LMFDB - Embedded newform 4018.2.a.bo.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, 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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.52046292.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 10x^{4} + 9x^{3} + 24x^{2} - 18x + 1 $ x^6 - x^5 - 10x^4 + 9x^3 + 24x^2 - 18x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.38442$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.63447 q^{3} +1.00000 q^{4} -2.84627 q^{5} +1.63447 q^{6} -1.00000 q^{8} -0.328504 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.63447 q^{3} +1.00000 q^{4} -2.84627 q^{5} +1.63447 q^{6} -1.00000 q^{8} -0.328504 q^{9} +2.84627 q^{10} +5.83771 q^{11} -1.63447 q^{12} +2.22364 q^{13} +4.65214 q^{15} +1.00000 q^{16} +1.51776 q^{17} +0.328504 q^{18} +1.82373 q^{19} -2.84627 q^{20} -5.83771 q^{22} -1.53174 q^{23} +1.63447 q^{24} +3.10122 q^{25} -2.22364 q^{26} +5.44034 q^{27} +3.43543 q^{29} -4.65214 q^{30} -7.63297 q^{31} -1.00000 q^{32} -9.54157 q^{33} -1.51776 q^{34} -0.328504 q^{36} +4.42196 q^{37} -1.82373 q^{38} -3.63447 q^{39} +2.84627 q^{40} +1.00000 q^{41} +4.53562 q^{43} +5.83771 q^{44} +0.935010 q^{45} +1.53174 q^{46} -1.02641 q^{47} -1.63447 q^{48} -3.10122 q^{50} -2.48074 q^{51} +2.22364 q^{52} +7.44758 q^{53} -5.44034 q^{54} -16.6157 q^{55} -2.98083 q^{57} -3.43543 q^{58} -0.382406 q^{59} +4.65214 q^{60} -10.4212 q^{61} +7.63297 q^{62} +1.00000 q^{64} -6.32906 q^{65} +9.54157 q^{66} -4.67162 q^{67} +1.51776 q^{68} +2.50359 q^{69} -10.3006 q^{71} +0.328504 q^{72} -13.9265 q^{73} -4.42196 q^{74} -5.06886 q^{75} +1.82373 q^{76} +3.63447 q^{78} +5.14907 q^{79} -2.84627 q^{80} -7.90657 q^{81} -1.00000 q^{82} -7.48985 q^{83} -4.31995 q^{85} -4.53562 q^{86} -5.61511 q^{87} -5.83771 q^{88} -8.71732 q^{89} -0.935010 q^{90} -1.53174 q^{92} +12.4759 q^{93} +1.02641 q^{94} -5.19081 q^{95} +1.63447 q^{96} +1.15610 q^{97} -1.91771 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + q^{3} + 6 q^{4} - q^{6} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + q^3 + 6 * q^4 - q^6 - 6 * q^8 + 5 * q^9	$ 6 q - 6 q^{2} + q^{3} + 6 q^{4} - q^{6} - 6 q^{8} + 5 q^{9} + q^{11} + q^{12} + 4 q^{13} + 2 q^{15} + 6 q^{16} - q^{17} - 5 q^{18} - 3 q^{19} - q^{22} + 21 q^{23} - q^{24} - 4 q^{26} + 13 q^{27} + 5 q^{29} - 2 q^{30} + 3 q^{31} - 6 q^{32} - 19 q^{33} + q^{34} + 5 q^{36} - 2 q^{37} + 3 q^{38} - 11 q^{39} + 6 q^{41} + 12 q^{43} + q^{44} + 28 q^{45} - 21 q^{46} - 18 q^{47} + q^{48} + 13 q^{51} + 4 q^{52} + 14 q^{53} - 13 q^{54} - 7 q^{55} + 5 q^{57} - 5 q^{58} + 16 q^{59} + 2 q^{60} - 20 q^{61} - 3 q^{62} + 6 q^{64} + 18 q^{65} + 19 q^{66} - 13 q^{67} - q^{68} + 15 q^{69} + 11 q^{71} - 5 q^{72} + q^{73} + 2 q^{74} - 23 q^{75} - 3 q^{76} + 11 q^{78} + 19 q^{79} - 6 q^{81} - 6 q^{82} + 15 q^{83} - 2 q^{85} - 12 q^{86} + 10 q^{87} - q^{88} - 14 q^{89} - 28 q^{90} + 21 q^{92} + 35 q^{93} + 18 q^{94} + 24 q^{95} - q^{96} + q^{97} + 10 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + q^3 + 6 * q^4 - q^6 - 6 * q^8 + 5 * q^9 + q^11 + q^12 + 4 * q^13 + 2 * q^15 + 6 * q^16 - q^17 - 5 * q^18 - 3 * q^19 - q^22 + 21 * q^23 - q^24 - 4 * q^26 + 13 * q^27 + 5 * q^29 - 2 * q^30 + 3 * q^31 - 6 * q^32 - 19 * q^33 + q^34 + 5 * q^36 - 2 * q^37 + 3 * q^38 - 11 * q^39 + 6 * q^41 + 12 * q^43 + q^44 + 28 * q^45 - 21 * q^46 - 18 * q^47 + q^48 + 13 * q^51 + 4 * q^52 + 14 * q^53 - 13 * q^54 - 7 * q^55 + 5 * q^57 - 5 * q^58 + 16 * q^59 + 2 * q^60 - 20 * q^61 - 3 * q^62 + 6 * q^64 + 18 * q^65 + 19 * q^66 - 13 * q^67 - q^68 + 15 * q^69 + 11 * q^71 - 5 * q^72 + q^73 + 2 * q^74 - 23 * q^75 - 3 * q^76 + 11 * q^78 + 19 * q^79 - 6 * q^81 - 6 * q^82 + 15 * q^83 - 2 * q^85 - 12 * q^86 + 10 * q^87 - q^88 - 14 * q^89 - 28 * q^90 + 21 * q^92 + 35 * q^93 + 18 * q^94 + 24 * q^95 - q^96 + q^97 + 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.63447	−0.943662	−0.471831	−	0.881689i	$-0.656407\pi$
$3$	−1.63447	−0.943662	−0.471831	+	0.881689i	$0.656407\pi$
$4$	1.00000	0.500000
$5$	−2.84627	−1.27289	−0.636444	−	0.771323i	$-0.719595\pi$
$5$	−2.84627	−1.27289	−0.636444	+	0.771323i	$0.719595\pi$
$6$	1.63447	0.667270
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−0.328504	−0.109501
$10$	2.84627	0.900068
$11$	5.83771	1.76014	0.880068	−	0.474848i	$-0.157497\pi$
$11$	5.83771	1.76014	0.880068	+	0.474848i	$0.157497\pi$
$12$	−1.63447	−0.471831
$13$	2.22364	0.616726	0.308363	−	0.951269i	$-0.400219\pi$
$13$	2.22364	0.616726	0.308363	+	0.951269i	$0.400219\pi$
$14$	0	0
$15$	4.65214	1.20118
$16$	1.00000	0.250000
$17$	1.51776	0.368111	0.184056	−	0.982916i	$-0.441077\pi$
$17$	1.51776	0.368111	0.184056	+	0.982916i	$0.441077\pi$
$18$	0.328504	0.0774292
$19$	1.82373	0.418392	0.209196	−	0.977874i	$-0.432915\pi$
$19$	1.82373	0.418392	0.209196	+	0.977874i	$0.432915\pi$
$20$	−2.84627	−0.636444
$21$	0	0
$22$	−5.83771	−1.24460
$23$	−1.53174	−0.319391	−0.159695	−	0.987166i	$-0.551051\pi$
$23$	−1.53174	−0.319391	−0.159695	+	0.987166i	$0.551051\pi$
$24$	1.63447	0.333635
$25$	3.10122	0.620245
$26$	−2.22364	−0.436091
$27$	5.44034	1.04699
$28$	0	0
$29$	3.43543	0.637944	0.318972	−	0.947764i	$-0.396662\pi$
$29$	3.43543	0.637944	0.318972	+	0.947764i	$0.396662\pi$
$30$	−4.65214	−0.849360
$31$	−7.63297	−1.37092	−0.685461	−	0.728110i	$-0.740399\pi$
$31$	−7.63297	−1.37092	−0.685461	+	0.728110i	$0.740399\pi$
$32$	−1.00000	−0.176777
$33$	−9.54157	−1.66097
$34$	−1.51776	−0.260294
$35$	0	0
$36$	−0.328504	−0.0547507
$37$	4.42196	0.726966	0.363483	−	0.931601i	$-0.381587\pi$
$37$	4.42196	0.726966	0.363483	+	0.931601i	$0.381587\pi$
$38$	−1.82373	−0.295848
$39$	−3.63447	−0.581981
$40$	2.84627	0.450034
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	4.53562	0.691675	0.345837	−	0.938294i	$-0.387595\pi$
