Properties

Label 768.2.o.b.95.3
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 95.3
Character \(\chi\) \(=\) 768.95
Dual form 768.2.o.b.671.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.25135 + 1.19755i) q^{3} +(2.18808 - 0.906333i) q^{5} +(-1.93241 - 1.93241i) q^{7} +(0.131733 - 2.99711i) q^{9} +O(q^{10})\) \(q+(-1.25135 + 1.19755i) q^{3} +(2.18808 - 0.906333i) q^{5} +(-1.93241 - 1.93241i) q^{7} +(0.131733 - 2.99711i) q^{9} +(-1.42447 + 0.590036i) q^{11} +(0.110405 - 0.266541i) q^{13} +(-1.65266 + 3.75448i) q^{15} -6.17031 q^{17} +(-7.34269 - 3.04144i) q^{19} +(4.73227 + 0.103949i) q^{21} +(1.85295 + 1.85295i) q^{23} +(0.430727 - 0.430727i) q^{25} +(3.42435 + 3.90817i) q^{27} +(-2.11574 + 5.10784i) q^{29} -3.42046i q^{31} +(1.07591 - 2.44422i) q^{33} +(-5.97967 - 2.47686i) q^{35} +(-2.52377 - 6.09293i) q^{37} +(0.181042 + 0.465751i) q^{39} +(-0.753641 + 0.753641i) q^{41} +(-1.57129 - 3.79343i) q^{43} +(-2.42813 - 6.67731i) q^{45} -1.54798i q^{47} +0.468394i q^{49} +(7.72119 - 7.38927i) q^{51} +(-5.12700 - 12.3777i) q^{53} +(-2.58210 + 2.58210i) q^{55} +(12.8305 - 4.98737i) q^{57} +(3.08775 + 7.45449i) q^{59} +(4.28571 + 1.77520i) q^{61} +(-6.04619 + 5.53707i) q^{63} -0.683277i q^{65} +(0.531731 - 1.28371i) q^{67} +(-4.53768 - 0.0996750i) q^{69} +(8.72539 - 8.72539i) q^{71} +(-2.73022 - 2.73022i) q^{73} +(-0.0231699 + 1.05481i) q^{75} +(3.89285 + 1.61247i) q^{77} -2.76080 q^{79} +(-8.96529 - 0.789635i) q^{81} +(-2.53133 + 6.11116i) q^{83} +(-13.5011 + 5.59235i) q^{85} +(-3.46939 - 8.92538i) q^{87} +(4.14369 + 4.14369i) q^{89} +(-0.728413 + 0.301719i) q^{91} +(4.09618 + 4.28017i) q^{93} -18.8230 q^{95} -10.3656 q^{97} +(1.58075 + 4.34703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

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
\(3\) −1.25135 + 1.19755i −0.722465 + 0.691408i
\(4\) 0 0
\(5\) 2.18808 0.906333i 0.978540 0.405324i 0.164655 0.986351i \(-0.447349\pi\)
0.813884 + 0.581027i \(0.197349\pi\)
\(6\) 0 0
\(7\) −1.93241 1.93241i −0.730381 0.730381i 0.240314 0.970695i \(-0.422750\pi\)
−0.970695 + 0.240314i \(0.922750\pi\)
\(8\) 0 0
\(9\) 0.131733 2.99711i 0.0439110 0.999035i
\(10\) 0 0
\(11\) −1.42447 + 0.590036i −0.429495 + 0.177903i −0.586949 0.809624i \(-0.699671\pi\)
0.157454 + 0.987526i \(0.449671\pi\)
\(12\) 0 0
\(13\) 0.110405 0.266541i 0.0306208 0.0739252i −0.907829 0.419340i \(-0.862262\pi\)
0.938450 + 0.345414i \(0.112262\pi\)
\(14\) 0 0
\(15\) −1.65266 + 3.75448i −0.426716 + 0.969402i
\(16\) 0 0
\(17\) −6.17031 −1.49652 −0.748260 0.663406i \(-0.769110\pi\)
−0.748260 + 0.663406i \(0.769110\pi\)
\(18\) 0 0
\(19\) −7.34269 3.04144i −1.68453 0.697755i −0.685004 0.728540i \(-0.740199\pi\)
−0.999526 + 0.0307845i \(0.990199\pi\)
\(20\) 0 0
\(21\) 4.73227 + 0.103949i 1.03267 + 0.0226836i
\(22\) 0 0
\(23\) 1.85295 + 1.85295i 0.386366 + 0.386366i 0.873389 0.487023i \(-0.161917\pi\)
−0.487023 + 0.873389i \(0.661917\pi\)
\(24\) 0 0
\(25\) 0.430727 0.430727i 0.0861453 0.0861453i
\(26\) 0 0
\(27\) 3.42435 + 3.90817i 0.659017 + 0.752128i
\(28\) 0 0
\(29\) −2.11574 + 5.10784i −0.392882 + 0.948501i 0.596427 + 0.802667i \(0.296587\pi\)
−0.989309 + 0.145834i \(0.953413\pi\)
\(30\) 0 0
\(31\) 3.42046i 0.614332i −0.951656 0.307166i \(-0.900619\pi\)
0.951656 0.307166i \(-0.0993807\pi\)
\(32\) 0 0
\(33\) 1.07591 2.44422i 0.187292 0.425485i
\(34\) 0 0
\(35\) −5.97967 2.47686i −1.01075 0.418666i
\(36\) 0 0
\(37\) −2.52377 6.09293i −0.414906 1.00167i −0.983801 0.179262i \(-0.942629\pi\)
0.568895 0.822410i \(-0.307371\pi\)
\(38\) 0 0
\(39\) 0.181042 + 0.465751i 0.0289900 + 0.0745798i
\(40\) 0 0
\(41\) −0.753641 + 0.753641i −0.117699 + 0.117699i −0.763503 0.645804i \(-0.776522\pi\)
0.645804 + 0.763503i \(0.276522\pi\)
\(42\) 0 0
\(43\) −1.57129 3.79343i −0.239619 0.578492i 0.757624 0.652691i \(-0.226360\pi\)
−0.997243 + 0.0741989i \(0.976360\pi\)
\(44\) 0 0
\(45\) −2.42813 6.67731i −0.361965 0.995394i
\(46\) 0 0
\(47\) 1.54798i 0.225796i −0.993607 0.112898i \(-0.963987\pi\)
0.993607 0.112898i \(-0.0360133\pi\)
\(48\) 0 0
\(49\) 0.468394i 0.0669135i
\(50\) 0 0
\(51\) 7.72119 7.38927i 1.08118 1.03471i
\(52\) 0 0
\(53\) −5.12700 12.3777i −0.704248 1.70020i −0.713897 0.700251i \(-0.753072\pi\)
0.00964932 0.999953i \(1.50307\pi\)
