Properties

Label 210.3.k.b.83.14
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 83.14
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(2.74188 - 1.21742i) q^{3} +2.00000i q^{4} +(3.32079 - 3.73796i) q^{5} +(3.95930 + 1.52446i) q^{6} +(2.29543 + 6.61294i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(6.03579 - 6.67602i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(2.74188 - 1.21742i) 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} +(2.43484 + 5.48376i) q^{12} +(-14.9899 + 14.9899i) q^{13} +(-4.31751 + 8.90837i) q^{14} +(4.55455 - 14.2918i) q^{15} -4.00000 q^{16} +(15.4921 - 15.4921i) q^{17} +(12.7118 - 0.640234i) 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} +(8.42188 - 25.6529i) q^{27} +(-13.2259 + 4.59086i) q^{28} -23.7038 q^{29} +(18.8464 - 9.73727i) q^{30} +33.1422i q^{31} +(-4.00000 - 4.00000i) q^{32} +(-12.8721 - 28.9907i) 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} +(-0.992874 + 29.6819i) q^{42} +(-22.8095 - 22.8095i) q^{43} +21.1466 q^{44} +(-4.91109 - 44.7312i) q^{45} -46.3507 q^{46} +(12.6291 - 12.6291i) q^{47} +(-10.9675 + 4.86967i) 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} +(47.5284 - 21.1030i) q^{57} +(-23.7038 - 23.7038i) q^{58} -31.0849i q^{59} +(28.5836 + 9.10910i) q^{60} -48.6492i q^{61} +(-33.1422 + 33.1422i) q^{62} +(58.0029 + 24.5900i) 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} +(1.28047 + 25.4236i) q^{72} +(-3.52743 + 3.52743i) q^{73} -35.2630 q^{74} +(-38.2975 - 64.4849i) q^{75} +34.6685i q^{76} +(69.9206 - 24.2703i) q^{77} +(-82.2009 + 36.4979i) 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} +(-64.9930 + 28.8574i) q^{87} +(21.1466 + 21.1466i) q^{88} +17.6839i q^{89} +(39.8201 - 49.6423i) q^{90} +(-133.535 - 64.7190i) q^{91} +(-46.3507 - 46.3507i) q^{92} +(40.3479 + 90.8718i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} + O(q^{10}) \) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} - 8q^{14} - 4q^{15} - 128q^{16} - 4q^{18} + 12q^{21} - 40q^{22} - 24q^{23} + 16q^{25} - 8q^{28} + 112q^{29} + 28q^{30} - 128q^{32} + 48q^{35} - 40q^{36} + 32q^{37} - 64q^{39} - 20q^{42} - 32q^{43} - 80q^{44} - 48q^{46} + 8q^{50} + 84q^{51} + 136q^{53} + 340q^{57} + 112q^{58} + 64q^{60} + 168q^{63} + 200q^{65} + 32q^{67} - 72q^{72} + 64q^{74} - 88q^{77} - 4q^{78} + 76q^{81} - 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} - 48q^{92} - 388q^{93} - 544q^{95} - 128q^{98} - 160q^{99} + O(q^{100}) \)

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
\(3\) 2.74188 1.21742i 0.913959 0.405806i
\(4\) 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 \(-0.840417\pi\)
0.876938 0.480604i \(-0.159583\pi\)
\(12\) 2.43484 + 5.48376i 0.202903 + 0.456980i
\(13\) −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
\(15\) 4.55455 14.2918i 0.303637 0.952788i
\(16\) −4.00000 −0.250000
\(17\) 15.4921 15.4921i 0.911302 0.911302i −0.0850728 0.996375i \(-0.527112\pi\)
0.996375 + 0.0850728i \(0.0271123\pi\)
\(18\) 12.7118 0.640234i 0.706212 0.0355686i
\(19\) 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
\(21\) 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 \(0.502436\pi\)
−0.999971 + 0.00765214i \(0.997564\pi\)
\(24\) −3.04892 + 7.91859i −0.127038 + 0.329941i
