Properties

Label 378.4.g.e.163.3
Level $378$
Weight $4$
Character 378.163
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 163.3
Root \(-1.44566 - 2.50395i\) of defining polynomial
Character \(\chi\) \(=\) 378.163
Dual form 378.4.g.e.109.3

$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

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

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 −0.808054 0.589108i \(-0.799479\pi\)
0.914210 + 0.405242i \(0.132813\pi\)
\(6\) 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 0.999117 + 0.0420115i \(0.0133766\pi\)
−0.463176 + 0.886267i \(0.653290\pi\)
\(12\) 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 0.643976 0.765046i \(-0.277284\pi\)
−0.984537 + 0.175177i \(0.943950\pi\)
\(18\) 0 0
\(19\) −59.8352 + 103.638i −0.722481 + 1.25137i 0.237521 + 0.971382i \(0.423665\pi\)
−0.960002 + 0.279992i \(0.909668\pi\)
\(20\) −9.49483 −0.106155
\(21\) 0 0
\(22\) 78.2108 0.757936
\(23\) −76.6464 + 132.755i −0.694864 + 1.20354i 0.275362 + 0.961341i \(0.411202\pi\)
−0.970226 + 0.242200i \(0.922131\pi\)
\(24\) 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 0.939041 0.343806i \(-0.111716\pi\)
−0.767265 + 0.641330i \(0.778383\pi\)
\(32\) 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 −0.532737 0.846281i \(-0.678837\pi\)
0.999269 + 0.0382238i \(0.0121700\pi\)
\(38\) 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 −0.632172 0.774828i \(-0.717836\pi\)
0.987107 + 0.160063i \(0.0511697\pi\)
\(48\) 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 0.996298 + 0.0859723i \(0.0273996\pi\)
−0.423695 + 0.905805i \(0.639267\pi\)
\(54\) 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 0.919648 + 0.392745i \(0.128474\pi\)
−0.119697 + 0.992810i \(0.538192\pi\)
\(60\) 0 0
\(61\) 170.880 295.973i 0.358671 0.621237i −0.629068 0.777351i \(-0.716563\pi\)
0.987739 + 0.156113i \(0.0498965\pi\)
\(62\) 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 0.728396 0.685156i \(-0.240266\pi\)
−0.957561 + 0.288231i \(0.906933\pi\)
\(68\) −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 0.813042 0.582206i \(-0.197810\pi\)
−0.910726 + 0.413012i \(0.864477\pi\)
\(74\) −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 0.427565 + 0.903985i \(0.359372\pi\)
−0.996656 + 0.0817107i \(0.973962\pi\)
\(80\) 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 −0.736027 0.676952i \(-0.763300\pi\)
0.954271 + 0.298942i \(0.0966336\pi\)
\(90\) 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 −0.996223 0.0868370i \(-0.972324\pi\)
0.422908 0.906173i \(-0.361009\pi\)
\(102\) 0 0
\(103\) −79.1611 + 137.111i −0.0757279 + 0.131165i −0.901403 0.432982i \(-0.857461\pi\)
0.825675 + 0.564147i \(0.190795\pi\)
\(104\) 195.514 0.184344
\(105\) 0 0
\(106\) 883.746 0.809783
\(107\) −79.6283 + 137.920i −0.0719436 + 0.124610i −0.899753 0.436399i \(-0.856253\pi\)
0.827809 + 0.561009i \(0.189587\pi\)
\(108\) 0 0
\(109\) 18.0923 + 31.3368i 0.0158984 + 0.0275369i 0.873865 0.486168i \(-0.161606\pi\)
−0.857967 + 0.513705i \(0.828272\pi\)
\(110\) 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 −0.918295 0.395896i \(-0.870434\pi\)
0.802004 + 0.597319i \(0.203767\pi\)
\(132\) 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 −0.997148 0.0754677i \(-0.975955\pi\)
0.433217 0.901290i \(-0.357378\pi\)
\(138\) 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 −0.0346375 + 0.999400i \(0.511028\pi\)
−0.848187 + 0.529697i \(0.822306\pi\)
\(150\) 0 0
\(151\) 1423.80 + 2466.09i 0.767331 + 1.32906i 0.939005 + 0.343902i \(0.111749\pi\)
−0.171675 + 0.985154i \(0.554918\pi\)
\(152\) 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 0.808778 0.588114i \(-0.200129\pi\)
−0.913711 + 0.406366i \(0.866796\pi\)
\(158\) 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 −0.999974 0.00717453i \(-0.997716\pi\)
0.506200 + 0.862416i \(0.331050\pi\)
\(164\) −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 −0.151325 0.988484i \(-0.548354\pi\)
0.931715 0.363191i \(-0.118313\pi\)
\(174\) 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 −0.902257 0.431200i \(-0.858090\pi\)
0.0776984 0.996977i \(-0.475243\pi\)
\(180\) 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 −0.784617 0.619981i \(-0.787140\pi\)
0.929228 + 0.369507i \(0.120474\pi\)
\(192\) 0 0
\(193\) 1365.76 + 2365.57i 0.509376 + 0.882266i 0.999941 + 0.0108609i \(0.00345719\pi\)
