Properties

Label 1200.3.bg.e.193.1
Level $1200$
Weight $3$
Character 1200.193
Analytic conductor $32.698$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1200.bg (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.6976317232\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 193.1
Root \(-1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1200.193
Dual form 1200.3.bg.e.1057.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 1.22474i) q^{3} +(-5.44949 + 5.44949i) q^{7} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.22474 - 1.22474i) q^{3} +(-5.44949 + 5.44949i) q^{7} +3.00000i q^{9} +6.44949 q^{11} +(-14.4495 - 14.4495i) q^{13} +(23.1464 - 23.1464i) q^{17} +16.6969i q^{19} +13.3485 q^{21} +(-6.65153 - 6.65153i) q^{23} +(3.67423 - 3.67423i) q^{27} +0.0454077i q^{29} -4.49490 q^{31} +(-7.89898 - 7.89898i) q^{33} +(-35.3485 + 35.3485i) q^{37} +35.3939i q^{39} +20.2929 q^{41} +(32.2929 + 32.2929i) q^{43} +(-50.5403 + 50.5403i) q^{47} -10.3939i q^{49} -56.6969 q^{51} +(5.50510 + 5.50510i) q^{53} +(20.4495 - 20.4495i) q^{57} +55.4393i q^{59} +47.8888 q^{61} +(-16.3485 - 16.3485i) q^{63} +(-85.2827 + 85.2827i) q^{67} +16.2929i q^{69} -48.4041 q^{71} +(21.9898 + 21.9898i) q^{73} +(-35.1464 + 35.1464i) q^{77} -126.697i q^{79} -9.00000 q^{81} +(94.9444 + 94.9444i) q^{83} +(0.0556128 - 0.0556128i) q^{87} +71.7980i q^{89} +157.485 q^{91} +(5.50510 + 5.50510i) q^{93} +(37.0000 - 37.0000i) q^{97} +19.3485i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 12 q^{7} + O(q^{10}) \) \( 4 q - 12 q^{7} + 16 q^{11} - 48 q^{13} + 24 q^{17} + 24 q^{21} - 56 q^{23} + 80 q^{31} - 12 q^{33} - 112 q^{37} - 56 q^{41} - 8 q^{43} - 16 q^{47} - 168 q^{51} + 120 q^{53} + 72 q^{57} - 24 q^{61} - 36 q^{63} - 8 q^{67} - 272 q^{71} - 108 q^{73} - 72 q^{77} - 36 q^{81} + 272 q^{83} + 108 q^{87} + 336 q^{91} + 120 q^{93} + 148 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).

\(n\) \(401\) \(577\) \(751\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.22474 1.22474i −0.408248 0.408248i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −5.44949 + 5.44949i −0.778499 + 0.778499i −0.979575 0.201077i \(-0.935556\pi\)
0.201077 + 0.979575i \(0.435556\pi\)
\(8\) 0 0
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) 6.44949 0.586317 0.293159 0.956064i \(-0.405294\pi\)
0.293159 + 0.956064i \(0.405294\pi\)
\(12\) 0 0
\(13\) −14.4495 14.4495i −1.11150 1.11150i −0.992948 0.118551i \(-0.962175\pi\)
−0.118551 0.992948i \(-0.537825\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 23.1464 23.1464i 1.36155 1.36155i 0.489617 0.871938i \(-0.337137\pi\)
0.871938 0.489617i \(-0.162863\pi\)
\(18\) 0 0
\(19\) 16.6969i 0.878786i 0.898295 + 0.439393i \(0.144806\pi\)
−0.898295 + 0.439393i \(0.855194\pi\)
\(20\) 0 0
\(21\) 13.3485 0.635641
\(22\) 0 0
\(23\) −6.65153 6.65153i −0.289197 0.289197i 0.547566 0.836763i \(-0.315555\pi\)
−0.836763 + 0.547566i \(0.815555\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) 0 0
\(29\) 0.0454077i 0.00156578i 1.00000 0.000782891i \(0.000249202\pi\)
−1.00000 0.000782891i \(0.999751\pi\)
\(30\) 0 0
\(31\) −4.49490 −0.144997 −0.0724983 0.997369i \(-0.523097\pi\)
−0.0724983 + 0.997369i \(0.523097\pi\)
\(32\) 0 0
\(33\) −7.89898 7.89898i −0.239363 0.239363i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −35.3485 + 35.3485i −0.955364 + 0.955364i −0.999046 0.0436815i \(-0.986091\pi\)
0.0436815 + 0.999046i \(0.486091\pi\)
\(38\) 0 0
\(39\) 35.3939i 0.907535i
\(40\) 0 0
\(41\) 20.2929 0.494948 0.247474 0.968895i \(-0.420400\pi\)
0.247474 + 0.968895i \(0.420400\pi\)
\(42\) 0 0
\(43\) 32.2929 + 32.2929i 0.750997 + 0.750997i 0.974665 0.223669i \(-0.0718033\pi\)
−0.223669 + 0.974665i \(0.571803\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −50.5403 + 50.5403i −1.07533 + 1.07533i −0.0784040 + 0.996922i \(0.524982\pi\)
