Properties

Label 378.3.s.d.53.2
Level $378$
Weight $3$
Character 378.53
Analytic conductor $10.300$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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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 53.2
Root \(-1.31664 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 378.53
Dual form 378.3.s.d.107.2

$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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 −0.155336 0.987862i \(-0.549646\pi\)
0.777845 + 0.628456i \(0.216313\pi\)
\(6\) 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 −0.266107 0.963944i \(-0.585737\pi\)
−0.967853 + 0.251517i \(0.919071\pi\)
\(12\) 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 −0.359791 0.933033i \(-0.617152\pi\)
−0.987926 + 0.154928i \(0.950485\pi\)
\(18\) 0 0
\(19\) 6.50000 + 11.2583i 0.342105 + 0.592544i 0.984823 0.173559i \(-0.0555267\pi\)
−0.642718 + 0.766103i \(0.722193\pi\)
\(20\) 7.18811i 0.359406i
\(21\) 0 0
\(22\) 22.1655 1.00752
\(23\) −17.8095 + 10.2823i −0.774325 + 0.447057i −0.834415 0.551136i \(-0.814195\pi\)
0.0600901 + 0.998193i \(0.480861\pi\)
\(24\) 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 \(-0.947711\pi\)
0.986538 0.163534i \(-0.0522895\pi\)
\(30\) 0 0
\(31\) −15.6655 + 27.1335i −0.505340 + 0.875274i 0.494641 + 0.869097i \(0.335299\pi\)
−0.999981 + 0.00617656i \(0.998034\pi\)
\(32\) 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 −0.958444 0.285280i \(-0.907913\pi\)
0.232162 0.972677i \(-0.425420\pi\)
\(38\) −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 \(-0.924501\pi\)
0.972003 0.234969i \(-0.0754988\pi\)
\(42\) 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 −0.263788 0.964581i \(-0.584972\pi\)
0.703457 + 0.710738i \(0.251639\pi\)
\(48\) 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 0.0806316 0.996744i \(-0.474306\pi\)
−0.822890 + 0.568201i \(0.807640\pi\)
\(54\) 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 −0.245227 0.969466i \(-0.578863\pi\)
−0.962195 + 0.272360i \(0.912196\pi\)
\(60\) 0 0
\(61\) −2.28967 3.96582i −0.0375356 0.0650135i 0.846647 0.532154i \(-0.178617\pi\)
−0.884183 + 0.467141i \(0.845284\pi\)
\(62\) 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 −0.328671 0.944444i \(-0.606601\pi\)
0.982248 0.187584i \(-0.0600658\pi\)
\(68\) −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 \(0.250371\pi\)
−0.706282 + 0.707931i \(0.749629\pi\)
\(72\) 0 0
\(73\) −29.9586 + 51.8898i −0.410392 + 0.710820i −0.994933 0.100545i \(-0.967941\pi\)
0.584541 + 0.811365i \(0.301275\pi\)
\(74\) 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 0.999257 0.0385318i \(-0.0122681\pi\)
−0.532998 + 0.846116i \(0.678935\pi\)
\(80\) −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 \(-0.817509\pi\)
0.840108 0.542419i \(-0.182491\pi\)
\(84\) 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 −0.966993 0.254804i \(-0.917989\pi\)
−0.262830 + 0.964842i \(0.584656\pi\)
\(90\) 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 0.969868 0.243630i \(-0.0783381\pi\)
0.273945 + 0.961745i \(0.411671\pi\)
\(102\) 0 0
\(103\) 3.12757 + 5.41711i 0.0303647 + 0.0525933i 0.880808 0.473473i \(-0.157000\pi\)
−0.850444 + 0.526066i \(0.823666\pi\)
\(104\) 37.0036i 0.355804i
\(105\) 0 0
\(106\) 64.2414 0.606051
\(107\) −30.6102 + 17.6728i −0.286077 + 0.165167i −0.636171 0.771548i \(-0.719483\pi\)
0.350094 + 0.936714i \(0.386150\pi\)
\(108\) 0 0
\(109\) 72.0414 124.779i 0.660930 1.14476i −0.319442 0.947606i \(-0.603495\pi\)
0.980372 0.197159i \(-0.0631714\pi\)
\(110\) 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 \(0.112717\pi\)
−0.937955 + 0.346756i \(0.887283\pi\)
\(114\) 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 0.317535 0.948247i \(-0.397145\pi\)
0.979973 + 0.199130i \(0.0638116\pi\)
\(132\) 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 0.420706 0.907197i \(-0.361782\pi\)
