Properties

Label 384.3.i.a.161.2
Level $384$
Weight $3$
Character 384.161
Analytic conductor $10.463$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.i (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.629407744.1
Defining polynomial: \(x^{8} - 2 x^{6} + 2 x^{4} - 8 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 161.2
Root \(-0.767178 + 1.18804i\) of defining polynomial
Character \(\chi\) \(=\) 384.161
Dual form 384.3.i.a.353.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.13234 + 2.77809i) q^{3} +(-6.28651 - 6.28651i) q^{5} -1.64575i q^{7} +(-6.43560 - 6.29150i) q^{9} +O(q^{10})\) \(q+(-1.13234 + 2.77809i) q^{3} +(-6.28651 - 6.28651i) q^{5} -1.64575i q^{7} +(-6.43560 - 6.29150i) q^{9} +(4.75216 + 4.75216i) q^{11} +(9.35425 + 9.35425i) q^{13} +(24.5830 - 10.3460i) q^{15} +11.4859i q^{17} +(8.58301 + 8.58301i) q^{19} +(4.57205 + 1.86355i) q^{21} +16.2381 q^{23} +54.0405i q^{25} +(24.7657 - 10.7546i) q^{27} +(10.7405 - 10.7405i) q^{29} +6.35425 q^{31} +(-18.5830 + 7.82087i) q^{33} +(-10.3460 + 10.3460i) q^{35} +(-27.2288 + 27.2288i) q^{37} +(-36.5792 + 15.3948i) q^{39} +1.98162 q^{41} +(19.4170 - 19.4170i) q^{43} +(0.905893 + 80.0091i) q^{45} +74.9474i q^{47} +46.2915 q^{49} +(-31.9090 - 13.0060i) q^{51} +(-4.00671 - 4.00671i) q^{53} -59.7490i q^{55} +(-33.5633 + 14.1255i) q^{57} +(27.9694 + 27.9694i) q^{59} +(-39.2288 - 39.2288i) q^{61} +(-10.3542 + 10.5914i) q^{63} -117.611i q^{65} +(68.6863 + 68.6863i) q^{67} +(-18.3871 + 45.1110i) q^{69} +40.6822 q^{71} -59.0405i q^{73} +(-150.130 - 61.1923i) q^{75} +(7.82087 - 7.82087i) q^{77} +17.3948 q^{79} +(1.83399 + 80.9792i) q^{81} +(75.1400 - 75.1400i) q^{83} +(72.2065 - 72.2065i) q^{85} +(17.6762 + 42.0000i) q^{87} +78.8051 q^{89} +(15.3948 - 15.3948i) q^{91} +(-7.19518 + 17.6527i) q^{93} -107.914i q^{95} -38.8340 q^{97} +(-0.684791 - 60.4812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{3} + O(q^{10}) \) \( 8q - 4q^{3} + 96q^{13} + 112q^{15} - 16q^{19} + 32q^{21} + 68q^{27} + 72q^{31} - 64q^{33} - 112q^{37} + 240q^{43} + 112q^{45} + 328q^{49} + 32q^{51} - 208q^{61} - 104q^{63} + 232q^{67} - 324q^{75} - 136q^{79} + 184q^{81} + 112q^{85} - 152q^{91} - 64q^{93} - 480q^{97} - 160q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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
\(3\) −1.13234 + 2.77809i −0.377447 + 0.926031i
\(4\) 0 0
\(5\) −6.28651 6.28651i −1.25730 1.25730i −0.952376 0.304927i \(-0.901368\pi\)
−0.304927 0.952376i \(-0.598632\pi\)
\(6\) 0 0
\(7\) 1.64575i 0.235107i −0.993067 0.117554i \(-0.962495\pi\)
0.993067 0.117554i \(-0.0375052\pi\)
\(8\) 0 0
\(9\) −6.43560 6.29150i −0.715067 0.699056i
\(10\) 0 0
\(11\) 4.75216 + 4.75216i 0.432014 + 0.432014i 0.889313 0.457299i \(-0.151183\pi\)
−0.457299 + 0.889313i \(0.651183\pi\)
\(12\) 0 0
\(13\) 9.35425 + 9.35425i 0.719558 + 0.719558i 0.968515 0.248957i \(-0.0800878\pi\)
−0.248957 + 0.968515i \(0.580088\pi\)
\(14\) 0 0
\(15\) 24.5830 10.3460i 1.63887 0.689736i
\(16\) 0 0
\(17\) 11.4859i 0.675644i 0.941210 + 0.337822i \(0.109690\pi\)
−0.941210 + 0.337822i \(0.890310\pi\)
\(18\) 0 0
\(19\) 8.58301 + 8.58301i 0.451737 + 0.451737i 0.895931 0.444194i \(-0.146510\pi\)
−0.444194 + 0.895931i \(0.646510\pi\)
\(20\) 0 0
\(21\) 4.57205 + 1.86355i 0.217717 + 0.0887406i
\(22\) 0 0
\(23\) 16.2381 0.706004 0.353002 0.935623i \(-0.385161\pi\)
0.353002 + 0.935623i \(0.385161\pi\)
\(24\) 0 0
\(25\) 54.0405i 2.16162i
\(26\) 0 0
\(27\) 24.7657 10.7546i 0.917248 0.398318i
\(28\) 0 0
\(29\) 10.7405 10.7405i 0.370362 0.370362i −0.497247 0.867609i \(-0.665656\pi\)
0.867609 + 0.497247i \(0.165656\pi\)
\(30\) 0 0
\(31\) 6.35425 0.204976 0.102488 0.994734i \(-0.467320\pi\)
0.102488 + 0.994734i \(0.467320\pi\)
\(32\) 0 0
\(33\) −18.5830 + 7.82087i −0.563121 + 0.236996i
\(34\) 0 0
\(35\) −10.3460 + 10.3460i −0.295601 + 0.295601i
\(36\) 0 0
\(37\) −27.2288 + 27.2288i −0.735912 + 0.735912i −0.971784 0.235872i \(-0.924205\pi\)
0.235872 + 0.971784i \(0.424205\pi\)
\(38\) 0 0
\(39\) −36.5792 + 15.3948i −0.937928 + 0.394738i
\(40\) 0 0
\(41\) 1.98162 0.0483323 0.0241662 0.999708i \(-0.492307\pi\)
0.0241662 + 0.999708i \(0.492307\pi\)
\(42\) 0 0