−0.996922 + 0.0784040i \(0.975018\pi\)
\(48\) 0 0
\(49\) 10.3939i 0.212120i
\(50\) 0 0
\(51\) −56.6969 −1.11170
\(52\) 0 0
\(53\) 5.50510 + 5.50510i 0.103870 + 0.103870i 0.757132 0.653262i \(-0.226600\pi\)
−0.653262 + 0.757132i \(0.726600\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 20.4495 20.4495i 0.358763 0.358763i
\(58\) 0 0
\(59\) 55.4393i 0.939649i 0.882760 + 0.469824i \(0.155683\pi\)
−0.882760 + 0.469824i \(0.844317\pi\)
\(60\) 0 0
\(61\) 47.8888 0.785062 0.392531 0.919739i \(-0.371600\pi\)
0.392531 + 0.919739i \(0.371600\pi\)
\(62\) 0 0
\(63\) −16.3485 16.3485i −0.259500 0.259500i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −85.2827 + 85.2827i −1.27288 + 1.27288i −0.328303 + 0.944573i \(0.606477\pi\)
−0.944573 + 0.328303i \(0.893523\pi\)
\(68\) 0 0
\(69\) 16.2929i 0.236128i
\(70\) 0 0
\(71\) −48.4041 −0.681748 −0.340874 0.940109i \(-0.610723\pi\)
−0.340874 + 0.940109i \(0.610723\pi\)
\(72\) 0 0
\(73\) 21.9898 + 21.9898i 0.301230 + 0.301230i 0.841495 0.540265i \(-0.181676\pi\)
−0.540265 + 0.841495i \(0.681676\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −35.1464 + 35.1464i −0.456447 + 0.456447i
\(78\) 0 0
\(79\) 126.697i 1.60376i −0.597486 0.801879i \(-0.703834\pi\)
0.597486 0.801879i \(-0.296166\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) 94.9444 + 94.9444i 1.14391 + 1.14391i 0.987729 + 0.156180i \(0.0499179\pi\)
0.156180 + 0.987729i \(0.450082\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.0556128 0.0556128i 0.000639228 0.000639228i
\(88\) 0 0
\(89\) 71.7980i 0.806719i 0.915042 + 0.403359i \(0.132158\pi\)
−0.915042 + 0.403359i \(0.867842\pi\)
\(90\) 0 0
\(91\) 157.485 1.73060
\(92\) 0 0
\(93\) 5.50510 + 5.50510i 0.0591947 + 0.0591947i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 37.0000 37.0000i 0.381443 0.381443i −0.490179 0.871622i \(-0.663068\pi\)
0.871622 + 0.490179i \(0.163068\pi\)
\(98\) 0 0
\(99\) 19.3485i 0.195439i
\(100\) 0 0
\(101\) 94.3383 0.934042 0.467021 0.884246i \(-0.345327\pi\)
0.467021 + 0.884246i \(0.345327\pi\)
\(102\) 0 0
\(103\) 72.6413 + 72.6413i 0.705256 + 0.705256i 0.965534 0.260278i \(-0.0838142\pi\)
−0.260278 + 0.965534i \(0.583814\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −13.0556 + 13.0556i −0.122015 + 0.122015i −0.765478 0.643463i \(-0.777497\pi\)
0.643463 + 0.765478i \(0.277497\pi\)
\(108\) 0 0
\(109\) 69.2827i 0.635621i 0.948154 + 0.317810i \(0.102948\pi\)
−0.948154 + 0.317810i \(0.897052\pi\)
\(110\) 0 0
\(111\) 86.5857 0.780051
\(112\) 0 0
\(113\) 102.136 + 102.136i 0.903860 + 0.903860i 0.995768 0.0919072i \(-0.0292963\pi\)
−0.0919072 + 0.995768i \(0.529296\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 43.3485 43.3485i 0.370500 0.370500i
\(118\) 0 0
\(119\) 252.272i 2.11994i
\(120\) 0 0
\(121\) −79.4041 −0.656232
\(122\) 0 0
\(123\) −24.8536 24.8536i −0.202062 0.202062i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 119.944 119.944i 0.944444 0.944444i −0.0540920 0.998536i \(-0.517226\pi\)
0.998536 + 0.0540920i \(0.0172264\pi\)
\(128\) 0 0
\(129\) 79.1010i 0.613186i
\(130\) 0 0
\(131\) −121.146 −0.924782 −0.462391 0.886676i \(-0.653008\pi\)
−0.462391 + 0.886676i \(0.653008\pi\)
\(132\) 0 0
\(133\) −90.9898 90.9898i −0.684134 0.684134i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −119.530 + 119.530i −0.872482 + 0.872482i −0.992742 0.120260i \(-0.961627\pi\)
0.120260 + 0.992742i \(0.461627\pi\)
\(138\) 0 0
\(139\) 140.788i 1.01286i 0.862281 + 0.506431i \(0.169035\pi\)
−0.862281 + 0.506431i \(0.830965\pi\)
\(140\) 0 0
\(141\) 123.798 0.878000
\(142\) 0 0
\(143\) −93.1918 93.1918i −0.651691 0.651691i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −12.7298 + 12.7298i −0.0865976 + 0.0865976i
\(148\) 0 0
