Properties

Label 1323.2.h.h.226.9
Level $1323$
Weight $2$
Character 1323.226
Analytic conductor $10.564$
Analytic rank $0$
Dimension $24$
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.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.9
Character \(\chi\) \(=\) 1323.226
Dual form 1323.2.h.h.802.9

$q$-expansion

\(f(q)\) \(=\) \(q+1.72661 q^{2} +0.981184 q^{4} +(1.75616 + 3.04175i) q^{5} -1.75910 q^{8} +O(q^{10})\) \(q+1.72661 q^{2} +0.981184 q^{4} +(1.75616 + 3.04175i) q^{5} -1.75910 q^{8} +(3.03220 + 5.25192i) q^{10} +(-3.04532 + 5.27465i) q^{11} +(0.560139 - 0.970190i) q^{13} -4.99965 q^{16} +(0.601978 + 1.04266i) q^{17} +(1.10269 - 1.90991i) q^{19} +(1.72311 + 2.98452i) q^{20} +(-5.25808 + 9.10727i) q^{22} +(-0.636695 - 1.10279i) q^{23} +(-3.66817 + 6.35345i) q^{25} +(0.967143 - 1.67514i) q^{26} +(3.10262 + 5.37390i) q^{29} -0.188404 q^{31} -5.11425 q^{32} +(1.03938 + 1.80026i) q^{34} +(-1.78835 + 3.09752i) q^{37} +(1.90391 - 3.29767i) q^{38} +(-3.08925 - 5.35074i) q^{40} +(-1.68320 + 2.91538i) q^{41} +(-1.90276 - 3.29567i) q^{43} +(-2.98802 + 5.17540i) q^{44} +(-1.09932 - 1.90408i) q^{46} +5.72070 q^{47} +(-6.33349 + 10.9699i) q^{50} +(0.549600 - 0.951935i) q^{52} +(-4.16913 - 7.22115i) q^{53} -21.3922 q^{55} +(5.35702 + 9.27862i) q^{58} +11.2685 q^{59} +12.0022 q^{61} -0.325300 q^{62} +1.16898 q^{64} +3.93477 q^{65} -7.91303 q^{67} +(0.590651 + 1.02304i) q^{68} +12.2052 q^{71} +(2.65737 + 4.60269i) q^{73} +(-3.08779 + 5.34820i) q^{74} +(1.08194 - 1.87397i) q^{76} +9.21711 q^{79} +(-8.78016 - 15.2077i) q^{80} +(-2.90623 + 5.03373i) q^{82} +(-0.624950 - 1.08245i) q^{83} +(-2.11433 + 3.66213i) q^{85} +(-3.28532 - 5.69034i) q^{86} +(5.35702 - 9.27862i) q^{88} +(2.77066 - 4.79892i) q^{89} +(-0.624715 - 1.08204i) q^{92} +9.87741 q^{94} +7.74596 q^{95} +(8.24277 + 14.2769i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{4} + 24q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{4} + 24q^{8} - 20q^{11} + 24q^{16} - 32q^{23} - 12q^{25} - 16q^{29} + 96q^{32} - 12q^{37} - 56q^{44} + 24q^{46} + 4q^{50} - 32q^{53} + 96q^{64} + 120q^{65} + 24q^{67} + 112q^{71} - 68q^{74} - 24q^{79} + 12q^{85} - 76q^{86} - 16q^{92} + 128q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.72661 1.22090 0.610449 0.792056i \(-0.290989\pi\)
0.610449 + 0.792056i \(0.290989\pi\)
\(3\) 0 0
\(4\) 0.981184 0.490592
\(5\) 1.75616 + 3.04175i 0.785377 + 1.36031i 0.928774 + 0.370647i \(0.120864\pi\)
−0.143397 + 0.989665i \(0.545803\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.75910 −0.621935
\(9\) 0 0
\(10\) 3.03220 + 5.25192i 0.958865 + 1.66080i
\(11\) −3.04532 + 5.27465i −0.918199 + 1.59037i −0.116049 + 0.993244i \(0.537023\pi\)
−0.802150 + 0.597123i \(0.796310\pi\)
\(12\) 0 0
\(13\) 0.560139 0.970190i 0.155355 0.269082i −0.777833 0.628471i \(-0.783681\pi\)
0.933188 + 0.359388i \(0.117015\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −4.99965 −1.24991
\(17\) 0.601978 + 1.04266i 0.146001 + 0.252881i 0.929746 0.368202i \(-0.120026\pi\)
−0.783745 + 0.621083i \(0.786693\pi\)
\(18\) 0 0
\(19\) 1.10269 1.90991i 0.252974 0.438163i −0.711370 0.702818i \(-0.751925\pi\)
0.964343 + 0.264655i \(0.0852581\pi\)
\(20\) 1.72311 + 2.98452i 0.385300 + 0.667359i
\(21\) 0 0
\(22\) −5.25808 + 9.10727i −1.12103 + 1.94168i
\(23\) −0.636695 1.10279i −0.132760 0.229947i 0.791980 0.610548i \(-0.209051\pi\)
−0.924740 + 0.380601i \(0.875717\pi\)
\(24\) 0 0
\(25\) −3.66817 + 6.35345i −0.733633 + 1.27069i
\(26\) 0.967143 1.67514i 0.189672 0.328522i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.10262 + 5.37390i 0.576142 + 0.997907i 0.995917 + 0.0902789i \(0.0287758\pi\)
−0.419774 + 0.907628i \(0.637891\pi\)
\(30\) 0 0
\(31\) −0.188404 −0.0338383 −0.0169192 0.999857i \(-0.505386\pi\)
−0.0169192 + 0.999857i \(0.505386\pi\)
\(32\) −5.11425 −0.904079
\(33\) 0 0
\(34\) 1.03938 + 1.80026i 0.178252 + 0.308742i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.78835 + 3.09752i −0.294003 + 0.509228i −0.974753 0.223288i \(-0.928321\pi\)
0.680749 + 0.732516i \(0.261654\pi\)
\(38\) 1.90391 3.29767i 0.308855 0.534953i
\(39\) 0 0
\(40\) −3.08925 5.35074i −0.488453 0.846026i
\(41\) −1.68320 + 2.91538i −0.262871 + 0.455307i −0.967004 0.254762i \(-0.918003\pi\)
0.704132 + 0.710069i \(0.251336\pi\)
\(42\) 0 0
\(43\) −1.90276 3.29567i −0.290168 0.502585i 0.683681 0.729781i \(-0.260378\pi\)
−0.973849 + 0.227195i \(0.927044\pi\)
