Properties

Label 1323.2.g.f.361.5
Level $1323$
Weight $2$
Character 1323.361
Analytic conductor $10.564$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.5
Root \(-1.02682 + 1.77851i\) of defining polynomial
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.f.667.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.02682 - 1.77851i) q^{2} +(-1.10873 - 1.92038i) q^{4} -0.146246 q^{5} -0.446582 q^{8} +O(q^{10})\) \(q+(1.02682 - 1.77851i) q^{2} +(-1.10873 - 1.92038i) q^{4} -0.146246 q^{5} -0.446582 q^{8} +(-0.150168 + 0.260099i) q^{10} -1.66404 q^{11} +(-0.0999454 + 0.173111i) q^{13} +(1.75890 - 3.04650i) q^{16} +(3.13555 - 5.43093i) q^{17} +(-3.45879 - 5.99080i) q^{19} +(0.162147 + 0.280847i) q^{20} +(-1.70867 + 2.95951i) q^{22} +6.18184 q^{23} -4.97861 q^{25} +(0.205252 + 0.355508i) q^{26} +(2.46757 + 4.27396i) q^{29} +(-1.25890 - 2.18047i) q^{31} +(-4.05873 - 7.02993i) q^{32} +(-6.43931 - 11.1532i) q^{34} +(-3.50023 - 6.06257i) q^{37} -14.2062 q^{38} +0.0653107 q^{40} +(1.15895 - 2.00736i) q^{41} +(-0.940993 - 1.62985i) q^{43} +(1.84497 + 3.19558i) q^{44} +(6.34765 - 10.9944i) q^{46} +(0.905887 - 1.56904i) q^{47} +(-5.11215 + 8.85451i) q^{50} +0.443250 q^{52} +(2.67307 - 4.62989i) q^{53} +0.243359 q^{55} +10.1350 q^{58} +(2.28549 + 3.95859i) q^{59} +(-0.339138 + 0.587404i) q^{61} -5.17066 q^{62} -9.63481 q^{64} +(0.0146166 - 0.0253167i) q^{65} +(3.09342 + 5.35796i) q^{67} -13.9059 q^{68} -1.27749 q^{71} +(0.778603 - 1.34858i) q^{73} -14.3765 q^{74} +(-7.66972 + 13.2843i) q^{76} +(-6.39787 + 11.0814i) q^{79} +(-0.257231 + 0.445537i) q^{80} +(-2.38008 - 4.12241i) q^{82} +(3.75687 + 6.50709i) q^{83} +(-0.458561 + 0.794251i) q^{85} -3.86493 q^{86} +0.743131 q^{88} +(4.53394 + 7.85301i) q^{89} +(-6.85398 - 11.8714i) q^{92} +(-1.86037 - 3.22226i) q^{94} +(0.505833 + 0.876128i) q^{95} +(3.98514 + 6.90246i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{2} - 4q^{4} - 8q^{5} + 6q^{8} + O(q^{10}) \) \( 10q - 2q^{2} - 4q^{4} - 8q^{5} + 6q^{8} + 7q^{10} + 8q^{11} + 8q^{13} + 2q^{16} + 12q^{17} - q^{19} + 5q^{20} - q^{22} + 6q^{23} + 2q^{25} + 11q^{26} - 7q^{29} + 3q^{31} + 2q^{32} - 3q^{34} - 40q^{38} - 6q^{40} + 5q^{41} - 7q^{43} + 10q^{44} + 3q^{46} + 27q^{47} - 19q^{50} - 20q^{52} + 21q^{53} - 4q^{55} + 20q^{58} + 30q^{59} + 14q^{61} - 12q^{62} - 50q^{64} + 11q^{65} - 2q^{67} - 54q^{68} + 6q^{71} - 15q^{73} - 72q^{74} - 5q^{76} - 4q^{79} + 20q^{80} + 5q^{82} + 9q^{83} - 6q^{85} - 16q^{86} + 36q^{88} + 28q^{89} - 27q^{92} + 3q^{94} + 14q^{95} + 12q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.02682 1.77851i 0.726073 1.25760i −0.232458 0.972607i \(-0.574677\pi\)
0.958531 0.284989i \(-0.0919900\pi\)
\(3\) 0 0
\(4\) −1.10873 1.92038i −0.554365 0.960188i
\(5\) −0.146246 −0.0654030 −0.0327015 0.999465i \(-0.510411\pi\)
−0.0327015 + 0.999465i \(0.510411\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −0.446582 −0.157891
\(9\) 0 0
\(10\) −0.150168 + 0.260099i −0.0474874 + 0.0822506i
\(11\) −1.66404 −0.501727 −0.250864 0.968022i \(-0.580715\pi\)
−0.250864 + 0.968022i \(0.580715\pi\)
\(12\) 0 0
\(13\) −0.0999454 + 0.173111i −0.0277199 + 0.0480122i −0.879553 0.475802i \(-0.842158\pi\)
0.851833 + 0.523814i \(0.175491\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.75890 3.04650i 0.439724 0.761625i
\(17\) 3.13555 5.43093i 0.760483 1.31720i −0.182119 0.983277i \(-0.558296\pi\)
0.942602 0.333919i \(-0.108371\pi\)
\(18\) 0 0
\(19\) −3.45879 5.99080i −0.793500 1.37438i −0.923787 0.382907i \(-0.874923\pi\)
0.130287 0.991476i \(-0.458410\pi\)
\(20\) 0.162147 + 0.280847i 0.0362571 + 0.0627992i
\(21\) 0 0
\(22\) −1.70867 + 2.95951i −0.364291 + 0.630970i
\(23\) 6.18184 1.28900 0.644501 0.764604i \(-0.277065\pi\)
0.644501 + 0.764604i \(0.277065\pi\)
\(24\) 0 0
\(25\) −4.97861 −0.995722
\(26\) 0.205252 + 0.355508i 0.0402533 + 0.0697208i
\(27\) 0 0
\(28\) 0 0
\(29\) 2.46757 + 4.27396i 0.458217 + 0.793655i 0.998867 0.0475930i \(-0.0151551\pi\)
−0.540650 + 0.841248i \(0.681822\pi\)
\(30\) 0 0
\(31\) −1.25890 2.18047i −0.226105 0.391625i 0.730546 0.682864i \(-0.239266\pi\)
−0.956650 + 0.291239i \(0.905932\pi\)
\(32\) −4.05873 7.02993i −0.717490 1.24273i
\(33\) 0 0
\(34\) −6.43931 11.1532i −1.10433 1.91276i
\(35\) 0 0
\(36\) 0 0
\(37\) −3.50023 6.06257i −0.575434 0.996681i −0.995994 0.0894162i \(-0.971500\pi\)
0.420560 0.907264i \(-0.361833\pi\)
\(38\) −14.2062 −2.30456
\(39\) 0 0
\(40\) 0.0653107 0.0103265
\(41\) 1.15895 2.00736i 0.180998 0.313498i −0.761223 0.648491i \(-0.775401\pi\)
