LMFDB - Embedded newform 289.6.a.j.1.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,6,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, 6, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 6 $
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:	$46.3509239260$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.27
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)

$f(q)$	$=$	$q+10.5085 q^{2} -25.0990 q^{3} +78.4279 q^{4} +55.7139 q^{5} -263.753 q^{6} -91.7804 q^{7} +487.886 q^{8} +386.962 q^{9} +O(q^{10})$	\(q+10.5085 q^{2} -25.0990 q^{3} +78.4279 q^{4} +55.7139 q^{5} -263.753 q^{6} -91.7804 q^{7} +487.886 q^{8} +386.962 q^{9} +585.468 q^{10} +39.2153 q^{11} -1968.47 q^{12} +243.603 q^{13} -964.471 q^{14} -1398.37 q^{15} +2617.24 q^{16} +4066.38 q^{18} +620.383 q^{19} +4369.53 q^{20} +2303.60 q^{21} +412.093 q^{22} +3748.31 q^{23} -12245.5 q^{24} -20.9596 q^{25} +2559.89 q^{26} -3613.31 q^{27} -7198.14 q^{28} -4569.03 q^{29} -14694.7 q^{30} +6666.42 q^{31} +11890.9 q^{32} -984.267 q^{33} -5113.44 q^{35} +30348.6 q^{36} +3052.25 q^{37} +6519.27 q^{38} -6114.20 q^{39} +27182.1 q^{40} +6773.72 q^{41} +24207.3 q^{42} +16032.4 q^{43} +3075.58 q^{44} +21559.2 q^{45} +39389.0 q^{46} +21852.3 q^{47} -65690.3 q^{48} -8383.37 q^{49} -220.253 q^{50} +19105.3 q^{52} +4754.78 q^{53} -37970.4 q^{54} +2184.84 q^{55} -44778.4 q^{56} -15571.0 q^{57} -48013.5 q^{58} +38999.6 q^{59} -109671. q^{60} -12199.9 q^{61} +70053.9 q^{62} -35515.5 q^{63} +41203.0 q^{64} +13572.1 q^{65} -10343.1 q^{66} -43024.2 q^{67} -94079.1 q^{69} -53734.5 q^{70} +58762.3 q^{71} +188793. q^{72} +47753.8 q^{73} +32074.5 q^{74} +526.065 q^{75} +48655.3 q^{76} -3599.20 q^{77} -64250.9 q^{78} -12919.1 q^{79} +145817. q^{80} -3341.15 q^{81} +71181.4 q^{82} -66422.1 q^{83} +180666. q^{84} +168476. q^{86} +114678. q^{87} +19132.6 q^{88} -72990.1 q^{89} +226554. q^{90} -22358.0 q^{91} +293972. q^{92} -167321. q^{93} +229634. q^{94} +34564.0 q^{95} -298450. q^{96} +83758.6 q^{97} -88096.4 q^{98} +15174.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 16 q^{2} + 448 q^{4} + 768 q^{8} + 2268 q^{9}+O(q^{10}) $ 28 * q + 16 * q^2 + 448 * q^4 + 768 * q^8 + 2268 * q^9	$ 28 q + 16 q^{2} + 448 q^{4} + 768 q^{8} + 2268 q^{9} + 304 q^{13} + 4392 q^{15} + 7176 q^{16} + 1896 q^{18} + 9288 q^{19} + 12032 q^{21} + 17692 q^{25} + 29600 q^{26} - 17784 q^{30} + 19032 q^{32} + 38800 q^{33} + 26056 q^{35} + 77816 q^{36} + 36384 q^{38} + 123904 q^{42} + 46520 q^{43} + 71808 q^{47} + 38748 q^{49} + 241632 q^{50} + 6008 q^{52} + 61360 q^{53} + 46680 q^{55} + 256920 q^{59} + 330504 q^{60} - 72496 q^{64} + 10736 q^{66} + 250608 q^{67} - 107696 q^{69} + 273320 q^{70} + 463640 q^{72} + 974048 q^{76} + 482672 q^{77} + 242060 q^{81} + 458584 q^{83} + 1605472 q^{84} + 718272 q^{86} + 1009400 q^{87} + 501088 q^{89} + 903248 q^{93} + 1315264 q^{94} - 156256 q^{98}+O(q^{100}) $ 28 * q + 16 * q^2 + 448 * q^4 + 768 * q^8 + 2268 * q^9 + 304 * q^13 + 4392 * q^15 + 7176 * q^16 + 1896 * q^18 + 9288 * q^19 + 12032 * q^21 + 17692 * q^25 + 29600 * q^26 - 17784 * q^30 + 19032 * q^32 + 38800 * q^33 + 26056 * q^35 + 77816 * q^36 + 36384 * q^38 + 123904 * q^42 + 46520 * q^43 + 71808 * q^47 + 38748 * q^49 + 241632 * q^50 + 6008 * q^52 + 61360 * q^53 + 46680 * q^55 + 256920 * q^59 + 330504 * q^60 - 72496 * q^64 + 10736 * q^66 + 250608 * q^67 - 107696 * q^69 + 273320 * q^70 + 463640 * q^72 + 974048 * q^76 + 482672 * q^77 + 242060 * q^81 + 458584 * q^83 + 1605472 * q^84 + 718272 * q^86 + 1009400 * q^87 + 501088 * q^89 + 903248 * q^93 + 1315264 * q^94 - 156256 * 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 $

$2$	10.5085	1.85765	0.928826	−	0.370516i	$-0.120819\pi$
$2$	10.5085	1.85765	0.928826	+	0.370516i	$0.120819\pi$
$3$	−25.0990	−1.61010	−0.805052	−	0.593204i	$-0.797863\pi$
$3$	−25.0990	−1.61010	−0.805052	+	0.593204i	$0.797863\pi$
$4$	78.4279	2.45087
$5$	55.7139	0.996641	0.498320	−	0.866993i	$-0.333950\pi$
$5$	55.7139	0.996641	0.498320	+	0.866993i	$0.333950\pi$
$6$	−263.753	−2.99101
$7$	−91.7804	−0.707953	−0.353977	−	0.935254i	$-0.615171\pi$
$7$	−91.7804	−0.707953	−0.353977	+	0.935254i	$0.615171\pi$
$8$	487.886	2.69522
$9$	386.962	1.59244
$10$	585.468	1.85141
$11$	39.2153	0.0977179	0.0488589	−	0.998806i	$-0.484442\pi$
$11$	39.2153	0.0977179	0.0488589	+	0.998806i	$0.484442\pi$
$12$	−1968.47	−3.94616
$13$	243.603	0.399783	0.199891	−	0.979818i	$-0.435941\pi$
$13$	243.603	0.399783	0.199891	+	0.979818i	$0.435941\pi$
$14$	−964.471	−1.31513
$15$	−1398.37	−1.60470
$16$	2617.24	2.55590
$17$	0	0
$17$	0	0
$18$	4066.38	2.95819
$19$	620.383	0.394254	0.197127	−	0.980378i	$-0.436839\pi$
$19$	620.383	0.394254	0.197127	+	0.980378i	$0.436839\pi$
$20$	4369.53	2.44264
$21$	2303.60	1.13988
$22$	412.093	0.181526
$23$	3748.31	1.47746	0.738731	−	0.674001i	$-0.235425\pi$
$23$	3748.31	1.47746	0.738731	+	0.674001i	$0.235425\pi$
$24$	−12245.5	−4.33958
$25$	−20.9596	−0.00670707
$26$	2559.89	0.742658
$27$	−3613.31	−0.953884
$28$	−7198.14	−1.73510
$29$	−4569.03	−1.00886	−0.504428	−	0.863454i	$-0.668297\pi$
$29$	−4569.03	−1.00886	−0.504428	+	0.863454i	$0.668297\pi$
$30$	−14694.7	−2.98097
$31$	6666.42	1.24592	0.622958	−	0.782255i	$-0.285931\pi$
$31$	6666.42	1.24592	0.622958	+	0.782255i	$0.285931\pi$
$32$	11890.9	2.05276
$33$	−984.267	−0.157336
$34$	0	0
$35$	−5113.44	−0.705575
$36$	30348.6	3.90286
$37$	3052.25	0.366536	0.183268	−	0.983063i	$-0.441332\pi$
$37$	3052.25	0.366536	0.183268	+	0.983063i	$0.441332\pi$
$38$	6519.27	0.732386
$39$	−6114.20	−0.643692
$40$	27182.1	2.68616
$41$	6773.72	0.629314	0.314657	−	0.949205i	$-0.398111\pi$
$41$	6773.72	0.629314	0.314657	+	0.949205i	$0.398111\pi$
$42$	24207.3	2.11750
$43$	16032.4	1.32229	0.661145	−	0.750258i	$-0.270071\pi$
$43$	16032.4	1.32229	0.661145	+	0.750258i	$0.270071\pi$
$44$	3075.58	0.239494
$45$	21559.2	1.58709
$46$	39389.0	2.74461
$47$	21852.3	1.44295	0.721476	−	0.692440i	$-0.243464\pi$
$47$	21852.3	1.44295	0.721476	+	0.692440i	$0.243464\pi$
$48$	−65690.3	−4.11527
