Properties

Label 320.6.l.a.81.15
Level 320
Weight 6
Character 320.81
Analytic conductor 51.323
Analytic rank 0
Dimension 80
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.l (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(51.3228223402\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 81.15
Character \(\chi\) \(=\) 320.81
Dual form 320.6.l.a.241.15

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.64986 - 5.64986i) q^{3} +(-17.6777 + 17.6777i) q^{5} -143.077i q^{7} -179.158i q^{9} +O(q^{10})\) \(q+(-5.64986 - 5.64986i) q^{3} +(-17.6777 + 17.6777i) q^{5} -143.077i q^{7} -179.158i q^{9} +(291.881 - 291.881i) q^{11} +(181.016 + 181.016i) q^{13} +199.753 q^{15} +1053.85 q^{17} +(421.682 + 421.682i) q^{19} +(-808.365 + 808.365i) q^{21} -340.870i q^{23} -625.000i q^{25} +(-2385.13 + 2385.13i) q^{27} +(1109.53 + 1109.53i) q^{29} -1054.61 q^{31} -3298.18 q^{33} +(2529.27 + 2529.27i) q^{35} +(2300.69 - 2300.69i) q^{37} -2045.43i q^{39} -13456.2i q^{41} +(2038.54 - 2038.54i) q^{43} +(3167.10 + 3167.10i) q^{45} -15149.3 q^{47} -3664.02 q^{49} +(-5954.12 - 5954.12i) q^{51} +(23031.5 - 23031.5i) q^{53} +10319.6i q^{55} -4764.89i q^{57} +(1167.72 - 1167.72i) q^{59} +(-38311.2 - 38311.2i) q^{61} -25633.4 q^{63} -6399.89 q^{65} +(19188.0 + 19188.0i) q^{67} +(-1925.87 + 1925.87i) q^{69} +39132.5i q^{71} -18613.3i q^{73} +(-3531.16 + 3531.16i) q^{75} +(-41761.5 - 41761.5i) q^{77} -89963.6 q^{79} -16584.1 q^{81} +(-50763.5 - 50763.5i) q^{83} +(-18629.6 + 18629.6i) q^{85} -12537.4i q^{87} +23162.0i q^{89} +(25899.3 - 25899.3i) q^{91} +(5958.40 + 5958.40i) q^{93} -14908.7 q^{95} -94202.7 q^{97} +(-52292.9 - 52292.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + O(q^{10}) \) \( 80q - 1208q^{11} + 1800q^{15} - 2360q^{19} + 7464q^{27} - 8144q^{29} + 21296q^{37} - 32072q^{43} + 88360q^{47} - 192080q^{49} + 5920q^{51} - 49456q^{53} - 44984q^{59} + 48080q^{61} - 158760q^{63} - 61160q^{67} - 22320q^{69} - 14896q^{77} - 177680q^{79} - 524880q^{81} + 329240q^{83} + 132400q^{85} - 364832q^{91} - 362352q^{93} - 288800q^{95} - 659000q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −5.64986 5.64986i −0.362439 0.362439i 0.502271 0.864710i \(-0.332498\pi\)
−0.864710 + 0.502271i \(0.832498\pi\)
\(4\) 0 0
\(5\) −17.6777 + 17.6777i −0.316228 + 0.316228i
\(6\) 0 0
\(7\) 143.077i 1.10363i −0.833966 0.551817i \(-0.813935\pi\)
0.833966 0.551817i \(-0.186065\pi\)
\(8\) 0 0
\(9\) 179.158i 0.737276i
\(10\) 0 0
\(11\) 291.881 291.881i 0.727318 0.727318i −0.242766 0.970085i \(-0.578055\pi\)
0.970085 + 0.242766i \(0.0780548\pi\)
\(12\) 0 0
\(13\) 181.016 + 181.016i 0.297070 + 0.297070i 0.839865 0.542795i \(-0.182634\pi\)
−0.542795 + 0.839865i \(0.682634\pi\)
\(14\) 0 0
\(15\) 199.753 0.229226
\(16\) 0 0
\(17\) 1053.85 0.884417 0.442209 0.896912i \(-0.354195\pi\)
0.442209 + 0.896912i \(0.354195\pi\)
\(18\) 0 0
\(19\) 421.682 + 421.682i 0.267979 + 0.267979i 0.828285 0.560306i \(-0.189317\pi\)
−0.560306 + 0.828285i \(0.689317\pi\)
\(20\) 0 0
\(21\) −808.365 + 808.365i −0.399999 + 0.399999i
\(22\) 0 0
\(23\) 340.870i 0.134360i −0.997741 0.0671798i \(-0.978600\pi\)
0.997741 0.0671798i \(-0.0214001\pi\)
\(24\) 0 0
\(25\) 625.000i 0.200000i
\(26\) 0 0
\(27\) −2385.13 + 2385.13i −0.629656 + 0.629656i
\(28\) 0 0
\(29\) 1109.53 + 1109.53i 0.244988 + 0.244988i 0.818910 0.573922i \(-0.194579\pi\)
−0.573922 + 0.818910i \(0.694579\pi\)
\(30\) 0 0
\(31\) −1054.61 −0.197101 −0.0985503 0.995132i \(-0.531421\pi\)
−0.0985503 + 0.995132i \(0.531421\pi\)
\(32\) 0 0
\(33\) −3298.18 −0.527217
\(34\) 0 0
\(35\) 2529.27 + 2529.27i 0.348999 + 0.348999i
\(36\) 0 0
\(37\) 2300.69 2300.69i 0.276283 0.276283i −0.555340 0.831623i \(-0.687412\pi\)
0.831623 + 0.555340i \(0.187412\pi\)
\(38\) 0 0
\(39\) 2045.43i 0.215340i
\(40\) 0 0
\(41\) 13456.2i 1.25015i −0.780565 0.625074i \(-0.785069\pi\)
0.780565 0.625074i \(-0.214931\pi\)
\(42\) 0 0
\(43\) 2038.54 2038.54i 0.168131 0.168131i −0.618026 0.786158i \(-0.712067\pi\)
