Properties

Label 2646.2.m.a.1763.4
Level $2646$
Weight $2$
Character 2646.1763
Analytic conductor $21.128$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.m (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + 2785 x^{8} - 2640 x^{7} - 2601 x^{6} + 10260 x^{5} - 10611 x^{4} - 1944 x^{3} + 16767 x^{2} - 17496 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1763.4
Root \(1.27866 + 1.16834i\) of defining polynomial
Character \(\chi\) \(=\) 2646.1763
Dual form 2646.2.m.a.881.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.77612 + 3.07634i) q^{5} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.77612 + 3.07634i) q^{5} -1.00000i q^{8} -3.55225i q^{10} +(2.61745 + 1.51119i) q^{11} +(0.888944 - 0.513232i) q^{13} +(-0.500000 + 0.866025i) q^{16} +1.61841 q^{17} +8.22889i q^{19} +(-1.77612 + 3.07634i) q^{20} +(-1.51119 - 2.61745i) q^{22} +(2.90837 - 1.67915i) q^{23} +(-3.80924 + 6.59779i) q^{25} -1.02646 q^{26} +(3.70319 + 2.13804i) q^{29} +(-5.18382 + 2.99288i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.40158 - 0.809204i) q^{34} -5.84647 q^{37} +(4.11444 - 7.12643i) q^{38} +(3.07634 - 1.77612i) q^{40} +(0.0472226 + 0.0817920i) q^{41} +(3.05899 - 5.29833i) q^{43} +3.02237i q^{44} -3.35830 q^{46} +(2.57023 - 4.45176i) q^{47} +(6.59779 - 3.80924i) q^{50} +(0.888944 + 0.513232i) q^{52} -3.18968i q^{53} +10.7362i q^{55} +(-2.13804 - 3.70319i) q^{58} +(4.42036 + 7.65628i) q^{59} +(4.06195 + 2.34517i) q^{61} +5.98576 q^{62} -1.00000 q^{64} +(3.15775 + 1.82313i) q^{65} +(0.187838 + 0.325345i) q^{67} +(0.809204 + 1.40158i) q^{68} -13.9868i q^{71} +1.31111i q^{73} +(5.06319 + 2.92323i) q^{74} +(-7.12643 + 4.11444i) q^{76} +(-0.462067 + 0.800324i) q^{79} -3.55225 q^{80} -0.0944452i q^{82} +(5.43209 - 9.40866i) q^{83} +(2.87450 + 4.97877i) q^{85} +(-5.29833 + 3.05899i) q^{86} +(1.51119 - 2.61745i) q^{88} +4.70989 q^{89} +(2.90837 + 1.67915i) q^{92} +(-4.45176 + 2.57023i) q^{94} +(-25.3148 + 14.6155i) q^{95} +(-13.3330 - 7.69782i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + O(q^{10}) \) \( 16 q + 8 q^{4} + 12 q^{11} - 6 q^{13} - 8 q^{16} + 36 q^{17} - 6 q^{23} - 8 q^{25} - 24 q^{26} - 6 q^{29} - 6 q^{31} + 4 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{46} + 18 q^{47} + 12 q^{50} - 6 q^{52} + 6 q^{58} - 30 q^{59} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} + 18 q^{68} + 18 q^{74} - 16 q^{79} - 12 q^{85} + 24 q^{86} + 48 q^{89} - 6 q^{92} - 66 q^{95} - 6 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.77612 + 3.07634i 0.794307 + 1.37578i 0.923278 + 0.384132i \(0.125499\pi\)
−0.128971 + 0.991648i \(0.541167\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 3.55225i 1.12332i
\(11\) 2.61745 + 1.51119i 0.789191 + 0.455639i 0.839678 0.543085i \(-0.182744\pi\)
−0.0504869 + 0.998725i \(0.516077\pi\)
\(12\) 0 0
\(13\) 0.888944 0.513232i 0.246549 0.142345i −0.371634 0.928379i \(-0.621202\pi\)
0.618183 + 0.786034i \(0.287869\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.61841 0.392522 0.196261 0.980552i \(-0.437120\pi\)
0.196261 + 0.980552i \(0.437120\pi\)
\(18\) 0 0
\(19\) 8.22889i 1.88784i 0.330179 + 0.943918i \(0.392891\pi\)
−0.330179 + 0.943918i \(0.607109\pi\)
\(20\) −1.77612 + 3.07634i −0.397154 + 0.687890i
\(21\) 0 0
\(22\) −1.51119 2.61745i −0.322186 0.558042i
\(23\) 2.90837 1.67915i 0.606438 0.350127i −0.165132 0.986271i \(-0.552805\pi\)
0.771570 + 0.636144i \(0.219472\pi\)
\(24\) 0 0
\(25\) −3.80924 + 6.59779i −0.761848 + 1.31956i
\(26\) −1.02646 −0.201306
\(27\) 0 0
\(28\) 0 0
\(29\) 3.70319 + 2.13804i 0.687666 + 0.397024i 0.802737 0.596333i \(-0.203376\pi\)
−0.115071 + 0.993357i \(0.536710\pi\)
\(30\) 0 0
\(31\) −5.18382 + 2.99288i −0.931041 + 0.537537i −0.887141 0.461499i \(-0.847312\pi\)
−0.0439006 + 0.999036i \(0.513978\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) −1.40158 0.809204i −0.240369 0.138777i
\(35\) 0 0
\(36\) 0 0
\(37\) −5.84647 −0.961154 −0.480577 0.876953i \(-0.659573\pi\)
−0.480577 + 0.876953i \(0.659573\pi\)
\(38\) 4.11444 7.12643i 0.667451 1.15606i
\(39\) 0 0
\(40\) 3.07634 1.77612i 0.486412 0.280830i
\(41\) 0.0472226 + 0.0817920i 0.00737493 + 0.0127738i 0.869689 0.493600i \(-0.164319\pi\)
−0.862314 + 0.506373i \(0.830986\pi\)
\(42\) 0 0
\(43\) 3.05899 5.29833i 0.466492 0.807988i −0.532775 0.846257i \(-0.678851\pi\)
0.999267 + 0.0382684i \(0.0121842\pi\)
\(44\) 3.02237i 0.455639i
\(45\) 0 0
