Properties

Label 192.9.e.f.65.1
Level $192$
Weight $9$
Character 192.65
Analytic conductor $78.217$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 192.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(78.2166931317\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-14}) \)
Defining polynomial: \( x^{2} + 14 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: no (minimal twist has level 3)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 65.1
Root \(3.74166i\) of defining polynomial
Character \(\chi\) \(=\) 192.65
Dual form 192.9.e.f.65.2

$q$-expansion

\(f(q)\) \(=\) \(q+(45.0000 - 67.3498i) q^{3} +224.499i q^{5} +1750.00 q^{7} +(-2511.00 - 6061.48i) q^{9} +O(q^{10})\) \(q+(45.0000 - 67.3498i) q^{3} +224.499i q^{5} +1750.00 q^{7} +(-2511.00 - 6061.48i) q^{9} +6959.48i q^{11} -25730.0 q^{13} +(15120.0 + 10102.5i) q^{15} +74893.0i q^{17} +18938.0 q^{19} +(78750.0 - 117862. i) q^{21} +470461. i q^{23} +340225. q^{25} +(-521235. - 103651. i) q^{27} -460897. i q^{29} +351478. q^{31} +(468720. + 313177. i) q^{33} +392874. i q^{35} -1.33517e6 q^{37} +(-1.15785e6 + 1.73291e6i) q^{39} +1.87547e6i q^{41} -3.52615e6 q^{43} +(1.36080e6 - 563718. i) q^{45} +4.08104e6i q^{47} -2.70230e6 q^{49} +(5.04403e6 + 3.37019e6i) q^{51} +6.60177e6i q^{53} -1.56240e6 q^{55} +(852210. - 1.27547e6i) q^{57} +1.37149e7i q^{59} -753602. q^{61} +(-4.39425e6 - 1.06076e7i) q^{63} -5.77637e6i q^{65} +2.26889e6 q^{67} +(3.16855e7 + 2.11707e7i) q^{69} -1.70220e7i q^{71} +2.76728e7 q^{73} +(1.53101e7 - 2.29141e7i) q^{75} +1.21791e7i q^{77} +2.29810e7 q^{79} +(-3.04365e7 + 3.04408e7i) q^{81} -4.63952e7i q^{83} -1.68134e7 q^{85} +(-3.10414e7 - 2.07404e7i) q^{87} +7.26152e7i q^{89} -4.50275e7 q^{91} +(1.58165e7 - 2.36720e7i) q^{93} +4.25157e6i q^{95} +1.47271e8 q^{97} +(4.21848e7 - 1.74753e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 90 q^{3} + 3500 q^{7} - 5022 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 90 q^{3} + 3500 q^{7} - 5022 q^{9} - 51460 q^{13} + 30240 q^{15} + 37876 q^{19} + 157500 q^{21} + 680450 q^{25} - 1042470 q^{27} + 702956 q^{31} + 937440 q^{33} - 2670340 q^{37} - 2315700 q^{39} - 7052300 q^{43} + 2721600 q^{45} - 5404602 q^{49} + 10088064 q^{51} - 3124800 q^{55} + 1704420 q^{57} - 1507204 q^{61} - 8788500 q^{63} + 4537780 q^{67} + 63370944 q^{69} + 55345540 q^{73} + 30620250 q^{75} + 45961964 q^{79} - 60872958 q^{81} - 33626880 q^{85} - 62082720 q^{87} - 90055000 q^{91} + 31633020 q^{93} + 294542020 q^{97} + 84369600 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(133\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(3\) 45.0000 67.3498i 0.555556 0.831479i
\(4\) 0 0
\(5\) 224.499i 0.359199i 0.983740 + 0.179600i \(0.0574802\pi\)
−0.983740 + 0.179600i \(0.942520\pi\)
\(6\) 0 0
\(7\) 1750.00 0.728863 0.364431 0.931230i \(-0.381263\pi\)
0.364431 + 0.931230i \(0.381263\pi\)
\(8\) 0 0
\(9\) −2511.00 6061.48i −0.382716 0.923866i
\(10\) 0 0
\(11\) 6959.48i 0.475342i 0.971346 + 0.237671i \(0.0763840\pi\)
−0.971346 + 0.237671i \(0.923616\pi\)
\(12\) 0 0
\(13\) −25730.0 −0.900879 −0.450439 0.892807i \(-0.648733\pi\)
−0.450439 + 0.892807i \(0.648733\pi\)
\(14\) 0 0
\(15\) 15120.0 + 10102.5i 0.298667 + 0.199555i
\(16\) 0 0
\(17\) 74893.0i 0.896697i 0.893859 + 0.448348i \(0.147988\pi\)
−0.893859 + 0.448348i \(0.852012\pi\)
\(18\) 0 0
\(19\) 18938.0 0.145318 0.0726590 0.997357i \(-0.476852\pi\)
0.0726590 + 0.997357i \(0.476852\pi\)
\(20\) 0 0
\(21\) 78750.0 117862.i 0.404924 0.606035i
\(22\) 0 0
\(23\) 470461.i 1.68117i 0.541678 + 0.840586i \(0.317789\pi\)
−0.541678 + 0.840586i \(0.682211\pi\)
\(24\) 0 0
\(25\) 340225. 0.870976
\(26\) 0 0
\(27\) −521235. 103651.i −0.980796 0.195038i
\(28\) 0 0
\(29\) 460897.i 0.651647i −0.945431 0.325823i \(-0.894359\pi\)
0.945431 0.325823i \(-0.105641\pi\)
\(30\) 0 0
\(31\) 351478. 0.380585 0.190292 0.981727i \(-0.439056\pi\)
0.190292 + 0.981727i \(0.439056\pi\)
\(32\) 0 0
\(33\) 468720. + 313177.i 0.395237 + 0.264079i
