LMFDB - Embedded newform 538.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,2,Mod(1,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("538.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	538.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:	$4.29595162874$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 15x^{5} + 16x^{4} + 49x^{3} - 53x^{2} - 44x + 48 $ x^7 - x^6 - 15x^5 + 16x^4 + 49x^3 - 53x^2 - 44*x + 48
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-3.33118$ of defining polynomial
Character	$\chi$	$=$	538.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +0.366193 q^{3} +1.00000 q^{4} -0.953965 q^{5} +0.366193 q^{6} +3.52894 q^{7} +1.00000 q^{8} -2.86590 q^{9} -0.953965 q^{10} +5.52181 q^{11} +0.366193 q^{12} -3.59708 q^{13} +3.52894 q^{14} -0.349336 q^{15} +1.00000 q^{16} +3.46821 q^{17} -2.86590 q^{18} +3.06529 q^{19} -0.953965 q^{20} +1.29227 q^{21} +5.52181 q^{22} +1.26761 q^{23} +0.366193 q^{24} -4.08995 q^{25} -3.59708 q^{26} -2.14806 q^{27} +3.52894 q^{28} -5.08210 q^{29} -0.349336 q^{30} +6.41035 q^{31} +1.00000 q^{32} +2.02205 q^{33} +3.46821 q^{34} -3.36648 q^{35} -2.86590 q^{36} +5.26979 q^{37} +3.06529 q^{38} -1.31723 q^{39} -0.953965 q^{40} -7.30413 q^{41} +1.29227 q^{42} -7.77528 q^{43} +5.52181 q^{44} +2.73397 q^{45} +1.26761 q^{46} +4.64032 q^{47} +0.366193 q^{48} +5.45340 q^{49} -4.08995 q^{50} +1.27004 q^{51} -3.59708 q^{52} +1.77008 q^{53} -2.14806 q^{54} -5.26761 q^{55} +3.52894 q^{56} +1.12249 q^{57} -5.08210 q^{58} -1.53880 q^{59} -0.349336 q^{60} -12.3708 q^{61} +6.41035 q^{62} -10.1136 q^{63} +1.00000 q^{64} +3.43148 q^{65} +2.02205 q^{66} -7.27990 q^{67} +3.46821 q^{68} +0.464192 q^{69} -3.36648 q^{70} -2.76845 q^{71} -2.86590 q^{72} -14.2747 q^{73} +5.26979 q^{74} -1.49771 q^{75} +3.06529 q^{76} +19.4861 q^{77} -1.31723 q^{78} +2.33688 q^{79} -0.953965 q^{80} +7.81110 q^{81} -7.30413 q^{82} -1.34837 q^{83} +1.29227 q^{84} -3.30855 q^{85} -7.77528 q^{86} -1.86103 q^{87} +5.52181 q^{88} -6.70123 q^{89} +2.73397 q^{90} -12.6939 q^{91} +1.26761 q^{92} +2.34743 q^{93} +4.64032 q^{94} -2.92418 q^{95} +0.366193 q^{96} -0.295411 q^{97} +5.45340 q^{98} -15.8250 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + q^{3} + 7 q^{4} + 7 q^{5} + q^{6} + 6 q^{7} + 7 q^{8} + 12 q^{9} + 7 q^{10} - 3 q^{11} + q^{12} - 9 q^{13} + 6 q^{14} + 8 q^{15} + 7 q^{16} + 8 q^{17} + 12 q^{18} - 11 q^{19} + 7 q^{20}+ \cdots - 37 q^{99}+O(q^{100}) $ 7 * q + 7 * q^2 + q^3 + 7 * q^4 + 7 * q^5 + q^6 + 6 * q^7 + 7 * q^8 + 12 * q^9 + 7 * q^10 - 3 * q^11 + q^12 - 9 * q^13 + 6 * q^14 + 8 * q^15 + 7 * q^16 + 8 * q^17 + 12 * q^18 - 11 * q^19 + 7 * q^20 - 6 * q^21 - 3 * q^22 + 12 * q^23 + q^24 + 22 * q^25 - 9 * q^26 - 14 * q^27 + 6 * q^28 - 5 * q^29 + 8 * q^30 + 14 * q^31 + 7 * q^32 - 4 * q^33 + 8 * q^34 - 4 * q^35 + 12 * q^36 + 13 * q^37 - 11 * q^38 - 18 * q^39 + 7 * q^40 + 12 * q^41 - 6 * q^42 - 11 * q^43 - 3 * q^44 + 3 * q^45 + 12 * q^46 + 2 * q^47 + q^48 + 15 * q^49 + 22 * q^50 - 26 * q^51 - 9 * q^52 + 19 * q^53 - 14 * q^54 - 40 * q^55 + 6 * q^56 - 12 * q^57 - 5 * q^58 - 9 * q^59 + 8 * q^60 - 3 * q^61 + 14 * q^62 - 26 * q^63 + 7 * q^64 - 10 * q^65 - 4 * q^66 - 33 * q^67 + 8 * q^68 - 64 * q^69 - 4 * q^70 + 28 * q^71 + 12 * q^72 - 14 * q^73 + 13 * q^74 - 45 * q^75 - 11 * q^76 + 10 * q^77 - 18 * q^78 + 2 * q^79 + 7 * q^80 + 15 * q^81 + 12 * q^82 - 7 * q^83 - 6 * q^84 - 16 * q^85 - 11 * q^86 + 16 * q^87 - 3 * q^88 + 18 * q^89 + 3 * q^90 - 26 * q^91 + 12 * q^92 + 6 * q^93 + 2 * q^94 - 34 * q^95 + q^96 - 4 * q^97 + 15 * q^98 - 37 * q^99

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
$3$	0.366193	0.211422	0.105711	−	0.994397i	$-0.466288\pi$
$3$	0.366193	0.211422	0.105711	+	0.994397i	$0.466288\pi$
$4$	1.00000	0.500000
$5$	−0.953965	−0.426626	−0.213313	−	0.976984i	$-0.568425\pi$
$5$	−0.953965	−0.426626	−0.213313	+	0.976984i	$0.568425\pi$
$6$	0.366193	0.149498
$7$	3.52894	1.33381	0.666907	−	0.745141i	$-0.267618\pi$
$7$	3.52894	1.33381	0.666907	+	0.745141i	$0.267618\pi$
$8$	1.00000	0.353553
$9$	−2.86590	−0.955301
$10$	−0.953965	−0.301670
$11$	5.52181	1.66489	0.832445	−	0.554108i	$-0.186941\pi$
$11$	5.52181	1.66489	0.832445	+	0.554108i	$0.186941\pi$
$12$	0.366193	0.105711
$13$	−3.59708	−0.997650	−0.498825	−	0.866703i	$-0.666235\pi$
$13$	−3.59708	−0.997650	−0.498825	+	0.866703i	$0.666235\pi$
$14$	3.52894	0.943148
$15$	−0.349336	−0.0901981
$16$	1.00000	0.250000
$17$	3.46821	0.841165	0.420583	−	0.907254i	$-0.361826\pi$
$17$	3.46821	0.841165	0.420583	+	0.907254i	$0.361826\pi$
$18$	−2.86590	−0.675500
$19$	3.06529	0.703226	0.351613	−	0.936145i	$-0.385633\pi$
$19$	3.06529	0.703226	0.351613	+	0.936145i	$0.385633\pi$
$20$	−0.953965	−0.213313
$21$	1.29227	0.281997
$22$	5.52181	1.17725
$23$	1.26761	0.264316	0.132158	−	0.991229i	$-0.457809\pi$
$23$	1.26761	0.264316	0.132158	+	0.991229i	$0.457809\pi$
$24$	0.366193	0.0747489
$25$	−4.08995	−0.817990
$26$	−3.59708	−0.705445
$27$	−2.14806	−0.413393
$28$	3.52894	0.666907
$29$	−5.08210	−0.943722	−0.471861	−	0.881673i	$-0.656418\pi$
$29$	−5.08210	−0.943722	−0.471861	+	0.881673i	$0.656418\pi$
$30$	−0.349336	−0.0637797
$31$	6.41035	1.15133	0.575666	−	0.817685i	$-0.304743\pi$
$31$	6.41035	1.15133	0.575666	+	0.817685i	$0.304743\pi$
$32$	1.00000	0.176777
$33$	2.02205	0.351994
$34$	3.46821	0.594794
$35$	−3.36648	−0.569039
$36$	−2.86590	−0.477650
$37$	5.26979	0.866349	0.433174	−	0.901310i	$-0.357393\pi$
$37$	5.26979	0.866349	0.433174	+	0.901310i	$0.357393\pi$
$38$	3.06529	0.497256
$39$	−1.31723	−0.210925
$40$	−0.953965	−0.150835
$41$	−7.30413	−1.14071	−0.570357	−	0.821397i	$-0.693195\pi$
$41$	−7.30413	−1.14071	−0.570357	+	0.821397i	$0.693195\pi$
$42$	1.29227	0.199402
$43$	−7.77528	−1.18572	−0.592860	−	0.805306i	$-0.702001\pi$
$43$	−7.77528	−1.18572	−0.592860	+	0.805306i	$0.702001\pi$
$44$	5.52181	0.832445
$45$	2.73397	0.407556
$46$	1.26761	0.186899
$47$	4.64032	0.676860	0.338430	−	0.940992i	$-0.390104\pi$
