Properties

Label 1323.2.h.h.226.10
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 226.10
Character \(\chi\) \(=\) 1323.226
Dual form 1323.2.h.h.802.10

$q$-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 \(-0.879136\pi\)
0.143397 0.989665i \(-0.454197\pi\)
\(6\) 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 −0.933188 0.359388i \(-0.882985\pi\)
0.777833 + 0.628471i \(0.216319\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −4.99965 −1.24991
\(17\) −0.601978 1.04266i −0.146001 0.252881i 0.783745 0.621083i \(-0.213307\pi\)
−0.929746 + 0.368202i \(0.879974\pi\)
\(18\) 0 0
\(19\) −1.10269 + 1.90991i −0.252974 + 0.438163i −0.964343 0.264655i \(-0.914742\pi\)
0.711370 + 0.702818i \(0.248075\pi\)
\(20\) −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 \(-0.494614\pi\)
0.0169192 + 0.999857i \(0.494614\pi\)
\(32\) −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 −0.704132 0.710069i \(-0.748664\pi\)
0.967004 + 0.254762i \(0.0819972\pi\)
\(42\) 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 \(-0.636997\pi\)
−0.417225 + 0.908803i \(0.636997\pi\)
\(48\) 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 \(-0.762123\pi\)
−0.733519 + 0.679669i \(0.762123\pi\)
\(60\) 0 0
\(61\) −12.0022 −1.53672 −0.768361 0.640017i \(-0.778927\pi\)
−0.768361 + 0.640017i \(0.778927\pi\)
\(62\) 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 0.667563 0.744554i \(-0.267338\pi\)
−0.978584 + 0.205849i \(0.934004\pi\)
\(74\) −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 0.898284 0.439415i \(-0.144814\pi\)
−0.829687 + 0.558229i \(0.811481\pi\)
\(84\) 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 −0.974679 0.223608i \(-0.928216\pi\)
0.680990 + 0.732293i \(0.261550\pi\)
\(90\) 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 \(-0.851017\pi\)
0.0555261 0.998457i \(-0.482316\pi\)
\(98\) 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 \(-0.610201\pi\)
0.984307 0.176463i \(-0.0564657\pi\)
\(102\) 0 0
\(103\) 1.35091 + 2.33984i 0.133109 + 0.230552i 0.924873 0.380275i \(-0.124171\pi\)
−0.791765 + 0.610826i \(0.790837\pi\)
\(104\) 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 \(0.0653519\pi\)
−0.312943 + 0.949772i \(0.601315\pi\)
\(132\) 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 −0.884030 0.467430i \(-0.845180\pi\)
0.846821 + 0.531878i \(0.178513\pi\)
\(140\) 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 \(-0.461194\pi\)
0.121611 + 0.992578i \(0.461194\pi\)
\(158\) 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 \(0.388829\pi\)
−0.984840 + 0.173464i \(0.944504\pi\)
\(168\) 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 \(-0.734120\pi\)
−0.670965 + 0.741489i \(0.734120\pi\)
\(174\) 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 \(-0.547184\pi\)
−0.147689 + 0.989034i \(0.547184\pi\)
\(182\) 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 0.955723 0.294268i \(-0.0950759\pi\)
−0.732705 + 0.680546i \(0.761743\pi\)
\(200\) 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 \(0.0664507\pi\)
−0.309662 + 0.950847i \(0.600216\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −7.26936 + 12.5909i −0.483551 + 0.837534i
\(227\) −1.80642 + 3.12880i −0.119896 + 0.207666i −0.919726 0.392560i \(-0.871589\pi\)
0.799830 + 0.600226i \(0.204923\pi\)
\(228\) 0 0
\(229\) 6.85733 + 11.8772i 0.453145 + 0.784870i 0.998579 0.0532835i \(-0.0169687\pi\)
−0.545435 + 0.838153i \(0.683635\pi\)
\(230\) −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 −0.677558 0.735469i \(-0.736962\pi\)
0.975714 + 0.219048i \(0.0702952\pi\)
\(242\) −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 \(-0.274030\pi\)
0.651763 + 0.758422i \(0.274030\pi\)
\(252\) 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 0.901643 0.432481i \(-0.142362\pi\)
−0.825361 + 0.564605i \(0.809028\pi\)
\(258\) 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 \(0.190842\pi\)
0.0758746 + 0.997117i \(0.475825\pi\)
\(270\) 0 0
\(271\) −12.3958 + 21.4701i −0.752989 + 1.30421i 0.193380 + 0.981124i \(0.438055\pi\)
−0.946368 + 0.323090i \(0.895278\pi\)
\(272\) 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 \(-0.187553\pi\)
0.831378 + 0.555708i \(0.187553\pi\)
\(284\) 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 −0.965634 0.259908i \(-0.916308\pi\)
0.707903 + 0.706309i \(0.249641\pi\)
\(294\) 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 \(-0.509587\pi\)
−0.0301152 + 0.999546i \(0.509587\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.571277 0.989481i −0.0324464 0.0561988i
\(311\) 3.07215 0.174206 0.0871029 0.996199i \(-0.472239\pi\)
0.0871029 + 0.996199i \(0.472239\pi\)
\(312\) 0 0
\(313\) −28.1621 −1.59181 −0.795907 0.605419i \(-0.793006\pi\)
