Properties

Label 210.3.k.b.83.3
Level 210
Weight 3
Character 210.83
Analytic conductor 5.722
Analytic rank 0
Dimension 32
CM no
Inner twists 4

Related objects

Downloads

Learn more about

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 83.3
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-2.74188 + 1.21742i) q^{3} +2.00000i q^{4} +(-3.32079 + 3.73796i) q^{5} +(-3.95930 - 1.52446i) q^{6} +(-6.61294 - 2.29543i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(6.03579 - 6.67602i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-2.74188 + 1.21742i) 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} +(-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} +(20.9264 - 1.75692i) q^{21} +(10.5733 - 10.5733i) q^{22} +(-23.1753 + 23.1753i) q^{23} +(3.04892 - 7.91859i) q^{24} +(-2.94466 - 24.8260i) q^{25} +29.9798 q^{26} +(-8.42188 + 25.6529i) q^{27} +(4.59086 - 13.2259i) 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} +(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} +(22.6833 + 19.1695i) 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} +(-55.2387 + 30.2934i) 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} +(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} +(-24.2703 + 69.9206i) 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} +(3.51384 + 41.8528i) 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} +(8.10289 + 68.8211i) q^{98} +(-70.5875 - 63.8182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} + O(q^{10}) \) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} - 8q^{14} - 4q^{15} - 128q^{16} - 4q^{18} + 12q^{21} - 40q^{22} - 24q^{23} + 16q^{25} - 8q^{28} + 112q^{29} + 28q^{30} - 128q^{32} + 48q^{35} - 40q^{36} + 32q^{37} - 64q^{39} - 20q^{42} - 32q^{43} - 80q^{44} - 48q^{46} + 8q^{50} + 84q^{51} + 136q^{53} + 340q^{57} + 112q^{58} + 64q^{60} + 168q^{63} + 200q^{65} + 32q^{67} - 72q^{72} + 64q^{74} - 88q^{77} - 4q^{78} + 76q^{81} - 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} - 48q^{92} - 388q^{93} - 544q^{95} - 128q^{98} - 160q^{99} + O(q^{100}) \)

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
\(7\) −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 \(-0.840417\pi\)
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 \(-0.446549\pi\)
0.985934 0.167134i \(-0.0534512\pi\)
\(14\) −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 −0.996375 0.0850728i \(-0.972888\pi\)
0.0850728 + 0.996375i \(0.472888\pi\)
\(18\) 12.7118 0.640234i 0.706212 0.0355686i
\(19\) −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
\(21\) 20.9264 1.75692i 0.996494 0.0836629i
\(22\) 10.5733 10.5733i 0.480604 0.480604i
\(23\) −23.1753 + 23.1753i −1.00762 + 1.00762i −0.00765214 + 0.999971i \(0.502436\pi\)
−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
\(28\) 4.59086 13.2259i 0.163959 0.472353i
\(29\) −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 \(-0.820481\pi\)
0.845136 0.534551i \(-0.179519\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 12.8721 + 28.9907i 0.390064 + 0.878505i
\(34\) −30.9843 −0.911302
\(35\) 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 \(-0.453890\pi\)
0.144352 + 0.989526i \(0.453890\pi\)
\(42\) 22.6833 + 19.1695i 0.540079 + 0.456416i
\(43\) −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 −0.828578 0.559874i \(-0.810850\pi\)
0.559874 + 0.828578i \(0.310850\pi\)
\(48\) 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 \(0.0848542\pi\)
−0.964678 + 0.263431i \(0.915146\pi\)
\(60\) 28.5836 + 9.10910i 0.476394 + 0.151818i
\(61\) 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
\(63\) −55.2387 + 30.2934i −0.876804 + 0.480848i
\(64\) 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 \(-0.859227\pi\)
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 −0.682533 0.730854i \(-0.739122\pi\)
0.730854 + 0.682533i \(0.239122\pi\)
\(74\) −35.2630 −0.476526
\(75\) 38.2975 + 64.4849i 0.510633 + 0.859799i