\(25\) −2.94466 24.8260i −0.117787 0.993039i
\(26\) −29.9798 −1.15307
\(27\) 8.42188 25.6529i 0.311922 0.950108i
\(28\) −13.2259 + 4.59086i −0.472353 + 0.163959i
\(29\) −23.7038 −0.817373 −0.408686 0.912675i \(-0.634013\pi\)
−0.408686 + 0.912675i \(0.634013\pi\)
\(30\) 18.8464 9.73727i 0.628212 0.324576i
\(31\) 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
\(33\) −12.8721 28.9907i −0.390064 0.878505i
\(34\) 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 \(-0.546110\pi\)
−0.144352 + 0.989526i \(0.546110\pi\)
\(42\) −0.992874 + 29.6819i −0.0236399 + 0.706712i
\(43\) −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
\(45\) −4.91109 44.7312i −0.109135 0.994027i
\(46\) −46.3507 −1.00762
\(47\) 12.6291 12.6291i 0.268704 0.268704i −0.559874 0.828578i \(-0.689150\pi\)
0.828578 + 0.559874i \(0.189150\pi\)
\(48\) −10.9675 + 4.86967i −0.228490 + 0.101451i
\(49\) −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 −0.836710 0.547646i \(-0.815524\pi\)
0.547646 + 0.836710i \(0.315524\pi\)
\(54\) 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
\(57\) 47.5284 21.1030i 0.833831 0.370228i
\(58\) −23.7038 23.7038i −0.408686 0.408686i
\(59\) 31.0849i 0.526863i −0.964678 0.263431i \(-0.915146\pi\)
0.964678 0.263431i \(-0.0848542\pi\)
\(60\) 28.5836 + 9.10910i 0.476394 + 0.151818i
\(61\) 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
\(63\) 58.0029 + 24.5900i 0.920681 + 0.390317i
\(64\) 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 \(-0.859227\pi\)
0.903790 0.427976i \(-0.140773\pi\)
\(72\) 1.28047 + 25.4236i 0.0177843 + 0.353106i
\(73\) −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
\(75\) −38.2975 64.4849i −0.510633 0.859799i
\(76\) 34.6685i 0.456164i
\(77\) 69.9206 24.2703i 0.908059 0.315198i
\(78\) −82.2009 + 36.4979i −1.05386 + 0.467922i
\(79\) 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
\(87\) −64.9930 + 28.8574i −0.747046 + 0.331695i
\(88\) 21.1466 + 21.1466i 0.240302 + 0.240302i
\(89\) 17.6839i 0.198695i 0.995053 + 0.0993477i \(0.0316756\pi\)
−0.995053 + 0.0993477i \(0.968324\pi\)
\(90\) 39.8201 49.6423i 0.442446 0.551581i
\(91\) −133.535 64.7190i −1.46742 0.711198i
\(92\) −46.3507 46.3507i −0.503811 0.503811i
\(93\) 40.3479 + 90.8718i 0.433848 + 0.977116i
\(94\) 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 \(-0.821587\pi\)
−0.846988 + 0.531612i \(0.821587\pi\)
\(102\) 84.9551 37.7208i 0.832893 0.369812i
\(103\) 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
\(105\) 104.966 2.68690i 0.999673 0.0255895i
\(106\) −30.6409 −0.289065
\(107\) 41.0523 + 41.0523i 0.383667 + 0.383667i 0.872421 0.488755i \(-0.162549\pi\)
−0.488755 + 0.872421i \(0.662549\pi\)
\(108\) 51.3058 + 16.8438i 0.475054 + 0.155961i
\(109\) 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 −0.618138 0.786070i \(-0.712113\pi\)
0.786070 + 0.618138i \(0.212113\pi\)
\(114\) 68.6314 + 26.4254i 0.602030 + 0.231801i
\(115\) 9.66794 + 163.589i 0.0840690 + 1.42251i
\(116\) 47.4076i 0.408686i
\(117\) 9.59704 + 190.549i 0.0820260 + 1.62862i
\(118\) 31.0849 31.0849i 0.263431 0.263431i
\(119\) 138.010 + 66.8874i 1.15975 + 0.562079i
\(120\) 19.4745 + 37.6927i 0.162288 + 0.314106i
\(121\) 9.20544 0.0760780
\(122\) 48.6492 48.6492i 0.398764 0.398764i
