Properties

Label 1050.3.q.e.199.15
Level $1050$
Weight $3$
Character 1050.199
Analytic conductor $28.610$
Analytic rank $0$
Dimension $32$
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: \(32\)
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 199.15
Character \(\chi\) \(=\) 1050.199
Dual form 1050.3.q.e.649.15

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-4.01037 + 5.73733i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-4.01037 + 5.73733i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(8.69259 - 15.0560i) q^{11} +(1.73205 + 3.00000i) q^{12} -7.22559 q^{13} +(-0.854777 + 9.86252i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(1.32600 - 2.29669i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-2.20128 + 1.27091i) q^{19} +(-5.13291 - 10.9842i) q^{21} -24.5864i q^{22} +(-34.7289 + 20.0507i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-8.84951 + 5.10926i) q^{26} +5.19615 q^{27} +(5.92697 + 12.6835i) q^{28} -47.0080 q^{29} +(34.9025 + 20.1510i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(15.0560 + 26.0778i) q^{33} -3.75049i q^{34} -6.00000 q^{36} +(28.1482 - 16.2514i) q^{37} +(-1.79734 + 3.11308i) q^{38} +(6.25755 - 10.8384i) q^{39} -70.6679i q^{41} +(-14.0535 - 9.82336i) q^{42} -37.3732i q^{43} +(-17.3852 - 30.1120i) q^{44} +(-28.3560 + 49.1141i) q^{46} +(-16.7242 - 28.9672i) q^{47} +6.92820 q^{48} +(-16.8339 - 46.0176i) q^{49} +(2.29669 + 3.97799i) q^{51} +(-7.22559 + 12.5151i) q^{52} +(-61.3911 - 35.4442i) q^{53} +(6.36396 - 3.67423i) q^{54} +(16.2276 + 11.3430i) q^{56} -4.40256i q^{57} +(-57.5728 + 33.2397i) q^{58} +(-87.0863 - 50.2793i) q^{59} +(-11.1621 + 6.44446i) q^{61} +56.9955 q^{62} +(20.9216 + 1.81326i) q^{63} -8.00000 q^{64} +(36.8795 + 21.2924i) q^{66} +(-81.4689 - 47.0361i) q^{67} +(-2.65199 - 4.59339i) q^{68} -69.4578i q^{69} -11.5793 q^{71} +(-7.34847 + 4.24264i) q^{72} +(-11.3345 + 19.6320i) q^{73} +(22.9829 - 39.8076i) q^{74} +5.08364i q^{76} +(51.5208 + 110.252i) q^{77} -17.6990i q^{78} +(-12.0542 - 20.8785i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-49.9698 - 86.5502i) q^{82} +111.664 q^{83} +(-24.1581 - 2.09377i) q^{84} +(-26.4268 - 45.7726i) q^{86} +(40.7101 - 70.5120i) q^{87} +(-42.5848 - 24.5864i) q^{88} +(110.770 - 63.9533i) q^{89} +(28.9773 - 41.4556i) q^{91} +80.2029i q^{92} +(-60.4529 + 34.9025i) q^{93} +(-40.9658 - 23.6516i) q^{94} +(8.48528 - 4.89898i) q^{96} +7.48256 q^{97} +(-53.1566 - 44.4565i) q^{98} -52.1556 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
\(7\) −4.01037 + 5.73733i −0.572910 + 0.819618i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 2.59808i −0.166667 0.288675i
\(10\) 0 0
\(11\) 8.69259 15.0560i 0.790236 1.36873i −0.135585 0.990766i \(-0.543291\pi\)
0.925821 0.377963i \(-0.123375\pi\)
\(12\) 1.73205 + 3.00000i 0.144338 + 0.250000i
\(13\) −7.22559 −0.555815 −0.277907 0.960608i \(-0.589641\pi\)
−0.277907 + 0.960608i \(0.589641\pi\)
\(14\) −0.854777 + 9.86252i −0.0610555 + 0.704466i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 1.32600 2.29669i 0.0779998 0.135100i −0.824387 0.566027i \(-0.808480\pi\)
0.902387 + 0.430927i \(0.141813\pi\)
\(18\) −3.67423 2.12132i −0.204124 0.117851i
\(19\) −2.20128 + 1.27091i −0.115857 + 0.0668900i −0.556809 0.830641i \(-0.687974\pi\)
0.440952 + 0.897531i \(0.354641\pi\)
\(20\) 0 0
\(21\) −5.13291 10.9842i −0.244424 0.523058i
\(22\) 24.5864i 1.11756i
\(23\) −34.7289 + 20.0507i −1.50995 + 0.871771i −0.510019 + 0.860163i \(0.670361\pi\)
−0.999933 + 0.0116074i \(0.996305\pi\)
\(24\) 4.24264 + 2.44949i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) −8.84951 + 5.10926i −0.340366 + 0.196510i
\(27\) 5.19615 0.192450
\(28\) 5.92697 + 12.6835i 0.211678 + 0.452982i
\(29\) −47.0080 −1.62096 −0.810482 0.585763i \(-0.800795\pi\)
−0.810482 + 0.585763i \(0.800795\pi\)
\(30\) 0 0
\(31\) 34.9025 + 20.1510i 1.12589 + 0.650031i 0.942897 0.333084i \(-0.108089\pi\)
0.182990 + 0.983115i \(0.441422\pi\)
\(32\) −4.89898 2.82843i −0.153093 0.0883883i
\(33\) 15.0560 + 26.0778i 0.456243 + 0.790236i
\(34\) 3.75049i 0.110308i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 28.1482 16.2514i 0.760762 0.439226i −0.0688071 0.997630i \(-0.521919\pi\)
0.829569 + 0.558404i \(0.188586\pi\)
\(38\) −1.79734 + 3.11308i −0.0472984 + 0.0819232i
\(39\) 6.25755 10.8384i 0.160450 0.277907i
\(40\) 0 0
\(41\) 70.6679i 1.72361i −0.507241 0.861804i \(-0.669335\pi\)
0.507241 0.861804i \(-0.330665\pi\)
\(42\) −14.0535 9.82336i −0.334608 0.233890i
\(43\) 37.3732i 0.869144i −0.900637 0.434572i \(-0.856900\pi\)
0.900637 0.434572i \(-0.143100\pi\)
\(44\) −17.3852 30.1120i −0.395118 0.684364i
\(45\) 0 0
\(46\) −28.3560 + 49.1141i −0.616435 + 1.06770i
\(47\) −16.7242 28.9672i −0.355835 0.616324i 0.631426 0.775436i \(-0.282470\pi\)
−0.987260 + 0.159113i \(0.949137\pi\)
\(48\) 6.92820 0.144338
\(49\) −16.8339 46.0176i −0.343548 0.939135i
\(50\) 0 0
\(51\) 2.29669 + 3.97799i 0.0450332 + 0.0779998i
\(52\) −7.22559 + 12.5151i −0.138954 + 0.240675i
\(53\) −61.3911 35.4442i −1.15832 0.668758i −0.207422 0.978252i \(-0.566507\pi\)
