Properties

Label 63.4.e.b.37.1
Level $63$
Weight $4$
Character 63.37
Analytic conductor $3.717$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 7)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 63.37
Dual form 63.4.e.b.46.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(2.00000 + 3.46410i) q^{4} +(3.50000 - 6.06218i) q^{5} +(14.0000 - 12.1244i) q^{7} +24.0000 q^{8} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(2.00000 + 3.46410i) q^{4} +(3.50000 - 6.06218i) q^{5} +(14.0000 - 12.1244i) q^{7} +24.0000 q^{8} +(-7.00000 - 12.1244i) q^{10} +(-2.50000 - 4.33013i) q^{11} -14.0000 q^{13} +(-7.00000 - 36.3731i) q^{14} +(8.00000 - 13.8564i) q^{16} +(-10.5000 - 18.1865i) q^{17} +(-24.5000 + 42.4352i) q^{19} +28.0000 q^{20} -10.0000 q^{22} +(-79.5000 + 137.698i) q^{23} +(38.0000 + 65.8179i) q^{25} +(-14.0000 + 24.2487i) q^{26} +(70.0000 + 24.2487i) q^{28} -58.0000 q^{29} +(-73.5000 - 127.306i) q^{31} +(80.0000 + 138.564i) q^{32} -42.0000 q^{34} +(-24.5000 - 127.306i) q^{35} +(-109.500 + 189.660i) q^{37} +(49.0000 + 84.8705i) q^{38} +(84.0000 - 145.492i) q^{40} -350.000 q^{41} -124.000 q^{43} +(10.0000 - 17.3205i) q^{44} +(159.000 + 275.396i) q^{46} +(262.500 - 454.663i) q^{47} +(49.0000 - 339.482i) q^{49} +152.000 q^{50} +(-28.0000 - 48.4974i) q^{52} +(151.500 + 262.406i) q^{53} -35.0000 q^{55} +(336.000 - 290.985i) q^{56} +(-58.0000 + 100.459i) q^{58} +(-52.5000 - 90.9327i) q^{59} +(206.500 - 357.668i) q^{61} -294.000 q^{62} +448.000 q^{64} +(-49.0000 + 84.8705i) q^{65} +(-207.500 - 359.401i) q^{67} +(42.0000 - 72.7461i) q^{68} +(-245.000 - 84.8705i) q^{70} +432.000 q^{71} +(556.500 + 963.886i) q^{73} +(219.000 + 379.319i) q^{74} -196.000 q^{76} +(-87.5000 - 30.3109i) q^{77} +(51.5000 - 89.2006i) q^{79} +(-56.0000 - 96.9948i) q^{80} +(-350.000 + 606.218i) q^{82} -1092.00 q^{83} -147.000 q^{85} +(-124.000 + 214.774i) q^{86} +(-60.0000 - 103.923i) q^{88} +(-164.500 + 284.922i) q^{89} +(-196.000 + 169.741i) q^{91} -636.000 q^{92} +(-525.000 - 909.327i) q^{94} +(171.500 + 297.047i) q^{95} -882.000 q^{97} +(-539.000 - 424.352i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 4q^{4} + 7q^{5} + 28q^{7} + 48q^{8} + O(q^{10}) \) \( 2q + 2q^{2} + 4q^{4} + 7q^{5} + 28q^{7} + 48q^{8} - 14q^{10} - 5q^{11} - 28q^{13} - 14q^{14} + 16q^{16} - 21q^{17} - 49q^{19} + 56q^{20} - 20q^{22} - 159q^{23} + 76q^{25} - 28q^{26} + 140q^{28} - 116q^{29} - 147q^{31} + 160q^{32} - 84q^{34} - 49q^{35} - 219q^{37} + 98q^{38} + 168q^{40} - 700q^{41} - 248q^{43} + 20q^{44} + 318q^{46} + 525q^{47} + 98q^{49} + 304q^{50} - 56q^{52} + 303q^{53} - 70q^{55} + 672q^{56} - 116q^{58} - 105q^{59} + 413q^{61} - 588q^{62} + 896q^{64} - 98q^{65} - 415q^{67} + 84q^{68} - 490q^{70} + 864q^{71} + 1113q^{73} + 438q^{74} - 392q^{76} - 175q^{77} + 103q^{79} - 112q^{80} - 700q^{82} - 2184q^{83} - 294q^{85} - 248q^{86} - 120q^{88} - 329q^{89} - 392q^{91} - 1272q^{92} - 1050q^{94} + 343q^{95} - 1764q^{97} - 1078q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 −0.633316 0.773893i \(-0.718307\pi\)
0.986869 + 0.161521i \(0.0516399\pi\)
\(3\) 0 0
\(4\) 2.00000 + 3.46410i 0.250000 + 0.433013i
\(5\) 3.50000 6.06218i 0.313050 0.542218i −0.665971 0.745977i \(-0.731983\pi\)
0.979021 + 0.203760i \(0.0653161\pi\)
\(6\) 0 0
\(7\) 14.0000 12.1244i 0.755929 0.654654i
\(8\) 24.0000 1.06066
\(9\) 0 0
\(10\) −7.00000 12.1244i −0.221359 0.383406i
\(11\) −2.50000 4.33013i −0.0685253 0.118689i 0.829727 0.558169i \(-0.188496\pi\)
−0.898252 + 0.439480i \(0.855163\pi\)
\(12\) 0 0
\(13\) −14.0000 −0.298685 −0.149342 0.988786i \(-0.547716\pi\)
−0.149342 + 0.988786i \(0.547716\pi\)
\(14\) −7.00000 36.3731i −0.133631 0.694365i
\(15\) 0 0
\(16\) 8.00000 13.8564i 0.125000 0.216506i
\(17\) −10.5000 18.1865i −0.149801 0.259464i 0.781353 0.624090i \(-0.214530\pi\)
−0.931154 + 0.364626i \(0.881197\pi\)
\(18\) 0 0
\(19\) −24.5000 + 42.4352i −0.295826 + 0.512385i −0.975177 0.221429i \(-0.928928\pi\)
0.679351 + 0.733813i \(0.262261\pi\)
\(20\) 28.0000 0.313050
\(21\) 0 0
\(22\) −10.0000 −0.0969094
\(23\) −79.5000 + 137.698i −0.720735 + 1.24835i 0.239971 + 0.970780i \(0.422862\pi\)
−0.960706 + 0.277569i \(0.910471\pi\)
\(24\) 0 0
\(25\) 38.0000 + 65.8179i 0.304000 + 0.526543i
\(26\) −14.0000 + 24.2487i −0.105601 + 0.182906i
\(27\) 0 0
\(28\) 70.0000 + 24.2487i 0.472456 + 0.163663i
\(29\) −58.0000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) −73.5000 127.306i −0.425838 0.737574i 0.570660 0.821186i \(-0.306687\pi\)
−0.996498 + 0.0836128i \(0.973354\pi\)
\(32\) 80.0000 + 138.564i 0.441942 + 0.765466i
\(33\) 0 0
\(34\) −42.0000 −0.211851
\(35\) −24.5000 127.306i −0.118322 0.614817i
\(36\) 0 0
\(37\) −109.500 + 189.660i −0.486532 + 0.842698i −0.999880 0.0154821i \(-0.995072\pi\)
