Properties

Label 768.2.o.b.95.11
Level 768
Weight 2
Character 768.95
Analytic conductor 6.133
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.o (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 95.11
Character \(\chi\) \(=\) 768.95
Dual form 768.2.o.b.671.11

$q$-expansion

\(f(q)\) \(=\) \(q+(1.29202 + 1.15356i) q^{3} +(-0.180206 + 0.0746437i) q^{5} +(-0.289055 - 0.289055i) q^{7} +(0.338620 + 2.98083i) q^{9} +O(q^{10})\) \(q+(1.29202 + 1.15356i) q^{3} +(-0.180206 + 0.0746437i) q^{5} +(-0.289055 - 0.289055i) q^{7} +(0.338620 + 2.98083i) q^{9} +(3.10859 - 1.28762i) q^{11} +(1.27981 - 3.08973i) q^{13} +(-0.318935 - 0.111436i) q^{15} +0.806332 q^{17} +(5.57935 + 2.31104i) q^{19} +(-0.0400233 - 0.706906i) q^{21} +(5.03681 + 5.03681i) q^{23} +(-3.50863 + 3.50863i) q^{25} +(-3.00105 + 4.24190i) q^{27} +(-3.64020 + 8.78822i) q^{29} -7.48336i q^{31} +(5.50170 + 1.92230i) q^{33} +(0.0736656 + 0.0305133i) q^{35} +(1.47112 + 3.55159i) q^{37} +(5.21770 - 2.51565i) q^{39} +(-2.62513 + 2.62513i) q^{41} +(-2.84744 - 6.87432i) q^{43} +(-0.283521 - 0.511886i) q^{45} -0.399772i q^{47} -6.83289i q^{49} +(1.04180 + 0.930149i) q^{51} +(1.42173 + 3.43237i) q^{53} +(-0.464073 + 0.464073i) q^{55} +(4.54271 + 9.42200i) q^{57} +(0.918629 + 2.21777i) q^{59} +(-8.81133 - 3.64977i) q^{61} +(0.763745 - 0.959504i) q^{63} +0.652316i q^{65} +(3.76613 - 9.09225i) q^{67} +(0.697409 + 12.3179i) q^{69} +(-2.86762 + 2.86762i) q^{71} +(-6.97993 - 6.97993i) q^{73} +(-8.58062 + 0.485813i) q^{75} +(-1.27075 - 0.526361i) q^{77} +8.01674 q^{79} +(-8.77067 + 2.01873i) q^{81} +(2.47115 - 5.96589i) q^{83} +(-0.145306 + 0.0601876i) q^{85} +(-14.8409 + 7.15536i) q^{87} +(-5.43308 - 5.43308i) q^{89} +(-1.26304 + 0.523167i) q^{91} +(8.63248 - 9.66864i) q^{93} -1.17794 q^{95} +2.61408 q^{97} +(4.89081 + 8.83016i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{8}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.29202 + 1.15356i 0.745947 + 0.666006i
\(4\) 0 0
\(5\) −0.180206 + 0.0746437i −0.0805904 + 0.0333817i −0.422614 0.906310i \(-0.638888\pi\)
0.342024 + 0.939691i \(0.388888\pi\)
\(6\) 0 0
\(7\) −0.289055 0.289055i −0.109253 0.109253i 0.650367 0.759620i \(-0.274615\pi\)
−0.759620 + 0.650367i \(0.774615\pi\)
\(8\) 0 0
\(9\) 0.338620 + 2.98083i 0.112873 + 0.993609i
\(10\) 0 0
\(11\) 3.10859 1.28762i 0.937276 0.388232i 0.138842 0.990315i \(-0.455662\pi\)
0.798434 + 0.602082i \(0.205662\pi\)
\(12\) 0 0
\(13\) 1.27981 3.08973i 0.354954 0.856936i −0.641039 0.767508i \(-0.721496\pi\)
0.995993 0.0894273i \(-0.0285037\pi\)
\(14\) 0 0
\(15\) −0.318935 0.111436i −0.0823486 0.0287727i
\(16\) 0 0
\(17\) 0.806332 0.195564 0.0977822 0.995208i \(-0.468825\pi\)
0.0977822 + 0.995208i \(0.468825\pi\)
\(18\) 0 0
\(19\) 5.57935 + 2.31104i 1.27999 + 0.530190i 0.915987 0.401208i \(-0.131409\pi\)
0.364004 + 0.931397i \(0.381409\pi\)
\(20\) 0 0
\(21\) −0.0400233 0.706906i −0.00873379 0.154260i
\(22\) 0 0
\(23\) 5.03681 + 5.03681i 1.05025 + 1.05025i 0.998669 + 0.0515792i \(0.0164254\pi\)
0.0515792 + 0.998669i \(0.483575\pi\)
\(24\) 0 0
\(25\) −3.50863 + 3.50863i −0.701726 + 0.701726i
\(26\) 0 0
\(27\) −3.00105 + 4.24190i −0.577552 + 0.816354i
\(28\) 0 0
\(29\) −3.64020 + 8.78822i −0.675968 + 1.63193i 0.0953212 + 0.995447i \(0.469612\pi\)
−0.771289 + 0.636485i \(0.780388\pi\)
\(30\) 0 0
\(31\) 7.48336i 1.34405i −0.740528 0.672026i \(-0.765424\pi\)
0.740528 0.672026i \(-0.234576\pi\)
\(32\) 0 0
\(33\) 5.50170 + 1.92230i 0.957723 + 0.334630i
\(34\) 0 0
\(35\) 0.0736656 + 0.0305133i 0.0124518 + 0.00515769i
\(36\) 0 0
\(37\) 1.47112 + 3.55159i 0.241850 + 0.583878i 0.997467 0.0711364i \(-0.0226626\pi\)
−0.755616 + 0.655014i \(0.772663\pi\)
\(38\) 0 0
\(39\) 5.21770 2.51565i 0.835501 0.402827i
\(40\) 0 0
\(41\) −2.62513 + 2.62513i −0.409976 + 0.409976i −0.881730 0.471754i \(-0.843621\pi\)
0.471754 + 0.881730i \(0.343621\pi\)
\(42\) 0 0
\(43\) −2.84744 6.87432i −0.434230 1.04832i −0.977909 0.209031i \(-0.932969\pi\)
0.543679 0.839293i \(-0.317031\pi\)
\(44\) 0 0
\(45\) −0.283521 0.511886i −0.0422648 0.0763075i
\(46\) 0 0
\(47\) 0.399772i 0.0583127i −0.999575 0.0291564i \(-0.990718\pi\)
0.999575 0.0291564i \(-0.00928208\pi\)
\(48\) 0 0
\(49\) 6.83289i 0.976128i
\(50\) 0 0
\(51\) 1.04180 + 0.930149i 0.145881 + 0.130247i
