Properties

Label 1050.3.q.b.199.3
Level $1050$
Weight $3$
Character 1050.199
Analytic conductor $28.610$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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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: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: 16.0.22986704741655040229376.1
Defining polynomial: \( x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.3
Root \(0.596002 + 2.22431i\) of defining polynomial
Character \(\chi\) \(=\) 1050.199
Dual form 1050.3.q.b.649.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.98615 + 0.440173i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.98615 + 0.440173i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.76860 + 6.52741i) q^{11} +(-1.73205 - 3.00000i) q^{12} +21.3906 q^{13} +(8.24500 - 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(10.4937 - 18.1757i) q^{17} +(3.67423 + 2.12132i) q^{18} +(-20.8728 + 12.0509i) q^{19} +(-5.38992 + 10.8604i) q^{21} -10.6592i q^{22} +(-4.83250 + 2.79005i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-26.1981 + 15.1255i) q^{26} -5.19615 q^{27} +(-6.22374 + 12.5405i) q^{28} +9.96625 q^{29} +(5.70073 + 3.29132i) q^{31} +(4.89898 + 2.82843i) q^{32} +(6.52741 + 11.3058i) q^{33} +29.6807i q^{34} -6.00000 q^{36} +(19.3960 - 11.1983i) q^{37} +(17.0426 - 29.5187i) q^{38} +(18.5248 - 32.0860i) q^{39} -51.0827i q^{41} +(-1.07820 - 17.1125i) q^{42} -34.7656i q^{43} +(7.53720 + 13.0548i) q^{44} +(3.94572 - 6.83419i) q^{46} +(-38.8246 - 67.2462i) q^{47} -6.92820 q^{48} +(48.6125 - 6.15023i) q^{49} +(-18.1757 - 31.4812i) q^{51} +(21.3906 - 37.0497i) q^{52} +(43.1262 + 24.8989i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} +41.7457i q^{57} +(-12.2061 + 7.04720i) q^{58} +(-72.9362 - 42.1098i) q^{59} +(-72.4404 + 41.8235i) q^{61} -9.30925 q^{62} +(11.6228 + 17.4903i) q^{63} -8.00000 q^{64} +(-15.9888 - 9.23115i) q^{66} +(-57.6618 - 33.2911i) q^{67} +(-20.9874 - 36.3513i) q^{68} +9.66501i q^{69} -68.1049 q^{71} +(7.34847 - 4.24264i) q^{72} +(43.8283 - 75.9128i) q^{73} +(-15.8368 + 27.4301i) q^{74} +48.2038i q^{76} +(23.4548 - 47.2603i) q^{77} +52.3962i q^{78} +(49.3730 + 85.5165i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(36.1209 + 62.5632i) q^{82} +26.9448 q^{83} +(13.4209 + 20.1960i) q^{84} +(24.5830 + 42.5790i) q^{86} +(8.63103 - 14.9494i) q^{87} +(-18.4623 - 10.6592i) q^{88} +(-12.0453 + 6.95436i) q^{89} +(-149.438 + 9.41559i) q^{91} +11.1602i q^{92} +(9.87395 - 5.70073i) q^{93} +(95.1005 + 54.9063i) q^{94} +(8.48528 - 4.89898i) q^{96} -3.69132 q^{97} +(-55.1890 + 41.9067i) q^{98} +22.6116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100}) \) 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
\(7\) −6.98615 + 0.440173i −0.998021 + 0.0628819i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 2.59808i −0.166667 0.288675i
\(10\) 0 0
\(11\) −3.76860 + 6.52741i −0.342600 + 0.593401i −0.984915 0.173040i \(-0.944641\pi\)
0.642315 + 0.766441i \(0.277974\pi\)
\(12\) −1.73205 3.00000i −0.144338 0.250000i
\(13\) 21.3906 1.64543 0.822717 0.568451i \(-0.192457\pi\)
0.822717 + 0.568451i \(0.192457\pi\)
\(14\) 8.24500 5.47905i 0.588928 0.391361i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 10.4937 18.1757i 0.617278 1.06916i −0.372703 0.927951i \(-0.621569\pi\)
0.989980 0.141205i \(-0.0450978\pi\)
\(18\) 3.67423 + 2.12132i 0.204124 + 0.117851i
\(19\) −20.8728 + 12.0509i −1.09857 + 0.634260i −0.935845 0.352411i \(-0.885362\pi\)
−0.162726 + 0.986671i \(0.552029\pi\)
\(20\) 0 0
\(21\) −5.38992 + 10.8604i −0.256663 + 0.517163i
\(22\) 10.6592i 0.484510i
\(23\) −4.83250 + 2.79005i −0.210109 + 0.121306i −0.601362 0.798977i \(-0.705375\pi\)
0.391253 + 0.920283i \(0.372042\pi\)
\(24\) 4.24264 + 2.44949i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) −26.1981 + 15.1255i −1.00762 + 0.581749i
\(27\) −5.19615 −0.192450
\(28\) −6.22374 + 12.5405i −0.222277 + 0.447876i
\(29\) 9.96625 0.343664 0.171832 0.985126i \(-0.445031\pi\)
0.171832 + 0.985126i \(0.445031\pi\)
\(30\) 0 0
\(31\) 5.70073 + 3.29132i 0.183894 + 0.106171i 0.589121 0.808045i \(-0.299474\pi\)
−0.405227 + 0.914216i \(0.632807\pi\)
\(32\) 4.89898 + 2.82843i 0.153093 + 0.0883883i
\(33\) 6.52741 + 11.3058i 0.197800 + 0.342600i
\(34\) 29.6807i 0.872962i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 19.3960 11.1983i 0.524216 0.302656i −0.214442 0.976737i \(-0.568793\pi\)
0.738658 + 0.674080i \(0.235460\pi\)
\(38\) 17.0426 29.5187i 0.448490 0.776807i
\(39\) 18.5248 32.0860i 0.474996 0.822717i
\(40\) 0 0
\(41\) 51.0827i 1.24592i −0.782254 0.622959i \(-0.785930\pi\)
0.782254 0.622959i \(-0.214070\pi\)
\(42\) −1.07820 17.1125i −0.0256714 0.407440i
\(43\) 34.7656i 0.808503i −0.914648 0.404252i \(-0.867532\pi\)
0.914648 0.404252i \(-0.132468\pi\)
\(44\) 7.53720 + 13.0548i 0.171300 + 0.296700i
\(45\) 0 0
\(46\) 3.94572 6.83419i 0.0857766 0.148569i
\(47\) −38.8246 67.2462i −0.826056 1.43077i −0.901110 0.433591i \(-0.857246\pi\)
0.0750536 0.997179i \(-0.476087\pi\)
\(48\) −6.92820 −0.144338
