Properties

Label 60.3.b.a.29.1
Level $60$
Weight $3$
Character 60.29
Analytic conductor $1.635$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 60.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.63488158616\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 29.1
Root \(-1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 60.29
Dual form 60.3.b.a.29.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.23607 - 2.00000i) q^{3} +(-2.23607 - 4.47214i) q^{5} -8.00000i q^{7} +(1.00000 + 8.94427i) q^{9} +O(q^{10})\) \(q+(-2.23607 - 2.00000i) q^{3} +(-2.23607 - 4.47214i) q^{5} -8.00000i q^{7} +(1.00000 + 8.94427i) q^{9} -8.94427i q^{11} +12.0000i q^{13} +(-3.94427 + 14.4721i) q^{15} +31.3050 q^{17} -6.00000 q^{19} +(-16.0000 + 17.8885i) q^{21} -4.47214 q^{23} +(-15.0000 + 20.0000i) q^{25} +(15.6525 - 22.0000i) q^{27} -26.8328i q^{29} +34.0000 q^{31} +(-17.8885 + 20.0000i) q^{33} +(-35.7771 + 17.8885i) q^{35} -44.0000i q^{37} +(24.0000 - 26.8328i) q^{39} +17.8885i q^{41} -28.0000i q^{43} +(37.7639 - 24.4721i) q^{45} -4.47214 q^{47} -15.0000 q^{49} +(-70.0000 - 62.6099i) q^{51} -40.2492 q^{53} +(-40.0000 + 20.0000i) q^{55} +(13.4164 + 12.0000i) q^{57} +98.3870i q^{59} +74.0000 q^{61} +(71.5542 - 8.00000i) q^{63} +(53.6656 - 26.8328i) q^{65} +92.0000i q^{67} +(10.0000 + 8.94427i) q^{69} +53.6656i q^{71} +56.0000i q^{73} +(73.5410 - 14.7214i) q^{75} -71.5542 q^{77} -78.0000 q^{79} +(-79.0000 + 17.8885i) q^{81} +102.859 q^{83} +(-70.0000 - 140.000i) q^{85} +(-53.6656 + 60.0000i) q^{87} -17.8885i q^{89} +96.0000 q^{91} +(-76.0263 - 68.0000i) q^{93} +(13.4164 + 26.8328i) q^{95} +32.0000i q^{97} +(80.0000 - 8.94427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{9} + O(q^{10}) \) \( 4q + 4q^{9} + 20q^{15} - 24q^{19} - 64q^{21} - 60q^{25} + 136q^{31} + 96q^{39} + 160q^{45} - 60q^{49} - 280q^{51} - 160q^{55} + 296q^{61} + 40q^{69} + 160q^{75} - 312q^{79} - 316q^{81} - 280q^{85} + 384q^{91} + 320q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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
\(3\) −2.23607 2.00000i −0.745356 0.666667i
\(4\) 0 0
\(5\) −2.23607 4.47214i −0.447214 0.894427i
\(6\) 0 0
\(7\) 8.00000i 1.14286i −0.820652 0.571429i \(-0.806389\pi\)
0.820652 0.571429i \(-0.193611\pi\)
\(8\) 0 0
\(9\) 1.00000 + 8.94427i 0.111111 + 0.993808i
\(10\) 0 0
\(11\) 8.94427i 0.813116i −0.913625 0.406558i \(-0.866729\pi\)
0.913625 0.406558i \(-0.133271\pi\)
\(12\) 0 0
\(13\) 12.0000i 0.923077i 0.887120 + 0.461538i \(0.152702\pi\)
−0.887120 + 0.461538i \(0.847298\pi\)
\(14\) 0 0
\(15\) −3.94427 + 14.4721i −0.262951 + 0.964809i
\(16\) 0 0
\(17\) 31.3050 1.84147 0.920734 0.390191i \(-0.127591\pi\)
0.920734 + 0.390191i \(0.127591\pi\)
\(18\) 0 0
\(19\) −6.00000 −0.315789 −0.157895 0.987456i \(-0.550471\pi\)
−0.157895 + 0.987456i \(0.550471\pi\)
\(20\) 0 0
\(21\) −16.0000 + 17.8885i −0.761905 + 0.851835i
\(22\) 0 0
\(23\) −4.47214 −0.194441 −0.0972203 0.995263i \(-0.530995\pi\)
−0.0972203 + 0.995263i \(0.530995\pi\)
\(24\) 0 0
\(25\) −15.0000 + 20.0000i −0.600000 + 0.800000i
\(26\) 0 0
\(27\) 15.6525 22.0000i 0.579721 0.814815i
\(28\) 0 0
\(29\) 26.8328i 0.925270i −0.886549 0.462635i \(-0.846904\pi\)
0.886549 0.462635i \(-0.153096\pi\)
\(30\) 0 0
\(31\) 34.0000 1.09677 0.548387 0.836225i \(-0.315242\pi\)
0.548387 + 0.836225i \(0.315242\pi\)
\(32\) 0 0
\(33\) −17.8885 + 20.0000i −0.542077 + 0.606061i
\(34\) 0 0
\(35\) −35.7771 + 17.8885i −1.02220 + 0.511101i
\(36\) 0 0
\(37\) 44.0000i 1.18919i −0.804026 0.594595i \(-0.797313\pi\)
0.804026 0.594595i \(-0.202687\pi\)
\(38\) 0 0
\(39\) 24.0000 26.8328i 0.615385 0.688021i
\(40\) 0 0
\(41\) 17.8885i 0.436306i 0.975915 + 0.218153i \(0.0700032\pi\)
−0.975915 + 0.218153i \(0.929997\pi\)
\(42\) 0 0
\(43\) 28.0000i 0.651163i −0.945514 0.325581i \(-0.894440\pi\)
0.945514 0.325581i \(-0.105560\pi\)
\(44\) 0 0
\(45\) 37.7639 24.4721i 0.839198 0.543825i
\(46\) 0 0
