Properties

Label 384.3.i.b.353.1
Level $384$
Weight $3$
Character 384.353
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 353.1
Root \(0.767178 + 1.18804i\) of defining polynomial
Character \(\chi\) \(=\) 384.353
Dual form 384.3.i.b.161.1

$q$-expansion

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

Character values

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

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

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
\(3\) −2.77809 1.13234i −0.926031 0.377447i
\(4\) 0 0
\(5\) 6.28651 6.28651i 1.25730 1.25730i 0.304927 0.952376i \(-0.401368\pi\)
0.952376 0.304927i \(-0.0986321\pi\)
\(6\) 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 −0.457299 0.889313i \(-0.651183\pi\)
0.889313 + 0.457299i \(0.151183\pi\)
\(12\) 0 0
\(13\) 9.35425 9.35425i 0.719558 0.719558i −0.248957 0.968515i \(-0.580088\pi\)
0.968515 + 0.248957i \(0.0800878\pi\)
\(14\) 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 \(-0.853490\pi\)
0.444194 + 0.895931i \(0.353490\pi\)
\(20\) 0 0
\(21\) −1.86355 + 4.57205i −0.0887406 + 0.217717i
\(22\) 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
\(27\) −10.7546 24.7657i −0.398318 0.917248i
\(28\) 0 0
\(29\) −10.7405 10.7405i −0.370362 0.370362i 0.497247 0.867609i \(-0.334344\pi\)
−0.867609 + 0.497247i \(0.834344\pi\)
\(30\) 0 0
\(31\) −6.35425 −0.204976 −0.102488 0.994734i \(-0.532680\pi\)
−0.102488 + 0.994734i \(0.532680\pi\)
\(32\) 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 0.235872 0.971784i \(-0.424205\pi\)
−0.971784 + 0.235872i \(0.924205\pi\)
\(38\) 0 0
\(39\) −36.5792 + 15.3948i −0.937928 + 0.394738i
\(40\) 0 0
\(41\) −1.98162 −0.0483323 −0.0241662 0.999708i \(-0.507693\pi\)
−0.0241662 + 0.999708i \(0.507693\pi\)
\(42\) 0 0
\(43\) −19.4170 19.4170i −0.451558 0.451558i 0.444313 0.895871i \(-0.353448\pi\)
−0.895871 + 0.444313i \(0.853448\pi\)
\(44\) 0 0
\(45\) 80.0091 0.905893i 1.77798 0.0201310i
\(46\) 0 0
\(47\) 74.9474i 1.59463i −0.603566 0.797313i \(-0.706254\pi\)
0.603566 0.797313i \(-0.293746\pi\)
\(48\) 0 0
\(49\) 46.2915 0.944725
\(50\) 0 0
\(51\) 13.0060 31.9090i 0.255020 0.625667i
\(52\) 0 0
\(53\) 4.00671 4.00671i 0.0755983 0.0755983i −0.668297 0.743895i \(-0.732976\pi\)
0.743895 + 0.668297i \(0.232976\pi\)
\(54\) 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 −0.429167 0.903225i \(-0.641193\pi\)
0.903225 + 0.429167i \(0.141193\pi\)
\(60\) 0 0
\(61\) −39.2288 + 39.2288i −0.643094 + 0.643094i −0.951315 0.308221i \(-0.900267\pi\)
0.308221 + 0.951315i \(0.400267\pi\)
\(62\) 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 −0.0254932 + 0.999675i \(0.508116\pi\)
−0.999675 + 0.0254932i \(0.991884\pi\)
\(68\) 0 0
\(69\) −45.1110 18.3871i −0.653782 0.266479i
\(70\) 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 \(0.132515\pi\)
−0.914588 + 0.404387i \(0.867485\pi\)
\(74\) 0 0
\(75\) −61.1923 + 150.130i −0.815898 + 2.00173i
\(76\) 0 0
\(77\) −7.82087 7.82087i −0.101570 0.101570i
