Properties

Label 300.3.f.b.199.8
Level $300$
Weight $3$
Character 300.199
Analytic conductor $8.174$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 5 x^{14} + 12 x^{12} + 25 x^{10} + 53 x^{8} + 100 x^{6} + 192 x^{4} + 320 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{24} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 199.8
Root \(-0.957636 + 1.04064i\) of defining polynomial
Character \(\chi\) \(=\) 300.199
Dual form 300.3.f.b.199.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.169449 + 1.99281i) q^{2} +1.73205 q^{3} +(-3.94257 - 0.675358i) q^{4} +(-0.293494 + 3.45165i) q^{6} -12.3959 q^{7} +(2.01392 - 7.74236i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(-0.169449 + 1.99281i) q^{2} +1.73205 q^{3} +(-3.94257 - 0.675358i) q^{4} +(-0.293494 + 3.45165i) q^{6} -12.3959 q^{7} +(2.01392 - 7.74236i) q^{8} +3.00000 q^{9} -11.0403i q^{11} +(-6.82874 - 1.16975i) q^{12} +2.82009i q^{13} +(2.10047 - 24.7027i) q^{14} +(15.0878 + 5.32529i) q^{16} -6.52606i q^{17} +(-0.508346 + 5.97843i) q^{18} -27.9928i q^{19} -21.4703 q^{21} +(22.0012 + 1.87077i) q^{22} -7.90421 q^{23} +(3.48822 - 13.4102i) q^{24} +(-5.61989 - 0.477860i) q^{26} +5.19615 q^{27} +(48.8718 + 8.37167i) q^{28} -50.7169 q^{29} -36.3467i q^{31} +(-13.1689 + 29.1647i) q^{32} -19.1224i q^{33} +(13.0052 + 1.10583i) q^{34} +(-11.8277 - 2.02607i) q^{36} +18.9279i q^{37} +(55.7842 + 4.74333i) q^{38} +4.88453i q^{39} +5.30410 q^{41} +(3.63812 - 42.7863i) q^{42} -45.5870 q^{43} +(-7.45616 + 43.5273i) q^{44} +(1.33936 - 15.7516i) q^{46} -11.7246 q^{47} +(26.1328 + 9.22368i) q^{48} +104.658 q^{49} -11.3035i q^{51} +(1.90457 - 11.1184i) q^{52} +41.1680i q^{53} +(-0.880481 + 10.3549i) q^{54} +(-24.9644 + 95.9735i) q^{56} -48.4849i q^{57} +(8.59391 - 101.069i) q^{58} +10.7008i q^{59} +56.1297 q^{61} +(72.4319 + 6.15889i) q^{62} -37.1877 q^{63} +(-55.8882 - 31.1850i) q^{64} +(38.1073 + 3.24026i) q^{66} +16.1709 q^{67} +(-4.40743 + 25.7295i) q^{68} -13.6905 q^{69} -66.1617i q^{71} +(6.04177 - 23.2271i) q^{72} +15.6330i q^{73} +(-37.7198 - 3.20731i) q^{74} +(-18.9051 + 110.363i) q^{76} +136.855i q^{77} +(-9.73394 - 0.827677i) q^{78} +123.057i q^{79} +9.00000 q^{81} +(-0.898773 + 10.5701i) q^{82} -99.6700 q^{83} +(84.6484 + 14.5002i) q^{84} +(7.72465 - 90.8461i) q^{86} -87.8443 q^{87} +(-85.4781 - 22.2343i) q^{88} -101.083 q^{89} -34.9575i q^{91} +(31.1629 + 5.33817i) q^{92} -62.9543i q^{93} +(1.98672 - 23.3649i) q^{94} +(-22.8092 + 50.5148i) q^{96} -127.293i q^{97} +(-17.7342 + 208.564i) q^{98} -33.1209i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 20q^{4} - 12q^{6} + 48q^{9} + O(q^{10}) \) \( 16q - 20q^{4} - 12q^{6} + 48q^{9} + 40q^{14} + 68q^{16} - 96q^{21} - 36q^{24} - 72q^{26} - 128q^{29} + 184q^{34} - 60q^{36} - 32q^{41} - 344q^{44} + 304q^{46} + 112q^{49} - 36q^{54} + 232q^{56} - 352q^{61} + 220q^{64} + 216q^{66} + 192q^{69} - 264q^{74} - 48q^{76} + 144q^{81} + 72q^{84} - 400q^{86} - 160q^{89} + 192q^{94} - 348q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.169449 + 1.99281i −0.0847243 + 0.996404i
\(3\) 1.73205 0.577350
\(4\) −3.94257 0.675358i −0.985644 0.168839i
\(5\) 0 0
\(6\) −0.293494 + 3.45165i −0.0489156 + 0.575274i
\(7\) −12.3959 −1.77084 −0.885422 0.464789i \(-0.846130\pi\)
−0.885422 + 0.464789i \(0.846130\pi\)
\(8\) 2.01392 7.74236i 0.251740 0.967795i
\(9\) 3.00000 0.333333
\(10\) 0 0
\(11\) 11.0403i 1.00366i −0.864965 0.501832i \(-0.832659\pi\)
0.864965 0.501832i \(-0.167341\pi\)
\(12\) −6.82874 1.16975i −0.569062 0.0974795i
\(13\) 2.82009i 0.216930i 0.994100 + 0.108465i \(0.0345935\pi\)
−0.994100 + 0.108465i \(0.965407\pi\)
\(14\) 2.10047 24.7027i 0.150034 1.76448i
\(15\) 0 0
\(16\) 15.0878 + 5.32529i 0.942987 + 0.332831i
\(17\) 6.52606i 0.383886i −0.981406 0.191943i \(-0.938521\pi\)
0.981406 0.191943i \(-0.0614789\pi\)
\(18\) −0.508346 + 5.97843i −0.0282414 + 0.332135i
\(19\) 27.9928i 1.47330i −0.676273 0.736651i \(-0.736406\pi\)
0.676273 0.736651i \(-0.263594\pi\)
\(20\) 0 0
\(21\) −21.4703 −1.02240
\(22\) 22.0012 + 1.87077i 1.00006 + 0.0850348i
\(23\) −7.90421 −0.343661 −0.171831 0.985126i \(-0.554968\pi\)
−0.171831 + 0.985126i \(0.554968\pi\)
\(24\) 3.48822 13.4102i 0.145342 0.558757i
\(25\) 0 0
\(26\) −5.61989 0.477860i −0.216150 0.0183792i
\(27\) 5.19615 0.192450
\(28\) 48.8718 + 8.37167i 1.74542 + 0.298988i
\(29\) −50.7169 −1.74886 −0.874429 0.485153i \(-0.838764\pi\)
−0.874429 + 0.485153i \(0.838764\pi\)
\(30\) 0 0
\(31\) 36.3467i 1.17247i −0.810140 0.586236i \(-0.800609\pi\)
0.810140 0.586236i \(-0.199391\pi\)
\(32\) −13.1689 + 29.1647i −0.411528 + 0.911397i
\(33\) 19.1224i 0.579466i
\(34\) 13.0052 + 1.10583i 0.382506 + 0.0325245i
\(35\) 0 0
\(36\) −11.8277 2.02607i −0.328548 0.0562798i
\(37\) 18.9279i 0.511566i 0.966734 + 0.255783i \(0.0823332\pi\)