0.942221 + 0.334993i \(0.108734\pi\)
\(42\) 0 0
\(43\) −0.940993 1.62985i −0.143500 0.248550i 0.785312 0.619100i \(-0.212502\pi\)
−0.928812 + 0.370550i \(0.879169\pi\)
\(44\) 1.84497 + 3.19558i 0.278140 + 0.481752i
\(45\) 0 0
\(46\) 6.34765 10.9944i 0.935910 1.62104i
\(47\) 0.905887 1.56904i 0.132137 0.228868i −0.792363 0.610050i \(-0.791149\pi\)
0.924500 + 0.381181i \(0.124483\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −5.11215 + 8.85451i −0.722967 + 1.25222i
\(51\) 0 0
\(52\) 0.443250 0.0614677
\(53\) 2.67307 4.62989i 0.367174 0.635964i −0.621948 0.783058i \(-0.713659\pi\)
0.989123 + 0.147094i \(0.0469920\pi\)
\(54\) 0 0
\(55\) 0.243359 0.0328145
\(56\) 0 0
\(57\) 0 0
\(58\) 10.1350 1.33080
\(59\) 2.28549 + 3.95859i 0.297546 + 0.515364i 0.975574 0.219672i \(-0.0704986\pi\)
−0.678028 + 0.735036i \(0.737165\pi\)
\(60\) 0 0
\(61\) −0.339138 + 0.587404i −0.0434221 + 0.0752094i −0.886920 0.461924i \(-0.847159\pi\)
0.843498 + 0.537133i \(0.180493\pi\)
\(62\) −5.17066 −0.656674
\(63\) 0 0
\(64\) −9.63481 −1.20435
\(65\) 0.0146166 0.0253167i 0.00181296 0.00314015i
\(66\) 0 0
\(67\) 3.09342 + 5.35796i 0.377921 + 0.654579i 0.990760 0.135630i \(-0.0433057\pi\)
−0.612838 + 0.790208i \(0.709972\pi\)
\(68\) −13.9059 −1.68634
\(69\) 0 0
\(70\) 0 0
\(71\) −1.27749 −0.151611 −0.0758053 0.997123i \(-0.524153\pi\)
−0.0758053 + 0.997123i \(0.524153\pi\)
\(72\) 0 0
\(73\) 0.778603 1.34858i 0.0911286 0.157839i −0.816858 0.576839i \(-0.804286\pi\)
0.907986 + 0.419000i \(0.137619\pi\)
\(74\) −14.3765 −1.67123
\(75\) 0 0
\(76\) −7.66972 + 13.2843i −0.879777 + 1.52382i
\(77\) 0 0
\(78\) 0 0
\(79\) −6.39787 + 11.0814i −0.719817 + 1.24676i 0.241255 + 0.970462i \(0.422441\pi\)
−0.961072 + 0.276298i \(0.910892\pi\)
\(80\) −0.257231 + 0.445537i −0.0287593 + 0.0498126i
\(81\) 0 0
\(82\) −2.38008 4.12241i −0.262835 0.455244i
\(83\) 3.75687 + 6.50709i 0.412370 + 0.714246i 0.995148 0.0983854i \(-0.0313678\pi\)
−0.582778 + 0.812631i \(0.698034\pi\)
\(84\) 0 0
\(85\) −0.458561 + 0.794251i −0.0497379 + 0.0861486i
\(86\) −3.86493 −0.416766
\(87\) 0 0
\(88\) 0.743131 0.0792181
\(89\) 4.53394 + 7.85301i 0.480597 + 0.832418i 0.999752 0.0222619i \(-0.00708678\pi\)
−0.519155 + 0.854680i \(0.673753\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −6.85398 11.8714i −0.714577 1.23768i
\(93\) 0 0
\(94\) −1.86037 3.22226i −0.191883 0.332350i
\(95\) 0.505833 + 0.876128i 0.0518973 + 0.0898888i
\(96\) 0 0
\(97\) 3.98514 + 6.90246i 0.404630 + 0.700839i 0.994278 0.106821i \(-0.0340671\pi\)
−0.589649 + 0.807660i \(0.700734\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 5.51993 + 9.56080i 0.551993 + 0.956080i
\(101\) 14.8430 1.47693 0.738467 0.674290i \(-0.235550\pi\)
0.738467 + 0.674290i \(0.235550\pi\)
\(102\) 0 0
\(103\) 0.203948 0.0200956 0.0100478 0.999950i \(-0.496802\pi\)
0.0100478 + 0.999950i \(0.496802\pi\)
\(104\) 0.0446339 0.0773081i 0.00437671 0.00758068i
\(105\) 0 0
\(106\) −5.48953 9.50815i −0.533191 0.923513i
\(107\) −3.48444 6.03524i −0.336854 0.583448i 0.646985 0.762503i \(-0.276030\pi\)
−0.983839 + 0.179054i \(0.942696\pi\)
\(108\) 0 0
\(109\) 3.33058 5.76874i 0.319012 0.552545i −0.661270 0.750148i \(-0.729982\pi\)
0.980282 + 0.197603i \(0.0633157\pi\)
\(110\) 0.249886 0.432816i 0.0238257 0.0412674i
\(111\) 0 0
\(112\) 0 0
\(113\) 0.0193234 0.0334691i 0.00181779 0.00314851i −0.865115 0.501573i \(-0.832755\pi\)
0.866933 + 0.498425i \(0.166088\pi\)
\(114\) 0 0
\(115\) −0.904067 −0.0843047
\(116\) 5.47174 9.47733i 0.508038 0.879948i
\(117\) 0 0
\(118\) 9.38718 0.864160
\(119\) 0 0
\(120\) 0 0
\(121\) −8.23097 −0.748270
\(122\) 0.696469 + 1.20632i 0.0630553 + 0.109215i
\(123\) 0 0
\(124\) −2.79155 + 4.83511i −0.250689 + 0.434206i
\(125\) 1.45933 0.130526
\(126\) 0 0
\(127\) 13.4788 1.19605 0.598027 0.801476i \(-0.295952\pi\)
0.598027 + 0.801476i \(0.295952\pi\)
\(128\) −1.77577 + 3.07572i −0.156957 + 0.271858i
\(129\) 0 0
\(130\) −0.0300173 0.0519914i −0.00263269 0.00455995i
\(131\) −19.8333 −1.73284 −0.866422 0.499312i \(-0.833586\pi\)
−0.866422 + 0.499312i \(0.833586\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 12.7056 1.09759
\(135\) 0 0
\(136\) −1.40028 + 2.42536i −0.120073 + 0.207973i
\(137\) 6.44509 0.550642 0.275321 0.961352i \(-0.411216\pi\)
0.275321 + 0.961352i \(0.411216\pi\)
\(138\) 0 0
\(139\) −6.26527 + 10.8518i −0.531413 + 0.920435i 0.467914 + 0.883774i \(0.345006\pi\)
−0.999328 + 0.0366611i \(0.988328\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.31176 + 2.27203i −0.110080 + 0.190665i
