LMFDB - Embedded newform 289.4.a.g.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,4,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	289.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:	$17.0515519917$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 58 x^{10} + 204 x^{9} + 1191 x^{8} - 3456 x^{7} - 10364 x^{6} + 21448 x^{5} + 38476 x^{4} - 32336 x^{3} - 57024 x^{2} - 15776 x + 1156 $ x^12 - 4x^11 - 58x^10 + 204x^9 + 1191x^8 - 3456x^7 - 10364x^6 + 21448x^5 + 38476x^4 - 32336x^3 - 57024x^2 - 15776*x + 1156
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$3.07564$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.227878 q^{2} -8.23916 q^{3} -7.94807 q^{4} -2.75144 q^{5} -1.87752 q^{6} +21.5220 q^{7} -3.63421 q^{8} +40.8838 q^{9} +O(q^{10})$	\(q+0.227878 q^{2} -8.23916 q^{3} -7.94807 q^{4} -2.75144 q^{5} -1.87752 q^{6} +21.5220 q^{7} -3.63421 q^{8} +40.8838 q^{9} -0.626993 q^{10} +54.5384 q^{11} +65.4854 q^{12} -52.4827 q^{13} +4.90438 q^{14} +22.6696 q^{15} +62.7564 q^{16} +9.31650 q^{18} -19.6304 q^{19} +21.8687 q^{20} -177.323 q^{21} +12.4281 q^{22} +13.9352 q^{23} +29.9428 q^{24} -117.430 q^{25} -11.9596 q^{26} -114.391 q^{27} -171.058 q^{28} +70.0221 q^{29} +5.16589 q^{30} -167.013 q^{31} +43.3745 q^{32} -449.350 q^{33} -59.2165 q^{35} -324.947 q^{36} +198.637 q^{37} -4.47334 q^{38} +432.414 q^{39} +9.99933 q^{40} -434.310 q^{41} -40.4079 q^{42} -127.141 q^{43} -433.475 q^{44} -112.489 q^{45} +3.17552 q^{46} +207.303 q^{47} -517.060 q^{48} +120.195 q^{49} -26.7596 q^{50} +417.136 q^{52} +312.078 q^{53} -26.0671 q^{54} -150.059 q^{55} -78.2154 q^{56} +161.738 q^{57} +15.9565 q^{58} -576.743 q^{59} -180.179 q^{60} +78.3874 q^{61} -38.0586 q^{62} +879.899 q^{63} -492.167 q^{64} +144.403 q^{65} -102.397 q^{66} -359.997 q^{67} -114.814 q^{69} -13.4941 q^{70} -213.190 q^{71} -148.580 q^{72} -29.0468 q^{73} +45.2650 q^{74} +967.521 q^{75} +156.024 q^{76} +1173.77 q^{77} +98.5374 q^{78} +855.508 q^{79} -172.671 q^{80} -161.379 q^{81} -98.9696 q^{82} +13.6871 q^{83} +1409.38 q^{84} -28.9727 q^{86} -576.923 q^{87} -198.204 q^{88} -651.126 q^{89} -25.6338 q^{90} -1129.53 q^{91} -110.758 q^{92} +1376.05 q^{93} +47.2397 q^{94} +54.0120 q^{95} -357.369 q^{96} -1198.65 q^{97} +27.3897 q^{98} +2229.73 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9}+O(q^{10}) $ 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9	$ 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9} - 8 q^{13} - 192 q^{15} - 184 q^{16} - 352 q^{19} - 256 q^{21} - 492 q^{25} - 784 q^{26} + 744 q^{30} + 24 q^{32} - 1400 q^{33} - 632 q^{35} - 856 q^{36} - 624 q^{38} - 1664 q^{42} - 1200 q^{43} - 1512 q^{47} - 1052 q^{49} - 2856 q^{50} + 792 q^{52} - 2504 q^{53} - 1424 q^{55} - 3408 q^{59} - 2808 q^{60} + 272 q^{64} + 272 q^{66} - 1080 q^{67} - 344 q^{69} + 2600 q^{70} + 248 q^{72} + 896 q^{76} + 848 q^{77} - 2404 q^{81} - 2960 q^{83} + 4768 q^{84} - 1200 q^{86} - 160 q^{87} - 2144 q^{89} + 3800 q^{93} + 5984 q^{94} + 3464 q^{98}+O(q^{100}) $ 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9 - 8 * q^13 - 192 * q^15 - 184 * q^16 - 352 * q^19 - 256 * q^21 - 492 * q^25 - 784 * q^26 + 744 * q^30 + 24 * q^32 - 1400 * q^33 - 632 * q^35 - 856 * q^36 - 624 * q^38 - 1664 * q^42 - 1200 * q^43 - 1512 * q^47 - 1052 * q^49 - 2856 * q^50 + 792 * q^52 - 2504 * q^53 - 1424 * q^55 - 3408 * q^59 - 2808 * q^60 + 272 * q^64 + 272 * q^66 - 1080 * q^67 - 344 * q^69 + 2600 * q^70 + 248 * q^72 + 896 * q^76 + 848 * q^77 - 2404 * q^81 - 2960 * q^83 + 4768 * q^84 - 1200 * q^86 - 160 * q^87 - 2144 * q^89 + 3800 * q^93 + 5984 * q^94 + 3464 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.227878	0.0805670	0.0402835	−	0.999188i	$-0.487174\pi$
$2$	0.227878	0.0805670	0.0402835	+	0.999188i	$0.487174\pi$
$3$	−8.23916	−1.58563	−0.792814	−	0.609464i	$-0.791385\pi$
$3$	−8.23916	−1.58563	−0.792814	+	0.609464i	$0.791385\pi$
$4$	−7.94807	−0.993509
$5$	−2.75144	−0.246097	−0.123048	−	0.992401i	$-0.539267\pi$
$5$	−2.75144	−0.246097	−0.123048	+	0.992401i	$0.539267\pi$
$6$	−1.87752	−0.127749
$7$	21.5220	1.16208	0.581038	−	0.813876i	$-0.302647\pi$
$7$	21.5220	1.16208	0.581038	+	0.813876i	$0.302647\pi$
$8$	−3.63421	−0.160611
$9$	40.8838	1.51421
$10$	−0.626993	−0.0198273
$11$	54.5384	1.49490	0.747452	−	0.664316i	$-0.231277\pi$
$11$	54.5384	1.49490	0.747452	+	0.664316i	$0.231277\pi$
$12$	65.4854	1.57533
$13$	−52.4827	−1.11970	−0.559850	−	0.828594i	$-0.689141\pi$
$13$	−52.4827	−1.11970	−0.559850	+	0.828594i	$0.689141\pi$
$14$	4.90438	0.0936250
$15$	22.6696	0.390217
$16$	62.7564	0.980569
$17$	0	0
$17$	0	0
$18$	9.31650	0.121996
$19$	−19.6304	−0.237028	−0.118514	−	0.992952i	$-0.537813\pi$
$19$	−19.6304	−0.237028	−0.118514	+	0.992952i	$0.537813\pi$
$20$	21.8687	0.244499
$21$	−177.323	−1.84262
$22$	12.4281	0.120440
$23$	13.9352	0.126334	0.0631670	−	0.998003i	$-0.479880\pi$
$23$	13.9352	0.126334	0.0631670	+	0.998003i	$0.479880\pi$
$24$	29.9428	0.254669
$25$	−117.430	−0.939436
$26$	−11.9596	−0.0902108
$27$	−114.391	−0.815351
$28$	−171.058	−1.15453
$29$	70.0221	0.448372	0.224186	−	0.974546i	$-0.428028\pi$
$29$	70.0221	0.448372	0.224186	+	0.974546i	$0.428028\pi$
$30$	5.16589	0.0314386
$31$	−167.013	−0.967627	−0.483813	−	0.875171i	$-0.660749\pi$
$31$	−167.013	−0.967627	−0.483813	+	0.875171i	$0.660749\pi$
$32$	43.3745	0.239612
$33$	−449.350	−2.37036
$34$	0	0
$35$	−59.2165	−0.285983
$36$	−324.947	−1.50438
$37$	198.637	0.882588	0.441294	−	0.897363i	$-0.354520\pi$
$37$	198.637	0.882588	0.441294	+	0.897363i	$0.354520\pi$
$38$	−4.47334	−0.0190966
$39$	432.414	1.77543
$40$	9.99933	0.0395258
$41$	−434.310	−1.65434	−0.827168	−	0.561954i	$-0.810050\pi$
$41$	−434.310	−1.65434	−0.827168	+	0.561954i	$0.810050\pi$
$42$	−40.4079	−0.148454
$43$	−127.141	−0.450904	−0.225452	−	0.974254i	$-0.572386\pi$
$43$	−127.141	−0.450904	−0.225452	+	0.974254i	$0.572386\pi$
