Properties

Label 63.4.p.a.17.8
Level $63$
Weight $4$
Character 63.17
Analytic conductor $3.717$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} - 1762200 x^{2} + 810000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.8
Root \(4.21355 - 2.43270i\) of defining polynomial
Character \(\chi\) \(=\) 63.17
Dual form 63.4.p.a.26.8

$q$-expansion

\(f(q)\) \(=\) \(q+(4.21355 - 2.43270i) q^{2} +(7.83601 - 13.5724i) q^{4} +(-6.38217 - 11.0542i) q^{5} +(2.53897 + 18.3454i) q^{7} -37.3274i q^{8} +O(q^{10})\) \(q+(4.21355 - 2.43270i) q^{2} +(7.83601 - 13.5724i) q^{4} +(-6.38217 - 11.0542i) q^{5} +(2.53897 + 18.3454i) q^{7} -37.3274i q^{8} +(-53.7832 - 31.0517i) q^{10} +(46.8633 + 27.0565i) q^{11} +8.85528i q^{13} +(55.3268 + 71.1228i) q^{14} +(-28.1181 - 48.7020i) q^{16} +(34.4587 - 59.6841i) q^{17} +(-141.898 + 81.9246i) q^{19} -200.043 q^{20} +263.281 q^{22} +(-81.3807 + 46.9852i) q^{23} +(-18.9642 + 32.8469i) q^{25} +(21.5422 + 37.3122i) q^{26} +(268.886 + 109.295i) q^{28} -119.620i q^{29} +(85.6311 + 49.4391i) q^{31} +(21.6577 + 12.5041i) q^{32} -335.310i q^{34} +(186.590 - 145.150i) q^{35} +(-47.0949 - 81.5708i) q^{37} +(-398.595 + 690.387i) q^{38} +(-412.626 + 238.230i) q^{40} -259.347 q^{41} +5.01418 q^{43} +(734.443 - 424.031i) q^{44} +(-228.601 + 395.949i) q^{46} +(-28.6747 - 49.6660i) q^{47} +(-330.107 + 93.1568i) q^{49} +184.536i q^{50} +(120.187 + 69.3901i) q^{52} +(-407.058 - 235.015i) q^{53} -690.718i q^{55} +(684.786 - 94.7731i) q^{56} +(-290.999 - 504.025i) q^{58} +(112.979 - 195.685i) q^{59} +(370.650 - 213.995i) q^{61} +481.082 q^{62} +571.564 q^{64} +(97.8884 - 56.5159i) q^{65} +(-81.9267 + 141.901i) q^{67} +(-540.037 - 935.372i) q^{68} +(433.103 - 1065.51i) q^{70} -79.8529i q^{71} +(666.447 + 384.774i) q^{73} +(-396.874 - 229.135i) q^{74} +2567.85i q^{76} +(-377.379 + 928.422i) q^{77} +(-267.408 - 463.165i) q^{79} +(-358.909 + 621.648i) q^{80} +(-1092.77 + 630.912i) q^{82} -438.520 q^{83} -879.684 q^{85} +(21.1275 - 12.1980i) q^{86} +(1009.95 - 1749.29i) q^{88} +(-12.8242 - 22.2121i) q^{89} +(-162.454 + 22.4833i) q^{91} +1472.71i q^{92} +(-241.644 - 139.513i) q^{94} +(1811.23 + 1045.71i) q^{95} +1381.00i q^{97} +(-1164.30 + 1195.57i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 32q^{4} + 56q^{7} + O(q^{10}) \) \( 16q + 32q^{4} + 56q^{7} - 72q^{10} - 188q^{16} - 612q^{19} + 528q^{22} - 20q^{25} + 1036q^{28} + 1128q^{31} - 1196q^{37} - 3204q^{40} + 328q^{43} - 1392q^{46} + 784q^{49} + 4452q^{52} - 3372q^{58} - 1632q^{61} + 5432q^{64} + 308q^{67} + 3612q^{70} + 4068q^{73} - 2176q^{79} - 10188q^{82} - 4608q^{85} + 708q^{88} + 924q^{91} - 2916q^{94} + O(q^{100}) \)

Character values

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

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.21355 2.43270i 1.48972 0.860088i 0.489785 0.871843i \(-0.337075\pi\)
0.999931 + 0.0117558i \(0.00374206\pi\)
\(3\) 0 0
\(4\) 7.83601 13.5724i 0.979502 1.69655i
\(5\) −6.38217 11.0542i −0.570839 0.988721i −0.996480 0.0838295i \(-0.973285\pi\)
0.425642 0.904892i \(-0.360048\pi\)
\(6\) 0 0
\(7\) 2.53897 + 18.3454i 0.137091 + 0.990558i
\(8\) 37.3274i 1.64965i
\(9\) 0 0
\(10\) −53.7832 31.0517i −1.70077 0.981942i
\(11\) 46.8633 + 27.0565i 1.28453 + 0.741623i 0.977673 0.210133i \(-0.0673897\pi\)
0.306856 + 0.951756i \(0.400723\pi\)
\(12\) 0 0
\(13\) 8.85528i 0.188924i 0.995528 + 0.0944620i \(0.0301131\pi\)
−0.995528 + 0.0944620i \(0.969887\pi\)
\(14\) 55.3268 + 71.1228i 1.05619 + 1.35774i
\(15\) 0 0
\(16\) −28.1181 48.7020i −0.439345 0.760968i
\(17\) 34.4587 59.6841i 0.491615 0.851502i −0.508339 0.861157i \(-0.669740\pi\)
0.999953 + 0.00965543i \(0.00307347\pi\)
\(18\) 0 0
\(19\) −141.898 + 81.9246i −1.71334 + 0.989199i −0.783383 + 0.621540i \(0.786508\pi\)
−0.929960 + 0.367660i \(0.880159\pi\)
\(20\) −200.043 −2.23655
\(21\) 0 0
\(22\) 263.281 2.55144
\(23\) −81.3807 + 46.9852i −0.737785 + 0.425960i −0.821263 0.570549i \(-0.806730\pi\)
0.0834783 + 0.996510i \(0.473397\pi\)
\(24\) 0 0
\(25\) −18.9642 + 32.8469i −0.151713 + 0.262775i
\(26\) 21.5422 + 37.3122i 0.162491 + 0.281443i
\(27\) 0 0
\(28\) 268.886 + 109.295i 1.81481 + 0.737672i
\(29\) 119.620i 0.765961i −0.923756 0.382981i \(-0.874898\pi\)
0.923756 0.382981i \(-0.125102\pi\)
\(30\) 0 0
\(31\) 85.6311 + 49.4391i 0.496123 + 0.286437i 0.727111 0.686520i \(-0.240863\pi\)
−0.230988 + 0.972957i \(0.574196\pi\)
\(32\) 21.6577 + 12.5041i 0.119643 + 0.0690760i
\(33\) 0 0
\(34\) 335.310i 1.69133i
\(35\) 186.590 145.150i 0.901129 0.700994i
\(36\) 0 0
\(37\) −47.0949 81.5708i −0.209253 0.362437i 0.742227 0.670149i \(-0.233770\pi\)
−0.951479 + 0.307712i \(0.900437\pi\)
\(38\) −398.595 + 690.387i −1.70160 + 2.94725i