−0.966734 + 0.255783i \(0.917667\pi\)
\(38\) 55.7842 + 4.74333i 1.46801 + 0.124825i
\(39\) 4.88453i 0.125244i
\(40\) 0 0
\(41\) 5.30410 0.129368 0.0646842 0.997906i \(-0.479396\pi\)
0.0646842 + 0.997906i \(0.479396\pi\)
\(42\) 3.63812 42.7863i 0.0866219 1.01872i
\(43\) −45.5870 −1.06016 −0.530081 0.847947i \(-0.677838\pi\)
−0.530081 + 0.847947i \(0.677838\pi\)
\(44\) −7.45616 + 43.5273i −0.169458 + 0.989256i
\(45\) 0 0
\(46\) 1.33936 15.7516i 0.0291165 0.342426i
\(47\) −11.7246 −0.249460 −0.124730 0.992191i \(-0.539806\pi\)
−0.124730 + 0.992191i \(0.539806\pi\)
\(48\) 26.1328 + 9.22368i 0.544434 + 0.192160i
\(49\) 104.658 2.13589
\(50\) 0 0
\(51\) 11.3035i 0.221637i
\(52\) 1.90457 11.1184i 0.0366263 0.213815i
\(53\) 41.1680i 0.776755i 0.921500 + 0.388378i \(0.126964\pi\)
−0.921500 + 0.388378i \(0.873036\pi\)
\(54\) −0.880481 + 10.3549i −0.0163052 + 0.191758i
\(55\) 0 0
\(56\) −24.9644 + 95.9735i −0.445793 + 1.71381i
\(57\) 48.4849i 0.850612i
\(58\) 8.59391 101.069i 0.148171 1.74257i
\(59\) 10.7008i 0.181370i 0.995880 + 0.0906848i \(0.0289056\pi\)
−0.995880 + 0.0906848i \(0.971094\pi\)
\(60\) 0 0
\(61\) 56.1297 0.920159 0.460080 0.887878i \(-0.347821\pi\)
0.460080 + 0.887878i \(0.347821\pi\)
\(62\) 72.4319 + 6.15889i 1.16826 + 0.0993370i
\(63\) −37.1877 −0.590281
\(64\) −55.8882 31.1850i −0.873254 0.487266i
\(65\) 0 0
\(66\) 38.1073 + 3.24026i 0.577383 + 0.0490949i
\(67\) 16.1709 0.241357 0.120679 0.992692i \(-0.461493\pi\)
0.120679 + 0.992692i \(0.461493\pi\)
\(68\) −4.40743 + 25.7295i −0.0648151 + 0.378375i
\(69\) −13.6905 −0.198413
\(70\) 0 0
\(71\) 66.1617i 0.931855i −0.884823 0.465928i \(-0.845721\pi\)
0.884823 0.465928i \(-0.154279\pi\)
\(72\) 6.04177 23.2271i 0.0839134 0.322598i
\(73\) 15.6330i 0.214150i 0.994251 + 0.107075i \(0.0341485\pi\)
−0.994251 + 0.107075i \(0.965851\pi\)
\(74\) −37.7198 3.20731i −0.509727 0.0433421i
\(75\) 0 0
\(76\) −18.9051 + 110.363i −0.248752 + 1.45215i
\(77\) 136.855i 1.77733i
\(78\) −9.73394 0.827677i −0.124794 0.0106112i
\(79\) 123.057i 1.55768i 0.627223 + 0.778840i \(0.284191\pi\)
−0.627223 + 0.778840i \(0.715809\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) −0.898773 + 10.5701i −0.0109606 + 0.128903i
\(83\) −99.6700 −1.20084 −0.600422 0.799684i \(-0.705001\pi\)
−0.600422 + 0.799684i \(0.705001\pi\)
\(84\) 84.6484 + 14.5002i 1.00772 + 0.172621i
\(85\) 0 0
\(86\) 7.72465 90.8461i 0.0898215 1.05635i
\(87\) −87.8443 −1.00970
\(88\) −85.4781 22.2343i −0.971342 0.252663i
\(89\) −101.083 −1.13576 −0.567881 0.823110i \(-0.692237\pi\)
−0.567881 + 0.823110i \(0.692237\pi\)
\(90\) 0 0
\(91\) 34.9575i 0.384148i
\(92\) 31.1629 + 5.33817i 0.338728 + 0.0580236i
\(93\) 62.9543i 0.676927i
\(94\) 1.98672 23.3649i 0.0211353 0.248563i
\(95\) 0 0
\(96\) −22.8092 + 50.5148i −0.237596 + 0.526195i
\(97\) 127.293i 1.31230i −0.754630 0.656151i \(-0.772183\pi\)
0.754630 0.656151i \(-0.227817\pi\)
\(98\) −17.7342 + 208.564i −0.180962 + 2.12821i
\(99\) 33.1209i 0.334555i
\(100\) 0 0
\(101\) −94.3535 −0.934193 −0.467096 0.884206i \(-0.654700\pi\)
−0.467096 + 0.884206i \(0.654700\pi\)
\(102\) 22.5257 + 1.91536i 0.220840 + 0.0187780i
\(103\) −31.8455 −0.309180 −0.154590 0.987979i \(-0.549406\pi\)
−0.154590 + 0.987979i \(0.549406\pi\)
\(104\) 21.8341 + 5.67943i 0.209943 + 0.0546099i
\(105\) 0 0
\(106\) −82.0400 6.97587i −0.773962 0.0658101i
\(107\) −33.7912 −0.315805 −0.157903 0.987455i \(-0.550473\pi\)
−0.157903 + 0.987455i \(0.550473\pi\)
\(108\) −20.4862 3.50926i −0.189687 0.0324932i
\(109\) 83.4266 0.765382 0.382691 0.923876i \(-0.374997\pi\)
0.382691 + 0.923876i \(0.374997\pi\)
\(110\) 0 0
\(111\) 32.7842i 0.295353i
\(112\) −187.027 66.0118i −1.66988 0.589391i
\(113\) 111.796i 0.989342i −0.869080 0.494671i \(-0.835289\pi\)
0.869080 0.494671i \(-0.164711\pi\)
\(114\) 96.6211 + 8.21569i 0.847553 + 0.0720675i
\(115\) 0 0
\(116\) 199.955 + 34.2520i 1.72375 + 0.295276i
\(117\) 8.46026i 0.0723099i
\(118\) −21.3247 1.81324i −0.180717 0.0153664i
\(119\) 80.8964i 0.679802i
\(120\) 0 0
\(121\) −0.888544 −0.00734334
\(122\) −9.51110 + 111.856i −0.0779599 + 0.916851i
\(123\) 9.18697 0.0746908
\(124\) −24.5470 + 143.299i −0.197960 + 1.15564i
\(125\) 0 0
\(126\) 6.30141 74.1080i 0.0500112 0.588159i
\(127\) −16.6855 −0.131382 −0.0656909 0.997840i \(-0.520925\pi\)
−0.0656909 + 0.997840i \(0.520925\pi\)
\(128\) 71.6160 106.090i 0.559500 0.828831i
\(129\) −78.9589 −0.612085
\(130\) 0 0
\(131\) 196.418i 1.49937i 0.661794 + 0.749686i \(0.269796\pi\)
−0.661794 + 0.749686i \(0.730204\pi\)
\(132\) −12.9144 + 75.3914i −0.0978367 + 0.571147i
\(133\) 346.995i 2.60899i
\(134\) −2.74015 + 32.2256i −0.0204488 + 0.240490i
\(135\) 0 0
\(136\) −50.5271 13.1430i −0.371523 0.0966396i
\(137\) 117.127i 0.854942i 0.904029 + 0.427471i \(0.140595\pi\)