\(52\) 0 0
\(53\) 1.42173 + 3.43237i 0.195290 + 0.471472i 0.990943 0.134280i \(-0.0428723\pi\)
−0.795653 + 0.605752i \(0.792872\pi\)
\(54\) 0 0
\(55\) −0.464073 + 0.464073i −0.0625756 + 0.0625756i
\(56\) 0 0
\(57\) 4.54271 + 9.42200i 0.601696 + 1.24797i
\(58\) 0 0
\(59\) 0.918629 + 2.21777i 0.119595 + 0.288729i 0.972328 0.233618i \(-0.0750566\pi\)
−0.852733 + 0.522347i \(0.825057\pi\)
\(60\) 0 0
\(61\) −8.81133 3.64977i −1.12818 0.467306i −0.261015 0.965335i \(-0.584057\pi\)
−0.867160 + 0.498029i \(0.834057\pi\)
\(62\) 0 0
\(63\) 0.763745 0.959504i 0.0962228 0.120886i
\(64\) 0 0
\(65\) 0.652316i 0.0809098i
\(66\) 0 0
\(67\) 3.76613 9.09225i 0.460107 1.11080i −0.508247 0.861212i \(-0.669706\pi\)
0.968353 0.249584i \(-0.0802938\pi\)
\(68\) 0 0
\(69\) 0.697409 + 12.3179i 0.0839581 + 1.48290i
\(70\) 0 0
\(71\) −2.86762 + 2.86762i −0.340324 + 0.340324i −0.856489 0.516165i \(-0.827359\pi\)
0.516165 + 0.856489i \(0.327359\pi\)
\(72\) 0 0
\(73\) −6.97993 6.97993i −0.816939 0.816939i 0.168725 0.985663i \(-0.446035\pi\)
−0.985663 + 0.168725i \(0.946035\pi\)
\(74\) 0 0
\(75\) −8.58062 + 0.485813i −0.990804 + 0.0560969i
\(76\) 0 0
\(77\) −1.27075 0.526361i −0.144815 0.0599845i
\(78\) 0 0
\(79\) 8.01674 0.901954 0.450977 0.892536i \(-0.351076\pi\)
0.450977 + 0.892536i \(0.351076\pi\)
\(80\) 0 0
\(81\) −8.77067 + 2.01873i −0.974519 + 0.224304i
\(82\) 0 0
\(83\) 2.47115 5.96589i 0.271244 0.654841i −0.728293 0.685266i \(-0.759686\pi\)
0.999537 + 0.0304247i \(0.00968596\pi\)
\(84\) 0 0
\(85\) −0.145306 + 0.0601876i −0.0157606 + 0.00652826i
\(86\) 0 0
\(87\) −14.8409 + 7.15536i −1.59111 + 0.767135i
\(88\) 0 0
\(89\) −5.43308 5.43308i −0.575905 0.575905i 0.357867 0.933773i \(-0.383504\pi\)
−0.933773 + 0.357867i \(0.883504\pi\)
\(90\) 0 0
\(91\) −1.26304 + 0.523167i −0.132402 + 0.0548428i
\(92\) 0 0
\(93\) 8.63248 9.66864i 0.895146 1.00259i
\(94\) 0 0
\(95\) −1.17794 −0.120854
\(96\) 0 0
\(97\) 2.61408 0.265419 0.132710 0.991155i \(-0.457632\pi\)
0.132710 + 0.991155i \(0.457632\pi\)
\(98\) 0 0
\(99\) 4.89081 + 8.83016i 0.491545 + 0.887465i
\(100\) 0 0
\(101\) 12.1420 5.02940i 1.20818 0.500444i 0.314546 0.949242i \(-0.398148\pi\)
0.893633 + 0.448798i \(0.148148\pi\)
\(102\) 0 0
\(103\) 8.46981 + 8.46981i 0.834555 + 0.834555i 0.988136 0.153581i \(-0.0490806\pi\)
−0.153581 + 0.988136i \(0.549081\pi\)
\(104\) 0 0
\(105\) 0.0599785 + 0.124401i 0.00585330 + 0.0121403i
\(106\) 0 0
\(107\) 1.03423 0.428394i 0.0999833 0.0414144i −0.332131 0.943233i \(-0.607768\pi\)
0.432114 + 0.901819i \(0.357768\pi\)
\(108\) 0 0
\(109\) 0.703211 1.69770i 0.0673554 0.162610i −0.886617 0.462504i \(-0.846951\pi\)
0.953973 + 0.299894i \(0.0969512\pi\)
\(110\) 0 0
\(111\) −2.19625 + 6.28573i −0.208459 + 0.596616i
\(112\) 0 0
\(113\) 1.39540 0.131268 0.0656339 0.997844i \(-0.479093\pi\)
0.0656339 + 0.997844i \(0.479093\pi\)
\(114\) 0 0
\(115\) −1.28363 0.531696i −0.119699 0.0495809i
\(116\) 0 0
\(117\) 9.64331 + 2.76864i 0.891524 + 0.255961i
\(118\) 0 0
\(119\) −0.233075 0.233075i −0.0213659 0.0213659i
\(120\) 0 0
\(121\) 0.227201 0.227201i 0.0206547 0.0206547i
\(122\) 0 0
\(123\) −6.41995 + 0.363481i −0.578867 + 0.0327740i
\(124\) 0 0
\(125\) 0.743597 1.79520i 0.0665093 0.160568i
\(126\) 0 0
\(127\) 6.87310i 0.609889i −0.952370 0.304944i \(-0.901362\pi\)
0.952370 0.304944i \(-0.0986379\pi\)
\(128\) 0 0
\(129\) 4.25097 12.1664i 0.374277 1.07119i
\(130\) 0 0
\(131\) −16.0581 6.65149i −1.40300 0.581143i −0.452474 0.891778i \(-0.649458\pi\)
−0.950529 + 0.310635i \(0.899458\pi\)
\(132\) 0 0
\(133\) −0.944722 2.28076i −0.0819178 0.197767i
\(134\) 0 0
\(135\) 0.224175 0.988424i 0.0192939 0.0850700i
\(136\) 0 0
\(137\) 10.7787 10.7787i 0.920890 0.920890i −0.0762022 0.997092i \(-0.524279\pi\)
0.997092 + 0.0762022i \(0.0242795\pi\)
\(138\) 0 0
\(139\) 1.41183 + 3.40847i 0.119750 + 0.289102i 0.972376 0.233419i \(-0.0749914\pi\)
−0.852626 + 0.522521i \(0.824991\pi\)
\(140\) 0 0
\(141\) 0.461159 0.516513i 0.0388366 0.0434982i
\(142\) 0 0
\(143\) 11.2526i 0.940990i
\(144\) 0 0
\(145\) 1.85541i 0.154083i
\(146\) 0 0
\(147\) 7.88212 8.82822i 0.650106 0.728139i
\(148\) 0 0
\(149\) −6.49923 15.6905i −0.532438 1.28542i −0.929904 0.367802i \(-0.880111\pi\)
0.397466 0.917617i \(1.63011\pi\)
\(150\) 0 0