\(49\) 48.6125 6.15023i 0.992092 0.125515i
\(50\) 0 0
\(51\) −18.1757 31.4812i −0.356385 0.617278i
\(52\) 21.3906 37.0497i 0.411359 0.712494i
\(53\) 43.1262 + 24.8989i 0.813703 + 0.469791i 0.848240 0.529612i \(-0.177662\pi\)
−0.0345374 + 0.999403i \(0.510996\pi\)
\(54\) 6.36396 3.67423i 0.117851 0.0680414i
\(55\) 0 0
\(56\) −1.24500 19.7598i −0.0222321 0.352854i
\(57\) 41.7457i 0.732381i
\(58\) −12.2061 + 7.04720i −0.210450 + 0.121504i
\(59\) −72.9362 42.1098i −1.23621 0.713725i −0.267890 0.963449i \(-0.586327\pi\)
−0.968317 + 0.249725i \(0.919660\pi\)
\(60\) 0 0
\(61\) −72.4404 + 41.8235i −1.18755 + 0.685631i −0.957749 0.287607i \(-0.907140\pi\)
−0.229799 + 0.973238i \(0.573807\pi\)
\(62\) −9.30925 −0.150149
\(63\) 11.6228 + 17.4903i 0.184489 + 0.277624i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) −15.9888 9.23115i −0.242255 0.139866i
\(67\) −57.6618 33.2911i −0.860625 0.496882i 0.00359682 0.999994i \(-0.498855\pi\)
−0.864221 + 0.503112i \(0.832188\pi\)
\(68\) −20.9874 36.3513i −0.308639 0.534578i
\(69\) 9.66501i 0.140073i
\(70\) 0 0
\(71\) −68.1049 −0.959224 −0.479612 0.877481i \(-0.659223\pi\)
−0.479612 + 0.877481i \(0.659223\pi\)
\(72\) 7.34847 4.24264i 0.102062 0.0589256i
\(73\) 43.8283 75.9128i 0.600387 1.03990i −0.392375 0.919805i \(-0.628346\pi\)
0.992762 0.120096i \(-0.0383202\pi\)
\(74\) −15.8368 + 27.4301i −0.214010 + 0.370677i
\(75\) 0 0
\(76\) 48.2038i 0.634260i
\(77\) 23.4548 47.2603i 0.304608 0.613770i
\(78\) 52.3962i 0.671746i
\(79\) 49.3730 + 85.5165i 0.624974 + 1.08249i 0.988546 + 0.150921i \(0.0482238\pi\)
−0.363572 + 0.931566i \(0.618443\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 36.1209 + 62.5632i 0.440499 + 0.762966i
\(83\) 26.9448 0.324636 0.162318 0.986739i \(-0.448103\pi\)
0.162318 + 0.986739i \(0.448103\pi\)
\(84\) 13.4209 + 20.1960i 0.159772 + 0.240429i
\(85\) 0 0
\(86\) 24.5830 + 42.5790i 0.285849 + 0.495105i
\(87\) 8.63103 14.9494i 0.0992072 0.171832i
\(88\) −18.4623 10.6592i −0.209799 0.121127i
\(89\) −12.0453 + 6.95436i −0.135341 + 0.0781389i −0.566142 0.824308i \(-0.691564\pi\)
0.430801 + 0.902447i \(0.358231\pi\)
\(90\) 0 0
\(91\) −149.438 + 9.41559i −1.64218 + 0.103468i
\(92\) 11.1602i 0.121306i
\(93\) 9.87395 5.70073i 0.106171 0.0612981i
\(94\) 95.1005 + 54.9063i 1.01171 + 0.584110i
\(95\) 0 0
\(96\) 8.48528 4.89898i 0.0883883 0.0510310i
\(97\) −3.69132 −0.0380549 −0.0190274 0.999819i \(-0.506057\pi\)
−0.0190274 + 0.999819i \(0.506057\pi\)
\(98\) −55.1890 + 41.9067i −0.563153 + 0.427619i
\(99\) 22.6116 0.228400
\(100\) 0 0
\(101\) −158.170 91.3195i −1.56604 0.904154i −0.996624 0.0821041i \(-0.973836\pi\)
−0.569416 0.822049i \(-0.692831\pi\)
\(102\) 44.5211 + 25.7043i 0.436481 + 0.252003i
\(103\) −45.5253 78.8521i −0.441993 0.765555i 0.555844 0.831287i \(-0.312395\pi\)
−0.997837 + 0.0657318i \(0.979062\pi\)
\(104\) 60.5019i 0.581749i
\(105\) 0 0
\(106\) −70.4249 −0.664385
\(107\) −44.6318 + 25.7682i −0.417120 + 0.240824i −0.693844 0.720125i \(-0.744084\pi\)
0.276724 + 0.960949i \(0.410751\pi\)
\(108\) −5.19615 + 9.00000i −0.0481125 + 0.0833333i
\(109\) 19.1807 33.2219i 0.175970 0.304788i −0.764527 0.644592i \(-0.777027\pi\)
0.940496 + 0.339804i \(0.110361\pi\)
\(110\) 0 0
\(111\) 38.7920i 0.349477i
\(112\) 15.4971 + 23.3204i 0.138367 + 0.208218i
\(113\) 198.558i 1.75715i −0.477608 0.878573i \(-0.658496\pi\)
0.477608 0.878573i \(-0.341504\pi\)
\(114\) −29.5187 51.1278i −0.258936 0.448490i
\(115\) 0 0
\(116\) 9.96625 17.2621i 0.0859160 0.148811i
\(117\) −32.0860 55.5745i −0.274239 0.474996i
\(118\) 119.104 1.00936
\(119\) −65.3102 + 131.597i −0.548825 + 1.10586i
\(120\) 0 0
\(121\) 32.0953 + 55.5907i 0.265250 + 0.459427i
\(122\) 59.1474 102.446i 0.484814 0.839723i
\(123\) −76.6240 44.2389i −0.622959 0.359666i
\(124\) 11.4015 6.58263i 0.0919472 0.0530857i
\(125\) 0 0
\(126\) −26.6025 13.2026i −0.211131 0.104782i
\(127\) 74.1132i 0.583569i 0.956484 + 0.291784i \(0.0942490\pi\)
−0.956484 + 0.291784i \(0.905751\pi\)
\(128\) 9.79796 5.65685i 0.0765466 0.0441942i
\(129\) −52.1485 30.1079i −0.404252 0.233395i
\(130\) 0 0
\(131\) 17.3500 10.0170i 0.132443 0.0764657i −0.432315 0.901723i \(-0.642303\pi\)
0.564757 + 0.825257i \(0.308970\pi\)
\(132\) 26.1096 0.197800
\(133\) 140.516 93.3773i 1.05651 0.702085i
\(134\) 94.1614 0.702697
\(135\) 0 0
\(136\) 51.4085 + 29.6807i 0.378004 + 0.218241i
\(137\) −74.6259 43.0853i −0.544715 0.314491i 0.202273 0.979329i \(-0.435167\pi\)
−0.746988 + 0.664838i \(0.768501\pi\)
\(138\) −6.83419 11.8372i −0.0495231 0.0857766i
\(139\) 232.502i 1.67268i −0.548213 0.836339i \(-0.684692\pi\)
0.548213 0.836339i \(-0.315308\pi\)
\(140\) 0 0
\(141\) −134.492 −0.953847
\(142\) 83.4111 48.1574i 0.587402 0.339137i
\(143\) −80.6128 + 139.625i −0.563726 + 0.976402i
\(144\) −6.00000 + 10.3923i −0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) 123.965i 0.849076i
\(147\) 32.8743 78.2450i 0.223635 0.532279i
\(148\) 44.7931i 0.302656i
\(149\) −109.963 190.462i −0.738008 1.27827i −0.953391 0.301738i \(-0.902433\pi\)
0.215383 0.976530i \(-0.430900\pi\)
