Properties

Label 80.6.a.f.1.1
Level 80
Weight 6
Character 80.1
Self dual yes
Analytic conductor 12.831
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 80.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(12.8307055850\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 40)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 80.1

$q$-expansion

\(f(q)\) \(=\) \(q+8.00000 q^{3} +25.0000 q^{5} +108.000 q^{7} -179.000 q^{9} +O(q^{10})\) \(q+8.00000 q^{3} +25.0000 q^{5} +108.000 q^{7} -179.000 q^{9} +604.000 q^{11} -306.000 q^{13} +200.000 q^{15} +930.000 q^{17} +1324.00 q^{19} +864.000 q^{21} +852.000 q^{23} +625.000 q^{25} -3376.00 q^{27} +5902.00 q^{29} +3320.00 q^{31} +4832.00 q^{33} +2700.00 q^{35} +10774.0 q^{37} -2448.00 q^{39} -17958.0 q^{41} -9264.00 q^{43} -4475.00 q^{45} +9796.00 q^{47} -5143.00 q^{49} +7440.00 q^{51} -31434.0 q^{53} +15100.0 q^{55} +10592.0 q^{57} -33228.0 q^{59} -40210.0 q^{61} -19332.0 q^{63} -7650.00 q^{65} -58864.0 q^{67} +6816.00 q^{69} +55312.0 q^{71} +27258.0 q^{73} +5000.00 q^{75} +65232.0 q^{77} -31456.0 q^{79} +16489.0 q^{81} -24552.0 q^{83} +23250.0 q^{85} +47216.0 q^{87} -90854.0 q^{89} -33048.0 q^{91} +26560.0 q^{93} +33100.0 q^{95} +154706. q^{97} -108116. q^{99} +O(q^{100})\)

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
\(3\) 8.00000 0.513200 0.256600 0.966518i \(-0.417398\pi\)
0.256600 + 0.966518i \(0.417398\pi\)
\(4\) 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
\(9\) −179.000 −0.736626
\(10\) 0 0
\(11\) 604.000 1.50506 0.752532 0.658555i \(-0.228832\pi\)
0.752532 + 0.658555i \(0.228832\pi\)
\(12\) 0 0
\(13\) −306.000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(14\) 0 0
\(15\) 200.000 0.229510
\(16\) 0 0
\(17\) 930.000 0.780478 0.390239 0.920714i \(-0.372392\pi\)
0.390239 + 0.920714i \(0.372392\pi\)
\(18\) 0 0
\(19\) 1324.00 0.841403 0.420701 0.907199i \(-0.361784\pi\)
0.420701 + 0.907199i \(0.361784\pi\)
\(20\) 0 0
\(21\) 864.000 0.427529
\(22\) 0 0
\(23\) 852.000 0.335830 0.167915 0.985801i \(-0.446297\pi\)
0.167915 + 0.985801i \(0.446297\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) −3376.00 −0.891237
\(28\) 0 0
\(29\) 5902.00 1.30318 0.651590 0.758572i \(-0.274102\pi\)
0.651590 + 0.758572i \(0.274102\pi\)
\(30\) 0 0
\(31\) 3320.00 0.620489 0.310244 0.950657i \(-0.399589\pi\)
0.310244 + 0.950657i \(0.399589\pi\)
\(32\) 0 0
\(33\) 4832.00 0.772400
\(34\) 0 0
\(35\) 2700.00 0.372558
\(36\) 0 0
\(37\) 10774.0 1.29382 0.646908 0.762568i \(-0.276062\pi\)
0.646908 + 0.762568i \(0.276062\pi\)
\(38\) 0 0
\(39\) −2448.00 −0.257721
\(40\) 0 0
\(41\) −17958.0 −1.66839 −0.834196 0.551467i \(-0.814068\pi\)
−0.834196 + 0.551467i \(0.814068\pi\)
\(42\) 0 0
\(43\) −9264.00 −0.764060 −0.382030 0.924150i \(-0.624775\pi\)
−0.382030 + 0.924150i \(0.624775\pi\)
\(44\) 0 0
\(45\) −4475.00 −0.329429
\(46\) 0 0
\(47\) 9796.00 0.646851 0.323425 0.946254i \(-0.395166\pi\)
0.323425 + 0.946254i \(0.395166\pi\)
\(48\) 0 0
\(49\) −5143.00 −0.306003
\(50\) 0 0
\(51\) 7440.00 0.400541
\(52\) 0 0
\(53\) −31434.0 −1.53713 −0.768564 0.639773i \(-0.779028\pi\)
−0.768564 + 0.639773i \(0.779028\pi\)
\(54\) 0 0
\(55\) 15100.0 0.673085
\(56\) 0 0
\(57\) 10592.0 0.431808
\(58\) 0 0
\(59\) −33228.0 −1.24272 −0.621361 0.783524i \(-0.713420\pi\)
−0.621361 + 0.783524i \(0.713420\pi\)
\(60\) 0 0
\(61\) −40210.0 −1.38360 −0.691798 0.722091i \(-0.743181\pi\)
−0.691798 + 0.722091i \(0.743181\pi\)
\(62\) 0 0
\(63\) −19332.0 −0.613657
\(64\) 0 0
\(65\) −7650.00 −0.224584
\(66\) 0 0
\(67\) −58864.0 −1.60200 −0.801000 0.598664i \(-0.795699\pi\)
−0.801000 + 0.598664i \(0.795699\pi\)
\(68\) 0 0
\(69\) 6816.00 0.172348
\(70\) 0 0
\(71\) 55312.0 1.30219 0.651094 0.758997i \(-0.274310\pi\)
0.651094 + 0.758997i \(0.274310\pi\)
\(72\) 0 0
\(73\) 27258.0 0.598669 0.299335 0.954148i \(-0.403235\pi\)
0.299335 + 0.954148i \(0.403235\pi\)
\(74\) 0 0
\(75\) 5000.00 0.102640
\(76\) 0 0
\(77\) 65232.0 1.25382
\(78\) 0 0
\(79\) −31456.0 −0.567069 −0.283534 0.958962i \(-0.591507\pi\)
−0.283534 + 0.958962i \(0.591507\pi\)
\(80\) 0 0
\(81\) 16489.0 0.279243
\(82\) 0 0
\(83\) −24552.0 −0.391194 −0.195597 0.980684i \(-0.562664\pi\)
−0.195597 + 0.980684i \(0.562664\pi\)
\(84\) 0 0
\(85\) 23250.0 0.349040
