Properties

Label 294.4.e.l.67.2
Level $294$
Weight $4$
Character 294.67
Analytic conductor $17.347$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3465615417\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(9.41856 + 16.3134i\) of defining polynomial
Character \(\chi\) \(=\) 294.67
Dual form 294.4.e.l.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(10.4186 + 18.0455i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(10.4186 + 18.0455i) q^{5} -6.00000 q^{6} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(20.8371 - 36.0910i) q^{10} +(-7.58144 + 13.1314i) q^{11} +(6.00000 + 10.3923i) q^{12} -2.16288 q^{13} +62.5114 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-59.6742 + 103.359i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(-16.7557 - 29.0217i) q^{19} -83.3485 q^{20} +30.3258 q^{22} +(-0.325758 - 0.564230i) q^{23} +(12.0000 - 20.7846i) q^{24} +(-154.593 + 267.763i) q^{25} +(2.16288 + 3.74622i) q^{26} -27.0000 q^{27} -163.208 q^{29} +(-62.5114 - 108.273i) q^{30} +(-111.663 + 193.406i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(22.7443 + 39.3943i) q^{33} +238.697 q^{34} +36.0000 q^{36} +(-84.2670 - 145.955i) q^{37} +(-33.5114 + 58.0434i) q^{38} +(-3.24432 + 5.61932i) q^{39} +(83.3485 + 144.364i) q^{40} +323.023 q^{41} +221.557 q^{43} +(-30.3258 - 52.5258i) q^{44} +(93.7670 - 162.409i) q^{45} +(-0.651517 + 1.12846i) q^{46} +(254.023 + 439.980i) q^{47} -48.0000 q^{48} +618.371 q^{50} +(179.023 + 310.076i) q^{51} +(4.32576 - 7.49243i) q^{52} +(88.2557 - 152.863i) q^{53} +(27.0000 + 46.7654i) q^{54} -315.951 q^{55} -100.534 q^{57} +(163.208 + 282.685i) q^{58} +(227.464 - 393.979i) q^{59} +(-125.023 + 216.546i) q^{60} +(19.3258 + 33.4732i) q^{61} +446.652 q^{62} +64.0000 q^{64} +(-22.5341 - 39.0302i) q^{65} +(45.4886 - 78.7886i) q^{66} +(-70.8958 + 122.795i) q^{67} +(-238.697 - 413.435i) q^{68} -1.95455 q^{69} +602.742 q^{71} +(-36.0000 - 62.3538i) q^{72} +(-551.150 + 954.619i) q^{73} +(-168.534 + 291.910i) q^{74} +(463.778 + 803.288i) q^{75} +134.045 q^{76} +12.9773 q^{78} +(58.1515 + 100.721i) q^{79} +(166.697 - 288.728i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-323.023 - 559.492i) q^{82} +568.928 q^{83} -2486.88 q^{85} +(-221.557 - 383.748i) q^{86} +(-244.812 + 424.028i) q^{87} +(-60.6515 + 105.052i) q^{88} +(-191.580 - 331.825i) q^{89} -375.068 q^{90} +2.60607 q^{92} +(334.989 + 580.217i) q^{93} +(508.045 - 879.961i) q^{94} +(349.140 - 604.728i) q^{95} +(48.0000 + 83.1384i) q^{96} -334.701 q^{97} +136.466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} + 6q^{3} - 8q^{4} + 5q^{5} - 24q^{6} + 32q^{8} - 18q^{9} + O(q^{10}) \) \( 4q - 4q^{2} + 6q^{3} - 8q^{4} + 5q^{5} - 24q^{6} + 32q^{8} - 18q^{9} + 10q^{10} - 67q^{11} + 24q^{12} - 82q^{13} + 30q^{15} - 32q^{16} - 92q^{17} - 36q^{18} + 43q^{19} - 40q^{20} + 268q^{22} - 148q^{23} + 48q^{24} - 435q^{25} + 82q^{26} - 108q^{27} + 154q^{29} - 30q^{30} - 520q^{31} - 64q^{32} + 201q^{33} + 368q^{34} + 144q^{36} - 7q^{37} + 86q^{38} - 123q^{39} + 40q^{40} + 852q^{41} - 214q^{43} - 268q^{44} + 45q^{45} - 296q^{46} + 576q^{47} - 192q^{48} + 1740q^{50} + 276q^{51} + 164q^{52} + 243q^{53} + 108q^{54} + 1010q^{55} + 258q^{57} - 154q^{58} - 7q^{59} - 60q^{60} + 224q^{61} + 2080q^{62} + 256q^{64} + 570q^{65} + 402q^{66} - 687q^{67} - 368q^{68} - 888q^{69} + 944q^{71} - 144q^{72} - 921q^{73} - 14q^{74} + 1305q^{75} - 344q^{76} + 492q^{78} + 526q^{79} + 80q^{80} - 162q^{81} - 852q^{82} + 442q^{83} - 5840q^{85} + 214q^{86} + 231q^{87} - 536q^{88} + 774q^{89} - 180q^{90} + 1184q^{92} + 1560q^{93} + 1152q^{94} + 1910q^{95} + 192q^{96} - 3906q^{97} + 1206q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 1.50000 2.59808i 0.288675 0.500000i
\(4\) −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 \(0.451515\pi\)
\(6\) −6.00000 −0.408248
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 20.8371 36.0910i 0.658928 1.14130i
\(11\) −7.58144 + 13.1314i −0.207808 + 0.359934i −0.951024 0.309118i \(-0.899966\pi\)
0.743216 + 0.669052i \(0.233300\pi\)
\(12\) 6.00000 + 10.3923i 0.144338 + 0.250000i
\(13\) −2.16288 −0.0461442 −0.0230721 0.999734i \(-0.507345\pi\)
