Properties

Label 210.3.k.a.83.11
Level 210
Weight 3
Character 210.83
Analytic conductor 5.722
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 83.11
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.a.167.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.21742 - 2.74188i) q^{3} +2.00000i q^{4} +(-3.32079 + 3.73796i) q^{5} +(-3.95930 + 1.52446i) q^{6} +(2.29543 + 6.61294i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-6.03579 - 6.67602i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.21742 - 2.74188i) q^{3} +2.00000i q^{4} +(-3.32079 + 3.73796i) q^{5} +(-3.95930 + 1.52446i) q^{6} +(2.29543 + 6.61294i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-6.03579 - 6.67602i) q^{9} +(7.05875 - 0.417165i) q^{10} +10.5733i q^{11} +(5.48376 + 2.43484i) q^{12} +(-14.9899 + 14.9899i) q^{13} +(4.31751 - 8.90837i) q^{14} +(6.20623 + 13.6559i) q^{15} -4.00000 q^{16} +(-15.4921 + 15.4921i) q^{17} +(-0.640234 + 12.7118i) q^{18} +17.3342 q^{19} +(-7.47592 - 6.64159i) q^{20} +(20.9264 + 1.75692i) q^{21} +(10.5733 - 10.5733i) q^{22} +(23.1753 - 23.1753i) q^{23} +(-3.04892 - 7.91859i) q^{24} +(-2.94466 - 24.8260i) q^{25} +29.9798 q^{26} +(-25.6529 + 8.42188i) q^{27} +(-13.2259 + 4.59086i) q^{28} +23.7038 q^{29} +(7.44963 - 19.8621i) q^{30} +33.1422i q^{31} +(4.00000 + 4.00000i) q^{32} +(28.9907 + 12.8721i) q^{33} +30.9843 q^{34} +(-32.3416 - 13.3800i) q^{35} +(13.3520 - 12.0716i) q^{36} +(-17.6315 + 17.6315i) q^{37} +(-17.3342 - 17.3342i) q^{38} +(22.8515 + 59.3494i) q^{39} +(0.834330 + 14.1175i) q^{40} +11.8368 q^{41} +(-19.1695 - 22.6833i) q^{42} +(-22.8095 - 22.8095i) q^{43} -21.1466 q^{44} +(44.9983 - 0.391834i) q^{45} -46.3507 q^{46} +(-12.6291 + 12.6291i) q^{47} +(-4.86967 + 10.9675i) q^{48} +(-38.4620 + 30.3591i) q^{49} +(-21.8813 + 27.7706i) q^{50} +(23.6171 + 61.3379i) q^{51} +(-29.9798 - 29.9798i) q^{52} +(15.3204 - 15.3204i) q^{53} +(34.0748 + 17.2310i) q^{54} +(-39.5225 - 35.1117i) q^{55} +(17.8167 + 8.63502i) q^{56} +(21.1030 - 47.5284i) q^{57} +(-23.7038 - 23.7038i) q^{58} +31.0849i q^{59} +(-27.3117 + 12.4125i) q^{60} -48.6492i q^{61} +(33.1422 - 33.1422i) q^{62} +(30.2934 - 55.2387i) q^{63} -8.00000i q^{64} +(-6.25326 - 105.810i) q^{65} +(-16.1186 - 41.8628i) q^{66} +(-77.5784 + 77.5784i) q^{67} +(-30.9843 - 30.9843i) q^{68} +(-35.3299 - 91.7580i) q^{69} +(18.9616 + 45.7215i) q^{70} +60.7725i q^{71} +(-25.4236 - 1.28047i) q^{72} +(-3.52743 + 3.52743i) q^{73} +35.2630 q^{74} +(-71.6547 - 22.1497i) q^{75} +34.6685i q^{76} +(-69.9206 + 24.2703i) q^{77} +(36.4979 - 82.2009i) q^{78} -99.4056i q^{79} +(13.2832 - 14.9518i) q^{80} +(-8.13854 + 80.5901i) q^{81} +(-11.8368 - 11.8368i) q^{82} +(-16.9196 - 16.9196i) q^{83} +(-3.51384 + 41.8528i) q^{84} +(-6.46278 - 109.355i) q^{85} +45.6189i q^{86} +(28.8574 - 64.9930i) q^{87} +(21.1466 + 21.1466i) q^{88} -17.6839i q^{89} +(-45.3901 - 44.6065i) q^{90} +(-133.535 - 64.7190i) q^{91} +(46.3507 + 46.3507i) q^{92} +(90.8718 + 40.3479i) q^{93} +25.2582 q^{94} +(-57.5634 + 64.7947i) q^{95} +(15.8372 - 6.09784i) q^{96} +(34.7968 + 34.7968i) q^{97} +(68.8211 + 8.10289i) q^{98} +(70.5875 - 63.8182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + O(q^{10}) \) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + 8q^{14} - 20q^{15} - 128q^{16} + 36q^{18} + 12q^{21} - 40q^{22} + 24q^{23} + 16q^{25} - 8q^{28} - 112q^{29} + 68q^{30} + 128q^{32} - 48q^{35} - 40q^{36} + 32q^{37} + 64q^{39} - 44q^{42} - 32q^{43} + 80q^{44} - 48q^{46} - 8q^{50} + 84q^{51} - 136q^{53} + 244q^{57} + 112q^{58} - 96q^{60} + 72q^{63} - 200q^{65} + 32q^{67} + 8q^{72} - 64q^{74} + 88q^{77} - 124q^{78} + 76q^{81} + 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} + 48q^{92} - 452q^{93} + 544q^{95} + 128q^{98} + 160q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) 1.21742 2.74188i 0.405806 0.913959i
\(4\) 2.00000i 0.500000i
\(5\) −3.32079 + 3.73796i −0.664159 + 0.747592i
\(6\) −3.95930 + 1.52446i −0.659883 + 0.254077i
\(7\) 2.29543 + 6.61294i 0.327919 + 0.944706i
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) −6.03579 6.67602i −0.670643 0.741780i
\(10\) 7.05875 0.417165i 0.705875 0.0417165i
\(11\) 10.5733i 0.961209i 0.876938 + 0.480604i \(0.159583\pi\)
−0.876938 + 0.480604i \(0.840417\pi\)
\(12\) 5.48376 + 2.43484i 0.456980 + 0.202903i
\(13\) −14.9899 + 14.9899i −1.15307 + 1.15307i −0.167134 + 0.985934i \(0.553451\pi\)
−0.985934 + 0.167134i \(0.946549\pi\)
\(14\) 4.31751 8.90837i 0.308394 0.636312i
\(15\) 6.20623 + 13.6559i 0.413749 + 0.910391i
\(16\) −4.00000 −0.250000
\(17\) −15.4921 + 15.4921i −0.911302 + 0.911302i −0.996375 0.0850728i \(-0.972888\pi\)
0.0850728 + 0.996375i \(0.472888\pi\)
\(18\) −0.640234 + 12.7118i −0.0355686 + 0.706212i
\(19\) 17.3342 0.912329 0.456164 0.889896i \(-0.349223\pi\)
0.456164 + 0.889896i \(0.349223\pi\)
\(20\) −7.47592 6.64159i −0.373796 0.332079i
\(21\) 20.9264 + 1.75692i 0.996494 + 0.0836629i
\(22\) 10.5733 10.5733i 0.480604 0.480604i
\(23\) 23.1753 23.1753i 1.00762 1.00762i 0.00765214 0.999971i \(-0.497564\pi\)
0.999971 0.00765214i \(-0.00243578\pi\)
\(24\) −3.04892 7.91859i −0.127038 0.329941i
\(25\) −2.94466 24.8260i −0.117787 0.993039i
\(26\) 29.9798 1.15307
\(27\) −25.6529 + 8.42188i −0.950108 + 0.311922i
\(28\) −13.2259 + 4.59086i −0.472353 + 0.163959i
\(29\) 23.7038 0.817373 0.408686 0.912675i \(-0.365987\pi\)
0.408686 + 0.912675i \(0.365987\pi\)
\(30\) 7.44963 19.8621i 0.248321 0.662070i
\(31\) 33.1422i 1.06910i 0.845136 + 0.534551i \(0.179519\pi\)
−0.845136 + 0.534551i \(0.820481\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 28.9907 + 12.8721i 0.878505 + 0.390064i
\(34\) 30.9843 0.911302
\(35\) −32.3416 13.3800i −0.924044 0.382285i
\(36\) 13.3520 12.0716i 0.370890 0.335322i
\(37\) −17.6315 + 17.6315i −0.476526 + 0.476526i −0.904019 0.427492i \(-0.859397\pi\)
