Properties

Label 300.3.c.d.151.8
Level $300$
Weight $3$
Character 300.151
Analytic conductor $8.174$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.85100625.1
Defining polynomial: \(x^{8} - x^{7} - 2 x^{6} + x^{5} + 3 x^{4} + 2 x^{3} - 8 x^{2} - 8 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.8
Root \(-1.34966 + 0.422403i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.d.151.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.99281 + 0.169449i) q^{2} +1.73205i q^{3} +(3.94257 + 0.675358i) q^{4} +(-0.293494 + 3.45165i) q^{6} +12.3959i q^{7} +(7.74236 + 2.01392i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(1.99281 + 0.169449i) q^{2} +1.73205i q^{3} +(3.94257 + 0.675358i) q^{4} +(-0.293494 + 3.45165i) q^{6} +12.3959i q^{7} +(7.74236 + 2.01392i) q^{8} -3.00000 q^{9} -11.0403i q^{11} +(-1.16975 + 6.82874i) q^{12} -2.82009 q^{13} +(-2.10047 + 24.7027i) q^{14} +(15.0878 + 5.32529i) q^{16} -6.52606 q^{17} +(-5.97843 - 0.508346i) q^{18} +27.9928i q^{19} -21.4703 q^{21} +(1.87077 - 22.0012i) q^{22} -7.90421i q^{23} +(-3.48822 + 13.4102i) q^{24} +(-5.61989 - 0.477860i) q^{26} -5.19615i q^{27} +(-8.37167 + 48.8718i) q^{28} +50.7169 q^{29} -36.3467i q^{31} +(29.1647 + 13.1689i) q^{32} +19.1224 q^{33} +(-13.0052 - 1.10583i) q^{34} +(-11.8277 - 2.02607i) q^{36} +18.9279 q^{37} +(-4.74333 + 55.7842i) q^{38} -4.88453i q^{39} +5.30410 q^{41} +(-42.7863 - 3.63812i) q^{42} -45.5870i q^{43} +(7.45616 - 43.5273i) q^{44} +(1.33936 - 15.7516i) q^{46} +11.7246i q^{47} +(-9.22368 + 26.1328i) q^{48} -104.658 q^{49} -11.3035i q^{51} +(-11.1184 - 1.90457i) q^{52} -41.1680 q^{53} +(0.880481 - 10.3549i) q^{54} +(-24.9644 + 95.9735i) q^{56} -48.4849 q^{57} +(101.069 + 8.59391i) q^{58} -10.7008i q^{59} +56.1297 q^{61} +(6.15889 - 72.4319i) q^{62} -37.1877i q^{63} +(55.8882 + 31.1850i) q^{64} +(38.1073 + 3.24026i) q^{66} -16.1709i q^{67} +(-25.7295 - 4.40743i) q^{68} +13.6905 q^{69} -66.1617i q^{71} +(-23.2271 - 6.04177i) q^{72} -15.6330 q^{73} +(37.7198 + 3.20731i) q^{74} +(-18.9051 + 110.363i) q^{76} +136.855 q^{77} +(0.827677 - 9.73394i) q^{78} -123.057i q^{79} +9.00000 q^{81} +(10.5701 + 0.898773i) q^{82} -99.6700i q^{83} +(-84.6484 - 14.5002i) q^{84} +(7.72465 - 90.8461i) q^{86} +87.8443i q^{87} +(22.2343 - 85.4781i) q^{88} +101.083 q^{89} -34.9575i q^{91} +(5.33817 - 31.1629i) q^{92} +62.9543 q^{93} +(-1.98672 + 23.3649i) q^{94} +(-22.8092 + 50.5148i) q^{96} -127.293 q^{97} +(-208.564 - 17.7342i) q^{98} +33.1209i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} + 10q^{4} - 6q^{6} + 20q^{8} - 24q^{9} + O(q^{10}) \) \( 8q - 4q^{2} + 10q^{4} - 6q^{6} + 20q^{8} - 24q^{9} - 16q^{13} - 20q^{14} + 34q^{16} + 12q^{18} - 48q^{21} - 68q^{22} + 18q^{24} - 36q^{26} - 28q^{28} + 64q^{29} + 76q^{32} - 92q^{34} - 30q^{36} + 112q^{37} + 40q^{38} - 16q^{41} - 108q^{42} + 172q^{44} + 152q^{46} - 48q^{48} - 56q^{49} + 128q^{52} - 352q^{53} + 18q^{54} + 116q^{56} - 144q^{57} + 204q^{58} - 176q^{61} + 56q^{62} - 110q^{64} + 108q^{66} + 184q^{68} - 96q^{69} - 60q^{72} + 240q^{73} + 132q^{74} - 24q^{76} + 288q^{77} + 240q^{78} + 72q^{81} - 40q^{82} - 36q^{84} - 200q^{86} - 140q^{88} + 80q^{89} - 144q^{92} - 144q^{93} - 96q^{94} - 174q^{96} - 432q^{97} - 660q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.99281 + 0.169449i 0.996404 + 0.0847243i
\(3\) 1.73205i 0.577350i
\(4\) 3.94257 + 0.675358i 0.985644 + 0.168839i
\(5\) 0 0
\(6\) −0.293494 + 3.45165i −0.0489156 + 0.575274i
\(7\) 12.3959i 1.77084i 0.464789 + 0.885422i \(0.346130\pi\)
−0.464789 + 0.885422i \(0.653870\pi\)
\(8\) 7.74236 + 2.01392i 0.967795 + 0.251740i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 11.0403i 1.00366i −0.864965 0.501832i \(-0.832659\pi\)
0.864965 0.501832i \(-0.167341\pi\)
\(12\) −1.16975 + 6.82874i −0.0974795 + 0.569062i
\(13\) −2.82009 −0.216930 −0.108465 0.994100i \(-0.534593\pi\)
−0.108465 + 0.994100i \(0.534593\pi\)
\(14\) −2.10047 + 24.7027i −0.150034 + 1.76448i
\(15\) 0 0
\(16\) 15.0878 + 5.32529i 0.942987 + 0.332831i
\(17\) −6.52606 −0.383886 −0.191943 0.981406i \(-0.561479\pi\)
−0.191943 + 0.981406i \(0.561479\pi\)
\(18\) −5.97843 0.508346i −0.332135 0.0282414i
\(19\) 27.9928i 1.47330i 0.676273 + 0.736651i \(0.263594\pi\)
−0.676273 + 0.736651i \(0.736406\pi\)
\(20\) 0 0
\(21\) −21.4703 −1.02240
\(22\) 1.87077 22.0012i 0.0850348 1.00006i
\(23\) 7.90421i 0.343661i −0.985126 0.171831i \(-0.945032\pi\)
0.985126 0.171831i \(-0.0549682\pi\)
\(24\) −3.48822 + 13.4102i −0.145342 + 0.558757i
\(25\) 0 0
\(26\) −5.61989 0.477860i −0.216150 0.0183792i
\(27\) 5.19615i 0.192450i
\(28\) −8.37167 + 48.8718i −0.298988 + 1.74542i
\(29\) 50.7169 1.74886 0.874429 0.485153i \(-0.161236\pi\)
0.874429 + 0.485153i \(0.161236\pi\)
\(30\) 0 0
\(31\) 36.3467i 1.17247i −0.810140 0.586236i \(-0.800609\pi\)
0.810140 0.586236i \(-0.199391\pi\)