\(123\) −32.4552 + 14.4104i −0.263863 + 0.117158i
\(124\) −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 \(0.107403\pi\)
\(132\) 57.9814 25.7442i 0.439253 0.195032i
\(133\) 39.7896 + 114.630i 0.299170 + 0.861882i
\(134\) −155.157 −1.15789
\(135\) −67.9222 116.669i −0.503127 0.864212i
\(136\) 61.9685i 0.455651i
\(137\) 139.005 + 139.005i 1.01463 + 1.01463i 0.999891 + 0.0147404i \(0.00469218\pi\)
0.0147404 + 0.999891i \(0.495308\pi\)
\(138\) −127.088 + 56.4281i −0.920926 + 0.408899i
\(139\) 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
\(147\) −68.4984 + 130.065i −0.465975 + 0.884798i
\(148\) −35.2630 35.2630i −0.238263 0.238263i
\(149\) −253.568 −1.70180 −0.850899 0.525329i \(-0.823942\pi\)
−0.850899 + 0.525329i \(0.823942\pi\)
\(150\) 26.1874 102.782i 0.174583 0.685216i
\(151\) 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
\(153\) −9.91860 196.933i −0.0648274 1.28714i
\(154\) 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
\(162\) 72.4516 88.7286i 0.447232 0.547708i
\(163\) 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
\(165\) −151.112 48.1566i −0.915828 0.291858i
\(166\) 33.8392i 0.203851i
\(167\) 81.7575 81.7575i 0.489566 0.489566i −0.418603 0.908169i \(-0.637480\pi\)
0.908169 + 0.418603i \(0.137480\pi\)
\(168\) −59.3638 1.98575i −0.353356 0.0118199i
\(169\) 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
\(175\) 157.413 76.4592i 0.899505 0.436910i
\(176\) 42.2932i 0.240302i
\(177\) −37.8433 85.2310i −0.213804 0.481531i
\(178\) −17.6839 + 17.6839i −0.0993477 + 0.0993477i
\(179\) −213.765 −1.19422 −0.597109 0.802160i \(-0.703684\pi\)
−0.597109 + 0.802160i \(0.703684\pi\)
\(180\) 89.4624 9.82218i 0.497013 0.0545677i
\(181\) 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
\(183\) −59.2264 133.390i −0.323642 0.728908i
\(184\) 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 \(-0.966226\pi\)
0.994376 0.105904i \(-0.0337735\pi\)
\(192\) −9.73934 21.9350i −0.0507257 0.114245i
\(193\) 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
\(195\) 145.960 + 282.505i 0.748515 + 1.44874i
\(196\) −60.7182 76.9240i −0.309787 0.392469i
\(197\) −98.2874 98.2874i −0.498921 0.498921i 0.412181 0.911102i \(-0.364767\pi\)
−0.911102 + 0.412181i \(0.864767\pi\)
\(198\) −6.76939 134.406i −0.0341888 0.678817i
\(199\) −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
\(207\) 14.8376 + 294.600i 0.0716794 + 1.42319i
\(208\) 59.9595 59.9595i 0.288267 0.288267i
\(209\) 183.280i 0.876938i
\(210\) 107.653 + 102.279i 0.512631 + 0.487042i
\(211\) 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
\(213\) −73.9856 166.631i −0.347350 0.782304i
\(214\) 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
\(222\) −96.6867 + 42.9298i −0.435526 + 0.193377i
\(223\) 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
\(225\) −183.512 130.186i −0.815609 0.578603i
\(226\) 37.9525 0.167932
\(227\) 139.705 139.705i 0.615443 0.615443i −0.328916 0.944359i \(-0.606683\pi\)
0.944359 + 0.328916i \(0.106683\pi\)
\(228\) 42.2060 + 95.0568i 0.185114 + 0.416916i
\(229\) −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
\(231\) 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 −0.634181 0.773185i \(-0.718663\pi\)
