Properties

Label 320.6.l.a.81.2
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 81.2
Character \(\chi\) \(=\) 320.81
Dual form 320.6.l.a.241.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-21.1465 - 21.1465i) q^{3} +(17.6777 - 17.6777i) q^{5} +100.160i q^{7} +651.346i q^{9} +O(q^{10})\) \(q+(-21.1465 - 21.1465i) q^{3} +(17.6777 - 17.6777i) q^{5} +100.160i q^{7} +651.346i q^{9} +(419.591 - 419.591i) q^{11} +(455.822 + 455.822i) q^{13} -747.641 q^{15} -662.910 q^{17} +(-1207.30 - 1207.30i) q^{19} +(2118.04 - 2118.04i) q^{21} -2571.76i q^{23} -625.000i q^{25} +(8635.09 - 8635.09i) q^{27} +(-2023.28 - 2023.28i) q^{29} -3150.05 q^{31} -17745.7 q^{33} +(1770.60 + 1770.60i) q^{35} +(2281.97 - 2281.97i) q^{37} -19278.1i q^{39} -3833.77i q^{41} +(-12989.2 + 12989.2i) q^{43} +(11514.3 + 11514.3i) q^{45} +15693.3 q^{47} +6774.93 q^{49} +(14018.2 + 14018.2i) q^{51} +(14775.3 - 14775.3i) q^{53} -14834.8i q^{55} +51060.5i q^{57} +(-24476.4 + 24476.4i) q^{59} +(-15192.1 - 15192.1i) q^{61} -65239.0 q^{63} +16115.7 q^{65} +(24925.1 + 24925.1i) q^{67} +(-54383.7 + 54383.7i) q^{69} -52032.9i q^{71} +37463.3i q^{73} +(-13216.5 + 13216.5i) q^{75} +(42026.3 + 42026.3i) q^{77} -88799.9 q^{79} -206926. q^{81} +(-61945.4 - 61945.4i) q^{83} +(-11718.7 + 11718.7i) q^{85} +85570.7i q^{87} -1923.83i q^{89} +(-45655.2 + 45655.2i) q^{91} +(66612.5 + 66612.5i) q^{93} -42684.7 q^{95} -57200.4 q^{97} +(273299. + 273299. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + O(q^{10}) \) \( 80q - 1208q^{11} + 1800q^{15} - 2360q^{19} + 7464q^{27} - 8144q^{29} + 21296q^{37} - 32072q^{43} + 88360q^{47} - 192080q^{49} + 5920q^{51} - 49456q^{53} - 44984q^{59} + 48080q^{61} - 158760q^{63} - 61160q^{67} - 22320q^{69} - 14896q^{77} - 177680q^{79} - 524880q^{81} + 329240q^{83} + 132400q^{85} - 364832q^{91} - 362352q^{93} - 288800q^{95} - 659000q^{99} + O(q^{100}) \)

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
\(3\) −21.1465 21.1465i −1.35655 1.35655i −0.878136 0.478410i \(-0.841213\pi\)
−0.478410 0.878136i \(-0.658787\pi\)
\(4\) 0 0
\(5\) 17.6777 17.6777i 0.316228 0.316228i
\(6\) 0 0
\(7\) 100.160i 0.772592i 0.922375 + 0.386296i \(0.126246\pi\)
−0.922375 + 0.386296i \(0.873754\pi\)
\(8\) 0 0
\(9\) 651.346i 2.68044i
\(10\) 0 0
\(11\) 419.591 419.591i 1.04555 1.04555i 0.0466369 0.998912i \(-0.485150\pi\)
0.998912 0.0466369i \(-0.0148504\pi\)
\(12\) 0 0
\(13\) 455.822 + 455.822i 0.748061 + 0.748061i 0.974115 0.226054i \(-0.0725826\pi\)
−0.226054 + 0.974115i \(0.572583\pi\)
\(14\) 0 0
\(15\) −747.641 −0.857955
\(16\) 0 0
\(17\) −662.910 −0.556329 −0.278165 0.960533i \(-0.589726\pi\)
−0.278165 + 0.960533i \(0.589726\pi\)
\(18\) 0 0
\(19\) −1207.30 1207.30i −0.767243 0.767243i 0.210377 0.977620i \(-0.432531\pi\)
−0.977620 + 0.210377i \(0.932531\pi\)
\(20\) 0 0
\(21\) 2118.04 2118.04i 1.04806 1.04806i
\(22\) 0 0
\(23\) 2571.76i 1.01370i −0.862033 0.506852i \(-0.830809\pi\)
0.862033 0.506852i \(-0.169191\pi\)
\(24\) 0 0
\(25\) 625.000i 0.200000i
\(26\) 0 0
\(27\) 8635.09 8635.09i 2.27959 2.27959i
\(28\) 0 0
\(29\) −2023.28 2023.28i −0.446747 0.446747i 0.447524 0.894272i \(-0.352306\pi\)
−0.894272 + 0.447524i \(0.852306\pi\)
\(30\) 0 0
\(31\) −3150.05 −0.588727 −0.294363 0.955694i \(-0.595108\pi\)
−0.294363 + 0.955694i \(0.595108\pi\)
\(32\) 0 0
\(33\) −17745.7 −2.83667
\(34\) 0 0
\(35\) 1770.60 + 1770.60i 0.244315 + 0.244315i
\(36\) 0 0
\(37\) 2281.97 2281.97i 0.274034 0.274034i −0.556688 0.830722i \(-0.687928\pi\)
0.830722 + 0.556688i \(0.187928\pi\)
\(38\) 0 0
\(39\) 19278.1i 2.02956i
\(40\) 0 0
\(41\) 3833.77i 0.356178i −0.984014 0.178089i \(-0.943009\pi\)
0.984014 0.178089i \(-0.0569914\pi\)
\(42\) 0 0
\(43\) −12989.2 + 12989.2i −1.07130 + 1.07130i −0.0740429 + 0.997255i \(0.523590\pi\)
−0.997255 + 0.0740429i \(0.976410\pi\)
\(44\) 0 0
\(45\) 11514.3 + 11514.3i 0.847629 + 0.847629i
\(46\) 0 0
\(47\) 15693.3 1.03626 0.518132 0.855301i \(-0.326628\pi\)
0.518132 + 0.855301i \(0.326628\pi\)
\(48\) 0 0
