Properties

Label 320.6.a.s.1.1
Level 320
Weight 6
Character 320.1
Self dual yes
Analytic conductor 51.323
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(51.3228223402\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{10}) \)
Defining polynomial: \(x^{2} - 10\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 160)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-3.16228\) of defining polynomial
Character \(\chi\) \(=\) 320.1

$q$-expansion

\(f(q)\) \(=\) \(q-6.32456 q^{3} -25.0000 q^{5} +44.2719 q^{7} -203.000 q^{9} +O(q^{10})\) \(q-6.32456 q^{3} -25.0000 q^{5} +44.2719 q^{7} -203.000 q^{9} +720.999 q^{11} +146.000 q^{13} +158.114 q^{15} -702.000 q^{17} -2732.21 q^{19} -280.000 q^{21} -4091.99 q^{23} +625.000 q^{25} +2820.75 q^{27} +4010.00 q^{29} +4566.33 q^{31} -4560.00 q^{33} -1106.80 q^{35} +14778.0 q^{37} -923.385 q^{39} -4350.00 q^{41} -12427.8 q^{43} +5075.00 q^{45} +6014.65 q^{47} -14847.0 q^{49} +4439.84 q^{51} +18154.0 q^{53} -18025.0 q^{55} +17280.0 q^{57} +19707.3 q^{59} +42130.0 q^{61} -8987.19 q^{63} -3650.00 q^{65} -16184.5 q^{67} +25880.0 q^{69} +45448.3 q^{71} +26266.0 q^{73} -3952.85 q^{75} +31920.0 q^{77} -8677.29 q^{79} +31489.0 q^{81} +98757.9 q^{83} +17550.0 q^{85} -25361.5 q^{87} +30570.0 q^{89} +6463.70 q^{91} -28880.0 q^{93} +68305.2 q^{95} +66882.0 q^{97} -146363. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 50q^{5} - 406q^{9} + O(q^{10}) \) \( 2q - 50q^{5} - 406q^{9} + 292q^{13} - 1404q^{17} - 560q^{21} + 1250q^{25} + 8020q^{29} - 9120q^{33} + 29556q^{37} - 8700q^{41} + 10150q^{45} - 29694q^{49} + 36308q^{53} + 34560q^{57} + 84260q^{61} - 7300q^{65} + 51760q^{69} + 52532q^{73} + 63840q^{77} + 62978q^{81} + 35100q^{85} + 61140q^{89} - 57760q^{93} + 133764q^{97} + O(q^{100}) \)

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
\(3\) −6.32456 −0.405720 −0.202860 0.979208i \(-0.565024\pi\)
−0.202860 + 0.979208i \(0.565024\pi\)
\(4\) 0 0
\(5\) −25.0000 −0.447214
\(6\) 0 0
\(7\) 44.2719 0.341494 0.170747 0.985315i \(-0.445382\pi\)
0.170747 + 0.985315i \(0.445382\pi\)
\(8\) 0 0
\(9\) −203.000 −0.835391
\(10\) 0 0
\(11\) 720.999 1.79661 0.898304 0.439375i \(-0.144800\pi\)
0.898304 + 0.439375i \(0.144800\pi\)
\(12\) 0 0
\(13\) 146.000 0.239604 0.119802 0.992798i \(-0.461774\pi\)
0.119802 + 0.992798i \(0.461774\pi\)
\(14\) 0 0
\(15\) 158.114 0.181444
\(16\) 0 0
\(17\) −702.000 −0.589135 −0.294567 0.955631i \(-0.595176\pi\)
−0.294567 + 0.955631i \(0.595176\pi\)
\(18\) 0 0
\(19\) −2732.21 −1.73632 −0.868160 0.496285i \(-0.834697\pi\)
−0.868160 + 0.496285i \(0.834697\pi\)
\(20\) 0 0
\(21\) −280.000 −0.138551
\(22\) 0 0
\(23\) −4091.99 −1.61293 −0.806463 0.591284i \(-0.798621\pi\)
−0.806463 + 0.591284i \(0.798621\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 2820.75 0.744656
\(28\) 0 0
\(29\) 4010.00 0.885420 0.442710 0.896665i \(-0.354017\pi\)
0.442710 + 0.896665i \(0.354017\pi\)
\(30\) 0 0
\(31\) 4566.33 0.853420 0.426710 0.904388i \(-0.359672\pi\)
0.426710 + 0.904388i \(0.359672\pi\)
\(32\) 0 0
\(33\) −4560.00 −0.728920
\(34\) 0 0
\(35\) −1106.80 −0.152721
\(36\) 0 0
\(37\) 14778.0 1.77464 0.887322 0.461150i \(-0.152563\pi\)
0.887322 + 0.461150i \(0.152563\pi\)
\(38\) 0 0
\(39\) −923.385 −0.0972123
\(40\) 0 0
\(41\) −4350.00 −0.404138 −0.202069 0.979371i \(-0.564767\pi\)
−0.202069 + 0.979371i \(0.564767\pi\)
\(42\) 0 0
\(43\) −12427.8 −1.02499 −0.512497 0.858689i \(-0.671279\pi\)
−0.512497 + 0.858689i \(0.671279\pi\)
\(44\) 0 0
\(45\) 5075.00 0.373598
\(46\) 0 0
\(47\) 6014.65 0.397160 0.198580 0.980085i \(-0.436367\pi\)
0.198580 + 0.980085i \(0.436367\pi\)
\(48\) 0 0
\(49\) −14847.0 −0.883382
\(50\) 0 0
\(51\) 4439.84 0.239024
\(52\) 0 0
\(53\) 18154.0 0.887734 0.443867 0.896093i \(-0.353606\pi\)
0.443867 + 0.896093i \(0.353606\pi\)
\(54\) 0 0
\(55\) −18025.0 −0.803467
\(56\) 0 0
\(57\) 17280.0 0.704460
\(58\) 0 0
\(59\) 19707.3 0.737051 0.368525 0.929618i \(-0.379863\pi\)
0.368525 + 0.929618i \(0.379863\pi\)
\(60\) 0 0
\(61\) 42130.0 1.44966 0.724831 0.688927i \(-0.241918\pi\)
0.724831 + 0.688927i \(0.241918\pi\)
\(62\) 0 0
\(63\) −8987.19 −0.285281
\(64\) 0 0
\(65\) −3650.00 −0.107154
\(66\) 0 0
\(67\) −16184.5 −0.440467 −0.220233 0.975447i \(-0.570682\pi\)
−0.220233 + 0.975447i \(0.570682\pi\)
\(68\) 0 0
\(69\) 25880.0 0.654397
\(70\) 0 0