\(34\) 0 0
\(35\) 392874.i 0.261807i
\(36\) 0 0
\(37\) −1.33517e6 −0.712409 −0.356205 0.934408i \(-0.615929\pi\)
−0.356205 + 0.934408i \(0.615929\pi\)
\(38\) 0 0
\(39\) −1.15785e6 + 1.73291e6i −0.500488 + 0.749062i
\(40\) 0 0
\(41\) 1.87547e6i 0.663704i 0.943331 + 0.331852i \(0.107673\pi\)
−0.943331 + 0.331852i \(0.892327\pi\)
\(42\) 0 0
\(43\) −3.52615e6 −1.03140 −0.515700 0.856769i \(-0.672468\pi\)
−0.515700 + 0.856769i \(0.672468\pi\)
\(44\) 0 0
\(45\) 1.36080e6 563718.i 0.331852 0.137471i
\(46\) 0 0
\(47\) 4.08104e6i 0.836333i 0.908370 + 0.418167i \(0.137327\pi\)
−0.908370 + 0.418167i \(0.862673\pi\)
\(48\) 0 0
\(49\) −2.70230e6 −0.468759
\(50\) 0 0
\(51\) 5.04403e6 + 3.37019e6i 0.745585 + 0.498165i
\(52\) 0 0
\(53\) 6.60177e6i 0.836675i 0.908292 + 0.418337i \(0.137387\pi\)
−0.908292 + 0.418337i \(0.862613\pi\)
\(54\) 0 0
\(55\) −1.56240e6 −0.170742
\(56\) 0 0
\(57\) 852210. 1.27547e6i 0.0807323 0.120829i
\(58\) 0 0
\(59\) 1.37149e7i 1.13184i 0.824461 + 0.565919i \(0.191479\pi\)
−0.824461 + 0.565919i \(0.808521\pi\)
\(60\) 0 0
\(61\) −753602. −0.0544280 −0.0272140 0.999630i \(-0.508664\pi\)
−0.0272140 + 0.999630i \(0.508664\pi\)
\(62\) 0 0
\(63\) −4.39425e6 1.06076e7i −0.278948 0.673372i
\(64\) 0 0
\(65\) 5.77637e6i 0.323595i
\(66\) 0 0
\(67\) 2.26889e6 0.112594 0.0562969 0.998414i \(-0.482071\pi\)
0.0562969 + 0.998414i \(0.482071\pi\)
\(68\) 0 0
\(69\) 3.16855e7 + 2.11707e7i 1.39786 + 0.933985i
\(70\) 0 0
\(71\) 1.70220e7i 0.669849i −0.942245 0.334925i \(-0.891289\pi\)
0.942245 0.334925i \(-0.108711\pi\)
\(72\) 0 0
\(73\) 2.76728e7 0.974454 0.487227 0.873275i \(-0.338008\pi\)
0.487227 + 0.873275i \(0.338008\pi\)
\(74\) 0 0
\(75\) 1.53101e7 2.29141e7i 0.483876 0.724199i
\(76\) 0 0
\(77\) 1.21791e7i 0.346459i
\(78\) 0 0
\(79\) 2.29810e7 0.590011 0.295006 0.955496i \(-0.404678\pi\)
0.295006 + 0.955496i \(0.404678\pi\)
\(80\) 0 0
\(81\) −3.04365e7 + 3.04408e7i −0.707057 + 0.707157i
\(82\) 0 0
\(83\) 4.63952e7i 0.977599i −0.872396 0.488799i \(-0.837435\pi\)
0.872396 0.488799i \(-0.162565\pi\)
\(84\) 0 0
\(85\) −1.68134e7 −0.322093
\(86\) 0 0
\(87\) −3.10414e7 2.07404e7i −0.541831 0.362026i
\(88\) 0 0
\(89\) 7.26152e7i 1.15736i 0.815555 + 0.578679i \(0.196432\pi\)
−0.815555 + 0.578679i \(0.803568\pi\)
\(90\) 0 0
\(91\) −4.50275e7 −0.656617
\(92\) 0 0
\(93\) 1.58165e7 2.36720e7i 0.211436 0.316448i
\(94\) 0 0
\(95\) 4.25157e6i 0.0521981i
\(96\) 0 0
\(97\) 1.47271e8 1.66353 0.831764 0.555129i \(-0.187331\pi\)
0.831764 + 0.555129i \(0.187331\pi\)
\(98\) 0 0
\(99\) 4.21848e7 1.74753e7i 0.439152 0.181921i
\(100\) 0 0
\(101\) 1.03545e8i 0.995045i 0.867451 + 0.497522i \(0.165757\pi\)
−0.867451 + 0.497522i \(0.834243\pi\)
\(102\) 0 0
\(103\) 1.66064e8 1.47545 0.737726 0.675100i \(-0.235899\pi\)
0.737726 + 0.675100i \(0.235899\pi\)
\(104\) 0 0
\(105\) 2.64600e7 + 1.76793e7i 0.217687 + 0.145448i
\(106\) 0 0
\(107\) 2.25540e7i 0.172063i −0.996292 0.0860316i \(-0.972581\pi\)
0.996292 0.0860316i \(-0.0274186\pi\)
\(108\) 0 0
\(109\) 1.09975e8 0.779091 0.389546 0.921007i \(-0.372632\pi\)
0.389546 + 0.921007i \(0.372632\pi\)
\(110\) 0 0
\(111\) −6.00826e7 + 8.99235e7i −0.395783 + 0.592354i
\(112\) 0 0
\(113\) 2.87748e8i 1.76481i 0.470490 + 0.882405i \(0.344077\pi\)
−0.470490 + 0.882405i \(0.655923\pi\)
\(114\) 0 0
\(115\) −1.05618e8 −0.603876
\(116\) 0 0
\(117\) 6.46080e7 + 1.55962e8i 0.344781 + 0.832291i
\(118\) 0 0
\(119\) 1.31063e8i 0.653569i
\(120\) 0 0
\(121\) 1.65924e8 0.774050
\(122\) 0 0
\(123\) 1.26312e8 + 8.43961e7i 0.551856 + 0.368724i
\(124\) 0 0
\(125\) 1.64075e8i 0.672053i
\(126\) 0 0
\(127\) −2.75994e8 −1.06092 −0.530462 0.847708i \(-0.677982\pi\)
−0.530462 + 0.847708i \(0.677982\pi\)
\(128\) 0 0
\(129\) −1.58677e8 + 2.37486e8i −0.573000 + 0.857588i
\(130\) 0 0
\(131\) 2.89118e8i 0.981725i 0.871237 + 0.490862i \(0.163318\pi\)
−0.871237 + 0.490862i \(0.836682\pi\)
\(132\) 0 0
\(133\) 3.31415e7 0.105917
\(134\) 0 0
\(135\) 2.32697e7 1.17017e8i 0.0700576 0.352301i
\(136\) 0 0
