LMFDB - Embedded newform 289.4.a.g.1.8

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			1.8
Root			$-0.619881$ 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	$-0.208615\pi$
$3$	8.23916	1.58563	0.792814	+	0.609464i	$0.208615\pi$
$4$	−7.94807	−0.993509
$5$	2.75144	0.246097	0.123048	−	0.992401i	$-0.460733\pi$
$5$	2.75144	0.246097	0.123048	+	0.992401i	$0.460733\pi$
$6$	1.87752	0.127749
$7$	−21.5220	−1.16208	−0.581038	−	0.813876i	$-0.697353\pi$
$7$	−21.5220	−1.16208	−0.581038	+	0.813876i	$0.697353\pi$
$8$	−3.63421	−0.160611
$9$	40.8838	1.51421
$10$	0.626993	0.0198273
$11$	−54.5384	−1.49490	−0.747452	−	0.664316i	$-0.768723\pi$
$11$	−54.5384	−1.49490	−0.747452	+	0.664316i	$0.768723\pi$
$12$	−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	$-0.520120\pi$
$23$	−13.9352	−0.126334	−0.0631670	+	0.998003i	$0.520120\pi$
$24$	−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	$-0.571972\pi$
$29$	−70.0221	−0.448372	−0.224186	+	0.974546i	$0.571972\pi$
$30$	5.16589	0.0314386
$31$	167.013	0.967627	0.483813	−	0.875171i	$-0.339251\pi$
$31$	167.013	0.967627	0.483813	+	0.875171i	$0.339251\pi$
$32$	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	$-0.645480\pi$
$37$	−198.637	−0.882588	−0.441294	+	0.897363i	$0.645480\pi$
$38$	−4.47334	−0.0190966
$39$	−432.414	−1.77543
$40$	−9.99933	−0.0395258
$41$	434.310	1.65434	0.827168	−	0.561954i	$-0.189950\pi$
$41$	434.310	1.65434	0.827168	+	0.561954i	$0.189950\pi$
$42$	−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	$-0.526216\pi$
$61$	−78.3874	−0.164533	−0.0822663	+	0.996610i	$0.526216\pi$
$62$	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	$-0.442980\pi$
$71$	213.190	0.356352	0.178176	+	0.983999i	$0.442980\pi$
$72$	−148.580	−0.243199
$73$	29.0468	0.0465708	0.0232854	−	0.999729i	$-0.492587\pi$
$73$	29.0468	0.0465708	0.0232854	+	0.999729i	$0.492587\pi$
$74$	−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	$-0.708506\pi$
$79$	−855.508	−1.21838	−0.609191	+	0.793024i	$0.708506\pi$
$80$	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	$-0.284142\pi$
$97$	1198.65	1.25469	0.627345	+	0.778742i	$0.284142\pi$
$98$	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	$-0.255583\pi$
$107$	1537.58	1.38919	0.694596	+	0.719400i	$0.255583\pi$
$108$	−909.184	−0.810058
$109$	103.880	0.0912839	0.0456419	−	0.998958i	$-0.485467\pi$
$109$	103.880	0.0912839	0.0456419	+	0.998958i	$0.485467\pi$
$110$	−34.1952	−0.0296398
$111$	−1636.60	−1.39946
$112$	−1350.64	−1.13950
$113$	368.211	0.306534	0.153267	−	0.988185i	$-0.451020\pi$
$113$	368.211	0.306534	0.153267	+	0.988185i	$0.451020\pi$
$114$	−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	$-0.273981\pi$
$131$	1954.81	1.30376	0.651879	+	0.758323i	$0.273981\pi$
$132$	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	$-0.479951\pi$
$139$	206.309	0.125891	0.0629456	+	0.998017i	$0.479951\pi$
$140$	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	$-0.349704\pi$
$163$	1893.00	0.909640	0.454820	+	0.890583i	$0.349704\pi$
$164$	−3451.93	−1.64360
$165$	−1236.36	−0.583337
$166$	3.11898	0.00145831
$167$	−108.478	−0.0502650	−0.0251325	−	0.999684i	$-0.508001\pi$
$167$	−108.478	−0.0502650	−0.0251325	+	0.999684i	$0.508001\pi$
$168$	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	$-0.707044\pi$
$173$	−2755.78	−1.21109	−0.605543	+	0.795813i	$0.707044\pi$
$174$	−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	$-0.334155\pi$
$181$	2424.21	0.995525	0.497762	+	0.867313i	$0.334155\pi$