\(49\) 6774.93 0.403102
\(50\) 0 0
\(51\) 14018.2 + 14018.2i 0.754687 + 0.754687i
\(52\) 0 0
\(53\) 14775.3 14775.3i 0.722515 0.722515i −0.246601 0.969117i \(-0.579314\pi\)
0.969117 + 0.246601i \(0.0793139\pi\)
\(54\) 0 0
\(55\) 14834.8i 0.661263i
\(56\) 0 0
\(57\) 51060.5i 2.08160i
\(58\) 0 0
\(59\) −24476.4 + 24476.4i −0.915413 + 0.915413i −0.996691 0.0812787i \(-0.974100\pi\)
0.0812787 + 0.996691i \(0.474100\pi\)
\(60\) 0 0
\(61\) −15192.1 15192.1i −0.522749 0.522749i 0.395652 0.918401i \(-0.370519\pi\)
−0.918401 + 0.395652i \(0.870519\pi\)
\(62\) 0 0
\(63\) −65239.0 −2.07088
\(64\) 0 0
\(65\) 16115.7 0.473115
\(66\) 0 0
\(67\) 24925.1 + 24925.1i 0.678343 + 0.678343i 0.959625 0.281282i \(-0.0907597\pi\)
−0.281282 + 0.959625i \(0.590760\pi\)
\(68\) 0 0
\(69\) −54383.7 + 54383.7i −1.37514 + 1.37514i
\(70\) 0 0
\(71\) 52032.9i 1.22499i −0.790475 0.612494i \(-0.790166\pi\)
0.790475 0.612494i \(-0.209834\pi\)
\(72\) 0 0
\(73\) 37463.3i 0.822808i 0.911453 + 0.411404i \(0.134961\pi\)
−0.911453 + 0.411404i \(0.865039\pi\)
\(74\) 0 0
\(75\) −13216.5 + 13216.5i −0.271309 + 0.271309i
\(76\) 0 0
\(77\) 42026.3 + 42026.3i 0.807783 + 0.807783i
\(78\) 0 0
\(79\) −88799.9 −1.60083 −0.800414 0.599448i \(-0.795387\pi\)
−0.800414 + 0.599448i \(0.795387\pi\)
\(80\) 0 0
\(81\) −206926. −3.50431
\(82\) 0 0
\(83\) −61945.4 61945.4i −0.986992 0.986992i 0.0129242 0.999916i \(-0.495886\pi\)
−0.999916 + 0.0129242i \(0.995886\pi\)
\(84\) 0 0
\(85\) −11718.7 + 11718.7i −0.175927 + 0.175927i
\(86\) 0 0
\(87\) 85570.7i 1.21207i
\(88\) 0 0
\(89\) 1923.83i 0.0257449i −0.999917 0.0128725i \(-0.995902\pi\)
0.999917 0.0128725i \(-0.00409754\pi\)
\(90\) 0 0
\(91\) −45655.2 + 45655.2i −0.577946 + 0.577946i
\(92\) 0 0
\(93\) 66612.5 + 66612.5i 0.798635 + 0.798635i
\(94\) 0 0
\(95\) −42684.7 −0.485247
\(96\) 0 0
\(97\) −57200.4 −0.617263 −0.308631 0.951182i \(-0.599871\pi\)
−0.308631 + 0.951182i \(0.599871\pi\)
\(98\) 0 0
\(99\) 273299. + 273299.i 2.80253 + 2.80253i
\(100\) 0 0
\(101\) 59911.1 59911.1i 0.584392 0.584392i −0.351715 0.936107i \(-0.614402\pi\)
0.936107 + 0.351715i \(0.114402\pi\)
\(102\) 0 0
\(103\) 163644.i 1.51987i 0.650000 + 0.759934i \(0.274769\pi\)
−0.650000 + 0.759934i \(0.725231\pi\)
\(104\) 0 0
\(105\) 74883.8i 0.662849i
\(106\) 0 0
\(107\) 48203.4 48203.4i 0.407022 0.407022i −0.473677 0.880699i \(-0.657073\pi\)
0.880699 + 0.473677i \(0.157073\pi\)
\(108\) 0 0
\(109\) −83668.5 83668.5i −0.674522 0.674522i 0.284233 0.958755i \(-0.408261\pi\)
−0.958755 + 0.284233i \(0.908261\pi\)
\(110\) 0 0
\(111\) −96511.0 −0.743480
\(112\) 0 0
\(113\) −43813.5 −0.322784 −0.161392 0.986890i \(-0.551598\pi\)
−0.161392 + 0.986890i \(0.551598\pi\)
\(114\) 0 0
\(115\) −45462.7 45462.7i −0.320561 0.320561i
\(116\) 0 0
\(117\) −296898. + 296898.i −2.00513 + 2.00513i
\(118\) 0 0
\(119\) 66397.2i 0.429816i
\(120\) 0 0
\(121\) 191062.i 1.18634i
\(122\) 0 0
\(123\) −81070.7 + 81070.7i −0.483172 + 0.483172i
\(124\) 0 0
\(125\) −11048.5 11048.5i −0.0632456 0.0632456i
\(126\) 0 0
\(127\) −150649. −0.828816 −0.414408 0.910091i \(-0.636011\pi\)
−0.414408 + 0.910091i \(0.636011\pi\)
\(128\) 0 0
\(129\) 549350. 2.90653
\(130\) 0 0
\(131\) −191515. 191515.i −0.975047 0.975047i 0.0246495 0.999696i \(-0.492153\pi\)
−0.999696 + 0.0246495i \(0.992153\pi\)
\(132\) 0 0
\(133\) 120924. 120924.i 0.592766 0.592766i
\(134\) 0 0
\(135\) 305296.i 1.44174i
\(136\) 0 0
\(137\) 127096.i 0.578537i −0.957248 0.289268i \(-0.906588\pi\)
0.957248 0.289268i \(-0.0934120\pi\)
\(138\) 0 0
\(139\) −8344.58 + 8344.58i −0.0366326 + 0.0366326i −0.725186 0.688553i \(-0.758246\pi\)
0.688553 + 0.725186i \(0.258246\pi\)
\(140\) 0 0
\(141\) −331859. 331859.i −1.40574 1.40574i
\(142\) 0 0
\(143\) 382518. 1.56427
\(144\) 0 0
\(145\) −71533.9 −0.282548
\(146\) 0 0
\(147\) −143266. 143266.i −0.546826 0.546826i
\(148\) 0 0
\(149\) −120025. + 120025.i −0.442900 + 0.442900i −0.892986 0.450085i \(-0.851394\pi\)
0.450085 + 0.892986i \(0.351394\pi\)
\(150\) 0 0
