Properties

Label 378.4.g.e.109.3
Level $378$
Weight $4$
Character 378.109
Analytic conductor $22.303$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 378.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.3027219822\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - x^{7} + 66x^{6} + 59x^{5} + 3770x^{4} + 721x^{3} + 29779x^{2} + 1374x + 209764 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.3
Root \(-1.44566 + 2.50395i\) of defining polynomial
Character \(\chi\) \(=\) 378.109
Dual form 378.4.g.e.163.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(1.18685 + 2.05569i) q^{5} +(9.15909 - 16.0969i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(1.18685 + 2.05569i) q^{5} +(9.15909 - 16.0969i) q^{7} -8.00000 q^{8} +(-2.37371 + 4.11138i) q^{10} +(19.5527 - 33.8662i) q^{11} -24.4393 q^{13} +(37.0398 - 0.232922i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-23.8709 + 41.3456i) q^{17} +(-59.8352 - 103.638i) q^{19} -9.49483 q^{20} +78.2108 q^{22} +(-76.6464 - 132.755i) q^{23} +(59.6828 - 103.374i) q^{25} +(-24.4393 - 42.3301i) q^{26} +(37.4432 + 63.9219i) q^{28} +215.634 q^{29} +(29.6485 - 51.3527i) q^{31} +(16.0000 - 27.7128i) q^{32} -95.4835 q^{34} +(43.9608 - 0.276444i) q^{35} +(104.999 + 181.863i) q^{37} +(119.670 - 207.275i) q^{38} +(-9.49483 - 16.4455i) q^{40} +415.622 q^{41} -452.341 q^{43} +(78.2108 + 135.465i) q^{44} +(153.293 - 265.511i) q^{46} +(114.366 + 198.087i) q^{47} +(-175.222 - 294.866i) q^{49} +238.731 q^{50} +(48.8786 - 84.6602i) q^{52} +(220.936 - 382.673i) q^{53} +92.8247 q^{55} +(-73.2727 + 128.775i) q^{56} +(215.634 + 373.488i) q^{58} +(362.528 - 627.916i) q^{59} +(170.880 + 295.973i) q^{61} +118.594 q^{62} +64.0000 q^{64} +(-29.0059 - 50.2396i) q^{65} +(-125.678 + 217.681i) q^{67} +(-95.4835 - 165.382i) q^{68} +(44.4396 + 75.8659i) q^{70} +209.119 q^{71} +(-60.9267 + 105.528i) q^{73} +(-209.997 + 363.726i) q^{74} +478.682 q^{76} +(-366.058 - 624.922i) q^{77} +(-399.598 - 692.123i) q^{79} +(18.9897 - 32.8910i) q^{80} +(415.622 + 719.879i) q^{82} +116.801 q^{83} -113.325 q^{85} +(-452.341 - 783.477i) q^{86} +(-156.422 + 270.930i) q^{88} +(183.244 + 317.387i) q^{89} +(-223.842 + 393.398i) q^{91} +613.171 q^{92} +(-228.731 + 396.174i) q^{94} +(142.031 - 246.005i) q^{95} -1045.65 q^{97} +(335.501 - 598.360i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} - 16 q^{4} - 4 q^{5} + 25 q^{7} - 64 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{2} - 16 q^{4} - 4 q^{5} + 25 q^{7} - 64 q^{8} + 8 q^{10} - 56 q^{11} - 18 q^{13} + 22 q^{14} - 64 q^{16} + 118 q^{17} + 37 q^{19} + 32 q^{20} - 224 q^{22} - 200 q^{23} - 104 q^{25} - 18 q^{26} - 56 q^{28} + 524 q^{29} + 276 q^{31} + 128 q^{32} + 472 q^{34} - 290 q^{35} - 185 q^{37} - 74 q^{38} + 32 q^{40} - 60 q^{41} - 1556 q^{43} - 224 q^{44} + 400 q^{46} - 30 q^{47} - 1159 q^{49} - 416 q^{50} + 36 q^{52} - 480 q^{53} + 1456 q^{55} - 200 q^{56} + 524 q^{58} + 296 q^{59} + 474 q^{61} + 1104 q^{62} + 512 q^{64} - 1542 q^{65} + 1319 q^{67} + 472 q^{68} - 32 q^{70} + 1852 q^{71} - 1423 q^{73} + 370 q^{74} - 296 q^{76} - 1228 q^{77} + 765 q^{79} - 64 q^{80} - 60 q^{82} + 1660 q^{83} - 584 q^{85} - 1556 q^{86} + 448 q^{88} + 864 q^{89} - 738 q^{91} + 1600 q^{92} + 60 q^{94} - 1766 q^{95} + 1088 q^{97} - 2704 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 + 1.73205i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 1.18685 + 2.05569i 0.106155 + 0.183866i 0.914210 0.405242i \(-0.132813\pi\)
−0.808054 + 0.589108i \(0.799479\pi\)
\(6\) 0 0
\(7\) 9.15909 16.0969i 0.494544 0.869152i
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −2.37371 + 4.11138i −0.0750632 + 0.130013i
\(11\) 19.5527 33.8662i 0.535942 0.928278i −0.463176 0.886267i \(-0.653290\pi\)
0.999117 0.0420115i \(-0.0133766\pi\)
\(12\) 0 0
\(13\) −24.4393 −0.521403 −0.260702 0.965419i \(-0.583954\pi\)
−0.260702 + 0.965419i \(0.583954\pi\)
\(14\) 37.0398 0.232922i 0.707093 0.00444650i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −23.8709 + 41.3456i −0.340561 + 0.589869i −0.984537 0.175177i \(-0.943950\pi\)
0.643976 + 0.765046i \(0.277284\pi\)
\(18\) 0 0
\(19\) −59.8352 103.638i −0.722481 1.25137i −0.960002 0.279992i \(-0.909668\pi\)
0.237521 0.971382i \(-0.423665\pi\)
\(20\) −9.49483 −0.106155
\(21\) 0 0
\(22\) 78.2108 0.757936
\(23\) −76.6464 132.755i −0.694864 1.20354i −0.970226 0.242200i \(-0.922131\pi\)
0.275362 0.961341i \(-0.411202\pi\)
\(24\) 0 0
\(25\) 59.6828 103.374i 0.477462 0.826989i
\(26\) −24.4393 42.3301i −0.184344 0.319293i
\(27\) 0 0
\(28\) 37.4432 + 63.9219i 0.252718 + 0.431432i
\(29\) 215.634 1.38076 0.690382 0.723445i \(-0.257443\pi\)
0.690382 + 0.723445i \(0.257443\pi\)
\(30\) 0 0
\(31\) 29.6485 51.3527i 0.171775 0.297523i −0.767265 0.641330i \(-0.778383\pi\)
