Properties

Label 882.3.s.i.863.3
Level $882$
Weight $3$
Character 882.863
Analytic conductor $24.033$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.0327593166\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.12745506816.5
Defining polynomial: \(x^{8} - 8 x^{6} + 55 x^{4} - 72 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 863.3
Root \(-1.00781 + 0.581861i\) of defining polynomial
Character \(\chi\) \(=\) 882.863
Dual form 882.3.s.i.557.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-5.25600 - 3.03455i) q^{5} +2.82843i q^{8} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-5.25600 - 3.03455i) q^{5} +2.82843i q^{8} +(-4.29150 - 7.43310i) q^{10} +(-10.5120 + 6.06910i) q^{11} +18.5830 q^{13} +(-2.00000 + 3.46410i) q^{16} +(9.44094 - 5.45073i) q^{17} +(10.0000 - 17.3205i) q^{19} -12.1382i q^{20} -17.1660 q^{22} +(10.5120 + 6.06910i) q^{23} +(5.91699 + 10.2485i) q^{25} +(22.7594 + 13.1402i) q^{26} +41.8367i q^{29} +(12.5830 + 21.7944i) q^{31} +(-4.89898 + 2.82843i) q^{32} +15.4170 q^{34} +(-19.0000 + 32.9090i) q^{37} +(24.4949 - 14.1421i) q^{38} +(8.58301 - 14.8662i) q^{40} +60.6337i q^{41} +83.4980 q^{43} +(-21.0240 - 12.1382i) q^{44} +(8.58301 + 14.8662i) q^{46} +(-14.6969 - 8.48528i) q^{47} +16.7358i q^{50} +(18.5830 + 32.1867i) q^{52} +(81.4431 - 47.0212i) q^{53} +73.6680 q^{55} +(-29.5830 + 51.2393i) q^{58} +(50.4179 - 29.1088i) q^{59} +(7.83399 - 13.5689i) q^{61} +35.5901i q^{62} -8.00000 q^{64} +(-97.6722 - 56.3911i) q^{65} +(66.3320 + 114.890i) q^{67} +(18.8819 + 10.9015i) q^{68} -12.1382i q^{71} +(-38.4575 - 66.6104i) q^{73} +(-46.5403 + 26.8701i) q^{74} +40.0000 q^{76} +(-16.8340 + 29.1573i) q^{79} +(21.0240 - 12.1382i) q^{80} +(-42.8745 + 74.2608i) q^{82} +60.5764i q^{83} -66.1621 q^{85} +(102.264 + 59.0420i) q^{86} +(-17.1660 - 29.7324i) q^{88} +(-4.13532 - 2.38753i) q^{89} +24.2764i q^{92} +(-12.0000 - 20.7846i) q^{94} +(-105.120 + 60.6910i) q^{95} +188.413 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} + O(q^{10}) \) \( 8 q + 8 q^{4} + 8 q^{10} + 64 q^{13} - 16 q^{16} + 80 q^{19} + 32 q^{22} + 132 q^{25} + 16 q^{31} + 208 q^{34} - 152 q^{37} - 16 q^{40} + 160 q^{43} - 16 q^{46} + 64 q^{52} + 928 q^{55} - 152 q^{58} + 232 q^{61} - 64 q^{64} + 192 q^{67} - 96 q^{73} + 320 q^{76} - 304 q^{79} - 216 q^{82} + 656 q^{85} + 32 q^{88} - 96 q^{94} + 576 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 0.707107i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) −5.25600 3.03455i −1.05120 0.606910i −0.128214 0.991746i \(-0.540925\pi\)
−0.922985 + 0.384836i \(0.874258\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) −4.29150 7.43310i −0.429150 0.743310i
\(11\) −10.5120 + 6.06910i −0.955636 + 0.551736i −0.894827 0.446413i \(-0.852701\pi\)
−0.0608086 + 0.998149i \(0.519368\pi\)
\(12\) 0 0
\(13\) 18.5830 1.42946 0.714731 0.699399i \(-0.246549\pi\)
0.714731 + 0.699399i \(0.246549\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 9.44094 5.45073i 0.555350 0.320631i −0.195927 0.980618i \(-0.562772\pi\)
0.751277 + 0.659987i \(0.229438\pi\)
\(18\) 0 0
\(19\) 10.0000 17.3205i 0.526316 0.911606i −0.473214 0.880947i \(-0.656906\pi\)
0.999530 0.0306583i \(-0.00976035\pi\)
\(20\) 12.1382i 0.606910i
\(21\) 0 0
\(22\) −17.1660 −0.780273
\(23\) 10.5120 + 6.06910i 0.457043 + 0.263874i 0.710800 0.703394i \(-0.248333\pi\)
−0.253757 + 0.967268i \(0.581666\pi\)
\(24\) 0 0
\(25\) 5.91699 + 10.2485i 0.236680 + 0.409941i
\(26\) 22.7594 + 13.1402i 0.875363 + 0.505391i
\(27\) 0 0
\(28\) 0 0
\(29\) 41.8367i 1.44264i 0.692600 + 0.721322i \(0.256465\pi\)
−0.692600 + 0.721322i \(0.743535\pi\)
\(30\) 0 0
\(31\) 12.5830 + 21.7944i 0.405903 + 0.703045i 0.994426 0.105435i \(-0.0336236\pi\)
−0.588523 + 0.808481i \(0.700290\pi\)
\(32\) −4.89898 + 2.82843i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 15.4170 0.453441
\(35\) 0 0
\(36\) 0 0
\(37\) −19.0000 + 32.9090i −0.513514 + 0.889431i 0.486364 + 0.873757i \(0.338323\pi\)
−0.999877 + 0.0156750i \(0.995010\pi\)
\(38\) 24.4949 14.1421i 0.644603 0.372161i
\(39\) 0 0
\(40\) 8.58301 14.8662i 0.214575 0.371655i
\(41\) 60.6337i 1.47887i 0.673227 + 0.739435i \(0.264908\pi\)
−0.673227 + 0.739435i \(0.735092\pi\)
\(42\) 0 0
\(43\) 83.4980 1.94181 0.970907 0.239455i \(-0.0769689\pi\)
0.970907 + 0.239455i \(0.0769689\pi\)
\(44\) −21.0240 12.1382i −0.477818 0.275868i
\(45\) 0 0
\(46\) 8.58301 + 14.8662i 0.186587 + 0.323178i