\(151\) 49519.6i 0.176740i 0.996088 + 0.0883699i \(0.0281658\pi\)
−0.996088 + 0.0883699i \(0.971834\pi\)
\(152\) 0 0
\(153\) 431784.i 1.49121i
\(154\) 0 0
\(155\) −55685.6 + 55685.6i −0.186172 + 0.186172i
\(156\) 0 0
\(157\) 143298. + 143298.i 0.463971 + 0.463971i 0.899955 0.435984i \(-0.143600\pi\)
−0.435984 + 0.899955i \(0.643600\pi\)
\(158\) 0 0
\(159\) −624892. −1.96025
\(160\) 0 0
\(161\) 257588. 0.783179
\(162\) 0 0
\(163\) 368607. + 368607.i 1.08666 + 1.08666i 0.995870 + 0.0907922i \(0.0289399\pi\)
0.0907922 + 0.995870i \(0.471060\pi\)
\(164\) 0 0
\(165\) −313703. + 313703.i −0.897034 + 0.897034i
\(166\) 0 0
\(167\) 373588.i 1.03658i 0.855206 + 0.518288i \(0.173430\pi\)
−0.855206 + 0.518288i \(0.826570\pi\)
\(168\) 0 0
\(169\) 44254.5i 0.119190i
\(170\) 0 0
\(171\) 786374. 786374.i 2.05655 2.05655i
\(172\) 0 0
\(173\) 1424.89 + 1424.89i 0.00361964 + 0.00361964i 0.708914 0.705295i \(-0.249185\pi\)
−0.705295 + 0.708914i \(0.749185\pi\)
\(174\) 0 0
\(175\) 62600.1 0.154518
\(176\) 0 0
\(177\) 1.03518e6 2.48360
\(178\) 0 0
\(179\) −171556. 171556.i −0.400196 0.400196i 0.478106 0.878302i \(-0.341324\pi\)
−0.878302 + 0.478106i \(0.841324\pi\)
\(180\) 0 0
\(181\) −189955. + 189955.i −0.430977 + 0.430977i −0.888961 0.457984i \(-0.848572\pi\)
0.457984 + 0.888961i \(0.348572\pi\)
\(182\) 0 0
\(183\) 642518.i 1.41827i
\(184\) 0 0
\(185\) 80679.7i 0.173314i
\(186\) 0 0
\(187\) −278151. + 278151.i −0.581670 + 0.581670i
\(188\) 0 0
\(189\) 864892. + 864892.i 1.76119 + 1.76119i
\(190\) 0 0
\(191\) −701235. −1.39085 −0.695425 0.718599i \(-0.744784\pi\)
−0.695425 + 0.718599i \(0.744784\pi\)
\(192\) 0 0
\(193\) −780783. −1.50882 −0.754409 0.656405i \(-0.772076\pi\)
−0.754409 + 0.656405i \(0.772076\pi\)
\(194\) 0 0
\(195\) −340791. 340791.i −0.641803 0.641803i
\(196\) 0 0
\(197\) −270606. + 270606.i −0.496788 + 0.496788i −0.910437 0.413649i \(-0.864254\pi\)
0.413649 + 0.910437i \(0.364254\pi\)
\(198\) 0 0
\(199\) 124497.i 0.222856i −0.993772 0.111428i \(-0.964458\pi\)
0.993772 0.111428i \(-0.0355425\pi\)
\(200\) 0 0
\(201\) 1.05415e6i 1.84041i
\(202\) 0 0
\(203\) 202653. 202653.i 0.345153 0.345153i
\(204\) 0 0
\(205\) −67772.2 67772.2i −0.112633 0.112633i
\(206\) 0 0
\(207\) 1.67511e6 2.71717
\(208\) 0 0
\(209\) −1.01315e6 −1.60438
\(210\) 0 0
\(211\) −74262.7 74262.7i −0.114832 0.114832i 0.647356 0.762188i \(-0.275875\pi\)
−0.762188 + 0.647356i \(0.775875\pi\)
\(212\) 0 0
\(213\) −1.10031e6 + 1.10031e6i −1.66175 + 1.66175i
\(214\) 0 0
\(215\) 459237.i 0.677548i
\(216\) 0 0
\(217\) 315510.i 0.454846i
\(218\) 0 0
\(219\) 792216. 792216.i 1.11618 1.11618i
\(220\) 0 0
\(221\) −302169. 302169.i −0.416168 0.416168i
\(222\) 0 0
\(223\) −873769. −1.17662 −0.588308 0.808637i \(-0.700206\pi\)
−0.588308 + 0.808637i \(0.700206\pi\)
\(224\) 0 0
\(225\) 407092. 0.536088
\(226\) 0 0
\(227\) 804882. + 804882.i 1.03673 + 1.03673i 0.999299 + 0.0374350i \(0.0119187\pi\)
0.0374350 + 0.999299i \(0.488081\pi\)
\(228\) 0 0
\(229\) 640029. 640029.i 0.806512 0.806512i −0.177592 0.984104i \(-0.556831\pi\)
0.984104 + 0.177592i \(0.0568308\pi\)
\(230\) 0 0
\(231\) 1.77742e6i 2.19159i
\(232\) 0 0
\(233\) 442511.i 0.533991i 0.963698 + 0.266996i \(0.0860309\pi\)
−0.963698 + 0.266996i \(0.913969\pi\)
\(234\) 0 0
\(235\) 277422. 277422.i 0.327696 0.327696i
\(236\) 0 0
\(237\) 1.87780e6 + 1.87780e6i 2.17160 + 2.17160i
\(238\) 0 0
\(239\) −779631. −0.882865 −0.441432 0.897294i \(-0.645530\pi\)
−0.441432 + 0.897294i \(0.645530\pi\)
\(240\) 0 0
\(241\) 1.17545e6 1.30365 0.651827 0.758368i \(-0.274003\pi\)
0.651827 + 0.758368i \(0.274003\pi\)
\(242\) 0 0
\(243\) 2.27743e6 + 2.27743e6i 2.47417 + 2.47417i
\(244\) 0 0
\(245\) 119765. 119765.i 0.127472 0.127472i
\(246\) 0 0
\(247\) 1.10063e6i 1.14789i
\(248\) 0 0
\(249\) 2.61985e6i 2.67780i
\(250\) 0 0
\(251\) −838767. + 838767.i −0.840344 + 0.840344i −0.988903 0.148559i \(-0.952536\pi\)
0.148559 + 0.988903i \(0.452536\pi\)
\(252\) 0 0
\(253\) −1.07909e6 1.07909e6i −1.05988 1.05988i