\(143\) 0.166313 0.288063i 0.0139078 0.0240890i
\(144\) 0 0
\(145\) −0.360872 0.625048i −0.0299688 0.0519074i
\(146\) −1.59897 2.76950i −0.132332 0.229206i
\(147\) 0 0
\(148\) −7.76161 + 13.4435i −0.638000 + 1.10505i
\(149\) −17.7673 −1.45555 −0.727776 0.685815i \(-0.759446\pi\)
−0.727776 + 0.685815i \(0.759446\pi\)
\(150\) 0 0
\(151\) 8.46599 0.688953 0.344476 0.938795i \(-0.388056\pi\)
0.344476 + 0.938795i \(0.388056\pi\)
\(152\) 1.54463 + 2.67538i 0.125286 + 0.217002i
\(153\) 0 0
\(154\) 0 0
\(155\) 0.184108 + 0.318885i 0.0147879 + 0.0256135i
\(156\) 0 0
\(157\) 2.84968 + 4.93579i 0.227429 + 0.393919i 0.957045 0.289938i \(-0.0936347\pi\)
−0.729616 + 0.683857i \(0.760301\pi\)
\(158\) 13.1390 + 22.7573i 1.04528 + 1.81048i
\(159\) 0 0
\(160\) 0.593572 + 1.02810i 0.0469260 + 0.0812782i
\(161\) 0 0
\(162\) 0 0
\(163\) −1.06267 1.84060i −0.0832349 0.144167i 0.821403 0.570349i \(-0.193192\pi\)
−0.904638 + 0.426181i \(0.859859\pi\)
\(164\) −5.13986 −0.401355
\(165\) 0 0
\(166\) 15.4306 1.19764
\(167\) −5.78723 + 10.0238i −0.447829 + 0.775663i −0.998244 0.0592278i \(-0.981136\pi\)
0.550415 + 0.834891i \(0.314470\pi\)
\(168\) 0 0
\(169\) 6.48002 + 11.2237i 0.498463 + 0.863364i
\(170\) 0.941721 + 1.63111i 0.0722267 + 0.125100i
\(171\) 0 0
\(172\) −2.08661 + 3.61412i −0.159103 + 0.275574i
\(173\) 7.95546 13.7793i 0.604842 1.04762i −0.387234 0.921981i \(-0.626570\pi\)
0.992076 0.125636i \(-0.0400971\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.92688 + 5.06950i −0.220622 + 0.382128i
\(177\) 0 0
\(178\) 18.6222 1.39579
\(179\) −3.87665 + 6.71456i −0.289755 + 0.501870i −0.973751 0.227615i \(-0.926907\pi\)
0.683996 + 0.729485i \(0.260240\pi\)
\(180\) 0 0
\(181\) 12.1618 0.903982 0.451991 0.892022i \(-0.350714\pi\)
0.451991 + 0.892022i \(0.350714\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −2.76070 −0.203521
\(185\) 0.511893 + 0.886625i 0.0376351 + 0.0651860i
\(186\) 0 0
\(187\) −5.21769 + 9.03730i −0.381555 + 0.660873i
\(188\) −4.01754 −0.293009
\(189\) 0 0
\(190\) 2.07760 0.150725
\(191\) −2.48383 + 4.30211i −0.179723 + 0.311290i −0.941786 0.336214i \(-0.890854\pi\)
0.762062 + 0.647504i \(0.224187\pi\)
\(192\) 0 0
\(193\) 7.45221 + 12.9076i 0.536422 + 0.929110i 0.999093 + 0.0425800i \(0.0135577\pi\)
−0.462671 + 0.886530i \(0.653109\pi\)
\(194\) 16.3681 1.17516
\(195\) 0 0
\(196\) 0 0
\(197\) 21.2608 1.51477 0.757386 0.652968i \(-0.226476\pi\)
0.757386 + 0.652968i \(0.226476\pi\)
\(198\) 0 0
\(199\) 9.97208 17.2722i 0.706902 1.22439i −0.259098 0.965851i \(-0.583425\pi\)
0.966001 0.258540i \(-0.0832413\pi\)
\(200\) 2.22336 0.157215
\(201\) 0 0
\(202\) 15.2411 26.3984i 1.07236 1.85739i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.169492 + 0.293568i −0.0118378 + 0.0205037i
\(206\) 0.209419 0.362724i 0.0145909 0.0252722i
\(207\) 0 0
\(208\) 0.351587 + 0.608967i 0.0243782 + 0.0422243i
\(209\) 5.75556 + 9.96893i 0.398121 + 0.689565i
\(210\) 0 0
\(211\) 11.7569 20.3636i 0.809381 1.40189i −0.103912 0.994587i \(-0.533136\pi\)
0.913293 0.407303i \(-0.133531\pi\)
\(212\) −11.8548 −0.814193
\(213\) 0 0
\(214\) −14.3116 −0.978323
\(215\) 0.137616 + 0.238358i 0.00938535 + 0.0162559i
\(216\) 0 0
\(217\) 0 0
\(218\) −6.83983 11.8469i −0.463252 0.802376i
\(219\) 0 0
\(220\) −0.269819 0.467340i −0.0181912 0.0315081i
\(221\) 0.626768 + 1.08559i 0.0421610 + 0.0730250i
\(222\) 0 0
\(223\) −2.03052 3.51696i −0.135974 0.235513i 0.789995 0.613113i \(-0.210083\pi\)
−0.925969 + 0.377600i \(0.876750\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −0.0396834 0.0687336i −0.00263970 0.00457209i
\(227\) −3.85285 −0.255723 −0.127861 0.991792i \(-0.540811\pi\)
−0.127861 + 0.991792i \(0.540811\pi\)
\(228\) 0 0
\(229\) −13.1162 −0.866746 −0.433373 0.901215i \(-0.642677\pi\)
−0.433373 + 0.901215i \(0.642677\pi\)
\(230\) −0.928316 + 1.60789i −0.0612113 + 0.106021i
\(231\) 0 0
\(232\) −1.10197 1.90868i −0.0723481 0.125311i
\(233\) 8.75115 + 15.1574i 0.573307 + 0.992997i 0.996223 + 0.0868284i \(0.0276732\pi\)
−0.422916 + 0.906169i \(0.638993\pi\)
\(234\) 0 0
\(235\) −0.132482 + 0.229466i −0.00864218 + 0.0149687i
\(236\) 5.06798 8.77801i 0.329898 0.571400i
\(237\) 0 0
\(238\) 0 0
\(239\) −3.65857 + 6.33683i −0.236653 + 0.409895i −0.959752 0.280849i \(-0.909384\pi\)
0.723099 + 0.690745i \(0.242717\pi\)
\(240\) 0 0
\(241\) −6.23107 −0.401378 −0.200689 0.979655i \(-0.564318\pi\)
−0.200689 + 0.979655i \(0.564318\pi\)