$49$	−8383.37	−0.498802
$50$	−220.253	−0.0124594
$51$	0	0
$52$	19105.3	0.979817
$53$	4754.78	0.232510	0.116255	−	0.993219i	$-0.462911\pi$
$53$	4754.78	0.232510	0.116255	+	0.993219i	$0.462911\pi$
$54$	−37970.4	−1.77199
$55$	2184.84	0.0973896
$56$	−44778.4	−1.90809
$57$	−15571.0	−0.634790
$58$	−48013.5	−1.87410
$59$	38999.6	1.45858	0.729291	−	0.684204i	$-0.239850\pi$
$59$	38999.6	1.45858	0.729291	+	0.684204i	$0.239850\pi$
$60$	−109671.	−3.93290
$61$	−12199.9	−0.419791	−0.209896	−	0.977724i	$-0.567312\pi$
$61$	−12199.9	−0.419791	−0.209896	+	0.977724i	$0.567312\pi$
$62$	70053.9	2.31448
$63$	−35515.5	−1.12737
$64$	41203.0	1.25742
$65$	13572.1	0.398440
$66$	−10343.1	−0.292276
$67$	−43024.2	−1.17092	−0.585458	−	0.810703i	$-0.699085\pi$
$67$	−43024.2	−1.17092	−0.585458	+	0.810703i	$0.699085\pi$
$68$	0	0
$69$	−94079.1	−2.37887
$70$	−53734.5	−1.31071
$71$	58762.3	1.38342	0.691709	−	0.722177i	$-0.256858\pi$
$71$	58762.3	1.38342	0.691709	+	0.722177i	$0.256858\pi$
$72$	188793.	4.29196
$73$	47753.8	1.04882	0.524409	−	0.851466i	$-0.324286\pi$
$73$	47753.8	1.04882	0.524409	+	0.851466i	$0.324286\pi$
$74$	32074.5	0.680896
$75$	526.065	0.0107991
$76$	48655.3	0.966265
$77$	−3599.20	−0.0691797
$78$	−64250.9	−1.19576
$79$	−12919.1	−0.232898	−0.116449	−	0.993197i	$-0.537151\pi$
$79$	−12919.1	−0.232898	−0.116449	+	0.993197i	$0.537151\pi$
$80$	145817.	2.54732
$81$	−3341.15	−0.0565827
$82$	71181.4	1.16905
$83$	−66422.1	−1.05832	−0.529160	−	0.848522i	$-0.677493\pi$
$83$	−66422.1	−1.05832	−0.529160	+	0.848522i	$0.677493\pi$
$84$	180666.	2.79370
$85$	0	0
$86$	168476.	2.45636
$87$	114678.	1.62436
$88$	19132.6	0.263371
$89$	−72990.1	−0.976763	−0.488381	−	0.872630i	$-0.662413\pi$
$89$	−72990.1	−0.976763	−0.488381	+	0.872630i	$0.662413\pi$
$90$	226554.	2.94826
$91$	−22358.0	−0.283028
$92$	293972.	3.62107
$93$	−167321.	−2.00605
$94$	229634.	2.68050
$95$	34564.0	0.392929
$96$	−298450.	−3.30516
$97$	83758.6	0.903858	0.451929	−	0.892054i	$-0.350736\pi$
$97$	83758.6	0.903858	0.451929	+	0.892054i	$0.350736\pi$
$98$	−88096.4	−0.926601
$99$	15174.8	0.155609
$100$	−1643.82	−0.0164382
$101$	−91093.1	−0.888551	−0.444275	−	0.895890i	$-0.646539\pi$
$101$	−91093.1	−0.888551	−0.444275	+	0.895890i	$0.646539\pi$
$102$	0	0
$103$	92993.8	0.863697	0.431848	−	0.901946i	$-0.357862\pi$
$103$	92993.8	0.863697	0.431848	+	0.901946i	$0.357862\pi$
$104$	118851.	1.07750
$105$	128343.	1.13605
$106$	49965.5	0.431922
$107$	−38460.1	−0.324752	−0.162376	−	0.986729i	$-0.551916\pi$
$107$	−38460.1	−0.324752	−0.162376	+	0.986729i	$0.551916\pi$
$108$	−283384.	−2.33785
$109$	−102431.	−0.825785	−0.412893	−	0.910780i	$-0.635482\pi$
$109$	−102431.	−0.825785	−0.412893	+	0.910780i	$0.635482\pi$
$110$	22959.3	0.180916
$111$	−76608.7	−0.590161
$112$	−240212.	−1.80946
$113$	−190807.	−1.40572	−0.702858	−	0.711330i	$-0.748093\pi$
$113$	−190807.	−1.40572	−0.702858	+	0.711330i	$0.748093\pi$
$114$	−163628.	−1.17922
$115$	208833.	1.47250
$116$	−358340.	−2.47258
$117$	94265.1	0.636629
$118$	409827.	2.70954
$119$	0	0
$120$	−682244.	−4.32500
$121$	−159513.	−0.990451
$122$	−128203.	−0.779826
$123$	−170014.	−1.01326
$124$	522834.	3.05358
$125$	−175274.	−1.00333
$126$	−373214.	−2.09426
$127$	−211847.	−1.16550	−0.582751	−	0.812651i	$-0.698024\pi$
$127$	−211847.	−1.16550	−0.582751	+	0.812651i	$0.698024\pi$
$128$	52472.8	0.283080
$129$	−402397.	−2.12903
$130$	142622.	0.740163
$131$	73275.1	0.373060	0.186530	−	0.982449i	$-0.440276\pi$
$131$	73275.1	0.373060	0.186530	+	0.982449i	$0.440276\pi$
$132$	−77194.0	−0.385610
$133$	−56938.9	−0.279113
$134$	−452118.	−2.17515
$135$	−201312.	−0.950680
$136$	0	0
$137$	44705.6	0.203498	0.101749	−	0.994810i	$-0.467556\pi$
$137$	44705.6	0.203498	0.101749	+	0.994810i	$0.467556\pi$
$138$	−988627.	−4.41911
$139$	110984.	0.487218	0.243609	−	0.969874i	$-0.421669\pi$
$139$	110984.	0.487218	0.243609	+	0.969874i	$0.421669\pi$
$140$	−401037.	−1.72927
$141$	−548471.	−2.32330
$142$	617502.	2.56991
$143$	9552.97	0.0390659
$144$	1.01277e6	4.07011
$145$	−254559.	−1.00547
$146$	501819.	1.94834
$147$	210415.	0.803124
$148$	239382.	0.898333
$149$	199107.	0.734720	0.367360	−	0.930079i	$-0.380262\pi$
$149$	199107.	0.734720	0.367360	+	0.930079i	$0.380262\pi$
$150$	5528.14	0.0200609
$151$	8828.12	0.0315084	0.0157542	−	0.999876i	$-0.494985\pi$
$151$	8828.12	0.0315084	0.0157542	+	0.999876i	$0.494985\pi$
$152$	302676.	1.06260
$153$	0	0
$154$	−37822.0	−0.128512
$155$	371412.	1.24173
$156$	−479524.	−1.57761
$157$	−68893.6	−0.223064	−0.111532	−	0.993761i	$-0.535576\pi$
$157$	−68893.6	−0.223064	−0.111532	+	0.993761i	$0.535576\pi$
$158$	−135760.	−0.432643
$159$	−119341.	−0.374365
$160$	662487.	2.04587
$161$	−344021.	−1.04597
$162$	−35110.4	−0.105111
$163$	−166914.	−0.492066	−0.246033	−	0.969261i	$-0.579127\pi$
$163$	−166914.	−0.492066	−0.246033	+	0.969261i	$0.579127\pi$
$164$	531248.	1.54237
$165$	−54837.4	−0.156807
$166$	−697994.	−1.96599
$167$	−574203.	−1.59321	−0.796607	−	0.604497i	$-0.793374\pi$
$167$	−574203.	−1.59321	−0.796607	+	0.604497i	$0.793374\pi$
$168$	1.12389e6	3.07222
$169$	−311951.	−0.840174
$170$	0	0
$171$	240065.	0.627824
$172$	1.25739e6	3.24076
$173$	−217487.	−0.552482	−0.276241	−	0.961088i	$-0.589089\pi$
$173$	−217487.	−0.552482	−0.276241	+	0.961088i	$0.589089\pi$
$174$	1.20509e6	3.01750
$175$	1923.68	0.00474829
$176$	102636.	0.249757
$177$	−978854.	−2.34847
$178$	−767015.	−1.81449
$179$	628318.	1.46571	0.732854	−	0.680386i	$-0.238188\pi$
$179$	628318.	1.46571	0.732854	+	0.680386i	$0.238188\pi$
$180$	1.69084e6	3.88975
$181$	−69023.1	−0.156602	−0.0783011	−	0.996930i	$-0.524950\pi$
$181$	−69023.1	−0.156602	−0.0783011	+	0.996930i	$0.524950\pi$
$182$	−234948.	−0.525767
$183$	306207.	0.675908
$184$	1.82875e6	3.98208
$185$	170053.	0.365305
$186$	−1.75829e6	−3.72655
$187$	0	0
$188$	1.71383e6	3.53649
$189$	331631.	0.675306
$190$	363214.	0.729926
$191$	−357545.	−0.709164	−0.354582	−	0.935025i	$-0.615377\pi$
$191$	−357545.	−0.709164	−0.354582	+	0.935025i	$0.615377\pi$
$192$	−1.03416e6	−2.02457