\(39\) 0 0
\(40\) −412.626 + 238.230i −1.63105 + 0.941686i
\(41\) −259.347 −0.987883 −0.493941 0.869495i \(-0.664444\pi\)
−0.493941 + 0.869495i \(0.664444\pi\)
\(42\) 0 0
\(43\) 5.01418 0.0177827 0.00889133 0.999960i \(-0.497170\pi\)
0.00889133 + 0.999960i \(0.497170\pi\)
\(44\) 734.443 424.031i 2.51640 1.45284i
\(45\) 0 0
\(46\) −228.601 + 395.949i −0.732727 + 1.26912i
\(47\) −28.6747 49.6660i −0.0889921 0.154139i 0.818093 0.575086i \(-0.195031\pi\)
−0.907085 + 0.420947i \(0.861698\pi\)
\(48\) 0 0
\(49\) −330.107 + 93.1568i −0.962412 + 0.271594i
\(50\) 184.536i 0.521947i
\(51\) 0 0
\(52\) 120.187 + 69.3901i 0.320518 + 0.185051i
\(53\) −407.058 235.015i −1.05497 0.609090i −0.130937 0.991391i \(-0.541798\pi\)
−0.924038 + 0.382301i \(0.875132\pi\)
\(54\) 0 0
\(55\) 690.718i 1.69339i
\(56\) 684.786 94.7731i 1.63408 0.226153i
\(57\) 0 0
\(58\) −290.999 504.025i −0.658794 1.14106i
\(59\) 112.979 195.685i 0.249299 0.431798i −0.714033 0.700112i \(-0.753133\pi\)
0.963331 + 0.268314i \(0.0864666\pi\)
\(60\) 0 0
\(61\) 370.650 213.995i 0.777982 0.449168i −0.0577325 0.998332i \(-0.518387\pi\)
0.835715 + 0.549164i \(0.185054\pi\)
\(62\) 481.082 0.985442
\(63\) 0 0
\(64\) 571.564 1.11634
\(65\) 97.8884 56.5159i 0.186793 0.107845i
\(66\) 0 0
\(67\) −81.9267 + 141.901i −0.149387 + 0.258746i −0.931001 0.365016i \(-0.881063\pi\)
0.781614 + 0.623762i \(0.214397\pi\)
\(68\) −540.037 935.372i −0.963075 1.66809i
\(69\) 0 0
\(70\) 433.103 1065.51i 0.739510 1.81933i
\(71\) 79.8529i 0.133476i −0.997771 0.0667380i \(-0.978741\pi\)
0.997771 0.0667380i \(-0.0212592\pi\)
\(72\) 0 0
\(73\) 666.447 + 384.774i 1.06852 + 0.616909i 0.927776 0.373138i \(-0.121718\pi\)
0.140741 + 0.990046i \(0.455051\pi\)
\(74\) −396.874 229.135i −0.623454 0.359952i
\(75\) 0 0
\(76\) 2567.85i 3.87569i
\(77\) −377.379 + 928.422i −0.558523 + 1.37407i
\(78\) 0 0
\(79\) −267.408 463.165i −0.380833 0.659622i 0.610349 0.792133i \(-0.291029\pi\)
−0.991182 + 0.132511i \(0.957696\pi\)
\(80\) −358.909 + 621.648i −0.501590 + 0.868780i
\(81\) 0 0
\(82\) −1092.77 + 630.912i −1.47166 + 0.849666i
\(83\) −438.520 −0.579926 −0.289963 0.957038i \(-0.593643\pi\)
−0.289963 + 0.957038i \(0.593643\pi\)
\(84\) 0 0
\(85\) −879.684 −1.12253
\(86\) 21.1275 12.1980i 0.0264911 0.0152947i
\(87\) 0 0
\(88\) 1009.95 1749.29i 1.22342 2.11903i
\(89\) −12.8242 22.2121i −0.0152737 0.0264548i 0.858288 0.513169i \(-0.171529\pi\)
−0.873561 + 0.486714i \(0.838195\pi\)
\(90\) 0 0
\(91\) −162.454 + 22.4833i −0.187140 + 0.0258999i
\(92\) 1472.71i 1.66892i
\(93\) 0 0
\(94\) −241.644 139.513i −0.265146 0.153082i
\(95\) 1811.23 + 1045.71i 1.95608 + 1.12935i
\(96\) 0 0
\(97\) 1381.00i 1.44555i 0.691081 + 0.722777i \(0.257135\pi\)
−0.691081 + 0.722777i \(0.742865\pi\)
\(98\) −1164.30 + 1195.57i −1.20013 + 1.23236i
\(99\) 0 0
\(100\) 297.207 + 514.777i 0.297207 + 0.514777i
\(101\) 356.808 618.009i 0.351522 0.608854i −0.634994 0.772517i \(-0.718998\pi\)
0.986516 + 0.163663i \(0.0523309\pi\)
\(102\) 0 0
\(103\) 1552.42 896.288i 1.48509 0.857416i 0.485232 0.874385i \(-0.338735\pi\)
0.999856 + 0.0169695i \(0.00540182\pi\)
\(104\) 330.544 0.311659
\(105\) 0 0
\(106\) −2286.88 −2.09548
\(107\) 19.5366 11.2794i 0.0176511 0.0101909i −0.491148 0.871076i \(-0.663423\pi\)
0.508800 + 0.860885i \(0.330089\pi\)
\(108\) 0 0
\(109\) −476.210 + 824.820i −0.418465 + 0.724802i −0.995785 0.0917154i \(-0.970765\pi\)
0.577320 + 0.816518i \(0.304098\pi\)
\(110\) −1680.31 2910.37i −1.45646 2.52267i
\(111\) 0 0
\(112\) 822.066 639.490i 0.693553 0.539519i
\(113\) 120.145i 0.100020i 0.998749 + 0.0500102i \(0.0159254\pi\)
−0.998749 + 0.0500102i \(0.984075\pi\)
\(114\) 0 0
\(115\) 1038.77 + 599.735i 0.842312 + 0.486309i
\(116\) −1623.53 937.344i −1.29949 0.750260i
\(117\) 0 0
\(118\) 1099.37i 0.857674i
\(119\) 1182.42 + 480.622i 0.910859 + 0.370240i
\(120\) 0 0
\(121\) 798.612 + 1383.24i 0.600009 + 1.03925i
\(122\) 1041.17 1803.36i 0.772648 1.33827i
\(123\) 0 0
\(124\) 1342.01 774.812i 0.971906 0.561130i
\(125\) −1111.41 −0.795262
\(126\) 0 0
\(127\) 884.302 0.617867 0.308934 0.951084i \(-0.400028\pi\)
0.308934 + 0.951084i \(0.400028\pi\)
\(128\) 2235.05 1290.41i 1.54338 0.891071i
\(129\) 0 0
\(130\) 274.972 476.265i 0.185512 0.321317i
\(131\) 803.439 + 1391.60i 0.535853 + 0.928125i 0.999122 + 0.0419070i \(0.0133433\pi\)
−0.463268 + 0.886218i \(0.653323\pi\)
\(132\) 0 0
\(133\) −1863.21 2395.16i −1.21474 1.56156i
\(134\) 797.210i 0.513944i
\(135\) 0 0
\(136\) −2227.85 1286.25i −1.40468 0.810994i
\(137\) 615.297 + 355.242i 0.383711 + 0.221535i 0.679431 0.733739i \(-0.262227\pi\)
−0.295721 + 0.955274i \(0.595560\pi\)
\(138\) 0 0
\(139\) 1531.91i 0.934782i −0.884051 0.467391i \(-0.845194\pi\)
