Properties

Label 378.3.s.d.107.2
Level $378$
Weight $3$
Character 378.107
Analytic conductor $10.300$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 378.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.2997539928\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.621801639936.1
Defining polynomial: \( x^{8} - 4x^{7} - 34x^{6} + 116x^{5} + 413x^{4} - 1024x^{3} - 1664x^{2} + 2196x + 4467 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.2
Root \(-1.31664 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 378.107
Dual form 378.3.s.d.53.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(3.11254 + 1.79703i) q^{5} +(-6.04138 - 3.53578i) q^{7} -2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(3.11254 + 1.79703i) q^{5} +(-6.04138 - 3.53578i) q^{7} -2.82843i q^{8} +(-2.54138 - 4.40180i) q^{10} +(-13.5736 + 7.83670i) q^{11} +13.0828 q^{13} +(4.89898 + 8.60233i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-22.9112 + 13.2278i) q^{17} +(6.50000 - 11.2583i) q^{19} +7.18811i q^{20} +22.1655 q^{22} +(-17.8095 - 10.2823i) q^{23} +(-6.04138 - 10.4640i) q^{25} +(-16.0230 - 9.25091i) q^{26} +(0.0827625 - 13.9998i) q^{28} +9.48500i q^{29} +(-15.6655 - 27.1335i) q^{31} +(4.89898 - 2.82843i) q^{32} +37.4138 q^{34} +(-12.4502 - 21.8618i) q^{35} +(-26.8724 + 46.5444i) q^{37} +(-15.9217 + 9.19239i) q^{38} +(5.08276 - 8.80360i) q^{40} +19.2674i q^{41} -76.7449 q^{43} +(-27.1471 - 15.6734i) q^{44} +(14.5414 + 25.1864i) q^{46} +(20.6644 + 11.9306i) q^{47} +(23.9966 + 42.7219i) q^{49} +17.0876i q^{50} +(13.0828 + 22.6600i) q^{52} +(-39.3397 + 22.7128i) q^{53} -56.3311 q^{55} +(-10.0007 + 17.0876i) q^{56} +(6.70691 - 11.6167i) q^{58} +(-71.2379 + 41.1292i) q^{59} +(-2.28967 + 3.96582i) q^{61} +44.3088i q^{62} -8.00000 q^{64} +(40.7207 + 23.5101i) q^{65} +(43.7897 + 75.8459i) q^{67} +(-45.8224 - 26.4556i) q^{68} +(-0.210331 + 35.5787i) q^{70} -100.526i q^{71} +(-29.9586 - 51.8898i) q^{73} +(65.8237 - 38.0034i) q^{74} +26.0000 q^{76} +(109.712 + 0.648585i) q^{77} +(36.8345 - 63.7992i) q^{79} +(-12.4502 + 7.18811i) q^{80} +(13.6241 - 23.5977i) q^{82} +90.0415i q^{83} -95.0828 q^{85} +(93.9929 + 54.2668i) q^{86} +(22.1655 + 38.3918i) q^{88} +(-109.454 - 63.1934i) q^{89} +(-79.0380 - 46.2577i) q^{91} -41.1292i q^{92} +(-16.8724 - 29.2239i) q^{94} +(40.4631 - 23.3614i) q^{95} -0.0827625 q^{97} +(0.819293 - 69.2916i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} - 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} - 24 q^{7} + 4 q^{10} + 56 q^{13} - 16 q^{16} + 52 q^{19} + 80 q^{22} - 24 q^{25} - 48 q^{28} - 28 q^{31} + 56 q^{34} + 4 q^{37} - 8 q^{40} - 176 q^{43} + 92 q^{46} - 100 q^{49} + 56 q^{52} - 256 q^{55} - 68 q^{58} + 152 q^{61} - 64 q^{64} + 180 q^{67} - 172 q^{70} - 264 q^{73} + 208 q^{76} + 392 q^{79} + 36 q^{82} - 712 q^{85} + 80 q^{88} - 316 q^{91} + 84 q^{94} + 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 0.707107i −0.612372 0.353553i
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) 3.11254 + 1.79703i 0.622509 + 0.359406i 0.777845 0.628456i \(-0.216313\pi\)
−0.155336 + 0.987862i \(0.549646\pi\)
\(6\) 0 0
\(7\) −6.04138 3.53578i −0.863054 0.505111i
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) −2.54138 4.40180i −0.254138 0.440180i
\(11\) −13.5736 + 7.83670i −1.23396 + 0.712427i −0.967853 0.251517i \(-0.919071\pi\)
−0.266107 + 0.963944i \(0.585737\pi\)
\(12\) 0 0
\(13\) 13.0828 1.00637 0.503183 0.864180i \(-0.332162\pi\)
0.503183 + 0.864180i \(0.332162\pi\)
\(14\) 4.89898 + 8.60233i 0.349927 + 0.614452i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −22.9112 + 13.2278i −1.34772 + 0.778105i −0.987926 0.154928i \(-0.950485\pi\)
−0.359791 + 0.933033i \(0.617152\pi\)
\(18\) 0 0
\(19\) 6.50000 11.2583i 0.342105 0.592544i −0.642718 0.766103i \(-0.722193\pi\)
0.984823 + 0.173559i \(0.0555267\pi\)
\(20\) 7.18811i 0.359406i
\(21\) 0 0
\(22\) 22.1655 1.00752
\(23\) −17.8095 10.2823i −0.774325 0.447057i 0.0600901 0.998193i \(-0.480861\pi\)
−0.834415 + 0.551136i \(0.814195\pi\)
\(24\) 0 0
\(25\) −6.04138 10.4640i −0.241655 0.418559i
\(26\) −16.0230 9.25091i −0.616271 0.355804i
\(27\) 0 0
\(28\) 0.0827625 13.9998i 0.00295580 0.499991i
\(29\) 9.48500i 0.327069i 0.986538 + 0.163534i \(0.0522895\pi\)
−0.986538 + 0.163534i \(0.947711\pi\)
\(30\) 0 0
\(31\) −15.6655 27.1335i −0.505340 0.875274i −0.999981 0.00617656i \(-0.998034\pi\)
0.494641 0.869097i \(-0.335299\pi\)
\(32\) 4.89898 2.82843i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 37.4138 1.10041
\(35\) −12.4502 21.8618i −0.355719 0.624623i
\(36\) 0 0
\(37\) −26.8724 + 46.5444i −0.726282 + 1.25796i 0.232162 + 0.972677i \(0.425420\pi\)
−0.958444 + 0.285280i \(0.907913\pi\)
\(38\) −15.9217 + 9.19239i −0.418992 + 0.241905i