$193$	141090.	0.272649	0.136325	−	0.990664i	$-0.456471\pi$
$193$	141090.	0.272649	0.136325	+	0.990664i	$0.456471\pi$
$194$	880175.	1.67905
$195$	−340646.	−0.641530
$196$	−657490.	−1.22250
$197$	−696431.	−1.27853	−0.639267	−	0.768985i	$-0.720762\pi$
$197$	−696431.	−1.27853	−0.639267	+	0.768985i	$0.720762\pi$
$198$	159464.	0.289068
$199$	−198110.	−0.354628	−0.177314	−	0.984154i	$-0.556741\pi$
$199$	−198110.	−0.354628	−0.177314	+	0.984154i	$0.556741\pi$
$200$	−10225.9	−0.0180770
$201$	1.07987e6	1.88530
$202$	−957249.	−1.65062
$203$	419347.	0.714223
$204$	0	0
$205$	377390.	0.627200
$206$	977223.	1.60445
$207$	1.45045e6	2.35276
$208$	637568.	1.02181
$209$	24328.5	0.0385256
$210$	1.34868e6	2.11039
$211$	−121671.	−0.188140	−0.0940700	−	0.995566i	$-0.529988\pi$
$211$	−121671.	−0.188140	−0.0940700	+	0.995566i	$0.529988\pi$
$212$	372908.	0.569852
$213$	−1.47488e6	−2.22745
$214$	−404157.	−0.603276
$215$	893226.	1.31785
$216$	−1.76288e6	−2.57093
$217$	−611847.	−0.882050
$218$	−1.07640e6	−1.53402
$219$	−1.19857e6	−1.68871
$220$	171352.	0.238690
$221$	0	0
$222$	−805040.	−1.09631
$223$	−566505.	−0.762854	−0.381427	−	0.924399i	$-0.624567\pi$
$223$	−566505.	−0.762854	−0.381427	+	0.924399i	$0.624567\pi$
$224$	−1.09135e6	−1.45326
$225$	−8110.56	−0.0106806
$226$	−2.00509e6	−2.61133
$227$	−918955.	−1.18367	−0.591833	−	0.806060i	$-0.701596\pi$
$227$	−918955.	−1.18367	−0.591833	+	0.806060i	$0.701596\pi$
$228$	−1.22120e6	−1.55579
$229$	1.45495e6	1.83341	0.916706	−	0.399562i	$-0.130838\pi$
$229$	1.45495e6	1.83341	0.916706	+	0.399562i	$0.130838\pi$
$230$	2.19452e6	2.73539
$231$	90336.4	0.111387
$232$	−2.22917e6	−2.71908
$233$	9096.89	0.0109775	0.00548875	−	0.999985i	$-0.498253\pi$
$233$	9096.89	0.0109775	0.00548875	+	0.999985i	$0.498253\pi$
$234$	990582.	1.18263
$235$	1.21747e6	1.43810
$236$	3.05866e6	3.57480
$237$	324258.	0.374990
$238$	0	0
$239$	−725823.	−0.821932	−0.410966	−	0.911651i	$-0.634808\pi$
$239$	−725823.	−0.821932	−0.410966	+	0.911651i	$0.634808\pi$
$240$	−3.65987e6	−4.10145
$241$	1.07312e6	1.19016	0.595081	−	0.803666i	$-0.297120\pi$
$241$	1.07312e6	1.19016	0.595081	+	0.803666i	$0.297120\pi$
$242$	−1.67624e6	−1.83991
$243$	961894.	1.04499
$244$	−956816.	−1.02885
$245$	−467070.	−0.497127
$246$	−1.78658e6	−1.88229
$247$	151127.	0.157616
$248$	3.25246e6	3.35801
$249$	1.66713e6	1.70401
$250$	−1.84186e6	−1.86383
$251$	1.39837e6	1.40099	0.700497	−	0.713655i	$-0.252962\pi$
$251$	1.39837e6	1.40099	0.700497	+	0.713655i	$0.252962\pi$
$252$	−2.78541e6	−2.76304
$253$	146991.	0.144374
$254$	−2.22619e6	−2.16510
$255$	0	0
$256$	−767088.	−0.731552
$257$	210631.	0.198925	0.0994627	−	0.995041i	$-0.468288\pi$
$257$	210631.	0.198925	0.0994627	+	0.995041i	$0.468288\pi$
$258$	−4.22858e6	−3.95499
$259$	−280137.	−0.259490
$260$	1.06443e6	0.976525
$261$	−1.76804e6	−1.60654
$262$	770009.	0.693015
$263$	307281.	0.273934	0.136967	−	0.990576i	$-0.456265\pi$
$263$	307281.	0.273934	0.136967	+	0.990576i	$0.456265\pi$
$264$	−480210.	−0.424055
$265$	264908.	0.231729
$266$	−598341.	−0.518495
$267$	1.83198e6	1.57269
$268$	−3.37430e6	−2.86977
$269$	25857.9	0.0217878	0.0108939	−	0.999941i	$-0.496532\pi$
$269$	25857.9	0.0217878	0.0108939	+	0.999941i	$0.496532\pi$
$270$	−2.11548e6	−1.76603
$271$	1.25525e6	1.03827	0.519133	−	0.854694i	$-0.326255\pi$
$271$	1.25525e6	1.03827	0.519133	+	0.854694i	$0.326255\pi$
$272$	0	0
$273$	561164.	0.455704
$274$	469787.	0.378029
$275$	−821.937	−0.000655400 0
$276$	−7.37843e6	−5.83030
$277$	1.23777e6	0.969259	0.484629	−	0.874720i	$-0.338954\pi$
$277$	1.23777e6	0.969259	0.484629	+	0.874720i	$0.338954\pi$
$278$	1.16627e6	0.905082
$279$	2.57965e6	1.98404
$280$	−2.49478e6	−1.90168
$281$	1.25678e6	0.949493	0.474747	−	0.880123i	$-0.342540\pi$
$281$	1.25678e6	0.949493	0.474747	+	0.880123i	$0.342540\pi$
$282$	−5.76359e6	−4.31589
$283$	20473.4	0.0151958	0.00759791	−	0.999971i	$-0.497581\pi$
$283$	20473.4	0.0151958	0.00759791	+	0.999971i	$0.497581\pi$
$284$	4.60861e6	3.39058
$285$	−867522.	−0.632657
$286$	100387.	0.0725709
$287$	−621694.	−0.445525
$288$	4.60132e6	3.26889
$289$	0	0
$290$	−2.67502e6	−1.86781
$291$	−2.10226e6	−1.45531
$292$	3.74523e6	2.57052
$293$	385468.	0.262313	0.131156	−	0.991362i	$-0.458131\pi$
$293$	385468.	0.262313	0.131156	+	0.991362i	$0.458131\pi$
$294$	2.21113e6	1.49192
$295$	2.17282e6	1.45368
$296$	1.48915e6	0.987894
$297$	−141697.	−0.0932116
$298$	2.09231e6	1.36485
$299$	913100.	0.590664
$300$	41258.2	0.0264672
$301$	−1.47146e6	−0.936120
$302$	92770.0	0.0585316
$303$	2.28635e6	1.43066
$304$	1.62369e6	1.00767
$305$	−679707.	−0.418381
$306$	0	0
$307$	−378716.	−0.229333	−0.114667	−	0.993404i	$-0.536580\pi$
$307$	−378716.	−0.229333	−0.114667	+	0.993404i	$0.536580\pi$
$308$	−282277.	−0.169551
$309$	−2.33406e6	−1.39064
$310$	3.90298e6	2.30670
$311$	−281786.	−0.165203	−0.0826016	−	0.996583i	$-0.526323\pi$
$311$	−281786.	−0.165203	−0.0826016	+	0.996583i	$0.526323\pi$
$312$	−2.98303e6	−1.73489
$313$	−1.42330e6	−0.821175	−0.410588	−	0.911821i	$-0.634676\pi$
$313$	−1.42330e6	−0.821175	−0.410588	+	0.911821i	$0.634676\pi$
$314$	−723967.	−0.414376
$315$	−1.97871e6	−1.12358
$316$	−1.01322e6	−0.570803
$317$	−1.61666e6	−0.903589	−0.451795	−	0.892122i	$-0.649216\pi$
$317$	−1.61666e6	−0.903589	−0.451795	+	0.892122i	$0.649216\pi$
$318$	−1.25409e6	−0.695440
$319$	−179176.	−0.0985832
$320$	2.29558e6	1.25319
$321$	965312.	0.522884
$322$	−3.61514e6	−1.94306
$323$	0	0
$324$	−262040.	−0.138677
$325$	−5105.82	−0.00268137
$326$	−1.75401e6	−0.914088
$327$	2.57093e6	1.32960
$328$	3.30480e6	1.69614
$329$	−2.00561e6	−1.02154
$330$	−576257.	−0.291294
$331$	−2.34866e6	−1.17829	−0.589143	−	0.808029i	$-0.700534\pi$
$331$	−2.34866e6	−1.17829	−0.589143	+	0.808029i	$0.700534\pi$
$332$	−5.20934e6	−2.59381
$333$	1.18111e6	0.583685
$334$	−6.03400e6	−2.95964
$335$	−2.39705e6	−1.16698
$336$	6.02908e6	2.91342
$337$	724801.	0.347651	0.173826	−	0.984776i	$-0.444387\pi$
$337$	724801.	0.347651	0.173826	+	0.984776i	$0.444387\pi$
$338$	−3.27812e6	−1.56075
