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Properties

Label 360.6.a.h.1.1
Level $360$
Weight $6$
Character 360.1
Self dual yes
Analytic conductor $57.738$
Analytic rank $0$
Dimension $1$
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] = [360,6,Mod(1,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("360.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 360.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: \(57.7381751327\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 120)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 360.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+25.0000 q^{5} +108.000 q^{7} +O(q^{10})\) \(q+25.0000 q^{5} +108.000 q^{7} +8.00000 q^{11} +162.000 q^{13} +714.000 q^{17} -532.000 q^{19} +4584.00 q^{23} +625.000 q^{25} -938.000 q^{29} -8360.00 q^{31} +2700.00 q^{35} +1090.00 q^{37} +11238.0 q^{41} -7692.00 q^{43} +13640.0 q^{47} -5143.00 q^{49} -19050.0 q^{53} +200.000 q^{55} +18936.0 q^{59} -1978.00 q^{61} +4050.00 q^{65} +44212.0 q^{67} +59744.0 q^{71} +56994.0 q^{73} +864.000 q^{77} -15128.0 q^{79} +21996.0 q^{83} +17850.0 q^{85} -14066.0 q^{89} +17496.0 q^{91} -13300.0 q^{95} +75938.0 q^{97} +O(q^{100})\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) 108.000 0.833065 0.416532 − 0.909121i \(-0.363245\pi\)
0.416532 + 0.909121i \(0.363245\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 8.00000 0.0199346 0.00996732 − 0.999950i \(-0.496827\pi\)
0.00996732 + 0.999950i \(0.496827\pi\)
\(12\) 0 0
\(13\) 162.000 0.265862 0.132931 − 0.991125i \(-0.457561\pi\)
0.132931 + 0.991125i \(0.457561\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 714.000 0.599206 0.299603 − 0.954064i \(-0.403146\pi\)
0.299603 + 0.954064i \(0.403146\pi\)
\(18\) 0 0
\(19\) −532.000 −0.338086 −0.169043 − 0.985609i \(-0.554068\pi\)
−0.169043 + 0.985609i \(0.554068\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4584.00 1.80686 0.903431 − 0.428733i \(-0.141040\pi\)
0.903431 + 0.428733i \(0.141040\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −938.000 −0.207113 −0.103557 − 0.994624i \(-0.533022\pi\)
−0.103557 + 0.994624i \(0.533022\pi\)
\(30\) 0 0
\(31\) −8360.00 −1.56244 −0.781218 − 0.624259i \(-0.785401\pi\)
−0.781218 + 0.624259i \(0.785401\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2700.00 0.372558
\(36\) 0 0
\(37\) 1090.00 0.130895 0.0654474 − 0.997856i \(-0.479153\pi\)
0.0654474 + 0.997856i \(0.479153\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 11238.0 1.04407 0.522035 − 0.852924i \(-0.325173\pi\)
0.522035 + 0.852924i \(0.325173\pi\)
\(42\) 0 0
\(43\) −7692.00 −0.634407 −0.317204 − 0.948357i \(-0.602744\pi\)
−0.317204 + 0.948357i \(0.602744\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 13640.0 0.900678 0.450339 − 0.892858i \(-0.351303\pi\)
0.450339 + 0.892858i \(0.351303\pi\)
\(48\) 0 0
\(49\) −5143.00 −0.306003
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −19050.0 −0.931548 −0.465774 − 0.884904i \(-0.654224\pi\)
−0.465774 + 0.884904i \(0.654224\pi\)
\(54\) 0 0
\(55\) 200.000 0.00891504
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 18936.0 0.708204 0.354102 − 0.935207i \(-0.384787\pi\)
0.354102 + 0.935207i \(0.384787\pi\)
\(60\) 0 0
\(61\) −1978.00 −0.0680615 −0.0340308 − 0.999421i \(-0.510834\pi\)
−0.0340308 + 0.999421i \(0.510834\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 4050.00 0.118897
\(66\) 0 0
\(67\) 44212.0 1.20324 0.601621 − 0.798782i \(-0.294522\pi\)
0.601621 + 0.798782i \(0.294522\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 59744.0 1.40653 0.703264 − 0.710929i \(-0.251725\pi\)
0.703264 + 0.710929i \(0.251725\pi\)
\(72\) 0 0
\(73\) 56994.0 1.25176 0.625881 − 0.779918i \(-0.284739\pi\)
0.625881 + 0.779918i \(0.284739\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 864.000 0.0166068
\(78\) 0 0
\(79\) −15128.0 −0.272718 −0.136359 − 0.990659i \(-0.543540\pi\)
−0.136359 + 0.990659i \(0.543540\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 21996.0 0.350468 0.175234 − 0.984527i \(-0.443932\pi\)
