Properties

Label 128.3.h.a.47.3
Level $128$
Weight $3$
Character 128.47
Analytic conductor $3.488$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 128.h (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.48774738381\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 47.3
Character \(\chi\) \(=\) 128.47
Dual form 128.3.h.a.79.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.527719 + 1.27403i) q^{3} +(-0.642823 - 1.55191i) q^{5} +(4.95044 + 4.95044i) q^{7} +(5.01930 + 5.01930i) q^{9} +O(q^{10})\) \(q+(-0.527719 + 1.27403i) q^{3} +(-0.642823 - 1.55191i) q^{5} +(4.95044 + 4.95044i) q^{7} +(5.01930 + 5.01930i) q^{9} +(4.27221 + 10.3140i) q^{11} +(1.68327 - 4.06379i) q^{13} +2.31641 q^{15} +28.6469i q^{17} +(-17.5460 - 7.26778i) q^{19} +(-8.91944 + 3.69455i) q^{21} +(24.3334 - 24.3334i) q^{23} +(15.6825 - 15.6825i) q^{25} +(-20.5098 + 8.49542i) q^{27} +(8.57286 + 3.55100i) q^{29} -5.73273i q^{31} -15.3949 q^{33} +(4.50039 - 10.8649i) q^{35} +(-26.1364 - 63.0989i) q^{37} +(4.28908 + 4.28908i) q^{39} +(-14.2561 - 14.2561i) q^{41} +(10.1365 + 24.4717i) q^{43} +(4.56299 - 11.0160i) q^{45} -57.9804 q^{47} +0.0137567i q^{49} +(-36.4969 - 15.1175i) q^{51} +(-46.3830 + 19.2124i) q^{53} +(13.2602 - 13.2602i) q^{55} +(18.5187 - 18.5187i) q^{57} +(27.6347 - 11.4467i) q^{59} +(76.3985 + 31.6453i) q^{61} +49.6955i q^{63} -7.38868 q^{65} +(36.1949 - 87.3821i) q^{67} +(18.1602 + 43.8425i) q^{69} +(5.39666 + 5.39666i) q^{71} +(-25.4031 - 25.4031i) q^{73} +(11.7039 + 28.2558i) q^{75} +(-29.9097 + 72.2084i) q^{77} -50.1674 q^{79} +33.2721i q^{81} +(100.805 + 41.7550i) q^{83} +(44.4574 - 18.4149i) q^{85} +(-9.04814 + 9.04814i) q^{87} +(10.6266 - 10.6266i) q^{89} +(28.4505 - 11.7846i) q^{91} +(7.30366 + 3.02527i) q^{93} +31.9017i q^{95} -14.3055 q^{97} +(-30.3257 + 73.2128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.527719 + 1.27403i −0.175906 + 0.424676i −0.987101 0.160101i \(-0.948818\pi\)
0.811194 + 0.584777i \(0.198818\pi\)
\(4\) 0 0
\(5\) −0.642823 1.55191i −0.128565 0.310382i 0.846470 0.532437i \(-0.178724\pi\)
−0.975034 + 0.222055i \(0.928724\pi\)
\(6\) 0 0
\(7\) 4.95044 + 4.95044i 0.707206 + 0.707206i 0.965947 0.258741i \(-0.0833075\pi\)
−0.258741 + 0.965947i \(0.583308\pi\)
\(8\) 0 0
\(9\) 5.01930 + 5.01930i 0.557700 + 0.557700i
\(10\) 0 0
\(11\) 4.27221 + 10.3140i 0.388383 + 0.937640i 0.990283 + 0.139068i \(0.0444106\pi\)
−0.601900 + 0.798572i \(0.705589\pi\)
\(12\) 0 0
\(13\) 1.68327 4.06379i 0.129483 0.312599i −0.845821 0.533467i \(-0.820889\pi\)
0.975304 + 0.220868i \(0.0708890\pi\)
\(14\) 0 0
\(15\) 2.31641 0.154427
\(16\) 0 0
\(17\) 28.6469i 1.68511i 0.538609 + 0.842556i \(0.318950\pi\)
−0.538609 + 0.842556i \(0.681050\pi\)
\(18\) 0 0
\(19\) −17.5460 7.26778i −0.923473 0.382515i −0.130274 0.991478i \(-0.541586\pi\)
−0.793199 + 0.608963i \(0.791586\pi\)
\(20\) 0 0
\(21\) −8.91944 + 3.69455i −0.424735 + 0.175931i
\(22\) 0 0
\(23\) 24.3334 24.3334i 1.05797 1.05797i 0.0597590 0.998213i \(-0.480967\pi\)
0.998213 0.0597590i \(-0.0190332\pi\)
\(24\) 0 0
\(25\) 15.6825 15.6825i 0.627298 0.627298i
\(26\) 0 0
\(27\) −20.5098 + 8.49542i −0.759621 + 0.314645i
\(28\) 0 0
\(29\) 8.57286 + 3.55100i 0.295616 + 0.122448i 0.525562 0.850755i \(-0.323855\pi\)
−0.229946 + 0.973203i \(0.573855\pi\)
\(30\) 0 0
\(31\) 5.73273i 0.184927i −0.995716 0.0924634i \(-0.970526\pi\)
0.995716 0.0924634i \(-0.0294741\pi\)
\(32\) 0 0
\(33\) −15.3949 −0.466512
\(34\) 0 0
\(35\) 4.50039 10.8649i 0.128583 0.310426i
\(36\) 0 0
\(37\) −26.1364 63.0989i −0.706390 1.70538i −0.708831 0.705379i \(-0.750777\pi\)
0.00244114 0.999997i \(-0.499223\pi\)
\(38\) 0 0
\(39\) 4.28908 + 4.28908i 0.109976 + 0.109976i
\(40\) 0 0
\(41\) −14.2561 14.2561i −0.347711 0.347711i 0.511545 0.859256i \(-0.329073\pi\)
−0.859256 + 0.511545i \(0.829073\pi\)
\(42\) 0 0
\(43\) 10.1365 + 24.4717i 0.235733 + 0.569109i 0.996833 0.0795253i \(-0.0253404\pi\)
−0.761100 + 0.648634i \(0.775340\pi\)
\(44\) 0 0
\(45\) 4.56299 11.0160i 0.101400 0.244801i
\(46\) 0 0
\(47\) −57.9804 −1.23363 −0.616813 0.787110i \(-0.711576\pi\)
−0.616813 + 0.787110i \(0.711576\pi\)
\(48\) 0 0
\(49\) 0.0137567i 0.000280749i
\(50\) 0 0
\(51\) −36.4969 15.1175i −0.715626 0.296422i