\(47\) −14.6969 8.48528i −0.312701 0.180538i 0.335434 0.942064i \(-0.391117\pi\)
−0.648134 + 0.761526i \(0.724451\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 16.7358i 0.334716i
\(51\) 0 0
\(52\) 18.5830 + 32.1867i 0.357365 + 0.618975i
\(53\) 81.4431 47.0212i 1.53666 0.887193i 0.537632 0.843180i \(-0.319319\pi\)
0.999031 0.0440129i \(-0.0140143\pi\)
\(54\) 0 0
\(55\) 73.6680 1.33942
\(56\) 0 0
\(57\) 0 0
\(58\) −29.5830 + 51.2393i −0.510052 + 0.883436i
\(59\) 50.4179 29.1088i 0.854540 0.493369i −0.00764008 0.999971i \(-0.502432\pi\)
0.862180 + 0.506602i \(0.169099\pi\)
\(60\) 0 0
\(61\) 7.83399 13.5689i 0.128426 0.222440i −0.794641 0.607080i \(-0.792341\pi\)
0.923067 + 0.384639i \(0.125674\pi\)
\(62\) 35.5901i 0.574034i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) −97.6722 56.3911i −1.50265 0.867555i
\(66\) 0 0
\(67\) 66.3320 + 114.890i 0.990030 + 1.71478i 0.617000 + 0.786964i \(0.288348\pi\)
0.373031 + 0.927819i \(0.378319\pi\)
\(68\) 18.8819 + 10.9015i 0.277675 + 0.160316i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.1382i 0.170961i −0.996340 0.0854803i \(-0.972758\pi\)
0.996340 0.0854803i \(-0.0272425\pi\)
\(72\) 0 0
\(73\) −38.4575 66.6104i −0.526815 0.912471i −0.999512 0.0312455i \(-0.990053\pi\)
0.472696 0.881225i \(-0.343281\pi\)
\(74\) −46.5403 + 26.8701i −0.628923 + 0.363109i
\(75\) 0 0
\(76\) 40.0000 0.526316
\(77\) 0 0
\(78\) 0 0
\(79\) −16.8340 + 29.1573i −0.213088 + 0.369080i −0.952680 0.303976i \(-0.901686\pi\)
0.739591 + 0.673056i \(0.235019\pi\)
\(80\) 21.0240 12.1382i 0.262800 0.151728i
\(81\) 0 0
\(82\) −42.8745 + 74.2608i −0.522860 + 0.905620i
\(83\) 60.5764i 0.729836i 0.931040 + 0.364918i \(0.118903\pi\)
−0.931040 + 0.364918i \(0.881097\pi\)
\(84\) 0 0
\(85\) −66.1621 −0.778377
\(86\) 102.264 + 59.0420i 1.18911 + 0.686535i
\(87\) 0 0
\(88\) −17.1660 29.7324i −0.195068 0.337868i
\(89\) −4.13532 2.38753i −0.0464643 0.0268262i 0.476588 0.879127i \(-0.341873\pi\)
−0.523052 + 0.852301i \(0.675207\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 24.2764i 0.263874i
\(93\) 0 0
\(94\) −12.0000 20.7846i −0.127660 0.221113i
\(95\) −105.120 + 60.6910i −1.10653 + 0.638853i
\(96\) 0 0
\(97\) 188.413 1.94240 0.971201 0.238260i \(-0.0765771\pi\)
0.971201 + 0.238260i \(0.0765771\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −11.8340 + 20.4971i −0.118340 + 0.204971i
\(101\) −92.4162 + 53.3565i −0.915012 + 0.528282i −0.882040 0.471174i \(-0.843830\pi\)
−0.0329716 + 0.999456i \(0.510497\pi\)
\(102\) 0 0
\(103\) 65.7490 113.881i 0.638340 1.10564i −0.347457 0.937696i \(-0.612955\pi\)
0.985797 0.167941i \(-0.0537119\pi\)
\(104\) 52.5607i 0.505391i
\(105\) 0 0
\(106\) 132.996 1.25468
\(107\) −71.3426 41.1897i −0.666753 0.384950i 0.128092 0.991762i \(-0.459115\pi\)
−0.794845 + 0.606812i \(0.792448\pi\)
\(108\) 0 0
\(109\) −16.9150 29.2977i −0.155184 0.268786i 0.777942 0.628336i \(-0.216264\pi\)
−0.933126 + 0.359550i \(0.882930\pi\)
\(110\) 90.2245 + 52.0911i 0.820223 + 0.473556i
\(111\) 0 0
\(112\) 0 0
\(113\) 28.5190i 0.252381i −0.992006 0.126190i \(-0.959725\pi\)
0.992006 0.126190i \(-0.0402750\pi\)
\(114\) 0 0
\(115\) −36.8340 63.7983i −0.320296 0.554768i
\(116\) −72.4633 + 41.8367i −0.624683 + 0.360661i
\(117\) 0 0
\(118\) 82.3320 0.697729
\(119\) 0 0
\(120\) 0 0
\(121\) 13.1680 22.8076i 0.108826 0.188493i
\(122\) 19.1893 11.0789i 0.157289 0.0908109i
\(123\) 0 0
\(124\) −25.1660 + 43.5888i −0.202952 + 0.351523i
\(125\) 79.9059i 0.639247i
\(126\) 0 0
\(127\) 129.668 1.02101 0.510504 0.859875i \(-0.329459\pi\)
0.510504 + 0.859875i \(0.329459\pi\)
\(128\) −9.79796 5.65685i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) −79.7490 138.129i −0.613454 1.06253i
\(131\) −128.187 74.0087i −0.978525 0.564952i −0.0767004 0.997054i \(-0.524438\pi\)
−0.901824 + 0.432103i \(0.857772\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 187.615i 1.40011i
\(135\) 0 0
\(136\) 15.4170 + 26.7030i 0.113360 + 0.196346i
\(137\) −66.6469 + 38.4786i −0.486474 + 0.280866i −0.723111 0.690732i \(-0.757288\pi\)
0.236637 + 0.971598i \(0.423955\pi\)
\(138\) 0 0
\(139\) −217.328 −1.56351 −0.781756 0.623585i \(-0.785676\pi\)
−0.781756 + 0.623585i \(0.785676\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 8.58301 14.8662i 0.0604437 0.104692i
\(143\) −195.344 + 112.782i −1.36604 + 0.788686i
\(144\) 0 0
\(145\) 126.956 219.893i 0.875555 1.51651i