$47$	4.64032	0.676860	0.338430	+	0.940992i	$0.390104\pi$
$48$	0.366193	0.0528555
$49$	5.45340	0.779058
$50$	−4.08995	−0.578407
$51$	1.27004	0.177841
$52$	−3.59708	−0.498825
$53$	1.77008	0.243140	0.121570	−	0.992583i	$-0.461207\pi$
$53$	1.77008	0.243140	0.121570	+	0.992583i	$0.461207\pi$
$54$	−2.14806	−0.292313
$55$	−5.26761	−0.710285
$56$	3.52894	0.471574
$57$	1.12249	0.148677
$58$	−5.08210	−0.667312
$59$	−1.53880	−0.200335	−0.100168	−	0.994971i	$-0.531938\pi$
$59$	−1.53880	−0.200335	−0.100168	+	0.994971i	$0.531938\pi$
$60$	−0.349336	−0.0450990
$61$	−12.3708	−1.58391	−0.791957	−	0.610576i	$-0.790938\pi$
$61$	−12.3708	−1.58391	−0.791957	+	0.610576i	$0.790938\pi$
$62$	6.41035	0.814115
$63$	−10.1136	−1.27419
$64$	1.00000	0.125000
$65$	3.43148	0.425623
$66$	2.02205	0.248897
$67$	−7.27990	−0.889382	−0.444691	−	0.895684i	$-0.646686\pi$
$67$	−7.27990	−0.889382	−0.444691	+	0.895684i	$0.646686\pi$
$68$	3.46821	0.420583
$69$	0.464192	0.0558821
$70$	−3.36648	−0.402372
$71$	−2.76845	−0.328554	−0.164277	−	0.986414i	$-0.552529\pi$
$71$	−2.76845	−0.328554	−0.164277	+	0.986414i	$0.552529\pi$
$72$	−2.86590	−0.337750
$73$	−14.2747	−1.67073	−0.835366	−	0.549693i	$-0.814745\pi$
$73$	−14.2747	−1.67073	−0.835366	+	0.549693i	$0.814745\pi$
$74$	5.26979	0.612601
$75$	−1.49771	−0.172941
$76$	3.06529	0.351613
$77$	19.4861	2.22065
$78$	−1.31723	−0.149147
$79$	2.33688	0.262919	0.131460	−	0.991322i	$-0.458034\pi$
$79$	2.33688	0.262919	0.131460	+	0.991322i	$0.458034\pi$
$80$	−0.953965	−0.106656
$81$	7.81110	0.867900
$82$	−7.30413	−0.806607
$83$	−1.34837	−0.148003	−0.0740013	−	0.997258i	$-0.523577\pi$
$83$	−1.34837	−0.148003	−0.0740013	+	0.997258i	$0.523577\pi$
$84$	1.29227	0.140999
$85$	−3.30855	−0.358863
$86$	−7.77528	−0.838430
$87$	−1.86103	−0.199523
$88$	5.52181	0.588627
$89$	−6.70123	−0.710328	−0.355164	−	0.934804i	$-0.615575\pi$
$89$	−6.70123	−0.710328	−0.355164	+	0.934804i	$0.615575\pi$
$90$	2.73397	0.288186
$91$	−12.6939	−1.33068
$92$	1.26761	0.132158
$93$	2.34743	0.243417
$94$	4.64032	0.478612
$95$	−2.92418	−0.300014
$96$	0.366193	0.0373745
$97$	−0.295411	−0.0299944	−0.0149972	−	0.999888i	$-0.504774\pi$
$97$	−0.295411	−0.0299944	−0.0149972	+	0.999888i	$0.504774\pi$
$98$	5.45340	0.550877
$99$	−15.8250	−1.59047
$100$	−4.08995	−0.408995
$101$	3.14362	0.312802	0.156401	−	0.987694i	$-0.450011\pi$
$101$	3.14362	0.312802	0.156401	+	0.987694i	$0.450011\pi$
$102$	1.27004	0.125752
$103$	−13.0436	−1.28523	−0.642613	−	0.766191i	$-0.722150\pi$
$103$	−13.0436	−1.28523	−0.642613	+	0.766191i	$0.722150\pi$
$104$	−3.59708	−0.352722
$105$	−1.23278	−0.120307
$106$	1.77008	0.171926
$107$	11.9783	1.15799	0.578995	−	0.815331i	$-0.303445\pi$
$107$	11.9783	1.15799	0.578995	+	0.815331i	$0.303445\pi$
$108$	−2.14806	−0.206697
$109$	−7.50255	−0.718614	−0.359307	−	0.933219i	$-0.616987\pi$
$109$	−7.50255	−0.718614	−0.359307	+	0.933219i	$0.616987\pi$
$110$	−5.26761	−0.502247
$111$	1.92976	0.183165
$112$	3.52894	0.333453
$113$	11.9300	1.12228	0.561139	−	0.827722i	$-0.310363\pi$
$113$	11.9300	1.12228	0.561139	+	0.827722i	$0.310363\pi$
$114$	1.12249	0.105131
$115$	−1.20926	−0.112764
$116$	−5.08210	−0.471861
$117$	10.3089	0.953056
$118$	−1.53880	−0.141658
$119$	12.2391	1.12196
$120$	−0.349336	−0.0318898
$121$	19.4904	1.77186
$122$	−12.3708	−1.12000
$123$	−2.67473	−0.241172
$124$	6.41035	0.575666
$125$	8.67149	0.775602
$126$	−10.1136	−0.900990
$127$	1.76310	0.156449	0.0782247	−	0.996936i	$-0.475075\pi$
$127$	1.76310	0.156449	0.0782247	+	0.996936i	$0.475075\pi$
$128$	1.00000	0.0883883
$129$	−2.84726	−0.250687
$130$	3.43148	0.300961
$131$	−8.08575	−0.706455	−0.353228	−	0.935537i	$-0.614916\pi$
$131$	−8.08575	−0.706455	−0.353228	+	0.935537i	$0.614916\pi$
$132$	2.02205	0.175997
$133$	10.8172	0.937972
$134$	−7.27990	−0.628888
$135$	2.04917	0.176364
$136$	3.46821	0.297397
$137$	−6.58186	−0.562326	−0.281163	−	0.959660i	$-0.590720\pi$
$137$	−6.58186	−0.562326	−0.281163	+	0.959660i	$0.590720\pi$
$138$	0.464192	0.0395146
$139$	−13.3633	−1.13346	−0.566728	−	0.823905i	$-0.691791\pi$
$139$	−13.3633	−1.13346	−0.566728	+	0.823905i	$0.691791\pi$
$140$	−3.36648	−0.284520
$141$	1.69925	0.143103
$142$	−2.76845	−0.232323
$143$	−19.8624	−1.66098
$144$	−2.86590	−0.238825
$145$	4.84814	0.402616
$146$	−14.2747	−1.18139
$147$	1.99700	0.164710
$148$	5.26979	0.433174
$149$	10.5913	0.867671	0.433835	−	0.900992i	$-0.357160\pi$
$149$	10.5913	0.867671	0.433835	+	0.900992i	$0.357160\pi$
$150$	−1.49771	−0.122288
$151$	8.26703	0.672761	0.336381	−	0.941726i	$-0.390797\pi$
$151$	8.26703	0.672761	0.336381	+	0.941726i	$0.390797\pi$
$152$	3.06529	0.248628
$153$	−9.93956	−0.803566
$154$	19.4861	1.57024
$155$	−6.11525	−0.491188
$156$	−1.31723	−0.105463
$157$	−18.0608	−1.44141	−0.720705	−	0.693242i	$-0.756182\pi$
$157$	−18.0608	−1.44141	−0.720705	+	0.693242i	$0.756182\pi$
$158$	2.33688	0.185912
$159$	0.648193	0.0514051
$160$	−0.953965	−0.0754175
$161$	4.47333	0.352548
$162$	7.81110	0.613698
$163$	−4.53006	−0.354822	−0.177411	−	0.984137i	$-0.556772\pi$
$163$	−4.53006	−0.354822	−0.177411	+	0.984137i	$0.556772\pi$
$164$	−7.30413	−0.570357
$165$	−1.92897	−0.150170
$166$	−1.34837	−0.104654
$167$	−11.6274	−0.899753	−0.449876	−	0.893091i	$-0.648532\pi$
$167$	−11.6274	−0.899753	−0.449876	+	0.893091i	$0.648532\pi$
$168$	1.29227	0.0997011
$169$	−0.0610353	−0.00469502
$170$	−3.30855	−0.253754
$171$	−8.78482	−0.671792
$172$	−7.77528	−0.592860
$173$	19.3718	1.47281	0.736406	−	0.676540i	$-0.236521\pi$
$173$	19.3718	1.47281	0.736406	+	0.676540i	$0.236521\pi$
$174$	−1.86103	−0.141084
$175$	−14.4332	−1.09105
$176$	5.52181	0.416222
$177$	−0.563500	−0.0423552
$178$	−6.70123	−0.502278
$179$	15.3979	1.15090	0.575448	−	0.817838i	$-0.304828\pi$
$179$	15.3979	1.15090	0.575448	+	0.817838i	$0.304828\pi$
$180$	2.73397	0.203778
$181$	4.31917	0.321041	0.160521	−	0.987032i	$-0.448683\pi$
$181$	4.31917	0.321041	0.160521	+	0.987032i	$0.448683\pi$
