Properties

Label 210.3.k.a.83.6
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 83.6
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.a.167.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.21742 + 2.74188i) q^{3} +2.00000i q^{4} +(3.32079 - 3.73796i) q^{5} +(3.95930 - 1.52446i) q^{6} +(-6.61294 - 2.29543i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-6.03579 - 6.67602i) q^{9} +O(q^{10})\) \(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} +(-6.61294 - 2.29543i) 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} +(14.3445 - 15.3374i) 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} +(4.59086 - 13.2259i) 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} +(-30.5404 + 17.0962i) 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} +(-29.6819 + 0.992874i) 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} +(24.5900 + 58.0029i) 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} +(47.6367 + 13.4442i) 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} +(24.2703 - 69.9206i) 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} +(30.6748 + 28.6890i) 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} +(-8.10289 - 68.8211i) 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
\(7\) −6.61294 2.29543i −0.944706 0.327919i
\(8\) 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 \(-0.446549\pi\)
0.985934 0.167134i \(-0.0534512\pi\)
\(14\) 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 −0.0850728 0.996375i \(-0.527112\pi\)
0.996375 + 0.0850728i \(0.0271123\pi\)
\(18\) −0.640234 + 12.7118i −0.0355686 + 0.706212i
\(19\) −17.3342 −0.912329 −0.456164 0.889896i \(-0.650777\pi\)
−0.456164 + 0.889896i \(0.650777\pi\)
\(20\) 7.47592 + 6.64159i 0.373796 + 0.332079i
\(21\) 14.3445 15.3374i 0.683072 0.730351i
\(22\) 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
\(28\) 4.59086 13.2259i 0.163959 0.472353i
\(29\) 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 \(-0.820481\pi\)
0.845136 0.534551i \(-0.179519\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −28.9907 12.8721i −0.878505 0.390064i
\(34\) −30.9843 −0.911302
\(35\) −30.5404 + 17.0962i −0.872584 + 0.488464i
\(36\) 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 \(-0.546110\pi\)
−0.144352 + 0.989526i \(0.546110\pi\)
\(42\) −29.6819 + 0.992874i −0.706712 + 0.0236399i
\(43\) −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 −0.559874 0.828578i \(-0.689150\pi\)
0.828578 + 0.559874i \(0.189150\pi\)
\(48\) 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 \(-0.915146\pi\)
0.964678 0.263431i \(-0.0848542\pi\)
\(60\) −27.3117 + 12.4125i −0.455196 + 0.206874i
\(61\) 48.6492i 0.797528i 0.917054 + 0.398764i \(0.130561\pi\)
−0.917054 + 0.398764i \(0.869439\pi\)
\(62\) −33.1422 + 33.1422i −0.534551 + 0.534551i
\(63\) 24.5900 + 58.0029i 0.390317 + 0.920681i
\(64\) 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
\(70\) 47.6367 + 13.4442i 0.680524 + 0.192060i
\(71\) 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 −0.682533 0.730854i \(-0.739122\pi\)
0.730854 + 0.682533i \(0.239122\pi\)
\(74\) 35.2630 0.476526
\(75\) 71.6547 + 22.1497i 0.955396 + 0.295329i
\(76\) 34.6685i 0.456164i
\(77\) 24.2703 69.9206i 0.315198 0.908059i
\(78\) 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 0.801648 0.597797i \(-0.203957\pi\)
−0.597797 + 0.801648i \(0.703957\pi\)
\(84\) 30.6748 + 28.6890i 0.365176 + 0.341536i
\(85\) −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 \(0.0316756\pi\)
−0.995053 + 0.0993477i \(0.968324\pi\)