\(86\) 0 0
\(87\) 47216.0 0.668792
\(88\) 0 0
\(89\) −90854.0 −1.21582 −0.607910 0.794006i \(-0.707992\pi\)
−0.607910 + 0.794006i \(0.707992\pi\)
\(90\) 0 0
\(91\) −33048.0 −0.418352
\(92\) 0 0
\(93\) 26560.0 0.318435
\(94\) 0 0
\(95\) 33100.0 0.376287
\(96\) 0 0
\(97\) 154706. 1.66947 0.834733 0.550654i \(-0.185622\pi\)
0.834733 + 0.550654i \(0.185622\pi\)
\(98\) 0 0
\(99\) −108116. −1.10867
\(100\) 0 0
\(101\) −72714.0 −0.709275 −0.354637 0.935004i \(-0.615396\pi\)
−0.354637 + 0.935004i \(0.615396\pi\)
\(102\) 0 0
\(103\) 129396. 1.20179 0.600894 0.799329i \(-0.294811\pi\)
0.600894 + 0.799329i \(0.294811\pi\)
\(104\) 0 0
\(105\) 21600.0 0.191197
\(106\) 0 0
\(107\) 206680. 1.74518 0.872588 0.488458i \(-0.162440\pi\)
0.872588 + 0.488458i \(0.162440\pi\)
\(108\) 0 0
\(109\) −70146.0 −0.565505 −0.282753 0.959193i \(-0.591248\pi\)
−0.282753 + 0.959193i \(0.591248\pi\)
\(110\) 0 0
\(111\) 86192.0 0.663987
\(112\) 0 0
\(113\) −151854. −1.11874 −0.559371 0.828917i \(-0.688957\pi\)
−0.559371 + 0.828917i \(0.688957\pi\)
\(114\) 0 0
\(115\) 21300.0 0.150188
\(116\) 0 0
\(117\) 54774.0 0.369922
\(118\) 0 0
\(119\) 100440. 0.650189
\(120\) 0 0
\(121\) 203765. 1.26522
\(122\) 0 0
\(123\) −143664. −0.856220
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) 336596. 1.85182 0.925912 0.377740i \(-0.123299\pi\)
0.925912 + 0.377740i \(0.123299\pi\)
\(128\) 0 0
\(129\) −74112.0 −0.392116
\(130\) 0 0
\(131\) −275308. −1.40165 −0.700827 0.713332i \(-0.747185\pi\)
−0.700827 + 0.713332i \(0.747185\pi\)
\(132\) 0 0
\(133\) 142992. 0.700943
\(134\) 0 0
\(135\) −84400.0 −0.398573
\(136\) 0 0
\(137\) −228502. −1.04013 −0.520066 0.854126i \(-0.674093\pi\)
−0.520066 + 0.854126i \(0.674093\pi\)
\(138\) 0 0
\(139\) −224284. −0.984603 −0.492302 0.870425i \(-0.663844\pi\)
−0.492302 + 0.870425i \(0.663844\pi\)
\(140\) 0 0
\(141\) 78368.0 0.331964
\(142\) 0 0
\(143\) −184824. −0.755820
\(144\) 0 0
\(145\) 147550. 0.582800
\(146\) 0 0
\(147\) −41144.0 −0.157041
\(148\) 0 0
\(149\) −183802. −0.678242 −0.339121 0.940743i \(-0.610130\pi\)
−0.339121 + 0.940743i \(0.610130\pi\)
\(150\) 0 0
\(151\) −296032. −1.05657 −0.528283 0.849069i \(-0.677164\pi\)
−0.528283 + 0.849069i \(0.677164\pi\)
\(152\) 0 0
\(153\) −166470. −0.574920
\(154\) 0 0
\(155\) 83000.0 0.277491
\(156\) 0 0
\(157\) 134766. 0.436346 0.218173 0.975910i \(-0.429990\pi\)
0.218173 + 0.975910i \(0.429990\pi\)
\(158\) 0 0
\(159\) −251472. −0.788854
\(160\) 0 0
\(161\) 92016.0 0.279768
\(162\) 0 0
\(163\) 60248.0 0.177613 0.0888063 0.996049i \(-0.471695\pi\)
0.0888063 + 0.996049i \(0.471695\pi\)
\(164\) 0 0
\(165\) 120800. 0.345428
\(166\) 0 0
\(167\) 62012.0 0.172062 0.0860309 0.996292i \(-0.472582\pi\)
0.0860309 + 0.996292i \(0.472582\pi\)
\(168\) 0 0
\(169\) −277657. −0.747811
\(170\) 0 0
\(171\) −236996. −0.619799
\(172\) 0 0
\(173\) −591682. −1.50305 −0.751524 0.659705i \(-0.770681\pi\)
−0.751524 + 0.659705i \(0.770681\pi\)
\(174\) 0 0
\(175\) 67500.0 0.166613
\(176\) 0 0
\(177\) −265824. −0.637766
\(178\) 0 0
\(179\) 241404. 0.563134 0.281567 0.959542i \(-0.409146\pi\)
0.281567 + 0.959542i \(0.409146\pi\)
\(180\) 0 0
\(181\) 187622. 0.425684 0.212842 0.977087i \(-0.431728\pi\)
0.212842 + 0.977087i \(0.431728\pi\)
\(182\) 0 0
\(183\) −321680. −0.710062
\(184\) 0 0
\(185\) 269350. 0.578612
\(186\) 0 0
\(187\) 561720. 1.17467
\(188\) 0 0
\(189\) −364608. −0.742458
\(190\) 0 0
\(191\) −37560.0 −0.0744976 −0.0372488 0.999306i \(-0.511859\pi\)
−0.0372488 + 0.999306i \(0.511859\pi\)
\(192\) 0 0
\(193\) 164434. 0.317759 0.158880 0.987298i \(-0.449212\pi\)
0.158880 + 0.987298i \(0.449212\pi\)
\(194\) 0 0
\(195\) −61200.0 −0.115256
\(196\) 0 0
\(197\) 360518. 0.661853 0.330926 0.943657i \(-0.392639\pi\)
0.330926 + 0.943657i \(0.392639\pi\)
\(198\) 0 0
\(199\) 654168. 1.17100 0.585500 0.810673i \(-0.300898\pi\)
0.585500 + 0.810673i \(0.300898\pi\)
\(200\) 0 0
\(201\) −470912. −0.822147
\(202\) 0 0
\(203\) 637416. 1.08563
\(204\) 0 0
\(205\) −448950. −0.746128
\(206\) 0 0
\(207\) −152508. −0.247381
\(208\) 0 0
\(209\) 799696. 1.26637
\(210\) 0 0
\(211\) 693156. 1.07183 0.535914 0.844273i \(-0.319967\pi\)
0.535914 + 0.844273i \(0.319967\pi\)
\(212\) 0 0
\(213\) 442496. 0.668283
\(214\) 0 0
\(215\) −231600. −0.341698
