Properties

Label 1323.2.o.e.440.20
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 440.20
Character \(\chi\) \(=\) 1323.440
Dual form 1323.2.o.e.881.20

$q$-expansion

\(f(q)\) \(=\) \(q+(1.28562 + 0.742253i) q^{2} +(0.101880 + 0.176462i) q^{4} +(0.154215 + 0.267109i) q^{5} -2.66653i q^{8} +O(q^{10})\) \(q+(1.28562 + 0.742253i) q^{2} +(0.101880 + 0.176462i) q^{4} +(0.154215 + 0.267109i) q^{5} -2.66653i q^{8} +0.457868i q^{10} +(2.73879 + 1.58124i) q^{11} +(3.00394 - 1.73432i) q^{13} +(2.18300 - 3.78107i) q^{16} -4.88248 q^{17} +5.34116i q^{19} +(-0.0314230 + 0.0544262i) q^{20} +(2.34736 + 4.06575i) q^{22} +(5.17269 - 2.98645i) q^{23} +(2.45244 - 4.24774i) q^{25} +5.14923 q^{26} +(-2.70372 - 1.56099i) q^{29} +(6.51414 - 3.76094i) q^{31} +(0.994457 - 0.574150i) q^{32} +(-6.27702 - 3.62404i) q^{34} +11.8514 q^{37} +(-3.96450 + 6.86671i) q^{38} +(0.712254 - 0.411220i) q^{40} +(-2.58920 - 4.48462i) q^{41} +(2.75159 - 4.76589i) q^{43} +0.644388i q^{44} +8.86682 q^{46} +(-4.23198 + 7.33000i) q^{47} +(6.30580 - 3.64066i) q^{50} +(0.612084 + 0.353387i) q^{52} +0.0855080i q^{53} +0.975406i q^{55} +(-2.31731 - 4.01369i) q^{58} +(1.04433 + 1.80884i) q^{59} +(4.69964 + 2.71334i) q^{61} +11.1663 q^{62} -7.02734 q^{64} +(0.926507 + 0.534919i) q^{65} +(0.0554134 + 0.0959787i) q^{67} +(-0.497429 - 0.861572i) q^{68} +7.78899i q^{71} +9.61495i q^{73} +(15.2364 + 8.79672i) q^{74} +(-0.942510 + 0.544159i) q^{76} +(-2.56825 + 4.44834i) q^{79} +1.34661 q^{80} -7.68736i q^{82} +(4.42464 - 7.66370i) q^{83} +(-0.752954 - 1.30416i) q^{85} +(7.07500 - 4.08475i) q^{86} +(4.21642 - 7.30306i) q^{88} -1.87377 q^{89} +(1.05399 + 0.608521i) q^{92} +(-10.8814 + 6.28240i) q^{94} +(-1.42667 + 0.823689i) q^{95} +(-10.9813 - 6.34007i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{4} + O(q^{10}) \) \( 48q + 24q^{4} + 24q^{11} - 24q^{16} + 48q^{23} - 24q^{25} - 120q^{32} - 48q^{50} - 48q^{64} - 120q^{65} + 168q^{74} - 24q^{79} - 24q^{85} - 24q^{86} + 144q^{92} - 96q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28562 + 0.742253i 0.909071 + 0.524852i 0.880132 0.474729i \(-0.157454\pi\)
0.0289389 + 0.999581i \(0.490787\pi\)
\(3\) 0 0
\(4\) 0.101880 + 0.176462i 0.0509401 + 0.0882308i
\(5\) 0.154215 + 0.267109i 0.0689672 + 0.119455i 0.898447 0.439082i \(-0.144696\pi\)
−0.829480 + 0.558537i \(0.811363\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.66653i 0.942761i
\(9\) 0 0
\(10\) 0.457868i 0.144790i
\(11\) 2.73879 + 1.58124i 0.825775 + 0.476761i 0.852404 0.522884i \(-0.175144\pi\)
−0.0266288 + 0.999645i \(0.508477\pi\)
\(12\) 0 0
\(13\) 3.00394 1.73432i 0.833143 0.481015i −0.0217849 0.999763i \(-0.506935\pi\)
0.854927 + 0.518748i \(0.173602\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.18300 3.78107i 0.545750 0.945267i
\(17\) −4.88248 −1.18418 −0.592088 0.805873i \(-0.701696\pi\)
−0.592088 + 0.805873i \(0.701696\pi\)
\(18\) 0 0
\(19\) 5.34116i 1.22535i 0.790336 + 0.612673i \(0.209906\pi\)
−0.790336 + 0.612673i \(0.790094\pi\)
\(20\) −0.0314230 + 0.0544262i −0.00702639 + 0.0121701i
\(21\) 0 0
\(22\) 2.34736 + 4.06575i 0.500459 + 0.866820i
\(23\) 5.17269 2.98645i 1.07858 0.622719i 0.148067 0.988977i \(-0.452695\pi\)
0.930513 + 0.366259i \(0.119361\pi\)
\(24\) 0 0
\(25\) 2.45244 4.24774i 0.490487 0.849548i
\(26\) 5.14923 1.00985
\(27\) 0 0
\(28\) 0 0
\(29\) −2.70372 1.56099i −0.502069 0.289869i 0.227499 0.973778i \(-0.426945\pi\)
−0.729567 + 0.683909i \(0.760279\pi\)
\(30\) 0 0
\(31\) 6.51414 3.76094i 1.16997 0.675485i 0.216300 0.976327i \(-0.430601\pi\)
0.953674 + 0.300842i \(0.0972678\pi\)
\(32\) 0.994457 0.574150i 0.175797 0.101496i
\(33\) 0 0
\(34\) −6.27702 3.62404i −1.07650 0.621518i
\(35\) 0 0
\(36\) 0 0
\(37\) 11.8514 1.94835 0.974176 0.225788i \(-0.0724957\pi\)
0.974176 + 0.225788i \(0.0724957\pi\)
\(38\) −3.96450 + 6.86671i −0.643126 + 1.11393i
\(39\) 0 0
\(40\) 0.712254 0.411220i 0.112617 0.0650196i
\(41\) −2.58920 4.48462i −0.404365 0.700380i 0.589883 0.807489i \(-0.299174\pi\)
−0.994247 + 0.107109i \(0.965841\pi\)
\(42\) 0 0
\(43\) 2.75159 4.76589i 0.419613 0.726792i −0.576287 0.817247i \(-0.695499\pi\)
0.995900 + 0.0904557i \(0.0288323\pi\)
\(44\) 0.644388i 0.0971451i
\(45\) 0 0
\(46\) 8.86682 1.30734
\(47\) −4.23198 + 7.33000i −0.617298 + 1.06919i 0.372679 + 0.927960i \(0.378439\pi\)
−0.989977 + 0.141231i \(0.954894\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 6.30580 3.64066i 0.891775 0.514867i
\(51\) 0 0