\(151\) −1.50166 + 1.50166i −0.122204 + 0.122204i −0.765564 0.643360i \(-0.777540\pi\)
0.643360 + 0.765564i \(0.277540\pi\)
\(152\) 0 0
\(153\) 0.273040 + 2.40354i 0.0220740 + 0.194315i
\(154\) 0 0
\(155\) 0.558586 + 1.34855i 0.0448667 + 0.108318i
\(156\) 0 0
\(157\) −12.7594 5.28511i −1.01831 0.421798i −0.189830 0.981817i \(-0.560794\pi\)
−0.828480 + 0.560019i \(0.810794\pi\)
\(158\) 0 0
\(159\) −2.12252 + 6.07473i −0.168327 + 0.481757i
\(160\) 0 0
\(161\) 2.91184i 0.229485i
\(162\) 0 0
\(163\) −3.02496 + 7.30291i −0.236933 + 0.572008i −0.996963 0.0778809i \(-0.975185\pi\)
0.760029 + 0.649889i \(0.225185\pi\)
\(164\) 0 0
\(165\) −1.13493 + 0.0642567i −0.0883538 + 0.00500237i
\(166\) 0 0
\(167\) −1.65109 + 1.65109i −0.127765 + 0.127765i −0.768098 0.640333i \(-0.778797\pi\)
0.640333 + 0.768098i \(0.278797\pi\)
\(168\) 0 0
\(169\) 1.28389 + 1.28389i 0.0987607 + 0.0987607i
\(170\) 0 0
\(171\) −4.99955 + 17.4137i −0.382325 + 1.33166i
\(172\) 0 0
\(173\) −9.81571 4.06580i −0.746275 0.309117i −0.0230541 0.999734i \(-0.507339\pi\)
−0.723221 + 0.690617i \(0.757339\pi\)
\(174\) 0 0
\(175\) 2.02838 0.153331
\(176\) 0 0
\(177\) −1.37143 + 3.92508i −0.103083 + 0.295027i
\(178\) 0 0
\(179\) −6.28126 + 15.1643i −0.469484 + 1.13343i 0.494906 + 0.868947i \(0.335203\pi\)
−0.964389 + 0.264487i \(0.914797\pi\)
\(180\) 0 0
\(181\) −4.93385 + 2.04367i −0.366730 + 0.151905i −0.558436 0.829548i \(-0.688598\pi\)
0.191705 + 0.981453i \(0.438598\pi\)
\(182\) 0 0
\(183\) −7.17418 14.8799i −0.530331 1.09996i
\(184\) 0 0
\(185\) −0.530208 0.530208i −0.0389816 0.0389816i
\(186\) 0 0
\(187\) 2.50656 1.03825i 0.183298 0.0759244i
\(188\) 0 0
\(189\) 2.09361 0.358675i 0.152288 0.0260898i
\(190\) 0 0
\(191\) −11.6455 −0.842637 −0.421318 0.906913i \(-0.638433\pi\)
−0.421318 + 0.906913i \(0.638433\pi\)
\(192\) 0 0
\(193\) −6.03220 −0.434207 −0.217104 0.976149i \(-0.569661\pi\)
−0.217104 + 0.976149i \(0.569661\pi\)
\(194\) 0 0
\(195\) −0.752482 + 0.842803i −0.0538864 + 0.0603544i
\(196\) 0 0
\(197\) −0.581435 + 0.240838i −0.0414255 + 0.0171590i −0.403300 0.915068i \(-0.632137\pi\)
0.361874 + 0.932227i \(0.382137\pi\)
\(198\) 0 0
\(199\) −13.6071 13.6071i −0.964583 0.964583i 0.0348110 0.999394i \(-0.488917\pi\)
−0.999394 + 0.0348110i \(0.988917\pi\)
\(200\) 0 0
\(201\) 15.3543 7.40291i 1.08301 0.522161i
\(202\) 0 0
\(203\) 3.59250 1.48806i 0.252144 0.104442i
\(204\) 0 0
\(205\) 0.277114 0.669012i 0.0193545 0.0467259i
\(206\) 0 0
\(207\) −13.3083 + 16.7194i −0.924991 + 1.16208i
\(208\) 0 0
\(209\) 20.3197 1.40554
\(210\) 0 0
\(211\) 6.94196 + 2.87545i 0.477904 + 0.197954i 0.608614 0.793466i \(-0.291726\pi\)
−0.130710 + 0.991421i \(0.541726\pi\)
\(212\) 0 0
\(213\) −7.01298 + 0.397057i −0.480521 + 0.0272059i
\(214\) 0 0
\(215\) 1.02625 + 1.02625i 0.0699896 + 0.0699896i
\(216\) 0 0
\(217\) −2.16311 + 2.16311i −0.146841 + 0.146841i
\(218\) 0 0
\(219\) −0.966457 17.0699i −0.0653071 1.15348i
\(220\) 0 0
\(221\) 1.03195 2.49135i 0.0694164 0.167586i
\(222\) 0 0
\(223\) 6.45182i 0.432046i 0.976388 + 0.216023i \(0.0693086\pi\)
−0.976388 + 0.216023i \(0.930691\pi\)
\(224\) 0 0
\(225\) −11.6467 9.27054i −0.776448 0.618036i
\(226\) 0 0
\(227\) −3.16606 1.31143i −0.210139 0.0870424i 0.275131 0.961407i \(-0.411279\pi\)
−0.485270 + 0.874364i \(0.661279\pi\)
\(228\) 0 0
\(229\) −8.63723 20.8521i −0.570764 1.37795i −0.900905 0.434015i \(-0.857096\pi\)
0.330141 0.943932i \(-0.392904\pi\)
\(230\) 0 0
\(231\) −1.03464 2.14595i −0.0680745 0.141193i
\(232\) 0 0
\(233\) −15.5223 + 15.5223i −1.01690 + 1.01690i −0.0170465 + 0.999855i \(0.505426\pi\)
−0.999855 + 0.0170465i \(0.994574\pi\)
\(234\) 0 0
\(235\) 0.0298404 + 0.0720412i 0.00194658 + 0.00469945i
\(236\) 0 0
\(237\) 10.3578 + 9.24776i 0.672810 + 0.600706i
\(238\) 0 0
\(239\) 22.3335i 1.44463i −0.691563 0.722316i \(-0.743078\pi\)
0.691563 0.722316i \(-0.256922\pi\)
\(240\) 0 0
\(241\) 10.0345i 0.646380i 0.946334 + 0.323190i \(0.104755\pi\)
−0.946334 + 0.323190i \(0.895245\pi\)
\(242\) 0 0
\(243\) −13.6606 7.50922i −0.876327 0.481717i
\(244\) 0 0
\(245\) 0.510032 + 1.23133i 0.0325848 + 0.0786666i
\(246\) 0 0
\(247\) 14.2810 14.2810i 0.908677 0.908677i
\(248\) 0 0
\(249\) 10.0748 4.85742i 0.638462 0.307827i
\(250\) 0 0
\(251\) −1.23078 2.97137i −0.0776862 0.187551i 0.880265 0.474483i \(-0.157365\pi\)
