Properties

Label 225.4.e.f.151.1
Level $225$
Weight $4$
Character 225.151
Analytic conductor $13.275$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 151.1
Character \(\chi\) \(=\) 225.151
Dual form 225.4.e.f.76.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.42567 + 4.20138i) q^{2} +(4.79753 + 1.99591i) q^{3} +(-7.76772 - 13.4541i) q^{4} +(-20.0228 + 15.3148i) q^{6} +(8.11924 - 14.0629i) q^{7} +36.5569 q^{8} +(19.0327 + 19.1509i) q^{9} +O(q^{10})\) \(q+(-2.42567 + 4.20138i) q^{2} +(4.79753 + 1.99591i) q^{3} +(-7.76772 - 13.4541i) q^{4} +(-20.0228 + 15.3148i) q^{6} +(8.11924 - 14.0629i) q^{7} +36.5569 q^{8} +(19.0327 + 19.1509i) q^{9} +(-29.7592 + 51.5445i) q^{11} +(-10.4127 - 80.0501i) q^{12} +(13.5395 + 23.4511i) q^{13} +(39.3891 + 68.2240i) q^{14} +(-26.5331 + 45.9567i) q^{16} -78.9077 q^{17} +(-126.627 + 33.5097i) q^{18} -142.290 q^{19} +(67.0207 - 51.2621i) q^{21} +(-144.372 - 250.060i) q^{22} +(42.8140 + 74.1561i) q^{23} +(175.383 + 72.9643i) q^{24} -131.369 q^{26} +(53.0864 + 129.865i) q^{27} -252.272 q^{28} +(-113.004 + 195.729i) q^{29} +(75.3561 + 130.521i) q^{31} +(17.5066 + 30.3223i) q^{32} +(-245.649 + 187.890i) q^{33} +(191.404 - 331.521i) q^{34} +(109.817 - 404.826i) q^{36} -234.171 q^{37} +(345.149 - 597.816i) q^{38} +(18.1499 + 139.531i) q^{39} +(-36.9290 - 63.9629i) q^{41} +(52.8017 + 405.924i) q^{42} +(133.539 - 231.296i) q^{43} +924.645 q^{44} -415.410 q^{46} +(133.013 - 230.385i) q^{47} +(-219.019 + 167.521i) q^{48} +(39.6560 + 68.6862i) q^{49} +(-378.563 - 157.493i) q^{51} +(210.342 - 364.323i) q^{52} +603.281 q^{53} +(-674.380 - 91.9724i) q^{54} +(296.814 - 514.097i) q^{56} +(-682.643 - 283.999i) q^{57} +(-548.222 - 949.548i) q^{58} +(-254.360 - 440.565i) q^{59} +(-39.1519 + 67.8131i) q^{61} -731.155 q^{62} +(423.849 - 112.164i) q^{63} -594.391 q^{64} +(-193.533 - 1487.82i) q^{66} +(244.101 + 422.796i) q^{67} +(612.933 + 1061.63i) q^{68} +(57.3928 + 441.219i) q^{69} -73.2487 q^{71} +(695.776 + 700.098i) q^{72} -115.831 q^{73} +(568.021 - 983.842i) q^{74} +(1105.27 + 1914.39i) q^{76} +(483.244 + 837.004i) q^{77} +(-630.249 - 262.202i) q^{78} +(-391.371 + 677.875i) q^{79} +(-4.51465 + 728.986i) q^{81} +358.310 q^{82} +(-135.732 + 235.095i) q^{83} +(-1210.28 - 503.512i) q^{84} +(647.840 + 1122.09i) q^{86} +(-932.801 + 713.471i) q^{87} +(-1087.91 + 1884.31i) q^{88} +211.511 q^{89} +439.722 q^{91} +(665.135 - 1152.05i) q^{92} +(101.016 + 776.581i) q^{93} +(645.289 + 1117.67i) q^{94} +(23.4678 + 180.414i) q^{96} +(833.050 - 1442.89i) q^{97} -384.769 q^{98} +(-1553.52 + 411.113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9} - 29 q^{11} + 77 q^{12} - 24 q^{13} + 69 q^{14} - 192 q^{16} - 158 q^{17} - 125 q^{18} - 150 q^{19} - 60 q^{21} + 18 q^{22} + 318 q^{23} + 342 q^{24} - 308 q^{26} + 394 q^{27} + 192 q^{28} - 106 q^{29} - 60 q^{31} + 914 q^{32} + 80 q^{33} + 108 q^{34} + 1303 q^{36} - 168 q^{37} + 640 q^{38} - 410 q^{39} + 353 q^{41} - 1521 q^{42} + 426 q^{43} + 1142 q^{44} + 540 q^{46} + 1210 q^{47} - 2680 q^{48} - 666 q^{49} - 1369 q^{51} + 75 q^{52} - 896 q^{53} - 2128 q^{54} + 570 q^{56} - 1544 q^{57} - 594 q^{58} - 482 q^{59} - 402 q^{61} - 5088 q^{62} + 1038 q^{63} + 1950 q^{64} + 2041 q^{66} + 201 q^{67} + 3437 q^{68} + 2856 q^{69} - 1888 q^{71} + 5493 q^{72} - 906 q^{73} - 10 q^{74} + 462 q^{76} + 2652 q^{77} + 4589 q^{78} - 258 q^{79} + 3071 q^{81} + 1746 q^{82} + 3012 q^{83} - 2703 q^{84} - 1952 q^{86} - 2708 q^{87} + 216 q^{88} - 1476 q^{89} - 1236 q^{91} + 5232 q^{92} - 3024 q^{93} - 63 q^{94} - 10424 q^{96} + 318 q^{97} - 15022 q^{98} - 1697 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42567 + 4.20138i −0.857603 + 1.48541i 0.0166066 + 0.999862i \(0.494714\pi\)
−0.874209 + 0.485549i \(0.838620\pi\)
\(3\) 4.79753 + 1.99591i 0.923286 + 0.384113i
\(4\) −7.76772 13.4541i −0.970965 1.68176i
\(5\) 0 0
\(6\) −20.0228 + 15.3148i −1.36238 + 1.04204i
\(7\) 8.11924 14.0629i 0.438398 0.759327i −0.559169 0.829054i \(-0.688880\pi\)
0.997566 + 0.0697271i \(0.0222129\pi\)
\(8\) 36.5569 1.61560
\(9\) 19.0327 + 19.1509i 0.704914 + 0.709293i
\(10\) 0 0
\(11\) −29.7592 + 51.5445i −0.815704 + 1.41284i 0.0931172 + 0.995655i \(0.470317\pi\)
−0.908821 + 0.417186i \(0.863016\pi\)
\(12\) −10.4127 80.0501i −0.250491 1.92571i
\(13\) 13.5395 + 23.4511i 0.288860 + 0.500321i 0.973538 0.228525i \(-0.0733903\pi\)
−0.684678 + 0.728846i \(0.740057\pi\)
\(14\) 39.3891 + 68.2240i 0.751942 + 1.30240i
\(15\) 0 0
\(16\) −26.5331 + 45.9567i −0.414580 + 0.718074i
\(17\) −78.9077 −1.12576 −0.562880 0.826538i \(-0.690307\pi\)
−0.562880 + 0.826538i \(0.690307\pi\)
\(18\) −126.627 + 33.5097i −1.65813 + 0.438796i
\(19\) −142.290 −1.71809 −0.859044 0.511902i \(-0.828941\pi\)
−0.859044 + 0.511902i \(0.828941\pi\)
\(20\) 0 0
\(21\) 67.0207 51.2621i 0.696434 0.532681i
\(22\) −144.372 250.060i −1.39910 2.42331i
\(23\) 42.8140 + 74.1561i 0.388145 + 0.672288i 0.992200 0.124655i \(-0.0397825\pi\)
−0.604055 + 0.796943i \(0.706449\pi\)
\(24\) 175.383 + 72.9643i 1.49166 + 0.620574i
\(25\) 0 0
\(26\) −131.369 −0.990910
\(27\) 53.0864 + 129.865i 0.378388 + 0.925647i
\(28\) −252.272 −1.70267
\(29\) −113.004 + 195.729i −0.723600 + 1.25331i 0.235948 + 0.971766i \(0.424180\pi\)
−0.959548 + 0.281546i \(0.909153\pi\)
