Properties

Label 1323.2.g.d.667.1
Level $1323$
Weight $2$
Character 1323.667
Analytic conductor $10.564$
Analytic rank $0$
Dimension $6$
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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 1323.667
Dual form 1323.2.g.d.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.439693 - 0.761570i) q^{2} +(0.613341 - 1.06234i) q^{4} -1.34730 q^{5} -2.83750 q^{8} +O(q^{10})\) \(q+(-0.439693 - 0.761570i) q^{2} +(0.613341 - 1.06234i) q^{4} -1.34730 q^{5} -2.83750 q^{8} +(0.592396 + 1.02606i) q^{10} -1.65270 q^{11} +(1.68479 + 2.91815i) q^{13} +(0.0209445 + 0.0362770i) q^{16} +(0.233956 + 0.405223i) q^{17} +(1.61334 - 2.79439i) q^{19} +(-0.826352 + 1.43128i) q^{20} +(0.726682 + 1.25865i) q^{22} -8.94356 q^{23} -3.18479 q^{25} +(1.48158 - 2.56617i) q^{26} +(3.13429 - 5.42874i) q^{29} +(-4.61721 + 7.99724i) q^{31} +(-2.81908 + 4.88279i) q^{32} +(0.205737 - 0.356347i) q^{34} +(-4.61721 + 7.99724i) q^{37} -2.83750 q^{38} +3.82295 q^{40} +(1.70574 + 2.95442i) q^{41} +(2.20574 - 3.82045i) q^{43} +(-1.01367 + 1.75573i) q^{44} +(3.93242 + 6.81115i) q^{46} +(4.67752 + 8.10170i) q^{47} +(1.40033 + 2.42544i) q^{50} +4.13341 q^{52} +(-0.286989 - 0.497079i) q^{53} +2.22668 q^{55} -5.51249 q^{58} +(-5.19846 + 9.00400i) q^{59} +(-3.81908 - 6.61484i) q^{61} +8.12061 q^{62} +5.04189 q^{64} +(-2.26991 - 3.93161i) q^{65} +(-0.298133 + 0.516382i) q^{67} +0.573978 q^{68} +0.554378 q^{71} +(-1.02481 - 1.77503i) q^{73} +8.12061 q^{74} +(-1.97906 - 3.42782i) q^{76} +(1.20187 + 2.08169i) q^{79} +(-0.0282185 - 0.0488759i) q^{80} +(1.50000 - 2.59808i) q^{82} +(-7.52481 + 13.0334i) q^{83} +(-0.315207 - 0.545955i) q^{85} -3.87939 q^{86} +4.68954 q^{88} +(4.54323 - 7.86911i) q^{89} +(-5.48545 + 9.50108i) q^{92} +(4.11334 - 7.12452i) q^{94} +(-2.17365 + 3.76487i) q^{95} +(0.949493 - 1.64457i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{2} - 3q^{4} - 6q^{5} - 12q^{8} + O(q^{10}) \) \( 6q + 3q^{2} - 3q^{4} - 6q^{5} - 12q^{8} - 12q^{11} + 3q^{13} - 3q^{16} + 6q^{17} + 3q^{19} - 6q^{20} - 9q^{22} - 24q^{23} - 12q^{25} - 3q^{26} + 9q^{29} + 3q^{31} - 9q^{34} + 3q^{37} - 12q^{38} - 18q^{40} + 3q^{43} + 15q^{44} + 3q^{47} - 6q^{50} - 42q^{52} + 6q^{53} - 18q^{58} - 3q^{59} - 6q^{61} + 60q^{62} + 24q^{64} + 15q^{65} + 12q^{67} - 12q^{68} - 18q^{71} + 21q^{73} + 60q^{74} - 15q^{76} + 21q^{79} - 15q^{80} + 9q^{82} - 18q^{83} - 9q^{85} - 12q^{86} + 54q^{88} + 12q^{89} + 3q^{92} + 18q^{94} - 12q^{95} + 3q^{97} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.439693 0.761570i −0.310910 0.538511i 0.667650 0.744475i \(-0.267300\pi\)
−0.978560 + 0.205964i \(0.933967\pi\)
\(3\) 0 0
\(4\) 0.613341 1.06234i 0.306670 0.531169i
\(5\) −1.34730 −0.602529 −0.301265 0.953541i \(-0.597409\pi\)
−0.301265 + 0.953541i \(0.597409\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −2.83750 −1.00321
\(9\) 0 0
\(10\) 0.592396 + 1.02606i 0.187332 + 0.324469i
\(11\) −1.65270 −0.498309 −0.249154 0.968464i \(-0.580153\pi\)
−0.249154 + 0.968464i \(0.580153\pi\)
\(12\) 0 0
\(13\) 1.68479 + 2.91815i 0.467277 + 0.809348i 0.999301 0.0373813i \(-0.0119016\pi\)
−0.532024 + 0.846729i \(0.678568\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.0209445 + 0.0362770i 0.00523613 + 0.00906925i
\(17\) 0.233956 + 0.405223i 0.0567426 + 0.0982810i 0.893001 0.450054i \(-0.148595\pi\)
−0.836259 + 0.548335i \(0.815262\pi\)
\(18\) 0 0
\(19\) 1.61334 2.79439i 0.370126 0.641077i −0.619459 0.785029i \(-0.712648\pi\)
0.989585 + 0.143953i \(0.0459813\pi\)
\(20\) −0.826352 + 1.43128i −0.184778 + 0.320045i
\(21\) 0 0
\(22\) 0.726682 + 1.25865i 0.154929 + 0.268345i
\(23\) −8.94356 −1.86486 −0.932431 0.361348i \(-0.882317\pi\)
−0.932431 + 0.361348i \(0.882317\pi\)
\(24\) 0 0
\(25\) −3.18479 −0.636959
\(26\) 1.48158 2.56617i 0.290562 0.503268i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.13429 5.42874i 0.582022 1.00809i −0.413217 0.910632i \(-0.635595\pi\)
0.995239 0.0974595i \(-0.0310717\pi\)
\(30\) 0 0
\(31\) −4.61721 + 7.99724i −0.829276 + 1.43635i 0.0693317 + 0.997594i \(0.477913\pi\)
−0.898607 + 0.438754i \(0.855420\pi\)
\(32\) −2.81908 + 4.88279i −0.498347 + 0.863163i
\(33\) 0 0
\(34\) 0.205737 0.356347i 0.0352836 0.0611130i
\(35\) 0 0
\(36\) 0 0
\(37\) −4.61721 + 7.99724i −0.759065 + 1.31474i 0.184263 + 0.982877i \(0.441010\pi\)
−0.943328 + 0.331862i \(0.892323\pi\)
\(38\) −2.83750 −0.460303
\(39\) 0 0
\(40\) 3.82295 0.604461
\(41\) 1.70574 + 2.95442i 0.266391 + 0.461403i 0.967927 0.251231i \(-0.0808353\pi\)
