Properties

Label 126.4.g.g.37.2
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 37.2
Root \(9.41856 - 16.3134i\) of defining polynomial
Character \(\chi\) \(=\) 126.37
Dual form 126.4.g.g.109.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(10.4186 - 18.0455i) q^{5} +(-18.3371 + 2.59808i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(10.4186 - 18.0455i) q^{5} +(-18.3371 + 2.59808i) q^{7} -8.00000 q^{8} +(-20.8371 - 36.0910i) q^{10} +(7.58144 + 13.1314i) q^{11} +2.16288 q^{13} +(-13.8371 + 34.3589i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-59.6742 - 103.359i) q^{17} +(16.7557 - 29.0217i) q^{19} -83.3485 q^{20} +30.3258 q^{22} +(0.325758 - 0.564230i) q^{23} +(-154.593 - 267.763i) q^{25} +(2.16288 - 3.74622i) q^{26} +(45.6742 + 58.3255i) q^{28} +163.208 q^{29} +(111.663 + 193.406i) q^{31} +(16.0000 + 27.7128i) q^{32} -238.697 q^{34} +(-144.163 + 357.970i) q^{35} +(-84.2670 + 145.955i) q^{37} +(-33.5114 - 58.0434i) q^{38} +(-83.3485 + 144.364i) q^{40} +323.023 q^{41} +221.557 q^{43} +(30.3258 - 52.5258i) q^{44} +(-0.651517 - 1.12846i) q^{46} +(254.023 - 439.980i) q^{47} +(329.500 - 95.2825i) q^{49} -618.371 q^{50} +(-4.32576 - 7.49243i) q^{52} +(-88.2557 - 152.863i) q^{53} +315.951 q^{55} +(146.697 - 20.7846i) q^{56} +(163.208 - 282.685i) q^{58} +(227.464 + 393.979i) q^{59} +(-19.3258 + 33.4732i) q^{61} +446.652 q^{62} +64.0000 q^{64} +(22.5341 - 39.0302i) q^{65} +(-70.8958 - 122.795i) q^{67} +(-238.697 + 413.435i) q^{68} +(475.860 + 607.668i) q^{70} -602.742 q^{71} +(551.150 + 954.619i) q^{73} +(168.534 + 291.910i) q^{74} -134.045 q^{76} +(-173.138 - 221.096i) q^{77} +(58.1515 - 100.721i) q^{79} +(166.697 + 288.728i) q^{80} +(323.023 - 559.492i) q^{82} +568.928 q^{83} -2486.88 q^{85} +(221.557 - 383.748i) q^{86} +(-60.6515 - 105.052i) q^{88} +(-191.580 + 331.825i) q^{89} +(-39.6610 + 5.61932i) q^{91} -2.60607 q^{92} +(-508.045 - 879.961i) q^{94} +(-349.140 - 604.728i) q^{95} +334.701 q^{97} +(164.466 - 665.993i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 8q^{4} + 5q^{5} - 32q^{8} + O(q^{10}) \) \( 4q + 4q^{2} - 8q^{4} + 5q^{5} - 32q^{8} - 10q^{10} + 67q^{11} + 82q^{13} + 18q^{14} - 32q^{16} - 92q^{17} - 43q^{19} - 40q^{20} + 268q^{22} + 148q^{23} - 435q^{25} + 82q^{26} + 36q^{28} - 154q^{29} + 520q^{31} + 64q^{32} - 368q^{34} - 650q^{35} - 7q^{37} + 86q^{38} - 40q^{40} + 852q^{41} - 214q^{43} + 268q^{44} - 296q^{46} + 576q^{47} + 1318q^{49} - 1740q^{50} - 164q^{52} - 243q^{53} - 1010q^{55} - 154q^{58} - 7q^{59} - 224q^{61} + 2080q^{62} + 256q^{64} - 570q^{65} - 687q^{67} - 368q^{68} + 1390q^{70} - 944q^{71} + 921q^{73} + 14q^{74} + 344q^{76} + 371q^{77} + 526q^{79} + 80q^{80} + 852q^{82} + 442q^{83} - 5840q^{85} - 214q^{86} - 536q^{88} + 774q^{89} + 1345q^{91} - 1184q^{92} - 1152q^{94} - 1910q^{95} + 3906q^{97} + 1318q^{98} + O(q^{100}) \)

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
\(5\) 10.4186 18.0455i 0.931864 1.61404i 0.151732 0.988422i \(-0.451515\pi\)
0.780132 0.625615i \(-0.215152\pi\)
\(6\) 0 0
\(7\) −18.3371 + 2.59808i −0.990111 + 0.140283i
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −20.8371 36.0910i −0.658928 1.14130i
\(11\) 7.58144 + 13.1314i 0.207808 + 0.359934i 0.951024 0.309118i \(-0.100034\pi\)
−0.743216 + 0.669052i \(0.766700\pi\)
\(12\) 0 0
\(13\) 2.16288 0.0461442 0.0230721 0.999734i \(-0.492655\pi\)
0.0230721 + 0.999734i \(0.492655\pi\)
\(14\) −13.8371 + 34.3589i −0.264152 + 0.655914i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −59.6742 103.359i −0.851361 1.47460i −0.879981 0.475009i \(-0.842445\pi\)
0.0286202 0.999590i \(-0.490889\pi\)
\(18\) 0 0
\(19\) 16.7557 29.0217i 0.202317 0.350423i −0.746958 0.664871i \(-0.768486\pi\)
0.949274 + 0.314449i \(0.101820\pi\)
\(20\) −83.3485 −0.931864
\(21\) 0 0
\(22\) 30.3258 0.293885
\(23\) 0.325758 0.564230i 0.00295327 0.00511522i −0.864545 0.502555i \(-0.832393\pi\)
0.867498 + 0.497440i \(0.165727\pi\)
\(24\) 0 0
\(25\) −154.593 267.763i −1.23674 2.14210i
\(26\) 2.16288 3.74622i 0.0163144 0.0282574i
\(27\) 0 0
\(28\) 45.6742 + 58.3255i 0.308272 + 0.393660i
\(29\) 163.208 1.04507 0.522535 0.852618i \(-0.324986\pi\)
0.522535 + 0.852618i \(0.324986\pi\)
\(30\) 0 0
\(31\) 111.663 + 193.406i 0.646943 + 1.12054i 0.983849 + 0.179000i \(0.0572863\pi\)
−0.336906 + 0.941538i \(0.609380\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −238.697 −1.20401
\(35\) −144.163 + 357.970i −0.696228 + 1.72880i
\(36\) 0 0
\(37\) −84.2670 + 145.955i −0.374417 + 0.648509i −0.990240 0.139376i \(-0.955490\pi\)
0.615823 + 0.787885i \(0.288824\pi\)
\(38\) −33.5114 58.0434i −0.143059 0.247786i
\(39\) 0 0
\(40\) −83.3485 + 144.364i −0.329464 + 0.570648i