\(150\) 0 0
\(151\) 130.461 225.965i 0.863980 1.49646i −0.00407633 0.999992i \(-0.501298\pi\)
0.868056 0.496466i \(-0.165369\pi\)
\(152\) −34.0852 59.0373i −0.224245 0.388403i
\(153\) −62.9623 −0.411518
\(154\) 4.69190 + 74.4668i 0.0304669 + 0.483551i
\(155\) 0 0
\(156\) −37.0497 64.1719i −0.237498 0.411359i
\(157\) −57.0954 + 98.8921i −0.363665 + 0.629886i −0.988561 0.150822i \(-0.951808\pi\)
0.624896 + 0.780708i \(0.285141\pi\)
\(158\) −120.939 69.8239i −0.765434 0.441923i
\(159\) 74.6968 43.1262i 0.469791 0.271234i
\(160\) 0 0
\(161\) 32.5325 21.6188i 0.202065 0.134278i
\(162\) 12.7279i 0.0785674i
\(163\) 42.1894 24.3581i 0.258831 0.149436i −0.364970 0.931019i \(-0.618921\pi\)
0.623801 + 0.781583i \(0.285588\pi\)
\(164\) −88.4777 51.0827i −0.539498 0.311480i
\(165\) 0 0
\(166\) −33.0005 + 19.0528i −0.198798 + 0.114776i
\(167\) 49.6127 0.297082 0.148541 0.988906i \(-0.452542\pi\)
0.148541 + 0.988906i \(0.452542\pi\)
\(168\) −30.7179 15.2450i −0.182845 0.0907440i
\(169\) 288.560 1.70745
\(170\) 0 0
\(171\) 62.6185 + 36.1528i 0.366190 + 0.211420i
\(172\) −60.2159 34.7656i −0.350092 0.202126i
\(173\) −117.670 203.811i −0.680176 1.17810i −0.974927 0.222525i \(-0.928570\pi\)
0.294751 0.955574i \(-0.404763\pi\)
\(174\) 24.4122i 0.140300i
\(175\) 0 0
\(176\) 30.1488 0.171300
\(177\) −126.329 + 72.9362i −0.713725 + 0.412069i
\(178\) 9.83495 17.0346i 0.0552525 0.0957002i
\(179\) −22.1049 + 38.2868i −0.123491 + 0.213893i −0.921142 0.389226i \(-0.872742\pi\)
0.797651 + 0.603119i \(0.206076\pi\)
\(180\) 0 0
\(181\) 117.049i 0.646679i 0.946283 + 0.323340i \(0.104806\pi\)
−0.946283 + 0.323340i \(0.895194\pi\)
\(182\) 176.366 117.200i 0.969043 0.643958i
\(183\) 144.881i 0.791699i
\(184\) −7.89145 13.6684i −0.0428883 0.0742847i
\(185\) 0 0
\(186\) −8.06204 + 13.9639i −0.0433443 + 0.0750746i
\(187\) 79.0933 + 136.994i 0.422959 + 0.732586i
\(188\) −155.299 −0.826056
\(189\) 36.3011 2.28721i 0.192069 0.0121016i
\(190\) 0 0
\(191\) −117.156 202.920i −0.613383 1.06241i −0.990666 0.136313i \(-0.956475\pi\)
0.377283 0.926098i \(-0.376858\pi\)
\(192\) −6.92820 + 12.0000i −0.0360844 + 0.0625000i
\(193\) 16.9438 + 9.78252i 0.0877918 + 0.0506866i 0.543253 0.839569i \(-0.317192\pi\)
−0.455461 + 0.890256i \(0.650526\pi\)
\(194\) 4.52093 2.61016i 0.0233037 0.0134544i
\(195\) 0 0
\(196\) 37.9600 90.3495i 0.193673 0.460967i
\(197\) 179.443i 0.910877i 0.890267 + 0.455438i \(0.150517\pi\)
−0.890267 + 0.455438i \(0.849483\pi\)
\(198\) −27.6934 + 15.9888i −0.139866 + 0.0807516i
\(199\) 221.630 + 127.958i 1.11372 + 0.643006i 0.939790 0.341753i \(-0.111021\pi\)
0.173928 + 0.984758i \(0.444354\pi\)
\(200\) 0 0
\(201\) −99.8732 + 57.6618i −0.496882 + 0.286875i
\(202\) 258.291 1.27867
\(203\) −69.6257 + 4.38688i −0.342984 + 0.0216102i
\(204\) −72.7026 −0.356385
\(205\) 0 0
\(206\) 111.514 + 64.3825i 0.541329 + 0.312536i
\(207\) 14.4975 + 8.37014i 0.0700363 + 0.0404355i
\(208\) −42.7813 74.0994i −0.205679 0.356247i
\(209\) 181.661i 0.869190i
\(210\) 0 0
\(211\) 196.891 0.933132 0.466566 0.884486i \(-0.345491\pi\)
0.466566 + 0.884486i \(0.345491\pi\)
\(212\) 86.2525 49.7979i 0.406851 0.234896i
\(213\) −58.9806 + 102.157i −0.276904 + 0.479612i
\(214\) 36.4417 63.1189i 0.170288 0.294948i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) −41.2749 20.4843i −0.190207 0.0943977i
\(218\) 54.2512i 0.248859i
\(219\) −75.9128 131.485i −0.346634 0.600387i
\(220\) 0 0
\(221\) 224.467 388.789i 1.01569 1.75923i
\(222\) 27.4301 + 47.5103i 0.123559 + 0.214010i
\(223\) 431.015 1.93280 0.966401 0.257039i \(-0.0827470\pi\)
0.966401 + 0.257039i \(0.0827470\pi\)
\(224\) −35.4700 17.6034i −0.158348 0.0785866i
\(225\) 0 0
\(226\) 140.401 + 243.182i 0.621245 + 1.07603i
\(227\) 87.5479 151.637i 0.385673 0.668006i −0.606189 0.795321i \(-0.707302\pi\)
0.991862 + 0.127315i \(0.0406358\pi\)
\(228\) 72.3057 + 41.7457i 0.317130 + 0.183095i
\(229\) −29.0717 + 16.7846i −0.126951 + 0.0732951i −0.562131 0.827048i \(-0.690018\pi\)
0.435180 + 0.900344i \(0.356685\pi\)
\(230\) 0 0
\(231\) −50.5779 76.1108i −0.218952 0.329484i
\(232\) 28.1888i 0.121504i
\(233\) −134.159 + 77.4567i −0.575790 + 0.332432i −0.759458 0.650556i \(-0.774536\pi\)
0.183669 + 0.982988i \(0.441203\pi\)
\(234\) 78.5942 + 45.3764i 0.335873 + 0.193916i
\(235\) 0 0
\(236\) −145.872 + 84.2195i −0.618104 + 0.356862i
\(237\) 171.033 0.721658
\(238\) −13.0647 207.354i −0.0548935 0.871235i
\(239\) −316.591 −1.32465 −0.662325 0.749217i \(-0.730430\pi\)
−0.662325 + 0.749217i \(0.730430\pi\)
\(240\) 0 0
\(241\) 202.219 + 116.751i 0.839084 + 0.484446i 0.856953 0.515395i \(-0.172355\pi\)
−0.0178685 + 0.999840i \(0.505688\pi\)
\(242\) −78.6171 45.3896i −0.324864 0.187560i
\(243\) 7.79423 + 13.5000i 0.0320750 + 0.0555556i
\(244\) 167.294i 0.685631i
\(245\) 0 0
\(246\) 125.126 0.508644
\(247\) −446.484 + 257.777i −1.80763 + 1.04363i
\(248\) −9.30925 + 16.1241i −0.0375373 + 0.0650165i
\(249\) 23.3349 40.4172i 0.0937143 0.162318i
\(250\) 0 0
\(251\) 56.6879i 0.225848i −0.993604 0.112924i \(-0.963978\pi\)
0.993604 0.112924i \(-0.0360217\pi\)
