Properties

Label 300.2.o.a.229.1
Level $300$
Weight $2$
Character 300.229
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 229.1
Character \(\chi\) \(=\) 300.229
Dual form 300.2.o.a.169.1

$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

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

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 \(-0.903550\pi\)
0.954444 0.298390i \(-0.0964496\pi\)
\(8\) 0 0
\(9\) −0.309017 0.951057i −0.103006 0.317019i
\(10\) 0 0
\(11\) 1.19917 3.69066i 0.361563 1.11278i −0.590543 0.807006i \(-0.701086\pi\)
0.952106 0.305769i \(-0.0989136\pi\)
\(12\) 0 0
\(13\) 0.326475 0.106078i 0.0905480 0.0294208i −0.263393 0.964689i \(-0.584841\pi\)
0.353941 + 0.935268i \(0.384841\pi\)
\(14\) 0 0
\(15\) 2.15854 0.583692i 0.557333 0.150709i
\(16\) 0 0
\(17\) −3.56817 4.91117i −0.865409 1.19113i −0.980253 0.197750i \(-0.936637\pi\)
0.114844 0.993384i \(-0.463363\pi\)
\(18\) 0 0
\(19\) 2.98680 2.17004i 0.685219 0.497841i −0.189866 0.981810i \(-0.560805\pi\)
0.875085 + 0.483969i \(0.160805\pi\)
\(20\) 0 0
\(21\) 1.27738 + 0.928073i 0.278748 + 0.202522i
\(22\) 0 0
\(23\) 1.32236 + 0.429662i 0.275732 + 0.0895906i 0.443619 0.896216i \(-0.353694\pi\)
−0.167887 + 0.985806i \(0.553694\pi\)
\(24\) 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 0.308860 0.951107i \(-0.400052\pi\)
−0.809114 + 0.587652i \(0.800052\pi\)
\(30\) 0 0
\(31\) 4.25135 3.08879i 0.763565 0.554763i −0.136437 0.990649i \(-0.543565\pi\)
0.900002 + 0.435886i \(0.143565\pi\)
\(32\) 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 −0.889121 0.457672i \(-0.848683\pi\)
−0.450301 + 0.892877i \(0.648683\pi\)
\(38\) 0 0
\(39\) −0.106078 + 0.326475i −0.0169861 + 0.0522779i
\(40\) 0 0
\(41\) −0.394970 1.21559i −0.0616839 0.189844i 0.915466 0.402396i \(-0.131822\pi\)
−0.977150 + 0.212552i \(0.931822\pi\)
\(42\) 0 0
\(43\) 1.42438i 0.217216i 0.994085 + 0.108608i \(0.0346394\pi\)
−0.994085 + 0.108608i \(0.965361\pi\)
\(44\) 0 0
\(45\) −0.796542 + 2.08938i −0.118742 + 0.311467i
\(46\) 0 0
\(47\) 0.220691 0.303755i 0.0321911 0.0443072i −0.792618 0.609718i \(-0.791283\pi\)
0.824809 + 0.565411i \(0.191283\pi\)
\(48\) 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 0.0540999 + 0.998536i \(0.482771\pi\)
−0.966382 + 0.257112i \(0.917229\pi\)
\(54\) 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 −0.857791 0.513999i \(-0.828163\pi\)
0.391846 0.920031i \(-0.371837\pi\)
\(60\) 0 0
\(61\) −3.38909 + 10.4305i −0.433928 + 1.33549i 0.460252 + 0.887788i \(0.347759\pi\)
−0.894181 + 0.447706i \(0.852241\pi\)
\(62\) 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 −0.997905 0.0646937i \(-0.979393\pi\)
0.246842 0.969056i \(-0.420607\pi\)
\(68\) 0 0
\(69\) −1.12487 + 0.817265i −0.135418 + 0.0983871i
\(70\) 0 0
\(71\) 8.19220 + 5.95198i 0.972235 + 0.706370i 0.955960 0.293498i \(-0.0948193\pi\)
0.0162750 + 0.999868i \(0.494819\pi\)
\(72\) 0 0
\(73\) 12.5444 + 4.07594i 1.46822 + 0.477052i 0.930569 0.366117i \(-0.119313\pi\)
0.537648 + 0.843170i \(0.319313\pi\)