−0.957951 + 0.286931i \(0.907365\pi\)
\(252\) 0 0
\(253\) 22.1429 + 9.17189i 1.39211 + 0.576632i
\(254\) 0 0
\(255\) −0.257167 0.0898547i −0.0161044 0.00562692i
\(256\) 0 0
\(257\) 22.7842i 1.42124i 0.703576 + 0.710620i \(0.251585\pi\)
−0.703576 + 0.710620i \(0.748415\pi\)
\(258\) 0 0
\(259\) 0.601372 1.45184i 0.0373675 0.0902130i
\(260\) 0 0
\(261\) −27.4288 7.87495i −1.69780 0.487447i
\(262\) 0 0
\(263\) −12.8553 + 12.8553i −0.792690 + 0.792690i −0.981931 0.189241i \(-0.939397\pi\)
0.189241 + 0.981931i \(0.439397\pi\)
\(264\) 0 0
\(265\) −0.512409 0.512409i −0.0314770 0.0314770i
\(266\) 0 0
\(267\) −0.752277 13.2870i −0.0460386 0.813151i
\(268\) 0 0
\(269\) 11.7742 + 4.87704i 0.717886 + 0.297358i 0.711564 0.702622i \(-0.247987\pi\)
0.00632279 + 0.999980i \(0.497987\pi\)
\(270\) 0 0
\(271\) −11.6627 −0.708457 −0.354228 0.935159i \(-0.615256\pi\)
−0.354228 + 0.935159i \(0.615256\pi\)
\(272\) 0 0
\(273\) −2.23537 0.781042i −0.135291 0.0472708i
\(274\) 0 0
\(275\) −6.38912 + 15.4247i −0.385278 + 0.930144i
\(276\) 0 0
\(277\) −8.48904 + 3.51628i −0.510057 + 0.211273i −0.622843 0.782347i \(-0.714023\pi\)
0.112786 + 0.993619i \(0.464023\pi\)
\(278\) 0 0
\(279\) 22.3066 2.53401i 1.33546 0.151707i
\(280\) 0 0
\(281\) −22.3102 22.3102i −1.33091 1.33091i −0.904553 0.426362i \(-0.859795\pi\)
−0.426362 0.904553i \(1.35979\pi\)
\(282\) 0 0
\(283\) 9.95203 4.12227i 0.591587 0.245043i −0.0667462 0.997770i \(-0.521262\pi\)
0.658333 + 0.752727i \(0.271262\pi\)
\(284\) 0 0
\(285\) −1.52191 1.35881i −0.0901504 0.0804892i
\(286\) 0 0
\(287\) 1.51762 0.0895820
\(288\) 0 0
\(289\) −16.3498 −0.961755
\(290\) 0 0
\(291\) 3.37744 + 3.01548i 0.197989 + 0.176771i
\(292\) 0 0
\(293\) 23.2108 9.61422i 1.35599 0.561669i 0.418035 0.908431i \(-0.362719\pi\)
0.937953 + 0.346762i \(0.112719\pi\)
\(294\) 0 0
\(295\) −0.331084 0.331084i −0.0192765 0.0192765i
\(296\) 0 0
\(297\) −3.86707 + 17.0505i −0.224390 + 0.989373i
\(298\) 0 0
\(299\) 22.0085 9.11622i 1.27279 0.527205i
\(300\) 0 0
\(301\) −1.16399 + 2.81013i −0.0670914 + 0.161973i
\(302\) 0 0
\(303\) 21.4894 + 7.50845i 1.23454 + 0.431349i
\(304\) 0 0
\(305\) 1.86029 0.106520
\(306\) 0 0
\(307\) −18.3982 7.62077i −1.05004 0.434940i −0.210133 0.977673i \(-0.567390\pi\)
−0.839906 + 0.542733i \(0.817390\pi\)
\(308\) 0 0
\(309\) 1.17275 + 20.7135i 0.0667154 + 1.17835i
\(310\) 0 0
\(311\) 0.938468 + 0.938468i 0.0532157 + 0.0532157i 0.733214 0.679998i \(-0.238019\pi\)
−0.679998 + 0.733214i \(0.738019\pi\)
\(312\) 0 0
\(313\) 11.2850 11.2850i 0.637867 0.637867i −0.312162 0.950029i \(-0.601053\pi\)
0.950029 + 0.312162i \(0.101053\pi\)
\(314\) 0 0
\(315\) −0.0660102 + 0.229917i −0.00371926 + 0.0129543i
\(316\) 0 0
\(317\) −7.57388 + 18.2850i −0.425391 + 1.02699i 0.555340 + 0.831623i \(0.312588\pi\)
−0.980731 + 0.195362i \(0.937412\pi\)
\(318\) 0 0
\(319\) 32.0062i 1.79200i
\(320\) 0 0
\(321\) 1.83043 + 0.639555i 0.102164 + 0.0356965i
\(322\) 0 0
\(323\) 4.49881 + 1.86347i 0.250321 + 0.103686i
\(324\) 0 0
\(325\) 6.35034 + 15.3311i 0.352253 + 0.850415i
\(326\) 0 0
\(327\) 2.86695 1.38227i 0.158543 0.0764395i
\(328\) 0 0
\(329\) −0.115556 + 0.115556i −0.00637082 + 0.00637082i
\(330\) 0 0
\(331\) 4.79305 + 11.5714i 0.263450 + 0.636024i 0.999147 0.0412860i \(-0.0131455\pi\)
−0.735698 + 0.677310i \(0.763145\pi\)
\(332\) 0 0
\(333\) −10.0885 + 5.58779i −0.552848 + 0.306209i
\(334\) 0 0
\(335\) 1.91959i 0.104879i
\(336\) 0 0
\(337\) 7.03034i 0.382967i −0.981496 0.191484i \(-0.938670\pi\)
0.981496 0.191484i \(-0.0613299\pi\)
\(338\) 0 0
\(339\) 1.80288 + 1.60967i 0.0979188 + 0.0874251i
\(340\) 0 0
\(341\) −9.63574 23.2627i −0.521804 1.25975i
\(342\) 0 0
\(343\) −3.99847 + 3.99847i −0.215897 + 0.215897i
\(344\) 0 0
\(345\) −1.04513 2.16770i −0.0562679 0.116705i
\(346\) 0 0
\(347\) 4.70857 + 11.3675i 0.252769 + 0.610240i 0.998426 0.0560914i \(-0.0178638\pi\)
−0.745656 + 0.666331i \(0.767864\pi\)
\(348\) 0 0
\(349\) 29.2204 + 12.1035i 1.56413 + 0.647885i 0.985801 0.167917i \(-0.0537039\pi\)
0.578332 + 0.815802i \(0.303704\pi\)
\(350\) 0 0
\(351\) 9.26554 + 14.7012i 0.494558 + 0.784693i
\(352\) 0 0
\(353\) 14.9632i 0.796411i 0.917296 + 0.398206i \(0.130367\pi\)
−0.917296 + 0.398206i \(0.869633\pi\)
\(354\) 0 0
\(355\) 0.302712 0.730811i 0.0160663 0.0387874i
\(356\) 0 0
