Properties

Label 320.6.f.d.289.14
Level 320
Weight 6
Character 320.289
Analytic conductor 51.323
Analytic rank 0
Dimension 32
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(51.3228223402\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 289.14
Character \(\chi\) \(=\) 320.289
Dual form 320.6.f.d.289.15

$q$-expansion

\(f(q)\) \(=\) \(q-4.76807 q^{3} +(-43.2814 - 35.3796i) q^{5} +82.4139i q^{7} -220.266 q^{9} +O(q^{10})\) \(q-4.76807 q^{3} +(-43.2814 - 35.3796i) q^{5} +82.4139i q^{7} -220.266 q^{9} +109.227i q^{11} -621.825 q^{13} +(206.369 + 168.693i) q^{15} +503.868i q^{17} -853.149i q^{19} -392.955i q^{21} +1424.25i q^{23} +(621.562 + 3062.56i) q^{25} +2208.88 q^{27} -275.098i q^{29} -6206.91 q^{31} -520.801i q^{33} +(2915.77 - 3566.99i) q^{35} +3668.93 q^{37} +2964.90 q^{39} -1266.95 q^{41} -7494.09 q^{43} +(9533.40 + 7792.91i) q^{45} -15862.9i q^{47} +10014.9 q^{49} -2402.48i q^{51} +10023.0 q^{53} +(3864.41 - 4727.49i) q^{55} +4067.88i q^{57} -27988.4i q^{59} -39901.8i q^{61} -18152.9i q^{63} +(26913.5 + 21999.9i) q^{65} +66510.4 q^{67} -6790.95i q^{69} -32714.8 q^{71} +71539.0i q^{73} +(-2963.65 - 14602.5i) q^{75} -9001.81 q^{77} -20741.8 q^{79} +42992.4 q^{81} +108500. q^{83} +(17826.7 - 21808.1i) q^{85} +1311.69i q^{87} +84870.1 q^{89} -51247.0i q^{91} +29595.0 q^{93} +(-30184.1 + 36925.5i) q^{95} +38393.1i q^{97} -24058.9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2944q^{9} + O(q^{10}) \) \( 32q + 2944q^{9} - 46528q^{25} - 36768q^{41} - 113920q^{49} + 25376q^{65} + 633472q^{81} + 968704q^{89} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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
\(3\) −4.76807 −0.305872 −0.152936 0.988236i \(-0.548873\pi\)
−0.152936 + 0.988236i \(0.548873\pi\)
\(4\) 0 0
\(5\) −43.2814 35.3796i −0.774242 0.632890i
\(6\) 0 0
\(7\) 82.4139i 0.635705i 0.948140 + 0.317852i \(0.102962\pi\)
−0.948140 + 0.317852i \(0.897038\pi\)
\(8\) 0 0
\(9\) −220.266 −0.906442
\(10\) 0 0
\(11\) 109.227i 0.272175i 0.990697 + 0.136087i \(0.0434528\pi\)
−0.990697 + 0.136087i \(0.956547\pi\)
\(12\) 0 0
\(13\) −621.825 −1.02049 −0.510246 0.860029i \(-0.670446\pi\)
−0.510246 + 0.860029i \(0.670446\pi\)
\(14\) 0 0
\(15\) 206.369 + 168.693i 0.236819 + 0.193583i
\(16\) 0 0
\(17\) 503.868i 0.422858i 0.977393 + 0.211429i \(0.0678118\pi\)
−0.977393 + 0.211429i \(0.932188\pi\)
\(18\) 0 0
\(19\) 853.149i 0.542177i −0.962554 0.271089i \(-0.912616\pi\)
0.962554 0.271089i \(-0.0873836\pi\)
\(20\) 0 0
\(21\) 392.955i 0.194444i
\(22\) 0 0
\(23\) 1424.25i 0.561394i 0.959796 + 0.280697i \(0.0905657\pi\)
−0.959796 + 0.280697i \(0.909434\pi\)
\(24\) 0 0
\(25\) 621.562 + 3062.56i 0.198900 + 0.980020i
\(26\) 0 0
\(27\) 2208.88 0.583127
\(28\) 0 0
\(29\) 275.098i 0.0607424i −0.999539 0.0303712i \(-0.990331\pi\)
0.999539 0.0303712i \(-0.00966894\pi\)
\(30\) 0 0
\(31\) −6206.91 −1.16004 −0.580018 0.814604i \(-0.696954\pi\)
−0.580018 + 0.814604i \(0.696954\pi\)
\(32\) 0 0
\(33\) 520.801i 0.0832505i
\(34\) 0 0
\(35\) 2915.77 3566.99i 0.402331 0.492189i
\(36\) 0 0
\(37\) 3668.93 0.440590 0.220295 0.975433i \(-0.429298\pi\)
0.220295 + 0.975433i \(0.429298\pi\)
\(38\) 0 0
\(39\) 2964.90 0.312140
\(40\) 0 0
\(41\) −1266.95 −0.117706 −0.0588530 0.998267i \(-0.518744\pi\)
−0.0588530 + 0.998267i \(0.518744\pi\)
\(42\) 0 0
\(43\) −7494.09 −0.618084 −0.309042 0.951048i \(-0.600008\pi\)
−0.309042 + 0.951048i \(0.600008\pi\)
\(44\) 0 0
\(45\) 9533.40 + 7792.91i 0.701805 + 0.573679i
\(46\) 0 0
\(47\) 15862.9i 1.04746i −0.851884 0.523731i \(-0.824540\pi\)
0.851884 0.523731i \(-0.175460\pi\)
\(48\) 0 0
\(49\) 10014.9 0.595880
\(50\) 0 0
\(51\) 2402.48i 0.129340i