\(52\) 0.612084 + 0.353387i 0.0848807 + 0.0490059i
\(53\) 0.0855080i 0.0117454i 0.999983 + 0.00587272i \(0.00186935\pi\)
−0.999983 + 0.00587272i \(0.998131\pi\)
\(54\) 0 0
\(55\) 0.975406i 0.131524i
\(56\) 0 0
\(57\) 0 0
\(58\) −2.31731 4.01369i −0.304277 0.527024i
\(59\) 1.04433 + 1.80884i 0.135960 + 0.235490i 0.925964 0.377612i \(-0.123255\pi\)
−0.790004 + 0.613102i \(0.789921\pi\)
\(60\) 0 0
\(61\) 4.69964 + 2.71334i 0.601727 + 0.347407i 0.769721 0.638381i \(-0.220396\pi\)
−0.167994 + 0.985788i \(0.553729\pi\)
\(62\) 11.1663 1.41812
\(63\) 0 0
\(64\) −7.02734 −0.878418
\(65\) 0.926507 + 0.534919i 0.114919 + 0.0663485i
\(66\) 0 0
\(67\) 0.0554134 + 0.0959787i 0.00676982 + 0.0117257i 0.869390 0.494126i \(-0.164512\pi\)
−0.862621 + 0.505851i \(0.831178\pi\)
\(68\) −0.497429 0.861572i −0.0603221 0.104481i
\(69\) 0 0
\(70\) 0 0
\(71\) 7.78899i 0.924384i 0.886780 + 0.462192i \(0.152937\pi\)
−0.886780 + 0.462192i \(0.847063\pi\)
\(72\) 0 0
\(73\) 9.61495i 1.12534i 0.826680 + 0.562672i \(0.190227\pi\)
−0.826680 + 0.562672i \(0.809773\pi\)
\(74\) 15.2364 + 8.79672i 1.77119 + 1.02260i
\(75\) 0 0
\(76\) −0.942510 + 0.544159i −0.108113 + 0.0624193i
\(77\) 0 0
\(78\) 0 0
\(79\) −2.56825 + 4.44834i −0.288951 + 0.500477i −0.973560 0.228433i \(-0.926640\pi\)
0.684609 + 0.728911i \(0.259973\pi\)
\(80\) 1.34661 0.150556
\(81\) 0 0
\(82\) 7.68736i 0.848927i
\(83\) 4.42464 7.66370i 0.485667 0.841201i −0.514197 0.857672i \(-0.671910\pi\)
0.999864 + 0.0164715i \(0.00524328\pi\)
\(84\) 0 0
\(85\) −0.752954 1.30416i −0.0816694 0.141455i
\(86\) 7.07500 4.08475i 0.762917 0.440470i
\(87\) 0 0
\(88\) 4.21642 7.30306i 0.449472 0.778508i
\(89\) −1.87377 −0.198619 −0.0993096 0.995057i \(-0.531663\pi\)
−0.0993096 + 0.995057i \(0.531663\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.05399 + 0.608521i 0.109886 + 0.0634427i
\(93\) 0 0
\(94\) −10.8814 + 6.28240i −1.12233 + 0.647980i
\(95\) −1.42667 + 0.823689i −0.146373 + 0.0845087i
\(96\) 0 0
\(97\) −10.9813 6.34007i −1.11498 0.643736i −0.174868 0.984592i \(-0.555950\pi\)
−0.940116 + 0.340855i \(0.889283\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.999418 0.0999418
\(101\) 3.68322 6.37952i 0.366494 0.634786i −0.622521 0.782603i \(-0.713891\pi\)
0.989015 + 0.147817i \(0.0472248\pi\)
\(102\) 0 0
\(103\) −6.91120 + 3.99019i −0.680981 + 0.393165i −0.800225 0.599700i \(-0.795286\pi\)
0.119244 + 0.992865i \(0.461953\pi\)
\(104\) −4.62463 8.01009i −0.453482 0.785454i
\(105\) 0 0
\(106\) −0.0634686 + 0.109931i −0.00616462 + 0.0106774i
\(107\) 16.7694i 1.62116i 0.585625 + 0.810582i \(0.300849\pi\)
−0.585625 + 0.810582i \(0.699151\pi\)
\(108\) 0 0
\(109\) −8.86509 −0.849122 −0.424561 0.905399i \(-0.639572\pi\)
−0.424561 + 0.905399i \(0.639572\pi\)
\(110\) −0.723998 + 1.25400i −0.0690305 + 0.119564i
\(111\) 0 0
\(112\) 0 0
\(113\) −13.5621 + 7.83007i −1.27581 + 0.736591i −0.976076 0.217430i \(-0.930233\pi\)
−0.299738 + 0.954022i \(0.596899\pi\)
\(114\) 0 0
\(115\) 1.59542 + 0.921114i 0.148773 + 0.0858943i
\(116\) 0.636138i 0.0590639i
\(117\) 0 0
\(118\) 3.10063i 0.285437i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.499366 0.864928i −0.0453969 0.0786298i
\(122\) 4.02797 + 6.97664i 0.364675 + 0.631635i
\(123\) 0 0
\(124\) 1.32732 + 0.766330i 0.119197 + 0.0688185i
\(125\) 3.05497 0.273245
\(126\) 0 0
\(127\) −6.78064 −0.601685 −0.300842 0.953674i \(-0.597268\pi\)
−0.300842 + 0.953674i \(0.597268\pi\)
\(128\) −11.0234 6.36437i −0.974341 0.562536i
\(129\) 0 0
\(130\) 0.794091 + 1.37541i 0.0696464 + 0.120631i
\(131\) −9.77105 16.9240i −0.853701 1.47865i −0.877845 0.478944i \(-0.841020\pi\)
0.0241447 0.999708i \(-0.492314\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.164523i 0.0142126i
\(135\) 0 0
\(136\) 13.0193i 1.11640i
\(137\) 1.37570 + 0.794262i 0.117534 + 0.0678584i 0.557615 0.830100i \(-0.311717\pi\)
−0.440080 + 0.897958i \(0.645050\pi\)
\(138\) 0 0
\(139\) 3.97274 2.29366i 0.336963 0.194546i −0.321965 0.946752i \(-0.604343\pi\)
0.658928 + 0.752206i \(0.271010\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −5.78141 + 10.0137i −0.485165 + 0.840330i
\(143\) 10.9695 0.917318
\(144\) 0 0
\(145\) 0.962918i 0.0799660i
\(146\) −7.13673 + 12.3612i −0.590640 + 1.02302i
\(147\) 0 0
\(148\) 1.20742 + 2.09131i 0.0992493 + 0.171905i
\(149\) −8.42966 + 4.86686i −0.690584 + 0.398709i −0.803831 0.594858i \(-0.797208\pi\)
0.113247 + 0.993567i \(0.463875\pi\)
\(150\) 0 0
