Properties

Label 768.2.o.b.95.1
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 95.1
Character \(\chi\) \(=\) 768.95
Dual form 768.2.o.b.671.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.72928 - 0.0979076i) q^{3} +(0.180206 - 0.0746437i) q^{5} +(-0.289055 - 0.289055i) q^{7} +(2.98083 + 0.338620i) q^{9} +O(q^{10})\) \(q+(-1.72928 - 0.0979076i) q^{3} +(0.180206 - 0.0746437i) q^{5} +(-0.289055 - 0.289055i) q^{7} +(2.98083 + 0.338620i) q^{9} +(-3.10859 + 1.28762i) q^{11} +(1.27981 - 3.08973i) q^{13} +(-0.318935 + 0.111436i) q^{15} -0.806332 q^{17} +(5.57935 + 2.31104i) q^{19} +(0.471557 + 0.528159i) q^{21} +(-5.03681 - 5.03681i) q^{23} +(-3.50863 + 3.50863i) q^{25} +(-5.12154 - 0.877415i) q^{27} +(3.64020 - 8.78822i) q^{29} -7.48336i q^{31} +(5.50170 - 1.92230i) q^{33} +(-0.0736656 - 0.0305133i) q^{35} +(1.47112 + 3.55159i) q^{37} +(-2.51565 + 5.21770i) q^{39} +(2.62513 - 2.62513i) q^{41} +(-2.84744 - 6.87432i) q^{43} +(0.562438 - 0.161479i) q^{45} +0.399772i q^{47} -6.83289i q^{49} +(1.39438 + 0.0789461i) q^{51} +(-1.42173 - 3.43237i) q^{53} +(-0.464073 + 0.464073i) q^{55} +(-9.42200 - 4.54271i) q^{57} +(-0.918629 - 2.21777i) q^{59} +(-8.81133 - 3.64977i) q^{61} +(-0.763745 - 0.959504i) q^{63} -0.652316i q^{65} +(3.76613 - 9.09225i) q^{67} +(8.21692 + 9.20321i) q^{69} +(2.86762 - 2.86762i) q^{71} +(-6.97993 - 6.97993i) q^{73} +(6.41093 - 5.72389i) q^{75} +(1.27075 + 0.526361i) q^{77} +8.01674 q^{79} +(8.77067 + 2.01873i) q^{81} +(-2.47115 + 5.96589i) q^{83} +(-0.145306 + 0.0601876i) q^{85} +(-7.15536 + 14.8409i) q^{87} +(5.43308 + 5.43308i) q^{89} +(-1.26304 + 0.523167i) q^{91} +(-0.732678 + 12.9408i) q^{93} +1.17794 q^{95} +2.61408 q^{97} +(-9.70219 + 2.78555i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

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
\(3\) −1.72928 0.0979076i −0.998401 0.0565270i
\(4\) 0 0
\(5\) 0.180206 0.0746437i 0.0805904 0.0333817i −0.342024 0.939691i \(-0.611112\pi\)
0.422614 + 0.906310i \(0.361112\pi\)
\(6\) 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
\(9\) 2.98083 + 0.338620i 0.993609 + 0.112873i
\(10\) 0 0
\(11\) −3.10859 + 1.28762i −0.937276 + 0.388232i −0.798434 0.602082i \(-0.794338\pi\)
−0.138842 + 0.990315i \(0.544338\pi\)
\(12\) 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 \(-0.531175\pi\)
−0.0977822 + 0.995208i \(0.531175\pi\)
\(18\) 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
\(21\) 0.471557 + 0.528159i 0.102902 + 0.115254i
\(22\) 0 0
\(23\) −5.03681 5.03681i −1.05025 1.05025i −0.998669 0.0515792i \(-0.983575\pi\)
−0.0515792 0.998669i \(1.48357\pi\)
\(24\) 0 0
\(25\) −3.50863 + 3.50863i −0.701726 + 0.701726i
\(26\) 0 0
\(27\) −5.12154 0.877415i −0.985640 0.168859i
\(28\) 0 0
\(29\) 3.64020 8.78822i 0.675968 1.63193i −0.0953212 0.995447i \(-0.530388\pi\)
0.771289 0.636485i \(-0.219612\pi\)
\(30\) 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
\(39\) −2.51565 + 5.21770i −0.402827 + 0.835501i
\(40\) 0 0
\(41\) 2.62513 2.62513i 0.409976 0.409976i −0.471754 0.881730i \(-0.656379\pi\)
0.881730 + 0.471754i \(0.156379\pi\)
\(42\) 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