0.786158 + 0.618026i \(0.212067\pi\)
\(44\) 0 0
\(45\) 3167.10 + 3167.10i 0.233147 + 0.233147i
\(46\) 0 0
\(47\) −15149.3 −1.00034 −0.500169 0.865928i \(-0.666729\pi\)
−0.500169 + 0.865928i \(0.666729\pi\)
\(48\) 0 0
\(49\) −3664.02 −0.218006
\(50\) 0 0
\(51\) −5954.12 5954.12i −0.320547 0.320547i
\(52\) 0 0
\(53\) 23031.5 23031.5i 1.12624 1.12624i 0.135462 0.990783i \(-0.456748\pi\)
0.990783 0.135462i \(-0.0432518\pi\)
\(54\) 0 0
\(55\) 10319.6i 0.459997i
\(56\) 0 0
\(57\) 4764.89i 0.194252i
\(58\) 0 0
\(59\) 1167.72 1167.72i 0.0436724 0.0436724i −0.684933 0.728606i \(-0.740169\pi\)
0.728606 + 0.684933i \(0.240169\pi\)
\(60\) 0 0
\(61\) −38311.2 38311.2i −1.31826 1.31826i −0.915152 0.403109i \(-0.867930\pi\)
−0.403109 0.915152i \(-0.632070\pi\)
\(62\) 0 0
\(63\) −25633.4 −0.813682
\(64\) 0 0
\(65\) −6399.89 −0.187884
\(66\) 0 0
\(67\) 19188.0 + 19188.0i 0.522206 + 0.522206i 0.918237 0.396031i \(-0.129613\pi\)
−0.396031 + 0.918237i \(0.629613\pi\)
\(68\) 0 0
\(69\) −1925.87 + 1925.87i −0.0486972 + 0.0486972i
\(70\) 0 0
\(71\) 39132.5i 0.921280i 0.887587 + 0.460640i \(0.152380\pi\)
−0.887587 + 0.460640i \(0.847620\pi\)
\(72\) 0 0
\(73\) 18613.3i 0.408805i −0.978887 0.204403i \(-0.934475\pi\)
0.978887 0.204403i \(-0.0655252\pi\)
\(74\) 0 0
\(75\) −3531.16 + 3531.16i −0.0724877 + 0.0724877i
\(76\) 0 0
\(77\) −41761.5 41761.5i −0.802693 0.802693i
\(78\) 0 0
\(79\) −89963.6 −1.62181 −0.810903 0.585180i \(-0.801024\pi\)
−0.810903 + 0.585180i \(0.801024\pi\)
\(80\) 0 0
\(81\) −16584.1 −0.280853
\(82\) 0 0
\(83\) −50763.5 50763.5i −0.808828 0.808828i 0.175629 0.984456i \(-0.443804\pi\)
−0.984456 + 0.175629i \(0.943804\pi\)
\(84\) 0 0
\(85\) −18629.6 + 18629.6i −0.279677 + 0.279677i
\(86\) 0 0
\(87\) 12537.4i 0.177586i
\(88\) 0 0
\(89\) 23162.0i 0.309956i 0.987918 + 0.154978i \(0.0495307\pi\)
−0.987918 + 0.154978i \(0.950469\pi\)
\(90\) 0 0
\(91\) 25899.3 25899.3i 0.327857 0.327857i
\(92\) 0 0
\(93\) 5958.40 + 5958.40i 0.0714369 + 0.0714369i
\(94\) 0 0
\(95\) −14908.7 −0.169485
\(96\) 0 0
\(97\) −94202.7 −1.01656 −0.508281 0.861191i \(-0.669719\pi\)
−0.508281 + 0.861191i \(0.669719\pi\)
\(98\) 0 0
\(99\) −52292.9 52292.9i −0.536235 0.536235i
\(100\) 0 0
\(101\) −90695.5 + 90695.5i −0.884672 + 0.884672i −0.994005 0.109333i \(-0.965129\pi\)
0.109333 + 0.994005i \(0.465129\pi\)
\(102\) 0 0
\(103\) 134854.i 1.25248i −0.779630 0.626241i \(-0.784593\pi\)
0.779630 0.626241i \(-0.215407\pi\)
\(104\) 0 0
\(105\) 28580.0i 0.252982i
\(106\) 0 0
\(107\) 95838.7 95838.7i 0.809248 0.809248i −0.175272 0.984520i \(-0.556081\pi\)
0.984520 + 0.175272i \(0.0560806\pi\)
\(108\) 0 0
\(109\) 141004. + 141004.i 1.13675 + 1.13675i 0.989028 + 0.147725i \(0.0471951\pi\)
0.147725 + 0.989028i \(0.452805\pi\)
\(110\) 0 0
\(111\) −25997.2 −0.200271
\(112\) 0 0
\(113\) −206889. −1.52420 −0.762099 0.647460i \(-0.775831\pi\)
−0.762099 + 0.647460i \(0.775831\pi\)
\(114\) 0 0
\(115\) 6025.78 + 6025.78i 0.0424883 + 0.0424883i
\(116\) 0 0
\(117\) 32430.5 32430.5i 0.219023 0.219023i
\(118\) 0 0
\(119\) 150782.i 0.976072i
\(120\) 0 0
\(121\) 9338.44i 0.0579844i
\(122\) 0 0
\(123\) −76025.5 + 76025.5i −0.453102 + 0.453102i
\(124\) 0 0
\(125\) 11048.5 + 11048.5i 0.0632456 + 0.0632456i
\(126\) 0 0
\(127\) −34606.3 −0.190391 −0.0951955 0.995459i \(-0.530348\pi\)
−0.0951955 + 0.995459i \(0.530348\pi\)
\(128\) 0 0
\(129\) −23035.0 −0.121875
\(130\) 0 0
\(131\) −207748. 207748.i −1.05769 1.05769i −0.998231 0.0594573i \(-0.981063\pi\)
−0.0594573 0.998231i \(-0.518937\pi\)
\(132\) 0 0
\(133\) 60333.0 60333.0i 0.295751 0.295751i
\(134\) 0 0
\(135\) 84327.2i 0.398230i
\(136\) 0 0
\(137\) 332218.i 1.51224i −0.654430 0.756122i \(-0.727091\pi\)
0.654430 0.756122i \(-0.272909\pi\)
\(138\) 0 0
\(139\) 245006. 245006.i 1.07557 1.07557i 0.0786730 0.996900i \(-0.474932\pi\)
0.996900 0.0786730i \(-0.0250683\pi\)
\(140\) 0 0
\(141\) 85591.3 + 85591.3i 0.362562 + 0.362562i
\(142\) 0 0
\(143\) 105671. 0.432130
\(144\) 0 0
\(145\) −39227.8 −0.154944
\(146\) 0 0