0.939041 + 0.343806i \(0.111716\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −95.4835 −0.481626
\(35\) 43.9608 0.276444i 0.212307 0.00133507i
\(36\) 0 0
\(37\) 104.999 + 181.863i 0.466532 + 0.808057i 0.999269 0.0382238i \(-0.0121700\pi\)
−0.532737 + 0.846281i \(0.678837\pi\)
\(38\) 119.670 207.275i 0.510871 0.884855i
\(39\) 0 0
\(40\) −9.49483 16.4455i −0.0375316 0.0650066i
\(41\) 415.622 1.58315 0.791577 0.611070i \(-0.209261\pi\)
0.791577 + 0.611070i \(0.209261\pi\)
\(42\) 0 0
\(43\) −452.341 −1.60422 −0.802109 0.597178i \(-0.796289\pi\)
−0.802109 + 0.597178i \(0.796289\pi\)
\(44\) 78.2108 + 135.465i 0.267971 + 0.464139i
\(45\) 0 0
\(46\) 153.293 265.511i 0.491343 0.851032i
\(47\) 114.366 + 198.087i 0.354935 + 0.614766i 0.987107 0.160063i \(-0.0511697\pi\)
−0.632172 + 0.774828i \(0.717836\pi\)
\(48\) 0 0
\(49\) −175.222 294.866i −0.510852 0.859669i
\(50\) 238.731 0.675233
\(51\) 0 0
\(52\) 48.8786 84.6602i 0.130351 0.225774i
\(53\) 220.936 382.673i 0.572603 0.991777i −0.423695 0.905805i \(-0.639267\pi\)
0.996298 0.0859723i \(-0.0273996\pi\)
\(54\) 0 0
\(55\) 92.8247 0.227572
\(56\) −73.2727 + 128.775i −0.174848 + 0.307292i
\(57\) 0 0
\(58\) 215.634 + 373.488i 0.488174 + 0.845542i
\(59\) 362.528 627.916i 0.799951 1.38556i −0.119697 0.992810i \(-0.538192\pi\)
0.919648 0.392745i \(-0.128474\pi\)
\(60\) 0 0
\(61\) 170.880 + 295.973i 0.358671 + 0.621237i 0.987739 0.156113i \(-0.0498965\pi\)
−0.629068 + 0.777351i \(0.716563\pi\)
\(62\) 118.594 0.242927
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −29.0059 50.2396i −0.0553497 0.0958686i
\(66\) 0 0
\(67\) −125.678 + 217.681i −0.229165 + 0.396925i −0.957561 0.288231i \(-0.906933\pi\)
0.728396 + 0.685156i \(0.240266\pi\)
\(68\) −95.4835 165.382i −0.170280 0.294934i
\(69\) 0 0
\(70\) 44.4396 + 75.8659i 0.0758793 + 0.129539i
\(71\) 209.119 0.349547 0.174773 0.984609i \(-0.444081\pi\)
0.174773 + 0.984609i \(0.444081\pi\)
\(72\) 0 0
\(73\) −60.9267 + 105.528i −0.0976841 + 0.169194i −0.910726 0.413012i \(-0.864477\pi\)
0.813042 + 0.582206i \(0.197810\pi\)
\(74\) −209.997 + 363.726i −0.329888 + 0.571382i
\(75\) 0 0
\(76\) 478.682 0.722481
\(77\) −366.058 624.922i −0.541768 0.924889i
\(78\) 0 0
\(79\) −399.598 692.123i −0.569092 0.985696i −0.996656 0.0817107i \(-0.973962\pi\)
0.427565 0.903985i \(-0.359372\pi\)
\(80\) 18.9897 32.8910i 0.0265388 0.0459666i
\(81\) 0 0
\(82\) 415.622 + 719.879i 0.559729 + 0.969479i
\(83\) 116.801 0.154465 0.0772324 0.997013i \(-0.475392\pi\)
0.0772324 + 0.997013i \(0.475392\pi\)
\(84\) 0 0
\(85\) −113.325 −0.144609
\(86\) −452.341 783.477i −0.567176 0.982378i
\(87\) 0 0
\(88\) −156.422 + 270.930i −0.189484 + 0.328196i
\(89\) 183.244 + 317.387i 0.218245 + 0.378011i 0.954271 0.298942i \(-0.0966336\pi\)
−0.736027 + 0.676952i \(0.763300\pi\)
\(90\) 0 0
\(91\) −223.842 + 393.398i −0.257857 + 0.453179i
\(92\) 613.171 0.694864
\(93\) 0 0
\(94\) −228.731 + 396.174i −0.250977 + 0.434705i
\(95\) 142.031 246.005i 0.153391 0.265680i
\(96\) 0 0
\(97\) −1045.65 −1.09454 −0.547268 0.836957i \(-0.684332\pi\)
−0.547268 + 0.836957i \(0.684332\pi\)
\(98\) 335.501 598.360i 0.345824 0.616770i
\(99\) 0 0
\(100\) 238.731 + 413.494i 0.238731 + 0.413494i
\(101\) −581.936 + 1007.94i −0.573314 + 0.993010i 0.422908 + 0.906173i \(0.361009\pi\)
−0.996223 + 0.0868370i \(0.972324\pi\)
\(102\) 0 0
\(103\) −79.1611 137.111i −0.0757279 0.131165i 0.825675 0.564147i \(-0.190795\pi\)
−0.901403 + 0.432982i \(0.857461\pi\)
\(104\) 195.514 0.184344
\(105\) 0 0
\(106\) 883.746 0.809783
\(107\) −79.6283 137.920i −0.0719436 0.124610i 0.827809 0.561009i \(-0.189587\pi\)
−0.899753 + 0.436399i \(0.856253\pi\)
\(108\) 0 0
\(109\) 18.0923 31.3368i 0.0158984 0.0275369i −0.857967 0.513705i \(-0.828272\pi\)
0.873865 + 0.486168i \(0.161606\pi\)
\(110\) 92.8247 + 160.777i 0.0804590 + 0.139359i
\(111\) 0 0
\(112\) −296.318 + 1.86337i −0.249995 + 0.00157207i
\(113\) 211.787 0.176312 0.0881561 0.996107i \(-0.471903\pi\)
0.0881561 + 0.996107i \(0.471903\pi\)
\(114\) 0 0
\(115\) 181.936 315.123i 0.147527 0.255525i
\(116\) −431.267 + 746.977i −0.345191 + 0.597888i
\(117\) 0 0
\(118\) 1450.11 1.13130
\(119\) 446.901 + 762.935i 0.344263 + 0.587716i
\(120\) 0 0
\(121\) −99.1152 171.673i −0.0744667 0.128980i
\(122\) −341.760 + 591.946i −0.253619 + 0.439281i
\(123\) 0 0
\(124\) 118.594 + 205.411i 0.0858876 + 0.148762i
\(125\) 580.052 0.415051
\(126\) 0 0
\(127\) −818.436 −0.571846 −0.285923 0.958253i \(-0.592300\pi\)
−0.285923 + 0.958253i \(0.592300\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 58.0117 100.479i 0.0391382 0.0677893i
\(131\) −174.364 302.007i −0.116292 0.201424i 0.802004 0.597319i \(-0.203767\pi\)
−0.918295 + 0.395896i \(0.870434\pi\)
\(132\) 0 0
\(133\) −2216.28 + 13.9369i −1.44493 + 0.00908635i
