Properties

Label 1050.3.q.e.199.10
Level $1050$
Weight $3$
Character 1050.199
Analytic conductor $28.610$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.10
Character \(\chi\) \(=\) 1050.199
Dual form 1050.3.q.e.649.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(2.86123 + 6.38854i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(2.86123 + 6.38854i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-9.98749 + 17.2988i) q^{11} +(-1.73205 - 3.00000i) q^{12} -3.49788 q^{13} +(8.02165 + 5.80113i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(9.12112 - 15.7982i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(21.3143 - 12.3058i) q^{19} +(12.0607 + 1.24079i) q^{21} +28.2489i q^{22} +(21.8155 - 12.5952i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-4.28401 + 2.47338i) q^{26} -5.19615 q^{27} +(13.9265 + 1.43274i) q^{28} +53.1223 q^{29} +(26.0944 + 15.0656i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(17.2988 + 29.9625i) q^{33} -25.7984i q^{34} -6.00000 q^{36} +(40.5034 - 23.3846i) q^{37} +(17.4030 - 30.1429i) q^{38} +(-3.02925 + 5.24682i) q^{39} -31.5250i q^{41} +(15.6487 - 7.00855i) q^{42} +64.4116i q^{43} +(19.9750 + 34.5977i) q^{44} +(17.8123 - 30.8518i) q^{46} +(14.0313 + 24.3029i) q^{47} -6.92820 q^{48} +(-32.6268 + 36.5581i) q^{49} +(-15.7982 - 27.3634i) q^{51} +(-3.49788 + 6.05851i) q^{52} +(56.1833 + 32.4374i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(18.0695 - 8.09277i) q^{56} -42.6285i q^{57} +(65.0613 - 37.5631i) q^{58} +(-86.7684 - 50.0958i) q^{59} +(6.94896 - 4.01198i) q^{61} +42.6119 q^{62} +(12.3061 - 17.0165i) q^{63} -8.00000 q^{64} +(42.3733 + 24.4642i) q^{66} +(14.0844 + 8.13165i) q^{67} +(-18.2422 - 31.5965i) q^{68} -43.6310i q^{69} -107.725 q^{71} +(-7.34847 + 4.24264i) q^{72} +(-25.8303 + 44.7395i) q^{73} +(33.0709 - 57.2804i) q^{74} -49.2232i q^{76} +(-139.091 - 14.3095i) q^{77} +8.56803i q^{78} +(-10.9877 - 19.0313i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-22.2916 - 38.6101i) q^{82} -0.417479 q^{83} +(14.2098 - 19.6489i) q^{84} +(45.5459 + 78.8878i) q^{86} +(46.0053 - 79.6835i) q^{87} +(48.9285 + 28.2489i) q^{88} +(96.3110 - 55.6052i) q^{89} +(-10.0082 - 22.3463i) q^{91} -50.3807i q^{92} +(45.1968 - 26.0944i) q^{93} +(34.3695 + 19.8432i) q^{94} +(-8.48528 + 4.89898i) q^{96} +74.2244 q^{97} +(-14.1090 + 67.8449i) q^{98} +59.9249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 0.707107i 0.612372 0.353553i
\(3\) 0.866025 1.50000i 0.288675 0.500000i
\(4\) 1.00000 1.73205i 0.250000 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) 2.86123 + 6.38854i 0.408747 + 0.912648i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 2.59808i −0.166667 0.288675i
\(10\) 0 0
\(11\) −9.98749 + 17.2988i −0.907953 + 1.57262i −0.0910503 + 0.995846i \(0.529022\pi\)
−0.816903 + 0.576775i \(0.804311\pi\)
\(12\) −1.73205 3.00000i −0.144338 0.250000i
\(13\) −3.49788 −0.269068 −0.134534 0.990909i \(-0.542954\pi\)
−0.134534 + 0.990909i \(0.542954\pi\)
\(14\) 8.02165 + 5.80113i 0.572975 + 0.414367i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 9.12112 15.7982i 0.536536 0.929308i −0.462551 0.886593i \(-0.653066\pi\)
0.999087 0.0427155i \(-0.0136009\pi\)
\(18\) −3.67423 2.12132i −0.204124 0.117851i
\(19\) 21.3143 12.3058i 1.12180 0.647673i 0.179942 0.983677i \(-0.442409\pi\)
0.941861 + 0.336004i \(0.109076\pi\)
\(20\) 0 0
\(21\) 12.0607 + 1.24079i 0.574319 + 0.0590854i
\(22\) 28.2489i 1.28404i
\(23\) 21.8155 12.5952i 0.948500 0.547617i 0.0558853 0.998437i \(-0.482202\pi\)
0.892615 + 0.450820i \(0.148869\pi\)
\(24\) −4.24264 2.44949i −0.176777 0.102062i
\(25\) 0 0
\(26\) −4.28401 + 2.47338i −0.164770 + 0.0951299i
\(27\) −5.19615 −0.192450
\(28\) 13.9265 + 1.43274i 0.497375 + 0.0511694i
\(29\) 53.1223 1.83180 0.915902 0.401402i \(-0.131477\pi\)
0.915902 + 0.401402i \(0.131477\pi\)
\(30\) 0 0
\(31\) 26.0944 + 15.0656i 0.841754 + 0.485987i 0.857860 0.513883i \(-0.171794\pi\)
−0.0161061 + 0.999870i \(0.505127\pi\)
\(32\) −4.89898 2.82843i −0.153093 0.0883883i
\(33\) 17.2988 + 29.9625i 0.524207 + 0.907953i
\(34\) 25.7984i 0.758777i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 40.5034 23.3846i 1.09469 0.632017i 0.159866 0.987139i \(-0.448894\pi\)
0.934820 + 0.355122i \(0.115561\pi\)
\(38\) 17.4030 30.1429i 0.457974 0.793234i
\(39\) −3.02925 + 5.24682i −0.0776732 + 0.134534i
\(40\) 0 0
\(41\) 31.5250i 0.768903i −0.923145 0.384452i \(-0.874391\pi\)
0.923145 0.384452i \(-0.125609\pi\)
\(42\) 15.6487 7.00855i 0.372587 0.166870i
\(43\) 64.4116i 1.49794i 0.662602 + 0.748972i \(0.269452\pi\)
−0.662602 + 0.748972i \(0.730548\pi\)
\(44\) 19.9750 + 34.5977i 0.453977 + 0.786311i
\(45\) 0 0
\(46\) 17.8123 30.8518i 0.387223 0.670691i
\(47\) 14.0313 + 24.3029i 0.298538 + 0.517083i 0.975802 0.218657i \(-0.0701677\pi\)
−0.677264 + 0.735740i \(0.736834\pi\)
\(48\) −6.92820 −0.144338
\(49\) −32.6268 + 36.5581i −0.665852 + 0.746084i
\(50\) 0 0
\(51\) −15.7982 27.3634i −0.309769 0.536536i
\(52\) −3.49788 + 6.05851i −0.0672670 + 0.116510i