0.175234 + 0.984527i \(0.443932\pi\)
\(84\) 0 0
\(85\) 17850.0 0.267973
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −14066.0 −0.188233 −0.0941165 − 0.995561i \(-0.530003\pi\)
−0.0941165 + 0.995561i \(0.530003\pi\)
\(90\) 0 0
\(91\) 17496.0 0.221480
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −13300.0 −0.151197
\(96\) 0 0
\(97\) 75938.0 0.819464 0.409732 − 0.912206i \(-0.365622\pi\)
0.409732 + 0.912206i \(0.365622\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3810.00 −0.0371639 −0.0185820 − 0.999827i \(-0.505915\pi\)
−0.0185820 + 0.999827i \(0.505915\pi\)
\(102\) 0 0
\(103\) 96828.0 0.899307 0.449653 − 0.893203i \(-0.351547\pi\)
0.449653 + 0.893203i \(0.351547\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 80276.0 0.677839 0.338919 − 0.940815i \(-0.389939\pi\)
0.338919 + 0.940815i \(0.389939\pi\)
\(108\) 0 0
\(109\) 157734. 1.27163 0.635813 − 0.771844i \(-0.280665\pi\)
0.635813 + 0.771844i \(0.280665\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −65022.0 −0.479032 −0.239516 − 0.970892i \(-0.576989\pi\)
−0.239516 + 0.970892i \(0.576989\pi\)
\(114\) 0 0
\(115\) 114600. 0.808053
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 77112.0 0.499177
\(120\) 0 0
\(121\) −160987. −0.999603
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) −64508.0 −0.354899 −0.177449 − 0.984130i \(-0.556785\pi\)
−0.177449 + 0.984130i \(0.556785\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 254968. 1.29810 0.649049 − 0.760747i \(-0.275167\pi\)
0.649049 + 0.760747i \(0.275167\pi\)
\(132\) 0 0
\(133\) −57456.0 −0.281648
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 391850. 1.78369 0.891843 − 0.452345i \(-0.149412\pi\)
0.891843 + 0.452345i \(0.149412\pi\)
\(138\) 0 0
\(139\) −102596. −0.450395 −0.225197 − 0.974313i \(-0.572303\pi\)
−0.225197 + 0.974313i \(0.572303\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1296.00 0.00529987
\(144\) 0 0
\(145\) −23450.0 −0.0926239
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 326102. 1.20334 0.601669 − 0.798745i \(-0.294503\pi\)
0.601669 + 0.798745i \(0.294503\pi\)
\(150\) 0 0
\(151\) 111496. 0.397939 0.198970 − 0.980006i \(-0.436240\pi\)
0.198970 + 0.980006i \(0.436240\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −209000. −0.698742
\(156\) 0 0
\(157\) −488574. −1.58191 −0.790954 − 0.611876i \(-0.790415\pi\)
−0.790954 + 0.611876i \(0.790415\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 495072. 1.50523
\(162\) 0 0
\(163\) 612196. 1.80477 0.902384 − 0.430932i \(-0.141815\pi\)
0.902384 + 0.430932i \(0.141815\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 334168. 0.927201 0.463600 − 0.886044i \(-0.346557\pi\)
0.463600 + 0.886044i \(0.346557\pi\)
\(168\) 0 0
\(169\) −345049. −0.929317
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −616162. −1.56524 −0.782618 − 0.622503i \(-0.786116\pi\)
−0.782618 + 0.622503i \(0.786116\pi\)
\(174\) 0 0
\(175\) 67500.0 0.166613
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 257952. 0.601736 0.300868 − 0.953666i \(-0.402724\pi\)
0.300868 + 0.953666i \(0.402724\pi\)
\(180\) 0 0
\(181\) −683074. −1.54978 −0.774892 − 0.632093i \(-0.782196\pi\)
−0.774892 + 0.632093i \(0.782196\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 27250.0 0.0585379
\(186\) 0 0
\(187\) 5712.00 0.0119449
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −283272. −0.561850 −0.280925 − 0.959730i \(-0.590641\pi\)
−0.280925 + 0.959730i \(0.590641\pi\)
\(192\) 0 0
\(193\) 11434.0 0.0220956 0.0110478 − 0.999939i \(-0.496483\pi\)
0.0110478 + 0.999939i \(0.496483\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −829354. −1.52256 −0.761280 − 0.648423i \(-0.775429\pi\)
−0.761280 + 0.648423i \(0.775429\pi\)
\(198\) 0 0
\(199\) 854232. 1.52913 0.764563 − 0.644549i \(-0.222955\pi\)
0.764563 + 0.644549i \(0.222955\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −101304. −0.172539
\(204\) 0 0
\(205\) 280950. 0.466922
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4256.00 −0.00673963
\(210\) 0 0
\(211\) 128004. 0.197933 0.0989663 − 0.995091i \(-0.468446\pi\)
