Properties

Label 126.4.g.g.109.1
Level $126$
Weight $4$
Character 126.109
Analytic conductor $7.434$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 126.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.43424066072\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{1345})\)
Defining polynomial: \(x^{4} - x^{3} + 337 x^{2} + 336 x + 112896\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(-8.91856 - 15.4474i\) of defining polynomial
Character \(\chi\) \(=\) 126.109
Dual form 126.4.g.g.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-7.91856 - 13.7153i) q^{5} +(18.3371 - 2.59808i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-7.91856 - 13.7153i) q^{5} +(18.3371 - 2.59808i) q^{7} -8.00000 q^{8} +(15.8371 - 27.4307i) q^{10} +(25.9186 - 44.8923i) q^{11} +38.8371 q^{13} +(22.8371 + 29.1627i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(13.6742 - 23.6845i) q^{17} +(-38.2557 - 66.2608i) q^{19} +63.3485 q^{20} +103.674 q^{22} +(73.6742 + 127.608i) q^{23} +(-62.9072 + 108.958i) q^{25} +(38.8371 + 67.2679i) q^{26} +(-27.6742 + 68.7178i) q^{28} -240.208 q^{29} +(148.337 - 256.927i) q^{31} +(16.0000 - 27.7128i) q^{32} +54.6970 q^{34} +(-180.837 - 230.927i) q^{35} +(80.7670 + 139.893i) q^{37} +(76.5114 - 132.522i) q^{38} +(63.3485 + 109.723i) q^{40} +102.977 q^{41} -328.557 q^{43} +(103.674 + 179.569i) q^{44} +(-147.348 + 255.215i) q^{46} +(33.9773 + 58.8504i) q^{47} +(329.500 - 95.2825i) q^{49} -251.629 q^{50} +(-77.6742 + 134.536i) q^{52} +(-33.2443 + 57.5808i) q^{53} -820.951 q^{55} +(-146.697 + 20.7846i) q^{56} +(-240.208 - 416.053i) q^{58} +(-230.964 + 400.041i) q^{59} +(-92.6742 - 160.516i) q^{61} +593.348 q^{62} +64.0000 q^{64} +(-307.534 - 532.665i) q^{65} +(-272.604 + 472.164i) q^{67} +(54.6970 + 94.7379i) q^{68} +(219.140 - 544.146i) q^{70} +130.742 q^{71} +(-90.6496 + 157.010i) q^{73} +(-161.534 + 279.785i) q^{74} +306.045 q^{76} +(358.638 - 890.533i) q^{77} +(204.848 + 354.808i) q^{79} +(-126.697 + 219.446i) q^{80} +(102.977 + 178.362i) q^{82} -347.928 q^{83} -433.121 q^{85} +(-328.557 - 569.077i) q^{86} +(-207.348 + 359.138i) q^{88} +(578.580 + 1002.13i) q^{89} +(712.161 - 100.902i) q^{91} -589.394 q^{92} +(-67.9546 + 117.701i) q^{94} +(-605.860 + 1049.38i) q^{95} +1618.30 q^{97} +(494.534 + 475.428i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 8q^{4} + 5q^{5} - 32q^{8} + O(q^{10}) \) \( 4q + 4q^{2} - 8q^{4} + 5q^{5} - 32q^{8} - 10q^{10} + 67q^{11} + 82q^{13} + 18q^{14} - 32q^{16} - 92q^{17} - 43q^{19} - 40q^{20} + 268q^{22} + 148q^{23} - 435q^{25} + 82q^{26} + 36q^{28} - 154q^{29} + 520q^{31} + 64q^{32} - 368q^{34} - 650q^{35} - 7q^{37} + 86q^{38} - 40q^{40} + 852q^{41} - 214q^{43} + 268q^{44} - 296q^{46} + 576q^{47} + 1318q^{49} - 1740q^{50} - 164q^{52} - 243q^{53} - 1010q^{55} - 154q^{58} - 7q^{59} - 224q^{61} + 2080q^{62} + 256q^{64} - 570q^{65} - 687q^{67} - 368q^{68} + 1390q^{70} - 944q^{71} + 921q^{73} + 14q^{74} + 344q^{76} + 371q^{77} + 526q^{79} + 80q^{80} + 852q^{82} + 442q^{83} - 5840q^{85} - 214q^{86} - 536q^{88} + 774q^{89} + 1345q^{91} - 1184q^{92} - 1152q^{94} - 1910q^{95} + 3906q^{97} + 1318q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −7.91856 13.7153i −0.708258 1.22674i −0.965503 0.260392i \(-0.916148\pi\)
0.257245 0.966346i \(-0.417185\pi\)
\(6\) 0 0
\(7\) 18.3371 2.59808i 0.990111 0.140283i
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 15.8371 27.4307i 0.500814 0.867435i
\(11\) 25.9186 44.8923i 0.710431 1.23050i −0.254265 0.967135i \(-0.581833\pi\)
0.964696 0.263368i \(-0.0848333\pi\)
\(12\) 0 0
\(13\) 38.8371 0.828575 0.414288 0.910146i \(-0.364031\pi\)
0.414288 + 0.910146i \(0.364031\pi\)
\(14\) 22.8371 + 29.1627i 0.435963 + 0.556719i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 13.6742 23.6845i 0.195088 0.337902i −0.751842 0.659344i \(-0.770834\pi\)
0.946929 + 0.321442i \(0.104168\pi\)
\(18\) 0 0
\(19\) −38.2557 66.2608i −0.461919 0.800067i 0.537138 0.843494i \(-0.319505\pi\)
−0.999057 + 0.0434278i \(0.986172\pi\)
\(20\) 63.3485 0.708258
\(21\) 0 0
\(22\) 103.674 1.00470
\(23\) 73.6742 + 127.608i 0.667919 + 1.15687i 0.978485 + 0.206318i \(0.0661482\pi\)
−0.310566 + 0.950552i \(0.600519\pi\)
\(24\) 0 0
\(25\) −62.9072 + 108.958i −0.503258 + 0.871668i
\(26\) 38.8371 + 67.2679i 0.292946 + 0.507397i
\(27\) 0 0
\(28\) −27.6742 + 68.7178i −0.186784 + 0.463802i
\(29\) −240.208 −1.53812 −0.769061 0.639175i \(-0.779276\pi\)
−0.769061 + 0.639175i \(0.779276\pi\)
\(30\) 0 0
\(31\) 148.337 256.927i 0.859424 1.48857i −0.0130559 0.999915i \(-0.504156\pi\)
0.872480 0.488651i \(-0.162511\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 54.6970 0.275896
\(35\) −180.837 230.927i −0.873344 1.11525i
\(36\) 0 0