\(216\) 0 0
\(217\) 358560. 0.516907
\(218\) 0 0
\(219\) 218064. 0.307237
\(220\) 0 0
\(221\) −284580. −0.391944
\(222\) 0 0
\(223\) −494756. −0.666237 −0.333119 0.942885i \(-0.608101\pi\)
−0.333119 + 0.942885i \(0.608101\pi\)
\(224\) 0 0
\(225\) −111875. −0.147325
\(226\) 0 0
\(227\) −907088. −1.16838 −0.584191 0.811616i \(-0.698588\pi\)
−0.584191 + 0.811616i \(0.698588\pi\)
\(228\) 0 0
\(229\) 1.08949e6 1.37289 0.686446 0.727181i \(-0.259170\pi\)
0.686446 + 0.727181i \(0.259170\pi\)
\(230\) 0 0
\(231\) 521856. 0.643459
\(232\) 0 0
\(233\) 499706. 0.603010 0.301505 0.953465i \(-0.402511\pi\)
0.301505 + 0.953465i \(0.402511\pi\)
\(234\) 0 0
\(235\) 244900. 0.289280
\(236\) 0 0
\(237\) −251648. −0.291020
\(238\) 0 0
\(239\) −1.62038e6 −1.83495 −0.917473 0.397799i \(-0.869774\pi\)
−0.917473 + 0.397799i \(0.869774\pi\)
\(240\) 0 0
\(241\) 1.00122e6 1.11042 0.555208 0.831711i \(-0.312638\pi\)
0.555208 + 0.831711i \(0.312638\pi\)
\(242\) 0 0
\(243\) 952280. 1.03454
\(244\) 0 0
\(245\) −128575. −0.136849
\(246\) 0 0
\(247\) −405144. −0.422539
\(248\) 0 0
\(249\) −196416. −0.200761
\(250\) 0 0
\(251\) −368980. −0.369674 −0.184837 0.982769i \(-0.559176\pi\)
−0.184837 + 0.982769i \(0.559176\pi\)
\(252\) 0 0
\(253\) 514608. 0.505447
\(254\) 0 0
\(255\) 186000. 0.179128
\(256\) 0 0
\(257\) 279010. 0.263504 0.131752 0.991283i \(-0.457940\pi\)
0.131752 + 0.991283i \(0.457940\pi\)
\(258\) 0 0
\(259\) 1.16359e6 1.07783
\(260\) 0 0
\(261\) −1.05646e6 −0.959955
\(262\) 0 0
\(263\) −811740. −0.723648 −0.361824 0.932246i \(-0.617846\pi\)
−0.361824 + 0.932246i \(0.617846\pi\)
\(264\) 0 0
\(265\) −785850. −0.687424
\(266\) 0 0
\(267\) −726832. −0.623959
\(268\) 0 0
\(269\) 353214. 0.297617 0.148808 0.988866i \(-0.452456\pi\)
0.148808 + 0.988866i \(0.452456\pi\)
\(270\) 0 0
\(271\) 1.71622e6 1.41954 0.709772 0.704432i \(-0.248798\pi\)
0.709772 + 0.704432i \(0.248798\pi\)
\(272\) 0 0
\(273\) −264384. −0.214698
\(274\) 0 0
\(275\) 377500. 0.301013
\(276\) 0 0
\(277\) −245882. −0.192543 −0.0962714 0.995355i \(-0.530692\pi\)
−0.0962714 + 0.995355i \(0.530692\pi\)
\(278\) 0 0
\(279\) −594280. −0.457068
\(280\) 0 0
\(281\) −1.67618e6 −1.26635 −0.633177 0.774007i \(-0.718250\pi\)
−0.633177 + 0.774007i \(0.718250\pi\)
\(282\) 0 0
\(283\) 1.25882e6 0.934321 0.467161 0.884173i \(-0.345277\pi\)
0.467161 + 0.884173i \(0.345277\pi\)
\(284\) 0 0
\(285\) 264800. 0.193110
\(286\) 0 0
\(287\) −1.93946e6 −1.38988
\(288\) 0 0
\(289\) −554957. −0.390854
\(290\) 0 0
\(291\) 1.23765e6 0.856771
\(292\) 0 0
\(293\) 719158. 0.489390 0.244695 0.969600i \(-0.421312\pi\)
0.244695 + 0.969600i \(0.421312\pi\)
\(294\) 0 0
\(295\) −830700. −0.555762
\(296\) 0 0
\(297\) −2.03910e6 −1.34137
\(298\) 0 0
\(299\) −260712. −0.168649
\(300\) 0 0
\(301\) −1.00051e6 −0.636511
\(302\) 0 0
\(303\) −581712. −0.364000
\(304\) 0 0
\(305\) −1.00525e6 −0.618763
\(306\) 0 0
\(307\) −1.86013e6 −1.12641 −0.563206 0.826317i \(-0.690432\pi\)
−0.563206 + 0.826317i \(0.690432\pi\)
\(308\) 0 0
\(309\) 1.03517e6 0.616758
\(310\) 0 0
\(311\) −278384. −0.163209 −0.0816043 0.996665i \(-0.526004\pi\)
−0.0816043 + 0.996665i \(0.526004\pi\)
\(312\) 0 0
\(313\) −474182. −0.273580 −0.136790 0.990600i \(-0.543679\pi\)
−0.136790 + 0.990600i \(0.543679\pi\)
\(314\) 0 0
\(315\) −483300. −0.274436
\(316\) 0 0
\(317\) −1.83738e6 −1.02695 −0.513476 0.858104i \(-0.671643\pi\)
−0.513476 + 0.858104i \(0.671643\pi\)
\(318\) 0 0
\(319\) 3.56481e6 1.96137
\(320\) 0 0
\(321\) 1.65344e6 0.895624
\(322\) 0 0
\(323\) 1.23132e6 0.656696
\(324\) 0 0
\(325\) −191250. −0.100437
\(326\) 0 0
\(327\) −561168. −0.290217
\(328\) 0 0
\(329\) 1.05797e6 0.538868
\(330\) 0 0
\(331\) −2.99743e6 −1.50376 −0.751880 0.659299i \(-0.770853\pi\)
−0.751880 + 0.659299i \(0.770853\pi\)
\(332\) 0 0
\(333\) −1.92855e6 −0.953058
\(334\) 0 0
\(335\) −1.47160e6 −0.716437
\(336\) 0 0
\(337\) 1.87531e6 0.899496 0.449748 0.893155i \(-0.351514\pi\)
0.449748 + 0.893155i \(0.351514\pi\)
\(338\) 0 0
\(339\) −1.21483e6 −0.574139
\(340\) 0 0
\(341\) 2.00528e6 0.933876
\(342\) 0 0
\(343\) −2.37060e6 −1.08799
\(344\) 0 0
\(345\) 170400. 0.0770765
\(346\) 0 0
\(347\) −180312. −0.0803898 −0.0401949 0.999192i \(-0.512798\pi\)
−0.0401949 + 0.999192i \(0.512798\pi\)