\(71\) 45448.3 1.06997 0.534985 0.844862i \(-0.320317\pi\)
0.534985 + 0.844862i \(0.320317\pi\)
\(72\) 0 0
\(73\) 26266.0 0.576882 0.288441 0.957498i \(-0.406863\pi\)
0.288441 + 0.957498i \(0.406863\pi\)
\(74\) 0 0
\(75\) −3952.85 −0.0811441
\(76\) 0 0
\(77\) 31920.0 0.613530
\(78\) 0 0
\(79\) −8677.29 −0.156429 −0.0782143 0.996937i \(-0.524922\pi\)
−0.0782143 + 0.996937i \(0.524922\pi\)
\(80\) 0 0
\(81\) 31489.0 0.533269
\(82\) 0 0
\(83\) 98757.9 1.57354 0.786768 0.617249i \(-0.211753\pi\)
0.786768 + 0.617249i \(0.211753\pi\)
\(84\) 0 0
\(85\) 17550.0 0.263469
\(86\) 0 0
\(87\) −25361.5 −0.359233
\(88\) 0 0
\(89\) 30570.0 0.409091 0.204546 0.978857i \(-0.434428\pi\)
0.204546 + 0.978857i \(0.434428\pi\)
\(90\) 0 0
\(91\) 6463.70 0.0818234
\(92\) 0 0
\(93\) −28880.0 −0.346250
\(94\) 0 0
\(95\) 68305.2 0.776506
\(96\) 0 0
\(97\) 66882.0 0.721739 0.360869 0.932616i \(-0.382480\pi\)
0.360869 + 0.932616i \(0.382480\pi\)
\(98\) 0 0
\(99\) −146363. −1.50087
\(100\) 0 0
\(101\) −42798.0 −0.417465 −0.208732 0.977973i \(-0.566934\pi\)
−0.208732 + 0.977973i \(0.566934\pi\)
\(102\) 0 0
\(103\) 10505.1 0.0975678 0.0487839 0.998809i \(-0.484465\pi\)
0.0487839 + 0.998809i \(0.484465\pi\)
\(104\) 0 0
\(105\) 7000.00 0.0619619
\(106\) 0 0
\(107\) −66856.9 −0.564529 −0.282265 0.959337i \(-0.591086\pi\)
−0.282265 + 0.959337i \(0.591086\pi\)
\(108\) 0 0
\(109\) 111714. 0.900620 0.450310 0.892872i \(-0.351314\pi\)
0.450310 + 0.892872i \(0.351314\pi\)
\(110\) 0 0
\(111\) −93464.3 −0.720009
\(112\) 0 0
\(113\) 216834. 1.59746 0.798732 0.601686i \(-0.205504\pi\)
0.798732 + 0.601686i \(0.205504\pi\)
\(114\) 0 0
\(115\) 102300. 0.721323
\(116\) 0 0
\(117\) −29638.0 −0.200163
\(118\) 0 0
\(119\) −31078.9 −0.201186
\(120\) 0 0
\(121\) 358789. 2.22780
\(122\) 0 0
\(123\) 27511.8 0.163967
\(124\) 0 0
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) 62277.9 0.342629 0.171315 0.985216i \(-0.445199\pi\)
0.171315 + 0.985216i \(0.445199\pi\)
\(128\) 0 0
\(129\) 78600.0 0.415861
\(130\) 0 0
\(131\) −176189. −0.897019 −0.448510 0.893778i \(-0.648045\pi\)
−0.448510 + 0.893778i \(0.648045\pi\)
\(132\) 0 0
\(133\) −120960. −0.592943
\(134\) 0 0
\(135\) −70518.8 −0.333020
\(136\) 0 0
\(137\) 99802.0 0.454295 0.227147 0.973860i \(-0.427060\pi\)
0.227147 + 0.973860i \(0.427060\pi\)
\(138\) 0 0
\(139\) 271475. 1.19177 0.595886 0.803069i \(-0.296801\pi\)
0.595886 + 0.803069i \(0.296801\pi\)
\(140\) 0 0
\(141\) −38040.0 −0.161136
\(142\) 0 0
\(143\) 105266. 0.430475
\(144\) 0 0
\(145\) −100250. −0.395972
\(146\) 0 0
\(147\) 93900.7 0.358406
\(148\) 0 0
\(149\) 413626. 1.52631 0.763154 0.646217i \(-0.223650\pi\)
0.763154 + 0.646217i \(0.223650\pi\)
\(150\) 0 0
\(151\) 172496. 0.615654 0.307827 0.951442i \(-0.400398\pi\)
0.307827 + 0.951442i \(0.400398\pi\)
\(152\) 0 0
\(153\) 142506. 0.492158
\(154\) 0 0
\(155\) −114158. −0.381661
\(156\) 0 0
\(157\) −179358. −0.580726 −0.290363 0.956917i \(-0.593776\pi\)
−0.290363 + 0.956917i \(0.593776\pi\)
\(158\) 0 0
\(159\) −114816. −0.360172
\(160\) 0 0
\(161\) −181160. −0.550805
\(162\) 0 0
\(163\) −465924. −1.37355 −0.686777 0.726868i \(-0.740975\pi\)
−0.686777 + 0.726868i \(0.740975\pi\)
\(164\) 0 0
\(165\) 114000. 0.325983
\(166\) 0 0
\(167\) −609567. −1.69134 −0.845669 0.533708i \(-0.820798\pi\)
−0.845669 + 0.533708i \(0.820798\pi\)
\(168\) 0 0
\(169\) −349977. −0.942590
\(170\) 0 0
\(171\) 554638. 1.45051
\(172\) 0 0
\(173\) −591086. −1.50153 −0.750767 0.660567i \(-0.770316\pi\)
−0.750767 + 0.660567i \(0.770316\pi\)
\(174\) 0 0
\(175\) 27669.9 0.0682988
\(176\) 0 0
\(177\) −124640. −0.299037
\(178\) 0 0
\(179\) −211215. −0.492711 −0.246355 0.969180i \(-0.579233\pi\)
−0.246355 + 0.969180i \(0.579233\pi\)
\(180\) 0 0
\(181\) 97538.0 0.221298 0.110649 0.993860i \(-0.464707\pi\)
0.110649 + 0.993860i \(0.464707\pi\)
\(182\) 0 0
\(183\) −266454. −0.588158
\(184\) 0 0
\(185\) −369450. −0.793645
\(186\) 0 0
\(187\) −506142. −1.05844
\(188\) 0 0
\(189\) 124880. 0.254295
\(190\) 0 0
\(191\) 307158. 0.609227 0.304613 0.952476i \(-0.401473\pi\)
0.304613 + 0.952476i \(0.401473\pi\)
\(192\) 0 0
\(193\) 12434.0 0.0240280 0.0120140 0.999928i \(-0.496176\pi\)
0.0120140 + 0.999928i \(0.496176\pi\)
\(194\) 0 0
\(195\) 23084.6 0.0434747
\(196\) 0 0
\(197\) 378858. 0.695522 0.347761 0.937583i \(-0.386942\pi\)