\(151\) 3.00916 5.21203i 0.244882 0.424149i −0.717216 0.696851i \(-0.754584\pi\)
0.962099 + 0.272702i \(0.0879173\pi\)
\(152\) 14.2424 1.15521
\(153\) 0 0
\(154\) 0 0
\(155\) 2.00916 + 1.15999i 0.161380 + 0.0931726i
\(156\) 0 0
\(157\) 14.1600 8.17531i 1.13009 0.652461i 0.186136 0.982524i \(-0.440403\pi\)
0.943959 + 0.330063i \(0.107070\pi\)
\(158\) −6.60359 + 3.81258i −0.525353 + 0.303313i
\(159\) 0 0
\(160\) 0.306721 + 0.177086i 0.0242484 + 0.0139998i
\(161\) 0 0
\(162\) 0 0
\(163\) −6.46471 −0.506355 −0.253177 0.967420i \(-0.581476\pi\)
−0.253177 + 0.967420i \(0.581476\pi\)
\(164\) 0.527576 0.913788i 0.0411968 0.0713549i
\(165\) 0 0
\(166\) 11.3768 6.56841i 0.883012 0.509807i
\(167\) −1.33556 2.31325i −0.103348 0.179005i 0.809714 0.586825i \(-0.199622\pi\)
−0.913062 + 0.407820i \(0.866289\pi\)
\(168\) 0 0
\(169\) −0.484236 + 0.838722i −0.0372489 + 0.0645171i
\(170\) 2.23553i 0.171457i
\(171\) 0 0
\(172\) 1.12133 0.0855006
\(173\) −10.0983 + 17.4908i −0.767760 + 1.32980i 0.171015 + 0.985268i \(0.445295\pi\)
−0.938775 + 0.344531i \(0.888038\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 11.9575 6.90369i 0.901334 0.520385i
\(177\) 0 0
\(178\) −2.40896 1.39081i −0.180559 0.104246i
\(179\) 21.9622i 1.64153i −0.571266 0.820765i \(-0.693548\pi\)
0.571266 0.820765i \(-0.306452\pi\)
\(180\) 0 0
\(181\) 2.50569i 0.186246i 0.995655 + 0.0931232i \(0.0296850\pi\)
−0.995655 + 0.0931232i \(0.970315\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −7.96347 13.7931i −0.587075 1.01684i
\(185\) 1.82766 + 3.16561i 0.134372 + 0.232740i
\(186\) 0 0
\(187\) −13.3721 7.72038i −0.977864 0.564570i
\(188\) −1.72462 −0.125781
\(189\) 0 0
\(190\) −2.44554 −0.177418
\(191\) 1.82276 + 1.05237i 0.131891 + 0.0761470i 0.564494 0.825437i \(-0.309071\pi\)
−0.432603 + 0.901584i \(0.642405\pi\)
\(192\) 0 0
\(193\) 2.97730 + 5.15683i 0.214311 + 0.371197i 0.953059 0.302784i \(-0.0979162\pi\)
−0.738748 + 0.673981i \(0.764583\pi\)
\(194\) −9.41187 16.3018i −0.675733 1.17040i
\(195\) 0 0
\(196\) 0 0
\(197\) 7.64511i 0.544692i 0.962199 + 0.272346i \(0.0877995\pi\)
−0.962199 + 0.272346i \(0.912200\pi\)
\(198\) 0 0
\(199\) 6.85193i 0.485720i −0.970061 0.242860i \(-0.921914\pi\)
0.970061 0.242860i \(-0.0780856\pi\)
\(200\) −11.3267 6.53949i −0.800921 0.462412i
\(201\) 0 0
\(202\) 9.47044 5.46776i 0.666338 0.384710i
\(203\) 0 0
\(204\) 0 0
\(205\) 0.798588 1.38320i 0.0557758 0.0966066i
\(206\) −11.8469 −0.825414
\(207\) 0 0
\(208\) 15.1441i 1.05006i
\(209\) −8.44565 + 14.6283i −0.584198 + 1.01186i
\(210\) 0 0
\(211\) −2.74784 4.75940i −0.189169 0.327651i 0.755804 0.654798i \(-0.227246\pi\)
−0.944974 + 0.327147i \(0.893913\pi\)
\(212\) −0.0150889 + 0.00871157i −0.00103631 + 0.000598313i
\(213\) 0 0
\(214\) −12.4472 + 21.5591i −0.850872 + 1.47375i
\(215\) 1.69735 0.115758
\(216\) 0 0
\(217\) 0 0
\(218\) −11.3971 6.58015i −0.771912 0.445664i
\(219\) 0 0
\(220\) −0.172122 + 0.0993745i −0.0116044 + 0.00669983i
\(221\) −14.6667 + 8.46781i −0.986588 + 0.569607i
\(222\) 0 0
\(223\) 17.6080 + 10.1660i 1.17912 + 0.680764i 0.955810 0.293985i \(-0.0949815\pi\)
0.223307 + 0.974748i \(0.428315\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −23.2476 −1.54641
\(227\) −0.161235 + 0.279268i −0.0107016 + 0.0185356i −0.871327 0.490704i \(-0.836740\pi\)
0.860625 + 0.509239i \(0.170073\pi\)
\(228\) 0 0
\(229\) −2.30171 + 1.32889i −0.152101 + 0.0878157i −0.574119 0.818772i \(-0.694655\pi\)
0.422018 + 0.906588i \(0.361322\pi\)
\(230\) 1.36740 + 2.36841i 0.0901637 + 0.156168i
\(231\) 0 0
\(232\) −4.16244 + 7.20956i −0.273278 + 0.473331i
\(233\) 23.2575i 1.52365i 0.647785 + 0.761823i \(0.275696\pi\)
−0.647785 + 0.761823i \(0.724304\pi\)
\(234\) 0 0
\(235\) −2.61055 −0.170293
\(236\) −0.212793 + 0.368569i −0.0138517 + 0.0239918i
\(237\) 0 0
\(238\) 0 0
\(239\) 0.291265 0.168162i 0.0188404 0.0108775i −0.490550 0.871413i \(-0.663204\pi\)
0.509391 + 0.860535i \(0.329871\pi\)
\(240\) 0 0
\(241\) −19.1846 11.0762i −1.23579 0.713483i −0.267558 0.963542i \(-0.586217\pi\)
−0.968231 + 0.250059i \(0.919550\pi\)
\(242\) 1.48263i 0.0953068i
\(243\) 0 0
\(244\) 1.10574i 0.0707878i
\(245\) 0 0
\(246\) 0 0
\(247\) 9.26331 + 16.0445i 0.589410 + 1.02089i
\(248\) −10.0287 17.3701i −0.636820 1.10301i
\(249\) 0 0
\(250\) 3.92753 + 2.26756i 0.248399 + 0.143413i
\(251\) −13.9800 −0.882409 −0.441205 0.897407i \(-0.645449\pi\)
−0.441205 + 0.897407i \(0.645449\pi\)
\(252\) 0 0
\(253\) 18.8892 1.18755