\(146\) 108.774i 0.745029i
\(147\) 0 0
\(148\) −76.0000 −0.513514
\(149\) −140.231 80.9623i −0.941147 0.543371i −0.0508272 0.998707i \(-0.516186\pi\)
−0.890320 + 0.455336i \(0.849519\pi\)
\(150\) 0 0
\(151\) 46.5830 + 80.6841i 0.308497 + 0.534332i 0.978034 0.208447i \(-0.0668408\pi\)
−0.669537 + 0.742779i \(0.733507\pi\)
\(152\) 48.9898 + 28.2843i 0.322301 + 0.186081i
\(153\) 0 0
\(154\) 0 0
\(155\) 152.735i 0.985388i
\(156\) 0 0
\(157\) −92.4980 160.211i −0.589159 1.02045i −0.994343 0.106219i \(-0.966126\pi\)
0.405183 0.914235i \(-0.367208\pi\)
\(158\) −41.2347 + 23.8069i −0.260979 + 0.150676i
\(159\) 0 0
\(160\) 34.3320 0.214575
\(161\) 0 0
\(162\) 0 0
\(163\) −43.4980 + 75.3408i −0.266859 + 0.462214i −0.968049 0.250761i \(-0.919319\pi\)
0.701190 + 0.712975i \(0.252652\pi\)
\(164\) −105.021 + 60.6337i −0.640370 + 0.369718i
\(165\) 0 0
\(166\) −42.8340 + 74.1906i −0.258036 + 0.446932i
\(167\) 60.5764i 0.362733i −0.983416 0.181366i \(-0.941948\pi\)
0.983416 0.181366i \(-0.0580520\pi\)
\(168\) 0 0
\(169\) 176.328 1.04336
\(170\) −81.0317 46.7837i −0.476657 0.275198i
\(171\) 0 0
\(172\) 83.4980 + 144.623i 0.485454 + 0.840830i
\(173\) 140.791 + 81.2858i 0.813822 + 0.469860i 0.848281 0.529546i \(-0.177638\pi\)
−0.0344594 + 0.999406i \(0.510971\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 48.5528i 0.275868i
\(177\) 0 0
\(178\) −3.37648 5.84823i −0.0189690 0.0328552i
\(179\) 193.202 111.545i 1.07934 0.623159i 0.148623 0.988894i \(-0.452516\pi\)
0.930719 + 0.365735i \(0.119182\pi\)
\(180\) 0 0
\(181\) −188.915 −1.04373 −0.521865 0.853028i \(-0.674763\pi\)
−0.521865 + 0.853028i \(0.674763\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −17.1660 + 29.7324i −0.0932935 + 0.161589i
\(185\) 199.728 115.313i 1.07961 0.623313i
\(186\) 0 0
\(187\) −66.1621 + 114.596i −0.353808 + 0.612813i
\(188\) 33.9411i 0.180538i
\(189\) 0 0
\(190\) −171.660 −0.903474
\(191\) 197.486 + 114.019i 1.03396 + 0.596957i 0.918117 0.396310i \(-0.129709\pi\)
0.115844 + 0.993267i \(0.463043\pi\)
\(192\) 0 0
\(193\) −67.0000 116.047i −0.347150 0.601282i 0.638592 0.769546i \(-0.279517\pi\)
−0.985742 + 0.168264i \(0.946184\pi\)
\(194\) 230.758 + 133.228i 1.18947 + 0.686743i
\(195\) 0 0
\(196\) 0 0
\(197\) 188.560i 0.957157i −0.878045 0.478579i \(-0.841152\pi\)
0.878045 0.478579i \(-0.158848\pi\)
\(198\) 0 0
\(199\) 51.2470 + 88.7625i 0.257523 + 0.446043i 0.965578 0.260115i \(-0.0837604\pi\)
−0.708055 + 0.706157i \(0.750427\pi\)
\(200\) −28.9872 + 16.7358i −0.144936 + 0.0836789i
\(201\) 0 0
\(202\) −150.915 −0.747104
\(203\) 0 0
\(204\) 0 0
\(205\) 183.996 318.691i 0.897542 1.55459i
\(206\) 161.052 92.9831i 0.781804 0.451375i
\(207\) 0 0
\(208\) −37.1660 + 64.3734i −0.178683 + 0.309488i
\(209\) 242.764i 1.16155i
\(210\) 0 0
\(211\) −84.5020 −0.400483 −0.200242 0.979747i \(-0.564173\pi\)
−0.200242 + 0.979747i \(0.564173\pi\)
\(212\) 162.886 + 94.0424i 0.768331 + 0.443596i
\(213\) 0 0
\(214\) −58.2510 100.894i −0.272201 0.471466i
\(215\) −438.865 253.379i −2.04123 1.17851i
\(216\) 0 0
\(217\) 0 0
\(218\) 47.8429i 0.219463i
\(219\) 0 0
\(220\) 73.6680 + 127.597i 0.334854 + 0.579985i
\(221\) 175.441 101.291i 0.793851 0.458330i
\(222\) 0 0
\(223\) 158.494 0.710736 0.355368 0.934727i \(-0.384356\pi\)
0.355368 + 0.934727i \(0.384356\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 20.1660 34.9286i 0.0892301 0.154551i
\(227\) −88.1816 + 50.9117i −0.388465 + 0.224281i −0.681495 0.731823i \(-0.738670\pi\)
0.293030 + 0.956103i \(0.405337\pi\)
\(228\) 0 0
\(229\) −134.458 + 232.887i −0.587151 + 1.01697i 0.407453 + 0.913226i \(0.366417\pi\)
−0.994604 + 0.103749i \(0.966916\pi\)
\(230\) 104.182i 0.452966i
\(231\) 0 0
\(232\) −118.332 −0.510052
\(233\) 22.7546 + 13.1374i 0.0976593 + 0.0563836i 0.548034 0.836456i \(-0.315376\pi\)
−0.450375 + 0.892840i \(0.648710\pi\)
\(234\) 0 0
\(235\) 51.4980 + 89.1972i 0.219141 + 0.379563i
\(236\) 100.836 + 58.2175i 0.427270 + 0.246684i
\(237\) 0 0
\(238\) 0 0
\(239\) 92.2733i 0.386081i 0.981191 + 0.193040i \(0.0618348\pi\)
−0.981191 + 0.193040i \(0.938165\pi\)
\(240\) 0 0
\(241\) 171.624 + 297.261i 0.712131 + 1.23345i 0.964056 + 0.265700i \(0.0856030\pi\)
−0.251925 + 0.967747i \(0.581064\pi\)
\(242\) 32.2548 18.6223i 0.133284 0.0769518i
\(243\) 0 0
\(244\) 31.3360 0.128426
\(245\) 0 0
\(246\) 0 0
\(247\) 185.830 321.867i 0.752348 1.30311i
\(248\) −61.6439 + 35.5901i −0.248564 + 0.143509i