\(147\) 20701.2 + 20701.2i 0.0790138 + 0.0790138i
\(148\) 0 0
\(149\) −184561. + 184561.i −0.681041 + 0.681041i −0.960235 0.279194i \(-0.909933\pi\)
0.279194 + 0.960235i \(0.409933\pi\)
\(150\) 0 0
\(151\) 436893.i 1.55931i 0.626208 + 0.779656i \(0.284606\pi\)
−0.626208 + 0.779656i \(0.715394\pi\)
\(152\) 0 0
\(153\) 188806.i 0.652060i
\(154\) 0 0
\(155\) 18643.1 18643.1i 0.0623287 0.0623287i
\(156\) 0 0
\(157\) −153307. 153307.i −0.496378 0.496378i 0.413930 0.910309i \(-0.364156\pi\)
−0.910309 + 0.413930i \(0.864156\pi\)
\(158\) 0 0
\(159\) −260250. −0.816389
\(160\) 0 0
\(161\) −48770.6 −0.148284
\(162\) 0 0
\(163\) 436208. + 436208.i 1.28595 + 1.28595i 0.937225 + 0.348725i \(0.113385\pi\)
0.348725 + 0.937225i \(0.386615\pi\)
\(164\) 0 0
\(165\) 58304.1 58304.1i 0.166721 0.166721i
\(166\) 0 0
\(167\) 552844.i 1.53395i 0.641677 + 0.766975i \(0.278239\pi\)
−0.641677 + 0.766975i \(0.721761\pi\)
\(168\) 0 0
\(169\) 305759.i 0.823498i
\(170\) 0 0
\(171\) 75547.8 75547.8i 0.197575 0.197575i
\(172\) 0 0
\(173\) 395062. + 395062.i 1.00357 + 1.00357i 0.999994 + 0.00358065i \(0.00113976\pi\)
0.00358065 + 0.999994i \(0.498860\pi\)
\(174\) 0 0
\(175\) −89423.1 −0.220727
\(176\) 0 0
\(177\) −13194.9 −0.0316572
\(178\) 0 0
\(179\) −290609. 290609.i −0.677918 0.677918i 0.281611 0.959529i \(-0.409131\pi\)
−0.959529 + 0.281611i \(0.909131\pi\)
\(180\) 0 0
\(181\) −93004.4 + 93004.4i −0.211012 + 0.211012i −0.804697 0.593685i \(-0.797672\pi\)
0.593685 + 0.804697i \(0.297672\pi\)
\(182\) 0 0
\(183\) 432906.i 0.955578i
\(184\) 0 0
\(185\) 81341.7i 0.174737i
\(186\) 0 0
\(187\) 307600. 307600.i 0.643253 0.643253i
\(188\) 0 0
\(189\) 341258. + 341258.i 0.694909 + 0.694909i
\(190\) 0 0
\(191\) −880503. −1.74642 −0.873208 0.487348i \(-0.837964\pi\)
−0.873208 + 0.487348i \(0.837964\pi\)
\(192\) 0 0
\(193\) 75295.8 0.145505 0.0727524 0.997350i \(-0.476822\pi\)
0.0727524 + 0.997350i \(0.476822\pi\)
\(194\) 0 0
\(195\) 36158.5 + 36158.5i 0.0680964 + 0.0680964i
\(196\) 0 0
\(197\) −118466. + 118466.i −0.217484 + 0.217484i −0.807437 0.589953i \(-0.799146\pi\)
0.589953 + 0.807437i \(0.299146\pi\)
\(198\) 0 0
\(199\) 342971.i 0.613939i −0.951719 0.306970i \(-0.900685\pi\)
0.951719 0.306970i \(-0.0993150\pi\)
\(200\) 0 0
\(201\) 216819.i 0.378536i
\(202\) 0 0
\(203\) 158748. 158748.i 0.270376 0.270376i
\(204\) 0 0
\(205\) 237874. + 237874.i 0.395332 + 0.395332i
\(206\) 0 0
\(207\) −61069.6 −0.0990602
\(208\) 0 0
\(209\) 246162. 0.389812
\(210\) 0 0
\(211\) 617232. + 617232.i 0.954426 + 0.954426i 0.999006 0.0445803i \(-0.0141950\pi\)
−0.0445803 + 0.999006i \(0.514195\pi\)
\(212\) 0 0
\(213\) 221093. 221093.i 0.333908 0.333908i
\(214\) 0 0
\(215\) 72073.4i 0.106336i
\(216\) 0 0
\(217\) 150891.i 0.217527i
\(218\) 0 0
\(219\) −105163. + 105163.i −0.148167 + 0.148167i
\(220\) 0 0
\(221\) 190764. + 190764.i 0.262734 + 0.262734i
\(222\) 0 0
\(223\) 403929. 0.543929 0.271965 0.962307i \(-0.412327\pi\)
0.271965 + 0.962307i \(0.412327\pi\)
\(224\) 0 0
\(225\) −111974. −0.147455
\(226\) 0 0
\(227\) −70307.4 70307.4i −0.0905601 0.0905601i 0.660375 0.750936i \(-0.270397\pi\)
−0.750936 + 0.660375i \(0.770397\pi\)
\(228\) 0 0
\(229\) 261814. 261814.i 0.329916 0.329916i −0.522638 0.852554i \(-0.675052\pi\)
0.852554 + 0.522638i \(0.175052\pi\)
\(230\) 0 0
\(231\) 471893.i 0.581854i
\(232\) 0 0
\(233\) 1.28860e6i 1.55500i −0.628884 0.777499i \(-0.716488\pi\)
0.628884 0.777499i \(-0.283512\pi\)
\(234\) 0 0
\(235\) 267804. 267804.i 0.316335 0.316335i
\(236\) 0 0
\(237\) 508282. + 508282.i 0.587806 + 0.587806i
\(238\) 0 0
\(239\) 366981. 0.415575 0.207787 0.978174i \(-0.433374\pi\)
0.207787 + 0.978174i \(0.433374\pi\)
\(240\) 0 0
\(241\) −1.37397e6 −1.52383 −0.761913 0.647679i \(-0.775740\pi\)
−0.761913 + 0.647679i \(0.775740\pi\)
\(242\) 0 0
\(243\) 673285. + 673285.i 0.731448 + 0.731448i
\(244\) 0 0
\(245\) 64771.4 64771.4i 0.0689395 0.0689395i
\(246\) 0 0
\(247\) 152663.i 0.159217i
\(248\) 0 0
\(249\) 573613.i 0.586301i
\(250\) 0 0