\(74\) 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 0.998557 0.0537055i \(-0.0171032\pi\)
0.257494 + 0.966280i \(0.417103\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 0 0
\(83\) 2.71826 + 3.74136i 0.298367 + 0.410668i 0.931709 0.363204i \(-0.118317\pi\)
−0.633342 + 0.773872i \(0.718317\pi\)
\(84\) 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 −0.758592 0.651566i \(-0.774112\pi\)
0.996695 0.0812387i \(-0.0258876\pi\)
\(90\) 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 −0.589138 0.808032i \(-0.700533\pi\)
0.950538 + 0.310608i \(0.100533\pi\)
\(98\) 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 −0.525692 0.850675i \(-0.676194\pi\)
0.971488 + 0.237090i \(0.0761936\pi\)
\(104\) 0 0
\(105\) −0.921610 3.40819i −0.0899399 0.332605i
\(106\) 0 0
\(107\) 18.0376i 1.74376i 0.489722 + 0.871878i \(0.337098\pi\)
−0.489722 + 0.871878i \(0.662902\pi\)
\(108\) 0 0
\(109\) −5.16860 15.9073i −0.495062 1.52364i −0.816861 0.576835i \(-0.804288\pi\)
0.321799 0.946808i \(-0.395712\pi\)
\(110\) 0 0
\(111\) 2.64725 8.14739i 0.251266 0.773316i
\(112\) 0 0
\(113\) 2.15793 0.701155i 0.203001 0.0659591i −0.205751 0.978604i \(-0.565964\pi\)
0.408753 + 0.912645i \(0.365964\pi\)
\(114\) 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 0.244725 0.969593i \(-0.421302\pi\)
−0.371926 + 0.928262i \(0.621302\pi\)
\(128\) 0 0
\(129\) −1.15235 0.837231i −0.101459 0.0737141i
\(130\) 0 0
\(131\) 12.8948 9.36859i 1.12662 0.818537i 0.141421 0.989950i \(-0.454833\pi\)
0.985199 + 0.171412i \(0.0548330\pi\)
\(132\) 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 −0.0792596 0.996854i \(-0.525256\pi\)
0.521814 + 0.853059i \(0.325256\pi\)
\(138\) 0 0
\(139\) 3.05409 9.39953i 0.259045 0.797258i −0.733961 0.679192i \(-0.762331\pi\)
0.993006 0.118066i \(-0.0376694\pi\)
\(140\) 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 \(-0.613920\pi\)
0.350300 0.936638i \(-0.386080\pi\)
\(158\) 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 −0.0770538 0.997027i \(-0.524551\pi\)
0.523700 + 0.851903i \(0.324551\pi\)
\(164\) 0 0
\(165\) 0.434245 8.66638i 0.0338059 0.674677i
\(166\) 0 0
\(167\) 3.76094 + 5.17649i 0.291030 + 0.400569i 0.929348 0.369204i \(-0.120370\pi\)
−0.638318 + 0.769773i \(0.720370\pi\)
\(168\) 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 0.491641 0.870798i \(-0.336397\pi\)
−0.114096 + 0.993470i \(0.536397\pi\)
\(174\) 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 0.993443 + 0.114329i \(0.0364718\pi\)
0.415724 + 0.909491i \(0.363528\pi\)
\(180\) 0 0
\(181\) −20.3662 + 14.7969i −1.51380 + 1.09984i −0.549350 + 0.835592i \(0.685125\pi\)
−0.964454 + 0.264251i \(0.914875\pi\)
\(182\) 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 0.999813 0.0193354i \(-0.00615503\pi\)
−0.820231 + 0.572033i \(0.806155\pi\)
\(192\) 0 0
\(193\) 20.2575i 1.45817i −0.684424 0.729084i \(-0.739946\pi\)
0.684424 0.729084i \(-0.260054\pi\)
\(194\) 0 0
\(195\) 0.642794 0.419536i 0.0460314 0.0300436i
\(196\) 0 0
\(197\) 11.7650 16.1931i 0.838221 1.15371i −0.148115 0.988970i \(-0.547321\pi\)
