Properties

Label 300.3.f.c.199.6
Level $300$
Weight $3$
Character 300.199
Analytic conductor $8.174$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 8 x^{14} - 14 x^{13} + 23 x^{12} - 26 x^{11} + 18 x^{10} - 10 x^{9} + 9 x^{8} - 20 x^{7} + 72 x^{6} - 208 x^{5} + 368 x^{4} - 448 x^{3} + 512 x^{2} - 512 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{20}\cdot 5^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 199.6
Root \(1.26238 + 0.637499i\) of defining polynomial
Character \(\chi\) \(=\) 300.199
Dual form 300.3.f.c.199.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.49110 + 1.33290i) q^{2} +1.73205 q^{3} +(0.446749 - 3.97497i) q^{4} +(-2.58266 + 2.30865i) q^{6} -6.56834 q^{7} +(4.63210 + 6.52255i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(-1.49110 + 1.33290i) q^{2} +1.73205 q^{3} +(0.446749 - 3.97497i) q^{4} +(-2.58266 + 2.30865i) q^{6} -6.56834 q^{7} +(4.63210 + 6.52255i) q^{8} +3.00000 q^{9} -2.26696i q^{11} +(0.773791 - 6.88486i) q^{12} +14.8772i q^{13} +(9.79404 - 8.75495i) q^{14} +(-15.6008 - 3.55163i) q^{16} +26.8250i q^{17} +(-4.47330 + 3.99870i) q^{18} +10.8680i q^{19} -11.3767 q^{21} +(3.02164 + 3.38027i) q^{22} +36.4610 q^{23} +(8.02303 + 11.2974i) q^{24} +(-19.8298 - 22.1834i) q^{26} +5.19615 q^{27} +(-2.93440 + 26.1090i) q^{28} +35.2510 q^{29} +23.8330i q^{31} +(27.9963 - 15.4985i) q^{32} -3.92650i q^{33} +(-35.7550 - 39.9987i) q^{34} +(1.34025 - 11.9249i) q^{36} +54.7495i q^{37} +(-14.4860 - 16.2053i) q^{38} +25.7680i q^{39} -23.8298 q^{41} +(16.9638 - 15.1640i) q^{42} -56.2515 q^{43} +(-9.01112 - 1.01276i) q^{44} +(-54.3670 + 48.5989i) q^{46} -51.4177 q^{47} +(-27.0214 - 6.15160i) q^{48} -5.85689 q^{49} +46.4622i q^{51} +(59.1364 + 6.64636i) q^{52} -30.6465i q^{53} +(-7.74797 + 6.92596i) q^{54} +(-30.4252 - 42.8423i) q^{56} +18.8240i q^{57} +(-52.5627 + 46.9861i) q^{58} -6.92483i q^{59} +107.426 q^{61} +(-31.7671 - 35.5374i) q^{62} -19.7050 q^{63} +(-21.0873 + 60.4262i) q^{64} +(5.23363 + 5.85479i) q^{66} -111.444 q^{67} +(106.629 + 11.9840i) q^{68} +63.1524 q^{69} +31.3190i q^{71} +(13.8963 + 19.5676i) q^{72} -110.909i q^{73} +(-72.9757 - 81.6369i) q^{74} +(43.2002 + 4.85528i) q^{76} +14.8902i q^{77} +(-34.3463 - 38.4227i) q^{78} +59.0065i q^{79} +9.00000 q^{81} +(35.5326 - 31.7628i) q^{82} +142.416 q^{83} +(-5.08253 + 45.2221i) q^{84} +(83.8765 - 74.9776i) q^{86} +61.0565 q^{87} +(14.7864 - 10.5008i) q^{88} -7.14798 q^{89} -97.7185i q^{91} +(16.2889 - 144.932i) q^{92} +41.2800i q^{93} +(76.6689 - 68.5347i) q^{94} +(48.4911 - 26.8443i) q^{96} -126.308i q^{97} +(8.73319 - 7.80665i) q^{98} -6.80089i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 16q^{4} - 12q^{6} + 48q^{9} + O(q^{10}) \) \( 16q + 16q^{4} - 12q^{6} + 48q^{9} - 44q^{14} + 80q^{16} + 48q^{21} + 72q^{24} - 132q^{26} + 64q^{29} - 248q^{34} + 48q^{36} - 32q^{41} - 80q^{44} - 152q^{46} - 32q^{49} - 36q^{54} - 344q^{56} + 272q^{61} - 32q^{64} - 216q^{66} + 192q^{69} + 216q^{74} + 240q^{76} + 144q^{81} + 288q^{84} + 428q^{86} - 256q^{89} - 24q^{94} + 192q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.49110 + 1.33290i −0.745549 + 0.666451i
\(3\) 1.73205 0.577350
\(4\) 0.446749 3.97497i 0.111687 0.993743i
\(5\) 0 0
\(6\) −2.58266 + 2.30865i −0.430443 + 0.384775i
\(7\) −6.56834 −0.938335 −0.469167 0.883109i \(-0.655446\pi\)
−0.469167 + 0.883109i \(0.655446\pi\)
\(8\) 4.63210 + 6.52255i 0.579013 + 0.815319i
\(9\) 3.00000 0.333333
\(10\) 0 0
\(11\) 2.26696i 0.206088i −0.994677 0.103044i \(-0.967142\pi\)
0.994677 0.103044i \(-0.0328582\pi\)
\(12\) 0.773791 6.88486i 0.0644826 0.573738i
\(13\) 14.8772i 1.14440i 0.820114 + 0.572200i \(0.193910\pi\)
−0.820114 + 0.572200i \(0.806090\pi\)
\(14\) 9.79404 8.75495i 0.699575 0.625354i
\(15\) 0 0
\(16\) −15.6008 3.55163i −0.975052 0.221977i
\(17\) 26.8250i 1.57794i 0.614432 + 0.788969i \(0.289385\pi\)
−0.614432 + 0.788969i \(0.710615\pi\)
\(18\) −4.47330 + 3.99870i −0.248516 + 0.222150i
\(19\) 10.8680i 0.572002i 0.958229 + 0.286001i \(0.0923260\pi\)
−0.958229 + 0.286001i \(0.907674\pi\)
\(20\) 0 0
\(21\) −11.3767 −0.541748
\(22\) 3.02164 + 3.38027i 0.137347 + 0.153648i
\(23\) 36.4610 1.58526 0.792631 0.609702i \(-0.208711\pi\)
0.792631 + 0.609702i \(0.208711\pi\)
\(24\) 8.02303 + 11.2974i 0.334293 + 0.470724i
\(25\) 0 0
\(26\) −19.8298 22.1834i −0.762685 0.853206i
\(27\) 5.19615 0.192450
\(28\) −2.93440 + 26.1090i −0.104800 + 0.932464i
\(29\) 35.2510 1.21555 0.607775 0.794109i \(-0.292062\pi\)
0.607775 + 0.794109i \(0.292062\pi\)
\(30\) 0 0
\(31\) 23.8330i 0.768808i 0.923165 + 0.384404i \(0.125593\pi\)
−0.923165 + 0.384404i \(0.874407\pi\)
\(32\) 27.9963 15.4985i 0.874886 0.484329i
\(33\) 3.92650i 0.118985i
\(34\) −35.7550 39.9987i −1.05162 1.17643i
\(35\) 0 0
\(36\) 1.34025 11.9249i 0.0372290 0.331248i