0.773185 + 0.634181i \(0.218663\pi\)
\(234\) −180.952 + 200.146i −0.773297 + 0.855323i
\(235\) −5.26842 89.1456i −0.0224188 0.379343i
\(236\) 62.1698 0.263431
\(237\) −121.018 272.558i −0.510625 1.15003i
\(238\) 71.1223 + 204.897i 0.298833 + 0.860912i
\(239\) 133.240 0.557489 0.278744 0.960365i \(-0.410082\pi\)
0.278744 + 0.960365i \(0.410082\pi\)
\(240\) −18.2182 + 57.1673i −0.0759092 + 0.238197i
\(241\) 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
\(243\) −120.427 211.060i −0.495583 0.868561i
\(244\) 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 \(-0.633961\pi\)
−0.408536 + 0.912742i \(0.633961\pi\)
\(252\) −49.1799 + 116.006i −0.195158 + 0.460340i
\(253\) 245.040 + 245.040i 0.968536 + 0.968536i
\(254\) 265.221 1.04418
\(255\) −150.851 291.970i −0.591573 1.14498i
\(256\) 16.0000 0.0625000
\(257\) −186.225 + 186.225i −0.724612 + 0.724612i −0.969541 0.244929i \(-0.921235\pi\)
0.244929 + 0.969541i \(0.421235\pi\)
\(258\) −55.5373 125.082i −0.215261 0.484812i
\(259\) −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 −0.204884 0.978786i \(-0.565682\pi\)
0.978786 + 0.204884i \(0.0656817\pi\)
\(264\) 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
\(267\) 21.5287 + 48.4871i 0.0806318 + 0.181599i
\(268\) −155.157 155.157i −0.578943 0.578943i
\(269\) 53.2780i 0.198060i −0.995084 0.0990298i \(-0.968426\pi\)
0.995084 0.0990298i \(-0.0315739\pi\)
\(270\) 48.7465 184.591i 0.180543 0.683670i
\(271\) 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
\(273\) −444.928 14.8831i −1.62977 0.0545167i
\(274\) 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 \(0.0127986\pi\)
−0.999192 + 0.0401971i \(0.987201\pi\)
\(282\) 69.2549 30.7498i 0.245585 0.109042i
\(283\) −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
\(285\) 78.9497 247.738i 0.277017 0.869256i
\(286\) 316.985i 1.10834i
\(287\) −27.1707 78.2763i −0.0946713 0.272740i
\(288\) −50.8472 + 2.56094i −0.176553 + 0.00889214i
\(289\) 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
\(297\) −271.236 89.0471i −0.913252 0.299822i
\(298\) −253.568 253.568i −0.850899 0.850899i
\(299\) 694.791i 2.32372i
\(300\) 128.970 76.5950i 0.429899 0.255317i
\(301\) 98.4801 203.195i 0.327176 0.675067i
\(302\) 196.889 + 196.889i 0.651952 + 0.651952i
\(303\) −469.112 + 208.290i −1.54823 + 0.687426i
\(304\) −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 \(-0.486633\pi\)
0.0419809 + 0.999118i \(0.486633\pi\)
\(312\) −72.9958 164.402i −0.233961 0.526929i
\(313\) 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
\(315\) 284.532 135.154i 0.903276 0.429061i
\(316\) 198.811 0.629150
\(317\) −368.411 368.411i −1.16218 1.16218i −0.983998 0.178182i \(-0.942978\pi\)
−0.178182 0.983998i \(-0.557022\pi\)
\(318\) −84.0135 + 37.3027i −0.264193 + 0.117304i
\(319\) 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
\(327\) 205.510 + 462.850i 0.628470 + 1.41544i
\(328\) 23.6737 23.6737i 0.0721759 0.0721759i
\(329\) 112.505 + 54.5262i 0.341959 + 0.165733i
\(330\) −102.955 199.268i −0.311985 0.603843i
\(331\) 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
\(333\) 11.2883 + 224.128i 0.0338987 + 0.673057i
\(334\) 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
\(342\) 220.350 11.0980i 0.644297 0.0324502i
