Properties

Label 1323.2.o.e.440.18
Level $1323$
Weight $2$
Character 1323.440
Analytic conductor $10.564$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 440.18
Character \(\chi\) \(=\) 1323.440
Dual form 1323.2.o.e.881.18

$q$-expansion

\(f(q)\) \(=\) \(q+(1.02035 + 0.589100i) q^{2} +(-0.305921 - 0.529871i) q^{4} +(2.16601 + 3.75164i) q^{5} -3.07728i q^{8} +O(q^{10})\) \(q+(1.02035 + 0.589100i) q^{2} +(-0.305921 - 0.529871i) q^{4} +(2.16601 + 3.75164i) q^{5} -3.07728i q^{8} +5.10399i q^{10} +(1.87238 + 1.08102i) q^{11} +(2.25256 - 1.30052i) q^{13} +(1.20098 - 2.08016i) q^{16} +1.17115 q^{17} +2.41658i q^{19} +(1.32526 - 2.29541i) q^{20} +(1.27366 + 2.20604i) q^{22} +(3.16186 - 1.82550i) q^{23} +(-6.88321 + 11.9221i) q^{25} +3.06454 q^{26} +(-0.589262 - 0.340210i) q^{29} +(5.67723 - 3.27775i) q^{31} +(-2.87915 + 1.66228i) q^{32} +(1.19499 + 0.689926i) q^{34} -5.10692 q^{37} +(-1.42361 + 2.46576i) q^{38} +(11.5448 - 6.66541i) q^{40} +(3.68473 + 6.38214i) q^{41} +(-2.12577 + 3.68194i) q^{43} -1.32283i q^{44} +4.30162 q^{46} +(-3.57157 + 6.18614i) q^{47} +(-14.0466 + 8.10980i) q^{50} +(-1.37821 - 0.795711i) q^{52} +3.23289i q^{53} +9.36601i q^{55} +(-0.400836 - 0.694269i) q^{58} +(-2.91810 - 5.05430i) q^{59} +(6.21638 + 3.58903i) q^{61} +7.72370 q^{62} -8.72092 q^{64} +(9.75814 + 5.63387i) q^{65} +(-3.32682 - 5.76221i) q^{67} +(-0.358281 - 0.620560i) q^{68} +1.95976i q^{71} -11.9069i q^{73} +(-5.21085 - 3.00849i) q^{74} +(1.28048 - 0.739283i) q^{76} +(4.87702 - 8.44725i) q^{79} +10.4054 q^{80} +8.68270i q^{82} +(-0.796736 + 1.37999i) q^{83} +(2.53673 + 4.39374i) q^{85} +(-4.33806 + 2.50458i) q^{86} +(3.32660 - 5.76184i) q^{88} +6.09921 q^{89} +(-1.93456 - 1.11692i) q^{92} +(-7.28851 + 4.20802i) q^{94} +(-9.06614 + 5.23434i) q^{95} +(-2.36387 - 1.36478i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{4} + O(q^{10}) \) \( 48q + 24q^{4} + 24q^{11} - 24q^{16} + 48q^{23} - 24q^{25} - 120q^{32} - 48q^{50} - 48q^{64} - 120q^{65} + 168q^{74} - 24q^{79} - 24q^{85} - 24q^{86} + 144q^{92} - 96q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.02035 + 0.589100i 0.721498 + 0.416557i 0.815304 0.579034i \(-0.196570\pi\)
−0.0938059 + 0.995591i \(0.529903\pi\)
\(3\) 0 0
\(4\) −0.305921 0.529871i −0.152961 0.264936i
\(5\) 2.16601 + 3.75164i 0.968670 + 1.67778i 0.699415 + 0.714716i \(0.253444\pi\)
0.269254 + 0.963069i \(0.413223\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 3.07728i 1.08798i
\(9\) 0 0
\(10\) 5.10399i 1.61402i
\(11\) 1.87238 + 1.08102i 0.564545 + 0.325940i 0.754968 0.655762i \(-0.227653\pi\)
−0.190423 + 0.981702i \(0.560986\pi\)
\(12\) 0 0
\(13\) 2.25256 1.30052i 0.624748 0.360698i −0.153967 0.988076i \(-0.549205\pi\)
0.778715 + 0.627378i \(0.215872\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.20098 2.08016i 0.300245 0.520040i
\(17\) 1.17115 0.284046 0.142023 0.989863i \(-0.454639\pi\)
0.142023 + 0.989863i \(0.454639\pi\)
\(18\) 0 0
\(19\) 2.41658i 0.554402i 0.960812 + 0.277201i \(0.0894067\pi\)
−0.960812 + 0.277201i \(0.910593\pi\)
\(20\) 1.32526 2.29541i 0.296337 0.513270i
\(21\) 0 0
\(22\) 1.27366 + 2.20604i 0.271545 + 0.470330i
\(23\) 3.16186 1.82550i 0.659294 0.380644i −0.132714 0.991154i \(-0.542369\pi\)
0.792008 + 0.610511i \(0.209036\pi\)
\(24\) 0 0
\(25\) −6.88321 + 11.9221i −1.37664 + 2.38441i
\(26\) 3.06454 0.601006
\(27\) 0 0
\(28\) 0 0
\(29\) −0.589262 0.340210i −0.109423 0.0631755i 0.444290 0.895883i \(-0.353456\pi\)
−0.553713 + 0.832708i \(0.686789\pi\)
\(30\) 0 0
\(31\) 5.67723 3.27775i 1.01966 0.588702i 0.105655 0.994403i \(-0.466306\pi\)
0.914006 + 0.405701i \(0.132973\pi\)
\(32\) −2.87915 + 1.66228i −0.508967 + 0.293852i
\(33\) 0 0
\(34\) 1.19499 + 0.689926i 0.204939 + 0.118321i
\(35\) 0 0
\(36\) 0 0
\(37\) −5.10692 −0.839572 −0.419786 0.907623i \(-0.637895\pi\)
−0.419786 + 0.907623i \(0.637895\pi\)
\(38\) −1.42361 + 2.46576i −0.230940 + 0.399999i
\(39\) 0 0
\(40\) 11.5448 6.66541i 1.82540 1.05389i
\(41\) 3.68473 + 6.38214i 0.575458 + 0.996723i 0.995992 + 0.0894458i \(0.0285096\pi\)
−0.420534 + 0.907277i \(0.638157\pi\)
\(42\) 0 0
\(43\) −2.12577 + 3.68194i −0.324176 + 0.561490i −0.981345 0.192253i \(-0.938420\pi\)
0.657169 + 0.753743i \(0.271754\pi\)
\(44\) 1.32283i 0.199424i
\(45\) 0 0
\(46\) 4.30162 0.634239
\(47\) −3.57157 + 6.18614i −0.520967 + 0.902341i 0.478736 + 0.877959i \(0.341095\pi\)