−0.950902 + 0.309493i \(0.899841\pi\)
\(54\) 6.36396 3.67423i 0.117851 0.0680414i
\(55\) 0 0
\(56\) 16.2276 + 11.3430i 0.289779 + 0.202554i
\(57\) 4.40256i 0.0772379i
\(58\) −57.5728 + 33.2397i −0.992634 + 0.573098i
\(59\) −87.0863 50.2793i −1.47604 0.852192i −0.476405 0.879226i \(-0.658060\pi\)
−0.999635 + 0.0270340i \(0.991394\pi\)
\(60\) 0 0
\(61\) −11.1621 + 6.44446i −0.182986 + 0.105647i −0.588695 0.808355i \(-0.700358\pi\)
0.405709 + 0.914002i \(0.367025\pi\)
\(62\) 56.9955 0.919283
\(63\) 20.9216 + 1.81326i 0.332088 + 0.0287819i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 36.8795 + 21.2924i 0.558781 + 0.322612i
\(67\) −81.4689 47.0361i −1.21595 0.702031i −0.251904 0.967752i \(-0.581057\pi\)
−0.964050 + 0.265721i \(0.914390\pi\)
\(68\) −2.65199 4.59339i −0.0389999 0.0675498i
\(69\) 69.4578i 1.00663i
\(70\) 0 0
\(71\) −11.5793 −0.163088 −0.0815440 0.996670i \(-0.525985\pi\)
−0.0815440 + 0.996670i \(0.525985\pi\)
\(72\) −7.34847 + 4.24264i −0.102062 + 0.0589256i
\(73\) −11.3345 + 19.6320i −0.155267 + 0.268931i −0.933156 0.359471i \(-0.882957\pi\)
0.777889 + 0.628402i \(0.216291\pi\)
\(74\) 22.9829 39.8076i 0.310580 0.537940i
\(75\) 0 0
\(76\) 5.08364i 0.0668900i
\(77\) 51.5208 + 110.252i 0.669101 + 1.43185i
\(78\) 17.6990i 0.226910i
\(79\) −12.0542 20.8785i −0.152585 0.264285i 0.779592 0.626287i \(-0.215426\pi\)
−0.932177 + 0.362003i \(0.882093\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −49.9698 86.5502i −0.609388 1.05549i
\(83\) 111.664 1.34535 0.672676 0.739937i \(-0.265145\pi\)
0.672676 + 0.739937i \(0.265145\pi\)
\(84\) −24.1581 2.09377i −0.287597 0.0249258i
\(85\) 0 0
\(86\) −26.4268 45.7726i −0.307289 0.532240i
\(87\) 40.7101 70.5120i 0.467932 0.810482i
\(88\) −42.5848 24.5864i −0.483919 0.279390i
\(89\) 110.770 63.9533i 1.24461 0.718577i 0.274582 0.961564i \(-0.411460\pi\)
0.970030 + 0.242987i \(0.0781272\pi\)
\(90\) 0 0
\(91\) 28.9773 41.4556i 0.318432 0.455556i
\(92\) 80.2029i 0.871771i
\(93\) −60.4529 + 34.9025i −0.650031 + 0.375296i
\(94\) −40.9658 23.6516i −0.435807 0.251613i
\(95\) 0 0
\(96\) 8.48528 4.89898i 0.0883883 0.0510310i
\(97\) 7.48256 0.0771398 0.0385699 0.999256i \(-0.487720\pi\)
0.0385699 + 0.999256i \(0.487720\pi\)
\(98\) −53.1566 44.4565i −0.542414 0.453638i
\(99\) −52.1556 −0.526824
\(100\) 0 0
\(101\) −81.9228 47.2982i −0.811117 0.468299i 0.0362267 0.999344i \(-0.488466\pi\)
−0.847344 + 0.531045i \(0.821799\pi\)
\(102\) 5.62573 + 3.24802i 0.0551542 + 0.0318433i
\(103\) 29.9109 + 51.8072i 0.290397 + 0.502982i 0.973904 0.226962i \(-0.0728794\pi\)
−0.683507 + 0.729944i \(0.739546\pi\)
\(104\) 20.4371i 0.196510i
\(105\) 0 0
\(106\) −100.251 −0.945767
\(107\) 5.59592 3.23081i 0.0522983 0.0301945i −0.473623 0.880728i \(-0.657054\pi\)
0.525921 + 0.850533i \(0.323721\pi\)
\(108\) 5.19615 9.00000i 0.0481125 0.0833333i
\(109\) −81.9201 + 141.890i −0.751560 + 1.30174i 0.195506 + 0.980703i \(0.437365\pi\)
−0.947066 + 0.321038i \(0.895968\pi\)
\(110\) 0 0
\(111\) 56.2964i 0.507175i
\(112\) 27.8954 + 2.41768i 0.249066 + 0.0215864i
\(113\) 105.434i 0.933040i 0.884511 + 0.466520i \(0.154492\pi\)
−0.884511 + 0.466520i \(0.845508\pi\)
\(114\) −3.11308 5.39202i −0.0273077 0.0472984i
\(115\) 0 0
\(116\) −47.0080 + 81.4202i −0.405241 + 0.701898i
\(117\) 10.8384 + 18.7726i 0.0926358 + 0.160450i
\(118\) −142.211 −1.20518
\(119\) 7.85915 + 16.8183i 0.0660433 + 0.141330i
\(120\) 0 0
\(121\) −90.6223 156.962i −0.748945 1.29721i
\(122\) −9.11384 + 15.7856i −0.0747036 + 0.129391i
\(123\) 106.002 + 61.2002i 0.861804 + 0.497563i
\(124\) 69.8050 40.3019i 0.562944 0.325016i
\(125\) 0 0
\(126\) 26.9058 12.5730i 0.213538 0.0997858i
\(127\) 53.7033i 0.422860i 0.977393 + 0.211430i \(0.0678121\pi\)
−0.977393 + 0.211430i \(0.932188\pi\)
\(128\) −9.79796 + 5.65685i −0.0765466 + 0.0441942i
\(129\) 56.0598 + 32.3661i 0.434572 + 0.250900i
\(130\) 0 0
\(131\) −50.6489 + 29.2421i −0.386632 + 0.223222i −0.680700 0.732562i \(-0.738324\pi\)
0.294068 + 0.955785i \(0.404991\pi\)
\(132\) 60.2240 0.456243
\(133\) 1.53632 17.7263i 0.0115513 0.133280i
\(134\) −133.038 −0.992822
\(135\) 0 0
\(136\) −6.49603 3.75049i −0.0477650 0.0275771i
\(137\) 10.4936 + 6.05848i 0.0765956 + 0.0442225i 0.537809 0.843067i \(-0.319252\pi\)
−0.461213 + 0.887289i \(0.652586\pi\)
\(138\) −49.1141 85.0680i −0.355899 0.616435i
\(139\) 45.2562i 0.325584i −0.986660 0.162792i \(-0.947950\pi\)
0.986660 0.162792i \(-0.0520500\pi\)
\(140\) 0 0
\(141\) 57.9344 0.410882
\(142\) −14.1816 + 8.18777i −0.0998706 + 0.0576603i
\(143\) −62.8091 + 108.789i −0.439225 + 0.760759i
\(144\) −6.00000 + 10.3923i −0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) 32.0589i 0.219581i
\(147\) 83.6050 + 14.6016i 0.568741 + 0.0993309i
\(148\) 65.0055i 0.439226i
\(149\) −25.4474 44.0762i −0.170788 0.295814i 0.767908 0.640561i \(-0.221298\pi\)
−0.938696 + 0.344747i \(0.887965\pi\)
\(150\) 0 0
\(151\) 78.8476 136.568i 0.522169 0.904424i −0.477498 0.878633i \(-0.658456\pi\)
0.999667 0.0257911i \(-0.00821047\pi\)