\(44\) −2.98802 + 5.17540i −0.450461 + 0.780221i
\(45\) 0 0
\(46\) −1.09932 1.90408i −0.162086 0.280742i
\(47\) 5.72070 0.834449 0.417225 0.908803i \(-0.363003\pi\)
0.417225 + 0.908803i \(0.363003\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −6.33349 + 10.9699i −0.895691 + 1.55138i
\(51\) 0 0
\(52\) 0.549600 0.951935i 0.0762158 0.132010i
\(53\) −4.16913 7.22115i −0.572675 0.991901i −0.996290 0.0860593i \(-0.972573\pi\)
0.423615 0.905842i \(-0.360761\pi\)
\(54\) 0 0
\(55\) −21.3922 −2.88453
\(56\) 0 0
\(57\) 0 0
\(58\) 5.35702 + 9.27862i 0.703411 + 1.21834i
\(59\) 11.2685 1.46704 0.733519 0.679669i \(-0.237877\pi\)
0.733519 + 0.679669i \(0.237877\pi\)
\(60\) 0 0
\(61\) 12.0022 1.53672 0.768361 0.640017i \(-0.221073\pi\)
0.768361 + 0.640017i \(0.221073\pi\)
\(62\) −0.325300 −0.0413131
\(63\) 0 0
\(64\) 1.16898 0.146123
\(65\) 3.93477 0.488048
\(66\) 0 0
\(67\) −7.91303 −0.966731 −0.483366 0.875419i \(-0.660586\pi\)
−0.483366 + 0.875419i \(0.660586\pi\)
\(68\) 0.590651 + 1.02304i 0.0716270 + 0.124062i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.2052 1.44850 0.724248 0.689540i \(-0.242187\pi\)
0.724248 + 0.689540i \(0.242187\pi\)
\(72\) 0 0
\(73\) 2.65737 + 4.60269i 0.311021 + 0.538704i 0.978584 0.205849i \(-0.0659957\pi\)
−0.667563 + 0.744554i \(0.732662\pi\)
\(74\) −3.08779 + 5.34820i −0.358948 + 0.621716i
\(75\) 0 0
\(76\) 1.08194 1.87397i 0.124107 0.214959i
\(77\) 0 0
\(78\) 0 0
\(79\) 9.21711 1.03701 0.518503 0.855076i \(-0.326490\pi\)
0.518503 + 0.855076i \(0.326490\pi\)
\(80\) −8.78016 15.2077i −0.981651 1.70027i
\(81\) 0 0
\(82\) −2.90623 + 5.03373i −0.320939 + 0.555883i
\(83\) −0.624950 1.08245i −0.0685972 0.118814i 0.829687 0.558229i \(-0.188519\pi\)
−0.898284 + 0.439415i \(0.855186\pi\)
\(84\) 0 0
\(85\) −2.11433 + 3.66213i −0.229332 + 0.397214i
\(86\) −3.28532 5.69034i −0.354265 0.613605i
\(87\) 0 0
\(88\) 5.35702 9.27862i 0.571060 0.989105i
\(89\) 2.77066 4.79892i 0.293689 0.508684i −0.680990 0.732293i \(-0.738450\pi\)
0.974679 + 0.223608i \(0.0717837\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.624715 1.08204i −0.0651310 0.112810i
\(93\) 0 0
\(94\) 9.87741 1.01878
\(95\) 7.74596 0.794718
\(96\) 0 0
\(97\) 8.24277 + 14.2769i 0.836926 + 1.44960i 0.892452 + 0.451142i \(0.148983\pi\)
−0.0555261 + 0.998457i \(0.517684\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.59915 + 6.23391i −0.359915 + 0.623391i
\(101\) −6.48192 + 11.2270i −0.644975 + 1.11713i 0.339332 + 0.940667i \(0.389799\pi\)
−0.984307 + 0.176463i \(0.943534\pi\)
\(102\) 0 0
\(103\) −1.35091 2.33984i −0.133109 0.230552i 0.791765 0.610826i \(-0.209163\pi\)
−0.924873 + 0.380275i \(0.875829\pi\)
\(104\) −0.985340 + 1.70666i −0.0966205 + 0.167352i
\(105\) 0 0
\(106\) −7.19847 12.4681i −0.699177 1.21101i
\(107\) −0.0892402 + 0.154569i −0.00862718 + 0.0149427i −0.870307 0.492510i \(-0.836079\pi\)
0.861680 + 0.507453i \(0.169413\pi\)
\(108\) 0 0
\(109\) −4.67927 8.10473i −0.448192 0.776292i 0.550076 0.835115i \(-0.314599\pi\)
−0.998268 + 0.0588226i \(0.981265\pi\)
\(110\) −36.9360 −3.52171
\(111\) 0 0
\(112\) 0 0
\(113\) −4.21019 + 7.29226i −0.396061 + 0.685998i −0.993236 0.116113i \(-0.962957\pi\)
0.597175 + 0.802111i \(0.296290\pi\)
\(114\) 0 0
\(115\) 2.23627 3.87333i 0.208533 0.361190i
\(116\) 3.04424 + 5.27278i 0.282651 + 0.489565i
\(117\) 0 0
\(118\) 19.4564 1.79110
\(119\) 0 0
\(120\) 0 0
\(121\) −13.0479 22.5997i −1.18618 2.05452i
\(122\) 20.7231 1.87618
\(123\) 0 0
\(124\) −0.184859 −0.0166008
\(125\) −8.20593 −0.733960
\(126\) 0 0
\(127\) −9.92438 −0.880647 −0.440323 0.897839i \(-0.645136\pi\)
−0.440323 + 0.897839i \(0.645136\pi\)
\(128\) 12.2469 1.08248
\(129\) 0 0
\(130\) 6.79381 0.595857
\(131\) −7.62335 13.2040i −0.666055 1.15364i −0.978998 0.203870i \(-0.934648\pi\)
0.312943 0.949772i \(-0.398685\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −13.6627 −1.18028
\(135\) 0 0
\(136\) −1.05894 1.83413i −0.0908032 0.157276i
\(137\) 3.07350 5.32346i 0.262587 0.454814i −0.704342 0.709861i \(-0.748758\pi\)
0.966929 + 0.255047i \(0.0820910\pi\)
\(138\) 0 0
\(139\) 0.438687 0.759829i 0.0372090 0.0644478i −0.846821 0.531878i \(-0.821487\pi\)
0.884030 + 0.467430i \(0.154820\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 21.0737 1.76847
\(143\) 3.41161 + 5.90908i 0.285293 + 0.494142i
\(144\) 0 0
\(145\) −10.8974 + 18.8748i −0.904977 + 1.56747i
\(146\) 4.58824 + 7.94706i 0.379725 + 0.657703i