−0.999703 + 0.0243819i \(0.992238\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −14.0466 + 8.10980i −1.98649 + 1.14690i
\(51\) 0 0
\(52\) −1.37821 0.795711i −0.191124 0.110345i
\(53\) 3.23289i 0.444071i 0.975039 + 0.222036i \(0.0712702\pi\)
−0.975039 + 0.222036i \(0.928730\pi\)
\(54\) 0 0
\(55\) 9.36601i 1.26291i
\(56\) 0 0
\(57\) 0 0
\(58\) −0.400836 0.694269i −0.0526324 0.0911619i
\(59\) −2.91810 5.05430i −0.379905 0.658014i 0.611143 0.791520i \(-0.290710\pi\)
−0.991048 + 0.133506i \(0.957377\pi\)
\(60\) 0 0
\(61\) 6.21638 + 3.58903i 0.795925 + 0.459528i 0.842044 0.539408i \(-0.181352\pi\)
−0.0461190 + 0.998936i \(0.514685\pi\)
\(62\) 7.72370 0.980911
\(63\) 0 0
\(64\) −8.72092 −1.09012
\(65\) 9.75814 + 5.63387i 1.21035 + 0.698795i
\(66\) 0 0
\(67\) −3.32682 5.76221i −0.406435 0.703966i 0.588052 0.808823i \(-0.299895\pi\)
−0.994487 + 0.104857i \(0.966562\pi\)
\(68\) −0.358281 0.620560i −0.0434479 0.0752540i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.95976i 0.232580i 0.993215 + 0.116290i \(0.0371003\pi\)
−0.993215 + 0.116290i \(0.962900\pi\)
\(72\) 0 0
\(73\) 11.9069i 1.39360i −0.717266 0.696799i \(-0.754607\pi\)
0.717266 0.696799i \(-0.245393\pi\)
\(74\) −5.21085 3.00849i −0.605749 0.349729i
\(75\) 0 0
\(76\) 1.28048 0.739283i 0.146881 0.0848016i
\(77\) 0 0
\(78\) 0 0
\(79\) 4.87702 8.44725i 0.548708 0.950390i −0.449656 0.893202i \(-0.648453\pi\)
0.998363 0.0571879i \(-0.0182134\pi\)
\(80\) 10.4054 1.16335
\(81\) 0 0
\(82\) 8.68270i 0.958844i
\(83\) −0.796736 + 1.37999i −0.0874531 + 0.151473i −0.906434 0.422348i \(-0.861206\pi\)
0.818981 + 0.573821i \(0.194539\pi\)
\(84\) 0 0
\(85\) 2.53673 + 4.39374i 0.275147 + 0.476568i
\(86\) −4.33806 + 2.50458i −0.467785 + 0.270076i
\(87\) 0 0
\(88\) 3.32660 5.76184i 0.354617 0.614214i
\(89\) 6.09921 0.646515 0.323258 0.946311i \(-0.395222\pi\)
0.323258 + 0.946311i \(0.395222\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.93456 1.11692i −0.201692 0.116447i
\(93\) 0 0
\(94\) −7.28851 + 4.20802i −0.751753 + 0.434025i
\(95\) −9.06614 + 5.23434i −0.930166 + 0.537032i
\(96\) 0 0
\(97\) −2.36387 1.36478i −0.240014 0.138572i 0.375169 0.926956i \(-0.377585\pi\)
−0.615183 + 0.788384i \(0.710918\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 8.42288 0.842288
\(101\) −7.99849 + 13.8538i −0.795880 + 1.37850i 0.126400 + 0.991979i \(0.459658\pi\)
−0.922279 + 0.386524i \(0.873676\pi\)
\(102\) 0 0
\(103\) −2.61251 + 1.50834i −0.257419 + 0.148621i −0.623156 0.782097i \(-0.714150\pi\)
0.365738 + 0.930718i \(0.380817\pi\)
\(104\) −4.00205 6.93175i −0.392433 0.679714i
\(105\) 0 0
\(106\) −1.90450 + 3.29868i −0.184981 + 0.320397i
\(107\) 11.8484i 1.14543i −0.819754 0.572716i \(-0.805890\pi\)
0.819754 0.572716i \(-0.194110\pi\)
\(108\) 0 0
\(109\) 7.16157 0.685954 0.342977 0.939344i \(-0.388565\pi\)
0.342977 + 0.939344i \(0.388565\pi\)
\(110\) −5.51752 + 9.55662i −0.526075 + 0.911188i
\(111\) 0 0
\(112\) 0 0
\(113\) −2.46102 + 1.42087i −0.231514 + 0.133664i −0.611270 0.791422i \(-0.709341\pi\)
0.379756 + 0.925086i \(0.376008\pi\)
\(114\) 0 0
\(115\) 13.6973 + 7.90812i 1.27728 + 0.737436i
\(116\) 0.416310i 0.0386535i
\(117\) 0 0
\(118\) 6.87623i 0.633008i
\(119\) 0 0
\(120\) 0 0
\(121\) −3.16279 5.47811i −0.287526 0.498010i
\(122\) 4.22859 + 7.32414i 0.382839 + 0.663096i
\(123\) 0 0
\(124\) −3.47357 2.00547i −0.311936 0.180096i
\(125\) −37.9763 −3.39670
\(126\) 0 0
\(127\) 18.5344 1.64466 0.822332 0.569009i \(-0.192673\pi\)
0.822332 + 0.569009i \(0.192673\pi\)
\(128\) −3.14011 1.81294i −0.277549 0.160243i
\(129\) 0 0
\(130\) 6.63783 + 11.4971i 0.582176 + 1.00836i
\(131\) −3.35221 5.80619i −0.292884 0.507289i 0.681607 0.731719i \(-0.261282\pi\)
−0.974490 + 0.224429i \(0.927948\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 7.83931i 0.677214i
\(135\) 0 0
\(136\) 3.60396i 0.309037i
\(137\) −11.8181 6.82316i −1.00969 0.582942i −0.0985856 0.995129i \(-0.531432\pi\)
−0.911099 + 0.412187i \(0.864765\pi\)
\(138\) 0 0
\(139\) 7.74126 4.46942i 0.656605 0.379091i −0.134377 0.990930i \(-0.542903\pi\)
0.790982 + 0.611839i \(0.209570\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.15449 + 1.99964i −0.0968830 + 0.167806i
\(143\) 5.62354 0.470264
\(144\) 0 0
\(145\) 2.94760i 0.244785i
\(146\) 7.01436 12.1492i 0.580513 1.00548i
\(147\) 0 0
\(148\) 1.56231 + 2.70601i 0.128421 + 0.222432i
\(149\) 3.29003 1.89950i 0.269530 0.155613i −0.359144 0.933282i \(-0.616931\pi\)
0.628674 + 0.777669i \(0.283598\pi\)