\(53\) 56.1833 + 32.4374i 1.06006 + 0.612027i 0.925449 0.378872i \(-0.123688\pi\)
0.134612 + 0.990898i \(0.457021\pi\)
\(54\) −6.36396 + 3.67423i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) 18.0695 8.09277i 0.322670 0.144514i
\(57\) 42.6285i 0.747869i
\(58\) 65.0613 37.5631i 1.12175 0.647640i
\(59\) −86.7684 50.0958i −1.47065 0.849081i −0.471194 0.882029i \(-0.656177\pi\)
−0.999457 + 0.0329486i \(0.989510\pi\)
\(60\) 0 0
\(61\) 6.94896 4.01198i 0.113917 0.0657702i −0.441959 0.897035i \(-0.645716\pi\)
0.555876 + 0.831265i \(0.312383\pi\)
\(62\) 42.6119 0.687289
\(63\) 12.3061 17.0165i 0.195334 0.270103i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 42.3733 + 24.4642i 0.642020 + 0.370670i
\(67\) 14.0844 + 8.13165i 0.210215 + 0.121368i 0.601411 0.798939i \(-0.294605\pi\)
−0.391196 + 0.920307i \(0.627939\pi\)
\(68\) −18.2422 31.5965i −0.268268 0.464654i
\(69\) 43.6310i 0.632333i
\(70\) 0 0
\(71\) −107.725 −1.51725 −0.758625 0.651528i \(-0.774128\pi\)
−0.758625 + 0.651528i \(0.774128\pi\)
\(72\) −7.34847 + 4.24264i −0.102062 + 0.0589256i
\(73\) −25.8303 + 44.7395i −0.353840 + 0.612870i −0.986919 0.161218i \(-0.948458\pi\)
0.633078 + 0.774088i \(0.281791\pi\)
\(74\) 33.0709 57.2804i 0.446904 0.774060i
\(75\) 0 0
\(76\) 49.2232i 0.647673i
\(77\) −139.091 14.3095i −1.80637 0.185838i
\(78\) 8.56803i 0.109846i
\(79\) −10.9877 19.0313i −0.139085 0.240903i 0.788065 0.615592i \(-0.211083\pi\)
−0.927151 + 0.374689i \(0.877750\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −22.2916 38.6101i −0.271848 0.470855i
\(83\) −0.417479 −0.00502987 −0.00251494 0.999997i \(-0.500801\pi\)
−0.00251494 + 0.999997i \(0.500801\pi\)
\(84\) 14.2098 19.6489i 0.169164 0.233916i
\(85\) 0 0
\(86\) 45.5459 + 78.8878i 0.529603 + 0.917300i
\(87\) 46.0053 79.6835i 0.528796 0.915902i
\(88\) 48.9285 + 28.2489i 0.556006 + 0.321010i
\(89\) 96.3110 55.6052i 1.08215 0.624778i 0.150672 0.988584i \(-0.451856\pi\)
0.931475 + 0.363806i \(0.118523\pi\)
\(90\) 0 0
\(91\) −10.0082 22.3463i −0.109981 0.245564i
\(92\) 50.3807i 0.547617i
\(93\) 45.1968 26.0944i 0.485987 0.280585i
\(94\) 34.3695 + 19.8432i 0.365633 + 0.211098i
\(95\) 0 0
\(96\) −8.48528 + 4.89898i −0.0883883 + 0.0510310i
\(97\) 74.2244 0.765200 0.382600 0.923914i \(-0.375029\pi\)
0.382600 + 0.923914i \(0.375029\pi\)
\(98\) −14.1090 + 67.8449i −0.143969 + 0.692295i
\(99\) 59.9249 0.605302
\(100\) 0 0
\(101\) 75.8587 + 43.7970i 0.751076 + 0.433634i 0.826083 0.563549i \(-0.190564\pi\)
−0.0750065 + 0.997183i \(0.523898\pi\)
\(102\) −38.6976 22.3421i −0.379388 0.219040i
\(103\) 69.5206 + 120.413i 0.674957 + 1.16906i 0.976482 + 0.215601i \(0.0691711\pi\)
−0.301525 + 0.953458i \(0.597496\pi\)
\(104\) 9.89350i 0.0951299i
\(105\) 0 0
\(106\) 91.7469 0.865537
\(107\) −131.800 + 76.0949i −1.23178 + 0.711168i −0.967400 0.253252i \(-0.918500\pi\)
−0.264378 + 0.964419i \(0.585167\pi\)
\(108\) −5.19615 + 9.00000i −0.0481125 + 0.0833333i
\(109\) 32.3777 56.0798i 0.297043 0.514494i −0.678415 0.734679i \(-0.737333\pi\)
0.975458 + 0.220185i \(0.0706662\pi\)
\(110\) 0 0
\(111\) 81.0068i 0.729791i
\(112\) 16.4081 22.6887i 0.146501 0.202577i
\(113\) 3.25860i 0.0288372i 0.999896 + 0.0144186i \(0.00458974\pi\)
−0.999896 + 0.0144186i \(0.995410\pi\)
\(114\) −30.1429 52.2090i −0.264411 0.457974i
\(115\) 0 0
\(116\) 53.1223 92.0105i 0.457951 0.793194i
\(117\) 5.24682 + 9.08776i 0.0448446 + 0.0776732i
\(118\) −141.692 −1.20078
\(119\) 127.025 + 13.0682i 1.06744 + 0.109817i
\(120\) 0 0
\(121\) −139.000 240.755i −1.14876 1.98971i
\(122\) 5.67380 9.82731i 0.0465066 0.0805517i
\(123\) −47.2875 27.3015i −0.384452 0.221963i
\(124\) 52.1887 30.1312i 0.420877 0.242993i
\(125\) 0 0
\(126\) 3.03931 29.5426i 0.0241215 0.234465i
\(127\) 88.5772i 0.697458i 0.937224 + 0.348729i \(0.113387\pi\)
−0.937224 + 0.348729i \(0.886613\pi\)
\(128\) −9.79796 + 5.65685i −0.0765466 + 0.0441942i
\(129\) 96.6174 + 55.7821i 0.748972 + 0.432419i
\(130\) 0 0
\(131\) −108.361 + 62.5621i −0.827181 + 0.477573i −0.852887 0.522096i \(-0.825150\pi\)
0.0257055 + 0.999670i \(0.491817\pi\)
\(132\) 69.1953 0.524207
\(133\) 139.601 + 100.957i 1.04963 + 0.759077i
\(134\) 22.9998 0.171640
\(135\) 0 0
\(136\) −44.6842 25.7984i −0.328560 0.189694i
\(137\) −33.7349 19.4769i −0.246240 0.142167i 0.371801 0.928312i \(-0.378740\pi\)
−0.618042 + 0.786145i \(0.712074\pi\)
\(138\) −30.8518 53.4368i −0.223564 0.387223i
\(139\) 98.9454i 0.711837i −0.934517 0.355919i \(-0.884168\pi\)
0.934517 0.355919i \(-0.115832\pi\)
\(140\) 0 0
\(141\) 48.6058 0.344722
\(142\) −131.935 + 76.1729i −0.929122 + 0.536429i
\(143\) 34.9351 60.5093i 0.244301 0.423142i
\(144\) −6.00000 + 10.3923i −0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) 73.0593i 0.500406i
\(147\) 26.5815 + 80.6004i 0.180827 + 0.548302i
\(148\) 93.5385i 0.632017i
\(149\) −93.2324 161.483i −0.625721 1.08378i −0.988401 0.151867i \(-0.951472\pi\)
0.362680 0.931914i \(-0.381862\pi\)
\(150\) 0 0
\(151\) −77.4202 + 134.096i −0.512716 + 0.888051i 0.487175 + 0.873304i \(0.338027\pi\)
−0.999891 + 0.0147462i \(0.995306\pi\)