\(54\) 0 0
\(55\) −2.58210 + 2.58210i −0.348170 + 0.348170i
\(56\) 0 0
\(57\) 12.8305 4.98737i 1.69945 0.660593i
\(58\) 0 0
\(59\) 3.08775 + 7.45449i 0.401991 + 0.970492i 0.987182 + 0.159597i \(0.0510195\pi\)
−0.585191 + 0.810895i \(0.698981\pi\)
\(60\) 0 0
\(61\) 4.28571 + 1.77520i 0.548728 + 0.227291i 0.639784 0.768555i \(-0.279024\pi\)
−0.0910552 + 0.995846i \(0.529024\pi\)
\(62\) 0 0
\(63\) −6.04619 + 5.53707i −0.761748 + 0.697605i
\(64\) 0 0
\(65\) 0.683277i 0.0847501i
\(66\) 0 0
\(67\) 0.531731 1.28371i 0.0649613 0.156831i −0.888065 0.459718i \(-0.847951\pi\)
0.953026 + 0.302887i \(0.0979506\pi\)
\(68\) 0 0
\(69\) −4.53768 0.0996750i −0.546272 0.0119995i
\(70\) 0 0
\(71\) 8.72539 8.72539i 1.03551 1.03551i 0.0361678 0.999346i \(-0.488485\pi\)
0.999346 0.0361678i \(-0.0115151\pi\)
\(72\) 0 0
\(73\) −2.73022 2.73022i −0.319548 0.319548i 0.529046 0.848593i \(-0.322550\pi\)
−0.848593 + 0.529046i \(0.822550\pi\)
\(74\) 0 0
\(75\) −0.0231699 + 1.05481i −0.00267543 + 0.121799i
\(76\) 0 0
\(77\) 3.89285 + 1.61247i 0.443632 + 0.183758i
\(78\) 0 0
\(79\) −2.76080 −0.310614 −0.155307 0.987866i \(-0.549637\pi\)
−0.155307 + 0.987866i \(0.549637\pi\)
\(80\) 0 0
\(81\) −8.96529 0.789635i −0.996144 0.0877372i
\(82\) 0 0
\(83\) −2.53133 + 6.11116i −0.277849 + 0.670787i −0.999776 0.0211827i \(-0.993257\pi\)
0.721927 + 0.691970i \(0.243257\pi\)
\(84\) 0 0
\(85\) −13.5011 + 5.59235i −1.46440 + 0.606576i
\(86\) 0 0
\(87\) −3.46939 8.92538i −0.371958 0.956901i
\(88\) 0 0
\(89\) 4.14369 + 4.14369i 0.439230 + 0.439230i 0.891753 0.452523i \(-0.149476\pi\)
−0.452523 + 0.891753i \(0.649476\pi\)
\(90\) 0 0
\(91\) −0.728413 + 0.301719i −0.0763585 + 0.0316287i
\(92\) 0 0
\(93\) 4.09618 + 4.28017i 0.424754 + 0.443833i
\(94\) 0 0
\(95\) −18.8230 −1.93120
\(96\) 0 0
\(97\) −10.3656 −1.05246 −0.526232 0.850341i \(-0.676396\pi\)
−0.526232 + 0.850341i \(0.676396\pi\)
\(98\) 0 0
\(99\) 1.58075 + 4.34703i 0.158872 + 0.436893i
\(100\) 0 0
\(101\) 10.5700 4.37825i 1.05176 0.435652i 0.211238 0.977435i \(-0.432250\pi\)
0.840519 + 0.541783i \(0.182250\pi\)
\(102\) 0 0
\(103\) −10.4823 10.4823i −1.03285 1.03285i −0.999442 0.0334101i \(-0.989363\pi\)
−0.0334101 0.999442i \(-0.510637\pi\)
\(104\) 0 0
\(105\) 10.4488 4.06156i 1.01970 0.396368i
\(106\) 0 0
\(107\) 9.39578 3.89186i 0.908325 0.376240i 0.120910 0.992664i \(-0.461419\pi\)
0.787415 + 0.616423i \(0.211419\pi\)
\(108\) 0 0
\(109\) −3.00588 + 7.25683i −0.287911 + 0.695078i −0.999975 0.00703600i \(-0.997760\pi\)
0.712064 + 0.702114i \(0.247760\pi\)
\(110\) 0 0
\(111\) 10.4547 + 4.60201i 0.992318 + 0.436803i
\(112\) 0 0
\(113\) 13.6372 1.28288 0.641438 0.767175i \(-0.278338\pi\)
0.641438 + 0.767175i \(0.278338\pi\)
\(114\) 0 0
\(115\) 5.73378 + 2.37501i 0.534678 + 0.221471i
\(116\) 0 0
\(117\) −0.784308 0.366008i −0.0725093 0.0338374i
\(118\) 0 0
\(119\) 11.9235 + 11.9235i 1.09303 + 1.09303i
\(120\) 0 0
\(121\) −6.09719 + 6.09719i −0.554290 + 0.554290i
\(122\) 0 0
\(123\) 0.0405404 1.84559i 0.00365540 0.166411i
\(124\) 0 0
\(125\) −3.97958 + 9.60756i −0.355945 + 0.859326i
\(126\) 0 0
\(127\) 7.75395i 0.688052i 0.938960 + 0.344026i \(0.111791\pi\)
−0.938960 + 0.344026i \(0.888209\pi\)
\(128\) 0 0
\(129\) 6.50906 + 2.86519i 0.573090 + 0.252266i
\(130\) 0 0
\(131\) 1.16782 + 0.483728i 0.102033 + 0.0422635i 0.433116 0.901338i \(-0.357414\pi\)
−0.331083 + 0.943602i \(0.607414\pi\)
\(132\) 0 0
\(133\) 8.31177 + 20.0664i 0.720722 + 1.73998i
\(134\) 0 0
\(135\) 11.0349 + 5.44780i 0.949730 + 0.468872i
\(136\) 0 0
\(137\) −7.54494 + 7.54494i −0.644608 + 0.644608i −0.951685 0.307077i \(-0.900649\pi\)
0.307077 + 0.951685i \(0.400649\pi\)
\(138\) 0 0
\(139\) −0.412435 0.995705i −0.0349822 0.0844546i 0.905423 0.424511i \(-0.139554\pi\)
−0.940405 + 0.340056i \(0.889554\pi\)
\(140\) 0 0
\(141\) 1.85379 + 1.93706i 0.156117 + 0.163130i
\(142\) 0 0
\(143\) 0.444824i 0.0371980i
\(144\) 0 0
\(145\) 13.0939i 1.08739i
\(146\) 0 0
\(147\) −0.560927 0.586123i −0.0462645 0.0483426i
\(148\) 0 0
\(149\) 0.458938 + 1.10798i 0.0375977 + 0.0907689i 0.941563 0.336837i \(-0.109357\pi\)
−0.903965 + 0.427606i \(0.859357\pi\)
\(150\) 0 0
\(151\) 9.80869 9.80869i 0.798220 0.798220i −0.184595 0.982815i \(-0.559097\pi\)
0.982815 + 0.184595i \(0.0590974\pi\)
