Properties

Label 384.7.h.e.65.4
Level $384$
Weight $7$
Character 384.65
Analytic conductor $88.341$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 384.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(88.3407681100\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - 172x^{6} + 13179x^{4} - 522628x^{2} + 8755681 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{26}\cdot 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 65.4
Root \(6.86097 - 3.28347i\) of defining polynomial
Character \(\chi\) \(=\) 384.65
Dual form 384.7.h.e.65.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-22.4164 + 15.0501i) q^{3} +122.733 q^{5} +206.594 q^{7} +(275.991 - 674.737i) q^{9} +O(q^{10})\) \(q+(-22.4164 + 15.0501i) q^{3} +122.733 q^{5} +206.594 q^{7} +(275.991 - 674.737i) q^{9} +142.827 q^{11} -3499.27i q^{13} +(-2751.23 + 1847.14i) q^{15} -3382.86i q^{17} +755.858i q^{19} +(-4631.09 + 3109.25i) q^{21} -16911.3i q^{23} -561.656 q^{25} +(3968.12 + 19278.9i) q^{27} -41131.3 q^{29} -22916.1 q^{31} +(-3201.66 + 2149.55i) q^{33} +25355.8 q^{35} -26835.0i q^{37} +(52664.2 + 78441.0i) q^{39} +40460.6i q^{41} +128319. i q^{43} +(33873.1 - 82812.4i) q^{45} -60668.5i q^{47} -74968.0 q^{49} +(50912.4 + 75831.7i) q^{51} +5295.60 q^{53} +17529.5 q^{55} +(-11375.7 - 16943.6i) q^{57} +97392.6 q^{59} +213477. i q^{61} +(57018.0 - 139397. i) q^{63} -429475. i q^{65} +385320. i q^{67} +(254517. + 379091. i) q^{69} +356373. i q^{71} -141507. q^{73} +(12590.3 - 8452.97i) q^{75} +29507.1 q^{77} -722207. q^{79} +(-379099. - 372442. i) q^{81} +8040.09 q^{83} -415188. i q^{85} +(922016. - 619029. i) q^{87} +410420. i q^{89} -722927. i q^{91} +(513697. - 344889. i) q^{93} +92768.6i q^{95} -1.52876e6 q^{97} +(39418.8 - 96370.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 72 q^{3} - 1656 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 72 q^{3} - 1656 q^{9} - 1648 q^{11} - 200 q^{25} - 21384 q^{27} - 22608 q^{33} - 136320 q^{35} + 105208 q^{49} - 275328 q^{51} - 391104 q^{57} - 836624 q^{59} - 1964944 q^{73} + 59400 q^{75} + 166536 q^{81} + 587024 q^{83} - 1477232 q^{97} + 1688976 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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
\(3\) −22.4164 + 15.0501i −0.830237 + 0.557410i
\(4\) 0 0
\(5\) 122.733 0.981863 0.490931 0.871198i \(-0.336657\pi\)
0.490931 + 0.871198i \(0.336657\pi\)
\(6\) 0 0
\(7\) 206.594 0.602315 0.301157 0.953574i \(-0.402627\pi\)
0.301157 + 0.953574i \(0.402627\pi\)
\(8\) 0 0
\(9\) 275.991 674.737i 0.378588 0.925565i
\(10\) 0 0
\(11\) 142.827 0.107308 0.0536539 0.998560i \(-0.482913\pi\)
0.0536539 + 0.998560i \(0.482913\pi\)
\(12\) 0 0
\(13\) 3499.27i 1.59275i −0.604804 0.796374i \(-0.706749\pi\)
0.604804 0.796374i \(-0.293251\pi\)
\(14\) 0 0
\(15\) −2751.23 + 1847.14i −0.815179 + 0.547300i
\(16\) 0 0
\(17\) 3382.86i 0.688554i −0.938868 0.344277i \(-0.888124\pi\)
0.938868 0.344277i \(-0.111876\pi\)
\(18\) 0 0
\(19\) 755.858i 0.110200i 0.998481 + 0.0550998i \(0.0175477\pi\)
−0.998481 + 0.0550998i \(0.982452\pi\)
\(20\) 0 0
\(21\) −4631.09 + 3109.25i −0.500064 + 0.335736i
\(22\) 0 0
\(23\) 16911.3i 1.38993i −0.719042 0.694967i \(-0.755419\pi\)
0.719042 0.694967i \(-0.244581\pi\)
\(24\) 0 0
\(25\) −561.656 −0.0359460
\(26\) 0 0
\(27\) 3968.12 + 19278.9i 0.201601 + 0.979468i
\(28\) 0 0
\(29\) −41131.3 −1.68647 −0.843235 0.537546i \(-0.819352\pi\)
−0.843235 + 0.537546i \(0.819352\pi\)
\(30\) 0 0
\(31\) −22916.1 −0.769229 −0.384615 0.923077i \(-0.625666\pi\)
−0.384615 + 0.923077i \(0.625666\pi\)
\(32\) 0 0
\(33\) −3201.66 + 2149.55i −0.0890909 + 0.0598144i
\(34\) 0 0
\(35\) 25355.8 0.591390
\(36\) 0 0
\(37\) 26835.0i 0.529780i −0.964279 0.264890i \(-0.914664\pi\)
0.964279 0.264890i \(-0.0853357\pi\)
\(38\) 0 0
\(39\) 52664.2 + 78441.0i 0.887814 + 1.32236i
\(40\) 0 0
\(41\) 40460.6i 0.587057i 0.955950 + 0.293528i \(0.0948296\pi\)