$44$	−433.475	−1.48520
$45$	−112.489	−0.372643
$46$	3.17552	0.0101784
$47$	207.303	0.643366	0.321683	−	0.946847i	$-0.395751\pi$
$47$	207.303	0.643366	0.321683	+	0.946847i	$0.395751\pi$
$48$	−517.060	−1.55482
$49$	120.195	0.350422
$50$	−26.7596	−0.0756875
$51$	0	0
$52$	417.136	1.11243
$53$	312.078	0.808817	0.404408	−	0.914579i	$-0.367477\pi$
$53$	312.078	0.808817	0.404408	+	0.914579i	$0.367477\pi$
$54$	−26.0671	−0.0656903
$55$	−150.059	−0.367891
$56$	−78.2154	−0.186642
$57$	161.738	0.375838
$58$	15.9565	0.0361239
$59$	−576.743	−1.27264	−0.636318	−	0.771427i	$-0.719543\pi$
$59$	−576.743	−1.27264	−0.636318	+	0.771427i	$0.719543\pi$
$60$	−180.179	−0.387684
$61$	78.3874	0.164533	0.0822663	−	0.996610i	$-0.473784\pi$
$61$	78.3874	0.164533	0.0822663	+	0.996610i	$0.473784\pi$
$62$	−38.0586	−0.0779587
$63$	879.899	1.75963
$64$	−492.167	−0.961264
$65$	144.403	0.275554
$66$	−102.397	−0.190973
$67$	−359.997	−0.656428	−0.328214	−	0.944603i	$-0.606447\pi$
$67$	−359.997	−0.656428	−0.328214	+	0.944603i	$0.606447\pi$
$68$	0	0
$69$	−114.814	−0.200319
$70$	−13.4941	−0.0230408
$71$	−213.190	−0.356352	−0.178176	−	0.983999i	$-0.557020\pi$
$71$	−213.190	−0.356352	−0.178176	+	0.983999i	$0.557020\pi$
$72$	−148.580	−0.243199
$73$	−29.0468	−0.0465708	−0.0232854	−	0.999729i	$-0.507413\pi$
$73$	−29.0468	−0.0465708	−0.0232854	+	0.999729i	$0.507413\pi$
$74$	45.2650	0.0711074
$75$	967.521	1.48960
$76$	156.024	0.235489
$77$	1173.77	1.73719
$78$	98.5374	0.143041
$79$	855.508	1.21838	0.609191	−	0.793024i	$-0.291494\pi$
$79$	855.508	1.21838	0.609191	+	0.793024i	$0.291494\pi$
$80$	−172.671	−0.241315
$81$	−161.379	−0.221371
$82$	−98.9696	−0.133285
$83$	13.6871	0.0181006	0.00905030	−	0.999959i	$-0.497119\pi$
$83$	13.6871	0.0181006	0.00905030	+	0.999959i	$0.497119\pi$
$84$	1409.38	1.83066
$85$	0	0
$86$	−28.9727	−0.0363280
$87$	−576.923	−0.710950
$88$	−198.204	−0.240098
$89$	−651.126	−0.775497	−0.387748	−	0.921765i	$-0.626747\pi$
$89$	−651.126	−0.775497	−0.387748	+	0.921765i	$0.626747\pi$
$90$	−25.6338	−0.0300227
$91$	−1129.53	−1.30118
$92$	−110.758	−0.125514
$93$	1376.05	1.53430
$94$	47.2397	0.0518341
$95$	54.0120	0.0583318
$96$	−357.369	−0.379936
$97$	−1198.65	−1.25469	−0.627345	−	0.778742i	$-0.715858\pi$
$97$	−1198.65	−1.25469	−0.627345	+	0.778742i	$0.715858\pi$
$98$	27.3897	0.0282325
$99$	2229.73	2.26360
$100$	933.339	0.933339
$101$	−89.2435	−0.0879214	−0.0439607	−	0.999033i	$-0.513998\pi$
$101$	−89.2435	−0.0879214	−0.0439607	+	0.999033i	$0.513998\pi$
$102$	0	0
$103$	−1242.17	−1.18830	−0.594150	−	0.804354i	$-0.702511\pi$
$103$	−1242.17	−1.18830	−0.594150	+	0.804354i	$0.702511\pi$
$104$	190.733	0.179836
$105$	487.894	0.453463
$106$	71.1158	0.0651639
$107$	−1537.58	−1.38919	−0.694596	−	0.719400i	$-0.744417\pi$
$107$	−1537.58	−1.38919	−0.694596	+	0.719400i	$0.744417\pi$
$108$	909.184	0.810058
$109$	−103.880	−0.0912839	−0.0456419	−	0.998958i	$-0.514533\pi$
$109$	−103.880	−0.0912839	−0.0456419	+	0.998958i	$0.514533\pi$
$110$	−34.1952	−0.0296398
$111$	−1636.60	−1.39946
$112$	1350.64	1.13950
$113$	−368.211	−0.306534	−0.153267	−	0.988185i	$-0.548980\pi$
$113$	−368.211	−0.306534	−0.153267	+	0.988185i	$0.548980\pi$
$114$	36.8566	0.0302801
$115$	−38.3418	−0.0310904
$116$	−556.541	−0.445461
$117$	−2145.69	−1.69546
$118$	−131.427	−0.102532
$119$	0	0
$120$	−82.3860	−0.0626732
$121$	1643.43	1.23474
$122$	17.8628	0.0132559
$123$	3578.35	2.62316
$124$	1327.43	0.961346
$125$	667.031	0.477289
$126$	200.509	0.141768
$127$	−1253.43	−0.875779	−0.437890	−	0.899029i	$-0.644274\pi$
$127$	−1253.43	−0.875779	−0.437890	+	0.899029i	$0.644274\pi$
$128$	−459.150	−0.317059
$129$	1047.54	0.714965
$130$	32.9063	0.0222006
$131$	−1954.81	−1.30376	−0.651879	−	0.758323i	$-0.726019\pi$
$131$	−1954.81	−1.30376	−0.651879	+	0.758323i	$0.726019\pi$
$132$	3571.47	2.35497
$133$	−422.486	−0.275445
$134$	−82.0354	−0.0528864
$135$	314.739	0.200655
$136$	0	0
$137$	1749.91	1.09127	0.545637	−	0.838022i	$-0.316288\pi$
$137$	1749.91	1.09127	0.545637	+	0.838022i	$0.316288\pi$
$138$	−26.1636	−0.0161391
$139$	−206.309	−0.125891	−0.0629456	−	0.998017i	$-0.520049\pi$
$139$	−206.309	−0.125891	−0.0629456	+	0.998017i	$0.520049\pi$
$140$	470.657	0.284127
$141$	−1708.00	−1.02014
$142$	−48.5812	−0.0287102
$143$	−2862.32	−1.67384
$144$	2565.72	1.48479
$145$	−192.662	−0.110343
$146$	−6.61911	−0.00375207
$147$	−990.304	−0.555639
$148$	−1578.78	−0.876859
$149$	−2013.39	−1.10700	−0.553501	−	0.832849i	$-0.686708\pi$
$149$	−2013.39	−1.10700	−0.553501	+	0.832849i	$0.686708\pi$
$150$	220.477	0.120012
$151$	75.6527	0.0407717	0.0203859	−	0.999792i	$-0.493511\pi$
$151$	75.6527	0.0407717	0.0203859	+	0.999792i	$0.493511\pi$
$152$	71.3412	0.0380693
$153$	0	0
$154$	267.477	0.139960
$155$	459.527	0.238130
$156$	−3436.85	−1.76390
$157$	2301.81	1.17009	0.585046	−	0.811000i	$-0.301076\pi$
$157$	2301.81	1.17009	0.585046	+	0.811000i	$0.301076\pi$
$158$	194.951	0.0981613
$159$	−2571.26	−1.28248
$160$	−119.342	−0.0589678
$161$	299.912	0.146810
$162$	−36.7748	−0.0178352
$163$	−1893.00	−0.909640	−0.454820	−	0.890583i	$-0.650296\pi$
$163$	−1893.00	−0.909640	−0.454820	+	0.890583i	$0.650296\pi$
$164$	3451.93	1.64360
$165$	1236.36	0.583337
$166$	3.11898	0.00145831
$167$	108.478	0.0502650	0.0251325	−	0.999684i	$-0.491999\pi$
$167$	108.478	0.0502650	0.0251325	+	0.999684i	$0.491999\pi$
$168$	644.429	0.295945
$169$	557.436	0.253726
$170$	0	0
$171$	−802.566	−0.358911
$172$	1010.53	0.447977
$173$	2755.78	1.21109	0.605543	−	0.795813i	$-0.292956\pi$
$173$	2755.78	1.21109	0.605543	+	0.795813i	$0.292956\pi$
$174$	−131.468	−0.0572791
$175$	−2527.31	−1.09170
$176$	3422.63	1.46586
$177$	4751.88	2.01793
$178$	−148.377	−0.0624794
$179$	2006.15	0.837691	0.418846	−	0.908058i	$-0.362435\pi$
$179$	2006.15	0.837691	0.418846	+	0.908058i	$0.362435\pi$
$180$	894.073	0.370224
$181$	−2424.21	−0.995525	−0.497762	−	0.867313i	$-0.665845\pi$
