$182$	−0.0468849	−0.00347534
$183$	−24.1312	−1.78383
$184$	2.85539	0.210502
$185$	−15.7312	−1.15658
$186$	−21.3513	−1.56555
$187$	0	0
$188$	−4.03114	−0.294001
$189$	9.17575	0.667438
$190$	−2.72353	−0.197586
$191$	6.44628	0.466437	0.233218	−	0.972424i	$-0.425074\pi$
$191$	6.44628	0.466437	0.233218	+	0.972424i	$0.425074\pi$
$192$	−9.30668	−0.671652
$193$	−1.43606	−0.103370	−0.0516849	−	0.998663i	$-0.516459\pi$
$193$	−1.43606	−0.103370	−0.0516849	+	0.998663i	$0.516459\pi$
$194$	4.41604	0.317053
$195$	0.586319	0.0419872
$196$	8.15713	0.582652
$197$	4.75399	0.338708	0.169354	−	0.985555i	$-0.445832\pi$
$197$	4.75399	0.338708	0.169354	+	0.985555i	$0.445832\pi$
$198$	0	0
$199$	−2.36002	−0.167298	−0.0836489	−	0.996495i	$-0.526657\pi$
$199$	−2.36002	−0.167298	−0.0836489	+	0.996495i	$0.526657\pi$
$200$	−19.0357	−1.34603
$201$	−33.6017	−2.37008
$202$	−6.24476	−0.439380
$203$	0.320107	0.0224671
$204$	18.8188	1.31758
$205$	41.9115	2.92722
$206$	4.82517	0.336185
$207$	−6.35189	−0.441487
$208$	0.0406011	0.00281518
$209$	0	0
$210$	−8.66467	−0.597919
$211$	24.5133	1.68756	0.843781	−	0.536687i	$-0.180324\pi$
$211$	24.5133	1.68756	0.843781	+	0.536687i	$0.180324\pi$
$212$	17.1491	1.17780
$213$	−40.2232	−2.75605
$214$	5.68536	0.388643
$215$	37.4590	2.55468
$216$	22.7393	1.54722
$217$	−9.80422	−0.665554
$218$	−6.08205	−0.411929
$219$	−33.2252	−2.24515
$220$	0	0
$221$	0.255509	0.0171874
$222$	−10.4705	−0.702734
$223$	8.47427	0.567479	0.283740	−	0.958901i	$-0.408425\pi$
$223$	8.47427	0.567479	0.283740	+	0.958901i	$0.408425\pi$
$224$	−6.24663	−0.417371
$225$	42.3456	2.82304
$226$	−0.335773	−0.0223353
$227$	−13.7491	−0.912558	−0.456279	−	0.889837i	$-0.650818\pi$
$227$	−13.7491	−0.912558	−0.456279	+	0.889837i	$0.650818\pi$
$228$	4.14852	0.274742
$229$	−1.99640	−0.131926	−0.0659629	−	0.997822i	$-0.521012\pi$
$229$	−1.99640	−0.131926	−0.0659629	+	0.997822i	$0.521012\pi$
$230$	2.94001	0.193859
$231$	0	0
$232$	0.793288	0.0520819
$233$	−11.3481	−0.743437	−0.371718	−	0.928346i	$-0.621231\pi$
$233$	−11.3481	−0.743437	−0.371718	+	0.928346i	$0.621231\pi$
$234$	0.258468	0.0168966
$235$	−10.1149	−0.659823
$236$	1.59478	0.103811
$237$	34.0537	2.21203
$238$	−3.77594	−0.244758
$239$	−5.21045	−0.337036	−0.168518	−	0.985699i	$-0.553898\pi$
$239$	−5.21045	−0.337036	−0.168518	+	0.985699i	$0.553898\pi$
$240$	7.50339	0.484341
$241$	−6.60827	−0.425676	−0.212838	−	0.977087i	$-0.568271\pi$
$241$	−6.60827	−0.425676	−0.212838	+	0.977087i	$0.568271\pi$
$242$	0	0
$243$	2.03139	0.130314
$244$	−11.2682	−0.721373
$245$	20.4678	1.30764
$246$	27.8957	1.77857
$247$	0.0563258	0.00358393
$248$	−24.2968	−1.54285
$249$	−41.6697	−2.64071
$250$	−5.98227	−0.378352
$251$	24.0024	1.51502	0.757510	−	0.652823i	$-0.226415\pi$
$251$	24.0024	1.51502	0.757510	+	0.652823i	$0.226415\pi$
$252$	8.74141	0.550657
$253$	0	0
$254$	2.44788	0.153593
$255$	47.2200	2.95703
$256$	−13.4739	−0.842117
$257$	−5.68903	−0.354872	−0.177436	−	0.984132i	$-0.556780\pi$
$257$	−5.68903	−0.354872	−0.177436	+	0.984132i	$0.556780\pi$
$258$	24.9322	1.55221
$259$	−4.80790	−0.298748
$260$	0.273785	0.0169794
$261$	−1.76469	−0.109232
$262$	−9.69481	−0.598948
$263$	−13.9857	−0.862395	−0.431197	−	0.902258i	$-0.641909\pi$
$263$	−13.9857	−0.862395	−0.431197	+	0.902258i	$0.641909\pi$
$264$	0	0
$265$	43.0303	2.64333
$266$	−0.832387	−0.0510369
$267$	0.546007	0.0334151
$268$	−15.6905	−0.958450
$269$	15.4020	0.939075	0.469538	−	0.882912i	$-0.344421\pi$
$269$	15.4020	0.939075	0.469538	+	0.882912i	$0.344421\pi$
$270$	23.4133	1.42489
$271$	25.3911	1.54240	0.771199	−	0.636595i	$-0.219658\pi$
$271$	25.3911	1.54240	0.771199	+	0.636595i	$0.219658\pi$
$272$	3.26987	0.198265
$273$	0.179196	0.0108454
$274$	10.7855	0.651577
$275$	0	0
$276$	−4.47827	−0.269560
$277$	−19.9798	−1.20047	−0.600235	−	0.799824i	$-0.704926\pi$
$277$	−19.9798	−1.20047	−0.600235	+	0.799824i	$0.704926\pi$
$278$	−12.4752	−0.748214
$279$	54.0490	3.23583
$280$	−9.86000	−0.589248
$281$	−6.18130	−0.368745	−0.184373	−	0.982856i	$-0.559025\pi$
$281$	−6.18130	−0.368745	−0.184373	+	0.982856i	$0.559025\pi$
$282$	−6.73235	−0.400906
$283$	7.12127	0.423316	0.211658	−	0.977344i	$-0.432114\pi$
$283$	7.12127	0.423316	0.211658	+	0.977344i	$0.432114\pi$
$284$	−18.7825	−1.11453
$285$	10.4094	0.616601
$286$	0	0
$287$	12.8093	0.756110
$288$	34.4366	2.02920
$289$	3.57781	0.210459