\(348\) 0 0
\(349\) −87058.0 −0.0382600 −0.0191300 0.999817i \(-0.506090\pi\)
−0.0191300 + 0.999817i \(0.506090\pi\)
\(350\) 0 0
\(351\) 1.03306e6 0.447565
\(352\) 0 0
\(353\) 2.65901e6 1.13575 0.567876 0.823114i \(-0.307765\pi\)
0.567876 + 0.823114i \(0.307765\pi\)
\(354\) 0 0
\(355\) 1.38280e6 0.582356
\(356\) 0 0
\(357\) 803520. 0.333677
\(358\) 0 0
\(359\) 2.14937e6 0.880186 0.440093 0.897952i \(-0.354945\pi\)
0.440093 + 0.897952i \(0.354945\pi\)
\(360\) 0 0
\(361\) −723123. −0.292041
\(362\) 0 0
\(363\) 1.63012e6 0.649311
\(364\) 0 0
\(365\) 681450. 0.267733
\(366\) 0 0
\(367\) 3.08258e6 1.19467 0.597337 0.801991i \(-0.296226\pi\)
0.597337 + 0.801991i \(0.296226\pi\)
\(368\) 0 0
\(369\) 3.21448e6 1.22898
\(370\) 0 0
\(371\) −3.39487e6 −1.28053
\(372\) 0 0
\(373\) 2.28727e6 0.851227 0.425613 0.904905i \(-0.360058\pi\)
0.425613 + 0.904905i \(0.360058\pi\)
\(374\) 0 0
\(375\) 125000. 0.0459020
\(376\) 0 0
\(377\) −1.80601e6 −0.654436
\(378\) 0 0
\(379\) 1.30154e6 0.465435 0.232718 0.972544i \(-0.425238\pi\)
0.232718 + 0.972544i \(0.425238\pi\)
\(380\) 0 0
\(381\) 2.69277e6 0.950356
\(382\) 0 0
\(383\) 2.03276e6 0.708093 0.354046 0.935228i \(-0.384806\pi\)
0.354046 + 0.935228i \(0.384806\pi\)
\(384\) 0 0
\(385\) 1.63080e6 0.560724
\(386\) 0 0
\(387\) 1.65826e6 0.562826
\(388\) 0 0
\(389\) 94230.0 0.0315730 0.0157865 0.999875i \(-0.494975\pi\)
0.0157865 + 0.999875i \(0.494975\pi\)
\(390\) 0 0
\(391\) 792360. 0.262108
\(392\) 0 0
\(393\) −2.20246e6 −0.719329
\(394\) 0 0
\(395\) −786400. −0.253601
\(396\) 0 0
\(397\) −5.55551e6 −1.76908 −0.884540 0.466465i \(-0.845527\pi\)
−0.884540 + 0.466465i \(0.845527\pi\)
\(398\) 0 0
\(399\) 1.14394e6 0.359724
\(400\) 0 0
\(401\) −784814. −0.243728 −0.121864 0.992547i \(-0.538887\pi\)
−0.121864 + 0.992547i \(0.538887\pi\)
\(402\) 0 0
\(403\) −1.01592e6 −0.311600
\(404\) 0 0
\(405\) 412225. 0.124881
\(406\) 0 0
\(407\) 6.50750e6 1.94728
\(408\) 0 0
\(409\) −4.59401e6 −1.35795 −0.678974 0.734162i \(-0.737575\pi\)
−0.678974 + 0.734162i \(0.737575\pi\)
\(410\) 0 0
\(411\) −1.82802e6 −0.533796
\(412\) 0 0
\(413\) −3.58862e6 −1.03527
\(414\) 0 0
\(415\) −613800. −0.174947
\(416\) 0 0
\(417\) −1.79427e6 −0.505299
\(418\) 0 0
\(419\) −1.41301e6 −0.393198 −0.196599 0.980484i \(-0.562990\pi\)
−0.196599 + 0.980484i \(0.562990\pi\)
\(420\) 0 0
\(421\) 5.94556e6 1.63489 0.817443 0.576010i \(-0.195391\pi\)
0.817443 + 0.576010i \(0.195391\pi\)
\(422\) 0 0
\(423\) −1.75348e6 −0.476487
\(424\) 0 0
\(425\) 581250. 0.156096
\(426\) 0 0
\(427\) −4.34268e6 −1.15263
\(428\) 0 0
\(429\) −1.47859e6 −0.387887
\(430\) 0 0
\(431\) 6.48114e6 1.68058 0.840289 0.542139i \(-0.182385\pi\)
0.840289 + 0.542139i \(0.182385\pi\)
\(432\) 0 0
\(433\) 4.05597e6 1.03962 0.519810 0.854282i \(-0.326003\pi\)
0.519810 + 0.854282i \(0.326003\pi\)
\(434\) 0 0
\(435\) 1.18040e6 0.299093
\(436\) 0 0
\(437\) 1.12805e6 0.282569
\(438\) 0 0
\(439\) 1.21450e6 0.300772 0.150386 0.988627i \(-0.451948\pi\)
0.150386 + 0.988627i \(0.451948\pi\)
\(440\) 0 0
\(441\) 920597. 0.225410
\(442\) 0 0
\(443\) 5.53154e6 1.33917 0.669586 0.742734i \(-0.266472\pi\)
0.669586 + 0.742734i \(0.266472\pi\)
\(444\) 0 0
\(445\) −2.27135e6 −0.543731
\(446\) 0 0
\(447\) −1.47042e6 −0.348074
\(448\) 0 0
\(449\) 2.20111e6 0.515258 0.257629 0.966244i \(-0.417059\pi\)
0.257629 + 0.966244i \(0.417059\pi\)
\(450\) 0 0
\(451\) −1.08466e7 −2.51104
\(452\) 0 0
\(453\) −2.36826e6 −0.542229
\(454\) 0 0
\(455\) −826200. −0.187093
\(456\) 0 0
\(457\) 3.29835e6 0.738764 0.369382 0.929278i \(-0.379569\pi\)
0.369382 + 0.929278i \(0.379569\pi\)
\(458\) 0 0
\(459\) −3.13968e6 −0.695591
\(460\) 0 0
\(461\) −3.94266e6 −0.864046 −0.432023 0.901863i \(-0.642200\pi\)
−0.432023 + 0.901863i \(0.642200\pi\)
\(462\) 0 0
\(463\) −8.82040e6 −1.91221 −0.956106 0.293021i \(-0.905339\pi\)
−0.956106 + 0.293021i \(0.905339\pi\)
\(464\) 0 0
\(465\) 664000. 0.142408
\(466\) 0 0
\(467\) 1.28709e6 0.273096 0.136548 0.990633i \(-0.456399\pi\)
0.136548 + 0.990633i \(0.456399\pi\)
\(468\) 0 0
\(469\) −6.35731e6 −1.33457
\(470\) 0 0
\(471\) 1.07813e6 0.223933
\(472\) 0 0
\(473\) −5.59546e6 −1.14996
\(474\) 0 0
\(475\) 827500. 0.168281
\(476\) 0 0
\(477\) 5.62669e6 1.13229
\(478\) 0 0