\(76\) 34.6685i 0.456164i
\(77\) −24.2703 + 69.9206i −0.315198 + 0.908059i
\(78\) −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 0.597797 0.801648i \(-0.296043\pi\)
−0.801648 + 0.597797i \(0.796043\pi\)
\(84\) 3.51384 + 41.8528i 0.0418315 + 0.498247i
\(85\) −6.46278 109.355i −0.0760327 1.28653i
\(86\) 45.6189i 0.530453i
\(87\) 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 \(-0.968324\pi\)
0.995053 0.0993477i \(-0.0316756\pi\)
\(90\) −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 0.504615 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 \(-0.178413\pi\)
0.846988 + 0.531612i \(0.178413\pi\)
\(102\) 84.9551 37.7208i 0.832893 0.369812i
\(103\) −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
\(105\) −62.9249 + 84.0563i −0.599284 + 0.800536i
\(106\) −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
\(112\) 26.4518 + 9.18172i 0.236176 + 0.0819797i
\(113\) 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
\(126\) −85.5321 24.9453i −0.678826 0.197978i
\(127\) 132.611 132.611i 1.04418 1.04418i 0.0452000 0.998978i \(-0.485607\pi\)
0.998978 0.0452000i \(-0.0143925\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 90.3094 + 34.7721i 0.700073 + 0.269551i
\(130\) −99.5566 + 112.063i −0.765820 + 0.862024i
\(131\) −247.227 −1.88723 −0.943613 0.331051i \(-0.892597\pi\)
−0.943613 + 0.331051i \(0.892597\pi\)
\(132\) −57.9814 + 25.7442i −0.439253 + 0.195032i
\(133\) 114.630 + 39.7896i 0.861882 + 0.299170i
\(134\) −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 \(-0.733808\pi\)
−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
\(147\) −142.418 36.4166i −0.968829 0.247732i
\(148\) −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 0.339988 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
\(162\) 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 −0.908169 0.418603i \(-0.862520\pi\)
0.418603 + 0.908169i \(0.362520\pi\)
\(168\) −38.3389 + 45.3666i −0.228208 + 0.270039i
\(169\) 280.393i 1.65913i
\(170\) 102.892 115.818i 0.605249 0.681282i
\(171\) −104.626 + 115.724i −0.611847 + 0.676747i
\(172\) 45.6189 45.6189i 0.265226 0.265226i
\(173\) −147.722 147.722i −0.853885 0.853885i 0.136724 0.990609i \(-0.456343\pi\)
−0.990609 + 0.136724i \(0.956343\pi\)
\(174\) 93.8504 + 36.1355i 0.539370 + 0.207675i
\(175\) −37.5134 + 170.932i −0.214362 + 0.976754i
\(176\) 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 \(-0.971934\pi\)
0.996115 0.0880587i \(-0.0280663\pi\)
\(182\) −198.254 68.8165i −1.08931 0.378113i
\(183\) −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
\(189\) 114.578 150.309i 0.606232 0.795288i
\(190\) 122.358 7.23124i 0.643990 0.0380592i
\(191\) 40.4552i 0.211808i −0.994376 0.105904i \(-0.966226\pi\)
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 \(-0.475569\pi\)
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
\(207\) 14.8376 + 294.600i 0.0716794 + 1.42319i
\(208\) −59.9595 + 59.9595i −0.288267 + 0.288267i
\(209\) 183.280i 0.876938i
\(210\) −146.981 + 21.1314i −0.699910 + 0.100626i
\(211\) 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
\(217\) −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
\(222\) 96.6867 42.9298i 0.435526 0.193377i
\(223\) −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
\(225\) −183.512 130.186i −0.815609 0.578603i
\(226\) 37.9525 0.167932
\(227\) −139.705 + 139.705i −0.615443 + 0.615443i −0.944359 0.328916i \(-0.893317\pi\)
0.328916 + 0.944359i \(0.393317\pi\)
\(228\) 42.2060 + 95.0568i 0.185114 + 0.416916i
\(229\) 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
\(231\) −18.5764 221.261i −0.0804175 0.957839i
\(232\) 47.4076 47.4076i 0.204343 0.204343i
\(233\) 32.3878 32.3878i 0.139003 0.139003i −0.634181 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
\(238\) 204.897 + 71.1223i 0.860912 + 0.298833i
\(239\) 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 \(0.219834\pi\)
−0.770845 + 0.637023i \(0.780166\pi\)
