Properties

Label 1900.2.i.g.201.1
Level $1900$
Weight $2$
Character 1900.201
Analytic conductor $15.172$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \( x^{20} + 20 x^{18} + 261 x^{16} + 1994 x^{14} + 11074 x^{12} + 39211 x^{10} + 99376 x^{8} + 134299 x^{6} + 124617 x^{4} + 24768 x^{2} + 4096 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.1
Root \(1.43632 + 2.48777i\) of defining polynomial
Character \(\chi\) \(=\) 1900.201
Dual form 1900.2.i.g.501.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.43632 + 2.48777i) q^{3} +3.54568 q^{7} +(-2.62601 - 4.54838i) q^{9} +O(q^{10})\) \(q+(-1.43632 + 2.48777i) q^{3} +3.54568 q^{7} +(-2.62601 - 4.54838i) q^{9} -1.81575 q^{11} +(-1.60681 - 2.78308i) q^{13} +(3.99638 - 6.92193i) q^{17} +(-0.863760 + 4.27246i) q^{19} +(-5.09271 + 8.82084i) q^{21} +(4.21480 + 7.30026i) q^{23} +6.46921 q^{27} +(4.29124 + 7.43265i) q^{29} -1.70874 q^{31} +(2.60799 - 4.51718i) q^{33} +5.50608 q^{37} +9.23155 q^{39} +(4.05694 - 7.02683i) q^{41} +(2.51363 - 4.35373i) q^{43} +(0.674543 + 1.16834i) q^{47} +5.57183 q^{49} +(11.4801 + 19.8842i) q^{51} +(1.10967 + 1.92201i) q^{53} +(-9.38828 - 8.28544i) q^{57} +(-0.960774 + 1.66411i) q^{59} +(2.83047 + 4.90251i) q^{61} +(-9.31098 - 16.1271i) q^{63} +(4.64397 + 8.04360i) q^{67} -24.2152 q^{69} +(-2.94365 + 5.09854i) q^{71} +(-1.63226 + 2.82716i) q^{73} -6.43807 q^{77} +(-2.08739 + 3.61546i) q^{79} +(-1.41381 + 2.44879i) q^{81} +6.30268 q^{83} -24.6543 q^{87} +(-2.73646 - 4.73968i) q^{89} +(-5.69723 - 9.86789i) q^{91} +(2.45429 - 4.25096i) q^{93} +(-3.99096 + 6.91255i) q^{97} +(4.76818 + 8.25873i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 10 q^{9} - 14 q^{19} - 8 q^{21} + 16 q^{29} + 8 q^{31} + 8 q^{39} + 26 q^{41} + 44 q^{49} + 26 q^{51} - 4 q^{59} + 2 q^{61} - 48 q^{69} - 2 q^{71} + 16 q^{79} + 26 q^{81} + 40 q^{89} - 4 q^{91} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) −1.43632 + 2.48777i −0.829257 + 1.43632i 0.0693641 + 0.997591i \(0.477903\pi\)
−0.898622 + 0.438725i \(0.855430\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 3.54568 1.34014 0.670070 0.742298i \(-0.266264\pi\)
0.670070 + 0.742298i \(0.266264\pi\)
\(8\) 0 0
\(9\) −2.62601 4.54838i −0.875336 1.51613i
\(10\) 0 0
\(11\) −1.81575 −0.547470 −0.273735 0.961805i \(-0.588259\pi\)
−0.273735 + 0.961805i \(0.588259\pi\)
\(12\) 0 0
\(13\) −1.60681 2.78308i −0.445649 0.771887i 0.552448 0.833547i \(-0.313694\pi\)
−0.998097 + 0.0616606i \(0.980360\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.99638 6.92193i 0.969264 1.67881i 0.271570 0.962419i \(-0.412457\pi\)
0.697694 0.716396i \(-0.254210\pi\)
\(18\) 0 0
\(19\) −0.863760 + 4.27246i −0.198160 + 0.980170i
\(20\) 0 0
\(21\) −5.09271 + 8.82084i −1.11132 + 1.92486i
\(22\) 0 0
\(23\) 4.21480 + 7.30026i 0.878848 + 1.52221i 0.852607 + 0.522553i \(0.175020\pi\)
0.0262406 + 0.999656i \(0.491646\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 6.46921 1.24500
\(28\) 0 0
\(29\) 4.29124 + 7.43265i 0.796863 + 1.38021i 0.921649 + 0.388024i \(0.126842\pi\)
−0.124786 + 0.992184i \(0.539824\pi\)
\(30\) 0 0
\(31\) −1.70874 −0.306899 −0.153450 0.988156i \(-0.549038\pi\)
−0.153450 + 0.988156i \(0.549038\pi\)
\(32\) 0 0
\(33\) 2.60799 4.51718i 0.453994 0.786340i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.50608 0.905193 0.452597 0.891715i \(-0.350498\pi\)
0.452597 + 0.891715i \(0.350498\pi\)
\(38\) 0 0
\(39\) 9.23155 1.47823
\(40\) 0 0
\(41\) 4.05694 7.02683i 0.633588 1.09741i −0.353224 0.935539i \(-0.614915\pi\)
0.986812 0.161868i \(-0.0517520\pi\)
\(42\) 0 0
\(43\) 2.51363 4.35373i 0.383325 0.663938i −0.608211 0.793776i \(-0.708112\pi\)
0.991535 + 0.129838i \(0.0414457\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.674543 + 1.16834i 0.0983922 + 0.170420i 0.911019 0.412364i \(-0.135297\pi\)
−0.812627 + 0.582784i \(0.801963\pi\)
\(48\) 0 0
\(49\) 5.57183 0.795976
\(50\) 0 0