\(37\) 80.7670 + 139.893i 0.358865 + 0.621573i 0.987772 0.155908i \(-0.0498304\pi\)
−0.628906 + 0.777481i \(0.716497\pi\)
\(38\) 76.5114 132.522i 0.326626 0.565733i
\(39\) 0 0
\(40\) 63.3485 + 109.723i 0.250407 + 0.433717i
\(41\) 102.977 0.392252 0.196126 0.980579i \(-0.437164\pi\)
0.196126 + 0.980579i \(0.437164\pi\)
\(42\) 0 0
\(43\) −328.557 −1.16522 −0.582610 0.812752i \(-0.697968\pi\)
−0.582610 + 0.812752i \(0.697968\pi\)
\(44\) 103.674 + 179.569i 0.355215 + 0.615251i
\(45\) 0 0
\(46\) −147.348 + 255.215i −0.472290 + 0.818031i
\(47\) 33.9773 + 58.8504i 0.105449 + 0.182643i 0.913921 0.405891i \(-0.133039\pi\)
−0.808473 + 0.588534i \(0.799705\pi\)
\(48\) 0 0
\(49\) 329.500 95.2825i 0.960641 0.277791i
\(50\) −251.629 −0.711714
\(51\) 0 0
\(52\) −77.6742 + 134.536i −0.207144 + 0.358784i
\(53\) −33.2443 + 57.5808i −0.0861596 + 0.149233i −0.905885 0.423524i \(-0.860793\pi\)
0.819725 + 0.572757i \(0.194126\pi\)
\(54\) 0 0
\(55\) −820.951 −2.01267
\(56\) −146.697 + 20.7846i −0.350057 + 0.0495975i
\(57\) 0 0
\(58\) −240.208 416.053i −0.543809 0.941904i
\(59\) −230.964 + 400.041i −0.509643 + 0.882728i 0.490294 + 0.871557i \(0.336889\pi\)
−0.999938 + 0.0111711i \(0.996444\pi\)
\(60\) 0 0
\(61\) −92.6742 160.516i −0.194520 0.336919i 0.752223 0.658909i \(-0.228982\pi\)
−0.946743 + 0.321990i \(0.895648\pi\)
\(62\) 593.348 1.21541
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −307.534 532.665i −0.586845 1.01644i
\(66\) 0 0
\(67\) −272.604 + 472.164i −0.497073 + 0.860956i −0.999994 0.00337637i \(-0.998925\pi\)
0.502921 + 0.864332i \(0.332259\pi\)
\(68\) 54.6970 + 94.7379i 0.0975438 + 0.168951i
\(69\) 0 0
\(70\) 219.140 544.146i 0.374175 0.929113i
\(71\) 130.742 0.218539 0.109270 0.994012i \(-0.465149\pi\)
0.109270 + 0.994012i \(0.465149\pi\)
\(72\) 0 0
\(73\) −90.6496 + 157.010i −0.145339 + 0.251734i −0.929499 0.368824i \(-0.879761\pi\)
0.784160 + 0.620558i \(0.213094\pi\)
\(74\) −161.534 + 279.785i −0.253756 + 0.439519i
\(75\) 0 0
\(76\) 306.045 0.461919
\(77\) 358.638 890.533i 0.530787 1.31800i
\(78\) 0 0
\(79\) 204.848 + 354.808i 0.291737 + 0.505304i 0.974221 0.225597i \(-0.0724333\pi\)
−0.682483 + 0.730901i \(0.739100\pi\)
\(80\) −126.697 + 219.446i −0.177064 + 0.306685i
\(81\) 0 0
\(82\) 102.977 + 178.362i 0.138682 + 0.240205i
\(83\) −347.928 −0.460121 −0.230061 0.973176i \(-0.573892\pi\)
−0.230061 + 0.973176i \(0.573892\pi\)
\(84\) 0 0
\(85\) −433.121 −0.552689
\(86\) −328.557 569.077i −0.411967 0.713548i
\(87\) 0 0
\(88\) −207.348 + 359.138i −0.251175 + 0.435048i
\(89\) 578.580 + 1002.13i 0.689093 + 1.19354i 0.972132 + 0.234436i \(0.0753243\pi\)
−0.283038 + 0.959109i \(0.591342\pi\)
\(90\) 0 0
\(91\) 712.161 100.902i 0.820382 0.116235i
\(92\) −589.394 −0.667919
\(93\) 0 0
\(94\) −67.9546 + 117.701i −0.0745636 + 0.129148i
\(95\) −605.860 + 1049.38i −0.654315 + 1.13331i
\(96\) 0 0
\(97\) 1618.30 1.69395 0.846976 0.531631i \(-0.178421\pi\)
0.846976 + 0.531631i \(0.178421\pi\)
\(98\) 494.534 + 475.428i 0.509750 + 0.490056i
\(99\) 0 0
\(100\) −251.629 435.834i −0.251629 0.435834i
\(101\) 359.371 622.449i 0.354047 0.613228i −0.632907 0.774228i \(-0.718139\pi\)
0.986954 + 0.161000i \(0.0514719\pi\)
\(102\) 0 0
\(103\) 805.790 + 1395.67i 0.770843 + 1.33514i 0.937102 + 0.349057i \(0.113498\pi\)
−0.166259 + 0.986082i \(0.553169\pi\)
\(104\) −310.697 −0.292946
\(105\) 0 0
\(106\) −132.977 −0.121848
\(107\) 467.335 + 809.448i 0.422234 + 0.731330i 0.996158 0.0875784i \(-0.0279128\pi\)
−0.573924 + 0.818909i \(0.694580\pi\)
\(108\) 0 0
\(109\) 598.509 1036.65i 0.525934 0.910944i −0.473610 0.880735i \(-0.657049\pi\)
0.999544 0.0302095i \(-0.00961746\pi\)
\(110\) −820.951 1421.93i −0.711587 1.23251i
\(111\) 0 0
\(112\) −182.697 233.302i −0.154136 0.196830i
\(113\) 2384.64 1.98521 0.992604 0.121400i \(-0.0387384\pi\)
0.992604 + 0.121400i \(0.0387384\pi\)
\(114\) 0 0
\(115\) 1166.79 2020.94i 0.946118 1.63872i
\(116\) 480.417 832.106i 0.384531 0.666027i
\(117\) 0 0
\(118\) −923.856 −0.720744
\(119\) 189.212 469.832i 0.145757 0.361928i
\(120\) 0 0
\(121\) −678.044 1174.41i −0.509424 0.882349i
\(122\) 185.348 321.033i 0.137546 0.238237i
\(123\) 0 0
\(124\) 593.348 + 1027.71i 0.429712 + 0.744283i
\(125\) 12.8977 0.00922883
\(126\) 0 0
\(127\) −2673.92 −1.86829 −0.934143 0.356898i \(-0.883834\pi\)
−0.934143 + 0.356898i \(0.883834\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 615.068 1065.33i 0.414962 0.718735i
\(131\) −19.4299 33.6536i −0.0129588 0.0224453i 0.859473 0.511181i \(-0.170792\pi\)
−0.872432 + 0.488735i \(0.837458\pi\)
\(132\) 0 0
\(133\) −873.650 1115.64i −0.569587 0.727356i
\(134\) −1090.42 −0.702968
\(135\) 0 0
\(136\) −109.394 + 189.476i −0.0689739 + 0.119466i
\(137\) −384.072 + 665.232i −0.239514 + 0.414851i −0.960575 0.278021i \(-0.910322\pi\)