$182$	−12.6939	−0.940932
$183$	−4.53010	−0.334874
$184$	1.26761	0.0934497
$185$	−5.02720	−0.369607
$186$	2.34743	0.172122
$187$	19.1508	1.40045
$188$	4.64032	0.338430
$189$	−7.58035	−0.551390
$190$	−2.92418	−0.212142
$191$	13.7202	0.992762	0.496381	−	0.868105i	$-0.334662\pi$
$191$	13.7202	0.992762	0.496381	+	0.868105i	$0.334662\pi$
$192$	0.366193	0.0264277
$193$	7.51242	0.540756	0.270378	−	0.962754i	$-0.412851\pi$
$193$	7.51242	0.540756	0.270378	+	0.962754i	$0.412851\pi$
$194$	−0.295411	−0.0212093
$195$	1.25659	0.0899861
$196$	5.45340	0.389529
$197$	−23.5591	−1.67852	−0.839258	−	0.543733i	$-0.817010\pi$
$197$	−23.5591	−1.67852	−0.839258	+	0.543733i	$0.817010\pi$
$198$	−15.8250	−1.12463
$199$	16.7895	1.19018	0.595088	−	0.803660i	$-0.297117\pi$
$199$	16.7895	1.19018	0.595088	+	0.803660i	$0.297117\pi$
$200$	−4.08995	−0.289203
$201$	−2.66585	−0.188035
$202$	3.14362	0.221185
$203$	−17.9344	−1.25875
$204$	1.27004	0.0889204
$205$	6.96789	0.486658
$206$	−13.0436	−0.908792
$207$	−3.63286	−0.252501
$208$	−3.59708	−0.249412
$209$	16.9260	1.17079
$210$	−1.23278	−0.0850702
$211$	12.8667	0.885778	0.442889	−	0.896577i	$-0.353954\pi$
$211$	12.8667	0.885778	0.442889	+	0.896577i	$0.353954\pi$
$212$	1.77008	0.121570
$213$	−1.01379	−0.0694636
$214$	11.9783	0.818822
$215$	7.41734	0.505859
$216$	−2.14806	−0.146157
$217$	22.6217	1.53566
$218$	−7.50255	−0.508137
$219$	−5.22732	−0.353230
$220$	−5.26761	−0.355142
$221$	−12.4754	−0.839188
$222$	1.92976	0.129517
$223$	18.0816	1.21083	0.605416	−	0.795909i	$-0.293007\pi$
$223$	18.0816	1.21083	0.605416	+	0.795909i	$0.293007\pi$
$224$	3.52894	0.235787
$225$	11.7214	0.781427
$226$	11.9300	0.793571
$227$	−4.79467	−0.318233	−0.159117	−	0.987260i	$-0.550865\pi$
$227$	−4.79467	−0.318233	−0.159117	+	0.987260i	$0.550865\pi$
$228$	1.12249	0.0743387
$229$	−20.1770	−1.33334	−0.666668	−	0.745354i	$-0.732280\pi$
$229$	−20.1770	−1.33334	−0.666668	+	0.745354i	$0.732280\pi$
$230$	−1.20926	−0.0797361
$231$	7.13570	0.469494
$232$	−5.08210	−0.333656
$233$	16.7595	1.09795	0.548976	−	0.835838i	$-0.315018\pi$
$233$	16.7595	1.09795	0.548976	+	0.835838i	$0.315018\pi$
$234$	10.3089	0.673912
$235$	−4.42670	−0.288766
$236$	−1.53880	−0.100168
$237$	0.855750	0.0555869
$238$	12.2391	0.793344
$239$	26.7477	1.73016	0.865082	−	0.501631i	$-0.167266\pi$
$239$	26.7477	1.73016	0.865082	+	0.501631i	$0.167266\pi$
$240$	−0.349336	−0.0225495
$241$	−3.58966	−0.231231	−0.115615	−	0.993294i	$-0.536884\pi$
$241$	−3.58966	−0.231231	−0.115615	+	0.993294i	$0.536884\pi$
$242$	19.4904	1.25289
$243$	9.30454	0.596887
$244$	−12.3708	−0.791957
$245$	−5.20235	−0.332366
$246$	−2.67473	−0.170534
$247$	−11.0261	−0.701573
$248$	6.41035	0.407058
$249$	−0.493763	−0.0312910
$250$	8.67149	0.548433
$251$	10.9688	0.692343	0.346171	−	0.938171i	$-0.387482\pi$
$251$	10.9688	0.692343	0.346171	+	0.938171i	$0.387482\pi$
$252$	−10.1136	−0.637096
$253$	6.99952	0.440056
$254$	1.76310	0.110627
$255$	−1.21157	−0.0758715
$256$	1.00000	0.0625000
$257$	2.02263	0.126168	0.0630842	−	0.998008i	$-0.479906\pi$
$257$	2.02263	0.126168	0.0630842	+	0.998008i	$0.479906\pi$
$258$	−2.84726	−0.177263
$259$	18.5968	1.15555
$260$	3.43148	0.212812
$261$	14.5648	0.901538
$262$	−8.08575	−0.499539
$263$	26.8669	1.65669	0.828343	−	0.560222i	$-0.189284\pi$
$263$	26.8669	1.65669	0.828343	+	0.560222i	$0.189284\pi$
$264$	2.02205	0.124449
$265$	−1.68860	−0.103730
$266$	10.8172	0.663246
$267$	−2.45395	−0.150179
$268$	−7.27990	−0.444691
$269$	−1.00000	−0.0609711
$269$	−1.00000	−0.0609711
$270$	2.04917	0.124708
$271$	−10.0261	−0.609042	−0.304521	−	0.952506i	$-0.598496\pi$
$271$	−10.0261	−0.609042	−0.304521	+	0.952506i	$0.598496\pi$
$272$	3.46821	0.210291
$273$	−4.64841	−0.281335
$274$	−6.58186	−0.397625
$275$	−22.5839	−1.36186
$276$	0.464192	0.0279411
$277$	12.9817	0.779996	0.389998	−	0.920816i	$-0.372476\pi$
$277$	12.9817	0.779996	0.389998	+	0.920816i	$0.372476\pi$
$278$	−13.3633	−0.801475
$279$	−18.3714	−1.09987
$280$	−3.36648	−0.201186
$281$	0.123363	0.00735920	0.00367960	−	0.999993i	$-0.498829\pi$
$281$	0.123363	0.00735920	0.00367960	+	0.999993i	$0.498829\pi$
$282$	1.69925	0.101189
$283$	−17.9921	−1.06952	−0.534761	−	0.845004i	$-0.679598\pi$
$283$	−17.9921	−1.06952	−0.534761	+	0.845004i	$0.679598\pi$
$284$	−2.76845	−0.164277
$285$	−1.07082	−0.0634296
$286$	−19.8624	−1.17449
$287$	−25.7758	−1.52150
$288$	−2.86590	−0.168875
$289$	−4.97150	−0.292441
$290$	4.84814	0.284693
$291$	−0.108178	−0.00634148
$292$	−14.2747	−0.835366
$293$	−24.1343	−1.40994	−0.704971	−	0.709236i	$-0.749040\pi$
$293$	−24.1343	−1.40994	−0.704971	+	0.709236i	$0.749040\pi$
$294$	1.99700	0.116467
$295$	1.46796	0.0854682
$296$	5.26979	0.306301
$297$	−11.8612	−0.688254
$298$	10.5913	0.613536
$299$	−4.55970	−0.263694
$300$	−1.49771	−0.0864705
$301$	−27.4385	−1.58153
$302$	8.26703	0.475714
$303$	1.15117	0.0661333
$304$	3.06529	0.175806
$305$	11.8013	0.675739
$306$	−9.93956	−0.568207
$307$	34.4288	1.96496	0.982479	−	0.186374i	$-0.0596738\pi$
$307$	34.4288	1.96496	0.982479	+	0.186374i	$0.0596738\pi$
$308$	19.4861	1.11033
$309$	−4.77649	−0.271725
$310$	−6.11525	−0.347323
$311$	9.08138	0.514958	0.257479	−	0.966284i	$-0.417108\pi$
$311$	9.08138	0.514958	0.257479	+	0.966284i	$0.417108\pi$
$312$	−1.31723	−0.0745733
$313$	−8.21382	−0.464273	−0.232136	−	0.972683i	$-0.574572\pi$
$313$	−8.21382	−0.464273	−0.232136	+	0.972683i	$0.574572\pi$
$314$	−18.0608	−1.01923
$315$	9.64801	0.543604
$316$	2.33688	0.131460
$317$	24.0949	1.35330	0.676652	−	0.736303i	$-0.263430\pi$
$317$	24.0949	1.35330	0.676652	+	0.736303i	$0.263430\pi$
$318$	0.648193	0.0363489
$319$	−28.0624	−1.57119
$320$	−0.953965	−0.0533282
$321$	4.38639	0.244824
$322$	4.47333	0.249289
$323$	10.6311	0.591529
$324$	7.81110	0.433950
$325$	14.7119	0.816068
$326$	−4.53006	−0.250897
$327$	−2.74739	−0.151931
$328$	−7.30413	−0.403303
$329$	16.3754	0.902804
$330$	−1.92897	−0.106186
$331$	−19.8778	−1.09259	−0.546293	−	0.837594i	$-0.683961\pi$