\(252\) 41.9169 2.64104i 0.166337 0.0104803i
\(253\) 42.0583i 0.166238i
\(254\) −52.4060 90.7698i −0.206323 0.357361i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −145.219 251.528i −0.565056 0.978706i −0.997044 0.0768270i \(-0.975521\pi\)
0.431988 0.901879i \(-0.357812\pi\)
\(258\) 85.1581 0.330070
\(259\) −130.574 + 86.7704i −0.504147 + 0.335021i
\(260\) 0 0
\(261\) −14.9494 25.8931i −0.0572773 0.0992072i
\(262\) −14.1662 + 24.5366i −0.0540694 + 0.0936510i
\(263\) 385.031 + 222.298i 1.46399 + 0.845238i 0.999193 0.0401768i \(-0.0127921\pi\)
0.464802 + 0.885415i \(0.346125\pi\)
\(264\) −31.9776 + 18.4623i −0.121127 + 0.0699329i
\(265\) 0 0
\(266\) −106.069 + 213.723i −0.398755 + 0.803471i
\(267\) 24.0906i 0.0902270i
\(268\) −115.324 + 66.5822i −0.430312 + 0.248441i
\(269\) 144.956 + 83.6902i 0.538869 + 0.311116i 0.744620 0.667488i \(-0.232631\pi\)
−0.205752 + 0.978604i \(0.565964\pi\)
\(270\) 0 0
\(271\) 2.24099 1.29384i 0.00826933 0.00477430i −0.495860 0.868403i \(-0.665147\pi\)
0.504129 + 0.863628i \(0.331814\pi\)
\(272\) −83.9498 −0.308639
\(273\) −115.294 + 232.311i −0.422322 + 0.850957i
\(274\) 121.864 0.444758
\(275\) 0 0
\(276\) 16.7403 + 9.66501i 0.0606532 + 0.0350181i
\(277\) −440.903 254.556i −1.59171 0.918973i −0.993014 0.117996i \(-0.962353\pi\)
−0.598694 0.800978i \(-0.704314\pi\)
\(278\) 164.404 + 284.756i 0.591381 + 1.02430i
\(279\) 19.7479i 0.0707810i
\(280\) 0 0
\(281\) 210.688 0.749779 0.374890 0.927069i \(-0.377681\pi\)
0.374890 + 0.927069i \(0.377681\pi\)
\(282\) 164.719 95.1005i 0.584110 0.337236i
\(283\) −19.7433 + 34.1964i −0.0697643 + 0.120835i −0.898797 0.438364i \(-0.855558\pi\)
0.829033 + 0.559199i \(0.188891\pi\)
\(284\) −68.1049 + 117.961i −0.239806 + 0.415356i
\(285\) 0 0
\(286\) 228.007i 0.797229i
\(287\) 22.4852 + 356.871i 0.0783457 + 1.24345i
\(288\) 16.9706i 0.0589256i
\(289\) −75.7363 131.179i −0.262063 0.453907i
\(290\) 0 0
\(291\) −3.19678 + 5.53698i −0.0109855 + 0.0190274i
\(292\) −87.6565 151.826i −0.300194 0.519951i
\(293\) 89.6023 0.305810 0.152905 0.988241i \(-0.451137\pi\)
0.152905 + 0.988241i \(0.451137\pi\)
\(294\) 15.0649 + 119.076i 0.0512412 + 0.405020i
\(295\) 0 0
\(296\) 31.6735 + 54.8602i 0.107005 + 0.185338i
\(297\) 19.5822 33.9174i 0.0659334 0.114200i
\(298\) 269.354 + 155.511i 0.903871 + 0.521850i
\(299\) −103.370 + 59.6809i −0.345720 + 0.199602i
\(300\) 0 0
\(301\) 15.3029 + 242.878i 0.0508402 + 0.806903i
\(302\) 368.999i 1.22185i
\(303\) −273.959 + 158.170i −0.904154 + 0.522013i
\(304\) 83.4914 + 48.2038i 0.274643 + 0.158565i
\(305\) 0 0
\(306\) 77.1128 44.5211i 0.252003 0.145494i
\(307\) −470.478 −1.53250 −0.766251 0.642542i \(-0.777880\pi\)
−0.766251 + 0.642542i \(0.777880\pi\)
\(308\) −58.4024 87.8852i −0.189618 0.285341i
\(309\) −157.704 −0.510370
\(310\) 0 0
\(311\) 217.631 + 125.649i 0.699778 + 0.404017i 0.807265 0.590189i \(-0.200947\pi\)
−0.107487 + 0.994207i \(0.534280\pi\)
\(312\) 90.7528 + 52.3962i 0.290874 + 0.167936i
\(313\) −194.231 336.417i −0.620545 1.07482i −0.989384 0.145322i \(-0.953578\pi\)
0.368839 0.929493i \(-0.379755\pi\)
\(314\) 161.490i 0.514300i
\(315\) 0 0
\(316\) 197.492 0.624974
\(317\) −129.366 + 74.6898i −0.408096 + 0.235614i −0.689971 0.723837i \(-0.742377\pi\)
0.281875 + 0.959451i \(0.409044\pi\)
\(318\) −60.9897 + 105.637i −0.191792 + 0.332193i
\(319\) −37.5588 + 65.0538i −0.117739 + 0.203930i
\(320\) 0 0
\(321\) 89.2636i 0.278080i
\(322\) −24.5572 + 49.4815i −0.0762645 + 0.153669i
\(323\) 505.837i 1.56606i
\(324\) 9.00000 + 15.5885i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) −34.4475 + 59.6648i −0.105667 + 0.183021i
\(327\) −33.2219 57.5420i −0.101596 0.175970i
\(328\) 144.484 0.440499
\(329\) 300.835 + 452.702i 0.914391 + 1.37600i
\(330\) 0 0
\(331\) 235.465 + 407.838i 0.711375 + 1.23214i 0.964341 + 0.264663i \(0.0852607\pi\)
−0.252966 + 0.967475i \(0.581406\pi\)
\(332\) 26.9448 46.6697i 0.0811590 0.140571i
\(333\) −58.1880 33.5948i −0.174739 0.100885i
\(334\) −60.7628 + 35.0814i −0.181925 + 0.105034i
\(335\) 0 0
\(336\) 48.4014 3.04961i 0.144052 0.00907622i
\(337\) 532.478i 1.58005i 0.613072 + 0.790027i \(0.289934\pi\)
−0.613072 + 0.790027i \(0.710066\pi\)
\(338\) −353.412 + 204.042i −1.04560 + 0.603676i
\(339\) −297.836 171.956i −0.878573 0.507244i
\(340\) 0 0
\(341\) −42.9675 + 24.8073i −0.126004 + 0.0727487i
\(342\) −102.256 −0.298993
\(343\) −336.907 + 64.3643i −0.982236 + 0.187651i
\(344\) 98.3321 0.285849
\(345\) 0 0
\(346\) 288.232 + 166.411i 0.833042 + 0.480957i
\(347\) 389.385 + 224.812i 1.12215 + 0.647872i 0.941948 0.335758i \(-0.108992\pi\)
0.180199 + 0.983630i \(0.442326\pi\)
\(348\) −17.2621 29.8988i −0.0496036 0.0859160i
\(349\) 330.676i 0.947495i 0.880661 + 0.473747i \(0.157099\pi\)
−0.880661 + 0.473747i \(0.842901\pi\)
\(350\) 0 0
\(351\) −111.149 −0.316664
\(352\) −36.9246 + 21.3184i −0.104899 + 0.0605637i
\(353\) −135.686 + 235.014i −0.384379 + 0.665763i −0.991683 0.128706i \(-0.958918\pi\)
0.607304 + 0.794469i \(0.292251\pi\)
\(354\) 103.147 178.657i 0.291377 0.504680i
