Properties

Label 300.3.c.e.151.7
Level $300$
Weight $3$
Character 300.151
Analytic conductor $8.174$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.4069419264.1
Defining polynomial: \(x^{8} - 7 x^{6} + 50 x^{4} - 84 x^{3} + 55 x^{2} - 12 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.7
Root \(0.151747 - 0.0876113i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.e.151.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.33290 - 1.49110i) q^{2} -1.73205i q^{3} +(-0.446749 - 3.97497i) q^{4} +(-2.58266 - 2.30865i) q^{6} -6.56834i q^{7} +(-6.52255 - 4.63210i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(1.33290 - 1.49110i) q^{2} -1.73205i q^{3} +(-0.446749 - 3.97497i) q^{4} +(-2.58266 - 2.30865i) q^{6} -6.56834i q^{7} +(-6.52255 - 4.63210i) q^{8} -3.00000 q^{9} +2.26696i q^{11} +(-6.88486 + 0.773791i) q^{12} -14.8772 q^{13} +(-9.79404 - 8.75495i) q^{14} +(-15.6008 + 3.55163i) q^{16} +26.8250 q^{17} +(-3.99870 + 4.47330i) q^{18} +10.8680i q^{19} -11.3767 q^{21} +(3.38027 + 3.02164i) q^{22} -36.4610i q^{23} +(-8.02303 + 11.2974i) q^{24} +(-19.8298 + 22.1834i) q^{26} +5.19615i q^{27} +(-26.1090 + 2.93440i) q^{28} -35.2510 q^{29} -23.8330i q^{31} +(-15.4985 + 27.9963i) q^{32} +3.92650 q^{33} +(35.7550 - 39.9987i) q^{34} +(1.34025 + 11.9249i) q^{36} +54.7495 q^{37} +(16.2053 + 14.4860i) q^{38} +25.7680i q^{39} -23.8298 q^{41} +(-15.1640 + 16.9638i) q^{42} +56.2515i q^{43} +(9.01112 - 1.01276i) q^{44} +(-54.3670 - 48.5989i) q^{46} -51.4177i q^{47} +(6.15160 + 27.0214i) q^{48} +5.85689 q^{49} -46.4622i q^{51} +(6.64636 + 59.1364i) q^{52} +30.6465 q^{53} +(7.74797 + 6.92596i) q^{54} +(-30.4252 + 42.8423i) q^{56} +18.8240 q^{57} +(-46.9861 + 52.5627i) q^{58} -6.92483i q^{59} +107.426 q^{61} +(-35.5374 - 31.7671i) q^{62} +19.7050i q^{63} +(21.0873 + 60.4262i) q^{64} +(5.23363 - 5.85479i) q^{66} -111.444i q^{67} +(-11.9840 - 106.629i) q^{68} -63.1524 q^{69} -31.3190i q^{71} +(19.5676 + 13.8963i) q^{72} +110.909 q^{73} +(72.9757 - 81.6369i) q^{74} +(43.2002 - 4.85528i) q^{76} +14.8902 q^{77} +(38.4227 + 34.3463i) q^{78} +59.0065i q^{79} +9.00000 q^{81} +(-31.7628 + 35.5326i) q^{82} -142.416i q^{83} +(5.08253 + 45.2221i) q^{84} +(83.8765 + 74.9776i) q^{86} +61.0565i q^{87} +(10.5008 - 14.7864i) q^{88} +7.14798 q^{89} +97.7185i q^{91} +(-144.932 + 16.2889i) q^{92} -41.2800 q^{93} +(-76.6689 - 68.5347i) q^{94} +(48.4911 + 26.8443i) q^{96} -126.308 q^{97} +(7.80665 - 8.73319i) q^{98} -6.80089i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{2} - 8q^{4} - 6q^{6} - 20q^{8} - 24q^{9} + O(q^{10}) \) \( 8q - 2q^{2} - 8q^{4} - 6q^{6} - 20q^{8} - 24q^{9} - 8q^{13} + 22q^{14} + 40q^{16} + 6q^{18} + 24q^{21} - 4q^{22} - 36q^{24} - 66q^{26} - 104q^{28} - 32q^{29} - 112q^{32} + 124q^{34} + 24q^{36} + 176q^{37} + 170q^{38} - 16q^{41} - 54q^{42} + 40q^{44} - 76q^{46} - 24q^{48} + 16q^{49} - 56q^{52} + 304q^{53} + 18q^{54} - 172q^{56} - 72q^{57} + 12q^{58} + 136q^{61} + 238q^{62} + 16q^{64} - 108q^{66} - 88q^{68} - 96q^{69} + 60q^{72} - 240q^{73} - 108q^{74} + 120q^{76} + 384q^{77} - 150q^{78} + 72q^{81} - 320q^{82} - 144q^{84} + 214q^{86} + 200q^{88} + 128q^{89} - 312q^{92} - 72q^{93} + 12q^{94} + 96q^{96} - 216q^{97} - 60q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.33290 1.49110i 0.666451 0.745549i
\(3\) 1.73205i 0.577350i
\(4\) −0.446749 3.97497i −0.111687 0.993743i
\(5\) 0 0
\(6\) −2.58266 2.30865i −0.430443 0.384775i
\(7\) 6.56834i 0.938335i −0.883109 0.469167i \(-0.844554\pi\)
0.883109 0.469167i \(-0.155446\pi\)
\(8\) −6.52255 4.63210i −0.815319 0.579013i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 2.26696i 0.206088i 0.994677 + 0.103044i \(0.0328582\pi\)
−0.994677 + 0.103044i \(0.967142\pi\)
\(12\) −6.88486 + 0.773791i −0.573738 + 0.0644826i
\(13\) −14.8772 −1.14440 −0.572200 0.820114i \(-0.693910\pi\)
−0.572200 + 0.820114i \(0.693910\pi\)
\(14\) −9.79404 8.75495i −0.699575 0.625354i
\(15\) 0 0
\(16\) −15.6008 + 3.55163i −0.975052 + 0.221977i
\(17\) 26.8250 1.57794 0.788969 0.614432i \(-0.210615\pi\)
0.788969 + 0.614432i \(0.210615\pi\)
\(18\) −3.99870 + 4.47330i −0.222150 + 0.248516i
\(19\) 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
\(22\) 3.38027 + 3.02164i 0.153648 + 0.137347i
\(23\) 36.4610i 1.58526i −0.609702 0.792631i \(-0.708711\pi\)
0.609702 0.792631i \(-0.291289\pi\)
\(24\) −8.02303 + 11.2974i −0.334293 + 0.470724i
\(25\) 0 0
\(26\) −19.8298 + 22.1834i −0.762685 + 0.853206i
\(27\) 5.19615i 0.192450i
\(28\) −26.1090 + 2.93440i −0.932464 + 0.104800i
\(29\) −35.2510 −1.21555 −0.607775 0.794109i \(-0.707938\pi\)
