Properties

Label 225.4.h.d.46.3
Level $225$
Weight $4$
Character 225.46
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 46.3
Character \(\chi\) \(=\) 225.46
Dual form 225.4.h.d.181.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.31991 + 4.06225i) q^{2} +(-8.28762 - 6.02131i) q^{4} +(-4.79821 + 10.0984i) q^{5} +33.6094 q^{7} +(7.75447 - 5.63395i) q^{8} +O(q^{10})\) \(q+(-1.31991 + 4.06225i) q^{2} +(-8.28762 - 6.02131i) q^{4} +(-4.79821 + 10.0984i) q^{5} +33.6094 q^{7} +(7.75447 - 5.63395i) q^{8} +(-34.6890 - 32.8205i) q^{10} +(-9.92549 + 30.5475i) q^{11} +(23.5572 + 72.5016i) q^{13} +(-44.3613 + 136.530i) q^{14} +(-12.6733 - 39.0045i) q^{16} +(-33.4899 + 24.3319i) q^{17} +(-2.91326 + 2.11660i) q^{19} +(100.571 - 54.8000i) q^{20} +(-110.991 - 80.6398i) q^{22} +(38.2254 - 117.646i) q^{23} +(-78.9543 - 96.9083i) q^{25} -325.613 q^{26} +(-278.542 - 202.372i) q^{28} +(153.999 + 111.887i) q^{29} +(-267.535 + 194.376i) q^{31} +251.854 q^{32} +(-54.6386 - 168.160i) q^{34} +(-161.265 + 339.400i) q^{35} +(-39.9391 - 122.920i) q^{37} +(-4.75296 - 14.6281i) q^{38} +(19.6862 + 105.340i) q^{40} +(-129.358 - 398.124i) q^{41} -41.9887 q^{43} +(266.195 - 193.402i) q^{44} +(427.452 + 310.562i) q^{46} +(-375.583 - 272.877i) q^{47} +786.592 q^{49} +(497.878 - 192.823i) q^{50} +(241.321 - 742.710i) q^{52} +(200.790 + 145.882i) q^{53} +(-260.856 - 246.805i) q^{55} +(260.623 - 189.354i) q^{56} +(-657.777 + 477.903i) q^{58} +(66.6949 + 205.266i) q^{59} +(57.9582 - 178.377i) q^{61} +(-436.482 - 1343.35i) q^{62} +(-231.037 + 711.060i) q^{64} +(-845.181 - 109.989i) q^{65} +(-223.332 + 162.260i) q^{67} +424.061 q^{68} +(-1165.88 - 1103.08i) q^{70} +(328.894 + 238.955i) q^{71} +(-161.479 + 496.983i) q^{73} +552.048 q^{74} +36.8887 q^{76} +(-333.590 + 1026.68i) q^{77} +(295.531 + 214.716i) q^{79} +(454.691 + 59.1718i) q^{80} +1788.02 q^{82} +(-550.242 + 399.774i) q^{83} +(-85.0205 - 454.944i) q^{85} +(55.4211 - 170.569i) q^{86} +(95.1364 + 292.800i) q^{88} +(-91.6049 + 281.931i) q^{89} +(791.743 + 2436.73i) q^{91} +(-1025.18 + 744.835i) q^{92} +(1604.23 - 1165.54i) q^{94} +(-7.39584 - 39.5751i) q^{95} +(-185.918 - 135.077i) q^{97} +(-1038.23 + 3195.33i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7} + O(q^{10}) \) \( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31991 + 4.06225i −0.466657 + 1.43622i 0.390229 + 0.920718i \(0.372396\pi\)
−0.856886 + 0.515506i \(0.827604\pi\)
\(3\) 0 0
\(4\) −8.28762 6.02131i −1.03595 0.752663i
\(5\) −4.79821 + 10.0984i −0.429165 + 0.903226i
\(6\) 0 0
\(7\) 33.6094 1.81474 0.907368 0.420336i \(-0.138088\pi\)
0.907368 + 0.420336i \(0.138088\pi\)
\(8\) 7.75447 5.63395i 0.342702 0.248988i
\(9\) 0 0
\(10\) −34.6890 32.8205i −1.09696 1.03787i
\(11\) −9.92549 + 30.5475i −0.272059 + 0.837312i 0.717924 + 0.696122i \(0.245093\pi\)
−0.989983 + 0.141190i \(0.954907\pi\)
\(12\) 0 0
\(13\) 23.5572 + 72.5016i 0.502584 + 1.54679i 0.804795 + 0.593553i \(0.202275\pi\)
−0.302211 + 0.953241i \(0.597725\pi\)
\(14\) −44.3613 + 136.530i −0.846860 + 2.60637i
\(15\) 0 0
\(16\) −12.6733 39.0045i −0.198021 0.609445i
\(17\) −33.4899 + 24.3319i −0.477794 + 0.347138i −0.800471 0.599371i \(-0.795417\pi\)
0.322677 + 0.946509i \(0.395417\pi\)
\(18\) 0 0
\(19\) −2.91326 + 2.11660i −0.0351761 + 0.0255570i −0.605234 0.796047i \(-0.706921\pi\)
0.570058 + 0.821604i \(0.306921\pi\)
\(20\) 100.571 54.8000i 1.12442 0.612682i
\(21\) 0 0
\(22\) −110.991 80.6398i −1.07561 0.781475i
\(23\) 38.2254 117.646i 0.346545 1.06656i −0.614206 0.789146i \(-0.710524\pi\)
0.960751 0.277411i \(-0.0894764\pi\)
\(24\) 0 0
\(25\) −78.9543 96.9083i −0.631635 0.775266i
\(26\) −325.613 −2.45608
\(27\) 0 0
\(28\) −278.542 202.372i −1.87998 1.36589i
\(29\) 153.999 + 111.887i 0.986100 + 0.716444i 0.959064 0.283191i \(-0.0913929\pi\)
0.0270367 + 0.999634i \(0.491393\pi\)
\(30\) 0 0
\(31\) −267.535 + 194.376i −1.55002 + 1.12616i −0.606390 + 0.795168i \(0.707383\pi\)
−0.943634 + 0.330990i \(0.892617\pi\)
\(32\) 251.854 1.39131
\(33\) 0 0
\(34\) −54.6386 168.160i −0.275601 0.848214i
\(35\) −161.265 + 339.400i −0.778822 + 1.63912i
\(36\) 0 0
\(37\) −39.9391 122.920i −0.177458 0.546160i 0.822279 0.569084i \(-0.192702\pi\)
−0.999737 + 0.0229247i \(0.992702\pi\)
\(38\) −4.75296 14.6281i −0.0202903 0.0624471i
\(39\) 0 0
\(40\) 19.6862 + 105.340i 0.0778165 + 0.416395i
\(41\) −129.358 398.124i −0.492741 1.51650i −0.820448 0.571721i \(-0.806276\pi\)
0.327708 0.944779i \(-0.393724\pi\)
\(42\) 0 0
\(43\) −41.9887 −0.148912 −0.0744559 0.997224i \(-0.523722\pi\)
−0.0744559 + 0.997224i \(0.523722\pi\)
\(44\) 266.195 193.402i 0.912054 0.662646i
\(45\) 0 0
\(46\) 427.452 + 310.562i 1.37010 + 0.995433i
\(47\) −375.583 272.877i −1.16563 0.846877i −0.175147 0.984542i \(-0.556040\pi\)
−0.990479 + 0.137666i \(0.956040\pi\)
\(48\) 0 0
\(49\) 786.592 2.29327