\(152\) −34.8060 60.2858i −0.228987 0.396617i
\(153\) −54.7267 −0.357691
\(154\) −180.469 + 80.8265i −1.17188 + 0.524847i
\(155\) 0 0
\(156\) 6.05851 + 10.4936i 0.0388366 + 0.0672670i
\(157\) −25.1019 + 43.4777i −0.159885 + 0.276928i −0.934827 0.355104i \(-0.884446\pi\)
0.774942 + 0.632032i \(0.217779\pi\)
\(158\) −26.9143 15.5390i −0.170344 0.0983481i
\(159\) 97.3123 56.1833i 0.612027 0.353354i
\(160\) 0 0
\(161\) 142.884 + 103.331i 0.887477 + 0.641810i
\(162\) 12.7279i 0.0785674i
\(163\) −100.295 + 57.9054i −0.615308 + 0.355248i −0.775040 0.631912i \(-0.782270\pi\)
0.159732 + 0.987160i \(0.448937\pi\)
\(164\) −54.6029 31.5250i −0.332945 0.192226i
\(165\) 0 0
\(166\) −0.511306 + 0.295202i −0.00308015 + 0.00177833i
\(167\) −61.3210 −0.367191 −0.183596 0.983002i \(-0.558774\pi\)
−0.183596 + 0.983002i \(0.558774\pi\)
\(168\) 3.50949 34.1128i 0.0208898 0.203052i
\(169\) −156.765 −0.927602
\(170\) 0 0
\(171\) −63.9428 36.9174i −0.373934 0.215891i
\(172\) 111.564 + 64.4116i 0.648629 + 0.374486i
\(173\) 15.8508 + 27.4544i 0.0916232 + 0.158696i 0.908194 0.418549i \(-0.137461\pi\)
−0.816571 + 0.577245i \(0.804128\pi\)
\(174\) 130.123i 0.747831i
\(175\) 0 0
\(176\) 79.8999 0.453977
\(177\) −150.287 + 86.7684i −0.849081 + 0.490217i
\(178\) 78.6376 136.204i 0.441784 0.765193i
\(179\) 65.9472 114.224i 0.368420 0.638122i −0.620899 0.783891i \(-0.713232\pi\)
0.989319 + 0.145768i \(0.0465655\pi\)
\(180\) 0 0
\(181\) 55.1431i 0.304658i 0.988330 + 0.152329i \(0.0486773\pi\)
−0.988330 + 0.152329i \(0.951323\pi\)
\(182\) −28.0588 20.2917i −0.154169 0.111493i
\(183\) 13.8979i 0.0759449i
\(184\) −35.6246 61.7035i −0.193612 0.335345i
\(185\) 0 0
\(186\) 36.9030 63.9179i 0.198403 0.343645i
\(187\) 182.194 + 315.569i 0.974300 + 1.68754i
\(188\) 56.1252 0.298538
\(189\) −14.8674 33.1958i −0.0786633 0.175639i
\(190\) 0 0
\(191\) −97.5822 169.017i −0.510901 0.884907i −0.999920 0.0126340i \(-0.995978\pi\)
0.489019 0.872273i \(-0.337355\pi\)
\(192\) −6.92820 + 12.0000i −0.0360844 + 0.0625000i
\(193\) −302.035 174.380i −1.56495 0.903523i −0.996744 0.0806348i \(-0.974305\pi\)
−0.568204 0.822888i \(-0.692361\pi\)
\(194\) 90.9060 52.4846i 0.468588 0.270539i
\(195\) 0 0
\(196\) 30.6937 + 93.0693i 0.156601 + 0.474843i
\(197\) 56.3808i 0.286197i 0.989708 + 0.143098i \(0.0457066\pi\)
−0.989708 + 0.143098i \(0.954293\pi\)
\(198\) 73.3927 42.3733i 0.370670 0.214007i
\(199\) −148.357 85.6540i −0.745513 0.430422i 0.0785571 0.996910i \(-0.474969\pi\)
−0.824070 + 0.566487i \(0.808302\pi\)
\(200\) 0 0
\(201\) 24.3950 14.0844i 0.121368 0.0700718i
\(202\) 123.877 0.613251
\(203\) 151.995 + 339.374i 0.748744 + 1.67179i
\(204\) −63.1930 −0.309769
\(205\) 0 0
\(206\) 170.290 + 98.3169i 0.826650 + 0.477267i
\(207\) −65.4465 37.7856i −0.316167 0.182539i
\(208\) 6.99576 + 12.1170i 0.0336335 + 0.0582549i
\(209\) 491.616i 2.35223i
\(210\) 0 0
\(211\) 162.038 0.767954 0.383977 0.923343i \(-0.374554\pi\)
0.383977 + 0.923343i \(0.374554\pi\)
\(212\) 112.367 64.8748i 0.530031 0.306013i
\(213\) −93.2923 + 161.587i −0.437992 + 0.758625i
\(214\) −107.614 + 186.394i −0.502871 + 0.870999i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) −21.5851 + 209.811i −0.0994707 + 0.966870i
\(218\) 91.5779i 0.420082i
\(219\) 44.7395 + 77.4910i 0.204290 + 0.353840i
\(220\) 0 0
\(221\) −31.9046 + 55.2604i −0.144365 + 0.250047i
\(222\) −57.2804 99.2126i −0.258020 0.446904i
\(223\) 365.329 1.63825 0.819123 0.573618i \(-0.194461\pi\)
0.819123 + 0.573618i \(0.194461\pi\)
\(224\) 4.05241 39.3901i 0.0180911 0.175849i
\(225\) 0 0
\(226\) 2.30418 + 3.99096i 0.0101955 + 0.0176591i
\(227\) 128.937 223.325i 0.568004 0.983811i −0.428759 0.903419i \(-0.641049\pi\)
0.996763 0.0803928i \(-0.0256175\pi\)
\(228\) −73.8347 42.6285i −0.323837 0.186967i
\(229\) 13.3634 7.71538i 0.0583556 0.0336916i −0.470538 0.882380i \(-0.655940\pi\)
0.528894 + 0.848688i \(0.322607\pi\)
\(230\) 0 0
\(231\) −141.920 + 196.244i −0.614374 + 0.849539i
\(232\) 150.253i 0.647640i
\(233\) −108.553 + 62.6734i −0.465895 + 0.268984i −0.714520 0.699615i \(-0.753355\pi\)
0.248625 + 0.968600i \(0.420021\pi\)
\(234\) 12.8520 + 7.42013i 0.0549232 + 0.0317100i
\(235\) 0 0
\(236\) −173.537 + 100.192i −0.735326 + 0.424540i
\(237\) −38.0626 −0.160602
\(238\) 164.814 73.8151i 0.692496 0.310148i
\(239\) 3.62565 0.0151701 0.00758503 0.999971i \(-0.497586\pi\)
0.00758503 + 0.999971i \(0.497586\pi\)
\(240\) 0 0
\(241\) 83.6915 + 48.3193i 0.347268 + 0.200495i 0.663481 0.748193i \(-0.269078\pi\)
−0.316213 + 0.948688i \(0.602412\pi\)
\(242\) −340.479 196.575i −1.40694 0.812295i
\(243\) 7.79423 + 13.5000i 0.0320750 + 0.0555556i
\(244\) 16.0479i 0.0657702i
\(245\) 0 0
\(246\) −77.2202 −0.313903
\(247\) −74.5548 + 43.0442i −0.301841 + 0.174268i
\(248\) 42.6119 73.8060i 0.171822 0.297605i
\(249\) −0.361548 + 0.626219i −0.00145200 + 0.00251494i
\(250\) 0 0
\(251\) 29.7311i 0.118450i −0.998245 0.0592252i \(-0.981137\pi\)
0.998245 0.0592252i \(-0.0188630\pi\)
\(252\) −17.1674 38.3312i −0.0681245 0.152108i
\(253\) 503.177i 1.98884i