\(479\) −6.51179e6 −1.29677 −0.648383 0.761314i \(-0.724555\pi\)
−0.648383 + 0.761314i \(0.724555\pi\)
\(480\) 0 0
\(481\) −3.29684e6 −0.649734
\(482\) 0 0
\(483\) 736128. 0.143577
\(484\) 0 0
\(485\) 3.86765e6 0.746608
\(486\) 0 0
\(487\) 5.79523e6 1.10726 0.553628 0.832764i \(-0.313243\pi\)
0.553628 + 0.832764i \(0.313243\pi\)
\(488\) 0 0
\(489\) 481984. 0.0911508
\(490\) 0 0
\(491\) −990276. −0.185376 −0.0926878 0.995695i \(-0.529546\pi\)
−0.0926878 + 0.995695i \(0.529546\pi\)
\(492\) 0 0
\(493\) 5.48886e6 1.01710
\(494\) 0 0
\(495\) −2.70290e6 −0.495812
\(496\) 0 0
\(497\) 5.97370e6 1.08481
\(498\) 0 0
\(499\) −2.91500e6 −0.524067 −0.262033 0.965059i \(-0.584393\pi\)
−0.262033 + 0.965059i \(0.584393\pi\)
\(500\) 0 0
\(501\) 496096. 0.0883022
\(502\) 0 0
\(503\) −2.47872e6 −0.436824 −0.218412 0.975857i \(-0.570088\pi\)
−0.218412 + 0.975857i \(0.570088\pi\)
\(504\) 0 0
\(505\) −1.81785e6 −0.317197
\(506\) 0 0
\(507\) −2.22126e6 −0.383777
\(508\) 0 0
\(509\) −6.75807e6 −1.15619 −0.578093 0.815971i \(-0.696203\pi\)
−0.578093 + 0.815971i \(0.696203\pi\)
\(510\) 0 0
\(511\) 2.94386e6 0.498730
\(512\) 0 0
\(513\) −4.46982e6 −0.749889
\(514\) 0 0
\(515\) 3.23490e6 0.537456
\(516\) 0 0
\(517\) 5.91678e6 0.973552
\(518\) 0 0
\(519\) −4.73346e6 −0.771365
\(520\) 0 0
\(521\) −6.33903e6 −1.02312 −0.511562 0.859246i \(-0.670933\pi\)
−0.511562 + 0.859246i \(0.670933\pi\)
\(522\) 0 0
\(523\) −231920. −0.0370752 −0.0185376 0.999828i \(-0.505901\pi\)
−0.0185376 + 0.999828i \(0.505901\pi\)
\(524\) 0 0
\(525\) 540000. 0.0855058
\(526\) 0 0
\(527\) 3.08760e6 0.484278
\(528\) 0 0
\(529\) −5.71044e6 −0.887218
\(530\) 0 0
\(531\) 5.94781e6 0.915421
\(532\) 0 0
\(533\) 5.49515e6 0.837841
\(534\) 0 0
\(535\) 5.16700e6 0.780466
\(536\) 0 0
\(537\) 1.93123e6 0.289001
\(538\) 0 0
\(539\) −3.10637e6 −0.460555
\(540\) 0 0
\(541\) −9.44440e6 −1.38733 −0.693667 0.720295i \(-0.744006\pi\)
−0.693667 + 0.720295i \(0.744006\pi\)
\(542\) 0 0
\(543\) 1.50098e6 0.218461
\(544\) 0 0
\(545\) −1.75365e6 −0.252902
\(546\) 0 0
\(547\) −3.10162e6 −0.443220 −0.221610 0.975135i \(-0.571131\pi\)
−0.221610 + 0.975135i \(0.571131\pi\)
\(548\) 0 0
\(549\) 7.19759e6 1.01919
\(550\) 0 0
\(551\) 7.81425e6 1.09650
\(552\) 0 0
\(553\) −3.39725e6 −0.472405
\(554\) 0 0
\(555\) 2.15480e6 0.296944
\(556\) 0 0
\(557\) −1.22330e6 −0.167068 −0.0835342 0.996505i \(-0.526621\pi\)
−0.0835342 + 0.996505i \(0.526621\pi\)
\(558\) 0 0
\(559\) 2.83478e6 0.383699
\(560\) 0 0
\(561\) 4.49376e6 0.602841
\(562\) 0 0
\(563\) 1.40896e7 1.87339 0.936693 0.350151i \(-0.113870\pi\)
0.936693 + 0.350151i \(0.113870\pi\)
\(564\) 0 0
\(565\) −3.79635e6 −0.500317
\(566\) 0 0
\(567\) 1.78081e6 0.232627
\(568\) 0 0
\(569\) 1.48468e6 0.192244 0.0961220 0.995370i \(-0.469356\pi\)
0.0961220 + 0.995370i \(0.469356\pi\)
\(570\) 0 0
\(571\) 2.86470e6 0.367696 0.183848 0.982955i \(-0.441145\pi\)
0.183848 + 0.982955i \(0.441145\pi\)
\(572\) 0 0
\(573\) −300480. −0.0382322
\(574\) 0 0
\(575\) 532500. 0.0671661
\(576\) 0 0
\(577\) 4.21728e6 0.527343 0.263671 0.964613i \(-0.415067\pi\)
0.263671 + 0.964613i \(0.415067\pi\)
\(578\) 0 0
\(579\) 1.31547e6 0.163074
\(580\) 0 0
\(581\) −2.65162e6 −0.325889
\(582\) 0 0
\(583\) −1.89861e7 −2.31348
\(584\) 0 0
\(585\) 1.36935e6 0.165434
\(586\) 0 0
\(587\) 2.01047e6 0.240826 0.120413 0.992724i \(-0.461578\pi\)
0.120413 + 0.992724i \(0.461578\pi\)
\(588\) 0 0
\(589\) 4.39568e6 0.522081
\(590\) 0 0
\(591\) 2.88414e6 0.339663
\(592\) 0 0
\(593\) 7.33691e6 0.856795 0.428397 0.903590i \(-0.359078\pi\)
0.428397 + 0.903590i \(0.359078\pi\)
\(594\) 0 0
\(595\) 2.51100e6 0.290773
\(596\) 0 0
\(597\) 5.23334e6 0.600957
\(598\) 0 0
\(599\) −1.14884e6 −0.130826 −0.0654128 0.997858i \(-0.520836\pi\)
−0.0654128 + 0.997858i \(0.520836\pi\)
\(600\) 0 0
\(601\) 1.16409e7 1.31462 0.657312 0.753618i \(-0.271693\pi\)
0.657312 + 0.753618i \(0.271693\pi\)
\(602\) 0 0
\(603\) 1.05367e7 1.18007
\(604\) 0 0
\(605\) 5.09412e6 0.565824
\(606\) 0 0
\(607\) 155540. 0.0171345 0.00856723 0.999963i \(-0.497273\pi\)
0.00856723 + 0.999963i \(0.497273\pi\)
\(608\) 0 0
\(609\) 5.09933e6 0.557147
\(610\) 0 0
\(611\) −2.99758e6 −0.324838
\(612\) 0 0
\(613\) −1.18137e7 −1.26980 −0.634899 0.772595i \(-0.718958\pi\)