0.721061 + 0.692872i \(0.243655\pi\)
\(138\) 0 0
\(139\) 1052.55 0.642274 0.321137 0.947033i \(-0.395935\pi\)
0.321137 + 0.947033i \(0.395935\pi\)
\(140\) 1161.63 164.584i 0.701254 0.0993564i
\(141\) 0 0
\(142\) 130.742 + 226.453i 0.0772652 + 0.133827i
\(143\) 1006.60 1743.49i 0.588646 1.01956i
\(144\) 0 0
\(145\) 1902.10 + 3294.54i 1.08939 + 1.88687i
\(146\) −362.598 −0.205540
\(147\) 0 0
\(148\) −646.136 −0.358865
\(149\) 180.489 + 312.615i 0.0992363 + 0.171882i 0.911369 0.411591i \(-0.135027\pi\)
−0.812132 + 0.583473i \(0.801693\pi\)
\(150\) 0 0
\(151\) −774.195 + 1340.95i −0.417239 + 0.722679i −0.995661 0.0930587i \(-0.970336\pi\)
0.578422 + 0.815738i \(0.303669\pi\)
\(152\) 306.045 + 530.086i 0.163313 + 0.282866i
\(153\) 0 0
\(154\) 1901.09 269.354i 0.994766 0.140942i
\(155\) −4698.47 −2.43477
\(156\) 0 0
\(157\) 483.534 837.506i 0.245798 0.425734i −0.716558 0.697528i \(-0.754283\pi\)
0.962356 + 0.271794i \(0.0876168\pi\)
\(158\) −409.697 + 709.616i −0.206289 + 0.357304i
\(159\) 0 0
\(160\) −506.788 −0.250407
\(161\) 1682.51 + 2148.54i 0.823604 + 1.05173i
\(162\) 0 0
\(163\) 663.250 + 1148.78i 0.318710 + 0.552022i 0.980219 0.197915i \(-0.0634170\pi\)
−0.661509 + 0.749937i \(0.730084\pi\)
\(164\) −205.955 + 356.724i −0.0980631 + 0.169850i
\(165\) 0 0
\(166\) −347.928 602.629i −0.162677 0.281766i
\(167\) −1416.70 −0.656451 −0.328225 0.944599i \(-0.606451\pi\)
−0.328225 + 0.944599i \(0.606451\pi\)
\(168\) 0 0
\(169\) −688.678 −0.313463
\(170\) −433.121 750.188i −0.195405 0.338452i
\(171\) 0 0
\(172\) 657.114 1138.15i 0.291305 0.504555i
\(173\) −518.299 897.721i −0.227778 0.394523i 0.729371 0.684118i \(-0.239813\pi\)
−0.957149 + 0.289595i \(0.906479\pi\)
\(174\) 0 0
\(175\) −870.454 + 2161.42i −0.376001 + 0.933647i
\(176\) −829.394 −0.355215
\(177\) 0 0
\(178\) −1157.16 + 2004.26i −0.487263 + 0.843964i
\(179\) −383.716 + 664.615i −0.160225 + 0.277518i −0.934949 0.354781i \(-0.884555\pi\)
0.774724 + 0.632299i \(0.217889\pi\)
\(180\) 0 0
\(181\) −3957.71 −1.62527 −0.812636 0.582772i \(-0.801968\pi\)
−0.812636 + 0.582772i \(0.801968\pi\)
\(182\) 886.928 + 1132.60i 0.361228 + 0.461284i
\(183\) 0 0
\(184\) −589.394 1020.86i −0.236145 0.409015i
\(185\) 1279.12 2215.50i 0.508338 0.880468i
\(186\) 0 0
\(187\) −708.833 1227.74i −0.277193 0.480112i
\(188\) −271.818 −0.105449
\(189\) 0 0
\(190\) −2423.44 −0.925341
\(191\) −902.648 1563.43i −0.341954 0.592282i 0.642841 0.765999i \(-0.277756\pi\)
−0.984796 + 0.173717i \(0.944422\pi\)
\(192\) 0 0
\(193\) −1685.42 + 2919.23i −0.628597 + 1.08876i 0.359237 + 0.933247i \(0.383037\pi\)
−0.987833 + 0.155515i \(0.950296\pi\)
\(194\) 1618.30 + 2802.98i 0.598903 + 1.03733i
\(195\) 0 0
\(196\) −328.932 + 1331.99i −0.119873 + 0.485418i
\(197\) 4612.31 1.66809 0.834044 0.551697i \(-0.186020\pi\)
0.834044 + 0.551697i \(0.186020\pi\)
\(198\) 0 0
\(199\) 1114.93 1931.12i 0.397163 0.687906i −0.596212 0.802827i \(-0.703328\pi\)
0.993375 + 0.114921i \(0.0366615\pi\)
\(200\) 503.258 871.668i 0.177928 0.308181i
\(201\) 0 0
\(202\) 1437.48 0.500698
\(203\) −4404.73 + 624.080i −1.52291 + 0.215772i
\(204\) 0 0
\(205\) −815.432 1412.37i −0.277816 0.481191i
\(206\) −1611.58 + 2791.34i −0.545068 + 0.944086i
\(207\) 0 0
\(208\) −310.697 538.143i −0.103572 0.179392i
\(209\) −3966.13 −1.31265
\(210\) 0 0
\(211\) 912.614 0.297758 0.148879 0.988855i \(-0.452434\pi\)
0.148879 + 0.988855i \(0.452434\pi\)
\(212\) −132.977 230.323i −0.0430798 0.0746164i
\(213\) 0 0
\(214\) −934.670 + 1618.90i −0.298564 + 0.517129i
\(215\) 2601.70 + 4506.27i 0.825276 + 1.42942i
\(216\) 0 0
\(217\) 2052.56 5096.70i 0.642105 1.59441i
\(218\) 2394.04 0.743783
\(219\) 0 0
\(220\) 1641.90 2843.86i 0.503168 0.871513i
\(221\) 531.068 919.837i 0.161645 0.279977i
\(222\) 0 0
\(223\) −4319.47 −1.29710 −0.648549 0.761173i \(-0.724624\pi\)
−0.648549 + 0.761173i \(0.724624\pi\)
\(224\) 221.394 549.742i 0.0660380 0.163979i
\(225\) 0 0
\(226\) 2384.64 + 4130.32i 0.701877 + 1.21569i
\(227\) 1030.64 1785.12i 0.301349 0.521951i −0.675093 0.737733i \(-0.735897\pi\)
0.976442 + 0.215782i \(0.0692299\pi\)
\(228\) 0 0
\(229\) 1737.32 + 3009.12i 0.501332 + 0.868333i 0.999999 + 0.00153905i \(0.000489896\pi\)
−0.498667 + 0.866794i \(0.666177\pi\)
\(230\) 4667.15 1.33801
\(231\) 0 0
\(232\) 1921.67 0.543809
\(233\) 388.049 + 672.121i 0.109107 + 0.188979i 0.915409 0.402525i \(-0.131868\pi\)
−0.806302 + 0.591505i \(0.798534\pi\)
\(234\) 0 0
\(235\) 538.102 932.020i 0.149370 0.258716i
\(236\) −923.856 1600.17i −0.254822 0.441364i
\(237\) 0 0
\(238\) 1002.98 142.107i 0.273167 0.0387035i
\(239\) −2006.80 −0.543133 −0.271567 0.962420i \(-0.587542\pi\)
−0.271567 + 0.962420i \(0.587542\pi\)
\(240\) 0 0