\(249\) 0 0
\(250\) −56.5020 + 97.8643i −0.226008 + 0.391457i
\(251\) 356.382i 1.41985i −0.704278 0.709924i \(-0.748729\pi\)
0.704278 0.709924i \(-0.251271\pi\)
\(252\) 0 0
\(253\) −147.336 −0.582356
\(254\) 158.810 + 91.6891i 0.625237 + 0.360981i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −220.603 127.365i −0.858377 0.495584i 0.00509129 0.999987i \(-0.498379\pi\)
−0.863469 + 0.504403i \(0.831713\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 225.564i 0.867555i
\(261\) 0 0
\(262\) −104.664 181.283i −0.399481 0.691922i
\(263\) 226.880 130.989i 0.862663 0.498059i −0.00224015 0.999997i \(-0.500713\pi\)
0.864903 + 0.501939i \(0.167380\pi\)
\(264\) 0 0
\(265\) −570.753 −2.15378
\(266\) 0 0
\(267\) 0 0
\(268\) −132.664 + 229.781i −0.495015 + 0.857391i
\(269\) −81.0813 + 46.8123i −0.301417 + 0.174023i −0.643079 0.765799i \(-0.722344\pi\)
0.341662 + 0.939823i \(0.389010\pi\)
\(270\) 0 0
\(271\) 0.583005 1.00979i 0.00215131 0.00372618i −0.864948 0.501862i \(-0.832649\pi\)
0.867099 + 0.498136i \(0.165982\pi\)
\(272\) 43.6058i 0.160316i
\(273\) 0 0
\(274\) −108.834 −0.397204
\(275\) −124.399 71.8217i −0.452359 0.261170i
\(276\) 0 0
\(277\) −16.0000 27.7128i −0.0577617 0.100046i 0.835699 0.549188i \(-0.185063\pi\)
−0.893460 + 0.449142i \(0.851730\pi\)
\(278\) −266.171 153.674i −0.957451 0.552785i
\(279\) 0 0
\(280\) 0 0
\(281\) 166.757i 0.593441i 0.954964 + 0.296721i \(0.0958930\pi\)
−0.954964 + 0.296721i \(0.904107\pi\)
\(282\) 0 0
\(283\) 8.16995 + 14.1508i 0.0288691 + 0.0500027i 0.880099 0.474790i \(-0.157476\pi\)
−0.851230 + 0.524793i \(0.824143\pi\)
\(284\) 21.0240 12.1382i 0.0740281 0.0427401i
\(285\) 0 0
\(286\) −318.996 −1.11537
\(287\) 0 0
\(288\) 0 0
\(289\) −85.0791 + 147.361i −0.294391 + 0.509901i
\(290\) 310.976 179.542i 1.07233 0.619111i
\(291\) 0 0
\(292\) 76.9150 133.221i 0.263408 0.456235i
\(293\) 368.921i 1.25912i −0.776953 0.629558i \(-0.783236\pi\)
0.776953 0.629558i \(-0.216764\pi\)
\(294\) 0 0
\(295\) −353.328 −1.19772
\(296\) −93.0806 53.7401i −0.314462 0.181554i
\(297\) 0 0
\(298\) −114.498 198.316i −0.384222 0.665491i
\(299\) 195.344 + 112.782i 0.653326 + 0.377198i
\(300\) 0 0
\(301\) 0 0
\(302\) 131.757i 0.436280i
\(303\) 0 0
\(304\) 40.0000 + 69.2820i 0.131579 + 0.227901i
\(305\) −82.3508 + 47.5453i −0.270003 + 0.155886i
\(306\) 0 0
\(307\) 192.664 0.627570 0.313785 0.949494i \(-0.398403\pi\)
0.313785 + 0.949494i \(0.398403\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 108.000 187.061i 0.348387 0.603424i
\(311\) −113.688 + 65.6380i −0.365557 + 0.211055i −0.671516 0.740990i \(-0.734356\pi\)
0.305959 + 0.952045i \(0.401023\pi\)
\(312\) 0 0
\(313\) 21.6640 37.5232i 0.0692142 0.119882i −0.829341 0.558742i \(-0.811284\pi\)
0.898556 + 0.438860i \(0.144617\pi\)
\(314\) 261.624i 0.833197i
\(315\) 0 0
\(316\) −67.3360 −0.213088
\(317\) 218.000 + 125.862i 0.687696 + 0.397042i 0.802748 0.596318i \(-0.203370\pi\)
−0.115052 + 0.993359i \(0.536703\pi\)
\(318\) 0 0
\(319\) −253.911 439.787i −0.795960 1.37864i
\(320\) 42.0480 + 24.2764i 0.131400 + 0.0758638i
\(321\) 0 0
\(322\) 0 0
\(323\) 218.029i 0.675013i
\(324\) 0 0
\(325\) 109.956 + 190.449i 0.338325 + 0.585996i
\(326\) −106.548 + 61.5155i −0.326834 + 0.188698i
\(327\) 0 0
\(328\) −171.498 −0.522860
\(329\) 0 0
\(330\) 0 0
\(331\) −180.745 + 313.060i −0.546058 + 0.945800i 0.452482 + 0.891774i \(0.350539\pi\)
−0.998540 + 0.0540260i \(0.982795\pi\)
\(332\) −104.921 + 60.5764i −0.316028 + 0.182459i
\(333\) 0 0
\(334\) 42.8340 74.1906i 0.128245 0.222128i
\(335\) 805.151i 2.40344i
\(336\) 0 0
\(337\) −298.834 −0.886748 −0.443374 0.896337i \(-0.646219\pi\)
−0.443374 + 0.896337i \(0.646219\pi\)
\(338\) 215.957 + 124.683i 0.638926 + 0.368884i
\(339\) 0 0
\(340\) −66.1621 114.596i −0.194594 0.337047i
\(341\) −264.545 152.735i −0.775791 0.447903i
\(342\) 0 0
\(343\) 0 0
\(344\) 236.168i 0.686535i
\(345\) 0 0
\(346\) 114.956 + 199.109i 0.332241 + 0.575459i
\(347\) 178.505 103.060i 0.514425 0.297003i −0.220226 0.975449i \(-0.570679\pi\)
0.734651 + 0.678446i \(0.237346\pi\)
\(348\) 0 0
\(349\) −434.324 −1.24448 −0.622241 0.782826i \(-0.713778\pi\)
−0.622241 + 0.782826i \(0.713778\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 34.3320 59.4648i 0.0975342 0.168934i
\(353\) 160.595 92.7197i 0.454944 0.262662i −0.254972 0.966948i \(-0.582066\pi\)
0.709916 + 0.704286i \(0.248733\pi\)
\(354\) 0 0