\(343\) −289.050 184.660i −0.842711 0.538366i
\(344\) 91.2379 0.265226
\(345\) 225.664 + 436.771i 0.654099 + 1.26600i
\(346\) 295.444i 0.853885i
\(347\) −200.513 200.513i −0.577846 0.577846i 0.356463 0.934309i \(-0.383982\pi\)
−0.934309 + 0.356463i \(0.883982\pi\)
\(348\) −57.7149 129.986i −0.165847 0.373523i
\(349\) −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 0.965768 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
\(357\) 459.836 + 15.3817i 1.28806 + 0.0430861i
\(358\) −213.765 213.765i −0.597109 0.597109i
\(359\) 267.685 0.745641 0.372821 0.927903i \(-0.378391\pi\)
0.372821 + 0.927903i \(0.378391\pi\)
\(360\) 99.2846 + 79.6402i 0.275791 + 0.221223i
\(361\) −60.5240 −0.167657
\(362\) −31.8772 + 31.8772i −0.0880587 + 0.0880587i
\(363\) 25.2402 11.2069i 0.0695322 0.0308729i
\(364\) 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
\(372\) −181.744 + 80.6957i −0.488558 + 0.216924i
\(373\) 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
\(375\) −368.220 70.9866i −0.981920 0.189298i
\(376\) 50.5164i 0.134352i
\(377\) 355.317 355.317i 0.942486 0.942486i
\(378\) 192.164 + 185.782i 0.508371 + 0.491487i
\(379\) 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
\(385\) 141.471 341.957i 0.367456 0.888199i
\(386\) 35.7541i 0.0926271i
\(387\) −289.950 + 14.6034i −0.749224 + 0.0377349i
\(388\) −69.5936 + 69.5936i −0.179365 + 0.179365i
\(389\) 77.4189 0.199020 0.0995101 0.995037i \(-0.468272\pi\)
0.0995101 + 0.995037i \(0.468272\pi\)
\(390\) −136.544 + 428.465i −0.350114 + 1.09863i
\(391\) 718.071i 1.83650i
\(392\) 16.2058 137.642i 0.0413413 0.351128i
\(393\) 677.865 300.978i 1.72485 0.765847i
\(394\) 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
\(399\) 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 \(0.104174\pi\)
−0.946923 + 0.321461i \(0.895826\pi\)
\(402\) −425.421 + 188.891i −1.05826 + 0.469877i
\(403\) −496.797 496.797i −1.23275 1.23275i
\(404\) 342.183i 0.846988i
\(405\) −328.269 237.202i −0.810540 0.585683i
\(406\) 102.341 211.162i 0.252073 0.520104i
\(407\) 186.423 + 186.423i 0.458041 + 0.458041i
\(408\) 75.4416 + 169.910i 0.184906 + 0.416446i
\(409\) 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
\(417\) 510.883 226.837i 1.22514 0.543973i
\(418\) 183.280 183.280i 0.438469 0.438469i
\(419\) 400.571i 0.956016i −0.878356 0.478008i \(-0.841359\pi\)
0.878356 0.478008i \(-0.158641\pi\)
\(420\) 5.37380 + 209.931i 0.0127948 + 0.499836i
\(421\) −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
\(423\) −8.08558 160.539i −0.0191148 0.379524i
\(424\) 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 \(-0.844570\pi\)
0.883133 0.469123i \(-0.155430\pi\)
\(432\) −33.6875 + 102.612i −0.0779804 + 0.237527i
\(433\) −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
\(435\) −107.960 + 338.771i −0.248184 + 0.778783i
\(436\) −337.615 −0.774347
\(437\) −401.727 + 401.727i −0.919283 + 0.919283i
\(438\) −19.3436 + 8.58872i −0.0441634 + 0.0196090i
\(439\) −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
\(441\) −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 −0.801023 0.598634i \(-0.795710\pi\)
0.598634 + 0.801023i \(0.295710\pi\)
\(444\) −139.616 53.7570i −0.314452 0.121074i
