Properties

Label 320.6.f.d.289.2
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 289.2
Character \(\chi\) \(=\) 320.289
Dual form 320.6.f.d.289.3

$q$-expansion

\(f(q)\) \(=\) \(q-28.5405 q^{3} +(-5.81388 - 55.5985i) q^{5} -92.3750i q^{7} +571.559 q^{9} +O(q^{10})\) \(q-28.5405 q^{3} +(-5.81388 - 55.5985i) q^{5} -92.3750i q^{7} +571.559 q^{9} -541.547i q^{11} +782.810 q^{13} +(165.931 + 1586.81i) q^{15} +1556.72i q^{17} -484.475i q^{19} +2636.43i q^{21} +1096.90i q^{23} +(-3057.40 + 646.487i) q^{25} -9377.22 q^{27} +597.650i q^{29} +8869.25 q^{31} +15456.0i q^{33} +(-5135.92 + 537.058i) q^{35} +13624.1 q^{37} -22341.8 q^{39} +14540.4 q^{41} -1828.39 q^{43} +(-3322.98 - 31777.8i) q^{45} +17951.8i q^{47} +8273.86 q^{49} -44429.6i q^{51} -1650.99 q^{53} +(-30109.3 + 3148.49i) q^{55} +13827.1i q^{57} +14453.6i q^{59} +24574.4i q^{61} -52797.7i q^{63} +(-4551.17 - 43523.1i) q^{65} +26842.8 q^{67} -31306.0i q^{69} +48050.6 q^{71} -60646.8i q^{73} +(87259.6 - 18451.0i) q^{75} -50025.5 q^{77} -28175.9 q^{79} +128742. q^{81} +24525.8 q^{83} +(86551.6 - 9050.61i) q^{85} -17057.2i q^{87} +117015. q^{89} -72312.1i q^{91} -253133. q^{93} +(-26936.1 + 2816.68i) q^{95} -37703.4i q^{97} -309526. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2944q^{9} + O(q^{10}) \) \( 32q + 2944q^{9} - 46528q^{25} - 36768q^{41} - 113920q^{49} + 25376q^{65} + 633472q^{81} + 968704q^{89} + O(q^{100}) \)

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
\(3\) −28.5405 −1.83087 −0.915436 0.402463i \(-0.868154\pi\)
−0.915436 + 0.402463i \(0.868154\pi\)
\(4\) 0 0
\(5\) −5.81388 55.5985i −0.104002 0.994577i
\(6\) 0 0
\(7\) 92.3750i 0.712540i −0.934383 0.356270i \(-0.884048\pi\)
0.934383 0.356270i \(-0.115952\pi\)
\(8\) 0 0
\(9\) 571.559 2.35209
\(10\) 0 0
\(11\) 541.547i 1.34944i −0.738072 0.674722i \(-0.764264\pi\)
0.738072 0.674722i \(-0.235736\pi\)
\(12\) 0 0
\(13\) 782.810 1.28469 0.642345 0.766416i \(-0.277962\pi\)
0.642345 + 0.766416i \(0.277962\pi\)
\(14\) 0 0
\(15\) 165.931 + 1586.81i 0.190414 + 1.82094i
\(16\) 0 0
\(17\) 1556.72i 1.30644i 0.757169 + 0.653219i \(0.226582\pi\)
−0.757169 + 0.653219i \(0.773418\pi\)
\(18\) 0 0
\(19\) 484.475i 0.307884i −0.988080 0.153942i \(-0.950803\pi\)
0.988080 0.153942i \(-0.0491969\pi\)
\(20\) 0 0
\(21\) 2636.43i 1.30457i
\(22\) 0 0
\(23\) 1096.90i 0.432361i 0.976353 + 0.216181i \(0.0693600\pi\)
−0.976353 + 0.216181i \(0.930640\pi\)
\(24\) 0 0
\(25\) −3057.40 + 646.487i −0.978367 + 0.206876i
\(26\) 0 0
\(27\) −9377.22 −2.47551
\(28\) 0 0
\(29\) 597.650i 0.131963i 0.997821 + 0.0659814i \(0.0210178\pi\)
−0.997821 + 0.0659814i \(0.978982\pi\)
\(30\) 0 0
\(31\) 8869.25 1.65761 0.828805 0.559537i \(-0.189021\pi\)
0.828805 + 0.559537i \(0.189021\pi\)
\(32\) 0 0
\(33\) 15456.0i 2.47066i
\(34\) 0 0
\(35\) −5135.92 + 537.058i −0.708676 + 0.0741056i
\(36\) 0 0
\(37\) 13624.1 1.63608 0.818039 0.575163i \(-0.195061\pi\)
0.818039 + 0.575163i \(0.195061\pi\)
\(38\) 0 0
\(39\) −22341.8 −2.35210
\(40\) 0 0
\(41\) 14540.4 1.35088 0.675441 0.737414i \(-0.263953\pi\)
0.675441 + 0.737414i \(0.263953\pi\)
\(42\) 0 0
\(43\) −1828.39 −0.150799 −0.0753993 0.997153i \(-0.524023\pi\)
−0.0753993 + 0.997153i \(0.524023\pi\)
\(44\) 0 0
\(45\) −3322.98 31777.8i −0.244622 2.33934i
\(46\) 0 0
\(47\) 17951.8i 1.18539i 0.805426 + 0.592697i \(0.201937\pi\)
−0.805426 + 0.592697i \(0.798063\pi\)
\(48\) 0 0
\(49\) 8273.86 0.492286
\(50\) 0 0
\(51\) 44429.6i 2.39192i
\(52\) 0 0
\(53\) −1650.99 −0.0807337 −0.0403669 0.999185i \(-0.512853\pi\)
−0.0403669 + 0.999185i \(0.512853\pi\)
\(54\) 0 0
\(55\) −30109.3 + 3148.49i −1.34213 + 0.140345i
\(56\) 0 0