−0.955950 + 0.293528i \(0.905170\pi\)
\(42\) 0 0
\(43\) 128319.i 1.61393i 0.590599 + 0.806965i \(0.298892\pi\)
−0.590599 + 0.806965i \(0.701108\pi\)
\(44\) 0 0
\(45\) 33873.1 82812.4i 0.371721 0.908778i
\(46\) 0 0
\(47\) 60668.5i 0.584345i −0.956366 0.292173i \(-0.905622\pi\)
0.956366 0.292173i \(-0.0943782\pi\)
\(48\) 0 0
\(49\) −74968.0 −0.637217
\(50\) 0 0
\(51\) 50912.4 + 75831.7i 0.383807 + 0.571663i
\(52\) 0 0
\(53\) 5295.60 0.0355703 0.0177852 0.999842i \(-0.494339\pi\)
0.0177852 + 0.999842i \(0.494339\pi\)
\(54\) 0 0
\(55\) 17529.5 0.105361
\(56\) 0 0
\(57\) −11375.7 16943.6i −0.0614263 0.0914917i
\(58\) 0 0
\(59\) 97392.6 0.474209 0.237105 0.971484i \(-0.423802\pi\)
0.237105 + 0.971484i \(0.423802\pi\)
\(60\) 0 0
\(61\) 213477.i 0.940506i 0.882532 + 0.470253i \(0.155837\pi\)
−0.882532 + 0.470253i \(0.844163\pi\)
\(62\) 0 0
\(63\) 57018.0 139397.i 0.228029 0.557481i
\(64\) 0 0
\(65\) 429475.i 1.56386i
\(66\) 0 0
\(67\) 385320.i 1.28114i 0.767898 + 0.640572i \(0.221303\pi\)
−0.767898 + 0.640572i \(0.778697\pi\)
\(68\) 0 0
\(69\) 254517. + 379091.i 0.774763 + 1.15397i
\(70\) 0 0
\(71\) 356373.i 0.995703i 0.867262 + 0.497851i \(0.165877\pi\)
−0.867262 + 0.497851i \(0.834123\pi\)
\(72\) 0 0
\(73\) −141507. −0.363754 −0.181877 0.983321i \(-0.558217\pi\)
−0.181877 + 0.983321i \(0.558217\pi\)
\(74\) 0 0
\(75\) 12590.3 8452.97i 0.0298437 0.0200367i
\(76\) 0 0
\(77\) 29507.1 0.0646330
\(78\) 0 0
\(79\) −722207. −1.46481 −0.732403 0.680871i \(-0.761601\pi\)
−0.732403 + 0.680871i \(0.761601\pi\)
\(80\) 0 0
\(81\) −379099. 372442.i −0.713342 0.700816i
\(82\) 0 0
\(83\) 8040.09 0.0140613 0.00703067 0.999975i \(-0.497762\pi\)
0.00703067 + 0.999975i \(0.497762\pi\)
\(84\) 0 0
\(85\) 415188.i 0.676065i
\(86\) 0 0
\(87\) 922016. 619029.i 1.40017 0.940055i
\(88\) 0 0
\(89\) 410420.i 0.582181i 0.956695 + 0.291091i \(0.0940182\pi\)
−0.956695 + 0.291091i \(0.905982\pi\)
\(90\) 0 0
\(91\) 722927.i 0.959335i
\(92\) 0 0
\(93\) 513697. 344889.i 0.638643 0.428776i
\(94\) 0 0
\(95\) 92768.6i 0.108201i
\(96\) 0 0
\(97\) −1.52876e6 −1.67504 −0.837520 0.546407i \(-0.815995\pi\)
−0.837520 + 0.546407i \(0.815995\pi\)
\(98\) 0 0
\(99\) 39418.8 96370.4i 0.0406254 0.0993203i
\(100\) 0 0
\(101\) −175149. −0.169998 −0.0849992 0.996381i \(-0.527089\pi\)
−0.0849992 + 0.996381i \(0.527089\pi\)
\(102\) 0 0
\(103\) −1.33846e6 −1.22488 −0.612440 0.790517i \(-0.709812\pi\)
−0.612440 + 0.790517i \(0.709812\pi\)
\(104\) 0 0
\(105\) −568387. + 381607.i −0.490994 + 0.329647i
\(106\) 0 0
\(107\) −1.06224e6 −0.867103 −0.433552 0.901129i \(-0.642740\pi\)
−0.433552 + 0.901129i \(0.642740\pi\)
\(108\) 0 0
\(109\) 390541.i 0.301570i 0.988567 + 0.150785i \(0.0481801\pi\)
−0.988567 + 0.150785i \(0.951820\pi\)
\(110\) 0 0
\(111\) 403868. + 601544.i 0.295305 + 0.439843i
\(112\) 0 0
\(113\) 2.53393e6i 1.75614i −0.478533 0.878070i \(-0.658831\pi\)
0.478533 0.878070i \(-0.341169\pi\)
\(114\) 0 0
\(115\) 2.07557e6i 1.36472i
\(116\) 0 0
\(117\) −2.36109e6 965765.i −1.47419 0.602995i
\(118\) 0 0
\(119\) 698879.i 0.414726i
\(120\) 0 0
\(121\) −1.75116e6 −0.988485
\(122\) 0 0
\(123\) −608934. 906980.i −0.327231 0.487397i
\(124\) 0 0
\(125\) −1.98663e6 −1.01716
\(126\) 0 0
\(127\) 2.59182e6 1.26530 0.632649 0.774439i \(-0.281968\pi\)
0.632649 + 0.774439i \(0.281968\pi\)
\(128\) 0 0
\(129\) −1.93121e6 2.87645e6i −0.899621 1.33995i
\(130\) 0 0
\(131\) −91522.7 −0.0407113 −0.0203557 0.999793i \(-0.506480\pi\)
−0.0203557 + 0.999793i \(0.506480\pi\)
\(132\) 0 0
\(133\) 156156.i 0.0663748i
\(134\) 0 0
\(135\) 487019. + 2.36615e6i 0.197945 + 0.961703i
\(136\) 0 0
\(137\) 2.50257e6i 0.973249i −0.873611 0.486624i \(-0.838228\pi\)
0.873611 0.486624i \(-0.161772\pi\)
\(138\) 0 0
\(139\) 988914.i 0.368226i −0.982905 0.184113i \(-0.941059\pi\)
0.982905 0.184113i \(-0.0589412\pi\)
\(140\) 0 0
\(141\) 913065. + 1.35997e6i 0.325720 + 0.485145i
\(142\) 0 0
\(143\) 499789.i 0.170914i