−0.607775 + 0.794109i \(0.707938\pi\)
\(30\) 0 0
\(31\) 23.8330i 0.768808i −0.923165 0.384404i \(-0.874407\pi\)
0.923165 0.384404i \(-0.125593\pi\)
\(32\) −15.4985 + 27.9963i −0.484329 + 0.874886i
\(33\) 3.92650 0.118985
\(34\) 35.7550 39.9987i 1.05162 1.17643i
\(35\) 0 0
\(36\) 1.34025 + 11.9249i 0.0372290 + 0.331248i
\(37\) 54.7495 1.47972 0.739858 0.672763i \(-0.234893\pi\)
0.739858 + 0.672763i \(0.234893\pi\)
\(38\) 16.2053 + 14.4860i 0.426455 + 0.381211i
\(39\) 25.7680i 0.660719i
\(40\) 0 0
\(41\) −23.8298 −0.581215 −0.290608 0.956842i \(-0.593857\pi\)
−0.290608 + 0.956842i \(0.593857\pi\)
\(42\) −15.1640 + 16.9638i −0.361048 + 0.403900i
\(43\) 56.2515i 1.30817i 0.756420 + 0.654087i \(0.226947\pi\)
−0.756420 + 0.654087i \(0.773053\pi\)
\(44\) 9.01112 1.01276i 0.204798 0.0230173i
\(45\) 0 0
\(46\) −54.3670 48.5989i −1.18189 1.05650i
\(47\) 51.4177i 1.09399i −0.837135 0.546997i \(-0.815771\pi\)
0.837135 0.546997i \(-0.184229\pi\)
\(48\) 6.15160 + 27.0214i 0.128158 + 0.562947i
\(49\) 5.85689 0.119528
\(50\) 0 0
\(51\) 46.4622i 0.911023i
\(52\) 6.64636 + 59.1364i 0.127815 + 1.13724i
\(53\) 30.6465 0.578236 0.289118 0.957293i \(-0.406638\pi\)
0.289118 + 0.957293i \(0.406638\pi\)
\(54\) 7.74797 + 6.92596i 0.143481 + 0.128258i
\(55\) 0 0
\(56\) −30.4252 + 42.8423i −0.543308 + 0.765042i
\(57\) 18.8240 0.330245
\(58\) −46.9861 + 52.5627i −0.810105 + 0.906253i
\(59\) 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 \(0.157182\pi\)
\(62\) −35.5374 31.7671i −0.573184 0.512372i
\(63\) 19.7050i 0.312778i
\(64\) 21.0873 + 60.4262i 0.329489 + 0.944160i
\(65\) 0 0
\(66\) 5.23363 5.85479i 0.0792975 0.0887090i
\(67\) 111.444i 1.66334i −0.555271 0.831670i \(-0.687385\pi\)
0.555271 0.831670i \(-0.312615\pi\)
\(68\) −11.9840 106.629i −0.176235 1.56807i
\(69\) −63.1524 −0.915251
\(70\) 0 0
\(71\) 31.3190i 0.441113i −0.975374 0.220556i \(-0.929213\pi\)
0.975374 0.220556i \(-0.0707873\pi\)
\(72\) 19.5676 + 13.8963i 0.271773 + 0.193004i
\(73\) 110.909 1.51930 0.759652 0.650330i \(-0.225369\pi\)
0.759652 + 0.650330i \(0.225369\pi\)
\(74\) 72.9757 81.6369i 0.986158 1.10320i
\(75\) 0 0
\(76\) 43.2002 4.85528i 0.568423 0.0638853i
\(77\) 14.8902 0.193379
\(78\) 38.4227 + 34.3463i 0.492599 + 0.440337i
\(79\) 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
\(82\) −31.7628 + 35.5326i −0.387351 + 0.433325i
\(83\) 142.416i 1.71586i −0.513767 0.857930i \(-0.671751\pi\)
0.513767 0.857930i \(-0.328249\pi\)
\(84\) 5.08253 + 45.2221i 0.0605063 + 0.538358i
\(85\) 0 0
\(86\) 83.8765 + 74.9776i 0.975308 + 0.871833i
\(87\) 61.0565i 0.701799i
\(88\) 10.5008 14.7864i 0.119327 0.168027i
\(89\) 7.14798 0.0803144 0.0401572 0.999193i \(-0.487214\pi\)
0.0401572 + 0.999193i \(0.487214\pi\)
\(90\) 0 0
\(91\) 97.7185i 1.07383i
\(92\) −144.932 + 16.2889i −1.57534 + 0.177053i
\(93\) −41.2800 −0.443871
\(94\) −76.6689 68.5347i −0.815626 0.729093i
\(95\) 0 0
\(96\) 48.4911 + 26.8443i 0.505116 + 0.279628i
\(97\) −126.308 −1.30214 −0.651070 0.759017i \(-0.725680\pi\)
−0.651070 + 0.759017i \(0.725680\pi\)
\(98\) 7.80665 8.73319i 0.0796597 0.0891142i
\(99\) 6.80089i 0.0686959i
\(100\) 0 0
\(101\) 86.7133 0.858547 0.429274 0.903174i \(-0.358770\pi\)
0.429274 + 0.903174i \(0.358770\pi\)
\(102\) −69.2797 61.9295i −0.679213 0.607152i
\(103\) 21.9281i 0.212895i 0.994318 + 0.106447i \(0.0339475\pi\)
−0.994318 + 0.106447i \(0.966052\pi\)
\(104\) 97.0372 + 68.9126i 0.933050 + 0.662622i
\(105\) 0 0
\(106\) 40.8488 45.6970i 0.385366 0.431104i
\(107\) 7.17725i 0.0670771i −0.999437 0.0335385i \(-0.989322\pi\)
0.999437 0.0335385i \(-0.0106777\pi\)
\(108\) 20.6546 2.32137i 0.191246 0.0214942i
\(109\) 25.4256 0.233262 0.116631 0.993175i \(-0.462790\pi\)
0.116631 + 0.993175i \(0.462790\pi\)
\(110\) 0 0
\(111\) 94.8289i 0.854315i
\(112\) 23.3283 + 102.472i 0.208288 + 0.914925i
\(113\) −78.3588 −0.693441 −0.346720 0.937968i \(-0.612705\pi\)
−0.346720 + 0.937968i \(0.612705\pi\)
\(114\) 25.0905 28.0684i 0.220092 0.246214i
\(115\) 0 0
\(116\) 15.7483 + 140.122i 0.135761 + 1.20795i
\(117\) 44.6316 0.381466
\(118\) −10.3256 9.23012i −0.0875052 0.0782214i
\(119\) 176.196i 1.48063i
\(120\) 0 0
\(121\) 115.861 0.957528
\(122\) 143.188 160.182i 1.17367 1.31297i
\(123\) 41.2745i 0.335565i
\(124\) −94.7357 + 10.6474i −0.763997 + 0.0858659i
\(125\) 0 0
\(126\) 29.3821 + 26.2649i 0.233192 + 0.208451i
\(127\) 71.6077i 0.563840i 0.959438 + 0.281920i \(0.0909713\pi\)
−0.959438 + 0.281920i \(0.909029\pi\)
\(128\) 118.209 + 49.0990i 0.923505 + 0.383586i
\(129\) 97.4304 0.755274
\(130\) 0 0
\(131\) 103.978i 0.793728i 0.917877 + 0.396864i \(0.129902\pi\)