\(355\) 0 0
\(356\) 27.8174i 0.0781389i
\(357\) 140.835 + 211.932i 0.394496 + 0.593646i
\(358\) 62.5221i 0.174643i
\(359\) −3.79200 6.56794i −0.0105627 0.0182951i 0.860696 0.509120i \(-0.170029\pi\)
−0.871258 + 0.490825i \(0.836696\pi\)
\(360\) 0 0
\(361\) 109.950 190.440i 0.304572 0.527534i
\(362\) −82.7661 143.355i −0.228636 0.396009i
\(363\) 111.181 0.306285
\(364\) −133.130 + 268.250i −0.365741 + 0.736951i
\(365\) 0 0
\(366\) −102.446 177.442i −0.279908 0.484814i
\(367\) 265.706 460.216i 0.723995 1.25400i −0.235392 0.971901i \(-0.575637\pi\)
0.959386 0.282095i \(-0.0910293\pi\)
\(368\) 19.3300 + 11.1602i 0.0525272 + 0.0303266i
\(369\) −132.717 + 76.6240i −0.359666 + 0.207653i
\(370\) 0 0
\(371\) −312.246 154.965i −0.841634 0.417695i
\(372\) 22.8029i 0.0612981i
\(373\) 497.937 287.484i 1.33495 0.770734i 0.348897 0.937161i \(-0.386556\pi\)
0.986054 + 0.166427i \(0.0532229\pi\)
\(374\) −193.738 111.855i −0.518016 0.299077i
\(375\) 0 0
\(376\) 190.201 109.813i 0.505854 0.292055i
\(377\) 213.185 0.565476
\(378\) −42.8423 + 28.4700i −0.113339 + 0.0753174i
\(379\) −627.464 −1.65558 −0.827789 0.561040i \(-0.810402\pi\)
−0.827789 + 0.561040i \(0.810402\pi\)
\(380\) 0 0
\(381\) 111.170 + 64.1839i 0.291784 + 0.168462i
\(382\) 286.973 + 165.684i 0.751238 + 0.433727i
\(383\) 33.3056 + 57.6870i 0.0869597 + 0.150619i 0.906225 0.422797i \(-0.138952\pi\)
−0.819265 + 0.573415i \(0.805618\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −27.6691 −0.0716817
\(387\) −90.3238 + 52.1485i −0.233395 + 0.134751i
\(388\) −3.69132 + 6.39356i −0.00951372 + 0.0164782i
\(389\) 274.525 475.491i 0.705719 1.22234i −0.260713 0.965416i \(-0.583957\pi\)
0.966431 0.256925i \(-0.0827092\pi\)
\(390\) 0 0
\(391\) 117.112i 0.299519i
\(392\) 17.3955 + 137.497i 0.0443762 + 0.350757i
\(393\) 34.7000i 0.0882950i
\(394\) −126.885 219.772i −0.322044 0.557796i
\(395\) 0 0
\(396\) 22.6116 39.1644i 0.0571000 0.0989001i
\(397\) 259.283 + 449.091i 0.653106 + 1.13121i 0.982365 + 0.186973i \(0.0598676\pi\)
−0.329259 + 0.944240i \(0.606799\pi\)
\(398\) −361.920 −0.909347
\(399\) −18.3753 291.642i −0.0460535 0.730931i
\(400\) 0 0
\(401\) 238.149 + 412.486i 0.593888 + 1.02864i 0.993703 + 0.112048i \(0.0357411\pi\)
−0.399815 + 0.916596i \(0.630926\pi\)
\(402\) 81.5462 141.242i 0.202851 0.351349i
\(403\) 121.942 + 70.4033i 0.302586 + 0.174698i
\(404\) −316.340 + 182.639i −0.783020 + 0.452077i
\(405\) 0 0
\(406\) 82.1717 54.6056i 0.202393 0.134497i
\(407\) 168.807i 0.414760i
\(408\) 89.0422 51.4085i 0.218241 0.126001i
\(409\) 93.2552 + 53.8409i 0.228008 + 0.131640i 0.609653 0.792669i \(-0.291309\pi\)
−0.381645 + 0.924309i \(0.624642\pi\)
\(410\) 0 0
\(411\) −129.256 + 74.6259i −0.314491 + 0.181572i
\(412\) −182.101 −0.441993
\(413\) 528.079 + 262.080i 1.27864 + 0.634577i
\(414\) −23.6743 −0.0571844
\(415\) 0 0
\(416\) 104.792 + 60.5019i 0.251905 + 0.145437i
\(417\) −348.753 201.353i −0.836339 0.482861i
\(418\) 128.454 + 222.488i 0.307305 + 0.532268i
\(419\) 323.811i 0.772818i −0.922328 0.386409i \(-0.873715\pi\)
0.922328 0.386409i \(-0.126285\pi\)
\(420\) 0 0
\(421\) −238.957 −0.567595 −0.283797 0.958884i \(-0.591594\pi\)
−0.283797 + 0.958884i \(0.591594\pi\)
\(422\) −241.141 + 139.223i −0.571424 + 0.329912i
\(423\) −116.474 + 201.739i −0.275352 + 0.476924i
\(424\) −70.4249 + 121.979i −0.166096 + 0.287687i
\(425\) 0 0
\(426\) 166.822i 0.391601i
\(427\) 487.670 324.071i 1.14208 0.758950i
\(428\) 103.073i 0.240824i
\(429\) 139.625 + 241.838i 0.325467 + 0.563726i
\(430\) 0 0
\(431\) 95.8960 166.097i 0.222497 0.385375i −0.733069 0.680154i \(-0.761913\pi\)
0.955565 + 0.294779i \(0.0952461\pi\)
\(432\) 10.3923 + 18.0000i 0.0240563 + 0.0416667i
\(433\) 122.083 0.281946 0.140973 0.990013i \(-0.454977\pi\)
0.140973 + 0.990013i \(0.454977\pi\)
\(434\) 65.0358 4.09768i 0.149852 0.00944166i
\(435\) 0 0
\(436\) −38.3614 66.4438i −0.0879848 0.152394i
\(437\) 67.2454 116.472i 0.153880 0.266527i
\(438\) 185.948 + 107.357i 0.424538 + 0.245107i
\(439\) 217.656 125.664i 0.495800 0.286250i −0.231177 0.972912i \(-0.574258\pi\)
0.726978 + 0.686661i \(0.240924\pi\)
\(440\) 0 0
\(441\) −88.8975 117.074i −0.201582 0.265473i
\(442\) 634.890i 1.43640i
\(443\) −95.0802 + 54.8946i −0.214628 + 0.123916i −0.603460 0.797393i \(-0.706212\pi\)
0.388832 + 0.921309i \(0.372879\pi\)
\(444\) −67.1897 38.7920i −0.151328 0.0873693i
\(445\) 0 0
\(446\) −527.883 + 304.773i −1.18359 + 0.683349i
\(447\) −380.924 −0.852178
\(448\) 55.8892 3.52139i 0.124753 0.00786024i
\(449\) −806.490 −1.79619 −0.898095 0.439801i \(-0.855049\pi\)
−0.898095 + 0.439801i \(0.855049\pi\)
\(450\) 0 0
\(451\) 333.437 + 192.510i 0.739329 + 0.426852i
\(452\) −343.912 198.558i −0.760867 0.439287i
\(453\) −225.965 391.383i −0.498819 0.863980i
\(454\) 247.623i 0.545425i
\(455\) 0 0
\(456\) −118.075 −0.258936
\(457\) −668.964 + 386.226i −1.46382 + 0.845135i −0.999185 0.0403698i \(-0.987146\pi\)
−0.464631 + 0.885504i \(0.653813\pi\)
\(458\) 23.7370 41.1137i 0.0518275 0.0897678i
\(459\) −54.5270 + 94.4435i −0.118795 + 0.205759i
\(460\) 0 0