\(242\) −8.45174 + 14.6389i −0.543299 + 0.941021i
\(243\) 0 0
\(244\) 1.50405 0.0962868
\(245\) 0 0
\(246\) 0 0
\(247\) 1.38276 0.0879829
\(248\) 0.562201 + 0.973761i 0.0356998 + 0.0618339i
\(249\) 0 0
\(250\) 1.49847 2.59543i 0.0947717 0.164149i
\(251\) 5.65283 0.356803 0.178402 0.983958i \(-0.442907\pi\)
0.178402 + 0.983958i \(0.442907\pi\)
\(252\) 0 0
\(253\) −10.2868 −0.646727
\(254\) 13.8404 23.9722i 0.868422 1.50415i
\(255\) 0 0
\(256\) −5.98801 10.3715i −0.374250 0.648221i
\(257\) 11.8016 0.736166 0.368083 0.929793i \(-0.380014\pi\)
0.368083 + 0.929793i \(0.380014\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.0648233 −0.00402017
\(261\) 0 0
\(262\) −20.3653 + 35.2737i −1.25817 + 2.17922i
\(263\) 22.2401 1.37138 0.685691 0.727893i \(-0.259500\pi\)
0.685691 + 0.727893i \(0.259500\pi\)
\(264\) 0 0
\(265\) −0.390925 + 0.677101i −0.0240143 + 0.0415940i
\(266\) 0 0
\(267\) 0 0
\(268\) 6.85953 11.8810i 0.419012 0.725750i
\(269\) −1.19442 + 2.06880i −0.0728251 + 0.126137i −0.900138 0.435604i \(-0.856535\pi\)
0.827313 + 0.561741i \(0.189868\pi\)
\(270\) 0 0
\(271\) 11.6129 + 20.1142i 0.705435 + 1.22185i 0.966534 + 0.256537i \(0.0825815\pi\)
−0.261100 + 0.965312i \(0.584085\pi\)
\(272\) −11.0302 19.1049i −0.668806 1.15841i
\(273\) 0 0
\(274\) 6.61797 11.4627i 0.399806 0.692484i
\(275\) 8.28461 0.499581
\(276\) 0 0
\(277\) −4.61800 −0.277469 −0.138734 0.990330i \(-0.544303\pi\)
−0.138734 + 0.990330i \(0.544303\pi\)
\(278\) 12.8666 + 22.2857i 0.771690 + 1.33661i
\(279\) 0 0
\(280\) 0 0
\(281\) −5.90841 10.2337i −0.352466 0.610489i 0.634215 0.773157i \(-0.281324\pi\)
−0.986681 + 0.162668i \(0.947990\pi\)
\(282\) 0 0
\(283\) 7.92483 + 13.7262i 0.471082 + 0.815939i 0.999453 0.0330753i \(-0.0105301\pi\)
−0.528370 + 0.849014i \(0.677197\pi\)
\(284\) 1.41639 + 2.45327i 0.0840475 + 0.145575i
\(285\) 0 0
\(286\) −0.341548 0.591579i −0.0201962 0.0349808i
\(287\) 0 0
\(288\) 0 0
\(289\) −11.1634 19.3355i −0.656669 1.13738i
\(290\) −1.48220 −0.0870381
\(291\) 0 0
\(292\) −3.45304 −0.202074
\(293\) 7.04804 12.2076i 0.411751 0.713173i −0.583330 0.812235i \(-0.698251\pi\)
0.995081 + 0.0990615i \(0.0315841\pi\)
\(294\) 0 0
\(295\) −0.334243 0.578927i −0.0194604 0.0337064i
\(296\) 1.56314 + 2.70744i 0.0908557 + 0.157367i
\(297\) 0 0
\(298\) −18.2438 + 31.5993i −1.05684 + 1.83050i
\(299\) −0.617846 + 1.07014i −0.0357310 + 0.0618878i
\(300\) 0 0
\(301\) 0 0
\(302\) 8.69307 15.0568i 0.500230 0.866424i
\(303\) 0 0
\(304\) −24.3346 −1.39569
\(305\) 0.0495974 0.0859053i 0.00283994 0.00491892i
\(306\) 0 0
\(307\) −27.3916 −1.56332 −0.781660 0.623704i \(-0.785627\pi\)
−0.781660 + 0.623704i \(0.785627\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.756186 0.0429485
\(311\) 7.02785 + 12.1726i 0.398513 + 0.690244i 0.993543 0.113459i \(-0.0361931\pi\)
−0.595030 + 0.803704i \(0.702860\pi\)
\(312\) 0 0
\(313\) 10.8723 18.8314i 0.614540 1.06441i −0.375925 0.926650i \(-0.622675\pi\)
0.990465 0.137764i \(-0.0439916\pi\)
\(314\) 11.7045 0.660520
\(315\) 0 0
\(316\) 28.3740 1.59616
\(317\) 4.28148 7.41575i 0.240472 0.416510i −0.720377 0.693583i \(-0.756031\pi\)
0.960849 + 0.277073i \(0.0893644\pi\)
\(318\) 0 0
\(319\) −4.10614 7.11204i −0.229900 0.398198i
\(320\) 1.40905 0.0787682
\(321\) 0 0
\(322\) 0 0
\(323\) −43.3808 −2.41377
\(324\) 0 0
\(325\) 0.497589 0.861850i 0.0276013 0.0478068i
\(326\) −4.36471 −0.241739
\(327\) 0 0
\(328\) −0.517568 + 0.896453i −0.0285779 + 0.0494984i
\(329\) 0 0
\(330\) 0 0
\(331\) −5.42360 + 9.39396i −0.298108 + 0.516339i −0.975703 0.219097i \(-0.929689\pi\)
0.677595 + 0.735435i \(0.263022\pi\)
\(332\) 8.33070 14.4292i 0.457207 0.791905i
\(333\) 0 0
\(334\) 11.8849 + 20.5853i 0.650314 + 1.12638i
\(335\) −0.452399 0.783578i −0.0247172 0.0428114i
\(336\) 0 0
\(337\) 1.67411 2.89964i 0.0911945 0.157954i −0.816819 0.576893i \(-0.804265\pi\)
0.908014 + 0.418940i \(0.137598\pi\)
\(338\) 26.6153 1.44768
\(339\) 0 0
\(340\) 2.03368 0.110292
\(341\) 2.09486 + 3.62840i 0.113443 + 0.196489i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.420231 + 0.727861i 0.0226573 + 0.0392437i
\(345\) 0 0
\(346\) −16.3377 28.2977i −0.878319 1.52129i
\(347\) −5.76652 9.98790i −0.309563 0.536178i 0.668704 0.743529i \(-0.266849\pi\)
−0.978267 + 0.207350i \(0.933516\pi\)
\(348\) 0 0
\(349\) 4.44917 + 7.70619i 0.238159 + 0.412503i 0.960186 0.279362i \(-0.0901228\pi\)
−0.722027 + 0.691865i \(0.756789\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 6.75390 + 11.6981i 0.359984 + 0.623511i