−0.701536 + 0.712634i \(0.747502\pi\)
\(42\) 0 0
\(43\) 2.20574 3.82045i 0.336372 0.582613i −0.647376 0.762171i \(-0.724133\pi\)
0.983747 + 0.179558i \(0.0574668\pi\)
\(44\) −1.01367 + 1.75573i −0.152817 + 0.264686i
\(45\) 0 0
\(46\) 3.93242 + 6.81115i 0.579803 + 1.00425i
\(47\) 4.67752 + 8.10170i 0.682286 + 1.18175i 0.974281 + 0.225335i \(0.0723475\pi\)
−0.291995 + 0.956420i \(0.594319\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.40033 + 2.42544i 0.198037 + 0.343009i
\(51\) 0 0
\(52\) 4.13341 0.573201
\(53\) −0.286989 0.497079i −0.0394210 0.0682791i 0.845642 0.533751i \(-0.179218\pi\)
−0.885063 + 0.465472i \(0.845885\pi\)
\(54\) 0 0
\(55\) 2.22668 0.300246
\(56\) 0 0
\(57\) 0 0
\(58\) −5.51249 −0.723825
\(59\) −5.19846 + 9.00400i −0.676782 + 1.17222i 0.299162 + 0.954202i \(0.403293\pi\)
−0.975945 + 0.218019i \(0.930041\pi\)
\(60\) 0 0
\(61\) −3.81908 6.61484i −0.488983 0.846943i 0.510937 0.859618i \(-0.329299\pi\)
−0.999920 + 0.0126752i \(0.995965\pi\)
\(62\) 8.12061 1.03132
\(63\) 0 0
\(64\) 5.04189 0.630236
\(65\) −2.26991 3.93161i −0.281548 0.487656i
\(66\) 0 0
\(67\) −0.298133 + 0.516382i −0.0364228 + 0.0630861i −0.883662 0.468125i \(-0.844930\pi\)
0.847239 + 0.531211i \(0.178263\pi\)
\(68\) 0.573978 0.0696051
\(69\) 0 0
\(70\) 0 0
\(71\) 0.554378 0.0657925 0.0328963 0.999459i \(-0.489527\pi\)
0.0328963 + 0.999459i \(0.489527\pi\)
\(72\) 0 0
\(73\) −1.02481 1.77503i −0.119946 0.207752i 0.799800 0.600266i \(-0.204939\pi\)
−0.919746 + 0.392514i \(0.871605\pi\)
\(74\) 8.12061 0.944002
\(75\) 0 0
\(76\) −1.97906 3.42782i −0.227013 0.393198i
\(77\) 0 0
\(78\) 0 0
\(79\) 1.20187 + 2.08169i 0.135221 + 0.234209i 0.925682 0.378303i \(-0.123492\pi\)
−0.790461 + 0.612512i \(0.790159\pi\)
\(80\) −0.0282185 0.0488759i −0.00315492 0.00546449i
\(81\) 0 0
\(82\) 1.50000 2.59808i 0.165647 0.286910i
\(83\) −7.52481 + 13.0334i −0.825956 + 1.43060i 0.0752309 + 0.997166i \(0.476031\pi\)
−0.901187 + 0.433431i \(0.857303\pi\)
\(84\) 0 0
\(85\) −0.315207 0.545955i −0.0341891 0.0592172i
\(86\) −3.87939 −0.418325
\(87\) 0 0
\(88\) 4.68954 0.499907
\(89\) 4.54323 7.86911i 0.481582 0.834124i −0.518195 0.855263i \(-0.673396\pi\)
0.999777 + 0.0211385i \(0.00672911\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −5.48545 + 9.50108i −0.571898 + 0.990556i
\(93\) 0 0
\(94\) 4.11334 7.12452i 0.424259 0.734838i
\(95\) −2.17365 + 3.76487i −0.223012 + 0.386267i
\(96\) 0 0
\(97\) 0.949493 1.64457i 0.0964064 0.166981i −0.813788 0.581161i \(-0.802598\pi\)
0.910195 + 0.414181i \(0.135932\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.95336 + 3.38332i −0.195336 + 0.338332i
\(101\) 1.70914 0.170066 0.0850329 0.996378i \(-0.472900\pi\)
0.0850329 + 0.996378i \(0.472900\pi\)
\(102\) 0 0
\(103\) −3.63816 −0.358478 −0.179239 0.983806i \(-0.557364\pi\)
−0.179239 + 0.983806i \(0.557364\pi\)
\(104\) −4.78059 8.28023i −0.468776 0.811943i
\(105\) 0 0
\(106\) −0.252374 + 0.437124i −0.0245127 + 0.0424573i
\(107\) 3.56418 6.17334i 0.344562 0.596799i −0.640712 0.767781i \(-0.721361\pi\)
0.985274 + 0.170982i \(0.0546941\pi\)
\(108\) 0 0
\(109\) −0.201867 0.349643i −0.0193353 0.0334898i 0.856196 0.516651i \(-0.172822\pi\)
−0.875531 + 0.483162i \(0.839488\pi\)
\(110\) −0.979055 1.69577i −0.0933493 0.161686i
\(111\) 0 0
\(112\) 0 0
\(113\) 7.18479 + 12.4444i 0.675888 + 1.17067i 0.976208 + 0.216835i \(0.0695732\pi\)
−0.300320 + 0.953839i \(0.597093\pi\)
\(114\) 0 0
\(115\) 12.0496 1.12363
\(116\) −3.84477 6.65934i −0.356978 0.618304i
\(117\) 0 0
\(118\) 9.14290 0.841672
\(119\) 0 0
\(120\) 0 0
\(121\) −8.26857 −0.751688
\(122\) −3.35844 + 5.81699i −0.304059 + 0.526646i
\(123\) 0 0
\(124\) 5.66385 + 9.81007i 0.508629 + 0.880971i
\(125\) 11.0273 0.986315
\(126\) 0 0
\(127\) −20.7716 −1.84318 −0.921589 0.388167i \(-0.873108\pi\)
−0.921589 + 0.388167i \(0.873108\pi\)
\(128\) 3.42127 + 5.92582i 0.302401 + 0.523774i
\(129\) 0 0
\(130\) −1.99613 + 3.45740i −0.175072 + 0.303234i
\(131\) 7.16519 0.626026 0.313013 0.949749i \(-0.398662\pi\)
0.313013 + 0.949749i \(0.398662\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.524348 0.0452968
\(135\) 0 0
\(136\) −0.663848 1.14982i −0.0569245 0.0985961i
\(137\) −2.56893 −0.219478 −0.109739 0.993960i \(-0.535002\pi\)
−0.109739 + 0.993960i \(0.535002\pi\)
\(138\) 0 0
\(139\) 3.06670 + 5.31169i 0.260114 + 0.450531i 0.966272 0.257523i \(-0.0829064\pi\)
−0.706158 + 0.708055i \(0.749573\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.243756 0.422197i −0.0204555 0.0354300i