\(39\) 0 0
\(40\) 5.08276 8.80360i 0.127069 0.220090i
\(41\) 19.2674i 0.469938i 0.972003 + 0.234969i \(0.0754988\pi\)
−0.972003 + 0.234969i \(0.924501\pi\)
\(42\) 0 0
\(43\) −76.7449 −1.78476 −0.892382 0.451281i \(-0.850967\pi\)
−0.892382 + 0.451281i \(0.850967\pi\)
\(44\) −27.1471 15.6734i −0.616980 0.356213i
\(45\) 0 0
\(46\) 14.5414 + 25.1864i 0.316117 + 0.547531i
\(47\) 20.6644 + 11.9306i 0.439669 + 0.253843i 0.703457 0.710738i \(-0.251639\pi\)
−0.263788 + 0.964581i \(0.584972\pi\)
\(48\) 0 0
\(49\) 23.9966 + 42.7219i 0.489726 + 0.871876i
\(50\) 17.0876i 0.341752i
\(51\) 0 0
\(52\) 13.0828 + 22.6600i 0.251592 + 0.435769i
\(53\) −39.3397 + 22.7128i −0.742258 + 0.428543i −0.822890 0.568201i \(-0.807640\pi\)
0.0806316 + 0.996744i \(0.474306\pi\)
\(54\) 0 0
\(55\) −56.3311 −1.02420
\(56\) −10.0007 + 17.0876i −0.178584 + 0.305136i
\(57\) 0 0
\(58\) 6.70691 11.6167i 0.115636 0.200288i
\(59\) −71.2379 + 41.1292i −1.20742 + 0.697106i −0.962195 0.272360i \(-0.912196\pi\)
−0.245227 + 0.969466i \(0.578863\pi\)
\(60\) 0 0
\(61\) −2.28967 + 3.96582i −0.0375356 + 0.0650135i −0.884183 0.467141i \(-0.845284\pi\)
0.846647 + 0.532154i \(0.178617\pi\)
\(62\) 44.3088i 0.714658i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) 40.7207 + 23.5101i 0.626472 + 0.361694i
\(66\) 0 0
\(67\) 43.7897 + 75.8459i 0.653577 + 1.13203i 0.982248 + 0.187584i \(0.0600658\pi\)
−0.328671 + 0.944444i \(0.606601\pi\)
\(68\) −45.8224 26.4556i −0.673858 0.389052i
\(69\) 0 0
\(70\) −0.210331 + 35.5787i −0.00300473 + 0.508267i
\(71\) 100.526i 1.41586i −0.706282 0.707931i \(-0.749629\pi\)
0.706282 0.707931i \(-0.250371\pi\)
\(72\) 0 0
\(73\) −29.9586 51.8898i −0.410392 0.710820i 0.584541 0.811365i \(-0.301275\pi\)
−0.994933 + 0.100545i \(0.967941\pi\)
\(74\) 65.8237 38.0034i 0.889510 0.513559i
\(75\) 0 0
\(76\) 26.0000 0.342105
\(77\) 109.712 + 0.648585i 1.42483 + 0.00842318i
\(78\) 0 0
\(79\) 36.8345 63.7992i 0.466259 0.807585i −0.532998 0.846116i \(-0.678935\pi\)
0.999257 + 0.0385318i \(0.0122681\pi\)
\(80\) −12.4502 + 7.18811i −0.155627 + 0.0898514i
\(81\) 0 0
\(82\) 13.6241 23.5977i 0.166148 0.287777i
\(83\) 90.0415i 1.08484i 0.840108 + 0.542419i \(0.182491\pi\)
−0.840108 + 0.542419i \(0.817509\pi\)
\(84\) 0 0
\(85\) −95.0828 −1.11862
\(86\) 93.9929 + 54.2668i 1.09294 + 0.631009i
\(87\) 0 0
\(88\) 22.1655 + 38.3918i 0.251881 + 0.436271i
\(89\) −109.454 63.1934i −1.22982 0.710039i −0.262830 0.964842i \(-0.584656\pi\)
−0.966993 + 0.254804i \(0.917989\pi\)
\(90\) 0 0
\(91\) −79.0380 46.2577i −0.868549 0.508327i
\(92\) 41.1292i 0.447057i
\(93\) 0 0
\(94\) −16.8724 29.2239i −0.179494 0.310893i
\(95\) 40.4631 23.3614i 0.425927 0.245909i
\(96\) 0 0
\(97\) −0.0827625 −0.000853222 −0.000426611 1.00000i \(-0.500136\pi\)
−0.000426611 1.00000i \(0.500136\pi\)
\(98\) 0.819293 69.2916i 0.00836013 0.707057i
\(99\) 0 0
\(100\) 12.0828 20.9280i 0.120828 0.209280i
\(101\) 125.625 72.5297i 1.24381 0.718116i 0.273945 0.961745i \(-0.411671\pi\)
0.969868 + 0.243630i \(0.0783381\pi\)
\(102\) 0 0
\(103\) 3.12757 5.41711i 0.0303647 0.0525933i −0.850444 0.526066i \(-0.823666\pi\)
0.880808 + 0.473473i \(0.157000\pi\)
\(104\) 37.0036i 0.355804i
\(105\) 0 0
\(106\) 64.2414 0.606051
\(107\) −30.6102 17.6728i −0.286077 0.165167i 0.350094 0.936714i \(-0.386150\pi\)
−0.636171 + 0.771548i \(0.719483\pi\)
\(108\) 0 0
\(109\) 72.0414 + 124.779i 0.660930 + 1.14476i 0.980372 + 0.197159i \(0.0631714\pi\)
−0.319442 + 0.947606i \(0.603495\pi\)
\(110\) 68.9912 + 39.8321i 0.627192 + 0.362110i
\(111\) 0 0
\(112\) 24.3311 13.8564i 0.217242 0.123718i
\(113\) 78.3670i 0.693513i −0.937955 0.346756i \(-0.887283\pi\)
0.937955 0.346756i \(-0.112717\pi\)
\(114\) 0 0
\(115\) −36.9552 64.0083i −0.321350 0.556594i
\(116\) −16.4285 + 9.48500i −0.141625 + 0.0817672i
\(117\) 0 0
\(118\) 116.331 0.985856
\(119\) 185.186 + 1.09476i 1.55618 + 0.00919970i
\(120\) 0 0
\(121\) 62.3276 107.955i 0.515104 0.892187i
\(122\) 5.60852 3.23808i 0.0459715 0.0265416i
\(123\) 0 0
\(124\) 31.3311 54.2670i 0.252670 0.437637i
\(125\) 133.278i 1.06622i
\(126\) 0 0
\(127\) 76.5793 0.602987 0.301493 0.953468i \(-0.402515\pi\)
0.301493 + 0.953468i \(0.402515\pi\)
\(128\) 9.79796 + 5.65685i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −33.2483 57.5877i −0.255756 0.442982i
\(131\) 169.974 + 98.1343i 1.29751 + 0.749117i 0.979973 0.199130i \(-0.0638116\pi\)
0.317535 + 0.948247i \(0.397145\pi\)
\(132\) 0 0
\(133\) −79.0759 + 45.0333i −0.594556 + 0.338596i
\(134\) 123.856i 0.924298i
\(135\) 0 0
\(136\) 37.4138 + 64.8026i 0.275102 + 0.476490i
\(137\) −21.1796 + 12.2281i −0.154596 + 0.0892559i −0.575302 0.817941i \(-0.695116\pi\)
0.420706 + 0.907197i \(0.361782\pi\)
\(138\) 0 0
