Properties

Label 300.2.o.a.169.1
Level $300$
Weight $2$
Character 300.169
Analytic conductor $2.396$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.o (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 169.1
Character \(\chi\) \(=\) 300.169
Dual form 300.2.o.a.229.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.587785 - 0.809017i) q^{3} +(-1.74098 + 1.40321i) q^{5} +1.57893i q^{7} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.587785 - 0.809017i) q^{3} +(-1.74098 + 1.40321i) q^{5} +1.57893i q^{7} +(-0.309017 + 0.951057i) q^{9} +(1.19917 + 3.69066i) q^{11} +(0.326475 + 0.106078i) q^{13} +(2.15854 + 0.583692i) q^{15} +(-3.56817 + 4.91117i) q^{17} +(2.98680 + 2.17004i) q^{19} +(1.27738 - 0.928073i) q^{21} +(1.32236 - 0.429662i) q^{23} +(1.06200 - 4.88592i) q^{25} +(0.951057 - 0.309017i) q^{27} +(-2.69395 + 1.95727i) q^{29} +(4.25135 + 3.08879i) q^{31} +(2.28095 - 3.13946i) q^{33} +(-2.21557 - 2.74888i) q^{35} +(-8.14739 - 2.64725i) q^{37} +(-0.106078 - 0.326475i) q^{39} +(-0.394970 + 1.21559i) q^{41} -1.42438i q^{43} +(-0.796542 - 2.08938i) q^{45} +(0.220691 + 0.303755i) q^{47} +4.50698 q^{49} +6.07054 q^{51} +(-6.64151 - 9.14125i) q^{53} +(-7.26650 - 4.74266i) q^{55} -3.69189i q^{57} +(-3.57899 + 11.0150i) q^{59} +(-3.38909 - 10.4305i) q^{61} +(-1.50165 - 0.487917i) q^{63} +(-0.717236 + 0.273434i) q^{65} +(-6.14771 + 8.46160i) q^{67} +(-1.12487 - 0.817265i) q^{69} +(8.19220 - 5.95198i) q^{71} +(12.5444 - 4.07594i) q^{73} +(-4.57701 + 2.01270i) q^{75} +(-5.82730 + 1.89340i) q^{77} +(11.1640 - 8.11114i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(2.71826 - 3.74136i) q^{83} +(-0.679305 - 13.5571i) q^{85} +(3.16693 + 1.02900i) q^{87} +(2.24626 + 6.91326i) q^{89} +(-0.167490 + 0.515482i) q^{91} -5.25496i q^{93} +(-8.24497 + 0.413129i) q^{95} +(3.55938 + 4.89906i) q^{97} -3.88059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{5} + 6q^{9} + O(q^{10}) \) \( 24q - 2q^{5} + 6q^{9} - 6q^{11} + 4q^{15} + 10q^{17} + 10q^{19} - 4q^{21} + 40q^{23} - 4q^{25} + 4q^{29} + 6q^{31} + 10q^{33} - 6q^{35} - 10q^{41} + 2q^{45} - 40q^{47} - 56q^{49} + 16q^{51} - 60q^{53} - 62q^{55} - 36q^{59} - 12q^{61} - 10q^{63} + 20q^{67} + 4q^{69} + 40q^{71} + 60q^{73} + 8q^{75} - 40q^{77} + 8q^{79} - 6q^{81} - 50q^{83} + 34q^{85} - 20q^{87} - 30q^{91} - 60q^{95} - 40q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.587785 0.809017i −0.339358 0.467086i
\(4\) 0 0
\(5\) −1.74098 + 1.40321i −0.778588 + 0.627535i
\(6\) 0 0
\(7\) 1.57893i 0.596780i 0.954444 + 0.298390i \(0.0964496\pi\)
−0.954444 + 0.298390i \(0.903550\pi\)
\(8\) 0 0
\(9\) −0.309017 + 0.951057i −0.103006 + 0.317019i
\(10\) 0 0
\(11\) 1.19917 + 3.69066i 0.361563 + 1.11278i 0.952106 + 0.305769i \(0.0989136\pi\)
−0.590543 + 0.807006i \(0.701086\pi\)
\(12\) 0 0
\(13\) 0.326475 + 0.106078i 0.0905480 + 0.0294208i 0.353941 0.935268i \(-0.384841\pi\)
−0.263393 + 0.964689i \(0.584841\pi\)
\(14\) 0 0
\(15\) 2.15854 + 0.583692i 0.557333 + 0.150709i
\(16\) 0 0
\(17\) −3.56817 + 4.91117i −0.865409 + 1.19113i 0.114844 + 0.993384i \(0.463363\pi\)
−0.980253 + 0.197750i \(0.936637\pi\)
\(18\) 0 0
\(19\) 2.98680 + 2.17004i 0.685219 + 0.497841i 0.875085 0.483969i \(-0.160805\pi\)
−0.189866 + 0.981810i \(0.560805\pi\)
\(20\) 0 0
\(21\) 1.27738 0.928073i 0.278748 0.202522i
\(22\) 0 0
\(23\) 1.32236 0.429662i 0.275732 0.0895906i −0.167887 0.985806i \(-0.553694\pi\)
0.443619 + 0.896216i \(0.353694\pi\)
\(24\) 0 0
\(25\) 1.06200 4.88592i 0.212399 0.977183i
\(26\) 0 0
\(27\) 0.951057 0.309017i 0.183031 0.0594703i
\(28\) 0 0
\(29\) −2.69395 + 1.95727i −0.500254 + 0.363455i −0.809114 0.587652i \(-0.800052\pi\)
0.308860 + 0.951107i \(0.400052\pi\)
\(30\) 0 0
\(31\) 4.25135 + 3.08879i 0.763565 + 0.554763i 0.900002 0.435886i \(-0.143565\pi\)
−0.136437 + 0.990649i \(0.543565\pi\)
\(32\) 0 0
\(33\) 2.28095 3.13946i 0.397063 0.546510i
\(34\) 0 0
\(35\) −2.21557 2.74888i −0.374500 0.464646i
\(36\) 0 0
\(37\) −8.14739 2.64725i −1.33942 0.435205i −0.450301 0.892877i \(-0.648683\pi\)
−0.889121 + 0.457672i \(0.848683\pi\)
\(38\) 0 0
\(39\) −0.106078 0.326475i −0.0169861 0.0522779i
\(40\) 0 0
\(41\) −0.394970 + 1.21559i −0.0616839 + 0.189844i −0.977150 0.212552i \(-0.931822\pi\)
0.915466 + 0.402396i \(0.131822\pi\)
\(42\) 0 0
\(43\) 1.42438i 0.217216i −0.994085 0.108608i \(-0.965361\pi\)
0.994085 0.108608i \(-0.0346394\pi\)
\(44\) 0 0