0.986337 0.164742i \(-0.0526793\pi\)
\(198\) 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 −0.815589 0.578631i \(-0.803587\pi\)
0.999937 + 0.0112687i \(0.00358702\pi\)
\(212\) 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 −0.113152 0.993578i \(-0.536095\pi\)
−0.675552 + 0.737312i \(0.736095\pi\)
\(224\) 0 0
\(225\) 4.31861 2.51985i 0.287907 0.167990i
\(226\) 0 0
\(227\) 17.3309 + 5.63116i 1.15029 + 0.373753i 0.821254 0.570563i \(-0.193275\pi\)
0.329040 + 0.944316i \(0.393275\pi\)
\(228\) 0 0
\(229\) 13.2812 + 9.64932i 0.877643 + 0.637645i 0.932627 0.360842i \(-0.117511\pi\)
−0.0549837 + 0.998487i \(0.517511\pi\)
\(230\) 0 0
\(231\) 4.95699 3.60147i 0.326146 0.236959i
\(232\) 0 0
\(233\) 3.01993 + 4.15658i 0.197842 + 0.272307i 0.896399 0.443248i \(-0.146174\pi\)
−0.698557 + 0.715555i \(0.746174\pi\)
\(234\) 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 0.332332 + 0.943162i \(0.392165\pi\)
−0.823239 + 0.567694i \(0.807835\pi\)
\(240\) 0 0
\(241\) 1.49413 + 4.59846i 0.0962454 + 0.296213i 0.987576 0.157141i \(-0.0502276\pi\)
−0.891331 + 0.453353i \(0.850228\pi\)
\(242\) 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 \(0.251774\pi\)
−0.703155 + 0.711036i \(0.748226\pi\)
\(258\) 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 −0.572562 0.819861i \(-0.694051\pi\)
0.0186895 + 0.999825i \(0.494051\pi\)
\(264\) 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 −0.463433 + 0.886132i \(0.653382\pi\)
−0.985970 + 0.166921i \(0.946618\pi\)
\(270\) 0 0
\(271\) −12.5303 9.10380i −0.761162 0.553016i 0.138105 0.990418i \(-0.455899\pi\)
−0.899266 + 0.437401i \(0.855899\pi\)
\(272\) 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 0.713453 0.700703i \(-0.247130\pi\)
0.165333 + 0.986238i \(0.447130\pi\)
\(278\) 0 0
\(279\) −4.25135 3.08879i −0.254522 0.184921i
\(280\) 0 0
\(281\) −3.13314 + 2.27636i −0.186908 + 0.135796i −0.677304 0.735703i \(-0.736852\pi\)
0.490397 + 0.871499i \(0.336852\pi\)
\(282\) 0 0
\(283\) −6.98697 9.61673i −0.415332 0.571655i 0.549177 0.835706i \(-0.314941\pi\)
−0.964509 + 0.264051i \(0.914941\pi\)
\(284\) 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 \(0.149140\pi\)
−0.892230 + 0.451581i \(0.850860\pi\)
\(294\) 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 \(0.274475\pi\)
−0.650702 + 0.759334i \(0.725525\pi\)
\(308\) 0 0
\(309\) 2.37858 + 7.32052i 0.135313 + 0.416450i
\(310\) 0 0
\(311\) −1.69361 + 5.21238i −0.0960356 + 0.295567i −0.987522 0.157480i \(-0.949663\pi\)
0.891487 + 0.453047i \(0.149663\pi\)
\(312\) 0 0
\(313\) 7.08632 2.30248i 0.400542 0.130144i −0.101817 0.994803i \(-0.532466\pi\)
0.502359 + 0.864659i \(0.332466\pi\)
\(314\) 0 0
\(315\) 3.29899 + 1.25769i 0.185877 + 0.0708626i
\(316\) 0 0
\(317\) 1.74481 + 2.40152i 0.0979981 + 0.134883i 0.855200 0.518298i \(-0.173434\pi\)
−0.757202 + 0.653181i \(0.773434\pi\)
\(318\) 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 −0.996072 0.0885426i \(-0.971779\pi\)
−0.223594 + 0.974682i \(0.571779\pi\)