\(355\) −36.8340 + 63.7983i −0.103758 + 0.179714i
\(356\) 9.55012i 0.0268262i
\(357\) 0 0
\(358\) 315.498 0.881279
\(359\) 447.533 + 258.383i 1.24661 + 0.719731i 0.970432 0.241376i \(-0.0775987\pi\)
0.276178 + 0.961106i \(0.410932\pi\)
\(360\) 0 0
\(361\) −19.5000 33.7750i −0.0540166 0.0935595i
\(362\) −231.373 133.583i −0.639151 0.369014i
\(363\) 0 0
\(364\) 0 0
\(365\) 466.805i 1.27892i
\(366\) 0 0
\(367\) −58.7451 101.749i −0.160068 0.277246i 0.774825 0.632176i \(-0.217838\pi\)
−0.934893 + 0.354930i \(0.884505\pi\)
\(368\) −42.0480 + 24.2764i −0.114261 + 0.0659685i
\(369\) 0 0
\(370\) 326.154 0.881498
\(371\) 0 0
\(372\) 0 0
\(373\) 201.332 348.717i 0.539764 0.934899i −0.459152 0.888358i \(-0.651847\pi\)
0.998916 0.0465413i \(-0.0148199\pi\)
\(374\) −162.063 + 93.5673i −0.433324 + 0.250180i
\(375\) 0 0
\(376\) 24.0000 41.5692i 0.0638298 0.110556i
\(377\) 777.451i 2.06221i
\(378\) 0 0
\(379\) 398.834 1.05233 0.526166 0.850382i \(-0.323629\pi\)
0.526166 + 0.850382i \(0.323629\pi\)
\(380\) −210.240 121.382i −0.553263 0.319426i
\(381\) 0 0
\(382\) 161.247 + 279.288i 0.422113 + 0.731121i
\(383\) 645.019 + 372.402i 1.68412 + 0.972329i 0.958869 + 0.283849i \(0.0916114\pi\)
0.725255 + 0.688481i \(0.241722\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 189.505i 0.490945i
\(387\) 0 0
\(388\) 188.413 + 326.341i 0.485601 + 0.841085i
\(389\) −463.464 + 267.581i −1.19142 + 0.687869i −0.958630 0.284656i \(-0.908121\pi\)
−0.232795 + 0.972526i \(0.574787\pi\)
\(390\) 0 0
\(391\) 132.324 0.338425
\(392\) 0 0
\(393\) 0 0
\(394\) 133.332 230.938i 0.338406 0.586137i
\(395\) 176.959 102.167i 0.447997 0.258651i
\(396\) 0 0
\(397\) −47.1621 + 81.6871i −0.118796 + 0.205761i −0.919291 0.393579i \(-0.871237\pi\)
0.800495 + 0.599340i \(0.204570\pi\)
\(398\) 144.949i 0.364192i
\(399\) 0 0
\(400\) −47.3360 −0.118340
\(401\) 89.7138 + 51.7963i 0.223725 + 0.129168i 0.607674 0.794187i \(-0.292103\pi\)
−0.383949 + 0.923354i \(0.625436\pi\)
\(402\) 0 0
\(403\) 233.830 + 405.006i 0.580223 + 1.00498i
\(404\) −184.832 106.713i −0.457506 0.264141i
\(405\) 0 0
\(406\) 0 0
\(407\) 461.252i 1.13330i
\(408\) 0 0
\(409\) −4.87844 8.44971i −0.0119277 0.0206594i 0.860000 0.510294i \(-0.170463\pi\)
−0.871928 + 0.489635i \(0.837130\pi\)
\(410\) 450.696 260.210i 1.09926 0.634658i
\(411\) 0 0
\(412\) 262.996 0.638340
\(413\) 0 0
\(414\) 0 0
\(415\) 183.822 318.389i 0.442945 0.767203i
\(416\) −91.0378 + 52.5607i −0.218841 + 0.126348i
\(417\) 0 0
\(418\) −171.660 + 297.324i −0.410670 + 0.711301i
\(419\) 339.411i 0.810051i −0.914305 0.405025i \(-0.867263\pi\)
0.914305 0.405025i \(-0.132737\pi\)
\(420\) 0 0
\(421\) −599.320 −1.42356 −0.711782 0.702401i \(-0.752111\pi\)
−0.711782 + 0.702401i \(0.752111\pi\)
\(422\) −103.493 59.7519i −0.245245 0.141592i
\(423\) 0 0
\(424\) 132.996 + 230.356i 0.313670 + 0.543292i
\(425\) 111.724 + 64.5039i 0.262880 + 0.151774i
\(426\) 0 0
\(427\) 0 0
\(428\) 164.759i 0.384950i
\(429\) 0 0
\(430\) −358.332 620.649i −0.833330 1.44337i
\(431\) 615.725 355.489i 1.42860 0.824800i 0.431586 0.902072i \(-0.357954\pi\)
0.997010 + 0.0772717i \(0.0246209\pi\)
\(432\) 0 0
\(433\) −377.984 −0.872943 −0.436471 0.899718i \(-0.643772\pi\)
−0.436471 + 0.899718i \(0.643772\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 33.8301 58.5954i 0.0775919 0.134393i
\(437\) 210.240 121.382i 0.481098 0.277762i
\(438\) 0 0
\(439\) 264.073 457.388i 0.601533 1.04189i −0.391056 0.920367i \(-0.627890\pi\)
0.992589 0.121519i \(-0.0387767\pi\)
\(440\) 208.365i 0.473556i
\(441\) 0 0
\(442\) 286.494 0.648177
\(443\) −31.7345 18.3219i −0.0716354 0.0413587i 0.463754 0.885964i \(-0.346502\pi\)
−0.535390 + 0.844605i \(0.679835\pi\)
\(444\) 0 0
\(445\) 14.4902 + 25.0977i 0.0325622 + 0.0563993i
\(446\) 194.115 + 112.072i 0.435235 + 0.251283i
\(447\) 0 0
\(448\) 0 0
\(449\) 397.612i 0.885550i −0.896633 0.442775i \(-0.853994\pi\)
0.896633 0.442775i \(-0.146006\pi\)
\(450\) 0 0
\(451\) −367.992 637.381i −0.815947 1.41326i
\(452\) 49.3964 28.5190i 0.109284 0.0630952i
\(453\) 0 0
\(454\) −144.000 −0.317181
\(455\) 0 0
\(456\) 0 0
\(457\) −172.162 + 298.193i −0.376722 + 0.652502i −0.990583 0.136912i \(-0.956282\pi\)
0.613861 + 0.789414i \(0.289616\pi\)
\(458\) −329.352 + 190.152i −0.719110 + 0.415178i
\(459\) 0 0
\(460\) 73.6680 127.597i 0.160148 0.277384i
\(461\) 370.936i 0.804634i 0.915500 + 0.402317i \(0.131795\pi\)