\(37\) 54.7495i 1.47972i 0.672763 + 0.739858i \(0.265107\pi\)
−0.672763 + 0.739858i \(0.734893\pi\)
\(38\) −14.4860 16.2053i −0.381211 0.426455i
\(39\) 25.7680i 0.660719i
\(40\) 0 0
\(41\) −23.8298 −0.581215 −0.290608 0.956842i \(-0.593857\pi\)
−0.290608 + 0.956842i \(0.593857\pi\)
\(42\) 16.9638 15.1640i 0.403900 0.361048i
\(43\) −56.2515 −1.30817 −0.654087 0.756420i \(-0.726947\pi\)
−0.654087 + 0.756420i \(0.726947\pi\)
\(44\) −9.01112 1.01276i −0.204798 0.0230173i
\(45\) 0 0
\(46\) −54.3670 + 48.5989i −1.18189 + 1.05650i
\(47\) −51.4177 −1.09399 −0.546997 0.837135i \(-0.684229\pi\)
−0.546997 + 0.837135i \(0.684229\pi\)
\(48\) −27.0214 6.15160i −0.562947 0.128158i
\(49\) −5.85689 −0.119528
\(50\) 0 0
\(51\) 46.4622i 0.911023i
\(52\) 59.1364 + 6.64636i 1.13724 + 0.127815i
\(53\) 30.6465i 0.578236i −0.957293 0.289118i \(-0.906638\pi\)
0.957293 0.289118i \(-0.0933620\pi\)
\(54\) −7.74797 + 6.92596i −0.143481 + 0.128258i
\(55\) 0 0
\(56\) −30.4252 42.8423i −0.543308 0.765042i
\(57\) 18.8240i 0.330245i
\(58\) −52.5627 + 46.9861i −0.906253 + 0.810105i
\(59\) 6.92483i 0.117370i −0.998277 0.0586850i \(-0.981309\pi\)
0.998277 0.0586850i \(-0.0186908\pi\)
\(60\) 0 0
\(61\) 107.426 1.76107 0.880537 0.473977i \(-0.157182\pi\)
0.880537 + 0.473977i \(0.157182\pi\)
\(62\) −31.7671 35.5374i −0.512372 0.573184i
\(63\) −19.7050 −0.312778
\(64\) −21.0873 + 60.4262i −0.329489 + 0.944160i
\(65\) 0 0
\(66\) 5.23363 + 5.85479i 0.0792975 + 0.0887090i
\(67\) −111.444 −1.66334 −0.831670 0.555271i \(-0.812615\pi\)
−0.831670 + 0.555271i \(0.812615\pi\)
\(68\) 106.629 + 11.9840i 1.56807 + 0.176235i
\(69\) 63.1524 0.915251
\(70\) 0 0
\(71\) 31.3190i 0.441113i 0.975374 + 0.220556i \(0.0707873\pi\)
−0.975374 + 0.220556i \(0.929213\pi\)
\(72\) 13.8963 + 19.5676i 0.193004 + 0.271773i
\(73\) 110.909i 1.51930i −0.650330 0.759652i \(-0.725369\pi\)
0.650330 0.759652i \(-0.274631\pi\)
\(74\) −72.9757 81.6369i −0.986158 1.10320i
\(75\) 0 0
\(76\) 43.2002 + 4.85528i 0.568423 + 0.0638853i
\(77\) 14.8902i 0.193379i
\(78\) −34.3463 38.4227i −0.440337 0.492599i
\(79\) 59.0065i 0.746917i 0.927647 + 0.373459i \(0.121828\pi\)
−0.927647 + 0.373459i \(0.878172\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 35.5326 31.7628i 0.433325 0.387351i
\(83\) 142.416 1.71586 0.857930 0.513767i \(-0.171751\pi\)
0.857930 + 0.513767i \(0.171751\pi\)
\(84\) −5.08253 + 45.2221i −0.0605063 + 0.538358i
\(85\) 0 0
\(86\) 83.8765 74.9776i 0.975308 0.871833i
\(87\) 61.0565 0.701799
\(88\) 14.7864 10.5008i 0.168027 0.119327i
\(89\) −7.14798 −0.0803144 −0.0401572 0.999193i \(-0.512786\pi\)
−0.0401572 + 0.999193i \(0.512786\pi\)
\(90\) 0 0
\(91\) 97.7185i 1.07383i
\(92\) 16.2889 144.932i 0.177053 1.57534i
\(93\) 41.2800i 0.443871i
\(94\) 76.6689 68.5347i 0.815626 0.729093i
\(95\) 0 0
\(96\) 48.4911 26.8443i 0.505116 0.279628i
\(97\) 126.308i 1.30214i −0.759017 0.651070i \(-0.774320\pi\)
0.759017 0.651070i \(-0.225680\pi\)
\(98\) 8.73319 7.80665i 0.0891142 0.0796597i
\(99\) 6.80089i 0.0686959i
\(100\) 0 0
\(101\) 86.7133 0.858547 0.429274 0.903174i \(-0.358770\pi\)
0.429274 + 0.903174i \(0.358770\pi\)
\(102\) −61.9295 69.2797i −0.607152 0.679213i
\(103\) −21.9281 −0.212895 −0.106447 0.994318i \(-0.533948\pi\)
−0.106447 + 0.994318i \(0.533948\pi\)
\(104\) −97.0372 + 68.9126i −0.933050 + 0.662622i
\(105\) 0 0
\(106\) 40.8488 + 45.6970i 0.385366 + 0.431104i
\(107\) −7.17725 −0.0670771 −0.0335385 0.999437i \(-0.510678\pi\)
−0.0335385 + 0.999437i \(0.510678\pi\)
\(108\) 2.32137 20.6546i 0.0214942 0.191246i
\(109\) −25.4256 −0.233262 −0.116631 0.993175i \(-0.537210\pi\)
−0.116631 + 0.993175i \(0.537210\pi\)
\(110\) 0 0
\(111\) 94.8289i 0.854315i
\(112\) 102.472 + 23.3283i 0.914925 + 0.208288i
\(113\) 78.3588i 0.693441i 0.937968 + 0.346720i \(0.112705\pi\)
−0.937968 + 0.346720i \(0.887295\pi\)
\(114\) −25.0905 28.0684i −0.220092 0.246214i
\(115\) 0 0
\(116\) 15.7483 140.122i 0.135761 1.20795i
\(117\) 44.6316i 0.381466i
\(118\) 9.23012 + 10.3256i 0.0782214 + 0.0875052i
\(119\) 176.196i 1.48063i
\(120\) 0 0
\(121\) 115.861 0.957528
\(122\) −160.182 + 143.188i −1.31297 + 1.17367i
\(123\) −41.2745 −0.335565
\(124\) 94.7357 + 10.6474i 0.763997 + 0.0858659i
\(125\) 0 0
\(126\) 29.3821 26.2649i 0.233192 0.208451i
\(127\) 71.6077 0.563840 0.281920 0.959438i \(-0.409029\pi\)
0.281920 + 0.959438i \(0.409029\pi\)
\(128\) −49.0990 118.209i −0.383586 0.923505i
\(129\) −97.4304 −0.755274
\(130\) 0 0
\(131\) 103.978i 0.793728i −0.917877 0.396864i \(-0.870098\pi\)
0.917877 0.396864i \(-0.129902\pi\)
\(132\) −15.6077 1.75416i −0.118240 0.0132891i
\(133\) 71.3850i 0.536729i
\(134\) 166.174 148.543i 1.24010 1.10853i
\(135\) 0 0
\(136\) −174.967 + 124.256i −1.28652 + 0.913647i
\(137\) 7.16645i 0.0523099i 0.999658 + 0.0261549i \(0.00832633\pi\)