\(41\) 323.023 1.23043 0.615216 0.788359i \(-0.289069\pi\)
0.615216 + 0.788359i \(0.289069\pi\)
\(42\) 0 0
\(43\) 221.557 0.785746 0.392873 0.919593i \(-0.371481\pi\)
0.392873 + 0.919593i \(0.371481\pi\)
\(44\) 30.3258 52.5258i 0.103904 0.179967i
\(45\) 0 0
\(46\) −0.651517 1.12846i −0.00208828 0.00361701i
\(47\) 254.023 439.980i 0.788362 1.36548i −0.138608 0.990347i \(-0.544263\pi\)
0.926970 0.375136i \(-0.122404\pi\)
\(48\) 0 0
\(49\) 329.500 95.2825i 0.960641 0.277791i
\(50\) −618.371 −1.74902
\(51\) 0 0
\(52\) −4.32576 7.49243i −0.0115361 0.0199810i
\(53\) −88.2557 152.863i −0.228733 0.396177i 0.728700 0.684833i \(-0.240125\pi\)
−0.957433 + 0.288656i \(0.906792\pi\)
\(54\) 0 0
\(55\) 315.951 0.774596
\(56\) 146.697 20.7846i 0.350057 0.0495975i
\(57\) 0 0
\(58\) 163.208 282.685i 0.369488 0.639972i
\(59\) 227.464 + 393.979i 0.501920 + 0.869351i 0.999998 + 0.00221868i \(0.000706227\pi\)
−0.498077 + 0.867133i \(0.665960\pi\)
\(60\) 0 0
\(61\) −19.3258 + 33.4732i −0.0405641 + 0.0702591i −0.885595 0.464459i \(-0.846249\pi\)
0.845031 + 0.534718i \(0.179582\pi\)
\(62\) 446.652 0.914916
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 22.5341 39.0302i 0.0430001 0.0744784i
\(66\) 0 0
\(67\) −70.8958 122.795i −0.129273 0.223908i 0.794122 0.607758i \(-0.207931\pi\)
−0.923395 + 0.383851i \(0.874598\pi\)
\(68\) −238.697 + 413.435i −0.425680 + 0.737300i
\(69\) 0 0
\(70\) 475.860 + 607.668i 0.812516 + 1.03757i
\(71\) −602.742 −1.00750 −0.503749 0.863850i \(-0.668046\pi\)
−0.503749 + 0.863850i \(0.668046\pi\)
\(72\) 0 0
\(73\) 551.150 + 954.619i 0.883660 + 1.53054i 0.847242 + 0.531207i \(0.178262\pi\)
0.0364183 + 0.999337i \(0.488405\pi\)
\(74\) 168.534 + 291.910i 0.264753 + 0.458565i
\(75\) 0 0
\(76\) −134.045 −0.202317
\(77\) −173.138 221.096i −0.256246 0.327223i
\(78\) 0 0
\(79\) 58.1515 100.721i 0.0828172 0.143444i −0.821642 0.570004i \(-0.806942\pi\)
0.904459 + 0.426561i \(0.140275\pi\)
\(80\) 166.697 + 288.728i 0.232966 + 0.403509i
\(81\) 0 0
\(82\) 323.023 559.492i 0.435023 0.753482i
\(83\) 568.928 0.752385 0.376193 0.926542i \(-0.377233\pi\)
0.376193 + 0.926542i \(0.377233\pi\)
\(84\) 0 0
\(85\) −2486.88 −3.17341
\(86\) 221.557 383.748i 0.277803 0.481169i
\(87\) 0 0
\(88\) −60.6515 105.052i −0.0734713 0.127256i
\(89\) −191.580 + 331.825i −0.228173 + 0.395207i −0.957267 0.289207i \(-0.906608\pi\)
0.729094 + 0.684414i \(0.239942\pi\)
\(90\) 0 0
\(91\) −39.6610 + 5.61932i −0.0456879 + 0.00647325i
\(92\) −2.60607 −0.00295327
\(93\) 0 0
\(94\) −508.045 879.961i −0.557456 0.965543i
\(95\) −349.140 604.728i −0.377063 0.653093i
\(96\) 0 0
\(97\) 334.701 0.350348 0.175174 0.984538i \(-0.443951\pi\)
0.175174 + 0.984538i \(0.443951\pi\)
\(98\) 164.466 665.993i 0.169526 0.686484i
\(99\) 0 0
\(100\) −618.371 + 1071.05i −0.618371 + 1.07105i
\(101\) −7.37121 12.7673i −0.00726201 0.0125782i 0.862372 0.506276i \(-0.168978\pi\)
−0.869634 + 0.493698i \(0.835645\pi\)
\(102\) 0 0
\(103\) 420.710 728.691i 0.402464 0.697088i −0.591559 0.806262i \(-0.701487\pi\)
0.994023 + 0.109174i \(0.0348205\pi\)
\(104\) −17.3030 −0.0163144
\(105\) 0 0
\(106\) −353.023 −0.323477
\(107\) −357.835 + 619.789i −0.323301 + 0.559974i −0.981167 0.193161i \(-0.938126\pi\)
0.657866 + 0.753135i \(0.271459\pi\)
\(108\) 0 0
\(109\) −300.009 519.632i −0.263630 0.456621i 0.703574 0.710622i \(-0.251587\pi\)
−0.967204 + 0.254001i \(0.918253\pi\)
\(110\) 315.951 547.243i 0.273861 0.474341i
\(111\) 0 0
\(112\) 110.697 274.871i 0.0933918 0.231901i
\(113\) −622.644 −0.518349 −0.259174 0.965831i \(-0.583450\pi\)
−0.259174 + 0.965831i \(0.583450\pi\)
\(114\) 0 0
\(115\) −6.78787 11.7569i −0.00550410 0.00953339i
\(116\) −326.417 565.370i −0.261267 0.452529i
\(117\) 0 0
\(118\) 909.856 0.709822
\(119\) 1362.79 + 1740.26i 1.04980 + 1.34059i
\(120\) 0 0
\(121\) 550.544 953.569i 0.413632 0.716431i
\(122\) 38.6515 + 66.9464i 0.0286831 + 0.0496807i
\(123\) 0 0
\(124\) 446.652 773.623i 0.323472 0.560269i
\(125\) −3837.90 −2.74618
\(126\) 0 0
\(127\) −180.076 −0.125820 −0.0629100 0.998019i \(-0.520038\pi\)
−0.0629100 + 0.998019i \(0.520038\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −45.0682 78.0604i −0.0304057 0.0526642i
\(131\) 108.930 188.672i 0.0726508 0.125835i −0.827411 0.561596i \(-0.810187\pi\)
0.900062 + 0.435761i \(0.143521\pi\)
\(132\) 0 0
\(133\) −231.850 + 575.707i −0.151158 + 0.375339i
\(134\) −283.583 −0.182820
\(135\) 0 0
\(136\) 477.394 + 826.871i 0.301001 + 0.521350i
\(137\) −1300.93 2253.27i −0.811283 1.40518i −0.911966 0.410265i \(-0.865436\pi\)
0.100683 0.994919i \(-0.467897\pi\)
\(138\) 0 0
\(139\) −2651.55 −1.61800 −0.808998 0.587811i \(-0.799990\pi\)
−0.808998 + 0.587811i \(0.799990\pi\)
\(140\) 1528.37 216.546i 0.922650 0.130725i
\(141\) 0 0