\(52\) 0 0
\(53\) −46.3830 + 19.2124i −0.875150 + 0.362499i −0.774614 0.632434i \(-0.782056\pi\)
−0.100536 + 0.994933i \(0.532056\pi\)
\(54\) 0 0
\(55\) 13.2602 13.2602i 0.241094 0.241094i
\(56\) 0 0
\(57\) 18.5187 18.5187i 0.324890 0.324890i
\(58\) 0 0
\(59\) 27.6347 11.4467i 0.468384 0.194011i −0.135992 0.990710i \(-0.543422\pi\)
0.604377 + 0.796699i \(0.293422\pi\)
\(60\) 0 0
\(61\) 76.3985 + 31.6453i 1.25243 + 0.518775i 0.907579 0.419881i \(-0.137928\pi\)
0.344855 + 0.938656i \(0.387928\pi\)
\(62\) 0 0
\(63\) 49.6955i 0.788818i
\(64\) 0 0
\(65\) −7.38868 −0.113672
\(66\) 0 0
\(67\) 36.1949 87.3821i 0.540222 1.30421i −0.384345 0.923190i \(-0.625573\pi\)
0.924566 0.381021i \(-0.124427\pi\)
\(68\) 0 0
\(69\) 18.1602 + 43.8425i 0.263191 + 0.635399i
\(70\) 0 0
\(71\) 5.39666 + 5.39666i 0.0760092 + 0.0760092i 0.744089 0.668080i \(-0.232884\pi\)
−0.668080 + 0.744089i \(0.732884\pi\)
\(72\) 0 0
\(73\) −25.4031 25.4031i −0.347988 0.347988i 0.511372 0.859360i \(-0.329137\pi\)
−0.859360 + 0.511372i \(0.829137\pi\)
\(74\) 0 0
\(75\) 11.7039 + 28.2558i 0.156053 + 0.376744i
\(76\) 0 0
\(77\) −29.9097 + 72.2084i −0.388438 + 0.937771i
\(78\) 0 0
\(79\) −50.1674 −0.635030 −0.317515 0.948253i \(-0.602848\pi\)
−0.317515 + 0.948253i \(0.602848\pi\)
\(80\) 0 0
\(81\) 33.2721i 0.410767i
\(82\) 0 0
\(83\) 100.805 + 41.7550i 1.21452 + 0.503072i 0.895665 0.444730i \(-0.146700\pi\)
0.318859 + 0.947802i \(0.396700\pi\)
\(84\) 0 0
\(85\) 44.4574 18.4149i 0.523029 0.216646i
\(86\) 0 0
\(87\) −9.04814 + 9.04814i −0.104002 + 0.104002i
\(88\) 0 0
\(89\) 10.6266 10.6266i 0.119400 0.119400i −0.644882 0.764282i \(-0.723094\pi\)
0.764282 + 0.644882i \(0.223094\pi\)
\(90\) 0 0
\(91\) 28.4505 11.7846i 0.312643 0.129501i
\(92\) 0 0
\(93\) 7.30366 + 3.02527i 0.0785339 + 0.0325298i
\(94\) 0 0
\(95\) 31.9017i 0.335807i
\(96\) 0 0
\(97\) −14.3055 −0.147479 −0.0737395 0.997278i \(-0.523493\pi\)
−0.0737395 + 0.997278i \(0.523493\pi\)
\(98\) 0 0
\(99\) −30.3257 + 73.2128i −0.306321 + 0.739523i
\(100\) 0 0
\(101\) 51.6638 + 124.728i 0.511523 + 1.23493i 0.942997 + 0.332801i \(0.107994\pi\)
−0.431474 + 0.902125i \(0.642006\pi\)
\(102\) 0 0
\(103\) −4.87593 4.87593i −0.0473392 0.0473392i 0.683041 0.730380i \(-0.260657\pi\)
−0.730380 + 0.683041i \(0.760657\pi\)
\(104\) 0 0
\(105\) 11.4672 + 11.4672i 0.109212 + 0.109212i
\(106\) 0 0
\(107\) 4.55603 + 10.9992i 0.0425797 + 0.102797i 0.943739 0.330692i \(-0.107282\pi\)
−0.901159 + 0.433489i \(0.857282\pi\)
\(108\) 0 0
\(109\) 11.0098 26.5800i 0.101007 0.243853i −0.865295 0.501263i \(-0.832869\pi\)
0.966302 + 0.257410i \(0.0828690\pi\)
\(110\) 0 0
\(111\) 94.1824 0.848490
\(112\) 0 0
\(113\) 120.275i 1.06438i −0.846624 0.532191i \(-0.821369\pi\)
0.846624 0.532191i \(-0.178631\pi\)
\(114\) 0 0
\(115\) −53.4052 22.1212i −0.464393 0.192358i
\(116\) 0 0
\(117\) 28.8462 11.9485i 0.246549 0.102124i
\(118\) 0 0
\(119\) −141.815 + 141.815i −1.19172 + 1.19172i
\(120\) 0 0
\(121\) −2.56759 + 2.56759i −0.0212197 + 0.0212197i
\(122\) 0 0
\(123\) 25.6860 10.6395i 0.208829 0.0864998i
\(124\) 0 0
\(125\) −73.2166 30.3273i −0.585733 0.242619i
\(126\) 0 0
\(127\) 128.040i 1.00819i −0.863648 0.504095i \(-0.831826\pi\)
0.863648 0.504095i \(-0.168174\pi\)
\(128\) 0 0
\(129\) −36.5268 −0.283154
\(130\) 0 0
\(131\) −20.1358 + 48.6121i −0.153708 + 0.371084i −0.981911 0.189345i \(-0.939364\pi\)
0.828203 + 0.560429i \(0.189364\pi\)
\(132\) 0 0
\(133\) −50.8816 122.839i −0.382569 0.923602i
\(134\) 0 0
\(135\) 26.3683 + 26.3683i 0.195321 + 0.195321i
\(136\) 0 0
\(137\) −1.66083 1.66083i −0.0121228 0.0121228i 0.701019 0.713142i \(-0.252729\pi\)
−0.713142 + 0.701019i \(0.752729\pi\)
\(138\) 0 0
\(139\) −75.6997 182.755i −0.544602 1.31479i −0.921445 0.388508i \(-0.872991\pi\)
0.376843 0.926277i \(-0.377009\pi\)
\(140\) 0 0
\(141\) 30.5974 73.8686i 0.217003 0.523891i
\(142\) 0 0
\(143\) 49.1053 0.343394
\(144\) 0 0
\(145\) 15.5870i 0.107496i
\(146\) 0 0
\(147\) −0.0175264 0.00725967i −0.000119227 4.93855e-5i
\(148\) 0 0
\(149\) −16.1203 + 6.67724i −0.108190 + 0.0448137i −0.436122 0.899888i \(-0.643648\pi\)
0.327932 + 0.944701i \(0.393648\pi\)
\(150\) 0 0
\(151\) 127.344 127.344i 0.843335 0.843335i −0.145956 0.989291i \(-0.546626\pi\)