\(150\) 0 0
\(151\) 1.91083 3.30965i 0.155501 0.269336i −0.777740 0.628586i \(-0.783634\pi\)
0.933241 + 0.359250i \(0.116967\pi\)
\(152\) 7.43648 0.603178
\(153\) 0 0
\(154\) 0 0
\(155\) 24.5939 + 14.1993i 1.97543 + 1.14051i
\(156\) 0 0
\(157\) −18.6081 + 10.7434i −1.48509 + 0.857417i −0.999856 0.0169675i \(-0.994599\pi\)
−0.485234 + 0.874384i \(0.661265\pi\)
\(158\) 9.95256 5.74611i 0.791783 0.457136i
\(159\) 0 0
\(160\) −12.4725 7.20102i −0.986041 0.569291i
\(161\) 0 0
\(162\) 0 0
\(163\) 12.5175 0.980447 0.490223 0.871597i \(-0.336915\pi\)
0.490223 + 0.871597i \(0.336915\pi\)
\(164\) 2.25448 3.90487i 0.176045 0.304919i
\(165\) 0 0
\(166\) −1.62590 + 0.938715i −0.126194 + 0.0728584i
\(167\) 7.70819 + 13.3510i 0.596477 + 1.03313i 0.993337 + 0.115250i \(0.0367668\pi\)
−0.396859 + 0.917880i \(0.629900\pi\)
\(168\) 0 0
\(169\) −3.11731 + 5.39935i −0.239793 + 0.415334i
\(170\) 5.97755i 0.458457i
\(171\) 0 0
\(172\) 2.60127 0.198345
\(173\) 4.30737 7.46059i 0.327483 0.567218i −0.654528 0.756037i \(-0.727133\pi\)
0.982012 + 0.188820i \(0.0604661\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4.49739 2.59657i 0.339004 0.195724i
\(177\) 0 0
\(178\) 6.22334 + 3.59305i 0.466459 + 0.269310i
\(179\) 19.1384i 1.43047i −0.698882 0.715237i \(-0.746319\pi\)
0.698882 0.715237i \(-0.253681\pi\)
\(180\) 0 0
\(181\) 7.69817i 0.572200i −0.958200 0.286100i \(-0.907641\pi\)
0.958200 0.286100i \(-0.0923590\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −5.61758 9.72993i −0.414133 0.717300i
\(185\) −11.0616 19.1593i −0.813268 1.40862i
\(186\) 0 0
\(187\) 2.19285 + 1.26604i 0.160357 + 0.0925820i
\(188\) 4.37047 0.318750
\(189\) 0 0
\(190\) −12.3342 −0.894817
\(191\) −16.1203 9.30704i −1.16642 0.673433i −0.213587 0.976924i \(-0.568515\pi\)
−0.952834 + 0.303491i \(0.901848\pi\)
\(192\) 0 0
\(193\) −9.05721 15.6875i −0.651952 1.12921i −0.982649 0.185477i \(-0.940617\pi\)
0.330696 0.943737i \(-0.392716\pi\)
\(194\) −1.60799 2.78511i −0.115447 0.199959i
\(195\) 0 0
\(196\) 0 0
\(197\) 16.5945i 1.18231i −0.806559 0.591154i \(-0.798672\pi\)
0.806559 0.591154i \(-0.201328\pi\)
\(198\) 0 0
\(199\) 2.71887i 0.192735i −0.995346 0.0963677i \(-0.969278\pi\)
0.995346 0.0963677i \(-0.0307225\pi\)
\(200\) 36.6875 + 21.1815i 2.59420 + 1.49776i
\(201\) 0 0
\(202\) −16.3225 + 9.42383i −1.14845 + 0.663058i
\(203\) 0 0
\(204\) 0 0
\(205\) −15.9623 + 27.6476i −1.11486 + 1.93099i
\(206\) −3.55425 −0.247636
\(207\) 0 0
\(208\) 6.24759i 0.433192i
\(209\) −2.61237 + 4.52476i −0.180702 + 0.312984i
\(210\) 0 0
\(211\) −13.9445 24.1526i −0.959979 1.66273i −0.722539 0.691330i \(-0.757025\pi\)
−0.237440 0.971402i \(-0.576308\pi\)
\(212\) 1.71301 0.989010i 0.117650 0.0679255i
\(213\) 0 0
\(214\) 6.97992 12.0896i 0.477138 0.826427i
\(215\) −18.4177 −1.25608
\(216\) 0 0
\(217\) 0 0
\(218\) 7.30732 + 4.21888i 0.494914 + 0.285739i
\(219\) 0 0
\(220\) 4.96278 2.86526i 0.334590 0.193176i
\(221\) 2.63809 1.52310i 0.177457 0.102455i
\(222\) 0 0
\(223\) 6.64349 + 3.83562i 0.444881 + 0.256852i 0.705666 0.708545i \(-0.250648\pi\)
−0.260785 + 0.965397i \(0.583981\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3.34815 −0.222715
\(227\) −1.16439 + 2.01677i −0.0772829 + 0.133858i −0.902077 0.431576i \(-0.857958\pi\)
0.824794 + 0.565434i \(0.191291\pi\)
\(228\) 0 0
\(229\) −10.3653 + 5.98443i −0.684961 + 0.395463i −0.801722 0.597698i \(-0.796082\pi\)
0.116760 + 0.993160i \(0.462749\pi\)
\(230\) 9.31735 + 16.1381i 0.614368 + 1.06412i
\(231\) 0 0
\(232\) −1.04692 + 1.81332i −0.0687337 + 0.119050i
\(233\) 2.52779i 0.165601i −0.996566 0.0828007i \(-0.973614\pi\)
0.996566 0.0828007i \(-0.0263865\pi\)
\(234\) 0 0
\(235\) −30.9442 −2.01858
\(236\) −1.78542 + 3.09244i −0.116221 + 0.201301i
\(237\) 0 0
\(238\) 0 0
\(239\) −17.4587 + 10.0798i −1.12931 + 0.652006i −0.943761 0.330630i \(-0.892739\pi\)
−0.185546 + 0.982636i \(0.559405\pi\)
\(240\) 0 0
\(241\) −18.1254 10.4647i −1.16756 0.674091i −0.214455 0.976734i \(-0.568798\pi\)
−0.953104 + 0.302643i \(0.902131\pi\)
\(242\) 7.45280i 0.479084i
\(243\) 0 0
\(244\) 4.39184i 0.281159i
\(245\) 0 0
\(246\) 0 0
\(247\) 3.14280 + 5.44349i 0.199972 + 0.346361i
\(248\) −10.0865 17.4704i −0.640496 1.10937i
\(249\) 0 0
\(250\) −38.7492 22.3718i −2.45071 1.41492i
\(251\) 25.5747 1.61426 0.807130 0.590374i \(-0.201020\pi\)
0.807130 + 0.590374i \(0.201020\pi\)
\(252\) 0 0
\(253\) 7.89363 0.496268
