Properties

Label 210.3.l.b.127.4
Level 210
Weight 3
Character 210.127
Analytic conductor 5.722
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.4
Root \(0.170157 + 0.170157i\) of \(x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + 1093889 x^{8} - 4595248 x^{7} + 18837632 x^{6} + 86081152 x^{5} + 178889856 x^{4} + 70149120 x^{3} + 10035200 x^{2} - 7168000 x + 2560000\)
Character \(\chi\) \(=\) 210.127
Dual form 210.3.l.b.43.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.80148 + 1.39490i) q^{5} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.80148 + 1.39490i) q^{5} +2.44949 q^{6} +(1.87083 + 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-3.40658 - 6.19639i) q^{10} -11.5078 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-7.70521 + 7.70521i) q^{13} -3.74166i q^{14} +(-7.58899 + 4.17219i) q^{15} -4.00000 q^{16} +(21.0749 + 21.0749i) q^{17} +(-3.00000 + 3.00000i) q^{18} +24.1173i q^{19} +(-2.78980 + 9.60297i) q^{20} -4.58258 q^{21} +(11.5078 + 11.5078i) q^{22} +(30.1762 - 30.1762i) q^{23} +4.89898i q^{24} +(21.1085 + 13.3952i) q^{25} +15.4104 q^{26} +(3.67423 + 3.67423i) q^{27} +(-3.74166 + 3.74166i) q^{28} +51.1392i q^{29} +(11.7612 + 3.41680i) q^{30} -46.9852 q^{31} +(4.00000 + 4.00000i) q^{32} +(14.0941 - 14.0941i) q^{33} -42.1499i q^{34} +(6.37313 + 11.5924i) q^{35} +6.00000 q^{36} +(-8.50020 - 8.50020i) q^{37} +(24.1173 - 24.1173i) q^{38} -18.8738i q^{39} +(12.3928 - 6.81316i) q^{40} +18.6089 q^{41} +(4.58258 + 4.58258i) q^{42} +(-26.1383 + 26.1383i) q^{43} -23.0156i q^{44} +(4.18471 - 14.4045i) q^{45} -60.3523 q^{46} +(50.1311 + 50.1311i) q^{47} +(4.89898 - 4.89898i) q^{48} +7.00000i q^{49} +(-7.71330 - 34.5037i) q^{50} -51.6228 q^{51} +(-15.4104 - 15.4104i) q^{52} +(7.08527 - 7.08527i) q^{53} -7.34847i q^{54} +(-55.2546 - 16.0523i) q^{55} +7.48331 q^{56} +(-29.5376 - 29.5376i) q^{57} +(51.1392 - 51.1392i) q^{58} -94.3487i q^{59} +(-8.34439 - 15.1780i) q^{60} +8.09003 q^{61} +(46.9852 + 46.9852i) q^{62} +(5.61249 - 5.61249i) q^{63} -8.00000i q^{64} +(-47.7445 + 26.2484i) q^{65} -28.1883 q^{66} +(-20.6469 - 20.6469i) q^{67} +(-42.1499 + 42.1499i) q^{68} +73.9162i q^{69} +(5.21925 - 17.9655i) q^{70} -63.7595 q^{71} +(-6.00000 - 6.00000i) q^{72} +(50.1883 - 50.1883i) q^{73} +17.0004i q^{74} +(-42.2582 + 9.44682i) q^{75} -48.2346 q^{76} +(-21.5292 - 21.5292i) q^{77} +(-18.8738 + 18.8738i) q^{78} +1.06121i q^{79} +(-19.2059 - 5.57961i) q^{80} -9.00000 q^{81} +(-18.6089 - 18.6089i) q^{82} +(53.6243 - 53.6243i) q^{83} -9.16515i q^{84} +(71.7935 + 130.588i) q^{85} +52.2765 q^{86} +(-62.6325 - 62.6325i) q^{87} +(-23.0156 + 23.0156i) q^{88} -145.154i q^{89} +(-18.5892 + 10.2197i) q^{90} -28.8303 q^{91} +(60.3523 + 60.3523i) q^{92} +(57.5449 - 57.5449i) q^{93} -100.262i q^{94} +(-33.6413 + 115.799i) q^{95} -9.79796 q^{96} +(23.7872 + 23.7872i) q^{97} +(7.00000 - 7.00000i) q^{98} +34.5235i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{2} - 16q^{5} + 32q^{8} + O(q^{10}) \) \( 16q - 16q^{2} - 16q^{5} + 32q^{8} + 24q^{10} + 8q^{11} - 32q^{13} - 12q^{15} - 64q^{16} + 56q^{17} - 48q^{18} - 16q^{20} - 8q^{22} + 24q^{23} + 40q^{25} + 64q^{26} - 112q^{31} + 64q^{32} + 24q^{33} + 28q^{35} + 96q^{36} - 152q^{37} - 16q^{40} + 24q^{45} - 48q^{46} + 80q^{47} - 72q^{50} - 72q^{51} - 64q^{52} + 48q^{53} - 24q^{55} + 24q^{57} + 96q^{58} + 24q^{60} + 96q^{61} + 112q^{62} + 16q^{65} - 48q^{66} - 80q^{67} - 112q^{68} + 536q^{71} - 96q^{72} - 288q^{75} - 168q^{77} - 48q^{78} + 64q^{80} - 144q^{81} - 256q^{83} + 40q^{85} - 144q^{87} + 16q^{88} + 24q^{90} + 48q^{92} + 192q^{93} + 360q^{95} + 688q^{97} + 112q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 4.80148 + 1.39490i 0.960297 + 0.278980i
\(6\) 2.44949 0.408248
\(7\) 1.87083 + 1.87083i 0.267261 + 0.267261i
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −3.40658 6.19639i −0.340658 0.619639i
\(11\) −11.5078 −1.04617 −0.523083 0.852282i \(-0.675218\pi\)
−0.523083 + 0.852282i \(0.675218\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −7.70521 + 7.70521i −0.592708 + 0.592708i −0.938362 0.345654i \(-0.887657\pi\)
0.345654 + 0.938362i \(0.387657\pi\)
\(14\) 3.74166i 0.267261i
\(15\) −7.58899 + 4.17219i −0.505933 + 0.278146i
\(16\) −4.00000 −0.250000
\(17\) 21.0749 + 21.0749i 1.23970 + 1.23970i 0.960123 + 0.279579i \(0.0901950\pi\)
0.279579 + 0.960123i \(0.409805\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 24.1173i 1.26933i 0.772786 + 0.634666i \(0.218862\pi\)
−0.772786 + 0.634666i \(0.781138\pi\)
\(20\) −2.78980 + 9.60297i −0.139490 + 0.480148i
\(21\) −4.58258 −0.218218
\(22\) 11.5078 + 11.5078i 0.523083 + 0.523083i
\(23\) 30.1762 30.1762i 1.31201 1.31201i 0.392073 0.919934i \(-0.371758\pi\)
0.919934 0.392073i \(-0.128242\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 21.1085 + 13.3952i 0.844340 + 0.535808i
\(26\) 15.4104 0.592708
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −3.74166 + 3.74166i −0.133631 + 0.133631i
\(29\) 51.1392i 1.76342i 0.471790 + 0.881711i \(0.343608\pi\)
−0.471790 + 0.881711i \(0.656392\pi\)
\(30\) 11.7612 + 3.41680i 0.392040 + 0.113893i
\(31\) −46.9852 −1.51565 −0.757826 0.652457i \(-0.773738\pi\)
−0.757826 + 0.652457i \(0.773738\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 14.0941 14.0941i 0.427095 0.427095i
\(34\) 42.1499i 1.23970i
\(35\) 6.37313 + 11.5924i 0.182089 + 0.331211i
\(36\) 6.00000 0.166667
\(37\) −8.50020 8.50020i −0.229735 0.229735i 0.582847 0.812582i \(-0.301939\pi\)
