Properties

Label 570.6.a.o.1.3
Level $570$
Weight $6$
Character 570.1
Self dual yes
Analytic conductor $91.419$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [570,6,Mod(1,570)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(570, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("570.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 570.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: \(91.4187772934\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 6052x^{3} - 41130x^{2} + 7064712x + 22607640 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{3}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(72.1421\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +46.3009 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +46.3009 q^{7} +64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} -592.198 q^{11} -144.000 q^{12} +661.340 q^{13} +185.204 q^{14} -225.000 q^{15} +256.000 q^{16} -1404.99 q^{17} +324.000 q^{18} +361.000 q^{19} +400.000 q^{20} -416.708 q^{21} -2368.79 q^{22} +4775.78 q^{23} -576.000 q^{24} +625.000 q^{25} +2645.36 q^{26} -729.000 q^{27} +740.814 q^{28} -178.254 q^{29} -900.000 q^{30} +5053.62 q^{31} +1024.00 q^{32} +5329.78 q^{33} -5619.98 q^{34} +1157.52 q^{35} +1296.00 q^{36} -3602.75 q^{37} +1444.00 q^{38} -5952.06 q^{39} +1600.00 q^{40} +15148.4 q^{41} -1666.83 q^{42} -22204.5 q^{43} -9475.16 q^{44} +2025.00 q^{45} +19103.1 q^{46} +12230.4 q^{47} -2304.00 q^{48} -14663.2 q^{49} +2500.00 q^{50} +12645.0 q^{51} +10581.4 q^{52} +9600.78 q^{53} -2916.00 q^{54} -14804.9 q^{55} +2963.26 q^{56} -3249.00 q^{57} -713.016 q^{58} +2191.79 q^{59} -3600.00 q^{60} +926.400 q^{61} +20214.5 q^{62} +3750.37 q^{63} +4096.00 q^{64} +16533.5 q^{65} +21319.1 q^{66} -17934.5 q^{67} -22479.9 q^{68} -42982.1 q^{69} +4630.09 q^{70} +43250.3 q^{71} +5184.00 q^{72} -13130.3 q^{73} -14411.0 q^{74} -5625.00 q^{75} +5776.00 q^{76} -27419.3 q^{77} -23808.2 q^{78} +109029. q^{79} +6400.00 q^{80} +6561.00 q^{81} +60593.5 q^{82} +5873.28 q^{83} -6667.33 q^{84} -35124.9 q^{85} -88818.1 q^{86} +1604.29 q^{87} -37900.6 q^{88} +66508.0 q^{89} +8100.00 q^{90} +30620.6 q^{91} +76412.6 q^{92} -45482.6 q^{93} +48921.4 q^{94} +9025.00 q^{95} -9216.00 q^{96} +145294. q^{97} -58652.9 q^{98} -47968.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + 20 q^{2} - 45 q^{3} + 80 q^{4} + 125 q^{5} - 180 q^{6} + 88 q^{7} + 320 q^{8} + 405 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q + 20 q^{2} - 45 q^{3} + 80 q^{4} + 125 q^{5} - 180 q^{6} + 88 q^{7} + 320 q^{8} + 405 q^{9} + 500 q^{10} - 112 q^{11} - 720 q^{12} - 44 q^{13} + 352 q^{14} - 1125 q^{15} + 1280 q^{16} + 2388 q^{17} + 1620 q^{18} + 1805 q^{19} + 2000 q^{20} - 792 q^{21} - 448 q^{22} + 3114 q^{23} - 2880 q^{24} + 3125 q^{25} - 176 q^{26} - 3645 q^{27} + 1408 q^{28} - 2966 q^{29} - 4500 q^{30} + 6930 q^{31} + 5120 q^{32} + 1008 q^{33} + 9552 q^{34} + 2200 q^{35} + 6480 q^{36} + 5608 q^{37} + 7220 q^{38} + 396 q^{39} + 8000 q^{40} + 20948 q^{41} - 3168 q^{42} + 3090 q^{43} - 1792 q^{44} + 10125 q^{45} + 12456 q^{46} + 16490 q^{47} - 11520 q^{48} + 2757 q^{49} + 12500 q^{50} - 21492 q^{51} - 704 q^{52} - 33060 q^{53} - 14580 q^{54} - 2800 q^{55} + 5632 q^{56} - 16245 q^{57} - 11864 q^{58} - 346 q^{59} - 18000 q^{60} + 57698 q^{61} + 27720 q^{62} + 7128 q^{63} + 20480 q^{64} - 1100 q^{65} + 4032 q^{66} + 12364 q^{67} + 38208 q^{68} - 28026 q^{69} + 8800 q^{70} + 9984 q^{71} + 25920 q^{72} + 28050 q^{73} + 22432 q^{74} - 28125 q^{75} + 28880 q^{76} + 235208 q^{77} + 1584 q^{78} + 36498 q^{79} + 32000 q^{80} + 32805 q^{81} + 83792 q^{82} + 89696 q^{83} - 12672 q^{84} + 59700 q^{85} + 12360 q^{86} + 26694 q^{87} - 7168 q^{88} + 114980 q^{89} + 40500 q^{90} + 267260 q^{91} + 49824 q^{92} - 62370 q^{93} + 65960 q^{94} + 45125 q^{95} - 46080 q^{96} + 317596 q^{97} + 11028 q^{98} - 9072 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 0.707107
\(3\) −9.00000 −0.577350
\(4\) 16.0000 0.500000
\(5\) 25.0000 0.447214
\(6\) −36.0000 −0.408248
\(7\) 46.3009 0.357145 0.178572 0.983927i \(-0.442852\pi\)
0.178572 + 0.983927i \(0.442852\pi\)
\(8\) 64.0000 0.353553
\(9\) 81.0000 0.333333
\(10\) 100.000 0.316228
\(11\) −592.198 −1.47566 −0.737828 0.674989i \(-0.764148\pi\)
−0.737828 + 0.674989i \(0.764148\pi\)
\(12\) −144.000 −0.288675
\(13\) 661.340 1.08534 0.542670 0.839946i \(-0.317413\pi\)
0.542670 + 0.839946i \(0.317413\pi\)
\(14\) 185.204 0.252539
\(15\) −225.000 −0.258199
\(16\) 256.000 0.250000
\(17\) −1404.99 −1.17910 −0.589552 0.807730i \(-0.700696\pi\)
−0.589552 + 0.807730i \(0.700696\pi\)
\(18\) 324.000 0.235702
\(19\) 361.000 0.229416
\(20\) 400.000 0.223607
\(21\) −416.708 −0.206198
\(22\) −2368.79 −1.04345
\(23\) 4775.78 1.88246 0.941229 0.337770i \(-0.109673\pi\)
0.941229 + 0.337770i \(0.109673\pi\)
\(24\) −576.000 −0.204124
\(25\) 625.000 0.200000
\(26\) 2645.36 0.767452
\(27\) −729.000 −0.192450
\(28\) 740.814 0.178572
\(29\) −178.254 −0.0393590 −0.0196795 0.999806i \(-0.506265\pi\)
−0.0196795 + 0.999806i \(0.506265\pi\)
\(30\) −900.000 −0.182574
\(31\) 5053.62 0.944492 0.472246 0.881467i \(-0.343443\pi\)
0.472246 + 0.881467i \(0.343443\pi\)
\(32\) 1024.00 0.176777
\(33\) 5329.78 0.851970
\(34\) −5619.98 −0.833753
\(35\) 1157.52 0.159720
\(36\) 1296.00 0.166667
\(37\) −3602.75 −0.432643 −0.216322 0.976322i \(-0.569406\pi\)
−0.216322 + 0.976322i \(0.569406\pi\)
\(38\) 1444.00 0.162221
\(39\) −5952.06 −0.626622