−0.0230721 + 0.999734i \(0.507345\pi\)
\(14\) 0 0
\(15\) 62.5114 1.07602
\(16\) −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 \(0.842445\pi\)
\(18\) −9.00000 + 15.5885i −0.117851 + 0.204124i
\(19\) −16.7557 29.0217i −0.202317 0.350423i 0.746958 0.664871i \(-0.231514\pi\)
−0.949274 + 0.314449i \(0.898180\pi\)
\(20\) −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 \(-0.167607\pi\)
−0.867498 + 0.497440i \(0.834273\pi\)
\(24\) 12.0000 20.7846i 0.102062 0.176777i
\(25\) −154.593 + 267.763i −1.23674 + 2.14210i
\(26\) 2.16288 + 3.74622i 0.0163144 + 0.0282574i
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −163.208 −1.04507 −0.522535 0.852618i \(-0.675014\pi\)
−0.522535 + 0.852618i \(0.675014\pi\)
\(30\) −62.5114 108.273i −0.380432 0.658928i
\(31\) −111.663 + 193.406i −0.646943 + 1.12054i 0.336906 + 0.941538i \(0.390620\pi\)
−0.983849 + 0.179000i \(0.942714\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 22.7443 + 39.3943i 0.119978 + 0.207808i
\(34\) 238.697 1.20401
\(35\) 0 0
\(36\) 36.0000 0.166667
\(37\) −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
\(39\) −3.24432 + 5.61932i −0.0133207 + 0.0230721i
\(40\) 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
\(45\) 93.7670 162.409i 0.310621 0.538012i
\(46\) −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 \(0.544263\pi\)
\(48\) −48.0000 −0.144338
\(49\) 0 0
\(50\) 618.371 1.74902
\(51\) 179.023 + 310.076i 0.491533 + 0.851361i
\(52\) 4.32576 7.49243i 0.0115361 0.0199810i
\(53\) 88.2557 152.863i 0.228733 0.396177i −0.728700 0.684833i \(-0.759875\pi\)
0.957433 + 0.288656i \(0.0932084\pi\)
\(54\) 27.0000 + 46.7654i 0.0680414 + 0.117851i
\(55\) −315.951 −0.774596
\(56\) 0 0
\(57\) −100.534 −0.233615
\(58\) 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 \(-0.000706227\pi\)
\(60\) −125.023 + 216.546i −0.269006 + 0.465932i
\(61\) 19.3258 + 33.4732i 0.0405641 + 0.0702591i 0.885595 0.464459i \(-0.153751\pi\)
−0.845031 + 0.534718i \(0.820418\pi\)
\(62\) 446.652 0.914916
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −22.5341 39.0302i −0.0430001 0.0744784i
\(66\) 45.4886 78.7886i 0.0848373 0.146943i
\(67\) −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
\(69\) −1.95455 −0.00341015
\(70\) 0 0
\(71\) 602.742 1.00750 0.503749 0.863850i \(-0.331954\pi\)
0.503749 + 0.863850i \(0.331954\pi\)
\(72\) −36.0000 62.3538i −0.0589256 0.102062i
\(73\) −551.150 + 954.619i −0.883660 + 1.53054i −0.0364183 + 0.999337i \(0.511595\pi\)
−0.847242 + 0.531207i \(0.821738\pi\)
\(74\) −168.534 + 291.910i −0.264753 + 0.458565i
\(75\) 463.778 + 803.288i 0.714034 + 1.23674i
\(76\) 134.045 0.202317
\(77\) 0 0
\(78\) 12.9773 0.0188383
\(79\) 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
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) −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
\(87\) −244.812 + 424.028i −0.301686 + 0.522535i
\(88\) −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 \(0.906608\pi\)
\(90\) −375.068 −0.439285
\(91\) 0 0
\(92\) 2.60607 0.00295327
\(93\) 334.989 + 580.217i 0.373513 + 0.646943i
\(94\) 508.045 879.961i 0.557456 0.965543i
\(95\) 349.140 604.728i 0.377063 0.653093i
\(96\) 48.0000 + 83.1384i 0.0510310 + 0.0883883i
\(97\) −334.701 −0.350348 −0.175174 0.984538i \(-0.556049\pi\)
−0.175174 + 0.984538i \(0.556049\pi\)
\(98\) 0 0
\(99\) 136.466 0.138539
\(100\) −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 \(0.168978\pi\)
\(102\) 358.045 620.153i 0.347566 0.602003i
\(103\) −420.710 728.691i −0.402464 0.697088i 0.591559 0.806262i \(-0.298513\pi\)
−0.994023 + 0.109174i \(0.965180\pi\)
\(104\) −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 \(-0.0618739\pi\)
−0.657866 + 0.753135i \(0.728541\pi\)
\(108\) 54.0000 93.5307i 0.0481125 0.0833333i
\(109\) −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
\(111\) −505.602 −0.432339
\(112\) 0 0
\(113\) 622.644 0.518349 0.259174 0.965831i \(-0.416550\pi\)
0.259174 + 0.965831i \(0.416550\pi\)
\(114\) 100.534 + 174.130i 0.0825954 + 0.143059i
\(115\) 6.78787 11.7569i 0.00550410 0.00953339i
\(116\) 326.417 565.370i 0.261267 0.452529i
\(117\) 9.73296 + 16.8580i 0.00769070 + 0.0133207i
\(118\) −909.856 −0.709822
