Properties

Label 588.4.k.c.521.1
Level $588$
Weight $4$
Character 588.521
Analytic conductor $34.693$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(34.6931230834\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 14 x^{10} - 32 x^{9} + 70 x^{8} + 224 x^{7} - 50 x^{6} + 2016 x^{5} + 5670 x^{4} - 23328 x^{3} - 91854 x^{2} + 531441\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{7} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 521.1
Root \(2.99268 + 0.209499i\) of defining polynomial
Character \(\chi\) \(=\) 588.521
Dual form 588.4.k.c.509.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.30758 + 2.90598i) q^{3} +(7.41560 + 12.8442i) q^{5} +(10.1105 - 25.0355i) q^{9} +O(q^{10})\) \(q+(-4.30758 + 2.90598i) q^{3} +(7.41560 + 12.8442i) q^{5} +(10.1105 - 25.0355i) q^{9} +(0.589052 + 0.340089i) q^{11} -52.4373i q^{13} +(-69.2683 - 33.7779i) q^{15} +(-51.6784 + 89.5096i) q^{17} +(-86.7417 + 50.0804i) q^{19} +(-3.63771 + 2.10024i) q^{23} +(-47.4824 + 82.2418i) q^{25} +(29.2008 + 137.224i) q^{27} +53.5367i q^{29} +(-235.952 - 136.227i) q^{31} +(-3.52568 + 0.246811i) q^{33} +(25.2855 + 43.7957i) q^{37} +(152.382 + 225.878i) q^{39} +318.804 q^{41} +168.515 q^{43} +(396.537 - 55.7917i) q^{45} +(-313.988 - 543.844i) q^{47} +(-37.5043 - 535.747i) q^{51} +(-625.481 - 361.121i) q^{53} +10.0879i q^{55} +(228.115 - 467.795i) q^{57} +(-263.093 + 455.691i) q^{59} +(-205.162 + 118.450i) q^{61} +(673.515 - 388.854i) q^{65} +(-149.359 + 258.697i) q^{67} +(9.56651 - 19.6181i) q^{69} -379.893i q^{71} +(559.469 + 323.010i) q^{73} +(-34.4592 - 492.246i) q^{75} +(-211.386 - 366.132i) q^{79} +(-524.554 - 506.245i) q^{81} -391.295 q^{83} -1532.91 q^{85} +(-155.577 - 230.614i) q^{87} +(-316.431 - 548.075i) q^{89} +(1412.26 - 98.8635i) q^{93} +(-1286.48 - 742.752i) q^{95} -1432.13i q^{97} +(14.4699 - 11.3087i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 84 q^{9} + O(q^{10}) \) \( 12 q - 84 q^{9} + 132 q^{15} - 204 q^{19} - 444 q^{25} - 1458 q^{31} + 108 q^{33} + 240 q^{37} - 432 q^{39} + 342 q^{45} - 300 q^{51} + 180 q^{57} - 2148 q^{61} + 1980 q^{67} + 3084 q^{73} + 3384 q^{75} - 438 q^{79} + 1008 q^{81} - 6144 q^{85} + 2898 q^{87} + 882 q^{93} + 9216 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) −4.30758 + 2.90598i −0.828995 + 0.559256i
\(4\) 0 0
\(5\) 7.41560 + 12.8442i 0.663272 + 1.14882i 0.979751 + 0.200221i \(0.0641660\pi\)
−0.316479 + 0.948600i \(0.602501\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 10.1105 25.0355i 0.374464 0.927241i
\(10\) 0 0
\(11\) 0.589052 + 0.340089i 0.0161460 + 0.00932189i 0.508051 0.861327i \(-0.330366\pi\)
−0.491905 + 0.870649i \(0.663699\pi\)
\(12\) 0 0
\(13\) 52.4373i 1.11873i −0.828921 0.559365i \(-0.811045\pi\)
0.828921 0.559365i \(-0.188955\pi\)
\(14\) 0 0
\(15\) −69.2683 33.7779i −1.19233 0.581427i
\(16\) 0 0
\(17\) −51.6784 + 89.5096i −0.737286 + 1.27702i 0.216428 + 0.976299i \(0.430559\pi\)
−0.953713 + 0.300717i \(0.902774\pi\)
\(18\) 0 0
\(19\) −86.7417 + 50.0804i −1.04736 + 0.604696i −0.921910 0.387404i \(-0.873372\pi\)
−0.125454 + 0.992099i \(0.540039\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.63771 + 2.10024i −0.0329790 + 0.0190404i −0.516399 0.856348i \(-0.672728\pi\)
0.483420 + 0.875389i \(0.339394\pi\)
\(24\) 0 0
\(25\) −47.4824 + 82.2418i −0.379859 + 0.657935i
\(26\) 0 0
\(27\) 29.2008 + 137.224i 0.208137 + 0.978100i
\(28\) 0 0
\(29\) 53.5367i 0.342811i 0.985201 + 0.171406i \(0.0548308\pi\)
−0.985201 + 0.171406i \(0.945169\pi\)
\(30\) 0 0
\(31\) −235.952 136.227i −1.36704 0.789261i −0.376492 0.926420i \(-0.622870\pi\)
−0.990549 + 0.137158i \(0.956203\pi\)
\(32\) 0 0
\(33\) −3.52568 + 0.246811i −0.0185983 + 0.00130195i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 25.2855 + 43.7957i 0.112349 + 0.194594i 0.916717 0.399538i \(-0.130829\pi\)
−0.804368 + 0.594131i \(0.797496\pi\)
\(38\) 0 0
\(39\) 152.382 + 225.878i 0.625657 + 0.927421i
\(40\) 0 0
\(41\) 318.804 1.21436 0.607181 0.794563i \(-0.292300\pi\)
0.607181 + 0.794563i \(0.292300\pi\)
\(42\) 0 0
\(43\) 168.515 0.597634 0.298817 0.954310i \(-0.403408\pi\)