\(353\) −2.64699 −0.140885 −0.0704424 0.997516i \(-0.522441\pi\)
−0.0704424 + 0.997516i \(0.522441\pi\)
\(354\) 0 0
\(355\) 0.186828 0.00991579
\(356\) 10.0538 17.4137i 0.532852 0.922926i
\(357\) 0 0
\(358\) 7.96127 + 13.7893i 0.420766 + 0.728789i
\(359\) 12.9835 + 22.4882i 0.685245 + 1.18688i 0.973360 + 0.229284i \(0.0736384\pi\)
−0.288114 + 0.957596i \(0.593028\pi\)
\(360\) 0 0
\(361\) −14.4264 + 24.9873i −0.759286 + 1.31512i
\(362\) 12.4880 21.6299i 0.656357 1.13684i
\(363\) 0 0
\(364\) 0 0
\(365\) −0.113867 + 0.197224i −0.00596009 + 0.0103232i
\(366\) 0 0
\(367\) −17.5874 −0.918056 −0.459028 0.888422i \(-0.651802\pi\)
−0.459028 + 0.888422i \(0.651802\pi\)
\(368\) 10.8732 18.8330i 0.566806 0.981736i
\(369\) 0 0
\(370\) 2.10249 0.109303
\(371\) 0 0
\(372\) 0 0
\(373\) 0.815075 0.0422030 0.0211015 0.999777i \(-0.493283\pi\)
0.0211015 + 0.999777i \(0.493283\pi\)
\(374\) 10.7153 + 18.5594i 0.554074 + 0.959684i
\(375\) 0 0
\(376\) −0.404553 + 0.700707i −0.0208632 + 0.0361362i
\(377\) −0.986490 −0.0508068
\(378\) 0 0
\(379\) −20.4312 −1.04948 −0.524741 0.851262i \(-0.675838\pi\)
−0.524741 + 0.851262i \(0.675838\pi\)
\(380\) 1.12166 1.94278i 0.0575401 0.0996624i
\(381\) 0 0
\(382\) 5.10090 + 8.83501i 0.260985 + 0.452039i
\(383\) 17.8928 0.914278 0.457139 0.889395i \(-0.348874\pi\)
0.457139 + 0.889395i \(0.348874\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 30.6084 1.55793
\(387\) 0 0
\(388\) 8.83688 15.3059i 0.448625 0.777041i
\(389\) −15.6278 −0.792363 −0.396181 0.918172i \(-0.629665\pi\)
−0.396181 + 0.918172i \(0.629665\pi\)
\(390\) 0 0
\(391\) 19.3835 33.5731i 0.980264 1.69787i
\(392\) 0 0
\(393\) 0 0
\(394\) 21.8311 37.8126i 1.09984 1.90497i
\(395\) 0.935661 1.62061i 0.0470782 0.0815419i
\(396\) 0 0
\(397\) −9.63064 16.6808i −0.483348 0.837183i 0.516469 0.856306i \(-0.327246\pi\)
−0.999817 + 0.0191225i \(0.993913\pi\)
\(398\) −20.4791 35.4709i −1.02653 1.77799i
\(399\) 0 0
\(400\) −8.75687 + 15.1673i −0.437843 + 0.758367i
\(401\) −14.3013 −0.714172 −0.357086 0.934072i \(-0.616230\pi\)
−0.357086 + 0.934072i \(0.616230\pi\)
\(402\) 0 0
\(403\) 0.503284 0.0250704
\(404\) −16.4569 28.5041i −0.818760 1.41813i
\(405\) 0 0
\(406\) 0 0
\(407\) 5.82452 + 10.0884i 0.288711 + 0.500062i
\(408\) 0 0
\(409\) 15.9305 + 27.5924i 0.787712 + 1.36436i 0.927366 + 0.374156i \(0.122068\pi\)
−0.139654 + 0.990200i \(0.544599\pi\)
\(410\) 0.348076 + 0.602885i 0.0171902 + 0.0297744i
\(411\) 0 0
\(412\) −0.226124 0.391657i −0.0111403 0.0192956i
\(413\) 0 0
\(414\) 0 0
\(415\) −0.549426 0.951633i −0.0269702 0.0467138i
\(416\) 1.62261 0.0795549
\(417\) 0 0
\(418\) 23.6398 1.15626
\(419\) 11.9480 20.6945i 0.583697 1.01099i −0.411339 0.911482i \(-0.634939\pi\)
0.995036 0.0995110i \(-0.0317278\pi\)
\(420\) 0 0
\(421\) −1.22251 2.11744i −0.0595813 0.103198i 0.834696 0.550711i \(-0.185643\pi\)
−0.894278 + 0.447513i \(0.852310\pi\)
\(422\) −24.1446 41.8197i −1.17534 2.03575i
\(423\) 0 0
\(424\) −1.19375 + 2.06763i −0.0579734 + 0.100413i
\(425\) −15.6107 + 27.0385i −0.757230 + 1.31156i
\(426\) 0 0
\(427\) 0 0
\(428\) −7.72661 + 13.3829i −0.373480 + 0.646886i
\(429\) 0 0
\(430\) 0.565230 0.0272578
\(431\) −2.46382 + 4.26746i −0.118678 + 0.205556i −0.919244 0.393688i \(-0.871199\pi\)
0.800566 + 0.599244i \(0.204532\pi\)
\(432\) 0 0
\(433\) −30.8539 −1.48274 −0.741371 0.671095i \(-0.765824\pi\)
−0.741371 + 0.671095i \(0.765824\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −14.7709 −0.707395
\(437\) −21.3817 37.0341i −1.02282 1.77158i
\(438\) 0 0
\(439\) 1.22411 2.12022i 0.0584235 0.101192i −0.835334 0.549742i \(-0.814726\pi\)
0.893758 + 0.448550i \(0.148059\pi\)
\(440\) −0.108680 −0.00518110
\(441\) 0 0
\(442\) 2.57432 0.122448
\(443\) −13.1475 + 22.7722i −0.624657 + 1.08194i 0.363950 + 0.931419i \(0.381428\pi\)
−0.988607 + 0.150520i \(0.951905\pi\)
\(444\) 0 0
\(445\) −0.663069 1.14847i −0.0314325 0.0544427i
\(446\) −8.33993 −0.394907
\(447\) 0 0
\(448\) 0 0
\(449\) 38.7077 1.82673 0.913365 0.407141i \(-0.133474\pi\)
0.913365 + 0.407141i \(0.133474\pi\)
\(450\) 0 0
\(451\) −1.92854 + 3.34034i −0.0908116 + 0.157290i
\(452\) −0.0856976 −0.00403087
\(453\) 0 0
\(454\) −3.95620 + 6.85233i −0.185673 + 0.321596i
\(455\) 0 0
\(456\) 0 0
\(457\) 4.57756 7.92856i 0.214129 0.370882i −0.738874 0.673844i \(-0.764642\pi\)
0.953003 + 0.302961i \(0.0979754\pi\)
\(458\) −13.4681 + 23.3274i −0.629321 + 1.09002i
\(459\) 0 0
\(460\) 1.00237 + 1.73615i 0.0467355 + 0.0809483i
\(461\) 14.6152 + 25.3143i 0.680698 + 1.17900i 0.974768 + 0.223220i \(0.0716568\pi\)