$290$	0.816800	0.0479641
$291$	−16.8782	−0.989420
$292$	−15.5147	−0.907929
$293$	−19.1342	−1.11783	−0.558916	−	0.829224i	$-0.688783\pi$
$293$	−19.1342	−1.11783	−0.558916	+	0.829224i	$0.688783\pi$
$294$	13.6231	0.794514
$295$	4.00159	0.232982
$296$	−11.9149	−0.692542
$297$	0	0
$298$	−8.86073	−0.513288
$299$	−0.0608030	−0.00351633
$300$	29.8549	1.72367
$301$	11.4485	0.659882
$302$	−3.63679	−0.209274
$303$	23.8677	1.37116
$304$	0.720827	0.0413422
$305$	−28.2740	−1.61897
$306$	20.8161	1.18998
$307$	−6.82573	−0.389565	−0.194782	−	0.980846i	$-0.562400\pi$
$307$	−6.82573	−0.389565	−0.194782	+	0.980846i	$0.562400\pi$
$308$	0	0
$309$	−18.4419	−1.04912
$310$	−25.0169	−1.42087
$311$	−12.8609	−0.729276	−0.364638	−	0.931149i	$-0.618807\pi$
$311$	−12.8609	−0.729276	−0.364638	+	0.931149i	$0.618807\pi$
$312$	0.444083	0.0251412
$313$	−3.01707	−0.170535	−0.0852673	−	0.996358i	$-0.527174\pi$
$313$	−3.01707	−0.170535	−0.0852673	+	0.996358i	$0.527174\pi$
$314$	−7.05930	−0.398380
$315$	21.9338	1.23583
$316$	15.9016	0.894534
$317$	17.7857	0.998943	0.499471	−	0.866330i	$-0.333528\pi$
$317$	17.7857	0.998943	0.499471	+	0.866330i	$0.333528\pi$
$318$	28.6404	1.60607
$319$	0	0
$320$	−10.9045	−0.609577
$321$	−21.7296	−1.21283
$322$	0.898551	0.0500743
$323$	4.53628	0.252405
$324$	−11.0942	−0.616346
$325$	0.405349	0.0224847
$326$	1.84640	0.102262
$327$	23.2458	1.28550
$328$	31.7441	1.75277
$329$	−3.09140	−0.170434
$330$	0	0
$331$	−26.3860	−1.45030	−0.725152	−	0.688589i	$-0.758230\pi$
$331$	−26.3860	−1.45030	−0.725152	+	0.688589i	$0.758230\pi$
$332$	−19.4579	−1.06789
$333$	26.5051	1.45247
$334$	7.23207	0.395722
$335$	−39.3704	−2.15104
$336$	2.29325	0.125107
$337$	13.2024	0.719181	0.359590	−	0.933110i	$-0.382916\pi$
$337$	13.2024	0.719181	0.359590	+	0.933110i	$0.382916\pi$
$338$	−10.1357	−0.551307
$339$	1.28334	0.0697012
$340$	22.0497	1.19581
$341$	0	0
$342$	4.58881	0.248134
$343$	13.7271	0.741191
$344$	28.3718	1.52970
$345$	−11.2368	−0.604970
$346$	−8.35786	−0.449321
$347$	−16.4809	−0.884740	−0.442370	−	0.896833i	$-0.645862\pi$
$347$	−16.4809	−0.884740	−0.442370	+	0.896833i	$0.645862\pi$
$348$	−1.24416	−0.0666940
$349$	19.0165	1.01793	0.508966	−	0.860787i	$-0.330028\pi$
$349$	19.0165	1.01793	0.508966	+	0.860787i	$0.330028\pi$
$350$	−5.99029	−0.320194
$351$	−0.484214	−0.0258455
$352$	0	0
$353$	13.1955	0.702325	0.351162	−	0.936315i	$-0.385787\pi$
$353$	13.1955	0.702325	0.351162	+	0.936315i	$0.385787\pi$
$354$	2.66341	0.141559
$355$	−47.1287	−2.50133
$356$	0.254961	0.0135129
$357$	14.4318	0.763810
$358$	−17.8641	−0.944148
$359$	2.88756	0.152400	0.0761998	−	0.997093i	$-0.475721\pi$
$359$	2.88756	0.152400	0.0761998	+	0.997093i	$0.475721\pi$
$360$	54.3565	2.86484
$361$	1.00000	0.0526316
$362$	4.60522	0.242045
$363$	0	0
$364$	0.0836765	0.00438584
$365$	−38.9293	−2.03765
$366$	−18.8188	−0.983676
$367$	−2.10833	−0.110054	−0.0550269	−	0.998485i	$-0.517524\pi$
$367$	−2.10833	−0.110054	−0.0550269	+	0.998485i	$0.517524\pi$
$368$	−0.778123	−0.0405624
$369$	−70.6156	−3.67610
$370$	−12.2681	−0.637787
$371$	13.1513	0.682780
$372$	38.1061	1.97571
$373$	−8.07305	−0.418007	−0.209003	−	0.977915i	$-0.567022\pi$
$373$	−8.07305	−0.418007	−0.209003	+	0.977915i	$0.567022\pi$
$374$	0	0
$375$	22.8644	1.18071
$376$	−7.66111	−0.395091
$377$	−0.0168924	−0.000870002 0
$378$	7.15576	0.368053
$379$	14.3355	0.736365	0.368183	−	0.929754i	$-0.379980\pi$
$379$	14.3355	0.736365	0.368183	+	0.929754i	$0.379980\pi$
$380$	4.86074	0.249351
$381$	−9.35586	−0.479315
$382$	5.02717	0.257212
$383$	−9.79867	−0.500689	−0.250344	−	0.968157i	$-0.580544\pi$
$383$	−9.79867	−0.500689	−0.250344	+	0.968157i	$0.580544\pi$
$384$	27.6299	1.40998
$385$	0	0
$386$	−1.11992	−0.0570024
$387$	−63.1138	−3.20825
$388$	−7.88139	−0.400117
$389$	−19.9236	−1.01016	−0.505082	−	0.863071i	$-0.668538\pi$
$389$	−19.9236	−1.01016	−0.505082	+	0.863071i	$0.668538\pi$
$390$	0.457244	0.0231535
$391$	−4.89685	−0.247644
$392$	15.5024	0.782992
$393$	37.0539	1.86912
$394$	3.70743	0.186778
$395$	39.9001	2.00759
$396$	0	0
$397$	13.9941	0.702342	0.351171	−	0.936311i	$-0.385784\pi$
$397$	13.9941	0.702342	0.351171	+	0.936311i	$0.385784\pi$
$398$	−1.84048	−0.0922549
$399$	3.18141	0.159270
$400$	5.18744	0.259372
$401$	−18.6293	−0.930301	−0.465151	−	0.885232i	$-0.654000\pi$
$401$	−18.6293	−0.930301	−0.465151	+	0.885232i	$0.654000\pi$