0.347761 + 0.937583i \(0.386942\pi\)
\(198\) 0 0
\(199\) 767194. 1.37332 0.686661 0.726978i \(-0.259076\pi\)
0.686661 + 0.726978i \(0.259076\pi\)
\(200\) 0 0
\(201\) 102360. 0.178706
\(202\) 0 0
\(203\) 177530. 0.302366
\(204\) 0 0
\(205\) 108750. 0.180736
\(206\) 0 0
\(207\) 830673. 1.34742
\(208\) 0 0
\(209\) −1.96992e6 −3.11948
\(210\) 0 0
\(211\) 864529. 1.33682 0.668411 0.743793i \(-0.266975\pi\)
0.668411 + 0.743793i \(0.266975\pi\)
\(212\) 0 0
\(213\) −287440. −0.434108
\(214\) 0 0
\(215\) 310694. 0.458391
\(216\) 0 0
\(217\) 202160. 0.291438
\(218\) 0 0
\(219\) −166121. −0.234053
\(220\) 0 0
\(221\) −102492. −0.141159
\(222\) 0 0
\(223\) −639710. −0.861432 −0.430716 0.902488i \(-0.641739\pi\)
−0.430716 + 0.902488i \(0.641739\pi\)
\(224\) 0 0
\(225\) −126875. −0.167078
\(226\) 0 0
\(227\) 980515. 1.26296 0.631480 0.775392i \(-0.282448\pi\)
0.631480 + 0.775392i \(0.282448\pi\)
\(228\) 0 0
\(229\) 1.01261e6 1.27601 0.638004 0.770033i \(-0.279760\pi\)
0.638004 + 0.770033i \(0.279760\pi\)
\(230\) 0 0
\(231\) −201880. −0.248922
\(232\) 0 0
\(233\) −706326. −0.852345 −0.426172 0.904642i \(-0.640138\pi\)
−0.426172 + 0.904642i \(0.640138\pi\)
\(234\) 0 0
\(235\) −150366. −0.177616
\(236\) 0 0
\(237\) 54880.0 0.0634663
\(238\) 0 0
\(239\) −1.19390e6 −1.35199 −0.675994 0.736907i \(-0.736285\pi\)
−0.675994 + 0.736907i \(0.736285\pi\)
\(240\) 0 0
\(241\) 404410. 0.448517 0.224259 0.974530i \(-0.428004\pi\)
0.224259 + 0.974530i \(0.428004\pi\)
\(242\) 0 0
\(243\) −884597. −0.961014
\(244\) 0 0
\(245\) 371175. 0.395060
\(246\) 0 0
\(247\) −398902. −0.416030
\(248\) 0 0
\(249\) −624600. −0.638416
\(250\) 0 0
\(251\) −1.43258e6 −1.43527 −0.717634 0.696420i \(-0.754775\pi\)
−0.717634 + 0.696420i \(0.754775\pi\)
\(252\) 0 0
\(253\) −2.95032e6 −2.89780
\(254\) 0 0
\(255\) −110996. −0.106895
\(256\) 0 0
\(257\) −987982. −0.933074 −0.466537 0.884502i \(-0.654499\pi\)
−0.466537 + 0.884502i \(0.654499\pi\)
\(258\) 0 0
\(259\) 654250. 0.606030
\(260\) 0 0
\(261\) −814030. −0.739672
\(262\) 0 0
\(263\) 2.06222e6 1.83842 0.919210 0.393767i \(-0.128828\pi\)
0.919210 + 0.393767i \(0.128828\pi\)
\(264\) 0 0
\(265\) −453850. −0.397007
\(266\) 0 0
\(267\) −193342. −0.165977
\(268\) 0 0
\(269\) 780386. 0.657550 0.328775 0.944408i \(-0.393364\pi\)
0.328775 + 0.944408i \(0.393364\pi\)
\(270\) 0 0
\(271\) −562291. −0.465091 −0.232545 0.972586i \(-0.574705\pi\)
−0.232545 + 0.972586i \(0.574705\pi\)
\(272\) 0 0
\(273\) −40880.0 −0.0331974
\(274\) 0 0
\(275\) 450625. 0.359321
\(276\) 0 0
\(277\) −386758. −0.302859 −0.151429 0.988468i \(-0.548388\pi\)
−0.151429 + 0.988468i \(0.548388\pi\)
\(278\) 0 0
\(279\) −926965. −0.712940
\(280\) 0 0
\(281\) 1.55485e6 1.17469 0.587344 0.809337i \(-0.300173\pi\)
0.587344 + 0.809337i \(0.300173\pi\)
\(282\) 0 0
\(283\) 1.75157e6 1.30005 0.650026 0.759912i \(-0.274758\pi\)
0.650026 + 0.759912i \(0.274758\pi\)
\(284\) 0 0
\(285\) −432000. −0.315044
\(286\) 0 0
\(287\) −192583. −0.138011
\(288\) 0 0
\(289\) −927053. −0.652920
\(290\) 0 0
\(291\) −422999. −0.292824
\(292\) 0 0
\(293\) −1.55309e6 −1.05689 −0.528444 0.848968i \(-0.677224\pi\)
−0.528444 + 0.848968i \(0.677224\pi\)
\(294\) 0 0
\(295\) −492683. −0.329619
\(296\) 0 0
\(297\) 2.03376e6 1.33785
\(298\) 0 0
\(299\) −597430. −0.386464
\(300\) 0 0
\(301\) −550200. −0.350029
\(302\) 0 0
\(303\) 270678. 0.169374
\(304\) 0 0
\(305\) −1.05325e6 −0.648309
\(306\) 0 0
\(307\) −2.60409e6 −1.57692 −0.788461 0.615085i \(-0.789122\pi\)
−0.788461 + 0.615085i \(0.789122\pi\)
\(308\) 0 0
\(309\) −66440.0 −0.0395853
\(310\) 0 0
\(311\) −302124. −0.177127 −0.0885634 0.996071i \(-0.528228\pi\)
−0.0885634 + 0.996071i \(0.528228\pi\)
\(312\) 0 0
\(313\) 2.09455e6 1.20846 0.604228 0.796812i \(-0.293482\pi\)
0.604228 + 0.796812i \(0.293482\pi\)
\(314\) 0 0
\(315\) 224680. 0.127581
\(316\) 0 0
\(317\) −1.07624e6 −0.601534 −0.300767 0.953698i \(-0.597243\pi\)
−0.300767 + 0.953698i \(0.597243\pi\)
\(318\) 0 0
\(319\) 2.89121e6 1.59075
\(320\) 0 0
\(321\) 422840. 0.229041
\(322\) 0 0
\(323\) 1.91801e6 1.02293
\(324\) 0 0
\(325\) 91250.0 0.0479208
\(326\) 0 0
\(327\) −706541. −0.365400
\(328\) 0 0
\(329\) 266280. 0.135628
\(330\) 0 0
\(331\) −313002. −0.157028 −0.0785141 0.996913i \(-0.525018\pi\)
−0.0785141 + 0.996913i \(0.525018\pi\)
\(332\) 0 0
