Properties

Label 1323.2.o.e.440.17
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 440.17
Character \(\chi\) \(=\) 1323.440
Dual form 1323.2.o.e.881.17

$q$-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 \(-0.746556\pi\)
−0.269254 0.963069i \(-0.586777\pi\)
\(6\) 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 −0.778715 0.627378i \(-0.784128\pi\)
0.153967 + 0.988076i \(0.450795\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.20098 2.08016i 0.300245 0.520040i
\(17\) −1.17115 −0.284046 −0.142023 0.989863i \(-0.545361\pi\)
−0.142023 + 0.989863i \(0.545361\pi\)
\(18\) 0 0
\(19\) 2.41658i 0.554402i −0.960812 0.277201i \(-0.910593\pi\)
0.960812 0.277201i \(-0.0894067\pi\)
\(20\) −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 −0.914006 0.405701i \(-0.867027\pi\)
−0.105655 + 0.994403i \(0.533694\pi\)
\(32\) −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 \(-0.971490\pi\)
0.420534 0.907277i \(-0.361843\pi\)
\(42\) 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 \(-0.658905\pi\)
0.999703 0.0243819i \(-0.00776176\pi\)
\(48\) 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 0.991048 0.133506i \(-0.0426234\pi\)
−0.611143 + 0.791520i \(0.709290\pi\)
\(60\) 0 0
\(61\) −6.21638 3.58903i −0.795925 0.459528i 0.0461190 0.998936i \(-0.485315\pi\)
−0.842044 + 0.539408i \(0.818648\pi\)
\(62\) −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 \(0.245393\pi\)
−0.717266 + 0.696799i \(0.754607\pi\)
\(74\) −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 −0.818981 0.573821i \(-0.805461\pi\)
0.906434 + 0.422348i \(0.138794\pi\)
\(84\) 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 \(-0.604778\pi\)
−0.323258 + 0.946311i \(0.604778\pi\)
\(90\) 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 0.615183 0.788384i \(-0.289082\pi\)
−0.375169 + 0.926956i \(0.622415\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 8.42288 0.842288
\(101\) 7.99849 13.8538i 0.795880 1.37850i −0.126400 0.991979i \(-0.540342\pi\)
0.922279 0.386524i \(-0.126324\pi\)
\(102\) 0 0
\(103\) 2.61251 1.50834i 0.257419 0.148621i −0.365738 0.930718i \(-0.619183\pi\)
0.623156 + 0.782097i \(0.285850\pi\)
\(104\) 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 0.974490 0.224429i \(-0.0720518\pi\)
−0.681607 + 0.731719i \(0.738718\pi\)
\(132\) 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 −0.790982 0.611839i \(-0.790430\pi\)
0.134377 + 0.990930i \(0.457097\pi\)
\(140\) 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 0.485234 0.874384i \(-0.338735\pi\)
0.999856 + 0.0169675i \(0.00540117\pi\)
\(158\) 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 \(-0.963233\pi\)
0.396859 0.917880i \(-0.370100\pi\)
\(168\) 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 −0.982012 0.188820i \(-0.939534\pi\)
0.654528 + 0.756037i \(0.272867\pi\)
\(174\) 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 \(0.0923590\pi\)
−0.958200 + 0.286100i \(0.907641\pi\)
\(182\) 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 \(0.0307225\pi\)
−0.995346 + 0.0963677i \(0.969278\pi\)
\(200\) 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 0.260785 0.965397i \(-0.416019\pi\)
−0.705666 + 0.708545i \(0.749352\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3.34815 −0.222715
\(227\) 1.16439 2.01677i 0.0772829 0.133858i −0.824794 0.565434i \(-0.808709\pi\)
0.902077 + 0.431576i \(0.142042\pi\)
\(228\) 0 0
\(229\) 10.3653 5.98443i 0.684961 0.395463i −0.116760 0.993160i \(-0.537251\pi\)
0.801722 + 0.597698i \(0.203918\pi\)
\(230\) −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 0.953104 0.302643i \(-0.0978690\pi\)
0.214455 + 0.976734i \(0.431202\pi\)
\(242\) 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 \(-0.798980\pi\)
−0.807130 + 0.590374i \(0.798980\pi\)
\(252\) 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 0.989620 0.143708i \(-0.0459026\pi\)
−0.619265 + 0.785182i \(0.712569\pi\)
\(258\) 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 \(-0.458870\pi\)
0.128853 + 0.991664i \(0.458870\pi\)
\(270\) 0 0
\(271\) 22.3943i 1.36036i 0.733046 + 0.680179i \(0.238098\pi\)
−0.733046 + 0.680179i \(0.761902\pi\)
\(272\) −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 −0.891090 0.453826i \(-0.850059\pi\)
−0.0525206 + 0.998620i \(0.516726\pi\)
\(284\) 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 0.988669 0.150112i \(-0.0479634\pi\)
−0.624335 + 0.781156i \(0.714630\pi\)
\(294\) 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 \(-0.791766\pi\)
0.793543 0.608514i \(-0.208234\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 16.7296 + 28.9765i 0.950178 + 1.64576i
\(311\) −3.92094 6.79126i −0.222336 0.385097i 0.733181 0.680034i \(-0.238035\pi\)
−0.955517 + 0.294936i \(0.904702\pi\)
\(312\) 0 0
\(313\) −8.57593 4.95131i −0.484740 0.279865i 0.237650 0.971351i \(-0.423623\pi\)