$43$	4.53562	0.691675	0.345837	+	0.938294i	$0.387595\pi$
$44$	5.83771	0.880068
$45$	0.935010	0.139383
$46$	1.53174	0.225843
$47$	−1.02641	−0.149717	−0.0748586	−	0.997194i	$-0.523851\pi$
$47$	−1.02641	−0.149717	−0.0748586	+	0.997194i	$0.523851\pi$
$48$	−1.63447	−0.235916
$49$	0	0
$50$	−3.10122	−0.438579
$51$	−2.48074	−0.347373
$52$	2.22364	0.308363
$53$	7.44758	1.02300	0.511502	−	0.859282i	$-0.329089\pi$
$53$	7.44758	1.02300	0.511502	+	0.859282i	$0.329089\pi$
$54$	−5.44034	−0.740337
$55$	−16.6157	−2.24046
$56$	0	0
$57$	−2.98083	−0.394821
$58$	−3.43543	−0.451094
$59$	−0.382406	−0.0497850	−0.0248925	−	0.999690i	$-0.507924\pi$
$59$	−0.382406	−0.0497850	−0.0248925	+	0.999690i	$0.507924\pi$
$60$	4.65214	0.600588
$61$	−10.4212	−1.33429	−0.667147	−	0.744926i	$-0.732485\pi$
$61$	−10.4212	−1.33429	−0.667147	+	0.744926i	$0.732485\pi$
$62$	7.63297	0.969388
$63$	0	0
$64$	1.00000	0.125000
$65$	−6.32906	−0.785023
$66$	9.54157	1.17449
$67$	−4.67162	−0.570729	−0.285364	−	0.958419i	$-0.592115\pi$
$67$	−4.67162	−0.570729	−0.285364	+	0.958419i	$0.592115\pi$
$68$	1.51776	0.184056
$69$	2.50359	0.301397
$70$	0	0
$71$	−10.3006	−1.22246	−0.611230	−	0.791453i	$-0.709325\pi$
$71$	−10.3006	−1.22246	−0.611230	+	0.791453i	$0.709325\pi$
$72$	0.328504	0.0387146
$73$	−13.9265	−1.62997	−0.814987	−	0.579479i	$-0.803256\pi$
$73$	−13.9265	−1.62997	−0.814987	+	0.579479i	$0.803256\pi$
$74$	−4.42196	−0.514043
$75$	−5.06886	−0.585302
$76$	1.82373	0.209196
$77$	0	0
$78$	3.63447	0.411523
$79$	5.14907	0.579316	0.289658	−	0.957130i	$-0.406458\pi$
$79$	5.14907	0.579316	0.289658	+	0.957130i	$0.406458\pi$
$80$	−2.84627	−0.318222
$81$	−7.90657	−0.878508
$82$	−1.00000	−0.110432
$83$	−7.48985	−0.822118	−0.411059	−	0.911609i	$-0.634841\pi$
$83$	−7.48985	−0.822118	−0.411059	+	0.911609i	$0.634841\pi$
$84$	0	0
$85$	−4.31995	−0.468564
$86$	−4.53562	−0.489088
$87$	−5.61511	−0.602003
$88$	−5.83771	−0.622302
$89$	−8.71732	−0.924034	−0.462017	−	0.886871i	$-0.652874\pi$
$89$	−8.71732	−0.924034	−0.462017	+	0.886871i	$0.652874\pi$
$90$	−0.935010	−0.0985587
$91$	0	0
$92$	−1.53174	−0.159695
$93$	12.4759	1.29369
$94$	1.02641	0.105866
$95$	−5.19081	−0.532566
$96$	1.63447	0.166818
$97$	1.15610	0.117385	0.0586923	−	0.998276i	$-0.481307\pi$
$97$	1.15610	0.117385	0.0586923	+	0.998276i	$0.481307\pi$
$98$	0	0
$99$	−1.91771	−0.192737
$100$	3.10122	0.310122
$101$	18.2950	1.82042	0.910211	−	0.414146i	$-0.135920\pi$
$101$	18.2950	1.82042	0.910211	+	0.414146i	$0.135920\pi$
$102$	2.48074	0.245629
$103$	0.509206	0.0501736	0.0250868	−	0.999685i	$-0.492014\pi$
$103$	0.509206	0.0501736	0.0250868	+	0.999685i	$0.492014\pi$
$104$	−2.22364	−0.218046
$105$	0	0
$106$	−7.44758	−0.723373
$107$	15.2827	1.47744	0.738719	−	0.674014i	$-0.235431\pi$
$107$	15.2827	1.47744	0.738719	+	0.674014i	$0.235431\pi$
$108$	5.44034	0.523497
$109$	−10.0728	−0.964799	−0.482399	−	0.875951i	$-0.660235\pi$
$109$	−10.0728	−0.964799	−0.482399	+	0.875951i	$0.660235\pi$
$110$	16.6157	1.58424
$111$	−7.22757	−0.686011
$112$	0	0
$113$	14.9473	1.40612	0.703062	−	0.711129i	$-0.251816\pi$
$113$	14.9473	1.40612	0.703062	+	0.711129i	$0.251816\pi$
$114$	2.98083	0.279180
$115$	4.35975	0.406549
$116$	3.43543	0.318972
$117$	−0.730474	−0.0675324
$118$	0.382406	0.0352033
$119$	0	0
$120$	−4.65214	−0.424680
$121$	23.0789	2.09808
$122$	10.4212	0.943489
$123$	−1.63447	−0.147375
$124$	−7.63297	−0.685461
$125$	5.40442	0.483386
$126$	0	0
$127$	13.7969	1.22428	0.612139	−	0.790750i	$-0.290309\pi$
$127$	13.7969	1.22428	0.612139	+	0.790750i	$0.290309\pi$
$128$	−1.00000	−0.0883883
$129$	−7.41333	−0.652708
$130$	6.32906	0.555095
$131$	6.16025	0.538223	0.269112	−	0.963109i	$-0.413270\pi$
$131$	6.16025	0.538223	0.269112	+	0.963109i	$0.413270\pi$
$132$	−9.54157	−0.830487
$133$	0	0
$134$	4.67162	0.403566
$135$	−15.4847	−1.33271
$136$	−1.51776	−0.130147
$137$	−12.8724	−1.09977	−0.549883	−	0.835241i	$-0.685328\pi$
$137$	−12.8724	−1.09977	−0.549883	+	0.835241i	$0.685328\pi$
$138$	−2.50359	−0.213120
$139$	−15.2698	−1.29517	−0.647584	−	0.761994i	$-0.724221\pi$
$139$	−15.2698	−1.29517	−0.647584	+	0.761994i	$0.724221\pi$
$140$	0	0
$141$	1.67764	0.141283
$142$	10.3006	0.864410
$143$	12.9810	1.08552
$144$	−0.328504	−0.0273754
$145$	−9.77815	−0.812031
$146$	13.9265	1.15257
$147$	0	0
$148$	4.42196	0.363483
$149$	14.0067	1.14747	0.573735	−	0.819041i	$-0.305494\pi$
$149$	14.0067	1.14747	0.573735	+	0.819041i	$0.305494\pi$
$150$	5.06886	0.413871
$151$	−6.80543	−0.553818	−0.276909	−	0.960896i	$-0.589310\pi$
$151$	−6.80543	−0.553818	−0.276909	+	0.960896i	$0.589310\pi$
$152$	−1.82373	−0.147924
$153$	−0.498591	−0.0403087
$154$	0	0
$155$	21.7254	1.74503
$156$	−3.63447	−0.290991
$157$	8.29315	0.661865	0.330933	−	0.943654i	$-0.392637\pi$
$157$	8.29315	0.661865	0.330933	+	0.943654i	$0.392637\pi$
$158$	−5.14907	−0.409638
$159$	−12.1729	−0.965371
$160$	2.84627	0.225017
$161$	0	0
$162$	7.90657	0.621199
$163$	−7.86592	−0.616106	−0.308053	−	0.951369i	$-0.599677\pi$
$163$	−7.86592	−0.616106	−0.308053	+	0.951369i	$0.599677\pi$
$164$	1.00000	0.0780869
$165$	27.1578	2.11423
$166$	7.48985	0.581325
$167$	19.4082	1.50185	0.750926	−	0.660387i	$-0.229608\pi$
$167$	19.4082	1.50185	0.750926	+	0.660387i	$0.229608\pi$
$168$	0	0
$169$	−8.05544	−0.619649
$170$	4.31995	0.331325
$171$	−0.599102	−0.0458145
$172$	4.53562	0.345837
$173$	−12.5308	−0.952696	−0.476348	−	0.879257i	$-0.658040\pi$
$173$	−12.5308	−0.952696	−0.476348	+	0.879257i	$0.658040\pi$
$174$	5.61511	0.425681
$175$	0	0
$176$	5.83771	0.440034
$177$	0.625031	0.0469802
$178$	8.71732	0.653390
$179$	−19.2533	−1.43906	−0.719530	−	0.694461i	$-0.755643\pi$
$179$	−19.2533	−1.43906	−0.719530	+	0.694461i	$0.755643\pi$
$180$	0.935010	0.0696915