$331$	−19.8778	−1.09259	−0.546293	+	0.837594i	$0.683961\pi$
$332$	−1.34837	−0.0740013
$333$	−15.1027	−0.827624
$334$	−11.6274	−0.636221
$335$	6.94477	0.379433
$336$	1.29227	0.0704993
$337$	35.6300	1.94089	0.970445	−	0.241321i	$-0.0775808\pi$
$337$	35.6300	1.94089	0.970445	+	0.241321i	$0.0775808\pi$
$338$	−0.0610353	−0.00331988
$339$	4.36868	0.237274
$340$	−3.30855	−0.179431
$341$	35.3967	1.91684
$342$	−8.78482	−0.475029
$343$	−5.45784	−0.294696
$344$	−7.77528	−0.419215
$345$	−0.442822	−0.0238408
$346$	19.3718	1.04143
$347$	−24.3435	−1.30683	−0.653414	−	0.757001i	$-0.726664\pi$
$347$	−24.3435	−1.30683	−0.653414	+	0.757001i	$0.726664\pi$
$348$	−1.86103	−0.0997617
$349$	11.5437	0.617922	0.308961	−	0.951075i	$-0.400019\pi$
$349$	11.5437	0.617922	0.308961	+	0.951075i	$0.400019\pi$
$350$	−14.4332	−0.771486
$351$	7.72672	0.412422
$352$	5.52181	0.294314
$353$	22.7530	1.21102	0.605509	−	0.795838i	$-0.292969\pi$
$353$	22.7530	1.21102	0.605509	+	0.795838i	$0.292969\pi$
$354$	−0.563500	−0.0299497
$355$	2.64100	0.140170
$356$	−6.70123	−0.355164
$357$	4.48188	0.237206
$358$	15.3979	0.813806
$359$	11.4035	0.601856	0.300928	−	0.953647i	$-0.402704\pi$
$359$	11.4035	0.601856	0.300928	+	0.953647i	$0.402704\pi$
$360$	2.73397	0.144093
$361$	−9.60399	−0.505473
$362$	4.31917	0.227010
$363$	7.13726	0.374609
$364$	−12.6939	−0.665339
$365$	13.6176	0.712778
$366$	−4.53010	−0.236792
$367$	20.4480	1.06738	0.533688	−	0.845682i	$-0.320806\pi$
$367$	20.4480	1.06738	0.533688	+	0.845682i	$0.320806\pi$
$368$	1.26761	0.0660789
$369$	20.9329	1.08973
$370$	−5.02720	−0.261351
$371$	6.24652	0.324303
$372$	2.34743	0.121708
$373$	1.94797	0.100862	0.0504310	−	0.998728i	$-0.483941\pi$
$373$	1.94797	0.100862	0.0504310	+	0.998728i	$0.483941\pi$
$374$	19.1508	0.990265
$375$	3.17544	0.163979
$376$	4.64032	0.239306
$377$	18.2807	0.941504
$378$	−7.58035	−0.389891
$379$	−28.6786	−1.47312	−0.736560	−	0.676373i	$-0.763551\pi$
$379$	−28.6786	−1.47312	−0.736560	+	0.676373i	$0.763551\pi$
$380$	−2.92418	−0.150007
$381$	0.645634	0.0330769
$382$	13.7202	0.701989
$383$	30.8761	1.57769	0.788847	−	0.614590i	$-0.210679\pi$
$383$	30.8761	1.57769	0.788847	+	0.614590i	$0.210679\pi$
$384$	0.366193	0.0186872
$385$	−18.5891	−0.947387
$386$	7.51242	0.382372
$387$	22.2832	1.13272
$388$	−0.295411	−0.0149972
$389$	8.80642	0.446503	0.223252	−	0.974761i	$-0.428333\pi$
$389$	8.80642	0.446503	0.223252	+	0.974761i	$0.428333\pi$
$390$	1.25659	0.0636298
$391$	4.39635	0.222333
$392$	5.45340	0.275439
$393$	−2.96095	−0.149360
$394$	−23.5591	−1.18689
$395$	−2.22930	−0.112168
$396$	−15.8250	−0.795235
$397$	−23.1484	−1.16178	−0.580892	−	0.813980i	$-0.697296\pi$
$397$	−23.1484	−1.16178	−0.580892	+	0.813980i	$0.697296\pi$
$398$	16.7895	0.841582
$399$	3.96120	0.198308
$400$	−4.08995	−0.204498
$401$	−34.8697	−1.74131	−0.870655	−	0.491894i	$-0.836305\pi$
$401$	−34.8697	−1.74131	−0.870655	+	0.491894i	$0.836305\pi$
$402$	−2.66585	−0.132961
$403$	−23.0585	−1.14863
$404$	3.14362	0.156401
$405$	−7.45152	−0.370269
$406$	−17.9344	−0.890070
$407$	29.0988	1.44237
$408$	1.27004	0.0628762
$409$	38.0864	1.88325	0.941626	−	0.336662i	$-0.109298\pi$
$409$	38.0864	1.88325	0.941626	+	0.336662i	$0.109298\pi$
$410$	6.96789	0.344119
$411$	−2.41023	−0.118888
$412$	−13.0436	−0.642613
$413$	−5.43034	−0.267210
$414$	−3.63286	−0.178545
$415$	1.28629	0.0631417
$416$	−3.59708	−0.176361
$417$	−4.89354	−0.239637
$418$	16.9260	0.827876
$419$	−25.0709	−1.22479	−0.612397	−	0.790550i	$-0.709795\pi$
$419$	−25.0709	−1.22479	−0.612397	+	0.790550i	$0.709795\pi$
$420$	−1.23278	−0.0601537
$421$	35.9462	1.75191	0.875954	−	0.482394i	$-0.160233\pi$
$421$	35.9462	1.75191	0.875954	+	0.482394i	$0.160233\pi$
$422$	12.8667	0.626339
$423$	−13.2987	−0.646605
$424$	1.77008	0.0859629
$425$	−14.1848	−0.688065
$426$	−1.01379	−0.0491182
$427$	−43.6557	−2.11265
$428$	11.9783	0.578995
$429$	−7.27348	−0.351167
$430$	7.41734	0.357696
$431$	4.34025	0.209063	0.104531	−	0.994522i	$-0.466666\pi$
$431$	4.34025	0.209063	0.104531	+	0.994522i	$0.466666\pi$
$432$	−2.14806	−0.103348
$433$	−34.4524	−1.65568	−0.827838	−	0.560967i	$-0.810429\pi$
$433$	−34.4524	−1.65568	−0.827838	+	0.560967i	$0.810429\pi$
$434$	22.6217	1.08588
$435$	1.77536	0.0851219
$436$	−7.50255	−0.359307
$437$	3.88560	0.185874
$438$	−5.22732	−0.249771
$439$	−35.3209	−1.68577	−0.842887	−	0.538091i	$-0.819146\pi$
$439$	−35.3209	−1.68577	−0.842887	+	0.538091i	$0.819146\pi$
$440$	−5.26761	−0.251124
$441$	−15.6289	−0.744235
$442$	−12.4754	−0.593396
$443$	13.5348	0.643057	0.321528	−	0.946900i	$-0.395803\pi$
$443$	13.5348	0.643057	0.321528	+	0.946900i	$0.395803\pi$
$444$	1.92976	0.0915825
$445$	6.39273	0.303045
$446$	18.0816	0.856188
$447$	3.87845	0.183445
$448$	3.52894	0.166727
$449$	−41.1462	−1.94181	−0.970906	−	0.239463i	$-0.923029\pi$
$449$	−41.1462	−1.94181	−0.970906	+	0.239463i	$0.923029\pi$
$450$	11.7214	0.552552
$451$	−40.3321	−1.89916
$452$	11.9300	0.561139
$453$	3.02733	0.142237
$454$	−4.79467	−0.225025
$455$	12.1095	0.567702
$456$	1.12249	0.0525654
$457$	19.1640	0.896454	0.448227	−	0.893920i	$-0.352056\pi$
$457$	19.1640	0.896454	0.448227	+	0.893920i	$0.352056\pi$
$458$	−20.1770	−0.942812
$459$	−7.44991	−0.347732
$460$	−1.20926	−0.0563819
$461$	16.5267	0.769723	0.384861	−	0.922974i	$-0.374249\pi$
$461$	16.5267	0.769723	0.384861	+	0.922974i	$0.374249\pi$
$462$	7.13570	0.331983
$463$	−1.24318	−0.0577753	−0.0288876	−	0.999583i	$-0.509197\pi$
$463$	−1.24318	−0.0577753	−0.0288876	+	0.999583i	$0.509197\pi$
$464$	−5.08210	−0.235930
$465$	−2.23936	−0.103848
$466$	16.7595	0.776369
$467$	−1.12302	−0.0519674	−0.0259837	−	0.999662i	$-0.508272\pi$
$467$	−1.12302	−0.0519674	−0.0259837	+	0.999662i	$0.508272\pi$
$468$	10.3089	0.476528
$469$	−25.6903	−1.18627
$470$	−4.42670	−0.204188
$471$	−6.61375	−0.304746
$472$	−1.53880	−0.0708292
$473$	−42.9337	−1.97409
$474$	0.855750	0.0393059
$475$	−12.5369	−0.575232