\(461\) 793.611i 1.72150i −0.509029 0.860749i \(-0.669995\pi\)
0.509029 0.860749i \(-0.330005\pi\)
\(462\) 115.764 + 57.4523i 0.250570 + 0.124356i
\(463\) 274.227i 0.592284i 0.955144 + 0.296142i \(0.0957001\pi\)
−0.955144 + 0.296142i \(0.904300\pi\)
\(464\) −19.9325 34.5241i −0.0429580 0.0744054i
\(465\) 0 0
\(466\) 109.540 189.730i 0.235065 0.407145i
\(467\) 198.815 + 344.357i 0.425727 + 0.737381i 0.996488 0.0837354i \(-0.0266851\pi\)
−0.570761 + 0.821116i \(0.693352\pi\)
\(468\) −128.344 −0.274239
\(469\) 417.488 + 207.195i 0.890166 + 0.441781i
\(470\) 0 0
\(471\) 98.8921 + 171.286i 0.209962 + 0.363665i
\(472\) 119.104 206.295i 0.252340 0.437065i
\(473\) 226.930 + 131.018i 0.479766 + 0.276993i
\(474\) −209.472 + 120.939i −0.441923 + 0.255145i
\(475\) 0 0
\(476\) 162.622 + 244.717i 0.341643 + 0.514112i
\(477\) 149.394i 0.313194i
\(478\) 387.743 223.864i 0.811179 0.468334i
\(479\) 165.573 + 95.5938i 0.345665 + 0.199570i 0.662774 0.748819i \(-0.269379\pi\)
−0.317110 + 0.948389i \(0.602712\pi\)
\(480\) 0 0
\(481\) 414.893 239.538i 0.862563 0.498001i
\(482\) −330.223 −0.685110
\(483\) −4.25428 67.5212i −0.00880803 0.139795i
\(484\) 128.381 0.265250
\(485\) 0 0
\(486\) −19.0919 11.0227i −0.0392837 0.0226805i
\(487\) 164.561 + 95.0092i 0.337907 + 0.195091i 0.659346 0.751840i \(-0.270833\pi\)
−0.321439 + 0.946930i \(0.604167\pi\)
\(488\) −118.295 204.892i −0.242407 0.419862i
\(489\) 84.3788i 0.172554i
\(490\) 0 0
\(491\) −211.384 −0.430517 −0.215258 0.976557i \(-0.569059\pi\)
−0.215258 + 0.976557i \(0.569059\pi\)
\(492\) −153.248 + 88.4777i −0.311480 + 0.179833i
\(493\) 104.583 181.143i 0.212136 0.367430i
\(494\) 364.552 631.423i 0.737960 1.27818i
\(495\) 0 0
\(496\) 26.3305i 0.0530857i
\(497\) 475.791 29.9779i 0.957325 0.0603178i
\(498\) 66.0010i 0.132532i
\(499\) −126.864 219.734i −0.254236 0.440349i 0.710452 0.703746i \(-0.248491\pi\)
−0.964688 + 0.263396i \(0.915157\pi\)
\(500\) 0 0
\(501\) 42.9658 74.4190i 0.0857601 0.148541i
\(502\) 40.0844 + 69.4282i 0.0798494 + 0.138303i
\(503\) −217.815 −0.433033 −0.216516 0.976279i \(-0.569469\pi\)
−0.216516 + 0.976279i \(0.569469\pi\)
\(504\) −49.4700 + 32.8743i −0.0981547 + 0.0652268i
\(505\) 0 0
\(506\) 29.7397 + 51.5107i 0.0587741 + 0.101800i
\(507\) 249.900 432.839i 0.492899 0.853727i
\(508\) 128.368 + 74.1132i 0.252693 + 0.145892i
\(509\) 24.6582 14.2364i 0.0484444 0.0279694i −0.475582 0.879671i \(-0.657763\pi\)
0.524027 + 0.851702i \(0.324429\pi\)
\(510\) 0 0
\(511\) −272.776 + 549.630i −0.533808 + 1.07560i
\(512\) 22.6274i 0.0441942i
\(513\) 108.458 62.6185i 0.211420 0.122063i
\(514\) 355.714 + 205.371i 0.692050 + 0.399555i
\(515\) 0 0
\(516\) −104.297 + 60.2159i −0.202126 + 0.116697i
\(517\) 585.258 1.13203
\(518\) 98.5640 198.601i 0.190278 0.383400i
\(519\) −407.622 −0.785399
\(520\) 0 0
\(521\) 671.401 + 387.634i 1.28868 + 0.744019i 0.978418 0.206633i \(-0.0662507\pi\)
0.310260 + 0.950652i \(0.399584\pi\)
\(522\) 36.6184 + 21.1416i 0.0701501 + 0.0405012i
\(523\) 51.2334 + 88.7388i 0.0979605 + 0.169673i 0.910840 0.412759i \(-0.135435\pi\)
−0.812880 + 0.582431i \(0.802101\pi\)
\(524\) 40.0681i 0.0764657i
\(525\) 0 0
\(526\) −628.752 −1.19535
\(527\) 119.644 69.0763i 0.227028 0.131075i
\(528\) 26.1096 45.2232i 0.0494501 0.0856500i
\(529\) −248.931 + 431.162i −0.470570 + 0.815050i
\(530\) 0 0
\(531\) 252.659i 0.475816i
\(532\) −21.2180 336.759i −0.0398835 0.633005i
\(533\) 1092.69i 2.05008i
\(534\) −17.0346 29.5049i −0.0319001 0.0552525i
\(535\) 0 0
\(536\) 94.1614 163.092i 0.175674 0.304277i
\(537\) 38.2868 + 66.3147i 0.0712976 + 0.123491i
\(538\) −236.712 −0.439984
\(539\) −143.056 + 340.491i −0.265410 + 0.631709i
\(540\) 0 0
\(541\) 408.868 + 708.180i 0.755763 + 1.30902i 0.944994 + 0.327088i \(0.106067\pi\)
−0.189231 + 0.981933i \(0.560599\pi\)
\(542\) −1.82976 + 3.16924i −0.00337594 + 0.00584730i
\(543\) 175.573 + 101.367i 0.323340 + 0.186680i
\(544\) 102.817 59.3614i 0.189002 0.109120i
\(545\) 0 0
\(546\) −23.0634 366.047i −0.0422406 0.670416i
\(547\) 204.209i 0.373325i −0.982424 0.186662i \(-0.940233\pi\)
0.982424 0.186662i \(-0.0597670\pi\)
\(548\) −149.252 + 86.1706i −0.272357 + 0.157246i
\(549\) 217.321 + 125.471i 0.395849 + 0.228544i
\(550\) 0 0
\(551\) −208.024 + 120.103i −0.377539 + 0.217972i
\(552\) −27.3368 −0.0495231
\(553\) −382.569 575.698i −0.691806 1.04105i
\(554\) 719.992 1.29962
\(555\) 0 0
\(556\) −402.706 232.502i −0.724291 0.418169i
\(557\) −464.253 268.036i −0.833487 0.481214i 0.0215578 0.999768i \(-0.493137\pi\)
−0.855045 + 0.518553i \(0.826471\pi\)
\(558\) 13.9639 + 24.1861i 0.0250249 + 0.0433443i
\(559\) 743.660i 1.33034i
\(560\) 0 0
\(561\) 273.987 0.488391
\(562\) −258.039 + 148.979i −0.459144 + 0.265087i
\(563\) −494.806 + 857.029i −0.878874 + 1.52225i −0.0262960 + 0.999654i \(0.508371\pi\)
−0.852578 + 0.522600i \(0.824962\pi\)
\(564\) −134.492 + 232.948i −0.238462 + 0.413028i
\(565\) 0 0
\(566\) 55.8424i 0.0986616i
\(567\) 28.0068 56.4324i 0.0493948 0.0995281i
\(568\) 192.630i 0.339137i
\(569\) 248.330 + 430.120i 0.436432 + 0.755922i 0.997411 0.0719076i \(-0.0229087\pi\)