\(241\) −402.824 + 697.711i −0.107669 + 0.186488i −0.914825 0.403850i \(-0.867672\pi\)
0.807157 + 0.590337i \(0.201005\pi\)
\(242\) 1356.09 2348.81i 0.360217 0.623915i
\(243\) 0 0
\(244\) 741.394 0.194520
\(245\) −3916.00 3764.71i −1.02116 0.981707i
\(246\) 0 0
\(247\) −1485.74 2573.38i −0.382734 0.662915i
\(248\) −1186.70 + 2055.42i −0.303852 + 0.526287i
\(249\) 0 0
\(250\) 12.8977 + 22.3394i 0.00326289 + 0.00565148i
\(251\) −1421.78 −0.357539 −0.178769 0.983891i \(-0.557212\pi\)
−0.178769 + 0.983891i \(0.557212\pi\)
\(252\) 0 0
\(253\) 7638.12 1.89804
\(254\) −2673.92 4631.37i −0.660539 1.14409i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −732.909 1269.44i −0.177890 0.308114i 0.763268 0.646082i \(-0.223594\pi\)
−0.941157 + 0.337968i \(0.890260\pi\)
\(258\) 0 0
\(259\) 1844.49 + 2355.39i 0.442513 + 0.565084i
\(260\) 2460.27 0.586845
\(261\) 0 0
\(262\) 38.8598 67.3072i 0.00916324 0.0158712i
\(263\) 3495.69 6054.72i 0.819596 1.41958i −0.0863847 0.996262i \(-0.527531\pi\)
0.905980 0.423320i \(-0.139135\pi\)
\(264\) 0 0
\(265\) 1052.99 0.244093
\(266\) 1058.70 2628.85i 0.244033 0.605958i
\(267\) 0 0
\(268\) −1090.42 1888.66i −0.248537 0.430478i
\(269\) 404.479 700.578i 0.0916786 0.158792i −0.816539 0.577290i \(-0.804110\pi\)
0.908218 + 0.418498i \(0.137443\pi\)
\(270\) 0 0
\(271\) −3330.88 5769.26i −0.746630 1.29320i −0.949429 0.313981i \(-0.898337\pi\)
0.202799 0.979220i \(-0.434996\pi\)
\(272\) −437.576 −0.0975438
\(273\) 0 0
\(274\) −1536.29 −0.338725
\(275\) 3260.93 + 5648.09i 0.715059 + 1.23852i
\(276\) 0 0
\(277\) 3765.73 6522.44i 0.816827 1.41479i −0.0911823 0.995834i \(-0.529065\pi\)
0.908009 0.418951i \(-0.137602\pi\)
\(278\) 1052.55 + 1823.07i 0.227078 + 0.393311i
\(279\) 0 0
\(280\) 1446.70 + 1847.42i 0.308774 + 0.394301i
\(281\) −1690.19 −0.358819 −0.179410 0.983774i \(-0.557419\pi\)
−0.179410 + 0.983774i \(0.557419\pi\)
\(282\) 0 0
\(283\) −1589.12 + 2752.43i −0.333792 + 0.578145i −0.983252 0.182251i \(-0.941662\pi\)
0.649460 + 0.760396i \(0.274995\pi\)
\(284\) −261.485 + 452.905i −0.0546348 + 0.0946302i
\(285\) 0 0
\(286\) 4026.41 0.832470
\(287\) 1888.31 267.543i 0.388374 0.0550263i
\(288\) 0 0
\(289\) 2082.53 + 3607.05i 0.423882 + 0.734184i
\(290\) −3804.21 + 6589.08i −0.770313 + 1.33422i
\(291\) 0 0
\(292\) −362.598 628.039i −0.0726694 0.125867i
\(293\) 2176.53 0.433974 0.216987 0.976174i \(-0.430377\pi\)
0.216987 + 0.976174i \(0.430377\pi\)
\(294\) 0 0
\(295\) 7315.61 1.44383
\(296\) −646.136 1119.14i −0.126878 0.219759i
\(297\) 0 0
\(298\) −360.977 + 625.231i −0.0701706 + 0.121539i
\(299\) 2861.30 + 4955.91i 0.553421 + 0.958554i
\(300\) 0 0
\(301\) −6024.79 + 853.616i −1.15370 + 0.163460i
\(302\) −3096.78 −0.590065
\(303\) 0 0
\(304\) −612.091 + 1060.17i −0.115480 + 0.200017i
\(305\) −1467.69 + 2542.12i −0.275541 + 0.477250i
\(306\) 0 0
\(307\) 623.504 0.115913 0.0579564 0.998319i \(-0.481542\pi\)
0.0579564 + 0.998319i \(0.481542\pi\)
\(308\) 2367.62 + 3023.43i 0.438012 + 0.559337i
\(309\) 0 0
\(310\) −4698.47 8137.98i −0.860822 1.49099i
\(311\) 233.996 405.293i 0.0426647 0.0738973i −0.843905 0.536493i \(-0.819749\pi\)
0.886569 + 0.462596i \(0.153082\pi\)
\(312\) 0 0
\(313\) −1806.41 3128.79i −0.326211 0.565014i 0.655546 0.755156i \(-0.272439\pi\)
−0.981757 + 0.190141i \(0.939105\pi\)
\(314\) 1934.14 0.347610
\(315\) 0 0
\(316\) −1638.79 −0.291737
\(317\) 2265.87 + 3924.60i 0.401463 + 0.695355i 0.993903 0.110260i \(-0.0351684\pi\)
−0.592439 + 0.805615i \(0.701835\pi\)
\(318\) 0 0
\(319\) −6225.85 + 10783.5i −1.09273 + 1.89266i
\(320\) −506.788 877.782i −0.0885322 0.153342i
\(321\) 0 0
\(322\) −2038.88 + 5062.73i −0.352864 + 0.876196i
\(323\) −2092.47 −0.360459
\(324\) 0 0
\(325\) −2443.13 + 4231.63i −0.416987 + 0.722242i
\(326\) −1326.50 + 2297.57i −0.225362 + 0.390339i
\(327\) 0 0
\(328\) −823.818 −0.138682
\(329\) 775.943 + 990.871i 0.130028 + 0.166044i
\(330\) 0 0
\(331\) 618.528 + 1071.32i 0.102711 + 0.177901i 0.912801 0.408405i \(-0.133915\pi\)
−0.810090 + 0.586306i \(0.800582\pi\)
\(332\) 695.856 1205.26i 0.115030 0.199238i
\(333\) 0 0
\(334\) −1416.70 2453.79i −0.232090 0.401992i
\(335\) 8634.53 1.40822
\(336\) 0 0
\(337\) −1867.83 −0.301921 −0.150960 0.988540i \(-0.548237\pi\)
−0.150960 + 0.988540i \(0.548237\pi\)
\(338\) −688.678 1192.83i −0.110826 0.191956i
\(339\) 0 0
\(340\) 866.242 1500.38i 0.138172 0.239322i
\(341\) −7689.37 13318.4i −1.22112 2.11505i
\(342\) 0 0
\(343\) 5794.53 2603.27i 0.912173 0.409806i
\(344\) 2628.45 0.411967
\(345\) 0 0
\(346\) 1036.60 1795.44i 0.161063 0.278970i
\(347\) −31.6819 + 54.8746i −0.00490136 + 0.00848940i −0.868466 0.495749i \(-0.834893\pi\)
0.863564 + 0.504239i \(0.168227\pi\)
\(348\) 0 0
\(349\) 1223.79 0.187702 0.0938508 0.995586i \(-0.470082\pi\)