\(152\) 3.59468 + 6.22616i 0.0236492 + 0.0409616i
\(153\) −7.95598 −0.0519999
\(154\) 141.060 + 98.6004i 0.915974 + 0.640263i
\(155\) 0 0
\(156\) −12.5151 21.6768i −0.0802249 0.138954i
\(157\) −83.9231 + 145.359i −0.534542 + 0.925854i 0.464643 + 0.885498i \(0.346183\pi\)
−0.999185 + 0.0403562i \(0.987151\pi\)
\(158\) −29.5266 17.0472i −0.186877 0.107894i
\(159\) 106.333 61.3911i 0.668758 0.386108i
\(160\) 0 0
\(161\) 24.2381 279.662i 0.150547 1.73703i
\(162\) 12.7279i 0.0785674i
\(163\) −239.517 + 138.285i −1.46943 + 0.848374i −0.999412 0.0342839i \(-0.989085\pi\)
−0.470015 + 0.882658i \(0.655752\pi\)
\(164\) −122.400 70.6679i −0.746344 0.430902i
\(165\) 0 0
\(166\) 136.760 78.9586i 0.823857 0.475654i
\(167\) 48.4258 0.289975 0.144987 0.989433i \(-0.453686\pi\)
0.144987 + 0.989433i \(0.453686\pi\)
\(168\) −31.0681 + 14.5181i −0.184929 + 0.0864170i
\(169\) −116.791 −0.691070
\(170\) 0 0
\(171\) 6.60384 + 3.81273i 0.0386190 + 0.0222967i
\(172\) −64.7323 37.3732i −0.376351 0.217286i
\(173\) 56.4843 + 97.8337i 0.326499 + 0.565513i 0.981815 0.189842i \(-0.0607977\pi\)
−0.655316 + 0.755355i \(0.727464\pi\)
\(174\) 115.146i 0.661756i
\(175\) 0 0
\(176\) −69.5407 −0.395118
\(177\) 150.838 87.0863i 0.852192 0.492013i
\(178\) 90.4437 156.653i 0.508111 0.880073i
\(179\) 165.708 287.015i 0.925744 1.60344i 0.135384 0.990793i \(-0.456773\pi\)
0.790360 0.612642i \(-0.209893\pi\)
\(180\) 0 0
\(181\) 213.328i 1.17861i 0.807912 + 0.589303i \(0.200598\pi\)
−0.807912 + 0.589303i \(0.799402\pi\)
\(182\) 6.17627 71.2626i 0.0339356 0.391553i
\(183\) 22.3243i 0.121991i
\(184\) 56.7120 + 98.2281i 0.308218 + 0.533848i
\(185\) 0 0
\(186\) −49.3596 + 85.4933i −0.265374 + 0.459642i
\(187\) −23.0527 39.9285i −0.123277 0.213521i
\(188\) −66.8969 −0.355835
\(189\) −20.8385 + 29.8120i −0.110257 + 0.157736i
\(190\) 0 0
\(191\) 33.4517 + 57.9400i 0.175140 + 0.303351i 0.940210 0.340596i \(-0.110629\pi\)
−0.765070 + 0.643947i \(0.777296\pi\)
\(192\) 6.92820 12.0000i 0.0360844 0.0625000i
\(193\) −97.5179 56.3020i −0.505274 0.291720i 0.225615 0.974217i \(-0.427561\pi\)
−0.730889 + 0.682497i \(0.760894\pi\)
\(194\) 9.16422 5.29097i 0.0472383 0.0272730i
\(195\) 0 0
\(196\) −96.5387 16.8605i −0.492544 0.0860231i
\(197\) 61.0211i 0.309752i −0.987934 0.154876i \(-0.950502\pi\)
0.987934 0.154876i \(-0.0494978\pi\)
\(198\) −63.8772 + 36.8795i −0.322612 + 0.186260i
\(199\) 165.554 + 95.5826i 0.831929 + 0.480314i 0.854513 0.519431i \(-0.173856\pi\)
−0.0225837 + 0.999745i \(0.507189\pi\)
\(200\) 0 0
\(201\) 141.108 81.4689i 0.702031 0.405318i
\(202\) −133.779 −0.662274
\(203\) 188.519 269.700i 0.928667 1.32857i
\(204\) 9.18678 0.0450332
\(205\) 0 0
\(206\) 73.2664 + 42.3004i 0.355662 + 0.205342i
\(207\) 104.187 + 60.1522i 0.503317 + 0.290590i
\(208\) 14.4512 + 25.0302i 0.0694768 + 0.120337i
\(209\) 44.1900i 0.211435i
\(210\) 0 0
\(211\) 280.115 1.32756 0.663781 0.747927i \(-0.268951\pi\)
0.663781 + 0.747927i \(0.268951\pi\)
\(212\) −122.782 + 70.8884i −0.579162 + 0.334379i
\(213\) 10.0279 17.3689i 0.0470795 0.0815440i
\(214\) 4.56905 7.91383i 0.0213507 0.0369805i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) −255.585 + 119.434i −1.17781 + 0.550388i
\(218\) 231.705i 1.06287i
\(219\) −19.6320 34.0036i −0.0896437 0.155267i
\(220\) 0 0
\(221\) −9.58111 + 16.5950i −0.0433535 + 0.0750904i
\(222\) 39.8076 + 68.9487i 0.179313 + 0.310580i
\(223\) 272.759 1.22313 0.611567 0.791192i \(-0.290539\pi\)
0.611567 + 0.791192i \(0.290539\pi\)
\(224\) 35.8743 16.7640i 0.160153 0.0748393i
\(225\) 0 0
\(226\) 74.5528 + 129.129i 0.329879 + 0.571368i
\(227\) −8.03620 + 13.9191i −0.0354018 + 0.0613176i −0.883183 0.469028i \(-0.844604\pi\)
0.847782 + 0.530345i \(0.177938\pi\)
\(228\) −7.62546 4.40256i −0.0334450 0.0193095i
\(229\) −128.261 + 74.0517i −0.560093 + 0.323370i −0.753183 0.657811i \(-0.771482\pi\)
0.193090 + 0.981181i \(0.438149\pi\)
\(230\) 0 0
\(231\) −209.997 18.2003i −0.909078 0.0787891i
\(232\) 132.959i 0.573098i
\(233\) 259.044 149.559i 1.11178 0.641885i 0.172488 0.985012i \(-0.444819\pi\)
0.939289 + 0.343127i \(0.111486\pi\)
\(234\) 26.5485 + 15.3278i 0.113455 + 0.0655034i
\(235\) 0 0
\(236\) −174.173 + 100.559i −0.738020 + 0.426096i
\(237\) 41.7570 0.176190
\(238\) 21.5178 + 15.0408i 0.0904108 + 0.0631968i
\(239\) 114.253 0.478046 0.239023 0.971014i \(-0.423173\pi\)
0.239023 + 0.971014i \(0.423173\pi\)
\(240\) 0 0
\(241\) −118.162 68.2209i −0.490299 0.283074i 0.234399 0.972140i \(-0.424688\pi\)
−0.724699 + 0.689066i \(0.758021\pi\)
\(242\) −221.978 128.159i −0.917266 0.529584i
\(243\) −7.79423 13.5000i −0.0320750 0.0555556i
\(244\) 25.7778i 0.105647i
\(245\) 0 0
\(246\) 173.100 0.703660
\(247\) 15.9056 9.18308i 0.0643950 0.0371785i
\(248\) 56.9955 98.7192i 0.229821 0.398061i
\(249\) −96.7041 + 167.496i −0.388370 + 0.672676i
\(250\) 0 0
\(251\) 457.024i 1.82081i 0.413717 + 0.910406i \(0.364230\pi\)
−0.413717 + 0.910406i \(0.635770\pi\)
\(252\) 24.0622 34.4240i 0.0954850 0.136603i
\(253\) 697.171i 2.75562i