\(50\) 497.878 192.823i 1.40821 0.545385i
\(51\) 0 0
\(52\) 241.321 742.710i 0.643562 1.98068i
\(53\) 200.790 + 145.882i 0.520388 + 0.378084i 0.816750 0.576992i \(-0.195774\pi\)
−0.296362 + 0.955076i \(0.595774\pi\)
\(54\) 0 0
\(55\) −260.856 246.805i −0.639523 0.605076i
\(56\) 260.623 189.354i 0.621915 0.451848i
\(57\) 0 0
\(58\) −657.777 + 477.903i −1.48914 + 1.08193i
\(59\) 66.6949 + 205.266i 0.147169 + 0.452938i 0.997283 0.0736590i \(-0.0234676\pi\)
−0.850115 + 0.526597i \(0.823468\pi\)
\(60\) 0 0
\(61\) 57.9582 178.377i 0.121652 0.374407i −0.871624 0.490175i \(-0.836933\pi\)
0.993276 + 0.115768i \(0.0369329\pi\)
\(62\) −436.482 1343.35i −0.894085 2.75171i
\(63\) 0 0
\(64\) −231.037 + 711.060i −0.451245 + 1.38879i
\(65\) −845.181 109.989i −1.61280 0.209883i
\(66\) 0 0
\(67\) −223.332 + 162.260i −0.407228 + 0.295869i −0.772479 0.635041i \(-0.780983\pi\)
0.365250 + 0.930909i \(0.380983\pi\)
\(68\) 424.061 0.756250
\(69\) 0 0
\(70\) −1165.88 1103.08i −1.99070 1.88347i
\(71\) 328.894 + 238.955i 0.549754 + 0.399419i 0.827695 0.561179i \(-0.189652\pi\)
−0.277941 + 0.960598i \(0.589652\pi\)
\(72\) 0 0
\(73\) −161.479 + 496.983i −0.258901 + 0.796814i 0.734136 + 0.679003i \(0.237588\pi\)
−0.993036 + 0.117811i \(0.962412\pi\)
\(74\) 552.048 0.867219
\(75\) 0 0
\(76\) 36.8887 0.0556766
\(77\) −333.590 + 1026.68i −0.493716 + 1.51950i
\(78\) 0 0
\(79\) 295.531 + 214.716i 0.420884 + 0.305790i 0.777993 0.628273i \(-0.216238\pi\)
−0.357109 + 0.934063i \(0.616238\pi\)
\(80\) 454.691 + 59.1718i 0.635450 + 0.0826951i
\(81\) 0 0
\(82\) 1788.02 2.40797
\(83\) −550.242 + 399.774i −0.727673 + 0.528686i −0.888827 0.458244i \(-0.848479\pi\)
0.161153 + 0.986929i \(0.448479\pi\)
\(84\) 0 0
\(85\) −85.0205 454.944i −0.108491 0.580536i
\(86\) 55.4211 170.569i 0.0694908 0.213871i
\(87\) 0 0
\(88\) 95.1364 + 292.800i 0.115245 + 0.354688i
\(89\) −91.6049 + 281.931i −0.109102 + 0.335782i −0.990671 0.136273i \(-0.956488\pi\)
0.881569 + 0.472055i \(0.156488\pi\)
\(90\) 0 0
\(91\) 791.743 + 2436.73i 0.912058 + 2.80702i
\(92\) −1025.18 + 744.835i −1.16176 + 0.844070i
\(93\) 0 0
\(94\) 1604.23 1165.54i 1.76025 1.27890i
\(95\) −7.39584 39.5751i −0.00798734 0.0427402i
\(96\) 0 0
\(97\) −185.918 135.077i −0.194609 0.141392i 0.486214 0.873840i \(-0.338378\pi\)
−0.680823 + 0.732448i \(0.738378\pi\)
\(98\) −1038.23 + 3195.33i −1.07017 + 3.29365i
\(99\) 0 0
\(100\) 70.8289 + 1278.55i 0.0708289 + 1.27855i
\(101\) 514.024 0.506409 0.253205 0.967413i \(-0.418515\pi\)
0.253205 + 0.967413i \(0.418515\pi\)
\(102\) 0 0
\(103\) 77.0965 + 56.0139i 0.0737528 + 0.0535846i 0.624051 0.781384i \(-0.285486\pi\)
−0.550298 + 0.834968i \(0.685486\pi\)
\(104\) 591.144 + 429.491i 0.557370 + 0.404953i
\(105\) 0 0
\(106\) −857.634 + 623.107i −0.785856 + 0.570958i
\(107\) −780.381 −0.705068 −0.352534 0.935799i \(-0.614680\pi\)
−0.352534 + 0.935799i \(0.614680\pi\)
\(108\) 0 0
\(109\) 190.124 + 585.140i 0.167069 + 0.514186i 0.999183 0.0404192i \(-0.0128693\pi\)
−0.832114 + 0.554605i \(0.812869\pi\)
\(110\) 1346.89 733.903i 1.16746 0.636136i
\(111\) 0 0
\(112\) −425.943 1310.92i −0.359356 1.10598i
\(113\) −130.179 400.650i −0.108374 0.333539i 0.882134 0.470999i \(-0.156106\pi\)
−0.990507 + 0.137459i \(0.956106\pi\)
\(114\) 0 0
\(115\) 1004.62 + 950.503i 0.814617 + 0.770738i
\(116\) −602.580 1854.55i −0.482312 1.48440i
\(117\) 0 0
\(118\) −921.873 −0.719198
\(119\) −1125.58 + 817.780i −0.867071 + 0.629964i
\(120\) 0 0
\(121\) 242.165 + 175.943i 0.181942 + 0.132189i
\(122\) 648.113 + 470.882i 0.480962 + 0.349440i
\(123\) 0 0
\(124\) 3387.62 2.45337
\(125\) 1357.46 332.324i 0.971316 0.237792i
\(126\) 0 0
\(127\) 354.912 1092.31i 0.247979 0.763202i −0.747153 0.664652i \(-0.768580\pi\)
0.995132 0.0985497i \(-0.0314204\pi\)
\(128\) −953.522 692.775i −0.658440 0.478384i
\(129\) 0 0
\(130\) 1562.36 3288.16i 1.05406 2.21839i
\(131\) −241.102 + 175.171i −0.160803 + 0.116830i −0.665277 0.746597i \(-0.731686\pi\)
0.504474 + 0.863427i \(0.331686\pi\)
\(132\) 0 0
\(133\) −97.9127 + 71.1378i −0.0638354 + 0.0463792i
\(134\) −364.364 1121.40i −0.234898 0.722940i
\(135\) 0 0
\(136\) −122.612 + 377.362i −0.0773082 + 0.237930i
\(137\) 674.262 + 2075.17i 0.420483 + 1.29411i 0.907254 + 0.420583i \(0.138174\pi\)
−0.486771 + 0.873529i \(0.661826\pi\)
\(138\) 0 0
\(139\) −656.504 + 2020.51i −0.400604 + 1.23293i 0.523907 + 0.851775i \(0.324474\pi\)
−0.924511 + 0.381156i \(0.875526\pi\)
\(140\) 3380.14 1841.79i 2.04053 1.11186i
\(141\) 0 0
\(142\) −1404.81 + 1020.65i −0.830202 + 0.603177i
\(143\) −2448.56 −1.43188
\(144\) 0 0
\(145\) −1868.80 + 1018.28i −1.07031 + 0.583199i
\(146\) −1805.73 1311.94i −1.02359 0.743678i
\(147\) 0 0
\(148\) −409.138 + 1259.20i −0.227236 + 0.699361i
\(149\) 2893.87 1.59111 0.795554 0.605882i \(-0.207180\pi\)
0.795554 + 0.605882i \(0.207180\pi\)
\(150\) 0 0