$402$	−26.2045	−1.30696
$403$	0.517380	0.0257725
$404$	11.1452	0.554492
$405$	−27.8375	−1.38326
$406$	0.249637	0.0123893
$407$	0	0
$408$	35.7648	1.77062
$409$	30.8428	1.52508	0.762540	−	0.646941i	$-0.223952\pi$
$409$	30.8428	1.52508	0.762540	+	0.646941i	$0.223952\pi$
$410$	32.6849	1.61419
$411$	−41.2226	−2.03336
$412$	−8.61157	−0.424262
$413$	1.22300	0.0601799
$414$	−4.95356	−0.243454
$415$	−48.8236	−2.39666
$416$	0.329642	0.0161620
$417$	47.6807	2.33493
$418$	0	0
$419$	37.9347	1.85323	0.926616	−	0.376009i	$-0.122704\pi$
$419$	37.9347	1.85323	0.926616	+	0.376009i	$0.122704\pi$
$420$	15.4640	0.754567
$421$	−18.4642	−0.899891	−0.449945	−	0.893056i	$-0.648557\pi$
$421$	−18.4642	−0.899891	−0.449945	+	0.893056i	$0.648557\pi$
$422$	19.1168	0.930592
$423$	17.0423	0.828627
$424$	32.5915	1.58278
$425$	32.6454	1.58353
$426$	−31.3683	−1.51980
$427$	−8.64134	−0.418184
$428$	−10.1468	−0.490463
$429$	0	0
$430$	29.2126	1.40876
$431$	−33.6742	−1.62203	−0.811013	−	0.585027i	$-0.801084\pi$
$431$	−33.6742	−1.62203	−0.811013	+	0.585027i	$0.801084\pi$
$432$	−6.19671	−0.298139
$433$	11.4041	0.548047	0.274024	−	0.961723i	$-0.411645\pi$
$433$	11.4041	0.548047	0.274024	+	0.961723i	$0.411645\pi$
$434$	−7.64588	−0.367014
$435$	−3.12183	−0.149680
$436$	10.8548	0.519849
$437$	−1.07949	−0.0516388
$438$	−25.9108	−1.23807
$439$	3.76890	0.179880	0.0899399	−	0.995947i	$-0.471333\pi$
$439$	3.76890	0.179880	0.0899399	+	0.995947i	$0.471333\pi$
$440$	0	0
$441$	−34.4856	−1.64217
$442$	0.199261	0.00947786
$443$	4.51841	0.214676	0.107338	−	0.994223i	$-0.465767\pi$
$443$	4.51841	0.214676	0.107338	+	0.994223i	$0.465767\pi$
$444$	18.6869	0.886842
$445$	0.639746	0.0303269
$446$	6.60871	0.312931
$447$	33.8660	1.60181
$448$	−3.33271	−0.157456
$449$	−37.3611	−1.76318	−0.881590	−	0.472016i	$-0.843526\pi$
$449$	−37.3611	−1.76318	−0.881590	+	0.472016i	$0.843526\pi$
$450$	33.0234	1.55674
$451$	0	0
$452$	0.599261	0.0281869
$453$	13.8999	0.653075
$454$	−10.7223	−0.503222
$455$	0.209960	0.00984308
$456$	7.88418	0.369210
$457$	−9.37773	−0.438672	−0.219336	−	0.975649i	$-0.570389\pi$
$457$	−9.37773	−0.438672	−0.219336	+	0.975649i	$0.570389\pi$
$458$	−1.55690	−0.0727494
$459$	−38.9969	−1.82022
$460$	−5.24710	−0.244648
$461$	−31.6785	−1.47542	−0.737708	−	0.675120i	$-0.764092\pi$
$461$	−31.6785	−1.47542	−0.737708	+	0.675120i	$0.764092\pi$
$462$	0	0
$463$	−37.1284	−1.72550	−0.862752	−	0.505628i	$-0.831261\pi$
$463$	−37.1284	−1.72550	−0.862752	+	0.505628i	$0.831261\pi$
$464$	−0.216179	−0.0100359
$465$	95.6155	4.43406
$466$	−8.84986	−0.409962
$467$	−15.9678	−0.738902	−0.369451	−	0.929250i	$-0.620454\pi$
$467$	−15.9678	−0.738902	−0.369451	+	0.929250i	$0.620454\pi$
$468$	−0.461294	−0.0213233
$469$	−12.0327	−0.555619
$470$	−7.88816	−0.363854
$471$	26.9809	1.24321
$472$	3.03084	0.139506
$473$	0	0
$474$	26.5570	1.21980
$475$	7.19651	0.330199
$476$	6.73900	0.308882
$477$	−72.5006	−3.31958
$478$	−4.06340	−0.185855
$479$	−28.1729	−1.28725	−0.643627	−	0.765340i	$-0.722571\pi$
$479$	−28.1729	−1.28725	−0.643627	+	0.765340i	$0.722571\pi$
$480$	60.9202	2.78061
$481$	0.253718	0.0115686
$482$	−5.15350	−0.234735
$483$	−3.43429	−0.156266
$484$	0	0
$485$	−19.7759	−0.897977
$486$	1.58419	0.0718604
$487$	24.0613	1.09032	0.545161	−	0.838331i	$-0.316468\pi$
$487$	24.0613	1.09032	0.545161	+	0.838331i	$0.316468\pi$
$488$	−21.4150	−0.969410
$489$	−7.05699	−0.319128
$490$	15.9619	0.721085
$491$	29.0197	1.30964	0.654821	−	0.755784i	$-0.272744\pi$
$491$	29.0197	1.30964	0.654821	+	0.755784i	$0.272744\pi$
$492$	−49.7861	−2.24453
$493$	−1.36045	−0.0612716
$494$	0.0439260	0.00197632
$495$	0	0
$496$	6.62114	0.297298
$497$	−14.4039	−0.646102
$498$	−32.4964	−1.45620
$499$	−15.0257	−0.672642	−0.336321	−	0.941747i	$-0.609183\pi$
$499$	−15.0257	−0.672642	−0.336321	+	0.941747i	$0.609183\pi$
$500$	10.6767	0.477476
$501$	−27.6412	−1.23492
$502$	18.7184	0.835445
$503$	28.7785	1.28317	0.641585	−	0.767052i	$-0.278277\pi$
$503$	28.7785	1.28317	0.641585	+	0.767052i	$0.278277\pi$
$504$	16.6129	0.739996
$505$	27.9653	1.24444
$506$	0	0
$507$	38.7388	1.72045
$508$	−4.36878	−0.193833
$509$	−10.4772	−0.464395	−0.232197	−	0.972669i	$-0.574592\pi$
$509$	−10.4772	−0.464395	−0.232197	+	0.972669i	$0.574592\pi$
$510$	36.8248	1.63063
$511$	−11.8979	−0.526332
$512$	8.03194	0.354965