−0.634899 + 0.772595i \(0.718958\pi\)
\(614\) 0 0
\(615\) −3.59160e6 −0.382913
\(616\) 0 0
\(617\) 6.42252e6 0.679192 0.339596 0.940571i \(-0.389710\pi\)
0.339596 + 0.940571i \(0.389710\pi\)
\(618\) 0 0
\(619\) −3.85252e6 −0.404128 −0.202064 0.979372i \(-0.564765\pi\)
−0.202064 + 0.979372i \(0.564765\pi\)
\(620\) 0 0
\(621\) −2.87635e6 −0.299304
\(622\) 0 0
\(623\) −9.81223e6 −1.01286
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 6.39757e6 0.649899
\(628\) 0 0
\(629\) 1.00198e7 1.00980
\(630\) 0 0
\(631\) 6.75136e6 0.675022 0.337511 0.941322i \(-0.390415\pi\)
0.337511 + 0.941322i \(0.390415\pi\)
\(632\) 0 0
\(633\) 5.54525e6 0.550062
\(634\) 0 0
\(635\) 8.41490e6 0.828161
\(636\) 0 0
\(637\) 1.57376e6 0.153670
\(638\) 0 0
\(639\) −9.90085e6 −0.959224
\(640\) 0 0
\(641\) −7.35493e6 −0.707022 −0.353511 0.935430i \(-0.615012\pi\)
−0.353511 + 0.935430i \(0.615012\pi\)
\(642\) 0 0
\(643\) −1.59694e7 −1.52322 −0.761610 0.648036i \(-0.775591\pi\)
−0.761610 + 0.648036i \(0.775591\pi\)
\(644\) 0 0
\(645\) −1.85280e6 −0.175359
\(646\) 0 0
\(647\) −1.72667e7 −1.62162 −0.810809 0.585311i \(-0.800972\pi\)
−0.810809 + 0.585311i \(0.800972\pi\)
\(648\) 0 0
\(649\) −2.00697e7 −1.87038
\(650\) 0 0
\(651\) 2.86848e6 0.265277
\(652\) 0 0
\(653\) −1.36251e6 −0.125043 −0.0625213 0.998044i \(-0.519914\pi\)
−0.0625213 + 0.998044i \(0.519914\pi\)
\(654\) 0 0
\(655\) −6.88270e6 −0.626838
\(656\) 0 0
\(657\) −4.87918e6 −0.440995
\(658\) 0 0
\(659\) 8.81808e6 0.790971 0.395485 0.918472i \(-0.370576\pi\)
0.395485 + 0.918472i \(0.370576\pi\)
\(660\) 0 0
\(661\) −1.52035e6 −0.135344 −0.0676720 0.997708i \(-0.521557\pi\)
−0.0676720 + 0.997708i \(0.521557\pi\)
\(662\) 0 0
\(663\) −2.27664e6 −0.201146
\(664\) 0 0
\(665\) 3.57480e6 0.313471
\(666\) 0 0
\(667\) 5.02850e6 0.437647
\(668\) 0 0
\(669\) −3.95805e6 −0.341913
\(670\) 0 0
\(671\) −2.42868e7 −2.08240
\(672\) 0 0
\(673\) −315086. −0.0268158 −0.0134079 0.999910i \(-0.504268\pi\)
−0.0134079 + 0.999910i \(0.504268\pi\)
\(674\) 0 0
\(675\) −2.11000e6 −0.178247
\(676\) 0 0
\(677\) −1.74092e6 −0.145985 −0.0729924 0.997332i \(-0.523255\pi\)
−0.0729924 + 0.997332i \(0.523255\pi\)
\(678\) 0 0
\(679\) 1.67082e7 1.39077
\(680\) 0 0
\(681\) −7.25670e6 −0.599614
\(682\) 0 0
\(683\) 1.98935e7 1.63177 0.815885 0.578214i \(-0.196250\pi\)
0.815885 + 0.578214i \(0.196250\pi\)
\(684\) 0 0
\(685\) −5.71255e6 −0.465161
\(686\) 0 0
\(687\) 8.71595e6 0.704568
\(688\) 0 0
\(689\) 9.61880e6 0.771921
\(690\) 0 0
\(691\) −2.01519e7 −1.60554 −0.802770 0.596289i \(-0.796641\pi\)
−0.802770 + 0.596289i \(0.796641\pi\)
\(692\) 0 0
\(693\) −1.16765e7 −0.923593
\(694\) 0 0
\(695\) −5.60710e6 −0.440328
\(696\) 0 0
\(697\) −1.67009e7 −1.30214
\(698\) 0 0
\(699\) 3.99765e6 0.309465
\(700\) 0 0
\(701\) 8.10766e6 0.623161 0.311581 0.950220i \(-0.399142\pi\)
0.311581 + 0.950220i \(0.399142\pi\)
\(702\) 0 0
\(703\) 1.42648e7 1.08862
\(704\) 0 0
\(705\) 1.95920e6 0.148459
\(706\) 0 0
\(707\) −7.85311e6 −0.590872
\(708\) 0 0
\(709\) −1.35613e7 −1.01317 −0.506587 0.862189i \(-0.669093\pi\)
−0.506587 + 0.862189i \(0.669093\pi\)
\(710\) 0 0
\(711\) 5.63062e6 0.417717
\(712\) 0 0
\(713\) 2.82864e6 0.208379
\(714\) 0 0
\(715\) −4.62060e6 −0.338013
\(716\) 0 0
\(717\) −1.29631e7 −0.941695
\(718\) 0 0
\(719\) −4.28314e6 −0.308987 −0.154493 0.987994i \(-0.549375\pi\)
−0.154493 + 0.987994i \(0.549375\pi\)
\(720\) 0 0
\(721\) 1.39748e7 1.00117
\(722\) 0 0
\(723\) 8.00974e6 0.569866
\(724\) 0 0
\(725\) 3.68875e6 0.260636
\(726\) 0 0
\(727\) −1.12084e7 −0.786515 −0.393258 0.919428i \(-0.628652\pi\)
−0.393258 + 0.919428i \(0.628652\pi\)
\(728\) 0 0
\(729\) 3.61141e6 0.251686
\(730\) 0 0
\(731\) −8.61552e6 −0.596332
\(732\) 0 0
\(733\) 4.70549e6 0.323478 0.161739 0.986834i \(-0.448290\pi\)
0.161739 + 0.986834i \(0.448290\pi\)
\(734\) 0 0
\(735\) −1.02860e6 −0.0702309
\(736\) 0 0
\(737\) −3.55539e7 −2.41112
\(738\) 0 0
\(739\) 2.31099e7 1.55663 0.778317 0.627872i \(-0.216074\pi\)
0.778317 + 0.627872i \(0.216074\pi\)
\(740\) 0 0
\(741\) −3.24115e6 −0.216847
\(742\) 0 0
\(743\) −5.75294e6 −0.382312 −0.191156 0.981560i \(-0.561224\pi\)
−0.191156 + 0.981560i \(0.561224\pi\)
\(744\) 0 0
\(745\) −4.59505e6 −0.303319
\(746\) 0 0
\(747\) 4.39481e6 0.288163
\(748\) 0 0