\(119\) 0 0
\(120\) 500.091 0.380432
\(121\) 550.544 + 953.569i 0.413632 + 0.716431i
\(122\) 38.6515 66.9464i 0.0286831 0.0496807i
\(123\) 484.534 839.238i 0.355195 0.615216i
\(124\) −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
\(129\) 332.335 575.621i 0.226825 0.392873i
\(130\) −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 \(0.810187\pi\)
\(132\) −181.955 −0.119978
\(133\) 0 0
\(134\) 283.583 0.182820
\(135\) −281.301 487.228i −0.179337 0.310621i
\(136\) −477.394 + 826.871i −0.301001 + 0.521350i
\(137\) 1300.93 2253.27i 0.811283 1.40518i −0.100683 0.994919i \(-0.532103\pi\)
0.911966 0.410265i \(-0.134564\pi\)
\(138\) 1.95455 + 3.38538i 0.00120567 + 0.00208828i
\(139\) 2651.55 1.61800 0.808998 0.587811i \(-0.200010\pi\)
0.808998 + 0.587811i \(0.200010\pi\)
\(140\) 0 0
\(141\) 1524.14 0.910322
\(142\) −602.742 1043.98i −0.356204 0.616964i
\(143\) 16.3977 28.4017i 0.00958914 0.0166089i
\(144\) −72.0000 + 124.708i −0.0416667 + 0.0721688i
\(145\) −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 \(-0.217729\pi\)
−0.934771 + 0.355251i \(0.884395\pi\)
\(150\) 927.557 1606.58i 0.504898 0.874509i
\(151\) 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
\(153\) 1074.14 0.567574
\(154\) 0 0
\(155\) −4653.47 −2.41145
\(156\) −12.9773 22.4773i −0.00666034 0.0115361i
\(157\) −153.466 + 265.811i −0.0780122 + 0.135121i −0.902392 0.430916i \(-0.858191\pi\)
0.824380 + 0.566037i \(0.191524\pi\)
\(158\) 116.303 201.443i 0.0585606 0.101430i
\(159\) −264.767 458.590i −0.132059 0.228733i
\(160\) −666.788 −0.329464
\(161\) 0 0
\(162\) 162.000 0.0785674
\(163\) −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
\(165\) −473.926 + 820.864i −0.223607 + 0.387298i
\(166\) −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
\(171\) −150.801 + 261.195i −0.0674389 + 0.116808i
\(172\) −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 \(0.724148\pi\)
\(174\) 979.250 0.426648
\(175\) 0 0
\(176\) 242.606 0.103904
\(177\) −682.392 1181.94i −0.289784 0.501920i
\(178\) −383.159 + 663.651i −0.161343 + 0.279454i
\(179\) −1706.72 + 2956.12i −0.712659 + 1.23436i 0.251197 + 0.967936i \(0.419176\pi\)
−0.963856 + 0.266425i \(0.914157\pi\)
\(180\) 375.068 + 649.637i 0.155311 + 0.269006i
\(181\) −1286.71 −0.528399 −0.264200 0.964468i \(-0.585108\pi\)
−0.264200 + 0.964468i \(0.585108\pi\)
\(182\) 0 0
\(183\) 115.955 0.0468394
\(184\) −2.60607 4.51384i −0.00104414 0.00180850i
\(185\) 1755.88 3041.28i 0.697811 1.20864i
\(186\) 669.977 1160.43i 0.264114 0.457458i
\(187\) −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 \(-0.230726\pi\)
−0.948493 + 0.316798i \(0.897392\pi\)
\(192\) 96.0000 166.277i 0.0360844 0.0625000i
\(193\) 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
\(195\) −135.205 −0.0496523
\(196\) 0 0
\(197\) 1622.31 0.586725 0.293363 0.956001i \(-0.405226\pi\)
0.293363 + 0.956001i \(0.405226\pi\)
\(198\) −136.466 236.366i −0.0489809 0.0848373i
\(199\) −1775.07 + 3074.51i −0.632318 + 1.09521i 0.354759 + 0.934958i \(0.384563\pi\)
−0.987077 + 0.160249i \(0.948770\pi\)
\(200\) −1236.74 + 2142.10i −0.437254 + 0.757347i
\(201\) 212.688 + 368.386i 0.0746359 + 0.129273i
\(202\) 29.4848 0.0102700
\(203\) 0 0
\(204\) −1432.18 −0.491533
\(205\) 3365.43 + 5829.10i 1.14659 + 1.98596i
\(206\) −841.420 + 1457.38i −0.284585 + 0.492916i
\(207\) −2.93183 + 5.07807i −0.000984425 + 0.00170507i
\(208\) 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
\(213\) 904.114 1565.97i 0.290840 0.503749i
\(214\) 715.670 1239.58i 0.228609 0.395962i
\(215\) 2308.30 + 3998.10i 0.732209 + 1.26822i
\(216\) −216.000 −0.0680414
\(217\) 0 0
\(218\) 1200.04 0.372829
\(219\) 1653.45 + 2863.86i 0.510181 + 0.883660i
\(220\) 631.901 1094.49i 0.193649 0.335410i
\(221\) 129.068 223.553i 0.0392854 0.0680442i
\(222\) 505.602 + 875.729i 0.152855 + 0.264753i
\(223\) 4649.53 1.39621 0.698107 0.715993i \(-0.254026\pi\)
0.698107 + 0.715993i \(0.254026\pi\)
\(224\) 0 0
\(225\) 2782.67 0.824495
\(226\) −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 \(-0.0409438\pi\)
\(228\) 201.068 348.260i 0.0584038 0.101158i
\(229\) 2131.82 + 3692.41i 0.615172 + 1.06551i 0.990354 + 0.138558i \(0.0442468\pi\)