0.298817 + 0.954310i \(0.403408\pi\)
\(44\) 0 0
\(45\) 396.537 55.7917i 1.31361 0.184821i
\(46\) 0 0
\(47\) −313.988 543.844i −0.974467 1.68783i −0.681684 0.731647i \(-0.738752\pi\)
−0.292782 0.956179i \(-0.594581\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −37.5043 535.747i −0.102974 1.47097i
\(52\) 0 0
\(53\) −625.481 361.121i −1.62106 0.935922i −0.986636 0.162939i \(-0.947903\pi\)
−0.634427 0.772982i \(-0.718764\pi\)
\(54\) 0 0
\(55\) 10.0879i 0.0247318i
\(56\) 0 0
\(57\) 228.115 467.795i 0.530079 1.08703i
\(58\) 0 0
\(59\) −263.093 + 455.691i −0.580539 + 1.00552i 0.414876 + 0.909878i \(0.363825\pi\)
−0.995415 + 0.0956456i \(0.969508\pi\)
\(60\) 0 0
\(61\) −205.162 + 118.450i −0.430627 + 0.248623i −0.699614 0.714521i \(-0.746645\pi\)
0.268987 + 0.963144i \(0.413311\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 673.515 388.854i 1.28522 0.742022i
\(66\) 0 0
\(67\) −149.359 + 258.697i −0.272344 + 0.471714i −0.969462 0.245243i \(-0.921132\pi\)
0.697117 + 0.716957i \(0.254466\pi\)
\(68\) 0 0
\(69\) 9.56651 19.6181i 0.0166909 0.0342281i
\(70\) 0 0
\(71\) 379.893i 0.634999i −0.948258 0.317500i \(-0.897157\pi\)
0.948258 0.317500i \(-0.102843\pi\)
\(72\) 0 0
\(73\) 559.469 + 323.010i 0.896999 + 0.517882i 0.876225 0.481902i \(-0.160054\pi\)
0.0207735 + 0.999784i \(0.493387\pi\)
\(74\) 0 0
\(75\) −34.4592 492.246i −0.0530533 0.757863i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −211.386 366.132i −0.301048 0.521431i 0.675325 0.737520i \(-0.264003\pi\)
−0.976374 + 0.216089i \(0.930670\pi\)
\(80\) 0 0
\(81\) −524.554 506.245i −0.719553 0.694438i
\(82\) 0 0
\(83\) −391.295 −0.517472 −0.258736 0.965948i \(-0.583306\pi\)
−0.258736 + 0.965948i \(0.583306\pi\)
\(84\) 0 0
\(85\) −1532.91 −1.95608
\(86\) 0 0
\(87\) −155.577 230.614i −0.191719 0.284189i
\(88\) 0 0
\(89\) −316.431 548.075i −0.376872 0.652762i 0.613733 0.789513i \(-0.289667\pi\)
−0.990605 + 0.136752i \(0.956334\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1412.26 98.8635i 1.57467 0.110233i
\(94\) 0 0
\(95\) −1286.48 742.752i −1.38937 0.802155i
\(96\) 0 0
\(97\) 1432.13i 1.49908i −0.661959 0.749540i \(-0.730275\pi\)
0.661959 0.749540i \(-0.269725\pi\)
\(98\) 0 0
\(99\) 14.4699 11.3087i 0.0146897 0.0114805i
\(100\) 0 0
\(101\) 445.537 771.692i 0.438936 0.760260i −0.558672 0.829389i \(-0.688689\pi\)
0.997608 + 0.0691294i \(0.0220221\pi\)
\(102\) 0 0
\(103\) −1067.48 + 616.313i −1.02119 + 0.589583i −0.914448 0.404704i \(-0.867375\pi\)
−0.106740 + 0.994287i \(0.534041\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 585.738 338.176i 0.529209 0.305539i −0.211485 0.977381i \(-0.567830\pi\)
0.740694 + 0.671842i \(0.234497\pi\)
\(108\) 0 0
\(109\) 497.209 861.191i 0.436917 0.756762i −0.560533 0.828132i \(-0.689404\pi\)
0.997450 + 0.0713697i \(0.0227370\pi\)
\(110\) 0 0
\(111\) −236.189 115.175i −0.201964 0.0984854i
\(112\) 0 0
\(113\) 707.915i 0.589337i 0.955600 + 0.294668i \(0.0952091\pi\)
−0.955600 + 0.294668i \(0.904791\pi\)
\(114\) 0 0
\(115\) −53.9517 31.1490i −0.0437480 0.0252579i
\(116\) 0 0
\(117\) −1312.80 530.169i −1.03733 0.418925i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −665.269 1152.28i −0.499826 0.865724i
\(122\) 0 0
\(123\) −1373.28 + 926.440i −1.00670 + 0.679140i
\(124\) 0 0
\(125\) 445.460 0.318745
\(126\) 0 0
\(127\) −885.551 −0.618740 −0.309370 0.950942i \(-0.600118\pi\)
−0.309370 + 0.950942i \(0.600118\pi\)
\(128\) 0 0
\(129\) −725.891 + 489.701i −0.495435 + 0.334231i
\(130\) 0 0
\(131\) −844.911 1463.43i −0.563513 0.976034i −0.997186 0.0749634i \(-0.976116\pi\)
0.433673 0.901070i \(-0.357217\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −1545.99 + 1392.66i −0.985610 + 0.887858i
\(136\) 0 0
\(137\) 1670.17 + 964.276i 1.04155 + 0.601340i 0.920273 0.391278i \(-0.127967\pi\)
0.121280 + 0.992618i \(0.461300\pi\)
\(138\) 0 0
\(139\) 402.721i 0.245744i −0.992423 0.122872i \(-0.960790\pi\)
0.992423 0.122872i \(-0.0392104\pi\)
\(140\) 0 0
\(141\) 2932.93 + 1430.21i 1.75176 + 0.854222i
\(142\) 0 0
\(143\) 17.8334 30.8883i 0.0104287 0.0180630i
\(144\) 0 0