\(51\) 11.4801 + 19.8842i 1.60754 + 2.78434i
\(52\) 0 0
\(53\) 1.10967 + 1.92201i 0.152426 + 0.264009i 0.932119 0.362153i \(-0.117958\pi\)
−0.779693 + 0.626162i \(0.784625\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −9.38828 8.28544i −1.24351 1.09743i
\(58\) 0 0
\(59\) −0.960774 + 1.66411i −0.125082 + 0.216649i −0.921765 0.387749i \(-0.873253\pi\)
0.796683 + 0.604398i \(0.206586\pi\)
\(60\) 0 0
\(61\) 2.83047 + 4.90251i 0.362404 + 0.627702i 0.988356 0.152159i \(-0.0486227\pi\)
−0.625952 + 0.779862i \(0.715289\pi\)
\(62\) 0 0
\(63\) −9.31098 16.1271i −1.17307 2.03182i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.64397 + 8.04360i 0.567352 + 0.982682i 0.996827 + 0.0796032i \(0.0253653\pi\)
−0.429475 + 0.903079i \(0.641301\pi\)
\(68\) 0 0
\(69\) −24.2152 −2.91516
\(70\) 0 0
\(71\) −2.94365 + 5.09854i −0.349346 + 0.605086i −0.986134 0.165954i \(-0.946930\pi\)
0.636787 + 0.771040i \(0.280263\pi\)
\(72\) 0 0
\(73\) −1.63226 + 2.82716i −0.191042 + 0.330894i −0.945596 0.325344i \(-0.894520\pi\)
0.754554 + 0.656238i \(0.227853\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.43807 −0.733687
\(78\) 0 0
\(79\) −2.08739 + 3.61546i −0.234850 + 0.406771i −0.959229 0.282630i \(-0.908793\pi\)
0.724379 + 0.689402i \(0.242126\pi\)
\(80\) 0 0
\(81\) −1.41381 + 2.44879i −0.157090 + 0.272087i
\(82\) 0 0
\(83\) 6.30268 0.691809 0.345905 0.938270i \(-0.387572\pi\)
0.345905 + 0.938270i \(0.387572\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −24.6543 −2.64322
\(88\) 0 0
\(89\) −2.73646 4.73968i −0.290064 0.502405i 0.683761 0.729706i \(-0.260343\pi\)
−0.973825 + 0.227301i \(0.927010\pi\)
\(90\) 0 0
\(91\) −5.69723 9.86789i −0.597232 1.03444i
\(92\) 0 0
\(93\) 2.45429 4.25096i 0.254499 0.440804i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −3.99096 + 6.91255i −0.405221 + 0.701863i −0.994347 0.106178i \(-0.966139\pi\)
0.589126 + 0.808041i \(0.299472\pi\)
\(98\) 0 0
\(99\) 4.76818 + 8.25873i 0.479220 + 0.830034i
\(100\) 0 0
\(101\) 2.46731 + 4.27351i 0.245507 + 0.425230i 0.962274 0.272082i \(-0.0877123\pi\)
−0.716767 + 0.697313i \(0.754379\pi\)
\(102\) 0 0
\(103\) 5.56291 0.548130 0.274065 0.961711i \(-0.411632\pi\)
0.274065 + 0.961711i \(0.411632\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.12251 0.881907 0.440953 0.897530i \(-0.354640\pi\)
0.440953 + 0.897530i \(0.354640\pi\)
\(108\) 0 0
\(109\) −7.57225 + 13.1155i −0.725290 + 1.25624i 0.233565 + 0.972341i \(0.424961\pi\)
−0.958855 + 0.283898i \(0.908372\pi\)
\(110\) 0 0
\(111\) −7.90847 + 13.6979i −0.750638 + 1.30014i
\(112\) 0 0
\(113\) 4.46091 0.419647 0.209823 0.977739i \(-0.432711\pi\)
0.209823 + 0.977739i \(0.432711\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −8.43899 + 14.6168i −0.780185 + 1.35132i
\(118\) 0 0
\(119\) 14.1699 24.5429i 1.29895 2.24985i
\(120\) 0 0
\(121\) −7.70304 −0.700277
\(122\) 0 0
\(123\) 11.6541 + 20.1855i 1.05082 + 1.82007i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0.104025 + 0.180177i 0.00923073 + 0.0159881i 0.870604 0.491985i \(-0.163728\pi\)
−0.861373 + 0.507973i \(0.830395\pi\)
\(128\) 0 0
\(129\) 7.22073 + 12.5067i 0.635750 + 1.10115i
\(130\) 0 0
\(131\) 7.55409 13.0841i 0.660004 1.14316i −0.320610 0.947211i \(-0.603888\pi\)
0.980614 0.195950i \(-0.0627789\pi\)
\(132\) 0 0
\(133\) −3.06261 + 15.1488i −0.265562 + 1.31356i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.63439 4.56291i −0.225072 0.389835i 0.731269 0.682089i \(-0.238928\pi\)
−0.956341 + 0.292253i \(0.905595\pi\)
\(138\) 0 0
\(139\) −3.38336 5.86016i −0.286973 0.497052i 0.686113 0.727495i \(-0.259316\pi\)
−0.973086 + 0.230443i \(0.925982\pi\)
\(140\) 0 0
\(141\) −3.87543 −0.326370
\(142\) 0 0
\(143\) 2.91757 + 5.05338i 0.243979 + 0.422585i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −8.00291 + 13.8614i −0.660069 + 1.14327i
\(148\) 0 0
\(149\) −4.83003 + 8.36586i −0.395692 + 0.685358i −0.993189 0.116513i \(-0.962828\pi\)