\(45\) 0.562438 0.161479i 0.0838433 0.0240718i
\(46\) 0 0
\(47\) 0.399772i 0.0583127i 0.999575 + 0.0291564i \(0.00928208\pi\)
−0.999575 + 0.0291564i \(0.990718\pi\)
\(48\) 0 0
\(49\) 6.83289i 0.976128i
\(50\) 0 0
\(51\) 1.39438 + 0.0789461i 0.195252 + 0.0110547i
\(52\) 0 0
\(53\) −1.42173 3.43237i −0.195290 0.471472i 0.795653 0.605752i \(-0.207128\pi\)
−0.990943 + 0.134280i \(0.957128\pi\)
\(54\) 0 0
\(55\) −0.464073 + 0.464073i −0.0625756 + 0.0625756i
\(56\) 0 0
\(57\) −9.42200 4.54271i −1.24797 0.601696i
\(58\) 0 0
\(59\) −0.918629 2.21777i −0.119595 0.288729i 0.852733 0.522347i \(-0.174943\pi\)
−0.972328 + 0.233618i \(0.924943\pi\)
\(60\) 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
\(69\) 8.21692 + 9.20321i 0.989201 + 1.10794i
\(70\) 0 0
\(71\) 2.86762 2.86762i 0.340324 0.340324i −0.516165 0.856489i \(-0.672641\pi\)
0.856489 + 0.516165i \(0.172641\pi\)
\(72\) 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
\(75\) 6.41093 5.72389i 0.740271 0.660938i
\(76\) 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 −0.999537 0.0304247i \(-0.990314\pi\)
0.728293 + 0.685266i \(0.240314\pi\)
\(84\) 0 0
\(85\) −0.145306 + 0.0601876i −0.0157606 + 0.00652826i
\(86\) 0 0
\(87\) −7.15536 + 14.8409i −0.767135 + 1.59111i
\(88\) 0 0
\(89\) 5.43308 + 5.43308i 0.575905 + 0.575905i 0.933773 0.357867i \(-0.116496\pi\)
−0.357867 + 0.933773i \(0.616496\pi\)
\(90\) 0 0
\(91\) −1.26304 + 0.523167i −0.132402 + 0.0548428i
\(92\) 0 0
\(93\) −0.732678 + 12.9408i −0.0759752 + 1.34190i
\(94\) 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
\(99\) −9.70219 + 2.78555i −0.975107 + 0.279958i
\(100\) 0 0
\(101\) −12.1420 + 5.02940i −1.20818 + 0.500444i −0.893633 0.448798i \(-0.851852\pi\)
−0.314546 + 0.949242i \(0.601852\pi\)
\(102\) 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
\(105\) 0.124401 + 0.0599785i 0.0121403 + 0.00585330i
\(106\) 0 0
\(107\) −1.03423 + 0.428394i −0.0999833 + 0.0414144i −0.432114 0.901819i \(-0.642232\pi\)
0.332131 + 0.943233i \(0.392232\pi\)
\(108\) 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 \(-0.520907\pi\)
−0.0656339 + 0.997844i \(0.520907\pi\)
\(114\) 0 0
\(115\) −1.28363 0.531696i −0.119699 0.0495809i
\(116\) 0 0
\(117\) 4.86112 8.77657i 0.449411 0.811394i
\(118\) 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
\(123\) −4.79661 + 4.28257i −0.432495 + 0.386146i
\(124\) 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 0.950529 0.310635i \(-0.100542\pi\)
0.452474 + 0.891778i \(0.350542\pi\)
\(132\) 0 0
\(133\) −0.944722 2.28076i −0.0819178 0.197767i
\(134\) 0 0
\(135\) −0.988424 + 0.224175i −0.0850700 + 0.0192939i
\(136\) 0 0
\(137\) −10.7787 + 10.7787i −0.920890 + 0.920890i −0.997092 0.0762022i \(-0.975721\pi\)
0.0762022 + 0.997092i \(0.475721\pi\)
\(138\) 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
\(141\) 0.0391407 0.691318i 0.00329624 0.0582195i
\(142\) 0 0
\(143\) 11.2526i 0.940990i
\(144\) 0 0
\(145\) 1.85541i 0.154083i
\(146\) 0 0
\(147\) −0.668992 + 11.8160i −0.0551776 + 0.974567i
\(148\) 0 0
\(149\) 6.49923 + 15.6905i 0.532438 + 1.28542i 0.929904 + 0.367802i \(0.119889\pi\)
−0.397466 + 0.917617i \(0.630111\pi\)
\(150\) 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