\(142\) −602.742 + 1043.98i −0.356204 + 0.616964i
\(143\) 16.3977 + 28.4017i 0.00958914 + 0.0166089i
\(144\) 0 0
\(145\) 1700.40 2945.17i 0.973863 1.68678i
\(146\) 2204.60 1.24968
\(147\) 0 0
\(148\) 674.136 0.374417
\(149\) 290.511 503.180i 0.159729 0.276659i −0.775042 0.631910i \(-0.782271\pi\)
0.934771 + 0.355251i \(0.115605\pi\)
\(150\) 0 0
\(151\) 307.695 + 532.943i 0.165827 + 0.287221i 0.936949 0.349467i \(-0.113637\pi\)
−0.771122 + 0.636688i \(0.780304\pi\)
\(152\) −134.045 + 232.174i −0.0715297 + 0.123893i
\(153\) 0 0
\(154\) −556.087 + 78.7886i −0.290979 + 0.0412271i
\(155\) 4653.47 2.41145
\(156\) 0 0
\(157\) 153.466 + 265.811i 0.0780122 + 0.135121i 0.902392 0.430916i \(-0.141809\pi\)
−0.824380 + 0.566037i \(0.808476\pi\)
\(158\) −116.303 201.443i −0.0585606 0.101430i
\(159\) 0 0
\(160\) 666.788 0.329464
\(161\) −4.50756 + 11.1927i −0.00220649 + 0.00547893i
\(162\) 0 0
\(163\) −1757.25 + 3043.65i −0.844408 + 1.46256i 0.0417271 + 0.999129i \(0.486714\pi\)
−0.886135 + 0.463428i \(0.846619\pi\)
\(164\) −646.045 1118.98i −0.307608 0.532792i
\(165\) 0 0
\(166\) 568.928 985.412i 0.266008 0.460740i
\(167\) −1123.30 −0.520502 −0.260251 0.965541i \(-0.583805\pi\)
−0.260251 + 0.965541i \(0.583805\pi\)
\(168\) 0 0
\(169\) −2192.32 −0.997871
\(170\) −2486.88 + 4307.40i −1.12197 + 1.94331i
\(171\) 0 0
\(172\) −443.114 767.495i −0.196437 0.340238i
\(173\) 765.299 1325.54i 0.336327 0.582536i −0.647412 0.762141i \(-0.724148\pi\)
0.983739 + 0.179605i \(0.0574818\pi\)
\(174\) 0 0
\(175\) 3530.45 + 4508.35i 1.52501 + 1.94742i
\(176\) −242.606 −0.103904
\(177\) 0 0
\(178\) 383.159 + 663.651i 0.161343 + 0.279454i
\(179\) 1706.72 + 2956.12i 0.712659 + 1.23436i 0.963856 + 0.266425i \(0.0858426\pi\)
−0.251197 + 0.967936i \(0.580824\pi\)
\(180\) 0 0
\(181\) 1286.71 0.528399 0.264200 0.964468i \(-0.414892\pi\)
0.264200 + 0.964468i \(0.414892\pi\)
\(182\) −29.9280 + 74.3142i −0.0121891 + 0.0302667i
\(183\) 0 0
\(184\) −2.60607 + 4.51384i −0.00104414 + 0.00180850i
\(185\) 1755.88 + 3041.28i 0.697811 + 1.20864i
\(186\) 0 0
\(187\) 904.833 1567.22i 0.353839 0.612868i
\(188\) −2032.18 −0.788362
\(189\) 0 0
\(190\) −1396.56 −0.533248
\(191\) 527.648 913.913i 0.199891 0.346222i −0.748602 0.663020i \(-0.769274\pi\)
0.948493 + 0.316798i \(0.102608\pi\)
\(192\) 0 0
\(193\) 2385.42 + 4131.67i 0.889670 + 1.54095i 0.840266 + 0.542175i \(0.182399\pi\)
0.0494044 + 0.998779i \(0.484268\pi\)
\(194\) 334.701 579.719i 0.123867 0.214543i
\(195\) 0 0
\(196\) −989.068 950.857i −0.360448 0.346522i
\(197\) −1622.31 −0.586725 −0.293363 0.956001i \(-0.594774\pi\)
−0.293363 + 0.956001i \(0.594774\pi\)
\(198\) 0 0
\(199\) 1775.07 + 3074.51i 0.632318 + 1.09521i 0.987077 + 0.160249i \(0.0512296\pi\)
−0.354759 + 0.934958i \(0.615437\pi\)
\(200\) 1236.74 + 2142.10i 0.437254 + 0.757347i
\(201\) 0 0
\(202\) −29.4848 −0.0102700
\(203\) −2992.77 + 424.028i −1.03474 + 0.146605i
\(204\) 0 0
\(205\) 3365.43 5829.10i 1.14659 1.98596i
\(206\) −841.420 1457.38i −0.284585 0.492916i
\(207\) 0 0
\(208\) −17.3030 + 29.9697i −0.00576803 + 0.00999051i
\(209\) 508.129 0.168172
\(210\) 0 0
\(211\) 4653.39 1.51826 0.759129 0.650941i \(-0.225625\pi\)
0.759129 + 0.650941i \(0.225625\pi\)
\(212\) −353.023 + 611.453i −0.114367 + 0.198089i
\(213\) 0 0
\(214\) 715.670 + 1239.58i 0.228609 + 0.395962i
\(215\) 2308.30 3998.10i 0.732209 1.26822i
\(216\) 0 0
\(217\) −2550.06 3256.40i −0.797739 1.01870i
\(218\) −1200.04 −0.372829
\(219\) 0 0
\(220\) −631.901 1094.49i −0.193649 0.335410i
\(221\) −129.068 223.553i −0.0392854 0.0680442i
\(222\) 0 0
\(223\) −4649.53 −1.39621 −0.698107 0.715993i \(-0.745974\pi\)
−0.698107 + 0.715993i \(0.745974\pi\)
\(224\) −365.394 466.604i −0.108991 0.139180i
\(225\) 0 0
\(226\) −622.644 + 1078.45i −0.183264 + 0.317423i
\(227\) 2075.86 + 3595.49i 0.606958 + 1.05128i 0.991739 + 0.128274i \(0.0409438\pi\)
−0.384780 + 0.923008i \(0.625723\pi\)
\(228\) 0 0
\(229\) −2131.82 + 3692.41i −0.615172 + 1.06551i 0.375182 + 0.926951i \(0.377580\pi\)
−0.990354 + 0.138558i \(0.955753\pi\)
\(230\) −27.1515 −0.00778398
\(231\) 0 0
\(232\) −1305.67 −0.369488
\(233\) 1524.95 2641.29i 0.428768 0.742647i −0.567996 0.823031i \(-0.692281\pi\)
0.996764 + 0.0803838i \(0.0256146\pi\)
\(234\) 0 0
\(235\) −5293.10 9167.92i −1.46929 2.54489i
\(236\) 909.856 1575.92i 0.250960 0.434676i
\(237\) 0 0
\(238\) 4377.02 620.153i 1.19210 0.168901i
\(239\) −3987.20 −1.07912 −0.539562 0.841946i \(-0.681410\pi\)
−0.539562 + 0.841946i \(0.681410\pi\)
\(240\) 0 0
\(241\) 312.324 + 540.961i 0.0834795 + 0.144591i 0.904742 0.425959i \(-0.140063\pi\)
−0.821263 + 0.570550i \(0.806730\pi\)
\(242\) −1101.09 1907.14i −0.292482 0.506593i
\(243\) 0 0
\(244\) 154.606 0.0405641