0.597498 + 0.801871i \(0.296162\pi\)
\(150\) 0 0
\(151\) −12.0256 −0.978631 −0.489316 0.872107i \(-0.662753\pi\)
−0.489316 + 0.872107i \(0.662753\pi\)
\(152\) 0 0
\(153\) −41.9781 −3.39373
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.788721 1.36610i 0.0629468 0.109027i −0.832835 0.553522i \(-0.813284\pi\)
0.895781 + 0.444495i \(0.146617\pi\)
\(158\) 0 0
\(159\) −6.37537 −0.505600
\(160\) 0 0
\(161\) 14.9443 + 25.8844i 1.17778 + 2.03997i
\(162\) 0 0
\(163\) −16.0641 −1.25823 −0.629117 0.777310i \(-0.716584\pi\)
−0.629117 + 0.777310i \(0.716584\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3.56125 + 6.16826i 0.275578 + 0.477314i 0.970281 0.241982i \(-0.0777976\pi\)
−0.694703 + 0.719297i \(0.744464\pi\)
\(168\) 0 0
\(169\) 1.33632 2.31458i 0.102794 0.178044i
\(170\) 0 0
\(171\) 21.7010 7.29081i 1.65952 0.557542i
\(172\) 0 0
\(173\) 8.58850 14.8757i 0.652972 1.13098i −0.329427 0.944181i \(-0.606855\pi\)
0.982398 0.186799i \(-0.0598113\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −2.75995 4.78038i −0.207451 0.359315i
\(178\) 0 0
\(179\) −3.38519 −0.253021 −0.126510 0.991965i \(-0.540378\pi\)
−0.126510 + 0.991965i \(0.540378\pi\)
\(180\) 0 0
\(181\) 10.4226 + 18.0524i 0.774704 + 1.34183i 0.934961 + 0.354751i \(0.115434\pi\)
−0.160257 + 0.987075i \(0.551232\pi\)
\(182\) 0 0
\(183\) −16.2618 −1.20210
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −7.25643 + 12.5685i −0.530643 + 0.919101i
\(188\) 0 0
\(189\) 22.9377 1.66847
\(190\) 0 0
\(191\) 4.58794 0.331972 0.165986 0.986128i \(-0.446919\pi\)
0.165986 + 0.986128i \(0.446919\pi\)
\(192\) 0 0
\(193\) −10.0596 + 17.4238i −0.724108 + 1.25419i 0.235232 + 0.971939i \(0.424415\pi\)
−0.959340 + 0.282252i \(0.908918\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −0.983439 −0.0700671 −0.0350336 0.999386i \(-0.511154\pi\)
−0.0350336 + 0.999386i \(0.511154\pi\)
\(198\) 0 0
\(199\) 5.84473 + 10.1234i 0.414322 + 0.717626i 0.995357 0.0962520i \(-0.0306855\pi\)
−0.581035 + 0.813878i \(0.697352\pi\)
\(200\) 0 0
\(201\) −26.6809 −1.88192
\(202\) 0 0
\(203\) 15.2154 + 26.3538i 1.06791 + 1.84967i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 22.1362 38.3411i 1.53857 2.66489i
\(208\) 0 0
\(209\) 1.56837 7.75773i 0.108487 0.536613i
\(210\) 0 0
\(211\) −5.35987 + 9.28357i −0.368989 + 0.639107i −0.989408 0.145163i \(-0.953629\pi\)
0.620419 + 0.784270i \(0.286963\pi\)
\(212\) 0 0
\(213\) −8.45601 14.6462i −0.579396 1.00354i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −6.05865 −0.411288
\(218\) 0 0
\(219\) −4.68888 8.12139i −0.316845 0.548792i
\(220\) 0 0
\(221\) −25.6857 −1.72781
\(222\) 0 0
\(223\) 10.2936 17.8291i 0.689313 1.19393i −0.282747 0.959195i \(-0.591246\pi\)
0.972060 0.234731i \(-0.0754210\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 7.47441 0.496094 0.248047 0.968748i \(-0.420211\pi\)
0.248047 + 0.968748i \(0.420211\pi\)
\(228\) 0 0
\(229\) −11.0863 −0.732604 −0.366302 0.930496i \(-0.619376\pi\)
−0.366302 + 0.930496i \(0.619376\pi\)
\(230\) 0 0
\(231\) 9.24711 16.0165i 0.608415 1.05381i
\(232\) 0 0
\(233\) 9.16743 15.8785i 0.600578 1.04023i −0.392155 0.919899i \(-0.628270\pi\)
0.992734 0.120333i \(-0.0383962\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −5.99630 10.3859i −0.389501 0.674636i
\(238\) 0 0
\(239\) 11.8518 0.766630 0.383315 0.923618i \(-0.374782\pi\)
0.383315 + 0.923618i \(0.374782\pi\)
\(240\) 0 0
\(241\) −2.34317 4.05850i −0.150937 0.261431i 0.780635 0.624987i \(-0.214896\pi\)
−0.931572 + 0.363556i \(0.881562\pi\)
\(242\) 0 0
\(243\) 5.64247 + 9.77304i 0.361964 + 0.626941i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 13.2785 4.46112i 0.844890 0.283854i
\(248\) 0 0
\(249\) −9.05264 + 15.6796i −0.573688 + 0.993657i
\(250\) 0 0
\(251\) 0.0510129 + 0.0883569i 0.00321990 + 0.00557704i 0.867631 0.497209i \(-0.165642\pi\)
−0.864411 + 0.502786i \(0.832308\pi\)
\(252\) 0 0
