Properties

Label 126.4.g.g.109.2
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 109.2
Root \(9.41856 + 16.3134i\) of defining polynomial
Character \(\chi\) \(=\) 126.109
Dual form 126.4.g.g.37.2

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

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

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
\(5\) 10.4186 + 18.0455i 0.931864 + 1.61404i 0.780132 + 0.625615i \(0.215152\pi\)
0.151732 + 0.988422i \(0.451515\pi\)
\(6\) 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 −0.743216 0.669052i \(-0.766700\pi\)
0.951024 + 0.309118i \(0.100034\pi\)
\(12\) 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 0.0286202 + 0.999590i \(0.490889\pi\)
−0.879981 + 0.475009i \(0.842445\pi\)
\(18\) 0 0
\(19\) 16.7557 + 29.0217i 0.202317 + 0.350423i 0.949274 0.314449i \(-0.101820\pi\)
−0.746958 + 0.664871i \(0.768486\pi\)
\(20\) −83.3485 −0.931864
\(21\) 0 0
\(22\) 30.3258 0.293885
\(23\) 0.325758 + 0.564230i 0.00295327 + 0.00511522i 0.867498 0.497440i \(-0.165727\pi\)
−0.864545 + 0.502555i \(0.832393\pi\)
\(24\) 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 −0.336906 0.941538i \(-0.609380\pi\)
0.983849 0.179000i \(-0.0572863\pi\)
\(32\) 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 0.615823 0.787885i \(-0.288824\pi\)
−0.990240 + 0.139376i \(0.955490\pi\)
\(38\) −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 0.926970 + 0.375136i \(0.122404\pi\)
−0.138608 + 0.990347i \(0.544263\pi\)
\(48\) 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 −0.957433 0.288656i \(-0.906792\pi\)
0.728700 + 0.684833i \(0.240125\pi\)
\(54\) 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 −0.498077 0.867133i \(-0.665960\pi\)
0.999998 0.00221868i \(-0.000706227\pi\)
\(60\) 0 0
\(61\) −19.3258 33.4732i −0.0405641 0.0702591i 0.845031 0.534718i \(-0.179582\pi\)
−0.885595 + 0.464459i \(0.846249\pi\)
\(62\) 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 −0.923395 0.383851i \(-0.874598\pi\)
0.794122 + 0.607758i \(0.207931\pi\)
\(68\) −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 0.0364183 0.999337i \(-0.488405\pi\)
0.847242 0.531207i \(-0.178262\pi\)
\(74\) 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 0.904459 0.426561i \(-0.140275\pi\)
−0.821642 + 0.570004i \(0.806942\pi\)
\(80\) 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 0.729094 0.684414i \(-0.239942\pi\)
−0.957267 + 0.289207i \(0.906608\pi\)
\(90\) 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 −0.869634 0.493698i \(-0.835645\pi\)
0.862372 + 0.506276i \(0.168978\pi\)
\(102\) 0 0
\(103\) 420.710 + 728.691i 0.402464 + 0.697088i 0.994023 0.109174i \(-0.0348205\pi\)
−0.591559 + 0.806262i \(0.701487\pi\)
\(104\) −17.3030 −0.0163144
\(105\) 0 0
\(106\) −353.023 −0.323477
\(107\) −357.835 619.789i −0.323301 0.559974i 0.657866 0.753135i \(-0.271459\pi\)
−0.981167 + 0.193161i \(0.938126\pi\)
\(108\) 0 0
\(109\) −300.009 + 519.632i −0.263630 + 0.456621i −0.967204 0.254001i \(-0.918253\pi\)
0.703574 + 0.710622i \(0.251587\pi\)
\(110\) 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 0.900062 0.435761i \(-0.143521\pi\)
−0.827411 + 0.561596i \(0.810187\pi\)
\(132\) 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 0.100683 + 0.994919i \(0.467897\pi\)
−0.911966 + 0.410265i \(0.865436\pi\)
\(138\) 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 0.934771 0.355251i \(-0.115605\pi\)
−0.775042 + 0.631910i \(0.782271\pi\)
\(150\) 0 0
\(151\) 307.695 532.943i 0.165827 0.287221i −0.771122 0.636688i \(-0.780304\pi\)
0.936949 + 0.349467i \(0.113637\pi\)
\(152\) −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 −0.824380 0.566037i \(-0.808476\pi\)
0.902392 + 0.430916i \(0.141809\pi\)
\(158\) −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 −0.886135 0.463428i \(-0.846619\pi\)
0.0417271 0.999129i \(-0.486714\pi\)
\(164\) −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 0.983739 0.179605i \(-0.0574818\pi\)
−0.647412 + 0.762141i \(0.724148\pi\)
\(174\) 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 −0.251197 0.967936i \(-0.580824\pi\)
0.963856 0.266425i \(-0.0858426\pi\)
\(180\) 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 0.948493 0.316798i \(-0.102608\pi\)
−0.748602 + 0.663020i \(0.769274\pi\)
\(192\) 0 0
\(193\) 2385.42 4131.67i 0.889670 1.54095i 0.0494044 0.998779i \(-0.484268\pi\)