\(251\) −278895. + 278895.i −0.279420 + 0.279420i −0.832877 0.553458i \(-0.813308\pi\)
0.553458 + 0.832877i \(0.313308\pi\)
\(252\) 0 0
\(253\) −99493.6 99493.6i −0.0977223 0.0977223i
\(254\) 0 0
\(255\) 210510. 0.202732
\(256\) 0 0
\(257\) 1.28986e6 1.21817 0.609087 0.793103i \(-0.291536\pi\)
0.609087 + 0.793103i \(0.291536\pi\)
\(258\) 0 0
\(259\) −329176. 329176.i −0.304915 0.304915i
\(260\) 0 0
\(261\) 198781. 198781.i 0.180624 0.180624i
\(262\) 0 0
\(263\) 1.44346e6i 1.28681i 0.765525 + 0.643406i \(0.222479\pi\)
−0.765525 + 0.643406i \(0.777521\pi\)
\(264\) 0 0
\(265\) 814287.i 0.712300i
\(266\) 0 0
\(267\) 130862. 130862.i 0.112340 0.112340i
\(268\) 0 0
\(269\) 1.39652e6 + 1.39652e6i 1.17671 + 1.17671i 0.980578 + 0.196127i \(0.0628366\pi\)
0.196127 + 0.980578i \(0.437163\pi\)
\(270\) 0 0
\(271\) 487103. 0.402900 0.201450 0.979499i \(-0.435435\pi\)
0.201450 + 0.979499i \(0.435435\pi\)
\(272\) 0 0
\(273\) −292655. −0.237656
\(274\) 0 0
\(275\) −182426. 182426.i −0.145464 0.145464i
\(276\) 0 0
\(277\) −159684. + 159684.i −0.125044 + 0.125044i −0.766859 0.641815i \(-0.778182\pi\)
0.641815 + 0.766859i \(0.278182\pi\)
\(278\) 0 0
\(279\) 188942.i 0.145318i
\(280\) 0 0
\(281\) 167923.i 0.126866i −0.997986 0.0634330i \(-0.979795\pi\)
0.997986 0.0634330i \(-0.0202049\pi\)
\(282\) 0 0
\(283\) 1.45221e6 1.45221e6i 1.07786 1.07786i 0.0811627 0.996701i \(-0.474137\pi\)
0.996701 0.0811627i \(-0.0258633\pi\)
\(284\) 0 0
\(285\) 84232.1 + 84232.1i 0.0614279 + 0.0614279i
\(286\) 0 0
\(287\) −1.92527e6 −1.37971
\(288\) 0 0
\(289\) −309253. −0.217806
\(290\) 0 0
\(291\) 532232. + 532232.i 0.368442 + 0.368442i
\(292\) 0 0
\(293\) 576523. 576523.i 0.392327 0.392327i −0.483189 0.875516i \(-0.660522\pi\)
0.875516 + 0.483189i \(0.160522\pi\)
\(294\) 0 0
\(295\) 41285.0i 0.0276209i
\(296\) 0 0
\(297\) 1.39235e6i 0.915921i
\(298\) 0 0
\(299\) 61703.0 61703.0i 0.0399143 0.0399143i
\(300\) 0 0
\(301\) −291669. 291669.i −0.185555 0.185555i
\(302\) 0 0
\(303\) 1.02483e6 0.641279
\(304\) 0 0
\(305\) 1.35451e6 0.833741
\(306\) 0 0
\(307\) 206791. + 206791.i 0.125223 + 0.125223i 0.766941 0.641718i \(-0.221778\pi\)
−0.641718 + 0.766941i \(0.721778\pi\)
\(308\) 0 0
\(309\) −761907. + 761907.i −0.453948 + 0.453948i
\(310\) 0 0
\(311\) 26746.0i 0.0156805i −0.999969 0.00784023i \(-0.997504\pi\)
0.999969 0.00784023i \(-0.00249565\pi\)
\(312\) 0 0
\(313\) 1.26947e6i 0.732424i −0.930531 0.366212i \(-0.880655\pi\)
0.930531 0.366212i \(-0.119345\pi\)
\(314\) 0 0
\(315\) 453139. 453139.i 0.257309 0.257309i
\(316\) 0 0
\(317\) −59452.2 59452.2i −0.0332292 0.0332292i 0.690297 0.723526i \(-0.257480\pi\)
−0.723526 + 0.690297i \(0.757480\pi\)
\(318\) 0 0
\(319\) 647702. 0.356368
\(320\) 0 0
\(321\) −1.08295e6 −0.586605
\(322\) 0 0
\(323\) 444390. + 444390.i 0.237005 + 0.237005i
\(324\) 0 0
\(325\) 113135. 113135.i 0.0594141 0.0594141i
\(326\) 0 0
\(327\) 1.59331e6i 0.824007i
\(328\) 0 0
\(329\) 2.16751e6i 1.10401i
\(330\) 0 0
\(331\) 172444. 172444.i 0.0865123 0.0865123i −0.662526 0.749039i \(-0.730516\pi\)
0.749039 + 0.662526i \(0.230516\pi\)
\(332\) 0 0
\(333\) −412188. 412188.i −0.203697 0.203697i
\(334\) 0 0
\(335\) −678397. −0.330272
\(336\) 0 0
\(337\) −1.28102e6 −0.614443 −0.307221 0.951638i \(-0.599399\pi\)
−0.307221 + 0.951638i \(0.599399\pi\)
\(338\) 0 0
\(339\) 1.16890e6 + 1.16890e6i 0.552429 + 0.552429i
\(340\) 0 0
\(341\) −307821. + 307821.i −0.143355 + 0.143355i
\(342\) 0 0
\(343\) 1.88046e6i 0.863035i
\(344\) 0 0
\(345\) 68089.7i 0.0307988i
\(346\) 0 0
\(347\) 241617. 241617.i 0.107722 0.107722i −0.651192 0.758913i \(-0.725731\pi\)
0.758913 + 0.651192i \(0.225731\pi\)
\(348\) 0 0
\(349\) −1.27223e6 1.27223e6i −0.559117 0.559117i 0.369939 0.929056i \(-0.379379\pi\)
−0.929056 + 0.369939i \(0.879379\pi\)
\(350\) 0 0
\(351\) −863497. −0.374104
\(352\) 0 0
\(353\) 4.07045e6 1.73863 0.869313 0.494263i \(-0.164562\pi\)
0.869313 + 0.494263i \(0.164562\pi\)
\(354\) 0 0
\(355\) −691771. 691771.i −0.291334 0.291334i
\(356\) 0 0