0.0989663 + 0.995091i \(0.468446\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −192300. −0.283716
\(216\) 0 0
\(217\) −902880. −1.30161
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 115668. 0.159306
\(222\) 0 0
\(223\) 524276. 0.705989 0.352994 − 0.935625i \(-0.385163\pi\)
0.352994 + 0.935625i \(0.385163\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −94396.0 −0.121588 −0.0607938 − 0.998150i \(-0.519363\pi\)
−0.0607938 + 0.998150i \(0.519363\pi\)
\(228\) 0 0
\(229\) 894086. 1.12665 0.563327 − 0.826234i \(-0.309521\pi\)
0.563327 + 0.826234i \(0.309521\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −857566. −1.03485 −0.517425 − 0.855728i \(-0.673110\pi\)
−0.517425 + 0.855728i \(0.673110\pi\)
\(234\) 0 0
\(235\) 341000. 0.402796
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −385320. −0.436342 −0.218171 − 0.975911i \(-0.570009\pi\)
−0.218171 + 0.975911i \(0.570009\pi\)
\(240\) 0 0
\(241\) −1.65011e6 −1.83008 −0.915040 − 0.403362i \(-0.867842\pi\)
−0.915040 + 0.403362i \(0.867842\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −128575. −0.136849
\(246\) 0 0
\(247\) −86184.0 −0.0898844
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −225488. −0.225912 −0.112956 − 0.993600i \(-0.536032\pi\)
−0.112956 + 0.993600i \(0.536032\pi\)
\(252\) 0 0
\(253\) 36672.0 0.0360191
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.08121e6 −1.02112 −0.510562 − 0.859841i \(-0.670563\pi\)
−0.510562 + 0.859841i \(0.670563\pi\)
\(258\) 0 0
\(259\) 117720. 0.109044
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.32943e6 −1.18516 −0.592580 − 0.805512i \(-0.701890\pi\)
−0.592580 + 0.805512i \(0.701890\pi\)
\(264\) 0 0
\(265\) −476250. −0.416601
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.61735e6 −1.36278 −0.681388 − 0.731923i \(-0.738623\pi\)
−0.681388 + 0.731923i \(0.738623\pi\)
\(270\) 0 0
\(271\) −15216.0 −0.0125857 −0.00629285 − 0.999980i \(-0.502003\pi\)
−0.00629285 + 0.999980i \(0.502003\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 5000.00 0.00398693
\(276\) 0 0
\(277\) 2.28215e6 1.78708 0.893540 − 0.448984i \(-0.148214\pi\)
0.893540 + 0.448984i \(0.148214\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 847598. 0.640360 0.320180 − 0.947357i \(-0.396257\pi\)
0.320180 + 0.947357i \(0.396257\pi\)
\(282\) 0 0
\(283\) −1.24978e6 −0.927614 −0.463807 − 0.885936i \(-0.653517\pi\)
−0.463807 + 0.885936i \(0.653517\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.21370e6 0.869777
\(288\) 0 0
\(289\) −910061. −0.640953
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.86190e6 −1.26703 −0.633515 − 0.773730i \(-0.718388\pi\)
−0.633515 + 0.773730i \(0.718388\pi\)
\(294\) 0 0
\(295\) 473400. 0.316718
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 742608. 0.480376
\(300\) 0 0
\(301\) −830736. −0.528502
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −49450.0 −0.0304380
\(306\) 0 0
\(307\) −2.60794e6 −1.57925 −0.789626 − 0.613588i \(-0.789726\pi\)
−0.789626 + 0.613588i \(0.789726\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.61363e6 −0.946027 −0.473013 − 0.881055i \(-0.656834\pi\)
−0.473013 + 0.881055i \(0.656834\pi\)
\(312\) 0 0
\(313\) −2.27469e6 −1.31238 −0.656192 − 0.754594i \(-0.727834\pi\)
−0.656192 + 0.754594i \(0.727834\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.26512e6 −0.707106 −0.353553 − 0.935415i \(-0.615027\pi\)
−0.353553 + 0.935415i \(0.615027\pi\)
\(318\) 0 0
\(319\) −7504.00 −0.00412873
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −379848. −0.202583
\(324\) 0 0
\(325\) 101250. 0.0531724
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.47312e6 0.750323
\(330\) 0 0
\(331\) 335876. 0.168504 0.0842518 − 0.996444i \(-0.473150\pi\)
0.0842518 + 0.996444i \(0.473150\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.10530e6 0.538106
\(336\) 0 0
\(337\) 1.62310e6 0.778520 0.389260 − 0.921128i \(-0.372731\pi\)
0.389260 + 0.921128i \(0.372731\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −66880.0 −0.0311466
\(342\) 0 0
\(343\) −2.37060e6 −1.08799