\(45\) −0.796542 2.08938i −0.118742 0.311467i
\(46\) 0 0
\(47\) 0.220691 + 0.303755i 0.0321911 + 0.0443072i 0.824809 0.565411i \(-0.191283\pi\)
−0.792618 + 0.609718i \(0.791283\pi\)
\(48\) 0 0
\(49\) 4.50698 0.643854
\(50\) 0 0
\(51\) 6.07054 0.850045
\(52\) 0 0
\(53\) −6.64151 9.14125i −0.912282 1.25565i −0.966382 0.257112i \(-0.917229\pi\)
0.0540999 0.998536i \(-0.482771\pi\)
\(54\) 0 0
\(55\) −7.26650 4.74266i −0.979814 0.639500i
\(56\) 0 0
\(57\) 3.69189i 0.489002i
\(58\) 0 0
\(59\) −3.57899 + 11.0150i −0.465945 + 1.43403i 0.391846 + 0.920031i \(0.371837\pi\)
−0.857791 + 0.513999i \(0.828163\pi\)
\(60\) 0 0
\(61\) −3.38909 10.4305i −0.433928 1.33549i −0.894181 0.447706i \(-0.852241\pi\)
0.460252 0.887788i \(-0.347759\pi\)
\(62\) 0 0
\(63\) −1.50165 0.487917i −0.189190 0.0614717i
\(64\) 0 0
\(65\) −0.717236 + 0.273434i −0.0889622 + 0.0339154i
\(66\) 0 0
\(67\) −6.14771 + 8.46160i −0.751063 + 1.03375i 0.246842 + 0.969056i \(0.420607\pi\)
−0.997905 + 0.0646937i \(0.979393\pi\)
\(68\) 0 0
\(69\) −1.12487 0.817265i −0.135418 0.0983871i
\(70\) 0 0
\(71\) 8.19220 5.95198i 0.972235 0.706370i 0.0162750 0.999868i \(-0.494819\pi\)
0.955960 + 0.293498i \(0.0948193\pi\)
\(72\) 0 0
\(73\) 12.5444 4.07594i 1.46822 0.477052i 0.537648 0.843170i \(-0.319313\pi\)
0.930569 + 0.366117i \(0.119313\pi\)
\(74\) 0 0
\(75\) −4.57701 + 2.01270i −0.528508 + 0.232406i
\(76\) 0 0
\(77\) −5.82730 + 1.89340i −0.664082 + 0.215773i
\(78\) 0 0
\(79\) 11.1640 8.11114i 1.25605 0.912574i 0.257494 0.966280i \(-0.417103\pi\)
0.998557 + 0.0537055i \(0.0171032\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 0 0
\(83\) 2.71826 3.74136i 0.298367 0.410668i −0.633342 0.773872i \(-0.718317\pi\)
0.931709 + 0.363204i \(0.118317\pi\)
\(84\) 0 0
\(85\) −0.679305 13.5571i −0.0736809 1.47048i
\(86\) 0 0
\(87\) 3.16693 + 1.02900i 0.339530 + 0.110320i
\(88\) 0 0
\(89\) 2.24626 + 6.91326i 0.238103 + 0.732805i 0.996695 + 0.0812387i \(0.0258876\pi\)
−0.758592 + 0.651566i \(0.774112\pi\)
\(90\) 0 0
\(91\) −0.167490 + 0.515482i −0.0175578 + 0.0540372i
\(92\) 0 0
\(93\) 5.25496i 0.544914i
\(94\) 0 0
\(95\) −8.24497 + 0.413129i −0.845916 + 0.0423862i
\(96\) 0 0
\(97\) 3.55938 + 4.89906i 0.361400 + 0.497424i 0.950538 0.310608i \(-0.100533\pi\)
−0.589138 + 0.808032i \(0.700533\pi\)
\(98\) 0 0
\(99\) −3.88059 −0.390014
\(100\) 0 0
\(101\) 3.23036 0.321432 0.160716 0.987001i \(-0.448620\pi\)
0.160716 + 0.987001i \(0.448620\pi\)
\(102\) 0 0
\(103\) 4.52433 + 6.22721i 0.445796 + 0.613585i 0.971488 0.237090i \(-0.0761936\pi\)
−0.525692 + 0.850675i \(0.676194\pi\)
\(104\) 0 0
\(105\) −0.921610 + 3.40819i −0.0899399 + 0.332605i
\(106\) 0 0
\(107\) 18.0376i 1.74376i −0.489722 0.871878i \(-0.662902\pi\)
0.489722 0.871878i \(-0.337098\pi\)
\(108\) 0 0
\(109\) −5.16860 + 15.9073i −0.495062 + 1.52364i 0.321799 + 0.946808i \(0.395712\pi\)
−0.816861 + 0.576835i \(0.804288\pi\)
\(110\) 0 0
\(111\) 2.64725 + 8.14739i 0.251266 + 0.773316i
\(112\) 0 0
\(113\) 2.15793 + 0.701155i 0.203001 + 0.0659591i 0.408753 0.912645i \(-0.365964\pi\)
−0.205751 + 0.978604i \(0.565964\pi\)
\(114\) 0 0
\(115\) −1.69929 + 2.60358i −0.158460 + 0.242785i
\(116\) 0 0
\(117\) −0.201773 + 0.277717i −0.0186539 + 0.0256749i
\(118\) 0 0
\(119\) −7.75440 5.63390i −0.710845 0.516459i
\(120\) 0 0
\(121\) −3.28377 + 2.38580i −0.298524 + 0.216891i
\(122\) 0 0
\(123\) 1.21559 0.394970i 0.109606 0.0356132i
\(124\) 0 0
\(125\) 5.00706 + 9.99646i 0.447845 + 0.894111i
\(126\) 0 0
\(127\) −1.43348 + 0.465767i −0.127201 + 0.0413301i −0.371926 0.928262i \(-0.621302\pi\)
0.244725 + 0.969593i \(0.421302\pi\)
\(128\) 0 0
\(129\) −1.15235 + 0.837231i −0.101459 + 0.0737141i
\(130\) 0 0
\(131\) 12.8948 + 9.36859i 1.12662 + 0.818537i 0.985199 0.171412i \(-0.0548330\pi\)
0.141421 + 0.989950i \(0.454833\pi\)
\(132\) 0 0
\(133\) −3.42634 + 4.71595i −0.297101 + 0.408925i
\(134\) 0 0
\(135\) −1.22215 + 1.87252i −0.105186 + 0.161161i
\(136\) 0 0
\(137\) 5.17996 + 1.68307i 0.442554 + 0.143795i 0.521814 0.853059i \(-0.325256\pi\)
−0.0792596 + 0.996854i \(0.525256\pi\)
\(138\) 0 0
\(139\) 3.05409 + 9.39953i 0.259045 + 0.797258i 0.993006 + 0.118066i \(0.0376694\pi\)
−0.733961 + 0.679192i \(0.762331\pi\)
\(140\) 0 0
\(141\) 0.116024 0.357085i 0.00977099 0.0300720i
\(142\) 0 0
\(143\) 1.33211i 0.111397i
\(144\) 0 0
\(145\) 1.94364 7.18773i 0.161410 0.596909i
\(146\) 0 0