\(357\) −851897. + 851897.i −0.353766 + 0.353766i
\(358\) 0 0
\(359\) 1.13485e6i 0.464731i −0.972629 0.232366i \(-0.925353\pi\)
0.972629 0.232366i \(-0.0746466\pi\)
\(360\) 0 0
\(361\) 2.12047e6i 0.856374i
\(362\) 0 0
\(363\) −52760.9 + 52760.9i −0.0210158 + 0.0210158i
\(364\) 0 0
\(365\) 329040. + 329040.i 0.129276 + 0.129276i
\(366\) 0 0
\(367\) −1.81372e6 −0.702920 −0.351460 0.936203i \(-0.614315\pi\)
−0.351460 + 0.936203i \(0.614315\pi\)
\(368\) 0 0
\(369\) −2.41078e6 −0.921705
\(370\) 0 0
\(371\) −3.29528e6 3.29528e6i −1.24296 1.24296i
\(372\) 0 0
\(373\) −13302.2 + 13302.2i −0.00495053 + 0.00495053i −0.709578 0.704627i \(-0.751114\pi\)
0.704627 + 0.709578i \(0.251114\pi\)
\(374\) 0 0
\(375\) 124845.i 0.0458453i
\(376\) 0 0
\(377\) 401686.i 0.145557i
\(378\) 0 0
\(379\) −2.23507e6 + 2.23507e6i −0.799269 + 0.799269i −0.982980 0.183712i \(-0.941189\pi\)
0.183712 + 0.982980i \(0.441189\pi\)
\(380\) 0 0
\(381\) 195521. + 195521.i 0.0690051 + 0.0690051i
\(382\) 0 0
\(383\) 1.73637e6 0.604846 0.302423 0.953174i \(-0.402204\pi\)
0.302423 + 0.953174i \(0.402204\pi\)
\(384\) 0 0
\(385\) 1.47649e6 0.507667
\(386\) 0 0
\(387\) −365222. 365222.i −0.123959 0.123959i
\(388\) 0 0
\(389\) −1.03858e6 + 1.03858e6i −0.347991 + 0.347991i −0.859361 0.511370i \(-0.829138\pi\)
0.511370 + 0.859361i \(0.329138\pi\)
\(390\) 0 0
\(391\) 359226.i 0.118830i
\(392\) 0 0
\(393\) 2.34749e6i 0.766694i
\(394\) 0 0
\(395\) 1.59035e6 1.59035e6i 0.512860 0.512860i
\(396\) 0 0
\(397\) −4.36652e6 4.36652e6i −1.39046 1.39046i −0.824279 0.566184i \(-0.808419\pi\)
−0.566184 0.824279i \(-0.691581\pi\)
\(398\) 0 0
\(399\) −681746. −0.214383
\(400\) 0 0
\(401\) −5.50255e6 −1.70885 −0.854423 0.519578i \(-0.826089\pi\)
−0.854423 + 0.519578i \(0.826089\pi\)
\(402\) 0 0
\(403\) −190902. 190902.i −0.0585527 0.0585527i
\(404\) 0 0
\(405\) 293168. 293168.i 0.0888134 0.0888134i
\(406\) 0 0
\(407\) 1.34306e6i 0.401891i
\(408\) 0 0
\(409\) 3.91372e6i 1.15686i −0.815731 0.578431i \(-0.803665\pi\)
0.815731 0.578431i \(-0.196335\pi\)
\(410\) 0 0
\(411\) −1.87699e6 + 1.87699e6i −0.548096 + 0.548096i
\(412\) 0 0
\(413\) −167073. 167073.i −0.0481983 0.0481983i
\(414\) 0 0
\(415\) 1.79476e6 0.511548
\(416\) 0 0
\(417\) −2.76850e6 −0.779659
\(418\) 0 0
\(419\) −2.90419e6 2.90419e6i −0.808147 0.808147i 0.176207 0.984353i \(-0.443617\pi\)
−0.984353 + 0.176207i \(0.943617\pi\)
\(420\) 0 0
\(421\) −936361. + 936361.i −0.257477 + 0.257477i −0.824027 0.566550i \(-0.808278\pi\)
0.566550 + 0.824027i \(0.308278\pi\)
\(422\) 0 0
\(423\) 2.71412e6i 0.737526i
\(424\) 0 0
\(425\) 658657.i 0.176883i
\(426\) 0 0
\(427\) −5.48145e6 + 5.48145e6i −1.45488 + 1.45488i
\(428\) 0 0
\(429\) −597024. 597024.i −0.156620 0.156620i
\(430\) 0 0
\(431\) −2.05364e6 −0.532513 −0.266257 0.963902i \(-0.585787\pi\)
−0.266257 + 0.963902i \(0.585787\pi\)
\(432\) 0 0
\(433\) 5.19369e6 1.33124 0.665620 0.746291i \(-0.268167\pi\)
0.665620 + 0.746291i \(0.268167\pi\)
\(434\) 0 0
\(435\) 221632. + 221632.i 0.0561576 + 0.0561576i
\(436\) 0 0
\(437\) 143739. 143739.i 0.0360056 0.0360056i
\(438\) 0 0
\(439\) 3.92534e6i 0.972111i −0.873928 0.486056i \(-0.838435\pi\)
0.873928 0.486056i \(-0.161565\pi\)
\(440\) 0 0
\(441\) 656440.i 0.160731i
\(442\) 0 0
\(443\) −2.44291e6 + 2.44291e6i −0.591423 + 0.591423i −0.938016 0.346593i \(-0.887339\pi\)
0.346593 + 0.938016i \(0.387339\pi\)
\(444\) 0 0
\(445\) −409450. 409450.i −0.0980168 0.0980168i
\(446\) 0 0
\(447\) 2.08548e6 0.493672
\(448\) 0 0
\(449\) 1.95234e6 0.457025 0.228513 0.973541i \(-0.426614\pi\)
0.228513 + 0.973541i \(0.426614\pi\)
\(450\) 0 0
\(451\) −3.92760e6 3.92760e6i −0.909256 0.909256i
\(452\) 0 0
\(453\) 2.46839e6 2.46839e6i 0.565155 0.565155i
\(454\) 0 0
\(455\) 915677.i 0.207355i
\(456\) 0 0
\(457\) 2.27789e6i 0.510201i 0.966915 + 0.255101i \(0.0821086\pi\)
−0.966915 + 0.255101i \(0.917891\pi\)
\(458\) 0 0
\(459\) −2.51358e6 + 2.51358e6i −0.556879 + 0.556879i
\(460\) 0 0
\(461\) −2.67379e6 2.67379e6i −0.585969 0.585969i 0.350568 0.936537i \(-0.385988\pi\)