\(151\) 2519.50 1.35784 0.678921 0.734212i \(-0.262448\pi\)
0.678921 + 0.734212i \(0.262448\pi\)
\(152\) −10.6659 + 32.8263i −0.00569157 + 0.0175169i
\(153\) 0 0
\(154\) −3730.34 2710.25i −1.95195 1.41817i
\(155\) −679.188 3634.33i −0.351959 1.88333i
\(156\) 0 0
\(157\) 2190.79 1.11366 0.556828 0.830628i \(-0.312018\pi\)
0.556828 + 0.830628i \(0.312018\pi\)
\(158\) −1262.30 + 917.117i −0.635591 + 0.461784i
\(159\) 0 0
\(160\) −1208.45 + 2543.32i −0.597102 + 1.25667i
\(161\) 1284.73 3954.00i 0.628889 1.93552i
\(162\) 0 0
\(163\) −150.794 464.095i −0.0724605 0.223010i 0.908267 0.418391i \(-0.137406\pi\)
−0.980728 + 0.195381i \(0.937406\pi\)
\(164\) −1325.15 + 4078.40i −0.630958 + 1.94189i
\(165\) 0 0
\(166\) −897.716 2762.89i −0.419737 1.29182i
\(167\) 2984.57 2168.42i 1.38295 1.00477i 0.386354 0.922351i \(-0.373734\pi\)
0.996597 0.0824226i \(-0.0262657\pi\)
\(168\) 0 0
\(169\) −2924.13 + 2124.50i −1.33096 + 0.967002i
\(170\) 1960.32 + 255.108i 0.884408 + 0.115093i
\(171\) 0 0
\(172\) 347.986 + 252.827i 0.154266 + 0.112080i
\(173\) 969.377 2983.44i 0.426014 1.31114i −0.476007 0.879442i \(-0.657916\pi\)
0.902020 0.431693i \(-0.142084\pi\)
\(174\) 0 0
\(175\) −2653.61 3257.03i −1.14625 1.40690i
\(176\) 1317.28 0.564169
\(177\) 0 0
\(178\) −1024.37 744.245i −0.431345 0.313391i
\(179\) 771.743 + 560.704i 0.322250 + 0.234128i 0.737135 0.675745i \(-0.236178\pi\)
−0.414885 + 0.909874i \(0.636178\pi\)
\(180\) 0 0
\(181\) 125.543 91.2125i 0.0515556 0.0374573i −0.561709 0.827335i \(-0.689856\pi\)
0.613265 + 0.789878i \(0.289856\pi\)
\(182\) −10943.7 −4.45713
\(183\) 0 0
\(184\) −366.392 1127.64i −0.146798 0.451797i
\(185\) 1432.93 + 186.476i 0.569464 + 0.0741079i
\(186\) 0 0
\(187\) −410.874 1264.54i −0.160674 0.494505i
\(188\) 1469.61 + 4523.00i 0.570119 + 1.75465i
\(189\) 0 0
\(190\) 170.526 + 22.1916i 0.0651118 + 0.00847340i
\(191\) 424.396 + 1306.16i 0.160776 + 0.494818i 0.998700 0.0509689i \(-0.0162309\pi\)
−0.837924 + 0.545787i \(0.816231\pi\)
\(192\) 0 0
\(193\) 2565.08 0.956676 0.478338 0.878176i \(-0.341239\pi\)
0.478338 + 0.878176i \(0.341239\pi\)
\(194\) 794.113 576.957i 0.293887 0.213521i
\(195\) 0 0
\(196\) −6518.97 4736.31i −2.37572 1.72606i
\(197\) −1114.76 809.922i −0.403165 0.292917i 0.367664 0.929959i \(-0.380158\pi\)
−0.770829 + 0.637042i \(0.780158\pi\)
\(198\) 0 0
\(199\) −988.966 −0.352291 −0.176146 0.984364i \(-0.556363\pi\)
−0.176146 + 0.984364i \(0.556363\pi\)
\(200\) −1158.23 306.647i −0.409495 0.108416i
\(201\) 0 0
\(202\) −678.464 + 2088.10i −0.236320 + 0.727317i
\(203\) 5175.82 + 3760.45i 1.78951 + 1.30016i
\(204\) 0 0
\(205\) 4641.09 + 603.974i 1.58121 + 0.205773i
\(206\) −329.303 + 239.252i −0.111377 + 0.0809199i
\(207\) 0 0
\(208\) 2529.34 1837.67i 0.843164 0.612595i
\(209\) −35.7415 110.001i −0.0118292 0.0364064i
\(210\) 0 0
\(211\) 606.537 1866.73i 0.197895 0.609057i −0.802036 0.597276i \(-0.796250\pi\)
0.999931 0.0117812i \(-0.00375017\pi\)
\(212\) −785.666 2418.03i −0.254527 0.783354i
\(213\) 0 0
\(214\) 1030.03 3170.11i 0.329025 1.01264i
\(215\) 201.470 424.017i 0.0639078 0.134501i
\(216\) 0 0
\(217\) −8991.70 + 6532.85i −2.81289 + 2.04368i
\(218\) −2627.93 −0.816450
\(219\) 0 0
\(220\) 675.785 + 3616.12i 0.207097 + 1.10818i
\(221\) −2553.03 1854.88i −0.777083 0.564584i
\(222\) 0 0
\(223\) 1063.53 3273.20i 0.319368 0.982913i −0.654551 0.756018i \(-0.727142\pi\)
0.973919 0.226895i \(-0.0728576\pi\)
\(224\) 8464.67 2.52486
\(225\) 0 0
\(226\) 1799.36 0.529610
\(227\) 518.565 1595.98i 0.151623 0.466647i −0.846180 0.532897i \(-0.821103\pi\)
0.997803 + 0.0662496i \(0.0211034\pi\)
\(228\) 0 0
\(229\) 436.125 + 316.863i 0.125851 + 0.0914363i 0.648930 0.760848i \(-0.275217\pi\)
−0.523079 + 0.852284i \(0.675217\pi\)
\(230\) −5187.18 + 2826.43i −1.48710 + 0.810301i
\(231\) 0 0
\(232\) 1824.55 0.516325
\(233\) −2488.89 + 1808.28i −0.699796 + 0.508431i −0.879866 0.475223i \(-0.842368\pi\)
0.180070 + 0.983654i \(0.442368\pi\)
\(234\) 0 0
\(235\) 4557.74 2483.46i 1.26517 0.689374i
\(236\) 683.227 2102.76i 0.188450 0.579990i
\(237\) 0 0
\(238\) −1836.37 5651.77i −0.500144 1.53929i
\(239\) −134.744 + 414.700i −0.0364681 + 0.112237i −0.967633 0.252360i \(-0.918793\pi\)
0.931165 + 0.364597i \(0.118793\pi\)
\(240\) 0 0
\(241\) 1239.98 + 3816.27i 0.331429 + 1.02003i 0.968455 + 0.249190i \(0.0801644\pi\)
−0.637026 + 0.770842i \(0.719836\pi\)
\(242\) −1034.36 + 751.508i −0.274758 + 0.199623i
\(243\) 0 0
\(244\) −1554.40 + 1129.34i −0.407828 + 0.296305i
\(245\) −3774.23 + 7943.30i −0.984191 + 2.07134i
\(246\) 0 0
\(247\) −222.085 161.354i −0.0572103 0.0415657i
\(248\) −979.490 + 3014.56i −0.250797 + 0.771874i
\(249\) 0 0
\(250\) −441.729 + 5952.97i −0.111750 + 1.50599i
\(251\) −4706.56 −1.18357 −0.591784 0.806097i \(-0.701576\pi\)
−0.591784 + 0.806097i \(0.701576\pi\)
\(252\) 0 0