\(143\) −2.78446 4.82283i −0.232848 0.403305i
\(144\) 0 0
\(145\) −4.22281 + 7.31412i −0.350685 + 0.607405i
\(146\) −0.901207 + 1.56094i −0.0745844 + 0.129184i
\(147\) 0 0
\(148\) 5.66385 + 9.81007i 0.465565 + 0.806383i
\(149\) −0.431074 −0.0353150 −0.0176575 0.999844i \(-0.505621\pi\)
−0.0176575 + 0.999844i \(0.505621\pi\)
\(150\) 0 0
\(151\) −2.47060 −0.201055 −0.100527 0.994934i \(-0.532053\pi\)
−0.100527 + 0.994934i \(0.532053\pi\)
\(152\) −4.57785 + 7.92907i −0.371313 + 0.643132i
\(153\) 0 0
\(154\) 0 0
\(155\) 6.22075 10.7747i 0.499663 0.865441i
\(156\) 0 0
\(157\) −5.06670 + 8.77579i −0.404367 + 0.700384i −0.994248 0.107106i \(-0.965841\pi\)
0.589881 + 0.807491i \(0.299175\pi\)
\(158\) 1.05690 1.83061i 0.0840828 0.145636i
\(159\) 0 0
\(160\) 3.79813 6.57856i 0.300269 0.520081i
\(161\) 0 0
\(162\) 0 0
\(163\) 1.29813 2.24843i 0.101678 0.176111i −0.810698 0.585464i \(-0.800912\pi\)
0.912376 + 0.409353i \(0.134246\pi\)
\(164\) 4.18479 0.326777
\(165\) 0 0
\(166\) 13.2344 1.02719
\(167\) −11.5915 20.0771i −0.896979 1.55361i −0.831337 0.555769i \(-0.812424\pi\)
−0.0656422 0.997843i \(-0.520910\pi\)
\(168\) 0 0
\(169\) 0.822948 1.42539i 0.0633037 0.109645i
\(170\) −0.277189 + 0.480105i −0.0212594 + 0.0368224i
\(171\) 0 0
\(172\) −2.70574 4.68647i −0.206311 0.357340i
\(173\) −2.37598 4.11532i −0.180643 0.312882i 0.761457 0.648215i \(-0.224484\pi\)
−0.942100 + 0.335333i \(0.891151\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.0346151 0.0599551i −0.00260921 0.00451929i
\(177\) 0 0
\(178\) −7.99050 −0.598914
\(179\) −4.26604 7.38901i −0.318859 0.552280i 0.661391 0.750041i \(-0.269966\pi\)
−0.980250 + 0.197761i \(0.936633\pi\)
\(180\) 0 0
\(181\) −17.2344 −1.28102 −0.640512 0.767948i \(-0.721278\pi\)
−0.640512 + 0.767948i \(0.721278\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 25.3773 1.87084
\(185\) 6.22075 10.7747i 0.457359 0.792169i
\(186\) 0 0
\(187\) −0.386659 0.669713i −0.0282753 0.0489743i
\(188\) 11.4757 0.836948
\(189\) 0 0
\(190\) 3.82295 0.277346
\(191\) 6.45471 + 11.1799i 0.467046 + 0.808948i 0.999291 0.0376425i \(-0.0119848\pi\)
−0.532245 + 0.846590i \(0.678651\pi\)
\(192\) 0 0
\(193\) 0.319078 0.552659i 0.0229677 0.0397813i −0.854313 0.519759i \(-0.826022\pi\)
0.877281 + 0.479977i \(0.159355\pi\)
\(194\) −1.66994 −0.119895
\(195\) 0 0
\(196\) 0 0
\(197\) −11.4456 −0.815467 −0.407733 0.913101i \(-0.633681\pi\)
−0.407733 + 0.913101i \(0.633681\pi\)
\(198\) 0 0
\(199\) 1.81908 + 3.15074i 0.128951 + 0.223350i 0.923270 0.384151i \(-0.125506\pi\)
−0.794319 + 0.607500i \(0.792172\pi\)
\(200\) 9.03684 0.639001
\(201\) 0 0
\(202\) −0.751497 1.30163i −0.0528751 0.0915824i
\(203\) 0 0
\(204\) 0 0
\(205\) −2.29813 3.98048i −0.160509 0.278009i
\(206\) 1.59967 + 2.77071i 0.111454 + 0.193045i
\(207\) 0 0
\(208\) −0.0705744 + 0.122238i −0.00489345 + 0.00847571i
\(209\) −2.66637 + 4.61830i −0.184437 + 0.319454i
\(210\) 0 0
\(211\) −2.91147 5.04282i −0.200434 0.347162i 0.748234 0.663435i \(-0.230902\pi\)
−0.948668 + 0.316273i \(0.897569\pi\)
\(212\) −0.704088 −0.0483570
\(213\) 0 0
\(214\) −6.26857 −0.428511
\(215\) −2.97178 + 5.14728i −0.202674 + 0.351041i
\(216\) 0 0
\(217\) 0 0
\(218\) −0.177519 + 0.307471i −0.0120231 + 0.0208246i
\(219\) 0 0
\(220\) 1.36571 2.36549i 0.0920765 0.159481i
\(221\) −0.788333 + 1.36543i −0.0530290 + 0.0918490i
\(222\) 0 0
\(223\) −3.54189 + 6.13473i −0.237182 + 0.410812i −0.959905 0.280327i \(-0.909557\pi\)
0.722722 + 0.691139i \(0.242891\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 6.31820 10.9434i 0.420280 0.727947i
\(227\) 11.9436 0.792722 0.396361 0.918095i \(-0.370273\pi\)
0.396361 + 0.918095i \(0.370273\pi\)
\(228\) 0 0
\(229\) −17.5526 −1.15991 −0.579955 0.814649i \(-0.696930\pi\)
−0.579955 + 0.814649i \(0.696930\pi\)
\(230\) −5.29813 9.17664i −0.349349 0.605089i
\(231\) 0 0
\(232\) −8.89352 + 15.4040i −0.583888 + 1.01132i
\(233\) 8.12701 14.0764i 0.532418 0.922175i −0.466865 0.884328i \(-0.654617\pi\)
0.999284 0.0378470i \(-0.0120499\pi\)
\(234\) 0 0
\(235\) −6.30200 10.9154i −0.411097 0.712042i
\(236\) 6.37686 + 11.0450i 0.415098 + 0.718971i
\(237\) 0 0
\(238\) 0 0
\(239\) −7.54963 13.0763i −0.488345 0.845838i 0.511565 0.859244i \(-0.329066\pi\)
−0.999910 + 0.0134062i \(0.995733\pi\)
\(240\) 0 0
\(241\) −15.6382 −1.00734 −0.503671 0.863896i \(-0.668018\pi\)
−0.503671 + 0.863896i \(0.668018\pi\)
\(242\) 3.63563 + 6.29710i 0.233707 + 0.404793i