$513$	−8.59667	−0.379552
$514$	−4.43662	−0.195691
$515$	−21.6081	−0.952165
$516$	−44.4971	−1.95888
$517$	0	0
$518$	−3.74947	−0.164742
$519$	31.9440	1.40219
$520$	0.520323	0.0228177
$521$	−24.7590	−1.08471	−0.542357	−	0.840148i	$-0.682468\pi$
$521$	−24.7590	−1.08471	−0.542357	+	0.840148i	$0.682468\pi$
$522$	−1.37621	−0.0602349
$523$	−14.8566	−0.649635	−0.324818	−	0.945777i	$-0.605303\pi$
$523$	−14.8566	−0.649635	−0.324818	+	0.945777i	$0.605303\pi$
$524$	17.3025	0.755865
$525$	22.8951	0.999223
$526$	−10.9068	−0.475560
$527$	41.6679	1.81508
$528$	0	0
$529$	−21.8347	−0.949335
$530$	33.5574	1.45764
$531$	−6.74219	−0.292586
$532$	1.48558	0.0644080
$533$	−0.675962	−0.0292792
$534$	0.425807	0.0184265
$535$	−25.4602	−1.10074
$536$	−29.8195	−1.28801
$537$	68.2773	2.94638
$538$	12.0113	0.517845
$539$	0	0
$540$	−41.7862	−1.79819
$541$	−3.88960	−0.167227	−0.0836134	−	0.996498i	$-0.526646\pi$
$541$	−3.88960	−0.167227	−0.0836134	+	0.996498i	$0.526646\pi$
$542$	19.8014	0.850541
$543$	−17.6013	−0.755343
$544$	26.5481	1.13824
$545$	27.2367	1.16669
$546$	0.139747	0.00598061
$547$	−17.5180	−0.749015	−0.374507	−	0.927224i	$-0.622188\pi$
$547$	−17.5180	−0.749015	−0.374507	+	0.927224i	$0.622188\pi$
$548$	−19.2491	−0.822283
$549$	47.6382	2.03315
$550$	0	0
$551$	−0.299905	−0.0127764
$552$	−8.51086	−0.362246
$553$	12.1946	0.518567
$554$	−15.5814	−0.661988
$555$	46.8890	1.99033
$556$	22.2648	0.944237
$557$	−28.9860	−1.22818	−0.614088	−	0.789237i	$-0.710476\pi$
$557$	−28.9860	−1.22818	−0.614088	+	0.789237i	$0.710476\pi$
$558$	42.1504	1.78437
$559$	−0.604152	−0.0255529
$560$	2.68695	0.113544
$561$	0	0
$562$	−4.82052	−0.203341
$563$	−29.6112	−1.24796	−0.623982	−	0.781438i	$-0.714486\pi$
$563$	−29.6112	−1.24796	−0.623982	+	0.781438i	$0.714486\pi$
$564$	12.0154	0.505938
$565$	1.50366	0.0632594
$566$	5.55356	0.233434
$567$	−8.50793	−0.357299
$568$	−35.6957	−1.49776
$569$	4.05818	0.170128	0.0850640	−	0.996375i	$-0.472891\pi$
$569$	4.05818	0.170128	0.0850640	+	0.996375i	$0.472891\pi$
$570$	8.11784	0.340019
$571$	−20.3380	−0.851117	−0.425559	−	0.904931i	$-0.639922\pi$
$571$	−20.3380	−0.851117	−0.425559	+	0.904931i	$0.639922\pi$
$572$	0	0
$573$	−19.2140	−0.802677
$574$	9.98942	0.416950
$575$	−7.76854	−0.323971
$576$	18.3726	0.765527
$577$	24.4768	1.01898	0.509492	−	0.860476i	$-0.329833\pi$
$577$	24.4768	1.01898	0.509492	+	0.860476i	$0.329833\pi$
$578$	2.79017	0.116056
$579$	4.28037	0.177886
$580$	−1.45776	−0.0605302
$581$	−14.9219	−0.619064
$582$	−13.1626	−0.545607
$583$	0	0
$584$	−29.4854	−1.22011
$585$	−1.15747	−0.0478556
$586$	−14.9219	−0.616419
$587$	−3.34628	−0.138116	−0.0690579	−	0.997613i	$-0.521999\pi$
$587$	−3.34628	−0.138116	−0.0690579	+	0.997613i	$0.521999\pi$
$588$	−24.3134	−1.00267
$589$	9.18548	0.378481
$590$	3.12067	0.128476
$591$	−14.1699	−0.582872
$592$	3.24695	0.133449
$593$	39.2063	1.61001	0.805006	−	0.593267i	$-0.202162\pi$
$593$	39.2063	1.61001	0.805006	+	0.593267i	$0.202162\pi$
$594$	0	0
$595$	16.9094	0.693219
$596$	15.8139	0.647764
$597$	7.03437	0.287898
$598$	−0.0474175	−0.00193905
$599$	5.72987	0.234116	0.117058	−	0.993125i	$-0.462654\pi$
$599$	5.72987	0.234116	0.117058	+	0.993125i	$0.462654\pi$
$600$	56.7386	2.31634
$601$	−13.9163	−0.567656	−0.283828	−	0.958875i	$-0.591605\pi$
$601$	−13.9163	−0.567656	−0.283828	+	0.958875i	$0.591605\pi$
$602$	8.92820	0.363886
$603$	66.3343	2.70134
$604$	6.49065	0.264101
$605$	0	0
$606$	18.6134	0.756116
$607$	−0.156175	−0.00633897	−0.00316948	−	0.999995i	$-0.501009\pi$
$607$	−0.156175	−0.00633897	−0.00316948	+	0.999995i	$0.501009\pi$
$608$	5.85241	0.237347
$609$	−0.954120	−0.0386629
$610$	−22.0497	−0.892765
$611$	0.163137	0.00659980
$612$	−37.1509	−1.50174
$613$	−40.1902	−1.62327	−0.811634	−	0.584166i	$-0.801422\pi$
$613$	−40.1902	−1.62327	−0.811634	+	0.584166i	$0.801422\pi$
$614$	−5.32308	−0.214822
$615$	−124.923	−5.03737
$616$	0	0
$617$	12.8606	0.517747	0.258874	−	0.965911i	$-0.416649\pi$
$617$	12.8606	0.517747	0.258874	+	0.965911i	$0.416649\pi$
$618$	−14.3820	−0.578531
$619$	−2.03398	−0.0817526	−0.0408763	−	0.999164i	$-0.513015\pi$
$619$	−2.03398	−0.0817526	−0.0408763	+	0.999164i	$0.513015\pi$
$620$	44.6482	1.79312
$621$	9.27999	0.372393
$622$	−10.0297	−0.402153
$623$	0.195524	0.00783352
$624$	−0.121017	−0.00484456
$625$	−9.19275	−0.367710
$626$	−2.35288	−0.0940398
$627$	0	0
