LMFDB - Embedded newform 289.4.a.f.1.6

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:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 54x^{6} - 20x^{5} + 677x^{4} + 380x^{3} - 2216x^{2} - 1000x + 476 $ x^8 - 54x^6 - 20x^5 + 677x^4 + 380x^3 - 2216x^2 - 1000x + 476
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.296379$ 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)

$f(q)$	$=$	$q+2.11783 q^{2} +8.38287 q^{3} -3.51478 q^{4} +14.3637 q^{5} +17.7535 q^{6} +4.54811 q^{7} -24.3864 q^{8} +43.2725 q^{9} +O(q^{10})$	\(q+2.11783 q^{2} +8.38287 q^{3} -3.51478 q^{4} +14.3637 q^{5} +17.7535 q^{6} +4.54811 q^{7} -24.3864 q^{8} +43.2725 q^{9} +30.4200 q^{10} +48.0908 q^{11} -29.4639 q^{12} -49.5377 q^{13} +9.63214 q^{14} +120.409 q^{15} -23.5281 q^{16} +91.6440 q^{18} +31.1112 q^{19} -50.4854 q^{20} +38.1262 q^{21} +101.848 q^{22} +41.8837 q^{23} -204.428 q^{24} +81.3170 q^{25} -104.913 q^{26} +136.410 q^{27} -15.9856 q^{28} -121.361 q^{29} +255.007 q^{30} -167.926 q^{31} +145.263 q^{32} +403.139 q^{33} +65.3279 q^{35} -152.093 q^{36} +356.317 q^{37} +65.8884 q^{38} -415.268 q^{39} -350.280 q^{40} -63.3621 q^{41} +80.7450 q^{42} -87.7863 q^{43} -169.028 q^{44} +621.555 q^{45} +88.7028 q^{46} -281.901 q^{47} -197.233 q^{48} -322.315 q^{49} +172.216 q^{50} +174.114 q^{52} -5.63254 q^{53} +288.894 q^{54} +690.763 q^{55} -110.912 q^{56} +260.801 q^{57} -257.022 q^{58} -134.352 q^{59} -423.212 q^{60} +598.035 q^{61} -355.640 q^{62} +196.808 q^{63} +495.867 q^{64} -711.547 q^{65} +853.781 q^{66} -951.761 q^{67} +351.106 q^{69} +138.354 q^{70} -332.263 q^{71} -1055.26 q^{72} +26.5290 q^{73} +754.620 q^{74} +681.670 q^{75} -109.349 q^{76} +218.722 q^{77} -879.470 q^{78} -33.1438 q^{79} -337.952 q^{80} -24.8476 q^{81} -134.190 q^{82} +283.887 q^{83} -134.005 q^{84} -185.917 q^{86} -1017.35 q^{87} -1172.76 q^{88} +191.442 q^{89} +1316.35 q^{90} -225.303 q^{91} -147.212 q^{92} -1407.70 q^{93} -597.020 q^{94} +446.874 q^{95} +1217.72 q^{96} +287.119 q^{97} -682.609 q^{98} +2081.01 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 36 q^{4} + 96 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 36 * q^4 + 96 * q^8 + 8 * q^9	$ 8 q + 8 q^{2} + 36 q^{4} + 96 q^{8} + 8 q^{9} + 88 q^{13} + 252 q^{15} + 420 q^{16} + 428 q^{18} - 52 q^{19} + 260 q^{21} - 140 q^{25} - 268 q^{26} + 120 q^{30} + 2336 q^{32} + 816 q^{33} + 1172 q^{35} - 264 q^{36} + 768 q^{38} - 136 q^{42} - 752 q^{43} + 368 q^{47} + 852 q^{49} + 468 q^{50} + 2564 q^{52} - 1156 q^{53} + 1996 q^{55} + 192 q^{59} - 3160 q^{60} + 3044 q^{64} + 1052 q^{66} + 764 q^{67} + 1812 q^{69} + 544 q^{70} - 1404 q^{72} + 896 q^{76} + 3084 q^{77} - 280 q^{81} + 496 q^{83} - 2952 q^{84} - 4244 q^{86} - 2860 q^{87} + 2156 q^{89} - 4012 q^{93} - 3392 q^{94} - 6728 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 36 * q^4 + 96 * q^8 + 8 * q^9 + 88 * q^13 + 252 * q^15 + 420 * q^16 + 428 * q^18 - 52 * q^19 + 260 * q^21 - 140 * q^25 - 268 * q^26 + 120 * q^30 + 2336 * q^32 + 816 * q^33 + 1172 * q^35 - 264 * q^36 + 768 * q^38 - 136 * q^42 - 752 * q^43 + 368 * q^47 + 852 * q^49 + 468 * q^50 + 2564 * q^52 - 1156 * q^53 + 1996 * q^55 + 192 * q^59 - 3160 * q^60 + 3044 * q^64 + 1052 * q^66 + 764 * q^67 + 1812 * q^69 + 544 * q^70 - 1404 * q^72 + 896 * q^76 + 3084 * q^77 - 280 * q^81 + 496 * q^83 - 2952 * q^84 - 4244 * q^86 - 2860 * q^87 + 2156 * q^89 - 4012 * q^93 - 3392 * q^94 - 6728 * 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 $

$2$	2.11783	0.748767	0.374384	−	0.927274i	$-0.377854\pi$
$2$	2.11783	0.748767	0.374384	+	0.927274i	$0.377854\pi$
$3$	8.38287	1.61328	0.806642	−	0.591040i	$-0.201283\pi$
$3$	8.38287	1.61328	0.806642	+	0.591040i	$0.201283\pi$
$4$	−3.51478	−0.439347
$5$	14.3637	1.28473	0.642366	−	0.766398i	$-0.277953\pi$
$5$	14.3637	1.28473	0.642366	+	0.766398i	$0.277953\pi$
$6$	17.7535	1.20797
$7$	4.54811	0.245575	0.122787	−	0.992433i	$-0.460817\pi$
$7$	4.54811	0.245575	0.122787	+	0.992433i	$0.460817\pi$
$8$	−24.3864	−1.07774
$9$	43.2725	1.60269
$10$	30.4200	0.961965
$11$	48.0908	1.31817	0.659087	−	0.752067i	$-0.270943\pi$
$11$	48.0908	1.31817	0.659087	+	0.752067i	$0.270943\pi$
$12$	−29.4639	−0.708792
$13$	−49.5377	−1.05687	−0.528434	−	0.848974i	$-0.677221\pi$
$13$	−49.5377	−1.05687	−0.528434	+	0.848974i	$0.677221\pi$
$14$	9.63214	0.183878
$15$	120.409	2.07264
$16$	−23.5281	−0.367627
$17$	0	0
$17$	0	0
$18$	91.6440	1.20004
$19$	31.1112	0.375653	0.187826	−	0.982202i	$-0.439856\pi$
$19$	31.1112	0.375653	0.187826	+	0.982202i	$0.439856\pi$
$20$	−50.4854	−0.564443
$21$	38.1262	0.396182
$22$	101.848	0.987006
$23$	41.8837	0.379711	0.189856	−	0.981812i	$-0.439198\pi$
$23$	41.8837	0.379711	0.189856	+	0.981812i	$0.439198\pi$
$24$	−204.428	−1.73870
$25$	81.3170	0.650536
$26$	−104.913	−0.791349
$27$	136.410	0.972303
$28$	−15.9856	−0.107893
$29$	−121.361	−0.777109	−0.388555	−	0.921426i	$-0.627025\pi$
$29$	−121.361	−0.777109	−0.388555	+	0.921426i	$0.627025\pi$
$30$	255.007	1.55192
$31$	−167.926	−0.972918	−0.486459	−	0.873703i	$-0.661712\pi$
$31$	−167.926	−0.972918	−0.486459	+	0.873703i	$0.661712\pi$
$32$	145.263	0.802470
$33$	403.139	2.12659
$34$	0	0
$35$	65.3279	0.315498
$36$	−152.093	−0.704136
$37$	356.317	1.58319	0.791596	−	0.611044i	$-0.209250\pi$
$37$	356.317	1.58319	0.791596	+	0.611044i	$0.209250\pi$
$38$	65.8884	0.281277
$39$	−415.268	−1.70503
$40$	−350.280	−1.38460
$41$	−63.3621	−0.241354	−0.120677	−	0.992692i	$-0.538506\pi$
$41$	−63.3621	−0.241354	−0.120677	+	0.992692i	$0.538506\pi$
$42$	80.7450	0.296648
$43$	−87.7863	−0.311332	−0.155666	−	0.987810i	$-0.549752\pi$
$43$	−87.7863	−0.311332	−0.155666	+	0.987810i	$0.549752\pi$
$44$	−169.028	−0.579136
$45$	621.555	2.05902
$46$	88.7028	0.284316
$47$	−281.901	−0.874884	−0.437442	−	0.899247i	$-0.644115\pi$
$47$	−281.901	−0.874884	−0.437442	+	0.899247i	$0.644115\pi$