\(243\) 0 0
\(244\) −9.36959 −0.599826
\(245\) 0 0
\(246\) 0 0
\(247\) 10.8726 0.691806
\(248\) 13.1013 22.6922i 0.831935 1.44095i
\(249\) 0 0
\(250\) −4.84864 8.39809i −0.306655 0.531142i
\(251\) −19.0651 −1.20338 −0.601690 0.798730i \(-0.705506\pi\)
−0.601690 + 0.798730i \(0.705506\pi\)
\(252\) 0 0
\(253\) 14.7811 0.929277
\(254\) 9.13310 + 15.8190i 0.573062 + 0.992572i
\(255\) 0 0
\(256\) 8.05051 13.9439i 0.503157 0.871493i
\(257\) −26.5817 −1.65812 −0.829061 0.559158i \(-0.811124\pi\)
−0.829061 + 0.559158i \(0.811124\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −5.56893 −0.345370
\(261\) 0 0
\(262\) −3.15048 5.45680i −0.194637 0.337122i
\(263\) 0.734118 0.0452676 0.0226338 0.999744i \(-0.492795\pi\)
0.0226338 + 0.999744i \(0.492795\pi\)
\(264\) 0 0
\(265\) 0.386659 + 0.669713i 0.0237523 + 0.0411402i
\(266\) 0 0
\(267\) 0 0
\(268\) 0.365715 + 0.633436i 0.0223396 + 0.0386933i
\(269\) −10.4251 18.0569i −0.635632 1.10095i −0.986381 0.164478i \(-0.947406\pi\)
0.350749 0.936470i \(-0.385927\pi\)
\(270\) 0 0
\(271\) −3.47906 + 6.02590i −0.211338 + 0.366047i −0.952133 0.305683i \(-0.901115\pi\)
0.740796 + 0.671730i \(0.234449\pi\)
\(272\) −0.00980018 + 0.0169744i −0.000594223 + 0.00102922i
\(273\) 0 0
\(274\) 1.12954 + 1.95642i 0.0682379 + 0.118191i
\(275\) 5.26352 0.317402
\(276\) 0 0
\(277\) 17.8726 1.07386 0.536930 0.843627i \(-0.319584\pi\)
0.536930 + 0.843627i \(0.319584\pi\)
\(278\) 2.69681 4.67102i 0.161744 0.280149i
\(279\) 0 0
\(280\) 0 0
\(281\) 11.1552 19.3214i 0.665465 1.15262i −0.313694 0.949524i \(-0.601567\pi\)
0.979159 0.203095i \(-0.0651001\pi\)
\(282\) 0 0
\(283\) 9.29726 16.1033i 0.552665 0.957243i −0.445417 0.895323i \(-0.646944\pi\)
0.998081 0.0619196i \(-0.0197222\pi\)
\(284\) 0.340022 0.588936i 0.0201766 0.0349469i
\(285\) 0 0
\(286\) −2.44862 + 4.24113i −0.144790 + 0.250783i
\(287\) 0 0
\(288\) 0 0
\(289\) 8.39053 14.5328i 0.493561 0.854872i
\(290\) 7.42696 0.436126
\(291\) 0 0
\(292\) −2.51424 −0.147135
\(293\) 6.54576 + 11.3376i 0.382407 + 0.662349i 0.991406 0.130822i \(-0.0417618\pi\)
−0.608998 + 0.793171i \(0.708428\pi\)
\(294\) 0 0
\(295\) 7.00387 12.1311i 0.407781 0.706298i
\(296\) 13.1013 22.6922i 0.761499 1.31895i
\(297\) 0 0
\(298\) 0.189540 + 0.328293i 0.0109798 + 0.0190175i
\(299\) −15.0680 26.0986i −0.871408 1.50932i
\(300\) 0 0
\(301\) 0 0
\(302\) 1.08630 + 1.88153i 0.0625098 + 0.108270i
\(303\) 0 0
\(304\) 0.135163 0.00775211
\(305\) 5.14543 + 8.91215i 0.294626 + 0.510308i
\(306\) 0 0
\(307\) 6.31046 0.360157 0.180078 0.983652i \(-0.442365\pi\)
0.180078 + 0.983652i \(0.442365\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −10.9409 −0.621400
\(311\) −4.76217 + 8.24833i −0.270038 + 0.467720i −0.968871 0.247565i \(-0.920370\pi\)
0.698833 + 0.715285i \(0.253703\pi\)
\(312\) 0 0
\(313\) 8.81433 + 15.2669i 0.498215 + 0.862934i 0.999998 0.00205946i \(-0.000655547\pi\)
−0.501782 + 0.864994i \(0.667322\pi\)
\(314\) 8.91117 0.502886
\(315\) 0 0
\(316\) 2.94862 0.165873
\(317\) 4.03849 + 6.99486i 0.226824 + 0.392871i 0.956865 0.290533i \(-0.0938325\pi\)
−0.730041 + 0.683403i \(0.760499\pi\)
\(318\) 0 0
\(319\) −5.18004 + 8.97210i −0.290027 + 0.502341i
\(320\) −6.79292 −0.379736
\(321\) 0 0
\(322\) 0 0
\(323\) 1.50980 0.0840075
\(324\) 0 0
\(325\) −5.36571 9.29369i −0.297636 0.515521i
\(326\) −2.28312 −0.126450
\(327\) 0 0
\(328\) −4.84002 8.38316i −0.267246 0.462883i
\(329\) 0 0
\(330\) 0 0
\(331\) −11.5248 19.9616i −0.633461 1.09719i −0.986839 0.161706i \(-0.948300\pi\)
0.353378 0.935481i \(-0.385033\pi\)
\(332\) 9.23055 + 15.9878i 0.506592 + 0.877444i
\(333\) 0 0
\(334\) −10.1934 + 17.6555i −0.557759 + 0.966066i
\(335\) 0.401674 0.695720i 0.0219458 0.0380112i
\(336\) 0 0
\(337\) −14.5116 25.1348i −0.790498 1.36918i −0.925659 0.378359i \(-0.876489\pi\)
0.135161 0.990824i \(-0.456845\pi\)
\(338\) −1.44738 −0.0787269
\(339\) 0 0
\(340\) −0.773318 −0.0419391
\(341\) 7.63088 13.2171i 0.413235 0.715745i
\(342\) 0 0
\(343\) 0 0
\(344\) −6.25877 + 10.8405i −0.337450 + 0.584481i
\(345\) 0 0
\(346\) −2.08940 + 3.61895i −0.112327 + 0.194556i
\(347\) 6.47313 11.2118i 0.347496 0.601880i −0.638308 0.769781i \(-0.720365\pi\)
0.985804 + 0.167901i \(0.0536988\pi\)
\(348\) 0 0
\(349\) −0.731429 + 1.26687i −0.0391525 + 0.0678141i −0.884938 0.465710i \(-0.845799\pi\)
0.845785 + 0.533524i \(0.179132\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.65910 8.06980i 0.248331 0.430122i
\(353\) −14.3327 −0.762855 −0.381428 0.924399i \(-0.624567\pi\)