\(52\) 0 0
\(53\) 10023.0 0.490127 0.245064 0.969507i \(-0.421191\pi\)
0.245064 + 0.969507i \(0.421191\pi\)
\(54\) 0 0
\(55\) 3864.41 4727.49i 0.172257 0.210729i
\(56\) 0 0
\(57\) 4067.88i 0.165837i
\(58\) 0 0
\(59\) 27988.4i 1.04676i −0.852098 0.523382i \(-0.824670\pi\)
0.852098 0.523382i \(-0.175330\pi\)
\(60\) 0 0
\(61\) 39901.8i 1.37299i −0.727134 0.686496i \(-0.759148\pi\)
0.727134 0.686496i \(-0.240852\pi\)
\(62\) 0 0
\(63\) 18152.9i 0.576230i
\(64\) 0 0
\(65\) 26913.5 + 21999.9i 0.790107 + 0.645859i
\(66\) 0 0
\(67\) 66510.4 1.81010 0.905049 0.425306i \(-0.139834\pi\)
0.905049 + 0.425306i \(0.139834\pi\)
\(68\) 0 0
\(69\) 6790.95i 0.171715i
\(70\) 0 0
\(71\) −32714.8 −0.770191 −0.385095 0.922877i \(-0.625831\pi\)
−0.385095 + 0.922877i \(0.625831\pi\)
\(72\) 0 0
\(73\) 71539.0i 1.57121i 0.618726 + 0.785607i \(0.287649\pi\)
−0.618726 + 0.785607i \(0.712351\pi\)
\(74\) 0 0
\(75\) −2963.65 14602.5i −0.0608379 0.299760i
\(76\) 0 0
\(77\) −9001.81 −0.173023
\(78\) 0 0
\(79\) −20741.8 −0.373920 −0.186960 0.982368i \(-0.559863\pi\)
−0.186960 + 0.982368i \(0.559863\pi\)
\(80\) 0 0
\(81\) 42992.4 0.728080
\(82\) 0 0
\(83\) 108500. 1.72876 0.864381 0.502838i \(-0.167711\pi\)
0.864381 + 0.502838i \(0.167711\pi\)
\(84\) 0 0
\(85\) 17826.7 21808.1i 0.267623 0.327394i
\(86\) 0 0
\(87\) 1311.69i 0.0185794i
\(88\) 0 0
\(89\) 84870.1 1.13574 0.567871 0.823117i \(-0.307767\pi\)
0.567871 + 0.823117i \(0.307767\pi\)
\(90\) 0 0
\(91\) 51247.0i 0.648731i
\(92\) 0 0
\(93\) 29595.0 0.354822
\(94\) 0 0
\(95\) −30184.1 + 36925.5i −0.343139 + 0.419776i
\(96\) 0 0
\(97\) 38393.1i 0.414309i 0.978308 + 0.207155i \(0.0664203\pi\)
−0.978308 + 0.207155i \(0.933580\pi\)
\(98\) 0 0
\(99\) 24058.9i 0.246711i
\(100\) 0 0
\(101\) 1331.92i 0.0129919i 0.999979 + 0.00649597i \(0.00206775\pi\)
−0.999979 + 0.00649597i \(0.997932\pi\)
\(102\) 0 0
\(103\) 114505.i 1.06348i −0.846907 0.531741i \(-0.821538\pi\)
0.846907 0.531741i \(-0.178462\pi\)
\(104\) 0 0
\(105\) −13902.6 + 17007.7i −0.123062 + 0.150547i
\(106\) 0 0
\(107\) 78186.5 0.660196 0.330098 0.943947i \(-0.392918\pi\)
0.330098 + 0.943947i \(0.392918\pi\)
\(108\) 0 0
\(109\) 48709.9i 0.392691i −0.980535 0.196346i \(-0.937093\pi\)
0.980535 0.196346i \(-0.0629075\pi\)
\(110\) 0 0
\(111\) −17493.7 −0.134764
\(112\) 0 0
\(113\) 162096.i 1.19420i 0.802168 + 0.597098i \(0.203680\pi\)
−0.802168 + 0.597098i \(0.796320\pi\)
\(114\) 0 0
\(115\) 50389.6 61643.8i 0.355301 0.434655i
\(116\) 0 0
\(117\) 136967. 0.925017
\(118\) 0 0
\(119\) −41525.8 −0.268813
\(120\) 0 0
\(121\) 149121. 0.925921
\(122\) 0 0
\(123\) 6040.88 0.0360029
\(124\) 0 0
\(125\) 81450.2 154543.i 0.466248 0.884654i
\(126\) 0 0
\(127\) 227166.i 1.24978i −0.780712 0.624891i \(-0.785143\pi\)
0.780712 0.624891i \(-0.214857\pi\)
\(128\) 0 0
\(129\) 35732.3 0.189055
\(130\) 0 0
\(131\) 194060.i 0.987999i −0.869462 0.494000i \(-0.835534\pi\)
0.869462 0.494000i \(-0.164466\pi\)
\(132\) 0 0
\(133\) 70311.4 0.344664
\(134\) 0 0
\(135\) −95603.6 78149.5i −0.451481 0.369055i
\(136\) 0 0
\(137\) 153702.i 0.699647i 0.936816 + 0.349823i \(0.113758\pi\)
−0.936816 + 0.349823i \(0.886242\pi\)
\(138\) 0 0
\(139\) 242909.i 1.06637i −0.846000 0.533183i \(-0.820996\pi\)
0.846000 0.533183i \(-0.179004\pi\)
\(140\) 0 0
\(141\) 75635.5i 0.320389i
\(142\) 0 0
\(143\) 67919.9i 0.277752i
\(144\) 0 0
\(145\) −9732.86 + 11906.6i −0.0384433 + 0.0470293i
\(146\) 0 0
\(147\) −47752.0 −0.182263
\(148\) 0 0
\(149\) 97400.3i 0.359414i 0.983720 + 0.179707i \(0.0575149\pi\)
−0.983720 + 0.179707i \(0.942485\pi\)
\(150\) 0 0
\(151\) 161098. 0.574972 0.287486 0.957785i \(-0.407181\pi\)
0.287486 + 0.957785i \(0.407181\pi\)