0.884051 0.467391i \(-0.154806\pi\)
\(140\) −507.903 3669.87i −0.306612 2.21543i
\(141\) 0 0
\(142\) −194.258 336.464i −0.114801 0.198841i
\(143\) −239.593 + 414.987i −0.140110 + 0.242678i
\(144\) 0 0
\(145\) −1322.31 + 763.435i −0.757322 + 0.437240i
\(146\) 3744.15 2.12238
\(147\) 0 0
\(148\) −1476.15 −0.819854
\(149\) −2079.39 + 1200.54i −1.14329 + 0.660079i −0.947243 0.320516i \(-0.896144\pi\)
−0.196046 + 0.980595i \(0.562810\pi\)
\(150\) 0 0
\(151\) −1233.99 + 2137.33i −0.665035 + 1.15188i 0.314240 + 0.949343i \(0.398250\pi\)
−0.979276 + 0.202532i \(0.935083\pi\)
\(152\) 3058.03 + 5296.67i 1.63184 + 2.82642i
\(153\) 0 0
\(154\) 668.463 + 4830.00i 0.349781 + 2.52735i
\(155\) 1262.12i 0.654036i
\(156\) 0 0
\(157\) 2109.74 + 1218.06i 1.07246 + 0.619184i 0.928852 0.370451i \(-0.120797\pi\)
0.143606 + 0.989635i \(0.454130\pi\)
\(158\) −2253.48 1301.05i −1.13466 0.655099i
\(159\) 0 0
\(160\) 319.213i 0.157725i
\(161\) −1068.59 1373.67i −0.523083 0.672424i
\(162\) 0 0
\(163\) −1638.50 2837.97i −0.787347 1.36372i −0.927587 0.373607i \(-0.878121\pi\)
0.140240 0.990118i \(-0.455213\pi\)
\(164\) −2032.25 + 3519.95i −0.967633 + 1.67599i
\(165\) 0 0
\(166\) −1847.73 + 1066.79i −0.863924 + 0.498787i
\(167\) 365.585 0.169400 0.0847000 0.996406i \(-0.473007\pi\)
0.0847000 + 0.996406i \(0.473007\pi\)
\(168\) 0 0
\(169\) 2118.58 0.964308
\(170\) −3706.59 + 2140.00i −1.67225 + 0.965475i
\(171\) 0 0
\(172\) 39.2912 68.0543i 0.0174182 0.0301691i
\(173\) −1046.47 1812.53i −0.459892 0.796557i 0.539062 0.842266i \(-0.318779\pi\)
−0.998955 + 0.0457089i \(0.985445\pi\)
\(174\) 0 0
\(175\) −650.739 264.508i −0.281093 0.114257i
\(176\) 3043.11i 1.30331i
\(177\) 0 0
\(178\) −108.071 62.3946i −0.0455070 0.0262735i
\(179\) 1524.01 + 879.890i 0.636370 + 0.367408i 0.783215 0.621751i \(-0.213578\pi\)
−0.146845 + 0.989160i \(0.546912\pi\)
\(180\) 0 0
\(181\) 3197.54i 1.31310i −0.754282 0.656551i \(-0.772015\pi\)
0.754282 0.656551i \(-0.227985\pi\)
\(182\) −629.812 + 489.934i −0.256510 + 0.199540i
\(183\) 0 0
\(184\) 1753.84 + 3037.73i 0.702687 + 1.21709i
\(185\) −601.135 + 1041.20i −0.238899 + 0.413786i
\(186\) 0 0
\(187\) 3229.69 1864.66i 1.26299 0.729186i
\(188\) −898.780 −0.348672
\(189\) 0 0
\(190\) 10175.6 3.88535
\(191\) 475.772 274.687i 0.180239 0.104061i −0.407166 0.913354i \(-0.633483\pi\)
0.587405 + 0.809293i \(0.300150\pi\)
\(192\) 0 0
\(193\) 352.238 610.094i 0.131371 0.227542i −0.792834 0.609437i \(-0.791395\pi\)
0.924205 + 0.381896i \(0.124729\pi\)
\(194\) 3359.54 + 5818.90i 1.24330 + 2.15347i
\(195\) 0 0
\(196\) −1322.37 + 5210.32i −0.481912 + 1.89880i
\(197\) 5317.81i 1.92324i −0.274384 0.961620i \(-0.588474\pi\)
0.274384 0.961620i \(-0.411526\pi\)
\(198\) 0 0
\(199\) −2155.80 1244.65i −0.767942 0.443371i 0.0641982 0.997937i \(-0.479551\pi\)
−0.832140 + 0.554566i \(0.812884\pi\)
\(200\) 1226.09 + 707.883i 0.433488 + 0.250274i
\(201\) 0 0
\(202\) 3472.02i 1.20936i
\(203\) 2194.48 303.711i 0.758729 0.105007i
\(204\) 0 0
\(205\) 1655.20 + 2866.88i 0.563922 + 0.976741i
\(206\) 4360.79 7553.11i 1.47491 2.55461i
\(207\) 0 0
\(208\) 431.269 248.993i 0.143765 0.0830029i
\(209\) −8866.38 −2.93445
\(210\) 0 0
\(211\) −3454.31 −1.12704 −0.563519 0.826103i \(-0.690553\pi\)
−0.563519 + 0.826103i \(0.690553\pi\)
\(212\) −6379.42 + 3683.16i −2.06670 + 1.19321i
\(213\) 0 0
\(214\) 54.8789 95.0530i 0.0175301 0.0303630i
\(215\) −32.0013 55.4279i −0.0101510 0.0175821i
\(216\) 0 0
\(217\) −689.566 + 1696.46i −0.215718 + 0.530706i
\(218\) 4633.90i 1.43967i
\(219\) 0 0
\(220\) −9374.68 5412.47i −2.87291 1.65868i
\(221\) 528.520 + 305.141i 0.160869 + 0.0928778i
\(222\) 0 0
\(223\) 3896.38i 1.17005i 0.811016 + 0.585024i \(0.198915\pi\)
−0.811016 + 0.585024i \(0.801085\pi\)
\(224\) −174.404 + 429.067i −0.0520218 + 0.127983i
\(225\) 0 0
\(226\) 292.277 + 506.238i 0.0860263 + 0.149002i
\(227\) 302.747 524.374i 0.0885201 0.153321i −0.818366 0.574698i \(-0.805120\pi\)
0.906886 + 0.421377i \(0.138453\pi\)
\(228\) 0 0
\(229\) −1912.98 + 1104.46i −0.552023 + 0.318711i −0.749938 0.661509i \(-0.769917\pi\)
0.197914 + 0.980219i \(0.436583\pi\)
\(230\) 5835.89 1.67307
\(231\) 0 0
\(232\) −4465.10 −1.26357
\(233\) 2065.77 1192.67i 0.580829 0.335342i −0.180634 0.983550i \(-0.557815\pi\)
0.761463 + 0.648209i \(0.224482\pi\)
\(234\) 0 0
\(235\) −366.013 + 633.953i −0.101600 + 0.175977i
\(236\) −1770.61 3066.79i −0.488377 0.845893i
\(237\) 0 0
\(238\) 6151.39 851.341i 1.67536 0.231866i
\(239\) 3017.95i 0.816798i −0.912803 0.408399i \(-0.866087\pi\)
0.912803 0.408399i \(-0.133913\pi\)
\(240\) 0 0
\(241\) −2178.48 1257.75i −0.582275 0.336176i 0.179762 0.983710i \(-0.442467\pi\)
−0.762037 + 0.647534i \(0.775800\pi\)