\(242\) 9.20544 + 9.20544i 0.0380390 + 0.0380390i
\(243\) 120.427 + 211.060i 0.495583 + 0.868561i
\(244\) −97.2984 −0.398764
\(245\) −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 \(-0.366039\pi\)
0.408536 + 0.912742i \(0.366039\pi\)
\(252\) −60.5868 110.477i −0.240424 0.438402i
\(253\) 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 −0.244929 0.969541i \(-0.578765\pi\)
0.969541 + 0.244929i \(0.0787646\pi\)
\(258\) 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 \(0.0315739\pi\)
−0.995084 + 0.0990298i \(0.968426\pi\)
\(270\) 48.7465 184.591i 0.180543 0.683670i
\(271\) 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
\(273\) 287.348 340.020i 1.05256 1.24549i
\(274\) 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 \(0.0127986\pi\)
−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 −0.301097 0.953594i \(-0.597353\pi\)
0.953594 + 0.301097i \(0.0973527\pi\)
\(284\) 121.545 0.427976
\(285\) −78.9497 + 247.738i −0.277017 + 0.869256i
\(286\) 316.985i 1.10834i
\(287\) −78.2763 27.1707i −0.272740 0.0946713i
\(288\) −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 0.788692 0.614789i \(-0.210759\pi\)
−0.614789 + 0.788692i \(0.710759\pi\)
\(294\) −106.001 178.834i −0.360548 0.608280i
\(295\) −116.194 103.227i −0.393878 0.349920i
\(296\) 70.5259i 0.238263i
\(297\) 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 0.811852 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 \(-0.513367\pi\)
−0.0419809 + 0.999118i \(0.513367\pi\)
\(312\) −72.9958 164.402i −0.233961 0.526929i
\(313\) −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
\(315\) 70.2007 307.078i 0.222859 0.974851i
\(316\) 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
\(322\) 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
\(327\) −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
\(336\) −83.7055 + 7.02769i −0.249124 + 0.0209157i
\(337\) −300.344 + 300.344i −0.891227 + 0.891227i −0.994639 0.103411i \(-0.967024\pi\)
0.103411 + 0.994639i \(0.467024\pi\)
\(338\) 280.393 280.393i 0.829566 0.829566i
\(339\) −28.9286 + 75.1327i −0.0853350 + 0.221630i
\(340\) 218.710 12.9256i 0.643265 0.0380163i
\(341\) −350.422 −1.02763
\(342\) −220.350 + 11.0980i −0.644297 + 0.0324502i
\(343\) −184.660 289.050i −0.538366 0.842711i
\(344\) 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 \(-0.297836\pi\)
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 0.259408 0.965768i \(-0.416473\pi\)
−0.965768 + 0.259408i \(0.916473\pi\)
\(354\) 47.3877 123.074i 0.133863 0.347667i
\(355\) 227.165 + 201.813i 0.639902 + 0.568487i
\(356\) 35.3678 0.0993477
\(357\) −296.976 + 351.413i −0.831865 + 0.984349i
\(358\) −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 \(-0.946692\pi\)
−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
\(372\) −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
\(378\) 264.887 35.7314i 0.700760 0.0945276i
\(379\) 364.774i 0.962465i 0.876593 + 0.481233i \(0.159811\pi\)
−0.876593 + 0.481233i \(0.840189\pi\)
\(380\) 129.589 + 115.127i 0.341025 + 0.302965i
\(381\) −202.160 + 525.045i −0.530603 + 1.37807i
\(382\) 40.4552 40.4552i 0.105904 0.105904i
\(383\) −113.130 113.130i −0.295378 0.295378i 0.543823 0.839200i \(-0.316976\pi\)
−0.839200 + 0.543823i \(0.816976\pi\)
\(384\) −12.1957 + 31.6744i −0.0317596 + 0.0824853i
\(385\) −180.764 322.913i −0.469516 0.838735i
\(386\) 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
\(392\) −137.642 + 16.2058i −0.351128 + 0.0413413i
\(393\) 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 0.0812649 0.996693i \(-0.474104\pi\)
−0.996693 + 0.0812649i \(0.974104\pi\)
\(398\) 30.5172 + 30.5172i 0.0766764 + 0.0766764i
\(399\) −362.743 + 30.4549i −0.909130 + 0.0763281i
\(400\) 11.7787 + 99.3039i 0.0294466 + 0.248260i
\(401\) 257.812i 0.642923i 0.946923 + 0.321461i \(0.104174\pi\)
−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 \(-0.705052\pi\)