\(332\) 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 −0.107754 0.994178i \(-0.534366\pi\)
0.497188 + 0.867643i \(0.334366\pi\)
\(338\) 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 −0.576704 0.816953i \(-0.695661\pi\)
0.955180 + 0.296026i \(0.0956614\pi\)
\(348\) 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 −0.214596 0.976703i \(-0.568844\pi\)
0.995214 0.0977244i \(-0.0311564\pi\)
\(354\) 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 0.944300 0.329086i \(-0.106741\pi\)
−0.957387 + 0.288810i \(0.906741\pi\)
\(360\) 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 0.494515 0.869169i \(-0.335346\pi\)
−0.979442 + 0.201724i \(0.935346\pi\)
\(368\) 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 0.218790 0.975772i \(-0.429789\pi\)
−0.396540 + 0.918018i \(0.629789\pi\)
\(374\) 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 0.986419 0.164249i \(-0.0525201\pi\)
0.148610 + 0.988896i \(0.452520\pi\)
\(380\) 0 0
\(381\) 1.21939 0.885941i 0.0624714 0.0453881i
\(382\) 0 0
\(383\) −11.3334 15.5991i −0.579112 0.797079i 0.414486 0.910056i \(-0.363961\pi\)
−0.993598 + 0.112977i \(0.963961\pi\)
\(384\) 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 −0.723876 0.689930i \(-0.757641\pi\)
0.991159 0.132682i \(-0.0423589\pi\)
\(390\) 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 −0.184499 0.982833i \(-0.559066\pi\)
0.991743 0.128243i \(-0.0409336\pi\)
\(398\) 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 −0.967921 0.251256i \(-0.919156\pi\)
0.635379 0.772200i \(-0.280844\pi\)
\(410\) 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 −0.673824 0.738892i \(-0.735349\pi\)
0.494505 + 0.869175i \(0.335349\pi\)
\(420\) 0 0
\(421\) −2.47193 1.79596i −0.120475 0.0875300i 0.525916 0.850536i \(-0.323722\pi\)
−0.646391 + 0.763006i \(0.723722\pi\)
\(422\) 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 −0.155181 0.987886i \(-0.549596\pi\)
0.891582 + 0.452860i \(0.149596\pi\)
\(432\) 0 0
\(433\) −2.00963 2.76602i −0.0965768 0.132927i 0.757994 0.652262i \(-0.226180\pi\)
−0.854571 + 0.519335i \(0.826180\pi\)
\(434\) 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 −0.897477 0.441061i \(-0.854602\pi\)
0.985323 + 0.170698i \(0.0546023\pi\)
\(440\) 0 0
\(441\) −1.39273 4.28639i −0.0663206 0.204114i
\(442\) 0 0
\(443\) 33.0705i 1.57122i −0.618719 0.785612i \(-0.712348\pi\)
0.618719 0.785612i \(-0.287652\pi\)
\(444\) 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 \(0.101212\pi\)
−0.949873 + 0.312635i \(0.898788\pi\)
\(458\) 0 0
\(459\) −1.87590 5.77342i −0.0875595 0.269480i
\(460\) 0 0
\(461\) −12.6568 + 38.9537i −0.589487 + 1.81425i −0.00903372 + 0.999959i \(0.502876\pi\)
−0.580453 + 0.814294i \(0.697124\pi\)
\(462\) 0 0
\(463\) 21.9961 7.14695i 1.02224 0.332147i 0.250524 0.968110i \(-0.419397\pi\)
0.771719 + 0.635963i \(0.219397\pi\)
\(464\) 0 0
\(465\) 7.37382 9.14876i 0.341953 0.424263i
\(466\) 0 0
\(467\) −17.8034 24.5043i −0.823845 1.13392i −0.989038 0.147664i \(-0.952825\pi\)
0.165193 0.986261i \(-0.447175\pi\)