$48$	−197.233	−0.593086
$49$	−322.315	−0.939693
$50$	172.216	0.487100
$51$	0	0
$52$	174.114	0.464332
$53$	−5.63254	−0.0145979	−0.00729895	−	0.999973i	$-0.502323\pi$
$53$	−5.63254	−0.0145979	−0.00729895	+	0.999973i	$0.502323\pi$
$54$	288.894	0.728029
$55$	690.763	1.69350
$56$	−110.912	−0.264665
$57$	260.801	0.606035
$58$	−257.022	−0.581874
$59$	−134.352	−0.296460	−0.148230	−	0.988953i	$-0.547358\pi$
$59$	−134.352	−0.296460	−0.148230	+	0.988953i	$0.547358\pi$
$60$	−423.212	−0.910608
$61$	598.035	1.25525	0.627627	−	0.778514i	$-0.284026\pi$
$61$	598.035	1.25525	0.627627	+	0.778514i	$0.284026\pi$
$62$	−355.640	−0.728490
$63$	196.808	0.393579
$64$	495.867	0.968490
$65$	−711.547	−1.35779
$66$	853.781	1.59232
$67$	−951.761	−1.73546	−0.867732	−	0.497032i	$-0.834423\pi$
$67$	−951.761	−1.73546	−0.867732	+	0.497032i	$0.834423\pi$
$68$	0	0
$69$	351.106	0.612582
$70$	138.354	0.236235
$71$	−332.263	−0.555385	−0.277693	−	0.960670i	$-0.589570\pi$
$71$	−332.263	−0.555385	−0.277693	+	0.960670i	$0.589570\pi$
$72$	−1055.26	−1.72727
$73$	26.5290	0.0425340	0.0212670	−	0.999774i	$-0.493230\pi$
$73$	26.5290	0.0425340	0.0212670	+	0.999774i	$0.493230\pi$
$74$	754.620	1.18544
$75$	681.670	1.04950
$76$	−109.349	−0.165042
$77$	218.722	0.323710
$78$	−879.470	−1.27667
$79$	−33.1438	−0.0472021	−0.0236010	−	0.999721i	$-0.507513\pi$
$79$	−33.1438	−0.0472021	−0.0236010	+	0.999721i	$0.507513\pi$
$80$	−337.952	−0.472302
$81$	−24.8476	−0.0340845
$82$	−134.190	−0.180718
$83$	283.887	0.375430	0.187715	−	0.982224i	$-0.439892\pi$
$83$	283.887	0.375430	0.187715	+	0.982224i	$0.439892\pi$
$84$	−134.005	−0.174062
$85$	0	0
$86$	−185.917	−0.233115
$87$	−1017.35	−1.25370
$88$	−1172.76	−1.42064
$89$	191.442	0.228009	0.114005	−	0.993480i	$-0.463632\pi$
$89$	191.442	0.228009	0.114005	+	0.993480i	$0.463632\pi$
$90$	1316.35	1.54173
$91$	−225.303	−0.259540
$92$	−147.212	−0.166825
$93$	−1407.70	−1.56959
$94$	−597.020	−0.655085
$95$	446.874	0.482613
$96$	1217.72	1.29461
$97$	287.119	0.300541	0.150271	−	0.988645i	$-0.451985\pi$
$97$	287.119	0.300541	0.150271	+	0.988645i	$0.451985\pi$
$98$	−682.609	−0.703612
$99$	2081.01	2.11262
$100$	−285.811	−0.285811
$101$	154.062	0.151780	0.0758899	−	0.997116i	$-0.475820\pi$
$101$	154.062	0.151780	0.0758899	+	0.997116i	$0.475820\pi$
$102$	0	0
$103$	765.082	0.731900	0.365950	−	0.930634i	$-0.380744\pi$
$103$	765.082	0.731900	0.365950	+	0.930634i	$0.380744\pi$
$104$	1208.05	1.13903
$105$	547.635	0.508988
$106$	−11.9288	−0.0109304
$107$	−395.483	−0.357315	−0.178658	−	0.983911i	$-0.557175\pi$
$107$	−395.483	−0.357315	−0.178658	+	0.983911i	$0.557175\pi$
$108$	−479.452	−0.427179
$109$	877.900	0.771446	0.385723	−	0.922615i	$-0.373952\pi$
$109$	877.900	0.771446	0.385723	+	0.922615i	$0.373952\pi$
$110$	1462.92	1.26804
$111$	2986.96	2.55414
$112$	−107.008	−0.0902799
$113$	−2046.06	−1.70334	−0.851669	−	0.524079i	$-0.824410\pi$
$113$	−2046.06	−1.70334	−0.851669	+	0.524079i	$0.824410\pi$
$114$	552.334	0.453779
$115$	601.607	0.487827
$116$	426.557	0.341421
$117$	−2143.62	−1.69383
$118$	−284.535	−0.221980
$119$	0	0
$120$	−2936.35	−2.23376
$121$	981.722	0.737582
$122$	1266.54	0.939894
$123$	−531.156	−0.389372
$124$	590.224	0.427449
$125$	−627.452	−0.448968
$126$	416.807	0.294699
$127$	2106.13	1.47156	0.735782	−	0.677218i	$-0.236815\pi$
$127$	2106.13	1.47156	0.735782	+	0.677218i	$0.236815\pi$
$128$	−111.936	−0.0772959
$129$	−735.901	−0.502267
$130$	−1506.94	−1.01667
$131$	−1390.56	−0.927434	−0.463717	−	0.885983i	$-0.653485\pi$
$131$	−1390.56	−0.927434	−0.463717	+	0.885983i	$0.653485\pi$
$132$	−1416.94	−0.934311
$133$	141.497	0.0922509
$134$	−2015.67	−1.29946
$135$	1959.36	1.24915
$136$	0	0
$137$	−2309.58	−1.44030	−0.720149	−	0.693820i	$-0.755926\pi$
$137$	−2309.58	−1.44030	−0.720149	+	0.693820i	$0.755926\pi$
$138$	743.584	0.458682
$139$	−2477.09	−1.51154	−0.755769	−	0.654838i	$-0.772737\pi$
$139$	−2477.09	−1.51154	−0.755769	+	0.654838i	$0.772737\pi$
$140$	−229.613	−0.138613
$141$	−2363.14	−1.41144
$142$	−703.678	−0.415855
$143$	−2382.31	−1.39314
$144$	−1018.12	−0.589190
$145$	−1743.20	−0.998377
$146$	56.1840	0.0318481
$147$	−2701.92	−1.51599
$148$	−1252.37	−0.695571
$149$	−1521.60	−0.836607	−0.418304	−	0.908307i	$-0.637375\pi$
$149$	−1521.60	−0.836607	−0.418304	+	0.908307i	$0.637375\pi$
$150$	1443.66	0.785831
$151$	−397.910	−0.214447	−0.107223	−	0.994235i	$-0.534196\pi$
$151$	−397.910	−0.214447	−0.107223	+	0.994235i	$0.534196\pi$
$152$	−758.691	−0.404855
$153$	0	0
$154$	463.217	0.242384
$155$	−2412.05	−1.24994
$156$	1459.58	0.749100
$157$	1068.19	0.543001	0.271501	−	0.962438i	$-0.412480\pi$
$157$	1068.19	0.543001	0.271501	+	0.962438i	$0.412480\pi$
$158$	−70.1930	−0.0353434
$159$	−47.2168	−0.0235505
$160$	2086.51	1.03096
$161$	190.492	0.0932476
$162$	−52.6231	−0.0255214
$163$	−845.422	−0.406249	−0.203124	−	0.979153i	$-0.565110\pi$
$163$	−845.422	−0.406249	−0.203124	+	0.979153i	$0.565110\pi$
$164$	222.704	0.106038
$165$	5790.58	2.73210
$166$	601.226	0.281109
$167$	2613.54	1.21103	0.605515	−	0.795834i	$-0.292967\pi$
$167$	2613.54	1.21103	0.605515	+	0.795834i	$0.292967\pi$
$168$	−929.761	−0.426980
$169$	256.987	0.116972
$170$	0	0
$171$	1346.26	0.602054
$172$	308.549	0.136783
$173$	−3084.82	−1.35569	−0.677846	−	0.735204i	$-0.737087\pi$
$173$	−3084.82	−1.35569	−0.677846	+	0.735204i	$0.737087\pi$
$174$	−2154.59	−0.938728
$175$	369.839	0.159755
$176$	−1131.48	−0.484596
$177$	−1126.26	−0.478274
$178$	405.443	0.170726
$179$	918.935	0.383712	0.191856	−	0.981423i	$-0.438549\pi$
$179$	918.935	0.383712	0.191856	+	0.981423i	$0.438549\pi$
$180$	−2184.63	−0.904625
$181$	2158.66	0.886475	0.443238	−	0.896404i	$-0.353830\pi$
$181$	2158.66	0.886475	0.443238	+	0.896404i	$0.353830\pi$
$182$	−477.155	−0.194335
$183$	5013.25	2.02508
$184$	−1021.39	−0.409229
$185$	5118.04	2.03398
$186$	−2981.29	−1.17526
$187$	0	0
$188$	990.821	0.384378