\(254\) 18.9116 + 10.9186i 1.18662 + 0.685096i
\(255\) 0 0
\(256\) 6.58491 + 11.4054i 0.411557 + 0.712837i
\(257\) −5.93725 10.2836i −0.370355 0.641474i 0.619265 0.785182i \(-0.287431\pi\)
−0.989620 + 0.143708i \(0.954097\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 6.89408i 0.427553i
\(261\) 0 0
\(262\) 7.89915i 0.488011i
\(263\) −19.3705 11.1836i −1.19444 0.689608i −0.235127 0.971965i \(-0.575550\pi\)
−0.959309 + 0.282357i \(0.908884\pi\)
\(264\) 0 0
\(265\) −12.1286 + 7.00247i −0.745056 + 0.430158i
\(266\) 0 0
\(267\) 0 0
\(268\) −2.03549 + 3.52557i −0.124337 + 0.215358i
\(269\) −4.22669 −0.257706 −0.128853 0.991664i \(-0.541130\pi\)
−0.128853 + 0.991664i \(0.541130\pi\)
\(270\) 0 0
\(271\) 22.3943i 1.36036i −0.733046 0.680179i \(-0.761902\pi\)
0.733046 0.680179i \(-0.238098\pi\)
\(272\) 1.40653 2.43619i 0.0852836 0.147715i
\(273\) 0 0
\(274\) −8.03905 13.9240i −0.485657 0.841183i
\(275\) −25.7760 + 14.8818i −1.55435 + 0.897405i
\(276\) 0 0
\(277\) −5.69230 + 9.85935i −0.342017 + 0.592391i −0.984807 0.173651i \(-0.944443\pi\)
0.642790 + 0.766042i \(0.277777\pi\)
\(278\) 10.5317 0.631652
\(279\) 0 0
\(280\) 0 0
\(281\) 0.702700 + 0.405704i 0.0419196 + 0.0242023i 0.520813 0.853671i \(-0.325629\pi\)
−0.478894 + 0.877873i \(0.658962\pi\)
\(282\) 0 0
\(283\) 15.8740 9.16486i 0.943611 0.544794i 0.0525206 0.998620i \(-0.483274\pi\)
0.891090 + 0.453826i \(0.149941\pi\)
\(284\) 1.03842 0.599532i 0.0616188 0.0355757i
\(285\) 0 0
\(286\) 5.73799 + 3.31283i 0.339294 + 0.195892i
\(287\) 0 0
\(288\) 0 0
\(289\) −15.6284 −0.919318
\(290\) 1.73643 3.00759i 0.101967 0.176612i
\(291\) 0 0
\(292\) −6.30913 + 3.64258i −0.369214 + 0.213166i
\(293\) −6.23639 10.8017i −0.364334 0.631044i 0.624335 0.781156i \(-0.285370\pi\)
−0.988669 + 0.150112i \(0.952037\pi\)
\(294\) 0 0
\(295\) 12.6413 21.8954i 0.736004 1.27480i
\(296\) 15.7154i 0.913438i
\(297\) 0 0
\(298\) 4.47599 0.259287
\(299\) 4.74819 8.22411i 0.274595 0.475613i
\(300\) 0 0
\(301\) 0 0
\(302\) 3.89943 2.25134i 0.224387 0.129550i
\(303\) 0 0
\(304\) 5.02688 + 2.90227i 0.288311 + 0.166457i
\(305\) 31.0955i 1.78052i
\(306\) 0 0
\(307\) 21.3241i 1.21703i 0.793543 + 0.608514i \(0.208234\pi\)
−0.793543 + 0.608514i \(0.791766\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 16.7296 + 28.9765i 0.950178 + 1.64576i
\(311\) 3.92094 + 6.79126i 0.222336 + 0.385097i 0.955517 0.294936i \(-0.0952985\pi\)
−0.733181 + 0.680034i \(0.761965\pi\)
\(312\) 0 0
\(313\) 8.57593 + 4.95131i 0.484740 + 0.279865i 0.722390 0.691486i \(-0.243044\pi\)
−0.237650 + 0.971351i \(0.576377\pi\)
\(314\) −25.3158 −1.42865
\(315\) 0 0
\(316\) −5.96794 −0.335723
\(317\) −20.8358 12.0296i −1.17025 0.675647i −0.216515 0.976279i \(-0.569469\pi\)
−0.953740 + 0.300632i \(0.902802\pi\)
\(318\) 0 0
\(319\) −0.735549 1.27401i −0.0411828 0.0713308i
\(320\) −18.8896 32.7178i −1.05596 1.82898i
\(321\) 0 0
\(322\) 0 0
\(323\) 2.83018i 0.157476i
\(324\) 0 0
\(325\) 35.8069i 1.98621i
\(326\) 12.7723 + 7.37407i 0.707390 + 0.408412i
\(327\) 0 0
\(328\) 19.6396 11.3389i 1.08442 0.626088i
\(329\) 0 0
\(330\) 0 0
\(331\) 4.53686 7.85807i 0.249368 0.431918i −0.713982 0.700164i \(-0.753110\pi\)
0.963351 + 0.268245i \(0.0864437\pi\)
\(332\) 0.974954 0.0535075
\(333\) 0 0
\(334\) 18.1636i 0.993867i
\(335\) 14.4118 24.9620i 0.787403 1.36382i
\(336\) 0 0
\(337\) 4.02012 + 6.96304i 0.218990 + 0.379301i 0.954499 0.298213i \(-0.0963906\pi\)
−0.735510 + 0.677514i \(0.763057\pi\)
\(338\) −6.36152 + 3.67282i −0.346021 + 0.199775i
\(339\) 0 0
\(340\) 1.55208 2.68828i 0.0841733 0.145792i
\(341\) 14.1733 0.767525
\(342\) 0 0
\(343\) 0 0
\(344\) 11.3303 + 6.54157i 0.610891 + 0.352698i
\(345\) 0 0
\(346\) 8.79007 5.07495i 0.472557 0.272831i
\(347\) 30.6345 17.6868i 1.64454 0.949478i 0.665356 0.746526i \(-0.268280\pi\)
0.979189 0.202952i \(-0.0650536\pi\)
\(348\) 0 0
\(349\) 21.1868 + 12.2322i 1.13411 + 0.654776i 0.944964 0.327174i \(-0.106096\pi\)
0.189141 + 0.981950i \(0.439430\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −7.18783 −0.383112
\(353\) 0.485949 0.841688i 0.0258644 0.0447985i −0.852803 0.522232i \(-0.825100\pi\)
0.878668 + 0.477433i \(0.158433\pi\)
\(354\) 0 0
\(355\) −7.35231 + 4.24486i −0.390220 + 0.225294i
\(356\) −1.86588 3.23180i −0.0988914 0.171285i
\(357\) 0 0
\(358\) 11.2745 19.5279i 0.595874 1.03208i
\(359\) 15.9210i 0.840276i 0.907460 + 0.420138i \(0.138018\pi\)
−0.907460 + 0.420138i \(0.861982\pi\)