\(145\) −687.637 + 397.007i −0.393828 + 0.227377i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1392.62 804.032i 0.765692 0.442073i −0.0656434 0.997843i \(-0.520910\pi\)
0.831336 + 0.555770i \(0.187577\pi\)
\(150\) 0 0
\(151\) −183.275 + 317.442i −0.0987731 + 0.171080i −0.911177 0.412015i \(-0.864825\pi\)
0.812404 + 0.583095i \(0.198158\pi\)
\(152\) 0 0
\(153\) 1718.42 + 2198.79i 0.908015 + 1.16184i
\(154\) 0 0
\(155\) 4040.82i 2.09398i
\(156\) 0 0
\(157\) −370.608 213.970i −0.188393 0.108769i 0.402837 0.915272i \(-0.368024\pi\)
−0.591230 + 0.806503i \(0.701357\pi\)
\(158\) 0 0
\(159\) 3743.72 262.075i 1.86727 0.130716i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 116.502 + 201.787i 0.0559823 + 0.0969643i 0.892658 0.450734i \(-0.148838\pi\)
−0.836676 + 0.547698i \(0.815504\pi\)
\(164\) 0 0
\(165\) −29.3152 43.4543i −0.0138314 0.0205025i
\(166\) 0 0
\(167\) 1013.86 0.469791 0.234896 0.972021i \(-0.424525\pi\)
0.234896 + 0.972021i \(0.424525\pi\)
\(168\) 0 0
\(169\) −552.672 −0.251558
\(170\) 0 0
\(171\) 376.782 + 2677.96i 0.168498 + 1.19760i
\(172\) 0 0
\(173\) 1657.13 + 2870.23i 0.728262 + 1.26139i 0.957617 + 0.288044i \(0.0930048\pi\)
−0.229356 + 0.973343i \(0.573662\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −190.933 2727.47i −0.0810816 1.15824i
\(178\) 0 0
\(179\) 1196.04 + 690.531i 0.499418 + 0.288339i 0.728473 0.685074i \(-0.240230\pi\)
−0.229055 + 0.973413i \(0.573564\pi\)
\(180\) 0 0
\(181\) 1558.38i 0.639963i 0.947424 + 0.319981i \(0.103677\pi\)
−0.947424 + 0.319981i \(0.896323\pi\)
\(182\) 0 0
\(183\) 539.537 1106.43i 0.217944 0.446938i
\(184\) 0 0
\(185\) −375.014 + 649.543i −0.149035 + 0.258137i
\(186\) 0 0
\(187\) −60.8825 + 35.1505i −0.0238084 + 0.0137458i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1884.48 + 1088.00i −0.713905 + 0.412173i −0.812505 0.582954i \(-0.801897\pi\)
0.0986002 + 0.995127i \(0.468564\pi\)
\(192\) 0 0
\(193\) −1749.63 + 3030.45i −0.652546 + 1.13024i 0.329957 + 0.943996i \(0.392966\pi\)
−0.982503 + 0.186247i \(0.940368\pi\)
\(194\) 0 0
\(195\) −1771.22 + 3632.25i −0.650460 + 1.33390i
\(196\) 0 0
\(197\) 1297.91i 0.469401i 0.972068 + 0.234700i \(0.0754109\pi\)
−0.972068 + 0.234700i \(0.924589\pi\)
\(198\) 0 0
\(199\) −3062.79 1768.30i −1.09103 0.629908i −0.157182 0.987570i \(-0.550241\pi\)
−0.933851 + 0.357661i \(0.883574\pi\)
\(200\) 0 0
\(201\) −108.393 1548.39i −0.0380372 0.543359i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2364.13 + 4094.79i 0.805452 + 1.39508i
\(206\) 0 0
\(207\) 15.8012 + 112.307i 0.00530561 + 0.0377094i
\(208\) 0 0
\(209\) −68.1271 −0.0225476
\(210\) 0 0
\(211\) −2131.02 −0.695286 −0.347643 0.937627i \(-0.613018\pi\)
−0.347643 + 0.937627i \(0.613018\pi\)
\(212\) 0 0
\(213\) 1103.96 + 1636.42i 0.355128 + 0.526411i
\(214\) 0 0
\(215\) 1249.64 + 2164.44i 0.396394 + 0.686574i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −3348.62 + 234.416i −1.03324 + 0.0723306i
\(220\) 0 0
\(221\) 4693.64 + 2709.88i 1.42864 + 0.824824i
\(222\) 0 0
\(223\) 6147.95i 1.84617i −0.384590 0.923087i \(-0.625657\pi\)
0.384590 0.923087i \(-0.374343\pi\)
\(224\) 0 0
\(225\) 1578.89 + 2020.25i 0.467821 + 0.598594i
\(226\) 0 0
\(227\) 1484.97 2572.05i 0.434190 0.752039i −0.563039 0.826430i \(-0.690368\pi\)
0.997229 + 0.0743914i \(0.0237014\pi\)
\(228\) 0 0
\(229\) −2479.18 + 1431.35i −0.715409 + 0.413042i −0.813061 0.582179i \(-0.802200\pi\)
0.0976515 + 0.995221i \(0.468867\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5177.16 + 2989.03i −1.45565 + 0.840421i −0.998793 0.0491180i \(-0.984359\pi\)
−0.456859 + 0.889539i \(0.651026\pi\)
\(234\) 0 0
\(235\) 4656.83 8065.86i 1.29267 2.23897i
\(236\) 0 0
\(237\) 1974.54 + 962.858i 0.541181 + 0.263900i
\(238\) 0 0
\(239\) 5571.82i 1.50800i 0.656876 + 0.753998i \(0.271877\pi\)
−0.656876 + 0.753998i \(0.728123\pi\)
\(240\) 0 0
\(241\) −3591.11 2073.33i −0.959851 0.554170i −0.0637236 0.997968i \(-0.520298\pi\)
−0.896127 + 0.443798i \(0.853631\pi\)
\(242\) 0 0
\(243\) 3730.70 + 656.348i 0.984874 + 0.173271i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2626.08 + 4548.50i 0.676492 + 1.17172i