\(152\) 0 0
\(153\) −0.812833 + 18.4931i −0.0657136 + 1.49508i
\(154\) 0 0
\(155\) −3.10007 7.48424i −0.249004 0.601148i
\(156\) 0 0
\(157\) −8.28207 3.43055i −0.660981 0.273787i 0.0268702 0.999639i \(-0.491446\pi\)
−0.687851 + 0.725852i \(0.741446\pi\)
\(158\) 0 0
\(159\) 21.2386 + 9.34890i 1.68433 + 0.741416i
\(160\) 0 0
\(161\) 7.16129i 0.564389i
\(162\) 0 0
\(163\) 1.15049 2.77752i 0.0901131 0.217552i −0.872397 0.488798i \(-0.837436\pi\)
0.962510 + 0.271246i \(0.0874355\pi\)
\(164\) 0 0
\(165\) 0.138898 6.32329i 0.0108132 0.492267i
\(166\) 0 0
\(167\) −1.86833 + 1.86833i −0.144576 + 0.144576i −0.775690 0.631114i \(-0.782598\pi\)
0.631114 + 0.775690i \(0.282598\pi\)
\(168\) 0 0
\(169\) 9.13353 + 9.13353i 0.702579 + 0.702579i
\(170\) 0 0
\(171\) −10.0828 + 21.6062i −0.771051 + 1.65227i
\(172\) 0 0
\(173\) 9.59196 + 3.97312i 0.729263 + 0.302071i 0.716249 0.697845i \(-0.245857\pi\)
0.0130138 + 0.999915i \(0.495857\pi\)
\(174\) 0 0
\(175\) −1.66468 −0.125838
\(176\) 0 0
\(177\) −12.7910 5.63040i −0.961430 0.423207i
\(178\) 0 0
\(179\) −0.00532113 + 0.0128464i −0.000397720 + 0.000960181i −0.924078 0.382203i \(-0.875165\pi\)
0.923681 + 0.383163i \(0.125165\pi\)
\(180\) 0 0
\(181\) 9.45181 3.91507i 0.702547 0.291005i −0.00266940 0.999996i \(-0.500850\pi\)
0.705217 + 0.708992i \(0.250850\pi\)
\(182\) 0 0
\(183\) −7.48879 + 2.91097i −0.553588 + 0.215185i
\(184\) 0 0
\(185\) −11.0444 11.0444i −0.812004 0.812004i
\(186\) 0 0
\(187\) 8.78944 3.64071i 0.642748 0.266235i
\(188\) 0 0
\(189\) 0.934943 14.1694i 0.0680071 1.03067i
\(190\) 0 0
\(191\) 7.77941 0.562898 0.281449 0.959576i \(-0.409185\pi\)
0.281449 + 0.959576i \(0.409185\pi\)
\(192\) 0 0
\(193\) −6.23528 −0.448825 −0.224413 0.974494i \(-0.572046\pi\)
−0.224413 + 0.974494i \(0.572046\pi\)
\(194\) 0 0
\(195\) 0.818261 + 0.855016i 0.0585969 + 0.0612290i
\(196\) 0 0
\(197\) −6.90773 + 2.86128i −0.492156 + 0.203858i −0.614937 0.788576i \(-0.710819\pi\)
0.122781 + 0.992434i \(0.460819\pi\)
\(198\) 0 0
\(199\) 12.4517 + 12.4517i 0.882681 + 0.882681i 0.993806 0.111125i \(-0.0354455\pi\)
−0.111125 + 0.993806i \(0.535445\pi\)
\(200\) 0 0
\(201\) 0.871935 + 2.24315i 0.0615015 + 0.158219i
\(202\) 0 0
\(203\) 13.9589 5.78196i 0.979721 0.405814i
\(204\) 0 0
\(205\) −0.965978 + 2.33208i −0.0674668 + 0.162879i
\(206\) 0 0
\(207\) 5.79757 5.30938i 0.402959 0.369028i
\(208\) 0 0
\(209\) 12.2540 0.847630
\(210\) 0 0
\(211\) 1.16851 + 0.484011i 0.0804432 + 0.0333207i 0.422542 0.906343i \(-0.361138\pi\)
−0.342099 + 0.939664i \(0.611138\pi\)
\(212\) 0 0
\(213\) −0.469362 + 21.3676i −0.0321602 + 1.46408i
\(214\) 0 0
\(215\) −6.87622 6.87622i −0.468954 0.468954i
\(216\) 0 0
\(217\) −6.60972 + 6.60972i −0.448697 + 0.448697i
\(218\) 0 0
\(219\) 6.68602 + 0.146866i 0.451800 + 0.00992426i
\(220\) 0 0
\(221\) −0.681233 + 1.64464i −0.0458247 + 0.110631i
\(222\) 0 0
\(223\) 10.5047i 0.703449i −0.936104 0.351724i \(-0.885595\pi\)
0.936104 0.351724i \(-0.114405\pi\)
\(224\) 0 0
\(225\) −1.23419 1.34767i −0.0822795 0.0898450i
\(226\) 0 0
\(227\) −16.7869 6.95334i −1.11418 0.461509i −0.251806 0.967778i \(-0.581025\pi\)
−0.862376 + 0.506268i \(0.831025\pi\)
\(228\) 0 0
\(229\) −5.87646 14.1870i −0.388327 0.937505i −0.990295 0.138984i \(-0.955616\pi\)
0.601967 0.798521i \(-0.294384\pi\)
\(230\) 0 0
\(231\) −6.80233 + 2.64414i −0.447560 + 0.173972i
\(232\) 0 0
\(233\) 2.54073 2.54073i 0.166449 0.166449i −0.618968 0.785416i \(-0.712449\pi\)
0.785416 + 0.618968i \(0.212449\pi\)
\(234\) 0 0
\(235\) −1.40298 3.38711i −0.0915206 0.220950i
\(236\) 0 0
\(237\) 3.45471 3.30620i 0.224408 0.214761i
\(238\) 0 0
\(239\) 17.6107i 1.13914i −0.821943 0.569570i \(-0.807110\pi\)
0.821943 0.569570i \(-0.192890\pi\)
\(240\) 0 0
\(241\) 6.18628i 0.398493i 0.979949 + 0.199247i \(0.0638495\pi\)
−0.979949 + 0.199247i \(0.936151\pi\)
\(242\) 0 0
\(243\) 12.1643 9.74831i 0.780341 0.625354i
\(244\) 0 0
\(245\) 0.424521 + 1.02489i 0.0271217 + 0.0654775i
\(246\) 0 0
\(247\) −1.62134 + 1.62134i −0.103163 + 0.103163i
\(248\) 0 0
\(249\) −4.15088 10.6786i −0.263051 0.676727i
\(250\) 0 0
\(251\) −9.18840 22.1828i −0.579967 1.40016i −0.892842 0.450369i \(-0.851292\pi\)
0.312876 0.949794i \(1.60129\pi\)
\(252\) 0 0