$339$	4.78907e6	2.26335
$340$	0	0
$341$	261426.	0.121748
$342$	2.52271e6	1.16628
$343$	2.31198e6	1.06108
$344$	7.82198e6	3.56386
$345$	−5.24151e6	−2.37088
$346$	−2.28545e6	−1.02632
$347$	−988484.	−0.440703	−0.220352	−	0.975421i	$-0.570720\pi$
$347$	−988484.	−0.440703	−0.220352	+	0.975421i	$0.570720\pi$
$348$	8.99398e6	3.98111
$349$	3.00138e6	1.31904	0.659519	−	0.751688i	$-0.270760\pi$
$349$	3.00138e6	1.31904	0.659519	+	0.751688i	$0.270760\pi$
$350$	20214.9	0.00882067
$351$	−880213.	−0.381347
$352$	466304.	0.200592
$353$	−755428.	−0.322668	−0.161334	−	0.986900i	$-0.551580\pi$
$353$	−755428.	−0.322668	−0.161334	+	0.986900i	$0.551580\pi$
$354$	−1.02863e7	−4.36264
$355$	3.27388e6	1.37877
$356$	−5.72446e6	−2.39392
$357$	0	0
$358$	6.60266e6	2.72277
$359$	−577718.	−0.236581	−0.118291	−	0.992979i	$-0.537741\pi$
$359$	−577718.	−0.236581	−0.118291	+	0.992979i	$0.537741\pi$
$360$	1.05184e7	4.27754
$361$	−2.09122e6	−0.844564
$362$	−725327.	−0.290913
$363$	4.00363e6	1.59473
$364$	−1.75349e6	−0.693664
$365$	2.66055e6	1.04530
$366$	3.21777e6	1.25560
$367$	1.61209e6	0.624777	0.312389	−	0.949954i	$-0.398871\pi$
$367$	1.61209e6	0.624777	0.312389	+	0.949954i	$0.398871\pi$
$368$	9.81025e6	3.77625
$369$	2.62117e6	1.00214
$370$	1.78700e6	0.678609
$371$	−436396.	−0.164606
$372$	−1.31226e7	−4.91658
$373$	4.75990e6	1.77144	0.885719	−	0.464222i	$-0.153666\pi$
$373$	4.75990e6	1.77144	0.885719	+	0.464222i	$0.153666\pi$
$374$	0	0
$375$	4.39920e6	1.61546
$376$	1.06614e7	3.88907
$377$	−1.11303e6	−0.403323
$378$	3.48493e6	1.25448
$379$	258919.	0.0925906	0.0462953	−	0.998928i	$-0.485258\pi$
$379$	258919.	0.0925906	0.0462953	+	0.998928i	$0.485258\pi$
$380$	2.71078e6	0.963019
$381$	5.31715e6	1.87658
$382$	−3.75725e6	−1.31738
$383$	−3.77627e6	−1.31542	−0.657712	−	0.753269i	$-0.728476\pi$
$383$	−3.77627e6	−1.31542	−0.657712	+	0.753269i	$0.728476\pi$
$384$	−1.31702e6	−0.455789
$385$	−200525.	−0.0689473
$386$	1.48264e6	0.506487
$387$	6.20392e6	2.10566
$388$	6.56902e6	2.21524
$389$	5.83173e6	1.95400	0.976998	−	0.213247i	$-0.0684040\pi$
$389$	5.83173e6	1.95400	0.976998	+	0.213247i	$0.0684040\pi$
$390$	−3.57967e6	−1.19174
$391$	0	0
$392$	−4.09013e6	−1.34438
$393$	−1.83914e6	−0.600665
$394$	−7.31842e6	−2.37507
$395$	−719775.	−0.232116
$396$	1.19013e6	0.381379
$397$	−4.95232e6	−1.57700	−0.788501	−	0.615034i	$-0.789142\pi$
$397$	−4.95232e6	−1.57700	−0.788501	+	0.615034i	$0.789142\pi$
$398$	−2.08183e6	−0.658776
$399$	1.42911e6	0.449401
$400$	−54856.4	−0.0171426
$401$	−4.41230e6	−1.37026	−0.685132	−	0.728419i	$-0.740256\pi$
$401$	−4.41230e6	−1.37026	−0.685132	+	0.728419i	$0.740256\pi$
$402$	1.13477e7	3.50223
$403$	1.62396e6	0.498096
$404$	−7.14425e6	−2.17772
$405$	−186149.	−0.0563926
$406$	4.40670e6	1.32678
$407$	119695.	0.0358171
$408$	0	0
$409$	3.93079e6	1.16191	0.580954	−	0.813936i	$-0.302679\pi$
$409$	3.93079e6	1.16191	0.580954	+	0.813936i	$0.302679\pi$
$410$	3.96579e6	1.16512
$411$	−1.12207e6	−0.327653
$412$	7.29331e6	2.11681
$413$	−3.57940e6	−1.03261
$414$	1.52421e7	4.37062
$415$	−3.70063e6	−1.05477
$416$	2.89665e6	0.820659
$417$	−2.78559e6	−0.784472
$418$	255655.	0.0715672
$419$	−5.92822e6	−1.64964	−0.824819	−	0.565396i	$-0.808723\pi$
$419$	−5.92822e6	−1.64964	−0.824819	+	0.565396i	$0.808723\pi$
$420$	1.00656e7	2.78431
$421$	−4.51963e6	−1.24279	−0.621395	−	0.783497i	$-0.713434\pi$
$421$	−4.51963e6	−1.24279	−0.621395	+	0.783497i	$0.713434\pi$
$422$	−1.27858e6	−0.349499
$423$	8.45599e6	2.29781
$424$	2.31979e6	0.626664
$425$	0	0
$426$	−1.54987e7	−4.13782
$427$	1.11972e6	0.297192
$428$	−3.01635e6	−0.795925
$429$	−239770.	−0.0629002
$430$	9.38644e6	2.44810
$431$	5.14428e6	1.33393	0.666963	−	0.745091i	$-0.267594\pi$
$431$	5.14428e6	1.33393	0.666963	+	0.745091i	$0.267594\pi$
$432$	−9.45692e6	−2.43804
$433$	5.56099e6	1.42539	0.712693	−	0.701476i	$-0.247475\pi$
$433$	5.56099e6	1.42539	0.712693	+	0.701476i	$0.247475\pi$
$434$	−6.42957e6	−1.63854
$435$	6.38918e6	1.61891
$436$	−8.03349e6	−2.02389
$437$	2.32539e6	0.582495
$438$	−1.25952e7	−3.13703
$439$	−5.87215e6	−1.45424	−0.727119	−	0.686511i	$-0.759141\pi$
$439$	−5.87215e6	−1.45424	−0.727119	+	0.686511i	$0.759141\pi$
$440$	1.06595e6	0.262486
$441$	−3.24404e6	−0.794311
$442$	0	0
$443$	−8.24535e6	−1.99618	−0.998090	−	0.0617826i	$-0.980321\pi$
$443$	−8.24535e6	−1.99618	−0.998090	+	0.0617826i	$0.980321\pi$
$444$	−6.00826e6	−1.44641
$445$	−4.06657e6	−0.973482
$446$	−5.95310e6	−1.41712
$447$	−4.99741e6	−1.18298
$448$	−3.78163e6	−0.890192
$449$	1.93885e6	0.453866	0.226933	−	0.973910i	$-0.427130\pi$
$449$	1.93885e6	0.453866	0.226933	+	0.973910i	$0.427130\pi$
$450$	−85229.6	−0.0198408
$451$	265633.	0.0614952
$452$	−1.49646e7	−3.44523
$453$	−221577.	−0.0507318
$454$	−9.65681e6	−2.19884
$455$	−1.24565e6	−0.282077
$456$	−7.59688e6	−1.71090
$457$	−6.52362e6	−1.46116	−0.730581	−	0.682826i	$-0.760751\pi$
$457$	−6.52362e6	−1.46116	−0.730581	+	0.682826i	$0.760751\pi$
$458$	1.52893e7	3.40584
$459$	0	0
$460$	1.63784e7	3.60891
$461$	1.85704e6	0.406976	0.203488	−	0.979077i	$-0.434772\pi$
$461$	1.85704e6	0.406976	0.203488	+	0.979077i	$0.434772\pi$
$462$	949297.	0.206917
$463$	1.55830e6	0.337830	0.168915	−	0.985631i	$-0.445974\pi$
$463$	1.55830e6	0.337830	0.168915	+	0.985631i	$0.445974\pi$
$464$	−1.19583e7	−2.57854
$465$	−9.32210e6	−1.99932
$466$	95594.4	0.0203924
$467$	−289142.	−0.0613507	−0.0306753	−	0.999529i	$-0.509766\pi$
$467$	−289142.	−0.0613507	−0.0306753	+	0.999529i	$0.509766\pi$
$468$	7.39301e6	1.56030
$469$	3.94878e6	0.828954
$470$	1.27938e7	2.67150
$471$	1.72916e6	0.359157
$472$	1.90274e7	3.93119
$473$	628715.	0.129211
$474$	3.40745e6	0.696601
$475$	−13003.0	−0.00264429
$476$	0	0
$477$	1.83992e6	0.370257
$478$	−7.62728e6	−1.52686
$479$	1.78964e6	0.356390	0.178195	−	0.983995i	$-0.442974\pi$
$479$	1.78964e6	0.356390	0.178195	+	0.983995i	$0.442974\pi$
$480$	−1.66278e7	−3.29406
$481$	743538.	0.146535
$482$	1.12769e7	2.21091
$483$	8.63461e6	1.68413
$484$	−1.25103e7	−2.42747
$485$	4.66652e6	0.900822
$486$	1.01080e7	1.94123