−0.375182 + 0.926951i \(0.622420\pi\)
\(230\) −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 \(-0.307719\pi\)
−0.996764 + 0.0803838i \(0.974385\pi\)
\(234\) 19.4659 33.7159i 0.00543815 0.00941915i
\(235\) −5293.10 + 9167.92i −1.46929 + 2.54489i
\(236\) 909.856 + 1575.92i 0.250960 + 0.434676i
\(237\) 348.909 0.0956290
\(238\) 0 0
\(239\) 3987.20 1.07912 0.539562 0.841946i \(-0.318590\pi\)
0.539562 + 0.841946i \(0.318590\pi\)
\(240\) −500.091 866.183i −0.134503 0.232966i
\(241\) −312.324 + 540.961i −0.0834795 + 0.144591i −0.904742 0.425959i \(-0.859937\pi\)
0.821263 + 0.570550i \(0.193270\pi\)
\(242\) 1101.09 1907.14i 0.292482 0.506593i
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) −154.606 −0.0405641
\(245\) 0 0
\(246\) −1938.14 −0.502321
\(247\) 36.2405 + 62.7704i 0.00933574 + 0.0161700i
\(248\) −893.303 + 1547.25i −0.228729 + 0.396170i
\(249\) 853.392 1478.12i 0.217195 0.376193i
\(250\) 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
\(255\) −3730.32 + 6461.10i −0.916085 + 1.58671i
\(256\) −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 \(0.961386\pi\)
\(258\) −1329.34 −0.320780
\(259\) 0 0
\(260\) 180.273 0.0430001
\(261\) 734.437 + 1272.08i 0.174178 + 0.301686i
\(262\) 217.860 377.344i 0.0513719 0.0889787i
\(263\) −1625.31 + 2815.11i −0.381067 + 0.660028i −0.991215 0.132260i \(-0.957777\pi\)
0.610148 + 0.792288i \(0.291110\pi\)
\(264\) 181.955 + 315.155i 0.0424187 + 0.0734713i
\(265\) 3677.99 0.852593
\(266\) 0 0
\(267\) −1149.48 −0.263471
\(268\) −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 \(0.0628921\pi\)
\(270\) −562.602 + 974.456i −0.126811 + 0.219643i
\(271\) −1198.38 2075.66i −0.268622 0.465268i 0.699884 0.714257i \(-0.253235\pi\)
−0.968506 + 0.248989i \(0.919902\pi\)
\(272\) 1909.58 0.425680
\(273\) 0 0
\(274\) −5203.71 −1.14733
\(275\) −2344.07 4060.05i −0.514010 0.890292i
\(276\) 3.90910 6.77076i 0.000852537 0.00147664i
\(277\) −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
\(279\) 2009.93 0.431296
\(280\) 0 0
\(281\) 3083.81 0.654679 0.327339 0.944907i \(-0.393848\pi\)
0.327339 + 0.944907i \(0.393848\pi\)
\(282\) −1524.14 2639.88i −0.321848 0.557456i
\(283\) 1277.38 2212.49i 0.268313 0.464732i −0.700113 0.714032i \(-0.746867\pi\)
0.968426 + 0.249300i \(0.0802005\pi\)
\(284\) −1205.48 + 2087.96i −0.251875 + 0.436259i
\(285\) −1047.42 1814.19i −0.217698 0.377063i
\(286\) −65.5910 −0.0135611
\(287\) 0 0
\(288\) 288.000 0.0589256
\(289\) −4665.53 8080.94i −0.949630 1.64481i
\(290\) −3400.79 + 5890.34i −0.688625 + 1.19273i
\(291\) −502.051 + 869.578i −0.101137 + 0.175174i
\(292\) −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
\(297\) 204.699 354.549i 0.0399927 0.0692694i
\(298\) −581.023 + 1006.36i −0.112945 + 0.195627i
\(299\) 0.704576 + 1.22036i 0.000136277 + 0.000236038i
\(300\) −3710.23 −0.714034
\(301\) 0 0
\(302\) −1230.78 −0.234515
\(303\) 22.1136 + 38.3019i 0.00419272 + 0.00726201i
\(304\) −268.091 + 464.347i −0.0505792 + 0.0876057i
\(305\) −402.693 + 697.485i −0.0756005 + 0.130944i
\(306\) −1074.14 1860.46i −0.200668 0.347566i
\(307\) −7041.50 −1.30905 −0.654527 0.756039i \(-0.727132\pi\)
−0.654527 + 0.756039i \(0.727132\pi\)
\(308\) 0 0
\(309\) −2524.26 −0.464726
\(310\) 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 \(0.245412\pi\)
\(312\) −25.9546 + 44.9546i −0.00470957 + 0.00815722i
\(313\) 1109.59 + 1921.87i 0.200377 + 0.347063i 0.948650 0.316328i \(-0.102450\pi\)
−0.748273 + 0.663391i \(0.769117\pi\)
\(314\) 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 \(-0.229715\pi\)
−0.947483 + 0.319807i \(0.896382\pi\)
\(318\) −529.534 + 917.180i −0.0933799 + 0.161739i
\(319\) 1237.35 2143.16i 0.217174 0.376157i
\(320\) 666.788 + 1154.91i 0.116483 + 0.201755i
\(321\) 2147.01 0.373316
\(322\) 0 0
\(323\) 3999.53 0.688978
\(324\) −162.000 280.592i −0.0277778 0.0481125i
\(325\) 334.366 579.138i 0.0570685 0.0988455i
\(326\) −3514.50 + 6087.29i −0.597086 + 1.03418i
\(327\) 900.028 + 1558.89i 0.152207 + 0.263630i
\(328\) 2584.18 0.435023
\(329\) 0 0
\(330\) 1895.70 0.316228
\(331\) −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
\(333\) −758.403 + 1313.59i −0.124806 + 0.216170i