\(47\) −4.47214 −0.0951518 −0.0475759 0.998868i \(-0.515150\pi\)
−0.0475759 + 0.998868i \(0.515150\pi\)
\(48\) 0 0
\(49\) −15.0000 −0.306122
\(50\) 0 0
\(51\) −70.0000 62.6099i −1.37255 1.22765i
\(52\) 0 0
\(53\) −40.2492 −0.759419 −0.379710 0.925106i \(-0.623976\pi\)
−0.379710 + 0.925106i \(0.623976\pi\)
\(54\) 0 0
\(55\) −40.0000 + 20.0000i −0.727273 + 0.363636i
\(56\) 0 0
\(57\) 13.4164 + 12.0000i 0.235376 + 0.210526i
\(58\) 0 0
\(59\) 98.3870i 1.66758i 0.552085 + 0.833788i \(0.313833\pi\)
−0.552085 + 0.833788i \(0.686167\pi\)
\(60\) 0 0
\(61\) 74.0000 1.21311 0.606557 0.795040i \(-0.292550\pi\)
0.606557 + 0.795040i \(0.292550\pi\)
\(62\) 0 0
\(63\) 71.5542 8.00000i 1.13578 0.126984i
\(64\) 0 0
\(65\) 53.6656 26.8328i 0.825625 0.412813i
\(66\) 0 0
\(67\) 92.0000i 1.37313i 0.727066 + 0.686567i \(0.240883\pi\)
−0.727066 + 0.686567i \(0.759117\pi\)
\(68\) 0 0
\(69\) 10.0000 + 8.94427i 0.144928 + 0.129627i
\(70\) 0 0
\(71\) 53.6656i 0.755854i 0.925835 + 0.377927i \(0.123363\pi\)
−0.925835 + 0.377927i \(0.876637\pi\)
\(72\) 0 0
\(73\) 56.0000i 0.767123i 0.923515 + 0.383562i \(0.125303\pi\)
−0.923515 + 0.383562i \(0.874697\pi\)
\(74\) 0 0
\(75\) 73.5410 14.7214i 0.980547 0.196285i
\(76\) 0 0
\(77\) −71.5542 −0.929275
\(78\) 0 0
\(79\) −78.0000 −0.987342 −0.493671 0.869649i \(-0.664345\pi\)
−0.493671 + 0.869649i \(0.664345\pi\)
\(80\) 0 0
\(81\) −79.0000 + 17.8885i −0.975309 + 0.220846i
\(82\) 0 0
\(83\) 102.859 1.23927 0.619633 0.784891i \(-0.287281\pi\)
0.619633 + 0.784891i \(0.287281\pi\)
\(84\) 0 0
\(85\) −70.0000 140.000i −0.823529 1.64706i
\(86\) 0 0
\(87\) −53.6656 + 60.0000i −0.616846 + 0.689655i
\(88\) 0 0
\(89\) 17.8885i 0.200995i −0.994937 0.100497i \(-0.967957\pi\)
0.994937 0.100497i \(-0.0320434\pi\)
\(90\) 0 0
\(91\) 96.0000 1.05495
\(92\) 0 0
\(93\) −76.0263 68.0000i −0.817487 0.731183i
\(94\) 0 0
\(95\) 13.4164 + 26.8328i 0.141225 + 0.282451i
\(96\) 0 0
\(97\) 32.0000i 0.329897i 0.986302 + 0.164948i \(0.0527458\pi\)
−0.986302 + 0.164948i \(0.947254\pi\)
\(98\) 0 0
\(99\) 80.0000 8.94427i 0.808081 0.0903462i
\(100\) 0 0
\(101\) 152.053i 1.50547i −0.658323 0.752736i \(-0.728734\pi\)
0.658323 0.752736i \(-0.271266\pi\)
\(102\) 0 0
\(103\) 104.000i 1.00971i −0.863205 0.504854i \(-0.831546\pi\)
0.863205 0.504854i \(-0.168454\pi\)
\(104\) 0 0
\(105\) 115.777 + 31.5542i 1.10264 + 0.300516i
\(106\) 0 0
\(107\) −147.580 −1.37926 −0.689628 0.724163i \(-0.742226\pi\)
−0.689628 + 0.724163i \(0.742226\pi\)
\(108\) 0 0
\(109\) 74.0000 0.678899 0.339450 0.940624i \(-0.389759\pi\)
0.339450 + 0.940624i \(0.389759\pi\)
\(110\) 0 0
\(111\) −88.0000 + 98.3870i −0.792793 + 0.886369i
\(112\) 0 0
\(113\) −40.2492 −0.356188 −0.178094 0.984013i \(-0.556993\pi\)
−0.178094 + 0.984013i \(0.556993\pi\)
\(114\) 0 0
\(115\) 10.0000 + 20.0000i 0.0869565 + 0.173913i
\(116\) 0 0
\(117\) −107.331 + 12.0000i −0.917361 + 0.102564i
\(118\) 0 0
\(119\) 250.440i 2.10453i
\(120\) 0 0
\(121\) 41.0000 0.338843
\(122\) 0 0
\(123\) 35.7771 40.0000i 0.290871 0.325203i
\(124\) 0 0
\(125\) 122.984 + 22.3607i 0.983870 + 0.178885i
\(126\) 0 0
\(127\) 16.0000i 0.125984i 0.998014 + 0.0629921i \(0.0200643\pi\)
−0.998014 + 0.0629921i \(0.979936\pi\)
\(128\) 0 0
\(129\) −56.0000 + 62.6099i −0.434109 + 0.485348i
\(130\) 0 0
\(131\) 80.4984i 0.614492i 0.951630 + 0.307246i \(0.0994074\pi\)
−0.951630 + 0.307246i \(0.900593\pi\)
\(132\) 0 0
\(133\) 48.0000i 0.360902i
\(134\) 0 0
\(135\) −133.387 20.8065i −0.988052 0.154122i
\(136\) 0 0
\(137\) 174.413 1.27309 0.636545 0.771240i \(-0.280363\pi\)
0.636545 + 0.771240i \(0.280363\pi\)
\(138\) 0 0
\(139\) −118.000 −0.848921 −0.424460 0.905446i \(-0.639536\pi\)
−0.424460 + 0.905446i \(0.639536\pi\)
\(140\) 0 0
\(141\) 10.0000 + 8.94427i 0.0709220 + 0.0634346i
\(142\) 0 0
\(143\) 107.331 0.750568
\(144\) 0 0
\(145\) −120.000 + 60.0000i −0.827586 + 0.413793i
\(146\) 0 0
\(147\) 33.5410 + 30.0000i 0.228170 + 0.204082i
\(148\) 0 0