\(253\) −7.65304 13.2555i −0.481143 0.833363i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.69424 + 13.3268i 0.479953 + 0.831303i 0.999736 0.0229953i \(-0.00732027\pi\)
−0.519782 + 0.854299i \(0.673987\pi\)
\(258\) 0 0
\(259\) 19.5228 1.21309
\(260\) 0 0
\(261\) 22.5377 39.0364i 1.39505 2.41629i
\(262\) 0 0
\(263\) 9.78416 16.9467i 0.603317 1.04498i −0.388998 0.921239i \(-0.627179\pi\)
0.992315 0.123737i \(-0.0394880\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 15.7217 0.962150
\(268\) 0 0
\(269\) −0.585331 + 1.01382i −0.0356883 + 0.0618139i −0.883318 0.468775i \(-0.844696\pi\)
0.847630 + 0.530588i \(0.178029\pi\)
\(270\) 0 0
\(271\) 6.40442 11.0928i 0.389041 0.673838i −0.603280 0.797529i \(-0.706140\pi\)
0.992321 + 0.123691i \(0.0394732\pi\)
\(272\) 0 0
\(273\) 32.7321 1.98104
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 11.0122 0.661656 0.330828 0.943691i \(-0.392672\pi\)
0.330828 + 0.943691i \(0.392672\pi\)
\(278\) 0 0
\(279\) 4.48717 + 7.77201i 0.268640 + 0.465298i
\(280\) 0 0
\(281\) −1.93481 3.35119i −0.115421 0.199915i 0.802527 0.596616i \(-0.203488\pi\)
−0.917948 + 0.396701i \(0.870155\pi\)
\(282\) 0 0
\(283\) 11.3099 19.5893i 0.672303 1.16446i −0.304947 0.952369i \(-0.598639\pi\)
0.977249 0.212093i \(-0.0680280\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 14.3846 24.9149i 0.849097 1.47068i
\(288\) 0 0
\(289\) −23.4421 40.6029i −1.37895 2.38840i
\(290\) 0 0
\(291\) −11.4646 19.8572i −0.672065 1.16405i
\(292\) 0 0
\(293\) −28.4482 −1.66196 −0.830980 0.556303i \(-0.812219\pi\)
−0.830980 + 0.556303i \(0.812219\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −11.7465 −0.681600
\(298\) 0 0
\(299\) 13.5448 23.4603i 0.783315 1.35674i
\(300\) 0 0
\(301\) 8.91251 15.4369i 0.513709 0.889770i
\(302\) 0 0
\(303\) −14.1754 −0.814353
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −7.05802 + 12.2248i −0.402822 + 0.697709i −0.994065 0.108785i \(-0.965304\pi\)
0.591243 + 0.806494i \(0.298637\pi\)
\(308\) 0 0
\(309\) −7.99010 + 13.8393i −0.454541 + 0.787288i
\(310\) 0 0
\(311\) 16.4672 0.933768 0.466884 0.884319i \(-0.345377\pi\)
0.466884 + 0.884319i \(0.345377\pi\)
\(312\) 0 0
\(313\) 12.4917 + 21.6363i 0.706073 + 1.22295i 0.966303 + 0.257408i \(0.0828685\pi\)
−0.260229 + 0.965547i \(0.583798\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.10281 1.91012i −0.0619399 0.107283i 0.833393 0.552681i \(-0.186395\pi\)
−0.895332 + 0.445398i \(0.853062\pi\)
\(318\) 0 0
\(319\) −7.79183 13.4958i −0.436259 0.755622i
\(320\) 0 0
\(321\) −13.1028 + 22.6947i −0.731328 + 1.26670i
\(322\) 0 0
\(323\) 26.1218 + 23.0533i 1.45345 + 1.28272i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −21.7523 37.6761i −1.20290 2.08349i
\(328\) 0 0
\(329\) 2.39171 + 4.14257i 0.131859 + 0.228387i
\(330\) 0 0
\(331\) −27.5415 −1.51382 −0.756910 0.653519i \(-0.773292\pi\)
−0.756910 + 0.653519i \(0.773292\pi\)
\(332\) 0 0
\(333\) −14.4590 25.0437i −0.792348 1.37239i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 9.20668 15.9464i 0.501520 0.868658i −0.498479 0.866902i \(-0.666108\pi\)
0.999998 0.00175582i \(-0.000558895\pi\)
\(338\) 0 0
\(339\) −6.40727 + 11.0977i −0.347995 + 0.602745i
\(340\) 0 0
\(341\) 3.10265 0.168018
\(342\) 0 0
\(343\) −5.06383 −0.273421
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −13.1677 + 22.8072i −0.706881 + 1.22435i 0.259128 + 0.965843i \(0.416565\pi\)
−0.966009 + 0.258510i \(0.916768\pi\)
\(348\) 0 0
\(349\) −7.40515 −0.396388 −0.198194 0.980163i \(-0.563508\pi\)
−0.198194 + 0.980163i \(0.563508\pi\)
\(350\) 0 0
\(351\) −10.3948 18.0043i −0.554833 0.960999i
\(352\) 0 0
\(353\) −2.42201 −0.128910 −0.0644552 0.997921i \(-0.520531\pi\)
−0.0644552 + 0.997921i \(0.520531\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 40.7048 + 70.5028i 2.15433 + 3.73140i
\(358\) 0 0
\(359\) −2.28083 + 3.95051i −0.120377 + 0.208500i −0.919917 0.392114i \(-0.871744\pi\)