−0.381428 + 0.924399i \(0.624567\pi\)
\(354\) 0 0
\(355\) −0.746911 −0.0396419
\(356\) −5.57310 9.65289i −0.295374 0.511602i
\(357\) 0 0
\(358\) −3.75150 + 6.49778i −0.198273 + 0.343418i
\(359\) −10.4684 + 18.1318i −0.552500 + 0.956958i 0.445593 + 0.895235i \(0.352993\pi\)
−0.998093 + 0.0617224i \(0.980341\pi\)
\(360\) 0 0
\(361\) 4.29426 + 7.43788i 0.226014 + 0.391467i
\(362\) 7.57785 + 13.1252i 0.398283 + 0.689846i
\(363\) 0 0
\(364\) 0 0
\(365\) 1.38073 + 2.39149i 0.0722707 + 0.125176i
\(366\) 0 0
\(367\) −12.0574 −0.629390 −0.314695 0.949193i \(-0.601902\pi\)
−0.314695 + 0.949193i \(0.601902\pi\)
\(368\) −0.187319 0.324446i −0.00976466 0.0169129i
\(369\) 0 0
\(370\) −10.9409 −0.568789
\(371\) 0 0
\(372\) 0 0
\(373\) −0.781059 −0.0404417 −0.0202209 0.999796i \(-0.506437\pi\)
−0.0202209 + 0.999796i \(0.506437\pi\)
\(374\) −0.340022 + 0.588936i −0.0175821 + 0.0304532i
\(375\) 0 0
\(376\) −13.2724 22.9885i −0.684474 1.18554i
\(377\) 21.1225 1.08786
\(378\) 0 0
\(379\) −6.92396 −0.355660 −0.177830 0.984061i \(-0.556908\pi\)
−0.177830 + 0.984061i \(0.556908\pi\)
\(380\) 2.66637 + 4.61830i 0.136782 + 0.236914i
\(381\) 0 0
\(382\) 5.67617 9.83142i 0.290418 0.503019i
\(383\) −7.73236 −0.395105 −0.197553 0.980292i \(-0.563299\pi\)
−0.197553 + 0.980292i \(0.563299\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.561185 −0.0285636
\(387\) 0 0
\(388\) −1.16473 2.01736i −0.0591300 0.102416i
\(389\) −5.39961 −0.273771 −0.136886 0.990587i \(-0.543709\pi\)
−0.136886 + 0.990587i \(0.543709\pi\)
\(390\) 0 0
\(391\) −2.09240 3.62414i −0.105817 0.183280i
\(392\) 0 0
\(393\) 0 0
\(394\) 5.03256 + 8.71664i 0.253536 + 0.439138i
\(395\) −1.61927 2.80466i −0.0814743 0.141118i
\(396\) 0 0
\(397\) 14.6172 25.3178i 0.733617 1.27066i −0.221711 0.975112i \(-0.571164\pi\)
0.955328 0.295549i \(-0.0955026\pi\)
\(398\) 1.59967 2.77071i 0.0801842 0.138883i
\(399\) 0 0
\(400\) −0.0667040 0.115535i −0.00333520 0.00577674i
\(401\) 27.3979 1.36818 0.684092 0.729396i \(-0.260199\pi\)
0.684092 + 0.729396i \(0.260199\pi\)
\(402\) 0 0
\(403\) −31.1162 −1.55001
\(404\) 1.04829 1.81568i 0.0521542 0.0903337i
\(405\) 0 0
\(406\) 0 0
\(407\) 7.63088 13.2171i 0.378249 0.655146i
\(408\) 0 0
\(409\) 4.51249 7.81586i 0.223128 0.386469i −0.732628 0.680629i \(-0.761706\pi\)
0.955756 + 0.294160i \(0.0950398\pi\)
\(410\) −2.02094 + 3.50038i −0.0998073 + 0.172871i
\(411\) 0 0
\(412\) −2.23143 + 3.86495i −0.109935 + 0.190412i
\(413\) 0 0
\(414\) 0 0
\(415\) 10.1382 17.5598i 0.497662 0.861977i
\(416\) −18.9982 −0.931466
\(417\) 0 0
\(418\) 4.68954 0.229373
\(419\) 0.0876485 + 0.151812i 0.00428191 + 0.00741649i 0.868158 0.496287i \(-0.165304\pi\)
−0.863877 + 0.503704i \(0.831970\pi\)
\(420\) 0 0
\(421\) 12.3525 21.3952i 0.602025 1.04274i −0.390490 0.920607i \(-0.627694\pi\)
0.992514 0.122130i \(-0.0389724\pi\)
\(422\) −2.56031 + 4.43458i −0.124634 + 0.215872i
\(423\) 0 0
\(424\) 0.814330 + 1.41046i 0.0395474 + 0.0684980i
\(425\) −0.745100 1.29055i −0.0361427 0.0626009i
\(426\) 0 0
\(427\) 0 0
\(428\) −4.37211 7.57272i −0.211334 0.366041i
\(429\) 0 0
\(430\) 5.22668 0.252053
\(431\) −14.6596 25.3911i −0.706126 1.22305i −0.966283 0.257481i \(-0.917108\pi\)
0.260157 0.965566i \(-0.416226\pi\)
\(432\) 0 0
\(433\) 19.6554 0.944578 0.472289 0.881444i \(-0.343428\pi\)
0.472289 + 0.881444i \(0.343428\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.495252 −0.0237183
\(437\) −14.4290 + 24.9918i −0.690233 + 1.19552i
\(438\) 0 0
\(439\) 10.9650 + 18.9919i 0.523330 + 0.906434i 0.999631 + 0.0271516i \(0.00864370\pi\)
−0.476302 + 0.879282i \(0.658023\pi\)
\(440\) −6.31820 −0.301208
\(441\) 0 0
\(442\) 1.38650 0.0659489
\(443\) −9.35504 16.2034i −0.444471 0.769847i 0.553544 0.832820i \(-0.313275\pi\)
−0.998015 + 0.0629732i \(0.979942\pi\)
\(444\) 0 0
\(445\) −6.12108 + 10.6020i −0.290167 + 0.502584i
\(446\) 6.22937 0.294969
\(447\) 0 0
\(448\) 0 0
\(449\) −6.68004 −0.315251 −0.157625 0.987499i \(-0.550384\pi\)
−0.157625 + 0.987499i \(0.550384\pi\)
\(450\) 0 0
\(451\) −2.81908 4.88279i −0.132745 0.229921i
\(452\) 17.6269 0.829100
\(453\) 0 0
\(454\) −5.25150 9.09586i −0.246465 0.426890i
\(455\) 0 0
\(456\) 0 0
\(457\) 9.71436 + 16.8258i 0.454418 + 0.787076i 0.998655 0.0518563i \(-0.0165138\pi\)
−0.544236 + 0.838932i \(0.683180\pi\)
\(458\) 7.71776 + 13.3676i 0.360627 + 0.624625i
\(459\) 0 0
\(460\) 7.39053 12.8008i 0.344585 0.596839i
\(461\) −0.482926 + 0.836452i −0.0224921 + 0.0389575i −0.877052 0.480395i \(-0.840493\pi\)