$181$	5.25741	0.390780	0.195390	−	0.980726i	$-0.437403\pi$
$181$	5.25741	0.390780	0.195390	+	0.980726i	$0.437403\pi$
$182$	0	0
$183$	17.0331	1.25912
$184$	1.53174	0.112922
$185$	−12.5861	−0.925347
$186$	−12.4759	−0.914775
$187$	8.86025	0.647925
$188$	−1.02641	−0.0748586
$189$	0	0
$190$	5.19081	0.376581
$191$	−10.7347	−0.776736	−0.388368	−	0.921504i	$-0.626961\pi$
$191$	−10.7347	−0.776736	−0.388368	+	0.921504i	$0.626961\pi$
$192$	−1.63447	−0.117958
$193$	22.3365	1.60781	0.803907	−	0.594755i	$-0.202751\pi$
$193$	22.3365	1.60781	0.803907	+	0.594755i	$0.202751\pi$
$194$	−1.15610	−0.0830034
$195$	10.3447	0.740797
$196$	0	0
$197$	10.0924	0.719051	0.359525	−	0.933135i	$-0.382939\pi$
$197$	10.0924	0.719051	0.359525	+	0.933135i	$0.382939\pi$
$198$	1.91771	0.136286
$199$	19.9925	1.41723	0.708617	−	0.705594i	$-0.249320\pi$
$199$	19.9925	1.41723	0.708617	+	0.705594i	$0.249320\pi$
$200$	−3.10122	−0.219290
$201$	7.63562	0.538575
$202$	−18.2950	−1.28723
$203$	0	0
$204$	−2.48074	−0.173686
$205$	−2.84627	−0.198792
$206$	−0.509206	−0.0354781
$207$	0.503184	0.0349737
$208$	2.22364	0.154182
$209$	10.6464	0.736426
$210$	0	0
$211$	−23.8390	−1.64115	−0.820573	−	0.571541i	$-0.806346\pi$
$211$	−23.8390	−1.64115	−0.820573	+	0.571541i	$0.806346\pi$
$212$	7.44758	0.511502
$213$	16.8361	1.15359
$214$	−15.2827	−1.04471
$215$	−12.9096	−0.880425
$216$	−5.44034	−0.370169
$217$	0	0
$218$	10.0728	0.682216
$219$	22.7625	1.53815
$220$	−16.6157	−1.12023
$221$	3.37495	0.227024
$222$	7.22757	0.485083
$223$	5.05921	0.338790	0.169395	−	0.985548i	$-0.445819\pi$
$223$	5.05921	0.338790	0.169395	+	0.985548i	$0.445819\pi$
$224$	0	0
$225$	−1.01877	−0.0679177
$226$	−14.9473	−0.994280
$227$	−14.5896	−0.968347	−0.484173	−	0.874972i	$-0.660880\pi$
$227$	−14.5896	−0.968347	−0.484173	+	0.874972i	$0.660880\pi$
$228$	−2.98083	−0.197410
$229$	−1.80304	−0.119148	−0.0595742	−	0.998224i	$-0.518974\pi$
$229$	−1.80304	−0.119148	−0.0595742	+	0.998224i	$0.518974\pi$
$230$	−4.35975	−0.287473
$231$	0	0
$232$	−3.43543	−0.225547
$233$	7.48405	0.490296	0.245148	−	0.969486i	$-0.421163\pi$
$233$	7.48405	0.490296	0.245148	+	0.969486i	$0.421163\pi$
$234$	0.730474	0.0477526
$235$	2.92143	0.190573
$236$	−0.382406	−0.0248925
$237$	−8.41601	−0.546679
$238$	0	0
$239$	4.45939	0.288454	0.144227	−	0.989545i	$-0.453931\pi$
$239$	4.45939	0.288454	0.144227	+	0.989545i	$0.453931\pi$
$240$	4.65214	0.300294
$241$	5.07297	0.326779	0.163389	−	0.986562i	$-0.447757\pi$
$241$	5.07297	0.326779	0.163389	+	0.986562i	$0.447757\pi$
$242$	−23.0789	−1.48357
$243$	−3.39797	−0.217980
$244$	−10.4212	−0.667147
$245$	0	0
$246$	1.63447	0.104210
$247$	4.05531	0.258033
$248$	7.63297	0.484694
$249$	12.2419	0.775801
$250$	−5.40442	−0.341805
$251$	28.0639	1.77138	0.885690	−	0.464277i	$-0.153686\pi$
$251$	28.0639	1.77138	0.885690	+	0.464277i	$0.153686\pi$
$252$	0	0
$253$	−8.94187	−0.562171
$254$	−13.7969	−0.865695
$255$	7.06083	0.442166
$256$	1.00000	0.0625000
$257$	26.1622	1.63196	0.815978	−	0.578084i	$-0.196199\pi$
$257$	26.1622	1.63196	0.815978	+	0.578084i	$0.196199\pi$
$258$	7.41333	0.461534
$259$	0	0
$260$	−6.32906	−0.392512
$261$	−1.12855	−0.0698557
$262$	−6.16025	−0.380581
$263$	20.5373	1.26638	0.633191	−	0.773996i	$-0.281745\pi$
$263$	20.5373	1.26638	0.633191	+	0.773996i	$0.281745\pi$
$264$	9.54157	0.587243
$265$	−21.1978	−1.30217
$266$	0	0
$267$	14.2482	0.871976
$268$	−4.67162	−0.285364
$269$	29.3297	1.78827	0.894133	−	0.447802i	$-0.147793\pi$
$269$	29.3297	1.78827	0.894133	+	0.447802i	$0.147793\pi$
$270$	15.4847	0.942366
$271$	26.0045	1.57966	0.789831	−	0.613324i	$-0.210168\pi$
$271$	26.0045	1.57966	0.789831	+	0.613324i	$0.210168\pi$
$272$	1.51776	0.0920278
$273$	0	0
$274$	12.8724	0.777653
$275$	18.1041	1.09172
$276$	2.50359	0.150698
$277$	−12.7929	−0.768648	−0.384324	−	0.923198i	$-0.625565\pi$
$277$	−12.7929	−0.768648	−0.384324	+	0.923198i	$0.625565\pi$
$278$	15.2698	0.915822
$279$	2.50746	0.150118
$280$	0	0
$281$	−33.1067	−1.97498	−0.987490	−	0.157679i	$-0.949599\pi$
$281$	−33.1067	−1.97498	−0.987490	+	0.157679i	$0.949599\pi$
$282$	−1.67764	−0.0999018
$283$	10.5385	0.626451	0.313225	−	0.949679i	$-0.398591\pi$
$283$	10.5385	0.626451	0.313225	+	0.949679i	$0.398591\pi$
$284$	−10.3006	−0.611230
$285$	8.48423	0.502563
$286$	−12.9810	−0.767580
$287$	0	0
$288$	0.328504	0.0193573
$289$	−14.6964	−0.864494
$290$	9.77815	0.574193
$291$	−1.88962	−0.110771
$292$	−13.9265	−0.814987
$293$	9.05154	0.528797	0.264398	−	0.964414i	$-0.414827\pi$
$293$	9.05154	0.528797	0.264398	+	0.964414i	$0.414827\pi$
$294$	0	0
$295$	1.08843	0.0633708
$296$	−4.42196	−0.257021
$297$	31.7592	1.84285
$298$	−14.0067	−0.811384
$299$	−3.40604	−0.196976
$300$	−5.06886	−0.292651
$301$	0	0
$302$	6.80543	0.391608
$303$	−29.9027	−1.71786
$304$	1.82373	0.104598
$305$	29.6614	1.69841
$306$	0.498591	0.0285025
$307$	−24.7876	−1.41470	−0.707351	−	0.706863i	$-0.750110\pi$
$307$	−24.7876	−1.41470	−0.707351	+	0.706863i	$0.750110\pi$
$308$	0	0
$309$	−0.832282	−0.0473469
$310$	−21.7254	−1.23392
$311$	−5.48426	−0.310984	−0.155492	−	0.987837i	$-0.549696\pi$
$311$	−5.48426	−0.310984	−0.155492	+	0.987837i	$0.549696\pi$
$312$	3.63447	0.205761
$313$	9.70418	0.548512	0.274256	−	0.961657i	$-0.411568\pi$
$313$	9.70418	0.548512	0.274256	+	0.961657i	$0.411568\pi$
$314$	−8.29315	−0.468009
$315$	0	0
$316$	5.14907	0.289658
$317$	11.5700	0.649838	0.324919	−	0.945742i	$-0.394663\pi$
$317$	11.5700	0.649838	0.324919	+	0.945742i	$0.394663\pi$
$318$	12.1729	0.682620
$319$	20.0551	1.12287
$320$	−2.84627	−0.159111
$321$	−24.9792	−1.39420
$322$	0	0
$323$	2.76798	0.154015
$324$	−7.90657	−0.439254
$325$	6.89600	0.382521
$326$	7.86592	0.435653
$327$	16.4637	0.910444
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	−27.1578	−1.49499