$628$	12.5989	0.502750
$629$	20.4336	0.814739
$630$	17.1052	0.681489
$631$	37.6984	1.50075	0.750375	−	0.661012i	$-0.229873\pi$
$631$	37.6984	1.50075	0.750375	+	0.661012i	$0.229873\pi$
$632$	30.2206	1.20211
$633$	−73.0651	−2.90408
$634$	13.8703	0.550858
$635$	−10.9621	−0.435017
$636$	−51.1151	−2.02685
$637$	−0.330111	−0.0130795
$638$	0	0
$639$	79.4060	3.14125
$640$	32.3734	1.27967
$641$	2.84360	0.112315	0.0561576	−	0.998422i	$-0.482115\pi$
$641$	2.84360	0.112315	0.0561576	+	0.998422i	$0.482115\pi$
$642$	−16.9460	−0.668804
$643$	30.6389	1.20828	0.604140	−	0.796878i	$-0.293517\pi$
$643$	30.6389	1.20828	0.604140	+	0.796878i	$0.293517\pi$
$644$	−1.60366	−0.0631932
$645$	−111.652	−4.39628
$646$	3.53764	0.139187
$647$	−6.76617	−0.266006	−0.133003	−	0.991116i	$-0.542462\pi$
$647$	−6.76617	−0.266006	−0.133003	+	0.991116i	$0.542462\pi$
$648$	−21.0844	−0.828272
$649$	0	0
$650$	0.316114	0.0123990
$651$	29.2228	1.14533
$652$	−3.29530	−0.129054
$653$	11.9015	0.465743	0.232872	−	0.972508i	$-0.425188\pi$
$653$	11.9015	0.465743	0.232872	+	0.972508i	$0.425188\pi$
$654$	18.1284	0.708876
$655$	43.4153	1.69638
$656$	−8.65059	−0.337749
$657$	65.5910	2.55895
$658$	−2.41085	−0.0939845
$659$	11.2353	0.437664	0.218832	−	0.975763i	$-0.429775\pi$
$659$	11.2353	0.437664	0.218832	+	0.975763i	$0.429775\pi$
$660$	0	0
$661$	−22.9273	−0.891768	−0.445884	−	0.895091i	$-0.647111\pi$
$661$	−22.9273	−0.891768	−0.445884	+	0.895091i	$0.647111\pi$
$662$	−20.5772	−0.799757
$663$	−0.761580	−0.0295773
$664$	−36.9794	−1.43508
$665$	3.72760	0.144550
$666$	20.6702	0.800953
$667$	0.323743	0.0125354
$668$	−12.9072	−0.499396
$669$	−25.2587	−0.976558
$670$	−30.7033	−1.18617
$671$	0	0
$672$	18.6189	0.718240
$673$	3.09828	0.119430	0.0597150	−	0.998215i	$-0.480981\pi$
$673$	3.09828	0.119430	0.0597150	+	0.998215i	$0.480981\pi$
$674$	10.2960	0.396586
$675$	−61.8661	−2.38123
$676$	18.0893	0.695743
$677$	−33.3985	−1.28361	−0.641804	−	0.766868i	$-0.721814\pi$
$677$	−33.3985	−1.28361	−0.641804	+	0.766868i	$0.721814\pi$
$678$	1.00082	0.0384361
$679$	−6.04407	−0.231950
$680$	41.9049	1.60698
$681$	40.9810	1.57039
$682$	0	0
$683$	6.01634	0.230209	0.115104	−	0.993353i	$-0.463280\pi$
$683$	6.01634	0.230209	0.115104	+	0.993353i	$0.463280\pi$
$684$	−8.18974	−0.313143
$685$	−48.2997	−1.84544
$686$	10.7051	0.408723
$687$	5.95054	0.227027
$688$	−7.73160	−0.294765
$689$	−0.694007	−0.0264396
$690$	−8.76310	−0.333606
$691$	−15.6730	−0.596227	−0.298114	−	0.954530i	$-0.596357\pi$
$691$	−15.6730	−0.596227	−0.298114	+	0.954530i	$0.596357\pi$
$692$	14.9164	0.567038
$693$	0	0
$694$	−12.8527	−0.487882
$695$	55.8665	2.11914
$696$	−2.36450	−0.0896262
$697$	−54.4395	−2.06204
$698$	14.8302	0.561330
$699$	33.8244	1.27936
$700$	10.6910	0.404082
$701$	−18.0567	−0.681992	−0.340996	−	0.940065i	$-0.610764\pi$
$701$	−18.0567	−0.681992	−0.340996	+	0.940065i	$0.610764\pi$
$702$	−0.377617	−0.0142523
$703$	4.50448	0.169890
$704$	0	0
$705$	30.1488	1.13547
$706$	10.2906	0.387291
$707$	8.54699	0.321442
$708$	−4.75344	−0.178645
$709$	16.2048	0.608586	0.304293	−	0.952579i	$-0.401580\pi$
$709$	16.2048	0.608586	0.304293	+	0.952579i	$0.401580\pi$
$710$	−36.7536	−1.37934
$711$	−67.2266	−2.52120
$712$	0.484549	0.0181592
$713$	−9.91560	−0.371342
$714$	11.2547	0.421196
$715$	0	0
$716$	31.8825	1.19150
$717$	15.5304	0.579995
$718$	2.25188	0.0840395
$719$	−27.9403	−1.04200	−0.520998	−	0.853558i	$-0.674440\pi$
$719$	−27.9403	−1.04200	−0.520998	+	0.853558i	$0.674440\pi$
$720$	−14.8127	−0.552037
$721$	−6.60403	−0.245947
$722$	0.779856	0.0290232
$723$	19.6968	0.732533
$724$	−8.21903	−0.305458
$725$	−2.15827	−0.0801561
$726$	0	0
$727$	−30.7020	−1.13867	−0.569337	−	0.822104i	$-0.692800\pi$
$727$	−30.7020	−1.13867	−0.569337	+	0.822104i	$0.692800\pi$
$728$	0.159025	0.00589387
$729$	−29.9678	−1.10992
$730$	−30.3592	−1.12365
$731$	−48.6562	−1.79961
$732$	33.5864	1.24139
$733$	−44.9333	−1.65965	−0.829826	−	0.558023i	$-0.811560\pi$
$733$	−44.9333	−1.65965	−0.829826	+	0.558023i	$0.811560\pi$
$734$	−1.64419	−0.0606882
$735$	−61.0069	−2.25027
$736$	−6.31760	−0.232870
$737$	0	0
$738$	−55.0700	−2.02715
$739$	3.19172	0.117409	0.0587047	−	0.998275i	$-0.481303\pi$
$739$	3.19172	0.117409	0.0587047	+	0.998275i	$0.481303\pi$
$740$	21.8951	0.804880
$741$	−0.167887	−0.00616747
$742$	10.2561	0.376513
$743$	−17.4348	−0.639619	−0.319810	−	0.947482i	$-0.603619\pi$