0.0938508 + 0.995586i \(0.470082\pi\)
\(350\) −4614.15 + 653.751i −0.704676 + 0.0998413i
\(351\) 0 0
\(352\) −829.394 1436.55i −0.125588 0.217524i
\(353\) −2257.81 + 3910.64i −0.340428 + 0.589638i −0.984512 0.175316i \(-0.943905\pi\)
0.644085 + 0.764954i \(0.277238\pi\)
\(354\) 0 0
\(355\) −1035.29 1793.18i −0.154782 0.268090i
\(356\) −4628.64 −0.689093
\(357\) 0 0
\(358\) −1534.86 −0.226592
\(359\) 1114.25 + 1929.93i 0.163810 + 0.283727i 0.936232 0.351383i \(-0.114288\pi\)
−0.772422 + 0.635109i \(0.780955\pi\)
\(360\) 0 0
\(361\) 502.506 870.365i 0.0732622 0.126894i
\(362\) −3957.71 6854.95i −0.574620 0.995271i
\(363\) 0 0
\(364\) −1074.79 + 2668.80i −0.154764 + 0.384295i
\(365\) 2871.26 0.411749
\(366\) 0 0
\(367\) 718.670 1244.77i 0.102219 0.177048i −0.810380 0.585905i \(-0.800739\pi\)
0.912598 + 0.408857i \(0.134072\pi\)
\(368\) 1178.79 2041.72i 0.166980 0.289217i
\(369\) 0 0
\(370\) 5116.47 0.718899
\(371\) −460.006 + 1142.24i −0.0643728 + 0.159844i
\(372\) 0 0
\(373\) 6118.71 + 10597.9i 0.849370 + 1.47115i 0.881771 + 0.471677i \(0.156351\pi\)
−0.0324014 + 0.999475i \(0.510315\pi\)
\(374\) 1417.67 2455.47i 0.196005 0.339490i
\(375\) 0 0
\(376\) −271.818 470.803i −0.0372818 0.0645740i
\(377\) −9329.00 −1.27445
\(378\) 0 0
\(379\) −10647.0 −1.44301 −0.721503 0.692411i \(-0.756549\pi\)
−0.721503 + 0.692411i \(0.756549\pi\)
\(380\) −2423.44 4197.52i −0.327157 0.566653i
\(381\) 0 0
\(382\) 1805.30 3126.86i 0.241798 0.418807i
\(383\) −3357.41 5815.20i −0.447925 0.775829i 0.550326 0.834950i \(-0.314504\pi\)
−0.998251 + 0.0591208i \(0.981170\pi\)
\(384\) 0 0
\(385\) −15053.9 + 2132.89i −1.99277 + 0.282344i
\(386\) −6741.68 −0.888970
\(387\) 0 0
\(388\) −3236.60 + 5605.95i −0.423488 + 0.733503i
\(389\) −5326.54 + 9225.83i −0.694258 + 1.20249i 0.276173 + 0.961108i \(0.410934\pi\)
−0.970430 + 0.241381i \(0.922400\pi\)
\(390\) 0 0
\(391\) 4029.76 0.521211
\(392\) −2636.00 + 762.260i −0.339638 + 0.0982141i
\(393\) 0 0
\(394\) 4612.31 + 7988.76i 0.589758 + 1.02149i
\(395\) 3244.21 5619.14i 0.413250 0.715771i
\(396\) 0 0
\(397\) −1610.52 2789.50i −0.203601 0.352648i 0.746085 0.665851i \(-0.231931\pi\)
−0.949686 + 0.313203i \(0.898598\pi\)
\(398\) 4459.73 0.561673
\(399\) 0 0
\(400\) 2013.03 0.251629
\(401\) 6242.50 + 10812.3i 0.777395 + 1.34649i 0.933438 + 0.358738i \(0.116793\pi\)
−0.156043 + 0.987750i \(0.549874\pi\)
\(402\) 0 0
\(403\) 5760.99 9978.32i 0.712097 1.23339i
\(404\) 1437.48 + 2489.80i 0.177024 + 0.306614i
\(405\) 0 0
\(406\) −5485.67 7005.14i −0.670564 0.856303i
\(407\) 8373.46 1.01980
\(408\) 0 0
\(409\) −3518.69 + 6094.56i −0.425399 + 0.736813i −0.996458 0.0840967i \(-0.973200\pi\)
0.571059 + 0.820909i \(0.306533\pi\)
\(410\) 1630.86 2824.74i 0.196445 0.340253i
\(411\) 0 0
\(412\) −6446.32 −0.770843
\(413\) −3195.88 + 7935.67i −0.380772 + 0.945493i
\(414\) 0 0
\(415\) 2755.09 + 4771.95i 0.325884 + 0.564448i
\(416\) 621.394 1076.29i 0.0732364 0.126849i
\(417\) 0 0
\(418\) −3966.13 6869.54i −0.464090 0.803828i
\(419\) 1549.66 0.180682 0.0903410 0.995911i \(-0.471204\pi\)
0.0903410 + 0.995911i \(0.471204\pi\)
\(420\) 0 0
\(421\) 5531.63 0.640369 0.320184 0.947355i \(-0.396255\pi\)
0.320184 + 0.947355i \(0.396255\pi\)
\(422\) 912.614 + 1580.69i 0.105273 + 0.182339i
\(423\) 0 0
\(424\) 265.955 460.647i 0.0304620 0.0527618i
\(425\) 1720.42 + 2979.85i 0.196359 + 0.340103i
\(426\) 0 0
\(427\) −2116.41 2702.64i −0.239860 0.306299i
\(428\) −3738.68 −0.422234
\(429\) 0 0
\(430\) −5203.39 + 9012.54i −0.583558 + 1.01075i
\(431\) −1014.97 + 1757.97i −0.113432 + 0.196470i −0.917152 0.398538i \(-0.869518\pi\)
0.803720 + 0.595008i \(0.202851\pi\)
\(432\) 0 0
\(433\) −327.739 −0.0363744 −0.0181872 0.999835i \(-0.505789\pi\)
−0.0181872 + 0.999835i \(0.505789\pi\)
\(434\) 10880.3 1541.56i 1.20339 0.170501i
\(435\) 0 0
\(436\) 2394.04 + 4146.60i 0.262967 + 0.455472i
\(437\) 5636.92 9763.43i 0.617049 1.06876i
\(438\) 0 0
\(439\) −3954.34 6849.12i −0.429910 0.744625i 0.566955 0.823749i \(-0.308121\pi\)
−0.996865 + 0.0791234i \(0.974788\pi\)
\(440\) 6567.61 0.711587
\(441\) 0 0
\(442\) 2124.27 0.228600
\(443\) −1460.41 2529.51i −0.156628 0.271288i 0.777023 0.629473i \(-0.216729\pi\)
−0.933651 + 0.358185i \(0.883396\pi\)
\(444\) 0 0
\(445\) 9163.03 15870.8i 0.976111 1.69067i
\(446\) −4319.47 7481.53i −0.458593 0.794307i
\(447\) 0 0
\(448\) 1173.58 166.277i 0.123764 0.0175354i
\(449\) 10240.2 1.07631 0.538156 0.842845i \(-0.319121\pi\)
0.538156 + 0.842845i \(0.319121\pi\)
\(450\) 0 0
\(451\) 2669.02 4622.88i 0.278668 0.482668i
\(452\) −4769.29 + 8260.65i −0.496302 + 0.859620i
\(453\) 0 0
\(454\) 4122.57 0.426171
\(455\) −7023.19 8968.54i −0.723632 0.924069i
\(456\) 0 0