−0.999658 + 0.0261549i \(0.991674\pi\)
\(138\) −94.1664 + 84.1758i −0.682365 + 0.609970i
\(139\) 146.909i 1.05690i 0.848965 + 0.528449i \(0.177226\pi\)
−0.848965 + 0.528449i \(0.822774\pi\)
\(140\) 0 0
\(141\) −89.0581 −0.631618
\(142\) −41.7451 46.6997i −0.293980 0.328871i
\(143\) 33.7261 0.235847
\(144\) −46.8025 10.6549i −0.325017 0.0739922i
\(145\) 0 0
\(146\) 147.831 + 165.376i 1.01254 + 1.13272i
\(147\) −10.1444 −0.0690097
\(148\) 217.628 + 24.4593i 1.47046 + 0.165265i
\(149\) −79.6054 −0.534265 −0.267132 0.963660i \(-0.586076\pi\)
−0.267132 + 0.963660i \(0.586076\pi\)
\(150\) 0 0
\(151\) 182.722i 1.21008i −0.796196 0.605039i \(-0.793158\pi\)
0.796196 0.605039i \(-0.206842\pi\)
\(152\) −70.8873 + 50.3418i −0.466364 + 0.331196i
\(153\) 80.4749i 0.525980i
\(154\) −19.8472 22.2027i −0.128878 0.144174i
\(155\) 0 0
\(156\) 102.427 + 11.5118i 0.656585 + 0.0737938i
\(157\) 212.182i 1.35148i −0.737141 0.675739i \(-0.763825\pi\)
0.737141 0.675739i \(-0.236175\pi\)
\(158\) −78.6498 87.9844i −0.497783 0.556864i
\(159\) 53.0813i 0.333845i
\(160\) 0 0
\(161\) −239.488 −1.48751
\(162\) −13.4199 + 11.9961i −0.0828388 + 0.0740501i
\(163\) −243.400 −1.49325 −0.746626 0.665244i \(-0.768327\pi\)
−0.746626 + 0.665244i \(0.768327\pi\)
\(164\) −10.6459 + 94.7229i −0.0649143 + 0.577579i
\(165\) 0 0
\(166\) −212.357 + 189.827i −1.27926 + 1.14354i
\(167\) 211.395 1.26584 0.632919 0.774218i \(-0.281857\pi\)
0.632919 + 0.774218i \(0.281857\pi\)
\(168\) −52.6980 74.2051i −0.313679 0.441697i
\(169\) −52.3307 −0.309649
\(170\) 0 0
\(171\) 32.6041i 0.190667i
\(172\) −25.1303 + 223.598i −0.146106 + 1.29999i
\(173\) 22.3138i 0.128982i −0.997918 0.0644909i \(-0.979458\pi\)
0.997918 0.0644909i \(-0.0205423\pi\)
\(174\) −91.0412 + 81.3823i −0.523225 + 0.467714i
\(175\) 0 0
\(176\) −8.05141 + 35.3665i −0.0457467 + 0.200946i
\(177\) 11.9942i 0.0677636i
\(178\) 10.6583 9.52755i 0.0598783 0.0535255i
\(179\) 94.5219i 0.528055i 0.964515 + 0.264028i \(0.0850510\pi\)
−0.964515 + 0.264028i \(0.914949\pi\)
\(180\) 0 0
\(181\) −80.6179 −0.445403 −0.222702 0.974887i \(-0.571488\pi\)
−0.222702 + 0.974887i \(0.571488\pi\)
\(182\) 130.249 + 145.708i 0.715654 + 0.800592i
\(183\) 186.067 1.01676
\(184\) 168.891 + 237.819i 0.917887 + 1.29249i
\(185\) 0 0
\(186\) −55.0222 61.5526i −0.295818 0.330928i
\(187\) 60.8112 0.325194
\(188\) −22.9708 + 204.384i −0.122185 + 1.08715i
\(189\) −34.1301 −0.180583
\(190\) 0 0
\(191\) 330.540i 1.73058i 0.501275 + 0.865288i \(0.332865\pi\)
−0.501275 + 0.865288i \(0.667135\pi\)
\(192\) −36.5242 + 104.661i −0.190230 + 0.545111i
\(193\) 103.609i 0.536836i 0.963303 + 0.268418i \(0.0865008\pi\)
−0.963303 + 0.268418i \(0.913499\pi\)
\(194\) 168.356 + 188.337i 0.867812 + 0.970810i
\(195\) 0 0
\(196\) −2.61656 + 23.2810i −0.0133498 + 0.118780i
\(197\) 160.633i 0.815394i 0.913117 + 0.407697i \(0.133668\pi\)
−0.913117 + 0.407697i \(0.866332\pi\)
\(198\) 9.06492 + 10.1408i 0.0457824 + 0.0512162i
\(199\) 27.5518i 0.138451i −0.997601 0.0692255i \(-0.977947\pi\)
0.997601 0.0692255i \(-0.0220528\pi\)
\(200\) 0 0
\(201\) −193.026 −0.960329
\(202\) −129.298 + 115.580i −0.640089 + 0.572179i
\(203\) −231.540 −1.14059
\(204\) 184.686 + 20.7569i 0.905324 + 0.101750i
\(205\) 0 0
\(206\) 32.6970 29.2280i 0.158723 0.141884i
\(207\) 109.383 0.528421
\(208\) 52.8382 232.097i 0.254030 1.11585i
\(209\) 24.6374 0.117883
\(210\) 0 0
\(211\) 269.808i 1.27871i −0.768911 0.639355i \(-0.779201\pi\)
0.768911 0.639355i \(-0.220799\pi\)
\(212\) −121.819 13.6913i −0.574618 0.0645816i
\(213\) 54.2461i 0.254677i
\(214\) 10.7020 9.56656i 0.0500093 0.0447036i
\(215\) 0 0
\(216\) 24.0691 + 33.8922i 0.111431 + 0.156908i
\(217\) 156.544i 0.721399i
\(218\) 37.9120 33.8898i 0.173908 0.155458i
\(219\) 192.100i 0.877170i
\(220\) 0 0
\(221\) −399.080 −1.80579
\(222\) −126.398 141.399i −0.569359 0.636934i
\(223\) 41.3345 0.185356 0.0926782 0.995696i \(-0.470457\pi\)
0.0926782 + 0.995696i \(0.470457\pi\)
\(224\) −183.890 + 101.800i −0.820935 + 0.454463i
\(225\) 0 0
\(226\) −104.445 116.841i −0.462144 0.516994i
\(227\) 149.837 0.660076 0.330038 0.943968i \(-0.392939\pi\)
0.330038 + 0.943968i \(0.392939\pi\)
\(228\) 74.8249 + 8.40959i 0.328179 + 0.0368842i
\(229\) 61.6770 0.269332 0.134666 0.990891i \(-0.457004\pi\)
0.134666 + 0.990891i \(0.457004\pi\)
\(230\) 0 0
\(231\) 25.7906i 0.111648i
\(232\) 163.286 + 229.926i 0.703819 + 0.991061i
\(233\) 405.585i 1.74071i 0.492425 + 0.870355i \(0.336110\pi\)
−0.492425 + 0.870355i \(0.663890\pi\)
\(234\) −59.4895 66.5501i −0.254228 0.284402i
\(235\) 0 0
\(236\) −27.5260 3.09366i −0.116636 0.0131087i
\(237\) 102.202i 0.431233i
\(238\) 234.851 + 262.725i 0.986770 + 1.10389i
\(239\) 267.769i 1.12037i −0.828367 0.560185i \(-0.810730\pi\)
0.828367 0.560185i \(-0.189270\pi\)
\(240\) 0 0