\(43\) 19.4170 19.4170i 0.451558 0.451558i −0.444313 0.895871i \(-0.646552\pi\)
0.895871 + 0.444313i \(0.146552\pi\)
\(44\) 0 0
\(45\) 0.905893 + 80.0091i 0.0201310 + 1.77798i
\(46\) 0 0
\(47\) 74.9474i 1.59463i 0.603566 + 0.797313i \(0.293746\pi\)
−0.603566 + 0.797313i \(0.706254\pi\)
\(48\) 0 0
\(49\) 46.2915 0.944725
\(50\) 0 0
\(51\) −31.9090 13.0060i −0.625667 0.255020i
\(52\) 0 0
\(53\) −4.00671 4.00671i −0.0755983 0.0755983i 0.668297 0.743895i \(-0.267024\pi\)
−0.743895 + 0.668297i \(0.767024\pi\)
\(54\) 0 0
\(55\) 59.7490i 1.08635i
\(56\) 0 0
\(57\) −33.5633 + 14.1255i −0.588830 + 0.247816i
\(58\) 0 0
\(59\) 27.9694 + 27.9694i 0.474058 + 0.474058i 0.903225 0.429167i \(-0.141193\pi\)
−0.429167 + 0.903225i \(0.641193\pi\)
\(60\) 0 0
\(61\) −39.2288 39.2288i −0.643094 0.643094i 0.308221 0.951315i \(-0.400267\pi\)
−0.951315 + 0.308221i \(0.900267\pi\)
\(62\) 0 0
\(63\) −10.3542 + 10.5914i −0.164353 + 0.168118i
\(64\) 0 0
\(65\) 117.611i 1.80940i
\(66\) 0 0
\(67\) 68.6863 + 68.6863i 1.02517 + 1.02517i 0.999675 + 0.0254932i \(0.00811562\pi\)
0.0254932 + 0.999675i \(0.491884\pi\)
\(68\) 0 0
\(69\) −18.3871 + 45.1110i −0.266479 + 0.653782i
\(70\) 0 0
\(71\) 40.6822 0.572988 0.286494 0.958082i \(-0.407510\pi\)
0.286494 + 0.958082i \(0.407510\pi\)
\(72\) 0 0
\(73\) 59.0405i 0.808774i −0.914588 0.404387i \(-0.867485\pi\)
0.914588 0.404387i \(-0.132515\pi\)
\(74\) 0 0
\(75\) −150.130 61.1923i −2.00173 0.815898i
\(76\) 0 0
\(77\) 7.82087 7.82087i 0.101570 0.101570i
\(78\) 0 0
\(79\) 17.3948 0.220187 0.110093 0.993921i \(-0.464885\pi\)
0.110093 + 0.993921i \(0.464885\pi\)
\(80\) 0 0
\(81\) 1.83399 + 80.9792i 0.0226418 + 0.999744i
\(82\) 0 0
\(83\) 75.1400 75.1400i 0.905301 0.905301i −0.0905874 0.995889i \(-0.528874\pi\)
0.995889 + 0.0905874i \(0.0288745\pi\)
\(84\) 0 0
\(85\) 72.2065 72.2065i 0.849489 0.849489i
\(86\) 0 0
\(87\) 17.6762 + 42.0000i 0.203174 + 0.482759i
\(88\) 0 0
\(89\) 78.8051 0.885450 0.442725 0.896657i \(-0.354012\pi\)
0.442725 + 0.896657i \(0.354012\pi\)
\(90\) 0 0
\(91\) 15.3948 15.3948i 0.169173 0.169173i
\(92\) 0 0
\(93\) −7.19518 + 17.6527i −0.0773675 + 0.189814i
\(94\) 0 0
\(95\) 107.914i 1.13594i
\(96\) 0 0
\(97\) −38.8340 −0.400350 −0.200175 0.979760i \(-0.564151\pi\)
−0.200175 + 0.979760i \(0.564151\pi\)
\(98\) 0 0
\(99\) −0.684791 60.4812i −0.00691708 0.610921i
\(100\) 0 0
\(101\) 41.5332 + 41.5332i 0.411220 + 0.411220i 0.882164 0.470943i \(-0.156086\pi\)
−0.470943 + 0.882164i \(0.656086\pi\)
\(102\) 0 0
\(103\) 98.8118i 0.959337i 0.877450 + 0.479669i \(0.159243\pi\)
−0.877450 + 0.479669i \(0.840757\pi\)
\(104\) 0 0
\(105\) −17.0270 40.4575i −0.162162 0.385310i
\(106\) 0 0
\(107\) 98.8480 + 98.8480i 0.923813 + 0.923813i 0.997296 0.0734837i \(-0.0234117\pi\)
−0.0734837 + 0.997296i \(0.523412\pi\)
\(108\) 0 0
\(109\) −68.8523 68.8523i −0.631672 0.631672i 0.316815 0.948487i \(-0.397387\pi\)
−0.948487 + 0.316815i \(0.897387\pi\)
\(110\) 0 0
\(111\) −44.8118 106.476i −0.403710 0.959246i
\(112\) 0 0
\(113\) 8.31160i 0.0735540i 0.999323 + 0.0367770i \(0.0117091\pi\)
−0.999323 + 0.0367770i \(0.988291\pi\)
\(114\) 0 0
\(115\) −102.081 102.081i −0.887661 0.887661i
\(116\) 0 0
\(117\) −1.34796 119.053i −0.0115210 1.01754i
\(118\) 0 0
\(119\) 18.9030 0.158849
\(120\) 0 0
\(121\) 75.8340i 0.626727i
\(122\) 0 0
\(123\) −2.24388 + 5.50514i −0.0182429 + 0.0447572i
\(124\) 0 0
\(125\) 182.564 182.564i 1.46051 1.46051i
\(126\) 0 0
\(127\) −195.933 −1.54278 −0.771391 0.636361i \(-0.780439\pi\)
−0.771391 + 0.636361i \(0.780439\pi\)
\(128\) 0 0
\(129\) 31.9555 + 75.9289i 0.247717 + 0.588596i
\(130\) 0 0
\(131\) −142.127 + 142.127i −1.08494 + 1.08494i −0.0888967 + 0.996041i \(0.528334\pi\)
−0.996041 + 0.0888967i \(0.971666\pi\)
\(132\) 0 0
\(133\) 14.1255 14.1255i 0.106207 0.106207i
\(134\) 0 0
\(135\) −223.299 88.0810i −1.65406 0.652452i
\(136\) 0 0
\(137\) −50.4847 −0.368501 −0.184251 0.982879i \(-0.558986\pi\)
−0.184251 + 0.982879i \(0.558986\pi\)
\(138\) 0 0
\(139\) −171.727 + 171.727i −1.23544 + 1.23544i −0.273601 + 0.961843i \(0.588215\pi\)
−0.961843 + 0.273601i \(0.911785\pi\)
\(140\) 0 0
\(141\) −208.211 84.8661i −1.47667 0.601887i
\(142\) 0 0