\(254\) 0 0
\(255\) 495618. 0.477306
\(256\) 0 0
\(257\) 26562.8 0.0250865 0.0125433 0.999921i \(-0.496007\pi\)
0.0125433 + 0.999921i \(0.496007\pi\)
\(258\) 0 0
\(259\) 228562. + 228562.i 0.211717 + 0.211717i
\(260\) 0 0
\(261\) 1.31786e6 1.31786e6i 1.19748 1.19748i
\(262\) 0 0
\(263\) 2.16147e6i 1.92690i −0.267885 0.963451i \(-0.586325\pi\)
0.267885 0.963451i \(-0.413675\pi\)
\(264\) 0 0
\(265\) 522386.i 0.456959i
\(266\) 0 0
\(267\) −40682.2 + 40682.2i −0.0349242 + 0.0349242i
\(268\) 0 0
\(269\) −553966. 553966.i −0.466770 0.466770i 0.434097 0.900866i \(-0.357068\pi\)
−0.900866 + 0.434097i \(0.857068\pi\)
\(270\) 0 0
\(271\) −1.04497e6 −0.864333 −0.432166 0.901794i \(-0.642251\pi\)
−0.432166 + 0.901794i \(0.642251\pi\)
\(272\) 0 0
\(273\) 1.93089e6 1.56802
\(274\) 0 0
\(275\) −262244. 262244.i −0.209110 0.209110i
\(276\) 0 0
\(277\) −758735. + 758735.i −0.594143 + 0.594143i −0.938748 0.344605i \(-0.888013\pi\)
0.344605 + 0.938748i \(0.388013\pi\)
\(278\) 0 0
\(279\) 2.05178e6i 1.57805i
\(280\) 0 0
\(281\) 209903.i 0.158582i −0.996852 0.0792908i \(-0.974734\pi\)
0.996852 0.0792908i \(-0.0252656\pi\)
\(282\) 0 0
\(283\) 355669. 355669.i 0.263986 0.263986i −0.562685 0.826671i \(-0.690232\pi\)
0.826671 + 0.562685i \(0.190232\pi\)
\(284\) 0 0
\(285\) 902630. + 902630.i 0.658260 + 0.658260i
\(286\) 0 0
\(287\) 383991. 0.275180
\(288\) 0 0
\(289\) −980408. −0.690498
\(290\) 0 0
\(291\) 1.20959e6 + 1.20959e6i 0.837346 + 0.837346i
\(292\) 0 0
\(293\) 1.42689e6 1.42689e6i 0.971006 0.971006i −0.0285852 0.999591i \(-0.509100\pi\)
0.999591 + 0.0285852i \(0.00910018\pi\)
\(294\) 0 0
\(295\) 865370.i 0.578958i
\(296\) 0 0
\(297\) 7.24641e6i 4.76685i
\(298\) 0 0
\(299\) 1.17227e6 1.17227e6i 0.758312 0.758312i
\(300\) 0 0
\(301\) −1.30100e6 1.30100e6i −0.827676 0.827676i
\(302\) 0 0
\(303\) −2.53382e6 −1.58551
\(304\) 0 0
\(305\) −537121. −0.330615
\(306\) 0 0
\(307\) −1.70499e6 1.70499e6i −1.03247 1.03247i −0.999455 0.0330100i \(-0.989491\pi\)
−0.0330100 0.999455i \(-0.510509\pi\)
\(308\) 0 0
\(309\) 3.46048e6 3.46048e6i 2.06177 2.06177i
\(310\) 0 0
\(311\) 101227.i 0.0593465i 0.999560 + 0.0296732i \(0.00944667\pi\)
−0.999560 + 0.0296732i \(0.990553\pi\)
\(312\) 0 0
\(313\) 98807.4i 0.0570071i 0.999594 + 0.0285035i \(0.00907419\pi\)
−0.999594 + 0.0285035i \(0.990926\pi\)
\(314\) 0 0
\(315\) −1.15327e6 + 1.15327e6i −0.654871 + 0.654871i
\(316\) 0 0
\(317\) −1.62863e6 1.62863e6i −0.910279 0.910279i 0.0860149 0.996294i \(-0.472587\pi\)
−0.996294 + 0.0860149i \(0.972587\pi\)
\(318\) 0 0
\(319\) −1.69790e6 −0.934192
\(320\) 0 0
\(321\) −2.03866e6 −1.10429
\(322\) 0 0
\(323\) 800334. + 800334.i 0.426840 + 0.426840i
\(324\) 0 0
\(325\) 284889. 284889.i 0.149612 0.149612i
\(326\) 0 0
\(327\) 3.53859e6i 1.83004i
\(328\) 0 0
\(329\) 1.57185e6i 0.800610i
\(330\) 0 0
\(331\) 1.03620e6 1.03620e6i 0.519843 0.519843i −0.397681 0.917524i \(-0.630185\pi\)
0.917524 + 0.397681i \(0.130185\pi\)
\(332\) 0 0
\(333\) 1.48635e6 + 1.48635e6i 0.734532 + 0.734532i
\(334\) 0 0
\(335\) 881234. 0.429022
\(336\) 0 0
\(337\) −1.54942e6 −0.743179 −0.371590 0.928397i \(-0.621187\pi\)
−0.371590 + 0.928397i \(0.621187\pi\)
\(338\) 0 0
\(339\) 926500. + 926500.i 0.437871 + 0.437871i
\(340\) 0 0
\(341\) −1.32173e6 + 1.32173e6i −0.615543 + 0.615543i
\(342\) 0 0
\(343\) 2.36197e6i 1.08403i
\(344\) 0 0
\(345\) 1.92275e6i 0.869712i
\(346\) 0 0
\(347\) −620879. + 620879.i −0.276811 + 0.276811i −0.831835 0.555024i \(-0.812709\pi\)
0.555024 + 0.831835i \(0.312709\pi\)
\(348\) 0 0
\(349\) 2.10966e6 + 2.10966e6i 0.927146 + 0.927146i 0.997521 0.0703743i \(-0.0224194\pi\)
−0.0703743 + 0.997521i \(0.522419\pi\)
\(350\) 0 0
\(351\) 7.87212e6 3.41055
\(352\) 0 0
\(353\) −2.90680e6 −1.24159 −0.620795 0.783973i \(-0.713190\pi\)
−0.620795 + 0.783973i \(0.713190\pi\)
\(354\) 0 0
\(355\) −919820. 919820.i −0.387376 0.387376i
\(356\) 0 0
\(357\) −1.40407e6 + 1.40407e6i −0.583065 + 0.583065i
\(358\) 0 0