0.840266 0.542175i \(-0.182399\pi\)
\(194\) 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 −0.354759 0.934958i \(-0.615437\pi\)
0.987077 0.160249i \(-0.0512296\pi\)
\(200\) 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 −0.384780 0.923008i \(-0.625723\pi\)
0.991739 0.128274i \(-0.0409438\pi\)
\(228\) 0 0
\(229\) −2131.82 3692.41i −0.615172 1.06551i −0.990354 0.138558i \(-0.955753\pi\)
0.375182 0.926951i \(-0.377580\pi\)
\(230\) −27.1515 −0.00778398
\(231\) 0 0
\(232\) −1305.67 −0.369488
\(233\) 1524.95 + 2641.29i 0.428768 + 0.742647i 0.996764 0.0803838i \(-0.0256146\pi\)
−0.567996 + 0.823031i \(0.692281\pi\)
\(234\) 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 −0.821263 0.570550i \(-0.806730\pi\)
0.904742 + 0.425959i \(0.140063\pi\)
\(242\) −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 0.601126 0.799154i \(-0.294719\pi\)
−0.992651 + 0.121013i \(0.961386\pi\)
\(258\) 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 −0.610148 0.792288i \(-0.708890\pi\)
0.991215 + 0.132260i \(0.0422233\pi\)
\(264\) 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 −0.660271 0.751027i \(-0.729559\pi\)
0.980544 + 0.196298i \(0.0628921\pi\)
\(270\) 0 0
\(271\) 1198.38 + 2075.66i 0.268622 + 0.465268i 0.968506 0.248989i \(-0.0800983\pi\)
−0.699884 + 0.714257i \(0.746765\pi\)
\(272\) 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 −0.947697 0.319170i \(-0.896596\pi\)
0.750258 + 0.661145i \(0.229929\pi\)
\(278\) −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 −0.968426 0.249300i \(-0.919800\pi\)
0.700113 + 0.714032i \(0.253133\pi\)
\(284\) 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 −0.962095 0.272715i \(-0.912078\pi\)
0.717226 + 0.696841i \(0.245412\pi\)
\(312\) 0 0
\(313\) −1109.59 1921.87i −0.200377 0.347063i 0.748273 0.663391i \(-0.230883\pi\)
−0.948650 + 0.316328i \(0.897550\pi\)
\(314\) 613.864 0.110326
\(315\) 0 0
\(316\) −465.212 −0.0828172
\(317\) 1110.63 + 1923.67i 0.196780 + 0.340833i 0.947483 0.319807i \(-0.103618\pi\)
−0.750703 + 0.660640i \(0.770285\pi\)
\(318\) 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 0.640431 0.768016i \(-0.278756\pi\)
−0.985337 + 0.170622i \(0.945422\pi\)
\(332\) −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 −0.999774 0.0212401i \(-0.993239\pi\)
0.518282 + 0.855210i \(0.326572\pi\)
\(348\) 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 −0.807271 0.590180i \(-0.799057\pi\)
0.914747 + 0.404027i \(0.132390\pi\)
\(354\) 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 0.572438 0.819948i \(-0.305998\pi\)
−0.996315 + 0.0857714i \(0.972665\pi\)
\(360\) 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 0.0838244 + 0.996481i \(0.473287\pi\)
−0.904890 + 0.425646i \(0.860047\pi\)
\(368\) 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 0.998368 0.0571033i \(-0.0181864\pi\)
−0.548637 + 0.836061i \(0.684853\pi\)
\(374\) −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 0.974022 0.226453i \(-0.0727130\pi\)
−0.683125 + 0.730301i \(0.739380\pi\)
\(384\) 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 0.0182021 + 0.999834i \(0.494206\pi\)
−0.874983 + 0.484154i \(0.839128\pi\)
\(390\) 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 0.999119 + 0.0419565i \(0.0133591\pi\)
−0.463224 + 0.886241i \(0.653308\pi\)
\(398\) 7100.27 0.894232
\(399\) 0 0
\(400\) 4946.97 0.618371
\(401\) 1401.50 + 2427.47i 0.174533 + 0.302299i 0.939999 0.341176i \(-0.110825\pi\)
−0.765467 + 0.643475i \(0.777492\pi\)
\(402\) 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 −0.605919 0.795526i \(-0.707194\pi\)
0.991906 + 0.126978i \(0.0405278\pi\)
\(410\) −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 −0.601836 0.798620i \(-0.705564\pi\)
0.992543 + 0.121895i \(0.0388972\pi\)
\(432\) 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 −0.999909 0.0135008i \(-0.995702\pi\)
0.488262 0.872697i \(-0.337631\pi\)
\(440\) −2527.61 −0.273861
\(441\) 0 0
\(442\) −516.273 −0.0555579
\(443\) −3129.09 5419.74i −0.335593 0.581263i 0.648006 0.761635i \(-0.275603\pi\)
−0.983598 + 0.180372i \(0.942270\pi\)
\(444\) 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 0.977709 + 0.209963i \(0.0673343\pi\)
−0.307022 + 0.951703i \(0.599332\pi\)
\(458\) 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 0.936239 + 0.351363i \(0.114282\pi\)