−0.812582 + 0.582847i \(0.801939\pi\)
\(38\) 24.1173 24.1173i 0.634666 0.634666i
\(39\) 18.8738i 0.483944i
\(40\) 12.3928 6.81316i 0.309819 0.170329i
\(41\) 18.6089 0.453875 0.226937 0.973909i \(-0.427129\pi\)
0.226937 + 0.973909i \(0.427129\pi\)
\(42\) 4.58258 + 4.58258i 0.109109 + 0.109109i
\(43\) −26.1383 + 26.1383i −0.607867 + 0.607867i −0.942388 0.334522i \(-0.891425\pi\)
0.334522 + 0.942388i \(0.391425\pi\)
\(44\) 23.0156i 0.523083i
\(45\) 4.18471 14.4045i 0.0929935 0.320099i
\(46\) −60.3523 −1.31201
\(47\) 50.1311 + 50.1311i 1.06662 + 1.06662i 0.997617 + 0.0690016i \(0.0219813\pi\)
0.0690016 + 0.997617i \(0.478019\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 7.00000i 0.142857i
\(50\) −7.71330 34.5037i −0.154266 0.690074i
\(51\) −51.6228 −1.01221
\(52\) −15.4104 15.4104i −0.296354 0.296354i
\(53\) 7.08527 7.08527i 0.133684 0.133684i −0.637098 0.770783i \(-0.719865\pi\)
0.770783 + 0.637098i \(0.219865\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −55.2546 16.0523i −1.00463 0.291860i
\(56\) 7.48331 0.133631
\(57\) −29.5376 29.5376i −0.518203 0.518203i
\(58\) 51.1392 51.1392i 0.881711 0.881711i
\(59\) 94.3487i 1.59913i −0.600579 0.799565i \(-0.705063\pi\)
0.600579 0.799565i \(-0.294937\pi\)
\(60\) −8.34439 15.1780i −0.139073 0.252966i
\(61\) 8.09003 0.132623 0.0663117 0.997799i \(-0.478877\pi\)
0.0663117 + 0.997799i \(0.478877\pi\)
\(62\) 46.9852 + 46.9852i 0.757826 + 0.757826i
\(63\) 5.61249 5.61249i 0.0890871 0.0890871i
\(64\) 8.00000i 0.125000i
\(65\) −47.7445 + 26.2484i −0.734530 + 0.403822i
\(66\) −28.1883 −0.427095
\(67\) −20.6469 20.6469i −0.308163 0.308163i 0.536034 0.844197i \(-0.319922\pi\)
−0.844197 + 0.536034i \(0.819922\pi\)
\(68\) −42.1499 + 42.1499i −0.619851 + 0.619851i
\(69\) 73.9162i 1.07125i
\(70\) 5.21925 17.9655i 0.0745607 0.256650i
\(71\) −63.7595 −0.898021 −0.449011 0.893526i \(-0.648223\pi\)
−0.449011 + 0.893526i \(0.648223\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) 50.1883 50.1883i 0.687511 0.687511i −0.274170 0.961681i \(-0.588403\pi\)
0.961681 + 0.274170i \(0.0884031\pi\)
\(74\) 17.0004i 0.229735i
\(75\) −42.2582 + 9.44682i −0.563443 + 0.125958i
\(76\) −48.2346 −0.634666
\(77\) −21.5292 21.5292i −0.279599 0.279599i
\(78\) −18.8738 + 18.8738i −0.241972 + 0.241972i
\(79\) 1.06121i 0.0134331i 0.999977 + 0.00671653i \(0.00213796\pi\)
−0.999977 + 0.00671653i \(0.997862\pi\)
\(80\) −19.2059 5.57961i −0.240074 0.0697451i
\(81\) −9.00000 −0.111111
\(82\) −18.6089 18.6089i −0.226937 0.226937i
\(83\) 53.6243 53.6243i 0.646075 0.646075i −0.305967 0.952042i \(-0.598980\pi\)
0.952042 + 0.305967i \(0.0989796\pi\)
\(84\) 9.16515i 0.109109i
\(85\) 71.7935 + 130.588i 0.844629 + 1.53633i
\(86\) 52.2765 0.607867
\(87\) −62.6325 62.6325i −0.719914 0.719914i
\(88\) −23.0156 + 23.0156i −0.261541 + 0.261541i
\(89\) 145.154i 1.63095i −0.578794 0.815473i \(-0.696477\pi\)
0.578794 0.815473i \(-0.303523\pi\)
\(90\) −18.5892 + 10.2197i −0.206546 + 0.113553i
\(91\) −28.8303 −0.316816
\(92\) 60.3523 + 60.3523i 0.656003 + 0.656003i
\(93\) 57.5449 57.5449i 0.618762 0.618762i
\(94\) 100.262i 1.06662i
\(95\) −33.6413 + 115.799i −0.354119 + 1.21894i
\(96\) −9.79796 −0.102062
\(97\) 23.7872 + 23.7872i 0.245229 + 0.245229i 0.819009 0.573780i \(-0.194524\pi\)
−0.573780 + 0.819009i \(0.694524\pi\)
\(98\) 7.00000 7.00000i 0.0714286 0.0714286i
\(99\) 34.5235i 0.348722i
\(100\) −26.7904 + 42.2170i −0.267904 + 0.422170i
\(101\) 50.1467 0.496502 0.248251 0.968696i \(-0.420144\pi\)
0.248251 + 0.968696i \(0.420144\pi\)
\(102\) 51.6228 + 51.6228i 0.506106 + 0.506106i
\(103\) 56.3876 56.3876i 0.547453 0.547453i −0.378251 0.925703i \(-0.623474\pi\)
0.925703 + 0.378251i \(0.123474\pi\)
\(104\) 30.8208i 0.296354i
\(105\) −22.0032 6.39224i −0.209554 0.0608785i
\(106\) −14.1705 −0.133684
\(107\) −135.365 135.365i −1.26510 1.26510i −0.948590 0.316506i \(-0.897490\pi\)
−0.316506 0.948590i \(-0.602510\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 100.934i 0.926001i −0.886358 0.463001i \(-0.846773\pi\)
0.886358 0.463001i \(-0.153227\pi\)
\(110\) 39.2023 + 71.3069i 0.356385 + 0.648245i
\(111\) 20.8211 0.187578
\(112\) −7.48331 7.48331i −0.0668153 0.0668153i
\(113\) 25.3174 25.3174i 0.224048 0.224048i −0.586153 0.810201i \(-0.699358\pi\)
0.810201 + 0.586153i \(0.199358\pi\)
\(114\) 59.0751i 0.518203i
\(115\) 186.983 102.798i 1.62594 0.893892i
\(116\) −102.278 −0.881711
\(117\) 23.1156 + 23.1156i 0.197569 + 0.197569i
\(118\) −94.3487 + 94.3487i −0.799565 + 0.799565i
\(119\) 78.8552i 0.662649i
\(120\) −6.83360 + 23.5224i −0.0569466 + 0.196020i
\(121\) 11.4299 0.0944623
\(122\) −8.09003 8.09003i −0.0663117 0.0663117i
\(123\) −22.7911 + 22.7911i −0.185294 + 0.185294i
\(124\) 93.9704i 0.757826i
\(125\) 82.6671 + 93.7611i 0.661337 + 0.750089i
\(126\) −11.2250 −0.0890871
\(127\) 116.746 + 116.746i 0.919262 + 0.919262i 0.996976 0.0777140i \(-0.0247621\pi\)
−0.0777140 + 0.996976i \(0.524762\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 64.0254i 0.496321i
\(130\) 73.9929 + 21.4960i 0.569176 + 0.165354i
\(131\) 34.8004 0.265652 0.132826 0.991139i \(-0.457595\pi\)
0.132826 + 0.991139i \(0.457595\pi\)
\(132\) 28.1883 + 28.1883i 0.213548 + 0.213548i
\(133\) −45.1194 + 45.1194i −0.339243 + 0.339243i
\(134\) 41.2938i 0.308163i
\(135\) 12.5166 + 22.7670i 0.0927154 + 0.168644i
\(136\) 84.2997 0.619851
\(137\) 131.552 + 131.552i 0.960235 + 0.960235i 0.999239 0.0390044i \(-0.0124186\pi\)