0.427492 + 0.904019i \(0.359397\pi\)
\(38\) −17.3342 17.3342i −0.456164 0.456164i
\(39\) 22.8515 + 59.3494i 0.585935 + 1.52178i
\(40\) 0.834330 + 14.1175i 0.0208583 + 0.352938i
\(41\) 11.8368 0.288703 0.144352 0.989526i \(-0.453890\pi\)
0.144352 + 0.989526i \(0.453890\pi\)
\(42\) −19.1695 22.6833i −0.456416 0.540079i
\(43\) −22.8095 22.8095i −0.530453 0.530453i 0.390254 0.920707i \(-0.372387\pi\)
−0.920707 + 0.390254i \(0.872387\pi\)
\(44\) −21.1466 −0.480604
\(45\) 44.9983 0.391834i 0.999962 0.00870743i
\(46\) −46.3507 −1.00762
\(47\) −12.6291 + 12.6291i −0.268704 + 0.268704i −0.828578 0.559874i \(-0.810850\pi\)
0.559874 + 0.828578i \(0.310850\pi\)
\(48\) −4.86967 + 10.9675i −0.101451 + 0.228490i
\(49\) −38.4620 + 30.3591i −0.784939 + 0.619574i
\(50\) −21.8813 + 27.7706i −0.437626 + 0.555413i
\(51\) 23.6171 + 61.3379i 0.463081 + 1.20270i
\(52\) −29.9798 29.9798i −0.576534 0.576534i
\(53\) 15.3204 15.3204i 0.289065 0.289065i −0.547646 0.836710i \(-0.684476\pi\)
0.836710 + 0.547646i \(0.184476\pi\)
\(54\) 34.0748 + 17.2310i 0.631015 + 0.319093i
\(55\) −39.5225 35.1117i −0.718592 0.638395i
\(56\) 17.8167 + 8.63502i 0.318156 + 0.154197i
\(57\) 21.1030 47.5284i 0.370228 0.833831i
\(58\) −23.7038 23.7038i −0.408686 0.408686i
\(59\) 31.0849i 0.526863i 0.964678 + 0.263431i \(0.0848542\pi\)
−0.964678 + 0.263431i \(0.915146\pi\)
\(60\) −27.3117 + 12.4125i −0.455196 + 0.206874i
\(61\) 48.6492i 0.797528i −0.917054 0.398764i \(-0.869439\pi\)
0.917054 0.398764i \(-0.130561\pi\)
\(62\) 33.1422 33.1422i 0.534551 0.534551i
\(63\) 30.2934 55.2387i 0.480848 0.876804i
\(64\) 8.00000i 0.125000i
\(65\) −6.25326 105.810i −0.0962039 1.62784i
\(66\) −16.1186 41.8628i −0.244221 0.634285i
\(67\) −77.5784 + 77.5784i −1.15789 + 1.15789i −0.172957 + 0.984929i \(0.555332\pi\)
−0.984929 + 0.172957i \(0.944668\pi\)
\(68\) −30.9843 30.9843i −0.455651 0.455651i
\(69\) −35.3299 91.7580i −0.512027 1.32983i
\(70\) 18.9616 + 45.7215i 0.270880 + 0.653165i
\(71\) 60.7725i 0.855951i 0.903790 + 0.427976i \(0.140773\pi\)
−0.903790 + 0.427976i \(0.859227\pi\)
\(72\) −25.4236 1.28047i −0.353106 0.0177843i
\(73\) −3.52743 + 3.52743i −0.0483210 + 0.0483210i −0.730854 0.682533i \(-0.760878\pi\)
0.682533 + 0.730854i \(0.260878\pi\)
\(74\) 35.2630 0.476526
\(75\) −71.6547 22.1497i −0.955396 0.295329i
\(76\) 34.6685i 0.456164i
\(77\) −69.9206 + 24.2703i −0.908059 + 0.315198i
\(78\) 36.4979 82.2009i 0.467922 1.05386i
\(79\) 99.4056i 1.25830i −0.777284 0.629150i \(-0.783403\pi\)
0.777284 0.629150i \(-0.216597\pi\)
\(80\) 13.2832 14.9518i 0.166040 0.186898i
\(81\) −8.13854 + 80.5901i −0.100476 + 0.994940i
\(82\) −11.8368 11.8368i −0.144352 0.144352i
\(83\) −16.9196 16.9196i −0.203851 0.203851i 0.597797 0.801648i \(-0.296043\pi\)
−0.801648 + 0.597797i \(0.796043\pi\)
\(84\) −3.51384 + 41.8528i −0.0418315 + 0.498247i
\(85\) −6.46278 109.355i −0.0760327 1.28653i
\(86\) 45.6189i 0.530453i
\(87\) 28.8574 64.9930i 0.331695 0.747046i
\(88\) 21.1466 + 21.1466i 0.240302 + 0.240302i
\(89\) 17.6839i 0.198695i −0.995053 0.0993477i \(-0.968324\pi\)
0.995053 0.0993477i \(-0.0316756\pi\)
\(90\) −45.3901 44.6065i −0.504335 0.495627i
\(91\) −133.535 64.7190i −1.46742 0.711198i
\(92\) 46.3507 + 46.3507i 0.503811 + 0.503811i
\(93\) 90.8718 + 40.3479i 0.977116 + 0.433848i
\(94\) 25.2582 0.268704
\(95\) −57.5634 + 64.7947i −0.605931 + 0.682049i
\(96\) 15.8372 6.09784i 0.164971 0.0635192i
\(97\) 34.7968 + 34.7968i 0.358730 + 0.358730i 0.863345 0.504615i \(-0.168365\pi\)
−0.504615 + 0.863345i \(0.668365\pi\)
\(98\) 68.8211 + 8.10289i 0.702256 + 0.0826825i
\(99\) 70.5875 63.8182i 0.713006 0.644628i
\(100\) 49.6519 5.88933i 0.496519 0.0588933i
\(101\) 171.092 1.69398 0.846988 0.531612i \(-0.178413\pi\)
0.846988 + 0.531612i \(0.178413\pi\)
\(102\) 37.7208 84.9551i 0.369812 0.832893i
\(103\) 35.4145 35.4145i 0.343831 0.343831i −0.513975 0.857805i \(-0.671828\pi\)
0.857805 + 0.513975i \(0.171828\pi\)
\(104\) 59.9595i 0.576534i
\(105\) −76.0595 + 72.3876i −0.724376 + 0.689405i
\(106\) −30.6409 −0.289065
\(107\) −41.0523 41.0523i −0.383667 0.383667i 0.488755 0.872421i \(-0.337451\pi\)
−0.872421 + 0.488755i \(0.837451\pi\)
\(108\) −16.8438 51.3058i −0.155961 0.475054i
\(109\) 168.808i 1.54869i 0.632761 + 0.774347i \(0.281922\pi\)
−0.632761 + 0.774347i \(0.718078\pi\)
\(110\) 4.41081 + 74.6343i 0.0400983 + 0.678493i
\(111\) 26.8785 + 69.8082i 0.242149 + 0.628903i
\(112\) −9.18172 26.4518i −0.0819797 0.236176i
\(113\) −18.9763 + 18.9763i −0.167932 + 0.167932i −0.786070 0.618138i \(-0.787887\pi\)
0.618138 + 0.786070i \(0.287887\pi\)
\(114\) −68.6314 + 26.4254i −0.602030 + 0.231801i
\(115\) 9.66794 + 163.589i 0.0840690 + 1.42251i
\(116\) 47.4076i 0.408686i
\(117\) 190.549 + 9.59704i 1.62862 + 0.0820260i
\(118\) 31.0849 31.0849i 0.263431 0.263431i
\(119\) −138.010 66.8874i −1.15975 0.562079i
\(120\) 39.7242 + 14.8993i 0.331035 + 0.124161i
\(121\) 9.20544 0.0760780
\(122\) −48.6492 + 48.6492i −0.398764 + 0.398764i
\(123\) 14.4104 32.4552i 0.117158 0.263863i
\(124\) −66.2843 −0.534551
\(125\) 102.577 + 71.4349i 0.820617 + 0.571479i
\(126\) −85.5321 + 24.9453i −0.678826 + 0.197978i
\(127\) 132.611 132.611i 1.04418 1.04418i 0.0452000 0.998978i \(-0.485607\pi\)
0.998978 0.0452000i \(-0.0143925\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) −90.3094 + 34.7721i −0.700073 + 0.269551i
\(130\) −99.5566 + 112.063i −0.765820 + 0.862024i
\(131\) −247.227 −1.88723 −0.943613 0.331051i \(-0.892597\pi\)
−0.943613 + 0.331051i \(0.892597\pi\)
\(132\) −25.7442 + 57.9814i −0.195032 + 0.439253i
\(133\) 39.7896 + 114.630i 0.299170 + 0.861882i
\(134\) 155.157 1.15789
\(135\) 53.7074 123.857i 0.397832 0.917458i
\(136\) 61.9685i 0.455651i
\(137\) −139.005 139.005i −1.01463 1.01463i −0.999891 0.0147404i \(-0.995308\pi\)