0.513348 + 0.858181i \(0.328405\pi\)
\(38\) 49.0000 + 84.8705i 0.209180 + 0.362311i
\(39\) 0 0
\(40\) 84.0000 145.492i 0.332039 0.575109i
\(41\) −350.000 −1.33319 −0.666595 0.745420i \(-0.732249\pi\)
−0.666595 + 0.745420i \(0.732249\pi\)
\(42\) 0 0
\(43\) −124.000 −0.439763 −0.219882 0.975527i \(-0.570567\pi\)
−0.219882 + 0.975527i \(0.570567\pi\)
\(44\) 10.0000 17.3205i 0.0342627 0.0593447i
\(45\) 0 0
\(46\) 159.000 + 275.396i 0.509636 + 0.882716i
\(47\) 262.500 454.663i 0.814671 1.41105i −0.0948921 0.995488i \(-0.530251\pi\)
0.909564 0.415565i \(-0.136416\pi\)
\(48\) 0 0
\(49\) 49.0000 339.482i 0.142857 0.989743i
\(50\) 152.000 0.429921
\(51\) 0 0
\(52\) −28.0000 48.4974i −0.0746712 0.129334i
\(53\) 151.500 + 262.406i 0.392644 + 0.680079i 0.992797 0.119806i \(-0.0382272\pi\)
−0.600153 + 0.799885i \(0.704894\pi\)
\(54\) 0 0
\(55\) −35.0000 −0.0858073
\(56\) 336.000 290.985i 0.801784 0.694365i
\(57\) 0 0
\(58\) −58.0000 + 100.459i −0.131306 + 0.227429i
\(59\) −52.5000 90.9327i −0.115846 0.200651i 0.802272 0.596959i \(-0.203625\pi\)
−0.918118 + 0.396308i \(0.870291\pi\)
\(60\) 0 0
\(61\) 206.500 357.668i 0.433436 0.750734i −0.563730 0.825959i \(-0.690634\pi\)
0.997167 + 0.0752252i \(0.0239676\pi\)
\(62\) −294.000 −0.602226
\(63\) 0 0
\(64\) 448.000 0.875000
\(65\) −49.0000 + 84.8705i −0.0935031 + 0.161952i
\(66\) 0 0
\(67\) −207.500 359.401i −0.378361 0.655340i 0.612463 0.790499i \(-0.290179\pi\)
−0.990824 + 0.135159i \(0.956845\pi\)
\(68\) 42.0000 72.7461i 0.0749007 0.129732i
\(69\) 0 0
\(70\) −245.000 84.8705i −0.418330 0.144914i
\(71\) 432.000 0.722098 0.361049 0.932547i \(-0.382419\pi\)
0.361049 + 0.932547i \(0.382419\pi\)
\(72\) 0 0
\(73\) 556.500 + 963.886i 0.892238 + 1.54540i 0.837186 + 0.546919i \(0.184199\pi\)
0.0550526 + 0.998483i \(0.482467\pi\)
\(74\) 219.000 + 379.319i 0.344030 + 0.595878i
\(75\) 0 0
\(76\) −196.000 −0.295826
\(77\) −87.5000 30.3109i −0.129501 0.0448603i
\(78\) 0 0
\(79\) 51.5000 89.2006i 0.0733443 0.127036i −0.827021 0.562171i \(-0.809966\pi\)
0.900365 + 0.435135i \(0.143299\pi\)
\(80\) −56.0000 96.9948i −0.0782624 0.135554i
\(81\) 0 0
\(82\) −350.000 + 606.218i −0.471354 + 0.816409i
\(83\) −1092.00 −1.44413 −0.722064 0.691827i \(-0.756806\pi\)
−0.722064 + 0.691827i \(0.756806\pi\)
\(84\) 0 0
\(85\) −147.000 −0.187581
\(86\) −124.000 + 214.774i −0.155480 + 0.269299i
\(87\) 0 0
\(88\) −60.0000 103.923i −0.0726821 0.125889i
\(89\) −164.500 + 284.922i −0.195921 + 0.339345i −0.947202 0.320637i \(-0.896103\pi\)
0.751281 + 0.659982i \(0.229436\pi\)
\(90\) 0 0
\(91\) −196.000 + 169.741i −0.225784 + 0.195535i
\(92\) −636.000 −0.720735
\(93\) 0 0
\(94\) −525.000 909.327i −0.576060 0.997765i
\(95\) 171.500 + 297.047i 0.185216 + 0.320804i
\(96\) 0 0
\(97\) −882.000 −0.923232 −0.461616 0.887080i \(-0.652730\pi\)
−0.461616 + 0.887080i \(0.652730\pi\)
\(98\) −539.000 424.352i −0.555584 0.437409i
\(99\) 0 0
\(100\) −152.000 + 263.272i −0.152000 + 0.263272i
\(101\) 689.500 + 1194.25i 0.679285 + 1.17656i 0.975196 + 0.221341i \(0.0710434\pi\)
−0.295911 + 0.955215i \(0.595623\pi\)
\(102\) 0 0
\(103\) 339.500 588.031i 0.324776 0.562529i −0.656691 0.754160i \(-0.728044\pi\)
0.981467 + 0.191631i \(0.0613777\pi\)
\(104\) −336.000 −0.316803
\(105\) 0 0
\(106\) 606.000 0.555282
\(107\) 228.500 395.774i 0.206448 0.357578i −0.744145 0.668018i \(-0.767143\pi\)
0.950593 + 0.310440i \(0.100476\pi\)
\(108\) 0 0
\(109\) 562.500 + 974.279i 0.494291 + 0.856137i 0.999978 0.00657959i \(-0.00209436\pi\)
−0.505687 + 0.862717i \(0.668761\pi\)
\(110\) −35.0000 + 60.6218i −0.0303374 + 0.0525460i
\(111\) 0 0
\(112\) −56.0000 290.985i −0.0472456 0.245495i
\(113\) 1538.00 1.28038 0.640190 0.768217i \(-0.278856\pi\)
0.640190 + 0.768217i \(0.278856\pi\)
\(114\) 0 0
\(115\) 556.500 + 963.886i 0.451251 + 0.781590i
\(116\) −116.000 200.918i −0.0928477 0.160817i
\(117\) 0 0
\(118\) −210.000 −0.163831
\(119\) −367.500 127.306i −0.283098 0.0980680i
\(120\) 0 0
\(121\) 653.000 1131.03i 0.490609 0.849759i
\(122\) −413.000 715.337i −0.306486 0.530849i
\(123\) 0 0
\(124\) 294.000 509.223i 0.212919 0.368787i
\(125\) 1407.00 1.00677
\(126\) 0 0
\(127\) 72.0000 0.0503068 0.0251534 0.999684i \(-0.491993\pi\)
0.0251534 + 0.999684i \(0.491993\pi\)
\(128\) −192.000 + 332.554i −0.132583 + 0.229640i
\(129\) 0 0
\(130\) 98.0000 + 169.741i 0.0661167 + 0.114517i
\(131\) 1074.50 1861.09i 0.716637 1.24125i −0.245687 0.969349i \(-0.579014\pi\)
0.962325 0.271903i \(-0.0876531\pi\)
\(132\) 0 0
\(133\) 171.500 + 891.140i 0.111812 + 0.580990i
\(134\) −830.000 −0.535083
\(135\) 0 0
\(136\) −252.000 436.477i −0.158888 0.275203i
\(137\) −562.500 974.279i −0.350786 0.607578i 0.635602 0.772017i \(-0.280752\pi\)
−0.986387 + 0.164439i \(0.947419\pi\)
\(138\) 0 0