−0.0390044 + 0.999239i \(0.512419\pi\)
\(138\) 73.9162 73.9162i 0.535625 0.535625i
\(139\) 89.4407i 0.643458i 0.946832 + 0.321729i \(0.104264\pi\)
−0.946832 + 0.321729i \(0.895736\pi\)
\(140\) −23.1848 + 12.7463i −0.165605 + 0.0910447i
\(141\) −122.795 −0.870890
\(142\) 63.7595 + 63.7595i 0.449011 + 0.449011i
\(143\) 88.6702 88.6702i 0.620071 0.620071i
\(144\) 12.0000i 0.0833333i
\(145\) −71.3342 + 245.544i −0.491960 + 1.69341i
\(146\) −100.377 −0.687511
\(147\) −8.57321 8.57321i −0.0583212 0.0583212i
\(148\) 17.0004 17.0004i 0.114868 0.114868i
\(149\) 55.7399i 0.374093i −0.982351 0.187047i \(-0.940108\pi\)
0.982351 0.187047i \(-0.0598915\pi\)
\(150\) 51.7050 + 32.8114i 0.344700 + 0.218743i
\(151\) 82.9665 0.549447 0.274724 0.961523i \(-0.411414\pi\)
0.274724 + 0.961523i \(0.411414\pi\)
\(152\) 48.2346 + 48.2346i 0.317333 + 0.317333i
\(153\) 63.2248 63.2248i 0.413234 0.413234i
\(154\) 43.0583i 0.279599i
\(155\) −225.599 65.5398i −1.45548 0.422837i
\(156\) 37.7477 0.241972
\(157\) −99.7950 99.7950i −0.635637 0.635637i 0.313839 0.949476i \(-0.398385\pi\)
−0.949476 + 0.313839i \(0.898385\pi\)
\(158\) 1.06121 1.06121i 0.00671653 0.00671653i
\(159\) 17.3553i 0.109153i
\(160\) 13.6263 + 24.7855i 0.0851645 + 0.154910i
\(161\) 112.909 0.701297
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) −45.3884 + 45.3884i −0.278457 + 0.278457i −0.832493 0.554036i \(-0.813087\pi\)
0.554036 + 0.832493i \(0.313087\pi\)
\(164\) 37.2177i 0.226937i
\(165\) 87.3328 48.0129i 0.529289 0.290987i
\(166\) −107.249 −0.646075
\(167\) −99.2501 99.2501i −0.594312 0.594312i 0.344481 0.938793i \(-0.388055\pi\)
−0.938793 + 0.344481i \(0.888055\pi\)
\(168\) −9.16515 + 9.16515i −0.0545545 + 0.0545545i
\(169\) 50.2595i 0.297393i
\(170\) 58.7949 202.382i 0.345853 1.19048i
\(171\) 72.3520 0.423111
\(172\) −52.2765 52.2765i −0.303933 0.303933i
\(173\) −80.5404 + 80.5404i −0.465551 + 0.465551i −0.900470 0.434919i \(-0.856777\pi\)
0.434919 + 0.900470i \(0.356777\pi\)
\(174\) 125.265i 0.719914i
\(175\) 14.4303 + 64.5505i 0.0824586 + 0.368860i
\(176\) 46.0313 0.261541
\(177\) 115.553 + 115.553i 0.652842 + 0.652842i
\(178\) −145.154 + 145.154i −0.815473 + 0.815473i
\(179\) 154.267i 0.861824i 0.902394 + 0.430912i \(0.141808\pi\)
−0.902394 + 0.430912i \(0.858192\pi\)
\(180\) 28.8089 + 8.36941i 0.160049 + 0.0464967i
\(181\) 166.548 0.920155 0.460078 0.887879i \(-0.347822\pi\)
0.460078 + 0.887879i \(0.347822\pi\)
\(182\) 28.8303 + 28.8303i 0.158408 + 0.158408i
\(183\) −9.90822 + 9.90822i −0.0541433 + 0.0541433i
\(184\) 120.705i 0.656003i
\(185\) −28.9566 52.6705i −0.156522 0.284705i
\(186\) −115.090 −0.618762
\(187\) −242.527 242.527i −1.29693 1.29693i
\(188\) −100.262 + 100.262i −0.533309 + 0.533309i
\(189\) 13.7477i 0.0727393i
\(190\) 149.440 82.1576i 0.786528 0.432409i
\(191\) −235.646 −1.23375 −0.616873 0.787063i \(-0.711601\pi\)
−0.616873 + 0.787063i \(0.711601\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) −16.2211 + 16.2211i −0.0840471 + 0.0840471i −0.747880 0.663833i \(-0.768928\pi\)
0.663833 + 0.747880i \(0.268928\pi\)
\(194\) 47.5744i 0.245229i
\(195\) 26.3271 90.6224i 0.135011 0.464730i
\(196\) −14.0000 −0.0714286
\(197\) −6.68134 6.68134i −0.0339154 0.0339154i 0.689946 0.723861i \(-0.257634\pi\)
−0.723861 + 0.689946i \(0.757634\pi\)
\(198\) 34.5235 34.5235i 0.174361 0.174361i
\(199\) 32.0712i 0.161162i −0.996748 0.0805808i \(-0.974322\pi\)
0.996748 0.0805808i \(-0.0256775\pi\)
\(200\) 69.0074 15.4266i 0.345037 0.0771330i
\(201\) 50.5744 0.251614
\(202\) −50.1467 50.1467i −0.248251 0.248251i
\(203\) −95.6728 + 95.6728i −0.471294 + 0.471294i
\(204\) 103.246i 0.506106i
\(205\) 89.3502 + 25.9575i 0.435855 + 0.126622i
\(206\) −112.775 −0.547453
\(207\) −90.5285 90.5285i −0.437336 0.437336i
\(208\) 30.8208 30.8208i 0.148177 0.148177i
\(209\) 277.538i 1.32793i
\(210\) 15.6109 + 28.3954i 0.0743377 + 0.135216i
\(211\) 123.531 0.585457 0.292728 0.956196i \(-0.405437\pi\)
0.292728 + 0.956196i \(0.405437\pi\)
\(212\) 14.1705 + 14.1705i 0.0668422 + 0.0668422i
\(213\) 78.0891 78.0891i 0.366616 0.366616i
\(214\) 270.731i 1.26510i
\(215\) −161.963 + 89.0421i −0.753315 + 0.414149i
\(216\) 14.6969 0.0680414
\(217\) −87.9013 87.9013i −0.405075 0.405075i
\(218\) −100.934 + 100.934i −0.463001 + 0.463001i
\(219\) 122.936i 0.561350i
\(220\) 32.1046 110.509i 0.145930 0.502315i
\(221\) −324.774 −1.46956
\(222\) −20.8211 20.8211i −0.0937890 0.0937890i
\(223\) −81.9590 + 81.9590i −0.367529 + 0.367529i −0.866575 0.499046i \(-0.833684\pi\)
0.499046 + 0.866575i \(0.333684\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 40.1856 63.3255i 0.178603 0.281447i
\(226\) −50.6348 −0.224048
\(227\) 93.6089 + 93.6089i 0.412374 + 0.412374i 0.882565 0.470191i \(-0.155815\pi\)
−0.470191 + 0.882565i \(0.655815\pi\)
\(228\) 59.0751 59.0751i 0.259101 0.259101i
\(229\) 348.973i 1.52390i −0.647635 0.761950i \(-0.724242\pi\)
0.647635 0.761950i \(-0.275758\pi\)
\(230\) −289.781 84.1856i −1.25992 0.366024i
\(231\) 52.7355 0.228292
\(232\) 102.278 + 102.278i 0.440856 + 0.440856i
\(233\) 208.319 208.319i 0.894074 0.894074i −0.100829 0.994904i \(-0.532150\pi\)
0.994904 + 0.100829i \(0.0321496\pi\)
\(234\) 46.2313i 0.197569i
\(235\) 170.776 + 310.631i 0.726704 + 1.32184i
\(236\) 188.697 0.799565
\(237\) −1.29971 1.29971i −0.00548403 0.00548403i
\(238\) 78.8552 78.8552i 0.331324 0.331324i
\(239\) 330.793i 1.38407i −0.721864 0.692035i \(-0.756715\pi\)
0.721864 0.692035i \(-0.243285\pi\)