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.48715e6 0.663026 0.331513 − 0.943451i \(-0.392441\pi\)
0.331513 + 0.943451i \(0.392441\pi\)
\(348\) 0 0
\(349\) 1.57924e6 0.694039 0.347020 − 0.937858i \(-0.387194\pi\)
0.347020 + 0.937858i \(0.387194\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.54855e6 0.661439 0.330719 − 0.943729i \(-0.392709\pi\)
0.330719 + 0.943729i \(0.392709\pi\)
\(354\) 0 0
\(355\) 1.49360e6 0.629019
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.33314e6 1.36495 0.682477 − 0.730907i \(-0.260903\pi\)
0.682477 + 0.730907i \(0.260903\pi\)
\(360\) 0 0
\(361\) −2.19308e6 −0.885698
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.42485e6 0.559805
\(366\) 0 0
\(367\) −919916. −0.356519 −0.178260 − 0.983983i \(-0.557047\pi\)
−0.178260 + 0.983983i \(0.557047\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2.05740e6 −0.776040
\(372\) 0 0
\(373\) −1.89172e6 −0.704019 −0.352009 − 0.935996i \(-0.614502\pi\)
−0.352009 + 0.935996i \(0.614502\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −151956. −0.0550636
\(378\) 0 0
\(379\) 628636. 0.224803 0.112401 − 0.993663i \(-0.464146\pi\)
0.112401 + 0.993663i \(0.464146\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5.28290e6 1.84025 0.920123 − 0.391630i \(-0.128089\pi\)
0.920123 + 0.391630i \(0.128089\pi\)
\(384\) 0 0
\(385\) 21600.0 0.00742680
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.93956e6 −0.984937 −0.492469 − 0.870330i \(-0.663905\pi\)
−0.492469 + 0.870330i \(0.663905\pi\)
\(390\) 0 0
\(391\) 3.27298e6 1.08268
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −378200. −0.121963
\(396\) 0 0
\(397\) 898826. 0.286220 0.143110 − 0.989707i \(-0.454290\pi\)
0.143110 + 0.989707i \(0.454290\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.94556e6 −0.604205 −0.302102 − 0.953275i \(-0.597688\pi\)
−0.302102 + 0.953275i \(0.597688\pi\)
\(402\) 0 0
\(403\) −1.35432e6 −0.415393
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 8720.00 0.00260934
\(408\) 0 0
\(409\) 4.60313e6 1.36065 0.680323 − 0.732913i \(-0.261840\pi\)
0.680323 + 0.732913i \(0.261840\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.04509e6 0.589979
\(414\) 0 0
\(415\) 549900. 0.156734
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −76056.0 −0.0211640 −0.0105820 − 0.999944i \(-0.503368\pi\)
−0.0105820 + 0.999944i \(0.503368\pi\)
\(420\) 0 0
\(421\) 4.31389e6 1.18622 0.593109 − 0.805122i \(-0.297900\pi\)
0.593109 + 0.805122i \(0.297900\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 446250. 0.119841
\(426\) 0 0
\(427\) −213624. −0.0566996
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6.68498e6 −1.73343 −0.866716 − 0.498802i \(-0.833773\pi\)
−0.866716 + 0.498802i \(0.833773\pi\)
\(432\) 0 0
\(433\) −4.27594e6 −1.09600 −0.548002 − 0.836477i \(-0.684611\pi\)
−0.548002 + 0.836477i \(0.684611\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.43869e6 −0.610875
\(438\) 0 0
\(439\) 7.08594e6 1.75484 0.877418 − 0.479727i \(-0.159264\pi\)
0.877418 + 0.479727i \(0.159264\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4.49952e6 −1.08932 −0.544662 − 0.838656i \(-0.683342\pi\)
−0.544662 + 0.838656i \(0.683342\pi\)
\(444\) 0 0
\(445\) −351650. −0.0841803
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.02484e6 1.17627 0.588134 − 0.808764i \(-0.299863\pi\)
0.588134 + 0.808764i \(0.299863\pi\)
\(450\) 0 0
\(451\) 89904.0 0.0208131
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 437400. 0.0990490
\(456\) 0 0
\(457\) 1.67129e6 0.374336 0.187168 − 0.982328i \(-0.440069\pi\)
0.187168 + 0.982328i \(0.440069\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 8.69406e6 1.90533 0.952665 − 0.304021i \(-0.0983292\pi\)
0.952665 + 0.304021i \(0.0983292\pi\)
\(462\) 0 0
\(463\) −6.57125e6 −1.42461 −0.712304 − 0.701871i \(-0.752348\pi\)
−0.712304 + 0.701871i \(0.752348\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −824596. −0.174964 −0.0874821 − 0.996166i \(-0.527882\pi\)
−0.0874821 + 0.996166i \(0.527882\pi\)
\(468\) 0 0
\(469\) 4.77490e6 1.00238