\(254\) 37.9739 + 65.7728i 0.149504 + 0.258948i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 24.9991 + 43.2997i 0.0972726 + 0.168481i 0.910555 0.413388i \(-0.135655\pi\)
−0.813282 + 0.581869i \(0.802321\pi\)
\(258\) 91.5453 0.354827
\(259\) −19.6453 + 226.669i −0.0758505 + 0.875172i
\(260\) 0 0
\(261\) 70.5120 + 122.130i 0.270161 + 0.467932i
\(262\) −41.3546 + 71.6283i −0.157842 + 0.273390i
\(263\) 157.857 + 91.1388i 0.600217 + 0.346535i 0.769127 0.639096i \(-0.220691\pi\)
−0.168910 + 0.985631i \(0.554025\pi\)
\(264\) 73.7591 42.5848i 0.279390 0.161306i
\(265\) 0 0
\(266\) −10.6528 22.7965i −0.0400480 0.0857012i
\(267\) 221.541i 0.829741i
\(268\) −162.938 + 94.0722i −0.607977 + 0.351016i
\(269\) 32.5814 + 18.8109i 0.121120 + 0.0699289i 0.559336 0.828941i \(-0.311056\pi\)
−0.438216 + 0.898870i \(0.644389\pi\)
\(270\) 0 0
\(271\) 175.576 101.369i 0.647880 0.374054i −0.139763 0.990185i \(-0.544634\pi\)
0.787644 + 0.616131i \(0.211301\pi\)
\(272\) −10.6080 −0.0389999
\(273\) 37.0883 + 79.3675i 0.135855 + 0.290724i
\(274\) 17.1360 0.0625401
\(275\) 0 0
\(276\) −120.304 69.4578i −0.435885 0.251659i
\(277\) −221.912 128.121i −0.801126 0.462530i 0.0427390 0.999086i \(-0.486392\pi\)
−0.843865 + 0.536556i \(0.819725\pi\)
\(278\) −32.0010 55.4273i −0.115111 0.199379i
\(279\) 120.906i 0.433354i
\(280\) 0 0
\(281\) −141.462 −0.503423 −0.251711 0.967802i \(-0.580993\pi\)
−0.251711 + 0.967802i \(0.580993\pi\)
\(282\) 70.9549 40.9658i 0.251613 0.145269i
\(283\) 271.684 470.571i 0.960014 1.66279i 0.237562 0.971372i \(-0.423652\pi\)
0.722452 0.691421i \(-0.243015\pi\)
\(284\) −11.5793 + 20.0559i −0.0407720 + 0.0706192i
\(285\) 0 0
\(286\) 177.651i 0.621157i
\(287\) 405.445 + 283.405i 1.41270 + 0.987472i
\(288\) 16.9706i 0.0589256i
\(289\) 140.983 + 244.191i 0.487832 + 0.844950i
\(290\) 0 0
\(291\) −6.48008 + 11.2238i −0.0222683 + 0.0385699i
\(292\) 22.6690 + 39.2639i 0.0776337 + 0.134466i
\(293\) −375.289 −1.28085 −0.640424 0.768021i \(-0.721241\pi\)
−0.640424 + 0.768021i \(0.721241\pi\)
\(294\) 112.720 41.2344i 0.383400 0.140253i
\(295\) 0 0
\(296\) −45.9658 79.6151i −0.155290 0.268970i
\(297\) 45.1680 78.2333i 0.152081 0.263412i
\(298\) −62.3332 35.9881i −0.209172 0.120765i
\(299\) 250.937 144.878i 0.839253 0.484543i
\(300\) 0 0
\(301\) 214.422 + 149.880i 0.712367 + 0.497942i
\(302\) 223.015i 0.738459i
\(303\) 141.894 81.9228i 0.468299 0.270372i
\(304\) 8.80512 + 5.08364i 0.0289642 + 0.0167225i
\(305\) 0 0
\(306\) −9.74405 + 5.62573i −0.0318433 + 0.0183847i
\(307\) −41.3436 −0.134670 −0.0673349 0.997730i \(-0.521450\pi\)
−0.0673349 + 0.997730i \(0.521450\pi\)
\(308\) 242.484 + 21.0159i 0.787284 + 0.0682333i
\(309\) −103.614 −0.335321
\(310\) 0 0
\(311\) −126.924 73.2794i −0.408115 0.235625i 0.281865 0.959454i \(-0.409047\pi\)
−0.689979 + 0.723829i \(0.742380\pi\)
\(312\) −30.6556 17.6990i −0.0982551 0.0567276i
\(313\) −112.435 194.744i −0.359218 0.622184i 0.628612 0.777719i \(-0.283623\pi\)
−0.987830 + 0.155535i \(0.950290\pi\)
\(314\) 237.370i 0.755957i
\(315\) 0 0
\(316\) −48.2168 −0.152585
\(317\) −195.918 + 113.113i −0.618038 + 0.356825i −0.776105 0.630604i \(-0.782807\pi\)
0.158067 + 0.987428i \(0.449474\pi\)
\(318\) 86.8202 150.377i 0.273019 0.472884i
\(319\) −408.621 + 707.753i −1.28094 + 2.21866i
\(320\) 0 0
\(321\) 11.1918i 0.0348656i
\(322\) −168.065 359.653i −0.521942 1.11694i
\(323\) 6.74089i 0.0208696i
\(324\) 9.00000 + 15.5885i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) −195.565 + 338.728i −0.599891 + 1.03904i
\(327\) −141.890 245.760i −0.433914 0.751560i
\(328\) −199.879 −0.609388
\(329\) 233.265 + 20.2169i 0.709011 + 0.0614495i
\(330\) 0 0
\(331\) −69.9082 121.085i −0.211203 0.365814i 0.740888 0.671628i \(-0.234405\pi\)
−0.952091 + 0.305814i \(0.901071\pi\)
\(332\) 111.664 193.408i 0.336338 0.582555i
\(333\) −84.4446 48.7541i −0.253587 0.146409i
\(334\) 59.3093 34.2422i 0.177573 0.102522i
\(335\) 0 0
\(336\) −27.7847 + 39.7494i −0.0826924 + 0.118302i
\(337\) 30.1128i 0.0893556i 0.999001 + 0.0446778i \(0.0142261\pi\)
−0.999001 + 0.0446778i \(0.985774\pi\)
\(338\) −143.039 + 82.5836i −0.423192 + 0.244330i
\(339\) −158.150 91.3081i −0.466520 0.269345i
\(340\) 0 0
\(341\) 606.786 350.328i 1.77943 1.02736i
\(342\) 10.7840 0.0315323
\(343\) 331.528 + 87.9664i 0.966554 + 0.256462i
\(344\) −105.707 −0.307289
\(345\) 0 0
\(346\) 138.358 + 79.8809i 0.399878 + 0.230870i
\(347\) 360.186 + 207.954i 1.03800 + 0.599290i 0.919266 0.393636i \(-0.128783\pi\)
0.118734 + 0.992926i \(0.462116\pi\)
\(348\) −81.4202 141.024i −0.233966 0.405241i
\(349\) 594.950i 1.70473i 0.522950 + 0.852363i \(0.324831\pi\)
−0.522950 + 0.852363i \(0.675169\pi\)
\(350\) 0 0
\(351\) −37.5453 −0.106967
\(352\) −85.1697 + 49.1727i −0.241959 + 0.139695i
\(353\) 182.159 315.509i 0.516031 0.893793i −0.483795 0.875181i \(-0.660742\pi\)
0.999827 0.0186116i \(-0.00592459\pi\)
\(354\) 123.159 213.317i 0.347906 0.602591i
\(355\) 0 0
\(356\) 255.813i 0.718577i
\(357\) −32.0336 2.77633i −0.0897301 0.00777684i
\(358\) 468.693i 1.30920i