\(149\) 98.3870i 0.660315i 0.943926 + 0.330158i \(0.107102\pi\)
−0.943926 + 0.330158i \(0.892898\pi\)
\(150\) 0 0
\(151\) 34.0000 0.225166 0.112583 0.993642i \(-0.464088\pi\)
0.112583 + 0.993642i \(0.464088\pi\)
\(152\) 0 0
\(153\) 31.3050 + 280.000i 0.204608 + 1.83007i
\(154\) 0 0
\(155\) −76.0263 152.053i −0.490492 0.980985i
\(156\) 0 0
\(157\) 92.0000i 0.585987i 0.956114 + 0.292994i \(0.0946515\pi\)
−0.956114 + 0.292994i \(0.905349\pi\)
\(158\) 0 0
\(159\) 90.0000 + 80.4984i 0.566038 + 0.506280i
\(160\) 0 0
\(161\) 35.7771i 0.222218i
\(162\) 0 0
\(163\) 68.0000i 0.417178i −0.978003 0.208589i \(-0.933113\pi\)
0.978003 0.208589i \(-0.0668871\pi\)
\(164\) 0 0
\(165\) 129.443 + 35.2786i 0.784501 + 0.213810i
\(166\) 0 0
\(167\) 67.0820 0.401689 0.200844 0.979623i \(-0.435631\pi\)
0.200844 + 0.979623i \(0.435631\pi\)
\(168\) 0 0
\(169\) 25.0000 0.147929
\(170\) 0 0
\(171\) −6.00000 53.6656i −0.0350877 0.313834i
\(172\) 0 0
\(173\) −76.0263 −0.439458 −0.219729 0.975561i \(-0.570517\pi\)
−0.219729 + 0.975561i \(0.570517\pi\)
\(174\) 0 0
\(175\) 160.000 + 120.000i 0.914286 + 0.685714i
\(176\) 0 0
\(177\) 196.774 220.000i 1.11172 1.24294i
\(178\) 0 0
\(179\) 259.384i 1.44907i 0.689237 + 0.724536i \(0.257946\pi\)
−0.689237 + 0.724536i \(0.742054\pi\)
\(180\) 0 0
\(181\) −166.000 −0.917127 −0.458564 0.888662i \(-0.651636\pi\)
−0.458564 + 0.888662i \(0.651636\pi\)
\(182\) 0 0
\(183\) −165.469 148.000i −0.904202 0.808743i
\(184\) 0 0
\(185\) −196.774 + 98.3870i −1.06364 + 0.531822i
\(186\) 0 0
\(187\) 280.000i 1.49733i
\(188\) 0 0
\(189\) −176.000 125.220i −0.931217 0.662539i
\(190\) 0 0
\(191\) 214.663i 1.12389i −0.827175 0.561944i \(-0.810054\pi\)
0.827175 0.561944i \(-0.189946\pi\)
\(192\) 0 0
\(193\) 32.0000i 0.165803i 0.996558 + 0.0829016i \(0.0264187\pi\)
−0.996558 + 0.0829016i \(0.973581\pi\)
\(194\) 0 0
\(195\) −173.666 47.3313i −0.890593 0.242724i
\(196\) 0 0
\(197\) −4.47214 −0.0227012 −0.0113506 0.999936i \(-0.503613\pi\)
−0.0113506 + 0.999936i \(0.503613\pi\)
\(198\) 0 0
\(199\) 114.000 0.572864 0.286432 0.958101i \(-0.407531\pi\)
0.286432 + 0.958101i \(0.407531\pi\)
\(200\) 0 0
\(201\) 184.000 205.718i 0.915423 1.02347i
\(202\) 0 0
\(203\) −214.663 −1.05745
\(204\) 0 0
\(205\) 80.0000 40.0000i 0.390244 0.195122i
\(206\) 0 0
\(207\) −4.47214 40.0000i −0.0216045 0.193237i
\(208\) 0 0
\(209\) 53.6656i 0.256773i
\(210\) 0 0
\(211\) −6.00000 −0.0284360 −0.0142180 0.999899i \(-0.504526\pi\)
−0.0142180 + 0.999899i \(0.504526\pi\)
\(212\) 0 0
\(213\) 107.331 120.000i 0.503903 0.563380i
\(214\) 0 0
\(215\) −125.220 + 62.6099i −0.582418 + 0.291209i
\(216\) 0 0
\(217\) 272.000i 1.25346i
\(218\) 0 0
\(219\) 112.000 125.220i 0.511416 0.571780i
\(220\) 0 0
\(221\) 375.659i 1.69982i
\(222\) 0 0
\(223\) 272.000i 1.21973i 0.792505 + 0.609865i \(0.208777\pi\)
−0.792505 + 0.609865i \(0.791223\pi\)
\(224\) 0 0
\(225\) −193.885 114.164i −0.861713 0.507396i
\(226\) 0 0
\(227\) 245.967 1.08356 0.541779 0.840521i \(-0.317751\pi\)
0.541779 + 0.840521i \(0.317751\pi\)
\(228\) 0 0
\(229\) 154.000 0.672489 0.336245 0.941775i \(-0.390843\pi\)
0.336245 + 0.941775i \(0.390843\pi\)
\(230\) 0 0
\(231\) 160.000 + 143.108i 0.692641 + 0.619517i
\(232\) 0 0
\(233\) −183.358 −0.786942 −0.393471 0.919337i \(-0.628726\pi\)
−0.393471 + 0.919337i \(0.628726\pi\)
\(234\) 0 0
\(235\) 10.0000 + 20.0000i 0.0425532 + 0.0851064i
\(236\) 0 0
\(237\) 174.413 + 156.000i 0.735921 + 0.658228i
\(238\) 0 0
\(239\) 178.885i 0.748475i −0.927333 0.374237i \(-0.877905\pi\)
0.927333 0.374237i \(-0.122095\pi\)
\(240\) 0 0
\(241\) −206.000 −0.854772 −0.427386 0.904069i \(-0.640565\pi\)
−0.427386 + 0.904069i \(0.640565\pi\)
\(242\) 0 0
\(243\) 212.426 + 118.000i 0.874183 + 0.485597i
\(244\) 0 0
\(245\) 33.5410 + 67.0820i 0.136902 + 0.273804i
\(246\) 0 0
\(247\) 72.0000i 0.291498i
\(248\) 0 0
\(249\) −230.000 205.718i −0.923695 0.826178i
\(250\) 0 0
\(251\) 26.8328i 0.106904i 0.998570 + 0.0534518i \(0.0170224\pi\)