\(240\) 30.3560 16.6888i 0.126483 0.0695366i
\(241\) 375.584 1.55844 0.779221 0.626749i \(-0.215615\pi\)
0.779221 + 0.626749i \(0.215615\pi\)
\(242\) −11.4299 11.4299i −0.0472312 0.0472312i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 16.1801i 0.0663117i
\(245\) −9.76432 + 33.6104i −0.0398543 + 0.137185i
\(246\) 45.5822 0.185294
\(247\) −185.829 185.829i −0.752344 0.752344i
\(248\) −93.9704 + 93.9704i −0.378913 + 0.378913i
\(249\) 131.352i 0.527518i
\(250\) 11.0940 176.428i 0.0443761 0.705713i
\(251\) 41.2876 0.164493 0.0822463 0.996612i \(-0.473791\pi\)
0.0822463 + 0.996612i \(0.473791\pi\)
\(252\) 11.2250 + 11.2250i 0.0445435 + 0.0445435i
\(253\) −347.262 + 347.262i −1.37258 + 1.37258i
\(254\) 233.492i 0.919262i
\(255\) −247.866 72.0088i −0.972024 0.282387i
\(256\) 16.0000 0.0625000
\(257\) −101.370 101.370i −0.394437 0.394437i 0.481828 0.876266i \(-0.339973\pi\)
−0.876266 + 0.481828i \(0.839973\pi\)
\(258\) −64.0254 + 64.0254i −0.248161 + 0.248161i
\(259\) 31.8048i 0.122799i
\(260\) −52.4969 95.4889i −0.201911 0.367265i
\(261\) 153.418 0.587807
\(262\) −34.8004 34.8004i −0.132826 0.132826i
\(263\) 164.594 164.594i 0.625833 0.625833i −0.321184 0.947017i \(-0.604081\pi\)
0.947017 + 0.321184i \(0.104081\pi\)
\(264\) 56.3766i 0.213548i
\(265\) 43.9031 24.1366i 0.165672 0.0910813i
\(266\) 90.2387 0.339243
\(267\) 177.777 + 177.777i 0.665831 + 0.665831i
\(268\) 41.2938 41.2938i 0.154081 0.154081i
\(269\) 254.148i 0.944788i 0.881387 + 0.472394i \(0.156610\pi\)
−0.881387 + 0.472394i \(0.843390\pi\)
\(270\) 10.2504 35.2836i 0.0379644 0.130680i
\(271\) 22.4723 0.0829237 0.0414619 0.999140i \(-0.486798\pi\)
0.0414619 + 0.999140i \(0.486798\pi\)
\(272\) −84.2997 84.2997i −0.309925 0.309925i
\(273\) 35.3097 35.3097i 0.129340 0.129340i
\(274\) 263.104i 0.960235i
\(275\) −242.913 154.150i −0.883319 0.560544i
\(276\) −147.832 −0.535625
\(277\) 47.3949 + 47.3949i 0.171101 + 0.171101i 0.787463 0.616362i \(-0.211394\pi\)
−0.616362 + 0.787463i \(0.711394\pi\)
\(278\) 89.4407 89.4407i 0.321729 0.321729i
\(279\) 140.956i 0.505217i
\(280\) 35.9310 + 10.4385i 0.128325 + 0.0372803i
\(281\) −18.8810 −0.0671920 −0.0335960 0.999435i \(-0.510696\pi\)
−0.0335960 + 0.999435i \(0.510696\pi\)
\(282\) 122.795 + 122.795i 0.435445 + 0.435445i
\(283\) −115.825 + 115.825i −0.409277 + 0.409277i −0.881486 0.472209i \(-0.843457\pi\)
0.472209 + 0.881486i \(0.343457\pi\)
\(284\) 127.519i 0.449011i
\(285\) −100.622 183.026i −0.353060 0.642197i
\(286\) −177.340 −0.620071
\(287\) 34.8140 + 34.8140i 0.121303 + 0.121303i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 599.306i 2.07372i
\(290\) 316.879 174.210i 1.09268 0.600724i
\(291\) −58.2665 −0.200228
\(292\) 100.377 + 100.377i 0.343756 + 0.343756i
\(293\) 224.451 224.451i 0.766043 0.766043i −0.211364 0.977407i \(-0.567791\pi\)
0.977407 + 0.211364i \(0.0677906\pi\)
\(294\) 17.1464i 0.0583212i
\(295\) 131.607 453.014i 0.446126 1.53564i
\(296\) −34.0008 −0.114868
\(297\) −42.2824 42.2824i −0.142365 0.142365i
\(298\) −55.7399 + 55.7399i −0.187047 + 0.187047i
\(299\) 465.027i 1.55528i
\(300\) −18.8936 84.5165i −0.0629788 0.281722i
\(301\) −97.8004 −0.324918
\(302\) −82.9665 82.9665i −0.274724 0.274724i
\(303\) −61.4169 + 61.4169i −0.202696 + 0.202696i
\(304\) 96.4693i 0.317333i
\(305\) 38.8441 + 11.2848i 0.127358 + 0.0369993i
\(306\) −126.450 −0.413234
\(307\) −42.5120 42.5120i −0.138476 0.138476i 0.634471 0.772947i \(-0.281218\pi\)
−0.772947 + 0.634471i \(0.781218\pi\)
\(308\) 43.0583 43.0583i 0.139800 0.139800i
\(309\) 138.121i 0.446993i
\(310\) 160.059 + 291.139i 0.516319 + 0.939157i
\(311\) −97.1353 −0.312332 −0.156166 0.987731i \(-0.549914\pi\)
−0.156166 + 0.987731i \(0.549914\pi\)
\(312\) −37.7477 37.7477i −0.120986 0.120986i
\(313\) −94.4913 + 94.4913i −0.301889 + 0.301889i −0.841753 0.539863i \(-0.818476\pi\)
0.539863 + 0.841753i \(0.318476\pi\)
\(314\) 199.590i 0.635637i
\(315\) 34.7771 19.1194i 0.110404 0.0606965i
\(316\) −2.12242 −0.00671653
\(317\) 146.150 + 146.150i 0.461040 + 0.461040i 0.898996 0.437956i \(-0.144297\pi\)
−0.437956 + 0.898996i \(0.644297\pi\)
\(318\) 17.3553 17.3553i 0.0545764 0.0545764i
\(319\) 588.501i 1.84483i
\(320\) 11.1592 38.4119i 0.0348726 0.120037i
\(321\) 331.576 1.03295
\(322\) −112.909 112.909i −0.350649 0.350649i
\(323\) −508.271 + 508.271i −1.57359 + 1.57359i
\(324\) 18.0000i 0.0555556i
\(325\) −265.858 + 59.4326i −0.818025 + 0.182869i
\(326\) 90.7768 0.278457
\(327\) 123.619 + 123.619i 0.378039 + 0.378039i
\(328\) 37.2177 37.2177i 0.113469 0.113469i
\(329\) 187.573i 0.570131i
\(330\) −135.346 39.3199i −0.410138 0.119151i
\(331\) 223.981 0.676679 0.338339 0.941024i \(-0.390135\pi\)
0.338339 + 0.941024i \(0.390135\pi\)
\(332\) 107.249 + 107.249i 0.323038 + 0.323038i
\(333\) −25.5006 + 25.5006i −0.0765784 + 0.0765784i
\(334\) 198.500i 0.594312i
\(335\) −70.3354 127.936i −0.209956 0.381899i
\(336\) 18.3303 0.0545545
\(337\) −41.7444 41.7444i −0.123871 0.123871i 0.642454 0.766324i \(-0.277916\pi\)
−0.766324 + 0.642454i \(0.777916\pi\)
\(338\) 50.2595 50.2595i 0.148697 0.148697i
\(339\) 62.0147i 0.182934i
\(340\) −261.177 + 143.587i −0.768167 + 0.422315i
\(341\) 540.697 1.58562
\(342\) −72.3520 72.3520i −0.211555 0.211555i
\(343\) −13.0958 + 13.0958i −0.0381802 + 0.0381802i
\(344\) 104.553i 0.303933i
\(345\) −103.106 + 354.907i −0.298858 + 1.02872i
\(346\) 161.081 0.465551
\(347\) 283.163 + 283.163i 0.816031 + 0.816031i 0.985530 0.169500i \(-0.0542152\pi\)