−0.936537 + 0.350568i \(0.885988\pi\)
\(462\) 0 0
\(463\) 8.69290e6 1.88457 0.942285 0.334811i \(-0.108672\pi\)
0.942285 + 0.334811i \(0.108672\pi\)
\(464\) 0 0
\(465\) −210661. −0.0451807
\(466\) 0 0
\(467\) 1.82222e6 + 1.82222e6i 0.386642 + 0.386642i 0.873488 0.486846i \(-0.161853\pi\)
−0.486846 + 0.873488i \(0.661853\pi\)
\(468\) 0 0
\(469\) 2.74536e6 2.74536e6i 0.576324 0.576324i
\(470\) 0 0
\(471\) 1.73233e6i 0.359813i
\(472\) 0 0
\(473\) 1.19003e6i 0.244570i
\(474\) 0 0
\(475\) 263551. 263551.i 0.0535958 0.0535958i
\(476\) 0 0
\(477\) −4.12628e6 4.12628e6i −0.830353 0.830353i
\(478\) 0 0
\(479\) −483261. −0.0962371 −0.0481186 0.998842i \(-0.515323\pi\)
−0.0481186 + 0.998842i \(0.515323\pi\)
\(480\) 0 0
\(481\) 832926. 0.164151
\(482\) 0 0
\(483\) 275547. + 275547.i 0.0537438 + 0.0537438i
\(484\) 0 0
\(485\) 1.66528e6 1.66528e6i 0.321465 0.321465i
\(486\) 0 0
\(487\) 649701.i 0.124134i 0.998072 + 0.0620671i \(0.0197693\pi\)
−0.998072 + 0.0620671i \(0.980231\pi\)
\(488\) 0 0
\(489\) 4.92902e6i 0.932156i
\(490\) 0 0
\(491\) −4.42640e6 + 4.42640e6i −0.828603 + 0.828603i −0.987324 0.158720i \(-0.949263\pi\)
0.158720 + 0.987324i \(0.449263\pi\)
\(492\) 0 0
\(493\) 1.16928e6 + 1.16928e6i 0.216671 + 0.216671i
\(494\) 0 0
\(495\) 1.84883e6 0.339145
\(496\) 0 0
\(497\) 5.59896e6 1.01676
\(498\) 0 0
\(499\) 3.11825e6 + 3.11825e6i 0.560608 + 0.560608i 0.929480 0.368872i \(-0.120256\pi\)
−0.368872 + 0.929480i \(0.620256\pi\)
\(500\) 0 0
\(501\) 3.12349e6 3.12349e6i 0.555963 0.555963i
\(502\) 0 0
\(503\) 7.75382e6i 1.36646i −0.730205 0.683228i \(-0.760575\pi\)
0.730205 0.683228i \(-0.239425\pi\)
\(504\) 0 0
\(505\) 3.20657e6i 0.559516i
\(506\) 0 0
\(507\) −1.72750e6 + 1.72750e6i −0.298468 + 0.298468i
\(508\) 0 0
\(509\) −4.66852e6 4.66852e6i −0.798703 0.798703i 0.184188 0.982891i \(-0.441034\pi\)
−0.982891 + 0.184188i \(0.941034\pi\)
\(510\) 0 0
\(511\) −2.66314e6 −0.451171
\(512\) 0 0
\(513\) −2.01154e6 −0.337469
\(514\) 0 0
\(515\) 2.38391e6 + 2.38391e6i 0.396069 + 0.396069i
\(516\) 0 0
\(517\) −4.42179e6 + 4.42179e6i −0.727565 + 0.727565i
\(518\) 0 0
\(519\) 4.46409e6i 0.727468i
\(520\) 0 0
\(521\) 8.27536e6i 1.33565i 0.744319 + 0.667825i \(0.232774\pi\)
−0.744319 + 0.667825i \(0.767226\pi\)
\(522\) 0 0
\(523\) 4.72044e6 4.72044e6i 0.754620 0.754620i −0.220717 0.975338i \(-0.570840\pi\)
0.975338 + 0.220717i \(0.0708399\pi\)
\(524\) 0 0
\(525\) 505228. + 505228.i 0.0799999 + 0.0799999i
\(526\) 0 0
\(527\) −1.11140e6 −0.174319
\(528\) 0 0
\(529\) 6.32015e6 0.981947
\(530\) 0 0
\(531\) −209206. 209206.i −0.0321986 0.0321986i
\(532\) 0 0
\(533\) 2.43579e6 2.43579e6i 0.371382 0.371382i
\(534\) 0 0
\(535\) 3.38841e6i 0.511813i
\(536\) 0 0
\(537\) 3.28380e6i 0.491407i
\(538\) 0 0
\(539\) −1.06946e6 + 1.06946e6i −0.158560 + 0.158560i
\(540\) 0 0
\(541\) 11776.0 + 11776.0i 0.00172984 + 0.00172984i 0.707971 0.706241i \(-0.249611\pi\)
−0.706241 + 0.707971i \(0.749611\pi\)
\(542\) 0 0
\(543\) 1.05092e6 0.152958
\(544\) 0 0
\(545\) −4.98526e6 −0.718946
\(546\) 0 0
\(547\) −1.39580e6 1.39580e6i −0.199459 0.199459i 0.600309 0.799768i \(-0.295044\pi\)
−0.799768 + 0.600309i \(0.795044\pi\)
\(548\) 0 0
\(549\) −6.86377e6 + 6.86377e6i −0.971922 + 0.971922i
\(550\) 0 0
\(551\) 935738.i 0.131303i
\(552\) 0 0
\(553\) 1.28717e7i 1.78988i
\(554\) 0 0
\(555\) 459570. 459570.i 0.0633314 0.0633314i
\(556\) 0 0
\(557\) −2.53880e6 2.53880e6i −0.346730 0.346730i 0.512160 0.858890i \(-0.328845\pi\)
−0.858890 + 0.512160i \(0.828845\pi\)
\(558\) 0 0
\(559\) 738019. 0.0998937
\(560\) 0 0
\(561\) −3.47579e6 −0.466280
\(562\) 0 0
\(563\) 592917. + 592917.i 0.0788357 + 0.0788357i 0.745425 0.666589i \(-0.232247\pi\)
−0.666589 + 0.745425i \(0.732247\pi\)
\(564\) 0 0
\(565\) 3.65732e6 3.65732e6i 0.481994 0.481994i
\(566\) 0 0
\(567\) 2.37280e6i 0.309958i
\(568\) 0 0
\(569\) 1.17265e7i 1.51841i 0.650851 + 0.759206i \(0.274412\pi\)
−0.650851 + 0.759206i \(0.725588\pi\)
\(570\) 0 0