\(445\) 66.1016 + 58.7245i 0.148543 + 0.131965i
\(446\) 141.877 0.318109
\(447\) −695.253 + 308.698i −1.55537 + 0.690600i
\(448\) 52.9035 18.3634i 0.118088 0.0409898i
\(449\) −335.741 −0.747752 −0.373876 0.927479i \(-0.621971\pi\)
−0.373876 + 0.927479i \(0.621971\pi\)
\(450\) −53.3265 313.698i −0.118503 0.697106i
\(451\) 125.154i 0.277504i
\(452\) 37.9525 + 37.9525i 0.0839658 + 0.0839658i
\(453\) 539.847 239.697i 1.19171 0.529132i
\(454\) 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 \(-0.508180\pi\)
−0.0256955 + 0.999670i \(0.508180\pi\)
\(462\) 313.835 + 10.4979i 0.679297 + 0.0227228i
\(463\) −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
\(465\) 473.662 + 150.948i 1.01863 + 0.324619i
\(466\) 64.7756 0.139003
\(467\) −359.835 + 359.835i −0.770525 + 0.770525i −0.978198 0.207673i \(-0.933411\pi\)
0.207673 + 0.978198i \(0.433411\pi\)
\(468\) −381.097 + 19.1941i −0.814310 + 0.0410130i
\(469\) −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
\(477\) 9.80866 + 194.750i 0.0205632 + 0.408282i
\(478\) 133.240 + 133.240i 0.278744 + 0.278744i
\(479\) 470.256i 0.981745i 0.871231 + 0.490873i \(0.163322\pi\)
−0.871231 + 0.490873i \(0.836678\pi\)
\(480\) −75.3855 + 38.9491i −0.157053 + 0.0811439i
\(481\) 528.588i 1.09893i
\(482\) 307.045 307.045i 0.637023 0.637023i
\(483\) −687.887 23.0102i −1.42420 0.0476401i
\(484\) 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 \(-0.998347\pi\)
0.999987 0.00519322i \(-0.00165306\pi\)
\(492\) −28.8208 64.9103i −0.0585788 0.131932i
\(493\) −367.223 + 367.223i −0.744874 + 0.744874i
\(494\) −519.677 −1.05198
\(495\) −472.956 + 51.9264i −0.955467 + 0.104902i
\(496\) 132.569i 0.267276i
\(497\) 401.885 139.499i 0.808622 0.280682i
\(498\) 41.1965 + 92.7830i 0.0827238 + 0.186311i
\(499\) 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
\(507\) −341.356 768.804i −0.673285 1.51638i
\(508\) 265.221 + 265.221i 0.522089 + 0.522089i
\(509\) 620.503i 1.21906i 0.792762 + 0.609531i \(0.208642\pi\)
−0.792762 + 0.609531i \(0.791358\pi\)
\(510\) 141.119 442.822i 0.276705 0.868277i
\(511\) −31.4237 15.2297i −0.0614945 0.0298038i
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 145.987 444.674i 0.284575 0.866811i
\(514\) −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 \(-0.397916\pi\)
0.315236 + 0.949013i \(0.397916\pi\)
\(522\) −301.318 + 15.1760i −0.577238 + 0.0290728i
\(523\) −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
\(525\) 338.526 401.280i 0.644811 0.764342i
\(526\) 407.073 0.773902
\(527\) 513.443 + 513.443i 0.974275 + 0.974275i
\(528\) 51.4885 + 115.963i 0.0975160 + 0.219626i
\(529\) 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
\(537\) −586.118 + 260.241i −1.09147 + 0.484621i
\(538\) 53.2780 53.2780i 0.0990298 0.0990298i
\(539\) 320.996 + 406.670i 0.595539 + 0.754490i
\(540\) 233.337 135.844i 0.432106 0.251564i
\(541\) −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
\(543\) 38.8079 + 87.4035i 0.0714695 + 0.160964i
\(544\) −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
\(552\) −112.856 254.176i −0.204450 0.460463i
\(553\) 657.364 228.179i 1.18872 0.412620i
\(554\) 461.740 0.833466
\(555\) 171.682 + 332.289i 0.309338 + 0.598720i
\(556\) 372.652i 0.670237i