\(144\) 0 0
\(145\) −5.04816e6 −1.65588
\(146\) 0 0
\(147\) 1.68051e6 1.12827e6i 0.529042 0.355191i
\(148\) 0 0
\(149\) 4.84935e6 1.46597 0.732985 0.680245i \(-0.238127\pi\)
0.732985 + 0.680245i \(0.238127\pi\)
\(150\) 0 0
\(151\) −3.63349e6 −1.05534 −0.527671 0.849449i \(-0.676935\pi\)
−0.527671 + 0.849449i \(0.676935\pi\)
\(152\) 0 0
\(153\) −2.28254e6 933639.i −0.637301 0.260678i
\(154\) 0 0
\(155\) −2.81256e6 −0.755278
\(156\) 0 0
\(157\) 4.51450e6i 1.16657i −0.812268 0.583285i \(-0.801767\pi\)
0.812268 0.583285i \(-0.198233\pi\)
\(158\) 0 0
\(159\) −118708. + 79699.2i −0.0295318 + 0.0198273i
\(160\) 0 0
\(161\) 3.49377e6i 0.837177i
\(162\) 0 0
\(163\) 5.64963e6i 1.30454i 0.757987 + 0.652269i \(0.226183\pi\)
−0.757987 + 0.652269i \(0.773817\pi\)
\(164\) 0 0
\(165\) −392949. + 263820.i −0.0874750 + 0.0587295i
\(166\) 0 0
\(167\) 4.42913e6i 0.950975i −0.879723 0.475487i \(-0.842272\pi\)
0.879723 0.475487i \(-0.157728\pi\)
\(168\) 0 0
\(169\) −7.41807e6 −1.53685
\(170\) 0 0
\(171\) 510006. + 208610.i 0.101997 + 0.0417202i
\(172\) 0 0
\(173\) 1.66599e6 0.321762 0.160881 0.986974i \(-0.448566\pi\)
0.160881 + 0.986974i \(0.448566\pi\)
\(174\) 0 0
\(175\) −116035. −0.0216508
\(176\) 0 0
\(177\) −2.18319e6 + 1.46577e6i −0.393706 + 0.264329i
\(178\) 0 0
\(179\) 4.85953e6 0.847296 0.423648 0.905827i \(-0.360749\pi\)
0.423648 + 0.905827i \(0.360749\pi\)
\(180\) 0 0
\(181\) 8.92904e6i 1.50581i 0.658132 + 0.752903i \(0.271347\pi\)
−0.658132 + 0.752903i \(0.728653\pi\)
\(182\) 0 0
\(183\) −3.21285e6 4.78539e6i −0.524248 0.780843i
\(184\) 0 0
\(185\) 3.29353e6i 0.520171i
\(186\) 0 0
\(187\) 483163.i 0.0738871i
\(188\) 0 0
\(189\) 819790. + 3.98289e6i 0.121427 + 0.589948i
\(190\) 0 0
\(191\) 7.88180e6i 1.13116i 0.824692 + 0.565582i \(0.191348\pi\)
−0.824692 + 0.565582i \(0.808652\pi\)
\(192\) 0 0
\(193\) −5.97521e6 −0.831154 −0.415577 0.909558i \(-0.636420\pi\)
−0.415577 + 0.909558i \(0.636420\pi\)
\(194\) 0 0
\(195\) 6.46363e6 + 9.62729e6i 0.871711 + 1.29837i
\(196\) 0 0
\(197\) 4.16081e6 0.544226 0.272113 0.962265i \(-0.412278\pi\)
0.272113 + 0.962265i \(0.412278\pi\)
\(198\) 0 0
\(199\) 1.21801e7 1.54558 0.772792 0.634660i \(-0.218860\pi\)
0.772792 + 0.634660i \(0.218860\pi\)
\(200\) 0 0
\(201\) −5.79910e6 8.63750e6i −0.714122 1.06365i
\(202\) 0 0
\(203\) −8.49747e6 −1.01578
\(204\) 0 0
\(205\) 4.96584e6i 0.576409i
\(206\) 0 0
\(207\) −1.14107e7 4.66737e6i −1.28647 0.526212i
\(208\) 0 0
\(209\) 107957.i 0.0118253i
\(210\) 0 0
\(211\) 1.27411e7i 1.35631i 0.734919 + 0.678154i \(0.237220\pi\)
−0.734919 + 0.678154i \(0.762780\pi\)
\(212\) 0 0
\(213\) −5.36344e6 7.98860e6i −0.555015 0.826669i
\(214\) 0 0
\(215\) 1.57489e7i 1.58466i
\(216\) 0 0
\(217\) −4.73433e6 −0.463318
\(218\) 0 0
\(219\) 3.17207e6 2.12969e6i 0.302003 0.202760i
\(220\) 0 0
\(221\) −1.18375e7 −1.09669
\(222\) 0 0
\(223\) 8.46685e6 0.763497 0.381749 0.924266i \(-0.375322\pi\)
0.381749 + 0.924266i \(0.375322\pi\)
\(224\) 0 0
\(225\) −155012. + 378970.i −0.0136087 + 0.0332704i
\(226\) 0 0
\(227\) 7.29952e6 0.624046 0.312023 0.950075i \(-0.398993\pi\)
0.312023 + 0.950075i \(0.398993\pi\)
\(228\) 0 0
\(229\) 1.83981e7i 1.53202i −0.642826 0.766012i \(-0.722238\pi\)
0.642826 0.766012i \(-0.277762\pi\)
\(230\) 0 0
\(231\) −661443. + 444084.i −0.0536607 + 0.0360271i
\(232\) 0 0
\(233\) 2.00421e7i 1.58444i −0.610237 0.792219i \(-0.708926\pi\)
0.610237 0.792219i \(-0.291074\pi\)
\(234\) 0 0
\(235\) 7.44601e6i 0.573747i
\(236\) 0 0
\(237\) 1.61893e7 1.08693e7i 1.21614 0.816498i
\(238\) 0 0
\(239\) 2.39694e7i 1.75575i −0.478887 0.877877i \(-0.658960\pi\)
0.478887 0.877877i \(-0.341040\pi\)
\(240\) 0 0
\(241\) 5.88680e6 0.420560 0.210280 0.977641i \(-0.432562\pi\)
0.210280 + 0.977641i \(0.432562\pi\)
\(242\) 0 0
\(243\) 1.41033e7 + 2.64335e6i 0.982885 + 0.184219i
\(244\) 0 0
\(245\) −9.20103e6 −0.625660
\(246\) 0 0
\(247\) 2.64495e6 0.175520