−0.917877 + 0.396864i \(0.870098\pi\)
\(132\) −1.75416 15.6077i −0.0132891 0.118240i
\(133\) 71.3850 0.536729
\(134\) −166.174 148.543i −1.24010 1.10853i
\(135\) 0 0
\(136\) −174.967 124.256i −1.28652 0.913647i
\(137\) 7.16645 0.0523099 0.0261549 0.999658i \(-0.491674\pi\)
0.0261549 + 0.999658i \(0.491674\pi\)
\(138\) −84.1758 + 94.1664i −0.609970 + 0.682365i
\(139\) 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
\(142\) −46.6997 41.7451i −0.328871 0.293980i
\(143\) 33.7261i 0.235847i
\(144\) 46.8025 10.6549i 0.325017 0.0739922i
\(145\) 0 0
\(146\) 147.831 165.376i 1.01254 1.13272i
\(147\) 10.1444i 0.0690097i
\(148\) −24.4593 217.628i −0.165265 1.47046i
\(149\) 79.6054 0.534265 0.267132 0.963660i \(-0.413924\pi\)
0.267132 + 0.963660i \(0.413924\pi\)
\(150\) 0 0
\(151\) 182.722i 1.21008i 0.796196 + 0.605039i \(0.206842\pi\)
−0.796196 + 0.605039i \(0.793158\pi\)
\(152\) 50.3418 70.8873i 0.331196 0.466364i
\(153\) −80.4749 −0.525980
\(154\) 19.8472 22.2027i 0.128878 0.144174i
\(155\) 0 0
\(156\) 102.427 11.5118i 0.656585 0.0737938i
\(157\) −212.182 −1.35148 −0.675739 0.737141i \(-0.736175\pi\)
−0.675739 + 0.737141i \(0.736175\pi\)
\(158\) 87.9844 + 78.6498i 0.556864 + 0.497783i
\(159\) 53.0813i 0.333845i
\(160\) 0 0
\(161\) −239.488 −1.48751
\(162\) 11.9961 13.4199i 0.0740501 0.0828388i
\(163\) 243.400i 1.49325i 0.665244 + 0.746626i \(0.268327\pi\)
−0.665244 + 0.746626i \(0.731673\pi\)
\(164\) 10.6459 + 94.7229i 0.0649143 + 0.577579i
\(165\) 0 0
\(166\) −212.357 189.827i −1.27926 1.14354i
\(167\) 211.395i 1.26584i 0.774218 + 0.632919i \(0.218143\pi\)
−0.774218 + 0.632919i \(0.781857\pi\)
\(168\) 74.2051 + 52.6980i 0.441697 + 0.313679i
\(169\) 52.3307 0.309649
\(170\) 0 0
\(171\) 32.6041i 0.190667i
\(172\) 223.598 25.1303i 1.29999 0.146106i
\(173\) 22.3138 0.128982 0.0644909 0.997918i \(-0.479458\pi\)
0.0644909 + 0.997918i \(0.479458\pi\)
\(174\) 91.0412 + 81.3823i 0.523225 + 0.467714i
\(175\) 0 0
\(176\) −8.05141 35.3665i −0.0457467 0.200946i
\(177\) −11.9942 −0.0677636
\(178\) 9.52755 10.6583i 0.0535255 0.0598783i
\(179\) 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 \(0.571488\pi\)
\(182\) 145.708 + 130.249i 0.800592 + 0.715654i
\(183\) 186.067i 1.01676i
\(184\) −168.891 + 237.819i −0.917887 + 1.29249i
\(185\) 0 0
\(186\) −55.0222 + 61.5526i −0.295818 + 0.330928i
\(187\) 60.8112i 0.325194i
\(188\) −204.384 + 22.9708i −1.08715 + 0.122185i
\(189\) 34.1301 0.180583
\(190\) 0 0
\(191\) 330.540i 1.73058i −0.501275 0.865288i \(-0.667135\pi\)
0.501275 0.865288i \(-0.332865\pi\)
\(192\) 104.661 36.5242i 0.545111 0.190230i
\(193\) −103.609 −0.536836 −0.268418 0.963303i \(-0.586501\pi\)
−0.268418 + 0.963303i \(0.586501\pi\)
\(194\) −168.356 + 188.337i −0.867812 + 0.970810i
\(195\) 0 0
\(196\) −2.61656 23.2810i −0.0133498 0.118780i
\(197\) 160.633 0.815394 0.407697 0.913117i \(-0.366332\pi\)
0.407697 + 0.913117i \(0.366332\pi\)
\(198\) −10.1408 9.06492i −0.0512162 0.0457824i
\(199\) 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
\(202\) 115.580 129.298i 0.572179 0.640089i
\(203\) 231.540i 1.14059i
\(204\) −184.686 + 20.7569i −0.905324 + 0.101750i
\(205\) 0 0
\(206\) 32.6970 + 29.2280i 0.158723 + 0.141884i
\(207\) 109.383i 0.528421i
\(208\) 232.097 52.8382i 1.11585 0.254030i
\(209\) −24.6374 −0.117883
\(210\) 0 0
\(211\) 269.808i 1.27871i 0.768911 + 0.639355i \(0.220799\pi\)
−0.768911 + 0.639355i \(0.779201\pi\)
\(212\) −13.6913 121.819i −0.0645816 0.574618i
\(213\) −54.2461 −0.254677
\(214\) −10.7020 9.56656i −0.0500093 0.0447036i
\(215\) 0 0
\(216\) 24.0691 33.8922i 0.111431 0.156908i
\(217\) −156.544 −0.721399
\(218\) 33.8898 37.9120i 0.155458 0.173908i
\(219\) 192.100i 0.877170i
\(220\) 0 0
\(221\) −399.080 −1.80579
\(222\) −141.399 126.398i −0.636934 0.569359i
\(223\) 41.3345i 0.185356i −0.995696 0.0926782i \(-0.970457\pi\)
0.995696 0.0926782i \(-0.0295428\pi\)
\(224\) 183.890 + 101.800i 0.820935 + 0.454463i
\(225\) 0 0
\(226\) −104.445 + 116.841i −0.462144 + 0.516994i
\(227\) 149.837i 0.660076i 0.943968 + 0.330038i \(0.107061\pi\)
−0.943968 + 0.330038i \(0.892939\pi\)
\(228\) −8.40959 74.8249i −0.0368842 0.328179i
\(229\) −61.6770 −0.269332 −0.134666 0.990891i \(-0.542996\pi\)
−0.134666 + 0.990891i \(0.542996\pi\)
\(230\) 0 0
\(231\) 25.7906i 0.111648i
\(232\) 229.926 + 163.286i 0.991061 + 0.703819i
\(233\) −405.585 −1.74071 −0.870355 0.492425i \(-0.836110\pi\)
−0.870355 + 0.492425i \(0.836110\pi\)
\(234\) 59.4895 66.5501i 0.254228 0.284402i
\(235\) 0 0
\(236\) −27.5260 + 3.09366i −0.116636 + 0.0131087i