0.799539 + 0.600614i \(0.205077\pi\)
\(360\) 0 0
\(361\) −17.5078 7.38076i −0.921465 0.388461i
\(362\) 0 0
\(363\) 11.0640 19.1634i 0.580710 1.00582i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 5.26242 + 9.11478i 0.274696 + 0.475788i 0.970058 0.242872i \(-0.0780894\pi\)
−0.695362 + 0.718659i \(0.744756\pi\)
\(368\) 0 0
\(369\) −42.6143 −2.21841
\(370\) 0 0
\(371\) 3.93455 + 6.81484i 0.204272 + 0.353809i
\(372\) 0 0
\(373\) 21.8633 1.13204 0.566019 0.824392i \(-0.308483\pi\)
0.566019 + 0.824392i \(0.308483\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 13.7904 23.8857i 0.710243 1.23018i
\(378\) 0 0
\(379\) 9.33617 0.479567 0.239783 0.970826i \(-0.422924\pi\)
0.239783 + 0.970826i \(0.422924\pi\)
\(380\) 0 0
\(381\) −0.597652 −0.0306186
\(382\) 0 0
\(383\) −2.75581 + 4.77320i −0.140815 + 0.243899i −0.927804 0.373068i \(-0.878306\pi\)
0.786989 + 0.616968i \(0.211639\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −26.4032 −1.34215
\(388\) 0 0
\(389\) −8.50605 14.7329i −0.431274 0.746988i 0.565709 0.824605i \(-0.308602\pi\)
−0.996983 + 0.0776163i \(0.975269\pi\)
\(390\) 0 0
\(391\) 67.3758 3.40734
\(392\) 0 0
\(393\) 21.7001 + 37.5857i 1.09463 + 1.89595i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 15.7110 27.2122i 0.788512 1.36574i −0.138366 0.990381i \(-0.544185\pi\)
0.926878 0.375362i \(-0.122482\pi\)
\(398\) 0 0
\(399\) −33.2878 29.3775i −1.66647 1.47071i
\(400\) 0 0
\(401\) 13.4762 23.3415i 0.672971 1.16562i −0.304087 0.952644i \(-0.598351\pi\)
0.977058 0.212976i \(-0.0683155\pi\)
\(402\) 0 0
\(403\) 2.74563 + 4.75556i 0.136769 + 0.236891i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −9.99767 −0.495566
\(408\) 0 0
\(409\) 17.0791 + 29.5819i 0.844509 + 1.46273i 0.886047 + 0.463596i \(0.153441\pi\)
−0.0415373 + 0.999137i \(0.513226\pi\)
\(410\) 0 0
\(411\) 15.1353 0.746569
\(412\) 0 0
\(413\) −3.40660 + 5.90040i −0.167628 + 0.290340i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 19.4383 0.951899
\(418\) 0 0
\(419\) 36.5998 1.78802 0.894009 0.448049i \(-0.147881\pi\)
0.894009 + 0.448049i \(0.147881\pi\)
\(420\) 0 0
\(421\) −4.85007 + 8.40057i −0.236378 + 0.409419i −0.959672 0.281121i \(-0.909294\pi\)
0.723294 + 0.690540i \(0.242627\pi\)
\(422\) 0 0
\(423\) 3.54271 6.13615i 0.172252 0.298350i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 10.0359 + 17.3827i 0.485672 + 0.841209i
\(428\) 0 0
\(429\) −16.7622 −0.809287
\(430\) 0 0
\(431\) −14.4779 25.0764i −0.697375 1.20789i −0.969373 0.245591i \(-0.921018\pi\)
0.271999 0.962298i \(-0.412315\pi\)
\(432\) 0 0
\(433\) −3.72388 6.44994i −0.178958 0.309965i 0.762566 0.646911i \(-0.223939\pi\)
−0.941524 + 0.336946i \(0.890606\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −34.8306 + 11.7019i −1.66618 + 0.559779i
\(438\) 0 0
\(439\) −5.70008 + 9.87283i −0.272050 + 0.471204i −0.969387 0.245539i \(-0.921035\pi\)
0.697337 + 0.716744i \(0.254368\pi\)
\(440\) 0 0
\(441\) −14.6317 25.3428i −0.696746 1.20680i
\(442\) 0 0
\(443\) −3.84540 6.66042i −0.182700 0.316446i 0.760099 0.649807i \(-0.225150\pi\)
−0.942799 + 0.333361i \(0.891817\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −13.8749 24.0320i −0.656260 1.13668i
\(448\) 0 0
\(449\) 37.0590 1.74892 0.874460 0.485097i \(-0.161216\pi\)
0.874460 + 0.485097i \(0.161216\pi\)
\(450\) 0 0
\(451\) −7.36641 + 12.7590i −0.346871 + 0.600797i
\(452\) 0 0
\(453\) 17.2726 29.9170i 0.811537 1.40562i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 22.1647 1.03682 0.518411 0.855131i \(-0.326524\pi\)
0.518411 + 0.855131i \(0.326524\pi\)
\(458\) 0 0
\(459\) 25.8534 44.7794i 1.20673 2.09012i
\(460\) 0 0
\(461\) 21.0779 36.5080i 0.981697 1.70035i 0.325914 0.945400i \(-0.394328\pi\)
0.655783 0.754949i \(-0.272339\pi\)
\(462\) 0 0
\(463\) −5.16758 −0.240158 −0.120079 0.992764i \(-0.538315\pi\)
−0.120079 + 0.992764i \(0.538315\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −12.7096 −0.588129 −0.294064 0.955786i \(-0.595008\pi\)