\(57\) 13827.1i 0.563697i
\(58\) 0 0
\(59\) 14453.6i 0.540564i 0.962781 + 0.270282i \(0.0871169\pi\)
−0.962781 + 0.270282i \(0.912883\pi\)
\(60\) 0 0
\(61\) 24574.4i 0.845588i 0.906226 + 0.422794i \(0.138951\pi\)
−0.906226 + 0.422794i \(0.861049\pi\)
\(62\) 0 0
\(63\) 52797.7i 1.67596i
\(64\) 0 0
\(65\) −4551.17 43523.1i −0.133610 1.27772i
\(66\) 0 0
\(67\) 26842.8 0.730535 0.365268 0.930903i \(-0.380978\pi\)
0.365268 + 0.930903i \(0.380978\pi\)
\(68\) 0 0
\(69\) 31306.0i 0.791598i
\(70\) 0 0
\(71\) 48050.6 1.13124 0.565618 0.824668i \(-0.308638\pi\)
0.565618 + 0.824668i \(0.308638\pi\)
\(72\) 0 0
\(73\) 60646.8i 1.33199i −0.745957 0.665994i \(-0.768007\pi\)
0.745957 0.665994i \(-0.231993\pi\)
\(74\) 0 0
\(75\) 87259.6 18451.0i 1.79127 0.378763i
\(76\) 0 0
\(77\) −50025.5 −0.961533
\(78\) 0 0
\(79\) −28175.9 −0.507937 −0.253969 0.967212i \(-0.581736\pi\)
−0.253969 + 0.967212i \(0.581736\pi\)
\(80\) 0 0
\(81\) 128742. 2.18025
\(82\) 0 0
\(83\) 24525.8 0.390777 0.195388 0.980726i \(-0.437403\pi\)
0.195388 + 0.980726i \(0.437403\pi\)
\(84\) 0 0
\(85\) 86551.6 9050.61i 1.29935 0.135872i
\(86\) 0 0
\(87\) 17057.2i 0.241607i
\(88\) 0 0
\(89\) 117015. 1.56591 0.782953 0.622081i \(-0.213713\pi\)
0.782953 + 0.622081i \(0.213713\pi\)
\(90\) 0 0
\(91\) 72312.1i 0.915393i
\(92\) 0 0
\(93\) −253133. −3.03487
\(94\) 0 0
\(95\) −26936.1 + 2816.68i −0.306215 + 0.0320205i
\(96\) 0 0
\(97\) 37703.4i 0.406865i −0.979089 0.203433i \(-0.934790\pi\)
0.979089 0.203433i \(-0.0652098\pi\)
\(98\) 0 0
\(99\) 309526.i 3.17402i
\(100\) 0 0
\(101\) 106605.i 1.03985i −0.854211 0.519927i \(-0.825959\pi\)
0.854211 0.519927i \(-0.174041\pi\)
\(102\) 0 0
\(103\) 140551.i 1.30539i −0.757619 0.652697i \(-0.773638\pi\)
0.757619 0.652697i \(-0.226362\pi\)
\(104\) 0 0
\(105\) 146581. 15327.9i 1.29750 0.135678i
\(106\) 0 0
\(107\) 78552.8 0.663289 0.331644 0.943405i \(-0.392397\pi\)
0.331644 + 0.943405i \(0.392397\pi\)
\(108\) 0 0
\(109\) 149209.i 1.20290i −0.798910 0.601450i \(-0.794590\pi\)
0.798910 0.601450i \(-0.205410\pi\)
\(110\) 0 0
\(111\) −388839. −2.99545
\(112\) 0 0
\(113\) 190766.i 1.40541i 0.711479 + 0.702707i \(0.248026\pi\)
−0.711479 + 0.702707i \(0.751974\pi\)
\(114\) 0 0
\(115\) 60986.0 6377.24i 0.430017 0.0449664i
\(116\) 0 0
\(117\) 447422. 3.02171
\(118\) 0 0
\(119\) 143802. 0.930890
\(120\) 0 0
\(121\) −132223. −0.820999
\(122\) 0 0
\(123\) −414991. −2.47329
\(124\) 0 0
\(125\) 53719.1 + 166228.i 0.307506 + 0.951546i
\(126\) 0 0
\(127\) 257744.i 1.41801i 0.705205 + 0.709004i \(0.250855\pi\)
−0.705205 + 0.709004i \(0.749145\pi\)
\(128\) 0 0
\(129\) 52183.1 0.276093
\(130\) 0 0
\(131\) 165038.i 0.840242i 0.907468 + 0.420121i \(0.138012\pi\)
−0.907468 + 0.420121i \(0.861988\pi\)
\(132\) 0 0
\(133\) −44753.4 −0.219380
\(134\) 0 0
\(135\) 54518.1 + 521360.i 0.257458 + 2.46209i
\(136\) 0 0
\(137\) 17244.2i 0.0784948i 0.999230 + 0.0392474i \(0.0124960\pi\)
−0.999230 + 0.0392474i \(0.987504\pi\)
\(138\) 0 0
\(139\) 140468.i 0.616654i 0.951280 + 0.308327i \(0.0997692\pi\)
−0.951280 + 0.308327i \(0.900231\pi\)
\(140\) 0 0
\(141\) 512352.i 2.17031i
\(142\) 0 0
\(143\) 423929.i 1.73362i
\(144\) 0 0
\(145\) 33228.5 3474.67i 0.131247 0.0137244i
\(146\) 0 0
\(147\) −236140. −0.901314
\(148\) 0 0
\(149\) 314120.i 1.15913i 0.814928 + 0.579563i \(0.196777\pi\)
−0.814928 + 0.579563i \(0.803223\pi\)
\(150\) 0 0
\(151\) −242427. −0.865242 −0.432621 0.901576i \(-0.642411\pi\)
−0.432621 + 0.901576i \(0.642411\pi\)
\(152\) 0 0
\(153\) 889759.i 3.07287i
\(154\) 0 0
\(155\) −51564.8 493117.i −0.172395 1.64862i
\(156\) 0 0
\(157\) −343720. −1.11290 −0.556450 0.830881i \(-0.687837\pi\)