\(46\) −3.35830 −0.495154
\(47\) 2.57023 4.45176i 0.374906 0.649356i −0.615407 0.788210i \(-0.711008\pi\)
0.990313 + 0.138853i \(0.0443416\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 6.59779 3.80924i 0.933069 0.538708i
\(51\) 0 0
\(52\) 0.888944 + 0.513232i 0.123274 + 0.0711725i
\(53\) 3.18968i 0.438137i −0.975709 0.219068i \(-0.929698\pi\)
0.975709 0.219068i \(-0.0703018\pi\)
\(54\) 0 0
\(55\) 10.7362i 1.44767i
\(56\) 0 0
\(57\) 0 0
\(58\) −2.13804 3.70319i −0.280738 0.486253i
\(59\) 4.42036 + 7.65628i 0.575481 + 0.996763i 0.995989 + 0.0894739i \(0.0285186\pi\)
−0.420508 + 0.907289i \(0.638148\pi\)
\(60\) 0 0
\(61\) 4.06195 + 2.34517i 0.520080 + 0.300268i 0.736967 0.675928i \(-0.236257\pi\)
−0.216887 + 0.976197i \(0.569590\pi\)
\(62\) 5.98576 0.760192
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 3.15775 + 1.82313i 0.391671 + 0.226131i
\(66\) 0 0
\(67\) 0.187838 + 0.325345i 0.0229480 + 0.0397472i 0.877271 0.479995i \(-0.159361\pi\)
−0.854323 + 0.519742i \(0.826028\pi\)
\(68\) 0.809204 + 1.40158i 0.0981304 + 0.169967i
\(69\) 0 0
\(70\) 0 0
\(71\) 13.9868i 1.65993i −0.557815 0.829966i \(-0.688360\pi\)
0.557815 0.829966i \(-0.311640\pi\)
\(72\) 0 0
\(73\) 1.31111i 0.153454i 0.997052 + 0.0767270i \(0.0244470\pi\)
−0.997052 + 0.0767270i \(0.975553\pi\)
\(74\) 5.06319 + 2.92323i 0.588584 + 0.339819i
\(75\) 0 0
\(76\) −7.12643 + 4.11444i −0.817457 + 0.471959i
\(77\) 0 0
\(78\) 0 0
\(79\) −0.462067 + 0.800324i −0.0519866 + 0.0900434i −0.890848 0.454302i \(-0.849889\pi\)
0.838861 + 0.544346i \(0.183222\pi\)
\(80\) −3.55225 −0.397154
\(81\) 0 0
\(82\) 0.0944452i 0.0104297i
\(83\) 5.43209 9.40866i 0.596250 1.03273i −0.397119 0.917767i \(-0.629990\pi\)
0.993369 0.114968i \(-0.0366765\pi\)
\(84\) 0 0
\(85\) 2.87450 + 4.97877i 0.311783 + 0.540024i
\(86\) −5.29833 + 3.05899i −0.571334 + 0.329860i
\(87\) 0 0
\(88\) 1.51119 2.61745i 0.161093 0.279021i
\(89\) 4.70989 0.499247 0.249624 0.968343i \(-0.419693\pi\)
0.249624 + 0.968343i \(0.419693\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.90837 + 1.67915i 0.303219 + 0.175063i
\(93\) 0 0
\(94\) −4.45176 + 2.57023i −0.459164 + 0.265099i
\(95\) −25.3148 + 14.6155i −2.59725 + 1.49952i
\(96\) 0 0
\(97\) −13.3330 7.69782i −1.35376 0.781595i −0.364988 0.931012i \(-0.618927\pi\)
−0.988774 + 0.149417i \(0.952260\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −7.61848 −0.761848
\(101\) −6.85234 + 11.8686i −0.681833 + 1.18097i 0.292588 + 0.956239i \(0.405484\pi\)
−0.974421 + 0.224731i \(0.927850\pi\)
\(102\) 0 0
\(103\) 2.64014 1.52429i 0.260141 0.150192i −0.364258 0.931298i \(-0.618677\pi\)
0.624399 + 0.781106i \(0.285344\pi\)
\(104\) −0.513232 0.888944i −0.0503266 0.0871682i
\(105\) 0 0
\(106\) −1.59484 + 2.76235i −0.154905 + 0.268303i
\(107\) 13.1267i 1.26901i 0.772920 + 0.634504i \(0.218796\pi\)
−0.772920 + 0.634504i \(0.781204\pi\)
\(108\) 0 0
\(109\) −10.5715 −1.01256 −0.506282 0.862368i \(-0.668980\pi\)
−0.506282 + 0.862368i \(0.668980\pi\)
\(110\) 5.36811 9.29783i 0.511829 0.886514i
\(111\) 0 0
\(112\) 0 0
\(113\) −10.6520 + 6.14993i −1.00205 + 0.578537i −0.908856 0.417111i \(-0.863043\pi\)
−0.0931992 + 0.995647i \(0.529709\pi\)
\(114\) 0 0
\(115\) 10.3313 + 5.96476i 0.963396 + 0.556217i
\(116\) 4.27608i 0.397024i
\(117\) 0 0
\(118\) 8.84071i 0.813853i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.932639 1.61538i −0.0847854 0.146853i
\(122\) −2.34517 4.06195i −0.212322 0.367752i
\(123\) 0 0
\(124\) −5.18382 2.99288i −0.465521 0.268768i
\(125\) −9.30148 −0.831950
\(126\) 0 0
\(127\) 0.287164 0.0254817 0.0127408 0.999919i \(-0.495944\pi\)
0.0127408 + 0.999919i \(0.495944\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −1.82313 3.15775i −0.159899 0.276953i
\(131\) 0.186474 + 0.322983i 0.0162923 + 0.0282192i 0.874057 0.485824i \(-0.161480\pi\)
−0.857764 + 0.514043i \(0.828147\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.375675i 0.0324534i
\(135\) 0 0
\(136\) 1.61841i 0.138777i
\(137\) 6.11607 + 3.53111i 0.522531 + 0.301683i 0.737969 0.674834i \(-0.235785\pi\)
−0.215439 + 0.976517i \(0.569118\pi\)
\(138\) 0 0
\(139\) 12.6320 7.29308i 1.07143 0.618591i 0.142858 0.989743i \(-0.454371\pi\)
0.928572 + 0.371152i \(0.121037\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −6.99341 + 12.1129i −0.586874 + 1.01650i
\(143\) 3.10236 0.259432
\(144\) 0 0
\(145\) 15.1897i 1.26144i
\(146\) 0.655556 1.13546i 0.0542542 0.0939710i