−0.0147404 0.999891i \(-0.504692\pi\)
\(138\) −56.4281 + 127.088i −0.408899 + 0.920926i
\(139\) 186.326 1.34047 0.670237 0.742147i \(-0.266192\pi\)
0.670237 + 0.742147i \(0.266192\pi\)
\(140\) 26.7600 64.6831i 0.191143 0.462022i
\(141\) 19.2525 + 50.0023i 0.136543 + 0.354626i
\(142\) 60.7725 60.7725i 0.427976 0.427976i
\(143\) −158.492 158.492i −1.10834 1.10834i
\(144\) 24.1432 + 26.7041i 0.167661 + 0.185445i
\(145\) −78.7155 + 88.6039i −0.542865 + 0.611061i
\(146\) 7.05487 0.0483210
\(147\) 36.4166 + 142.418i 0.247732 + 0.968829i
\(148\) −35.2630 35.2630i −0.238263 0.238263i
\(149\) 253.568 1.70180 0.850899 0.525329i \(-0.176058\pi\)
0.850899 + 0.525329i \(0.176058\pi\)
\(150\) 49.5050 + 93.8043i 0.330033 + 0.625362i
\(151\) 196.889 1.30390 0.651952 0.758261i \(-0.273951\pi\)
0.651952 + 0.758261i \(0.273951\pi\)
\(152\) 34.6685 34.6685i 0.228082 0.228082i
\(153\) 196.933 + 9.91860i 1.28714 + 0.0648274i
\(154\) 94.1908 + 45.6503i 0.611629 + 0.296431i
\(155\) −123.884 110.058i −0.799252 0.710053i
\(156\) −118.699 + 45.7030i −0.760889 + 0.292968i
\(157\) 94.2693 + 94.2693i 0.600442 + 0.600442i 0.940430 0.339988i \(-0.110423\pi\)
−0.339988 + 0.940430i \(0.610423\pi\)
\(158\) −99.4056 + 99.4056i −0.629150 + 0.629150i
\(159\) −23.3554 60.6581i −0.146889 0.381498i
\(160\) −28.2350 + 1.66866i −0.176469 + 0.0104291i
\(161\) 206.454 + 100.060i 1.28233 + 0.621489i
\(162\) 88.7286 72.4516i 0.547708 0.447232i
\(163\) 144.119 + 144.119i 0.884164 + 0.884164i 0.993955 0.109791i \(-0.0350181\pi\)
−0.109791 + 0.993955i \(0.535018\pi\)
\(164\) 23.6737i 0.144352i
\(165\) −144.387 + 65.6203i −0.875076 + 0.397699i
\(166\) 33.8392i 0.203851i
\(167\) −81.7575 + 81.7575i −0.489566 + 0.489566i −0.908169 0.418603i \(-0.862520\pi\)
0.418603 + 0.908169i \(0.362520\pi\)
\(168\) 45.3666 38.3389i 0.270039 0.228208i
\(169\) 280.393i 1.65913i
\(170\) −102.892 + 115.818i −0.605249 + 0.681282i
\(171\) −104.626 115.724i −0.611847 0.676747i
\(172\) 45.6189 45.6189i 0.265226 0.265226i
\(173\) −147.722 147.722i −0.853885 0.853885i 0.136724 0.990609i \(-0.456343\pi\)
−0.990609 + 0.136724i \(0.956343\pi\)
\(174\) −93.8504 + 36.1355i −0.539370 + 0.207675i
\(175\) 157.413 76.4592i 0.899505 0.436910i
\(176\) 42.2932i 0.240302i
\(177\) 85.2310 + 37.8433i 0.481531 + 0.213804i
\(178\) −17.6839 + 17.6839i −0.0993477 + 0.0993477i
\(179\) 213.765 1.19422 0.597109 0.802160i \(-0.296316\pi\)
0.597109 + 0.802160i \(0.296316\pi\)
\(180\) 0.783669 + 89.9966i 0.00435371 + 0.499981i
\(181\) 31.8772i 0.176117i 0.996115 + 0.0880587i \(0.0280663\pi\)
−0.996115 + 0.0880587i \(0.971934\pi\)
\(182\) 68.8165 + 198.254i 0.378113 + 1.08931i
\(183\) −133.390 59.2264i −0.728908 0.323642i
\(184\) 92.7013i 0.503811i
\(185\) −7.35524 124.456i −0.0397580 0.672736i
\(186\) −50.5239 131.220i −0.271634 0.705482i
\(187\) −163.803 163.803i −0.875951 0.875951i
\(188\) −25.2582 25.2582i −0.134352 0.134352i
\(189\) −114.578 150.309i −0.606232 0.795288i
\(190\) 122.358 7.23124i 0.643990 0.0380592i
\(191\) 40.4552i 0.211808i 0.994376 + 0.105904i \(0.0337735\pi\)
−0.994376 + 0.105904i \(0.966226\pi\)
\(192\) −21.9350 9.73934i −0.114245 0.0507257i
\(193\) 17.8770 + 17.8770i 0.0926271 + 0.0926271i 0.751902 0.659275i \(-0.229137\pi\)
−0.659275 + 0.751902i \(0.729137\pi\)
\(194\) 69.5936i 0.358730i
\(195\) −297.731 111.669i −1.52682 0.572662i
\(196\) −60.7182 76.9240i −0.309787 0.392469i
\(197\) 98.2874 + 98.2874i 0.498921 + 0.498921i 0.911102 0.412181i \(-0.135233\pi\)
−0.412181 + 0.911102i \(0.635233\pi\)
\(198\) −134.406 6.76939i −0.678817 0.0341888i
\(199\) −30.5172 −0.153353 −0.0766764 0.997056i \(-0.524431\pi\)
−0.0766764 + 0.997056i \(0.524431\pi\)
\(200\) −55.5413 43.7626i −0.277706 0.218813i
\(201\) 118.265 + 307.156i 0.588384 + 1.52814i
\(202\) −171.092 171.092i −0.846988 0.846988i
\(203\) 54.4105 + 156.752i 0.268032 + 0.772177i
\(204\) −122.676 + 47.2343i −0.601352 + 0.231541i
\(205\) −39.3077 + 44.2456i −0.191745 + 0.215832i
\(206\) −70.8291 −0.343831
\(207\) −294.600 14.8376i −1.42319 0.0716794i
\(208\) 59.9595 59.9595i 0.288267 0.288267i
\(209\) 183.280i 0.876938i
\(210\) 148.447 + 3.67192i 0.706891 + 0.0174853i
\(211\) 30.5075 0.144585 0.0722926 0.997383i \(-0.476968\pi\)
0.0722926 + 0.997383i \(0.476968\pi\)
\(212\) 30.6409 + 30.6409i 0.144532 + 0.144532i
\(213\) 166.631 + 73.9856i 0.782304 + 0.347350i
\(214\) 82.1046i 0.383667i
\(215\) 161.006 9.51531i 0.748867 0.0442573i
\(216\) −34.4621 + 68.1496i −0.159547 + 0.315507i
\(217\) −219.167 + 76.0756i −1.00999 + 0.350579i
\(218\) 168.808 168.808i 0.774347 0.774347i
\(219\) 5.37743 + 13.9662i 0.0245545 + 0.0637724i
\(220\) 70.2234 79.0451i 0.319197 0.359296i
\(221\) 464.451i 2.10159i
\(222\) 42.9298 96.6867i 0.193377 0.435526i
\(223\) 70.9384 70.9384i 0.318109 0.318109i −0.529931 0.848041i \(-0.677782\pi\)
0.848041 + 0.529931i \(0.177782\pi\)
\(224\) −17.2700 + 35.6335i −0.0770984 + 0.159078i
\(225\) −147.965 + 169.503i −0.657624 + 0.753346i
\(226\) 37.9525 0.167932
\(227\) −139.705 + 139.705i −0.615443 + 0.615443i −0.944359 0.328916i \(-0.893317\pi\)
0.328916 + 0.944359i \(0.393317\pi\)
\(228\) 95.0568 + 42.2060i 0.416916 + 0.185114i
\(229\) −19.0520 −0.0831966 −0.0415983 0.999134i \(-0.513245\pi\)
−0.0415983 + 0.999134i \(0.513245\pi\)
\(230\) 153.921 173.257i 0.669221 0.753290i
\(231\) −18.5764 + 221.261i −0.0804175 + 0.957839i
\(232\) 47.4076 47.4076i 0.204343 0.204343i
\(233\) −32.3878 + 32.3878i −0.139003 + 0.139003i −0.773185 0.634181i \(-0.781337\pi\)
0.634181 + 0.773185i \(0.281337\pi\)
\(234\) −180.952 200.146i −0.773297 0.855323i
\(235\) −5.26842 89.1456i −0.0224188 0.379343i
\(236\) −62.1698 −0.263431
\(237\) −272.558 121.018i −1.15003 0.510625i
\(238\) 71.1223 + 204.897i 0.298833 + 0.860912i