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −61536.0 −0.0126467
\(474\) 0 0
\(475\) −332500. −0.0676173
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6.28593e6 1.25179 0.625894 − 0.779908i \(-0.284734\pi\)
0.625894 + 0.779908i \(0.284734\pi\)
\(480\) 0 0
\(481\) 176580. 0.0348000
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.89845e6 0.366475
\(486\) 0 0
\(487\) 4.93824e6 0.943518 0.471759 − 0.881728i \(-0.343619\pi\)
0.471759 + 0.881728i \(0.343619\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −8.84554e6 −1.65585 −0.827924 − 0.560840i \(-0.810478\pi\)
−0.827924 + 0.560840i \(0.810478\pi\)
\(492\) 0 0
\(493\) −669732. −0.124103
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.45235e6 1.17173
\(498\) 0 0
\(499\) 1.22350e6 0.219965 0.109982 − 0.993934i \(-0.464921\pi\)
0.109982 + 0.993934i \(0.464921\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.64710e6 0.818960 0.409480 − 0.912319i \(-0.365710\pi\)
0.409480 + 0.912319i \(0.365710\pi\)
\(504\) 0 0
\(505\) −95250.0 −0.0166202
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4.09500e6 0.700582 0.350291 − 0.936641i \(-0.386083\pi\)
0.350291 + 0.936641i \(0.386083\pi\)
\(510\) 0 0
\(511\) 6.15535e6 1.04280
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.42070e6 0.402182
\(516\) 0 0
\(517\) 109120. 0.0179547
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 4.10389e6 0.662370 0.331185 − 0.943566i \(-0.392551\pi\)
0.331185 + 0.943566i \(0.392551\pi\)
\(522\) 0 0
\(523\) −7.21508e6 −1.15342 −0.576709 − 0.816950i \(-0.695663\pi\)
−0.576709 + 0.816950i \(0.695663\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.96904e6 −0.936220
\(528\) 0 0
\(529\) 1.45767e7 2.26475
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.82056e6 0.277579
\(534\) 0 0
\(535\) 2.00690e6 0.303139
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −41144.0 −0.00610007
\(540\) 0 0
\(541\) −3.86937e6 −0.568391 −0.284195 − 0.958766i \(-0.591726\pi\)
−0.284195 + 0.958766i \(0.591726\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3.94335e6 0.568688
\(546\) 0 0
\(547\) −9.81378e6 −1.40239 −0.701194 − 0.712971i \(-0.747349\pi\)
−0.701194 + 0.712971i \(0.747349\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 499016. 0.0700222
\(552\) 0 0
\(553\) −1.63382e6 −0.227192
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.33130e6 −0.181818 −0.0909091 − 0.995859i \(-0.528977\pi\)
−0.0909091 + 0.995859i \(0.528977\pi\)
\(558\) 0 0
\(559\) −1.24610e6 −0.168665
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 8.83100e6 1.17419 0.587095 − 0.809518i \(-0.300271\pi\)
0.587095 + 0.809518i \(0.300271\pi\)
\(564\) 0 0
\(565\) −1.62555e6 −0.214229
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.17054e6 0.669507 0.334754 − 0.942306i \(-0.391347\pi\)
0.334754 + 0.942306i \(0.391347\pi\)
\(570\) 0 0
\(571\) −1.39730e7 −1.79349 −0.896746 − 0.442545i \(-0.854076\pi\)
−0.896746 + 0.442545i \(0.854076\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.86500e6 0.361372
\(576\) 0 0
\(577\) 5.36583e6 0.670961 0.335480 − 0.942047i \(-0.391101\pi\)
0.335480 + 0.942047i \(0.391101\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2.37557e6 0.291963
\(582\) 0 0
\(583\) −152400. −0.0185701
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.19604e6 −0.143269 −0.0716344 − 0.997431i \(-0.522821\pi\)
−0.0716344 + 0.997431i \(0.522821\pi\)
\(588\) 0 0
\(589\) 4.44752e6 0.528238
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −9.44657e6 −1.10316 −0.551579 − 0.834123i \(-0.685974\pi\)
−0.551579 + 0.834123i \(0.685974\pi\)
\(594\) 0 0
\(595\) 1.92780e6 0.223239
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −200296. −0.0228089 −0.0114045 − 0.999935i \(-0.503630\pi\)
−0.0114045 + 0.999935i \(0.503630\pi\)
\(600\) 0 0
\(601\) 1.72481e6 0.194785 0.0973924 − 0.995246i \(-0.468950\pi\)
0.0973924 + 0.995246i \(0.468950\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4.02468e6 −0.447036
\(606\) 0 0
\(607\) −8.67213e6 −0.955332 −0.477666 − 0.878542i \(-0.658517\pi\)