\(30\) 0 0
\(31\) 75.3561 + 130.521i 0.436592 + 0.756200i 0.997424 0.0717300i \(-0.0228520\pi\)
−0.560832 + 0.827930i \(0.689519\pi\)
\(32\) 17.5066 + 30.3223i 0.0967112 + 0.167509i
\(33\) −245.649 + 187.890i −1.29582 + 0.991133i
\(34\) 191.404 331.521i 0.965455 1.67222i
\(35\) 0 0
\(36\) 109.817 404.826i 0.508414 1.87419i
\(37\) −234.171 −1.04047 −0.520237 0.854022i \(-0.674156\pi\)
−0.520237 + 0.854022i \(0.674156\pi\)
\(38\) 345.149 597.816i 1.47344 2.55207i
\(39\) 18.1499 + 139.531i 0.0745208 + 0.572894i
\(40\) 0 0
\(41\) −36.9290 63.9629i −0.140667 0.243642i 0.787081 0.616850i \(-0.211591\pi\)
−0.927748 + 0.373207i \(0.878258\pi\)
\(42\) 52.8017 + 405.924i 0.193988 + 1.49132i
\(43\) 133.539 231.296i 0.473592 0.820285i −0.525951 0.850515i \(-0.676290\pi\)
0.999543 + 0.0302295i \(0.00962383\pi\)
\(44\) 924.645 3.16808
\(45\) 0 0
\(46\) −415.410 −1.33150
\(47\) 133.013 230.385i 0.412806 0.715001i −0.582389 0.812910i \(-0.697882\pi\)
0.995195 + 0.0979088i \(0.0312154\pi\)
\(48\) −219.019 + 167.521i −0.658598 + 0.503742i
\(49\) 39.6560 + 68.6862i 0.115615 + 0.200251i
\(50\) 0 0
\(51\) −378.563 157.493i −1.03940 0.432420i
\(52\) 210.342 364.323i 0.560946 0.971588i
\(53\) 603.281 1.56353 0.781765 0.623574i \(-0.214320\pi\)
0.781765 + 0.623574i \(0.214320\pi\)
\(54\) −674.380 91.9724i −1.69947 0.231775i
\(55\) 0 0
\(56\) 296.814 514.097i 0.708276 1.22677i
\(57\) −682.643 283.999i −1.58629 0.659940i
\(58\) −548.222 949.548i −1.24112 2.14969i
\(59\) −254.360 440.565i −0.561270 0.972148i −0.997386 0.0722573i \(-0.976980\pi\)
0.436116 0.899890i \(-0.356354\pi\)
\(60\) 0 0
\(61\) −39.1519 + 67.8131i −0.0821786 + 0.142337i −0.904185 0.427140i \(-0.859521\pi\)
0.822007 + 0.569478i \(0.192854\pi\)
\(62\) −731.155 −1.49769
\(63\) 423.849 112.164i 0.847618 0.224308i
\(64\) −594.391 −1.16092
\(65\) 0 0
\(66\) −193.533 1487.82i −0.360943 2.77482i
\(67\) 244.101 + 422.796i 0.445101 + 0.770937i 0.998059 0.0622718i \(-0.0198346\pi\)
−0.552959 + 0.833209i \(0.686501\pi\)
\(68\) 612.933 + 1061.63i 1.09307 + 1.89326i
\(69\) 57.3928 + 441.219i 0.100135 + 0.769805i
\(70\) 0 0
\(71\) −73.2487 −0.122437 −0.0612184 0.998124i \(-0.519499\pi\)
−0.0612184 + 0.998124i \(0.519499\pi\)
\(72\) 695.776 + 700.098i 1.13886 + 1.14594i
\(73\) −115.831 −0.185712 −0.0928558 0.995680i \(-0.529600\pi\)
−0.0928558 + 0.995680i \(0.529600\pi\)
\(74\) 568.021 983.842i 0.892313 1.54553i
\(75\) 0 0
\(76\) 1105.27 + 1914.39i 1.66820 + 2.88941i
\(77\) 483.244 + 837.004i 0.715205 + 1.23877i
\(78\) −630.249 262.202i −0.914893 0.380622i
\(79\) −391.371 + 677.875i −0.557376 + 0.965404i 0.440338 + 0.897832i \(0.354859\pi\)
−0.997714 + 0.0675718i \(0.978475\pi\)
\(80\) 0 0
\(81\) −4.51465 + 728.986i −0.00619293 + 0.999981i
\(82\) 358.310 0.482545
\(83\) −135.732 + 235.095i −0.179501 + 0.310904i −0.941710 0.336427i \(-0.890782\pi\)
0.762209 + 0.647331i \(0.224115\pi\)
\(84\) −1210.28 503.512i −1.57206 0.654020i
\(85\) 0 0
\(86\) 647.840 + 1122.09i 0.812307 + 1.40696i
\(87\) −932.801 + 713.471i −1.14950 + 0.879220i
\(88\) −1087.91 + 1884.31i −1.31785 + 2.28259i
\(89\) 211.511 0.251911 0.125955 0.992036i \(-0.459800\pi\)
0.125955 + 0.992036i \(0.459800\pi\)
\(90\) 0 0
\(91\) 439.722 0.506543
\(92\) 665.135 1152.05i 0.753751 1.30553i
\(93\) 101.016 + 776.581i 0.112633 + 0.865889i
\(94\) 645.289 + 1117.67i 0.708047 + 1.22637i
\(95\) 0 0
\(96\) 23.4678 + 180.414i 0.0249498 + 0.191806i
\(97\) 833.050 1442.89i 0.871994 1.51034i 0.0120642 0.999927i \(-0.496160\pi\)
0.859930 0.510411i \(-0.170507\pi\)
\(98\) −384.769 −0.396607
\(99\) −1553.52 + 411.113i −1.57712 + 0.417358i
\(100\) 0 0
\(101\) 228.292 395.413i 0.224910 0.389555i −0.731383 0.681967i \(-0.761125\pi\)
0.956292 + 0.292412i \(0.0944580\pi\)
\(102\) 1579.95 1208.46i 1.53371 1.17309i
\(103\) 82.9660 + 143.701i 0.0793678 + 0.137469i 0.902977 0.429688i \(-0.141377\pi\)
−0.823610 + 0.567157i \(0.808043\pi\)
\(104\) 494.963 + 857.300i 0.466683 + 0.808319i
\(105\) 0 0
\(106\) −1463.36 + 2534.61i −1.34089 + 2.32248i
\(107\) −452.071 −0.408443 −0.204221 0.978925i \(-0.565466\pi\)
−0.204221 + 0.978925i \(0.565466\pi\)
\(108\) 1334.85 1722.98i 1.18931 1.53513i
\(109\) −463.243 −0.407070 −0.203535 0.979068i \(-0.565243\pi\)
−0.203535 + 0.979068i \(0.565243\pi\)
\(110\) 0 0
\(111\) −1123.44 467.385i −0.960655 0.399660i
\(112\) 430.857 + 746.267i 0.363502 + 0.629604i
\(113\) 475.041 + 822.795i 0.395470 + 0.684974i 0.993161 0.116753i \(-0.0372485\pi\)
−0.597691 + 0.801726i \(0.703915\pi\)
\(114\) 2849.05 2179.15i 2.34069 1.79032i
\(115\) 0 0
\(116\) 3511.14 2.81036
\(117\) −191.417 + 705.632i −0.151252 + 0.557570i
\(118\) 2467.97 1.92539
\(119\) −640.670 + 1109.67i −0.493531 + 0.854820i
\(120\) 0 0
\(121\) −1105.72 1915.17i −0.830746 1.43889i
\(122\) −189.939 328.984i −0.140953 0.244138i
\(123\) −49.5038 380.571i −0.0362895 0.278983i
\(124\) 1170.69 2027.69i 0.847831 1.46849i
\(125\) 0 0
\(126\) −556.871 + 2052.82i −0.393730 + 1.45143i
\(127\) −210.383 −0.146996 −0.0734979 0.997295i \(-0.523416\pi\)
−0.0734979 + 0.997295i \(0.523416\pi\)
\(128\) 1301.74 2254.68i 0.898896 1.55693i
\(129\) 1102.30 843.118i 0.752343 0.575445i
\(130\) 0 0
\(131\) 462.388 + 800.879i 0.308389 + 0.534146i 0.978010 0.208557i \(-0.0668767\pi\)