\(749\) 2.23214e7 1.45384
\(750\) 0 0
\(751\) 1.92424e7 1.24497 0.622485 0.782632i \(-0.286123\pi\)
0.622485 + 0.782632i \(0.286123\pi\)
\(752\) 0 0
\(753\) −2.95184e6 −0.189717
\(754\) 0 0
\(755\) −7.40080e6 −0.472510
\(756\) 0 0
\(757\) 4.49210e6 0.284911 0.142456 0.989801i \(-0.454500\pi\)
0.142456 + 0.989801i \(0.454500\pi\)
\(758\) 0 0
\(759\) 4.11686e6 0.259395
\(760\) 0 0
\(761\) 7.33500e6 0.459133 0.229567 0.973293i \(-0.426269\pi\)
0.229567 + 0.973293i \(0.426269\pi\)
\(762\) 0 0
\(763\) −7.57577e6 −0.471102
\(764\) 0 0
\(765\) −4.16175e6 −0.257112
\(766\) 0 0
\(767\) 1.01678e7 0.624076
\(768\) 0 0
\(769\) −5.85526e6 −0.357051 −0.178526 0.983935i \(-0.557133\pi\)
−0.178526 + 0.983935i \(0.557133\pi\)
\(770\) 0 0
\(771\) 2.23208e6 0.135230
\(772\) 0 0
\(773\) 1.34557e7 0.809952 0.404976 0.914327i \(-0.367280\pi\)
0.404976 + 0.914327i \(0.367280\pi\)
\(774\) 0 0
\(775\) 2.07500e6 0.124098
\(776\) 0 0
\(777\) 9.30874e6 0.553144
\(778\) 0 0
\(779\) −2.37764e7 −1.40379
\(780\) 0 0
\(781\) 3.34084e7 1.95988
\(782\) 0 0
\(783\) −1.99252e7 −1.16144
\(784\) 0 0
\(785\) 3.36915e6 0.195140
\(786\) 0 0
\(787\) −1.00706e7 −0.579587 −0.289794 0.957089i \(-0.593587\pi\)
−0.289794 + 0.957089i \(0.593587\pi\)
\(788\) 0 0
\(789\) −6.49392e6 −0.371377
\(790\) 0 0
\(791\) −1.64002e7 −0.931985
\(792\) 0 0
\(793\) 1.23043e7 0.694820
\(794\) 0 0
\(795\) −6.28680e6 −0.352786
\(796\) 0 0
\(797\) −1.18844e7 −0.662723 −0.331362 0.943504i \(-0.607508\pi\)
−0.331362 + 0.943504i \(0.607508\pi\)
\(798\) 0 0
\(799\) 9.11028e6 0.504853
\(800\) 0 0
\(801\) 1.62629e7 0.895604
\(802\) 0 0
\(803\) 1.64638e7 0.901036
\(804\) 0 0
\(805\) 2.30040e6 0.125116
\(806\) 0 0
\(807\) 2.82571e6 0.152737
\(808\) 0 0
\(809\) 1.06053e7 0.569705 0.284852 0.958571i \(-0.408055\pi\)
0.284852 + 0.958571i \(0.408055\pi\)
\(810\) 0 0
\(811\) 1.38944e6 0.0741799 0.0370900 0.999312i \(-0.488191\pi\)
0.0370900 + 0.999312i \(0.488191\pi\)
\(812\) 0 0
\(813\) 1.37297e7 0.728510
\(814\) 0 0
\(815\) 1.50620e6 0.0794307
\(816\) 0 0
\(817\) −1.22655e7 −0.642882
\(818\) 0 0
\(819\) 5.91559e6 0.308169
\(820\) 0 0
\(821\) −1.12661e7 −0.583334 −0.291667 0.956520i \(-0.594210\pi\)
−0.291667 + 0.956520i \(0.594210\pi\)
\(822\) 0 0
\(823\) 2.77093e7 1.42602 0.713011 0.701152i \(-0.247331\pi\)
0.713011 + 0.701152i \(0.247331\pi\)
\(824\) 0 0
\(825\) 3.02000e6 0.154480
\(826\) 0 0
\(827\) −1.23662e7 −0.628740 −0.314370 0.949300i \(-0.601793\pi\)
−0.314370 + 0.949300i \(0.601793\pi\)
\(828\) 0 0
\(829\) 1.23182e7 0.622530 0.311265 0.950323i \(-0.399247\pi\)
0.311265 + 0.950323i \(0.399247\pi\)
\(830\) 0 0
\(831\) −1.96706e6 −0.0988130
\(832\) 0 0
\(833\) −4.78299e6 −0.238829
\(834\) 0 0
\(835\) 1.55030e6 0.0769484
\(836\) 0 0
\(837\) −1.12083e7 −0.553002
\(838\) 0 0
\(839\) 1.17277e7 0.575183 0.287592 0.957753i \(-0.407145\pi\)
0.287592 + 0.957753i \(0.407145\pi\)
\(840\) 0 0
\(841\) 1.43225e7 0.698277
\(842\) 0 0
\(843\) −1.34095e7 −0.649894
\(844\) 0 0
\(845\) −6.94142e6 −0.334431
\(846\) 0 0
\(847\) 2.20066e7 1.05401
\(848\) 0 0
\(849\) 1.00705e7 0.479494
\(850\) 0 0
\(851\) 9.17945e6 0.434503
\(852\) 0 0
\(853\) 1.57059e7 0.739077 0.369538 0.929215i \(-0.379516\pi\)
0.369538 + 0.929215i \(0.379516\pi\)
\(854\) 0 0
\(855\) −5.92490e6 −0.277182
\(856\) 0 0
\(857\) 2.52390e7 1.17387 0.586935 0.809634i \(-0.300334\pi\)
0.586935 + 0.809634i \(0.300334\pi\)
\(858\) 0 0
\(859\) −3.66248e6 −0.169353 −0.0846763 0.996409i \(-0.526986\pi\)
−0.0846763 + 0.996409i \(0.526986\pi\)
\(860\) 0 0
\(861\) −1.55157e7 −0.713286
\(862\) 0 0
\(863\) 4.17938e7 1.91023 0.955113 0.296243i \(-0.0957338\pi\)
0.955113 + 0.296243i \(0.0957338\pi\)
\(864\) 0 0
\(865\) −1.47921e7 −0.672184
\(866\) 0 0
\(867\) −4.43966e6 −0.200586
\(868\) 0 0
\(869\) −1.89994e7 −0.853475
\(870\) 0 0
\(871\) 1.80124e7 0.804500
\(872\) 0 0
\(873\) −2.76924e7 −1.22977
\(874\) 0 0
\(875\) 1.68750e6 0.0745116
\(876\) 0 0
\(877\) 1.08990e7 0.478505 0.239253 0.970957i \(-0.423098\pi\)
0.239253 + 0.970957i \(0.423098\pi\)
\(878\) 0 0
\(879\) 5.75326e6 0.251155
\(880\) 0 0
\(881\) −3.04336e7 −1.32103 −0.660517 0.750811i \(-0.729663\pi\)
−0.660517 + 0.750811i \(0.729663\pi\)
\(882\) 0 0
\(883\) −6.09028e6 −0.262867 −0.131433 0.991325i \(-0.541958\pi\)