−0.477666 + 0.878542i \(0.658517\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.20968e6 0.239456
\(612\) 0 0
\(613\) −1.66852e7 −1.79342 −0.896709 − 0.442621i \(-0.854049\pi\)
−0.896709 + 0.442621i \(0.854049\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.88635e6 −0.199485 −0.0997423 − 0.995013i \(-0.531802\pi\)
−0.0997423 + 0.995013i \(0.531802\pi\)
\(618\) 0 0
\(619\) 2.87390e6 0.301471 0.150735 − 0.988574i \(-0.451836\pi\)
0.150735 + 0.988574i \(0.451836\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.51913e6 −0.156810
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 778260. 0.0784329
\(630\) 0 0
\(631\) −9.02440e6 −0.902287 −0.451144 − 0.892451i \(-0.648984\pi\)
−0.451144 + 0.892451i \(0.648984\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.61270e6 −0.158715
\(636\) 0 0
\(637\) −833166. −0.0813548
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.41199e7 −1.35734 −0.678669 − 0.734445i \(-0.737443\pi\)
−0.678669 + 0.734445i \(0.737443\pi\)
\(642\) 0 0
\(643\) −5.87280e6 −0.560167 −0.280083 − 0.959976i \(-0.590362\pi\)
−0.280083 + 0.959976i \(0.590362\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2.15131e6 −0.202042 −0.101021 − 0.994884i \(-0.532211\pi\)
−0.101021 + 0.994884i \(0.532211\pi\)
\(648\) 0 0
\(649\) 151488. 0.0141178
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8.66951e6 −0.795630 −0.397815 − 0.917466i \(-0.630231\pi\)
−0.397815 + 0.917466i \(0.630231\pi\)
\(654\) 0 0
\(655\) 6.37420e6 0.580527
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.19684e6 −0.107355 −0.0536775 − 0.998558i \(-0.517094\pi\)
−0.0536775 + 0.998558i \(0.517094\pi\)
\(660\) 0 0
\(661\) −1.53050e6 −0.136248 −0.0681238 − 0.997677i \(-0.521701\pi\)
−0.0681238 + 0.997677i \(0.521701\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.43640e6 −0.125957
\(666\) 0 0
\(667\) −4.29979e6 −0.374225
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −15824.0 −0.00135678
\(672\) 0 0
\(673\) 9.79465e6 0.833588 0.416794 − 0.909001i \(-0.363154\pi\)
0.416794 + 0.909001i \(0.363154\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.72991e6 0.145061 0.0725307 − 0.997366i \(-0.476892\pi\)
0.0725307 + 0.997366i \(0.476892\pi\)
\(678\) 0 0
\(679\) 8.20130e6 0.682666
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.83465e7 −1.50488 −0.752438 − 0.658663i \(-0.771122\pi\)
−0.752438 + 0.658663i \(0.771122\pi\)
\(684\) 0 0
\(685\) 9.79625e6 0.797689
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −3.08610e6 −0.247663
\(690\) 0 0
\(691\) −1.66145e7 −1.32370 −0.661852 − 0.749635i \(-0.730229\pi\)
−0.661852 + 0.749635i \(0.730229\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.56490e6 −0.201423
\(696\) 0 0
\(697\) 8.02393e6 0.625612
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 9.83372e6 0.755828 0.377914 − 0.925841i \(-0.376642\pi\)
0.377914 + 0.925841i \(0.376642\pi\)
\(702\) 0 0
\(703\) −579880. −0.0442537
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −411480. −0.0309599
\(708\) 0 0
\(709\) 1.62390e7 1.21323 0.606615 − 0.794996i \(-0.292527\pi\)
0.606615 + 0.794996i \(0.292527\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.83222e7 −2.82311
\(714\) 0 0
\(715\) 32400.0 0.00237017
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −5.79024e6 −0.417709 −0.208855 − 0.977947i \(-0.566974\pi\)
−0.208855 + 0.977947i \(0.566974\pi\)
\(720\) 0 0
\(721\) 1.04574e7 0.749181
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −586250. −0.0414226
\(726\) 0 0
\(727\) 2.41350e7 1.69360 0.846800 − 0.531911i \(-0.178526\pi\)
0.846800 + 0.531911i \(0.178526\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −5.49209e6 −0.380140
\(732\) 0 0
\(733\) −9.56034e6 −0.657224 −0.328612 − 0.944465i \(-0.606581\pi\)
−0.328612 + 0.944465i \(0.606581\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 353696. 0.0239862
\(738\) 0 0
\(739\) −1.12796e7 −0.759772 −0.379886 − 0.925033i \(-0.624037\pi\)
−0.379886 + 0.925033i \(0.624037\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 4.26632e6 0.283518 0.141759 − 0.989901i \(-0.454724\pi\)