−0.998570 + 0.0534518i \(0.982978\pi\)
\(252\) 0 0
\(253\) 40.0000i 0.158103i
\(254\) 0 0
\(255\) −123.475 + 453.050i −0.484217 + 1.77666i
\(256\) 0 0
\(257\) −40.2492 −0.156612 −0.0783059 0.996929i \(-0.524951\pi\)
−0.0783059 + 0.996929i \(0.524951\pi\)
\(258\) 0 0
\(259\) −352.000 −1.35907
\(260\) 0 0
\(261\) 240.000 26.8328i 0.919540 0.102808i
\(262\) 0 0
\(263\) 210.190 0.799203 0.399602 0.916689i \(-0.369149\pi\)
0.399602 + 0.916689i \(0.369149\pi\)
\(264\) 0 0
\(265\) 90.0000 + 180.000i 0.339623 + 0.679245i
\(266\) 0 0
\(267\) −35.7771 + 40.0000i −0.133997 + 0.149813i
\(268\) 0 0
\(269\) 134.164i 0.498751i −0.968407 0.249376i \(-0.919775\pi\)
0.968407 0.249376i \(-0.0802254\pi\)
\(270\) 0 0
\(271\) −398.000 −1.46863 −0.734317 0.678806i \(-0.762498\pi\)
−0.734317 + 0.678806i \(0.762498\pi\)
\(272\) 0 0
\(273\) −214.663 192.000i −0.786310 0.703297i
\(274\) 0 0
\(275\) 178.885 + 134.164i 0.650493 + 0.487869i
\(276\) 0 0
\(277\) 292.000i 1.05415i 0.849818 + 0.527076i \(0.176712\pi\)
−0.849818 + 0.527076i \(0.823288\pi\)
\(278\) 0 0
\(279\) 34.0000 + 304.105i 0.121864 + 1.08998i
\(280\) 0 0
\(281\) 53.6656i 0.190981i 0.995430 + 0.0954904i \(0.0304419\pi\)
−0.995430 + 0.0954904i \(0.969558\pi\)
\(282\) 0 0
\(283\) 52.0000i 0.183746i 0.995771 + 0.0918728i \(0.0292853\pi\)
−0.995771 + 0.0918728i \(0.970715\pi\)
\(284\) 0 0
\(285\) 23.6656 86.8328i 0.0830373 0.304677i
\(286\) 0 0
\(287\) 143.108 0.498635
\(288\) 0 0
\(289\) 691.000 2.39100
\(290\) 0 0
\(291\) 64.0000 71.5542i 0.219931 0.245891i
\(292\) 0 0
\(293\) 389.076 1.32790 0.663952 0.747775i \(-0.268878\pi\)
0.663952 + 0.747775i \(0.268878\pi\)
\(294\) 0 0
\(295\) 440.000 220.000i 1.49153 0.745763i
\(296\) 0 0
\(297\) −196.774 140.000i −0.662539 0.471380i
\(298\) 0 0
\(299\) 53.6656i 0.179484i
\(300\) 0 0
\(301\) −224.000 −0.744186
\(302\) 0 0
\(303\) −304.105 + 340.000i −1.00365 + 1.12211i
\(304\) 0 0
\(305\) −165.469 330.938i −0.542521 1.08504i
\(306\) 0 0
\(307\) 492.000i 1.60261i 0.598259 + 0.801303i \(0.295859\pi\)
−0.598259 + 0.801303i \(0.704141\pi\)
\(308\) 0 0
\(309\) −208.000 + 232.551i −0.673139 + 0.752592i
\(310\) 0 0
\(311\) 482.991i 1.55302i −0.630102 0.776512i \(-0.716987\pi\)
0.630102 0.776512i \(-0.283013\pi\)
\(312\) 0 0
\(313\) 568.000i 1.81470i −0.420380 0.907348i \(-0.638103\pi\)
0.420380 0.907348i \(-0.361897\pi\)
\(314\) 0 0
\(315\) −195.777 302.111i −0.621515 0.959084i
\(316\) 0 0
\(317\) −612.683 −1.93275 −0.966376 0.257132i \(-0.917223\pi\)
−0.966376 + 0.257132i \(0.917223\pi\)
\(318\) 0 0
\(319\) −240.000 −0.752351
\(320\) 0 0
\(321\) 330.000 + 295.161i 1.02804 + 0.919505i
\(322\) 0 0
\(323\) −187.830 −0.581516
\(324\) 0 0
\(325\) −240.000 180.000i −0.738462 0.553846i
\(326\) 0 0
\(327\) −165.469 148.000i −0.506021 0.452599i
\(328\) 0 0
\(329\) 35.7771i 0.108745i
\(330\) 0 0
\(331\) 202.000 0.610272 0.305136 0.952309i \(-0.401298\pi\)
0.305136 + 0.952309i \(0.401298\pi\)
\(332\) 0 0
\(333\) 393.548 44.0000i 1.18183 0.132132i
\(334\) 0 0
\(335\) 411.437 205.718i 1.22817 0.614084i
\(336\) 0 0
\(337\) 368.000i 1.09199i −0.837789 0.545994i \(-0.816152\pi\)
0.837789 0.545994i \(-0.183848\pi\)
\(338\) 0 0
\(339\) 90.0000 + 80.4984i 0.265487 + 0.237459i
\(340\) 0 0
\(341\) 304.105i 0.891804i
\(342\) 0 0
\(343\) 272.000i 0.793003i
\(344\) 0 0
\(345\) 17.6393 64.7214i 0.0511285 0.187598i
\(346\) 0 0
\(347\) −254.912 −0.734616 −0.367308 0.930099i \(-0.619720\pi\)
−0.367308 + 0.930099i \(0.619720\pi\)
\(348\) 0 0
\(349\) −118.000 −0.338109 −0.169054 0.985607i \(-0.554071\pi\)
−0.169054 + 0.985607i \(0.554071\pi\)
\(350\) 0 0
\(351\) 264.000 + 187.830i 0.752137 + 0.535127i
\(352\) 0 0
\(353\) 31.3050 0.0886826 0.0443413 0.999016i \(-0.485881\pi\)
0.0443413 + 0.999016i \(0.485881\pi\)
\(354\) 0 0
\(355\) 240.000 120.000i 0.676056 0.338028i
\(356\) 0 0
\(357\) −500.879 + 560.000i −1.40302 + 1.56863i
\(358\) 0 0