−0.560979 + 0.827830i \(0.689575\pi\)
\(570\) 0 0
\(571\) 71.0244 123.018i 0.124386 0.215443i −0.797107 0.603838i \(-0.793637\pi\)
0.921493 + 0.388395i \(0.126971\pi\)
\(572\) 161.226 + 279.251i 0.281863 + 0.488201i
\(573\) −405.841 −0.708274
\(574\) −279.884 421.176i −0.487604 0.733757i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) 189.689 328.551i 0.328751 0.569413i −0.653514 0.756915i \(-0.726706\pi\)
0.982264 + 0.187502i \(0.0600391\pi\)
\(578\) 185.515 + 107.107i 0.320961 + 0.185307i
\(579\) 29.3476 16.9438i 0.0506866 0.0292639i
\(580\) 0 0
\(581\) −188.240 + 11.8604i −0.323993 + 0.0204137i
\(582\) 9.04185i 0.0155358i
\(583\) −325.051 + 187.668i −0.557549 + 0.321901i
\(584\) 214.714 + 123.965i 0.367661 + 0.212269i
\(585\) 0 0
\(586\) −109.740 + 63.3584i −0.187269 + 0.108120i
\(587\) 234.204 0.398984 0.199492 0.979899i \(-0.436071\pi\)
0.199492 + 0.979899i \(0.436071\pi\)
\(588\) −102.650 135.185i −0.174575 0.229906i
\(589\) −158.654 −0.269361
\(590\) 0 0
\(591\) 269.164 + 155.402i 0.455438 + 0.262948i
\(592\) −77.5840 44.7931i −0.131054 0.0756641i
\(593\) 286.272 + 495.838i 0.482753 + 0.836152i 0.999804 0.0198023i \(-0.00630369\pi\)
−0.517051 + 0.855954i \(0.672970\pi\)
\(594\) 55.3869i 0.0932439i
\(595\) 0 0
\(596\) −439.853 −0.738008
\(597\) 383.874 221.630i 0.643006 0.371239i
\(598\) 84.4016 146.188i 0.141140 0.244461i
\(599\) 46.7105 80.9049i 0.0779807 0.135067i −0.824398 0.566011i \(-0.808486\pi\)
0.902379 + 0.430944i \(0.141819\pi\)
\(600\) 0 0
\(601\) 167.140i 0.278103i 0.990285 + 0.139051i \(0.0444053\pi\)
−0.990285 + 0.139051i \(0.955595\pi\)
\(602\) −190.483 286.643i −0.316417 0.476151i
\(603\) 199.746i 0.331255i
\(604\) −260.922 451.930i −0.431990 0.748229i
\(605\) 0 0
\(606\) 223.686 387.436i 0.369119 0.639333i
\(607\) −459.572 796.002i −0.757120 1.31137i −0.944314 0.329047i \(-0.893273\pi\)
0.187194 0.982323i \(-0.440061\pi\)
\(608\) −136.341 −0.224245
\(609\) −53.7173 + 108.238i −0.0882058 + 0.177730i
\(610\) 0 0
\(611\) −830.484 1438.44i −1.35922 2.35424i
\(612\) −62.9623 + 109.054i −0.102880 + 0.178193i
\(613\) −675.011 389.718i −1.10116 0.635755i −0.164635 0.986355i \(-0.552644\pi\)
−0.936525 + 0.350600i \(0.885978\pi\)
\(614\) 576.215 332.678i 0.938462 0.541821i
\(615\) 0 0
\(616\) 133.672 + 66.3402i 0.217000 + 0.107695i
\(617\) 510.821i 0.827911i 0.910297 + 0.413956i \(0.135853\pi\)
−0.910297 + 0.413956i \(0.864147\pi\)
\(618\) 193.148 111.514i 0.312536 0.180443i
\(619\) 808.792 + 466.956i 1.30661 + 0.754372i 0.981529 0.191314i \(-0.0612749\pi\)
0.325082 + 0.945686i \(0.394608\pi\)
\(620\) 0 0
\(621\) 25.1104 14.4975i 0.0404355 0.0233454i
\(622\) −355.390 −0.571367
\(623\) 81.0892 53.8862i 0.130159 0.0864947i
\(624\) −148.199 −0.237498
\(625\) 0 0
\(626\) 475.766 + 274.684i 0.760009 + 0.438792i
\(627\) −272.491 157.323i −0.434595 0.250914i
\(628\) 114.191 + 197.784i 0.181832 + 0.314943i
\(629\) 470.047i 0.747292i
\(630\) 0 0
\(631\) −614.861 −0.974423 −0.487212 0.873284i \(-0.661986\pi\)
−0.487212 + 0.873284i \(0.661986\pi\)
\(632\) −241.877 + 139.648i −0.382717 + 0.220962i
\(633\) 170.512 295.336i 0.269372 0.466566i
\(634\) 105.627 182.952i 0.166605 0.288568i
\(635\) 0 0
\(636\) 172.505i 0.271234i
\(637\) 1039.85 131.557i 1.63242 0.206526i
\(638\) 106.232i 0.166508i
\(639\) 102.157 + 176.942i 0.159871 + 0.276904i
\(640\) 0 0
\(641\) 94.1724 163.111i 0.146915 0.254464i −0.783171 0.621807i \(-0.786399\pi\)
0.930086 + 0.367343i \(0.119732\pi\)
\(642\) −63.1189 109.325i −0.0983161 0.170288i
\(643\) 23.8831 0.0371432 0.0185716 0.999828i \(-0.494088\pi\)
0.0185716 + 0.999828i \(0.494088\pi\)
\(644\) −4.91242 77.9667i −0.00762798 0.121066i
\(645\) 0 0
\(646\) −357.681 619.521i −0.553685 0.959011i
\(647\) 542.667 939.928i 0.838744 1.45275i −0.0522010 0.998637i \(-0.516624\pi\)
0.890945 0.454111i \(-0.150043\pi\)
\(648\) −22.0454 12.7279i −0.0340207 0.0196419i
\(649\) 549.735 317.390i 0.847049 0.489044i
\(650\) 0 0
\(651\) −66.4715 + 44.1724i −0.102107 + 0.0678531i
\(652\) 97.4323i 0.149436i
\(653\) 550.536 317.852i 0.843087 0.486756i −0.0152254 0.999884i \(-0.504847\pi\)
0.858312 + 0.513128i \(0.171513\pi\)
\(654\) 81.3767 + 46.9829i 0.124429 + 0.0718393i
\(655\) 0 0
\(656\) −176.955 + 102.165i −0.269749 + 0.155740i
\(657\) −262.970 −0.400258
\(658\) −688.555 341.723i −1.04644 0.519336i
\(659\) 888.955 1.34895 0.674473 0.738300i \(-0.264371\pi\)
0.674473 + 0.738300i \(0.264371\pi\)
\(660\) 0 0
\(661\) −656.362 378.951i −0.992983 0.573299i −0.0868187 0.996224i \(-0.527670\pi\)
−0.906165 + 0.422925i \(0.861003\pi\)
\(662\) −576.770 332.998i −0.871253 0.503018i
\(663\) −388.789 673.402i −0.586409 1.01569i
\(664\) 76.2114i 0.114776i
\(665\) 0 0
\(666\) 95.0206 0.142674
\(667\) −48.1620 + 27.8063i −0.0722068 + 0.0416886i
\(668\) 49.6127 85.9316i 0.0742704 0.128640i
\(669\) 373.270 646.522i 0.557952 0.966401i
\(670\) 0 0
\(671\) 630.464i 0.939589i
\(672\) −57.1230 + 37.9600i −0.0850045 + 0.0564881i
\(673\) 936.839i 1.39203i −0.718026 0.696017i \(-0.754954\pi\)