\(239\) −133.240 −0.557489 −0.278744 0.960365i \(-0.589918\pi\)
−0.278744 + 0.960365i \(0.589918\pi\)
\(240\) −24.8249 54.6235i −0.103437 0.227598i
\(241\) 307.045i 1.27405i −0.770845 0.637023i \(-0.780166\pi\)
0.770845 0.637023i \(-0.219834\pi\)
\(242\) −9.20544 9.20544i −0.0380390 0.0380390i
\(243\) 211.060 + 120.427i 0.868561 + 0.495583i
\(244\) 97.2984 0.398764
\(245\) 14.2433 244.586i 0.0581357 0.998309i
\(246\) −46.8656 + 18.0448i −0.190510 + 0.0733528i
\(247\) −259.838 + 259.838i −1.05198 + 1.05198i
\(248\) 66.2843 + 66.2843i 0.267276 + 0.267276i
\(249\) −66.9897 + 25.7933i −0.269035 + 0.103587i
\(250\) −31.1422 174.012i −0.124569 0.696048i
\(251\) 205.085 0.817072 0.408536 0.912742i \(-0.366039\pi\)
0.408536 + 0.912742i \(0.366039\pi\)
\(252\) 110.477 + 60.5868i 0.438402 + 0.240424i
\(253\) 245.040 + 245.040i 0.968536 + 0.968536i
\(254\) −265.221 −1.04418
\(255\) −307.706 115.411i −1.20669 0.452591i
\(256\) 16.0000 0.0625000
\(257\) 186.225 186.225i 0.724612 0.724612i −0.244929 0.969541i \(-0.578765\pi\)
0.969541 + 0.244929i \(0.0787646\pi\)
\(258\) 125.082 + 55.5373i 0.484812 + 0.215261i
\(259\) −157.068 76.1241i −0.606439 0.293915i
\(260\) 211.620 12.5065i 0.813922 0.0481020i
\(261\) −143.071 158.247i −0.548165 0.606311i
\(262\) 247.227 + 247.227i 0.943613 + 0.943613i
\(263\) −203.536 + 203.536i −0.773902 + 0.773902i −0.978786 0.204884i \(-0.934318\pi\)
0.204884 + 0.978786i \(0.434318\pi\)
\(264\) 83.7256 32.2371i 0.317142 0.122110i
\(265\) 6.39115 + 108.143i 0.0241175 + 0.408087i
\(266\) 74.8408 154.420i 0.281356 0.580526i
\(267\) −48.4871 21.5287i −0.181599 0.0806318i
\(268\) −155.157 155.157i −0.578943 0.578943i
\(269\) 53.2780i 0.198060i 0.995084 + 0.0990298i \(0.0315739\pi\)
−0.995084 + 0.0990298i \(0.968426\pi\)
\(270\) −177.564 + 70.1495i −0.657645 + 0.259813i
\(271\) 312.775i 1.15415i −0.816691 0.577076i \(-0.804194\pi\)
0.816691 0.577076i \(-0.195806\pi\)
\(272\) 61.9685 61.9685i 0.227825 0.227825i
\(273\) −340.020 + 287.348i −1.24549 + 1.05256i
\(274\) 278.009i 1.01463i
\(275\) 262.492 31.1348i 0.954518 0.113217i
\(276\) 183.516 70.6597i 0.664913 0.256013i
\(277\) 230.870 230.870i 0.833466 0.833466i −0.154523 0.987989i \(-0.549384\pi\)
0.987989 + 0.154523i \(0.0493842\pi\)
\(278\) −186.326 186.326i −0.670237 0.670237i
\(279\) 221.258 200.039i 0.793039 0.716986i
\(280\) −91.4431 + 37.9231i −0.326582 + 0.135440i
\(281\) 22.5908i 0.0803942i −0.999192 0.0401971i \(-0.987201\pi\)
0.999192 0.0401971i \(-0.0127986\pi\)
\(282\) 30.7498 69.2549i 0.109042 0.245585i
\(283\) −184.657 + 184.657i −0.652497 + 0.652497i −0.953594 0.301097i \(-0.902647\pi\)
0.301097 + 0.953594i \(0.402647\pi\)
\(284\) −121.545 −0.427976
\(285\) 107.580 + 236.714i 0.377475 + 0.830576i
\(286\) 316.985i 1.10834i
\(287\) 27.1707 + 78.2763i 0.0946713 + 0.272740i
\(288\) 2.56094 50.8472i 0.00889214 0.176553i
\(289\) 191.012i 0.660943i
\(290\) 167.319 9.88840i 0.576963 0.0340979i
\(291\) 137.771 53.0463i 0.473439 0.182290i
\(292\) −7.05487 7.05487i −0.0241605 0.0241605i
\(293\) 50.9535 + 50.9535i 0.173903 + 0.173903i 0.788692 0.614789i \(-0.210759\pi\)
−0.614789 + 0.788692i \(0.710759\pi\)
\(294\) 106.001 178.834i 0.360548 0.608280i
\(295\) −116.194 103.227i −0.393878 0.349920i
\(296\) 70.5259i 0.238263i
\(297\) −89.0471 271.236i −0.299822 0.913252i
\(298\) −253.568 253.568i −0.850899 0.850899i
\(299\) 694.791i 2.32372i
\(300\) 44.2993 143.309i 0.147664 0.477698i
\(301\) 98.4801 203.195i 0.327176 0.675067i
\(302\) −196.889 196.889i −0.651952 0.651952i
\(303\) 208.290 469.112i 0.687426 1.54823i
\(304\) −69.3370 −0.228082
\(305\) 181.849 + 161.554i 0.596225 + 0.529685i
\(306\) −187.014 206.852i −0.611158 0.675986i
\(307\) −69.9923 69.9923i −0.227988 0.227988i 0.583864 0.811852i \(-0.301540\pi\)
−0.811852 + 0.583864i \(0.801540\pi\)
\(308\) −48.5405 139.841i −0.157599 0.454030i
\(309\) −53.9881 140.217i −0.174719 0.453776i
\(310\) 13.8258 + 233.942i 0.0445992 + 0.754653i
\(311\) −26.1121 −0.0839618 −0.0419809 0.999118i \(-0.513367\pi\)
−0.0419809 + 0.999118i \(0.513367\pi\)
\(312\) 164.402 + 72.9958i 0.526929 + 0.233961i
\(313\) 57.8685 57.8685i 0.184884 0.184884i −0.608596 0.793480i \(-0.708267\pi\)
0.793480 + 0.608596i \(0.208267\pi\)
\(314\) 188.539i 0.600442i
\(315\) 105.882 + 296.672i 0.336132 + 0.941815i
\(316\) 198.811 0.629150
\(317\) 368.411 + 368.411i 1.16218 + 1.16218i 0.983998 + 0.178182i \(0.0570215\pi\)
0.178182 + 0.983998i \(0.442978\pi\)
\(318\) −37.3027 + 84.0135i −0.117304 + 0.264193i
\(319\) 250.627i 0.785666i
\(320\) 29.9037 + 26.5663i 0.0934490 + 0.0830198i
\(321\) −162.538 + 62.5826i −0.506350 + 0.194961i
\(322\) −106.395 306.514i −0.330418 0.951907i
\(323\) −268.544 + 268.544i −0.831407 + 0.831407i
\(324\) −161.180 16.2771i −0.497470 0.0502379i
\(325\) 416.279 + 327.998i 1.28086 + 1.00923i
\(326\) 288.237i 0.884164i
\(327\) 462.850 + 205.510i 1.41544 + 0.628470i
\(328\) 23.6737 23.6737i 0.0721759 0.0721759i
\(329\) −112.505 54.5262i −0.341959 0.165733i
\(330\) 210.008 + 78.7672i 0.636387 + 0.238688i
\(331\) 172.781 0.521996 0.260998 0.965339i \(-0.415948\pi\)
0.260998 + 0.965339i \(0.415948\pi\)
\(332\) 33.8392 33.8392i 0.101925 0.101925i
\(333\) 224.128 + 11.2883i 0.673057 + 0.0338987i
\(334\) 163.515 0.489566
\(335\) −32.3630 547.606i −0.0966059 1.63465i
\(336\) −83.7055 7.02769i −0.249124 0.0209157i
\(337\) −300.344 + 300.344i −0.891227 + 0.891227i −0.994639 0.103411i \(-0.967024\pi\)
0.103411 + 0.994639i \(0.467024\pi\)
\(338\) −280.393 + 280.393i −0.829566 + 0.829566i
\(339\) 28.9286 + 75.1327i 0.0853350 + 0.221630i
\(340\) 218.710 12.9256i 0.643265 0.0380163i
\(341\) −350.422 −1.02763
\(342\) −11.0980 + 220.350i −0.0324502 + 0.644297i
\(343\) −289.050 184.660i −0.842711 0.538366i
\(344\) −91.2379 −0.265226
\(345\) 460.311 + 172.648i 1.33423 + 0.500428i