\(147\) −2.64913 3.64622i −0.218497 0.300735i
\(148\) 0 0
\(149\) −0.0649364 −0.00531979 −0.00265990 0.999996i \(-0.500847\pi\)
−0.00265990 + 0.999996i \(0.500847\pi\)
\(150\) 0 0
\(151\) −12.1221 −0.986481 −0.493240 0.869893i \(-0.664188\pi\)
−0.493240 + 0.869893i \(0.664188\pi\)
\(152\) 0 0
\(153\) −3.56817 4.91117i −0.288470 0.397044i
\(154\) 0 0
\(155\) −11.7357 + 0.588040i −0.942636 + 0.0472325i
\(156\) 0 0
\(157\) 23.4721i 1.87328i 0.350300 + 0.936638i \(0.386080\pi\)
−0.350300 + 0.936638i \(0.613920\pi\)
\(158\) 0 0
\(159\) −3.49165 + 10.7462i −0.276906 + 0.852228i
\(160\) 0 0
\(161\) 0.678406 + 2.08792i 0.0534659 + 0.164551i
\(162\) 0 0
\(163\) 5.70240 + 1.85282i 0.446646 + 0.145124i 0.523700 0.851903i \(-0.324551\pi\)
−0.0770538 + 0.997027i \(0.524551\pi\)
\(164\) 0 0
\(165\) 0.434245 + 8.66638i 0.0338059 + 0.674677i
\(166\) 0 0
\(167\) 3.76094 5.17649i 0.291030 0.400569i −0.638318 0.769773i \(-0.720370\pi\)
0.929348 + 0.369204i \(0.120370\pi\)
\(168\) 0 0
\(169\) −10.4219 7.57194i −0.801684 0.582457i
\(170\) 0 0
\(171\) −2.98680 + 2.17004i −0.228406 + 0.165947i
\(172\) 0 0
\(173\) 4.96583 1.61350i 0.377545 0.122672i −0.114096 0.993470i \(-0.536397\pi\)
0.491641 + 0.870798i \(0.336397\pi\)
\(174\) 0 0
\(175\) 7.71452 + 1.67682i 0.583163 + 0.126755i
\(176\) 0 0
\(177\) 11.0150 3.57899i 0.827937 0.269013i
\(178\) 0 0
\(179\) 18.8534 13.6978i 1.40917 1.02382i 0.415724 0.909491i \(-0.363528\pi\)
0.993443 0.114329i \(-0.0364718\pi\)
\(180\) 0 0
\(181\) −20.3662 14.7969i −1.51380 1.09984i −0.964454 0.264251i \(-0.914875\pi\)
−0.549350 0.835592i \(-0.685125\pi\)
\(182\) 0 0
\(183\) −6.44643 + 8.87275i −0.476534 + 0.655893i
\(184\) 0 0
\(185\) 17.8991 6.82372i 1.31596 0.501690i
\(186\) 0 0
\(187\) −22.4043 7.27959i −1.63836 0.532336i
\(188\) 0 0
\(189\) 0.487917 + 1.50165i 0.0354907 + 0.109229i
\(190\) 0 0
\(191\) 2.48188 7.63843i 0.179582 0.552697i −0.820231 0.572033i \(-0.806155\pi\)
0.999813 + 0.0193354i \(0.00615503\pi\)
\(192\) 0 0
\(193\) 20.2575i 1.45817i 0.684424 + 0.729084i \(0.260054\pi\)
−0.684424 + 0.729084i \(0.739946\pi\)
\(194\) 0 0
\(195\) 0.642794 + 0.419536i 0.0460314 + 0.0300436i
\(196\) 0 0
\(197\) 11.7650 + 16.1931i 0.838221 + 1.15371i 0.986337 + 0.164742i \(0.0526793\pi\)
−0.148115 + 0.988970i \(0.547321\pi\)
\(198\) 0 0
\(199\) 22.4180 1.58917 0.794585 0.607153i \(-0.207689\pi\)
0.794585 + 0.607153i \(0.207689\pi\)
\(200\) 0 0
\(201\) 10.4591 0.737729
\(202\) 0 0
\(203\) −3.09039 4.25356i −0.216903 0.298541i
\(204\) 0 0
\(205\) −1.01810 2.67054i −0.0711072 0.186519i
\(206\) 0 0
\(207\) 1.39041i 0.0966404i
\(208\) 0 0
\(209\) −4.42719 + 13.6255i −0.306235 + 0.942495i
\(210\) 0 0
\(211\) 2.67780 + 8.24142i 0.184347 + 0.567363i 0.999937 0.0112687i \(-0.00358702\pi\)
−0.815589 + 0.578631i \(0.803587\pi\)
\(212\) 0 0
\(213\) −9.63050 3.12914i −0.659871 0.214405i
\(214\) 0 0
\(215\) 1.99871 + 2.47982i 0.136311 + 0.169122i
\(216\) 0 0
\(217\) −4.87698 + 6.71259i −0.331071 + 0.455680i
\(218\) 0 0
\(219\) −10.6709 7.75289i −0.721076 0.523892i
\(220\) 0 0
\(221\) −1.68589 + 1.22487i −0.113405 + 0.0823937i
\(222\) 0 0
\(223\) −11.7779 + 3.82686i −0.788705 + 0.256266i −0.675552 0.737312i \(-0.736095\pi\)
−0.113152 + 0.993578i \(0.536095\pi\)
\(224\) 0 0
\(225\) 4.31861 + 2.51985i 0.287907 + 0.167990i
\(226\) 0 0
\(227\) 17.3309 5.63116i 1.15029 0.373753i 0.329040 0.944316i \(-0.393275\pi\)
0.821254 + 0.570563i \(0.193275\pi\)
\(228\) 0 0
\(229\) 13.2812 9.64932i 0.877643 0.637645i −0.0549837 0.998487i \(-0.517511\pi\)
0.932627 + 0.360842i \(0.117511\pi\)
\(230\) 0 0
\(231\) 4.95699 + 3.60147i 0.326146 + 0.236959i
\(232\) 0 0
\(233\) 3.01993 4.15658i 0.197842 0.272307i −0.698557 0.715555i \(-0.746174\pi\)
0.896399 + 0.443248i \(0.146174\pi\)
\(234\) 0 0
\(235\) −0.810450 0.219154i −0.0528679 0.0142960i
\(236\) 0 0
\(237\) −13.1241 4.26428i −0.852502 0.276995i
\(238\) 0 0
\(239\) −7.58924 23.3573i −0.490907 1.51086i −0.823239 0.567694i \(-0.807835\pi\)
0.332332 0.943162i \(-0.392165\pi\)
\(240\) 0 0
\(241\) 1.49413 4.59846i 0.0962454 0.296213i −0.891331 0.453353i \(-0.850228\pi\)
0.987576 + 0.157141i \(0.0502276\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −7.84654 + 6.32424i −0.501297 + 0.404041i
\(246\) 0 0
\(247\) 0.744923 + 1.02530i 0.0473983 + 0.0652382i
\(248\) 0 0
\(249\) −4.62458 −0.293071
\(250\) 0 0
\(251\) −15.1395 −0.955594 −0.477797 0.878470i \(-0.658565\pi\)