\(137\) 2.07562e8i 0.589205i −0.955620 0.294602i \(-0.904813\pi\)
0.955620 0.294602i \(-0.0951872\pi\)
\(138\) 0 0
\(139\) −1.42668e8 −0.382180 −0.191090 0.981573i \(-0.561202\pi\)
−0.191090 + 0.981573i \(0.561202\pi\)
\(140\) 0 0
\(141\) 2.74857e8 + 1.83647e8i 0.695394 + 0.464630i
\(142\) 0 0
\(143\) 1.79067e8i 0.428226i
\(144\) 0 0
\(145\) 1.03471e8 0.234071
\(146\) 0 0
\(147\) −1.21604e8 + 1.82000e8i −0.260422 + 0.389763i
\(148\) 0 0
\(149\) 8.19236e8i 1.66213i 0.556179 + 0.831063i \(0.312267\pi\)
−0.556179 + 0.831063i \(0.687733\pi\)
\(150\) 0 0
\(151\) −4.23861e8 −0.815296 −0.407648 0.913139i \(-0.633651\pi\)
−0.407648 + 0.913139i \(0.633651\pi\)
\(152\) 0 0
\(153\) 4.53963e8 1.88056e8i 0.828428 0.343180i
\(154\) 0 0
\(155\) 7.89066e7i 0.136706i
\(156\) 0 0
\(157\) 7.59851e8 1.25063 0.625316 0.780371i \(-0.284970\pi\)
0.625316 + 0.780371i \(0.284970\pi\)
\(158\) 0 0
\(159\) 4.44628e8 + 2.97079e8i 0.695678 + 0.464819i
\(160\) 0 0
\(161\) 8.23307e8i 1.22534i
\(162\) 0 0
\(163\) 6.68160e8 0.946520 0.473260 0.880923i \(-0.343077\pi\)
0.473260 + 0.880923i \(0.343077\pi\)
\(164\) 0 0
\(165\) −7.03080e7 + 1.05227e8i −0.0948569 + 0.141969i
\(166\) 0 0
\(167\) 1.96306e8i 0.252387i −0.992006 0.126194i \(-0.959724\pi\)
0.992006 0.126194i \(-0.0402761\pi\)
\(168\) 0 0
\(169\) −1.53698e8 −0.188417
\(170\) 0 0
\(171\) −4.75533e7 1.14792e8i −0.0556156 0.134254i
\(172\) 0 0
\(173\) 1.02319e9i 1.14228i −0.820852 0.571141i \(-0.806501\pi\)
0.820852 0.571141i \(-0.193499\pi\)
\(174\) 0 0
\(175\) 5.95394e8 0.634822
\(176\) 0 0
\(177\) 9.23696e8 + 6.17170e8i 0.941100 + 0.628799i
\(178\) 0 0
\(179\) 1.28895e9i 1.25552i −0.778408 0.627759i \(-0.783972\pi\)
0.778408 0.627759i \(-0.216028\pi\)
\(180\) 0 0
\(181\) −4.71707e8 −0.439499 −0.219749 0.975556i \(-0.570524\pi\)
−0.219749 + 0.975556i \(0.570524\pi\)
\(182\) 0 0
\(183\) −3.39121e7 + 5.07550e7i −0.0302378 + 0.0452558i
\(184\) 0 0
\(185\) 2.99745e8i 0.255897i
\(186\) 0 0
\(187\) −5.21217e8 −0.426238
\(188\) 0 0
\(189\) −9.12161e8 1.81390e8i −0.714866 0.142156i
\(190\) 0 0
\(191\) 1.61787e8i 0.121565i 0.998151 + 0.0607827i \(0.0193597\pi\)
−0.998151 + 0.0607827i \(0.980640\pi\)
\(192\) 0 0
\(193\) −1.58840e9 −1.14480 −0.572401 0.819974i \(-0.693988\pi\)
−0.572401 + 0.819974i \(0.693988\pi\)
\(194\) 0 0
\(195\) −3.89038e8 2.59937e8i −0.269062 0.179775i
\(196\) 0 0
\(197\) 5.37769e8i 0.357052i 0.983935 + 0.178526i \(0.0571328\pi\)
−0.983935 + 0.178526i \(0.942867\pi\)
\(198\) 0 0
\(199\) −6.47586e8 −0.412938 −0.206469 0.978453i \(-0.566197\pi\)
−0.206469 + 0.978453i \(0.566197\pi\)
\(200\) 0 0
\(201\) 1.02100e8 1.52809e8i 0.0625521 0.0936194i
\(202\) 0 0
\(203\) 8.06570e8i 0.474961i
\(204\) 0 0
\(205\) −4.21042e8 −0.238402
\(206\) 0 0
\(207\) 2.85169e9 1.18133e9i 1.55318 0.643412i
\(208\) 0 0
\(209\) 1.31799e8i 0.0690758i
\(210\) 0 0
\(211\) 5.81104e7 0.0293173 0.0146586 0.999893i \(-0.495334\pi\)
0.0146586 + 0.999893i \(0.495334\pi\)
\(212\) 0 0
\(213\) −1.14643e9 7.65990e8i −0.556966 0.372139i
\(214\) 0 0
\(215\) 7.91619e8i 0.370478i
\(216\) 0 0
\(217\) 6.15086e8 0.277394
\(218\) 0 0
\(219\) 1.24527e9 1.86376e9i 0.541363 0.810238i
\(220\) 0 0
\(221\) 1.92700e9i 0.807815i
\(222\) 0 0
\(223\) −4.40200e9 −1.78004 −0.890021 0.455920i \(-0.849310\pi\)
−0.890021 + 0.455920i \(0.849310\pi\)
\(224\) 0 0
\(225\) −8.54305e8 2.06227e9i −0.333336 0.804665i
\(226\) 0 0
\(227\) 3.53592e9i 1.33168i 0.746095 + 0.665839i \(0.231926\pi\)
−0.746095 + 0.665839i \(0.768074\pi\)
\(228\) 0 0
\(229\) 1.86569e9 0.678420 0.339210 0.940711i \(-0.389840\pi\)
0.339210 + 0.940711i \(0.389840\pi\)
\(230\) 0 0
\(231\) 8.20260e8 + 5.48059e8i 0.288074 + 0.192477i
\(232\) 0 0
\(233\) 2.72132e9i 0.923328i −0.887055 0.461664i \(-0.847253\pi\)
0.887055 0.461664i \(-0.152747\pi\)
\(234\) 0 0
\(235\) −9.16191e8 −0.300410
\(236\) 0 0
\(237\) 1.03414e9 1.54777e9i 0.327784 0.490582i
\(238\) 0 0
\(239\) 2.27461e9i 0.697132i 0.937284 + 0.348566i \(0.113331\pi\)