\(346\) 295.444i 0.853885i
\(347\) 200.513 + 200.513i 0.577846 + 0.577846i 0.934309 0.356463i \(-0.116018\pi\)
−0.356463 + 0.934309i \(0.616018\pi\)
\(348\) 129.986 + 57.7149i 0.373523 + 0.165847i
\(349\) −414.103 −1.18654 −0.593270 0.805003i \(-0.702164\pi\)
−0.593270 + 0.805003i \(0.702164\pi\)
\(350\) −233.873 80.9542i −0.668208 0.231298i
\(351\) 258.291 510.777i 0.735872 1.45521i
\(352\) −42.2932 + 42.2932i −0.120151 + 0.120151i
\(353\) −249.345 249.345i −0.706360 0.706360i 0.259408 0.965768i \(-0.416473\pi\)
−0.965768 + 0.259408i \(0.916473\pi\)
\(354\) −47.3877 123.074i −0.133863 0.347667i
\(355\) −227.165 201.813i −0.639902 0.568487i
\(356\) 35.3678 0.0993477
\(357\) −351.413 + 296.976i −0.984349 + 0.831865i
\(358\) −213.765 213.765i −0.597109 0.597109i
\(359\) −267.685 −0.745641 −0.372821 0.927903i \(-0.621609\pi\)
−0.372821 + 0.927903i \(0.621609\pi\)
\(360\) 89.2129 90.7803i 0.247814 0.252167i
\(361\) −60.5240 −0.167657
\(362\) 31.8772 31.8772i 0.0880587 0.0880587i
\(363\) 11.2069 25.2402i 0.0308729 0.0695322i
\(364\) 129.438 267.071i 0.355599 0.733711i
\(365\) −1.47152 24.8993i −0.00403157 0.0682172i
\(366\) 74.1638 + 192.617i 0.202633 + 0.526275i
\(367\) 423.041 + 423.041i 1.15270 + 1.15270i 0.986009 + 0.166690i \(0.0533079\pi\)
0.166690 + 0.986009i \(0.446692\pi\)
\(368\) −92.7013 + 92.7013i −0.251906 + 0.251906i
\(369\) −71.4447 79.0230i −0.193617 0.214155i
\(370\) −117.101 + 131.811i −0.316489 + 0.356247i
\(371\) 136.480 + 66.1461i 0.367871 + 0.178291i
\(372\) −80.6957 + 181.744i −0.216924 + 0.488558i
\(373\) 53.4661 + 53.4661i 0.143341 + 0.143341i 0.775136 0.631795i \(-0.217682\pi\)
−0.631795 + 0.775136i \(0.717682\pi\)
\(374\) 327.606i 0.875951i
\(375\) 320.745 194.288i 0.855320 0.518101i
\(376\) 50.5164i 0.134352i
\(377\) −355.317 + 355.317i −0.942486 + 0.942486i
\(378\) −35.7314 + 264.887i −0.0945276 + 0.700760i
\(379\) 364.774i 0.962465i 0.876593 + 0.481233i \(0.159811\pi\)
−0.876593 + 0.481233i \(0.840189\pi\)
\(380\) −129.589 115.127i −0.341025 0.302965i
\(381\) −202.160 525.045i −0.530603 1.37807i
\(382\) 40.4552 40.4552i 0.105904 0.105904i
\(383\) −113.130 113.130i −0.295378 0.295378i 0.543823 0.839200i \(-0.316976\pi\)
−0.839200 + 0.543823i \(0.816976\pi\)
\(384\) 12.1957 + 31.6744i 0.0317596 + 0.0824853i
\(385\) 141.471 341.957i 0.367456 0.888199i
\(386\) 35.7541i 0.0926271i
\(387\) −14.6034 + 289.950i −0.0377349 + 0.749224i
\(388\) −69.5936 + 69.5936i −0.179365 + 0.179365i
\(389\) −77.4189 −0.199020 −0.0995101 0.995037i \(-0.531728\pi\)
−0.0995101 + 0.995037i \(0.531728\pi\)
\(390\) 186.061 + 409.400i 0.477080 + 1.04974i
\(391\) 718.071i 1.83650i
\(392\) −16.2058 + 137.642i −0.0413413 + 0.351128i
\(393\) −300.978 + 677.865i −0.765847 + 1.72485i
\(394\) 196.575i 0.498921i
\(395\) 371.574 + 330.106i 0.940694 + 0.835710i
\(396\) 127.636 + 141.175i 0.322314 + 0.356503i
\(397\) 363.425 + 363.425i 0.915428 + 0.915428i 0.996693 0.0812649i \(-0.0258960\pi\)
−0.0812649 + 0.996693i \(0.525896\pi\)
\(398\) 30.5172 + 30.5172i 0.0766764 + 0.0766764i
\(399\) 362.743 + 30.4549i 0.909130 + 0.0763281i
\(400\) 11.7787 + 99.3039i 0.0294466 + 0.248260i
\(401\) 257.812i 0.642923i −0.946923 0.321461i \(-0.895826\pi\)
0.946923 0.321461i \(-0.104174\pi\)
\(402\) 188.891 425.421i 0.469877 1.05826i
\(403\) −496.797 496.797i −1.23275 1.23275i
\(404\) 342.183i 0.846988i
\(405\) −274.216 298.045i −0.677077 0.735913i
\(406\) 102.341 211.162i 0.252073 0.520104i
\(407\) −186.423 186.423i −0.458041 0.458041i
\(408\) 169.910 + 75.4416i 0.416446 + 0.184906i
\(409\) 491.252 1.20110 0.600552 0.799586i \(-0.294948\pi\)
0.600552 + 0.799586i \(0.294948\pi\)
\(410\) 83.5533 4.93792i 0.203789 0.0120437i
\(411\) −550.360 + 211.907i −1.33908 + 0.515588i
\(412\) 70.8291 + 70.8291i 0.171915 + 0.171915i
\(413\) −205.563 + 71.3532i −0.497730 + 0.172768i
\(414\) 279.763 + 309.438i 0.675755 + 0.747435i
\(415\) 119.431 7.05827i 0.287786 0.0170079i
\(416\) −119.919 −0.288267
\(417\) 226.837 510.883i 0.543973 1.22514i
\(418\) 183.280 183.280i 0.438469 0.438469i
\(419\) 400.571i 0.956016i 0.878356 + 0.478008i \(0.158641\pi\)
−0.878356 + 0.478008i \(0.841359\pi\)
\(420\) −144.775 152.119i −0.344703 0.362188i
\(421\) −281.156 −0.667828 −0.333914 0.942604i \(-0.608369\pi\)
−0.333914 + 0.942604i \(0.608369\pi\)
\(422\) −30.5075 30.5075i −0.0722926 0.0722926i
\(423\) 160.539 + 8.08558i 0.379524 + 0.0191148i
\(424\) 61.2817i 0.144532i
\(425\) 430.226 + 338.988i 1.01230 + 0.797619i
\(426\) −92.6453 240.616i −0.217477 0.564827i
\(427\) 321.714 111.671i 0.753429 0.261524i
\(428\) 82.1046 82.1046i 0.191833 0.191833i
\(429\) −627.518 + 241.615i −1.46275 + 0.563206i
\(430\) −170.522 151.491i −0.396562 0.352305i
\(431\) 404.384i 0.938246i 0.883133 + 0.469123i \(0.155430\pi\)
−0.883133 + 0.469123i \(0.844570\pi\)
\(432\) 102.612 33.6875i 0.237527 0.0779804i
\(433\) −43.6114 + 43.6114i −0.100719 + 0.100719i −0.755671 0.654952i \(-0.772689\pi\)
0.654952 + 0.755671i \(0.272689\pi\)
\(434\) 295.243 + 143.092i 0.680283 + 0.329704i
\(435\) 147.111 + 323.696i 0.338187 + 0.744129i
\(436\) −337.615 −0.774347
\(437\) 401.727 401.727i 0.919283 0.919283i
\(438\) 8.58872 19.3436i 0.0196090 0.0441634i
\(439\) −605.567 −1.37942 −0.689712 0.724084i \(-0.742263\pi\)
−0.689712 + 0.724084i \(0.742263\pi\)
\(440\) −149.269 + 8.82162i −0.339247 + 0.0200491i
\(441\) 434.826 + 73.5320i 0.986001 + 0.166739i
\(442\) −464.451 + 464.451i −1.05079 + 1.05079i
\(443\) 89.6580 89.6580i 0.202388 0.202388i −0.598634 0.801023i \(-0.704290\pi\)
0.801023 + 0.598634i \(0.204290\pi\)
\(444\) −139.616 + 53.7570i −0.314452 + 0.121074i
\(445\) 66.1016 + 58.7245i 0.148543 + 0.131965i
\(446\) −141.877 −0.318109
\(447\) 308.698 695.253i 0.690600 1.55537i
\(448\) 52.9035 18.3634i 0.118088 0.0409898i