$181$	−2424.21	−0.995525	−0.497762	+	0.867313i	$0.665845\pi$
$182$	−257.395	−0.104832
$183$	−645.847	−0.260887
$184$	−50.6433	−0.0202906
$185$	−546.539	−0.217202
$186$	313.571	0.123614
$187$	0	0
$188$	−1647.66	−0.639190
$189$	−2461.91	−0.947500
$190$	12.3081	0.00469961
$191$	−4153.64	−1.57354	−0.786772	−	0.617243i	$-0.788249\pi$
$191$	−4153.64	−1.57354	−0.786772	+	0.617243i	$0.788249\pi$
$192$	4055.04	1.52421
$193$	−2076.42	−0.774425	−0.387212	−	0.921991i	$-0.626562\pi$
$193$	−2076.42	−0.774425	−0.387212	+	0.921991i	$0.626562\pi$
$194$	−273.147	−0.101087
$195$	−1189.76	−0.436926
$196$	−955.317	−0.348148
$197$	3803.50	1.37558	0.687788	−	0.725912i	$-0.258582\pi$
$197$	3803.50	1.37558	0.687788	+	0.725912i	$0.258582\pi$
$198$	508.107	0.182372
$199$	3621.89	1.29020	0.645098	−	0.764100i	$-0.276817\pi$
$199$	3621.89	1.29020	0.645098	+	0.764100i	$0.276817\pi$
$200$	426.764	0.150884
$201$	2966.08	1.04085
$202$	−20.3366	−0.00708356
$203$	1507.01	0.521042
$204$	0	0
$205$	1194.98	0.407127
$206$	−283.063	−0.0957377
$207$	569.722	0.191297
$208$	−3293.63	−1.09794
$209$	−1070.61	−0.354334
$210$	111.180	0.0365341
$211$	632.505	0.206367	0.103183	−	0.994662i	$-0.467097\pi$
$211$	632.505	0.206367	0.103183	+	0.994662i	$0.467097\pi$
$212$	−2480.42	−0.803567
$213$	1756.51	0.565041
$214$	−350.380	−0.111923
$215$	349.822	0.110966
$216$	415.719	0.130954
$217$	−3594.45	−1.12446
$218$	−23.6721	−0.00735447
$219$	239.321	0.0738439
$220$	1192.68	0.365503
$221$	0	0
$222$	−372.946	−0.112750
$223$	−533.811	−0.160299	−0.0801494	−	0.996783i	$-0.525540\pi$
$223$	−533.811	−0.160299	−0.0801494	+	0.996783i	$0.525540\pi$
$224$	933.504	0.278448
$225$	−4800.96	−1.42251
$226$	−83.9071	−0.0246965
$227$	−588.842	−0.172171	−0.0860855	−	0.996288i	$-0.527436\pi$
$227$	−588.842	−0.172171	−0.0860855	+	0.996288i	$0.527436\pi$
$228$	−1285.51	−0.373398
$229$	2641.15	0.762148	0.381074	−	0.924545i	$-0.375554\pi$
$229$	2641.15	0.762148	0.381074	+	0.924545i	$0.375554\pi$
$230$	−8.73725	−0.00250486
$231$	−9670.90	−2.75454
$232$	−254.475	−0.0720134
$233$	383.377	0.107794	0.0538968	−	0.998547i	$-0.482836\pi$
$233$	383.377	0.107794	0.0538968	+	0.998547i	$0.482836\pi$
$234$	−488.955	−0.136598
$235$	−570.382	−0.158330
$236$	4583.99	1.26438
$237$	−7048.67	−1.93190
$238$	0	0
$239$	−4344.62	−1.17586	−0.587929	−	0.808913i	$-0.700056\pi$
$239$	−4344.62	−1.17586	−0.587929	+	0.808913i	$0.700056\pi$
$240$	1422.66	0.382635
$241$	2053.67	0.548915	0.274458	−	0.961599i	$-0.411502\pi$
$241$	2053.67	0.548915	0.274458	+	0.961599i	$0.411502\pi$
$242$	374.502	0.0994790
$243$	4418.18	1.16636
$244$	−623.029	−0.163465
$245$	−330.709	−0.0862377
$246$	815.426	0.211340
$247$	1030.26	0.265400
$248$	606.961	0.155411
$249$	−112.770	−0.0287008
$250$	152.002	0.0384537
$251$	907.953	0.228325	0.114162	−	0.993462i	$-0.463582\pi$
$251$	907.953	0.228325	0.114162	+	0.993462i	$0.463582\pi$
$252$	−6993.50	−1.74821
$253$	760.001	0.188857
$254$	−285.629	−0.0705589
$255$	0	0
$256$	3832.71	0.935720
$257$	−7490.82	−1.81815	−0.909075	−	0.416633i	$-0.863210\pi$
$257$	−7490.82	−1.81815	−0.909075	+	0.416633i	$0.863210\pi$
$258$	238.711	0.0576026
$259$	4275.06	1.02564
$260$	−1147.73	−0.273765
$261$	2862.77	0.678930
$262$	−445.457	−0.105040
$263$	−7860.69	−1.84301	−0.921503	−	0.388371i	$-0.873038\pi$
$263$	−7860.69	−1.84301	−0.921503	+	0.388371i	$0.873038\pi$
$264$	1633.03	0.380706
$265$	−858.666	−0.199047
$266$	−96.2751	−0.0221917
$267$	5364.73	1.22965
$268$	2861.29	0.652167
$269$	−7553.86	−1.71215	−0.856073	−	0.516856i	$-0.827102\pi$
$269$	−7553.86	−1.71215	−0.856073	+	0.516856i	$0.827102\pi$
$270$	71.7221	0.0161662
$271$	−6394.46	−1.43334	−0.716672	−	0.697411i	$-0.754335\pi$
$271$	−6394.46	−1.43334	−0.716672	+	0.697411i	$0.754335\pi$
$272$	0	0
$273$	9306.39	2.06318
$274$	398.765	0.0879206
$275$	−6404.42	−1.40437
$276$	912.551	0.199018
$277$	6762.61	1.46688	0.733440	−	0.679754i	$-0.237913\pi$
$277$	6762.61	1.46688	0.733440	+	0.679754i	$0.237913\pi$
$278$	−47.0132	−0.0101427
$279$	−6828.12	−1.46519
$280$	215.205	0.0459320
$281$	−6298.04	−1.33704	−0.668522	−	0.743692i	$-0.733073\pi$
$281$	−6298.04	−1.33704	−0.668522	+	0.743692i	$0.733073\pi$
$282$	−389.216	−0.0821895
$283$	−2672.62	−0.561381	−0.280690	−	0.959798i	$-0.590563\pi$
$283$	−2672.62	−0.561381	−0.280690	+	0.959798i	$0.590563\pi$
$284$	1694.45	0.354039
$285$	−445.014	−0.0924924
$286$	−652.260	−0.134856
$287$	−9347.20	−1.92247
$288$	1773.31	0.362824
$289$	0	0
$290$	−43.9033	−0.00888998
$291$	9875.90	1.98947
$292$	230.866	0.0462685
$293$	−2183.30	−0.435323	−0.217661	−	0.976024i	$-0.569843\pi$
$293$	−2183.30	−0.435323	−0.217661	+	0.976024i	$0.569843\pi$
$294$	−225.668	−0.0447661
$295$	1586.88	0.313191
$296$	−721.890	−0.141753
$297$	−6238.68	−1.21887
$298$	−458.806	−0.0891877
$299$	−731.356	−0.141456
$300$	−7689.93	−1.47993
$301$	−2736.33	−0.523985
$302$	17.2396	0.00328485
$303$	735.292	0.139411
$304$	−1231.94	−0.232422
$305$	−215.679	−0.0404909
$306$	0	0
$307$	−3905.30	−0.726018	−0.363009	−	0.931786i	$-0.618250\pi$
$307$	−3905.30	−0.726018	−0.363009	+	0.931786i	$0.618250\pi$
$308$	−9329.23	−1.72592
$309$	10234.5	1.88420
$310$	104.716	0.0191854
$311$	−7367.41	−1.34330	−0.671652	−	0.740867i	$-0.734415\pi$
$311$	−7367.41	−1.34330	−0.671652	+	0.740867i	$0.734415\pi$
$312$	−1571.48	−0.285153
$313$	2326.83	0.420192	0.210096	−	0.977681i	$-0.432622\pi$
$313$	2326.83	0.420192	0.210096	+	0.977681i	$0.432622\pi$
$314$	524.532	0.0942708
$315$	−2420.99	−0.433039
$316$	−6799.64	−1.21047
$317$	7470.26	1.32357	0.661785	−	0.749694i	$-0.269799\pi$
$317$	7470.26	1.32357	0.661785	+	0.749694i	$0.269799\pi$
$318$	−585.934	−0.103326
$319$	3818.89	0.670272
$320$	1354.17	0.236564
$321$	12668.4	2.20274
$322$	68.3433	0.0118280
$323$	0	0
$324$	1282.66	0.219934
$325$	6163.02	1.05189
$326$	−431.373	−0.0732869
$327$	855.888	0.144742
$328$	1578.37	0.265705
$329$	4461.56	0.747641