\(241\) −89.5377 −0.371526 −0.185763 0.982595i \(-0.559476\pi\)
−0.185763 + 0.982595i \(0.559476\pi\)
\(242\) −172.760 + 154.431i −0.713884 + 0.638145i
\(243\) 15.5885 0.0641500
\(244\) 47.9922 427.014i 0.196689 1.75006i
\(245\) 0 0
\(246\) 61.5443 55.0148i 0.250180 0.223637i
\(247\) −161.686 −0.654598
\(248\) −155.452 + 110.397i −0.626823 + 0.445149i
\(249\) 246.672 0.990652
\(250\) 0 0
\(251\) 227.844i 0.907745i −0.891067 0.453873i \(-0.850042\pi\)
0.891067 0.453873i \(-0.149958\pi\)
\(252\) −8.80319 + 78.3270i −0.0349333 + 0.310821i
\(253\) 82.6559i 0.326703i
\(254\) −106.774 + 95.4460i −0.420371 + 0.375772i
\(255\) 0 0
\(256\) 230.772 + 110.817i 0.901453 + 0.432878i
\(257\) 442.129i 1.72035i −0.510003 0.860173i \(-0.670356\pi\)
0.510003 0.860173i \(-0.329644\pi\)
\(258\) 145.278 129.865i 0.563094 0.503353i
\(259\) 359.614i 1.38847i
\(260\) 0 0
\(261\) 105.753 0.405184
\(262\) 138.593 + 155.042i 0.528981 + 0.591763i
\(263\) −34.1556 −0.129869 −0.0649346 0.997890i \(-0.520684\pi\)
−0.0649346 + 0.997890i \(0.520684\pi\)
\(264\) 25.6108 18.1879i 0.0970105 0.0688937i
\(265\) 0 0
\(266\) 95.1491 + 106.442i 0.357703 + 0.400158i
\(267\) −12.3807 −0.0463695
\(268\) −49.7873 + 442.986i −0.185774 + 1.65293i
\(269\) 9.96085 0.0370292 0.0185146 0.999829i \(-0.494106\pi\)
0.0185146 + 0.999829i \(0.494106\pi\)
\(270\) 0 0
\(271\) 56.5791i 0.208779i 0.994536 + 0.104390i \(0.0332889\pi\)
−0.994536 + 0.104390i \(0.966711\pi\)
\(272\) 95.2723 418.492i 0.350266 1.53857i
\(273\) 169.253i 0.619976i
\(274\) −9.55218 10.6859i −0.0348620 0.0389996i
\(275\) 0 0
\(276\) 28.2132 251.029i 0.102222 0.909525i
\(277\) 103.794i 0.374708i 0.982292 + 0.187354i \(0.0599911\pi\)
−0.982292 + 0.187354i \(0.940009\pi\)
\(278\) −195.815 219.056i −0.704370 0.787969i
\(279\) 71.4991i 0.256269i
\(280\) 0 0
\(281\) 393.069 1.39882 0.699411 0.714720i \(-0.253446\pi\)
0.699411 + 0.714720i \(0.253446\pi\)
\(282\) 132.794 118.706i 0.470902 0.420942i
\(283\) 114.027 0.402923 0.201462 0.979496i \(-0.435431\pi\)
0.201462 + 0.979496i \(0.435431\pi\)
\(284\) 124.492 + 13.9917i 0.438353 + 0.0492666i
\(285\) 0 0
\(286\) −50.2889 + 44.9535i −0.175835 + 0.157180i
\(287\) 156.522 0.545374
\(288\) 83.9890 46.4956i 0.291629 0.161443i
\(289\) −430.579 −1.48989
\(290\) 0 0
\(291\) 218.771i 0.751791i
\(292\) −440.861 49.5485i −1.50980 0.169687i
\(293\) 126.796i 0.432750i −0.976310 0.216375i \(-0.930577\pi\)
0.976310 0.216375i \(-0.0694234\pi\)
\(294\) 15.1263 13.5215i 0.0514501 0.0459915i
\(295\) 0 0
\(296\) −357.106 + 253.605i −1.20644 + 0.856775i
\(297\) 11.7795i 0.0396616i
\(298\) 118.700 106.106i 0.398321 0.356061i
\(299\) 542.438i 1.81417i
\(300\) 0 0
\(301\) 369.479 1.22750
\(302\) 243.550 + 272.456i 0.806457 + 0.902172i
\(303\) 150.192 0.495683
\(304\) 38.5992 169.550i 0.126971 0.557732i
\(305\) 0 0
\(306\) −107.265 119.996i −0.350539 0.392144i
\(307\) −408.420 −1.33036 −0.665180 0.746683i \(-0.731645\pi\)
−0.665180 + 0.746683i \(0.731645\pi\)
\(308\) 59.1881 + 6.65217i 0.192169 + 0.0215980i
\(309\) −37.9806 −0.122915
\(310\) 0 0
\(311\) 472.495i 1.51928i 0.650345 + 0.759639i \(0.274624\pi\)
−0.650345 + 0.759639i \(0.725376\pi\)
\(312\) −168.073 + 119.360i −0.538697 + 0.382565i
\(313\) 54.6519i 0.174607i −0.996182 0.0873033i \(-0.972175\pi\)
0.996182 0.0873033i \(-0.0278249\pi\)
\(314\) 282.818 + 316.384i 0.900693 + 1.00759i
\(315\) 0 0
\(316\) 234.549 + 26.3611i 0.742244 + 0.0834211i
\(317\) 63.3734i 0.199916i −0.994992 0.0999581i \(-0.968129\pi\)
0.994992 0.0999581i \(-0.0318709\pi\)
\(318\) 70.7522 + 79.1495i 0.222491 + 0.248898i
\(319\) 79.9127i 0.250510i
\(320\) 0 0
\(321\) −12.4314 −0.0387270
\(322\) 357.101 319.215i 1.10901 0.991349i
\(323\) −291.535 −0.902584
\(324\) 4.02074 35.7748i 0.0124097 0.110416i
\(325\) 0 0
\(326\) 362.933 324.428i 1.11329 0.995179i
\(327\) −44.0384 −0.134674
\(328\) −110.382 155.431i −0.336531 0.473876i
\(329\) 337.729 1.02653
\(330\) 0 0
\(331\) 431.595i 1.30391i −0.758257 0.651955i \(-0.773949\pi\)
0.758257 0.651955i \(-0.226051\pi\)
\(332\) 63.6243 566.101i 0.191639 1.70512i
\(333\) 164.249i 0.493239i
\(334\) −315.211 + 281.768i −0.943744 + 0.843618i
\(335\) 0 0
\(336\) 177.486 + 40.4058i 0.528232 + 0.120255i
\(337\) 486.091i 1.44241i 0.692723 + 0.721203i \(0.256411\pi\)
−0.692723 + 0.721203i \(0.743589\pi\)
\(338\) 78.0303 69.7517i 0.230859 0.206366i
\(339\) 135.721i 0.400358i
\(340\) 0 0
\(341\) 54.0286 0.158442
\(342\) −43.4581 48.6159i −0.127070 0.142152i
\(343\) 360.319 1.05049
\(344\) −260.562 366.903i −0.757449 1.06658i
\(345\) 0 0
\(346\) 29.7422 + 33.2721i 0.0859600 + 0.0961623i
\(347\) −294.297 −0.848119 −0.424060 0.905634i \(-0.639395\pi\)
−0.424060 + 0.905634i \(0.639395\pi\)
\(348\) 27.2769 242.698i 0.0783819 0.697408i
\(349\) −83.0428 −0.237945 −0.118972 0.992898i \(-0.537960\pi\)