$487$	−2.29704e6	−0.438880	−0.219440	−	0.975626i	$-0.570423\pi$
$487$	−2.29704e6	−0.438880	−0.219440	+	0.975626i	$0.570423\pi$
$488$	−5.95219e6	−1.13143
$489$	4.18938e6	0.792278
$490$	−4.90819e6	−0.923488
$491$	−5.01563e6	−0.938905	−0.469452	−	0.882958i	$-0.655549\pi$
$491$	−5.01563e6	−0.938905	−0.469452	+	0.882958i	$0.655549\pi$
$492$	−1.33338e7	−2.48337
$493$	0	0
$494$	1.58811e6	0.292795
$495$	845450.	0.155087
$496$	1.74477e7	3.18444
$497$	−5.39323e6	−0.979395
$498$	1.75190e7	3.16545
$499$	−6.02420e6	−1.08305	−0.541524	−	0.840685i	$-0.682153\pi$
$499$	−6.02420e6	−1.08305	−0.541524	+	0.840685i	$0.682153\pi$
$500$	−1.37464e7	−2.45902
$501$	1.44119e7	2.56524
$502$	1.46947e7	2.60256
$503$	−1.65203e6	−0.291137	−0.145569	−	0.989348i	$-0.546501\pi$
$503$	−1.65203e6	−0.291137	−0.145569	+	0.989348i	$0.546501\pi$
$504$	−1.73275e7	−3.03851
$505$	−5.07516e6	−0.885566
$506$	1.54465e6	0.268197
$507$	7.82966e6	1.35277
$508$	−1.66147e7	−2.85649
$509$	−88594.7	−0.0151570	−0.00757850	−	0.999971i	$-0.502412\pi$
$509$	−88594.7	−0.0151570	−0.00757850	+	0.999971i	$0.502412\pi$
$510$	0	0
$511$	−4.38286e6	−0.742515
$512$	−9.74005e6	−1.64205
$513$	−2.24164e6	−0.376072
$514$	2.21341e6	0.369534
$515$	5.18105e6	0.860795
$516$	−3.15592e7	−5.21797
$517$	856943.	0.141002
$518$	−2.94381e6	−0.482043
$519$	5.45871e6	0.889553
$520$	6.62163e6	1.07388
$521$	−6.98311e6	−1.12708	−0.563540	−	0.826089i	$-0.690561\pi$
$521$	−6.98311e6	−1.12708	−0.563540	+	0.826089i	$0.690561\pi$
$522$	−1.85794e7	−2.98439
$523$	4.70205e6	0.751680	0.375840	−	0.926685i	$-0.377354\pi$
$523$	4.70205e6	0.751680	0.375840	+	0.926685i	$0.377354\pi$
$524$	5.74681e6	0.914321
$525$	−48282.5	−0.00764524
$526$	3.22905e6	0.508874
$527$	0	0
$528$	−2.57607e6	−0.402135
$529$	7.61351e6	1.18289
$530$	2.78377e6	0.430471
$531$	1.50914e7	2.32270
$532$	−4.46560e6	−0.684071
$533$	1.65010e6	0.251589
$534$	1.92513e7	2.92151
$535$	−2.14276e6	−0.323661
$536$	−2.09909e7	−3.15587
$537$	−1.57702e7	−2.35994
$538$	271727.	0.0404741
$539$	−328756.	−0.0487419
$540$	−1.57885e7	−2.33000
$541$	1.03093e7	1.51439	0.757193	−	0.653191i	$-0.226570\pi$
$541$	1.03093e7	1.51439	0.757193	+	0.653191i	$0.226570\pi$
$542$	1.31908e7	1.92874
$543$	1.73241e6	0.252146
$544$	0	0
$545$	−5.70686e6	−0.823011
$546$	5.89697e6	0.846540
$547$	8.53248e6	1.21929	0.609645	−	0.792675i	$-0.291312\pi$
$547$	8.53248e6	1.21929	0.609645	+	0.792675i	$0.291312\pi$
$548$	3.50616e6	0.498748
$549$	−4.72091e6	−0.668491
$550$	−8637.30	−0.00121751
$551$	−2.83455e6	−0.397745
$552$	−4.58999e7	−6.41156
$553$	1.18572e6	0.164881
$554$	1.30070e7	1.80055
$555$	−4.26817e6	−0.588179
$556$	8.70424e6	1.19411
$557$	−1.10890e7	−1.51445	−0.757224	−	0.653156i	$-0.773445\pi$
$557$	−1.10890e7	−1.51445	−0.757224	+	0.653156i	$0.773445\pi$
$558$	2.71082e7	3.68566
$559$	3.90553e6	0.528629
$560$	−1.33831e7	−1.80338
$561$	0	0
$562$	1.32068e7	1.76383
$563$	−1.18645e7	−1.57753	−0.788765	−	0.614695i	$-0.789279\pi$
$563$	−1.18645e7	−1.57753	−0.788765	+	0.614695i	$0.789279\pi$
$564$	−4.30154e7	−5.69412
$565$	−1.06306e7	−1.40099
$566$	215144.	0.0282286
$567$	306652.	0.0400579
$568$	2.86693e7	3.72861
$569$	4.61227e6	0.597220	0.298610	−	0.954375i	$-0.403477\pi$
$569$	4.61227e6	0.597220	0.298610	+	0.954375i	$0.403477\pi$
$570$	−9.11633e6	−1.17526
$571$	−4.14651e6	−0.532222	−0.266111	−	0.963942i	$-0.585739\pi$
$571$	−4.14651e6	−0.532222	−0.266111	+	0.963942i	$0.585739\pi$
$572$	749219.	0.0957456
$573$	8.97403e6	1.14183
$574$	−6.53305e6	−0.827630
$575$	−78563.1	−0.00990943
$576$	1.59440e7	2.00236
$577$	3.84164e6	0.480372	0.240186	−	0.970727i	$-0.422792\pi$
$577$	3.84164e6	0.480372	0.240186	+	0.970727i	$0.422792\pi$
$578$	0	0
$579$	−3.54123e6	−0.438993
$580$	−1.99645e7	−2.46427
$581$	6.09624e6	0.749241
$582$	−2.20916e7	−2.70345
$583$	186460.	0.0227204
$584$	2.32984e7	2.82679
$585$	5.25188e6	0.634490
$586$	4.05068e6	0.487286
$587$	7.59787e6	0.910115	0.455058	−	0.890462i	$-0.349619\pi$
$587$	7.59787e6	0.910115	0.455058	+	0.890462i	$0.349619\pi$
$588$	1.65024e7	1.96835
$589$	4.13573e6	0.491207
$590$	2.28330e7	2.70044
$591$	1.74797e7	2.05857
$592$	7.98850e6	0.936830
$593$	−5.19082e6	−0.606176	−0.303088	−	0.952963i	$-0.598018\pi$
$593$	−5.19082e6	−0.606176	−0.303088	+	0.952963i	$0.598018\pi$
$594$	−1.48902e6	−0.173155
$595$	0	0
$596$	1.56156e7	1.80070
$597$	4.97237e6	0.570989
$598$	9.59528e6	1.09725
$599$	2.90719e6	0.331059	0.165530	−	0.986205i	$-0.447067\pi$
$599$	2.90719e6	0.331059	0.165530	+	0.986205i	$0.447067\pi$
$600$	256660.	0.0291059
$601$	1.62974e7	1.84049	0.920244	−	0.391346i	$-0.127990\pi$
$601$	1.62974e7	1.84049	0.920244	+	0.391346i	$0.127990\pi$
$602$	−1.54628e7	−1.73898
$603$	−1.66487e7	−1.86461
$604$	692371.	0.0772230
$605$	−8.88710e6	−0.987124
$606$	2.40260e7	2.65767
$607$	−5.21457e6	−0.574443	−0.287221	−	0.957864i	$-0.592732\pi$
$607$	−5.21457e6	−0.574443	−0.287221	+	0.957864i	$0.592732\pi$
$608$	7.37689e6	0.809309
$609$	−1.05252e7	−1.14997
$610$	−7.14268e6	−0.777206
$611$	5.32327e6	0.576867
$612$	0	0
$613$	−4.70208e6	−0.505404	−0.252702	−	0.967544i	$-0.581319\pi$
$613$	−4.70208e6	−0.505404	−0.252702	+	0.967544i	$0.581319\pi$
$614$	−3.97972e6	−0.426022
$615$	−9.47213e6	−1.00986
$616$	−1.75600e6	−0.186454
$617$	−2.49670e6	−0.264031	−0.132015	−	0.991248i	$-0.542145\pi$
$617$	−2.49670e6	−0.264031	−0.132015	+	0.991248i	$0.542145\pi$
$618$	−2.45274e7	−2.58333
$619$	1.43885e7	1.50935	0.754674	−	0.656100i	$-0.227795\pi$
$619$	1.43885e7	1.50935	0.754674	+	0.656100i	$0.227795\pi$
$620$	2.91291e7	3.04332
$621$	−1.35438e7	−1.40933
$622$	−2.96114e6	−0.306890
$623$	6.69906e6	0.691502
$624$	−1.60024e7	−1.64521
$625$	−9.69969e6	−0.993248
$626$	−1.49567e7	−1.52546
$627$	−610622.	−0.0620303
$628$	−5.40318e6	−0.546702
$629$	0	0
$630$	−2.07932e7	−2.08723
$631$	9.85263e6	0.985096	0.492548	−	0.870285i	$-0.336066\pi$
$631$	9.85263e6	0.985096	0.492548	+	0.870285i	$0.336066\pi$
$632$	−6.30307e6	−0.627710
$633$	3.05383e6	0.302925
$634$	−1.69886e7	−1.67855
$635$	−1.18028e7	−1.16159
$636$	−9.35963e6	−0.917521