\(152\) 0 0
\(153\) 110985.i 0.383297i
\(154\) 0 0
\(155\) 268644. + 219598.i 0.898147 + 0.734175i
\(156\) 0 0
\(157\) 168524. 0.545647 0.272824 0.962064i \(-0.412042\pi\)
0.272824 + 0.962064i \(0.412042\pi\)
\(158\) 0 0
\(159\) −47790.5 −0.149916
\(160\) 0 0
\(161\) −117378. −0.356881
\(162\) 0 0
\(163\) −231681. −0.683000 −0.341500 0.939882i \(-0.610935\pi\)
−0.341500 + 0.939882i \(0.610935\pi\)
\(164\) 0 0
\(165\) −18425.8 + 22541.0i −0.0526885 + 0.0644560i
\(166\) 0 0
\(167\) 674343.i 1.87107i 0.353238 + 0.935534i \(0.385081\pi\)
−0.353238 + 0.935534i \(0.614919\pi\)
\(168\) 0 0
\(169\) 15372.9 0.0414037
\(170\) 0 0
\(171\) 187919.i 0.491452i
\(172\) 0 0
\(173\) −637772. −1.62013 −0.810065 0.586340i \(-0.800568\pi\)
−0.810065 + 0.586340i \(0.800568\pi\)
\(174\) 0 0
\(175\) −252398. + 51225.4i −0.623003 + 0.126442i
\(176\) 0 0
\(177\) 133451.i 0.320176i
\(178\) 0 0
\(179\) 341699.i 0.797096i 0.917147 + 0.398548i \(0.130486\pi\)
−0.917147 + 0.398548i \(0.869514\pi\)
\(180\) 0 0
\(181\) 123083.i 0.279256i −0.990204 0.139628i \(-0.955409\pi\)
0.990204 0.139628i \(-0.0445907\pi\)
\(182\) 0 0
\(183\) 190255.i 0.419960i
\(184\) 0 0
\(185\) −158796. 129805.i −0.341123 0.278845i
\(186\) 0 0
\(187\) −55035.9 −0.115091
\(188\) 0 0
\(189\) 182043.i 0.370697i
\(190\) 0 0
\(191\) −354073. −0.702279 −0.351139 0.936323i \(-0.614206\pi\)
−0.351139 + 0.936323i \(0.614206\pi\)
\(192\) 0 0
\(193\) 357838.i 0.691502i −0.938326 0.345751i \(-0.887624\pi\)
0.938326 0.345751i \(-0.112376\pi\)
\(194\) 0 0
\(195\) −128325. 104897.i −0.241672 0.197550i
\(196\) 0 0
\(197\) −418271. −0.767878 −0.383939 0.923359i \(-0.625433\pi\)
−0.383939 + 0.923359i \(0.625433\pi\)
\(198\) 0 0
\(199\) 969952. 1.73627 0.868136 0.496326i \(-0.165318\pi\)
0.868136 + 0.496326i \(0.165318\pi\)
\(200\) 0 0
\(201\) −317126. −0.553658
\(202\) 0 0
\(203\) 22671.9 0.0386142
\(204\) 0 0
\(205\) 54835.2 + 44824.1i 0.0911328 + 0.0744949i
\(206\) 0 0
\(207\) 313714.i 0.508872i
\(208\) 0 0
\(209\) 93186.8 0.147567
\(210\) 0 0
\(211\) 545362.i 0.843293i 0.906760 + 0.421647i \(0.138548\pi\)
−0.906760 + 0.421647i \(0.861452\pi\)
\(212\) 0 0
\(213\) 155986. 0.235580
\(214\) 0 0
\(215\) 324355. + 265138.i 0.478546 + 0.391179i
\(216\) 0 0
\(217\) 511536.i 0.737440i
\(218\) 0 0
\(219\) 341103.i 0.480590i
\(220\) 0 0
\(221\) 313318.i 0.431523i
\(222\) 0 0
\(223\) 627315.i 0.844741i −0.906423 0.422370i \(-0.861198\pi\)
0.906423 0.422370i \(-0.138802\pi\)
\(224\) 0 0
\(225\) −136909. 674577.i −0.180291 0.888332i
\(226\) 0 0
\(227\) −1.00091e6 −1.28923 −0.644615 0.764508i \(-0.722982\pi\)
−0.644615 + 0.764508i \(0.722982\pi\)
\(228\) 0 0
\(229\) 920954.i 1.16051i 0.814435 + 0.580255i \(0.197047\pi\)
−0.814435 + 0.580255i \(0.802953\pi\)
\(230\) 0 0
\(231\) 42921.3 0.0529228
\(232\) 0 0
\(233\) 185771.i 0.224176i −0.993698 0.112088i \(-0.964246\pi\)
0.993698 0.112088i \(-0.0357538\pi\)
\(234\) 0 0
\(235\) −561224. + 686570.i −0.662929 + 0.810989i
\(236\) 0 0
\(237\) 98898.3 0.114371
\(238\) 0 0
\(239\) 665553. 0.753682 0.376841 0.926278i \(-0.377010\pi\)
0.376841 + 0.926278i \(0.377010\pi\)
\(240\) 0 0
\(241\) −761168. −0.844186 −0.422093 0.906553i \(-0.638704\pi\)
−0.422093 + 0.906553i \(0.638704\pi\)
\(242\) 0 0
\(243\) −741749. −0.805826
\(244\) 0 0
\(245\) −433461. 354325.i −0.461355 0.377126i
\(246\) 0 0
\(247\) 530509.i 0.553287i
\(248\) 0 0
\(249\) −517336. −0.528780
\(250\) 0 0
\(251\) 1.24971e6i 1.25206i 0.779799 + 0.626030i \(0.215321\pi\)
−0.779799 + 0.626030i \(0.784679\pi\)
\(252\) 0 0
\(253\) −155567. −0.152797
\(254\) 0 0
\(255\) −84998.9 + 103983.i −0.0818583 + 0.100141i
\(256\) 0 0