−0.477797 + 0.878470i \(0.658565\pi\)
\(252\) 0 0
\(253\) 3.17147 + 4.36515i 0.199388 + 0.274435i
\(254\) 0 0
\(255\) −10.5687 + 8.51825i −0.661835 + 0.533433i
\(256\) 0 0
\(257\) 22.7976i 1.42207i −0.703155 0.711036i \(-0.748226\pi\)
0.703155 0.711036i \(-0.251774\pi\)
\(258\) 0 0
\(259\) 4.17982 12.8642i 0.259722 0.799341i
\(260\) 0 0
\(261\) −1.02900 3.16693i −0.0636933 0.196028i
\(262\) 0 0
\(263\) −8.98231 2.91853i −0.553873 0.179964i 0.0186895 0.999825i \(-0.494051\pi\)
−0.572562 + 0.819861i \(0.694051\pi\)
\(264\) 0 0
\(265\) 24.3898 + 6.59526i 1.49825 + 0.405144i
\(266\) 0 0
\(267\) 4.27263 5.88077i 0.261481 0.359898i
\(268\) 0 0
\(269\) −23.7720 17.2714i −1.44940 1.05305i −0.985970 0.166921i \(-0.946618\pi\)
−0.463433 0.886132i \(-0.653382\pi\)
\(270\) 0 0
\(271\) −12.5303 + 9.10380i −0.761162 + 0.553016i −0.899266 0.437401i \(-0.855899\pi\)
0.138105 + 0.990418i \(0.455899\pi\)
\(272\) 0 0
\(273\) 0.515482 0.167490i 0.0311984 0.0101370i
\(274\) 0 0
\(275\) 19.3058 1.93957i 1.16418 0.116960i
\(276\) 0 0
\(277\) 14.6259 4.75225i 0.878786 0.285535i 0.165333 0.986238i \(-0.447130\pi\)
0.713453 + 0.700703i \(0.247130\pi\)
\(278\) 0 0
\(279\) −4.25135 + 3.08879i −0.254522 + 0.184921i
\(280\) 0 0
\(281\) −3.13314 2.27636i −0.186908 0.135796i 0.490397 0.871499i \(-0.336852\pi\)
−0.677304 + 0.735703i \(0.736852\pi\)
\(282\) 0 0
\(283\) −6.98697 + 9.61673i −0.415332 + 0.571655i −0.964509 0.264051i \(-0.914941\pi\)
0.549177 + 0.835706i \(0.314941\pi\)
\(284\) 0 0
\(285\) 5.18050 + 6.42749i 0.306866 + 0.380731i
\(286\) 0 0
\(287\) −1.91934 0.623630i −0.113295 0.0368117i
\(288\) 0 0
\(289\) −6.13443 18.8798i −0.360849 1.11058i
\(290\) 0 0
\(291\) 1.87127 5.75919i 0.109696 0.337610i
\(292\) 0 0
\(293\) 15.4596i 0.903161i −0.892230 0.451581i \(-0.850860\pi\)
0.892230 0.451581i \(-0.149140\pi\)
\(294\) 0 0
\(295\) −9.22543 24.1989i −0.537125 1.40892i
\(296\) 0 0
\(297\) 2.28095 + 3.13946i 0.132354 + 0.182170i
\(298\) 0 0
\(299\) 0.477297 0.0276028
\(300\) 0 0
\(301\) 2.24900 0.129630
\(302\) 0 0
\(303\) −1.89876 2.61341i −0.109081 0.150137i
\(304\) 0 0
\(305\) 20.5366 + 13.4037i 1.17592 + 0.767495i
\(306\) 0 0
\(307\) 26.6092i 1.51867i −0.650702 0.759334i \(-0.725525\pi\)
0.650702 0.759334i \(-0.274475\pi\)
\(308\) 0 0
\(309\) 2.37858 7.32052i 0.135313 0.416450i
\(310\) 0 0
\(311\) −1.69361 5.21238i −0.0960356 0.295567i 0.891487 0.453047i \(-0.149663\pi\)
−0.987522 + 0.157480i \(0.949663\pi\)
\(312\) 0 0
\(313\) 7.08632 + 2.30248i 0.400542 + 0.130144i 0.502359 0.864659i \(-0.332466\pi\)
−0.101817 + 0.994803i \(0.532466\pi\)
\(314\) 0 0
\(315\) 3.29899 1.25769i 0.185877 0.0708626i
\(316\) 0 0
\(317\) 1.74481 2.40152i 0.0979981 0.134883i −0.757202 0.653181i \(-0.773434\pi\)
0.855200 + 0.518298i \(0.173434\pi\)
\(318\) 0 0
\(319\) −10.4541 7.59535i −0.585317 0.425258i
\(320\) 0 0
\(321\) −14.5927 + 10.6022i −0.814485 + 0.591758i
\(322\) 0 0
\(323\) −21.3148 + 6.92561i −1.18599 + 0.385351i
\(324\) 0 0
\(325\) 0.865005 1.48248i 0.0479818 0.0822330i
\(326\) 0 0
\(327\) 15.9073 5.16860i 0.879676 0.285824i
\(328\) 0 0
\(329\) −0.479608 + 0.348456i −0.0264416 + 0.0192110i
\(330\) 0 0
\(331\) −22.1899 16.1219i −1.21967 0.886140i −0.223594 0.974682i \(-0.571779\pi\)
−0.996072 + 0.0885426i \(0.971779\pi\)
\(332\) 0 0
\(333\) 5.03536 6.93058i 0.275936 0.379794i
\(334\) 0 0
\(335\) −1.17039 23.3580i −0.0639455 1.27618i
\(336\) 0 0
\(337\) 7.14905 + 2.32287i 0.389433 + 0.126535i 0.497188 0.867643i \(-0.334366\pi\)
−0.107754 + 0.994178i \(0.534366\pi\)
\(338\) 0 0
\(339\) −0.701155 2.15793i −0.0380815 0.117203i
\(340\) 0 0
\(341\) −6.30157 + 19.3943i −0.341249 + 1.05026i
\(342\) 0 0
\(343\) 18.1687i 0.981019i
\(344\) 0 0
\(345\) 3.10516 0.155590i 0.167176 0.00837668i
\(346\) 0 0
\(347\) 7.05022 + 9.70380i 0.378476 + 0.520927i 0.955180 0.296026i \(-0.0956614\pi\)
−0.576704 + 0.816953i \(0.695661\pi\)
\(348\) 0 0
\(349\) 3.50169 0.187441 0.0937207 0.995599i \(-0.470124\pi\)
0.0937207 + 0.995599i \(0.470124\pi\)
\(350\) 0 0
\(351\) 0.343277 0.0183227
\(352\) 0 0
\(353\) 14.6665 + 20.1867i 0.780617 + 1.07443i 0.995214 + 0.0977244i \(0.0311564\pi\)
−0.214596 + 0.976703i \(0.568844\pi\)
\(354\) 0 0
\(355\) −5.91053 + 21.8576i −0.313698 + 1.16008i
\(356\) 0 0
\(357\) 9.58496i 0.507290i
\(358\) 0 0
\(359\) −0.247954 + 0.763123i −0.0130865 + 0.0402761i −0.957387 0.288810i \(-0.906741\pi\)