\(139\) −64.5725 −0.464550 −0.232275 0.972650i \(-0.574617\pi\)
−0.232275 + 0.972650i \(0.574617\pi\)
\(140\) 25.4156 43.4261i 0.181540 0.310187i
\(141\) 0 0
\(142\) −71.0828 + 123.119i −0.500583 + 0.867035i
\(143\) −177.580 + 102.526i −1.24182 + 0.716963i
\(144\) 0 0
\(145\) −17.0448 + 29.5225i −0.117550 + 0.203603i
\(146\) 84.7358i 0.580382i
\(147\) 0 0
\(148\) −107.490 −0.726282
\(149\) 174.374 + 100.675i 1.17030 + 0.675671i 0.953750 0.300602i \(-0.0971875\pi\)
0.216546 + 0.976272i \(0.430521\pi\)
\(150\) 0 0
\(151\) −56.8242 98.4224i −0.376319 0.651804i 0.614204 0.789147i \(-0.289477\pi\)
−0.990524 + 0.137343i \(0.956144\pi\)
\(152\) −31.8434 18.3848i −0.209496 0.120952i
\(153\) 0 0
\(154\) −133.910 78.3723i −0.869548 0.508911i
\(155\) 112.606i 0.726487i
\(156\) 0 0
\(157\) 64.6173 + 111.920i 0.411575 + 0.712869i 0.995062 0.0992534i \(-0.0316454\pi\)
−0.583487 + 0.812122i \(0.698312\pi\)
\(158\) −90.2257 + 52.0918i −0.571049 + 0.329695i
\(159\) 0 0
\(160\) 20.3311 0.127069
\(161\) 71.2379 + 125.090i 0.442472 + 0.776955i
\(162\) 0 0
\(163\) 48.5000 84.0045i 0.297546 0.515365i −0.678028 0.735036i \(-0.737165\pi\)
0.975574 + 0.219671i \(0.0704985\pi\)
\(164\) −33.3722 + 19.2674i −0.203489 + 0.117484i
\(165\) 0 0
\(166\) 63.6689 110.278i 0.383548 0.664324i
\(167\) 159.328i 0.954061i −0.878887 0.477031i \(-0.841713\pi\)
0.878887 0.477031i \(-0.158287\pi\)
\(168\) 0 0
\(169\) 2.15868 0.0127732
\(170\) 116.452 + 67.2337i 0.685013 + 0.395492i
\(171\) 0 0
\(172\) −76.7449 132.926i −0.446191 0.772826i
\(173\) −173.251 100.026i −1.00145 0.578187i −0.0927725 0.995687i \(-0.529573\pi\)
−0.908677 + 0.417500i \(0.862906\pi\)
\(174\) 0 0
\(175\) −0.500000 + 84.5779i −0.00285714 + 0.483302i
\(176\) 62.6936i 0.356213i
\(177\) 0 0
\(178\) 89.3690 + 154.792i 0.502073 + 0.869616i
\(179\) 190.896 110.214i 1.06646 0.615718i 0.139245 0.990258i \(-0.455533\pi\)
0.927211 + 0.374540i \(0.122199\pi\)
\(180\) 0 0
\(181\) 274.311 1.51553 0.757764 0.652529i \(-0.226292\pi\)
0.757764 + 0.652529i \(0.226292\pi\)
\(182\) 64.0922 + 112.542i 0.352155 + 0.618364i
\(183\) 0 0
\(184\) −29.0828 + 50.3728i −0.158058 + 0.273765i
\(185\) −167.283 + 96.5810i −0.904234 + 0.522060i
\(186\) 0 0
\(187\) 207.324 359.096i 1.10869 1.92030i
\(188\) 47.7224i 0.253843i
\(189\) 0 0
\(190\) −66.0759 −0.347768
\(191\) 150.175 + 86.7035i 0.786256 + 0.453945i 0.838643 0.544682i \(-0.183350\pi\)
−0.0523868 + 0.998627i \(0.516683\pi\)
\(192\) 0 0
\(193\) 94.6173 + 163.882i 0.490245 + 0.849129i 0.999937 0.0112277i \(-0.00357395\pi\)
−0.509692 + 0.860357i \(0.670241\pi\)
\(194\) 0.101363 + 0.0585219i 0.000522490 + 0.000301660i
\(195\) 0 0
\(196\) −50.0000 + 84.2852i −0.255102 + 0.430027i
\(197\) 180.083i 0.914127i −0.889434 0.457063i \(-0.848901\pi\)
0.889434 0.457063i \(-0.151099\pi\)
\(198\) 0 0
\(199\) 2.86901 + 4.96927i 0.0144171 + 0.0249712i 0.873144 0.487462i \(-0.162077\pi\)
−0.858727 + 0.512434i \(0.828744\pi\)
\(200\) −29.5966 + 17.0876i −0.147983 + 0.0854380i
\(201\) 0 0
\(202\) −205.145 −1.01557
\(203\) 33.5368 57.3025i 0.165206 0.282278i
\(204\) 0 0
\(205\) −34.6241 + 59.9708i −0.168898 + 0.292540i
\(206\) −7.66095 + 4.42305i −0.0371891 + 0.0214711i
\(207\) 0 0
\(208\) −26.1655 + 45.3200i −0.125796 + 0.217885i
\(209\) 203.754i 0.974900i
\(210\) 0 0
\(211\) −75.7517 −0.359013 −0.179506 0.983757i \(-0.557450\pi\)
−0.179506 + 0.983757i \(0.557450\pi\)
\(212\) −78.6794 45.4256i −0.371129 0.214271i
\(213\) 0 0
\(214\) 24.9932 + 43.2894i 0.116790 + 0.202287i
\(215\) −238.872 137.913i −1.11103 0.641454i
\(216\) 0 0
\(217\) −1.29652 + 219.314i −0.00597474 + 1.01066i
\(218\) 203.764i 0.934696i
\(219\) 0 0
\(220\) −56.3311 97.5682i −0.256050 0.443492i
\(221\) −299.742 + 173.056i −1.35630 + 0.783058i
\(222\) 0 0
\(223\) −249.235 −1.11764 −0.558822 0.829288i \(-0.688746\pi\)
−0.558822 + 0.829288i \(0.688746\pi\)
\(224\) −39.5973 0.234088i −0.176774 0.00104503i
\(225\) 0 0
\(226\) −55.4138 + 95.9795i −0.245194 + 0.424688i
\(227\) −248.138 + 143.262i −1.09312 + 0.631112i −0.934405 0.356213i \(-0.884068\pi\)
−0.158713 + 0.987325i \(0.550734\pi\)
\(228\) 0 0
\(229\) −109.831 + 190.233i −0.479612 + 0.830712i −0.999727 0.0233846i \(-0.992556\pi\)
0.520115 + 0.854096i \(0.325889\pi\)
\(230\) 104.525i 0.454457i
\(231\) 0 0
\(232\) 26.8276 0.115636
\(233\) 221.320 + 127.779i 0.949871 + 0.548408i 0.893041 0.449976i \(-0.148567\pi\)
0.0568299 + 0.998384i \(0.481901\pi\)
\(234\) 0 0
\(235\) 42.8793 + 74.2691i 0.182465 + 0.316039i
\(236\) −142.476 82.2585i −0.603711 0.348553i
\(237\) 0 0
\(238\) −226.031 132.287i −0.949711 0.555827i
\(239\) 162.113i 0.678296i −0.940733 0.339148i \(-0.889861\pi\)
0.940733 0.339148i \(-0.110139\pi\)
\(240\) 0 0
\(241\) 38.3724 + 66.4630i 0.159222 + 0.275780i 0.934588 0.355731i \(-0.115768\pi\)