\(253\) −3.73278 1.54617i −0.234678 0.0972067i
\(254\) 0 0
\(255\) 10.1975 23.1663i 0.638589 1.45073i
\(256\) 0 0
\(257\) 11.8836i 0.741276i 0.928777 + 0.370638i \(0.120861\pi\)
−0.928777 + 0.370638i \(0.879139\pi\)
\(258\) 0 0
\(259\) −6.89706 + 16.6510i −0.428563 + 1.03464i
\(260\) 0 0
\(261\) 15.0300 + 7.01395i 0.930335 + 0.434153i
\(262\) 0 0
\(263\) −11.6191 + 11.6191i −0.716464 + 0.716464i −0.967879 0.251415i \(-0.919104\pi\)
0.251415 + 0.967879i \(0.419104\pi\)
\(264\) 0 0
\(265\) −22.4366 22.4366i −1.37827 1.37827i
\(266\) 0 0
\(267\) −10.1475 0.222900i −0.621015 0.0136413i
\(268\) 0 0
\(269\) −13.7480 5.69459i −0.838228 0.347205i −0.0780733 0.996948i \(-0.524877\pi\)
−0.760155 + 0.649742i \(0.774877\pi\)
\(270\) 0 0
\(271\) 7.07297 0.429652 0.214826 0.976652i \(-0.431081\pi\)
0.214826 + 0.976652i \(0.431081\pi\)
\(272\) 0 0
\(273\) 0.550173 1.24987i 0.0332980 0.0756455i
\(274\) 0 0
\(275\) −0.359414 + 0.867703i −0.0216735 + 0.0523245i
\(276\) 0 0
\(277\) 1.13397 0.469705i 0.0681335 0.0282218i −0.348356 0.937362i \(-0.613260\pi\)
0.416490 + 0.909140i \(0.363260\pi\)
\(278\) 0 0
\(279\) −10.2515 0.450587i −0.613740 0.0269759i
\(280\) 0 0
\(281\) −12.0212 12.0212i −0.717122 0.717122i 0.250893 0.968015i \(-0.419276\pi\)
−0.968015 + 0.250893i \(0.919276\pi\)
\(282\) 0 0
\(283\) −12.8158 + 5.30848i −0.761821 + 0.315557i −0.729555 0.683923i \(-0.760273\pi\)
−0.0322666 + 0.999479i \(0.510273\pi\)
\(284\) 0 0
\(285\) 23.5541 22.5415i 1.39522 1.33524i
\(286\) 0 0
\(287\) 2.91268 0.171930
\(288\) 0 0
\(289\) 21.0727 1.23957
\(290\) 0 0
\(291\) 12.9709 12.4133i 0.760369 0.727682i
\(292\) 0 0
\(293\) −24.7412 + 10.2481i −1.44539 + 0.598702i −0.961099 0.276203i \(-0.910924\pi\)
−0.484295 + 0.874905i \(0.660924\pi\)
\(294\) 0 0
\(295\) 13.5125 + 13.5125i 0.786729 + 0.786729i
\(296\) 0 0
\(297\) −7.18386 3.54660i −0.416850 0.205795i
\(298\) 0 0
\(299\) 0.698461 0.289312i 0.0403930 0.0167313i
\(300\) 0 0
\(301\) −4.29408 + 10.3668i −0.247506 + 0.597533i
\(302\) 0 0
\(303\) −7.98357 + 18.1369i −0.458644 + 1.04194i
\(304\) 0 0
\(305\) 10.9864 0.629079
\(306\) 0 0
\(307\) 0.664375 + 0.275193i 0.0379179 + 0.0157061i 0.401562 0.915832i \(-0.368468\pi\)
−0.363644 + 0.931538i \(0.618468\pi\)
\(308\) 0 0
\(309\) 25.6701 + 0.563871i 1.46032 + 0.0320775i
\(310\) 0 0
\(311\) 3.60638 + 3.60638i 0.204499 + 0.204499i 0.801924 0.597425i \(-0.203810\pi\)
−0.597425 + 0.801924i \(0.703810\pi\)
\(312\) 0 0
\(313\) 23.2233 23.2233i 1.31266 1.31266i 0.393210 0.919449i \(-0.371365\pi\)
0.919449 0.393210i \(-0.128635\pi\)
\(314\) 0 0
\(315\) −8.21113 + 17.5954i −0.462645 + 0.991389i
\(316\) 0 0
\(317\) −1.42053 + 3.42947i −0.0797850 + 0.192618i −0.958738 0.284289i \(-0.908242\pi\)
0.878954 + 0.476907i \(0.158242\pi\)
\(318\) 0 0
\(319\) 8.52434i 0.477271i
\(320\) 0 0
\(321\) −7.09666 + 16.1220i −0.396097 + 0.899843i
\(322\) 0 0
\(323\) 45.3067 + 18.7666i 2.52093 + 1.04420i
\(324\) 0 0
\(325\) −0.0672520 0.162361i −0.00373047 0.00900615i
\(326\) 0 0
\(327\) −4.92905 12.6805i −0.272577 0.701233i
\(328\) 0 0
\(329\) −2.99133 + 2.99133i −0.164917 + 0.164917i
\(330\) 0 0
\(331\) 3.25086 + 7.84826i 0.178683 + 0.431380i 0.987691 0.156419i \(-0.0499949\pi\)
−0.809008 + 0.587798i \(0.799995\pi\)
\(332\) 0 0
\(333\) −18.5936 + 6.76138i −1.01892 + 0.370521i
\(334\) 0 0
\(335\) 3.29079i 0.179795i
\(336\) 0 0
\(337\) 24.2771i 1.32246i −0.750183 0.661230i \(-0.770035\pi\)
0.750183 0.661230i \(-0.229965\pi\)
\(338\) 0 0
\(339\) −17.0648 + 16.3312i −0.926833 + 0.886990i
\(340\) 0 0
\(341\) 2.01819 + 4.87235i 0.109291 + 0.263853i
\(342\) 0 0
\(343\) −12.6217 + 12.6217i −0.681509 + 0.681509i
\(344\) 0 0
\(345\) −10.0191 + 3.89455i −0.539413 + 0.209676i
\(346\) 0 0
\(347\) 1.37907 + 3.32937i 0.0740325 + 0.178730i 0.956564 0.291524i \(-0.0941623\pi\)
−0.882531 + 0.470254i \(0.844162\pi\)
\(348\) 0 0
\(349\) −10.7378 4.44775i −0.574782 0.238083i 0.0763062 0.997084i \(-0.475687\pi\)
−0.651089 + 0.759002i \(0.725687\pi\)
\(350\) 0 0
\(351\) 1.41975 0.481249i 0.0757809 0.0256871i
\(352\) 0 0
\(353\) 5.62531i 0.299405i 0.988731 + 0.149703i \(0.0478316\pi\)
−0.988731 + 0.149703i \(0.952168\pi\)
\(354\) 0 0
\(355\) 11.1838 27.0000i 0.593572 1.43301i
\(356\) 0 0
\(357\) −29.1996 0.641400i −1.54540 0.0339465i