\(147\) 0 0
\(148\) −2.92323 5.06319i −0.240288 0.416192i
\(149\) −9.26832 + 5.35107i −0.759290 + 0.438376i −0.829041 0.559188i \(-0.811113\pi\)
0.0697505 + 0.997564i \(0.477780\pi\)
\(150\) 0 0
\(151\) −8.00065 + 13.8575i −0.651084 + 1.12771i 0.331777 + 0.943358i \(0.392352\pi\)
−0.982860 + 0.184352i \(0.940981\pi\)
\(152\) 8.22889 0.667451
\(153\) 0 0
\(154\) 0 0
\(155\) −18.4142 10.6315i −1.47907 0.853939i
\(156\) 0 0
\(157\) 9.98239 5.76334i 0.796681 0.459964i −0.0456280 0.998958i \(-0.514529\pi\)
0.842309 + 0.538994i \(0.181196\pi\)
\(158\) 0.800324 0.462067i 0.0636703 0.0367601i
\(159\) 0 0
\(160\) 3.07634 + 1.77612i 0.243206 + 0.140415i
\(161\) 0 0
\(162\) 0 0
\(163\) −2.74773 −0.215219 −0.107609 0.994193i \(-0.534320\pi\)
−0.107609 + 0.994193i \(0.534320\pi\)
\(164\) −0.0472226 + 0.0817920i −0.00368747 + 0.00638688i
\(165\) 0 0
\(166\) −9.40866 + 5.43209i −0.730254 + 0.421612i
\(167\) −2.76946 4.79685i −0.214307 0.371191i 0.738751 0.673979i \(-0.235416\pi\)
−0.953058 + 0.302788i \(0.902083\pi\)
\(168\) 0 0
\(169\) −5.97319 + 10.3459i −0.459476 + 0.795835i
\(170\) 5.74899i 0.440927i
\(171\) 0 0
\(172\) 6.11799 0.466492
\(173\) −5.60253 + 9.70387i −0.425953 + 0.737772i −0.996509 0.0834869i \(-0.973394\pi\)
0.570556 + 0.821259i \(0.306728\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.61745 + 1.51119i −0.197298 + 0.113910i
\(177\) 0 0
\(178\) −4.07888 2.35495i −0.305725 0.176511i
\(179\) 2.74178i 0.204930i −0.994737 0.102465i \(-0.967327\pi\)
0.994737 0.102465i \(-0.0326730\pi\)
\(180\) 0 0
\(181\) 22.2899i 1.65679i 0.560142 + 0.828397i \(0.310747\pi\)
−0.560142 + 0.828397i \(0.689253\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.67915 2.90837i −0.123789 0.214408i
\(185\) −10.3841 17.9857i −0.763451 1.32234i
\(186\) 0 0
\(187\) 4.23610 + 2.44571i 0.309774 + 0.178848i
\(188\) 5.14045 0.374906
\(189\) 0 0
\(190\) 29.2311 2.12064
\(191\) 4.44499 + 2.56632i 0.321628 + 0.185692i 0.652118 0.758117i \(-0.273881\pi\)
−0.330490 + 0.943810i \(0.607214\pi\)
\(192\) 0 0
\(193\) −7.99235 13.8432i −0.575302 0.996452i −0.996009 0.0892557i \(-0.971551\pi\)
0.420707 0.907197i \(-0.361782\pi\)
\(194\) 7.69782 + 13.3330i 0.552671 + 0.957254i
\(195\) 0 0
\(196\) 0 0
\(197\) 4.72572i 0.336694i 0.985728 + 0.168347i \(0.0538428\pi\)
−0.985728 + 0.168347i \(0.946157\pi\)
\(198\) 0 0
\(199\) 2.12095i 0.150350i 0.997170 + 0.0751749i \(0.0239515\pi\)
−0.997170 + 0.0751749i \(0.976048\pi\)
\(200\) 6.59779 + 3.80924i 0.466534 + 0.269354i
\(201\) 0 0
\(202\) 11.8686 6.85234i 0.835072 0.482129i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.167747 + 0.290545i −0.0117159 + 0.0202926i
\(206\) −3.04857 −0.212404
\(207\) 0 0
\(208\) 1.02646i 0.0711725i
\(209\) −12.4354 + 21.5387i −0.860173 + 1.48986i
\(210\) 0 0
\(211\) −13.8079 23.9160i −0.950578 1.64645i −0.744179 0.667981i \(-0.767159\pi\)
−0.206399 0.978468i \(-0.566174\pi\)
\(212\) 2.76235 1.59484i 0.189719 0.109534i
\(213\) 0 0
\(214\) 6.56336 11.3681i 0.448662 0.777105i
\(215\) 21.7326 1.48215
\(216\) 0 0
\(217\) 0 0
\(218\) 9.15516 + 5.28574i 0.620066 + 0.357995i
\(219\) 0 0
\(220\) −9.29783 + 5.36811i −0.626860 + 0.361918i
\(221\) 1.43867 0.830619i 0.0967757 0.0558735i
\(222\) 0 0
\(223\) 17.6209 + 10.1734i 1.17998 + 0.681264i 0.956011 0.293331i \(-0.0947638\pi\)
0.223973 + 0.974595i \(0.428097\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 12.2999 0.818174
\(227\) −2.08000 + 3.60266i −0.138054 + 0.239117i −0.926760 0.375654i \(-0.877418\pi\)
0.788706 + 0.614771i \(0.210752\pi\)
\(228\) 0 0
\(229\) −5.16986 + 2.98482i −0.341634 + 0.197242i −0.660994 0.750391i \(-0.729865\pi\)
0.319361 + 0.947633i \(0.396532\pi\)
\(230\) −5.96476 10.3313i −0.393305 0.681224i
\(231\) 0 0
\(232\) 2.13804 3.70319i 0.140369 0.243126i
\(233\) 4.48720i 0.293966i 0.989139 + 0.146983i \(0.0469563\pi\)
−0.989139 + 0.146983i \(0.953044\pi\)
\(234\) 0 0
\(235\) 18.2602 1.19116
\(236\) −4.42036 + 7.65628i −0.287741 + 0.498381i
\(237\) 0 0
\(238\) 0 0
\(239\) 3.02944 1.74905i 0.195958 0.113136i −0.398811 0.917033i \(-0.630577\pi\)
0.594769 + 0.803897i \(0.297244\pi\)
\(240\) 0 0
\(241\) 10.0170 + 5.78332i 0.645252 + 0.372537i 0.786635 0.617419i \(-0.211821\pi\)
−0.141383 + 0.989955i \(0.545155\pi\)
\(242\) 1.86528i 0.119905i
\(243\) 0 0
\(244\) 4.69034i 0.300268i
\(245\) 0 0
\(246\) 0 0
\(247\) 4.22333 + 7.31502i 0.268724 + 0.465444i
\(248\) 2.99288 + 5.18382i 0.190048 + 0.329173i