$189$	620.409	0.238773
$190$	946.404	0.361365
$191$	−1349.67	−0.511302	−0.255651	−	0.966769i	$-0.582290\pi$
$191$	−1349.67	−0.511302	−0.255651	+	0.966769i	$0.582290\pi$
$192$	4156.79	1.56245
$193$	3509.11	1.30876	0.654382	−	0.756164i	$-0.272929\pi$
$193$	3509.11	1.30876	0.654382	+	0.756164i	$0.272929\pi$
$194$	608.070	0.225036
$195$	−5964.81	−2.19051
$196$	1132.86	0.412852
$197$	3548.60	1.28339	0.641694	−	0.766961i	$-0.278232\pi$
$197$	3548.60	1.28339	0.641694	+	0.766961i	$0.278232\pi$
$198$	4407.23	1.58186
$199$	−3071.91	−1.09428	−0.547141	−	0.837041i	$-0.684284\pi$
$199$	−3071.91	−1.09428	−0.547141	+	0.837041i	$0.684284\pi$
$200$	−1983.03	−0.701106
$201$	−7978.49	−2.79980
$202$	326.278	0.113648
$203$	−551.963	−0.190838
$204$	0	0
$205$	−910.116	−0.310075
$206$	1620.32	0.548023
$207$	1812.41	0.608558
$208$	1165.53	0.388533
$209$	1496.16	0.495176
$210$	1159.80	0.381113
$211$	6021.99	1.96479	0.982395	−	0.186817i	$-0.0598170\pi$
$211$	6021.99	1.96479	0.982395	+	0.186817i	$0.0598170\pi$
$212$	19.7971	0.00641354
$213$	−2785.32	−0.895995
$214$	−837.567	−0.267546
$215$	−1260.94	−0.399978
$216$	−3326.56	−1.04789
$217$	−763.748	−0.238924
$218$	1859.25	0.577634
$219$	222.389	0.0686194
$220$	−2427.88	−0.744035
$221$	0	0
$222$	6325.88	1.91246
$223$	−3581.06	−1.07536	−0.537680	−	0.843149i	$-0.680699\pi$
$223$	−3581.06	−1.07536	−0.537680	+	0.843149i	$0.680699\pi$
$224$	660.670	0.197066
$225$	3518.79	1.04260
$226$	−4333.22	−1.27540
$227$	4244.38	1.24101	0.620506	−	0.784202i	$-0.286927\pi$
$227$	4244.38	1.24101	0.620506	+	0.784202i	$0.286927\pi$
$228$	−916.659	−0.266260
$229$	5146.73	1.48518	0.742589	−	0.669748i	$-0.233598\pi$
$229$	5146.73	1.48518	0.742589	+	0.669748i	$0.233598\pi$
$230$	1274.10	0.365269
$231$	1833.52	0.522237
$232$	2959.56	0.837519
$233$	2847.35	0.800584	0.400292	−	0.916388i	$-0.368909\pi$
$233$	2847.35	0.800584	0.400292	+	0.916388i	$0.368909\pi$
$234$	−4539.84	−1.26828
$235$	−4049.16	−1.12399
$236$	472.218	0.130249
$237$	−277.840	−0.0761504
$238$	0	0
$239$	3984.47	1.07839	0.539193	−	0.842182i	$-0.318729\pi$
$239$	3984.47	1.07839	0.539193	+	0.842182i	$0.318729\pi$
$240$	−2833.00	−0.761957
$241$	1794.52	0.479648	0.239824	−	0.970816i	$-0.422910\pi$
$241$	1794.52	0.479648	0.239824	+	0.970816i	$0.422910\pi$
$242$	2079.12	0.552278
$243$	−3891.37	−1.02729
$244$	−2101.96	−0.551493
$245$	−4629.64	−1.20725
$246$	−1124.90	−0.291549
$247$	−1541.18	−0.397016
$248$	4095.12	1.04855
$249$	2379.79	0.605675
$250$	−1328.84	−0.336173
$251$	4658.75	1.17154	0.585772	−	0.810476i	$-0.300791\pi$
$251$	4658.75	1.17154	0.585772	+	0.810476i	$0.300791\pi$
$252$	−691.737	−0.172918
$253$	2014.22	0.500526
$254$	4460.43	1.10186
$255$	0	0
$256$	−4204.00	−1.02637
$257$	6235.43	1.51345	0.756723	−	0.653736i	$-0.226799\pi$
$257$	6235.43	1.51345	0.756723	+	0.653736i	$0.226799\pi$
$258$	−1558.52	−0.376081
$259$	1620.57	0.388792
$260$	2500.93	0.596543
$261$	−5251.59	−1.24546
$262$	−2944.98	−0.694432
$263$	149.037	0.0349430	0.0174715	−	0.999847i	$-0.494438\pi$
$263$	149.037	0.0349430	0.0174715	+	0.999847i	$0.494438\pi$
$264$	−9831.10	−2.29190
$265$	−80.9043	−0.0187544
$266$	299.668	0.0690745
$267$	1604.83	0.367844
$268$	3345.23	0.762472
$269$	3110.04	0.704915	0.352458	−	0.935828i	$-0.385346\pi$
$269$	3110.04	0.704915	0.352458	+	0.935828i	$0.385346\pi$
$270$	4149.60	0.935322
$271$	4725.42	1.05922	0.529610	−	0.848241i	$-0.322338\pi$
$271$	4725.42	1.05922	0.529610	+	0.848241i	$0.322338\pi$
$272$	0	0
$273$	−1888.69	−0.418713
$274$	−4891.31	−1.07845
$275$	3910.60	0.857519
$276$	−1234.06	−0.269136
$277$	−900.145	−0.195251	−0.0976254	−	0.995223i	$-0.531125\pi$
$277$	−900.145	−0.195251	−0.0976254	+	0.995223i	$0.531125\pi$
$278$	−5246.06	−1.13179
$279$	−7266.60	−1.55928
$280$	−1593.11	−0.340024
$281$	9165.72	1.94584	0.972920	−	0.231143i	$-0.0742465\pi$
$281$	9165.72	1.94584	0.972920	+	0.231143i	$0.0742465\pi$
$282$	−5004.75	−1.05684
$283$	−3541.31	−0.743847	−0.371924	−	0.928263i	$-0.621302\pi$
$283$	−3541.31	−0.743847	−0.371924	+	0.928263i	$0.621302\pi$
$284$	1167.83	0.244007
$285$	3746.08	0.778592
$286$	−5045.33	−1.04314
$287$	−288.178	−0.0592704
$288$	6285.87	1.28611
$289$	0	0
$290$	−3691.80	−0.747552
$291$	2406.88	0.484859
$292$	−93.2435	−0.0186872
$293$	−1268.29	−0.252882	−0.126441	−	0.991974i	$-0.540355\pi$
$293$	−1268.29	−0.252882	−0.126441	+	0.991974i	$0.540355\pi$
$294$	−5722.22	−1.13513
$295$	−1929.80	−0.380872
$296$	−8689.28	−1.70626
$297$	6560.08	1.28166
$298$	−3222.50	−0.626424
$299$	−2074.83	−0.401305
$300$	−2395.92	−0.461095
$301$	−399.262	−0.0764554
$302$	−842.708	−0.160571
$303$	1291.48	0.244864
$304$	−731.988	−0.138100
$305$	8590.02	1.61267
$306$	0	0
$307$	9924.22	1.84497	0.922484	−	0.386034i	$-0.126155\pi$
$307$	9924.22	1.84497	0.922484	+	0.386034i	$0.126155\pi$
$308$	−768.760	−0.142221
$309$	6413.58	1.18076
$310$	−5108.32	−0.935914
$311$	1458.67	0.265959	0.132980	−	0.991119i	$-0.457546\pi$
$311$	1458.67	0.265959	0.132980	+	0.991119i	$0.457546\pi$
$312$	10126.9	1.83757
$313$	797.861	0.144082	0.0720412	−	0.997402i	$-0.477049\pi$
$313$	797.861	0.144082	0.0720412	+	0.997402i	$0.477049\pi$
$314$	2262.26	0.406582
$315$	2826.90	0.505644
$316$	116.493	0.0207381
$317$	3852.53	0.682586	0.341293	−	0.939957i	$-0.389135\pi$
$317$	3852.53	0.682586	0.341293	+	0.939957i	$0.389135\pi$
$318$	−99.9974	−0.0176339
$319$	−5836.34	−1.02436
$320$	7122.50	1.24425
$321$	−3315.28	−0.576451
$322$	403.430	0.0698208
$323$	0	0
$324$	87.3338	0.0149749
$325$	−4028.26	−0.687531
$326$	−1790.46	−0.304186
$327$	7359.32	1.24456
$328$	1545.17	0.260115
$329$	−1282.12	−0.214850
$330$	12263.5	2.04570
$331$	−8470.40	−1.40657	−0.703286	−	0.710907i	$-0.748285\pi$
$331$	−8470.40	−1.40657	−0.703286	+	0.710907i	$0.748285\pi$
$332$	−997.800	−0.164944
$333$	15418.7	2.53736
$334$	5535.05	0.906780
$335$	−13670.8	−2.22961