\(357\) −0.0322721 0.570001i −0.00170802 0.0301677i
\(358\) 0 0
\(359\) 19.5707 19.5707i 1.03290 1.03290i 0.0334594 0.999440i \(-0.489348\pi\)
0.999440 0.0334594i \(-0.0106524\pi\)
\(360\) 0 0
\(361\) 12.3532 + 12.3532i 0.650170 + 0.650170i
\(362\) 0 0
\(363\) 0.555638 0.0314588i 0.0291634 0.00165116i
\(364\) 0 0
\(365\) 1.77883 + 0.736815i 0.0931082 + 0.0385667i
\(366\) 0 0
\(367\) −21.5484 −1.12482 −0.562410 0.826859i \(-0.690126\pi\)
−0.562410 + 0.826859i \(0.690126\pi\)
\(368\) 0 0
\(369\) −8.71398 6.93614i −0.453632 0.361081i
\(370\) 0 0
\(371\) 0.581184 1.40310i 0.0301736 0.0728455i
\(372\) 0 0
\(373\) 27.1858 11.2607i 1.40763 0.583059i 0.455910 0.890026i \(-0.349314\pi\)
0.951720 + 0.306967i \(0.0993141\pi\)
\(374\) 0 0
\(375\) 3.03160 1.46165i 0.156551 0.0754794i
\(376\) 0 0
\(377\) 22.4944 + 22.4944i 1.15852 + 1.15852i
\(378\) 0 0
\(379\) 11.5245 4.77361i 0.591975 0.245204i −0.0665251 0.997785i \(-0.521191\pi\)
0.658500 + 0.752581i \(0.271191\pi\)
\(380\) 0 0
\(381\) 7.92850 8.88016i 0.406189 0.454945i
\(382\) 0 0
\(383\) 33.6911 1.72154 0.860768 0.508998i \(-0.169984\pi\)
0.860768 + 0.508998i \(0.169984\pi\)
\(384\) 0 0
\(385\) 0.268286 0.0136731
\(386\) 0 0
\(387\) 19.5270 10.8155i 0.992612 0.549783i
\(388\) 0 0
\(389\) −34.0564 + 14.1066i −1.72673 + 0.715233i −0.727139 + 0.686490i \(0.759151\pi\)
−0.999587 + 0.0287433i \(0.990849\pi\)
\(390\) 0 0
\(391\) 4.06135 + 4.06135i 0.205391 + 0.205391i
\(392\) 0 0
\(393\) −13.0745 27.1178i −0.659521 1.36791i
\(394\) 0 0
\(395\) −1.44466 + 0.598399i −0.0726889 + 0.0301087i
\(396\) 0 0
\(397\) −11.3891 + 27.4958i −0.571604 + 1.37997i 0.328586 + 0.944474i \(0.393428\pi\)
−0.900189 + 0.435499i \(0.856572\pi\)
\(398\) 0 0
\(399\) 1.41039 4.03657i 0.0706077 0.202081i
\(400\) 0 0
\(401\) −9.31753 −0.465295 −0.232648 0.972561i \(-0.574739\pi\)
−0.232648 + 0.972561i \(0.574739\pi\)
\(402\) 0 0
\(403\) −23.1215 9.57726i −1.15177 0.477077i
\(404\) 0 0
\(405\) 1.42984 1.01846i 0.0710493 0.0506078i
\(406\) 0 0
\(407\) 9.14621 + 9.14621i 0.453361 + 0.453361i
\(408\) 0 0
\(409\) 17.7916 17.7916i 0.879736 0.879736i −0.113771 0.993507i \(-0.536293\pi\)
0.993507 + 0.113771i \(0.0362930\pi\)
\(410\) 0 0
\(411\) 26.3602 1.49245i 1.30025 0.0736171i
\(412\) 0 0
\(413\) 0.375523 0.906592i 0.0184783 0.0446105i
\(414\) 0 0
\(415\) 1.25954i 0.0618285i
\(416\) 0 0
\(417\) −2.10774 + 6.03242i −0.103217 + 0.295409i
\(418\) 0 0
\(419\) 9.75715 + 4.04154i 0.476668 + 0.197442i 0.608065 0.793888i \(-0.291946\pi\)
−0.131397 + 0.991330i \(0.541946\pi\)
\(420\) 0 0
\(421\) −1.73340 4.18479i −0.0844806 0.203954i 0.875994 0.482322i \(-0.160207\pi\)
−0.960474 + 0.278368i \(0.910207\pi\)
\(422\) 0 0
\(423\) 1.19165 0.135371i 0.0579401 0.00658195i
\(424\) 0 0
\(425\) −2.82912 + 2.82912i −0.137233 + 0.137233i
\(426\) 0 0
\(427\) 1.49198 + 3.60195i 0.0722018 + 0.174311i
\(428\) 0 0
\(429\) 12.9805 14.5386i 0.626704 0.701928i
\(430\) 0 0
\(431\) 24.2865i 1.16984i 0.811092 + 0.584919i \(0.198874\pi\)
−0.811092 + 0.584919i \(0.801126\pi\)
\(432\) 0 0
\(433\) 21.4987i 1.03316i 0.856239 + 0.516580i \(0.172795\pi\)
−0.856239 + 0.516580i \(0.827205\pi\)
\(434\) 0 0
\(435\) 2.14031 2.39722i 0.102620 0.114938i
\(436\) 0 0
\(437\) 16.4619 + 39.7424i 0.787478 + 1.90114i
\(438\) 0 0
\(439\) −1.71247 + 1.71247i −0.0817316 + 0.0817316i −0.746791 0.665059i \(-0.768406\pi\)
0.665059 + 0.746791i \(0.268406\pi\)
\(440\) 0 0
\(441\) 20.3677 2.31375i 0.969890 0.110179i
\(442\) 0 0
\(443\) 1.69988 + 4.10388i 0.0807639 + 0.194981i 0.959103 0.283056i \(-0.0913483\pi\)
−0.878339 + 0.478037i \(0.841348\pi\)
\(444\) 0 0
\(445\) 1.38462 + 0.573527i 0.0656371 + 0.0271878i
\(446\) 0 0
\(447\) 9.70278 27.7697i 0.458926 1.31346i
\(448\) 0 0
\(449\) 6.34782i 0.299572i −0.988718 0.149786i \(-0.952142\pi\)
0.988718 0.149786i \(-0.0478585\pi\)
\(450\) 0 0
\(451\) −4.78028 + 11.5406i −0.225095 + 0.543427i
\(452\) 0 0
\(453\) −3.67242 + 0.207924i −0.172546 + 0.00976910i
\(454\) 0 0
\(455\) 0.188555 0.188555i 0.00883961 0.00883961i
\(456\) 0 0
\(457\) 10.0211 + 10.0211i 0.468765 + 0.468765i 0.901514 0.432749i \(-0.142456\pi\)
−0.432749 + 0.901514i \(0.642456\pi\)
\(458\) 0 0
\(459\) −2.41984 + 3.42038i −0.112949 + 0.159650i
\(460\) 0 0
\(461\) −19.1656 7.93865i −0.892631 0.369740i −0.111249 0.993793i \(-0.535485\pi\)