\(237\) 102.202 0.431233
\(238\) −262.725 234.851i −1.10389 0.986770i
\(239\) 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 \(0.559476\pi\)
\(242\) 154.431 172.760i 0.638145 0.713884i
\(243\) 15.5885i 0.0641500i
\(244\) −47.9922 427.014i −0.196689 1.75006i
\(245\) 0 0
\(246\) 61.5443 + 55.0148i 0.250180 + 0.223637i
\(247\) 161.686i 0.654598i
\(248\) −110.397 + 155.452i −0.445149 + 0.626823i
\(249\) −246.672 −0.990652
\(250\) 0 0
\(251\) 227.844i 0.907745i 0.891067 + 0.453873i \(0.149958\pi\)
−0.891067 + 0.453873i \(0.850042\pi\)
\(252\) 78.3270 8.80319i 0.310821 0.0349333i
\(253\) 82.6559 0.326703
\(254\) 106.774 + 95.4460i 0.420371 + 0.375772i
\(255\) 0 0
\(256\) 230.772 110.817i 0.901453 0.432878i
\(257\) −442.129 −1.72035 −0.860173 0.510003i \(-0.829644\pi\)
−0.860173 + 0.510003i \(0.829644\pi\)
\(258\) 129.865 145.278i 0.503353 0.563094i
\(259\) 359.614i 1.38847i
\(260\) 0 0
\(261\) 105.753 0.405184
\(262\) 155.042 + 138.593i 0.591763 + 0.528981i
\(263\) 34.1556i 0.129869i 0.997890 + 0.0649346i \(0.0206839\pi\)
−0.997890 + 0.0649346i \(0.979316\pi\)
\(264\) −25.6108 18.1879i −0.0970105 0.0688937i
\(265\) 0 0
\(266\) 95.1491 106.442i 0.357703 0.400158i
\(267\) 12.3807i 0.0463695i
\(268\) −442.986 + 49.7873i −1.65293 + 0.185774i
\(269\) −9.96085 −0.0370292 −0.0185146 0.999829i \(-0.505894\pi\)
−0.0185146 + 0.999829i \(0.505894\pi\)
\(270\) 0 0
\(271\) 56.5791i 0.208779i −0.994536 0.104390i \(-0.966711\pi\)
0.994536 0.104390i \(-0.0332889\pi\)
\(272\) −418.492 + 95.2723i −1.53857 + 0.350266i
\(273\) 169.253 0.619976
\(274\) 9.55218 10.6859i 0.0348620 0.0389996i
\(275\) 0 0
\(276\) 28.2132 + 251.029i 0.102222 + 0.909525i
\(277\) 103.794 0.374708 0.187354 0.982292i \(-0.440009\pi\)
0.187354 + 0.982292i \(0.440009\pi\)
\(278\) 219.056 + 195.815i 0.787969 + 0.704370i
\(279\) 71.4991i 0.256269i
\(280\) 0 0
\(281\) 393.069 1.39882 0.699411 0.714720i \(-0.253446\pi\)
0.699411 + 0.714720i \(0.253446\pi\)
\(282\) −118.706 + 132.794i −0.420942 + 0.470902i
\(283\) 114.027i 0.402923i −0.979496 0.201462i \(-0.935431\pi\)
0.979496 0.201462i \(-0.0645692\pi\)
\(284\) −124.492 + 13.9917i −0.438353 + 0.0492666i
\(285\) 0 0
\(286\) −50.2889 44.9535i −0.175835 0.157180i
\(287\) 156.522i 0.545374i
\(288\) 46.4956 83.9890i 0.161443 0.291629i
\(289\) 430.579 1.48989
\(290\) 0 0
\(291\) 218.771i 0.751791i
\(292\) −49.5485 440.861i −0.169687 1.50980i
\(293\) 126.796 0.432750 0.216375 0.976310i \(-0.430577\pi\)
0.216375 + 0.976310i \(0.430577\pi\)
\(294\) −15.1263 13.5215i −0.0514501 0.0459915i
\(295\) 0 0
\(296\) −357.106 253.605i −1.20644 0.856775i
\(297\) −11.7795 −0.0396616
\(298\) 106.106 118.700i 0.356061 0.398321i
\(299\) 542.438i 1.81417i
\(300\) 0 0
\(301\) 369.479 1.22750
\(302\) 272.456 + 243.550i 0.902172 + 0.806457i
\(303\) 150.192i 0.495683i
\(304\) −38.5992 169.550i −0.126971 0.557732i
\(305\) 0 0
\(306\) −107.265 + 119.996i −0.350539 + 0.392144i
\(307\) 408.420i 1.33036i −0.746683 0.665180i \(-0.768355\pi\)
0.746683 0.665180i \(-0.231645\pi\)
\(308\) −6.65217 59.1881i −0.0215980 0.192169i
\(309\) 37.9806 0.122915
\(310\) 0 0
\(311\) 472.495i 1.51928i −0.650345 0.759639i \(-0.725376\pi\)
0.650345 0.759639i \(-0.274624\pi\)
\(312\) 119.360 168.073i 0.382565 0.538697i
\(313\) 54.6519 0.174607 0.0873033 0.996182i \(-0.472175\pi\)
0.0873033 + 0.996182i \(0.472175\pi\)
\(314\) −282.818 + 316.384i −0.900693 + 1.00759i
\(315\) 0 0
\(316\) 234.549 26.3611i 0.742244 0.0834211i
\(317\) −63.3734 −0.199916 −0.0999581 0.994992i \(-0.531871\pi\)
−0.0999581 + 0.994992i \(0.531871\pi\)
\(318\) −79.1495 70.7522i −0.248898 0.222491i
\(319\) 79.9127i 0.250510i
\(320\) 0 0
\(321\) −12.4314 −0.0387270
\(322\) −319.215 + 357.101i −0.991349 + 1.10901i
\(323\) 291.535i 0.902584i
\(324\) −4.02074 35.7748i −0.0124097 0.110416i
\(325\) 0 0
\(326\) 362.933 + 324.428i 1.11329 + 0.995179i
\(327\) 44.0384i 0.134674i
\(328\) 155.431 + 110.382i 0.473876 + 0.336531i
\(329\) −337.729 −1.02653
\(330\) 0 0
\(331\) 431.595i 1.30391i 0.758257 + 0.651955i \(0.226051\pi\)
−0.758257 + 0.651955i \(0.773949\pi\)
\(332\) −566.101 + 63.6243i −1.70512 + 0.191639i
\(333\) −164.249 −0.493239
\(334\) 315.211 + 281.768i 0.943744 + 0.843618i
\(335\) 0 0
\(336\) 177.486 40.4058i 0.528232 0.120255i
\(337\) 486.091 1.44241 0.721203 0.692723i \(-0.243589\pi\)
0.721203 + 0.692723i \(0.243589\pi\)
\(338\) 69.7517 78.0303i 0.206366 0.230859i
\(339\) 135.721i 0.400358i
\(340\) 0 0
\(341\) 54.0286 0.158442
\(342\) −48.6159 43.4581i −0.142152 0.127070i
\(343\) 360.319i 1.05049i
\(344\) 260.562 366.903i 0.757449 1.06658i
