Properties

Label 225.4.h.d.181.3
Level $225$
Weight $4$
Character 225.181
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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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 181.3
Character \(\chi\) \(=\) 225.181
Dual form 225.4.h.d.46.3

$q$-expansion

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

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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 −0.856886 0.515506i \(-0.827604\pi\)
0.390229 0.920718i \(-0.372396\pi\)
\(3\) 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 −0.989983 0.141190i \(-0.954907\pi\)
0.717924 0.696122i \(-0.245093\pi\)
\(12\) 0 0
\(13\) 23.5572 72.5016i 0.502584 1.54679i −0.302211 0.953241i \(-0.597725\pi\)
0.804795 0.593553i \(-0.202275\pi\)
\(14\) −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 0.322677 0.946509i \(-0.395417\pi\)
−0.800471 + 0.599371i \(0.795417\pi\)
\(18\) 0 0
\(19\) −2.91326 2.11660i −0.0351761 0.0255570i 0.570058 0.821604i \(-0.306921\pi\)
−0.605234 + 0.796047i \(0.706921\pi\)
\(20\) 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 0.960751 + 0.277411i \(0.0894764\pi\)
−0.614206 + 0.789146i \(0.710524\pi\)
\(24\) 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 0.0270367 0.999634i \(-0.491393\pi\)
0.959064 + 0.283191i \(0.0913929\pi\)
\(30\) 0 0
\(31\) −267.535 194.376i −1.55002 1.12616i −0.943634 0.330990i \(-0.892617\pi\)
−0.606390 0.795168i \(-0.707383\pi\)
\(32\) 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 −0.999737 0.0229247i \(-0.992702\pi\)
0.822279 + 0.569084i \(0.192702\pi\)
\(38\) −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 0.327708 + 0.944779i \(0.393724\pi\)
−0.820448 + 0.571721i \(0.806276\pi\)
\(42\) 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 −0.990479 0.137666i \(-0.956040\pi\)
−0.175147 + 0.984542i \(0.556040\pi\)
\(48\) 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 −0.296362 0.955076i \(-0.595774\pi\)
0.816750 + 0.576992i \(0.195774\pi\)
\(54\) 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 −0.850115 0.526597i \(-0.823468\pi\)
0.997283 + 0.0736590i \(0.0234676\pi\)
\(60\) 0 0
\(61\) 57.9582 + 178.377i 0.121652 + 0.374407i 0.993276 0.115768i \(-0.0369329\pi\)
−0.871624 + 0.490175i \(0.836933\pi\)
\(62\) −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 0.365250 0.930909i \(-0.380983\pi\)
−0.772479 + 0.635041i \(0.780983\pi\)
\(68\) 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 −0.277941 0.960598i \(-0.589652\pi\)
0.827695 + 0.561179i \(0.189652\pi\)
\(72\) 0 0
\(73\) −161.479 496.983i −0.258901 0.796814i −0.993036 0.117811i \(-0.962412\pi\)
0.734136 0.679003i \(-0.237588\pi\)
\(74\) 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 −0.357109 0.934063i \(-0.616238\pi\)
0.777993 + 0.628273i \(0.216238\pi\)
\(80\) 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 0.161153 0.986929i \(-0.448479\pi\)
−0.888827 + 0.458244i \(0.848479\pi\)
\(84\) 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 0.881569 0.472055i \(-0.156488\pi\)
−0.990671 + 0.136273i \(0.956488\pi\)
\(90\) 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 −0.680823 0.732448i \(-0.738378\pi\)
0.486214 + 0.873840i \(0.338378\pi\)
\(98\) −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 −0.550298 0.834968i \(-0.685486\pi\)
0.624051 + 0.781384i \(0.285486\pi\)
\(104\) 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 −0.832114 0.554605i \(-0.812869\pi\)
0.999183 + 0.0404192i \(0.0128693\pi\)
\(110\) 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 −0.990507 0.137459i \(-0.956106\pi\)
0.882134 + 0.470999i \(0.156106\pi\)
\(114\) 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 0.995132 + 0.0985497i \(0.0314204\pi\)