\(257\) 1.80658e6i 1.70617i −0.521769 0.853087i \(-0.674728\pi\)
0.521769 0.853087i \(-0.325272\pi\)
\(258\) 0 0
\(259\) 302371.i 0.280085i
\(260\) 0 0
\(261\) 60594.5i 0.0550595i
\(262\) 0 0
\(263\) 1.14041e6i 1.01665i 0.861166 + 0.508324i \(0.169735\pi\)
−0.861166 + 0.508324i \(0.830265\pi\)
\(264\) 0 0
\(265\) −433811. 354611.i −0.379477 0.310197i
\(266\) 0 0
\(267\) −404667. −0.347392
\(268\) 0 0
\(269\) 1.86107e6i 1.56813i 0.620679 + 0.784065i \(0.286857\pi\)
−0.620679 + 0.784065i \(0.713143\pi\)
\(270\) 0 0
\(271\) −1.08713e6 −0.899204 −0.449602 0.893229i \(-0.648434\pi\)
−0.449602 + 0.893229i \(0.648434\pi\)
\(272\) 0 0
\(273\) 244349.i 0.198429i
\(274\) 0 0
\(275\) −334514. + 67891.3i −0.266736 + 0.0541355i
\(276\) 0 0
\(277\) −628877. −0.492455 −0.246227 0.969212i \(-0.579191\pi\)
−0.246227 + 0.969212i \(0.579191\pi\)
\(278\) 0 0
\(279\) 1.36717e6 1.05150
\(280\) 0 0
\(281\) −817929. −0.617945 −0.308972 0.951071i \(-0.599985\pi\)
−0.308972 + 0.951071i \(0.599985\pi\)
\(282\) 0 0
\(283\) −519909. −0.385888 −0.192944 0.981210i \(-0.561804\pi\)
−0.192944 + 0.981210i \(0.561804\pi\)
\(284\) 0 0
\(285\) 143920. 176063.i 0.104956 0.128398i
\(286\) 0 0
\(287\) 104414.i 0.0748262i
\(288\) 0 0
\(289\) 1.16597e6 0.821191
\(290\) 0 0
\(291\) 183061.i 0.126725i
\(292\) 0 0
\(293\) −61931.1 −0.0421444 −0.0210722 0.999778i \(-0.506708\pi\)
−0.0210722 + 0.999778i \(0.506708\pi\)
\(294\) 0 0
\(295\) −990221. + 1.21138e6i −0.662486 + 0.810448i
\(296\) 0 0
\(297\) 241269.i 0.158712i
\(298\) 0 0
\(299\) 885637.i 0.572898i
\(300\) 0 0
\(301\) 617617.i 0.392919i
\(302\) 0 0
\(303\) 6350.68i 0.00397387i
\(304\) 0 0
\(305\) −1.41171e6 + 1.72701e6i −0.868953 + 1.06303i
\(306\) 0 0
\(307\) 2.02897e6 1.22865 0.614327 0.789051i \(-0.289427\pi\)
0.614327 + 0.789051i \(0.289427\pi\)
\(308\) 0 0
\(309\) 545966.i 0.325289i
\(310\) 0 0
\(311\) 1.44330e6 0.846166 0.423083 0.906091i \(-0.360948\pi\)
0.423083 + 0.906091i \(0.360948\pi\)
\(312\) 0 0
\(313\) 210398.i 0.121389i −0.998156 0.0606947i \(-0.980668\pi\)
0.998156 0.0606947i \(-0.0193316\pi\)
\(314\) 0 0
\(315\) −642244. + 785685.i −0.364690 + 0.446141i
\(316\) 0 0
\(317\) −719655. −0.402231 −0.201116 0.979567i \(-0.564457\pi\)
−0.201116 + 0.979567i \(0.564457\pi\)
\(318\) 0 0
\(319\) 30048.0 0.0165325
\(320\) 0 0
\(321\) −372799. −0.201935
\(322\) 0 0
\(323\) 429875. 0.229264
\(324\) 0 0
\(325\) −386503. 1.90438e6i −0.202976 1.00010i
\(326\) 0 0
\(327\) 232252.i 0.120113i
\(328\) 0 0
\(329\) 1.30733e6 0.665877
\(330\) 0 0
\(331\) 1.34910e6i 0.676822i −0.940998 0.338411i \(-0.890111\pi\)
0.940998 0.338411i \(-0.109889\pi\)
\(332\) 0 0
\(333\) −808138. −0.399370
\(334\) 0 0
\(335\) −2.87866e6 2.35311e6i −1.40145 1.14559i
\(336\) 0 0
\(337\) 1.81431e6i 0.870234i 0.900374 + 0.435117i \(0.143293\pi\)
−0.900374 + 0.435117i \(0.856707\pi\)
\(338\) 0 0
\(339\) 772884.i 0.365271i
\(340\) 0 0
\(341\) 677961.i 0.315732i
\(342\) 0 0
\(343\) 2.21050e6i 1.01451i
\(344\) 0 0
\(345\) −240261. + 293922.i −0.108677 + 0.132949i
\(346\) 0 0
\(347\) −826969. −0.368693 −0.184347 0.982861i \(-0.559017\pi\)
−0.184347 + 0.982861i \(0.559017\pi\)
\(348\) 0 0
\(349\) 1.90016e6i 0.835077i 0.908659 + 0.417538i \(0.137107\pi\)
−0.908659 + 0.417538i \(0.862893\pi\)
\(350\) 0 0
\(351\) −1.37354e6 −0.595076
\(352\) 0 0
\(353\) 1.54658e6i 0.660595i −0.943877 0.330298i \(-0.892851\pi\)
0.943877 0.330298i \(-0.107149\pi\)
\(354\) 0 0
\(355\) 1.41594e6 + 1.15744e6i 0.596314 + 0.487446i
\(356\) 0 0
\(357\) 197998. 0.0822223
\(358\) 0 0
\(359\) 4.20737e6 1.72296 0.861479 0.507792i \(-0.169538\pi\)
0.861479 + 0.507792i \(0.169538\pi\)
\(360\) 0 0
\(361\) 1.74824e6 0.706044
\(362\) 0 0