\(242\) 6729.99 + 3885.56i 1.78769 + 1.03212i
\(243\) 0 0
\(244\) 6707.47i 1.75984i
\(245\) 3136.58 + 3054.54i 0.817913 + 0.796521i
\(246\) 0 0
\(247\) −725.465 1256.54i −0.186883 0.323692i
\(248\) 1845.44 3196.39i 0.472521 0.818431i
\(249\) 0 0
\(250\) −4682.99 + 2703.73i −1.18471 + 0.683995i
\(251\) 1306.11 0.328451 0.164226 0.986423i \(-0.447488\pi\)
0.164226 + 0.986423i \(0.447488\pi\)
\(252\) 0 0
\(253\) −5085.03 −1.26361
\(254\) 3726.05 2151.24i 0.920447 0.531420i
\(255\) 0 0
\(256\) 3992.09 6914.50i 0.974630 1.68811i
\(257\) 3735.91 + 6470.79i 0.906770 + 1.57057i 0.818524 + 0.574473i \(0.194793\pi\)
0.0882460 + 0.996099i \(0.471874\pi\)
\(258\) 0 0
\(259\) 1376.88 1071.08i 0.330328 0.256964i
\(260\) 1771.44i 0.422538i
\(261\) 0 0
\(262\) 6770.66 + 3909.04i 1.59654 + 0.921762i
\(263\) −1330.77 768.318i −0.312010 0.180139i 0.335816 0.941928i \(-0.390988\pi\)
−0.647825 + 0.761789i \(0.724321\pi\)
\(264\) 0 0
\(265\) 5999.62i 1.39077i
\(266\) −13677.4 5559.51i −3.15270 1.28149i
\(267\) 0 0
\(268\) 1283.96 + 2223.88i 0.292650 + 0.506884i
\(269\) 1958.09 3391.52i 0.443818 0.768715i −0.554151 0.832416i \(-0.686957\pi\)
0.997969 + 0.0637010i \(0.0202904\pi\)
\(270\) 0 0
\(271\) 3117.42 1799.84i 0.698780 0.403441i −0.108113 0.994139i \(-0.534481\pi\)
0.806893 + 0.590698i \(0.201147\pi\)
\(272\) −3875.65 −0.863955
\(273\) 0 0
\(274\) 3456.78 0.762159
\(275\) −1777.45 + 1026.21i −0.389760 + 0.225028i
\(276\) 0 0
\(277\) −142.040 + 246.021i −0.0308100 + 0.0533645i −0.881019 0.473080i \(-0.843142\pi\)
0.850209 + 0.526445i \(0.176475\pi\)
\(278\) −3726.67 6454.77i −0.803995 1.39256i
\(279\) 0 0
\(280\) −5418.07 6964.93i −1.15640 1.48655i
\(281\) 321.256i 0.0682011i 0.999418 + 0.0341006i \(0.0108566\pi\)
−0.999418 + 0.0341006i \(0.989143\pi\)
\(282\) 0 0
\(283\) 5891.40 + 3401.40i 1.23748 + 0.714460i 0.968579 0.248707i \(-0.0800057\pi\)
0.268903 + 0.963167i \(0.413339\pi\)
\(284\) −1083.79 625.728i −0.226448 0.130740i
\(285\) 0 0
\(286\) 2331.43i 0.482029i
\(287\) −658.474 4757.82i −0.135430 0.978556i
\(288\) 0 0
\(289\) 81.7017 + 141.511i 0.0166297 + 0.0288035i
\(290\) −3714.41 + 6433.55i −0.752130 + 1.30273i
\(291\) 0 0
\(292\) 10444.6 6030.18i 2.09323 1.20853i
\(293\) 3180.05 0.634063 0.317031 0.948415i \(-0.397314\pi\)
0.317031 + 0.948415i \(0.397314\pi\)
\(294\) 0 0
\(295\) −2884.20 −0.569237
\(296\) −3044.83 + 1757.93i −0.597895 + 0.345195i
\(297\) 0 0
\(298\) −5841.07 + 10117.0i −1.13545 + 1.96666i
\(299\) −416.067 720.649i −0.0804741 0.139385i
\(300\) 0 0
\(301\) 12.7308 + 91.9871i 0.00243785 + 0.0176148i
\(302\) 12007.6i 2.28795i
\(303\) 0 0
\(304\) 7979.78 + 4607.13i 1.50550 + 0.869200i
\(305\) −4731.11 2731.51i −0.888204 0.512805i
\(306\) 0 0
\(307\) 2976.39i 0.553328i 0.960967 + 0.276664i \(0.0892289\pi\)
−0.960967 + 0.276664i \(0.910771\pi\)
\(308\) 9643.74 + 12397.0i 1.78410 + 2.29346i
\(309\) 0 0
\(310\) −3070.34 5317.99i −0.562528 0.974328i
\(311\) −2340.89 + 4054.55i −0.426817 + 0.739268i −0.996588 0.0825352i \(-0.973698\pi\)
0.569772 + 0.821803i \(0.307032\pi\)
\(312\) 0 0
\(313\) −850.477 + 491.023i −0.153584 + 0.0886718i −0.574823 0.818278i \(-0.694929\pi\)
0.421238 + 0.906950i \(0.361596\pi\)
\(314\) 11852.7 2.13021
\(315\) 0 0
\(316\) −8381.66 −1.49211
\(317\) 4269.80 2465.17i 0.756516 0.436775i −0.0715272 0.997439i \(-0.522787\pi\)
0.828044 + 0.560664i \(0.189454\pi\)
\(318\) 0 0
\(319\) 3236.50 5605.79i 0.568055 0.983899i
\(320\) −3647.82 6318.21i −0.637248 1.10375i
\(321\) 0 0
\(322\) −7844.26 3188.48i −1.35759 0.551823i
\(323\) 11292.0i 1.94522i
\(324\) 0 0
\(325\) −290.868 167.933i −0.0496445 0.0286623i
\(326\) −13807.8 7971.96i −2.34585 1.35437i
\(327\) 0 0
\(328\) 9680.75i 1.62966i
\(329\) 838.338 652.148i 0.140483 0.109283i
\(330\) 0 0
\(331\) 2017.25 + 3493.99i 0.334980 + 0.580202i 0.983481 0.181012i \(-0.0579372\pi\)
−0.648501 + 0.761214i \(0.724604\pi\)
\(332\) −3436.25 + 5951.76i −0.568038 + 0.983871i
\(333\) 0 0
\(334\) 1540.41 889.356i 0.252358 0.145699i
\(335\) 2091.48 0.341104
\(336\) 0 0
\(337\) 2771.62 0.448011 0.224006 0.974588i \(-0.428087\pi\)
0.224006 + 0.974588i \(0.428087\pi\)
\(338\) 8926.76 5153.87i 1.43654 0.829389i
\(339\) 0 0
\(340\) −6893.21 + 11939.4i −1.09952 + 1.90443i
\(341\) 2675.30 + 4633.76i 0.424856 + 0.735872i
\(342\) 0 0
\(343\) −2547.13 5819.43i −0.400968 0.916092i
\(344\) 187.166i 0.0293352i
\(345\) 0 0
\(346\) −8818.68 5091.47i −1.37022 0.791095i
\(347\) −3743.15 2161.11i −0.579085 0.334335i 0.181685 0.983357i \(-0.441845\pi\)
−0.760770 + 0.649022i \(0.775178\pi\)
\(348\) 0 0
\(349\) 1331.65i 0.204245i −0.994772 0.102122i \(-0.967437\pi\)
0.994772 0.102122i \(-0.0325634\pi\)
\(350\) −3385.39 + 468.531i −0.517019 + 0.0715545i