0.944300 + 0.329086i \(0.106741\pi\)
\(360\) 0 0
\(361\) −1.65941 5.10714i −0.0873374 0.268797i
\(362\) 0 0
\(363\) 3.86030 + 1.25429i 0.202613 + 0.0658330i
\(364\) 0 0
\(365\) −16.1202 + 24.6986i −0.843769 + 1.29278i
\(366\) 0 0
\(367\) −9.28986 + 12.7864i −0.484927 + 0.667445i −0.979442 0.201724i \(-0.935346\pi\)
0.494515 + 0.869169i \(0.335346\pi\)
\(368\) 0 0
\(369\) −1.03404 0.751277i −0.0538302 0.0391099i
\(370\) 0 0
\(371\) 14.4334 10.4865i 0.749346 0.544431i
\(372\) 0 0
\(373\) −3.43291 + 1.11542i −0.177750 + 0.0577543i −0.396540 0.918018i \(-0.629789\pi\)
0.218790 + 0.975772i \(0.429789\pi\)
\(374\) 0 0
\(375\) 5.14423 9.92657i 0.265647 0.512606i
\(376\) 0 0
\(377\) −1.08713 + 0.353230i −0.0559901 + 0.0181923i
\(378\) 0 0
\(379\) 22.0967 16.0542i 1.13503 0.824647i 0.148610 0.988896i \(-0.452520\pi\)
0.986419 + 0.164249i \(0.0525201\pi\)
\(380\) 0 0
\(381\) 1.21939 + 0.885941i 0.0624714 + 0.0453881i
\(382\) 0 0
\(383\) −11.3334 + 15.5991i −0.579112 + 0.797079i −0.993598 0.112977i \(-0.963961\pi\)
0.414486 + 0.910056i \(0.363961\pi\)
\(384\) 0 0
\(385\) 7.48834 11.4733i 0.381641 0.584733i
\(386\) 0 0
\(387\) 1.35467 + 0.440159i 0.0688617 + 0.0223745i
\(388\) 0 0
\(389\) 5.27164 + 16.2244i 0.267283 + 0.822612i 0.991159 + 0.132682i \(0.0423589\pi\)
−0.723876 + 0.689930i \(0.757641\pi\)
\(390\) 0 0
\(391\) −2.60828 + 8.02745i −0.131906 + 0.405966i
\(392\) 0 0
\(393\) 15.9388i 0.804006i
\(394\) 0 0
\(395\) −8.05466 + 29.7868i −0.405274 + 1.49874i
\(396\) 0 0
\(397\) 16.0842 + 22.1380i 0.807243 + 1.11108i 0.991743 + 0.128243i \(0.0409336\pi\)
−0.184499 + 0.982833i \(0.559066\pi\)
\(398\) 0 0
\(399\) 5.82924 0.291827
\(400\) 0 0
\(401\) −14.7793 −0.738042 −0.369021 0.929421i \(-0.620307\pi\)
−0.369021 + 0.929421i \(0.620307\pi\)
\(402\) 0 0
\(403\) 1.06031 + 1.45939i 0.0528177 + 0.0726974i
\(404\) 0 0
\(405\) 2.23327 0.111902i 0.110972 0.00556045i
\(406\) 0 0
\(407\) 33.2437i 1.64783i
\(408\) 0 0
\(409\) −6.72523 + 20.6981i −0.332541 + 1.02346i 0.635379 + 0.772200i \(0.280844\pi\)
−0.967921 + 0.251256i \(0.919156\pi\)
\(410\) 0 0
\(411\) −1.68307 5.17996i −0.0830198 0.255509i
\(412\) 0 0
\(413\) −17.3919 5.65098i −0.855800 0.278066i
\(414\) 0 0
\(415\) 0.517499 + 10.3279i 0.0254030 + 0.506977i
\(416\) 0 0
\(417\) 5.80923 7.99572i 0.284479 0.391552i
\(418\) 0 0
\(419\) −3.67055 2.66681i −0.179318 0.130282i 0.494505 0.869175i \(-0.335349\pi\)
−0.673824 + 0.738892i \(0.735349\pi\)
\(420\) 0 0
\(421\) −2.47193 + 1.79596i −0.120475 + 0.0875300i −0.646391 0.763006i \(-0.723722\pi\)
0.525916 + 0.850536i \(0.323722\pi\)
\(422\) 0 0
\(423\) −0.357085 + 0.116024i −0.0173621 + 0.00564128i
\(424\) 0 0
\(425\) 20.2062 + 22.6494i 0.980143 + 1.09866i
\(426\) 0 0
\(427\) 16.4691 5.35114i 0.796996 0.258960i
\(428\) 0 0
\(429\) 1.07770 0.782997i 0.0520320 0.0378035i
\(430\) 0 0
\(431\) 15.2881 + 11.1074i 0.736400 + 0.535026i 0.891582 0.452860i \(-0.149596\pi\)
−0.155181 + 0.987886i \(0.549596\pi\)
\(432\) 0 0
\(433\) −2.00963 + 2.76602i −0.0965768 + 0.132927i −0.854571 0.519335i \(-0.826180\pi\)
0.757994 + 0.652262i \(0.226180\pi\)
\(434\) 0 0
\(435\) −6.95744 + 2.65241i −0.333584 + 0.127173i
\(436\) 0 0
\(437\) 4.88201 + 1.58626i 0.233538 + 0.0758812i
\(438\) 0 0
\(439\) 1.84058 + 5.66473i 0.0878462 + 0.270363i 0.985323 0.170698i \(-0.0546023\pi\)
−0.897477 + 0.441061i \(0.854602\pi\)
\(440\) 0 0
\(441\) −1.39273 + 4.28639i −0.0663206 + 0.204114i
\(442\) 0 0
\(443\) 33.0705i 1.57122i 0.618719 + 0.785612i \(0.287652\pi\)
−0.618719 + 0.785612i \(0.712348\pi\)
\(444\) 0 0
\(445\) −13.6115 8.88386i −0.645245 0.421135i
\(446\) 0 0
\(447\) 0.0381686 + 0.0525346i 0.00180531 + 0.00248480i
\(448\) 0 0
\(449\) 8.68077 0.409671 0.204835 0.978796i \(-0.434334\pi\)
0.204835 + 0.978796i \(0.434334\pi\)
\(450\) 0 0
\(451\) −4.95997 −0.233556
\(452\) 0 0
\(453\) 7.12518 + 9.80697i 0.334770 + 0.460771i
\(454\) 0 0
\(455\) −0.431734 1.13247i −0.0202400 0.0530909i
\(456\) 0 0
\(457\) 13.3667i 0.625269i −0.949873 0.312635i \(-0.898788\pi\)
0.949873 0.312635i \(-0.101212\pi\)
\(458\) 0 0
\(459\) −1.87590 + 5.77342i −0.0875595 + 0.269480i
\(460\) 0 0
\(461\) −12.6568 38.9537i −0.589487 1.81425i −0.580453 0.814294i \(-0.697124\pi\)
−0.00903372 0.999959i \(-0.502876\pi\)
\(462\) 0 0
\(463\) 21.9961 + 7.14695i 1.02224 + 0.332147i 0.771719 0.635963i \(-0.219397\pi\)