\(253\) 3214.38 + 2335.38i 0.798760 + 0.580333i
\(254\) 3968.78 + 2883.49i 0.980407 + 0.712308i
\(255\) 0 0
\(256\) −766.121 + 556.620i −0.187041 + 0.135893i
\(257\) 573.257 0.139139 0.0695696 0.997577i \(-0.477837\pi\)
0.0695696 + 0.997577i \(0.477837\pi\)
\(258\) 0 0
\(259\) −1342.33 4131.26i −0.322040 0.991136i
\(260\) 6342.26 + 6000.63i 1.51281 + 1.43132i
\(261\) 0 0
\(262\) −393.357 1210.63i −0.0927544 0.285469i
\(263\) 1428.46 + 4396.36i 0.334915 + 1.03076i 0.966764 + 0.255672i \(0.0822966\pi\)
−0.631848 + 0.775092i \(0.717703\pi\)
\(264\) 0 0
\(265\) −2436.60 + 1327.67i −0.564828 + 0.307768i
\(266\) −159.744 491.642i −0.0368216 0.113325i
\(267\) 0 0
\(268\) 2827.90 0.644559
\(269\) −5498.69 + 3995.03i −1.24632 + 0.905507i −0.998003 0.0631703i \(-0.979879\pi\)
−0.248321 + 0.968678i \(0.579879\pi\)
\(270\) 0 0
\(271\) −4062.81 2951.81i −0.910695 0.661659i 0.0304957 0.999535i \(-0.490291\pi\)
−0.941190 + 0.337876i \(0.890291\pi\)
\(272\) 1373.48 + 997.893i 0.306175 + 0.222449i
\(273\) 0 0
\(274\) −9319.81 −2.05486
\(275\) 3743.97 1450.00i 0.820981 0.317957i
\(276\) 0 0
\(277\) −1967.28 + 6054.66i −0.426723 + 1.31332i 0.474612 + 0.880195i \(0.342589\pi\)
−0.901335 + 0.433123i \(0.857411\pi\)
\(278\) −7341.30 5333.77i −1.58382 1.15071i
\(279\) 0 0
\(280\) 661.641 + 3540.43i 0.141216 + 0.755647i
\(281\) 1793.59 1303.12i 0.380771 0.276646i −0.380892 0.924619i \(-0.624383\pi\)
0.761663 + 0.647973i \(0.224383\pi\)
\(282\) 0 0
\(283\) 5646.82 4102.66i 1.18611 0.861759i 0.193261 0.981147i \(-0.438093\pi\)
0.992848 + 0.119389i \(0.0380935\pi\)
\(284\) −1286.92 3960.74i −0.268890 0.827559i
\(285\) 0 0
\(286\) 3231.87 9946.68i 0.668198 2.05650i
\(287\) −4347.65 13380.7i −0.894195 2.75205i
\(288\) 0 0
\(289\) −988.664 + 3042.79i −0.201234 + 0.619335i
\(290\) −1669.89 8935.56i −0.338136 1.80936i
\(291\) 0 0
\(292\) 4330.76 3146.48i 0.867941 0.630596i
\(293\) 8443.08 1.68345 0.841724 0.539908i \(-0.181541\pi\)
0.841724 + 0.539908i \(0.181541\pi\)
\(294\) 0 0
\(295\) −2392.87 311.399i −0.472265 0.0614588i
\(296\) −1002.23 728.164i −0.196802 0.142985i
\(297\) 0 0
\(298\) −3819.64 + 11755.6i −0.742503 + 2.28519i
\(299\) 9429.98 1.82391
\(300\) 0 0
\(301\) −1411.21 −0.270236
\(302\) −3325.50 + 10234.8i −0.633647 + 1.95016i
\(303\) 0 0
\(304\) 119.478 + 86.8056i 0.0225412 + 0.0163771i
\(305\) 1523.22 + 1441.17i 0.285965 + 0.270562i
\(306\) 0 0
\(307\) −2853.33 −0.530450 −0.265225 0.964187i \(-0.585446\pi\)
−0.265225 + 0.964187i \(0.585446\pi\)
\(308\) 8946.64 6500.12i 1.65514 1.20253i
\(309\) 0 0
\(310\) 15660.0 + 2037.94i 2.86913 + 0.373377i
\(311\) −2085.97 + 6419.96i −0.380336 + 1.17055i 0.559471 + 0.828850i \(0.311004\pi\)
−0.939807 + 0.341705i \(0.888996\pi\)
\(312\) 0 0
\(313\) 1021.84 + 3144.90i 0.184530 + 0.567924i 0.999940 0.0109593i \(-0.00348854\pi\)
−0.815410 + 0.578884i \(0.803489\pi\)
\(314\) −2891.64 + 8899.54i −0.519696 + 1.59946i
\(315\) 0 0
\(316\) −1156.38 3558.96i −0.205859 0.633568i
\(317\) 2682.89 1949.24i 0.475351 0.345363i −0.324172 0.945998i \(-0.605086\pi\)
0.799523 + 0.600635i \(0.205086\pi\)
\(318\) 0 0
\(319\) −4946.39 + 3593.76i −0.868164 + 0.630758i
\(320\) −6071.98 5744.92i −1.06073 1.00360i
\(321\) 0 0
\(322\) 14366.4 + 10437.8i 2.48636 + 1.80645i
\(323\) 46.0638 141.770i 0.00793517 0.0244219i
\(324\) 0 0
\(325\) 5166.06 8007.20i 0.881728 1.36665i
\(326\) 2084.30 0.354107
\(327\) 0 0
\(328\) −3246.12 2358.44i −0.546454 0.397022i
\(329\) −12623.1 9171.23i −2.11530 1.53686i
\(330\) 0 0
\(331\) 6061.25 4403.76i 1.00651 0.731276i 0.0430396 0.999073i \(-0.486296\pi\)
0.963475 + 0.267798i \(0.0862958\pi\)
\(332\) 6967.36 1.15176
\(333\) 0 0
\(334\) 4869.31 + 14986.2i 0.797714 + 2.45511i
\(335\) −566.969 3033.84i −0.0924682 0.494796i
\(336\) 0 0
\(337\) −2497.93 7687.83i −0.403771 1.24268i −0.921917 0.387387i \(-0.873378\pi\)
0.518146 0.855292i \(-0.326622\pi\)
\(338\) −4770.70 14682.7i −0.767727 2.36282i
\(339\) 0 0
\(340\) −2034.74 + 4282.33i −0.324556 + 0.683065i
\(341\) −3282.28 10101.8i −0.521247 1.60423i
\(342\) 0 0
\(343\) 14908.8 2.34694
\(344\) −325.600 + 236.562i −0.0510325 + 0.0370773i
\(345\) 0 0
\(346\) 10840.0 + 7875.71i 1.68428 + 1.22370i
\(347\) 8214.67 + 5968.31i 1.27086 + 0.923330i 0.999236 0.0390745i \(-0.0124410\pi\)
0.271619 + 0.962405i \(0.412441\pi\)
\(348\) 0 0
\(349\) 915.035 0.140346 0.0701729 0.997535i \(-0.477645\pi\)
0.0701729 + 0.997535i \(0.477645\pi\)
\(350\) 16733.4 6480.65i 2.55554 0.989730i
\(351\) 0 0
\(352\) −2499.78 + 7693.52i −0.378519 + 1.16496i
\(353\) −64.3813 46.7758i −0.00970728 0.00705275i 0.582921 0.812529i \(-0.301910\pi\)
−0.592628 + 0.805476i \(0.701910\pi\)
\(354\) 0 0
\(355\) −3991.16 + 2174.73i −0.596701 + 0.325135i
\(356\) 2456.78 1784.95i 0.365756 0.265737i
\(357\) 0 0
\(358\) −3296.35 + 2394.94i −0.486641 + 0.353565i