\(334\) 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
\(339\) 933.966 1617.68i 0.149634 0.259174i
\(340\) 4973.76 8614.80i 0.793353 1.37413i
\(341\) −1693.13 2932.59i −0.268880 0.465714i
\(342\) 603.205 0.0953730
\(343\) 0 0
\(344\) 1772.45 0.277803
\(345\) −20.3636 35.2708i −0.00317780 0.00550410i
\(346\) 1530.60 2651.07i 0.237819 0.411915i
\(347\) 3112.32 5390.69i 0.481493 0.833970i −0.518282 0.855210i \(-0.673428\pi\)
0.999774 + 0.0212401i \(0.00676143\pi\)
\(348\) −979.250 1696.11i −0.150843 0.261267i
\(349\) −9732.21 −1.49270 −0.746352 0.665552i \(-0.768196\pi\)
−0.746352 + 0.665552i \(0.768196\pi\)
\(350\) 0 0
\(351\) 58.3977 0.00888046
\(352\) −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 \(0.132390\pi\)
\(354\) −1364.78 + 2363.88i −0.204908 + 0.354911i
\(355\) 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 \(-0.0273355\pi\)
−0.572438 + 0.819948i \(0.694002\pi\)
\(360\) 750.136 1299.27i 0.109821 0.190216i
\(361\) 2867.99 4967.51i 0.418136 0.724233i
\(362\) 1286.71 + 2228.64i 0.186817 + 0.323577i
\(363\) 3303.26 0.477621
\(364\) 0 0
\(365\) −22968.7 −3.29381
\(366\) −115.955 200.839i −0.0165602 0.0286831i
\(367\) 5772.67 9998.56i 0.821065 1.42213i −0.0838244 0.996481i \(-0.526713\pi\)
0.904890 0.425646i \(-0.139953\pi\)
\(368\) −5.21213 + 9.02768i −0.000738319 + 0.00127881i
\(369\) −1453.60 2517.71i −0.205072 0.355195i
\(370\) −7023.53 −0.986854
\(371\) 0 0
\(372\) −2679.91 −0.373513
\(373\) 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
\(375\) −5756.85 + 9971.15i −0.792753 + 1.37309i
\(376\) 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
\(381\) −270.114 + 467.851i −0.0363211 + 0.0629100i
\(382\) −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 \(0.739380\pi\)
\(384\) −384.000 −0.0510310
\(385\) 0 0
\(386\) −9541.68 −1.25818
\(387\) −997.006 1726.86i −0.130958 0.226825i
\(388\) 669.402 1159.44i 0.0875869 0.151705i
\(389\) 6573.46 11385.6i 0.856781 1.48399i −0.0182021 0.999834i \(-0.505794\pi\)
0.874983 0.484154i \(-0.160872\pi\)
\(390\) 135.205 + 234.181i 0.0175547 + 0.0304057i
\(391\) 77.7575 0.0100572
\(392\) 0 0
\(393\) 653.580 0.0838899
\(394\) −1622.31 2809.92i −0.207439 0.359294i
\(395\) −1211.71 + 2098.74i −0.154349 + 0.267340i
\(396\) −272.932 + 472.732i −0.0346347 + 0.0599891i
\(397\) −4239.02 7342.20i −0.535895 0.928198i −0.999119 0.0419565i \(-0.986641\pi\)
0.463224 0.886241i \(-0.346692\pi\)
\(398\) 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 \(-0.222508\pi\)
−0.939999 + 0.341176i \(0.889175\pi\)
\(402\) 425.375 736.771i 0.0527756 0.0914100i
\(403\) 241.513 418.313i 0.0298527 0.0517064i
\(404\) −29.4848 51.0692i −0.00363100 0.00628908i
\(405\) −1687.81 −0.207081
\(406\) 0 0
\(407\) 2555.46 0.311227
\(408\) 1432.18 + 2480.61i 0.173783 + 0.301001i
\(409\) −3192.69 + 5529.91i −0.385987 + 0.668548i −0.991906 0.126978i \(-0.959472\pi\)
0.605919 + 0.795526i \(0.292806\pi\)
\(410\) 6730.86 11658.2i 0.810765 1.40429i
\(411\) −3902.78 6759.82i −0.468395 0.811283i
\(412\) 3365.68 0.402464
\(413\) 0 0
\(414\) 11.7273 0.00139219
\(415\) 5927.41 + 10266.6i 0.701121 + 1.21438i
\(416\) 34.6061 59.9395i 0.00407861 0.00706436i
\(417\) 3977.32 6888.93i 0.467075 0.808998i
\(418\) −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
\(423\) 2286.20 3959.82i 0.262787 0.455161i
\(424\) 706.045 1222.91i 0.0808693 0.140070i
\(425\) −18450.4 31957.1i −2.10583 3.64740i
\(426\) −3616.45 −0.411309
\(427\) 0 0
\(428\) −2862.68 −0.323301
\(429\) −49.1932 85.2051i −0.00553630 0.00958914i
\(430\) 4616.61 7996.20i 0.517750 0.896769i
\(431\) −3495.97 + 6055.19i −0.390707 + 0.676725i −0.992543 0.121895i \(-0.961103\pi\)
0.601836 + 0.798620i \(0.294436\pi\)
\(432\) 216.000 + 374.123i 0.0240563 + 0.0416667i
\(433\) 7699.26 0.854510 0.427255 0.904131i \(-0.359481\pi\)
0.427255 + 0.904131i \(0.359481\pi\)
\(434\) 0 0
\(435\) −10202.4 −1.12452
\(436\) −1200.04 2078.53i −0.131815 0.228310i
\(437\) −10.9166 + 18.9081i −0.00119499 + 0.00206979i
\(438\) 3306.90 5727.71i 0.360753 0.624842i
\(439\) 4706.16 + 8151.31i 0.511646 + 0.886198i 0.999909 + 0.0135008i \(0.00429758\pi\)
−0.488262 + 0.872697i \(0.662369\pi\)