\(249\) 0 0
\(250\) 8.05532 + 4.65074i 0.509463 + 0.294139i
\(251\) 26.7426 1.68798 0.843988 0.536361i \(-0.180202\pi\)
0.843988 + 0.536361i \(0.180202\pi\)
\(252\) 0 0
\(253\) 10.1500 0.638127
\(254\) −0.248691 0.143582i −0.0156043 0.00900913i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 2.60614 + 4.51396i 0.162566 + 0.281573i 0.935788 0.352562i \(-0.114690\pi\)
−0.773222 + 0.634135i \(0.781356\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 3.64626i 0.226131i
\(261\) 0 0
\(262\) 0.372949i 0.0230409i
\(263\) −13.0228 7.51869i −0.803018 0.463622i 0.0415076 0.999138i \(-0.486784\pi\)
−0.844525 + 0.535516i \(0.820117\pi\)
\(264\) 0 0
\(265\) 9.81255 5.66528i 0.602780 0.348015i
\(266\) 0 0
\(267\) 0 0
\(268\) −0.187838 + 0.325345i −0.0114740 + 0.0198736i
\(269\) 23.1313 1.41034 0.705170 0.709038i \(-0.250870\pi\)
0.705170 + 0.709038i \(0.250870\pi\)
\(270\) 0 0
\(271\) 9.91496i 0.602291i −0.953578 0.301146i \(-0.902631\pi\)
0.953578 0.301146i \(-0.0973690\pi\)
\(272\) −0.809204 + 1.40158i −0.0490652 + 0.0849834i
\(273\) 0 0
\(274\) −3.53111 6.11607i −0.213322 0.369485i
\(275\) −19.9410 + 11.5129i −1.20249 + 0.694256i
\(276\) 0 0
\(277\) 4.29721 7.44299i 0.258195 0.447206i −0.707564 0.706650i \(-0.750206\pi\)
0.965758 + 0.259443i \(0.0835391\pi\)
\(278\) −14.5862 −0.874819
\(279\) 0 0
\(280\) 0 0
\(281\) 17.9508 + 10.3639i 1.07085 + 0.618258i 0.928415 0.371545i \(-0.121172\pi\)
0.142440 + 0.989803i \(0.454505\pi\)
\(282\) 0 0
\(283\) 2.04997 1.18355i 0.121858 0.0703547i −0.437832 0.899057i \(-0.644254\pi\)
0.559690 + 0.828702i \(0.310920\pi\)
\(284\) 12.1129 6.99341i 0.718771 0.414983i
\(285\) 0 0
\(286\) −2.68672 1.55118i −0.158869 0.0917231i
\(287\) 0 0
\(288\) 0 0
\(289\) −14.3808 −0.845927
\(290\) 7.59485 13.1547i 0.445985 0.772468i
\(291\) 0 0
\(292\) −1.13546 + 0.655556i −0.0664475 + 0.0383635i
\(293\) 8.83774 + 15.3074i 0.516306 + 0.894268i 0.999821 + 0.0189321i \(0.00602664\pi\)
−0.483515 + 0.875336i \(0.660640\pi\)
\(294\) 0 0
\(295\) −15.7022 + 27.1970i −0.914218 + 1.58347i
\(296\) 5.84647i 0.339819i
\(297\) 0 0
\(298\) 10.7021 0.619958
\(299\) 1.72359 2.98534i 0.0996777 0.172647i
\(300\) 0 0
\(301\) 0 0
\(302\) 13.8575 8.00065i 0.797411 0.460386i
\(303\) 0 0
\(304\) −7.12643 4.11444i −0.408729 0.235980i
\(305\) 16.6613i 0.954021i
\(306\) 0 0
\(307\) 1.28155i 0.0731422i −0.999331 0.0365711i \(-0.988356\pi\)
0.999331 0.0365711i \(-0.0116435\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 10.6315 + 18.4142i 0.603826 + 1.04586i
\(311\) −6.26643 10.8538i −0.355336 0.615461i 0.631839 0.775100i \(-0.282300\pi\)
−0.987175 + 0.159639i \(0.948967\pi\)
\(312\) 0 0
\(313\) −7.58105 4.37692i −0.428507 0.247398i 0.270204 0.962803i \(-0.412909\pi\)
−0.698710 + 0.715405i \(0.746242\pi\)
\(314\) −11.5267 −0.650488
\(315\) 0 0
\(316\) −0.924134 −0.0519866
\(317\) 11.8458 + 6.83920i 0.665329 + 0.384128i 0.794304 0.607520i \(-0.207836\pi\)
−0.128976 + 0.991648i \(0.541169\pi\)
\(318\) 0 0
\(319\) 6.46195 + 11.1924i 0.361799 + 0.626655i
\(320\) −1.77612 3.07634i −0.0992884 0.171973i
\(321\) 0 0
\(322\) 0 0
\(323\) 13.3177i 0.741017i
\(324\) 0 0
\(325\) 7.82009i 0.433781i
\(326\) 2.37960 + 1.37386i 0.131794 + 0.0760912i
\(327\) 0 0
\(328\) 0.0817920 0.0472226i 0.00451621 0.00260743i
\(329\) 0 0
\(330\) 0 0
\(331\) 5.44858 9.43721i 0.299481 0.518716i −0.676536 0.736409i \(-0.736520\pi\)
0.976017 + 0.217693i \(0.0698532\pi\)
\(332\) 10.8642 0.596250
\(333\) 0 0
\(334\) 5.53892i 0.303076i
\(335\) −0.667247 + 1.15570i −0.0364556 + 0.0631429i
\(336\) 0 0
\(337\) 12.8090 + 22.1858i 0.697749 + 1.20854i 0.969245 + 0.246098i \(0.0791484\pi\)
−0.271496 + 0.962440i \(0.587518\pi\)
\(338\) 10.3459 5.97319i 0.562741 0.324898i
\(339\) 0 0
\(340\) −2.87450 + 4.97877i −0.155891 + 0.270012i
\(341\) −18.0912 −0.979692
\(342\) 0 0
\(343\) 0 0
\(344\) −5.29833 3.05899i −0.285667 0.164930i
\(345\) 0 0
\(346\) 9.70387 5.60253i 0.521683 0.301194i
\(347\) 14.5166 8.38116i 0.779291 0.449924i −0.0568878 0.998381i \(-0.518118\pi\)
0.836179 + 0.548457i \(0.184784\pi\)
\(348\) 0 0
\(349\) −14.4455 8.34010i −0.773249 0.446435i 0.0607835 0.998151i \(-0.480640\pi\)
−0.834032 + 0.551716i \(0.813973\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 3.02237 0.161093
\(353\) −17.9568 + 31.1021i −0.955746 + 1.65540i −0.223093 + 0.974797i \(0.571615\pi\)
−0.732653 + 0.680603i \(0.761718\pi\)
\(354\) 0 0