\(32\) 29.1647 + 13.1689i 0.911397 + 0.411528i
\(33\) 19.1224 0.579466
\(34\) −13.0052 1.10583i −0.382506 0.0325245i
\(35\) 0 0
\(36\) −11.8277 2.02607i −0.328548 0.0562798i
\(37\) 18.9279 0.511566 0.255783 0.966734i \(-0.417667\pi\)
0.255783 + 0.966734i \(0.417667\pi\)
\(38\) −4.74333 + 55.7842i −0.124825 + 1.46801i
\(39\) 4.88453i 0.125244i
\(40\) 0 0
\(41\) 5.30410 0.129368 0.0646842 0.997906i \(-0.479396\pi\)
0.0646842 + 0.997906i \(0.479396\pi\)
\(42\) −42.7863 3.63812i −1.01872 0.0866219i
\(43\) 45.5870i 1.06016i −0.847947 0.530081i \(-0.822162\pi\)
0.847947 0.530081i \(-0.177838\pi\)
\(44\) 7.45616 43.5273i 0.169458 0.989256i
\(45\) 0 0
\(46\) 1.33936 15.7516i 0.0291165 0.342426i
\(47\) 11.7246i 0.249460i 0.992191 + 0.124730i \(0.0398064\pi\)
−0.992191 + 0.124730i \(0.960194\pi\)
\(48\) −9.22368 + 26.1328i −0.192160 + 0.544434i
\(49\) −104.658 −2.13589
\(50\) 0 0
\(51\) 11.3035i 0.221637i
\(52\) −11.1184 1.90457i −0.213815 0.0366263i
\(53\) −41.1680 −0.776755 −0.388378 0.921500i \(-0.626964\pi\)
−0.388378 + 0.921500i \(0.626964\pi\)
\(54\) 0.880481 10.3549i 0.0163052 0.191758i
\(55\) 0 0
\(56\) −24.9644 + 95.9735i −0.445793 + 1.71381i
\(57\) −48.4849 −0.850612
\(58\) 101.069 + 8.59391i 1.74257 + 0.148171i
\(59\) 10.7008i 0.181370i −0.995880 0.0906848i \(-0.971094\pi\)
0.995880 0.0906848i \(-0.0289056\pi\)
\(60\) 0 0
\(61\) 56.1297 0.920159 0.460080 0.887878i \(-0.347821\pi\)
0.460080 + 0.887878i \(0.347821\pi\)
\(62\) 6.15889 72.4319i 0.0993370 1.16826i
\(63\) 37.1877i 0.590281i
\(64\) 55.8882 + 31.1850i 0.873254 + 0.487266i
\(65\) 0 0
\(66\) 38.1073 + 3.24026i 0.577383 + 0.0490949i
\(67\) 16.1709i 0.241357i −0.992692 0.120679i \(-0.961493\pi\)
0.992692 0.120679i \(-0.0385071\pi\)
\(68\) −25.7295 4.40743i −0.378375 0.0648151i
\(69\) 13.6905 0.198413
\(70\) 0 0
\(71\) 66.1617i 0.931855i −0.884823 0.465928i \(-0.845721\pi\)
0.884823 0.465928i \(-0.154279\pi\)
\(72\) −23.2271 6.04177i −0.322598 0.0839134i
\(73\) −15.6330 −0.214150 −0.107075 0.994251i \(-0.534149\pi\)
−0.107075 + 0.994251i \(0.534149\pi\)
\(74\) 37.7198 + 3.20731i 0.509727 + 0.0433421i
\(75\) 0 0
\(76\) −18.9051 + 110.363i −0.248752 + 1.45215i
\(77\) 136.855 1.77733
\(78\) 0.827677 9.73394i 0.0106112 0.124794i
\(79\) 123.057i 1.55768i −0.627223 0.778840i \(-0.715809\pi\)
0.627223 0.778840i \(-0.284191\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 10.5701 + 0.898773i 0.128903 + 0.0109606i
\(83\) 99.6700i 1.20084i −0.799684 0.600422i \(-0.794999\pi\)
0.799684 0.600422i \(-0.205001\pi\)
\(84\) −84.6484 14.5002i −1.00772 0.172621i
\(85\) 0 0
\(86\) 7.72465 90.8461i 0.0898215 1.05635i
\(87\) 87.8443i 1.00970i
\(88\) 22.2343 85.4781i 0.252663 0.971342i
\(89\) 101.083 1.13576 0.567881 0.823110i \(-0.307763\pi\)
0.567881 + 0.823110i \(0.307763\pi\)
\(90\) 0 0
\(91\) 34.9575i 0.384148i
\(92\) 5.33817 31.1629i 0.0580236 0.338728i
\(93\) 62.9543 0.676927
\(94\) −1.98672 + 23.3649i −0.0211353 + 0.248563i
\(95\) 0 0
\(96\) −22.8092 + 50.5148i −0.237596 + 0.526195i
\(97\) −127.293 −1.31230 −0.656151 0.754630i \(-0.727817\pi\)
−0.656151 + 0.754630i \(0.727817\pi\)
\(98\) −208.564 17.7342i −2.12821 0.180962i
\(99\) 33.1209i 0.334555i
\(100\) 0 0
\(101\) −94.3535 −0.934193 −0.467096 0.884206i \(-0.654700\pi\)
−0.467096 + 0.884206i \(0.654700\pi\)
\(102\) 1.91536 22.5257i 0.0187780 0.220840i
\(103\) 31.8455i 0.309180i −0.987979 0.154590i \(-0.950594\pi\)
0.987979 0.154590i \(-0.0494056\pi\)
\(104\) −21.8341 5.67943i −0.209943 0.0546099i
\(105\) 0 0
\(106\) −82.0400 6.97587i −0.773962 0.0658101i
\(107\) 33.7912i 0.315805i 0.987455 + 0.157903i \(0.0504732\pi\)
−0.987455 + 0.157903i \(0.949527\pi\)
\(108\) 3.50926 20.4862i 0.0324932 0.189687i
\(109\) −83.4266 −0.765382 −0.382691 0.923876i \(-0.625003\pi\)
−0.382691 + 0.923876i \(0.625003\pi\)
\(110\) 0 0
\(111\) 32.7842i 0.295353i
\(112\) −66.0118 + 187.027i −0.589391 + 1.66988i
\(113\) 111.796 0.989342 0.494671 0.869080i \(-0.335289\pi\)
0.494671 + 0.869080i \(0.335289\pi\)
\(114\) −96.6211 8.21569i −0.847553 0.0720675i
\(115\) 0 0
\(116\) 199.955 + 34.2520i 1.72375 + 0.295276i
\(117\) 8.46026 0.0723099
\(118\) 1.81324 21.3247i 0.0153664 0.180717i
\(119\) 80.8964i 0.679802i
\(120\) 0 0
\(121\) −0.888544 −0.00734334
\(122\) 111.856 + 9.51110i 0.916851 + 0.0779599i
\(123\) 9.18697i 0.0746908i
\(124\) 24.5470 143.299i 0.197960 1.15564i
\(125\) 0 0
\(126\) 6.30141 74.1080i 0.0500112 0.588159i
\(127\) 16.6855i 0.131382i 0.997840 + 0.0656909i \(0.0209251\pi\)
−0.997840 + 0.0656909i \(0.979075\pi\)
\(128\) 106.090 + 71.6160i 0.828831 + 0.559500i
\(129\) 78.9589 0.612085
\(130\) 0 0
\(131\) 196.418i 1.49937i 0.661794 + 0.749686i \(0.269796\pi\)
−0.661794 + 0.749686i \(0.730204\pi\)
\(132\) 75.3914 + 12.9144i 0.571147 + 0.0978367i
\(133\) −346.995 −2.60899
\(134\) 2.74015 32.2256i 0.0204488 0.240490i