−0.775367 + 0.631511i \(0.782435\pi\)
\(242\) −152.671 + 88.1446i −0.630871 + 0.364234i
\(243\) 0 0
\(244\) −9.15868 −0.0375356
\(245\) −2.08214 + 176.096i −0.00849851 + 0.718761i
\(246\) 0 0
\(247\) 85.0380 147.290i 0.344283 0.596316i
\(248\) −76.7451 + 44.3088i −0.309456 + 0.178665i
\(249\) 0 0
\(250\) −94.2414 + 163.231i −0.376966 + 0.652924i
\(251\) 343.815i 1.36978i 0.728646 + 0.684890i \(0.240150\pi\)
−0.728646 + 0.684890i \(0.759850\pi\)
\(252\) 0 0
\(253\) 322.317 1.27398
\(254\) −93.7902 54.1498i −0.369253 0.213188i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −192.277 111.011i −0.748158 0.431949i 0.0768701 0.997041i \(-0.475507\pi\)
−0.825028 + 0.565092i \(0.808841\pi\)
\(258\) 0 0
\(259\) 326.917 186.178i 1.26223 0.718833i
\(260\) 94.0404i 0.361694i
\(261\) 0 0
\(262\) −138.783 240.379i −0.529705 0.917477i
\(263\) −273.718 + 158.031i −1.04075 + 0.600879i −0.920046 0.391810i \(-0.871849\pi\)
−0.120706 + 0.992688i \(0.538516\pi\)
\(264\) 0 0
\(265\) −163.262 −0.616083
\(266\) 128.691 + 0.760785i 0.483801 + 0.00286010i
\(267\) 0 0
\(268\) −87.5793 + 151.692i −0.326789 + 0.566014i
\(269\) −239.645 + 138.359i −0.890872 + 0.514345i −0.874228 0.485516i \(-0.838632\pi\)
−0.0166443 + 0.999861i \(0.505298\pi\)
\(270\) 0 0
\(271\) −224.786 + 389.341i −0.829470 + 1.43668i 0.0689854 + 0.997618i \(0.478024\pi\)
−0.898455 + 0.439066i \(0.855310\pi\)
\(272\) 105.822i 0.389052i
\(273\) 0 0
\(274\) 34.5862 0.126227
\(275\) 164.006 + 94.6889i 0.596386 + 0.344323i
\(276\) 0 0
\(277\) 135.366 + 234.460i 0.488684 + 0.846426i 0.999915 0.0130172i \(-0.00414362\pi\)
−0.511231 + 0.859443i \(0.670810\pi\)
\(278\) 79.0848 + 45.6596i 0.284478 + 0.164243i
\(279\) 0 0
\(280\) −61.8345 + 35.2144i −0.220837 + 0.125766i
\(281\) 550.948i 1.96067i −0.197340 0.980335i \(-0.563230\pi\)
0.197340 0.980335i \(-0.436770\pi\)
\(282\) 0 0
\(283\) −91.9449 159.253i −0.324894 0.562732i 0.656597 0.754241i \(-0.271995\pi\)
−0.981491 + 0.191509i \(0.938662\pi\)
\(284\) 174.116 100.526i 0.613086 0.353966i
\(285\) 0 0
\(286\) 289.986 1.01394
\(287\) 68.1254 116.402i 0.237371 0.405582i
\(288\) 0 0
\(289\) 205.448 355.847i 0.710894 1.23130i
\(290\) 41.7511 24.1050i 0.143969 0.0831207i
\(291\) 0 0
\(292\) 59.9172 103.780i 0.205196 0.355410i
\(293\) 66.7998i 0.227986i 0.993482 + 0.113993i \(0.0363641\pi\)
−0.993482 + 0.113993i \(0.963636\pi\)
\(294\) 0 0
\(295\) −295.642 −1.00217
\(296\) 131.647 + 76.0067i 0.444755 + 0.256779i
\(297\) 0 0
\(298\) −142.376 246.602i −0.477771 0.827524i
\(299\) −232.997 134.521i −0.779255 0.449903i
\(300\) 0 0
\(301\) 463.645 + 271.353i 1.54035 + 0.901504i
\(302\) 160.723i 0.532196i
\(303\) 0 0
\(304\) 26.0000 + 45.0333i 0.0855263 + 0.148136i
\(305\) −14.2534 + 8.22920i −0.0467324 + 0.0269810i
\(306\) 0 0
\(307\) −165.331 −0.538538 −0.269269 0.963065i \(-0.586782\pi\)
−0.269269 + 0.963065i \(0.586782\pi\)
\(308\) 108.588 + 190.675i 0.352560 + 0.619075i
\(309\) 0 0
\(310\) −79.6241 + 137.913i −0.256852 + 0.444881i
\(311\) −316.499 + 182.731i −1.01768 + 0.587559i −0.913432 0.406992i \(-0.866578\pi\)
−0.104251 + 0.994551i \(0.533245\pi\)
\(312\) 0 0
\(313\) 28.1689 48.7901i 0.0899966 0.155879i −0.817513 0.575910i \(-0.804648\pi\)
0.907509 + 0.420032i \(0.137981\pi\)
\(314\) 182.765i 0.582055i
\(315\) 0 0
\(316\) 147.338 0.466259
\(317\) −363.116 209.645i −1.14548 0.661341i −0.197695 0.980264i \(-0.563346\pi\)
−0.947781 + 0.318923i \(0.896679\pi\)
\(318\) 0 0
\(319\) −74.3311 128.745i −0.233013 0.403590i
\(320\) −24.9003 14.3762i −0.0778136 0.0449257i
\(321\) 0 0
\(322\) 1.20348 203.576i 0.00373752 0.632223i
\(323\) 343.922i 1.06477i
\(324\) 0 0
\(325\) −79.0380 136.898i −0.243194 0.421224i
\(326\) −118.800 + 68.5894i −0.364418 + 0.210397i
\(327\) 0 0
\(328\) 54.4966 0.166148
\(329\) −82.6577 145.142i −0.251239 0.441162i
\(330\) 0 0
\(331\) 237.366 411.129i 0.717117 1.24208i −0.245021 0.969518i \(-0.578795\pi\)
0.962138 0.272565i \(-0.0878718\pi\)
\(332\) −155.956 + 90.0415i −0.469748 + 0.271209i
\(333\) 0 0
\(334\) −112.662 + 195.136i −0.337312 + 0.584241i
\(335\) 314.765i 0.939597i
\(336\) 0 0
\(337\) 467.304 1.38666 0.693329 0.720621i \(-0.256143\pi\)
0.693329 + 0.720621i \(0.256143\pi\)
\(338\) −2.64383 1.52641i −0.00782197 0.00451602i
\(339\) 0 0
\(340\) −95.0828 164.688i −0.279655 0.484377i
\(341\) 425.274 + 245.532i 1.24714 + 0.720035i
\(342\) 0 0
\(343\) 6.08276 342.946i 0.0177340 0.999843i
\(344\) 217.067i 0.631009i
\(345\) 0 0
\(346\) 141.459 + 245.014i 0.408840 + 0.708132i
\(347\) −41.9370 + 24.2124i −0.120856 + 0.0697762i −0.559209 0.829026i \(-0.688895\pi\)
0.438353 + 0.898803i \(0.355562\pi\)
\(348\) 0 0
\(349\) −199.345 −0.571188 −0.285594 0.958351i \(-0.592191\pi\)
