Properties

Label 768.2.o.b.95.8
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 95.8
Character \(\chi\) \(=\) 768.95
Dual form 768.2.o.b.671.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0380372 + 1.73163i) q^{3} +(-2.18808 + 0.906333i) q^{5} +(-1.93241 - 1.93241i) q^{7} +(-2.99711 + 0.131733i) q^{9} +O(q^{10})\) \(q+(0.0380372 + 1.73163i) q^{3} +(-2.18808 + 0.906333i) q^{5} +(-1.93241 - 1.93241i) q^{7} +(-2.99711 + 0.131733i) q^{9} +(1.42447 - 0.590036i) q^{11} +(0.110405 - 0.266541i) q^{13} +(-1.65266 - 3.75448i) q^{15} +6.17031 q^{17} +(-7.34269 - 3.04144i) q^{19} +(3.27272 - 3.41972i) q^{21} +(-1.85295 - 1.85295i) q^{23} +(0.430727 - 0.430727i) q^{25} +(-0.342114 - 5.18488i) q^{27} +(2.11574 - 5.10784i) q^{29} -3.42046i q^{31} +(1.07591 + 2.44422i) q^{33} +(5.97967 + 2.47686i) q^{35} +(-2.52377 - 6.09293i) q^{37} +(0.465751 + 0.181042i) q^{39} +(0.753641 - 0.753641i) q^{41} +(-1.57129 - 3.79343i) q^{43} +(6.43852 - 3.00462i) q^{45} +1.54798i q^{47} +0.468394i q^{49} +(0.234701 + 10.6847i) q^{51} +(5.12700 + 12.3777i) q^{53} +(-2.58210 + 2.58210i) q^{55} +(4.98737 - 12.8305i) q^{57} +(-3.08775 - 7.45449i) q^{59} +(4.28571 + 1.77520i) q^{61} +(6.04619 + 5.53707i) q^{63} +0.683277i q^{65} +(0.531731 - 1.28371i) q^{67} +(3.13814 - 3.27910i) q^{69} +(-8.72539 + 8.72539i) q^{71} +(-2.73022 - 2.73022i) q^{73} +(0.762244 + 0.729477i) q^{75} +(-3.89285 - 1.61247i) q^{77} -2.76080 q^{79} +(8.96529 - 0.789635i) q^{81} +(2.53133 - 6.11116i) q^{83} +(-13.5011 + 5.59235i) q^{85} +(8.92538 + 3.46939i) q^{87} +(-4.14369 - 4.14369i) q^{89} +(-0.728413 + 0.301719i) q^{91} +(5.92298 - 0.130105i) q^{93} +18.8230 q^{95} -10.3656 q^{97} +(-4.19157 + 1.95605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

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
\(3\) 0.0380372 + 1.73163i 0.0219608 + 0.999759i
\(4\) 0 0
\(5\) −2.18808 + 0.906333i −0.978540 + 0.405324i −0.813884 0.581027i \(-0.802651\pi\)
−0.164655 + 0.986351i \(0.552651\pi\)
\(6\) 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
\(9\) −2.99711 + 0.131733i −0.999035 + 0.0439110i
\(10\) 0 0
\(11\) 1.42447 0.590036i 0.429495 0.177903i −0.157454 0.987526i \(-0.550329\pi\)
0.586949 + 0.809624i \(0.300329\pi\)
\(12\) 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 \(-0.230890\pi\)
0.748260 + 0.663406i \(0.230890\pi\)
\(18\) 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
\(21\) 3.27272 3.41972i 0.714165 0.746245i
\(22\) 0 0
\(23\) −1.85295 1.85295i −0.386366 0.386366i 0.487023 0.873389i \(-0.338083\pi\)
−0.873389 + 0.487023i \(0.838083\pi\)
\(24\) 0 0
\(25\) 0.430727 0.430727i 0.0861453 0.0861453i
\(26\) 0 0
\(27\) −0.342114 5.18488i −0.0658400 0.997830i
\(28\) 0 0
\(29\) 2.11574 5.10784i 0.392882 0.948501i −0.596427 0.802667i \(-0.703413\pi\)
0.989309 0.145834i \(-0.0465866\pi\)
\(30\) 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
\(39\) 0.465751 + 0.181042i 0.0745798 + 0.0289900i
\(40\) 0 0
\(41\) 0.753641 0.753641i 0.117699 0.117699i −0.645804 0.763503i \(-0.723478\pi\)
0.763503 + 0.645804i \(0.223478\pi\)
\(42\) 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
\(45\) 6.43852 3.00462i 0.959798 0.447902i