\(135\) 0 0
\(136\) −50.5271 13.1430i −0.371523 0.0966396i
\(137\) 117.127 0.854942 0.427471 0.904029i \(-0.359405\pi\)
0.427471 + 0.904029i \(0.359405\pi\)
\(138\) 27.2825 + 2.31984i 0.197700 + 0.0168104i
\(139\) 187.238i 1.34704i 0.739170 + 0.673519i \(0.235218\pi\)
−0.739170 + 0.673519i \(0.764782\pi\)
\(140\) 0 0
\(141\) −20.3076 −0.144026
\(142\) 11.2110 131.848i 0.0789508 0.928505i
\(143\) 31.1346i 0.217725i
\(144\) −45.2634 15.9759i −0.314329 0.110944i
\(145\) 0 0
\(146\) −31.1535 2.64899i −0.213380 0.0181437i
\(147\) 181.274i 1.23315i
\(148\) 74.6248 + 12.7831i 0.504222 + 0.0863725i
\(149\) −50.2274 −0.337096 −0.168548 0.985693i \(-0.553908\pi\)
−0.168548 + 0.985693i \(0.553908\pi\)
\(150\) 0 0
\(151\) 213.160i 1.41166i 0.708382 + 0.705829i \(0.249425\pi\)
−0.708382 + 0.705829i \(0.750575\pi\)
\(152\) −56.3752 + 216.730i −0.370890 + 1.42585i
\(153\) 19.5782 0.127962
\(154\) 272.725 + 23.1898i 1.77094 + 0.150583i
\(155\) 0 0
\(156\) 3.29880 19.2576i 0.0211462 0.123446i
\(157\) −203.918 −1.29884 −0.649419 0.760431i \(-0.724988\pi\)
−0.649419 + 0.760431i \(0.724988\pi\)
\(158\) 20.8518 245.228i 0.131973 1.55208i
\(159\) 71.3051i 0.448460i
\(160\) 0 0
\(161\) 97.9798 0.608570
\(162\) 17.9353 + 1.52504i 0.110712 + 0.00941381i
\(163\) 215.898i 1.32452i 0.749272 + 0.662262i \(0.230404\pi\)
−0.749272 + 0.662262i \(0.769596\pi\)
\(164\) 20.9118 + 3.58216i 0.127511 + 0.0218425i
\(165\) 0 0
\(166\) 16.8889 198.623i 0.101741 1.19653i
\(167\) 255.029i 1.52712i −0.645737 0.763560i \(-0.723450\pi\)
0.645737 0.763560i \(-0.276550\pi\)
\(168\) −166.231 43.2396i −0.989470 0.257378i
\(169\) −161.047 −0.952942
\(170\) 0 0
\(171\) 83.9783i 0.491101i
\(172\) 30.7875 179.730i 0.178997 1.04494i
\(173\) 235.426 1.36084 0.680421 0.732822i \(-0.261797\pi\)
0.680421 + 0.732822i \(0.261797\pi\)
\(174\) −14.8851 + 175.057i −0.0855465 + 1.00607i
\(175\) 0 0
\(176\) 58.7929 166.574i 0.334051 0.946443i
\(177\) 18.5343 0.104714
\(178\) 201.439 + 17.1284i 1.13168 + 0.0962267i
\(179\) 102.669i 0.573572i 0.957995 + 0.286786i \(0.0925869\pi\)
−0.957995 + 0.286786i \(0.907413\pi\)
\(180\) 0 0
\(181\) −56.8222 −0.313935 −0.156967 0.987604i \(-0.550172\pi\)
−0.156967 + 0.987604i \(0.550172\pi\)
\(182\) 5.92350 69.6636i 0.0325467 0.382767i
\(183\) 97.2195i 0.531254i
\(184\) 15.9185 61.1972i 0.0865134 0.332594i
\(185\) 0 0
\(186\) 125.456 + 10.6675i 0.674493 + 0.0573522i
\(187\) 72.0498i 0.385293i
\(188\) −7.91830 + 46.2251i −0.0421186 + 0.245878i
\(189\) 64.4110 0.340799
\(190\) 0 0
\(191\) 158.493i 0.829808i −0.909865 0.414904i \(-0.863815\pi\)
0.909865 0.414904i \(-0.136185\pi\)
\(192\) −54.0140 + 96.8013i −0.281323 + 0.504173i
\(193\) 156.732 0.812084 0.406042 0.913854i \(-0.366909\pi\)
0.406042 + 0.913854i \(0.366909\pi\)
\(194\) −253.671 21.5697i −1.30758 0.111184i
\(195\) 0 0
\(196\) −412.624 70.6819i −2.10522 0.360622i
\(197\) −260.127 −1.32044 −0.660221 0.751072i \(-0.729537\pi\)
−0.660221 + 0.751072i \(0.729537\pi\)
\(198\) −5.61230 + 66.0037i −0.0283449 + 0.333352i
\(199\) 14.0326i 0.0705157i 0.999378 + 0.0352579i \(0.0112253\pi\)
−0.999378 + 0.0352579i \(0.988775\pi\)
\(200\) 0 0
\(201\) 28.0089 0.139348
\(202\) −188.028 15.9881i −0.930834 0.0791489i
\(203\) 628.682i 3.09696i
\(204\) 7.63389 44.5648i 0.0374210 0.218455i
\(205\) 0 0
\(206\) 5.39618 63.4620i 0.0261950 0.308068i
\(207\) 23.7126i 0.114554i
\(208\) −42.5488 15.0178i −0.204562 0.0722009i
\(209\) 309.049 1.47870
\(210\) 0 0
\(211\) 74.4941i 0.353052i −0.984296 0.176526i \(-0.943514\pi\)
0.984296 0.176526i \(-0.0564860\pi\)
\(212\) −162.308 27.8031i −0.765604 0.131147i
\(213\) 114.595 0.538007
\(214\) −5.72587 + 67.3393i −0.0267564 + 0.314670i
\(215\) 0 0
\(216\) 10.4646 40.2305i 0.0484474 0.186252i
\(217\) 450.550 2.07627
\(218\) −166.253 14.1365i −0.762630 0.0648465i
\(219\) 27.0771i 0.123640i
\(220\) 0 0
\(221\) 18.4041 0.0832763
\(222\) −5.55523 + 65.3326i −0.0250236 + 0.294291i
\(223\) 159.996i 0.717471i 0.933439 + 0.358736i \(0.116792\pi\)
−0.933439 + 0.358736i \(0.883208\pi\)
\(224\) −163.240 + 361.523i −0.728752 + 1.61394i
\(225\) 0 0
\(226\) 222.787 + 18.9436i 0.985784 + 0.0838213i
\(227\) 175.978i 0.775236i 0.921820 + 0.387618i \(0.126702\pi\)
−0.921820 + 0.387618i \(0.873298\pi\)
\(228\) −191.155 32.7446i −0.838400 0.143617i
\(229\) −114.170 −0.498560 −0.249280 0.968431i \(-0.580194\pi\)
−0.249280 + 0.968431i \(0.580194\pi\)
\(230\) 0 0
\(231\) 237.039i 1.02614i
\(232\) 392.668 + 102.140i 1.69254 + 0.440258i
\(233\) −260.062 −1.11615 −0.558073 0.829792i \(-0.688459\pi\)
−0.558073 + 0.829792i \(0.688459\pi\)
\(234\) 16.8597 + 1.43358i 0.0720499 + 0.00612641i
\(235\) 0 0
\(236\) 7.22687 42.1887i 0.0306223 0.178766i
\(237\) 213.140 0.899327
\(238\) 13.7078 161.211i 0.0575958 0.677358i
\(239\) 140.089i 0.586147i 0.956090 + 0.293073i \(0.0946780\pi\)