\(245\) 1713.50 6938.69i 0.446822 1.80937i
\(246\) 0 0
\(247\) 36.2405 62.7704i 0.00933574 0.0161700i
\(248\) −893.303 1547.25i −0.228729 0.396170i
\(249\) 0 0
\(250\) −3837.90 + 6647.43i −0.970920 + 1.68168i
\(251\) 1328.78 0.334152 0.167076 0.985944i \(-0.446568\pi\)
0.167076 + 0.985944i \(0.446568\pi\)
\(252\) 0 0
\(253\) 9.87887 0.00245486
\(254\) −180.076 + 311.900i −0.0444841 + 0.0770487i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −1613.09 + 2793.96i −0.391525 + 0.678141i −0.992651 0.121013i \(-0.961386\pi\)
0.601126 + 0.799154i \(0.294719\pi\)
\(258\) 0 0
\(259\) 1166.01 2895.32i 0.279740 0.694620i
\(260\) −180.273 −0.0430001
\(261\) 0 0
\(262\) −217.860 377.344i −0.0513719 0.0889787i
\(263\) 1625.31 + 2815.11i 0.381067 + 0.660028i 0.991215 0.132260i \(-0.0422233\pi\)
−0.610148 + 0.792288i \(0.708890\pi\)
\(264\) 0 0
\(265\) −3677.99 −0.852593
\(266\) 765.303 + 977.283i 0.176405 + 0.225267i
\(267\) 0 0
\(268\) −283.583 + 491.181i −0.0646366 + 0.111954i
\(269\) 1413.02 + 2447.42i 0.320273 + 0.554729i 0.980544 0.196298i \(-0.0628921\pi\)
−0.660271 + 0.751027i \(0.729559\pi\)
\(270\) 0 0
\(271\) 1198.38 2075.66i 0.268622 0.465268i −0.699884 0.714257i \(-0.746765\pi\)
0.968506 + 0.248989i \(0.0800983\pi\)
\(272\) 1909.58 0.425680
\(273\) 0 0
\(274\) −5203.71 −1.14733
\(275\) 2344.07 4060.05i 0.514010 0.890292i
\(276\) 0 0
\(277\) −910.233 1576.57i −0.197439 0.341974i 0.750258 0.661145i \(-0.229929\pi\)
−0.947697 + 0.319170i \(0.896596\pi\)
\(278\) −2651.55 + 4592.62i −0.572048 + 0.990816i
\(279\) 0 0
\(280\) 1153.30 2863.76i 0.246154 0.611223i
\(281\) −3083.81 −0.654679 −0.327339 0.944907i \(-0.606152\pi\)
−0.327339 + 0.944907i \(0.606152\pi\)
\(282\) 0 0
\(283\) −1277.38 2212.49i −0.268313 0.464732i 0.700113 0.714032i \(-0.253133\pi\)
−0.968426 + 0.249300i \(0.919800\pi\)
\(284\) 1205.48 + 2087.96i 0.251875 + 0.436259i
\(285\) 0 0
\(286\) 65.5910 0.0135611
\(287\) −5923.31 + 839.238i −1.21826 + 0.172608i
\(288\) 0 0
\(289\) −4665.53 + 8080.94i −0.949630 + 1.64481i
\(290\) −3400.79 5890.34i −0.688625 1.19273i
\(291\) 0 0
\(292\) 2204.60 3818.48i 0.441830 0.765272i
\(293\) 1846.47 0.368163 0.184081 0.982911i \(-0.441069\pi\)
0.184081 + 0.982911i \(0.441069\pi\)
\(294\) 0 0
\(295\) 9479.39 1.87089
\(296\) 674.136 1167.64i 0.132376 0.229282i
\(297\) 0 0
\(298\) −581.023 1006.36i −0.112945 0.195627i
\(299\) 0.704576 1.22036i 0.000136277 0.000236038i
\(300\) 0 0
\(301\) −4062.71 + 575.621i −0.777977 + 0.110227i
\(302\) 1230.78 0.234515
\(303\) 0 0
\(304\) 268.091 + 464.347i 0.0505792 + 0.0876057i
\(305\) 402.693 + 697.485i 0.0756005 + 0.130944i
\(306\) 0 0
\(307\) 7041.50 1.30905 0.654527 0.756039i \(-0.272868\pi\)
0.654527 + 0.756039i \(0.272868\pi\)
\(308\) −419.621 + 1041.96i −0.0776303 + 0.192764i
\(309\) 0 0
\(310\) 4653.47 8060.04i 0.852578 1.47671i
\(311\) −1343.00 2326.14i −0.244869 0.424126i 0.717226 0.696841i \(-0.245412\pi\)
−0.962095 + 0.272715i \(0.912078\pi\)
\(312\) 0 0
\(313\) −1109.59 + 1921.87i −0.200377 + 0.347063i −0.948650 0.316328i \(-0.897550\pi\)
0.748273 + 0.663391i \(0.230883\pi\)
\(314\) 613.864 0.110326
\(315\) 0 0
\(316\) −465.212 −0.0828172
\(317\) 1110.63 1923.67i 0.196780 0.340833i −0.750703 0.660640i \(-0.770285\pi\)
0.947483 + 0.319807i \(0.103618\pi\)
\(318\) 0 0
\(319\) 1237.35 + 2143.16i 0.217174 + 0.376157i
\(320\) 666.788 1154.91i 0.116483 0.201755i
\(321\) 0 0
\(322\) 14.8788 + 19.0000i 0.00257503 + 0.00328829i
\(323\) −3999.53 −0.688978
\(324\) 0 0
\(325\) −334.366 579.138i −0.0570685 0.0988455i
\(326\) 3514.50 + 6087.29i 0.597086 + 1.03418i
\(327\) 0 0
\(328\) −2584.18 −0.435023
\(329\) −3514.94 + 8727.94i −0.589012 + 1.46257i
\(330\) 0 0
\(331\) −2077.03 + 3597.52i −0.344906 + 0.597394i −0.985337 0.170622i \(-0.945422\pi\)
0.640431 + 0.768016i \(0.278756\pi\)
\(332\) −1137.86 1970.82i −0.188096 0.325792i
\(333\) 0 0
\(334\) −1123.30 + 1945.62i −0.184025 + 0.318741i
\(335\) −2954.53 −0.481860
\(336\) 0 0
\(337\) −254.167 −0.0410841 −0.0205420 0.999789i \(-0.506539\pi\)
−0.0205420 + 0.999789i \(0.506539\pi\)
\(338\) −2192.32 + 3797.21i −0.352801 + 0.611069i
\(339\) 0 0
\(340\) 4973.76 + 8614.80i 0.793353 + 1.37413i
\(341\) −1693.13 + 2932.59i −0.268880 + 0.465714i
\(342\) 0 0
\(343\) −5794.53 + 2603.27i −0.912173 + 0.409806i
\(344\) −1772.45 −0.277803
\(345\) 0 0
\(346\) −1530.60 2651.07i −0.237819 0.411915i
\(347\) −3112.32 5390.69i −0.481493 0.833970i 0.518282 0.855210i \(-0.326572\pi\)
−0.999774 + 0.0212401i \(0.993239\pi\)
\(348\) 0 0
\(349\) 9732.21 1.49270 0.746352 0.665552i \(-0.231804\pi\)
0.746352 + 0.665552i \(0.231804\pi\)
\(350\) 11339.1 1606.58i 1.73172 0.245357i
\(351\) 0 0
\(352\) −242.606 + 420.206i −0.0367356 + 0.0636280i