\(359\) −306.381 530.668i −0.853430 1.47818i −0.878094 0.478488i \(-0.841185\pi\)
0.0246647 0.999696i \(-0.492148\pi\)
\(360\) 0 0
\(361\) −177.270 + 307.040i −0.491051 + 0.850526i
\(362\) 150.846 + 261.272i 0.416700 + 0.721746i
\(363\) 313.925 0.864807
\(364\) −42.8259 91.6457i −0.117654 0.251774i
\(365\) 0 0
\(366\) −15.7856 27.3415i −0.0431302 0.0747036i
\(367\) 246.509 426.967i 0.671687 1.16340i −0.305738 0.952116i \(-0.598903\pi\)
0.977425 0.211281i \(-0.0677635\pi\)
\(368\) 138.916 + 80.2029i 0.377488 + 0.217943i
\(369\) −183.601 + 106.002i −0.497563 + 0.287268i
\(370\) 0 0
\(371\) 449.556 210.077i 1.21174 0.566245i
\(372\) 139.610i 0.375296i
\(373\) −143.243 + 82.7013i −0.384029 + 0.221719i −0.679570 0.733611i \(-0.737834\pi\)
0.295541 + 0.955330i \(0.404500\pi\)
\(374\) −56.4674 32.6015i −0.150982 0.0871697i
\(375\) 0 0
\(376\) −81.9317 + 47.3033i −0.217903 + 0.125807i
\(377\) 339.660 0.900956
\(378\) −4.44155 + 51.2472i −0.0117501 + 0.135575i
\(379\) 179.349 0.473215 0.236608 0.971605i \(-0.423964\pi\)
0.236608 + 0.971605i \(0.423964\pi\)
\(380\) 0 0
\(381\) −80.5549 46.5084i −0.211430 0.122069i
\(382\) 81.9395 + 47.3078i 0.214501 + 0.123842i
\(383\) −134.585 233.108i −0.351396 0.608636i 0.635098 0.772432i \(-0.280960\pi\)
−0.986494 + 0.163795i \(0.947626\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −159.246 −0.412554
\(387\) −97.0984 + 56.0598i −0.250900 + 0.144857i
\(388\) 7.48256 12.9602i 0.0192849 0.0334025i
\(389\) −236.874 + 410.277i −0.608930 + 1.05470i 0.382487 + 0.923961i \(0.375068\pi\)
−0.991417 + 0.130737i \(0.958266\pi\)
\(390\) 0 0
\(391\) 106.349i 0.271992i
\(392\) −130.157 + 47.6133i −0.332034 + 0.121463i
\(393\) 101.298i 0.257755i
\(394\) −43.1484 74.7353i −0.109514 0.189683i
\(395\) 0 0
\(396\) −52.1556 + 90.3361i −0.131706 + 0.228121i
\(397\) −256.967 445.080i −0.647271 1.12111i −0.983772 0.179424i \(-0.942577\pi\)
0.336500 0.941683i \(-0.390757\pi\)
\(398\) 270.348 0.679267
\(399\) 25.2589 + 17.6559i 0.0633056 + 0.0442504i
\(400\) 0 0
\(401\) 203.367 + 352.242i 0.507150 + 0.878410i 0.999966 + 0.00827591i \(0.00263433\pi\)
−0.492816 + 0.870134i \(0.664032\pi\)
\(402\) 115.214 199.557i 0.286603 0.496411i
\(403\) −252.191 145.603i −0.625785 0.361297i
\(404\) −163.846 + 94.5963i −0.405558 + 0.234149i
\(405\) 0 0
\(406\) 40.1814 463.617i 0.0989689 1.14191i
\(407\) 565.066i 1.38837i
\(408\) 11.2515 6.49603i 0.0275771 0.0159217i
\(409\) 422.173 + 243.742i 1.03221 + 0.595946i 0.917617 0.397467i \(-0.130111\pi\)
0.114592 + 0.993413i \(0.463444\pi\)
\(410\) 0 0
\(411\) −18.1755 + 10.4936i −0.0442225 + 0.0255319i
\(412\) 119.643 0.290397
\(413\) 637.717 298.004i 1.54411 0.721560i
\(414\) 170.136 0.410957
\(415\) 0 0
\(416\) 35.3980 + 20.4371i 0.0850914 + 0.0491275i
\(417\) 67.8843 + 39.1930i 0.162792 + 0.0939881i
\(418\) 31.2471 + 54.1215i 0.0747537 + 0.129477i
\(419\) 552.257i 1.31804i 0.752127 + 0.659018i \(0.229028\pi\)
−0.752127 + 0.659018i \(0.770972\pi\)
\(420\) 0 0
\(421\) −74.6870 −0.177404 −0.0887019 0.996058i \(-0.528272\pi\)
−0.0887019 + 0.996058i \(0.528272\pi\)
\(422\) 343.070 198.072i 0.812962 0.469364i
\(423\) −50.1727 + 86.9016i −0.118612 + 0.205441i
\(424\) −100.251 + 173.640i −0.236442 + 0.409529i
\(425\) 0 0
\(426\) 28.3633i 0.0665804i
\(427\) 7.79031 89.8855i 0.0182443 0.210505i
\(428\) 12.9232i 0.0301945i
\(429\) −108.789 188.427i −0.253586 0.439225i
\(430\) 0 0
\(431\) −242.339 + 419.743i −0.562271 + 0.973881i 0.435027 + 0.900417i \(0.356739\pi\)
−0.997298 + 0.0734641i \(0.976595\pi\)
\(432\) −10.3923 18.0000i −0.0240563 0.0416667i
\(433\) 458.196 1.05819 0.529094 0.848563i \(-0.322532\pi\)
0.529094 + 0.848563i \(0.322532\pi\)
\(434\) −228.573 + 327.002i −0.526667 + 0.753461i
\(435\) 0 0
\(436\) 163.840 + 283.779i 0.375780 + 0.650870i
\(437\) 50.9653 88.2746i 0.116626 0.202001i
\(438\) −48.0883 27.7638i −0.109791 0.0633877i
\(439\) −121.167 + 69.9559i −0.276007 + 0.159353i −0.631614 0.775283i \(-0.717607\pi\)
0.355607 + 0.934635i \(0.384274\pi\)
\(440\) 0 0
\(441\) −94.3065 + 112.762i −0.213847 + 0.255696i
\(442\) 27.0995i 0.0613110i
\(443\) 13.9364 8.04616i 0.0314591 0.0181629i −0.484188 0.874964i \(-0.660885\pi\)
0.515647 + 0.856801i \(0.327552\pi\)
\(444\) 97.5082 + 56.2964i 0.219613 + 0.126794i
\(445\) 0 0
\(446\) 334.060 192.870i 0.749014 0.432444i
\(447\) 88.1524 0.197209
\(448\) 32.0830 45.8986i 0.0716138 0.102452i
\(449\) 329.314 0.733439 0.366720 0.930332i \(-0.380481\pi\)
0.366720 + 0.930332i \(0.380481\pi\)
\(450\) 0 0
\(451\) −1063.98 614.288i −2.35915 1.36206i
\(452\) 182.616 + 105.434i 0.404018 + 0.233260i
\(453\) 136.568 + 236.543i 0.301475 + 0.522169i
\(454\) 22.7298i 0.0500657i
\(455\) 0 0
\(456\) −12.4523 −0.0273077
\(457\) −771.557 + 445.459i −1.68831 + 0.974745i −0.732494 + 0.680773i \(0.761644\pi\)
−0.955814 + 0.293972i \(0.905023\pi\)
\(458\) −104.725 + 181.389i −0.228657 + 0.396046i
\(459\) 6.89008 11.9340i 0.0150111 0.0259999i
\(460\) 0 0
\(461\) 534.019i 1.15839i −0.815188 0.579196i \(-0.803367\pi\)
0.815188 0.579196i \(-0.196633\pi\)
\(462\) −270.062 + 126.200i −0.584550 + 0.273159i