0.854560 + 0.519352i \(0.173827\pi\)
\(462\) 0 0
\(463\) 0.222811 + 0.385920i 0.0103549 + 0.0179352i 0.871156 0.491006i \(-0.163371\pi\)
−0.860802 + 0.508941i \(0.830037\pi\)
\(464\) 0.262585 0.0121902
\(465\) 0 0
\(466\) −14.2935 −0.662136
\(467\) −17.1074 + 29.6309i −0.791637 + 1.37115i 0.133317 + 0.991074i \(0.457437\pi\)
−0.924953 + 0.380081i \(0.875896\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −5.54189 + 9.59883i −0.255628 + 0.442761i
\(471\) 0 0
\(472\) 14.7506 25.5488i 0.678952 1.17598i
\(473\) −3.64543 + 6.31407i −0.167617 + 0.290321i
\(474\) 0 0
\(475\) −5.13816 + 8.89955i −0.235755 + 0.408339i
\(476\) 0 0
\(477\) 0 0
\(478\) −6.63903 + 11.4991i −0.303662 + 0.525959i
\(479\) 21.7929 0.995744 0.497872 0.867251i \(-0.334115\pi\)
0.497872 + 0.867251i \(0.334115\pi\)
\(480\) 0 0
\(481\) −31.1162 −1.41878
\(482\) 6.87598 + 11.9095i 0.313192 + 0.542465i
\(483\) 0 0
\(484\) −5.07145 + 8.78401i −0.230521 + 0.399273i
\(485\) −1.27925 + 2.21572i −0.0580877 + 0.100611i
\(486\) 0 0
\(487\) −9.69640 16.7947i −0.439386 0.761039i 0.558256 0.829669i \(-0.311471\pi\)
−0.997642 + 0.0686297i \(0.978137\pi\)
\(488\) 10.8366 + 18.7696i 0.490551 + 0.849659i
\(489\) 0 0
\(490\) 0 0
\(491\) 13.0783 + 22.6523i 0.590216 + 1.02228i 0.994203 + 0.107519i \(0.0342908\pi\)
−0.403987 + 0.914765i \(0.632376\pi\)
\(492\) 0 0
\(493\) 2.93313 0.132102
\(494\) −4.78059 8.28023i −0.215089 0.372545i
\(495\) 0 0
\(496\) −0.386821 −0.0173688
\(497\) 0 0
\(498\) 0 0
\(499\) −14.3013 −0.640214 −0.320107 0.947381i \(-0.603719\pi\)
−0.320107 + 0.947381i \(0.603719\pi\)
\(500\) 6.76352 11.7148i 0.302474 0.523900i
\(501\) 0 0
\(502\) 8.38279 + 14.5194i 0.374142 + 0.648033i
\(503\) −18.7033 −0.833937 −0.416969 0.908921i \(-0.636908\pi\)
−0.416969 + 0.908921i \(0.636908\pi\)
\(504\) 0 0
\(505\) −2.30272 −0.102470
\(506\) −6.49912 11.2568i −0.288921 0.500426i
\(507\) 0 0
\(508\) −12.7400 + 22.0664i −0.565248 + 0.979039i
\(509\) 25.6091 1.13510 0.567551 0.823338i \(-0.307891\pi\)
0.567551 + 0.823338i \(0.307891\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.473897 −0.0209435
\(513\) 0 0
\(514\) 11.6878 + 20.2438i 0.515526 + 0.892917i
\(515\) 4.90167 0.215994
\(516\) 0 0
\(517\) −7.73055 13.3897i −0.339989 0.588879i
\(518\) 0 0
\(519\) 0 0
\(520\) 6.44087 + 11.1559i 0.282451 + 0.489220i
\(521\) −10.6061 18.3702i −0.464660 0.804815i 0.534526 0.845152i \(-0.320490\pi\)
−0.999186 + 0.0403370i \(0.987157\pi\)
\(522\) 0 0
\(523\) −10.4029 + 18.0183i −0.454885 + 0.787884i −0.998682 0.0513330i \(-0.983653\pi\)
0.543796 + 0.839217i \(0.316986\pi\)
\(524\) 4.39470 7.61185i 0.191984 0.332525i
\(525\) 0 0
\(526\) −0.322786 0.559082i −0.0140741 0.0243771i
\(527\) −4.32089 −0.188221
\(528\) 0 0
\(529\) 56.9873 2.47771
\(530\) 0.340022 0.588936i 0.0147696 0.0255817i
\(531\) 0 0
\(532\) 0 0
\(533\) −5.74763 + 9.95518i −0.248957 + 0.431207i
\(534\) 0 0
\(535\) −4.80200 + 8.31731i −0.207609 + 0.359589i
\(536\) 0.845952 1.46523i 0.0365396 0.0632884i
\(537\) 0 0
\(538\) −9.16772 + 15.8790i −0.395248 + 0.684590i
\(539\) 0 0
\(540\) 0 0
\(541\) −13.3648 + 23.1486i −0.574599 + 0.995235i 0.421486 + 0.906835i \(0.361509\pi\)
−0.996085 + 0.0884001i \(0.971825\pi\)
\(542\) 6.11886 0.262828
\(543\) 0 0
\(544\) −2.63816 −0.113110
\(545\) 0.271974 + 0.471073i 0.0116501 + 0.0201786i
\(546\) 0 0
\(547\) −18.3812 + 31.8372i −0.785923 + 1.36126i 0.142523 + 0.989792i \(0.454479\pi\)
−0.928446 + 0.371467i \(0.878855\pi\)
\(548\) −1.57563 + 2.72907i −0.0673074 + 0.116580i
\(549\) 0 0
\(550\) −2.31433 4.00854i −0.0986834 0.170925i
\(551\) −10.1133 17.5168i −0.430843 0.746242i
\(552\) 0 0
\(553\) 0 0
\(554\) −7.85844 13.6112i −0.333873 0.578285i
\(555\) 0 0
\(556\) 7.52374 0.319078
\(557\) 16.1694 + 28.0062i 0.685118 + 1.18666i 0.973400 + 0.229114i \(0.0735827\pi\)
−0.288282 + 0.957546i \(0.593084\pi\)
\(558\) 0 0
\(559\) 14.8648 0.628716
\(560\) 0 0
\(561\) 0 0
\(562\) −19.6195 −0.827598
\(563\) −8.87093 + 15.3649i −0.373865 + 0.647553i −0.990156 0.139965i \(-0.955301\pi\)
0.616291 + 0.787518i \(0.288634\pi\)
\(564\) 0 0
\(565\) −9.68004 16.7663i −0.407243 0.705365i
\(566\) −16.3517 −0.687315
\(567\) 0 0
\(568\) −1.57304 −0.0660035
\(569\) −13.3007 23.0374i −0.557593 0.965779i −0.997697 0.0678320i \(-0.978392\pi\)
0.440104 0.897947i \(-0.354942\pi\)
\(570\) 0 0
\(571\) 5.00862 8.67518i 0.209604 0.363045i −0.741986 0.670416i \(-0.766116\pi\)
0.951590 + 0.307371i \(0.0994491\pi\)
\(572\) −6.83130 −0.285631