\(359\) −1932.90 5948.86i −0.284163 0.874565i −0.986648 0.162866i \(-0.947926\pi\)
0.702485 0.711699i \(-0.252074\pi\)
\(360\) 0 0
\(361\) −2115.54 + 6510.96i −0.308433 + 0.949259i
\(362\) 204.823 + 630.380i 0.0297383 + 0.0915250i
\(363\) 0 0
\(364\) 8110.66 24962.1i 1.16790 3.59441i
\(365\) −4243.90 4015.31i −0.608592 0.575810i
\(366\) 0 0
\(367\) 2077.48 1509.38i 0.295487 0.214684i −0.430157 0.902754i \(-0.641542\pi\)
0.725644 + 0.688070i \(0.241542\pi\)
\(368\) −5073.15 −0.718631
\(369\) 0 0
\(370\) −2648.84 + 5574.78i −0.372180 + 0.783295i
\(371\) 6748.41 + 4903.01i 0.944367 + 0.686123i
\(372\) 0 0
\(373\) 2876.24 8852.16i 0.399266 1.22881i −0.526323 0.850285i \(-0.676430\pi\)
0.925589 0.378530i \(-0.123570\pi\)
\(374\) 5679.20 0.785199
\(375\) 0 0
\(376\) −4449.82 −0.610325
\(377\) −4484.19 + 13800.9i −0.612593 + 1.88537i
\(378\) 0 0
\(379\) 1786.14 + 1297.71i 0.242079 + 0.175880i 0.702209 0.711971i \(-0.252197\pi\)
−0.460130 + 0.887851i \(0.652197\pi\)
\(380\) −177.000 + 372.515i −0.0238944 + 0.0502885i
\(381\) 0 0
\(382\) −5866.10 −0.785696
\(383\) −10414.5 + 7566.60i −1.38945 + 1.00949i −0.393520 + 0.919316i \(0.628743\pi\)
−0.995926 + 0.0901754i \(0.971257\pi\)
\(384\) 0 0
\(385\) −8767.21 8294.96i −1.16057 1.09805i
\(386\) −3385.66 + 10420.0i −0.446440 + 1.37400i
\(387\) 0 0
\(388\) 727.475 + 2238.94i 0.0951855 + 0.292951i
\(389\) −3872.47 + 11918.2i −0.504735 + 1.55341i 0.296481 + 0.955039i \(0.404187\pi\)
−0.801216 + 0.598376i \(0.795813\pi\)
\(390\) 0 0
\(391\) 1582.37 + 4870.04i 0.204665 + 0.629894i
\(392\) 6099.60 4431.62i 0.785909 0.570996i
\(393\) 0 0
\(394\) 4761.49 3459.43i 0.608834 0.442344i
\(395\) −3586.30 + 1954.13i −0.456826 + 0.248919i
\(396\) 0 0
\(397\) −10322.4 7499.67i −1.30496 0.948105i −0.304964 0.952364i \(-0.598645\pi\)
−0.999991 + 0.00425835i \(0.998645\pi\)
\(398\) 1305.34 4017.43i 0.164399 0.505969i
\(399\) 0 0
\(400\) −2779.24 + 4307.72i −0.347405 + 0.538466i
\(401\) −4960.15 −0.617700 −0.308850 0.951111i \(-0.599944\pi\)
−0.308850 + 0.951111i \(0.599944\pi\)
\(402\) 0 0
\(403\) −20394.9 14817.8i −2.52095 1.83158i
\(404\) −4260.04 3095.10i −0.524616 0.381156i
\(405\) 0 0
\(406\) −22107.5 + 16062.0i −2.70241 + 1.96341i
\(407\) 4151.31 0.505585
\(408\) 0 0
\(409\) 3499.05 + 10769.0i 0.423025 + 1.30194i 0.904873 + 0.425682i \(0.139966\pi\)
−0.481848 + 0.876255i \(0.660034\pi\)
\(410\) −8579.30 + 18056.1i −1.03342 + 2.17494i
\(411\) 0 0
\(412\) −301.669 928.443i −0.0360733 0.111022i
\(413\) 2241.58 + 6898.86i 0.267072 + 0.821963i
\(414\) 0 0
\(415\) −1396.89 7474.75i −0.165231 0.884147i
\(416\) 5932.98 + 18259.8i 0.699251 + 2.15207i
\(417\) 0 0
\(418\) 494.028 0.0578079
\(419\) −9318.52 + 6770.30i −1.08649 + 0.789382i −0.978803 0.204803i \(-0.934345\pi\)
−0.107688 + 0.994185i \(0.534345\pi\)
\(420\) 0 0
\(421\) 1968.58 + 1430.26i 0.227892 + 0.165574i 0.695872 0.718166i \(-0.255018\pi\)
−0.467980 + 0.883739i \(0.655018\pi\)
\(422\) 6782.56 + 4927.82i 0.782393 + 0.568442i
\(423\) 0 0
\(424\) 2378.91 0.272477
\(425\) 5002.14 + 1324.35i 0.570916 + 0.151153i
\(426\) 0 0
\(427\) 1947.94 5995.14i 0.220767 0.679450i
\(428\) 6467.50 + 4698.91i 0.730417 + 0.530679i
\(429\) 0 0
\(430\) 1456.54 + 1378.09i 0.163351 + 0.154552i
\(431\) 7111.10 5166.51i 0.794732 0.577407i −0.114632 0.993408i \(-0.536569\pi\)
0.909364 + 0.416001i \(0.136569\pi\)
\(432\) 0 0
\(433\) −6196.51 + 4502.03i −0.687726 + 0.499662i −0.875912 0.482471i \(-0.839739\pi\)
0.188186 + 0.982133i \(0.439739\pi\)
\(434\) −14669.9 45149.3i −1.62253 4.99363i
\(435\) 0 0
\(436\) 1947.64 5994.21i 0.213933 0.658419i
\(437\) 137.649 + 423.640i 0.0150678 + 0.0463740i
\(438\) 0 0
\(439\) 1589.15 4890.90i 0.172770 0.531731i −0.826755 0.562563i \(-0.809815\pi\)
0.999525 + 0.0308313i \(0.00981546\pi\)
\(440\) −3413.29 444.192i −0.369823 0.0481273i
\(441\) 0 0
\(442\) 10904.8 7922.78i 1.17350 0.852598i
\(443\) −3847.00 −0.412588 −0.206294 0.978490i \(-0.566140\pi\)
−0.206294 + 0.978490i \(0.566140\pi\)
\(444\) 0 0
\(445\) −2407.50 2277.83i −0.256464 0.242650i
\(446\) 11892.8 + 8640.63i 1.26265 + 0.917367i
\(447\) 0 0
\(448\) −7765.02 + 23898.3i −0.818890 + 2.52029i
\(449\) 1690.99 0.177735 0.0888674 0.996043i \(-0.471675\pi\)
0.0888674 + 0.996043i \(0.471675\pi\)
\(450\) 0 0
\(451\) 13445.6 1.40384
\(452\) −1333.56 + 4104.28i −0.138773 + 0.427100i
\(453\) 0 0
\(454\) 5798.82 + 4213.09i 0.599454 + 0.435529i
\(455\) −28406.0 3696.65i −2.92680 0.380883i
\(456\) 0 0
\(457\) −369.186 −0.0377895 −0.0188947 0.999821i \(-0.506015\pi\)
−0.0188947 + 0.999821i \(0.506015\pi\)
\(458\) −1862.82 + 1353.42i −0.190052 + 0.138081i
\(459\) 0 0
\(460\) −2602.60 13926.5i −0.263798 1.41158i
\(461\) 812.481 2500.56i 0.0820846 0.252630i −0.901589 0.432595i \(-0.857598\pi\)
0.983673 + 0.179964i \(0.0575982\pi\)
\(462\) 0 0