−0.118972 + 0.992898i \(0.537960\pi\)
\(350\) 0 0
\(351\) 77.3041i 0.220240i
\(352\) −35.1346 63.4667i −0.0998143 0.180303i
\(353\) 570.733i 1.61681i −0.588628 0.808404i \(-0.700332\pi\)
0.588628 0.808404i \(-0.299668\pi\)
\(354\) 15.9870 + 17.8845i 0.0451611 + 0.0505211i
\(355\) 0 0
\(356\) −3.19335 + 28.4130i −0.00897008 + 0.0798119i
\(357\) 305.180i 0.854845i
\(358\) −125.988 140.941i −0.351923 0.393691i
\(359\) 558.265i 1.55506i 0.628848 + 0.777528i \(0.283527\pi\)
−0.628848 + 0.777528i \(0.716473\pi\)
\(360\) 0 0
\(361\) 242.886 0.672814
\(362\) 120.209 107.456i 0.332070 0.296839i
\(363\) 200.677 0.552829
\(364\) −388.428 43.6556i −1.06711 0.119933i
\(365\) 0 0
\(366\) −277.444 + 248.008i −0.758042 + 0.677618i
\(367\) 446.467 1.21653 0.608265 0.793734i \(-0.291866\pi\)
0.608265 + 0.793734i \(0.291866\pi\)
\(368\) −568.822 129.496i −1.54571 0.351891i
\(369\) −71.4895 −0.193738
\(370\) 0 0
\(371\) 201.297i 0.542579i
\(372\) 164.087 + 18.4418i 0.441094 + 0.0495747i
\(373\) 112.924i 0.302744i −0.988477 0.151372i \(-0.951631\pi\)
0.988477 0.151372i \(-0.0483692\pi\)
\(374\) −90.6755 + 81.0554i −0.242448 + 0.216726i
\(375\) 0 0
\(376\) −238.172 335.375i −0.633436 0.891954i
\(377\) 524.435i 1.39108i
\(378\) 50.8913 45.4921i 0.134633 0.120349i
\(379\) 321.457i 0.848173i 0.905622 + 0.424086i \(0.139405\pi\)
−0.905622 + 0.424086i \(0.860595\pi\)
\(380\) 0 0
\(381\) 124.028 0.325533
\(382\) −440.577 492.868i −1.15334 1.29023i
\(383\) −89.2269 −0.232968 −0.116484 0.993193i \(-0.537162\pi\)
−0.116484 + 0.993193i \(0.537162\pi\)
\(384\) −85.0419 204.743i −0.221463 0.533186i
\(385\) 0 0
\(386\) −138.101 154.492i −0.357775 0.400238i
\(387\) −168.754 −0.436058
\(388\) −502.069 56.4278i −1.29399 0.145432i
\(389\) −260.714 −0.670217 −0.335108 0.942180i \(-0.608773\pi\)
−0.335108 + 0.942180i \(0.608773\pi\)
\(390\) 0 0
\(391\) 978.066i 2.50145i
\(392\) −27.1297 38.2018i −0.0692084 0.0974536i
\(393\) 180.096i 0.458259i
\(394\) −214.107 239.519i −0.543420 0.607916i
\(395\) 0 0
\(396\) −27.0334 3.03829i −0.0682661 0.00767245i
\(397\) 112.607i 0.283644i −0.989892 0.141822i \(-0.954704\pi\)
0.989892 0.141822i \(-0.0452960\pi\)
\(398\) 36.7238 + 41.0824i 0.0922708 + 0.103222i
\(399\) 123.642i 0.309881i
\(400\) 0 0
\(401\) 577.513 1.44018 0.720091 0.693880i \(-0.244100\pi\)
0.720091 + 0.693880i \(0.244100\pi\)
\(402\) 287.821 257.285i 0.715973 0.640012i
\(403\) −354.569 −0.879823
\(404\) 38.7390 344.683i 0.0958887 0.853176i
\(405\) 0 0
\(406\) 345.250 308.621i 0.850368 0.760149i
\(407\) 124.115 0.304951
\(408\) −303.052 + 215.218i −0.742774 + 0.527494i
\(409\) 276.255 0.675441 0.337721 0.941246i \(-0.390344\pi\)
0.337721 + 0.941246i \(0.390344\pi\)
\(410\) 0 0
\(411\) 12.4127i 0.0302011i
\(412\) −9.79636 + 87.1638i −0.0237776 + 0.211563i
\(413\) 45.4847i 0.110132i
\(414\) −163.101 + 145.797i −0.393964 + 0.352166i
\(415\) 0 0
\(416\) 230.575 + 416.507i 0.554266 + 1.00122i
\(417\) 254.454i 0.610200i
\(418\) −36.7369 + 32.8393i −0.0878872 + 0.0785629i
\(419\) 247.520i 0.590739i −0.955383 0.295370i \(-0.904557\pi\)
0.955383 0.295370i \(-0.0954428\pi\)
\(420\) 0 0
\(421\) −77.7303 −0.184632 −0.0923162 0.995730i \(-0.529427\pi\)
−0.0923162 + 0.995730i \(0.529427\pi\)
\(422\) 359.627 + 402.310i 0.852197 + 0.953342i
\(423\) −154.253 −0.364665
\(424\) 199.893 141.958i 0.471447 0.334806i
\(425\) 0 0
\(426\) −72.3047 80.8863i −0.169729 0.189874i
\(427\) −705.608 −1.65248
\(428\) −3.20643 + 28.5294i −0.00749165 + 0.0666574i
\(429\) 58.4152 0.136166
\(430\) 0 0
\(431\) 317.184i 0.735926i −0.929840 0.367963i \(-0.880055\pi\)
0.929840 0.367963i \(-0.119945\pi\)
\(432\) −81.0643 18.4548i −0.187649 0.0427194i
\(433\) 82.9688i 0.191614i −0.995400 0.0958069i \(-0.969457\pi\)
0.995400 0.0958069i \(-0.0305431\pi\)
\(434\) 208.657 + 233.422i 0.480777 + 0.537838i
\(435\) 0 0
\(436\) −11.3588 + 101.066i −0.0260524 + 0.231803i
\(437\) 396.260i 0.906773i
\(438\) 256.051 + 286.440i 0.584591 + 0.653974i
\(439\) 117.621i 0.267930i −0.990986 0.133965i \(-0.957229\pi\)
0.990986 0.133965i \(-0.0427709\pi\)
\(440\) 0 0
\(441\) −17.5707 −0.0398428
\(442\) 595.068 531.934i 1.34631 1.20347i
\(443\) −35.1780 −0.0794086 −0.0397043 0.999211i \(-0.512642\pi\)
−0.0397043 + 0.999211i \(0.512642\pi\)
\(444\) 376.943 + 42.3647i 0.848970 + 0.0954160i
\(445\) 0 0
\(446\) −61.6337 + 55.0948i −0.138192 + 0.123531i
\(447\) −137.881 −0.308458
\(448\) 138.508 396.900i 0.309171 0.885938i
\(449\) 67.4253 0.150168 0.0750838 0.997177i \(-0.476078\pi\)
0.0750838 + 0.997177i \(0.476078\pi\)
\(450\) 0 0
\(451\) 54.0214i 0.119781i
\(452\) 311.474 + 35.0067i 0.689102 + 0.0774484i
\(453\) 316.483i 0.698638i
\(454\) −223.422 + 199.718i −0.492119 + 0.439908i
\(455\) 0 0
\(456\) −122.780 + 87.1946i −0.269255 + 0.191216i