−0.285594 + 0.958351i \(0.592191\pi\)
\(350\) 60.4180 103.233i 0.172623 0.294951i
\(351\) 0 0
\(352\) −44.3311 + 76.7836i −0.125940 + 0.218135i
\(353\) 502.129 289.904i 1.42246 0.821258i 0.425952 0.904746i \(-0.359939\pi\)
0.996509 + 0.0834878i \(0.0266060\pi\)
\(354\) 0 0
\(355\) 180.648 312.892i 0.508869 0.881387i
\(356\) 252.774i 0.710039i
\(357\) 0 0
\(358\) −311.731 −0.870757
\(359\) 493.142 + 284.715i 1.37365 + 0.793079i 0.991386 0.130973i \(-0.0418100\pi\)
0.382267 + 0.924052i \(0.375143\pi\)
\(360\) 0 0
\(361\) 96.0000 + 166.277i 0.265928 + 0.460601i
\(362\) −335.960 193.967i −0.928067 0.535820i
\(363\) 0 0
\(364\) 1.08276 183.155i 0.00297462 0.503174i
\(365\) 215.346i 0.589989i
\(366\) 0 0
\(367\) −114.110 197.645i −0.310928 0.538542i 0.667636 0.744488i \(-0.267306\pi\)
−0.978563 + 0.205946i \(0.933973\pi\)
\(368\) 71.2379 41.1292i 0.193581 0.111764i
\(369\) 0 0
\(370\) 273.172 0.738304
\(371\) 317.973 + 1.87977i 0.857071 + 0.00506676i
\(372\) 0 0
\(373\) −208.811 + 361.670i −0.559814 + 0.969626i 0.437698 + 0.899122i \(0.355794\pi\)
−0.997512 + 0.0705036i \(0.977539\pi\)
\(374\) −507.839 + 293.201i −1.35786 + 0.783959i
\(375\) 0 0
\(376\) 33.7449 58.4478i 0.0897470 0.155446i
\(377\) 124.090i 0.329151i
\(378\) 0 0
\(379\) −235.552 −0.621509 −0.310755 0.950490i \(-0.600582\pi\)
−0.310755 + 0.950490i \(0.600582\pi\)
\(380\) 80.9261 + 46.7227i 0.212964 + 0.122955i
\(381\) 0 0
\(382\) −122.617 212.379i −0.320988 0.555967i
\(383\) −224.010 129.332i −0.584883 0.337682i 0.178189 0.983996i \(-0.442976\pi\)
−0.763072 + 0.646314i \(0.776310\pi\)
\(384\) 0 0
\(385\) 340.317 + 199.174i 0.883941 + 0.517335i
\(386\) 267.618i 0.693311i
\(387\) 0 0
\(388\) −0.0827625 0.143349i −0.000213305 0.000369456i
\(389\) −153.123 + 88.4055i −0.393632 + 0.227263i −0.683733 0.729733i \(-0.739645\pi\)
0.290101 + 0.956996i \(0.406311\pi\)
\(390\) 0 0
\(391\) 544.049 1.39143
\(392\) 120.836 67.8726i 0.308255 0.173144i
\(393\) 0 0
\(394\) −127.338 + 220.556i −0.323193 + 0.559786i
\(395\) 229.298 132.385i 0.580501 0.335152i
\(396\) 0 0
\(397\) −54.7999 + 94.9163i −0.138035 + 0.239084i −0.926753 0.375672i \(-0.877412\pi\)
0.788718 + 0.614756i \(0.210745\pi\)
\(398\) 8.11478i 0.0203889i
\(399\) 0 0
\(400\) 48.3311 0.120828
\(401\) 204.541 + 118.092i 0.510077 + 0.294493i 0.732865 0.680374i \(-0.238183\pi\)
−0.222788 + 0.974867i \(0.571516\pi\)
\(402\) 0 0
\(403\) −204.948 354.981i −0.508557 0.880846i
\(404\) 251.250 + 145.059i 0.621907 + 0.359058i
\(405\) 0 0
\(406\) −81.5930 + 46.4668i −0.200968 + 0.114450i
\(407\) 842.364i 2.06969i
\(408\) 0 0
\(409\) 209.114 + 362.196i 0.511281 + 0.885564i 0.999915 + 0.0130754i \(0.00416214\pi\)
−0.488634 + 0.872489i \(0.662505\pi\)
\(410\) 84.8115 48.9659i 0.206857 0.119429i
\(411\) 0 0
\(412\) 12.5103 0.0303647
\(413\) 575.799 + 3.40396i 1.39419 + 0.00824203i
\(414\) 0 0
\(415\) −161.807 + 280.258i −0.389897 + 0.675321i
\(416\) 64.0922 37.0036i 0.154068 0.0889511i
\(417\) 0 0
\(418\) 144.076 249.547i 0.344679 0.597002i
\(419\) 572.537i 1.36644i −0.730214 0.683219i \(-0.760580\pi\)
0.730214 0.683219i \(-0.239420\pi\)
\(420\) 0 0
\(421\) −237.407 −0.563912 −0.281956 0.959427i \(-0.590983\pi\)
−0.281956 + 0.959427i \(0.590983\pi\)
\(422\) 92.7765 + 53.5645i 0.219850 + 0.126930i
\(423\) 0 0
\(424\) 64.2414 + 111.269i 0.151513 + 0.262428i
\(425\) 276.830 + 159.828i 0.651366 + 0.376066i
\(426\) 0 0
\(427\) 27.8550 15.8633i 0.0652342 0.0371506i
\(428\) 70.6913i 0.165167i
\(429\) 0 0
\(430\) 195.038 + 337.816i 0.453577 + 0.785618i
\(431\) 492.297 284.228i 1.14222 0.659461i 0.195241 0.980755i \(-0.437451\pi\)
0.946980 + 0.321294i \(0.104118\pi\)
\(432\) 0 0
\(433\) −739.724 −1.70837 −0.854185 0.519969i \(-0.825943\pi\)
−0.854185 + 0.519969i \(0.825943\pi\)
\(434\) 156.666 267.686i 0.360982 0.616789i
\(435\) 0 0
\(436\) −144.083 + 249.559i −0.330465 + 0.572382i
\(437\) −231.523 + 133.670i −0.529802 + 0.305881i
\(438\) 0 0
\(439\) −363.521 + 629.637i −0.828066 + 1.43425i 0.0714879 + 0.997441i \(0.477225\pi\)
−0.899554 + 0.436810i \(0.856108\pi\)
\(440\) 159.328i 0.362110i
\(441\) 0 0
\(442\) 489.476 1.10741
\(443\) −687.128 396.714i −1.55108 0.895516i −0.998054 0.0623521i \(-0.980140\pi\)
−0.553026 0.833164i \(-0.686527\pi\)
\(444\) 0 0
\(445\) −227.121 393.385i −0.510384 0.884010i
\(446\) 305.249 + 176.235i 0.684414 + 0.395147i
\(447\) 0 0
\(448\) 48.3311 + 28.2862i 0.107882 + 0.0631389i
\(449\) 81.6882i 0.181934i −0.995854 0.0909668i \(-0.971004\pi\)
0.995854 0.0909668i \(-0.0289957\pi\)
\(450\) 0 0
\(451\) −150.993 261.528i −0.334796 0.579884i
\(452\) 135.736 78.3670i 0.300300 0.173378i
\(453\) 0 0
\(454\) 405.207 0.892527
\(455\) −162.883 286.013i −0.357984 0.628599i
\(456\) 0 0