$182$	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	$-0.373438\pi$
$193$	2076.42	0.774425	0.387212	+	0.921991i	$0.373438\pi$
$194$	273.147	0.101087
$195$	−1189.76	−0.436926
$196$	−955.317	−0.348148
$197$	−3803.50	−1.37558	−0.687788	−	0.725912i	$-0.741418\pi$
$197$	−3803.50	−1.37558	−0.687788	+	0.725912i	$0.741418\pi$
$198$	−508.107	−0.182372
$199$	−3621.89	−1.29020	−0.645098	−	0.764100i	$-0.723183\pi$
$199$	−3621.89	−1.29020	−0.645098	+	0.764100i	$0.723183\pi$
$200$	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	$-0.532903\pi$
$211$	−632.505	−0.206367	−0.103183	+	0.994662i	$0.532903\pi$
$212$	−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	$-0.472564\pi$
$227$	588.842	0.172171	0.0860855	+	0.996288i	$0.472564\pi$
$228$	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	$-0.517164\pi$
$233$	−383.377	−0.107794	−0.0538968	+	0.998547i	$0.517164\pi$
$234$	−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	$-0.588498\pi$
$241$	−2053.67	−0.548915	−0.274458	+	0.961599i	$0.588498\pi$
$242$	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	$-0.172898\pi$
$269$	7553.86	1.71215	0.856073	+	0.516856i	$0.172898\pi$
$270$	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	$-0.762087\pi$
$277$	−6762.61	−1.46688	−0.733440	+	0.679754i	$0.762087\pi$
$278$	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	$-0.409437\pi$
$283$	2672.62	0.561381	0.280690	+	0.959798i	$0.409437\pi$
$284$	−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	$-0.265585\pi$
$311$	7367.41	1.34330	0.671652	+	0.740867i	$0.265585\pi$
$312$	1571.48	0.285153
$313$	−2326.83	−0.420192	−0.210096	−	0.977681i	$-0.567378\pi$
$313$	−2326.83	−0.420192	−0.210096	+	0.977681i	$0.567378\pi$
$314$	524.532	0.0942708
$315$	−2420.99	−0.433039
$316$	6799.64	1.21047
$317$	−7470.26	−1.32357	−0.661785	−	0.749694i	$-0.730201\pi$
$317$	−7470.26	−1.32357	−0.661785	+	0.749694i	$0.730201\pi$
$318$	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	$-0.689671\pi$
$337$	−6944.09	−1.12246	−0.561229	+	0.827660i	$0.689671\pi$
$338$	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	$-0.440312\pi$
$347$	2409.98	0.372838	0.186419	+	0.982470i	$0.440312\pi$
$348$	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	$-0.762394\pi$
$367$	−10322.4	−1.46819	−0.734096	+	0.679046i	$0.762394\pi$
$368$	−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	$-0.642913\pi$
$379$	−6405.00	−0.868082	−0.434041	+	0.900893i	$0.642913\pi$
$380$	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	$-0.547761\pi$
$397$	−2364.86	−0.298965	−0.149483	+	0.988764i	$0.547761\pi$
$398$	−825.348	−0.103947
$399$	3480.93	0.436753
$400$	−7369.46	−0.921182
$401$	−2063.74	−0.257003	−0.128502	−	0.991709i	$-0.541017\pi$
$401$	−2063.74	−0.257003	−0.128502	+	0.991709i	$0.541017\pi$
$402$	−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	$-0.577884\pi$
$419$	−4155.37	−0.484494	−0.242247	+	0.970215i	$0.577884\pi$
$420$	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	$-0.919786\pi$
$431$	−17330.4	−1.93683	−0.968416	+	0.249341i	$0.919786\pi$
$432$	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	$-0.410077\pi$
$439$	5128.08	0.557516	0.278758	+	0.960361i	$0.410077\pi$
$440$	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	$-0.288154\pi$
$449$	11749.6	1.23496	0.617480	+	0.786586i	$0.288154\pi$
$450$	−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	$-0.504291\pi$
$479$	−282.615	−0.0269583	−0.0134791	+	0.999909i	$0.504291\pi$