0.989291 + 0.145956i \(0.0466258\pi\)
\(152\) 0 0
\(153\) −143.787 + 143.787i −0.939787 + 0.939787i
\(154\) 0 0
\(155\) −8.89669 + 3.68513i −0.0573980 + 0.0237750i
\(156\) 0 0
\(157\) −236.255 97.8598i −1.50481 0.623311i −0.530328 0.847793i \(-0.677931\pi\)
−0.974478 + 0.224482i \(0.927931\pi\)
\(158\) 0 0
\(159\) 69.2319i 0.435421i
\(160\) 0 0
\(161\) 240.922 1.49641
\(162\) 0 0
\(163\) −38.0947 + 91.9687i −0.233710 + 0.564225i −0.996608 0.0822932i \(-0.973776\pi\)
0.762898 + 0.646518i \(0.223776\pi\)
\(164\) 0 0
\(165\) 9.89619 + 23.8915i 0.0599769 + 0.144797i
\(166\) 0 0
\(167\) −223.831 223.831i −1.34031 1.34031i −0.895750 0.444558i \(-0.853361\pi\)
−0.444558 0.895750i \(-0.646639\pi\)
\(168\) 0 0
\(169\) 105.820 + 105.820i 0.626154 + 0.626154i
\(170\) 0 0
\(171\) −51.5894 124.548i −0.301692 0.728350i
\(172\) 0 0
\(173\) 13.2654 32.0254i 0.0766784 0.185118i −0.880892 0.473317i \(-0.843056\pi\)
0.957571 + 0.288199i \(0.0930565\pi\)
\(174\) 0 0
\(175\) 155.270 0.887259
\(176\) 0 0
\(177\) 41.2480i 0.233039i
\(178\) 0 0
\(179\) 13.8305 + 5.72877i 0.0772652 + 0.0320043i 0.420981 0.907069i \(-0.361686\pi\)
−0.343716 + 0.939074i \(0.611686\pi\)
\(180\) 0 0
\(181\) 153.596 63.6217i 0.848599 0.351501i 0.0843605 0.996435i \(-0.473115\pi\)
0.764238 + 0.644934i \(0.223115\pi\)
\(182\) 0 0
\(183\) −80.6339 + 80.6339i −0.440623 + 0.440623i
\(184\) 0 0
\(185\) −81.1228 + 81.1228i −0.438502 + 0.438502i
\(186\) 0 0
\(187\) −295.465 + 122.386i −1.58003 + 0.654469i
\(188\) 0 0
\(189\) −143.588 59.4763i −0.759727 0.314689i
\(190\) 0 0
\(191\) 2.00135i 0.0104783i 0.999986 + 0.00523914i \(0.00166768\pi\)
−0.999986 + 0.00523914i \(0.998332\pi\)
\(192\) 0 0
\(193\) −107.502 −0.557003 −0.278502 0.960436i \(-0.589838\pi\)
−0.278502 + 0.960436i \(0.589838\pi\)
\(194\) 0 0
\(195\) 3.89915 9.41338i 0.0199956 0.0482738i
\(196\) 0 0
\(197\) 35.9828 + 86.8701i 0.182654 + 0.440965i 0.988512 0.151144i \(-0.0482956\pi\)
−0.805858 + 0.592109i \(0.798296\pi\)
\(198\) 0 0
\(199\) 228.742 + 228.742i 1.14946 + 1.14946i 0.986659 + 0.162799i \(0.0520521\pi\)
0.162799 + 0.986659i \(0.447948\pi\)
\(200\) 0 0
\(201\) 92.2265 + 92.2265i 0.458838 + 0.458838i
\(202\) 0 0
\(203\) 24.8605 + 60.0185i 0.122465 + 0.295658i
\(204\) 0 0
\(205\) −12.9601 + 31.2885i −0.0632200 + 0.152627i
\(206\) 0 0
\(207\) 244.273 1.18006
\(208\) 0 0
\(209\) 212.019i 1.01445i
\(210\) 0 0
\(211\) 244.800 + 101.400i 1.16019 + 0.480567i 0.877938 0.478773i \(-0.158918\pi\)
0.282252 + 0.959340i \(0.408918\pi\)
\(212\) 0 0
\(213\) −9.72341 + 4.02757i −0.0456498 + 0.0189088i
\(214\) 0 0
\(215\) 31.4619 31.4619i 0.146335 0.146335i
\(216\) 0 0
\(217\) 28.3796 28.3796i 0.130781 0.130781i
\(218\) 0 0
\(219\) 45.7700 18.9585i 0.208995 0.0865687i
\(220\) 0 0
\(221\) 116.415 + 48.2206i 0.526764 + 0.218193i
\(222\) 0 0
\(223\) 110.575i 0.495853i 0.968779 + 0.247927i \(0.0797492\pi\)
−0.968779 + 0.247927i \(0.920251\pi\)
\(224\) 0 0
\(225\) 157.430 0.699689
\(226\) 0 0
\(227\) −153.333 + 370.178i −0.675475 + 1.63074i 0.0966861 + 0.995315i \(0.469176\pi\)
−0.772161 + 0.635427i \(0.780824\pi\)
\(228\) 0 0
\(229\) −24.0559 58.0760i −0.105047 0.253607i 0.862612 0.505865i \(-0.168827\pi\)
−0.967660 + 0.252258i \(0.918827\pi\)
\(230\) 0 0
\(231\) −76.2115 76.2115i −0.329920 0.329920i
\(232\) 0 0
\(233\) −104.978 104.978i −0.450547 0.450547i 0.444989 0.895536i \(-0.353208\pi\)
−0.895536 + 0.444989i \(0.853208\pi\)
\(234\) 0 0
\(235\) 37.2711 + 89.9804i 0.158600 + 0.382895i
\(236\) 0 0
\(237\) 26.4743 63.9146i 0.111706 0.269682i
\(238\) 0 0
\(239\) −122.643 −0.513151 −0.256576 0.966524i \(-0.582594\pi\)
−0.256576 + 0.966524i \(0.582594\pi\)
\(240\) 0 0
\(241\) 188.784i 0.783335i 0.920107 + 0.391668i \(0.128102\pi\)
−0.920107 + 0.391668i \(0.871898\pi\)
\(242\) 0 0
\(243\) −226.977 94.0171i −0.934063 0.386902i
\(244\) 0 0
\(245\) 0.0213492 0.00884311i 8.71395e−5 3.60943e-5i
\(246\) 0 0
\(247\) −59.0694 + 59.0694i −0.239147 + 0.239147i
\(248\) 0 0
\(249\) −106.394 + 106.394i −0.427285 + 0.427285i
\(250\) 0 0
\(251\) 355.365 147.197i 1.41580 0.586443i 0.461997 0.886881i \(-0.347133\pi\)
0.953801 + 0.300439i \(0.0971330\pi\)
\(252\) 0 0