\(46\) 0 0
\(47\) 1.54798i 0.225796i 0.993607 + 0.112898i \(0.0360133\pi\)
−0.993607 + 0.112898i \(0.963987\pi\)
\(48\) 0 0
\(49\) 0.468394i 0.0669135i
\(50\) 0 0
\(51\) 0.234701 + 10.6847i 0.0328647 + 1.49616i
\(52\) 0 0
\(53\) 5.12700 + 12.3777i 0.704248 + 1.70020i 0.713897 + 0.700251i \(0.246928\pi\)
−0.00964932 + 0.999953i \(0.503072\pi\)
\(54\) 0 0
\(55\) −2.58210 + 2.58210i −0.348170 + 0.348170i
\(56\) 0 0
\(57\) 4.98737 12.8305i 0.660593 1.69945i
\(58\) 0 0
\(59\) −3.08775 7.45449i −0.401991 0.970492i −0.987182 0.159597i \(-0.948981\pi\)
0.585191 0.810895i \(1.69898\pi\)
\(60\) 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
\(69\) 3.13814 3.27910i 0.377788 0.394758i
\(70\) 0 0
\(71\) −8.72539 + 8.72539i −1.03551 + 1.03551i −0.0361678 + 0.999346i \(0.511515\pi\)
−0.999346 + 0.0361678i \(0.988485\pi\)
\(72\) 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
\(75\) 0.762244 + 0.729477i 0.0880164 + 0.0842327i
\(76\) 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 −0.721927 0.691970i \(-0.756743\pi\)
0.999776 + 0.0211827i \(0.00674318\pi\)
\(84\) 0 0
\(85\) −13.5011 + 5.59235i −1.46440 + 0.606576i
\(86\) 0 0
\(87\) 8.92538 + 3.46939i 0.956901 + 0.371958i
\(88\) 0 0
\(89\) −4.14369 4.14369i −0.439230 0.439230i 0.452523 0.891753i \(-0.350524\pi\)
−0.891753 + 0.452523i \(0.850524\pi\)
\(90\) 0 0
\(91\) −0.728413 + 0.301719i −0.0763585 + 0.0316287i
\(92\) 0 0
\(93\) 5.92298 0.130105i 0.614184 0.0134912i
\(94\) 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
\(99\) −4.19157 + 1.95605i −0.421269 + 0.196591i
\(100\) 0 0
\(101\) −10.5700 + 4.37825i −1.05176 + 0.435652i −0.840519 0.541783i \(-0.817750\pi\)
−0.211238 + 0.977435i \(0.567750\pi\)
\(102\) 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
\(105\) −4.06156 + 10.4488i −0.396368 + 1.01970i
\(106\) 0 0
\(107\) −9.39578 + 3.89186i −0.908325 + 0.376240i −0.787415 0.616423i \(-0.788581\pi\)
−0.120910 + 0.992664i \(0.538581\pi\)
\(108\) 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 \(-0.721662\pi\)
−0.641438 + 0.767175i \(0.721662\pi\)
\(114\) 0 0
\(115\) 5.73378 + 2.37501i 0.534678 + 0.221471i
\(116\) 0 0
\(117\) −0.295783 + 0.813396i −0.0273452 + 0.0751985i
\(118\) 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
\(123\) 1.33370 + 1.27636i 0.120255 + 0.115086i
\(124\) 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 0.331083 0.943602i \(-0.392586\pi\)
−0.433116 + 0.901338i \(0.642586\pi\)
\(132\) 0 0
\(133\) 8.31177 + 20.0664i 0.720722 + 1.73998i
\(134\) 0 0
\(135\) 5.44780 + 11.0349i 0.468872 + 0.949730i
\(136\) 0 0
\(137\) 7.54494 7.54494i 0.644608 0.644608i −0.307077 0.951685i \(-0.599351\pi\)
0.951685 + 0.307077i \(0.0993509\pi\)
\(138\) 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
\(141\) −2.68053 + 0.0588808i −0.225742 + 0.00495866i
\(142\) 0 0
\(143\) 0.444824i 0.0371980i
\(144\) 0 0
\(145\) 13.0939i 1.08739i
\(146\) 0 0
\(147\) −0.811087 + 0.0178164i −0.0668973 + 0.00146947i
\(148\) 0 0
\(149\) −0.458938 1.10798i −0.0375977 0.0907689i 0.903965 0.427606i \(-0.140643\pi\)
−0.941563 + 0.336837i \(0.890643\pi\)
\(150\) 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