\(134\) −502.713 −0.324088
\(135\) 0 0
\(136\) 190.967 330.764i 0.120406 0.208550i
\(137\) −904.288 + 1566.27i −0.563931 + 0.976757i 0.433217 + 0.901290i \(0.357378\pi\)
−0.997148 + 0.0754677i \(0.975955\pi\)
\(138\) 0 0
\(139\) 1673.29 1.02106 0.510528 0.859861i \(-0.329450\pi\)
0.510528 + 0.859861i \(0.329450\pi\)
\(140\) −86.9639 + 152.838i −0.0524985 + 0.0922652i
\(141\) 0 0
\(142\) 209.119 + 362.204i 0.123583 + 0.214053i
\(143\) −477.854 + 827.667i −0.279442 + 0.484007i
\(144\) 0 0
\(145\) 255.925 + 443.276i 0.146575 + 0.253876i
\(146\) −243.707 −0.138146
\(147\) 0 0
\(148\) −839.989 −0.466532
\(149\) −1605.66 2781.09i −0.882824 1.52910i −0.848187 0.529697i \(-0.822306\pi\)
−0.0346375 0.999400i \(-0.511028\pi\)
\(150\) 0 0
\(151\) 1423.80 2466.09i 0.767331 1.32906i −0.171675 0.985154i \(-0.554918\pi\)
0.939005 0.343902i \(-0.111749\pi\)
\(152\) 478.682 + 829.101i 0.255436 + 0.442428i
\(153\) 0 0
\(154\) 716.339 1258.95i 0.374833 0.658762i
\(155\) 140.754 0.0729394
\(156\) 0 0
\(157\) −206.423 + 357.536i −0.104932 + 0.181748i −0.913711 0.406366i \(-0.866796\pi\)
0.808778 + 0.588114i \(0.200129\pi\)
\(158\) 799.195 1384.25i 0.402409 0.696992i
\(159\) 0 0
\(160\) 75.9586 0.0375316
\(161\) −2838.97 + 17.8526i −1.38970 + 0.00873903i
\(162\) 0 0
\(163\) −1027.57 1779.80i −0.493774 0.855241i 0.506200 0.862416i \(-0.331050\pi\)
−0.999974 + 0.00717453i \(0.997716\pi\)
\(164\) −831.244 + 1439.76i −0.395788 + 0.685525i
\(165\) 0 0
\(166\) 116.801 + 202.305i 0.0546116 + 0.0945900i
\(167\) −3780.59 −1.75180 −0.875900 0.482493i \(-0.839732\pi\)
−0.875900 + 0.482493i \(0.839732\pi\)
\(168\) 0 0
\(169\) −1599.72 −0.728139
\(170\) −113.325 196.284i −0.0511272 0.0885549i
\(171\) 0 0
\(172\) 904.682 1566.95i 0.401054 0.694646i
\(173\) 1775.75 + 3075.68i 0.780390 + 1.35168i 0.931715 + 0.363191i \(0.118313\pi\)
−0.151325 + 0.988484i \(0.548354\pi\)
\(174\) 0 0
\(175\) −1117.36 1907.52i −0.482653 0.823970i
\(176\) −625.686 −0.267971
\(177\) 0 0
\(178\) −366.487 + 634.774i −0.154322 + 0.267294i
\(179\) −1974.70 + 3420.28i −0.824558 + 1.42818i 0.0776984 + 0.996977i \(0.475243\pi\)
−0.902257 + 0.431200i \(0.858090\pi\)
\(180\) 0 0
\(181\) −2448.62 −1.00555 −0.502774 0.864418i \(-0.667687\pi\)
−0.502774 + 0.864418i \(0.667687\pi\)
\(182\) −905.226 + 5.69245i −0.368680 + 0.00231842i
\(183\) 0 0
\(184\) 613.171 + 1062.04i 0.245672 + 0.425516i
\(185\) −249.236 + 431.689i −0.0990497 + 0.171559i
\(186\) 0 0
\(187\) 933.479 + 1616.83i 0.365041 + 0.632270i
\(188\) −914.925 −0.354935
\(189\) 0 0
\(190\) 568.125 0.216927
\(191\) 381.726 + 661.169i 0.144611 + 0.250474i 0.929228 0.369507i \(-0.120474\pi\)
−0.784617 + 0.619981i \(0.787140\pi\)
\(192\) 0 0
\(193\) 1365.76 2365.57i 0.509376 0.882266i −0.490565 0.871405i \(-0.663209\pi\)
0.999941 0.0108609i \(-0.00345719\pi\)
\(194\) −1045.65 1811.12i −0.386977 0.670264i
\(195\) 0 0
\(196\) 1371.89 17.2547i 0.499960 0.00628817i
\(197\) 3476.58 1.25734 0.628671 0.777671i \(-0.283599\pi\)
0.628671 + 0.777671i \(0.283599\pi\)
\(198\) 0 0
\(199\) −1627.72 + 2819.30i −0.579831 + 1.00430i 0.415668 + 0.909517i \(0.363548\pi\)
−0.995498 + 0.0947796i \(0.969785\pi\)
\(200\) −477.462 + 826.989i −0.168808 + 0.292385i
\(201\) 0 0
\(202\) −2327.74 −0.810789
\(203\) 1975.01 3471.04i 0.682849 1.20009i
\(204\) 0 0
\(205\) 493.282 + 854.390i 0.168060 + 0.291089i
\(206\) 158.322 274.222i 0.0535477 0.0927473i
\(207\) 0 0
\(208\) 195.514 + 338.641i 0.0651754 + 0.112887i
\(209\) −4679.76 −1.54883
\(210\) 0 0
\(211\) 1596.29 0.520822 0.260411 0.965498i \(-0.416142\pi\)
0.260411 + 0.965498i \(0.416142\pi\)
\(212\) 883.746 + 1530.69i 0.286301 + 0.495889i
\(213\) 0 0
\(214\) 159.257 275.841i 0.0508718 0.0881125i
\(215\) −536.862 929.873i −0.170296 0.294962i
\(216\) 0 0
\(217\) −555.068 947.594i −0.173643 0.296437i
\(218\) 72.3693 0.0224838
\(219\) 0 0
\(220\) −185.649 + 321.554i −0.0568931 + 0.0985417i
\(221\) 583.387 1010.46i 0.177570 0.307559i
\(222\) 0 0
\(223\) 5869.21 1.76247 0.881236 0.472677i \(-0.156712\pi\)
0.881236 + 0.472677i \(0.156712\pi\)
\(224\) −299.546 511.375i −0.0893493 0.152534i
\(225\) 0 0
\(226\) 211.787 + 366.827i 0.0623358 + 0.107969i
\(227\) −2979.05 + 5159.86i −0.871041 + 1.50869i −0.0101189 + 0.999949i \(0.503221\pi\)
−0.860922 + 0.508738i \(0.830112\pi\)
\(228\) 0 0
\(229\) −319.983 554.227i −0.0923366 0.159932i 0.816157 0.577830i \(-0.196100\pi\)
−0.908494 + 0.417898i \(0.862767\pi\)
\(230\) 727.744 0.208635
\(231\) 0 0
\(232\) −1725.07 −0.488174
\(233\) −20.5054 35.5163i −0.00576545 0.00998606i 0.863128 0.504985i \(-0.168502\pi\)
−0.868894 + 0.494999i \(0.835169\pi\)
\(234\) 0 0
\(235\) −271.470 + 470.201i −0.0753565 + 0.130521i
\(236\) 1450.11 + 2511.67i 0.399975 + 0.692778i
\(237\) 0 0