−0.294064 + 0.955786i \(0.595008\pi\)
\(468\) 0 0
\(469\) 16.4660 + 28.5200i 0.760331 + 1.31693i
\(470\) 0 0
\(471\) 2.26570 + 3.92431i 0.104398 + 0.180823i
\(472\) 0 0
\(473\) −4.56413 + 7.90530i −0.209859 + 0.363486i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 5.82803 10.0944i 0.266847 0.462193i
\(478\) 0 0
\(479\) 11.0555 + 19.1487i 0.505140 + 0.874928i 0.999982 + 0.00594539i \(0.00189249\pi\)
−0.494842 + 0.868983i \(0.664774\pi\)
\(480\) 0 0
\(481\) −8.84722 15.3238i −0.403399 0.698707i
\(482\) 0 0
\(483\) −85.8592 −3.90673
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −28.3389 −1.28416 −0.642078 0.766639i \(-0.721928\pi\)
−0.642078 + 0.766639i \(0.721928\pi\)
\(488\) 0 0
\(489\) 23.0731 39.9637i 1.04340 1.80722i
\(490\) 0 0
\(491\) −4.33288 + 7.50477i −0.195540 + 0.338686i −0.947077 0.321005i \(-0.895979\pi\)
0.751537 + 0.659691i \(0.229313\pi\)
\(492\) 0 0
\(493\) 68.5977 3.08948
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −10.4372 + 18.0778i −0.468173 + 0.810900i
\(498\) 0 0
\(499\) 8.07784 13.9912i 0.361614 0.626334i −0.626613 0.779331i \(-0.715559\pi\)
0.988227 + 0.152997i \(0.0488925\pi\)
\(500\) 0 0
\(501\) −20.4603 −0.914099
\(502\) 0 0
\(503\) 12.8900 + 22.3262i 0.574737 + 0.995474i 0.996070 + 0.0885682i \(0.0282291\pi\)
−0.421333 + 0.906906i \(0.638438\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3.83876 + 6.64893i 0.170485 + 0.295289i
\(508\) 0 0
\(509\) 6.15335 + 10.6579i 0.272743 + 0.472404i 0.969563 0.244842i \(-0.0787359\pi\)
−0.696821 + 0.717246i \(0.745403\pi\)
\(510\) 0 0
\(511\) −5.78747 + 10.0242i −0.256023 + 0.443444i
\(512\) 0 0
\(513\) −5.58784 + 27.6394i −0.246709 + 1.22031i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −1.22480 2.12142i −0.0538668 0.0933000i
\(518\) 0 0
\(519\) 24.6716 + 42.7325i 1.08296 + 1.87575i
\(520\) 0 0
\(521\) 17.0934 0.748875 0.374438 0.927252i \(-0.377836\pi\)
0.374438 + 0.927252i \(0.377836\pi\)
\(522\) 0 0
\(523\) −1.32368 2.29269i −0.0578806 0.100252i 0.835633 0.549288i \(-0.185101\pi\)
−0.893514 + 0.449036i \(0.851768\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.82878 + 11.8278i −0.297466 + 0.515227i
\(528\) 0 0
\(529\) −24.0292 + 41.6197i −1.04475 + 1.80955i
\(530\) 0 0
\(531\) 10.0920 0.437956
\(532\) 0 0
\(533\) −26.0750 −1.12943
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 4.86220 8.42158i 0.209820 0.363418i
\(538\) 0 0
\(539\) −10.1171 −0.435773
\(540\) 0 0
\(541\) −5.06701 8.77631i −0.217848 0.377323i 0.736302 0.676653i \(-0.236570\pi\)
−0.954150 + 0.299330i \(0.903237\pi\)
\(542\) 0 0
\(543\) −59.8804 −2.56972
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −11.2375 19.4639i −0.480480 0.832217i 0.519269 0.854611i \(-0.326204\pi\)
−0.999749 + 0.0223944i \(0.992871\pi\)
\(548\) 0 0
\(549\) 14.8656 25.7481i 0.634450 1.09890i
\(550\) 0 0
\(551\) −35.4623 + 11.9141i −1.51074 + 0.507559i
\(552\) 0 0
\(553\) −7.40121 + 12.8193i −0.314731 + 0.545131i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.22948 + 3.86157i 0.0944659 + 0.163620i 0.909386 0.415954i \(-0.136552\pi\)
−0.814920 + 0.579574i \(0.803219\pi\)
\(558\) 0 0
\(559\) −16.1557 −0.683313
\(560\) 0 0
\(561\) −20.8451 36.1047i −0.880079 1.52434i
\(562\) 0 0
\(563\) −10.0514 −0.423616 −0.211808 0.977311i \(-0.567935\pi\)
−0.211808 + 0.977311i \(0.567935\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −5.01291 + 8.68261i −0.210522 + 0.364635i
\(568\) 0 0
\(569\) −5.41442 −0.226984 −0.113492 0.993539i \(-0.536204\pi\)
−0.113492 + 0.993539i \(0.536204\pi\)
\(570\) 0 0
\(571\) −24.0418 −1.00612 −0.503059 0.864252i \(-0.667792\pi\)
−0.503059 + 0.864252i \(0.667792\pi\)
\(572\) 0 0
\(573\) −6.58973 + 11.4138i −0.275290 + 0.476816i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1.40727 −0.0585855 −0.0292928 0.999571i \(-0.509326\pi\)
−0.0292928 + 0.999571i \(0.509326\pi\)