−0.169500 + 0.985530i \(0.554215\pi\)
\(348\) 125.265 125.265i 0.359957 0.359957i
\(349\) 73.8529i 0.211613i 0.994387 + 0.105807i \(0.0337424\pi\)
−0.994387 + 0.105807i \(0.966258\pi\)
\(350\) 50.1203 78.9808i 0.143201 0.225659i
\(351\) −56.6215 −0.161315
\(352\) −46.0313 46.0313i −0.130771 0.130771i
\(353\) −221.700 + 221.700i −0.628047 + 0.628047i −0.947576 0.319530i \(-0.896475\pi\)
0.319530 + 0.947576i \(0.396475\pi\)
\(354\) 231.106i 0.652842i
\(355\) −306.140 88.9383i −0.862367 0.250530i
\(356\) 290.309 0.815473
\(357\) −96.5775 96.5775i −0.270525 0.270525i
\(358\) 154.267 154.267i 0.430912 0.430912i
\(359\) 351.735i 0.979764i 0.871789 + 0.489882i \(0.162960\pi\)
−0.871789 + 0.489882i \(0.837040\pi\)
\(360\) −20.4395 37.1783i −0.0567764 0.103273i
\(361\) −220.645 −0.611205
\(362\) −166.548 166.548i −0.460078 0.460078i
\(363\) −13.9988 + 13.9988i −0.0385641 + 0.0385641i
\(364\) 57.6605i 0.158408i
\(365\) 310.986 170.971i 0.852017 0.468413i
\(366\) 19.8164 0.0541433
\(367\) 9.03767 + 9.03767i 0.0246258 + 0.0246258i 0.719312 0.694687i \(-0.244457\pi\)
−0.694687 + 0.719312i \(0.744457\pi\)
\(368\) −120.705 + 120.705i −0.328002 + 0.328002i
\(369\) 55.8266i 0.151292i
\(370\) −23.7139 + 81.6271i −0.0640916 + 0.220614i
\(371\) 26.5107 0.0714573
\(372\) 115.090 + 115.090i 0.309381 + 0.309381i
\(373\) −151.095 + 151.095i −0.405079 + 0.405079i −0.880019 0.474939i \(-0.842470\pi\)
0.474939 + 0.880019i \(0.342470\pi\)
\(374\) 485.053i 1.29693i
\(375\) −216.080 13.5873i −0.576212 0.0362329i
\(376\) 200.524 0.533309
\(377\) −394.039 394.039i −1.04520 1.04520i
\(378\) 13.7477 13.7477i 0.0363696 0.0363696i
\(379\) 268.787i 0.709201i 0.935018 + 0.354601i \(0.115383\pi\)
−0.935018 + 0.354601i \(0.884617\pi\)
\(380\) −231.598 67.2826i −0.609468 0.177059i
\(381\) −285.969 −0.750574
\(382\) 235.646 + 235.646i 0.616873 + 0.616873i
\(383\) 304.341 304.341i 0.794625 0.794625i −0.187618 0.982242i \(-0.560077\pi\)
0.982242 + 0.187618i \(0.0600766\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −73.3408 133.403i −0.190496 0.346501i
\(386\) 32.4422 0.0840471
\(387\) 78.4148 + 78.4148i 0.202622 + 0.202622i
\(388\) −47.5744 + 47.5744i −0.122614 + 0.122614i
\(389\) 50.0127i 0.128567i −0.997932 0.0642837i \(-0.979524\pi\)
0.997932 0.0642837i \(-0.0204763\pi\)
\(390\) −116.950 + 64.2952i −0.299871 + 0.164860i
\(391\) 1271.92 3.25299
\(392\) 14.0000 + 14.0000i 0.0357143 + 0.0357143i
\(393\) −42.6216 + 42.6216i −0.108452 + 0.108452i
\(394\) 13.3627i 0.0339154i
\(395\) −1.48029 + 5.09539i −0.00374756 + 0.0128997i
\(396\) −69.0469 −0.174361
\(397\) −325.002 325.002i −0.818644 0.818644i 0.167268 0.985912i \(-0.446506\pi\)
−0.985912 + 0.167268i \(0.946506\pi\)
\(398\) −32.0712 + 32.0712i −0.0805808 + 0.0805808i
\(399\) 110.519i 0.276991i
\(400\) −84.4340 53.5808i −0.211085 0.133952i
\(401\) −462.981 −1.15457 −0.577283 0.816544i \(-0.695887\pi\)
−0.577283 + 0.816544i \(0.695887\pi\)
\(402\) −50.5744 50.5744i −0.125807 0.125807i
\(403\) 362.031 362.031i 0.898340 0.898340i
\(404\) 100.293i 0.248251i
\(405\) −43.2134 12.5541i −0.106700 0.0309978i
\(406\) 191.346 0.471294
\(407\) 97.8188 + 97.8188i 0.240341 + 0.240341i
\(408\) −103.246 + 103.246i −0.253053 + 0.253053i
\(409\) 131.630i 0.321834i 0.986968 + 0.160917i \(0.0514451\pi\)
−0.986968 + 0.160917i \(0.948555\pi\)
\(410\) −63.3926 115.308i −0.154616 0.281238i
\(411\) −322.236 −0.784028
\(412\) 112.775 + 112.775i 0.273726 + 0.273726i
\(413\) 176.510 176.510i 0.427386 0.427386i
\(414\) 181.057i 0.437336i
\(415\) 332.277 182.675i 0.800667 0.440182i
\(416\) −61.6417 −0.148177
\(417\) −109.542 109.542i −0.262691 0.262691i
\(418\) −277.538 + 277.538i −0.663966 + 0.663966i
\(419\) 536.418i 1.28023i 0.768277 + 0.640117i \(0.221114\pi\)
−0.768277 + 0.640117i \(0.778886\pi\)
\(420\) 12.7845 44.0063i 0.0304393 0.104777i
\(421\) −508.770 −1.20848 −0.604240 0.796803i \(-0.706523\pi\)
−0.604240 + 0.796803i \(0.706523\pi\)
\(422\) −123.531 123.531i −0.292728 0.292728i
\(423\) 150.393 150.393i 0.355539 0.355539i
\(424\) 28.3411i 0.0668422i
\(425\) 162.557 + 727.163i 0.382487 + 1.71097i
\(426\) −156.178 −0.366616
\(427\) 15.1351 + 15.1351i 0.0354451 + 0.0354451i
\(428\) 270.731 270.731i 0.632548 0.632548i
\(429\) 217.197i 0.506286i
\(430\) 251.005 + 72.9206i 0.583732 + 0.169583i
\(431\) 467.561 1.08483 0.542414 0.840111i \(-0.317510\pi\)
0.542414 + 0.840111i \(0.317510\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) −129.391 + 129.391i −0.298825 + 0.298825i −0.840554 0.541729i \(-0.817770\pi\)
0.541729 + 0.840554i \(0.317770\pi\)
\(434\) 175.803i 0.405075i
\(435\) −213.363 388.095i −0.490489 0.892173i
\(436\) 201.868 0.463001
\(437\) 727.768 + 727.768i 1.66537 + 1.66537i
\(438\) 122.936 122.936i 0.280675 0.280675i
\(439\) 51.7818i 0.117954i −0.998259 0.0589770i \(-0.981216\pi\)
0.998259 0.0589770i \(-0.0187839\pi\)
\(440\) −142.614 + 78.4047i −0.324122 + 0.178192i
\(441\) 21.0000 0.0476190
\(442\) 324.774 + 324.774i 0.734782 + 0.734782i
\(443\) 357.514 357.514i 0.807029 0.807029i −0.177154 0.984183i \(-0.556689\pi\)
0.984183 + 0.177154i \(0.0566891\pi\)
\(444\) 41.6423i 0.0937890i
\(445\) 202.476 696.956i 0.455002 1.56619i
\(446\) 163.918 0.367529
\(447\) 68.2671 + 68.2671i 0.152723 + 0.152723i
\(448\) 14.9666 14.9666i 0.0334077 0.0334077i
\(449\) 615.742i 1.37136i −0.727902 0.685681i \(-0.759504\pi\)
0.727902 0.685681i \(-0.240496\pi\)
\(450\) −103.511 + 23.1399i −0.230025 + 0.0514220i