\(153\) −18.4931 + 0.812833i −1.49508 + 0.0657136i
\(154\) 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
\(165\) −4.56946 4.37303i −0.355732 0.340440i
\(166\) 0 0
\(167\) 1.86833 1.86833i 0.144576 0.144576i −0.631114 0.775690i \(-0.717402\pi\)
0.775690 + 0.631114i \(0.217402\pi\)
\(168\) 0 0
\(169\) 9.13353 + 9.13353i 0.702579 + 0.702579i
\(170\) 0 0
\(171\) 22.4075 + 8.14826i 1.71354 + 0.623113i
\(172\) 0 0
\(173\) −9.59196 3.97312i −0.729263 0.302071i −0.0130138 0.999915i \(-0.504143\pi\)
−0.716249 + 0.697845i \(0.754143\pi\)
\(174\) 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 −0.923681 0.383163i \(-0.874835\pi\)
0.924078 + 0.382203i \(0.124835\pi\)
\(180\) 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
\(183\) −2.91097 + 7.48879i −0.215185 + 0.553588i
\(184\) 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
\(189\) −9.35819 + 10.6804i −0.680708 + 0.776885i
\(190\) 0 0
\(191\) −7.77941 −0.562898 −0.281449 0.959576i \(-0.590815\pi\)
−0.281449 + 0.959576i \(0.590815\pi\)
\(192\) 0 0
\(193\) −6.23528 −0.448825 −0.224413 0.974494i \(-0.572046\pi\)
−0.224413 + 0.974494i \(0.572046\pi\)
\(194\) 0 0
\(195\) −1.18319 + 0.0259899i −0.0847297 + 0.00186118i
\(196\) 0 0
\(197\) 6.90773 2.86128i 0.492156 0.203858i −0.122781 0.992434i \(-0.539181\pi\)
0.614937 + 0.788576i \(0.289181\pi\)
\(198\) 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
\(201\) 2.24315 + 0.871935i 0.158219 + 0.0615015i
\(202\) 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
\(213\) −15.4411 14.7773i −1.05800 1.01252i
\(214\) 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
\(219\) 4.62388 4.83158i 0.312453 0.326488i
\(220\) 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 0.862376 0.506268i \(-0.168975\pi\)
0.251806 + 0.967778i \(0.418975\pi\)
\(228\) 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
\(231\) 2.64414 6.80233i 0.173972 0.447560i
\(232\) 0 0
\(233\) −2.54073 + 2.54073i −0.166449 + 0.166449i −0.785416 0.618968i \(-0.787551\pi\)
0.618968 + 0.785416i \(0.287551\pi\)
\(234\) 0 0
\(235\) −1.40298 3.38711i −0.0915206 0.220950i
\(236\) 0 0
\(237\) −0.105013 4.78069i −0.00682132 0.310539i
\(238\) 0 0
\(239\) 17.6107i 1.13914i 0.821943 + 0.569570i \(0.192890\pi\)
−0.821943 + 0.569570i \(0.807110\pi\)
\(240\) 0 0
\(241\) 6.18628i 0.398493i 0.979949 + 0.199247i \(0.0638495\pi\)
−0.979949 + 0.199247i \(0.936151\pi\)
\(242\) 0 0
\(243\) 1.70837 + 15.4946i 0.109592 + 0.993977i
\(244\) 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
\(249\) 10.6786 + 4.15088i 0.676727 + 0.263051i
\(250\) 0 0
\(251\) 9.18840 + 22.1828i 0.579967 + 1.40016i 0.892842 + 0.450369i \(0.148708\pi\)
−0.312876 + 0.949794i \(0.601292\pi\)
\(252\) 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 \(-0.879139\pi\)
0.928777 0.370638i \(-0.120861\pi\)
\(258\) 0 0
\(259\) −6.89706 + 16.6510i −0.428563 + 1.03464i
\(260\) 0 0
\(261\) −5.66821 + 15.5874i −0.350854 + 0.964838i
\(262\) 0 0
\(263\) 11.6191 11.6191i 0.716464 0.716464i −0.251415 0.967879i \(-0.580896\pi\)
0.967879 + 0.251415i \(0.0808959\pi\)
\(264\) 0 0
\(265\) −22.4366 22.4366i −1.37827 1.37827i
\(266\) 0 0