\(254\) 62.6336 + 108.484i 0.246589 + 0.427104i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −220.811 382.457i −0.859189 1.48816i −0.872704 0.488250i \(-0.837636\pi\)
0.0135154 0.999909i \(-0.495698\pi\)
\(258\) 157.776 0.611533
\(259\) 265.283 + 191.848i 1.02426 + 0.740728i
\(260\) 0 0
\(261\) −79.6835 138.016i −0.305301 0.528796i
\(262\) −88.4762 + 153.245i −0.337695 + 0.584905i
\(263\) −297.087 171.523i −1.12961 0.652180i −0.185772 0.982593i \(-0.559479\pi\)
−0.943836 + 0.330413i \(0.892812\pi\)
\(264\) 84.7466 48.9285i 0.321010 0.185335i
\(265\) 0 0
\(266\) 242.363 + 24.9341i 0.911139 + 0.0937371i
\(267\) 192.622i 0.721431i
\(268\) 28.1689 16.2633i 0.105108 0.0606840i
\(269\) −401.274 231.676i −1.49172 0.861247i −0.491769 0.870726i \(-0.663650\pi\)
−0.999955 + 0.00947852i \(0.996983\pi\)
\(270\) 0 0
\(271\) 211.814 122.291i 0.781600 0.451257i −0.0553967 0.998464i \(-0.517642\pi\)
0.836997 + 0.547207i \(0.184309\pi\)
\(272\) −72.9689 −0.268268
\(273\) −42.1869 4.34015i −0.154531 0.0158980i
\(274\) −55.0889 −0.201054
\(275\) 0 0
\(276\) −75.5711 43.6310i −0.273808 0.158083i
\(277\) 122.126 + 70.5092i 0.440887 + 0.254546i 0.703974 0.710226i \(-0.251407\pi\)
−0.263087 + 0.964772i \(0.584741\pi\)
\(278\) −69.9650 121.183i −0.251673 0.435910i
\(279\) 90.3935i 0.323991i
\(280\) 0 0
\(281\) 84.9953 0.302475 0.151237 0.988497i \(-0.451674\pi\)
0.151237 + 0.988497i \(0.451674\pi\)
\(282\) 59.5297 34.3695i 0.211098 0.121878i
\(283\) 58.3392 101.047i 0.206146 0.357055i −0.744351 0.667788i \(-0.767241\pi\)
0.950497 + 0.310733i \(0.100575\pi\)
\(284\) −107.725 + 186.585i −0.379312 + 0.656988i
\(285\) 0 0
\(286\) 98.8112i 0.345494i
\(287\) 201.399 90.2003i 0.701738 0.314287i
\(288\) 16.9706i 0.0589256i
\(289\) −21.8896 37.9138i −0.0757424 0.131190i
\(290\) 0 0
\(291\) 64.2802 111.337i 0.220894 0.382600i
\(292\) 51.6607 + 89.4789i 0.176920 + 0.306435i
\(293\) −131.882 −0.450110 −0.225055 0.974346i \(-0.572256\pi\)
−0.225055 + 0.974346i \(0.572256\pi\)
\(294\) 89.5487 + 79.9189i 0.304587 + 0.271833i
\(295\) 0 0
\(296\) −66.1417 114.561i −0.223452 0.387030i
\(297\) 51.8965 89.8874i 0.174736 0.302651i
\(298\) −228.372 131.851i −0.766348 0.442451i
\(299\) −76.3080 + 44.0565i −0.255211 + 0.147346i
\(300\) 0 0
\(301\) −411.496 + 184.296i −1.36710 + 0.612280i
\(302\) 218.977i 0.725090i
\(303\) 131.391 75.8587i 0.433634 0.250359i
\(304\) −85.2570 49.2232i −0.280451 0.161918i
\(305\) 0 0
\(306\) −67.0263 + 38.6976i −0.219040 + 0.126463i
\(307\) 429.871 1.40023 0.700115 0.714030i \(-0.253132\pi\)
0.700115 + 0.714030i \(0.253132\pi\)
\(308\) −163.875 + 226.603i −0.532063 + 0.735723i
\(309\) 240.826 0.779373
\(310\) 0 0
\(311\) −217.786 125.739i −0.700277 0.404305i 0.107174 0.994240i \(-0.465820\pi\)
−0.807451 + 0.589935i \(0.799153\pi\)
\(312\) 14.8403 + 8.56803i 0.0475649 + 0.0274616i
\(313\) 6.85166 + 11.8674i 0.0218903 + 0.0379151i 0.876763 0.480923i \(-0.159698\pi\)
−0.854873 + 0.518838i \(0.826365\pi\)
\(314\) 70.9988i 0.226111i
\(315\) 0 0
\(316\) −43.9509 −0.139085
\(317\) 28.5183 16.4651i 0.0899632 0.0519403i −0.454343 0.890827i \(-0.650126\pi\)
0.544307 + 0.838886i \(0.316793\pi\)
\(318\) 79.4551 137.620i 0.249859 0.432768i
\(319\) −530.558 + 918.954i −1.66319 + 2.88073i
\(320\) 0 0
\(321\) 263.601i 0.821186i
\(322\) 248.063 + 25.5204i 0.770381 + 0.0792560i
\(323\) 448.970i 1.39000i
\(324\) 9.00000 + 15.5885i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) −81.8906 + 141.839i −0.251198 + 0.435088i
\(327\) −56.0798 97.1331i −0.171498 0.297043i
\(328\) −89.1662 −0.271848
\(329\) −115.113 + 159.176i −0.349888 + 0.483816i
\(330\) 0 0
\(331\) 208.940 + 361.895i 0.631240 + 1.09334i 0.987299 + 0.158876i \(0.0507869\pi\)
−0.356059 + 0.934464i \(0.615880\pi\)
\(332\) −0.417479 + 0.723095i −0.00125747 + 0.00217800i
\(333\) −121.510 70.1539i −0.364895 0.210672i
\(334\) −75.1025 + 43.3605i −0.224858 + 0.129822i
\(335\) 0 0
\(336\) −19.8232 44.2611i −0.0589975 0.131729i
\(337\) 286.688i 0.850705i 0.905028 + 0.425353i \(0.139850\pi\)
−0.905028 + 0.425353i \(0.860150\pi\)
\(338\) −191.997 + 110.849i −0.568038 + 0.327957i
\(339\) 4.88790 + 2.82203i 0.0144186 + 0.00832458i
\(340\) 0 0
\(341\) −521.234 + 300.935i −1.52855 + 0.882507i
\(342\) −104.418 −0.305316
\(343\) −326.905 103.836i −0.953077 0.302729i
\(344\) 182.184 0.529603
\(345\) 0 0
\(346\) 38.8264 + 22.4164i 0.112215 + 0.0647874i
\(347\) 265.693 + 153.398i 0.765685 + 0.442069i 0.831333 0.555774i \(-0.187578\pi\)
−0.0656479 + 0.997843i \(0.520911\pi\)
\(348\) −92.0105 159.367i −0.264398 0.457951i
\(349\) 340.162i 0.974676i 0.873214 + 0.487338i \(0.162032\pi\)
−0.873214 + 0.487338i \(0.837968\pi\)
\(350\) 0 0
\(351\) 18.1755 0.0517821
\(352\) 97.8570 56.4978i 0.278003 0.160505i
\(353\) 187.501 324.761i 0.531165 0.920004i −0.468174 0.883636i \(-0.655088\pi\)
0.999338 0.0363676i \(-0.0115787\pi\)
\(354\) −122.709 + 212.538i −0.346636 + 0.600391i
\(355\) 0 0
\(356\) 222.421i 0.624778i
\(357\) 129.609 179.220i 0.363051 0.502018i
\(358\) 186.527i 0.521025i