\(147\) 0 0
\(148\) −1.75470 + 3.03923i −0.144236 + 0.249823i
\(149\) 2.88776 + 5.00175i 0.236575 + 0.409760i 0.959729 0.280927i \(-0.0906418\pi\)
−0.723154 + 0.690686i \(0.757308\pi\)
\(150\) 0 0
\(151\) 1.01321 1.75494i 0.0824541 0.142815i −0.821849 0.569705i \(-0.807058\pi\)
0.904304 + 0.426890i \(0.140391\pi\)
\(152\) −1.93973 + 3.35972i −0.157333 + 0.272509i
\(153\) 0 0
\(154\) 0 0
\(155\) −0.330866 0.573077i −0.0265758 0.0460307i
\(156\) 0 0
\(157\) −3.04756 −0.243222 −0.121611 0.992578i \(-0.538806\pi\)
−0.121611 + 0.992578i \(0.538806\pi\)
\(158\) 15.9144 1.26608
\(159\) 0 0
\(160\) −8.98141 15.5563i −0.710043 1.22983i
\(161\) 0 0
\(162\) 0 0
\(163\) 2.69445 4.66693i 0.211046 0.365542i −0.740996 0.671509i \(-0.765646\pi\)
0.952042 + 0.305967i \(0.0989797\pi\)
\(164\) −1.65153 + 2.86053i −0.128963 + 0.223370i
\(165\) 0 0
\(166\) −1.07905 1.86896i −0.0837502 0.145060i
\(167\) 8.30480 14.3843i 0.642645 1.11309i −0.342196 0.939629i \(-0.611171\pi\)
0.984840 0.173464i \(-0.0554961\pi\)
\(168\) 0 0
\(169\) 5.87249 + 10.1714i 0.451730 + 0.782419i
\(170\) −3.65063 + 6.32308i −0.279991 + 0.484958i
\(171\) 0 0
\(172\) −1.86696 3.23366i −0.142354 0.246564i
\(173\) 17.6503 1.34193 0.670965 0.741489i \(-0.265880\pi\)
0.670965 + 0.741489i \(0.265880\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 15.2255 26.3714i 1.14767 1.98782i
\(177\) 0 0
\(178\) 4.78384 8.28586i 0.358564 0.621051i
\(179\) 1.31422 + 2.27630i 0.0982294 + 0.170138i 0.910952 0.412513i \(-0.135349\pi\)
−0.812722 + 0.582651i \(0.802015\pi\)
\(180\) 0 0
\(181\) 3.97391 0.295378 0.147689 0.989034i \(-0.452816\pi\)
0.147689 + 0.989034i \(0.452816\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1.12001 + 1.93991i 0.0825681 + 0.143012i
\(185\) −12.5625 −0.923613
\(186\) 0 0
\(187\) −7.33286 −0.536232
\(188\) 5.61306 0.409374
\(189\) 0 0
\(190\) 13.3743 0.970270
\(191\) 18.2059 1.31733 0.658666 0.752435i \(-0.271121\pi\)
0.658666 + 0.752435i \(0.271121\pi\)
\(192\) 0 0
\(193\) −0.202385 −0.0145680 −0.00728401 0.999973i \(-0.502319\pi\)
−0.00728401 + 0.999973i \(0.502319\pi\)
\(194\) 14.2321 + 24.6506i 1.02180 + 1.76981i
\(195\) 0 0
\(196\) 0 0
\(197\) 1.63136 0.116229 0.0581147 0.998310i \(-0.481491\pi\)
0.0581147 + 0.998310i \(0.481491\pi\)
\(198\) 0 0
\(199\) −3.14605 5.44912i −0.223018 0.386278i 0.732705 0.680546i \(-0.238257\pi\)
−0.955723 + 0.294268i \(0.904924\pi\)
\(200\) 6.45266 11.1763i 0.456272 0.790287i
\(201\) 0 0
\(202\) −11.1918 + 19.3847i −0.787449 + 1.36390i
\(203\) 0 0
\(204\) 0 0
\(205\) −11.8238 −0.825812
\(206\) −2.33249 4.04000i −0.162512 0.281480i
\(207\) 0 0
\(208\) −2.80050 + 4.85061i −0.194180 + 0.336329i
\(209\) 6.71607 + 11.6326i 0.464560 + 0.804642i
\(210\) 0 0
\(211\) 8.14368 14.1053i 0.560634 0.971046i −0.436807 0.899555i \(-0.643891\pi\)
0.997441 0.0714912i \(-0.0227758\pi\)
\(212\) −4.09069 7.08528i −0.280950 0.486619i
\(213\) 0 0
\(214\) −0.154083 + 0.266880i −0.0105329 + 0.0182435i
\(215\) 6.68308 11.5754i 0.455782 0.789438i
\(216\) 0 0
\(217\) 0 0
\(218\) −8.07927 13.9937i −0.547197 0.947773i
\(219\) 0 0
\(220\) −20.9897 −1.41513
\(221\) 1.34877 0.0907278
\(222\) 0 0
\(223\) −9.98472 17.2940i −0.668626 1.15809i −0.978288 0.207248i \(-0.933549\pi\)
0.309662 0.950847i \(-0.399784\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −7.26936 + 12.5909i −0.483551 + 0.837534i
\(227\) 1.80642 3.12880i 0.119896 0.207666i −0.799830 0.600226i \(-0.795077\pi\)
0.919726 + 0.392560i \(0.128411\pi\)
\(228\) 0 0
\(229\) −6.85733 11.8772i −0.453145 0.784870i 0.545435 0.838153i \(-0.316365\pi\)
−0.998579 + 0.0532835i \(0.983031\pi\)
\(230\) 3.86117 6.68774i 0.254598 0.440976i
\(231\) 0 0
\(232\) −5.45781 9.45321i −0.358323 0.620634i
\(233\) −12.6271 + 21.8707i −0.827227 + 1.43280i 0.0729776 + 0.997334i \(0.476750\pi\)
−0.900205 + 0.435466i \(0.856583\pi\)
\(234\) 0 0
\(235\) 10.0464 + 17.4009i 0.655357 + 1.13511i
\(236\) 11.0565 0.719717
\(237\) 0 0
\(238\) 0 0
\(239\) 4.49495 7.78549i 0.290754 0.503601i −0.683234 0.730200i \(-0.739427\pi\)
0.973988 + 0.226598i \(0.0727604\pi\)
\(240\) 0 0
\(241\) −4.62862 + 8.01701i −0.298156 + 0.516421i −0.975714 0.219048i \(-0.929705\pi\)
0.677558 + 0.735469i \(0.263038\pi\)
\(242\) −22.5287 39.0209i −1.44820 2.50836i
\(243\) 0 0
\(244\) 11.7763 0.753903
\(245\) 0 0
\(246\) 0 0
\(247\) −1.23532 2.13963i −0.0786013 0.136141i
\(248\) 0.331421 0.0210452
\(249\) 0 0