−0.956090 + 0.293073i \(0.905322\pi\)
\(240\) 0 0
\(241\) 105.920 0.439503 0.219752 0.975556i \(-0.429475\pi\)
0.219752 + 0.975556i \(0.429475\pi\)
\(242\) −1.77070 0.150563i −0.00731693 0.000622159i
\(243\) 15.5885i 0.0641500i
\(244\) 221.296 + 37.9076i 0.906949 + 0.155359i
\(245\) 0 0
\(246\) −1.55672 + 18.3079i −0.00632813 + 0.0744223i
\(247\) 78.9419i 0.319603i
\(248\) 73.1993 281.409i 0.295159 1.13471i
\(249\) 172.633 0.693307
\(250\) 0 0
\(251\) 167.879i 0.668839i 0.942424 + 0.334420i \(0.108540\pi\)
−0.942424 + 0.334420i \(0.891460\pi\)
\(252\) 25.1150 146.615i 0.0996627 0.581807i
\(253\) −87.2650 −0.344921
\(254\) −2.82733 + 33.2510i −0.0111312 + 0.130909i
\(255\) 0 0
\(256\) 199.282 + 160.694i 0.778447 + 0.627710i
\(257\) −198.849 −0.773732 −0.386866 0.922136i \(-0.626442\pi\)
−0.386866 + 0.922136i \(0.626442\pi\)
\(258\) 157.350 + 13.3795i 0.609884 + 0.0518585i
\(259\) 234.629i 0.905903i
\(260\) 0 0
\(261\) −152.151 −0.582953
\(262\) −33.2827 + 391.423i −0.127033 + 1.49398i
\(263\) 480.528i 1.82710i −0.406722 0.913552i \(-0.633328\pi\)
0.406722 0.913552i \(-0.366672\pi\)
\(264\) 148.052 + 38.5110i 0.560804 + 0.145875i
\(265\) 0 0
\(266\) −691.496 58.7979i −2.59961 0.221045i
\(267\) 175.081i 0.655733i
\(268\) 10.9212 63.7552i 0.0407506 0.237892i
\(269\) −291.496 −1.08363 −0.541815 0.840498i \(-0.682263\pi\)
−0.541815 + 0.840498i \(0.682263\pi\)
\(270\) 0 0
\(271\) 174.063i 0.642299i 0.947029 + 0.321150i \(0.104069\pi\)
−0.947029 + 0.321150i \(0.895931\pi\)
\(272\) −98.4638 34.7532i −0.361999 0.127769i
\(273\) 60.5482 0.221788
\(274\) 233.412 + 19.8470i 0.851868 + 0.0724344i
\(275\) 0 0
\(276\) 53.9758 + 9.24598i 0.195564 + 0.0334999i
\(277\) 50.5203 0.182384 0.0911918 0.995833i \(-0.470932\pi\)
0.0911918 + 0.995833i \(0.470932\pi\)
\(278\) −31.7273 + 373.130i −0.114127 + 1.34219i
\(279\) 109.040i 0.390824i
\(280\) 0 0
\(281\) −66.0514 −0.235058 −0.117529 0.993069i \(-0.537497\pi\)
−0.117529 + 0.993069i \(0.537497\pi\)
\(282\) −40.4692 3.44110i −0.143508 0.0122025i
\(283\) 116.934i 0.413196i 0.978426 + 0.206598i \(0.0662392\pi\)
−0.978426 + 0.206598i \(0.933761\pi\)
\(284\) 44.6828 260.848i 0.157334 0.918477i
\(285\) 0 0
\(286\) −5.27572 + 62.0454i −0.0184466 + 0.216942i
\(287\) 65.7491i 0.229091i
\(288\) −87.4941 39.5067i −0.303799 0.137176i
\(289\) −246.411 −0.852631
\(290\) 0 0
\(291\) 220.478i 0.757658i
\(292\) −61.6341 10.5578i −0.211076 0.0361570i
\(293\) 68.3732 0.233356 0.116678 0.993170i \(-0.462776\pi\)
0.116678 + 0.993170i \(0.462776\pi\)
\(294\) 30.7166 361.244i 0.104478 1.22872i
\(295\) 0 0
\(296\) 146.547 + 38.1194i 0.495091 + 0.128782i
\(297\) −57.3672 −0.193155
\(298\) −100.094 8.51096i −0.335884 0.0285603i
\(299\) 22.2905i 0.0745503i
\(300\) 0 0
\(301\) 565.092 1.87738
\(302\) −36.1197 + 424.788i −0.119602 + 1.40658i
\(303\) 163.425i 0.539356i
\(304\) −149.070 + 422.349i −0.490361 + 1.38930i
\(305\) 0 0
\(306\) 39.0156 + 3.31750i 0.127502 + 0.0108415i
\(307\) 369.497i 1.20357i −0.798657 0.601786i \(-0.794456\pi\)
0.798657 0.601786i \(-0.205544\pi\)
\(308\) 539.560 + 92.4258i 1.75182 + 0.300084i
\(309\) 55.1580 0.178505
\(310\) 0 0
\(311\) 303.446i 0.975712i 0.872924 + 0.487856i \(0.162221\pi\)
−0.872924 + 0.487856i \(0.837779\pi\)
\(312\) 9.83707 37.8178i 0.0315291 0.121211i
\(313\) −297.693 −0.951097 −0.475549 0.879689i \(-0.657750\pi\)
−0.475549 + 0.879689i \(0.657750\pi\)
\(314\) −406.369 34.5536i −1.29417 0.110043i
\(315\) 0 0
\(316\) 83.1072 485.160i 0.262998 1.53532i
\(317\) −264.678 −0.834948 −0.417474 0.908689i \(-0.637084\pi\)
−0.417474 + 0.908689i \(0.637084\pi\)
\(318\) 12.0826 142.097i 0.0379955 0.446847i
\(319\) 559.931i 1.75527i
\(320\) 0 0
\(321\) −58.5280 −0.182330
\(322\) 195.255 + 16.6026i 0.606382 + 0.0515607i
\(323\) 182.682i 0.565580i
\(324\) 35.4832 + 6.07822i 0.109516 + 0.0187599i
\(325\) 0 0
\(326\) −36.5835 + 430.243i −0.112219 + 1.31976i
\(327\) 144.499i 0.441893i
\(328\) 41.0663 + 10.6820i 0.125202 + 0.0325672i
\(329\) −145.337 −0.441754
\(330\) 0 0
\(331\) 473.426i 1.43029i −0.698976 0.715145i \(-0.746361\pi\)
0.698976 0.715145i \(-0.253639\pi\)
\(332\) 67.3129 392.956i 0.202750 1.18360i
\(333\) −56.7838 −0.170522
\(334\) 43.2143 508.224i 0.129384 1.52163i
\(335\) 0 0
\(336\) −323.940 114.336i −0.964107 0.340285i
\(337\) −29.7588 −0.0883051 −0.0441526 0.999025i \(-0.514059\pi\)
−0.0441526 + 0.999025i \(0.514059\pi\)
\(338\) −320.936 27.2892i −0.949515 0.0807373i
\(339\) 193.636i 0.571197i
\(340\) 0 0
\(341\) −401.278 −1.17677
\(342\) 14.2300 167.353i 0.0416082 0.489335i
\(343\) 689.937i 2.01148i
\(344\) 91.8086 352.951i 0.266885 1.02602i
\(345\) 0 0
\(346\) 469.158 + 39.8925i 1.35595 + 0.115296i
\(347\) 306.190i 0.882391i 0.897411 + 0.441195i \(0.145445\pi\)
−0.897411 + 0.441195i \(0.854555\pi\)