\(238\) −874.541 + 1536.99i −0.238185 + 0.418606i
\(239\) 2995.72 0.810783 0.405391 0.914143i \(-0.367135\pi\)
0.405391 + 0.914143i \(0.367135\pi\)
\(240\) 0 0
\(241\) 332.680 576.218i 0.0889203 0.154014i −0.818135 0.575027i \(-0.804992\pi\)
0.907055 + 0.421012i \(0.138325\pi\)
\(242\) 198.230 343.345i 0.0526559 0.0912027i
\(243\) 0 0
\(244\) −1367.04 −0.358671
\(245\) 398.191 710.166i 0.103835 0.185187i
\(246\) 0 0
\(247\) 1462.33 + 2532.83i 0.376704 + 0.652470i
\(248\) −237.188 + 410.822i −0.0607317 + 0.105190i
\(249\) 0 0
\(250\) 580.052 + 1004.68i 0.146743 + 0.254166i
\(251\) −611.679 −0.153820 −0.0769100 0.997038i \(-0.524505\pi\)
−0.0769100 + 0.997038i \(0.524505\pi\)
\(252\) 0 0
\(253\) −5994.57 −1.48963
\(254\) −818.436 1417.57i −0.202178 0.350183i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −1049.17 1817.21i −0.254651 0.441069i 0.710149 0.704051i \(-0.248627\pi\)
−0.964801 + 0.262982i \(0.915294\pi\)
\(258\) 0 0
\(259\) 3889.13 24.4565i 0.933045 0.00586738i
\(260\) 232.047 0.0553497
\(261\) 0 0
\(262\) 348.728 604.014i 0.0822308 0.142428i
\(263\) 2070.93 3586.95i 0.485547 0.840992i −0.514315 0.857601i \(-0.671954\pi\)
0.999862 + 0.0166096i \(0.00528725\pi\)
\(264\) 0 0
\(265\) 1048.88 0.243140
\(266\) −2240.42 3824.78i −0.516425 0.881625i
\(267\) 0 0
\(268\) −502.713 870.725i −0.114582 0.198463i
\(269\) −1941.13 + 3362.14i −0.439974 + 0.762058i −0.997687 0.0679765i \(-0.978346\pi\)
0.557713 + 0.830034i \(0.311679\pi\)
\(270\) 0 0
\(271\) 698.842 + 1210.43i 0.156648 + 0.271322i 0.933658 0.358166i \(-0.116598\pi\)
−0.777010 + 0.629488i \(0.783264\pi\)
\(272\) 763.868 0.170280
\(273\) 0 0
\(274\) −3617.15 −0.797519
\(275\) −2333.92 4042.46i −0.511784 0.886435i
\(276\) 0 0
\(277\) −3305.04 + 5724.50i −0.716898 + 1.24170i 0.245325 + 0.969441i \(0.421105\pi\)
−0.962223 + 0.272262i \(0.912228\pi\)
\(278\) 1673.29 + 2898.23i 0.360998 + 0.625267i
\(279\) 0 0
\(280\) −351.686 + 2.21155i −0.0750617 + 0.000472020i
\(281\) 7076.82 1.50238 0.751188 0.660088i \(-0.229481\pi\)
0.751188 + 0.660088i \(0.229481\pi\)
\(282\) 0 0
\(283\) 937.326 1623.50i 0.196884 0.341013i −0.750632 0.660720i \(-0.770251\pi\)
0.947517 + 0.319707i \(0.103584\pi\)
\(284\) −418.238 + 724.409i −0.0873867 + 0.151358i
\(285\) 0 0
\(286\) −1911.42 −0.395190
\(287\) 3806.72 6690.24i 0.782939 1.37600i
\(288\) 0 0
\(289\) 1316.86 + 2280.87i 0.268037 + 0.464253i
\(290\) −511.851 + 886.551i −0.103645 + 0.179518i
\(291\) 0 0
\(292\) −243.707 422.113i −0.0488420 0.0845969i
\(293\) 6964.76 1.38869 0.694344 0.719643i \(-0.255694\pi\)
0.694344 + 0.719643i \(0.255694\pi\)
\(294\) 0 0
\(295\) 1721.07 0.339676
\(296\) −839.989 1454.90i −0.164944 0.285691i
\(297\) 0 0
\(298\) 3211.32 5562.17i 0.624251 1.08123i
\(299\) 1873.18 + 3244.45i 0.362305 + 0.627530i
\(300\) 0 0
\(301\) −4143.03 + 7281.30i −0.793356 + 1.39431i
\(302\) 5695.19 1.08517
\(303\) 0 0
\(304\) −957.364 + 1658.20i −0.180620 + 0.312844i
\(305\) −405.619 + 702.553i −0.0761498 + 0.131895i
\(306\) 0 0
\(307\) 5750.23 1.06900 0.534500 0.845169i \(-0.320500\pi\)
0.534500 + 0.845169i \(0.320500\pi\)
\(308\) 2896.91 18.2170i 0.535931 0.00337016i
\(309\) 0 0
\(310\) 140.754 + 243.793i 0.0257880 + 0.0446661i
\(311\) −2392.17 + 4143.35i −0.436165 + 0.755460i −0.997390 0.0722036i \(-0.976997\pi\)
0.561225 + 0.827663i \(0.310330\pi\)
\(312\) 0 0
\(313\) 4449.28 + 7706.39i 0.803477 + 1.39166i 0.917314 + 0.398164i \(0.130353\pi\)
−0.113837 + 0.993499i \(0.536314\pi\)
\(314\) −825.693 −0.148397
\(315\) 0 0
\(316\) 3196.78 0.569092
\(317\) −2036.68 3527.63i −0.360856 0.625021i 0.627246 0.778821i \(-0.284182\pi\)
−0.988102 + 0.153800i \(0.950849\pi\)
\(318\) 0 0
\(319\) 4216.22 7302.70i 0.740009 1.28173i
\(320\) 75.9586 + 131.564i 0.0132694 + 0.0229833i
\(321\) 0 0
\(322\) −2869.89 4899.38i −0.496685 0.847925i
\(323\) 5713.27 0.984195
\(324\) 0 0
\(325\) −1458.60 + 2526.38i −0.248950 + 0.431194i
\(326\) 2055.13 3559.59i 0.349151 0.604747i
\(327\) 0 0
\(328\) −3324.98 −0.559729
\(329\) 4236.08 26.6383i 0.709856 0.00446387i
\(330\) 0 0
\(331\) −1613.95 2795.44i −0.268008 0.464203i 0.700340 0.713810i \(-0.253032\pi\)
−0.968347 + 0.249607i \(0.919699\pi\)
\(332\) −233.602 + 404.611i −0.0386162 + 0.0668853i
\(333\) 0 0
\(334\) −3780.59 6548.17i −0.619355 1.07275i
\(335\) −596.647 −0.0973083
\(336\) 0 0
\(337\) 9639.76 1.55819 0.779097 0.626904i \(-0.215678\pi\)
0.779097 + 0.626904i \(0.215678\pi\)
\(338\) −1599.72 2770.80i −0.257436 0.445892i
\(339\) 0 0
\(340\) 226.650 392.569i 0.0361524 0.0626177i
\(341\) −1159.42 2008.17i −0.184123 0.318910i
\(342\) 0 0
\(343\) −6351.32 + 119.832i −0.999822 + 0.0188639i
\(344\) 3618.73 0.567176
\(345\) 0 0
\(346\) −3551.49 + 6151.37i −0.551819 + 0.955779i
\(347\) 832.775 1442.41i 0.128835 0.223149i −0.794391 0.607407i \(-0.792210\pi\)