−0.915500 + 0.402317i \(0.868205\pi\)
\(462\) 0 0
\(463\) 78.3320 0.169184 0.0845918 0.996416i \(-0.473041\pi\)
0.0845918 + 0.996416i \(0.473041\pi\)
\(464\) −144.927 83.6734i −0.312342 0.180331i
\(465\) 0 0
\(466\) 18.5791 + 32.1799i 0.0398692 + 0.0690556i
\(467\) −346.201 199.879i −0.741330 0.428007i 0.0812229 0.996696i \(-0.474117\pi\)
−0.822553 + 0.568689i \(0.807451\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 145.658i 0.309912i
\(471\) 0 0
\(472\) 82.3320 + 142.603i 0.174432 + 0.302126i
\(473\) −877.731 + 506.758i −1.85567 + 1.07137i
\(474\) 0 0
\(475\) 236.680 0.498273
\(476\) 0 0
\(477\) 0 0
\(478\) −65.2470 + 113.011i −0.136500 + 0.236425i
\(479\) 609.100 351.664i 1.27161 0.734163i 0.296317 0.955090i \(-0.404241\pi\)
0.975290 + 0.220927i \(0.0709081\pi\)
\(480\) 0 0
\(481\) −353.077 + 611.547i −0.734048 + 1.27141i
\(482\) 485.425i 1.00711i
\(483\) 0 0
\(484\) 52.6719 0.108826
\(485\) −990.298 571.749i −2.04185 1.17886i
\(486\) 0 0
\(487\) 41.2549 + 71.4556i 0.0847124 + 0.146726i 0.905269 0.424840i \(-0.139670\pi\)
−0.820556 + 0.571566i \(0.806336\pi\)
\(488\) 38.3786 + 22.1579i 0.0786446 + 0.0454055i
\(489\) 0 0
\(490\) 0 0
\(491\) 184.203i 0.375158i −0.982249 0.187579i \(-0.939936\pi\)
0.982249 0.187579i \(-0.0600641\pi\)
\(492\) 0 0
\(493\) 228.041 + 394.978i 0.462557 + 0.801172i
\(494\) 455.189 262.803i 0.921435 0.531991i
\(495\) 0 0
\(496\) −100.664 −0.202952
\(497\) 0 0
\(498\) 0 0
\(499\) −376.405 + 651.953i −0.754319 + 1.30652i 0.191393 + 0.981513i \(0.438699\pi\)
−0.945712 + 0.325005i \(0.894634\pi\)
\(500\) −138.401 + 79.9059i −0.276802 + 0.159812i
\(501\) 0 0
\(502\) 252.000 436.477i 0.501992 0.869476i
\(503\) 662.540i 1.31718i 0.752504 + 0.658588i \(0.228846\pi\)
−0.752504 + 0.658588i \(0.771154\pi\)
\(504\) 0 0
\(505\) 647.652 1.28248
\(506\) −180.449 104.182i −0.356618 0.205894i
\(507\) 0 0
\(508\) 129.668 + 224.592i 0.255252 + 0.442109i
\(509\) 821.958 + 474.557i 1.61485 + 0.932333i 0.988225 + 0.153010i \(0.0488968\pi\)
0.626623 + 0.779322i \(0.284437\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) −180.122 311.980i −0.350431 0.606964i
\(515\) −691.153 + 399.037i −1.34204 + 0.774830i
\(516\) 0 0
\(517\) 205.992 0.398437
\(518\) 0 0
\(519\) 0 0
\(520\) 159.498 276.259i 0.306727 0.531267i
\(521\) −618.640 + 357.172i −1.18741 + 0.685551i −0.957717 0.287712i \(-0.907105\pi\)
−0.229692 + 0.973263i \(0.573772\pi\)
\(522\) 0 0
\(523\) −116.000 + 200.918i −0.221797 + 0.384164i −0.955354 0.295464i \(-0.904526\pi\)
0.733556 + 0.679629i \(0.237859\pi\)
\(524\) 296.035i 0.564952i
\(525\) 0 0
\(526\) 370.494 0.704361
\(527\) 237.591 + 137.173i 0.450837 + 0.260291i
\(528\) 0 0
\(529\) −190.832 330.531i −0.360741 0.624822i
\(530\) −699.027 403.583i −1.31892 0.761478i
\(531\) 0 0
\(532\) 0 0
\(533\) 1126.76i 2.11399i
\(534\) 0 0
\(535\) 249.984 + 432.985i 0.467260 + 0.809319i
\(536\) −324.959 + 187.615i −0.606267 + 0.350029i
\(537\) 0 0
\(538\) −132.405 −0.246106
\(539\) 0 0
\(540\) 0 0
\(541\) −82.8340 + 143.473i −0.153113 + 0.265199i −0.932370 0.361505i \(-0.882263\pi\)
0.779257 + 0.626704i \(0.215596\pi\)
\(542\) 1.42807 0.824494i 0.00263481 0.00152121i
\(543\) 0 0
\(544\) −30.8340 + 53.4060i −0.0566801 + 0.0981729i
\(545\) 205.318i 0.376730i
\(546\) 0 0
\(547\) 295.676 0.540541 0.270270 0.962784i \(-0.412887\pi\)
0.270270 + 0.962784i \(0.412887\pi\)
\(548\) −133.294 76.9573i −0.243237 0.140433i
\(549\) 0 0
\(550\) −101.571 175.926i −0.184675 0.319866i
\(551\) 724.633 + 418.367i 1.31512 + 0.759287i
\(552\) 0 0
\(553\) 0 0
\(554\) 45.2548i 0.0816874i
\(555\) 0 0
\(556\) −217.328 376.423i −0.390878 0.677020i
\(557\) 66.5477 38.4213i 0.119475 0.0689790i −0.439071 0.898452i \(-0.644693\pi\)
0.558547 + 0.829473i \(0.311359\pi\)
\(558\) 0 0
\(559\) 1551.64 2.77575
\(560\) 0 0
\(561\) 0 0
\(562\) −117.915 + 204.235i −0.209813 + 0.363407i
\(563\) −880.170 + 508.167i −1.56336 + 0.902605i −0.566444 + 0.824100i \(0.691681\pi\)
−0.996914 + 0.0785049i \(0.974985\pi\)
\(564\) 0 0
\(565\) −86.5425 + 149.896i −0.153173 + 0.265303i
\(566\) 23.1081i 0.0408270i
\(567\) 0 0
\(568\) 34.3320 0.0604437
\(569\) 507.952 + 293.266i 0.892710 + 0.515406i 0.874828 0.484434i \(-0.160974\pi\)
0.0178822 + 0.999840i \(0.494308\pi\)
\(570\) 0 0
\(571\) −475.822 824.148i −0.833314 1.44334i −0.895396 0.445271i \(-0.853107\pi\)
0.0620822 0.998071i \(-0.480226\pi\)
\(572\) −390.689 225.564i −0.683022 0.394343i