$330$	281.739	0.0469977
$331$	9353.18	1.55316	0.776582	−	0.630016i	$-0.216952\pi$
$331$	9353.18	1.55316	0.776582	+	0.630016i	$0.216952\pi$
$332$	−108.786	−0.0179831
$333$	8121.04	1.33643
$334$	24.7197	0.00404970
$335$	990.512	0.161545
$336$	−11128.1	−1.80682
$337$	6944.09	1.12246	0.561229	−	0.827660i	$-0.310329\pi$
$337$	6944.09	1.12246	0.561229	+	0.827660i	$0.310329\pi$
$338$	127.027	0.0204419
$339$	3033.75	0.486049
$340$	0	0
$341$	−9108.62	−1.44651
$342$	−182.887	−0.0289164
$343$	−4795.20	−0.754859
$344$	462.058	0.0724201
$345$	315.904	0.0492977
$346$	627.981	0.0975735
$347$	−2409.98	−0.372838	−0.186419	−	0.982470i	$-0.559688\pi$
$347$	−2409.98	−0.372838	−0.186419	+	0.982470i	$0.559688\pi$
$348$	4585.43	0.706335
$349$	11005.3	1.68797	0.843985	−	0.536367i	$-0.180204\pi$
$349$	11005.3	1.68797	0.843985	+	0.536367i	$0.180204\pi$
$350$	−575.919	−0.0879547
$351$	6003.53	0.912948
$352$	2365.57	0.358197
$353$	7713.23	1.16299	0.581493	−	0.813552i	$-0.302469\pi$
$353$	7713.23	1.16299	0.581493	+	0.813552i	$0.302469\pi$
$354$	1082.85	0.162578
$355$	586.580	0.0876970
$356$	5175.20	0.770463
$357$	0	0
$358$	457.157	0.0674902
$359$	−10220.1	−1.50249	−0.751245	−	0.660023i	$-0.770546\pi$
$359$	−10220.1	−1.50249	−0.751245	+	0.660023i	$0.770546\pi$
$360$	408.810	0.0598505
$361$	−6473.65	−0.943818
$362$	−552.423	−0.0802064
$363$	−13540.5	−1.95783
$364$	8977.59	1.29273
$365$	79.9205	0.0114609
$366$	−147.174	−0.0210189
$367$	10322.4	1.46819	0.734096	−	0.679046i	$-0.237606\pi$
$367$	10322.4	1.46819	0.734096	+	0.679046i	$0.237606\pi$
$368$	874.521	0.123879
$369$	−17756.2	−2.50502
$370$	−124.544	−0.0174993
$371$	6716.54	0.939907
$372$	−10936.9	−1.52434
$373$	2744.09	0.380921	0.190461	−	0.981695i	$-0.439002\pi$
$373$	2744.09	0.380921	0.190461	+	0.981695i	$0.439002\pi$
$374$	0	0
$375$	−5495.78	−0.756802
$376$	−753.382	−0.103332
$377$	−3674.95	−0.502041
$378$	−561.014	−0.0763372
$379$	6405.00	0.868082	0.434041	−	0.900893i	$-0.357087\pi$
$379$	6405.00	0.868082	0.434041	+	0.900893i	$0.357087\pi$
$380$	−429.291	−0.0579531
$381$	10327.2	1.38866
$382$	−946.523	−0.126776
$383$	3692.83	0.492676	0.246338	−	0.969184i	$-0.420773\pi$
$383$	3692.83	0.492676	0.246338	+	0.969184i	$0.420773\pi$
$384$	3783.01	0.502737
$385$	−3229.57	−0.427517
$386$	−473.170	−0.0623930
$387$	−5198.01	−0.682765
$388$	9526.99	1.24654
$389$	−2132.95	−0.278007	−0.139004	−	0.990292i	$-0.544390\pi$
$389$	−2132.95	−0.278007	−0.139004	+	0.990292i	$0.544390\pi$
$390$	−271.120	−0.0352018
$391$	0	0
$392$	−436.813	−0.0562816
$393$	16106.0	2.06727
$394$	866.734	0.110826
$395$	−2353.88	−0.299840
$396$	−17722.1	−2.24891
$397$	2364.86	0.298965	0.149483	−	0.988764i	$-0.452239\pi$
$397$	2364.86	0.298965	0.149483	+	0.988764i	$0.452239\pi$
$398$	825.348	0.103947
$399$	3480.93	0.436753
$400$	−7369.46	−0.921182
$401$	2063.74	0.257003	0.128502	−	0.991709i	$-0.458983\pi$
$401$	2063.74	0.257003	0.128502	+	0.991709i	$0.458983\pi$
$402$	675.903	0.0838581
$403$	8765.30	1.08345
$404$	709.314	0.0873507
$405$	444.026	0.0544786
$406$	343.415	0.0419788
$407$	10833.4	1.31938
$408$	0	0
$409$	9245.03	1.11769	0.558847	−	0.829271i	$-0.311244\pi$
$409$	9245.03	1.11769	0.558847	+	0.829271i	$0.311244\pi$
$410$	272.309	0.0328009
$411$	−14417.8	−1.73035
$412$	9872.87	1.18059
$413$	−12412.6	−1.47890
$414$	129.827	0.0154122
$415$	−37.6592	−0.00445449
$416$	−2276.41	−0.268294
$417$	1699.81	0.199617
$418$	−243.969	−0.0285476
$419$	4155.37	0.484494	0.242247	−	0.970215i	$-0.422116\pi$
$419$	4155.37	0.484494	0.242247	+	0.970215i	$0.422116\pi$
$420$	−3877.82	−0.450519
$421$	4609.26	0.533591	0.266795	−	0.963753i	$-0.414035\pi$
$421$	4609.26	0.533591	0.266795	+	0.963753i	$0.414035\pi$
$422$	144.134	0.0166264
$423$	8475.32	0.974194
$424$	−1134.16	−0.129905
$425$	0	0
$426$	400.269	0.0455237
$427$	1687.05	0.191199
$428$	12220.8	1.38017
$429$	23583.1	2.65409
$430$	79.7167	0.00894018
$431$	17330.4	1.93683	0.968416	−	0.249341i	$-0.0802141\pi$
$431$	17330.4	1.93683	0.968416	+	0.249341i	$0.0802141\pi$
$432$	−7178.74	−0.799508
$433$	11353.9	1.26012	0.630061	−	0.776545i	$-0.283030\pi$
$433$	11353.9	1.26012	0.630061	+	0.776545i	$0.283030\pi$
$434$	−819.095	−0.0905940
$435$	1587.37	0.174962
$436$	825.649	0.0906914
$437$	−273.553	−0.0299447
$438$	54.5359	0.00594938
$439$	−5128.08	−0.557516	−0.278758	−	0.960361i	$-0.589923\pi$
$439$	−5128.08	−0.557516	−0.278758	+	0.960361i	$0.589923\pi$
$440$	545.347	0.0590873
$441$	4914.02	0.530614
$442$	0	0
$443$	−3133.00	−0.336012	−0.168006	−	0.985786i	$-0.553733\pi$
$443$	−3133.00	−0.336012	−0.168006	+	0.985786i	$0.553733\pi$
$444$	13007.8	1.39037
$445$	1791.54	0.190847
$446$	−121.644	−0.0129148
$447$	16588.6	1.75529
$448$	−10592.4	−1.11706
$449$	−11749.6	−1.23496	−0.617480	−	0.786586i	$-0.711846\pi$
$449$	−11749.6	−1.23496	−0.617480	+	0.786586i	$0.711846\pi$
$450$	−1094.03	−0.114607
$451$	−23686.6	−2.47307
$452$	2926.57	0.304545
$453$	−623.315	−0.0646488
$454$	−134.184	−0.0138713
$455$	3107.84	0.320215
$456$	−587.791	−0.0603637
$457$	−12408.7	−1.27014	−0.635072	−	0.772453i	$-0.719030\pi$
$457$	−12408.7	−1.27014	−0.635072	+	0.772453i	$0.719030\pi$
$458$	601.859	0.0614039
$459$	0	0
$460$	304.744	0.0308886
$461$	−7370.49	−0.744638	−0.372319	−	0.928105i	$-0.621437\pi$
$461$	−7370.49	−0.744638	−0.372319	+	0.928105i	$0.621437\pi$
$462$	−2203.78	−0.221925
$463$	11446.9	1.14899	0.574495	−	0.818508i	$-0.305198\pi$
$463$	11446.9	1.14899	0.574495	+	0.818508i	$0.305198\pi$
$464$	4394.34	0.439659
$465$	−3786.12	−0.377585
$466$	87.3632	0.00868460
$467$	4418.29	0.437803	0.218901	−	0.975747i	$-0.429753\pi$
$467$	4418.29	0.437803	0.218901	+	0.975747i	$0.429753\pi$
$468$	17054.1	1.68446
$469$	−7747.85	−0.762820
$470$	−129.977	−0.0127562
$471$	−18965.0	−1.85533
$472$	2096.01	0.204399
$473$	−6934.08	−0.674058
$474$	−1606.23	−0.155647
$475$	2305.19	0.222673
$476$	0	0
$477$	12758.9	1.22472
$478$	−990.042	−0.0947353