\(449\) 335.741 0.747752 0.373876 0.927479i \(-0.378029\pi\)
0.373876 + 0.927479i \(0.378029\pi\)
\(450\) 317.468 21.5376i 0.705485 0.0478613i
\(451\) 125.154i 0.277504i
\(452\) −37.9525 37.9525i −0.0839658 0.0839658i
\(453\) 239.697 539.847i 0.529132 1.19171i
\(454\) 279.411 0.615443
\(455\) 685.360 284.232i 1.50629 0.624685i
\(456\) −52.8507 137.263i −0.115901 0.301015i
\(457\) 429.732 429.732i 0.940332 0.940332i −0.0579859 0.998317i \(-0.518468\pi\)
0.998317 + 0.0579859i \(0.0184678\pi\)
\(458\) 19.0520 + 19.0520i 0.0415983 + 0.0415983i
\(459\) 266.945 527.891i 0.581580 1.15009i
\(460\) −327.178 + 19.3359i −0.711256 + 0.0420345i
\(461\) 23.6913 0.0513911 0.0256955 0.999670i \(-0.491820\pi\)
0.0256955 + 0.999670i \(0.491820\pi\)
\(462\) 239.837 202.684i 0.519128 0.438711i
\(463\) −228.050 228.050i −0.492548 0.492548i 0.416560 0.909108i \(-0.363236\pi\)
−0.909108 + 0.416560i \(0.863236\pi\)
\(464\) −94.8153 −0.204343
\(465\) −452.585 + 205.688i −0.973301 + 0.442340i
\(466\) 64.7756 0.139003
\(467\) 359.835 359.835i 0.770525 0.770525i −0.207673 0.978198i \(-0.566589\pi\)
0.978198 + 0.207673i \(0.0665891\pi\)
\(468\) −19.1941 + 381.097i −0.0410130 + 0.814310i
\(469\) −691.097 334.945i −1.47355 0.714169i
\(470\) −83.8772 + 94.4140i −0.178462 + 0.200881i
\(471\) 373.240 143.710i 0.792442 0.305116i
\(472\) 62.1698 + 62.1698i 0.131716 + 0.131716i
\(473\) 241.171 241.171i 0.509876 0.509876i
\(474\) 151.540 + 393.576i 0.319704 + 0.830330i
\(475\) −51.0435 430.339i −0.107460 0.905978i
\(476\) 133.775 276.019i 0.281040 0.579873i
\(477\) −194.750 9.80866i −0.408282 0.0205632i
\(478\) 133.240 + 133.240i 0.278744 + 0.278744i
\(479\) 470.256i 0.981745i −0.871231 0.490873i \(-0.836678\pi\)
0.871231 0.490873i \(-0.163322\pi\)
\(480\) −29.7985 + 79.4484i −0.0620803 + 0.165517i
\(481\) 528.588i 1.09893i
\(482\) −307.045 + 307.045i −0.637023 + 0.637023i
\(483\) 525.693 444.258i 1.08839 0.919790i
\(484\) 18.4109i 0.0380390i
\(485\) −245.622 + 14.5160i −0.506437 + 0.0299299i
\(486\) −90.6335 331.487i −0.186489 0.682072i
\(487\) −246.237 + 246.237i −0.505621 + 0.505621i −0.913179 0.407558i \(-0.866380\pi\)
0.407558 + 0.913179i \(0.366380\pi\)
\(488\) −97.2984 97.2984i −0.199382 0.199382i
\(489\) 570.609 219.703i 1.16689 0.449291i
\(490\) −258.829 + 230.342i −0.528222 + 0.470086i
\(491\) 5.09974i 0.0103864i 0.999987 + 0.00519322i \(0.00165306\pi\)
−0.999987 + 0.00519322i \(0.998347\pi\)
\(492\) 64.9103 + 28.8208i 0.131932 + 0.0585788i
\(493\) −367.223 + 367.223i −0.744874 + 0.744874i
\(494\) 519.677 1.05198
\(495\) 4.14298 + 475.780i 0.00836966 + 0.961172i
\(496\) 132.569i 0.267276i
\(497\) −401.885 + 139.499i −0.808622 + 0.280682i
\(498\) 92.7830 + 41.1965i 0.186311 + 0.0827238i
\(499\) 678.365i 1.35945i 0.733467 + 0.679725i \(0.237901\pi\)
−0.733467 + 0.679725i \(0.762099\pi\)
\(500\) −142.870 + 205.154i −0.285740 + 0.410308i
\(501\) 124.636 + 323.702i 0.248775 + 0.646112i
\(502\) −205.085 205.085i −0.408536 0.408536i
\(503\) 501.769 + 501.769i 0.997552 + 0.997552i 0.999997 0.00244509i \(-0.000778296\pi\)
−0.00244509 + 0.999997i \(0.500778\pi\)
\(504\) −49.8905 171.064i −0.0989891 0.339413i
\(505\) −568.160 + 639.533i −1.12507 + 1.26640i
\(506\) 490.079i 0.968536i
\(507\) −768.804 341.356i −1.51638 0.673285i
\(508\) 265.221 + 265.221i 0.522089 + 0.522089i
\(509\) 620.503i 1.21906i −0.792762 0.609531i \(-0.791358\pi\)
0.792762 0.609531i \(-0.208642\pi\)
\(510\) 192.296 + 423.117i 0.377050 + 0.829641i
\(511\) −31.4237 15.2297i −0.0614945 0.0298038i
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −444.674 + 145.987i −0.866811 + 0.284575i
\(514\) −372.451 −0.724612
\(515\) 14.7737 + 249.982i 0.0286868 + 0.485403i
\(516\) −69.5442 180.619i −0.134776 0.350037i
\(517\) −133.531 133.531i −0.258281 0.258281i
\(518\) 80.9437 + 233.192i 0.156262 + 0.450177i
\(519\) −584.876 + 225.197i −1.12693 + 0.433905i
\(520\) −224.126 199.113i −0.431012 0.382910i
\(521\) −328.476 −0.630471 −0.315236 0.949013i \(-0.602084\pi\)
−0.315236 + 0.949013i \(0.602084\pi\)
\(522\) −15.1760 + 301.318i −0.0290728 + 0.577238i
\(523\) −167.734 + 167.734i −0.320714 + 0.320714i −0.849041 0.528327i \(-0.822820\pi\)
0.528327 + 0.849041i \(0.322820\pi\)
\(524\) 494.453i 0.943613i
\(525\) −18.0039 524.691i −0.0342931 0.999412i
\(526\) 407.073 0.773902
\(527\) −513.443 513.443i −0.974275 0.974275i
\(528\) −115.963 51.4885i −0.219626 0.0975160i
\(529\) 545.191i 1.03061i
\(530\) 101.752 114.534i 0.191985 0.216102i
\(531\) 207.523 187.622i 0.390816 0.353337i
\(532\) −229.261 + 79.5791i −0.430941 + 0.149585i
\(533\) −177.433 + 177.433i −0.332895 + 0.332895i
\(534\) 26.9584 + 70.0157i 0.0504839 + 0.131116i
\(535\) 289.778 17.1256i 0.541641 0.0320105i
\(536\) 310.313i 0.578943i
\(537\) 260.241 586.118i 0.484621 1.09147i
\(538\) 53.2780 53.2780i 0.0990298 0.0990298i
\(539\) −320.996 406.670i −0.595539 0.754490i
\(540\) 247.714 + 107.415i 0.458729 + 0.198916i
\(541\) −850.320 −1.57176 −0.785878 0.618381i \(-0.787789\pi\)
−0.785878 + 0.618381i \(0.787789\pi\)
\(542\) −312.775 + 312.775i −0.577076 + 0.577076i
\(543\) 87.4035 + 38.8079i 0.160964 + 0.0714695i
\(544\) −123.937 −0.227825
\(545\) −630.996 560.576i −1.15779 1.02858i
\(546\) 627.368 + 52.6721i 1.14903 + 0.0964690i
\(547\) 141.618 141.618i 0.258899 0.258899i −0.565707 0.824606i \(-0.691397\pi\)
0.824606 + 0.565707i \(0.191397\pi\)
\(548\) 278.009 278.009i 0.507316 0.507316i
\(549\) −324.783 + 293.636i −0.591590 + 0.534857i
\(550\) −293.627 231.358i −0.533868 0.420650i
\(551\) 410.888 0.745713
\(552\) −254.176 112.856i −0.460463 0.204450i
\(553\) 657.364 228.179i 1.18872 0.412620i
\(554\) −461.740 −0.833466
\(555\) −350.198 131.348i −0.630988 0.236663i
\(556\) 372.652i 0.670237i