\(78\) 0 0
\(79\) −17.3948 −0.220187 −0.110093 0.993921i \(-0.535115\pi\)
−0.110093 + 0.993921i \(0.535115\pi\)
\(80\) 0 0
\(81\) 1.83399 + 80.9792i 0.0226418 + 0.999744i
\(82\) 0 0
\(83\) 75.1400 + 75.1400i 0.905301 + 0.905301i 0.995889 0.0905874i \(-0.0288745\pi\)
−0.0905874 + 0.995889i \(0.528874\pi\)
\(84\) 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 \(-0.645988\pi\)
−0.442725 + 0.896657i \(0.645988\pi\)
\(90\) 0 0
\(91\) −15.3948 15.3948i −0.169173 0.169173i
\(92\) 0 0
\(93\) 17.6527 + 7.19518i 0.189814 + 0.0773675i
\(94\) 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
\(99\) 60.4812 0.684791i 0.610921 0.00691708i
\(100\) 0 0
\(101\) −41.5332 + 41.5332i −0.411220 + 0.411220i −0.882164 0.470943i \(-0.843914\pi\)
0.470943 + 0.882164i \(0.343914\pi\)
\(102\) 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 −0.0734837 0.997296i \(-0.523412\pi\)
0.997296 + 0.0734837i \(0.0234117\pi\)
\(108\) 0 0
\(109\) −68.8523 + 68.8523i −0.631672 + 0.631672i −0.948487 0.316815i \(-0.897387\pi\)
0.316815 + 0.948487i \(0.397387\pi\)
\(110\) 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
\(117\) 119.053 1.34796i 1.01754 0.0115210i
\(118\) 0 0
\(119\) 18.9030 0.158849
\(120\) 0 0
\(121\) 75.8340i 0.626727i
\(122\) 0 0
\(123\) 5.50514 + 2.24388i 0.0447572 + 0.0182429i
\(124\) 0 0
\(125\) −182.564 182.564i −1.46051 1.46051i
\(126\) 0 0
\(127\) 195.933 1.54278 0.771391 0.636361i \(-0.219561\pi\)
0.771391 + 0.636361i \(0.219561\pi\)
\(128\) 0 0
\(129\) 31.9555 + 75.9289i 0.247717 + 0.588596i
\(130\) 0 0
\(131\) −142.127 142.127i −1.08494 1.08494i −0.996041 0.0888967i \(-0.971666\pi\)
−0.0888967 0.996041i \(-0.528334\pi\)
\(132\) 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 \(-0.441014\pi\)
0.184251 + 0.982879i \(0.441014\pi\)
\(138\) 0 0
\(139\) 171.727 + 171.727i 1.23544 + 1.23544i 0.961843 + 0.273601i \(0.0882149\pi\)
0.273601 + 0.961843i \(0.411785\pi\)
\(140\) 0 0
\(141\) −84.8661 + 208.211i −0.601887 + 1.47667i
\(142\) 0 0
\(143\) 88.9057i 0.621718i
\(144\) 0 0
\(145\) −135.041 −0.931314
\(146\) 0 0
\(147\) −128.602 52.4178i −0.874844 0.356584i
\(148\) 0 0
\(149\) 84.4952 84.4952i 0.567082 0.567082i −0.364228 0.931310i \(-0.618667\pi\)
0.931310 + 0.364228i \(0.118667\pi\)
\(150\) 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 0.168928 0.985628i \(-0.445970\pi\)
0.985628 0.168928i \(-0.0540305\pi\)
\(158\) 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 0.262581 0.964910i \(-0.415426\pi\)
0.964910 0.262581i \(-0.0845737\pi\)
\(164\) 0 0
\(165\) −67.6563 + 165.988i −0.410038 + 1.00599i
\(166\) 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
\(171\) −109.237 + 1.23682i −0.638812 + 0.00723287i
\(172\) 0 0
\(173\) 40.8313 + 40.8313i 0.236019 + 0.236019i 0.815199 0.579181i \(-0.196627\pi\)
−0.579181 + 0.815199i \(0.696627\pi\)
\(174\) 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 0.990451 0.137866i \(-0.0440245\pi\)
−0.137866 + 0.990451i \(0.544024\pi\)
\(180\) 0 0