$336$	−897.038	−0.145647
$337$	1922.89	0.310821	0.155411	−	0.987850i	$-0.450330\pi$
$337$	1922.89	0.310821	0.155411	+	0.987850i	$0.450330\pi$
$338$	544.256	0.0875848
$339$	−17151.9	−2.74797
$340$	0	0
$341$	−8075.71	−1.28248
$342$	2851.16	0.450798
$343$	−3025.92	−0.476340
$344$	2140.79	0.335534
$345$	5043.19	0.787004
$346$	−6533.15	−1.01510
$347$	2564.08	0.396677	0.198339	−	0.980134i	$-0.436445\pi$
$347$	2564.08	0.396677	0.198339	+	0.980134i	$0.436445\pi$
$348$	3575.77	0.550809
$349$	−283.156	−0.0434298	−0.0217149	−	0.999764i	$-0.506913\pi$
$349$	−283.156	−0.0434298	−0.0217149	+	0.999764i	$0.506913\pi$
$350$	783.257	0.119620
$351$	−6757.46	−1.02760
$352$	6985.79	1.05779
$353$	−10695.1	−1.61259	−0.806295	−	0.591514i	$-0.798530\pi$
$353$	−10695.1	−1.61259	−0.806295	+	0.591514i	$0.798530\pi$
$354$	−2385.22	−0.358116
$355$	−4772.54	−0.713521
$356$	−672.877	−0.100175
$357$	0	0
$358$	1946.15	0.287311
$359$	8702.38	1.27937	0.639685	−	0.768637i	$-0.279065\pi$
$359$	8702.38	1.27937	0.639685	+	0.768637i	$0.279065\pi$
$360$	−15157.5	−2.21908
$361$	−5891.09	−0.858885
$362$	4571.69	0.663764
$363$	8229.65	1.18993
$364$	791.890	0.114028
$365$	381.055	0.0546448
$366$	10617.2	1.51632
$367$	−11921.7	−1.69566	−0.847831	−	0.530266i	$-0.822092\pi$
$367$	−11921.7	−1.69566	−0.847831	+	0.530266i	$0.822092\pi$
$368$	−985.445	−0.139592
$369$	−2741.84	−0.386814
$370$	10839.2	1.52298
$371$	−25.6174	−0.00358488
$372$	4947.77	0.689597
$373$	−11054.6	−1.53454	−0.767270	−	0.641324i	$-0.778385\pi$
$373$	−11054.6	−1.53454	−0.767270	+	0.641324i	$0.778385\pi$
$374$	0	0
$375$	−5259.85	−0.724313
$376$	6874.56	0.942894
$377$	6011.95	0.821302
$378$	1313.92	0.178786
$379$	11548.5	1.56519	0.782596	−	0.622529i	$-0.213895\pi$
$379$	11548.5	1.56519	0.782596	+	0.622529i	$0.213895\pi$
$380$	−1570.66	−0.212035
$381$	17655.4	2.37405
$382$	−2858.38	−0.382847
$383$	10238.7	1.36599	0.682995	−	0.730423i	$-0.260677\pi$
$383$	10238.7	1.36599	0.682995	+	0.730423i	$0.260677\pi$
$384$	−938.349	−0.124700
$385$	3141.67	0.415881
$386$	7431.72	0.979960
$387$	−3798.73	−0.498968
$388$	−1009.16	−0.132042
$389$	4378.48	0.570688	0.285344	−	0.958425i	$-0.407892\pi$
$389$	4378.48	0.570688	0.285344	+	0.958425i	$0.407892\pi$
$390$	−12632.5	−1.64018
$391$	0	0
$392$	7860.09	1.01274
$393$	−11656.9	−1.49621
$394$	7515.35	0.960959
$395$	−476.068	−0.0606420
$396$	−7314.28	−0.928173
$397$	10055.9	1.27126	0.635629	−	0.771995i	$-0.280741\pi$
$397$	10055.9	1.27126	0.635629	+	0.771995i	$0.280741\pi$
$398$	−6505.80	−0.819363
$399$	1186.15	0.148827
$400$	−1913.23	−0.239154
$401$	−8216.40	−1.02321	−0.511605	−	0.859221i	$-0.670949\pi$
$401$	−8216.40	−1.02321	−0.511605	+	0.859221i	$0.670949\pi$
$402$	−16897.1	−2.09640
$403$	8318.69	1.02825
$404$	−541.495	−0.0666841
$405$	−356.904	−0.0437894
$406$	−1168.97	−0.142894
$407$	17135.6	2.08692
$408$	0	0
$409$	−5402.57	−0.653154	−0.326577	−	0.945171i	$-0.605895\pi$
$409$	−5402.57	−0.653154	−0.326577	+	0.945171i	$0.605895\pi$
$410$	−1927.48	−0.232174
$411$	−19360.9	−2.32361
$412$	−2689.09	−0.321558
$413$	−611.048	−0.0728031
$414$	3838.39	0.455668
$415$	4077.68	0.482326
$416$	−7195.98	−0.848105
$417$	−20765.1	−2.43854
$418$	3168.63	0.370772
$419$	6305.19	0.735152	0.367576	−	0.929993i	$-0.380188\pi$
$419$	6305.19	0.735152	0.367576	+	0.929993i	$0.380188\pi$
$420$	−1924.82	−0.223622
$421$	6492.45	0.751598	0.375799	−	0.926701i	$-0.377368\pi$
$421$	6492.45	0.751598	0.375799	+	0.926701i	$0.377368\pi$
$422$	12753.6	1.47117
$423$	−12198.6	−1.40216
$424$	137.357	0.0157327
$425$	0	0
$426$	−5898.84	−0.670892
$427$	2719.93	0.308259
$428$	1390.03	0.156986
$429$	−19970.6	−2.24753
$430$	−2670.46	−0.299491
$431$	−13477.5	−1.50624	−0.753118	−	0.657886i	$-0.771451\pi$
$431$	−13477.5	−1.50624	−0.753118	+	0.657886i	$0.771451\pi$
$432$	−3209.48	−0.357445
$433$	−13237.8	−1.46921	−0.734605	−	0.678495i	$-0.762633\pi$
$433$	−13237.8	−1.46921	−0.734605	+	0.678495i	$0.762633\pi$
$434$	−1617.49	−0.178899
$435$	−14613.0	−1.61067
$436$	−3085.63	−0.338933
$437$	1303.05	0.142640
$438$	470.983	0.0513800
$439$	10249.1	1.11426	0.557130	−	0.830425i	$-0.311902\pi$
$439$	10249.1	1.11426	0.557130	+	0.830425i	$0.311902\pi$
$440$	−16845.2	−1.82515
$441$	−13947.4	−1.50603
$442$	0	0
$443$	−8163.30	−0.875508	−0.437754	−	0.899095i	$-0.644226\pi$
$443$	−8163.30	−0.875508	−0.437754	+	0.899095i	$0.644226\pi$
$444$	−10498.5	−1.12215
$445$	2749.82	0.292931
$446$	−7584.09	−0.805195
$447$	−12755.4	−1.34969
$448$	2255.26	0.237837
$449$	−4382.67	−0.460648	−0.230324	−	0.973114i	$-0.573979\pi$
$449$	−4382.67	−0.460648	−0.230324	+	0.973114i	$0.573979\pi$
$450$	7452.21	0.780668
$451$	−3047.13	−0.318146
$452$	7191.45	0.748357
$453$	−3335.63	−0.345964
$454$	8988.90	0.929229
$455$	−3236.19	−0.333440
$456$	−6360.01	−0.653146
$457$	−10463.4	−1.07102	−0.535509	−	0.844530i	$-0.679880\pi$
$457$	−10463.4	−1.07102	−0.535509	+	0.844530i	$0.679880\pi$
$458$	10899.9	1.11205
$459$	0	0
$460$	−2114.52	−0.214326
$461$	−7540.64	−0.761828	−0.380914	−	0.924610i	$-0.624391\pi$
$461$	−7540.64	−0.761828	−0.380914	+	0.924610i	$0.624391\pi$
$462$	3883.09	0.391034
$463$	12962.0	1.30107	0.650536	−	0.759475i	$-0.274544\pi$
$463$	12962.0	1.30107	0.650536	+	0.759475i	$0.274544\pi$
$464$	2855.39	0.285686
$465$	−20219.9	−2.01651
$466$	6030.21	0.599451
$467$	12536.8	1.24226	0.621130	−	0.783707i	$-0.286674\pi$
$467$	12536.8	1.24226	0.621130	+	0.783707i	$0.286674\pi$
$468$	7534.36	0.744179
$469$	−4328.71	−0.426186
$470$	−8575.45	−0.841608
$471$	8954.53	0.876015
$472$	3276.36	0.319506
$473$	−4221.71	−0.410390
$474$	−588.419	−0.0570189
$475$	2529.87	0.244376
$476$	0	0
$477$	−243.734	−0.0233958
$478$	8438.46	0.807460
$479$	−1048.55	−0.100020	−0.0500099	−	0.998749i	$-0.515925\pi$
$479$	−1048.55	−0.100020	−0.0500099	+	0.998749i	$0.515925\pi$
$480$	17491.0	1.66323
$481$	−17651.1	−1.67323
$482$	3800.50	0.359145