−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
\(417\) 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 \(0.158641\pi\)
−0.878356 + 0.478008i \(0.841359\pi\)
\(420\) −168.113 125.850i −0.400268 0.299642i
\(421\) −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
\(427\) 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 \(-0.844570\pi\)
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 −0.654952 0.755671i \(-0.727311\pi\)
0.755671 + 0.654952i \(0.227311\pi\)
\(434\) −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 \(-0.257737\pi\)
0.689712 + 0.724084i \(0.257737\pi\)
\(440\) −149.269 + 8.82162i −0.339247 + 0.0200491i
\(441\) 434.826 73.5320i 0.986001 0.166739i
\(442\) −464.451 + 464.451i −1.05079 + 1.05079i
\(443\) −89.6580 + 89.6580i −0.202388 + 0.202388i −0.801023 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
\(448\) −18.3634 + 52.9035i −0.0409898 + 0.118088i
\(449\) −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
\(455\) 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 \(-0.491820\pi\)
0.0256955 + 0.999670i \(0.491820\pi\)
\(462\) 202.684 239.837i 0.438711 0.519128i
\(463\) −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 −0.207673 0.978198i \(-0.566589\pi\)
0.978198 + 0.207673i \(0.0665891\pi\)
\(468\) 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 \(-0.836678\pi\)
0.871231 0.490873i \(-0.163322\pi\)
\(480\) −75.3855 + 38.9491i −0.157053 + 0.0811439i
\(481\) 528.588i 1.09893i
\(482\) −307.045 + 307.045i −0.637023 + 0.637023i
\(483\) −444.258 + 525.693i −0.919790 + 1.08839i
\(484\) 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 \(-0.998347\pi\)
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
\(497\) −139.499 + 401.885i −0.280682 + 0.808622i
\(498\) 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 0.999997 0.00244509i \(-0.000778296\pi\)
−0.00244509 + 0.999997i \(0.500778\pi\)
\(504\) 49.8905 171.064i 0.0989891 0.339413i
\(505\) −568.160 + 639.533i −1.12507 + 1.26640i
\(506\) 490.079i 0.968536i
\(507\) 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 \(-0.791358\pi\)
0.792762 0.609531i \(-0.208642\pi\)
\(510\) −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
\(518\) 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 \(-0.602084\pi\)
−0.315236 + 0.949013i \(0.602084\pi\)
\(522\) −301.318 + 15.1760i −0.577238 + 0.0290728i
\(523\) 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
\(525\) −105.238 514.344i −0.200454 0.979703i
\(526\) 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
\(532\) −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
\(537\) 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
\(546\) 627.368 52.6721i 1.14903 0.0964690i
\(547\) 141.618 141.618i 0.258899 0.258899i −0.565707 0.824606i \(-0.691397\pi\)
0.824606 + 0.565707i \(0.191397\pi\)
\(548\) −278.009 + 278.009i −0.507316 + 0.507316i
\(549\) 324.783 + 293.636i 0.591590 + 0.534857i
\(550\) −293.627 231.358i −0.533868 0.420650i
\(551\) 410.888 0.745713
\(552\) 112.856 + 254.176i 0.204450 + 0.460463i
\(553\) −228.179 + 657.364i −0.412620 + 1.18872i
\(554\) 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
\(560\) −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 0.694802 0.719201i \(-0.255492\pi\)
−0.719201 + 0.694802i \(0.755492\pi\)
\(564\) 100.005 + 38.5051i 0.177313 + 0.0682714i
\(565\) 7.91624 + 133.949i 0.0140110 + 0.237077i
\(566\) 369.313 0.652497
\(567\) −131.169 + 551.619i −0.231339 + 0.972873i
\(568\) 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 0.880324 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
\(582\) 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 \(0.547166\pi\)
−0.989042 + 0.147635i \(0.952834\pi\)
\(588\) 72.8333 284.836i 0.123866 0.484414i
\(589\) 574.494i 0.975372i
\(590\) −12.9675 219.421i −0.0219789 0.371899i
\(591\) 389.149 + 149.835i 0.658459 + 0.253528i
\(592\) 70.5259 70.5259i 0.119132 0.119132i