$476$	12.2391	0.560979
$477$	−5.07289	−0.232272
$478$	26.7477	1.22341
$479$	3.92860	0.179502	0.0897512	−	0.995964i	$-0.471393\pi$
$479$	3.92860	0.179502	0.0897512	+	0.995964i	$0.471393\pi$
$480$	−0.349336	−0.0159449
$481$	−18.9559	−0.864313
$482$	−3.58966	−0.163505
$483$	1.63810	0.0745363
$484$	19.4904	0.885928
$485$	0.281812	0.0127964
$486$	9.30454	0.422063
$487$	22.0296	0.998258	0.499129	−	0.866528i	$-0.333653\pi$
$487$	22.0296	0.998258	0.499129	+	0.866528i	$0.333653\pi$
$488$	−12.3708	−0.559998
$489$	−1.65888	−0.0750172
$490$	−5.20235	−0.235018
$491$	−40.3244	−1.81982	−0.909908	−	0.414811i	$-0.863848\pi$
$491$	−40.3244	−1.81982	−0.909908	+	0.414811i	$0.863848\pi$
$492$	−2.67473	−0.120586
$493$	−17.6258	−0.793826
$494$	−11.0261	−0.496087
$495$	15.0965	0.678536
$496$	6.41035	0.287833
$497$	−9.76968	−0.438230
$498$	−0.493763	−0.0221261
$499$	−11.2449	−0.503390	−0.251695	−	0.967807i	$-0.580988\pi$
$499$	−11.2449	−0.503390	−0.251695	+	0.967807i	$0.580988\pi$
$500$	8.67149	0.387801
$501$	−4.25787	−0.190227
$502$	10.9688	0.489560
$503$	10.6249	0.473739	0.236870	−	0.971541i	$-0.423879\pi$
$503$	10.6249	0.473739	0.236870	+	0.971541i	$0.423879\pi$
$504$	−10.1136	−0.450495
$505$	−2.99891	−0.133450
$506$	6.99952	0.311167
$507$	−0.0223507	−0.000992630 0
$508$	1.76310	0.0782247
$509$	−30.7681	−1.36377	−0.681886	−	0.731459i	$-0.738840\pi$
$509$	−30.7681	−1.36377	−0.681886	+	0.731459i	$0.738840\pi$
$510$	−1.21157	−0.0536492
$511$	−50.3747	−2.22845
$512$	1.00000	0.0441942
$513$	−6.58441	−0.290709
$514$	2.02263	0.0892146
$515$	12.4432	0.548311
$516$	−2.84726	−0.125344
$517$	25.6230	1.12690
$518$	18.5968	0.817095
$519$	7.09383	0.311385
$520$	3.43148	0.150481
$521$	−29.6851	−1.30053	−0.650264	−	0.759709i	$-0.725342\pi$
$521$	−29.6851	−1.30053	−0.650264	+	0.759709i	$0.725342\pi$
$522$	14.5648	0.637484
$523$	2.68567	0.117436	0.0587180	−	0.998275i	$-0.481299\pi$
$523$	2.68567	0.117436	0.0587180	+	0.998275i	$0.481299\pi$
$524$	−8.08575	−0.353228
$525$	−5.28534	−0.230671
$526$	26.8669	1.17145
$527$	22.2325	0.968461
$528$	2.02205	0.0879985
$529$	−21.3932	−0.930137
$530$	−1.68860	−0.0733480
$531$	4.41006	0.191380
$532$	10.8172	0.468986
$533$	26.2735	1.13803
$534$	−2.45395	−0.106193
$535$	−11.4269	−0.494028
$536$	−7.27990	−0.314444
$537$	5.63862	0.243325
$538$	−1.00000	−0.0431131
$539$	30.1127	1.29704
$540$	2.04917	0.0881822
$541$	1.40108	0.0602370	0.0301185	−	0.999546i	$-0.490412\pi$
$541$	1.40108	0.0602370	0.0301185	+	0.999546i	$0.490412\pi$
$542$	−10.0261	−0.430658
$543$	1.58165	0.0678751
$544$	3.46821	0.148698
$545$	7.15717	0.306580
$546$	−4.64841	−0.198934
$547$	−5.48870	−0.234680	−0.117340	−	0.993092i	$-0.537437\pi$
$547$	−5.48870	−0.234680	−0.117340	+	0.993092i	$0.537437\pi$
$548$	−6.58186	−0.281163
$549$	35.4534	1.51312
$550$	−22.5839	−0.962983
$551$	−15.5781	−0.663649
$552$	0.464192	0.0197573
$553$	8.24670	0.350685
$554$	12.9817	0.551541
$555$	−1.84093	−0.0781430
$556$	−13.3633	−0.566728
$557$	−41.2445	−1.74759	−0.873793	−	0.486298i	$-0.838347\pi$
$557$	−41.2445	−1.74759	−0.873793	+	0.486298i	$0.838347\pi$
$558$	−18.3714	−0.777725
$559$	27.9683	1.18293
$560$	−3.36648	−0.142260
$561$	7.01291	0.296085
$562$	0.123363	0.00520374
$563$	−12.2378	−0.515763	−0.257881	−	0.966177i	$-0.583024\pi$
$563$	−12.2378	−0.515763	−0.257881	+	0.966177i	$0.583024\pi$
$564$	1.69925	0.0715515
$565$	−11.3808	−0.478793
$566$	−17.9921	−0.756266
$567$	27.5649	1.15762
$568$	−2.76845	−0.116162
$569$	−21.5337	−0.902740	−0.451370	−	0.892337i	$-0.649065\pi$
$569$	−21.5337	−0.902740	−0.451370	+	0.892337i	$0.649065\pi$
$570$	−1.07082	−0.0448515
$571$	−39.3756	−1.64782	−0.823908	−	0.566724i	$-0.808211\pi$
$571$	−39.3756	−1.64782	−0.823908	+	0.566724i	$0.808211\pi$
$572$	−19.8624	−0.830488
$573$	5.02426	0.209892
$574$	−25.7758	−1.07586
$575$	−5.18448	−0.216208
$576$	−2.86590	−0.119413
$577$	37.6215	1.56620	0.783101	−	0.621894i	$-0.213637\pi$
$577$	37.6215	1.56620	0.783101	+	0.621894i	$0.213637\pi$
$578$	−4.97150	−0.206787
$579$	2.75100	0.114328
$580$	4.84814	0.201308
$581$	−4.75830	−0.197408
$582$	−0.108178	−0.00448411
$583$	9.77408	0.404801
$584$	−14.2747	−0.590693
$585$	−9.83430	−0.406598
$586$	−24.1343	−0.996980
$587$	−10.1725	−0.419865	−0.209933	−	0.977716i	$-0.567325\pi$
$587$	−10.1725	−0.419865	−0.209933	+	0.977716i	$0.567325\pi$
$588$	1.99700	0.0823549
$589$	19.6496	0.809647
$590$	1.46796	0.0604351
$591$	−8.62719	−0.354875
$592$	5.26979	0.216587
$593$	−20.4503	−0.839795	−0.419897	−	0.907572i	$-0.637934\pi$
$593$	−20.4503	−0.839795	−0.419897	+	0.907572i	$0.637934\pi$
$594$	−11.8612	−0.486669
$595$	−11.6757	−0.478656
$596$	10.5913	0.433835
$597$	6.14821	0.251629
$598$	−4.55970	−0.186460
$599$	−13.3902	−0.547108	−0.273554	−	0.961857i	$-0.588199\pi$
$599$	−13.3902	−0.547108	−0.273554	+	0.961857i	$0.588199\pi$
$600$	−1.49771	−0.0611439
$601$	−21.4300	−0.874150	−0.437075	−	0.899425i	$-0.643986\pi$
$601$	−21.4300	−0.874150	−0.437075	+	0.899425i	$0.643986\pi$
$602$	−27.4385	−1.11831
$603$	20.8635	0.849627
$604$	8.26703	0.336381
$605$	−18.5932	−0.755919
$606$	1.15117	0.0467633
$607$	−18.8668	−0.765780	−0.382890	−	0.923794i	$-0.625071\pi$
$607$	−18.8668	−0.765780	−0.382890	+	0.923794i	$0.625071\pi$
$608$	3.06529	0.124314
$609$	−6.56746	−0.266127
$610$	11.8013	0.477820
$611$	−16.6916	−0.675269
$612$	−9.93956	−0.401783
$613$	−46.5134	−1.87866	−0.939330	−	0.343014i	$-0.888552\pi$
$613$	−46.5134	−1.87866	−0.939330	+	0.343014i	$0.888552\pi$
$614$	34.4288	1.38943
$615$	2.55159	0.102890
$616$	19.4861	0.785119
$617$	13.3038	0.535590	0.267795	−	0.963476i	$-0.413705\pi$
$617$	13.3038	0.535590	0.267795	+	0.963476i	$0.413705\pi$
$618$	−4.77649	−0.192139
$619$	8.74154	0.351352	0.175676	−	0.984448i	$-0.443789\pi$
$619$	8.74154	0.351352	0.175676	+	0.984448i	$0.443789\pi$
$620$	−6.11525	−0.245594
$621$	−2.72290	−0.109266
$622$	9.08138	0.364130
$623$	−23.6482	−0.947446
$624$	−1.31723	−0.0527313
$625$	12.1775	0.487099