\(359\) 53.6656i 0.149486i 0.997203 + 0.0747432i \(0.0238137\pi\)
−0.997203 + 0.0747432i \(0.976186\pi\)
\(360\) 0 0
\(361\) −325.000 −0.900277
\(362\) 0 0
\(363\) −91.6788 82.0000i −0.252559 0.225895i
\(364\) 0 0
\(365\) 250.440 125.220i 0.686136 0.343068i
\(366\) 0 0
\(367\) 352.000i 0.959128i 0.877507 + 0.479564i \(0.159205\pi\)
−0.877507 + 0.479564i \(0.840795\pi\)
\(368\) 0 0
\(369\) −160.000 + 17.8885i −0.433604 + 0.0484784i
\(370\) 0 0
\(371\) 321.994i 0.867908i
\(372\) 0 0
\(373\) 132.000i 0.353887i 0.984221 + 0.176944i \(0.0566211\pi\)
−0.984221 + 0.176944i \(0.943379\pi\)
\(374\) 0 0
\(375\) −230.279 295.967i −0.614076 0.789247i
\(376\) 0 0
\(377\) 321.994 0.854095
\(378\) 0 0
\(379\) 394.000 1.03958 0.519789 0.854295i \(-0.326011\pi\)
0.519789 + 0.854295i \(0.326011\pi\)
\(380\) 0 0
\(381\) 32.0000 35.7771i 0.0839895 0.0939031i
\(382\) 0 0
\(383\) −76.0263 −0.198502 −0.0992511 0.995062i \(-0.531645\pi\)
−0.0992511 + 0.995062i \(0.531645\pi\)
\(384\) 0 0
\(385\) 160.000 + 320.000i 0.415584 + 0.831169i
\(386\) 0 0
\(387\) 250.440 28.0000i 0.647131 0.0723514i
\(388\) 0 0
\(389\) 277.272i 0.712783i 0.934337 + 0.356391i \(0.115993\pi\)
−0.934337 + 0.356391i \(0.884007\pi\)
\(390\) 0 0
\(391\) −140.000 −0.358056
\(392\) 0 0
\(393\) 160.997 180.000i 0.409661 0.458015i
\(394\) 0 0
\(395\) 174.413 + 348.827i 0.441553 + 0.883105i
\(396\) 0 0
\(397\) 652.000i 1.64232i 0.570700 + 0.821159i \(0.306672\pi\)
−0.570700 + 0.821159i \(0.693328\pi\)
\(398\) 0 0
\(399\) 96.0000 107.331i 0.240602 0.269001i
\(400\) 0 0
\(401\) 178.885i 0.446098i −0.974807 0.223049i \(-0.928399\pi\)
0.974807 0.223049i \(-0.0716011\pi\)
\(402\) 0 0
\(403\) 408.000i 1.01241i
\(404\) 0 0
\(405\) 256.649 + 313.299i 0.633702 + 0.773577i
\(406\) 0 0
\(407\) −393.548 −0.966948
\(408\) 0 0
\(409\) −206.000 −0.503667 −0.251834 0.967771i \(-0.581034\pi\)
−0.251834 + 0.967771i \(0.581034\pi\)
\(410\) 0 0
\(411\) −390.000 348.827i −0.948905 0.848727i
\(412\) 0 0
\(413\) 787.096 1.90580
\(414\) 0 0
\(415\) −230.000 460.000i −0.554217 1.10843i
\(416\) 0 0
\(417\) 263.856 + 236.000i 0.632748 + 0.565947i
\(418\) 0 0
\(419\) 205.718i 0.490974i −0.969400 0.245487i \(-0.921052\pi\)
0.969400 0.245487i \(-0.0789479\pi\)
\(420\) 0 0
\(421\) −38.0000 −0.0902613 −0.0451306 0.998981i \(-0.514370\pi\)
−0.0451306 + 0.998981i \(0.514370\pi\)
\(422\) 0 0
\(423\) −4.47214 40.0000i −0.0105724 0.0945626i
\(424\) 0 0
\(425\) −469.574 + 626.099i −1.10488 + 1.47317i
\(426\) 0 0
\(427\) 592.000i 1.38642i
\(428\) 0 0
\(429\) −240.000 214.663i −0.559441 0.500379i
\(430\) 0 0
\(431\) 608.210i 1.41116i 0.708630 + 0.705581i \(0.249314\pi\)
−0.708630 + 0.705581i \(0.750686\pi\)
\(432\) 0 0
\(433\) 272.000i 0.628176i 0.949394 + 0.314088i \(0.101699\pi\)
−0.949394 + 0.314088i \(0.898301\pi\)
\(434\) 0 0
\(435\) 388.328 + 105.836i 0.892708 + 0.243301i
\(436\) 0 0
\(437\) 26.8328 0.0614023
\(438\) 0 0
\(439\) −366.000 −0.833713 −0.416856 0.908972i \(-0.636868\pi\)
−0.416856 + 0.908972i \(0.636868\pi\)
\(440\) 0 0
\(441\) −15.0000 134.164i −0.0340136 0.304227i
\(442\) 0 0
\(443\) −576.906 −1.30227 −0.651135 0.758962i \(-0.725707\pi\)
−0.651135 + 0.758962i \(0.725707\pi\)
\(444\) 0 0
\(445\) −80.0000 + 40.0000i −0.179775 + 0.0898876i
\(446\) 0 0
\(447\) 196.774 220.000i 0.440210 0.492170i
\(448\) 0 0
\(449\) 429.325i 0.956181i −0.878311 0.478090i \(-0.841329\pi\)
0.878311 0.478090i \(-0.158671\pi\)
\(450\) 0 0
\(451\) 160.000 0.354767
\(452\) 0 0
\(453\) −76.0263 68.0000i −0.167829 0.150110i
\(454\) 0 0
\(455\) −214.663 429.325i −0.471786 0.943572i
\(456\) 0 0
\(457\) 104.000i 0.227571i −0.993505 0.113786i \(-0.963702\pi\)
0.993505 0.113786i \(-0.0362977\pi\)
\(458\) 0 0
\(459\) 490.000 688.709i 1.06754 1.50046i
\(460\) 0 0
\(461\) 509.823i 1.10591i 0.833212 + 0.552954i \(0.186499\pi\)
−0.833212 + 0.552954i \(0.813501\pi\)
\(462\) 0 0
\(463\) 96.0000i 0.207343i 0.994612 + 0.103672i \(0.0330591\pi\)