\(90\) 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 0.504615 0.863345i \(-0.331635\pi\)
−0.863345 + 0.504615i \(0.831635\pi\)
\(98\) −8.10289 68.8211i −0.0826825 0.702256i
\(99\) 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 \(-0.821587\pi\)
−0.846988 + 0.531612i \(0.821587\pi\)
\(102\) 37.7208 84.9551i 0.369812 0.832893i
\(103\) −35.4145 + 35.4145i −0.343831 + 0.343831i −0.857805 0.513975i \(-0.828172\pi\)
0.513975 + 0.857805i \(0.328172\pi\)
\(104\) 59.9595i 0.576534i
\(105\) −9.69535 104.551i −0.0923366 0.995728i
\(106\) −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
\(112\) 26.4518 + 9.18172i 0.236176 + 0.0819797i
\(113\) −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
\(126\) 33.4129 82.5928i 0.265182 0.655499i
\(127\) 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 \(-0.107403\pi\)
0.943613 + 0.331051i \(0.107403\pi\)
\(132\) 25.7442 57.9814i 0.195032 0.439253i
\(133\) 114.630 + 39.7896i 0.861882 + 0.299170i
\(134\) 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 \(-0.733808\pi\)
−0.670237 + 0.742147i \(0.733808\pi\)
\(140\) −34.1925 61.0809i −0.244232 0.436292i
\(141\) 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
\(147\) −130.065 + 68.4984i −0.884798 + 0.465975i
\(148\) −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 0.339988 0.940430i \(-0.389577\pi\)
−0.940430 + 0.339988i \(0.889577\pi\)
\(158\) −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 −0.418603 0.908169i \(-0.637480\pi\)
0.908169 + 0.418603i \(0.137480\pi\)
\(168\) −1.98575 59.3638i −0.0118199 0.353356i
\(169\) 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 0.990609 0.136724i \(-0.0436573\pi\)
−0.136724 + 0.990609i \(0.543657\pi\)
\(174\) 93.8504 36.1355i 0.539370 0.207675i
\(175\) −37.5134 + 170.932i −0.214362 + 0.976754i
\(176\) 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 \(-0.971934\pi\)
0.996115 0.0880587i \(-0.0280663\pi\)
\(182\) 198.254 + 68.8165i 1.08931 + 0.378113i
\(183\) −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
\(189\) −188.973 3.19107i −0.999857 0.0168840i
\(190\) 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 \(-0.475569\pi\)
0.0766764 + 0.997056i \(0.475569\pi\)
\(200\) −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
\(203\) −156.752 54.4105i −0.772177 0.268032i
\(204\) −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
\(210\) −94.8561 + 114.247i −0.451696 + 0.544032i
\(211\) 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
\(217\) −76.0756 + 219.167i −0.350579 + 1.00999i
\(218\) 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 −0.848041 0.529931i \(-0.822218\pi\)
0.529931 + 0.848041i \(0.322218\pi\)
\(224\) −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 −0.328916 0.944359i \(-0.606683\pi\)
0.944359 + 0.328916i \(0.106683\pi\)
\(228\) 95.0568 + 42.2060i 0.416916 + 0.185114i
\(229\) 19.0520 0.0831966 0.0415983 0.999134i \(-0.486755\pi\)
0.0415983 + 0.999134i \(0.486755\pi\)
\(230\) −153.921 + 173.257i −0.669221 + 0.753290i
\(231\) 162.167 + 151.669i 0.702020 + 0.656574i
\(232\) 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
\(238\) 204.897 + 71.1223i 0.860912 + 0.298833i
\(239\) −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 \(0.219834\pi\)
−0.770845 + 0.637023i \(0.780166\pi\)
\(242\) −9.20544 9.20544i −0.0380390 0.0380390i
\(243\) −211.060 120.427i −0.868561 0.495583i
\(244\) −97.2984 −0.398764
\(245\) 241.205 42.9530i 0.984512 0.175318i
\(246\) −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 \(-0.633961\pi\)
−0.408536 + 0.912742i \(0.633961\pi\)
\(252\) −116.006 + 49.1799i −0.460340 + 0.195158i