−0.781382 + 0.624053i \(0.785485\pi\)
\(462\) 0 0
\(463\) 30.9634 1.43899 0.719496 0.694496i \(-0.244373\pi\)
0.719496 + 0.694496i \(0.244373\pi\)
\(464\) 0 0
\(465\) −0.833919 + 2.38670i −0.0386721 + 0.110681i
\(466\) 0 0
\(467\) 2.87599 6.94326i 0.133085 0.321296i −0.843263 0.537502i \(-0.819368\pi\)
0.976348 + 0.216206i \(0.0693682\pi\)
\(468\) 0 0
\(469\) −3.71679 + 1.53954i −0.171625 + 0.0710895i
\(470\) 0 0
\(471\) −10.3887 21.5471i −0.478685 0.992839i
\(472\) 0 0
\(473\) −17.7030 17.7030i −0.813987 0.813987i
\(474\) 0 0
\(475\) −27.6845 + 11.4673i −1.27025 + 0.526155i
\(476\) 0 0
\(477\) −9.74987 + 5.40021i −0.446416 + 0.247259i
\(478\) 0 0
\(479\) 12.3852 0.565894 0.282947 0.959136i \(-0.408688\pi\)
0.282947 + 0.959136i \(0.408688\pi\)
\(480\) 0 0
\(481\) 12.8562 0.586192
\(482\) 0 0
\(483\) 3.35896 3.76214i 0.152838 0.171183i
\(484\) 0 0
\(485\) −0.471072 + 0.195124i −0.0213903 + 0.00886014i
\(486\) 0 0
\(487\) −8.82766 8.82766i −0.400019 0.400019i 0.478220 0.878240i \(-0.341282\pi\)
−0.878240 + 0.478220i \(0.841282\pi\)
\(488\) 0 0
\(489\) −12.3326 + 5.94602i −0.557700 + 0.268889i
\(490\) 0 0
\(491\) −9.13225 + 3.78270i −0.412133 + 0.170711i −0.579109 0.815250i \(-0.696600\pi\)
0.166977 + 0.985961i \(0.446600\pi\)
\(492\) 0 0
\(493\) −2.93521 + 7.08623i −0.132195 + 0.319148i
\(494\) 0 0
\(495\) −1.54047 1.22618i −0.0692389 0.0551126i
\(496\) 0 0
\(497\) 1.65780 0.0743626
\(498\) 0 0
\(499\) 4.86758 + 2.01622i 0.217903 + 0.0902583i 0.488965 0.872304i \(-0.337375\pi\)
−0.271062 + 0.962562i \(0.587375\pi\)
\(500\) 0 0
\(501\) −4.03786 + 0.228613i −0.180398 + 0.0102137i
\(502\) 0 0
\(503\) 0.926311 + 0.926311i 0.0413022 + 0.0413022i 0.727456 0.686154i \(-0.240702\pi\)
−0.686154 + 0.727456i \(0.740702\pi\)
\(504\) 0 0
\(505\) −1.81265 + 1.81265i −0.0806620 + 0.0806620i
\(506\) 0 0
\(507\) 0.177770 + 3.13984i 0.00789505 + 0.139445i
\(508\) 0 0
\(509\) 1.79808 4.34096i 0.0796987 0.192410i −0.879008 0.476808i \(-0.841794\pi\)
0.958706 + 0.284398i \(0.0917938\pi\)
\(510\) 0 0
\(511\) 4.03517i 0.178505i
\(512\) 0 0
\(513\) −26.5471 + 16.7315i −1.17208 + 0.738714i
\(514\) 0 0
\(515\) −2.15853 0.894090i −0.0951160 0.0393983i
\(516\) 0 0
\(517\) −0.514755 1.24273i −0.0226389 0.0546551i
\(518\) 0 0
\(519\) −7.99195 16.5761i −0.350807 0.727608i
\(520\) 0 0
\(521\) 12.3969 12.3969i 0.543120 0.543120i −0.381322 0.924442i \(-0.624531\pi\)
0.924442 + 0.381322i \(0.124531\pi\)
\(522\) 0 0
\(523\) 5.71533 + 13.7980i 0.249914 + 0.603346i 0.998196 0.0600346i \(-0.0191211\pi\)
−0.748282 + 0.663380i \(0.769121\pi\)
\(524\) 0 0
\(525\) 2.62070 + 2.33985i 0.114377 + 0.102119i
\(526\) 0 0
\(527\) 6.03408i 0.262849i
\(528\) 0 0
\(529\) 27.7390i 1.20604i
\(530\) 0 0
\(531\) −6.29971 + 3.48925i −0.273384 + 0.151421i
\(532\) 0 0
\(533\) 4.75127 + 11.4706i 0.205800 + 0.496846i
\(534\) 0 0
\(535\) −0.154398 + 0.154398i −0.00667521 + 0.00667521i
\(536\) 0 0
\(537\) −25.6084 + 12.3468i −1.10508 + 0.532802i
\(538\) 0 0
\(539\) −8.79818 21.2407i −0.378964 0.914901i
\(540\) 0 0
\(541\) −16.5235 6.84424i −0.710399 0.294257i −0.00192927 0.999998i \(-0.500614\pi\)
−0.708470 + 0.705741i \(0.750614\pi\)
\(542\) 0 0
\(543\) −8.73211 3.05102i −0.374731 0.130932i
\(544\) 0 0
\(545\) 0.358426i 0.0153533i
\(546\) 0 0
\(547\) −2.24912 + 5.42985i −0.0961654 + 0.232164i −0.964641 0.263569i \(-0.915100\pi\)
0.868475 + 0.495733i \(0.165100\pi\)
\(548\) 0 0
\(549\) 7.89566 27.5010i 0.336978 1.17371i
\(550\) 0 0
\(551\) −40.6199 + 40.6199i −1.73047 + 1.73047i
\(552\) 0 0
\(553\) −2.31728 2.31728i −0.0985409 0.0985409i
\(554\) 0 0
\(555\) −0.0734137 1.29666i −0.00311624 0.0550402i
\(556\) 0 0
\(557\) 17.5896 + 7.28584i 0.745294 + 0.308711i 0.722820 0.691036i \(-0.242846\pi\)
0.0224743 + 0.999747i \(0.492846\pi\)
\(558\) 0 0
\(559\) −24.8839 −1.05248
\(560\) 0 0
\(561\) 4.43620 + 1.55002i 0.187296 + 0.0654417i
\(562\) 0 0
\(563\) 7.04761 17.0144i 0.297021 0.717073i −0.702962 0.711228i \(-0.748139\pi\)
0.999983 0.00584493i \(-0.00186051\pi\)
\(564\) 0 0
\(565\) −0.251458 + 0.104157i −0.0105789 + 0.00438194i
\(566\) 0 0
\(567\) 3.11874 + 1.95168i 0.130975 + 0.0819630i
\(568\) 0 0
\(569\) 15.9856 + 15.9856i 0.670152 + 0.670152i 0.957751 0.287599i \(-0.0928571\pi\)