\(345\) 0 0
\(346\) 29.7422 33.2721i 0.0859600 0.0961623i
\(347\) 294.297i 0.848119i −0.905634 0.424060i \(-0.860605\pi\)
0.905634 0.424060i \(-0.139395\pi\)
\(348\) 242.698 27.2769i 0.697408 0.0783819i
\(349\) 83.0428 0.237945 0.118972 0.992898i \(-0.462040\pi\)
0.118972 + 0.992898i \(0.462040\pi\)
\(350\) 0 0
\(351\) 77.3041i 0.220240i
\(352\) −63.4667 35.1346i −0.180303 0.0998143i
\(353\) 570.733 1.61681 0.808404 0.588628i \(-0.200332\pi\)
0.808404 + 0.588628i \(0.200332\pi\)
\(354\) −15.9870 + 17.8845i −0.0451611 + 0.0505211i
\(355\) 0 0
\(356\) −3.19335 28.4130i −0.00897008 0.0798119i
\(357\) −305.180 −0.854845
\(358\) 140.941 + 125.988i 0.393691 + 0.351923i
\(359\) 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
\(362\) −107.456 + 120.209i −0.296839 + 0.332070i
\(363\) 200.677i 0.552829i
\(364\) 388.428 43.6556i 1.06711 0.119933i
\(365\) 0 0
\(366\) −277.444 248.008i −0.758042 0.677618i
\(367\) 446.467i 1.21653i 0.793734 + 0.608265i \(0.208134\pi\)
−0.793734 + 0.608265i \(0.791866\pi\)
\(368\) 129.496 + 568.822i 0.351891 + 1.54571i
\(369\) 71.4895 0.193738
\(370\) 0 0
\(371\) 201.297i 0.542579i
\(372\) 18.4418 + 164.087i 0.0495747 + 0.441094i
\(373\) 112.924 0.302744 0.151372 0.988477i \(-0.451631\pi\)
0.151372 + 0.988477i \(0.451631\pi\)
\(374\) 90.6755 + 81.0554i 0.242448 + 0.216726i
\(375\) 0 0
\(376\) −238.172 + 335.375i −0.633436 + 0.891954i
\(377\) 524.435 1.39108
\(378\) 45.4921 50.8913i 0.120349 0.134633i
\(379\) 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
\(382\) −492.868 440.577i −1.29023 1.15334i
\(383\) 89.2269i 0.232968i 0.993193 + 0.116484i \(0.0371624\pi\)
−0.993193 + 0.116484i \(0.962838\pi\)
\(384\) 85.0419 204.743i 0.221463 0.533186i
\(385\) 0 0
\(386\) −138.101 + 154.492i −0.357775 + 0.400238i
\(387\) 168.754i 0.436058i
\(388\) 56.4278 + 502.069i 0.145432 + 1.29399i
\(389\) 260.714 0.670217 0.335108 0.942180i \(-0.391227\pi\)
0.335108 + 0.942180i \(0.391227\pi\)
\(390\) 0 0
\(391\) 978.066i 2.50145i
\(392\) −38.2018 27.1297i −0.0974536 0.0692084i
\(393\) 180.096 0.458259
\(394\) 214.107 239.519i 0.543420 0.607916i
\(395\) 0 0
\(396\) −27.0334 + 3.03829i −0.0682661 + 0.00767245i
\(397\) −112.607 −0.283644 −0.141822 0.989892i \(-0.545296\pi\)
−0.141822 + 0.989892i \(0.545296\pi\)
\(398\) −41.0824 36.7238i −0.103222 0.0922708i
\(399\) 123.642i 0.309881i
\(400\) 0 0
\(401\) 577.513 1.44018 0.720091 0.693880i \(-0.244100\pi\)
0.720091 + 0.693880i \(0.244100\pi\)
\(402\) −257.285 + 287.821i −0.640012 + 0.715973i
\(403\) 354.569i 0.879823i
\(404\) −38.7390 344.683i −0.0958887 0.853176i
\(405\) 0 0
\(406\) 345.250 + 308.621i 0.850368 + 0.760149i
\(407\) 124.115i 0.304951i
\(408\) −215.218 + 303.052i −0.527494 + 0.742774i
\(409\) −276.255 −0.675441 −0.337721 0.941246i \(-0.609656\pi\)
−0.337721 + 0.941246i \(0.609656\pi\)
\(410\) 0 0
\(411\) 12.4127i 0.0302011i
\(412\) 87.1638 9.79636i 0.211563 0.0237776i
\(413\) −45.4847 −0.110132
\(414\) 163.101 + 145.797i 0.393964 + 0.352166i
\(415\) 0 0
\(416\) 230.575 416.507i 0.554266 1.00122i
\(417\) 254.454 0.610200
\(418\) −32.8393 + 36.7369i −0.0785629 + 0.0878872i
\(419\) 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 \(0.529427\pi\)
\(422\) 402.310 + 359.627i 0.953342 + 0.852197i
\(423\) 154.253i 0.364665i
\(424\) −199.893 141.958i −0.471447 0.334806i
\(425\) 0 0
\(426\) −72.3047 + 80.8863i −0.169729 + 0.189874i
\(427\) 705.608i 1.65248i
\(428\) −28.5294 + 3.20643i −0.0666574 + 0.00749165i
\(429\) −58.4152 −0.136166
\(430\) 0 0
\(431\) 317.184i 0.735926i 0.929840 + 0.367963i \(0.119945\pi\)
−0.929840 + 0.367963i \(0.880055\pi\)
\(432\) −18.4548 81.0643i −0.0427194 0.187649i
\(433\) 82.9688 0.191614 0.0958069 0.995400i \(-0.469457\pi\)
0.0958069 + 0.995400i \(0.469457\pi\)
\(434\) −208.657 + 233.422i −0.480777 + 0.537838i
\(435\) 0 0
\(436\) −11.3588 101.066i −0.0260524 0.231803i
\(437\) 396.260 0.906773
\(438\) −286.440 256.051i −0.653974 0.584591i
\(439\) 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
\(442\) −531.934 + 595.068i −1.20347 + 1.34631i
\(443\) 35.1780i 0.0794086i 0.999211 + 0.0397043i \(0.0126416\pi\)
−0.999211 + 0.0397043i \(0.987358\pi\)
\(444\) −376.943 + 42.3647i −0.848970 + 0.0954160i
\(445\) 0 0
\(446\) −61.6337 55.0948i −0.138192 0.123531i
\(447\) 137.881i 0.308458i
\(448\) 396.900 138.508i 0.885938 0.309171i
\(449\) −67.4253 −0.150168 −0.0750838 0.997177i \(-0.523922\pi\)
−0.0750838 + 0.997177i \(0.523922\pi\)
\(450\) 0 0
\(451\) 54.0214i 0.119781i
\(452\) 35.0067 + 311.474i 0.0774484 + 0.689102i
\(453\) 316.483 0.698638