\(181\) −166.601 166.601i −0.920449 0.920449i 0.0766118 0.997061i \(-0.475590\pi\)
−0.997061 + 0.0766118i \(0.975590\pi\)
\(182\) 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
\(189\) −40.7582 + 17.6994i −0.215652 + 0.0936474i
\(190\) 0 0
\(191\) 14.3434i 0.0750963i 0.999295 + 0.0375482i \(0.0119548\pi\)
−0.999295 + 0.0375482i \(0.988045\pi\)
\(192\) 0 0
\(193\) 207.373 1.07447 0.537235 0.843433i \(-0.319469\pi\)
0.537235 + 0.843433i \(0.319469\pi\)
\(194\) 0 0
\(195\) −133.176 + 326.735i −0.682954 + 1.67556i
\(196\) 0 0
\(197\) −97.2608 + 97.2608i −0.493710 + 0.493710i −0.909473 0.415763i \(-0.863514\pi\)
0.415763 + 0.909473i \(0.363514\pi\)
\(198\) 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 \(-0.986184\pi\)
0.0433911 + 0.999058i \(0.486184\pi\)
\(212\) 0 0
\(213\) −113.019 46.0661i −0.530605 0.216273i
\(214\) 0 0
\(215\) −244.130 −1.13549
\(216\) 0 0
\(217\) 10.4575i 0.0481913i
\(218\) 0 0
\(219\) 66.8541 164.020i 0.305270 0.748950i
\(220\) 0 0
\(221\) 107.442 + 107.442i 0.486164 + 0.486164i
\(222\) 0 0
\(223\) −233.261 −1.04602 −0.523008 0.852328i \(-0.675190\pi\)
−0.523008 + 0.852328i \(0.675190\pi\)
\(224\) 0 0
\(225\) 339.996 347.783i 1.51109 1.54570i
\(226\) 0 0
\(227\) 94.3599 + 94.3599i 0.415682 + 0.415682i 0.883712 0.468030i \(-0.155036\pi\)
−0.468030 + 0.883712i \(0.655036\pi\)
\(228\) 0 0
\(229\) 138.063 + 138.063i 0.602894 + 0.602894i 0.941080 0.338185i \(-0.109813\pi\)
−0.338185 + 0.941080i \(0.609813\pi\)
\(230\) 0 0
\(231\) 12.8712 + 30.5830i 0.0557195 + 0.132394i
\(232\) 0 0
\(233\) 396.796 1.70299 0.851493 0.524366i \(-0.175697\pi\)
0.851493 + 0.524366i \(0.175697\pi\)
\(234\) 0 0
\(235\) −471.158 471.158i −2.00493 2.00493i
\(236\) 0 0
\(237\) 48.3243 + 19.6968i 0.203900 + 0.0831090i
\(238\) 0 0
\(239\) 284.813i 1.19168i −0.803102 0.595842i \(-0.796818\pi\)
0.803102 0.595842i \(-0.203182\pi\)
\(240\) 0 0
\(241\) −266.531 −1.10594 −0.552968 0.833202i \(-0.686505\pi\)
−0.552968 + 0.833202i \(0.686505\pi\)
\(242\) 0 0
\(243\) 86.6012 227.045i 0.356383 0.934340i
\(244\) 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 −0.943811 0.330485i \(-0.892788\pi\)
0.330485 + 0.943811i \(0.392788\pi\)
\(252\) 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
\(261\) −1.54772 136.695i −0.00592995 0.523737i
\(262\) 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
\(267\) 218.928 + 89.2343i 0.819954 + 0.334211i
\(268\) 0 0
\(269\) 229.830 + 229.830i 0.854388 + 0.854388i 0.990670 0.136282i \(-0.0435152\pi\)
−0.136282 + 0.990670i \(0.543515\pi\)
\(270\) 0 0
\(271\) −228.731 −0.844025 −0.422012 0.906590i \(-0.638676\pi\)
−0.422012 + 0.906590i \(0.638676\pi\)
\(272\) 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 0.868496 0.495697i \(-0.165087\pi\)
−0.495697 + 0.868496i \(0.665087\pi\)
\(278\) 0 0
\(279\) −40.8934 39.9778i −0.146571 0.143290i
\(280\) 0 0
\(281\) 283.552 1.00908 0.504540 0.863388i \(-0.331662\pi\)
0.504540 + 0.863388i \(0.331662\pi\)
\(282\) 0 0