\(463\) 587.970 + 1809.58i 0.0590178 + 0.181638i 0.976219 0.216786i \(-0.0695573\pi\)
−0.917201 + 0.398424i \(0.869557\pi\)
\(464\) 2412.41 7424.64i 0.241365 0.742845i
\(465\) 0 0
\(466\) −4060.60 12497.2i −0.403656 1.24233i
\(467\) 8903.30 6468.62i 0.882217 0.640968i −0.0516199 0.998667i \(-0.516438\pi\)
0.933837 + 0.357698i \(0.116438\pi\)
\(468\) 0 0
\(469\) −7506.04 + 5453.46i −0.739012 + 0.536924i
\(470\) 4072.64 + 21792.6i 0.399695 + 2.13876i
\(471\) 0 0
\(472\) 1673.64 + 1215.97i 0.163211 + 0.118580i
\(473\) 416.758 1282.65i 0.0405128 0.124686i
\(474\) 0 0
\(475\) 435.131 + 115.203i 0.0420319 + 0.0111282i
\(476\) 14252.5 1.37239
\(477\) 0 0
\(478\) −1506.77 1094.73i −0.144180 0.104753i
\(479\) 11054.3 + 8031.41i 1.05445 + 0.766106i 0.973054 0.230576i \(-0.0740610\pi\)
0.0813995 + 0.996682i \(0.474061\pi\)
\(480\) 0 0
\(481\) 7971.03 5791.30i 0.755609 0.548982i
\(482\) −17139.3 −1.61966
\(483\) 0 0
\(484\) −947.564 2916.30i −0.0889899 0.273883i
\(485\) 2256.14 1229.34i 0.211229 0.115096i
\(486\) 0 0
\(487\) −1524.98 4693.40i −0.141896 0.436711i 0.854703 0.519118i \(-0.173739\pi\)
−0.996599 + 0.0824064i \(0.973739\pi\)
\(488\) −555.532 1709.75i −0.0515323 0.158600i
\(489\) 0 0
\(490\) −27286.0 25816.3i −2.51563 2.38013i
\(491\) 134.582 + 414.201i 0.0123699 + 0.0380705i 0.957051 0.289920i \(-0.0936287\pi\)
−0.944681 + 0.327990i \(0.893629\pi\)
\(492\) 0 0
\(493\) −7879.84 −0.719858
\(494\) 948.594 689.194i 0.0863953 0.0627698i
\(495\) 0 0
\(496\) 10972.1 + 7971.69i 0.993269 + 0.721652i
\(497\) 11053.9 + 8031.14i 0.997658 + 0.724841i
\(498\) 0 0
\(499\) 3428.76 0.307600 0.153800 0.988102i \(-0.450849\pi\)
0.153800 + 0.988102i \(0.450849\pi\)
\(500\) −13251.1 5419.48i −1.18521 0.484733i
\(501\) 0 0
\(502\) 6212.22 19119.2i 0.552320 1.69987i
\(503\) −3567.05 2591.62i −0.316197 0.229731i 0.418354 0.908284i \(-0.362607\pi\)
−0.734551 + 0.678553i \(0.762607\pi\)
\(504\) 0 0
\(505\) −2466.40 + 5190.81i −0.217333 + 0.457402i
\(506\) −13729.6 + 9975.13i −1.20623 + 0.876381i
\(507\) 0 0
\(508\) −9518.50 + 6915.59i −0.831329 + 0.603996i
\(509\) −1764.24 5429.77i −0.153632 0.472830i 0.844388 0.535732i \(-0.179964\pi\)
−0.998020 + 0.0629024i \(0.979964\pi\)
\(510\) 0 0
\(511\) −5427.23 + 16703.3i −0.469836 + 1.44601i
\(512\) −4163.63 12814.3i −0.359391 1.10609i
\(513\) 0 0
\(514\) −756.645 + 2328.72i −0.0649303 + 0.199835i
\(515\) −935.574 + 509.783i −0.0800511 + 0.0436189i
\(516\) 0 0
\(517\) 12063.6 8764.69i 1.02622 0.745592i
\(518\) 18554.0 1.57377
\(519\) 0 0
\(520\) −7173.60 + 3908.81i −0.604968 + 0.329639i
\(521\) −1640.89 1192.18i −0.137982 0.100250i 0.516653 0.856195i \(-0.327178\pi\)
−0.654635 + 0.755945i \(0.727178\pi\)
\(522\) 0 0
\(523\) −1067.09 + 3284.16i −0.0892171 + 0.274582i −0.985703 0.168489i \(-0.946111\pi\)
0.896486 + 0.443071i \(0.146111\pi\)
\(524\) 3052.92 0.254518
\(525\) 0 0
\(526\) −19744.5 −1.63670
\(527\) 4230.21 13019.3i 0.349660 1.07614i
\(528\) 0 0
\(529\) −2536.00 1842.51i −0.208433 0.151435i
\(530\) −2177.26 11650.5i −0.178442 0.954841i
\(531\) 0 0
\(532\) 1239.81 0.101038
\(533\) 25817.3 18757.4i 2.09807 1.52434i
\(534\) 0 0
\(535\) 3744.43 7880.58i 0.302591 0.636836i
\(536\) −817.654 + 2516.48i −0.0658904 + 0.202790i
\(537\) 0 0
\(538\) −8971.08 27610.2i −0.718905 2.21256i
\(539\) −7807.31 + 24028.4i −0.623905 + 1.92018i
\(540\) 0 0
\(541\) 6762.35 + 20812.4i 0.537405 + 1.65396i 0.738394 + 0.674370i \(0.235585\pi\)
−0.200988 + 0.979594i \(0.564415\pi\)
\(542\) 17353.5 12608.1i 1.37527 0.999194i
\(543\) 0 0
\(544\) −8434.58 + 6128.08i −0.664761 + 0.482977i
\(545\) −6821.22 887.687i −0.536126 0.0697694i
\(546\) 0 0
\(547\) −6842.63 4971.46i −0.534862 0.388600i 0.287311 0.957837i \(-0.407239\pi\)
−0.822173 + 0.569237i \(0.807239\pi\)
\(548\) 6907.18 21258.1i 0.538431 1.65712i
\(549\) 0 0
\(550\) 948.569 + 17122.8i 0.0735402 + 1.32749i
\(551\) −685.459 −0.0529973
\(552\) 0 0
\(553\) 9932.62 + 7216.47i 0.763793 + 0.554928i
\(554\) −21998.9 15983.2i −1.68709 1.22574i
\(555\) 0 0
\(556\) 17607.0 12792.2i 1.34299 0.975738i
\(557\) −16513.1 −1.25616 −0.628080 0.778149i \(-0.716159\pi\)
−0.628080 + 0.778149i \(0.716159\pi\)
\(558\) 0 0
\(559\) −989.135 3044.24i −0.0748407 0.230336i
\(560\) 15281.9 + 1988.73i 1.15318 + 0.150070i
\(561\) 0 0
\(562\) 2926.23 + 9006.01i 0.219636 + 0.675971i
\(563\) −5502.05 16933.6i −0.411872 1.26761i −0.915019 0.403410i \(-0.867825\pi\)
0.503147 0.864201i \(-0.332175\pi\)
\(564\) 0 0
\(565\) 4670.54 + 607.806i 0.347772 + 0.0452577i
\(566\) 9212.76 + 28354.0i 0.684172 + 2.10566i
\(567\) 0 0
\(568\) 3896.66 0.287853
\(569\) 3984.70 2895.05i 0.293580 0.213299i −0.431239 0.902238i \(-0.641923\pi\)
0.724819 + 0.688939i \(0.241923\pi\)
\(570\) 0 0
\(571\) −10205.8 7414.97i −0.747987 0.543444i 0.147215 0.989104i \(-0.452969\pi\)
−0.895202 + 0.445660i \(0.852969\pi\)
\(572\) 20292.7 + 14743.5i 1.48336 + 1.07772i