$626$	−8.21382	−0.328290
$627$	6.19818	0.247531
$628$	−18.0608	−0.720705
$629$	18.2768	0.728742
$630$	9.64801	0.384386
$631$	44.8284	1.78459	0.892296	−	0.451451i	$-0.149094\pi$
$631$	44.8284	1.78459	0.892296	+	0.451451i	$0.149094\pi$
$632$	2.33688	0.0929560
$633$	4.71169	0.187273
$634$	24.0949	0.956931
$635$	−1.68193	−0.0667454
$636$	0.648193	0.0257025
$637$	−19.6163	−0.777227
$638$	−28.0624	−1.11100
$639$	7.93410	0.313868
$640$	−0.953965	−0.0377088
$641$	−24.7311	−0.976821	−0.488411	−	0.872614i	$-0.662423\pi$
$641$	−24.7311	−0.976821	−0.488411	+	0.872614i	$0.662423\pi$
$642$	4.38639	0.173117
$643$	26.6842	1.05232	0.526161	−	0.850385i	$-0.323631\pi$
$643$	26.6842	1.05232	0.526161	+	0.850385i	$0.323631\pi$
$644$	4.47333	0.176274
$645$	2.71618	0.106950
$646$	10.6311	0.418274
$647$	24.7663	0.973664	0.486832	−	0.873496i	$-0.338152\pi$
$647$	24.7663	0.973664	0.486832	+	0.873496i	$0.338152\pi$
$648$	7.81110	0.306849
$649$	−8.49699	−0.333536
$650$	14.7119	0.577047
$651$	8.28393	0.324673
$652$	−4.53006	−0.177411
$653$	3.58804	0.140411	0.0702055	−	0.997533i	$-0.477634\pi$
$653$	3.58804	0.140411	0.0702055	+	0.997533i	$0.477634\pi$
$654$	−2.74739	−0.107431
$655$	7.71352	0.301392
$656$	−7.30413	−0.285179
$657$	40.9100	1.59605
$658$	16.3754	0.638379
$659$	46.3745	1.80649	0.903247	−	0.429120i	$-0.141176\pi$
$659$	46.3745	1.80649	0.903247	+	0.429120i	$0.141176\pi$
$660$	−1.92897	−0.0750849
$661$	13.4389	0.522711	0.261356	−	0.965243i	$-0.415831\pi$
$661$	13.4389	0.522711	0.261356	+	0.965243i	$0.415831\pi$
$662$	−19.8778	−0.772574
$663$	−4.56842	−0.177423
$664$	−1.34837	−0.0523268
$665$	−10.3192	−0.400163
$666$	−15.1027	−0.585218
$667$	−6.44213	−0.249440
$668$	−11.6274	−0.449876
$669$	6.62136	0.255996
$670$	6.94477	0.268300
$671$	−68.3091	−2.63704
$672$	1.29227	0.0498506
$673$	42.0333	1.62027	0.810133	−	0.586246i	$-0.199395\pi$
$673$	42.0333	1.62027	0.810133	+	0.586246i	$0.199395\pi$
$674$	35.6300	1.37242
$675$	8.78544	0.338152
$676$	−0.0610353	−0.00234751
$677$	29.0946	1.11819	0.559097	−	0.829102i	$-0.311148\pi$
$677$	29.0946	1.11819	0.559097	+	0.829102i	$0.311148\pi$
$678$	4.36868	0.167778
$679$	−1.04249	−0.0400070
$680$	−3.30855	−0.126877
$681$	−1.75578	−0.0672815
$682$	35.3967	1.35541
$683$	22.4564	0.859270	0.429635	−	0.903003i	$-0.358642\pi$
$683$	22.4564	0.859270	0.429635	+	0.903003i	$0.358642\pi$
$684$	−8.78482	−0.335896
$685$	6.27886	0.239903
$686$	−5.45784	−0.208381
$687$	−7.38870	−0.281897
$688$	−7.77528	−0.296430
$689$	−6.36713	−0.242568
$690$	−0.442822	−0.0168580
$691$	−43.8859	−1.66950	−0.834749	−	0.550630i	$-0.814388\pi$
$691$	−43.8859	−1.66950	−0.834749	+	0.550630i	$0.814388\pi$
$692$	19.3718	0.736406
$693$	−55.8454	−2.12139
$694$	−24.3435	−0.924066
$695$	12.7481	0.483562
$696$	−1.86103	−0.0705422
$697$	−25.3323	−0.959529
$698$	11.5437	0.436937
$699$	6.13722	0.232131
$700$	−14.4332	−0.545523
$701$	11.9976	0.453144	0.226572	−	0.973994i	$-0.427248\pi$
$701$	11.9976	0.453144	0.226572	+	0.973994i	$0.427248\pi$
$702$	7.72672	0.291626
$703$	16.1534	0.609239
$704$	5.52181	0.208111
$705$	−1.62103	−0.0610514
$706$	22.7530	0.856320
$707$	11.0937	0.417220
$708$	−0.563500	−0.0211776
$709$	30.2648	1.13662	0.568308	−	0.822816i	$-0.307598\pi$
$709$	30.2648	1.13662	0.568308	+	0.822816i	$0.307598\pi$
$710$	2.64100	0.0991150
$711$	−6.69727	−0.251167
$712$	−6.70123	−0.251139
$713$	8.12584	0.304315
$714$	4.48188	0.167730
$715$	18.9480	0.708615
$716$	15.3979	0.575448
$717$	9.79483	0.365795
$718$	11.4035	0.425576
$719$	40.3460	1.50465	0.752326	−	0.658791i	$-0.228932\pi$
$719$	40.3460	1.50465	0.752326	+	0.658791i	$0.228932\pi$
$720$	2.73397	0.101889
$721$	−46.0301	−1.71425
$722$	−9.60399	−0.357424
$723$	−1.31451	−0.0488872
$724$	4.31917	0.160521
$725$	20.7855	0.771955
$726$	7.13726	0.264889
$727$	−4.67361	−0.173335	−0.0866673	−	0.996237i	$-0.527622\pi$
$727$	−4.67361	−0.173335	−0.0866673	+	0.996237i	$0.527622\pi$
$728$	−12.6939	−0.470466
$729$	−20.0260	−0.741705
$730$	13.6176	0.504010
$731$	−26.9663	−0.997386
$732$	−4.53010	−0.167437
$733$	−27.6280	−1.02046	−0.510231	−	0.860037i	$-0.670440\pi$
$733$	−27.6280	−1.02046	−0.510231	+	0.860037i	$0.670440\pi$
$734$	20.4480	0.754748
$735$	−1.90507	−0.0702695
$736$	1.26761	0.0467248
$737$	−40.1983	−1.48072
$738$	20.9329	0.770552
$739$	43.1959	1.58899	0.794493	−	0.607273i	$-0.207737\pi$
$739$	43.1959	1.58899	0.794493	+	0.607273i	$0.207737\pi$
$740$	−5.02720	−0.184803
$741$	−4.03768	−0.148328
$742$	6.24652	0.229317
$743$	29.1755	1.07034	0.535172	−	0.844743i	$-0.320247\pi$
$743$	29.1755	1.07034	0.535172	+	0.844743i	$0.320247\pi$
$744$	2.34743	0.0860609
$745$	−10.1037	−0.370171
$746$	1.94797	0.0713201
$747$	3.86429	0.141387
$748$	19.1508	0.700223
$749$	42.2708	1.54454
$750$	3.17544	0.115951
$751$	15.7867	0.576066	0.288033	−	0.957621i	$-0.406999\pi$
$751$	15.7867	0.576066	0.288033	+	0.957621i	$0.406999\pi$
$752$	4.64032	0.169215
$753$	4.01669	0.146376
$754$	18.2807	0.665744
$755$	−7.88645	−0.287017
$756$	−7.58035	−0.275695
$757$	−45.5058	−1.65394	−0.826969	−	0.562247i	$-0.809937\pi$
$757$	−45.5058	−1.65394	−0.826969	+	0.562247i	$0.809937\pi$
$758$	−28.6786	−1.04165
$759$	2.56318	0.0930375
$760$	−2.92418	−0.106071
$761$	−22.8181	−0.827156	−0.413578	−	0.910469i	$-0.635721\pi$
$761$	−22.8181	−0.827156	−0.413578	+	0.910469i	$0.635721\pi$
$762$	0.645634	0.0233889
$763$	−26.4761	−0.958497
$764$	13.7202	0.496381
$765$	9.48199	0.342822
$766$	30.8761	1.11560
$767$	5.53520	0.199864
$768$	0.366193	0.0132139
$769$	−8.05192	−0.290360	−0.145180	−	0.989405i	$-0.546376\pi$
$769$	−8.05192	−0.290360	−0.145180	+	0.989405i	$0.546376\pi$
$770$	−18.5891	−0.669904
$771$	0.740676	0.0266748
$772$	7.51242	0.270378
$773$	9.05695	0.325756	0.162878	−	0.986646i	$-0.447922\pi$
$773$	9.05695	0.325756	0.162878	+	0.986646i	$0.447922\pi$
$774$	22.2832	0.800953
$775$	−26.2180	−0.941779
$776$	−0.295411	−0.0106046
$777$	6.81002	0.244308
$778$	8.80642	0.315725