−0.556450 + 0.830881i \(0.687837\pi\)
\(158\) 0 0
\(159\) 47120.1 0.147813
\(160\) 0 0
\(161\) 101326. 0.308075
\(162\) 0 0
\(163\) −154899. −0.456647 −0.228324 0.973585i \(-0.573324\pi\)
−0.228324 + 0.973585i \(0.573324\pi\)
\(164\) 0 0
\(165\) 859332. 89859.5i 2.45726 0.256953i
\(166\) 0 0
\(167\) 41199.1i 0.114313i −0.998365 0.0571567i \(-0.981797\pi\)
0.998365 0.0571567i \(-0.0182035\pi\)
\(168\) 0 0
\(169\) 241499. 0.650427
\(170\) 0 0
\(171\) 276906.i 0.724172i
\(172\) 0 0
\(173\) −707204. −1.79651 −0.898255 0.439475i \(-0.855164\pi\)
−0.898255 + 0.439475i \(0.855164\pi\)
\(174\) 0 0
\(175\) 59719.2 + 282427.i 0.147407 + 0.697126i
\(176\) 0 0
\(177\) 412513.i 0.989703i
\(178\) 0 0
\(179\) 385923.i 0.900259i −0.892963 0.450130i \(-0.851378\pi\)
0.892963 0.450130i \(-0.148622\pi\)
\(180\) 0 0
\(181\) 283701.i 0.643672i 0.946795 + 0.321836i \(0.104300\pi\)
−0.946795 + 0.321836i \(0.895700\pi\)
\(182\) 0 0
\(183\) 701366.i 1.54816i
\(184\) 0 0
\(185\) −79209.0 757481.i −0.170155 1.62721i
\(186\) 0 0
\(187\) 843040. 1.76297
\(188\) 0 0
\(189\) 866221.i 1.76390i
\(190\) 0 0
\(191\) 749997. 1.48756 0.743782 0.668422i \(-0.233030\pi\)
0.743782 + 0.668422i \(0.233030\pi\)
\(192\) 0 0
\(193\) 232810.i 0.449892i −0.974371 0.224946i \(-0.927779\pi\)
0.974371 0.224946i \(-0.0722206\pi\)
\(194\) 0 0
\(195\) 129893. + 1.24217e6i 0.244623 + 2.33935i
\(196\) 0 0
\(197\) 88921.6 0.163246 0.0816228 0.996663i \(-0.473990\pi\)
0.0816228 + 0.996663i \(0.473990\pi\)
\(198\) 0 0
\(199\) 194624. 0.348388 0.174194 0.984711i \(-0.444268\pi\)
0.174194 + 0.984711i \(0.444268\pi\)
\(200\) 0 0
\(201\) −766107. −1.33752
\(202\) 0 0
\(203\) 55207.9 0.0940288
\(204\) 0 0
\(205\) −84536.4 808427.i −0.140494 1.34356i
\(206\) 0 0
\(207\) 626942.i 1.01695i
\(208\) 0 0
\(209\) −262366. −0.415472
\(210\) 0 0
\(211\) 932681.i 1.44220i 0.692828 + 0.721102i \(0.256364\pi\)
−0.692828 + 0.721102i \(0.743636\pi\)
\(212\) 0 0
\(213\) −1.37139e6 −2.07115
\(214\) 0 0
\(215\) 10630.0 + 101656.i 0.0156833 + 0.149981i
\(216\) 0 0
\(217\) 819297.i 1.18111i
\(218\) 0 0
\(219\) 1.73089e6i 2.43870i
\(220\) 0 0
\(221\) 1.21862e6i 1.67837i
\(222\) 0 0
\(223\) 1.37279e6i 1.84860i −0.381666 0.924300i \(-0.624649\pi\)
0.381666 0.924300i \(-0.375351\pi\)
\(224\) 0 0
\(225\) −1.74748e6 + 369505.i −2.30121 + 0.486591i
\(226\) 0 0
\(227\) 1.38224e6 1.78040 0.890200 0.455569i \(-0.150564\pi\)
0.890200 + 0.455569i \(0.150564\pi\)
\(228\) 0 0
\(229\) 330003.i 0.415843i −0.978146 0.207922i \(-0.933330\pi\)
0.978146 0.207922i \(-0.0666699\pi\)
\(230\) 0 0
\(231\) 1.42775e6 1.76044
\(232\) 0 0
\(233\) 1.14254e6i 1.37874i −0.724409 0.689370i \(-0.757887\pi\)
0.724409 0.689370i \(-0.242113\pi\)
\(234\) 0 0
\(235\) 998093. 104370.i 1.17897 0.123283i
\(236\) 0 0
\(237\) 804154. 0.929969
\(238\) 0 0
\(239\) −441560. −0.500029 −0.250015 0.968242i \(-0.580435\pi\)
−0.250015 + 0.968242i \(0.580435\pi\)
\(240\) 0 0
\(241\) 509548. 0.565122 0.282561 0.959249i \(-0.408816\pi\)
0.282561 + 0.959249i \(0.408816\pi\)
\(242\) 0 0
\(243\) −1.39568e6 −1.51625
\(244\) 0 0
\(245\) −48103.3 460015.i −0.0511987 0.489617i
\(246\) 0 0
\(247\) 379252.i 0.395536i
\(248\) 0 0
\(249\) −699979. −0.715462
\(250\) 0 0
\(251\) 253562.i 0.254039i −0.991900 0.127019i \(-0.959459\pi\)
0.991900 0.127019i \(-0.0405411\pi\)
\(252\) 0 0
\(253\) 594023. 0.583447
\(254\) 0 0
\(255\) −2.47022e6 + 258309.i −2.37895 + 0.248765i
\(256\) 0 0
\(257\) 203987.i 0.192650i −0.995350 0.0963252i \(-0.969291\pi\)
0.995350 0.0963252i \(-0.0307089\pi\)
\(258\) 0 0
\(259\) 1.25853e6i 1.16577i
\(260\) 0 0
\(261\) 341592.i 0.310389i