\(40\) 1600.00 0.158114
\(41\) 15148.4 1.40736 0.703682 0.710515i \(-0.251538\pi\)
0.703682 + 0.710515i \(0.251538\pi\)
\(42\) −1666.83 −0.145804
\(43\) −22204.5 −1.83135 −0.915673 0.401925i \(-0.868341\pi\)
−0.915673 + 0.401925i \(0.868341\pi\)
\(44\) −9475.16 −0.737828
\(45\) 2025.00 0.149071
\(46\) 19103.1 1.33110
\(47\) 12230.4 0.807596 0.403798 0.914848i \(-0.367690\pi\)
0.403798 + 0.914848i \(0.367690\pi\)
\(48\) −2304.00 −0.144338
\(49\) −14663.2 −0.872448
\(50\) 2500.00 0.141421
\(51\) 12645.0 0.680757
\(52\) 10581.4 0.542670
\(53\) 9600.78 0.469480 0.234740 0.972058i \(-0.424576\pi\)
0.234740 + 0.972058i \(0.424576\pi\)
\(54\) −2916.00 −0.136083
\(55\) −14804.9 −0.659933
\(56\) 2963.26 0.126270
\(57\) −3249.00 −0.132453
\(58\) −713.016 −0.0278310
\(59\) 2191.79 0.0819726 0.0409863 0.999160i \(-0.486950\pi\)
0.0409863 + 0.999160i \(0.486950\pi\)
\(60\) −3600.00 −0.129099
\(61\) 926.400 0.0318768 0.0159384 0.999873i \(-0.494926\pi\)
0.0159384 + 0.999873i \(0.494926\pi\)
\(62\) 20214.5 0.667856
\(63\) 3750.37 0.119048
\(64\) 4096.00 0.125000
\(65\) 16533.5 0.485379
\(66\) 21319.1 0.602434
\(67\) −17934.5 −0.488094 −0.244047 0.969763i \(-0.578475\pi\)
−0.244047 + 0.969763i \(0.578475\pi\)
\(68\) −22479.9 −0.589552
\(69\) −42982.1 −1.08684
\(70\) 4630.09 0.112939
\(71\) 43250.3 1.01822 0.509112 0.860700i \(-0.329974\pi\)
0.509112 + 0.860700i \(0.329974\pi\)
\(72\) 5184.00 0.117851
\(73\) −13130.3 −0.288381 −0.144190 0.989550i \(-0.546058\pi\)
−0.144190 + 0.989550i \(0.546058\pi\)
\(74\) −14411.0 −0.305925
\(75\) −5625.00 −0.115470
\(76\) 5776.00 0.114708
\(77\) −27419.3 −0.527022
\(78\) −23808.2 −0.443089
\(79\) 109029. 1.96551 0.982755 0.184913i \(-0.0592002\pi\)
0.982755 + 0.184913i \(0.0592002\pi\)
\(80\) 6400.00 0.111803
\(81\) 6561.00 0.111111
\(82\) 60593.5 0.995157
\(83\) 5873.28 0.0935806 0.0467903 0.998905i \(-0.485101\pi\)
0.0467903 + 0.998905i \(0.485101\pi\)
\(84\) −6667.33 −0.103099
\(85\) −35124.9 −0.527312
\(86\) −88818.1 −1.29496
\(87\) 1604.29 0.0227239
\(88\) −37900.6 −0.521723
\(89\) 66508.0 0.890018 0.445009 0.895526i \(-0.353200\pi\)
0.445009 + 0.895526i \(0.353200\pi\)
\(90\) 8100.00 0.105409
\(91\) 30620.6 0.387624
\(92\) 76412.6 0.941229
\(93\) −45482.6 −0.545302
\(94\) 48921.4 0.571057
\(95\) 9025.00 0.102598
\(96\) −9216.00 −0.102062
\(97\) 145294. 1.56790 0.783949 0.620825i \(-0.213202\pi\)
0.783949 + 0.620825i \(0.213202\pi\)
\(98\) −58652.9 −0.616914
\(99\) −47968.0 −0.491885
\(100\) 10000.0 0.100000
\(101\) 2653.33 0.0258814 0.0129407 0.999916i \(-0.495881\pi\)
0.0129407 + 0.999916i \(0.495881\pi\)
\(102\) 50579.8 0.481368
\(103\) 32721.2 0.303904 0.151952 0.988388i \(-0.451444\pi\)
0.151952 + 0.988388i \(0.451444\pi\)
\(104\) 42325.7 0.383726
\(105\) −10417.7 −0.0922144
\(106\) 38403.1 0.331972
\(107\) −119594. −1.00983 −0.504916 0.863169i \(-0.668476\pi\)
−0.504916 + 0.863169i \(0.668476\pi\)
\(108\) −11664.0 −0.0962250
\(109\) 107852. 0.869485 0.434742 0.900555i \(-0.356839\pi\)
0.434742 + 0.900555i \(0.356839\pi\)
\(110\) −59219.8 −0.466643
\(111\) 32424.8 0.249787
\(112\) 11853.0 0.0892862
\(113\) 259806. 1.91405 0.957026 0.290002i \(-0.0936558\pi\)
0.957026 + 0.290002i \(0.0936558\pi\)
\(114\) −12996.0 −0.0936586
\(115\) 119395. 0.841861
\(116\) −2852.06 −0.0196795
\(117\) 53568.5 0.361780
\(118\) 8767.15 0.0579634
\(119\) −65052.5 −0.421111
\(120\) −14400.0 −0.0912871
\(121\) 189647. 1.17756
\(122\) 3705.60 0.0225403
\(123\) −136335. −0.812542
\(124\) 80857.9 0.472246
\(125\) 15625.0 0.0894427
\(126\) 15001.5 0.0841798
\(127\) −162333. −0.893095 −0.446548 0.894760i \(-0.647347\pi\)
−0.446548 + 0.894760i \(0.647347\pi\)
\(128\) 16384.0 0.0883883
\(129\) 199841. 1.05733
\(130\) 66134.0 0.343215
\(131\) 260155. 1.32450 0.662252 0.749281i \(-0.269601\pi\)
0.662252 + 0.749281i \(0.269601\pi\)
\(132\) 85276.4 0.425985
\(133\) 16714.6 0.0819346
\(134\) −71738.2 −0.345135
\(135\) −18225.0 −0.0860663
\(136\) −89919.7 −0.416877
\(137\) 75669.6 0.344445 0.172223 0.985058i \(-0.444905\pi\)
0.172223 + 0.985058i \(0.444905\pi\)
\(138\) −171928. −0.768510
\(139\) −79493.2 −0.348974 −0.174487 0.984659i \(-0.555827\pi\)
−0.174487 + 0.984659i \(0.555827\pi\)
\(140\) 18520.4 0.0798600
\(141\) −110073. −0.466266
\(142\) 173001. 0.719993
\(143\) −391644. −1.60159
\(144\) 20736.0 0.0833333
\(145\) −4456.35 −0.0176019
\(146\) −52521.0 −0.203916
\(147\) 131969. 0.503708
\(148\) −57644.0 −0.216322
\(149\) 490284. 1.80918 0.904590 0.426283i \(-0.140177\pi\)
0.904590 + 0.426283i \(0.140177\pi\)
\(150\) −22500.0 −0.0816497
\(151\) −210024. −0.749595 −0.374797 0.927107i \(-0.622288\pi\)
−0.374797 + 0.927107i \(0.622288\pi\)
\(152\) 23104.0 0.0811107
\(153\) −113805. −0.393035
\(154\) −109677. −0.372661
\(155\) 126340. 0.422389
\(156\) −95232.9 −0.313311
\(157\) 13799.4 0.0446797 0.0223399 0.999750i \(-0.492888\pi\)
0.0223399 + 0.999750i \(0.492888\pi\)
\(158\) 436117. 1.38983
\(159\) −86407.0 −0.271054
\(160\) 25600.0 0.0790569
\(161\) 221123. 0.672310
\(162\) 26244.0 0.0785674
\(163\) 7959.84 0.0234658 0.0117329 0.999931i \(-0.496265\pi\)
0.0117329 + 0.999931i \(0.496265\pi\)
\(164\) 242374. 0.703682
\(165\) 133244. 0.381013
\(166\) 23493.1 0.0661715
\(167\) 408123. 1.13240 0.566200 0.824268i \(-0.308413\pi\)
0.566200 + 0.824268i \(0.308413\pi\)
\(168\) −26669.3 −0.0729018
\(169\) 66077.0 0.177965
\(170\) −140499. −0.372866
\(171\) 29241.0 0.0764719
\(172\) −355272. −0.915673