0.250524 + 0.968110i \(0.419397\pi\)
\(464\) 0 0
\(465\) 7.37382 + 9.14876i 0.341953 + 0.424263i
\(466\) 0 0
\(467\) −17.8034 + 24.5043i −0.823845 + 1.13392i 0.165193 + 0.986261i \(0.447175\pi\)
−0.989038 + 0.147664i \(0.952825\pi\)
\(468\) 0 0
\(469\) −13.3603 9.70682i −0.616921 0.448219i
\(470\) 0 0
\(471\) 18.9893 13.7965i 0.874981 0.635711i
\(472\) 0 0
\(473\) 5.25691 1.70807i 0.241713 0.0785373i
\(474\) 0 0
\(475\) 13.7746 12.2887i 0.632021 0.563843i
\(476\) 0 0
\(477\) 10.7462 3.49165i 0.492034 0.159872i
\(478\) 0 0
\(479\) −19.4809 + 14.1537i −0.890107 + 0.646700i −0.935906 0.352250i \(-0.885417\pi\)
0.0457990 + 0.998951i \(0.485417\pi\)
\(480\) 0 0
\(481\) −2.37911 1.72852i −0.108478 0.0788138i
\(482\) 0 0
\(483\) 1.29040 1.77609i 0.0587155 0.0808149i
\(484\) 0 0
\(485\) −13.0712 3.53459i −0.593533 0.160497i
\(486\) 0 0
\(487\) −2.14446 0.696777i −0.0971747 0.0315740i 0.260026 0.965602i \(-0.416269\pi\)
−0.357201 + 0.934028i \(0.616269\pi\)
\(488\) 0 0
\(489\) −1.85282 5.70240i −0.0837875 0.257871i
\(490\) 0 0
\(491\) −8.84093 + 27.2096i −0.398986 + 1.22795i 0.526828 + 0.849972i \(0.323381\pi\)
−0.925814 + 0.377980i \(0.876619\pi\)
\(492\) 0 0
\(493\) 20.2143i 0.910406i
\(494\) 0 0
\(495\) 6.75601 5.44528i 0.303660 0.244747i
\(496\) 0 0
\(497\) 9.39777 + 12.9349i 0.421547 + 0.580210i
\(498\) 0 0
\(499\) 26.9489 1.20640 0.603199 0.797590i \(-0.293892\pi\)
0.603199 + 0.797590i \(0.293892\pi\)
\(500\) 0 0
\(501\) −6.39850 −0.285864
\(502\) 0 0
\(503\) −0.245105 0.337358i −0.0109287 0.0150421i 0.803518 0.595281i \(-0.202959\pi\)
−0.814446 + 0.580239i \(0.802959\pi\)
\(504\) 0 0
\(505\) −5.62397 + 4.53287i −0.250263 + 0.201710i
\(506\) 0 0
\(507\) 12.8822i 0.572117i
\(508\) 0 0
\(509\) −4.14176 + 12.7470i −0.183580 + 0.565002i −0.999921 0.0125684i \(-0.995999\pi\)
0.816341 + 0.577571i \(0.195999\pi\)
\(510\) 0 0
\(511\) 6.43563 + 19.8068i 0.284695 + 0.876202i
\(512\) 0 0
\(513\) 3.51119 + 1.14086i 0.155023 + 0.0503700i
\(514\) 0 0
\(515\) −16.6148 4.49283i −0.732138 0.197978i
\(516\) 0 0
\(517\) −0.856410 + 1.17875i −0.0376649 + 0.0518412i
\(518\) 0 0
\(519\) −4.22419 3.06905i −0.185421 0.134716i
\(520\) 0 0
\(521\) −17.0496 + 12.3872i −0.746956 + 0.542695i −0.894882 0.446303i \(-0.852740\pi\)
0.147926 + 0.988998i \(0.452740\pi\)
\(522\) 0 0
\(523\) −11.2943 + 3.66974i −0.493866 + 0.160467i −0.545352 0.838207i \(-0.683604\pi\)
0.0514866 + 0.998674i \(0.483604\pi\)
\(524\) 0 0
\(525\) −3.17791 7.22679i −0.138695 0.315403i
\(526\) 0 0
\(527\) −30.3391 + 9.85777i −1.32159 + 0.429411i
\(528\) 0 0
\(529\) −17.0434 + 12.3827i −0.741016 + 0.538379i
\(530\) 0 0
\(531\) −9.36991 6.80764i −0.406620 0.295426i
\(532\) 0 0
\(533\) −0.257896 + 0.354963i −0.0111707 + 0.0153752i
\(534\) 0 0
\(535\) 25.3105 + 31.4030i 1.09427 + 1.35767i
\(536\) 0 0
\(537\) −22.1635 7.20135i −0.956424 0.310761i
\(538\) 0 0
\(539\) 5.40462 + 16.6337i 0.232793 + 0.716464i
\(540\) 0 0
\(541\) 11.2993 34.7757i 0.485796 1.49513i −0.345029 0.938592i \(-0.612131\pi\)
0.830825 0.556534i \(-0.187869\pi\)
\(542\) 0 0
\(543\) 25.1739i 1.08032i
\(544\) 0 0
\(545\) −13.3229 34.9469i −0.570691 1.49696i
\(546\) 0 0
\(547\) −23.2652 32.0219i −0.994750 1.36916i −0.928492 0.371353i \(-0.878894\pi\)
−0.0662579 0.997803i \(-0.521106\pi\)
\(548\) 0 0
\(549\) 10.9673 0.468074
\(550\) 0 0
\(551\) −12.2936 −0.523726
\(552\) 0 0
\(553\) 12.8069 + 17.6272i 0.544606 + 0.749586i
\(554\) 0 0
\(555\) −16.0413 10.4698i −0.680915 0.444417i
\(556\) 0 0
\(557\) 12.1804i 0.516102i −0.966131 0.258051i \(-0.916920\pi\)
0.966131 0.258051i \(-0.0830802\pi\)
\(558\) 0 0
\(559\) 0.151096 0.465026i 0.00639068 0.0196685i
\(560\) 0 0
\(561\) 7.27959 + 22.4043i 0.307345 + 0.945909i
\(562\) 0 0
\(563\) 34.7979 + 11.3065i 1.46656 + 0.476513i 0.930065 0.367394i \(-0.119750\pi\)
0.536490 + 0.843907i \(0.319750\pi\)
\(564\) 0 0
\(565\) −4.74078 + 1.80734i −0.199446 + 0.0760355i
\(566\) 0 0
\(567\) 0.928073 1.27738i 0.0389754 0.0536450i
\(568\) 0 0
\(569\) −27.3735 19.8880i −1.14756 0.833749i −0.159403 0.987214i \(-0.550957\pi\)
−0.988154 + 0.153464i \(0.950957\pi\)
\(570\) 0 0
\(571\) 0.974239 0.707826i 0.0407706 0.0296216i −0.567213 0.823571i \(-0.691978\pi\)
0.607984 + 0.793949i \(0.291978\pi\)
\(572\) 0 0
\(573\) −7.63843 + 2.48188i −0.319100 + 0.103682i
\(574\) 0 0
\(575\) −0.694947 6.91725i −0.0289813 0.288469i
\(576\) 0 0