\(248\) 0 0
\(249\) −180230. + 121004.i −0.0116743 + 0.00783793i
\(250\) 0 0
\(251\) −2.80782e7 −1.77561 −0.887807 0.460217i \(-0.847772\pi\)
−0.887807 + 0.460217i \(0.847772\pi\)
\(252\) 0 0
\(253\) 2.41539e6i 0.149151i
\(254\) 0 0
\(255\) 6.24862e6 + 9.30703e6i 0.376845 + 0.561294i
\(256\) 0 0
\(257\) 1.62429e7i 0.956894i 0.878116 + 0.478447i \(0.158800\pi\)
−0.878116 + 0.478447i \(0.841200\pi\)
\(258\) 0 0
\(259\) 5.54394e6i 0.319094i
\(260\) 0 0
\(261\) −1.13519e7 + 2.77528e7i −0.638477 + 1.56094i
\(262\) 0 0
\(263\) 572672.i 0.0314803i −0.999876 0.0157401i \(-0.994990\pi\)
0.999876 0.0157401i \(-0.00501045\pi\)
\(264\) 0 0
\(265\) 649944. 0.0349252
\(266\) 0 0
\(267\) −6.17685e6 9.20014e6i −0.324514 0.483349i
\(268\) 0 0
\(269\) −1.60268e7 −0.823358 −0.411679 0.911329i \(-0.635057\pi\)
−0.411679 + 0.911329i \(0.635057\pi\)
\(270\) 0 0
\(271\) −2.21330e7 −1.11207 −0.556035 0.831159i \(-0.687678\pi\)
−0.556035 + 0.831159i \(0.687678\pi\)
\(272\) 0 0
\(273\) 1.08801e7 + 1.62054e7i 0.534743 + 0.796476i
\(274\) 0 0
\(275\) −80219.5 −0.00385728
\(276\) 0 0
\(277\) 329177.i 0.0154878i −0.999970 0.00774392i \(-0.997535\pi\)
0.999970 0.00774392i \(-0.00246499\pi\)
\(278\) 0 0
\(279\) −6.32463e6 + 1.54624e7i −0.291221 + 0.711972i
\(280\) 0 0
\(281\) 2.42415e7i 1.09255i 0.837607 + 0.546274i \(0.183954\pi\)
−0.837607 + 0.546274i \(0.816046\pi\)
\(282\) 0 0
\(283\) 2.32930e7i 1.02770i −0.857880 0.513850i \(-0.828219\pi\)
0.857880 0.513850i \(-0.171781\pi\)
\(284\) 0 0
\(285\) −1.39617e6 2.07954e6i −0.0603122 0.0898323i
\(286\) 0 0
\(287\) 8.35890e6i 0.353593i
\(288\) 0 0
\(289\) 1.26938e7 0.525894
\(290\) 0 0
\(291\) 3.42694e7 2.30080e7i 1.39068 0.933684i
\(292\) 0 0
\(293\) 1.21239e7 0.481993 0.240996 0.970526i \(-0.422526\pi\)
0.240996 + 0.970526i \(0.422526\pi\)
\(294\) 0 0
\(295\) 1.19533e7 0.465608
\(296\) 0 0
\(297\) 566753. + 2.75353e6i 0.0216334 + 0.105104i
\(298\) 0 0
\(299\) −5.91772e7 −2.21381
\(300\) 0 0
\(301\) 2.65099e7i 0.972094i
\(302\) 0 0
\(303\) 3.92622e6 2.63601e6i 0.141139 0.0947588i
\(304\) 0 0
\(305\) 2.62006e7i 0.923448i
\(306\) 0 0
\(307\) 1.04782e7i 0.362136i 0.983471 + 0.181068i \(0.0579555\pi\)
−0.983471 + 0.181068i \(0.942045\pi\)
\(308\) 0 0
\(309\) 3.00035e7 2.01439e7i 1.01694 0.682761i
\(310\) 0 0
\(311\) 5.87497e7i 1.95310i −0.215292 0.976550i \(-0.569070\pi\)
0.215292 0.976550i \(-0.430930\pi\)
\(312\) 0 0
\(313\) 5.12380e7 1.67093 0.835467 0.549540i \(-0.185197\pi\)
0.835467 + 0.549540i \(0.185197\pi\)
\(314\) 0 0
\(315\) 6.99798e6 1.71085e7i 0.223893 0.547370i
\(316\) 0 0
\(317\) 5.13280e7 1.61130 0.805651 0.592390i \(-0.201816\pi\)
0.805651 + 0.592390i \(0.201816\pi\)
\(318\) 0 0
\(319\) −5.87464e6 −0.180971
\(320\) 0 0
\(321\) 2.38116e7 1.59868e7i 0.719901 0.483332i
\(322\) 0 0
\(323\) 2.55697e6 0.0758783
\(324\) 0 0
\(325\) 1.96539e6i 0.0572529i
\(326\) 0 0
\(327\) −5.87768e6 8.75454e6i −0.168098 0.250374i
\(328\) 0 0
\(329\) 1.25337e7i 0.351960i
\(330\) 0 0
\(331\) 5.26211e7i 1.45103i −0.688207 0.725515i \(-0.741602\pi\)
0.688207 0.725515i \(-0.258398\pi\)
\(332\) 0 0
\(333\) −1.81065e7 7.40620e6i −0.490346 0.200569i
\(334\) 0 0
\(335\) 4.72915e7i 1.25791i
\(336\) 0 0
\(337\) 3.13406e7 0.818876 0.409438 0.912338i \(-0.365725\pi\)
0.409438 + 0.912338i \(0.365725\pi\)
\(338\) 0 0
\(339\) 3.81358e7 + 5.68016e7i 0.978890 + 1.45801i
\(340\) 0 0
\(341\) −3.27303e6 −0.0825443
\(342\) 0 0
\(343\) −3.97935e7 −0.986120
\(344\) 0 0
\(345\) 3.12375e7 + 4.65269e7i 0.760710 + 1.13304i
\(346\) 0 0
\(347\) −5.67725e7 −1.35878 −0.679391 0.733777i \(-0.737756\pi\)
−0.679391 + 0.733777i \(0.737756\pi\)
\(348\) 0 0
\(349\) 9.45512e6i 0.222429i −0.993796 0.111214i \(-0.964526\pi\)
0.993796 0.111214i \(-0.0354740\pi\)
\(350\) 0 0
\(351\) 6.74619e7 1.38855e7i 1.56005 0.321100i
\(352\) 0 0
\(353\) 1.84722e7i 0.419948i −0.977707 0.209974i \(-0.932662\pi\)
0.977707 0.209974i \(-0.0673379\pi\)