−0.747153 + 0.664652i \(0.768580\pi\)
\(128\) −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 0.504474 0.863427i \(-0.331686\pi\)
−0.665277 + 0.746597i \(0.731686\pi\)
\(132\) 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 −0.486771 0.873529i \(-0.661826\pi\)
0.907254 0.420583i \(-0.138174\pi\)
\(138\) 0 0
\(139\) −656.504 2020.51i −0.400604 1.23293i −0.924511 0.381156i \(-0.875526\pi\)
0.523907 0.851775i \(-0.324474\pi\)
\(140\) 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 −0.980728 0.195381i \(-0.937406\pi\)
0.908267 + 0.418391i \(0.137406\pi\)
\(164\) −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 0.996597 + 0.0824226i \(0.0262657\pi\)
0.386354 + 0.922351i \(0.373734\pi\)
\(168\) 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 0.902020 + 0.431693i \(0.142084\pi\)
−0.476007 + 0.879442i \(0.657916\pi\)
\(174\) 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 −0.414885 0.909874i \(-0.636178\pi\)
0.737135 + 0.675745i \(0.236178\pi\)
\(180\) 0 0
\(181\) 125.543 + 91.2125i 0.0515556 + 0.0374573i 0.613265 0.789878i \(-0.289856\pi\)
−0.561709 + 0.827335i \(0.689856\pi\)
\(182\) −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 −0.837924 0.545787i \(-0.816231\pi\)
0.998700 + 0.0509689i \(0.0162309\pi\)
\(192\) 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 −0.770829 0.637042i \(-0.780158\pi\)
0.367664 + 0.929959i \(0.380158\pi\)
\(198\) 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 0.999931 + 0.0117812i \(0.00375017\pi\)
−0.802036 + 0.597276i \(0.796250\pi\)
\(212\) −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 0.973919 + 0.226895i \(0.0728576\pi\)
−0.654551 + 0.756018i \(0.727142\pi\)
\(224\) 8464.67 2.52486
\(225\) 0 0
\(226\) 1799.36 0.529610
\(227\) 518.565 + 1595.98i 0.151623 + 0.466647i 0.997803 0.0662496i \(-0.0211034\pi\)
−0.846180 + 0.532897i \(0.821103\pi\)
\(228\) 0 0
\(229\) 436.125 316.863i 0.125851 0.0914363i −0.523079 0.852284i \(-0.675217\pi\)
0.648930 + 0.760848i \(0.275217\pi\)
\(230\) −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 0.180070 0.983654i \(-0.442368\pi\)
−0.879866 + 0.475223i \(0.842368\pi\)
\(234\) 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 0.931165 0.364597i \(-0.118793\pi\)
−0.967633 + 0.252360i \(0.918793\pi\)
\(240\) 0 0
\(241\) 1239.98 3816.27i 0.331429 1.02003i −0.637026 0.770842i \(-0.719836\pi\)
0.968455 0.249190i \(-0.0801644\pi\)
\(242\) −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 −0.631848 0.775092i \(-0.717703\pi\)
0.966764 0.255672i \(-0.0822966\pi\)
\(264\) 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 −0.248321 0.968678i \(-0.579879\pi\)
−0.998003 + 0.0631703i \(0.979879\pi\)
\(270\) 0 0
\(271\) −4062.81 + 2951.81i −0.910695 + 0.661659i −0.941190 0.337876i \(-0.890291\pi\)
0.0304957 + 0.999535i \(0.490291\pi\)
\(272\) 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 −0.901335 0.433123i \(-0.857411\pi\)
0.474612 0.880195i \(-0.342589\pi\)
\(278\) −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 0.761663 0.647973i \(-0.224383\pi\)
−0.380892 + 0.924619i \(0.624383\pi\)
\(282\) 0 0
\(283\) 5646.82 + 4102.66i 1.18611 + 0.861759i 0.992848 0.119389i \(-0.0380935\pi\)
0.193261 + 0.981147i \(0.438093\pi\)
\(284\) −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 −0.939807 0.341705i \(-0.888996\pi\)
0.559471 0.828850i \(-0.311004\pi\)
\(312\) 0 0
\(313\) 1021.84 3144.90i 0.184530 0.567924i −0.815410 0.578884i \(-0.803489\pi\)
0.999940 + 0.0109593i \(0.00348854\pi\)
\(314\) −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 0.799523 0.600635i \(-0.205086\pi\)
−0.324172 + 0.945998i \(0.605086\pi\)
\(318\) 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 0.963475 0.267798i \(-0.0862958\pi\)
0.0430396 + 0.999073i \(0.486296\pi\)