−0.287599 + 0.957751i \(0.592857\pi\)
\(570\) 0 0
\(571\) 21.2300 8.79375i 0.888447 0.368007i 0.108680 0.994077i \(-0.465337\pi\)
0.779767 + 0.626070i \(0.215337\pi\)
\(572\) 0 0
\(573\) −15.0462 13.4337i −0.628562 0.561201i
\(574\) 0 0
\(575\) −35.3446 −1.47397
\(576\) 0 0
\(577\) 21.1703 0.881332 0.440666 0.897671i \(-0.354742\pi\)
0.440666 + 0.897671i \(0.354742\pi\)
\(578\) 0 0
\(579\) −7.79371 6.95848i −0.323896 0.289185i
\(580\) 0 0
\(581\) −2.43877 + 1.01017i −0.101177 + 0.0419090i
\(582\) 0 0
\(583\) 8.83917 + 8.83917i 0.366081 + 0.366081i
\(584\) 0 0
\(585\) −1.94444 + 0.220887i −0.0803927 + 0.00913255i
\(586\) 0 0
\(587\) 14.4081 5.96803i 0.594686 0.246327i −0.0649791 0.997887i \(-0.520698\pi\)
0.659665 + 0.751560i \(0.270698\pi\)
\(588\) 0 0
\(589\) 17.2944 41.7523i 0.712603 1.72037i
\(590\) 0 0
\(591\) −1.02905 0.359550i −0.0423293 0.0147899i
\(592\) 0 0
\(593\) −20.5777 −0.845025 −0.422512 0.906357i \(-0.638852\pi\)
−0.422512 + 0.906357i \(0.638852\pi\)
\(594\) 0 0
\(595\) 0.0593989 + 0.0246038i 0.00243512 + 0.00100866i
\(596\) 0 0
\(597\) −1.88407 33.2772i −0.0771100 1.36195i
\(598\) 0 0
\(599\) −14.6016 14.6016i −0.596604 0.596604i 0.342803 0.939407i \(-0.388624\pi\)
−0.939407 + 0.342803i \(0.888624\pi\)
\(600\) 0 0
\(601\) −22.7394 + 22.7394i −0.927561 + 0.927561i −0.997548 0.0699869i \(-0.977704\pi\)
0.0699869 + 0.997548i \(0.477704\pi\)
\(602\) 0 0
\(603\) 28.3777 + 8.14738i 1.15563 + 0.331787i
\(604\) 0 0
\(605\) −0.0239839 + 0.0579021i −0.000975082 + 0.00235406i
\(606\) 0 0
\(607\) 40.2640i 1.63426i −0.576451 0.817132i \(-0.695563\pi\)
0.576451 0.817132i \(-0.304437\pi\)
\(608\) 0 0
\(609\) 6.35814 + 2.22155i 0.257645 + 0.0900216i
\(610\) 0 0
\(611\) −1.23519 0.511631i −0.0499703 0.0206984i
\(612\) 0 0
\(613\) 6.76173 + 16.3243i 0.273104 + 0.659331i 0.999613 0.0278260i \(-0.00885845\pi\)
−0.726509 + 0.687157i \(0.758858\pi\)
\(614\) 0 0
\(615\) 1.12978 0.544710i 0.0455571 0.0219648i
\(616\) 0 0
\(617\) −5.19834 + 5.19834i −0.209277 + 0.209277i −0.803960 0.594683i \(-0.797278\pi\)
0.594683 + 0.803960i \(0.297278\pi\)
\(618\) 0 0
\(619\) −8.07299 19.4899i −0.324481 0.783366i −0.998983 0.0450932i \(-0.985642\pi\)
0.674502 0.738273i \(-0.264358\pi\)
\(620\) 0 0
\(621\) −36.4814 + 6.24994i −1.46395 + 0.250801i
\(622\) 0 0
\(623\) 3.14092i 0.125838i
\(624\) 0 0
\(625\) 24.4308i 0.977230i
\(626\) 0 0
\(627\) 26.2534 + 23.4399i 1.04846 + 0.936098i
\(628\) 0 0
\(629\) 1.18621 + 2.86376i 0.0472973 + 0.114186i
\(630\) 0 0
\(631\) −22.5327 + 22.5327i −0.897012 + 0.897012i −0.995171 0.0981592i \(-0.968705\pi\)
0.0981592 + 0.995171i \(0.468705\pi\)
\(632\) 0 0
\(633\) 5.65214 + 11.7231i 0.224652 + 0.465950i
\(634\) 0 0
\(635\) 0.513033 + 1.23857i 0.0203591 + 0.0491512i
\(636\) 0 0
\(637\) −21.1118 8.74478i −0.836479 0.346481i
\(638\) 0 0
\(639\) −9.51892 7.57685i −0.376563 0.299736i
\(640\) 0 0
\(641\) 41.6012i 1.64315i −0.570100 0.821575i \(-0.693096\pi\)
0.570100 0.821575i \(-0.306904\pi\)
\(642\) 0 0
\(643\) −7.11746 + 17.1831i −0.280685 + 0.677634i −0.999852 0.0172036i \(-0.994524\pi\)
0.719167 + 0.694837i \(0.244524\pi\)
\(644\) 0 0
\(645\) 0.142097 + 2.50977i 0.00559506 + 0.0988220i
\(646\) 0 0
\(647\) 31.4452 31.4452i 1.23624 1.23624i 0.274714 0.961526i \(-0.411417\pi\)
0.961526 0.274714i \(-0.0885833\pi\)
\(648\) 0 0
\(649\) 5.71128 + 5.71128i 0.224187 + 0.224187i
\(650\) 0 0
\(651\) −5.29004 + 0.299509i −0.207333 + 0.0117387i
\(652\) 0 0
\(653\) 5.38622 + 2.23104i 0.210779 + 0.0873075i 0.485575 0.874195i \(-0.338610\pi\)
−0.274796 + 0.961503i \(0.588610\pi\)
\(654\) 0 0
\(655\) 3.39025 0.132468
\(656\) 0 0
\(657\) 18.4424 23.1695i 0.719507 0.903928i
\(658\) 0 0
\(659\) 7.05977 17.0438i 0.275010 0.663932i −0.724674 0.689092i \(-0.758010\pi\)
0.999683 + 0.0251602i \(0.00800958\pi\)
\(660\) 0 0
\(661\) −25.7857 + 10.6808i −1.00295 + 0.415435i −0.822878 0.568219i \(-0.807633\pi\)
−0.180071 + 0.983654i \(0.557633\pi\)
\(662\) 0 0
\(663\) 4.20720 2.02845i 0.163394 0.0787786i
\(664\) 0 0
\(665\) 0.340489 + 0.340489i 0.0132036 + 0.0132036i
\(666\) 0 0
\(667\) −62.5996 + 25.9296i −2.42387 + 1.00400i
\(668\) 0 0
\(669\) −7.44253 + 8.33586i −0.287745 + 0.322283i
\(670\) 0 0
\(671\) −32.0904 −1.23883
\(672\) 0 0
\(673\) 18.5829 0.716319 0.358160 0.933660i \(-0.383404\pi\)