\(468\) 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 0.0457990 0.998951i \(-0.485417\pi\)
−0.935906 + 0.352250i \(0.885417\pi\)
\(480\) 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 −0.357201 0.934028i \(-0.616269\pi\)
0.260026 + 0.965602i \(0.416269\pi\)
\(488\) 0 0
\(489\) −1.85282 + 5.70240i −0.0837875 + 0.257871i
\(490\) 0 0
\(491\) −8.84093 27.2096i −0.398986 1.22795i −0.925814 0.377980i \(-0.876619\pi\)
0.526828 0.849972i \(-0.323381\pi\)
\(492\) 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 −0.814446 0.580239i \(-0.802959\pi\)
0.803518 + 0.595281i \(0.202959\pi\)
\(504\) 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 0.816341 0.577571i \(-0.195999\pi\)
−0.999921 + 0.0125684i \(0.995999\pi\)
\(510\) 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 0.147926 0.988998i \(-0.452740\pi\)
−0.894882 + 0.446303i \(0.852740\pi\)
\(522\) 0 0
\(523\) −11.2943 3.66974i −0.493866 0.160467i 0.0514866 0.998674i \(-0.483604\pi\)
−0.545352 + 0.838207i \(0.683604\pi\)
\(524\) 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 0.830825 + 0.556534i \(0.187869\pi\)
−0.345029 + 0.938592i \(0.612131\pi\)
\(542\) 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 −0.0662579 + 0.997803i \(0.521106\pi\)
−0.928492 + 0.371353i \(0.878894\pi\)
\(548\) 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 \(0.0830802\pi\)
−0.966131 + 0.258051i \(0.916920\pi\)
\(558\) 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 0.536490 0.843907i \(-0.319750\pi\)
0.930065 + 0.367394i \(0.119750\pi\)
\(564\) 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 −0.988154 0.153464i \(-0.950957\pi\)
−0.159403 + 0.987214i \(0.550957\pi\)
\(570\) 0 0
\(571\) 0.974239 + 0.707826i 0.0407706 + 0.0296216i 0.607984 0.793949i \(-0.291978\pi\)
−0.567213 + 0.823571i \(0.691978\pi\)
\(572\) 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 0.615187 0.788381i \(-0.289080\pi\)
0.0342981 + 0.999412i \(0.489080\pi\)
\(578\) 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 0.439182 0.898398i \(-0.355268\pi\)
0.883371 + 0.468674i \(0.155268\pi\)
\(588\) 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 \(0.230112\pi\)
−0.749878 + 0.661576i \(0.769888\pi\)
\(594\) 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 \(-0.894060\pi\)
0.945124 0.326710i \(-0.105940\pi\)
\(608\) 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 −0.981285 0.192559i \(-0.938321\pi\)
−0.680693 + 0.732569i \(0.738321\pi\)
\(614\) 0 0
\(615\) −1.56209 2.39337i −0.0629896 0.0965098i
\(616\) 0 0
\(617\) −0.931550 1.28217i −0.0375028 0.0516182i 0.789854 0.613295i \(-0.210156\pi\)
−0.827357 + 0.561677i \(0.810156\pi\)
\(618\) 0 0
\(619\) −10.9048 + 7.92281i −0.438301 + 0.318444i −0.784960 0.619547i \(-0.787316\pi\)
0.346658 + 0.937991i \(0.387316\pi\)
\(620\) 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 −0.00594245 0.999982i \(-0.501892\pi\)
0.949203 + 0.314663i \(0.101892\pi\)
\(632\) 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 −0.999411 0.0343242i \(-0.989072\pi\)
0.788365 0.615208i \(-0.210928\pi\)