\(267\) 7.01773 7.33296i 0.429478 0.448770i
\(268\) 0 0
\(269\) 13.7480 + 5.69459i 0.838228 + 0.347205i 0.760155 0.649742i \(-0.225123\pi\)
0.0780733 + 0.996948i \(0.475123\pi\)
\(270\) 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
\(279\) 0.450587 + 10.2515i 0.0269759 + 0.613740i
\(280\) 0 0
\(281\) 12.0212 + 12.0212i 0.717122 + 0.717122i 0.968015 0.250893i \(-0.0807241\pi\)
−0.250893 + 0.968015i \(0.580724\pi\)
\(282\) 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
\(285\) 0.715973 + 32.5945i 0.0424106 + 1.93073i
\(286\) 0 0
\(287\) −2.91268 −0.171930
\(288\) 0 0
\(289\) 21.0727 1.23957
\(290\) 0 0
\(291\) −0.394277 17.9494i −0.0231129 1.05221i
\(292\) 0 0
\(293\) 24.7412 10.2481i 1.44539 0.598702i 0.484295 0.874905i \(-0.339076\pi\)
0.961099 + 0.276203i \(0.0890763\pi\)
\(294\) 0 0
\(295\) 13.5125 + 13.5125i 0.786729 + 0.786729i
\(296\) 0 0
\(297\) −3.54660 7.18386i −0.205795 0.416850i
\(298\) 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
\(309\) 17.7528 18.5502i 1.00992 1.05528i
\(310\) 0 0
\(311\) −3.60638 3.60638i −0.204499 0.204499i 0.597425 0.801924i \(-0.296190\pi\)
−0.801924 + 0.597425i \(0.796190\pi\)
\(312\) 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
\(315\) −18.2480 6.63569i −1.02816 0.373879i
\(316\) 0 0
\(317\) 1.42053 3.42947i 0.0797850 0.192618i −0.878954 0.476907i \(-0.841758\pi\)
0.958738 + 0.284289i \(0.0917577\pi\)
\(318\) 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
\(327\) −12.6805 4.92905i −0.701233 0.272577i
\(328\) 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
\(333\) 8.36666 + 17.9287i 0.458490 + 0.982487i
\(334\) 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
\(339\) −0.518719 23.6146i −0.0281730 1.28257i
\(340\) 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
\(345\) −3.89455 + 10.0191i −0.209676 + 0.539413i
\(346\) 0 0
\(347\) −1.37907 3.32937i −0.0740325 0.178730i 0.882531 0.470254i \(-0.155838\pi\)
−0.956564 + 0.291524i \(0.905838\pi\)
\(348\) 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 \(-0.952168\pi\)
0.988731 0.149703i \(-0.0478316\pi\)
\(354\) 0 0
\(355\) 11.1838 27.0000i 0.593572 1.43301i
\(356\) 0 0
\(357\) 20.1937 21.1007i 1.06876 1.11677i
\(358\) 0 0
\(359\) 22.3781 22.3781i 1.18107 1.18107i 0.201603 0.979467i \(-0.435385\pi\)
0.979467 0.201603i \(-0.0646152\pi\)
\(360\) 0 0
\(361\) 31.2298 + 31.2298i 1.64367 + 1.64367i
\(362\) 0 0
\(363\) −10.7900 10.3262i −0.566329 0.541984i
\(364\) 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
\(375\) 16.7881 + 6.52573i 0.866936 + 0.336987i
\(376\) 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
\(381\) −13.4270 + 0.294938i −0.687886 + 0.0151101i
\(382\) 0 0
\(383\) 5.25906 0.268725 0.134363 0.990932i \(-0.457101\pi\)
0.134363 + 0.990932i \(0.457101\pi\)
\(384\) 0 0
\(385\) 9.97932 0.508593
\(386\) 0 0
\(387\) 5.20904 + 11.1623i 0.264790 + 0.567412i
\(388\) 0 0
\(389\) −25.9373 + 10.7436i −1.31507 + 0.544721i −0.926360 0.376639i \(-0.877080\pi\)
−0.388712 + 0.921359i \(0.627080\pi\)
\(390\) 0 0
\(391\) −11.4333 11.4333i −0.578204 0.578204i
\(392\) 0 0
\(393\) 0.793219 2.04064i 0.0400126 0.102937i
\(394\) 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 \(-0.790954\pi\)