\(262\) 0 0
\(263\) 1.49608e6i 1.33372i 0.745181 + 0.666862i \(0.232363\pi\)
−0.745181 + 0.666862i \(0.767637\pi\)
\(264\) 0 0
\(265\) 9598.67 + 91792.7i 0.00839646 + 0.0802959i
\(266\) 0 0
\(267\) −3.33966e6 −2.86697
\(268\) 0 0
\(269\) 522744.i 0.440462i 0.975448 + 0.220231i \(0.0706811\pi\)
−0.975448 + 0.220231i \(0.929319\pi\)
\(270\) 0 0
\(271\) −1.43490e6 −1.18686 −0.593429 0.804886i \(-0.702226\pi\)
−0.593429 + 0.804886i \(0.702226\pi\)
\(272\) 0 0
\(273\) 2.06382e6i 1.67597i
\(274\) 0 0
\(275\) 350103. + 1.65573e6i 0.279167 + 1.32025i
\(276\) 0 0
\(277\) −360298. −0.282139 −0.141069 0.990000i \(-0.545054\pi\)
−0.141069 + 0.990000i \(0.545054\pi\)
\(278\) 0 0
\(279\) 5.06930e6 3.89886
\(280\) 0 0
\(281\) −982971. −0.742634 −0.371317 0.928506i \(-0.621094\pi\)
−0.371317 + 0.928506i \(0.621094\pi\)
\(282\) 0 0
\(283\) 597953. 0.443814 0.221907 0.975068i \(-0.428772\pi\)
0.221907 + 0.975068i \(0.428772\pi\)
\(284\) 0 0
\(285\) 768769. 80389.4i 0.560640 0.0586255i
\(286\) 0 0
\(287\) 1.34317e6i 0.962558i
\(288\) 0 0
\(289\) −1.00353e6 −0.706783
\(290\) 0 0
\(291\) 1.07607e6i 0.744919i
\(292\) 0 0
\(293\) −1.14992e6 −0.782529 −0.391264 0.920278i \(-0.627962\pi\)
−0.391264 + 0.920278i \(0.627962\pi\)
\(294\) 0 0
\(295\) 803601. 84031.7i 0.537632 0.0562197i
\(296\) 0 0
\(297\) 5.07821e6i 3.34056i
\(298\) 0 0
\(299\) 858663.i 0.555450i
\(300\) 0 0
\(301\) 168897.i 0.107450i
\(302\) 0 0
\(303\) 3.04255e6i 1.90384i
\(304\) 0 0
\(305\) 1.36630e6 142873.i 0.841003 0.0879428i
\(306\) 0 0
\(307\) −1.78536e6 −1.08114 −0.540568 0.841300i \(-0.681791\pi\)
−0.540568 + 0.841300i \(0.681791\pi\)
\(308\) 0 0
\(309\) 4.01140e6i 2.39001i
\(310\) 0 0
\(311\) 669162. 0.392311 0.196155 0.980573i \(-0.437154\pi\)
0.196155 + 0.980573i \(0.437154\pi\)
\(312\) 0 0
\(313\) 1.22019e6i 0.703989i −0.936002 0.351994i \(-0.885504\pi\)
0.936002 0.351994i \(-0.114496\pi\)
\(314\) 0 0
\(315\) −2.93548e6 + 306960.i −1.66687 + 0.174303i
\(316\) 0 0
\(317\) 1.63087e6 0.911529 0.455764 0.890101i \(-0.349366\pi\)
0.455764 + 0.890101i \(0.349366\pi\)
\(318\) 0 0
\(319\) 323656. 0.178076
\(320\) 0 0
\(321\) −2.24194e6 −1.21440
\(322\) 0 0
\(323\) 754194. 0.402232
\(324\) 0 0
\(325\) −2.39336e6 + 506077.i −1.25690 + 0.265771i
\(326\) 0 0
\(327\) 4.25851e6i 2.20236i
\(328\) 0 0
\(329\) 1.65830e6 0.844641
\(330\) 0 0
\(331\) 1.47491e6i 0.739936i 0.929044 + 0.369968i \(0.120631\pi\)
−0.929044 + 0.369968i \(0.879369\pi\)
\(332\) 0 0
\(333\) 7.78698e6 3.84821
\(334\) 0 0
\(335\) −156061. 1.49242e6i −0.0759771 0.726573i
\(336\) 0 0
\(337\) 3.04284e6i 1.45950i −0.683713 0.729751i \(-0.739636\pi\)
0.683713 0.729751i \(-0.260364\pi\)
\(338\) 0 0
\(339\) 5.44455e6i 2.57314i
\(340\) 0 0
\(341\) 4.80312e6i 2.23685i
\(342\) 0 0
\(343\) 2.31684e6i 1.06331i
\(344\) 0 0
\(345\) −1.74057e6 + 182009.i −0.787306 + 0.0823277i
\(346\) 0 0
\(347\) 3.03217e6 1.35185 0.675927 0.736968i \(-0.263743\pi\)
0.675927 + 0.736968i \(0.263743\pi\)
\(348\) 0 0
\(349\) 142845.i 0.0627773i 0.999507 + 0.0313887i \(0.00999296\pi\)
−0.999507 + 0.0313887i \(0.990007\pi\)
\(350\) 0 0
\(351\) −7.34059e6 −3.18026
\(352\) 0 0
\(353\) 955673.i 0.408200i −0.978950 0.204100i \(-0.934573\pi\)
0.978950 0.204100i \(-0.0654267\pi\)
\(354\) 0 0
\(355\) −279361. 2.67154e6i −0.117651 1.12510i
\(356\) 0 0
\(357\) −4.10419e6 −1.70434
\(358\) 0 0
\(359\) 1.33046e6 0.544837 0.272418 0.962179i \(-0.412177\pi\)
0.272418 + 0.962179i \(0.412177\pi\)
\(360\) 0 0
\(361\) 2.24138e6 0.905207
\(362\) 0 0
\(363\) 3.77370e6 1.50314
\(364\) 0 0
\(365\) −3.37187e6 + 352593.i −1.32477 + 0.138529i
\(366\) 0 0