−0.904029 + 0.427471i \(0.859405\pi\)
\(138\) 2.31984 27.2825i 0.0168104 0.197700i
\(139\) 187.238i 1.34704i −0.739170 0.673519i \(-0.764782\pi\)
0.739170 0.673519i \(-0.235218\pi\)
\(140\) 0 0
\(141\) −20.3076 −0.144026
\(142\) 131.848 + 11.2110i 0.928505 + 0.0789508i
\(143\) 31.1346 0.217725
\(144\) 45.2634 + 15.9759i 0.314329 + 0.110944i
\(145\) 0 0
\(146\) −31.1535 2.64899i −0.213380 0.0181437i
\(147\) 181.274 1.23315
\(148\) 12.7831 74.6248i 0.0863725 0.504222i
\(149\) 50.2274 0.337096 0.168548 0.985693i \(-0.446092\pi\)
0.168548 + 0.985693i \(0.446092\pi\)
\(150\) 0 0
\(151\) 213.160i 1.41166i 0.708382 + 0.705829i \(0.249425\pi\)
−0.708382 + 0.705829i \(0.750575\pi\)
\(152\) −216.730 56.3752i −1.42585 0.370890i
\(153\) 19.5782i 0.127962i
\(154\) −272.725 23.1898i −1.77094 0.150583i
\(155\) 0 0
\(156\) 3.29880 19.2576i 0.0211462 0.123446i
\(157\) 203.918i 1.29884i −0.760431 0.649419i \(-0.775012\pi\)
0.760431 0.649419i \(-0.224988\pi\)
\(158\) −245.228 20.8518i −1.55208 0.131973i
\(159\) 71.3051i 0.448460i
\(160\) 0 0
\(161\) 97.9798 0.608570
\(162\) −1.52504 + 17.9353i −0.00941381 + 0.110712i
\(163\) 215.898 1.32452 0.662262 0.749272i \(-0.269596\pi\)
0.662262 + 0.749272i \(0.269596\pi\)
\(164\) −20.9118 3.58216i −0.127511 0.0218425i
\(165\) 0 0
\(166\) 16.8889 198.623i 0.101741 1.19653i
\(167\) 255.029 1.52712 0.763560 0.645737i \(-0.223450\pi\)
0.763560 + 0.645737i \(0.223450\pi\)
\(168\) −43.2396 + 166.231i −0.257378 + 0.989470i
\(169\) 161.047 0.952942
\(170\) 0 0
\(171\) 83.9783i 0.491101i
\(172\) 179.730 + 30.7875i 1.04494 + 0.178997i
\(173\) 235.426i 1.36084i −0.732822 0.680421i \(-0.761797\pi\)
0.732822 0.680421i \(-0.238203\pi\)
\(174\) 14.8851 175.057i 0.0855465 1.00607i
\(175\) 0 0
\(176\) 58.7929 166.574i 0.334051 0.946443i
\(177\) 18.5343i 0.104714i
\(178\) 17.1284 201.439i 0.0962267 1.13168i
\(179\) 102.669i 0.573572i −0.957995 0.286786i \(-0.907413\pi\)
0.957995 0.286786i \(-0.0925869\pi\)
\(180\) 0 0
\(181\) −56.8222 −0.313935 −0.156967 0.987604i \(-0.550172\pi\)
−0.156967 + 0.987604i \(0.550172\pi\)
\(182\) 69.6636 + 5.92350i 0.382767 + 0.0325467i
\(183\) 97.2195 0.531254
\(184\) −15.9185 + 61.1972i −0.0865134 + 0.332594i
\(185\) 0 0
\(186\) 125.456 + 10.6675i 0.674493 + 0.0573522i
\(187\) −72.0498 −0.385293
\(188\) 46.2251 + 7.91830i 0.245878 + 0.0421186i
\(189\) −64.4110 −0.340799
\(190\) 0 0
\(191\) 158.493i 0.829808i −0.909865 0.414904i \(-0.863815\pi\)
0.909865 0.414904i \(-0.136185\pi\)
\(192\) −96.8013 54.0140i −0.504173 0.281323i
\(193\) 156.732i 0.812084i −0.913854 0.406042i \(-0.866909\pi\)
0.913854 0.406042i \(-0.133091\pi\)
\(194\) 253.671 + 21.5697i 1.30758 + 0.111184i
\(195\) 0 0
\(196\) −412.624 70.6819i −2.10522 0.360622i
\(197\) 260.127i 1.32044i −0.751072 0.660221i \(-0.770463\pi\)
0.751072 0.660221i \(-0.229537\pi\)
\(198\) 66.0037 + 5.61230i 0.333352 + 0.0283449i
\(199\) 14.0326i 0.0705157i −0.999378 0.0352579i \(-0.988775\pi\)
0.999378 0.0352579i \(-0.0112253\pi\)
\(200\) 0 0
\(201\) 28.0089 0.139348
\(202\) 15.9881 188.028i 0.0791489 0.930834i
\(203\) 628.682 3.09696
\(204\) −7.63389 + 44.5648i −0.0374210 + 0.218455i
\(205\) 0 0
\(206\) 5.39618 63.4620i 0.0261950 0.308068i
\(207\) −23.7126 −0.114554
\(208\) −15.0178 + 42.5488i −0.0722009 + 0.204562i
\(209\) −309.049 −1.47870
\(210\) 0 0
\(211\) 74.4941i 0.353052i −0.984296 0.176526i \(-0.943514\pi\)
0.984296 0.176526i \(-0.0564860\pi\)
\(212\) 27.8031 162.308i 0.131147 0.765604i
\(213\) 114.595i 0.538007i
\(214\) 5.72587 67.3393i 0.0267564 0.314670i
\(215\) 0 0
\(216\) 10.4646 40.2305i 0.0484474 0.186252i
\(217\) 450.550i 2.07627i
\(218\) −14.1365 + 166.253i −0.0648465 + 0.762630i
\(219\) 27.0771i 0.123640i
\(220\) 0 0
\(221\) 18.4041 0.0832763
\(222\) −65.3326 5.55523i −0.294291 0.0250236i
\(223\) 159.996 0.717471 0.358736 0.933439i \(-0.383208\pi\)
0.358736 + 0.933439i \(0.383208\pi\)
\(224\) 163.240 361.523i 0.728752 1.61394i
\(225\) 0 0
\(226\) 222.787 + 18.9436i 0.985784 + 0.0838213i
\(227\) −175.978 −0.775236 −0.387618 0.921820i \(-0.626702\pi\)
−0.387618 + 0.921820i \(0.626702\pi\)
\(228\) −32.7446 + 191.155i −0.143617 + 0.838400i
\(229\) 114.170 0.498560 0.249280 0.968431i \(-0.419806\pi\)
0.249280 + 0.968431i \(0.419806\pi\)
\(230\) 0 0
\(231\) 237.039i 1.02614i
\(232\) −102.140 + 392.668i −0.440258 + 1.69254i
\(233\) 260.062i 1.11615i 0.829792 + 0.558073i \(0.188459\pi\)
−0.829792 + 0.558073i \(0.811541\pi\)
\(234\) −16.8597 1.43358i −0.0720499 0.00612641i
\(235\) 0 0
\(236\) 7.22687 42.1887i 0.0306223 0.178766i
\(237\) 213.140i 0.899327i
\(238\) −161.211 13.7078i −0.677358 0.0575958i
\(239\) 140.089i 0.586147i −0.956090 0.293073i \(-0.905322\pi\)
0.956090 0.293073i \(-0.0946780\pi\)
\(240\) 0 0
\(241\) 105.920 0.439503 0.219752 0.975556i \(-0.429475\pi\)