\(363\) −711017. −0.283213
\(364\) 0 0
\(365\) 2.53102e6 3.09631e6i 0.994406 1.21650i
\(366\) 0 0
\(367\) 3.08199e6i 1.19445i −0.802075 0.597223i \(-0.796271\pi\)
0.802075 0.597223i \(-0.203729\pi\)
\(368\) 0 0
\(369\) 279064. 0.106694
\(370\) 0 0
\(371\) 826036.i 0.311576i
\(372\) 0 0
\(373\) 3.22578e6 1.20050 0.600252 0.799811i \(-0.295067\pi\)
0.600252 + 0.799811i \(0.295067\pi\)
\(374\) 0 0
\(375\) −388361. + 736870.i −0.142612 + 0.270591i
\(376\) 0 0
\(377\) 171063.i 0.0619871i
\(378\) 0 0
\(379\) 3.54075e6i 1.26619i −0.774076 0.633093i \(-0.781785\pi\)
0.774076 0.633093i \(-0.218215\pi\)
\(380\) 0 0
\(381\) 1.08314e6i 0.382273i
\(382\) 0 0
\(383\) 4.84417e6i 1.68742i −0.536803 0.843708i \(-0.680368\pi\)
0.536803 0.843708i \(-0.319632\pi\)
\(384\) 0 0
\(385\) 389611. + 318481.i 0.133961 + 0.109504i
\(386\) 0 0
\(387\) 1.65069e6 0.560258
\(388\) 0 0
\(389\) 2.70292e6i 0.905648i 0.891600 + 0.452824i \(0.149583\pi\)
−0.891600 + 0.452824i \(0.850417\pi\)
\(390\) 0 0
\(391\) −717637. −0.237390
\(392\) 0 0
\(393\) 925289.i 0.302201i
\(394\) 0 0
\(395\) 897733. + 733837.i 0.289504 + 0.236650i
\(396\) 0 0
\(397\) 2.85969e6 0.910631 0.455316 0.890330i \(-0.349526\pi\)
0.455316 + 0.890330i \(0.349526\pi\)
\(398\) 0 0
\(399\) −335250. −0.105423
\(400\) 0 0
\(401\) 2.78230e6 0.864058 0.432029 0.901860i \(-0.357798\pi\)
0.432029 + 0.901860i \(0.357798\pi\)
\(402\) 0 0
\(403\) 3.85961e6 1.18381
\(404\) 0 0
\(405\) −1.86077e6 1.52106e6i −0.563710 0.460795i
\(406\) 0 0
\(407\) 400745.i 0.119917i
\(408\) 0 0
\(409\) 6.46827e6 1.91196 0.955982 0.293425i \(-0.0947950\pi\)
0.955982 + 0.293425i \(0.0947950\pi\)
\(410\) 0 0
\(411\) 732863.i 0.214002i
\(412\) 0 0
\(413\) 2.30664e6 0.665432
\(414\) 0 0
\(415\) −4.69604e6 3.83870e6i −1.33848 1.09412i
\(416\) 0 0
\(417\) 1.15821e6i 0.326171i
\(418\) 0 0
\(419\) 5.24272e6i 1.45889i −0.684041 0.729444i \(-0.739779\pi\)
0.684041 0.729444i \(-0.260221\pi\)
\(420\) 0 0
\(421\) 4.34887e6i 1.19583i −0.801558 0.597917i \(-0.795995\pi\)
0.801558 0.597917i \(-0.204005\pi\)
\(422\) 0 0
\(423\) 3.49405e6i 0.949464i
\(424\) 0 0
\(425\) −1.54313e6 + 313186.i −0.414409 + 0.0841065i
\(426\) 0 0
\(427\) 3.28846e6 0.872817
\(428\) 0 0
\(429\) 323847.i 0.0849565i
\(430\) 0 0
\(431\) −5.96989e6 −1.54801 −0.774003 0.633181i \(-0.781749\pi\)
−0.774003 + 0.633181i \(0.781749\pi\)
\(432\) 0 0
\(433\) 6.35336e6i 1.62848i 0.580525 + 0.814242i \(0.302847\pi\)
−0.580525 + 0.814242i \(0.697153\pi\)
\(434\) 0 0
\(435\) 46407.0 56771.6i 0.0117587 0.0143849i
\(436\) 0 0
\(437\) 1.21510e6 0.304375
\(438\) 0 0
\(439\) 6.83485e6 1.69265 0.846326 0.532666i \(-0.178810\pi\)
0.846326 + 0.532666i \(0.178810\pi\)
\(440\) 0 0
\(441\) −2.20595e6 −0.540131
\(442\) 0 0
\(443\) 6.02270e6 1.45808 0.729041 0.684470i \(-0.239966\pi\)
0.729041 + 0.684470i \(0.239966\pi\)
\(444\) 0 0
\(445\) −3.67330e6 3.00267e6i −0.879339 0.718800i
\(446\) 0 0
\(447\) 464412.i 0.109935i
\(448\) 0 0
\(449\) 4.11636e6 0.963602 0.481801 0.876281i \(-0.339983\pi\)
0.481801 + 0.876281i \(0.339983\pi\)
\(450\) 0 0
\(451\) 138384.i 0.0320366i
\(452\) 0 0
\(453\) −768124. −0.175868
\(454\) 0 0
\(455\) −1.81310e6 + 2.21804e6i −0.410576 + 0.502275i
\(456\) 0 0
\(457\) 7.61258e6i 1.70507i 0.522673 + 0.852533i \(0.324935\pi\)
−0.522673 + 0.852533i \(0.675065\pi\)
\(458\) 0 0
\(459\) 1.11299e6i 0.246580i
\(460\) 0 0
\(461\) 4.54787e6i 0.996680i −0.866982 0.498340i \(-0.833943\pi\)
0.866982 0.498340i \(-0.166057\pi\)
\(462\) 0 0
\(463\) 3.15983e6i 0.685033i −0.939512 0.342516i \(-0.888721\pi\)
0.939512 0.342516i \(-0.111279\pi\)
\(464\) 0 0
\(465\) −1.28091e6 1.04706e6i −0.274718 0.224563i
\(466\) 0 0
