Properties

Label 384.7.h.e.65.1
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: \(x^{8} - 172 x^{6} + 13179 x^{4} - 522628 x^{2} + 8755681\)
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 65.1
Root \(-6.86097 + 3.28347i\) of defining polynomial
Character \(\chi\) \(=\) 384.65
Dual form 384.7.h.e.65.3

$q$-expansion

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

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 \(-0.663343\pi\)
−0.490931 + 0.871198i \(0.663343\pi\)
\(6\) 0 0
\(7\) −206.594 −0.602315 −0.301157 0.953574i \(-0.597373\pi\)
−0.301157 + 0.953574i \(0.597373\pi\)
\(8\) 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 \(0.111876\pi\)
−0.938868 + 0.344277i \(0.888124\pi\)
\(18\) 0 0
\(19\) 755.858i 0.110200i −0.998481 0.0550998i \(-0.982452\pi\)
0.998481 0.0550998i \(-0.0175477\pi\)
\(20\) 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 \(-0.180648\pi\)
0.843235 + 0.537546i \(0.180648\pi\)
\(30\) 0 0
\(31\) 22916.1 0.769229 0.384615 0.923077i \(-0.374334\pi\)
0.384615 + 0.923077i \(0.374334\pi\)
\(32\) 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 \(-0.905170\pi\)
0.955950 0.293528i \(-0.0948296\pi\)
\(42\) 0 0
\(43\) 128319.i 1.61393i −0.590599 0.806965i \(-0.701108\pi\)
0.590599 0.806965i \(-0.298892\pi\)
\(44\) 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 \(-0.505661\pi\)
−0.0177852 + 0.999842i \(0.505661\pi\)
\(54\) 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 \(-0.778697\pi\)
0.767898 0.640572i \(-0.221303\pi\)
\(68\) 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 \(-0.238399\pi\)
0.732403 + 0.680871i \(0.238399\pi\)
\(80\) 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 \(-0.905982\pi\)
0.956695 0.291091i \(-0.0940182\pi\)
\(90\) 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 \(-0.472911\pi\)
0.0849992 + 0.996381i \(0.472911\pi\)
\(102\) 0 0
\(103\) 1.33846e6 1.22488 0.612440 0.790517i \(-0.290188\pi\)
0.612440 + 0.790517i \(0.290188\pi\)
\(104\) 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 \(0.341169\pi\)
−0.478533 + 0.878070i \(0.658831\pi\)
\(114\) 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 \(-0.718032\pi\)
−0.632649 + 0.774439i \(0.718032\pi\)
\(128\) 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 \(0.161772\pi\)
−0.873611 + 0.486624i \(0.838228\pi\)
\(138\) 0 0
\(139\) 988914.i 0.368226i 0.982905 + 0.184113i \(0.0589412\pi\)
−0.982905 + 0.184113i \(0.941059\pi\)
\(140\) 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 \(-0.761873\pi\)
−0.732985 + 0.680245i \(0.761873\pi\)
\(150\) 0 0
\(151\) 3.63349e6 1.05534 0.527671 0.849449i \(-0.323065\pi\)
0.527671 + 0.849449i \(0.323065\pi\)
\(152\) 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 \(-0.773817\pi\)
0.757987 0.652269i \(-0.226183\pi\)
\(164\) 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 \(-0.551434\pi\)
−0.160881 + 0.986974i \(0.551434\pi\)
\(174\) 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 \(-0.587722\pi\)
−0.272113 + 0.962265i \(0.587722\pi\)
\(198\) 0 0
\(199\) −1.21801e7 −1.54558 −0.772792 0.634660i \(-0.781140\pi\)
−0.772792 + 0.634660i \(0.781140\pi\)
\(200\) 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 \(-0.762780\pi\)
0.734919 0.678154i \(-0.237220\pi\)
\(212\) 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 \(-0.624678\pi\)
−0.381749 + 0.924266i \(0.624678\pi\)
\(224\) 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 \(0.291074\pi\)
−0.610237 + 0.792219i \(0.708926\pi\)
\(234\) 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 \(-0.841200\pi\)
0.878116 0.478447i \(-0.158800\pi\)
\(258\) 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 \(-0.364943\pi\)
0.411679 + 0.911329i \(0.364943\pi\)
\(270\) 0 0
\(271\) 2.21330e7 1.11207 0.556035 0.831159i \(-0.312322\pi\)
0.556035 + 0.831159i \(0.312322\pi\)
\(272\) 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 \(-0.816046\pi\)
0.837607 0.546274i \(-0.183954\pi\)
\(282\) 0 0
\(283\) 2.32930e7i 1.02770i 0.857880 + 0.513850i \(0.171781\pi\)
−0.857880 + 0.513850i \(0.828219\pi\)
\(284\) 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 \(-0.577474\pi\)
−0.240996 + 0.970526i \(0.577474\pi\)
\(294\) 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 \(-0.942045\pi\)
0.983471 0.181068i \(-0.0579555\pi\)
\(308\) 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 \(-0.798184\pi\)