\(463\) 158.679i 0.342719i −0.985209 0.171359i \(-0.945184\pi\)
0.985209 0.171359i \(-0.0548159\pi\)
\(464\) 94.0160 + 162.840i 0.202621 + 0.350949i
\(465\) 0 0
\(466\) 211.509 366.344i 0.453881 0.786145i
\(467\) −56.0995 97.1671i −0.120127 0.208067i 0.799690 0.600413i \(-0.204997\pi\)
−0.919818 + 0.392346i \(0.871664\pi\)
\(468\) 43.3535 0.0926358
\(469\) 596.582 278.782i 1.27203 0.594417i
\(470\) 0 0
\(471\) −145.359 251.769i −0.308618 0.534542i
\(472\) −142.211 + 246.317i −0.301295 + 0.521859i
\(473\) −562.691 324.870i −1.18962 0.686829i
\(474\) 51.1416 29.5266i 0.107894 0.0622925i
\(475\) 0 0
\(476\) 36.9893 + 3.20583i 0.0777085 + 0.00673494i
\(477\) 212.665i 0.445839i
\(478\) 139.931 80.7891i 0.292742 0.169015i
\(479\) 598.669 + 345.642i 1.24983 + 0.721590i 0.971076 0.238772i \(-0.0767450\pi\)
0.278755 + 0.960362i \(0.410078\pi\)
\(480\) 0 0
\(481\) −203.387 + 117.426i −0.422843 + 0.244128i
\(482\) −192.958 −0.400328
\(483\) 398.502 + 278.551i 0.825056 + 0.576711i
\(484\) −362.489 −0.748945
\(485\) 0 0
\(486\) −19.0919 11.0227i −0.0392837 0.0226805i
\(487\) −624.248 360.410i −1.28182 0.740062i −0.304643 0.952467i \(-0.598537\pi\)
−0.977182 + 0.212405i \(0.931870\pi\)
\(488\) 18.2277 + 31.5713i 0.0373518 + 0.0646953i
\(489\) 479.033i 0.979618i
\(490\) 0 0
\(491\) 589.995 1.20162 0.600809 0.799392i \(-0.294845\pi\)
0.600809 + 0.799392i \(0.294845\pi\)
\(492\) 212.004 122.400i 0.430902 0.248781i
\(493\) −62.3325 + 107.963i −0.126435 + 0.218992i
\(494\) 12.9868 22.4939i 0.0262891 0.0455341i
\(495\) 0 0
\(496\) 161.208i 0.325016i
\(497\) 46.4371 66.4340i 0.0934348 0.133670i
\(498\) 273.521i 0.549238i
\(499\) −437.845 758.370i −0.877445 1.51978i −0.854135 0.520052i \(-0.825913\pi\)
−0.0233104 0.999728i \(-0.507421\pi\)
\(500\) 0 0
\(501\) −41.9380 + 72.6387i −0.0837085 + 0.144987i
\(502\) 323.165 + 559.737i 0.643754 + 1.11501i
\(503\) −817.809 −1.62586 −0.812931 0.582360i \(-0.802129\pi\)
−0.812931 + 0.582360i \(0.802129\pi\)
\(504\) 5.12866 59.1751i 0.0101759 0.117411i
\(505\) 0 0
\(506\) 492.974 + 853.857i 0.974258 + 1.68746i
\(507\) 101.144 175.186i 0.199495 0.345535i
\(508\) 93.0168 + 53.7033i 0.183104 + 0.105715i
\(509\) 657.585 379.657i 1.29191 0.745887i 0.312921 0.949779i \(-0.398692\pi\)
0.978993 + 0.203892i \(0.0653591\pi\)
\(510\) 0 0
\(511\) −67.1794 143.761i −0.131467 0.281333i
\(512\) 22.6274i 0.0441942i
\(513\) −11.4382 + 6.60384i −0.0222967 + 0.0128730i
\(514\) 61.2350 + 35.3540i 0.119134 + 0.0687821i
\(515\) 0 0
\(516\) 112.120 64.7323i 0.217286 0.125450i
\(517\) −581.508 −1.12477
\(518\) 136.219 + 291.504i 0.262971 + 0.562748i
\(519\) −195.667 −0.377009
\(520\) 0 0
\(521\) −153.671 88.7220i −0.294954 0.170292i 0.345220 0.938522i \(-0.387804\pi\)
−0.640174 + 0.768230i \(0.721138\pi\)
\(522\) 172.718 + 99.7190i 0.330878 + 0.191033i
\(523\) −52.6094 91.1221i −0.100592 0.174230i 0.811337 0.584579i \(-0.198740\pi\)
−0.911929 + 0.410349i \(0.865407\pi\)
\(524\) 116.969i 0.223222i
\(525\) 0 0
\(526\) 257.780 0.490075
\(527\) 92.5612 53.4403i 0.175638 0.101405i
\(528\) 60.2240 104.311i 0.114061 0.197559i
\(529\) 539.563 934.551i 1.01997 1.76664i
\(530\) 0 0
\(531\) 301.676i 0.568128i
\(532\) −29.1665 20.3873i −0.0548243 0.0383220i
\(533\) 510.618i 0.958007i
\(534\) 156.653 + 271.331i 0.293358 + 0.508111i
\(535\) 0 0
\(536\) −133.038 + 230.429i −0.248206 + 0.429905i
\(537\) 287.015 + 497.125i 0.534479 + 0.925744i
\(538\) 53.2051 0.0988943
\(539\) −839.172 146.562i −1.55690 0.271914i
\(540\) 0 0
\(541\) 138.181 + 239.337i 0.255419 + 0.442398i 0.965009 0.262216i \(-0.0844534\pi\)
−0.709591 + 0.704614i \(0.751120\pi\)
\(542\) 143.357 248.301i 0.264496 0.458121i
\(543\) −319.992 184.747i −0.589303 0.340234i
\(544\) −12.9921 + 7.50097i −0.0238825 + 0.0137886i
\(545\) 0 0
\(546\) 101.545 + 70.9796i 0.185980 + 0.129999i
\(547\) 918.409i 1.67899i 0.543366 + 0.839496i \(0.317150\pi\)
−0.543366 + 0.839496i \(0.682850\pi\)
\(548\) 20.9872 12.1170i 0.0382978 0.0221113i
\(549\) 33.4864 + 19.3334i 0.0609953 + 0.0352156i
\(550\) 0 0
\(551\) 103.478 59.7429i 0.187800 0.108426i
\(552\) −196.456 −0.355899
\(553\) 168.128 + 14.5716i 0.304030 + 0.0263500i
\(554\) −362.380 −0.654116
\(555\) 0 0
\(556\) −78.3861 45.2562i −0.140982 0.0813961i
\(557\) −636.538 367.505i −1.14280 0.659794i −0.195675 0.980669i \(-0.562690\pi\)
−0.947122 + 0.320875i \(0.896023\pi\)
\(558\) −85.4933 148.079i −0.153214 0.265374i
\(559\) 270.044i 0.483083i
\(560\) 0 0
\(561\) 79.8569 0.142347
\(562\) −173.255 + 100.029i −0.308282 + 0.177987i
\(563\) 413.283 715.827i 0.734073 1.27145i −0.221056 0.975261i \(-0.570950\pi\)
0.955129 0.296191i \(-0.0957164\pi\)
\(564\) 57.9344 100.345i 0.102721 0.177917i
\(565\) 0 0
\(566\) 768.438i 1.35767i
\(567\) −26.6714 57.0757i −0.0470395 0.100663i
\(568\) 32.7511i 0.0576603i
\(569\) −216.546 375.069i −0.380573 0.659172i 0.610571 0.791961i \(-0.290940\pi\)
−0.991144 + 0.132790i \(0.957607\pi\)
\(570\) 0 0
\(571\) −240.036 + 415.754i −0.420378 + 0.728116i −0.995976 0.0896166i \(-0.971436\pi\)