\(143\) 88.9057i 0.621718i
\(144\) 0 0
\(145\) −135.041 −0.931314
\(146\) 0 0
\(147\) −52.4178 + 128.602i −0.356584 + 0.874844i
\(148\) 0 0
\(149\) −84.4952 84.4952i −0.567082 0.567082i 0.364228 0.931310i \(-0.381333\pi\)
−0.931310 + 0.364228i \(0.881333\pi\)
\(150\) 0 0
\(151\) 30.1033i 0.199359i −0.995020 0.0996797i \(-0.968218\pi\)
0.995020 0.0996797i \(-0.0317818\pi\)
\(152\) 0 0
\(153\) 72.2638 73.9190i 0.472313 0.483130i
\(154\) 0 0
\(155\) −39.9461 39.9461i −0.257717 0.257717i
\(156\) 0 0
\(157\) 181.265 + 181.265i 1.15456 + 1.15456i 0.985628 + 0.168928i \(0.0540305\pi\)
0.168928 + 0.985628i \(0.445970\pi\)
\(158\) 0 0
\(159\) 15.6680 6.59405i 0.0985407 0.0414720i
\(160\) 0 0
\(161\) 26.7239i 0.165987i
\(162\) 0 0
\(163\) −200.081 200.081i −1.22749 1.22749i −0.964910 0.262581i \(-0.915426\pi\)
−0.262581 0.964910i \(-0.584574\pi\)
\(164\) 0 0
\(165\) 165.988 + 67.6563i 1.00599 + 0.410038i
\(166\) 0 0
\(167\) 172.656 1.03387 0.516933 0.856026i \(-0.327074\pi\)
0.516933 + 0.856026i \(0.327074\pi\)
\(168\) 0 0
\(169\) 6.00394i 0.0355263i
\(170\) 0 0
\(171\) −1.23682 109.237i −0.00723287 0.638812i
\(172\) 0 0
\(173\) −40.8313 + 40.8313i −0.236019 + 0.236019i −0.815199 0.579181i \(-0.803373\pi\)
0.579181 + 0.815199i \(0.303373\pi\)
\(174\) 0 0
\(175\) 88.9373 0.508213
\(176\) 0 0
\(177\) −109.373 + 46.0307i −0.617924 + 0.260060i
\(178\) 0 0
\(179\) 152.613 152.613i 0.852584 0.852584i −0.137866 0.990451i \(-0.544024\pi\)
0.990451 + 0.137866i \(0.0440245\pi\)
\(180\) 0 0
\(181\) −166.601 + 166.601i −0.920449 + 0.920449i −0.997061 0.0766118i \(-0.975590\pi\)
0.0766118 + 0.997061i \(0.475590\pi\)
\(182\) 0 0
\(183\) 153.402 64.5608i 0.838260 0.352791i
\(184\) 0 0
\(185\) 342.348 1.85053
\(186\) 0 0
\(187\) −54.5830 + 54.5830i −0.291888 + 0.291888i
\(188\) 0 0
\(189\) −17.6994 40.7582i −0.0936474 0.215652i
\(190\) 0 0
\(191\) 14.3434i 0.0750963i −0.999295 0.0375482i \(-0.988045\pi\)
0.999295 0.0375482i \(-0.0119548\pi\)
\(192\) 0 0
\(193\) 207.373 1.07447 0.537235 0.843433i \(-0.319469\pi\)
0.537235 + 0.843433i \(0.319469\pi\)
\(194\) 0 0
\(195\) 326.735 + 133.176i 1.67556 + 0.682954i
\(196\) 0 0
\(197\) 97.2608 + 97.2608i 0.493710 + 0.493710i 0.909473 0.415763i \(-0.136486\pi\)
−0.415763 + 0.909473i \(0.636486\pi\)
\(198\) 0 0
\(199\) 82.7673i 0.415916i 0.978138 + 0.207958i \(0.0666818\pi\)
−0.978138 + 0.207958i \(0.933318\pi\)
\(200\) 0 0
\(201\) −268.593 + 113.041i −1.33628 + 0.562391i
\(202\) 0 0
\(203\) −17.6762 17.6762i −0.0870748 0.0870748i
\(204\) 0 0
\(205\) −12.4575 12.4575i −0.0607684 0.0607684i
\(206\) 0 0
\(207\) −104.502 102.162i −0.504840 0.493536i
\(208\) 0 0
\(209\) 81.5756i 0.390314i
\(210\) 0 0
\(211\) 201.646 + 201.646i 0.955667 + 0.955667i 0.999058 0.0433911i \(-0.0138162\pi\)
−0.0433911 + 0.999058i \(0.513816\pi\)
\(212\) 0 0
\(213\) −46.0661 + 113.019i −0.216273 + 0.530605i
\(214\) 0 0
\(215\) −244.130 −1.13549
\(216\) 0 0
\(217\) 10.4575i 0.0481913i
\(218\) 0 0
\(219\) 164.020 + 66.8541i 0.748950 + 0.305270i
\(220\) 0 0
\(221\) −107.442 + 107.442i −0.486164 + 0.486164i
\(222\) 0 0
\(223\) 233.261 1.04602 0.523008 0.852328i \(-0.324810\pi\)
0.523008 + 0.852328i \(0.324810\pi\)
\(224\) 0 0
\(225\) 339.996 347.783i 1.51109 1.54570i
\(226\) 0 0
\(227\) 94.3599 94.3599i 0.415682 0.415682i −0.468030 0.883712i \(-0.655036\pi\)
0.883712 + 0.468030i \(0.155036\pi\)
\(228\) 0 0
\(229\) 138.063 138.063i 0.602894 0.602894i −0.338185 0.941080i \(-0.609813\pi\)
0.941080 + 0.338185i \(0.109813\pi\)
\(230\) 0 0
\(231\) 12.8712 + 30.5830i 0.0557195 + 0.132394i
\(232\) 0 0
\(233\) −396.796 −1.70299 −0.851493 0.524366i \(-0.824303\pi\)
−0.851493 + 0.524366i \(0.824303\pi\)
\(234\) 0 0
\(235\) 471.158 471.158i 2.00493 2.00493i
\(236\) 0 0
\(237\) −19.6968 + 48.3243i −0.0831090 + 0.203900i
\(238\) 0 0
\(239\) 284.813i 1.19168i 0.803102 + 0.595842i \(0.203182\pi\)
−0.803102 + 0.595842i \(0.796818\pi\)
\(240\) 0 0
\(241\) −266.531 −1.10594 −0.552968 0.833202i \(-0.686505\pi\)
−0.552968 + 0.833202i \(0.686505\pi\)
\(242\) 0 0
\(243\) −227.045 86.6012i −0.934340 0.356383i
\(244\) 0 0
\(245\) −291.012 291.012i −1.18780 1.18780i
\(246\) 0 0