−0.994612 + 0.103672i \(0.966941\pi\)
\(464\) 0 0
\(465\) −134.105 + 492.053i −0.288398 + 1.05818i
\(466\) 0 0
\(467\) −147.580 −0.316018 −0.158009 0.987438i \(-0.550508\pi\)
−0.158009 + 0.987438i \(0.550508\pi\)
\(468\) 0 0
\(469\) 736.000 1.56930
\(470\) 0 0
\(471\) 184.000 205.718i 0.390658 0.436769i
\(472\) 0 0
\(473\) −250.440 −0.529471
\(474\) 0 0
\(475\) 90.0000 120.000i 0.189474 0.252632i
\(476\) 0 0
\(477\) −40.2492 360.000i −0.0843799 0.754717i
\(478\) 0 0
\(479\) 572.433i 1.19506i 0.801847 + 0.597530i \(0.203851\pi\)
−0.801847 + 0.597530i \(0.796149\pi\)
\(480\) 0 0
\(481\) 528.000 1.09771
\(482\) 0 0
\(483\) 71.5542 80.0000i 0.148145 0.165631i
\(484\) 0 0
\(485\) 143.108 71.5542i 0.295069 0.147534i
\(486\) 0 0
\(487\) 648.000i 1.33060i −0.746578 0.665298i \(-0.768305\pi\)
0.746578 0.665298i \(-0.231695\pi\)
\(488\) 0 0
\(489\) −136.000 + 152.053i −0.278119 + 0.310946i
\(490\) 0 0
\(491\) 134.164i 0.273247i 0.990623 + 0.136623i \(0.0436250\pi\)
−0.990623 + 0.136623i \(0.956375\pi\)
\(492\) 0 0
\(493\) 840.000i 1.70385i
\(494\) 0 0
\(495\) −218.885 337.771i −0.442193 0.682365i
\(496\) 0 0
\(497\) 429.325 0.863833
\(498\) 0 0
\(499\) −486.000 −0.973948 −0.486974 0.873416i \(-0.661899\pi\)
−0.486974 + 0.873416i \(0.661899\pi\)
\(500\) 0 0
\(501\) −150.000 134.164i −0.299401 0.267793i
\(502\) 0 0
\(503\) −791.568 −1.57369 −0.786847 0.617148i \(-0.788288\pi\)
−0.786847 + 0.617148i \(0.788288\pi\)
\(504\) 0 0
\(505\) −680.000 + 340.000i −1.34653 + 0.673267i
\(506\) 0 0
\(507\) −55.9017 50.0000i −0.110260 0.0986193i
\(508\) 0 0
\(509\) 26.8328i 0.0527167i −0.999653 0.0263584i \(-0.991609\pi\)
0.999653 0.0263584i \(-0.00839110\pi\)
\(510\) 0 0
\(511\) 448.000 0.876712
\(512\) 0 0
\(513\) −93.9149 + 132.000i −0.183070 + 0.257310i
\(514\) 0 0
\(515\) −465.102 + 232.551i −0.903111 + 0.451555i
\(516\) 0 0
\(517\) 40.0000i 0.0773694i
\(518\) 0 0
\(519\) 170.000 + 152.053i 0.327553 + 0.292972i
\(520\) 0 0
\(521\) 983.870i 1.88843i −0.329336 0.944213i \(-0.606825\pi\)
0.329336 0.944213i \(-0.393175\pi\)
\(522\) 0 0
\(523\) 292.000i 0.558317i 0.960245 + 0.279159i \(0.0900556\pi\)
−0.960245 + 0.279159i \(0.909944\pi\)
\(524\) 0 0
\(525\) −117.771 588.328i −0.224325 1.12063i
\(526\) 0 0
\(527\) 1064.37 2.01967
\(528\) 0 0
\(529\) −509.000 −0.962193
\(530\) 0 0
\(531\) −880.000 + 98.3870i −1.65725 + 0.185286i
\(532\) 0 0
\(533\) −214.663 −0.402744
\(534\) 0 0
\(535\) 330.000 + 660.000i 0.616822 + 1.23364i
\(536\) 0 0
\(537\) 518.768 580.000i 0.966048 1.08007i
\(538\) 0 0
\(539\) 134.164i 0.248913i
\(540\) 0 0
\(541\) −86.0000 −0.158965 −0.0794824 0.996836i \(-0.525327\pi\)
−0.0794824 + 0.996836i \(0.525327\pi\)
\(542\) 0 0
\(543\) 371.187 + 332.000i 0.683586 + 0.611418i
\(544\) 0 0
\(545\) −165.469 330.938i −0.303613 0.607226i
\(546\) 0 0
\(547\) 164.000i 0.299817i −0.988700 0.149909i \(-0.952102\pi\)
0.988700 0.149909i \(-0.0478979\pi\)
\(548\) 0 0
\(549\) 74.0000 + 661.876i 0.134791 + 1.20560i
\(550\) 0 0
\(551\) 160.997i 0.292190i
\(552\) 0 0
\(553\) 624.000i 1.12839i
\(554\) 0 0
\(555\) 636.774 + 173.548i 1.14734 + 0.312699i
\(556\) 0 0
\(557\) −362.243 −0.650347 −0.325173 0.945654i \(-0.605423\pi\)
−0.325173 + 0.945654i \(0.605423\pi\)
\(558\) 0 0
\(559\) 336.000 0.601073
\(560\) 0 0
\(561\) −560.000 + 626.099i −0.998217 + 1.11604i
\(562\) 0 0
\(563\) 997.286 1.77138 0.885689 0.464278i \(-0.153686\pi\)
0.885689 + 0.464278i \(0.153686\pi\)
\(564\) 0 0
\(565\) 90.0000 + 180.000i 0.159292 + 0.318584i
\(566\) 0 0
\(567\) 143.108 + 632.000i 0.252396 + 1.11464i
\(568\) 0 0
\(569\) 626.099i 1.10035i 0.835049 + 0.550175i \(0.185439\pi\)
−0.835049 + 0.550175i \(0.814561\pi\)
\(570\) 0 0
\(571\) 394.000 0.690018 0.345009 0.938599i \(-0.387876\pi\)
0.345009 + 0.938599i \(0.387876\pi\)
\(572\) 0 0
\(573\) −429.325 + 480.000i −0.749258 + 0.837696i
\(574\) 0 0
\(575\) 67.0820 89.4427i 0.116664 0.155553i
\(576\) 0 0