−0.669621 + 0.742703i \(0.733543\pi\)
\(132\) 4436.02 + 1845.51i 2.92504 + 1.21690i
\(133\) −1155.29 + 2001.02i −0.753205 + 1.30459i
\(134\) −2368.44 −1.52688
\(135\) 0 0
\(136\) −2884.62 −1.81878
\(137\) −968.837 + 1678.07i −0.604185 + 1.04648i 0.387995 + 0.921661i \(0.373168\pi\)
−0.992180 + 0.124817i \(0.960166\pi\)
\(138\) −1992.95 829.122i −1.22935 0.511446i
\(139\) 985.256 + 1706.51i 0.601211 + 1.04133i 0.992638 + 0.121119i \(0.0386481\pi\)
−0.391427 + 0.920209i \(0.628019\pi\)
\(140\) 0 0
\(141\) 1097.96 839.797i 0.655780 0.501586i
\(142\) 177.677 307.745i 0.105002 0.181869i
\(143\) −1611.70 −0.942498
\(144\) −1385.11 + 366.546i −0.801568 + 0.212121i
\(145\) 0 0
\(146\) 280.966 486.648i 0.159267 0.275858i
\(147\) 53.1594 + 408.674i 0.0298266 + 0.229298i
\(148\) 1818.98 + 3150.56i 1.01026 + 1.74983i
\(149\) −798.166 1382.46i −0.438848 0.760106i 0.558753 0.829334i \(-0.311280\pi\)
−0.997601 + 0.0692276i \(0.977947\pi\)
\(150\) 0 0
\(151\) 1836.48 3180.88i 0.989741 1.71428i 0.371141 0.928576i \(-0.378967\pi\)
0.618600 0.785706i \(-0.287700\pi\)
\(152\) −5201.70 −2.77575
\(153\) −1501.82 1511.15i −0.793564 0.798494i
\(154\) −4688.76 −2.45345
\(155\) 0 0
\(156\) 1736.28 1328.03i 0.891114 0.681586i
\(157\) 525.779 + 910.676i 0.267272 + 0.462929i 0.968156 0.250346i \(-0.0805444\pi\)
−0.700884 + 0.713275i \(0.747211\pi\)
\(158\) −1898.67 3288.60i −0.956014 1.65587i
\(159\) 2894.26 + 1204.10i 1.44358 + 0.600573i
\(160\) 0 0
\(161\) 1390.47 0.680648
\(162\) −3051.79 1787.24i −1.48007 0.866785i
\(163\) 1998.77 0.960463 0.480232 0.877142i \(-0.340553\pi\)
0.480232 + 0.877142i \(0.340553\pi\)
\(164\) −573.708 + 993.691i −0.273165 + 0.473136i
\(165\) 0 0
\(166\) −658.483 1140.53i −0.307881 0.533265i
\(167\) 1240.51 + 2148.63i 0.574813 + 0.995606i 0.996062 + 0.0886604i \(0.0282586\pi\)
−0.421249 + 0.906945i \(0.638408\pi\)
\(168\) 2450.07 1873.98i 1.12516 0.860601i
\(169\) 731.863 1267.62i 0.333119 0.576980i
\(170\) 0 0
\(171\) −2708.17 2724.99i −1.21110 1.21863i
\(172\) −4149.16 −1.83936
\(173\) −1313.04 + 2274.25i −0.577042 + 0.999466i 0.418774 + 0.908090i \(0.362460\pi\)
−0.995816 + 0.0913761i \(0.970873\pi\)
\(174\) −734.899 5649.69i −0.320187 2.46151i
\(175\) 0 0
\(176\) −1579.21 2735.27i −0.676349 1.17147i
\(177\) −340.974 2621.31i −0.144798 1.11316i
\(178\) −513.054 + 888.636i −0.216039 + 0.374191i
\(179\) −3231.72 −1.34944 −0.674720 0.738074i \(-0.735736\pi\)
−0.674720 + 0.738074i \(0.735736\pi\)
\(180\) 0 0
\(181\) 337.854 0.138743 0.0693714 0.997591i \(-0.477901\pi\)
0.0693714 + 0.997591i \(0.477901\pi\)
\(182\) −1066.62 + 1847.44i −0.434412 + 0.752424i
\(183\) −323.182 + 247.192i −0.130548 + 0.0998523i
\(184\) 1565.15 + 2710.92i 0.627088 + 1.08615i
\(185\) 0 0
\(186\) −3507.74 1459.32i −1.38280 0.575283i
\(187\) 2348.23 4067.26i 0.918288 1.59052i
\(188\) −4132.82 −1.60328
\(189\) 2257.30 + 307.852i 0.868753 + 0.118481i
\(190\) 0 0
\(191\) −505.253 + 875.124i −0.191407 + 0.331527i −0.945717 0.324992i \(-0.894639\pi\)
0.754309 + 0.656519i \(0.227972\pi\)
\(192\) −2851.61 1186.35i −1.07186 0.445925i
\(193\) −746.079 1292.25i −0.278259 0.481958i 0.692693 0.721232i \(-0.256424\pi\)
−0.970952 + 0.239274i \(0.923091\pi\)
\(194\) 4041.41 + 6999.92i 1.49565 + 2.59054i
\(195\) 0 0
\(196\) 616.073 1067.07i 0.224516 0.388874i
\(197\) 3313.50 1.19836 0.599181 0.800613i \(-0.295493\pi\)
0.599181 + 0.800613i \(0.295493\pi\)
\(198\) 2041.08 7524.15i 0.732593 2.70060i
\(199\) 2165.17 0.771279 0.385640 0.922649i \(-0.373981\pi\)
0.385640 + 0.922649i \(0.373981\pi\)
\(200\) 0 0
\(201\) 327.222 + 2515.58i 0.114828 + 0.882764i
\(202\) 1107.52 + 1918.28i 0.385766 + 0.668167i
\(203\) 1835.02 + 3178.35i 0.634449 + 1.09890i
\(204\) 821.645 + 6316.57i 0.281993 + 2.16788i
\(205\) 0 0
\(206\) −804.991 −0.272264
\(207\) −605.291 + 2231.32i −0.203240 + 0.749214i
\(208\) −1436.98 −0.479023
\(209\) 4234.45 7334.29i 1.40145 2.42738i
\(210\) 0 0
\(211\) 1279.85 + 2216.77i 0.417576 + 0.723263i 0.995695 0.0926897i \(-0.0295464\pi\)
−0.578119 + 0.815952i \(0.696213\pi\)
\(212\) −4686.12 8116.59i −1.51813 2.62948i
\(213\) −351.413 146.198i −0.113044 0.0470296i
\(214\) 1096.57 1899.32i 0.350282 0.606706i
\(215\) 0 0
\(216\) 1940.67 + 4747.45i 0.611325 + 1.49548i
\(217\) 2447.34 0.765604
\(218\) 1123.67 1946.26i 0.349104 0.604666i
\(219\) −555.701 231.188i −0.171465 0.0713343i
\(220\) 0 0
\(221\) −1068.37 1850.47i −0.325188 0.563242i
\(222\) 4688.76 3586.30i 1.41752 1.08422i
\(223\) 707.218 1224.94i 0.212371 0.367838i −0.740085 0.672514i \(-0.765215\pi\)
0.952456 + 0.304675i \(0.0985480\pi\)
\(224\) 568.561 0.169592
\(225\) 0 0
\(226\) −4609.16 −1.35662
\(227\) 813.532 1409.08i 0.237868 0.411999i −0.722234 0.691648i \(-0.756885\pi\)
0.960102 + 0.279649i \(0.0902181\pi\)
\(228\) 1481.63 + 11390.4i 0.430366 + 3.30853i
\(229\) 3309.78 + 5732.71i 0.955093 + 1.65427i 0.734154 + 0.678983i \(0.237579\pi\)
0.220939 + 0.975288i \(0.429088\pi\)
\(230\) 0 0
\(231\) 647.796 + 4980.07i 0.184510 + 1.41846i
\(232\) −4131.09 + 7155.26i −1.16905 + 2.02485i
\(233\) 1911.28 0.537390 0.268695 0.963225i \(-0.413408\pi\)
0.268695 + 0.963225i \(0.413408\pi\)
\(234\) −2500.31 2515.84i −0.698506 0.702845i
\(235\) 0 0
\(236\) −3951.60 + 6844.37i −1.08995 + 1.88784i