\(250\) −14.1684 −0.896091
\(251\) −20.6517 −1.30353 −0.651763 0.758422i \(-0.725970\pi\)
−0.651763 + 0.758422i \(0.725970\pi\)
\(252\) 0 0
\(253\) 7.75576 0.487600
\(254\) −17.1355 −1.07518
\(255\) 0 0
\(256\) 18.8076 1.17548
\(257\) −1.22289 2.11811i −0.0762819 0.132124i 0.825361 0.564605i \(-0.190972\pi\)
−0.901643 + 0.432481i \(0.857638\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 3.86073 0.239432
\(261\) 0 0
\(262\) −13.1626 22.7982i −0.813186 1.40848i
\(263\) −12.2814 + 21.2720i −0.757302 + 1.31169i 0.186919 + 0.982375i \(0.440150\pi\)
−0.944222 + 0.329311i \(0.893184\pi\)
\(264\) 0 0
\(265\) 14.6433 25.3629i 0.899531 1.55803i
\(266\) 0 0
\(267\) 0 0
\(268\) −7.76415 −0.474271
\(269\) −14.7851 25.6086i −0.901466 1.56139i −0.825592 0.564268i \(-0.809158\pi\)
−0.0758746 0.997117i \(-0.524175\pi\)
\(270\) 0 0
\(271\) 12.3958 21.4701i 0.752989 1.30421i −0.193380 0.981124i \(-0.561945\pi\)
0.946368 0.323090i \(-0.104722\pi\)
\(272\) −3.00968 5.21291i −0.182488 0.316079i
\(273\) 0 0
\(274\) 5.30674 9.19154i 0.320592 0.555281i
\(275\) −22.3415 38.6966i −1.34724 2.33349i
\(276\) 0 0
\(277\) −0.939249 + 1.62683i −0.0564340 + 0.0977466i −0.892862 0.450330i \(-0.851306\pi\)
0.836428 + 0.548076i \(0.184640\pi\)
\(278\) 0.757442 1.31193i 0.0454284 0.0786842i
\(279\) 0 0
\(280\) 0 0
\(281\) −6.03965 10.4610i −0.360295 0.624049i 0.627714 0.778444i \(-0.283991\pi\)
−0.988009 + 0.154395i \(0.950657\pi\)
\(282\) 0 0
\(283\) −27.9719 −1.66276 −0.831378 0.555708i \(-0.812447\pi\)
−0.831378 + 0.555708i \(0.812447\pi\)
\(284\) 11.9756 0.710620
\(285\) 0 0
\(286\) 5.89052 + 10.2027i 0.348314 + 0.603297i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.77524 13.4671i 0.457367 0.792183i
\(290\) −18.8155 + 32.5894i −1.10488 + 1.91372i
\(291\) 0 0
\(292\) 2.60736 + 4.51609i 0.152584 + 0.264284i
\(293\) 4.41163 7.64117i 0.257730 0.446402i −0.707903 0.706309i \(-0.750359\pi\)
0.965634 + 0.259908i \(0.0836921\pi\)
\(294\) 0 0
\(295\) 19.7893 + 34.2761i 1.15218 + 1.99563i
\(296\) 3.14589 5.44883i 0.182851 0.316707i
\(297\) 0 0
\(298\) 4.98604 + 8.63608i 0.288834 + 0.500275i
\(299\) −1.42655 −0.0824996
\(300\) 0 0
\(301\) 0 0
\(302\) 1.74942 3.03009i 0.100668 0.174362i
\(303\) 0 0
\(304\) −5.51304 + 9.54887i −0.316195 + 0.547665i
\(305\) 21.0777 + 36.5076i 1.20691 + 2.09042i
\(306\) 0 0
\(307\) 1.05532 0.0602304 0.0301152 0.999546i \(-0.490413\pi\)
0.0301152 + 0.999546i \(0.490413\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.571277 0.989481i −0.0324464 0.0561988i
\(311\) −3.07215 −0.174206 −0.0871029 0.996199i \(-0.527761\pi\)
−0.0871029 + 0.996199i \(0.527761\pi\)
\(312\) 0 0
\(313\) 28.1621 1.59181 0.795907 0.605419i \(-0.206994\pi\)
0.795907 + 0.605419i \(0.206994\pi\)
\(314\) −5.26196 −0.296949
\(315\) 0 0
\(316\) 9.04368 0.508747
\(317\) −12.8465 −0.721530 −0.360765 0.932657i \(-0.617484\pi\)
−0.360765 + 0.932657i \(0.617484\pi\)
\(318\) 0 0
\(319\) −37.7939 −2.11605
\(320\) 2.05291 + 3.55575i 0.114761 + 0.198772i
\(321\) 0 0
\(322\) 0 0
\(323\) 2.65517 0.147738
\(324\) 0 0
\(325\) 4.10937 + 7.11763i 0.227947 + 0.394815i
\(326\) 4.65227 8.05797i 0.257665 0.446290i
\(327\) 0 0
\(328\) 2.96091 5.12845i 0.163489 0.283171i
\(329\) 0 0
\(330\) 0 0
\(331\) −21.5560 −1.18483 −0.592413 0.805634i \(-0.701825\pi\)
−0.592413 + 0.805634i \(0.701825\pi\)
\(332\) −0.613191 1.06208i −0.0336532 0.0582891i
\(333\) 0 0
\(334\) 14.3392 24.8361i 0.784604 1.35897i
\(335\) −13.8965 24.0695i −0.759248 1.31506i
\(336\) 0 0
\(337\) 6.30340 10.9178i 0.343368 0.594731i −0.641688 0.766966i \(-0.721766\pi\)
0.985056 + 0.172235i \(0.0550989\pi\)
\(338\) 10.1395 + 17.5621i 0.551516 + 0.955254i
\(339\) 0 0
\(340\) −2.07455 + 3.59323i −0.112508 + 0.194870i
\(341\) 0.573750 0.993764i 0.0310703 0.0538153i
\(342\) 0 0
\(343\) 0 0
\(344\) 3.34714 + 5.79741i 0.180466 + 0.312575i
\(345\) 0 0
\(346\) 30.4752 1.63836
\(347\) −23.1366 −1.24204 −0.621020 0.783795i \(-0.713281\pi\)
−0.621020 + 0.783795i \(0.713281\pi\)
\(348\) 0 0
\(349\) 8.24346 + 14.2781i 0.441262 + 0.764289i 0.997783 0.0665448i \(-0.0211975\pi\)
−0.556521 + 0.830833i \(0.687864\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 15.5745 26.9759i 0.830124 1.43782i
\(353\) −12.2438 + 21.2068i −0.651669 + 1.12872i 0.331049 + 0.943614i \(0.392598\pi\)
−0.982718 + 0.185110i \(0.940736\pi\)
\(354\) 0 0
\(355\) 21.4343 + 37.1253i 1.13761 + 1.97041i
\(356\) 2.71852 4.70862i 0.144081 0.249556i