0.575598 + 0.817733i \(0.304769\pi\)
\(572\) 125.618 + 217.577i 0.219612 + 0.380380i
\(573\) −115.880 −0.202234
\(574\) 696.964 + 60.4054i 1.21422 + 0.105236i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) 43.5695 75.4646i 0.0755104 0.130788i −0.825798 0.563966i \(-0.809275\pi\)
0.901308 + 0.433179i \(0.142608\pi\)
\(578\) 345.338 + 199.381i 0.597470 + 0.344949i
\(579\) 168.906 97.5179i 0.291720 0.168425i
\(580\) 0 0
\(581\) −447.815 + 640.655i −0.770766 + 1.10268i
\(582\) 18.3284i 0.0314922i
\(583\) −1067.30 + 616.204i −1.83070 + 1.05695i
\(584\) 55.5276 + 32.0589i 0.0950815 + 0.0548953i
\(585\) 0 0
\(586\) −459.633 + 265.369i −0.784356 + 0.452848i
\(587\) −104.332 −0.177737 −0.0888687 0.996043i \(-0.528325\pi\)
−0.0888687 + 0.996043i \(0.528325\pi\)
\(588\) 108.896 130.206i 0.185197 0.221439i
\(589\) −102.440 −0.173922
\(590\) 0 0
\(591\) 91.5316 + 52.8458i 0.154876 + 0.0894176i
\(592\) −112.593 65.0055i −0.190191 0.109807i
\(593\) −145.735 252.421i −0.245760 0.425668i 0.716585 0.697499i \(-0.245704\pi\)
−0.962345 + 0.271831i \(0.912371\pi\)
\(594\) 127.754i 0.215075i
\(595\) 0 0
\(596\) −101.790 −0.170788
\(597\) −286.748 + 165.554i −0.480314 + 0.277310i
\(598\) 204.889 354.878i 0.342624 0.593442i
\(599\) 298.839 517.604i 0.498896 0.864114i −0.501103 0.865388i \(-0.667072\pi\)
0.999999 + 0.00127378i \(0.000405456\pi\)
\(600\) 0 0
\(601\) 447.444i 0.744499i 0.928133 + 0.372250i \(0.121413\pi\)
−0.928133 + 0.372250i \(0.878587\pi\)
\(602\) 368.594 + 31.9458i 0.612283 + 0.0530661i
\(603\) 282.217i 0.468021i
\(604\) −157.695 273.136i −0.261085 0.452212i
\(605\) 0 0
\(606\) 115.856 200.669i 0.191182 0.331137i
\(607\) 308.155 + 533.739i 0.507668 + 0.879307i 0.999961 + 0.00887709i \(0.00282570\pi\)
−0.492293 + 0.870430i \(0.663841\pi\)
\(608\) 14.3787 0.0236492
\(609\) 241.288 + 516.346i 0.396203 + 0.847859i
\(610\) 0 0
\(611\) 120.842 + 209.305i 0.197778 + 0.342562i
\(612\) −7.95598 + 13.7802i −0.0130000 + 0.0225166i
\(613\) −110.052 63.5384i −0.179530 0.103651i 0.407542 0.913186i \(-0.366386\pi\)
−0.587072 + 0.809535i \(0.699719\pi\)
\(614\) −50.6354 + 29.2344i −0.0824681 + 0.0476130i
\(615\) 0 0
\(616\) 311.841 145.723i 0.506235 0.236563i
\(617\) 68.5630i 0.111123i 0.998455 + 0.0555616i \(0.0176949\pi\)
−0.998455 + 0.0555616i \(0.982305\pi\)
\(618\) −126.901 + 73.2664i −0.205342 + 0.118554i
\(619\) −833.529 481.238i −1.34657 0.777445i −0.358812 0.933410i \(-0.616818\pi\)
−0.987763 + 0.155965i \(0.950151\pi\)
\(620\) 0 0
\(621\) −180.457 + 104.187i −0.290590 + 0.167772i
\(622\) −207.265 −0.333224
\(623\) −77.3092 + 892.003i −0.124092 + 1.43179i
\(624\) −50.0604 −0.0802249
\(625\) 0 0
\(626\) −275.409 159.008i −0.439951 0.254006i
\(627\) −66.2850 38.2697i −0.105718 0.0610362i
\(628\) 167.846 + 290.718i 0.267271 + 0.462927i
\(629\) 86.1971i 0.137038i
\(630\) 0 0
\(631\) 412.586 0.653860 0.326930 0.945048i \(-0.393986\pi\)
0.326930 + 0.945048i \(0.393986\pi\)
\(632\) −59.0533 + 34.0944i −0.0934387 + 0.0539469i
\(633\) −242.587 + 420.173i −0.383234 + 0.663781i
\(634\) −159.966 + 277.070i −0.252313 + 0.437019i
\(635\) 0 0
\(636\) 245.565i 0.386108i
\(637\) 121.635 + 332.504i 0.190949 + 0.521985i
\(638\) 1155.76i 1.81153i
\(639\) 17.3689 + 30.0838i 0.0271813 + 0.0470795i
\(640\) 0 0
\(641\) 71.3374 123.560i 0.111291 0.192761i −0.805000 0.593275i \(-0.797835\pi\)
0.916291 + 0.400513i \(0.131168\pi\)
\(642\) 7.91383 + 13.7072i 0.0123268 + 0.0213507i
\(643\) −239.942 −0.373160 −0.186580 0.982440i \(-0.559740\pi\)
−0.186580 + 0.982440i \(0.559740\pi\)
\(644\) −460.150 321.643i −0.714519 0.499446i
\(645\) 0 0
\(646\) 4.76653 + 8.25588i 0.00737853 + 0.0127800i
\(647\) 74.3724 128.817i 0.114950 0.199098i −0.802810 0.596235i \(-0.796663\pi\)
0.917760 + 0.397136i \(0.129996\pi\)
\(648\) 22.0454 + 12.7279i 0.0340207 + 0.0196419i
\(649\) −1514.01 + 874.115i −2.33284 + 1.34686i
\(650\) 0 0
\(651\) 42.1915 486.810i 0.0648102 0.747788i
\(652\) 553.140i 0.848374i
\(653\) −249.434 + 144.011i −0.381982 + 0.220537i −0.678680 0.734434i \(-0.737448\pi\)
0.296698 + 0.954971i \(0.404114\pi\)
\(654\) −347.557 200.662i −0.531433 0.306823i
\(655\) 0 0
\(656\) −244.801 + 141.336i −0.373172 + 0.215451i
\(657\) 68.0071 0.103512
\(658\) 299.985 140.183i 0.455905 0.213043i
\(659\) 175.647 0.266536 0.133268 0.991080i \(-0.457453\pi\)
0.133268 + 0.991080i \(0.457453\pi\)
\(660\) 0 0
\(661\) −615.015 355.079i −0.930432 0.537185i −0.0434835 0.999054i \(-0.513846\pi\)
−0.886948 + 0.461869i \(0.847179\pi\)
\(662\) −171.239 98.8651i −0.258670 0.149343i
\(663\) −16.5950 28.7433i −0.0250301 0.0433535i
\(664\) 315.834i 0.475654i
\(665\) 0 0
\(666\) −137.897 −0.207053
\(667\) 1632.53 942.544i 2.44758 1.41311i
\(668\) 48.4258 83.8760i 0.0724937 0.125563i
\(669\) −236.216 + 409.139i −0.353089 + 0.611567i
\(670\) 0 0
\(671\) 224.076i 0.333944i
\(672\) −5.92207 + 68.3296i −0.00881261 + 0.101681i
\(673\) 1173.04i 1.74301i 0.490389 + 0.871504i \(0.336855\pi\)
−0.490389 + 0.871504i \(0.663145\pi\)
\(674\) 21.2930 + 36.8806i 0.0315920 + 0.0547189i