\(139\) 252.000 0.153772 0.0768862 0.997040i \(-0.475502\pi\)
0.0768862 + 0.997040i \(0.475502\pi\)
\(140\) 392.000 339.482i 0.236643 0.204939i
\(141\) 0 0
\(142\) 432.000 748.246i 0.255300 0.442193i
\(143\) 35.0000 + 60.6218i 0.0204675 + 0.0354507i
\(144\) 0 0
\(145\) −203.000 + 351.606i −0.116264 + 0.201375i
\(146\) 2226.00 1.26182
\(147\) 0 0
\(148\) −876.000 −0.486532
\(149\) −100.500 + 174.071i −0.0552569 + 0.0957078i −0.892331 0.451382i \(-0.850931\pi\)
0.837074 + 0.547090i \(0.184264\pi\)
\(150\) 0 0
\(151\) −809.500 1402.10i −0.436266 0.755635i 0.561132 0.827726i \(-0.310366\pi\)
−0.997398 + 0.0720914i \(0.977033\pi\)
\(152\) −588.000 + 1018.45i −0.313770 + 0.543466i
\(153\) 0 0
\(154\) −140.000 + 121.244i −0.0732566 + 0.0634421i
\(155\) −1029.00 −0.533234
\(156\) 0 0
\(157\) −339.500 588.031i −0.172580 0.298917i 0.766741 0.641956i \(-0.221877\pi\)
−0.939321 + 0.343039i \(0.888544\pi\)
\(158\) −103.000 178.401i −0.0518623 0.0898281i
\(159\) 0 0
\(160\) 1120.00 0.553399
\(161\) 556.500 + 2891.66i 0.272412 + 1.41549i
\(162\) 0 0
\(163\) 233.500 404.434i 0.112203 0.194342i −0.804455 0.594014i \(-0.797543\pi\)
0.916658 + 0.399672i \(0.130876\pi\)
\(164\) −700.000 1212.44i −0.333298 0.577288i
\(165\) 0 0
\(166\) −1092.00 + 1891.40i −0.510576 + 0.884344i
\(167\) −1204.00 −0.557894 −0.278947 0.960306i \(-0.589985\pi\)
−0.278947 + 0.960306i \(0.589985\pi\)
\(168\) 0 0
\(169\) −2001.00 −0.910787
\(170\) −147.000 + 254.611i −0.0663199 + 0.114869i
\(171\) 0 0
\(172\) −248.000 429.549i −0.109941 0.190423i
\(173\) −1410.50 + 2443.06i −0.619875 + 1.07365i 0.369633 + 0.929178i \(0.379483\pi\)
−0.989508 + 0.144477i \(0.953850\pi\)
\(174\) 0 0
\(175\) 1330.00 + 460.726i 0.574506 + 0.199015i
\(176\) −80.0000 −0.0342627
\(177\) 0 0
\(178\) 329.000 + 569.845i 0.138537 + 0.239953i
\(179\) −1626.50 2817.18i −0.679164 1.17635i −0.975233 0.221180i \(-0.929009\pi\)
0.296069 0.955166i \(-0.404324\pi\)
\(180\) 0 0
\(181\) 1582.00 0.649664 0.324832 0.945772i \(-0.394692\pi\)
0.324832 + 0.945772i \(0.394692\pi\)
\(182\) 98.0000 + 509.223i 0.0399134 + 0.207396i
\(183\) 0 0
\(184\) −1908.00 + 3304.75i −0.764454 + 1.32407i
\(185\) 766.500 + 1327.62i 0.304617 + 0.527613i
\(186\) 0 0
\(187\) −52.5000 + 90.9327i −0.0205304 + 0.0355597i
\(188\) 2100.00 0.814671
\(189\) 0 0
\(190\) 686.000 0.261935
\(191\) 1278.50 2214.43i 0.484340 0.838902i −0.515498 0.856891i \(-0.672393\pi\)
0.999838 + 0.0179887i \(0.00572630\pi\)
\(192\) 0 0
\(193\) 198.500 + 343.812i 0.0740329 + 0.128229i 0.900665 0.434514i \(-0.143080\pi\)
−0.826632 + 0.562742i \(0.809746\pi\)
\(194\) −882.000 + 1527.67i −0.326412 + 0.565362i
\(195\) 0 0
\(196\) 1274.00 509.223i 0.464286 0.185577i
\(197\) −2914.00 −1.05388 −0.526939 0.849903i \(-0.676660\pi\)
−0.526939 + 0.849903i \(0.676660\pi\)
\(198\) 0 0
\(199\) −1669.50 2891.66i −0.594712 1.03007i −0.993587 0.113066i \(-0.963933\pi\)
0.398875 0.917005i \(-0.369401\pi\)
\(200\) 912.000 + 1579.63i 0.322441 + 0.558484i
\(201\) 0 0
\(202\) 2758.00 0.960654
\(203\) −812.000 + 703.213i −0.280745 + 0.243132i
\(204\) 0 0
\(205\) −1225.00 + 2121.76i −0.417355 + 0.722880i
\(206\) −679.000 1176.06i −0.229651 0.397768i
\(207\) 0 0
\(208\) −112.000 + 193.990i −0.0373356 + 0.0646671i
\(209\) 245.000 0.0810861
\(210\) 0 0
\(211\) 1780.00 0.580759 0.290380 0.956911i \(-0.406218\pi\)
0.290380 + 0.956911i \(0.406218\pi\)
\(212\) −606.000 + 1049.62i −0.196322 + 0.340040i
\(213\) 0 0
\(214\) −457.000 791.547i −0.145981 0.252846i
\(215\) −434.000 + 751.710i −0.137668 + 0.238447i
\(216\) 0 0
\(217\) −2572.50 891.140i −0.804759 0.278777i
\(218\) 2250.00 0.699033
\(219\) 0 0
\(220\) −70.0000 121.244i −0.0214518 0.0371556i
\(221\) 147.000 + 254.611i 0.0447434 + 0.0774978i
\(222\) 0 0
\(223\) −1400.00 −0.420408 −0.210204 0.977658i \(-0.567413\pi\)
−0.210204 + 0.977658i \(0.567413\pi\)
\(224\) 2800.00 + 969.948i 0.835191 + 0.289319i
\(225\) 0 0
\(226\) 1538.00 2663.89i 0.452682 0.784069i
\(227\) −1102.50 1909.59i −0.322359 0.558342i 0.658615 0.752480i \(-0.271142\pi\)
−0.980974 + 0.194138i \(0.937809\pi\)
\(228\) 0 0
\(229\) −143.500 + 248.549i −0.0414094 + 0.0717231i −0.885987 0.463710i \(-0.846518\pi\)
0.844578 + 0.535433i \(0.179851\pi\)
\(230\) 2226.00 0.638166
\(231\) 0 0
\(232\) −1392.00 −0.393919
\(233\) 2293.50 3972.46i 0.644859 1.11693i −0.339475 0.940615i \(-0.610249\pi\)
0.984334 0.176314i \(-0.0564173\pi\)
\(234\) 0 0
\(235\) −1837.50 3182.64i −0.510065 0.883459i
\(236\) 210.000 363.731i 0.0579230 0.100326i
\(237\) 0 0
\(238\) −588.000 + 509.223i −0.160144 + 0.138689i
\(239\) −1668.00 −0.451439 −0.225720 0.974192i \(-0.572473\pi\)
−0.225720 + 0.974192i \(0.572473\pi\)
\(240\) 0 0
\(241\) 1704.50 + 2952.28i 0.455587 + 0.789100i 0.998722 0.0505456i \(-0.0160960\pi\)