$483$	1596.87	0.150435
$484$	−3450.54	−0.324055
$485$	4124.10	0.386115
$486$	−8241.28	−0.769202
$487$	−903.684	−0.0840859	−0.0420429	−	0.999116i	$-0.513387\pi$
$487$	−903.684	−0.0840859	−0.0420429	+	0.999116i	$0.513387\pi$
$488$	−14583.9	−1.35283
$489$	−7087.06	−0.655394
$490$	−9804.82	−0.903952
$491$	14922.5	1.37158	0.685789	−	0.727800i	$-0.259457\pi$
$491$	14922.5	1.37158	0.685789	+	0.727800i	$0.259457\pi$
$492$	1866.90	0.171069
$493$	0	0
$494$	−3263.96	−0.297273
$495$	29891.1	2.71415
$496$	3950.99	0.357671
$497$	−1511.17	−0.136389
$498$	5040.00	0.453509
$499$	2628.41	0.235799	0.117900	−	0.993026i	$-0.462384\pi$
$499$	2628.41	0.235799	0.117900	+	0.993026i	$0.462384\pi$
$500$	2205.35	0.197253
$501$	21909.0	1.95373
$502$	9866.45	0.877214
$503$	6500.03	0.576187	0.288093	−	0.957602i	$-0.406979\pi$
$503$	6500.03	0.576187	0.288093	+	0.957602i	$0.406979\pi$
$504$	−4799.44	−0.424175
$505$	2212.91	0.194996
$506$	4265.79	0.374777
$507$	2154.29	0.188709
$508$	−7402.58	−0.646528
$509$	−1931.57	−0.168203	−0.0841013	−	0.996457i	$-0.526802\pi$
$509$	−1931.57	−0.168203	−0.0841013	+	0.996457i	$0.526802\pi$
$510$	0	0
$511$	120.657	0.0104453
$512$	−8007.88	−0.691214
$513$	4243.89	0.365249
$514$	13205.6	1.13322
$515$	10989.4	0.940296
$516$	2586.53	0.220670
$517$	−13556.9	−1.15325
$518$	3432.10	0.291115
$519$	−25859.7	−2.18712
$520$	17352.1	1.46334
$521$	−5287.08	−0.444589	−0.222295	−	0.974980i	$-0.571355\pi$
$521$	−5287.08	−0.444589	−0.222295	+	0.974980i	$0.571355\pi$
$522$	−11122.0	−0.932561
$523$	−8406.61	−0.702859	−0.351430	−	0.936214i	$-0.614304\pi$
$523$	−8406.61	−0.702859	−0.351430	+	0.936214i	$0.614304\pi$
$524$	4887.51	0.407466
$525$	3100.31	0.257731
$526$	315.635	0.0261642
$527$	0	0
$528$	−9485.09	−0.781791
$529$	−10412.8	−0.855819
$530$	−171.342	−0.0140427
$531$	−5813.75	−0.475132
$532$	−497.332	−0.0405302
$533$	3138.81	0.255079
$534$	3398.77	0.275429
$535$	−5680.61	−0.459054
$536$	23210.0	1.87037
$537$	7703.31	0.619036
$538$	6586.54	0.527818
$539$	−15500.4	−1.23868
$540$	−6886.72	−0.548810
$541$	11319.4	0.899553	0.449776	−	0.893141i	$-0.351504\pi$
$541$	11319.4	0.899553	0.449776	+	0.893141i	$0.351504\pi$
$542$	10007.6	0.793110
$543$	18095.8	1.43014
$544$	0	0
$545$	12609.9	0.991101
$546$	−3999.93	−0.313518
$547$	−1201.61	−0.0939251	−0.0469626	−	0.998897i	$-0.514954\pi$
$547$	−1201.61	−0.0939251	−0.0469626	+	0.998897i	$0.514954\pi$
$548$	8117.66	0.632791
$549$	25878.5	2.01178
$550$	8281.99	0.642082
$551$	−3775.69	−0.291923
$552$	−8562.21	−0.660202
$553$	−150.742	−0.0115916
$554$	−1906.36	−0.146197
$555$	42903.9	3.28138
$556$	8706.41	0.664090
$557$	5277.38	0.401454	0.200727	−	0.979647i	$-0.435670\pi$
$557$	5277.38	0.401454	0.200727	+	0.979647i	$0.435670\pi$
$558$	−15389.4	−1.16754
$559$	4348.73	0.329037
$560$	−1537.04	−0.115985
$561$	0	0
$562$	19411.5	1.45698
$563$	2341.00	0.175243	0.0876213	−	0.996154i	$-0.472073\pi$
$563$	2341.00	0.175243	0.0876213	+	0.996154i	$0.472073\pi$
$564$	8305.92	0.620111
$565$	−29389.1	−2.18833
$566$	−7499.90	−0.556969
$567$	−113.010	−0.00837030
$568$	8102.70	0.598559
$569$	−3732.25	−0.274981	−0.137490	−	0.990503i	$-0.543904\pi$
$569$	−3732.25	−0.274981	−0.137490	+	0.990503i	$0.543904\pi$
$570$	7933.58	0.582985
$571$	−4505.21	−0.330187	−0.165094	−	0.986278i	$-0.552793\pi$
$571$	−4505.21	−0.330187	−0.165094	+	0.986278i	$0.552793\pi$
$572$	8373.28	0.612071
$573$	−11314.1	−0.824876
$574$	−610.313	−0.0443797
$575$	3405.86	0.247016
$576$	21457.4	1.55218
$577$	−15292.7	−1.10337	−0.551685	−	0.834053i	$-0.686015\pi$
$577$	−15292.7	−1.10337	−0.551685	+	0.834053i	$0.686015\pi$
$578$	0	0
$579$	29416.4	2.11141
$580$	6126.95	0.438634
$581$	1291.15	0.0921961
$582$	5097.37	0.363046
$583$	−270.873	−0.0192426
$584$	−646.946	−0.0458405
$585$	−30790.4	−2.17612
$586$	−2686.03	−0.189350
$587$	−11208.5	−0.788116	−0.394058	−	0.919086i	$-0.628929\pi$
$587$	−11208.5	−0.788116	−0.394058	+	0.919086i	$0.628929\pi$
$588$	9496.66	0.666047
$589$	−5224.40	−0.365480
$590$	−4086.99	−0.285184
$591$	29747.5	2.07047
$592$	−8383.46	−0.582024
$593$	10220.6	0.707774	0.353887	−	0.935288i	$-0.384860\pi$
$593$	10220.6	0.707774	0.353887	+	0.935288i	$0.384860\pi$
$594$	13893.2	0.959669
$595$	0	0
$596$	5348.09	0.367561
$597$	−25751.4	−1.76539
$598$	−4394.14	−0.300484
$599$	−9068.76	−0.618597	−0.309298	−	0.950965i	$-0.600094\pi$
$599$	−9068.76	−0.618597	−0.309298	+	0.950965i	$0.600094\pi$
$600$	−16623.5	−1.13108
$601$	−14293.5	−0.970122	−0.485061	−	0.874480i	$-0.661203\pi$
$601$	−14293.5	−0.970122	−0.485061	+	0.874480i	$0.661203\pi$
$602$	−845.570	−0.0572473
$603$	−41185.1	−2.78140
$604$	1398.57	0.0942167
$605$	14101.2	0.947595
$606$	2735.15	0.183346
$607$	13055.6	0.873000	0.436500	−	0.899704i	$-0.356218\pi$
$607$	13055.6	0.873000	0.436500	+	0.899704i	$0.356218\pi$
$608$	4519.30	0.301450
$609$	−4627.03	−0.307877
$610$	18192.2	1.20751
$611$	13964.8	0.924638
$612$	0	0
$613$	−15590.7	−1.02725	−0.513623	−	0.858016i	$-0.671697\pi$
$613$	−15590.7	−1.02725	−0.513623	+	0.858016i	$0.671697\pi$
$614$	21017.9	1.38145
$615$	−7629.39	−0.500238
$616$	−5333.84	−0.348874
$617$	25884.6	1.68894	0.844469	−	0.535605i	$-0.179916\pi$
$617$	25884.6	1.68894	0.844469	+	0.535605i	$0.179916\pi$
$618$	13582.9	0.884117
$619$	−448.382	−0.0291147	−0.0145574	−	0.999894i	$-0.504634\pi$
$619$	−448.382	−0.0291147	−0.0145574	+	0.999894i	$0.504634\pi$
$620$	8477.82	0.549157
$621$	5713.38	0.369195
$622$	3089.21	0.199142
$623$	870.700	0.0559933
$624$	9770.48	0.626814
$625$	−19177.2	−1.22734
$626$	1689.74	0.107884
$627$	12542.1	0.798859
$628$	−3754.47	−0.238566
$629$	0	0
$630$	5986.91	0.378610
$631$	−6811.18	−0.429713	−0.214856	−	0.976646i	$-0.568928\pi$
$631$	−6811.18	−0.429713	−0.214856	+	0.976646i	$0.568928\pi$
$632$	808.257	0.0508714
$633$	50481.5	3.16976
$634$	8159.03	0.511098
$635$	30251.9	1.89057
$636$	165.957	0.0103469