−0.575302 + 0.817941i \(0.695116\pi\)
\(138\) 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 0.216546 0.976272i \(-0.430521\pi\)
0.953750 + 0.300602i \(0.0971875\pi\)
\(150\) 0 0
\(151\) −56.8242 + 98.4224i −0.376319 + 0.651804i −0.990524 0.137343i \(-0.956144\pi\)
0.614204 + 0.789147i \(0.289477\pi\)
\(152\) −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 −0.583487 0.812122i \(-0.698312\pi\)
0.995062 + 0.0992534i \(0.0316454\pi\)
\(158\) −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 0.975574 0.219671i \(-0.0704985\pi\)
−0.678028 + 0.735036i \(0.737165\pi\)
\(164\) −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 \(0.158287\pi\)
−0.878887 + 0.477031i \(0.841713\pi\)
\(168\) 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 −0.908677 0.417500i \(-0.862906\pi\)
−0.0927725 + 0.995687i \(0.529573\pi\)
\(174\) 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 0.927211 0.374540i \(-0.122199\pi\)
0.139245 + 0.990258i \(0.455533\pi\)
\(180\) 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 −0.0523868 0.998627i \(-0.516683\pi\)
0.838643 + 0.544682i \(0.183350\pi\)
\(192\) 0 0
\(193\) 94.6173 163.882i 0.490245 0.849129i −0.509692 0.860357i \(-0.670241\pi\)
0.999937 + 0.0112277i \(0.00357395\pi\)
\(194\) 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 \(0.151099\pi\)
−0.889434 + 0.457063i \(0.848901\pi\)
\(198\) 0 0
\(199\) 2.86901 4.96927i 0.0144171 0.0249712i −0.858727 0.512434i \(-0.828744\pi\)
0.873144 + 0.487462i \(0.162077\pi\)
\(200\) −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 −0.158713 0.987325i \(-0.550734\pi\)
−0.934405 + 0.356213i \(0.884068\pi\)
\(228\) 0 0
\(229\) −109.831 190.233i −0.479612 0.830712i 0.520115 0.854096i \(-0.325889\pi\)
−0.999727 + 0.0233846i \(0.992556\pi\)
\(230\) 104.525i 0.454457i
\(231\) 0 0
\(232\) 26.8276 0.115636
\(233\) 221.320 127.779i 0.949871 0.548408i 0.0568299 0.998384i \(-0.481901\pi\)
0.893041 + 0.449976i \(0.148567\pi\)
\(234\) 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 \(0.110139\pi\)
−0.940733 + 0.339148i \(0.889861\pi\)
\(240\) 0 0
\(241\) 38.3724 66.4630i 0.159222 0.275780i −0.775367 0.631511i \(-0.782435\pi\)
0.934588 + 0.355731i \(0.115768\pi\)
\(242\) −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 \(-0.759850\pi\)
0.728646 0.684890i \(-0.240150\pi\)
\(252\) 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 −0.825028 0.565092i \(-0.808841\pi\)
0.0768701 + 0.997041i \(0.475507\pi\)
\(258\) 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 −0.120706 0.992688i \(-0.538516\pi\)
−0.920046 + 0.391810i \(0.871849\pi\)
\(264\) 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 −0.0166443 0.999861i \(-0.505298\pi\)
−0.874228 + 0.485516i \(0.838632\pi\)
\(270\) 0 0
\(271\) −224.786 389.341i −0.829470 1.43668i −0.898455 0.439066i \(-0.855310\pi\)
0.0689854 0.997618i \(-0.478024\pi\)
\(272\) 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 −0.511231 0.859443i \(-0.670810\pi\)
0.999915 + 0.0130172i \(0.00414362\pi\)
\(278\) 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 \(0.436770\pi\)
−0.197340 + 0.980335i \(0.563230\pi\)
\(282\) 0 0
\(283\) −91.9449 + 159.253i −0.324894 + 0.562732i −0.981491 0.191509i \(-0.938662\pi\)
0.656597 + 0.754241i \(0.271995\pi\)
\(284\) 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 \(-0.963636\pi\)
0.993482 0.113993i \(-0.0363641\pi\)
\(294\) 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 −0.104251 0.994551i \(-0.533245\pi\)
−0.913432 + 0.406992i \(0.866578\pi\)
\(312\) 0 0
\(313\) 28.1689 + 48.7901i 0.0899966 + 0.155879i 0.907509 0.420032i \(-0.137981\pi\)
−0.817513 + 0.575910i \(0.804648\pi\)
\(314\) 182.765i 0.582055i
\(315\) 0 0
\(316\) 147.338 0.466259
\(317\) −363.116 + 209.645i −1.14548 + 0.661341i −0.947781 0.318923i \(-0.896679\pi\)
−0.197695 + 0.980264i \(0.563346\pi\)