\(467\) −5.77790e6 −1.22596 −0.612982 0.790097i \(-0.710030\pi\)
−0.612982 + 0.790097i \(0.710030\pi\)
\(468\) 0 0
\(469\) 5.48138e6i 1.15069i
\(470\) 0 0
\(471\) −803533. −0.166898
\(472\) 0 0
\(473\) 818555.i 0.168227i
\(474\) 0 0
\(475\) 2.61282e6 530285.i 0.531344 0.107839i
\(476\) 0 0
\(477\) −2.20773e6 −0.444272
\(478\) 0 0
\(479\) 4.83200e6 0.962250 0.481125 0.876652i \(-0.340228\pi\)
0.481125 + 0.876652i \(0.340228\pi\)
\(480\) 0 0
\(481\) −2.28143e6 −0.449619
\(482\) 0 0
\(483\) 559668. 0.109160
\(484\) 0 0
\(485\) 1.35834e6 1.66171e6i 0.262212 0.320775i
\(486\) 0 0
\(487\) 2.82344e6i 0.539455i 0.962937 + 0.269728i \(0.0869337\pi\)
−0.962937 + 0.269728i \(0.913066\pi\)
\(488\) 0 0
\(489\) 1.10467e6 0.208911
\(490\) 0 0
\(491\) 425391.i 0.0796314i 0.999207 + 0.0398157i \(0.0126771\pi\)
−0.999207 + 0.0398157i \(0.987323\pi\)
\(492\) 0 0
\(493\) 138613. 0.0256854
\(494\) 0 0
\(495\) −851195. + 1.04130e6i −0.156141 + 0.191014i
\(496\) 0 0
\(497\) 2.69615e6i 0.489614i
\(498\) 0 0
\(499\) 1.09645e7i 1.97122i −0.169022 0.985612i \(-0.554061\pi\)
0.169022 0.985612i \(-0.445939\pi\)
\(500\) 0 0
\(501\) 3.21531e6i 0.572307i
\(502\) 0 0
\(503\) 673131.i 0.118626i 0.998239 + 0.0593130i \(0.0188910\pi\)
−0.998239 + 0.0593130i \(0.981109\pi\)
\(504\) 0 0
\(505\) 47122.8 57647.3i 0.00822247 0.0100589i
\(506\) 0 0
\(507\) −73299.1 −0.0126642
\(508\) 0 0
\(509\) 1.03530e7i 1.77122i 0.464434 + 0.885608i \(0.346258\pi\)
−0.464434 + 0.885608i \(0.653742\pi\)
\(510\) 0 0
\(511\) −5.89580e6 −0.998828
\(512\) 0 0
\(513\) 1.88451e6i 0.316158i
\(514\) 0 0
\(515\) −4.05113e6 + 4.95592e6i −0.673067 + 0.823392i
\(516\) 0 0
\(517\) 1.73266e6 0.285093
\(518\) 0 0
\(519\) 3.04094e6 0.495552
\(520\) 0 0
\(521\) −5.28373e6 −0.852799 −0.426399 0.904535i \(-0.640218\pi\)
−0.426399 + 0.904535i \(0.640218\pi\)
\(522\) 0 0
\(523\) 208807. 0.0333803 0.0166901 0.999861i \(-0.494687\pi\)
0.0166901 + 0.999861i \(0.494687\pi\)
\(524\) 0 0
\(525\) 1.20345e6 244246.i 0.190559 0.0386749i
\(526\) 0 0
\(527\) 3.12747e6i 0.490530i
\(528\) 0 0
\(529\) 4.40784e6 0.684836
\(530\) 0 0
\(531\) 6.16489e6i 0.948831i
\(532\) 0 0
\(533\) 787818. 0.120118
\(534\) 0 0
\(535\) −3.38402e6 2.76621e6i −0.511151 0.417831i
\(536\) 0 0
\(537\) 1.62924e6i 0.243809i
\(538\) 0 0
\(539\) 1.09390e6i 0.162183i
\(540\) 0 0
\(541\) 7.19366e6i 1.05671i −0.849023 0.528356i \(-0.822809\pi\)
0.849023 0.528356i \(-0.177191\pi\)
\(542\) 0 0
\(543\) 586870.i 0.0854165i
\(544\) 0 0
\(545\) −1.72334e6 + 2.10824e6i −0.248531 + 0.304038i
\(546\) 0 0
\(547\) 1.32353e6 0.189133 0.0945664 0.995519i \(-0.469854\pi\)
0.0945664 + 0.995519i \(0.469854\pi\)
\(548\) 0 0
\(549\) 8.78899e6i 1.24454i
\(550\) 0 0
\(551\) −234699. −0.0329331
\(552\) 0 0
\(553\) 1.70941e6i 0.237702i
\(554\) 0 0
\(555\) 757152. + 618921.i 0.104340 + 0.0852909i
\(556\) 0 0
\(557\) 919685. 0.125603 0.0628017 0.998026i \(-0.479996\pi\)
0.0628017 + 0.998026i \(0.479996\pi\)
\(558\) 0 0
\(559\) 4.66001e6 0.630750
\(560\) 0 0
\(561\) 262415. 0.0352032
\(562\) 0 0
\(563\) −9.78497e6 −1.30103 −0.650517 0.759492i \(-0.725448\pi\)
−0.650517 + 0.759492i \(0.725448\pi\)
\(564\) 0 0
\(565\) 5.73489e6 7.01574e6i 0.755795 0.924596i
\(566\) 0 0
\(567\) 3.54317e6i 0.462844i
\(568\) 0 0
\(569\) −289576. −0.0374958 −0.0187479 0.999824i \(-0.505968\pi\)
−0.0187479 + 0.999824i \(0.505968\pi\)
\(570\) 0 0
\(571\) 1.52990e6i 0.196369i −0.995168 0.0981845i \(-0.968696\pi\)
0.995168 0.0981845i \(-0.0313035\pi\)
\(572\) 0 0
\(573\) 1.68825e6 0.214807
\(574\) 0 0
\(575\) −4.36187e6 + 885263.i −0.550178 + 0.111661i
\(576\) 0 0
\(577\) 3.25795e6i 0.407385i −0.979035 0.203692i \(-0.934706\pi\)