$637$	15966.7	0.993132
$638$	−12360.4	−0.767011
$639$	−14377.9	−0.890108
$640$	−1607.83	−0.0993045
$641$	−14093.7	−0.868434	−0.434217	−	0.900808i	$-0.642975\pi$
$641$	−14093.7	−0.868434	−0.434217	+	0.900808i	$0.642975\pi$
$642$	−7021.21	−0.431628
$643$	−8650.68	−0.530559	−0.265280	−	0.964172i	$-0.585464\pi$
$643$	−8650.68	−0.530559	−0.265280	+	0.964172i	$0.585464\pi$
$644$	−669.537	−0.0409681
$645$	−10570.3	−0.645279
$646$	0	0
$647$	−10310.7	−0.626515	−0.313258	−	0.949668i	$-0.601420\pi$
$647$	−10310.7	−0.626515	−0.313258	+	0.949668i	$0.601420\pi$
$648$	605.943	0.0367341
$649$	−6461.09	−0.390786
$650$	−8531.18	−0.514801
$651$	−6402.40	−0.385453
$652$	2971.47	0.178484
$653$	−8590.34	−0.514803	−0.257401	−	0.966305i	$-0.582866\pi$
$653$	−8590.34	−0.514803	−0.257401	+	0.966305i	$0.582866\pi$
$654$	15585.8	0.931887
$655$	−19973.6	−1.19150
$656$	1490.79	0.0887280
$657$	1147.98	0.0681686
$658$	−2715.32	−0.160872
$659$	4635.27	0.273998	0.136999	−	0.990571i	$-0.456254\pi$
$659$	4635.27	0.273998	0.136999	+	0.990571i	$0.456254\pi$
$660$	−20352.6	−1.20034
$661$	27861.5	1.63946	0.819732	−	0.572747i	$-0.194122\pi$
$661$	27861.5	1.63946	0.819732	+	0.572747i	$0.194122\pi$
$662$	−17938.9	−1.05320
$663$	0	0
$664$	−6922.98	−0.404614
$665$	2032.43	0.118518
$666$	32654.3	1.89989
$667$	−5083.05	−0.295077
$668$	−9186.02	−0.532063
$669$	−30019.6	−1.73486
$670$	−28952.6	−1.66946
$671$	28760.0	1.65464
$672$	5538.31	0.317924
$673$	−8480.12	−0.485713	−0.242856	−	0.970062i	$-0.578084\pi$
$673$	−8480.12	−0.485713	−0.242856	+	0.970062i	$0.578084\pi$
$674$	4072.37	0.232733
$675$	11092.5	0.632518
$676$	−903.253	−0.0513913
$677$	−11284.7	−0.640627	−0.320314	−	0.947312i	$-0.603788\pi$
$677$	−11284.7	−0.640627	−0.320314	+	0.947312i	$0.603788\pi$
$678$	−36324.8	−2.05759
$679$	1305.85	0.0738054
$680$	0	0
$681$	35580.1	2.00210
$682$	−17103.0	−0.960276
$683$	−2315.69	−0.129733	−0.0648665	−	0.997894i	$-0.520662\pi$
$683$	−2315.69	−0.129733	−0.0648665	+	0.997894i	$0.520662\pi$
$684$	−4731.81	−0.264511
$685$	−33174.2	−1.85040
$686$	−6408.41	−0.356668
$687$	43144.4	2.39601
$688$	2065.45	0.114454
$689$	279.023	0.0154281
$690$	10680.6	0.589283
$691$	−8175.26	−0.450074	−0.225037	−	0.974350i	$-0.572250\pi$
$691$	−8175.26	−0.450074	−0.225037	+	0.974350i	$0.572250\pi$
$692$	10842.5	0.595620
$693$	9464.66	0.518806
$694$	5430.30	0.297019
$695$	−35580.2	−1.94192
$696$	24809.6	1.35116
$697$	0	0
$698$	−599.677	−0.0325188
$699$	23868.9	1.29157
$700$	−1299.90	−0.0701880
$701$	22583.3	1.21677	0.608387	−	0.793640i	$-0.291817\pi$
$701$	22583.3	1.21677	0.608387	+	0.793640i	$0.291817\pi$
$702$	−14311.2	−0.769431
$703$	11085.5	0.594731
$704$	23846.6	1.27664
$705$	−33943.6	−1.81332
$706$	−22650.5	−1.20745
$707$	700.692	0.0372733
$708$	3958.54	0.210129
$709$	−23125.7	−1.22497	−0.612484	−	0.790483i	$-0.709830\pi$
$709$	−23125.7	−1.22497	−0.612484	+	0.790483i	$0.709830\pi$
$710$	−10107.4	−0.534262
$711$	−1434.21	−0.0756501
$712$	−4668.58	−0.245734
$713$	−7033.38	−0.369428
$714$	0	0
$715$	−34218.8	−1.78981
$716$	−3229.85	−0.168583
$717$	33401.3	1.73974
$718$	18430.2	0.957951
$719$	−34843.0	−1.80727	−0.903634	−	0.428305i	$-0.859111\pi$
$719$	−34843.0	−1.80727	−0.903634	+	0.428305i	$0.859111\pi$
$720$	−14624.0	−0.756951
$721$	3479.68	0.179736
$722$	−12476.4	−0.643105
$723$	15043.2	0.773809
$724$	−7587.22	−0.389471
$725$	−9868.70	−0.505537
$726$	17429.0	0.890981
$727$	−11782.3	−0.601077	−0.300538	−	0.953770i	$-0.597166\pi$
$727$	−11782.3	−0.601077	−0.300538	+	0.953770i	$0.597166\pi$
$728$	5494.33	0.279716
$729$	−31950.0	−1.62323
$730$	807.012	0.0409162
$731$	0	0
$732$	−17620.5	−0.889715
$733$	−20099.0	−1.01279	−0.506394	−	0.862302i	$-0.669022\pi$
$733$	−20099.0	−1.01279	−0.506394	+	0.862302i	$0.669022\pi$
$734$	−25248.2	−1.26966
$735$	−38809.7	−1.94764
$736$	6084.14	0.304707
$737$	−45770.9	−2.28764
$738$	−5806.75	−0.289634
$739$	12538.4	0.624132	0.312066	−	0.950060i	$-0.398979\pi$
$739$	12538.4	0.624132	0.312066	+	0.950060i	$0.398979\pi$
$740$	−17988.8	−0.893623
$741$	−12919.5	−0.640500
$742$	−54.2534	−0.00268424
$743$	3294.68	0.162679	0.0813393	−	0.996686i	$-0.474080\pi$
$743$	3294.68	0.162679	0.0813393	+	0.996686i	$0.474080\pi$
$744$	34328.8	1.69161
$745$	−21855.9	−1.07482
$746$	−23411.7	−1.14901
$747$	12284.5	0.601696
$748$	0	0
$749$	−1798.70	−0.0877477
$750$	−11139.5	−0.542342
$751$	7252.15	0.352376	0.176188	−	0.984357i	$-0.443623\pi$
$751$	7252.15	0.352376	0.176188	+	0.984357i	$0.443623\pi$
$752$	6632.61	0.321631
$753$	39053.7	1.89003
$754$	12732.3	0.614965
$755$	−5715.48	−0.275507
$756$	−2180.60	−0.104904
$757$	26725.2	1.28315	0.641574	−	0.767061i	$-0.278282\pi$
$757$	26725.2	1.28315	0.641574	+	0.767061i	$0.278282\pi$
$758$	24457.9	1.17197
$759$	16885.0	0.807490
$760$	−10897.6	−0.520130
$761$	−1638.39	−0.0780443	−0.0390222	−	0.999238i	$-0.512424\pi$
$761$	−1638.39	−0.0780443	−0.0390222	+	0.999238i	$0.512424\pi$
$762$	37391.2	1.77761
$763$	3992.79	0.189448
$764$	4743.79	0.224639
$765$	0	0
$766$	21683.9	1.02281
$767$	6655.50	0.313319
$768$	−35241.6	−1.65582
$769$	−9542.58	−0.447483	−0.223741	−	0.974649i	$-0.571827\pi$
$769$	−9542.58	−0.447483	−0.223741	+	0.974649i	$0.571827\pi$
$770$	6653.53	0.311398
$771$	52270.8	2.44162
$772$	−12333.8	−0.575002
$773$	10640.1	0.495080	0.247540	−	0.968878i	$-0.420378\pi$
$773$	10640.1	0.495080	0.247540	+	0.968878i	$0.420378\pi$
$774$	−8045.09	−0.373611
$775$	−13655.3	−0.632918
$776$	−7001.80	−0.323904
$777$	13585.0	0.627233
$778$	9272.90	0.427313
$779$	−1971.27	−0.0906652
$780$	20965.0	0.962393
$781$	−15978.8	−0.732095
$782$	0	0
$783$	−16554.9	−0.755586
$784$	7583.45	0.345456
$785$	15343.3	0.697611
$786$	−24687.4	−1.12032
$787$	−4358.23	−0.197400	−0.0987002	−	0.995117i	$-0.531468\pi$
$787$	−4358.23	−0.197400	−0.0987002	+	0.995117i	$0.531468\pi$
$788$	−12472.5	−0.563853
$789$	1249.36	0.0563730