\(354\) 0 0
\(355\) 4.37386e7i 0.977643i
\(356\) 0 0
\(357\) 1.05182e7 + 1.56664e7i 0.231172 + 0.344321i
\(358\) 0 0
\(359\) 8.02076e7i 1.73353i 0.498714 + 0.866767i \(0.333806\pi\)
−0.498714 + 0.866767i \(0.666194\pi\)
\(360\) 0 0
\(361\) 4.64746e7 0.987856
\(362\) 0 0
\(363\) 3.92548e7 2.63551e7i 0.820677 0.550992i
\(364\) 0 0
\(365\) −1.73675e7 −0.357157
\(366\) 0 0
\(367\) 6.88440e6 0.139273 0.0696366 0.997572i \(-0.477816\pi\)
0.0696366 + 0.997572i \(0.477816\pi\)
\(368\) 0 0
\(369\) 2.73002e7 + 1.11667e7i 0.543360 + 0.222253i
\(370\) 0 0
\(371\) 1.09404e6 0.0214245
\(372\) 0 0
\(373\) 4.53815e7i 0.874485i 0.899344 + 0.437243i \(0.144045\pi\)
−0.899344 + 0.437243i \(0.855955\pi\)
\(374\) 0 0
\(375\) 4.45332e7 2.98990e7i 0.844481 0.566973i
\(376\) 0 0
\(377\) 1.43929e8i 2.68612i
\(378\) 0 0
\(379\) 1.51053e7i 0.277467i 0.990330 + 0.138734i \(0.0443032\pi\)
−0.990330 + 0.138734i \(0.955697\pi\)
\(380\) 0 0
\(381\) −5.80992e7 + 3.90070e7i −1.05050 + 0.705290i
\(382\) 0 0
\(383\) 2.37036e7i 0.421908i −0.977496 0.210954i \(-0.932343\pi\)
0.977496 0.210954i \(-0.0676570\pi\)
\(384\) 0 0
\(385\) 3.62149e6 0.0634607
\(386\) 0 0
\(387\) 8.65814e7 + 3.54148e7i 1.49380 + 0.611015i
\(388\) 0 0
\(389\) −3.21550e7 −0.546261 −0.273130 0.961977i \(-0.588059\pi\)
−0.273130 + 0.961977i \(0.588059\pi\)
\(390\) 0 0
\(391\) −5.72087e7 −0.957044
\(392\) 0 0
\(393\) 2.05161e6 1.37742e6i 0.0338000 0.0226929i
\(394\) 0 0
\(395\) −8.86385e7 −1.43824
\(396\) 0 0
\(397\) 1.01939e8i 1.62918i −0.580035 0.814591i \(-0.696961\pi\)
0.580035 0.814591i \(-0.303039\pi\)
\(398\) 0 0
\(399\) −2.35015e6 3.50045e6i −0.0369980 0.0551068i
\(400\) 0 0
\(401\) 2.78698e7i 0.432215i 0.976370 + 0.216108i \(0.0693362\pi\)
−0.976370 + 0.216108i \(0.930664\pi\)
\(402\) 0 0
\(403\) 8.01896e7i 1.22519i
\(404\) 0 0
\(405\) −4.65279e7 4.57109e7i −0.700404 0.688105i
\(406\) 0 0
\(407\) 3.83275e6i 0.0568495i
\(408\) 0 0
\(409\) 1.07187e8 1.56665 0.783326 0.621611i \(-0.213522\pi\)
0.783326 + 0.621611i \(0.213522\pi\)
\(410\) 0 0
\(411\) 3.76638e7 + 5.60986e7i 0.542499 + 0.808028i
\(412\) 0 0
\(413\) 2.01207e7 0.285623
\(414\) 0 0
\(415\) 986783. 0.0138063
\(416\) 0 0
\(417\) 1.48832e7 + 2.21679e7i 0.205253 + 0.305715i
\(418\) 0 0
\(419\) −6.69022e6 −0.0909491 −0.0454745 0.998965i \(-0.514480\pi\)
−0.0454745 + 0.998965i \(0.514480\pi\)
\(420\) 0 0
\(421\) 5.45684e7i 0.731299i −0.930753 0.365649i \(-0.880847\pi\)
0.930753 0.365649i \(-0.119153\pi\)
\(422\) 0 0
\(423\) −4.09353e7 1.67439e7i −0.540850 0.221226i
\(424\) 0 0
\(425\) 1.90001e6i 0.0247508i
\(426\) 0 0
\(427\) 4.41031e7i 0.566481i
\(428\) 0 0
\(429\) 7.52185e6 + 1.12035e7i 0.0952693 + 0.141899i
\(430\) 0 0
\(431\) 4.58145e7i 0.572231i −0.958195 0.286115i \(-0.907636\pi\)
0.958195 0.286115i \(-0.0923641\pi\)
\(432\) 0 0
\(433\) −6.27032e6 −0.0772372 −0.0386186 0.999254i \(-0.512296\pi\)
−0.0386186 + 0.999254i \(0.512296\pi\)
\(434\) 0 0
\(435\) 1.13162e8 7.59752e7i 1.37477 0.923005i
\(436\) 0 0
\(437\) 1.27826e7 0.153170
\(438\) 0 0
\(439\) 4.02491e7 0.475732 0.237866 0.971298i \(-0.423552\pi\)
0.237866 + 0.971298i \(0.423552\pi\)
\(440\) 0 0
\(441\) −2.06905e7 + 5.05837e7i −0.241243 + 0.589786i
\(442\) 0 0
\(443\) −7.03746e7 −0.809477 −0.404739 0.914432i \(-0.632637\pi\)
−0.404739 + 0.914432i \(0.632637\pi\)
\(444\) 0 0
\(445\) 5.03720e7i 0.571622i
\(446\) 0 0
\(447\) −1.08705e8 + 7.29831e7i −1.21710 + 0.817146i
\(448\) 0 0
\(449\) 1.22328e8i 1.35141i −0.737170 0.675707i \(-0.763838\pi\)
0.737170 0.675707i \(-0.236162\pi\)
\(450\) 0 0
\(451\) 5.77884e6i 0.0629958i
\(452\) 0 0
\(453\) 8.14498e7 5.46843e7i 0.876184 0.588258i
\(454\) 0 0
\(455\) 8.87269e7i 0.941935i
\(456\) 0 0
\(457\) −1.10853e6 −0.0116144 −0.00580722 0.999983i \(-0.501849\pi\)
−0.00580722 + 0.999983i \(0.501849\pi\)
\(458\) 0 0
\(459\) 6.52178e7 1.34236e7i 0.674416 0.138813i
\(460\) 0 0
\(461\) 4.08136e7 0.416583 0.208292 0.978067i \(-0.433210\pi\)