\(440\) −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 \(-0.0577301\pi\)
−0.648006 + 0.761635i \(0.724397\pi\)
\(444\) 1011.20 1751.46i 0.108085 0.187208i
\(445\) 3991.97 6914.29i 0.425252 0.736559i
\(446\) −4649.53 8053.23i −0.493636 0.855003i
\(447\) −1743.07 −0.184439
\(448\) 0 0
\(449\) −11633.8 −1.22279 −0.611396 0.791325i \(-0.709392\pi\)
−0.611396 + 0.791325i \(0.709392\pi\)
\(450\) −2782.67 4819.73i −0.291503 0.504898i
\(451\) −2448.98 + 4241.75i −0.255694 + 0.442874i
\(452\) −1245.29 + 2156.90i −0.129587 + 0.224452i
\(453\) −923.085 1598.83i −0.0957402 0.165827i
\(454\) −8303.43 −0.858369
\(455\) 0 0
\(456\) −804.273 −0.0825954
\(457\) 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
\(459\) 1611.20 2790.69i 0.163844 0.283787i
\(460\) 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
\(465\) −6980.20 + 12090.1i −0.696127 + 1.20573i
\(466\) −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 \(0.552385\pi\)
\(468\) −77.8637 −0.00769070
\(469\) 0 0
\(470\) 21172.4 2.07789
\(471\) 460.398 + 797.432i 0.0450404 + 0.0780122i
\(472\) 1819.71 3151.83i 0.177456 0.307362i
\(473\) −1679.72 + 2909.36i −0.163285 + 0.282817i
\(474\) −348.909 604.328i −0.0338100 0.0585606i
\(475\) 10361.2 1.00085
\(476\) 0 0
\(477\) −1588.60 −0.152489
\(478\) −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 \(0.298763\pi\)
\(480\) −1000.18 + 1732.37i −0.0951080 + 0.164732i
\(481\) 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
\(486\) 243.000 420.888i 0.0226805 0.0392837i
\(487\) 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
\(489\) −10543.5 −0.975038
\(490\) 0 0
\(491\) 13927.9 1.28016 0.640079 0.768309i \(-0.278902\pi\)
0.640079 + 0.768309i \(0.278902\pi\)
\(492\) 1938.14 + 3356.95i 0.177597 + 0.307608i
\(493\) 9739.33 16869.0i 0.889731 1.54106i
\(494\) 72.4810 125.541i 0.00660137 0.0114339i
\(495\) 1421.78 + 2462.59i 0.129099 + 0.223607i
\(496\) 3573.21 0.323472
\(497\) 0 0
\(498\) −3413.57 −0.307160
\(499\) 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
\(501\) −1684.95 + 2918.43i −0.150256 + 0.260251i
\(502\) −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
\(507\) −3288.48 + 5695.82i −0.288060 + 0.498935i
\(508\) 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 \(0.722593\pi\)
\(510\) 14921.3 1.29554
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 452.403 + 783.586i 0.0389359 + 0.0674389i
\(514\) −3226.18 + 5587.91i −0.276850 + 0.479518i
\(515\) 8766.39 15183.8i 0.750084 1.29918i
\(516\) 1329.34 + 2302.49i 0.113413 + 0.196437i
\(517\) −7703.43 −0.655312
\(518\) 0 0
\(519\) 4591.80 0.388357
\(520\) −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 \(0.246563\pi\)
\(522\) 1468.87 2544.17i 0.123163 0.213324i
\(523\) 3954.03 + 6848.58i 0.330588 + 0.572595i 0.982627 0.185590i \(-0.0594196\pi\)
−0.652039 + 0.758185i \(0.726086\pi\)
\(524\) −871.439 −0.0726508
\(525\) 0 0
\(526\) 6501.23 0.538911
\(527\) −13326.8 23082.7i −1.10156 1.90797i
\(528\) 363.909 630.309i 0.0299945 0.0519520i
\(529\) 6083.29 10536.6i 0.499983 0.865995i
\(530\) −3677.99 6370.46i −0.301437 0.522104i
\(531\) −4094.35 −0.334613
\(532\) 0 0
\(533\) −698.659 −0.0567773
\(534\) 1149.48 + 1990.95i 0.0931512 + 0.161343i
\(535\) −7456.26 + 12914.6i −0.602546 + 1.04364i
\(536\) −567.167 + 982.362i −0.0457050 + 0.0791633i
\(537\) 5120.15 + 8868.36i 0.411454 + 0.712659i
\(538\) −5652.08 −0.452934
\(539\) 0 0
\(540\) 2250.41 0.179337
\(541\) 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
\(543\) −1930.06 + 3342.97i −0.152536 + 0.264200i
\(544\) −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
\(549\) 173.932 301.259i 0.0135214 0.0234197i
\(550\) −4688.14 + 8120.10i −0.363460 + 0.629532i
\(551\) 2734.67 + 4736.58i 0.211435 + 0.366216i
\(552\) −15.6364 −0.00120567
\(553\) 0 0
\(554\) 3640.93 0.279221
\(555\) −5267.65 9123.83i −0.402881 0.697811i
\(556\) −5303.10 + 9185.24i −0.404499 + 0.700613i
\(557\) −11266.0 + 19513.3i −0.857011 + 1.48439i 0.0177556 + 0.999842i \(0.494348\pi\)
−0.874767 + 0.484544i \(0.838985\pi\)
\(558\) −2009.93 3481.30i −0.152486 0.264114i
\(559\) −479.201 −0.0362577
\(560\) 0 0
\(561\) −5429.00 −0.408579
