Properties

Label 1008.2.r.l.337.4
Level $1008$
Weight $2$
Character 1008.337
Analytic conductor $8.049$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.2091141441.1
Defining polynomial: \(x^{8} - x^{7} + x^{6} + 3 x^{5} - 15 x^{4} + 9 x^{3} + 9 x^{2} - 27 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 337.4
Root \(0.335492 - 1.69925i\) of defining polynomial
Character \(\chi\) \(=\) 1008.337
Dual form 1008.2.r.l.673.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.30385 + 1.14017i) q^{3} +(-0.164508 + 0.284936i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(0.400030 + 2.97321i) q^{9} +O(q^{10})\) \(q+(1.30385 + 1.14017i) q^{3} +(-0.164508 + 0.284936i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(0.400030 + 2.97321i) q^{9} +(-0.664508 - 1.15096i) q^{11} +(-1.53937 + 2.66626i) q^{13} +(-0.539368 + 0.183946i) q^{15} +7.35741 q^{17} +2.93671 q^{19} +(0.335492 - 1.69925i) q^{21} +(-3.34321 + 5.79062i) q^{23} +(2.44587 + 4.23638i) q^{25} +(-2.86838 + 4.33271i) q^{27} +(3.88258 + 6.72483i) q^{29} +(-1.63555 + 2.83286i) q^{31} +(0.445874 - 2.25833i) q^{33} +0.329016 q^{35} +0.329016 q^{37} +(-5.04709 + 1.72126i) q^{39} +(-0.135552 + 0.234783i) q^{41} +(-5.48255 - 9.49606i) q^{43} +(-0.912983 - 0.375134i) q^{45} +(0.571014 + 0.989025i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(9.59293 + 8.38869i) q^{51} +6.42828 q^{53} +0.437267 q^{55} +(3.82902 + 3.34834i) q^{57} +(0.372170 - 0.644618i) q^{59} +(-4.42195 - 7.65904i) q^{61} +(2.37486 - 1.83304i) q^{63} +(-0.506476 - 0.877243i) q^{65} +(4.28640 - 7.42426i) q^{67} +(-10.9613 + 3.73825i) q^{69} -1.60769 q^{71} -13.4941 q^{73} +(-1.64114 + 8.31230i) q^{75} +(-0.664508 + 1.15096i) q^{77} +(-0.628926 - 1.08933i) q^{79} +(-8.67995 + 2.37875i) q^{81} +(-0.0316459 - 0.0548124i) q^{83} +(-1.21035 + 2.09639i) q^{85} +(-2.60515 + 13.1949i) q^{87} +11.3071 q^{89} +3.07874 q^{91} +(-5.36245 + 1.82881i) q^{93} +(-0.483112 + 0.836774i) q^{95} +(5.51420 + 9.55087i) q^{97} +(3.15623 - 2.43614i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{3} - 3q^{5} - 4q^{7} - q^{9} + O(q^{10}) \) \( 8q + q^{3} - 3q^{5} - 4q^{7} - q^{9} - 7q^{11} + 3q^{13} + 11q^{15} + 6q^{17} + 8q^{19} + q^{21} - 2q^{23} - 5q^{25} - 11q^{27} - 9q^{29} - 3q^{31} - 21q^{33} + 6q^{35} + 6q^{37} - 2q^{39} + 9q^{41} - 8q^{43} + 7q^{45} - 3q^{47} - 4q^{49} + 18q^{51} + 12q^{53} + 56q^{55} + 34q^{57} - 10q^{59} + 20q^{61} + 2q^{63} + q^{65} - 11q^{67} - 17q^{69} + 6q^{71} - 48q^{73} - 52q^{75} - 7q^{77} - 21q^{79} - 25q^{81} - 8q^{83} + 9q^{85} + 15q^{87} + 12q^{89} - 6q^{91} + 29q^{93} - 36q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) 1.30385 + 1.14017i 0.752776 + 0.658277i
\(4\) 0 0
\(5\) −0.164508 + 0.284936i −0.0735702 + 0.127427i −0.900464 0.434931i \(-0.856773\pi\)
0.826893 + 0.562359i \(0.190106\pi\)
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) 0 0
\(9\) 0.400030 + 2.97321i 0.133343 + 0.991070i
\(10\) 0 0
\(11\) −0.664508 1.15096i −0.200357 0.347028i 0.748287 0.663375i \(-0.230877\pi\)
−0.948643 + 0.316348i \(0.897543\pi\)
\(12\) 0 0
\(13\) −1.53937 + 2.66626i −0.426944 + 0.739489i −0.996600 0.0823948i \(-0.973743\pi\)
0.569656 + 0.821883i \(0.307076\pi\)
\(14\) 0 0
\(15\) −0.539368 + 0.183946i −0.139264 + 0.0474946i
\(16\) 0 0
\(17\) 7.35741 1.78443 0.892217 0.451606i \(-0.149149\pi\)
0.892217 + 0.451606i \(0.149149\pi\)
\(18\) 0 0
\(19\) 2.93671 0.673727 0.336864 0.941553i \(-0.390634\pi\)
0.336864 + 0.941553i \(0.390634\pi\)
\(20\) 0 0
\(21\) 0.335492 1.69925i 0.0732104 0.370806i
\(22\) 0 0