\(173\) 563088. 1.43041 0.715206 0.698914i \(-0.246333\pi\)
0.715206 + 0.698914i \(0.246333\pi\)
\(174\) 6417.14 0.0160683
\(175\) 28938.1 0.0714289
\(176\) −151603. −0.368914
\(177\) −19726.1 −0.0473269
\(178\) 266032. 0.629338
\(179\) −705880. −1.64664 −0.823319 0.567579i \(-0.807880\pi\)
−0.823319 + 0.567579i \(0.807880\pi\)
\(180\) 32400.0 0.0745356
\(181\) 28650.5 0.0650034 0.0325017 0.999472i \(-0.489653\pi\)
0.0325017 + 0.999472i \(0.489653\pi\)
\(182\) 122482. 0.274091
\(183\) −8337.60 −0.0184041
\(184\) 305650. 0.665549
\(185\) −90068.8 −0.193484
\(186\) −181930. −0.385587
\(187\) 832035. 1.73995
\(188\) 195686. 0.403798
\(189\) −33753.3 −0.0687325
\(190\) 36100.0 0.0725476
\(191\) 137123. 0.271974 0.135987 0.990711i \(-0.456579\pi\)
0.135987 + 0.990711i \(0.456579\pi\)
\(192\) −36864.0 −0.0721688
\(193\) 930902. 1.79892 0.899458 0.437008i \(-0.143962\pi\)
0.899458 + 0.437008i \(0.143962\pi\)
\(194\) 581175. 1.10867
\(195\) −148801. −0.280234
\(196\) −234612. −0.436224
\(197\) −1812.91 −0.00332820 −0.00166410 0.999999i \(-0.500530\pi\)
−0.00166410 + 0.999999i \(0.500530\pi\)
\(198\) −191872. −0.347815
\(199\) 605207. 1.08336 0.541678 0.840586i \(-0.317789\pi\)
0.541678 + 0.840586i \(0.317789\pi\)
\(200\) 40000.0 0.0707107
\(201\) 161411. 0.281801
\(202\) 10613.3 0.0183009
\(203\) −8253.32 −0.0140569
\(204\) 202319. 0.340378
\(205\) 378709. 0.629392
\(206\) 130885. 0.214892
\(207\) 386839. 0.627486
\(208\) 169303. 0.271335
\(209\) −213783. −0.338539
\(210\) −41670.8 −0.0652054
\(211\) −1.06405e6 −1.64534 −0.822669 0.568520i \(-0.807516\pi\)
−0.822669 + 0.568520i \(0.807516\pi\)
\(212\) 153613. 0.234740
\(213\) −389253. −0.587872
\(214\) −478375. −0.714058
\(215\) −555113. −0.819002
\(216\) −46656.0 −0.0680414
\(217\) 233987. 0.337320
\(218\) 431408. 0.614819
\(219\) 118172. 0.166497
\(220\) −236879. −0.329967
\(221\) −929179. −1.27973
\(222\) 129699. 0.176626
\(223\) −339331. −0.456942 −0.228471 0.973551i \(-0.573373\pi\)
−0.228471 + 0.973551i \(0.573373\pi\)
\(224\) 47412.1 0.0631349
\(225\) 50625.0 0.0666667
\(226\) 1.03923e6 1.35344
\(227\) −563086. −0.725287 −0.362643 0.931928i \(-0.618126\pi\)
−0.362643 + 0.931928i \(0.618126\pi\)
\(228\) −51984.0 −0.0662266
\(229\) −143103. −0.180327 −0.0901633 0.995927i \(-0.528739\pi\)
−0.0901633 + 0.995927i \(0.528739\pi\)
\(230\) 477578. 0.595285
\(231\) 246773. 0.304277
\(232\) −11408.3 −0.0139155
\(233\) −149712. −0.180663 −0.0903313 0.995912i \(-0.528793\pi\)
−0.0903313 + 0.995912i \(0.528793\pi\)
\(234\) 214274. 0.255817
\(235\) 305759. 0.361168
\(236\) 35068.6 0.0409863
\(237\) −981263. −1.13479
\(238\) −260210. −0.297770
\(239\) −881537. −0.998265 −0.499133 0.866526i \(-0.666348\pi\)
−0.499133 + 0.866526i \(0.666348\pi\)
\(240\) −57600.0 −0.0645497
\(241\) −889167. −0.986145 −0.493072 0.869988i \(-0.664126\pi\)
−0.493072 + 0.869988i \(0.664126\pi\)
\(242\) 758588. 0.832659
\(243\) −59049.0 −0.0641500
\(244\) 14822.4 0.0159384
\(245\) −366581. −0.390170
\(246\) −545341. −0.574554
\(247\) 238744. 0.248994
\(248\) 323431. 0.333928
\(249\) −52859.5 −0.0540288
\(250\) 62500.0 0.0632456
\(251\) 119596. 0.119820 0.0599102 0.998204i \(-0.480919\pi\)
0.0599102 + 0.998204i \(0.480919\pi\)
\(252\) 60005.9 0.0595241
\(253\) −2.82821e6 −2.77786
\(254\) −649332. −0.631514
\(255\) 316124. 0.304444
\(256\) 65536.0 0.0625000
\(257\) −339118. −0.320272 −0.160136 0.987095i \(-0.551193\pi\)
−0.160136 + 0.987095i \(0.551193\pi\)
\(258\) 799363. 0.747644
\(259\) −166811. −0.154516
\(260\) 264536. 0.242690
\(261\) −14438.6 −0.0131197
\(262\) 1.04062e6 0.936566
\(263\) 65039.2 0.0579810 0.0289905 0.999580i \(-0.490771\pi\)
0.0289905 + 0.999580i \(0.490771\pi\)
\(264\) 341106. 0.301217
\(265\) 240020. 0.209958
\(266\) 66858.5 0.0579365
\(267\) −598572. −0.513852
\(268\) −286953. −0.244047
\(269\) −1.33562e6 −1.12539 −0.562695 0.826665i \(-0.690235\pi\)
−0.562695 + 0.826665i \(0.690235\pi\)
\(270\) −72900.0 −0.0608581
\(271\) −1.43923e6 −1.19044 −0.595218 0.803564i \(-0.702934\pi\)
−0.595218 + 0.803564i \(0.702934\pi\)
\(272\) −359679. −0.294776
\(273\) −275585. −0.223795
\(274\) 302678. 0.243559
\(275\) −370123. −0.295131
\(276\) −687713. −0.543419
\(277\) −1.13151e6 −0.886054 −0.443027 0.896508i \(-0.646095\pi\)
−0.443027 + 0.896508i \(0.646095\pi\)
\(278\) −317973. −0.246762
\(279\) 409343. 0.314831
\(280\) 74081.4 0.0564695
\(281\) 1.28968e6 0.974349 0.487175 0.873305i \(-0.338028\pi\)
0.487175 + 0.873305i \(0.338028\pi\)
\(282\) −440293. −0.329700
\(283\) 1.20910e6 0.897418 0.448709 0.893678i \(-0.351884\pi\)
0.448709 + 0.893678i \(0.351884\pi\)
\(284\) 692004. 0.509112
\(285\) −81225.0 −0.0592349
\(286\) −1.56657e6 −1.13249
\(287\) 701383. 0.502632
\(288\) 82944.0 0.0589256
\(289\) 554154. 0.390288
\(290\) −17825.4 −0.0124464
\(291\) −1.30764e6 −0.905226
\(292\) −210084. −0.144190
\(293\) 399283. 0.271714 0.135857 0.990728i \(-0.456621\pi\)
0.135857 + 0.990728i \(0.456621\pi\)
\(294\) 527876. 0.356175
\(295\) 54794.7 0.0366592
\(296\) −230576. −0.152963
\(297\) 431712. 0.283990
\(298\) 1.96113e6 1.27928
\(299\) 3.15842e6 2.04311
\(300\) −90000.0 −0.0577350
\(301\) −1.02809e6 −0.654055
\(302\) −840096. −0.530043
\(303\) −23879.9 −0.0149426
\(304\) 92416.0 0.0573539
\(305\) 23160.0 0.0142557
\(306\) −455218. −0.277918
\(307\) 1.59355e6 0.964982 0.482491 0.875901i \(-0.339732\pi\)
0.482491 + 0.875901i \(0.339732\pi\)
\(308\) −438708. −0.263511