\(247\) 160.575i 0.650102i
\(248\) 0 0
\(249\) 123.662 + 293.830i 0.496633 + 1.18004i
\(250\) 0 0
\(251\) −153.945 153.945i −0.613327 0.613327i 0.330485 0.943811i \(-0.392788\pi\)
−0.943811 + 0.330485i \(0.892788\pi\)
\(252\) 0 0
\(253\) 77.1660 + 77.1660i 0.305004 + 0.305004i
\(254\) 0 0
\(255\) 118.834 + 282.359i 0.466016 + 1.10729i
\(256\) 0 0
\(257\) 240.167i 0.934503i −0.884125 0.467251i \(-0.845244\pi\)
0.884125 0.467251i \(-0.154756\pi\)
\(258\) 0 0
\(259\) 44.8118 + 44.8118i 0.173018 + 0.173018i
\(260\) 0 0
\(261\) −136.695 + 1.54772i −0.523737 + 0.00592995i
\(262\) 0 0
\(263\) 140.707 0.535009 0.267505 0.963557i \(-0.413801\pi\)
0.267505 + 0.963557i \(0.413801\pi\)
\(264\) 0 0
\(265\) 50.3765i 0.190100i
\(266\) 0 0
\(267\) −89.2343 + 218.928i −0.334211 + 0.819954i
\(268\) 0 0
\(269\) −229.830 + 229.830i −0.854388 + 0.854388i −0.990670 0.136282i \(-0.956485\pi\)
0.136282 + 0.990670i \(0.456485\pi\)
\(270\) 0 0
\(271\) 228.731 0.844025 0.422012 0.906590i \(-0.361324\pi\)
0.422012 + 0.906590i \(0.361324\pi\)
\(272\) 0 0
\(273\) 25.3360 + 60.2002i 0.0928057 + 0.220514i
\(274\) 0 0
\(275\) −256.809 + 256.809i −0.933851 + 0.933851i
\(276\) 0 0
\(277\) 103.265 103.265i 0.372799 0.372799i −0.495697 0.868496i \(-0.665087\pi\)
0.868496 + 0.495697i \(0.165087\pi\)
\(278\) 0 0
\(279\) −40.8934 39.9778i −0.146571 0.143290i
\(280\) 0 0
\(281\) −283.552 −1.00908 −0.504540 0.863388i \(-0.668338\pi\)
−0.504540 + 0.863388i \(0.668338\pi\)
\(282\) 0 0
\(283\) −23.4758 + 23.4758i −0.0829534 + 0.0829534i −0.747366 0.664413i \(-0.768682\pi\)
0.664413 + 0.747366i \(0.268682\pi\)
\(284\) 0 0
\(285\) 299.796 + 122.196i 1.05192 + 0.428758i
\(286\) 0 0
\(287\) 3.26126i 0.0113633i
\(288\) 0 0
\(289\) 157.073 0.543506
\(290\) 0 0
\(291\) 43.9734 107.884i 0.151111 0.370737i
\(292\) 0 0
\(293\) 381.409 + 381.409i 1.30174 + 1.30174i 0.927220 + 0.374516i \(0.122191\pi\)
0.374516 + 0.927220i \(0.377809\pi\)
\(294\) 0 0
\(295\) 351.660i 1.19207i
\(296\) 0 0
\(297\) 168.798 + 66.5830i 0.568343 + 0.224185i
\(298\) 0 0
\(299\) 151.895 + 151.895i 0.508011 + 0.508011i
\(300\) 0 0
\(301\) −31.9555 31.9555i −0.106165 0.106165i
\(302\) 0 0
\(303\) −162.413 + 68.3534i −0.536017 + 0.225589i
\(304\) 0 0
\(305\) 493.224i 1.61713i
\(306\) 0 0
\(307\) 209.055 + 209.055i 0.680960 + 0.680960i 0.960217 0.279256i \(-0.0900879\pi\)
−0.279256 + 0.960217i \(0.590088\pi\)
\(308\) 0 0
\(309\) −274.508 111.889i −0.888376 0.362099i
\(310\) 0 0
\(311\) −111.176 −0.357478 −0.178739 0.983897i \(-0.557202\pi\)
−0.178739 + 0.983897i \(0.557202\pi\)
\(312\) 0 0
\(313\) 282.280i 0.901852i 0.892561 + 0.450926i \(0.148906\pi\)
−0.892561 + 0.450926i \(0.851094\pi\)
\(314\) 0 0
\(315\) 131.675 1.49088i 0.418016 0.00473294i
\(316\) 0 0
\(317\) 206.983 206.983i 0.652943 0.652943i −0.300758 0.953701i \(-0.597240\pi\)
0.953701 + 0.300758i \(0.0972395\pi\)
\(318\) 0 0
\(319\) 102.081 0.320003
\(320\) 0 0
\(321\) −386.539 + 162.679i −1.20417 + 0.506789i
\(322\) 0 0
\(323\) −98.5839 + 98.5839i −0.305213 + 0.305213i
\(324\) 0 0
\(325\) −505.508 + 505.508i −1.55541 + 1.55541i
\(326\) 0 0
\(327\) 269.242 113.314i 0.823371 0.346525i
\(328\) 0 0
\(329\) 123.345 0.374908
\(330\) 0 0
\(331\) −127.431 + 127.431i −0.384989 + 0.384989i −0.872896 0.487907i \(-0.837761\pi\)
0.487907 + 0.872896i \(0.337761\pi\)
\(332\) 0 0
\(333\) 346.543 3.92369i 1.04067 0.0117829i
\(334\) 0 0
\(335\) 863.594i 2.57789i
\(336\) 0 0
\(337\) 68.9595 0.204628 0.102314 0.994752i \(-0.467375\pi\)
0.102314 + 0.994752i \(0.467375\pi\)
\(338\) 0 0
\(339\) −23.0904 9.41157i −0.0681133 0.0277627i
\(340\) 0 0
\(341\) 30.1964 + 30.1964i 0.0885525 + 0.0885525i
\(342\) 0 0
\(343\) 156.826i 0.457219i
\(344\) 0 0
\(345\) 399.181 168.000i 1.15705 0.486957i
\(346\) 0 0
\(347\) −54.0628 54.0628i −0.155801 0.155801i 0.624902 0.780703i \(-0.285139\pi\)
−0.780703 + 0.624902i \(0.785139\pi\)
\(348\) 0 0
\(349\) −0.107201 0.107201i −0.000307168 0.000307168i 0.706953 0.707260i \(-0.250069\pi\)
−0.707260 + 0.706953i \(0.750069\pi\)
\(350\) 0 0
\(351\) 332.265 + 131.063i 0.946625 + 0.373400i
\(352\) 0 0
\(353\) 194.223i 0.550208i 0.961414 + 0.275104i \(0.0887123\pi\)