\(248\) 0 0
\(249\) 1685.54 1137.10i 0.428982 0.289400i
\(250\) 0 0
\(251\) −7611.35 −1.91404 −0.957021 0.290020i \(-0.906338\pi\)
−0.957021 + 0.290020i \(0.906338\pi\)
\(252\) 0 0
\(253\) −2.85707 −0.000709970
\(254\) 0 0
\(255\) 6603.12 4454.60i 1.62158 1.09395i
\(256\) 0 0
\(257\) 1174.76 + 2034.74i 0.285134 + 0.493867i 0.972642 0.232310i \(-0.0746284\pi\)
−0.687507 + 0.726177i \(0.741295\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1340.32 + 541.285i 0.317869 + 0.128371i
\(262\) 0 0
\(263\) −4441.42 2564.25i −1.04133 0.601211i −0.121119 0.992638i \(-0.538648\pi\)
−0.920209 + 0.391426i \(0.871982\pi\)
\(264\) 0 0
\(265\) 10711.7i 2.48308i
\(266\) 0 0
\(267\) 2955.75 + 1441.33i 0.677486 + 0.330368i
\(268\) 0 0
\(269\) −20.2532 + 35.0795i −0.00459055 + 0.00795107i −0.868312 0.496019i \(-0.834795\pi\)
0.863721 + 0.503970i \(0.168128\pi\)
\(270\) 0 0
\(271\) −2807.84 + 1621.11i −0.629389 + 0.363378i −0.780515 0.625137i \(-0.785043\pi\)
0.151127 + 0.988514i \(0.451710\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −55.9391 + 32.2965i −0.0122664 + 0.00708200i
\(276\) 0 0
\(277\) 1107.85 1918.85i 0.240304 0.416219i −0.720497 0.693458i \(-0.756086\pi\)
0.960801 + 0.277239i \(0.0894195\pi\)
\(278\) 0 0
\(279\) −5796.12 + 4529.86i −1.24374 + 0.972027i
\(280\) 0 0
\(281\) 5882.33i 1.24879i 0.781108 + 0.624395i \(0.214655\pi\)
−0.781108 + 0.624395i \(0.785345\pi\)
\(282\) 0 0
\(283\) 1323.79 + 764.290i 0.278060 + 0.160538i 0.632545 0.774524i \(-0.282010\pi\)
−0.354485 + 0.935062i \(0.615344\pi\)
\(284\) 0 0
\(285\) 7700.06 539.034i 1.60039 0.112034i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −2884.82 4996.65i −0.587180 1.01703i
\(290\) 0 0
\(291\) 4161.74 + 6169.02i 0.838370 + 1.24273i
\(292\) 0 0
\(293\) 6038.37 1.20398 0.601989 0.798505i \(-0.294375\pi\)
0.601989 + 0.798505i \(0.294375\pi\)
\(294\) 0 0
\(295\) −7803.98 −1.54022
\(296\) 0 0
\(297\) −29.4675 + 90.7627i −0.00575716 + 0.0177326i
\(298\) 0 0
\(299\) 110.131 + 190.752i 0.0213011 + 0.0368946i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 323.337 + 4618.85i 0.0613044 + 0.875729i
\(304\) 0 0
\(305\) −3042.79 1756.76i −0.571246 0.329809i
\(306\) 0 0
\(307\) 7231.98i 1.34447i 0.740340 + 0.672233i \(0.234665\pi\)
−0.740340 + 0.672233i \(0.765335\pi\)
\(308\) 0 0
\(309\) 2807.29 5756.91i 0.516831 1.05987i
\(310\) 0 0
\(311\) −859.000 + 1487.83i −0.156622 + 0.271277i −0.933648 0.358191i \(-0.883394\pi\)
0.777027 + 0.629468i \(0.216727\pi\)
\(312\) 0 0
\(313\) 4787.88 2764.28i 0.864622 0.499190i −0.000935213 1.00000i \(-0.500298\pi\)
0.865557 + 0.500810i \(0.166964\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1541.66 + 890.076i −0.273149 + 0.157702i −0.630318 0.776337i \(-0.717075\pi\)
0.357169 + 0.934040i \(0.383742\pi\)
\(318\) 0 0
\(319\) −18.2073 + 31.5359i −0.00319565 + 0.00553502i
\(320\) 0 0
\(321\) −1540.38 + 3158.86i −0.267837 + 0.549254i
\(322\) 0 0
\(323\) 10352.3i 1.78333i
\(324\) 0 0
\(325\) 4312.54 + 2489.85i 0.736052 + 0.424960i
\(326\) 0 0
\(327\) 360.837 + 5154.53i 0.0610224 + 0.871701i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 3219.65 + 5576.59i 0.534646 + 0.926034i 0.999180 + 0.0404789i \(0.0128884\pi\)
−0.464534 + 0.885555i \(0.653778\pi\)
\(332\) 0 0
\(333\) 1352.10 190.236i 0.222506 0.0313060i
\(334\) 0 0
\(335\) −4430.34 −0.722553
\(336\) 0 0
\(337\) 2095.32 0.338692 0.169346 0.985557i \(-0.445834\pi\)
0.169346 + 0.985557i \(0.445834\pi\)
\(338\) 0 0
\(339\) −2057.19 3049.40i −0.329590 0.488557i
\(340\) 0 0
\(341\) −92.6587 160.490i −0.0147148 0.0254868i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 322.920 22.6057i 0.0503925 0.00352767i
\(346\) 0 0
\(347\) 2115.84 + 1221.58i 0.327332 + 0.188985i 0.654656 0.755927i \(-0.272814\pi\)
−0.327324 + 0.944912i \(0.606147\pi\)
\(348\) 0 0
\(349\) 1583.72i 0.242907i 0.992597 + 0.121453i \(0.0387555\pi\)
−0.992597 + 0.121453i \(0.961244\pi\)
\(350\) 0 0
\(351\) 7195.64 1531.21i 1.09423 0.232849i
\(352\) 0 0
\(353\) −4032.35 + 6984.23i −0.607989 + 1.05307i 0.383583 + 0.923507i \(0.374690\pi\)
−0.991571 + 0.129561i \(0.958643\pi\)