\(348\) −59.3263 + 346.333i −0.170478 + 0.995208i
\(349\) 649.149 1.86002 0.930012 0.367528i \(-0.119796\pi\)
0.930012 + 0.367528i \(0.119796\pi\)
\(350\) 0 0
\(351\) 14.6536i 0.0417481i
\(352\) 145.389 321.988i 0.413036 0.914737i
\(353\) 275.547 0.780587 0.390293 0.920691i \(-0.372374\pi\)
0.390293 + 0.920691i \(0.372374\pi\)
\(354\) 36.9354 + 3.14062i 0.104337 + 0.00887181i
\(355\) 0 0
\(356\) 398.527 + 68.2671i 1.11946 + 0.191761i
\(357\) 140.117 0.392484
\(358\) −17.3972 + 204.600i −0.0485955 + 0.571510i
\(359\) 507.672i 1.41413i −0.707149 0.707065i \(-0.750019\pi\)
0.707149 0.707065i \(-0.249981\pi\)
\(360\) 0 0
\(361\) −422.594 −1.17062
\(362\) −113.236 9.62845i −0.312806 0.0265979i
\(363\) 1.53900i 0.00423968i
\(364\) 23.6088 137.823i 0.0648594 0.378633i
\(365\) 0 0
\(366\) −16.4737 + 193.740i −0.0450102 + 0.529344i
\(367\) 62.7671i 0.171028i −0.996337 0.0855138i \(-0.972747\pi\)
0.996337 0.0855138i \(-0.0272532\pi\)
\(368\) 42.0923 119.257i 0.114381 0.324068i
\(369\) −15.9123 −0.0431228
\(370\) 0 0
\(371\) 510.315i 1.37551i
\(372\) 248.202 + 42.5166i 0.667209 + 0.114292i
\(373\) 272.776 0.731302 0.365651 0.930752i \(-0.380846\pi\)
0.365651 + 0.930752i \(0.380846\pi\)
\(374\) −12.2087 + 143.581i −0.0326437 + 0.383908i
\(375\) 0 0
\(376\) −23.6124 + 90.7761i −0.0627990 + 0.241426i
\(377\) −143.026 −0.379379
\(378\) 128.359 + 10.9144i 0.339574 + 0.0288740i
\(379\) 376.828i 0.994270i −0.867673 0.497135i \(-0.834385\pi\)
0.867673 0.497135i \(-0.165615\pi\)
\(380\) 0 0
\(381\) −28.9001 −0.0758533
\(382\) 26.8565 315.847i 0.0703049 0.826825i
\(383\) 412.206i 1.07625i −0.842864 0.538127i \(-0.819132\pi\)
0.842864 0.538127i \(-0.180868\pi\)
\(384\) −124.042 + 183.754i −0.323027 + 0.478526i
\(385\) 0 0
\(386\) 312.337 + 26.5581i 0.809164 + 0.0688032i
\(387\) 136.761i 0.353387i
\(388\) −501.863 85.9685i −1.29346 0.221568i
\(389\) −161.289 −0.414623 −0.207312 0.978275i \(-0.566471\pi\)
−0.207312 + 0.978275i \(0.566471\pi\)
\(390\) 0 0
\(391\) 51.5834i 0.131927i
\(392\) −810.303 210.774i −2.06710 0.537689i
\(393\) −340.206 −0.865663
\(394\) −518.383 44.0782i −1.31569 0.111874i
\(395\) 0 0
\(396\) −22.3685 + 130.582i −0.0564861 + 0.329752i
\(397\) 186.505 0.469785 0.234893 0.972021i \(-0.424526\pi\)
0.234893 + 0.972021i \(0.424526\pi\)
\(398\) −2.37781 + 27.9643i −0.00597440 + 0.0702622i
\(399\) 601.014i 1.50630i
\(400\) 0 0
\(401\) 239.061 0.596162 0.298081 0.954541i \(-0.403653\pi\)
0.298081 + 0.954541i \(0.403653\pi\)
\(402\) 55.8164 + 4.74607i 0.138847 + 0.0118061i
\(403\) 102.501i 0.254344i
\(404\) −371.996 63.7223i −0.920781 0.157729i
\(405\) 0 0
\(406\) −106.529 + 1252.84i −0.262387 + 3.08582i
\(407\) 208.970i 0.513441i
\(408\) 22.7643 87.5155i 0.0557949 0.214499i
\(409\) 47.8016 0.116874 0.0584372 0.998291i \(-0.481388\pi\)
0.0584372 + 0.998291i \(0.481388\pi\)
\(410\) 0 0
\(411\) 202.870i 0.493601i
\(412\) 21.5071 125.553i 0.0522017 0.304741i
\(413\) 132.646 0.321177
\(414\) −4.01807 + 47.2547i −0.00970549 + 0.114142i
\(415\) 0 0
\(416\) −82.2470 37.1374i −0.197709 0.0892726i
\(417\) −324.306 −0.777713
\(418\) 615.875 + 52.3679i 1.47339 + 0.125282i
\(419\) 239.009i 0.570428i 0.958464 + 0.285214i \(0.0920647\pi\)
−0.958464 + 0.285214i \(0.907935\pi\)
\(420\) 0 0
\(421\) −257.592 −0.611857 −0.305929 0.952054i \(-0.598967\pi\)
−0.305929 + 0.952054i \(0.598967\pi\)
\(422\) 12.6229 148.452i 0.0299121 0.351783i
\(423\) 35.1738i 0.0831532i
\(424\) −318.738 82.9092i −0.751740 0.195541i
\(425\) 0 0
\(426\) 228.367 + 19.4181i 0.536073 + 0.0455823i
\(427\) 695.779i 1.62946i
\(428\) −22.8211 + 133.224i −0.0533204 + 0.311271i
\(429\) −53.9268 −0.125703
\(430\) 0 0
\(431\) 343.164i 0.796205i −0.917341 0.398103i \(-0.869669\pi\)
0.917341 0.398103i \(-0.130331\pi\)
\(432\) 27.6710 78.3984i 0.0640533 0.181478i
\(433\) 234.760 0.542171 0.271085 0.962555i \(-0.412617\pi\)
0.271085 + 0.962555i \(0.412617\pi\)
\(434\) 897.859 + 76.3450i 2.06880 + 0.175910i
\(435\) 0 0
\(436\) −328.916 56.3428i −0.754394 0.129227i
\(437\) 221.261 0.506317
\(438\) 4.58818 53.9595i 0.0104753 0.123195i
\(439\) 374.473i 0.853013i 0.904484 + 0.426507i \(0.140256\pi\)
−0.904484 + 0.426507i \(0.859744\pi\)
\(440\) 0 0
\(441\) 313.975 0.711962
\(442\) 36.6758 + 3.11854i 0.0829768 + 0.00705553i
\(443\) 108.557i 0.245050i 0.992465 + 0.122525i \(0.0390992\pi\)
−0.992465 + 0.122525i \(0.960901\pi\)
\(444\) −22.1410 + 129.254i −0.0498672 + 0.291113i
\(445\) 0 0
\(446\) −27.1111 + 318.842i −0.0607873 + 0.714891i
\(447\) 86.9963i 0.194623i
\(448\) −386.566 + 692.785i −0.862872 + 1.54640i
\(449\) −431.511 −0.961050 −0.480525 0.876981i \(-0.659554\pi\)
−0.480525 + 0.876981i \(0.659554\pi\)
\(450\) 0 0
\(451\) 58.5589i 0.129842i
\(452\) 440.762 + 75.5020i 0.975138 + 0.167040i
\(453\) −369.205 −0.815021
\(454\) −29.8193 + 350.692i −0.0656813 + 0.772448i