\(562\) −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 \(-0.171933\pi\)
\(564\) −3048.27 + 5279.76i −0.227581 + 0.394181i
\(565\) 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 \(0.112812\pi\)
−0.168384 + 0.985721i \(0.553855\pi\)
\(570\) −2094.84 + 3628.37i −0.153935 + 0.266624i
\(571\) −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
\(573\) −3165.89 −0.230815
\(574\) 0 0
\(575\) 201.440 0.0146098
\(576\) −288.000 498.831i −0.0208333 0.0360844i
\(577\) 1227.20 2125.57i 0.0885422 0.153360i −0.818353 0.574716i \(-0.805113\pi\)
0.906895 + 0.421356i \(0.138446\pi\)
\(578\) −9331.06 + 16161.9i −0.671490 + 1.16305i
\(579\) −7156.26 12395.0i −0.513651 0.889670i
\(580\) 13603.2 0.973863
\(581\) 0 0
\(582\) 2008.20 0.143029
\(583\) 1338.21 + 2317.85i 0.0950652 + 0.164658i
\(584\) −4409.20 + 7636.95i −0.312421 + 0.541129i
\(585\) −202.807 + 351.272i −0.0143334 + 0.0248261i
\(586\) −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
\(591\) 2433.47 4214.89i 0.169373 0.293363i
\(592\) −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 \(0.631461\pi\)
\(594\) −818.795 −0.0565582
\(595\) 0 0
\(596\) 2324.09 0.159729
\(597\) 5325.20 + 9223.52i 0.365069 + 0.632318i
\(598\) 1.40915 2.44072i 9.63621e−5 0.000166904i
\(599\) −11632.4 + 20147.9i −0.793469 + 1.37433i 0.130338 + 0.991470i \(0.458394\pi\)
−0.923807 + 0.382859i \(0.874940\pi\)
\(600\) 3710.23 + 6426.30i 0.252449 + 0.437254i
\(601\) −25322.3 −1.71867 −0.859334 0.511416i \(-0.829121\pi\)
−0.859334 + 0.511416i \(0.829121\pi\)
\(602\) 0 0
\(603\) 1276.13 0.0861821
\(604\) 1230.78 + 2131.77i 0.0829135 + 0.143610i
\(605\) −11471.7 + 19869.6i −0.770897 + 1.33523i
\(606\) 44.2272 76.6038i 0.00296470 0.00513501i
\(607\) −10867.2 18822.5i −0.726665 1.25862i −0.958285 0.285814i \(-0.907736\pi\)
0.231620 0.972806i \(-0.425597\pi\)
\(608\) 1072.36 0.0715297
\(609\) 0 0
\(610\) 1610.77 0.106915
\(611\) −549.420 951.624i −0.0363784 0.0630092i
\(612\) −2148.27 + 3720.92i −0.141893 + 0.245767i
\(613\) 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
\(615\) 20192.6 1.32397
\(616\) 0 0
\(617\) −8497.12 −0.554427 −0.277213 0.960808i \(-0.589411\pi\)
−0.277213 + 0.960808i \(0.589411\pi\)
\(618\) 2524.26 + 4372.15i 0.164305 + 0.284585i
\(619\) −11491.5 + 19903.8i −0.746173 + 1.29241i 0.203472 + 0.979081i \(0.434777\pi\)
−0.949645 + 0.313329i \(0.898556\pi\)
\(620\) 9306.93 16120.1i 0.602863 1.04419i
\(621\) 8.79548 + 15.2342i 0.000568358 + 0.000984425i
\(622\) 5371.98 0.346297
\(623\) 0 0
\(624\) 103.818 0.00666034
\(625\) −20661.3 35786.4i −1.32232 2.29033i
\(626\) 2219.19 3843.75i 0.141688 0.245411i
\(627\) 762.193 1320.16i 0.0485471 0.0840861i
\(628\) −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
\(633\) 6980.08 12089.9i 0.438283 0.759129i
\(634\) −2221.26 + 3847.34i −0.139144 + 0.241005i
\(635\) −1876.13 3249.55i −0.117247 0.203078i
\(636\) 2118.14 0.132059
\(637\) 0 0
\(638\) −4949.42 −0.307131
\(639\) −2712.34 4697.91i −0.167916 0.290840i
\(640\) 1333.58 2309.82i 0.0823660 0.142662i
\(641\) −14553.7 + 25207.7i −0.896780 + 1.55327i −0.0651930 + 0.997873i \(0.520766\pi\)
−0.831587 + 0.555395i \(0.812567\pi\)
\(642\) −2147.01 3718.73i −0.131987 0.228609i
\(643\) 3112.26 0.190880 0.0954398 0.995435i \(-0.469574\pi\)
0.0954398 + 0.995435i \(0.469574\pi\)
\(644\) 0 0
\(645\) 13849.8 0.845482
\(646\) −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 \(0.243397\pi\)
\(648\) −324.000 + 561.184i −0.0196419 + 0.0340207i
\(649\) 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 \(0.0322224\pi\)
−0.409923 + 0.912120i \(0.634444\pi\)
\(654\) 1800.06 3117.79i 0.107627 0.186415i
\(655\) −2269.79 + 3931.38i −0.135401 + 0.234522i
\(656\) −2584.18 4475.93i −0.153804 0.266396i
\(657\) 9920.69 0.589107
\(658\) 0 0
\(659\) 664.061 0.0392536 0.0196268 0.999807i \(-0.493752\pi\)
0.0196268 + 0.999807i \(0.493752\pi\)
\(660\) −1895.70 3283.46i −0.111803 0.193649i
\(661\) 7960.82 13788.5i 0.468442 0.811365i −0.530908 0.847430i \(-0.678149\pi\)
0.999349 + 0.0360650i \(0.0114823\pi\)
\(662\) −4154.06 + 7195.04i −0.243885 + 0.422422i
\(663\) −387.205 670.658i −0.0226814 0.0392854i
\(664\) 4551.42 0.266008
\(665\) 0 0
\(666\) 3033.61 0.176502