\(354\) 0 0
\(355\) 4879.42 2817.13i 0.729500 0.421177i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5312.56 + 3067.21i −0.781020 + 0.450922i −0.836792 0.547522i \(-0.815571\pi\)
0.0557719 + 0.998444i \(0.482238\pi\)
\(360\) 0 0
\(361\) 1586.58 2748.04i 0.231314 0.400648i
\(362\) 0 0
\(363\) 6214.20 + 3030.28i 0.898515 + 0.438150i
\(364\) 0 0
\(365\) 9581.25i 1.37399i
\(366\) 0 0
\(367\) 3351.77 + 1935.14i 0.476733 + 0.275242i 0.719054 0.694954i \(-0.244575\pi\)
−0.242321 + 0.970196i \(0.577909\pi\)
\(368\) 0 0
\(369\) 3223.28 7981.43i 0.454736 1.12601i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −3644.06 6311.70i −0.505851 0.876160i −0.999977 0.00676929i \(-0.997845\pi\)
0.494126 0.869390i \(-0.335488\pi\)
\(374\) 0 0
\(375\) −1918.85 + 1294.50i −0.264238 + 0.178260i
\(376\) 0 0
\(377\) 2807.32 0.383513
\(378\) 0 0
\(379\) −3203.69 −0.434201 −0.217101 0.976149i \(-0.569660\pi\)
−0.217101 + 0.976149i \(0.569660\pi\)
\(380\) 0 0
\(381\) 3814.59 2573.40i 0.512932 0.346034i
\(382\) 0 0
\(383\) 2096.49 + 3631.22i 0.279701 + 0.484456i 0.971310 0.237816i \(-0.0764314\pi\)
−0.691610 + 0.722272i \(0.743098\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1703.77 4218.85i 0.223793 0.554151i
\(388\) 0 0
\(389\) 5025.75 + 2901.62i 0.655053 + 0.378195i 0.790390 0.612605i \(-0.209878\pi\)
−0.135336 + 0.990800i \(0.543212\pi\)
\(390\) 0 0
\(391\) 434.147i 0.0561529i
\(392\) 0 0
\(393\) 7892.22 + 3848.55i 1.01300 + 0.493978i
\(394\) 0 0
\(395\) 3135.11 5430.18i 0.399354 0.691701i
\(396\) 0 0
\(397\) −13668.1 + 7891.30i −1.72792 + 0.997614i −0.829440 + 0.558596i \(0.811340\pi\)
−0.898478 + 0.439018i \(0.855327\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6782.69 3915.99i 0.844667 0.487669i −0.0141808 0.999899i \(-0.504514\pi\)
0.858848 + 0.512231i \(0.171181\pi\)
\(402\) 0 0
\(403\) −7143.38 + 12372.7i −0.882971 + 1.52935i
\(404\) 0 0
\(405\) 2612.43 10491.6i 0.320525 1.28724i
\(406\) 0 0
\(407\) 34.3972i 0.00418921i
\(408\) 0 0
\(409\) −11913.3 6878.12i −1.44028 0.831543i −0.442408 0.896814i \(-0.645876\pi\)
−0.997868 + 0.0652706i \(0.979209\pi\)
\(410\) 0 0
\(411\) −9996.58 + 699.800i −1.19974 + 0.0839868i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −2901.69 5025.87i −0.343225 0.594483i
\(416\) 0 0
\(417\) 1170.30 + 1734.76i 0.137434 + 0.203720i
\(418\) 0 0
\(419\) 9478.94 1.10519 0.552597 0.833448i \(-0.313637\pi\)
0.552597 + 0.833448i \(0.313637\pi\)
\(420\) 0 0
\(421\) −7360.46 −0.852082 −0.426041 0.904704i \(-0.640092\pi\)
−0.426041 + 0.904704i \(0.640092\pi\)
\(422\) 0 0
\(423\) −16790.0 + 2362.31i −1.92992 + 0.271535i
\(424\) 0 0
\(425\) −4907.62 8500.26i −0.560129 0.970172i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 12.9421 + 184.877i 0.00145653 + 0.0208064i
\(430\) 0 0
\(431\) 76.0396 + 43.9015i 0.00849814 + 0.00490641i 0.504243 0.863562i \(-0.331772\pi\)
−0.495745 + 0.868468i \(0.665105\pi\)
\(432\) 0 0
\(433\) 1782.09i 0.197787i −0.995098 0.0988936i \(-0.968470\pi\)
0.995098 0.0988936i \(-0.0315303\pi\)
\(434\) 0 0
\(435\) 1808.36 3708.40i 0.199320 0.408745i
\(436\) 0 0
\(437\) 210.361 364.356i 0.0230273 0.0398845i
\(438\) 0 0
\(439\) −8035.74 + 4639.44i −0.873634 + 0.504393i −0.868554 0.495595i \(-0.834950\pi\)
−0.00507951 + 0.999987i \(0.501617\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4831.09 + 2789.23i −0.518131 + 0.299143i −0.736170 0.676797i \(-0.763367\pi\)
0.218039 + 0.975940i \(0.430034\pi\)
\(444\) 0 0
\(445\) 4693.05 8128.61i 0.499937 0.865917i
\(446\) 0 0
\(447\) −3662.34 + 7510.37i −0.387523 + 0.794694i
\(448\) 0 0
\(449\) 5410.98i 0.568730i −0.958716 0.284365i \(-0.908217\pi\)
0.958716 0.284365i \(-0.0917827\pi\)
\(450\) 0 0
\(451\) 187.792 + 108.422i 0.0196071 + 0.0113201i
\(452\) 0 0
\(453\) −133.008 1900.00i −0.0137952 0.197064i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 3971.67 + 6879.13i 0.406536 + 0.704140i 0.994499 0.104747i \(-0.0334034\pi\)
−0.587963 + 0.808888i \(0.700070\pi\)
\(458\) 0 0
\(459\) −13791.9 4477.75i −1.40251 0.455345i
\(460\) 0 0
\(461\) −2715.21 −0.274317 −0.137159 0.990549i \(-0.543797\pi\)