$479$	282.615	0.0269583	0.0134791	−	0.999909i	$-0.495709\pi$
$479$	282.615	0.0269583	0.0134791	+	0.999909i	$0.495709\pi$
$480$	983.281	0.0935009
$481$	−10425.0	−0.988233
$482$	467.986	0.0442244
$483$	−2471.02	−0.232786
$484$	−13062.1	−1.22672
$485$	3298.03	0.308775
$486$	1006.80	0.0939703
$487$	−7602.13	−0.707362	−0.353681	−	0.935366i	$-0.615070\pi$
$487$	−7602.13	−0.707362	−0.353681	+	0.935366i	$0.615070\pi$
$488$	−284.877	−0.0264257
$489$	15596.7	1.44235
$490$	−75.3613	−0.00694791
$491$	−12834.9	−1.17970	−0.589850	−	0.807513i	$-0.700813\pi$
$491$	−12834.9	−1.17970	−0.589850	+	0.807513i	$0.700813\pi$
$492$	−28441.0	−2.60613
$493$	0	0
$494$	234.773	0.0213825
$495$	−6134.99	−0.557065
$496$	−10481.1	−0.948825
$497$	−4588.27	−0.414108
$498$	−25.6977	−0.00231234
$499$	−2717.22	−0.243767	−0.121883	−	0.992544i	$-0.538893\pi$
$499$	−2717.22	−0.243767	−0.121883	+	0.992544i	$0.538893\pi$
$500$	−5301.61	−0.474191
$501$	−893.765	−0.0797016
$502$	206.902	0.0183954
$503$	8214.44	0.728159	0.364079	−	0.931368i	$-0.381384\pi$
$503$	8214.44	0.728159	0.364079	+	0.931368i	$0.381384\pi$
$504$	−3197.74	−0.282616
$505$	245.548	0.0216372
$506$	173.187	0.0152157
$507$	−4592.80	−0.402315
$508$	9962.35	0.870094
$509$	−8243.18	−0.717824	−0.358912	−	0.933371i	$-0.616852\pi$
$509$	−8243.18	−0.717824	−0.358912	+	0.933371i	$0.616852\pi$
$510$	0	0
$511$	−625.144	−0.0541188
$512$	4546.59	0.392447
$513$	2245.54	0.193261
$514$	−1706.99	−0.146483
$515$	3417.77	0.292436
$516$	−8325.90	−0.710325
$517$	11306.0	0.961771
$518$	974.192	0.0826323
$519$	−22705.3	−1.92033
$520$	−524.792	−0.0442570
$521$	−8953.14	−0.752868	−0.376434	−	0.926443i	$-0.622850\pi$
$521$	−8953.14	−0.752868	−0.376434	+	0.926443i	$0.622850\pi$
$522$	652.361	0.0546993
$523$	−15665.1	−1.30973	−0.654864	−	0.755747i	$-0.727274\pi$
$523$	−15665.1	−1.30973	−0.654864	+	0.755747i	$0.727274\pi$
$524$	15536.9	1.29530
$525$	20822.9	1.73102
$526$	−1791.28	−0.148485
$527$	0	0
$528$	−28199.6	−2.32430
$529$	−11972.8	−0.984040
$530$	−195.671	−0.0160366
$531$	−23579.4	−1.92704
$532$	3357.95	0.273657
$533$	22793.8	1.85236
$534$	1222.50	0.0990691
$535$	4230.57	0.341875
$536$	1308.31	0.105430
$537$	−16529.0	−1.32827
$538$	−1721.36	−0.137942
$539$	6555.23	0.523847
$540$	−2501.57	−0.199353
$541$	−9269.95	−0.736684	−0.368342	−	0.929690i	$-0.620074\pi$
$541$	−9269.95	−0.736684	−0.368342	+	0.929690i	$0.620074\pi$
$542$	−1457.16	−0.115480
$543$	19973.4	1.57853
$544$	0	0
$545$	285.821	0.0224647
$546$	2120.72	0.166224
$547$	15692.5	1.22662	0.613312	−	0.789840i	$-0.289837\pi$
$547$	15692.5	1.22662	0.613312	+	0.789840i	$0.289837\pi$
$548$	−13908.4	−1.08419
$549$	3204.77	0.249137
$550$	−1459.42	−0.113146
$551$	−1374.56	−0.106277
$552$	417.259	0.0321734
$553$	18412.2	1.41585
$554$	1541.05	0.118182
$555$	4503.02	0.344401
$556$	1639.76	0.125074
$557$	3540.22	0.269307	0.134654	−	0.990893i	$-0.457008\pi$
$557$	3540.22	0.269307	0.134654	+	0.990893i	$0.457008\pi$
$558$	−1555.98	−0.118046
$559$	6672.72	0.504877
$560$	−3716.21	−0.280426
$561$	0	0
$562$	−1435.18	−0.107722
$563$	315.012	0.0235811	0.0117906	−	0.999930i	$-0.496247\pi$
$563$	315.012	0.0235811	0.0117906	+	0.999930i	$0.496247\pi$
$564$	13575.3	1.01352
$565$	1013.11	0.0754371
$566$	−609.031	−0.0452287
$567$	−3473.20	−0.257250
$568$	774.777	0.0572340
$569$	−8531.61	−0.628583	−0.314291	−	0.949327i	$-0.601767\pi$
$569$	−8531.61	−0.628583	−0.314291	+	0.949327i	$0.601767\pi$
$570$	−101.409	−0.00745183
$571$	−8828.53	−0.647044	−0.323522	−	0.946221i	$-0.604867\pi$
$571$	−8828.53	−0.647044	−0.323522	+	0.946221i	$0.604867\pi$
$572$	22749.9	1.66298
$573$	34222.5	2.49505
$574$	−2130.02	−0.154887
$575$	−1636.40	−0.118683
$576$	−20121.7	−1.45556
$577$	21726.1	1.56754	0.783769	−	0.621052i	$-0.213295\pi$
$577$	21726.1	1.56754	0.783769	+	0.621052i	$0.213295\pi$
$578$	0	0
$579$	17108.0	1.22795
$580$	1531.29	0.109626
$581$	294.572	0.0210343
$582$	2250.50	0.160286
$583$	17020.3	1.20910
$584$	105.562	0.00747978
$585$	5903.75	0.417248
$586$	−497.525	−0.0350726
$587$	24674.7	1.73498	0.867489	−	0.497456i	$-0.165732\pi$
$587$	24674.7	1.73498	0.867489	+	0.497456i	$0.165732\pi$
$588$	7871.01	0.552032
$589$	3278.54	0.229355
$590$	361.614	0.0252329
$591$	−31337.7	−2.18115
$592$	12465.8	0.865439
$593$	9437.74	0.653561	0.326781	−	0.945100i	$-0.394036\pi$
$593$	9437.74	0.653561	0.326781	+	0.945100i	$0.394036\pi$
$594$	−1421.66	−0.0982007
$595$	0	0
$596$	16002.6	1.09982
$597$	−29841.3	−2.04577
$598$	−166.660	−0.0113967
$599$	−28257.9	−1.92753	−0.963763	−	0.266759i	$-0.914047\pi$
$599$	−28257.9	−1.92753	−0.963763	+	0.266759i	$0.914047\pi$
$600$	−3516.18	−0.239245
$601$	−17440.7	−1.18373	−0.591863	−	0.806038i	$-0.701607\pi$
$601$	−17440.7	−1.18373	−0.591863	+	0.806038i	$0.701607\pi$
$602$	−623.549	−0.0422159
$603$	−14718.0	−0.993972
$604$	−601.293	−0.0405071
$605$	−4521.82	−0.303864
$606$	167.557	0.0112319
$607$	452.598	0.0302642	0.0151321	−	0.999886i	$-0.495183\pi$
$607$	452.598	0.0302642	0.0151321	+	0.999886i	$0.495183\pi$
$608$	−851.460	−0.0567948
$609$	−12416.5	−0.826179
$610$	−49.1484	−0.00326223
$611$	−10879.8	−0.720377
$612$	0	0
$613$	−10731.9	−0.707106	−0.353553	−	0.935415i	$-0.615027\pi$
$613$	−10731.9	−0.707106	−0.353553	+	0.935415i	$0.615027\pi$
$614$	−889.932	−0.0584930
$615$	−9845.62	−0.645551
$616$	−4265.74	−0.279012
$617$	−20161.0	−1.31548	−0.657741	−	0.753244i	$-0.728488\pi$
$617$	−20161.0	−1.31548	−0.657741	+	0.753244i	$0.728488\pi$
$618$	2332.20	0.151804
$619$	−2592.80	−0.168358	−0.0841790	−	0.996451i	$-0.526827\pi$
$619$	−2592.80	−0.168358	−0.0841790	+	0.996451i	$0.526827\pi$
$620$	−3652.35	−0.236584
$621$	−1594.05	−0.103007
$622$	−1678.87	−0.108226
$623$	−14013.5	−0.901187
$624$	27136.7	1.74093
$625$	12843.4	0.821977
$626$	530.232	0.0338536
$627$	8820.95	0.561841
$628$	−18295.0	−1.16250
$629$	0	0
$630$	−551.690	−0.0348887