\(454\) 223.422 + 199.718i 0.492119 + 0.439908i
\(455\) 0 0
\(456\) −122.780 87.1946i −0.269255 0.191216i
\(457\) 204.153 0.446724 0.223362 0.974736i \(-0.428297\pi\)
0.223362 + 0.974736i \(0.428297\pi\)
\(458\) −82.2094 + 91.9665i −0.179496 + 0.200800i
\(459\) 139.387i 0.303674i
\(460\) 0 0
\(461\) 125.762 0.272802 0.136401 0.990654i \(-0.456446\pi\)
0.136401 + 0.990654i \(0.456446\pi\)
\(462\) −38.4563 34.3763i −0.0832387 0.0744076i
\(463\) 553.629i 1.19574i −0.801592 0.597871i \(-0.796013\pi\)
0.801592 0.597871i \(-0.203987\pi\)
\(464\) 549.944 125.198i 1.18523 0.269824i
\(465\) 0 0
\(466\) −540.605 + 604.768i −1.16010 + 1.29778i
\(467\) 625.772i 1.33998i −0.742369 0.669991i \(-0.766298\pi\)
0.742369 0.669991i \(-0.233702\pi\)
\(468\) −19.9391 177.409i −0.0426049 0.379080i
\(469\) −732.000 −1.56077
\(470\) 0 0
\(471\) 367.510i 0.780276i
\(472\) −32.0765 + 45.1676i −0.0679588 + 0.0956940i
\(473\) −127.520 −0.269598
\(474\) 136.225 152.394i 0.287395 0.321505i
\(475\) 0 0
\(476\) −700.373 + 78.7151i −1.47137 + 0.165368i
\(477\) −91.9396 −0.192745
\(478\) −399.269 356.909i −0.835291 0.746672i
\(479\) 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
\(482\) −119.345 + 133.509i −0.247604 + 0.276991i
\(483\) 414.806i 0.858812i
\(484\) −51.7607 460.544i −0.106944 0.951537i
\(485\) 0 0
\(486\) −23.2439 20.7779i −0.0478270 0.0427528i
\(487\) 609.476i 1.25149i 0.780027 + 0.625746i \(0.215205\pi\)
−0.780027 + 0.625746i \(0.784795\pi\)
\(488\) −700.689 497.606i −1.43584 1.01968i
\(489\) 421.581 0.862129
\(490\) 0 0
\(491\) 689.074i 1.40341i 0.712468 + 0.701705i \(0.247578\pi\)
−0.712468 + 0.701705i \(0.752422\pi\)
\(492\) 164.065 18.4393i 0.333465 0.0374783i
\(493\) −945.606 −1.91806
\(494\) −241.089 215.511i −0.488035 0.436257i
\(495\) 0 0
\(496\) 84.6461 + 371.815i 0.170657 + 0.749627i
\(497\) −205.714 −0.413911
\(498\) −328.790 + 367.813i −0.660220 + 0.738580i
\(499\) 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
\(502\) 339.738 + 303.694i 0.676769 + 0.604967i
\(503\) 943.945i 1.87663i −0.345782 0.938315i \(-0.612386\pi\)
0.345782 0.938315i \(-0.387614\pi\)
\(504\) 91.2757 128.527i 0.181103 0.255014i
\(505\) 0 0
\(506\) 110.172 123.248i 0.217731 0.243573i
\(507\) 90.6395i 0.178776i
\(508\) 284.639 31.9906i 0.560313 0.0629737i
\(509\) −357.147 −0.701665 −0.350832 0.936438i \(-0.614101\pi\)
−0.350832 + 0.936438i \(0.614101\pi\)
\(510\) 0 0
\(511\) 728.489i 1.42562i
\(512\) 142.358 491.811i 0.278042 0.960569i
\(513\) −56.4720 −0.110082
\(514\) −589.314 + 659.258i −1.14653 + 1.28260i
\(515\) 0 0
\(516\) −43.5269 387.283i −0.0843544 0.750549i
\(517\) 116.562 0.225459
\(518\) −536.219 479.329i −1.03517 0.925346i
\(519\) 38.6487i 0.0744677i
\(520\) 0 0
\(521\) −88.8415 −0.170521 −0.0852605 0.996359i \(-0.527172\pi\)
−0.0852605 + 0.996359i \(0.527172\pi\)
\(522\) 140.958 157.688i 0.270035 0.302084i
\(523\) 220.427i 0.421467i −0.977544 0.210734i \(-0.932415\pi\)
0.977544 0.210734i \(-0.0675852\pi\)
\(524\) 413.311 46.4522i 0.788762 0.0886492i
\(525\) 0 0
\(526\) 50.9294 + 45.5261i 0.0968239 + 0.0865514i
\(527\) 639.320i 1.21313i
\(528\) −61.2566 + 13.9455i −0.116016 + 0.0264119i
\(529\) −800.407 −1.51306
\(530\) 0 0
\(531\) 20.7745i 0.0391234i
\(532\) −31.8911 283.753i −0.0599457 0.533371i
\(533\) 354.521 0.665142
\(534\) −18.4608 16.5022i −0.0345708 0.0309030i
\(535\) 0 0
\(536\) −516.219 + 726.897i −0.963094 + 1.35615i
\(537\) 163.717 0.304873
\(538\) −13.2768 + 14.8526i −0.0246781 + 0.0276071i
\(539\) 13.2774i 0.0246333i
\(540\) 0 0
\(541\) −411.560 −0.760740 −0.380370 0.924834i \(-0.624203\pi\)
−0.380370 + 0.924834i \(0.624203\pi\)
\(542\) −84.3651 75.4144i −0.155655 0.139141i
\(543\) 139.634i 0.257154i
\(544\) −415.748 + 751.001i −0.764242 + 1.38052i
\(545\) 0 0
\(546\) 225.598 252.373i 0.413183 0.462222i
\(547\) 851.537i 1.55674i 0.627806 + 0.778370i \(0.283953\pi\)
−0.627806 + 0.778370i \(0.716047\pi\)
\(548\) −3.20160 28.4865i −0.00584234 0.0519826i
\(549\) −322.277 −0.587025
\(550\) 0 0
\(551\) 383.109i 0.695297i
\(552\) 411.914 + 292.528i 0.746222 + 0.529942i
\(553\) 387.575 0.700858
\(554\) 138.347 154.767i 0.249724 0.279363i
\(555\) 0 0
\(556\) 583.959 65.6313i 1.05029 0.118042i
\(557\) −211.553 −0.379808 −0.189904 0.981803i \(-0.560818\pi\)
−0.189904 + 0.981803i \(0.560818\pi\)
\(558\) 106.612 + 95.3012i 0.191061 + 0.170791i
\(559\) 836.864i 1.49707i
\(560\) 0 0
\(561\) 105.328 0.187751
\(562\) 523.922 586.104i 0.932246 1.04289i
\(563\) 404.044i 0.717663i 0.933402 + 0.358832i \(0.116825\pi\)
−0.933402 + 0.358832i \(0.883175\pi\)
\(564\) 39.7866 + 354.004i 0.0705436 + 0.627666i