\(573\) 0 0
\(574\) 0 0
\(575\) 28.4834 1.18784
\(576\) 0 0
\(577\) 16.4572 + 28.5048i 0.685124 + 1.18667i 0.973398 + 0.229121i \(0.0735852\pi\)
−0.288274 + 0.957548i \(0.593082\pi\)
\(578\) −14.7570 −0.613811
\(579\) 0 0
\(580\) 5.18004 + 8.97210i 0.215090 + 0.372546i
\(581\) 0 0
\(582\) 0 0
\(583\) 0.474308 + 0.821525i 0.0196438 + 0.0340241i
\(584\) 2.90791 + 5.03665i 0.120330 + 0.208418i
\(585\) 0 0
\(586\) 5.75624 9.97011i 0.237788 0.411861i
\(587\) −7.53643 + 13.0535i −0.311062 + 0.538774i −0.978592 0.205808i \(-0.934018\pi\)
0.667531 + 0.744582i \(0.267351\pi\)
\(588\) 0 0
\(589\) 14.8983 + 25.8046i 0.613873 + 1.06326i
\(590\) −12.3182 −0.507132
\(591\) 0 0
\(592\) −0.386821 −0.0158983
\(593\) 20.5005 35.5079i 0.841853 1.45813i −0.0464729 0.998920i \(-0.514798\pi\)
0.888326 0.459213i \(-0.151869\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.264396 + 0.457947i −0.0108301 + 0.0187582i
\(597\) 0 0
\(598\) −13.2506 + 22.9507i −0.541858 + 0.938526i
\(599\) 3.03684 5.25996i 0.124082 0.214916i −0.797292 0.603594i \(-0.793735\pi\)
0.921374 + 0.388678i \(0.127068\pi\)
\(600\) 0 0
\(601\) 7.06758 12.2414i 0.288293 0.499338i −0.685110 0.728440i \(-0.740246\pi\)
0.973402 + 0.229102i \(0.0735791\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1.51532 + 2.62461i −0.0616575 + 0.106794i
\(605\) 11.1402 0.452914
\(606\) 0 0
\(607\) 46.0898 1.87073 0.935363 0.353689i \(-0.115073\pi\)
0.935363 + 0.353689i \(0.115073\pi\)
\(608\) 9.09627 + 15.7552i 0.368902 + 0.638958i
\(609\) 0 0
\(610\) 4.52481 7.83721i 0.183204 0.317319i
\(611\) −15.7613 + 27.2994i −0.637634 + 1.10441i
\(612\) 0 0
\(613\) 13.2469 + 22.9443i 0.535038 + 0.926712i 0.999162 + 0.0409421i \(0.0130359\pi\)
−0.464124 + 0.885770i \(0.653631\pi\)
\(614\) −2.77466 4.80586i −0.111976 0.193949i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.12495 1.94847i −0.0452889 0.0784426i 0.842492 0.538708i \(-0.181087\pi\)
−0.887781 + 0.460266i \(0.847754\pi\)
\(618\) 0 0
\(619\) 6.19078 0.248828 0.124414 0.992230i \(-0.460295\pi\)
0.124414 + 0.992230i \(0.460295\pi\)
\(620\) −7.63088 13.2171i −0.306464 0.530811i
\(621\) 0 0
\(622\) 8.37557 0.335830
\(623\) 0 0
\(624\) 0 0
\(625\) 1.06687 0.0426746
\(626\) 7.75119 13.4255i 0.309800 0.536589i
\(627\) 0 0
\(628\) 6.21523 + 10.7651i 0.248015 + 0.429574i
\(629\) −4.32089 −0.172285
\(630\) 0 0
\(631\) 26.1661 1.04166 0.520829 0.853661i \(-0.325623\pi\)
0.520829 + 0.853661i \(0.325623\pi\)
\(632\) −3.41029 5.90680i −0.135654 0.234960i
\(633\) 0 0
\(634\) 3.55138 6.15118i 0.141043 0.244295i
\(635\) 27.9855 1.11057
\(636\) 0 0
\(637\) 0 0
\(638\) 9.11051 0.360689
\(639\) 0 0
\(640\) −4.60947 7.98384i −0.182205 0.315589i
\(641\) −4.88888 −0.193099 −0.0965496 0.995328i \(-0.530781\pi\)
−0.0965496 + 0.995328i \(0.530781\pi\)
\(642\) 0 0
\(643\) 20.1839 + 34.9596i 0.795976 + 1.37867i 0.922218 + 0.386671i \(0.126375\pi\)
−0.126242 + 0.992000i \(0.540291\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.663848 1.14982i −0.0261188 0.0452390i
\(647\) −1.14038 1.97519i −0.0448329 0.0776528i 0.842738 0.538324i \(-0.180942\pi\)
−0.887571 + 0.460671i \(0.847609\pi\)
\(648\) 0 0
\(649\) 8.59152 14.8809i 0.337247 0.584128i
\(650\) −4.71853 + 8.17273i −0.185076 + 0.320561i
\(651\) 0 0
\(652\) −1.59240 2.75811i −0.0623631 0.108016i
\(653\) −23.4793 −0.918815 −0.459407 0.888226i \(-0.651938\pi\)
−0.459407 + 0.888226i \(0.651938\pi\)
\(654\) 0 0
\(655\) −9.65364 −0.377199
\(656\) −0.0714517 + 0.123758i −0.00278972 + 0.00483194i
\(657\) 0 0
\(658\) 0 0
\(659\) −23.9812 + 41.5366i −0.934174 + 1.61804i −0.158073 + 0.987427i \(0.550528\pi\)
−0.776101 + 0.630609i \(0.782805\pi\)
\(660\) 0 0
\(661\) −14.6545 + 25.3824i −0.569995 + 0.987260i 0.426571 + 0.904454i \(0.359721\pi\)
−0.996566 + 0.0828055i \(0.973612\pi\)
\(662\) −10.1348 + 17.5539i −0.393898 + 0.682252i
\(663\) 0 0
\(664\) 21.3516 36.9821i 0.828604 1.43518i
\(665\) 0 0
\(666\) 0 0
\(667\) −28.0317 + 48.5523i −1.08539 + 1.87995i
\(668\) −28.4382 −1.10031
\(669\) 0 0
\(670\) −0.706452 −0.0272926
\(671\) 6.31180 + 10.9324i 0.243664 + 0.422039i
\(672\) 0 0
\(673\) −13.1591 + 22.7922i −0.507246 + 0.878576i 0.492719 + 0.870189i \(0.336003\pi\)
−0.999965 + 0.00838731i \(0.997330\pi\)
\(674\) −12.7613 + 22.1032i −0.491547 + 0.851384i
\(675\) 0 0
\(676\) −1.00950 1.74850i −0.0388267 0.0672499i
\(677\) 17.9454 + 31.0823i 0.689697 + 1.19459i 0.971936 + 0.235246i \(0.0755895\pi\)