$790$	−1008.23	−0.0454068
$791$	−9305.71	−0.418297
$792$	−50748.3	−2.27685
$793$	−29625.3	−1.32664
$794$	21296.7	0.951876
$795$	−678.210	−0.0302561
$796$	10797.1	0.480770
$797$	19901.9	0.884517	0.442259	−	0.896888i	$-0.354177\pi$
$797$	19901.9	0.884517	0.442259	+	0.896888i	$0.354177\pi$
$798$	2512.08	0.111437
$799$	0	0
$800$	11812.3	0.522035
$801$	8284.18	0.365427
$802$	−17401.0	−0.766147
$803$	1275.80	0.0560672
$804$	28042.6	1.23008
$805$	2736.18	0.119798
$806$	17617.6	0.769918
$807$	26071.0	1.13723
$808$	−3757.02	−0.163579
$809$	−28136.7	−1.22279	−0.611394	−	0.791326i	$-0.709391\pi$
$809$	−28136.7	−1.22279	−0.611394	+	0.791326i	$0.709391\pi$
$810$	−755.864	−0.0327881
$811$	−213.599	−0.00924845	−0.00462422	−	0.999989i	$-0.501472\pi$
$811$	−213.599	−0.00924845	−0.00462422	+	0.999989i	$0.501472\pi$
$812$	1940.03	0.0838444
$813$	39612.6	1.70882
$814$	36290.3	1.56262
$815$	−12143.4	−0.521921
$816$	0	0
$817$	−2731.14	−0.116953
$818$	−11441.8	−0.489061
$819$	−9749.43	−0.415962
$820$	3198.86	0.136230
$821$	10422.0	0.443033	0.221517	−	0.975157i	$-0.428899\pi$
$821$	10422.0	0.443033	0.221517	+	0.975157i	$0.428899\pi$
$822$	−41003.2	−1.73984
$823$	25083.0	1.06238	0.531189	−	0.847253i	$-0.321745\pi$
$823$	25083.0	1.06238	0.531189	+	0.847253i	$0.321745\pi$
$824$	−18657.6	−0.788796
$825$	32782.0	1.38342
$826$	−1294.10	−0.0545126
$827$	−27880.2	−1.17230	−0.586148	−	0.810204i	$-0.699356\pi$
$827$	−27880.2	−1.17230	−0.586148	+	0.810204i	$0.699356\pi$
$828$	−6370.24	−0.267368
$829$	−28128.7	−1.17847	−0.589235	−	0.807962i	$-0.700571\pi$
$829$	−28128.7	−1.17847	−0.589235	+	0.807962i	$0.700571\pi$
$830$	8635.85	0.361150
$831$	−7545.80	−0.314995
$832$	−24564.1	−1.02357
$833$	0	0
$834$	−43977.0	−1.82590
$835$	37540.2	1.55585
$836$	−5258.68	−0.217554
$837$	−22906.9	−0.945971
$838$	13353.4	0.550458
$839$	39229.0	1.61422	0.807112	−	0.590398i	$-0.201029\pi$
$839$	39229.0	1.61422	0.807112	+	0.590398i	$0.201029\pi$
$840$	−13354.8	−0.548555
$841$	−9660.52	−0.396101
$842$	13749.9	0.562772
$843$	76835.0	3.13919
$844$	−21165.9	−0.863225
$845$	3691.30	0.150278
$846$	−25834.6	−1.04989
$847$	4464.98	0.181132
$848$	132.523	0.00536657
$849$	−29686.3	−1.20004
$850$	0	0
$851$	14923.9	0.601156
$852$	9789.78	0.393653
$853$	−38686.5	−1.55287	−0.776436	−	0.630196i	$-0.782974\pi$
$853$	−38686.5	−1.55287	−0.776436	+	0.630196i	$0.782974\pi$
$854$	5760.36	0.230814
$855$	19337.3	0.773477
$856$	9644.39	0.385092
$857$	9417.90	0.375390	0.187695	−	0.982227i	$-0.439898\pi$
$857$	9417.90	0.375390	0.187695	+	0.982227i	$0.439898\pi$
$858$	−42294.4	−1.68287
$859$	43890.4	1.74333	0.871666	−	0.490101i	$-0.163040\pi$
$859$	43890.4	1.74333	0.871666	+	0.490101i	$0.163040\pi$
$860$	4431.92	0.175729
$861$	−2415.76	−0.0956199
$862$	−28543.1	−1.12782
$863$	6822.88	0.269123	0.134562	−	0.990905i	$-0.457037\pi$
$863$	6822.88	0.269123	0.134562	+	0.990905i	$0.457037\pi$
$864$	19815.3	0.780244
$865$	−44309.6	−1.74170
$866$	−28035.5	−1.10010
$867$	0	0
$868$	2684.40	0.104971
$869$	−1593.91	−0.0622206
$870$	−30947.9	−1.20601
$871$	47148.1	1.83416
$872$	−21408.8	−0.831415
$873$	12424.4	0.481673
$874$	2759.65	0.106804
$875$	−2853.72	−0.110255
$876$	−781.648	−0.0301478
$877$	34548.2	1.33023	0.665114	−	0.746742i	$-0.268383\pi$
$877$	34548.2	1.33023	0.665114	+	0.746742i	$0.268383\pi$
$878$	21705.8	0.834322
$879$	−10631.9	−0.407970
$880$	−16252.4	−0.622576
$881$	−30611.4	−1.17063	−0.585315	−	0.810806i	$-0.699029\pi$
$881$	−30611.4	−1.17063	−0.585315	+	0.810806i	$0.699029\pi$
$882$	−29538.2	−1.12767
$883$	42598.5	1.62350	0.811751	−	0.584003i	$-0.198514\pi$
$883$	42598.5	1.62350	0.811751	+	0.584003i	$0.198514\pi$
$884$	0	0
$885$	−16177.2	−0.614454
$886$	−17288.5	−0.655552
$887$	−19049.1	−0.721091	−0.360545	−	0.932742i	$-0.617409\pi$
$887$	−19049.1	−0.721091	−0.360545	+	0.932742i	$0.617409\pi$
$888$	−72841.1	−2.75269
$889$	9578.91	0.361379
$890$	5823.67	0.219337
$891$	−1194.94	−0.0449293
$892$	12586.6	0.472457
$893$	−8770.30	−0.328653
$894$	−27013.8	−1.01060
$895$	13199.3	0.492967
$896$	−509.099	−0.0189819
$897$	−17393.0	−0.647419
$898$	−9281.77	−0.344918
$899$	20379.7	0.756064
$900$	−12367.8	−0.458065
$901$	0	0
$902$	−6453.32	−0.238217
$903$	−3346.96	−0.123344
$904$	49896.1	1.83575
$905$	31006.4	1.13888
$906$	−7064.31	−0.259047
$907$	−8388.99	−0.307113	−0.153557	−	0.988140i	$-0.549073\pi$
$907$	−8388.99	−0.307113	−0.153557	+	0.988140i	$0.549073\pi$
$908$	−14918.1	−0.545235
$909$	6666.66	0.243255
$910$	−6853.72	−0.249669
$911$	−10467.7	−0.380694	−0.190347	−	0.981717i	$-0.560961\pi$
$911$	−10467.7	−0.380694	−0.190347	+	0.981717i	$0.560961\pi$
$912$	−6136.16	−0.222795
$913$	13652.3	0.494882
$914$	−22159.6	−0.801943
$915$	72009.0	2.60169
$916$	−18089.6	−0.652509
$917$	−6324.42	−0.227754
$918$	0	0
$919$	−16180.4	−0.580787	−0.290394	−	0.956907i	$-0.593786\pi$
$919$	−16180.4	−0.580787	−0.290394	+	0.956907i	$0.593786\pi$
$920$	−14671.0	−0.525749
$921$	83193.5	2.97646
$922$	−15969.8	−0.570432
$923$	16459.6	0.586970
$924$	−6444.41	−0.229443
$925$	28974.6	1.02992
$926$	27451.4	0.974201
$927$	33107.0	1.17301
$928$	−17629.2	−0.623606
$929$	−14214.9	−0.502020	−0.251010	−	0.967985i	$-0.580763\pi$
$929$	−14214.9	−0.502020	−0.251010	+	0.967985i	$0.580763\pi$
$930$	−42822.4	−1.50989
$931$	−10027.6	−0.352998
$932$	−10007.8	−0.351734
$933$	12227.8	0.429068
$934$	26550.9	0.930164
$935$	0	0
$936$	52275.2	1.82550
$937$	49244.5	1.71691	0.858456	−	0.512887i	$-0.171424\pi$
$937$	49244.5	1.71691	0.858456	+	0.512887i	$0.171424\pi$
$938$	−9167.50	−0.319115
$939$	6688.37	0.232446
$940$	14231.9	0.493823
$941$	15645.1	0.541993	0.270997	−	0.962580i	$-0.412647\pi$
$941$	15645.1	0.541993	0.270997	+	0.962580i	$0.412647\pi$
$942$	18964.2	0.655932
$943$	−2653.84	−0.0916447
$944$	3161.05	0.108987
$945$	8911.40	0.306760
$946$	−8940.88	−0.307287
$947$	33064.5	1.13459	0.567293	−	0.823516i	$-0.307991\pi$