\(355\) 43.0282 24.8424i 2.28370 1.31850i
\(356\) 2.35495 + 4.07888i 0.124812 + 0.216180i
\(357\) 0 0
\(358\) −1.37089 + 2.37445i −0.0724538 + 0.125494i
\(359\) 28.5498i 1.50680i −0.657563 0.753399i \(-0.728413\pi\)
0.657563 0.753399i \(-0.271587\pi\)
\(360\) 0 0
\(361\) −48.7146 −2.56393
\(362\) 11.1449 19.3036i 0.585765 1.01457i
\(363\) 0 0
\(364\) 0 0
\(365\) −4.03342 + 2.32870i −0.211119 + 0.121890i
\(366\) 0 0
\(367\) 0.310665 + 0.179362i 0.0162166 + 0.00936264i 0.508086 0.861306i \(-0.330353\pi\)
−0.491870 + 0.870669i \(0.663686\pi\)
\(368\) 3.35830i 0.175063i
\(369\) 0 0
\(370\) 20.7681i 1.07968i
\(371\) 0 0
\(372\) 0 0
\(373\) −12.6854 21.9718i −0.656826 1.13766i −0.981433 0.191807i \(-0.938565\pi\)
0.324606 0.945849i \(-0.394768\pi\)
\(374\) −2.44571 4.23610i −0.126465 0.219044i
\(375\) 0 0
\(376\) −4.45176 2.57023i −0.229582 0.132549i
\(377\) 4.38924 0.226057
\(378\) 0 0
\(379\) 26.9063 1.38209 0.691043 0.722814i \(-0.257152\pi\)
0.691043 + 0.722814i \(0.257152\pi\)
\(380\) −25.3148 14.6155i −1.29862 0.749761i
\(381\) 0 0
\(382\) −2.56632 4.44499i −0.131304 0.227426i
\(383\) −6.28586 10.8874i −0.321192 0.556322i 0.659542 0.751668i \(-0.270750\pi\)
−0.980734 + 0.195346i \(0.937417\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 15.9847i 0.813600i
\(387\) 0 0
\(388\) 15.3956i 0.781595i
\(389\) −14.0805 8.12937i −0.713909 0.412175i 0.0985980 0.995127i \(-0.468564\pi\)
−0.812507 + 0.582952i \(0.801898\pi\)
\(390\) 0 0
\(391\) 4.70694 2.71755i 0.238040 0.137432i
\(392\) 0 0
\(393\) 0 0
\(394\) 2.36286 4.09259i 0.119039 0.206182i
\(395\) −3.28275 −0.165173
\(396\) 0 0
\(397\) 14.6938i 0.737463i 0.929536 + 0.368732i \(0.120208\pi\)
−0.929536 + 0.368732i \(0.879792\pi\)
\(398\) 1.06047 1.83679i 0.0531567 0.0920701i
\(399\) 0 0
\(400\) −3.80924 6.59779i −0.190462 0.329890i
\(401\) 14.4162 8.32318i 0.719909 0.415640i −0.0948099 0.995495i \(-0.530224\pi\)
0.814719 + 0.579855i \(0.196891\pi\)
\(402\) 0 0
\(403\) −3.07208 + 5.32101i −0.153031 + 0.265058i
\(404\) −13.7047 −0.681833
\(405\) 0 0
\(406\) 0 0
\(407\) −15.3028 8.83510i −0.758534 0.437940i
\(408\) 0 0
\(409\) 2.43254 1.40443i 0.120282 0.0694446i −0.438652 0.898657i \(-0.644544\pi\)
0.558934 + 0.829212i \(0.311211\pi\)
\(410\) 0.290545 0.167747i 0.0143490 0.00828441i
\(411\) 0 0
\(412\) 2.64014 + 1.52429i 0.130070 + 0.0750962i
\(413\) 0 0
\(414\) 0 0
\(415\) 38.5923 1.89442
\(416\) 0.513232 0.888944i 0.0251633 0.0435841i
\(417\) 0 0
\(418\) 21.5387 12.4354i 1.05349 0.608234i
\(419\) 7.47362 + 12.9447i 0.365110 + 0.632390i 0.988794 0.149287i \(-0.0476980\pi\)
−0.623684 + 0.781677i \(0.714365\pi\)
\(420\) 0 0
\(421\) −7.80336 + 13.5158i −0.380312 + 0.658720i −0.991107 0.133069i \(-0.957517\pi\)
0.610794 + 0.791789i \(0.290850\pi\)
\(422\) 27.6159i 1.34432i
\(423\) 0 0
\(424\) −3.18968 −0.154905
\(425\) −6.16490 + 10.6779i −0.299042 + 0.517955i
\(426\) 0 0
\(427\) 0 0
\(428\) −11.3681 + 6.56336i −0.549496 + 0.317252i
\(429\) 0 0
\(430\) −18.8210 10.8663i −0.907629 0.524020i
\(431\) 16.1758i 0.779163i −0.920992 0.389581i \(-0.872620\pi\)
0.920992 0.389581i \(-0.127380\pi\)
\(432\) 0 0
\(433\) 27.2499i 1.30955i −0.755824 0.654774i \(-0.772764\pi\)
0.755824 0.654774i \(-0.227236\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −5.28574 9.15516i −0.253141 0.438453i
\(437\) 13.8175 + 23.9327i 0.660983 + 1.14486i
\(438\) 0 0
\(439\) −28.6955 16.5674i −1.36956 0.790717i −0.378690 0.925523i \(-0.623625\pi\)
−0.990872 + 0.134806i \(0.956959\pi\)
\(440\) 10.7362 0.511829
\(441\) 0 0
\(442\) −1.66124 −0.0790171
\(443\) 19.2808 + 11.1318i 0.916060 + 0.528887i 0.882376 0.470545i \(-0.155943\pi\)
0.0336837 + 0.999433i \(0.489276\pi\)
\(444\) 0 0
\(445\) 8.36535 + 14.4892i 0.396556 + 0.686855i
\(446\) −10.1734 17.6209i −0.481727 0.834375i
\(447\) 0 0
\(448\) 0 0
\(449\) 6.80819i 0.321298i −0.987012 0.160649i \(-0.948641\pi\)
0.987012 0.160649i \(-0.0513588\pi\)
\(450\) 0 0
\(451\) 0.285448i 0.0134412i
\(452\) −10.6520 6.14993i −0.501027 0.289268i
\(453\) 0 0
\(454\) 3.60266 2.08000i 0.169081 0.0976192i
\(455\) 0 0
\(456\) 0 0
\(457\) −7.61298 + 13.1861i −0.356120 + 0.616818i −0.987309 0.158811i \(-0.949234\pi\)
0.631189 + 0.775629i \(0.282567\pi\)
\(458\) 5.96964 0.278943
\(459\) 0 0
\(460\) 11.9295i 0.556217i
\(461\) 0.103381 0.179060i 0.00481492 0.00833968i −0.863608 0.504164i \(-0.831801\pi\)
0.868423 + 0.495824i \(0.165134\pi\)
\(462\) 0 0