\(357\) 0 0
\(358\) 2.26915 + 3.93028i 0.119928 + 0.207722i
\(359\) 10.2389 17.7342i 0.540386 0.935977i −0.458495 0.888697i \(-0.651611\pi\)
0.998882 0.0472797i \(-0.0150552\pi\)
\(360\) 0 0
\(361\) 7.06816 + 12.2424i 0.372009 + 0.644338i
\(362\) 6.86139 0.360627
\(363\) 0 0
\(364\) 0 0
\(365\) −9.33349 + 16.1661i −0.488537 + 0.846172i
\(366\) 0 0
\(367\) −11.1269 + 19.2724i −0.580821 + 1.00601i 0.414561 + 0.910021i \(0.363935\pi\)
−0.995382 + 0.0959900i \(0.969398\pi\)
\(368\) 3.18325 + 5.51355i 0.165938 + 0.287414i
\(369\) 0 0
\(370\) −21.6905 −1.12764
\(371\) 0 0
\(372\) 0 0
\(373\) 16.2684 + 28.1777i 0.842347 + 1.45899i 0.887905 + 0.460027i \(0.152160\pi\)
−0.0455576 + 0.998962i \(0.514506\pi\)
\(374\) −12.6610 −0.654685
\(375\) 0 0
\(376\) −10.0633 −0.518973
\(377\) 6.95160 0.358026
\(378\) 0 0
\(379\) 1.54440 0.0793306 0.0396653 0.999213i \(-0.487371\pi\)
0.0396653 + 0.999213i \(0.487371\pi\)
\(380\) 7.60021 0.389883
\(381\) 0 0
\(382\) 31.4345 1.60833
\(383\) 15.8147 + 27.3919i 0.808093 + 1.39966i 0.914183 + 0.405302i \(0.132834\pi\)
−0.106090 + 0.994357i \(0.533833\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.349441 −0.0177861
\(387\) 0 0
\(388\) 8.08767 + 14.0083i 0.410589 + 0.711162i
\(389\) −2.62313 + 4.54340i −0.132998 + 0.230359i −0.924831 0.380378i \(-0.875794\pi\)
0.791833 + 0.610738i \(0.209127\pi\)
\(390\) 0 0
\(391\) 0.766552 1.32771i 0.0387662 0.0671451i
\(392\) 0 0
\(393\) 0 0
\(394\) 2.81672 0.141904
\(395\) 16.1867 + 28.0362i 0.814440 + 1.41065i
\(396\) 0 0
\(397\) −0.0138175 + 0.0239325i −0.000693478 + 0.00120114i −0.866372 0.499399i \(-0.833554\pi\)
0.865678 + 0.500600i \(0.166887\pi\)
\(398\) −5.43201 9.40851i −0.272282 0.471606i
\(399\) 0 0
\(400\) 18.3395 31.7650i 0.916977 1.58825i
\(401\) 6.06885 + 10.5115i 0.303064 + 0.524922i 0.976828 0.214024i \(-0.0686572\pi\)
−0.673765 + 0.738946i \(0.735324\pi\)
\(402\) 0 0
\(403\) −0.105532 + 0.182787i −0.00525694 + 0.00910529i
\(404\) −6.35996 + 11.0158i −0.316420 + 0.548055i
\(405\) 0 0
\(406\) 0 0
\(407\) −10.8922 18.8659i −0.539907 0.935146i
\(408\) 0 0
\(409\) 31.3453 1.54993 0.774963 0.632007i \(-0.217769\pi\)
0.774963 + 0.632007i \(0.217769\pi\)
\(410\) −20.4152 −1.00823
\(411\) 0 0
\(412\) −1.32549 2.29582i −0.0653022 0.113107i
\(413\) 0 0
\(414\) 0 0
\(415\) 2.19502 3.80189i 0.107749 0.186627i
\(416\) −2.86469 + 4.96179i −0.140453 + 0.243272i
\(417\) 0 0
\(418\) 11.5960 + 20.0849i 0.567181 + 0.982385i
\(419\) −7.44319 + 12.8920i −0.363623 + 0.629814i −0.988554 0.150866i \(-0.951794\pi\)
0.624931 + 0.780680i \(0.285127\pi\)
\(420\) 0 0
\(421\) −4.54213 7.86721i −0.221370 0.383424i 0.733854 0.679307i \(-0.237720\pi\)
−0.955224 + 0.295883i \(0.904386\pi\)
\(422\) 14.0610 24.3543i 0.684477 1.18555i
\(423\) 0 0
\(424\) 7.33392 + 12.7027i 0.356166 + 0.616898i
\(425\) −8.83262 −0.428445
\(426\) 0 0
\(427\) 0 0
\(428\) −0.0875611 + 0.151660i −0.00423243 + 0.00733078i
\(429\) 0 0
\(430\) 11.5391 19.9863i 0.556463 0.963823i
\(431\) −8.31776 14.4068i −0.400652 0.693950i 0.593152 0.805090i \(-0.297883\pi\)
−0.993805 + 0.111140i \(0.964550\pi\)
\(432\) 0 0
\(433\) 19.7423 0.948756 0.474378 0.880321i \(-0.342673\pi\)
0.474378 + 0.880321i \(0.342673\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4.59122 7.95223i −0.219880 0.380843i
\(437\) −2.80830 −0.134339
\(438\) 0 0
\(439\) −6.73514 −0.321451 −0.160725 0.986999i \(-0.551383\pi\)
−0.160725 + 0.986999i \(0.551383\pi\)
\(440\) 37.6310 1.79399
\(441\) 0 0
\(442\) 2.32879 0.110769
\(443\) −28.6403 −1.36074 −0.680372 0.732867i \(-0.738182\pi\)
−0.680372 + 0.732867i \(0.738182\pi\)
\(444\) 0 0
\(445\) 19.4628 0.922626
\(446\) −17.2397 29.8601i −0.816324 1.41392i
\(447\) 0 0
\(448\) 0 0
\(449\) 6.66872 0.314716 0.157358 0.987542i \(-0.449702\pi\)
0.157358 + 0.987542i \(0.449702\pi\)
\(450\) 0 0
\(451\) −10.2518 17.7566i −0.482736 0.836124i
\(452\) −4.13097 + 7.15505i −0.194305 + 0.336545i
\(453\) 0 0
\(454\) 3.11898 5.40223i 0.146381 0.253539i
\(455\) 0 0
\(456\) 0 0
\(457\) −28.6573 −1.34053 −0.670266 0.742121i \(-0.733820\pi\)
−0.670266 + 0.742121i \(0.733820\pi\)
\(458\) −11.8399 20.5074i −0.553244 0.958246i
\(459\) 0 0
\(460\) 2.19419 3.80045i 0.102305 0.177197i
\(461\) 10.0087 + 17.3355i 0.466150 + 0.807395i 0.999253 0.0386554i \(-0.0123075\pi\)
−0.533103 + 0.846050i \(0.678974\pi\)
\(462\) 0 0
\(463\) −4.95789 + 8.58731i −0.230413 + 0.399086i −0.957930 0.287003i \(-0.907341\pi\)