\(318\) 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 0.962138 + 0.272565i \(0.0878718\pi\)
−0.245021 + 0.969518i \(0.578795\pi\)
\(332\) −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 0.438353 0.898803i \(-0.355562\pi\)
−0.559209 + 0.829026i \(0.688895\pi\)
\(348\) 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 0.996509 0.0834878i \(-0.0266060\pi\)
0.425952 + 0.904746i \(0.359939\pi\)
\(354\) 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 0.382267 0.924052i \(-0.375143\pi\)
0.991386 + 0.130973i \(0.0418100\pi\)
\(360\) 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 −0.978563 0.205946i \(-0.933973\pi\)
0.667636 + 0.744488i \(0.267306\pi\)
\(368\) 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 −0.997512 0.0705036i \(-0.977539\pi\)
0.437698 0.899122i \(-0.355794\pi\)
\(374\) −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 −0.763072 0.646314i \(-0.776310\pi\)
0.178189 + 0.983996i \(0.442976\pi\)
\(384\) 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 0.290101 0.956996i \(-0.406311\pi\)
−0.683733 + 0.729733i \(0.739645\pi\)
\(390\) 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 0.788718 0.614756i \(-0.210745\pi\)
−0.926753 + 0.375672i \(0.877412\pi\)
\(398\) 8.11478i 0.0203889i
\(399\) 0 0
\(400\) 48.3311 0.120828
\(401\) 204.541 118.092i 0.510077 0.294493i −0.222788 0.974867i \(-0.571516\pi\)
0.732865 + 0.680374i \(0.238183\pi\)
\(402\) 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 −0.488634 0.872489i \(-0.662505\pi\)
0.999915 0.0130754i \(-0.00416214\pi\)
\(410\) 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 \(0.239420\pi\)
−0.730214 + 0.683219i \(0.760580\pi\)
\(420\) 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 0.946980 0.321294i \(-0.104118\pi\)
0.195241 + 0.980755i \(0.437451\pi\)
\(432\) 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 −0.899554 0.436810i \(-0.856108\pi\)
0.0714879 0.997441i \(-0.477225\pi\)
\(440\) 159.328i 0.362110i
\(441\) 0 0
\(442\) 489.476 1.10741
\(443\) −687.128 + 396.714i −1.55108 + 0.895516i −0.553026 + 0.833164i \(0.686527\pi\)
−0.998054 + 0.0623521i \(0.980140\pi\)
\(444\) 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 \(0.0289957\pi\)
−0.995854 + 0.0909668i \(0.971004\pi\)
\(450\) 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 −0.972466 0.233045i \(-0.925131\pi\)
0.284410 0.958703i \(-0.408202\pi\)
\(458\) 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 \(-0.810063\pi\)
0.827192 0.561919i \(-0.189937\pi\)
\(462\) 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 −0.406545 0.913631i \(-0.633267\pi\)
0.587955 + 0.808894i \(0.299933\pi\)
\(468\) 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 0.780911 0.624642i \(-0.214755\pi\)
−0.150500 + 0.988610i \(0.548088\pi\)
\(480\) 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 −0.418889 0.908037i \(-0.637580\pi\)
0.995828 0.0912499i \(-0.0290862\pi\)
\(488\) 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 \(-0.705232\pi\)
0.601004 0.799246i \(-0.294768\pi\)
\(492\) 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 0.938184 + 0.346136i \(0.112507\pi\)
−0.169329 + 0.985560i \(0.554160\pi\)
\(500\) 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 \(0.0598019\pi\)
−0.982404 + 0.186770i \(0.940198\pi\)
\(504\) 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 −0.595670 0.803229i \(-0.703113\pi\)
0.397782 + 0.917480i \(0.369780\pi\)
\(510\) 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 0.182869 0.983137i \(-0.441462\pi\)
−0.759988 + 0.649937i \(0.774795\pi\)
\(522\) 0 0
\(523\) −464.221 804.054i −0.887612 1.53739i −0.842691 0.538398i \(-0.819030\pi\)
−0.0449209 0.998991i \(-0.514304\pi\)
\(524\) 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 0.891848 + 0.452335i \(0.149409\pi\)
−0.0541909 + 0.998531i \(0.517258\pi\)
\(542\) 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 0.321334 0.946966i \(-0.395869\pi\)