$631$	20929.5	1.32043	0.660215	−	0.751077i	$-0.270465\pi$
$631$	20929.5	1.32043	0.660215	+	0.751077i	$0.270465\pi$
$632$	−3109.10	−0.195685
$633$	−5211.31	−0.327221
$634$	1702.31	0.106636
$635$	3448.74	0.215526
$636$	20436.6	1.27416
$637$	−6308.15	−0.392367
$638$	870.240	0.0540018
$639$	−8716.01	−0.539593
$640$	1263.32	0.0780270
$641$	−9715.01	−0.598627	−0.299313	−	0.954155i	$-0.596758\pi$
$641$	−9715.01	−0.598627	−0.299313	+	0.954155i	$0.596758\pi$
$642$	2886.84	0.177468
$643$	−24219.0	−1.48539	−0.742693	−	0.669632i	$-0.766452\pi$
$643$	−24219.0	−1.48539	−0.742693	+	0.669632i	$0.766452\pi$
$644$	−2383.72	−0.145857
$645$	−2882.24	−0.175951
$646$	0	0
$647$	5143.07	0.312511	0.156256	−	0.987717i	$-0.450058\pi$
$647$	5143.07	0.312511	0.156256	+	0.987717i	$0.450058\pi$
$648$	586.487	0.0355546
$649$	−31454.6	−1.90247
$650$	1404.42	0.0847473
$651$	29615.2	1.78297
$652$	15045.7	0.903736
$653$	2922.83	0.175160	0.0875799	−	0.996157i	$-0.472087\pi$
$653$	2922.83	0.175160	0.0875799	+	0.996157i	$0.472087\pi$
$654$	195.038	0.0116614
$655$	5378.54	0.320850
$656$	−27255.7	−1.62219
$657$	−1187.54	−0.0705181
$658$	1016.69	0.0602352
$659$	−17368.4	−1.02667	−0.513336	−	0.858188i	$-0.671591\pi$
$659$	−17368.4	−1.02667	−0.513336	+	0.858188i	$0.671591\pi$
$660$	−9826.69	−0.579551
$661$	8041.13	0.473167	0.236584	−	0.971611i	$-0.423972\pi$
$661$	8041.13	0.473167	0.236584	+	0.971611i	$0.423972\pi$
$662$	2131.38	0.125134
$663$	0	0
$664$	−49.7417	−0.00290715
$665$	1162.44	0.0677860
$666$	1850.60	0.107672
$667$	975.769	0.0566446
$668$	−862.189	−0.0499387
$669$	4398.16	0.254174
$670$	225.716	0.0130152
$671$	4275.12	0.245960
$672$	−7691.29	−0.441515
$673$	9076.35	0.519863	0.259931	−	0.965627i	$-0.416300\pi$
$673$	9076.35	0.519863	0.259931	+	0.965627i	$0.416300\pi$
$674$	1582.40	0.0904331
$675$	13432.8	0.765970
$676$	−4430.54	−0.252079
$677$	−24957.6	−1.41684	−0.708418	−	0.705794i	$-0.750591\pi$
$677$	−24957.6	−1.41684	−0.708418	+	0.705794i	$0.750591\pi$
$678$	691.324	0.0391595
$679$	−25797.4	−1.45805
$680$	0	0
$681$	4851.56	0.272999
$682$	−2075.65	−0.116541
$683$	6068.62	0.339984	0.169992	−	0.985445i	$-0.445626\pi$
$683$	6068.62	0.339984	0.169992	+	0.985445i	$0.445626\pi$
$684$	6378.85	0.356581
$685$	−4814.77	−0.268559
$686$	−1092.72	−0.0608167
$687$	−21760.8	−1.20848
$688$	−7978.93	−0.442142
$689$	−16378.7	−0.905631
$690$	71.9876	0.00397177
$691$	17355.6	0.955484	0.477742	−	0.878500i	$-0.341455\pi$
$691$	17355.6	0.955484	0.477742	+	0.878500i	$0.341455\pi$
$692$	−21903.1	−1.20322
$693$	47988.2	2.63048
$694$	−549.182	−0.0300384
$695$	567.647	0.0309814
$696$	2096.66	0.114186
$697$	0	0
$698$	2507.87	0.135995
$699$	−3158.71	−0.170920
$700$	20087.3	1.08461
$701$	34827.5	1.87649	0.938243	−	0.345976i	$-0.112452\pi$
$701$	34827.5	1.87649	0.938243	+	0.345976i	$0.112452\pi$
$702$	1368.07	0.0735534
$703$	−3899.34	−0.209198
$704$	−26842.0	−1.43700
$705$	4699.47	0.251053
$706$	1757.67	0.0936982
$707$	−1920.70	−0.102171
$708$	−37768.3	−2.00483
$709$	−25687.0	−1.36064	−0.680322	−	0.732913i	$-0.738160\pi$
$709$	−25687.0	−1.36064	−0.680322	+	0.732913i	$0.738160\pi$
$710$	133.669	0.00706548
$711$	34976.4	1.84489
$712$	2366.33	0.124553
$713$	−2327.35	−0.122244
$714$	0	0
$715$	7875.52	0.411927
$716$	−15945.0	−0.832254
$717$	35796.0	1.86447
$718$	−2328.92	−0.121051
$719$	18176.3	0.942783	0.471392	−	0.881924i	$-0.343752\pi$
$719$	18176.3	0.942783	0.471392	+	0.881924i	$0.343752\pi$
$720$	−7059.43	−0.365402
$721$	−26734.0	−1.38090
$722$	−1475.20	−0.0760405
$723$	−16920.5	−0.870375
$724$	19267.8	0.989063
$725$	−8222.66	−0.421217
$726$	−3085.58	−0.157737
$727$	−8657.73	−0.441674	−0.220837	−	0.975311i	$-0.570879\pi$
$727$	−8657.73	−0.441674	−0.220837	+	0.975311i	$0.570879\pi$
$728$	4104.95	0.208983
$729$	−32044.8	−1.62805
$730$	18.2121	0.000923371 0
$731$	0	0
$732$	5133.24	0.259194
$733$	11299.2	0.569366	0.284683	−	0.958622i	$-0.408112\pi$
$733$	11299.2	0.569366	0.284683	+	0.958622i	$0.408112\pi$
$734$	2352.25	0.118288
$735$	2724.77	0.136741
$736$	604.431	0.0302712
$737$	−19633.7	−0.981297
$738$	−4046.25	−0.201822
$739$	12566.0	0.625503	0.312752	−	0.949835i	$-0.398749\pi$
$739$	12566.0	0.625503	0.312752	+	0.949835i	$0.398749\pi$
$740$	4343.93	0.215792
$741$	−8488.47	−0.420825
$742$	1530.55	0.0757254
$743$	14049.4	0.693707	0.346854	−	0.937919i	$-0.387250\pi$
$743$	14049.4	0.693707	0.346854	+	0.937919i	$0.387250\pi$
$744$	−5000.85	−0.246425
$745$	5539.72	0.272429
$746$	625.317	0.0306897
$747$	559.578	0.0274082
$748$	0	0
$749$	−33091.7	−1.61435
$750$	−1252.37	−0.0609732
$751$	8131.49	0.395103	0.197551	−	0.980293i	$-0.436701\pi$
$751$	8131.49	0.395103	0.197551	+	0.980293i	$0.436701\pi$
$752$	13009.6	0.630865
$753$	−7480.77	−0.362038
$754$	−837.439	−0.0404479
$755$	−208.154	−0.0100338
$756$	19567.4	0.941350
$757$	−22973.8	−1.10304	−0.551518	−	0.834163i	$-0.685951\pi$
$757$	−22973.8	−1.10304	−0.551518	+	0.834163i	$0.685951\pi$
$758$	1459.56	0.0699387
$759$	−6261.77	−0.299457
$760$	−196.291	−0.00936872
$761$	15071.9	0.717946	0.358973	−	0.933348i	$-0.383127\pi$
$761$	15071.9	0.717946	0.358973	+	0.933348i	$0.383127\pi$
$762$	2353.34	0.111880
$763$	−2235.71	−0.106079
$764$	33013.4	1.56333
$765$	0	0
$766$	841.515	0.0396934
$767$	30269.0	1.42497
$768$	−31578.3	−1.48370
$769$	−10392.1	−0.487321	−0.243660	−	0.969861i	$-0.578348\pi$
$769$	−10392.1	−0.487321	−0.243660	+	0.969861i	$0.578348\pi$
$770$	−735.947	−0.0344438
$771$	61718.1	2.88291
$772$	16503.5	0.769398
$773$	−34388.6	−1.60009	−0.800047	−	0.599937i	$-0.795192\pi$
$773$	−34388.6	−1.60009	−0.800047	+	0.599937i	$0.795192\pi$
$774$	−1184.51	−0.0550083
$775$	19612.3	0.909024
$776$	4356.16	0.201517
$777$	−35222.9	−1.62627
$778$	−486.052	−0.0223982
$779$	8525.69	0.392124
$780$	9456.31	0.434090
$781$	−11627.0	−0.532712
$782$	0	0
$783$	−8009.87	−0.365580
$784$	7543.00	0.343613
$785$	−6333.30	−0.287956
$786$	3670.19	0.166554