\(359\) 322431.i 0.132038i −0.997818 0.0660192i \(-0.978970\pi\)
0.997818 0.0660192i \(-0.0210299\pi\)
\(360\) 0 0
\(361\) 439070.i 0.177323i
\(362\) 0 0
\(363\) −4.04029e6 + 4.04029e6i −1.60933 + 1.60933i
\(364\) 0 0
\(365\) 662263. + 662263.i 0.260195 + 0.260195i
\(366\) 0 0
\(367\) 540469. 0.209462 0.104731 0.994501i \(-0.466602\pi\)
0.104731 + 0.994501i \(0.466602\pi\)
\(368\) 0 0
\(369\) 2.49711e6 0.954712
\(370\) 0 0
\(371\) 1.47990e6 + 1.47990e6i 0.558210 + 0.558210i
\(372\) 0 0
\(373\) −1.77590e6 + 1.77590e6i −0.660914 + 0.660914i −0.955596 0.294681i \(-0.904787\pi\)
0.294681 + 0.955596i \(0.404787\pi\)
\(374\) 0 0
\(375\) 467275.i 0.171591i
\(376\) 0 0
\(377\) 1.84452e6i 0.668388i
\(378\) 0 0
\(379\) 2.43945e6 2.43945e6i 0.872357 0.872357i −0.120371 0.992729i \(-0.538409\pi\)
0.992729 + 0.120371i \(0.0384086\pi\)
\(380\) 0 0
\(381\) 3.18570e6 + 3.18570e6i 1.12433 + 1.12433i
\(382\) 0 0
\(383\) −1.05785e6 −0.368490 −0.184245 0.982880i \(-0.558984\pi\)
−0.184245 + 0.982880i \(0.558984\pi\)
\(384\) 0 0
\(385\) 1.48585e6 0.510887
\(386\) 0 0
\(387\) −8.46045e6 8.46045e6i −2.87155 2.87155i
\(388\) 0 0
\(389\) −2.38220e6 + 2.38220e6i −0.798186 + 0.798186i −0.982809 0.184624i \(-0.940893\pi\)
0.184624 + 0.982809i \(0.440893\pi\)
\(390\) 0 0
\(391\) 1.70484e6i 0.563953i
\(392\) 0 0
\(393\) 8.09975e6i 2.64539i
\(394\) 0 0
\(395\) −1.56977e6 + 1.56977e6i −0.506226 + 0.506226i
\(396\) 0 0
\(397\) −4.13447e6 4.13447e6i −1.31657 1.31657i −0.916473 0.400096i \(-0.868977\pi\)
−0.400096 0.916473i \(-0.631023\pi\)
\(398\) 0 0
\(399\) −5.11423e6 −1.60823
\(400\) 0 0
\(401\) 456569. 0.141790 0.0708951 0.997484i \(-0.477414\pi\)
0.0708951 + 0.997484i \(0.477414\pi\)
\(402\) 0 0
\(403\) −1.43586e6 1.43586e6i −0.440403 0.440403i
\(404\) 0 0
\(405\) −3.65797e6 + 3.65797e6i −1.10816 + 1.10816i
\(406\) 0 0
\(407\) 1.91498e6i 0.573032i
\(408\) 0 0
\(409\) 4.96200e6i 1.46673i 0.679838 + 0.733363i \(0.262050\pi\)
−0.679838 + 0.733363i \(0.737950\pi\)
\(410\) 0 0
\(411\) −2.68763e6 + 2.68763e6i −0.784812 + 0.784812i
\(412\) 0 0
\(413\) −2.45156e6 2.45156e6i −0.707240 0.707240i
\(414\) 0 0
\(415\) −2.19010e6 −0.624229
\(416\) 0 0
\(417\) 352917. 0.0993876
\(418\) 0 0
\(419\) −119480. 119480.i −0.0332476 0.0332476i 0.690288 0.723535i \(-0.257484\pi\)
−0.723535 + 0.690288i \(0.757484\pi\)
\(420\) 0 0
\(421\) 2.01225e6 2.01225e6i 0.553321 0.553321i −0.374077 0.927398i \(-0.622040\pi\)
0.927398 + 0.374077i \(0.122040\pi\)
\(422\) 0 0
\(423\) 1.02218e7i 2.77764i
\(424\) 0 0
\(425\) 414319.i 0.111266i
\(426\) 0 0
\(427\) 1.52164e6 1.52164e6i 0.403871 0.403871i
\(428\) 0 0
\(429\) −8.08890e6 8.08890e6i −2.12200 2.12200i
\(430\) 0 0
\(431\) 2.42671e6 0.629253 0.314626 0.949216i \(-0.398121\pi\)
0.314626 + 0.949216i \(0.398121\pi\)
\(432\) 0 0
\(433\) 2.83723e6 0.727234 0.363617 0.931548i \(-0.381542\pi\)
0.363617 + 0.931548i \(0.381542\pi\)
\(434\) 0 0
\(435\) 1.51269e6 + 1.51269e6i 0.383289 + 0.383289i
\(436\) 0 0
\(437\) −3.10490e6 + 3.10490e6i −0.777757 + 0.777757i
\(438\) 0 0
\(439\) 2.45058e6i 0.606886i −0.952850 0.303443i \(-0.901864\pi\)
0.952850 0.303443i \(-0.0981361\pi\)
\(440\) 0 0
\(441\) 4.41283e6i 1.08049i
\(442\) 0 0
\(443\) 3.37357e6 3.37357e6i 0.816734 0.816734i −0.168899 0.985633i \(-0.554021\pi\)
0.985633 + 0.168899i \(0.0540212\pi\)
\(444\) 0 0
\(445\) −34008.8 34008.8i −0.00814125 0.00814125i
\(446\) 0 0
\(447\) 5.07621e6 1.20163
\(448\) 0 0
\(449\) −4.06254e6 −0.951002 −0.475501 0.879715i \(-0.657733\pi\)
−0.475501 + 0.879715i \(0.657733\pi\)
\(450\) 0 0
\(451\) −1.60862e6 1.60862e6i −0.372401 0.372401i
\(452\) 0 0
\(453\) 1.04716e6 1.04716e6i 0.239756 0.239756i
\(454\) 0 0
\(455\) 1.61416e6i 0.365525i
\(456\) 0 0
\(457\) 5.58191e6i 1.25024i −0.780530 0.625119i \(-0.785051\pi\)
0.780530 0.625119i \(-0.214949\pi\)
\(458\) 0 0
\(459\) −5.72428e6 + 5.72428e6i −1.26820 + 1.26820i
\(460\) 0 0
\(461\) −1.91750e6 1.91750e6i −0.420227 0.420227i 0.465055 0.885282i \(-0.346034\pi\)
−0.885282 + 0.465055i \(0.846034\pi\)