\(565\) 0 0
\(566\) −170.026 151.987i −0.300399 0.268529i
\(567\) 59.1151i 0.104259i
\(568\) −145.073 + 204.280i −0.255410 + 0.359647i
\(569\) 230.465 0.405036 0.202518 0.979279i \(-0.435088\pi\)
0.202518 + 0.979279i \(0.435088\pi\)
\(570\) 0 0
\(571\) 351.234i 0.615121i −0.951529 0.307560i \(-0.900487\pi\)
0.951529 0.307560i \(-0.0995126\pi\)
\(572\) −134.060 + 15.0671i −0.234371 + 0.0263410i
\(573\) −572.512 −0.999149
\(574\) 233.390 + 208.629i 0.406603 + 0.363465i
\(575\) 0 0
\(576\) −63.2618 181.279i −0.109830 0.314720i
\(577\) 638.575 1.10672 0.553358 0.832944i \(-0.313346\pi\)
0.553358 + 0.832944i \(0.313346\pi\)
\(578\) 573.919 642.035i 0.992939 1.11079i
\(579\) 179.457i 0.309942i
\(580\) 0 0
\(581\) −935.439 −1.61005
\(582\) 326.209 + 291.600i 0.560497 + 0.501032i
\(583\) 69.4746i 0.119167i
\(584\) −723.410 513.742i −1.23872 0.879696i
\(585\) 0 0
\(586\) 169.006 189.065i 0.288407 0.322637i
\(587\) 105.047i 0.178956i −0.995989 0.0894779i \(-0.971480\pi\)
0.995989 0.0894779i \(-0.0285198\pi\)
\(588\) −40.3238 + 4.53201i −0.0685779 + 0.00770749i
\(589\) 259.018 0.439759
\(590\) 0 0
\(591\) 278.224i 0.470768i
\(592\) −854.138 + 194.450i −1.44280 + 0.328463i
\(593\) −990.175 −1.66977 −0.834886 0.550422i \(-0.814467\pi\)
−0.834886 + 0.550422i \(0.814467\pi\)
\(594\) −15.7009 + 17.5644i −0.0264325 + 0.0295697i
\(595\) 0 0
\(596\) −35.5636 316.429i −0.0596705 0.530922i
\(597\) −47.7210 −0.0799347
\(598\) 808.828 + 723.016i 1.35255 + 1.20906i
\(599\) 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 \(0.671426\pi\)
\(602\) 492.479 550.929i 0.818071 0.915165i
\(603\) 334.331i 0.554446i
\(604\) 726.314 81.6306i 1.20251 0.135150i
\(605\) 0 0
\(606\) −223.951 200.191i −0.369556 0.330348i
\(607\) 226.520i 0.373179i −0.982438 0.186590i \(-0.940257\pi\)
0.982438 0.186590i \(-0.0597435\pi\)
\(608\) −304.265 168.439i −0.500436 0.277037i
\(609\) 401.040 0.658522
\(610\) 0 0
\(611\) 764.951i 1.25197i
\(612\) 35.9520 + 319.886i 0.0587452 + 0.522689i
\(613\) −732.519 −1.19497 −0.597487 0.801879i \(-0.703834\pi\)
−0.597487 + 0.801879i \(0.703834\pi\)
\(614\) −608.995 544.384i −0.991848 0.886619i
\(615\) 0 0
\(616\) −97.1220 68.9729i −0.157666 0.111969i
\(617\) −350.585 −0.568209 −0.284105 0.958793i \(-0.591696\pi\)
−0.284105 + 0.958793i \(0.591696\pi\)
\(618\) 50.6245 56.6329i 0.0819166 0.0916390i
\(619\) 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
\(622\) −704.537 629.790i −1.13270 1.01252i
\(623\) 46.9504i 0.0753617i
\(624\) −91.5185 402.003i −0.146664 0.644235i
\(625\) 0 0
\(626\) 72.8455 81.4913i 0.116367 0.130178i
\(627\) 42.6733i 0.0680595i
\(628\) 94.7920 + 843.417i 0.150943 + 1.34302i
\(629\) 1468.65 2.33490
\(630\) 0 0
\(631\) 200.923i 0.318419i 0.987245 + 0.159210i \(0.0508946\pi\)
−0.987245 + 0.159210i \(0.949105\pi\)
\(632\) 273.324 384.873i 0.432475 0.608976i
\(633\) 467.321 0.738264
\(634\) −84.4705 + 94.4960i −0.133234 + 0.149047i
\(635\) 0 0
\(636\) −210.997 + 23.7140i −0.331756 + 0.0372862i
\(637\) −87.1340 −0.136788
\(638\) −119.158 106.516i −0.186768 0.166953i
\(639\) 93.9570i 0.147038i
\(640\) 0 0
\(641\) 216.861 0.338316 0.169158 0.985589i \(-0.445895\pi\)
0.169158 + 0.985589i \(0.445895\pi\)
\(642\) −16.5698 + 18.5364i −0.0258096 + 0.0288729i
\(643\) 37.5349i 0.0583746i −0.999574 0.0291873i \(-0.990708\pi\)
0.999574 0.0291873i \(-0.00929193\pi\)
\(644\) 106.991 + 951.960i 0.166135 + 1.47820i
\(645\) 0 0
\(646\) 434.707 + 388.587i 0.672921 + 0.601528i
\(647\) 1192.56i 1.84321i 0.388125 + 0.921607i \(0.373123\pi\)
−0.388125 + 0.921607i \(0.626877\pi\)
\(648\) −58.7029 41.6889i −0.0905910 0.0643347i
\(649\) 15.6984 0.0241885
\(650\) 0 0
\(651\) 271.141i 0.416500i
\(652\) 967.509 108.739i 1.48391 0.166777i
\(653\) 1087.78 1.66582 0.832908 0.553412i \(-0.186675\pi\)
0.832908 + 0.553412i \(0.186675\pi\)
\(654\) −65.6656 58.6988i −0.100406 0.0897535i
\(655\) 0 0
\(656\) 371.765 84.6347i 0.566715 0.129016i
\(657\) −332.727 −0.506435
\(658\) −450.160 + 503.587i −0.684133 + 0.765330i
\(659\) 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 \(0.624746\pi\)
\(662\) 643.550 + 575.273i 0.972130 + 0.868992i
\(663\) 691.227i 1.04257i
\(664\) −659.687 + 928.917i −0.993504 + 1.39897i
\(665\) 0 0
\(666\) −218.927 + 244.911i −0.328719 + 0.367734i
\(667\) 1285.29i 1.92697i
\(668\) 840.289 94.4403i 1.25792 0.141378i
\(669\) −71.5934 −0.107016
\(670\) 0 0
\(671\) 243.530i 0.362936i
\(672\) 176.322 318.506i 0.262384 0.473967i
\(673\) 902.689 1.34129 0.670646 0.741778i \(-0.266017\pi\)
0.670646 + 0.741778i \(0.266017\pi\)