$787$	−25621.7	−1.16050	−0.580252	−	0.814437i	$-0.697046\pi$
$787$	−25621.7	−1.16050	−0.580252	+	0.814437i	$0.697046\pi$
$788$	−30230.5	−1.36665
$789$	64765.5	2.92232
$790$	−536.397	−0.0241572
$791$	−7924.63	−0.356216
$792$	−8103.32	−0.363559
$793$	−4113.99	−0.184227
$794$	538.900	0.0240867
$795$	7074.69	0.315614
$796$	−28787.0	−1.28182
$797$	28437.6	1.26388	0.631940	−	0.775017i	$-0.282259\pi$
$797$	28437.6	1.26388	0.631940	+	0.775017i	$0.282259\pi$
$798$	793.226	0.0351878
$799$	0	0
$800$	−5093.45	−0.225101
$801$	−26620.5	−1.17427
$802$	470.281	0.0207060
$803$	−1584.16	−0.0696188
$804$	−23574.6	−1.03409
$805$	−825.191	−0.0361294
$806$	1997.42	0.0872903
$807$	62237.5	2.71482
$808$	324.330	0.0141211
$809$	22354.1	0.971481	0.485741	−	0.874103i	$-0.338550\pi$
$809$	22354.1	0.971481	0.485741	+	0.874103i	$0.338550\pi$
$810$	101.184	0.00438918
$811$	−6031.85	−0.261167	−0.130584	−	0.991437i	$-0.541685\pi$
$811$	−6031.85	−0.261167	−0.130584	+	0.991437i	$0.541685\pi$
$812$	−11977.8	−0.517660
$813$	52685.0	2.27275
$814$	2468.68	0.106299
$815$	5208.49	0.223859
$816$	0	0
$817$	2495.84	0.106877
$818$	2106.74	0.0900493
$819$	−46179.5	−1.97026
$820$	−9497.78	−0.404484
$821$	−12662.5	−0.538276	−0.269138	−	0.963102i	$-0.586739\pi$
$821$	−12662.5	−0.538276	−0.269138	+	0.963102i	$0.586739\pi$
$822$	−3285.49	−0.139409
$823$	−11029.9	−0.467166	−0.233583	−	0.972337i	$-0.575045\pi$
$823$	−11029.9	−0.467166	−0.233583	+	0.972337i	$0.575045\pi$
$824$	4514.32	0.190854
$825$	52767.0	2.22680
$826$	−2828.57	−0.119151
$827$	28646.5	1.20452	0.602258	−	0.798301i	$-0.294268\pi$
$827$	28646.5	1.20452	0.602258	+	0.798301i	$0.294268\pi$
$828$	−4528.19	−0.190055
$829$	−15663.7	−0.656239	−0.328120	−	0.944636i	$-0.606415\pi$
$829$	−15663.7	−0.656239	−0.328120	+	0.944636i	$0.606415\pi$
$830$	−8.58169	−0.000358885 0
$831$	−55718.2	−2.32593
$832$	25830.3	1.07633
$833$	0	0
$834$	387.349	0.0160825
$835$	−298.470	−0.0123700
$836$	8509.30	0.352034
$837$	19104.7	0.788955
$838$	946.916	0.0390342
$839$	−22653.3	−0.932158	−0.466079	−	0.884743i	$-0.654334\pi$
$839$	−22653.3	−0.932158	−0.466079	+	0.884743i	$0.654334\pi$
$840$	−1773.11	−0.0728311
$841$	−19485.9	−0.798963
$842$	1050.35	0.0429898
$843$	51890.6	2.12005
$844$	−5027.19	−0.205027
$845$	−1533.75	−0.0624411
$846$	1931.34	0.0784879
$847$	35369.9	1.43486
$848$	19584.9	0.793100
$849$	22020.1	0.890141
$850$	0	0
$851$	2768.04	0.111501
$852$	−13960.8	−0.561374
$853$	4449.94	0.178620	0.0893102	−	0.996004i	$-0.471534\pi$
$853$	4449.94	0.178620	0.0893102	+	0.996004i	$0.471534\pi$
$854$	384.442	0.0154044
$855$	2208.22	0.0883267
$856$	5587.89	0.223119
$857$	22724.0	0.905762	0.452881	−	0.891571i	$-0.350396\pi$
$857$	22724.0	0.905762	0.452881	+	0.891571i	$0.350396\pi$
$858$	5374.07	0.213832
$859$	42049.4	1.67021	0.835104	−	0.550092i	$-0.185408\pi$
$859$	42049.4	1.67021	0.835104	+	0.550092i	$0.185408\pi$
$860$	−2780.41	−0.110246
$861$	77013.1	3.04831
$862$	3949.21	0.156045
$863$	−7875.51	−0.310644	−0.155322	−	0.987864i	$-0.549641\pi$
$863$	−7875.51	−0.310644	−0.155322	+	0.987864i	$0.549641\pi$
$864$	−4961.63	−0.195368
$865$	−7582.37	−0.298044
$866$	2587.30	0.101524
$867$	0	0
$868$	28568.9	1.11716
$869$	46658.0	1.82136
$870$	361.727	0.0140962
$871$	18893.6	0.735002
$872$	377.524	0.0146612
$873$	−49005.5	−1.89987
$874$	−62.3368	−0.00241255
$875$	14355.8	0.554646
$876$	−1902.14	−0.0733646
$877$	−26126.7	−1.00597	−0.502986	−	0.864295i	$-0.667765\pi$
$877$	−26126.7	−1.00597	−0.502986	+	0.864295i	$0.667765\pi$
$878$	−1168.57	−0.0449174
$879$	17988.5	0.690259
$880$	−9417.18	−0.360742
$881$	6400.01	0.244747	0.122373	−	0.992484i	$-0.460949\pi$
$881$	6400.01	0.244747	0.122373	+	0.992484i	$0.460949\pi$
$882$	1119.80	0.0427500
$883$	43393.3	1.65379	0.826897	−	0.562354i	$-0.190104\pi$
$883$	43393.3	1.65379	0.826897	+	0.562354i	$0.190104\pi$
$884$	0	0
$885$	−13074.5	−0.496605
$886$	−713.941	−0.0270714
$887$	−20465.4	−0.774704	−0.387352	−	0.921932i	$-0.626610\pi$
$887$	−20465.4	−0.774704	−0.387352	+	0.921932i	$0.626610\pi$
$888$	5947.77	0.224768
$889$	−26976.3	−1.01772
$890$	408.251	0.0153760
$891$	−8801.37	−0.330928
$892$	4242.77	0.159258
$893$	−4069.44	−0.152496
$894$	3780.18	0.141418
$895$	−5519.81	−0.206153
$896$	−9881.81	−0.368446
$897$	6025.76	0.224297
$898$	−2677.47	−0.0994970
$899$	−11694.6	−0.433856
$900$	38158.4	1.41327
$901$	0	0
$902$	−5397.64	−0.199248
$903$	22545.1	0.830845
$904$	1338.16	0.0492328
$905$	6670.07	0.244995
$906$	−142.040	−0.00520856
$907$	30194.7	1.10540	0.552701	−	0.833379i	$-0.313597\pi$
$907$	30194.7	1.10540	0.552701	+	0.833379i	$0.313597\pi$
$908$	4680.16	0.171053
$909$	−3648.61	−0.133132
$910$	708.208	0.0257987
$911$	22997.2	0.836368	0.418184	−	0.908362i	$-0.362667\pi$
$911$	22997.2	0.836368	0.418184	+	0.908362i	$0.362667\pi$
$912$	10150.1	0.368535
$913$	746.470	0.0270586
$914$	−2827.68	−0.102332
$915$	1777.01	0.0642034
$916$	−20992.0	−0.757201
$917$	−42071.3	−1.51507
$918$	0	0
$919$	−40432.8	−1.45131	−0.725656	−	0.688057i	$-0.758464\pi$
$919$	−40432.8	−1.45131	−0.725656	+	0.688057i	$0.758464\pi$
$920$	139.342	0.00499346
$921$	32176.4	1.15119
$922$	−1679.57	−0.0599932
$923$	11188.8	0.399007
$924$	76865.0	2.73666
$925$	−23325.9	−0.829135
$926$	2608.49	0.0925707
$927$	−50784.7	−1.79934
$928$	3037.17	0.107435
$929$	−34086.1	−1.20380	−0.601899	−	0.798572i	$-0.705589\pi$
$929$	−34086.1	−1.20380	−0.601899	+	0.798572i	$0.705589\pi$
$930$	−862.772	−0.0304209
$931$	−2359.48	−0.0830599
$932$	−3047.11	−0.107094
$933$	60701.3	2.12998
$934$	1006.83	0.0352724
$935$	0	0
$936$	7797.89	0.272310
$937$	763.643	0.0266245	0.0133122	−	0.999911i	$-0.495762\pi$
$937$	763.643	0.0266245	0.0133122	+	0.999911i	$0.495762\pi$
$938$	−1765.56	−0.0614581
$939$	−19171.1	−0.666268
$940$	4533.44	0.157303
$941$	444.965	0.0154149	0.00770746	−	0.999970i	$-0.497547\pi$
$941$	444.965	0.0154149	0.00770746	+	0.999970i	$0.497547\pi$