$331$	−13.8810	−0.762971	−0.381486	−	0.924375i	$-0.624587\pi$
$331$	−13.8810	−0.762971	−0.381486	+	0.924375i	$0.624587\pi$
$332$	−7.48985	−0.411059
$333$	−1.45263	−0.0796038
$334$	−19.4082	−1.06197
$335$	13.2967	0.726474
$336$	0	0
$337$	19.3243	1.05266	0.526332	−	0.850279i	$-0.323567\pi$
$337$	19.3243	1.05266	0.526332	+	0.850279i	$0.323567\pi$
$338$	8.05544	0.438158
$339$	−24.4309	−1.32691
$340$	−4.31995	−0.234282
$341$	−44.5591	−2.41301
$342$	0.599102	0.0323957
$343$	0	0
$344$	−4.53562	−0.244544
$345$	−7.12588	−0.383645
$346$	12.5308	0.673658
$347$	16.1830	0.868749	0.434375	−	0.900732i	$-0.356969\pi$
$347$	16.1830	0.868749	0.434375	+	0.900732i	$0.356969\pi$
$348$	−5.61511	−0.301002
$349$	−0.606891	−0.0324861	−0.0162431	−	0.999868i	$-0.505171\pi$
$349$	−0.606891	−0.0324861	−0.0162431	+	0.999868i	$0.505171\pi$
$350$	0	0
$351$	12.0974	0.645709
$352$	−5.83771	−0.311151
$353$	−18.2435	−0.971002	−0.485501	−	0.874236i	$-0.661363\pi$
$353$	−18.2435	−0.971002	−0.485501	+	0.874236i	$0.661363\pi$
$354$	−0.625031	−0.0332200
$355$	29.3183	1.55606
$356$	−8.71732	−0.462017
$357$	0	0
$358$	19.2533	1.01757
$359$	30.1101	1.58915	0.794575	−	0.607166i	$-0.207694\pi$
$359$	30.1101	1.58915	0.794575	+	0.607166i	$0.207694\pi$
$360$	−0.935010	−0.0492794
$361$	−15.6740	−0.824948
$362$	−5.25741	−0.276323
$363$	−37.7217	−1.97988
$364$	0	0
$365$	39.6385	2.07478
$366$	−17.0331	−0.890335
$367$	14.1259	0.737368	0.368684	−	0.929555i	$-0.379808\pi$
$367$	14.1259	0.737368	0.368684	+	0.929555i	$0.379808\pi$
$368$	−1.53174	−0.0798476
$369$	−0.328504	−0.0171012
$370$	12.5861	0.654319
$371$	0	0
$372$	12.4759	0.646843
$373$	−6.66104	−0.344896	−0.172448	−	0.985019i	$-0.555168\pi$
$373$	−6.66104	−0.344896	−0.172448	+	0.985019i	$0.555168\pi$
$374$	−8.86025	−0.458152
$375$	−8.83336	−0.456153
$376$	1.02641	0.0529330
$377$	7.63915	0.393436
$378$	0	0
$379$	21.0246	1.07996	0.539981	−	0.841677i	$-0.318431\pi$
$379$	21.0246	1.07996	0.539981	+	0.841677i	$0.318431\pi$
$380$	−5.19081	−0.266283
$381$	−22.5507	−1.15531
$382$	10.7347	0.549235
$383$	−29.8778	−1.52668	−0.763341	−	0.645995i	$-0.776443\pi$
$383$	−29.8778	−1.52668	−0.763341	+	0.645995i	$0.776443\pi$
$384$	1.63447	0.0834088
$385$	0	0
$386$	−22.3365	−1.13690
$387$	−1.48997	−0.0757394
$388$	1.15610	0.0586923
$389$	2.29210	0.116214	0.0581070	−	0.998310i	$-0.481494\pi$
$389$	2.29210	0.116214	0.0581070	+	0.998310i	$0.481494\pi$
$390$	−10.3447	−0.523823
$391$	−2.32482	−0.117571
$392$	0	0
$393$	−10.0687	−0.507901
$394$	−10.0924	−0.508446
$395$	−14.6556	−0.737405
$396$	−1.91771	−0.0963687
$397$	−3.26132	−0.163681	−0.0818404	−	0.996645i	$-0.526080\pi$
$397$	−3.26132	−0.163681	−0.0818404	+	0.996645i	$0.526080\pi$
$398$	−19.9925	−1.00214
$399$	0	0
$400$	3.10122	0.155061
$401$	2.38940	0.119321	0.0596606	−	0.998219i	$-0.480998\pi$
$401$	2.38940	0.119321	0.0596606	+	0.998219i	$0.480998\pi$
$402$	−7.63562	−0.380830
$403$	−16.9730	−0.845483
$404$	18.2950	0.910211
$405$	22.5042	1.11824
$406$	0	0
$407$	25.8141	1.27956
$408$	2.48074	0.122815
$409$	−14.9274	−0.738111	−0.369055	−	0.929407i	$-0.620319\pi$
$409$	−14.9274	−0.738111	−0.369055	+	0.929407i	$0.620319\pi$
$410$	2.84627	0.140567
$411$	21.0396	1.03781
$412$	0.509206	0.0250868
$413$	0	0
$414$	−0.503184	−0.0247302
$415$	21.3181	1.04646
$416$	−2.22364	−0.109023
$417$	24.9581	1.22220
$418$	−10.6464	−0.520732
$419$	30.3037	1.48043	0.740217	−	0.672368i	$-0.234723\pi$
$419$	30.3037	1.48043	0.740217	+	0.672368i	$0.234723\pi$
$420$	0	0
$421$	−13.9612	−0.680428	−0.340214	−	0.940348i	$-0.610500\pi$
$421$	−13.9612	−0.680428	−0.340214	+	0.940348i	$0.610500\pi$
$422$	23.8390	1.16047
$423$	0.337180	0.0163942
$424$	−7.44758	−0.361687
$425$	4.70692	0.228319
$426$	−16.8361	−0.815711
$427$	0	0
$428$	15.2827	0.738719
$429$	−21.2170	−1.02437
$430$	12.9096	0.622554
$431$	34.9582	1.68388	0.841939	−	0.539573i	$-0.181414\pi$
$431$	34.9582	1.68388	0.841939	+	0.539573i	$0.181414\pi$
$432$	5.44034	0.261749
$433$	38.8725	1.86809	0.934046	−	0.357153i	$-0.116252\pi$
$433$	38.8725	1.86809	0.934046	+	0.357153i	$0.116252\pi$
$434$	0	0
$435$	15.9821	0.766283
$436$	−10.0728	−0.482399
$437$	−2.79348	−0.133630
$438$	−22.7625	−1.08763
$439$	22.3459	1.06651	0.533256	−	0.845954i	$-0.320968\pi$
$439$	22.3459	1.06651	0.533256	+	0.845954i	$0.320968\pi$
$440$	16.6157	0.792121
$441$	0	0
$442$	−3.37495	−0.160530
$443$	9.68852	0.460315	0.230158	−	0.973153i	$-0.426076\pi$
$443$	9.68852	0.460315	0.230158	+	0.973153i	$0.426076\pi$
$444$	−7.22757	−0.343005
$445$	24.8118	1.17619
$446$	−5.05921	−0.239560
$447$	−22.8935	−1.08282
$448$	0	0
$449$	−26.5317	−1.25211	−0.626053	−	0.779780i	$-0.715331\pi$
$449$	−26.5317	−1.25211	−0.626053	+	0.779780i	$0.715331\pi$
$450$	1.01877	0.0480251
$451$	5.83771	0.274887
$452$	14.9473	0.703062
$453$	11.1233	0.522617
$454$	14.5896	0.684725
$455$	0	0
$456$	2.98083	0.139590
$457$	0.677200	0.0316781	0.0158390	−	0.999875i	$-0.494958\pi$
$457$	0.677200	0.0316781	0.0158390	+	0.999875i	$0.494958\pi$
$458$	1.80304	0.0842506
$459$	8.25714	0.385410
$460$	4.35975	0.203274
$461$	−7.39900	−0.344606	−0.172303	−	0.985044i	$-0.555121\pi$
$461$	−7.39900	−0.344606	−0.172303	+	0.985044i	$0.555121\pi$
$462$	0	0
$463$	24.0999	1.12002	0.560009	−	0.828486i	$-0.310798\pi$
$463$	24.0999	1.12002	0.560009	+	0.828486i	$0.310798\pi$
$464$	3.43543	0.159486
$465$	−35.5096	−1.64672
$466$	−7.48405	−0.346692
$467$	−7.05288	−0.326368	−0.163184	−	0.986596i	$-0.552176\pi$
$467$	−7.05288	−0.326368	−0.163184	+	0.986596i	$0.552176\pi$
$468$	−0.730474	−0.0337662
$469$	0	0
$470$	−2.92143	−0.134756
$471$	−13.5549	−0.624577
$472$	0.382406	0.0176017
$473$	26.4776	1.21744
$474$	8.41601	0.386560
$475$	5.65579	0.259505
$476$	0	0
$477$	−2.44656	−0.112020
$478$	−4.45939	−0.203968