\(642\) 0 0
\(643\) 46.8857i 1.84899i 0.381190 + 0.924497i \(0.375514\pi\)
−0.381190 + 0.924497i \(0.624486\pi\)
\(644\) 0 0
\(645\) 0.831401 + 3.07459i 0.0327364 + 0.121062i
\(646\) 0 0
\(647\) 8.46236 11.6474i 0.332690 0.457908i −0.609599 0.792710i \(-0.708669\pi\)
0.942288 + 0.334802i \(0.108669\pi\)
\(648\) 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 0.263195 + 0.964743i \(0.415224\pi\)
−0.998857 + 0.0478084i \(0.984776\pi\)
\(654\) 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 −0.998295 0.0583742i \(-0.981408\pi\)
0.773326 0.634009i \(-0.218592\pi\)
\(660\) 0 0
\(661\) −0.209866 + 0.645901i −0.00816284 + 0.0251226i −0.955055 0.296429i \(-0.904204\pi\)
0.946892 + 0.321551i \(0.104204\pi\)
\(662\) 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 0.438999 0.898488i \(-0.355333\pi\)
−0.172961 + 0.984929i \(0.555333\pi\)
\(674\) 0 0
\(675\) −0.499813 + 4.97496i −0.0192378 + 0.191486i
\(676\) 0 0
\(677\) −32.2918 10.4922i −1.24107 0.403249i −0.386359 0.922348i \(-0.626267\pi\)
−0.854714 + 0.519099i \(0.826267\pi\)
\(678\) 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 0.998236 0.0593717i \(-0.0189097\pi\)
−0.364938 + 0.931032i \(0.618910\pi\)
\(684\) 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 0.992643 + 0.121076i \(0.0386344\pi\)
−0.731899 + 0.681413i \(0.761366\pi\)
\(692\) 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 0.832852 0.553496i \(-0.186707\pi\)
−0.999128 + 0.0417503i \(0.986707\pi\)
\(710\) 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 −0.394992 0.918685i \(-0.629253\pi\)
0.751662 + 0.659549i \(0.229253\pi\)
\(720\) 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 0.330740 0.943722i \(-0.392702\pi\)
−0.287131 + 0.957891i \(0.592702\pi\)
\(728\) 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 0.591305 0.806448i \(-0.298613\pi\)
−0.949701 + 0.313159i \(0.898613\pi\)
\(734\) 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 −0.808504 0.588491i \(-0.799722\pi\)
1.00000 0.000872485i \(-0.000277721\pi\)
\(740\) 0 0
\(741\) 0.391629 + 1.20531i 0.0143869 + 0.0442782i
\(742\) 0 0
\(743\) 11.8940i 0.436347i 0.975910 + 0.218174i \(0.0700099\pi\)
−0.975910 + 0.218174i \(0.929990\pi\)
\(744\) 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 \(-0.798461\pi\)
0.806166 0.591690i \(-0.201539\pi\)
\(758\) 0 0
\(759\) 1.66734 + 5.13154i 0.0605206 + 0.186263i
\(760\) 0 0
\(761\) −3.35824 + 10.3356i −0.121736 + 0.374665i −0.993292 0.115631i \(-0.963111\pi\)
0.871556 + 0.490295i \(0.163111\pi\)
\(762\) 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 −0.622017 0.783004i \(-0.713687\pi\)
0.552467 + 0.833535i \(0.313687\pi\)
\(770\) 0 0
\(771\) −18.4436 13.4001i −0.664230 0.482592i
\(772\) 0 0
\(773\) 35.4118 + 11.5060i 1.27367 + 0.413841i 0.866347 0.499442i \(-0.166462\pi\)
0.407325 + 0.913283i \(0.366462\pi\)
\(774\) 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 −0.670242 0.742143i \(-0.733809\pi\)
−0.106016 + 0.994364i \(0.533809\pi\)
\(788\) 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 +