\(457\) −2946.31 5103.17i −0.301582 0.522355i 0.674913 0.737897i \(-0.264181\pi\)
−0.976494 + 0.215543i \(0.930848\pi\)
\(458\) −3474.63 + 6018.24i −0.354495 + 0.614004i
\(459\) 0 0
\(460\) 4667.15 + 8083.74i 0.473059 + 0.819362i
\(461\) 12643.4 1.27735 0.638677 0.769475i \(-0.279482\pi\)
0.638677 + 0.769475i \(0.279482\pi\)
\(462\) 0 0
\(463\) 15093.2 1.51499 0.757494 0.652842i \(-0.226423\pi\)
0.757494 + 0.652842i \(0.226423\pi\)
\(464\) 1921.67 + 3328.42i 0.192265 + 0.333013i
\(465\) 0 0
\(466\) −776.099 + 1344.24i −0.0771504 + 0.133628i
\(467\) −1410.12 2442.39i −0.139727 0.242014i 0.787666 0.616102i \(-0.211289\pi\)
−0.927393 + 0.374088i \(0.877956\pi\)
\(468\) 0 0
\(469\) −3772.06 + 9366.38i −0.371380 + 0.922173i
\(470\) 2152.41 0.211241
\(471\) 0 0
\(472\) 1847.71 3200.33i 0.180186 0.312091i
\(473\) −8515.72 + 14749.7i −0.827808 + 1.43381i
\(474\) 0 0
\(475\) 9626.23 0.929856
\(476\) 1249.12 + 1595.11i 0.120280 + 0.153596i
\(477\) 0 0
\(478\) −2006.80 3475.87i −0.192027 0.332600i
\(479\) −8224.25 + 14244.8i −0.784500 + 1.35879i 0.144798 + 0.989461i \(0.453747\pi\)
−0.929297 + 0.369332i \(0.879586\pi\)
\(480\) 0 0
\(481\) 3136.76 + 5433.03i 0.297347 + 0.515020i
\(482\) −1611.30 −0.152267
\(483\) 0 0
\(484\) 5424.35 0.509424
\(485\) −12814.6 22195.5i −1.19975 2.07804i
\(486\) 0 0
\(487\) −3165.53 + 5482.87i −0.294546 + 0.510169i −0.974879 0.222734i \(-0.928502\pi\)
0.680333 + 0.732903i \(0.261835\pi\)
\(488\) 741.394 + 1284.13i 0.0687732 + 0.119119i
\(489\) 0 0
\(490\) 2604.67 10547.4i 0.240136 0.972416i
\(491\) 9286.90 0.853588 0.426794 0.904349i \(-0.359643\pi\)
0.426794 + 0.904349i \(0.359643\pi\)
\(492\) 0 0
\(493\) −3284.67 + 5689.21i −0.300069 + 0.519735i
\(494\) 2971.48 5146.76i 0.270634 0.468752i
\(495\) 0 0
\(496\) −4746.79 −0.429712
\(497\) 2397.44 339.679i 0.216378 0.0306573i
\(498\) 0 0
\(499\) 121.725 + 210.835i 0.0109202 + 0.0189143i 0.871434 0.490513i \(-0.163191\pi\)
−0.860514 + 0.509427i \(0.829857\pi\)
\(500\) −25.7954 + 44.6789i −0.00230721 + 0.00399620i
\(501\) 0 0
\(502\) −1421.78 2462.60i −0.126409 0.218947i
\(503\) −8499.30 −0.753409 −0.376705 0.926333i \(-0.622943\pi\)
−0.376705 + 0.926333i \(0.622943\pi\)
\(504\) 0 0
\(505\) −11382.8 −1.00303
\(506\) 7638.12 + 13229.6i 0.671059 + 1.16231i
\(507\) 0 0
\(508\) 5347.85 9262.75i 0.467072 0.808992i
\(509\) −3841.55 6653.76i −0.334526 0.579416i 0.648868 0.760901i \(-0.275243\pi\)
−0.983394 + 0.181485i \(0.941910\pi\)
\(510\) 0 0
\(511\) −1254.33 + 3114.62i −0.108588 + 0.269634i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 1465.82 2538.87i 0.125787 0.217869i
\(515\) 12761.4 22103.4i 1.09191 1.89124i
\(516\) 0 0
\(517\) 3522.57 0.299656
\(518\) −2235.17 + 5550.13i −0.189590 + 0.470770i
\(519\) 0 0
\(520\) 2460.27 + 4261.32i 0.207481 + 0.359368i
\(521\) −10765.3 + 18646.1i −0.905253 + 1.56794i −0.0846750 + 0.996409i \(0.526985\pi\)
−0.820578 + 0.571535i \(0.806348\pi\)
\(522\) 0 0
\(523\) 8423.53 + 14590.0i 0.704274 + 1.21984i 0.966953 + 0.254955i \(0.0820606\pi\)
−0.262679 + 0.964883i \(0.584606\pi\)
\(524\) 155.439 0.0129588
\(525\) 0 0
\(526\) 13982.8 1.15908
\(527\) −4056.80 7026.58i −0.335326 0.580802i
\(528\) 0 0
\(529\) −4772.29 + 8265.84i −0.392232 + 0.679366i
\(530\) 1052.99 + 1823.83i 0.0862998 + 0.149476i
\(531\) 0 0
\(532\) 5611.99 795.129i 0.457351 0.0647993i
\(533\) 3999.34 0.325011
\(534\) 0 0
\(535\) 7401.24 12819.3i 0.598100 1.03594i
\(536\) 2180.83 3777.31i 0.175742 0.304394i
\(537\) 0 0
\(538\) 1617.92 0.129653
\(539\) 4262.72 17261.6i 0.340646 1.37942i
\(540\) 0 0
\(541\) −8720.02 15103.5i −0.692981 1.20028i −0.970856 0.239662i \(-0.922963\pi\)
0.277875 0.960617i \(-0.410370\pi\)
\(542\) 6661.77 11538.5i 0.527947 0.914432i
\(543\) 0 0
\(544\) −437.576 757.903i −0.0344870 0.0597332i
\(545\) −18957.3 −1.48999
\(546\) 0 0
\(547\) 11520.7 0.900530 0.450265 0.892895i \(-0.351329\pi\)
0.450265 + 0.892895i \(0.351329\pi\)
\(548\) −1536.29 2660.93i −0.119757 0.207426i
\(549\) 0 0
\(550\) −6521.86 + 11296.2i −0.505623 + 0.875765i
\(551\) 9189.33 + 15916.4i 0.710488 + 1.23060i
\(552\) 0 0
\(553\) 4678.15 + 5973.94i 0.359738 + 0.459382i
\(554\) 15062.9 1.15517
\(555\) 0 0
\(556\) −2105.10 + 3646.14i −0.160568 + 0.278113i
\(557\) 5746.51 9953.25i 0.437141 0.757151i −0.560327 0.828272i \(-0.689324\pi\)
0.997468 + 0.0711212i \(0.0226577\pi\)
\(558\) 0 0
\(559\) −12760.2 −0.965472
\(560\) −1753.12 + 4353.17i −0.132291 + 0.328491i
\(561\) 0 0
\(562\) −1690.19 2927.49i −0.126862 0.219731i
\(563\) 9055.65 15684.8i 0.677886 1.17413i −0.297730 0.954650i \(-0.596230\pi\)
0.975616 0.219483i \(-0.0704372\pi\)
\(564\) 0 0
\(565\) −18882.9 32706.2i −1.40604 2.43533i
\(566\) −6356.46 −0.472053
\(567\) 0 0
\(568\) −1045.94 −0.0772652
