Properties

Label 126.4.g.g.37.1
Level $126$
Weight $4$
Character 126.37
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 37.1
Root \(-8.91856 + 15.4474i\) of defining polynomial
Character \(\chi\) \(=\) 126.37
Dual form 126.4.g.g.109.1

$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 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 0.257245 + 0.966346i \(0.417185\pi\)
−0.965503 + 0.260392i \(0.916148\pi\)
\(6\) 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 0.964696 + 0.263368i \(0.0848333\pi\)
−0.254265 + 0.967135i \(0.581833\pi\)
\(12\) 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 0.946929 0.321442i \(-0.104168\pi\)
−0.751842 + 0.659344i \(0.770834\pi\)
\(18\) 0 0
\(19\) −38.2557 + 66.2608i −0.461919 + 0.800067i −0.999057 0.0434278i \(-0.986172\pi\)
0.537138 + 0.843494i \(0.319505\pi\)
\(20\) 63.3485 0.708258
\(21\) 0 0
\(22\) 103.674 1.00470
\(23\) 73.6742 127.608i 0.667919 1.15687i −0.310566 0.950552i \(-0.600519\pi\)
0.978485 0.206318i \(-0.0661482\pi\)
\(24\) 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 0.872480 + 0.488651i \(0.162511\pi\)
−0.0130559 + 0.999915i \(0.504156\pi\)
\(32\) 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 −0.628906 0.777481i \(-0.716497\pi\)
0.987772 + 0.155908i \(0.0498304\pi\)
\(38\) 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 −0.808473 0.588534i \(-0.799705\pi\)
0.913921 + 0.405891i \(0.133039\pi\)
\(48\) 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 0.819725 0.572757i \(-0.194126\pi\)
−0.905885 + 0.423524i \(0.860793\pi\)
\(54\) 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 −0.999938 0.0111711i \(-0.996444\pi\)
0.490294 0.871557i \(-0.336889\pi\)
\(60\) 0 0
\(61\) −92.6742 + 160.516i −0.194520 + 0.336919i −0.946743 0.321990i \(-0.895648\pi\)
0.752223 + 0.658909i \(0.228982\pi\)
\(62\) 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 0.502921 0.864332i \(-0.332259\pi\)
−0.999994 + 0.00337637i \(0.998925\pi\)
\(68\) 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 0.784160 0.620558i \(-0.213094\pi\)
−0.929499 + 0.368824i \(0.879761\pi\)
\(74\) −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 −0.682483 0.730901i \(-0.739100\pi\)
0.974221 + 0.225597i \(0.0724333\pi\)
\(80\) −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 −0.283038 0.959109i \(-0.591342\pi\)
0.972132 0.234436i \(-0.0753243\pi\)
\(90\) 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 0.986954 0.161000i \(-0.0514719\pi\)
−0.632907 + 0.774228i \(0.718139\pi\)
\(102\) 0 0
\(103\) 805.790 1395.67i 0.770843 1.33514i −0.166259 0.986082i \(-0.553169\pi\)
0.937102 0.349057i \(-0.113498\pi\)
\(104\) −310.697 −0.292946
\(105\) 0 0
\(106\) −132.977 −0.121848
\(107\) 467.335 809.448i 0.422234 0.731330i −0.573924 0.818909i \(-0.694580\pi\)
0.996158 + 0.0875784i \(0.0279128\pi\)
\(108\) 0 0
\(109\) 598.509 + 1036.65i 0.525934 + 0.910944i 0.999544 + 0.0302095i \(0.00961746\pi\)
−0.473610 + 0.880735i \(0.657049\pi\)
\(110\) −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 −0.872432 0.488735i \(-0.837458\pi\)
0.859473 + 0.511181i \(0.170792\pi\)
\(132\) 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 0.721061 0.692872i \(-0.243655\pi\)
−0.960575 + 0.278021i \(0.910322\pi\)
\(138\) 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 −0.812132 0.583473i \(-0.801693\pi\)
0.911369 + 0.411591i \(0.135027\pi\)
\(150\) 0 0
\(151\) −774.195 1340.95i −0.417239 0.722679i 0.578422 0.815738i \(-0.303669\pi\)
−0.995661 + 0.0930587i \(0.970336\pi\)
\(152\) 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 0.962356 0.271794i \(-0.0876168\pi\)
−0.716558 + 0.697528i \(0.754283\pi\)
\(158\) −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 −0.661509 0.749937i \(-0.730084\pi\)
0.980219 + 0.197915i \(0.0634170\pi\)
\(164\) −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 −0.957149 0.289595i \(-0.906479\pi\)
0.729371 + 0.684118i \(0.239813\pi\)
\(174\) 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 0.774724 0.632299i \(-0.217889\pi\)
−0.934949 + 0.354781i \(0.884555\pi\)
\(180\) 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 −0.984796 0.173717i \(-0.944422\pi\)
0.642841 + 0.765999i \(0.277756\pi\)
\(192\) 0 0
\(193\) −1685.42 2919.23i −0.628597 1.08876i −0.987833 0.155515i \(-0.950296\pi\)
0.359237 0.933247i \(-0.383037\pi\)