\(351\) 0 0
\(352\) 676.635 + 1171.97i 0.102457 + 0.177460i
\(353\) −5674.26 + 9828.10i −0.855553 + 1.48186i 0.0205782 + 0.999788i \(0.493449\pi\)
−0.876131 + 0.482073i \(0.839884\pi\)
\(354\) 0 0
\(355\) −882.713 + 509.634i −0.131970 + 0.0761932i
\(356\) −401.962 −0.0598425
\(357\) 0 0
\(358\) 8562.02 1.26401
\(359\) −7247.49 + 4184.34i −1.06548 + 0.615156i −0.926943 0.375201i \(-0.877574\pi\)
−0.138538 + 0.990357i \(0.544240\pi\)
\(360\) 0 0
\(361\) 9993.77 17309.7i 1.45703 2.52365i
\(362\) −7778.64 13473.0i −1.12938 1.95615i
\(363\) 0 0
\(364\) −967.837 + 2381.06i −0.139364 + 0.342861i
\(365\) 9822.76i 1.40862i
\(366\) 0 0
\(367\) 2351.31 + 1357.53i 0.334434 + 0.193086i 0.657808 0.753186i \(-0.271484\pi\)
−0.323374 + 0.946271i \(0.604817\pi\)
\(368\) 4576.54 + 2642.27i 0.648285 + 0.374287i
\(369\) 0 0
\(370\) 5849.52i 0.821897i
\(371\) 3277.93 8064.33i 0.458711 1.12851i
\(372\) 0 0
\(373\) −3048.56 5280.25i −0.423186 0.732979i 0.573063 0.819511i \(-0.305755\pi\)
−0.996249 + 0.0865320i \(0.972422\pi\)
\(374\) 9072.32 15713.7i 1.25433 2.17256i
\(375\) 0 0
\(376\) −1853.90 + 1070.35i −0.254276 + 0.146806i
\(377\) 1059.27 0.144708
\(378\) 0 0
\(379\) −9922.24 −1.34478 −0.672389 0.740198i \(-0.734732\pi\)
−0.672389 + 0.740198i \(0.734732\pi\)
\(380\) 28385.6 16388.4i 3.83198 2.21239i
\(381\) 0 0
\(382\) 1336.46 2314.82i 0.179003 0.310043i
\(383\) −609.532 1055.74i −0.0813202 0.140851i 0.822497 0.568769i \(-0.192580\pi\)
−0.903817 + 0.427919i \(0.859247\pi\)
\(384\) 0 0
\(385\) 12671.5 1753.71i 1.67740 0.232149i
\(386\) 3427.55i 0.451963i
\(387\) 0 0
\(388\) 18743.4 + 10821.5i 2.45245 + 1.41592i
\(389\) 11374.6 + 6567.15i 1.48256 + 0.855958i 0.999804 0.0197949i \(-0.00630133\pi\)
0.482759 + 0.875753i \(0.339635\pi\)
\(390\) 0 0
\(391\) 6476.19i 0.837634i
\(392\) 3477.30 + 12322.0i 0.448036 + 1.58765i
\(393\) 0 0
\(394\) −12936.6 22406.9i −1.65416 2.86508i
\(395\) −3413.29 + 5911.99i −0.434788 + 0.753075i
\(396\) 0 0
\(397\) 2697.68 1557.51i 0.341040 0.196900i −0.319692 0.947522i \(-0.603579\pi\)
0.660732 + 0.750622i \(0.270246\pi\)
\(398\) −12111.4 −1.52535
\(399\) 0 0
\(400\) 2132.94 0.266618
\(401\) −9724.47 + 5614.42i −1.21101 + 0.699179i −0.962980 0.269572i \(-0.913118\pi\)
−0.248034 + 0.968751i \(0.579784\pi\)
\(402\) 0 0
\(403\) −437.797 + 758.287i −0.0541147 + 0.0937295i
\(404\) −5591.90 9685.46i −0.688633 1.19275i
\(405\) 0 0
\(406\) 8507.70 6618.20i 1.03998 0.809004i
\(407\) 5096.90i 0.620747i
\(408\) 0 0
\(409\) −10739.4 6200.41i −1.29836 0.749610i −0.318242 0.948010i \(-0.603092\pi\)
−0.980121 + 0.198399i \(0.936426\pi\)
\(410\) 13948.5 + 8053.18i 1.68017 + 0.970044i
\(411\) 0 0
\(412\) 28093.3i 3.35936i
\(413\) 3876.78 + 1575.81i 0.461898 + 0.187749i
\(414\) 0 0
\(415\) 2798.71 + 4847.51i 0.331044 + 0.573385i
\(416\) −110.727 + 191.785i −0.0130501 + 0.0226035i
\(417\) 0 0
\(418\) −37359.0 + 21569.2i −4.37150 + 2.52389i
\(419\) −8260.19 −0.963095 −0.481547 0.876420i \(-0.659925\pi\)
−0.481547 + 0.876420i \(0.659925\pi\)
\(420\) 0 0
\(421\) 5571.81 0.645020 0.322510 0.946566i \(-0.395473\pi\)
0.322510 + 0.946566i \(0.395473\pi\)
\(422\) −14554.9 + 8403.30i −1.67896 + 0.969351i
\(423\) 0 0
\(424\) −8772.49 + 15194.4i −1.00479 + 1.74034i
\(425\) 1306.96 + 2263.72i 0.149169 + 0.258368i
\(426\) 0 0
\(427\) 4866.89 + 6256.40i 0.551582 + 0.709060i
\(428\) 353.543i 0.0399279i
\(429\) 0 0
\(430\) −269.678 155.699i −0.0302443 0.0174616i
\(431\) −6094.88 3518.88i −0.681160 0.393268i 0.119132 0.992878i \(-0.461989\pi\)
−0.800292 + 0.599611i \(0.795322\pi\)
\(432\) 0 0
\(433\) 9212.26i 1.02243i 0.859452 + 0.511216i \(0.170805\pi\)
−0.859452 + 0.511216i \(0.829195\pi\)
\(434\) 1221.45 + 8825.63i 0.135096 + 0.976138i
\(435\) 0 0
\(436\) 7463.18 + 12926.6i 0.819774 + 1.41989i
\(437\) 7698.48 13334.2i 0.842719 1.45963i
\(438\) 0 0
\(439\) −7345.30 + 4240.81i −0.798570 + 0.461054i −0.842971 0.537959i \(-0.819195\pi\)
0.0444012 + 0.999014i \(0.485862\pi\)
\(440\) −25782.7 −2.79350
\(441\) 0 0
\(442\) 2969.26 0.319532
\(443\) 11305.9 6527.49i 1.21255 0.700068i 0.249239 0.968442i \(-0.419820\pi\)
0.963315 + 0.268374i \(0.0864863\pi\)
\(444\) 0 0
\(445\) −163.692 + 283.523i −0.0174376 + 0.0302029i
\(446\) 9478.70 + 16417.6i 1.00634 + 1.74304i
\(447\) 0 0
\(448\) 1451.18 + 10485.6i 0.153040 + 1.10580i
\(449\) 14114.0i 1.48348i 0.670689 + 0.741738i \(0.265998\pi\)
−0.670689 + 0.741738i \(0.734002\pi\)
\(450\) 0 0
\(451\) −12153.9 7017.03i −1.26896 0.732637i
\(452\) 1630.66 + 941.459i 0.169689 + 0.0979702i
\(453\) 0 0
\(454\) 2945.97i 0.304540i
\(455\) 1285.34 + 1652.31i 0.132435 + 0.170245i
\(456\) 0 0
\(457\) 4486.87 + 7771.49i 0.459271 + 0.795481i 0.998923 0.0464073i \(-0.0147772\pi\)