\(360\) 0 0
\(361\) 13.1601 0.692639
\(362\) 4.53499 7.85484i 0.238354 0.412841i
\(363\) 0 0
\(364\) 0 0
\(365\) 44.6704 25.7905i 2.33816 1.34994i
\(366\) 0 0
\(367\) −21.3983 12.3543i −1.11698 0.644891i −0.176355 0.984327i \(-0.556431\pi\)
−0.940629 + 0.339435i \(0.889764\pi\)
\(368\) 8.76958i 0.457146i
\(369\) 0 0
\(370\) 26.0657i 1.35509i
\(371\) 0 0
\(372\) 0 0
\(373\) 4.71810 + 8.17200i 0.244294 + 0.423130i 0.961933 0.273286i \(-0.0881104\pi\)
−0.717639 + 0.696416i \(0.754777\pi\)
\(374\) 1.49165 + 2.58361i 0.0771314 + 0.133595i
\(375\) 0 0
\(376\) 19.0364 + 10.9907i 0.981730 + 0.566802i
\(377\) −1.76980 −0.0911492
\(378\) 0 0
\(379\) 20.8031 1.06858 0.534292 0.845300i \(-0.320578\pi\)
0.534292 + 0.845300i \(0.320578\pi\)
\(380\) 5.54705 + 3.20259i 0.284558 + 0.164289i
\(381\) 0 0
\(382\) −10.9656 18.9929i −0.561047 0.971761i
\(383\) 3.23008 + 5.59467i 0.165050 + 0.285874i 0.936673 0.350205i \(-0.113888\pi\)
−0.771623 + 0.636080i \(0.780555\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 21.3424i 1.08630i
\(387\) 0 0
\(388\) 1.67006i 0.0847845i
\(389\) 0.0445846 + 0.0257409i 0.00226053 + 0.00130512i 0.501130 0.865372i \(-0.332918\pi\)
−0.498869 + 0.866677i \(0.666251\pi\)
\(390\) 0 0
\(391\) 3.70303 2.13794i 0.187270 0.108120i
\(392\) 0 0
\(393\) 0 0
\(394\) 9.77582 16.9322i 0.492499 0.853033i
\(395\) 42.2547 2.12607
\(396\) 0 0
\(397\) 12.7131i 0.638052i 0.947746 + 0.319026i \(0.103356\pi\)
−0.947746 + 0.319026i \(0.896644\pi\)
\(398\) 1.60169 2.77420i 0.0802853 0.139058i
\(399\) 0 0
\(400\) 16.5332 + 28.6364i 0.826660 + 1.43182i
\(401\) 2.19725 1.26858i 0.109725 0.0633500i −0.444133 0.895961i \(-0.646488\pi\)
0.553858 + 0.832611i \(0.313155\pi\)
\(402\) 0 0
\(403\) 8.52554 14.7667i 0.424687 0.735580i
\(404\) 9.78764 0.486953
\(405\) 0 0
\(406\) 0 0
\(407\) −9.56210 5.52068i −0.473976 0.273650i
\(408\) 0 0
\(409\) −0.0495655 + 0.0286167i −0.00245086 + 0.00141500i −0.501225 0.865317i \(-0.667117\pi\)
0.498774 + 0.866732i \(0.333784\pi\)
\(410\) −32.5744 + 18.8068i −1.60873 + 0.928803i
\(411\) 0 0
\(412\) 1.59845 + 0.922864i 0.0787499 + 0.0454663i
\(413\) 0 0
\(414\) 0 0
\(415\) −6.90295 −0.338853
\(416\) −4.32364 + 7.48876i −0.211984 + 0.367167i
\(417\) 0 0
\(418\) −5.33108 + 3.07790i −0.260752 + 0.150545i
\(419\) −3.08007 5.33484i −0.150471 0.260624i 0.780930 0.624619i \(-0.214746\pi\)
−0.931401 + 0.363995i \(0.881412\pi\)
\(420\) 0 0
\(421\) 15.0693 26.1007i 0.734431 1.27207i −0.220542 0.975378i \(-0.570783\pi\)
0.954973 0.296694i \(-0.0958842\pi\)
\(422\) 32.8588i 1.59954i
\(423\) 0 0
\(424\) 9.94849 0.483141
\(425\) −8.06128 + 13.9626i −0.391030 + 0.677283i
\(426\) 0 0
\(427\) 0 0
\(428\) −6.27815 + 3.62469i −0.303466 + 0.175206i
\(429\) 0 0
\(430\) −18.7926 10.8499i −0.906258 0.523228i
\(431\) 8.07140i 0.388785i 0.980924 + 0.194393i \(0.0622736\pi\)
−0.980924 + 0.194393i \(0.937726\pi\)
\(432\) 0 0
\(433\) 28.4938i 1.36933i 0.728860 + 0.684663i \(0.240051\pi\)
−0.728860 + 0.684663i \(0.759949\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2.19088 3.79471i −0.104924 0.181734i
\(437\) 4.41147 + 7.64090i 0.211029 + 0.365514i
\(438\) 0 0
\(439\) 1.77067 + 1.02230i 0.0845096 + 0.0487916i 0.541659 0.840598i \(-0.317796\pi\)
−0.457150 + 0.889390i \(0.651130\pi\)
\(440\) 28.8218 1.37402
\(441\) 0 0
\(442\) 3.58904 0.170713
\(443\) 21.1324 + 12.2008i 1.00403 + 0.579677i 0.909438 0.415839i \(-0.136512\pi\)
0.0945924 + 0.995516i \(0.469845\pi\)
\(444\) 0 0
\(445\) 13.2110 + 22.8821i 0.626260 + 1.08471i
\(446\) 4.51913 + 7.82737i 0.213987 + 0.370637i
\(447\) 0 0
\(448\) 0 0
\(449\) 0.293539i 0.0138529i 0.999976 + 0.00692647i \(0.00220478\pi\)
−0.999976 + 0.00692647i \(0.997795\pi\)
\(450\) 0 0
\(451\) 15.9331i 0.750259i
\(452\) 1.50576 + 0.869351i 0.0708250 + 0.0408908i
\(453\) 0 0
\(454\) −2.37616 + 1.37188i −0.111519 + 0.0643855i
\(455\) 0 0
\(456\) 0 0
\(457\) −8.27470 + 14.3322i −0.387074 + 0.670432i −0.992055 0.125808i \(-0.959848\pi\)
0.604981 + 0.796240i \(0.293181\pi\)
\(458\) −14.1017 −0.658931
\(459\) 0 0
\(460\) 9.67705i 0.451195i
\(461\) −10.0560 + 17.4175i −0.468354 + 0.811213i −0.999346 0.0361638i \(-0.988486\pi\)
0.530992 + 0.847377i \(0.321820\pi\)
\(462\) 0 0
\(463\) 9.34602 + 16.1878i 0.434346 + 0.752310i 0.997242 0.0742181i \(-0.0236461\pi\)
−0.562896 + 0.826528i \(0.690313\pi\)
\(464\) −1.41538 + 0.817173i −0.0657076 + 0.0379363i
\(465\) 0 0