\(309\) −294491. −0.175459
\(310\) 505362. 0.298674
\(311\) −895028. −0.524730 −0.262365 0.964969i \(-0.584502\pi\)
−0.262365 + 0.964969i \(0.584502\pi\)
\(312\) −380932. −0.221544
\(313\) 593284. 0.342296 0.171148 0.985245i \(-0.445252\pi\)
0.171148 + 0.985245i \(0.445252\pi\)
\(314\) 55197.5 0.0315933
\(315\) 93759.3 0.0532400
\(316\) 1.74447e6 0.982755
\(317\) 3.44435e6 1.92513 0.962564 0.271054i \(-0.0873723\pi\)
0.962564 + 0.271054i \(0.0873723\pi\)
\(318\) −345628. −0.191664
\(319\) 105562. 0.0580803
\(320\) 102400. 0.0559017
\(321\) 1.07634e6 0.583026
\(322\) 884492. 0.475395
\(323\) −507203. −0.270505
\(324\) 104976. 0.0555556
\(325\) 413337. 0.217068
\(326\) 31839.4 0.0165928
\(327\) −970668. −0.501997
\(328\) 969496. 0.497578
\(329\) 566276. 0.288429
\(330\) 532978. 0.269417
\(331\) 2.39189e6 1.19997 0.599986 0.800011i \(-0.295173\pi\)
0.599986 + 0.800011i \(0.295173\pi\)
\(332\) 93972.5 0.0467903
\(333\) −291823. −0.144214
\(334\) 1.63249e6 0.800728
\(335\) −448364. −0.218282
\(336\) −106677. −0.0515494
\(337\) −1.00905e6 −0.483992 −0.241996 0.970277i \(-0.577802\pi\)
−0.241996 + 0.970277i \(0.577802\pi\)
\(338\) 264308. 0.125840
\(339\) −2.33826e6 −1.10508
\(340\) −561998. −0.263656
\(341\) −2.99274e6 −1.39374
\(342\) 116964. 0.0540738
\(343\) −1.45710e6 −0.668735
\(344\) −1.42109e6 −0.647478
\(345\) −1.07455e6 −0.486048
\(346\) 2.25235e6 1.01145
\(347\) 558349. 0.248933 0.124466 0.992224i \(-0.460278\pi\)
0.124466 + 0.992224i \(0.460278\pi\)
\(348\) 25668.6 0.0113620
\(349\) 1.60518e6 0.705441 0.352721 0.935729i \(-0.385257\pi\)
0.352721 + 0.935729i \(0.385257\pi\)
\(350\) 115752. 0.0505079
\(351\) −482117. −0.208874
\(352\) −606410. −0.260861
\(353\) −2.25469e6 −0.963053 −0.481527 0.876432i \(-0.659918\pi\)
−0.481527 + 0.876432i \(0.659918\pi\)
\(354\) −78904.4 −0.0334652
\(355\) 1.08126e6 0.455363
\(356\) 1.06413e6 0.445009
\(357\) 585473. 0.243129
\(358\) −2.82352e6 −1.16435
\(359\) −3.72457e6 −1.52525 −0.762623 0.646843i \(-0.776089\pi\)
−0.762623 + 0.646843i \(0.776089\pi\)
\(360\) 129600. 0.0527046
\(361\) 130321. 0.0526316
\(362\) 114602. 0.0459643
\(363\) −1.70682e6 −0.679864
\(364\) 489930. 0.193812
\(365\) −328256. −0.128968
\(366\) −33350.4 −0.0130136
\(367\) −608999. −0.236021 −0.118011 0.993012i \(-0.537652\pi\)
−0.118011 + 0.993012i \(0.537652\pi\)
\(368\) 1.22260e6 0.470614
\(369\) 1.22702e6 0.469121
\(370\) −360275. −0.136814
\(371\) 444525. 0.167672
\(372\) −727721. −0.272651
\(373\) −1.14524e6 −0.426212 −0.213106 0.977029i \(-0.568358\pi\)
−0.213106 + 0.977029i \(0.568358\pi\)
\(374\) 3.32814e6 1.23033
\(375\) −140625. −0.0516398
\(376\) 782743. 0.285528
\(377\) −117886. −0.0427180
\(378\) −135013. −0.0486012
\(379\) −3.85601e6 −1.37892 −0.689461 0.724323i \(-0.742153\pi\)
−0.689461 + 0.724323i \(0.742153\pi\)
\(380\) 144400. 0.0512989
\(381\) 1.46100e6 0.515629
\(382\) 548492. 0.192315
\(383\) 366401. 0.127632 0.0638160 0.997962i \(-0.479673\pi\)
0.0638160 + 0.997962i \(0.479673\pi\)
\(384\) −147456. −0.0510310
\(385\) −685482. −0.235692
\(386\) 3.72361e6 1.27203
\(387\) −1.79857e6 −0.610448
\(388\) 2.32470e6 0.783949
\(389\) −1.72920e6 −0.579389 −0.289695 0.957119i \(-0.593554\pi\)
−0.289695 + 0.957119i \(0.593554\pi\)
\(390\) −595206. −0.198155
\(391\) −6.70995e6 −2.21961
\(392\) −938447. −0.308457
\(393\) −2.34139e6 −0.764703
\(394\) −7251.63 −0.00235340
\(395\) 2.72573e6 0.879003
\(396\) −767488. −0.245943
\(397\) −495411. −0.157757 −0.0788787 0.996884i \(-0.525134\pi\)
−0.0788787 + 0.996884i \(0.525134\pi\)
\(398\) 2.42083e6 0.766049
\(399\) −150432. −0.0473050
\(400\) 160000. 0.0500000
\(401\) −616557. −0.191475 −0.0957376 0.995407i \(-0.530521\pi\)
−0.0957376 + 0.995407i \(0.530521\pi\)
\(402\) 645644. 0.199263
\(403\) 3.34216e6 1.02510
\(404\) 42453.2 0.0129407
\(405\) 164025. 0.0496904
\(406\) −33013.3 −0.00993971
\(407\) 2.13354e6 0.638432
\(408\) 809277. 0.240684
\(409\) 4.43760e6 1.31172 0.655859 0.754884i \(-0.272307\pi\)
0.655859 + 0.754884i \(0.272307\pi\)
\(410\) 1.51484e6 0.445048
\(411\) −681026. −0.198865
\(412\) 523539. 0.151952
\(413\) 101482. 0.0292761
\(414\) 1.54735e6 0.443699
\(415\) 146832. 0.0418505
\(416\) 677212. 0.191863
\(417\) 715439. 0.201480
\(418\) −855133. −0.239383
\(419\) 5.99895e6 1.66932 0.834662 0.550763i \(-0.185663\pi\)
0.834662 + 0.550763i \(0.185663\pi\)
\(420\) −166683. −0.0461072
\(421\) −2.34020e6 −0.643500 −0.321750 0.946825i \(-0.604271\pi\)
−0.321750 + 0.946825i \(0.604271\pi\)
\(422\) −4.25619e6 −1.16343
\(423\) 990659. 0.269199
\(424\) 614450. 0.165986
\(425\) −878122. −0.235821
\(426\) −1.55701e6 −0.415688
\(427\) 42893.2 0.0113846
\(428\) −1.91350e6 −0.504916
\(429\) 3.52479e6 0.924678
\(430\) −2.22045e6 −0.579122
\(431\) −3.18571e6 −0.826064 −0.413032 0.910717i \(-0.635530\pi\)
−0.413032 + 0.910717i \(0.635530\pi\)
\(432\) −186624. −0.0481125
\(433\) −3.76503e6 −0.965048 −0.482524 0.875883i \(-0.660280\pi\)
−0.482524 + 0.875883i \(0.660280\pi\)
\(434\) 935948. 0.238521
\(435\) 40107.2 0.0101625
\(436\) 1.72563e6 0.434742
\(437\) 1.72406e6 0.431865
\(438\) 472689. 0.117731
\(439\) −3.73627e6 −0.925287 −0.462644 0.886544i \(-0.653099\pi\)
−0.462644 + 0.886544i \(0.653099\pi\)
\(440\) −947516. −0.233322
\(441\) −1.18772e6 −0.290816
\(442\) −3.71672e6 −0.904906
\(443\) 1.62775e6 0.394075 0.197037 0.980396i \(-0.436868\pi\)
0.197037 + 0.980396i \(0.436868\pi\)
\(444\) 518796. 0.124893
\(445\) 1.66270e6 0.398028