$480$	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	$-0.384930\pi$
$487$	7602.13	0.707362	0.353681	+	0.935366i	$0.384930\pi$
$488$	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	$-0.461107\pi$
$499$	2717.22	0.243767	0.121883	+	0.992544i	$0.461107\pi$
$500$	5301.61	0.474191
$501$	−893.765	−0.0797016
$502$	206.902	0.0183954
$503$	−8214.44	−0.728159	−0.364079	−	0.931368i	$-0.618616\pi$
$503$	−8214.44	−0.728159	−0.364079	+	0.931368i	$0.618616\pi$
$504$	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	$-0.377150\pi$
$521$	8953.14	0.752868	0.376434	+	0.926443i	$0.377150\pi$
$522$	−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	$-0.379926\pi$
$541$	9269.95	0.736684	0.368342	+	0.929690i	$0.379926\pi$
$542$	−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	$-0.710163\pi$
$547$	−15692.5	−1.22662	−0.613312	+	0.789840i	$0.710163\pi$
$548$	−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	$-0.395133\pi$
$571$	8828.53	0.647044	0.323522	+	0.946221i	$0.395133\pi$
$572$	−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	$-0.298393\pi$
$601$	17440.7	1.18373	0.591863	+	0.806038i	$0.298393\pi$
$602$	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	$-0.504817\pi$
$607$	−452.598	−0.0302642	−0.0151321	+	0.999886i	$0.504817\pi$
$608$	−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	$-0.271512\pi$
$617$	20161.0	1.31548	0.657741	+	0.753244i	$0.271512\pi$
$618$	−2332.20	−0.151804
$619$	2592.80	0.168358	0.0841790	−	0.996451i	$-0.473173\pi$
$619$	2592.80	0.168358	0.0841790	+	0.996451i	$0.473173\pi$
$620$	−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	$-0.403242\pi$
$641$	9715.01	0.598627	0.299313	+	0.954155i	$0.403242\pi$
$642$	2886.84	0.177468
$643$	24219.0	1.48539	0.742693	−	0.669632i	$-0.233548\pi$
$643$	24219.0	1.48539	0.742693	+	0.669632i	$0.233548\pi$
$644$	−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	$-0.527913\pi$
$653$	−2922.83	−0.175160	−0.0875799	+	0.996157i	$0.527913\pi$
$654$	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	$-0.583700\pi$
$673$	−9076.35	−0.519863	−0.259931	+	0.965627i	$0.583700\pi$
$674$	−1582.40	−0.0904331
$675$	−13432.8	−0.765970
$676$	−4430.54	−0.252079
$677$	24957.6	1.41684	0.708418	−	0.705794i	$-0.249409\pi$
$677$	24957.6	1.41684	0.708418	+	0.705794i	$0.249409\pi$
$678$	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	$-0.554374\pi$
$683$	−6068.62	−0.339984	−0.169992	+	0.985445i	$0.554374\pi$
$684$	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	$-0.658545\pi$
$691$	−17355.6	−0.955484	−0.477742	+	0.878500i	$0.658545\pi$
$692$	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	$-0.261840\pi$
$709$	25687.0	1.36064	0.680322	+	0.732913i	$0.261840\pi$
$710$	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	$-0.656248\pi$
$719$	−18176.3	−0.942783	−0.471392	+	0.881924i	$0.656248\pi$
$720$	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	$-0.612750\pi$
$743$	−14049.4	−0.693707	−0.346854	+	0.937919i	$0.612750\pi$
$744$	−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	$-0.563299\pi$
$751$	−8131.49	−0.395103	−0.197551	+	0.980293i	$0.563299\pi$
$752$	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	$-0.302954\pi$
$787$	25621.7	1.16050	0.580252	+	0.814437i	$0.302954\pi$
$788$	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	$-0.661450\pi$
$809$	−22354.1	−0.971481	−0.485741	+	0.874103i	$0.661450\pi$
$810$	−101.184	−0.00438918