\(577\) 608.000i 1.05373i −0.849950 0.526863i \(-0.823368\pi\)
0.849950 0.526863i \(-0.176632\pi\)
\(578\) 0 0
\(579\) 64.0000 71.5542i 0.110535 0.123582i
\(580\) 0 0
\(581\) 822.873i 1.41630i
\(582\) 0 0
\(583\) 360.000i 0.617496i
\(584\) 0 0
\(585\) 293.666 + 453.167i 0.501993 + 0.774645i
\(586\) 0 0
\(587\) 711.070 1.21136 0.605681 0.795707i \(-0.292901\pi\)
0.605681 + 0.795707i \(0.292901\pi\)
\(588\) 0 0
\(589\) −204.000 −0.346350
\(590\) 0 0
\(591\) 10.0000 + 8.94427i 0.0169205 + 0.0151341i
\(592\) 0 0
\(593\) 603.738 1.01811 0.509054 0.860734i \(-0.329995\pi\)
0.509054 + 0.860734i \(0.329995\pi\)
\(594\) 0 0
\(595\) −1120.00 + 560.000i −1.88235 + 0.941176i
\(596\) 0 0
\(597\) −254.912 228.000i −0.426988 0.381910i
\(598\) 0 0
\(599\) 53.6656i 0.0895920i −0.998996 0.0447960i \(-0.985736\pi\)
0.998996 0.0447960i \(-0.0142638\pi\)
\(600\) 0 0
\(601\) 434.000 0.722130 0.361065 0.932541i \(-0.382413\pi\)
0.361065 + 0.932541i \(0.382413\pi\)
\(602\) 0 0
\(603\) −822.873 + 92.0000i −1.36463 + 0.152570i
\(604\) 0 0
\(605\) −91.6788 183.358i −0.151535 0.303070i
\(606\) 0 0
\(607\) 656.000i 1.08072i 0.841432 + 0.540362i \(0.181713\pi\)
−0.841432 + 0.540362i \(0.818287\pi\)
\(608\) 0 0
\(609\) 480.000 + 429.325i 0.788177 + 0.704967i
\(610\) 0 0
\(611\) 53.6656i 0.0878325i
\(612\) 0 0
\(613\) 844.000i 1.37684i −0.725315 0.688418i \(-0.758306\pi\)
0.725315 0.688418i \(-0.241694\pi\)
\(614\) 0 0
\(615\) −258.885 70.5573i −0.420952 0.114727i
\(616\) 0 0
\(617\) 460.630 0.746564 0.373282 0.927718i \(-0.378232\pi\)
0.373282 + 0.927718i \(0.378232\pi\)
\(618\) 0 0
\(619\) −1046.00 −1.68982 −0.844911 0.534907i \(-0.820347\pi\)
−0.844911 + 0.534907i \(0.820347\pi\)
\(620\) 0 0
\(621\) −70.0000 + 98.3870i −0.112721 + 0.158433i
\(622\) 0 0
\(623\) −143.108 −0.229708
\(624\) 0 0
\(625\) −175.000 600.000i −0.280000 0.960000i
\(626\) 0 0
\(627\) 107.331 120.000i 0.171182 0.191388i
\(628\) 0 0
\(629\) 1377.42i 2.18985i
\(630\) 0 0
\(631\) −46.0000 −0.0729002 −0.0364501 0.999335i \(-0.511605\pi\)
−0.0364501 + 0.999335i \(0.511605\pi\)
\(632\) 0 0
\(633\) 13.4164 + 12.0000i 0.0211950 + 0.0189573i
\(634\) 0 0
\(635\) 71.5542 35.7771i 0.112684 0.0563419i
\(636\) 0 0
\(637\) 180.000i 0.282575i
\(638\) 0 0
\(639\) −480.000 + 53.6656i −0.751174 + 0.0839838i
\(640\) 0 0
\(641\) 1144.87i 1.78606i 0.449994 + 0.893032i \(0.351426\pi\)
−0.449994 + 0.893032i \(0.648574\pi\)
\(642\) 0 0
\(643\) 804.000i 1.25039i −0.780469 0.625194i \(-0.785020\pi\)
0.780469 0.625194i \(-0.214980\pi\)
\(644\) 0 0
\(645\) 405.220 + 110.440i 0.628248 + 0.171224i
\(646\) 0 0
\(647\) −576.906 −0.891662 −0.445831 0.895117i \(-0.647092\pi\)
−0.445831 + 0.895117i \(0.647092\pi\)
\(648\) 0 0
\(649\) 880.000 1.35593
\(650\) 0 0
\(651\) −544.000 + 608.210i −0.835637 + 0.934271i
\(652\) 0 0
\(653\) −1077.78 −1.65051 −0.825256 0.564758i \(-0.808969\pi\)
−0.825256 + 0.564758i \(0.808969\pi\)
\(654\) 0 0
\(655\) 360.000 180.000i 0.549618 0.274809i
\(656\) 0 0
\(657\) −500.879 + 56.0000i −0.762373 + 0.0852359i
\(658\) 0 0
\(659\) 813.929i 1.23510i −0.786533 0.617548i \(-0.788126\pi\)
0.786533 0.617548i \(-0.211874\pi\)
\(660\) 0 0
\(661\) 1082.00 1.63691 0.818457 0.574568i \(-0.194830\pi\)
0.818457 + 0.574568i \(0.194830\pi\)
\(662\) 0 0
\(663\) 751.319 840.000i 1.13321 1.26697i
\(664\) 0 0
\(665\) 214.663 107.331i 0.322801 0.161400i
\(666\) 0 0
\(667\) 120.000i 0.179910i
\(668\) 0 0
\(669\) 544.000 608.210i 0.813154 0.909134i
\(670\) 0 0
\(671\) 661.876i 0.986403i
\(672\) 0 0
\(673\) 1056.00i 1.56909i 0.620070 + 0.784547i \(0.287104\pi\)
−0.620070 + 0.784547i \(0.712896\pi\)
\(674\) 0 0
\(675\) 205.213 + 643.050i 0.304019 + 0.952666i
\(676\) 0 0
\(677\) −612.683 −0.904996 −0.452498 0.891765i \(-0.649467\pi\)
−0.452498 + 0.891765i \(0.649467\pi\)
\(678\) 0 0
\(679\) 256.000 0.377025
\(680\) 0 0
\(681\) −550.000 491.935i −0.807636 0.722371i
\(682\) 0 0
\(683\) 317.522 0.464893 0.232446 0.972609i \(-0.425327\pi\)