$637$	−2.04221e6	−0.199413
$638$	−1.88287e6	−0.183133
$639$	2.27388e7	2.20300
$640$	2.92347e6	0.282129
$641$	−1.65245e6	−0.158849	−0.0794243	−	0.996841i	$-0.525308\pi$
$641$	−1.65245e6	−0.158849	−0.0794243	+	0.996841i	$0.525308\pi$
$642$	1.01440e7	0.971337
$643$	−1.26355e7	−1.20522	−0.602609	−	0.798037i	$-0.705872\pi$
$643$	−1.26355e7	−1.20522	−0.602609	+	0.798037i	$0.705872\pi$
$644$	−2.69809e7	−2.56355
$645$	−2.24191e7	−2.12187
$646$	0	0
$647$	2.03508e6	0.191126	0.0955630	−	0.995423i	$-0.469535\pi$
$647$	2.03508e6	0.191126	0.0955630	+	0.995423i	$0.469535\pi$
$648$	−1.63010e6	−0.152503
$649$	1.52938e6	0.142529
$650$	−53654.3	−0.00498105
$651$	1.53568e7	1.42019
$652$	−1.30907e7	−1.20599
$653$	−1.28934e7	−1.18328	−0.591638	−	0.806204i	$-0.701518\pi$
$653$	−1.28934e7	−1.18328	−0.591638	+	0.806204i	$0.701518\pi$
$654$	2.70166e7	2.46994
$655$	4.08244e6	0.371806
$656$	1.77285e7	1.60847
$657$	1.84789e7	1.67018
$658$	−2.10759e7	−1.89767
$659$	9.82029e6	0.880868	0.440434	−	0.897785i	$-0.354825\pi$
$659$	9.82029e6	0.880868	0.440434	+	0.897785i	$0.354825\pi$
$660$	−4.30078e6	−0.384315
$661$	5.98007e6	0.532356	0.266178	−	0.963924i	$-0.414239\pi$
$661$	5.98007e6	0.532356	0.266178	+	0.963924i	$0.414239\pi$
$662$	−2.46808e7	−2.18884
$663$	0	0
$664$	−3.24064e7	−2.85240
$665$	−3.17229e6	−0.278176
$666$	1.24116e7	1.08428
$667$	−1.71262e7	−1.49055
$668$	−4.50336e7	−3.90477
$669$	1.42187e7	1.22827
$670$	−2.51893e7	−2.16785
$671$	−478425.	−0.0410211
$672$	2.73918e7	2.33990
$673$	4.37408e6	0.372262	0.186131	−	0.982525i	$-0.440405\pi$
$673$	4.37408e6	0.372262	0.186131	+	0.982525i	$0.440405\pi$
$674$	7.61655e6	0.645815
$675$	75733.5	0.00639777
$676$	−2.44656e7	−2.05916
$677$	−1.16472e6	−0.0976674	−0.0488337	−	0.998807i	$-0.515550\pi$
$677$	−1.16472e6	−0.0976674	−0.0488337	+	0.998807i	$0.515550\pi$
$678$	5.03258e7	4.20452
$679$	−7.68740e6	−0.639889
$680$	0	0
$681$	2.30649e7	1.90583
$682$	2.74719e6	0.226166
$683$	−7.13327e6	−0.585109	−0.292555	−	0.956249i	$-0.594505\pi$
$683$	−7.13327e6	−0.585109	−0.292555	+	0.956249i	$0.594505\pi$
$684$	1.88278e7	1.53872
$685$	2.49072e6	0.202814
$686$	2.42954e7	1.97112
$687$	−3.65179e7	−2.95199
$688$	4.19606e7	3.37965
$689$	1.15828e6	0.0929534
$690$	−5.50803e7	−4.40426
$691$	2.58026e6	0.205574	0.102787	−	0.994703i	$-0.467224\pi$
$691$	2.58026e6	0.205574	0.102787	+	0.994703i	$0.467224\pi$
$692$	−1.70570e7	−1.35406
$693$	−1.39275e6	−0.110164
$694$	−1.03875e7	−0.818673
$695$	6.18335e6	0.485581
$696$	5.59500e7	4.37801
$697$	0	0
$698$	3.15399e7	2.45031
$699$	−228323.	−0.0176749
$700$	150870.	0.0116375
$701$	8.38631e6	0.644578	0.322289	−	0.946641i	$-0.395548\pi$
$701$	8.38631e6	0.644578	0.322289	+	0.946641i	$0.395548\pi$
$702$	−9.24969e6	−0.708410
$703$	1.89357e6	0.144508
$704$	1.61579e6	0.122872
$705$	−3.05575e7	−2.31550
$706$	−7.93839e6	−0.599405
$707$	8.36056e6	0.629052
$708$	−7.67695e7	−5.75580
$709$	−6.64715e6	−0.496615	−0.248307	−	0.968681i	$-0.579874\pi$
$709$	−6.64715e6	−0.496615	−0.248307	+	0.968681i	$0.579874\pi$
$710$	3.44035e7	2.56128
$711$	−4.99921e6	−0.370875
$712$	−3.56109e7	−2.63259
$713$	2.49878e7	1.84079
$714$	0	0
$715$	532233.	0.0389347
$716$	4.92777e7	3.59226
$717$	1.82175e7	1.32340
$718$	−6.07094e6	−0.439486
$719$	1.98127e7	1.42929	0.714647	−	0.699485i	$-0.246587\pi$
$719$	1.98127e7	1.42929	0.714647	+	0.699485i	$0.246587\pi$
$720$	5.64256e7	4.05644
$721$	−8.53501e6	−0.611457
$722$	−2.19756e7	−1.56891
$723$	−2.69343e7	−1.91629
$724$	−5.41334e6	−0.383812
$725$	95765.0	0.00676646
$726$	4.20720e7	2.96245
$727$	−9.55304e6	−0.670356	−0.335178	−	0.942155i	$-0.608797\pi$
$727$	−9.55304e6	−0.670356	−0.335178	+	0.942155i	$0.608797\pi$
$728$	−1.09081e7	−0.762821
$729$	−2.33307e7	−1.62596
$730$	2.79583e7	1.94180
$731$	0	0
$732$	2.40152e7	1.65656
$733$	−5.29912e6	−0.364287	−0.182144	−	0.983272i	$-0.558304\pi$
$733$	−5.29912e6	−0.364287	−0.182144	+	0.983272i	$0.558304\pi$
$734$	1.69406e7	1.16062
$735$	1.17230e7	0.800426
$736$	4.45707e7	3.03288
$737$	−1.68721e6	−0.114419
$738$	2.75445e7	1.86163
$739$	−8.93627e6	−0.601929	−0.300964	−	0.953635i	$-0.597309\pi$
$739$	−8.93627e6	−0.601929	−0.300964	+	0.953635i	$0.597309\pi$
$740$	1.33369e7	0.895315
$741$	−3.79314e6	−0.253778
$742$	−4.58585e6	−0.305781
$743$	−570526.	−0.0379143	−0.0189572	−	0.999820i	$-0.506035\pi$
$743$	−570526.	−0.0379143	−0.0189572	+	0.999820i	$0.506035\pi$
$744$	−8.16335e7	−5.40675
$745$	1.10931e7	0.732252
$746$	5.00193e7	3.29072
$747$	−2.57028e7	−1.68531
$748$	0	0
$749$	3.52988e6	0.229909
$750$	4.62289e7	3.00096
$751$	6.99921e6	0.452845	0.226422	−	0.974029i	$-0.427297\pi$
$751$	6.99921e6	0.452845	0.226422	+	0.974029i	$0.427297\pi$
$752$	5.71927e7	3.68804
$753$	−3.50976e7	−2.25575
$754$	−1.16962e7	−0.749234
$755$	491849.	0.0314025
$756$	2.60091e7	1.65509
$757$	−2.02906e7	−1.28693	−0.643465	−	0.765476i	$-0.722504\pi$
$757$	−2.02906e7	−1.28693	−0.643465	+	0.765476i	$0.722504\pi$
$758$	2.72085e6	0.172001
$759$	−3.68934e6	−0.232458
$760$	1.68633e7	1.05903
$761$	−1.78173e7	−1.11527	−0.557636	−	0.830085i	$-0.688292\pi$
$761$	−1.78173e7	−1.11527	−0.557636	+	0.830085i	$0.688292\pi$
$762$	5.58751e7	3.48603
$763$	9.40119e6	0.584617
$764$	−2.80415e7	−1.73807
$765$	0	0
$766$	−3.96828e7	−2.44360
$767$	9.50043e6	0.583116
$768$	1.92532e7	1.17788
$769$	−7.00151e6	−0.426949	−0.213475	−	0.976949i	$-0.568478\pi$
$769$	−7.00151e6	−0.426949	−0.213475	+	0.976949i	$0.568478\pi$
$770$	−2.10721e6	−0.128080
$771$	−5.28665e6	−0.320291
$772$	1.10654e7	0.668228
$773$	−1.14209e7	−0.687469	−0.343734	−	0.939067i	$-0.611692\pi$
$773$	−1.14209e7	−0.687469	−0.343734	+	0.939067i	$0.611692\pi$
$774$	6.51937e7	3.91159
$775$	−139725.	−0.00835644
$776$	4.08647e7	2.43609
$777$	7.03117e6	0.417806
$778$	6.12826e7	3.62985
$779$	4.20230e6	0.248109
$780$	−2.67162e7	−1.57231
$781$	2.30438e6	0.135185
$782$	0	0
$783$	1.65093e7	0.962332
$784$	−2.19413e7	−1.27489
$785$	−3.83833e6	−0.222315
$786$	−1.93265e7	−1.11583
$787$	7.23244e6	0.416244	0.208122	−	0.978103i	$-0.433265\pi$