\(451\) −214.148 −0.474828
\(452\) 50.6348 + 50.6348i 0.112024 + 0.112024i
\(453\) −101.613 + 101.613i −0.224311 + 0.224311i
\(454\) 187.218i 0.412374i
\(455\) −138.428 40.2154i −0.304237 0.0883855i
\(456\) −118.150 −0.259101
\(457\) −502.144 502.144i −1.09878 1.09878i −0.994553 0.104230i \(-0.966762\pi\)
−0.104230 0.994553i \(-0.533238\pi\)
\(458\) −348.973 + 348.973i −0.761950 + 0.761950i
\(459\) 154.868i 0.337404i
\(460\) 205.595 + 373.966i 0.446946 + 0.812970i
\(461\) 100.965 0.219012 0.109506 0.993986i \(-0.465073\pi\)
0.109506 + 0.993986i \(0.465073\pi\)
\(462\) −52.7355 52.7355i −0.114146 0.114146i
\(463\) 312.235 312.235i 0.674374 0.674374i −0.284347 0.958721i \(-0.591777\pi\)
0.958721 + 0.284347i \(0.0917768\pi\)
\(464\) 204.557i 0.440856i
\(465\) 356.570 196.031i 0.766818 0.421573i
\(466\) −416.639 −0.894074
\(467\) 502.571 + 502.571i 1.07617 + 1.07617i 0.996849 + 0.0793198i \(0.0252748\pi\)
0.0793198 + 0.996849i \(0.474725\pi\)
\(468\) −46.2313 + 46.2313i −0.0987847 + 0.0987847i
\(469\) 77.2537i 0.164720i
\(470\) 139.856 481.407i 0.297566 1.02427i
\(471\) 244.447 0.518995
\(472\) −188.697 188.697i −0.399783 0.399783i
\(473\) 300.794 300.794i 0.635929 0.635929i
\(474\) 2.59943i 0.00548403i
\(475\) −323.056 + 509.080i −0.680119 + 1.07175i
\(476\) −157.710 −0.331324
\(477\) −21.2558 21.2558i −0.0445614 0.0445614i
\(478\) −330.793 + 330.793i −0.692035 + 0.692035i
\(479\) 270.133i 0.563952i 0.959421 + 0.281976i \(0.0909899\pi\)
−0.959421 + 0.281976i \(0.909010\pi\)
\(480\) −47.0447 13.6672i −0.0980099 0.0284733i
\(481\) 130.992 0.272332
\(482\) −375.584 375.584i −0.779221 0.779221i
\(483\) −138.285 + 138.285i −0.286303 + 0.286303i
\(484\) 22.8599i 0.0472312i
\(485\) 81.0330 + 147.395i 0.167078 + 0.303906i
\(486\) −22.0454 −0.0453609
\(487\) −227.632 227.632i −0.467417 0.467417i 0.433660 0.901077i \(-0.357222\pi\)
−0.901077 + 0.433660i \(0.857222\pi\)
\(488\) 16.1801 16.1801i 0.0331559 0.0331559i
\(489\) 111.178i 0.227359i
\(490\) 43.3747 23.8461i 0.0885198 0.0486655i
\(491\) −23.2563 −0.0473652 −0.0236826 0.999720i \(-0.507539\pi\)
−0.0236826 + 0.999720i \(0.507539\pi\)
\(492\) −45.5822 45.5822i −0.0926468 0.0926468i
\(493\) −1077.76 + 1077.76i −2.18612 + 2.18612i
\(494\) 371.658i 0.752344i
\(495\) −48.1569 + 165.764i −0.0972866 + 0.334876i
\(496\) 187.941 0.378913
\(497\) −119.283 119.283i −0.240006 0.240006i
\(498\) 131.352 131.352i 0.263759 0.263759i
\(499\) 319.077i 0.639433i 0.947513 + 0.319717i \(0.103588\pi\)
−0.947513 + 0.319717i \(0.896412\pi\)
\(500\) −187.522 + 165.334i −0.375045 + 0.330668i
\(501\) 243.112 0.485254
\(502\) −41.2876 41.2876i −0.0822463 0.0822463i
\(503\) 585.731 585.731i 1.16448 1.16448i 0.180990 0.983485i \(-0.442070\pi\)
0.983485 0.180990i \(-0.0579302\pi\)
\(504\) 22.4499i 0.0445435i
\(505\) 240.779 + 69.9498i 0.476789 + 0.138514i
\(506\) 694.524 1.37258
\(507\) −61.5551 61.5551i −0.121410 0.121410i
\(508\) −233.492 + 233.492i −0.459631 + 0.459631i
\(509\) 266.157i 0.522902i 0.965217 + 0.261451i \(0.0842009\pi\)
−0.965217 + 0.261451i \(0.915799\pi\)
\(510\) 175.857 + 319.875i 0.344818 + 0.627206i
\(511\) 187.787 0.367490
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −88.6127 + 88.6127i −0.172734 + 0.172734i
\(514\) 202.741i 0.394437i
\(515\) 349.399 192.089i 0.678446 0.372988i
\(516\) 128.051 0.248161
\(517\) −576.899 576.899i −1.11586 1.11586i
\(518\) −31.8048 + 31.8048i −0.0613993 + 0.0613993i
\(519\) 197.283i 0.380121i
\(520\) −42.9921 + 147.986i −0.0826770 + 0.284588i
\(521\) −1.52542 −0.00292786 −0.00146393 0.999999i \(-0.500466\pi\)
−0.00146393 + 0.999999i \(0.500466\pi\)
\(522\) −153.418 153.418i −0.293904 0.293904i
\(523\) 260.120 260.120i 0.497362 0.497362i −0.413254 0.910616i \(-0.635608\pi\)
0.910616 + 0.413254i \(0.135608\pi\)
\(524\) 69.6007i 0.132826i
\(525\) −96.7313 61.3845i −0.184250 0.116923i
\(526\) −329.188 −0.625833
\(527\) −990.210 990.210i −1.87896 1.87896i
\(528\) −56.3766 + 56.3766i −0.106774 + 0.106774i
\(529\) 1292.20i 2.44272i
\(530\) −68.0396 19.7665i −0.128377 0.0372953i
\(531\) −283.046 −0.533044
\(532\) −90.2387 90.2387i −0.169622 0.169622i
\(533\) −143.385 + 143.385i −0.269015 + 0.269015i
\(534\) 355.554i 0.665831i
\(535\) −461.133 838.776i −0.861931 1.56781i
\(536\) −82.5877 −0.154081
\(537\) −188.937 188.937i −0.351838 0.351838i
\(538\) 254.148 254.148i 0.472394 0.472394i
\(539\) 80.5547i 0.149452i
\(540\) −45.5340 + 25.0332i −0.0843221 + 0.0463577i
\(541\) −273.648 −0.505820 −0.252910 0.967490i \(-0.581388\pi\)
−0.252910 + 0.967490i \(0.581388\pi\)
\(542\) −22.4723 22.4723i −0.0414619 0.0414619i
\(543\) −203.979 + 203.979i −0.375652 + 0.375652i
\(544\) 168.599i 0.309925i
\(545\) 140.793 484.634i 0.258336 0.889236i
\(546\) −70.6194 −0.129340
\(547\) 355.490 + 355.490i 0.649890 + 0.649890i 0.952966 0.303077i \(-0.0980138\pi\)
−0.303077 + 0.952966i \(0.598014\pi\)
\(548\) −263.104 + 263.104i −0.480117 + 0.480117i
\(549\) 24.2701i 0.0442078i
\(550\) 88.7632 + 397.062i 0.161388 + 0.721932i
\(551\) −1233.34 −2.23837
\(552\) 147.832 + 147.832i 0.267812 + 0.267812i
\(553\) −1.98535 + 1.98535i −0.00359014 + 0.00359014i
\(554\) 94.7898i 0.171101i
\(555\) 99.9724 + 29.0435i 0.180130 + 0.0523306i
\(556\) −178.881 −0.321729
\(557\) −270.897 270.897i −0.486350 0.486350i 0.420802 0.907152i \(-0.361749\pi\)
−0.907152 + 0.420802i \(0.861749\pi\)
\(558\) 140.956 140.956i 0.252609 0.252609i
\(559\) 402.802i 0.720575i
\(560\) −25.4925 46.3695i −0.0455224 0.0828027i