0.727517 + 0.686090i \(0.240674\pi\)
\(464\) −15.5120 26.8676i −0.720127 1.24730i
\(465\) 0 0
\(466\) −21.8020 + 37.7623i −1.00996 + 1.74930i
\(467\) −8.04035 + 13.9263i −0.372063 + 0.644432i −0.989883 0.141888i \(-0.954683\pi\)
0.617820 + 0.786320i \(0.288016\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 17.3463 + 30.0446i 0.800124 + 1.38586i
\(471\) 0 0
\(472\) −19.8225 −0.912402
\(473\) 23.1780 1.06573
\(474\) 0 0
\(475\) 8.08967 + 14.0117i 0.371180 + 0.642902i
\(476\) 0 0
\(477\) 0 0
\(478\) 7.76103 13.4425i 0.354981 0.614846i
\(479\) 4.10128 7.10362i 0.187392 0.324573i −0.756988 0.653429i \(-0.773330\pi\)
0.944380 + 0.328856i \(0.106663\pi\)
\(480\) 0 0
\(481\) 2.00345 + 3.47008i 0.0913496 + 0.158222i
\(482\) −7.99183 + 13.8423i −0.364018 + 0.630497i
\(483\) 0 0
\(484\) −12.8024 22.1745i −0.581929 1.00793i
\(485\) −28.9512 + 50.1449i −1.31460 + 2.27696i
\(486\) 0 0
\(487\) −1.36840 2.37014i −0.0620081 0.107401i 0.833355 0.552738i \(-0.186417\pi\)
−0.895363 + 0.445337i \(0.853084\pi\)
\(488\) −21.1130 −0.955741
\(489\) 0 0
\(490\) 0 0
\(491\) −9.85482 + 17.0690i −0.444742 + 0.770315i −0.998034 0.0626719i \(-0.980038\pi\)
0.553293 + 0.832987i \(0.313371\pi\)
\(492\) 0 0
\(493\) −3.73542 + 6.46993i −0.168235 + 0.291391i
\(494\) −2.13291 3.69431i −0.0959642 0.166215i
\(495\) 0 0
\(496\) 0.941952 0.0422949
\(497\) 0 0
\(498\) 0 0
\(499\) 16.5480 + 28.6619i 0.740789 + 1.28309i 0.952136 + 0.305674i \(0.0988817\pi\)
−0.211347 + 0.977411i \(0.567785\pi\)
\(500\) −8.05153 −0.360075
\(501\) 0 0
\(502\) −35.6575 −1.59147
\(503\) 12.1860 0.543346 0.271673 0.962390i \(-0.412423\pi\)
0.271673 + 0.962390i \(0.412423\pi\)
\(504\) 0 0
\(505\) −45.5331 −2.02619
\(506\) 13.3912 0.595310
\(507\) 0 0
\(508\) −9.73765 −0.432038
\(509\) −6.81965 11.8120i −0.302276 0.523557i 0.674375 0.738389i \(-0.264413\pi\)
−0.976651 + 0.214832i \(0.931080\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 7.97968 0.352656
\(513\) 0 0
\(514\) −2.11146 3.65715i −0.0931325 0.161310i
\(515\) 4.74481 8.21826i 0.209081 0.362140i
\(516\) 0 0
\(517\) −17.4214 + 30.1747i −0.766190 + 1.32708i
\(518\) 0 0
\(519\) 0 0
\(520\) −6.92164 −0.303534
\(521\) 17.7745 + 30.7863i 0.778714 + 1.34877i 0.932683 + 0.360697i \(0.117461\pi\)
−0.153969 + 0.988076i \(0.549206\pi\)
\(522\) 0 0
\(523\) 13.3593 23.1391i 0.584163 1.01180i −0.410816 0.911718i \(-0.634756\pi\)
0.994979 0.100082i \(-0.0319105\pi\)
\(524\) −7.47991 12.9556i −0.326761 0.565967i
\(525\) 0 0
\(526\) −21.2052 + 36.7284i −0.924589 + 1.60143i
\(527\) −0.113415 0.196440i −0.00494043 0.00855708i
\(528\) 0 0
\(529\) 10.6892 18.5143i 0.464750 0.804970i
\(530\) 25.2833 43.7919i 1.09824 1.90220i
\(531\) 0 0
\(532\) 0 0
\(533\) 1.88565 + 3.26604i 0.0816766 + 0.141468i
\(534\) 0 0
\(535\) −0.626879 −0.0271023
\(536\) 13.9198 0.601244
\(537\) 0 0
\(538\) −25.5282 44.2161i −1.10060 1.90629i
\(539\) 0 0
\(540\) 0 0
\(541\) −18.7927 + 32.5500i −0.807963 + 1.39943i 0.106309 + 0.994333i \(0.466097\pi\)
−0.914272 + 0.405100i \(0.867237\pi\)
\(542\) 21.4026 37.0705i 0.919322 1.59231i
\(543\) 0 0
\(544\) −3.07866 5.33240i −0.131997 0.228625i
\(545\) 16.4350 28.4663i 0.704000 1.21936i
\(546\) 0 0
\(547\) −9.13381 15.8202i −0.390533 0.676424i 0.601986 0.798506i \(-0.294376\pi\)
−0.992520 + 0.122082i \(0.961043\pi\)
\(548\) 3.01567 5.22329i 0.128823 0.223128i
\(549\) 0 0
\(550\) −38.5750 66.8139i −1.64485 2.84896i
\(551\) 13.6849 0.582995
\(552\) 0 0
\(553\) 0 0
\(554\) −1.62172 + 2.80890i −0.0689002 + 0.119339i
\(555\) 0 0
\(556\) 0.430433 0.745532i 0.0182544 0.0316176i
\(557\) −1.94636 3.37119i −0.0824698 0.142842i 0.821840 0.569718i \(-0.192947\pi\)
−0.904310 + 0.426876i \(0.859614\pi\)
\(558\) 0 0
\(559\) −4.26324 −0.180316
\(560\) 0 0
\(561\) 0 0
\(562\) −10.4281 18.0620i −0.439884 0.761901i
\(563\) −3.32855 −0.140282 −0.0701409 0.997537i \(-0.522345\pi\)
−0.0701409 + 0.997537i \(0.522345\pi\)
\(564\) 0 0
\(565\) −29.5750 −1.24423
\(566\) −48.2965 −2.03006
\(567\) 0 0
\(568\) −21.4702 −0.900870
\(569\) 36.6244 1.53538 0.767688 0.640824i \(-0.221407\pi\)
0.767688 + 0.640824i \(0.221407\pi\)
\(570\) 0 0
\(571\) −22.5824 −0.945044 −0.472522 0.881319i \(-0.656656\pi\)
−0.472522 + 0.881319i \(0.656656\pi\)
\(572\) 3.34742 + 5.79789i 0.139962 + 0.242422i
\(573\) 0 0
\(574\) 0 0
\(575\) 9.34201 0.389589
\(576\) 0 0