0.923225 + 0.384259i \(0.125543\pi\)
\(348\) 0 0
\(349\) 4441.18 0.681177 0.340589 0.940212i \(-0.389374\pi\)
0.340589 + 0.940212i \(0.389374\pi\)
\(350\) 2186.56 3842.84i 0.333933 0.586881i
\(351\) 0 0
\(352\) −625.686 1083.72i −0.0947420 0.164098i
\(353\) 4399.42 7620.02i 0.663336 1.14893i −0.316397 0.948627i \(-0.602473\pi\)
0.979734 0.200305i \(-0.0641933\pi\)
\(354\) 0 0
\(355\) 248.193 + 429.883i 0.0371063 + 0.0642700i
\(356\) −1465.95 −0.218245
\(357\) 0 0
\(358\) −7898.79 −1.16610
\(359\) 2769.49 + 4796.89i 0.407153 + 0.705210i 0.994569 0.104075i \(-0.0331883\pi\)
−0.587417 + 0.809285i \(0.699855\pi\)
\(360\) 0 0
\(361\) −3731.01 + 6462.30i −0.543958 + 0.942163i
\(362\) −2448.62 4241.13i −0.355515 0.615770i
\(363\) 0 0
\(364\) −915.086 1562.21i −0.131768 0.224950i
\(365\) −289.244 −0.0414788
\(366\) 0 0
\(367\) 5721.93 9910.68i 0.813848 1.40963i −0.0963034 0.995352i \(-0.530702\pi\)
0.910152 0.414275i \(-0.135965\pi\)
\(368\) −1226.34 + 2124.09i −0.173716 + 0.300885i
\(369\) 0 0
\(370\) −996.944 −0.140077
\(371\) −4136.29 7061.34i −0.578828 0.988157i
\(372\) 0 0
\(373\) −6187.63 10717.3i −0.858936 1.48772i −0.872945 0.487819i \(-0.837792\pi\)
0.0140082 0.999902i \(-0.495541\pi\)
\(374\) −1866.96 + 3233.67i −0.258123 + 0.447083i
\(375\) 0 0
\(376\) −914.925 1584.70i −0.125488 0.217352i
\(377\) −5269.93 −0.719935
\(378\) 0 0
\(379\) 621.352 0.0842129 0.0421064 0.999113i \(-0.486593\pi\)
0.0421064 + 0.999113i \(0.486593\pi\)
\(380\) 568.125 + 984.021i 0.0766953 + 0.132840i
\(381\) 0 0
\(382\) −763.452 + 1322.34i −0.102256 + 0.177112i
\(383\) 4673.97 + 8095.56i 0.623574 + 1.08006i 0.988815 + 0.149149i \(0.0476533\pi\)
−0.365241 + 0.930913i \(0.619013\pi\)
\(384\) 0 0
\(385\) 850.189 1494.19i 0.112545 0.197795i
\(386\) 5463.04 0.720367
\(387\) 0 0
\(388\) 2091.31 3622.25i 0.273634 0.473948i
\(389\) 575.571 996.918i 0.0750195 0.129938i −0.826075 0.563560i \(-0.809431\pi\)
0.901095 + 0.433622i \(0.142765\pi\)
\(390\) 0 0
\(391\) 7318.46 0.946575
\(392\) 1401.78 + 2358.93i 0.180613 + 0.303939i
\(393\) 0 0
\(394\) 3476.58 + 6021.62i 0.444538 + 0.769962i
\(395\) 948.527 1642.90i 0.120824 0.209274i
\(396\) 0 0
\(397\) 2714.27 + 4701.26i 0.343137 + 0.594331i 0.985014 0.172477i \(-0.0551771\pi\)
−0.641876 + 0.766808i \(0.721844\pi\)
\(398\) −6510.90 −0.820004
\(399\) 0 0
\(400\) −1909.85 −0.238731
\(401\) −2182.88 3780.87i −0.271841 0.470842i 0.697493 0.716592i \(-0.254299\pi\)
−0.969333 + 0.245750i \(0.920966\pi\)
\(402\) 0 0
\(403\) −724.589 + 1255.02i −0.0895641 + 0.155130i
\(404\) −2327.74 4031.77i −0.286657 0.496505i
\(405\) 0 0
\(406\) 7987.02 50.2258i 0.976328 0.00613956i
\(407\) 8212.03 1.00014
\(408\) 0 0
\(409\) −1654.33 + 2865.38i −0.200003 + 0.346415i −0.948529 0.316690i \(-0.897428\pi\)
0.748526 + 0.663105i \(0.230762\pi\)
\(410\) −986.565 + 1708.78i −0.118837 + 0.205831i
\(411\) 0 0
\(412\) 633.288 0.0757279
\(413\) −6787.10 11586.7i −0.808648 1.38050i
\(414\) 0 0
\(415\) 138.626 + 240.107i 0.0163973 + 0.0284009i
\(416\) −391.029 + 677.282i −0.0460860 + 0.0798232i
\(417\) 0 0
\(418\) −4679.76 8105.58i −0.547594 0.948461i
\(419\) −3249.72 −0.378900 −0.189450 0.981890i \(-0.560670\pi\)
−0.189450 + 0.981890i \(0.560670\pi\)
\(420\) 0 0
\(421\) −2932.21 −0.339447 −0.169724 0.985492i \(-0.554287\pi\)
−0.169724 + 0.985492i \(0.554287\pi\)
\(422\) 1596.29 + 2764.86i 0.184138 + 0.318937i
\(423\) 0 0
\(424\) −1767.49 + 3061.39i −0.202446 + 0.350646i
\(425\) 2849.36 + 4935.23i 0.325210 + 0.563280i
\(426\) 0 0
\(427\) 6329.36 39.8017i 0.717329 0.00451087i
\(428\) 637.027 0.0719436
\(429\) 0 0
\(430\) 1073.72 1859.75i 0.120418 0.208569i
\(431\) 3981.70 6896.50i 0.444992 0.770749i −0.553059 0.833142i \(-0.686540\pi\)
0.998052 + 0.0623926i \(0.0198731\pi\)
\(432\) 0 0
\(433\) −7441.66 −0.825920 −0.412960 0.910749i \(-0.635505\pi\)
−0.412960 + 0.910749i \(0.635505\pi\)
\(434\) 1086.21 1909.00i 0.120138 0.211140i
\(435\) 0 0
\(436\) 72.3693 + 125.347i 0.00794922 + 0.0137685i
\(437\) −9172.31 + 15886.9i −1.00405 + 1.73907i
\(438\) 0 0
\(439\) −2822.84 4889.30i −0.306895 0.531557i 0.670787 0.741650i \(-0.265957\pi\)
−0.977681 + 0.210093i \(0.932623\pi\)
\(440\) −742.597 −0.0804590
\(441\) 0 0
\(442\) 2333.55 0.251121
\(443\) −6952.30 12041.7i −0.745630 1.29147i −0.949900 0.312554i \(-0.898816\pi\)
0.204270 0.978915i \(-0.434518\pi\)
\(444\) 0 0
\(445\) −434.966 + 753.384i −0.0463357 + 0.0802558i
\(446\) 5869.21 + 10165.8i 0.623128 + 1.07929i
\(447\) 0 0
\(448\) 586.182 1030.20i 0.0618180 0.108644i
\(449\) 15582.7 1.63784 0.818921 0.573906i \(-0.194573\pi\)
0.818921 + 0.573906i \(0.194573\pi\)
\(450\) 0 0
\(451\) 8126.53 14075.6i 0.848477 1.46961i
\(452\) −423.575 + 733.653i −0.0440781 + 0.0763454i
\(453\) 0 0