\(446\) −1.35732e6 −0.323107
\(447\) −4.41255e6 −1.04453
\(448\) 189648. 0.0446431
\(449\) 737503. 0.172643 0.0863213 0.996267i \(-0.472489\pi\)
0.0863213 + 0.996267i \(0.472489\pi\)
\(450\) 202500. 0.0471405
\(451\) −8.97083e6 −2.07678
\(452\) 4.15690e6 0.957026
\(453\) 1.89022e6 0.432779
\(454\) −2.25234e6 −0.512855
\(455\) 765515. 0.173351
\(456\) −207936. −0.0468293
\(457\) −893631. −0.200156 −0.100078 0.994980i \(-0.531909\pi\)
−0.100078 + 0.994980i \(0.531909\pi\)
\(458\) −572412. −0.127510
\(459\) 1.02424e6 0.226919
\(460\) 1.91031e6 0.420930
\(461\) −5.46587e6 −1.19786 −0.598931 0.800801i \(-0.704408\pi\)
−0.598931 + 0.800801i \(0.704408\pi\)
\(462\) 987094. 0.215156
\(463\) −4.05984e6 −0.880149 −0.440074 0.897961i \(-0.645048\pi\)
−0.440074 + 0.897961i \(0.645048\pi\)
\(464\) −45633.0 −0.00983976
\(465\) −1.13706e6 −0.243867
\(466\) −598850. −0.127748
\(467\) 5.53201e6 1.17379 0.586895 0.809663i \(-0.300350\pi\)
0.586895 + 0.809663i \(0.300350\pi\)
\(468\) 857096. 0.180890
\(469\) −830385. −0.174320
\(470\) 1.22304e6 0.255384
\(471\) −124194. −0.0257958
\(472\) 140274. 0.0289817
\(473\) 1.31495e7 2.70243
\(474\) −3.92505e6 −0.802416
\(475\) 225625. 0.0458831
\(476\) −1.04084e6 −0.210556
\(477\) 777663. 0.156493
\(478\) −3.52615e6 −0.705880
\(479\) 1.07783e6 0.214640 0.107320 0.994225i \(-0.465773\pi\)
0.107320 + 0.994225i \(0.465773\pi\)
\(480\) −230400. −0.0456435
\(481\) −2.38264e6 −0.469566
\(482\) −3.55667e6 −0.697310
\(483\) −1.99011e6 −0.388158
\(484\) 3.03435e6 0.588779
\(485\) 3.63235e6 0.701185
\(486\) −236196. −0.0453609
\(487\) −5.51455e6 −1.05363 −0.526814 0.849980i \(-0.676614\pi\)
−0.526814 + 0.849980i \(0.676614\pi\)
\(488\) 59289.6 0.0112701
\(489\) −71638.6 −0.0135480
\(490\) −1.46632e6 −0.275892
\(491\) −9.17738e6 −1.71797 −0.858984 0.512003i \(-0.828904\pi\)
−0.858984 + 0.512003i \(0.828904\pi\)
\(492\) −2.18137e6 −0.406271
\(493\) 250446. 0.0464084
\(494\) 954974. 0.176066
\(495\) −1.19920e6 −0.219978
\(496\) 1.29373e6 0.236123
\(497\) 2.00253e6 0.363653
\(498\) −211438. −0.0382041
\(499\) −8.41157e6 −1.51226 −0.756129 0.654423i \(-0.772912\pi\)
−0.756129 + 0.654423i \(0.772912\pi\)
\(500\) 250000. 0.0447214
\(501\) −3.67311e6 −0.653792
\(502\) 478383. 0.0847259
\(503\) −2.49352e6 −0.439433 −0.219717 0.975564i \(-0.570513\pi\)
−0.219717 + 0.975564i \(0.570513\pi\)
\(504\) 240024. 0.0420899
\(505\) 66333.1 0.0115745
\(506\) −1.13128e7 −1.96424
\(507\) −594693. −0.102748
\(508\) −2.59733e6 −0.446548
\(509\) −5.47906e6 −0.937370 −0.468685 0.883365i \(-0.655272\pi\)
−0.468685 + 0.883365i \(0.655272\pi\)
\(510\) 1.26450e6 0.215274
\(511\) −607942. −0.102994
\(512\) 262144. 0.0441942
\(513\) −263169. −0.0441511
\(514\) −1.35647e6 −0.226466
\(515\) 818030. 0.135910
\(516\) 3.19745e6 0.528664
\(517\) −7.24279e6 −1.19173
\(518\) −667242. −0.109260
\(519\) −5.06779e6 −0.825848
\(520\) 1.05814e6 0.171607
\(521\) −9.26335e6 −1.49511 −0.747556 0.664199i \(-0.768773\pi\)
−0.747556 + 0.664199i \(0.768773\pi\)
\(522\) −57754.3 −0.00927701
\(523\) −1.81815e6 −0.290654 −0.145327 0.989384i \(-0.546423\pi\)
−0.145327 + 0.989384i \(0.546423\pi\)
\(524\) 4.16248e6 0.662252
\(525\) −260442. −0.0412395
\(526\) 260157. 0.0409988
\(527\) −7.10031e6 −1.11365
\(528\) 1.36442e6 0.212992
\(529\) 1.63718e7 2.54365
\(530\) 960078. 0.148463
\(531\) 177535. 0.0273242
\(532\) 267434. 0.0409673
\(533\) 1.00182e7 1.52747
\(534\) −2.39429e6 −0.363348
\(535\) −2.98984e6 −0.451610
\(536\) −1.14781e6 −0.172567
\(537\) 6.35292e6 0.950687
\(538\) −5.34249e6 −0.795770
\(539\) 8.68353e6 1.28743
\(540\) −291600. −0.0430331
\(541\) 1.05448e7 1.54898 0.774491 0.632585i \(-0.218006\pi\)
0.774491 + 0.632585i \(0.218006\pi\)
\(542\) −5.75690e6 −0.841765
\(543\) −257855. −0.0375297
\(544\) −1.43871e6 −0.208438
\(545\) 2.69630e6 0.388845
\(546\) −1.10234e6 −0.158247
\(547\) −1.27881e7 −1.82742 −0.913711 0.406365i \(-0.866796\pi\)
−0.913711 + 0.406365i \(0.866796\pi\)
\(548\) 1.21071e6 0.172223
\(549\) 75038.4 0.0106256
\(550\) −1.48049e6 −0.208689
\(551\) −64349.7 −0.00902958
\(552\) −2.75085e6 −0.384255
\(553\) 5.04815e6 0.701971
\(554\) −4.52605e6 −0.626534
\(555\) 810619. 0.111708
\(556\) −1.27189e6 −0.174487
\(557\) −2.52948e6 −0.345457 −0.172728 0.984970i \(-0.555258\pi\)
−0.172728 + 0.984970i \(0.555258\pi\)
\(558\) 1.63737e6 0.222619
\(559\) −1.46847e7 −1.98763
\(560\) 296326. 0.0399300
\(561\) −7.48831e6 −1.00456
\(562\) 5.15870e6 0.688969
\(563\) 549145. 0.0730156 0.0365078 0.999333i \(-0.488377\pi\)
0.0365078 + 0.999333i \(0.488377\pi\)
\(564\) −1.76117e6 −0.233133
\(565\) 6.49516e6 0.855990
\(566\) 4.83638e6 0.634570
\(567\) 303780. 0.0396827
\(568\) 2.76802e6 0.359996
\(569\) 1.17774e7 1.52499 0.762496 0.646992i \(-0.223973\pi\)
0.762496 + 0.646992i \(0.223973\pi\)
\(570\) −324900. −0.0418854
\(571\) 1.46636e7 1.88213 0.941065 0.338226i \(-0.109827\pi\)
0.941065 + 0.338226i \(0.109827\pi\)
\(572\) −6.26630e6 −0.800794
\(573\) −1.23411e6 −0.157024
\(574\) 2.80553e6 0.355415
\(575\) 2.98487e6 0.376491
\(576\) 331776. 0.0416667
\(577\) −1.56628e7 −1.95853 −0.979264 0.202590i \(-0.935064\pi\)
−0.979264 + 0.202590i \(0.935064\pi\)
\(578\) 2.21661e6 0.275976
\(579\) −8.37812e6 −1.03860
\(580\) −71301.6 −0.00880095
\(581\) 271938. 0.0334218
\(582\) −5.23058e6 −0.640092
\(583\) −5.68556e6 −0.692790
\(584\) −840336. −0.101958
\(585\) 1.33921e6 0.161793
\(586\) 1.59713e6 0.192131
\(587\) 909404. 0.108934 0.0544668 0.998516i \(-0.482654\pi\)