\(578\) 0 0
\(579\) −28.8976 50.0521i −1.20094 2.08010i
\(580\) 0 0
\(581\) 22.3473 0.927121
\(582\) 0 0
\(583\) −2.01489 3.48990i −0.0834484 0.144537i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.129501 0.224303i 0.00534510 0.00925798i −0.863340 0.504622i \(-0.831632\pi\)
0.868686 + 0.495364i \(0.164965\pi\)
\(588\) 0 0
\(589\) 1.47594 7.30054i 0.0608152 0.300813i
\(590\) 0 0
\(591\) 1.41253 2.44657i 0.0581037 0.100639i
\(592\) 0 0
\(593\) −1.48405 2.57044i −0.0609425 0.105555i 0.833944 0.551848i \(-0.186077\pi\)
−0.894887 + 0.446293i \(0.852744\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −33.5795 −1.37432
\(598\) 0 0
\(599\) −23.7083 41.0640i −0.968696 1.67783i −0.699338 0.714791i \(-0.746522\pi\)
−0.269359 0.963040i \(-0.586812\pi\)
\(600\) 0 0
\(601\) −22.2047 −0.905747 −0.452874 0.891575i \(-0.649601\pi\)
−0.452874 + 0.891575i \(0.649601\pi\)
\(602\) 0 0
\(603\) 24.3902 42.2451i 0.993247 1.72035i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 37.6580 1.52849 0.764246 0.644925i \(-0.223112\pi\)
0.764246 + 0.644925i \(0.223112\pi\)
\(608\) 0 0
\(609\) −87.4162 −3.54228
\(610\) 0 0
\(611\) 2.16772 3.75461i 0.0876968 0.151895i
\(612\) 0 0
\(613\) −22.1526 + 38.3694i −0.894734 + 1.54973i −0.0606013 + 0.998162i \(0.519302\pi\)
−0.834133 + 0.551563i \(0.814031\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11.6190 + 20.1247i 0.467764 + 0.810190i 0.999321 0.0368317i \(-0.0117265\pi\)
−0.531558 + 0.847022i \(0.678393\pi\)
\(618\) 0 0
\(619\) −28.8420 −1.15926 −0.579630 0.814880i \(-0.696803\pi\)
−0.579630 + 0.814880i \(0.696803\pi\)
\(620\) 0 0
\(621\) 27.2665 + 47.2269i 1.09417 + 1.89515i
\(622\) 0 0
\(623\) −9.70259 16.8054i −0.388726 0.673294i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 17.0468 + 15.0443i 0.680783 + 0.600812i
\(628\) 0 0
\(629\) 22.0044 38.1127i 0.877371 1.51965i
\(630\) 0 0
\(631\) 6.79323 + 11.7662i 0.270434 + 0.468406i 0.968973 0.247166i \(-0.0794994\pi\)
−0.698539 + 0.715572i \(0.746166\pi\)
\(632\) 0 0
\(633\) −15.3969 26.6683i −0.611973 1.05997i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −8.95287 15.5068i −0.354726 0.614403i
\(638\) 0 0
\(639\) 30.9201 1.22318
\(640\) 0 0
\(641\) 3.15731 5.46863i 0.124706 0.215998i −0.796912 0.604096i \(-0.793534\pi\)
0.921618 + 0.388098i \(0.126868\pi\)
\(642\) 0 0
\(643\) −6.85067 + 11.8657i −0.270164 + 0.467938i −0.968904 0.247438i \(-0.920411\pi\)
0.698740 + 0.715376i \(0.253745\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8.50227 −0.334259 −0.167129 0.985935i \(-0.553450\pi\)
−0.167129 + 0.985935i \(0.553450\pi\)
\(648\) 0 0
\(649\) 1.74453 3.02161i 0.0684787 0.118609i
\(650\) 0 0
\(651\) 8.70214 15.0725i 0.341064 0.590740i
\(652\) 0 0
\(653\) 6.89369 0.269771 0.134885 0.990861i \(-0.456933\pi\)
0.134885 + 0.990861i \(0.456933\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 17.1453 0.668902
\(658\) 0 0
\(659\) 10.9585 + 18.9807i 0.426884 + 0.739384i 0.996594 0.0824611i \(-0.0262780\pi\)
−0.569711 + 0.821845i \(0.692945\pi\)
\(660\) 0 0
\(661\) 15.5768 + 26.9797i 0.605866 + 1.04939i 0.991914 + 0.126912i \(0.0405065\pi\)
−0.386048 + 0.922479i \(0.626160\pi\)
\(662\) 0 0
\(663\) 36.8928 63.9001i 1.43280 2.48168i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −36.1735 + 62.6543i −1.40064 + 2.42598i
\(668\) 0 0
\(669\) 29.5699 + 51.2165i 1.14324 + 1.98014i
\(670\) 0 0
\(671\) −5.13943 8.90175i −0.198405 0.343648i
\(672\) 0 0
\(673\) 24.5193 0.945150 0.472575 0.881290i \(-0.343325\pi\)
0.472575 + 0.881290i \(0.343325\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.89395 −0.303389 −0.151695 0.988427i \(-0.548473\pi\)
−0.151695 + 0.988427i \(0.548473\pi\)
\(678\) 0 0
\(679\) −14.1507 + 24.5097i −0.543053 + 0.940595i
\(680\) 0 0
\(681\) −10.7356 + 18.5946i −0.411390 + 0.712548i
\(682\) 0 0
\(683\) −44.3352 −1.69644 −0.848220 0.529644i \(-0.822325\pi\)