−0.137159 + 0.990549i \(0.543797\pi\)
\(462\) 0 0
\(463\) −11587.7 −1.16313 −0.581563 0.813502i \(-0.697558\pi\)
−0.581563 + 0.813502i \(0.697558\pi\)
\(464\) 0 0
\(465\) 11742.6 + 17406.2i 1.17107 + 1.73590i
\(466\) 0 0
\(467\) 1879.76 + 3255.83i 0.186263 + 0.322617i 0.944001 0.329942i \(-0.107029\pi\)
−0.757738 + 0.652558i \(0.773696\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 2218.22 155.284i 0.217006 0.0151913i
\(472\) 0 0
\(473\) 99.2639 + 57.3100i 0.00964938 + 0.00557107i
\(474\) 0 0
\(475\) 9511.73i 0.918796i
\(476\) 0 0
\(477\) −15364.8 + 12008.1i −1.47486 + 1.15265i
\(478\) 0 0
\(479\) −2666.10 + 4617.82i −0.254316 + 0.440488i −0.964709 0.263317i \(-0.915184\pi\)
0.710394 + 0.703804i \(0.248517\pi\)
\(480\) 0 0
\(481\) 2296.53 1325.90i 0.217698 0.125688i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 18394.6 10620.1i 1.72217 0.994297i
\(486\) 0 0
\(487\) −521.790 + 903.766i −0.0485514 + 0.0840935i −0.889280 0.457364i \(-0.848794\pi\)
0.840728 + 0.541457i \(0.182127\pi\)
\(488\) 0 0
\(489\) −1088.23 530.662i −0.100637 0.0490744i
\(490\) 0 0
\(491\) 13213.2i 1.21446i −0.794525 0.607232i \(-0.792280\pi\)
0.794525 0.607232i \(-0.207720\pi\)
\(492\) 0 0
\(493\) −4792.05 2766.69i −0.437775 0.252750i
\(494\) 0 0
\(495\) 252.555 + 101.994i 0.0229323 + 0.00926117i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 874.489 + 1514.66i 0.0784519 + 0.135883i 0.902582 0.430518i \(-0.141669\pi\)
−0.824130 + 0.566400i \(0.808336\pi\)
\(500\) 0 0
\(501\) −4367.30 + 2946.27i −0.389454 + 0.262734i
\(502\) 0 0
\(503\) −12215.5 −1.08283 −0.541414 0.840756i \(-0.682111\pi\)
−0.541414 + 0.840756i \(0.682111\pi\)
\(504\) 0 0
\(505\) 13215.7 1.16454
\(506\) 0 0
\(507\) 2380.68 1606.05i 0.208540 0.140685i
\(508\) 0 0
\(509\) −8483.69 14694.2i −0.738768 1.27958i −0.953050 0.302812i \(-0.902074\pi\)
0.214282 0.976772i \(-0.431259\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −9405.13 10440.6i −0.809448 0.898567i
\(514\) 0 0
\(515\) −15832.1 9140.66i −1.35465 0.782108i
\(516\) 0 0
\(517\) 427.136i 0.0363355i
\(518\) 0 0
\(519\) −15479.1 7548.18i −1.30916 0.638397i
\(520\) 0 0
\(521\) 2103.60 3643.55i 0.176892 0.306385i −0.763923 0.645308i \(-0.776729\pi\)
0.940814 + 0.338922i \(0.110062\pi\)
\(522\) 0 0
\(523\) 5104.44 2947.05i 0.426772 0.246397i −0.271199 0.962523i \(-0.587420\pi\)
0.697970 + 0.716127i \(0.254087\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 24387.3 14080.0i 2.01580 1.16382i
\(528\) 0 0
\(529\) −6074.68 + 10521.7i −0.499275 + 0.864770i
\(530\) 0 0
\(531\) 8748.44 + 11194.0i 0.714972 + 0.914833i
\(532\) 0 0
\(533\) 16717.2i 1.35854i
\(534\) 0 0
\(535\) 8687.20 + 5015.56i 0.702019 + 0.405311i
\(536\) 0 0
\(537\) −7158.69 + 501.136i −0.575271 + 0.0402712i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −8059.86 13960.1i −0.640518 1.10941i −0.985317 0.170734i \(-0.945386\pi\)
0.344799 0.938677i \(-0.387947\pi\)
\(542\) 0 0
\(543\) −4528.61 6712.84i −0.357903 0.530526i
\(544\) 0 0
\(545\) 14748.4 1.15918
\(546\) 0 0
\(547\) 14061.3 1.09912 0.549558 0.835456i \(-0.314796\pi\)
0.549558 + 0.835456i \(0.314796\pi\)
\(548\) 0 0
\(549\) 891.165 + 6333.92i 0.0692787 + 0.492396i
\(550\) 0 0
\(551\) −2681.14 4643.87i −0.207296 0.359048i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −272.157 3887.74i −0.0208152 0.297343i
\(556\) 0 0
\(557\) −7010.50 4047.52i −0.533294 0.307897i 0.209063 0.977902i \(-0.432959\pi\)
−0.742357 + 0.670005i \(0.766292\pi\)
\(558\) 0 0
\(559\) 8836.46i 0.668591i
\(560\) 0 0
\(561\) 160.110 328.337i 0.0120496 0.0247102i
\(562\) 0 0
\(563\) 5149.34 8918.92i 0.385469 0.667651i −0.606366 0.795186i \(-0.707373\pi\)
0.991834 + 0.127535i \(0.0407065\pi\)
\(564\) 0 0
\(565\) −9092.60 + 5249.62i −0.677042 + 0.390890i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2507.30 1447.59i 0.184730 0.106654i −0.404783 0.914413i \(-0.632653\pi\)
0.589513 + 0.807759i \(0.299320\pi\)
\(570\) 0 0
\(571\) 310.198 537.278i 0.0227345 0.0393772i −0.854434 0.519559i \(-0.826096\pi\)
0.877169 + 0.480182i \(0.159429\pi\)
\(572\) 0 0