−0.795907 + 0.605419i \(0.793006\pi\)
\(314\) 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 0.556521 0.830833i \(-0.312136\pi\)
−0.997783 + 0.0665448i \(0.978802\pi\)
\(350\) 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 \(-0.607402\pi\)
0.982718 0.185110i \(-0.0592642\pi\)
\(354\) 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 \(-0.636065\pi\)
0.995382 0.0959900i \(-0.0306017\pi\)
\(368\) 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 \(-0.867166\pi\)
0.106090 0.994357i \(-0.466167\pi\)
\(384\) 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 −0.865678 0.500600i \(-0.833113\pi\)
0.866372 + 0.499399i \(0.166446\pi\)
\(398\) 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 \(-0.782231\pi\)
−0.774963 + 0.632007i \(0.782231\pi\)
\(410\) −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 −0.624931 0.780680i \(-0.714873\pi\)
0.988554 + 0.150866i \(0.0482061\pi\)
\(420\) 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 \(-0.657327\pi\)
−0.474378 + 0.880321i \(0.657327\pi\)
\(434\) 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 \(-0.448617\pi\)
0.160725 + 0.986999i \(0.448617\pi\)
\(440\) −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 0.533103 0.846050i \(-0.321026\pi\)
−0.999253 + 0.0386554i \(0.987693\pi\)
\(462\) 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 −0.617820 0.786320i \(-0.711984\pi\)
0.989883 + 0.141888i \(0.0453172\pi\)
\(468\) 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 −0.944380 0.328856i \(-0.893337\pi\)
0.756988 + 0.653429i \(0.226670\pi\)
\(480\) 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 \(-0.587577\pi\)
−0.271673 + 0.962390i \(0.587577\pi\)
\(504\) 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 0.976651 0.214832i \(-0.0689204\pi\)
−0.674375 + 0.738389i \(0.735587\pi\)
\(510\) 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 \(-0.882539\pi\)
0.153969 0.988076i \(-0.450794\pi\)
\(522\) 0 0
\(523\) −13.3593 + 23.1391i −0.584163 + 1.01180i 0.410816 + 0.911718i \(0.365244\pi\)
−0.994979 + 0.100082i \(0.968089\pi\)
\(524\) 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 \(-0.477655\pi\)
0.0701409 + 0.997537i \(0.477655\pi\)
\(564\) 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 0.999383 0.0351177i \(-0.0111806\pi\)
−0.530104 + 0.847932i \(0.677847\pi\)
\(578\) 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 \(-0.999913\pi\)
0.499763 0.866162i \(-0.333421\pi\)
\(588\) 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 \(-0.445081\pi\)
0.767328 0.641255i \(-0.221586\pi\)
\(594\) 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 0.675671 0.737203i \(-0.263854\pi\)
−0.976272 + 0.216547i \(0.930521\pi\)
\(602\) 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 0.797733 0.603011i \(-0.206033\pi\)
−0.921089 + 0.389351i \(0.872699\pi\)
\(608\) 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 −0.964145 0.265377i \(-0.914504\pi\)
0.711896 + 0.702285i \(0.247837\pi\)
\(620\) −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 −0.945192 0.326516i \(-0.894125\pi\)
0.755367 + 0.655302i \(0.227459\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 4.58445 0.180373
\(647\) 3.90607 + 6.76551i 0.153564 + 0.265980i 0.932535 0.361079i \(-0.117592\pi\)
−0.778972 + 0.627059i \(0.784258\pi\)
\(648\) 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 \(-0.679810\pi\)
−0.535324 + 0.844647i \(0.679810\pi\)
\(662\) −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 \(-0.628948\pi\)
−0.394112 + 0.919062i \(0.628948\pi\)
\(678\) 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 \(-0.616837\pi\)
−0.358868 + 0.933388i \(0.616837\pi\)
\(692\) −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 −0.635323 0.772246i \(-0.719133\pi\)
0.986447 + 0.164083i \(0.0524665\pi\)
\(720\) 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 \(0.0913996\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(728\) 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 0.985076 0.172123i \(-0.0550625\pi\)
−0.641600 + 0.767039i \(0.721729\pi\)
\(734\) 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 \(0.0921216\pi\)
−0.232055 + 0.972703i \(0.574545\pi\)
\(762\) 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 \(0.467608\pi\)
−0.912339 + 0.409436i \(0.865726\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.198577 −0.00714695
\(773\) 12.1781 + 21.0930i 0.438014 + 0.758663i 0.997536 0.0701524i \(-0.0223485\pi\)
−0.559522 + 0.828816i \(0.689015\pi\)
\(774\) 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 \(-0.765209\pi\)
−0.740073 + 0.672526i \(0.765209\pi\)
\(788\) 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