\(254\) −8.71734 5.03296i −0.546974 0.315796i
\(255\) 0 0
\(256\) −2.42061 4.19261i −0.151288 0.262038i
\(257\) 9.69064 + 16.7847i 0.604486 + 1.04700i 0.992133 + 0.125192i \(0.0399547\pi\)
−0.387647 + 0.921808i \(0.626712\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0.217991i 0.0135192i
\(261\) 0 0
\(262\) 29.0104i 1.79227i
\(263\) −4.40776 2.54482i −0.271794 0.156920i 0.357909 0.933757i \(-0.383490\pi\)
−0.629703 + 0.776836i \(0.716823\pi\)
\(264\) 0 0
\(265\) −0.0228400 + 0.0131867i −0.00140305 + 0.000810050i
\(266\) 0 0
\(267\) 0 0
\(268\) −0.0112910 + 0.0195567i −0.000689710 + 0.00119461i
\(269\) 5.05601 0.308270 0.154135 0.988050i \(-0.450741\pi\)
0.154135 + 0.988050i \(0.450741\pi\)
\(270\) 0 0
\(271\) 31.3809i 1.90626i 0.302567 + 0.953128i \(0.402156\pi\)
−0.302567 + 0.953128i \(0.597844\pi\)
\(272\) −10.6585 + 18.4610i −0.646265 + 1.11936i
\(273\) 0 0
\(274\) 1.17909 + 2.04224i 0.0712313 + 0.123376i
\(275\) 13.4334 7.75577i 0.810064 0.467691i
\(276\) 0 0
\(277\) −13.0279 + 22.5650i −0.782771 + 1.35580i 0.147551 + 0.989054i \(0.452861\pi\)
−0.930322 + 0.366744i \(0.880473\pi\)
\(278\) 6.80991 0.408431
\(279\) 0 0
\(280\) 0 0
\(281\) 4.14335 + 2.39217i 0.247172 + 0.142705i 0.618469 0.785810i \(-0.287753\pi\)
−0.371297 + 0.928514i \(0.621087\pi\)
\(282\) 0 0
\(283\) 0.927241 0.535343i 0.0551188 0.0318228i −0.472187 0.881498i \(-0.656535\pi\)
0.527306 + 0.849675i \(0.323202\pi\)
\(284\) −1.37446 + 0.793544i −0.0815591 + 0.0470882i
\(285\) 0 0
\(286\) 14.1026 + 8.14217i 0.833907 + 0.481457i
\(287\) 0 0
\(288\) 0 0
\(289\) 6.83866 0.402274
\(290\) 0.714729 1.23795i 0.0419703 0.0726947i
\(291\) 0 0
\(292\) −1.69667 + 0.979573i −0.0992901 + 0.0573252i
\(293\) 1.36267 + 2.36021i 0.0796079 + 0.137885i 0.903081 0.429471i \(-0.141300\pi\)
−0.823473 + 0.567356i \(0.807967\pi\)
\(294\) 0 0
\(295\) −0.322104 + 0.557900i −0.0187536 + 0.0324822i
\(296\) 31.6020i 1.83683i
\(297\) 0 0
\(298\) −14.4498 −0.837054
\(299\) 10.3590 17.9422i 0.599074 1.03763i
\(300\) 0 0
\(301\) 0 0
\(302\) 7.73729 4.46713i 0.445231 0.257054i
\(303\) 0 0
\(304\) 20.1953 + 11.6598i 1.15828 + 0.668733i
\(305\) 1.67375i 0.0958388i
\(306\) 0 0
\(307\) 8.31294i 0.474444i 0.971455 + 0.237222i \(0.0762369\pi\)
−0.971455 + 0.237222i \(0.923763\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1.72201 + 2.98261i 0.0978037 + 0.169401i
\(311\) −3.00023 5.19656i −0.170128 0.294670i 0.768337 0.640046i \(-0.221085\pi\)
−0.938464 + 0.345376i \(0.887751\pi\)
\(312\) 0 0
\(313\) −10.2410 5.91263i −0.578854 0.334201i 0.181824 0.983331i \(-0.441800\pi\)
−0.760678 + 0.649130i \(0.775133\pi\)
\(314\) 24.2726 1.36978
\(315\) 0 0
\(316\) −1.04662 −0.0588767
\(317\) −25.6726 14.8221i −1.44192 0.832491i −0.443940 0.896057i \(-0.646420\pi\)
−0.997978 + 0.0635652i \(0.979753\pi\)
\(318\) 0 0
\(319\) −4.93661 8.55046i −0.276397 0.478734i
\(320\) −1.08372 1.87707i −0.0605821 0.104931i
\(321\) 0 0
\(322\) 0 0
\(323\) 26.0781i 1.45103i
\(324\) 0 0
\(325\) 17.0133i 0.943727i
\(326\) −8.31116 4.79845i −0.460313 0.265762i
\(327\) 0 0
\(328\) −11.9584 + 6.90417i −0.660291 + 0.381219i
\(329\) 0 0
\(330\) 0 0
\(331\) 8.52504 14.7658i 0.468579 0.811602i −0.530776 0.847512i \(-0.678100\pi\)
0.999355 + 0.0359097i \(0.0114329\pi\)
\(332\) 1.80313 0.0989598
\(333\) 0 0
\(334\) 3.96529i 0.216971i
\(335\) −0.0170912 + 0.0296028i −0.000933791 + 0.00161737i
\(336\) 0 0
\(337\) 10.1065 + 17.5050i 0.550536 + 0.953556i 0.998236 + 0.0593723i \(0.0189099\pi\)
−0.447700 + 0.894184i \(0.647757\pi\)
\(338\) −1.24509 + 0.718852i −0.0677239 + 0.0391004i
\(339\) 0 0
\(340\) 0.153422 0.265735i 0.00832049 0.0144115i
\(341\) 23.7878 1.28818
\(342\) 0 0
\(343\) 0 0
\(344\) −12.7084 7.33719i −0.685191 0.395595i
\(345\) 0 0
\(346\) −25.9652 + 14.9910i −1.39590 + 0.805921i
\(347\) −15.3128 + 8.84086i −0.822036 + 0.474602i −0.851118 0.524975i \(-0.824075\pi\)
0.0290824 + 0.999577i \(0.490741\pi\)
\(348\) 0 0
\(349\) 3.62628 + 2.09363i 0.194110 + 0.112070i 0.593905 0.804535i \(-0.297585\pi\)
−0.399795 + 0.916605i \(0.630919\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 3.63148 0.193558
\(353\) 15.2477 26.4097i 0.811551 1.40565i −0.100227 0.994965i \(-0.531957\pi\)
0.911778 0.410684i \(-0.134710\pi\)
\(354\) 0 0
\(355\) −2.08051 + 1.20118i −0.110422 + 0.0637522i
\(356\) −0.190900 0.330649i −0.0101177 0.0175243i
\(357\) 0 0
\(358\) 16.3015 28.2350i 0.861561 1.49227i