\(457\) −314.441 + 544.629i −0.688056 + 1.19175i 0.284410 + 0.958703i \(0.408202\pi\)
−0.972466 + 0.233045i \(0.925131\pi\)
\(458\) 269.030 155.325i 0.587402 0.339137i
\(459\) 0 0
\(460\) 73.9104 128.017i 0.160675 0.278297i
\(461\) 518.090i 1.12384i 0.827192 + 0.561919i \(0.189937\pi\)
−0.827192 + 0.561919i \(0.810063\pi\)
\(462\) 0 0
\(463\) −591.062 −1.27659 −0.638296 0.769791i \(-0.720360\pi\)
−0.638296 + 0.769791i \(0.720360\pi\)
\(464\) −32.8570 18.9700i −0.0708125 0.0408836i
\(465\) 0 0
\(466\) −180.707 312.994i −0.387783 0.671660i
\(467\) 84.7185 + 48.9123i 0.181410 + 0.104737i 0.587955 0.808894i \(-0.299933\pi\)
−0.406545 + 0.913631i \(0.633267\pi\)
\(468\) 0 0
\(469\) 3.62414 613.045i 0.00772739 1.30713i
\(470\) 121.281i 0.258045i
\(471\) 0 0
\(472\) 116.331 + 201.491i 0.246464 + 0.426888i
\(473\) 1041.70 601.426i 2.20233 1.27151i
\(474\) 0 0
\(475\) −157.076 −0.330686
\(476\) 183.290 + 321.846i 0.385062 + 0.676147i
\(477\) 0 0
\(478\) −114.631 + 198.547i −0.239814 + 0.415370i
\(479\) 301.967 174.341i 0.630411 0.363968i −0.150500 0.988610i \(-0.548088\pi\)
0.780911 + 0.624642i \(0.214755\pi\)
\(480\) 0 0
\(481\) −351.566 + 608.930i −0.730906 + 1.26597i
\(482\) 108.534i 0.225173i
\(483\) 0 0
\(484\) 249.311 0.515104
\(485\) −0.257602 0.148727i −0.000531138 0.000306653i
\(486\) 0 0
\(487\) 280.969 + 486.653i 0.576939 + 0.999287i 0.995828 + 0.0912499i \(0.0290862\pi\)
−0.418889 + 0.908037i \(0.637580\pi\)
\(488\) 11.2170 + 6.47616i 0.0229857 + 0.0132708i
\(489\) 0 0
\(490\) 127.069 214.201i 0.259325 0.437145i
\(491\) 784.859i 1.59849i 0.601004 + 0.799246i \(0.294768\pi\)
−0.601004 + 0.799246i \(0.705232\pi\)
\(492\) 0 0
\(493\) −125.465 217.313i −0.254494 0.440796i
\(494\) −208.300 + 120.262i −0.421659 + 0.243445i
\(495\) 0 0
\(496\) 125.324 0.252670
\(497\) −355.438 + 607.317i −0.715167 + 1.22197i
\(498\) 0 0
\(499\) 383.659 664.516i 0.768855 1.33170i −0.169329 0.985560i \(-0.554160\pi\)
0.938184 0.346136i \(-0.112507\pi\)
\(500\) 230.843 133.278i 0.461687 0.266555i
\(501\) 0 0
\(502\) 243.114 421.086i 0.484291 0.838816i
\(503\) 187.891i 0.373540i −0.982404 0.186770i \(-0.940198\pi\)
0.982404 0.186770i \(-0.0598019\pi\)
\(504\) 0 0
\(505\) 521.352 1.03238
\(506\) −394.757 227.913i −0.780151 0.450421i
\(507\) 0 0
\(508\) 76.5793 + 132.639i 0.150747 + 0.261101i
\(509\) −100.725 58.1535i −0.197888 0.114250i 0.397782 0.917480i \(-0.369780\pi\)
−0.595670 + 0.803229i \(0.703113\pi\)
\(510\) 0 0
\(511\) −2.47945 + 419.413i −0.00485215 + 0.820770i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) 156.993 + 271.920i 0.305434 + 0.529027i
\(515\) 19.4694 11.2407i 0.0378046 0.0218265i
\(516\) 0 0
\(517\) −373.986 −0.723378
\(518\) −532.038 3.14525i −1.02710 0.00607192i
\(519\) 0 0
\(520\) 66.4966 115.175i 0.127878 0.221491i
\(521\) −300.679 + 173.597i −0.577119 + 0.333200i −0.759988 0.649937i \(-0.774795\pi\)
0.182869 + 0.983137i \(0.441462\pi\)
\(522\) 0 0
\(523\) −464.221 + 804.054i −0.887612 + 1.53739i −0.0449209 + 0.998991i \(0.514304\pi\)
−0.842691 + 0.538398i \(0.819030\pi\)
\(524\) 392.537i 0.749117i
\(525\) 0 0
\(526\) 446.979 0.849771
\(527\) 717.832 + 414.440i 1.36211 + 0.786414i
\(528\) 0 0
\(529\) −53.0482 91.8822i −0.100280 0.173690i
\(530\) 199.954 + 115.444i 0.377272 + 0.217818i
\(531\) 0 0
\(532\) −157.076 91.9302i −0.295255 0.172801i
\(533\) 252.071i 0.472930i
\(534\) 0 0
\(535\) −63.5171 110.015i −0.118724 0.205635i
\(536\) 214.525 123.856i 0.400233 0.231074i
\(537\) 0 0
\(538\) 391.338 0.727394
\(539\) −660.518 391.835i −1.22545 0.726966i
\(540\) 0 0
\(541\) 453.173 784.918i 0.837657 1.45087i −0.0541909 0.998531i \(-0.517258\pi\)
0.891848 0.452335i \(-0.149409\pi\)
\(542\) 550.612 317.896i 1.01589 0.586524i
\(543\) 0 0
\(544\) −74.8276 + 129.605i −0.137551 + 0.238245i
\(545\) 517.841i 0.950168i
\(546\) 0 0
\(547\) 833.263 1.52333 0.761666 0.647970i \(-0.224382\pi\)
0.761666 + 0.647970i \(0.224382\pi\)
\(548\) −42.3593 24.4561i −0.0772979 0.0446280i
\(549\) 0 0
\(550\) −133.910 231.940i −0.243473 0.421708i
\(551\) 106.785 + 61.6525i 0.193803 + 0.111892i
\(552\) 0 0
\(553\) −448.111 + 255.197i −0.810327 + 0.461477i
\(554\) 382.872i 0.691104i
\(555\) 0 0
\(556\) −64.5725 111.843i −0.116138 0.201156i
\(557\) −188.320 + 108.726i −0.338096 + 0.195200i −0.659430 0.751766i \(-0.729202\pi\)
0.321334 + 0.946966i \(0.395869\pi\)
\(558\) 0 0
\(559\) −1004.03 −1.79613
\(560\) 100.632 + 0.594906i 0.179700 + 0.00106233i
\(561\) 0 0
\(562\) −389.579 + 674.771i −0.693202 + 1.20066i
\(563\) −70.9803 + 40.9805i −0.126075 + 0.0727895i −0.561711 0.827333i \(-0.689857\pi\)
0.435636 + 0.900123i \(0.356523\pi\)
\(564\) 0 0
\(565\) 140.828 243.921i 0.249252 0.431718i
\(566\) 260.060i 0.459469i
\(567\) 0 0
\(568\) −284.331 −0.500583