0.208292 + 0.978067i \(0.433210\pi\)
\(462\) 0 0
\(463\) −3.22650e7 −0.325079 −0.162540 0.986702i \(-0.551969\pi\)
−0.162540 + 0.986702i \(0.551969\pi\)
\(464\) 0 0
\(465\) 6.30475e7 4.23292e7i 0.627060 0.420999i
\(466\) 0 0
\(467\) −9.16957e7 −0.900323 −0.450162 0.892947i \(-0.648634\pi\)
−0.450162 + 0.892947i \(0.648634\pi\)
\(468\) 0 0
\(469\) 7.96049e7i 0.771651i
\(470\) 0 0
\(471\) 6.79435e7 + 1.01199e8i 0.650257 + 0.968529i
\(472\) 0 0
\(473\) 1.83273e7i 0.173187i
\(474\) 0 0
\(475\) 424533.i 0.00396123i
\(476\) 0 0
\(477\) 1.46154e6 3.57314e6i 0.0134665 0.0329227i
\(478\) 0 0
\(479\) 3.72123e7i 0.338594i −0.985565 0.169297i \(-0.945850\pi\)
0.985565 0.169297i \(-0.0541498\pi\)
\(480\) 0 0
\(481\) −9.39027e7 −0.843807
\(482\) 0 0
\(483\) 5.25816e7 + 7.83179e7i 0.466651 + 0.695056i
\(484\) 0 0
\(485\) −1.87629e8 −1.64466
\(486\) 0 0
\(487\) 1.89081e8 1.63705 0.818525 0.574471i \(-0.194792\pi\)
0.818525 + 0.574471i \(0.194792\pi\)
\(488\) 0 0
\(489\) −8.50273e7 1.26644e8i −0.727163 1.08308i
\(490\) 0 0
\(491\) −1.81333e8 −1.53190 −0.765952 0.642898i \(-0.777732\pi\)
−0.765952 + 0.642898i \(0.777732\pi\)
\(492\) 0 0
\(493\) 1.39142e8i 1.16122i
\(494\) 0 0
\(495\) 4.83798e6 1.18278e7i 0.0398886 0.0975189i
\(496\) 0 0
\(497\) 7.36245e7i 0.599726i
\(498\) 0 0
\(499\) 1.73596e8i 1.39713i −0.715546 0.698566i \(-0.753822\pi\)
0.715546 0.698566i \(-0.246178\pi\)
\(500\) 0 0
\(501\) 6.66587e7 + 9.92852e7i 0.530083 + 0.789535i
\(502\) 0 0
\(503\) 8.79058e7i 0.690739i 0.938467 + 0.345369i \(0.112246\pi\)
−0.938467 + 0.345369i \(0.887754\pi\)
\(504\) 0 0
\(505\) −2.14966e7 −0.166915
\(506\) 0 0
\(507\) 1.66286e8 1.11642e8i 1.27595 0.856654i
\(508\) 0 0
\(509\) 1.69584e8 1.28597 0.642987 0.765877i \(-0.277695\pi\)
0.642987 + 0.765877i \(0.277695\pi\)
\(510\) 0 0
\(511\) −2.92344e7 −0.219095
\(512\) 0 0
\(513\) −1.45721e7 + 2.99934e6i −0.107937 + 0.0222164i
\(514\) 0 0
\(515\) −1.64273e8 −1.20266
\(516\) 0 0
\(517\) 8.66507e6i 0.0627048i
\(518\) 0 0
\(519\) −3.73456e7 + 2.50733e7i −0.267139 + 0.179354i
\(520\) 0 0
\(521\) 1.96877e8i 1.39213i −0.717977 0.696067i \(-0.754932\pi\)
0.717977 0.696067i \(-0.245068\pi\)
\(522\) 0 0
\(523\) 1.70811e8i 1.19402i −0.802235 0.597008i \(-0.796356\pi\)
0.802235 0.597008i \(-0.203644\pi\)
\(524\) 0 0
\(525\) 2.60108e6 1.74633e6i 0.0179753 0.0120684i
\(526\) 0 0
\(527\) 7.75221e7i 0.529656i
\(528\) 0 0
\(529\) −1.37957e8 −0.931914
\(530\) 0 0
\(531\) 2.68795e7 6.57144e7i 0.179530 0.438912i
\(532\) 0 0
\(533\) 1.41582e8 0.935034
\(534\) 0 0
\(535\) −1.30372e8 −0.851376
\(536\) 0 0
\(537\) −1.08933e8 + 7.31363e7i −0.703457 + 0.472291i
\(538\) 0 0
\(539\) −1.07074e7 −0.0683783
\(540\) 0 0
\(541\) 1.09184e8i 0.689555i −0.938684 0.344778i \(-0.887954\pi\)
0.938684 0.344778i \(-0.112046\pi\)
\(542\) 0 0
\(543\) −1.34383e8 2.00157e8i −0.839351 1.25018i
\(544\) 0 0
\(545\) 4.79323e7i 0.296100i
\(546\) 0 0
\(547\) 2.10962e7i 0.128897i 0.997921 + 0.0644483i \(0.0205287\pi\)
−0.997921 + 0.0644483i \(0.979471\pi\)
\(548\) 0 0
\(549\) 1.44041e8 + 5.89177e7i 0.870500 + 0.356064i
\(550\) 0 0
\(551\) 3.10894e7i 0.185848i
\(552\) 0 0
\(553\) −1.49203e8 −0.882274
\(554\) 0 0
\(555\) 4.95679e7 + 7.38291e7i 0.289949 + 0.431866i
\(556\) 0 0
\(557\) −2.31350e8 −1.33876 −0.669381 0.742919i \(-0.733441\pi\)
−0.669381 + 0.742919i \(0.733441\pi\)
\(558\) 0 0
\(559\) 4.49022e8 2.57058
\(560\) 0 0
\(561\) 7.27164e6 + 1.08308e7i 0.0411854 + 0.0613439i
\(562\) 0 0
\(563\) −2.49317e8 −1.39709 −0.698547 0.715564i \(-0.746170\pi\)
−0.698547 + 0.715564i \(0.746170\pi\)
\(564\) 0 0
\(565\) 3.10996e8i 1.72429i
\(566\) 0 0
\(567\) −7.83196e7 7.69443e7i −0.429656 0.422112i
\(568\) 0 0
\(569\) 1.88477e8i 1.02311i −0.859252 0.511553i \(-0.829070\pi\)
0.859252 0.511553i \(-0.170930\pi\)
\(570\) 0 0
\(571\) 6.38897e7i 0.343181i −0.985168 0.171590i \(-0.945109\pi\)