\(149\) 53.5301i 0.359262i 0.983734 + 0.179631i \(0.0574904\pi\)
−0.983734 + 0.179631i \(0.942510\pi\)
\(150\) 0 0
\(151\) 232.606 1.54044 0.770219 0.637780i \(-0.220147\pi\)
0.770219 + 0.637780i \(0.220147\pi\)
\(152\) 0 0
\(153\) 69.4393 + 69.4393i 0.453852 + 0.453852i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −128.631 + 128.631i −0.819306 + 0.819306i −0.986007 0.166701i \(-0.946689\pi\)
0.166701 + 0.986007i \(0.446689\pi\)
\(158\) 0 0
\(159\) 13.4847i 0.0848094i
\(160\) 0 0
\(161\) 72.4949 0.450279
\(162\) 0 0
\(163\) −117.576 117.576i −0.721322 0.721322i 0.247552 0.968875i \(-0.420374\pi\)
−0.968875 + 0.247552i \(0.920374\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −33.6617 + 33.6617i −0.201567 + 0.201567i −0.800671 0.599104i \(-0.795524\pi\)
0.599104 + 0.800671i \(0.295524\pi\)
\(168\) 0 0
\(169\) 248.576i 1.47086i
\(170\) 0 0
\(171\) −50.0908 −0.292929
\(172\) 0 0
\(173\) −28.2474 28.2474i −0.163280 0.163280i 0.620738 0.784018i \(-0.286833\pi\)
−0.784018 + 0.620738i \(0.786833\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 67.8990 67.8990i 0.383610 0.383610i
\(178\) 0 0
\(179\) 45.2372i 0.252722i −0.991984 0.126361i \(-0.959670\pi\)
0.991984 0.126361i \(-0.0403298\pi\)
\(180\) 0 0
\(181\) −260.656 −1.44009 −0.720045 0.693928i \(-0.755879\pi\)
−0.720045 + 0.693928i \(0.755879\pi\)
\(182\) 0 0
\(183\) −58.6515 58.6515i −0.320500 0.320500i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 149.283 149.283i 0.798303 0.798303i
\(188\) 0 0
\(189\) 40.0454i 0.211880i
\(190\) 0 0
\(191\) 51.8684 0.271562 0.135781 0.990739i \(-0.456646\pi\)
0.135781 + 0.990739i \(0.456646\pi\)
\(192\) 0 0
\(193\) −16.6163 16.6163i −0.0860950 0.0860950i 0.662748 0.748843i \(-0.269390\pi\)
−0.748843 + 0.662748i \(0.769390\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −86.0908 + 86.0908i −0.437009 + 0.437009i −0.891004 0.453995i \(-0.849998\pi\)
0.453995 + 0.891004i \(0.349998\pi\)
\(198\) 0 0
\(199\) 28.5653i 0.143544i 0.997421 + 0.0717721i \(0.0228654\pi\)
−0.997421 + 0.0717721i \(0.977135\pi\)
\(200\) 0 0
\(201\) 208.899 1.03930
\(202\) 0 0
\(203\) −0.247449 0.247449i −0.00121896 0.00121896i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 19.9546 19.9546i 0.0963990 0.0963990i
\(208\) 0 0
\(209\) 107.687i 0.515248i
\(210\) 0 0
\(211\) 197.151 0.934365 0.467183 0.884161i \(-0.345269\pi\)
0.467183 + 0.884161i \(0.345269\pi\)
\(212\) 0 0
\(213\) 59.2827 + 59.2827i 0.278322 + 0.278322i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 24.4949 24.4949i 0.112880 0.112880i
\(218\) 0 0
\(219\) 53.8638i 0.245953i
\(220\) 0 0
\(221\) −668.908 −3.02673
\(222\) 0 0
\(223\) 287.338 + 287.338i 1.28851 + 1.28851i 0.935690 + 0.352822i \(0.114778\pi\)
0.352822 + 0.935690i \(0.385222\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −234.384 + 234.384i −1.03253 + 1.03253i −0.0330743 + 0.999453i \(0.510530\pi\)
−0.999453 + 0.0330743i \(0.989470\pi\)
\(228\) 0 0
\(229\) 284.969i 1.24441i 0.782855 + 0.622204i \(0.213763\pi\)
−0.782855 + 0.622204i \(0.786237\pi\)
\(230\) 0 0
\(231\) 86.0908 0.372688
\(232\) 0 0
\(233\) 241.530 + 241.530i 1.03661 + 1.03661i 0.999304 + 0.0373060i \(0.0118776\pi\)
0.0373060 + 0.999304i \(0.488122\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −155.171 + 155.171i −0.654732 + 0.654732i
\(238\) 0 0
\(239\) 327.737i 1.37128i −0.727939 0.685642i \(-0.759522\pi\)
0.727939 0.685642i \(-0.240478\pi\)
\(240\) 0 0
\(241\) 269.131 1.11672 0.558362 0.829597i \(-0.311430\pi\)
0.558362 + 0.829597i \(0.311430\pi\)
\(242\) 0 0
\(243\) 11.0227 + 11.0227i 0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 241.262 241.262i 0.976770 0.976770i
\(248\) 0 0
\(249\) 232.565i 0.933997i
\(250\) 0 0
\(251\) −186.136 −0.741579 −0.370789 0.928717i \(-0.620913\pi\)