−0.791987 + 0.610537i \(0.790954\pi\)
\(402\) 0 0
\(403\) −0.911693 0.377635i −0.0454146 0.0188114i
\(404\) 0 0
\(405\) −18.9011 + 9.85333i −0.939204 + 0.489616i
\(406\) 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
\(411\) 13.3521 + 12.7781i 0.658608 + 0.630296i
\(412\) 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 0.330634 0.943759i \(-0.392737\pi\)
−0.433544 + 0.901132i \(0.642737\pi\)
\(420\) 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
\(423\) −0.203920 4.63946i −0.00991492 0.225578i
\(424\) 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
\(429\) 0.770272 0.0169198i 0.0371891 0.000816898i
\(430\) 0 0
\(431\) 2.95351i 0.142266i 0.997467 + 0.0711329i \(0.0226614\pi\)
−0.997467 + 0.0711329i \(0.977339\pi\)
\(432\) 0 0
\(433\) 31.3472i 1.50645i −0.657764 0.753224i \(-0.728497\pi\)
0.657764 0.753224i \(-0.271503\pi\)
\(434\) 0 0
\(435\) −22.6739 + 0.498056i −1.08713 + 0.0238800i
\(436\) 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
\(441\) −0.0617029 1.40383i −0.00293824 0.0668489i
\(442\) 0 0
\(443\) 3.50021 + 8.45026i 0.166300 + 0.401484i 0.984957 0.172799i \(-0.0552810\pi\)
−0.818657 + 0.574283i \(0.805281\pi\)
\(444\) 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 \(0.192453\pi\)
−0.822725 + 0.568439i \(0.807547\pi\)
\(450\) 0 0
\(451\) 0.628866 1.51822i 0.0296121 0.0714901i
\(452\) 0 0
\(453\) 17.3581 + 16.6120i 0.815557 + 0.780498i
\(454\) 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
\(459\) −2.11095 31.9923i −0.0985308 1.49327i
\(460\) 0 0
\(461\) −26.4361 10.9502i −1.23125 0.510001i −0.330282 0.943882i \(-0.607144\pi\)
−0.900970 + 0.433881i \(0.857144\pi\)
\(462\) 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 −0.875315 0.483553i \(-0.839346\pi\)
0.960865 + 0.277018i \(0.0893460\pi\)
\(468\) 0 0
\(469\) −3.50818 + 1.45313i −0.161993 + 0.0670995i
\(470\) 0 0
\(471\) 5.62542 14.4720i 0.259206 0.666834i
\(472\) 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
\(477\) −16.9967 36.4218i −0.778226 1.66764i
\(478\) 0 0
\(479\) −15.8988 −0.726433 −0.363216 0.931705i \(-0.618321\pi\)
−0.363216 + 0.931705i \(0.618321\pi\)
\(480\) 0 0
\(481\) −1.90265 −0.0867535
\(482\) 0 0
\(483\) −12.4007 + 0.272395i −0.564253 + 0.0123944i
\(484\) 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
\(489\) 4.85341 + 1.88657i 0.219479 + 0.0853138i
\(490\) 0 0
\(491\) 0.306137 0.126806i 0.0138158 0.00572268i −0.375765 0.926715i \(-0.622620\pi\)
0.389581 + 0.920992i \(0.372620\pi\)
\(492\) 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
\(501\) 3.30633 + 3.16419i 0.147716 + 0.141366i
\(502\) 0 0
\(503\) 10.6198 + 10.6198i 0.473513 + 0.473513i 0.903050 0.429536i \(-0.141323\pi\)
−0.429536 + 0.903050i \(0.641323\pi\)
\(504\) 0 0
\(505\) 19.1599 19.1599i 0.852605 0.852605i
\(506\) 0 0
\(507\) −15.4685 + 16.1633i −0.686981 + 0.717839i
\(508\) 0 0
\(509\) −2.01172 + 4.85673i −0.0891681 + 0.215271i −0.962172 0.272442i \(-0.912169\pi\)
0.873004 + 0.487713i \(0.162169\pi\)
\(510\) 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
\(519\) 6.51513 16.7609i 0.285983 0.735721i
\(520\) 0 0