0.0544668 + 0.998516i \(0.482654\pi\)
\(588\) 2.11150e6 0.251854
\(589\) 1.82436e6 0.216681
\(590\) 219179. 0.0259220
\(591\) 16316.2 0.00192154
\(592\) −922305. −0.108161
\(593\) −1.47954e7 −1.72779 −0.863896 0.503670i \(-0.831983\pi\)
−0.863896 + 0.503670i \(0.831983\pi\)
\(594\) 1.72685e6 0.200811
\(595\) −1.62631e6 −0.188327
\(596\) 7.84454e6 0.904590
\(597\) −5.44686e6 −0.625476
\(598\) 1.26337e7 1.44470
\(599\) 1.42416e7 1.62178 0.810888 0.585202i \(-0.198985\pi\)
0.810888 + 0.585202i \(0.198985\pi\)
\(600\) −360000. −0.0408248
\(601\) 1.40092e6 0.158208 0.0791040 0.996866i \(-0.474794\pi\)
0.0791040 + 0.996866i \(0.474794\pi\)
\(602\) −4.11236e6 −0.462487
\(603\) −1.45270e6 −0.162698
\(604\) −3.36038e6 −0.374797
\(605\) 4.74117e6 0.526620
\(606\) −95519.7 −0.0105660
\(607\) 1.00463e7 1.10671 0.553356 0.832945i \(-0.313347\pi\)
0.553356 + 0.832945i \(0.313347\pi\)
\(608\) 369664. 0.0405554
\(609\) 74279.9 0.00811574
\(610\) 92640.0 0.0100803
\(611\) 8.08842e6 0.876517
\(612\) −1.82087e6 −0.196517
\(613\) −4.38057e6 −0.470847 −0.235424 0.971893i \(-0.575648\pi\)
−0.235424 + 0.971893i \(0.575648\pi\)
\(614\) 6.37419e6 0.682345
\(615\) −3.40838e6 −0.363380
\(616\) −1.75483e6 −0.186331
\(617\) −3.77700e6 −0.399424 −0.199712 0.979855i \(-0.564001\pi\)
−0.199712 + 0.979855i \(0.564001\pi\)
\(618\) −1.17796e6 −0.124068
\(619\) −1.55698e7 −1.63327 −0.816633 0.577157i \(-0.804162\pi\)
−0.816633 + 0.577157i \(0.804162\pi\)
\(620\) 2.02145e6 0.211195
\(621\) −3.48155e6 −0.362279
\(622\) −3.58011e6 −0.371040
\(623\) 3.07938e6 0.317865
\(624\) −1.52373e6 −0.156655
\(625\) 390625. 0.0400000
\(626\) 2.37314e6 0.242040
\(627\) 1.92405e6 0.195455
\(628\) 220790. 0.0223399
\(629\) 5.06185e6 0.510132
\(630\) 375037. 0.0376464
\(631\) −1.44580e6 −0.144556 −0.0722778 0.997385i \(-0.523027\pi\)
−0.0722778 + 0.997385i \(0.523027\pi\)
\(632\) 6.97787e6 0.694913
\(633\) 9.57643e6 0.949936
\(634\) 1.37774e7 1.36127
\(635\) −4.05833e6 −0.399404
\(636\) −1.38251e6 −0.135527
\(637\) −9.69737e6 −0.946903
\(638\) 422246. 0.0410690
\(639\) 3.50327e6 0.339408
\(640\) 409600. 0.0395285
\(641\) 1.41495e7 1.36018 0.680092 0.733127i \(-0.261940\pi\)
0.680092 + 0.733127i \(0.261940\pi\)
\(642\) 4.30537e6 0.412262
\(643\) −3.07758e6 −0.293550 −0.146775 0.989170i \(-0.546889\pi\)
−0.146775 + 0.989170i \(0.546889\pi\)
\(644\) 3.53797e6 0.336155
\(645\) 4.99602e6 0.472851
\(646\) −2.02881e6 −0.191276
\(647\) 1.66462e7 1.56335 0.781673 0.623688i \(-0.214367\pi\)
0.781673 + 0.623688i \(0.214367\pi\)
\(648\) 419904. 0.0392837
\(649\) −1.29797e6 −0.120963
\(650\) 1.65335e6 0.153490
\(651\) −2.10588e6 −0.194752
\(652\) 127357. 0.0117329
\(653\) −1.12480e7 −1.03227 −0.516133 0.856509i \(-0.672629\pi\)
−0.516133 + 0.856509i \(0.672629\pi\)
\(654\) −3.88267e6 −0.354966
\(655\) 6.50387e6 0.592337
\(656\) 3.87798e6 0.351841
\(657\) −1.06355e6 −0.0961269
\(658\) 2.26510e6 0.203950
\(659\) 4.63676e6 0.415912 0.207956 0.978138i \(-0.433319\pi\)
0.207956 + 0.978138i \(0.433319\pi\)
\(660\) 2.13191e6 0.190506
\(661\) −1.86324e7 −1.65869 −0.829346 0.558736i \(-0.811287\pi\)
−0.829346 + 0.558736i \(0.811287\pi\)
\(662\) 9.56756e6 0.848508
\(663\) 8.36261e6 0.738853
\(664\) 375890. 0.0330857
\(665\) 417865. 0.0366423
\(666\) −1.16729e6 −0.101975
\(667\) −851303. −0.0740917
\(668\) 6.52997e6 0.566200
\(669\) 3.05398e6 0.263816
\(670\) −1.79345e6 −0.154349
\(671\) −548612. −0.0470391
\(672\) −426709. −0.0364509
\(673\) 8.43418e6 0.717803 0.358901 0.933376i \(-0.383151\pi\)
0.358901 + 0.933376i \(0.383151\pi\)
\(674\) −4.03620e6 −0.342234
\(675\) −455625. −0.0384900
\(676\) 1.05723e6 0.0889823
\(677\) −1.49945e6 −0.125736 −0.0628679 0.998022i \(-0.520025\pi\)
−0.0628679 + 0.998022i \(0.520025\pi\)
\(678\) −9.35303e6 −0.781409
\(679\) 6.72723e6 0.559966
\(680\) −2.24799e6 −0.186433
\(681\) 5.06777e6 0.418745
\(682\) −1.19710e7 −0.985526
\(683\) −1.78268e6 −0.146225 −0.0731124 0.997324i \(-0.523293\pi\)
−0.0731124 + 0.997324i \(0.523293\pi\)
\(684\) 467856. 0.0382360
\(685\) 1.89174e6 0.154041
\(686\) −5.82840e6 −0.472867
\(687\) 1.28793e6 0.104112
\(688\) −5.68436e6 −0.457836
\(689\) 6.34938e6 0.509546
\(690\) −4.29821e6 −0.343688
\(691\) −4.90602e6 −0.390872 −0.195436 0.980716i \(-0.562612\pi\)
−0.195436 + 0.980716i \(0.562612\pi\)
\(692\) 9.00941e6 0.715206
\(693\) −2.22096e6 −0.175674
\(694\) 2.23340e6 0.176022
\(695\) −1.98733e6 −0.156066
\(696\) 102674. 0.00803413
\(697\) −2.12834e7 −1.65943
\(698\) 6.42073e6 0.498822
\(699\) 1.34741e6 0.104306
\(700\) 463009. 0.0357145
\(701\) 1.07045e7 0.822756 0.411378 0.911465i \(-0.365048\pi\)
0.411378 + 0.911465i \(0.365048\pi\)
\(702\) −1.92847e6 −0.147696
\(703\) −1.30059e6 −0.0992552
\(704\) −2.42564e6 −0.184457
\(705\) −2.75183e6 −0.208521
\(706\) −9.01876e6 −0.680981
\(707\) 122851. 0.00924339
\(708\) −315617. −0.0236634
\(709\) −1.25861e7 −0.940319 −0.470159 0.882581i \(-0.655804\pi\)
−0.470159 + 0.882581i \(0.655804\pi\)
\(710\) 4.32503e6 0.321990
\(711\) 8.83137e6 0.655170
\(712\) 4.25651e6 0.314669
\(713\) 2.41350e7 1.77797
\(714\) 2.34189e6 0.171918
\(715\) −9.79109e6 −0.716252
\(716\) −1.12941e7 −0.823319
\(717\) 7.93384e6 0.576349
\(718\) −1.48983e7 −1.07851
\(719\) −1.28196e7 −0.924810 −0.462405 0.886669i \(-0.653013\pi\)
−0.462405 + 0.886669i \(0.653013\pi\)
\(720\) 518400. 0.0372678
\(721\) 1.51502e6 0.108538
\(722\) 521284. 0.0372161
\(723\) 8.00250e6 0.569351