\(283\) 23.4758 + 23.4758i 0.0829534 + 0.0829534i 0.747366 0.664413i \(-0.231318\pi\)
−0.664413 + 0.747366i \(0.731318\pi\)
\(284\) 0 0
\(285\) 122.196 299.796i 0.428758 1.05192i
\(286\) 0 0
\(287\) 3.26126i 0.0113633i
\(288\) 0 0
\(289\) 157.073 0.543506
\(290\) 0 0
\(291\) 107.884 + 43.9734i 0.370737 + 0.151111i
\(292\) 0 0
\(293\) −381.409 + 381.409i −1.30174 + 1.30174i −0.374516 + 0.927220i \(0.622191\pi\)
−0.927220 + 0.374516i \(0.877809\pi\)
\(294\) 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 \(-0.909912\pi\)
0.279256 + 0.960217i \(0.409912\pi\)
\(308\) 0 0
\(309\) 111.889 274.508i 0.362099 0.888376i
\(310\) 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 \(-0.851094\pi\)
0.892561 0.450926i \(-0.148906\pi\)
\(314\) 0 0
\(315\) −1.49088 131.675i −0.00473294 0.418016i
\(316\) 0 0
\(317\) −206.983 206.983i −0.652943 0.652943i 0.300758 0.953701i \(-0.402760\pi\)
−0.953701 + 0.300758i \(0.902760\pi\)
\(318\) 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 \(-0.162239\pi\)
−0.487907 + 0.872896i \(0.662239\pi\)
\(332\) 0 0
\(333\) −3.92369 346.543i −0.0117829 1.04067i
\(334\) 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
\(339\) 9.41157 23.0904i 0.0277627 0.0681133i
\(340\) 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 −0.780703 0.624902i \(-0.785139\pi\)
0.624902 + 0.780703i \(0.285139\pi\)
\(348\) 0 0
\(349\) −0.107201 + 0.107201i −0.000307168 + 0.000307168i −0.707260 0.706953i \(-0.750069\pi\)
0.706953 + 0.707260i \(0.250069\pi\)
\(350\) 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
\(357\) −52.5143 21.4047i −0.147099 0.0599570i
\(358\) 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
\(363\) 85.8700 210.674i 0.236556 0.580369i
\(364\) 0 0
\(365\) 371.159 + 371.159i 1.01687 + 1.01687i
\(366\) 0 0
\(367\) 246.678 0.672148 0.336074 0.941836i \(-0.390901\pi\)
0.336074 + 0.941836i \(0.390901\pi\)
\(368\) 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 0.998157 0.0606816i \(-0.0193274\pi\)
−0.0606816 + 0.998157i \(0.519327\pi\)
\(374\) 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 \(-0.105088\pi\)
−0.324180 + 0.945995i \(0.605088\pi\)
\(380\) 0 0
\(381\) −544.321 221.864i −1.42866 0.582319i
\(382\) 0 0
\(383\) 64.2130i 0.167658i −0.996480 0.0838290i \(-0.973285\pi\)
0.996480 0.0838290i \(-0.0267149\pi\)
\(384\) 0 0
\(385\) −98.3320 −0.255408
\(386\) 0 0
\(387\) −2.79801 247.122i −0.00723000 0.638559i
\(388\) 0 0
\(389\) 273.321 273.321i 0.702624 0.702624i −0.262349 0.964973i \(-0.584497\pi\)
0.964973 + 0.262349i \(0.0844973\pi\)
\(390\) 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 −0.862659 0.505786i \(-0.831202\pi\)
0.505786 + 0.862659i \(0.331202\pi\)
\(398\) 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
\(405\) 520.607 + 497.548i 1.28545 + 1.22851i
\(406\) 0 0
\(407\) −258.791 −0.635849
\(408\) 0 0
\(409\) 420.826i 1.02891i −0.857516 0.514457i \(-0.827993\pi\)
0.857516 0.514457i \(-0.172007\pi\)
\(410\) 0 0
\(411\) −140.251 57.1659i −0.341244 0.139090i