$743$	−17.4348	−0.639619	−0.319810	+	0.947482i	$0.603619\pi$
$744$	72.4199	2.65504
$745$	39.6801	1.45377
$746$	−6.29581	−0.230506
$747$	82.2617	3.00980
$748$	0	0
$749$	−7.78135	−0.284324
$750$	17.8310	0.651095
$751$	9.55633	0.348715	0.174358	−	0.984682i	$-0.444215\pi$
$751$	9.55633	0.348715	0.174358	+	0.984682i	$0.444215\pi$
$752$	2.08773	0.0761317
$753$	−71.5425	−2.60715
$754$	−0.0131736	−0.000479755 0
$755$	16.2863	0.592718
$756$	−12.7710	−0.464478
$757$	−48.5259	−1.76370	−0.881852	−	0.471527i	$-0.843703\pi$
$757$	−48.5259	−1.76370	−0.881852	+	0.471527i	$0.843703\pi$
$758$	11.1796	0.406062
$759$	0	0
$760$	9.23774	0.335088
$761$	−38.6035	−1.39937	−0.699687	−	0.714449i	$-0.746677\pi$
$761$	−38.6035	−1.39937	−0.699687	+	0.714449i	$0.746677\pi$
$762$	−7.29622	−0.264314
$763$	8.32429	0.301360
$764$	−8.97210	−0.324599
$765$	−93.2187	−3.37033
$766$	−7.64155	−0.276101
$767$	−0.0645391	−0.00233037
$768$	40.1607	1.44917
$769$	−53.2658	−1.92081	−0.960406	−	0.278603i	$-0.910129\pi$
$769$	−53.2658	−1.92081	−0.960406	+	0.278603i	$0.910129\pi$
$770$	0	0
$771$	16.9569	0.610688
$772$	1.99874	0.0719363
$773$	9.31748	0.335126	0.167563	−	0.985861i	$-0.446410\pi$
$773$	9.31748	0.335126	0.167563	+	0.985861i	$0.446410\pi$
$774$	−49.2196	−1.76916
$775$	66.1034	2.37451
$776$	−14.9784	−0.537694
$777$	14.3306	0.514107
$778$	−15.5375	−0.557047
$779$	−12.0009	−0.429978
$780$	−0.816053	−0.0292194
$781$	0	0
$782$	−3.81884	−0.136561
$783$	2.57818	0.0921367
$784$	−4.22458	−0.150878
$785$	31.6130	1.12832
$786$	28.8967	1.03071
$787$	15.0616	0.536889	0.268444	−	0.963295i	$-0.413490\pi$
$787$	15.0616	0.536889	0.268444	+	0.963295i	$0.413490\pi$
$788$	−6.61672	−0.235711
$789$	41.6862	1.48407
$790$	31.1163	1.10707
$791$	0.459561	0.0163401
$792$	0	0
$793$	0.456013	0.0161935
$794$	10.9133	0.387300
$795$	−128.257	−4.54882
$796$	3.28474	0.116425
$797$	−19.0593	−0.675114	−0.337557	−	0.941305i	$-0.609601\pi$
$797$	−19.0593	−0.675114	−0.337557	+	0.941305i	$0.609601\pi$
$798$	2.48104	0.0878279
$799$	13.1384	0.464804
$800$	42.1169	1.48906
$801$	−1.07789	−0.0380855
$802$	−14.5281	−0.513006
$803$	0	0
$804$	46.7676	1.64937
$805$	−4.02389	−0.141824
$806$	0.403481	0.0142120
$807$	−45.9077	−1.61603
$808$	21.1811	0.745150
$809$	15.2273	0.535363	0.267681	−	0.963507i	$-0.413743\pi$
$809$	15.2273	0.535363	0.267681	+	0.963507i	$0.413743\pi$
$810$	−21.7093	−0.762785
$811$	43.3354	1.52171	0.760857	−	0.648920i	$-0.224779\pi$
$811$	43.3354	1.52171	0.760857	+	0.648920i	$0.224779\pi$
$812$	−0.445532	−0.0156351
$813$	−75.6814	−2.65426
$814$	0	0
$815$	−8.26854	−0.289634
$816$	−9.74628	−0.341188
$817$	−10.7260	−0.375256
$818$	24.0530	0.840992
$819$	−0.353756	−0.0123612
$820$	−58.3334	−2.03709
$821$	−19.4279	−0.678040	−0.339020	−	0.940779i	$-0.610095\pi$
$821$	−19.4279	−0.678040	−0.339020	+	0.940779i	$0.610095\pi$
$822$	−32.1477	−1.12128
$823$	2.35683	0.0821539	0.0410769	−	0.999156i	$-0.486921\pi$
$823$	2.35683	0.0821539	0.0410769	+	0.999156i	$0.486921\pi$
$824$	−16.3661	−0.570141
$825$	0	0
$826$	0.953763	0.0331857
$827$	29.8127	1.03669	0.518344	−	0.855172i	$-0.326549\pi$
$827$	29.8127	1.03669	0.518344	+	0.855172i	$0.326549\pi$
$828$	8.84072	0.307236
$829$	52.6510	1.82864	0.914322	−	0.404988i	$-0.132724\pi$
$829$	52.6510	1.82864	0.914322	+	0.404988i	$0.132724\pi$
$830$	−38.0754	−1.32162
$831$	59.5524	2.06585
$832$	0.175871	0.00609722
$833$	−26.5859	−0.921148
$834$	37.1841	1.28758
$835$	−32.3867	−1.12079
$836$	0	0
$837$	−78.9645	−2.72941
$838$	29.5836	1.02195
$839$	29.7892	1.02844	0.514218	−	0.857660i	$-0.328082\pi$
$839$	29.7892	1.02844	0.514218	+	0.857660i	$0.328082\pi$
$840$	29.3890	1.01402
$841$	−28.9101	−0.996899
$842$	−14.3994	−0.496237
$843$	18.4242	0.634563
$844$	−34.1182	−1.17440
$845$	45.3895	1.56145
$846$	13.2906	0.456939
$847$	0	0
$848$	−8.88152	−0.304992
$849$	−21.2259	−0.728471
$850$	25.4587	0.873226
$851$	−4.86252	−0.166685
$852$	55.9836	1.91797
$853$	35.2393	1.20657	0.603285	−	0.797526i	$-0.293858\pi$
$853$	35.2393	1.20657	0.603285	+	0.797526i	$0.293858\pi$
$854$	−6.73900	−0.230604
$855$	−20.5496	−0.702782
$856$	−19.2837	−0.659105
$857$	21.5877	0.737421	0.368711	−	0.929544i	$-0.379799\pi$
$857$	21.5877	0.737421	0.368711	+	0.929544i	$0.379799\pi$
$858$	0	0
$859$	27.7669	0.947396	0.473698	−	0.880687i	$-0.342919\pi$