\(332\) 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 0.518146 + 0.855292i \(0.326622\pi\)
−0.921917 + 0.387387i \(0.873378\pi\)
\(338\) −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 0.271619 0.962405i \(-0.412441\pi\)
0.999236 + 0.0390745i \(0.0124410\pi\)
\(348\) 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 −0.592628 0.805476i \(-0.701910\pi\)
0.582921 + 0.812529i \(0.301910\pi\)
\(354\) 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 0.702485 + 0.711699i \(0.252074\pi\)
−0.986648 + 0.162866i \(0.947926\pi\)
\(360\) 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 0.725644 0.688070i \(-0.241542\pi\)
−0.430157 + 0.902754i \(0.641542\pi\)
\(368\) −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 0.925589 + 0.378530i \(0.123570\pi\)
−0.526323 + 0.850285i \(0.676430\pi\)
\(374\) 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 −0.460130 0.887851i \(-0.652197\pi\)
0.702209 + 0.711971i \(0.252197\pi\)
\(380\) −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 −0.995926 0.0901754i \(-0.971257\pi\)
−0.393520 0.919316i \(-0.628743\pi\)
\(384\) 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 −0.801216 0.598376i \(-0.795813\pi\)
0.296481 0.955039i \(-0.404187\pi\)
\(390\) 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 −0.999991 0.00425835i \(-0.998645\pi\)
−0.304964 + 0.952364i \(0.598645\pi\)
\(398\) 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 −0.481848 0.876255i \(-0.660034\pi\)
0.904873 0.425682i \(-0.139966\pi\)
\(410\) −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 −0.107688 0.994185i \(-0.534345\pi\)
−0.978803 + 0.204803i \(0.934345\pi\)
\(420\) 0 0
\(421\) 1968.58 1430.26i 0.227892 0.165574i −0.467980 0.883739i \(-0.655018\pi\)
0.695872 + 0.718166i \(0.255018\pi\)
\(422\) 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 0.909364 0.416001i \(-0.136569\pi\)
−0.114632 + 0.993408i \(0.536569\pi\)
\(432\) 0 0
\(433\) −6196.51 4502.03i −0.687726 0.499662i 0.188186 0.982133i \(-0.439739\pi\)
−0.875912 + 0.482471i \(0.839739\pi\)
\(434\) −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 0.999525 0.0308313i \(-0.00981546\pi\)
−0.826755 + 0.562563i \(0.809815\pi\)
\(440\) −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 0.983673 0.179964i \(-0.0575982\pi\)
−0.901589 + 0.432595i \(0.857598\pi\)
\(462\) 0 0
\(463\) 587.970 1809.58i 0.0590178 0.181638i −0.917201 0.398424i \(-0.869557\pi\)
0.976219 + 0.216786i \(0.0695573\pi\)
\(464\) 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 0.933837 0.357698i \(-0.116438\pi\)
−0.0516199 + 0.998667i \(0.516438\pi\)
\(468\) 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 0.0813995 0.996682i \(-0.474061\pi\)
0.973054 + 0.230576i \(0.0740610\pi\)
\(480\) 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 −0.996599 0.0824064i \(-0.973739\pi\)
0.854703 + 0.519118i \(0.173739\pi\)
\(488\) −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 −0.944681 0.327990i \(-0.893629\pi\)
0.957051 + 0.289920i \(0.0936287\pi\)
\(492\) 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 −0.734551 0.678553i \(-0.762607\pi\)
0.418354 + 0.908284i \(0.362607\pi\)
\(504\) 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 −0.998020 0.0629024i \(-0.979964\pi\)
0.844388 + 0.535732i \(0.179964\pi\)
\(510\) 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 −0.654635 0.755945i \(-0.727178\pi\)
0.516653 + 0.856195i \(0.327178\pi\)
\(522\) 0 0
\(523\) −1067.09 3284.16i −0.0892171 0.274582i 0.896486 0.443071i \(-0.146111\pi\)
−0.985703 + 0.168489i \(0.946111\pi\)
\(524\) 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 −0.200988 0.979594i \(-0.564415\pi\)
0.738394 0.674370i \(-0.235585\pi\)
\(542\) 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 −0.822173 0.569237i \(-0.807239\pi\)