\(412\) 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 0.893661 0.448742i \(-0.148128\pi\)
−0.448742 + 0.893661i \(0.648128\pi\)
\(420\) 0 0
\(421\) 186.889 + 186.889i 0.443917 + 0.443917i 0.893326 0.449409i \(-0.148366\pi\)
−0.449409 + 0.893326i \(0.648366\pi\)
\(422\) 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
\(429\) −100.672 + 246.988i −0.234666 + 0.575731i
\(430\) 0 0
\(431\) 128.395i 0.297901i −0.988845 0.148950i \(-0.952411\pi\)
0.988845 0.148950i \(-0.0475895\pi\)
\(432\) 0 0
\(433\) 684.737 1.58138 0.790690 0.612217i \(-0.209722\pi\)
0.790690 + 0.612217i \(0.209722\pi\)
\(434\) 0 0
\(435\) 375.155 + 152.912i 0.862426 + 0.351522i
\(436\) 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 −0.964453 0.264253i \(-0.914875\pi\)
0.264253 + 0.964453i \(0.414875\pi\)
\(444\) 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
\(453\) −34.0872 + 83.6297i −0.0752477 + 0.184613i
\(454\) 0 0
\(455\) −193.559 −0.425404
\(456\) 0 0
\(457\) 289.579i 0.633652i 0.948484 + 0.316826i \(0.102617\pi\)
−0.948484 + 0.316826i \(0.897383\pi\)
\(458\) 0 0
\(459\) 284.457 123.526i 0.619732 0.269121i
\(460\) 0 0
\(461\) 160.511 + 160.511i 0.348180 + 0.348180i 0.859431 0.511251i \(-0.170818\pi\)
−0.511251 + 0.859431i \(0.670818\pi\)
\(462\) 0 0
\(463\) 197.573 0.426723 0.213361 0.976973i \(-0.431559\pi\)
0.213361 + 0.976973i \(0.431559\pi\)
\(464\) 0 0
\(465\) 156.207 65.7413i 0.335928 0.141379i
\(466\) 0 0
\(467\) −52.7645 52.7645i −0.112986 0.112986i 0.648353 0.761339i \(-0.275458\pi\)
−0.761339 + 0.648353i \(0.775458\pi\)
\(468\) 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
\(477\) 50.9938 0.577371i 0.106905 0.00121042i
\(478\) 0 0
\(479\) 175.985i 0.367401i 0.982982 + 0.183700i \(0.0588076\pi\)
−0.982982 + 0.183700i \(0.941192\pi\)
\(480\) 0 0
\(481\) −509.409 −1.05906
\(482\) 0 0
\(483\) −30.2606 + 74.2414i −0.0626513 + 0.153709i
\(484\) 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 −0.256775 + 0.966471i \(0.582660\pi\)
−0.966471 + 0.256775i \(0.917340\pi\)
\(492\) 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 \(-0.773300\pi\)
0.653501 + 0.756926i \(0.273300\pi\)
\(500\) 0 0
\(501\) −479.653 195.505i −0.957391 0.390230i
\(502\) 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
\(507\) −6.79851 + 16.6795i −0.0134093 + 0.0328984i
\(508\) 0 0
\(509\) −128.457 128.457i −0.252372 0.252372i 0.569570 0.821942i \(-0.307110\pi\)
−0.821942 + 0.569570i \(0.807110\pi\)
\(510\) 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 \(-0.724856\pi\)
−0.649103 + 0.760700i \(0.724856\pi\)
\(522\) 0 0
\(523\) −600.494 600.494i −1.14817 1.14817i −0.986912 0.161260i \(-0.948444\pi\)
−0.161260 0.986912i \(-0.551556\pi\)
\(524\) 0 0
\(525\) 247.076 + 100.707i 0.470621 + 0.191824i
\(526\) 0 0
\(527\) 72.9845i 0.138491i
\(528\) 0 0
\(529\) −265.324 −0.501558
\(530\) 0 0
\(531\) 355.970 4.03042i 0.670376 0.00759025i
\(532\) 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 −0.746149 0.665779i \(-0.768099\pi\)