$859$	27.7669	0.947396	0.473698	+	0.880687i	$0.342919\pi$
$860$	−52.1364	−1.77784
$861$	−38.1799	−1.30117
$862$	−26.2610	−0.894453
$863$	7.11774	0.242291	0.121145	−	0.992635i	$-0.461343\pi$
$863$	7.11774	0.242291	0.121145	+	0.992635i	$0.461343\pi$
$864$	−50.3112	−1.71162
$865$	37.4282	1.27260
$866$	8.89357	0.302216
$867$	−10.6641	−0.362173
$868$	13.6458	0.463167
$869$	0	0
$870$	−2.43458	−0.0825400
$871$	0.634980	0.0215155
$872$	20.6293	0.698595
$873$	33.3199	1.12771
$874$	−0.841844	−0.0284758
$875$	8.18772	0.276796
$876$	46.2436	1.56243
$877$	44.1031	1.48925	0.744627	−	0.667481i	$-0.232627\pi$
$877$	44.1031	1.48925	0.744627	+	0.667481i	$0.232627\pi$
$878$	2.93920	0.0991931
$879$	57.0321	1.92364
$880$	0	0
$881$	−37.9204	−1.27757	−0.638785	−	0.769385i	$-0.720563\pi$
$881$	−37.9204	−1.27757	−0.638785	+	0.769385i	$0.720563\pi$
$882$	−26.8938	−0.905562
$883$	4.85252	0.163300	0.0816502	−	0.996661i	$-0.473981\pi$
$883$	4.85252	0.163300	0.0816502	+	0.996661i	$0.473981\pi$
$884$	−0.355624	−0.0119609
$885$	−11.9273	−0.400931
$886$	3.52371	0.118381
$887$	−11.2754	−0.378591	−0.189295	−	0.981920i	$-0.560620\pi$
$887$	−11.2754	−0.378591	−0.189295	+	0.981920i	$0.560620\pi$
$888$	35.5141	1.19177
$889$	−3.35032	−0.112366
$890$	0.498910	0.0167235
$891$	0	0
$892$	−11.7947	−0.394916
$893$	2.89630	0.0969210
$894$	26.4106	0.883302
$895$	79.9991	2.67408
$896$	9.89423	0.330543
$897$	0.181231	0.00605114
$898$	−29.1363	−0.972290
$899$	−2.75477	−0.0918767
$900$	−58.9376	−1.96459
$901$	−55.8928	−1.86206
$902$	0	0
$903$	−34.1239	−1.13557
$904$	1.13888	0.0378787
$905$	−20.6231	−0.685534
$906$	10.8399	0.360133
$907$	24.0191	0.797540	0.398770	−	0.917051i	$-0.369437\pi$
$907$	24.0191	0.797540	0.398770	+	0.917051i	$0.369437\pi$
$908$	19.1363	0.635061
$909$	−47.1181	−1.56281
$910$	0.163739	0.00542788
$911$	7.48540	0.248002	0.124001	−	0.992282i	$-0.460427\pi$
$911$	7.48540	0.248002	0.124001	+	0.992282i	$0.460427\pi$
$912$	−2.14852	−0.0711446
$913$	0	0
$914$	−7.31328	−0.241902
$915$	84.2745	2.78603
$916$	2.77864	0.0918089
$917$	13.2689	0.438179
$918$	−30.4119	−1.00374
$919$	−40.0187	−1.32009	−0.660047	−	0.751224i	$-0.729464\pi$
$919$	−40.0187	−1.32009	−0.660047	+	0.751224i	$0.729464\pi$
$920$	−9.97201	−0.328768
$921$	20.3450	0.670390
$922$	−24.7047	−0.813605
$923$	0.760108	0.0250193
$924$	0	0
$925$	32.4165	1.06585
$926$	−28.9548	−0.951514
$927$	36.4069	1.19576
$928$	−1.75517	−0.0576161
$929$	−32.3099	−1.06005	−0.530027	−	0.847981i	$-0.677818\pi$
$929$	−32.3099	−1.06005	−0.530027	+	0.847981i	$0.677818\pi$
$930$	74.5663	2.44513
$931$	−5.86074	−0.192078
$932$	15.7945	0.517367
$933$	38.3337	1.25499
$934$	−12.4526	−0.407461
$935$	0	0
$936$	−0.876679	−0.0286552
$937$	54.1000	1.76737	0.883684	−	0.468083i	$-0.155055\pi$
$937$	54.1000	1.76737	0.883684	+	0.468083i	$0.155055\pi$
$938$	−9.38378	−0.306391
$939$	8.99277	0.293468
$940$	14.0782	0.459179
$941$	−26.6955	−0.870248	−0.435124	−	0.900371i	$-0.643295\pi$
$941$	−26.6955	−0.870248	−0.435124	+	0.900371i	$0.643295\pi$
$942$	21.0412	0.685559
$943$	12.9548	0.421868
$944$	−0.825935	−0.0268819
$945$	−32.0449	−1.04242
$946$	0	0
$947$	−39.4463	−1.28183	−0.640916	−	0.767611i	$-0.721445\pi$
$947$	−39.4463	−1.28183	−0.640916	+	0.767611i	$0.721445\pi$
$948$	−47.3968	−1.53938
$949$	0.627865	0.0203814
$950$	5.61224	0.182085
$951$	−53.0126	−1.71905
$952$	12.8073	0.415088
$953$	48.7523	1.57924	0.789621	−	0.613595i	$-0.210277\pi$
$953$	48.7523	1.57924	0.789621	+	0.613595i	$0.210277\pi$
$954$	−56.5400	−1.83055
$955$	−22.5127	−0.728493
$956$	7.25203	0.234547
$957$	0	0
$958$	−21.9708	−0.709845
$959$	−14.7618	−0.476682
$960$	32.5022	1.04900
$961$	53.3730	1.72171
$962$	0.197864	0.00637938
$963$	42.8972	1.38234
$964$	9.19755	0.296233
$965$	5.01522	0.161446
$966$	−2.67825	−0.0861713
$967$	1.39478	0.0448532	0.0224266	−	0.999748i	$-0.492861\pi$
$967$	1.39478	0.0448532	0.0224266	+	0.999748i	$0.492861\pi$
$968$	0	0
$969$	−13.5210	−0.434356
$970$	−15.4224	−0.495182
$971$	−3.11733	−0.100040	−0.0500200	−	0.998748i	$-0.515929\pi$
$971$	−3.11733	−0.100040	−0.0500200	+	0.998748i	$0.515929\pi$
$972$	−2.82734	−0.0906870
$973$	17.0744	0.547380
$974$	18.7644	0.601249
$975$	−1.20820	−0.0386933
$976$	5.83580	0.186800
$977$	−22.3690	−0.715647	−0.357823	−	0.933789i	$-0.616481\pi$
$977$	−22.3690	−0.715647	−0.357823	+	0.933789i	$0.616481\pi$