−0.937284 + 0.348566i \(0.886669\pi\)
\(240\) 0 0
\(241\) −1.74667e9 −0.517778 −0.258889 0.965907i \(-0.583356\pi\)
−0.258889 + 0.965907i \(0.583356\pi\)
\(242\) 0 0
\(243\) 6.80540e8 + 3.41973e9i 0.195177 + 0.980768i
\(244\) 0 0
\(245\) 6.06665e8i 0.168378i
\(246\) 0 0
\(247\) −4.87275e8 −0.130914
\(248\) 0 0
\(249\) −3.12471e9 2.08778e9i −0.812853 0.543110i
\(250\) 0 0
\(251\) 1.37549e9i 0.346547i 0.984874 + 0.173274i \(0.0554345\pi\)
−0.984874 + 0.173274i \(0.944566\pi\)
\(252\) 0 0
\(253\) −3.27417e9 −0.799132
\(254\) 0 0
\(255\) −7.56605e8 + 1.13238e9i −0.178940 + 0.267813i
\(256\) 0 0
\(257\) 7.93672e9i 1.81932i −0.415356 0.909659i \(-0.636343\pi\)
0.415356 0.909659i \(-0.363657\pi\)
\(258\) 0 0
\(259\) −2.33655e9 −0.519249
\(260\) 0 0
\(261\) −2.79372e9 + 1.15731e9i −0.602034 + 0.249396i
\(262\) 0 0
\(263\) 3.22555e8i 0.0674187i −0.999432 0.0337093i \(-0.989268\pi\)
0.999432 0.0337093i \(-0.0107320\pi\)
\(264\) 0 0
\(265\) −1.48209e9 −0.300533
\(266\) 0 0
\(267\) 4.89062e9 + 3.26769e9i 0.962319 + 0.642977i
\(268\) 0 0
\(269\) 3.47314e9i 0.663304i −0.943402 0.331652i \(-0.892394\pi\)
0.943402 0.331652i \(-0.107606\pi\)
\(270\) 0 0
\(271\) 1.44216e9 0.267385 0.133693 0.991023i \(-0.457317\pi\)
0.133693 + 0.991023i \(0.457317\pi\)
\(272\) 0 0
\(273\) −2.02624e9 + 3.03259e9i −0.364787 + 0.545964i
\(274\) 0 0
\(275\) 2.36779e9i 0.414012i
\(276\) 0 0
\(277\) −3.38046e9 −0.574192 −0.287096 0.957902i \(-0.592690\pi\)
−0.287096 + 0.957902i \(0.592690\pi\)
\(278\) 0 0
\(279\) −8.82561e8 2.13048e9i −0.145656 0.351609i
\(280\) 0 0
\(281\) 4.02262e9i 0.645184i 0.946538 + 0.322592i \(0.104554\pi\)
−0.946538 + 0.322592i \(0.895446\pi\)
\(282\) 0 0
\(283\) −1.04253e10 −1.62533 −0.812666 0.582730i \(-0.801984\pi\)
−0.812666 + 0.582730i \(0.801984\pi\)
\(284\) 0 0
\(285\) 2.86343e8 + 1.91321e8i 0.0434017 + 0.0289990i
\(286\) 0 0
\(287\) 3.28207e9i 0.483749i
\(288\) 0 0
\(289\) 1.36679e9 0.195935
\(290\) 0 0
\(291\) 6.62720e9 9.91868e9i 0.924183 1.38319i
\(292\) 0 0
\(293\) 1.03927e10i 1.41012i −0.709146 0.705061i \(-0.750919\pi\)
0.709146 0.705061i \(-0.249081\pi\)
\(294\) 0 0
\(295\) −3.07899e9 −0.406555
\(296\) 0 0
\(297\) 7.21360e8 3.62753e9i 0.0927099 0.466213i
\(298\) 0 0
\(299\) 1.21050e10i 1.51453i
\(300\) 0 0
\(301\) −6.17076e9 −0.751749
\(302\) 0 0
\(303\) 6.97372e9 + 4.65951e9i 0.827359 + 0.552803i
\(304\) 0 0
\(305\) 1.69183e8i 0.0195505i
\(306\) 0 0
\(307\) −2.99309e9 −0.336951 −0.168476 0.985706i \(-0.553884\pi\)
−0.168476 + 0.985706i \(0.553884\pi\)
\(308\) 0 0
\(309\) 7.47286e9 1.11843e10i 0.819696 1.22681i
\(310\) 0 0
\(311\) 6.44832e9i 0.689295i −0.938732 0.344647i \(-0.887998\pi\)
0.938732 0.344647i \(-0.112002\pi\)
\(312\) 0 0
\(313\) 3.27737e7 0.00341467 0.00170733 0.999999i \(-0.499457\pi\)
0.00170733 + 0.999999i \(0.499457\pi\)
\(314\) 0 0
\(315\) 2.38140e9 9.86507e8i 0.241875 0.100198i
\(316\) 0 0
\(317\) 1.17797e10i 1.16653i 0.812282 + 0.583264i \(0.198225\pi\)
−0.812282 + 0.583264i \(0.801775\pi\)
\(318\) 0 0
\(319\) 3.20761e9 0.309755
\(320\) 0 0
\(321\) −1.51901e9 1.01493e9i −0.143067 0.0955907i
\(322\) 0 0
\(323\) 1.41832e9i 0.130306i
\(324\) 0 0
\(325\) −8.75399e9 −0.784644
\(326\) 0 0
\(327\) 4.94888e9 7.40680e9i 0.432829 0.647798i
\(328\) 0 0
\(329\) 7.14182e9i 0.609573i
\(330\) 0 0
\(331\) −1.20100e10 −1.00053 −0.500265 0.865872i \(-0.666764\pi\)
−0.500265 + 0.865872i \(0.666764\pi\)
\(332\) 0 0
\(333\) 3.35261e9 + 8.09311e9i 0.272651 + 0.658171i
\(334\) 0 0
\(335\) 5.09365e8i 0.0404436i
\(336\) 0 0
\(337\) 1.59214e10 1.23441 0.617207 0.786801i \(-0.288264\pi\)
0.617207 + 0.786801i \(0.288264\pi\)
\(338\) 0 0
\(339\) 1.93798e10 + 1.29486e10i 1.46740 + 0.980451i
\(340\) 0 0
\(341\) 2.44611e9i 0.180908i
\(342\) 0 0
\(343\) −1.48174e10 −1.07052
\(344\) 0 0
\(345\) −4.75282e9 + 7.11337e9i −0.335487 + 0.502110i
\(346\) 0 0
\(347\) 4.94792e9i 0.341275i −0.985334 0.170638i \(-0.945417\pi\)
0.985334 0.170638i \(-0.0545828\pi\)
\(348\) 0 0
\(349\) 7.29567e9 0.491772 0.245886 0.969299i \(-0.420921\pi\)