0.358160 + 0.933660i \(0.383404\pi\)
\(674\) 0 0
\(675\) −4.35369 25.4128i −0.167574 0.978140i
\(676\) 0 0
\(677\) 22.9138 9.49122i 0.880650 0.364777i 0.103901 0.994588i \(-0.466867\pi\)
0.776749 + 0.629810i \(0.216867\pi\)
\(678\) 0 0
\(679\) −0.755613 0.755613i −0.0289978 0.0289978i
\(680\) 0 0
\(681\) −2.57781 5.34661i −0.0987817 0.204883i
\(682\) 0 0
\(683\) −34.5480 + 14.3103i −1.32194 + 0.547567i −0.928346 0.371717i \(-0.878769\pi\)
−0.393597 + 0.919283i \(0.628769\pi\)
\(684\) 0 0
\(685\) −1.13783 + 2.74696i −0.0434741 + 0.104956i
\(686\) 0 0
\(687\) 12.8946 36.9048i 0.491960 1.40801i
\(688\) 0 0
\(689\) 12.4246 0.473340
\(690\) 0 0
\(691\) 29.9717 + 12.4147i 1.14018 + 0.472277i 0.871228 0.490878i \(-0.163324\pi\)
0.268948 + 0.963155i \(0.413324\pi\)
\(692\) 0 0
\(693\) 1.13869 3.96612i 0.0432554 0.150660i
\(694\) 0 0
\(695\) −0.508841 0.508841i −0.0193014 0.0193014i
\(696\) 0 0
\(697\) −2.11673 + 2.11673i −0.0801767 + 0.0801767i
\(698\) 0 0
\(699\) −37.9610 + 2.14926i −1.43582 + 0.0812924i
\(700\) 0 0
\(701\) 6.56454 15.8482i 0.247939 0.598578i −0.750090 0.661336i \(-0.769990\pi\)
0.998029 + 0.0627582i \(0.0199897\pi\)
\(702\) 0 0
\(703\) 23.2154i 0.875585i
\(704\) 0 0
\(705\) −0.0445491 + 0.127501i −0.00167782 + 0.00480197i
\(706\) 0 0
\(707\) −4.96350 2.05595i −0.186672 0.0773219i
\(708\) 0 0
\(709\) 11.6861 + 28.2128i 0.438882 + 1.05955i 0.976336 + 0.216261i \(0.0693863\pi\)
−0.537454 + 0.843293i \(0.680614\pi\)
\(710\) 0 0
\(711\) 2.71463 + 23.8965i 0.101806 + 0.896190i
\(712\) 0 0
\(713\) 37.6923 37.6923i 1.41159 1.41159i
\(714\) 0 0
\(715\) 0.839935 + 2.02778i 0.0314118 + 0.0758348i
\(716\) 0 0
\(717\) 25.7629 28.8552i 0.962133 1.07762i
\(718\) 0 0
\(719\) 32.6392i 1.21724i 0.793463 + 0.608619i \(0.208276\pi\)
−0.793463 + 0.608619i \(0.791724\pi\)
\(720\) 0 0
\(721\) 4.89649i 0.182355i
\(722\) 0 0
\(723\) −11.5754 + 12.9648i −0.430493 + 0.482165i
\(724\) 0 0
\(725\) −18.0625 43.6067i −0.670825 1.61951i
\(726\) 0 0
\(727\) −11.8938 + 11.8938i −0.441118 + 0.441118i −0.892388 0.451270i \(-0.850971\pi\)
0.451270 + 0.892388i \(0.350971\pi\)
\(728\) 0 0
\(729\) −8.98742 25.4603i −0.332867 0.942974i
\(730\) 0 0
\(731\) −2.29598 5.54299i −0.0849199 0.205015i
\(732\) 0 0
\(733\) 14.2498 + 5.90246i 0.526328 + 0.218012i 0.629994 0.776600i \(-0.283057\pi\)
−0.103666 + 0.994612i \(0.533057\pi\)
\(734\) 0 0
\(735\) −0.761433 + 2.17925i −0.0280859 + 0.0803827i
\(736\) 0 0
\(737\) 33.1135i 1.21975i
\(738\) 0 0
\(739\) 1.65560 3.99698i 0.0609024 0.147031i −0.890499 0.454986i \(-0.849644\pi\)
0.951401 + 0.307954i \(0.0996444\pi\)
\(740\) 0 0
\(741\) 34.9252 1.97738i 1.28301 0.0726408i
\(742\) 0 0
\(743\) 15.0005 15.0005i 0.550313 0.550313i −0.376218 0.926531i \(-0.622776\pi\)
0.926531 + 0.376218i \(0.122776\pi\)
\(744\) 0 0
\(745\) 2.34240 + 2.34240i 0.0858188 + 0.0858188i
\(746\) 0 0
\(747\) 18.6201 + 5.34591i 0.681273 + 0.195597i
\(748\) 0 0
\(749\) −0.422781 0.175122i −0.0154481 0.00639880i
\(750\) 0 0
\(751\) 10.9267 0.398720 0.199360 0.979926i \(-0.436114\pi\)
0.199360 + 0.979926i \(0.436114\pi\)
\(752\) 0 0
\(753\) 1.83745 5.25884i 0.0669603 0.191643i
\(754\) 0 0
\(755\) 0.158519 0.382698i 0.00576908 0.0139278i
\(756\) 0 0
\(757\) 19.8634 8.22770i 0.721948 0.299041i 0.00870961 0.999962i \(-0.497228\pi\)
0.713239 + 0.700921i \(0.247228\pi\)
\(758\) 0 0
\(759\) 18.0287 + 37.3933i 0.654402 + 1.35729i
\(760\) 0 0
\(761\) −8.07215 8.07215i −0.292615 0.292615i 0.545497 0.838112i \(-0.316341\pi\)
−0.838112 + 0.545497i \(0.816341\pi\)
\(762\) 0 0
\(763\) −0.693996 + 0.287463i −0.0251243 + 0.0104068i
\(764\) 0 0
\(765\) −0.228612 0.412751i −0.00826549 0.0149230i
\(766\) 0 0
\(767\) 8.02795 0.289873
\(768\) 0 0
\(769\) −7.21321 −0.260115 −0.130057 0.991506i \(-0.541516\pi\)
−0.130057 + 0.991506i \(0.541516\pi\)
\(770\) 0 0
\(771\) −26.2828 + 29.4376i −0.946554 + 1.06017i
\(772\) 0 0
\(773\) −29.1506 + 12.0746i −1.04848 + 0.434293i −0.839347 0.543595i \(-0.817063\pi\)
−0.209128 + 0.977888i \(0.567063\pi\)
\(774\) 0 0
\(775\) 26.2564 + 26.2564i 0.943157 + 0.943157i
\(776\) 0 0
\(777\) 2.45176 1.18209i 0.0879565 0.0424072i
\(778\) 0 0
\(779\) −20.7133 + 8.57973i −0.742131 + 0.307401i
\(780\) 0 0
\(781\) −5.22185 + 12.6067i −0.186853 + 0.451102i
\(782\) 0 0
\(783\) −26.3543