0.979035 0.203692i \(-0.0652942\pi\)
\(578\) 0 0
\(579\) 1.70620e6i 0.211511i
\(580\) 0 0
\(581\) 8.94192e6i 1.09898i
\(582\) 0 0
\(583\) 1.09478e6i 0.133400i
\(584\) 0 0
\(585\) −5.92811e6 4.84583e6i −0.716187 0.585434i
\(586\) 0 0
\(587\) −902249. −0.108076 −0.0540382 0.998539i \(-0.517209\pi\)
−0.0540382 + 0.998539i \(0.517209\pi\)
\(588\) 0 0
\(589\) 5.29542e6i 0.628944i
\(590\) 0 0
\(591\) 1.99434e6 0.234872
\(592\) 0 0
\(593\) 1.13280e7i 1.32287i −0.750004 0.661433i \(-0.769949\pi\)
0.750004 0.661433i \(-0.230051\pi\)
\(594\) 0 0
\(595\) 1.79729e6 + 1.46917e6i 0.208126 + 0.170129i
\(596\) 0 0
\(597\) −4.62480e6 −0.531077
\(598\) 0 0
\(599\) 1.65503e7 1.88468 0.942342 0.334651i \(-0.108618\pi\)
0.942342 + 0.334651i \(0.108618\pi\)
\(600\) 0 0
\(601\) 204374. 0.0230802 0.0115401 0.999933i \(-0.496327\pi\)
0.0115401 + 0.999933i \(0.496327\pi\)
\(602\) 0 0
\(603\) −1.46499e7 −1.64075
\(604\) 0 0
\(605\) −6.45415e6 5.27583e6i −0.716886 0.586006i
\(606\) 0 0
\(607\) 5.18844e6i 0.571565i −0.958295 0.285782i \(-0.907747\pi\)
0.958295 0.285782i \(-0.0922534\pi\)
\(608\) 0 0
\(609\) −108101. −0.0118110
\(610\) 0 0
\(611\) 9.86396e6i 1.06893i
\(612\) 0 0
\(613\) −1.06424e7 −1.14390 −0.571951 0.820288i \(-0.693813\pi\)
−0.571951 + 0.820288i \(0.693813\pi\)
\(614\) 0 0
\(615\) −261458. 213724.i −0.0278750 0.0227859i
\(616\) 0 0
\(617\) 6.94619e6i 0.734571i −0.930108 0.367286i \(-0.880287\pi\)
0.930108 0.367286i \(-0.119713\pi\)
\(618\) 0 0
\(619\) 2.38878e6i 0.250582i 0.992120 + 0.125291i \(0.0399864\pi\)
−0.992120 + 0.125291i \(0.960014\pi\)
\(620\) 0 0
\(621\) 3.14601e6i 0.327364i
\(622\) 0 0
\(623\) 6.99448e6i 0.721997i
\(624\) 0 0
\(625\) −8.99295e6 + 3.80715e6i −0.920878 + 0.389852i
\(626\) 0 0
\(627\) −444321. −0.0451365
\(628\) 0 0
\(629\) 1.84866e6i 0.186307i
\(630\) 0 0
\(631\) 1.38123e6 0.138100 0.0690499 0.997613i \(-0.478003\pi\)
0.0690499 + 0.997613i \(0.478003\pi\)
\(632\) 0 0
\(633\) 2.60032e6i 0.257940i
\(634\) 0 0
\(635\) −8.03705e6 + 9.83207e6i −0.790975 + 0.967633i
\(636\) 0 0
\(637\) −6.22754e6 −0.608090
\(638\) 0 0
\(639\) 7.20594e6 0.698133
\(640\) 0 0
\(641\) −1.39783e7 −1.34372 −0.671861 0.740677i \(-0.734505\pi\)
−0.671861 + 0.740677i \(0.734505\pi\)
\(642\) 0 0
\(643\) 1.28822e6 0.122875 0.0614373 0.998111i \(-0.480432\pi\)
0.0614373 + 0.998111i \(0.480432\pi\)
\(644\) 0 0
\(645\) −1.54655e6 1.26420e6i −0.146374 0.119651i
\(646\) 0 0
\(647\) 1.51716e7i 1.42485i 0.701746 + 0.712427i \(0.252404\pi\)
−0.701746 + 0.712427i \(0.747596\pi\)
\(648\) 0 0
\(649\) 3.05709e6 0.284902
\(650\) 0 0
\(651\) 2.43904e6i 0.225562i
\(652\) 0 0
\(653\) −1.46639e7 −1.34575 −0.672877 0.739754i \(-0.734942\pi\)
−0.672877 + 0.739754i \(0.734942\pi\)
\(654\) 0 0
\(655\) −6.86576e6 + 8.39917e6i −0.625295 + 0.764950i
\(656\) 0 0
\(657\) 1.57576e7i 1.42422i
\(658\) 0 0
\(659\) 91638.5i 0.00821986i 0.999992 + 0.00410993i \(0.00130824\pi\)
−0.999992 + 0.00410993i \(0.998692\pi\)
\(660\) 0 0
\(661\) 3.06350e6i 0.272718i −0.990659 0.136359i \(-0.956460\pi\)
0.990659 0.136359i \(-0.0435400\pi\)
\(662\) 0 0
\(663\) 1.49392e6i 0.131991i
\(664\) 0 0
\(665\) −3.04318e6 2.48759e6i −0.266854 0.218135i
\(666\) 0 0
\(667\) 391809. 0.0341004
\(668\) 0 0
\(669\) 2.99108e6i 0.258382i
\(670\) 0 0
\(671\) 4.35835e6 0.373694
\(672\) 0 0
\(673\) 1.55354e7i 1.32216i 0.750316 + 0.661079i \(0.229901\pi\)
−0.750316 + 0.661079i \(0.770099\pi\)
\(674\) 0 0
\(675\) 1.37296e6 + 6.76484e6i 0.115984 + 0.571476i
\(676\) 0 0
\(677\) −5.41038e6 −0.453687 −0.226843 0.973931i \(-0.572841\pi\)
−0.226843 + 0.973931i \(0.572841\pi\)
\(678\) 0 0
\(679\) −3.16413e6 −0.263378
\(680\) 0 0
\(681\) 4.77241e6 0.394339