\(253\) 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 −0.969541 0.244929i \(-0.921235\pi\)
0.244929 + 0.969541i \(0.421235\pi\)
\(258\) −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 \(-0.968426\pi\)
0.995084 0.0990298i \(-0.0315739\pi\)
\(270\) −177.564 + 70.1495i −0.657645 + 0.259813i
\(271\) 312.775i 1.15415i 0.816691 + 0.577076i \(0.195806\pi\)
−0.816691 + 0.577076i \(0.804194\pi\)
\(272\) −61.9685 + 61.9685i −0.227825 + 0.227825i
\(273\) −14.8831 444.928i −0.0545167 1.62977i
\(274\) 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
\(280\) −26.8884 + 95.2734i −0.0960299 + 0.340262i
\(281\) 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 −0.301097 0.953594i \(-0.597353\pi\)
0.953594 + 0.301097i \(0.0973527\pi\)
\(284\) −121.545 −0.427976
\(285\) −107.580 236.714i −0.377475 0.830576i
\(286\) 316.985i 1.10834i
\(287\) 78.2763 + 27.1707i 0.272740 + 0.0946713i
\(288\) 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 0.614789 0.788692i \(-0.289241\pi\)
−0.788692 + 0.614789i \(0.789241\pi\)
\(294\) 198.564 + 61.5669i 0.675387 + 0.209411i
\(295\) −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 0.811852 0.583864i \(-0.198460\pi\)
−0.583864 + 0.811852i \(0.698460\pi\)
\(308\) 139.841 + 48.5405i 0.454030 + 0.157599i
\(309\) −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 \(-0.486633\pi\)
0.0419809 + 0.999118i \(0.486633\pi\)
\(312\) 164.402 + 72.9958i 0.526929 + 0.233961i
\(313\) −57.8685 + 57.8685i −0.184884 + 0.184884i −0.793480 0.608596i \(-0.791733\pi\)
0.608596 + 0.793480i \(0.291733\pi\)
\(314\) 188.539i 0.600442i
\(315\) 298.471 + 100.699i 0.947525 + 0.319680i
\(316\) 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
\(322\) 306.514 + 106.395i 0.951907 + 0.330418i
\(323\) −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
\(336\) −57.3780 + 61.3495i −0.170768 + 0.182588i
\(337\) −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
\(343\) −184.660 289.050i −0.538366 0.842711i
\(344\) −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 \(-0.297836\pi\)
0.593270 + 0.805003i \(0.297836\pi\)
\(350\) 208.445 133.419i 0.595558 0.381196i
\(351\) 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 0.965768 0.259408i \(-0.0835273\pi\)
−0.259408 + 0.965768i \(0.583527\pi\)
\(354\) −47.3877 123.074i −0.133863 0.347667i
\(355\) 227.165 + 201.813i 0.639902 + 0.568487i
\(356\) −35.3678 −0.0993477
\(357\) −15.3817 459.836i −0.0430861 1.28806i
\(358\) −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 \(-0.946692\pi\)
−0.166690 0.986009i \(-0.553308\pi\)
\(368\) −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
\(378\) 185.782 + 192.164i 0.491487 + 0.508371i
\(379\) 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 0.839200 0.543823i \(-0.183024\pi\)
−0.543823 + 0.839200i \(0.683024\pi\)
\(384\) −12.1957 31.6744i −0.0317596 0.0824853i
\(385\) −180.764 322.913i −0.469516 0.838735i
\(386\) 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
\(392\) 137.642 16.2058i 0.351128 0.0413413i
\(393\) −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 0.0812649 0.996693i \(-0.474104\pi\)
−0.996693 + 0.0812649i \(0.974104\pi\)
\(398\) −30.5172 30.5172i −0.0766764 0.0766764i
\(399\) −248.651 + 265.862i −0.623186 + 0.666320i
\(400\) 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 \(-0.705052\pi\)
−0.600552 + 0.799586i \(0.705052\pi\)
\(410\) 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
\(413\) −71.3532 + 205.563i −0.172768 + 0.497730i
\(414\) 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 \(-0.841359\pi\)