0.245886 + 0.969299i \(0.420921\pi\)
\(350\) 0 0
\(351\) 1.34114e10 + 2.66695e9i 0.883578 + 0.175706i
\(352\) 0 0
\(353\) 6.93875e9i 0.446871i −0.974719 0.223436i \(-0.928273\pi\)
0.974719 0.223436i \(-0.0717272\pi\)
\(354\) 0 0
\(355\) 3.82143e9 0.240609
\(356\) 0 0
\(357\) 8.82706e9 + 5.89782e9i 0.543429 + 0.363094i
\(358\) 0 0
\(359\) 1.60096e10i 0.963838i −0.876216 0.481919i \(-0.839940\pi\)
0.876216 0.481919i \(-0.160060\pi\)
\(360\) 0 0
\(361\) −1.66249e10 −0.978883
\(362\) 0 0
\(363\) 7.46660e9 1.11750e10i 0.430028 0.643607i
\(364\) 0 0
\(365\) 6.21252e9i 0.350023i
\(366\) 0 0
\(367\) −1.36364e10 −0.751686 −0.375843 0.926683i \(-0.622647\pi\)
−0.375843 + 0.926683i \(0.622647\pi\)
\(368\) 0 0
\(369\) 1.13681e10 4.70930e9i 0.613173 0.254010i
\(370\) 0 0
\(371\) 1.15531e10i 0.609821i
\(372\) 0 0
\(373\) 2.44062e10 1.26085 0.630427 0.776248i \(-0.282880\pi\)
0.630427 + 0.776248i \(0.282880\pi\)
\(374\) 0 0
\(375\) 1.10505e10 + 7.38339e9i 0.558798 + 0.373363i
\(376\) 0 0
\(377\) 1.18589e10i 0.587055i
\(378\) 0 0
\(379\) −1.98392e10 −0.961542 −0.480771 0.876846i \(-0.659643\pi\)
−0.480771 + 0.876846i \(0.659643\pi\)
\(380\) 0 0
\(381\) −1.24197e10 + 1.85881e10i −0.589403 + 0.882137i
\(382\) 0 0
\(383\) 1.51133e10i 0.702366i 0.936307 + 0.351183i \(0.114220\pi\)
−0.936307 + 0.351183i \(0.885780\pi\)
\(384\) 0 0
\(385\) −2.73420e9 −0.124448
\(386\) 0 0
\(387\) 8.85416e9 + 2.13737e10i 0.394733 + 0.952875i
\(388\) 0 0
\(389\) 1.79991e10i 0.786056i 0.919527 + 0.393028i \(0.128572\pi\)
−0.919527 + 0.393028i \(0.871428\pi\)
\(390\) 0 0
\(391\) −3.52342e10 −1.50750
\(392\) 0 0
\(393\) 1.94720e10 + 1.30103e10i 0.816284 + 0.545403i
\(394\) 0 0
\(395\) 5.15922e9i 0.211931i
\(396\) 0 0
\(397\) 2.35673e10 0.948739 0.474370 0.880326i \(-0.342676\pi\)
0.474370 + 0.880326i \(0.342676\pi\)
\(398\) 0 0
\(399\) 1.49137e9 2.23207e9i 0.0588428 0.0880678i
\(400\) 0 0
\(401\) 1.37692e10i 0.532515i 0.963902 + 0.266257i \(0.0857871\pi\)
−0.963902 + 0.266257i \(0.914213\pi\)
\(402\) 0 0
\(403\) −9.04353e9 −0.342861
\(404\) 0 0
\(405\) −6.83394e9 6.83297e9i −0.254010 0.253974i
\(406\) 0 0
\(407\) 9.29209e9i 0.338638i
\(408\) 0 0
\(409\) 3.58480e10 1.28107 0.640533 0.767931i \(-0.278714\pi\)
0.640533 + 0.767931i \(0.278714\pi\)
\(410\) 0 0
\(411\) −1.39793e10 9.34031e9i −0.489912 0.327336i
\(412\) 0 0
\(413\) 2.40011e10i 0.824955i
\(414\) 0 0
\(415\) 1.04157e10 0.351153
\(416\) 0 0
\(417\) −6.42007e9 + 9.60868e9i −0.212322 + 0.317775i
\(418\) 0 0
\(419\) 2.23996e10i 0.726750i 0.931643 + 0.363375i \(0.118376\pi\)
−0.931643 + 0.363375i \(0.881624\pi\)
\(420\) 0 0
\(421\) 1.49535e10 0.476008 0.238004 0.971264i \(-0.423507\pi\)
0.238004 + 0.971264i \(0.423507\pi\)
\(422\) 0 0
\(423\) 2.47372e10 1.02475e10i 0.772660 0.320078i
\(424\) 0 0
\(425\) 2.54805e10i 0.781001i
\(426\) 0 0
\(427\) −1.31880e9 −0.0396706
\(428\) 0 0
\(429\) −1.20602e10 8.05804e9i −0.356061 0.237903i
\(430\) 0 0
\(431\) 6.40436e10i 1.85595i 0.372640 + 0.927976i \(0.378453\pi\)
−0.372640 + 0.927976i \(0.621547\pi\)
\(432\) 0 0
\(433\) −5.22954e9 −0.148769 −0.0743843 0.997230i \(-0.523699\pi\)
−0.0743843 + 0.997230i \(0.523699\pi\)
\(434\) 0 0
\(435\) 4.65620e9 6.96877e9i 0.130039 0.194625i
\(436\) 0 0
\(437\) 8.90959e9i 0.244305i
\(438\) 0 0
\(439\) −4.34801e10 −1.17066 −0.585332 0.810793i \(-0.699036\pi\)
−0.585332 + 0.810793i \(0.699036\pi\)
\(440\) 0 0
\(441\) 6.78548e9 + 1.63800e10i 0.179402 + 0.433070i
\(442\) 0 0
\(443\) 3.78737e10i 0.983383i −0.870770 0.491691i \(-0.836379\pi\)
0.870770 0.491691i \(-0.163621\pi\)
\(444\) 0 0
\(445\) −1.63021e10 −0.415722
\(446\) 0 0
\(447\) 5.51754e10 + 3.68656e10i 1.38202 + 0.923403i
\(448\) 0 0
\(449\) 2.95505e10i 0.727076i 0.931579 + 0.363538i \(0.118431\pi\)
−0.931579 + 0.363538i \(0.881569\pi\)
\(450\) 0 0
\(451\) −1.30523e10 −0.315486
\(452\) 0 0
\(453\) −1.90737e10 + 2.85469e10i −0.452942 + 0.677902i
\(454\) 0 0
\(455\) 1.01086e10i 0.235856i
\(456\) 0 0