\(367\) 1.97269e6i 0.764527i −0.924053 0.382263i \(-0.875145\pi\)
0.924053 0.382263i \(-0.124855\pi\)
\(368\) 0 0
\(369\) 8.31071e6 3.17740
\(370\) 0 0
\(371\) 152510.i 0.0575260i
\(372\) 0 0
\(373\) −386597. −0.143875 −0.0719377 0.997409i \(-0.522918\pi\)
−0.0719377 + 0.997409i \(0.522918\pi\)
\(374\) 0 0
\(375\) −1.53317e6 4.74423e6i −0.563004 1.74216i
\(376\) 0 0
\(377\) 467846.i 0.169531i
\(378\) 0 0
\(379\) 3.21349e6i 1.14915i −0.818450 0.574577i \(-0.805167\pi\)
0.818450 0.574577i \(-0.194833\pi\)
\(380\) 0 0
\(381\) 7.35612e6i 2.59619i
\(382\) 0 0
\(383\) 2.09419e6i 0.729488i 0.931108 + 0.364744i \(0.118844\pi\)
−0.931108 + 0.364744i \(0.881156\pi\)
\(384\) 0 0
\(385\) 290842. + 2.78134e6i 0.100001 + 0.956319i
\(386\) 0 0
\(387\) −1.04503e6 −0.354692
\(388\) 0 0
\(389\) 944090.i 0.316329i 0.987413 + 0.158165i \(0.0505577\pi\)
−0.987413 + 0.158165i \(0.949442\pi\)
\(390\) 0 0
\(391\) −1.70757e6 −0.564854
\(392\) 0 0
\(393\) 4.71025e6i 1.53838i
\(394\) 0 0
\(395\) 163811. + 1.56654e6i 0.0528265 + 0.505183i
\(396\) 0 0
\(397\) −3.62777e6 −1.15522 −0.577608 0.816314i \(-0.696014\pi\)
−0.577608 + 0.816314i \(0.696014\pi\)
\(398\) 0 0
\(399\) 1.27728e6 0.401657
\(400\) 0 0
\(401\) −3.56035e6 −1.10569 −0.552843 0.833285i \(-0.686457\pi\)
−0.552843 + 0.833285i \(0.686457\pi\)
\(402\) 0 0
\(403\) 6.94294e6 2.12952
\(404\) 0 0
\(405\) −748489. 7.15785e6i −0.226750 2.16843i
\(406\) 0 0
\(407\) 7.37811e6i 2.20780i
\(408\) 0 0
\(409\) 4.04814e6 1.19660 0.598298 0.801273i \(-0.295844\pi\)
0.598298 + 0.801273i \(0.295844\pi\)
\(410\) 0 0
\(411\) 492157.i 0.143714i
\(412\) 0 0
\(413\) 1.33515e6 0.385173
\(414\) 0 0
\(415\) −142590. 1.36360e6i −0.0406415 0.388657i
\(416\) 0 0
\(417\) 4.00904e6i 1.12902i
\(418\) 0 0
\(419\) 4.13360e6i 1.15025i 0.818064 + 0.575127i \(0.195047\pi\)
−0.818064 + 0.575127i \(0.804953\pi\)
\(420\) 0 0
\(421\) 1.98891e6i 0.546902i 0.961886 + 0.273451i \(0.0881651\pi\)
−0.961886 + 0.273451i \(0.911835\pi\)
\(422\) 0 0
\(423\) 1.02605e7i 2.78816i
\(424\) 0 0
\(425\) −1.00640e6 4.75952e6i −0.270271 1.27818i
\(426\) 0 0
\(427\) 2.27006e6 0.602516
\(428\) 0 0
\(429\) 1.20991e7i 3.17403i
\(430\) 0 0
\(431\) −2.17585e6 −0.564203 −0.282101 0.959385i \(-0.591031\pi\)
−0.282101 + 0.959385i \(0.591031\pi\)
\(432\) 0 0
\(433\) 3.97546e6i 1.01899i −0.860475 0.509493i \(-0.829833\pi\)
0.860475 0.509493i \(-0.170167\pi\)
\(434\) 0 0
\(435\) −948356. + 99168.6i −0.240297 + 0.0251276i
\(436\) 0 0
\(437\) 531420. 0.133117
\(438\) 0 0
\(439\) 2.62877e6 0.651017 0.325508 0.945539i \(-0.394465\pi\)
0.325508 + 0.945539i \(0.394465\pi\)
\(440\) 0 0
\(441\) 4.72900e6 1.15790
\(442\) 0 0
\(443\) −3.63413e6 −0.879814 −0.439907 0.898043i \(-0.644989\pi\)
−0.439907 + 0.898043i \(0.644989\pi\)
\(444\) 0 0
\(445\) −680310. 6.50585e6i −0.162857 1.55741i
\(446\) 0 0
\(447\) 8.96515e6i 2.12221i
\(448\) 0 0
\(449\) −1.40882e6 −0.329792 −0.164896 0.986311i \(-0.552729\pi\)
−0.164896 + 0.986311i \(0.552729\pi\)
\(450\) 0 0
\(451\) 7.87433e6i 1.82294i
\(452\) 0 0
\(453\) 6.91897e6 1.58415
\(454\) 0 0
\(455\) −4.02045e6 + 420414.i −0.910429 + 0.0952026i
\(456\) 0 0
\(457\) 7.07341e6i 1.58430i 0.610325 + 0.792151i \(0.291039\pi\)
−0.610325 + 0.792151i \(0.708961\pi\)
\(458\) 0 0
\(459\) 1.45977e7i 3.23410i
\(460\) 0 0
\(461\) 1.57690e6i 0.345582i 0.984958 + 0.172791i \(0.0552786\pi\)
−0.984958 + 0.172791i \(0.944721\pi\)
\(462\) 0 0
\(463\) 5.38641e6i 1.16774i 0.811847 + 0.583871i \(0.198463\pi\)
−0.811847 + 0.583871i \(0.801537\pi\)
\(464\) 0 0
\(465\) 1.47168e6 + 1.40738e7i 0.315633 + 3.01842i
\(466\) 0 0
\(467\) 1.22575e6 0.260082 0.130041 0.991509i \(-0.458489\pi\)