$779$	−22.3893	−0.802180
$780$	1.25659	0.0449930
$781$	−15.2869	−0.547007
$782$	4.39635	0.157213
$783$	10.9166	0.390128
$784$	5.45340	0.194764
$785$	17.2294	0.614943
$786$	−2.96095	−0.105614
$787$	−12.6861	−0.452211	−0.226105	−	0.974103i	$-0.572599\pi$
$787$	−12.6861	−0.452211	−0.226105	+	0.974103i	$0.572599\pi$
$788$	−23.5591	−0.839258
$789$	9.83849	0.350260
$790$	−2.22930	−0.0793149
$791$	42.1002	1.49691
$792$	−15.8250	−0.562316
$793$	44.4986	1.58019
$794$	−23.1484	−0.821506
$795$	−0.618354	−0.0219307
$796$	16.7895	0.595088
$797$	44.7835	1.58631	0.793156	−	0.609018i	$-0.208436\pi$
$797$	44.7835	1.58631	0.793156	+	0.609018i	$0.208436\pi$
$798$	3.96120	0.140225
$799$	16.0936	0.569351
$800$	−4.08995	−0.144602
$801$	19.2051	0.678577
$802$	−34.8697	−1.23129
$803$	−78.8225	−2.78158
$804$	−2.66585	−0.0940174
$805$	−4.26740	−0.150406
$806$	−23.0585	−0.812202
$807$	−0.366193	−0.0128906
$808$	3.14362	0.110592
$809$	33.7900	1.18799	0.593996	−	0.804468i	$-0.297549\pi$
$809$	33.7900	1.18799	0.593996	+	0.804468i	$0.297549\pi$
$810$	−7.45152	−0.261820
$811$	−34.8186	−1.22265	−0.611323	−	0.791382i	$-0.709362\pi$
$811$	−34.8186	−1.22265	−0.611323	+	0.791382i	$0.709362\pi$
$812$	−17.9344	−0.629374
$813$	−3.67149	−0.128765
$814$	29.0988	1.01991
$815$	4.32152	0.151376
$816$	1.27004	0.0444602
$817$	−23.8335	−0.833829
$818$	38.0864	1.33166
$819$	36.3794	1.27120
$820$	6.96789	0.243329
$821$	−10.1228	−0.353288	−0.176644	−	0.984275i	$-0.556524\pi$
$821$	−10.1228	−0.353288	−0.176644	+	0.984275i	$0.556524\pi$
$822$	−2.41023	−0.0840665
$823$	46.4948	1.62071	0.810354	−	0.585941i	$-0.199275\pi$
$823$	46.4948	1.62071	0.810354	+	0.585941i	$0.199275\pi$
$824$	−13.0436	−0.454396
$825$	−8.27009	−0.287928
$826$	−5.43034	−0.188946
$827$	11.2198	0.390151	0.195075	−	0.980788i	$-0.437505\pi$
$827$	11.2198	0.390151	0.195075	+	0.980788i	$0.437505\pi$
$828$	−3.63286	−0.126250
$829$	30.1694	1.04783	0.523913	−	0.851772i	$-0.324472\pi$
$829$	30.1694	1.04783	0.523913	+	0.851772i	$0.324472\pi$
$830$	1.28629	0.0446479
$831$	4.75382	0.164908
$832$	−3.59708	−0.124706
$833$	18.9136	0.655316
$834$	−4.89354	−0.169449
$835$	11.0921	0.383858
$836$	16.9260	0.585397
$837$	−13.7698	−0.475953
$838$	−25.0709	−0.866060
$839$	−37.7762	−1.30418	−0.652089	−	0.758142i	$-0.726107\pi$
$839$	−37.7762	−1.30418	−0.652089	+	0.758142i	$0.726107\pi$
$840$	−1.23278	−0.0425351
$841$	−3.17229	−0.109389
$842$	35.9462	1.23879
$843$	0.0451746	0.00155590
$844$	12.8667	0.442889
$845$	0.0582255	0.00200302
$846$	−13.2987	−0.457218
$847$	68.7805	2.36332
$848$	1.77008	0.0607850
$849$	−6.58860	−0.226120
$850$	−14.1848	−0.486535
$851$	6.68006	0.228989
$852$	−1.01379	−0.0347318
$853$	0.179928	0.00616062	0.00308031	−	0.999995i	$-0.499020\pi$
$853$	0.179928	0.00616062	0.00308031	+	0.999995i	$0.499020\pi$
$854$	−43.6557	−1.49387
$855$	8.38041	0.286604
$856$	11.9783	0.409411
$857$	18.0604	0.616931	0.308466	−	0.951235i	$-0.400185\pi$
$857$	18.0604	0.616931	0.308466	+	0.951235i	$0.400185\pi$
$858$	−7.27348	−0.248312
$859$	13.8764	0.473457	0.236729	−	0.971576i	$-0.423925\pi$
$859$	13.8764	0.473457	0.236729	+	0.971576i	$0.423925\pi$
$860$	7.41734	0.252929
$861$	−9.43895	−0.321678
$862$	4.34025	0.147830
$863$	23.2651	0.791953	0.395976	−	0.918261i	$-0.370406\pi$
$863$	23.2651	0.791953	0.395976	+	0.918261i	$0.370406\pi$
$864$	−2.14806	−0.0730783
$865$	−18.4800	−0.628340
$866$	−34.4524	−1.17074
$867$	−1.82053	−0.0618284
$868$	22.6217	0.767831
$869$	12.9038	0.437732
$870$	1.77536	0.0601902
$871$	26.1864	0.887291
$872$	−7.50255	−0.254069
$873$	0.846619	0.0286537
$874$	3.88560	0.131432
$875$	30.6012	1.03451
$876$	−5.22732	−0.176615
$877$	39.2517	1.32544	0.662718	−	0.748869i	$-0.269403\pi$
$877$	39.2517	1.32544	0.662718	+	0.748869i	$0.269403\pi$
$878$	−35.3209	−1.19202
$879$	−8.83783	−0.298093
$880$	−5.26761	−0.177571
$881$	33.1392	1.11649	0.558243	−	0.829677i	$-0.311476\pi$
$881$	33.1392	1.11649	0.558243	+	0.829677i	$0.311476\pi$
$882$	−15.6289	−0.526253
$883$	16.2361	0.546387	0.273194	−	0.961959i	$-0.411920\pi$
$883$	16.2361	0.546387	0.273194	+	0.961959i	$0.411920\pi$
$884$	−12.4754	−0.419594
$885$	0.537559	0.0180698
$886$	13.5348	0.454710
$887$	49.0229	1.64603	0.823013	−	0.568022i	$-0.192291\pi$
$887$	49.0229	1.64603	0.823013	+	0.568022i	$0.192291\pi$
$888$	1.92976	0.0647586
$889$	6.22186	0.208674
$890$	6.39273	0.214285
$891$	43.1314	1.44496
$892$	18.0816	0.605416
$893$	14.2239	0.475985
$894$	3.87845	0.129715
$895$	−14.6891	−0.491002
$896$	3.52894	0.117894
$897$	−1.66973	−0.0557508
$898$	−41.1462	−1.37307
$899$	−32.5780	−1.08654
$900$	11.7214	0.390713
$901$	6.13903	0.204521
$902$	−40.3321	−1.34291
$903$	−10.0478	−0.334370
$904$	11.9300	0.396785
$905$	−4.12033	−0.136964
$906$	3.02733	0.100576
$907$	28.2851	0.939191	0.469596	−	0.882882i	$-0.344400\pi$
$907$	28.2851	0.939191	0.469596	+	0.882882i	$0.344400\pi$
$908$	−4.79467	−0.159117
$909$	−9.00932	−0.298820
$910$	12.1095	0.401426
$911$	−9.52689	−0.315640	−0.157820	−	0.987468i	$-0.550447\pi$
$911$	−9.52689	−0.315640	−0.157820	+	0.987468i	$0.550447\pi$
$912$	1.12249	0.0371693
$913$	−7.44543	−0.246408
$914$	19.1640	0.633889
$915$	4.32155	0.142866
$916$	−20.1770	−0.666668
$917$	−28.5341	−0.942279
$918$	−7.44991	−0.245884
$919$	−45.8904	−1.51379	−0.756893	−	0.653539i	$-0.773283\pi$
$919$	−45.8904	−1.51379	−0.756893	+	0.653539i	$0.773283\pi$
$920$	−1.20926	−0.0398680
$921$	12.6076	0.415435
$922$	16.5267	0.544276
$923$	9.95832	0.327782
$924$	7.13570	0.234747
$925$	−21.5532	−0.708665
$926$	−1.24318	−0.0408533
$927$	37.3818	1.22778
$928$	−5.08210	−0.166828
$929$	−34.0802	−1.11814	−0.559068	−	0.829122i	$-0.688841\pi$
$929$	−34.0802	−1.11814	−0.559068	+	0.829122i	$0.688841\pi$
$930$	−2.23936	−0.0734316
$931$	16.7163	0.547854
$932$	16.7595	0.548976
$933$	3.32554	0.108873
$934$	−1.12302	−0.0367465
$935$	−18.2692	−0.597467
$936$	10.3089	0.336956
$937$	23.8272	0.778400	0.389200	−	0.921153i	$-0.372751\pi$