\(463\) −7.60217 13.1673i −0.353303 0.611938i 0.633523 0.773724i \(-0.281608\pi\)
−0.986826 + 0.161785i \(0.948275\pi\)
\(464\) −3.70319 + 2.13804i −0.171916 + 0.0992560i
\(465\) 0 0
\(466\) 2.24360 3.88603i 0.103933 0.180017i
\(467\) −2.30849 −0.106824 −0.0534120 0.998573i \(-0.517010\pi\)
−0.0534120 + 0.998573i \(0.517010\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −15.8138 9.13009i −0.729435 0.421139i
\(471\) 0 0
\(472\) 7.65628 4.42036i 0.352409 0.203463i
\(473\) 16.0135 9.24541i 0.736303 0.425105i
\(474\) 0 0
\(475\) −54.2925 31.3458i −2.49111 1.43824i
\(476\) 0 0
\(477\) 0 0
\(478\) −3.49809 −0.159999
\(479\) 6.21659 10.7674i 0.284043 0.491977i −0.688334 0.725394i \(-0.741657\pi\)
0.972377 + 0.233417i \(0.0749908\pi\)
\(480\) 0 0
\(481\) −5.19719 + 3.00060i −0.236971 + 0.136815i
\(482\) −5.78332 10.0170i −0.263423 0.456262i
\(483\) 0 0
\(484\) 0.932639 1.61538i 0.0423927 0.0734263i
\(485\) 54.6891i 2.48331i
\(486\) 0 0
\(487\) 37.3007 1.69026 0.845128 0.534565i \(-0.179524\pi\)
0.845128 + 0.534565i \(0.179524\pi\)
\(488\) 2.34517 4.06195i 0.106161 0.183876i
\(489\) 0 0
\(490\) 0 0
\(491\) 11.8191 6.82377i 0.533389 0.307952i −0.209006 0.977914i \(-0.567023\pi\)
0.742396 + 0.669962i \(0.233690\pi\)
\(492\) 0 0
\(493\) 5.99328 + 3.46022i 0.269924 + 0.155840i
\(494\) 8.44666i 0.380033i
\(495\) 0 0
\(496\) 5.98576i 0.268768i
\(497\) 0 0
\(498\) 0 0
\(499\) 10.5010 + 18.1882i 0.470088 + 0.814216i 0.999415 0.0342021i \(-0.0108890\pi\)
−0.529327 + 0.848418i \(0.677556\pi\)
\(500\) −4.65074 8.05532i −0.207987 0.360245i
\(501\) 0 0
\(502\) −23.1598 13.3713i −1.03367 0.596790i
\(503\) −22.3018 −0.994388 −0.497194 0.867639i \(-0.665636\pi\)
−0.497194 + 0.867639i \(0.665636\pi\)
\(504\) 0 0
\(505\) −48.6824 −2.16634
\(506\) −8.79018 5.07501i −0.390771 0.225612i
\(507\) 0 0
\(508\) 0.143582 + 0.248691i 0.00637042 + 0.0110339i
\(509\) −10.9589 18.9814i −0.485746 0.841337i 0.514120 0.857719i \(-0.328119\pi\)
−0.999866 + 0.0163813i \(0.994785\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 5.21227i 0.229904i
\(515\) 9.37844 + 5.41465i 0.413264 + 0.238598i
\(516\) 0 0
\(517\) 13.4549 7.76818i 0.591745 0.341644i
\(518\) 0 0
\(519\) 0 0
\(520\) 1.82313 3.15775i 0.0799495 0.138477i
\(521\) −26.7678 −1.17272 −0.586358 0.810052i \(-0.699439\pi\)
−0.586358 + 0.810052i \(0.699439\pi\)
\(522\) 0 0
\(523\) 17.1561i 0.750184i −0.926988 0.375092i \(-0.877611\pi\)
0.926988 0.375092i \(-0.122389\pi\)
\(524\) −0.186474 + 0.322983i −0.00814617 + 0.0141096i
\(525\) 0 0
\(526\) 7.51869 + 13.0228i 0.327831 + 0.567819i
\(527\) −8.38954 + 4.84370i −0.365454 + 0.210995i
\(528\) 0 0
\(529\) −5.86091 + 10.1514i −0.254822 + 0.441365i
\(530\) −11.3306 −0.492168
\(531\) 0 0
\(532\) 0 0
\(533\) 0.0839566 + 0.0484723i 0.00363656 + 0.00209957i
\(534\) 0 0
\(535\) −40.3822 + 23.3147i −1.74588 + 1.00798i
\(536\) 0.325345 0.187838i 0.0140527 0.00811336i
\(537\) 0 0
\(538\) −20.0323 11.5657i −0.863654 0.498631i
\(539\) 0 0
\(540\) 0 0
\(541\) 28.8182 1.23899 0.619496 0.785000i \(-0.287337\pi\)
0.619496 + 0.785000i \(0.287337\pi\)
\(542\) −4.95748 + 8.58661i −0.212942 + 0.368827i
\(543\) 0 0
\(544\) 1.40158 0.809204i 0.0600924 0.0346943i
\(545\) −18.7763 32.5214i −0.804286 1.39306i
\(546\) 0 0
\(547\) −16.4045 + 28.4135i −0.701407 + 1.21487i 0.266565 + 0.963817i \(0.414111\pi\)
−0.967972 + 0.251056i \(0.919222\pi\)
\(548\) 7.06222i 0.301683i
\(549\) 0 0
\(550\) 23.0259 0.981826
\(551\) −17.5937 + 30.4732i −0.749516 + 1.29820i
\(552\) 0 0
\(553\) 0 0
\(554\) −7.44299 + 4.29721i −0.316223 + 0.182571i
\(555\) 0 0
\(556\) 12.6320 + 7.29308i 0.535715 + 0.309295i
\(557\) 46.2508i 1.95971i −0.199708 0.979855i \(-0.563999\pi\)
0.199708 0.979855i \(-0.436001\pi\)
\(558\) 0 0
\(559\) 6.27990i 0.265611i
\(560\) 0 0
\(561\) 0 0
\(562\) −10.3639 17.9508i −0.437174 0.757208i
\(563\) −0.988637 1.71237i −0.0416661 0.0721678i 0.844440 0.535650i \(-0.179933\pi\)
−0.886106 + 0.463482i \(0.846600\pi\)
\(564\) 0 0
\(565\) −37.8385 21.8461i −1.59188 0.919071i
\(566\) −2.36710 −0.0994966
\(567\) 0 0
\(568\) −13.9868 −0.586874
\(569\) −28.5702 16.4950i −1.19773 0.691508i −0.237679 0.971344i \(-0.576387\pi\)
−0.960048 + 0.279836i \(0.909720\pi\)
\(570\) 0 0
\(571\) −7.40326 12.8228i −0.309817 0.536618i 0.668505 0.743707i \(-0.266934\pi\)
−0.978322 + 0.207089i \(0.933601\pi\)
\(572\) 1.55118 + 2.68672i 0.0648580 + 0.112337i
\(573\) 0 0