0.985168 0.171590i \(-0.0548905\pi\)
\(572\) 0 0
\(573\) −1.18622e8 1.76682e8i −0.630522 0.939134i
\(574\) 0 0
\(575\) 9.49835e6i 0.0499625i
\(576\) 0 0
\(577\) −2.64150e8 −1.37506 −0.687531 0.726155i \(-0.741306\pi\)
−0.687531 + 0.726155i \(0.741306\pi\)
\(578\) 0 0
\(579\) 1.33943e8 8.99274e7i 0.690055 0.463294i
\(580\) 0 0
\(581\) 1.66103e6 0.00846935
\(582\) 0 0
\(583\) 756353. 0.00381697
\(584\) 0 0
\(585\) −2.89783e8 1.18531e8i −1.44745 0.592059i
\(586\) 0 0
\(587\) −6.84017e7 −0.338184 −0.169092 0.985600i \(-0.554083\pi\)
−0.169092 + 0.985600i \(0.554083\pi\)
\(588\) 0 0
\(589\) 1.73213e7i 0.0847687i
\(590\) 0 0
\(591\) −9.32704e7 + 6.26205e7i −0.451837 + 0.303357i
\(592\) 0 0
\(593\) 2.30466e7i 0.110521i −0.998472 0.0552604i \(-0.982401\pi\)
0.998472 0.0552604i \(-0.0175989\pi\)
\(594\) 0 0
\(595\) 8.57754e7i 0.407204i
\(596\) 0 0
\(597\) −2.73035e8 + 1.83312e8i −1.28320 + 0.861524i
\(598\) 0 0
\(599\) 2.25012e8i 1.04695i 0.852042 + 0.523474i \(0.175364\pi\)
−0.852042 + 0.523474i \(0.824636\pi\)
\(600\) 0 0
\(601\) −8.08740e7 −0.372551 −0.186275 0.982498i \(-0.559642\pi\)
−0.186275 + 0.982498i \(0.559642\pi\)
\(602\) 0 0
\(603\) 2.59990e8 + 1.06345e8i 1.18578 + 0.485026i
\(604\) 0 0
\(605\) −2.14925e8 −0.970556
\(606\) 0 0
\(607\) −2.86741e8 −1.28211 −0.641054 0.767496i \(-0.721502\pi\)
−0.641054 + 0.767496i \(0.721502\pi\)
\(608\) 0 0
\(609\) 1.90483e8 1.27888e8i 0.843343 0.566209i
\(610\) 0 0
\(611\) −2.12295e8 −0.930715
\(612\) 0 0
\(613\) 3.51391e8i 1.52549i 0.646699 + 0.762745i \(0.276149\pi\)
−0.646699 + 0.762745i \(0.723851\pi\)
\(614\) 0 0
\(615\) −7.47362e7 1.11316e8i −0.321296 0.478556i
\(616\) 0 0
\(617\) 3.46355e8i 1.47457i −0.675580 0.737287i \(-0.736107\pi\)
0.675580 0.737287i \(-0.263893\pi\)
\(618\) 0 0
\(619\) 3.14225e8i 1.32486i 0.749126 + 0.662428i \(0.230474\pi\)
−0.749126 + 0.662428i \(0.769526\pi\)
\(620\) 0 0
\(621\) 3.26031e8 6.71062e7i 1.36139 0.280213i
\(622\) 0 0
\(623\) 8.47902e7i 0.350656i
\(624\) 0 0
\(625\) −2.35049e8 −0.962762
\(626\) 0 0
\(627\) −1.62476e6 2.42000e6i −0.00659152 0.00981777i
\(628\) 0 0
\(629\) −9.07791e7 −0.364782
\(630\) 0 0
\(631\) −5.41176e7 −0.215402 −0.107701 0.994183i \(-0.534349\pi\)
−0.107701 + 0.994183i \(0.534349\pi\)
\(632\) 0 0
\(633\) −1.91754e8 2.85609e8i −0.756020 1.12606i
\(634\) 0 0
\(635\) 3.18101e8 1.24235
\(636\) 0 0
\(637\) 2.62333e8i 1.01493i
\(638\) 0 0
\(639\) 2.40458e8 + 9.83556e7i 0.921588 + 0.376961i
\(640\) 0 0
\(641\) 1.42947e8i 0.542751i −0.962474 0.271375i \(-0.912522\pi\)
0.962474 0.271375i \(-0.0874785\pi\)
\(642\) 0 0
\(643\) 5.21812e7i 0.196282i 0.995173 + 0.0981411i \(0.0312897\pi\)
−0.995173 + 0.0981411i \(0.968710\pi\)
\(644\) 0 0
\(645\) −2.37022e8 3.53034e8i −0.883304 1.31564i
\(646\) 0 0
\(647\) 4.37963e8i 1.61705i −0.588460 0.808526i \(-0.700266\pi\)
0.588460 0.808526i \(-0.299734\pi\)
\(648\) 0 0
\(649\) 1.39103e7 0.0508863
\(650\) 0 0
\(651\) 1.06127e8 7.12520e7i 0.384664 0.258258i
\(652\) 0 0
\(653\) −2.41321e7 −0.0866674 −0.0433337 0.999061i \(-0.513798\pi\)
−0.0433337 + 0.999061i \(0.513798\pi\)
\(654\) 0 0
\(655\) −1.12328e7 −0.0399729
\(656\) 0 0
\(657\) −3.90545e7 + 9.54798e7i −0.137713 + 0.336679i
\(658\) 0 0
\(659\) −2.76788e8 −0.967142 −0.483571 0.875305i \(-0.660661\pi\)
−0.483571 + 0.875305i \(0.660661\pi\)
\(660\) 0 0
\(661\) 3.29605e8i 1.14127i −0.821203 0.570636i \(-0.806697\pi\)
0.821203 0.570636i \(-0.193303\pi\)
\(662\) 0 0
\(663\) 2.65355e8 1.78156e8i 0.910515 0.611308i
\(664\) 0 0
\(665\) 1.91654e7i 0.0651709i
\(666\) 0 0
\(667\) 6.95584e8i 2.34408i
\(668\) 0 0
\(669\) −1.89796e8 + 1.27427e8i −0.633884 + 0.425581i
\(670\) 0 0
\(671\) 3.04902e7i 0.100924i
\(672\) 0 0
\(673\) −2.21755e8 −0.727493 −0.363746 0.931498i \(-0.618503\pi\)
−0.363746 + 0.931498i \(0.618503\pi\)
\(674\) 0 0
\(675\) −2.22872e6 1.08281e7i −0.00724677 0.0352079i
\(676\) 0 0
\(677\) 5.76656e8 1.85845 0.929225 0.369513i \(-0.120476\pi\)