\(466\) 1.48912 2.57924i 0.0689824 0.119481i
\(467\) −29.3605 −1.35864 −0.679322 0.733841i \(-0.737726\pi\)
−0.679322 + 0.733841i \(0.737726\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −31.5740 18.2293i −1.45640 0.840853i
\(471\) 0 0
\(472\) −15.5535 + 8.97981i −0.715907 + 0.413329i
\(473\) −7.96050 + 4.59599i −0.366024 + 0.211324i
\(474\) 0 0
\(475\) −28.8106 16.6338i −1.32192 0.763212i
\(476\) 0 0
\(477\) 0 0
\(478\) −23.7520 −1.08639
\(479\) −10.9660 + 18.9938i −0.501051 + 0.867847i 0.498948 + 0.866632i \(0.333720\pi\)
−0.999999 + 0.00121455i \(0.999613\pi\)
\(480\) 0 0
\(481\) −11.5036 + 6.64163i −0.524521 + 0.302832i
\(482\) −12.3295 21.3554i −0.561594 0.972710i
\(483\) 0 0
\(484\) −1.93513 + 3.35174i −0.0879604 + 0.152352i
\(485\) 11.8245i 0.536923i
\(486\) 0 0
\(487\) 1.07779 0.0488394 0.0244197 0.999702i \(-0.492226\pi\)
0.0244197 + 0.999702i \(0.492226\pi\)
\(488\) 11.0444 19.1295i 0.499957 0.865952i
\(489\) 0 0
\(490\) 0 0
\(491\) −16.3708 + 9.45168i −0.738804 + 0.426549i −0.821634 0.570015i \(-0.806937\pi\)
0.0828305 + 0.996564i \(0.473604\pi\)
\(492\) 0 0
\(493\) −0.690115 0.398438i −0.0310812 0.0179448i
\(494\) 7.40570i 0.333198i
\(495\) 0 0
\(496\) 15.7461i 0.707020i
\(497\) 0 0
\(498\) 0 0
\(499\) 8.34290 + 14.4503i 0.373479 + 0.646885i 0.990098 0.140377i \(-0.0448314\pi\)
−0.616619 + 0.787262i \(0.711498\pi\)
\(500\) 11.6178 + 20.1225i 0.519562 + 0.899908i
\(501\) 0 0
\(502\) 26.0952 + 15.0661i 1.16468 + 0.672431i
\(503\) −21.2386 −0.946981 −0.473491 0.880799i \(-0.657006\pi\)
−0.473491 + 0.880799i \(0.657006\pi\)
\(504\) 0 0
\(505\) −69.2993 −3.08378
\(506\) 8.05428 + 4.65014i 0.358056 + 0.206724i
\(507\) 0 0
\(508\) −5.67007 9.82085i −0.251569 0.435730i
\(509\) 5.72252 + 9.91170i 0.253646 + 0.439328i 0.964527 0.263984i \(-0.0850367\pi\)
−0.710881 + 0.703313i \(0.751703\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.7685i 1.00623i
\(513\) 0 0
\(514\) 13.9905i 0.617096i
\(515\) −11.3175 6.53414i −0.498707 0.287929i
\(516\) 0 0
\(517\) −13.3747 + 7.72188i −0.588218 + 0.339608i
\(518\) 0 0
\(519\) 0 0
\(520\) 17.3370 30.0285i 0.760276 1.31684i
\(521\) −20.7998 −0.911254 −0.455627 0.890171i \(-0.650585\pi\)
−0.455627 + 0.890171i \(0.650585\pi\)
\(522\) 0 0
\(523\) 14.9338i 0.653009i −0.945196 0.326505i \(-0.894129\pi\)
0.945196 0.326505i \(-0.105871\pi\)
\(524\) −2.05102 + 3.55248i −0.0895994 + 0.155191i
\(525\) 0 0
\(526\) −13.1765 22.8223i −0.574522 0.995101i
\(527\) 6.64890 3.83875i 0.289631 0.167218i
\(528\) 0 0
\(529\) −4.83508 + 8.37460i −0.210221 + 0.364113i
\(530\) −16.5006 −0.716742
\(531\) 0 0
\(532\) 0 0
\(533\) 16.6002 + 9.58410i 0.719033 + 0.415134i
\(534\) 0 0
\(535\) 44.4511 25.6639i 1.92179 1.10955i
\(536\) −17.7319 + 10.2375i −0.765902 + 0.442194i
\(537\) 0 0
\(538\) −4.31272 2.48995i −0.185934 0.107349i
\(539\) 0 0
\(540\) 0 0
\(541\) 31.1677 1.34000 0.670002 0.742360i \(-0.266293\pi\)
0.670002 + 0.742360i \(0.266293\pi\)
\(542\) 13.1925 22.8501i 0.566667 0.981496i
\(543\) 0 0
\(544\) −3.37192 + 1.94678i −0.144570 + 0.0834675i
\(545\) 15.5120 + 26.8676i 0.664462 + 1.15088i
\(546\) 0 0
\(547\) −15.7410 + 27.2642i −0.673035 + 1.16573i 0.304004 + 0.952671i \(0.401677\pi\)
−0.977039 + 0.213061i \(0.931657\pi\)
\(548\) 8.34940i 0.356669i
\(549\) 0 0
\(550\) −35.0674 −1.49528
\(551\) 0.822146 1.42400i 0.0350246 0.0606644i
\(552\) 0 0
\(553\) 0 0
\(554\) −11.6163 + 6.70667i −0.493529 + 0.284939i
\(555\) 0 0
\(556\) −4.73643 2.73458i −0.200870 0.115972i
\(557\) 27.2389i 1.15415i −0.816692 0.577074i \(-0.804194\pi\)
0.816692 0.577074i \(-0.195806\pi\)
\(558\) 0 0
\(559\) 11.0584i 0.467720i
\(560\) 0 0
\(561\) 0 0
\(562\) 0.478001 + 0.827922i 0.0201633 + 0.0349238i
\(563\) −14.1871 24.5728i −0.597916 1.03562i −0.993128 0.117031i \(-0.962662\pi\)
0.395212 0.918590i \(-0.370671\pi\)
\(564\) 0 0
\(565\) −10.6612 6.15525i −0.448521 0.258953i
\(566\) 21.5961 0.907751
\(567\) 0 0
\(568\) 6.03071 0.253043
\(569\) −29.4616 17.0097i −1.23509 0.713082i −0.267007 0.963695i \(-0.586035\pi\)
−0.968087 + 0.250613i \(0.919368\pi\)
\(570\) 0 0
\(571\) 22.3455 + 38.7035i 0.935130 + 1.61969i 0.774402 + 0.632693i \(0.218051\pi\)
0.160727 + 0.986999i \(0.448616\pi\)
\(572\) −1.72036 2.97975i −0.0719319 0.124590i
\(573\) 0 0
\(574\) 0 0
\(575\) 50.2613i 2.09604i
\(576\) 0 0
\(577\) 7.34738i 0.305875i 0.988236 + 0.152938i \(0.0488734\pi\)
−0.988236 + 0.152938i \(0.951127\pi\)