−0.370789 + 0.928717i \(0.620913\pi\)
\(252\) 0 0
\(253\) −42.8990 42.8990i −0.169561 0.169561i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −138.268 + 138.268i −0.538007 + 0.538007i −0.922943 0.384936i \(-0.874224\pi\)
0.384936 + 0.922943i \(0.374224\pi\)
\(258\) 0 0
\(259\) 385.262i 1.48750i
\(260\) 0 0
\(261\) −0.136223 −0.000521927
\(262\) 0 0
\(263\) −163.146 163.146i −0.620329 0.620329i 0.325287 0.945615i \(-0.394539\pi\)
−0.945615 + 0.325287i \(0.894539\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 87.9342 87.9342i 0.329342 0.329342i
\(268\) 0 0
\(269\) 108.227i 0.402331i −0.979557 0.201165i \(-0.935527\pi\)
0.979557 0.201165i \(-0.0644729\pi\)
\(270\) 0 0
\(271\) −324.384 −1.19699 −0.598494 0.801127i \(-0.704234\pi\)
−0.598494 + 0.801127i \(0.704234\pi\)
\(272\) 0 0
\(273\) −192.879 192.879i −0.706515 0.706515i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 165.864 165.864i 0.598786 0.598786i −0.341203 0.939990i \(-0.610834\pi\)
0.939990 + 0.341203i \(0.110834\pi\)
\(278\) 0 0
\(279\) 13.4847i 0.0483322i
\(280\) 0 0
\(281\) 300.434 1.06916 0.534579 0.845118i \(-0.320470\pi\)
0.534579 + 0.845118i \(0.320470\pi\)
\(282\) 0 0
\(283\) −352.161 352.161i −1.24439 1.24439i −0.958163 0.286223i \(-0.907600\pi\)
−0.286223 0.958163i \(-0.592400\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −110.586 + 110.586i −0.385316 + 0.385316i
\(288\) 0 0
\(289\) 782.514i 2.70766i
\(290\) 0 0
\(291\) −90.6311 −0.311447
\(292\) 0 0
\(293\) 109.414 + 109.414i 0.373428 + 0.373428i 0.868724 0.495296i \(-0.164941\pi\)
−0.495296 + 0.868724i \(0.664941\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 23.6969 23.6969i 0.0797877 0.0797877i
\(298\) 0 0
\(299\) 192.222i 0.642884i
\(300\) 0 0
\(301\) −351.959 −1.16930
\(302\) 0 0
\(303\) −115.540 115.540i −0.381321 0.381321i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 110.627 110.627i 0.360347 0.360347i −0.503594 0.863941i \(-0.667989\pi\)
0.863941 + 0.503594i \(0.167989\pi\)
\(308\) 0 0
\(309\) 177.934i 0.575839i
\(310\) 0 0
\(311\) −2.38367 −0.00766454 −0.00383227 0.999993i \(-0.501220\pi\)
−0.00383227 + 0.999993i \(0.501220\pi\)
\(312\) 0 0
\(313\) −132.959 132.959i −0.424790 0.424790i 0.462059 0.886849i \(-0.347111\pi\)
−0.886849 + 0.462059i \(0.847111\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 37.1464 37.1464i 0.117181 0.117181i −0.646085 0.763266i \(-0.723595\pi\)
0.763266 + 0.646085i \(0.223595\pi\)
\(318\) 0 0
\(319\) 0.292856i 0.000918045i
\(320\) 0 0
\(321\) 31.9796 0.0996249
\(322\) 0 0
\(323\) 386.474 + 386.474i 1.19652 + 1.19652i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 84.8536 84.8536i 0.259491 0.259491i
\(328\) 0 0
\(329\) 550.838i 1.67428i
\(330\) 0 0
\(331\) −21.6459 −0.0653955 −0.0326978 0.999465i \(-0.510410\pi\)
−0.0326978 + 0.999465i \(0.510410\pi\)
\(332\) 0 0
\(333\) −106.045 106.045i −0.318455 0.318455i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 136.757 136.757i 0.405808 0.405808i −0.474466 0.880274i \(-0.657359\pi\)
0.880274 + 0.474466i \(0.157359\pi\)
\(338\) 0 0
\(339\) 250.182i 0.737999i
\(340\) 0 0
\(341\) −28.9898 −0.0850141
\(342\) 0 0
\(343\) −210.384 210.384i −0.613363 0.613363i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 33.8480 33.8480i 0.0975445 0.0975445i −0.656650 0.754195i \(-0.728027\pi\)
0.754195 + 0.656650i \(0.228027\pi\)
\(348\) 0 0
\(349\) 241.283i 0.691354i 0.938354 + 0.345677i \(0.112351\pi\)
−0.938354 + 0.345677i \(0.887649\pi\)
\(350\) 0 0
\(351\) −106.182 −0.302512
\(352\) 0 0
\(353\) −126.833 126.833i −0.359301 0.359301i 0.504254 0.863555i \(-0.331767\pi\)
−0.863555 + 0.504254i \(0.831767\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 308.969 308.969i 0.865460 0.865460i
\(358\) 0 0
\(359\) 22.1112i 0.0615912i −0.999526 0.0307956i \(-0.990196\pi\)