−0.490565 + 0.871405i \(0.663209\pi\)
\(194\) −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 −0.995498 0.0947796i \(-0.969785\pi\)
0.415668 0.909517i \(-0.363548\pi\)
\(200\) −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 −0.860922 0.508738i \(-0.830112\pi\)
−0.0101189 0.999949i \(-0.503221\pi\)
\(228\) 0 0
\(229\) −319.983 + 554.227i −0.0923366 + 0.159932i −0.908494 0.417898i \(-0.862767\pi\)
0.816157 + 0.577830i \(0.196100\pi\)
\(230\) 727.744 0.208635
\(231\) 0 0
\(232\) −1725.07 −0.488174
\(233\) −20.5054 + 35.5163i −0.00576545 + 0.00998606i −0.868894 0.494999i \(-0.835169\pi\)
0.863128 + 0.504985i \(0.168502\pi\)
\(234\) 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 0.907055 0.421012i \(-0.138325\pi\)
−0.818135 + 0.575027i \(0.804992\pi\)
\(242\) 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 −0.964801 0.262982i \(-0.915294\pi\)
0.710149 + 0.704051i \(0.248627\pi\)
\(258\) 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 0.999862 0.0166096i \(-0.00528725\pi\)
−0.514315 + 0.857601i \(0.671954\pi\)
\(264\) 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 0.557713 0.830034i \(-0.311679\pi\)
−0.997687 + 0.0679765i \(0.978346\pi\)
\(270\) 0 0
\(271\) 698.842 1210.43i 0.156648 0.271322i −0.777010 0.629488i \(-0.783264\pi\)
0.933658 + 0.358166i \(0.116598\pi\)
\(272\) 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 −0.962223 0.272262i \(-0.912228\pi\)
0.245325 0.969441i \(-0.421105\pi\)
\(278\) 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 0.947517 0.319707i \(-0.103584\pi\)
−0.750632 + 0.660720i \(0.770251\pi\)
\(284\) −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 0.561225 0.827663i \(-0.310330\pi\)
−0.997390 + 0.0722036i \(0.976997\pi\)
\(312\) 0 0
\(313\) 4449.28 7706.39i 0.803477 1.39166i −0.113837 0.993499i \(-0.536314\pi\)
0.917314 0.398164i \(-0.130353\pi\)
\(314\) −825.693 −0.148397
\(315\) 0 0
\(316\) 3196.78 0.569092
\(317\) −2036.68 + 3527.63i −0.360856 + 0.625021i −0.988102 0.153800i \(-0.950849\pi\)
0.627246 + 0.778821i \(0.284182\pi\)
\(318\) 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 −0.968347 0.249607i \(-0.919699\pi\)
0.700340 + 0.713810i \(0.253032\pi\)
\(332\) −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 0.923225 0.384259i \(-0.125543\pi\)
−0.794391 + 0.607407i \(0.792210\pi\)
\(348\) 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 0.979734 + 0.200305i \(0.0641933\pi\)
−0.316397 + 0.948627i \(0.602473\pi\)
\(354\) 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 −0.587417 0.809285i \(-0.699855\pi\)
0.994569 + 0.104075i \(0.0331883\pi\)
\(360\) 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 0.910152 + 0.414275i \(0.135965\pi\)
−0.0963034 + 0.995352i \(0.530702\pi\)
\(368\) −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 0.0140082 + 0.999902i \(0.495541\pi\)
−0.872945 + 0.487819i \(0.837792\pi\)
\(374\) −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 −0.365241 0.930913i \(-0.619013\pi\)
0.988815 0.149149i \(-0.0476533\pi\)
\(384\) 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 0.901095 0.433622i \(-0.142765\pi\)
−0.826075 + 0.563560i \(0.809431\pi\)
\(390\) 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 −0.641876 0.766808i \(-0.721844\pi\)
0.985014 + 0.172477i \(0.0551771\pi\)
\(398\) −6510.90 −0.820004
\(399\) 0 0
\(400\) −1909.85 −0.238731
\(401\) −2182.88 + 3780.87i −0.271841 + 0.470842i −0.969333 0.245750i \(-0.920966\pi\)
0.697493 + 0.716592i \(0.254299\pi\)
\(402\) 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 0.748526 0.663105i \(-0.230762\pi\)
−0.948529 + 0.316690i \(0.897428\pi\)
\(410\) −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 0.998052 0.0623926i \(-0.0198731\pi\)
−0.553059 + 0.833142i \(0.686540\pi\)
\(432\) 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 −0.977681 0.210093i \(-0.932623\pi\)
0.670787 + 0.741650i \(0.265957\pi\)
\(440\) −742.597 −0.0804590
\(441\) 0 0
\(442\) 2333.55 0.251121
\(443\) −6952.30 + 12041.7i −0.745630 + 1.29147i 0.204270 + 0.978915i \(0.434518\pi\)
−0.949900 + 0.312554i \(0.898816\pi\)
\(444\) 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 −0.999710 0.0240700i \(-0.992338\pi\)
0.520700 + 0.853740i \(0.325671\pi\)
\(458\) 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 −0.447623 0.894223i \(-0.647729\pi\)