\(454\) −11916.2 −1.23184
\(455\) −1074.37 + 6.75610i −0.110697 + 0.000696111i
\(456\) 0 0
\(457\) −4679.71 8105.49i −0.479010 0.829670i 0.520700 0.853740i \(-0.325671\pi\)
−0.999710 + 0.0240700i \(0.992338\pi\)
\(458\) 639.966 1108.45i 0.0652918 0.113089i
\(459\) 0 0
\(460\) 727.744 + 1260.49i 0.0737636 + 0.127762i
\(461\) −1558.11 −0.157415 −0.0787074 0.996898i \(-0.525079\pi\)
−0.0787074 + 0.996898i \(0.525079\pi\)
\(462\) 0 0
\(463\) 12753.6 1.28015 0.640074 0.768313i \(-0.278904\pi\)
0.640074 + 0.768313i \(0.278904\pi\)
\(464\) −1725.07 2987.91i −0.172595 0.298944i
\(465\) 0 0
\(466\) 41.0107 71.0326i 0.00407679 0.00706121i
\(467\) 5556.71 + 9624.51i 0.550608 + 0.953681i 0.998231 + 0.0594586i \(0.0189374\pi\)
−0.447623 + 0.894223i \(0.647729\pi\)
\(468\) 0 0
\(469\) 2352.90 + 4016.80i 0.231656 + 0.395476i
\(470\) −1085.88 −0.106570
\(471\) 0 0
\(472\) −2900.22 + 5023.33i −0.282825 + 0.489868i
\(473\) −8844.48 + 15319.1i −0.859767 + 1.48916i
\(474\) 0 0
\(475\) −14284.5 −1.37983
\(476\) −3536.69 + 22.2402i −0.340554 + 0.00214155i
\(477\) 0 0
\(478\) 2995.72 + 5188.74i 0.286655 + 0.496501i
\(479\) −9495.17 + 16446.1i −0.905731 + 1.56877i −0.0857987 + 0.996312i \(0.527344\pi\)
−0.819933 + 0.572460i \(0.805989\pi\)
\(480\) 0 0
\(481\) −2566.09 4444.61i −0.243251 0.421323i
\(482\) 1330.72 0.125752
\(483\) 0 0
\(484\) 792.922 0.0744667
\(485\) −1241.04 2149.54i −0.116191 0.201249i
\(486\) 0 0
\(487\) −2474.13 + 4285.31i −0.230212 + 0.398739i −0.957870 0.287201i \(-0.907275\pi\)
0.727658 + 0.685940i \(0.240609\pi\)
\(488\) −1367.04 2367.78i −0.126810 0.219641i
\(489\) 0 0
\(490\) 1628.23 20.4789i 0.150114 0.00188804i
\(491\) 9178.86 0.843658 0.421829 0.906675i \(-0.361388\pi\)
0.421829 + 0.906675i \(0.361388\pi\)
\(492\) 0 0
\(493\) −5147.36 + 8915.49i −0.470234 + 0.814469i
\(494\) −2924.66 + 5065.66i −0.266370 + 0.461366i
\(495\) 0 0
\(496\) −948.752 −0.0858876
\(497\) 1915.34 3366.17i 0.172866 0.303810i
\(498\) 0 0
\(499\) 8374.31 + 14504.7i 0.751274 + 1.30125i 0.947205 + 0.320627i \(0.103894\pi\)
−0.195931 + 0.980618i \(0.562773\pi\)
\(500\) −1160.10 + 2009.36i −0.103763 + 0.179723i
\(501\) 0 0
\(502\) −611.679 1059.46i −0.0543836 0.0941952i
\(503\) −10162.0 −0.900794 −0.450397 0.892828i \(-0.648718\pi\)
−0.450397 + 0.892828i \(0.648718\pi\)
\(504\) 0 0
\(505\) −2762.69 −0.243442
\(506\) −5994.57 10382.9i −0.526663 0.912206i
\(507\) 0 0
\(508\) 1636.87 2835.14i 0.142961 0.247617i
\(509\) 2831.68 + 4904.62i 0.246586 + 0.427099i 0.962576 0.271011i \(-0.0873580\pi\)
−0.715991 + 0.698110i \(0.754025\pi\)
\(510\) 0 0
\(511\) 1140.65 + 1947.28i 0.0987461 + 0.168576i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 2098.34 3634.43i 0.180066 0.311883i
\(515\) 187.905 325.461i 0.0160778 0.0278476i
\(516\) 0 0
\(517\) 8944.62 0.760898
\(518\) 3931.49 + 6711.71i 0.333474 + 0.569297i
\(519\) 0 0
\(520\) 232.047 + 401.917i 0.0195691 + 0.0338947i
\(521\) 839.858 1454.68i 0.0706235 0.122324i −0.828551 0.559913i \(-0.810834\pi\)
0.899175 + 0.437590i \(0.144168\pi\)
\(522\) 0 0
\(523\) 3522.27 + 6100.76i 0.294490 + 0.510072i 0.974866 0.222791i \(-0.0715169\pi\)
−0.680376 + 0.732863i \(0.738184\pi\)
\(524\) 1394.91 0.116292
\(525\) 0 0
\(526\) 8283.70 0.686667
\(527\) 1415.47 + 2451.67i 0.117000 + 0.202650i
\(528\) 0 0
\(529\) −5665.85 + 9813.53i −0.465673 + 0.806570i
\(530\) 1048.88 + 1816.71i 0.0859628 + 0.148892i
\(531\) 0 0
\(532\) 4384.29 7705.31i 0.357299 0.627946i
\(533\) −10157.5 −0.825461
\(534\) 0 0
\(535\) 189.014 327.382i 0.0152744 0.0264560i
\(536\) 1005.43 1741.45i 0.0810220 0.140334i
\(537\) 0 0
\(538\) −7764.54 −0.622217
\(539\) −13412.1 + 168.688i −1.07180 + 0.0134804i
\(540\) 0 0
\(541\) −884.613 1532.20i −0.0703004 0.121764i 0.828733 0.559645i \(-0.189062\pi\)
−0.899033 + 0.437881i \(0.855729\pi\)
\(542\) −1397.68 + 2420.86i −0.110767 + 0.191854i
\(543\) 0 0
\(544\) 763.868 + 1323.06i 0.0602032 + 0.104275i
\(545\) 85.8917 0.00675082
\(546\) 0 0
\(547\) 5279.46 0.412676 0.206338 0.978481i \(-0.433845\pi\)
0.206338 + 0.978481i \(0.433845\pi\)
\(548\) −3617.15 6265.09i −0.281966 0.488379i
\(549\) 0 0
\(550\) 4667.83 8084.92i 0.361886 0.626804i
\(551\) −12902.5 22347.8i −0.997576 1.72785i
\(552\) 0 0
\(553\) −14801.0 + 93.0750i −1.13816 + 0.00715724i
\(554\) −13220.2 −1.01385
\(555\) 0 0
\(556\) −3346.59 + 5796.46i −0.255264 + 0.442131i
\(557\) −10662.5 + 18468.1i −0.811107 + 1.40488i 0.100984 + 0.994888i \(0.467801\pi\)
−0.912090 + 0.409990i \(0.865532\pi\)
\(558\) 0 0
\(559\) 11054.9 0.836444
\(560\) −355.517 606.927i −0.0268274 0.0457988i
\(561\) 0 0
\(562\) 7076.82 + 12257.4i 0.531170 + 0.920014i
\(563\) −12490.1 + 21633.4i −0.934979 + 1.61943i −0.160308 + 0.987067i \(0.551249\pi\)
−0.774671 + 0.632364i \(0.782085\pi\)
\(564\) 0 0