\(359\) 5.39131i 0.284542i −0.989828 0.142271i \(-0.954559\pi\)
0.989828 0.142271i \(-0.0454405\pi\)
\(360\) 0 0
\(361\) −9.52801 −0.501474
\(362\) −1.85986 + 3.22137i −0.0977519 + 0.169311i
\(363\) 0 0
\(364\) 0 0
\(365\) −2.56824 + 1.48277i −0.134428 + 0.0776119i
\(366\) 0 0
\(367\) −17.3218 10.0007i −0.904188 0.522033i −0.0256317 0.999671i \(-0.508160\pi\)
−0.878557 + 0.477638i \(0.841493\pi\)
\(368\) 26.0777i 1.35940i
\(369\) 0 0
\(370\) 5.42636i 0.282103i
\(371\) 0 0
\(372\) 0 0
\(373\) 13.0474 + 22.5988i 0.675571 + 1.17012i 0.976302 + 0.216414i \(0.0694363\pi\)
−0.300730 + 0.953709i \(0.597230\pi\)
\(374\) −11.4609 19.8509i −0.592632 1.02647i
\(375\) 0 0
\(376\) 19.5457 + 11.2847i 1.00799 + 0.581964i
\(377\) −10.8291 −0.557726
\(378\) 0 0
\(379\) 30.5222 1.56782 0.783910 0.620875i \(-0.213222\pi\)
0.783910 + 0.620875i \(0.213222\pi\)
\(380\) −0.290699 0.167835i −0.0149126 0.00860977i
\(381\) 0 0
\(382\) 1.56225 + 2.70590i 0.0799319 + 0.138446i
\(383\) −11.3543 19.6662i −0.580177 1.00490i −0.995458 0.0952034i \(-0.969650\pi\)
0.415280 0.909693i \(-0.363683\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 8.83964i 0.449926i
\(387\) 0 0
\(388\) 2.58371i 0.131168i
\(389\) 3.89121 + 2.24659i 0.197292 + 0.113907i 0.595392 0.803436i \(-0.296997\pi\)
−0.398100 + 0.917342i \(0.630330\pi\)
\(390\) 0 0
\(391\) −25.2556 + 14.5813i −1.27723 + 0.737409i
\(392\) 0 0
\(393\) 0 0
\(394\) −5.67461 + 9.82872i −0.285883 + 0.495164i
\(395\) −1.58425 −0.0797125
\(396\) 0 0
\(397\) 9.65161i 0.484400i −0.970226 0.242200i \(-0.922131\pi\)
0.970226 0.242200i \(-0.0778691\pi\)
\(398\) 5.08587 8.80898i 0.254931 0.441554i
\(399\) 0 0
\(400\) −10.7073 18.5457i −0.535367 0.927283i
\(401\) 17.2356 9.95098i 0.860705 0.496928i −0.00354346 0.999994i \(-0.501128\pi\)
0.864248 + 0.503066i \(0.167795\pi\)
\(402\) 0 0
\(403\) 13.0454 22.5953i 0.649837 1.12555i
\(404\) 1.50099 0.0746769
\(405\) 0 0
\(406\) 0 0
\(407\) 32.4584 + 18.7398i 1.60890 + 0.928900i
\(408\) 0 0
\(409\) −2.10072 + 1.21285i −0.103874 + 0.0599718i −0.551037 0.834481i \(-0.685768\pi\)
0.447163 + 0.894453i \(0.352434\pi\)
\(410\) 2.05336 1.18551i 0.101408 0.0585482i
\(411\) 0 0
\(412\) −1.40823 0.813042i −0.0693785 0.0400557i
\(413\) 0 0
\(414\) 0 0
\(415\) 2.72939 0.133981
\(416\) 1.99153 3.44942i 0.0976426 0.169122i
\(417\) 0 0
\(418\) −21.7158 + 12.5376i −1.06216 + 0.613236i
\(419\) 14.6878 + 25.4399i 0.717544 + 1.24282i 0.961970 + 0.273155i \(0.0880671\pi\)
−0.244426 + 0.969668i \(0.578600\pi\)
\(420\) 0 0
\(421\) −18.2078 + 31.5368i −0.887392 + 1.53701i −0.0444443 + 0.999012i \(0.514152\pi\)
−0.842948 + 0.537996i \(0.819182\pi\)
\(422\) 8.15838i 0.397144i
\(423\) 0 0
\(424\) 0.228010 0.0110731
\(425\) −11.9740 + 20.7395i −0.580823 + 1.00602i
\(426\) 0 0
\(427\) 0 0
\(428\) −2.95916 + 1.70847i −0.143037 + 0.0825822i
\(429\) 0 0
\(430\) 2.18215 + 1.25986i 0.105232 + 0.0607560i
\(431\) 19.4520i 0.936968i 0.883472 + 0.468484i \(0.155200\pi\)
−0.883472 + 0.468484i \(0.844800\pi\)
\(432\) 0 0
\(433\) 9.94623i 0.477985i −0.971021 0.238993i \(-0.923183\pi\)
0.971021 0.238993i \(-0.0768172\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.903178 1.56435i −0.0432544 0.0749188i
\(437\) 15.9511 + 27.6282i 0.763046 + 1.32163i
\(438\) 0 0
\(439\) 6.38746 + 3.68780i 0.304857 + 0.176009i 0.644623 0.764501i \(-0.277014\pi\)
−0.339766 + 0.940510i \(0.610348\pi\)
\(440\) 2.60095 0.123995
\(441\) 0 0
\(442\) −25.1411 −1.19584
\(443\) −0.744629 0.429911i −0.0353784 0.0204257i 0.482207 0.876058i \(-0.339835\pi\)
−0.517585 + 0.855632i \(0.673169\pi\)
\(444\) 0 0
\(445\) −0.288964 0.500501i −0.0136982 0.0237260i
\(446\) 15.0914 + 26.1392i 0.714601 + 1.23772i
\(447\) 0 0
\(448\) 0 0
\(449\) 15.6497i 0.738556i 0.929319 + 0.369278i \(0.120395\pi\)
−0.929319 + 0.369278i \(0.879605\pi\)
\(450\) 0 0
\(451\) 16.3766i 0.771142i
\(452\) −2.76342 1.59546i −0.129980 0.0750441i
\(453\) 0 0
\(454\) −0.414575 + 0.239355i −0.0194570 + 0.0112335i
\(455\) 0 0
\(456\) 0 0
\(457\) 2.81559 4.87675i 0.131708 0.228125i −0.792627 0.609707i \(-0.791287\pi\)
0.924335 + 0.381582i \(0.124621\pi\)
\(458\) −3.94550 −0.184361
\(459\) 0 0
\(460\) 0.375373i 0.0175019i
\(461\) 11.3342 19.6314i 0.527886 0.914326i −0.471585 0.881821i \(-0.656318\pi\)
0.999472 0.0325056i \(-0.0103487\pi\)
\(462\) 0 0
\(463\) −21.0052 36.3821i −0.976194 1.69082i −0.675937 0.736960i \(-0.736261\pi\)
−0.300257 0.953858i \(-0.597073\pi\)
\(464\) −11.8045 + 6.81531i −0.548008 + 0.316393i