\(153\) −2.40354 0.273040i −0.194315 0.0220740i
\(154\) 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
\(165\) 0.847950 0.757077i 0.0660128 0.0589384i
\(166\) 0 0
\(167\) 1.65109 1.65109i 0.127765 0.127765i −0.640333 0.768098i \(-0.721203\pi\)
0.768098 + 0.640333i \(0.221203\pi\)
\(168\) 0 0
\(169\) 1.28389 + 1.28389i 0.0987607 + 0.0987607i
\(170\) 0 0
\(171\) 15.8485 + 8.77810i 1.21197 + 0.671278i
\(172\) 0 0
\(173\) 9.81571 + 4.06580i 0.746275 + 0.309117i 0.723221 0.690617i \(-0.242661\pi\)
0.0230541 + 0.999734i \(0.492661\pi\)
\(174\) 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 \(-0.664797\pi\)
0.964389 0.264487i \(-0.0852026\pi\)
\(180\) 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
\(183\) 14.8799 + 7.17418i 1.09996 + 0.530331i
\(184\) 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
\(189\) 1.22679 + 1.73403i 0.0892356 + 0.126132i
\(190\) 0 0
\(191\) 11.6455 0.842637 0.421318 0.906913i \(-0.361567\pi\)
0.421318 + 0.906913i \(0.361567\pi\)
\(192\) 0 0
\(193\) −6.03220 −0.434207 −0.217104 0.976149i \(-0.569661\pi\)
−0.217104 + 0.976149i \(0.569661\pi\)
\(194\) 0 0
\(195\) −0.0638667 + 1.12804i −0.00457359 + 0.0807804i
\(196\) 0 0
\(197\) 0.581435 0.240838i 0.0414255 0.0171590i −0.361874 0.932227i \(-0.617863\pi\)
0.403300 + 0.915068i \(0.367863\pi\)
\(198\) 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
\(201\) −7.40291 + 15.3543i −0.522161 + 1.08301i
\(202\) 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
\(213\) −5.23969 + 4.67816i −0.359017 + 0.320542i
\(214\) 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
\(219\) 11.3869 + 12.7536i 0.769453 + 0.861811i
\(220\) 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 0.485270 0.874364i \(-0.338721\pi\)
−0.275131 + 0.961407i \(0.588721\pi\)
\(228\) 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
\(231\) −2.14595 1.03464i −0.141193 0.0680745i
\(232\) 0 0
\(233\) 15.5223 15.5223i 1.01690 1.01690i 0.0170465 0.999855i \(-0.494574\pi\)
0.999855 0.0170465i \(-0.00542634\pi\)
\(234\) 0 0
\(235\) 0.0298404 + 0.0720412i 0.00194658 + 0.00469945i
\(236\) 0 0
\(237\) −13.8632 0.784900i −0.900512 0.0509847i
\(238\) 0 0
\(239\) 22.3335i 1.44463i 0.691563 + 0.722316i \(0.256922\pi\)
−0.691563 + 0.722316i \(0.743078\pi\)
\(240\) 0 0
\(241\) 10.0345i 0.646380i 0.946334 + 0.323190i \(0.104755\pi\)
−0.946334 + 0.323190i \(0.895245\pi\)
\(242\) 0 0
\(243\) −14.9693 4.34968i −0.960282 0.279032i
\(244\) 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
\(249\) 4.85742 10.0748i 0.307827 0.638462i
\(250\) 0 0
\(251\) 1.23078 + 2.97137i 0.0776862 + 0.187551i 0.957951 0.286931i \(-0.0926352\pi\)
−0.880265 + 0.474483i \(0.842635\pi\)
\(252\) 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 \(-0.748415\pi\)
0.703576 0.710620i \(-0.251585\pi\)
\(258\) 0 0
\(259\) 0.601372 1.45184i 0.0373675 0.0902130i
\(260\) 0 0
\(261\) 13.8267 24.9635i 0.855850 1.54520i
\(262\) 0 0
\(263\) 12.8553 12.8553i 0.792690 0.792690i −0.189241 0.981931i \(-0.560603\pi\)
0.981931 + 0.189241i \(0.0606027\pi\)
\(264\) 0 0
\(265\) −0.512409 0.512409i −0.0314770 0.0314770i
\(266\) 0 0