\(457\) 204.153i 0.446724i 0.974736 + 0.223362i \(0.0717032\pi\)
−0.974736 + 0.223362i \(0.928297\pi\)
\(458\) −91.9665 + 82.2094i −0.200800 + 0.179496i
\(459\) 139.387i 0.303674i
\(460\) 0 0
\(461\) 125.762 0.272802 0.136401 0.990654i \(-0.456446\pi\)
0.136401 + 0.990654i \(0.456446\pi\)
\(462\) −34.3763 38.4563i −0.0744076 0.0832387i
\(463\) 553.629 1.19574 0.597871 0.801592i \(-0.296013\pi\)
0.597871 + 0.801592i \(0.296013\pi\)
\(464\) −549.944 125.198i −1.18523 0.269824i
\(465\) 0 0
\(466\) −540.605 604.768i −1.16010 1.29778i
\(467\) −625.772 −1.33998 −0.669991 0.742369i \(-0.733702\pi\)
−0.669991 + 0.742369i \(0.733702\pi\)
\(468\) 177.409 + 19.9391i 0.379080 + 0.0426049i
\(469\) 732.000 1.56077
\(470\) 0 0
\(471\) 367.510i 0.780276i
\(472\) 45.1676 32.0765i 0.0956940 0.0679588i
\(473\) 127.520i 0.269598i
\(474\) −136.225 152.394i −0.287395 0.321505i
\(475\) 0 0
\(476\) −700.373 78.7151i −1.47137 0.165368i
\(477\) 91.9396i 0.192745i
\(478\) 356.909 + 399.269i 0.746672 + 0.835291i
\(479\) 488.207i 1.01922i −0.860405 0.509610i \(-0.829790\pi\)
0.860405 0.509610i \(-0.170210\pi\)
\(480\) 0 0
\(481\) −814.519 −1.69339
\(482\) 133.509 119.345i 0.276991 0.247604i
\(483\) −414.806 −0.858812
\(484\) 51.7607 460.544i 0.106944 0.951537i
\(485\) 0 0
\(486\) −23.2439 + 20.7779i −0.0478270 + 0.0427528i
\(487\) 609.476 1.25149 0.625746 0.780027i \(-0.284795\pi\)
0.625746 + 0.780027i \(0.284795\pi\)
\(488\) 497.606 + 700.689i 1.01968 + 1.43584i
\(489\) −421.581 −0.862129
\(490\) 0 0
\(491\) 689.074i 1.40341i −0.712468 0.701705i \(-0.752422\pi\)
0.712468 0.701705i \(-0.247578\pi\)
\(492\) −18.4393 + 164.065i −0.0374783 + 0.333465i
\(493\) 945.606i 1.91806i
\(494\) 241.089 215.511i 0.488035 0.436257i
\(495\) 0 0
\(496\) 84.6461 371.815i 0.170657 0.749627i
\(497\) 205.714i 0.413911i
\(498\) −367.813 + 328.790i −0.738580 + 0.660220i
\(499\) 700.401i 1.40361i 0.712370 + 0.701804i \(0.247622\pi\)
−0.712370 + 0.701804i \(0.752378\pi\)
\(500\) 0 0
\(501\) 366.147 0.730832
\(502\) 303.694 + 339.738i 0.604967 + 0.676769i
\(503\) 943.945 1.87663 0.938315 0.345782i \(-0.112386\pi\)
0.938315 + 0.345782i \(0.112386\pi\)
\(504\) −91.2757 128.527i −0.181103 0.255014i
\(505\) 0 0
\(506\) 110.172 + 123.248i 0.217731 + 0.243573i
\(507\) −90.6395 −0.178776
\(508\) 31.9906 284.639i 0.0629737 0.560313i
\(509\) 357.147 0.701665 0.350832 0.936438i \(-0.385899\pi\)
0.350832 + 0.936438i \(0.385899\pi\)
\(510\) 0 0
\(511\) 728.489i 1.42562i
\(512\) −491.811 + 142.358i −0.960569 + 0.278042i
\(513\) 56.4720i 0.110082i
\(514\) 589.314 + 659.258i 1.14653 + 1.28260i
\(515\) 0 0
\(516\) −43.5269 + 387.283i −0.0843544 + 0.750549i
\(517\) 116.562i 0.225459i
\(518\) 479.329 + 536.219i 0.925346 + 1.03517i
\(519\) 38.6487i 0.0744677i
\(520\) 0 0
\(521\) −88.8415 −0.170521 −0.0852605 0.996359i \(-0.527172\pi\)
−0.0852605 + 0.996359i \(0.527172\pi\)
\(522\) −157.688 + 140.958i −0.302084 + 0.270035i
\(523\) 220.427 0.421467 0.210734 0.977544i \(-0.432415\pi\)
0.210734 + 0.977544i \(0.432415\pi\)
\(524\) −413.311 46.4522i −0.788762 0.0886492i
\(525\) 0 0
\(526\) 50.9294 45.5261i 0.0968239 0.0865514i
\(527\) −639.320 −1.21313
\(528\) −13.9455 + 61.2566i −0.0264119 + 0.116016i
\(529\) 800.407 1.51306
\(530\) 0 0
\(531\) 20.7745i 0.0391234i
\(532\) −283.753 31.8911i −0.533371 0.0599457i
\(533\) 354.521i 0.665142i
\(534\) 18.4608 16.5022i 0.0345708 0.0309030i
\(535\) 0 0
\(536\) −516.219 726.897i −0.963094 1.35615i
\(537\) 163.717i 0.304873i
\(538\) −14.8526 + 13.2768i −0.0276071 + 0.0246781i
\(539\) 13.2774i 0.0246333i
\(540\) 0 0
\(541\) −411.560 −0.760740 −0.380370 0.924834i \(-0.624203\pi\)
−0.380370 + 0.924834i \(0.624203\pi\)
\(542\) −75.4144 84.3651i −0.139141 0.155655i
\(543\) −139.634 −0.257154
\(544\) 415.748 + 751.001i 0.764242 + 1.38052i
\(545\) 0 0
\(546\) 225.598 + 252.373i 0.413183 + 0.462222i
\(547\) 851.537 1.55674 0.778370 0.627806i \(-0.216047\pi\)
0.778370 + 0.627806i \(0.216047\pi\)
\(548\) 28.4865 + 3.20160i 0.0519826 + 0.00584234i
\(549\) 322.277 0.587025
\(550\) 0 0
\(551\) 383.109i 0.695297i
\(552\) 292.528 + 411.914i 0.529942 + 0.746222i
\(553\) 387.575i 0.700858i
\(554\) −138.347 154.767i −0.249724 0.279363i
\(555\) 0 0
\(556\) 583.959 + 65.6313i 1.05029 + 0.118042i
\(557\) 211.553i 0.379808i −0.981803 0.189904i \(-0.939182\pi\)
0.981803 0.189904i \(-0.0608177\pi\)
\(558\) −95.3012 106.612i −0.170791 0.191061i
\(559\) 836.864i 1.49707i
\(560\) 0 0
\(561\) 105.328 0.187751
\(562\) −586.104 + 523.922i −1.04289 + 0.932246i
\(563\) −404.044 −0.717663 −0.358832 0.933402i \(-0.616825\pi\)
−0.358832 + 0.933402i \(0.616825\pi\)
\(564\) −39.7866 + 354.004i −0.0705436 + 0.627666i
\(565\) 0 0
\(566\) −170.026 + 151.987i −0.300399 + 0.268529i
\(567\) −59.1151 −0.104259
\(568\) −204.280 + 145.073i −0.359647 + 0.255410i