0.929225 + 0.369513i \(0.120476\pi\)
\(678\) 0 0
\(679\) −3.15833e8 −1.00890
\(680\) 0 0
\(681\) −1.63629e8 + 1.09858e8i −0.518106 + 0.347850i
\(682\) 0 0
\(683\) 8.03596e7 0.252218 0.126109 0.992016i \(-0.459751\pi\)
0.126109 + 0.992016i \(0.459751\pi\)
\(684\) 0 0
\(685\) 3.07147e8i 0.955597i
\(686\) 0 0
\(687\) 2.76892e8 + 4.12418e8i 0.853965 + 1.27194i
\(688\) 0 0
\(689\) 1.85307e7i 0.0566546i
\(690\) 0 0
\(691\) 2.40157e8i 0.727884i −0.931422 0.363942i \(-0.881431\pi\)
0.931422 0.363942i \(-0.118569\pi\)
\(692\) 0 0
\(693\) 8.14369e6 1.99095e7i 0.0244693 0.0598221i
\(694\) 0 0
\(695\) 1.21372e8i 0.361547i
\(696\) 0 0
\(697\) 1.36873e8 0.404220
\(698\) 0 0
\(699\) 3.01635e8 + 4.49271e8i 0.883181 + 1.31546i
\(700\) 0 0
\(701\) 4.71751e8 1.36949 0.684744 0.728784i \(-0.259914\pi\)
0.684744 + 0.728784i \(0.259914\pi\)
\(702\) 0 0
\(703\) 2.02834e7 0.0583815
\(704\) 0 0
\(705\) 1.12063e8 + 1.66913e8i 0.319812 + 0.476346i
\(706\) 0 0
\(707\) −3.61848e7 −0.102392
\(708\) 0 0
\(709\) 3.03570e8i 0.851765i 0.904779 + 0.425882i \(0.140036\pi\)
−0.904779 + 0.425882i \(0.859964\pi\)
\(710\) 0 0
\(711\) −1.99322e8 + 4.87300e8i −0.554558 + 1.35577i
\(712\) 0 0
\(713\) 3.87542e8i 1.06918i
\(714\) 0 0
\(715\) 6.13405e7i 0.167814i
\(716\) 0 0
\(717\) 3.60741e8 + 5.37308e8i 0.978675 + 1.45769i
\(718\) 0 0
\(719\) 2.70537e8i 0.727846i −0.931429 0.363923i \(-0.881437\pi\)
0.931429 0.363923i \(-0.118563\pi\)
\(720\) 0 0
\(721\) −2.76518e8 −0.737763
\(722\) 0 0
\(723\) −1.31961e8 + 8.85967e7i −0.349164 + 0.234424i
\(724\) 0 0
\(725\) 2.31017e7 0.0606218
\(726\) 0 0
\(727\) 3.96563e8 1.03207 0.516035 0.856567i \(-0.327407\pi\)
0.516035 + 0.856567i \(0.327407\pi\)
\(728\) 0 0
\(729\) −3.55929e8 + 1.53002e8i −0.918714 + 0.394924i
\(730\) 0 0
\(731\) 4.34085e8 1.11128
\(732\) 0 0
\(733\) 1.12080e8i 0.284589i −0.989824 0.142295i \(-0.954552\pi\)
0.989824 0.142295i \(-0.0454480\pi\)
\(734\) 0 0
\(735\) 2.06254e8 1.38476e8i 0.519446 0.348749i
\(736\) 0 0
\(737\) 5.50340e7i 0.137477i
\(738\) 0 0
\(739\) 2.33774e8i 0.579245i −0.957141 0.289622i \(-0.906470\pi\)
0.957141 0.289622i \(-0.0935297\pi\)
\(740\) 0 0
\(741\) −5.92903e7 + 3.98067e7i −0.145723 + 0.0978367i
\(742\) 0 0
\(743\) 6.99167e8i 1.70457i 0.523078 + 0.852285i \(0.324783\pi\)
−0.523078 + 0.852285i \(0.675217\pi\)
\(744\) 0 0
\(745\) 5.95175e8 1.43938
\(746\) 0 0
\(747\) 2.21899e6 5.42495e6i 0.00532346 0.0130147i
\(748\) 0 0
\(749\) −2.19452e8 −0.522269
\(750\) 0 0
\(751\) −5.11140e8 −1.20676 −0.603379 0.797455i \(-0.706179\pi\)
−0.603379 + 0.797455i \(0.706179\pi\)
\(752\) 0 0
\(753\) 6.29413e8 4.22579e8i 1.47418 0.989745i
\(754\) 0 0
\(755\) −4.45948e8 −1.03620
\(756\) 0 0
\(757\) 5.13325e8i 1.18333i 0.806185 + 0.591664i \(0.201529\pi\)
−0.806185 + 0.591664i \(0.798471\pi\)
\(758\) 0 0
\(759\) 3.63517e7 + 5.41443e7i 0.0831380 + 0.123830i
\(760\) 0 0
\(761\) 9.53837e7i 0.216431i 0.994127 + 0.108216i \(0.0345137\pi\)
−0.994127 + 0.108216i \(0.965486\pi\)
\(762\) 0 0
\(763\) 8.06835e7i 0.181640i
\(764\) 0 0
\(765\) −2.80143e8 1.14588e8i −0.625742 0.255950i
\(766\) 0 0
\(767\) 3.40803e8i 0.755296i
\(768\) 0 0
\(769\) −1.74508e8 −0.383740 −0.191870 0.981420i \(-0.561455\pi\)
−0.191870 + 0.981420i \(0.561455\pi\)
\(770\) 0 0
\(771\) −2.44457e8 3.64107e8i −0.533382 0.794449i
\(772\) 0 0
\(773\) −4.01318e8 −0.868860 −0.434430 0.900706i \(-0.643050\pi\)
−0.434430 + 0.900706i \(0.643050\pi\)
\(774\) 0 0
\(775\) 1.28710e7 0.0276507
\(776\) 0 0
\(777\) 8.34367e7 + 1.24275e8i 0.177866 + 0.264924i
\(778\) 0 0
\(779\) −3.05825e7 −0.0646934
\(780\) 0 0
\(781\) 5.08995e7i 0.106847i
\(782\) 0 0
\(783\) −1.63214e8 7.92965e8i −0.339995 1.65184i
\(784\) 0 0
\(785\) 5.54077e8i 1.14541i
\(786\) 0 0
\(787\) 7.87876e7i 0.161634i 0.996729 + 0.0808172i \(0.0257530\pi\)
−0.996729 + 0.0808172i \(0.974247\pi\)
\(788\) 0 0
\(789\) 8.61875e6 + 1.28372e7i 0.0175474 + 0.0261361i