\(267\) −8.86338 9.92726i −0.542430 0.607539i
\(268\) 0 0
\(269\) −11.7742 4.87704i −0.717886 0.297358i −0.00632279 0.999980i \(-0.502013\pi\)
−0.711564 + 0.702622i \(0.752013\pi\)
\(270\) 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
\(279\) 2.53401 22.3066i 0.151707 1.33546i
\(280\) 0 0
\(281\) 22.3102 + 22.3102i 1.33091 + 1.33091i 0.904553 + 0.426362i \(0.140205\pi\)
0.426362 + 0.904553i \(0.359795\pi\)
\(282\) 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
\(285\) −2.03698 0.115329i −0.120660 0.00683150i
\(286\) 0 0
\(287\) −1.51762 −0.0895820
\(288\) 0 0
\(289\) −16.3498 −0.961755
\(290\) 0 0
\(291\) −4.52048 0.255938i −0.264995 0.0150034i
\(292\) 0 0
\(293\) −23.2108 + 9.61422i −1.35599 + 0.561669i −0.937953 0.346762i \(-0.887281\pi\)
−0.418035 + 0.908431i \(0.637281\pi\)
\(294\) 0 0
\(295\) −0.331084 0.331084i −0.0192765 0.0192765i
\(296\) 0 0
\(297\) 17.0505 3.86707i 0.989373 0.224390i
\(298\) 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
\(309\) −13.8174 15.4759i −0.786046 0.880395i
\(310\) 0 0
\(311\) −0.938468 0.938468i −0.0532157 0.0532157i 0.679998 0.733214i \(-0.261981\pi\)
−0.733214 + 0.679998i \(0.761981\pi\)
\(312\) 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
\(315\) −0.209252 0.115899i −0.0117900 0.00653020i
\(316\) 0 0
\(317\) 7.57388 18.2850i 0.425391 1.02699i −0.555340 0.831623i \(-0.687412\pi\)
0.980731 0.195362i \(-0.0625881\pi\)
\(318\) 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
\(327\) −1.38227 + 2.86695i −0.0764395 + 0.158543i
\(328\) 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
\(333\) 3.18251 + 11.0848i 0.174400 + 0.607445i
\(334\) 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
\(339\) 2.41303 + 0.136620i 0.131058 + 0.00742018i
\(340\) 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
\(345\) 2.16770 + 1.04513i 0.116705 + 0.0562679i
\(346\) 0 0
\(347\) −4.70857 11.3675i −0.252769 0.610240i 0.745656 0.666331i \(-0.232136\pi\)
−0.998426 + 0.0560914i \(0.982136\pi\)
\(348\) 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 \(-0.869633\pi\)
0.917296 0.398206i \(-0.130367\pi\)
\(354\) 0 0
\(355\) 0.302712 0.730811i 0.0160663 0.0387874i
\(356\) 0 0
\(357\) −0.380232 0.425872i −0.0201240 0.0225395i
\(358\) 0 0
\(359\) −19.5707 + 19.5707i −1.03290 + 1.03290i −0.0334594 + 0.999440i \(0.510652\pi\)
−0.999440 + 0.0334594i \(0.989348\pi\)
\(360\) 0 0
\(361\) 12.3532 + 12.3532i 0.650170 + 0.650170i
\(362\) 0 0
\(363\) −0.415140 + 0.370650i −0.0217892 + 0.0194541i
\(364\) 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
\(375\) 1.46165 3.03160i 0.0754794 0.156551i
\(376\) 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
\(381\) −0.672929 + 11.8855i −0.0344752 + 0.608914i
\(382\) 0 0
\(383\) −33.6911 −1.72154 −0.860768 0.508998i \(-0.830016\pi\)
−0.860768 + 0.508998i \(0.830016\pi\)
\(384\) 0 0
\(385\) 0.268286 0.0136731
\(386\) 0 0
\(387\) −6.15994 21.4554i −0.313127 1.09064i
\(388\) 0 0
\(389\) 34.0564 14.1066i 1.72673 0.715233i 0.727139 0.686490i \(-0.240849\pi\)
0.999587 0.0287433i \(-0.00915052\pi\)
\(390\) 0 0
\(391\) 4.06135 + 4.06135i 0.205391 + 0.205391i
\(392\) 0 0
\(393\) −27.1178 13.0745i −1.36791 0.659521i