0.141759 + 0.989901i \(0.454724\pi\)
\(744\) 0 0
\(745\) 8.15255e6 0.538149
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 8.66981e6 0.564683
\(750\) 0 0
\(751\) −693592. −0.0448750 −0.0224375 − 0.999748i \(-0.507143\pi\)
−0.0224375 + 0.999748i \(0.507143\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.78740e6 0.177964
\(756\) 0 0
\(757\) −2.88601e7 −1.83045 −0.915224 − 0.402945i \(-0.867987\pi\)
−0.915224 + 0.402945i \(0.867987\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.98319e7 −1.24137 −0.620686 − 0.784059i \(-0.713146\pi\)
−0.620686 + 0.784059i \(0.713146\pi\)
\(762\) 0 0
\(763\) 1.70353e7 1.05935
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.06763e6 0.188285
\(768\) 0 0
\(769\) −2.20619e7 −1.34532 −0.672662 − 0.739950i \(-0.734849\pi\)
−0.672662 + 0.739950i \(0.734849\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.63410e7 −0.983627 −0.491813 − 0.870701i \(-0.663666\pi\)
−0.491813 + 0.870701i \(0.663666\pi\)
\(774\) 0 0
\(775\) −5.22500e6 −0.312487
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.97862e6 −0.352986
\(780\) 0 0
\(781\) 477952. 0.0280386
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.22144e7 −0.707451
\(786\) 0 0
\(787\) −1.69147e7 −0.973479 −0.486740 − 0.873547i \(-0.661814\pi\)
−0.486740 + 0.873547i \(0.661814\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −7.02238e6 −0.399064
\(792\) 0 0
\(793\) −320436. −0.0180950
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.34548e7 0.750296 0.375148 − 0.926965i \(-0.377592\pi\)
0.375148 + 0.926965i \(0.377592\pi\)
\(798\) 0 0
\(799\) 9.73896e6 0.539692
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 455952. 0.0249534
\(804\) 0 0
\(805\) 1.23768e7 0.673161
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.34629e7 0.723215 0.361607 − 0.932330i \(-0.382228\pi\)
0.361607 + 0.932330i \(0.382228\pi\)
\(810\) 0 0
\(811\) −3.20723e7 −1.71229 −0.856146 − 0.516733i \(-0.827148\pi\)
−0.856146 + 0.516733i \(0.827148\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.53049e7 0.807117
\(816\) 0 0
\(817\) 4.09214e6 0.214484
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.41016e7 1.24793 0.623963 − 0.781454i \(-0.285522\pi\)
0.623963 + 0.781454i \(0.285522\pi\)
\(822\) 0 0
\(823\) 3.03888e7 1.56392 0.781960 − 0.623329i \(-0.214220\pi\)
0.781960 + 0.623329i \(0.214220\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.59452e7 −0.810711 −0.405356 − 0.914159i \(-0.632852\pi\)
−0.405356 + 0.914159i \(0.632852\pi\)
\(828\) 0 0
\(829\) −6.76087e6 −0.341678 −0.170839 − 0.985299i \(-0.554648\pi\)
−0.170839 + 0.985299i \(0.554648\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −3.67210e6 −0.183359
\(834\) 0 0
\(835\) 8.35420e6 0.414657
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −1.55965e7 −0.764931 −0.382466 − 0.923970i \(-0.624925\pi\)
−0.382466 + 0.923970i \(0.624925\pi\)
\(840\) 0 0
\(841\) −1.96313e7 −0.957104
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −8.62622e6 −0.415603
\(846\) 0 0
\(847\) −1.73866e7 −0.832734
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4.99656e6 0.236509
\(852\) 0 0
\(853\) −3.05784e7 −1.43894 −0.719468 − 0.694526i \(-0.755614\pi\)
−0.719468 + 0.694526i \(0.755614\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.91911e7 0.892580 0.446290 − 0.894888i \(-0.352745\pi\)
0.446290 + 0.894888i \(0.352745\pi\)
\(858\) 0 0
\(859\) 1.26255e7 0.583801 0.291900 − 0.956449i \(-0.405712\pi\)
0.291900 + 0.956449i \(0.405712\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.77531e7 0.811422 0.405711 − 0.914002i \(-0.367024\pi\)
0.405711 + 0.914002i \(0.367024\pi\)
\(864\) 0 0
\(865\) −1.54040e7 −0.699995
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −121024. −0.00543653
\(870\) 0 0
\(871\) 7.16234e6 0.319897
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.68750e6 0.0745116
\(876\) 0 0
\(877\) −1.37705e7 −0.604575 −0.302288 − 0.953217i \(-0.597750\pi\)
−0.302288 + 0.953217i \(0.597750\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.47471e7 1.07420 0.537098 − 0.843520i \(-0.319520\pi\)