\(465\) 0 0
\(466\) −17.2629 + 29.9003i −0.799690 + 1.38510i
\(467\) −24.8033 −1.14776 −0.573879 0.818940i \(-0.694562\pi\)
−0.573879 + 0.818940i \(0.694562\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −3.35617 1.93769i −0.154809 0.0893788i
\(471\) 0 0
\(472\) 4.82331 2.78474i 0.222011 0.128178i
\(473\) 15.0720 8.70184i 0.693013 0.400111i
\(474\) 0 0
\(475\) 22.6879 + 13.0989i 1.04099 + 0.601017i
\(476\) 0 0
\(477\) 0 0
\(478\) 0.499275 0.0228363
\(479\) −1.64647 + 2.85177i −0.0752291 + 0.130301i −0.901186 0.433433i \(-0.857302\pi\)
0.825957 + 0.563733i \(0.190635\pi\)
\(480\) 0 0
\(481\) 35.6008 20.5541i 1.62326 0.937187i
\(482\) −16.4427 28.4797i −0.748946 1.29721i
\(483\) 0 0
\(484\) 0.101751 0.176238i 0.00462505 0.00801082i
\(485\) 3.91094i 0.177587i
\(486\) 0 0
\(487\) 10.4448 0.473299 0.236650 0.971595i \(-0.423951\pi\)
0.236650 + 0.971595i \(0.423951\pi\)
\(488\) 7.23519 12.5317i 0.327522 0.567284i
\(489\) 0 0
\(490\) 0 0
\(491\) 26.2797 15.1726i 1.18599 0.684731i 0.228596 0.973521i \(-0.426587\pi\)
0.957392 + 0.288791i \(0.0932532\pi\)
\(492\) 0 0
\(493\) 13.2009 + 7.62153i 0.594538 + 0.343257i
\(494\) 27.5029i 1.23741i
\(495\) 0 0
\(496\) 32.8405i 1.47458i
\(497\) 0 0
\(498\) 0 0
\(499\) −0.984757 1.70565i −0.0440838 0.0763554i 0.843142 0.537692i \(-0.180704\pi\)
−0.887225 + 0.461336i \(0.847370\pi\)
\(500\) 0.311241 + 0.539085i 0.0139191 + 0.0241086i
\(501\) 0 0
\(502\) −17.9730 10.3767i −0.802173 0.463135i
\(503\) 17.3024 0.771477 0.385739 0.922608i \(-0.373947\pi\)
0.385739 + 0.922608i \(0.373947\pi\)
\(504\) 0 0
\(505\) 2.27203 0.101104
\(506\) 24.2843 + 14.0206i 1.07957 + 0.623290i
\(507\) 0 0
\(508\) −0.690813 1.19652i −0.0306499 0.0530872i
\(509\) 0.240892 + 0.417237i 0.0106774 + 0.0184937i 0.871315 0.490725i \(-0.163268\pi\)
−0.860637 + 0.509218i \(0.829935\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 18.2707i 0.807457i
\(513\) 0 0
\(514\) 28.7717i 1.26906i
\(515\) −2.13163 1.23070i −0.0939307 0.0542309i
\(516\) 0 0
\(517\) −23.1810 + 13.3835i −1.01950 + 0.588607i
\(518\) 0 0
\(519\) 0 0
\(520\) 1.42638 2.47056i 0.0625508 0.108341i
\(521\) −14.4154 −0.631550 −0.315775 0.948834i \(-0.602265\pi\)
−0.315775 + 0.948834i \(0.602265\pi\)
\(522\) 0 0
\(523\) 6.81956i 0.298198i −0.988822 0.149099i \(-0.952363\pi\)
0.988822 0.149099i \(-0.0476374\pi\)
\(524\) 1.99095 3.44843i 0.0869752 0.150645i
\(525\) 0 0
\(526\) −3.77780 6.54334i −0.164720 0.285303i
\(527\) −31.8052 + 18.3627i −1.38546 + 0.799893i
\(528\) 0 0
\(529\) 6.33781 10.9774i 0.275557 0.477278i
\(530\) −0.0391514 −0.00170063
\(531\) 0 0
\(532\) 0 0
\(533\) −15.5556 8.98102i −0.673787 0.389011i
\(534\) 0 0
\(535\) −4.47927 + 2.58611i −0.193656 + 0.111807i
\(536\) 0.255930 0.147761i 0.0110545 0.00638232i
\(537\) 0 0
\(538\) 6.50011 + 3.75284i 0.280240 + 0.161796i
\(539\) 0 0
\(540\) 0 0
\(541\) −17.8226 −0.766252 −0.383126 0.923696i \(-0.625153\pi\)
−0.383126 + 0.923696i \(0.625153\pi\)
\(542\) −23.2926 + 40.3440i −1.00050 + 1.73292i
\(543\) 0 0
\(544\) −4.85542 + 2.80328i −0.208175 + 0.120190i
\(545\) −1.36713 2.36795i −0.0585616 0.101432i
\(546\) 0 0
\(547\) −6.79325 + 11.7663i −0.290458 + 0.503089i −0.973918 0.226900i \(-0.927141\pi\)
0.683460 + 0.729988i \(0.260474\pi\)
\(548\) 0.323678i 0.0138268i
\(549\) 0 0
\(550\) 23.0270 0.981874
\(551\) 8.33752 14.4410i 0.355191 0.615208i
\(552\) 0 0
\(553\) 0 0
\(554\) −33.4979 + 19.3400i −1.42319 + 0.821678i
\(555\) 0 0
\(556\) 0.809487 + 0.467357i 0.0343299 + 0.0198204i
\(557\) 7.21412i 0.305672i −0.988252 0.152836i \(-0.951159\pi\)
0.988252 0.152836i \(-0.0488406\pi\)
\(558\) 0 0
\(559\) 19.0886i 0.807361i
\(560\) 0 0
\(561\) 0 0
\(562\) 3.55119 + 6.15084i 0.149798 + 0.259457i
\(563\) 11.5472 + 20.0004i 0.486657 + 0.842915i 0.999882 0.0153392i \(-0.00488280\pi\)
−0.513225 + 0.858254i \(0.671549\pi\)
\(564\) 0 0
\(565\) −4.18296 2.41504i −0.175979 0.101601i
\(566\) 1.58944 0.0668092
\(567\) 0 0
\(568\) 20.7696 0.871473
\(569\) 22.6039 + 13.0504i 0.947605 + 0.547100i 0.892336 0.451372i \(-0.149065\pi\)
0.0552688 + 0.998472i \(0.482398\pi\)
\(570\) 0 0
\(571\) 12.3318 + 21.3594i 0.516071 + 0.893862i 0.999826 + 0.0186582i \(0.00593945\pi\)
−0.483754 + 0.875204i \(0.660727\pi\)
\(572\) 1.11758 + 1.93570i 0.0467283 + 0.0809357i
\(573\) 0 0
\(574\) 0 0
\(575\) 29.2963i 1.22174i
\(576\) 0 0
\(577\) 19.3300i 0.804719i 0.915482 + 0.402360i \(0.131810\pi\)