−0.539651 + 0.841889i \(0.681444\pi\)
\(458\) −5373.63 + 9307.40i −0.548238 + 0.949577i
\(459\) 0 0
\(460\) 16279.7 9399.06i 1.65009 0.952682i
\(461\) 955.010 0.0964842 0.0482421 0.998836i \(-0.484638\pi\)
0.0482421 + 0.998836i \(0.484638\pi\)
\(462\) 0 0
\(463\) 12004.5 1.20496 0.602479 0.798135i \(-0.294180\pi\)
0.602479 + 0.798135i \(0.294180\pi\)
\(464\) −5825.73 + 3363.49i −0.582872 + 0.336521i
\(465\) 0 0
\(466\) 5802.82 10050.8i 0.576846 0.999127i
\(467\) 2532.46 + 4386.34i 0.250938 + 0.434638i 0.963784 0.266683i \(-0.0859276\pi\)
−0.712846 + 0.701320i \(0.752594\pi\)
\(468\) 0 0
\(469\) −2811.24 1142.69i −0.276783 0.112505i
\(470\) 3561.59i 0.349540i
\(471\) 0 0
\(472\) −7304.43 4217.21i −0.712317 0.411256i
\(473\) 234.981 + 135.666i 0.0228423 + 0.0131880i
\(474\) 0 0
\(475\) 6214.52i 0.600299i
\(476\) 15788.6 12282.1i 1.52032 1.18266i
\(477\) 0 0
\(478\) −7341.75 12716.3i −0.702518 1.21680i
\(479\) −7606.85 + 13175.5i −0.725607 + 1.25679i 0.233116 + 0.972449i \(0.425108\pi\)
−0.958724 + 0.284340i \(0.908226\pi\)
\(480\) 0 0
\(481\) 722.332 417.038i 0.0684730 0.0395329i
\(482\) −12238.8 −1.15656
\(483\) 0 0
\(484\) 25031.7 2.35084
\(485\) 15265.9 8813.75i 1.42925 0.825179i
\(486\) 0 0
\(487\) −7905.92 + 13693.5i −0.735629 + 1.27415i 0.218817 + 0.975766i \(0.429780\pi\)
−0.954447 + 0.298382i \(0.903553\pi\)
\(488\) −7987.88 13835.4i −0.740972 1.28340i
\(489\) 0 0
\(490\) 20646.9 + 5240.14i 1.90354 + 0.483113i
\(491\) 18064.2i 1.66034i −0.557512 0.830169i \(-0.688244\pi\)
0.557512 0.830169i \(-0.311756\pi\)
\(492\) 0 0
\(493\) −7139.42 4121.94i −0.652217 0.376558i
\(494\) −6113.57 3529.67i −0.556806 0.321472i
\(495\) 0 0
\(496\) 5560.54i 0.503378i
\(497\) 1464.93 202.744i 0.132216 0.0182984i
\(498\) 0 0
\(499\) 5262.33 + 9114.62i 0.472092 + 0.817688i 0.999490 0.0319305i \(-0.0101655\pi\)
−0.527398 + 0.849619i \(0.676832\pi\)
\(500\) −8709.04 + 15084.5i −0.778960 + 1.34920i
\(501\) 0 0
\(502\) 5503.38 3177.38i 0.489299 0.282497i
\(503\) 7790.82 0.690607 0.345304 0.938491i \(-0.387776\pi\)
0.345304 + 0.938491i \(0.387776\pi\)
\(504\) 0 0
\(505\) −9108.83 −0.802649
\(506\) −21426.0 + 12370.3i −1.88242 + 1.08681i
\(507\) 0 0
\(508\) 6929.41 12002.1i 0.605202 1.04824i
\(509\) −5098.24 8830.41i −0.443960 0.768961i 0.554019 0.832504i \(-0.313093\pi\)
−0.997979 + 0.0635430i \(0.979760\pi\)
\(510\) 0 0
\(511\) −5366.74 + 13203.2i −0.464600 + 1.14300i
\(512\) 18199.6i 1.57093i
\(513\) 0 0
\(514\) 31482.9 + 18176.7i 2.70166 + 1.55980i
\(515\) −19815.6 11440.5i −1.69549 0.978892i
\(516\) 0 0
\(517\) 3103.35i 0.263994i
\(518\) 3195.93 7862.57i 0.271083 0.666914i
\(519\) 0 0
\(520\) −2109.59 3653.92i −0.177907 0.308144i
\(521\) −963.789 + 1669.33i −0.0810449 + 0.140374i −0.903699 0.428168i \(-0.859159\pi\)
0.822654 + 0.568542i \(0.192492\pi\)
\(522\) 0 0
\(523\) −6716.70 + 3877.89i −0.561569 + 0.324222i −0.753775 0.657133i \(-0.771769\pi\)
0.192206 + 0.981355i \(0.438436\pi\)
\(524\) 25183.0 2.09948
\(525\) 0 0
\(526\) −7476.33 −0.619741
\(527\) 5901.47 3407.21i 0.487803 0.281633i
\(528\) 0 0
\(529\) −1668.28 + 2889.55i −0.137115 + 0.237491i
\(530\) 14595.2 + 25279.7i 1.19618 + 2.07185i
\(531\) 0 0
\(532\) −47108.2 + 6519.68i −3.83910 + 0.531324i
\(533\) 2296.59i 0.186635i
\(534\) 0 0
\(535\) −249.371 143.975i −0.0201519 0.0116347i
\(536\) 5296.80 + 3058.11i 0.426841 + 0.246437i
\(537\) 0 0
\(538\) 19053.8i 1.52689i
\(539\) −17990.4 4565.93i −1.43767 0.364876i
\(540\) 0 0
\(541\) −8380.42 14515.3i −0.665993 1.15353i −0.979015 0.203788i \(-0.934675\pi\)
0.313022 0.949746i \(-0.398659\pi\)
\(542\) 8756.93 15167.4i 0.693989 1.20202i
\(543\) 0 0
\(544\) 1492.59 861.748i 0.117637 0.0679176i
\(545\) 12157.0 0.955503
\(546\) 0 0
\(547\) 5869.79 0.458819 0.229410 0.973330i \(-0.426320\pi\)
0.229410 + 0.973330i \(0.426320\pi\)
\(548\) 9642.95 5567.36i 0.751690 0.433989i
\(549\) 0 0
\(550\) −4992.91 + 8647.97i −0.387088 + 0.670456i
\(551\) 9799.82 + 16973.8i 0.757688 + 1.31235i
\(552\) 0 0
\(553\) 7818.00 6081.67i 0.601185 0.467666i
\(554\) 1382.16i 0.105997i
\(555\) 0 0
\(556\) −20791.6 12004.1i −1.58590 0.915621i
\(557\) 18756.5 + 10829.1i 1.42682 + 0.823774i 0.996868 0.0790779i \(-0.0251976\pi\)
0.429951 + 0.902852i \(0.358531\pi\)
\(558\) 0 0
\(559\) 44.4019i 0.00335957i
\(560\) −12315.6 5005.98i −0.929341 0.377752i
\(561\) 0 0
\(562\) 781.517 + 1353.63i 0.0586589 + 0.101600i
\(563\) −4795.36 + 8305.80i −0.358970 + 0.621755i −0.987789 0.155797i \(-0.950205\pi\)
0.628819 + 0.777552i \(0.283539\pi\)
\(564\) 0 0
\(565\) 1328.11 766.787i 0.0988923 0.0570955i
\(566\) 33098.3 2.45799
\(567\) 0 0
\(568\) −2980.70 −0.220189
\(569\) −14405.5 + 8317.01i −1.06135 + 0.612772i −0.925806 0.377999i \(-0.876612\pi\)