\(577\) 15.6012 5.06913i 0.649485 0.211031i 0.0342981 0.999412i \(-0.489080\pi\)
0.615187 + 0.788381i \(0.289080\pi\)
\(578\) 0 0
\(579\) 16.3887 11.9071i 0.681090 0.494841i
\(580\) 0 0
\(581\) 5.90735 + 4.29194i 0.245078 + 0.178060i
\(582\) 0 0
\(583\) 25.7730 35.4734i 1.06741 1.46916i
\(584\) 0 0
\(585\) −0.0384133 0.766628i −0.00158819 0.0316962i
\(586\) 0 0
\(587\) 32.0429 + 10.4114i 1.32255 + 0.429724i 0.883371 0.468674i \(-0.155268\pi\)
0.439182 + 0.898398i \(0.355268\pi\)
\(588\) 0 0
\(589\) 5.99515 + 18.4512i 0.247026 + 0.760267i
\(590\) 0 0
\(591\) 6.18522 19.0362i 0.254426 0.783043i
\(592\) 0 0
\(593\) 32.2208i 1.32315i −0.749878 0.661576i \(-0.769888\pi\)
0.749878 0.661576i \(-0.230112\pi\)
\(594\) 0 0
\(595\) 21.4058 1.07258i 0.877551 0.0439713i
\(596\) 0 0
\(597\) −13.1770 18.1365i −0.539297 0.742279i
\(598\) 0 0
\(599\) 14.7284 0.601784 0.300892 0.953658i \(-0.402716\pi\)
0.300892 + 0.953658i \(0.402716\pi\)
\(600\) 0 0
\(601\) 35.5643 1.45070 0.725348 0.688382i \(-0.241679\pi\)
0.725348 + 0.688382i \(0.241679\pi\)
\(602\) 0 0
\(603\) −6.14771 8.46160i −0.250354 0.344583i
\(604\) 0 0
\(605\) 2.36918 8.76143i 0.0963210 0.356203i
\(606\) 0 0
\(607\) 16.0986i 0.653421i 0.945124 + 0.326710i \(0.105940\pi\)
−0.945124 + 0.326710i \(0.894060\pi\)
\(608\) 0 0
\(609\) −1.62471 + 5.00036i −0.0658368 + 0.202625i
\(610\) 0 0
\(611\) 0.0398283 + 0.122579i 0.00161128 + 0.00495902i
\(612\) 0 0
\(613\) −41.1487 13.3700i −1.66198 0.540010i −0.680693 0.732569i \(-0.738321\pi\)
−0.981285 + 0.192559i \(0.938321\pi\)
\(614\) 0 0
\(615\) −1.56209 + 2.39337i −0.0629896 + 0.0965098i
\(616\) 0 0
\(617\) −0.931550 + 1.28217i −0.0375028 + 0.0516182i −0.827357 0.561677i \(-0.810156\pi\)
0.789854 + 0.613295i \(0.210156\pi\)
\(618\) 0 0
\(619\) −10.9048 7.92281i −0.438301 0.318444i 0.346658 0.937991i \(-0.387316\pi\)
−0.784960 + 0.619547i \(0.787316\pi\)
\(620\) 0 0
\(621\) 1.12487 0.817265i 0.0451394 0.0327957i
\(622\) 0 0
\(623\) −10.9156 + 3.54668i −0.437323 + 0.142095i
\(624\) 0 0
\(625\) −22.7443 10.3776i −0.909773 0.415105i
\(626\) 0 0
\(627\) 13.6255 4.42719i 0.544150 0.176805i
\(628\) 0 0
\(629\) 42.0724 30.5674i 1.67754 1.21880i
\(630\) 0 0
\(631\) 23.6944 + 17.2150i 0.943261 + 0.685319i 0.949203 0.314663i \(-0.101892\pi\)
−0.00594245 + 0.999982i \(0.501892\pi\)
\(632\) 0 0
\(633\) 5.09348 7.01057i 0.202448 0.278645i
\(634\) 0 0
\(635\) 1.84209 2.82237i 0.0731011 0.112002i
\(636\) 0 0
\(637\) 1.47142 + 0.478092i 0.0582997 + 0.0189427i
\(638\) 0 0
\(639\) 3.12914 + 9.63050i 0.123787 + 0.380977i
\(640\) 0 0
\(641\) −5.34325 + 16.4448i −0.211046 + 0.649532i 0.788365 + 0.615208i \(0.210928\pi\)
−0.999411 + 0.0343242i \(0.989072\pi\)
\(642\) 0 0
\(643\) 46.8857i 1.84899i −0.381190 0.924497i \(-0.624486\pi\)
0.381190 0.924497i \(-0.375514\pi\)
\(644\) 0 0
\(645\) 0.831401 3.07459i 0.0327364 0.121062i
\(646\) 0 0
\(647\) 8.46236 + 11.6474i 0.332690 + 0.457908i 0.942288 0.334802i \(-0.108669\pi\)
−0.609599 + 0.792710i \(0.708669\pi\)
\(648\) 0 0
\(649\) −44.9444 −1.76422
\(650\) 0 0
\(651\) 8.29722 0.325194
\(652\) 0 0
\(653\) −18.7990 25.8746i −0.735661 1.01255i −0.998857 0.0478084i \(-0.984776\pi\)
0.263195 0.964743i \(-0.415224\pi\)
\(654\) 0 0
\(655\) −35.5956 + 1.78358i −1.39083 + 0.0696903i
\(656\) 0 0
\(657\) 13.1900i 0.514591i
\(658\) 0 0
\(659\) −5.77517 + 17.7742i −0.224969 + 0.692383i 0.773326 + 0.634009i \(0.218592\pi\)
−0.998295 + 0.0583742i \(0.981408\pi\)
\(660\) 0 0
\(661\) −0.209866 0.645901i −0.00816284 0.0251226i 0.946892 0.321551i \(-0.104204\pi\)
−0.955055 + 0.296429i \(0.904204\pi\)
\(662\) 0 0
\(663\) 1.98188 + 0.643952i 0.0769699 + 0.0250090i
\(664\) 0 0
\(665\) −0.652303 13.0182i −0.0252952 0.504826i
\(666\) 0 0
\(667\) −2.72141 + 3.74570i −0.105373 + 0.145034i
\(668\) 0 0
\(669\) 10.0189 + 7.27912i 0.387351 + 0.281427i
\(670\) 0 0
\(671\) 34.4315 25.0159i 1.32921 0.965730i
\(672\) 0 0
\(673\) 6.90162 2.24247i 0.266038 0.0864410i −0.172961 0.984929i \(-0.555333\pi\)
0.438999 + 0.898488i \(0.355333\pi\)
\(674\) 0 0
\(675\) −0.499813 4.97496i −0.0192378 0.191486i
\(676\) 0 0
\(677\) −32.2918 + 10.4922i −1.24107 + 0.403249i −0.854714 0.519099i \(-0.826267\pi\)
−0.386359 + 0.922348i \(0.626267\pi\)
\(678\) 0 0
\(679\) −7.73528 + 5.62001i −0.296853 + 0.215676i
\(680\) 0 0
\(681\) −14.7426 10.7111i −0.564936 0.410450i
\(682\) 0 0
\(683\) 16.5508 22.7802i 0.633298 0.871660i −0.364938 0.931032i \(-0.618910\pi\)