\(394\) 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 \(-0.425261\pi\)
0.232648 + 0.972561i \(0.425261\pi\)
\(402\) 0 0
\(403\) −23.1215 9.57726i −1.15177 0.477077i
\(404\) 0 0
\(405\) 1.73121 0.290888i 0.0860246 0.0144543i
\(406\) 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
\(411\) 19.6948 17.5842i 0.971473 0.867363i
\(412\) 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 0.131397 0.991330i \(-0.458054\pi\)
−0.608065 + 0.793888i \(0.708054\pi\)
\(420\) 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
\(423\) −0.135371 + 1.19165i −0.00658195 + 0.0579401i
\(424\) 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
\(429\) 1.10172 19.4589i 0.0531913 0.939485i
\(430\) 0 0
\(431\) 24.2865i 1.16984i −0.811092 0.584919i \(-0.801126\pi\)
0.811092 0.584919i \(-0.198874\pi\)
\(432\) 0 0
\(433\) 21.4987i 1.03316i 0.856239 + 0.516580i \(0.172795\pi\)
−0.856239 + 0.516580i \(0.827205\pi\)
\(434\) 0 0
\(435\) −0.181658 + 3.20852i −0.00870985 + 0.153837i
\(436\) 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
\(441\) 2.31375 20.3677i 0.110179 0.969890i
\(442\) 0 0
\(443\) −1.69988 4.10388i −0.0807639 0.194981i 0.878339 0.478037i \(-0.158652\pi\)
−0.959103 + 0.283056i \(0.908652\pi\)
\(444\) 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 \(0.0478585\pi\)
−0.988718 + 0.149786i \(0.952142\pi\)
\(450\) 0 0
\(451\) −4.78028 + 11.5406i −0.225095 + 0.543427i
\(452\) 0 0
\(453\) 2.74382 2.44977i 0.128916 0.115100i
\(454\) 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
\(459\) 4.12966 + 0.707488i 0.192756 + 0.0330227i
\(460\) 0 0
\(461\) 19.1656 + 7.93865i 0.892631 + 0.369740i 0.781382 0.624053i \(-0.214515\pi\)
0.111249 + 0.993793i \(0.464515\pi\)
\(462\) 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 −0.976348 0.216206i \(-0.930632\pi\)
0.843263 + 0.537502i \(0.180632\pi\)
\(468\) 0 0
\(469\) −3.71679 + 1.53954i −0.171625 + 0.0710895i
\(470\) 0 0
\(471\) 21.5471 + 10.3887i 0.992839 + 0.478685i
\(472\) 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
\(477\) −3.07567 10.7127i −0.140825 0.490502i
\(478\) 0 0
\(479\) −12.3852 −0.565894 −0.282947 0.959136i \(-0.591312\pi\)
−0.282947 + 0.959136i \(0.591312\pi\)
\(480\) 0 0
\(481\) 12.8562 0.586192
\(482\) 0 0
\(483\) 0.285091 5.03538i 0.0129721 0.229118i
\(484\) 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
\(489\) 5.94602 12.3326i 0.268889 0.557700i
\(490\) 0 0
\(491\) 9.13225 3.78270i 0.412133 0.170711i −0.166977 0.985961i \(-0.553400\pi\)
0.579109 + 0.815250i \(0.303400\pi\)
\(492\) 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
\(501\) −3.01685 + 2.69354i −0.134783 + 0.120339i
\(502\) 0 0
\(503\) −0.926311 0.926311i −0.0413022 0.0413022i 0.686154 0.727456i \(-0.259298\pi\)
−0.727456 + 0.686154i \(0.759298\pi\)
\(504\) 0 0
\(505\) −1.81265 + 1.81265i −0.0806620 + 0.0806620i
\(506\) 0 0
\(507\) −2.09450 2.34591i −0.0930201 0.104185i
\(508\) 0 0
\(509\) −1.79808 + 4.34096i −0.0796987 + 0.192410i −0.958706 0.284398i \(-0.908206\pi\)
0.879008 + 0.476808i \(0.158206\pi\)
\(510\) 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
\(519\) −16.5761 7.99195i −0.727608 0.350807i
\(520\) 0 0