−0.659430 + 0.751766i \(0.729202\pi\)
\(558\) 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 0.435636 0.900123i \(-0.356523\pi\)
−0.561711 + 0.827333i \(0.689857\pi\)
\(564\) 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 −0.978241 0.207472i \(-0.933476\pi\)
−0.309445 + 0.950917i \(0.600143\pi\)
\(570\) 0 0
\(571\) −312.759 + 541.714i −0.547739 + 0.948711i 0.450690 + 0.892680i \(0.351178\pi\)
−0.998429 + 0.0560310i \(0.982155\pi\)
\(572\) −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 −0.965863 0.259053i \(-0.916590\pi\)
0.707278 + 0.706935i \(0.249923\pi\)
\(578\) −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 \(0.133033\pi\)
−0.913928 + 0.405875i \(0.866967\pi\)
\(588\) 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 −0.691655 0.722229i \(-0.743118\pi\)
0.279641 + 0.960105i \(0.409785\pi\)
\(594\) 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 −0.0323567 0.999476i \(-0.510301\pi\)
−0.881750 + 0.471716i \(0.843635\pi\)
\(600\) 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 0.803898 0.594767i \(-0.202756\pi\)
−0.917032 + 0.398813i \(0.869422\pi\)
\(608\) 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 −0.562202 0.827000i \(-0.690046\pi\)
0.997304 + 0.0733818i \(0.0233792\pi\)
\(614\) 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 \(-0.955382\pi\)
0.990192 0.139714i \(-0.0446184\pi\)
\(618\) 0 0
\(619\) 361.293 625.778i 0.583672 1.01095i −0.411367 0.911470i \(-0.634949\pi\)
0.995040 0.0994803i \(-0.0317180\pi\)
\(620\) 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 0.534014 0.845476i \(-0.320683\pi\)
−0.465196 + 0.885208i \(0.654016\pi\)
\(642\) 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 −0.280916 0.959732i \(-0.590638\pi\)
−0.971611 + 0.236586i \(0.923972\pi\)
\(648\) 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 −0.940409 0.340046i \(-0.889557\pi\)
−0.175716 + 0.984441i \(0.556224\pi\)
\(654\) 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 \(-0.808907\pi\)
0.825146 0.564920i \(-0.191093\pi\)
\(660\) 0 0
\(661\) −591.817 + 1025.06i −0.895336 + 1.55077i −0.0619486 + 0.998079i \(0.519732\pi\)
−0.833388 + 0.552689i \(0.813602\pi\)
\(662\) −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 −0.701300 0.712866i \(-0.747397\pi\)
0.266710 + 0.963777i \(0.414063\pi\)
\(678\) 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 0.0613823 0.998114i \(-0.480449\pi\)
−0.833701 + 0.552216i \(0.813782\pi\)
\(684\) 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 0.997750 + 0.0670410i \(0.0213558\pi\)
−0.440816 + 0.897598i \(0.645311\pi\)
\(692\) 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 \(-0.616094\pi\)
0.356687 0.934224i \(-0.383906\pi\)
\(702\) 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 0.694447 0.719544i \(-0.255649\pi\)
−0.970367 + 0.241636i \(0.922316\pi\)
\(710\) −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 −0.610537 0.791988i \(-0.709046\pi\)
0.380613 + 0.924734i \(0.375713\pi\)
\(720\) 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 0.972047 0.234786i \(-0.0754390\pi\)
−0.689354 + 0.724424i \(0.742106\pi\)
\(734\) 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 −0.972944 0.231041i \(-0.925787\pi\)
0.686560 + 0.727074i \(0.259120\pi\)
\(740\) −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 \(-0.900971\pi\)
0.951995 0.306113i \(-0.0990286\pi\)
\(744\) 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 0.770063 0.637967i \(-0.220225\pi\)
−0.937528 + 0.347911i \(0.886891\pi\)
\(752\) −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 0.0798052 0.996810i \(-0.474570\pi\)
0.903166 + 0.429292i \(0.141237\pi\)
\(762\) 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 0.957443 0.288621i \(-0.0931969\pi\)
0.228768 + 0.973481i \(0.426530\pi\)
\(774\) 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