0.130041 + 0.991509i \(0.458489\pi\)
\(468\) 0 0
\(469\) 2.47961e6i 0.520536i
\(470\) 0 0
\(471\) 9.80994e6 2.03758
\(472\) 0 0
\(473\) 990159.i 0.203494i
\(474\) 0 0
\(475\) 313207. + 1.48123e6i 0.0636938 + 0.301224i
\(476\) 0 0
\(477\) −943638. −0.189893
\(478\) 0 0
\(479\) −2.58563e6 −0.514906 −0.257453 0.966291i \(-0.582883\pi\)
−0.257453 + 0.966291i \(0.582883\pi\)
\(480\) 0 0
\(481\) 1.06651e7 2.10185
\(482\) 0 0
\(483\) −2.89189e6 −0.564046
\(484\) 0 0
\(485\) −2.09625e6 + 219203.i −0.404659 + 0.0423148i
\(486\) 0 0
\(487\) 8.96610e6i 1.71309i 0.516069 + 0.856547i \(0.327395\pi\)
−0.516069 + 0.856547i \(0.672605\pi\)
\(488\) 0 0
\(489\) 4.42090e6 0.836063
\(490\) 0 0
\(491\) 2.48071e6i 0.464378i −0.972671 0.232189i \(-0.925411\pi\)
0.972671 0.232189i \(-0.0745889\pi\)
\(492\) 0 0
\(493\) −930375. −0.172401
\(494\) 0 0
\(495\) −1.72092e7 + 1.79955e6i −3.15681 + 0.330104i
\(496\) 0 0
\(497\) 4.43867e6i 0.806051i
\(498\) 0 0
\(499\) 2.82421e6i 0.507744i 0.967238 + 0.253872i \(0.0817043\pi\)
−0.967238 + 0.253872i \(0.918296\pi\)
\(500\) 0 0
\(501\) 1.17584e6i 0.209293i
\(502\) 0 0
\(503\) 1.47261e6i 0.259517i −0.991546 0.129759i \(-0.958580\pi\)
0.991546 0.129759i \(-0.0414203\pi\)
\(504\) 0 0
\(505\) −5.92706e6 + 619787.i −1.03422 + 0.108147i
\(506\) 0 0
\(507\) −6.89250e6 −1.19085
\(508\) 0 0
\(509\) 5.12155e6i 0.876207i −0.898924 0.438104i \(-0.855650\pi\)
0.898924 0.438104i \(-0.144350\pi\)
\(510\) 0 0
\(511\) −5.60225e6 −0.949096
\(512\) 0 0
\(513\) 4.54303e6i 0.762171i
\(514\) 0 0
\(515\) −7.81444e6 + 817148.i −1.29831 + 0.135763i
\(516\) 0 0
\(517\) 9.72174e6 1.59962
\(518\) 0 0
\(519\) 2.01839e7 3.28918
\(520\) 0 0
\(521\) −2.85592e6 −0.460948 −0.230474 0.973078i \(-0.574028\pi\)
−0.230474 + 0.973078i \(0.574028\pi\)
\(522\) 0 0
\(523\) −5.00538e6 −0.800171 −0.400086 0.916478i \(-0.631020\pi\)
−0.400086 + 0.916478i \(0.631020\pi\)
\(524\) 0 0
\(525\) −1.70442e6 8.06060e6i −0.269884 1.27635i
\(526\) 0 0
\(527\) 1.38070e7i 2.16557i
\(528\) 0 0
\(529\) 5.23316e6 0.813064
\(530\) 0 0
\(531\) 8.26110e6i 1.27146i
\(532\) 0 0
\(533\) 1.13824e7 1.73547
\(534\) 0 0
\(535\) −456697. 4.36742e6i −0.0689833 0.659692i
\(536\) 0 0
\(537\) 1.10144e7i 1.64826i
\(538\) 0 0
\(539\) 4.48069e6i 0.664313i
\(540\) 0 0
\(541\) 6.29808e6i 0.925157i 0.886578 + 0.462578i \(0.153076\pi\)
−0.886578 + 0.462578i \(0.846924\pi\)
\(542\) 0 0
\(543\) 8.09696e6i 1.17848i
\(544\) 0 0
\(545\) −8.29582e6 + 867486.i −1.19638 + 0.125104i
\(546\) 0 0
\(547\) −1.56773e6 −0.224029 −0.112014 0.993707i \(-0.535730\pi\)
−0.112014 + 0.993707i \(0.535730\pi\)
\(548\) 0 0
\(549\) 1.40457e7i 1.98890i
\(550\) 0 0
\(551\) 289546. 0.0406293
\(552\) 0 0
\(553\) 2.60275e6i 0.361926i
\(554\) 0 0
\(555\) 2.26066e6 + 2.16189e7i 0.311533 + 2.97921i
\(556\) 0 0
\(557\) −8.52468e6 −1.16423 −0.582117 0.813105i \(-0.697775\pi\)
−0.582117 + 0.813105i \(0.697775\pi\)
\(558\) 0 0
\(559\) −1.43128e6 −0.193729
\(560\) 0 0
\(561\) −2.40608e7 −3.22777
\(562\) 0 0
\(563\) −935676. −0.124410 −0.0622049 0.998063i \(-0.519813\pi\)
−0.0622049 + 0.998063i \(0.519813\pi\)
\(564\) 0 0
\(565\) 1.06063e7 1.10909e6i 1.39779 0.146166i
\(566\) 0 0
\(567\) 1.18925e7i 1.55352i
\(568\) 0 0
\(569\) −9.09876e6 −1.17815 −0.589076 0.808077i \(-0.700508\pi\)
−0.589076 + 0.808077i \(0.700508\pi\)
\(570\) 0 0
\(571\) 1.41349e6i 0.181427i 0.995877 + 0.0907136i \(0.0289148\pi\)
−0.995877 + 0.0907136i \(0.971085\pi\)
\(572\) 0 0
\(573\) −2.14053e7 −2.72354
\(574\) 0 0
\(575\) −709131. 3.35365e6i −0.0894451 0.423008i
\(576\) 0 0
\(577\) 1.18400e7i 1.48052i −0.672322 0.740259i \(-0.734703\pi\)
0.672322 0.740259i \(-0.265297\pi\)