0.878356 0.478008i \(-0.158641\pi\)
\(420\) 209.103 19.3907i 0.497864 0.0461683i
\(421\) −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
\(427\) 111.671 321.714i 0.261524 0.753429i
\(428\) 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 −0.654952 0.755671i \(-0.727311\pi\)
0.755671 + 0.654952i \(0.227311\pi\)
\(434\) 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 \(-0.257737\pi\)
0.689712 + 0.724084i \(0.257737\pi\)
\(440\) 149.269 8.82162i 0.339247 0.0200491i
\(441\) −29.4704 440.014i −0.0668262 0.997765i
\(442\) −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
\(448\) −18.3634 + 52.9035i −0.0409898 + 0.118088i
\(449\) 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
\(455\) −201.527 + 714.068i −0.442916 + 1.56938i
\(456\) −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 \(-0.508180\pi\)
−0.0256955 + 0.999670i \(0.508180\pi\)
\(462\) −10.4979 313.835i −0.0227228 0.679297i
\(463\) −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 −0.978198 0.207673i \(-0.933411\pi\)
0.207673 + 0.978198i \(0.433411\pi\)
\(468\) 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 \(0.163322\pi\)
−0.871231 + 0.490873i \(0.836678\pi\)
\(480\) −29.7985 + 79.4484i −0.0620803 + 0.165517i
\(481\) 528.588i 1.09893i
\(482\) 307.045 307.045i 0.637023 0.637023i
\(483\) −23.0102 687.887i −0.0476401 1.42420i
\(484\) 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
\(490\) −284.158 198.252i −0.579915 0.404597i
\(491\) 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
\(497\) 139.499 401.885i 0.280682 0.808622i
\(498\) 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 0.00244509 0.999997i \(-0.499222\pi\)
−0.999997 + 0.00244509i \(0.999222\pi\)
\(504\) 165.186 + 66.8258i 0.327749 + 0.132591i
\(505\) −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 \(0.208642\pi\)
−0.792762 + 0.609531i \(0.791358\pi\)
\(510\) −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
\(518\) −233.192 80.9437i −0.450177 0.156262i
\(519\) −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 \(-0.397916\pi\)
0.315236 + 0.949013i \(0.397916\pi\)
\(522\) −15.1760 + 301.318i −0.0290728 + 0.577238i
\(523\) 167.734 167.734i 0.320714 0.320714i −0.528327 0.849041i \(-0.677180\pi\)
0.849041 + 0.528327i \(0.177180\pi\)
\(524\) 494.453i 0.943613i
\(525\) −423.005 310.953i −0.805724 0.592291i
\(526\) 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
\(532\) −79.5791 + 229.261i −0.149585 + 0.430941i
\(533\) −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
\(546\) −430.045 + 459.811i −0.787628 + 0.842145i
\(547\) 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
\(553\) −228.179 + 657.364i −0.412620 + 1.18872i
\(554\) −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
\(560\) 122.162 68.3850i 0.218146 0.122116i
\(561\) −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 0.719201 0.694802i \(-0.244508\pi\)
−0.694802 + 0.719201i \(0.744508\pi\)
\(564\) −100.005 + 38.5051i −0.177313 + 0.0682714i
\(565\) 7.91624 + 133.949i 0.0140110 + 0.237077i
\(566\) −369.313 −0.652497
\(567\) 238.809 514.256i 0.421179 0.906977i
\(568\) 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 0.880324 0.474373i \(-0.157325\pi\)
−0.474373 + 0.880324i \(0.657325\pi\)
\(578\) −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 \(-0.452834\pi\)
0.989042 0.147635i \(-0.0471661\pi\)
\(588\) −136.997 260.131i −0.232988 0.442399i
\(589\) 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 \(0.00346921\pi\)
0.0108986 + 0.999941i \(0.496531\pi\)
\(594\) 182.189 360.283i 0.306715 0.606537i