\(359\) −164.750 285.356i −0.458915 0.794863i 0.539989 0.841672i \(-0.318428\pi\)
−0.998904 + 0.0468084i \(0.985095\pi\)
\(360\) 0 0
\(361\) 122.365 211.942i 0.338961 0.587098i
\(362\) 38.9920 + 67.5362i 0.107713 + 0.186564i
\(363\) −481.509 −1.32647
\(364\) −48.7132 5.01157i −0.133828 0.0137681i
\(365\) 0 0
\(366\) −9.82731 17.0214i −0.0268506 0.0465066i
\(367\) 13.5772 23.5163i 0.0369950 0.0640772i −0.846935 0.531696i \(-0.821555\pi\)
0.883930 + 0.467619i \(0.154888\pi\)
\(368\) −87.2620 50.3807i −0.237125 0.136904i
\(369\) −81.9044 + 47.2875i −0.221963 + 0.128151i
\(370\) 0 0
\(371\) −46.4745 + 451.740i −0.125268 + 1.21763i
\(372\) 104.377i 0.280585i
\(373\) 110.416 63.7488i 0.296022 0.170908i −0.344633 0.938738i \(-0.611996\pi\)
0.640654 + 0.767829i \(0.278663\pi\)
\(374\) 446.283 + 257.661i 1.19327 + 0.688934i
\(375\) 0 0
\(376\) 68.7390 39.6865i 0.182817 0.105549i
\(377\) −185.816 −0.492880
\(378\) −41.6817 30.1436i −0.110269 0.0797449i
\(379\) −319.795 −0.843785 −0.421893 0.906646i \(-0.638634\pi\)
−0.421893 + 0.906646i \(0.638634\pi\)
\(380\) 0 0
\(381\) 132.866 + 76.7101i 0.348729 + 0.201339i
\(382\) −239.027 138.002i −0.625724 0.361262i
\(383\) 204.471 + 354.155i 0.533867 + 0.924686i 0.999217 + 0.0395587i \(0.0125952\pi\)
−0.465350 + 0.885127i \(0.654071\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −493.221 −1.27777
\(387\) 167.346 96.6174i 0.432419 0.249657i
\(388\) 74.2244 128.560i 0.191300 0.331341i
\(389\) 193.576 335.284i 0.497626 0.861913i −0.502370 0.864652i \(-0.667539\pi\)
0.999996 + 0.00273932i \(0.000871952\pi\)
\(390\) 0 0
\(391\) 459.529i 1.17526i
\(392\) 103.402 + 92.2824i 0.263780 + 0.235414i
\(393\) 216.721i 0.551454i
\(394\) 39.8672 + 69.0521i 0.101186 + 0.175259i
\(395\) 0 0
\(396\) 59.9249 103.793i 0.151326 0.262104i
\(397\) −15.0556 26.0771i −0.0379234 0.0656853i 0.846441 0.532483i \(-0.178741\pi\)
−0.884364 + 0.466798i \(0.845408\pi\)
\(398\) −242.266 −0.608709
\(399\) 272.334 121.970i 0.682541 0.305689i
\(400\) 0 0
\(401\) −68.3852 118.447i −0.170537 0.295378i 0.768071 0.640365i \(-0.221217\pi\)
−0.938608 + 0.344987i \(0.887883\pi\)
\(402\) 19.9184 34.4997i 0.0495482 0.0858201i
\(403\) −91.2750 52.6977i −0.226489 0.130763i
\(404\) 151.717 87.5941i 0.375538 0.216817i
\(405\) 0 0
\(406\) 426.129 + 308.170i 1.04958 + 0.759038i
\(407\) 934.215i 2.29537i
\(408\) −77.3952 + 44.6842i −0.189694 + 0.109520i
\(409\) 426.838 + 246.435i 1.04361 + 0.602531i 0.920855 0.389906i \(-0.127493\pi\)
0.122759 + 0.992437i \(0.460826\pi\)
\(410\) 0 0
\(411\) −58.4306 + 33.7349i −0.142167 + 0.0820801i
\(412\) 278.082 0.674957
\(413\) 71.7744 697.659i 0.173788 1.68925i
\(414\) −106.874 −0.258149
\(415\) 0 0
\(416\) 17.1361 + 9.89350i 0.0411924 + 0.0237825i
\(417\) −148.418 85.6892i −0.355919 0.205490i
\(418\) 347.625 + 602.104i 0.831638 + 1.44044i
\(419\) 311.640i 0.743771i 0.928279 + 0.371885i \(0.121289\pi\)
−0.928279 + 0.371885i \(0.878711\pi\)
\(420\) 0 0
\(421\) −539.935 −1.28250 −0.641252 0.767330i \(-0.721585\pi\)
−0.641252 + 0.767330i \(0.721585\pi\)
\(422\) 198.456 114.578i 0.470274 0.271513i
\(423\) 42.0939 72.9087i 0.0995127 0.172361i
\(424\) 91.7469 158.910i 0.216384 0.374788i
\(425\) 0 0
\(426\) 263.871i 0.619414i
\(427\) 45.5132 + 32.9145i 0.106588 + 0.0770831i
\(428\) 304.380i 0.711168i
\(429\) −60.5093 104.805i −0.141047 0.244301i
\(430\) 0 0
\(431\) 314.021 543.900i 0.728586 1.26195i −0.228895 0.973451i \(-0.573511\pi\)
0.957481 0.288497i \(-0.0931555\pi\)
\(432\) 10.3923 + 18.0000i 0.0240563 + 0.0416667i
\(433\) −706.789 −1.63231 −0.816153 0.577836i \(-0.803897\pi\)
−0.816153 + 0.577836i \(0.803897\pi\)
\(434\) 121.922 + 272.228i 0.280927 + 0.627253i
\(435\) 0 0
\(436\) −64.7554 112.160i −0.148522 0.257247i
\(437\) 309.987 536.914i 0.709353 1.22864i
\(438\) 109.589 + 63.2712i 0.250203 + 0.144455i
\(439\) −564.452 + 325.886i −1.28577 + 0.742338i −0.977896 0.209090i \(-0.932950\pi\)
−0.307871 + 0.951428i \(0.599617\pi\)
\(440\) 0 0
\(441\) 143.921 + 29.9297i 0.326351 + 0.0678677i
\(442\) 90.2398i 0.204162i
\(443\) −20.4605 + 11.8129i −0.0461863 + 0.0266657i −0.522915 0.852385i \(-0.675156\pi\)
0.476729 + 0.879050i \(0.341822\pi\)
\(444\) −140.308 81.0068i −0.316009 0.182448i
\(445\) 0 0
\(446\) 447.435 258.326i 1.00322 0.579207i
\(447\) −322.967 −0.722520
\(448\) −22.8898 51.1083i −0.0510933 0.114081i
\(449\) 55.1499 0.122828 0.0614141 0.998112i \(-0.480439\pi\)
0.0614141 + 0.998112i \(0.480439\pi\)
\(450\) 0 0
\(451\) 545.346 + 314.856i 1.20919 + 0.698128i
\(452\) 5.64407 + 3.25860i 0.0124869 + 0.00720930i
\(453\) 134.096 + 232.260i 0.296017 + 0.512716i
\(454\) 364.689i 0.803279i
\(455\) 0 0
\(456\) −120.572 −0.264411
\(457\) −303.778 + 175.386i −0.664723 + 0.383778i −0.794074 0.607821i \(-0.792044\pi\)
0.129351 + 0.991599i \(0.458710\pi\)
\(458\) 10.9112 18.8987i 0.0238236 0.0412636i
\(459\) −47.3947 + 82.0901i −0.103256 + 0.178845i
\(460\) 0 0
\(461\) 471.598i 1.02299i −0.859287 0.511494i \(-0.829092\pi\)
0.859287 0.511494i \(-0.170908\pi\)