\(578\) 0 0
\(579\) 6.64451e6i 0.823695i
\(580\) 0 0
\(581\) 2.26557e6i 0.278444i
\(582\) 0 0
\(583\) 894090.i 0.108946i
\(584\) 0 0
\(585\) −2.60126e6 2.48760e7i −0.314264 3.00532i
\(586\) 0 0
\(587\) 3.37505e6 0.404283 0.202141 0.979356i \(-0.435210\pi\)
0.202141 + 0.979356i \(0.435210\pi\)
\(588\) 0 0
\(589\) 4.29693e6i 0.510352i
\(590\) 0 0
\(591\) −2.53786e6 −0.298882
\(592\) 0 0
\(593\) 1.32900e7i 1.55199i 0.630737 + 0.775997i \(0.282753\pi\)
−0.630737 + 0.775997i \(0.717247\pi\)
\(594\) 0 0
\(595\) −836050. 7.99520e6i −0.0968144 0.925842i
\(596\) 0 0
\(597\) −5.55466e6 −0.637855
\(598\) 0 0
\(599\) 8.21563e6 0.935565 0.467783 0.883844i \(-0.345053\pi\)
0.467783 + 0.883844i \(0.345053\pi\)
\(600\) 0 0
\(601\) 4.66795e6 0.527157 0.263579 0.964638i \(-0.415097\pi\)
0.263579 + 0.964638i \(0.415097\pi\)
\(602\) 0 0
\(603\) 1.53422e7 1.71829
\(604\) 0 0
\(605\) 768727. + 7.35139e6i 0.0853855 + 0.816547i
\(606\) 0 0
\(607\) 280377.i 0.0308867i 0.999881 + 0.0154433i \(0.00491596\pi\)
−0.999881 + 0.0154433i \(0.995084\pi\)
\(608\) 0 0
\(609\) −1.57566e6 −0.172155
\(610\) 0 0
\(611\) 1.40528e7i 1.52286i
\(612\) 0 0
\(613\) −963624. −0.103575 −0.0517877 0.998658i \(-0.516492\pi\)
−0.0517877 + 0.998658i \(0.516492\pi\)
\(614\) 0 0
\(615\) 2.41271e6 + 2.30729e7i 0.257227 + 2.45988i
\(616\) 0 0
\(617\) 1.00959e7i 1.06766i 0.845593 + 0.533829i \(0.179247\pi\)
−0.845593 + 0.533829i \(0.820753\pi\)
\(618\) 0 0
\(619\) 1.57741e7i 1.65469i −0.561691 0.827347i \(-0.689849\pi\)
0.561691 0.827347i \(-0.310151\pi\)
\(620\) 0 0
\(621\) 1.02859e7i 1.07031i
\(622\) 0 0
\(623\) 1.08092e7i 1.11577i
\(624\) 0 0
\(625\) 8.92973e6 3.95314e6i 0.914405 0.404801i
\(626\) 0 0
\(627\) 7.48806e6 0.760677
\(628\) 0 0
\(629\) 2.12090e7i 2.13744i
\(630\) 0 0
\(631\) −1.60364e7 −1.60337 −0.801685 0.597747i \(-0.796063\pi\)
−0.801685 + 0.597747i \(0.796063\pi\)
\(632\) 0 0
\(633\) 2.66192e7i 2.64049i
\(634\) 0 0
\(635\) 1.43302e7 1.49849e6i 1.41032 0.147475i
\(636\) 0 0
\(637\) 6.47686e6 0.632435
\(638\) 0 0
\(639\) 2.74637e7 2.66077
\(640\) 0 0
\(641\) 9.42961e6 0.906460 0.453230 0.891394i \(-0.350272\pi\)
0.453230 + 0.891394i \(0.350272\pi\)
\(642\) 0 0
\(643\) 102240. 0.00975200 0.00487600 0.999988i \(-0.498448\pi\)
0.00487600 + 0.999988i \(0.498448\pi\)
\(644\) 0 0
\(645\) −303386. 2.90130e6i −0.0287142 0.274596i
\(646\) 0 0
\(647\) 7.52613e6i 0.706824i 0.935468 + 0.353412i \(0.114979\pi\)
−0.935468 + 0.353412i \(0.885021\pi\)
\(648\) 0 0
\(649\) 7.82733e6 0.729460
\(650\) 0 0
\(651\) 2.33831e7i 2.16247i
\(652\) 0 0
\(653\) −1.11241e7 −1.02090 −0.510450 0.859907i \(-0.670521\pi\)
−0.510450 + 0.859907i \(0.670521\pi\)
\(654\) 0 0
\(655\) 9.17585e6 959509.i 0.835686 0.0873868i
\(656\) 0 0
\(657\) 3.46632e7i 3.13296i
\(658\) 0 0
\(659\) 9.90902e6i 0.888827i 0.895822 + 0.444413i \(0.146588\pi\)
−0.895822 + 0.444413i \(0.853412\pi\)
\(660\) 0 0
\(661\) 1.94571e7i 1.73211i −0.499950 0.866054i \(-0.666648\pi\)
0.499950 0.866054i \(-0.333352\pi\)
\(662\) 0 0
\(663\) 3.47800e7i 3.07288i
\(664\) 0 0
\(665\) 260191. + 2.48822e6i 0.0228159 + 0.218190i
\(666\) 0 0
\(667\) −655561. −0.0570556
\(668\) 0 0
\(669\) 3.91802e7i 3.38455i
\(670\) 0 0
\(671\) 1.33082e7 1.14107
\(672\) 0 0
\(673\) 1.66792e7i 1.41951i 0.704450 + 0.709754i \(0.251194\pi\)
−0.704450 + 0.709754i \(0.748806\pi\)
\(674\) 0 0
\(675\) 2.86699e7 6.06225e6i 2.42196 0.512123i
\(676\) 0 0
\(677\) 1.43143e7 1.20033 0.600163 0.799878i \(-0.295102\pi\)
0.600163 + 0.799878i \(0.295102\pi\)
\(678\) 0 0
\(679\) −3.48285e6 −0.289908
\(680\) 0 0
\(681\) −3.94497e7 −3.25969
\(682\) 0 0