\(462\) 0 0
\(463\) −847727. −0.183782 −0.0918911 0.995769i \(-0.529291\pi\)
−0.0918911 + 0.995769i \(0.529291\pi\)
\(464\) 0 0
\(465\) 2.35511e6 0.505101
\(466\) 0 0
\(467\) 971517. + 971517.i 0.206138 + 0.206138i 0.802624 0.596486i \(-0.203437\pi\)
−0.596486 + 0.802624i \(0.703437\pi\)
\(468\) 0 0
\(469\) −2.49650e6 + 2.49650e6i −0.524082 + 0.524082i
\(470\) 0 0
\(471\) 6.06049e6i 1.25880i
\(472\) 0 0
\(473\) 1.09003e7i 2.24019i
\(474\) 0 0
\(475\) −754565. + 754565.i −0.153449 + 0.153449i
\(476\) 0 0
\(477\) 9.62385e6 + 9.62385e6i 1.93666 + 1.93666i
\(478\) 0 0
\(479\) 2.09178e6 0.416559 0.208280 0.978069i \(-0.433214\pi\)
0.208280 + 0.978069i \(0.433214\pi\)
\(480\) 0 0
\(481\) 2.08034e6 0.409989
\(482\) 0 0
\(483\) −5.44708e6 5.44708e6i −1.06242 1.06242i
\(484\) 0 0
\(485\) −1.01117e6 + 1.01117e6i −0.195196 + 0.195196i
\(486\) 0 0
\(487\) 1.79078e6i 0.342153i 0.985258 + 0.171076i \(0.0547245\pi\)
−0.985258 + 0.171076i \(0.945276\pi\)
\(488\) 0 0
\(489\) 1.55895e7i 2.94822i
\(490\) 0 0
\(491\) 584391. 584391.i 0.109396 0.109396i −0.650290 0.759686i \(-0.725353\pi\)
0.759686 + 0.650290i \(0.225353\pi\)
\(492\) 0 0
\(493\) 1.34126e6 + 1.34126e6i 0.248539 + 0.248539i
\(494\) 0 0
\(495\) 9.66258e6 1.77247
\(496\) 0 0
\(497\) 5.21163e6 0.946417
\(498\) 0 0
\(499\) −541829. 541829.i −0.0974116 0.0974116i 0.656722 0.754133i \(-0.271943\pi\)
−0.754133 + 0.656722i \(0.771943\pi\)
\(500\) 0 0
\(501\) 7.90006e6 7.90006e6i 1.40616 1.40616i
\(502\) 0 0
\(503\) 3.68224e6i 0.648922i 0.945899 + 0.324461i \(0.105183\pi\)
−0.945899 + 0.324461i \(0.894817\pi\)
\(504\) 0 0
\(505\) 2.11818e6i 0.369602i
\(506\) 0 0
\(507\) 935826. 935826.i 0.161687 0.161687i
\(508\) 0 0
\(509\) −3.31091e6 3.31091e6i −0.566438 0.566438i 0.364690 0.931129i \(-0.381175\pi\)
−0.931129 + 0.364690i \(0.881175\pi\)
\(510\) 0 0
\(511\) −3.75233e6 −0.635695
\(512\) 0 0
\(513\) −2.08504e7 −3.49800
\(514\) 0 0
\(515\) 2.89284e6 + 2.89284e6i 0.480624 + 0.480624i
\(516\) 0 0
\(517\) 6.58478e6 6.58478e6i 1.08347 1.08347i
\(518\) 0 0
\(519\) 60262.8i 0.00982043i
\(520\) 0 0
\(521\) 6.70813e6i 1.08270i 0.840798 + 0.541348i \(0.182086\pi\)
−0.840798 + 0.541348i \(0.817914\pi\)
\(522\) 0 0
\(523\) 46922.8 46922.8i 0.00750118 0.00750118i −0.703346 0.710847i \(-0.748312\pi\)
0.710847 + 0.703346i \(0.248312\pi\)
\(524\) 0 0
\(525\) −1.32377e6 1.32377e6i −0.209611 0.209611i
\(526\) 0 0
\(527\) 2.08820e6 0.327526
\(528\) 0 0
\(529\) −177608. −0.0275945
\(530\) 0 0
\(531\) −1.59426e7 1.59426e7i −2.45371 2.45371i
\(532\) 0 0
\(533\) 1.74752e6 1.74752e6i 0.266443 0.266443i
\(534\) 0 0
\(535\) 1.70425e6i 0.257424i
\(536\) 0 0
\(537\) 7.25561e6i 1.08577i
\(538\) 0 0
\(539\) 2.84270e6 2.84270e6i 0.421463 0.421463i
\(540\) 0 0
\(541\) −4.04930e6 4.04930e6i −0.594822 0.594822i 0.344108 0.938930i \(-0.388181\pi\)
−0.938930 + 0.344108i \(0.888181\pi\)
\(542\) 0 0
\(543\) 8.03375e6 1.16928
\(544\) 0 0
\(545\) −2.95813e6 −0.426605
\(546\) 0 0
\(547\) −5.29104e6 5.29104e6i −0.756089 0.756089i 0.219519 0.975608i \(-0.429551\pi\)
−0.975608 + 0.219519i \(0.929551\pi\)
\(548\) 0 0
\(549\) 9.89531e6 9.89531e6i 1.40120 1.40120i
\(550\) 0 0
\(551\) 4.88544e6i 0.685528i
\(552\) 0 0
\(553\) 8.89422e6i 1.23679i
\(554\) 0 0
\(555\) −1.70609e6 + 1.70609e6i −0.235109 + 0.235109i
\(556\) 0 0
\(557\) −2.03827e6 2.03827e6i −0.278371 0.278371i 0.554087 0.832458i \(-0.313067\pi\)
−0.832458 + 0.554087i \(0.813067\pi\)
\(558\) 0 0
\(559\) −1.18415e7 −1.60279
\(560\) 0 0
\(561\) 1.17638e7 1.57812
\(562\) 0 0
\(563\) 6.46130e6 + 6.46130e6i 0.859111 + 0.859111i 0.991233 0.132123i \(-0.0421793\pi\)
−0.132123 + 0.991233i \(0.542179\pi\)
\(564\) 0 0
\(565\) −774520. + 774520.i −0.102073 + 0.102073i
\(566\) 0 0
\(567\) 2.07258e7i 2.70740i
\(568\) 0 0
\(569\) 3.86309e6i 0.500212i −0.968218 0.250106i \(-0.919535\pi\)
0.968218 0.250106i \(-0.0804655\pi\)
\(570\) 0 0
\(571\) 3.01051e6 3.01051e6i 0.386411 0.386411i −0.486994 0.873405i \(-0.661907\pi\)
0.873405 + 0.486994i \(0.161907\pi\)