0.219752 + 0.975556i \(0.429475\pi\)
\(242\) 0.150563 1.77070i 0.000622159 0.00731693i
\(243\) 15.5885 0.0641500
\(244\) −221.296 37.9076i −0.906949 0.155359i
\(245\) 0 0
\(246\) −1.55672 + 18.3079i −0.00632813 + 0.0744223i
\(247\) 78.9419 0.319603
\(248\) −281.409 73.1993i −1.13471 0.295159i
\(249\) −172.633 −0.693307
\(250\) 0 0
\(251\) 167.879i 0.668839i 0.942424 + 0.334420i \(0.108540\pi\)
−0.942424 + 0.334420i \(0.891460\pi\)
\(252\) 146.615 + 25.1150i 0.581807 + 0.0996627i
\(253\) 87.2650i 0.344921i
\(254\) 2.82733 33.2510i 0.0111312 0.130909i
\(255\) 0 0
\(256\) 199.282 + 160.694i 0.778447 + 0.627710i
\(257\) 198.849i 0.773732i −0.922136 0.386866i \(-0.873558\pi\)
0.922136 0.386866i \(-0.126442\pi\)
\(258\) 13.3795 157.350i 0.0518585 0.609884i
\(259\) 234.629i 0.905903i
\(260\) 0 0
\(261\) −152.151 −0.582953
\(262\) −391.423 33.2827i −1.49398 0.127033i
\(263\) −480.528 −1.82710 −0.913552 0.406722i \(-0.866672\pi\)
−0.913552 + 0.406722i \(0.866672\pi\)
\(264\) −148.052 38.5110i −0.560804 0.145875i
\(265\) 0 0
\(266\) −691.496 58.7979i −2.59961 0.221045i
\(267\) −175.081 −0.655733
\(268\) −63.7552 10.9212i −0.237892 0.0407506i
\(269\) 291.496 1.08363 0.541815 0.840498i \(-0.317737\pi\)
0.541815 + 0.840498i \(0.317737\pi\)
\(270\) 0 0
\(271\) 174.063i 0.642299i 0.947029 + 0.321150i \(0.104069\pi\)
−0.947029 + 0.321150i \(0.895931\pi\)
\(272\) 34.7532 98.4638i 0.127769 0.361999i
\(273\) 60.5482i 0.221788i
\(274\) −233.412 19.8470i −0.851868 0.0724344i
\(275\) 0 0
\(276\) 53.9758 + 9.24598i 0.195564 + 0.0334999i
\(277\) 50.5203i 0.182384i 0.995833 + 0.0911918i \(0.0290676\pi\)
−0.995833 + 0.0911918i \(0.970932\pi\)
\(278\) 373.130 + 31.7273i 1.34219 + 0.114127i
\(279\) 109.040i 0.390824i
\(280\) 0 0
\(281\) −66.0514 −0.235058 −0.117529 0.993069i \(-0.537497\pi\)
−0.117529 + 0.993069i \(0.537497\pi\)
\(282\) 3.44110 40.4692i 0.0122025 0.143508i
\(283\) 116.934 0.413196 0.206598 0.978426i \(-0.433761\pi\)
0.206598 + 0.978426i \(0.433761\pi\)
\(284\) −44.6828 + 260.848i −0.157334 + 0.918477i
\(285\) 0 0
\(286\) −5.27572 + 62.0454i −0.0184466 + 0.216942i
\(287\) −65.7491 −0.229091
\(288\) −39.5067 + 87.4941i −0.137176 + 0.303799i
\(289\) 246.411 0.852631
\(290\) 0 0
\(291\) 220.478i 0.757658i
\(292\) 10.5578 61.6341i 0.0361570 0.211076i
\(293\) 68.3732i 0.233356i −0.993170 0.116678i \(-0.962776\pi\)
0.993170 0.116678i \(-0.0372245\pi\)
\(294\) −30.7166 + 361.244i −0.104478 + 1.22872i
\(295\) 0 0
\(296\) 146.547 + 38.1194i 0.495091 + 0.128782i
\(297\) 57.3672i 0.193155i
\(298\) −8.51096 + 100.094i −0.0285603 + 0.335884i
\(299\) 22.2905i 0.0745503i
\(300\) 0 0
\(301\) 565.092 1.87738
\(302\) −424.788 36.1197i −1.40658 0.119602i
\(303\) −163.425 −0.539356
\(304\) 149.070 422.349i 0.490361 1.38930i
\(305\) 0 0
\(306\) 39.0156 + 3.31750i 0.127502 + 0.0108415i
\(307\) 369.497 1.20357 0.601786 0.798657i \(-0.294456\pi\)
0.601786 + 0.798657i \(0.294456\pi\)
\(308\) 92.4258 539.560i 0.300084 1.75182i
\(309\) −55.1580 −0.178505
\(310\) 0 0
\(311\) 303.446i 0.975712i 0.872924 + 0.487856i \(0.162221\pi\)
−0.872924 + 0.487856i \(0.837779\pi\)
\(312\) 37.8178 + 9.83707i 0.121211 + 0.0315291i
\(313\) 297.693i 0.951097i 0.879689 + 0.475549i \(0.157750\pi\)
−0.879689 + 0.475549i \(0.842250\pi\)
\(314\) 406.369 + 34.5536i 1.29417 + 0.110043i
\(315\) 0 0
\(316\) 83.1072 485.160i 0.262998 1.53532i
\(317\) 264.678i 0.834948i −0.908689 0.417474i \(-0.862916\pi\)
0.908689 0.417474i \(-0.137084\pi\)
\(318\) −142.097 12.0826i −0.446847 0.0379955i
\(319\) 559.931i 1.75527i
\(320\) 0 0
\(321\) −58.5280 −0.182330
\(322\) −16.6026 + 195.255i −0.0515607 + 0.606382i
\(323\) −182.682 −0.565580
\(324\) −35.4832 6.07822i −0.109516 0.0187599i
\(325\) 0 0
\(326\) −36.5835 + 430.243i −0.112219 + 1.31976i
\(327\) 144.499 0.441893
\(328\) 10.6820 41.0663i 0.0325672 0.125202i
\(329\) 145.337 0.441754
\(330\) 0 0
\(331\) 473.426i 1.43029i −0.698976 0.715145i \(-0.746361\pi\)
0.698976 0.715145i \(-0.253639\pi\)
\(332\) 392.956 + 67.3129i 1.18360 + 0.202750i
\(333\) 56.7838i 0.170522i
\(334\) −43.2143 + 508.224i −0.129384 + 1.52163i
\(335\) 0 0
\(336\) −323.940 114.336i −0.964107 0.340285i
\(337\) 29.7588i 0.0883051i −0.999025 0.0441526i \(-0.985941\pi\)
0.999025 0.0441526i \(-0.0140588\pi\)
\(338\) −27.2892 + 320.936i −0.0807373 + 0.949515i
\(339\) 193.636i 0.571197i
\(340\) 0 0
\(341\) −401.278 −1.17677
\(342\) 167.353 + 14.2300i 0.489335 + 0.0416082i
\(343\) −689.937 −2.01148
\(344\) −91.8086 + 352.951i −0.266885 + 1.02602i
\(345\) 0 0
\(346\) 469.158 + 39.8925i 1.35595 + 0.115296i
\(347\) −306.190 −0.882391 −0.441195 0.897411i \(-0.645445\pi\)
−0.441195 + 0.897411i \(0.645445\pi\)
\(348\) 346.333 + 59.3263i 0.995208 + 0.170478i
\(349\) −649.149 −1.86002 −0.930012 0.367528i \(-0.880204\pi\)