\(577\) −11.2725 19.5245i −0.469279 0.812815i 0.530104 0.847932i \(-0.322153\pi\)
−0.999383 + 0.0351177i \(0.988819\pi\)
\(578\) 13.4248 23.2525i 0.558399 0.967175i
\(579\) 0 0
\(580\) −10.6923 + 18.5197i −0.443975 + 0.768987i
\(581\) 0 0
\(582\) 0 0
\(583\) 50.7854 2.10332
\(584\) −4.67457 8.09659i −0.193435 0.335039i
\(585\) 0 0
\(586\) 7.61717 13.1933i 0.314662 0.545011i
\(587\) 12.1198 + 20.9921i 0.500237 + 0.866436i 1.00000 0.000273884i \(8.71801e-5\pi\)
−0.499763 + 0.866162i \(0.666579\pi\)
\(588\) 0 0
\(589\) −0.207750 + 0.359834i −0.00856020 + 0.0148267i
\(590\) 34.1684 + 59.1814i 1.40669 + 2.43646i
\(591\) 0 0
\(592\) 8.94112 15.4865i 0.367478 0.636490i
\(593\) −22.8663 + 39.6056i −0.939007 + 1.62641i −0.171680 + 0.985153i \(0.554919\pi\)
−0.767328 + 0.641255i \(0.778414\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 2.83343 + 4.90764i 0.116062 + 0.201025i
\(597\) 0 0
\(598\) −2.46310 −0.100724
\(599\) 30.1668 1.23258 0.616290 0.787519i \(-0.288635\pi\)
0.616290 + 0.787519i \(0.288635\pi\)
\(600\) 0 0
\(601\) 7.36933 + 12.7641i 0.300601 + 0.520657i 0.976272 0.216547i \(-0.0694794\pi\)
−0.675671 + 0.737203i \(0.736146\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.994149 1.72192i 0.0404513 0.0700638i
\(605\) 45.8285 79.3772i 1.86319 3.22714i
\(606\) 0 0
\(607\) 3.03918 + 5.26401i 0.123356 + 0.213660i 0.921089 0.389351i \(-0.127301\pi\)
−0.797733 + 0.603011i \(0.793967\pi\)
\(608\) −5.63941 + 9.76774i −0.228708 + 0.396134i
\(609\) 0 0
\(610\) 36.3930 + 63.0345i 1.47351 + 2.55219i
\(611\) 3.20439 5.55016i 0.129636 0.224535i
\(612\) 0 0
\(613\) −5.88668 10.1960i −0.237761 0.411814i 0.722311 0.691569i \(-0.243080\pi\)
−0.960071 + 0.279755i \(0.909747\pi\)
\(614\) 1.82213 0.0735352
\(615\) 0 0
\(616\) 0 0
\(617\) 16.0319 27.7680i 0.645418 1.11790i −0.338786 0.940863i \(-0.610016\pi\)
0.984205 0.177034i \(-0.0566503\pi\)
\(618\) 0 0
\(619\) 6.27588 10.8701i 0.252249 0.436908i −0.711896 0.702285i \(-0.752163\pi\)
0.964145 + 0.265377i \(0.0854965\pi\)
\(620\) −0.324641 0.562294i −0.0130379 0.0225823i
\(621\) 0 0
\(622\) −5.30441 −0.212688
\(623\) 0 0
\(624\) 0 0
\(625\) 3.92995 + 6.80687i 0.157198 + 0.272275i
\(626\) 48.6249 1.94344
\(627\) 0 0
\(628\) −2.99022 −0.119323
\(629\) −4.30619 −0.171699
\(630\) 0 0
\(631\) 33.4642 1.33219 0.666095 0.745867i \(-0.267964\pi\)
0.666095 + 0.745867i \(0.267964\pi\)
\(632\) −16.2138 −0.644950
\(633\) 0 0
\(634\) −22.1809 −0.880915
\(635\) −17.4288 30.1875i −0.691639 1.19795i
\(636\) 0 0
\(637\) 0 0
\(638\) −65.2553 −2.58348
\(639\) 0 0
\(640\) 21.5074 + 37.2519i 0.850155 + 1.47251i
\(641\) −9.49183 + 16.4403i −0.374905 + 0.649354i −0.990313 0.138855i \(-0.955658\pi\)
0.615408 + 0.788209i \(0.288991\pi\)
\(642\) 0 0
\(643\) 4.81347 8.33718i 0.189825 0.328786i −0.755367 0.655302i \(-0.772541\pi\)
0.945192 + 0.326516i \(0.105875\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 4.58445 0.180373
\(647\) −3.90607 6.76551i −0.153564 0.265980i 0.778972 0.627059i \(-0.215742\pi\)
−0.932535 + 0.361079i \(0.882408\pi\)
\(648\) 0 0
\(649\) −34.3163 + 59.4375i −1.34703 + 2.33313i
\(650\) 7.09528 + 12.2894i 0.278300 + 0.482029i
\(651\) 0 0
\(652\) 2.64376 4.57912i 0.103537 0.179332i
\(653\) 15.8714 + 27.4901i 0.621097 + 1.07577i 0.989282 + 0.146019i \(0.0466461\pi\)
−0.368185 + 0.929753i \(0.620021\pi\)
\(654\) 0 0
\(655\) 26.7756 46.3767i 1.04621 1.81209i
\(656\) 8.41540 14.5759i 0.328566 0.569093i
\(657\) 0 0
\(658\) 0 0
\(659\) −3.10685 5.38122i −0.121026 0.209623i 0.799147 0.601136i \(-0.205285\pi\)
−0.920172 + 0.391513i \(0.871952\pi\)
\(660\) 0 0
\(661\) 27.5263 1.07065 0.535324 0.844647i \(-0.320190\pi\)
0.535324 + 0.844647i \(0.320190\pi\)
\(662\) −37.2189 −1.44655
\(663\) 0 0
\(664\) 1.09935 + 1.90413i 0.0426630 + 0.0738945i
\(665\) 0 0
\(666\) 0 0
\(667\) 3.95084 6.84306i 0.152977 0.264964i
\(668\) 8.14854 14.1137i 0.315276 0.546075i
\(669\) 0 0
\(670\) −23.9939 41.5586i −0.926965 1.60555i
\(671\) −36.5505 + 63.3073i −1.41102 + 2.44395i
\(672\) 0 0
\(673\) −8.10894 14.0451i −0.312577 0.541399i 0.666343 0.745646i \(-0.267859\pi\)
−0.978919 + 0.204247i \(0.934526\pi\)
\(674\) 10.8835 18.8508i 0.419217 0.726106i
\(675\) 0 0
\(676\) 5.76199 + 9.98006i 0.221615 + 0.383849i
\(677\) 20.5090 0.788225 0.394112 0.919062i \(-0.371052\pi\)
0.394112 + 0.919062i \(0.371052\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 3.71932 6.44205i 0.142629 0.247041i
\(681\) 0 0