\(569\) 2208.81 + 3825.77i 0.162738 + 0.281871i 0.935850 0.352399i \(-0.114634\pi\)
−0.773112 + 0.634270i \(0.781301\pi\)
\(570\) 0 0
\(571\) −6609.87 + 11448.6i −0.484439 + 0.839073i −0.999840 0.0178762i \(-0.994310\pi\)
0.515401 + 0.856949i \(0.327643\pi\)
\(572\) 4026.41 + 6973.95i 0.294323 + 0.509782i
\(573\) 0 0
\(574\) 2351.70 + 3003.10i 0.171007 + 0.218375i
\(575\) −18538.6 −1.34454
\(576\) 0 0
\(577\) 8748.20 15152.3i 0.631182 1.09324i −0.356128 0.934437i \(-0.615903\pi\)
0.987310 0.158803i \(-0.0507634\pi\)
\(578\) −4165.06 + 7214.10i −0.299730 + 0.519147i
\(579\) 0 0
\(580\) −15216.8 −1.08939
\(581\) −6380.00 + 903.944i −0.455571 + 0.0645472i
\(582\) 0 0
\(583\) 1723.29 + 2984.83i 0.122421 + 0.212039i
\(584\) 725.197 1256.08i 0.0513850 0.0890015i
\(585\) 0 0
\(586\) 2176.53 + 3769.87i 0.153433 + 0.265754i
\(587\) 4280.53 0.300982 0.150491 0.988611i \(-0.451915\pi\)
0.150491 + 0.988611i \(0.451915\pi\)
\(588\) 0 0
\(589\) −22699.0 −1.58794
\(590\) 7315.61 + 12671.0i 0.510473 + 0.884165i
\(591\) 0 0
\(592\) 1292.27 2238.28i 0.0897164 0.155393i
\(593\) −795.466 1377.79i −0.0550858 0.0954114i 0.837168 0.546946i \(-0.184210\pi\)
−0.892253 + 0.451535i \(0.850877\pi\)
\(594\) 0 0
\(595\) −7942.20 + 1125.28i −0.547224 + 0.0775329i
\(596\) −1443.91 −0.0992363
\(597\) 0 0
\(598\) −5722.59 + 9911.82i −0.391328 + 0.677800i
\(599\) −6961.42 + 12057.5i −0.474851 + 0.822467i −0.999585 0.0287997i \(-0.990831\pi\)
0.524734 + 0.851266i \(0.324165\pi\)
\(600\) 0 0
\(601\) 12559.7 0.852446 0.426223 0.904618i \(-0.359844\pi\)
0.426223 + 0.904618i \(0.359844\pi\)
\(602\) −7503.29 9581.62i −0.507992 0.648700i
\(603\) 0 0
\(604\) −3096.78 5363.78i −0.208620 0.361340i
\(605\) −10738.3 + 18599.2i −0.721607 + 1.24986i
\(606\) 0 0
\(607\) −3839.19 6649.66i −0.256718 0.444648i 0.708643 0.705567i \(-0.249308\pi\)
−0.965361 + 0.260919i \(0.915974\pi\)
\(608\) −2448.36 −0.163313
\(609\) 0 0
\(610\) −5870.77 −0.389673
\(611\) 1319.58 + 2285.58i 0.0873723 + 0.151333i
\(612\) 0 0
\(613\) −3079.19 + 5333.31i −0.202883 + 0.351403i −0.949456 0.313900i \(-0.898364\pi\)
0.746573 + 0.665303i \(0.231698\pi\)
\(614\) 623.504 + 1079.94i 0.0409814 + 0.0709818i
\(615\) 0 0
\(616\) −2869.11 + 7124.27i −0.187662 + 0.465982i
\(617\) −8813.12 −0.575045 −0.287523 0.957774i \(-0.592832\pi\)
−0.287523 + 0.957774i \(0.592832\pi\)
\(618\) 0 0
\(619\) −11595.0 + 20083.1i −0.752894 + 1.30405i 0.193521 + 0.981096i \(0.438009\pi\)
−0.946415 + 0.322954i \(0.895324\pi\)
\(620\) 9396.93 16276.0i 0.608693 1.05429i
\(621\) 0 0
\(622\) 935.985 0.0603369
\(623\) 13213.1 + 16873.0i 0.849713 + 1.08507i
\(624\) 0 0
\(625\) 7761.27 + 13442.9i 0.496721 + 0.860346i
\(626\) 3612.81 6257.57i 0.230666 0.399525i
\(627\) 0 0
\(628\) 1934.14 + 3350.02i 0.122899 + 0.212867i
\(629\) 4417.71 0.280041
\(630\) 0 0
\(631\) 7936.94 0.500736 0.250368 0.968151i \(-0.419448\pi\)
0.250368 + 0.968151i \(0.419448\pi\)
\(632\) −1638.79 2838.46i −0.103145 0.178652i
\(633\) 0 0
\(634\) −4531.74 + 7849.20i −0.283877 + 0.491690i
\(635\) 21173.6 + 36673.8i 1.32323 + 2.29190i
\(636\) 0 0
\(637\) 12796.8 3700.50i 0.795964 0.230171i
\(638\) −24903.4 −1.54535
\(639\) 0 0
\(640\) 1013.58 1755.56i 0.0626017 0.108429i
\(641\) 16057.3 27812.1i 0.989432 1.71375i 0.369146 0.929371i \(-0.379650\pi\)
0.620286 0.784376i \(-0.287016\pi\)
\(642\) 0 0
\(643\) −24786.7 −1.52021 −0.760104 0.649802i \(-0.774852\pi\)
−0.760104 + 0.649802i \(0.774852\pi\)
\(644\) −10807.8 + 1531.29i −0.661314 + 0.0936977i
\(645\) 0 0
\(646\) −2092.47 3624.26i −0.127441 0.220735i
\(647\) 3772.80 6534.67i 0.229249 0.397070i −0.728337 0.685219i \(-0.759706\pi\)
0.957586 + 0.288149i \(0.0930398\pi\)
\(648\) 0 0
\(649\) 11972.5 + 20737.0i 0.724133 + 1.25423i
\(650\) −9772.54 −0.589708
\(651\) 0 0
\(652\) −5306.00 −0.318710
\(653\) −2444.49 4233.99i −0.146494 0.253735i 0.783435 0.621473i \(-0.213466\pi\)
−0.929929 + 0.367738i \(0.880132\pi\)
\(654\) 0 0
\(655\) −307.714 + 532.976i −0.0183563 + 0.0317941i
\(656\) −823.818 1426.89i −0.0490316 0.0849251i
\(657\) 0 0
\(658\) −940.295 + 2334.84i −0.0557090 + 0.138331i
\(659\) −25895.9 −1.53075 −0.765374 0.643586i \(-0.777446\pi\)
−0.765374 + 0.643586i \(0.777446\pi\)
\(660\) 0 0
\(661\) −4091.68 + 7087.00i −0.240769 + 0.417023i −0.960933 0.276780i \(-0.910733\pi\)
0.720165 + 0.693803i \(0.244066\pi\)
\(662\) −1237.06 + 2142.65i −0.0726278 + 0.125795i
\(663\) 0 0
\(664\) 2783.42 0.162677
\(665\) −8383.36 + 20816.7i −0.488861 + 1.21389i
\(666\) 0 0
\(667\) −17697.2 30652.4i −1.02734 1.77941i
\(668\) 2833.39 4907.58i 0.164113 0.284252i
\(669\) 0 0
\(670\) 8634.53 + 14955.4i 0.497882 + 0.862357i
\(671\) −9607.93 −0.552772
\(672\) 0 0
\(673\) −4635.02 −0.265478 −0.132739 0.991151i \(-0.542377\pi\)