$479$	7.68410	0.351095	0.175548	−	0.984471i	$-0.443830\pi$
$479$	7.68410	0.351095	0.175548	+	0.984471i	$0.443830\pi$
$480$	−4.65214	−0.212340
$481$	9.83284	0.448339
$482$	−5.07297	−0.231068
$483$	0	0
$484$	23.0789	1.04904
$485$	−3.29058	−0.149417
$486$	3.39797	0.154135
$487$	36.9817	1.67580	0.837901	−	0.545822i	$-0.183783\pi$
$487$	36.9817	1.67580	0.837901	+	0.545822i	$0.183783\pi$
$488$	10.4212	0.471744
$489$	12.8566	0.581396
$490$	0	0
$491$	28.8179	1.30053	0.650267	−	0.759706i	$-0.274657\pi$
$491$	28.8179	1.30053	0.650267	+	0.759706i	$0.274657\pi$
$492$	−1.63447	−0.0736876
$493$	5.21416	0.234834
$494$	−4.05531	−0.182457
$495$	5.45832	0.245333
$496$	−7.63297	−0.342730
$497$	0	0
$498$	−12.2419	−0.548574
$499$	27.1059	1.21343	0.606714	−	0.794920i	$-0.292487\pi$
$499$	27.1059	1.21343	0.606714	+	0.794920i	$0.292487\pi$
$500$	5.40442	0.241693
$501$	−31.7221	−1.41724
$502$	−28.0639	−1.25255
$503$	2.36757	0.105565	0.0527823	−	0.998606i	$-0.483191\pi$
$503$	2.36757	0.105565	0.0527823	+	0.998606i	$0.483191\pi$
$504$	0	0
$505$	−52.0724	−2.31719
$506$	8.94187	0.397515
$507$	13.1664	0.584739
$508$	13.7969	0.612139
$509$	2.78525	0.123454	0.0617271	−	0.998093i	$-0.480339\pi$
$509$	2.78525	0.123454	0.0617271	+	0.998093i	$0.480339\pi$
$510$	−7.06083	−0.312659
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	9.92171	0.438054
$514$	−26.1622	−1.15397
$515$	−1.44934	−0.0638653
$516$	−7.41333	−0.326354
$517$	−5.99188	−0.263523
$518$	0	0
$519$	20.4812	0.899024
$520$	6.32906	0.277548
$521$	−22.0999	−0.968215	−0.484108	−	0.875009i	$-0.660856\pi$
$521$	−22.0999	−0.968215	−0.484108	+	0.875009i	$0.660856\pi$
$522$	1.12855	0.0493955
$523$	−17.9731	−0.785911	−0.392955	−	0.919558i	$-0.628547\pi$
$523$	−17.9731	−0.785911	−0.392955	+	0.919558i	$0.628547\pi$
$524$	6.16025	0.269112
$525$	0	0
$526$	−20.5373	−0.895467
$527$	−11.5850	−0.504651
$528$	−9.54157	−0.415243
$529$	−20.6538	−0.897990
$530$	21.1978	0.920773
$531$	0.125622	0.00545153
$532$	0	0
$533$	2.22364	0.0963164
$534$	−14.2482	−0.616580
$535$	−43.4987	−1.88061
$536$	4.67162	0.201783
$537$	31.4690	1.35799
$538$	−29.3297	−1.26449
$539$	0	0
$540$	−15.4847	−0.666354
$541$	−5.52017	−0.237331	−0.118665	−	0.992934i	$-0.537862\pi$
$541$	−5.52017	−0.237331	−0.118665	+	0.992934i	$0.537862\pi$
$542$	−26.0045	−1.11699
$543$	−8.59308	−0.368764
$544$	−1.51776	−0.0650735
$545$	28.6698	1.22808
$546$	0	0
$547$	−30.7025	−1.31274	−0.656372	−	0.754438i	$-0.727910\pi$
$547$	−30.7025	−1.31274	−0.656372	+	0.754438i	$0.727910\pi$
$548$	−12.8724	−0.549883
$549$	3.42340	0.146107
$550$	−18.1041	−0.771959
$551$	6.26529	0.266910
$552$	−2.50359	−0.106560
$553$	0	0
$554$	12.7929	0.543516
$555$	20.5716	0.873215
$556$	−15.2698	−0.647584
$557$	16.1518	0.684374	0.342187	−	0.939632i	$-0.388832\pi$
$557$	16.1518	0.684374	0.342187	+	0.939632i	$0.388832\pi$
$558$	−2.50746	−0.106149
$559$	10.0856	0.426574
$560$	0	0
$561$	−14.4818	−0.611423
$562$	33.1067	1.39652
$563$	−7.57295	−0.319162	−0.159581	−	0.987185i	$-0.551014\pi$
$563$	−7.57295	−0.319162	−0.159581	+	0.987185i	$0.551014\pi$
$564$	1.67764	0.0706413
$565$	−42.5440	−1.78984
$566$	−10.5385	−0.442967
$567$	0	0
$568$	10.3006	0.432205
$569$	31.2893	1.31172	0.655858	−	0.754884i	$-0.272307\pi$
$569$	31.2893	1.31172	0.655858	+	0.754884i	$0.272307\pi$
$570$	−8.48423	−0.355365
$571$	−39.9471	−1.67173	−0.835866	−	0.548933i	$-0.815034\pi$
$571$	−39.9471	−1.67173	−0.835866	+	0.548933i	$0.815034\pi$
$572$	12.9810	0.542761
$573$	17.5456	0.732977
$574$	0	0
$575$	−4.75028	−0.198100
$576$	−0.328504	−0.0136877
$577$	−2.99333	−0.124614	−0.0623070	−	0.998057i	$-0.519846\pi$
$577$	−2.99333	−0.124614	−0.0623070	+	0.998057i	$0.519846\pi$
$578$	14.6964	0.611290
$579$	−36.5083	−1.51723
$580$	−9.77815	−0.406016
$581$	0	0
$582$	1.88962	0.0783272
$583$	43.4768	1.80063
$584$	13.9265	0.576283
$585$	2.07912	0.0859612
$586$	−9.05154	−0.373916
$587$	10.8383	0.447344	0.223672	−	0.974665i	$-0.428196\pi$
$587$	10.8383	0.447344	0.223672	+	0.974665i	$0.428196\pi$
$588$	0	0
$589$	−13.9205	−0.573582
$590$	−1.08843	−0.0448099
$591$	−16.4957	−0.678541
$592$	4.42196	0.181742
$593$	47.7990	1.96287	0.981435	−	0.191794i	$-0.0614307\pi$
$593$	47.7990	1.96287	0.981435	+	0.191794i	$0.0614307\pi$
$594$	−31.7592	−1.30309
$595$	0	0
$596$	14.0067	0.573735
$597$	−32.6772	−1.33739
$598$	3.40604	0.139283
$599$	−18.4533	−0.753981	−0.376991	−	0.926217i	$-0.623041\pi$
$599$	−18.4533	−0.753981	−0.376991	+	0.926217i	$0.623041\pi$
$600$	5.06886	0.206935
$601$	−16.3870	−0.668440	−0.334220	−	0.942495i	$-0.608473\pi$
$601$	−16.3870	−0.668440	−0.334220	+	0.942495i	$0.608473\pi$
$602$	0	0
$603$	1.53465	0.0624956
$604$	−6.80543	−0.276909
$605$	−65.6886	−2.67062
$606$	29.9027	1.21471
$607$	24.1272	0.979294	0.489647	−	0.871921i	$-0.337126\pi$
$607$	24.1272	0.979294	0.489647	+	0.871921i	$0.337126\pi$
$608$	−1.82373	−0.0739619
$609$	0	0
$610$	−29.6614	−1.20096
$611$	−2.28236	−0.0923345
$612$	−0.498591	−0.0201543
$613$	−33.7142	−1.36170	−0.680852	−	0.732421i	$-0.738390\pi$
$613$	−33.7142	−1.36170	−0.680852	+	0.732421i	$0.738390\pi$
$614$	24.7876	1.00035
$615$	4.65214	0.187592
$616$	0	0
$617$	−45.5703	−1.83459	−0.917296	−	0.398205i	$-0.869633\pi$
$617$	−45.5703	−1.83459	−0.917296	+	0.398205i	$0.869633\pi$
$618$	0.832282	0.0334793
$619$	−12.9355	−0.519922	−0.259961	−	0.965619i	$-0.583710\pi$
$619$	−12.9355	−0.519922	−0.259961	+	0.965619i	$0.583710\pi$
$620$	21.7254	0.872515
$621$	−8.33321	−0.334400
$622$	5.48426	0.219899
$623$	0	0
$624$	−3.63447	−0.145495
$625$	−30.8885	−1.23554
$626$	−9.70418	−0.387857
$627$	−17.4012	−0.694938
$628$	8.29315	0.330933
$629$	6.71148	0.267604
$630$	0	0
$631$	1.55161	0.0617686	0.0308843	−	0.999523i	$-0.490168\pi$