\(455\) 0 0
\(456\) −375.387 97.6448i −0.823218 0.214133i
\(457\) −219.747 −0.480847 −0.240424 0.970668i \(-0.577286\pi\)
−0.240424 + 0.970668i \(0.577286\pi\)
\(458\) −227.520 19.3460i −0.496768 0.0422402i
\(459\) 33.9104i 0.0738789i
\(460\) 0 0
\(461\) 223.434 0.484673 0.242337 0.970192i \(-0.422086\pi\)
0.242337 + 0.970192i \(0.422086\pi\)
\(462\) −40.1660 + 472.374i −0.0869394 + 1.02245i
\(463\) 740.855i 1.60012i −0.599921 0.800059i \(-0.704802\pi\)
0.599921 0.800059i \(-0.295198\pi\)
\(464\) 765.206 + 270.082i 1.64915 + 0.582074i
\(465\) 0 0
\(466\) −518.254 44.0672i −1.11213 0.0945648i
\(467\) 249.381i 0.534007i −0.963696 0.267004i \(-0.913966\pi\)
0.963696 0.267004i \(-0.0860336\pi\)
\(468\) 33.3552 + 5.71370i 0.0712718 + 0.0122088i
\(469\) 200.454 0.427406
\(470\) 0 0
\(471\) 353.196i 0.749885i
\(472\) 21.5506 82.8495i 0.0456580 0.175529i
\(473\) −503.294 −1.06405
\(474\) 424.748 + 36.1164i 0.896093 + 0.0761948i
\(475\) 0 0
\(476\) 54.6340 318.940i 0.114777 0.670043i
\(477\) 123.504 0.258918
\(478\) −23.7379 + 279.171i −0.0496609 + 0.584039i
\(479\) 210.915i 0.440324i −0.975463 0.220162i \(-0.929341\pi\)
0.975463 0.220162i \(-0.0706587\pi\)
\(480\) 0 0
\(481\) −53.3784 −0.110974
\(482\) 211.079 + 17.9480i 0.437923 + 0.0372366i
\(483\) 169.706i 0.351358i
\(484\) −3.50315 0.600085i −0.00723791 0.00123984i
\(485\) 0 0
\(486\) −2.64144 + 31.0648i −0.00543507 + 0.0639194i
\(487\) 710.541i 1.45902i 0.683972 + 0.729508i \(0.260251\pi\)
−0.683972 + 0.729508i \(0.739749\pi\)
\(488\) 434.576 + 113.041i 0.890525 + 0.231641i
\(489\) −373.946 −0.764715
\(490\) 0 0
\(491\) 697.876i 1.42134i −0.703528 0.710668i \(-0.748393\pi\)
0.703528 0.710668i \(-0.251607\pi\)
\(492\) −6.20449 + 36.2203i −0.0126108 + 0.0736185i
\(493\) −330.982 −0.671363
\(494\) 13.3766 157.316i 0.0270781 0.318454i
\(495\) 0 0
\(496\) 193.557 548.390i 0.390235 1.10563i
\(497\) 820.135 1.65017
\(498\) 344.025 + 29.2525i 0.690814 + 0.0587400i
\(499\) 875.602i 1.75471i 0.479838 + 0.877357i \(0.340695\pi\)
−0.479838 + 0.877357i \(0.659305\pi\)
\(500\) 0 0
\(501\) 441.723 0.881683
\(502\) −28.4468 + 334.550i −0.0566670 + 0.666434i
\(503\) 142.849i 0.283995i 0.989867 + 0.141997i \(0.0453524\pi\)
−0.989867 + 0.141997i \(0.954648\pi\)
\(504\) 74.8932 287.921i 0.148598 0.571271i
\(505\) 0 0
\(506\) −173.902 14.7869i −0.343681 0.0292232i
\(507\) 278.942i 0.550181i
\(508\) −11.2687 + 65.7837i −0.0221824 + 0.129496i
\(509\) −147.662 −0.290102 −0.145051 0.989424i \(-0.546335\pi\)
−0.145051 + 0.989424i \(0.546335\pi\)
\(510\) 0 0
\(511\) 193.785i 0.379227i
\(512\) 369.903 + 354.000i 0.722466 + 0.691407i
\(513\) 145.455 0.283537
\(514\) −396.268 33.6947i −0.770950 0.0655539i
\(515\) 0 0
\(516\) 311.301 + 53.3255i 0.603297 + 0.103344i
\(517\) 129.443 0.250374
\(518\) −39.7576 + 467.571i −0.0767520 + 0.902646i
\(519\) 407.769i 0.785682i
\(520\) 0 0
\(521\) −348.592 −0.669082 −0.334541 0.942381i \(-0.608581\pi\)
−0.334541 + 0.942381i \(0.608581\pi\)
\(522\) −303.207 25.7817i −0.580857 0.0493903i
\(523\) 370.317i 0.708063i 0.935233 + 0.354032i \(0.115189\pi\)
−0.935233 + 0.354032i \(0.884811\pi\)
\(524\) −132.652 + 774.392i −0.253153 + 1.47785i
\(525\) 0 0
\(526\) 81.4249 957.601i 0.154800 1.82053i
\(527\) 237.201i 0.450096i
\(528\) 288.514 + 101.832i 0.546429 + 0.192864i
\(529\) 466.523 0.881897
\(530\) 0 0
\(531\) 32.1024i 0.0604565i
\(532\) −1368.06 234.346i −2.57153 0.440500i
\(533\) −14.9580 −0.0280638
\(534\) −29.6672 + 348.902i −0.0555565 + 0.653375i
\(535\) 0 0
\(536\) 32.5670 125.201i 0.0607594 0.233584i
\(537\) −177.829 −0.331152
\(538\) −580.897 49.3937i −1.07973 0.0918098i
\(539\) 1155.46i 2.14371i
\(540\) 0 0
\(541\) −279.719 −0.517041 −0.258520 0.966006i \(-0.583235\pi\)
−0.258520 + 0.966006i \(0.583235\pi\)
\(542\) −29.4947 + 346.874i −0.0544183 + 0.639990i
\(543\) 98.4190i 0.181250i
\(544\) −190.331 85.9411i −0.349873 0.157980i
\(545\) 0 0
\(546\) 120.661 + 10.2598i 0.220991 + 0.0187909i
\(547\) 387.716i 0.708804i −0.935093 0.354402i \(-0.884685\pi\)
0.935093 0.354402i \(-0.115315\pi\)
\(548\) 461.782 + 79.1026i 0.842668 + 0.144348i
\(549\) −168.389 −0.306720
\(550\) 0 0
\(551\) 1419.71i 2.57660i
\(552\) 105.997 + 27.5716i 0.192023 + 0.0499485i
\(553\) 1525.40 2.75841
\(554\) 100.677 + 8.56059i 0.181728 + 0.0154523i
\(555\) 0 0
\(556\) −126.453 + 738.201i −0.227433 + 1.32770i
\(557\) −43.5564 −0.0781983 −0.0390991 0.999235i \(-0.512449\pi\)
−0.0390991 + 0.999235i \(0.512449\pi\)
\(558\) −18.4767 + 217.296i −0.0331123 + 0.389419i
\(559\) 128.559i 0.229981i
\(560\) 0 0
\(561\) −124.794 −0.222449
\(562\) −131.628 11.1923i −0.234213 0.0199152i
\(563\) 361.646i 0.642355i −0.947019 0.321178i \(-0.895921\pi\)
0.947019 0.321178i \(-0.104079\pi\)
\(564\) −80.0642 13.7149i −0.141958 0.0243172i
\(565\) 0 0
\(566\) −19.8144 + 233.028i −0.0350078 + 0.411710i