0.287311 + 0.957837i \(0.407239\pi\)
\(548\) 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 0.503147 + 0.864201i \(0.332175\pi\)
−0.915019 + 0.403410i \(0.867825\pi\)
\(564\) 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 0.724819 0.688939i \(-0.241923\pi\)
−0.431239 + 0.902238i \(0.641923\pi\)
\(570\) 0 0
\(571\) −10205.8 + 7414.97i −0.747987 + 0.543444i −0.895202 0.445660i \(-0.852969\pi\)
0.147215 + 0.989104i \(0.452969\pi\)
\(572\) 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 0.985991 + 0.166801i \(0.0533439\pi\)
−0.699640 + 0.714496i \(0.746656\pi\)
\(578\) −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 −0.849375 0.527790i \(-0.823021\pi\)
0.997386 + 0.0722593i \(0.0230209\pi\)
\(588\) 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 −0.998511 0.0545546i \(-0.982626\pi\)
0.839879 + 0.542774i \(0.182626\pi\)
\(614\) 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 0.877593 + 0.479406i \(0.159148\pi\)
0.727134 + 0.686496i \(0.240852\pi\)
\(618\) 0 0
\(619\) 16760.8 + 12177.5i 1.08833 + 0.790716i 0.979116 0.203302i \(-0.0651674\pi\)
0.109212 + 0.994019i \(0.465167\pi\)
\(620\) −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 0.991102 0.133101i \(-0.0424935\pi\)
0.179681 + 0.983725i \(0.442493\pi\)
\(632\) 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 0.636238 + 0.771493i \(0.280490\pi\)
−0.968199 + 0.250180i \(0.919510\pi\)
\(642\) 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 −0.623227 0.782041i \(-0.714179\pi\)
0.551177 + 0.834388i \(0.314179\pi\)
\(648\) 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 −0.413244 0.910620i \(-0.635605\pi\)
0.738352 + 0.674416i \(0.235605\pi\)
\(654\) 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 −0.939821 0.341667i \(-0.889008\pi\)
0.961158 + 0.275998i \(0.0890084\pi\)
\(660\) 0 0
\(661\) 811.577 + 2497.78i 0.0477559 + 0.146978i 0.972091 0.234604i \(-0.0753794\pi\)
−0.924335 + 0.381582i \(0.875379\pi\)
\(662\) 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 −0.958252 0.285926i \(-0.907699\pi\)
0.607179 0.794565i \(-0.292301\pi\)
\(674\) 34527.0 1.97319
\(675\) 0 0
\(676\) 37026.4 2.10664
\(677\) 1227.06 + 3776.51i 0.0696600 + 0.214392i 0.979826 0.199852i \(-0.0640462\pi\)
−0.910166 + 0.414244i \(0.864046\pi\)
\(678\) 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 0.820092 0.572231i \(-0.193922\pi\)
−0.290802 + 0.956783i \(0.593922\pi\)
\(684\) 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 0.134181 + 0.990957i \(0.457160\pi\)
−0.691024 + 0.722831i \(0.742840\pi\)
\(692\) −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 −0.422338 0.906438i \(-0.638791\pi\)
0.874470 0.485080i \(-0.161209\pi\)
\(710\) −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 0.696797 0.717268i \(-0.254608\pi\)
−0.466840 + 0.884342i \(0.654608\pi\)
\(720\) 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 −0.946020 0.324109i \(-0.894936\pi\)
0.574840 0.818266i \(-0.305064\pi\)
\(728\) 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 0.421697 0.906737i \(-0.361435\pi\)
−0.732046 + 0.681255i \(0.761435\pi\)
\(734\) 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 −0.999954 0.00956656i \(-0.996955\pi\)
0.803357 0.595498i \(-0.203045\pi\)
\(740\) −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 0.885189 + 0.465231i \(0.154029\pi\)
−0.442678 + 0.896681i \(0.645971\pi\)
\(762\) 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 0.733780 0.679387i \(-0.237754\pi\)
−0.419385 + 0.907808i \(0.637754\pi\)
\(770\) 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 0.921907 0.387412i \(-0.126631\pi\)
−0.973553 + 0.228461i \(0.926631\pi\)
\(774\) 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 &