\(333\) −2.99993e6 −1.48252
\(334\) 0 0
\(335\) 404613. 0.196983
\(336\) 0 0
\(337\) 1.55400e6 0.745378 0.372689 0.927956i \(-0.378436\pi\)
0.372689 + 0.927956i \(0.378436\pi\)
\(338\) 0 0
\(339\) −1.37138e6 −0.648124
\(340\) 0 0
\(341\) 3.29232e6 1.53326
\(342\) 0 0
\(343\) −1.40138e6 −0.643163
\(344\) 0 0
\(345\) −647000. −0.292655
\(346\) 0 0
\(347\) 2.22208e6 0.990684 0.495342 0.868698i \(-0.335043\pi\)
0.495342 + 0.868698i \(0.335043\pi\)
\(348\) 0 0
\(349\) 774570. 0.340406 0.170203 0.985409i \(-0.445558\pi\)
0.170203 + 0.985409i \(0.445558\pi\)
\(350\) 0 0
\(351\) 411830. 0.178423
\(352\) 0 0
\(353\) −2.26217e6 −0.966249 −0.483125 0.875552i \(-0.660498\pi\)
−0.483125 + 0.875552i \(0.660498\pi\)
\(354\) 0 0
\(355\) −1.13621e6 −0.478505
\(356\) 0 0
\(357\) 196560. 0.0816253
\(358\) 0 0
\(359\) −869601. −0.356110 −0.178055 0.984021i \(-0.556980\pi\)
−0.178055 + 0.984021i \(0.556980\pi\)
\(360\) 0 0
\(361\) 4.98886e6 2.01481
\(362\) 0 0
\(363\) −2.26918e6 −0.903863
\(364\) 0 0
\(365\) −656650. −0.257989
\(366\) 0 0
\(367\) −1.25361e6 −0.485844 −0.242922 0.970046i \(-0.578106\pi\)
−0.242922 + 0.970046i \(0.578106\pi\)
\(368\) 0 0
\(369\) 883050. 0.337613
\(370\) 0 0
\(371\) 803712. 0.303156
\(372\) 0 0
\(373\) −175206. −0.0652044 −0.0326022 0.999468i \(-0.510379\pi\)
−0.0326022 + 0.999468i \(0.510379\pi\)
\(374\) 0 0
\(375\) 98821.2 0.0362887
\(376\) 0 0
\(377\) 585460. 0.212150
\(378\) 0 0
\(379\) 796945. 0.284990 0.142495 0.989795i \(-0.454487\pi\)
0.142495 + 0.989795i \(0.454487\pi\)
\(380\) 0 0
\(381\) −393880. −0.139012
\(382\) 0 0
\(383\) −3.36129e6 −1.17087 −0.585436 0.810719i \(-0.699077\pi\)
−0.585436 + 0.810719i \(0.699077\pi\)
\(384\) 0 0
\(385\) −798000. −0.274379
\(386\) 0 0
\(387\) 2.52283e6 0.856271
\(388\) 0 0
\(389\) 5.51959e6 1.84941 0.924705 0.380685i \(-0.124312\pi\)
0.924705 + 0.380685i \(0.124312\pi\)
\(390\) 0 0
\(391\) 2.87258e6 0.950232
\(392\) 0 0
\(393\) 1.11432e6 0.363939
\(394\) 0 0
\(395\) 216932. 0.0699570
\(396\) 0 0
\(397\) 1.74738e6 0.556430 0.278215 0.960519i \(-0.410257\pi\)
0.278215 + 0.960519i \(0.410257\pi\)
\(398\) 0 0
\(399\) 765018. 0.240569
\(400\) 0 0
\(401\) 541122. 0.168048 0.0840242 0.996464i \(-0.473223\pi\)
0.0840242 + 0.996464i \(0.473223\pi\)
\(402\) 0 0
\(403\) 666684. 0.204483
\(404\) 0 0
\(405\) −787225. −0.238485
\(406\) 0 0
\(407\) 1.06549e7 3.18834
\(408\) 0 0
\(409\) 3.79699e6 1.12236 0.561179 0.827694i \(-0.310348\pi\)
0.561179 + 0.827694i \(0.310348\pi\)
\(410\) 0 0
\(411\) −631203. −0.184317
\(412\) 0 0
\(413\) 872480. 0.251698
\(414\) 0 0
\(415\) −2.46895e6 −0.703707
\(416\) 0 0
\(417\) −1.71696e6 −0.483526
\(418\) 0 0
\(419\) 3.88108e6 1.07998 0.539992 0.841670i \(-0.318427\pi\)
0.539992 + 0.841670i \(0.318427\pi\)
\(420\) 0 0
\(421\) 6.66081e6 1.83156 0.915781 0.401677i \(-0.131573\pi\)
0.915781 + 0.401677i \(0.131573\pi\)
\(422\) 0 0
\(423\) −1.22097e6 −0.331784
\(424\) 0 0
\(425\) −438750. −0.117827
\(426\) 0 0
\(427\) 1.86517e6 0.495051
\(428\) 0 0
\(429\) −665760. −0.174652
\(430\) 0 0
\(431\) −4.65337e6 −1.20663 −0.603315 0.797503i \(-0.706154\pi\)
−0.603315 + 0.797503i \(0.706154\pi\)
\(432\) 0 0
\(433\) −6.23873e6 −1.59910 −0.799552 0.600597i \(-0.794930\pi\)
−0.799552 + 0.600597i \(0.794930\pi\)
\(434\) 0 0
\(435\) 634037. 0.160654
\(436\) 0 0
\(437\) 1.11802e7 2.80056
\(438\) 0 0
\(439\) −4.75743e6 −1.17818 −0.589089 0.808068i \(-0.700513\pi\)
−0.589089 + 0.808068i \(0.700513\pi\)
\(440\) 0 0
\(441\) 3.01394e6 0.737969
\(442\) 0 0
\(443\) −5.77073e6 −1.39708 −0.698541 0.715570i \(-0.746167\pi\)
−0.698541 + 0.715570i \(0.746167\pi\)
\(444\) 0 0
\(445\) −764250. −0.182951
\(446\) 0 0
\(447\) −2.61600e6 −0.619254
\(448\) 0 0
\(449\) −4.22765e6 −0.989654 −0.494827 0.868991i \(-0.664769\pi\)
−0.494827 + 0.868991i \(0.664769\pi\)
\(450\) 0 0
\(451\) −3.13635e6 −0.726077
\(452\) 0 0
\(453\) −1.09096e6 −0.249783
\(454\) 0 0
\(455\) −161592. −0.0365925
\(456\) 0 0
\(457\) 4.31374e6 0.966192 0.483096 0.875567i \(-0.339512\pi\)
0.483096 + 0.875567i \(0.339512\pi\)
\(458\) 0 0
\(459\) −1.98017e6 −0.438703
\(460\) 0 0
\(461\) 5.94820e6 1.30357 0.651784 0.758405i \(-0.274021\pi\)
0.651784 + 0.758405i \(0.274021\pi\)
\(462\) 0 0
\(463\) 8.39722e6 1.82047 0.910234 0.414094i \(-0.135902\pi\)
0.910234 + 0.414094i \(0.135902\pi\)
\(464\) 0 0