−0.961414 + 0.275104i \(0.911288\pi\)
\(354\) 0 0
\(355\) −255.749 255.749i −0.720420 0.720420i
\(356\) 0 0
\(357\) −21.4047 + 52.5143i −0.0599570 + 0.147099i
\(358\) 0 0
\(359\) −437.689 −1.21919 −0.609595 0.792713i \(-0.708668\pi\)
−0.609595 + 0.792713i \(0.708668\pi\)
\(360\) 0 0
\(361\) 213.664i 0.591867i
\(362\) 0 0
\(363\) 210.674 + 85.8700i 0.580369 + 0.236556i
\(364\) 0 0
\(365\) −371.159 + 371.159i −1.01687 + 1.01687i
\(366\) 0 0
\(367\) −246.678 −0.672148 −0.336074 0.941836i \(-0.609099\pi\)
−0.336074 + 0.941836i \(0.609099\pi\)
\(368\) 0 0
\(369\) −12.7530 12.4674i −0.0345608 0.0337870i
\(370\) 0 0
\(371\) −6.59405 + 6.59405i −0.0177737 + 0.0177737i
\(372\) 0 0
\(373\) 349.678 349.678i 0.937476 0.937476i −0.0606816 0.998157i \(-0.519327\pi\)
0.998157 + 0.0606816i \(0.0193274\pi\)
\(374\) 0 0
\(375\) 300.454 + 713.903i 0.801212 + 1.90374i
\(376\) 0 0
\(377\) 200.938 0.532993
\(378\) 0 0
\(379\) −235.668 + 235.668i −0.621815 + 0.621815i −0.945995 0.324180i \(-0.894912\pi\)
0.324180 + 0.945995i \(0.394912\pi\)
\(380\) 0 0
\(381\) 221.864 544.321i 0.582319 1.42866i
\(382\) 0 0
\(383\) 64.2130i 0.167658i 0.996480 + 0.0838290i \(0.0267149\pi\)
−0.996480 + 0.0838290i \(0.973285\pi\)
\(384\) 0 0
\(385\) −98.3320 −0.255408
\(386\) 0 0
\(387\) −247.122 + 2.79801i −0.638559 + 0.00723000i
\(388\) 0 0
\(389\) −273.321 273.321i −0.702624 0.702624i 0.262349 0.964973i \(-0.415503\pi\)
−0.964973 + 0.262349i \(0.915503\pi\)
\(390\) 0 0
\(391\) 186.510i 0.477007i
\(392\) 0 0
\(393\) −233.905 555.778i −0.595179 1.41419i
\(394\) 0 0
\(395\) −109.352 109.352i −0.276842 0.276842i
\(396\) 0 0
\(397\) −141.678 141.678i −0.356873 0.356873i 0.505786 0.862659i \(-0.331202\pi\)
−0.862659 + 0.505786i \(0.831202\pi\)
\(398\) 0 0
\(399\) 23.2470 + 55.2368i 0.0582633 + 0.138438i
\(400\) 0 0
\(401\) 194.801i 0.485788i 0.970053 + 0.242894i \(0.0780967\pi\)
−0.970053 + 0.242894i \(0.921903\pi\)
\(402\) 0 0
\(403\) 59.4392 + 59.4392i 0.147492 + 0.147492i
\(404\) 0 0
\(405\) 497.548 520.607i 1.22851 1.28545i
\(406\) 0 0
\(407\) −258.791 −0.635849
\(408\) 0 0
\(409\) 420.826i 1.02891i 0.857516 + 0.514457i \(0.172007\pi\)
−0.857516 + 0.514457i \(0.827993\pi\)
\(410\) 0 0
\(411\) 57.1659 140.251i 0.139090 0.341244i
\(412\) 0 0
\(413\) 46.0307 46.0307i 0.111454 0.111454i
\(414\) 0 0
\(415\) −944.737 −2.27648
\(416\) 0 0
\(417\) −282.620 671.526i −0.677745 1.61038i
\(418\) 0 0
\(419\) 186.421 186.421i 0.444919 0.444919i −0.448742 0.893661i \(-0.648128\pi\)
0.893661 + 0.448742i \(0.148128\pi\)
\(420\) 0 0
\(421\) 186.889 186.889i 0.443917 0.443917i −0.449409 0.893326i \(-0.648366\pi\)
0.893326 + 0.449409i \(0.148366\pi\)
\(422\) 0 0
\(423\) 471.532 482.332i 1.11473 1.14026i
\(424\) 0 0
\(425\) −620.706 −1.46049
\(426\) 0 0
\(427\) −64.5608 + 64.5608i −0.151196 + 0.151196i
\(428\) 0 0
\(429\) −246.988 100.672i −0.575731 0.234666i
\(430\) 0 0
\(431\) 128.395i 0.297901i 0.988845 + 0.148950i \(0.0475895\pi\)
−0.988845 + 0.148950i \(0.952411\pi\)
\(432\) 0 0
\(433\) 684.737 1.58138 0.790690 0.612217i \(-0.209722\pi\)
0.790690 + 0.612217i \(0.209722\pi\)
\(434\) 0 0
\(435\) 152.912 375.155i 0.351522 0.862426i
\(436\) 0 0
\(437\) 139.372 + 139.372i 0.318928 + 0.318928i
\(438\) 0 0
\(439\) 239.107i 0.544663i −0.962203 0.272332i \(-0.912205\pi\)
0.962203 0.272332i \(-0.0877948\pi\)
\(440\) 0 0
\(441\) −297.914 291.243i −0.675541 0.660415i
\(442\) 0 0
\(443\) −310.189 310.189i −0.700200 0.700200i 0.264253 0.964453i \(-0.414875\pi\)
−0.964453 + 0.264253i \(0.914875\pi\)
\(444\) 0 0
\(445\) −495.409 495.409i −1.11328 1.11328i
\(446\) 0 0
\(447\) 330.413 139.058i 0.739179 0.311092i
\(448\) 0 0
\(449\) 545.902i 1.21582i −0.794007 0.607908i \(-0.792009\pi\)
0.794007 0.607908i \(-0.207991\pi\)
\(450\) 0 0
\(451\) 9.41699 + 9.41699i 0.0208803 + 0.0208803i
\(452\) 0 0
\(453\) 83.6297 + 34.0872i 0.184613 + 0.0752477i
\(454\) 0 0
\(455\) −193.559 −0.425404
\(456\) 0 0
\(457\) 289.579i 0.633652i −0.948484 0.316826i \(-0.897383\pi\)
0.948484 0.316826i \(-0.102617\pi\)
\(458\) 0 0
\(459\) 123.526 + 284.457i 0.269121 + 0.619732i
\(460\) 0 0
\(461\) −160.511 + 160.511i −0.348180 + 0.348180i −0.859431 0.511251i \(-0.829182\pi\)