\(569\) −230.465 −0.405036 −0.202518 0.979279i \(-0.564912\pi\)
−0.202518 + 0.979279i \(0.564912\pi\)
\(570\) 0 0
\(571\) 351.234i 0.615121i 0.951529 + 0.307560i \(0.0995126\pi\)
−0.951529 + 0.307560i \(0.900487\pi\)
\(572\) 15.0671 134.060i 0.0263410 0.234371i
\(573\) 572.512i 0.999149i
\(574\) −233.390 + 208.629i −0.406603 + 0.363465i
\(575\) 0 0
\(576\) −63.2618 + 181.279i −0.109830 + 0.314720i
\(577\) 638.575i 1.10672i 0.832944 + 0.553358i \(0.186654\pi\)
−0.832944 + 0.553358i \(0.813346\pi\)
\(578\) 642.035 573.919i 1.11079 0.992939i
\(579\) 179.457i 0.309942i
\(580\) 0 0
\(581\) −935.439 −1.61005
\(582\) 291.600 + 326.209i 0.501032 + 0.560497i
\(583\) −69.4746 −0.119167
\(584\) 723.410 513.742i 1.23872 0.879696i
\(585\) 0 0
\(586\) 169.006 + 189.065i 0.288407 + 0.322637i
\(587\) −105.047 −0.178956 −0.0894779 0.995989i \(-0.528520\pi\)
−0.0894779 + 0.995989i \(0.528520\pi\)
\(588\) −4.53201 + 40.3238i −0.00770749 + 0.0685779i
\(589\) −259.018 −0.439759
\(590\) 0 0
\(591\) 278.224i 0.470768i
\(592\) 194.450 854.138i 0.328463 1.44280i
\(593\) 990.175i 1.66977i 0.550422 + 0.834886i \(0.314467\pi\)
−0.550422 + 0.834886i \(0.685533\pi\)
\(594\) 15.7009 + 17.5644i 0.0264325 + 0.0295697i
\(595\) 0 0
\(596\) −35.5636 + 316.429i −0.0596705 + 0.530922i
\(597\) 47.7210i 0.0799347i
\(598\) −723.016 808.828i −1.20906 1.35255i
\(599\) 78.0745i 0.130341i −0.997874 0.0651707i \(-0.979241\pi\)
0.997874 0.0651707i \(-0.0207592\pi\)
\(600\) 0 0
\(601\) −616.498 −1.02579 −0.512893 0.858452i \(-0.671426\pi\)
−0.512893 + 0.858452i \(0.671426\pi\)
\(602\) −550.929 + 492.479i −0.915165 + 0.818071i
\(603\) −334.331 −0.554446
\(604\) −726.314 81.6306i −1.20251 0.135150i
\(605\) 0 0
\(606\) −223.951 + 200.191i −0.369556 + 0.330348i
\(607\) −226.520 −0.373179 −0.186590 0.982438i \(-0.559743\pi\)
−0.186590 + 0.982438i \(0.559743\pi\)
\(608\) 168.439 + 304.265i 0.277037 + 0.500436i
\(609\) −401.040 −0.658522
\(610\) 0 0
\(611\) 764.951i 1.25197i
\(612\) 319.886 + 35.9520i 0.522689 + 0.0587452i
\(613\) 732.519i 1.19497i 0.801879 + 0.597487i \(0.203834\pi\)
−0.801879 + 0.597487i \(0.796166\pi\)
\(614\) 608.995 544.384i 0.991848 0.886619i
\(615\) 0 0
\(616\) −97.1220 + 68.9729i −0.157666 + 0.111969i
\(617\) 350.585i 0.568209i −0.958793 0.284105i \(-0.908304\pi\)
0.958793 0.284105i \(-0.0916963\pi\)
\(618\) 56.6329 50.6245i 0.0916390 0.0819166i
\(619\) 237.923i 0.384367i −0.981359 0.192184i \(-0.938443\pi\)
0.981359 0.192184i \(-0.0615569\pi\)
\(620\) 0 0
\(621\) 189.457 0.305084
\(622\) −629.790 704.537i −1.01252 1.13270i
\(623\) 46.9504 0.0753617
\(624\) 91.5185 402.003i 0.146664 0.644235i
\(625\) 0 0
\(626\) 72.8455 + 81.4913i 0.116367 + 0.130178i
\(627\) 42.6733 0.0680595
\(628\) −843.417 94.7920i −1.34302 0.150943i
\(629\) −1468.65 −2.33490
\(630\) 0 0
\(631\) 200.923i 0.318419i −0.987245 0.159210i \(-0.949105\pi\)
0.987245 0.159210i \(-0.0508946\pi\)
\(632\) −384.873 + 273.324i −0.608976 + 0.432475i
\(633\) 467.321i 0.738264i
\(634\) 84.4705 + 94.4960i 0.133234 + 0.149047i
\(635\) 0 0
\(636\) −210.997 23.7140i −0.331756 0.0372862i
\(637\) 87.1340i 0.136788i
\(638\) 106.516 + 119.158i 0.166953 + 0.186768i
\(639\) 93.9570i 0.147038i
\(640\) 0 0
\(641\) 216.861 0.338316 0.169158 0.985589i \(-0.445895\pi\)
0.169158 + 0.985589i \(0.445895\pi\)
\(642\) 18.5364 16.5698i 0.0288729 0.0258096i
\(643\) 37.5349 0.0583746 0.0291873 0.999574i \(-0.490708\pi\)
0.0291873 + 0.999574i \(0.490708\pi\)
\(644\) −106.991 + 951.960i −0.166135 + 1.47820i
\(645\) 0 0
\(646\) 434.707 388.587i 0.672921 0.601528i
\(647\) 1192.56 1.84321 0.921607 0.388125i \(-0.126877\pi\)
0.921607 + 0.388125i \(0.126877\pi\)
\(648\) 41.6889 + 58.7029i 0.0643347 + 0.0905910i
\(649\) −15.6984 −0.0241885
\(650\) 0 0
\(651\) 271.141i 0.416500i
\(652\) −108.739 + 967.509i −0.166777 + 1.48391i
\(653\) 1087.78i 1.66582i −0.553412 0.832908i \(-0.686675\pi\)
0.553412 0.832908i \(-0.313325\pi\)
\(654\) 65.6656 58.6988i 0.100406 0.0897535i
\(655\) 0 0
\(656\) 371.765 + 84.6347i 0.566715 + 0.129016i
\(657\) 332.727i 0.506435i
\(658\) −503.587 + 450.160i −0.765330 + 0.684133i
\(659\) 852.957i 1.29432i −0.762354 0.647160i \(-0.775956\pi\)
0.762354 0.647160i \(-0.224044\pi\)
\(660\) 0 0
\(661\) −504.933 −0.763892 −0.381946 0.924185i \(-0.624746\pi\)
−0.381946 + 0.924185i \(0.624746\pi\)
\(662\) 575.273 + 643.550i 0.868992 + 0.972130i
\(663\) −691.227 −1.04257
\(664\) 659.687 + 928.917i 0.993504 + 1.39897i
\(665\) 0 0
\(666\) −218.927 244.911i −0.328719 0.367734i
\(667\) 1285.29 1.92697
\(668\) 94.4403 840.289i 0.141378 1.25792i
\(669\) 71.5934 0.107016
\(670\) 0 0
\(671\) 243.530i 0.362936i
\(672\) −318.506 + 176.322i −0.473967 + 0.262384i
\(673\) 902.689i 1.34129i −0.741778 0.670646i \(-0.766017\pi\)
0.741778 0.670646i \(-0.233983\pi\)