−0.915482 + 0.402360i \(0.868190\pi\)
\(578\) 8.79192 + 5.07602i 0.365696 + 0.211135i
\(579\) 0 0
\(580\) 0.169918 0.0981022i 0.00705546 0.00407347i
\(581\) 0 0
\(582\) 0 0
\(583\) −0.135209 + 0.234188i −0.00559977 + 0.00969908i
\(584\) 25.6386 1.06093
\(585\) 0 0
\(586\) 4.04578i 0.167130i
\(587\) −7.65692 + 13.2622i −0.316035 + 0.547389i −0.979657 0.200679i \(-0.935685\pi\)
0.663622 + 0.748068i \(0.269018\pi\)
\(588\) 0 0
\(589\) 20.0878 + 34.7931i 0.827703 + 1.43362i
\(590\) −0.828207 + 0.478166i −0.0340967 + 0.0196858i
\(591\) 0 0
\(592\) 25.8716 44.8108i 1.06331 1.84171i
\(593\) −39.2391 −1.61136 −0.805678 0.592354i \(-0.798199\pi\)
−0.805678 + 0.592354i \(0.798199\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.71763 0.991674i −0.0703569 0.0406206i
\(597\) 0 0
\(598\) 26.6354 15.3779i 1.08920 0.628851i
\(599\) 29.7113 17.1538i 1.21397 0.700887i 0.250350 0.968155i \(-0.419454\pi\)
0.963622 + 0.267269i \(0.0861211\pi\)
\(600\) 0 0
\(601\) −24.0139 13.8644i −0.979547 0.565541i −0.0774133 0.996999i \(-0.524666\pi\)
−0.902133 + 0.431458i \(0.857999\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.22630 0.0498973
\(605\) 0.154020 0.266770i 0.00626180 0.0108458i
\(606\) 0 0
\(607\) −13.0526 + 7.53592i −0.529788 + 0.305873i −0.740930 0.671582i \(-0.765615\pi\)
0.211142 + 0.977455i \(0.432282\pi\)
\(608\) 3.06663 + 5.31156i 0.124368 + 0.215412i
\(609\) 0 0
\(610\) −1.24235 + 2.15181i −0.0503012 + 0.0871243i
\(611\) 29.3585i 1.18772i
\(612\) 0 0
\(613\) 9.65889 0.390119 0.195059 0.980791i \(-0.437510\pi\)
0.195059 + 0.980791i \(0.437510\pi\)
\(614\) −6.17031 + 10.6873i −0.249013 + 0.431304i
\(615\) 0 0
\(616\) 0 0
\(617\) −15.9761 + 9.22381i −0.643174 + 0.371337i −0.785836 0.618435i \(-0.787767\pi\)
0.142662 + 0.989771i \(0.454434\pi\)
\(618\) 0 0
\(619\) 29.3519 + 16.9463i 1.17975 + 0.681130i 0.955957 0.293506i \(-0.0948220\pi\)
0.223795 + 0.974636i \(0.428155\pi\)
\(620\) 0.472720i 0.0189849i
\(621\) 0 0
\(622\) 8.90774i 0.357168i
\(623\) 0 0
\(624\) 0 0
\(625\) −11.7911 20.4227i −0.471642 0.816908i
\(626\) −8.77733 15.2028i −0.350813 0.607626i
\(627\) 0 0
\(628\) 2.88526 + 1.66580i 0.115134 + 0.0664728i
\(629\) −57.8641 −2.30719
\(630\) 0 0
\(631\) −10.0134 −0.398629 −0.199314 0.979936i \(-0.563871\pi\)
−0.199314 + 0.979936i \(0.563871\pi\)
\(632\) 11.8616 + 6.84831i 0.471830 + 0.272411i
\(633\) 0 0
\(634\) −22.0035 38.1112i −0.873870 1.51359i
\(635\) −1.04568 1.81117i −0.0414965 0.0718741i
\(636\) 0 0
\(637\) 0 0
\(638\) 14.6569i 0.580271i
\(639\) 0 0
\(640\) 3.92594i 0.155186i
\(641\) 34.7673 + 20.0729i 1.37323 + 0.792833i 0.991333 0.131373i \(-0.0419387\pi\)
0.381894 + 0.924206i \(0.375272\pi\)
\(642\) 0 0
\(643\) 30.0552 17.3524i 1.18526 0.684311i 0.228036 0.973653i \(-0.426770\pi\)
0.957226 + 0.289342i \(0.0934364\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 19.3566 33.5266i 0.761575 1.31909i
\(647\) 14.3693 0.564916 0.282458 0.959280i \(-0.408850\pi\)
0.282458 + 0.959280i \(0.408850\pi\)
\(648\) 0 0
\(649\) 6.60535i 0.259283i
\(650\) 12.6282 21.8726i 0.495317 0.857915i
\(651\) 0 0
\(652\) −0.658626 1.14077i −0.0257938 0.0446761i
\(653\) 0.971455 0.560870i 0.0380160 0.0219485i −0.480872 0.876791i \(-0.659680\pi\)
0.518888 + 0.854843i \(0.326346\pi\)
\(654\) 0 0
\(655\) 3.01369 5.21987i 0.117755 0.203957i
\(656\) −22.6089 −0.882729
\(657\) 0 0
\(658\) 0 0
\(659\) 5.45240 + 3.14795i 0.212395 + 0.122627i 0.602424 0.798176i \(-0.294202\pi\)
−0.390029 + 0.920803i \(0.627535\pi\)
\(660\) 0 0
\(661\) −37.6913 + 21.7611i −1.46602 + 0.846409i −0.999278 0.0379828i \(-0.987907\pi\)
−0.466745 + 0.884392i \(0.654573\pi\)
\(662\) 21.9199 12.6555i 0.851943 0.491869i
\(663\) 0 0
\(664\) −20.4355 11.7984i −0.793051 0.457868i
\(665\) 0 0
\(666\) 0 0
\(667\) −18.6474 −0.722028
\(668\) 0.272134 0.471349i 0.0105292 0.0182370i
\(669\) 0 0
\(670\) −0.0439456 + 0.0253720i −0.00169776 + 0.000980205i
\(671\) 8.58086 + 14.8625i 0.331261 + 0.573760i
\(672\) 0 0
\(673\) −11.6052 + 20.1008i −0.447347 + 0.774827i −0.998212 0.0597668i \(-0.980964\pi\)
0.550866 + 0.834594i \(0.314298\pi\)
\(674\) 30.0063i 1.15580i
\(675\) 0 0
\(676\) −0.197336 −0.00758986
\(677\) 22.8213 39.5276i 0.877093 1.51917i 0.0225758 0.999745i \(-0.492813\pi\)
0.854517 0.519424i \(-0.173853\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −3.47757 + 2.00778i −0.133359 + 0.0769947i
\(681\) 0 0
\(682\) 30.5821 + 17.6566i 1.17105 + 0.676104i