−0.722390 + 0.691486i \(0.756956\pi\)
\(314\) 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 −0.189141 0.981950i \(-0.560570\pi\)
−0.944964 + 0.327174i \(0.893904\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −7.18783 −0.383112
\(353\) −0.485949 + 0.841688i −0.0258644 + 0.0447985i −0.878668 0.477433i \(-0.841567\pi\)
0.852803 + 0.522232i \(0.174900\pi\)
\(354\) 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 0.940629 0.339435i \(-0.110236\pi\)
0.176355 + 0.984327i \(0.443569\pi\)
\(368\) 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 0.771623 0.636080i \(-0.219445\pi\)
−0.936673 + 0.350205i \(0.886112\pi\)
\(384\) 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 \(-0.896644\pi\)
0.947746 0.319026i \(-0.103356\pi\)
\(398\) −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 −0.498774 0.866732i \(-0.666216\pi\)
0.501225 + 0.865317i \(0.332883\pi\)
\(410\) −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 0.931401 0.363995i \(-0.118588\pi\)
−0.780930 + 0.624619i \(0.785254\pi\)
\(420\) 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 \(-0.759949\pi\)
0.728860 0.684663i \(-0.240051\pi\)
\(434\) 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 0.457150 0.889390i \(-0.348870\pi\)
−0.541659 + 0.840598i \(0.682204\pi\)
\(440\) −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 −0.530992 0.847377i \(-0.678180\pi\)
0.999346 + 0.0361638i \(0.0115138\pi\)
\(462\) 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 \(-0.262274\pi\)
0.679322 + 0.733841i \(0.262274\pi\)
\(468\) 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 \(-0.666280\pi\)
0.999999 0.00121455i \(-0.000386605\pi\)
\(480\) 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 \(-0.342994\pi\)
0.473491 + 0.880799i \(0.342994\pi\)
\(504\) 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 0.710881 0.703313i \(-0.248297\pi\)
−0.964527 + 0.263984i \(0.914963\pi\)
\(510\) 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 \(-0.349415\pi\)
0.455627 + 0.890171i \(0.349415\pi\)
\(522\) 0 0
\(523\) 14.9338i 0.653009i 0.945196 + 0.326505i \(0.105871\pi\)
−0.945196 + 0.326505i \(0.894129\pi\)
\(524\) 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 \(0.0373377\pi\)
−0.395212 + 0.918590i \(0.629329\pi\)
\(564\) 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 \(-0.951127\pi\)
0.988236 0.152938i \(-0.0488734\pi\)
\(578\) −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 \(-0.650982\pi\)
0.998786 0.0492535i \(-0.0156842\pi\)
\(588\) 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 \(-0.440013\pi\)
0.187343 + 0.982295i \(0.440013\pi\)
\(594\) 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 0.0595840 0.998223i \(-0.481023\pi\)
−0.834695 + 0.550713i \(0.814356\pi\)
\(602\) 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 \(0.693632\pi\)
−0.996414 + 0.0846136i \(0.973034\pi\)
\(608\) 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 −0.245949 0.969283i \(-0.579100\pi\)
−0.962398 + 0.271643i \(0.912433\pi\)
\(620\) 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 −0.680207 0.733020i \(-0.738110\pi\)
0.294710 + 0.955587i \(0.404777\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −1.66726 + 2.88778i −0.0655976 + 0.113618i
\(647\) 5.08677 0.199982 0.0999909 0.994988i \(-0.468119\pi\)
0.0999909 + 0.994988i \(0.468119\pi\)
\(648\) 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 0.481854 0.876251i \(-0.339963\pi\)
0.999783 + 0.0208274i \(0.00663005\pi\)
\(662\) 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 −0.851475 0.524395i \(-0.824291\pi\)
0.879877 + 0.475201i \(0.157625\pi\)
\(678\) 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 0.369559 0.929207i \(-0.379509\pi\)
−0.619937 + 0.784651i \(0.712842\pi\)
\(692\) 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 \(-0.584975\pi\)
−0.263797 + 0.964578i \(0.584975\pi\)
\(720\) 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 0.999938 0.0110955i \(-0.00353187\pi\)
0.490360 + 0.871520i \(0.336865\pi\)
\(728\) 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 −0.0136726 0.999907i \(-0.504352\pi\)
0.859108 + 0.511794i \(0.171019\pi\)
\(734\) 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 0.806436 0.591322i \(-0.201394\pi\)
−0.915318 + 0.402733i \(0.868060\pi\)
\(762\) 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 0.124166 0.992262i \(-0.460375\pi\)
0.921406 + 0.388600i \(0.127041\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −5.54159 + 9.59831i −0.199446 + 0.345451i
\(773\) −36.2016 −1.30208 −0.651040 0.759043i \(-0.725667\pi\)
−0.651040 + 0.759043i \(0.725667\pi\)
\(774\) 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 −0.225232 0.974305i \(-0.572314\pi\)
0.731157 + 0.682209i \(0.238981\pi\)
\(788\) −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