0.511251 + 0.859431i \(0.329182\pi\)
\(462\) 0 0
\(463\) −197.573 −0.426723 −0.213361 0.976973i \(-0.568441\pi\)
−0.213361 + 0.976973i \(0.568441\pi\)
\(464\) 0 0
\(465\) 156.207 65.7413i 0.335928 0.141379i
\(466\) 0 0
\(467\) −52.7645 + 52.7645i −0.112986 + 0.112986i −0.761339 0.648353i \(-0.775458\pi\)
0.648353 + 0.761339i \(0.275458\pi\)
\(468\) 0 0
\(469\) 113.041 113.041i 0.241025 0.241025i
\(470\) 0 0
\(471\) −708.826 + 298.318i −1.50494 + 0.633371i
\(472\) 0 0
\(473\) 184.545 0.390159
\(474\) 0 0
\(475\) −463.830 + 463.830i −0.976484 + 0.976484i
\(476\) 0 0
\(477\) 0.577371 + 50.9938i 0.00121042 + 0.106905i
\(478\) 0 0
\(479\) 175.985i 0.367401i −0.982982 0.183700i \(-0.941192\pi\)
0.982982 0.183700i \(-0.0588076\pi\)
\(480\) 0 0
\(481\) −509.409 −1.05906
\(482\) 0 0
\(483\) 74.2414 + 30.2606i 0.153709 + 0.0626513i
\(484\) 0 0
\(485\) 244.130 + 244.130i 0.503362 + 0.503362i
\(486\) 0 0
\(487\) 965.217i 1.98196i 0.133991 + 0.990982i \(0.457221\pi\)
−0.133991 + 0.990982i \(0.542779\pi\)
\(488\) 0 0
\(489\) 782.404 329.284i 1.60001 0.673382i
\(490\) 0 0
\(491\) −600.614 600.614i −1.22325 1.22325i −0.966471 0.256775i \(-0.917340\pi\)
−0.256775 0.966471i \(-0.582660\pi\)
\(492\) 0 0
\(493\) 123.365 + 123.365i 0.250233 + 0.250233i
\(494\) 0 0
\(495\) −375.911 + 384.521i −0.759416 + 0.776810i
\(496\) 0 0
\(497\) 66.9527i 0.134714i
\(498\) 0 0
\(499\) 51.6092 + 51.6092i 0.103425 + 0.103425i 0.756926 0.653501i \(-0.226700\pi\)
−0.653501 + 0.756926i \(0.726700\pi\)
\(500\) 0 0
\(501\) −195.505 + 479.653i −0.390230 + 0.957391i
\(502\) 0 0
\(503\) 847.530 1.68495 0.842475 0.538735i \(-0.181098\pi\)
0.842475 + 0.538735i \(0.181098\pi\)
\(504\) 0 0
\(505\) 522.199i 1.03406i
\(506\) 0 0
\(507\) −16.6795 6.79851i −0.0328984 0.0134093i
\(508\) 0 0
\(509\) 128.457 128.457i 0.252372 0.252372i −0.569570 0.821942i \(-0.692890\pi\)
0.821942 + 0.569570i \(0.192890\pi\)
\(510\) 0 0
\(511\) −97.1660 −0.190149
\(512\) 0 0
\(513\) 304.871 + 120.257i 0.594290 + 0.234420i
\(514\) 0 0
\(515\) 621.182 621.182i 1.20618 1.20618i
\(516\) 0 0
\(517\) −356.162 + 356.162i −0.688901 + 0.688901i
\(518\) 0 0
\(519\) −67.1981 159.668i −0.129476 0.307645i
\(520\) 0 0
\(521\) 676.366 1.29821 0.649103 0.760700i \(-0.275144\pi\)
0.649103 + 0.760700i \(0.275144\pi\)
\(522\) 0 0
\(523\) 600.494 600.494i 1.14817 1.14817i 0.161260 0.986912i \(-0.448444\pi\)
0.986912 0.161260i \(-0.0515559\pi\)
\(524\) 0 0
\(525\) −100.707 + 247.076i −0.191824 + 0.470621i
\(526\) 0 0
\(527\) 72.9845i 0.138491i
\(528\) 0 0
\(529\) −265.324 −0.501558
\(530\) 0 0
\(531\) −4.03042 355.970i −0.00759025 0.670376i
\(532\) 0 0
\(533\) 18.5366 + 18.5366i 0.0347779 + 0.0347779i
\(534\) 0 0
\(535\) 1242.82i 2.32302i
\(536\) 0 0
\(537\) 251.162 + 596.782i 0.467714 + 1.11133i
\(538\) 0 0
\(539\) 219.985 + 219.985i 0.408135 + 0.408135i
\(540\) 0 0
\(541\) −43.4797 43.4797i −0.0803692 0.0803692i 0.665779 0.746149i \(-0.268099\pi\)
−0.746149 + 0.665779i \(0.768099\pi\)
\(542\) 0 0
\(543\) −274.184 651.484i −0.504943 1.19979i
\(544\) 0 0
\(545\) 865.682i 1.58841i
\(546\) 0 0
\(547\) 125.498 + 125.498i 0.229430 + 0.229430i 0.812454 0.583025i \(-0.198131\pi\)
−0.583025 + 0.812454i \(0.698131\pi\)
\(548\) 0 0
\(549\) 5.65291 + 499.269i 0.0102967 + 0.909414i
\(550\) 0 0
\(551\) 184.371 0.334612
\(552\) 0 0
\(553\) 28.6275i 0.0517676i
\(554\) 0 0
\(555\) −387.655 + 951.074i −0.698477 + 1.71365i
\(556\) 0 0
\(557\) 184.272 184.272i 0.330829 0.330829i −0.522072 0.852901i \(-0.674841\pi\)
0.852901 + 0.522072i \(0.174841\pi\)
\(558\) 0 0
\(559\) 363.263 0.649844
\(560\) 0 0
\(561\) −89.8301 213.443i −0.160125 0.380469i
\(562\) 0 0
\(563\) −523.489 + 523.489i −0.929820 + 0.929820i −0.997694 0.0678736i \(-0.978379\pi\)
0.0678736 + 0.997694i \(0.478379\pi\)
\(564\) 0 0
\(565\) 52.2510 52.2510i 0.0924796 0.0924796i
\(566\) 0 0
\(567\) 133.272 3.01829i 0.235047 0.00532326i
\(568\) 0 0
\(569\) −52.6214 −0.0924805 −0.0462403 0.998930i \(-0.514724\pi\)
−0.0462403 + 0.998930i \(0.514724\pi\)
\(570\) 0 0
\(571\) 114.561 114.561i 0.200632 0.200632i −0.599639 0.800271i \(-0.704689\pi\)
0.800271 + 0.599639i \(0.204689\pi\)
\(572\) 0 0