\(573\) 0 0
\(574\) 0 0
\(575\) 143.643i 0.249815i
\(576\) 0 0
\(577\) −74.3360 128.754i −0.128832 0.223143i 0.794392 0.607405i \(-0.207789\pi\)
−0.923224 + 0.384262i \(0.874456\pi\)
\(578\) −208.400 + 120.320i −0.360554 + 0.208166i
\(579\) 0 0
\(580\) 507.822 0.875555
\(581\) 0 0
\(582\) 0 0
\(583\) −570.753 + 988.573i −0.978993 + 1.69567i
\(584\) 188.403 108.774i 0.322607 0.186257i
\(585\) 0 0
\(586\) 260.867 451.834i 0.445165 0.771048i
\(587\) 332.564i 0.566548i −0.959039 0.283274i \(-0.908579\pi\)
0.959039 0.283274i \(-0.0914206\pi\)
\(588\) 0 0
\(589\) 503.320 0.854533
\(590\) −432.737 249.841i −0.733452 0.423459i
\(591\) 0 0
\(592\) −76.0000 131.636i −0.128378 0.222358i
\(593\) 188.145 + 108.625i 0.317276 + 0.183180i 0.650178 0.759782i \(-0.274694\pi\)
−0.332902 + 0.942962i \(0.608028\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 323.849i 0.543371i
\(597\) 0 0
\(598\) 159.498 + 276.259i 0.266719 + 0.461971i
\(599\) −149.111 + 86.0896i −0.248934 + 0.143722i −0.619276 0.785173i \(-0.712574\pi\)
0.370342 + 0.928895i \(0.379240\pi\)
\(600\) 0 0
\(601\) 418.000 0.695507 0.347754 0.937586i \(-0.386945\pi\)
0.347754 + 0.937586i \(0.386945\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −93.1660 + 161.368i −0.154248 + 0.267166i
\(605\) −138.422 + 79.9178i −0.228796 + 0.132096i
\(606\) 0 0
\(607\) 313.579 543.135i 0.516605 0.894786i −0.483209 0.875505i \(-0.660529\pi\)
0.999814 0.0192808i \(-0.00613765\pi\)
\(608\) 113.137i 0.186081i
\(609\) 0 0
\(610\) −134.478 −0.220456
\(611\) −273.113 157.682i −0.446994 0.258072i
\(612\) 0 0
\(613\) 139.664 + 241.905i 0.227837 + 0.394625i 0.957167 0.289537i \(-0.0935014\pi\)
−0.729330 + 0.684162i \(0.760168\pi\)
\(614\) 235.964 + 136.234i 0.384307 + 0.221880i
\(615\) 0 0
\(616\) 0 0
\(617\) 358.380i 0.580843i 0.956899 + 0.290422i \(0.0937955\pi\)
−0.956899 + 0.290422i \(0.906204\pi\)
\(618\) 0 0
\(619\) −491.822 851.861i −0.794543 1.37619i −0.923129 0.384491i \(-0.874377\pi\)
0.128586 0.991698i \(-0.458956\pi\)
\(620\) 264.545 152.735i 0.426685 0.246347i
\(621\) 0 0
\(622\) −185.652 −0.298476
\(623\) 0 0
\(624\) 0 0
\(625\) 390.403 676.198i 0.624645 1.08192i
\(626\) 53.0658 30.6376i 0.0847697 0.0489418i
\(627\) 0 0
\(628\) 184.996 320.423i 0.294580 0.510227i
\(629\) 414.256i 0.658594i
\(630\) 0 0
\(631\) −298.996 −0.473845 −0.236922 0.971529i \(-0.576139\pi\)
−0.236922 + 0.971529i \(0.576139\pi\)
\(632\) −82.4694 47.6137i −0.130490 0.0753382i
\(633\) 0 0
\(634\) 177.996 + 308.298i 0.280751 + 0.486275i
\(635\) −681.534 393.484i −1.07328 0.619660i
\(636\) 0 0
\(637\) 0 0
\(638\) 718.169i 1.12566i
\(639\) 0 0
\(640\) 34.3320 + 59.4648i 0.0536438 + 0.0929138i
\(641\) −270.163 + 155.979i −0.421471 + 0.243336i −0.695706 0.718326i \(-0.744909\pi\)
0.274236 + 0.961663i \(0.411575\pi\)
\(642\) 0 0
\(643\) 604.000 0.939347 0.469673 0.882840i \(-0.344372\pi\)
0.469673 + 0.882840i \(0.344372\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 154.170 267.030i 0.238653 0.413359i
\(647\) −155.538 + 89.7998i −0.240398 + 0.138794i −0.615360 0.788246i \(-0.710989\pi\)
0.374961 + 0.927040i \(0.377656\pi\)
\(648\) 0 0
\(649\) −353.328 + 611.982i −0.544419 + 0.942962i
\(650\) 311.001i 0.478463i
\(651\) 0 0
\(652\) −173.992 −0.266859
\(653\) −417.331 240.946i −0.639097 0.368983i 0.145169 0.989407i \(-0.453627\pi\)
−0.784267 + 0.620424i \(0.786961\pi\)
\(654\) 0 0
\(655\) 449.166 + 777.978i 0.685750 + 1.18775i
\(656\) −210.041 121.267i −0.320185 0.184859i
\(657\) 0 0
\(658\) 0 0
\(659\) 877.408i 1.33142i 0.746209 + 0.665711i \(0.231872\pi\)
−0.746209 + 0.665711i \(0.768128\pi\)
\(660\) 0 0
\(661\) −260.822 451.757i −0.394587 0.683445i 0.598461 0.801152i \(-0.295779\pi\)
−0.993048 + 0.117707i \(0.962446\pi\)
\(662\) −442.733 + 255.612i −0.668781 + 0.386121i
\(663\) 0 0
\(664\) −171.336 −0.258036
\(665\) 0 0
\(666\) 0 0
\(667\) −253.911 + 439.787i −0.380676 + 0.659351i
\(668\) 104.921 60.5764i 0.157068 0.0906832i
\(669\) 0 0
\(670\) 569.328 986.105i 0.849743 1.47180i
\(671\) 190.181i 0.283429i
\(672\) 0 0
\(673\) −659.992 −0.980672 −0.490336 0.871534i \(-0.663126\pi\)
−0.490336 + 0.871534i \(0.663126\pi\)
\(674\) −365.995 211.308i −0.543020 0.313513i
\(675\) 0 0
\(676\) 176.328 + 305.409i 0.260840 + 0.451789i
\(677\) 880.121 + 508.138i 1.30003 + 0.750573i 0.980409 0.196972i \(-0.0631108\pi\)