\(253\) 354.932 + 147.018i 1.40289 + 0.581098i
\(254\) 0 0
\(255\) 66.3579i 0.260227i
\(256\) 0 0
\(257\) 84.4316 0.328528 0.164264 0.986416i \(-0.447475\pi\)
0.164264 + 0.986416i \(0.447475\pi\)
\(258\) 0 0
\(259\) 182.981 441.754i 0.706489 1.70561i
\(260\) 0 0
\(261\) 25.2063 + 60.8533i 0.0965758 + 0.233155i
\(262\) 0 0
\(263\) 37.2079 + 37.2079i 0.141475 + 0.141475i 0.774297 0.632822i \(-0.218104\pi\)
−0.632822 + 0.774297i \(0.718104\pi\)
\(264\) 0 0
\(265\) 59.6320 + 59.6320i 0.225027 + 0.225027i
\(266\) 0 0
\(267\) 7.93072 + 19.1464i 0.0297031 + 0.0717095i
\(268\) 0 0
\(269\) −90.5201 + 218.535i −0.336506 + 0.812398i 0.661540 + 0.749910i \(0.269903\pi\)
−0.998046 + 0.0624874i \(0.980097\pi\)
\(270\) 0 0
\(271\) −312.612 −1.15355 −0.576775 0.816903i \(-0.695689\pi\)
−0.576775 + 0.816903i \(0.695689\pi\)
\(272\) 0 0
\(273\) 42.4657i 0.155552i
\(274\) 0 0
\(275\) 228.748 + 94.7506i 0.831812 + 0.344548i
\(276\) 0 0
\(277\) −199.434 + 82.6083i −0.719978 + 0.298225i −0.712426 0.701747i \(-0.752404\pi\)
−0.00755172 + 0.999971i \(0.502404\pi\)
\(278\) 0 0
\(279\) 28.7743 28.7743i 0.103134 0.103134i
\(280\) 0 0
\(281\) 237.700 237.700i 0.845909 0.845909i −0.143711 0.989620i \(-0.545904\pi\)
0.989620 + 0.143711i \(0.0459036\pi\)
\(282\) 0 0
\(283\) −58.7408 + 24.3312i −0.207565 + 0.0859761i −0.484044 0.875044i \(-0.660832\pi\)
0.276479 + 0.961020i \(0.410832\pi\)
\(284\) 0 0
\(285\) −40.6436 16.8351i −0.142609 0.0590707i
\(286\) 0 0
\(287\) 141.148i 0.491807i
\(288\) 0 0
\(289\) −531.645 −1.83960
\(290\) 0 0
\(291\) 7.54927 18.2256i 0.0259425 0.0626308i
\(292\) 0 0
\(293\) 47.5607 + 114.822i 0.162323 + 0.391883i 0.984024 0.178036i \(-0.0569745\pi\)
−0.821701 + 0.569919i \(0.806974\pi\)
\(294\) 0 0
\(295\) −35.5284 35.5284i −0.120435 0.120435i
\(296\) 0 0
\(297\) −175.244 175.244i −0.590048 0.590048i
\(298\) 0 0
\(299\) −57.9258 139.845i −0.193732 0.467710i
\(300\) 0 0
\(301\) −70.9655 + 171.326i −0.235766 + 0.569189i
\(302\) 0 0
\(303\) −186.170 −0.614423
\(304\) 0 0
\(305\) 138.906i 0.455429i
\(306\) 0 0
\(307\) −407.254 168.690i −1.32656 0.549480i −0.396889 0.917867i \(-0.629910\pi\)
−0.929673 + 0.368387i \(0.879910\pi\)
\(308\) 0 0
\(309\) 8.78520 3.63895i 0.0284311 0.0117765i
\(310\) 0 0
\(311\) −149.458 + 149.458i −0.480572 + 0.480572i −0.905314 0.424742i \(-0.860365\pi\)
0.424742 + 0.905314i \(0.360365\pi\)
\(312\) 0 0
\(313\) 295.452 295.452i 0.943937 0.943937i −0.0545726 0.998510i \(-0.517380\pi\)
0.998510 + 0.0545726i \(0.0173796\pi\)
\(314\) 0 0
\(315\) 77.1231 31.9454i 0.244835 0.101414i
\(316\) 0 0
\(317\) −222.852 92.3084i −0.703004 0.291194i 0.00240221 0.999997i \(-0.499235\pi\)
−0.705406 + 0.708803i \(0.749235\pi\)
\(318\) 0 0
\(319\) 103.591i 0.324738i
\(320\) 0 0
\(321\) −16.4176 −0.0511453
\(322\) 0 0
\(323\) 208.199 502.638i 0.644580 1.55615i
\(324\) 0 0
\(325\) −37.3323 90.1281i −0.114868 0.277317i
\(326\) 0 0
\(327\) 28.0535 + 28.0535i 0.0857906 + 0.0857906i
\(328\) 0 0
\(329\) −287.029 287.029i −0.872427 0.872427i
\(330\) 0 0
\(331\) 200.624 + 484.350i 0.606115 + 1.46329i 0.867192 + 0.497974i \(0.165923\pi\)
−0.261076 + 0.965318i \(0.584077\pi\)
\(332\) 0 0
\(333\) 185.526 447.899i 0.557135 1.34504i
\(334\) 0 0
\(335\) −158.876 −0.474257
\(336\) 0 0
\(337\) 248.089i 0.736169i 0.929792 + 0.368085i \(0.119986\pi\)
−0.929792 + 0.368085i \(0.880014\pi\)
\(338\) 0 0
\(339\) 153.234 + 63.4715i 0.452017 + 0.187232i
\(340\) 0 0
\(341\) 59.1276 24.4914i 0.173395 0.0718224i
\(342\) 0 0
\(343\) 242.504 242.504i 0.707007 0.707007i
\(344\) 0 0
\(345\) 56.3660 56.3660i 0.163380 0.163380i
\(346\) 0 0
\(347\) 101.462 42.0270i 0.292398 0.121115i −0.231662 0.972796i \(-0.574416\pi\)
0.524061 + 0.851681i \(0.324416\pi\)
\(348\) 0 0
\(349\) 489.895 + 202.921i 1.40371 + 0.581436i 0.950712 0.310076i \(-0.100354\pi\)
0.452998 + 0.891512i \(0.350354\pi\)
\(350\) 0 0
\(351\) 97.6474i 0.278198i
\(352\) 0 0
\(353\) −185.627 −0.525856 −0.262928 0.964815i \(-0.584688\pi\)
−0.262928 + 0.964815i \(0.584688\pi\)
\(354\) 0 0
\(355\) 4.90604 11.8442i 0.0138198 0.0333640i
\(356\) 0 0
\(357\) −105.838 255.514i −0.296464 0.715727i
\(358\) 0 0
\(359\) −222.847 222.847i −0.620743 0.620743i 0.324978 0.945722i \(-0.394643\pi\)