$631$	1.55161	0.0617686	0.0308843	+	0.999523i	$0.490168\pi$
$632$	−5.14907	−0.204819
$633$	38.9642	1.54869
$634$	−11.5700	−0.459505
$635$	−39.2697	−1.55837
$636$	−12.1729	−0.482685
$637$	0	0
$638$	−20.0551	−0.793987
$639$	3.38380	0.133861
$640$	2.84627	0.112509
$641$	−32.9839	−1.30279	−0.651393	−	0.758740i	$-0.725815\pi$
$641$	−32.9839	−1.30279	−0.651393	+	0.758740i	$0.725815\pi$
$642$	24.9792	0.985850
$643$	26.0179	1.02605	0.513023	−	0.858375i	$-0.328525\pi$
$643$	26.0179	1.02605	0.513023	+	0.858375i	$0.328525\pi$
$644$	0	0
$645$	21.1003	0.830824
$646$	−2.76798	−0.108905
$647$	30.8795	1.21400	0.606999	−	0.794703i	$-0.292373\pi$
$647$	30.8795	1.21400	0.606999	+	0.794703i	$0.292373\pi$
$648$	7.90657	0.310599
$649$	−2.23237	−0.0876284
$650$	−6.89600	−0.270483
$651$	0	0
$652$	−7.86592	−0.308053
$653$	42.7492	1.67290	0.836452	−	0.548040i	$-0.184626\pi$
$653$	42.7492	1.67290	0.836452	+	0.548040i	$0.184626\pi$
$654$	−16.4637	−0.643781
$655$	−17.5337	−0.685098
$656$	1.00000	0.0390434
$657$	4.57492	0.178485
$658$	0	0
$659$	4.75083	0.185066	0.0925330	−	0.995710i	$-0.470504\pi$
$659$	4.75083	0.185066	0.0925330	+	0.995710i	$0.470504\pi$
$660$	27.1578	1.05712
$661$	−8.77914	−0.341469	−0.170734	−	0.985317i	$-0.554614\pi$
$661$	−8.77914	−0.341469	−0.170734	+	0.985317i	$0.554614\pi$
$662$	13.8810	0.539502
$663$	−5.51626	−0.214234
$664$	7.48985	0.290662
$665$	0	0
$666$	1.45263	0.0562884
$667$	−5.26220	−0.203753
$668$	19.4082	0.750926
$669$	−8.26913	−0.319703
$670$	−13.2967	−0.513695
$671$	−60.8358	−2.34854
$672$	0	0
$673$	−39.9093	−1.53839	−0.769194	−	0.639015i	$-0.779342\pi$
$673$	−39.9093	−1.53839	−0.769194	+	0.639015i	$0.779342\pi$
$674$	−19.3243	−0.744346
$675$	16.8717	0.649393
$676$	−8.05544	−0.309824
$677$	−31.9096	−1.22639	−0.613193	−	0.789933i	$-0.710115\pi$
$677$	−31.9096	−1.22639	−0.613193	+	0.789933i	$0.710115\pi$
$678$	24.4309	0.938264
$679$	0	0
$680$	4.31995	0.165662
$681$	23.8463	0.913792
$682$	44.5591	1.70625
$683$	16.5609	0.633687	0.316843	−	0.948478i	$-0.397377\pi$
$683$	16.5609	0.633687	0.316843	+	0.948478i	$0.397377\pi$
$684$	−0.599102	−0.0229072
$685$	36.6384	1.39988
$686$	0	0
$687$	2.94702	0.112436
$688$	4.53562	0.172919
$689$	16.5607	0.630913
$690$	7.12588	0.271278
$691$	−41.1701	−1.56618	−0.783092	−	0.621906i	$-0.786359\pi$
$691$	−41.1701	−1.56618	−0.783092	+	0.621906i	$0.786359\pi$
$692$	−12.5308	−0.476348
$693$	0	0
$694$	−16.1830	−0.614299
$695$	43.4619	1.64860
$696$	5.61511	0.212840
$697$	1.51776	0.0574893
$698$	0.606891	0.0229712
$699$	−12.2325	−0.462674
$700$	0	0
$701$	−7.68501	−0.290259	−0.145129	−	0.989413i	$-0.546360\pi$
$701$	−7.68501	−0.290259	−0.145129	+	0.989413i	$0.546360\pi$
$702$	−12.0974	−0.456585
$703$	8.06446	0.304157
$704$	5.83771	0.220017
$705$	−4.77500	−0.179837
$706$	18.2435	0.686602
$707$	0	0
$708$	0.625031	0.0234901
$709$	2.78791	0.104702	0.0523510	−	0.998629i	$-0.483329\pi$
$709$	2.78791	0.104702	0.0523510	+	0.998629i	$0.483329\pi$
$710$	−29.3183	−1.10030
$711$	−1.69149	−0.0634359
$712$	8.71732	0.326695
$713$	11.6917	0.437859
$714$	0	0
$715$	−36.9472	−1.38175
$716$	−19.2533	−0.719530
$717$	−7.28874	−0.272203
$718$	−30.1101	−1.12370
$719$	24.0908	0.898434	0.449217	−	0.893423i	$-0.351703\pi$
$719$	24.0908	0.898434	0.449217	+	0.893423i	$0.351703\pi$
$720$	0.935010	0.0348458
$721$	0	0
$722$	15.6740	0.583327
$723$	−8.29162	−0.308369
$724$	5.25741	0.195390
$725$	10.6540	0.395681
$726$	37.7217	1.39998
$727$	−3.61107	−0.133927	−0.0669635	−	0.997755i	$-0.521331\pi$
$727$	−3.61107	−0.133927	−0.0669635	+	0.997755i	$0.521331\pi$
$728$	0	0
$729$	29.2736	1.08421
$730$	−39.6385	−1.46709
$731$	6.88398	0.254613
$732$	17.0331	0.629562
$733$	23.6186	0.872373	0.436186	−	0.899856i	$-0.356329\pi$
$733$	23.6186	0.872373	0.436186	+	0.899856i	$0.356329\pi$
$734$	−14.1259	−0.521398
$735$	0	0
$736$	1.53174	0.0564608
$737$	−27.2715	−1.00456
$738$	0.328504	0.0120924
$739$	19.7211	0.725452	0.362726	−	0.931896i	$-0.381846\pi$
$739$	19.7211	0.725452	0.362726	+	0.931896i	$0.381846\pi$
$740$	−12.5861	−0.462674
$741$	−6.62829	−0.243496
$742$	0	0
$743$	43.6375	1.60090	0.800452	−	0.599397i	$-0.204593\pi$
$743$	43.6375	1.60090	0.800452	+	0.599397i	$0.204593\pi$
$744$	−12.4759	−0.457387
$745$	−39.8667	−1.46060
$746$	6.66104	0.243878
$747$	2.46045	0.0900230
$748$	8.86025	0.323963
$749$	0	0
$750$	8.83336	0.322549
$751$	48.4691	1.76866	0.884331	−	0.466860i	$-0.154615\pi$
$751$	48.4691	1.76866	0.884331	+	0.466860i	$0.154615\pi$
$752$	−1.02641	−0.0374293
$753$	−45.8697	−1.67158
$754$	−7.63915	−0.278202
$755$	19.3700	0.704948
$756$	0	0
$757$	−17.9222	−0.651395	−0.325698	−	0.945474i	$-0.605599\pi$
$757$	−17.9222	−0.651395	−0.325698	+	0.945474i	$0.605599\pi$
$758$	−21.0246	−0.763649
$759$	14.6152	0.530499
$760$	5.19081	0.188291
$761$	37.3650	1.35448	0.677240	−	0.735762i	$-0.263176\pi$
$761$	37.3650	1.35448	0.677240	+	0.735762i	$0.263176\pi$
$762$	22.5507	0.816924
$763$	0	0
$764$	−10.7347	−0.388368
$765$	1.41912	0.0513085
$766$	29.8778	1.07953
$767$	−0.850332	−0.0307037
$768$	−1.63447	−0.0589789
$769$	−32.8494	−1.18458	−0.592289	−	0.805725i	$-0.701776\pi$
$769$	−32.8494	−1.18458	−0.592289	+	0.805725i	$0.701776\pi$
$770$	0	0
$771$	−42.7614	−1.54001
$772$	22.3365	0.803907
$773$	−41.4054	−1.48925	−0.744625	−	0.667483i	$-0.767372\pi$
$773$	−41.4054	−1.48925	−0.744625	+	0.667483i	$0.767372\pi$
$774$	1.48997	0.0535558
$775$	−23.6715	−0.850307
$776$	−1.15610	−0.0415017
$777$	0	0
$778$	−2.29210	−0.0821757
$779$	1.82373	0.0653418
$780$	10.3447	0.370399
$781$	−60.1321	−2.15170
$782$	2.32482	0.0831354
$783$	18.6899	0.667924
$784$	0	0
$785$	−23.6045	−0.842480
$786$	10.0687	0.359140
$787$	28.1479	1.00336	0.501681	−	0.865052i	$-0.332715\pi$
$787$	28.1479	1.00336	0.501681	+	0.865052i	$0.332715\pi$