0.319622 + 0.947545i \(0.396444\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 187.135i 0.275198i
\(681\) 0 0
\(682\) −216.000 374.123i −0.316716 0.548567i
\(683\) −203.615 + 117.557i −0.298119 + 0.172119i −0.641597 0.767042i \(-0.721728\pi\)
0.343479 + 0.939160i \(0.388395\pi\)
\(684\) 0 0
\(685\) 467.061 0.681841
\(686\) 0 0
\(687\) 0 0
\(688\) −166.996 + 289.246i −0.242727 + 0.420415i
\(689\) 1513.46 873.795i 2.19660 1.26821i
\(690\) 0 0
\(691\) −25.4902 + 44.1502i −0.0368888 + 0.0638933i −0.883880 0.467713i \(-0.845078\pi\)
0.846992 + 0.531606i \(0.178411\pi\)
\(692\) 325.143i 0.469860i
\(693\) 0 0
\(694\) 291.498 0.420026
\(695\) 1142.28 + 659.493i 1.64356 + 0.948911i
\(696\) 0 0
\(697\) 330.498 + 572.439i 0.474172 + 0.821290i
\(698\) −531.936 307.114i −0.762086 0.439991i
\(699\) 0 0
\(700\) 0 0
\(701\) 141.530i 0.201898i 0.994892 + 0.100949i \(0.0321879\pi\)
−0.994892 + 0.100949i \(0.967812\pi\)
\(702\) 0 0
\(703\) 380.000 + 658.179i 0.540541 + 0.936244i
\(704\) 84.0959 48.5528i 0.119454 0.0689671i
\(705\) 0 0
\(706\) 262.251 0.371460
\(707\) 0 0
\(708\) 0 0
\(709\) 27.7490 48.0627i 0.0391382 0.0677894i −0.845793 0.533512i \(-0.820872\pi\)
0.884931 + 0.465722i \(0.154205\pi\)
\(710\) −90.2245 + 52.0911i −0.127077 + 0.0733678i
\(711\) 0 0
\(712\) 6.75295 11.6965i 0.00948448 0.0164276i
\(713\) 305.470i 0.428429i
\(714\) 0 0
\(715\) 1368.97 1.91465
\(716\) 386.405 + 223.091i 0.539671 + 0.311579i
\(717\) 0 0
\(718\) 365.409 + 632.907i 0.508926 + 0.881486i
\(719\) −873.843 504.514i −1.21536 0.701688i −0.251438 0.967874i \(-0.580903\pi\)
−0.963922 + 0.266185i \(0.914237\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 55.1543i 0.0763910i
\(723\) 0 0
\(724\) −188.915 327.210i −0.260932 0.451948i
\(725\) −428.765 + 247.547i −0.591400 + 0.341445i
\(726\) 0 0
\(727\) 365.182 0.502313 0.251157 0.967946i \(-0.419189\pi\)
0.251157 + 0.967946i \(0.419189\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −330.081 + 571.717i −0.452166 + 0.783174i
\(731\) 788.300 455.125i 1.07839 0.622606i
\(732\) 0 0
\(733\) −176.539 + 305.774i −0.240844 + 0.417154i −0.960955 0.276705i \(-0.910758\pi\)
0.720111 + 0.693859i \(0.244091\pi\)
\(734\) 166.156i 0.226371i
\(735\) 0 0
\(736\) −68.6640 −0.0932935
\(737\) −1394.56 805.151i −1.89222 1.09247i
\(738\) 0 0
\(739\) −164.842 285.514i −0.223061 0.386352i 0.732675 0.680579i \(-0.238271\pi\)
−0.955736 + 0.294226i \(0.904938\pi\)
\(740\) 399.456 + 230.626i 0.539805 + 0.311657i
\(741\) 0 0
\(742\) 0 0
\(743\) 112.061i 0.150822i −0.997153 0.0754112i \(-0.975973\pi\)
0.997153 0.0754112i \(-0.0240270\pi\)
\(744\) 0 0
\(745\) 491.369 + 851.075i 0.659555 + 1.14238i
\(746\) 493.161 284.726i 0.661073 0.381671i
\(747\) 0 0
\(748\) −264.648 −0.353808
\(749\) 0 0
\(750\) 0 0
\(751\) 72.4131 125.423i 0.0964222 0.167008i −0.813779 0.581174i \(-0.802593\pi\)
0.910201 + 0.414166i \(0.135927\pi\)
\(752\) 58.7878 33.9411i 0.0781752 0.0451345i
\(753\) 0 0
\(754\) −549.741 + 952.180i −0.729100 + 1.26284i
\(755\) 565.434i 0.748919i
\(756\) 0 0
\(757\) 78.1699 0.103263 0.0516314 0.998666i \(-0.483558\pi\)
0.0516314 + 0.998666i \(0.483558\pi\)
\(758\) 488.470 + 282.018i 0.644419 + 0.372056i
\(759\) 0 0
\(760\) −171.660 297.324i −0.225869 0.391216i
\(761\) 1269.16 + 732.752i 1.66776 + 0.962880i 0.968843 + 0.247676i \(0.0796667\pi\)
0.698915 + 0.715205i \(0.253667\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 456.076i 0.596957i
\(765\) 0 0
\(766\) 526.656 + 912.195i 0.687541 + 1.19086i
\(767\) 936.915 540.928i 1.22153 0.705252i
\(768\) 0 0
\(769\) −729.320 −0.948401 −0.474200 0.880417i \(-0.657263\pi\)
−0.474200 + 0.880417i \(0.657263\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 134.000 232.095i 0.173575 0.300641i
\(773\) 376.339 217.280i 0.486855 0.281086i −0.236414 0.971653i \(-0.575972\pi\)
0.723269 + 0.690566i \(0.242639\pi\)
\(774\) 0 0
\(775\) −148.907 + 257.915i −0.192138 + 0.332793i
\(776\) 532.913i 0.686743i
\(777\) 0 0
\(778\) −756.834 −0.972794
\(779\) 1050.21 + 606.337i 1.34815 + 0.778353i
\(780\) 0 0
\(781\) 73.6680 + 127.597i 0.0943252 + 0.163376i
\(782\) 162.063 + 93.5673i 0.207242 + 0.119651i
\(783\) 0 0
\(784\) 0 0
\(785\) 1122.76i 1.43027i
\(786\) 0 0
\(787\) −7.67585 13.2950i −0.00975331 0.0168932i 0.861108 0.508423i \(-0.169771\pi\)
−0.870861 + 0.491530i \(0.836438\pi\)
\(788\) 326.595 188.560i 0.414461 0.239289i
\(789\) 0 0
\(790\) 288.972 0.365788
\(791\) 0 0
\(792\) 0