\(353\) 712.807 + 1234.62i 0.107476 + 0.186153i 0.914747 0.404027i \(-0.132390\pi\)
−0.807271 + 0.590180i \(0.799057\pi\)
\(354\) 0 0
\(355\) −6279.71 + 10876.8i −0.938852 + 1.62614i
\(356\) 1532.64 0.228173
\(357\) 0 0
\(358\) 6826.86 1.00785
\(359\) −2883.25 + 4993.93i −0.423877 + 0.734177i −0.996315 0.0857714i \(-0.972665\pi\)
0.572438 + 0.819948i \(0.305998\pi\)
\(360\) 0 0
\(361\) 2867.99 + 4967.51i 0.418136 + 0.724233i
\(362\) 1286.71 2228.64i 0.186817 0.323577i
\(363\) 0 0
\(364\) 98.7879 + 126.151i 0.0142250 + 0.0181651i
\(365\) 22968.7 3.29381
\(366\) 0 0
\(367\) −5772.67 9998.56i −0.821065 1.42213i −0.904890 0.425646i \(-0.860047\pi\)
0.0838244 0.996481i \(-0.473287\pi\)
\(368\) 5.21213 + 9.02768i 0.000738319 + 0.00127881i
\(369\) 0 0
\(370\) 7023.53 0.986854
\(371\) 2015.51 + 2573.78i 0.282048 + 0.360172i
\(372\) 0 0
\(373\) 3239.79 5611.47i 0.449731 0.778957i −0.548637 0.836061i \(-0.684853\pi\)
0.998368 + 0.0571033i \(0.0181864\pi\)
\(374\) −1809.67 3134.43i −0.250202 0.433363i
\(375\) 0 0
\(376\) −2032.18 + 3519.84i −0.278728 + 0.482771i
\(377\) 353.000 0.0482239
\(378\) 0 0
\(379\) 611.996 0.0829449 0.0414725 0.999140i \(-0.486795\pi\)
0.0414725 + 0.999140i \(0.486795\pi\)
\(380\) −1396.56 + 2418.91i −0.188532 + 0.326546i
\(381\) 0 0
\(382\) −1055.30 1827.83i −0.141345 0.244816i
\(383\) 2180.41 3776.57i 0.290897 0.503848i −0.683125 0.730301i \(-0.739380\pi\)
0.974022 + 0.226453i \(0.0727130\pi\)
\(384\) 0 0
\(385\) −5793.63 + 820.864i −0.766937 + 0.108663i
\(386\) 9541.68 1.25818
\(387\) 0 0
\(388\) −669.402 1159.44i −0.0875869 0.151705i
\(389\) −6573.46 11385.6i −0.856781 1.48399i −0.874983 0.484154i \(-0.839128\pi\)
0.0182021 0.999834i \(-0.494206\pi\)
\(390\) 0 0
\(391\) −77.7575 −0.0100572
\(392\) −2636.00 + 762.260i −0.339638 + 0.0982141i
\(393\) 0 0
\(394\) −1622.31 + 2809.92i −0.207439 + 0.359294i
\(395\) −1211.71 2098.74i −0.154349 0.267340i
\(396\) 0 0
\(397\) 4239.02 7342.20i 0.535895 0.928198i −0.463224 0.886241i \(-0.653308\pi\)
0.999119 0.0419565i \(-0.0133591\pi\)
\(398\) 7100.27 0.894232
\(399\) 0 0
\(400\) 4946.97 0.618371
\(401\) 1401.50 2427.47i 0.174533 0.302299i −0.765467 0.643475i \(-0.777492\pi\)
0.939999 + 0.341176i \(0.110825\pi\)
\(402\) 0 0
\(403\) 241.513 + 418.313i 0.0298527 + 0.0517064i
\(404\) −29.4848 + 51.0692i −0.00363100 + 0.00628908i
\(405\) 0 0
\(406\) −2258.33 + 5607.66i −0.276057 + 0.685476i
\(407\) −2555.46 −0.311227
\(408\) 0 0
\(409\) 3192.69 + 5529.91i 0.385987 + 0.668548i 0.991906 0.126978i \(-0.0405278\pi\)
−0.605919 + 0.795526i \(0.707194\pi\)
\(410\) −6730.86 11658.2i −0.810765 1.40429i
\(411\) 0 0
\(412\) −3365.68 −0.402464
\(413\) −5194.62 6633.48i −0.618912 0.790344i
\(414\) 0 0
\(415\) 5927.41 10266.6i 0.701121 1.21438i
\(416\) 34.6061 + 59.9395i 0.00407861 + 0.00706436i
\(417\) 0 0
\(418\) 508.129 880.105i 0.0594579 0.102984i
\(419\) −4831.66 −0.563346 −0.281673 0.959510i \(-0.590889\pi\)
−0.281673 + 0.959510i \(0.590889\pi\)
\(420\) 0 0
\(421\) 7475.37 0.865385 0.432693 0.901542i \(-0.357564\pi\)
0.432693 + 0.901542i \(0.357564\pi\)
\(422\) 4653.39 8059.90i 0.536785 0.929739i
\(423\) 0 0
\(424\) 706.045 + 1222.91i 0.0808693 + 0.140070i
\(425\) −18450.4 + 31957.1i −2.10583 + 3.64740i
\(426\) 0 0
\(427\) 267.413 664.012i 0.0303068 0.0752548i
\(428\) 2862.68 0.323301
\(429\) 0 0
\(430\) −4616.61 7996.20i −0.517750 0.896769i
\(431\) 3495.97 + 6055.19i 0.390707 + 0.676725i 0.992543 0.121895i \(-0.0388972\pi\)
−0.601836 + 0.798620i \(0.705564\pi\)
\(432\) 0 0
\(433\) −7699.26 −0.854510 −0.427255 0.904131i \(-0.640519\pi\)
−0.427255 + 0.904131i \(0.640519\pi\)
\(434\) −8190.30 + 1160.43i −0.905869 + 0.128347i
\(435\) 0 0
\(436\) −1200.04 + 2078.53i −0.131815 + 0.228310i
\(437\) −10.9166 18.9081i −0.00119499 0.00206979i
\(438\) 0 0
\(439\) −4706.16 + 8151.31i −0.511646 + 0.886198i 0.488262 + 0.872697i \(0.337631\pi\)
−0.999909 + 0.0135008i \(0.995702\pi\)
\(440\) −2527.61 −0.273861
\(441\) 0 0
\(442\) −516.273 −0.0555579
\(443\) −3129.09 + 5419.74i −0.335593 + 0.581263i −0.983598 0.180372i \(-0.942270\pi\)
0.648006 + 0.761635i \(0.275603\pi\)
\(444\) 0 0
\(445\) 3991.97 + 6914.29i 0.425252 + 0.736559i
\(446\) −4649.53 + 8053.23i −0.493636 + 0.855003i
\(447\) 0 0
\(448\) −1173.58 + 166.277i −0.123764 + 0.0175354i
\(449\) 11633.8 1.22279 0.611396 0.791325i \(-0.290608\pi\)
0.611396 + 0.791325i \(0.290608\pi\)
\(450\) 0 0
\(451\) 2448.98 + 4241.75i 0.255694 + 0.442874i
\(452\) 1245.29 + 2156.90i 0.129587 + 0.224452i
\(453\) 0 0
\(454\) 8303.43 0.858369
\(455\) −311.807 + 774.246i −0.0321269 + 0.0797741i
\(456\) 0 0
\(457\) 6552.31 11348.9i 0.670688 1.16167i −0.307022 0.951703i \(-0.599332\pi\)