−0.294070 + 0.955784i \(0.595010\pi\)
\(462\) 0 0
\(463\) −8.21031 + 14.2207i −0.381565 + 0.660891i −0.991286 0.131726i \(-0.957948\pi\)
0.609721 + 0.792616i \(0.291282\pi\)
\(464\) 17.3608 0.805956
\(465\) 0 0
\(466\) 35.9435 1.66505
\(467\) 7.68632 + 13.3131i 0.355680 + 0.616057i 0.987234 0.159276i \(-0.0509158\pi\)
−0.631554 + 0.775332i \(0.717582\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0.272071 + 0.471241i 0.0125497 + 0.0217367i
\(471\) 0 0
\(472\) −1.02066 1.76784i −0.0469797 0.0813713i
\(473\) 1.56585 + 2.71213i 0.0719979 + 0.124704i
\(474\) 0 0
\(475\) 17.2200 + 29.8259i 0.790106 + 1.36850i
\(476\) 0 0
\(477\) 0 0
\(478\) 7.51341 + 13.0136i 0.343655 + 0.595228i
\(479\) −37.9291 −1.73303 −0.866513 0.499155i \(-0.833644\pi\)
−0.866513 + 0.499155i \(0.833644\pi\)
\(480\) 0 0
\(481\) 1.39933 0.0638038
\(482\) −6.39820 + 11.0820i −0.291430 + 0.504772i
\(483\) 0 0
\(484\) 9.12591 + 15.8065i 0.414814 + 0.718479i
\(485\) −0.582809 1.00946i −0.0264640 0.0458370i
\(486\) 0 0
\(487\) 2.30247 3.98800i 0.104335 0.180714i −0.809131 0.587628i \(-0.800062\pi\)
0.913466 + 0.406914i \(0.133395\pi\)
\(488\) 0.151453 0.262324i 0.00685595 0.0118749i
\(489\) 0 0
\(490\) 0 0
\(491\) 15.1876 26.3056i 0.685405 1.18716i −0.287904 0.957659i \(-0.592958\pi\)
0.973309 0.229497i \(-0.0737082\pi\)
\(492\) 0 0
\(493\) 30.9488 1.39386
\(494\) 1.41985 2.45925i 0.0638820 0.110647i
\(495\) 0 0
\(496\) −8.85709 −0.397695
\(497\) 0 0
\(498\) 0 0
\(499\) 9.26871 0.414925 0.207462 0.978243i \(-0.433480\pi\)
0.207462 + 0.978243i \(0.433480\pi\)
\(500\) −1.61800 2.80246i −0.0723592 0.125330i
\(501\) 0 0
\(502\) 5.80445 10.0536i 0.259065 0.448715i
\(503\) −22.4230 −0.999791 −0.499896 0.866086i \(-0.666628\pi\)
−0.499896 + 0.866086i \(0.666628\pi\)
\(504\) 0 0
\(505\) −2.17072 −0.0965960
\(506\) −10.5627 + 18.2952i −0.469571 + 0.813321i
\(507\) 0 0
\(508\) −14.9444 25.8844i −0.663050 1.14844i
\(509\) −37.6414 −1.66843 −0.834213 0.551443i \(-0.814077\pi\)
−0.834213 + 0.551443i \(0.814077\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −31.6976 −1.40085
\(513\) 0 0
\(514\) 12.1182 20.9893i 0.534511 0.925800i
\(515\) −0.0298266 −0.00131432
\(516\) 0 0
\(517\) −1.50743 + 2.61095i −0.0662969 + 0.114830i
\(518\) 0 0
\(519\) 0 0
\(520\) −0.00652751 + 0.0113060i −0.000286250 + 0.000495800i
\(521\) 17.4641 30.2488i 0.765117 1.32522i −0.175067 0.984556i \(-0.556014\pi\)
0.940185 0.340666i \(-0.110652\pi\)
\(522\) 0 0
\(523\) 11.8735 + 20.5656i 0.519194 + 0.899270i 0.999751 + 0.0223069i \(0.00710109\pi\)
−0.480557 + 0.876963i \(0.659566\pi\)
\(524\) 21.9898 + 38.0874i 0.960628 + 1.66386i
\(525\) 0 0
\(526\) 22.8366 39.5542i 0.995723 1.72464i
\(527\) −15.7894 −0.687795
\(528\) 0 0
\(529\) 15.2151 0.661526
\(530\) 0.802820 + 1.39053i 0.0348723 + 0.0604006i
\(531\) 0 0
\(532\) 0 0
\(533\) 0.231664 + 0.401254i 0.0100345 + 0.0173802i
\(534\) 0 0
\(535\) 0.509585 + 0.882627i 0.0220313 + 0.0381593i
\(536\) −1.38147 2.39277i −0.0596702 0.103352i
\(537\) 0 0
\(538\) 2.45292 + 4.24857i 0.105753 + 0.183169i
\(539\) 0 0
\(540\) 0 0
\(541\) 8.58542 + 14.8704i 0.369116 + 0.639328i 0.989428 0.145028i \(-0.0463271\pi\)
−0.620311 + 0.784356i \(0.712994\pi\)
\(542\) 47.6976 2.04879
\(543\) 0 0
\(544\) −50.9055 −2.18255
\(545\) −0.487083 + 0.843653i −0.0208643 + 0.0361381i
\(546\) 0 0
\(547\) −10.0046 17.3284i −0.427765 0.740910i 0.568910 0.822400i \(-0.307365\pi\)
−0.996674 + 0.0814901i \(0.974032\pi\)
\(548\) −7.14586 12.3770i −0.305256 0.528719i
\(549\) 0 0
\(550\) 8.50683 14.7343i 0.362732 0.628271i
\(551\) 17.0696 29.5654i 0.727190 1.25953i
\(552\) 0 0
\(553\) 0 0
\(554\) −4.74187 + 8.21316i −0.201463 + 0.348944i
\(555\) 0 0
\(556\) 27.7860 1.17839
\(557\) 0.122740 0.212593i 0.00520068 0.00900784i −0.863413 0.504497i \(-0.831678\pi\)
0.868614 + 0.495489i \(0.165011\pi\)
\(558\) 0 0
\(559\) 0.376192 0.0159112
\(560\) 0 0
\(561\) 0 0
\(562\) −24.2676 −1.02367
\(563\) 22.1255 + 38.3224i 0.932477 + 1.61510i 0.779073 + 0.626934i \(0.215690\pi\)
0.153404 + 0.988164i \(0.450976\pi\)
\(564\) 0 0
\(565\) −0.00282596 + 0.00489471i −0.000118889 + 0.000205922i
\(566\) 32.5496 1.36816
\(567\) 0 0
\(568\) 0.570506 0.0239379
\(569\) −2.76767 + 4.79374i −0.116027 + 0.200964i −0.918190 0.396141i \(-0.870349\pi\)
0.802163 + 0.597105i \(0.203682\pi\)
\(570\) 0 0
\(571\) 2.05191 + 3.55400i 0.0858696 + 0.148730i 0.905761 0.423788i \(-0.139300\pi\)
−0.819892 + 0.572518i \(0.805966\pi\)