$787$	7.23244e6	0.416244	0.208122	+	0.978103i	$0.433265\pi$
$788$	−5.46196e7	−3.13352
$789$	−7.71245e6	−0.441062
$790$	−7.56374e6	−0.431190
$791$	1.75123e7	0.995182
$792$	7.40360e6	0.419401
$793$	−2.97194e6	−0.167825
$794$	−5.20413e7	−2.92952
$795$	−6.64893e6	−0.373107
$796$	−1.55373e7	−0.869149
$797$	−2.10646e7	−1.17465	−0.587324	−	0.809352i	$-0.699819\pi$
$797$	−2.10646e7	−1.17465	−0.587324	+	0.809352i	$0.699819\pi$
$798$	1.50178e7	0.834831
$799$	0	0
$800$	−249228.	−0.0137680
$801$	−2.82444e7	−1.55543
$802$	−4.63665e7	−2.54547
$803$	1.87268e6	0.102488
$804$	8.46917e7	4.62062
$805$	−1.91668e7	−1.04246
$806$	1.70653e7	0.925289
$807$	−649009.	−0.0350806
$808$	−4.44431e7	−2.39484
$809$	4.12289e6	0.221478	0.110739	−	0.993850i	$-0.464678\pi$
$809$	4.12289e6	0.221478	0.110739	+	0.993850i	$0.464678\pi$
$810$	−1.95614e6	−0.104758
$811$	−7.45417e6	−0.397967	−0.198984	−	0.980003i	$-0.563764\pi$
$811$	−7.45417e6	−0.397967	−0.198984	+	0.980003i	$0.563764\pi$
$812$	3.28885e7	1.75047
$813$	−3.15057e7	−1.67172
$814$	1.25781e6	0.0665357
$815$	−9.29943e6	−0.490413
$816$	0	0
$817$	9.94621e6	0.521318
$818$	4.13066e7	2.15842
$819$	−8.65168e6	−0.450703
$820$	2.95979e7	1.53719
$821$	2.38165e7	1.23316	0.616581	−	0.787292i	$-0.288517\pi$
$821$	2.38165e7	1.23316	0.616581	+	0.787292i	$0.288517\pi$
$822$	−1.17912e7	−0.608666
$823$	−2.95580e7	−1.52116	−0.760582	−	0.649242i	$-0.775086\pi$
$823$	−2.95580e7	−1.52116	−0.760582	+	0.649242i	$0.775086\pi$
$824$	4.53704e7	2.32785
$825$	20629.8	0.00105526
$826$	−3.76140e7	−1.91823
$827$	3.28549e7	1.67046	0.835231	−	0.549899i	$-0.185334\pi$
$827$	3.28549e7	1.67046	0.835231	+	0.549899i	$0.185334\pi$
$828$	1.13756e8	5.76632
$829$	351675.	0.0177728	0.00888640	−	0.999961i	$-0.497171\pi$
$829$	351675.	0.0177728	0.00888640	+	0.999961i	$0.497171\pi$
$830$	−3.88880e7	−1.95939
$831$	−3.10668e7	−1.56061
$832$	1.00372e7	0.502694
$833$	0	0
$834$	−2.92723e7	−1.45728
$835$	−3.19911e7	−1.58786
$836$	1.90803e6	0.0944214
$837$	−2.40878e7	−1.18846
$838$	−6.22965e7	−3.06446
$839$	3.05399e7	1.49783	0.748915	−	0.662666i	$-0.230575\pi$
$839$	3.05399e7	1.49783	0.748915	+	0.662666i	$0.230575\pi$
$840$	6.26166e7	3.06190
$841$	364895.	0.0177901
$842$	−4.74944e7	−2.30867
$843$	−3.15439e7	−1.52878
$844$	−9.54241e6	−0.461107
$845$	−1.73800e7	−0.837351
$846$	8.88596e7	4.26853
$847$	1.46402e7	0.701193
$848$	1.24444e7	0.594272
$849$	−513863.	−0.0244669
$850$	0	0
$851$	1.14408e7	0.541543
$852$	−1.15672e8	−5.45919
$853$	−6.72309e6	−0.316371	−0.158185	−	0.987409i	$-0.550564\pi$
$853$	−6.72309e6	−0.316371	−0.158185	+	0.987409i	$0.550564\pi$
$854$	1.17665e7	0.552080
$855$	1.33749e7	0.625715
$856$	−1.87642e7	−0.875276
$857$	3.83745e7	1.78480	0.892402	−	0.451241i	$-0.149019\pi$
$857$	3.83745e7	1.78480	0.892402	+	0.451241i	$0.149019\pi$
$858$	−2.51962e6	−0.116847
$859$	2.40545e7	1.11228	0.556140	−	0.831089i	$-0.312282\pi$
$859$	2.40545e7	1.11228	0.556140	+	0.831089i	$0.312282\pi$
$860$	7.00539e7	3.22988
$861$	1.56039e7	0.717342
$862$	5.40586e7	2.47797
$863$	−367366.	−0.0167908	−0.00839540	−	0.999965i	$-0.502672\pi$
$863$	−367366.	−0.0167908	−0.00839540	+	0.999965i	$0.502672\pi$
$864$	−4.29654e7	−1.95810
$865$	−1.21171e7	−0.550626
$866$	5.84375e7	2.64787
$867$	0	0
$868$	−4.79859e7	−2.16179
$869$	−506628.	−0.0227583
$870$	6.71405e7	3.00737
$871$	−1.04808e7	−0.468112
$872$	−4.99749e7	−2.22567
$873$	3.24114e7	1.43934
$874$	2.44363e7	1.08207
$875$	1.60867e7	0.710308
$876$	−9.40016e7	−4.13881
$877$	−6.61357e6	−0.290360	−0.145180	−	0.989405i	$-0.546376\pi$
$877$	−6.61357e6	−0.290360	−0.145180	+	0.989405i	$0.546376\pi$
$878$	−6.17073e7	−2.70147
$879$	−9.67487e6	−0.422351
$880$	5.71826e6	0.248918
$881$	3432.14	0.000148979 0	7.44895e−5	−	1.00000i	$-0.499976\pi$
$881$	3432.14	0.000148979 0	7.44895e−5		1.00000i	$0.499976\pi$
$882$	−3.40899e7	−1.47555
$883$	−4.47460e7	−1.93131	−0.965655	−	0.259826i	$-0.916335\pi$
$883$	−4.47460e7	−1.93131	−0.965655	+	0.259826i	$0.916335\pi$
$884$	0	0
$885$	−5.45358e7	−2.34058
$886$	−8.66460e7	−3.70821
$887$	−3.38852e7	−1.44611	−0.723055	−	0.690790i	$-0.757263\pi$
$887$	−3.38852e7	−1.44611	−0.723055	+	0.690790i	$0.757263\pi$
$888$	−3.73763e7	−1.59061
$889$	1.94434e7	0.825120
$890$	−4.27334e7	−1.80839
$891$	−131024.	−0.00552914
$892$	−4.44298e7	−1.86966
$893$	1.35568e7	0.568889
$894$	−5.25151e7	−2.19756
$895$	3.50061e7	1.46078
$896$	−4.81597e6	−0.200408
$897$	−2.29179e7	−0.951030
$898$	2.03743e7	0.843125
$899$	−3.04591e7	−1.25695
$900$	−636095.	−0.0261767
$901$	0	0
$902$	2.79140e6	0.114237
$903$	3.69322e7	1.50725
$904$	−9.30920e7	−3.78871
$905$	−3.84555e6	−0.156076
$906$	−2.32844e6	−0.0942420
$907$	−1.52397e7	−0.615117	−0.307558	−	0.951529i	$-0.599512\pi$
$907$	−1.52397e7	−0.615117	−0.307558	+	0.951529i	$0.599512\pi$
$908$	−7.20717e7	−2.90102
$909$	−3.52496e7	−1.41496
$910$	−1.30899e7	−0.524001
$911$	−1.28387e7	−0.512539	−0.256269	−	0.966605i	$-0.582493\pi$
$911$	−1.28387e7	−0.512539	−0.256269	+	0.966605i	$0.582493\pi$
$912$	−4.07532e7	−1.62246
$913$	−2.60476e6	−0.103417
$914$	−6.85533e7	−2.71433
$915$	1.70600e7	0.673637
$916$	1.14109e8	4.49346
$917$	−6.72521e6	−0.264109
$918$	0	0
$919$	−3.68255e7	−1.43833	−0.719167	−	0.694837i	$-0.755477\pi$
$919$	−3.68255e7	−1.43833	−0.719167	+	0.694837i	$0.755477\pi$
$920$	1.01887e8	3.96870
$921$	9.50540e6	0.369251
$922$	1.95147e7	0.756021
$923$	1.43147e7	0.553066
$924$	7.08489e6	0.272994
$925$	−63974.0	−0.00245838
$926$	1.63753e7	0.627571
$927$	3.59851e7	1.37538
$928$	−5.43298e7	−2.07094
$929$	−7.85506e6	−0.298614	−0.149307	−	0.988791i	$-0.547704\pi$
$929$	−7.85506e6	−0.298614	−0.149307	+	0.988791i	$0.547704\pi$
$930$	−9.79610e7	−3.71403
$931$	−5.20090e6	−0.196655
$932$	713450.	0.0269044
$933$	7.07256e6	0.265994
$934$	−3.03844e6	−0.113968
$935$	0	0
$936$	4.59906e7	1.71585
$937$	3.43040e7	1.27643	0.638213	−	0.769860i	$-0.279674\pi$
$937$	3.43040e7	1.27643	0.638213	+	0.769860i	$0.279674\pi$
$938$	4.14956e7	1.53991
$939$	3.57235e7	1.32218
$940$	9.54840e7	3.52461
$941$	−3.64166e7	−1.34068	−0.670341	−	0.742053i	$-0.733852\pi$