0.977709 0.209963i \(-0.0673343\pi\)
\(458\) 4263.63 + 7384.83i 0.434992 + 0.753429i
\(459\) 0 0
\(460\) −27.1515 + 47.0277i −0.00275205 + 0.00476669i
\(461\) 2594.63 0.262134 0.131067 0.991373i \(-0.458160\pi\)
0.131067 + 0.991373i \(0.458160\pi\)
\(462\) 0 0
\(463\) −14136.2 −1.41893 −0.709465 0.704741i \(-0.751063\pi\)
−0.709465 + 0.704741i \(0.751063\pi\)
\(464\) −1305.67 + 2261.48i −0.130634 + 0.226264i
\(465\) 0 0
\(466\) −3049.90 5282.58i −0.303184 0.525131i
\(467\) 7795.12 13501.5i 0.772409 1.33785i −0.163830 0.986489i \(-0.552385\pi\)
0.936239 0.351363i \(-0.114282\pi\)
\(468\) 0 0
\(469\) 1619.06 + 2067.52i 0.159405 + 0.203559i
\(470\) −21172.4 −2.07789
\(471\) 0 0
\(472\) −1819.71 3151.83i −0.177456 0.307362i
\(473\) 1679.72 + 2909.36i 0.163285 + 0.282817i
\(474\) 0 0
\(475\) −10361.2 −1.00085
\(476\) 3302.88 8201.37i 0.318040 0.789725i
\(477\) 0 0
\(478\) −3987.20 + 6906.04i −0.381528 + 0.660826i
\(479\) −4226.75 7320.95i −0.403184 0.698336i 0.590924 0.806727i \(-0.298763\pi\)
−0.994108 + 0.108391i \(0.965430\pi\)
\(480\) 0 0
\(481\) −182.259 + 315.683i −0.0172772 + 0.0299249i
\(482\) 1249.30 0.118058
\(483\) 0 0
\(484\) −4404.35 −0.413632
\(485\) 3487.10 6039.83i 0.326476 0.565474i
\(486\) 0 0
\(487\) 2005.53 + 3473.69i 0.186611 + 0.323219i 0.944118 0.329607i \(-0.106916\pi\)
−0.757507 + 0.652827i \(0.773583\pi\)
\(488\) 154.606 267.786i 0.0143416 0.0248403i
\(489\) 0 0
\(490\) −10304.7 9906.56i −0.950035 0.913332i
\(491\) −13927.9 −1.28016 −0.640079 0.768309i \(-0.721098\pi\)
−0.640079 + 0.768309i \(0.721098\pi\)
\(492\) 0 0
\(493\) −9739.33 16869.0i −0.889731 1.54106i
\(494\) −72.4810 125.541i −0.00660137 0.0114339i
\(495\) 0 0
\(496\) −3573.21 −0.323472
\(497\) 11052.6 1565.97i 0.997535 0.141335i
\(498\) 0 0
\(499\) 1973.77 3418.68i 0.177071 0.306695i −0.763805 0.645447i \(-0.776671\pi\)
0.940876 + 0.338751i \(0.110005\pi\)
\(500\) 7675.80 + 13294.9i 0.686544 + 1.18913i
\(501\) 0 0
\(502\) 1328.78 2301.52i 0.118141 0.204625i
\(503\) 13725.3 1.21666 0.608331 0.793684i \(-0.291839\pi\)
0.608331 + 0.793684i \(0.291839\pi\)
\(504\) 0 0
\(505\) −307.190 −0.0270688
\(506\) 9.87887 17.1107i 0.000867924 0.00150329i
\(507\) 0 0
\(508\) 360.152 + 623.801i 0.0314550 + 0.0544817i
\(509\) 3915.05 6781.07i 0.340926 0.590502i −0.643679 0.765296i \(-0.722593\pi\)
0.984605 + 0.174794i \(0.0559259\pi\)
\(510\) 0 0
\(511\) −12586.7 16073.0i −1.08963 1.39145i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 3226.18 + 5587.91i 0.276850 + 0.479518i
\(515\) −8766.39 15183.8i −0.750084 1.29918i
\(516\) 0 0
\(517\) 7703.43 0.655312
\(518\) −3848.83 4914.92i −0.326463 0.416890i
\(519\) 0 0
\(520\) −180.273 + 312.241i −0.0152028 + 0.0263321i
\(521\) −2953.69 5115.95i −0.248376 0.430199i 0.714700 0.699431i \(-0.246563\pi\)
−0.963075 + 0.269232i \(0.913230\pi\)
\(522\) 0 0
\(523\) −3954.03 + 6848.58i −0.330588 + 0.572595i −0.982627 0.185590i \(-0.940580\pi\)
0.652039 + 0.758185i \(0.273914\pi\)
\(524\) −871.439 −0.0726508
\(525\) 0 0
\(526\) 6501.23 0.538911
\(527\) 13326.8 23082.7i 1.10156 1.90797i
\(528\) 0 0
\(529\) 6083.29 + 10536.6i 0.499983 + 0.865995i
\(530\) −3677.99 + 6370.46i −0.301437 + 0.522104i
\(531\) 0 0
\(532\) 2458.01 348.260i 0.200316 0.0283816i
\(533\) 698.659 0.0567773
\(534\) 0 0
\(535\) 7456.26 + 12914.6i 0.602546 + 1.04364i
\(536\) 567.167 + 982.362i 0.0457050 + 0.0791633i
\(537\) 0 0
\(538\) 5652.08 0.452934
\(539\) 3749.28 + 3604.43i 0.299616 + 0.288040i
\(540\) 0 0
\(541\) 1970.52 3413.04i 0.156598 0.271235i −0.777042 0.629449i \(-0.783281\pi\)
0.933640 + 0.358214i \(0.116614\pi\)
\(542\) −2396.77 4151.33i −0.189945 0.328994i
\(543\) 0 0
\(544\) 1909.58 3307.48i 0.150501 0.260675i
\(545\) −12502.7 −0.982670
\(546\) 0 0
\(547\) −1828.71 −0.142943 −0.0714717 0.997443i \(-0.522770\pi\)
−0.0714717 + 0.997443i \(0.522770\pi\)
\(548\) −5203.71 + 9013.09i −0.405642 + 0.702592i
\(549\) 0 0
\(550\) −4688.14 8120.10i −0.363460 0.629532i
\(551\) 2734.67 4736.58i 0.211435 0.366216i
\(552\) 0 0
\(553\) −804.650 + 1998.02i −0.0618756 + 0.153643i
\(554\) −3640.93 −0.279221
\(555\) 0 0
\(556\) 5303.10 + 9185.24i 0.404499 + 0.700613i
\(557\) 11266.0 + 19513.3i 0.857011 + 1.48439i 0.874767 + 0.484544i \(0.161015\pi\)
−0.0177556 + 0.999842i \(0.505652\pi\)
\(558\) 0 0
\(559\) 479.201 0.0362577
\(560\) −3806.88 4861.34i −0.287268 0.366838i
\(561\) 0 0
\(562\) −3083.81 + 5341.32i −0.231464 + 0.400907i
\(563\) 11677.9 + 20226.6i 0.874179 + 1.51412i 0.857635 + 0.514260i \(0.171933\pi\)
0.0165446 + 0.999863i \(0.494733\pi\)
\(564\) 0 0
\(565\) −6487.05 + 11235.9i −0.483031 + 0.836634i
\(566\) −5109.54 −0.379452
\(567\) 0 0
\(568\) 4821.94 0.356204
\(569\) −10443.8 + 18089.2i −0.769468 + 1.33276i 0.168384 + 0.985721i \(0.446145\pi\)