\(521\) 19.9974 19.9974i 0.876102 0.876102i −0.117027 0.993129i \(-0.537336\pi\)
0.993129 + 0.117027i \(0.0373363\pi\)
\(522\) 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
\(525\) −0.0633197 2.88261i −0.00276350 0.125808i
\(526\) 0 0
\(527\) 21.1053i 0.919360i
\(528\) 0 0
\(529\) 16.1332i 0.701443i
\(530\) 0 0
\(531\) 10.2363 + 21.9352i 0.444219 + 0.951905i
\(532\) 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
\(537\) 0.0224476 + 0.00872561i 0.000968684 + 0.000376538i
\(538\) 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
\(549\) −13.0786 4.75589i −0.558180 0.202976i
\(550\) 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
\(555\) −18.7048 + 19.5450i −0.793976 + 0.829640i
\(556\) 0 0
\(557\) −9.30090 3.85256i −0.394092 0.163238i 0.176832 0.984241i \(-0.443415\pi\)
−0.570924 + 0.821003i \(0.693415\pi\)
\(558\) 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 −0.947882 0.318620i \(-0.896780\pi\)
0.895553 + 0.444955i \(0.146780\pi\)
\(564\) 0 0
\(565\) 29.8392 12.3598i 1.25535 0.519981i
\(566\) 0 0
\(567\) −18.8505 15.7987i −0.791646 0.663483i
\(568\) 0 0
\(569\) 28.3250 + 28.3250i 1.18745 + 1.18745i 0.977771 + 0.209674i \(0.0672404\pi\)
0.209674 + 0.977771i \(0.432760\pi\)
\(570\) 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
\(573\) −0.295907 13.4711i −0.0123617 0.562763i
\(574\) 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
\(579\) −0.237172 10.7972i −0.00985655 0.448717i
\(580\) 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
\(585\) −0.0900101 2.04785i −0.00372146 0.0846684i
\(586\) 0 0
\(587\) −1.77252 + 0.734203i −0.0731599 + 0.0303038i −0.418963 0.908003i \(-0.637606\pi\)
0.345803 + 0.938307i \(0.387606\pi\)
\(588\) 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 \(-0.334729\pi\)
0.496197 + 0.868210i \(0.334729\pi\)
\(594\) 0 0
\(595\) 36.8964 + 15.2830i 1.51260 + 0.626541i
\(596\) 0 0
\(597\) −21.0882 + 22.0355i −0.863084 + 0.901853i
\(598\) 0 0
\(599\) −11.6692 11.6692i −0.476789 0.476789i 0.427314 0.904103i \(-0.359460\pi\)
−0.904103 + 0.427314i \(0.859460\pi\)
\(600\) 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
\(603\) −1.42455 + 3.91747i −0.0580121 + 0.159532i
\(604\) 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
\(615\) −4.07504 1.58401i −0.164322 0.0638736i
\(616\) 0 0
\(617\) −13.5933 + 13.5933i −0.547246 + 0.547246i −0.925643 0.378397i \(-0.876475\pi\)
0.378397 + 0.925643i \(0.376475\pi\)
\(618\) 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
\(621\) −8.97338 + 10.2412i −0.360089 + 0.410966i
\(622\) 0 0
\(623\) 16.0146i 0.641611i
\(624\) 0 0
\(625\) 27.6746i 1.10699i
\(626\) 0 0
\(627\) −0.466109 21.2195i −0.0186146 0.847425i
\(628\) 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
\(633\) −0.793682 + 2.04183i −0.0315460 + 0.0811556i
\(634\) 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 \(-0.988544\pi\)
0.999352 0.0359830i \(-0.0114562\pi\)
\(642\) 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
\(645\) −11.6455 + 12.1686i −0.458542 + 0.479140i
\(646\) 0 0
\(647\) −27.3258 + 27.3258i −1.07429 + 1.07429i −0.0772785 + 0.997010i \(0.524623\pi\)
−0.997010 + 0.0772785i \(0.975377\pi\)