−0.945722 + 0.324978i \(0.894643\pi\)
\(360\) 0 0
\(361\) −0.224842 0.224842i −0.000622830 0.000622830i
\(362\) 0 0
\(363\) −1.91621 4.62614i −0.00527882 0.0127442i
\(364\) 0 0
\(365\) −23.0937 + 55.7530i −0.0632703 + 0.152748i
\(366\) 0 0
\(367\) −532.771 −1.45169 −0.725846 0.687857i \(-0.758552\pi\)
−0.725846 + 0.687857i \(0.758552\pi\)
\(368\) 0 0
\(369\) 143.112i 0.387837i
\(370\) 0 0
\(371\) −324.726 134.506i −0.875273 0.362550i
\(372\) 0 0
\(373\) −277.629 + 114.998i −0.744313 + 0.308305i −0.722419 0.691456i \(-0.756970\pi\)
−0.0218944 + 0.999760i \(0.506970\pi\)
\(374\) 0 0
\(375\) 77.2757 77.2757i 0.206068 0.206068i
\(376\) 0 0
\(377\) 28.8610 28.8610i 0.0765543 0.0765543i
\(378\) 0 0
\(379\) −306.344 + 126.892i −0.808296 + 0.334807i −0.748274 0.663390i \(-0.769117\pi\)
−0.0600223 + 0.998197i \(0.519117\pi\)
\(380\) 0 0
\(381\) 163.127 + 67.5692i 0.428154 + 0.177347i
\(382\) 0 0
\(383\) 163.336i 0.426465i 0.977001 + 0.213233i \(0.0683992\pi\)
−0.977001 + 0.213233i \(0.931601\pi\)
\(384\) 0 0
\(385\) 131.288 0.341007
\(386\) 0 0
\(387\) −71.9526 + 173.709i −0.185924 + 0.448861i
\(388\) 0 0
\(389\) −27.0717 65.3568i −0.0695930 0.168012i 0.885256 0.465104i \(-0.153983\pi\)
−0.954849 + 0.297092i \(0.903983\pi\)
\(390\) 0 0
\(391\) 697.075 + 697.075i 1.78280 + 1.78280i
\(392\) 0 0
\(393\) −51.3071 51.3071i −0.130552 0.130552i
\(394\) 0 0
\(395\) 32.2487 + 77.8553i 0.0816423 + 0.197102i
\(396\) 0 0
\(397\) −153.949 + 371.666i −0.387781 + 0.936187i 0.602628 + 0.798022i \(0.294120\pi\)
−0.990409 + 0.138165i \(0.955880\pi\)
\(398\) 0 0
\(399\) 183.352 0.459528
\(400\) 0 0
\(401\) 287.838i 0.717801i 0.933376 + 0.358900i \(0.116848\pi\)
−0.933376 + 0.358900i \(0.883152\pi\)
\(402\) 0 0
\(403\) −23.2966 9.64976i −0.0578079 0.0239448i
\(404\) 0 0
\(405\) 51.6353 21.3881i 0.127495 0.0528100i
\(406\) 0 0
\(407\) 539.144 539.144i 1.32468 1.32468i
\(408\) 0 0
\(409\) −134.641 + 134.641i −0.329195 + 0.329195i −0.852280 0.523085i \(-0.824781\pi\)
0.523085 + 0.852280i \(0.324781\pi\)
\(410\) 0 0
\(411\) 2.99239 1.23949i 0.00728076 0.00301579i
\(412\) 0 0
\(413\) 193.470 + 80.1378i 0.468450 + 0.194038i
\(414\) 0 0
\(415\) 183.282i 0.441644i
\(416\) 0 0
\(417\) 272.783 0.654156
\(418\) 0 0
\(419\) −94.1979 + 227.414i −0.224816 + 0.542754i −0.995532 0.0944249i \(-0.969899\pi\)
0.770716 + 0.637179i \(0.219899\pi\)
\(420\) 0 0
\(421\) −151.850 366.598i −0.360689 0.870779i −0.995200 0.0978656i \(-0.968798\pi\)
0.634511 0.772914i \(-0.281202\pi\)
\(422\) 0 0
\(423\) −291.021 291.021i −0.687993 0.687993i
\(424\) 0 0
\(425\) 449.254 + 449.254i 1.05707 + 1.05707i
\(426\) 0 0
\(427\) 221.548 + 534.864i 0.518848 + 1.25261i
\(428\) 0 0
\(429\) −25.9138 + 62.5615i −0.0604052 + 0.145831i
\(430\) 0 0
\(431\) 691.406 1.60419 0.802095 0.597196i \(-0.203719\pi\)
0.802095 + 0.597196i \(0.203719\pi\)
\(432\) 0 0
\(433\) 580.011i 1.33952i 0.742579 + 0.669758i \(0.233602\pi\)
−0.742579 + 0.669758i \(0.766398\pi\)
\(434\) 0 0
\(435\) 19.8582 + 8.22556i 0.0456511 + 0.0189093i
\(436\) 0 0
\(437\) −603.802 + 250.103i −1.38170 + 0.572318i
\(438\) 0 0
\(439\) −411.067 + 411.067i −0.936371 + 0.936371i −0.998093 0.0617227i \(-0.980341\pi\)
0.0617227 + 0.998093i \(0.480341\pi\)
\(440\) 0 0
\(441\) −0.0690490 + 0.0690490i −0.000156574 + 0.000156574i
\(442\) 0 0
\(443\) 34.4767 14.2807i 0.0778256 0.0322364i −0.343431 0.939178i \(-0.611589\pi\)
0.421257 + 0.906941i \(0.361589\pi\)
\(444\) 0 0
\(445\) −23.3226 9.66052i −0.0524102 0.0217090i
\(446\) 0 0
\(447\) 24.0614i 0.0538286i
\(448\) 0 0
\(449\) 185.456 0.413043 0.206521 0.978442i \(-0.433786\pi\)
0.206521 + 0.978442i \(0.433786\pi\)
\(450\) 0 0
\(451\) 86.1331 207.944i 0.190982 0.461073i
\(452\) 0 0
\(453\) 95.0375 + 229.441i 0.209796 + 0.506492i
\(454\) 0 0
\(455\) −36.5772 36.5772i −0.0803895 0.0803895i
\(456\) 0 0
\(457\) 386.211 + 386.211i 0.845100 + 0.845100i 0.989517 0.144417i \(-0.0461306\pi\)
−0.144417 + 0.989517i \(0.546131\pi\)
\(458\) 0 0
\(459\) −243.367 587.541i −0.530212 1.28005i
\(460\) 0 0
\(461\) 268.824 648.999i 0.583133 1.40781i −0.306826 0.951766i \(-0.599267\pi\)
0.889958 0.456042i \(-0.150733\pi\)
\(462\) 0 0