\(682\) 0 0
\(683\) 1.26434e6 0.103708 0.0518542 0.998655i \(-0.483487\pi\)
0.0518542 + 0.998655i \(0.483487\pi\)
\(684\) 0 0
\(685\) 5.43793e6 6.65245e6i 0.442800 0.541696i
\(686\) 0 0
\(687\) 4.39117e6i 0.354968i
\(688\) 0 0
\(689\) −6.23256e6 −0.500171
\(690\) 0 0
\(691\) 867712.i 0.0691323i 0.999402 + 0.0345661i \(0.0110049\pi\)
−0.999402 + 0.0345661i \(0.988995\pi\)
\(692\) 0 0
\(693\) 1.98279e6 0.156835
\(694\) 0 0
\(695\) −8.59402e6 + 1.05134e7i −0.674892 + 0.825624i
\(696\) 0 0
\(697\) 638374.i 0.0497729i
\(698\) 0 0
\(699\) 885770.i 0.0685690i
\(700\) 0 0
\(701\) 6.82392e6i 0.524492i 0.965001 + 0.262246i \(0.0844632\pi\)
−0.965001 + 0.262246i \(0.915537\pi\)
\(702\) 0 0
\(703\) 3.13014e6i 0.238878i
\(704\) 0 0
\(705\) 2.67596e6 3.27361e6i 0.202771 0.248059i
\(706\) 0 0
\(707\) −109769. −0.00825904
\(708\) 0 0
\(709\) 1.03780e7i 0.775350i 0.921796 + 0.387675i \(0.126722\pi\)
−0.921796 + 0.387675i \(0.873278\pi\)
\(710\) 0 0
\(711\) 4.56870e6 0.338937
\(712\) 0 0
\(713\) 8.84022e6i 0.651237i
\(714\) 0 0
\(715\) −2.40298e6 + 2.93967e6i −0.175786 + 0.215047i
\(716\) 0 0
\(717\) −3.17341e6 −0.230530
\(718\) 0 0
\(719\) 5.77556e6 0.416650 0.208325 0.978060i \(-0.433199\pi\)
0.208325 + 0.978060i \(0.433199\pi\)
\(720\) 0 0
\(721\) 9.43677e6 0.676060
\(722\) 0 0
\(723\) 3.62930e6 0.258213
\(724\) 0 0
\(725\) 842504. 170990.i 0.0595288 0.0120817i
\(726\) 0 0
\(727\) 1.08256e7i 0.759653i −0.925058 0.379827i \(-0.875984\pi\)
0.925058 0.379827i \(-0.124016\pi\)
\(728\) 0 0
\(729\) −6.91044e6 −0.481601
\(730\) 0 0
\(731\) 3.77603e6i 0.261362i
\(732\) 0 0
\(733\) 2.58032e7 1.77383 0.886917 0.461929i \(-0.152842\pi\)
0.886917 + 0.461929i \(0.152842\pi\)
\(734\) 0 0
\(735\) 2.06677e6 + 1.68945e6i 0.141115 + 0.115352i
\(736\) 0 0
\(737\) 7.26471e6i 0.492663i
\(738\) 0 0
\(739\) 1.32347e7i 0.891459i −0.895168 0.445730i \(-0.852944\pi\)
0.895168 0.445730i \(-0.147056\pi\)
\(740\) 0 0
\(741\) 2.52951e6i 0.169235i
\(742\) 0 0
\(743\) 1.33971e7i 0.890304i −0.895455 0.445152i \(-0.853150\pi\)
0.895455 0.445152i \(-0.146850\pi\)
\(744\) 0 0
\(745\) 3.44599e6 4.21562e6i 0.227469 0.278273i
\(746\) 0 0
\(747\) −2.38988e7 −1.56702
\(748\) 0 0
\(749\) 6.44366e6i 0.419689i
\(750\) 0 0
\(751\) −3.63485e6 −0.235173 −0.117586 0.993063i \(-0.537516\pi\)
−0.117586 + 0.993063i \(0.537516\pi\)
\(752\) 0 0
\(753\) 5.95870e6i 0.382970i
\(754\) 0 0
\(755\) −6.97253e6 5.69957e6i −0.445167 0.363894i
\(756\) 0 0
\(757\) 2.53597e7 1.60844 0.804219 0.594332i \(-0.202584\pi\)
0.804219 + 0.594332i \(0.202584\pi\)
\(758\) 0 0
\(759\) 741753. 0.0467364
\(760\) 0 0
\(761\) −9.42741e6 −0.590107 −0.295053 0.955481i \(-0.595337\pi\)
−0.295053 + 0.955481i \(0.595337\pi\)
\(762\) 0 0
\(763\) 4.01438e6 0.249636
\(764\) 0 0
\(765\) −3.92660e6 + 4.80358e6i −0.242585 + 0.296764i
\(766\) 0 0
\(767\) 1.74039e7i 1.06821i
\(768\) 0 0
\(769\) 1.77861e7 1.08459 0.542293 0.840189i \(-0.317556\pi\)
0.542293 + 0.840189i \(0.317556\pi\)
\(770\) 0 0
\(771\) 8.61388e6i 0.521871i
\(772\) 0 0
\(773\) −2.23501e7 −1.34534 −0.672668 0.739944i \(-0.734852\pi\)
−0.672668 + 0.739944i \(0.734852\pi\)
\(774\) 0 0
\(775\) −3.85798e6 1.90090e7i −0.230731 1.13686i
\(776\) 0 0
\(777\) 1.44172e6i 0.0856702i
\(778\) 0 0
\(779\) 1.08089e6i 0.0638174i
\(780\) 0 0
\(781\) 3.57333e6i 0.209626i
\(782\) 0 0
\(783\) 607659.i 0.0354205i
\(784\) 0 0
\(785\) −7.29395e6 5.96231e6i −0.422463 0.345335i
\(786\) 0 0
\(787\) 1.53456e7 0.883177 0.441589 0.897218i \(-0.354415\pi\)
0.441589 + 0.897218i \(0.354415\pi\)
\(788\) 0 0
\(789\) 5.43754e6i 0.310964i
\(790\) 0 0
\(791\) −1.33589e7 −0.759156
\(792\) 0 0
\(793\) 2.48119e7i 1.40113i
\(794\) 0 0