−0.543135 + 0.839646i \(0.682763\pi\)
\(242\) −1306.00 2262.06i −0.346913 0.600870i
\(243\) 0 0
\(244\) 1652.00 0.433436
\(245\) −1886.50 1485.23i −0.491935 0.387298i
\(246\) 0 0
\(247\) 343.000 594.093i 0.0883586 0.153042i
\(248\) −1764.00 3055.34i −0.451670 0.782315i
\(249\) 0 0
\(250\) 1407.00 2437.00i 0.355946 0.616517i
\(251\) 4760.00 1.19701 0.598503 0.801121i \(-0.295762\pi\)
0.598503 + 0.801121i \(0.295762\pi\)
\(252\) 0 0
\(253\) 795.000 0.197554
\(254\) 72.0000 124.708i 0.0177861 0.0308065i
\(255\) 0 0
\(256\) 2176.00 + 3768.94i 0.531250 + 0.920152i
\(257\) −402.500 + 697.150i −0.0976936 + 0.169210i −0.910730 0.413003i \(-0.864480\pi\)
0.813036 + 0.582213i \(0.197813\pi\)
\(258\) 0 0
\(259\) 766.500 + 3982.85i 0.183892 + 0.955530i
\(260\) −392.000 −0.0935031
\(261\) 0 0
\(262\) −2149.00 3722.18i −0.506739 0.877698i
\(263\) −128.500 222.569i −0.0301279 0.0521831i 0.850568 0.525865i \(-0.176258\pi\)
−0.880696 + 0.473681i \(0.842925\pi\)
\(264\) 0 0
\(265\) 2121.00 0.491668
\(266\) 1715.00 + 594.093i 0.395314 + 0.136941i
\(267\) 0 0
\(268\) 830.000 1437.60i 0.189180 0.327670i
\(269\) 1795.50 + 3109.90i 0.406965 + 0.704884i 0.994548 0.104280i \(-0.0332538\pi\)
−0.587583 + 0.809164i \(0.699920\pi\)
\(270\) 0 0
\(271\) −696.500 + 1206.37i −0.156123 + 0.270413i −0.933467 0.358662i \(-0.883233\pi\)
0.777344 + 0.629075i \(0.216566\pi\)
\(272\) −336.000 −0.0749007
\(273\) 0 0
\(274\) −2250.00 −0.496086
\(275\) 190.000 329.090i 0.0416634 0.0721631i
\(276\) 0 0
\(277\) −207.500 359.401i −0.0450089 0.0779577i 0.842643 0.538472i \(-0.180998\pi\)
−0.887652 + 0.460514i \(0.847665\pi\)
\(278\) 252.000 436.477i 0.0543667 0.0941660i
\(279\) 0 0
\(280\) −588.000 3055.34i −0.125499 0.652112i
\(281\) 4954.00 1.05171 0.525856 0.850574i \(-0.323745\pi\)
0.525856 + 0.850574i \(0.323745\pi\)
\(282\) 0 0
\(283\) 2138.50 + 3703.99i 0.449190 + 0.778019i 0.998333 0.0577087i \(-0.0183795\pi\)
−0.549144 + 0.835728i \(0.685046\pi\)
\(284\) 864.000 + 1496.49i 0.180525 + 0.312678i
\(285\) 0 0
\(286\) 140.000 0.0289454
\(287\) −4900.00 + 4243.52i −1.00780 + 0.872778i
\(288\) 0 0
\(289\) 2236.00 3872.87i 0.455119 0.788289i
\(290\) 406.000 + 703.213i 0.0822108 + 0.142393i
\(291\) 0 0
\(292\) −2226.00 + 3855.55i −0.446119 + 0.772701i
\(293\) −7742.00 −1.54366 −0.771830 0.635829i \(-0.780658\pi\)
−0.771830 + 0.635829i \(0.780658\pi\)
\(294\) 0 0
\(295\) −735.000 −0.145062
\(296\) −2628.00 + 4551.83i −0.516045 + 0.893817i
\(297\) 0 0
\(298\) 201.000 + 348.142i 0.0390725 + 0.0676756i
\(299\) 1113.00 1927.77i 0.215272 0.372863i
\(300\) 0 0
\(301\) −1736.00 + 1503.42i −0.332430 + 0.287893i
\(302\) −3238.00 −0.616973
\(303\) 0 0
\(304\) 392.000 + 678.964i 0.0739564 + 0.128096i
\(305\) −1445.50 2503.68i −0.271374 0.470034i
\(306\) 0 0
\(307\) −7364.00 −1.36901 −0.684504 0.729009i \(-0.739981\pi\)
−0.684504 + 0.729009i \(0.739981\pi\)
\(308\) −70.0000 363.731i −0.0129501 0.0672905i
\(309\) 0 0
\(310\) −1029.00 + 1782.28i −0.188527 + 0.326538i
\(311\) 4987.50 + 8638.60i 0.909374 + 1.57508i 0.814936 + 0.579550i \(0.196772\pi\)
0.0944372 + 0.995531i \(0.469895\pi\)
\(312\) 0 0
\(313\) 2376.50 4116.22i 0.429162 0.743330i −0.567637 0.823279i \(-0.692142\pi\)
0.996799 + 0.0799485i \(0.0254756\pi\)
\(314\) −1358.00 −0.244065
\(315\) 0 0
\(316\) 412.000 0.0733443
\(317\) −1738.50 + 3011.17i −0.308025 + 0.533515i −0.977930 0.208932i \(-0.933001\pi\)
0.669905 + 0.742447i \(0.266335\pi\)
\(318\) 0 0
\(319\) 145.000 + 251.147i 0.0254497 + 0.0440801i
\(320\) 1568.00 2715.86i 0.273918 0.474440i
\(321\) 0 0
\(322\) 5565.00 + 1927.77i 0.963122 + 0.333635i
\(323\) 1029.00 0.177260
\(324\) 0 0
\(325\) −532.000 921.451i −0.0908002 0.157270i
\(326\) −467.000 808.868i −0.0793397 0.137420i
\(327\) 0 0
\(328\) −8400.00 −1.41406
\(329\) −1837.50 9547.93i −0.307917 1.59998i
\(330\) 0 0
\(331\) −1670.50 + 2893.39i −0.277399 + 0.480469i −0.970738 0.240143i \(-0.922806\pi\)
0.693339 + 0.720612i \(0.256139\pi\)
\(332\) −2184.00 3782.80i −0.361032 0.625325i
\(333\) 0 0
\(334\) −1204.00 + 2085.39i −0.197245 + 0.341639i
\(335\) −2905.00 −0.473782
\(336\) 0 0
\(337\) 7366.00 1.19066 0.595329 0.803482i \(-0.297022\pi\)
0.595329 + 0.803482i \(0.297022\pi\)
\(338\) −2001.00 + 3465.83i −0.322012 + 0.557741i
\(339\) 0 0
\(340\) −294.000 509.223i −0.0468953 0.0812250i
\(341\) −367.500 + 636.529i −0.0583614 + 0.101085i
\(342\) 0 0
\(343\) −3430.00 5346.84i −0.539949 0.841698i
\(344\) −2976.00 −0.466439
\(345\) 0 0
\(346\) 2821.00 + 4886.12i 0.438318 + 0.759188i
\(347\) 3707.50 + 6421.58i 0.573571 + 0.993454i 0.996195 + 0.0871487i \(0.0277755\pi\)
−0.422625 + 0.906305i \(0.638891\pi\)
\(348\) 0 0
\(349\) −3878.00 −0.594798 −0.297399 0.954753i \(-0.596119\pi\)