\(569\) −732.693 423.021i −1.28769 0.743446i −0.309445 0.950917i \(-0.600143\pi\)
−0.978241 + 0.207472i \(0.933476\pi\)
\(570\) 0 0
\(571\) −312.759 541.714i −0.547739 0.948711i −0.998429 0.0560310i \(-0.982155\pi\)
0.450690 0.892680i \(-0.351178\pi\)
\(572\) −355.159 205.051i −0.620908 0.358481i
\(573\) 0 0
\(574\) −165.745 + 94.3908i −0.288754 + 0.164444i
\(575\) 248.477i 0.432135i
\(576\) 0 0
\(577\) −149.203 258.428i −0.258585 0.447882i 0.707278 0.706935i \(-0.249923\pi\)
−0.965863 + 0.259053i \(0.916590\pi\)
\(578\) −503.244 + 290.548i −0.870664 + 0.502678i
\(579\) 0 0
\(580\) −68.1792 −0.117550
\(581\) 318.367 543.975i 0.547963 0.936274i
\(582\) 0 0
\(583\) 355.986 616.586i 0.610611 1.05761i
\(584\) −146.767 + 84.7358i −0.251313 + 0.145095i
\(585\) 0 0
\(586\) 47.2346 81.8127i 0.0806051 0.139612i
\(587\) 476.498i 0.811751i −0.913928 0.405875i \(-0.866967\pi\)
0.913928 0.405875i \(-0.133033\pi\)
\(588\) 0 0
\(589\) −407.304 −0.691517
\(590\) 362.085 + 209.050i 0.613704 + 0.354322i
\(591\) 0 0
\(592\) −107.490 186.178i −0.181570 0.314489i
\(593\) −244.324 141.061i −0.412014 0.237876i 0.279641 0.960105i \(-0.409785\pi\)
−0.691655 + 0.722229i \(0.743118\pi\)
\(594\) 0 0
\(595\) 574.431 + 336.191i 0.965431 + 0.565027i
\(596\) 402.700i 0.675671i
\(597\) 0 0
\(598\) 190.241 + 329.508i 0.318129 + 0.551016i
\(599\) −547.550 + 316.128i −0.914107 + 0.527760i −0.881750 0.471716i \(-0.843635\pi\)
−0.0323567 + 0.999476i \(0.510301\pi\)
\(600\) 0 0
\(601\) −629.738 −1.04782 −0.523908 0.851775i \(-0.675527\pi\)
−0.523908 + 0.851775i \(0.675527\pi\)
\(602\) −375.972 660.184i −0.624537 1.09665i
\(603\) 0 0
\(604\) 113.648 196.845i 0.188160 0.325902i
\(605\) 387.995 224.009i 0.641314 0.370263i
\(606\) 0 0
\(607\) −68.6724 + 118.944i −0.113134 + 0.195954i −0.917032 0.398813i \(-0.869422\pi\)
0.803898 + 0.594767i \(0.202756\pi\)
\(608\) 73.5391i 0.120952i
\(609\) 0 0
\(610\) 23.2757 0.0381569
\(611\) 270.348 + 156.085i 0.442468 + 0.255459i
\(612\) 0 0
\(613\) 266.717 + 461.968i 0.435101 + 0.753618i 0.997304 0.0733818i \(-0.0233792\pi\)
−0.562202 + 0.827000i \(0.690046\pi\)
\(614\) 202.488 + 116.907i 0.329786 + 0.190402i
\(615\) 0 0
\(616\) 1.83447 310.312i 0.00297804 0.503753i
\(617\) 172.407i 0.279428i 0.990192 + 0.139714i \(0.0446184\pi\)
−0.990192 + 0.139714i \(0.955382\pi\)
\(618\) 0 0
\(619\) 361.293 + 625.778i 0.583672 + 1.01095i 0.995040 + 0.0994803i \(0.0317180\pi\)
−0.411367 + 0.911470i \(0.634949\pi\)
\(620\) 195.039 112.606i 0.314578 0.181622i
\(621\) 0 0
\(622\) 516.841 0.830935
\(623\) 437.817 + 768.781i 0.702756 + 1.23400i
\(624\) 0 0
\(625\) 88.4689 153.233i 0.141550 0.245172i
\(626\) −68.9996 + 39.8369i −0.110223 + 0.0636372i
\(627\) 0 0
\(628\) −129.235 + 223.841i −0.205788 + 0.356435i
\(629\) 1421.85i 2.26049i
\(630\) 0 0
\(631\) −204.772 −0.324520 −0.162260 0.986748i \(-0.551878\pi\)
−0.162260 + 0.986748i \(0.551878\pi\)
\(632\) −180.451 104.184i −0.285524 0.164848i
\(633\) 0 0
\(634\) 296.483 + 513.523i 0.467639 + 0.809974i
\(635\) 238.357 + 137.615i 0.375365 + 0.216717i
\(636\) 0 0
\(637\) 313.941 + 558.921i 0.492844 + 0.877427i
\(638\) 210.240i 0.329530i
\(639\) 0 0
\(640\) 20.3311 + 35.2144i 0.0317673 + 0.0550225i
\(641\) 44.1121 25.4682i 0.0688177 0.0397319i −0.465196 0.885208i \(-0.654016\pi\)
0.534014 + 0.845476i \(0.320683\pi\)
\(642\) 0 0
\(643\) 114.034 0.177347 0.0886736 0.996061i \(-0.471737\pi\)
0.0886736 + 0.996061i \(0.471737\pi\)
\(644\) −145.424 + 248.477i −0.225813 + 0.385834i
\(645\) 0 0
\(646\) 243.190 421.217i 0.376455 0.652039i
\(647\) −810.385 + 467.876i −1.25253 + 0.723147i −0.971611 0.236586i \(-0.923972\pi\)
−0.280916 + 0.959732i \(0.590638\pi\)
\(648\) 0 0
\(649\) 644.635 1116.54i 0.993274 1.72040i
\(650\) 223.553i 0.343928i
\(651\) 0 0
\(652\) 194.000 0.297546
\(653\) −728.829 420.790i −1.11612 0.644395i −0.175716 0.984441i \(-0.556224\pi\)
−0.940409 + 0.340046i \(0.889557\pi\)
\(654\) 0 0
\(655\) 352.700 + 610.894i 0.538473 + 0.932663i
\(656\) −66.7444 38.5349i −0.101745 0.0587422i
\(657\) 0 0
\(658\) −1.39641 + 236.210i −0.00212220 + 0.358982i
\(659\) 744.564i 1.12984i 0.825146 + 0.564920i \(0.191093\pi\)
−0.825146 + 0.564920i \(0.808907\pi\)
\(660\) 0 0
\(661\) −591.817 1025.06i −0.895336 1.55077i −0.833388 0.552689i \(-0.813602\pi\)
−0.0619486 0.998079i \(-0.519732\pi\)
\(662\) −581.425 + 335.686i −0.878285 + 0.507078i
\(663\) 0 0
\(664\) 254.676 0.383548
\(665\) −327.053 1.93345i −0.491810 0.00290744i
\(666\) 0 0
\(667\) 97.5277 168.923i 0.146218 0.253258i
\(668\) 275.965 159.328i 0.413121 0.238515i
\(669\) 0 0
\(670\) 222.572 385.507i 0.332198 0.575383i
\(671\) 71.7738i 0.106965i
\(672\) 0 0
\(673\) −247.724 −0.368090 −0.184045 0.982918i \(-0.558919\pi\)
−0.184045 + 0.982918i \(0.558919\pi\)