\(573\) 0 0
\(574\) 60094.3 4.36984
\(575\) −14418.9 + 5584.28i −1.04576 + 0.405009i
\(576\) 0 0
\(577\) 3968.83 12214.8i 0.286351 0.881297i −0.699640 0.714496i \(-0.746656\pi\)
0.985991 0.166801i \(-0.0533439\pi\)
\(578\) −11055.7 8032.41i −0.795597 0.578035i
\(579\) 0 0
\(580\) 21619.3 + 2813.45i 1.54774 + 0.201417i
\(581\) −18493.3 + 13436.2i −1.32054 + 0.959425i
\(582\) 0 0
\(583\) −6449.27 + 4685.67i −0.458150 + 0.332866i
\(584\) 1547.79 + 4763.61i 0.109671 + 0.337533i
\(585\) 0 0
\(586\) −11144.1 + 34297.9i −0.785593 + 2.41781i
\(587\) 2104.99 + 6478.50i 0.148011 + 0.455530i 0.997386 0.0722593i \(-0.0230209\pi\)
−0.849375 + 0.527790i \(0.823021\pi\)
\(588\) 0 0
\(589\) 367.982 1132.53i 0.0257427 0.0792278i
\(590\) 4423.34 9309.42i 0.308655 0.649598i
\(591\) 0 0
\(592\) −4288.27 + 3115.61i −0.297714 + 0.216302i
\(593\) 20641.3 1.42941 0.714703 0.699428i \(-0.246562\pi\)
0.714703 + 0.699428i \(0.246562\pi\)
\(594\) 0 0
\(595\) −2857.49 15290.4i −0.196883 1.05352i
\(596\) −23983.3 17424.9i −1.64831 1.19757i
\(597\) 0 0
\(598\) −12446.7 + 38307.0i −0.851142 + 2.61955i
\(599\) 15650.0 1.06751 0.533757 0.845638i \(-0.320780\pi\)
0.533757 + 0.845638i \(0.320780\pi\)
\(600\) 0 0
\(601\) −17812.8 −1.20898 −0.604491 0.796612i \(-0.706623\pi\)
−0.604491 + 0.796612i \(0.706623\pi\)
\(602\) 1862.67 5732.71i 0.126108 0.388119i
\(603\) 0 0
\(604\) −20880.6 15170.7i −1.40666 1.02200i
\(605\) −2938.70 + 1601.26i −0.197480 + 0.107604i
\(606\) 0 0
\(607\) −22919.5 −1.53258 −0.766290 0.642495i \(-0.777899\pi\)
−0.766290 + 0.642495i \(0.777899\pi\)
\(608\) −733.716 + 533.076i −0.0489409 + 0.0355577i
\(609\) 0 0
\(610\) −7864.93 + 4285.50i −0.522035 + 0.284450i
\(611\) 10936.3 33658.6i 0.724119 2.22861i
\(612\) 0 0
\(613\) −2407.59 7409.79i −0.158632 0.488220i 0.839879 0.542774i \(-0.182626\pi\)
−0.998511 + 0.0545546i \(0.982626\pi\)
\(614\) 3766.13 11591.0i 0.247538 0.761845i
\(615\) 0 0
\(616\) 3197.48 + 9840.82i 0.209140 + 0.643666i
\(617\) 24594.0 17868.6i 1.60473 1.16590i 0.727134 0.686496i \(-0.240852\pi\)
0.877593 0.479406i \(-0.159148\pi\)
\(618\) 0 0
\(619\) 16760.8 12177.5i 1.08833 0.790716i 0.109212 0.994019i \(-0.465167\pi\)
0.979116 + 0.203302i \(0.0651674\pi\)
\(620\) −16254.5 + 34209.5i −1.05290 + 2.21595i
\(621\) 0 0
\(622\) −23326.2 16947.5i −1.50369 1.09250i
\(623\) −3078.79 + 9475.53i −0.197992 + 0.609356i
\(624\) 0 0
\(625\) −3157.43 + 15302.7i −0.202075 + 0.979370i
\(626\) −14124.1 −0.901778
\(627\) 0 0
\(628\) −18156.4 13191.4i −1.15369 0.838208i
\(629\) 4328.43 + 3144.79i 0.274381 + 0.199350i
\(630\) 0 0
\(631\) 18557.5 13482.8i 1.17078 0.850624i 0.179681 0.983725i \(-0.442493\pi\)
0.991102 + 0.133101i \(0.0424935\pi\)
\(632\) 3501.38 0.220376
\(633\) 0 0
\(634\) 4377.12 + 13471.4i 0.274192 + 0.843876i
\(635\) 9327.59 + 8825.16i 0.582920 + 0.551521i
\(636\) 0 0
\(637\) 18529.9 + 57029.1i 1.15256 + 3.54722i
\(638\) −8070.00 24836.9i −0.500775 1.54123i
\(639\) 0 0
\(640\) 11571.1 6304.95i 0.714669 0.389414i
\(641\) −5387.35 16580.5i −0.331962 1.02167i −0.968199 0.250180i \(-0.919510\pi\)
0.636238 0.771493i \(-0.280490\pi\)
\(642\) 0 0
\(643\) 29188.0 1.79014 0.895072 0.445921i \(-0.147124\pi\)
0.895072 + 0.445921i \(0.147124\pi\)
\(644\) −34455.6 + 25033.5i −2.10829 + 1.53176i
\(645\) 0 0
\(646\) 515.105 + 374.246i 0.0313724 + 0.0227934i
\(647\) −1185.75 861.499i −0.0720506 0.0523478i 0.551177 0.834388i \(-0.314179\pi\)
−0.623227 + 0.782041i \(0.714179\pi\)
\(648\) 0 0
\(649\) −6932.35 −0.419289
\(650\) 25708.6 + 31554.6i 1.55134 + 1.90411i
\(651\) 0 0
\(652\) −1544.74 + 4754.21i −0.0927862 + 0.285567i
\(653\) 5424.96 + 3941.46i 0.325107 + 0.236204i 0.738352 0.674416i \(-0.235605\pi\)
−0.413244 + 0.910620i \(0.635605\pi\)
\(654\) 0 0
\(655\) −612.083 3275.25i −0.0365131 0.195381i
\(656\) −13889.2 + 10091.1i −0.826651 + 0.600597i
\(657\) 0 0
\(658\) 53917.2 39173.1i 3.19439 2.32086i
\(659\) 360.964 + 1110.93i 0.0213371 + 0.0656689i 0.961158 0.275998i \(-0.0890084\pi\)
−0.939821 + 0.341667i \(0.889008\pi\)
\(660\) 0 0
\(661\) 811.577 2497.78i 0.0477559 0.146978i −0.924335 0.381582i \(-0.875379\pi\)
0.972091 + 0.234604i \(0.0753794\pi\)
\(662\) 9888.89 + 30434.9i 0.580578 + 1.78684i
\(663\) 0 0
\(664\) −2014.53 + 6200.07i −0.117739 + 0.362364i
\(665\) −248.570 1330.09i −0.0144949 0.0775621i
\(666\) 0 0
\(667\) 19049.7 13840.4i 1.10586 0.803452i
\(668\) −37791.7 −2.18893
\(669\) 0 0
\(670\) 13072.6 + 1701.22i 0.753788 + 0.0980951i
\(671\) 4873.71 + 3540.96i 0.280399 + 0.203722i
\(672\) 0 0
\(673\) −6129.43 + 18864.4i −0.351073 + 1.08049i 0.607179 + 0.794565i \(0.292301\pi\)
−0.958252 + 0.285926i \(0.907699\pi\)
\(674\) 34527.0 1.97319
\(675\) 0 0
\(676\) 37026.4 2.10664
\(677\) 1227.06 3776.51i 0.0696600 0.214392i −0.910166 0.414244i \(-0.864046\pi\)
0.979826 + 0.199852i \(0.0640462\pi\)