\(358\) 0 0
\(359\) −22.3781 + 22.3781i −1.18107 + 1.18107i −0.201603 + 0.979467i \(0.564615\pi\)
−0.979467 + 0.201603i \(0.935385\pi\)
\(360\) 0 0
\(361\) 31.2298 + 31.2298i 1.64367 + 1.64367i
\(362\) 0 0
\(363\) 0.327984 14.9314i 0.0172147 0.783696i
\(364\) 0 0
\(365\) −8.44842 3.49945i −0.442211 0.183170i
\(366\) 0 0
\(367\) −26.0135 −1.35789 −0.678946 0.734188i \(-0.737563\pi\)
−0.678946 + 0.734188i \(0.737563\pi\)
\(368\) 0 0
\(369\) 2.15946 + 2.35802i 0.112417 + 0.122754i
\(370\) 0 0
\(371\) −14.0113 + 33.8262i −0.727428 + 1.75617i
\(372\) 0 0
\(373\) 16.7694 6.94611i 0.868286 0.359656i 0.0963434 0.995348i \(-0.469285\pi\)
0.771942 + 0.635692i \(0.219285\pi\)
\(374\) 0 0
\(375\) −6.52573 16.7881i −0.336987 0.866936i
\(376\) 0 0
\(377\) 1.12786 + 1.12786i 0.0580878 + 0.0580878i
\(378\) 0 0
\(379\) −11.8673 + 4.91559i −0.609582 + 0.252497i −0.666050 0.745907i \(-0.732016\pi\)
0.0564681 + 0.998404i \(0.482016\pi\)
\(380\) 0 0
\(381\) −9.28576 9.70287i −0.475724 0.497093i
\(382\) 0 0
\(383\) −5.25906 −0.268725 −0.134363 0.990932i \(-0.542899\pi\)
−0.134363 + 0.990932i \(0.542899\pi\)
\(384\) 0 0
\(385\) 9.97932 0.508593
\(386\) 0 0
\(387\) −11.5763 + 4.20960i −0.588456 + 0.213986i
\(388\) 0 0
\(389\) 25.9373 10.7436i 1.31507 0.544721i 0.388712 0.921359i \(-0.372920\pi\)
0.926360 + 0.376639i \(0.122920\pi\)
\(390\) 0 0
\(391\) −11.4333 11.4333i −0.578204 0.578204i
\(392\) 0 0
\(393\) −2.04064 + 0.793219i −0.102937 + 0.0400126i
\(394\) 0 0
\(395\) −6.04085 + 2.50220i −0.303948 + 0.125899i
\(396\) 0 0
\(397\) 14.4580 34.9046i 0.725624 1.75181i 0.0689699 0.997619i \(-0.478029\pi\)
0.656654 0.754192i \(-0.271971\pi\)
\(398\) 0 0
\(399\) −34.4315 15.1562i −1.72373 0.758759i
\(400\) 0 0
\(401\) 31.7191 1.58397 0.791987 0.610537i \(-0.209046\pi\)
0.791987 + 0.610537i \(0.209046\pi\)
\(402\) 0 0
\(403\) −0.911693 0.377635i −0.0454146 0.0188114i
\(404\) 0 0
\(405\) −20.3325 + 6.39776i −1.01033 + 0.317907i
\(406\) 0 0
\(407\) 7.19010 + 7.19010i 0.356400 + 0.356400i
\(408\) 0 0
\(409\) −17.8308 + 17.8308i −0.881677 + 0.881677i −0.993705 0.112028i \(-0.964265\pi\)
0.112028 + 0.993705i \(0.464265\pi\)
\(410\) 0 0
\(411\) 0.405863 18.4768i 0.0200197 0.911393i
\(412\) 0 0
\(413\) 8.43832 20.3719i 0.415223 1.00244i
\(414\) 0 0
\(415\) 15.6659i 0.769011i
\(416\) 0 0
\(417\) 1.70851 + 0.752059i 0.0836660 + 0.0368285i
\(418\) 0 0
\(419\) 2.10652 + 0.872548i 0.102910 + 0.0426268i 0.433544 0.901132i \(-0.357263\pi\)
−0.330634 + 0.943759i \(0.607263\pi\)
\(420\) 0 0
\(421\) 0.169965 + 0.410331i 0.00828357 + 0.0199983i 0.927967 0.372662i \(-0.121555\pi\)
−0.919684 + 0.392660i \(0.871555\pi\)
\(422\) 0 0
\(423\) −4.63946 0.203920i −0.225578 0.00991492i
\(424\) 0 0
\(425\) −2.65772 + 2.65772i −0.128918 + 0.128918i
\(426\) 0 0
\(427\) −4.85132 11.7121i −0.234772 0.566790i
\(428\) 0 0
\(429\) −0.532700 0.556628i −0.0257190 0.0268743i
\(430\) 0 0
\(431\) 2.95351i 0.142266i −0.997467 0.0711329i \(-0.977339\pi\)
0.997467 0.0711329i \(-0.0226614\pi\)
\(432\) 0 0
\(433\) 31.3472i 1.50645i −0.657764 0.753224i \(-0.728497\pi\)
0.657764 0.753224i \(-0.271503\pi\)
\(434\) 0 0
\(435\) −15.6807 16.3850i −0.751830 0.785602i
\(436\) 0 0
\(437\) −7.96999 19.2413i −0.381256 0.920434i
\(438\) 0 0
\(439\) −7.44392 + 7.44392i −0.355279 + 0.355279i −0.862069 0.506791i \(-0.830832\pi\)
0.506791 + 0.862069i \(0.330832\pi\)
\(440\) 0 0
\(441\) 1.40383 + 0.0617029i 0.0668489 + 0.00293824i
\(442\) 0 0
\(443\) −3.50021 8.45026i −0.166300 0.401484i 0.818657 0.574283i \(-0.194719\pi\)
−0.984957 + 0.172799i \(0.944719\pi\)
\(444\) 0 0
\(445\) 12.8223 + 5.31117i 0.607835 + 0.251773i
\(446\) 0 0
\(447\) −1.90115 0.836857i −0.0899213 0.0395820i
\(448\) 0 0
\(449\) 24.0900i 1.13688i −0.822725 0.568439i \(-0.807547\pi\)
0.822725 0.568439i \(-0.192453\pi\)
\(450\) 0 0
\(451\) 0.628866 1.51822i 0.0296121 0.0714901i
\(452\) 0 0
\(453\) −0.527636 + 24.0205i −0.0247905 + 1.12858i
\(454\) 0 0
\(455\) −1.32037 + 1.32037i −0.0618999 + 0.0618999i
\(456\) 0 0
\(457\) −13.8807 13.8807i −0.649311 0.649311i 0.303515 0.952827i \(-0.401840\pi\)
−0.952827 + 0.303515i \(0.901840\pi\)
\(458\) 0 0
\(459\) −21.1293 24.1146i −0.986231 1.12557i
\(460\) 0 0
\(461\) 26.4361 + 10.9502i 1.23125 + 0.510001i 0.900970 0.433881i \(-0.142856\pi\)