\(457\) −2.02181e10 −0.463529 −0.231764 0.972772i \(-0.574450\pi\)
−0.231764 + 0.972772i \(0.574450\pi\)
\(458\) 0 0
\(459\) 7.76277e9 3.90369e10i 0.174890 0.879476i
\(460\) 0 0
\(461\) 7.01826e10i 1.55391i −0.629556 0.776955i \(-0.716763\pi\)
0.629556 0.776955i \(-0.283237\pi\)
\(462\) 0 0
\(463\) −4.16009e9 −0.0905271 −0.0452635 0.998975i \(-0.514413\pi\)
−0.0452635 + 0.998975i \(0.514413\pi\)
\(464\) 0 0
\(465\) 5.31435e9 + 3.55080e9i 0.113668 + 0.0759476i
\(466\) 0 0
\(467\) 2.88138e10i 0.605806i 0.953021 + 0.302903i \(0.0979558\pi\)
−0.953021 + 0.302903i \(0.902044\pi\)
\(468\) 0 0
\(469\) 3.97056e9 0.0820654
\(470\) 0 0
\(471\) 3.41933e10 5.11758e10i 0.694796 1.03988i
\(472\) 0 0
\(473\) 2.45402e10i 0.490268i
\(474\) 0 0
\(475\) 6.44318e9 0.126569
\(476\) 0 0
\(477\) 4.00165e10 1.65770e10i 0.772975 0.320209i
\(478\) 0 0
\(479\) 4.47149e10i 0.849395i −0.905335 0.424698i \(-0.860380\pi\)
0.905335 0.424698i \(-0.139620\pi\)
\(480\) 0 0
\(481\) 3.43539e10 0.641795
\(482\) 0 0
\(483\) 5.54496e10 + 3.70488e10i 1.01885 + 0.680747i
\(484\) 0 0
\(485\) 3.30623e10i 0.597538i
\(486\) 0 0
\(487\) −5.72836e10 −1.01839 −0.509195 0.860651i \(-0.670057\pi\)
−0.509195 + 0.860651i \(0.670057\pi\)
\(488\) 0 0
\(489\) 3.00672e10 4.50005e10i 0.525845 0.787012i
\(490\) 0 0
\(491\) 7.25262e10i 1.24787i −0.781477 0.623934i \(-0.785533\pi\)
0.781477 0.623934i \(-0.214467\pi\)
\(492\) 0 0
\(493\) 3.45180e10 0.584330
\(494\) 0 0
\(495\) 3.92319e9 + 9.47046e9i 0.0653459 + 0.157743i
\(496\) 0 0
\(497\) 2.97885e10i 0.488228i
\(498\) 0 0
\(499\) −2.64368e10 −0.426389 −0.213195 0.977010i \(-0.568387\pi\)
−0.213195 + 0.977010i \(0.568387\pi\)
\(500\) 0 0
\(501\) −1.32212e10 8.83376e9i −0.209855 0.140215i
\(502\) 0 0
\(503\) 7.52828e10i 1.17604i −0.808845 0.588022i \(-0.799907\pi\)
0.808845 0.588022i \(-0.200093\pi\)
\(504\) 0 0
\(505\) −2.32457e10 −0.357419
\(506\) 0 0
\(507\) −6.91640e9 + 1.03515e10i −0.104676 + 0.156665i
\(508\) 0 0
\(509\) 6.45184e10i 0.961197i 0.876941 + 0.480599i \(0.159581\pi\)
−0.876941 + 0.480599i \(0.840419\pi\)
\(510\) 0 0
\(511\) 4.84273e10 0.710243
\(512\) 0 0
\(513\) −9.87115e9 1.96295e9i −0.142527 0.0283426i
\(514\) 0 0
\(515\) 3.72812e10i 0.529981i
\(516\) 0 0
\(517\) −2.84019e10 −0.397544
\(518\) 0 0
\(519\) −6.89119e10 4.60437e10i −0.949783 0.634601i
\(520\) 0 0
\(521\) 7.65146e10i 1.03847i −0.854632 0.519235i \(-0.826217\pi\)
0.854632 0.519235i \(-0.173783\pi\)
\(522\) 0 0
\(523\) −8.46771e10 −1.13177 −0.565886 0.824483i \(-0.691466\pi\)
−0.565886 + 0.824483i \(0.691466\pi\)
\(524\) 0 0
\(525\) 2.67927e10 4.00997e10i 0.352679 0.527842i
\(526\) 0 0
\(527\) 2.63232e10i 0.341269i
\(528\) 0 0
\(529\) −1.43023e11 −1.82634
\(530\) 0 0
\(531\) 8.31326e10 3.44381e10i 1.04567 0.433173i
\(532\) 0 0
\(533\) 4.82558e10i 0.597917i
\(534\) 0 0
\(535\) 5.06336e9 0.0618050
\(536\) 0 0
\(537\) −8.68104e10 5.80026e10i −1.04394 0.697510i
\(538\) 0 0
\(539\) 1.88066e10i 0.222821i
\(540\) 0 0
\(541\) −1.43470e11 −1.67483 −0.837415 0.546568i \(-0.815934\pi\)
−0.837415 + 0.546568i \(0.815934\pi\)
\(542\) 0 0
\(543\) −2.12268e10 + 3.17694e10i −0.244166 + 0.365434i
\(544\) 0 0
\(545\) 2.46893e10i 0.279849i
\(546\) 0 0
\(547\) 1.64171e11 1.83378 0.916892 0.399134i \(-0.130689\pi\)
0.916892 + 0.399134i \(0.130689\pi\)
\(548\) 0 0
\(549\) 1.89229e9 + 4.56795e9i 0.0208305 + 0.0502842i
\(550\) 0 0
\(551\) 8.72847e9i 0.0946961i
\(552\) 0 0
\(553\) 4.02167e10 0.430037
\(554\) 0 0
\(555\) −2.01878e10 1.34885e10i −0.212773 0.142165i
\(556\) 0 0
\(557\) 1.54420e11i 1.60429i −0.597130 0.802145i \(-0.703692\pi\)
0.597130 0.802145i \(-0.296308\pi\)
\(558\) 0 0
\(559\) 9.07278e10 0.929166
\(560\) 0 0
\(561\) −2.34547e10 + 3.51039e10i −0.236799 + 0.354408i
\(562\) 0 0
\(563\) 1.54622e11i 1.53900i 0.638646 + 0.769500i \(0.279495\pi\)
−0.638646 + 0.769500i \(0.720505\pi\)
\(564\) 0 0
\(565\) −6.45992e10 −0.633919
\(566\) 0 0
\(567\) −5.32638e10 + 5.32714e10i −0.515348 + 0.515420i
\(568\) 0 0