−0.930012 + 0.367528i \(0.880204\pi\)
\(350\) 0 0
\(351\) 14.6536i 0.0417481i
\(352\) 321.988 + 145.389i 0.914737 + 0.413036i
\(353\) 275.547i 0.780587i −0.920691 0.390293i \(-0.872374\pi\)
0.920691 0.390293i \(-0.127626\pi\)
\(354\) −36.9354 3.14062i −0.104337 0.00887181i
\(355\) 0 0
\(356\) 398.527 + 68.2671i 1.11946 + 0.191761i
\(357\) 140.117i 0.392484i
\(358\) 204.600 + 17.3972i 0.571510 + 0.0485955i
\(359\) 507.672i 1.41413i 0.707149 + 0.707065i \(0.249981\pi\)
−0.707149 + 0.707065i \(0.750019\pi\)
\(360\) 0 0
\(361\) −422.594 −1.17062
\(362\) 9.62845 113.236i 0.0265979 0.312806i
\(363\) −1.53900 −0.00423968
\(364\) −23.6088 + 137.823i −0.0648594 + 0.378633i
\(365\) 0 0
\(366\) −16.4737 + 193.740i −0.0450102 + 0.529344i
\(367\) 62.7671 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(368\) −119.257 42.0923i −0.324068 0.114381i
\(369\) 15.9123 0.0431228
\(370\) 0 0
\(371\) 510.315i 1.37551i
\(372\) −42.5166 + 248.202i −0.114292 + 0.667209i
\(373\) 272.776i 0.731302i −0.930752 0.365651i \(-0.880846\pi\)
0.930752 0.365651i \(-0.119154\pi\)
\(374\) 12.2087 143.581i 0.0326437 0.383908i
\(375\) 0 0
\(376\) −23.6124 + 90.7761i −0.0627990 + 0.241426i
\(377\) 143.026i 0.379379i
\(378\) 10.9144 128.359i 0.0288740 0.339574i
\(379\) 376.828i 0.994270i 0.867673 + 0.497135i \(0.165615\pi\)
−0.867673 + 0.497135i \(0.834385\pi\)
\(380\) 0 0
\(381\) −28.9001 −0.0758533
\(382\) 315.847 + 26.8565i 0.826825 + 0.0703049i
\(383\) −412.206 −1.07625 −0.538127 0.842864i \(-0.680868\pi\)
−0.538127 + 0.842864i \(0.680868\pi\)
\(384\) 124.042 183.754i 0.323027 0.478526i
\(385\) 0 0
\(386\) 312.337 + 26.5581i 0.809164 + 0.0688032i
\(387\) −136.761 −0.353387
\(388\) −85.9685 + 501.863i −0.221568 + 1.29346i
\(389\) 161.289 0.414623 0.207312 0.978275i \(-0.433529\pi\)
0.207312 + 0.978275i \(0.433529\pi\)
\(390\) 0 0
\(391\) 51.5834i 0.131927i
\(392\) 210.774 810.303i 0.537689 2.06710i
\(393\) 340.206i 0.865663i
\(394\) 518.383 + 44.0782i 1.31569 + 0.111874i
\(395\) 0 0
\(396\) −22.3685 + 130.582i −0.0564861 + 0.329752i
\(397\) 186.505i 0.469785i 0.972021 + 0.234893i \(0.0754738\pi\)
−0.972021 + 0.234893i \(0.924526\pi\)
\(398\) 27.9643 + 2.37781i 0.0702622 + 0.00597440i
\(399\) 601.014i 1.50630i
\(400\) 0 0
\(401\) 239.061 0.596162 0.298081 0.954541i \(-0.403653\pi\)
0.298081 + 0.954541i \(0.403653\pi\)
\(402\) −4.74607 + 55.8164i −0.0118061 + 0.138847i
\(403\) 102.501 0.254344
\(404\) 371.996 + 63.7223i 0.920781 + 0.157729i
\(405\) 0 0
\(406\) −106.529 + 1252.84i −0.262387 + 3.08582i
\(407\) 208.970 0.513441
\(408\) −87.5155 22.7643i −0.214499 0.0557949i
\(409\) −47.8016 −0.116874 −0.0584372 0.998291i \(-0.518612\pi\)
−0.0584372 + 0.998291i \(0.518612\pi\)
\(410\) 0 0
\(411\) 202.870i 0.493601i
\(412\) 125.553 + 21.5071i 0.304741 + 0.0522017i
\(413\) 132.646i 0.321177i
\(414\) 4.01807 47.2547i 0.00970549 0.114142i
\(415\) 0 0
\(416\) −82.2470 37.1374i −0.197709 0.0892726i
\(417\) 324.306i 0.777713i
\(418\) 52.3679 615.875i 0.125282 1.47339i
\(419\) 239.009i 0.570428i −0.958464 0.285214i \(-0.907935\pi\)
0.958464 0.285214i \(-0.0920647\pi\)
\(420\) 0 0
\(421\) −257.592 −0.611857 −0.305929 0.952054i \(-0.598967\pi\)
−0.305929 + 0.952054i \(0.598967\pi\)
\(422\) 148.452 + 12.6229i 0.351783 + 0.0299121i
\(423\) −35.1738 −0.0831532
\(424\) 318.738 + 82.9092i 0.751740 + 0.195541i
\(425\) 0 0
\(426\) 228.367 + 19.4181i 0.536073 + 0.0455823i
\(427\) −695.779 −1.62946
\(428\) 133.224 + 22.8211i 0.311271 + 0.0533204i
\(429\) 53.9268 0.125703
\(430\) 0 0
\(431\) 343.164i 0.796205i −0.917341 0.398103i \(-0.869669\pi\)
0.917341 0.398103i \(-0.130331\pi\)
\(432\) 78.3984 + 27.6710i 0.181478 + 0.0640533i
\(433\) 234.760i 0.542171i −0.962555 0.271085i \(-0.912617\pi\)
0.962555 0.271085i \(-0.0873826\pi\)
\(434\) −897.859 76.3450i −2.06880 0.175910i
\(435\) 0 0
\(436\) −328.916 56.3428i −0.754394 0.129227i
\(437\) 221.261i 0.506317i
\(438\) −53.9595 4.58818i −0.123195 0.0104753i
\(439\) 374.473i 0.853013i −0.904484 0.426507i \(-0.859744\pi\)
0.904484 0.426507i \(-0.140256\pi\)
\(440\) 0 0
\(441\) 313.975 0.711962
\(442\) −3.11854 + 36.6758i −0.00705553 + 0.0829768i
\(443\) 108.557 0.245050 0.122525 0.992465i \(-0.460901\pi\)
0.122525 + 0.992465i \(0.460901\pi\)
\(444\) 22.1410 129.254i 0.0498672 0.291113i
\(445\) 0 0
\(446\) −27.1111 + 318.842i −0.0607873 + 0.714891i
\(447\) 86.9963 0.194623
\(448\) 692.785 + 386.566i 1.54640 + 0.862872i
\(449\) 431.511 0.961050 0.480525 0.876981i \(-0.340446\pi\)
0.480525 + 0.876981i \(0.340446\pi\)
\(450\) 0 0
\(451\) 58.5589i 0.129842i
\(452\) −75.5020 + 440.762i −0.167040 + 0.975138i
\(453\) 369.205i 0.815021i
\(454\) 29.8193 350.692i 0.0656813 0.772448i
\(455\) 0 0
\(456\) −375.387 97.6448i −0.823218 0.214133i
\(457\) 219.747i 0.480847i −0.970668 0.240424i \(-0.922714\pi\)