\(463\) −49.4705 −0.106848 −0.0534238 0.998572i \(-0.517013\pi\)
−0.0534238 + 0.998572i \(0.517013\pi\)
\(464\) 0 0
\(465\) 13.2793i 0.0285577i
\(466\) 0 0
\(467\) 192.753 + 79.8411i 0.412748 + 0.170966i 0.579388 0.815052i \(-0.303292\pi\)
−0.166640 + 0.986018i \(0.553292\pi\)
\(468\) 0 0
\(469\) 611.761 253.400i 1.30439 0.540297i
\(470\) 0 0
\(471\) 249.352 249.352i 0.529410 0.529410i
\(472\) 0 0
\(473\) −209.097 + 209.097i −0.442065 + 0.442065i
\(474\) 0 0
\(475\) −389.141 + 161.187i −0.819244 + 0.339342i
\(476\) 0 0
\(477\) −329.243 136.377i −0.690237 0.285906i
\(478\) 0 0
\(479\) 256.988i 0.536509i 0.963348 + 0.268254i \(0.0864468\pi\)
−0.963348 + 0.268254i \(0.913553\pi\)
\(480\) 0 0
\(481\) −300.415 −0.624564
\(482\) 0 0
\(483\) −127.139 + 306.941i −0.263228 + 0.635488i
\(484\) 0 0
\(485\) 9.19588 + 22.2008i 0.0189606 + 0.0457749i
\(486\) 0 0
\(487\) 10.7898 + 10.7898i 0.0221557 + 0.0221557i 0.718098 0.695942i \(-0.245013\pi\)
−0.695942 + 0.718098i \(0.745013\pi\)
\(488\) 0 0
\(489\) −97.0673 97.0673i −0.198502 0.198502i
\(490\) 0 0
\(491\) −58.0314 140.100i −0.118190 0.285336i 0.853702 0.520761i \(-0.174352\pi\)
−0.971893 + 0.235425i \(0.924352\pi\)
\(492\) 0 0
\(493\) −101.725 + 245.586i −0.206339 + 0.498146i
\(494\) 0 0
\(495\) 133.114 0.268917
\(496\) 0 0
\(497\) 53.4317i 0.107508i
\(498\) 0 0
\(499\) 72.1133 + 29.8703i 0.144516 + 0.0598603i 0.453769 0.891119i \(-0.350079\pi\)
−0.309253 + 0.950980i \(0.600079\pi\)
\(500\) 0 0
\(501\) 403.288 167.047i 0.804965 0.333428i
\(502\) 0 0
\(503\) −151.600 + 151.600i −0.301393 + 0.301393i −0.841559 0.540166i \(-0.818361\pi\)
0.540166 + 0.841559i \(0.318361\pi\)
\(504\) 0 0
\(505\) 160.355 160.355i 0.317535 0.317535i
\(506\) 0 0
\(507\) −190.661 + 78.9744i −0.376057 + 0.155768i
\(508\) 0 0
\(509\) −562.711 233.082i −1.10552 0.457922i −0.246128 0.969237i \(-0.579158\pi\)
−0.859393 + 0.511315i \(0.829158\pi\)
\(510\) 0 0
\(511\) 251.513i 0.492198i
\(512\) 0 0
\(513\) 421.607 0.821845
\(514\) 0 0
\(515\) −4.43266 + 10.7014i −0.00860710 + 0.0207794i
\(516\) 0 0
\(517\) −247.705 598.012i −0.479119 1.15670i
\(518\) 0 0
\(519\) 33.8009 + 33.8009i 0.0651270 + 0.0651270i
\(520\) 0 0
\(521\) −224.985 224.985i −0.431833 0.431833i 0.457418 0.889252i \(-0.348774\pi\)
−0.889252 + 0.457418i \(0.848774\pi\)
\(522\) 0 0
\(523\) 9.30771 + 22.4708i 0.0177968 + 0.0429652i 0.932528 0.361097i \(-0.117598\pi\)
−0.914731 + 0.404063i \(0.867598\pi\)
\(524\) 0 0
\(525\) −81.9391 + 197.819i −0.156075 + 0.376797i
\(526\) 0 0
\(527\) 164.225 0.311622
\(528\) 0 0
\(529\) 655.224i 1.23861i
\(530\) 0 0
\(531\) 196.161 + 81.2525i 0.369418 + 0.153018i
\(532\) 0 0
\(533\) −81.9309 + 33.9369i −0.153717 + 0.0636715i
\(534\) 0 0
\(535\) 14.1411 14.1411i 0.0264320 0.0264320i
\(536\) 0 0
\(537\) −14.5972 + 14.5972i −0.0271829 + 0.0271829i
\(538\) 0 0
\(539\) −0.141887 + 0.0587715i −0.000263241 + 0.000109038i
\(540\) 0 0
\(541\) −357.866 148.233i −0.661490 0.273998i 0.0265752 0.999647i \(-0.491540\pi\)
−0.688066 + 0.725649i \(0.741540\pi\)
\(542\) 0 0
\(543\) 229.260i 0.422211i
\(544\) 0 0
\(545\) −48.3271 −0.0886735
\(546\) 0 0
\(547\) −187.175 + 451.879i −0.342184 + 0.826105i 0.655311 + 0.755360i \(0.272538\pi\)
−0.997494 + 0.0707454i \(0.977462\pi\)
\(548\) 0 0
\(549\) 224.630 + 542.304i 0.409162 + 0.987804i
\(550\) 0 0
\(551\) −124.611 124.611i −0.226155 0.226155i
\(552\) 0 0
\(553\) −248.351 248.351i −0.449097 0.449097i
\(554\) 0 0
\(555\) −60.5426 146.163i −0.109086 0.263356i
\(556\) 0 0
\(557\) 307.716 742.891i 0.552452 1.33374i −0.363181 0.931719i \(-0.618309\pi\)
0.915632 0.402017i \(-0.131691\pi\)
\(558\) 0 0
\(559\) 116.510 0.208426
\(560\) 0 0
\(561\) 441.016i 0.786125i
\(562\) 0 0
\(563\) −706.303 292.560i −1.25454 0.519646i −0.346307 0.938121i \(-0.612565\pi\)
−0.908228 + 0.418476i \(0.862565\pi\)
\(564\) 0 0
\(565\) −186.656 + 77.3156i −0.330365 + 0.136842i
\(566\) 0 0
\(567\) −164.712 + 164.712i −0.290497 + 0.290497i
\(568\) 0 0
\(569\) −552.550 + 552.550i −0.971089 + 0.971089i −0.999594 0.0285048i \(-0.990925\pi\)
0.0285048 + 0.999594i \(0.490925\pi\)
\(570\) 0 0
\(571\) 476.739 197.472i 0.834919 0.345835i 0.0760707 0.997102i \(-0.475763\pi\)
0.758848 + 0.651268i \(0.225763\pi\)