\(572\) −0.737585 −0.0308400
\(573\) 0 0
\(574\) 0 0
\(575\) −30.7770 −1.28349
\(576\) 0 0
\(577\) 2.82275 4.88915i 0.117513 0.203538i −0.801269 0.598305i \(-0.795841\pi\)
0.918781 + 0.394767i \(0.129175\pi\)
\(578\) −45.8512 −1.90716
\(579\) 0 0
\(580\) −0.800218 + 1.38602i −0.0332272 + 0.0575513i
\(581\) 0 0
\(582\) 0 0
\(583\) −4.44809 + 7.70433i −0.184221 + 0.319081i
\(584\) −0.347710 + 0.602252i −0.0143884 + 0.0249214i
\(585\) 0 0
\(586\) −14.4742 25.0700i −0.597923 1.03563i
\(587\) 9.36644 + 16.2232i 0.386595 + 0.669601i 0.991989 0.126324i \(-0.0403180\pi\)
−0.605394 + 0.795926i \(0.706985\pi\)
\(588\) 0 0
\(589\) −8.70852 + 15.0836i −0.358828 + 0.621509i
\(590\) −1.37283 −0.0565187
\(591\) 0 0
\(592\) −24.6262 −1.01213
\(593\) −9.43516 16.3422i −0.387456 0.671093i 0.604651 0.796491i \(-0.293313\pi\)
−0.992107 + 0.125398i \(0.959979\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 19.6991 + 34.1198i 0.806906 + 1.39760i
\(597\) 0 0
\(598\) 1.26884 + 2.19769i 0.0518866 + 0.0898702i
\(599\) 1.33726 + 2.31620i 0.0546388 + 0.0946372i 0.892051 0.451934i \(-0.149266\pi\)
−0.837412 + 0.546572i \(0.815933\pi\)
\(600\) 0 0
\(601\) 6.60716 + 11.4439i 0.269511 + 0.466808i 0.968736 0.248095i \(-0.0798044\pi\)
−0.699224 + 0.714902i \(0.746471\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −9.38650 16.2579i −0.381931 0.661524i
\(605\) 1.20374 0.0489391
\(606\) 0 0
\(607\) −25.8052 −1.04740 −0.523701 0.851902i \(-0.675449\pi\)
−0.523701 + 0.851902i \(0.675449\pi\)
\(608\) −28.0766 + 48.6301i −1.13866 + 1.97221i
\(609\) 0 0
\(610\) −0.101856 0.176419i −0.00412401 0.00714299i
\(611\) 0.181079 + 0.313637i 0.00732565 + 0.0126884i
\(612\) 0 0
\(613\) 13.4766 23.3422i 0.544316 0.942784i −0.454333 0.890832i \(-0.650122\pi\)
0.998650 0.0519519i \(-0.0165443\pi\)
\(614\) −28.1263 + 48.7162i −1.13509 + 1.96603i
\(615\) 0 0
\(616\) 0 0
\(617\) 4.76588 8.25474i 0.191867 0.332323i −0.754002 0.656872i \(-0.771879\pi\)
0.945869 + 0.324549i \(0.105212\pi\)
\(618\) 0 0
\(619\) −34.7071 −1.39500 −0.697499 0.716586i \(-0.745704\pi\)
−0.697499 + 0.716586i \(0.745704\pi\)
\(620\) 0.408253 0.707114i 0.0163958 0.0283984i
\(621\) 0 0
\(622\) 28.8654 1.15740
\(623\) 0 0
\(624\) 0 0
\(625\) 24.6796 0.987186
\(626\) −22.3279 38.6730i −0.892402 1.54568i
\(627\) 0 0
\(628\) 6.31904 10.9449i 0.252157 0.436749i
\(629\) −43.9006 −1.75043
\(630\) 0 0
\(631\) −36.7963 −1.46484 −0.732419 0.680854i \(-0.761609\pi\)
−0.732419 + 0.680854i \(0.761609\pi\)
\(632\) 2.85718 4.94877i 0.113652 0.196852i
\(633\) 0 0
\(634\) −8.79265 15.2293i −0.349201 0.604833i
\(635\) −1.97122 −0.0782256
\(636\) 0 0
\(637\) 0 0
\(638\) −16.8651 −0.667696
\(639\) 0 0
\(640\) 0.259699 0.449811i 0.0102655 0.0177804i
\(641\) 44.1844 1.74518 0.872590 0.488454i \(-0.162439\pi\)
0.872590 + 0.488454i \(0.162439\pi\)
\(642\) 0 0
\(643\) −7.24065 + 12.5412i −0.285543 + 0.494575i −0.972741 0.231895i \(-0.925507\pi\)
0.687197 + 0.726471i \(0.258841\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −44.5444 + 77.1532i −1.75258 + 3.03555i
\(647\) −16.6536 + 28.8448i −0.654719 + 1.13401i 0.327245 + 0.944940i \(0.393880\pi\)
−0.981964 + 0.189068i \(0.939453\pi\)
\(648\) 0 0
\(649\) −3.80315 6.58725i −0.149287 0.258572i
\(650\) −1.02187 1.76993i −0.0400811 0.0694225i
\(651\) 0 0
\(652\) −2.35643 + 4.08146i −0.0922850 + 0.159842i
\(653\) 9.06643 0.354797 0.177398 0.984139i \(-0.443232\pi\)
0.177398 + 0.984139i \(0.443232\pi\)
\(654\) 0 0
\(655\) 2.90054 0.113333
\(656\) −4.07696 7.06150i −0.159178 0.275705i
\(657\) 0 0
\(658\) 0 0
\(659\) −16.1806 28.0256i −0.630305 1.09172i −0.987489 0.157686i \(-0.949596\pi\)
0.357184 0.934034i \(-0.383737\pi\)
\(660\) 0 0
\(661\) −4.32958 7.49905i −0.168401 0.291679i 0.769457 0.638699i \(-0.220527\pi\)
−0.937858 + 0.347020i \(0.887194\pi\)
\(662\) 11.1382 + 19.2919i 0.432897 + 0.749799i
\(663\) 0 0
\(664\) −1.67775 2.90595i −0.0651094 0.112773i
\(665\) 0 0
\(666\) 0 0
\(667\) 15.2541 + 26.4209i 0.590642 + 1.02302i
\(668\) 25.6659 0.993043
\(669\) 0 0
\(670\) −1.85813 −0.0717860
\(671\) 0.564339 0.977464i 0.0217861 0.0377346i
\(672\) 0 0
\(673\) 7.24842 + 12.5546i 0.279406 + 0.483946i 0.971237 0.238114i \(-0.0765291\pi\)
−0.691831 + 0.722059i \(0.743196\pi\)
\(674\) −3.43803 5.95484i −0.132428 0.229372i
\(675\) 0 0
\(676\) 14.3692 24.8881i 0.552661 0.957236i
\(677\) −19.1657 + 33.1960i −0.736600 + 1.27583i 0.217418 + 0.976078i \(0.430236\pi\)