0.999526 0.0307956i \(-0.00980409\pi\)
\(360\) 0 0
\(361\) 82.2122 0.227735
\(362\) 0 0
\(363\) 97.2497 + 97.2497i 0.267906 + 0.267906i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −213.944 + 213.944i −0.582955 + 0.582955i −0.935714 0.352759i \(-0.885243\pi\)
0.352759 + 0.935714i \(0.385243\pi\)
\(368\) 0 0
\(369\) 60.8786i 0.164983i
\(370\) 0 0
\(371\) −60.0000 −0.161725
\(372\) 0 0
\(373\) −210.025 210.025i −0.563070 0.563070i 0.367108 0.930178i \(-0.380348\pi\)
−0.930178 + 0.367108i \(0.880348\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.656118 0.656118i 0.00174037 0.00174037i
\(378\) 0 0
\(379\) 124.343i 0.328081i −0.986454 0.164041i \(-0.947547\pi\)
0.986454 0.164041i \(-0.0524528\pi\)
\(380\) 0 0
\(381\) −293.803 −0.771135
\(382\) 0 0
\(383\) 418.540 + 418.540i 1.09279 + 1.09279i 0.995229 + 0.0975654i \(0.0311055\pi\)
0.0975654 + 0.995229i \(0.468894\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −96.8786 + 96.8786i −0.250332 + 0.250332i
\(388\) 0 0
\(389\) 369.884i 0.950859i 0.879754 + 0.475430i \(0.157707\pi\)
−0.879754 + 0.475430i \(0.842293\pi\)
\(390\) 0 0
\(391\) −307.918 −0.787515
\(392\) 0 0
\(393\) 148.373 + 148.373i 0.377541 + 0.377541i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 373.984 373.984i 0.942026 0.942026i −0.0563835 0.998409i \(-0.517957\pi\)
0.998409 + 0.0563835i \(0.0179570\pi\)
\(398\) 0 0
\(399\) 222.879i 0.558593i
\(400\) 0 0
\(401\) 113.151 0.282172 0.141086 0.989997i \(-0.454941\pi\)
0.141086 + 0.989997i \(0.454941\pi\)
\(402\) 0 0
\(403\) 64.9490 + 64.9490i 0.161164 + 0.161164i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −227.980 + 227.980i −0.560146 + 0.560146i
\(408\) 0 0
\(409\) 90.3837i 0.220987i −0.993877 0.110493i \(-0.964757\pi\)
0.993877 0.110493i \(-0.0352431\pi\)
\(410\) 0 0
\(411\) 292.788 0.712379
\(412\) 0 0
\(413\) −302.116 302.116i −0.731515 0.731515i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 172.429 172.429i 0.413499 0.413499i
\(418\) 0 0
\(419\) 334.772i 0.798978i 0.916738 + 0.399489i \(0.130812\pi\)
−0.916738 + 0.399489i \(0.869188\pi\)
\(420\) 0 0
\(421\) 57.2735 0.136042 0.0680208 0.997684i \(-0.478332\pi\)
0.0680208 + 0.997684i \(0.478332\pi\)
\(422\) 0 0
\(423\) −151.621 151.621i −0.358442 0.358442i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −260.969 + 260.969i −0.611170 + 0.611170i
\(428\) 0 0
\(429\) 228.272i 0.532104i
\(430\) 0 0
\(431\) −442.656 −1.02704 −0.513522 0.858076i \(-0.671660\pi\)
−0.513522 + 0.858076i \(0.671660\pi\)
\(432\) 0 0
\(433\) 14.8684 + 14.8684i 0.0343380 + 0.0343380i 0.724067 0.689729i \(-0.242270\pi\)
−0.689729 + 0.724067i \(0.742270\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 111.060 111.060i 0.254142 0.254142i
\(438\) 0 0
\(439\) 233.818i 0.532616i 0.963888 + 0.266308i \(0.0858038\pi\)
−0.963888 + 0.266308i \(0.914196\pi\)
\(440\) 0 0
\(441\) 31.1816 0.0707066
\(442\) 0 0
\(443\) −246.747 246.747i −0.556991 0.556991i 0.371459 0.928449i \(-0.378858\pi\)
−0.928449 + 0.371459i \(0.878858\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 65.5607 65.5607i 0.146668 0.146668i
\(448\) 0 0
\(449\) 282.758i 0.629751i 0.949133 + 0.314875i \(0.101963\pi\)
−0.949133 + 0.314875i \(0.898037\pi\)
\(450\) 0 0
\(451\) 130.879 0.290196
\(452\) 0 0
\(453\) −284.883 284.883i −0.628881 0.628881i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 298.171 298.171i 0.652454 0.652454i −0.301129 0.953583i \(-0.597364\pi\)
0.953583 + 0.301129i \(0.0973636\pi\)
\(458\) 0 0
\(459\) 170.091i 0.370568i
\(460\) 0 0
\(461\) −264.318 −0.573358 −0.286679 0.958027i \(-0.592551\pi\)
−0.286679 + 0.958027i \(0.592551\pi\)
\(462\) 0 0
\(463\) 135.116 + 135.116i 0.291827 + 0.291827i 0.837802 0.545975i \(-0.183841\pi\)