\(521\) −12.3969 + 12.3969i −0.543120 + 0.543120i −0.924442 0.381322i \(-0.875469\pi\)
0.381322 + 0.924442i \(0.375469\pi\)
\(522\) 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
\(525\) −3.50764 0.198594i −0.153086 0.00866734i
\(526\) 0 0
\(527\) 6.03408i 0.262849i
\(528\) 0 0
\(529\) 27.7390i 1.20604i
\(530\) 0 0
\(531\) −1.98730 6.92184i −0.0862413 0.300382i
\(532\) 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
\(537\) −12.3468 + 25.6084i −0.532802 + 1.10508i
\(538\) 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
\(549\) −25.0292 13.8630i −1.06822 0.591660i
\(550\) 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
\(555\) −0.864967 0.968789i −0.0367158 0.0411228i
\(556\) 0 0
\(557\) −17.5896 7.28584i −0.745294 0.308711i −0.0224743 0.999747i \(-0.507154\pi\)
−0.722820 + 0.691036i \(0.757154\pi\)
\(558\) 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 \(0.251861\pi\)
−0.999983 + 0.00584493i \(0.998139\pi\)
\(564\) 0 0
\(565\) −0.251458 + 0.104157i −0.0105789 + 0.00438194i
\(566\) 0 0
\(567\) −1.95168 3.11874i −0.0819630 0.130975i
\(568\) 0 0
\(569\) −15.9856 15.9856i −0.670152 0.670152i 0.287599 0.957751i \(-0.407143\pi\)
−0.957751 + 0.287599i \(0.907143\pi\)
\(570\) 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
\(573\) −20.1383 1.14018i −0.841290 0.0476317i
\(574\) 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
\(579\) 10.4314 + 0.590599i 0.433513 + 0.0245444i
\(580\) 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
\(585\) 0.220887 1.94444i 0.00913255 0.0803927i
\(586\) 0 0
\(587\) −14.4081 + 5.96803i −0.594686 + 0.246327i −0.659665 0.751560i \(-0.729302\pi\)
0.0649791 + 0.997887i \(0.479302\pi\)
\(588\) 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 \(-0.361148\pi\)
0.422512 + 0.906357i \(0.361148\pi\)
\(594\) 0 0
\(595\) 0.0593989 + 0.0246038i 0.00243512 + 0.00100866i
\(596\) 0 0
\(597\) 22.1983 + 24.8628i 0.908516 + 1.01757i
\(598\) 0 0
\(599\) 14.6016 + 14.6016i 0.596604 + 0.596604i 0.939407 0.342803i \(-0.111376\pi\)
−0.342803 + 0.939407i \(0.611376\pi\)
\(600\) 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
\(603\) 14.3050 25.8272i 0.582545 1.05176i
\(604\) 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
\(615\) −0.544710 + 1.12978i −0.0219648 + 0.0455571i
\(616\) 0 0
\(617\) 5.19834 5.19834i 0.209277 0.209277i −0.594683 0.803960i \(-0.702722\pi\)
0.803960 + 0.594683i \(0.202722\pi\)
\(618\) 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
\(621\) 21.3769 + 30.2156i 0.857824 + 1.21251i
\(622\) 0 0
\(623\) 3.14092i 0.125838i
\(624\) 0 0
\(625\) 24.4308i 0.977230i
\(626\) 0 0
\(627\) 35.1384 + 1.98945i 1.40329 + 0.0794510i
\(628\) 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
\(633\) −11.7231 5.65214i −0.465950 0.224652i
\(634\) 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 \(0.306904\pi\)
−0.570100 + 0.821575i \(0.693096\pi\)
\(642\) 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
\(645\) 1.67420 + 1.87515i 0.0659214 + 0.0738340i
\(646\) 0 0
\(647\) −31.4452 + 31.4452i −1.23624 + 1.23624i −0.274714 + 0.961526i \(0.588583\pi\)
−0.961526 + 0.274714i \(0.911417\pi\)
\(648\) 0 0