\(724\) 458408. 0.0325017
\(725\) −111409. −0.00787181
\(726\) −6.82729e6 −0.480736
\(727\) 2.14041e7 1.50197 0.750985 0.660320i \(-0.229579\pi\)
0.750985 + 0.660320i \(0.229579\pi\)
\(728\) 1.95972e6 0.137046
\(729\) 531441. 0.0370370
\(730\) −1.31303e6 −0.0911940
\(731\) 3.11972e7 2.15935
\(732\) −133402. −0.00920203
\(733\) 2.20700e7 1.51720 0.758599 0.651558i \(-0.225884\pi\)
0.758599 + 0.651558i \(0.225884\pi\)
\(734\) −2.43600e6 −0.166892
\(735\) 3.29923e6 0.225265
\(736\) 4.89040e6 0.332775
\(737\) 1.06208e7 0.720258
\(738\) 4.90807e6 0.331719
\(739\) −1.34951e7 −0.909004 −0.454502 0.890746i \(-0.650183\pi\)
−0.454502 + 0.890746i \(0.650183\pi\)
\(740\) −1.44110e6 −0.0967420
\(741\) −2.14869e6 −0.143757
\(742\) 1.77810e6 0.118562
\(743\) 2.01371e7 1.33821 0.669107 0.743166i \(-0.266677\pi\)
0.669107 + 0.743166i \(0.266677\pi\)
\(744\) −2.91088e6 −0.192794
\(745\) 1.22571e7 0.809090
\(746\) −4.58097e6 −0.301377
\(747\) 475736. 0.0311935
\(748\) 1.33126e7 0.869976
\(749\) −5.53729e6 −0.360656
\(750\) −562500. −0.0365148
\(751\) −1.94257e7 −1.25683 −0.628414 0.777879i \(-0.716296\pi\)
−0.628414 + 0.777879i \(0.716296\pi\)
\(752\) 3.13097e6 0.201899
\(753\) −1.07636e6 −0.0691784
\(754\) −471546. −0.0302062
\(755\) −5.25060e6 −0.335229
\(756\) −540053. −0.0343663
\(757\) 6.77650e6 0.429799 0.214900 0.976636i \(-0.431058\pi\)
0.214900 + 0.976636i \(0.431058\pi\)
\(758\) −1.54240e7 −0.975045
\(759\) 2.54539e7 1.60380
\(760\) 577600. 0.0362738
\(761\) −3.45254e6 −0.216111 −0.108056 0.994145i \(-0.534462\pi\)
−0.108056 + 0.994145i \(0.534462\pi\)
\(762\) 5.84399e6 0.364605
\(763\) 4.99364e6 0.310532
\(764\) 2.19397e6 0.135987
\(765\) −2.84511e6 −0.175771
\(766\) 1.46560e6 0.0902494
\(767\) 1.44952e6 0.0889682
\(768\) −589824. −0.0360844
\(769\) 3.09539e7 1.88756 0.943779 0.330578i \(-0.107244\pi\)
0.943779 + 0.330578i \(0.107244\pi\)
\(770\) −2.74193e6 −0.166659
\(771\) 3.05206e6 0.184909
\(772\) 1.48944e7 0.899458
\(773\) 5.07221e6 0.305315 0.152658 0.988279i \(-0.451217\pi\)
0.152658 + 0.988279i \(0.451217\pi\)
\(774\) −7.19426e6 −0.431652
\(775\) 3.15851e6 0.188898
\(776\) 9.29880e6 0.554336
\(777\) 1.50130e6 0.0892100
\(778\) −6.91679e6 −0.409690
\(779\) 5.46856e6 0.322871
\(780\) −2.38082e6 −0.140117
\(781\) −2.56127e7 −1.50255
\(782\) −2.68398e7 −1.56950
\(783\) 129947. 0.00757465
\(784\) −3.75379e6 −0.218112
\(785\) 344984. 0.0199814
\(786\) −9.36557e6 −0.540727
\(787\) −1.04173e7 −0.599542 −0.299771 0.954011i \(-0.596910\pi\)
−0.299771 + 0.954011i \(0.596910\pi\)
\(788\) −29006.5 −0.00166410
\(789\) −585353. −0.0334753
\(790\) 1.09029e7 0.621549
\(791\) 1.20293e7 0.683594
\(792\) −3.06995e6 −0.173908
\(793\) 612665. 0.0345971
\(794\) −1.98164e6 −0.111551
\(795\) −2.16018e6 −0.121219
\(796\) 9.68332e6 0.541678
\(797\) 2.74038e7 1.52815 0.764074 0.645129i \(-0.223196\pi\)
0.764074 + 0.645129i \(0.223196\pi\)
\(798\) −601726. −0.0334497
\(799\) −1.71836e7 −0.952241
\(800\) 640000. 0.0353553
\(801\) 5.38715e6 0.296673
\(802\) −2.46623e6 −0.135393
\(803\) 7.77571e6 0.425550
\(804\) 2.58257e6 0.140901
\(805\) 5.52808e6 0.300666
\(806\) 1.33686e7 0.724852
\(807\) 1.20206e7 0.649744
\(808\) 169813. 0.00915044
\(809\) 3.67103e7 1.97205 0.986023 0.166607i \(-0.0532811\pi\)
0.986023 + 0.166607i \(0.0532811\pi\)
\(810\) 656100. 0.0351364
\(811\) 2.46123e7 1.31401 0.657006 0.753885i \(-0.271823\pi\)
0.657006 + 0.753885i \(0.271823\pi\)
\(812\) −132053. −0.00702843
\(813\) 1.29530e7 0.687298
\(814\) 8.53416e6 0.451440
\(815\) 198996. 0.0104942
\(816\) 3.23711e6 0.170189
\(817\) −8.01583e6 −0.420139
\(818\) 1.77504e7 0.927524
\(819\) 2.48027e6 0.129208
\(820\) 6.05935e6 0.314696
\(821\) 1.19995e7 0.621305 0.310653 0.950523i \(-0.399452\pi\)
0.310653 + 0.950523i \(0.399452\pi\)
\(822\) −2.72411e6 −0.140619
\(823\) 2.80911e7 1.44567 0.722834 0.691022i \(-0.242839\pi\)
0.722834 + 0.691022i \(0.242839\pi\)
\(824\) 2.09416e6 0.107446
\(825\) 3.33111e6 0.170394
\(826\) 405927. 0.0207013
\(827\) 1.74273e7 0.886066 0.443033 0.896505i \(-0.353902\pi\)
0.443033 + 0.896505i \(0.353902\pi\)
\(828\) 6.18942e6 0.313743
\(829\) 1.76895e7 0.893981 0.446990 0.894539i \(-0.352496\pi\)
0.446990 + 0.894539i \(0.352496\pi\)
\(830\) 587328. 0.0295928
\(831\) 1.01836e7 0.511563
\(832\) 2.70885e6 0.135668
\(833\) 2.06018e7 1.02871
\(834\) 2.86175e6 0.142468
\(835\) 1.02031e7 0.506425
\(836\) −3.42053e6 −0.169269
\(837\) −3.68409e6 −0.181767
\(838\) 2.39958e7 1.18039
\(839\) −3.44796e7 −1.69106 −0.845528 0.533931i \(-0.820714\pi\)
−0.845528 + 0.533931i \(0.820714\pi\)
\(840\) −666733. −0.0326027
\(841\) −2.04794e7 −0.998451
\(842\) −9.36082e6 −0.455023
\(843\) −1.16071e7 −0.562541
\(844\) −1.70248e7 −0.822669
\(845\) 1.65193e6 0.0795882
\(846\) 3.96263e6 0.190352
\(847\) 8.78082e6 0.420559
\(848\) 2.45780e6 0.117370
\(849\) −1.08819e7 −0.518124
\(850\) −3.51249e6 −0.166751
\(851\) −1.72060e7 −0.814433
\(852\) −6.22804e6 −0.293936
\(853\) 2.17229e7 1.02222 0.511110 0.859515i \(-0.329234\pi\)
0.511110 + 0.859515i \(0.329234\pi\)
\(854\) 171573. 0.00805014
\(855\) 731025. 0.0341993
\(856\) −7.65399e6 −0.357029
\(857\) 1.25946e7 0.585778 0.292889 0.956147i \(-0.405383\pi\)
0.292889 + 0.956147i \(0.405383\pi\)
\(858\) 1.40992e7 0.653846
\(859\) −2.38444e7 −1.10256 −0.551281 0.834320i \(-0.685861\pi\)
−0.551281 + 0.834320i \(0.685861\pi\)
\(860\) −8.88181e6 −0.409501
\(861\) −6.31245e6 −0.290195
\(862\) −1.27429e7 −0.584115