−0.132739 + 0.991151i \(0.542377\pi\)
\(674\) −1867.83 3235.18i −0.106745 0.184888i
\(675\) 0 0
\(676\) 1377.36 2385.65i 0.0783657 0.135733i
\(677\) −12192.9 21118.7i −0.692187 1.19890i −0.971120 0.238593i \(-0.923314\pi\)
0.278932 0.960311i \(-0.410020\pi\)
\(678\) 0 0
\(679\) 29674.9 4204.46i 1.67720 0.237633i
\(680\) 3464.97 0.195405
\(681\) 0 0
\(682\) 15378.7 26636.8i 0.863464 1.49556i
\(683\) −9196.71 + 15929.2i −0.515230 + 0.892405i 0.484613 + 0.874728i \(0.338960\pi\)
−0.999844 + 0.0176767i \(0.994373\pi\)
\(684\) 0 0
\(685\) 12165.2 0.678552
\(686\) 10303.5 + 7433.15i 0.573456 + 0.413701i
\(687\) 0 0
\(688\) 2628.45 + 4552.62i 0.145652 + 0.252277i
\(689\) −1291.11 + 2236.27i −0.0713897 + 0.123651i
\(690\) 0 0
\(691\) 7449.44 + 12902.8i 0.410116 + 0.710341i 0.994902 0.100846i \(-0.0321550\pi\)
−0.584786 + 0.811187i \(0.698822\pi\)
\(692\) 4146.39 0.227778
\(693\) 0 0
\(694\) −126.727 −0.00693157
\(695\) −8334.67 14436.1i −0.454895 0.787902i
\(696\) 0 0
\(697\) 1408.14 2438.96i 0.0765236 0.132543i
\(698\) 1223.79 + 2119.66i 0.0663625 + 0.114943i
\(699\) 0 0
\(700\) −5746.48 7338.19i −0.310281 0.396225i
\(701\) 5725.70 0.308497 0.154249 0.988032i \(-0.450704\pi\)
0.154249 + 0.988032i \(0.450704\pi\)
\(702\) 0 0
\(703\) 6179.60 10703.4i 0.331533 0.574232i
\(704\) 1658.79 2873.10i 0.0888039 0.153813i
\(705\) 0 0
\(706\) −9031.23 −0.481437
\(707\) 4972.66 12347.6i 0.264521 0.656831i
\(708\) 0 0
\(709\) 11728.4 + 20314.2i 0.621255 + 1.07604i 0.989252 + 0.146218i \(0.0467101\pi\)
−0.367998 + 0.929827i \(0.619957\pi\)
\(710\) 2070.58 3586.36i 0.109447 0.189568i
\(711\) 0 0
\(712\) −4628.64 8017.03i −0.243631 0.421982i
\(713\) 43714.5 2.29610
\(714\) 0 0
\(715\) −31883.4 −1.66765
\(716\) −1534.86 2658.46i −0.0801125 0.138759i
\(717\) 0 0
\(718\) −2228.49 + 3859.86i −0.115831 + 0.200625i
\(719\) −4229.50 7325.71i −0.219379 0.379976i 0.735239 0.677808i \(-0.237070\pi\)
−0.954618 + 0.297832i \(0.903737\pi\)
\(720\) 0 0
\(721\) 18401.9 + 23499.0i 0.950518 + 1.21380i
\(722\) 2010.02 0.103608
\(723\) 0 0
\(724\) 7915.42 13709.9i 0.406318 0.703763i
\(725\) 15110.8 26172.7i 0.774072 1.34073i
\(726\) 0 0
\(727\) −11822.2 −0.603111 −0.301555 0.953449i \(-0.597506\pi\)
−0.301555 + 0.953449i \(0.597506\pi\)
\(728\) −5697.29 + 807.214i −0.290049 + 0.0410953i
\(729\) 0 0
\(730\) 2871.26 + 4973.16i 0.145575 + 0.252144i
\(731\) −4492.77 + 7781.70i −0.227320 + 0.393730i
\(732\) 0 0
\(733\) −2514.48 4355.20i −0.126704 0.219458i 0.795694 0.605699i \(-0.207107\pi\)
−0.922398 + 0.386241i \(0.873773\pi\)
\(734\) 2874.68 0.144559
\(735\) 0 0
\(736\) 4715.15 0.236145
\(737\) 14131.0 + 24475.6i 0.706272 + 1.22330i
\(738\) 0 0
\(739\) 8871.95 15366.7i 0.441624 0.764914i −0.556187 0.831057i \(-0.687736\pi\)
0.997810 + 0.0661431i \(0.0210694\pi\)
\(740\) 5116.47 + 8861.99i 0.254169 + 0.440234i
\(741\) 0 0
\(742\) −2438.42 + 345.485i −0.120643 + 0.0170932i
\(743\) 13202.3 0.651877 0.325938 0.945391i \(-0.394320\pi\)
0.325938 + 0.945391i \(0.394320\pi\)
\(744\) 0 0
\(745\) 2858.42 4950.93i 0.140570 0.243474i
\(746\) −12237.4 + 21195.8i −0.600595 + 1.04026i
\(747\) 0 0
\(748\) 5670.67 0.277193
\(749\) 10672.6 + 13628.8i 0.520652 + 0.664866i
\(750\) 0 0
\(751\) −7800.49 13510.8i −0.379020 0.656482i 0.611900 0.790935i \(-0.290406\pi\)
−0.990920 + 0.134453i \(0.957072\pi\)
\(752\) 543.636 941.606i 0.0263622 0.0456607i
\(753\) 0 0
\(754\) −9329.00 16158.3i −0.450586 0.780439i
\(755\) 24522.0 1.18205
\(756\) 0 0
\(757\) 2948.08 0.141545 0.0707725 0.997492i \(-0.477454\pi\)
0.0707725 + 0.997492i \(0.477454\pi\)
\(758\) −10647.0 18441.1i −0.510180 0.883657i
\(759\) 0 0
\(760\) 4846.88 8395.04i 0.231335 0.400684i
\(761\) 848.515 + 1469.67i 0.0404187 + 0.0700073i 0.885527 0.464588i \(-0.153797\pi\)
−0.845108 + 0.534595i \(0.820464\pi\)
\(762\) 0 0
\(763\) 8281.65 20564.1i 0.392943 0.975716i
\(764\) 7221.18 0.341954
\(765\) 0 0
\(766\) 6714.81 11630.4i 0.316731 0.548594i
\(767\) −8969.98 + 15536.5i −0.422278 + 0.731407i
\(768\) 0 0
\(769\) −96.7799 −0.00453833 −0.00226916 0.999997i \(-0.500722\pi\)
−0.00226916 + 0.999997i \(0.500722\pi\)
\(770\) −18748.2 23941.2i −0.877450 1.12049i
\(771\) 0 0
\(772\) −6741.68 11676.9i −0.314298 0.544381i
\(773\) 18163.4 31459.9i 0.845138 1.46382i −0.0403629 0.999185i \(-0.512851\pi\)
0.885501 0.464637i \(-0.153815\pi\)
\(774\) 0 0
\(775\) 18662.9 + 32325.2i 0.865023 + 1.49826i
\(776\) −12946.4 −0.598903
\(777\) 0 0
\(778\) −21306.2 −0.981828
\(779\) −3939.47 6823.35i −0.181189 0.313828i
\(780\) 0 0
\(781\) 3388.66 5869.32i 0.155257 0.268913i
\(782\) 4029.76 + 6979.74i 0.184276 + 0.319175i
\(783\) 0 0
\(784\) −3956.27 3803.43i −0.180224 0.173261i
\(785\) −15315.6 −0.696352
\(786\) 0 0
\(787\) −3548.23 + 6145.72i