\(578\) −15.9465 9.20670i −0.663286 0.382948i
\(579\) 0 0
\(580\) −1.56185 + 0.901733i −0.0648522 + 0.0374424i
\(581\) 0 0
\(582\) 0 0
\(583\) −3.49482 + 6.05320i −0.144741 + 0.250698i
\(584\) −36.6408 −1.51621
\(585\) 0 0
\(586\) 14.6954i 0.607063i
\(587\) −13.1328 + 22.7466i −0.542048 + 0.938855i 0.456738 + 0.889601i \(0.349018\pi\)
−0.998786 + 0.0492535i \(0.984316\pi\)
\(588\) 0 0
\(589\) 7.92095 + 13.7195i 0.326377 + 0.565302i
\(590\) 25.7971 14.8940i 1.06205 0.613175i
\(591\) 0 0
\(592\) −6.13331 + 10.6232i −0.252078 + 0.436611i
\(593\) −9.12418 −0.374685 −0.187343 0.982295i \(-0.559987\pi\)
−0.187343 + 0.982295i \(0.559987\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −2.01298 1.16220i −0.0824550 0.0476054i
\(597\) 0 0
\(598\) 9.68966 5.59433i 0.396240 0.228769i
\(599\) 20.0987 11.6040i 0.821210 0.474126i −0.0296234 0.999561i \(-0.509431\pi\)
0.850834 + 0.525435i \(0.176097\pi\)
\(600\) 0 0
\(601\) 19.0021 + 10.9709i 0.775111 + 0.447510i 0.834695 0.550713i \(-0.185644\pi\)
−0.0595840 + 0.998223i \(0.518977\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −2.33825 −0.0951421
\(605\) 13.7013 23.7313i 0.557036 0.964815i
\(606\) 0 0
\(607\) 38.6289 22.3024i 1.56790 0.905226i 0.571484 0.820613i \(-0.306368\pi\)
0.996414 0.0846136i \(-0.0269656\pi\)
\(608\) −4.01703 6.95770i −0.162912 0.282172i
\(609\) 0 0
\(610\) −18.3184 + 31.7283i −0.741689 + 1.28464i
\(611\) 18.5795i 0.751647i
\(612\) 0 0
\(613\) 11.6560 0.470780 0.235390 0.971901i \(-0.424363\pi\)
0.235390 + 0.971901i \(0.424363\pi\)
\(614\) −12.5620 + 21.7580i −0.506961 + 0.878083i
\(615\) 0 0
\(616\) 0 0
\(617\) −36.6143 + 21.1393i −1.47403 + 0.851034i −0.999572 0.0292416i \(-0.990691\pi\)
−0.474462 + 0.880276i \(0.657357\pi\)
\(618\) 0 0
\(619\) 30.0633 + 17.3571i 1.20835 + 0.697640i 0.962398 0.271643i \(-0.0875670\pi\)
0.245949 + 0.969283i \(0.420900\pi\)
\(620\) 17.3755i 0.697815i
\(621\) 0 0
\(622\) 9.23930i 0.370462i
\(623\) 0 0
\(624\) 0 0
\(625\) −47.8410 82.8631i −1.91364 3.31452i
\(626\) 5.83364 + 10.1042i 0.233159 + 0.403844i
\(627\) 0 0
\(628\) 11.3852 + 6.57327i 0.454321 + 0.262302i
\(629\) −5.98098 −0.238477
\(630\) 0 0
\(631\) −12.8860 −0.512982 −0.256491 0.966547i \(-0.582566\pi\)
−0.256491 + 0.966547i \(0.582566\pi\)
\(632\) −25.9945 15.0079i −1.03401 0.596984i
\(633\) 0 0
\(634\) −14.1732 24.5488i −0.562891 0.974956i
\(635\) 40.1457 + 69.5345i 1.59314 + 2.75939i
\(636\) 0 0
\(637\) 0 0
\(638\) 1.73325i 0.0686200i
\(639\) 0 0
\(640\) 15.7074i 0.620890i
\(641\) 16.5666 + 9.56474i 0.654342 + 0.377785i 0.790118 0.612955i \(-0.210019\pi\)
−0.135776 + 0.990740i \(0.543353\pi\)
\(642\) 0 0
\(643\) 9.77521 5.64372i 0.385497 0.222567i −0.294710 0.955587i \(-0.595223\pi\)
0.680207 + 0.733020i \(0.261890\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −1.66726 + 2.88778i −0.0655976 + 0.113618i
\(647\) −5.08677 −0.199982 −0.0999909 0.994988i \(-0.531881\pi\)
−0.0999909 + 0.994988i \(0.531881\pi\)
\(648\) 0 0
\(649\) 12.6181i 0.495305i
\(650\) −21.0939 + 36.5356i −0.827369 + 1.43305i
\(651\) 0 0
\(652\) −3.82937 6.63267i −0.149970 0.259755i
\(653\) 32.9044 18.9974i 1.28765 0.743424i 0.309414 0.950927i \(-0.399867\pi\)
0.978234 + 0.207503i \(0.0665338\pi\)
\(654\) 0 0
\(655\) 14.5218 25.1526i 0.567415 0.982792i
\(656\) 17.7012 0.691115
\(657\) 0 0
\(658\) 0 0
\(659\) −9.97949 5.76166i −0.388746 0.224442i 0.292871 0.956152i \(-0.405389\pi\)
−0.681617 + 0.731710i \(0.738723\pi\)
\(660\) 0 0
\(661\) −38.0928 + 21.9929i −1.48164 + 0.855424i −0.999783 0.0208274i \(-0.993370\pi\)
−0.481854 + 0.876251i \(0.660037\pi\)
\(662\) 9.25838 5.34533i 0.359837 0.207752i
\(663\) 0 0
\(664\) 4.24660 + 2.45178i 0.164800 + 0.0951473i
\(665\) 0 0
\(666\) 0 0
\(667\) −2.48422 −0.0961894
\(668\) 4.71620 8.16869i 0.182475 0.316056i
\(669\) 0 0
\(670\) 29.4103 16.9800i 1.13622 0.655996i
\(671\) 7.75962 + 13.4401i 0.299557 + 0.518848i
\(672\) 0 0
\(673\) −21.9316 + 37.9866i −0.845400 + 1.46428i 0.0398735 + 0.999205i \(0.487305\pi\)
−0.885273 + 0.465071i \(0.846029\pi\)
\(674\) 9.47301i 0.364887i
\(675\) 0 0
\(676\) 3.81461 0.146716
\(677\) −0.738999 + 1.27998i −0.0284020 + 0.0491938i −0.879877 0.475201i \(-0.842375\pi\)
0.851475 + 0.524395i \(0.175709\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 13.5208 7.80621i 0.518497 0.299355i
\(681\) 0 0
\(682\) 14.4617 + 8.34948i 0.553768 + 0.319718i
\(683\) 10.3259i 0.395111i 0.980292 + 0.197555i \(0.0633002\pi\)