$937$	23.8272	0.778400	0.389200	+	0.921153i	$0.372751\pi$
$938$	−25.6903	−0.838819
$939$	−3.00785	−0.0981574
$940$	−4.42670	−0.144383
$941$	−26.0700	−0.849858	−0.424929	−	0.905227i	$-0.639701\pi$
$941$	−26.0700	−0.849858	−0.424929	+	0.905227i	$0.639701\pi$
$942$	−6.61375	−0.215488
$943$	−9.25882	−0.301509
$944$	−1.53880	−0.0500838
$945$	7.23139	0.235237
$946$	−42.9337	−1.39589
$947$	−16.8556	−0.547733	−0.273866	−	0.961768i	$-0.588303\pi$
$947$	−16.8556	−0.547733	−0.273866	+	0.961768i	$0.588303\pi$
$948$	0.855750	0.0277935
$949$	51.3474	1.66681
$950$	−12.5369	−0.406750
$951$	8.82340	0.286118
$952$	12.2391	0.396672
$953$	−26.3030	−0.852036	−0.426018	−	0.904715i	$-0.640084\pi$
$953$	−26.3030	−0.852036	−0.426018	+	0.904715i	$0.640084\pi$
$954$	−5.07289	−0.164241
$955$	−13.0886	−0.423538
$956$	26.7477	0.865082
$957$	−10.2763	−0.332184
$958$	3.92860	0.126927
$959$	−23.2270	−0.750038
$960$	−0.349336	−0.0112748
$961$	10.0926	0.325567
$962$	−18.9559	−0.611161
$963$	−34.3287	−1.10623
$964$	−3.58966	−0.115615
$965$	−7.16658	−0.230700
$966$	1.63810	0.0527051
$967$	−26.4603	−0.850906	−0.425453	−	0.904980i	$-0.639885\pi$
$967$	−26.4603	−0.850906	−0.425453	+	0.904980i	$0.639885\pi$
$968$	19.4904	0.626446
$969$	3.89303	0.125062
$970$	0.281812	0.00904843
$971$	46.7631	1.50070	0.750349	−	0.661041i	$-0.229885\pi$
$971$	46.7631	1.50070	0.750349	+	0.661041i	$0.229885\pi$
$972$	9.30454	0.298443
$973$	−47.1581	−1.51182
$974$	22.0296	0.705875
$975$	5.38739	0.172535
$976$	−12.3708	−0.395979
$977$	32.4480	1.03810	0.519051	−	0.854743i	$-0.326285\pi$
$977$	32.4480	1.03810	0.519051	+	0.854743i	$0.326285\pi$
$978$	−1.65888	−0.0530451
$979$	−37.0029	−1.18262
$980$	−5.20235	−0.166183
$981$	21.5016	0.686493
$982$	−40.3244	−1.28680
$983$	20.9853	0.669327	0.334664	−	0.942338i	$-0.391377\pi$
$983$	20.9853	0.669327	0.334664	+	0.942338i	$0.391377\pi$
$984$	−2.67473	−0.0852672
$985$	22.4745	0.716098
$986$	−17.6258	−0.561320
$987$	5.99656	0.190873
$988$	−11.0261	−0.350787
$989$	−9.85605	−0.313404
$990$	15.0965	0.479797
$991$	27.7877	0.882707	0.441353	−	0.897333i	$-0.354499\pi$
$991$	27.7877	0.882707	0.441353	+	0.897333i	$0.354499\pi$
$992$	6.41035	0.203529
$993$	−7.27914	−0.230996
$994$	−9.76968	−0.309876
$995$	−16.0166	−0.507760
$996$	−0.493763	−0.0156455
$997$	−7.07698	−0.224130	−0.112065	−	0.993701i	$-0.535747\pi$
$997$	−7.07698	−0.224130	−0.112065	+	0.993701i	$0.535747\pi$
$998$	−11.2449	−0.355950
$999$	−11.3198	−0.358143

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.2.a.e.1.4	✓	7
3.2	odd	2		4842.2.a.n.1.6		7
4.3	odd	2		4304.2.a.h.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.2.a.e.1.4	✓	7	1.1	even	1	trivial
4304.2.a.h.1.4		7	4.3	odd	2
4842.2.a.n.1.6		7	3.2	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	538.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.366193 q^{3} +1.00000 q^{4} -0.953965 q^{5} +0.366193 q^{6} +3.52894 q^{7} +1.00000 q^{8} -2.86590 q^{9} -0.953965 q^{10} +5.52181 q^{11} +0.366193 q^{12} -3.59708 q^{13} +3.52894 q^{14} -0.349336 q^{15} +1.00000 q^{16} +3.46821 q^{17} -2.86590 q^{18} +3.06529 q^{19} -0.953965 q^{20} +1.29227 q^{21} +5.52181 q^{22} +1.26761 q^{23} +0.366193 q^{24} -4.08995 q^{25} -3.59708 q^{26} -2.14806 q^{27} +3.52894 q^{28} -5.08210 q^{29} -0.349336 q^{30} +6.41035 q^{31} +1.00000 q^{32} +2.02205 q^{33} +3.46821 q^{34} -3.36648 q^{35} -2.86590 q^{36} +5.26979 q^{37} +3.06529 q^{38} -1.31723 q^{39} -0.953965 q^{40} -7.30413 q^{41} +1.29227 q^{42} -7.77528 q^{43} +5.52181 q^{44} +2.73397 q^{45} +1.26761 q^{46} +4.64032 q^{47} +0.366193 q^{48} +5.45340 q^{49} -4.08995 q^{50} +1.27004 q^{51} -3.59708 q^{52} +1.77008 q^{53} -2.14806 q^{54} -5.26761 q^{55} +3.52894 q^{56} +1.12249 q^{57} -5.08210 q^{58} -1.53880 q^{59} -0.349336 q^{60} -12.3708 q^{61} +6.41035 q^{62} -10.1136 q^{63} +1.00000 q^{64} +3.43148 q^{65} +2.02205 q^{66} -7.27990 q^{67} +3.46821 q^{68} +0.464192 q^{69} -3.36648 q^{70} -2.76845 q^{71} -2.86590 q^{72} -14.2747 q^{73} +5.26979 q^{74} -1.49771 q^{75} +3.06529 q^{76} +19.4861 q^{77} -1.31723 q^{78} +2.33688 q^{79} -0.953965 q^{80} +7.81110 q^{81} -7.30413 q^{82} -1.34837 q^{83} +1.29227 q^{84} -3.30855 q^{85} -7.77528 q^{86} -1.86103 q^{87} +5.52181 q^{88} -6.70123 q^{89} +2.73397 q^{90} -12.6939 q^{91} +1.26761 q^{92} +2.34743 q^{93} +4.64032 q^{94} -2.92418 q^{95} +0.366193 q^{96} -0.295411 q^{97} +5.45340 q^{98} -15.8250 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + q^{3} + 7 q^{4} + 7 q^{5} + q^{6} + 6 q^{7} + 7 q^{8} + 12 q^{9} + 7 q^{10} - 3 q^{11} + q^{12} - 9 q^{13} + 6 q^{14} + 8 q^{15} + 7 q^{16} + 8 q^{17} + 12 q^{18} - 11 q^{19} + 7 q^{20}+ \cdots - 37 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + q^3 + 7 * q^4 + 7 * q^5 + q^6 + 6 * q^7 + 7 * q^8 + 12 * q^9 + 7 * q^10 - 3 * q^11 + q^12 - 9 * q^13 + 6 * q^14 + 8 * q^15 + 7 * q^16 + 8 * q^17 + 12 * q^18 - 11 * q^19 + 7 * q^20 - 6 * q^21 - 3 * q^22 + 12 * q^23 + q^24 + 22 * q^25 - 9 * q^26 - 14 * q^27 + 6 * q^28 - 5 * q^29 + 8 * q^30 + 14 * q^31 + 7 * q^32 - 4 * q^33 + 8 * q^34 - 4 * q^35 + 12 * q^36 + 13 * q^37 - 11 * q^38 - 18 * q^39 + 7 * q^40 + 12 * q^41 - 6 * q^42 - 11 * q^43 - 3 * q^44 + 3 * q^45 + 12 * q^46 + 2 * q^47 + q^48 + 15 * q^49 + 22 * q^50 - 26 * q^51 - 9 * q^52 + 19 * q^53 - 14 * q^54 - 40 * q^55 + 6 * q^56 - 12 * q^57 - 5 * q^58 - 9 * q^59 + 8 * q^60 - 3 * q^61 + 14 * q^62 - 26 * q^63 + 7 * q^64 - 10 * q^65 - 4 * q^66 - 33 * q^67 + 8 * q^68 - 64 * q^69 - 4 * q^70 + 28 * q^71 + 12 * q^72 - 14 * q^73 + 13 * q^74 - 45 * q^75 - 11 * q^76 + 10 * q^77 - 18 * q^78 + 2 * q^79 + 7 * q^80 + 15 * q^81 + 12 * q^82 - 7 * q^83 - 6 * q^84 - 16 * q^85 - 11 * q^86 + 16 * q^87 - 3 * q^88 + 18 * q^89 + 3 * q^90 - 26 * q^91 + 12 * q^92 + 6 * q^93 + 2 * q^94 - 34 * q^95 + q^96 - 4 * q^97 + 15 * q^98 - 37 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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