0.330282 + 0.943882i \(0.392856\pi\)
\(462\) 0 0
\(463\) 35.7558 1.66171 0.830857 0.556485i \(-0.187850\pi\)
0.830857 + 0.556485i \(0.187850\pi\)
\(464\) 0 0
\(465\) 12.8420 + 5.65287i 0.595535 + 0.262145i
\(466\) 0 0
\(467\) −1.84875 + 4.46327i −0.0855498 + 0.206536i −0.960865 0.277018i \(-0.910654\pi\)
0.875315 + 0.483553i \(0.160654\pi\)
\(468\) 0 0
\(469\) −3.50818 + 1.45313i −0.161993 + 0.0670995i
\(470\) 0 0
\(471\) 14.4720 5.62542i 0.666834 0.259206i
\(472\) 0 0
\(473\) 4.47652 + 4.47652i 0.205831 + 0.205831i
\(474\) 0 0
\(475\) −4.47273 + 1.85266i −0.205223 + 0.0850060i
\(476\) 0 0
\(477\) −37.7726 + 13.7356i −1.72949 + 0.628911i
\(478\) 0 0
\(479\) 15.8988 0.726433 0.363216 0.931705i \(-0.381679\pi\)
0.363216 + 0.931705i \(0.381679\pi\)
\(480\) 0 0
\(481\) −1.90265 −0.0867535
\(482\) 0 0
\(483\) 8.57603 + 8.96126i 0.390223 + 0.407751i
\(484\) 0 0
\(485\) −22.6807 + 9.39466i −1.02988 + 0.426590i
\(486\) 0 0
\(487\) −10.4283 10.4283i −0.472552 0.472552i 0.430187 0.902740i \(-0.358448\pi\)
−0.902740 + 0.430187i \(0.858448\pi\)
\(488\) 0 0
\(489\) 1.88657 + 4.85341i 0.0853138 + 0.219479i
\(490\) 0 0
\(491\) −0.306137 + 0.126806i −0.0138158 + 0.00572268i −0.389581 0.920992i \(-0.627380\pi\)
0.375765 + 0.926715i \(0.377380\pi\)
\(492\) 0 0
\(493\) 13.0547 31.5169i 0.587956 1.41945i
\(494\) 0 0
\(495\) 7.39867 + 8.07896i 0.332545 + 0.363122i
\(496\) 0 0
\(497\) −33.7220 −1.51264
\(498\) 0 0
\(499\) −5.62549 2.33015i −0.251831 0.104312i 0.253197 0.967415i \(-0.418518\pi\)
−0.505028 + 0.863103i \(0.668518\pi\)
\(500\) 0 0
\(501\) 0.100502 4.57535i 0.00449012 0.204411i
\(502\) 0 0
\(503\) −10.6198 10.6198i −0.473513 0.473513i 0.429536 0.903050i \(-0.358677\pi\)
−0.903050 + 0.429536i \(0.858677\pi\)
\(504\) 0 0
\(505\) 19.1599 19.1599i 0.852605 0.852605i
\(506\) 0 0
\(507\) −22.3671 0.491317i −0.993358 0.0218202i
\(508\) 0 0
\(509\) 2.01172 4.85673i 0.0891681 0.215271i −0.873004 0.487713i \(-0.837831\pi\)
0.962172 + 0.272442i \(0.0878313\pi\)
\(510\) 0 0
\(511\) 10.5518i 0.466783i
\(512\) 0 0
\(513\) −13.2575 39.1115i −0.585332 1.72681i
\(514\) 0 0
\(515\) −32.4366 13.4357i −1.42933 0.592046i
\(516\) 0 0
\(517\) 0.913364 + 2.20506i 0.0401697 + 0.0969783i
\(518\) 0 0
\(519\) −16.7609 + 6.51513i −0.735721 + 0.285983i
\(520\) 0 0
\(521\) −19.9974 + 19.9974i −0.876102 + 0.876102i −0.993129 0.117027i \(-0.962664\pi\)
0.117027 + 0.993129i \(0.462664\pi\)
\(522\) 0 0
\(523\) 15.2948 + 36.9248i 0.668793 + 1.61461i 0.783632 + 0.621225i \(0.213365\pi\)
−0.114839 + 0.993384i \(0.536635\pi\)
\(524\) 0 0
\(525\) 2.08309 1.99354i 0.0909134 0.0870053i
\(526\) 0 0
\(527\) 21.1053i 0.919360i
\(528\) 0 0
\(529\) 16.1332i 0.701443i
\(530\) 0 0
\(531\) 22.7487 8.27232i 0.987208 0.358988i
\(532\) 0 0
\(533\) 0.117671 + 0.284082i 0.00509688 + 0.0123050i
\(534\) 0 0
\(535\) 17.0314 17.0314i 0.736332 0.736332i
\(536\) 0 0
\(537\) −0.00872561 0.0224476i −0.000376538 0.000968684i
\(538\) 0 0
\(539\) −0.276370 0.667216i −0.0119041 0.0287390i
\(540\) 0 0
\(541\) 35.6786 + 14.7786i 1.53394 + 0.635380i 0.980325 0.197391i \(-0.0632468\pi\)
0.553618 + 0.832771i \(0.313247\pi\)
\(542\) 0 0
\(543\) −7.13898 + 16.2181i −0.306363 + 0.695987i
\(544\) 0 0
\(545\) 18.6029i 0.796859i
\(546\) 0 0
\(547\) −12.4112 + 29.9634i −0.530666 + 1.28114i 0.400416 + 0.916333i \(0.368865\pi\)
−0.931083 + 0.364808i \(0.881135\pi\)
\(548\) 0 0
\(549\) 5.88502 12.6109i 0.251167 0.538219i
\(550\) 0 0
\(551\) 31.0704 31.0704i 1.32364 1.32364i
\(552\) 0 0
\(553\) 5.33499 + 5.33499i 0.226867 + 0.226867i
\(554\) 0 0
\(555\) 27.0467 + 0.594111i 1.14807 + 0.0252186i
\(556\) 0 0
\(557\) 9.30090 + 3.85256i 0.394092 + 0.163238i 0.570924 0.821003i \(-0.306585\pi\)
−0.176832 + 0.984241i \(0.556585\pi\)
\(558\) 0 0
\(559\) −1.18458 −0.0501025
\(560\) 0 0
\(561\) −6.63869 + 15.0816i −0.280286 + 0.636746i
\(562\) 0 0
\(563\) 1.24166 2.99763i 0.0523297 0.126335i −0.895553 0.444955i \(-0.853220\pi\)
0.947882 + 0.318620i \(0.103220\pi\)
\(564\) 0 0
\(565\) 29.8392 12.3598i 1.25535 0.519981i
\(566\) 0 0
\(567\) 15.7987 + 18.8505i 0.663483 + 0.791646i
\(568\) 0 0
\(569\) −28.3250 28.3250i −1.18745 1.18745i −0.977771 0.209674i \(-0.932760\pi\)
−0.209674 0.977771i \(1.43276\pi\)