\(572\) 0 0
\(573\) −2.54978 1.05615i −0.00444988 0.00184320i
\(574\) 0 0
\(575\) 763.214i 1.32733i
\(576\) 0 0
\(577\) −188.090 −0.325980 −0.162990 0.986628i \(-0.552114\pi\)
−0.162990 + 0.986628i \(0.552114\pi\)
\(578\) 0 0
\(579\) 56.7307 136.960i 0.0979805 0.236546i
\(580\) 0 0
\(581\) 292.326 + 705.737i 0.503143 + 1.21469i
\(582\) 0 0
\(583\) −396.316 396.316i −0.679787 0.679787i
\(584\) 0 0
\(585\) −37.0860 37.0860i −0.0633949 0.0633949i
\(586\) 0 0
\(587\) −229.302 553.585i −0.390634 0.943075i −0.989802 0.142451i \(-0.954502\pi\)
0.599167 0.800624i \(-0.295498\pi\)
\(588\) 0 0
\(589\) −41.6642 + 100.586i −0.0707372 + 0.170775i
\(590\) 0 0
\(591\) −129.664 −0.219397
\(592\) 0 0
\(593\) 378.708i 0.638630i −0.947649 0.319315i \(-0.896547\pi\)
0.947649 0.319315i \(-0.103453\pi\)
\(594\) 0 0
\(595\) 311.246 + 128.922i 0.523102 + 0.216676i
\(596\) 0 0
\(597\) −412.135 + 170.712i −0.690344 + 0.285950i
\(598\) 0 0
\(599\) −745.316 + 745.316i −1.24427 + 1.24427i −0.286055 + 0.958213i \(0.592344\pi\)
−0.958213 + 0.286055i \(0.907656\pi\)
\(600\) 0 0
\(601\) 130.996 130.996i 0.217963 0.217963i −0.589676 0.807640i \(-0.700745\pi\)
0.807640 + 0.589676i \(0.200745\pi\)
\(602\) 0 0
\(603\) 620.270 256.924i 1.02864 0.426077i
\(604\) 0 0
\(605\) 5.63517 + 2.33416i 0.00931433 + 0.00385812i
\(606\) 0 0
\(607\) 732.344i 1.20650i −0.797553 0.603249i \(-0.793873\pi\)
0.797553 0.603249i \(-0.206127\pi\)
\(608\) 0 0
\(609\) −89.5845 −0.147101
\(610\) 0 0
\(611\) −97.5969 + 235.620i −0.159733 + 0.385630i
\(612\) 0 0
\(613\) 208.204 + 502.648i 0.339647 + 0.819981i 0.997749 + 0.0670521i \(0.0213594\pi\)
−0.658102 + 0.752928i \(0.728641\pi\)
\(614\) 0 0
\(615\) −33.0230 33.0230i −0.0536960 0.0536960i
\(616\) 0 0
\(617\) 209.834 + 209.834i 0.340087 + 0.340087i 0.856400 0.516313i \(-0.172696\pi\)
−0.516313 + 0.856400i \(0.672696\pi\)
\(618\) 0 0
\(619\) −175.433 423.533i −0.283414 0.684222i 0.716497 0.697590i \(-0.245744\pi\)
−0.999911 + 0.0133688i \(0.995744\pi\)
\(620\) 0 0
\(621\) −292.349 + 705.793i −0.470772 + 1.13654i
\(622\) 0 0
\(623\) 105.213 0.168881
\(624\) 0 0
\(625\) 421.338i 0.674141i
\(626\) 0 0
\(627\) 270.118 + 111.887i 0.430811 + 0.178448i
\(628\) 0 0
\(629\) 1807.59 748.727i 2.87375 1.19035i
\(630\) 0 0
\(631\) −232.756 + 232.756i −0.368868 + 0.368868i −0.867064 0.498196i \(-0.833996\pi\)
0.498196 + 0.867064i \(0.333996\pi\)
\(632\) 0 0
\(633\) −258.372 + 258.372i −0.408170 + 0.408170i
\(634\) 0 0
\(635\) −198.707 + 82.3071i −0.312924 + 0.129617i
\(636\) 0 0
\(637\) 0.0559042 + 0.0231563i 8.77618e−5 + 3.63521e-5i
\(638\) 0 0
\(639\) 54.1749i 0.0847807i
\(640\) 0 0
\(641\) −123.632 −0.192873 −0.0964366 0.995339i \(-0.530744\pi\)
−0.0964366 + 0.995339i \(0.530744\pi\)
\(642\) 0 0
\(643\) 351.513 848.628i 0.546677 1.31979i −0.373260 0.927727i \(-0.621760\pi\)
0.919936 0.392068i \(-0.128240\pi\)
\(644\) 0 0
\(645\) 23.4803 + 56.6864i 0.0364035 + 0.0878859i
\(646\) 0 0
\(647\) 191.561 + 191.561i 0.296076 + 0.296076i 0.839475 0.543399i \(-0.182863\pi\)
−0.543399 + 0.839475i \(0.682863\pi\)
\(648\) 0 0
\(649\) 236.122 + 236.122i 0.363825 + 0.363825i
\(650\) 0 0
\(651\) 21.1799 + 51.1328i 0.0325344 + 0.0785450i
\(652\) 0 0
\(653\) −89.1964 + 215.339i −0.136595 + 0.329769i −0.977344 0.211655i \(-0.932115\pi\)
0.840750 + 0.541424i \(0.182115\pi\)
\(654\) 0 0
\(655\) 88.3853 0.134939
\(656\) 0 0
\(657\) 255.012i 0.388146i
\(658\) 0 0
\(659\) 911.099 + 377.389i 1.38255 + 0.572670i 0.945161 0.326604i \(-0.105904\pi\)
0.437386 + 0.899274i \(0.355904\pi\)
\(660\) 0 0
\(661\) −496.993 + 205.861i −0.751880 + 0.311439i −0.725509 0.688213i \(-0.758395\pi\)
−0.0263718 + 0.999652i \(0.508395\pi\)
\(662\) 0 0
\(663\) −122.869 + 122.869i −0.185322 + 0.185322i
\(664\) 0 0
\(665\) −157.928 + 157.928i −0.237485 + 0.237485i
\(666\) 0 0
\(667\) 295.014 122.199i 0.442300 0.183207i
\(668\) 0 0
\(669\) −140.876 58.3527i −0.210577 0.0872238i
\(670\) 0 0
\(671\) 923.172i 1.37582i
\(672\) 0 0
\(673\) 374.150 0.555944 0.277972 0.960589i \(-0.410338\pi\)
0.277972 + 0.960589i \(0.410338\pi\)
\(674\) 0 0
\(675\) −188.414 + 454.873i −0.279132 + 0.673885i
\(676\) 0 0
\(677\) 12.3571 + 29.8326i 0.0182527 + 0.0440659i 0.932743 0.360542i \(-0.117408\pi\)