0.665779 + 0.746149i \(0.268099\pi\)
\(542\) 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 \(-0.801869\pi\)
0.583025 + 0.812454i \(0.301869\pi\)
\(548\) 0 0
\(549\) −499.269 + 5.65291i −0.909414 + 0.0102967i
\(550\) 0 0
\(551\) 184.371 0.334612
\(552\) 0 0
\(553\) 28.6275i 0.0517676i
\(554\) 0 0
\(555\) 951.074 + 387.655i 1.71365 + 0.698477i
\(556\) 0 0
\(557\) −184.272 184.272i −0.330829 0.330829i 0.522072 0.852901i \(-0.325159\pi\)
−0.852901 + 0.522072i \(0.825159\pi\)
\(558\) 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 0.0678736 0.997694i \(-0.478379\pi\)
−0.997694 + 0.0678736i \(0.978379\pi\)
\(564\) 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 \(-0.485276\pi\)
0.0462403 + 0.998930i \(0.485276\pi\)
\(570\) 0 0
\(571\) −114.561 114.561i −0.200632 0.200632i 0.599639 0.800271i \(-0.295311\pi\)
−0.800271 + 0.599639i \(0.795311\pi\)
\(572\) 0 0
\(573\) 16.2416 39.8473i 0.0283449 0.0695415i
\(574\) 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
\(579\) −576.100 234.817i −0.994992 0.405555i
\(580\) 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 −0.798435 0.602081i \(-0.794338\pi\)
0.602081 + 0.798435i \(0.294338\pi\)
\(588\) 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
\(597\) 93.7209 229.935i 0.156986 0.385151i
\(598\) 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 \(0.0227368\pi\)
−0.997450 + 0.0713690i \(0.977263\pi\)
\(602\) 0 0
\(603\) −874.177 + 9.89776i −1.44971 + 0.0164142i
\(604\) 0 0
\(605\) 476.731 + 476.731i 0.787986 + 0.787986i
\(606\) 0 0
\(607\) −685.217 −1.12886 −0.564429 0.825482i \(-0.690904\pi\)
−0.564429 + 0.825482i \(0.690904\pi\)
\(608\) 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 0.994391 0.105767i \(-0.0337296\pi\)
−0.105767 + 0.994391i \(0.533730\pi\)
\(614\) 0 0
\(615\) 48.7143 20.5020i 0.0792102 0.0333365i
\(616\) 0 0
\(617\) 383.577 0.621681 0.310840 0.950462i \(-0.399390\pi\)
0.310840 + 0.950462i \(0.399390\pi\)
\(618\) 0 0
\(619\) 81.7634 + 81.7634i 0.132089 + 0.132089i 0.770060 0.637971i \(-0.220226\pi\)
−0.637971 + 0.770060i \(0.720226\pi\)
\(620\) 0 0
\(621\) −174.634 402.148i −0.281214 0.647581i
\(622\) 0 0
\(623\) 129.694i 0.208176i
\(624\) 0 0
\(625\) −944.365 −1.51098
\(626\) 0 0
\(627\) 92.3715 226.625i 0.147323 0.361443i
\(628\) 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 0.274195 0.961674i \(-0.411588\pi\)
0.961674 0.274195i \(-0.0884115\pi\)
\(644\) 0 0
\(645\) 678.217 + 276.439i 1.05150 + 0.428588i
\(646\) 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
\(651\) 11.8415 29.0519i 0.0181897 0.0446266i
\(652\) 0 0
\(653\) −829.478 829.478i −1.27026 1.27026i −0.945953 0.324305i \(-0.894870\pi\)
−0.324305 0.945953i \(-0.605130\pi\)
\(654\) 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 0.999971 0.00762509i \(-0.00242716\pi\)
−0.00762509 + 0.999971i \(0.502427\pi\)
\(660\) 0 0
\(661\) −734.342 734.342i −1.11096 1.11096i −0.993021 0.117936i \(-0.962372\pi\)