\(194\) 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 0.993375 0.114921i \(-0.0366615\pi\)
−0.596212 + 0.802827i \(0.703328\pi\)
\(200\) 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 0.976442 0.215782i \(-0.0692299\pi\)
−0.675093 + 0.737733i \(0.735897\pi\)
\(228\) 0 0
\(229\) 1737.32 3009.12i 0.501332 0.868333i −0.498667 0.866794i \(-0.666177\pi\)
0.999999 0.00153905i \(-0.000489896\pi\)
\(230\) 4667.15 1.33801
\(231\) 0 0
\(232\) 1921.67 0.543809
\(233\) 388.049 672.121i 0.109107 0.188979i −0.806302 0.591505i \(-0.798534\pi\)
0.915409 + 0.402525i \(0.131868\pi\)
\(234\) 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 0.807157 0.590337i \(-0.201005\pi\)
−0.914825 + 0.403850i \(0.867672\pi\)
\(242\) 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 −0.941157 0.337968i \(-0.890260\pi\)
0.763268 + 0.646082i \(0.223594\pi\)
\(258\) 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 0.905980 + 0.423320i \(0.139135\pi\)
−0.0863847 + 0.996262i \(0.527531\pi\)
\(264\) 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 0.908218 0.418498i \(-0.137443\pi\)
−0.816539 + 0.577290i \(0.804110\pi\)
\(270\) 0 0
\(271\) −3330.88 + 5769.26i −0.746630 + 1.29320i 0.202799 + 0.979220i \(0.434996\pi\)
−0.949429 + 0.313981i \(0.898337\pi\)
\(272\) −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 0.908009 + 0.418951i \(0.137602\pi\)
−0.0911823 + 0.995834i \(0.529065\pi\)
\(278\) 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 0.649460 0.760396i \(-0.274995\pi\)
−0.983252 + 0.182251i \(0.941662\pi\)
\(284\) −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 0.886569 0.462596i \(-0.153082\pi\)
−0.843905 + 0.536493i \(0.819749\pi\)
\(312\) 0 0
\(313\) −1806.41 + 3128.79i −0.326211 + 0.565014i −0.981757 0.190141i \(-0.939105\pi\)
0.655546 + 0.755156i \(0.272439\pi\)
\(314\) 1934.14 0.347610
\(315\) 0 0
\(316\) −1638.79 −0.291737
\(317\) 2265.87 3924.60i 0.401463 0.695355i −0.592439 0.805615i \(-0.701835\pi\)
0.993903 + 0.110260i \(0.0351684\pi\)
\(318\) 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 −0.810090 0.586306i \(-0.800582\pi\)
0.912801 + 0.408405i \(0.133915\pi\)
\(332\) 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 0.863564 0.504239i \(-0.168227\pi\)
−0.868466 + 0.495749i \(0.834893\pi\)
\(348\) 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 0.644085 0.764954i \(-0.277238\pi\)
−0.984512 + 0.175316i \(0.943905\pi\)
\(354\) 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 −0.772422 0.635109i \(-0.780955\pi\)
0.936232 + 0.351383i \(0.114288\pi\)
\(360\) 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 0.912598 0.408857i \(-0.134072\pi\)
−0.810380 + 0.585905i \(0.800739\pi\)
\(368\) 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 −0.0324014 0.999475i \(-0.510315\pi\)
0.881771 0.471677i \(-0.156351\pi\)
\(374\) 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 −0.998251 0.0591208i \(-0.981170\pi\)
0.550326 + 0.834950i \(0.314504\pi\)
\(384\) 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 −0.970430 0.241381i \(-0.922400\pi\)
0.276173 0.961108i \(-0.410934\pi\)
\(390\) 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 −0.949686 0.313203i \(-0.898598\pi\)
0.746085 + 0.665851i \(0.231931\pi\)
\(398\) 4459.73 0.561673
\(399\) 0 0
\(400\) 2013.03 0.251629
\(401\) 6242.50 10812.3i 0.777395 1.34649i −0.156043 0.987750i \(-0.549874\pi\)
0.933438 0.358738i \(-0.116793\pi\)
\(402\) 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 0.571059 0.820909i \(-0.306533\pi\)
−0.996458 + 0.0840967i \(0.973200\pi\)
\(410\) 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 0.803720 0.595008i \(-0.202851\pi\)
−0.917152 + 0.398538i \(0.869518\pi\)
\(432\) 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 −0.996865 0.0791234i \(-0.974788\pi\)
0.566955 + 0.823749i \(0.308121\pi\)
\(440\) 6567.61 0.711587
\(441\) 0 0
\(442\) 2124.27 0.228600
\(443\) −1460.41 + 2529.51i −0.156628 + 0.271288i −0.933651 0.358185i \(-0.883396\pi\)
0.777023 + 0.629473i \(0.216729\pi\)
\(444\) 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 −0.976494 0.215543i \(-0.930848\pi\)
0.674913 + 0.737897i \(0.264181\pi\)
\(458\) −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 −0.927393 0.374088i \(-0.877956\pi\)
0.787666 + 0.616102i \(0.211289\pi\)