\(593\) −599.428 599.428i −1.01084 1.01084i −0.999941 0.0108986i \(-0.996531\pi\)
−0.0108986 0.999941i \(-0.503469\pi\)
\(594\) 182.189 + 360.283i 0.306715 + 0.606537i
\(595\) −208.279 + 737.994i −0.350049 + 1.24033i
\(596\) 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 \(-0.990895\pi\)
0.999591 0.0286009i \(-0.00910520\pi\)
\(602\) −104.715 + 301.675i −0.173945 + 0.501122i
\(603\) 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 0.537113 0.843510i \(-0.319515\pi\)
−0.843510 + 0.537113i \(0.819515\pi\)
\(608\) 69.3370 + 69.3370i 0.114041 + 0.114041i
\(609\) −496.035 + 41.6457i −0.814507 + 0.0683838i
\(610\) −20.2947 343.403i −0.0332701 0.562955i
\(611\) 378.617i 0.619668i
\(612\) −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 \(-0.476641\pi\)
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
\(627\) −223.128 502.532i −0.355867 0.801486i
\(628\) 188.539 188.539i 0.300221 0.300221i
\(629\) 546.298i 0.868519i
\(630\) 377.279 236.877i 0.598855 0.375996i
\(631\) −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
\(637\) 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 \(0.126384\pi\)
−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 −0.538325 0.842737i \(-0.680943\pi\)
0.842737 + 0.538325i \(0.180943\pi\)
\(644\) 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 −0.0925538 0.995708i \(-0.529503\pi\)
0.995708 + 0.0925538i \(0.0295030\pi\)
\(648\) 177.457 + 144.903i 0.273854 + 0.223616i
\(649\) 328.670 0.506425
\(650\) −88.2804 744.277i −0.135816 1.14504i
\(651\) −58.2282 693.545i −0.0894442 1.06535i
\(652\) −288.237 + 288.237i −0.442082 + 0.442082i
\(653\) 25.5558 25.5558i 0.0391360 0.0391360i −0.687268 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
\(658\) 167.031 + 57.9784i 0.253846 + 0.0881131i
\(659\) 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 \(-0.848807\pi\)
0.889298 0.457328i \(-0.151193\pi\)
\(662\) 172.781 + 172.781i 0.260998 + 0.260998i
\(663\) −565.430 1273.47i −0.852836 1.92076i
\(664\) 67.6784 0.101925
\(665\) −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
\(672\) −90.7332 76.6778i −0.135020 0.114104i
\(673\) 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 −0.784538 0.620080i \(-0.787100\pi\)
0.620080 + 0.784538i \(0.287100\pi\)
\(678\) −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 \(0.0552712\pi\)
−0.984962 + 0.172768i \(0.944729\pi\)
\(692\) 295.444 295.444i 0.426943 0.426943i
\(693\) 320.301 + 584.055i 0.462195 + 0.842792i
\(694\) 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 \(-0.566676\pi\)
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
\(707\) −1131.42 392.729i −1.60031 0.555487i
\(708\) 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
\(714\) −648.388 + 54.4369i −0.908107 + 0.0762422i
\(715\) 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 \(0.263349\pi\)
−0.676840 + 0.736130i \(0.736651\pi\)
\(720\) −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 0.605068 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
\(732\) 266.780 118.453i 0.364454 0.161821i
\(733\) −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
\(735\) 609.064 411.420i 0.828658 0.559755i
\(736\) 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
\(742\) 202.626 + 70.3340i 0.273081 + 0.0947897i
\(743\) −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
\(756\) 300.619 + 229.156i 0.397644 + 0.303116i
\(757\) 581.912 581.912i 0.768708 0.768708i −0.209171 0.977879i \(-0.567077\pi\)
0.977879 + 0.209171i \(0.0670766\pi\)
\(758\) −364.774 + 364.774i −0.481233 + 0.481233i
\(759\) −970.184 373.553i −1.27824 0.492165i
\(760\) 14.4625 + 244.716i 0.0190296 + 0.321995i
\(761\) −863.872 −1.13518 −0.567590 0.823311i \(-0.692124\pi\)
−0.567590 + 0.823311i \(0.692124\pi\)
\(762\) −727.204 + 322.885i −0.954336 + 0.423734i
\(763\) 387.487 1116.32i 0.507846 1.46306i
\(764\) 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 +