−0.282239 + 0.959344i \(0.591077\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.894400 + 1.54915i 0.0342987 + 0.0594070i
\(681\) 0 0
\(682\) −13.4210 −0.513915
\(683\) 17.5321 + 30.3665i 0.670847 + 1.16194i 0.977664 + 0.210172i \(0.0674025\pi\)
−0.306818 + 0.951768i \(0.599264\pi\)
\(684\) 0 0
\(685\) 3.46110 0.132242
\(686\) 0 0
\(687\) 0 0
\(688\) 0.184793 0.00704515
\(689\) 0.967034 1.67495i 0.0368411 0.0638106i
\(690\) 0 0
\(691\) −1.03343 1.78996i −0.0393136 0.0680932i 0.845699 0.533660i \(-0.179184\pi\)
−0.885013 + 0.465567i \(0.845850\pi\)
\(692\) −5.82915 −0.221591
\(693\) 0 0
\(694\) −11.3847 −0.432159
\(695\) −4.13176 7.15642i −0.156727 0.271458i
\(696\) 0 0
\(697\) −0.798133 + 1.38241i −0.0302315 + 0.0523624i
\(698\) 1.28642 0.0486916
\(699\) 0 0
\(700\) 0 0
\(701\) 7.36009 0.277987 0.138993 0.990293i \(-0.455613\pi\)
0.138993 + 0.990293i \(0.455613\pi\)
\(702\) 0 0
\(703\) 14.8983 + 25.8046i 0.561899 + 0.973237i
\(704\) −8.33275 −0.314052
\(705\) 0 0
\(706\) 6.30200 + 10.9154i 0.237179 + 0.410806i
\(707\) 0 0
\(708\) 0 0
\(709\) −4.55438 7.88841i −0.171043 0.296256i 0.767742 0.640760i \(-0.221380\pi\)
−0.938785 + 0.344504i \(0.888047\pi\)
\(710\) 0.328411 + 0.568825i 0.0123251 + 0.0213476i
\(711\) 0 0
\(712\) −12.8914 + 22.3286i −0.483126 + 0.836799i
\(713\) 41.2943 71.5239i 1.54648 2.67859i
\(714\) 0 0
\(715\) 3.75150 + 6.49778i 0.140298 + 0.243003i
\(716\) −10.4662 −0.391139
\(717\) 0 0
\(718\) 18.4115 0.687110
\(719\) −12.9768 + 22.4765i −0.483954 + 0.838233i −0.999830 0.0184300i \(-0.994133\pi\)
0.515876 + 0.856663i \(0.327467\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3.77631 6.54076i 0.140540 0.243422i
\(723\) 0 0
\(724\) −10.5706 + 18.3088i −0.392852 + 0.680440i
\(725\) −9.98205 + 17.2894i −0.370724 + 0.642113i
\(726\) 0 0
\(727\) 5.08007 8.79894i 0.188409 0.326335i −0.756311 0.654213i \(-0.773000\pi\)
0.944720 + 0.327878i \(0.106333\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 1.21419 2.10304i 0.0449393 0.0778372i
\(731\) 2.06418 0.0763464
\(732\) 0 0
\(733\) 40.6614 1.50186 0.750931 0.660381i \(-0.229605\pi\)
0.750931 + 0.660381i \(0.229605\pi\)
\(734\) 5.30154 + 9.18253i 0.195683 + 0.338933i
\(735\) 0 0
\(736\) 25.2126 43.6695i 0.929349 1.60968i
\(737\) 0.492726 0.853427i 0.0181498 0.0314364i
\(738\) 0 0
\(739\) 12.6809 + 21.9640i 0.466475 + 0.807959i 0.999267 0.0382877i \(-0.0121903\pi\)
−0.532791 + 0.846247i \(0.678857\pi\)
\(740\) −7.63088 13.2171i −0.280517 0.485869i
\(741\) 0 0
\(742\) 0 0
\(743\) −11.2221 19.4372i −0.411699 0.713083i 0.583377 0.812202i \(-0.301731\pi\)
−0.995076 + 0.0991184i \(0.968398\pi\)
\(744\) 0 0
\(745\) 0.580785 0.0212783
\(746\) 0.343426 + 0.594831i 0.0125737 + 0.0217783i
\(747\) 0 0
\(748\) −0.948615 −0.0346848
\(749\) 0 0
\(750\) 0 0
\(751\) 24.2172 0.883698 0.441849 0.897090i \(-0.354323\pi\)
0.441849 + 0.897090i \(0.354323\pi\)
\(752\) −0.195937 + 0.339373i −0.00714508 + 0.0123756i
\(753\) 0 0
\(754\) −9.28740 16.0862i −0.338227 0.585827i
\(755\) 3.32863 0.121141
\(756\) 0 0
\(757\) 9.11793 0.331397 0.165698 0.986176i \(-0.447012\pi\)
0.165698 + 0.986176i \(0.447012\pi\)
\(758\) 3.04442 + 5.27308i 0.110578 + 0.191527i
\(759\) 0 0
\(760\) 6.16772 10.6828i 0.223727 0.387506i
\(761\) 18.2722 0.662366 0.331183 0.943566i \(-0.392552\pi\)
0.331183 + 0.943566i \(0.392552\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 15.8357 0.572917
\(765\) 0 0
\(766\) 3.39986 + 5.88874i 0.122842 + 0.212769i
\(767\) −35.0333 −1.26498
\(768\) 0 0
\(769\) −9.26470 16.0469i −0.334094 0.578667i 0.649217 0.760604i \(-0.275097\pi\)
−0.983310 + 0.181936i \(0.941764\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.391407 0.677937i −0.0140870 0.0243995i
\(773\) −1.48040 2.56413i −0.0532463 0.0922253i 0.838174 0.545403i \(-0.183624\pi\)
−0.891420 + 0.453178i \(0.850290\pi\)
\(774\) 0 0
\(775\) 14.7049 25.4696i 0.528214 0.914894i
\(776\) −2.69418 + 4.66646i −0.0967155 + 0.167516i
\(777\) 0 0
\(778\) 2.37417 + 4.11218i 0.0851181 + 0.147429i
\(779\) 11.0077 0.394393
\(780\) 0 0
\(781\) −0.916222 −0.0327850
\(782\) −1.84002 + 3.18701i −0.0657991 + 0.113967i
\(783\) 0 0
\(784\) 0 0
\(785\) 6.82635 11.8236i 0.243643 0.422002i
\(786\) 0 0
\(787\) 16.7010 28.9270i 0.595326 1.03113i −0.398175 0.917310i \(-0.630356\pi\)
0.993501 0.113825i \(-0.0363104\pi\)
\(788\) −7.02007 + 12.1591i −0.250080 + 0.433150i
\(789\) 0 0
\(790\) −1.42396 + 2.46638i −0.0506623 + 0.0877497i
\(791\) 0 0
\(792\) 0 0
\(793\) 12.8687 22.2893i 0.456981 0.791515i
\(794\) −25.7083