−0.937852 + 0.347036i \(0.887188\pi\)
\(570\) 0 0
\(571\) −11872.6 20564.0i −0.870147 1.50714i −0.861844 0.507173i \(-0.830690\pi\)
−0.00830301 0.999966i \(-0.502643\pi\)
\(572\) 65.5910 113.607i 0.00479457 0.00830444i
\(573\) 0 0
\(574\) −4469.70 + 11098.7i −0.325021 + 0.807058i
\(575\) −201.440 −0.0146098
\(576\) 0 0
\(577\) −1227.20 2125.57i −0.0885422 0.153360i 0.818353 0.574716i \(-0.194887\pi\)
−0.906895 + 0.421356i \(0.861554\pi\)
\(578\) 9331.06 + 16161.9i 0.671490 + 1.16305i
\(579\) 0 0
\(580\) −13603.2 −0.973863
\(581\) −10432.5 + 1478.12i −0.744945 + 0.105547i
\(582\) 0 0
\(583\) 1338.21 2317.85i 0.0950652 0.164658i
\(584\) −4409.20 7636.95i −0.312421 0.541129i
\(585\) 0 0
\(586\) 1846.47 3198.17i 0.130165 0.225453i
\(587\) −18567.5 −1.30556 −0.652780 0.757547i \(-0.726397\pi\)
−0.652780 + 0.757547i \(0.726397\pi\)
\(588\) 0 0
\(589\) 7483.95 0.523550
\(590\) 9479.39 16418.8i 0.661458 1.14568i
\(591\) 0 0
\(592\) −1348.27 2335.28i −0.0936042 0.162127i
\(593\) 8556.47 14820.2i 0.592533 1.02630i −0.401357 0.915922i \(-0.631461\pi\)
0.993890 0.110375i \(-0.0352053\pi\)
\(594\) 0 0
\(595\) 45602.2 6461.10i 3.14203 0.445175i
\(596\) −2324.09 −0.159729
\(597\) 0 0
\(598\) −1.40915 2.44072i −9.63621e−5 0.000166904i
\(599\) 11632.4 + 20147.9i 0.793469 + 1.37433i 0.923807 + 0.382859i \(0.125060\pi\)
−0.130338 + 0.991470i \(0.541606\pi\)
\(600\) 0 0
\(601\) 25322.3 1.71867 0.859334 0.511416i \(-0.170879\pi\)
0.859334 + 0.511416i \(0.170879\pi\)
\(602\) −3065.71 + 7612.45i −0.207556 + 0.515382i
\(603\) 0 0
\(604\) 1230.78 2131.77i 0.0829135 0.143610i
\(605\) −11471.7 19869.6i −0.770897 1.33523i
\(606\) 0 0
\(607\) 10867.2 18822.5i 0.726665 1.25862i −0.231620 0.972806i \(-0.574403\pi\)
0.958285 0.285814i \(-0.0922639\pi\)
\(608\) 1072.36 0.0715297
\(609\) 0 0
\(610\) 1610.77 0.106915
\(611\) 549.420 951.624i 0.0363784 0.0630092i
\(612\) 0 0
\(613\) 6786.19 + 11754.0i 0.447131 + 0.774454i 0.998198 0.0600072i \(-0.0191124\pi\)
−0.551067 + 0.834461i \(0.685779\pi\)
\(614\) 7041.50 12196.2i 0.462820 0.801628i
\(615\) 0 0
\(616\) 1385.11 + 1768.76i 0.0905966 + 0.115691i
\(617\) 8497.12 0.554427 0.277213 0.960808i \(-0.410589\pi\)
0.277213 + 0.960808i \(0.410589\pi\)
\(618\) 0 0
\(619\) 11491.5 + 19903.8i 0.746173 + 1.29241i 0.949645 + 0.313329i \(0.101444\pi\)
−0.203472 + 0.979081i \(0.565223\pi\)
\(620\) −9306.93 16120.1i −0.602863 1.04419i
\(621\) 0 0
\(622\) −5371.98 −0.346297
\(623\) 2650.91 6582.46i 0.170476 0.423308i
\(624\) 0 0
\(625\) −20661.3 + 35786.4i −1.32232 + 2.29033i
\(626\) 2219.19 + 3843.75i 0.141688 + 0.245411i
\(627\) 0 0
\(628\) 613.864 1063.24i 0.0390061 0.0675605i
\(629\) 20114.3 1.27505
\(630\) 0 0
\(631\) −15717.9 −0.991635 −0.495817 0.868427i \(-0.665131\pi\)
−0.495817 + 0.868427i \(0.665131\pi\)
\(632\) −465.212 + 805.771i −0.0292803 + 0.0507150i
\(633\) 0 0
\(634\) −2221.26 3847.34i −0.139144 0.241005i
\(635\) −1876.13 + 3249.55i −0.117247 + 0.203078i
\(636\) 0 0
\(637\) 712.669 206.084i 0.0443280 0.0128185i
\(638\) 4949.42 0.307131
\(639\) 0 0
\(640\) −1333.58 2309.82i −0.0823660 0.142662i
\(641\) 14553.7 + 25207.7i 0.896780 + 1.55327i 0.831587 + 0.555395i \(0.187433\pi\)
0.0651930 + 0.997873i \(0.479234\pi\)
\(642\) 0 0
\(643\) −3112.26 −0.190880 −0.0954398 0.995435i \(-0.530426\pi\)
−0.0954398 + 0.995435i \(0.530426\pi\)
\(644\) 47.7878 6.77076i 0.00292407 0.000414294i
\(645\) 0 0
\(646\) −3999.53 + 6927.39i −0.243590 + 0.421911i
\(647\) −3928.80 6804.87i −0.238728 0.413489i 0.721622 0.692288i \(-0.243397\pi\)
−0.960349 + 0.278799i \(0.910064\pi\)
\(648\) 0 0
\(649\) −3449.01 + 5973.86i −0.208606 + 0.361317i
\(650\) −1337.46 −0.0807071
\(651\) 0 0
\(652\) 14058.0 0.844408
\(653\) −9761.01 + 16906.6i −0.584958 + 1.01318i 0.409923 + 0.912120i \(0.365556\pi\)
−0.994881 + 0.101057i \(0.967778\pi\)
\(654\) 0 0
\(655\) −2269.79 3931.38i −0.135401 0.234522i
\(656\) −2584.18 + 4475.93i −0.153804 + 0.266396i
\(657\) 0 0
\(658\) 11602.3 + 14816.0i 0.687393 + 0.877793i
\(659\) −664.061 −0.0392536 −0.0196268 0.999807i \(-0.506248\pi\)
−0.0196268 + 0.999807i \(0.506248\pi\)
\(660\) 0 0
\(661\) −7960.82 13788.5i −0.468442 0.811365i 0.530908 0.847430i \(-0.321851\pi\)
−0.999349 + 0.0360650i \(0.988518\pi\)
\(662\) 4154.06 + 7195.04i 0.243885 + 0.422422i
\(663\) 0 0
\(664\) −4551.42 −0.266008
\(665\) 7973.36 + 10181.9i 0.464953 + 0.593739i
\(666\) 0 0
\(667\) 53.1665 92.0870i 0.00308638 0.00534576i
\(668\) 2246.61 + 3891.24i 0.130125 + 0.225384i
\(669\) 0 0
\(670\) −2954.53 + 5117.40i −0.170363 + 0.295078i
\(671\) −586.068 −0.0337182
\(672\) 0 0
\(673\) 24631.0 1.41078 0.705391 0.708819i \(-0.250771\pi\)
0.705391 + 0.708819i \(0.250771\pi\)