\(572\) 0 0
\(573\) 1.48286e7 + 1.48286e7i 1.88675 + 1.88675i
\(574\) 0 0
\(575\) −1.60735e6 −0.202741
\(576\) 0 0
\(577\) −6.06843e6 −0.758816 −0.379408 0.925229i \(-0.623872\pi\)
−0.379408 + 0.925229i \(0.623872\pi\)
\(578\) 0 0
\(579\) 1.65108e7 + 1.65108e7i 2.04678 + 2.04678i
\(580\) 0 0
\(581\) 6.20446e6 6.20446e6i 0.762542 0.762542i
\(582\) 0 0
\(583\) 1.23992e7i 1.51085i
\(584\) 0 0
\(585\) 1.04969e7i 1.26816i
\(586\) 0 0
\(587\) 8.94817e6 8.94817e6i 1.07186 1.07186i 0.0746522 0.997210i \(-0.476215\pi\)
0.997210 0.0746522i \(-0.0237847\pi\)
\(588\) 0 0
\(589\) 3.80307e6 + 3.80307e6i 0.451696 + 0.451696i
\(590\) 0 0
\(591\) 1.14447e7 1.34783
\(592\) 0 0
\(593\) 6.63893e6 0.775285 0.387643 0.921810i \(-0.373289\pi\)
0.387643 + 0.921810i \(0.373289\pi\)
\(594\) 0 0
\(595\) −1.17375e6 1.17375e6i −0.135920 0.135920i
\(596\) 0 0
\(597\) −2.63266e6 + 2.63266e6i −0.302315 + 0.302315i
\(598\) 0 0
\(599\) 1.55670e7i 1.77271i 0.463003 + 0.886357i \(0.346772\pi\)
−0.463003 + 0.886357i \(0.653228\pi\)
\(600\) 0 0
\(601\) 7.58219e6i 0.856265i 0.903716 + 0.428133i \(0.140828\pi\)
−0.903716 + 0.428133i \(0.859172\pi\)
\(602\) 0 0
\(603\) −1.62349e7 + 1.62349e7i −1.81826 + 1.81826i
\(604\) 0 0
\(605\) −3.37753e6 3.37753e6i −0.375155 0.375155i
\(606\) 0 0
\(607\) −1.10026e7 −1.21206 −0.606030 0.795442i \(-0.707239\pi\)
−0.606030 + 0.795442i \(0.707239\pi\)
\(608\) 0 0
\(609\) −8.57078e6 −0.936433
\(610\) 0 0
\(611\) 7.15337e6 + 7.15337e6i 0.775189 + 0.775189i
\(612\) 0 0
\(613\) −1.92065e6 + 1.92065e6i −0.206441 + 0.206441i −0.802753 0.596312i \(-0.796632\pi\)
0.596312 + 0.802753i \(0.296632\pi\)
\(614\) 0 0
\(615\) 2.86628e6i 0.305585i
\(616\) 0 0
\(617\) 666574.i 0.0704913i 0.999379 + 0.0352456i \(0.0112214\pi\)
−0.999379 + 0.0352456i \(0.988779\pi\)
\(618\) 0 0
\(619\) −776525. + 776525.i −0.0814571 + 0.0814571i −0.746661 0.665204i \(-0.768344\pi\)
0.665204 + 0.746661i \(0.268344\pi\)
\(620\) 0 0
\(621\) −2.22074e7 2.22074e7i −2.31083 2.31083i
\(622\) 0 0
\(623\) 192691. 0.0198903
\(624\) 0 0
\(625\) −390625. −0.0400000
\(626\) 0 0
\(627\) 2.14245e7 + 2.14245e7i 2.17642 + 2.17642i
\(628\) 0 0
\(629\) −1.51274e6 + 1.51274e6i −0.152453 + 0.152453i
\(630\) 0 0
\(631\) 8.87851e6i 0.887700i −0.896101 0.443850i \(-0.853612\pi\)
0.896101 0.443850i \(-0.146388\pi\)
\(632\) 0 0
\(633\) 3.14079e6i 0.311551i
\(634\) 0 0
\(635\) −2.66313e6 + 2.66313e6i −0.262095 + 0.262095i
\(636\) 0 0
\(637\) 3.08816e6 + 3.08816e6i 0.301545 + 0.301545i
\(638\) 0 0
\(639\) 3.38914e7 3.28351
\(640\) 0 0
\(641\) 9.05119e6 0.870083 0.435041 0.900411i \(-0.356734\pi\)
0.435041 + 0.900411i \(0.356734\pi\)
\(642\) 0 0
\(643\) 1.05074e7 + 1.05074e7i 1.00224 + 1.00224i 0.999997 + 0.00223776i \(0.000712300\pi\)
0.00223776 + 0.999997i \(0.499288\pi\)
\(644\) 0 0
\(645\) 9.71123e6 9.71123e6i 0.919126 0.919126i
\(646\) 0 0
\(647\) 1.63451e7i 1.53507i 0.641007 + 0.767535i \(0.278517\pi\)
−0.641007 + 0.767535i \(0.721483\pi\)
\(648\) 0 0
\(649\) 2.05401e7i 1.91422i
\(650\) 0 0
\(651\) −6.67192e6 + 6.67192e6i −0.617019 + 0.617019i
\(652\) 0 0
\(653\) −5.46500e6 5.46500e6i −0.501542 0.501542i 0.410375 0.911917i \(-0.365398\pi\)
−0.911917 + 0.410375i \(0.865398\pi\)
\(654\) 0 0
\(655\) −6.77109e6 −0.616674
\(656\) 0 0
\(657\) −2.44016e7 −2.20549
\(658\) 0 0
\(659\) −1.11299e7 1.11299e7i −0.998334 0.998334i 0.00166454 0.999999i \(-0.499470\pi\)
−0.999999 + 0.00166454i \(0.999470\pi\)
\(660\) 0 0
\(661\) 8.50684e6 8.50684e6i 0.757295 0.757295i −0.218535 0.975829i \(-0.570128\pi\)
0.975829 + 0.218535i \(0.0701277\pi\)
\(662\) 0 0
\(663\) 1.27796e7i 1.12910i
\(664\) 0 0
\(665\) 4.27531e6i 0.374898i
\(666\) 0 0
\(667\) −5.20340e6 + 5.20340e6i −0.452869 + 0.452869i
\(668\) 0 0
\(669\) 1.84771e7 + 1.84771e7i 1.59613 + 1.59613i
\(670\) 0 0
\(671\) −1.27489e7 −1.09312
\(672\) 0 0
\(673\) 1.91012e7 1.62563 0.812816 0.582521i \(-0.197933\pi\)
0.812816 + 0.582521i \(0.197933\pi\)
\(674\) 0 0
\(675\) −5.39693e6 5.39693e6i −0.455919 0.455919i