\(465\) 722000. 0.154848
\(466\) 0 0
\(467\) −5.30976e6 −1.12663 −0.563317 0.826241i \(-0.690475\pi\)
−0.563317 + 0.826241i \(0.690475\pi\)
\(468\) 0 0
\(469\) −716520. −0.150417
\(470\) 0 0
\(471\) 1.13436e6 0.235613
\(472\) 0 0
\(473\) −8.96040e6 −1.84151
\(474\) 0 0
\(475\) −1.70763e6 −0.347264
\(476\) 0 0
\(477\) −3.68526e6 −0.741605
\(478\) 0 0
\(479\) 5.83653e6 1.16229 0.581147 0.813799i \(-0.302604\pi\)
0.581147 + 0.813799i \(0.302604\pi\)
\(480\) 0 0
\(481\) 2.15759e6 0.425212
\(482\) 0 0
\(483\) 1.14576e6 0.223473
\(484\) 0 0
\(485\) −1.67205e6 −0.322771
\(486\) 0 0
\(487\) −8.75327e6 −1.67243 −0.836215 0.548402i \(-0.815236\pi\)
−0.836215 + 0.548402i \(0.815236\pi\)
\(488\) 0 0
\(489\) 2.94676e6 0.557279
\(490\) 0 0
\(491\) 5.16834e6 0.967492 0.483746 0.875209i \(-0.339276\pi\)
0.483746 + 0.875209i \(0.339276\pi\)
\(492\) 0 0
\(493\) −2.81502e6 −0.521632
\(494\) 0 0
\(495\) 3.65907e6 0.671209
\(496\) 0 0
\(497\) 2.01208e6 0.365388
\(498\) 0 0
\(499\) 5.36171e6 0.963943 0.481972 0.876187i \(-0.339921\pi\)
0.481972 + 0.876187i \(0.339921\pi\)
\(500\) 0 0
\(501\) 3.85524e6 0.686210
\(502\) 0 0
\(503\) −5.26635e6 −0.928089 −0.464045 0.885812i \(-0.653602\pi\)
−0.464045 + 0.885812i \(0.653602\pi\)
\(504\) 0 0
\(505\) 1.06995e6 0.186696
\(506\) 0 0
\(507\) 2.21345e6 0.382428
\(508\) 0 0
\(509\) −5.46847e6 −0.935559 −0.467780 0.883845i \(-0.654946\pi\)
−0.467780 + 0.883845i \(0.654946\pi\)
\(510\) 0 0
\(511\) 1.16285e6 0.197002
\(512\) 0 0
\(513\) −7.70688e6 −1.29296
\(514\) 0 0
\(515\) −262627. −0.0436337
\(516\) 0 0
\(517\) 4.33656e6 0.713541
\(518\) 0 0
\(519\) 3.73836e6 0.609203
\(520\) 0 0
\(521\) −3.05762e6 −0.493503 −0.246751 0.969079i \(-0.579363\pi\)
−0.246751 + 0.969079i \(0.579363\pi\)
\(522\) 0 0
\(523\) 9.64117e6 1.54126 0.770629 0.637284i \(-0.219942\pi\)
0.770629 + 0.637284i \(0.219942\pi\)
\(524\) 0 0
\(525\) −175000. −0.0277102
\(526\) 0 0
\(527\) −3.20556e6 −0.502780
\(528\) 0 0
\(529\) 1.03080e7 1.60153
\(530\) 0 0
\(531\) −4.00058e6 −0.615726
\(532\) 0 0
\(533\) −635100. −0.0968332
\(534\) 0 0
\(535\) 1.67142e6 0.252465
\(536\) 0 0
\(537\) 1.33584e6 0.199903
\(538\) 0 0
\(539\) −1.07047e7 −1.58709
\(540\) 0 0
\(541\) 4.15820e6 0.610819 0.305409 0.952221i \(-0.401207\pi\)
0.305409 + 0.952221i \(0.401207\pi\)
\(542\) 0 0
\(543\) −616884. −0.0897851
\(544\) 0 0
\(545\) −2.79285e6 −0.402769
\(546\) 0 0
\(547\) −5.32628e6 −0.761125 −0.380562 0.924755i \(-0.624270\pi\)
−0.380562 + 0.924755i \(0.624270\pi\)
\(548\) 0 0
\(549\) −8.55239e6 −1.21103
\(550\) 0 0
\(551\) −1.09562e7 −1.53737
\(552\) 0 0
\(553\) −384160. −0.0534194
\(554\) 0 0
\(555\) 2.33661e6 0.321998
\(556\) 0 0
\(557\) −999102. −0.136449 −0.0682247 0.997670i \(-0.521733\pi\)
−0.0682247 + 0.997670i \(0.521733\pi\)
\(558\) 0 0
\(559\) −1.81445e6 −0.245593
\(560\) 0 0
\(561\) 3.20112e6 0.429432
\(562\) 0 0
\(563\) −5.31886e6 −0.707208 −0.353604 0.935395i \(-0.615044\pi\)
−0.353604 + 0.935395i \(0.615044\pi\)
\(564\) 0 0
\(565\) −5.42085e6 −0.714408
\(566\) 0 0
\(567\) 1.39408e6 0.182108
\(568\) 0 0
\(569\) 6.56759e6 0.850404 0.425202 0.905099i \(-0.360203\pi\)
0.425202 + 0.905099i \(0.360203\pi\)
\(570\) 0 0
\(571\) 164173. 0.0210723 0.0105361 0.999944i \(-0.496646\pi\)
0.0105361 + 0.999944i \(0.496646\pi\)
\(572\) 0 0
\(573\) −1.94264e6 −0.247176
\(574\) 0 0
\(575\) −2.55749e6 −0.322585
\(576\) 0 0
\(577\) 9.27762e6 1.16010 0.580052 0.814579i \(-0.303032\pi\)
0.580052 + 0.814579i \(0.303032\pi\)
\(578\) 0 0
\(579\) −78639.5 −0.00974865
\(580\) 0 0
\(581\) 4.37220e6 0.537353
\(582\) 0 0
\(583\) 1.30890e7 1.59491
\(584\) 0 0
\(585\) 740950. 0.0895157
\(586\) 0 0
\(587\) 5.44474e6 0.652202 0.326101 0.945335i \(-0.394265\pi\)
0.326101 + 0.945335i \(0.394265\pi\)
\(588\) 0 0
\(589\) −1.24762e7 −1.48181
\(590\) 0 0
\(591\) −2.39611e6 −0.282187
\(592\) 0 0
\(593\) −1.50978e7 −1.76310 −0.881548 0.472094i \(-0.843498\pi\)
−0.881548 + 0.472094i \(0.843498\pi\)
\(594\) 0 0
\(595\) 776972. 0.0899731
\(596\) 0 0
\(597\) −4.85216e6 −0.557185
\(598\) 0 0
\(599\) −6.98593e6 −0.795531 −0.397765 0.917487i \(-0.630214\pi\)
−0.397765 + 0.917487i \(0.630214\pi\)
\(600\) 0 0
\(601\) 6.16941e6 0.696719 0.348359 0.937361i \(-0.386739\pi\)
0.348359 + 0.937361i \(0.386739\pi\)
\(602\) 0 0
\(603\) 3.28546e6 0.367962
\(604\) 0 0
\(605\) −8.96972e6 −0.996301