\(570\) 0 0
\(571\) 37.5476 15.5527i 1.57132 0.650862i 0.584310 0.811530i \(-0.301365\pi\)
0.987008 + 0.160669i \(0.0513651\pi\)
\(572\) 0 0
\(573\) −9.73473 + 9.31626i −0.406674 + 0.389192i
\(574\) 0 0
\(575\) 1.59623 0.0665673
\(576\) 0 0
\(577\) 5.37886 0.223925 0.111962 0.993712i \(-0.464286\pi\)
0.111962 + 0.993712i \(0.464286\pi\)
\(578\) 0 0
\(579\) 7.80249 7.46708i 0.324260 0.310321i
\(580\) 0 0
\(581\) 16.7008 6.91770i 0.692866 0.286994i
\(582\) 0 0
\(583\) 14.6066 + 14.6066i 0.604942 + 0.604942i
\(584\) 0 0
\(585\) −2.04785 0.0900101i −0.0846684 0.00372146i
\(586\) 0 0
\(587\) 1.77252 0.734203i 0.0731599 0.0303038i −0.345803 0.938307i \(-0.612394\pi\)
0.418963 + 0.908003i \(0.362394\pi\)
\(588\) 0 0
\(589\) −10.4031 + 25.1154i −0.428653 + 1.03486i
\(590\) 0 0
\(591\) 5.21743 11.8528i 0.214616 0.487560i
\(592\) 0 0
\(593\) −24.1664 −0.992394 −0.496197 0.868210i \(-0.665271\pi\)
−0.496197 + 0.868210i \(0.665271\pi\)
\(594\) 0 0
\(595\) 36.8964 + 15.2830i 1.51260 + 0.626541i
\(596\) 0 0
\(597\) −30.4931 0.669813i −1.24800 0.0274136i
\(598\) 0 0
\(599\) 11.6692 + 11.6692i 0.476789 + 0.476789i 0.904103 0.427314i \(-0.140540\pi\)
−0.427314 + 0.904103i \(0.640540\pi\)
\(600\) 0 0
\(601\) −8.80143 + 8.80143i −0.359018 + 0.359018i −0.863451 0.504433i \(-0.831702\pi\)
0.504433 + 0.863451i \(0.331702\pi\)
\(602\) 0 0
\(603\) −3.77738 1.76276i −0.153827 0.0717852i
\(604\) 0 0
\(605\) −7.81507 + 18.8672i −0.317728 + 0.767062i
\(606\) 0 0
\(607\) 31.9215i 1.29565i −0.761788 0.647826i \(-0.775678\pi\)
0.761788 0.647826i \(-0.224322\pi\)
\(608\) 0 0
\(609\) −10.5432 + 23.9517i −0.427231 + 0.970573i
\(610\) 0 0
\(611\) −0.412600 0.170905i −0.0166920 0.00691406i
\(612\) 0 0
\(613\) −7.35458 17.7555i −0.297049 0.717139i −0.999983 0.00588391i \(-0.998127\pi\)
0.702934 0.711255i \(-0.251873\pi\)
\(614\) 0 0
\(615\) −1.58401 4.07504i −0.0638736 0.164322i
\(616\) 0 0
\(617\) 13.5933 13.5933i 0.547246 0.547246i −0.378397 0.925643i \(-0.623525\pi\)
0.925643 + 0.378397i \(0.123525\pi\)
\(618\) 0 0
\(619\) 3.75210 + 9.05838i 0.150810 + 0.364087i 0.981172 0.193137i \(-0.0618663\pi\)
−0.830362 + 0.557224i \(0.811866\pi\)
\(620\) 0 0
\(621\) −0.896498 + 13.5868i −0.0359752 + 0.545219i
\(622\) 0 0
\(623\) 16.0146i 0.641611i
\(624\) 0 0
\(625\) 27.6746i 1.10699i
\(626\) 0 0
\(627\) −15.3340 + 14.6749i −0.612383 + 0.586058i
\(628\) 0 0
\(629\) 15.5725 + 37.5953i 0.620915 + 1.49902i
\(630\) 0 0
\(631\) 5.39207 5.39207i 0.214655 0.214655i −0.591587 0.806242i \(-0.701498\pi\)
0.806242 + 0.591587i \(0.201498\pi\)
\(632\) 0 0
\(633\) −2.04183 + 0.793682i −0.0811556 + 0.0315460i
\(634\) 0 0
\(635\) 7.02766 + 16.9663i 0.278884 + 0.673286i
\(636\) 0 0
\(637\) 0.124846 + 0.0517131i 0.00494659 + 0.00204895i
\(638\) 0 0
\(639\) −25.0015 27.3003i −0.989044 1.07999i
\(640\) 0 0
\(641\) 1.82203i 0.0719659i 0.999352 + 0.0359830i \(0.0114562\pi\)
−0.999352 + 0.0359830i \(0.988544\pi\)
\(642\) 0 0
\(643\) 10.4095 25.1308i 0.410511 0.991062i −0.574489 0.818512i \(-0.694799\pi\)
0.985001 0.172550i \(-0.0552007\pi\)
\(644\) 0 0
\(645\) 16.8392 + 0.369890i 0.663041 + 0.0145644i
\(646\) 0 0
\(647\) 27.3258 27.3258i 1.07429 1.07429i 0.0772785 0.997010i \(-0.475377\pi\)
0.997010 0.0772785i \(-0.0246231\pi\)
\(648\) 0 0
\(649\) −8.79684 8.79684i −0.345306 0.345306i
\(650\) 0 0
\(651\) 0.355554 16.1865i 0.0139353 0.634400i
\(652\) 0 0
\(653\) −21.5061 8.90811i −0.841598 0.348601i −0.0801145 0.996786i \(-0.525529\pi\)
−0.761483 + 0.648184i \(0.775529\pi\)
\(654\) 0 0
\(655\) 2.99371 0.116974
\(656\) 0 0
\(657\) −8.54241 + 7.82309i −0.333271 + 0.305208i
\(658\) 0 0
\(659\) 17.2778 41.7123i 0.673048 1.62488i −0.103355 0.994644i \(-0.532958\pi\)
0.776403 0.630237i \(-0.217042\pi\)
\(660\) 0 0
\(661\) −44.7407 + 18.5322i −1.74021 + 0.720819i −0.741453 + 0.671005i \(0.765863\pi\)
−0.998759 + 0.0498140i \(0.984137\pi\)
\(662\) 0 0
\(663\) −1.11709 2.87383i −0.0433841 0.111610i
\(664\) 0 0
\(665\) 36.3736 + 36.3736i 1.41051 + 1.41051i
\(666\) 0 0
\(667\) −13.3849 + 5.54420i −0.518265 + 0.214672i
\(668\) 0 0
\(669\) 12.5800 + 13.1451i 0.486370 + 0.508217i
\(670\) 0 0
\(671\) −7.15231 −0.276112
\(672\) 0 0
\(673\) −10.8139 −0.416844 −0.208422 0.978039i \(-0.566833\pi\)