−0.545975 + 0.837802i \(0.683841\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 558.631 558.631i 1.19621 1.19621i 0.220920 0.975292i \(-0.429094\pi\)
0.975292 0.220920i \(-0.0709061\pi\)
\(468\) 0 0
\(469\) 929.494i 1.98186i
\(470\) 0 0
\(471\) 315.081 0.668961
\(472\) 0 0
\(473\) 208.272 + 208.272i 0.440322 + 0.440322i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −16.5153 + 16.5153i −0.0346233 + 0.0346233i
\(478\) 0 0
\(479\) 456.141i 0.952277i −0.879370 0.476139i \(-0.842036\pi\)
0.879370 0.476139i \(-0.157964\pi\)
\(480\) 0 0
\(481\) 1021.53 2.12377
\(482\) 0 0
\(483\) −88.7878 88.7878i −0.183826 0.183826i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 11.9444 11.9444i 0.0245265 0.0245265i −0.694737 0.719264i \(-0.744479\pi\)
0.719264 + 0.694737i \(0.244479\pi\)
\(488\) 0 0
\(489\) 288.000i 0.588957i
\(490\) 0 0
\(491\) −822.468 −1.67509 −0.837544 0.546370i \(-0.816009\pi\)
−0.837544 + 0.546370i \(0.816009\pi\)
\(492\) 0 0
\(493\) 1.05103 + 1.05103i 0.00213190 + 0.00213190i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 263.778 263.778i 0.530740 0.530740i
\(498\) 0 0
\(499\) 312.474i 0.626201i 0.949720 + 0.313101i \(0.101368\pi\)
−0.949720 + 0.313101i \(0.898632\pi\)
\(500\) 0 0
\(501\) 82.4541 0.164579
\(502\) 0 0
\(503\) −371.530 371.530i −0.738628 0.738628i 0.233684 0.972313i \(-0.424922\pi\)
−0.972313 + 0.233684i \(0.924922\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 304.442 304.442i 0.600476 0.600476i
\(508\) 0 0
\(509\) 171.228i 0.336401i −0.985753 0.168200i \(-0.946204\pi\)
0.985753 0.168200i \(-0.0537956\pi\)
\(510\) 0 0
\(511\) −239.666 −0.469014
\(512\) 0 0
\(513\) 61.3485 + 61.3485i 0.119588 + 0.119588i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −325.959 + 325.959i −0.630482 + 0.630482i
\(518\) 0 0
\(519\) 69.1918i 0.133318i
\(520\) 0 0
\(521\) −206.313 −0.395995 −0.197997 0.980203i \(-0.563444\pi\)
−0.197997 + 0.980203i \(0.563444\pi\)
\(522\) 0 0
\(523\) −135.526 135.526i −0.259131 0.259131i 0.565570 0.824701i \(-0.308656\pi\)
−0.824701 + 0.565570i \(0.808656\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −104.041 + 104.041i −0.197421 + 0.197421i
\(528\) 0 0
\(529\) 440.514i 0.832730i
\(530\) 0 0
\(531\) −166.318 −0.313216
\(532\) 0 0
\(533\) −293.221 293.221i −0.550134 0.550134i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −55.4041 + 55.4041i −0.103173 + 0.103173i
\(538\) 0 0
\(539\) 67.0352i 0.124370i
\(540\) 0 0
\(541\) 303.485 0.560970 0.280485 0.959858i \(-0.409505\pi\)
0.280485 + 0.959858i \(0.409505\pi\)
\(542\) 0 0
\(543\) 319.237 + 319.237i 0.587914 + 0.587914i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −71.3939 + 71.3939i −0.130519 + 0.130519i −0.769348 0.638829i \(-0.779419\pi\)
0.638829 + 0.769348i \(0.279419\pi\)
\(548\) 0 0
\(549\) 143.666i 0.261687i
\(550\) 0 0
\(551\) −0.758169 −0.00137599
\(552\) 0 0
\(553\) 690.434 + 690.434i 1.24852 + 1.24852i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −753.019 + 753.019i −1.35192 + 1.35192i −0.468407 + 0.883513i \(0.655172\pi\)
−0.883513 + 0.468407i \(0.844828\pi\)
\(558\) 0 0
\(559\) 933.231i 1.66946i
\(560\) 0 0
\(561\) −365.666 −0.651812
\(562\) 0 0
\(563\) 703.464 + 703.464i 1.24949 + 1.24949i 0.955944 + 0.293548i \(0.0948361\pi\)
0.293548 + 0.955944i \(0.405164\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 49.0454 49.0454i 0.0864998 0.0864998i
\(568\) 0 0
\(569\) 434.504i 0.763628i −0.924239 0.381814i \(-0.875300\pi\)
0.924239 0.381814i \(-0.124700\pi\)
\(570\) 0 0
\(571\) 131.040 0.229492 0.114746 0.993395i \(-0.463395\pi\)
0.114746 + 0.993395i \(0.463395\pi\)
\(572\) 0 0
\(573\) −63.5255 63.5255i −0.110865 0.110865i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −290.444 + 290.444i −0.503369 + 0.503369i −0.912483 0.409114i \(-0.865838\pi\)
0.409114 + 0.912483i \(0.365838\pi\)