\(606\) 0 0
\(607\) 1.00769e7 1.11009 0.555043 0.831822i \(-0.312702\pi\)
0.555043 + 0.831822i \(0.312702\pi\)
\(608\) 0 0
\(609\) −1.12280e6 −0.122676
\(610\) 0 0
\(611\) 878139. 0.0951613
\(612\) 0 0
\(613\) −5.26885e6 −0.566324 −0.283162 0.959072i \(-0.591383\pi\)
−0.283162 + 0.959072i \(0.591383\pi\)
\(614\) 0 0
\(615\) −687795. −0.0733283
\(616\) 0 0
\(617\) −1.38112e7 −1.46056 −0.730280 0.683148i \(-0.760610\pi\)
−0.730280 + 0.683148i \(0.760610\pi\)
\(618\) 0 0
\(619\) 3.20903e6 0.336625 0.168313 0.985734i \(-0.446168\pi\)
0.168313 + 0.985734i \(0.446168\pi\)
\(620\) 0 0
\(621\) −1.15425e7 −1.20108
\(622\) 0 0
\(623\) 1.35339e6 0.139702
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 1.24589e7 1.26564
\(628\) 0 0
\(629\) −1.03742e7 −1.04551
\(630\) 0 0
\(631\) 6.07204e6 0.607102 0.303551 0.952815i \(-0.401828\pi\)
0.303551 + 0.952815i \(0.401828\pi\)
\(632\) 0 0
\(633\) −5.46776e6 −0.542376
\(634\) 0 0
\(635\) −1.55695e6 −0.153229
\(636\) 0 0
\(637\) −2.16766e6 −0.211662
\(638\) 0 0
\(639\) −9.22600e6 −0.893843
\(640\) 0 0
\(641\) −2.02767e6 −0.194918 −0.0974591 0.995240i \(-0.531072\pi\)
−0.0974591 + 0.995240i \(0.531072\pi\)
\(642\) 0 0
\(643\) −1.19769e7 −1.14240 −0.571199 0.820811i \(-0.693522\pi\)
−0.571199 + 0.820811i \(0.693522\pi\)
\(644\) 0 0
\(645\) −1.96500e6 −0.185979
\(646\) 0 0
\(647\) 1.44768e6 0.135961 0.0679803 0.997687i \(-0.478344\pi\)
0.0679803 + 0.997687i \(0.478344\pi\)
\(648\) 0 0
\(649\) 1.42090e7 1.32419
\(650\) 0 0
\(651\) −1.27857e6 −0.118242
\(652\) 0 0
\(653\) −4.82477e6 −0.442785 −0.221393 0.975185i \(-0.571060\pi\)
−0.221393 + 0.975185i \(0.571060\pi\)
\(654\) 0 0
\(655\) 4.40474e6 0.401159
\(656\) 0 0
\(657\) −5.33200e6 −0.481922
\(658\) 0 0
\(659\) 4.37616e6 0.392536 0.196268 0.980550i \(-0.437118\pi\)
0.196268 + 0.980550i \(0.437118\pi\)
\(660\) 0 0
\(661\) 7.34953e6 0.654268 0.327134 0.944978i \(-0.393917\pi\)
0.327134 + 0.944978i \(0.393917\pi\)
\(662\) 0 0
\(663\) 648216. 0.0572712
\(664\) 0 0
\(665\) 3.02400e6 0.265172
\(666\) 0 0
\(667\) −1.64089e7 −1.42812
\(668\) 0 0
\(669\) 4.04588e6 0.349500
\(670\) 0 0
\(671\) 3.03757e7 2.60447
\(672\) 0 0
\(673\) −1.75692e7 −1.49525 −0.747626 0.664119i \(-0.768807\pi\)
−0.747626 + 0.664119i \(0.768807\pi\)
\(674\) 0 0
\(675\) 1.76297e6 0.148931
\(676\) 0 0
\(677\) −5.60338e6 −0.469871 −0.234935 0.972011i \(-0.575488\pi\)
−0.234935 + 0.972011i \(0.575488\pi\)
\(678\) 0 0
\(679\) 2.96099e6 0.246469
\(680\) 0 0
\(681\) −6.20132e6 −0.512409
\(682\) 0 0
\(683\) 5.05809e6 0.414892 0.207446 0.978246i \(-0.433485\pi\)
0.207446 + 0.978246i \(0.433485\pi\)
\(684\) 0 0
\(685\) −2.49505e6 −0.203167
\(686\) 0 0
\(687\) −6.40431e6 −0.517703
\(688\) 0 0
\(689\) 2.65048e6 0.212705
\(690\) 0 0
\(691\) 1.47421e7 1.17453 0.587267 0.809393i \(-0.300204\pi\)
0.587267 + 0.809393i \(0.300204\pi\)
\(692\) 0 0
\(693\) −6.47976e6 −0.512538
\(694\) 0 0
\(695\) −6.78688e6 −0.532977
\(696\) 0 0
\(697\) 3.05370e6 0.238092
\(698\) 0 0
\(699\) 4.46720e6 0.345814
\(700\) 0 0
\(701\) 8.83317e6 0.678925 0.339462 0.940620i \(-0.389755\pi\)
0.339462 + 0.940620i \(0.389755\pi\)
\(702\) 0 0
\(703\) −4.03766e7 −3.08135
\(704\) 0 0
\(705\) 951000. 0.0720622
\(706\) 0 0
\(707\) −1.89475e6 −0.142562
\(708\) 0 0
\(709\) 1.93101e6 0.144268 0.0721338 0.997395i \(-0.477019\pi\)
0.0721338 + 0.997395i \(0.477019\pi\)
\(710\) 0 0
\(711\) 1.76149e6 0.130679
\(712\) 0 0
\(713\) −1.86854e7 −1.37650
\(714\) 0 0
\(715\) −2.63165e6 −0.192514
\(716\) 0 0
\(717\) 7.55088e6 0.548529
\(718\) 0 0
\(719\) 7.22373e6 0.521122 0.260561 0.965457i \(-0.416093\pi\)
0.260561 + 0.965457i \(0.416093\pi\)
\(720\) 0 0
\(721\) 465080. 0.0333188
\(722\) 0 0
\(723\) −2.55771e6 −0.181973
\(724\) 0 0
\(725\) 2.50625e6 0.177084
\(726\) 0 0
\(727\) −9.81106e6 −0.688462 −0.344231 0.938885i \(-0.611860\pi\)
−0.344231 + 0.938885i \(0.611860\pi\)
\(728\) 0 0
\(729\) −2.05715e6 −0.143366
\(730\) 0 0
\(731\) 8.72428e6 0.603860
\(732\) 0 0
\(733\) 2.40813e7 1.65547 0.827733 0.561122i \(-0.189630\pi\)
0.827733 + 0.561122i \(0.189630\pi\)
\(734\) 0 0
\(735\) −2.34752e6 −0.160284
\(736\) 0 0
\(737\) −1.16690e7 −0.791346
\(738\) 0 0
\(739\) −2.40518e7 −1.62008 −0.810040 0.586374i \(-0.800555\pi\)
−0.810040 + 0.586374i \(0.800555\pi\)
\(740\) 0 0
\(741\) 2.52288e6 0.168792
\(742\) 0 0