−0.208422 + 0.978039i \(0.566833\pi\)
\(674\) 0 0
\(675\) 3.15831 + 0.208395i 0.121564 + 0.00802114i
\(676\) 0 0
\(677\) 16.7436 6.93541i 0.643507 0.266549i −0.0369727 0.999316i \(-0.511771\pi\)
0.680480 + 0.732767i \(0.261771\pi\)
\(678\) 0 0
\(679\) 20.0305 + 20.0305i 0.768701 + 0.768701i
\(680\) 0 0
\(681\) 29.3332 11.4021i 1.12405 0.436930i
\(682\) 0 0
\(683\) −43.5660 + 18.0456i −1.66701 + 0.690497i −0.998580 0.0532798i \(-0.983032\pi\)
−0.668428 + 0.743777i \(0.733032\pi\)
\(684\) 0 0
\(685\) −9.67071 + 23.3472i −0.369499 + 0.892049i
\(686\) 0 0
\(687\) 24.3432 + 10.7155i 0.928751 + 0.408822i
\(688\) 0 0
\(689\) −3.86521 −0.147253
\(690\) 0 0
\(691\) 5.29763 + 2.19435i 0.201531 + 0.0834771i 0.481166 0.876629i \(-0.340213\pi\)
−0.279635 + 0.960106i \(0.590213\pi\)
\(692\) 0 0
\(693\) 5.34557 11.4549i 0.203061 0.435135i
\(694\) 0 0
\(695\) −1.80488 1.80488i −0.0684630 0.0684630i
\(696\) 0 0
\(697\) 4.65020 4.65020i 0.176139 0.176139i
\(698\) 0 0
\(699\) −0.136673 + 6.22199i −0.00516943 + 0.235337i
\(700\) 0 0
\(701\) 13.7184 33.1190i 0.518135 1.25089i −0.420912 0.907101i \(-0.638290\pi\)
0.939047 0.343787i \(-0.111710\pi\)
\(702\) 0 0
\(703\) 52.4144i 1.97685i
\(704\) 0 0
\(705\) 5.81186 + 2.55829i 0.218887 + 0.0963508i
\(706\) 0 0
\(707\) −28.8861 11.9650i −1.08638 0.449991i
\(708\) 0 0
\(709\) 1.39804 + 3.37516i 0.0525044 + 0.126757i 0.947955 0.318403i \(-0.103147\pi\)
−0.895451 + 0.445160i \(0.853147\pi\)
\(710\) 0 0
\(711\) −0.363688 + 8.27440i −0.0136394 + 0.310314i
\(712\) 0 0
\(713\) 6.33792 6.33792i 0.237357 0.237357i
\(714\) 0 0
\(715\) 0.403158 + 0.973311i 0.0150773 + 0.0363998i
\(716\) 0 0
\(717\) 21.0897 + 22.0371i 0.787610 + 0.822989i
\(718\) 0 0
\(719\) 25.3851i 0.946706i 0.880873 + 0.473353i \(0.156956\pi\)
−0.880873 + 0.473353i \(0.843044\pi\)
\(720\) 0 0
\(721\) 40.5121i 1.50875i
\(722\) 0 0
\(723\) −7.40840 7.74117i −0.275521 0.287897i
\(724\) 0 0
\(725\) 1.28878 + 3.11138i 0.0478640 + 0.115554i
\(726\) 0 0
\(727\) −32.5294 + 32.5294i −1.20645 + 1.20645i −0.234280 + 0.972169i \(0.575273\pi\)
−0.972169 + 0.234280i \(0.924727\pi\)
\(728\) 0 0
\(729\) −3.54764 + 26.7659i −0.131394 + 0.991330i
\(730\) 0 0
\(731\) 9.69534 + 23.4066i 0.358595 + 0.865725i
\(732\) 0 0
\(733\) −26.3419 10.9112i −0.972961 0.403014i −0.161147 0.986930i \(-0.551519\pi\)
−0.811814 + 0.583917i \(0.801519\pi\)
\(734\) 0 0
\(735\) −1.75858 0.774099i −0.0648661 0.0285531i
\(736\) 0 0
\(737\) 2.14236i 0.0789147i
\(738\) 0 0
\(739\) −13.4201 + 32.3991i −0.493668 + 1.19182i 0.459172 + 0.888347i \(0.348146\pi\)
−0.952840 + 0.303473i \(0.901854\pi\)
\(740\) 0 0
\(741\) 0.0872162 3.97050i 0.00320397 0.145860i
\(742\) 0 0
\(743\) 5.42669 5.42669i 0.199086 0.199086i −0.600522 0.799608i \(-0.705041\pi\)
0.799608 + 0.600522i \(0.205041\pi\)
\(744\) 0 0
\(745\) 2.00839 + 2.00839i 0.0735817 + 0.0735817i
\(746\) 0 0
\(747\) 17.9823 + 8.39169i 0.657939 + 0.307036i
\(748\) 0 0
\(749\) −25.6771 10.6358i −0.938222 0.388624i
\(750\) 0 0
\(751\) 3.67683 0.134170 0.0670848 0.997747i \(-0.478630\pi\)
0.0670848 + 0.997747i \(0.478630\pi\)
\(752\) 0 0
\(753\) 38.0629 + 16.7547i 1.38709 + 0.610576i
\(754\) 0 0
\(755\) 12.5723 30.3521i 0.457552 1.10463i
\(756\) 0 0
\(757\) 13.0816 5.41857i 0.475458 0.196941i −0.132068 0.991241i \(-0.542162\pi\)
0.607526 + 0.794299i \(0.292162\pi\)
\(758\) 0 0
\(759\) 6.52262 2.53541i 0.236756 0.0920296i
\(760\) 0 0
\(761\) 25.8277 + 25.8277i 0.936254 + 0.936254i 0.998087 0.0618325i \(-0.0196945\pi\)
−0.0618325 + 0.998087i \(0.519694\pi\)
\(762\) 0 0
\(763\) 19.8317 8.21457i 0.717957 0.297387i
\(764\) 0 0
\(765\) 14.9823 + 41.2010i 0.541688 + 1.48963i
\(766\) 0 0
\(767\) 2.32783 0.0840532
\(768\) 0 0
\(769\) −22.8386 −0.823580 −0.411790 0.911279i \(-0.635096\pi\)
−0.411790 + 0.911279i \(0.635096\pi\)
\(770\) 0 0
\(771\) −14.2312 14.8704i −0.512524 0.535546i
\(772\) 0 0
\(773\) 8.07057 3.34294i 0.290278 0.120237i −0.232793 0.972526i \(-0.574786\pi\)
0.523071 + 0.852289i \(0.324786\pi\)
\(774\) 0 0
\(775\) −1.47328 1.47328i −0.0529219 0.0529219i
\(776\) 0 0
\(777\) −11.3098 29.0957i −0.405738 1.04380i
\(778\) 0 0
\(779\) 7.82591 3.24160i 0.280392 0.116142i
\(780\) 0 0
\(781\) −7.28079 + 17.5774i −0.260527 + 0.628968i
\(782\) 0 0
\(783\) −27.2073 +