\(557\) 596.862 + 596.862i 1.07157 + 1.07157i 0.997234 + 0.0743321i \(0.0236825\pi\)
0.0743321 + 0.997234i \(0.476318\pi\)
\(558\) −421.297 21.2188i −0.755012 0.0380264i
\(559\) 683.823 1.22330
\(560\) 129.366 + 53.5199i 0.231011 + 0.0955713i
\(561\) −648.544 + 249.711i −1.15605 + 0.445118i
\(562\) −22.5908 + 22.5908i −0.0401971 + 0.0401971i
\(563\) −13.7370 13.7370i −0.0243996 0.0243996i 0.694802 0.719201i \(-0.255492\pi\)
−0.719201 + 0.694802i \(0.755492\pi\)
\(564\) −100.005 + 38.5051i −0.177313 + 0.0682714i
\(565\) −7.91624 133.949i −0.0140110 0.237077i
\(566\) 369.313 0.652497
\(567\) −551.619 + 131.169i −0.972873 + 0.231339i
\(568\) 121.545 + 121.545i 0.213988 + 0.213988i
\(569\) 1040.51 1.82866 0.914331 0.404969i \(-0.132718\pi\)
0.914331 + 0.404969i \(0.132718\pi\)
\(570\) 129.134 344.294i 0.226550 0.604025i
\(571\) 42.2507 0.0739942 0.0369971 0.999315i \(-0.488221\pi\)
0.0369971 + 0.999315i \(0.488221\pi\)
\(572\) 316.985 316.985i 0.554169 0.554169i
\(573\) 110.923 + 49.2509i 0.193583 + 0.0859527i
\(574\) 51.1057 105.447i 0.0890343 0.183706i
\(575\) −643.594 507.106i −1.11929 0.881924i
\(576\) −53.4082 + 48.2863i −0.0927225 + 0.0838304i
\(577\) −234.233 234.233i −0.405950 0.405950i 0.474373 0.880324i \(-0.342675\pi\)
−0.880324 + 0.474373i \(0.842675\pi\)
\(578\) −191.012 + 191.012i −0.330471 + 0.330471i
\(579\) 70.7804 27.2528i 0.122246 0.0470688i
\(580\) −177.208 157.431i −0.305531 0.271433i
\(581\) 73.0506 150.726i 0.125732 0.259425i
\(582\) −190.817 84.7245i −0.327865 0.145575i
\(583\) 161.987 + 161.987i 0.277851 + 0.277851i
\(584\) 14.1097i 0.0241605i
\(585\) −668.646 + 680.393i −1.14298 + 1.16306i
\(586\) 101.907i 0.173903i
\(587\) −667.229 + 667.229i −1.13668 + 1.13668i −0.147635 + 0.989042i \(0.547166\pi\)
−0.989042 + 0.147635i \(0.952834\pi\)
\(588\) −284.836 + 72.8333i −0.484414 + 0.123866i
\(589\) 574.494i 0.975372i
\(590\) 12.9675 + 219.421i 0.0219789 + 0.371899i
\(591\) 389.149 149.835i 0.658459 0.253528i
\(592\) 70.5259 70.5259i 0.119132 0.119132i
\(593\) −599.428 599.428i −1.01084 1.01084i −0.999941 0.0108986i \(-0.996531\pi\)
−0.0108986 0.999941i \(-0.503469\pi\)
\(594\) −182.189 + 360.283i −0.306715 + 0.606537i
\(595\) 708.324 293.755i 1.19046 0.493706i
\(596\) 507.136i 0.850899i
\(597\) −37.1522 + 83.6745i −0.0622315 + 0.140158i
\(598\) 694.791 694.791i 1.16186 1.16186i
\(599\) −303.628 −0.506892 −0.253446 0.967350i \(-0.581564\pi\)
−0.253446 + 0.967350i \(0.581564\pi\)
\(600\) −187.609 + 99.0100i −0.312681 + 0.165017i
\(601\) 34.3783i 0.0572019i 0.999591 + 0.0286009i \(0.00910520\pi\)
−0.999591 + 0.0286009i \(0.990895\pi\)
\(602\) −301.675 + 104.715i −0.501122 + 0.173945i
\(603\) 986.161 + 49.6683i 1.63543 + 0.0823687i
\(604\) 393.779i 0.651952i
\(605\) −30.5694 + 34.4096i −0.0505279 + 0.0568753i
\(606\) −677.402 + 260.822i −1.11783 + 0.430400i
\(607\) 185.983 + 185.983i 0.306397 + 0.306397i 0.843510 0.537113i \(-0.180485\pi\)
−0.537113 + 0.843510i \(0.680485\pi\)
\(608\) 69.3370 + 69.3370i 0.114041 + 0.114041i
\(609\) 496.035 + 41.6457i 0.814507 + 0.0683838i
\(610\) −20.2947 343.403i −0.0332701 0.562955i
\(611\) 378.617i 0.619668i
\(612\) −19.8372 + 393.866i −0.0324137 + 0.643572i
\(613\) −121.390 121.390i −0.198027 0.198027i 0.601127 0.799154i \(-0.294719\pi\)
−0.799154 + 0.601127i \(0.794719\pi\)
\(614\) 139.985i 0.227988i
\(615\) 73.4622 + 161.642i 0.119451 + 0.262833i
\(616\) −91.3006 + 188.382i −0.148215 + 0.305814i
\(617\) 585.706 + 585.706i 0.949281 + 0.949281i 0.998774 0.0494938i \(-0.0157608\pi\)
−0.0494938 + 0.998774i \(0.515761\pi\)
\(618\) −86.2286 + 194.205i −0.139528 + 0.314247i
\(619\) −90.7688 −0.146638 −0.0733189 0.997309i \(-0.523359\pi\)
−0.0733189 + 0.997309i \(0.523359\pi\)
\(620\) 220.117 247.768i 0.355027 0.399626i
\(621\) −399.335 + 789.694i −0.643051 + 1.27165i
\(622\) 26.1121 + 26.1121i 0.0419809 + 0.0419809i
\(623\) 116.943 40.5921i 0.187709 0.0651559i
\(624\) −91.4059 237.398i −0.146484 0.380445i
\(625\) −607.658 + 146.208i −0.972253 + 0.233933i
\(626\) −115.737 −0.184884
\(627\) 502.532 + 223.128i 0.801486 + 0.355867i
\(628\) −188.539 + 188.539i −0.300221 + 0.300221i
\(629\) 546.298i 0.868519i
\(630\) 190.790 402.553i 0.302841 0.638974i
\(631\) −293.524 −0.465173 −0.232587 0.972576i \(-0.574719\pi\)
−0.232587 + 0.972576i \(0.574719\pi\)
\(632\) −198.811 198.811i −0.314575 0.314575i
\(633\) 37.1404 83.6478i 0.0586735 0.132145i
\(634\) 736.822i 1.16218i
\(635\) 55.3205 + 936.065i 0.0871189 + 1.47412i
\(636\) 121.316 46.7108i 0.190749 0.0734446i
\(637\) 121.461 1031.62i 0.190677 1.61950i
\(638\) 250.627 250.627i 0.392833 0.392833i
\(639\) 405.719 366.810i 0.634928 0.574038i
\(640\) −3.33732 56.4700i −0.00521456 0.0882344i
\(641\) 495.745i 0.773393i −0.922207 0.386697i \(-0.873616\pi\)
0.922207 0.386697i \(-0.126384\pi\)
\(642\) 225.121 + 99.9556i 0.350656 + 0.155694i
\(643\) −195.737 + 195.737i −0.304412 + 0.304412i −0.842737 0.538325i \(-0.819057\pi\)
0.538325 + 0.842737i \(0.319057\pi\)
\(644\) −200.119 + 412.909i −0.310744 + 0.641163i
\(645\) 169.922 453.044i 0.263445 0.702394i
\(646\) 537.089 0.831407
\(647\) 584.341 584.341i 0.903154 0.903154i −0.0925538 0.995708i \(-0.529503\pi\)
0.995708 + 0.0925538i \(0.0295030\pi\)
\(648\) 144.903 + 177.457i 0.223616 + 0.273854i
\(649\) −328.670 −0.506425
\(650\) −88.2804 744.277i −0.135816 1.14504i
\(651\) −58.2282 + 693.545i −0.0894442 + 1.06535i
\(652\) −288.237 + 288.237i −0.442082 + 0.442082i
\(653\) −25.5558 + 25.5558i −0.0391360 + 0.0391360i −0.726404 0.687268i \(-0.758810\pi\)
0.687268 + 0.726404i \(0.258810\pi\)
\(654\) −257.341 668.360i −0.393487 1.02196i
\(655\) 820.988 924.122i 1.25342 1.41087i
\(656\) −47.3474 −0.0721759
\(657\) 44.8401 + 2.25838i 0.0682497 + 0.00343742i
\(658\) 57.9784 + 167.031i 0.0881131 + 0.253846i