\(683\) 4.40243i 0.168454i 0.996447 + 0.0842272i \(0.0268421\pi\)
−0.996447 + 0.0842272i \(0.973158\pi\)
\(684\) 0 0
\(685\) 0.489950i 0.0187200i
\(686\) 0 0
\(687\) 0 0
\(688\) −12.0134 20.8079i −0.458008 0.793294i
\(689\) 0.148299 + 0.256861i 0.00564973 + 0.00978562i
\(690\) 0 0
\(691\) 8.08070 + 4.66539i 0.307404 + 0.177480i 0.645764 0.763537i \(-0.276539\pi\)
−0.338360 + 0.941017i \(0.609872\pi\)
\(692\) −4.11527 −0.156439
\(693\) 0 0
\(694\) −26.2486 −0.996385
\(695\) 1.22531 + 0.707436i 0.0464788 + 0.0268346i
\(696\) 0 0
\(697\) 12.6417 + 21.8961i 0.478839 + 0.829374i
\(698\) 3.10802 + 5.38324i 0.117640 + 0.203759i
\(699\) 0 0
\(700\) 0 0
\(701\) 22.9051i 0.865116i 0.901606 + 0.432558i \(0.142389\pi\)
−0.901606 + 0.432558i \(0.857611\pi\)
\(702\) 0 0
\(703\) 63.3001i 2.38741i
\(704\) −19.2464 11.1119i −0.725376 0.418796i
\(705\) 0 0
\(706\) 39.2054 22.6353i 1.47552 0.851889i
\(707\) 0 0
\(708\) 0 0
\(709\) −2.78180 + 4.81822i −0.104473 + 0.180952i −0.913523 0.406788i \(-0.866649\pi\)
0.809050 + 0.587740i \(0.199982\pi\)
\(710\) −3.56633 −0.133842
\(711\) 0 0
\(712\) 4.99647i 0.187250i
\(713\) 22.4637 38.9083i 0.841274 1.45713i
\(714\) 0 0
\(715\) 1.69167 + 2.93006i 0.0632649 + 0.109578i
\(716\) 3.87548 2.23751i 0.144834 0.0836197i
\(717\) 0 0
\(718\) 4.00172 6.93118i 0.149343 0.258669i
\(719\) 19.9978 0.745790 0.372895 0.927873i \(-0.378365\pi\)
0.372895 + 0.927873i \(0.378365\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −12.2494 7.07220i −0.455876 0.263200i
\(723\) 0 0
\(724\) −0.442158 + 0.255280i −0.0164327 + 0.00948741i
\(725\) −13.2614 + 7.65648i −0.492516 + 0.284354i
\(726\) 0 0
\(727\) −25.0380 14.4557i −0.928610 0.536133i −0.0422381 0.999108i \(-0.513449\pi\)
−0.886372 + 0.462975i \(0.846782\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −4.40237 −0.162939
\(731\) −13.4346 + 23.2694i −0.496896 + 0.860650i
\(732\) 0 0
\(733\) 27.5498 15.9059i 1.01757 0.587496i 0.104173 0.994559i \(-0.466780\pi\)
0.913400 + 0.407063i \(0.133447\pi\)
\(734\) −14.8461 25.7143i −0.547981 0.949131i
\(735\) 0 0
\(736\) 3.42935 5.93980i 0.126407 0.218944i
\(737\) 0.350487i 0.0129104i
\(738\) 0 0
\(739\) 22.7871 0.838236 0.419118 0.907932i \(-0.362339\pi\)
0.419118 + 0.907932i \(0.362339\pi\)
\(740\) −0.372405 + 0.645025i −0.0136899 + 0.0237116i
\(741\) 0 0
\(742\) 0 0
\(743\) −11.8554 + 6.84471i −0.434932 + 0.251108i −0.701446 0.712723i \(-0.747462\pi\)
0.266513 + 0.963831i \(0.414128\pi\)
\(744\) 0 0
\(745\) −2.59997 1.50109i −0.0952554 0.0549957i
\(746\) 38.7380i 1.41830i
\(747\) 0 0
\(748\) 3.14621i 0.115037i
\(749\) 0 0
\(750\) 0 0
\(751\) −10.2030 17.6721i −0.372312 0.644864i 0.617608 0.786486i \(-0.288102\pi\)
−0.989921 + 0.141622i \(0.954768\pi\)
\(752\) 18.4768 + 32.0028i 0.673781 + 1.16702i
\(753\) 0 0
\(754\) −13.9221 8.03793i −0.507013 0.292724i
\(755\) 1.85624 0.0675554
\(756\) 0 0
\(757\) −4.02306 −0.146221 −0.0731104 0.997324i \(-0.523293\pi\)
−0.0731104 + 0.997324i \(0.523293\pi\)
\(758\) 39.2400 + 22.6552i 1.42526 + 0.822874i
\(759\) 0 0
\(760\) 2.19639 + 3.80426i 0.0796715 + 0.137995i
\(761\) 22.9595 + 39.7670i 0.832280 + 1.44155i 0.896226 + 0.443598i \(0.146298\pi\)
−0.0639453 + 0.997953i \(0.520368\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.428864i 0.0155157i
\(765\) 0 0
\(766\) 33.7111i 1.21803i
\(767\) 6.27422 + 3.62242i 0.226549 + 0.130798i
\(768\) 0 0
\(769\) −5.22983 + 3.01944i −0.188592 + 0.108884i −0.591323 0.806434i \(-0.701394\pi\)
0.402731 + 0.915318i \(0.368061\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.606656 + 1.05076i −0.0218340 + 0.0378176i
\(773\) −38.2314 −1.37509 −0.687545 0.726142i \(-0.741311\pi\)
−0.687545 + 0.726142i \(0.741311\pi\)
\(774\) 0 0
\(775\) 36.8938i 1.32527i
\(776\) −16.9060 + 29.2820i −0.606889 + 1.05116i
\(777\) 0 0
\(778\) 3.33508 + 5.77653i 0.119568 + 0.207098i
\(779\) 23.9531 13.8293i 0.858209 0.495487i
\(780\) 0 0
\(781\) −12.3163 + 21.3324i −0.440711 + 0.763333i
\(782\) −43.2921 −1.54812
\(783\) 0 0
\(784\) 0 0
\(785\) 4.36739 + 2.52152i 0.155879 + 0.0899968i
\(786\) 0 0
\(787\) 41.7875 24.1260i 1.48957 0.860001i 0.489636 0.871927i \(-0.337130\pi\)
0.999929 + 0.0119261i \(0.00379628\pi\)
\(788\) −1.34907 + 0.778886i −0.0480586 + 0.0277467i
\(789\) 0 0
\(790\) −2.03675 1.17592i −0.0724643 0.0418373i
\(791\) 0 0
\(792\) 0 0
\(793\) 18.8232 0.668432
\(794\) 7.16394 12.4083i 0.254239 0.440354i
\(795\) 0 0
\(796\) 1.20910 0.698076i 0.0428555 0.0247426i