\(578\) 0 0
\(579\) 40.7015i 0.0702962i
\(580\) 0 0
\(581\) −1034.80 −1.78106
\(582\) 0 0
\(583\) 35.5051 + 35.5051i 0.0609007 + 0.0609007i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 180.288 180.288i 0.307135 0.307135i −0.536662 0.843797i \(-0.680315\pi\)
0.843797 + 0.536662i \(0.180315\pi\)
\(588\) 0 0
\(589\) 75.0510i 0.127421i
\(590\) 0 0
\(591\) 210.879 0.356817
\(592\) 0 0
\(593\) 25.0556 + 25.0556i 0.0422523 + 0.0422523i 0.727917 0.685665i \(-0.240488\pi\)
−0.685665 + 0.727917i \(0.740488\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 34.9852 34.9852i 0.0586017 0.0586017i
\(598\) 0 0
\(599\) 509.807i 0.851097i 0.904936 + 0.425549i \(0.139919\pi\)
−0.904936 + 0.425549i \(0.860081\pi\)
\(600\) 0 0
\(601\) 179.757 0.299097 0.149548 0.988754i \(-0.452218\pi\)
0.149548 + 0.988754i \(0.452218\pi\)
\(602\) 0 0
\(603\) −255.848 255.848i −0.424292 0.424292i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 33.1566 33.1566i 0.0546238 0.0546238i −0.679267 0.733891i \(-0.737702\pi\)
0.733891 + 0.679267i \(0.237702\pi\)
\(608\) 0 0
\(609\) 0.606123i 0.000995276i
\(610\) 0 0
\(611\) 1460.56 2.39045
\(612\) 0 0
\(613\) 261.712 + 261.712i 0.426936 + 0.426936i 0.887583 0.460647i \(-0.152383\pi\)
−0.460647 + 0.887583i \(0.652383\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 762.075 762.075i 1.23513 1.23513i 0.273161 0.961968i \(-0.411931\pi\)
0.961968 0.273161i \(-0.0880693\pi\)
\(618\) 0 0
\(619\) 81.6367i 0.131885i −0.997823 0.0659424i \(-0.978995\pi\)
0.997823 0.0659424i \(-0.0210054\pi\)
\(620\) 0 0
\(621\) −48.8786 −0.0787095
\(622\) 0 0
\(623\) −391.262 391.262i −0.628029 0.628029i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 131.889 131.889i 0.210349 0.210349i
\(628\) 0 0
\(629\) 1636.38i 2.60156i
\(630\) 0 0
\(631\) 16.4133 0.0260115 0.0130057 0.999915i \(-0.495860\pi\)
0.0130057 + 0.999915i \(0.495860\pi\)
\(632\) 0 0
\(633\) −241.460 241.460i −0.381453 0.381453i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −150.186 + 150.186i −0.235771 + 0.235771i
\(638\) 0 0
\(639\) 145.212i 0.227249i
\(640\) 0 0
\(641\) −546.041 −0.851858 −0.425929 0.904757i \(-0.640053\pi\)
−0.425929 + 0.904757i \(0.640053\pi\)
\(642\) 0 0
\(643\) −142.879 142.879i −0.222206 0.222206i 0.587221 0.809427i \(-0.300222\pi\)
−0.809427 + 0.587221i \(0.800222\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −649.691 + 649.691i −1.00416 + 1.00416i −0.00416838 + 0.999991i \(0.501327\pi\)
−0.999991 + 0.00416838i \(0.998673\pi\)
\(648\) 0 0
\(649\) 357.555i 0.550932i
\(650\) 0 0
\(651\) −60.0000 −0.0921659
\(652\) 0 0
\(653\) 150.904 + 150.904i 0.231093 + 0.231093i 0.813149 0.582056i \(-0.197752\pi\)
−0.582056 + 0.813149i \(0.697752\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −65.9694 + 65.9694i −0.100410 + 0.100410i
\(658\) 0 0
\(659\) 268.802i 0.407893i −0.978982 0.203947i \(-0.934623\pi\)
0.978982 0.203947i \(-0.0653769\pi\)
\(660\) 0 0
\(661\) 311.162 0.470745 0.235372 0.971905i \(-0.424369\pi\)
0.235372 + 0.971905i \(0.424369\pi\)
\(662\) 0 0
\(663\) 819.242 + 819.242i 1.23566 + 1.23566i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.302031 0.302031i 0.000452820 0.000452820i
\(668\) 0 0
\(669\) 703.832i 1.05207i
\(670\) 0 0
\(671\) 308.858 0.460295
\(672\) 0 0
\(673\) 547.756 + 547.756i 0.813902 + 0.813902i 0.985216 0.171314i \(-0.0548014\pi\)
−0.171314 + 0.985216i \(0.554801\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −696.257 + 696.257i −1.02844 + 1.02844i −0.0288606 + 0.999583i \(0.509188\pi\)
−0.999583 + 0.0288606i \(0.990812\pi\)
\(678\) 0 0
\(679\) 403.262i 0.593906i
\(680\) 0 0
\(681\) 574.120 0.843055
\(682\) 0 0
\(683\) −84.0250 84.0250i −0.123023 0.123023i 0.642915 0.765938i \(-0.277725\pi\)