\(573\) 4955.82 10162.9i 0.361313 0.740946i
\(574\) 0 0
\(575\) 398.897i 0.0289307i
\(576\) 0 0
\(577\) 8241.62 + 4758.30i 0.594633 + 0.343312i 0.766927 0.641734i \(-0.221785\pi\)
−0.172294 + 0.985046i \(0.555118\pi\)
\(578\) 0 0
\(579\) −1269.75 18138.3i −0.0911385 1.30191i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −245.627 425.438i −0.0174491 0.0302227i
\(584\) 0 0
\(585\) −2925.56 20793.3i −0.206764 1.46957i
\(586\) 0 0
\(587\) −1093.47 −0.0768861 −0.0384431 0.999261i \(-0.512240\pi\)
−0.0384431 + 0.999261i \(0.512240\pi\)
\(588\) 0 0
\(589\) 27289.2 1.90905
\(590\) 0 0
\(591\) −3771.69 5590.83i −0.262515 0.389131i
\(592\) 0 0
\(593\) −4882.36 8456.49i −0.338102 0.585610i 0.645974 0.763360i \(-0.276451\pi\)
−0.984076 + 0.177750i \(0.943118\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 18331.9 1283.30i 1.25674 0.0879768i
\(598\) 0 0
\(599\) 12740.2 + 7355.53i 0.869029 + 0.501734i 0.867026 0.498264i \(-0.166029\pi\)
0.00200376 + 0.999998i \(0.499362\pi\)
\(600\) 0 0
\(601\) 14047.5i 0.953425i 0.879059 + 0.476713i \(0.158172\pi\)
−0.879059 + 0.476713i \(0.841828\pi\)
\(602\) 0 0
\(603\) 4966.51 + 6354.83i 0.335409 + 0.429169i
\(604\) 0 0
\(605\) 9866.74 17089.7i 0.663041 1.14842i
\(606\) 0 0
\(607\) 14931.5 8620.73i 0.998439 0.576449i 0.0906530 0.995883i \(-0.471105\pi\)
0.907786 + 0.419434i \(0.137771\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −28517.7 + 16464.7i −1.88822 + 1.09017i
\(612\) 0 0
\(613\) −3608.26 + 6249.69i −0.237742 + 0.411782i −0.960066 0.279773i \(-0.909741\pi\)
0.722324 + 0.691555i \(0.243074\pi\)
\(614\) 0 0
\(615\) −22083.0 10768.5i −1.44793 0.706063i
\(616\) 0 0
\(617\) 25662.2i 1.67443i 0.546877 + 0.837213i \(0.315817\pi\)
−0.546877 + 0.837213i \(0.684183\pi\)
\(618\) 0 0
\(619\) 10818.3 + 6245.96i 0.702464 + 0.405568i 0.808265 0.588820i \(-0.200407\pi\)
−0.105800 + 0.994387i \(0.533740\pi\)
\(620\) 0 0
\(621\) −394.426 437.852i −0.0254876 0.0282937i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 9238.65 + 16001.8i 0.591273 + 1.02412i
\(626\) 0 0
\(627\) 293.463 197.976i 0.0186919 0.0126099i
\(628\) 0 0
\(629\) −5226.85 −0.331332
\(630\) 0 0
\(631\) −11952.7 −0.754091 −0.377046 0.926195i \(-0.623060\pi\)
−0.377046 + 0.926195i \(0.623060\pi\)
\(632\) 0 0
\(633\) 9179.54 6192.70i 0.576388 0.388843i
\(634\) 0 0
\(635\) −6566.90 11374.2i −0.410393 0.710821i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −9510.81 3840.92i −0.588798 0.237785i
\(640\) 0 0
\(641\) −12156.4 7018.51i −0.749063 0.432472i 0.0762922 0.997086i \(-0.475692\pi\)
−0.825355 + 0.564614i \(0.809025\pi\)
\(642\) 0 0
\(643\) 12089.9i 0.741493i 0.928734 + 0.370747i \(0.120898\pi\)
−0.928734 + 0.370747i \(0.879102\pi\)
\(644\) 0 0
\(645\) −11672.7 5692.06i −0.712579 0.347480i
\(646\) 0 0
\(647\) −2411.27 + 4176.44i −0.146517 + 0.253775i −0.929938 0.367716i \(-0.880140\pi\)
0.783421 + 0.621492i \(0.213473\pi\)
\(648\) 0 0
\(649\) −309.951 + 178.950i −0.0187467 + 0.0108234i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2592.48 1496.77i 0.155362 0.0896983i −0.420303 0.907384i \(-0.638076\pi\)
0.575666 + 0.817685i \(0.304743\pi\)
\(654\) 0 0
\(655\) 12531.1 21704.4i 0.747525 1.29475i
\(656\) 0 0
\(657\) 13743.2 10740.8i 0.816096 0.637806i
\(658\) 0 0
\(659\) 4336.79i 0.256354i 0.991751 + 0.128177i \(0.0409125\pi\)
−0.991751 + 0.128177i \(0.959087\pi\)
\(660\) 0 0
\(661\) −16220.2 9364.73i −0.954451 0.551053i −0.0599904 0.998199i \(-0.519107\pi\)
−0.894461 + 0.447146i \(0.852440\pi\)
\(662\) 0 0
\(663\) −28093.1 + 1966.63i −1.64562 + 0.115200i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −112.440 194.751i −0.00652726 0.0113056i
\(668\) 0 0
\(669\) 17865.8 + 26482.8i 1.03249 + 1.53047i
\(670\) 0 0
\(671\) −161.134 −0.00927053
\(672\) 0 0
\(673\) −19919.4 −1.14092 −0.570459 0.821326i \(-0.693235\pi\)
−0.570459 + 0.821326i \(0.693235\pi\)
\(674\) 0 0
\(675\) −12672.0 4114.17i −0.722588 0.234599i
\(676\) 0 0
\(677\) 15019.2 + 26014.1i 0.852638 + 1.47681i 0.878819 + 0.477155i \(0.158332\pi\)
−0.0261815 + 0.999657i \(0.508335\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1077.68 + 15394.6i 0.0606415 + 0.866259i