−0.954018 + 0.299749i \(0.903097\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.204785 0.354698i 0.00785315 0.0136021i
\(681\) 0 0
\(682\) 8.60418 0.329471
\(683\) 3.31659 5.74450i 0.126906 0.219807i −0.795570 0.605861i \(-0.792829\pi\)
0.922476 + 0.386054i \(0.126162\pi\)
\(684\) 0 0
\(685\) −0.942567 −0.0360136
\(686\) 0 0
\(687\) 0 0
\(688\) −6.62044 −0.252402
\(689\) 0.534322 + 0.925472i 0.0203560 + 0.0352577i
\(690\) 0 0
\(691\) −11.6938 + 20.2542i −0.444852 + 0.770506i −0.998042 0.0625490i \(-0.980077\pi\)
0.553190 + 0.833055i \(0.313410\pi\)
\(692\) −35.2818 −1.34121
\(693\) 0 0
\(694\) −23.6848 −0.899061
\(695\) 0.916269 1.58702i 0.0347561 0.0601992i
\(696\) 0 0
\(697\) −7.26791 12.5884i −0.275292 0.476819i
\(698\) 18.2740 0.691683
\(699\) 0 0
\(700\) 0 0
\(701\) −9.26736 −0.350023 −0.175012 0.984566i \(-0.555996\pi\)
−0.175012 + 0.984566i \(0.555996\pi\)
\(702\) 0 0
\(703\) −24.2131 + 41.9383i −0.913214 + 1.58173i
\(704\) 16.0327 0.604256
\(705\) 0 0
\(706\) −2.71799 + 4.70769i −0.102293 + 0.177176i
\(707\) 0 0
\(708\) 0 0
\(709\) −7.11775 + 12.3283i −0.267313 + 0.462999i −0.968167 0.250305i \(-0.919469\pi\)
0.700854 + 0.713305i \(0.252802\pi\)
\(710\) 0.191839 0.332275i 0.00719959 0.0124701i
\(711\) 0 0
\(712\) −2.02478 3.50702i −0.0758817 0.131431i
\(713\) −7.78230 13.4793i −0.291449 0.504805i
\(714\) 0 0
\(715\) −0.0243226 + 0.0421280i −0.000909613 + 0.00157550i
\(716\) 17.1926 0.642519
\(717\) 0 0
\(718\) 53.3272 1.99015
\(719\) 6.92848 + 12.0005i 0.258389 + 0.447542i 0.965810 0.259249i \(-0.0834752\pi\)
−0.707422 + 0.706792i \(0.750142\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 29.6268 + 51.3151i 1.10259 + 1.90975i
\(723\) 0 0
\(724\) −13.4842 23.3553i −0.501136 0.867993i
\(725\) −12.2851 21.2784i −0.456257 0.790260i
\(726\) 0 0
\(727\) −15.7000 27.1932i −0.582280 1.00854i −0.995208 0.0977755i \(-0.968827\pi\)
0.412928 0.910764i \(-0.364506\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0.233843 + 0.405028i 0.00865492 + 0.0149908i
\(731\) −11.8021 −0.436518
\(732\) 0 0
\(733\) 26.6006 0.982515 0.491257 0.871014i \(-0.336537\pi\)
0.491257 + 0.871014i \(0.336537\pi\)
\(734\) −18.0592 + 31.2794i −0.666576 + 1.15454i
\(735\) 0 0
\(736\) −25.0904 43.4579i −0.924845 1.60188i
\(737\) −5.14757 8.91586i −0.189613 0.328420i
\(738\) 0 0
\(739\) 16.5019 28.5822i 0.607034 1.05141i −0.384693 0.923045i \(-0.625693\pi\)
0.991727 0.128368i \(-0.0409740\pi\)
\(740\) 1.13510 1.96605i 0.0417272 0.0722736i
\(741\) 0 0
\(742\) 0 0
\(743\) −19.3008 + 33.4299i −0.708076 + 1.22642i 0.257493 + 0.966280i \(0.417103\pi\)
−0.965570 + 0.260144i \(0.916230\pi\)
\(744\) 0 0
\(745\) 2.59839 0.0951975
\(746\) 0.836938 1.44962i 0.0306425 0.0530743i
\(747\) 0 0
\(748\) 23.1400 0.846082
\(749\) 0 0
\(750\) 0 0
\(751\) −37.8996 −1.38297 −0.691487 0.722389i \(-0.743044\pi\)
−0.691487 + 0.722389i \(0.743044\pi\)
\(752\) −3.18673 5.51957i −0.116208 0.201278i
\(753\) 0 0
\(754\) −1.01295 + 1.75448i −0.0368895 + 0.0638944i
\(755\) −1.23811 −0.0450596
\(756\) 0 0
\(757\) 22.5927 0.821147 0.410573 0.911828i \(-0.365329\pi\)
0.410573 + 0.911828i \(0.365329\pi\)
\(758\) −20.9793 + 36.3371i −0.762001 + 1.31982i
\(759\) 0 0
\(760\) −0.225896 0.391263i −0.00819411 0.0141926i
\(761\) 27.7470 1.00583 0.502913 0.864337i \(-0.332261\pi\)
0.502913 + 0.864337i \(0.332261\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 11.0156 0.398529
\(765\) 0 0
\(766\) 18.3727 31.8224i 0.663832 1.14979i
\(767\) −0.913698 −0.0329917
\(768\) 0 0
\(769\) 6.07668 10.5251i 0.219131 0.379546i −0.735412 0.677621i \(-0.763011\pi\)
0.954542 + 0.298075i \(0.0963445\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 16.5250 28.6221i 0.594747 1.03013i
\(773\) −20.7795 + 35.9912i −0.747388 + 1.29451i 0.201682 + 0.979451i \(0.435359\pi\)
−0.949071 + 0.315063i \(0.897974\pi\)
\(774\) 0 0
\(775\) 6.26756 + 10.8557i 0.225137 + 0.389950i
\(776\) −1.77969 3.08252i −0.0638873 0.110656i
\(777\) 0 0
\(778\) −16.0470 + 27.7942i −0.575313 + 0.996472i
\(779\) −16.0343 −0.574488
\(780\) 0 0
\(781\) 2.12580 0.0760671
\(782\) −39.8068 68.9473i −1.42349 2.46555i
\(783\) 0 0
\(784\) 0 0
\(785\) −0.416753 0.721837i −0.0148746 0.0257635i
\(786\) 0 0
\(787\) −10.4484 18.0972i −0.372446 0.645096i 0.617495 0.786575i \(-0.288148\pi\)
−0.989941 + 0.141479i \(0.954814\pi\)
\(788\) −23.5725 40.8288i −0.839736 1.45447i
\(789\) 0 0
\(790\) −1.92152 3.32816i −0.0683645 0.118411i
\(791\) 0 0
\(792\) 0 0
\(793\) −0.0677905 0.117417i −0.00240731 0.00416959i
\(794\) −39.5558 −1.40378
\(795\) 0