−0.297399 + 0.954753i \(0.596119\pi\)
\(350\) 2128.00 1842.90i 0.324990 0.281449i
\(351\) 0 0
\(352\) 400.000 692.820i 0.0605684 0.104908i
\(353\) 633.500 + 1097.25i 0.0955179 + 0.165442i 0.909825 0.414993i \(-0.136216\pi\)
−0.814307 + 0.580435i \(0.802883\pi\)
\(354\) 0 0
\(355\) 1512.00 2618.86i 0.226052 0.391534i
\(356\) −1316.00 −0.195921
\(357\) 0 0
\(358\) −6506.00 −0.960483
\(359\) 2342.50 4057.33i 0.344380 0.596484i −0.640861 0.767657i \(-0.721422\pi\)
0.985241 + 0.171173i \(0.0547558\pi\)
\(360\) 0 0
\(361\) 2229.00 + 3860.74i 0.324974 + 0.562872i
\(362\) 1582.00 2740.10i 0.229691 0.397836i
\(363\) 0 0
\(364\) −980.000 339.482i −0.141115 0.0488838i
\(365\) 7791.00 1.11726
\(366\) 0 0
\(367\) 2320.50 + 4019.22i 0.330052 + 0.571667i 0.982522 0.186148i \(-0.0596004\pi\)
−0.652470 + 0.757815i \(0.726267\pi\)
\(368\) 1272.00 + 2203.17i 0.180184 + 0.312087i
\(369\) 0 0
\(370\) 3066.00 0.430794
\(371\) 5302.50 + 1836.84i 0.742027 + 0.257046i
\(372\) 0 0
\(373\) 4398.50 7618.43i 0.610578 1.05755i −0.380565 0.924754i \(-0.624270\pi\)
0.991143 0.132798i \(-0.0423963\pi\)
\(374\) 105.000 + 181.865i 0.0145172 + 0.0251445i
\(375\) 0 0
\(376\) 6300.00 10911.9i 0.864090 1.49665i
\(377\) 812.000 0.110929
\(378\) 0 0
\(379\) 13680.0 1.85407 0.927037 0.374969i \(-0.122347\pi\)
0.927037 + 0.374969i \(0.122347\pi\)
\(380\) −686.000 + 1188.19i −0.0926080 + 0.160402i
\(381\) 0 0
\(382\) −2557.00 4428.85i −0.342480 0.593193i
\(383\) 4882.50 8456.74i 0.651395 1.12825i −0.331390 0.943494i \(-0.607518\pi\)
0.982785 0.184755i \(-0.0591490\pi\)
\(384\) 0 0
\(385\) −490.000 + 424.352i −0.0648642 + 0.0561740i
\(386\) 794.000 0.104698
\(387\) 0 0
\(388\) −1764.00 3055.34i −0.230808 0.399771i
\(389\) 865.500 + 1499.09i 0.112809 + 0.195390i 0.916902 0.399113i \(-0.130682\pi\)
−0.804093 + 0.594504i \(0.797349\pi\)
\(390\) 0 0
\(391\) 3339.00 0.431868
\(392\) 1176.00 8147.57i 0.151523 1.04978i
\(393\) 0 0
\(394\) −2914.00 + 5047.20i −0.372602 + 0.645366i
\(395\) −360.500 624.404i −0.0459208 0.0795372i
\(396\) 0 0
\(397\) −5491.50 + 9511.56i −0.694233 + 1.20245i 0.276206 + 0.961099i \(0.410923\pi\)
−0.970439 + 0.241348i \(0.922410\pi\)
\(398\) −6678.00 −0.841050
\(399\) 0 0
\(400\) 1216.00 0.152000
\(401\) 3301.50 5718.37i 0.411145 0.712124i −0.583870 0.811847i \(-0.698462\pi\)
0.995015 + 0.0997232i \(0.0317957\pi\)
\(402\) 0 0
\(403\) 1029.00 + 1782.28i 0.127191 + 0.220302i
\(404\) −2758.00 + 4777.00i −0.339643 + 0.588278i
\(405\) 0 0
\(406\) 406.000 + 2109.64i 0.0496292 + 0.257881i
\(407\) 1095.00 0.133359
\(408\) 0 0
\(409\) −5477.50 9487.31i −0.662213 1.14699i −0.980033 0.198835i \(-0.936284\pi\)
0.317820 0.948151i \(-0.397049\pi\)
\(410\) 2450.00 + 4243.52i 0.295114 + 0.511153i
\(411\) 0 0
\(412\) 2716.00 0.324776
\(413\) −1837.50 636.529i −0.218928 0.0758391i
\(414\) 0 0
\(415\) −3822.00 + 6619.90i −0.452083 + 0.783031i
\(416\) −1120.00 1939.90i −0.132001 0.228633i
\(417\) 0 0
\(418\) 245.000 424.352i 0.0286683 0.0496549i
\(419\) −6636.00 −0.773723 −0.386861 0.922138i \(-0.626441\pi\)
−0.386861 + 0.922138i \(0.626441\pi\)
\(420\) 0 0
\(421\) −16630.0 −1.92517 −0.962585 0.270980i \(-0.912652\pi\)
−0.962585 + 0.270980i \(0.912652\pi\)
\(422\) 1780.00 3083.05i 0.205329 0.355641i
\(423\) 0 0
\(424\) 3636.00 + 6297.74i 0.416462 + 0.721333i
\(425\) 798.000 1382.18i 0.0910793 0.157754i
\(426\) 0 0
\(427\) −1445.50 7511.04i −0.163824 0.851252i
\(428\) 1828.00 0.206448
\(429\) 0 0
\(430\) 868.000 + 1503.42i 0.0973458 + 0.168608i
\(431\) 2461.50 + 4263.44i 0.275096 + 0.476480i 0.970159 0.242468i \(-0.0779571\pi\)
−0.695064 + 0.718948i \(0.744624\pi\)
\(432\) 0 0
\(433\) 8974.00 0.995988 0.497994 0.867180i \(-0.334070\pi\)
0.497994 + 0.867180i \(0.334070\pi\)
\(434\) −4116.00 + 3564.56i −0.455240 + 0.394250i
\(435\) 0 0
\(436\) −2250.00 + 3897.11i −0.247146 + 0.428069i
\(437\) −3895.50 6747.20i −0.426423 0.738587i
\(438\) 0 0
\(439\) 2089.50 3619.12i 0.227167 0.393465i −0.729800 0.683660i \(-0.760387\pi\)
0.956967 + 0.290195i \(0.0937203\pi\)
\(440\) −840.000 −0.0910123
\(441\) 0 0
\(442\) 588.000 0.0632767
\(443\) −6463.50 + 11195.1i −0.693206 + 1.20067i 0.277576 + 0.960704i \(0.410469\pi\)
−0.970782 + 0.239964i \(0.922864\pi\)
\(444\) 0 0
\(445\) 1151.50 + 1994.46i 0.122666 + 0.212464i
\(446\) −1400.00 + 2424.87i −0.148637 + 0.257446i
\(447\) 0 0
\(448\) 6272.00 5431.71i 0.661438 0.572822i
\(449\) 2826.00 0.297032 0.148516 0.988910i \(-0.452550\pi\)
0.148516 + 0.988910i \(0.452550\pi\)
\(450\) 0 0
\(451\) 875.000 + 1515.54i 0.0913573 + 0.158235i
\(452\) 3076.00 + 5327.79i 0.320095 + 0.554421i
\(453\) 0 0
\(454\) −4410.00 −0.455884
\(455\) 343.000 + 1782.28i 0.0353409 + 0.183636i
\(456\) 0 0
\(457\) −4239.50 + 7343.03i −0.433951 + 0.751625i −0.997209 0.0746560i \(-0.976214\pi\)