\(659\) −54.2782 −0.0823645 −0.0411823 0.999152i \(-0.513112\pi\)
−0.0411823 + 0.999152i \(0.513112\pi\)
\(660\) −131.241 288.775i −0.198849 0.437538i
\(661\) 604.587i 0.914655i 0.889298 + 0.457328i \(0.151193\pi\)
−0.889298 + 0.457328i \(0.848807\pi\)
\(662\) −172.781 172.781i −0.260998 0.260998i
\(663\) −1273.47 565.430i −1.92076 0.852836i
\(664\) −67.6784 −0.101925
\(665\) −560.616 231.932i −0.843032 0.348770i
\(666\) −212.840 235.416i −0.319579 0.353478i
\(667\) 549.344 549.344i 0.823604 0.823604i
\(668\) −163.515 163.515i −0.244783 0.244783i
\(669\) −108.143 280.866i −0.161648 0.419829i
\(670\) −515.243 + 579.969i −0.769020 + 0.865626i
\(671\) 514.382 0.766591
\(672\) 76.6778 + 90.7332i 0.114104 + 0.135020i
\(673\) 653.084 + 653.084i 0.970407 + 0.970407i 0.999575 0.0291677i \(-0.00928567\pi\)
−0.0291677 + 0.999575i \(0.509286\pi\)
\(674\) 600.687 0.891227
\(675\) 284.621 + 612.059i 0.421660 + 0.906754i
\(676\) 560.786 0.829566
\(677\) −111.338 + 111.338i −0.164458 + 0.164458i −0.784538 0.620080i \(-0.787100\pi\)
0.620080 + 0.784538i \(0.287100\pi\)
\(678\) 46.2041 104.061i 0.0681476 0.153483i
\(679\) −150.236 + 309.983i −0.221260 + 0.456529i
\(680\) −231.636 205.785i −0.340641 0.302625i
\(681\) 212.975 + 553.135i 0.312739 + 0.812240i
\(682\) 350.422 + 350.422i 0.513815 + 0.513815i
\(683\) 420.406 420.406i 0.615528 0.615528i −0.328853 0.944381i \(-0.606662\pi\)
0.944381 + 0.328853i \(0.106662\pi\)
\(684\) 231.448 209.252i 0.338374 0.305923i
\(685\) 981.199 57.9878i 1.43241 0.0846538i
\(686\) 104.390 + 473.710i 0.152172 + 0.690539i
\(687\) −23.1943 + 52.2383i −0.0337617 + 0.0760383i
\(688\) 91.2379 + 91.2379i 0.132613 + 0.132613i
\(689\) 459.303i 0.666622i
\(690\) −287.663 632.958i −0.416903 0.917331i
\(691\) 238.766i 0.345537i −0.984962 0.172768i \(-0.944729\pi\)
0.984962 0.172768i \(-0.0552712\pi\)
\(692\) 295.444 295.444i 0.426943 0.426943i
\(693\) 584.055 + 320.301i 0.842792 + 0.462195i
\(694\) 401.025i 0.577846i
\(695\) −618.750 + 696.479i −0.890288 + 1.00213i
\(696\) −72.2710 187.701i −0.103838 0.269685i
\(697\) −183.378 + 183.378i −0.263096 + 0.263096i
\(698\) 414.103 + 414.103i 0.593270 + 0.593270i
\(699\) 49.3739 + 128.233i 0.0706350 + 0.183452i
\(700\) 152.918 + 314.827i 0.218455 + 0.449753i
\(701\) 1371.35i 1.95628i 0.207939 + 0.978142i \(0.433324\pi\)
−0.207939 + 0.978142i \(0.566676\pi\)
\(702\) −769.068 + 252.486i −1.09554 + 0.359667i
\(703\) −305.628 + 305.628i −0.434749 + 0.434749i
\(704\) 84.5864 0.120151
\(705\) −250.840 94.0821i −0.355802 0.133450i
\(706\) 498.690i 0.706360i
\(707\) 392.729 + 1131.42i 0.555487 + 1.60031i
\(708\) −75.6866 + 170.462i −0.106902 + 0.240765i
\(709\) 403.787i 0.569516i −0.958600 0.284758i \(-0.908087\pi\)
0.958600 0.284758i \(-0.0919132\pi\)
\(710\) 25.3522 + 428.978i 0.0357073 + 0.604195i
\(711\) −663.634 + 599.991i −0.933381 + 0.843870i
\(712\) −35.3678 35.3678i −0.0496738 0.0496738i
\(713\) 768.081 + 768.081i 1.07725 + 1.07725i
\(714\) 648.388 + 54.4369i 0.908107 + 0.0762422i
\(715\) 1118.76 66.1175i 1.56470 0.0924721i
\(716\) 427.530i 0.597109i
\(717\) −162.208 + 365.327i −0.226232 + 0.509522i
\(718\) 267.685 + 267.685i 0.372821 + 0.372821i
\(719\) 1058.56i 1.47226i 0.676840 + 0.736130i \(0.263349\pi\)
−0.676840 + 0.736130i \(0.736651\pi\)
\(720\) −179.993 + 1.56734i −0.249991 + 0.00217686i
\(721\) 315.486 + 152.903i 0.437567 + 0.212070i
\(722\) 60.5240 + 60.5240i 0.0838283 + 0.0838283i
\(723\) −841.880 373.802i −1.16443 0.517015i
\(724\) −63.7545 −0.0880587
\(725\) −69.7998 588.470i −0.0962756 0.811683i
\(726\) −36.4471 + 14.0333i −0.0502026 + 0.0193297i
\(727\) 138.934 + 138.934i 0.191106 + 0.191106i 0.796174 0.605068i \(-0.206854\pi\)
−0.605068 + 0.796174i \(0.706854\pi\)
\(728\) −396.509 + 137.633i −0.544655 + 0.189056i
\(729\) 587.144 432.092i 0.805410 0.592718i
\(730\) −23.4278 + 26.3708i −0.0320928 + 0.0361244i
\(731\) 706.735 0.966805
\(732\) 118.453 266.780i 0.161821 0.364454i
\(733\) 777.200 777.200i 1.06030 1.06030i 0.0622385 0.998061i \(-0.480176\pi\)
0.998061 0.0622385i \(-0.0198239\pi\)
\(734\) 846.081i 1.15270i
\(735\) −653.284 336.816i −0.888822 0.458253i
\(736\) 185.403 0.251906
\(737\) −820.259 820.259i −1.11297 1.11297i
\(738\) −7.57835 + 150.468i −0.0102688 + 0.203886i
\(739\) 1369.25i 1.85285i 0.376485 + 0.926423i \(0.377133\pi\)
−0.376485 + 0.926423i \(0.622867\pi\)
\(740\) 248.912 14.7105i 0.336368 0.0198790i
\(741\) 396.113 + 1028.78i 0.534566 + 1.38836i
\(742\) −70.3340 202.626i −0.0947897 0.273081i
\(743\) 903.427 903.427i 1.21592 1.21592i 0.246870 0.969049i \(-0.420598\pi\)
0.969049 0.246870i \(-0.0794019\pi\)
\(744\) 262.439 101.048i 0.352741 0.135817i
\(745\) −842.047 + 947.827i −1.13026 + 1.27225i
\(746\) 106.932i 0.143341i
\(747\) −10.8325 + 215.079i −0.0145014 + 0.287923i
\(748\) 327.606 327.606i 0.437976 0.437976i
\(749\) 177.244 365.709i 0.236641 0.488263i
\(750\) −515.033 126.457i −0.686710 0.168610i
\(751\) 303.273 0.403825 0.201913 0.979404i \(-0.435284\pi\)
0.201913 + 0.979404i \(0.435284\pi\)
\(752\) 50.5164 50.5164i 0.0671760 0.0671760i
\(753\) 249.674 562.318i 0.331573 0.746771i
\(754\) 710.635 0.942486
\(755\) −653.829 + 735.964i −0.865999 + 0.974787i
\(756\) 300.619 229.156i 0.397644 0.303116i
\(757\) 581.912 581.912i 0.768708 0.768708i −0.209171 0.977879i \(-0.567077\pi\)
0.977879 + 0.209171i \(0.0670766\pi\)
\(758\) 364.774 364.774i 0.481233 0.481233i
\(759\) 970.184 373.553i 1.27824 0.492165i
\(760\) 14.4625 + 244.716i 0.0190296 + 0.321995i
\(761\) −863.872 −1.13518 −0.567590 0.823311i \(-0.692124\pi\)
−0.567590 + 0.823311i \(0.692124\pi\)
\(762\) −322.885 + 727.204i −0.423734 + 0.954336i
\(763\) −1116.32 + 387.487i −1.46306 + 0.507846i
\(764\) −80.9105 −0.105904
\(765\) −691.049 + 703.190i −0.903332 + 0.919203i
\(766\) 226.259i 0.295378i
\(767\) −465.959