\(678\) 0 0
\(679\) −6248.59 4539.87i −0.353165 0.256589i
\(680\) −3222.42 3048.85i −0.181727 0.171938i
\(681\) 0 0
\(682\) 45368.4 2.54728
\(683\) 9447.69 6864.15i 0.529291 0.384552i −0.290802 0.956783i \(-0.593922\pi\)
0.820092 + 0.572231i \(0.193922\pi\)
\(684\) 0 0
\(685\) −24191.1 3148.13i −1.34933 0.175597i
\(686\) −19678.3 + 60563.5i −1.09522 + 3.37074i
\(687\) 0 0
\(688\) 532.136 + 1637.75i 0.0294876 + 0.0907536i
\(689\) −5846.65 + 17994.1i −0.323279 + 0.994952i
\(690\) 0 0
\(691\) −10114.6 31129.6i −0.556844 1.71379i −0.691024 0.722831i \(-0.742840\pi\)
0.134181 0.990957i \(-0.457160\pi\)
\(692\) −25998.0 + 18888.7i −1.42817 + 1.03763i
\(693\) 0 0
\(694\) −35087.4 + 25492.5i −1.91916 + 1.39435i
\(695\) −17253.8 16324.5i −0.941691 0.890967i
\(696\) 0 0
\(697\) 14019.3 + 10185.6i 0.761863 + 0.553526i
\(698\) −1207.76 + 3717.10i −0.0654934 + 0.201568i
\(699\) 0 0
\(700\) 2380.52 + 42971.2i 0.128536 + 2.32023i
\(701\) 25681.6 1.38371 0.691855 0.722036i \(-0.256794\pi\)
0.691855 + 0.722036i \(0.256794\pi\)
\(702\) 0 0
\(703\) 376.525 + 273.562i 0.0202005 + 0.0146765i
\(704\) −19428.0 14115.2i −1.04008 0.755665i
\(705\) 0 0
\(706\) 274.992 199.794i 0.0146593 0.0106506i
\(707\) 17276.0 0.918999
\(708\) 0 0
\(709\) 8535.60 + 26269.9i 0.452132 + 1.39152i 0.874470 + 0.485080i \(0.161209\pi\)
−0.422338 + 0.906438i \(0.638791\pi\)
\(710\) −3566.36 19083.6i −0.188512 1.00872i
\(711\) 0 0
\(712\) 878.038 + 2702.32i 0.0462161 + 0.142239i
\(713\) 12640.8 + 38904.4i 0.663958 + 2.04345i
\(714\) 0 0
\(715\) 11748.7 24726.5i 0.614513 1.29331i
\(716\) −3019.74 9293.80i −0.157616 0.485092i
\(717\) 0 0
\(718\) 26717.0 1.38868
\(719\) 4433.43 3221.08i 0.229957 0.167074i −0.466840 0.884342i \(-0.654608\pi\)
0.696797 + 0.717268i \(0.254608\pi\)
\(720\) 0 0
\(721\) 2591.17 + 1882.59i 0.133842 + 0.0972419i
\(722\) −23656.9 17187.7i −1.21942 0.885957i
\(723\) 0 0
\(724\) −1589.67 −0.0816018
\(725\) −1316.13 23757.7i −0.0674205 1.21702i
\(726\) 0 0
\(727\) −7275.89 + 22392.9i −0.371180 + 1.14237i 0.574840 + 0.818266i \(0.305064\pi\)
−0.946020 + 0.324109i \(0.894936\pi\)
\(728\) 19868.0 + 14434.9i 1.01148 + 0.734883i
\(729\) 0 0
\(730\) 21912.8 11940.0i 1.11100 0.605368i
\(731\) 1406.20 1021.66i 0.0711493 0.0516930i
\(732\) 0 0
\(733\) −6158.96 + 4474.74i −0.310350 + 0.225482i −0.732046 0.681255i \(-0.761435\pi\)
0.421697 + 0.906737i \(0.361435\pi\)
\(734\) 3389.40 + 10431.5i 0.170443 + 0.524570i
\(735\) 0 0
\(736\) 9627.22 29629.5i 0.482152 1.48391i
\(737\) −2739.96 8432.74i −0.136944 0.421471i
\(738\) 0 0
\(739\) −3949.52 + 12155.4i −0.196597 + 0.605064i 0.803357 + 0.595498i \(0.203045\pi\)
−0.999954 + 0.00956656i \(0.996955\pi\)
\(740\) −10752.7 10173.5i −0.534159 0.505387i
\(741\) 0 0
\(742\) −28824.5 + 20942.3i −1.42612 + 1.03614i
\(743\) 8636.53 0.426438 0.213219 0.977004i \(-0.431605\pi\)
0.213219 + 0.977004i \(0.431605\pi\)
\(744\) 0 0
\(745\) −13885.4 + 29223.4i −0.682848 + 1.43713i
\(746\) 32163.4 + 23368.1i 1.57853 + 1.14687i
\(747\) 0 0
\(748\) −4209.02 + 12954.0i −0.205745 + 0.633217i
\(749\) −26228.1 −1.27951
\(750\) 0 0
\(751\) −13862.3 −0.673558 −0.336779 0.941584i \(-0.609338\pi\)
−0.336779 + 0.941584i \(0.609338\pi\)
\(752\) −5883.54 + 18107.7i −0.285307 + 0.878084i
\(753\) 0 0
\(754\) −50144.1 36431.8i −2.42194 1.75964i
\(755\) −12089.1 + 25442.9i −0.582738 + 1.22644i
\(756\) 0 0
\(757\) −34297.7 −1.64673 −0.823364 0.567514i \(-0.807905\pi\)
−0.823364 + 0.567514i \(0.807905\pi\)
\(758\) −7629.15 + 5542.90i −0.365571 + 0.265603i
\(759\) 0 0
\(760\) −280.315 265.216i −0.0133791 0.0126584i
\(761\) 9289.71 28590.8i 0.442512 1.36191i −0.442678 0.896681i \(-0.645971\pi\)
0.885189 0.465231i \(-0.154029\pi\)
\(762\) 0 0
\(763\) 6389.94 + 19666.2i 0.303186 + 0.933112i
\(764\) 4347.54 13380.3i 0.205875 0.633618i
\(765\) 0 0
\(766\) −16991.2 52293.7i −0.801460 2.46664i
\(767\) −13311.0 + 9670.98i −0.626638 + 0.455279i
\(768\) 0 0
\(769\) 6704.47 4871.08i 0.314395 0.228421i −0.419385 0.907808i \(-0.637754\pi\)
0.733780 + 0.679387i \(0.237754\pi\)
\(770\) 45268.1 24666.0i 2.11864 1.15442i
\(771\) 0 0
\(772\) −21258.4 15445.1i −0.991070 0.720055i
\(773\) −1109.96 + 3416.11i −0.0516463 + 0.158951i −0.973553 0.228461i \(-0.926631\pi\)
0.921907 + 0.387412i \(0.126631\pi\)
\(774\) 0 0
\(775\) 39959.7 + 10579.6i 1.85212 + 0.490360i
\(776\) −2202.72 −0.101898
\(777\) 0 0
\(778\) −43303.6 31461.9i −1.99551 1.44982i
\(779\) 1219.52 + 886.036i 0.0560898 + 0.0407516i
\(780\) 0 0
\(781\) −10563.9 + 7675.14i −0.484004 + 0.351649i
\(782\) −21871.9 −1.00018
\(783\) 0 0
\(784\) −9968.73 30680.6i −0.454115 1.39762i
\(785\) −10511.9 + 22123.4i −0.477942 + 1.00588i
\(786\) 0 0
\(787\) 692.596 + 2131.59i 0.0313702 + 0.0965477i 0.965516 0.260345i \(-0.0838362\pi\)
−0.934145 + 0.356893i \(0.883836\pi\)
\(788\) 4361.93