\(649\) 5.71128 + 5.71128i 0.224187 + 0.224187i
\(650\) 0 0
\(651\) 3.95240 3.52884i 0.154907 0.138306i
\(652\) 0 0
\(653\) −5.38622 2.23104i −0.210779 0.0873075i 0.274796 0.961503i \(-0.411390\pi\)
−0.485575 + 0.874195i \(0.661390\pi\)
\(654\) 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 −0.999683 0.0251602i \(-0.991990\pi\)
0.724674 + 0.689092i \(0.241990\pi\)
\(660\) 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
\(663\) 2.02845 4.20720i 0.0787786 0.163394i
\(664\) 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
\(669\) 0.631682 11.1570i 0.0244222 0.431355i
\(670\) 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
\(675\) 21.0481 14.8911i 0.810142 0.573157i
\(676\) 0 0
\(677\) −22.9138 + 9.49122i −0.880650 + 0.364777i −0.776749 0.629810i \(-0.783133\pi\)
−0.103901 + 0.994588i \(0.533133\pi\)
\(678\) 0 0
\(679\) −0.755613 0.755613i −0.0289978 0.0289978i
\(680\) 0 0
\(681\) −5.34661 2.57781i −0.204883 0.0987817i
\(682\) 0 0
\(683\) 34.5480 14.3103i 1.32194 0.547567i 0.393597 0.919283i \(-0.371231\pi\)
0.928346 + 0.371717i \(0.121231\pi\)
\(684\) 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
\(693\) 3.60965 + 1.99929i 0.137119 + 0.0759469i
\(694\) 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
\(699\) −28.3622 + 25.3227i −1.07276 + 0.957793i
\(700\) 0 0
\(701\) −6.56454 + 15.8482i −0.247939 + 0.598578i −0.998029 0.0627582i \(-0.980010\pi\)
0.750090 + 0.661336i \(0.230010\pi\)
\(702\) 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
\(711\) 23.8965 + 2.71463i 0.896190 + 0.101806i
\(712\) 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
\(717\) 2.18662 38.6208i 0.0816607 1.44232i
\(718\) 0 0
\(719\) 32.6392i 1.21724i −0.793463 0.608619i \(-0.791724\pi\)
0.793463 0.608619i \(-0.208276\pi\)
\(720\) 0 0
\(721\) 4.89649i 0.182355i
\(722\) 0 0
\(723\) 0.982456 17.3525i 0.0365379 0.645347i
\(724\) 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
\(729\) 25.4603 + 8.98742i 0.942974 + 0.332867i
\(730\) 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
\(741\) −26.0940 + 23.2976i −0.958589 + 0.855859i
\(742\) 0 0
\(743\) −15.0005 + 15.0005i −0.550313 + 0.550313i −0.926531 0.376218i \(-0.877224\pi\)
0.376218 + 0.926531i \(0.377224\pi\)
\(744\) 0 0
\(745\) 2.34240 + 2.34240i 0.0858188 + 0.0858188i
\(746\) 0 0
\(747\) −9.38625 + 16.9465i −0.343425 + 0.620040i
\(748\) 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
\(759\) −37.3933 18.0287i −1.35729 0.654402i
\(760\) 0 0
\(761\) 8.07215 + 8.07215i 0.292615 + 0.292615i 0.838112 0.545497i \(-0.183659\pi\)
−0.545497 + 0.838112i \(0.683659\pi\)
\(762\) 0 0
\(763\) −0.693996 + 0.287463i −0.0251243 + 0.0104068i
\(764\) 0 0
\(765\) −0.453512 + 0.130206i −0.0163968 + 0.00470759i
\(766\) 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
\(771\) −2.23075 + 39.4003i −0.0803384 + 1.41897i
\(772\) 0 0
\(773\) 29.1506 12.0746i 1.04848 0.434293i 0.209128 0.977888i \(-0.432937\pi\)
0.839347 + 0.543595i \(0.182937\pi\)
\(774\) 0 0
\(775\) 26.2564 + 26.2564i 0.943157 + 0.943157i
\(776\) 0 0
\(777\) −1.18209 + 2.45176i −0.0424072 + 0.0879565i
\(778\) 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
\(783\)