0.563259 + 0.826281i \(0.309547\pi\)
\(458\) 287.000 + 497.099i 0.0292808 + 0.0507159i
\(459\) 0 0
\(460\) −2226.00 + 3855.55i −0.225626 + 0.390795i
\(461\) −9338.00 −0.943414 −0.471707 0.881755i \(-0.656362\pi\)
−0.471707 + 0.881755i \(0.656362\pi\)
\(462\) 0 0
\(463\) −4016.00 −0.403109 −0.201554 0.979477i \(-0.564599\pi\)
−0.201554 + 0.979477i \(0.564599\pi\)
\(464\) −464.000 + 803.672i −0.0464238 + 0.0804084i
\(465\) 0 0
\(466\) −4587.00 7944.92i −0.455984 0.789788i
\(467\) −2929.50 + 5074.04i −0.290281 + 0.502781i −0.973876 0.227080i \(-0.927082\pi\)
0.683595 + 0.729861i \(0.260415\pi\)
\(468\) 0 0
\(469\) −7262.50 2515.80i −0.715034 0.247695i
\(470\) −7350.00 −0.721341
\(471\) 0 0
\(472\) −1260.00 2182.38i −0.122873 0.212823i
\(473\) 310.000 + 536.936i 0.0301349 + 0.0521952i
\(474\) 0 0
\(475\) −3724.00 −0.359724
\(476\) −294.000 1527.67i −0.0283098 0.147102i
\(477\) 0 0
\(478\) −1668.00 + 2889.06i −0.159608 + 0.276449i
\(479\) 3251.50 + 5631.76i 0.310156 + 0.537206i 0.978396 0.206740i \(-0.0662853\pi\)
−0.668240 + 0.743946i \(0.732952\pi\)
\(480\) 0 0
\(481\) 1533.00 2655.23i 0.145320 0.251701i
\(482\) 6818.00 0.644297
\(483\) 0 0
\(484\) 5224.00 0.490609
\(485\) −3087.00 + 5346.84i −0.289017 + 0.500593i
\(486\) 0 0
\(487\) 8024.50 + 13898.8i 0.746663 + 1.29326i 0.949414 + 0.314028i \(0.101678\pi\)
−0.202751 + 0.979230i \(0.564988\pi\)
\(488\) 4956.00 8584.04i 0.459729 0.796273i
\(489\) 0 0
\(490\) −4459.00 + 1782.28i −0.411096 + 0.164317i
\(491\) −8864.00 −0.814718 −0.407359 0.913268i \(-0.633550\pi\)
−0.407359 + 0.913268i \(0.633550\pi\)
\(492\) 0 0
\(493\) 609.000 + 1054.82i 0.0556348 + 0.0963624i
\(494\) −686.000 1188.19i −0.0624789 0.108217i
\(495\) 0 0
\(496\) −2352.00 −0.212919
\(497\) 6048.00 5237.72i 0.545855 0.472724i
\(498\) 0 0
\(499\) 5105.50 8842.99i 0.458023 0.793319i −0.540833 0.841130i \(-0.681891\pi\)
0.998856 + 0.0478104i \(0.0152243\pi\)
\(500\) 2814.00 + 4873.99i 0.251692 + 0.435943i
\(501\) 0 0
\(502\) 4760.00 8244.56i 0.423206 0.733014i
\(503\) 1680.00 0.148921 0.0744607 0.997224i \(-0.476276\pi\)
0.0744607 + 0.997224i \(0.476276\pi\)
\(504\) 0 0
\(505\) 9653.00 0.850600
\(506\) 795.000 1376.98i 0.0698460 0.120977i
\(507\) 0 0
\(508\) 144.000 + 249.415i 0.0125767 + 0.0217835i
\(509\) −4728.50 + 8190.00i −0.411762 + 0.713193i −0.995083 0.0990489i \(-0.968420\pi\)
0.583320 + 0.812242i \(0.301753\pi\)
\(510\) 0 0
\(511\) 19477.5 + 6747.20i 1.68617 + 0.584107i
\(512\) 5632.00 0.486136
\(513\) 0 0
\(514\) 805.000 + 1394.30i 0.0690798 + 0.119650i
\(515\) −2376.50 4116.22i −0.203342 0.352199i
\(516\) 0 0
\(517\) −2625.00 −0.223302
\(518\) 7665.00 + 2655.23i 0.650156 + 0.225221i
\(519\) 0 0
\(520\) −1176.00 + 2036.89i −0.0991750 + 0.171776i
\(521\) −9040.50 15658.6i −0.760214 1.31673i −0.942740 0.333528i \(-0.891761\pi\)
0.182526 0.983201i \(-0.441573\pi\)
\(522\) 0 0
\(523\) −10188.5 + 17647.0i −0.851839 + 1.47543i 0.0277071 + 0.999616i \(0.491179\pi\)
−0.879546 + 0.475813i \(0.842154\pi\)
\(524\) 8596.00 0.716637
\(525\) 0 0
\(526\) −514.000 −0.0426073
\(527\) −1543.50 + 2673.42i −0.127582 + 0.220979i
\(528\) 0 0
\(529\) −6557.00 11357.1i −0.538917 0.933431i
\(530\) 2121.00 3673.68i 0.173831 0.301084i
\(531\) 0 0
\(532\) −2744.00 + 2376.37i −0.223623 + 0.193663i
\(533\) 4900.00 0.398204
\(534\) 0 0
\(535\) −1599.50 2770.42i −0.129257 0.223879i
\(536\) −4980.00 8625.61i −0.401312 0.695093i
\(537\) 0 0
\(538\) 7182.00 0.575535
\(539\) −1592.50 + 636.529i −0.127261 + 0.0508668i
\(540\) 0 0
\(541\) 3096.50 5363.30i 0.246079 0.426222i −0.716355 0.697736i \(-0.754191\pi\)
0.962435 + 0.271514i \(0.0875243\pi\)
\(542\) 1393.00 + 2412.75i 0.110396 + 0.191211i
\(543\) 0 0
\(544\) 1680.00 2909.85i 0.132407 0.229336i
\(545\) 7875.00 0.618950
\(546\) 0 0
\(547\) −18464.0 −1.44326 −0.721630 0.692279i \(-0.756607\pi\)
−0.721630 + 0.692279i \(0.756607\pi\)
\(548\) 2250.00 3897.11i 0.175393 0.303789i
\(549\) 0 0
\(550\) −380.000 658.179i −0.0294605 0.0510270i
\(551\) 1421.00 2461.24i 0.109867 0.190295i
\(552\) 0 0
\(553\) −360.500 1873.21i −0.0277216 0.144045i
\(554\) −830.000 −0.0636522
\(555\) 0 0
\(556\) 504.000 + 872.954i 0.0384431 + 0.0665854i
\(557\) −4706.50 8151.90i −0.358027 0.620120i 0.629604 0.776916i \(-0.283217\pi\)
−0.987631 + 0.156796i \(0.949884\pi\)
\(558\) 0 0
\(559\) 1736.00 0.131351
\(560\) −1960.00 678.964i −0.147902 0.0512348i
\(561\) 0 0
\(562\) 4954.00 8580.58i 0.371836 0.644039i
\(563\) 1599.50 + 2770.42i 0.119735 + 0.207387i 0.919663 0.392709i \(-0.128462\pi\)
−0.799928 + 0.600097i \(0.795129\pi\)
\(564\) 0 0
\(565\) 5383.00 9323.63i 0.400822 0.694244i
\(566\) 8554.00 0.635250
\(567\) 0 0
\(568\) 10368.0 0.765901