\(567\) 111.563i 0.196760i
\(568\) 133.245 512.248i 0.234586 0.901845i
\(569\) 888.559 1.56161 0.780807 0.624772i \(-0.214808\pi\)
0.780807 + 0.624772i \(0.214808\pi\)
\(570\) 0 0
\(571\) 447.745i 0.784142i 0.919935 + 0.392071i \(0.128241\pi\)
−0.919935 + 0.392071i \(0.871759\pi\)
\(572\) −21.0270 + 122.751i −0.0367605 + 0.214599i
\(573\) 274.519 0.479090
\(574\) −11.1411 + 131.025i −0.0194096 + 0.228267i
\(575\) 0 0
\(576\) −167.665 93.5551i −0.291085 0.162422i
\(577\) −1069.90 −1.85425 −0.927124 0.374756i \(-0.877727\pi\)
−0.927124 + 0.374756i \(0.877727\pi\)
\(578\) −491.049 41.7539i −0.849566 0.0722386i
\(579\) 271.468i 0.468857i
\(580\) 0 0
\(581\) 1235.50 2.12651
\(582\) 37.3598 439.371i 0.0641921 0.754934i
\(583\) 454.508i 0.779602i
\(584\) −121.036 31.4836i −0.207253 0.0539102i
\(585\) 0 0
\(586\) 136.255 + 11.5857i 0.232517 + 0.0197709i
\(587\) 129.637i 0.220847i −0.993885 0.110424i \(-0.964779\pi\)
0.993885 0.110424i \(-0.0352208\pi\)
\(588\) 122.425 714.685i 0.208205 1.21545i
\(589\) 1017.44 1.72741
\(590\) 0 0
\(591\) 450.553i 0.762357i
\(592\) 285.581 + 100.797i 0.482400 + 0.170265i
\(593\) −892.757 −1.50549 −0.752746 0.658311i \(-0.771271\pi\)
−0.752746 + 0.658311i \(0.771271\pi\)
\(594\) −114.322 9.72079i −0.192461 0.0163650i
\(595\) 0 0
\(596\) −198.025 33.9214i −0.332257 0.0569151i
\(597\) −24.3052 −0.0407123
\(598\) −3.77710 + 44.4208i −0.00631623 + 0.0742823i
\(599\) 1030.62i 1.72057i −0.509816 0.860284i \(-0.670286\pi\)
0.509816 0.860284i \(-0.329714\pi\)
\(600\) 0 0
\(601\) −815.961 −1.35767 −0.678836 0.734289i \(-0.737515\pi\)
−0.678836 + 0.734289i \(0.737515\pi\)
\(602\) 1126.12 + 95.7540i 1.87063 + 0.159060i
\(603\) 48.5128i 0.0804525i
\(604\) −143.959 + 840.401i −0.238343 + 1.39139i
\(605\) 0 0
\(606\) 27.6921 325.675i 0.0456966 0.537417i
\(607\) 842.678i 1.38827i −0.719847 0.694133i \(-0.755788\pi\)
0.719847 0.694133i \(-0.244212\pi\)
\(608\) −368.634 + 816.400i −0.606305 + 1.34276i
\(609\) −1088.91 −1.78803
\(610\) 0 0
\(611\) 33.0644i 0.0541152i
\(612\) 77.1885 + 13.2223i 0.126125 + 0.0216050i
\(613\) 731.088 1.19264 0.596320 0.802747i \(-0.296629\pi\)
0.596320 + 0.802747i \(0.296629\pi\)
\(614\) 62.6107 736.336i 0.101972 1.19924i
\(615\) 0 0
\(616\) 1059.58 + 275.615i 1.72009 + 0.447426i
\(617\) 919.609 1.49045 0.745226 0.666812i \(-0.232342\pi\)
0.745226 + 0.666812i \(0.232342\pi\)
\(618\) 109.919 + 9.34645i 0.177863 + 0.0151237i
\(619\) 688.974i 1.11304i −0.830833 0.556522i \(-0.812135\pi\)
0.830833 0.556522i \(-0.187865\pi\)
\(620\) 0 0
\(621\) −41.0715 −0.0661377
\(622\) −51.4186 + 604.711i −0.0826665 + 0.972203i
\(623\) 1253.01i 2.01126i
\(624\) 26.0116 73.6968i 0.0416852 0.118104i
\(625\) 0 0
\(626\) −593.246 50.4438i −0.947678 0.0805811i
\(627\) 535.288i 0.853729i
\(628\) −803.960 137.717i −1.28019 0.219295i
\(629\) −123.525 −0.196383
\(630\) 0 0
\(631\) 418.968i 0.663975i −0.943284 0.331987i \(-0.892281\pi\)
0.943284 0.331987i \(-0.107719\pi\)
\(632\) 247.827 952.749i 0.392131 1.50751i
\(633\) 129.027 0.203835
\(634\) −527.454 44.8494i −0.831946 0.0707404i
\(635\) 0 0
\(636\) 48.1565 281.126i 0.0757177 0.442022i
\(637\) 295.146 0.463337
\(638\) 94.8795 1115.83i 0.148714 1.74896i
\(639\) 198.485i 0.310618i
\(640\) 0 0
\(641\) −47.2426 −0.0737014 −0.0368507 0.999321i \(-0.511733\pi\)
−0.0368507 + 0.999321i \(0.511733\pi\)
\(642\) −116.635 9.91749i −0.181675 0.0154478i
\(643\) 710.880i 1.10557i 0.833325 + 0.552784i \(0.186435\pi\)
−0.833325 + 0.552784i \(0.813565\pi\)
\(644\) 386.293 + 66.1714i 0.599834 + 0.102751i
\(645\) 0 0
\(646\) 30.9553 364.051i 0.0479184 0.563547i
\(647\) 468.195i 0.723641i 0.932248 + 0.361820i \(0.117845\pi\)
−0.932248 + 0.361820i \(0.882155\pi\)
\(648\) 69.6812 + 18.1253i 0.107533 + 0.0279711i
\(649\) −118.140 −0.182034
\(650\) 0 0
\(651\) 780.375i 1.19873i
\(652\) −145.808 + 851.192i −0.223632 + 1.30551i
\(653\) −551.066 −0.843900 −0.421950 0.906619i \(-0.638654\pi\)
−0.421950 + 0.906619i \(0.638654\pi\)
\(654\) 24.4852 287.959i 0.0374391 0.440304i
\(655\) 0 0
\(656\) 80.0271 + 28.2459i 0.121993 + 0.0430578i
\(657\) 46.8989 0.0713834
\(658\) −289.629 24.6272i −0.440165 0.0374273i
\(659\) 158.259i 0.240151i 0.992765 + 0.120075i \(0.0383136\pi\)
−0.992765 + 0.120075i \(0.961686\pi\)
\(660\) 0 0
\(661\) 92.4953 0.139932 0.0699662 0.997549i \(-0.477711\pi\)
0.0699662 + 0.997549i \(0.477711\pi\)
\(662\) 80.2214 943.447i 0.121180 1.42515i
\(663\) 31.8768i 0.0480796i
\(664\) 200.728 771.681i 0.302301 1.16217i
\(665\) 0 0
\(666\) −113.159 9.62194i −0.169909 0.0144474i
\(667\) 400.877i 0.601015i
\(668\) 172.236 1005.47i 0.257838 1.50520i
\(669\) −277.121 −0.414232
\(670\) 0 0
\(671\) 619.690i 0.923532i
\(672\) −626.176 282.741i −0.931810 0.420745i
\(673\) −956.062 −1.42060 −0.710299 0.703900i \(-0.751440\pi\)