\(571\) 8.44620e6 8.44620e6i 1.08410 1.08410i 0.0879828 0.996122i \(-0.471958\pi\)
0.996122 0.0879828i \(-0.0280420\pi\)
\(572\) 0 0
\(573\) 4.97472e6 + 4.97472e6i 0.632969 + 0.632969i
\(574\) 0 0
\(575\) −213044. −0.0268719
\(576\) 0 0
\(577\) 1.04084e7 1.30150 0.650751 0.759291i \(-0.274454\pi\)
0.650751 + 0.759291i \(0.274454\pi\)
\(578\) 0 0
\(579\) −425411. 425411.i −0.0527366 0.0527366i
\(580\) 0 0
\(581\) −7.26308e6 + 7.26308e6i −0.892649 + 0.892649i
\(582\) 0 0
\(583\) 1.34449e7i 1.63828i
\(584\) 0 0
\(585\) 1.14659e6i 0.138522i
\(586\) 0 0
\(587\) −2.10564e6 + 2.10564e6i −0.252226 + 0.252226i −0.821883 0.569657i \(-0.807076\pi\)
0.569657 + 0.821883i \(0.307076\pi\)
\(588\) 0 0
\(589\) −444710. 444710.i −0.0528188 0.0528188i
\(590\) 0 0
\(591\) 1.33863e6 0.157650
\(592\) 0 0
\(593\) 8.80654e6 1.02841 0.514207 0.857666i \(-0.328086\pi\)
0.514207 + 0.857666i \(0.328086\pi\)
\(594\) 0 0
\(595\) 2.66547e6 + 2.66547e6i 0.308661 + 0.308661i
\(596\) 0 0
\(597\) −1.93774e6 + 1.93774e6i −0.222515 + 0.222515i
\(598\) 0 0
\(599\) 9.65722e6i 1.09973i 0.835255 + 0.549864i \(0.185320\pi\)
−0.835255 + 0.549864i \(0.814680\pi\)
\(600\) 0 0
\(601\) 3.77039e6i 0.425795i 0.977075 + 0.212897i \(0.0682900\pi\)
−0.977075 + 0.212897i \(0.931710\pi\)
\(602\) 0 0
\(603\) 3.43768e6 3.43768e6i 0.385010 0.385010i
\(604\) 0 0
\(605\) 165082. + 165082.i 0.0183363 + 0.0183363i
\(606\) 0 0
\(607\) 6.18205e6 0.681021 0.340511 0.940241i \(-0.389400\pi\)
0.340511 + 0.940241i \(0.389400\pi\)
\(608\) 0 0
\(609\) −1.79381e6 −0.195990
\(610\) 0 0
\(611\) −2.74227e6 2.74227e6i −0.297171 0.297171i
\(612\) 0 0
\(613\) 6.39097e6 6.39097e6i 0.686935 0.686935i −0.274618 0.961553i \(-0.588552\pi\)
0.961553 + 0.274618i \(0.0885515\pi\)
\(614\) 0 0
\(615\) 2.68791e6i 0.286567i
\(616\) 0 0
\(617\) 538688.i 0.0569672i −0.999594 0.0284836i \(-0.990932\pi\)
0.999594 0.0284836i \(-0.00906783\pi\)
\(618\) 0 0
\(619\) 302602. 302602.i 0.0317428 0.0317428i −0.691057 0.722800i \(-0.742855\pi\)
0.722800 + 0.691057i \(0.242855\pi\)
\(620\) 0 0
\(621\) 813021. + 813021.i 0.0846004 + 0.0846004i
\(622\) 0 0
\(623\) 3.31395e6 0.342078
\(624\) 0 0
\(625\) −390625. −0.0400000
\(626\) 0 0
\(627\) −1.39078e6 1.39078e6i −0.141283 0.141283i
\(628\) 0 0
\(629\) 2.42459e6 2.42459e6i 0.244349 0.244349i
\(630\) 0 0
\(631\) 1.13112e7i 1.13093i 0.824772 + 0.565465i \(0.191303\pi\)
−0.824772 + 0.565465i \(0.808697\pi\)
\(632\) 0 0
\(633\) 6.97455e6i 0.691842i
\(634\) 0 0
\(635\) 611760. 611760.i 0.0602069 0.0602069i
\(636\) 0 0
\(637\) −663248. 663248.i −0.0647631 0.0647631i
\(638\) 0 0
\(639\) 7.01091e6 0.679238
\(640\) 0 0
\(641\) −1.42270e7 −1.36763 −0.683814 0.729656i \(-0.739680\pi\)
−0.683814 + 0.729656i \(0.739680\pi\)
\(642\) 0 0
\(643\) 3.57817e6 + 3.57817e6i 0.341298 + 0.341298i 0.856855 0.515557i \(-0.172415\pi\)
−0.515557 + 0.856855i \(0.672415\pi\)
\(644\) 0 0
\(645\) 407204. 407204.i 0.0385401 0.0385401i
\(646\) 0 0
\(647\) 1.77065e7i 1.66292i −0.555585 0.831460i \(-0.687506\pi\)
0.555585 0.831460i \(-0.312494\pi\)
\(648\) 0 0
\(649\) 681669.i 0.0635275i
\(650\) 0 0
\(651\) 852510. 852510.i 0.0788401 0.0788401i
\(652\) 0 0
\(653\) 1.48482e7 + 1.48482e7i 1.36267 + 1.36267i 0.870501 + 0.492166i \(0.163795\pi\)
0.492166 + 0.870501i \(0.336205\pi\)
\(654\) 0 0
\(655\) 7.34498e6 0.668941
\(656\) 0 0
\(657\) −3.33473e6 −0.301402
\(658\) 0 0
\(659\) 1.21574e7 + 1.21574e7i 1.09051 + 1.09051i 0.995474 + 0.0950310i \(0.0302950\pi\)
0.0950310 + 0.995474i \(0.469705\pi\)
\(660\) 0 0
\(661\) 6.00382e6 6.00382e6i 0.534471 0.534471i −0.387429 0.921900i \(-0.626637\pi\)
0.921900 + 0.387429i \(0.126637\pi\)
\(662\) 0 0
\(663\) 2.15558e6i 0.190450i
\(664\) 0 0
\(665\) 2.13309e6i 0.187049i
\(666\) 0 0
\(667\) 378205. 378205.i 0.0329165 0.0329165i
\(668\) 0 0
\(669\) −2.28214e6 2.28214e6i −0.197141 0.197141i
\(670\) 0 0
\(671\) −2.23647e7 −1.91759
\(672\) 0 0
\(673\) 1.02278e7 0.870451 0.435226 0.900321i \(-0.356669\pi\)
0.435226 + 0.900321i \(0.356669\pi\)
\(674\) 0 0
\(675\) 1.49071e6 + 1.49071e6i 0.125931 + 0.125931i