$811$	6031.85	0.261167	0.130584	−	0.991437i	$-0.458315\pi$
$811$	6031.85	0.261167	0.130584	+	0.991437i	$0.458315\pi$
$812$	−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	$-0.413261\pi$
$821$	12662.5	0.538276	0.269138	+	0.963102i	$0.413261\pi$
$822$	3285.49	0.139409
$823$	11029.9	0.467166	0.233583	−	0.972337i	$-0.424955\pi$
$823$	11029.9	0.467166	0.233583	+	0.972337i	$0.424955\pi$
$824$	4514.32	0.190854
$825$	52767.0	2.22680
$826$	2828.57	0.119151
$827$	−28646.5	−1.20452	−0.602258	−	0.798301i	$-0.705732\pi$
$827$	−28646.5	−1.20452	−0.602258	+	0.798301i	$0.705732\pi$
$828$	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	$-0.345666\pi$
$839$	22653.3	0.932158	0.466079	+	0.884743i	$0.345666\pi$
$840$	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	$-0.528466\pi$
$853$	−4449.94	−0.178620	−0.0893102	+	0.996004i	$0.528466\pi$
$854$	384.442	0.0154044
$855$	−2208.22	−0.0883267
$856$	−5587.89	−0.223119
$857$	−22724.0	−0.905762	−0.452881	−	0.891571i	$-0.649604\pi$
$857$	−22724.0	−0.905762	−0.452881	+	0.891571i	$0.649604\pi$
$858$	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	$-0.332235\pi$
$877$	26126.7	1.00597	0.502986	+	0.864295i	$0.332235\pi$
$878$	1168.57	0.0449174
$879$	−17988.5	−0.690259
$880$	−9417.18	−0.360742
$881$	−6400.01	−0.244747	−0.122373	−	0.992484i	$-0.539051\pi$
$881$	−6400.01	−0.244747	−0.122373	+	0.992484i	$0.539051\pi$
$882$	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	$-0.373390\pi$
$887$	20465.4	0.774704	0.387352	+	0.921932i	$0.373390\pi$
$888$	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	$-0.686403\pi$
$907$	−30194.7	−1.10540	−0.552701	+	0.833379i	$0.686403\pi$
$908$	−4680.16	−0.171053
$909$	−3648.61	−0.133132
$910$	708.208	0.0257987
$911$	−22997.2	−0.836368	−0.418184	−	0.908362i	$-0.637333\pi$
$911$	−22997.2	−0.836368	−0.418184	+	0.908362i	$0.637333\pi$
$912$	−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	$-0.294411\pi$
$929$	34086.1	1.20380	0.601899	+	0.798572i	$0.294411\pi$
$930$	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	$-0.502453\pi$
$941$	−444.965	−0.0154149	−0.00770746	+	0.999970i	$0.502453\pi$
$942$	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	$-0.438707\pi$
$947$	11153.9	0.382739	0.191369	+	0.981518i	$0.438707\pi$
$948$	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	$-0.266722\pi$
$983$	41237.1	1.33800	0.669002	+	0.743261i	$0.266722\pi$
$984$	−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	$-0.677907\pi$
$991$	−33085.1	−1.06053	−0.530264	+	0.847832i	$0.677907\pi$
$992$	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	$-0.442642\pi$
$997$	11284.0	0.358442	0.179221	+	0.983809i	$0.442642\pi$
$998$	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.1.8		12
17.4	even	4		289.4.b.e.288.5		12
17.10	odd	16		17.4.d.a.15.2	yes	12
17.12	odd	16		17.4.d.a.8.2	✓	12
17.13	even	4		289.4.b.e.288.6		12
17.16	even	2	inner	289.4.a.g.1.7		12
51.29	even	16		153.4.l.a.127.2		12
51.44	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	17.12	odd	16
17.4.d.a.15.2	yes	12	17.10	odd	16
153.4.l.a.100.2		12	51.44	even	16
153.4.l.a.127.2		12	51.29	even	16
289.4.a.g.1.7		12	17.16	even	2	inner
289.4.a.g.1.8		12	1.1	even	1	trivial
289.4.b.e.288.5		12	17.4	even	4
289.4.b.e.288.6		12	17.13	even	4

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
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

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Database

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