\(561\) 594.066 1.05894
\(562\) 18.8810 + 18.8810i 0.0335960 + 0.0335960i
\(563\) 73.1143 73.1143i 0.129866 0.129866i −0.639186 0.769052i \(-0.720729\pi\)
0.769052 + 0.639186i \(0.220729\pi\)
\(564\) 245.591i 0.435445i
\(565\) 156.876 86.2458i 0.277657 0.152647i
\(566\) 231.651 0.409277
\(567\) −16.8375 16.8375i −0.0296957 0.0296957i
\(568\) −127.519 + 127.519i −0.224505 + 0.224505i
\(569\) 1018.55i 1.79007i −0.445992 0.895037i \(-0.647149\pi\)
0.445992 0.895037i \(-0.352851\pi\)
\(570\) −82.4040 + 283.648i −0.144568 + 0.497629i
\(571\) −621.517 −1.08847 −0.544236 0.838932i \(-0.683180\pi\)
−0.544236 + 0.838932i \(0.683180\pi\)
\(572\) 177.340 + 177.340i 0.310036 + 0.310036i
\(573\) 288.606 288.606i 0.503675 0.503675i
\(574\) 69.6280i 0.121303i
\(575\) 1041.19 232.758i 1.81076 0.404796i
\(576\) −24.0000 −0.0416667
\(577\) 760.301 + 760.301i 1.31768 + 1.31768i 0.915608 + 0.402071i \(0.131710\pi\)
0.402071 + 0.915608i \(0.368290\pi\)
\(578\) 599.306 599.306i 1.03686 1.03686i
\(579\) 39.7334i 0.0686242i
\(580\) −491.089 142.668i −0.846704 0.245980i
\(581\) 200.644 0.345342
\(582\) 58.2665 + 58.2665i 0.100114 + 0.100114i
\(583\) −81.5360 + 81.5360i −0.139856 + 0.139856i
\(584\) 200.753i 0.343756i
\(585\) 78.7453 + 143.233i 0.134607 + 0.244843i
\(586\) −448.901 −0.766043
\(587\) 5.94607 + 5.94607i 0.0101296 + 0.0101296i 0.712153 0.702024i \(-0.247720\pi\)
−0.702024 + 0.712153i \(0.747720\pi\)
\(588\) 17.1464 17.1464i 0.0291606 0.0291606i
\(589\) 1133.16i 1.92387i
\(590\) −584.621 + 321.407i −0.990883 + 0.544757i
\(591\) 16.3659 0.0276918
\(592\) 34.0008 + 34.0008i 0.0574338 + 0.0574338i
\(593\) −463.916 + 463.916i −0.782320 + 0.782320i −0.980222 0.197902i \(-0.936587\pi\)
0.197902 + 0.980222i \(0.436587\pi\)
\(594\) 84.5649i 0.142365i
\(595\) −109.995 + 378.622i −0.184866 + 0.636339i
\(596\) 111.480 0.187047
\(597\) 39.2790 + 39.2790i 0.0657940 + 0.0657940i
\(598\) 465.027 465.027i 0.777638 0.777638i
\(599\) 660.745i 1.10308i 0.834148 + 0.551540i \(0.185960\pi\)
−0.834148 + 0.551540i \(0.814040\pi\)
\(600\) −65.6228 + 103.410i −0.109371 + 0.172350i
\(601\) −905.439 −1.50655 −0.753277 0.657704i \(-0.771528\pi\)
−0.753277 + 0.657704i \(0.771528\pi\)
\(602\) 97.8004 + 97.8004i 0.162459 + 0.162459i
\(603\) −61.9407 + 61.9407i −0.102721 + 0.102721i
\(604\) 165.933i 0.274724i
\(605\) 54.8807 + 15.9436i 0.0907119 + 0.0263531i
\(606\) 122.834 0.202696
\(607\) 518.514 + 518.514i 0.854224 + 0.854224i 0.990650 0.136426i \(-0.0435615\pi\)
−0.136426 + 0.990650i \(0.543562\pi\)
\(608\) −96.4693 + 96.4693i −0.158667 + 0.158667i
\(609\) 234.349i 0.384810i
\(610\) −27.5593 50.1289i −0.0451792 0.0821786i
\(611\) −772.541 −1.26439
\(612\) 126.450 + 126.450i 0.206617 + 0.206617i
\(613\) −500.739 + 500.739i −0.816867 + 0.816867i −0.985653 0.168786i \(-0.946015\pi\)
0.168786 + 0.985653i \(0.446015\pi\)
\(614\) 85.0240i 0.138476i
\(615\) −141.223 + 77.6398i −0.229630 + 0.126244i
\(616\) −86.1166 −0.139800
\(617\) 122.242 + 122.242i 0.198123 + 0.198123i 0.799195 0.601072i \(-0.205260\pi\)
−0.601072 + 0.799195i \(0.705260\pi\)
\(618\) 138.121 138.121i 0.223497 0.223497i
\(619\) 320.914i 0.518440i −0.965818 0.259220i \(-0.916534\pi\)
0.965818 0.259220i \(-0.0834655\pi\)
\(620\) 131.080 451.198i 0.211419 0.727738i
\(621\) 221.749 0.357083
\(622\) 97.1353 + 97.1353i 0.156166 + 0.156166i
\(623\) 271.559 271.559i 0.435889 0.435889i
\(624\) 75.4953i 0.120986i
\(625\) 266.137 + 565.505i 0.425820 + 0.904808i
\(626\) 188.983 0.301889
\(627\) 339.913 + 339.913i 0.542126 + 0.542126i
\(628\) 199.590 199.590i 0.317818 0.317818i
\(629\) 358.282i 0.569606i
\(630\) −53.8965 15.6577i −0.0855500 0.0248536i
\(631\) −636.141 −1.00815 −0.504074 0.863661i \(-0.668166\pi\)
−0.504074 + 0.863661i \(0.668166\pi\)
\(632\) 2.12242 + 2.12242i 0.00335827 + 0.00335827i
\(633\) −151.294 + 151.294i −0.239012 + 0.239012i
\(634\) 292.300i 0.461040i
\(635\) 397.706 + 723.405i 0.626308 + 1.13922i
\(636\) −34.7106 −0.0545764
\(637\) −53.9365 53.9365i −0.0846726 0.0846726i
\(638\) −588.501 + 588.501i −0.922416 + 0.922416i
\(639\) 191.278i 0.299340i
\(640\) −49.5711 + 27.2527i −0.0774548 + 0.0425823i
\(641\) −682.051 −1.06404 −0.532021 0.846731i \(-0.678567\pi\)
−0.532021 + 0.846731i \(0.678567\pi\)
\(642\) −331.576 331.576i −0.516474 0.516474i
\(643\) −5.33298 + 5.33298i −0.00829390 + 0.00829390i −0.711242 0.702948i \(-0.751867\pi\)
0.702948 + 0.711242i \(0.251867\pi\)
\(644\) 225.818i 0.350649i
\(645\) 89.3092 307.417i 0.138464 0.476615i
\(646\) 1016.54 1.57359
\(647\) 285.931 + 285.931i 0.441933 + 0.441933i 0.892661 0.450728i \(-0.148836\pi\)
−0.450728 + 0.892661i \(0.648836\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 1085.75i 1.67296i
\(650\) 325.291 + 206.426i 0.500447 + 0.317578i
\(651\) 215.313 0.330742
\(652\) −90.7768 90.7768i −0.139228 0.139228i
\(653\) 199.462 199.462i 0.305455 0.305455i −0.537689 0.843144i \(-0.680702\pi\)
0.843144 + 0.537689i \(0.180702\pi\)
\(654\) 247.237i 0.378039i
\(655\) 167.093 + 48.5431i 0.255104 + 0.0741116i
\(656\) −74.4355 −0.113469
\(657\) −150.565 150.565i −0.229170 0.229170i
\(658\) 187.573 187.573i 0.285066 0.285066i
\(659\) 204.685i 0.310599i −0.987867 0.155300i \(-0.950366\pi\)
0.987867 0.155300i \(-0.0496343\pi\)
\(660\) 96.0257 + 174.666i 0.145494 + 0.264645i
\(661\) 143.044 0.216406 0.108203 0.994129i \(-0.465490\pi\)
0.108203 + 0.994129i \(0.465490\pi\)
\(662\) −223.981 223.981i −0.338339 0.338339i