\(743\) 4.70160e6 0.312445 0.156223 0.987722i \(-0.450068\pi\)
0.156223 + 0.987722i \(0.450068\pi\)
\(744\) 0 0
\(745\) −1.03406e7 −0.682586
\(746\) 0 0
\(747\) −2.00479e7 −1.31452
\(748\) 0 0
\(749\) −2.95988e6 −0.192783
\(750\) 0 0
\(751\) −2.31282e7 −1.49638 −0.748189 0.663485i \(-0.769077\pi\)
−0.748189 + 0.663485i \(0.769077\pi\)
\(752\) 0 0
\(753\) 9.06040e6 0.582318
\(754\) 0 0
\(755\) −4.31240e6 −0.275329
\(756\) 0 0
\(757\) 1.26635e7 0.803181 0.401591 0.915819i \(-0.368458\pi\)
0.401591 + 0.915819i \(0.368458\pi\)
\(758\) 0 0
\(759\) 1.86595e7 1.17570
\(760\) 0 0
\(761\) −4.33524e6 −0.271363 −0.135682 0.990752i \(-0.543322\pi\)
−0.135682 + 0.990752i \(0.543322\pi\)
\(762\) 0 0
\(763\) 4.94579e6 0.307556
\(764\) 0 0
\(765\) −3.56265e6 −0.220100
\(766\) 0 0
\(767\) 2.87727e6 0.176600
\(768\) 0 0
\(769\) −364270. −0.0222130 −0.0111065 0.999938i \(-0.503535\pi\)
−0.0111065 + 0.999938i \(0.503535\pi\)
\(770\) 0 0
\(771\) 6.24855e6 0.378567
\(772\) 0 0
\(773\) 1.03051e6 0.0620300 0.0310150 0.999519i \(-0.490126\pi\)
0.0310150 + 0.999519i \(0.490126\pi\)
\(774\) 0 0
\(775\) 2.85396e6 0.170684
\(776\) 0 0
\(777\) −4.13784e6 −0.245879
\(778\) 0 0
\(779\) 1.18851e7 0.701713
\(780\) 0 0
\(781\) 3.27682e7 1.92231
\(782\) 0 0
\(783\) 1.13112e7 0.659333
\(784\) 0 0
\(785\) 4.48395e6 0.259709
\(786\) 0 0
\(787\) 1.95300e7 1.12400 0.561999 0.827138i \(-0.310032\pi\)
0.561999 + 0.827138i \(0.310032\pi\)
\(788\) 0 0
\(789\) −1.30426e7 −0.745885
\(790\) 0 0
\(791\) 9.59965e6 0.545524
\(792\) 0 0
\(793\) 6.15098e6 0.347345
\(794\) 0 0
\(795\) 2.87040e6 0.161074
\(796\) 0 0
\(797\) −7.86344e6 −0.438497 −0.219249 0.975669i \(-0.570361\pi\)
−0.219249 + 0.975669i \(0.570361\pi\)
\(798\) 0 0
\(799\) −4.22229e6 −0.233981
\(800\) 0 0
\(801\) −6.20571e6 −0.341751
\(802\) 0 0
\(803\) 1.89378e7 1.03643
\(804\) 0 0
\(805\) 4.52900e6 0.246327
\(806\) 0 0
\(807\) −4.93559e6 −0.266781
\(808\) 0 0
\(809\) −1.05014e7 −0.564127 −0.282064 0.959396i \(-0.591019\pi\)
−0.282064 + 0.959396i \(0.591019\pi\)
\(810\) 0 0
\(811\) −1.87803e7 −1.00265 −0.501325 0.865259i \(-0.667154\pi\)
−0.501325 + 0.865259i \(0.667154\pi\)
\(812\) 0 0
\(813\) 3.55624e6 0.188697
\(814\) 0 0
\(815\) 1.16481e7 0.614272
\(816\) 0 0
\(817\) 3.39552e7 1.77972
\(818\) 0 0
\(819\) −1.31213e6 −0.0683545
\(820\) 0 0
\(821\) −2.00557e7 −1.03844 −0.519220 0.854641i \(-0.673777\pi\)
−0.519220 + 0.854641i \(0.673777\pi\)
\(822\) 0 0
\(823\) 1.02444e7 0.527212 0.263606 0.964630i \(-0.415088\pi\)
0.263606 + 0.964630i \(0.415088\pi\)
\(824\) 0 0
\(825\) −2.85000e6 −0.145784
\(826\) 0 0
\(827\) −827524. −0.0420743 −0.0210371 0.999779i \(-0.506697\pi\)
−0.0210371 + 0.999779i \(0.506697\pi\)
\(828\) 0 0
\(829\) 3.80328e7 1.92208 0.961041 0.276407i \(-0.0891436\pi\)
0.961041 + 0.276407i \(0.0891436\pi\)
\(830\) 0 0
\(831\) 2.44607e6 0.122876
\(832\) 0 0
\(833\) 1.04226e7 0.520431
\(834\) 0 0
\(835\) 1.52392e7 0.756389
\(836\) 0 0
\(837\) 1.28805e7 0.635504
\(838\) 0 0
\(839\) −3.57628e7 −1.75399 −0.876993 0.480503i \(-0.840454\pi\)
−0.876993 + 0.480503i \(0.840454\pi\)
\(840\) 0 0
\(841\) −4.43105e6 −0.216031
\(842\) 0 0
\(843\) −9.83373e6 −0.476595
\(844\) 0 0
\(845\) 8.74943e6 0.421539
\(846\) 0 0
\(847\) 1.58843e7 0.760779
\(848\) 0 0
\(849\) −1.10779e7 −0.527457
\(850\) 0 0
\(851\) −6.04714e7 −2.86237
\(852\) 0 0
\(853\) −970214. −0.0456557 −0.0228278 0.999739i \(-0.507267\pi\)
−0.0228278 + 0.999739i \(0.507267\pi\)
\(854\) 0 0
\(855\) −1.38660e7 −0.648686
\(856\) 0 0
\(857\) 1.86468e6 0.0867267 0.0433633 0.999059i \(-0.486193\pi\)
0.0433633 + 0.999059i \(0.486193\pi\)
\(858\) 0 0
\(859\) −1.05785e6 −0.0489147 −0.0244573 0.999701i \(-0.507786\pi\)
−0.0244573 + 0.999701i \(0.507786\pi\)
\(860\) 0 0
\(861\) 1.21800e6 0.0559937
\(862\) 0 0
\(863\) 8.24333e6 0.376769 0.188385 0.982095i \(-0.439675\pi\)
0.188385 + 0.982095i \(0.439675\pi\)
\(864\) 0 0
\(865\) 1.47772e7 0.671507
\(866\) 0 0
\(867\) 5.86320e6 0.264903
\(868\) 0 0
\(869\) −6.25632e6 −0.281041
\(870\) 0 0
\(871\) −2.36294e6 −0.105538
\(872\) 0 0
\(873\) −1.35770e7 −0.602934
\(874\) 0 0
\(875\) −691748. −0.0305441
\(876\) 0 0
\(877\) 2.40362e7 1.05528 0.527640 0.849468i \(-0.323077\pi\)
0.527640 + 0.849468i \(0.323077\pi\)
\(878\) 0 0
\(879\) 9.82263e6 0.428801
\(880\) 0 0
\(881\) 3.68605e7 1.60000 0.800002 0.599997i \(-0.204831\pi\)