\(573\) 39.8473 + 16.2416i 0.0695415 + 0.0283449i
\(574\) 0 0
\(575\) 877.515i 1.52611i
\(576\) 0 0
\(577\) 496.442 0.860384 0.430192 0.902737i \(-0.358446\pi\)
0.430192 + 0.902737i \(0.358446\pi\)
\(578\) 0 0
\(579\) −234.817 + 576.100i −0.405555 + 0.994992i
\(580\) 0 0
\(581\) −123.662 123.662i −0.212843 0.212843i
\(582\) 0 0
\(583\) 38.0810i 0.0653191i
\(584\) 0 0
\(585\) −739.951 + 756.899i −1.26487 + 1.29384i
\(586\) 0 0
\(587\) −115.260 115.260i −0.196354 0.196354i 0.602081 0.798435i \(-0.294338\pi\)
−0.798435 + 0.602081i \(0.794338\pi\)
\(588\) 0 0
\(589\) 54.5385 + 54.5385i 0.0925952 + 0.0925952i
\(590\) 0 0
\(591\) −380.332 + 160.067i −0.643540 + 0.270841i
\(592\) 0 0
\(593\) 227.756i 0.384074i 0.981388 + 0.192037i \(0.0615094\pi\)
−0.981388 + 0.192037i \(0.938491\pi\)
\(594\) 0 0
\(595\) −118.834 118.834i −0.199721 0.199721i
\(596\) 0 0
\(597\) −229.935 93.7209i −0.385151 0.156986i
\(598\) 0 0
\(599\) −760.308 −1.26930 −0.634648 0.772802i \(-0.718855\pi\)
−0.634648 + 0.772802i \(0.718855\pi\)
\(600\) 0 0
\(601\) 85.7856i 0.142738i −0.997450 0.0713690i \(-0.977263\pi\)
0.997450 0.0713690i \(-0.0227368\pi\)
\(602\) 0 0
\(603\) −9.89776 874.177i −0.0164142 1.44971i
\(604\) 0 0
\(605\) −476.731 + 476.731i −0.787986 + 0.787986i
\(606\) 0 0
\(607\) 685.217 1.12886 0.564429 0.825482i \(-0.309096\pi\)
0.564429 + 0.825482i \(0.309096\pi\)
\(608\) 0 0
\(609\) 69.1216 29.0906i 0.113500 0.0477678i
\(610\) 0 0
\(611\) −701.077 + 701.077i −1.14743 + 1.14743i
\(612\) 0 0
\(613\) 544.727 544.727i 0.888624 0.888624i −0.105767 0.994391i \(-0.533730\pi\)
0.994391 + 0.105767i \(0.0337296\pi\)
\(614\) 0 0
\(615\) 48.7143 20.5020i 0.0792102 0.0333365i
\(616\) 0 0
\(617\) −383.577 −0.621681 −0.310840 0.950462i \(-0.600610\pi\)
−0.310840 + 0.950462i \(0.600610\pi\)
\(618\) 0 0
\(619\) −81.7634 + 81.7634i −0.132089 + 0.132089i −0.770060 0.637971i \(-0.779774\pi\)
0.637971 + 0.770060i \(0.279774\pi\)
\(620\) 0 0
\(621\) 402.148 174.634i 0.647581 0.281214i
\(622\) 0 0
\(623\) 129.694i 0.208176i
\(624\) 0 0
\(625\) −944.365 −1.51098
\(626\) 0 0
\(627\) −226.625 92.3715i −0.361443 0.147323i
\(628\) 0 0
\(629\) −312.748 312.748i −0.497214 0.497214i
\(630\) 0 0
\(631\) 944.242i 1.49642i 0.663461 + 0.748211i \(0.269087\pi\)
−0.663461 + 0.748211i \(0.730913\pi\)
\(632\) 0 0
\(633\) −788.523 + 331.859i −1.24569 + 0.524263i
\(634\) 0 0
\(635\) 1231.74 + 1231.74i 1.93974 + 1.93974i
\(636\) 0 0
\(637\) 433.022 + 433.022i 0.679784 + 0.679784i
\(638\) 0 0
\(639\) −261.814 255.952i −0.409725 0.400551i
\(640\) 0 0
\(641\) 1102.48i 1.71994i −0.510344 0.859970i \(-0.670482\pi\)
0.510344 0.859970i \(-0.329518\pi\)
\(642\) 0 0
\(643\) −794.664 794.664i −1.23587 1.23587i −0.961674 0.274195i \(-0.911588\pi\)
−0.274195 0.961674i \(-0.588412\pi\)
\(644\) 0 0
\(645\) 276.439 678.217i 0.428588 1.05150i
\(646\) 0 0
\(647\) −768.446 −1.18771 −0.593853 0.804574i \(-0.702394\pi\)
−0.593853 + 0.804574i \(0.702394\pi\)
\(648\) 0 0
\(649\) 265.830i 0.409599i
\(650\) 0 0
\(651\) 29.0519 + 11.8415i 0.0446266 + 0.0181897i
\(652\) 0 0
\(653\) 829.478 829.478i 1.27026 1.27026i 0.324305 0.945953i \(-0.394870\pi\)
0.945953 0.324305i \(-0.105130\pi\)
\(654\) 0 0
\(655\) 1786.96 2.72819
\(656\) 0 0
\(657\) −371.454 + 379.961i −0.565378 + 0.578328i
\(658\) 0 0
\(659\) 653.956 653.956i 0.992346 0.992346i −0.00762509 0.999971i \(-0.502427\pi\)
0.999971 + 0.00762509i \(0.00242716\pi\)
\(660\) 0 0
\(661\) −734.342 + 734.342i −1.11096 + 1.11096i −0.117936 + 0.993021i \(0.537628\pi\)
−0.993021 + 0.117936i \(0.962372\pi\)
\(662\) 0 0
\(663\) −176.823 420.146i −0.266702 0.633705i
\(664\) 0 0
\(665\) −177.600 −0.267068
\(666\) 0 0
\(667\) 174.405 174.405i 0.261477 0.261477i
\(668\) 0 0
\(669\) −264.132 + 648.022i −0.394816 + 0.968643i
\(670\) 0 0
\(671\) 372.842i 0.555652i
\(672\) 0 0
\(673\) 514.259 0.764129 0.382065 0.924136i \(-0.375213\pi\)
0.382065 + 0.924136i \(0.375213\pi\)
\(674\) 0 0
\(675\) 581.183 + 1338.35i 0.861012 + 1.98274i
\(676\) 0 0
\(677\) −662.519 662.519i −0.978610 0.978610i 0.0211661 0.999776i \(-0.493262\pi\)
−0.999776 + 0.0211661i \(0.993262\pi\)
\(678\) 0 0
\(679\) 63.9111i 0.0941253i
\(680\) 0 0