$941$	−3.64166e7	−1.34068	−0.670341	+	0.742053i	$0.733852\pi$
$942$	1.81709e7	0.667188
$943$	2.53900e7	0.929787
$944$	1.02072e8	3.72799
$945$	1.84765e7	0.673037
$946$	6.60683e6	0.240030
$947$	2.86479e7	1.03805	0.519024	−	0.854760i	$-0.326295\pi$
$947$	2.86479e7	1.03805	0.519024	+	0.854760i	$0.326295\pi$
$948$	2.54309e7	0.919052
$949$	1.16330e7	0.419300
$950$	−136641.	−0.00491216
$951$	4.05767e7	1.45487
$952$	0	0
$953$	−8.06993e6	−0.287831	−0.143915	−	0.989590i	$-0.545969\pi$
$953$	−8.06993e6	−0.287831	−0.143915	+	0.989590i	$0.545969\pi$
$954$	1.93348e7	0.687809
$955$	−1.99202e7	−0.706782
$956$	−5.69247e7	−2.01445
$957$	4.49715e6	0.158729
$958$	1.88063e7	0.662050
$959$	−4.10309e6	−0.144067
$960$	−5.76169e7	−2.01777
$961$	1.58120e7	0.552305
$962$	7.81345e6	0.272211
$963$	−1.48826e7	−0.517146
$964$	8.41627e7	2.91694
$965$	7.86070e6	0.271733
$966$	9.07365e7	3.12852
$967$	1.89152e7	0.650495	0.325248	−	0.945629i	$-0.394552\pi$
$967$	1.89152e7	0.650495	0.325248	+	0.945629i	$0.394552\pi$
$968$	−7.78243e7	−2.66948
$969$	0	0
$970$	4.90380e7	1.67341
$971$	2.00268e7	0.681652	0.340826	−	0.940126i	$-0.389293\pi$
$971$	2.00268e7	0.681652	0.340826	+	0.940126i	$0.389293\pi$
$972$	7.54393e7	2.56113
$973$	−1.01862e7	−0.344928
$974$	−2.41383e7	−0.815286
$975$	128151.	0.00431729
$976$	−3.19302e7	−1.07295
$977$	4.96053e7	1.66261	0.831307	−	0.555813i	$-0.187593\pi$
$977$	4.96053e7	1.66261	0.831307	+	0.555813i	$0.187593\pi$
$978$	4.40240e7	1.47178
$979$	−2.86233e6	−0.0954472
$980$	−3.66313e7	−1.21839
$981$	−3.96371e7	−1.31501
$982$	−5.27066e7	−1.74416
$983$	1.22095e7	0.403008	0.201504	−	0.979488i	$-0.435417\pi$
$983$	1.22095e7	0.403008	0.201504	+	0.979488i	$0.435417\pi$
$984$	−8.29474e7	−2.73096
$985$	−3.88009e7	−1.27424
$986$	0	0
$987$	5.03388e7	1.64479
$988$	1.18526e7	0.386296
$989$	6.00944e7	1.95363
$990$	8.88438e6	0.288097
$991$	−1.64521e7	−0.532153	−0.266077	−	0.963952i	$-0.585727\pi$
$991$	−1.64521e7	−0.532153	−0.266077	+	0.963952i	$0.585727\pi$
$992$	7.92696e7	2.55757
$993$	5.89492e7	1.89716
$994$	−5.66746e7	−1.81938
$995$	−1.10375e7	−0.353437
$996$	1.30750e8	4.17630
$997$	−5.49706e6	−0.175143	−0.0875714	−	0.996158i	$-0.527911\pi$
$997$	−5.49706e6	−0.175143	−0.0875714	+	0.996158i	$0.527911\pi$
$998$	−6.33051e7	−2.01193
$999$	−1.10287e7	−0.349633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.6.a.j.1.27		28
17.10	odd	16		17.6.d.a.15.1	yes	28
17.12	odd	16		17.6.d.a.8.1	✓	28
17.16	even	2	inner	289.6.a.j.1.28		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.6.d.a.8.1	✓	28	17.12	odd	16
17.6.d.a.15.1	yes	28	17.10	odd	16
289.6.a.j.1.27		28	1.1	even	1	trivial
289.6.a.j.1.28		28	17.16	even	2	inner

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+10.5085 q^{2} -25.0990 q^{3} +78.4279 q^{4} +55.7139 q^{5} -263.753 q^{6} -91.7804 q^{7} +487.886 q^{8} +386.962 q^{9} +O(q^{10})\)	\(q+10.5085 q^{2} -25.0990 q^{3} +78.4279 q^{4} +55.7139 q^{5} -263.753 q^{6} -91.7804 q^{7} +487.886 q^{8} +386.962 q^{9} +585.468 q^{10} +39.2153 q^{11} -1968.47 q^{12} +243.603 q^{13} -964.471 q^{14} -1398.37 q^{15} +2617.24 q^{16} +4066.38 q^{18} +620.383 q^{19} +4369.53 q^{20} +2303.60 q^{21} +412.093 q^{22} +3748.31 q^{23} -12245.5 q^{24} -20.9596 q^{25} +2559.89 q^{26} -3613.31 q^{27} -7198.14 q^{28} -4569.03 q^{29} -14694.7 q^{30} +6666.42 q^{31} +11890.9 q^{32} -984.267 q^{33} -5113.44 q^{35} +30348.6 q^{36} +3052.25 q^{37} +6519.27 q^{38} -6114.20 q^{39} +27182.1 q^{40} +6773.72 q^{41} +24207.3 q^{42} +16032.4 q^{43} +3075.58 q^{44} +21559.2 q^{45} +39389.0 q^{46} +21852.3 q^{47} -65690.3 q^{48} -8383.37 q^{49} -220.253 q^{50} +19105.3 q^{52} +4754.78 q^{53} -37970.4 q^{54} +2184.84 q^{55} -44778.4 q^{56} -15571.0 q^{57} -48013.5 q^{58} +38999.6 q^{59} -109671. q^{60} -12199.9 q^{61} +70053.9 q^{62} -35515.5 q^{63} +41203.0 q^{64} +13572.1 q^{65} -10343.1 q^{66} -43024.2 q^{67} -94079.1 q^{69} -53734.5 q^{70} +58762.3 q^{71} +188793. q^{72} +47753.8 q^{73} +32074.5 q^{74} +526.065 q^{75} +48655.3 q^{76} -3599.20 q^{77} -64250.9 q^{78} -12919.1 q^{79} +145817. q^{80} -3341.15 q^{81} +71181.4 q^{82} -66422.1 q^{83} +180666. q^{84} +168476. q^{86} +114678. q^{87} +19132.6 q^{88} -72990.1 q^{89} +226554. q^{90} -22358.0 q^{91} +293972. q^{92} -167321. q^{93} +229634. q^{94} +34564.0 q^{95} -298450. q^{96} +83758.6 q^{97} -88096.4 q^{98} +15174.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 16 q^{2} + 448 q^{4} + 768 q^{8} + 2268 q^{9}+O(q^{10}) \) 28 * q + 16 * q^2 + 448 * q^4 + 768 * q^8 + 2268 * q^9	\( 28 q + 16 q^{2} + 448 q^{4} + 768 q^{8} + 2268 q^{9} + 304 q^{13} + 4392 q^{15} + 7176 q^{16} + 1896 q^{18} + 9288 q^{19} + 12032 q^{21} + 17692 q^{25} + 29600 q^{26} - 17784 q^{30} + 19032 q^{32} + 38800 q^{33} + 26056 q^{35} + 77816 q^{36} + 36384 q^{38} + 123904 q^{42} + 46520 q^{43} + 71808 q^{47} + 38748 q^{49} + 241632 q^{50} + 6008 q^{52} + 61360 q^{53} + 46680 q^{55} + 256920 q^{59} + 330504 q^{60} - 72496 q^{64} + 10736 q^{66} + 250608 q^{67} - 107696 q^{69} + 273320 q^{70} + 463640 q^{72} + 974048 q^{76} + 482672 q^{77} + 242060 q^{81} + 458584 q^{83} + 1605472 q^{84} + 718272 q^{86} + 1009400 q^{87} + 501088 q^{89} + 903248 q^{93} + 1315264 q^{94} - 156256 q^{98}+O(q^{100}) \) 28 * q + 16 * q^2 + 448 * q^4 + 768 * q^8 + 2268 * q^9 + 304 * q^13 + 4392 * q^15 + 7176 * q^16 + 1896 * q^18 + 9288 * q^19 + 12032 * q^21 + 17692 * q^25 + 29600 * q^26 - 17784 * q^30 + 19032 * q^32 + 38800 * q^33 + 26056 * q^35 + 77816 * q^36 + 36384 * q^38 + 123904 * q^42 + 46520 * q^43 + 71808 * q^47 + 38748 * q^49 + 241632 * q^50 + 6008 * q^52 + 61360 * q^53 + 46680 * q^55 + 256920 * q^59 + 330504 * q^60 - 72496 * q^64 + 10736 * q^66 + 250608 * q^67 - 107696 * q^69 + 273320 * q^70 + 463640 * q^72 + 974048 * q^76 + 482672 * q^77 + 242060 * q^81 + 458584 * q^83 + 1605472 * q^84 + 718272 * q^86 + 1009400 * q^87 + 501088 * q^89 + 903248 * q^93 + 1315264 * q^94 - 156256 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more