$788$	10.0924	0.359525
$789$	−33.5676	−1.19504
$790$	14.6556	0.521424
$791$	0	0
$792$	1.91771	0.0681430
$793$	−23.1729	−0.822894
$794$	3.26132	0.115740
$795$	34.6472	1.22881
$796$	19.9925	0.708617
$797$	12.1746	0.431245	0.215623	−	0.976477i	$-0.430822\pi$
$797$	12.1746	0.431245	0.215623	+	0.976477i	$0.430822\pi$
$798$	0	0
$799$	−1.55784	−0.0551126
$800$	−3.10122	−0.109645
$801$	2.86368	0.101183
$802$	−2.38940	−0.0843728
$803$	−81.2989	−2.86898
$804$	7.63562	0.269288
$805$	0	0
$806$	16.9730	0.597847
$807$	−47.9386	−1.68752
$808$	−18.2950	−0.643616
$809$	10.0254	0.352474	0.176237	−	0.984348i	$-0.443608\pi$
$809$	10.0254	0.352474	0.176237	+	0.984348i	$0.443608\pi$
$810$	−22.5042	−0.790717
$811$	28.5475	1.00244	0.501219	−	0.865320i	$-0.332885\pi$
$811$	28.5475	1.00244	0.501219	+	0.865320i	$0.332885\pi$
$812$	0	0
$813$	−42.5036	−1.49067
$814$	−25.8141	−0.904785
$815$	22.3885	0.784234
$816$	−2.48074	−0.0868431
$817$	8.27173	0.289391
$818$	14.9274	0.521923
$819$	0	0
$820$	−2.84627	−0.0993959
$821$	19.7982	0.690963	0.345481	−	0.938426i	$-0.387716\pi$
$821$	19.7982	0.690963	0.345481	+	0.938426i	$0.387716\pi$
$822$	−21.0396	−0.733842
$823$	24.2207	0.844281	0.422140	−	0.906530i	$-0.361279\pi$
$823$	24.2207	0.844281	0.422140	+	0.906530i	$0.361279\pi$
$824$	−0.509206	−0.0177390
$825$	−29.5905	−1.03021
$826$	0	0
$827$	−35.9318	−1.24947	−0.624735	−	0.780836i	$-0.714793\pi$
$827$	−35.9318	−1.24947	−0.624735	+	0.780836i	$0.714793\pi$
$828$	0.503184	0.0174869
$829$	10.2158	0.354809	0.177405	−	0.984138i	$-0.443230\pi$
$829$	10.2158	0.354809	0.177405	+	0.984138i	$0.443230\pi$
$830$	−21.3181	−0.739962
$831$	20.9095	0.725344
$832$	2.22364	0.0770908
$833$	0	0
$834$	−24.9581	−0.864227
$835$	−55.2409	−1.91169
$836$	10.6464	0.368213
$837$	−41.5260	−1.43535
$838$	−30.3037	−1.04682
$839$	−21.6531	−0.747547	−0.373774	−	0.927520i	$-0.621936\pi$
$839$	−21.6531	−0.747547	−0.373774	+	0.927520i	$0.621936\pi$
$840$	0	0
$841$	−17.1978	−0.593028
$842$	13.9612	0.481135
$843$	54.1120	1.86372
$844$	−23.8390	−0.820573
$845$	22.9279	0.788744
$846$	−0.337180	−0.0115925
$847$	0	0
$848$	7.44758	0.255751
$849$	−17.2249	−0.591158
$850$	−4.70692	−0.161446
$851$	−6.77331	−0.232186
$852$	16.8361	0.576795
$853$	−9.59159	−0.328410	−0.164205	−	0.986426i	$-0.552506\pi$
$853$	−9.59159	−0.328410	−0.164205	+	0.986426i	$0.552506\pi$
$854$	0	0
$855$	1.70520	0.0583167
$856$	−15.2827	−0.522353
$857$	12.9047	0.440817	0.220408	−	0.975408i	$-0.429261\pi$
$857$	12.9047	0.440817	0.220408	+	0.975408i	$0.429261\pi$
$858$	21.2170	0.724336
$859$	43.8089	1.49474	0.747370	−	0.664408i	$-0.231316\pi$
$859$	43.8089	1.49474	0.747370	+	0.664408i	$0.231316\pi$
$860$	−12.9096	−0.440212
$861$	0	0
$862$	−34.9582	−1.19068
$863$	−6.63615	−0.225897	−0.112949	−	0.993601i	$-0.536030\pi$
$863$	−6.63615	−0.225897	−0.112949	+	0.993601i	$0.536030\pi$
$864$	−5.44034	−0.185084
$865$	35.6659	1.21268
$866$	−38.8725	−1.32094
$867$	24.0208	0.815791
$868$	0	0
$869$	30.0588	1.01967
$870$	−15.9821	−0.541844
$871$	−10.3880	−0.351983
$872$	10.0728	0.341108
$873$	−0.379785	−0.0128538
$874$	2.79348	0.0944910
$875$	0	0
$876$	22.7625	0.769073
$877$	−55.8284	−1.88519	−0.942596	−	0.333936i	$-0.891623\pi$
$877$	−55.8284	−1.88519	−0.942596	+	0.333936i	$0.891623\pi$
$878$	−22.3459	−0.754138
$879$	−14.7945	−0.499006
$880$	−16.6157	−0.560114
$881$	−18.9613	−0.638823	−0.319412	−	0.947616i	$-0.603485\pi$
$881$	−18.9613	−0.638823	−0.319412	+	0.947616i	$0.603485\pi$
$882$	0	0
$883$	28.7970	0.969097	0.484548	−	0.874765i	$-0.338984\pi$
$883$	28.7970	0.969097	0.484548	+	0.874765i	$0.338984\pi$
$884$	3.37495	0.113512
$885$	−1.77900	−0.0598006
$886$	−9.68852	−0.325492
$887$	10.0932	0.338895	0.169448	−	0.985539i	$-0.445802\pi$
$887$	10.0932	0.338895	0.169448	+	0.985539i	$0.445802\pi$
$888$	7.22757	0.242541
$889$	0	0
$890$	−24.8118	−0.831693
$891$	−46.1563	−1.54629
$892$	5.05921	0.169395
$893$	−1.87189	−0.0626405
$894$	22.8935	0.765672
$895$	54.8001	1.83176
$896$	0	0
$897$	5.56708	0.185879
$898$	26.5317	0.885373
$899$	−26.2225	−0.874571
$900$	−1.01877	−0.0339588
$901$	11.3037	0.376579
$902$	−5.83771	−0.194374
$903$	0	0
$904$	−14.9473	−0.497140
$905$	−14.9640	−0.497419
$906$	−11.1233	−0.369546
$907$	59.1289	1.96334	0.981672	−	0.190580i	$-0.0610367\pi$
$907$	59.1289	1.96334	0.981672	+	0.190580i	$0.0610367\pi$
$908$	−14.5896	−0.484173
$909$	−6.00999	−0.199339
$910$	0	0
$911$	−29.8969	−0.990529	−0.495265	−	0.868742i	$-0.664929\pi$
$911$	−29.8969	−0.990529	−0.495265	+	0.868742i	$0.664929\pi$
$912$	−2.98083	−0.0987051
$913$	−43.7236	−1.44704
$914$	−0.677200	−0.0223998
$915$	−48.4807	−1.60272
$916$	−1.80304	−0.0595742
$917$	0	0
$918$	−8.25714	−0.272526
$919$	−23.8655	−0.787249	−0.393625	−	0.919271i	$-0.628779\pi$
$919$	−23.8655	−0.787249	−0.393625	+	0.919271i	$0.628779\pi$
$920$	−4.35975	−0.143737
$921$	40.5146	1.33500
$922$	7.39900	0.243673
$923$	−22.9049	−0.753923
$924$	0	0
$925$	13.7135	0.450897
$926$	−24.0999	−0.791973
$927$	−0.167276	−0.00549408
$928$	−3.43543	−0.112774
$929$	25.4903	0.836309	0.418154	−	0.908376i	$-0.362677\pi$
$929$	25.4903	0.836309	0.418154	+	0.908376i	$0.362677\pi$
$930$	35.5096	1.16441
$931$	0	0
$932$	7.48405	0.245148
$933$	8.96386	0.293464
$934$	7.05288	0.230777
$935$	−25.2186	−0.824737
$936$	0.730474	0.0238763
$937$	47.3211	1.54591	0.772957	−	0.634458i	$-0.218777\pi$
$937$	47.3211	1.54591	0.772957	+	0.634458i	$0.218777\pi$
$938$	0	0
$939$	−15.8612	−0.517611
$940$	2.92143	0.0952867
$941$	5.48718	0.178877	0.0894384	−	0.995992i	$-0.471493\pi$
$941$	5.48718	0.178877	0.0894384	+	0.995992i	$0.471493\pi$
$942$	13.5549	0.441643
$943$	−1.53174	−0.0498804
$944$	−0.382406	−0.0124463
$945$	0	0
$946$	−26.4776	−0.860861
$947$	58.5346	1.90212	0.951060	−	0.309007i	$-0.0999966\pi$