\(681\) 155.293 + 368.988i 0.228037 + 0.541833i
\(682\) 0 0
\(683\) 280.446 + 280.446i 0.410608 + 0.410608i 0.881950 0.471342i \(-0.156230\pi\)
−0.471342 + 0.881950i \(0.656230\pi\)
\(684\) 0 0
\(685\) 317.373 + 317.373i 0.463318 + 0.463318i
\(686\) 0 0
\(687\) 227.217 + 539.885i 0.330738 + 0.785859i
\(688\) 0 0
\(689\) 74.9595i 0.108795i
\(690\) 0 0
\(691\) 631.830 + 631.830i 0.914371 + 0.914371i 0.996612 0.0822418i \(-0.0262080\pi\)
−0.0822418 + 0.996612i \(0.526208\pi\)
\(692\) 0 0
\(693\) −99.5370 + 1.12700i −0.143632 + 0.00162626i
\(694\) 0 0
\(695\) 2159.13 3.10666
\(696\) 0 0
\(697\) 22.7608i 0.0326554i
\(698\) 0 0
\(699\) 449.309 1102.34i 0.642788 1.57702i
\(700\) 0 0
\(701\) −160.480 + 160.480i −0.228930 + 0.228930i −0.812246 0.583315i \(-0.801755\pi\)
0.583315 + 0.812246i \(0.301755\pi\)
\(702\) 0 0
\(703\) −467.409 −0.664878
\(704\) 0 0
\(705\) 775.409 + 1842.43i 1.09987 + 2.61338i
\(706\) 0 0
\(707\) 68.3534 68.3534i 0.0966809 0.0966809i
\(708\) 0 0
\(709\) 410.261 410.261i 0.578648 0.578648i −0.355883 0.934531i \(-0.615820\pi\)
0.934531 + 0.355883i \(0.115820\pi\)
\(710\) 0 0
\(711\) −111.946 109.439i −0.157448 0.153923i
\(712\) 0 0
\(713\) 103.181 0.144714
\(714\) 0 0
\(715\) 558.907 558.907i 0.781688 0.781688i
\(716\) 0 0
\(717\) −791.236 322.505i −1.10354 0.449798i
\(718\) 0 0
\(719\) 1069.18i 1.48704i −0.668716 0.743518i \(-0.733156\pi\)
0.668716 0.743518i \(-0.266844\pi\)
\(720\) 0 0
\(721\) 162.620 0.225547
\(722\) 0 0
\(723\) 301.804 740.447i 0.417433 1.02413i
\(724\) 0 0
\(725\) 580.422 + 580.422i 0.800582 + 0.800582i
\(726\) 0 0
\(727\) 148.864i 0.204765i 0.994745 + 0.102382i \(0.0326466\pi\)
−0.994745 + 0.102382i \(0.967353\pi\)
\(728\) 0 0
\(729\) 497.678 532.689i 0.682686 0.730712i
\(730\) 0 0
\(731\) 223.022 + 223.022i 0.305092 + 0.305092i
\(732\) 0 0
\(733\) 690.136 + 690.136i 0.941522 + 0.941522i 0.998382 0.0568598i \(-0.0181088\pi\)
−0.0568598 + 0.998382i \(0.518109\pi\)
\(734\) 0 0
\(735\) 1137.98 478.934i 1.54828 0.651610i
\(736\) 0 0
\(737\) 652.816i 0.885775i
\(738\) 0 0
\(739\) 535.593 + 535.593i 0.724754 + 0.724754i 0.969570 0.244815i \(-0.0787274\pi\)
−0.244815 + 0.969570i \(0.578727\pi\)
\(740\) 0 0
\(741\) −446.093 181.826i −0.602014 0.245379i
\(742\) 0 0
\(743\) 20.5116 0.0276065 0.0138032 0.999905i \(-0.495606\pi\)
0.0138032 + 0.999905i \(0.495606\pi\)
\(744\) 0 0
\(745\) 1062.36i 1.42599i
\(746\) 0 0
\(747\) −956.315 + 10.8278i −1.28021 + 0.0144950i
\(748\) 0 0
\(749\) 162.679 162.679i 0.217195 0.217195i
\(750\) 0 0
\(751\) −15.8000 −0.0210385 −0.0105193 0.999945i \(-0.503348\pi\)
−0.0105193 + 0.999945i \(0.503348\pi\)
\(752\) 0 0
\(753\) 601.992 253.355i 0.799458 0.336461i
\(754\) 0 0
\(755\) −189.245 + 189.245i −0.250655 + 0.250655i
\(756\) 0 0
\(757\) −810.497 + 810.497i −1.07067 + 1.07067i −0.0733640 + 0.997305i \(0.523373\pi\)
−0.997305 + 0.0733640i \(0.976627\pi\)
\(758\) 0 0
\(759\) −301.753 + 126.996i −0.397566 + 0.167320i
\(760\) 0 0
\(761\) 212.194 0.278836 0.139418 0.990234i \(-0.455477\pi\)
0.139418 + 0.990234i \(0.455477\pi\)
\(762\) 0 0
\(763\) −113.314 + 113.314i −0.148511 + 0.148511i
\(764\) 0 0
\(765\) −918.980 + 10.4050i −1.20128 + 0.0136014i
\(766\) 0 0
\(767\) 523.266i 0.682224i
\(768\) 0 0
\(769\) −883.681 −1.14913 −0.574565 0.818459i \(-0.694829\pi\)
−0.574565 + 0.818459i \(0.694829\pi\)
\(770\) 0 0
\(771\) 667.207 + 271.951i 0.865378 + 0.352725i
\(772\) 0 0
\(773\) 515.805 + 515.805i 0.667277 + 0.667277i 0.957085 0.289808i \(-0.0935914\pi\)
−0.289808 + 0.957085i \(0.593591\pi\)
\(774\) 0 0
\(775\) 343.387i 0.443080i
\(776\) 0 0
\(777\) −175.233 + 73.7490i −0.225526 + 0.0949151i
\(778\) 0 0
\(779\) 17.0083 + 17.0083i 0.0218335 + 0.0218335i
\(780\) 0 0
\(781\) 193.328 + 193.328i 0.247539 + 0.247539i
\(782\) 0 0
\(783\) 150.486 381.505i 0.192192 0.487235i
\(784\) 0 0
\(785\) 2279.05i 2.90325i
\(786\) 0 0
\(787\) −279.150 279.150i −0.354702 0.354702i 0.507154 0.861856i \(-0.330698\pi\)
−0.861856 + 0.507154i \(0.830698\pi\)
\(788\) 0 0
\(789\) −159.329 + 390.898i −0.201938 + 0.495435i
\(790\) 0 0
\(791\) 13.6788 0.0172931
\(792\) 0 0
\(793\) 733.911i 0.925487i
\(794\) 0 0
\(795\) −139.951