\(237\) −3230.60 + 2470.99i −0.885442 + 0.677248i
\(238\) −3108.11 5383.40i −0.846507 1.46619i
\(239\) −1443.35 2499.95i −0.390637 0.676603i 0.601897 0.798574i \(-0.294412\pi\)
−0.992534 + 0.121971i \(0.961079\pi\)
\(240\) 0 0
\(241\) 644.326 1116.01i 0.172219 0.298291i −0.766977 0.641675i \(-0.778240\pi\)
0.939195 + 0.343384i \(0.111573\pi\)
\(242\) 10728.5 2.84980
\(243\) −1476.65 + 3488.32i −0.389824 + 0.920889i
\(244\) 1216.48 0.319170
\(245\) 0 0
\(246\) 1719.00 + 715.154i 0.445527 + 0.185352i
\(247\) −1926.54 3336.87i −0.496287 0.859595i
\(248\) 2754.79 + 4771.43i 0.705359 + 1.22172i
\(249\) −1120.41 + 856.968i −0.285153 + 0.218105i
\(250\) 0 0
\(251\) 4356.21 1.09546 0.547732 0.836654i \(-0.315491\pi\)
0.547732 + 0.836654i \(0.315491\pi\)
\(252\) −4801.41 4831.23i −1.20024 1.20769i
\(253\) −5096.45 −1.26645
\(254\) 510.319 883.898i 0.126064 0.218349i
\(255\) 0 0
\(256\) 3937.62 + 6820.15i 0.961332 + 1.66508i
\(257\) −1618.26 2802.91i −0.392780 0.680314i 0.600035 0.799973i \(-0.295153\pi\)
−0.992815 + 0.119659i \(0.961820\pi\)
\(258\) 868.439 + 6676.31i 0.209561 + 1.61104i
\(259\) −1901.29 + 3293.13i −0.456141 + 0.790060i
\(260\) 0 0
\(261\) −5899.17 + 1561.12i −1.39904 + 0.370232i
\(262\) −4486.40 −1.05790
\(263\) −690.768 + 1196.44i −0.161956 + 0.280517i −0.935570 0.353141i \(-0.885114\pi\)
0.773614 + 0.633657i \(0.218447\pi\)
\(264\) −8980.17 + 6868.67i −2.09353 + 1.60128i
\(265\) 0 0
\(266\) −5604.70 9707.62i −1.29190 2.23764i
\(267\) 1014.73 + 422.156i 0.232586 + 0.0967623i
\(268\) 3792.22 6568.32i 0.864354 1.49710i
\(269\) 721.063 0.163435 0.0817175 0.996656i \(-0.473959\pi\)
0.0817175 + 0.996656i \(0.473959\pi\)
\(270\) 0 0
\(271\) 3816.82 0.855554 0.427777 0.903884i \(-0.359297\pi\)
0.427777 + 0.903884i \(0.359297\pi\)
\(272\) 2093.67 3626.34i 0.466718 0.808379i
\(273\) 2109.58 + 877.646i 0.467684 + 0.194570i
\(274\) −4700.15 8140.90i −1.03630 1.79493i
\(275\) 0 0
\(276\) 5490.39 4199.44i 1.19740 0.915856i
\(277\) 964.393 1670.38i 0.209187 0.362322i −0.742272 0.670099i \(-0.766252\pi\)
0.951459 + 0.307777i \(0.0995850\pi\)
\(278\) −9559.61 −2.06240
\(279\) −1065.36 + 3927.29i −0.228607 + 0.842727i
\(280\) 0 0
\(281\) −2471.93 + 4281.50i −0.524778 + 0.908943i 0.474805 + 0.880091i \(0.342518\pi\)
−0.999584 + 0.0288518i \(0.990815\pi\)
\(282\) 865.019 + 6650.01i 0.182664 + 1.40426i
\(283\) −3171.79 5493.70i −0.666231 1.15395i −0.978950 0.204100i \(-0.934573\pi\)
0.312719 0.949846i \(-0.398760\pi\)
\(284\) 568.975 + 985.494i 0.118882 + 0.205909i
\(285\) 0 0
\(286\) 3909.45 6771.37i 0.808289 1.40000i
\(287\) −1199.34 −0.246672
\(288\) −247.503 + 912.382i −0.0506397 + 0.186676i
\(289\) 1313.43 0.267337
\(290\) 0 0
\(291\) 6876.46 5259.60i 1.38524 1.05953i
\(292\) 899.739 + 1558.39i 0.180319 + 0.312322i
\(293\) 753.429 + 1304.98i 0.150225 + 0.260197i 0.931310 0.364228i \(-0.118667\pi\)
−0.781085 + 0.624424i \(0.785334\pi\)
\(294\) −1845.94 767.964i −0.366182 0.152342i
\(295\) 0 0
\(296\) −8560.58 −1.68099
\(297\) −8273.62 1128.36i −1.61644 0.220452i
\(298\) 7744.34 1.50543
\(299\) −1159.36 + 2008.07i −0.224240 + 0.388394i
\(300\) 0 0
\(301\) −2168.46 3755.89i −0.415243 0.719222i
\(302\) 8909.40 + 15431.5i 1.69761 + 2.94035i
\(303\) 1884.45 1441.36i 0.357289 0.273280i
\(304\) 3775.41 6539.20i 0.712285 1.23371i
\(305\) 0 0
\(306\) 9991.86 2644.18i 1.86666 0.493979i
\(307\) 8239.13 1.53170 0.765850 0.643019i \(-0.222319\pi\)
0.765850 + 0.643019i \(0.222319\pi\)
\(308\) 7507.41 13003.2i 1.38888 2.40561i
\(309\) 111.217 + 855.005i 0.0204755 + 0.157409i
\(310\) 0 0
\(311\) 402.948 + 697.927i 0.0734698 + 0.127253i 0.900420 0.435022i \(-0.143259\pi\)
−0.826950 + 0.562275i \(0.809926\pi\)
\(312\) 663.504 + 5100.83i 0.120396 + 0.925569i
\(313\) −2030.70 + 3517.28i −0.366716 + 0.635171i −0.989050 0.147581i \(-0.952851\pi\)
0.622334 + 0.782752i \(0.286185\pi\)
\(314\) −5101.46 −0.916853
\(315\) 0 0
\(316\) 12160.2 2.16477
\(317\) −503.804 + 872.615i −0.0892633 + 0.154609i −0.907200 0.420700i \(-0.861785\pi\)
0.817937 + 0.575308i \(0.195118\pi\)
\(318\) −12079.4 + 9239.16i −2.13012 + 1.62926i
\(319\) −6725.85 11649.5i −1.18049 2.04466i
\(320\) 0 0
\(321\) −2168.83 902.295i −0.377110 0.156888i
\(322\) −3372.81 + 5841.89i −0.583726 + 1.01104i
\(323\) 11227.8 1.93416
\(324\) 9842.91 5601.82i 1.68774 0.960531i
\(325\) 0 0
\(326\) −4848.34 + 8397.57i −0.823696 + 1.42668i
\(327\) −2222.42 924.591i −0.375842 0.156361i
\(328\) −1350.01 2338.29i −0.227262 0.393629i
\(329\) −2159.92 3741.10i −0.361946 0.626910i
\(330\) 0 0
\(331\) −4647.21 + 8049.20i −0.771702 + 1.33663i 0.164927 + 0.986306i \(0.447261\pi\)
−0.936629 + 0.350322i \(0.886072\pi\)
\(332\) 4217.32 0.697155
\(333\) −4456.91 4484.59i −0.733444 0.738001i
\(334\) −12036.3 −1.97185
\(335\) 0 0
\(336\) 577.570 + 4440.19i 0.0937769 + 0.720930i
\(337\) 1697.85 + 2940.77i 0.274445 + 0.475352i 0.969995 0.243125i \(-0.0781726\pi\)
−0.695550 + 0.718478i \(0.744839\pi\)
\(338\) 3550.51 + 6149.67i 0.571368 + 0.989639i
\(339\) 636.799 + 4895.53i 0.102024 + 0.784332i
\(340\) 0 0
\(341\) −8970.16 −1.42452
\(342\) 18017.8 4768.11i 2.84881 0.753889i
\(343\) 6857.70 1.07954
\(344\) 4881.76 8455.46i 0.765136 1.32525i
\(345\) 0 0