\(468\) 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 −0.929297 0.369332i \(-0.879586\pi\)
0.144798 0.989461i \(-0.453747\pi\)
\(480\) 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 0.680333 0.732903i \(-0.261835\pi\)
−0.974879 + 0.222734i \(0.928502\pi\)
\(488\) 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 −0.860514 0.509427i \(-0.829857\pi\)
0.871434 + 0.490513i \(0.163191\pi\)
\(500\) −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 −0.983394 0.181485i \(-0.941910\pi\)
0.648868 + 0.760901i \(0.275243\pi\)
\(510\) 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 −0.820578 0.571535i \(-0.806348\pi\)
−0.0846750 0.996409i \(-0.526985\pi\)
\(522\) 0 0
\(523\) 8423.53 14590.0i 0.704274 1.21984i −0.262679 0.964883i \(-0.584606\pi\)
0.966953 0.254955i \(-0.0820606\pi\)
\(524\) 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 0.277875 + 0.960617i \(0.410370\pi\)
−0.970856 + 0.239662i \(0.922963\pi\)
\(542\) 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 0.997468 0.0711212i \(-0.0226577\pi\)
−0.560327 + 0.828272i \(0.689324\pi\)
\(558\) 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 0.975616 + 0.219483i \(0.0704372\pi\)
−0.297730 + 0.954650i \(0.596230\pi\)
\(564\) 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 −0.773112 0.634270i \(-0.781301\pi\)
0.935850 + 0.352399i \(0.114634\pi\)
\(570\) 0 0
\(571\) −6609.87 11448.6i −0.484439 0.839073i 0.515401 0.856949i \(-0.327643\pi\)
−0.999840 + 0.0178762i \(0.994310\pi\)
\(572\) 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 0.987310 + 0.158803i \(0.0507634\pi\)
−0.356128 + 0.934437i \(0.615903\pi\)
\(578\) −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 −0.892253 0.451535i \(-0.850877\pi\)
0.837168 + 0.546946i \(0.184210\pi\)
\(594\) 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 0.524734 0.851266i \(-0.324165\pi\)
−0.999585 + 0.0287997i \(0.990831\pi\)
\(600\) 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 −0.965361 0.260919i \(-0.915974\pi\)
0.708643 + 0.705567i \(0.249308\pi\)
\(608\) −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 0.746573 0.665303i \(-0.231698\pi\)
−0.949456 + 0.313900i \(0.898364\pi\)
\(614\) 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 −0.946415 0.322954i \(-0.895324\pi\)
0.193521 0.981096i \(-0.438009\pi\)
\(620\) 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 0.620286 + 0.784376i \(0.287016\pi\)
0.369146 + 0.929371i \(0.379650\pi\)
\(642\) 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 0.957586 0.288149i \(-0.0930398\pi\)
−0.728337 + 0.685219i \(0.759706\pi\)
\(648\) 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 −0.929929 0.367738i \(-0.880132\pi\)
0.783435 + 0.621473i \(0.213466\pi\)
\(654\) 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 0.720165 0.693803i \(-0.244066\pi\)
−0.960933 + 0.276780i \(0.910733\pi\)
\(662\) −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 0.278932 + 0.960311i \(0.410020\pi\)
−0.971120 + 0.238593i \(0.923314\pi\)
\(678\) 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 −0.999844 0.0176767i \(-0.994373\pi\)
0.484613 0.874728i \(-0.338960\pi\)
\(684\) 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 −0.584786 0.811187i \(-0.698822\pi\)
0.994902 + 0.100846i \(0.0321550\pi\)
\(692\) 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 −0.367998 0.929827i \(-0.619957\pi\)
0.989252 0.146218i \(-0.0467101\pi\)
\(710\) 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 −0.954618 0.297832i \(-0.903737\pi\)
0.735239 + 0.677808i \(0.237070\pi\)
\(720\) 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 −0.922398 0.386241i \(-0.873773\pi\)
0.795694 + 0.605699i \(0.207107\pi\)
\(734\) 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 0.997810 0.0661431i \(-0.0210694\pi\)
−0.556187 + 0.831057i \(0.687736\pi\)
\(740\) 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 −0.990920 0.134453i \(-0.957072\pi\)
0.611900 + 0.790935i \(0.290406\pi\)
\(752\) 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 −0.845108 0.534595i \(-0.820464\pi\)
0.885527 + 0.464588i \(0.153797\pi\)
\(762\) 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 0.885501 + 0.464637i \(0.153815\pi\)
−0.0403629 + 0.999185i \(0.512851\pi\)
\(774\) 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
\(787\)