0.718026 0.696017i \(-0.245046\pi\)
\(674\) −376.519 652.150i −0.558634 0.967582i
\(675\) 0 0
\(676\) 288.560 499.800i 0.426863 0.739349i
\(677\) 123.589 + 214.062i 0.182554 + 0.316192i 0.942749 0.333502i \(-0.108230\pi\)
−0.760196 + 0.649694i \(0.774897\pi\)
\(678\) 486.365 0.717352
\(679\) 25.7881 1.62482i 0.0379795 0.00239296i
\(680\) 0 0
\(681\) −151.637 262.644i −0.222669 0.385673i
\(682\) 35.0828 60.7652i 0.0514411 0.0890986i
\(683\) −607.755 350.887i −0.889831 0.513744i −0.0159438 0.999873i \(-0.505075\pi\)
−0.873887 + 0.486129i \(0.838409\pi\)
\(684\) 125.237 72.3057i 0.183095 0.105710i
\(685\) 0 0
\(686\) 367.112 317.059i 0.535149 0.462185i
\(687\) 58.1435i 0.0846339i
\(688\) −120.432 + 69.5313i −0.175046 + 0.101063i
\(689\) 922.498 + 532.604i 1.33889 + 0.773011i
\(690\) 0 0
\(691\) −530.850 + 306.486i −0.768234 + 0.443540i −0.832244 0.554409i \(-0.812944\pi\)
0.0640104 + 0.997949i \(0.479611\pi\)
\(692\) −470.682 −0.680176
\(693\) −157.968 + 9.95302i −0.227948 + 0.0143622i
\(694\) −635.863 −0.916230
\(695\) 0 0
\(696\) 42.2832 + 24.4122i 0.0607518 + 0.0350750i
\(697\) −928.461 536.047i −1.33208 0.769078i
\(698\) −233.823 404.993i −0.334990 0.580220i
\(699\) 268.318i 0.383860i
\(700\) 0 0
\(701\) 161.307 0.230110 0.115055 0.993359i \(-0.463296\pi\)
0.115055 + 0.993359i \(0.463296\pi\)
\(702\) 136.129 78.5942i 0.193916 0.111958i
\(703\) −269.900 + 467.480i −0.383926 + 0.664979i
\(704\) 30.1488 52.2193i 0.0428250 0.0741751i
\(705\) 0 0
\(706\) 383.777i 0.543593i
\(707\) 1145.20 + 568.349i 1.61980 + 0.803889i
\(708\) 291.745i 0.412069i
\(709\) 285.175 + 493.938i 0.402222 + 0.696669i 0.993994 0.109436i \(-0.0349046\pi\)
−0.591772 + 0.806106i \(0.701571\pi\)
\(710\) 0 0
\(711\) 148.119 256.549i 0.208325 0.360829i
\(712\) −19.6699 34.0693i −0.0276263 0.0478501i
\(713\) −36.7317 −0.0515171
\(714\) −322.345 159.977i −0.451464 0.224057i
\(715\) 0 0
\(716\) 44.2098 + 76.5736i 0.0617455 + 0.106946i
\(717\) −274.176 + 474.887i −0.382393 + 0.662325i
\(718\) 9.28847 + 5.36270i 0.0129366 + 0.00746894i
\(719\) −431.817 + 249.310i −0.600580 + 0.346745i −0.769270 0.638924i \(-0.779380\pi\)
0.168690 + 0.985669i \(0.446046\pi\)
\(720\) 0 0
\(721\) 352.755 + 530.834i 0.489258 + 0.736246i
\(722\) 310.987i 0.430730i
\(723\) 350.254 202.219i 0.484446 0.279695i
\(724\) 202.735 + 117.049i 0.280020 + 0.161670i
\(725\) 0 0
\(726\) −136.169 + 78.6171i −0.187560 + 0.108288i
\(727\) 1058.79 1.45638 0.728190 0.685375i \(-0.240362\pi\)
0.728190 + 0.685375i \(0.240362\pi\)
\(728\) −26.6313 422.675i −0.0365815 0.580597i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) −631.888 364.821i −0.864416 0.499071i
\(732\) 250.941 + 144.881i 0.342816 + 0.197925i
\(733\) −7.56721 13.1068i −0.0103236 0.0178810i 0.860817 0.508914i \(-0.169953\pi\)
−0.871141 + 0.491033i \(0.836620\pi\)
\(734\) 751.530i 1.02388i
\(735\) 0 0
\(736\) −31.5658 −0.0428883
\(737\) 434.609 250.922i 0.589700 0.340463i
\(738\) 108.363 187.690i 0.146833 0.254322i
\(739\) −81.3819 + 140.958i −0.110124 + 0.190741i −0.915820 0.401588i \(-0.868458\pi\)
0.805696 + 0.592329i \(0.201792\pi\)
\(740\) 0 0
\(741\) 892.967i 1.20508i
\(742\) 491.998 30.9991i 0.663071 0.0417778i
\(743\) 338.071i 0.455009i −0.973777 0.227504i \(-0.926943\pi\)
0.973777 0.227504i \(-0.0730566\pi\)
\(744\) 16.1241 + 27.9277i 0.0216722 + 0.0375373i
\(745\) 0 0
\(746\) −406.564 + 704.189i −0.544991 + 0.943953i
\(747\) −40.4172 70.0046i −0.0541060 0.0937143i
\(748\) 316.373 0.422959
\(749\) 300.462 199.666i 0.401151 0.266577i
\(750\) 0 0
\(751\) −239.087 414.111i −0.318359 0.551413i 0.661787 0.749692i \(-0.269798\pi\)
−0.980146 + 0.198279i \(0.936465\pi\)
\(752\) −155.299 + 268.985i −0.206514 + 0.357693i
\(753\) −85.0319 49.0932i −0.112924 0.0651968i
\(754\) −261.097 + 150.744i −0.346282 + 0.199926i
\(755\) 0 0
\(756\) 32.3395 65.1625i 0.0427771 0.0861938i
\(757\) 397.788i 0.525479i −0.964867 0.262739i \(-0.915374\pi\)
0.964867 0.262739i \(-0.0846260\pi\)
\(758\) 768.483 443.684i 1.01383 0.585335i
\(759\) −63.0874 36.4236i −0.0831192 0.0479889i
\(760\) 0 0
\(761\) −1264.02 + 729.785i −1.66100 + 0.958981i −0.688767 + 0.724983i \(0.741848\pi\)
−0.972237 + 0.233998i \(0.924819\pi\)
\(762\) −181.540 −0.238241
\(763\) −119.376 + 240.536i −0.156456 + 0.315250i
\(764\) −468.625 −0.613383
\(765\) 0 0
\(766\) −81.5817 47.1012i −0.106503 0.0614898i
\(767\) −1560.15 900.755i −2.03410 1.17439i
\(768\) 13.8564 + 24.0000i 0.0180422 + 0.0312500i
\(769\) 2.10093i 0.00273203i 0.999999 + 0.00136602i \(0.000434817\pi\)
−0.999999 + 0.00136602i \(0.999565\pi\)
\(770\) 0 0
\(771\) −503.055 −0.652471
\(772\) 33.8876 19.5650i 0.0438959 0.0253433i
\(773\) 226.305 391.972i 0.292762 0.507079i −0.681700 0.731632i \(-0.738759\pi\)
0.974462 + 0.224553i \(0.0720923\pi\)
\(774\) 73.7491 127.737i 0.0952830 0.165035i
\(775\) 0 0
\(776\) 10.4406i 0.0134544i
\(777\) 17.0752 + 271.007i 0.0219758 + 0.348786i
\(778\) 776.473i 0.998037i
\(779\) 615.594 + 1066.24i 0.790236 + 1.36873i
\(780\) 0 0
\(781\) 256.660 444.548i 0.328630 0.569204i