0.232446 + 0.972609i \(0.425327\pi\)
\(684\) 0 0
\(685\) −390.000 780.000i −0.569343 1.13869i
\(686\) 0 0
\(687\) −344.354 308.000i −0.501244 0.448326i
\(688\) 0 0
\(689\) 482.991i 0.701002i
\(690\) 0 0
\(691\) 922.000 1.33430 0.667149 0.744924i \(-0.267514\pi\)
0.667149 + 0.744924i \(0.267514\pi\)
\(692\) 0 0
\(693\) −71.5542 640.000i −0.103253 0.923521i
\(694\) 0 0
\(695\) 263.856 + 527.712i 0.379649 + 0.759298i
\(696\) 0 0
\(697\) 560.000i 0.803443i
\(698\) 0 0
\(699\) 410.000 + 366.715i 0.586552 + 0.524628i
\(700\) 0 0
\(701\) 474.046i 0.676243i 0.941102 + 0.338122i \(0.109791\pi\)
−0.941102 + 0.338122i \(0.890209\pi\)
\(702\) 0 0
\(703\) 264.000i 0.375533i
\(704\) 0 0
\(705\) 17.6393 64.7214i 0.0250203 0.0918033i
\(706\) 0 0
\(707\) −1216.42 −1.72054
\(708\) 0 0
\(709\) −966.000 −1.36248 −0.681241 0.732059i \(-0.738559\pi\)
−0.681241 + 0.732059i \(0.738559\pi\)
\(710\) 0 0
\(711\) −78.0000 697.653i −0.109705 0.981228i
\(712\) 0 0
\(713\) −152.053 −0.213258
\(714\) 0 0
\(715\) −240.000 480.000i −0.335664 0.671329i
\(716\) 0 0
\(717\) −357.771 + 400.000i −0.498983 + 0.557880i
\(718\) 0 0
\(719\) 1109.09i 1.54254i 0.636505 + 0.771272i \(0.280379\pi\)
−0.636505 + 0.771272i \(0.719621\pi\)
\(720\) 0 0
\(721\) −832.000 −1.15395
\(722\) 0 0
\(723\) 460.630 + 412.000i 0.637109 + 0.569848i
\(724\) 0 0
\(725\) 536.656 + 402.492i 0.740216 + 0.555162i
\(726\) 0 0
\(727\) 408.000i 0.561210i −0.959823 0.280605i \(-0.909465\pi\)
0.959823 0.280605i \(-0.0905352\pi\)
\(728\) 0 0
\(729\) −239.000 688.709i −0.327846 0.944731i
\(730\) 0 0
\(731\) 876.539i 1.19910i
\(732\) 0 0
\(733\) 164.000i 0.223738i −0.993723 0.111869i \(-0.964316\pi\)
0.993723 0.111869i \(-0.0356837\pi\)
\(734\) 0 0
\(735\) 59.1641 217.082i 0.0804953 0.295350i
\(736\) 0 0
\(737\) 822.873 1.11652
\(738\) 0 0
\(739\) 1082.00 1.46414 0.732070 0.681229i \(-0.238554\pi\)
0.732070 + 0.681229i \(0.238554\pi\)
\(740\) 0 0
\(741\) −144.000 + 160.997i −0.194332 + 0.217270i
\(742\) 0 0
\(743\) 1140.39 1.53485 0.767426 0.641138i \(-0.221537\pi\)
0.767426 + 0.641138i \(0.221537\pi\)
\(744\) 0 0
\(745\) 440.000 220.000i 0.590604 0.295302i
\(746\) 0 0
\(747\) 102.859 + 920.000i 0.137696 + 1.23159i
\(748\) 0 0
\(749\) 1180.64i 1.57629i
\(750\) 0 0
\(751\) −958.000 −1.27563 −0.637816 0.770189i \(-0.720162\pi\)
−0.637816 + 0.770189i \(0.720162\pi\)
\(752\) 0 0
\(753\) 53.6656 60.0000i 0.0712691 0.0796813i
\(754\) 0 0
\(755\) −76.0263 152.053i −0.100697 0.201394i
\(756\) 0 0
\(757\) 772.000i 1.01982i 0.860229 + 0.509908i \(0.170320\pi\)
−0.860229 + 0.509908i \(0.829680\pi\)
\(758\) 0 0
\(759\) 80.0000 89.4427i 0.105402 0.117843i
\(760\) 0 0
\(761\) 1126.98i 1.48092i 0.672102 + 0.740459i \(0.265392\pi\)
−0.672102 + 0.740459i \(0.734608\pi\)
\(762\) 0 0
\(763\) 592.000i 0.775885i
\(764\) 0 0
\(765\) 1182.20 766.099i 1.54536 1.00144i
\(766\) 0 0
\(767\) −1180.64 −1.53930
\(768\) 0 0
\(769\) −1326.00 −1.72432 −0.862159 0.506638i \(-0.830888\pi\)
−0.862159 + 0.506638i \(0.830888\pi\)
\(770\) 0 0
\(771\) 90.0000 + 80.4984i 0.116732 + 0.104408i
\(772\) 0 0
\(773\) −147.580 −0.190919 −0.0954596 0.995433i \(-0.530432\pi\)
−0.0954596 + 0.995433i \(0.530432\pi\)
\(774\) 0 0
\(775\) −510.000 + 680.000i −0.658065 + 0.877419i
\(776\) 0 0
\(777\) 787.096 + 704.000i 1.01299 + 0.906049i
\(778\) 0 0
\(779\) 107.331i 0.137781i
\(780\) 0 0
\(781\) 480.000 0.614597
\(782\) 0 0
\(783\) −590.322 420.000i −0.753923 0.536398i
\(784\) 0 0
\(785\) 411.437 205.718i 0.524123 0.262061i
\(786\) 0 0
\(787\) 1132.00i 1.43837i 0.694817 + 0.719187i \(0.255485\pi\)
−0.694817 + 0.719187i \(0.744515\pi\)
\(788\) 0 0
\(789\) −470.000 420.381i −0.595691 0.532802i
\(790\) 0 0
\(791\) 321.994i 0.407072i
\(792\) 0 0
\(793\) 888.000i 1.11980i
\(794\) 0 0
\(795\) 158.754 582.492i 0.199690 0.732695i
\(796\) 0 0
\(797\) −612.683 −0.768736 −0.384368 0.923180i \(-0.625581\pi\)
−0.384368 + 0.923180i \(0.625581\pi\)
\(798\) 0 0