0.970668 0.240424i \(-0.0772864\pi\)
\(458\) −19.3460 + 227.520i −0.0422402 + 0.496768i
\(459\) 33.9104i 0.0738789i
\(460\) 0 0
\(461\) 223.434 0.484673 0.242337 0.970192i \(-0.422086\pi\)
0.242337 + 0.970192i \(0.422086\pi\)
\(462\) −472.374 40.1660i −1.02245 0.0869394i
\(463\) −740.855 −1.60012 −0.800059 0.599921i \(-0.795198\pi\)
−0.800059 + 0.599921i \(0.795198\pi\)
\(464\) −765.206 270.082i −1.64915 0.582074i
\(465\) 0 0
\(466\) −518.254 44.0672i −1.11213 0.0945648i
\(467\) 249.381 0.534007 0.267004 0.963696i \(-0.413966\pi\)
0.267004 + 0.963696i \(0.413966\pi\)
\(468\) 5.71370 33.3552i 0.0122088 0.0712718i
\(469\) −200.454 −0.427406
\(470\) 0 0
\(471\) 353.196i 0.749885i
\(472\) 82.8495 + 21.5506i 0.175529 + 0.0456580i
\(473\) 503.294i 1.06405i
\(474\) −424.748 36.1164i −0.896093 0.0761948i
\(475\) 0 0
\(476\) 54.6340 318.940i 0.114777 0.670043i
\(477\) 123.504i 0.258918i
\(478\) 279.171 + 23.7379i 0.584039 + 0.0496609i
\(479\) 210.915i 0.440324i 0.975463 + 0.220162i \(0.0706587\pi\)
−0.975463 + 0.220162i \(0.929341\pi\)
\(480\) 0 0
\(481\) −53.3784 −0.110974
\(482\) −17.9480 + 211.079i −0.0372366 + 0.437923i
\(483\) 169.706 0.351358
\(484\) 3.50315 + 0.600085i 0.00723791 + 0.00123984i
\(485\) 0 0
\(486\) −2.64144 + 31.0648i −0.00543507 + 0.0639194i
\(487\) −710.541 −1.45902 −0.729508 0.683972i \(-0.760251\pi\)
−0.729508 + 0.683972i \(0.760251\pi\)
\(488\) 113.041 434.576i 0.231641 0.890525i
\(489\) 373.946 0.764715
\(490\) 0 0
\(491\) 697.876i 1.42134i −0.703528 0.710668i \(-0.748393\pi\)
0.703528 0.710668i \(-0.251607\pi\)
\(492\) −36.2203 6.20449i −0.0736185 0.0126108i
\(493\) 330.982i 0.671363i
\(494\) −13.3766 + 157.316i −0.0270781 + 0.318454i
\(495\) 0 0
\(496\) 193.557 548.390i 0.390235 1.10563i
\(497\) 820.135i 1.65017i
\(498\) 29.2525 344.025i 0.0587400 0.690814i
\(499\) 875.602i 1.75471i −0.479838 0.877357i \(-0.659305\pi\)
0.479838 0.877357i \(-0.340695\pi\)
\(500\) 0 0
\(501\) 441.723 0.881683
\(502\) −334.550 28.4468i −0.666434 0.0566670i
\(503\) 142.849 0.283995 0.141997 0.989867i \(-0.454648\pi\)
0.141997 + 0.989867i \(0.454648\pi\)
\(504\) −74.8932 + 287.921i −0.148598 + 0.571271i
\(505\) 0 0
\(506\) −173.902 14.7869i −0.343681 0.0292232i
\(507\) 278.942 0.550181
\(508\) 65.7837 + 11.2687i 0.129496 + 0.0221824i
\(509\) 147.662 0.290102 0.145051 0.989424i \(-0.453665\pi\)
0.145051 + 0.989424i \(0.453665\pi\)
\(510\) 0 0
\(511\) 193.785i 0.379227i
\(512\) −354.000 + 369.903i −0.691407 + 0.722466i
\(513\) 145.455i 0.283537i
\(514\) 396.268 + 33.6947i 0.770950 + 0.0655539i
\(515\) 0 0
\(516\) 311.301 + 53.3255i 0.603297 + 0.103344i
\(517\) 129.443i 0.250374i
\(518\) 467.571 + 39.7576i 0.902646 + 0.0767520i
\(519\) 407.769i 0.785682i
\(520\) 0 0
\(521\) −348.592 −0.669082 −0.334541 0.942381i \(-0.608581\pi\)
−0.334541 + 0.942381i \(0.608581\pi\)
\(522\) 25.7817 303.207i 0.0493903 0.580857i
\(523\) 370.317 0.708063 0.354032 0.935233i \(-0.384811\pi\)
0.354032 + 0.935233i \(0.384811\pi\)
\(524\) 132.652 774.392i 0.253153 1.47785i
\(525\) 0 0
\(526\) 81.4249 957.601i 0.154800 1.82053i
\(527\) −237.201 −0.450096
\(528\) 101.832 288.514i 0.192864 0.546429i
\(529\) −466.523 −0.881897
\(530\) 0 0
\(531\) 32.1024i 0.0604565i
\(532\) 234.346 1368.06i 0.440500 2.57153i
\(533\) 14.9580i 0.0280638i
\(534\) 29.6672 348.902i 0.0555565 0.653375i
\(535\) 0 0
\(536\) 32.5670 125.201i 0.0607594 0.233584i
\(537\) 177.829i 0.331152i
\(538\) −49.3937 + 580.897i −0.0918098 + 1.07973i
\(539\) 1155.46i 2.14371i
\(540\) 0 0
\(541\) −279.719 −0.517041 −0.258520 0.966006i \(-0.583235\pi\)
−0.258520 + 0.966006i \(0.583235\pi\)
\(542\) −346.874 29.4947i −0.639990 0.0544183i
\(543\) −98.4190 −0.181250
\(544\) 190.331 + 85.9411i 0.349873 + 0.157980i
\(545\) 0 0
\(546\) 120.661 + 10.2598i 0.220991 + 0.0187909i
\(547\) 387.716 0.708804 0.354402 0.935093i \(-0.384685\pi\)
0.354402 + 0.935093i \(0.384685\pi\)
\(548\) 79.1026 461.782i 0.144348 0.842668i
\(549\) 168.389 0.306720
\(550\) 0 0
\(551\) 1419.71i 2.57660i
\(552\) −27.5716 + 105.997i −0.0499485 + 0.192023i
\(553\) 1525.40i 2.75841i
\(554\) −100.677 8.56059i −0.181728 0.0154523i
\(555\) 0 0
\(556\) −126.453 + 738.201i −0.227433 + 1.32770i
\(557\) 43.5564i 0.0781983i −0.999235 0.0390991i \(-0.987551\pi\)
0.999235 0.0390991i \(-0.0124488\pi\)
\(558\) 217.296 + 18.4767i 0.389419 + 0.0331123i
\(559\) 128.559i 0.229981i
\(560\) 0 0
\(561\) −124.794 −0.222449
\(562\) 11.1923 131.628i 0.0199152 0.234213i
\(563\) −361.646 −0.642355 −0.321178 0.947019i \(-0.604079\pi\)
−0.321178 + 0.947019i \(0.604079\pi\)
\(564\) 80.0642 + 13.7149i 0.141958 + 0.0243172i
\(565\) 0 0
\(566\) −19.8144 + 233.028i −0.0350078 + 0.411710i
\(567\) −111.563 −0.196760
\(568\) −512.248 133.245i −0.901845 0.234586i