$978$	−5.50343	−0.175980
$979$	0	0
$980$	−28.4875	−0.910001
$981$	−45.8904	−1.46517
$982$	22.6312	0.722191
$983$	42.2421	1.34731	0.673657	−	0.739044i	$-0.264723\pi$
$983$	42.2421	1.34731	0.673657	+	0.739044i	$0.264723\pi$
$984$	−94.6174	−3.01629
$985$	−16.6026	−0.529003
$986$	−1.06096	−0.0337877
$987$	9.21433	0.293295
$988$	−0.0783957	−0.00249410
$989$	11.5786	0.368178
$990$	0	0
$991$	−1.69828	−0.0539477	−0.0269738	−	0.999636i	$-0.508587\pi$
$991$	−1.69828	−0.0539477	−0.0269738	+	0.999636i	$0.508587\pi$
$992$	53.7572	1.70679
$993$	78.6469	2.49578
$994$	−11.2329	−0.356287
$995$	8.24203	0.261290
$996$	57.9970	1.83770
$997$	−18.9376	−0.599759	−0.299879	−	0.953977i	$-0.596946\pi$
$997$	−18.9376	−0.599759	−0.299879	+	0.953977i	$0.596946\pi$
$998$	−11.7179	−0.370923
$999$	−38.7235	−1.22516

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2299.2.a.n.1.4		5
11.10	odd	2		209.2.a.c.1.2	✓	5
33.32	even	2		1881.2.a.k.1.4		5
44.43	even	2		3344.2.a.t.1.5		5
55.54	odd	2		5225.2.a.h.1.4		5
209.208	even	2		3971.2.a.h.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.a.c.1.2	✓	5	11.10	odd	2
1881.2.a.k.1.4		5	33.32	even	2
2299.2.a.n.1.4		5	1.1	even	1	trivial
3344.2.a.t.1.5		5	44.43	even	2
3971.2.a.h.1.4		5	209.208	even	2
5225.2.a.h.1.4		5	55.54	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:	\( N \)	\(=\)	\( 2299 = 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2299.a (trivial)

\(f(q)\)	\(=\)	\(q+0.779856 q^{2} -2.98063 q^{3} -1.39182 q^{4} -3.49235 q^{5} -2.32446 q^{6} -1.06736 q^{7} -2.64513 q^{8} +5.88418 q^{9} -2.72353 q^{10} +4.14852 q^{12} +0.0563258 q^{13} -0.832387 q^{14} +10.4094 q^{15} +0.720827 q^{16} +4.53628 q^{17} +4.58881 q^{18} +1.00000 q^{19} +4.86074 q^{20} +3.18141 q^{21} -1.07949 q^{23} +7.88418 q^{24} +7.19651 q^{25} +0.0439260 q^{26} -8.59667 q^{27} +1.48558 q^{28} -0.299905 q^{29} +8.11784 q^{30} +9.18548 q^{31} +5.85241 q^{32} +3.53764 q^{34} +3.72760 q^{35} -8.18974 q^{36} +4.50448 q^{37} +0.779856 q^{38} -0.167887 q^{39} +9.23774 q^{40} -12.0009 q^{41} +2.48104 q^{42} -10.7260 q^{43} -20.5496 q^{45} -0.841844 q^{46} +2.89630 q^{47} -2.14852 q^{48} -5.86074 q^{49} +5.61224 q^{50} -13.5210 q^{51} -0.0783957 q^{52} -12.3213 q^{53} -6.70416 q^{54} +2.82331 q^{56} -2.98063 q^{57} -0.233882 q^{58} -1.14582 q^{59} -14.4881 q^{60} +8.09599 q^{61} +7.16335 q^{62} -6.28054 q^{63} +3.12238 q^{64} -0.196709 q^{65} +11.2733 q^{67} -6.31370 q^{68} +3.21755 q^{69} +2.90699 q^{70} +13.4948 q^{71} -15.5644 q^{72} +11.1470 q^{73} +3.51284 q^{74} -21.4502 q^{75} -1.39182 q^{76} -0.130927 q^{78} -11.4250 q^{79} -2.51738 q^{80} +7.97100 q^{81} -9.35899 q^{82} +13.9802 q^{83} -4.42797 q^{84} -15.8423 q^{85} -8.36475 q^{86} +0.893906 q^{87} -0.183185 q^{89} -16.0257 q^{90} -0.0601200 q^{91} +1.50246 q^{92} -27.3785 q^{93} +2.25870 q^{94} -3.49235 q^{95} -17.4439 q^{96} +5.66263 q^{97} -4.57053 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + q^{3} + 6 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} - 6 q^{8} + 4 q^{9} - 12 q^{10} + 6 q^{12} - 4 q^{13} - 14 q^{14} + 3 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} + 5 q^{19} - 8 q^{20} - 10 q^{21}+ \cdots + 10 q^{98}+O(q^{100}) \) 5 * q - 2 * q^2 + q^3 + 6 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 - 6 * q^8 + 4 * q^9 - 12 * q^10 + 6 * q^12 - 4 * q^13 - 14 * q^14 + 3 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 + 5 * q^19 - 8 * q^20 - 10 * q^21 + 3 * q^23 + 14 * q^24 + 6 * q^25 - 6 * q^26 - 11 * q^27 + 10 * q^28 - 10 * q^29 - 6 * q^30 + 11 * q^31 - 14 * q^32 - 4 * q^34 + 8 * q^35 - 26 * q^36 + q^37 - 2 * q^38 - 2 * q^39 + 16 * q^40 - 2 * q^41 - 16 * q^42 - 20 * q^43 - 28 * q^45 + 4 * q^46 - 20 * q^47 + 4 * q^48 + 3 * q^49 + 32 * q^50 - 24 * q^51 - 6 * q^52 - 14 * q^53 - 16 * q^54 - 38 * q^56 + q^57 - 6 * q^58 + 3 * q^59 - 40 * q^60 + 10 * q^61 + 6 * q^62 - 24 * q^63 + 9 * q^67 - 24 * q^68 - 5 * q^69 + 50 * q^70 + 23 * q^71 + 12 * q^72 - 8 * q^74 - 18 * q^75 + 6 * q^76 - 22 * q^78 - 44 * q^79 - 18 * q^80 + q^81 - 30 * q^82 + 14 * q^83 - 14 * q^84 + 12 * q^85 + 52 * q^86 - 28 * q^87 - 27 * q^89 - 26 * q^90 + 24 * q^91 + 58 * q^92 - 27 * q^93 + 8 * q^94 - 5 * q^95 - 50 * q^96 + 15 * q^97 + 10 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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