0.998236 + 0.0593717i \(0.0189097\pi\)
\(684\) 0 0
\(685\) −11.3799 + 4.33840i −0.434804 + 0.165762i
\(686\) 0 0
\(687\) −15.6129 5.07295i −0.595670 0.193545i
\(688\) 0 0
\(689\) −1.19860 3.68892i −0.0456631 0.140536i
\(690\) 0 0
\(691\) 6.85416 21.0949i 0.260745 0.802489i −0.731899 0.681413i \(-0.761366\pi\)
0.992643 0.121076i \(-0.0386344\pi\)
\(692\) 0 0
\(693\) 6.12718i 0.232752i
\(694\) 0 0
\(695\) −18.5066 12.0788i −0.701996 0.458176i
\(696\) 0 0
\(697\) −4.56066 6.27721i −0.172747 0.237766i
\(698\) 0 0
\(699\) −5.13782 −0.194330
\(700\) 0 0
\(701\) 16.9652 0.640768 0.320384 0.947288i \(-0.396188\pi\)
0.320384 + 0.947288i \(0.396188\pi\)
\(702\) 0 0
\(703\) −18.5900 25.5869i −0.701135 0.965030i
\(704\) 0 0
\(705\) 0.299071 + 0.784483i 0.0112637 + 0.0295453i
\(706\) 0 0
\(707\) 5.10051i 0.191824i
\(708\) 0 0
\(709\) −4.42745 + 13.6263i −0.166276 + 0.511746i −0.999128 0.0417503i \(-0.986707\pi\)
0.832852 + 0.553496i \(0.186707\pi\)
\(710\) 0 0
\(711\) 4.26428 + 13.1241i 0.159923 + 0.492192i
\(712\) 0 0
\(713\) 6.94896 + 2.25785i 0.260241 + 0.0845573i
\(714\) 0 0
\(715\) −1.86924 2.31918i −0.0699056 0.0867324i
\(716\) 0 0
\(717\) −14.4356 + 19.8689i −0.539107 + 0.742017i
\(718\) 0 0
\(719\) 9.56382 + 6.94852i 0.356670 + 0.259136i 0.751662 0.659549i \(-0.229253\pi\)
−0.394992 + 0.918685i \(0.629253\pi\)
\(720\) 0 0
\(721\) −9.83234 + 7.14361i −0.366175 + 0.266042i
\(722\) 0 0
\(723\) −4.59846 + 1.49413i −0.171019 + 0.0555673i
\(724\) 0 0
\(725\) 6.70208 + 15.2410i 0.248909 + 0.566037i
\(726\) 0 0
\(727\) 1.17583 0.382051i 0.0436092 0.0141695i −0.287131 0.957891i \(-0.592702\pi\)
0.330740 + 0.943722i \(0.392702\pi\)
\(728\) 0 0
\(729\) 0.809017 0.587785i 0.0299636 0.0217698i
\(730\) 0 0
\(731\) 6.99538 + 5.08244i 0.258734 + 0.187981i
\(732\) 0 0
\(733\) −9.70319 + 13.3553i −0.358395 + 0.493289i −0.949701 0.313159i \(-0.898613\pi\)
0.591305 + 0.806448i \(0.298613\pi\)
\(734\) 0 0
\(735\) 9.72850 + 2.63069i 0.358841 + 0.0970343i
\(736\) 0 0
\(737\) −38.6010 12.5422i −1.42189 0.461999i
\(738\) 0 0
\(739\) 5.20573 + 16.0216i 0.191496 + 0.589363i 1.00000 0.000872485i \(0.000277721\pi\)
−0.808504 + 0.588491i \(0.799722\pi\)
\(740\) 0 0
\(741\) 0.391629 1.20531i 0.0143869 0.0442782i
\(742\) 0 0
\(743\) 11.8940i 0.436347i −0.975910 0.218174i \(-0.929990\pi\)
0.975910 0.218174i \(-0.0700099\pi\)
\(744\) 0 0
\(745\) 0.113053 0.0911194i 0.00414193 0.00333836i
\(746\) 0 0
\(747\) 2.71826 + 3.74136i 0.0994558 + 0.136889i
\(748\) 0 0
\(749\) 28.4801 1.04064
\(750\) 0 0
\(751\) 0.821377 0.0299725 0.0149862 0.999888i \(-0.495230\pi\)
0.0149862 + 0.999888i \(0.495230\pi\)
\(752\) 0 0
\(753\) 8.89875 + 12.2481i 0.324288 + 0.446345i
\(754\) 0 0
\(755\) 21.1042 17.0098i 0.768062 0.619051i
\(756\) 0 0
\(757\) 32.5591i 1.18338i 0.806166 + 0.591690i \(0.201539\pi\)
−0.806166 + 0.591690i \(0.798461\pi\)
\(758\) 0 0
\(759\) 1.66734 5.13154i 0.0605206 0.186263i
\(760\) 0 0
\(761\) −3.35824 10.3356i −0.121736 0.374665i 0.871556 0.490295i \(-0.163111\pi\)
−0.993292 + 0.115631i \(0.963111\pi\)
\(762\) 0 0
\(763\) −25.1165 8.16086i −0.909280 0.295443i
\(764\) 0 0
\(765\) 13.1035 + 3.54333i 0.473758 + 0.128109i
\(766\) 0 0
\(767\) −2.33690 + 3.21647i −0.0843807 + 0.116140i
\(768\) 0 0
\(769\) −1.92870 1.40128i −0.0695505 0.0505314i 0.552467 0.833535i \(-0.313687\pi\)
−0.622017 + 0.783004i \(0.713687\pi\)
\(770\) 0 0
\(771\) −18.4436 + 13.4001i −0.664230 + 0.482592i
\(772\) 0 0
\(773\) 35.4118 11.5060i 1.27367 0.413841i 0.407325 0.913283i \(-0.366462\pi\)
0.866347 + 0.499442i \(0.166462\pi\)
\(774\) 0 0
\(775\) 19.6065 17.4915i 0.704285 0.628312i
\(776\) 0 0
\(777\) −12.8642 + 4.17982i −0.461500 + 0.149950i
\(778\) 0 0
\(779\) −3.81757 + 2.77363i −0.136779 + 0.0993756i
\(780\) 0 0
\(781\) 31.7905 + 23.0972i 1.13755 + 0.826482i
\(782\) 0 0
\(783\) −1.95727 + 2.69395i −0.0699470 + 0.0962738i
\(784\) 0 0
\(785\) −32.9363 40.8643i −1.17555 1.45851i
\(786\) 0 0
\(787\) −21.7768 7.07570i −0.776258 0.252221i −0.106016 0.994364i \(-0.533809\pi\)
−0.670242 + 0.742143i \(0.733809\pi\)
\(788\) 0 0
\(789\) 2.91853 + 8.98231i 0.103902 + 0.319779i
\(790\) 0 0
\(791\) −1.10708 + 3.40723i −0.0393631 + 0.121147i
\(792\) 0 0
\(793\) 3.76483i 0.133693i
\(794\) 0 0
\(795\) −9.00030 23.6084i −0.319208 0.837303i
\(796\) 0 0
\(797\) −5.21641 7.17977i −0.184775 0.254321i 0.706574 &minu