−0.117936 0.993021i \(-0.537628\pi\)
\(662\) 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
\(669\) 648.022 + 264.132i 0.968643 + 0.394816i
\(670\) 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
\(675\) −1338.35 + 581.183i −1.98274 + 0.861012i
\(676\) 0 0
\(677\) 662.519 662.519i 0.978610 0.978610i −0.0211661 0.999776i \(-0.506738\pi\)
0.999776 + 0.0211661i \(0.00673787\pi\)
\(678\) 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 −0.471342 0.881950i \(-0.656230\pi\)
0.881950 + 0.471342i \(0.156230\pi\)
\(684\) 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 \(-0.973792\pi\)
0.0822418 + 0.996612i \(0.473792\pi\)
\(692\) 0 0
\(693\) −1.12700 99.5370i −0.00162626 0.143632i
\(694\) 0 0
\(695\) 2159.13 3.10666
\(696\) 0 0
\(697\) 22.7608i 0.0326554i
\(698\) 0 0
\(699\) −1102.34 449.309i −1.57702 0.642788i
\(700\) 0 0
\(701\) 160.480 + 160.480i 0.228930 + 0.228930i 0.812246 0.583315i \(-0.198245\pi\)
−0.583315 + 0.812246i \(0.698245\pi\)
\(702\) 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 0.934531 0.355883i \(-0.115820\pi\)
−0.355883 + 0.934531i \(0.615820\pi\)
\(710\) 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
\(717\) −322.505 + 791.236i −0.449798 + 1.10354i
\(718\) 0 0
\(719\) 1069.18i 1.48704i 0.668716 + 0.743518i \(0.266844\pi\)
−0.668716 + 0.743518i \(0.733156\pi\)
\(720\) 0 0
\(721\) 162.620 0.225547
\(722\) 0 0
\(723\) 740.447 + 301.804i 1.02413 + 0.417433i
\(724\) 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 −0.0568598 0.998382i \(-0.518109\pi\)
0.998382 + 0.0568598i \(0.0181088\pi\)
\(734\) 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 \(-0.921273\pi\)
0.244815 + 0.969570i \(0.421273\pi\)
\(740\) 0 0
\(741\) 181.826 446.093i 0.245379 0.602014i
\(742\) 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
\(747\) 10.8278 + 956.315i 0.0144950 + 1.28021i
\(748\) 0 0
\(749\) −162.679 162.679i −0.217195 0.217195i
\(750\) 0 0
\(751\) 15.8000 0.0210385 0.0105193 0.999945i \(-0.496652\pi\)
0.0105193 + 0.999945i \(0.496652\pi\)
\(752\) 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 −0.997305 0.0733640i \(-0.976627\pi\)
−0.0733640 0.997305i \(-0.523373\pi\)
\(758\) 0 0
\(759\) −301.753 + 126.996i −0.397566 + 0.167320i
\(760\) 0 0
\(761\) −212.194 −0.278836 −0.139418 0.990234i \(-0.544523\pi\)
−0.139418 + 0.990234i \(0.544523\pi\)
\(762\) 0 0
\(763\) 113.314 + 113.314i 0.148511 + 0.148511i
\(764\) 0 0
\(765\) 10.4050 + 918.980i 0.0136014 + 1.20128i
\(766\) 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
\(771\) −271.951 + 667.207i −0.352725 + 0.865378i
\(772\) 0 0
\(773\) −515.805 + 515.805i −0.667277 + 0.667277i −0.957085 0.289808i \(-0.906409\pi\)
0.289808 + 0.957085i \(0.406409\pi\)
\(774\) 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 \(-0.669302\pi\)
0.861856 + 0.507154i \(0.169302\pi\)
\(788\) 0 0
\(789\) −390.898 159.329i −0.495435 0.201938i
\(790\) 0 0
\(791\) 13.6788 0.0172931
\(792\) 0 0
\(793\) 733.911i 0.925487i
\(794\) 0 0
\(795\) −57.0434 +