−0.805651 + 0.592390i \(0.798184\pi\)
\(318\) 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 \(0.258398\pi\)
−0.688207 + 0.725515i \(0.741602\pi\)
\(332\) 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 \(0.0673379\pi\)
−0.977707 + 0.209974i \(0.932662\pi\)
\(354\) 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 \(-0.522184\pi\)
−0.0696366 + 0.997572i \(0.522184\pi\)
\(368\) 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 \(-0.955697\pi\)
0.990330 0.138734i \(-0.0443032\pi\)
\(380\) 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 \(-0.411941\pi\)
0.273130 + 0.961977i \(0.411941\pi\)
\(390\) 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 \(-0.930664\pi\)
0.976370 0.216108i \(-0.0693362\pi\)
\(402\) 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 \(-0.576448\pi\)
−0.237866 + 0.971298i \(0.576448\pi\)
\(440\) 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 \(0.236162\pi\)
−0.737170 + 0.675707i \(0.763838\pi\)
\(450\) 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 \(-0.566790\pi\)
−0.208292 + 0.978067i \(0.566790\pi\)
\(462\) 0 0
\(463\) 3.22650e7 0.325079 0.162540 0.986702i \(-0.448031\pi\)
0.162540 + 0.986702i \(0.448031\pi\)
\(464\) 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 \(-0.805208\pi\)
−0.818525 + 0.574471i \(0.805208\pi\)
\(488\) 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 \(0.246178\pi\)
−0.715546 + 0.698566i \(0.753822\pi\)
\(500\) 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 \(-0.722305\pi\)
−0.642987 + 0.765877i \(0.722305\pi\)
\(510\) 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 \(0.245068\pi\)
−0.717977 + 0.696067i \(0.754932\pi\)
\(522\) 0 0
\(523\) 1.70811e8i 1.19402i 0.802235 + 0.597008i \(0.203644\pi\)
−0.802235 + 0.597008i \(0.796356\pi\)
\(524\) 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 \(-0.979471\pi\)
0.997921 0.0644483i \(-0.0205287\pi\)
\(548\) 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 \(-0.266559\pi\)
0.669381 + 0.742919i \(0.266559\pi\)
\(558\) 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 \(0.170930\pi\)
−0.859252 + 0.511553i \(0.829070\pi\)
\(570\) 0 0
\(571\) 6.38897e7i 0.343181i 0.985168 + 0.171590i \(0.0548905\pi\)
−0.985168 + 0.171590i \(0.945109\pi\)
\(572\) 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 \(0.0175989\pi\)
−0.998472 + 0.0552604i \(0.982401\pi\)
\(594\) 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 \(-0.278498\pi\)
0.641054 + 0.767496i \(0.278498\pi\)
\(608\) 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 \(0.263893\pi\)
−0.675580 + 0.737287i \(0.736107\pi\)
\(618\) 0 0
\(619\) 3.14225e8i 1.32486i −0.749126 0.662428i \(-0.769526\pi\)
0.749126 0.662428i \(-0.230474\pi\)
\(620\) 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 \(-0.465651\pi\)
0.107701 + 0.994183i \(0.465651\pi\)
\(632\) 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 \(0.0874785\pi\)
−0.962474 + 0.271375i \(0.912522\pi\)
\(642\) 0 0
\(643\) 5.21812e7i 0.196282i −0.995173 0.0981411i \(-0.968710\pi\)
0.995173 0.0981411i \(-0.0312897\pi\)
\(644\) 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 \(-0.486202\pi\)
0.0433337 + 0.999061i \(0.486202\pi\)
\(654\) 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 \(-0.879524\pi\)
−0.929225 + 0.369513i \(0.879524\pi\)
\(678\) 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 \(0.118569\pi\)
−0.931422 + 0.363942i \(0.881431\pi\)
\(692\) 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 \(-0.740086\pi\)
−0.684744 + 0.728784i \(0.740086\pi\)
\(702\) 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 \(-0.672593\pi\)
−0.516035 + 0.856567i \(0.672593\pi\)
\(728\) 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 \(0.0935297\pi\)
−0.957141 + 0.289622i \(0.906470\pi\)
\(740\) 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 \(-0.293821\pi\)
0.603379 + 0.797455i \(0.293821\pi\)
\(752\) 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 \(-0.965486\pi\)
0.994127 0.108216i \(-0.0345137\pi\)
\(762\) 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 \(-0.356950\pi\)
0.434430 + 0.900706i \(0.356950\pi\)
\(774\) 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 \(-0.974247\pi\)
0.996729 0.0808172i \(-0.0257530\pi\)
\(788\) 0 0
\(789\) −8.61875e6 + 1.28372e7i −0.0175474 + 0.0261361i
\(790\) 0 0
\(791\) 5.23494e8i 1.05775i