−0.135546 + 0.990771i \(0.543279\pi\)
\(570\) 0 0
\(571\) −3165.51 + 5482.83i −0.232001 + 0.401838i −0.958397 0.285439i \(-0.907861\pi\)
0.726396 + 0.687277i \(0.241194\pi\)
\(572\) 3754.91 + 6503.69i 0.274477 + 0.475408i
\(573\) 0 0
\(574\) −14348.8 18445.5i −1.04340 1.34129i
\(575\) 3564.14i 0.258495i
\(576\) 0 0
\(577\) 8431.94 + 4868.18i 0.608364 + 0.351239i 0.772325 0.635228i \(-0.219094\pi\)
−0.163961 + 0.986467i \(0.552427\pi\)
\(578\) 688.509 + 397.511i 0.0495470 + 0.0286060i
\(579\) 0 0
\(580\) 23929.1i 1.71311i
\(581\) −1113.39 8044.83i −0.0795028 0.574450i
\(582\) 0 0
\(583\) −12717.4 22027.1i −0.903430 1.56479i
\(584\) 14362.6 24876.8i 1.01769 1.76268i
\(585\) 0 0
\(586\) 13399.3 7736.09i 0.944573 0.545350i
\(587\) −10940.3 −0.769255 −0.384628 0.923072i \(-0.625670\pi\)
−0.384628 + 0.923072i \(0.625670\pi\)
\(588\) 0 0
\(589\) −16201.1 −1.13337
\(590\) −12152.7 + 7016.39i −0.848001 + 0.489594i
\(591\) 0 0
\(592\) −2648.44 + 4587.23i −0.183869 + 0.318470i
\(593\) −12430.4 21530.0i −0.860799 1.49095i −0.871159 0.491000i \(-0.836631\pi\)
0.0103608 0.999946i \(-0.496702\pi\)
\(594\) 0 0
\(595\) −2233.49 16138.2i −0.153889 1.11193i
\(596\) 37629.6i 2.58619i
\(597\) 0 0
\(598\) −3506.24 2024.33i −0.239767 0.138430i
\(599\) −20207.8 11667.0i −1.37841 0.795825i −0.386442 0.922314i \(-0.626296\pi\)
−0.991968 + 0.126488i \(0.959629\pi\)
\(600\) 0 0
\(601\) 13012.4i 0.883175i 0.897218 + 0.441587i \(0.145584\pi\)
−0.897218 + 0.441587i \(0.854416\pi\)
\(602\) 277.419 + 356.622i 0.0187820 + 0.0241442i
\(603\) 0 0
\(604\) 19339.1 + 33496.2i 1.30281 + 2.25653i
\(605\) 10193.8 17656.1i 0.685017 1.18648i
\(606\) 0 0
\(607\) 7355.69 4246.81i 0.491859 0.283975i −0.233486 0.972360i \(-0.575013\pi\)
0.725345 + 0.688385i \(0.241680\pi\)
\(608\) −4097.57 −0.273320
\(609\) 0 0
\(610\) −26579.7 −1.76423
\(611\) 439.806 253.922i 0.0291205 0.0168127i
\(612\) 0 0
\(613\) 4569.79 7915.11i 0.301097 0.521514i −0.675288 0.737554i \(-0.735981\pi\)
0.976385 + 0.216040i \(0.0693140\pi\)
\(614\) 7240.66 + 12541.2i 0.475911 + 0.824302i
\(615\) 0 0
\(616\) 34655.6 + 14086.6i 2.26674 + 0.921370i
\(617\) 7360.91i 0.480290i 0.970737 + 0.240145i \(0.0771950\pi\)
−0.970737 + 0.240145i \(0.922805\pi\)
\(618\) 0 0
\(619\) 19878.5 + 11476.9i 1.29077 + 0.745225i 0.978790 0.204864i \(-0.0656753\pi\)
0.311978 + 0.950089i \(0.399009\pi\)
\(620\) −17129.9 9889.96i −1.10960 0.640629i
\(621\) 0 0
\(622\) 22778.7i 1.46840i
\(623\) 374.930 291.660i 0.0241112 0.0187562i
\(624\) 0 0
\(625\) 9463.74 + 16391.7i 0.605679 + 1.04907i
\(626\) −2389.02 + 4137.91i −0.152531 + 0.264192i
\(627\) 0 0
\(628\) 33064.0 19089.5i 2.10095 1.21298i
\(629\) −6491.31 −0.411487
\(630\) 0 0
\(631\) 21126.0 1.33282 0.666412 0.745584i \(-0.267829\pi\)
0.666412 + 0.745584i \(0.267829\pi\)
\(632\) −17288.7 + 9981.66i −1.08815 + 0.628242i
\(633\) 0 0
\(634\) 11994.0 20774.2i 0.751330 1.30134i
\(635\) −5643.77 9775.29i −0.352703 0.610899i
\(636\) 0 0
\(637\) −824.929 2923.19i −0.0513106 0.181823i
\(638\) 31493.7i 1.95431i
\(639\) 0 0
\(640\) −28529.0 16471.2i −1.76204 1.01732i
\(641\) 15447.5 + 8918.61i 0.951855 + 0.549554i 0.893657 0.448751i \(-0.148131\pi\)
0.0581985 + 0.998305i \(0.481464\pi\)
\(642\) 0 0
\(643\) 25449.0i 1.56082i −0.625266 0.780412i \(-0.715009\pi\)
0.625266 0.780412i \(-0.284991\pi\)
\(644\) −27017.4 + 3739.16i −1.65316 + 0.228794i
\(645\) 0 0
\(646\) 27470.1 + 47579.6i 1.67306 + 2.89782i
\(647\) 13149.2 22775.1i 0.798993 1.38390i −0.121280 0.992618i \(-0.538700\pi\)
0.920273 0.391277i \(-0.127967\pi\)
\(648\) 0 0
\(649\) 10589.1 6113.64i 0.640462 0.369771i
\(650\) −1634.12 −0.0986083
\(651\) 0 0
\(652\) −51357.4 −3.08483
\(653\) −8203.79 + 4736.46i −0.491637 + 0.283847i −0.725253 0.688482i \(-0.758277\pi\)
0.233616 + 0.972329i \(0.424944\pi\)
\(654\) 0 0
\(655\) 10255.4 17762.8i 0.611771 1.05962i
\(656\) 7292.34 + 12630.7i 0.434022 + 0.751747i
\(657\) 0 0
\(658\) 1945.90 4787.28i 0.115287 0.283629i
\(659\) 22384.5i 1.32318i 0.749865 + 0.661591i \(0.230118\pi\)
−0.749865 + 0.661591i \(0.769882\pi\)
\(660\) 0 0
\(661\) −19857.3 11464.6i −1.16847 0.674618i −0.215153 0.976580i \(-0.569025\pi\)
−0.953320 + 0.301962i \(0.902359\pi\)
\(662\) 16999.6 + 9814.73i 0.998049 + 0.576224i
\(663\) 0 0
\(664\) 16368.8i 0.956677i
\(665\) −14585.4 + 35882.7i −0.850521 + 2.09244i
\(666\) 0 0
\(667\) 5620.37 + 9734.77i 0.326269 + 0.565115i
\(668\) 2864.73 4961.85i 0.165928 0.287395i
\(669\) 0 0
\(670\) 8812.56 5087.93i 0.508147 0.293379i
\(671\) 23159.9 1.33245
\(672\) 0 0
\(673\) −4873.86 −0.279158 −0.139579 0.990211i \(-0.544575\pi\)
−0.139579 + 0.990211i \(0.544575\pi\)
\(674\) 11678.4 6742.51i 0.667409 0.385329i