\(676\) 0 0
\(677\) 1.35318e7 1.35318e7i 1.13470 1.13470i 0.145319 0.989385i \(-0.453579\pi\)
0.989385 0.145319i \(-0.0464209\pi\)
\(678\) 0 0
\(679\) 5.72921e6i 0.476892i
\(680\) 0 0
\(681\) 3.40408e7i 2.81276i
\(682\) 0 0
\(683\) −4506.05 + 4506.05i −0.000369610 + 0.000369610i −0.707292 0.706922i \(-0.750083\pi\)
0.706922 + 0.707292i \(0.250083\pi\)
\(684\) 0 0
\(685\) −2.24676e6 2.24676e6i −0.182949 0.182949i
\(686\) 0 0
\(687\) −2.70687e7 −2.18814
\(688\) 0 0
\(689\) 1.34698e7 1.08097
\(690\) 0 0
\(691\) −8.92380e6 8.92380e6i −0.710976 0.710976i 0.255764 0.966739i \(-0.417673\pi\)
−0.966739 + 0.255764i \(0.917673\pi\)
\(692\) 0 0
\(693\) −2.73737e7 + 2.73737e7i −2.16521 + 2.16521i
\(694\) 0 0
\(695\) 295025.i 0.0231685i
\(696\) 0 0
\(697\) 2.54144e6i 0.198152i
\(698\) 0 0
\(699\) 9.35755e6 9.35755e6i 0.724384 0.724384i
\(700\) 0 0
\(701\) 5.86907e6 + 5.86907e6i 0.451101 + 0.451101i 0.895720 0.444619i \(-0.146661\pi\)
−0.444619 + 0.895720i \(0.646661\pi\)
\(702\) 0 0
\(703\) −5.51006e6 −0.420502
\(704\) 0 0
\(705\) −1.17330e7 −0.889069
\(706\) 0 0
\(707\) 6.00071e6 + 6.00071e6i 0.451496 + 0.451496i
\(708\) 0 0
\(709\) 1.26108e7 1.26108e7i 0.942166 0.942166i −0.0562506 0.998417i \(-0.517915\pi\)
0.998417 + 0.0562506i \(0.0179146\pi\)
\(710\) 0 0
\(711\) 5.78395e7i 4.29092i
\(712\) 0 0
\(713\) 8.10118e6i 0.596794i
\(714\) 0 0
\(715\) 6.76202e6 6.76202e6i 0.494665 0.494665i
\(716\) 0 0
\(717\) 1.64864e7 + 1.64864e7i 1.19765 + 1.19765i
\(718\) 0 0
\(719\) 2.40190e7 1.73274 0.866368 0.499407i \(-0.166449\pi\)
0.866368 + 0.499407i \(0.166449\pi\)
\(720\) 0 0
\(721\) −1.63906e7 −1.17424
\(722\) 0 0
\(723\) −2.48567e7 2.48567e7i −1.76847 1.76847i
\(724\) 0 0
\(725\) −1.26455e6 + 1.26455e6i −0.0893495 + 0.0893495i
\(726\) 0 0
\(727\) 1.69795e7i 1.19149i 0.803175 + 0.595743i \(0.203142\pi\)
−0.803175 + 0.595743i \(0.796858\pi\)
\(728\) 0 0
\(729\) 4.60361e7i 3.20834i
\(730\) 0 0
\(731\) 8.61065e6 8.61065e6i 0.595995 0.595995i
\(732\) 0 0
\(733\) 6.03684e6 + 6.03684e6i 0.415001 + 0.415001i 0.883477 0.468475i \(-0.155196\pi\)
−0.468475 + 0.883477i \(0.655196\pi\)
\(734\) 0 0
\(735\) −5.06521e6 −0.345843
\(736\) 0 0
\(737\) 2.09167e7 1.41848
\(738\) 0 0
\(739\) −6.99975e6 6.99975e6i −0.471489 0.471489i 0.430908 0.902396i \(-0.358194\pi\)
−0.902396 + 0.430908i \(0.858194\pi\)
\(740\) 0 0
\(741\) −2.32745e7 + 2.32745e7i −1.55716 + 1.55716i
\(742\) 0 0
\(743\) 1.72605e7i 1.14705i −0.819188 0.573525i \(-0.805575\pi\)
0.819188 0.573525i \(-0.194425\pi\)
\(744\) 0 0
\(745\) 4.24352e6i 0.280115i
\(746\) 0 0
\(747\) 4.03479e7 4.03479e7i 2.64557 2.64557i
\(748\) 0 0
\(749\) 4.82806e6 + 4.82806e6i 0.314462 + 0.314462i
\(750\) 0 0
\(751\) 2.57275e7 1.66455 0.832277 0.554360i \(-0.187037\pi\)
0.832277 + 0.554360i \(0.187037\pi\)
\(752\) 0 0
\(753\) 3.54739e7 2.27993
\(754\) 0 0
\(755\) 875391. + 875391.i 0.0558901 + 0.0558901i
\(756\) 0 0
\(757\) 6.50319e6 6.50319e6i 0.412464 0.412464i −0.470132 0.882596i \(-0.655794\pi\)
0.882596 + 0.470132i \(0.155794\pi\)
\(758\) 0 0
\(759\) 4.56378e7i 2.87554i
\(760\) 0 0
\(761\) 1.22816e7i 0.768766i 0.923174 + 0.384383i \(0.125586\pi\)
−0.923174 + 0.384383i \(0.874414\pi\)
\(762\) 0 0
\(763\) 8.38026e6 8.38026e6i 0.521130 0.521130i
\(764\) 0 0
\(765\) −7.63293e6 7.63293e6i −0.471561 0.471561i
\(766\) 0 0
\(767\) −2.23137e7 −1.36957
\(768\) 0 0
\(769\) −6.88429e6 −0.419801 −0.209900 0.977723i \(-0.567314\pi\)
−0.209900 + 0.977723i \(0.567314\pi\)
\(770\) 0 0
\(771\) −561709. 561709.i −0.0340311 0.0340311i
\(772\) 0 0
\(773\) −7.34275e6 + 7.34275e6i −0.441987 + 0.441987i −0.892679 0.450692i \(-0.851177\pi\)
0.450692 + 0.892679i \(0.351177\pi\)
\(774\) 0 0
\(775\) 1.96878e6i 0.117745i
\(776\) 0 0
\(777\) 9.66657e6i 0.574407i
\(778\) 0 0
\(779\) −4.62853e6 + 4.62853e6i −0.273275 + 0.273275i
\(780\) 0 0
\(781\) −2.18325e7 2.18325e7i −1.28079 1.28079i
\(782\) 0 0
\(783\) −3.49425e7 −2.03680
\(784\) 0 0
\(785\) 5.06634e6 0.293441
\(786\) 0 0