−0.765938 + 0.642915i \(0.777725\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 349.015 349.015i 0.508027 0.508027i
\(688\) 0 0
\(689\) 159.092i 0.230903i
\(690\) 0 0
\(691\) −1157.06 −1.67447 −0.837236 0.546842i \(-0.815830\pi\)
−0.837236 + 0.546842i \(0.815830\pi\)
\(692\) 0 0
\(693\) −105.439 105.439i −0.152149 0.152149i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 469.707 469.707i 0.673898 0.673898i
\(698\) 0 0
\(699\) 591.626i 0.846388i
\(700\) 0 0
\(701\) 843.691 1.20355 0.601777 0.798664i \(-0.294460\pi\)
0.601777 + 0.798664i \(0.294460\pi\)
\(702\) 0 0
\(703\) −590.211 590.211i −0.839561 0.839561i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −514.095 + 514.095i −0.727150 + 0.727150i
\(708\) 0 0
\(709\) 170.686i 0.240741i 0.992729 + 0.120371i \(0.0384083\pi\)
−0.992729 + 0.120371i \(0.961592\pi\)
\(710\) 0 0
\(711\) 380.091 0.534586
\(712\) 0 0
\(713\) 29.8979 + 29.8979i 0.0419326 + 0.0419326i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −401.394 + 401.394i −0.559824 + 0.559824i
\(718\) 0 0
\(719\) 605.435i 0.842051i −0.907049 0.421026i \(-0.861670\pi\)
0.907049 0.421026i \(-0.138330\pi\)
\(720\) 0 0
\(721\) −791.716 −1.09808
\(722\) 0 0
\(723\) −329.616 329.616i −0.455901 0.455901i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −50.8025 + 50.8025i −0.0698797 + 0.0698797i −0.741183 0.671303i \(-0.765735\pi\)
0.671303 + 0.741183i \(0.265735\pi\)
\(728\) 0 0
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) 1494.93 2.04505
\(732\) 0 0
\(733\) −516.529 516.529i −0.704678 0.704678i 0.260733 0.965411i \(-0.416036\pi\)
−0.965411 + 0.260733i \(0.916036\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −550.030 + 550.030i −0.746309 + 0.746309i
\(738\) 0 0
\(739\) 650.109i 0.879715i 0.898068 + 0.439857i \(0.144971\pi\)
−0.898068 + 0.439857i \(0.855029\pi\)
\(740\) 0 0
\(741\) −590.969 −0.797530
\(742\) 0 0
\(743\) 90.6811 + 90.6811i 0.122047 + 0.122047i 0.765492 0.643445i \(-0.222496\pi\)
−0.643445 + 0.765492i \(0.722496\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −284.833 + 284.833i −0.381303 + 0.381303i
\(748\) 0 0
\(749\) 142.293i 0.189977i
\(750\) 0 0
\(751\) 300.050 0.399534 0.199767 0.979843i \(-0.435981\pi\)
0.199767 + 0.979843i \(0.435981\pi\)
\(752\) 0 0
\(753\) 227.969 + 227.969i 0.302748 + 0.302748i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −523.176 + 523.176i −0.691118 + 0.691118i −0.962478 0.271360i \(-0.912527\pi\)
0.271360 + 0.962478i \(0.412527\pi\)
\(758\) 0 0
\(759\) 105.081i 0.138446i
\(760\) 0 0
\(761\) −724.130 −0.951550 −0.475775 0.879567i \(-0.657832\pi\)
−0.475775 + 0.879567i \(0.657832\pi\)
\(762\) 0 0
\(763\) −377.555 377.555i −0.494830 0.494830i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 801.069 801.069i 1.04442 1.04442i
\(768\) 0 0
\(769\) 13.7775i 0.0179162i 0.999960 + 0.00895809i \(0.00285149\pi\)
−0.999960 + 0.00895809i \(0.997149\pi\)
\(770\) 0 0
\(771\) 338.686 0.439281
\(772\) 0 0
\(773\) 564.207 + 564.207i 0.729892 + 0.729892i 0.970598 0.240706i \(-0.0773789\pi\)
−0.240706 + 0.970598i \(0.577379\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −471.848 + 471.848i −0.607269 + 0.607269i
\(778\) 0 0
\(779\) 338.829i 0.434953i
\(780\) 0 0
\(781\) −312.182 −0.399720
\(782\) 0 0
\(783\) 0.166838 + 0.166838i 0.000213076 + 0.000213076i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −212.424 + 212.424i −0.269917 + 0.269917i −0.829067 0.559150i \(-0.811128\pi\)
0.559150 + 0.829067i \(0.311128\pi\)
\(788\) 0 0
\(789\) 399.626i 0.506496i
\(790\) 0 0
\(791\) −1113.18 −1.40731
\(792\) 0 0
\(793\) −691.968 691.968i −0.872596 0.872596i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 15.6617 15.6617i 0.0196509 0.0196509i −0.697213 0.716864i \(-0.745577\pi\)
0.716864 + 0.697213i \(0.245577\pi\)
\(798\) 0 0
\(799\) 2339.66i 2.92823i