\(676\) 0 0
\(677\) −8.41995e6 + 8.41995e6i −0.706054 + 0.706054i −0.965703 0.259649i \(-0.916393\pi\)
0.259649 + 0.965703i \(0.416393\pi\)
\(678\) 0 0
\(679\) 1.34782e7i 1.12191i
\(680\) 0 0
\(681\) 794455.i 0.0656449i
\(682\) 0 0
\(683\) −6.71475e6 + 6.71475e6i −0.550780 + 0.550780i −0.926666 0.375886i \(-0.877338\pi\)
0.375886 + 0.926666i \(0.377338\pi\)
\(684\) 0 0
\(685\) 5.87284e6 + 5.87284e6i 0.478214 + 0.478214i
\(686\) 0 0
\(687\) −2.95842e6 −0.239149
\(688\) 0 0
\(689\) 8.33816e6 0.669148
\(690\) 0 0
\(691\) −1.05194e7 1.05194e7i −0.838098 0.838098i 0.150510 0.988608i \(-0.451908\pi\)
−0.988608 + 0.150510i \(0.951908\pi\)
\(692\) 0 0
\(693\) −7.48191e6 + 7.48191e6i −0.591806 + 0.591806i
\(694\) 0 0
\(695\) 8.66228e6i 0.680252i
\(696\) 0 0
\(697\) 1.41808e7i 1.10565i
\(698\) 0 0
\(699\) −7.28044e6 + 7.28044e6i −0.563591 + 0.563591i
\(700\) 0 0
\(701\) 1.40028e7 + 1.40028e7i 1.07626 + 1.07626i 0.996841 + 0.0794224i \(0.0253076\pi\)
0.0794224 + 0.996841i \(0.474692\pi\)
\(702\) 0 0
\(703\) 1.94032e6 0.148076
\(704\) 0 0
\(705\) −3.02611e6 −0.229304
\(706\) 0 0
\(707\) 1.29764e7 + 1.29764e7i 0.976354 + 0.976354i
\(708\) 0 0
\(709\) 5.58854e6 5.58854e6i 0.417525 0.417525i −0.466825 0.884350i \(-0.654602\pi\)
0.884350 + 0.466825i \(0.154602\pi\)
\(710\) 0 0
\(711\) 1.61177e7i 1.19572i
\(712\) 0 0
\(713\) 359485.i 0.0264824i
\(714\) 0 0
\(715\) −1.86801e6 + 1.86801e6i −0.136651 + 0.136651i
\(716\) 0 0
\(717\) −2.07339e6 2.07339e6i −0.150620 0.150620i
\(718\) 0 0
\(719\) 8.53642e6 0.615820 0.307910 0.951416i \(-0.400370\pi\)
0.307910 + 0.951416i \(0.400370\pi\)
\(720\) 0 0
\(721\) −1.92945e7 −1.38228
\(722\) 0 0
\(723\) 7.76275e6 + 7.76275e6i 0.552294 + 0.552294i
\(724\) 0 0
\(725\) 693456. 693456.i 0.0489975 0.0489975i
\(726\) 0 0
\(727\) 8.88434e6i 0.623432i −0.950175 0.311716i \(-0.899096\pi\)
0.950175 0.311716i \(-0.100904\pi\)
\(728\) 0 0
\(729\) 3.57801e6i 0.249358i
\(730\) 0 0
\(731\) 2.14832e6 2.14832e6i 0.148698 0.148698i
\(732\) 0 0
\(733\) −7.63896e6 7.63896e6i −0.525139 0.525139i 0.393980 0.919119i \(-0.371098\pi\)
−0.919119 + 0.393980i \(0.871098\pi\)
\(734\) 0 0
\(735\) −731899. −0.0499727
\(736\) 0 0
\(737\) 1.12012e7 0.759621
\(738\) 0 0
\(739\) 2.83232e6 + 2.83232e6i 0.190779 + 0.190779i 0.796033 0.605254i \(-0.206928\pi\)
−0.605254 + 0.796033i \(0.706928\pi\)
\(740\) 0 0
\(741\) 862523. 862523.i 0.0577065 0.0577065i
\(742\) 0 0
\(743\) 4.95901e6i 0.329551i 0.986331 + 0.164776i \(0.0526900\pi\)
−0.986331 + 0.164776i \(0.947310\pi\)
\(744\) 0 0
\(745\) 6.52520e6i 0.430728i
\(746\) 0 0
\(747\) −9.09469e6 + 9.09469e6i −0.596330 + 0.596330i
\(748\) 0 0
\(749\) −1.37123e7 1.37123e7i −0.893112 0.893112i
\(750\) 0 0
\(751\) −746560. −0.0483020 −0.0241510 0.999708i \(-0.507688\pi\)
−0.0241510 + 0.999708i \(0.507688\pi\)
\(752\) 0 0
\(753\) 3.15144e6 0.202545
\(754\) 0 0
\(755\) −7.72325e6 7.72325e6i −0.493098 0.493098i
\(756\) 0 0
\(757\) 4.70246e6 4.70246e6i 0.298254 0.298254i −0.542076 0.840330i \(-0.682361\pi\)
0.840330 + 0.542076i \(0.182361\pi\)
\(758\) 0 0
\(759\) 1.12425e6i 0.0708367i
\(760\) 0 0
\(761\) 1.17758e7i 0.737102i −0.929607 0.368551i \(-0.879854\pi\)
0.929607 0.368551i \(-0.120146\pi\)
\(762\) 0 0
\(763\) 2.01745e7 2.01745e7i 1.25456 1.25456i
\(764\) 0 0
\(765\) 3.33765e6 + 3.33765e6i 0.206199 + 0.206199i
\(766\) 0 0
\(767\) 422751. 0.0259476
\(768\) 0 0
\(769\) −5.11272e6 −0.311771 −0.155886 0.987775i \(-0.549823\pi\)
−0.155886 + 0.987775i \(0.549823\pi\)
\(770\) 0 0
\(771\) −7.28752e6 7.28752e6i −0.441513 0.441513i
\(772\) 0 0
\(773\) 7.11366e6 7.11366e6i 0.428198 0.428198i −0.459816 0.888014i \(-0.652085\pi\)
0.888014 + 0.459816i \(0.152085\pi\)
\(774\) 0 0
\(775\) 659132.i 0.0394201i
\(776\) 0 0
\(777\) 3.71960e6i 0.221026i
\(778\) 0 0
\(779\) 5.67422e6 5.67422e6i 0.335014 0.335014i
\(780\) 0 0
\(781\) 1.14220e7 + 1.14220e7i 0.670064 + 0.670064i
\(782\) 0 0
\(783\) −5.29276e6 −0.308516
\(784\) 0 0
\(785\) 5.42022e6 0.313937
\(786\) 0 0