\(569\) −888.559 −1.56161 −0.780807 0.624772i \(-0.785192\pi\)
−0.780807 + 0.624772i \(0.785192\pi\)
\(570\) 0 0
\(571\) 447.745i 0.784142i 0.919935 + 0.392071i \(0.128241\pi\)
−0.919935 + 0.392071i \(0.871759\pi\)
\(572\) −122.751 21.0270i −0.214599 0.0367605i
\(573\) 274.519i 0.479090i
\(574\) 11.1411 131.025i 0.0194096 0.228267i
\(575\) 0 0
\(576\) −167.665 93.5551i −0.291085 0.162422i
\(577\) 1069.90i 1.85425i −0.374756 0.927124i \(-0.622273\pi\)
0.374756 0.927124i \(-0.377727\pi\)
\(578\) −41.7539 + 491.049i −0.0722386 + 0.849566i
\(579\) 271.468i 0.468857i
\(580\) 0 0
\(581\) 1235.50 2.12651
\(582\) 439.371 + 37.3598i 0.754934 + 0.0641921i
\(583\) 454.508 0.779602
\(584\) 121.036 + 31.4836i 0.207253 + 0.0539102i
\(585\) 0 0
\(586\) 136.255 + 11.5857i 0.232517 + 0.0197709i
\(587\) 129.637 0.220847 0.110424 0.993885i \(-0.464779\pi\)
0.110424 + 0.993885i \(0.464779\pi\)
\(588\) −714.685 122.425i −1.21545 0.208205i
\(589\) −1017.44 −1.72741
\(590\) 0 0
\(591\) 450.553i 0.762357i
\(592\) −100.797 + 285.581i −0.170265 + 0.482400i
\(593\) 892.757i 1.50549i 0.658311 + 0.752746i \(0.271271\pi\)
−0.658311 + 0.752746i \(0.728729\pi\)
\(594\) 114.322 + 9.72079i 0.192461 + 0.0163650i
\(595\) 0 0
\(596\) −198.025 33.9214i −0.332257 0.0569151i
\(597\) 24.3052i 0.0407123i
\(598\) 44.4208 + 3.77710i 0.0742823 + 0.00631623i
\(599\) 1030.62i 1.72057i 0.509816 + 0.860284i \(0.329714\pi\)
−0.509816 + 0.860284i \(0.670286\pi\)
\(600\) 0 0
\(601\) −815.961 −1.35767 −0.678836 0.734289i \(-0.737515\pi\)
−0.678836 + 0.734289i \(0.737515\pi\)
\(602\) −95.7540 + 1126.12i −0.159060 + 1.87063i
\(603\) 48.5128 0.0804525
\(604\) 143.959 840.401i 0.238343 1.39139i
\(605\) 0 0
\(606\) 27.6921 325.675i 0.0456966 0.537417i
\(607\) 842.678 1.38827 0.694133 0.719847i \(-0.255788\pi\)
0.694133 + 0.719847i \(0.255788\pi\)
\(608\) 816.400 + 368.634i 1.34276 + 0.606305i
\(609\) 1088.91 1.78803
\(610\) 0 0
\(611\) 33.0644i 0.0541152i
\(612\) −13.2223 + 77.1885i −0.0216050 + 0.126125i
\(613\) 731.088i 1.19264i −0.802747 0.596320i \(-0.796629\pi\)
0.802747 0.596320i \(-0.203371\pi\)
\(614\) −62.6107 + 736.336i −0.101972 + 1.19924i
\(615\) 0 0
\(616\) 1059.58 + 275.615i 1.72009 + 0.447426i
\(617\) 919.609i 1.49045i 0.666812 + 0.745226i \(0.267658\pi\)
−0.666812 + 0.745226i \(0.732342\pi\)
\(618\) 9.34645 109.919i 0.0151237 0.177863i
\(619\) 688.974i 1.11304i 0.830833 + 0.556522i \(0.187865\pi\)
−0.830833 + 0.556522i \(0.812135\pi\)
\(620\) 0 0
\(621\) −41.0715 −0.0661377
\(622\) −604.711 51.4186i −0.972203 0.0826665i
\(623\) 1253.01 2.01126
\(624\) −26.0116 + 73.6968i −0.0416852 + 0.118104i
\(625\) 0 0
\(626\) −593.246 50.4438i −0.947678 0.0805811i
\(627\) −535.288 −0.853729
\(628\) −137.717 + 803.960i −0.219295 + 1.28019i
\(629\) 123.525 0.196383
\(630\) 0 0
\(631\) 418.968i 0.663975i −0.943284 0.331987i \(-0.892281\pi\)
0.943284 0.331987i \(-0.107719\pi\)
\(632\) 952.749 + 247.827i 1.50751 + 0.392131i
\(633\) 129.027i 0.203835i
\(634\) 527.454 + 44.8494i 0.831946 + 0.0707404i
\(635\) 0 0
\(636\) 48.1565 281.126i 0.0757177 0.442022i
\(637\) 295.146i 0.463337i
\(638\) −1115.83 94.8795i −1.74896 0.148714i
\(639\) 198.485i 0.310618i
\(640\) 0 0
\(641\) −47.2426 −0.0737014 −0.0368507 0.999321i \(-0.511733\pi\)
−0.0368507 + 0.999321i \(0.511733\pi\)
\(642\) 9.91749 116.635i 0.0154478 0.181675i
\(643\) 710.880 1.10557 0.552784 0.833325i \(-0.313565\pi\)
0.552784 + 0.833325i \(0.313565\pi\)
\(644\) −386.293 66.1714i −0.599834 0.102751i
\(645\) 0 0
\(646\) 30.9553 364.051i 0.0479184 0.563547i
\(647\) −468.195 −0.723641 −0.361820 0.932248i \(-0.617845\pi\)
−0.361820 + 0.932248i \(0.617845\pi\)
\(648\) 18.1253 69.6812i 0.0279711 0.107533i
\(649\) 118.140 0.182034
\(650\) 0 0
\(651\) 780.375i 1.19873i
\(652\) −851.192 145.808i −1.30551 0.223632i
\(653\) 551.066i 0.843900i 0.906619 + 0.421950i \(0.138654\pi\)
−0.906619 + 0.421950i \(0.861346\pi\)
\(654\) −24.4852 + 287.959i −0.0374391 + 0.440304i
\(655\) 0 0
\(656\) 80.0271 + 28.2459i 0.121993 + 0.0430578i
\(657\) 46.8989i 0.0713834i
\(658\) −24.6272 + 289.629i −0.0374273 + 0.440165i
\(659\) 158.259i 0.240151i −0.992765 0.120075i \(-0.961686\pi\)
0.992765 0.120075i \(-0.0383136\pi\)
\(660\) 0 0
\(661\) 92.4953 0.139932 0.0699662 0.997549i \(-0.477711\pi\)
0.0699662 + 0.997549i \(0.477711\pi\)
\(662\) 943.447 + 80.2214i 1.42515 + 0.121180i
\(663\) 31.8768 0.0480796
\(664\) −200.728 + 771.681i −0.302301 + 1.16217i
\(665\) 0 0
\(666\) −113.159 9.62194i −0.169909 0.0144474i
\(667\) 400.877 0.601015
\(668\) −1005.47 172.236i −1.50520 0.257838i
\(669\) 277.121 0.414232
\(670\) 0 0
\(671\) 619.690i 0.923532i
\(672\) 282.741 626.176i 0.420745 0.931810i
\(673\) 956.062i 1.42060i 0.703900 + 0.710299i \(0.251440\pi\)
−0.703900 + 0.710299i \(0.748560\pi\)