$947$	58.5346	1.90212	0.951060	+	0.309007i	$0.0999966\pi$
$948$	−8.41601	−0.273339
$949$	−30.9675	−1.00525
$950$	−5.65579	−0.183498
$951$	−18.9109	−0.613228
$952$	0	0
$953$	−46.0020	−1.49015	−0.745075	−	0.666980i	$-0.767586\pi$
$953$	−46.0020	−1.49015	−0.745075	+	0.666980i	$0.767586\pi$
$954$	2.44656	0.0792104
$955$	30.5538	0.988699
$956$	4.45939	0.144227
$957$	−32.7794	−1.05961
$958$	−7.68410	−0.248262
$959$	0	0
$960$	4.65214	0.150147
$961$	27.2622	0.879426
$962$	−9.83284	−0.317024
$963$	−5.02044	−0.161782
$964$	5.07297	0.163389
$965$	−63.5755	−2.04657
$966$	0	0
$967$	−43.9625	−1.41374	−0.706869	−	0.707345i	$-0.749893\pi$
$967$	−43.9625	−1.41374	−0.706869	+	0.707345i	$0.749893\pi$
$968$	−23.0789	−0.741783
$969$	−4.52419	−0.145338
$970$	3.29058	0.105654
$971$	−34.6759	−1.11280	−0.556402	−	0.830913i	$-0.687818\pi$
$971$	−34.6759	−1.11280	−0.556402	+	0.830913i	$0.687818\pi$
$972$	−3.39797	−0.108990
$973$	0	0
$974$	−36.9817	−1.18497
$975$	−11.2713	−0.360971
$976$	−10.4212	−0.333574
$977$	53.0423	1.69697	0.848487	−	0.529217i	$-0.177514\pi$
$977$	53.0423	1.69697	0.848487	+	0.529217i	$0.177514\pi$
$978$	−12.8566	−0.411109
$979$	−50.8892	−1.62642
$980$	0	0
$981$	3.30896	0.105647
$982$	−28.8179	−0.919617
$983$	23.6336	0.753796	0.376898	−	0.926255i	$-0.376991\pi$
$983$	23.6336	0.753796	0.376898	+	0.926255i	$0.376991\pi$
$984$	1.63447	0.0521050
$985$	−28.7255	−0.915272
$986$	−5.21416	−0.166053
$987$	0	0
$988$	4.05531	0.129017
$989$	−6.94740	−0.220914
$990$	−5.45832	−0.173477
$991$	−19.9545	−0.633875	−0.316938	−	0.948446i	$-0.602655\pi$
$991$	−19.9545	−0.633875	−0.316938	+	0.948446i	$0.602655\pi$
$992$	7.63297	0.242347
$993$	22.6882	0.719987
$994$	0	0
$995$	−56.9041	−1.80398
$996$	12.2419	0.387901
$997$	−24.2081	−0.766677	−0.383339	−	0.923608i	$-0.625226\pi$
$997$	−24.2081	−0.766677	−0.383339	+	0.923608i	$0.625226\pi$
$998$	−27.1059	−0.858024
$999$	24.0570	0.761130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bo.1.2		6
7.2	even	3		574.2.e.g.165.5	✓	12
7.4	even	3		574.2.e.g.247.5	yes	12
7.6	odd	2		4018.2.a.bn.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.g.165.5	✓	12	7.2	even	3
574.2.e.g.247.5	yes	12	7.4	even	3
4018.2.a.bn.1.5		6	7.6	odd	2
4018.2.a.bo.1.2		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.63447 q^{3} +1.00000 q^{4} -2.84627 q^{5} +1.63447 q^{6} -1.00000 q^{8} -0.328504 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.63447 q^{3} +1.00000 q^{4} -2.84627 q^{5} +1.63447 q^{6} -1.00000 q^{8} -0.328504 q^{9} +2.84627 q^{10} +5.83771 q^{11} -1.63447 q^{12} +2.22364 q^{13} +4.65214 q^{15} +1.00000 q^{16} +1.51776 q^{17} +0.328504 q^{18} +1.82373 q^{19} -2.84627 q^{20} -5.83771 q^{22} -1.53174 q^{23} +1.63447 q^{24} +3.10122 q^{25} -2.22364 q^{26} +5.44034 q^{27} +3.43543 q^{29} -4.65214 q^{30} -7.63297 q^{31} -1.00000 q^{32} -9.54157 q^{33} -1.51776 q^{34} -0.328504 q^{36} +4.42196 q^{37} -1.82373 q^{38} -3.63447 q^{39} +2.84627 q^{40} +1.00000 q^{41} +4.53562 q^{43} +5.83771 q^{44} +0.935010 q^{45} +1.53174 q^{46} -1.02641 q^{47} -1.63447 q^{48} -3.10122 q^{50} -2.48074 q^{51} +2.22364 q^{52} +7.44758 q^{53} -5.44034 q^{54} -16.6157 q^{55} -2.98083 q^{57} -3.43543 q^{58} -0.382406 q^{59} +4.65214 q^{60} -10.4212 q^{61} +7.63297 q^{62} +1.00000 q^{64} -6.32906 q^{65} +9.54157 q^{66} -4.67162 q^{67} +1.51776 q^{68} +2.50359 q^{69} -10.3006 q^{71} +0.328504 q^{72} -13.9265 q^{73} -4.42196 q^{74} -5.06886 q^{75} +1.82373 q^{76} +3.63447 q^{78} +5.14907 q^{79} -2.84627 q^{80} -7.90657 q^{81} -1.00000 q^{82} -7.48985 q^{83} -4.31995 q^{85} -4.53562 q^{86} -5.61511 q^{87} -5.83771 q^{88} -8.71732 q^{89} -0.935010 q^{90} -1.53174 q^{92} +12.4759 q^{93} +1.02641 q^{94} -5.19081 q^{95} +1.63447 q^{96} +1.15610 q^{97} -1.91771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + q^{3} + 6 q^{4} - q^{6} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + q^3 + 6 * q^4 - q^6 - 6 * q^8 + 5 * q^9	\( 6 q - 6 q^{2} + q^{3} + 6 q^{4} - q^{6} - 6 q^{8} + 5 q^{9} + q^{11} + q^{12} + 4 q^{13} + 2 q^{15} + 6 q^{16} - q^{17} - 5 q^{18} - 3 q^{19} - q^{22} + 21 q^{23} - q^{24} - 4 q^{26} + 13 q^{27} + 5 q^{29} - 2 q^{30} + 3 q^{31} - 6 q^{32} - 19 q^{33} + q^{34} + 5 q^{36} - 2 q^{37} + 3 q^{38} - 11 q^{39} + 6 q^{41} + 12 q^{43} + q^{44} + 28 q^{45} - 21 q^{46} - 18 q^{47} + q^{48} + 13 q^{51} + 4 q^{52} + 14 q^{53} - 13 q^{54} - 7 q^{55} + 5 q^{57} - 5 q^{58} + 16 q^{59} + 2 q^{60} - 20 q^{61} - 3 q^{62} + 6 q^{64} + 18 q^{65} + 19 q^{66} - 13 q^{67} - q^{68} + 15 q^{69} + 11 q^{71} - 5 q^{72} + q^{73} + 2 q^{74} - 23 q^{75} - 3 q^{76} + 11 q^{78} + 19 q^{79} - 6 q^{81} - 6 q^{82} + 15 q^{83} - 2 q^{85} - 12 q^{86} + 10 q^{87} - q^{88} - 14 q^{89} - 28 q^{90} + 21 q^{92} + 35 q^{93} + 18 q^{94} + 24 q^{95} - q^{96} + q^{97} + 10 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + q^3 + 6 * q^4 - q^6 - 6 * q^8 + 5 * q^9 + q^11 + q^12 + 4 * q^13 + 2 * q^15 + 6 * q^16 - q^17 - 5 * q^18 - 3 * q^19 - q^22 + 21 * q^23 - q^24 - 4 * q^26 + 13 * q^27 + 5 * q^29 - 2 * q^30 + 3 * q^31 - 6 * q^32 - 19 * q^33 + q^34 + 5 * q^36 - 2 * q^37 + 3 * q^38 - 11 * q^39 + 6 * q^41 + 12 * q^43 + q^44 + 28 * q^45 - 21 * q^46 - 18 * q^47 + q^48 + 13 * q^51 + 4 * q^52 + 14 * q^53 - 13 * q^54 - 7 * q^55 + 5 * q^57 - 5 * q^58 + 16 * q^59 + 2 * q^60 - 20 * q^61 - 3 * q^62 + 6 * q^64 + 18 * q^65 + 19 * q^66 - 13 * q^67 - q^68 + 15 * q^69 + 11 * q^71 - 5 * q^72 + q^73 + 2 * q^74 - 23 * q^75 - 3 * q^76 + 11 * q^78 + 19 * q^79 - 6 * q^81 - 6 * q^82 + 15 * q^83 - 2 * q^85 - 12 * q^86 + 10 * q^87 - q^88 - 14 * q^89 - 28 * q^90 + 21 * q^92 + 35 * q^93 + 18 * q^94 + 24 * q^95 - q^96 + q^97 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more