\(565\) 251.361 + 435.369i 0.0187165 + 0.0324179i
\(566\) 3749.30 0.278436
\(567\) 0 0
\(568\) −1672.95 −0.123583
\(569\) −8527.32 14769.7i −0.628267 1.08819i −0.987899 0.155096i \(-0.950431\pi\)
0.359633 0.933094i \(-0.382902\pi\)
\(570\) 0 0
\(571\) −7455.68 + 12913.6i −0.546429 + 0.946442i 0.452087 + 0.891974i \(0.350680\pi\)
−0.998516 + 0.0544681i \(0.982654\pi\)
\(572\) −1911.42 3310.67i −0.139721 0.242004i
\(573\) 0 0
\(574\) 15394.6 96.8075i 1.11944 0.00703949i
\(575\) −18297.9 −1.32709
\(576\) 0 0
\(577\) −11224.7 + 19441.7i −0.809860 + 1.40272i 0.103100 + 0.994671i \(0.467124\pi\)
−0.912960 + 0.408048i \(0.866210\pi\)
\(578\) −2633.73 + 4561.75i −0.189530 + 0.328276i
\(579\) 0 0
\(580\) −2047.40 −0.146575
\(581\) 1069.79 1880.14i 0.0763897 0.134254i
\(582\) 0 0
\(583\) −8639.80 14964.6i −0.613763 1.06307i
\(584\) 487.414 844.226i 0.0345365 0.0598190i
\(585\) 0 0
\(586\) 6964.76 + 12063.3i 0.490976 + 0.850395i
\(587\) 7613.92 0.535367 0.267683 0.963507i \(-0.413742\pi\)
0.267683 + 0.963507i \(0.413742\pi\)
\(588\) 0 0
\(589\) −7096.10 −0.496417
\(590\) 1721.07 + 2980.98i 0.120094 + 0.208008i
\(591\) 0 0
\(592\) 1679.98 2909.81i 0.116633 0.202014i
\(593\) 6920.65 + 11986.9i 0.479253 + 0.830090i 0.999717 0.0237934i \(-0.00757438\pi\)
−0.520464 + 0.853884i \(0.674241\pi\)
\(594\) 0 0
\(595\) −1037.95 + 1824.18i −0.0715158 + 0.125688i
\(596\) 12845.3 0.882824
\(597\) 0 0
\(598\) −3746.37 + 6488.90i −0.256188 + 0.443731i
\(599\) −3038.99 + 5263.69i −0.207295 + 0.359046i −0.950862 0.309616i \(-0.899799\pi\)
0.743566 + 0.668662i \(0.233133\pi\)
\(600\) 0 0
\(601\) −5719.48 −0.388190 −0.194095 0.980983i \(-0.562177\pi\)
−0.194095 + 0.980983i \(0.562177\pi\)
\(602\) −16754.6 + 105.360i −1.13433 + 0.00713315i
\(603\) 0 0
\(604\) 5695.19 + 9864.35i 0.383665 + 0.664528i
\(605\) 235.270 407.500i 0.0158101 0.0273839i
\(606\) 0 0
\(607\) −14768.8 25580.3i −0.987558 1.71050i −0.629966 0.776623i \(-0.716931\pi\)
−0.357592 0.933878i \(-0.616402\pi\)
\(608\) −3829.45 −0.255436
\(609\) 0 0
\(610\) −1622.48 −0.107692
\(611\) −2795.02 4841.11i −0.185064 0.320541i
\(612\) 0 0
\(613\) −10569.8 + 18307.5i −0.696429 + 1.20625i 0.273267 + 0.961938i \(0.411896\pi\)
−0.969697 + 0.244312i \(0.921438\pi\)
\(614\) 5750.23 + 9959.69i 0.377949 + 0.654626i
\(615\) 0 0
\(616\) 2928.46 + 4999.38i 0.191544 + 0.326998i
\(617\) 6754.03 0.440692 0.220346 0.975422i \(-0.429281\pi\)
0.220346 + 0.975422i \(0.429281\pi\)
\(618\) 0 0
\(619\) 13387.6 23188.0i 0.869292 1.50566i 0.00657132 0.999978i \(-0.497908\pi\)
0.862721 0.505680i \(-0.168758\pi\)
\(620\) −281.507 + 487.585i −0.0182349 + 0.0315837i
\(621\) 0 0
\(622\) −9568.66 −0.616830
\(623\) 6787.30 42.6814i 0.436481 0.00274478i
\(624\) 0 0
\(625\) −6771.91 11729.3i −0.433402 0.750675i
\(626\) −8898.57 + 15412.8i −0.568144 + 0.984055i
\(627\) 0 0
\(628\) −825.693 1430.14i −0.0524662 0.0908741i
\(629\) −10025.6 −0.635530
\(630\) 0 0
\(631\) 17990.3 1.13500 0.567499 0.823374i \(-0.307911\pi\)
0.567499 + 0.823374i \(0.307911\pi\)
\(632\) 3196.78 + 5536.99i 0.201204 + 0.348496i
\(633\) 0 0
\(634\) 4073.36 7055.27i 0.255164 0.441957i
\(635\) −971.363 1682.45i −0.0607045 0.105143i
\(636\) 0 0
\(637\) 4282.31 + 7206.33i 0.266360 + 0.448234i
\(638\) 16864.9 1.04653
\(639\) 0 0
\(640\) −151.917 + 263.128i −0.00938290 + 0.0162517i
\(641\) 4678.17 8102.83i 0.288263 0.499287i −0.685132 0.728419i \(-0.740256\pi\)
0.973395 + 0.229132i \(0.0735888\pi\)
\(642\) 0 0
\(643\) 14794.8 0.907388 0.453694 0.891158i \(-0.350106\pi\)
0.453694 + 0.891158i \(0.350106\pi\)
\(644\) 5616.09 9870.17i 0.343641 0.603943i
\(645\) 0 0
\(646\) 5713.27 + 9895.68i 0.347966 + 0.602694i
\(647\) 13672.9 23682.2i 0.830816 1.43902i −0.0665758 0.997781i \(-0.521207\pi\)
0.897392 0.441234i \(-0.145459\pi\)
\(648\) 0 0
\(649\) −14176.8 24554.9i −0.857454 1.48515i
\(650\) −5834.42 −0.352069
\(651\) 0 0
\(652\) 8220.52 0.493774
\(653\) 3351.78 + 5805.46i 0.200866 + 0.347910i 0.948808 0.315854i \(-0.102291\pi\)
−0.747942 + 0.663764i \(0.768958\pi\)
\(654\) 0 0
\(655\) 413.889 716.876i 0.0246900 0.0427644i
\(656\) −3324.98 5759.03i −0.197894 0.342763i
\(657\) 0 0
\(658\) 4282.22 + 7310.47i 0.253706 + 0.433118i
\(659\) 13321.2 0.787433 0.393717 0.919232i \(-0.371189\pi\)
0.393717 + 0.919232i \(0.371189\pi\)
\(660\) 0 0
\(661\) 9509.03 16470.1i 0.559544 0.969158i −0.437991 0.898980i \(-0.644310\pi\)
0.997534 0.0701787i \(-0.0223570\pi\)
\(662\) 3227.89 5590.88i 0.189510 0.328241i
\(663\) 0 0
\(664\) −934.409 −0.0546116
\(665\) −2659.05 4539.45i −0.155058 0.264710i
\(666\) 0 0
\(667\) −16527.5 28626.5i −0.959444 1.66181i
\(668\) 7561.17 13096.3i 0.437950 0.758552i
\(669\) 0 0
\(670\) −596.647 1033.42i −0.0344037 0.0595890i
\(671\) 13364.7 0.768908
\(672\) 0 0