−0.914490 + 0.404608i \(0.867408\pi\)
\(678\) 0 0
\(679\) −70.8184 70.8184i −0.104298 0.104298i
\(680\) 0 0
\(681\) −390.701 390.701i −0.573716 0.573716i
\(682\) 0 0
\(683\) −22.0894 53.3285i −0.0323417 0.0780799i 0.906883 0.421382i \(-0.138455\pi\)
−0.939225 + 0.343302i \(0.888455\pi\)
\(684\) 0 0
\(685\) −1.50984 + 3.64508i −0.00220415 + 0.00532128i
\(686\) 0 0
\(687\) 86.6852 0.126179
\(688\) 0 0
\(689\) 220.830i 0.320508i
\(690\) 0 0
\(691\) 622.510 + 257.852i 0.900883 + 0.373158i 0.784560 0.620053i \(-0.212889\pi\)
0.116323 + 0.993211i \(0.462889\pi\)
\(692\) 0 0
\(693\) −512.562 + 212.310i −0.739627 + 0.306364i
\(694\) 0 0
\(695\) −234.958 + 234.958i −0.338069 + 0.338069i
\(696\) 0 0
\(697\) 408.394 408.394i 0.585932 0.585932i
\(698\) 0 0
\(699\) 189.143 78.3456i 0.270591 0.112082i
\(700\) 0 0
\(701\) −34.0835 14.1179i −0.0486213 0.0201396i 0.358240 0.933629i \(-0.383377\pi\)
−0.406862 + 0.913490i \(0.633377\pi\)
\(702\) 0 0
\(703\) 1297.09i 1.84507i
\(704\) 0 0
\(705\) −134.306 −0.190505
\(706\) 0 0
\(707\) −361.698 + 873.215i −0.511595 + 1.23510i
\(708\) 0 0
\(709\) 285.114 + 688.325i 0.402135 + 0.970840i 0.987147 + 0.159815i \(0.0510898\pi\)
−0.585012 + 0.811025i \(0.698910\pi\)
\(710\) 0 0
\(711\) −251.805 251.805i −0.354156 0.354156i
\(712\) 0 0
\(713\) −139.497 139.497i −0.195647 0.195647i
\(714\) 0 0
\(715\) −31.5660 76.2071i −0.0441483 0.106583i
\(716\) 0 0
\(717\) 64.7212 156.251i 0.0902666 0.217923i
\(718\) 0 0
\(719\) 478.037 0.664863 0.332432 0.943127i \(-0.392131\pi\)
0.332432 + 0.943127i \(0.392131\pi\)
\(720\) 0 0
\(721\) 48.2761i 0.0669571i
\(722\) 0 0
\(723\) −240.516 99.6249i −0.332664 0.137794i
\(724\) 0 0
\(725\) 190.132 78.7553i 0.262251 0.108628i
\(726\) 0 0
\(727\) 408.395 408.395i 0.561753 0.561753i −0.368052 0.929805i \(-0.619975\pi\)
0.929805 + 0.368052i \(0.119975\pi\)
\(728\) 0 0
\(729\) 27.8184 27.8184i 0.0381597 0.0381597i
\(730\) 0 0
\(731\) −701.038 + 290.379i −0.959012 + 0.397236i
\(732\) 0 0
\(733\) 747.573 + 309.655i 1.01988 + 0.422449i 0.829050 0.559174i \(-0.188882\pi\)
0.190831 + 0.981623i \(0.438882\pi\)
\(734\) 0 0
\(735\) 0.0318661i 4.33552e-5i
\(736\) 0 0
\(737\) 1055.89 1.43269
\(738\) 0 0
\(739\) 348.876 842.261i 0.472092 1.13973i −0.491145 0.871078i \(-0.663421\pi\)
0.963237 0.268653i \(-0.0865786\pi\)
\(740\) 0 0
\(741\) −44.0840 106.428i −0.0594925 0.143628i
\(742\) 0 0
\(743\) 345.072 + 345.072i 0.464430 + 0.464430i 0.900104 0.435674i \(-0.143490\pi\)
−0.435674 + 0.900104i \(0.643490\pi\)
\(744\) 0 0
\(745\) 20.7250 + 20.7250i 0.0278187 + 0.0278187i
\(746\) 0 0
\(747\) 296.392 + 715.554i 0.396777 + 0.957903i
\(748\) 0 0
\(749\) −31.8967 + 77.0054i −0.0425857 + 0.102811i
\(750\) 0 0
\(751\) −642.659 −0.855737 −0.427869 0.903841i \(-0.640735\pi\)
−0.427869 + 0.903841i \(0.640735\pi\)
\(752\) 0 0
\(753\) 530.424i 0.704414i
\(754\) 0 0
\(755\) −279.485 115.767i −0.370179 0.153333i
\(756\) 0 0
\(757\) 241.802 100.158i 0.319422 0.132309i −0.217211 0.976125i \(-0.569696\pi\)
0.536633 + 0.843816i \(0.319696\pi\)
\(758\) 0 0
\(759\) −374.609 + 374.609i −0.493556 + 0.493556i
\(760\) 0 0
\(761\) −253.025 + 253.025i −0.332490 + 0.332490i −0.853531 0.521042i \(-0.825544\pi\)
0.521042 + 0.853531i \(0.325544\pi\)
\(762\) 0 0
\(763\) 186.086 77.0793i 0.243887 0.101021i
\(764\) 0 0
\(765\) 315.575 + 130.716i 0.412517 + 0.170870i
\(766\) 0 0
\(767\) 131.569i 0.171537i
\(768\) 0 0
\(769\) −1066.22 −1.38650 −0.693248 0.720699i \(-0.743821\pi\)
−0.693248 + 0.720699i \(0.743821\pi\)
\(770\) 0 0
\(771\) −44.5562 + 107.568i −0.0577902 + 0.139518i
\(772\) 0 0
\(773\) −497.702 1201.56i −0.643857 1.55441i −0.821435 0.570302i \(-0.806826\pi\)
0.177578 0.984107i \(-0.443174\pi\)
\(774\) 0 0
\(775\) −89.9033 89.9033i −0.116004 0.116004i
\(776\) 0 0
\(777\) 466.245 + 466.245i 0.600057 + 0.600057i
\(778\) 0 0
\(779\) 146.527 + 353.749i 0.188097 + 0.454106i
\(780\) 0 0
\(781\) −32.6056 + 78.7170i −0.0417486 + 0.100790i
\(782\) 0 0
\(783\) −205.995 −0.263084
\(784\) 0 0
\(785\) 429.553i 0.547201i
\(786\) 0 0
\(787\) −307.578 127.403i −0.390823 0.161884i 0.178614 0.983919i \(-0.442839\pi\)
−0.569437 + 0.822035i \(0.692839\pi\)
\(788\) 0 0