\(663\) 397.765 397.765i 0.599947 0.599947i
\(664\) 214.497i 0.323038i
\(665\) −279.577 + 153.703i −0.420417 + 0.231132i
\(666\) 51.0012 0.0765784
\(667\) 1543.19 + 1543.19i 2.31362 + 2.31362i
\(668\) 198.500 198.500i 0.297156 0.297156i
\(669\) 200.758i 0.300086i
\(670\) −57.6008 + 198.272i −0.0859714 + 0.295928i
\(671\) −93.0986 −0.138746
\(672\) −18.3303 18.3303i −0.0272772 0.0272772i
\(673\) −317.527 + 317.527i −0.471808 + 0.471808i −0.902499 0.430691i \(-0.858270\pi\)
0.430691 + 0.902499i \(0.358270\pi\)
\(674\) 83.4888i 0.123871i
\(675\) 28.3405 + 126.775i 0.0419859 + 0.187814i
\(676\) −100.519 −0.148697
\(677\) −272.663 272.663i −0.402752 0.402752i 0.476450 0.879202i \(-0.341923\pi\)
−0.879202 + 0.476450i \(0.841923\pi\)
\(678\) 62.0147 62.0147i 0.0914671 0.0914671i
\(679\) 89.0035i 0.131080i
\(680\) 404.764 + 117.590i 0.595241 + 0.172926i
\(681\) −229.294 −0.336702
\(682\) −540.697 540.697i −0.792812 0.792812i
\(683\) −449.231 + 449.231i −0.657732 + 0.657732i −0.954843 0.297111i \(-0.903977\pi\)
0.297111 + 0.954843i \(0.403977\pi\)
\(684\) 144.704i 0.211555i
\(685\) 448.143 + 815.148i 0.654224 + 1.19000i
\(686\) 26.1916 0.0381802
\(687\) 427.403 + 427.403i 0.622130 + 0.622130i
\(688\) 104.553 104.553i 0.151967 0.151967i
\(689\) 109.187i 0.158472i
\(690\) 458.013 251.802i 0.663787 0.364930i
\(691\) 1004.13 1.45316 0.726578 0.687084i \(-0.241109\pi\)
0.726578 + 0.687084i \(0.241109\pi\)
\(692\) −161.081 161.081i −0.232776 0.232776i
\(693\) −64.5875 + 64.5875i −0.0931998 + 0.0931998i
\(694\) 566.325i 0.816031i
\(695\) −124.761 + 429.448i −0.179512 + 0.617911i
\(696\) −250.530 −0.359957
\(697\) 392.181 + 392.181i 0.562669 + 0.562669i
\(698\) 73.8529 73.8529i 0.105807 0.105807i
\(699\) 510.276i 0.730009i
\(700\) −129.101 + 28.8605i −0.184430 + 0.0412293i
\(701\) −869.248 −1.24001 −0.620006 0.784597i \(-0.712870\pi\)
−0.620006 + 0.784597i \(0.712870\pi\)
\(702\) 56.6215 + 56.6215i 0.0806574 + 0.0806574i
\(703\) 205.002 205.002i 0.291610 0.291610i
\(704\) 92.0626i 0.130771i
\(705\) −589.601 171.288i −0.836313 0.242961i
\(706\) 443.401 0.628047
\(707\) 93.8159 + 93.8159i 0.132696 + 0.132696i
\(708\) −231.106 + 231.106i −0.326421 + 0.326421i
\(709\) 79.6980i 0.112409i −0.998419 0.0562045i \(-0.982100\pi\)
0.998419 0.0562045i \(-0.0178999\pi\)
\(710\) 217.202 + 395.078i 0.305918 + 0.556449i
\(711\) 3.18364 0.00447769
\(712\) −290.309 290.309i −0.407737 0.407737i
\(713\) −1417.83 + 1417.83i −1.98855 + 1.98855i
\(714\) 193.155i 0.270525i
\(715\) 549.435 302.062i 0.768440 0.422465i
\(716\) −308.533 −0.430912
\(717\) 405.136 + 405.136i 0.565044 + 0.565044i
\(718\) 351.735 351.735i 0.489882 0.489882i
\(719\) 1081.03i 1.50351i −0.659440 0.751757i \(-0.729207\pi\)
0.659440 0.751757i \(-0.270793\pi\)
\(720\) −16.7388 + 57.6178i −0.0232484 + 0.0800247i
\(721\) 210.983 0.292626
\(722\) 220.645 + 220.645i 0.305603 + 0.305603i
\(723\) −459.995 + 459.995i −0.636231 + 0.636231i
\(724\) 333.096i 0.460078i
\(725\) −685.020 + 1079.47i −0.944856 + 1.48893i
\(726\) 27.9975 0.0385641
\(727\) 281.701 + 281.701i 0.387484 + 0.387484i 0.873789 0.486305i \(-0.161656\pi\)
−0.486305 + 0.873789i \(0.661656\pi\)
\(728\) −57.6605 + 57.6605i −0.0792040 + 0.0792040i
\(729\) 27.0000i 0.0370370i
\(730\) −481.957 140.016i −0.660215 0.191802i
\(731\) −1101.72 −1.50715
\(732\) −19.8164 19.8164i −0.0270716 0.0270716i
\(733\) 1016.28 1016.28i 1.38647 1.38647i 0.553858 0.832611i \(-0.313155\pi\)
0.832611 0.553858i \(-0.186845\pi\)
\(734\) 18.0753i 0.0246258i
\(735\) −29.2054 53.1229i −0.0397352 0.0722761i
\(736\) 241.409 0.328002
\(737\) 237.601 + 237.601i 0.322389 + 0.322389i
\(738\) −55.8266 + 55.8266i −0.0756458 + 0.0756458i
\(739\) 289.140i 0.391258i −0.980678 0.195629i \(-0.937325\pi\)
0.980678 0.195629i \(-0.0626749\pi\)
\(740\) 105.341 57.9132i 0.142353 0.0782611i
\(741\) 455.186 0.614286
\(742\) −26.5107 26.5107i −0.0357286 0.0357286i
\(743\) 290.501 290.501i 0.390984 0.390984i −0.484054 0.875038i \(-0.660836\pi\)
0.875038 + 0.484054i \(0.160836\pi\)
\(744\) 230.180i 0.309381i
\(745\) 77.7517 267.634i 0.104365 0.359240i
\(746\) 302.189 0.405079
\(747\) −160.873 160.873i −0.215358 0.215358i
\(748\) 485.053 485.053i 0.648467 0.648467i
\(749\) 506.491i 0.676223i
\(750\) 202.492 + 229.667i 0.269990 + 0.306223i
\(751\) 688.089 0.916231 0.458115 0.888893i \(-0.348525\pi\)
0.458115 + 0.888893i \(0.348525\pi\)
\(752\) −200.524 200.524i −0.266655 0.266655i
\(753\) −50.5668 + 50.5668i −0.0671538 + 0.0671538i
\(754\) 788.077i 1.04520i
\(755\) 398.363 + 115.730i 0.527632 + 0.153285i
\(756\) −27.4955 −0.0363696
\(757\) 180.960 + 180.960i 0.239049 + 0.239049i 0.816456 0.577408i \(-0.195936\pi\)
−0.577408 + 0.816456i \(0.695936\pi\)
\(758\) 268.787 268.787i 0.354601 0.354601i
\(759\) 850.614i 1.12070i
\(760\) 164.315 + 298.880i 0.216204 + 0.393264i
\(761\) 1096.09 1.44033 0.720163 0.693805i \(-0.244067\pi\)
0.720163 + 0.693805i \(0.244067\pi\)
\(762\) 285.969 + 285.969i 0.375287 + 0.375287i
\(763\) 188.831 188.831i 0.247484 0.247484i
\(764\) 471.291i 0.616873i
\(765\) 391.765 215.380i 0.512111 0.281543i
\(766\) −608.682 −0.794625
\(767\) 726.977 + 726.977i 0.947818 + 0.947818i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 892.540i 1.16065i 0.814385 + 0.580325i \(0.197075\pi\)
−0.814385 + 0.580325i \(0.802925\pi\)
\(770\) −60.0621 + 206.744i −0.0780028 + 0.268499i
\(771\) 248.306 0.322057
\(772\) −32.4422 32.4422i −0.0420235 0.0420235i
\(773\) 836.773