\(557\) −596.862 596.862i −1.07157 1.07157i −0.997234 0.0743321i \(-0.976318\pi\)
−0.0743321 0.997234i \(-0.523682\pi\)
\(558\) 21.2188 + 421.297i 0.0380264 + 0.755012i
\(559\) 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 0.719201 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
\(567\) 514.256 238.809i 0.906977 0.421179i
\(568\) 121.545 + 121.545i 0.213988 + 0.213988i
\(569\) −1040.51 −1.82866 −0.914331 0.404969i \(-0.867282\pi\)
−0.914331 + 0.404969i \(0.867282\pi\)
\(570\) 326.688 168.788i 0.573136 0.296120i
\(571\) 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
\(573\) −49.2509 110.923i −0.0859527 0.193583i
\(574\) 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
\(582\) 84.7245 + 190.817i 0.145575 + 0.327865i
\(583\) 161.987 + 161.987i 0.277851 + 0.277851i
\(584\) 14.1097i 0.0241605i
\(585\) 744.132 + 596.899i 1.27202 + 1.02034i
\(586\) 101.907i 0.173903i
\(587\) 667.229 667.229i 1.13668 1.13668i 0.147635 0.989042i \(-0.452834\pi\)
0.989042 0.147635i \(-0.0471661\pi\)
\(588\) −260.131 136.997i −0.442399 0.232988i
\(589\) 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
\(595\) 708.324 293.755i 1.19046 0.493706i
\(596\) 507.136i 0.850899i
\(597\) −83.6745 + 37.1522i −0.140158 + 0.0622315i
\(598\) 694.791 694.791i 1.16186 1.16186i
\(599\) 303.628 0.506892 0.253446 0.967350i \(-0.418436\pi\)
0.253446 + 0.967350i \(0.418436\pi\)
\(600\) 205.565 + 52.3748i 0.342608 + 0.0872913i
\(601\) 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
\(603\) 49.6683 + 986.161i 0.0823687 + 1.63543i
\(604\) 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
\(609\) −340.019 363.554i −0.558324 0.596969i
\(610\) −20.2947 343.403i −0.0332701 0.562955i
\(611\) 378.617i 0.619668i
\(612\) 393.866 19.8372i 0.643572 0.0324137i
\(613\) −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
\(615\) −53.9115 + 169.170i −0.0876610 + 0.275073i
\(616\) −91.3006 + 188.382i −0.148215 + 0.305814i
\(617\) −585.706 585.706i −0.949281 0.949281i 0.0494938 0.998774i \(-0.484239\pi\)
−0.998774 + 0.0494938i \(0.984239\pi\)
\(618\) 194.205 86.2286i 0.314247 0.139528i
\(619\) −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
\(627\) −223.128 502.532i −0.355867 0.801486i
\(628\) −188.539 + 188.539i −0.300221 + 0.300221i
\(629\) 546.298i 0.868519i
\(630\) 419.686 + 149.378i 0.666168 + 0.237107i
\(631\) −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
\(633\) 83.6478 37.1404i 0.132145 0.0586735i
\(634\) 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 \(0.126384\pi\)
−0.922207 + 0.386697i \(0.873616\pi\)
\(642\) 99.9556 + 225.121i 0.155694 + 0.350656i
\(643\) −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
\(645\) −429.876 + 222.102i −0.666474 + 0.344344i
\(646\) 537.089 0.831407
\(647\) −584.341 + 584.341i −0.903154 + 0.903154i −0.995708 0.0925538i \(-0.970497\pi\)
0.0925538 + 0.995708i \(0.470497\pi\)
\(648\) 177.457 + 144.903i 0.273854 + 0.223616i
\(649\) −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 −0.687268 0.726404i \(-0.741190\pi\)
0.726404 + 0.687268i \(0.241190\pi\)
\(654\) −257.341 + 668.360i −0.393487 + 1.02196i
\(655\) 820.988 924.122i 1.25342 1.41087i
\(656\) 47.3474 0.0721759
\(657\) 2.25838 + 44.8401i 0.00343742 + 0.0682497i
\(658\) 57.9784 + 167.031i 0.0881131 + 0.253846i