0.998231 0.0594586i \(-0.0189374\pi\)
\(468\) 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 −0.819933 0.572460i \(-0.805989\pi\)
−0.0857987 0.996312i \(-0.527344\pi\)
\(480\) 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 0.727658 0.685940i \(-0.240609\pi\)
−0.957870 + 0.287201i \(0.907275\pi\)
\(488\) −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 −0.195931 0.980618i \(-0.562773\pi\)
0.947205 0.320627i \(-0.103894\pi\)
\(500\) −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 −0.715991 0.698110i \(-0.754025\pi\)
0.962576 + 0.271011i \(0.0873580\pi\)
\(510\) 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 0.899175 0.437590i \(-0.144168\pi\)
−0.828551 + 0.559913i \(0.810834\pi\)
\(522\) 0 0
\(523\) 3522.27 6100.76i 0.294490 0.510072i −0.680376 0.732863i \(-0.738184\pi\)
0.974866 + 0.222791i \(0.0715169\pi\)
\(524\) 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 −0.899033 0.437881i \(-0.855729\pi\)
0.828733 + 0.559645i \(0.189062\pi\)
\(542\) −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 −0.912090 0.409990i \(-0.865532\pi\)
0.100984 0.994888i \(-0.467801\pi\)
\(558\) 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 −0.774671 0.632364i \(-0.782085\pi\)
−0.160308 0.987067i \(-0.551249\pi\)
\(564\) 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 0.359633 + 0.933094i \(0.382902\pi\)
−0.987899 + 0.155096i \(0.950431\pi\)
\(570\) 0 0
\(571\) −7455.68 12913.6i −0.546429 0.946442i −0.998516 0.0544681i \(-0.982654\pi\)
0.452087 0.891974i \(-0.350680\pi\)
\(572\) −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 −0.912960 0.408048i \(-0.866210\pi\)
0.103100 0.994671i \(-0.467124\pi\)
\(578\) −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 −0.520464 0.853884i \(-0.674241\pi\)
0.999717 + 0.0237934i \(0.00757438\pi\)
\(594\) 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 0.743566 0.668662i \(-0.233133\pi\)
−0.950862 + 0.309616i \(0.899799\pi\)
\(600\) 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 −0.357592 + 0.933878i \(0.616402\pi\)
−0.629966 + 0.776623i \(0.716931\pi\)
\(608\) −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 −0.969697 0.244312i \(-0.921438\pi\)
0.273267 0.961938i \(-0.411896\pi\)
\(614\) 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 0.862721 + 0.505680i \(0.168758\pi\)
0.00657132 + 0.999978i \(0.497908\pi\)
\(620\) −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 0.973395 0.229132i \(-0.0735888\pi\)
−0.685132 + 0.728419i \(0.740256\pi\)
\(642\) 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 0.897392 + 0.441234i \(0.145459\pi\)
−0.0665758 + 0.997781i \(0.521207\pi\)
\(648\) 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 −0.747942 0.663764i \(-0.768958\pi\)
0.948808 + 0.315854i \(0.102291\pi\)
\(654\) 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 0.997534 + 0.0701787i \(0.0223570\pi\)
−0.437991 + 0.898980i \(0.644310\pi\)
\(662\) 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 −0.707273 0.706941i \(-0.750075\pi\)
0.965865 + 0.259046i \(0.0834081\pi\)
\(678\) 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 −0.997143 0.0755422i \(-0.975931\pi\)
0.433150 0.901322i \(-0.357402\pi\)
\(684\) 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 −0.00464517 0.999989i \(-0.501479\pi\)
0.868339 0.495972i \(-0.165188\pi\)
\(692\) −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 −0.977428 0.211271i \(-0.932240\pi\)
0.671680 + 0.740842i \(0.265573\pi\)
\(710\) −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 −0.840608 0.541645i \(-0.817802\pi\)
0.889382 + 0.457165i \(0.151135\pi\)
\(720\) 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 0.246451 + 0.969155i \(0.420736\pi\)
−0.962539 + 0.271145i \(0.912598\pi\)
\(734\) 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 0.768825 0.639460i \(-0.220842\pi\)
−0.938201 + 0.346092i \(0.887509\pi\)
\(740\) −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 −0.998030 0.0627375i \(-0.980017\pi\)
0.553347 + 0.832951i \(0.313350\pi\)
\(752\) 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 0.411641 + 0.911346i \(0.364956\pi\)
−0.995069 + 0.0991813i \(0.968378\pi\)
\(762\) 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 0.899115 + 0.437711i \(0.144211\pi\)
−0.0704885 + 0.997513i \(0.522456\pi\)
\(774\) 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