\(675\) 0 0
\(676\) 16601.3 28754.2i 0.944541 1.63599i
\(677\) −8123.71 14070.7i −0.461181 0.798789i 0.537839 0.843048i \(-0.319241\pi\)
−0.999020 + 0.0442583i \(0.985908\pi\)
\(678\) 0 0
\(679\) −25334.9 + 3506.30i −1.43191 + 0.198173i
\(680\) 32836.3i 1.85179i
\(681\) 0 0
\(682\) 22545.1 + 13016.4i 1.26583 + 0.730827i
\(683\) 18786.2 + 10846.2i 1.05247 + 0.607641i 0.923339 0.383987i \(-0.125449\pi\)
0.129127 + 0.991628i \(0.458783\pi\)
\(684\) 0 0
\(685\) 9068.85i 0.505844i
\(686\) −24889.4 18324.1i −1.38525 1.01985i
\(687\) 0 0
\(688\) −140.989 244.200i −0.00781273 0.0135320i
\(689\) 2081.12 3604.61i 0.115072 0.199310i
\(690\) 0 0
\(691\) −19499.9 + 11258.3i −1.07353 + 0.619803i −0.929144 0.369718i \(-0.879454\pi\)
−0.144387 + 0.989521i \(0.546121\pi\)
\(692\) −32800.5 −1.80186
\(693\) 0 0
\(694\) −21029.2 −1.15023
\(695\) −16934.1 + 9776.90i −0.924239 + 0.533610i
\(696\) 0 0
\(697\) −8936.75 + 15478.9i −0.485658 + 0.841184i
\(698\) −3239.49 5610.97i −0.175669 0.304267i
\(699\) 0 0
\(700\) −8689.20 + 6759.38i −0.469173 + 0.364972i
\(701\) 33929.0i 1.82807i 0.405631 + 0.914037i \(0.367052\pi\)
−0.405631 + 0.914037i \(0.632948\pi\)
\(702\) 0 0
\(703\) 13365.3 + 7716.46i 0.717044 + 0.413986i
\(704\) 26785.4 + 15464.5i 1.43397 + 0.827901i
\(705\) 0 0
\(706\) 55214.9i 2.94340i
\(707\) 12243.6 + 4976.68i 0.651296 + 0.264734i
\(708\) 0 0
\(709\) −9593.62 16616.6i −0.508175 0.880185i −0.999955 0.00946553i \(-0.996987\pi\)
0.491780 0.870719i \(-0.336346\pi\)
\(710\) −2479.57 + 4294.74i −0.131066 + 0.227012i
\(711\) 0 0
\(712\) −829.121 + 478.693i −0.0436413 + 0.0251963i
\(713\) −9291.63 −0.488043
\(714\) 0 0
\(715\) 6116.49 0.319922
\(716\) 23884.4 13789.7i 1.24665 0.719754i
\(717\) 0 0
\(718\) −20358.4 + 35261.8i −1.05818 + 1.83281i
\(719\) −6883.43 11922.4i −0.357036 0.618404i 0.630429 0.776247i \(-0.282879\pi\)
−0.987464 + 0.157844i \(0.949546\pi\)
\(720\) 0 0
\(721\) 20384.3 + 26204.0i 1.05291 + 1.35352i
\(722\) 97247.2i 5.01269i
\(723\) 0 0
\(724\) −43398.2 25056.0i −2.22774 1.28618i
\(725\) 3929.15 + 2268.49i 0.201276 + 0.116207i
\(726\) 0 0
\(727\) 12226.1i 0.623717i −0.950129 0.311858i \(-0.899049\pi\)
0.950129 0.311858i \(-0.100951\pi\)
\(728\) 839.242 + 6063.97i 0.0427258 + 0.308717i
\(729\) 0 0
\(730\) −23895.8 41388.7i −1.21154 2.09845i
\(731\) 172.782 299.267i 0.00874222 0.0151420i
\(732\) 0 0
\(733\) 2256.76 1302.94i 0.113718 0.0656553i −0.442062 0.896984i \(-0.645753\pi\)
0.555780 + 0.831329i \(0.312420\pi\)
\(734\) 13209.8 0.664282
\(735\) 0 0
\(736\) −2350.03 −0.117695
\(737\) −7678.71 + 4433.30i −0.383784 + 0.221578i
\(738\) 0 0
\(739\) −16871.7 + 29222.7i −0.839833 + 1.45463i 0.0502016 + 0.998739i \(0.484014\pi\)
−0.890034 + 0.455894i \(0.849320\pi\)
\(740\) 9421.01 + 16317.7i 0.468004 + 0.810607i
\(741\) 0 0
\(742\) −5806.31 41953.7i −0.287273 2.07570i
\(743\) 14586.9i 0.720244i 0.932905 + 0.360122i \(0.117265\pi\)
−0.932905 + 0.360122i \(0.882735\pi\)
\(744\) 0 0
\(745\) 26542.0 + 15324.0i 1.30527 + 0.753597i
\(746\) −25690.5 14832.4i −1.26085 0.727953i
\(747\) 0 0
\(748\) 58446.1i 2.85695i
\(749\) 256.528 + 329.768i 0.0125145 + 0.0160874i
\(750\) 0 0
\(751\) 3757.62 + 6508.39i 0.182580 + 0.316238i 0.942758 0.333477i \(-0.108222\pi\)
−0.760178 + 0.649714i \(0.774889\pi\)
\(752\) −1612.55 + 2793.02i −0.0781965 + 0.135440i
\(753\) 0 0
\(754\) 4463.28 2576.88i 0.215574 0.124462i
\(755\) 31502.0 1.51851
\(756\) 0 0
\(757\) 23917.4 1.14834 0.574169 0.818737i \(-0.305325\pi\)
0.574169 + 0.818737i \(0.305325\pi\)
\(758\) −41807.9 + 24137.8i −2.00334 + 1.15663i
\(759\) 0 0
\(760\) 39033.7 67608.4i 1.86303 3.22686i
\(761\) 6099.27 + 10564.2i 0.290537 + 0.503224i 0.973937 0.226820i \(-0.0728328\pi\)
−0.683400 + 0.730044i \(0.739500\pi\)
\(762\) 0 0
\(763\) −16340.7 6642.07i −0.775327 0.315150i
\(764\) 8609.80i 0.407712i
\(765\) 0 0
\(766\) −5136.59 2965.61i −0.242288 0.139885i
\(767\) 1732.85 + 1000.46i 0.0815769 + 0.0470985i
\(768\) 0 0
\(769\) 2013.08i 0.0943999i −0.998885 0.0471999i \(-0.984970\pi\)
0.998885 0.0471999i \(-0.0150298\pi\)
\(770\) 49125.7 38215.2i 2.29918 1.78855i
\(771\) 0 0
\(772\) −5520.28 9561.41i −0.257357 0.445755i
\(773\) 15139.1 26221.7i 0.704418 1.22009i −0.262483 0.964937i \(-0.584541\pi\)
0.966901 0.255152i \(-0.0821254\pi\)
\(774\) 0 0
\(775\) −3247.85 + 1875.14i −0.150537 + 0.0869125i
\(776\) 51549.0 2.38467
\(777\) 0 0
\(778\) 63903.5 2.94480
\(779\) 36800.7 21246.9i 1.69258 0.977213i
\(780\) 0 0
\(781\) 2160.54 3742.17i 0.0989888 0.171454i
\(782\) 15754.6 + 27287.8i 0.720439 + 1.24784i
\(783\) 0 0
\(784\) 13818.9 + 13457.5i 0.629506 + 0.613041i
\(785\) 31095.5i 1.41382i
\(786\) 0 0
\(787\) 24839.3 + 14341.0i