\(683\) −2.35057e7 −1.92806 −0.964032 0.265786i \(-0.914369\pi\)
−0.964032 + 0.265786i \(0.914369\pi\)
\(684\) 0 0
\(685\) 958751. 100256.i 0.0780691 0.00816361i
\(686\) 0 0
\(687\) 9.41845e6i 0.761355i
\(688\) 0 0
\(689\) −1.29241e6 −0.103718
\(690\) 0 0
\(691\) 9.02428e6i 0.718981i −0.933149 0.359490i \(-0.882951\pi\)
0.933149 0.359490i \(-0.117049\pi\)
\(692\) 0 0
\(693\) −2.85925e7 −2.26162
\(694\) 0 0
\(695\) 7.80984e6 816667.i 0.613310 0.0641332i
\(696\) 0 0
\(697\) 2.26354e7i 1.76485i
\(698\) 0 0
\(699\) 3.26087e7i 2.52430i
\(700\) 0 0
\(701\) 2.56364e6i 0.197044i 0.995135 + 0.0985218i \(0.0314114\pi\)
−0.995135 + 0.0985218i \(0.968589\pi\)
\(702\) 0 0
\(703\) 6.60054e6i 0.503723i
\(704\) 0 0
\(705\) −2.84860e7 + 2.97876e6i −2.15854 + 0.225716i
\(706\) 0 0
\(707\) −9.84760e6 −0.740938
\(708\) 0 0
\(709\) 1.83762e6i 0.137290i 0.997641 + 0.0686450i \(0.0218676\pi\)
−0.997641 + 0.0686450i \(0.978132\pi\)
\(710\) 0 0
\(711\) −1.61042e7 −1.19472
\(712\) 0 0
\(713\) 9.72866e6i 0.716687i
\(714\) 0 0
\(715\) −2.35698e7 + 2.46467e6i −1.72422 + 0.180299i
\(716\) 0 0
\(717\) 1.26023e7 0.915489
\(718\) 0 0
\(719\) 9.48236e6 0.684060 0.342030 0.939689i \(-0.388885\pi\)
0.342030 + 0.939689i \(0.388885\pi\)
\(720\) 0 0
\(721\) −1.29834e7 −0.930145
\(722\) 0 0
\(723\) −1.45427e7 −1.03467
\(724\) 0 0
\(725\) −386373. 1.82725e6i −0.0272999 0.129108i
\(726\) 0 0
\(727\) 2.49674e6i 0.175201i 0.996156 + 0.0876007i \(0.0279200\pi\)
−0.996156 + 0.0876007i \(0.972080\pi\)
\(728\) 0 0
\(729\) 8.54920e6 0.595809
\(730\) 0 0
\(731\) 2.84629e6i 0.197009i
\(732\) 0 0
\(733\) −2.33505e7 −1.60522 −0.802612 0.596502i \(-0.796557\pi\)
−0.802612 + 0.596502i \(0.796557\pi\)
\(734\) 0 0
\(735\) 1.37289e6 + 1.31290e7i 0.0937384 + 0.896426i
\(736\) 0 0
\(737\) 1.45367e7i 0.985816i
\(738\) 0 0
\(739\) 2.42153e7i 1.63109i −0.578692 0.815546i \(-0.696437\pi\)
0.578692 0.815546i \(-0.303563\pi\)
\(740\) 0 0
\(741\) 1.08240e7i 0.724175i
\(742\) 0 0
\(743\) 1.99899e7i 1.32843i 0.747542 + 0.664214i \(0.231234\pi\)
−0.747542 + 0.664214i \(0.768766\pi\)
\(744\) 0 0
\(745\) 1.74646e7 1.82626e6i 1.15284 0.120551i
\(746\) 0 0
\(747\) 1.40180e7 0.919143
\(748\) 0 0
\(749\) 7.25632e6i 0.472620i
\(750\) 0 0
\(751\) −4.33613e6 −0.280545 −0.140272 0.990113i \(-0.544798\pi\)
−0.140272 + 0.990113i \(0.544798\pi\)
\(752\) 0 0
\(753\) 7.23679e6i 0.465113i
\(754\) 0 0
\(755\) 1.40944e6 + 1.34786e7i 0.0899869 + 0.860550i
\(756\) 0 0
\(757\) 1.47258e7 0.933984 0.466992 0.884262i \(-0.345338\pi\)
0.466992 + 0.884262i \(0.345338\pi\)
\(758\) 0 0
\(759\) −1.69537e7 −1.06822
\(760\) 0 0
\(761\) −366653. −0.0229506 −0.0114753 0.999934i \(-0.503653\pi\)
−0.0114753 + 0.999934i \(0.503653\pi\)
\(762\) 0 0
\(763\) −1.37832e7 −0.857115
\(764\) 0 0
\(765\) 4.94693e7 5.17295e6i 3.05620 0.319584i
\(766\) 0 0
\(767\) 1.13145e7i 0.694457i
\(768\) 0 0
\(769\) 5.25862e6 0.320668 0.160334 0.987063i \(-0.448743\pi\)
0.160334 + 0.987063i \(0.448743\pi\)
\(770\) 0 0
\(771\) 5.82189e6i 0.352718i
\(772\) 0 0
\(773\) 249509. 0.0150189 0.00750943 0.999972i \(-0.497610\pi\)
0.00750943 + 0.999972i \(0.497610\pi\)
\(774\) 0 0
\(775\) −2.71168e7 + 5.73385e6i −1.62175 + 0.342920i
\(776\) 0 0
\(777\) 3.59190e7i 2.13438i
\(778\) 0 0
\(779\) 7.04448e6i 0.415915i
\(780\) 0 0
\(781\) 2.60217e7i 1.52654i
\(782\) 0 0
\(783\) 5.60429e6i 0.326675i
\(784\) 0 0
\(785\) 1.99835e6 + 1.91104e7i 0.115744 + 1.10686i
\(786\) 0 0
\(787\) −1.94586e6 −0.111989 −0.0559945 0.998431i \(-0.517833\pi\)
−0.0559945 + 0.998431i \(0.517833\pi\)
\(788\) 0 0
\(789\) 4.26989e7i 2.44188i
\(790\) 0 0
\(791\) 1.76220e7 1.00141
\(792\) 0 0
\(793\) 1.92371e7i 1.08632i
\(794\) 0 0