0.800002 + 0.599997i \(0.204831\pi\)
\(882\) 0 0
\(883\) −1.67403e7 −0.722541 −0.361271 0.932461i \(-0.617657\pi\)
−0.361271 + 0.932461i \(0.617657\pi\)
\(884\) 0 0
\(885\) 3.11600e6 0.133733
\(886\) 0 0
\(887\) −9.25364e6 −0.394915 −0.197457 0.980311i \(-0.563268\pi\)
−0.197457 + 0.980311i \(0.563268\pi\)
\(888\) 0 0
\(889\) 2.75716e6 0.117006
\(890\) 0 0
\(891\) 2.27035e7 0.958075
\(892\) 0 0
\(893\) −1.64333e7 −0.689597
\(894\) 0 0
\(895\) 5.28037e6 0.220347
\(896\) 0 0
\(897\) 3.77848e6 0.156796
\(898\) 0 0
\(899\) 1.83110e7 0.755635
\(900\) 0 0
\(901\) −1.27441e7 −0.522995
\(902\) 0 0
\(903\) 3.47977e6 0.142014
\(904\) 0 0
\(905\) −2.43845e6 −0.0989675
\(906\) 0 0
\(907\) 1.03030e7 0.415859 0.207929 0.978144i \(-0.433328\pi\)
0.207929 + 0.978144i \(0.433328\pi\)
\(908\) 0 0
\(909\) 8.68799e6 0.348746
\(910\) 0 0
\(911\) −3.82374e7 −1.52649 −0.763243 0.646111i \(-0.776394\pi\)
−0.763243 + 0.646111i \(0.776394\pi\)
\(912\) 0 0
\(913\) 7.12044e7 2.82703
\(914\) 0 0
\(915\) 6.66134e6 0.263032
\(916\) 0 0
\(917\) −7.80024e6 −0.306327
\(918\) 0 0
\(919\) 7.72150e6 0.301587 0.150794 0.988565i \(-0.451817\pi\)
0.150794 + 0.988565i \(0.451817\pi\)
\(920\) 0 0
\(921\) 1.64697e7 0.639790
\(922\) 0 0
\(923\) 6.63545e6 0.256369
\(924\) 0 0
\(925\) 9.23625e6 0.354929
\(926\) 0 0
\(927\) −2.13253e6 −0.0815073
\(928\) 0 0
\(929\) 3.39039e6 0.128888 0.0644438 0.997921i \(-0.479473\pi\)
0.0644438 + 0.997921i \(0.479473\pi\)
\(930\) 0 0
\(931\) 4.05651e7 1.53383
\(932\) 0 0
\(933\) 1.91080e6 0.0718640
\(934\) 0 0
\(935\) 1.26535e7 0.473351
\(936\) 0 0
\(937\) −7.67490e6 −0.285577 −0.142789 0.989753i \(-0.545607\pi\)
−0.142789 + 0.989753i \(0.545607\pi\)
\(938\) 0 0
\(939\) −1.32471e7 −0.490295
\(940\) 0 0
\(941\) −4.55115e7 −1.67551 −0.837756 0.546045i \(-0.816133\pi\)
−0.837756 + 0.546045i \(0.816133\pi\)
\(942\) 0 0
\(943\) 1.78001e7 0.651845
\(944\) 0 0
\(945\) −3.12200e6 −0.113724
\(946\) 0 0
\(947\) −2.28294e7 −0.827218 −0.413609 0.910455i \(-0.635732\pi\)
−0.413609 + 0.910455i \(0.635732\pi\)
\(948\) 0 0
\(949\) 3.83484e6 0.138223
\(950\) 0 0
\(951\) 6.80673e6 0.244055
\(952\) 0 0
\(953\) 4.64478e7 1.65666 0.828330 0.560241i \(-0.189291\pi\)
0.828330 + 0.560241i \(0.189291\pi\)
\(954\) 0 0
\(955\) −7.67896e6 −0.272454
\(956\) 0 0
\(957\) −1.82856e7 −0.645401
\(958\) 0 0
\(959\) 4.41842e6 0.155139
\(960\) 0 0
\(961\) −7.77779e6 −0.271674
\(962\) 0 0
\(963\) 1.35719e7 0.471603
\(964\) 0 0
\(965\) −310850. −0.0107456
\(966\) 0 0
\(967\) 2.63000e7 0.904460 0.452230 0.891901i \(-0.350629\pi\)
0.452230 + 0.891901i \(0.350629\pi\)
\(968\) 0 0
\(969\) −1.21306e7 −0.415022
\(970\) 0 0
\(971\) 2.19967e7 0.748704 0.374352 0.927287i \(-0.377865\pi\)
0.374352 + 0.927287i \(0.377865\pi\)
\(972\) 0 0
\(973\) 1.20187e7 0.406983
\(974\) 0 0
\(975\) −577116. −0.0194425
\(976\) 0 0
\(977\) 4.46750e7 1.49737 0.748683 0.662929i \(-0.230687\pi\)
0.748683 + 0.662929i \(0.230687\pi\)
\(978\) 0 0
\(979\) 2.20409e7 0.734977
\(980\) 0 0
\(981\) −2.26779e7 −0.752369
\(982\) 0 0
\(983\) −2.02740e7 −0.669201 −0.334600 0.942360i \(-0.608601\pi\)
−0.334600 + 0.942360i \(0.608601\pi\)
\(984\) 0 0
\(985\) −9.47145e6 −0.311047
\(986\) 0 0
\(987\) −1.68410e6 −0.0550270
\(988\) 0 0
\(989\) 5.08542e7 1.65324
\(990\) 0 0
\(991\) 1.49135e7 0.482386 0.241193 0.970477i \(-0.422461\pi\)
0.241193 + 0.970477i \(0.422461\pi\)
\(992\) 0 0
\(993\) 1.97960e6 0.0637095
\(994\) 0 0
\(995\) −1.91798e7 −0.614168
\(996\) 0 0
\(997\) −3.17032e7 −1.01010 −0.505052 0.863089i \(-0.668527\pi\)
−0.505052 + 0.863089i \(0.668527\pi\)
\(998\) 0 0
\(999\) 4.16851e7 1.32150
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 320.6.a.s.1.1 2
4.3 odd 2 inner 320.6.a.s.1.2 2
8.3 odd 2 160.6.a.d.1.1 2
8.5 even 2 160.6.a.d.1.2 yes 2
40.3 even 4 800.6.c.i.449.2 4
40.13 odd 4 800.6.c.i.449.3 4
40.19 odd 2 800.6.a.h.1.2 2
40.27 even 4 800.6.c.i.449.4 4
40.29 even 2 800.6.a.h.1.1 2
40.37 odd 4 800.6.c.i.449.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.6.a.d.1.1 2 8.3 odd 2
160.6.a.d.1.2 yes 2 8.5 even 2
320.6.a.s.1.1 2 1.1 even 1 trivial
320.6.a.s.1.2 2 4.3 odd 2 inner
800.6.a.h.1.1 2 40.29 even 2
800.6.a.h.1.2 2 40.19 odd 2
800.6.c.i.449.1 4 40.37 odd 4
800.6.c.i.449.2 4 40.3 even 4
800.6.c.i.449.3 4 40.13 odd 4
800.6.c.i.449.4 4 40.27 even 4