\(569\) 1.15380e11i 1.10073i −0.834925 0.550364i \(-0.814489\pi\)
0.834925 0.550364i \(-0.185511\pi\)
\(570\) 0 0
\(571\) −1.63410e11 −1.53722 −0.768608 0.639720i \(-0.779050\pi\)
−0.768608 + 0.639720i \(0.779050\pi\)
\(572\) 0 0
\(573\) 1.08963e10 + 7.28041e9i 0.101079 + 0.0675363i
\(574\) 0 0
\(575\) 1.60063e11i 1.46426i
\(576\) 0 0
\(577\) 7.42282e10 0.669678 0.334839 0.942275i \(-0.391318\pi\)
0.334839 + 0.942275i \(0.391318\pi\)
\(578\) 0 0
\(579\) −7.14779e10 + 1.06978e11i −0.636001 + 0.951879i
\(580\) 0 0
\(581\) 8.11916e10i 0.712535i
\(582\) 0 0
\(583\) −4.59449e10 −0.397707
\(584\) 0 0
\(585\) −3.50134e10 + 1.45045e10i −0.298958 + 0.123845i
\(586\) 0 0
\(587\) 6.72877e10i 0.566739i −0.959011 0.283369i \(-0.908548\pi\)
0.959011 0.283369i \(-0.0914523\pi\)
\(588\) 0 0
\(589\) 6.65629e9 0.0553059
\(590\) 0 0
\(591\) 3.62187e10 + 2.41996e10i 0.296881 + 0.198362i
\(592\) 0 0
\(593\) 2.36444e10i 0.191210i −0.995419 0.0956048i \(-0.969521\pi\)
0.995419 0.0956048i \(-0.0304785\pi\)
\(594\) 0 0
\(595\) −2.94235e10 −0.234761
\(596\) 0 0
\(597\) −2.91414e10 + 4.36148e10i −0.229410 + 0.343350i
\(598\) 0 0
\(599\) 3.03370e10i 0.235649i −0.993034 0.117825i \(-0.962408\pi\)
0.993034 0.117825i \(-0.0375921\pi\)
\(600\) 0 0
\(601\) 3.37911e10 0.259003 0.129501 0.991579i \(-0.458662\pi\)
0.129501 + 0.991579i \(0.458662\pi\)
\(602\) 0 0
\(603\) −5.69718e9 1.37528e10i −0.0430914 0.104022i
\(604\) 0 0
\(605\) 3.72500e10i 0.278038i
\(606\) 0 0
\(607\) 3.82366e10 0.281660 0.140830 0.990034i \(-0.455023\pi\)
0.140830 + 0.990034i \(0.455023\pi\)
\(608\) 0 0
\(609\) −5.43224e10 3.62957e10i −0.394920 0.263867i
\(610\) 0 0
\(611\) 1.05005e11i 0.753435i
\(612\) 0 0
\(613\) −1.08066e11 −0.765330 −0.382665 0.923887i \(-0.624994\pi\)
−0.382665 + 0.923887i \(0.624994\pi\)
\(614\) 0 0
\(615\) −1.89469e10 + 2.83571e10i −0.132445 + 0.198226i
\(616\) 0 0
\(617\) 4.72538e9i 0.0326059i −0.999867 0.0163029i \(-0.994810\pi\)
0.999867 0.0163029i \(-0.00518962\pi\)
\(618\) 0 0
\(619\) 2.29845e10 0.156557 0.0782786 0.996932i \(-0.475058\pi\)
0.0782786 + 0.996932i \(0.475058\pi\)
\(620\) 0 0
\(621\) 4.87639e10 2.45221e11i 0.327893 1.64889i
\(622\) 0 0
\(623\) 1.27077e11i 0.843555i
\(624\) 0 0
\(625\) 9.60656e10 0.629575
\(626\) 0 0
\(627\) 8.87662e9 + 5.93094e9i 0.0574351 + 0.0383754i
\(628\) 0 0
\(629\) 9.99949e10i 0.638815i
\(630\) 0 0
\(631\) 1.01892e11 0.642722 0.321361 0.946957i \(-0.395860\pi\)
0.321361 + 0.946957i \(0.395860\pi\)
\(632\) 0 0
\(633\) 2.61497e9 3.91372e9i 0.0162874 0.0243767i
\(634\) 0 0
\(635\) 6.19605e10i 0.381083i
\(636\) 0 0
\(637\) 6.95302e10 0.422295
\(638\) 0 0
\(639\) −1.03179e11 + 4.27422e10i −0.618851 + 0.256362i
\(640\) 0 0
\(641\) 1.17803e11i 0.697791i 0.937162 + 0.348896i \(0.113443\pi\)
−0.937162 + 0.348896i \(0.886557\pi\)
\(642\) 0 0
\(643\) −2.62680e10 −0.153668 −0.0768339 0.997044i \(-0.524481\pi\)
−0.0768339 + 0.997044i \(0.524481\pi\)
\(644\) 0 0
\(645\) −5.33154e10 3.56228e10i −0.308045 0.205821i
\(646\) 0 0
\(647\) 3.10527e11i 1.77208i −0.463612 0.886038i \(-0.653447\pi\)
0.463612 0.886038i \(-0.346553\pi\)
\(648\) 0 0
\(649\) −9.54486e10 −0.538010
\(650\) 0 0
\(651\) 2.76789e10 4.14260e10i 0.154108 0.230648i
\(652\) 0 0
\(653\) 3.48345e10i 0.191583i −0.995401 0.0957914i \(-0.969462\pi\)
0.995401 0.0957914i \(-0.0305382\pi\)
\(654\) 0 0
\(655\) −6.49068e10 −0.352635
\(656\) 0 0
\(657\) −6.94863e10 1.67738e11i −0.372939 0.900265i
\(658\) 0 0
\(659\) 3.77120e10i 0.199957i 0.994990 + 0.0999787i \(0.0318775\pi\)
−0.994990 + 0.0999787i \(0.968123\pi\)
\(660\) 0 0
\(661\) 1.39619e11 0.731372 0.365686 0.930738i \(-0.380834\pi\)
0.365686 + 0.930738i \(0.380834\pi\)
\(662\) 0 0
\(663\) −1.29783e11 8.67149e10i −0.671682 0.448786i
\(664\) 0 0
\(665\) 7.44025e9i 0.0380453i
\(666\) 0 0
\(667\) 2.16834e11 1.09553
\(668\) 0 0
\(669\) −1.98090e11 + 2.96474e11i −0.988912 + 1.48007i
\(670\) 0 0
\(671\) 5.24468e9i 0.0258719i
\(672\) 0 0
\(673\) −1.29783e11 −0.632642 −0.316321 0.948652i \(-0.602448\pi\)