−0.848220 + 0.529644i \(0.822325\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 15.9234 27.5802i 0.607517 1.05225i
\(688\) 0 0
\(689\) 3.56607 6.17662i 0.135857 0.235311i
\(690\) 0 0
\(691\) 44.2501 1.68335 0.841676 0.539982i \(-0.181569\pi\)
0.841676 + 0.539982i \(0.181569\pi\)
\(692\) 0 0
\(693\) 16.9064 + 29.2828i 0.642222 + 1.11236i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −32.4262 56.1638i −1.22823 2.12735i
\(698\) 0 0
\(699\) 26.3347 + 45.6130i 0.996068 + 1.72524i
\(700\) 0 0
\(701\) −9.27840 + 16.0707i −0.350440 + 0.606980i −0.986327 0.164802i \(-0.947301\pi\)
0.635886 + 0.771783i \(0.280635\pi\)
\(702\) 0 0
\(703\) −4.75593 + 23.5245i −0.179373 + 0.887243i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.74830 + 15.1525i 0.329014 + 0.569868i
\(708\) 0 0
\(709\) −21.4349 37.1263i −0.805003 1.39431i −0.916289 0.400518i \(-0.868830\pi\)
0.111285 0.993788i \(-0.464503\pi\)
\(710\) 0 0
\(711\) 21.9260 0.822289
\(712\) 0 0
\(713\) −7.20202 12.4743i −0.269718 0.467165i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −17.0230 + 29.4846i −0.635734 + 1.10112i
\(718\) 0 0
\(719\) 17.5024 30.3150i 0.652728 1.13056i −0.329730 0.944075i \(-0.606958\pi\)
0.982458 0.186483i \(-0.0597088\pi\)
\(720\) 0 0
\(721\) 19.7243 0.734571
\(722\) 0 0
\(723\) 13.4622 0.500663
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −0.252064 + 0.436587i −0.00934852 + 0.0161921i −0.870662 0.491882i \(-0.836309\pi\)
0.861313 + 0.508074i \(0.169642\pi\)
\(728\) 0 0
\(729\) −40.9003 −1.51483
\(730\) 0 0
\(731\) −20.0908 34.7983i −0.743086 1.28706i
\(732\) 0 0
\(733\) 26.5745 0.981553 0.490777 0.871285i \(-0.336713\pi\)
0.490777 + 0.871285i \(0.336713\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −8.43231 14.6052i −0.310608 0.537989i
\(738\) 0 0
\(739\) −12.8643 + 22.2817i −0.473222 + 0.819645i −0.999530 0.0306492i \(-0.990243\pi\)
0.526308 + 0.850294i \(0.323576\pi\)
\(740\) 0 0
\(741\) −7.97384 + 39.4414i −0.292926 + 1.44892i
\(742\) 0 0
\(743\) 2.13851 3.70400i 0.0784542 0.135887i −0.824129 0.566402i \(-0.808335\pi\)
0.902583 + 0.430516i \(0.141668\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −16.5509 28.6670i −0.605565 1.04887i
\(748\) 0 0
\(749\) 32.3455 1.18188
\(750\) 0 0
\(751\) −7.26869 12.5897i −0.265238 0.459406i 0.702388 0.711795i \(-0.252117\pi\)
−0.967626 + 0.252388i \(0.918784\pi\)
\(752\) 0 0
\(753\) −0.293082 −0.0106805
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 8.16844 14.1482i 0.296887 0.514224i −0.678535 0.734568i \(-0.737385\pi\)
0.975422 + 0.220345i \(0.0707182\pi\)
\(758\) 0 0
\(759\) 43.9687 1.59596
\(760\) 0 0
\(761\) −21.9812 −0.796819 −0.398409 0.917208i \(-0.630438\pi\)
−0.398409 + 0.917208i \(0.630438\pi\)
\(762\) 0 0
\(763\) −26.8488 + 46.5034i −0.971990 + 1.68354i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6.17513 0.222971
\(768\) 0 0
\(769\) −23.1977 40.1796i −0.836530 1.44891i −0.892778 0.450496i \(-0.851247\pi\)
0.0562477 0.998417i \(-0.482086\pi\)
\(770\) 0 0
\(771\) −44.2054 −1.59202
\(772\) 0 0
\(773\) 12.4954 + 21.6426i 0.449428 + 0.778431i 0.998349 0.0574426i \(-0.0182946\pi\)
−0.548921 + 0.835874i \(0.684961\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −28.0409 + 48.5682i −1.00596 + 1.74238i
\(778\) 0 0
\(779\) 26.5176 + 23.4026i 0.950093 + 0.838486i
\(780\) 0 0
\(781\) 5.34493 9.25769i 0.191257 0.331266i
\(782\) 0 0
\(783\) 27.7609 + 48.0834i 0.992095 + 1.71836i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −36.4986 −1.30103 −0.650517 0.759492i \(-0.725448\pi\)
−0.650517 + 0.759492i \(0.725448\pi\)
\(788\) 0 0
\(789\) 28.1063 + 48.6815i 1.00061 + 1.73311i
\(790\) 0 0
\(791\) 15.8169 0.562385
\(792\) 0 0
\(793\) 9.09604 15.7548i 0.323010 0.559470i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −11.9753 −0.424188 −0.212094 0.977249i \(-0.568028\pi\)
−0.212094 + 0.977249i \(0.568028\pi\)
\(798\) 0 0
\(799\) 10.7829 0.381472
\(800\) 0