0.537098 + 0.843520i \(0.319520\pi\)
\(882\) 0 0
\(883\) −1.75283e7 −0.756553 −0.378276 − 0.925693i \(-0.623483\pi\)
−0.378276 + 0.925693i \(0.623483\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.35319e6 −0.0577498 −0.0288749 − 0.999583i \(-0.509192\pi\)
−0.0288749 + 0.999583i \(0.509192\pi\)
\(888\) 0 0
\(889\) −6.96686e6 −0.295653
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −7.25648e6 −0.304507
\(894\) 0 0
\(895\) 6.44880e6 0.269105
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 7.84168e6 0.323601
\(900\) 0 0
\(901\) −1.36017e7 −0.558189
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.70768e7 −0.693085
\(906\) 0 0
\(907\) 4.25300e7 1.71663 0.858315 − 0.513123i \(-0.171511\pi\)
0.858315 + 0.513123i \(0.171511\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 4.07575e7 1.62709 0.813544 − 0.581503i \(-0.197535\pi\)
0.813544 + 0.581503i \(0.197535\pi\)
\(912\) 0 0
\(913\) 175968. 0.00698645
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.75365e7 1.08140
\(918\) 0 0
\(919\) 4.60039e7 1.79682 0.898412 − 0.439154i \(-0.144722\pi\)
0.898412 + 0.439154i \(0.144722\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 9.67853e6 0.373943
\(924\) 0 0
\(925\) 681250. 0.0261789
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.38595e7 1.66734 0.833671 − 0.552262i \(-0.186235\pi\)
0.833671 + 0.552262i \(0.186235\pi\)
\(930\) 0 0
\(931\) 2.73608e6 0.103456
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 142800. 0.00534194
\(936\) 0 0
\(937\) −4.37237e7 −1.62693 −0.813463 − 0.581617i \(-0.802420\pi\)
−0.813463 + 0.581617i \(0.802420\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.05385e7 0.387976 0.193988 − 0.981004i \(-0.437858\pi\)
0.193988 + 0.981004i \(0.437858\pi\)
\(942\) 0 0
\(943\) 5.15150e7 1.88649
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −3.60743e7 −1.30714 −0.653572 − 0.756865i \(-0.726730\pi\)
−0.653572 + 0.756865i \(0.726730\pi\)
\(948\) 0 0
\(949\) 9.23303e6 0.332796
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −1.39245e7 −0.496647 −0.248323 − 0.968677i \(-0.579880\pi\)
−0.248323 + 0.968677i \(0.579880\pi\)
\(954\) 0 0
\(955\) −7.08180e6 −0.251267
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 4.23198e7 1.48593
\(960\) 0 0
\(961\) 4.12604e7 1.44120
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 285850. 0.00988143
\(966\) 0 0
\(967\) 1.62789e7 0.559834 0.279917 − 0.960024i \(-0.409693\pi\)
0.279917 + 0.960024i \(0.409693\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −5.14320e6 −0.175059 −0.0875297 − 0.996162i \(-0.527897\pi\)
−0.0875297 + 0.996162i \(0.527897\pi\)
\(972\) 0 0
\(973\) −1.10804e7 −0.375208
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −8.74612e6 −0.293143 −0.146571 − 0.989200i \(-0.546824\pi\)
−0.146571 + 0.989200i \(0.546824\pi\)
\(978\) 0 0
\(979\) −112528. −0.00375235
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −14896.0 −0.000491684 0 −0.000245842 − 1.00000i \(-0.500078\pi\)
−0.000245842 1.00000i \(0.500078\pi\)
\(984\) 0 0
\(985\) −2.07338e7 −0.680909
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −3.52601e7 −1.14629
\(990\) 0 0
\(991\) −2.73555e7 −0.884830 −0.442415 − 0.896810i \(-0.645878\pi\)
−0.442415 + 0.896810i \(0.645878\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 2.13558e7 0.683846
\(996\) 0 0
\(997\) 3.17345e7 1.01110 0.505550 − 0.862797i \(-0.331290\pi\)
0.505550 + 0.862797i \(0.331290\pi\)
\(998\) 0 0
\(999\) 0 0
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 360.6.a.h.1.1 1
3.2 odd 2 120.6.a.b.1.1 ✓ 1
4.3 odd 2 720.6.a.n.1.1 1
12.11 even 2 240.6.a.h.1.1 1
15.2 even 4 600.6.f.g.49.2 2
15.8 even 4 600.6.f.g.49.1 2
15.14 odd 2 600.6.a.f.1.1 1
24.5 odd 2 960.6.a.ba.1.1 1
24.11 even 2 960.6.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.6.a.b.1.1 ✓ 1 3.2 odd 2
240.6.a.h.1.1 1 12.11 even 2
360.6.a.h.1.1 1 1.1 even 1 trivial
600.6.a.f.1.1 1 15.14 odd 2
600.6.f.g.49.1 2 15.8 even 4
600.6.f.g.49.2 2 15.2 even 4
720.6.a.n.1.1 1 4.3 odd 2
960.6.a.h.1.1 1 24.11 even 2
960.6.a.ba.1.1 1 24.5 odd 2