\(674\) −572.328 330.434i −0.849151 0.490258i
\(675\) 0 0
\(676\) 2.15868 + 3.73894i 0.00319331 + 0.00553097i
\(677\) −294.218 169.867i −0.434590 0.250911i 0.266710 0.963777i \(-0.414063\pi\)
−0.701300 + 0.712866i \(0.747397\pi\)
\(678\) 0 0
\(679\) 0.500000 + 0.292630i 0.000736377 + 0.000430972i
\(680\) 268.935i 0.395492i
\(681\) 0 0
\(682\) −347.235 601.428i −0.509142 0.881859i
\(683\) −527.494 + 304.549i −0.772319 + 0.445899i −0.833701 0.552216i \(-0.813782\pi\)
0.0613823 + 0.998114i \(0.480449\pi\)
\(684\) 0 0
\(685\) −87.8967 −0.128316
\(686\) −249.949 + 415.720i −0.364358 + 0.606006i
\(687\) 0 0
\(688\) 153.490 265.852i 0.223096 0.386413i
\(689\) −514.672 + 297.146i −0.746984 + 0.431271i
\(690\) 0 0
\(691\) 384.842 666.565i 0.556934 0.964639i −0.440816 0.897598i \(-0.645311\pi\)
0.997750 0.0670410i \(-0.0213558\pi\)
\(692\) 400.105i 0.578187i
\(693\) 0 0
\(694\) 68.4829 0.0986785
\(695\) −200.985 116.039i −0.289187 0.166962i
\(696\) 0 0
\(697\) −254.866 441.440i −0.365661 0.633343i
\(698\) 244.146 + 140.958i 0.349780 + 0.201946i
\(699\) 0 0
\(700\) −146.993 + 83.7118i −0.209990 + 0.119588i
\(701\) 1309.78i 1.86845i 0.356687 + 0.934224i \(0.383906\pi\)
−0.356687 + 0.934224i \(0.616094\pi\)
\(702\) 0 0
\(703\) 349.342 + 605.077i 0.496930 + 0.860708i
\(704\) 108.588 62.6936i 0.154245 0.0890534i
\(705\) 0 0
\(706\) −819.973 −1.16143
\(707\) −1015.40 6.00274i −1.43621 0.00849044i
\(708\) 0 0
\(709\) −195.628 + 338.837i −0.275920 + 0.477908i −0.970367 0.241636i \(-0.922316\pi\)
0.694447 + 0.719544i \(0.255649\pi\)
\(710\) −442.496 + 255.475i −0.623234 + 0.359825i
\(711\) 0 0
\(712\) −178.738 + 309.583i −0.251037 + 0.434808i
\(713\) 644.311i 0.903662i
\(714\) 0 0
\(715\) −736.966 −1.03072
\(716\) 381.791 + 220.427i 0.533228 + 0.307859i
\(717\) 0 0
\(718\) −402.648 697.407i −0.560792 0.971320i
\(719\) −165.315 95.4449i −0.229924 0.132747i 0.380613 0.924734i \(-0.375713\pi\)
−0.610537 + 0.791988i \(0.709046\pi\)
\(720\) 0 0
\(721\) −38.0485 + 21.6684i −0.0527719 + 0.0300533i
\(722\) 271.529i 0.376079i
\(723\) 0 0
\(724\) 274.311 + 475.120i 0.378882 + 0.656243i
\(725\) 99.2508 57.3025i 0.136898 0.0790379i
\(726\) 0 0
\(727\) −125.131 −0.172119 −0.0860596 0.996290i \(-0.527428\pi\)
−0.0860596 + 0.996290i \(0.527428\pi\)
\(728\) −130.837 + 223.553i −0.179721 + 0.307078i
\(729\) 0 0
\(730\) −152.273 + 263.744i −0.208593 + 0.361293i
\(731\) 1758.32 1015.16i 2.40536 1.38873i
\(732\) 0 0
\(733\) 207.214 358.905i 0.282693 0.489638i −0.689354 0.724424i \(-0.742106\pi\)
0.972047 + 0.234786i \(0.0754390\pi\)
\(734\) 322.753i 0.439718i
\(735\) 0 0
\(736\) −116.331 −0.158058
\(737\) −1188.76 686.333i −1.61298 0.931252i
\(738\) 0 0
\(739\) −211.638 366.568i −0.286384 0.496032i 0.686560 0.727074i \(-0.259120\pi\)
−0.972944 + 0.231041i \(0.925787\pi\)
\(740\) −334.566 193.162i −0.452117 0.261030i
\(741\) 0 0
\(742\) −388.107 227.143i −0.523055 0.306123i
\(743\) 454.884i 0.612226i 0.951995 + 0.306113i \(0.0990286\pi\)
−0.951995 + 0.306113i \(0.900971\pi\)
\(744\) 0 0
\(745\) 361.831 + 626.710i 0.485680 + 0.841222i
\(746\) 511.479 295.303i 0.685629 0.395848i
\(747\) 0 0
\(748\) 829.297 1.10869
\(749\) 122.441 + 214.999i 0.163473 + 0.287048i
\(750\) 0 0
\(751\) −125.766 + 217.833i −0.167464 + 0.290057i −0.937528 0.347911i \(-0.886891\pi\)
0.770063 + 0.637967i \(0.220225\pi\)
\(752\) −82.6577 + 47.7224i −0.109917 + 0.0634607i
\(753\) 0 0
\(754\) 87.7449 151.979i 0.116372 0.201563i
\(755\) 408.459i 0.541005i
\(756\) 0 0
\(757\) 485.572 0.641443 0.320722 0.947174i \(-0.396075\pi\)
0.320722 + 0.947174i \(0.396075\pi\)
\(758\) 288.491 + 166.560i 0.380595 + 0.219737i
\(759\) 0 0
\(760\) −66.0759 114.447i −0.0869420 0.150588i
\(761\) 748.041 + 431.882i 0.982971 + 0.567519i 0.903166 0.429292i \(-0.141237\pi\)
0.0798052 + 0.996810i \(0.474570\pi\)
\(762\) 0 0
\(763\) 5.96233 1008.56i 0.00781432 1.32184i
\(764\) 346.814i 0.453945i
\(765\) 0 0
\(766\) 182.904 + 316.798i 0.238777 + 0.413575i
\(767\) −931.989 + 538.084i −1.21511 + 0.701544i
\(768\) 0 0
\(769\) 696.910 0.906255 0.453128 0.891446i \(-0.350308\pi\)
0.453128 + 0.891446i \(0.350308\pi\)
\(770\) −275.965 484.578i −0.358396 0.629322i
\(771\) 0 0
\(772\) −189.235 + 327.764i −0.245123 + 0.424565i
\(773\) 916.941 529.396i 1.18621 0.684859i 0.228768 0.973481i \(-0.426530\pi\)
0.957443 + 0.288621i \(0.0931969\pi\)
\(774\) 0 0
\(775\) −189.283 + 327.847i −0.244236 + 0.423029i
\(776\) 0.234088i 0.000301660i
\(777\) 0 0
\(778\) 250.049 0.321399
\(779\) 216.919 + 125.238i 0.278459 + 0.160768i
\(780\) 0 0
\(781\) 787.793 + 1364.50i 1.00870 + 1.74712i
\(782\) −666.321 384.700i −0.852072 0.491944i
\(783\) 0 0
\(784\) −195.986 2.31731i −0.249983 0.00295575i
\(785\) 464.476i 0.591690i