\(863\) −3.48578e7 −1.59321 −0.796604 0.604501i \(-0.793373\pi\)
−0.796604 + 0.604501i \(0.793373\pi\)
\(864\) −746496. −0.0340207
\(865\) 1.40772e7 0.639699
\(866\) −1.50601e7 −0.682392
\(867\) −4.98738e6 −0.225333
\(868\) 3.74379e6 0.168660
\(869\) −6.45668e7 −2.90041
\(870\) 160429. 0.00718594
\(871\) −1.18608e7 −0.529748
\(872\) 6.90253e6 0.307409
\(873\) 1.17688e7 0.522633
\(874\) 6.89623e6 0.305375
\(875\) 723451. 0.0319440
\(876\) 1.89076e6 0.0832483
\(877\) −1.07520e7 −0.472052 −0.236026 0.971747i \(-0.575845\pi\)
−0.236026 + 0.971747i \(0.575845\pi\)
\(878\) −1.49451e7 −0.654277
\(879\) −3.59355e6 −0.156874
\(880\) −3.79006e6 −0.164983
\(881\) −2.91868e7 −1.26691 −0.633457 0.773778i \(-0.718365\pi\)
−0.633457 + 0.773778i \(0.718365\pi\)
\(882\) −4.75089e6 −0.205638
\(883\) 1.27529e6 0.0550436 0.0275218 0.999621i \(-0.491238\pi\)
0.0275218 + 0.999621i \(0.491238\pi\)
\(884\) −1.48669e7 −0.639865
\(885\) −493152. −0.0211652
\(886\) 6.51100e6 0.278653
\(887\) 2.02105e6 0.0862517 0.0431258 0.999070i \(-0.486268\pi\)
0.0431258 + 0.999070i \(0.486268\pi\)
\(888\) 2.07519e6 0.0883130
\(889\) −7.51616e6 −0.318964
\(890\) 6.65080e6 0.281448
\(891\) −3.88541e6 −0.163962
\(892\) −5.42929e6 −0.228471
\(893\) 4.41516e6 0.185275
\(894\) −1.76502e7 −0.738595
\(895\) −1.76470e7 −0.736399
\(896\) 758594. 0.0315674
\(897\) −2.84257e7 −1.17959
\(898\) 2.95001e6 0.122077
\(899\) −900828. −0.0371743
\(900\) 810000. 0.0333333
\(901\) −1.34890e7 −0.553566
\(902\) −3.58833e7 −1.46851
\(903\) 9.25280e6 0.377619
\(904\) 1.66276e7 0.676720
\(905\) 716263. 0.0290704
\(906\) 7.56086e6 0.306021
\(907\) 1.65529e6 0.0668122 0.0334061 0.999442i \(-0.489365\pi\)
0.0334061 + 0.999442i \(0.489365\pi\)
\(908\) −9.00937e6 −0.362643
\(909\) 214919. 0.00862712
\(910\) 3.06206e6 0.122577
\(911\) −3.22406e7 −1.28708 −0.643542 0.765411i \(-0.722536\pi\)
−0.643542 + 0.765411i \(0.722536\pi\)
\(912\) −831744. −0.0331133
\(913\) −3.47814e6 −0.138093
\(914\) −3.57452e6 −0.141531
\(915\) −208440. −0.00823054
\(916\) −2.28965e6 −0.0901633
\(917\) 1.20454e7 0.473040
\(918\) 4.09697e6 0.160456
\(919\) 4.54273e7 1.77431 0.887153 0.461475i \(-0.152680\pi\)
0.887153 + 0.461475i \(0.152680\pi\)
\(920\) 7.64126e6 0.297643
\(921\) −1.43419e7 −0.557133
\(922\) −2.18635e7 −0.847017
\(923\) 2.86031e7 1.10512
\(924\) 3.94837e6 0.152138
\(925\) −2.25172e6 −0.0865287
\(926\) −1.62393e7 −0.622359
\(927\) 2.65042e6 0.101301
\(928\) −182532. −0.00695776
\(929\) −1.91920e7 −0.729593 −0.364796 0.931087i \(-0.618861\pi\)
−0.364796 + 0.931087i \(0.618861\pi\)
\(930\) −4.54826e6 −0.172440
\(931\) −5.29343e6 −0.200153
\(932\) −2.39540e6 −0.0903313
\(933\) 8.05525e6 0.302953
\(934\) 2.21280e7 0.829995
\(935\) 2.08009e7 0.778130
\(936\) 3.42838e6 0.127909
\(937\) −1.24587e7 −0.463578 −0.231789 0.972766i \(-0.574458\pi\)
−0.231789 + 0.972766i \(0.574458\pi\)
\(938\) −3.32154e6 −0.123263
\(939\) −5.33956e6 −0.197625
\(940\) 4.89214e6 0.180584
\(941\) 1.53659e7 0.565699 0.282849 0.959164i \(-0.408720\pi\)
0.282849 + 0.959164i \(0.408720\pi\)
\(942\) −496777. −0.0182404
\(943\) 7.23454e7 2.64930
\(944\) 561098. 0.0204931
\(945\) −843834. −0.0307381
\(946\) 5.25978e7 1.91091
\(947\) 1.55748e7 0.564349 0.282175 0.959363i \(-0.408944\pi\)
0.282175 + 0.959363i \(0.408944\pi\)
\(948\) −1.57002e7 −0.567394
\(949\) −8.68356e6 −0.312991
\(950\) 902500. 0.0324443
\(951\) −3.09992e7 −1.11147
\(952\) −4.16336e6 −0.148885
\(953\) 3.55359e7 1.26746 0.633731 0.773554i \(-0.281523\pi\)
0.633731 + 0.773554i \(0.281523\pi\)
\(954\) 3.11065e6 0.110657
\(955\) 3.42808e6 0.121630
\(956\) −1.41046e7 −0.499133
\(957\) −950054. −0.0335327
\(958\) 4.31131e6 0.151773
\(959\) 3.50357e6 0.123017
\(960\) −921600. −0.0322749
\(961\) −3.09011e6 −0.107936
\(962\) −9.53057e6 −0.332033
\(963\) −9.68709e6 −0.336610
\(964\) −1.42267e7 −0.493072
\(965\) 2.32726e7 0.804499
\(966\) −7.96043e6 −0.274469
\(967\) −2.87843e7 −0.989895 −0.494948 0.868923i \(-0.664813\pi\)
−0.494948 + 0.868923i \(0.664813\pi\)
\(968\) 1.21374e7 0.416330
\(969\) 4.56483e6 0.156176
\(970\) 1.45294e7 0.495813
\(971\) −2.81369e6 −0.0957697 −0.0478849 0.998853i \(-0.515248\pi\)
−0.0478849 + 0.998853i \(0.515248\pi\)
\(972\) −944784. −0.0320750
\(973\) −3.68060e6 −0.124634
\(974\) −2.20582e7 −0.745028
\(975\) −3.72004e6 −0.125324
\(976\) 237159. 0.00796919
\(977\) 3.57564e7 1.19844 0.599222 0.800583i \(-0.295477\pi\)
0.599222 + 0.800583i \(0.295477\pi\)
\(978\) −286554. −0.00957987
\(979\) −3.93859e7 −1.31336
\(980\) −5.86529e6 −0.195085
\(981\) 8.73601e6 0.289828
\(982\) −3.67095e7 −1.21479
\(983\) −2.56559e7 −0.846845 −0.423422 0.905932i \(-0.639171\pi\)
−0.423422 + 0.905932i \(0.639171\pi\)
\(984\) −8.72546e6 −0.287277
\(985\) −45322.7 −0.00148842
\(986\) 1.00178e6 0.0328157
\(987\) −5.09649e6 −0.166524
\(988\) 3.81990e6 0.124497
\(989\) −1.06044e8 −3.44743
\(990\) −4.79680e6 −0.155548
\(991\) −1.79995e7 −0.582205 −0.291103 0.956692i \(-0.594022\pi\)
−0.291103 + 0.956692i \(0.594022\pi\)
\(992\) 5.17490e6 0.166964
\(993\) −2.15270e7 −0.692804
\(994\) 8.01010e6 0.257142
\(995\) 1.51302e7 0.484492
\(996\) −845753. −0.0270144
\(997\) 5.65443e7 1.80157 0.900785 0.434266i \(-0.142992\pi\)
0.900785 + 0.434266i \(0.142992\pi\)
\(998\) −3.36463e7 −1.06933
\(999\) 2.62641e6 0.0832623
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 570.6.a.o.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.6.a.o.1.3 5 1.1 even 1 trivial