\(569\) 10791.5 18691.4i 0.795085 1.37713i −0.127701 0.991813i \(-0.540760\pi\)
0.922785 0.385314i \(-0.125907\pi\)
\(570\) 0 0
\(571\) −10133.5 17551.7i −0.742686 1.28637i −0.951268 0.308365i \(-0.900218\pi\)
0.208582 0.978005i \(-0.433115\pi\)
\(572\) −140.000 + 242.487i −0.0102337 + 0.0177253i
\(573\) 0 0
\(574\) 2450.00 + 12730.6i 0.178155 + 0.925721i
\(575\) −12084.0 −0.876413
\(576\) 0 0
\(577\) −6975.50 12081.9i −0.503282 0.871710i −0.999993 0.00379418i \(-0.998792\pi\)
0.496711 0.867916i \(-0.334541\pi\)
\(578\) −4472.00 7745.73i −0.321818 0.557405i
\(579\) 0 0
\(580\) −1624.00 −0.116264
\(581\) −15288.0 + 13239.8i −1.09166 + 0.945403i
\(582\) 0 0
\(583\) 757.500 1312.03i 0.0538121 0.0932053i
\(584\) 13356.0 + 23133.3i 0.946362 + 1.63915i
\(585\) 0 0
\(586\) −7742.00 + 13409.5i −0.545766 + 0.945295i
\(587\) 20972.0 1.47463 0.737314 0.675550i \(-0.236094\pi\)
0.737314 + 0.675550i \(0.236094\pi\)
\(588\) 0 0
\(589\) 7203.00 0.503895
\(590\) −735.000 + 1273.06i −0.0512872 + 0.0888321i
\(591\) 0 0
\(592\) 1752.00 + 3034.55i 0.121633 + 0.210675i
\(593\) −94.5000 + 163.679i −0.00654410 + 0.0113347i −0.869279 0.494322i \(-0.835416\pi\)
0.862735 + 0.505657i \(0.168750\pi\)
\(594\) 0 0
\(595\) −2058.00 + 1782.28i −0.141798 + 0.122801i
\(596\) −804.000 −0.0552569
\(597\) 0 0
\(598\) −2226.00 3855.55i −0.152221 0.263654i
\(599\) −5140.50 8903.61i −0.350643 0.607331i 0.635719 0.771920i \(-0.280704\pi\)
−0.986362 + 0.164589i \(0.947370\pi\)
\(600\) 0 0
\(601\) −6090.00 −0.413338 −0.206669 0.978411i \(-0.566262\pi\)
−0.206669 + 0.978411i \(0.566262\pi\)
\(602\) 868.000 + 4510.26i 0.0587658 + 0.305356i
\(603\) 0 0
\(604\) 3238.00 5608.38i 0.218133 0.377817i
\(605\) −4571.00 7917.20i −0.307170 0.532033i
\(606\) 0 0
\(607\) −2474.50 + 4285.96i −0.165464 + 0.286593i −0.936820 0.349812i \(-0.886246\pi\)
0.771356 + 0.636404i \(0.219579\pi\)
\(608\) −7840.00 −0.522951
\(609\) 0 0
\(610\) −5782.00 −0.383781
\(611\) −3675.00 + 6365.29i −0.243330 + 0.421460i
\(612\) 0 0
\(613\) 7898.50 + 13680.6i 0.520420 + 0.901394i 0.999718 + 0.0237416i \(0.00755791\pi\)
−0.479298 + 0.877652i \(0.659109\pi\)
\(614\) −7364.00 + 12754.8i −0.484018 + 0.838343i
\(615\) 0 0
\(616\) −2100.00 727.461i −0.137356 0.0475816i
\(617\) 9378.00 0.611903 0.305951 0.952047i \(-0.401025\pi\)
0.305951 + 0.952047i \(0.401025\pi\)
\(618\) 0 0
\(619\) 12176.5 + 21090.3i 0.790654 + 1.36945i 0.925562 + 0.378595i \(0.123593\pi\)
−0.134908 + 0.990858i \(0.543074\pi\)
\(620\) −2058.00 3564.56i −0.133308 0.230897i
\(621\) 0 0
\(622\) 19950.0 1.28605
\(623\) 1151.50 + 5983.37i 0.0740512 + 0.384781i
\(624\) 0 0
\(625\) 174.500 302.243i 0.0111680 0.0193435i
\(626\) −4753.00 8232.44i −0.303463 0.525614i
\(627\) 0 0
\(628\) 1358.00 2352.12i 0.0862900 0.149459i
\(629\) 4599.00 0.291533
\(630\) 0 0
\(631\) −12640.0 −0.797449 −0.398725 0.917071i \(-0.630547\pi\)
−0.398725 + 0.917071i \(0.630547\pi\)
\(632\) 1236.00 2140.81i 0.0777934 0.134742i
\(633\) 0 0
\(634\) 3477.00 + 6022.34i 0.217806 + 0.377252i
\(635\) 252.000 436.477i 0.0157485 0.0272772i
\(636\) 0 0
\(637\) −686.000 + 4752.75i −0.0426692 + 0.295621i
\(638\) 580.000 0.0359913
\(639\) 0 0
\(640\) 1344.00 + 2327.88i 0.0830098 + 0.143777i
\(641\) −520.500 901.532i −0.0320726 0.0555513i 0.849544 0.527518i \(-0.176877\pi\)
−0.881616 + 0.471967i \(0.843544\pi\)
\(642\) 0 0
\(643\) 9548.00 0.585593 0.292797 0.956175i \(-0.405414\pi\)
0.292797 + 0.956175i \(0.405414\pi\)
\(644\) −8904.00 + 7711.09i −0.544824 + 0.471832i
\(645\) 0 0
\(646\) 1029.00 1782.28i 0.0626710 0.108549i
\(647\) −1620.50 2806.79i −0.0984674 0.170551i 0.812583 0.582845i \(-0.198061\pi\)
−0.911050 + 0.412295i \(0.864727\pi\)
\(648\) 0 0
\(649\) −262.500 + 454.663i −0.0158768 + 0.0274994i
\(650\) −2128.00 −0.128411
\(651\) 0 0
\(652\) 1868.00 0.112203
\(653\) −4426.50 + 7666.92i −0.265272 + 0.459464i −0.967635 0.252355i \(-0.918795\pi\)
0.702363 + 0.711819i \(0.252128\pi\)
\(654\) 0 0
\(655\) −7521.50 13027.6i −0.448686 0.777147i
\(656\) −2800.00 + 4849.74i −0.166649 + 0.288644i
\(657\) 0 0
\(658\) −18375.0 6365.29i −1.08865 0.377120i
\(659\) −7044.00 −0.416381 −0.208191 0.978088i \(-0.566757\pi\)
−0.208191 + 0.978088i \(0.566757\pi\)
\(660\) 0 0
\(661\) 6044.50 + 10469.4i 0.355679 + 0.616054i 0.987234 0.159277i \(-0.0509163\pi\)
−0.631555 + 0.775331i \(0.717583\pi\)
\(662\) 3341.00 + 5786.78i 0.196151 + 0.339743i
\(663\) 0 0
\(664\) −26208.0 −1.53173
\(665\) 6002.50 + 2079.33i 0.350026 + 0.121252i
\(666\) 0 0
\(667\) 4611.00 7986.49i 0.267674 0.463625i
\(668\) −2408.00 4170.78i −0.139474 0.241575i
\(669\) 0 0
\(670\) −2905.00 + 5031.61i −0.167507 + 0.290131i
\(671\) −2065.00 −0.118805
\(672\) 0 0
\(673\) 982.000 0.0562456 0.0281228 0.999604i \(-0.491047\pi\)
0.0281228 + 0.999604i \(0.491047\pi\)