\(667\) 53.1665 + 92.0870i 0.00308638 + 0.00534576i
\(668\) 2246.61 3891.24i 0.130125 0.225384i
\(669\) 6974.30 12079.8i 0.403052 0.698107i
\(670\) 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
\(675\) 4174.01 7229.59i 0.238011 0.412247i
\(676\) 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 \(0.672089\pi\)
\(678\) −3735.86 −0.211615
\(679\) 0 0
\(680\) −19895.0 −1.12197
\(681\) −6227.57 10786.5i −0.350428 0.606958i
\(682\) −3386.26 + 5865.18i −0.190127 + 0.329310i
\(683\) 9581.79 16596.1i 0.536804 0.929771i −0.462270 0.886739i \(-0.652965\pi\)
0.999074 0.0430322i \(-0.0137018\pi\)
\(684\) −603.205 1044.78i −0.0337194 0.0584038i
\(685\) 54215.2 3.02402
\(686\) 0 0
\(687\) 12790.9 0.710339
\(688\) −1772.45 3069.98i −0.0982183 0.170119i
\(689\) −190.886 + 330.625i −0.0105547 + 0.0182813i
\(690\) −40.7272 + 70.5416i −0.00224704 + 0.00389199i
\(691\) 4047.94 + 7011.23i 0.222852 + 0.385991i 0.955673 0.294431i \(-0.0951300\pi\)
−0.732821 + 0.680422i \(0.761797\pi\)
\(692\) −6122.39 −0.336327
\(693\) 0 0
\(694\) −12449.3 −0.680934
\(695\) 27625.3 + 47848.5i 1.50775 + 2.61150i
\(696\) −1958.50 + 3392.22i −0.106662 + 0.184744i
\(697\) −19276.1 + 33387.2i −1.04754 + 1.81439i
\(698\) 9732.21 + 16856.7i 0.527750 + 0.914090i
\(699\) −9149.70 −0.495098
\(700\) 0 0
\(701\) 12354.7 0.665664 0.332832 0.942986i \(-0.391996\pi\)
0.332832 + 0.942986i \(0.391996\pi\)
\(702\) −58.3977 101.148i −0.00313972 0.00543815i
\(703\) −2823.90 + 4891.14i −0.151501 + 0.262408i
\(704\) −485.212 + 840.412i −0.0259760 + 0.0449918i
\(705\) 15879.3 + 27503.8i 0.848297 + 1.46929i
\(706\) −2851.23 −0.151993
\(707\) 0 0
\(708\) 5459.14 0.289784
\(709\) −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
\(711\) 523.364 906.492i 0.0276057 0.0478145i
\(712\) −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
\(717\) 5980.81 10359.1i 0.311516 0.539562i
\(718\) 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 \(0.823236\pi\)
\(720\) −3000.55 −0.155311
\(721\) 0 0
\(722\) −11472.0 −0.591333
\(723\) 936.972 + 1622.88i 0.0481969 + 0.0834795i
\(724\) 2573.42 4457.29i 0.132100 0.228804i
\(725\) 25230.8 43701.1i 1.29248 2.23864i
\(726\) −3303.26 5721.42i −0.168864 0.292482i
\(727\) −6368.21 −0.324875 −0.162437 0.986719i \(-0.551936\pi\)
−0.162437 + 0.986719i \(0.551936\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 22968.7 + 39783.0i 1.16454 + 2.01704i
\(731\) −13221.2 + 22899.9i −0.668954 + 1.15866i
\(732\) −231.909 + 401.678i −0.0117098 + 0.0202820i
\(733\) −12577.0 21784.0i −0.633753 1.09769i −0.986778 0.162079i \(-0.948180\pi\)
0.353024 0.935614i \(-0.385153\pi\)
\(734\) −23090.7 −1.16116
\(735\) 0 0
\(736\) 20.8485 0.00104414
\(737\) −1074.98 1861.93i −0.0537281 0.0930597i
\(738\) −2907.20 + 5035.43i −0.145008 + 0.251161i
\(739\) 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
\(741\) 217.443 0.0107800
\(742\) 0 0
\(743\) 28166.3 1.39074 0.695370 0.718652i \(-0.255240\pi\)
0.695370 + 0.718652i \(0.255240\pi\)
\(744\) 2679.91 + 4641.74i 0.132057 + 0.228729i
\(745\) 6053.42 10484.8i 0.297691 0.515617i
\(746\) 6479.57 11222.9i 0.318008 0.550806i
\(747\) −2560.18 4434.36i −0.125398 0.217195i
\(748\) 7238.67 0.353839
\(749\) 0 0
\(750\) 23027.4 1.12112
\(751\) −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
\(753\) 1993.18 3452.28i 0.0964613 0.167076i
\(754\) −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
\(759\) 14.8183 25.6661i 0.000708657 0.00122743i
\(760\) 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 \(0.798153\pi\)
\(762\) 1080.45 0.0513658
\(763\) 0 0
\(764\) 4221.18 0.199891
\(765\) 11191.0 + 19383.3i 0.528902 + 0.916085i
\(766\) 4360.81 7553.15i 0.205695 0.356274i
\(767\) −491.977 + 852.129i −0.0231607 + 0.0401155i
\(768\) 384.000 + 665.108i 0.0180422 + 0.0312500i
\(769\) −33276.8 −1.56046 −0.780228 0.625495i \(-0.784897\pi\)
−0.780228 + 0.625495i \(0.784897\pi\)
\(770\) 0 0
\(771\) −9678.55 −0.452094
\(772\) 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 \(0.987480\pi\)
\(774\) −1994.01 + 3453.73i −0.0926011 + 0.160390i
\(775\) −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
\(780\) 270.409 468.362i 0.0124131 0.0215001i