\(595\) −208.279 + 737.994i −0.350049 + 1.24033i
\(596\) 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 \(-0.990895\pi\)
0.999591 0.0286009i \(-0.00910520\pi\)
\(602\) 104.715 301.675i 0.173945 0.501122i
\(603\) 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 0.537113 0.843510i \(-0.319515\pi\)
−0.843510 + 0.537113i \(0.819515\pi\)
\(608\) −69.3370 69.3370i −0.114041 0.114041i
\(609\) 340.019 363.554i 0.558324 0.596969i
\(610\) −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 \(-0.476641\pi\)
0.0733189 + 0.997309i \(0.476641\pi\)
\(620\) 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
\(623\) 40.5921 116.943i 0.0651559 0.187709i
\(624\) −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
\(630\) −197.771 399.170i −0.313923 0.633603i
\(631\) −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
\(637\) 1031.62 121.461i 1.61950 0.190677i
\(638\) 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 −0.538325 0.842737i \(-0.680943\pi\)
0.842737 + 0.538325i \(0.180943\pi\)
\(644\) −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 −0.995708 0.0925538i \(-0.970497\pi\)
0.0925538 + 0.995708i \(0.470497\pi\)
\(648\) 144.903 + 177.457i 0.223616 + 0.273854i
\(649\) 328.670 0.506425
\(650\) 88.2804 + 744.277i 0.135816 + 1.14504i
\(651\) −508.314 475.408i −0.780820 0.730273i
\(652\) −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
\(658\) 167.031 + 57.9784i 0.253846 + 0.0881131i
\(659\) −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 \(-0.848807\pi\)
0.889298 0.457328i \(-0.151193\pi\)
\(662\) −172.781 172.781i −0.260998 0.260998i
\(663\) 1273.47 + 565.430i 1.92076 + 0.852836i
\(664\) 67.6784 0.101925
\(665\) 529.395 296.351i 0.796083 0.445640i
\(666\) −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
\(672\) 118.728 3.97150i 0.176678 0.00590996i
\(673\) 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 −0.620080 0.784538i \(-0.712900\pi\)
0.784538 + 0.620080i \(0.212900\pi\)
\(678\) −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 \(0.0552712\pi\)
−0.984962 + 0.172768i \(0.944729\pi\)
\(692\) −295.444 + 295.444i −0.426943 + 0.426943i
\(693\) −613.282 + 259.997i −0.884966 + 0.375176i
\(694\) 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
\(700\) −341.864 75.0268i −0.488377 0.107181i
\(701\) 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
\(707\) 1131.42 + 392.729i 1.60031 + 0.555487i
\(708\) −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
\(714\) −444.454 + 475.217i −0.622485 + 0.665571i
\(715\) 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 \(-0.736651\pi\)
0.676840 0.736130i \(-0.263349\pi\)
\(720\) 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 0.605068 0.796174i \(-0.293146\pi\)
−0.796174 + 0.605068i \(0.793146\pi\)
\(728\) −137.633 + 396.509i −0.189056 + 0.544655i
\(729\) 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 \(0.519824\pi\)
−0.998061 + 0.0622385i \(0.980176\pi\)
\(734\) 846.081i 1.15270i
\(735\) −175.876 + 713.647i −0.239287 + 0.970949i
\(736\) 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
\(742\) 202.626 + 70.3340i 0.273081 + 0.0947897i
\(743\) 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
\(756\) 6.38214 377.946i 0.00844198 0.499929i
\(757\) 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 \(-0.307876\pi\)
0.567590 + 0.823311i \(0.307876\pi\)
\(762\) 322.885 727.204i 0.423734 0.954336i
\(763\) 387.487 1116.32i 0.507846 1.46306i
\(764\) −80.9105 −0.105904
\(765\) −691.049 + 703.190i −0.903332 + 0.919203i
\(766\) 226.259i 0.295378i
\(767\) −465.959