\(462\) −35.0510 + 340.701i −0.0758680 + 0.737448i
\(463\) 387.112i 0.836094i 0.908425 + 0.418047i \(0.137285\pi\)
−0.908425 + 0.418047i \(0.862715\pi\)
\(464\) −106.245 184.021i −0.228975 0.396597i
\(465\) 0 0
\(466\) −88.6336 + 153.518i −0.190201 + 0.329437i
\(467\) 146.673 + 254.045i 0.314075 + 0.543994i 0.979240 0.202702i \(-0.0649724\pi\)
−0.665166 + 0.746696i \(0.731639\pi\)
\(468\) 20.9873 0.0448446
\(469\) −11.6506 + 113.245i −0.0248413 + 0.241461i
\(470\) 0 0
\(471\) 43.4777 + 75.3056i 0.0923094 + 0.159885i
\(472\) −141.692 + 245.418i −0.300195 + 0.519954i
\(473\) −1114.25 643.310i −2.35570 1.36006i
\(474\) −46.6170 + 26.9143i −0.0983481 + 0.0567813i
\(475\) 0 0
\(476\) 149.660 206.946i 0.314412 0.434760i
\(477\) 194.625i 0.408018i
\(478\) 4.44049 2.56372i 0.00928973 0.00536343i
\(479\) 660.805 + 381.516i 1.37955 + 0.796484i 0.992105 0.125409i \(-0.0400242\pi\)
0.387445 + 0.921893i \(0.373358\pi\)
\(480\) 0 0
\(481\) −141.676 + 81.7967i −0.294545 + 0.170056i
\(482\) 136.668 0.283543
\(483\) 278.738 124.838i 0.577098 0.258464i
\(484\) −555.999 −1.14876
\(485\) 0 0
\(486\) 19.0919 + 11.0227i 0.0392837 + 0.0226805i
\(487\) −193.893 111.944i −0.398138 0.229865i 0.287542 0.957768i \(-0.407162\pi\)
−0.685680 + 0.727903i \(0.740495\pi\)
\(488\) −11.3476 19.6546i −0.0232533 0.0402759i
\(489\) 200.590i 0.410205i
\(490\) 0 0
\(491\) −837.694 −1.70610 −0.853049 0.521830i \(-0.825249\pi\)
−0.853049 + 0.521830i \(0.825249\pi\)
\(492\) −94.5751 + 54.6029i −0.192226 + 0.110982i
\(493\) 484.535 839.239i 0.982829 1.70231i
\(494\) −60.8737 + 105.436i −0.123226 + 0.213434i
\(495\) 0 0
\(496\) 120.525i 0.242993i
\(497\) −308.225 688.203i −0.620171 1.38471i
\(498\) 1.02261i 0.00205344i
\(499\) 87.3234 + 151.249i 0.174997 + 0.303103i 0.940160 0.340733i \(-0.110675\pi\)
−0.765163 + 0.643836i \(0.777342\pi\)
\(500\) 0 0
\(501\) −53.1055 + 91.9814i −0.105999 + 0.183596i
\(502\) −21.0230 36.4130i −0.0418786 0.0725358i
\(503\) 747.962 1.48700 0.743501 0.668734i \(-0.233164\pi\)
0.743501 + 0.668734i \(0.233164\pi\)
\(504\) −48.1299 34.8068i −0.0954958 0.0690611i
\(505\) 0 0
\(506\) 355.800 + 616.263i 0.703162 + 1.21791i
\(507\) −135.762 + 235.147i −0.267776 + 0.463801i
\(508\) 153.420 + 88.5772i 0.302008 + 0.174365i
\(509\) 203.021 117.214i 0.398863 0.230284i −0.287130 0.957892i \(-0.592701\pi\)
0.685993 + 0.727608i \(0.259368\pi\)
\(510\) 0 0
\(511\) −359.726 37.0083i −0.703965 0.0724233i
\(512\) 22.6274i 0.0441942i
\(513\) −110.752 + 63.9428i −0.215891 + 0.124645i
\(514\) −540.875 312.275i −1.05229 0.607538i
\(515\) 0 0
\(516\) 193.235 111.564i 0.374486 0.216210i
\(517\) −560.549 −1.08423
\(518\) 460.561 + 47.3821i 0.889114 + 0.0914712i
\(519\) 54.9088 0.105797
\(520\) 0 0
\(521\) 186.068 + 107.427i 0.357137 + 0.206193i 0.667824 0.744319i \(-0.267226\pi\)
−0.310687 + 0.950512i \(0.600559\pi\)
\(522\) −195.184 112.689i −0.373915 0.215880i
\(523\) 462.520 + 801.108i 0.884360 + 1.53176i 0.846446 + 0.532475i \(0.178738\pi\)
0.0379137 + 0.999281i \(0.487929\pi\)
\(524\) 250.248i 0.477573i
\(525\) 0 0
\(526\) −485.141 −0.922321
\(527\) 476.020 274.830i 0.903263 0.521499i
\(528\) 69.1953 119.850i 0.131052 0.226988i
\(529\) 52.7773 91.4130i 0.0997681 0.172803i
\(530\) 0 0
\(531\) 300.575i 0.566054i
\(532\) 314.464 140.839i 0.591098 0.264734i
\(533\) 110.271i 0.206887i
\(534\) −136.204 235.913i −0.255064 0.441784i
\(535\) 0 0
\(536\) 22.9998 39.8368i 0.0429100 0.0743224i
\(537\) −114.224 197.842i −0.212707 0.368420i
\(538\) −655.277 −1.21799
\(539\) −306.553 929.528i −0.568744 1.72454i
\(540\) 0 0
\(541\) 57.1560 + 98.9971i 0.105649 + 0.182989i 0.914003 0.405707i \(-0.132975\pi\)
−0.808354 + 0.588696i \(0.799641\pi\)
\(542\) 172.945 299.550i 0.319087 0.552675i
\(543\) 82.7146 + 47.7553i 0.152329 + 0.0879472i
\(544\) −89.3683 + 51.5968i −0.164280 + 0.0948471i
\(545\) 0 0
\(546\) −54.7371 + 24.5151i −0.100251 + 0.0448994i
\(547\) 57.7698i 0.105612i 0.998605 + 0.0528060i \(0.0168165\pi\)
−0.998605 + 0.0528060i \(0.983183\pi\)
\(548\) −67.4699 + 38.9538i −0.123120 + 0.0710835i
\(549\) −20.8469 12.0359i −0.0379725 0.0219234i
\(550\) 0 0
\(551\) 1132.26 653.712i 2.05492 1.18641i
\(552\) −123.407 −0.223564
\(553\) 90.1438 124.648i 0.163009 0.225404i
\(554\) 199.430 0.359982
\(555\) 0 0
\(556\) −171.378 98.9454i −0.308235 0.177959i
\(557\) −351.738 203.076i −0.631487 0.364589i 0.149841 0.988710i \(-0.452124\pi\)
−0.781328 + 0.624121i \(0.785457\pi\)
\(558\) −63.9179 110.709i −0.114548 0.198403i
\(559\) 225.304i 0.403049i
\(560\) 0 0
\(561\) 631.139 1.12502
\(562\) 104.098 60.1008i 0.185227 0.106941i
\(563\) 214.146 370.911i 0.380366 0.658813i −0.610749 0.791824i \(-0.709131\pi\)
0.991114 + 0.133012i \(0.0424648\pi\)
\(564\) 48.6058 84.1878i 0.0861805 0.149269i
\(565\) 0 0
\(566\) 165.008i 0.291534i
\(567\) −62.6692 6.44735i −0.110528 0.0113710i
\(568\) 304.691i 0.536429i
\(569\) −457.897 793.100i −0.804739 1.39385i −0.916467 0.400110i \(-0.868972\pi\)
0.111728 0.993739i \(-0.464362\pi\)
\(570\) 0 0
\(571\) 356.947 618.250i 0.625125 1.08275i −0.363391 0.931637i \(-0.618381\pi\)