\(673\) −12786.8 −0.732386 −0.366193 0.930539i \(-0.619339\pi\)
−0.366193 + 0.930539i \(0.619339\pi\)
\(674\) 9639.76 + 16696.6i 0.550905 + 0.954195i
\(675\) 0 0
\(676\) 3199.44 5541.60i 0.182035 0.315293i
\(677\) 4555.10 + 7889.67i 0.258592 + 0.447895i 0.965865 0.259046i \(-0.0834081\pi\)
−0.707273 + 0.706941i \(0.750075\pi\)
\(678\) 0 0
\(679\) −9577.23 + 16831.8i −0.541297 + 0.951319i
\(680\) 906.599 0.0511272
\(681\) 0 0
\(682\) 2318.83 4016.34i 0.130195 0.225504i
\(683\) −10067.1 + 17436.7i −0.563993 + 0.976864i 0.433150 + 0.901322i \(0.357402\pi\)
−0.997143 + 0.0755422i \(0.975931\pi\)
\(684\) 0 0
\(685\) −4293.03 −0.239457
\(686\) −6558.87 10881.0i −0.365042 0.605594i
\(687\) 0 0
\(688\) 3618.73 + 6267.82i 0.200527 + 0.347323i
\(689\) −5399.53 + 9352.26i −0.298557 + 0.517116i
\(690\) 0 0
\(691\) 15688.3 + 27173.0i 0.863693 + 1.49596i 0.868339 + 0.495972i \(0.165188\pi\)
−0.00464517 + 0.999989i \(0.501479\pi\)
\(692\) −14206.0 −0.780390
\(693\) 0 0
\(694\) 3331.10 0.182200
\(695\) 1985.95 + 3439.77i 0.108391 + 0.187738i
\(696\) 0 0
\(697\) −9921.26 + 17184.1i −0.539160 + 0.933852i
\(698\) 4441.18 + 7692.35i 0.240833 + 0.417134i
\(699\) 0 0
\(700\) 8842.55 55.6057i 0.477453 0.00300242i
\(701\) 22364.5 1.20498 0.602492 0.798125i \(-0.294174\pi\)
0.602492 + 0.798125i \(0.294174\pi\)
\(702\) 0 0
\(703\) 12565.2 21763.6i 0.674121 1.16761i
\(704\) 1251.37 2167.44i 0.0669927 0.116035i
\(705\) 0 0
\(706\) 17597.7 0.938099
\(707\) 10894.8 + 18599.2i 0.579547 + 0.989385i
\(708\) 0 0
\(709\) −5772.08 9997.54i −0.305748 0.529571i 0.671680 0.740842i \(-0.265573\pi\)
−0.977428 + 0.211271i \(0.932240\pi\)
\(710\) −496.387 + 859.767i −0.0262381 + 0.0454457i
\(711\) 0 0
\(712\) −1465.95 2539.10i −0.0771611 0.133647i
\(713\) −9089.81 −0.477442
\(714\) 0 0
\(715\) −2268.57 −0.118657
\(716\) −7898.79 13681.1i −0.412279 0.714088i
\(717\) 0 0
\(718\) −5538.97 + 9593.78i −0.287901 + 0.498658i
\(719\) 940.338 + 1628.71i 0.0487742 + 0.0844795i 0.889382 0.457165i \(-0.151135\pi\)
−0.840608 + 0.541645i \(0.817802\pi\)
\(720\) 0 0
\(721\) −2932.11 + 18.4383i −0.151453 + 0.000952399i
\(722\) −14924.0 −0.769273
\(723\) 0 0
\(724\) 4897.23 8482.26i 0.251387 0.435415i
\(725\) 12869.6 22290.8i 0.659262 1.14188i
\(726\) 0 0
\(727\) −2783.27 −0.141988 −0.0709942 0.997477i \(-0.522617\pi\)
−0.0709942 + 0.997477i \(0.522617\pi\)
\(728\) 1790.73 3147.18i 0.0911662 0.160223i
\(729\) 0 0
\(730\) −289.244 500.986i −0.0146650 0.0254004i
\(731\) 10797.8 18702.3i 0.546334 0.946278i
\(732\) 0 0
\(733\) −14210.9 24614.0i −0.716088 1.24030i −0.962539 0.271145i \(-0.912598\pi\)
0.246451 0.969155i \(-0.420736\pi\)
\(734\) 22887.7 1.15096
\(735\) 0 0
\(736\) −4905.37 −0.245672
\(737\) 4914.70 + 8512.51i 0.245638 + 0.425458i
\(738\) 0 0
\(739\) −3402.66 + 5893.58i −0.169376 + 0.293368i −0.938201 0.346092i \(-0.887509\pi\)
0.768825 + 0.639460i \(0.220842\pi\)
\(740\) −996.944 1726.76i −0.0495249 0.0857796i
\(741\) 0 0
\(742\) 8094.31 14225.6i 0.400473 0.703825i
\(743\) −4302.19 −0.212426 −0.106213 0.994343i \(-0.533872\pi\)
−0.106213 + 0.994343i \(0.533872\pi\)
\(744\) 0 0
\(745\) 3811.37 6601.48i 0.187433 0.324644i
\(746\) 12375.3 21434.6i 0.607360 1.05198i
\(747\) 0 0
\(748\) −7467.83 −0.365041
\(749\) −2949.42 + 18.5472i −0.143884 + 0.000904805i
\(750\) 0 0
\(751\) −9151.88 15851.5i −0.444683 0.770213i 0.553347 0.832951i \(-0.313350\pi\)
−0.998030 + 0.0627375i \(0.980017\pi\)
\(752\) 1829.85 3169.39i 0.0887338 0.153691i
\(753\) 0 0
\(754\) −5269.93 9127.79i −0.254535 0.440868i
\(755\) 6759.35 0.325825
\(756\) 0 0
\(757\) 4475.34 0.214873 0.107437 0.994212i \(-0.465736\pi\)
0.107437 + 0.994212i \(0.465736\pi\)
\(758\) 621.352 + 1076.21i 0.0297738 + 0.0515696i
\(759\) 0 0
\(760\) −1136.25 + 1968.04i −0.0542317 + 0.0939321i
\(761\) −12248.0 21214.1i −0.583428 1.01053i −0.995069 0.0991813i \(-0.968378\pi\)
0.411641 0.911346i \(-0.364956\pi\)
\(762\) 0 0
\(763\) −338.717 578.247i −0.0160713 0.0274364i
\(764\) −3053.81 −0.144611
\(765\) 0 0
\(766\) −9347.94 + 16191.1i −0.440933 + 0.763719i
\(767\) −8859.92 + 15345.8i −0.417097 + 0.722433i
\(768\) 0 0
\(769\) −11671.0 −0.547290 −0.273645 0.961831i \(-0.588229\pi\)
−0.273645 + 0.961831i \(0.588229\pi\)
\(770\) 3438.21 21.6209i 0.160915 0.00101190i
\(771\) 0 0
\(772\) 5463.04 + 9462.27i 0.254688 + 0.441133i
\(773\) 17808.5 30845.3i 0.828627 1.43522i −0.0704885 0.997513i \(-0.522456\pi\)
0.899115 0.437711i \(-0.144211\pi\)
\(774\) 0 0
\(775\) −3539.01 6129.75i −0.164032 0.284112i
\(776\) 8365.23 0.386977
\(777\) 0 0
\(778\) 2302.28 0.106094
\(779\) −24868.8 43074.1i −1.14380 1.98112i
\(780\) 0 0
\(781\) 4088.83 7082.07i 0.187337 0.324477i
\(782\) 7318.46 + 12676.0i 0.334665 + 0.579656i
\(783\) 0 0
\(784\) −2684.01 + 4786.88i −0.122267 + 0.218061i