\(574\) 0 0
\(575\) 25.5851i 1.06697i
\(576\) 0 0
\(577\) 18.4180i 0.766752i −0.923592 0.383376i \(-0.874761\pi\)
0.923592 0.383376i \(-0.125239\pi\)
\(578\) 12.4541 + 7.19038i 0.518022 + 0.299080i
\(579\) 0 0
\(580\) −13.1547 + 7.59485i −0.546218 + 0.315359i
\(581\) 0 0
\(582\) 0 0
\(583\) 4.82020 8.34884i 0.199632 0.345774i
\(584\) 1.31111 0.0542542
\(585\) 0 0
\(586\) 17.6755i 0.730167i
\(587\) 23.1065 40.0216i 0.953707 1.65187i 0.216406 0.976304i \(-0.430567\pi\)
0.737301 0.675565i \(-0.236100\pi\)
\(588\) 0 0
\(589\) −24.6281 42.6571i −1.01478 1.75765i
\(590\) 27.1970 15.7022i 1.11968 0.646450i
\(591\) 0 0
\(592\) 2.92323 5.06319i 0.120144 0.208096i
\(593\) −13.6093 −0.558867 −0.279434 0.960165i \(-0.590147\pi\)
−0.279434 + 0.960165i \(0.590147\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −9.26832 5.35107i −0.379645 0.219188i
\(597\) 0 0
\(598\) −2.98534 + 1.72359i −0.122080 + 0.0704827i
\(599\) 20.4214 11.7903i 0.834396 0.481739i −0.0209595 0.999780i \(-0.506672\pi\)
0.855355 + 0.518042i \(0.173339\pi\)
\(600\) 0 0
\(601\) 31.0765 + 17.9420i 1.26764 + 0.731871i 0.974540 0.224212i \(-0.0719808\pi\)
0.293097 + 0.956083i \(0.405314\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −16.0013 −0.651084
\(605\) 3.31297 5.73823i 0.134691 0.233292i
\(606\) 0 0
\(607\) −16.8502 + 9.72845i −0.683928 + 0.394866i −0.801333 0.598218i \(-0.795876\pi\)
0.117406 + 0.993084i \(0.462542\pi\)
\(608\) 4.11444 + 7.12643i 0.166863 + 0.289015i
\(609\) 0 0
\(610\) 8.33063 14.4291i 0.337297 0.584216i
\(611\) 5.27649i 0.213464i
\(612\) 0 0
\(613\) 42.2421 1.70614 0.853071 0.521795i \(-0.174738\pi\)
0.853071 + 0.521795i \(0.174738\pi\)
\(614\) −0.640777 + 1.10986i −0.0258597 + 0.0447902i
\(615\) 0 0
\(616\) 0 0
\(617\) −9.63660 + 5.56369i −0.387955 + 0.223986i −0.681274 0.732029i \(-0.738574\pi\)
0.293319 + 0.956015i \(0.405240\pi\)
\(618\) 0 0
\(619\) 8.71387 + 5.03096i 0.350240 + 0.202211i 0.664791 0.747029i \(-0.268521\pi\)
−0.314551 + 0.949241i \(0.601854\pi\)
\(620\) 21.2629i 0.853939i
\(621\) 0 0
\(622\) 12.5329i 0.502522i
\(623\) 0 0
\(624\) 0 0
\(625\) 2.52560 + 4.37447i 0.101024 + 0.174979i
\(626\) 4.37692 + 7.58105i 0.174937 + 0.303000i
\(627\) 0 0
\(628\) 9.98239 + 5.76334i 0.398341 + 0.229982i
\(629\) −9.46198 −0.377274
\(630\) 0 0
\(631\) 10.3528 0.412139 0.206070 0.978537i \(-0.433933\pi\)
0.206070 + 0.978537i \(0.433933\pi\)
\(632\) 0.800324 + 0.462067i 0.0318352 + 0.0183800i
\(633\) 0 0
\(634\) −6.83920 11.8458i −0.271619 0.470459i
\(635\) 0.510039 + 0.883413i 0.0202403 + 0.0350572i
\(636\) 0 0
\(637\) 0 0
\(638\) 12.9239i 0.511662i
\(639\) 0 0
\(640\) 3.55225i 0.140415i
\(641\) −23.0678 13.3182i −0.911123 0.526037i −0.0303310 0.999540i \(-0.509656\pi\)
−0.880792 + 0.473503i \(0.842989\pi\)
\(642\) 0 0
\(643\) −40.0493 + 23.1225i −1.57939 + 0.911861i −0.584446 + 0.811433i \(0.698688\pi\)
−0.994944 + 0.100429i \(0.967979\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.65885 11.5335i 0.261989 0.453778i
\(647\) 31.4063 1.23471 0.617355 0.786684i \(-0.288204\pi\)
0.617355 + 0.786684i \(0.288204\pi\)
\(648\) 0 0
\(649\) 26.7199i 1.04885i
\(650\) 3.91005 6.77240i 0.153365 0.265635i
\(651\) 0 0
\(652\) −1.37386 2.37960i −0.0538046 0.0931923i
\(653\) 39.9639 23.0732i 1.56391 0.902924i 0.567054 0.823681i \(-0.308083\pi\)
0.996855 0.0792429i \(-0.0252503\pi\)
\(654\) 0 0
\(655\) −0.662404 + 1.14732i −0.0258823 + 0.0448294i
\(656\) −0.0944452 −0.00368747
\(657\) 0 0
\(658\) 0 0
\(659\) −1.18052 0.681575i −0.0459867 0.0265504i 0.476830 0.878995i \(-0.341786\pi\)
−0.522817 + 0.852445i \(0.675119\pi\)
\(660\) 0 0
\(661\) −6.23888 + 3.60202i −0.242664 + 0.140102i −0.616401 0.787433i \(-0.711410\pi\)
0.373736 + 0.927535i \(0.378076\pi\)
\(662\) −9.43721 + 5.44858i −0.366788 + 0.211765i
\(663\) 0 0
\(664\) −9.40866 5.43209i −0.365127 0.210806i
\(665\) 0 0
\(666\) 0 0
\(667\) 14.3604 0.556035
\(668\) 2.76946 4.79685i 0.107154 0.185596i
\(669\) 0 0
\(670\) 1.15570 0.667247i 0.0446488 0.0257780i
\(671\) 7.08797 + 12.2767i 0.273628 + 0.473938i
\(672\) 0 0
\(673\) 19.4709 33.7246i 0.750548 1.29999i −0.197010 0.980402i \(-0.563123\pi\)
0.947558 0.319585i \(-0.103544\pi\)
\(674\) 25.6180i 0.986767i
\(675\) 0 0
\(676\) −11.9464 −0.459476
\(677\) −1.20505 + 2.08722i −0.0463140 + 0.0802182i −0.888253 0.459354i \(-0.848081\pi\)
0.841939 + 0.539573i \(0.181414\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 4.97877 2.87450i 0.190927 0.110232i