\(674\) −647.911 724.810i −0.961293 1.07539i
\(675\) 0 0
\(676\) −23.3787 + 208.013i −0.0345838 + 0.307712i
\(677\) 930.750i 1.37482i −0.726272 0.687408i \(-0.758748\pi\)
0.726272 0.687408i \(-0.241252\pi\)
\(678\) −180.903 202.374i −0.266819 0.298487i
\(679\) 829.632i 1.22184i
\(680\) 0 0
\(681\) 259.526 0.381095
\(682\) −80.5620 + 72.0148i −0.118126 + 0.105594i
\(683\) 64.9023 0.0950253 0.0475127 0.998871i \(-0.484871\pi\)
0.0475127 + 0.998871i \(0.484871\pi\)
\(684\) 129.600 + 14.5658i 0.189474 + 0.0212951i
\(685\) 0 0
\(686\) −537.271 + 480.269i −0.783193 + 0.700101i
\(687\) 106.828 0.155499
\(688\) 877.570 + 199.784i 1.27554 + 0.290384i
\(689\) 455.934 0.661733
\(690\) 0 0
\(691\) 348.329i 0.504094i −0.967715 0.252047i \(-0.918896\pi\)
0.967715 0.252047i \(-0.0811038\pi\)
\(692\) −88.6970 9.96868i −0.128175 0.0144056i
\(693\) 44.6706i 0.0644597i
\(694\) 438.826 392.269i 0.632315 0.565230i
\(695\) 0 0
\(696\) 282.820 + 398.244i 0.406350 + 0.572189i
\(697\) 639.234i 0.917122i
\(698\) 123.825 110.688i 0.177400 0.158579i
\(699\) 702.494i 1.00500i
\(700\) 0 0
\(701\) 815.159 1.16285 0.581426 0.813600i \(-0.302495\pi\)
0.581426 + 0.813600i \(0.302495\pi\)
\(702\) −103.039 115.268i −0.146779 0.164200i
\(703\) −595.020 −0.846401
\(704\) 136.984 + 47.8041i 0.194580 + 0.0679036i
\(705\) 0 0
\(706\) 760.731 + 851.020i 1.07752 + 1.20541i
\(707\) −569.562 −0.805605
\(708\) −47.6765 5.35838i −0.0673397 0.00756833i
\(709\) −1300.08 −1.83368 −0.916839 0.399257i \(-0.869268\pi\)
−0.916839 + 0.399257i \(0.869268\pi\)
\(710\) 0 0
\(711\) 177.019i 0.248972i
\(712\) −33.1102 46.6230i −0.0465030 0.0654818i
\(713\) 868.977i 1.21876i
\(714\) 406.774 + 455.053i 0.569712 + 0.637329i
\(715\) 0 0
\(716\) 375.722 + 42.2275i 0.524751 + 0.0589770i
\(717\) 463.789i 0.646846i
\(718\) −744.112 832.428i −1.03637 1.15937i
\(719\) 782.612i 1.08847i 0.838932 + 0.544237i \(0.183181\pi\)
−0.838932 + 0.544237i \(0.816819\pi\)
\(720\) 0 0
\(721\) 144.031 0.199766
\(722\) −362.167 + 323.743i −0.501616 + 0.448397i
\(723\) −155.084 −0.214500
\(724\) −36.0160 + 320.454i −0.0497458 + 0.442616i
\(725\) 0 0
\(726\) −299.229 + 267.483i −0.412161 + 0.368433i
\(727\) 850.638 1.17007 0.585033 0.811009i \(-0.301081\pi\)
0.585033 + 0.811009i \(0.301081\pi\)
\(728\) 637.373 452.642i 0.875513 0.621761i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 1508.94i 2.06422i
\(732\) 83.1250 739.610i 0.113559 1.01040i
\(733\) 365.781i 0.499019i 0.968372 + 0.249510i \(0.0802694\pi\)
−0.968372 + 0.249510i \(0.919731\pi\)
\(734\) −665.726 + 595.096i −0.906984 + 0.810758i
\(735\) 0 0
\(736\) 1020.78 565.093i 1.38692 0.767789i
\(737\) 252.639i 0.342794i
\(738\) 106.598 95.2884i 0.144442 0.129117i
\(739\) 727.328i 0.984205i −0.870537 0.492103i \(-0.836228\pi\)
0.870537 0.492103i \(-0.163772\pi\)
\(740\) 0 0
\(741\) −280.048 −0.377933
\(742\) −268.309 300.153i −0.361602 0.404519i
\(743\) 481.526 0.648083 0.324041 0.946043i \(-0.394958\pi\)
0.324041 + 0.946043i \(0.394958\pi\)
\(744\) −269.251 + 191.213i −0.361896 + 0.257007i
\(745\) 0 0
\(746\) 150.516 + 168.380i 0.201764 + 0.225711i
\(747\) 427.249 0.571953
\(748\) 27.1673 241.723i 0.0363200 0.323159i
\(749\) 47.1426 0.0629408
\(750\) 0 0
\(751\) 1316.30i 1.75273i 0.481647 + 0.876365i \(0.340039\pi\)
−0.481647 + 0.876365i \(0.659961\pi\)
\(752\) 802.159 + 182.617i 1.06670 + 0.242841i
\(753\) 394.637i 0.524087i
\(754\) −699.021 781.985i −0.927083 1.03711i
\(755\) 0 0
\(756\) −15.2476 + 135.666i −0.0201688 + 0.179453i
\(757\) 483.813i 0.639118i −0.947566 0.319559i \(-0.896465\pi\)
0.947566 0.319559i \(-0.103535\pi\)
\(758\) −428.471 479.325i −0.565265 0.632354i
\(759\) 143.164i 0.188622i
\(760\) 0 0
\(761\) 1027.03 1.34958 0.674789 0.738011i \(-0.264235\pi\)
0.674789 + 0.738011i \(0.264235\pi\)
\(762\) −184.938 + 165.317i −0.242701 + 0.216952i
\(763\) 167.004 0.218878
\(764\) 1313.89 + 147.668i 1.71975 + 0.193283i
\(765\) 0 0
\(766\) 133.046 118.931i 0.173689 0.155262i
\(767\) 103.022 0.134318
\(768\) 399.709 + 191.940i 0.520454 + 0.249922i
\(769\) −1024.79 −1.33263 −0.666314 0.745671i \(-0.732129\pi\)
−0.666314 + 0.745671i \(0.732129\pi\)
\(770\) 0 0
\(771\) 765.790i 0.993242i
\(772\) 411.844 + 46.2873i 0.533477 + 0.0599577i
\(773\) 1092.74i 1.41364i −0.707395 0.706819i \(-0.750130\pi\)
0.707395 0.706819i \(-0.249870\pi\)
\(774\) 251.629 224.933i 0.325103 0.290611i
\(775\) 0 0
\(776\) 823.848 585.070i 1.06166 0.753956i
\(777\) 622.869i 0.801633i
\(778\) 388.751 347.506i 0.499679 0.446666i
\(779\) 258.983i 0.332456i
\(780\) 0 0
\(781\) 70.9991 0.0909079
\(782\) −1303.66 1458.39i −1.66709 1.86495i
\(783\) 183.169 0.233933
\(784\) 91.3723 + 20.8015i 0.116546 + 0.0265325i
\(785\) 0 0
\(786\) 240.050 + 268.541i 0.305407 + 0.341655i
\(787\) −1385.63 −1.76064