\(682\) 0.990642 1.71584i 0.0379337 0.0657030i
\(683\) −0.0561542 0.0972618i −0.00214868 0.00372162i 0.864949 0.501860i \(-0.167351\pi\)
−0.867098 + 0.498138i \(0.834017\pi\)
\(684\) 0 0
\(685\) 21.5902 0.824918
\(686\) 0 0
\(687\) 0 0
\(688\) 9.51311 + 16.4772i 0.362684 + 0.628187i
\(689\) −9.34118 −0.355871
\(690\) 0 0
\(691\) 18.8670 0.717735 0.358868 0.933388i \(-0.383163\pi\)
0.358868 + 0.933388i \(0.383163\pi\)
\(692\) 17.3182 0.658340
\(693\) 0 0
\(694\) −39.9480 −1.51640
\(695\) 3.08161 0.116892
\(696\) 0 0
\(697\) −4.05299 −0.153518
\(698\) 14.2332 + 24.6527i 0.538736 + 0.933118i
\(699\) 0 0
\(700\) 0 0
\(701\) 3.16006 0.119354 0.0596770 0.998218i \(-0.480993\pi\)
0.0596770 + 0.998218i \(0.480993\pi\)
\(702\) 0 0
\(703\) 3.94398 + 6.83118i 0.148750 + 0.257643i
\(704\) −3.55992 + 6.16596i −0.134170 + 0.232388i
\(705\) 0 0
\(706\) −21.1402 + 36.6159i −0.795622 + 1.37806i
\(707\) 0 0
\(708\) 0 0
\(709\) −21.5211 −0.808243 −0.404121 0.914705i \(-0.632423\pi\)
−0.404121 + 0.914705i \(0.632423\pi\)
\(710\) 37.0087 + 64.1009i 1.38891 + 2.40567i
\(711\) 0 0
\(712\) −4.87385 + 8.44176i −0.182655 + 0.316368i
\(713\) 0.119956 + 0.207769i 0.00449237 + 0.00778102i
\(714\) 0 0
\(715\) −11.9826 + 20.7545i −0.448125 + 0.776175i
\(716\) 1.28949 + 2.23347i 0.0481906 + 0.0834685i
\(717\) 0 0
\(718\) 17.6785 30.6201i 0.659757 1.14273i
\(719\) −9.41508 + 16.3074i −0.351123 + 0.608163i −0.986447 0.164083i \(-0.947533\pi\)
0.635323 + 0.772246i \(0.280867\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 12.2040 + 21.1379i 0.454185 + 0.786671i
\(723\) 0 0
\(724\) 3.89914 0.144910
\(725\) −45.5237 −1.69071
\(726\) 0 0
\(727\) −19.5426 33.8489i −0.724797 1.25538i −0.959058 0.283211i \(-0.908600\pi\)
0.234261 0.972174i \(-0.424733\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −16.1153 + 27.9125i −0.596454 + 1.03309i
\(731\) 2.29084 3.96784i 0.0847296 0.146756i
\(732\) 0 0
\(733\) −9.29924 16.1068i −0.343475 0.594917i 0.641600 0.767039i \(-0.278271\pi\)
−0.985076 + 0.172123i \(0.944937\pi\)
\(734\) −19.2119 + 33.2759i −0.709123 + 1.22824i
\(735\) 0 0
\(736\) 3.25621 + 5.63993i 0.120026 + 0.207890i
\(737\) 24.0977 41.7385i 0.887651 1.53746i
\(738\) 0 0
\(739\) −2.75068 4.76432i −0.101185 0.175258i 0.810988 0.585063i \(-0.198930\pi\)
−0.912173 + 0.409805i \(0.865597\pi\)
\(740\) −12.3261 −0.453117
\(741\) 0 0
\(742\) 0 0
\(743\) −10.2326 + 17.7234i −0.375399 + 0.650210i −0.990387 0.138327i \(-0.955828\pi\)
0.614988 + 0.788537i \(0.289161\pi\)
\(744\) 0 0
\(745\) −10.1427 + 17.5677i −0.371601 + 0.643631i
\(746\) 28.0892 + 48.6520i 1.02842 + 1.78128i
\(747\) 0 0
\(748\) −7.19489 −0.263071
\(749\) 0 0
\(750\) 0 0
\(751\) −19.0230 32.9488i −0.694159 1.20232i −0.970463 0.241248i \(-0.922443\pi\)
0.276305 0.961070i \(-0.410890\pi\)
\(752\) −28.6015 −1.04299
\(753\) 0 0
\(754\) 12.0027 0.437113
\(755\) 7.11744 0.259030
\(756\) 0 0
\(757\) −51.0780 −1.85646 −0.928230 0.372006i \(-0.878670\pi\)
−0.928230 + 0.372006i \(0.878670\pi\)
\(758\) 2.66658 0.0968546
\(759\) 0 0
\(760\) −13.6259 −0.494263
\(761\) −20.0375 34.7059i −0.726357 1.25809i −0.958413 0.285385i \(-0.907878\pi\)
0.232055 0.972703i \(-0.425455\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 17.8633 0.646273
\(765\) 0 0
\(766\) 27.3058 + 47.2951i 0.986599 + 1.70884i
\(767\) 6.31195 10.9326i 0.227911 0.394754i
\(768\) 0 0
\(769\) 22.4828 38.9414i 0.810751 1.40426i −0.101587 0.994827i \(-0.532392\pi\)
0.912339 0.409436i \(-0.134274\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.198577 −0.00714695
\(773\) −12.1781 21.0930i −0.438014 0.758663i 0.559522 0.828816i \(-0.310985\pi\)
−0.997536 + 0.0701524i \(0.977651\pi\)
\(774\) 0 0
\(775\) 0.691096 1.19701i 0.0248249 0.0429980i
\(776\) −14.4998 25.1145i −0.520514 0.901556i
\(777\) 0 0
\(778\) −4.52913 + 7.84468i −0.162377 + 0.281245i
\(779\) 3.71208 + 6.42951i 0.132999 + 0.230361i
\(780\) 0 0
\(781\) −37.1689 + 64.3784i −1.33001 + 2.30364i
\(782\) 1.32354 2.29243i 0.0473296 0.0819773i
\(783\) 0 0
\(784\) 0 0
\(785\) −5.35200 9.26993i −0.191021 0.330858i
\(786\) 0 0
\(787\) 41.5233 1.48015 0.740073 0.672526i \(-0.234791\pi\)
0.740073 + 0.672526i \(0.234791\pi\)
\(788\) 1.60066 0.0570212
\(789\) 0 0
\(790\) 27.9481 + 48.4075i 0.994349 + 1.72226i
\(791\) 0 0
\(792\) 0 0
\(793\) 6.72289 11.6444i 0.238737 0.413504i
\(794\) −0.0238574 + 0.0413222i −0.000846666 + 0.00146647i
\(795\) 0 0
\(796\) −3.08686 5.34659i −0