\(674\) 647.911 724.810i 0.961293 1.07539i
\(675\) 0 0
\(676\) −23.3787 208.013i −0.0345838 0.307712i
\(677\) −930.750 −1.37482 −0.687408 0.726272i \(-0.741252\pi\)
−0.687408 + 0.726272i \(0.741252\pi\)
\(678\) 202.374 + 180.903i 0.298487 + 0.266819i
\(679\) 829.632i 1.22184i
\(680\) 0 0
\(681\) 259.526 0.381095
\(682\) 72.0148 80.5620i 0.105594 0.118126i
\(683\) 64.9023i 0.0950253i −0.998871 0.0475127i \(-0.984871\pi\)
0.998871 0.0475127i \(-0.0151294\pi\)
\(684\) −129.600 + 14.5658i −0.189474 + 0.0212951i
\(685\) 0 0
\(686\) −537.271 480.269i −0.783193 0.700101i
\(687\) 106.828i 0.155499i
\(688\) −199.784 877.570i −0.290384 1.27554i
\(689\) −455.934 −0.661733
\(690\) 0 0
\(691\) 348.329i 0.504094i 0.967715 + 0.252047i \(0.0811038\pi\)
−0.967715 + 0.252047i \(0.918896\pi\)
\(692\) −9.96868 88.6970i −0.0144056 0.128175i
\(693\) −44.6706 −0.0644597
\(694\) −438.826 392.269i −0.632315 0.565230i
\(695\) 0 0
\(696\) 282.820 398.244i 0.406350 0.572189i
\(697\) −639.234 −0.917122
\(698\) 110.688 123.825i 0.158579 0.177400i
\(699\) 702.494i 1.00500i
\(700\) 0 0
\(701\) 815.159 1.16285 0.581426 0.813600i \(-0.302495\pi\)
0.581426 + 0.813600i \(0.302495\pi\)
\(702\) −115.268 103.039i −0.164200 0.146779i
\(703\) 595.020i 0.846401i
\(704\) −136.984 + 47.8041i −0.194580 + 0.0679036i
\(705\) 0 0
\(706\) 760.731 851.020i 1.07752 1.20541i
\(707\) 569.562i 0.805605i
\(708\) 5.35838 + 47.6765i 0.00756833 + 0.0673397i
\(709\) 1300.08 1.83368 0.916839 0.399257i \(-0.130732\pi\)
0.916839 + 0.399257i \(0.130732\pi\)
\(710\) 0 0
\(711\) 177.019i 0.248972i
\(712\) −46.6230 33.1102i −0.0654818 0.0465030i
\(713\) −868.977 −1.21876
\(714\) −406.774 + 455.053i −0.569712 + 0.637329i
\(715\) 0 0
\(716\) 375.722 42.2275i 0.524751 0.0589770i
\(717\) −463.789 −0.646846
\(718\) 832.428 + 744.112i 1.15937 + 1.03637i
\(719\) 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
\(722\) 323.743 362.167i 0.448397 0.501616i
\(723\) 155.084i 0.214500i
\(724\) 36.0160 + 320.454i 0.0497458 + 0.442616i
\(725\) 0 0
\(726\) −299.229 267.483i −0.412161 0.368433i
\(727\) 850.638i 1.17007i 0.811009 + 0.585033i \(0.198919\pi\)
−0.811009 + 0.585033i \(0.801081\pi\)
\(728\) 452.642 637.373i 0.621761 0.875513i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 1508.94i 2.06422i
\(732\) −739.610 + 83.1250i −1.01040 + 0.113559i
\(733\) −365.781 −0.499019 −0.249510 0.968372i \(-0.580269\pi\)
−0.249510 + 0.968372i \(0.580269\pi\)
\(734\) 665.726 + 595.096i 0.906984 + 0.810758i
\(735\) 0 0
\(736\) 1020.78 + 565.093i 1.38692 + 0.767789i
\(737\) 252.639 0.342794
\(738\) 95.2884 106.598i 0.129117 0.144442i
\(739\) 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
\(742\) −300.153 268.309i −0.404519 0.361602i
\(743\) 481.526i 0.648083i −0.946043 0.324041i \(-0.894958\pi\)
0.946043 0.324041i \(-0.105042\pi\)
\(744\) 269.251 + 191.213i 0.361896 + 0.257007i
\(745\) 0 0
\(746\) 150.516 168.380i 0.201764 0.225711i
\(747\) 427.249i 0.571953i
\(748\) 241.723 27.1673i 0.323159 0.0363200i
\(749\) −47.1426 −0.0629408
\(750\) 0 0
\(751\) 1316.30i 1.75273i −0.481647 0.876365i \(-0.659961\pi\)
0.481647 0.876365i \(-0.340039\pi\)
\(752\) 182.617 + 802.159i 0.242841 + 1.06670i
\(753\) 394.637 0.524087
\(754\) 699.021 781.985i 0.927083 1.03711i
\(755\) 0 0
\(756\) −15.2476 135.666i −0.0201688 0.179453i
\(757\) −483.813 −0.639118 −0.319559 0.947566i \(-0.603535\pi\)
−0.319559 + 0.947566i \(0.603535\pi\)
\(758\) 479.325 + 428.471i 0.632354 + 0.565265i
\(759\) 143.164i 0.188622i
\(760\) 0 0
\(761\) 1027.03 1.34958 0.674789 0.738011i \(-0.264235\pi\)
0.674789 + 0.738011i \(0.264235\pi\)
\(762\) 165.317 184.938i 0.216952 0.242701i
\(763\) 167.004i 0.218878i
\(764\) −1313.89 + 147.668i −1.71975 + 0.193283i
\(765\) 0 0
\(766\) 133.046 + 118.931i 0.173689 + 0.155262i
\(767\) 103.022i 0.134318i
\(768\) −191.940 399.709i −0.249922 0.520454i
\(769\) 1024.79 1.33263 0.666314 0.745671i \(-0.267871\pi\)
0.666314 + 0.745671i \(0.267871\pi\)
\(770\) 0 0
\(771\) 765.790i 0.993242i
\(772\) 46.2873 + 411.844i 0.0599577 + 0.533477i
\(773\) 1092.74 1.41364 0.706819 0.707395i \(-0.250130\pi\)
0.706819 + 0.707395i \(0.250130\pi\)
\(774\) −251.629 224.933i −0.325103 0.290611i
\(775\) 0 0
\(776\) 823.848 + 585.070i 1.06166 + 0.753956i
\(777\) −622.869 −0.801633
\(778\) 347.506 388.751i 0.446666 0.499679i
\(779\) 258.983i 0.332456i
\(780\) 0 0
\(781\) 70.9991 0.0909079
\(782\) −1458.39 1303.66i −1.86495 1.66709i
\(783\) 183.169i 0.233933i
\(784\) −91.3723 + 20.8015i −0.116546 + 0.0265325i
\(785\) 0 0
\(786\) 240.050 268.541i 0.305407 0.341655i
\(787\) &minus