\(674\) 7366.00 12758.3i 0.420961 0.729126i
\(675\) 0 0
\(676\) −4002.00 6931.67i −0.227697 0.394383i
\(677\) −15256.5 + 26425.0i −0.866108 + 1.50014i −0.000164659 1.00000i \(0.500052\pi\)
−0.865943 + 0.500143i \(0.833281\pi\)
\(678\) 0 0
\(679\) −12348.0 + 10693.7i −0.697898 + 0.604397i
\(680\) −3528.00 −0.198960
\(681\) 0 0
\(682\) 735.000 + 1273.06i 0.0412677 + 0.0714778i
\(683\) 5737.50 + 9937.64i 0.321434 + 0.556740i 0.980784 0.195096i \(-0.0625019\pi\)
−0.659350 + 0.751836i \(0.729169\pi\)
\(684\) 0 0
\(685\) −7875.00 −0.439253
\(686\) −12691.0 + 594.093i −0.706333 + 0.0330650i
\(687\) 0 0
\(688\) −992.000 + 1718.19i −0.0549704 + 0.0952116i
\(689\) −2121.00 3673.68i −0.117277 0.203129i
\(690\) 0 0
\(691\) 14157.5 24521.5i 0.779416 1.34999i −0.152862 0.988248i \(-0.548849\pi\)
0.932279 0.361741i \(-0.117818\pi\)
\(692\) −11284.0 −0.619875
\(693\) 0 0
\(694\) 14830.0 0.811151
\(695\) 882.000 1527.67i 0.0481384 0.0833781i
\(696\) 0 0
\(697\) 3675.00 + 6365.29i 0.199714 + 0.345915i
\(698\) −3878.00 + 6716.89i −0.210293 + 0.364238i
\(699\) 0 0
\(700\) 1064.00 + 5528.71i 0.0574506 + 0.298522i
\(701\) −10614.0 −0.571876 −0.285938 0.958248i \(-0.592305\pi\)
−0.285938 + 0.958248i \(0.592305\pi\)
\(702\) 0 0
\(703\) −5365.50 9293.32i −0.287857 0.498583i
\(704\) −1120.00 1939.90i −0.0599596 0.103853i
\(705\) 0 0
\(706\) 2534.00 0.135083
\(707\) 24132.5 + 8359.74i 1.28373 + 0.444697i
\(708\) 0 0
\(709\) −5149.50 + 8919.20i −0.272769 + 0.472451i −0.969570 0.244814i \(-0.921273\pi\)
0.696801 + 0.717265i \(0.254606\pi\)
\(710\) −3024.00 5237.72i −0.159843 0.276857i
\(711\) 0 0
\(712\) −3948.00 + 6838.14i −0.207806 + 0.359930i
\(713\) 23373.0 1.22767
\(714\) 0 0
\(715\) 490.000 0.0256293
\(716\) 6506.00 11268.7i 0.339582 0.588173i
\(717\) 0 0
\(718\) −4685.00 8114.66i −0.243513 0.421778i
\(719\) 16264.5 28170.9i 0.843621 1.46119i −0.0431924 0.999067i \(-0.513753\pi\)
0.886813 0.462128i \(-0.152914\pi\)
\(720\) 0 0
\(721\) −2376.50 12348.7i −0.122754 0.637847i
\(722\) 8916.00 0.459583
\(723\) 0 0
\(724\) 3164.00 + 5480.21i 0.162416 + 0.281313i
\(725\) −2204.00 3817.44i −0.112903 0.195553i
\(726\) 0 0
\(727\) 29456.0 1.50270 0.751350 0.659904i \(-0.229403\pi\)
0.751350 + 0.659904i \(0.229403\pi\)
\(728\) −4704.00 + 4073.78i −0.239481 + 0.207396i
\(729\) 0 0
\(730\) 7791.00 13494.4i 0.395011 0.684179i
\(731\) 1302.00 + 2255.13i 0.0658772 + 0.114103i
\(732\) 0 0
\(733\) −13933.5 + 24133.5i −0.702109 + 1.21609i 0.265616 + 0.964079i \(0.414425\pi\)
−0.967725 + 0.252009i \(0.918909\pi\)
\(734\) 9282.00 0.466764
\(735\) 0 0
\(736\) −25440.0 −1.27409
\(737\) −1037.50 + 1797.00i −0.0518546 + 0.0898147i
\(738\) 0 0
\(739\) −9769.50 16921.3i −0.486302 0.842299i 0.513574 0.858045i \(-0.328321\pi\)
−0.999876 + 0.0157460i \(0.994988\pi\)
\(740\) −3066.00 + 5310.47i −0.152309 + 0.263806i
\(741\) 0 0
\(742\) 8484.00 7347.36i 0.419754 0.363518i
\(743\) −1248.00 −0.0616214 −0.0308107 0.999525i \(-0.509809\pi\)
−0.0308107 + 0.999525i \(0.509809\pi\)
\(744\) 0 0
\(745\) 703.500 + 1218.50i 0.0345963 + 0.0599226i
\(746\) −8797.00 15236.9i −0.431744 0.747803i
\(747\) 0 0
\(748\) −420.000 −0.0205304
\(749\) −1599.50 8311.25i −0.0780300 0.405456i
\(750\) 0 0
\(751\) −14046.5 + 24329.3i −0.682509 + 1.18214i 0.291704 + 0.956509i \(0.405778\pi\)
−0.974213 + 0.225631i \(0.927556\pi\)
\(752\) −4200.00 7274.61i −0.203668 0.352763i
\(753\) 0 0
\(754\) 812.000 1406.43i 0.0392192 0.0679297i
\(755\) −11333.0 −0.546292
\(756\) 0 0
\(757\) 35954.0 1.72625 0.863124 0.504991i \(-0.168504\pi\)
0.863124 + 0.504991i \(0.168504\pi\)
\(758\) 13680.0 23694.5i 0.655514 1.13538i
\(759\) 0 0
\(760\) 4116.00 + 7129.12i 0.196451 + 0.340264i
\(761\) −430.500 + 745.648i −0.0205067 + 0.0355187i −0.876097 0.482136i \(-0.839861\pi\)
0.855590 + 0.517654i \(0.173195\pi\)
\(762\) 0 0
\(763\) 19687.5 + 6819.95i 0.934122 + 0.323589i
\(764\) 10228.0 0.484340
\(765\) 0 0
\(766\) −9765.00 16913.5i −0.460605 0.797792i
\(767\) 735.000 + 1273.06i 0.0346014 + 0.0599315i
\(768\) 0 0
\(769\) 24710.0 1.15873 0.579366 0.815067i \(-0.303300\pi\)
0.579366 + 0.815067i \(0.303300\pi\)
\(770\) 245.000 + 1273.06i 0.0114665 + 0.0595816i
\(771\) 0 0
\(772\) −794.000 + 1375.25i −0.0370164 + 0.0641143i
\(773\) 8249.50 + 14288.6i 0.383847 + 0.664843i 0.991609 0.129277i \(-0.0412656\pi\)
−0.607761 + 0.794120i \(0.707932\pi\)
\(774\) 0 0
\(775\) 5586.00 9675.24i 0.258910 0.448445i
\(776\) −21168.0 −0.979236
\(777\) 0 0
\(778\) 3462.00 0.159536
\(779\) 8575.00 14852.3i 0.394392 0.683107i
\(780\) 0 0
\(781\) −1080.00 1870.61i −0.0494820 0.0857053i
\(782\) 3339.00 5783.32i 0.152688 0.264464i
\(783\) 0 0
\(784\) −4312.00 3394.82i −0.196429 0.154647i
\(785\) −4753.00 −0.216104
\(786\) 0 0
\(787\)