−0.710299 + 0.703900i \(0.751440\pi\)
\(674\) −59.3037 5.04259i −0.0879876 0.00748159i
\(675\) 0 0
\(676\) −634.940 108.764i −0.939261 0.160894i
\(677\) −1116.67 −1.64944 −0.824719 0.565543i \(-0.808667\pi\)
−0.824719 + 0.565543i \(0.808667\pi\)
\(678\) −32.8113 + 385.879i −0.0483942 + 0.569143i
\(679\) 1577.92i 2.32388i
\(680\) 0 0
\(681\) −304.804 −0.447583
\(682\) −799.671 67.9961i −1.17254 0.0997010i
\(683\) 826.776i 1.21051i 0.796033 + 0.605254i \(0.206928\pi\)
−0.796033 + 0.605254i \(0.793072\pi\)
\(684\) 56.7153 331.090i 0.0829172 0.484050i
\(685\) 0 0
\(686\) 116.909 1374.91i 0.170421 2.00424i
\(687\) 197.749i 0.287844i
\(688\) 242.764 687.806i 0.352855 0.999718i
\(689\) 116.097 0.168501
\(690\) 0 0
\(691\) 965.432i 1.39715i 0.715536 + 0.698576i \(0.246182\pi\)
−0.715536 + 0.698576i \(0.753818\pi\)
\(692\) 928.183 + 158.996i 1.34130 + 0.229764i
\(693\) −410.564 −0.592444
\(694\) −51.8834 + 610.177i −0.0747600 + 0.879218i
\(695\) 0 0
\(696\) −176.912 + 680.122i −0.254183 + 0.977186i
\(697\) −34.6149 −0.0496627
\(698\) 1293.63 + 109.997i 1.85334 + 0.157589i
\(699\) 450.441i 0.644408i
\(700\) 0 0
\(701\) −1109.94 −1.58337 −0.791686 0.610928i \(-0.790797\pi\)
−0.791686 + 0.610928i \(0.790797\pi\)
\(702\) −2.48303 + 29.2018i −0.00353708 + 0.0415980i
\(703\) 529.845i 0.753691i
\(704\) 344.292 617.024i 0.489052 0.876454i
\(705\) 0 0
\(706\) 549.113 + 46.6911i 0.777780 + 0.0661347i
\(707\) 1169.60i 1.65431i
\(708\) 73.0730 + 12.5173i 0.103210 + 0.0176798i
\(709\) −964.244 −1.36001 −0.680003 0.733210i \(-0.738021\pi\)
−0.680003 + 0.733210i \(0.738021\pi\)
\(710\) 0 0
\(711\) 369.170i 0.519226i
\(712\) 782.620 + 203.573i 1.09919 + 0.285917i
\(713\) −287.292 −0.402934
\(714\) 279.226 + 23.7426i 0.391073 + 0.0332529i
\(715\) 0 0
\(716\) −69.3385 + 404.782i −0.0968415 + 0.565338i
\(717\) −242.641 −0.338412
\(718\) 86.0244 1011.69i 0.119811 1.40904i
\(719\) 190.820i 0.265396i 0.991157 + 0.132698i \(0.0423641\pi\)
−0.991157 + 0.132698i \(0.957636\pi\)
\(720\) 0 0
\(721\) 394.754 0.547509
\(722\) −842.149 71.6080i −1.16641 0.0991801i
\(723\) 183.459i 0.253747i
\(724\) −224.026 38.3753i −0.309428 0.0530046i
\(725\) 0 0
\(726\) 0.260782 3.06694i 0.000359204 0.00422443i
\(727\) 202.134i 0.278039i −0.990290 0.139019i \(-0.955605\pi\)
0.990290 0.139019i \(-0.0443951\pi\)
\(728\) 70.4017 270.654i 0.0967056 0.371777i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 297.503i 0.406981i
\(732\) −65.6579 + 383.295i −0.0896966 + 0.523627i
\(733\) 962.435 1.31301 0.656504 0.754322i \(-0.272034\pi\)
0.656504 + 0.754322i \(0.272034\pi\)
\(734\) 10.6358 125.083i 0.0144902 0.170413i
\(735\) 0 0
\(736\) 104.090 230.524i 0.141426 0.313212i
\(737\) −178.532 −0.242242
\(738\) −31.7102 2.69632i −0.0429677 0.00365355i
\(739\) 932.112i 1.26132i 0.776061 + 0.630658i \(0.217215\pi\)
−0.776061 + 0.630658i \(0.782785\pi\)
\(740\) 0 0
\(741\) 136.731 0.184523
\(742\) 86.4722 1016.96i 0.116539 1.37057i
\(743\) 1153.70i 1.55276i −0.630266 0.776379i \(-0.717054\pi\)
0.630266 0.776379i \(-0.282946\pi\)
\(744\) 487.414 + 126.785i 0.655127 + 0.170410i
\(745\) 0 0
\(746\) 543.590 + 46.2215i 0.728672 + 0.0619591i
\(747\) 299.010i 0.400281i
\(748\) −48.6594 + 284.062i −0.0650526 + 0.379762i
\(749\) −418.872 −0.559242
\(750\) 0 0
\(751\) 204.359i 0.272116i 0.990701 + 0.136058i \(0.0434434\pi\)
−0.990701 + 0.136058i \(0.956557\pi\)
\(752\) −62.4369 + 176.898i −0.0830279 + 0.235237i
\(753\) −290.774 −0.386155
\(754\) −285.023 24.2356i −0.378015 0.0321427i
\(755\) 0 0
\(756\) 253.945 + 43.5005i 0.335906 + 0.0575403i
\(757\) 216.739 0.286314 0.143157 0.989700i \(-0.454275\pi\)
0.143157 + 0.989700i \(0.454275\pi\)
\(758\) 63.8530 750.947i 0.0842388 0.990695i
\(759\) 151.147i 0.199140i
\(760\) 0 0
\(761\) 1324.78 1.74085 0.870424 0.492303i \(-0.163845\pi\)
0.870424 + 0.492303i \(0.163845\pi\)
\(762\) −57.5924 4.89708i −0.0755805 0.00642662i
\(763\) 1034.15i 1.35537i
\(764\) 107.040 624.872i 0.140104 0.817895i
\(765\) 0 0
\(766\) 69.8477 821.447i 0.0911849 1.07238i
\(767\) 30.1772i 0.0393444i
\(768\) −278.330 + 345.167i −0.362409 + 0.449437i
\(769\) 444.088 0.577488 0.288744 0.957406i \(-0.406762\pi\)
0.288744 + 0.957406i \(0.406762\pi\)
\(770\) 0 0
\(771\) 344.417i 0.446714i
\(772\) 617.928 + 105.850i 0.800425 + 0.137112i
\(773\) 751.987 0.972817 0.486408 0.873732i \(-0.338307\pi\)
0.486408 + 0.873732i \(0.338307\pi\)
\(774\) −23.1739 + 272.538i −0.0299405 + 0.352117i
\(775\) 0 0
\(776\) −985.550 256.359i −1.27004 0.330359i
\(777\) −406.389 −0.523023
\(778\) −321.417 27.3301i −0.413133 0.0351287i
\(779\) 148.476i 0.190599i
\(780\) 0 0
\(781\) −730.446 −0.935271
\(782\) −8.74073 + 102.796i −0.0111774 + 0.131452i
\(783\) 263.533i 0.336568i
\(784\) −1579.06 557.337i −2.01411 0.710889i
\(785\) 0 0
\(786\) −677.965 57.6474i −0.862550 0.0733427i
\(787\)