\(648\) 0 0
\(649\) −8.79684 8.79684i −0.345306 0.345306i
\(650\) 0 0
\(651\) −11.6970 11.1942i −0.458442 0.438735i
\(652\) 0 0
\(653\) 21.5061 + 8.90811i 0.841598 + 0.348601i 0.761483 0.648184i \(-0.224471\pi\)
0.0801145 + 0.996786i \(0.474471\pi\)
\(654\) 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 \(0.467042\pi\)
−0.776403 + 0.630237i \(0.782958\pi\)
\(660\) 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
\(663\) 2.87383 + 1.11709i 0.111610 + 0.0433841i
\(664\) 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
\(669\) 18.1903 0.399570i 0.703279 0.0154483i
\(670\) 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
\(675\) −2.38062 2.08591i −0.0916302 0.0802866i
\(676\) 0 0
\(677\) −16.7436 + 6.93541i −0.643507 + 0.266549i −0.680480 0.732767i \(-0.738229\pi\)
0.0369727 + 0.999316i \(0.488229\pi\)
\(678\) 0 0
\(679\) 20.0305 + 20.0305i 0.768701 + 0.768701i
\(680\) 0 0
\(681\) −11.4021 + 29.3332i −0.436930 + 1.12405i
\(682\) 0 0
\(683\) 43.5660 18.0456i 1.66701 0.690497i 0.668428 0.743777i \(-0.266968\pi\)
0.998580 + 0.0532798i \(0.0169675\pi\)
\(684\) 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
\(693\) 11.8797 + 4.31994i 0.451273 + 0.164101i
\(694\) 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
\(699\) −4.49625 4.30297i −0.170064 0.162753i
\(700\) 0 0
\(701\) −13.7184 + 33.1190i −0.518135 + 1.25089i 0.420912 + 0.907101i \(0.361710\pi\)
−0.939047 + 0.343787i \(0.888290\pi\)
\(702\) 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
\(711\) 8.27440 0.363688i 0.310314 0.0136394i
\(712\) 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
\(717\) −30.4952 + 0.669861i −1.13887 + 0.0250164i
\(718\) 0 0
\(719\) 25.3851i 0.946706i −0.880873 0.473353i \(-0.843044\pi\)
0.880873 0.473353i \(-0.156956\pi\)
\(720\) 0 0
\(721\) 40.5121i 1.50875i
\(722\) 0 0
\(723\) −10.7124 + 0.235309i −0.398397 + 0.00875122i
\(724\) 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
\(729\) −26.7659 + 3.54764i −0.991330 + 0.131394i
\(730\) 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
\(741\) −2.86924 2.74589i −0.105404 0.100873i
\(742\) 0 0
\(743\) −5.42669 + 5.42669i −0.199086 + 0.199086i −0.799608 0.600522i \(-0.794959\pi\)
0.600522 + 0.799608i \(0.294959\pi\)
\(744\) 0 0
\(745\) 2.00839 + 2.00839i 0.0735817 + 0.0735817i
\(746\) 0 0
\(747\) −6.78161 + 18.6493i −0.248126 + 0.682341i
\(748\) 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
\(759\) 2.53541 6.52262i 0.0920296 0.236756i
\(760\) 0 0
\(761\) −25.8277 25.8277i −0.936254 0.936254i 0.0618325 0.998087i \(-0.480306\pi\)
−0.998087 + 0.0618325i \(0.980306\pi\)
\(762\) 0 0
\(763\) 19.8317 8.21457i 0.717957 0.297387i
\(764\) 0 0
\(765\) 39.7276 18.5394i 1.43636 0.670294i
\(766\) 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
\(771\) 20.5780 0.452017i 0.741097 0.0162790i
\(772\) 0 0
\(773\) −8.07057 + 3.34294i −0.290278 + 0.120237i −0.523071 0.852289i \(-0.675214\pi\)
0.232793 + 0.972526i \(0.425214\pi\)
\(774\) 0 0
\(775\) −1.47328 1.47328i −0.0529219 0.0529219i
\(776\) 0 0
\(777\) −29.0957 11.3098i −1.04380 0.405738i
\(778\) 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
\(783\)