\(346\) −6369.98 11033.1i −0.989746 1.71429i
\(347\) 4086.81 + 7078.56i 0.632252 + 1.09509i 0.987090 + 0.160165i \(0.0512026\pi\)
−0.354838 + 0.934928i \(0.615464\pi\)
\(348\) 16844.8 + 7007.93i 2.59476 + 1.07950i
\(349\) 2787.95 4828.88i 0.427609 0.740641i −0.569051 0.822302i \(-0.692689\pi\)
0.996660 + 0.0816612i \(0.0260225\pi\)
\(350\) 0 0
\(351\) −2326.71 + 3003.24i −0.353819 + 0.456698i
\(352\) −2083.93 −0.315551
\(353\) 1611.89 2791.87i 0.243037 0.420953i −0.718541 0.695485i \(-0.755190\pi\)
0.961578 + 0.274532i \(0.0885230\pi\)
\(354\) 11840.2 + 4925.86i 1.77768 + 0.739566i
\(355\) 0 0
\(356\) −1642.95 2845.68i −0.244597 0.423654i
\(357\) −5288.45 + 4044.98i −0.784018 + 0.599672i
\(358\) 7839.07 13577.7i 1.15728 2.00447i
\(359\) −2593.48 −0.381278 −0.190639 0.981660i \(-0.561056\pi\)
−0.190639 + 0.981660i \(0.561056\pi\)
\(360\) 0 0
\(361\) 13387.6 1.95182
\(362\) −819.520 + 1419.45i −0.118986 + 0.206090i
\(363\) −1482.24 11395.0i −0.214318 1.64761i
\(364\) −3415.64 5916.06i −0.491835 0.851883i
\(365\) 0 0
\(366\) −254.616 1957.41i −0.0363634 0.279551i
\(367\) 884.083 1531.28i 0.125746 0.217798i −0.796278 0.604930i \(-0.793201\pi\)
0.922024 + 0.387132i \(0.126534\pi\)
\(368\) −4543.96 −0.643669
\(369\) 522.090 1924.61i 0.0736556 0.271521i
\(370\) 0 0
\(371\) 4898.18 8483.90i 0.685447 1.18723i
\(372\) 9663.52 7391.34i 1.34686 1.03017i
\(373\) −1514.74 2623.61i −0.210269 0.364197i 0.741529 0.670920i \(-0.234101\pi\)
−0.951799 + 0.306723i \(0.900767\pi\)
\(374\) 11392.1 + 19731.6i 1.57505 + 2.72807i
\(375\) 0 0
\(376\) 4862.53 8422.15i 0.666931 1.15516i
\(377\) −6120.10 −0.836077
\(378\) −6768.86 + 8737.02i −0.921038 + 1.18885i
\(379\) 9435.84 1.27886 0.639428 0.768851i \(-0.279171\pi\)
0.639428 + 0.768851i \(0.279171\pi\)
\(380\) 0 0
\(381\) −1009.32 419.906i −0.135719 0.0564630i
\(382\) −2451.15 4245.52i −0.328303 0.568638i
\(383\) −4849.33 8399.29i −0.646969 1.12058i −0.983843 0.179034i \(-0.942703\pi\)
0.336874 0.941550i \(-0.390631\pi\)
\(384\) 10745.3 8218.75i 1.42798 1.09222i
\(385\) 0 0
\(386\) 7238.96 0.954542
\(387\) 6971.12 1844.79i 0.915664 0.242315i
\(388\) −25883.6 −3.38670
\(389\) −6379.36 + 11049.4i −0.831481 + 1.44017i 0.0653822 + 0.997860i \(0.479173\pi\)
−0.896863 + 0.442308i \(0.854160\pi\)
\(390\) 0 0
\(391\) −3378.36 5851.49i −0.436959 0.756835i
\(392\) 1449.70 + 2510.95i 0.186788 + 0.323526i
\(393\) 619.838 + 4765.13i 0.0795590 + 0.611626i
\(394\) −8037.46 + 13921.3i −1.02772 + 1.78006i
\(395\) 0 0
\(396\) 17598.5 + 17707.8i 2.23322 + 2.24710i
\(397\) −14088.8 −1.78111 −0.890553 0.454879i \(-0.849682\pi\)
−0.890553 + 0.454879i \(0.849682\pi\)
\(398\) −5251.97 + 9096.68i −0.661451 + 1.14567i
\(399\) −9536.40 + 7294.11i −1.19653 + 0.915193i
\(400\) 0 0
\(401\) 3582.63 + 6205.30i 0.446155 + 0.772763i 0.998132 0.0610961i \(-0.0194596\pi\)
−0.551977 + 0.833860i \(0.686126\pi\)
\(402\) −11362.6 4727.19i −1.40974 0.586494i
\(403\) −2040.57 + 3534.37i −0.252228 + 0.436872i
\(404\) −7093.22 −0.873517
\(405\) 0 0
\(406\) −17804.6 −2.17642
\(407\) 6968.76 12070.2i 0.848719 1.47002i
\(408\) −13839.1 5757.45i −1.67926 0.698618i
\(409\) −1019.82 1766.39i −0.123293 0.213550i 0.797771 0.602960i \(-0.206012\pi\)
−0.921065 + 0.389410i \(0.872679\pi\)
\(410\) 0 0
\(411\) −7997.31 + 6116.91i −0.959802 + 0.734123i
\(412\) 1288.91 2232.46i 0.154127 0.266955i
\(413\) −8260.85 −0.984237
\(414\) −7906.37 7955.49i −0.938591 0.944422i
\(415\) 0 0
\(416\) −474.061 + 821.099i −0.0558721 + 0.0967732i
\(417\) 1320.75 + 10153.5i 0.155102 + 1.19238i
\(418\) 20542.7 + 35581.1i 2.40378 + 4.16346i
\(419\) −6596.83 11426.0i −0.769156 1.33222i −0.938021 0.346578i \(-0.887344\pi\)
0.168865 0.985639i \(-0.445990\pi\)
\(420\) 0 0
\(421\) −5621.08 + 9735.99i −0.650724 + 1.12709i 0.332224 + 0.943201i \(0.392201\pi\)
−0.982948 + 0.183886i \(0.941132\pi\)
\(422\) −12418.0 −1.43246
\(423\) 6943.66 1837.52i 0.798138 0.211214i
\(424\) 22054.1 2.52604
\(425\) 0 0
\(426\) 1466.64 1121.79i 0.166805 0.127584i
\(427\) 635.768 + 1101.18i 0.0720538 + 0.124801i
\(428\) 3511.56 + 6082.21i 0.396584 + 0.686903i
\(429\) −7732.19 3216.81i −0.870195 0.362026i
\(430\) 0 0
\(431\) −5546.88 −0.619916 −0.309958 0.950750i \(-0.600315\pi\)
−0.309958 + 0.950750i \(0.600315\pi\)
\(432\) −7376.70 1006.04i −0.821555 0.112044i
\(433\) 4484.74 0.497744 0.248872 0.968536i \(-0.419940\pi\)
0.248872 + 0.968536i \(0.419940\pi\)
\(434\) −5936.42 + 10282.2i −0.656584 + 1.13724i
\(435\) 0 0
\(436\) 3598.34 + 6232.50i 0.395250 + 0.684594i
\(437\) −6092.03 10551.7i −0.666868 1.15505i
\(438\) 2319.25 1773.93i 0.253009 0.193519i
\(439\) −2634.86 + 4563.71i −0.286458 + 0.496159i −0.972962 0.230967i \(-0.925811\pi\)
0.686504 + 0.727126i \(0.259144\pi\)
\(440\) 0 0
\(441\) −560.643 + 2066.73i −0.0605381 + 0.223165i
\(442\) 10366.1 1.11553
\(443\) 3700.66 6409.74i 0.396894 0.687440i −0.596447 0.802652i \(-0.703422\pi\)
0.993341 + 0.115212i \(0.0367549\pi\)
\(444\) 2438.36 + 18745.4i 0.260630 + 2.00365i
\(445\) 0 0
\(446\) 3430.95 + 5942.58i 0.364261 + 0.630918i
\(447\) −1069.95 8225.49i −0.113215 0.870363i
\(448\) −4826.00 + 8358.87i −0.508944 + 0.881517i
\(449\) −938.733 −0.0986672 −0.0493336 0.998782i \(-0.515710\pi\)
−0.0493336 + 0.998782i \(0.515710\pi\)
\(450\) 0 0