\(681\) 0 0
\(682\) 15.6674 + 9.04559i 0.599937 + 0.346374i
\(683\) 28.3251i 1.08383i 0.840433 + 0.541915i \(0.182300\pi\)
−0.840433 + 0.541915i \(0.817700\pi\)
\(684\) 0 0
\(685\) 25.0868i 0.958517i
\(686\) 0 0
\(687\) 0 0
\(688\) 3.05899 + 5.29833i 0.116623 + 0.201997i
\(689\) −1.63705 2.83545i −0.0623666 0.108022i
\(690\) 0 0
\(691\) 2.95334 + 1.70511i 0.112350 + 0.0648655i 0.555122 0.831769i \(-0.312672\pi\)
−0.442772 + 0.896634i \(0.646005\pi\)
\(692\) −11.2051 −0.425953
\(693\) 0 0
\(694\) −16.7623 −0.636289
\(695\) 44.8719 + 25.9068i 1.70209 + 0.982702i
\(696\) 0 0
\(697\) 0.0764255 + 0.132373i 0.00289482 + 0.00501398i
\(698\) 8.34010 + 14.4455i 0.315678 + 0.546769i
\(699\) 0 0
\(700\) 0 0
\(701\) 51.4943i 1.94491i −0.233087 0.972456i \(-0.574883\pi\)
0.233087 0.972456i \(-0.425117\pi\)
\(702\) 0 0
\(703\) 48.1099i 1.81450i
\(704\) −2.61745 1.51119i −0.0986488 0.0569549i
\(705\) 0 0
\(706\) 31.1021 17.9568i 1.17054 0.675814i
\(707\) 0 0
\(708\) 0 0
\(709\) −5.04218 + 8.73331i −0.189363 + 0.327986i −0.945038 0.326960i \(-0.893976\pi\)
0.755675 + 0.654947i \(0.227309\pi\)
\(710\) −49.6847 −1.86463
\(711\) 0 0
\(712\) 4.70989i 0.176511i
\(713\) −10.0510 + 17.4088i −0.376412 + 0.651965i
\(714\) 0 0
\(715\) 5.51017 + 9.54389i 0.206069 + 0.356921i
\(716\) 2.37445 1.37089i 0.0887375 0.0512326i
\(717\) 0 0
\(718\) −14.2749 + 24.7248i −0.532734 + 0.922722i
\(719\) 31.9168 1.19030 0.595148 0.803616i \(-0.297093\pi\)
0.595148 + 0.803616i \(0.297093\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 42.1881 + 24.3573i 1.57008 + 0.906485i
\(723\) 0 0
\(724\) −19.3036 + 11.1449i −0.717413 + 0.414198i
\(725\) −28.2127 + 16.2886i −1.04779 + 0.604943i
\(726\) 0 0
\(727\) 17.9336 + 10.3540i 0.665120 + 0.384007i 0.794225 0.607624i \(-0.207877\pi\)
−0.129105 + 0.991631i \(0.541210\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 4.65739 0.172378
\(731\) 4.95070 8.57487i 0.183108 0.317153i
\(732\) 0 0
\(733\) 7.69996 4.44558i 0.284405 0.164201i −0.351011 0.936371i \(-0.614162\pi\)
0.635416 + 0.772170i \(0.280829\pi\)
\(734\) −0.179362 0.310665i −0.00662038 0.0114668i
\(735\) 0 0
\(736\) 1.67915 2.90837i 0.0618943 0.107204i
\(737\) 1.13543i 0.0418241i
\(738\) 0 0
\(739\) 32.7763 1.20570 0.602848 0.797856i \(-0.294032\pi\)
0.602848 + 0.797856i \(0.294032\pi\)
\(740\) 10.3841 17.9857i 0.381726 0.661168i
\(741\) 0 0
\(742\) 0 0
\(743\) 6.68055 3.85702i 0.245086 0.141500i −0.372426 0.928062i \(-0.621474\pi\)
0.617512 + 0.786562i \(0.288141\pi\)
\(744\) 0 0
\(745\) −32.9234 19.0083i −1.20622 0.696411i
\(746\) 25.3708i 0.928893i
\(747\) 0 0
\(748\) 4.89143i 0.178848i
\(749\) 0 0
\(750\) 0 0
\(751\) −15.3804 26.6397i −0.561239 0.972095i −0.997389 0.0722207i \(-0.976991\pi\)
0.436149 0.899874i \(-0.356342\pi\)
\(752\) 2.57023 + 4.45176i 0.0937265 + 0.162339i
\(753\) 0 0
\(754\) −3.80120 2.19462i −0.138431 0.0799234i
\(755\) −56.8406 −2.06864
\(756\) 0 0
\(757\) 46.4611 1.68866 0.844328 0.535827i \(-0.180000\pi\)
0.844328 + 0.535827i \(0.180000\pi\)
\(758\) −23.3016 13.4532i −0.846351 0.488641i
\(759\) 0 0
\(760\) 14.6155 + 25.3148i 0.530161 + 0.918266i
\(761\) −18.5959 32.2090i −0.674099 1.16757i −0.976731 0.214467i \(-0.931199\pi\)
0.302632 0.953107i \(-0.402135\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 5.13264i 0.185692i
\(765\) 0 0
\(766\) 12.5717i 0.454235i
\(767\) 7.85890 + 4.53734i 0.283768 + 0.163834i
\(768\) 0 0
\(769\) 12.2312 7.06166i 0.441067 0.254650i −0.262983 0.964800i \(-0.584706\pi\)
0.704050 + 0.710150i \(0.251373\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 7.99235 13.8432i 0.287651 0.498226i
\(773\) −30.9455 −1.11303 −0.556517 0.830836i \(-0.687862\pi\)
−0.556517 + 0.830836i \(0.687862\pi\)
\(774\) 0 0
\(775\) 45.6024i 1.63809i
\(776\) −7.69782 + 13.3330i −0.276336 + 0.478627i
\(777\) 0 0
\(778\) 8.12937 + 14.0805i 0.291452 + 0.504810i
\(779\) −0.673057 + 0.388590i −0.0241148 + 0.0139227i
\(780\) 0 0
\(781\) 21.1367 36.6098i 0.756330 1.31000i
\(782\) −5.43510 −0.194359
\(783\) 0 0
\(784\) 0 0
\(785\) 35.4599 + 20.4728i 1.26562 + 0.730706i
\(786\) 0 0
\(787\) 15.8704 9.16280i 0.565720 0.326619i −0.189718 0.981839i \(-0.560757\pi\)
0.755438 + 0.655220i \(0.227424\pi\)
\(788\) −4.09259 + 2.36286i −0.145793 + 0.0841734i
\(789\) 0 0
\(790\) 2.84295 + 1.64138i 0.101148 + 0.0583976i
\(791\) 0 0
\(792\) 0 0
\(793\) 4.81447 0.170967