−0.163830 + 0.986489i \(0.552385\pi\)
\(468\) 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 −0.994108 0.108391i \(-0.965430\pi\)
0.590924 + 0.806727i \(0.298763\pi\)
\(480\) 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 −0.757507 0.652827i \(-0.773583\pi\)
0.944118 + 0.329607i \(0.106916\pi\)
\(488\) 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 0.940876 0.338751i \(-0.110005\pi\)
−0.763805 + 0.645447i \(0.776671\pi\)
\(500\) 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 0.984605 0.174794i \(-0.0559259\pi\)
−0.643679 + 0.765296i \(0.722593\pi\)
\(510\) 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 −0.963075 0.269232i \(-0.913230\pi\)
0.714700 + 0.699431i \(0.246563\pi\)
\(522\) 0 0
\(523\) −3954.03 6848.58i −0.330588 0.572595i 0.652039 0.758185i \(-0.273914\pi\)
−0.982627 + 0.185590i \(0.940580\pi\)
\(524\) −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 0.933640 0.358214i \(-0.116614\pi\)
−0.777042 + 0.629449i \(0.783281\pi\)
\(542\) −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 −0.0177556 0.999842i \(-0.505652\pi\)
0.874767 0.484544i \(-0.161015\pi\)
\(558\) 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 0.0165446 0.999863i \(-0.494733\pi\)
0.857635 0.514260i \(-0.171933\pi\)
\(564\) 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 −0.937852 0.347036i \(-0.887188\pi\)
0.168384 0.985721i \(-0.446145\pi\)
\(570\) 0 0
\(571\) −11872.6 + 20564.0i −0.870147 + 1.50714i −0.00830301 + 0.999966i \(0.502643\pi\)
−0.861844 + 0.507173i \(0.830690\pi\)
\(572\) 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 −0.906895 0.421356i \(-0.861554\pi\)
0.818353 + 0.574716i \(0.194887\pi\)
\(578\) 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 0.993890 + 0.110375i \(0.0352053\pi\)
−0.401357 + 0.915922i \(0.631461\pi\)
\(594\) 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 −0.130338 0.991470i \(-0.541606\pi\)
0.923807 0.382859i \(-0.125060\pi\)
\(600\) 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 0.958285 + 0.285814i \(0.0922639\pi\)
−0.231620 + 0.972806i \(0.574403\pi\)
\(608\) 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 −0.551067 0.834461i \(-0.685779\pi\)
0.998198 + 0.0600072i \(0.0191124\pi\)
\(614\) 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 −0.203472 0.979081i \(-0.565223\pi\)
0.949645 0.313329i \(-0.101444\pi\)
\(620\) −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 0.0651930 0.997873i \(-0.479234\pi\)
0.831587 0.555395i \(-0.187433\pi\)
\(642\) 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 −0.960349 0.278799i \(-0.910064\pi\)
0.721622 + 0.692288i \(0.243397\pi\)
\(648\) 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 −0.994881 0.101057i \(-0.967778\pi\)
0.409923 0.912120i \(-0.365556\pi\)
\(654\) 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 −0.999349 0.0360650i \(-0.988518\pi\)
0.530908 + 0.847430i \(0.321851\pi\)
\(662\) 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 0.999855 0.0170329i \(-0.00542200\pi\)
−0.514678 + 0.857383i \(0.672089\pi\)
\(678\) 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 0.462270 + 0.886739i \(0.347035\pi\)
−0.999074 + 0.0430322i \(0.986298\pi\)
\(684\) 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 0.732821 0.680422i \(-0.238203\pi\)
−0.955673 + 0.294431i \(0.904870\pi\)
\(692\) −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 0.810858 0.585243i \(-0.199001\pi\)
−0.912264 + 0.409602i \(0.865668\pi\)
\(710\) 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 0.881449 0.472280i \(-0.156569\pi\)
−0.849731 + 0.527217i \(0.823236\pi\)
\(720\) 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 0.986778 + 0.162079i \(0.0518199\pi\)
−0.353024 + 0.935614i \(0.614847\pi\)
\(734\) −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 −0.700876 0.713283i \(-0.747207\pi\)
0.968159 + 0.250335i \(0.0805408\pi\)
\(740\) 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 −0.969771 0.244018i \(-0.921534\pi\)
0.273559 0.961855i \(-0.411799\pi\)
\(752\) 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 0.915890 0.401429i \(-0.131486\pi\)
−0.805593 + 0.592470i \(0.798153\pi\)
\(762\) 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 0.465558 + 0.885017i \(0.345853\pi\)
−0.999227 + 0.0393231i \(0.987480\pi\)
\(774\) 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