−0.131433 + 0.991325i \(0.541958\pi\)
\(884\) 0 0
\(885\) −6.64560e6 −0.285217
\(886\) 0 0
\(887\) −2.77908e7 −1.18602 −0.593010 0.805195i \(-0.702060\pi\)
−0.593010 + 0.805195i \(0.702060\pi\)
\(888\) 0 0
\(889\) 3.63524e7 1.54269
\(890\) 0 0
\(891\) 9.95936e6 0.420278
\(892\) 0 0
\(893\) 1.29699e7 0.544262
\(894\) 0 0
\(895\) 6.03510e6 0.251841
\(896\) 0 0
\(897\) −2.08570e6 −0.0865506
\(898\) 0 0
\(899\) 1.95946e7 0.808608
\(900\) 0 0
\(901\) −2.92336e7 −1.19969
\(902\) 0 0
\(903\) −8.00410e6 −0.326658
\(904\) 0 0
\(905\) 4.69055e6 0.190372
\(906\) 0 0
\(907\) −3.71510e7 −1.49952 −0.749761 0.661709i \(-0.769831\pi\)
−0.749761 + 0.661709i \(0.769831\pi\)
\(908\) 0 0
\(909\) 1.30158e7 0.522470
\(910\) 0 0
\(911\) 7.85959e6 0.313765 0.156882 0.987617i \(-0.449856\pi\)
0.156882 + 0.987617i \(0.449856\pi\)
\(912\) 0 0
\(913\) −1.48294e7 −0.588772
\(914\) 0 0
\(915\) −8.04200e6 −0.317549
\(916\) 0 0
\(917\) −2.97333e7 −1.16767
\(918\) 0 0
\(919\) 1.62693e7 0.635448 0.317724 0.948183i \(-0.397081\pi\)
0.317724 + 0.948183i \(0.397081\pi\)
\(920\) 0 0
\(921\) −1.48810e7 −0.578074
\(922\) 0 0
\(923\) −1.69255e7 −0.653938
\(924\) 0 0
\(925\) 6.73375e6 0.258763
\(926\) 0 0
\(927\) −2.31619e7 −0.885268
\(928\) 0 0
\(929\) −3.69365e7 −1.40416 −0.702079 0.712099i \(-0.747745\pi\)
−0.702079 + 0.712099i \(0.747745\pi\)
\(930\) 0 0
\(931\) −6.80933e6 −0.257472
\(932\) 0 0
\(933\) −2.22707e6 −0.0837587
\(934\) 0 0
\(935\) 1.40430e7 0.525328
\(936\) 0 0
\(937\) 4.89705e6 0.182216 0.0911078 0.995841i \(-0.470959\pi\)
0.0911078 + 0.995841i \(0.470959\pi\)
\(938\) 0 0
\(939\) −3.79346e6 −0.140401
\(940\) 0 0
\(941\) −6.83943e6 −0.251794 −0.125897 0.992043i \(-0.540181\pi\)
−0.125897 + 0.992043i \(0.540181\pi\)
\(942\) 0 0
\(943\) −1.53002e7 −0.560297
\(944\) 0 0
\(945\) −9.11520e6 −0.332037
\(946\) 0 0
\(947\) −1.03790e7 −0.376082 −0.188041 0.982161i \(-0.560214\pi\)
−0.188041 + 0.982161i \(0.560214\pi\)
\(948\) 0 0
\(949\) −8.34095e6 −0.300642
\(950\) 0 0
\(951\) −1.46990e7 −0.527032
\(952\) 0 0
\(953\) 2.59587e7 0.925873 0.462937 0.886391i \(-0.346796\pi\)
0.462937 + 0.886391i \(0.346796\pi\)
\(954\) 0 0
\(955\) −939000. −0.0333163
\(956\) 0 0
\(957\) 2.85185e7 1.00658
\(958\) 0 0
\(959\) −2.46782e7 −0.866497
\(960\) 0 0
\(961\) −1.76068e7 −0.614994
\(962\) 0 0
\(963\) −3.69957e7 −1.28554
\(964\) 0 0
\(965\) 4.11085e6 0.142106
\(966\) 0 0
\(967\) 3.92120e7 1.34851 0.674253 0.738501i \(-0.264466\pi\)
0.674253 + 0.738501i \(0.264466\pi\)
\(968\) 0 0
\(969\) 9.85056e6 0.337017
\(970\) 0 0
\(971\) 1.06876e7 0.363774 0.181887 0.983319i \(-0.441779\pi\)
0.181887 + 0.983319i \(0.441779\pi\)
\(972\) 0 0
\(973\) −2.42227e7 −0.820238
\(974\) 0 0
\(975\) −1.53000e6 −0.0515442
\(976\) 0 0
\(977\) 2.77266e7 0.929308 0.464654 0.885492i \(-0.346179\pi\)
0.464654 + 0.885492i \(0.346179\pi\)
\(978\) 0 0
\(979\) −5.48758e7 −1.82989
\(980\) 0 0
\(981\) 1.25561e7 0.416566
\(982\) 0 0
\(983\) 9.49272e6 0.313334 0.156667 0.987652i \(-0.449925\pi\)
0.156667 + 0.987652i \(0.449925\pi\)
\(984\) 0 0
\(985\) 9.01295e6 0.295990
\(986\) 0 0
\(987\) 8.46374e6 0.276547
\(988\) 0 0
\(989\) −7.89293e6 −0.256595
\(990\) 0 0
\(991\) 2.03243e7 0.657403 0.328702 0.944434i \(-0.393389\pi\)
0.328702 + 0.944434i \(0.393389\pi\)
\(992\) 0 0
\(993\) −2.39794e7 −0.771730
\(994\) 0 0
\(995\) 1.63542e7 0.523687
\(996\) 0 0
\(997\) 4.70508e7 1.49909 0.749547 0.661951i \(-0.230271\pi\)
0.749547 + 0.661951i \(0.230271\pi\)
\(998\) 0 0
\(999\) −3.63730e7 −1.15310
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 80.6.a.f.1.1 1
3.2 odd 2 720.6.a.h.1.1 1
4.3 odd 2 40.6.a.b.1.1 1
5.2 odd 4 400.6.c.h.49.1 2
5.3 odd 4 400.6.c.h.49.2 2
5.4 even 2 400.6.a.f.1.1 1
8.3 odd 2 320.6.a.l.1.1 1
8.5 even 2 320.6.a.e.1.1 1
12.11 even 2 360.6.a.b.1.1 1
20.3 even 4 200.6.c.c.49.1 2
20.7 even 4 200.6.c.c.49.2 2
20.19 odd 2 200.6.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.6.a.b.1.1 1 4.3 odd 2
80.6.a.f.1.1 1 1.1 even 1 trivial
200.6.a.c.1.1 1 20.19 odd 2
200.6.c.c.49.1 2 20.3 even 4
200.6.c.c.49.2 2 20.7 even 4
320.6.a.e.1.1 1 8.5 even 2
320.6.a.l.1.1 1 8.3 odd 2
360.6.a.b.1.1 1 12.11 even 2
400.6.a.f.1.1 1 5.4 even 2
400.6.c.h.49.1 2 5.2 odd 4
400.6.c.h.49.2 2 5.3 odd 4
720.6.a.h.1.1 1 3.2 odd 2