\(451\) 4395.91 0.458970
\(452\) 7379.97 12782.5i 0.767974 1.33017i
\(453\) 15159.4 11594.9i 1.57229 1.20260i
\(454\) 3946.71 + 6835.91i 0.407992 + 0.706663i
\(455\) 0 0
\(456\) −24955.3 10382.1i −2.56281 1.06620i
\(457\) −2153.58 + 3730.11i −0.220438 + 0.381810i −0.954941 0.296795i \(-0.904082\pi\)
0.734503 + 0.678605i \(0.237415\pi\)
\(458\) −32113.7 −3.27636
\(459\) −4188.93 10247.3i −0.425975 1.04206i
\(460\) 0 0
\(461\) −2621.39 + 4540.38i −0.264838 + 0.458713i −0.967521 0.252790i \(-0.918652\pi\)
0.702683 + 0.711503i \(0.251985\pi\)
\(462\) −22494.5 9358.35i −2.26523 0.942402i
\(463\) −4274.77 7404.13i −0.429083 0.743194i 0.567709 0.823230i \(-0.307830\pi\)
−0.996792 + 0.0800354i \(0.974497\pi\)
\(464\) −5996.72 10386.6i −0.599980 1.03920i
\(465\) 0 0
\(466\) −4636.12 + 8029.99i −0.460867 + 0.798245i
\(467\) −12706.2 −1.25904 −0.629522 0.776983i \(-0.716749\pi\)
−0.629522 + 0.776983i \(0.716749\pi\)
\(468\) 10980.5 2905.80i 1.08456 0.287010i
\(469\) 7927.67 0.780524
\(470\) 0 0
\(471\) 704.814 + 5418.41i 0.0689514 + 0.530079i
\(472\) −9298.63 16105.7i −0.906788 1.57060i
\(473\) 7948.01 + 13766.4i 0.772622 + 1.33822i
\(474\) −2545.20 19566.7i −0.246635 1.89606i
\(475\) 0 0
\(476\) 19906.2 1.91680
\(477\) 11482.1 + 11553.4i 1.10215 + 1.10900i
\(478\) 14004.3 1.34005
\(479\) 9178.08 15896.9i 0.875485 1.51638i 0.0192388 0.999815i \(-0.493876\pi\)
0.856246 0.516569i \(-0.172791\pi\)
\(480\) 0 0
\(481\) −3170.57 5491.58i −0.300552 0.520571i
\(482\) 3125.84 + 5414.11i 0.295390 + 0.511631i
\(483\) 6670.82 + 2775.25i 0.628433 + 0.261446i
\(484\) −17177.9 + 29753.0i −1.61325 + 2.79423i
\(485\) 0 0
\(486\) −11073.9 14665.5i −1.03359 1.36881i
\(487\) 15195.3 1.41389 0.706945 0.707268i \(-0.250073\pi\)
0.706945 + 0.707268i \(0.250073\pi\)
\(488\) −1431.27 + 2479.04i −0.132768 + 0.229961i
\(489\) 9589.15 + 3989.36i 0.886782 + 0.368927i
\(490\) 0 0
\(491\) −3971.95 6879.62i −0.365075 0.632328i 0.623713 0.781653i \(-0.285623\pi\)
−0.988788 + 0.149325i \(0.952290\pi\)
\(492\) −4735.70 + 3622.20i −0.433947 + 0.331913i
\(493\) 8916.92 15444.6i 0.814600 1.41093i
\(494\) 18692.6 1.70247
\(495\) 0 0
\(496\) −7997.73 −0.724009
\(497\) −594.723 + 1030.09i −0.0536760 + 0.0929696i
\(498\) −882.705 6785.98i −0.0794277 0.610617i
\(499\) 9578.93 + 16591.2i 0.859343 + 1.48843i 0.872557 + 0.488512i \(0.162460\pi\)
−0.0132143 + 0.999913i \(0.504206\pi\)
\(500\) 0 0
\(501\) 1662.93 + 12784.1i 0.148291 + 1.14002i
\(502\) −10566.7 + 18302.1i −0.939474 + 1.62722i
\(503\) −11203.5 −0.993119 −0.496559 0.868003i \(-0.665403\pi\)
−0.496559 + 0.868003i \(0.665403\pi\)
\(504\) 15494.6 4100.38i 1.36941 0.362392i
\(505\) 0 0
\(506\) 12362.3 21412.1i 1.08611 1.88119i
\(507\) 6041.20 4620.74i 0.529190 0.404762i
\(508\) 1634.19 + 2830.51i 0.142728 + 0.247212i
\(509\) −3544.02 6138.42i −0.308617 0.534540i 0.669443 0.742863i \(-0.266533\pi\)
−0.978060 + 0.208323i \(0.933199\pi\)
\(510\) 0 0
\(511\) −940.456 + 1628.92i −0.0814155 + 0.141016i
\(512\) −17377.5 −1.49997
\(513\) −7553.68 18478.5i −0.650104 1.59034i
\(514\) 15701.5 1.34740
\(515\) 0 0
\(516\) −19905.7 8281.36i −1.69826 0.706524i
\(517\) 7916.71 + 13712.1i 0.673455 + 1.16646i
\(518\) −9223.80 15976.1i −0.782376 1.35511i
\(519\) −10838.5 + 8290.07i −0.916683 + 0.701144i
\(520\) 0 0
\(521\) −9739.55 −0.818997 −0.409499 0.912311i \(-0.634296\pi\)
−0.409499 + 0.912311i \(0.634296\pi\)
\(522\) 7750.58 28571.4i 0.649873 2.39566i
\(523\) −14153.1 −1.18331 −0.591656 0.806190i \(-0.701526\pi\)
−0.591656 + 0.806190i \(0.701526\pi\)
\(524\) 7183.40 12442.0i 0.598871 1.03727i
\(525\) 0 0
\(526\) −3351.14 5804.35i −0.277789 0.481144i
\(527\) −5946.18 10299.1i −0.491498 0.851300i
\(528\) −2116.95 16274.5i −0.174486 1.34140i
\(529\) 2417.42 4187.09i 0.198686 0.344135i
\(530\) 0 0
\(531\) 3596.07 13256.4i 0.293891 1.08338i
\(532\) 35895.9 2.92534
\(533\) 1000.00 1732.05i 0.0812661 0.140757i
\(534\) −4235.03 + 3239.25i −0.343198 + 0.262502i
\(535\) 0 0
\(536\) 8923.59 + 15456.1i 0.719106 + 1.24553i
\(537\) −15504.3 6450.22i −1.24592 0.518338i
\(538\) −1749.06 + 3029.46i −0.140162 + 0.242768i
\(539\) −4720.52 −0.377231
\(540\) 0 0
\(541\) −12175.5 −0.967592 −0.483796 0.875181i \(-0.660742\pi\)
−0.483796 + 0.875181i \(0.660742\pi\)
\(542\) −9258.33 + 16035.9i −0.733725 + 1.27085i
\(543\) 1620.86 + 674.326i 0.128099 + 0.0532930i
\(544\) −1381.41 2392.66i −0.108874 0.188575i
\(545\) 0 0
\(546\) −8804.47 + 6734.27i −0.690103 + 0.527839i
\(547\) −609.617 + 1055.89i −0.0476515 + 0.0825348i −0.888867 0.458165i \(-0.848507\pi\)
0.841216 + 0.540699i \(0.181840\pi\)
\(548\) 30102.6 2.34657
\(549\) −2043.85 + 540.870i −0.158888 + 0.0420470i
\(550\) 0 0
\(551\) 16079.4 27850.4i 1.24321 2.15330i
\(552\) 2098.10 + 16129.6i 0.161778 + 1.24370i
\(553\) 6355.27 + 11007.7i 0.488705 + 0.846461i
\(554\) 4678.59 + 8103.56i 0.358798 + 0.621457i
\(555\) 0 0
\(556\) 15306.4 26511.4i 1.16751 2.02218i
\(557\) −12672.4 −0.963995 −0.481998 0.876172i \(-0.660089\pi\)
−0.481998 + 0.876172i \(0.660089\pi\)
\(558\) −13915.8 14002.3i −1.05574 1.06230i
\(559\) 7232.19 0.547208
\(560\) 0 0
\(561\) 19383.6 14825.9i 1.45878 1.11578i
\(562\) −11992.1 20771.0i −0.900102 1.55902i
\(563\) 4116.80 + 7130.50i 0.308175 + 0.533774i 0.977963 0.208778i \(-0.0669486\pi\)