\(674\) −254.167 + 440.230i −0.0145254 + 0.0251588i
\(675\) 0 0
\(676\) 4384.64 + 7594.43i 0.249468 + 0.432091i
\(677\) 8546.39 14802.8i 0.485177 0.840350i −0.514678 0.857383i \(-0.672089\pi\)
0.999855 + 0.0170329i \(0.00542200\pi\)
\(678\) 0 0
\(679\) −6137.45 + 869.578i −0.346883 + 0.0491478i
\(680\) 19895.0 1.12197
\(681\) 0 0
\(682\) 3386.26 + 5865.18i 0.190127 + 0.329310i
\(683\) −9581.79 16596.1i −0.536804 0.929771i −0.999074 0.0430322i \(-0.986298\pi\)
0.462270 0.886739i \(-0.347035\pi\)
\(684\) 0 0
\(685\) −54215.2 −3.02402
\(686\) −1285.53 + 12639.7i −0.0715478 + 0.703478i
\(687\) 0 0
\(688\) −1772.45 + 3069.98i −0.0982183 + 0.170119i
\(689\) −190.886 330.625i −0.0105547 0.0182813i
\(690\) 0 0
\(691\) −4047.94 + 7011.23i −0.222852 + 0.385991i −0.955673 0.294431i \(-0.904870\pi\)
0.732821 + 0.680422i \(0.238203\pi\)
\(692\) −6122.39 −0.336327
\(693\) 0 0
\(694\) −12449.3 −0.680934
\(695\) −27625.3 + 47848.5i −1.50775 + 2.61150i
\(696\) 0 0
\(697\) −19276.1 33387.2i −1.04754 1.81439i
\(698\) 9732.21 16856.7i 0.527750 0.914090i
\(699\) 0 0
\(700\) 8556.48 21246.6i 0.462006 1.14721i
\(701\) −12354.7 −0.665664 −0.332832 0.942986i \(-0.608004\pi\)
−0.332832 + 0.942986i \(0.608004\pi\)
\(702\) 0 0
\(703\) 2823.90 + 4891.14i 0.151501 + 0.262408i
\(704\) 485.212 + 840.412i 0.0259760 + 0.0449918i
\(705\) 0 0
\(706\) 2851.23 0.151993
\(707\) 168.337 + 214.965i 0.00895470 + 0.0114350i
\(708\) 0 0
\(709\) −1914.41 + 3315.85i −0.101406 + 0.175641i −0.912264 0.409602i \(-0.865668\pi\)
0.810858 + 0.585243i \(0.199001\pi\)
\(710\) 12559.4 + 21753.5i 0.663868 + 1.14985i
\(711\) 0 0
\(712\) 1532.64 2654.60i 0.0806713 0.139727i
\(713\) 145.500 0.00764241
\(714\) 0 0
\(715\) 683.363 0.0357431
\(716\) 6826.86 11824.5i 0.356329 0.617181i
\(717\) 0 0
\(718\) 5766.49 + 9987.86i 0.299726 + 0.519141i
\(719\) 611.500 1059.15i 0.0317178 0.0549368i −0.849731 0.527217i \(-0.823236\pi\)
0.881449 + 0.472280i \(0.156569\pi\)
\(720\) 0 0
\(721\) −5821.42 + 14455.1i −0.300695 + 0.746654i
\(722\) 11472.0 0.591333
\(723\) 0 0
\(724\) −2573.42 4457.29i −0.132100 0.228804i
\(725\) −25230.8 43701.1i −1.29248 2.23864i
\(726\) 0 0
\(727\) 6368.21 0.324875 0.162437 0.986719i \(-0.448064\pi\)
0.162437 + 0.986719i \(0.448064\pi\)
\(728\) 317.288 44.9546i 0.0161531 0.00228864i
\(729\) 0 0
\(730\) 22968.7 39783.0i 1.16454 2.01704i
\(731\) −13221.2 22899.9i −0.668954 1.15866i
\(732\) 0 0
\(733\) 12577.0 21784.0i 0.633753 1.09769i −0.353024 0.935614i \(-0.614847\pi\)
0.986778 0.162079i \(-0.0518199\pi\)
\(734\) −23090.7 −1.16116
\(735\) 0 0
\(736\) 20.8485 0.00104414
\(737\) 1074.98 1861.93i 0.0537281 0.0930597i
\(738\) 0 0
\(739\) 5369.55 + 9300.34i 0.267283 + 0.462948i 0.968159 0.250335i \(-0.0805408\pi\)
−0.700876 + 0.713283i \(0.747207\pi\)
\(740\) 7023.53 12165.1i 0.348906 0.604322i
\(741\) 0 0
\(742\) 6473.42 917.180i 0.320279 0.0453783i
\(743\) −28166.3 −1.39074 −0.695370 0.718652i \(-0.744760\pi\)
−0.695370 + 0.718652i \(0.744760\pi\)
\(744\) 0 0
\(745\) −6053.42 10484.8i −0.297691 0.515617i
\(746\) −6479.57 11222.9i −0.318008 0.550806i
\(747\) 0 0
\(748\) −7238.67 −0.353839
\(749\) 4951.41 12294.8i 0.241549 0.599791i
\(750\) 0 0
\(751\) −14328.5 + 24817.7i −0.696211 + 1.20587i 0.273559 + 0.961855i \(0.411799\pi\)
−0.969771 + 0.244018i \(0.921534\pi\)
\(752\) 4064.36 + 7039.68i 0.197091 + 0.341371i
\(753\) 0 0
\(754\) 353.000 611.414i 0.0170497 0.0295310i
\(755\) 12823.0 0.618113
\(756\) 0 0
\(757\) −23604.1 −1.13330 −0.566648 0.823960i \(-0.691760\pi\)
−0.566648 + 0.823960i \(0.691760\pi\)
\(758\) 611.996 1060.01i 0.0293255 0.0507932i
\(759\) 0 0
\(760\) 2793.12 + 4837.83i 0.133312 + 0.230903i
\(761\) 2315.48 4010.54i 0.110297 0.191041i −0.805593 0.592470i \(-0.798153\pi\)
0.915890 + 0.401429i \(0.131486\pi\)
\(762\) 0 0
\(763\) 6851.35 + 8749.10i 0.325079 + 0.415123i
\(764\) −4221.18 −0.199891
\(765\) 0 0
\(766\) −4360.81 7553.15i −0.205695 0.356274i
\(767\) 491.977 + 852.129i 0.0231607 + 0.0401155i
\(768\) 0 0
\(769\) 33276.8 1.56046 0.780228 0.625495i \(-0.215103\pi\)
0.780228 + 0.625495i \(0.215103\pi\)
\(770\) −4371.85 + 10855.7i −0.204611 + 0.508069i
\(771\) 0 0
\(772\) 9541.68 16526.7i 0.444835 0.770477i
\(773\) −11469.4 19865.6i −0.533668 0.924340i −0.999227 0.0393231i \(-0.987480\pi\)
0.465558 0.885017i \(-0.345853\pi\)
\(774\) 0 0
\(775\) 34524.6 59798.3i 1.60020 2.77164i
\(776\) −2677.61 −0.123867
\(777\) 0 0
\(778\) −26293.8 −1.21167
\(779\) 5412.47 9374.67i 0.248937 0.431171i
\(780\) 0 0
\(781\) −4569.66 7914.88i −0.209366 0.362633i
\(782\) −77.7575 + 134.680i −0.00355576 + 0.00615876i
\(783\) 0 0
\(784\) −1315.73 + 5327.95i −0.0599366 + 0.242709i
\(785\) 6395.58 0.290787
\(786\) 0 0
\(787\) 67