0.988517 0.151112i \(-0.0482855\pi\)
\(572\) −69.8701 121.019i −0.122151 0.211571i
\(573\) −338.035 −0.589938
\(574\) 182.881 252.883i 0.318608 0.440562i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) −43.7973 + 75.8591i −0.0759052 + 0.131472i −0.901480 0.432822i \(-0.857518\pi\)
0.825574 + 0.564293i \(0.190851\pi\)
\(578\) −53.6183 30.9565i −0.0927652 0.0535580i
\(579\) −523.140 + 302.035i −0.903523 + 0.521649i
\(580\) 0 0
\(581\) −1.19450 2.66708i −0.00205594 0.00459050i
\(582\) 181.812i 0.312392i
\(583\) −1122.26 + 647.937i −1.92497 + 1.11138i
\(584\) 126.542 + 73.0593i 0.216682 + 0.125101i
\(585\) 0 0
\(586\) −161.522 + 93.2548i −0.275635 + 0.159138i
\(587\) −169.908 −0.289452 −0.144726 0.989472i \(-0.546230\pi\)
−0.144726 + 0.989472i \(0.546230\pi\)
\(588\) 166.186 + 34.5598i 0.282628 + 0.0587752i
\(589\) 741.576 1.25904
\(590\) 0 0
\(591\) 84.5712 + 48.8272i 0.143098 + 0.0826179i
\(592\) −162.014 93.5385i −0.273671 0.158004i
\(593\) 100.126 + 173.424i 0.168847 + 0.292452i 0.938015 0.346595i \(-0.112662\pi\)
−0.769168 + 0.639047i \(0.779329\pi\)
\(594\) 146.785i 0.247114i
\(595\) 0 0
\(596\) −372.930 −0.625721
\(597\) −256.962 + 148.357i −0.430422 + 0.248504i
\(598\) −62.3053 + 107.916i −0.104189 + 0.180461i
\(599\) −350.201 + 606.566i −0.584643 + 1.01263i 0.410277 + 0.911961i \(0.365432\pi\)
−0.994920 + 0.100671i \(0.967901\pi\)
\(600\) 0 0
\(601\) 1039.21i 1.72914i 0.502515 + 0.864569i \(0.332408\pi\)
−0.502515 + 0.864569i \(0.667592\pi\)
\(602\) −373.660 + 516.687i −0.620698 + 0.858285i
\(603\) 48.7899i 0.0809119i
\(604\) 154.840 + 268.191i 0.256358 + 0.444025i
\(605\) 0 0
\(606\) 107.280 185.815i 0.177030 0.306626i
\(607\) −30.5796 52.9655i −0.0503783 0.0872578i 0.839737 0.542994i \(-0.182709\pi\)
−0.890115 + 0.455736i \(0.849376\pi\)
\(608\) −139.224 −0.228987
\(609\) 640.692 + 65.9138i 1.05204 + 0.108233i
\(610\) 0 0
\(611\) −49.0798 85.0087i −0.0803270 0.139130i
\(612\) −54.7267 + 94.7894i −0.0894227 + 0.154885i
\(613\) 452.688 + 261.359i 0.738479 + 0.426361i 0.821516 0.570185i \(-0.193129\pi\)
−0.0830371 + 0.996546i \(0.526462\pi\)
\(614\) 526.482 303.965i 0.857462 0.495056i
\(615\) 0 0
\(616\) −40.4734 + 393.408i −0.0657036 + 0.638649i
\(617\) 608.200i 0.985738i 0.870104 + 0.492869i \(0.164052\pi\)
−0.870104 + 0.492869i \(0.835948\pi\)
\(618\) 294.951 170.290i 0.477267 0.275550i
\(619\) −902.671 521.157i −1.45827 0.841934i −0.459346 0.888257i \(-0.651916\pi\)
−0.998927 + 0.0463229i \(0.985250\pi\)
\(620\) 0 0
\(621\) −113.357 + 65.4465i −0.182539 + 0.105389i
\(622\) −355.643 −0.571774
\(623\) 630.804 + 456.187i 1.01253 + 0.732243i
\(624\) 24.2340 0.0388366
\(625\) 0 0
\(626\) 16.7831 + 9.68972i 0.0268100 + 0.0154788i
\(627\) 737.424 + 425.752i 1.17611 + 0.679030i
\(628\) 50.2037 + 86.9554i 0.0799423 + 0.138464i
\(629\) 853.176i 1.35640i
\(630\) 0 0
\(631\) −235.274 −0.372859 −0.186430 0.982468i \(-0.559692\pi\)
−0.186430 + 0.982468i \(0.559692\pi\)
\(632\) −53.8287 + 31.0780i −0.0851720 + 0.0491741i
\(633\) 140.329 243.057i 0.221689 0.383977i
\(634\) 23.2851 40.3310i 0.0367273 0.0636136i
\(635\) 0 0
\(636\) 224.733i 0.353354i
\(637\) 114.125 127.876i 0.179159 0.200747i
\(638\) 1500.65i 2.35211i
\(639\) 161.587 + 279.877i 0.252875 + 0.437992i
\(640\) 0 0
\(641\) 58.4900 101.308i 0.0912481 0.158046i −0.816788 0.576937i \(-0.804248\pi\)
0.908037 + 0.418891i \(0.137581\pi\)
\(642\) 186.394 + 322.843i 0.290333 + 0.502871i
\(643\) 874.209 1.35958 0.679789 0.733408i \(-0.262071\pi\)
0.679789 + 0.733408i \(0.262071\pi\)
\(644\) 321.859 144.151i 0.499781 0.223837i
\(645\) 0 0
\(646\) −317.470 549.874i −0.491439 0.851198i
\(647\) −5.84189 + 10.1185i −0.00902920 + 0.0156390i −0.870505 0.492160i \(-0.836207\pi\)
0.861476 + 0.507799i \(0.169541\pi\)
\(648\) 22.0454 + 12.7279i 0.0340207 + 0.0196419i
\(649\) 1733.20 1000.66i 2.67057 1.54185i
\(650\) 0 0
\(651\) 296.023 + 214.079i 0.454720 + 0.328847i
\(652\) 231.622i 0.355248i
\(653\) 552.641 319.067i 0.846311 0.488618i −0.0130935 0.999914i \(-0.504168\pi\)
0.859404 + 0.511296i \(0.170835\pi\)
\(654\) −137.367 79.3088i −0.210041 0.121267i
\(655\) 0 0
\(656\) −109.206 + 63.0500i −0.166472 + 0.0961129i
\(657\) 154.982 0.235894
\(658\) −28.4303 + 276.347i −0.0432071 + 0.419980i
\(659\) −870.363 −1.32073 −0.660367 0.750943i \(-0.729599\pi\)
−0.660367 + 0.750943i \(0.729599\pi\)
\(660\) 0 0
\(661\) 417.571 + 241.085i 0.631727 + 0.364728i 0.781420 0.624005i \(-0.214495\pi\)
−0.149694 + 0.988732i \(0.547829\pi\)
\(662\) 511.797 + 295.486i 0.773108 + 0.446354i
\(663\) 55.2604 + 95.7138i 0.0833490 + 0.144365i
\(664\) 1.18081i 0.00177833i
\(665\) 0 0
\(666\) −198.425 −0.297936
\(667\) 1158.89 669.085i 1.73747 1.00313i
\(668\) −61.3210 + 106.211i −0.0917978 + 0.158999i
\(669\) 316.384 547.993i 0.472921 0.819123i
\(670\) 0 0
\(671\) 160.279i 0.238865i
\(672\) −55.5756 40.1914i −0.0827018 0.0598087i
\(673\) 399.323i 0.593347i −0.954979 0.296674i \(-0.904123\pi\)
0.954979 0.296674i \(-0.0958773\pi\)
\(674\) 202.719 + 351.119i 0.300770 + 0.520948i