−0.669788 + 0.742552i \(0.733615\pi\)
\(564\) −19827.3 8248.74i −1.48029 0.615842i
\(565\) 0 0
\(566\) 30774.8 2.28545
\(567\) 10215.0 + 5982.30i 0.756597 + 0.443092i
\(568\) −2677.75 −0.197809
\(569\) −1974.55 + 3420.02i −0.145479 + 0.251977i −0.929552 0.368692i \(-0.879806\pi\)
0.784073 + 0.620669i \(0.213139\pi\)
\(570\) 0 0
\(571\) 1955.13 + 3386.38i 0.143292 + 0.248189i 0.928734 0.370746i \(-0.120898\pi\)
−0.785442 + 0.618935i \(0.787565\pi\)
\(572\) 12519.2 + 21684.0i 0.915133 + 1.58506i
\(573\) −4170.64 + 3190.00i −0.304068 + 0.232572i
\(574\) 2909.20 5038.88i 0.211547 0.366409i
\(575\) 0 0
\(576\) −11312.8 11383.1i −0.818348 0.823432i
\(577\) −18788.9 −1.35562 −0.677810 0.735237i \(-0.737071\pi\)
−0.677810 + 0.735237i \(0.737071\pi\)
\(578\) −3185.94 + 5518.21i −0.229269 + 0.397106i
\(579\) −1000.13 7688.71i −0.0717858 0.551868i
\(580\) 0 0
\(581\) 2204.09 + 3817.59i 0.157385 + 0.272599i
\(582\) 5417.56 + 41648.6i 0.385851 + 2.96631i
\(583\) −17953.2 + 31095.8i −1.27538 + 2.20902i
\(584\) −4234.41 −0.300036
\(585\) 0 0
\(586\) −7310.27 −0.515332
\(587\) 2200.11 3810.70i 0.154699 0.267946i −0.778251 0.627954i \(-0.783893\pi\)
0.932949 + 0.360008i \(0.117226\pi\)
\(588\) 5085.41 3889.68i 0.356664 0.272802i
\(589\) −10722.4 18571.8i −0.750103 1.29922i
\(590\) 0 0
\(591\) 15896.7 + 6613.46i 1.10643 + 0.460307i
\(592\) 6213.30 10761.7i 0.431360 0.747137i
\(593\) −13311.2 −0.921798 −0.460899 0.887453i \(-0.652473\pi\)
−0.460899 + 0.887453i \(0.652473\pi\)
\(594\) 24809.7 32023.6i 1.71373 2.21203i
\(595\) 0 0
\(596\) −12399.9 + 21477.2i −0.852211 + 1.47607i
\(597\) 10387.5 + 4321.48i 0.712111 + 0.296259i
\(598\) −5624.45 9741.84i −0.384617 0.666176i
\(599\) 7966.01 + 13797.5i 0.543377 + 0.941156i 0.998707 + 0.0508333i \(0.0161877\pi\)
−0.455331 + 0.890322i \(0.650479\pi\)
\(600\) 0 0
\(601\) −11754.9 + 20360.2i −0.797828 + 1.38188i 0.123201 + 0.992382i \(0.460684\pi\)
−0.921028 + 0.389496i \(0.872649\pi\)
\(602\) 21039.9 1.42445
\(603\) −3451.03 + 12721.7i −0.233062 + 0.859151i
\(604\) −57061.2 −3.84402
\(605\) 0 0
\(606\) 1484.65 + 11413.5i 0.0995208 + 0.765087i
\(607\) 4876.00 + 8445.49i 0.326048 + 0.564731i 0.981724 0.190311i \(-0.0609497\pi\)
−0.655676 + 0.755042i \(0.727616\pi\)
\(608\) −2491.02 4314.57i −0.166158 0.287795i
\(609\) 2459.87 + 18910.8i 0.163676 + 1.25830i
\(610\) 0 0
\(611\) 7203.71 0.476973
\(612\) −8665.44 + 31943.9i −0.572353 + 2.10989i
\(613\) −24076.3 −1.58635 −0.793176 0.608992i \(-0.791574\pi\)
−0.793176 + 0.608992i \(0.791574\pi\)
\(614\) −19985.4 + 34615.7i −1.31359 + 2.27520i
\(615\) 0 0
\(616\) 17665.9 + 30598.3i 1.15549 + 2.00136i
\(617\) −3324.25 5757.76i −0.216903 0.375687i 0.736957 0.675940i \(-0.236262\pi\)
−0.953860 + 0.300253i \(0.902929\pi\)
\(618\) −3861.97 1606.69i −0.251378 0.104580i
\(619\) 4100.83 7102.85i 0.266278 0.461208i −0.701619 0.712552i \(-0.747539\pi\)
0.967898 + 0.251344i \(0.0808726\pi\)
\(620\) 0 0
\(621\) −7357.41 + 9496.71i −0.475431 + 0.613671i
\(622\) −3909.67 −0.252031
\(623\) 1717.30 2974.46i 0.110437 0.191283i
\(624\) −6893.97 2868.09i −0.442275 0.183999i
\(625\) 0 0
\(626\) −9851.62 17063.5i −0.628994 1.08945i
\(627\) 34953.5 26734.9i 2.22633 1.70285i
\(628\) 8168.21 14147.7i 0.519024 0.898975i
\(629\) 18477.9 1.17132
\(630\) 0 0
\(631\) 28159.1 1.77654 0.888269 0.459323i \(-0.151908\pi\)
0.888269 + 0.459323i \(0.151908\pi\)
\(632\) −14307.3 + 24781.0i −0.900498 + 1.55971i
\(633\) 1715.66 + 13189.5i 0.107727 + 0.828175i
\(634\) −2444.12 4233.35i −0.153105 0.265186i
\(635\) 0 0
\(636\) −6281.81 48292.7i −0.391651 3.01090i
\(637\) −1073.85 + 1859.95i −0.0667932 + 0.115689i
\(638\) 65258.6 4.04955
\(639\) −1394.12 1402.78i −0.0863075 0.0868436i
\(640\) 0 0
\(641\) −5777.99 + 10007.8i −0.356032 + 0.616666i −0.987294 0.158904i \(-0.949204\pi\)
0.631262 + 0.775570i \(0.282537\pi\)
\(642\) 9051.74 6923.40i 0.556454 0.425615i
\(643\) 6901.87 + 11954.4i 0.423302 + 0.733180i 0.996260 0.0864042i \(-0.0275376\pi\)
−0.572958 + 0.819585i \(0.694204\pi\)
\(644\) −10800.8 18707.5i −0.660885 1.14469i
\(645\) 0 0
\(646\) −27234.9 + 47172.3i −1.65874 + 2.87302i
\(647\) 24257.1 1.47395 0.736974 0.675921i \(-0.236254\pi\)
0.736974 + 0.675921i \(0.236254\pi\)
\(648\) −165.041 + 26649.5i −0.0100053 + 1.61557i
\(649\) 30278.3 1.83132
\(650\) 0 0
\(651\) 11741.2 + 4884.67i 0.706871 + 0.294079i
\(652\) −15525.9 26891.6i −0.932576 1.61527i
\(653\) −3249.10 5627.61i −0.194712 0.337252i 0.752094 0.659056i \(-0.229044\pi\)
−0.946806 + 0.321804i \(0.895711\pi\)
\(654\) 9275.41 7094.49i 0.554583 0.424184i
\(655\) 0 0
\(656\) 3919.37 0.233271
\(657\) −2204.57 2218.26i −0.130911 0.131724i
\(658\) 20957.0 1.24162
\(659\) −1901.37 + 3293.26i −0.112393 + 0.194670i −0.916734 0.399497i \(-0.869185\pi\)
0.804342 + 0.594167i \(0.202518\pi\)
\(660\) 0 0
\(661\) −4837.05 8378.01i −0.284628 0.492991i 0.687891 0.725814i \(-0.258537\pi\)
−0.972519 + 0.232824i \(0.925204\pi\)
\(662\) −22545.1 39049.3i −1.32363 2.29259i
\(663\) −1432.17 11010.1i −0.0838926 0.644942i
\(664\) −4961.95 + 8594.35i −0.290002 + 0.502298i
\(665\) 0 0
\(666\) 29652.4 7847.02i 1.72524 0.456555i
\(667\) −19352.7 −1.12345
\(668\) 19271.9 33379.9i 1.11625 1.93340i
\(669\) 5837.77 4465.14i 0.337371 0.258045i