\(675\) 0 0
\(676\) −116.791 + 202.288i −0.172768 + 0.299242i
\(677\) 338.731 + 586.699i 0.500341 + 0.866616i 1.00000 0.000393478i \(0.000125248\pi\)
−0.499659 + 0.866222i \(0.666541\pi\)
\(678\) −258.258 −0.380912
\(679\) −30.0078 + 42.9299i −0.0441941 + 0.0632252i
\(680\) 0 0
\(681\) −13.9191 24.1086i −0.0204392 0.0354018i
\(682\) 495.439 858.126i 0.726450 1.25825i
\(683\) −719.691 415.514i −1.05372 0.608366i −0.130032 0.991510i \(-0.541508\pi\)
−0.923689 + 0.383144i \(0.874841\pi\)
\(684\) 13.2077 7.62546i 0.0193095 0.0111483i
\(685\) 0 0
\(686\) 468.239 126.689i 0.682564 0.184679i
\(687\) 256.523i 0.373395i
\(688\) −129.465 + 74.7464i −0.188175 + 0.108643i
\(689\) 443.587 + 256.105i 0.643813 + 0.371706i
\(690\) 0 0
\(691\) 541.436 312.598i 0.783554 0.452385i −0.0541345 0.998534i \(-0.517240\pi\)
0.837688 + 0.546149i \(0.183907\pi\)
\(692\) 225.937 0.326499
\(693\) 209.163 299.233i 0.301823 0.431794i
\(694\) 588.181 0.847524
\(695\) 0 0
\(696\) −199.438 115.146i −0.286549 0.165439i
\(697\) −162.303 93.7055i −0.232859 0.134441i
\(698\) 420.693 + 728.661i 0.602712 + 1.04393i
\(699\) 518.088i 0.741185i
\(700\) 0 0
\(701\) 1030.02 1.46936 0.734678 0.678416i \(-0.237333\pi\)
0.734678 + 0.678416i \(0.237333\pi\)
\(702\) −45.9834 + 26.5485i −0.0655034 + 0.0378184i
\(703\) −41.3081 + 71.5477i −0.0587597 + 0.101775i
\(704\) −69.5407 + 120.448i −0.0987795 + 0.171091i
\(705\) 0 0
\(706\) 515.224i 0.729779i
\(707\) 599.906 280.335i 0.848523 0.396513i
\(708\) 348.345i 0.492013i
\(709\) −329.126 570.062i −0.464211 0.804037i 0.534955 0.844881i \(-0.320329\pi\)
−0.999166 + 0.0408438i \(0.986995\pi\)
\(710\) 0 0
\(711\) −36.1626 + 62.6354i −0.0508616 + 0.0880949i
\(712\) −180.887 313.306i −0.254055 0.440037i
\(713\) −1616.17 −2.26671
\(714\) −41.1962 + 19.2509i −0.0576978 + 0.0269621i
\(715\) 0 0
\(716\) −331.416 574.030i −0.462872 0.801718i
\(717\) −98.9461 + 171.380i −0.138000 + 0.239023i
\(718\) −750.478 433.288i −1.04523 0.603466i
\(719\) 1166.99 673.760i 1.62307 0.937079i 0.636975 0.770884i \(-0.280185\pi\)
0.986093 0.166195i \(-0.0531481\pi\)
\(720\) 0 0
\(721\) −417.188 36.1574i −0.578625 0.0501490i
\(722\) 501.394i 0.694452i
\(723\) 204.663 118.162i 0.283074 0.163433i
\(724\) 369.495 + 213.328i 0.510352 + 0.294652i
\(725\) 0 0
\(726\) 384.478 221.978i 0.529584 0.305755i
\(727\) 1126.18 1.54907 0.774536 0.632530i \(-0.217983\pi\)
0.774536 + 0.632530i \(0.217983\pi\)
\(728\) −117.254 81.9602i −0.161063 0.112583i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) −85.8348 49.5568i −0.117421 0.0677931i
\(732\) −38.6668 22.3243i −0.0528235 0.0304976i
\(733\) −303.337 525.395i −0.413829 0.716773i 0.581476 0.813564i \(-0.302476\pi\)
−0.995305 + 0.0967907i \(0.969142\pi\)
\(734\) 697.233i 0.949909i
\(735\) 0 0
\(736\) 226.848 0.308218
\(737\) −1416.35 + 817.731i −1.92178 + 1.10954i
\(738\) −149.909 + 259.651i −0.203129 + 0.351830i
\(739\) 461.084 798.622i 0.623930 1.08068i −0.364817 0.931079i \(-0.618868\pi\)
0.988747 0.149599i \(-0.0477984\pi\)
\(740\) 0 0
\(741\) 31.8111i 0.0429300i
\(742\) 402.045 575.175i 0.541840 0.775168i
\(743\) 13.3994i 0.0180342i −0.999959 0.00901712i \(-0.997130\pi\)
0.999959 0.00901712i \(-0.00287028\pi\)
\(744\) 98.7192 + 170.987i 0.132687 + 0.229821i
\(745\) 0 0
\(746\) −116.957 + 202.576i −0.156779 + 0.271550i
\(747\) −167.496 290.112i −0.224225 0.388370i
\(748\) −92.2108 −0.123277
\(749\) −3.90552 + 45.0624i −0.00521431 + 0.0601634i
\(750\) 0 0
\(751\) −538.071 931.967i −0.716473 1.24097i −0.962389 0.271676i \(-0.912422\pi\)
0.245916 0.969291i \(-0.420911\pi\)
\(752\) −66.8969 + 115.869i −0.0889587 + 0.154081i
\(753\) −685.536 395.794i −0.910406 0.525623i
\(754\) 415.997 240.176i 0.551721 0.318536i
\(755\) 0 0
\(756\) 30.7975 + 65.9054i 0.0407374 + 0.0871764i
\(757\) 254.117i 0.335690i −0.985813 0.167845i \(-0.946319\pi\)
0.985813 0.167845i \(-0.0536807\pi\)
\(758\) 219.656 126.819i 0.289784 0.167307i
\(759\) −1045.76 603.768i −1.37781 0.795478i
\(760\) 0 0
\(761\) −685.095 + 395.540i −0.900256 + 0.519763i −0.877283 0.479973i \(-0.840646\pi\)
−0.0229729 + 0.999736i \(0.507313\pi\)
\(762\) −131.546 −0.172632
\(763\) −485.538 1039.03i −0.636354 1.36177i
\(764\) 133.807 0.175140
\(765\) 0 0
\(766\) −329.664 190.332i −0.430371 0.248475i
\(767\) 629.250 + 363.298i 0.820405 + 0.473661i
\(768\) −13.8564 24.0000i −0.0180422 0.0312500i
\(769\) 464.403i 0.603905i −0.953323 0.301952i \(-0.902362\pi\)
0.953323 0.301952i \(-0.0976384\pi\)
\(770\) 0 0
\(771\) −86.5993 −0.112321
\(772\) −195.036 + 112.604i −0.252637 + 0.145860i
\(773\) 390.063 675.608i 0.504609 0.874008i −0.495377 0.868678i \(-0.664970\pi\)
0.999986 0.00533002i \(-0.00169661\pi\)
\(774\) −79.2805 + 137.318i −0.102430 + 0.177413i
\(775\) 0 0
\(776\) 21.1639i 0.0272730i
\(777\) −322.991 225.769i −0.415690 0.290566i
\(778\) 669.980i 0.861157i
\(779\) 89.8126 + 155.560i 0.115292 + 0.199692i
\(780\) 0 0
\(781\) −100.654 + 174.337i −0.128878 + 0.223223i
\(782\) 75.2000 + 130.250i 0.0961637 + 0.166560i
\(783\) −244.261