\(674\) 59.3037 + 5.04259i 0.0879876 + 0.00748159i
\(675\) 0 0
\(676\) −634.940 108.764i −0.939261 0.160894i
\(677\) 1116.67i 1.64944i −0.565543 0.824719i \(-0.691333\pi\)
0.565543 0.824719i \(-0.308667\pi\)
\(678\) 385.879 + 32.8113i 0.569143 + 0.0483942i
\(679\) 1577.92i 2.32388i
\(680\) 0 0
\(681\) −304.804 −0.447583
\(682\) 67.9961 799.671i 0.0997010 1.17254i
\(683\) 826.776 1.21051 0.605254 0.796033i \(-0.293072\pi\)
0.605254 + 0.796033i \(0.293072\pi\)
\(684\) −56.7153 + 331.090i −0.0829172 + 0.484050i
\(685\) 0 0
\(686\) 116.909 1374.91i 0.170421 2.00424i
\(687\) 197.749 0.287844
\(688\) −687.806 242.764i −0.999718 0.352855i
\(689\) −116.097 −0.168501
\(690\) 0 0
\(691\) 965.432i 1.39715i 0.715536 + 0.698576i \(0.246182\pi\)
−0.715536 + 0.698576i \(0.753818\pi\)
\(692\) −158.996 + 928.183i −0.229764 + 1.34130i
\(693\) 410.564i 0.592444i
\(694\) 51.8834 610.177i 0.0747600 0.879218i
\(695\) 0 0
\(696\) −176.912 + 680.122i −0.254183 + 0.977186i
\(697\) 34.6149i 0.0496627i
\(698\) 109.997 1293.63i 0.157589 1.85334i
\(699\) 450.441i 0.644408i
\(700\) 0 0
\(701\) −1109.94 −1.58337 −0.791686 0.610928i \(-0.790797\pi\)
−0.791686 + 0.610928i \(0.790797\pi\)
\(702\) −29.2018 2.48303i −0.0415980 0.00353708i
\(703\) 529.845 0.753691
\(704\) −344.292 + 617.024i −0.489052 + 0.876454i
\(705\) 0 0
\(706\) 549.113 + 46.6911i 0.777780 + 0.0661347i
\(707\) 1169.60 1.65431
\(708\) 12.5173 73.0730i 0.0176798 0.103210i
\(709\) 964.244 1.36001 0.680003 0.733210i \(-0.261979\pi\)
0.680003 + 0.733210i \(0.261979\pi\)
\(710\) 0 0
\(711\) 369.170i 0.519226i
\(712\) −203.573 + 782.620i −0.285917 + 1.09919i
\(713\) 287.292i 0.402934i
\(714\) −279.226 23.7426i −0.391073 0.0332529i
\(715\) 0 0
\(716\) −69.3385 + 404.782i −0.0968415 + 0.565338i
\(717\) 242.641i 0.338412i
\(718\) −1011.69 86.0244i −1.40904 0.119811i
\(719\) 190.820i 0.265396i −0.991157 0.132698i \(-0.957636\pi\)
0.991157 0.132698i \(-0.0423641\pi\)
\(720\) 0 0
\(721\) 394.754 0.547509
\(722\) 71.6080 842.149i 0.0991801 1.16641i
\(723\) 183.459 0.253747
\(724\) 224.026 + 38.3753i 0.309428 + 0.0530046i
\(725\) 0 0
\(726\) 0.260782 3.06694i 0.000359204 0.00422443i
\(727\) 202.134 0.278039 0.139019 0.990290i \(-0.455605\pi\)
0.139019 + 0.990290i \(0.455605\pi\)
\(728\) −270.654 70.4017i −0.371777 0.0967056i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 297.503i 0.406981i
\(732\) −383.295 65.6579i −0.523627 0.0896966i
\(733\) 962.435i 1.31301i −0.754322 0.656504i \(-0.772034\pi\)
0.754322 0.656504i \(-0.227966\pi\)
\(734\) −10.6358 + 125.083i −0.0144902 + 0.170413i
\(735\) 0 0
\(736\) 104.090 230.524i 0.141426 0.313212i
\(737\) 178.532i 0.242242i
\(738\) −2.69632 + 31.7102i −0.00365355 + 0.0429677i
\(739\) 932.112i 1.26132i −0.776061 0.630658i \(-0.782785\pi\)
0.776061 0.630658i \(-0.217215\pi\)
\(740\) 0 0
\(741\) 136.731 0.184523
\(742\) 1016.96 + 86.4722i 1.37057 + 0.116539i
\(743\) −1153.70 −1.55276 −0.776379 0.630266i \(-0.782946\pi\)
−0.776379 + 0.630266i \(0.782946\pi\)
\(744\) −487.414 126.785i −0.655127 0.170410i
\(745\) 0 0
\(746\) 543.590 + 46.2215i 0.728672 + 0.0619591i
\(747\) −299.010 −0.400281
\(748\) 284.062 + 48.6594i 0.379762 + 0.0650526i
\(749\) 418.872 0.559242
\(750\) 0 0
\(751\) 204.359i 0.272116i 0.990701 + 0.136058i \(0.0434434\pi\)
−0.990701 + 0.136058i \(0.956557\pi\)
\(752\) −176.898 62.4369i −0.235237 0.0830279i
\(753\) 290.774i 0.386155i
\(754\) 285.023 + 24.2356i 0.378015 + 0.0321427i
\(755\) 0 0
\(756\) 253.945 + 43.5005i 0.335906 + 0.0575403i
\(757\) 216.739i 0.286314i 0.989700 + 0.143157i \(0.0457253\pi\)
−0.989700 + 0.143157i \(0.954275\pi\)
\(758\) −750.947 63.8530i −0.990695 0.0842388i
\(759\) 151.147i 0.199140i
\(760\) 0 0
\(761\) 1324.78 1.74085 0.870424 0.492303i \(-0.163845\pi\)
0.870424 + 0.492303i \(0.163845\pi\)
\(762\) 4.89708 57.5924i 0.00642662 0.0755805i
\(763\) −1034.15 −1.35537
\(764\) −107.040 + 624.872i −0.140104 + 0.817895i
\(765\) 0 0
\(766\) 69.8477 821.447i 0.0911849 1.07238i
\(767\) −30.1772 −0.0393444
\(768\) 345.167 + 278.330i 0.449437 + 0.362409i
\(769\) −444.088 −0.577488 −0.288744 0.957406i \(-0.593238\pi\)
−0.288744 + 0.957406i \(0.593238\pi\)
\(770\) 0 0
\(771\) 344.417i 0.446714i
\(772\) −105.850 + 617.928i −0.137112 + 0.800425i
\(773\) 751.987i 0.972817i −0.873732 0.486408i \(-0.838307\pi\)
0.873732 0.486408i \(-0.161693\pi\)
\(774\) 23.1739 272.538i 0.0299405 0.352117i
\(775\) 0 0
\(776\) −985.550 256.359i −1.27004 0.330359i
\(777\) 406.389i 0.523023i
\(778\) −27.3301 + 321.417i −0.0351287 + 0.413133i
\(779\) 148.476i 0.190599i
\(780\) 0 0
\(781\) −730.446 −0.935271
\(782\) −102.796 8.74073i −0.131452 0.0111774i
\(783\) −263.533 −0.336568
\(784\) 1579.06 + 557.337i 2.01411 + 0.710889i
\(785\) 0 0
\(786\) −677.965 57.6474i −0.862550 0.0733427i
\(787\) −442.296 −0.562002