$942$	−4321.70	−0.149478
$943$	−6052.18	−0.208999
$944$	−36194.3	−1.24791
$945$	6773.80	0.233177
$946$	−1580.12	−0.0543068
$947$	−11153.9	−0.382739	−0.191369	−	0.981518i	$-0.561293\pi$
$947$	−11153.9	−0.382739	−0.191369	+	0.981518i	$0.561293\pi$
$948$	56023.3	1.91936
$949$	1524.45	0.0521453
$950$	525.302	0.0179401
$951$	−61548.7	−2.09869
$952$	0	0
$953$	48344.2	1.64325	0.821627	−	0.570026i	$-0.193067\pi$
$953$	48344.2	1.64325	0.821627	+	0.570026i	$0.193067\pi$
$954$	2907.48	0.0986720
$955$	11428.5	0.387244
$956$	34531.3	1.16822
$957$	−31464.5	−1.06280
$958$	64.4017	0.00217195
$959$	37661.4	1.26814
$960$	−11157.2	−0.375102
$961$	−1897.64	−0.0636985
$962$	−2375.63	−0.0796189
$963$	−62862.1	−2.10353
$964$	−16322.7	−0.545352
$965$	5713.15	0.190583
$966$	−563.092	−0.0187548
$967$	−874.287	−0.0290746	−0.0145373	−	0.999894i	$-0.504628\pi$
$967$	−874.287	−0.0290746	−0.0145373	+	0.999894i	$0.504628\pi$
$968$	−5972.59	−0.198312
$969$	0	0
$970$	751.547	0.0248770
$971$	−28878.7	−0.954441	−0.477220	−	0.878784i	$-0.658356\pi$
$971$	−28878.7	−0.954441	−0.477220	+	0.878784i	$0.658356\pi$
$972$	−35116.0	−1.15879
$973$	−4440.17	−0.146295
$974$	−1732.36	−0.0569900
$975$	−50778.1	−1.66790
$976$	4919.31	0.161335
$977$	−4446.04	−0.145590	−0.0727950	−	0.997347i	$-0.523192\pi$
$977$	−4446.04	−0.145590	−0.0727950	+	0.997347i	$0.523192\pi$
$978$	3554.15	0.116206
$979$	−35511.3	−1.15929
$980$	2628.50	0.0856779
$981$	−4247.02	−0.138223
$982$	−2924.80	−0.0950448
$983$	−41237.1	−1.33800	−0.669002	−	0.743261i	$-0.733278\pi$
$983$	−41237.1	−1.33800	−0.669002	+	0.743261i	$0.733278\pi$
$984$	−13004.5	−0.421308
$985$	−10465.1	−0.338524
$986$	0	0
$987$	−36759.5	−1.18548
$988$	−8188.57	−0.263677
$989$	−1771.74	−0.0569645
$990$	−1398.03	−0.0448810
$991$	33085.1	1.06053	0.530264	−	0.847832i	$-0.322093\pi$
$991$	33085.1	1.06053	0.530264	+	0.847832i	$0.322093\pi$
$992$	−7244.10	−0.231855
$993$	−77062.3	−2.46274
$994$	−1045.56	−0.0333634
$995$	−9965.42	−0.317513
$996$	896.303	0.0285145
$997$	−11284.0	−0.358442	−0.179221	−	0.983809i	$-0.557358\pi$
$997$	−11284.0	−0.358442	−0.179221	+	0.983809i	$0.557358\pi$
$998$	−619.195	−0.0196395
$999$	−22722.2	−0.719619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.g.1.7		12
17.4	even	4		289.4.b.e.288.6		12
17.5	odd	16		17.4.d.a.8.2	✓	12
17.7	odd	16		17.4.d.a.15.2	yes	12
17.13	even	4		289.4.b.e.288.5		12
17.16	even	2	inner	289.4.a.g.1.8		12
51.5	even	16		153.4.l.a.127.2		12
51.41	even	16		153.4.l.a.100.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.8.2	✓	12	17.5	odd	16
17.4.d.a.15.2	yes	12	17.7	odd	16
153.4.l.a.100.2		12	51.41	even	16
153.4.l.a.127.2		12	51.5	even	16
289.4.a.g.1.7		12	1.1	even	1	trivial
289.4.a.g.1.8		12	17.16	even	2	inner
289.4.b.e.288.5		12	17.13	even	4
289.4.b.e.288.6		12	17.4	even	4

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+0.227878 q^{2} -8.23916 q^{3} -7.94807 q^{4} -2.75144 q^{5} -1.87752 q^{6} +21.5220 q^{7} -3.63421 q^{8} +40.8838 q^{9} +O(q^{10})\)	\(q+0.227878 q^{2} -8.23916 q^{3} -7.94807 q^{4} -2.75144 q^{5} -1.87752 q^{6} +21.5220 q^{7} -3.63421 q^{8} +40.8838 q^{9} -0.626993 q^{10} +54.5384 q^{11} +65.4854 q^{12} -52.4827 q^{13} +4.90438 q^{14} +22.6696 q^{15} +62.7564 q^{16} +9.31650 q^{18} -19.6304 q^{19} +21.8687 q^{20} -177.323 q^{21} +12.4281 q^{22} +13.9352 q^{23} +29.9428 q^{24} -117.430 q^{25} -11.9596 q^{26} -114.391 q^{27} -171.058 q^{28} +70.0221 q^{29} +5.16589 q^{30} -167.013 q^{31} +43.3745 q^{32} -449.350 q^{33} -59.2165 q^{35} -324.947 q^{36} +198.637 q^{37} -4.47334 q^{38} +432.414 q^{39} +9.99933 q^{40} -434.310 q^{41} -40.4079 q^{42} -127.141 q^{43} -433.475 q^{44} -112.489 q^{45} +3.17552 q^{46} +207.303 q^{47} -517.060 q^{48} +120.195 q^{49} -26.7596 q^{50} +417.136 q^{52} +312.078 q^{53} -26.0671 q^{54} -150.059 q^{55} -78.2154 q^{56} +161.738 q^{57} +15.9565 q^{58} -576.743 q^{59} -180.179 q^{60} +78.3874 q^{61} -38.0586 q^{62} +879.899 q^{63} -492.167 q^{64} +144.403 q^{65} -102.397 q^{66} -359.997 q^{67} -114.814 q^{69} -13.4941 q^{70} -213.190 q^{71} -148.580 q^{72} -29.0468 q^{73} +45.2650 q^{74} +967.521 q^{75} +156.024 q^{76} +1173.77 q^{77} +98.5374 q^{78} +855.508 q^{79} -172.671 q^{80} -161.379 q^{81} -98.9696 q^{82} +13.6871 q^{83} +1409.38 q^{84} -28.9727 q^{86} -576.923 q^{87} -198.204 q^{88} -651.126 q^{89} -25.6338 q^{90} -1129.53 q^{91} -110.758 q^{92} +1376.05 q^{93} +47.2397 q^{94} +54.0120 q^{95} -357.369 q^{96} -1198.65 q^{97} +27.3897 q^{98} +2229.73 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9}+O(q^{10}) \) 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9	\( 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9} - 8 q^{13} - 192 q^{15} - 184 q^{16} - 352 q^{19} - 256 q^{21} - 492 q^{25} - 784 q^{26} + 744 q^{30} + 24 q^{32} - 1400 q^{33} - 632 q^{35} - 856 q^{36} - 624 q^{38} - 1664 q^{42} - 1200 q^{43} - 1512 q^{47} - 1052 q^{49} - 2856 q^{50} + 792 q^{52} - 2504 q^{53} - 1424 q^{55} - 3408 q^{59} - 2808 q^{60} + 272 q^{64} + 272 q^{66} - 1080 q^{67} - 344 q^{69} + 2600 q^{70} + 248 q^{72} + 896 q^{76} + 848 q^{77} - 2404 q^{81} - 2960 q^{83} + 4768 q^{84} - 1200 q^{86} - 160 q^{87} - 2144 q^{89} + 3800 q^{93} + 5984 q^{94} + 3464 q^{98}+O(q^{100}) \) 12 * q - 8 * q^2 + 16 * q^4 - 96 * q^8 - 36 * q^9 - 8 * q^13 - 192 * q^15 - 184 * q^16 - 352 * q^19 - 256 * q^21 - 492 * q^25 - 784 * q^26 + 744 * q^30 + 24 * q^32 - 1400 * q^33 - 632 * q^35 - 856 * q^36 - 624 * q^38 - 1664 * q^42 - 1200 * q^43 - 1512 * q^47 - 1052 * q^49 - 2856 * q^50 + 792 * q^52 - 2504 * q^53 - 1424 * q^55 - 3408 * q^59 - 2808 * q^60 + 272 * q^64 + 272 * q^66 - 1080 * q^67 - 344 * q^69 + 2600 * q^70 + 248 * q^72 + 896 * q^76 + 848 * q^77 - 2404 * q^81 - 2960 * q^83 + 4768 * q^84 - 1200 * q^86 - 160 * q^87 - 2144 * q^89 + 3800 * q^93 + 5984 * q^94 + 3464 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more