\(659\) 54.2782 0.0823645 0.0411823 0.999152i \(-0.486888\pi\)
0.0411823 + 0.999152i \(0.486888\pi\)
\(660\) 96.3132 302.223i 0.145929 0.457914i
\(661\) 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
\(663\) 565.430 + 1273.47i 0.852836 + 1.92076i
\(664\) −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
\(672\) 3.97150 118.728i 0.00590996 0.176678i
\(673\) 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
\(675\) −661.658 133.542i −0.980234 0.197840i
\(676\) 560.786 0.829566
\(677\) 111.338 111.338i 0.164458 0.164458i −0.620080 0.784538i \(-0.712900\pi\)
0.784538 + 0.620080i \(0.212900\pi\)
\(678\) 104.061 46.2041i 0.153483 0.0681476i
\(679\) −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 −0.944381 0.328853i \(-0.893338\pi\)
0.328853 + 0.944381i \(0.393338\pi\)
\(684\) 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
\(687\) −52.2383 + 23.1943i −0.0760383 + 0.0337617i
\(688\) 91.2379 + 91.2379i 0.132613 + 0.132613i
\(689\) 459.303i 0.666622i
\(690\) −211.106 + 662.435i −0.305951 + 0.960051i
\(691\) 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
\(693\) 259.997 613.282i 0.375176 0.884966i
\(694\) 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 \(-0.566676\pi\)
0.207939 0.978142i \(-0.433324\pi\)
\(702\) −252.486 + 769.068i −0.359667 + 1.09554i
\(703\) −305.628 + 305.628i −0.434749 + 0.434749i
\(704\) −84.5864 −0.120151
\(705\) −122.973 238.013i −0.174430 0.337606i
\(706\) 498.690i 0.706360i
\(707\) −392.729 1131.42i −0.555487 1.60031i
\(708\) 170.462 75.6866i 0.240765 0.106902i
\(709\) 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
\(717\) 365.327 162.208i 0.509522 0.226232i
\(718\) 267.685 + 267.685i 0.372821 + 0.372821i
\(719\) 1058.56i 1.47226i −0.676840 0.736130i \(-0.736651\pi\)
0.676840 0.736130i \(-0.263349\pi\)
\(720\) 19.6444 + 178.925i 0.0272838 + 0.248507i
\(721\) 315.486 + 152.903i 0.437567 + 0.212070i
\(722\) −60.5240 60.5240i −0.0838283 0.0838283i
\(723\) −373.802 841.880i −0.517015 1.16443i
\(724\) −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
\(732\) 266.780 118.453i 0.364454 0.161821i
\(733\) 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
\(735\) 258.710 + 687.964i 0.351986 + 0.936005i
\(736\) 185.403 0.251906
\(737\) 820.259 + 820.259i 1.11297 + 1.11297i
\(738\) −150.468 + 7.57835i −0.203886 + 0.0102688i
\(739\) 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 \(0.579402\pi\)
−0.969049 + 0.246870i \(0.920598\pi\)
\(744\) −262.439 101.048i −0.352741 0.135817i
\(745\) −842.047 + 947.827i −1.13026 + 1.27225i
\(746\) 106.932i 0.143341i
\(747\) 215.079 10.8325i 0.287923 0.0145014i
\(748\) 327.606 327.606i 0.437976 0.437976i
\(749\) −177.244 + 365.709i −0.236641 + 0.488263i
\(750\) −297.233 439.206i −0.396311 0.585609i
\(751\) 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
\(753\) −562.318 + 249.674i −0.746771 + 0.331573i
\(754\) 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 \(0.307876\pi\)
\(762\) 727.204 322.885i 0.954336 0.423734i
\(763\) −1116.32 + 387.487i −1.46306 + 0.507846i
\(764\) 80.9105 0.105904
\(765\) −769.065 616.899i −1.00531 0.806403i
\(766\) 226.259i 0.295378i
\(767\) 465.959 + 465.959i 0.607508 + 0.607508i
\(768\) 43.8700