−0.980292 + 0.197555i \(0.936700\pi\)
\(684\) 0 0
\(685\) 59.1162i 2.25871i
\(686\) 0 0
\(687\) 0 0
\(688\) 5.10601 + 8.84388i 0.194665 + 0.337170i
\(689\) 4.20442 + 7.28228i 0.160176 + 0.277433i
\(690\) 0 0
\(691\) 6.58166 + 3.79992i 0.250378 + 0.144556i 0.619937 0.784651i \(-0.287158\pi\)
−0.369559 + 0.929207i \(0.620491\pi\)
\(692\) −5.27087 −0.200368
\(693\) 0 0
\(694\) 41.6773 1.58205
\(695\) 33.5353 + 19.3616i 1.27207 + 0.734428i
\(696\) 0 0
\(697\) 4.31538 + 7.47446i 0.163457 + 0.283115i
\(698\) 14.4120 + 24.9624i 0.545503 + 0.944839i
\(699\) 0 0
\(700\) 0 0
\(701\) 6.35907i 0.240179i −0.992763 0.120089i \(-0.961682\pi\)
0.992763 0.120089i \(-0.0383181\pi\)
\(702\) 0 0
\(703\) 12.3413i 0.465460i
\(704\) −16.3289 9.42749i −0.615419 0.355312i
\(705\) 0 0
\(706\) 0.991677 0.572545i 0.0373223 0.0215480i
\(707\) 0 0
\(708\) 0 0
\(709\) 23.8048 41.2311i 0.894007 1.54847i 0.0589776 0.998259i \(-0.481216\pi\)
0.835029 0.550206i \(-0.185451\pi\)
\(710\) −10.0026 −0.375390
\(711\) 0 0
\(712\) 18.7690i 0.703396i
\(713\) 11.9671 20.7276i 0.448171 0.776255i
\(714\) 0 0
\(715\) 12.1806 + 21.0975i 0.455530 + 0.789002i
\(716\) −10.1409 + 5.85486i −0.378983 + 0.218806i
\(717\) 0 0
\(718\) −9.37904 + 16.2450i −0.350023 + 0.606257i
\(719\) 14.1470 0.527594 0.263797 0.964578i \(-0.415025\pi\)
0.263797 + 0.964578i \(0.415025\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 13.4280 + 7.75264i 0.499737 + 0.288524i
\(723\) 0 0
\(724\) −4.07904 + 2.35503i −0.151596 + 0.0875241i
\(725\) 8.11202 4.68348i 0.301273 0.173940i
\(726\) 0 0
\(727\) −40.1828 23.1996i −1.49030 0.860424i −0.490360 0.871520i \(-0.663135\pi\)
−0.999938 + 0.0110955i \(0.996468\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 60.7728 2.24930
\(731\) −2.48960 + 4.31211i −0.0920811 + 0.159489i
\(732\) 0 0
\(733\) −22.8893 + 13.2151i −0.845436 + 0.488112i −0.859108 0.511794i \(-0.828981\pi\)
0.0136726 + 0.999907i \(0.495648\pi\)
\(734\) −14.5559 25.2115i −0.537268 0.930575i
\(735\) 0 0
\(736\) −6.06899 + 10.5118i −0.223706 + 0.387470i
\(737\) 14.3854i 0.529894i
\(738\) 0 0
\(739\) −46.2670 −1.70196 −0.850979 0.525200i \(-0.823991\pi\)
−0.850979 + 0.525200i \(0.823991\pi\)
\(740\) −6.76798 + 11.7225i −0.248796 + 0.430927i
\(741\) 0 0
\(742\) 0 0
\(743\) 36.5640 21.1102i 1.34140 0.774458i 0.354388 0.935098i \(-0.384689\pi\)
0.987013 + 0.160640i \(0.0513558\pi\)
\(744\) 0 0
\(745\) 14.2525 + 8.22868i 0.522171 + 0.301476i
\(746\) 11.1177i 0.407050i
\(747\) 0 0
\(748\) 1.54923i 0.0566456i
\(749\) 0 0
\(750\) 0 0
\(751\) 8.02320 + 13.8966i 0.292771 + 0.507094i 0.974464 0.224544i \(-0.0720894\pi\)
−0.681693 + 0.731638i \(0.738756\pi\)
\(752\) 8.57877 + 14.8589i 0.312836 + 0.541847i
\(753\) 0 0
\(754\) −1.80582 1.04259i −0.0657639 0.0379688i
\(755\) 16.5555 0.602516
\(756\) 0 0
\(757\) 25.0149 0.909183 0.454591 0.890700i \(-0.349785\pi\)
0.454591 + 0.890700i \(0.349785\pi\)
\(758\) 21.2265 + 12.2551i 0.770981 + 0.445126i
\(759\) 0 0
\(760\) 16.1075 + 27.8990i 0.584281 + 1.01200i
\(761\) 3.00365 + 5.20247i 0.108882 + 0.188589i 0.915318 0.402733i \(-0.131940\pi\)
−0.806436 + 0.591322i \(0.798606\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 11.3889i 0.412035i
\(765\) 0 0
\(766\) 7.61138i 0.275010i
\(767\) −13.1464 7.59008i −0.474689 0.274062i
\(768\) 0 0
\(769\) −28.9946 + 16.7400i −1.04557 + 0.603661i −0.921406 0.388600i \(-0.872959\pi\)
−0.124166 + 0.992262i \(0.539625\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −5.54159 + 9.59831i −0.199446 + 0.345451i
\(773\) 36.2016 1.30208 0.651040 0.759043i \(-0.274333\pi\)
0.651040 + 0.759043i \(0.274333\pi\)
\(774\) 0 0
\(775\) 90.2458i 3.24172i
\(776\) −4.19980 + 7.27427i −0.150764 + 0.261131i
\(777\) 0 0
\(778\) 0.0303280 + 0.0525296i 0.00108731 + 0.00188328i
\(779\) −15.4230 + 8.90445i −0.552585 + 0.319035i
\(780\) 0 0
\(781\) −2.11854 + 3.66942i −0.0758073 + 0.131302i
\(782\) 5.03785 0.180153
\(783\) 0 0
\(784\) 0 0
\(785\) −80.6108 46.5407i −2.87712 1.66111i
\(786\) 0 0
\(787\) −14.1930 + 8.19433i −0.505926 + 0.292096i −0.731157 0.682209i \(-0.761019\pi\)
0.225232 + 0.974305i \(0.427686\pi\)
\(788\) −8.79294 + 5.07661i −0.313236 + 0.180847i
\(789\) 0 0
\(790\) 43.1147 + 24.8923i 1.53395 + 0.885628i
\(791\) 0 0
\(792\) 0 0
\(793\) 18.6703 0.663004
\(794\) −7.48929 + 12.9718i −0.265785 + 0.460353i
\(795\) 0 0
\(796\) −1.44065 + 0.831760i −0.0510625 + 0.0294809i