\(675\) 0 0
\(676\) −156.765 + 271.525i −0.231901 + 0.401664i
\(677\) −70.6707 122.405i −0.104388 0.180805i 0.809100 0.587671i \(-0.199955\pi\)
−0.913488 + 0.406866i \(0.866622\pi\)
\(678\) 7.98191 0.0117727
\(679\) 212.373 + 474.185i 0.312773 + 0.698358i
\(680\) 0 0
\(681\) −223.325 386.811i −0.327937 0.568004i
\(682\) −425.586 + 737.137i −0.624026 + 1.08085i
\(683\) −855.785 494.088i −1.25298 0.723408i −0.281279 0.959626i \(-0.590759\pi\)
−0.971700 + 0.236218i \(0.924092\pi\)
\(684\) −127.886 + 73.8347i −0.186967 + 0.107946i
\(685\) 0 0
\(686\) −473.799 + 103.984i −0.690669 + 0.151580i
\(687\) 26.7268i 0.0389037i
\(688\) 223.128 128.823i 0.324314 0.187243i
\(689\) −196.522 113.462i −0.285228 0.164677i
\(690\) 0 0
\(691\) 303.829 175.415i 0.439694 0.253857i −0.263774 0.964585i \(-0.584967\pi\)
0.703468 + 0.710727i \(0.251634\pi\)
\(692\) 63.4033 0.0916232
\(693\) 171.459 + 382.832i 0.247415 + 0.552428i
\(694\) 433.875 0.625180
\(695\) 0 0
\(696\) −225.379 130.123i −0.323820 0.186958i
\(697\) −498.040 287.543i −0.714548 0.412544i
\(698\) 240.531 + 416.611i 0.344600 + 0.596864i
\(699\) 217.107i 0.310597i
\(700\) 0 0
\(701\) 307.500 0.438659 0.219330 0.975651i \(-0.429613\pi\)
0.219330 + 0.975651i \(0.429613\pi\)
\(702\) 22.2604 12.8520i 0.0317100 0.0183077i
\(703\) 575.533 996.852i 0.818681 1.41800i
\(704\) 79.8999 138.391i 0.113494 0.196578i
\(705\) 0 0
\(706\) 530.333i 0.751180i
\(707\) −62.7500 + 609.939i −0.0887552 + 0.862715i
\(708\) 347.074i 0.490217i
\(709\) −49.0712 84.9938i −0.0692118 0.119878i 0.829343 0.558740i \(-0.188715\pi\)
−0.898555 + 0.438862i \(0.855382\pi\)
\(710\) 0 0
\(711\) −32.9632 + 57.0939i −0.0463617 + 0.0803009i
\(712\) −157.275 272.409i −0.220892 0.382597i
\(713\) 759.016 1.06454
\(714\) 32.0105 311.147i 0.0448326 0.435780i
\(715\) 0 0
\(716\) −131.894 228.448i −0.184210 0.319061i
\(717\) 3.13990 5.43847i 0.00437922 0.00758503i
\(718\) −403.554 232.992i −0.562053 0.324502i
\(719\) −612.340 + 353.535i −0.851655 + 0.491703i −0.861209 0.508251i \(-0.830292\pi\)
0.00955403 + 0.999954i \(0.496959\pi\)
\(720\) 0 0
\(721\) −570.349 + 788.664i −0.791053 + 1.09385i
\(722\) 346.100i 0.479363i
\(723\) 144.958 83.6915i 0.200495 0.115756i
\(724\) 95.5106 + 55.1431i 0.131921 + 0.0761645i
\(725\) 0 0
\(726\) −589.726 + 340.479i −0.812295 + 0.468979i
\(727\) −1353.85 −1.86225 −0.931123 0.364705i \(-0.881170\pi\)
−0.931123 + 0.364705i \(0.881170\pi\)
\(728\) −63.2050 + 28.3076i −0.0868201 + 0.0388840i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 1017.59 + 587.506i 1.39205 + 0.803701i
\(732\) −24.0719 13.8979i −0.0328851 0.0189862i
\(733\) −276.517 478.941i −0.377240 0.653398i 0.613420 0.789757i \(-0.289793\pi\)
−0.990660 + 0.136359i \(0.956460\pi\)
\(734\) 38.4020i 0.0523188i
\(735\) 0 0
\(736\) −142.498 −0.193612
\(737\) −281.336 + 162.429i −0.381732 + 0.220393i
\(738\) −66.8747 + 115.830i −0.0906161 + 0.156952i
\(739\) 466.739 808.416i 0.631582 1.09393i −0.355646 0.934621i \(-0.615739\pi\)
0.987228 0.159312i \(-0.0509276\pi\)
\(740\) 0 0
\(741\) 149.110i 0.201227i
\(742\) 262.509 + 586.128i 0.353785 + 0.789930i
\(743\) 554.921i 0.746865i 0.927657 + 0.373432i \(0.121819\pi\)
−0.927657 + 0.373432i \(0.878181\pi\)
\(744\) −73.8060 127.836i −0.0992016 0.171822i
\(745\) 0 0
\(746\) 90.1544 156.152i 0.120850 0.209319i
\(747\) 0.626219 + 1.08464i 0.000838312 + 0.00145200i
\(748\) 728.776 0.974300
\(749\) −863.246 624.286i −1.15253 0.833492i
\(750\) 0 0
\(751\) −363.974 630.421i −0.484652 0.839442i 0.515192 0.857075i \(-0.327721\pi\)
−0.999845 + 0.0176322i \(0.994387\pi\)
\(752\) 56.1252 97.2117i 0.0746345 0.129271i
\(753\) −44.5966 25.7479i −0.0592252 0.0341937i
\(754\) −227.577 + 131.391i −0.301826 + 0.174259i
\(755\) 0 0
\(756\) −72.3642 7.44476i −0.0957198 0.00984756i
\(757\) 667.167i 0.881330i −0.897672 0.440665i \(-0.854743\pi\)
0.897672 0.440665i \(-0.145257\pi\)
\(758\) −391.667 + 226.129i −0.516711 + 0.298323i
\(759\) 754.765 + 435.764i 0.994421 + 0.574129i
\(760\) 0 0
\(761\) −630.061 + 363.766i −0.827938 + 0.478010i −0.853146 0.521672i \(-0.825309\pi\)
0.0252080 + 0.999682i \(0.491975\pi\)
\(762\) 216.969 0.284736
\(763\) 450.908 + 46.3890i 0.590967 + 0.0607981i
\(764\) −390.329 −0.510901
\(765\) 0 0
\(766\) 500.850 + 289.166i 0.653851 + 0.377501i
\(767\) 303.506 + 175.229i 0.395705 + 0.228460i
\(768\) 13.8564 + 24.0000i 0.0180422 + 0.0312500i
\(769\) 1374.28i 1.78709i −0.448969 0.893547i \(-0.648209\pi\)
0.448969 0.893547i \(-0.351791\pi\)
\(770\) 0 0
\(771\) −764.913 −0.992106
\(772\) −604.070 + 348.760i −0.782474 + 0.451761i
\(773\) −46.3356 + 80.2556i −0.0599425 + 0.103824i −0.894439 0.447189i \(-0.852425\pi\)
0.834497 + 0.551013i \(0.185758\pi\)
\(774\) 136.638 236.663i 0.176534 0.305767i
\(775\) 0 0
\(776\) 209.938i 0.270539i
\(777\) 517.514 231.779i 0.666042 0.298300i
\(778\) 547.517i 0.703749i
\(779\) −387.940 671.932i −0.497998 0.862558i
\(780\) 0 0
\(781\) 1075.90 1863.51i 1.37759 2.38606i
\(782\) −324.936 562.805i −0.415519 0.719700i
\(783\) −276.032