$947$	33064.5	1.13459	0.567293	+	0.823516i	$0.307991\pi$
$948$	976.546	0.0334565
$949$	−1314.19	−0.0449529
$950$	5357.85	0.182981
$951$	32295.3	1.10121
$952$	0	0
$953$	−47771.2	−1.62378	−0.811890	−	0.583811i	$-0.801561\pi$
$953$	−47771.2	−1.62378	−0.811890	+	0.583811i	$0.801561\pi$
$954$	−516.188	−0.0175180
$955$	−19386.3	−0.656886
$956$	−14004.5	−0.473786
$957$	−48925.3	−1.65259
$958$	−2220.65	−0.0748915
$959$	−10504.2	−0.353701
$960$	59707.0	2.00733
$961$	−1591.73	−0.0534300
$962$	−37382.2	−1.25286
$963$	−17113.5	−0.572664
$964$	−6307.34	−0.210732
$965$	50404.0	1.68141
$966$	3381.90	0.112641
$967$	−29494.2	−0.980837	−0.490418	−	0.871487i	$-0.663156\pi$
$967$	−29494.2	−0.980837	−0.490418	+	0.871487i	$0.663156\pi$
$968$	−23940.7	−0.794919
$969$	0	0
$970$	8734.16	0.289110
$971$	32058.3	1.05953	0.529763	−	0.848146i	$-0.322281\pi$
$971$	32058.3	1.05953	0.529763	+	0.848146i	$0.322281\pi$
$972$	13677.3	0.451338
$973$	−11266.1	−0.371196
$974$	−1913.85	−0.0629608
$975$	−33768.4	−1.10918
$976$	−14070.6	−0.461465
$977$	−47602.0	−1.55878	−0.779388	−	0.626542i	$-0.784470\pi$
$977$	−47602.0	−1.55878	−0.779388	+	0.626542i	$0.784470\pi$
$978$	−15009.2	−0.490738
$979$	9206.60	0.300556
$980$	16272.2	0.530404
$981$	37989.0	1.23639
$982$	31603.5	1.02699
$983$	−28860.0	−0.936410	−0.468205	−	0.883620i	$-0.655099\pi$
$983$	−28860.0	−0.936410	−0.468205	+	0.883620i	$0.655099\pi$
$984$	12953.0	0.419640
$985$	50971.2	1.64881
$986$	0	0
$987$	−10747.8	−0.346613
$988$	5416.91	0.174428
$989$	−3676.82	−0.118216
$990$	63304.3	2.03227
$991$	−4704.04	−0.150786	−0.0753930	−	0.997154i	$-0.524021\pi$
$991$	−4704.04	−0.150786	−0.0753930	+	0.997154i	$0.524021\pi$
$992$	−24393.4	−0.780737
$993$	−71006.3	−2.26920
$994$	−3200.41	−0.102123
$995$	−44124.1	−1.40586
$996$	−8364.43	−0.266102
$997$	32982.5	1.04771	0.523854	−	0.851808i	$-0.324494\pi$
$997$	32982.5	1.04771	0.523854	+	0.851808i	$0.324494\pi$
$998$	5566.54	0.176559
$999$	48605.3	1.53934

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.f.1.6		8
17.4	even	4		289.4.b.c.288.3		8
17.8	even	8		17.4.c.a.13.2	yes	8
17.13	even	4		289.4.b.c.288.4		8
17.15	even	8		17.4.c.a.4.3	✓	8
17.16	even	2	inner	289.4.a.f.1.5		8
51.8	odd	8		153.4.f.a.64.3		8
51.32	odd	8		153.4.f.a.55.2		8
68.15	odd	8		272.4.o.e.225.4		8
68.59	odd	8		272.4.o.e.81.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.c.a.4.3	✓	8	17.15	even	8
17.4.c.a.13.2	yes	8	17.8	even	8
153.4.f.a.55.2		8	51.32	odd	8
153.4.f.a.64.3		8	51.8	odd	8
272.4.o.e.81.4		8	68.59	odd	8
272.4.o.e.225.4		8	68.15	odd	8
289.4.a.f.1.5		8	17.16	even	2	inner
289.4.a.f.1.6		8	1.1	even	1	trivial
289.4.b.c.288.3		8	17.4	even	4
289.4.b.c.288.4		8	17.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.11783 q^{2} +8.38287 q^{3} -3.51478 q^{4} +14.3637 q^{5} +17.7535 q^{6} +4.54811 q^{7} -24.3864 q^{8} +43.2725 q^{9} +O(q^{10})\)	\(q+2.11783 q^{2} +8.38287 q^{3} -3.51478 q^{4} +14.3637 q^{5} +17.7535 q^{6} +4.54811 q^{7} -24.3864 q^{8} +43.2725 q^{9} +30.4200 q^{10} +48.0908 q^{11} -29.4639 q^{12} -49.5377 q^{13} +9.63214 q^{14} +120.409 q^{15} -23.5281 q^{16} +91.6440 q^{18} +31.1112 q^{19} -50.4854 q^{20} +38.1262 q^{21} +101.848 q^{22} +41.8837 q^{23} -204.428 q^{24} +81.3170 q^{25} -104.913 q^{26} +136.410 q^{27} -15.9856 q^{28} -121.361 q^{29} +255.007 q^{30} -167.926 q^{31} +145.263 q^{32} +403.139 q^{33} +65.3279 q^{35} -152.093 q^{36} +356.317 q^{37} +65.8884 q^{38} -415.268 q^{39} -350.280 q^{40} -63.3621 q^{41} +80.7450 q^{42} -87.7863 q^{43} -169.028 q^{44} +621.555 q^{45} +88.7028 q^{46} -281.901 q^{47} -197.233 q^{48} -322.315 q^{49} +172.216 q^{50} +174.114 q^{52} -5.63254 q^{53} +288.894 q^{54} +690.763 q^{55} -110.912 q^{56} +260.801 q^{57} -257.022 q^{58} -134.352 q^{59} -423.212 q^{60} +598.035 q^{61} -355.640 q^{62} +196.808 q^{63} +495.867 q^{64} -711.547 q^{65} +853.781 q^{66} -951.761 q^{67} +351.106 q^{69} +138.354 q^{70} -332.263 q^{71} -1055.26 q^{72} +26.5290 q^{73} +754.620 q^{74} +681.670 q^{75} -109.349 q^{76} +218.722 q^{77} -879.470 q^{78} -33.1438 q^{79} -337.952 q^{80} -24.8476 q^{81} -134.190 q^{82} +283.887 q^{83} -134.005 q^{84} -185.917 q^{86} -1017.35 q^{87} -1172.76 q^{88} +191.442 q^{89} +1316.35 q^{90} -225.303 q^{91} -147.212 q^{92} -1407.70 q^{93} -597.020 q^{94} +446.874 q^{95} +1217.72 q^{96} +287.119 q^{97} -682.609 q^{98} +2081.01 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 36 q^{4} + 96 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 36 * q^4 + 96 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 36 q^{4} + 96 q^{8} + 8 q^{9} + 88 q^{13} + 252 q^{15} + 420 q^{16} + 428 q^{18} - 52 q^{19} + 260 q^{21} - 140 q^{25} - 268 q^{26} + 120 q^{30} + 2336 q^{32} + 816 q^{33} + 1172 q^{35} - 264 q^{36} + 768 q^{38} - 136 q^{42} - 752 q^{43} + 368 q^{47} + 852 q^{49} + 468 q^{50} + 2564 q^{52} - 1156 q^{53} + 1996 q^{55} + 192 q^{59} - 3160 q^{60} + 3044 q^{64} + 1052 q^{66} + 764 q^{67} + 1812 q^{69} + 544 q^{70} - 1404 q^{72} + 896 q^{76} + 3084 q^{77} - 280 q^{81} + 496 q^{83} - 2952 q^{84} - 4244 q^{86} - 2860 q^{87} + 2156 q^{89} - 4012 q^{93} - 3392 q^{94} - 6728 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 36 * q^4 + 96 * q^8 + 8 * q^9 + 88 * q^13 + 252 * q^15 + 420 * q^16 + 428 * q^18 - 52 * q^19 + 260 * q^21 - 140 * q^25 - 268 * q^26 + 120 * q^30 + 2336 * q^32 + 816 * q^33 + 1172 * q^35 - 264 * q^36 + 768 * q^38 - 136 * q^42 - 752 * q^43 + 368 * q^47 + 852 * q^49 + 468 * q^50 + 2564 * q^52 - 1156 * q^53 + 1996 * q^55 + 192 * q^59 - 3160 * q^60 + 3044 * q^64 + 1052 * q^66 + 764 * q^67 + 1812 * q^69 + 544 * q^70 - 1404 * q^72 + 896 * q^76 + 3084 * q^77 - 280 * q^81 + 496 * q^83 - 2952 * q^84 - 4244 * q^86 - 2860 * q^87 + 2156 * q^89 - 4012 * q^93 - 3392 * q^94 - 6728 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more