\(670\) 0 0
\(671\) −2330.26 4036.13i −0.134067 0.232210i
\(672\) 2727.69 + 1134.80i 0.156582 + 0.0651425i
\(673\) −1016.47 + 1760.57i −0.0582198 + 0.100840i −0.893666 0.448732i \(-0.851876\pi\)
0.835447 + 0.549572i \(0.185209\pi\)
\(674\) −16473.7 −0.941458
\(675\) 0 0
\(676\) −22739.6 −1.29379
\(677\) 4499.50 7793.36i 0.255435 0.442427i −0.709578 0.704627i \(-0.751114\pi\)
0.965014 + 0.262199i \(0.0844478\pi\)
\(678\) −22112.6 9199.48i −1.25255 0.521097i
\(679\) −13527.5 23430.3i −0.764561 1.32426i
\(680\) 0 0
\(681\) 6715.34 5136.37i 0.377875 0.289025i
\(682\) 21758.6 37687.0i 1.22167 2.11600i
\(683\) 23826.0 1.33481 0.667407 0.744693i \(-0.267404\pi\)
0.667407 + 0.744693i \(0.267404\pi\)
\(684\) −15626.0 + 57602.9i −0.873500 + 3.22003i
\(685\) 0 0
\(686\) −16634.5 + 28811.8i −0.925814 + 1.60356i
\(687\) 4436.81 + 34108.9i 0.246397 + 1.89423i
\(688\) 7086.39 + 12274.0i 0.392684 + 0.680148i
\(689\) 8168.13 + 14147.6i 0.451642 + 0.782266i
\(690\) 0 0
\(691\) 2939.49 5091.35i 0.161828 0.280295i −0.773696 0.633557i \(-0.781594\pi\)
0.935524 + 0.353262i \(0.114928\pi\)
\(692\) 40797.2 2.24115
\(693\) −6831.95 + 25185.0i −0.374494 + 1.38052i
\(694\) −39653.0 −2.16888
\(695\) 0 0
\(696\) −34100.3 + 26082.3i −1.85714 + 1.42047i
\(697\) 2913.98 + 5047.17i 0.158357 + 0.274283i
\(698\) 13525.3 + 23426.5i 0.733438 + 1.27035i
\(699\) 9169.41 + 3814.74i 0.496164 + 0.206419i
\(700\) 0 0
\(701\) −24961.0 −1.34489 −0.672443 0.740148i \(-0.734755\pi\)
−0.672443 + 0.740148i \(0.734755\pi\)
\(702\) −6973.93 17060.2i −0.374949 0.917233i
\(703\) 33320.3 1.78762
\(704\) 17688.6 30637.6i 0.946966 1.64019i
\(705\) 0 0
\(706\) 7819.80 + 13544.3i 0.416859 + 0.722020i
\(707\) −3707.11 6420.90i −0.197200 0.341560i
\(708\) −32618.7 + 24949.1i −1.73148 + 1.32436i
\(709\) 5754.43 9966.96i 0.304813 0.527951i −0.672407 0.740182i \(-0.734739\pi\)
0.977220 + 0.212231i \(0.0680728\pi\)
\(710\) 0 0
\(711\) −20430.8 + 5406.66i −1.07766 + 0.285184i
\(712\) 7732.17 0.406988
\(713\) −6452.60 + 11176.2i −0.338922 + 0.587031i
\(714\) −4166.46 32030.5i −0.218384 1.67887i
\(715\) 0 0
\(716\) 25103.1 + 43479.8i 1.31026 + 2.26943i
\(717\) −1934.83 14874.4i −0.100777 0.774747i
\(718\) 6290.92 10896.2i 0.326985 0.566355i
\(719\) 16503.6 0.856022 0.428011 0.903773i \(-0.359214\pi\)
0.428011 + 0.903773i \(0.359214\pi\)
\(720\) 0 0
\(721\) 2694.48 0.139179
\(722\) −32473.8 + 56246.2i −1.67389 + 2.89926i
\(723\) 5318.62 4068.06i 0.273585 0.209257i
\(724\) −2624.35 4545.51i −0.134714 0.233332i
\(725\) 0 0
\(726\) 51470.2 + 21413.1i 2.63118 + 1.09465i
\(727\) 19224.0 33296.9i 0.980713 1.69865i 0.321090 0.947049i \(-0.395951\pi\)
0.659623 0.751597i \(-0.270716\pi\)
\(728\) 16074.9 0.818372
\(729\) −14046.7 + 13788.1i −0.713645 + 0.700508i
\(730\) 0 0
\(731\) −10537.2 + 18251.0i −0.533151 + 0.923445i
\(732\) 5836.13 + 2428.00i 0.294685 + 0.122597i
\(733\) −17220.7 29827.1i −0.867750 1.50299i −0.864290 0.502993i \(-0.832232\pi\)
−0.00345985 0.999994i \(-0.501101\pi\)
\(734\) 4288.98 + 7428.73i 0.215680 + 0.373569i
\(735\) 0 0
\(736\) −1499.06 + 2596.44i −0.0750760 + 0.130035i
\(737\) −29057.1 −1.45228
\(738\) 6819.59 + 6861.96i 0.340153 + 0.342266i
\(739\) 4619.83 0.229964 0.114982 0.993368i \(-0.463319\pi\)
0.114982 + 0.993368i \(0.463319\pi\)
\(740\) 0 0
\(741\) −2582.56 19854.0i −0.128033 0.984283i
\(742\) 23762.7 + 41158.2i 1.17568 + 2.03634i
\(743\) −296.537 513.617i −0.0146418 0.0253604i 0.858612 0.512627i \(-0.171327\pi\)
−0.873253 + 0.487266i \(0.837994\pi\)
\(744\) 3692.83 + 28389.4i 0.181970 + 1.39893i
\(745\) 0 0
\(746\) 14697.1 0.721310
\(747\) −7085.64 + 1875.09i −0.347055 + 0.0918422i
\(748\) −72961.6 −3.56650
\(749\) −3670.48 + 6357.45i −0.179060 + 0.310142i
\(750\) 0 0
\(751\) 11099.8 + 19225.4i 0.539331 + 0.934150i 0.998940 + 0.0460280i \(0.0146563\pi\)
−0.459609 + 0.888122i \(0.652010\pi\)
\(752\) 7058.48 + 12225.6i 0.342282 + 0.592850i
\(753\) 20899.1 + 8694.61i 1.01143 + 0.420783i
\(754\) 14845.3 25712.8i 0.717022 1.24192i
\(755\) 0 0
\(756\) −13392.2 32761.2i −0.644272 1.57608i
\(757\) 9329.48 0.447934 0.223967 0.974597i \(-0.428099\pi\)
0.223967 + 0.974597i \(0.428099\pi\)
\(758\) −22888.2 + 39643.5i −1.09675 + 1.89963i
\(759\) −24450.4 10172.1i −1.16929 0.486459i
\(760\) 0 0
\(761\) −11435.9 19807.5i −0.544745 0.943526i −0.998623 0.0524619i \(-0.983293\pi\)
0.453878 0.891064i \(-0.350040\pi\)
\(762\) 4212.45 3221.98i 0.200264 0.153176i
\(763\) −3761.18 + 6514.55i −0.178458 + 0.309099i
\(764\) 15698.7 0.743400
\(765\) 0 0
\(766\) 47051.4 2.21937
\(767\) 6887.83 11930.1i 0.324257 0.561630i
\(768\) 5278.43 + 40579.0i 0.248006 + 1.90660i
\(769\) 6416.15 + 11113.1i 0.300874 + 0.521130i 0.976334 0.216267i \(-0.0693882\pi\)
−0.675460 + 0.737397i \(0.736055\pi\)
\(770\) 0 0
\(771\) −2169.30 16677.0i −0.101330 0.778997i
\(772\) −11590.7 + 20075.6i −0.540359 + 0.935929i
\(773\) −10821.5 −0.503523 −0.251762 0.967789i \(-0.581010\pi\)
−0.251762 + 0.967789i \(0.581010\pi\)
\(774\) −9158.96 + 33763.2i −0.425338 + 1.56795i
\(775\) 0 0
\(776\) 30453.7 52747.4i 1.40880 2.44011i
\(777\) −15694.3 + 12004.1i −0.724621 + 0.554241i
\(778\) −30948.4 53604.2i −1.42616 2.47018i
\(779\) 5254.64 + 9101.31i 0.241678 + 0.418598i
\(780\) 0