−0.316321 + 0.948652i \(0.602448\pi\)
\(674\) 0 0
\(675\) −1.77337e11 3.52648e10i −0.854249 0.169874i
\(676\) 0 0
\(677\) 3.40648e11i 1.62163i 0.585306 + 0.810813i \(0.300975\pi\)
−0.585306 + 0.810813i \(0.699025\pi\)
\(678\) 0 0
\(679\) 2.57724e11 1.21248
\(680\) 0 0
\(681\) 2.38144e11 + 1.59117e11i 1.10726 + 0.739821i
\(682\) 0 0
\(683\) 1.02876e11i 0.472750i 0.971662 + 0.236375i \(0.0759593\pi\)
−0.971662 + 0.236375i \(0.924041\pi\)
\(684\) 0 0
\(685\) 4.65976e10 0.211642
\(686\) 0 0
\(687\) 8.39562e10 1.25654e11i 0.376900 0.564092i
\(688\) 0 0
\(689\) 1.69863e11i 0.753742i
\(690\) 0 0
\(691\) 3.58259e11 1.57140 0.785698 0.618611i \(-0.212304\pi\)
0.785698 + 0.618611i \(0.212304\pi\)
\(692\) 0 0
\(693\) 7.38234e10 3.05817e10i 0.320082 0.132595i
\(694\) 0 0
\(695\) 3.20289e10i 0.137279i
\(696\) 0 0
\(697\) −1.40459e11 −0.595141
\(698\) 0 0
\(699\) −1.83280e11 1.22459e11i −0.767728 0.512960i
\(700\) 0 0
\(701\) 2.49323e11i 1.03250i 0.856438 + 0.516250i \(0.172673\pi\)
−0.856438 + 0.516250i \(0.827327\pi\)
\(702\) 0 0
\(703\) −2.52854e10 −0.103526
\(704\) 0 0
\(705\) −4.12286e10 + 6.17053e10i −0.166895 + 0.249785i
\(706\) 0 0
\(707\) 1.81203e11i 0.725251i
\(708\) 0 0
\(709\) 3.88874e11 1.53895 0.769474 0.638678i \(-0.220518\pi\)
0.769474 + 0.638678i \(0.220518\pi\)
\(710\) 0 0
\(711\) −5.77052e10 1.39299e11i −0.225807 0.545091i
\(712\) 0 0
\(713\) 1.65357e11i 0.639829i
\(714\) 0 0
\(715\) 4.02006e10 0.153818
\(716\) 0 0
\(717\) 1.53195e11 + 1.02357e11i 0.579651 + 0.387296i
\(718\) 0 0
\(719\) 3.35735e10i 0.125626i −0.998025 0.0628132i \(-0.979993\pi\)
0.998025 0.0628132i \(-0.0200072\pi\)
\(720\) 0 0
\(721\) 2.90611e11 1.07540
\(722\) 0 0
\(723\) −7.86002e10 + 1.17638e11i −0.287654 + 0.430521i
\(724\) 0 0
\(725\) 1.56809e11i 0.567569i
\(726\) 0 0
\(727\) −2.53113e11 −0.906102 −0.453051 0.891485i \(-0.649664\pi\)
−0.453051 + 0.891485i \(0.649664\pi\)
\(728\) 0 0
\(729\) 2.60942e11 + 1.08053e11i 0.923920 + 0.382586i
\(730\) 0 0
\(731\) 2.64084e11i 0.924853i
\(732\) 0 0
\(733\) −2.07602e11 −0.719144 −0.359572 0.933117i \(-0.617077\pi\)
−0.359572 + 0.933117i \(0.617077\pi\)
\(734\) 0 0
\(735\) −4.08588e10 2.72999e10i −0.140003 0.0935432i
\(736\) 0 0
\(737\) 1.57903e10i 0.0535205i
\(738\) 0 0
\(739\) 4.15014e11 1.39151 0.695753 0.718281i \(-0.255071\pi\)
0.695753 + 0.718281i \(0.255071\pi\)
\(740\) 0 0
\(741\) −2.19274e10 + 3.28179e10i −0.0727300 + 0.108852i
\(742\) 0 0
\(743\) 3.30690e11i 1.08509i 0.840027 + 0.542545i \(0.182539\pi\)
−0.840027 + 0.542545i \(0.817461\pi\)
\(744\) 0 0
\(745\) −1.83918e11 −0.597034
\(746\) 0 0
\(747\) −2.81224e11 + 1.16498e11i −0.903170 + 0.374143i
\(748\) 0 0
\(749\) 3.94695e10i 0.125411i
\(750\) 0 0
\(751\) 4.77978e11 1.50262 0.751308 0.659952i \(-0.229423\pi\)
0.751308 + 0.659952i \(0.229423\pi\)
\(752\) 0 0
\(753\) 9.26390e10 + 6.18970e10i 0.288147 + 0.192526i
\(754\) 0 0
\(755\) 9.51565e10i 0.292854i
\(756\) 0 0
\(757\) 8.95066e10 0.272566 0.136283 0.990670i \(-0.456484\pi\)
0.136283 + 0.990670i \(0.456484\pi\)
\(758\) 0 0
\(759\) −1.47337e11 + 2.20514e11i −0.443962 + 0.664462i
\(760\) 0 0
\(761\) 5.71473e11i 1.70395i 0.523581 + 0.851976i \(0.324596\pi\)
−0.523581 + 0.851976i \(0.675404\pi\)
\(762\) 0 0
\(763\) 1.92456e11 0.567851
\(764\) 0 0
\(765\) 4.22185e10 + 1.01914e11i 0.123270 + 0.297570i
\(766\) 0 0
\(767\) 3.52884e11i 1.01965i
\(768\) 0 0
\(769\) 2.56194e11 0.732596 0.366298 0.930498i \(-0.380625\pi\)
0.366298 + 0.930498i \(0.380625\pi\)
\(770\) 0 0
\(771\) −5.34537e11 3.57152e11i −1.51273 1.01073i
\(772\) 0 0
\(773\) 1.00523e11i 0.281543i 0.990042 + 0.140772i \(0.0449584\pi\)
−0.990042 + 0.140772i \(0.955042\pi\)
\(774\) 0 0
\(775\) 1.19582e11 0.331480
\(776\) 0 0
\(777\) −1.05145e11 + 1.57366e11i −0.288472 + 0.431745i
\(778\) 0 0
\(779\) 3.55176e10i 0.0964482i
\(780\) 0 0
\(781\) 1.18464e11 0.318408
\(782\) 0 0
\(783\) −4.77727e10 + 2.40236e11i −0.127096 + 0.639132i
\(784\) 0 0
\(785\) 1.70586e11i 0.449226i
\(786\) 0 0