\(682\) 0 0
\(683\) 3348.00 + 1932.97i 0.187566 + 0.108291i 0.590843 0.806787i \(-0.298795\pi\)
−0.403277 + 0.915078i \(0.632129\pi\)
\(684\) 0 0
\(685\) 28602.7i 1.59541i
\(686\) 0 0
\(687\) 6519.78 13370.1i 0.362074 0.742507i
\(688\) 0 0
\(689\) −18936.2 + 32798.5i −1.04704 + 1.81353i
\(690\) 0 0
\(691\) 5762.10 3326.75i 0.317222 0.183148i −0.332931 0.942951i \(-0.608038\pi\)
0.650154 + 0.759803i \(0.274704\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5172.64 2986.42i 0.282315 0.162995i
\(696\) 0 0
\(697\) −16475.3 + 28536.1i −0.895332 + 1.55076i
\(698\) 0 0
\(699\) 13615.0 27920.2i 0.736717 1.51079i
\(700\) 0 0
\(701\) 21100.3i 1.13687i −0.822728 0.568435i \(-0.807549\pi\)
0.822728 0.568435i \(-0.192451\pi\)
\(702\) 0 0
\(703\) −4386.61 2532.61i −0.235340 0.135874i
\(704\) 0 0
\(705\) 3379.58 + 48277.0i 0.180542 + 2.57903i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −11715.1 20291.1i −0.620548 1.07482i −0.989384 0.145326i \(-0.953577\pi\)
0.368836 0.929494i \(-0.379756\pi\)
\(710\) 0 0
\(711\) −11303.5 + 1590.38i −0.596224 + 0.0838871i
\(712\) 0 0
\(713\) 1144.44 0.0601114
\(714\) 0 0
\(715\) 528.981 0.0276682
\(716\) 0 0
\(717\) −16191.6 24001.1i −0.843357 1.25012i
\(718\) 0 0
\(719\) 4247.60 + 7357.06i 0.220318 + 0.381603i 0.954905 0.296913i \(-0.0959571\pi\)
−0.734586 + 0.678515i \(0.762624\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 21494.1 1504.67i 1.10563 0.0773987i
\(724\) 0 0
\(725\) −4402.96 2542.05i −0.225547 0.130220i
\(726\) 0 0
\(727\) 2662.18i 0.135811i 0.997692 + 0.0679057i \(0.0216317\pi\)
−0.997692 + 0.0679057i \(0.978368\pi\)
\(728\) 0 0
\(729\) −17977.6 + 8014.07i −0.913358 + 0.407157i
\(730\) 0 0
\(731\) −8708.57 + 15083.7i −0.440627 + 0.763188i
\(732\) 0 0
\(733\) 17425.1 10060.4i 0.878052 0.506943i 0.00803608 0.999968i \(-0.497442\pi\)
0.870015 + 0.493024i \(0.164109\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −175.960 + 101.590i −0.00879453 + 0.00507752i
\(738\) 0 0
\(739\) 4889.49 8468.84i 0.243387 0.421558i −0.718290 0.695744i \(-0.755075\pi\)
0.961677 + 0.274186i \(0.0884083\pi\)
\(740\) 0 0
\(741\) −24529.9 11961.7i −1.21610 0.593015i
\(742\) 0 0
\(743\) 35045.8i 1.73043i 0.501404 + 0.865213i \(0.332817\pi\)
−0.501404 + 0.865213i \(0.667183\pi\)
\(744\) 0 0
\(745\) 20654.3 + 11924.8i 1.01572 + 0.586429i
\(746\) 0 0
\(747\) −3956.20 + 9796.27i −0.193775 + 0.479822i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −10043.6 17396.0i −0.488011 0.845260i 0.511894 0.859049i \(-0.328944\pi\)
−0.999905 + 0.0137887i \(0.995611\pi\)
\(752\) 0 0
\(753\) 32786.5 22118.5i 1.58673 1.07044i
\(754\) 0 0
\(755\) −5436.39 −0.262054
\(756\) 0 0
\(757\) −2813.68 −0.135092 −0.0675462 0.997716i \(-0.521517\pi\)
−0.0675462 + 0.997716i \(0.521517\pi\)
\(758\) 0 0
\(759\) 12.3071 8.30259i 0.000588561 0.000397055i
\(760\) 0 0
\(761\) 10857.5 + 18805.7i 0.517191 + 0.895801i 0.999801 + 0.0199656i \(0.00635567\pi\)
−0.482610 + 0.875836i \(0.660311\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −15498.5 + 38377.1i −0.732483 + 1.81376i
\(766\) 0 0
\(767\) 23895.2 + 13795.9i 1.12491 + 0.649467i
\(768\) 0 0
\(769\) 15956.6i 0.748257i 0.927377 + 0.374128i \(0.122058\pi\)
−0.927377 + 0.374128i \(0.877942\pi\)
\(770\) 0 0
\(771\) −10973.3 5351.00i −0.512573 0.249950i
\(772\) 0 0
\(773\) −3910.77 + 6773.65i −0.181967 + 0.315176i −0.942550 0.334064i \(-0.891580\pi\)
0.760583 + 0.649240i \(0.224913\pi\)
\(774\) 0 0
\(775\) 22407.1 12936.8i 1.03857 0.599616i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −27653.6 + 15965.8i −1.27188 + 0.734320i
\(780\) 0 0
\(781\) 129.197 223.776i 0.00591939 0.0102527i
\(782\) 0 0
\(783\) −7346.50 + 1563.31i −0.335304 + 0.0713516i
\(784\) 0 0
\(785\) 6346.88i 0.288573i
\(786\) 0 0
\(787\) 21587.3 + 12463.4i 0.977767 + 0.564514i 0.901595 0.432581i \(-0.142397\pi\)
0.0761716 + 0.997095i \(0.475730\pi\)
\(788\) 0 0
\(789\) 26583.4 1860.94i 1.19949 0.0839688i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6211.21 + 10758.1i 0.278142 + 0.481756i
\(794\) 0 0
\(795\) 31128.1 + 46141.7i