\(23\) −3.34321 + 5.79062i −0.697108 + 1.20743i 0.272356 + 0.962196i \(0.412197\pi\)
−0.969465 + 0.245231i \(0.921136\pi\)
\(24\) 0 0
\(25\) 2.44587 + 4.23638i 0.489175 + 0.847276i
\(26\) 0 0
\(27\) −2.86838 + 4.33271i −0.552021 + 0.833830i
\(28\) 0 0
\(29\) 3.88258 + 6.72483i 0.720977 + 1.24877i 0.960608 + 0.277906i \(0.0896402\pi\)
−0.239631 + 0.970864i \(0.577026\pi\)
\(30\) 0 0
\(31\) −1.63555 + 2.83286i −0.293754 + 0.508796i −0.974694 0.223542i \(-0.928238\pi\)
0.680940 + 0.732339i \(0.261571\pi\)
\(32\) 0 0
\(33\) 0.445874 2.25833i 0.0776168 0.393124i
\(34\) 0 0
\(35\) 0.329016 0.0556138
\(36\) 0 0
\(37\) 0.329016 0.0540899 0.0270449 0.999634i \(-0.491390\pi\)
0.0270449 + 0.999634i \(0.491390\pi\)
\(38\) 0 0
\(39\) −5.04709 + 1.72126i −0.808181 + 0.275622i
\(40\) 0 0
\(41\) −0.135552 + 0.234783i −0.0211696 + 0.0366669i −0.876416 0.481555i \(-0.840072\pi\)
0.855247 + 0.518221i \(0.173406\pi\)
\(42\) 0 0
\(43\) −5.48255 9.49606i −0.836081 1.44814i −0.893147 0.449765i \(-0.851508\pi\)
0.0570654 0.998370i \(-0.481826\pi\)
\(44\) 0 0
\(45\) −0.912983 0.375134i −0.136099 0.0559216i
\(46\) 0 0
\(47\) 0.571014 + 0.989025i 0.0832910 + 0.144264i 0.904662 0.426131i \(-0.140124\pi\)
−0.821371 + 0.570395i \(0.806790\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0 0
\(51\) 9.59293 + 8.38869i 1.34328 + 1.17465i
\(52\) 0 0
\(53\) 6.42828 0.882992 0.441496 0.897263i \(-0.354448\pi\)
0.441496 + 0.897263i \(0.354448\pi\)
\(54\) 0 0
\(55\) 0.437267 0.0589611
\(56\) 0 0
\(57\) 3.82902 + 3.34834i 0.507166 + 0.443499i
\(58\) 0 0
\(59\) 0.372170 0.644618i 0.0484525 0.0839221i −0.840782 0.541374i \(-0.817904\pi\)
0.889234 + 0.457452i \(0.151238\pi\)
\(60\) 0 0
\(61\) −4.42195 7.65904i −0.566173 0.980640i −0.996940 0.0781767i \(-0.975090\pi\)
0.430767 0.902463i \(-0.358243\pi\)
\(62\) 0 0
\(63\) 2.37486 1.83304i 0.299204 0.230941i
\(64\) 0 0
\(65\) −0.506476 0.877243i −0.0628207 0.108809i
\(66\) 0 0
\(67\) 4.28640 7.42426i 0.523667 0.907018i −0.475954 0.879470i \(-0.657897\pi\)
0.999620 0.0275474i \(-0.00876971\pi\)
\(68\) 0 0
\(69\) −10.9613 + 3.73825i −1.31959 + 0.450032i
\(70\) 0 0
\(71\) −1.60769 −0.190798 −0.0953990 0.995439i \(-0.530413\pi\)
−0.0953990 + 0.995439i \(0.530413\pi\)
\(72\) 0 0
\(73\) −13.4941 −1.57936 −0.789680 0.613519i \(-0.789754\pi\)
−0.789680 + 0.613519i \(0.789754\pi\)
\(74\) 0 0
\(75\) −1.64114 + 8.31230i −0.189503 + 0.959821i
\(76\) 0 0
\(77\) −0.664508 + 1.15096i −0.0757277 + 0.131164i
\(78\) 0 0
\(79\) −0.628926 1.08933i −0.0707597 0.122559i 0.828475 0.560026i \(-0.189209\pi\)
−0.899234 + 0.437467i \(0.855876\pi\)
\(80\) 0 0
\(81\) −8.67995 + 2.37875i −0.964439 + 0.264305i
\(82\) 0 0
\(83\) −0.0316459 0.0548124i −0.00347359 0.00601644i 0.864283 0.503005i \(-0.167772\pi\)
−0.867757 + 0.496989i \(0.834439\pi\)
\(84\) 0 0
\(85\) −1.21035 + 2.09639i −0.131281 + 0.227386i
\(86\) 0 0
\(87\) −2.60515 + 13.1949i −0.279302 + 1.41465i
\(88\) 0 0
\(89\) 11.3071 1.19855 0.599274 0.800544i \(-0.295456\pi\)
0.599274 + 0.800544i \(0.295456\pi\)
\(90\) 0 0
\(91\) 3.07874 0.322739
\(92\) 0 0
\(93\) −5.36245 + 1.82881i −0.556060 + 0.189638i
\(94\) 0 0
\(95\) −0.483112 + 0.836774i −0.0495662 + 0.0858512i
\(96\) 0 0
\(97\) 5.51420 + 9.55087i 0.559882 + 0.969744i 0.997506 + 0.0705859i \(0.0224869\pi\)
−0.437624 + 0.899158i \(0.644180\pi\)
\(98\) 0 0
\(99\) 3.15623 2.43614i 0.317213 0.244841i
\(100\) 0 0
\(101\) −7.12079 12.3336i −0.708546 1.22724i −0.965397 0.260786i \(-0.916018\pi\)
0.256851 0.966451i \(-0.417315\pi\)
\(102\) 0 0
\(103\) 5.29288 9.16753i 0.521522 0.903303i −0.478164 0.878270i \(-0.658698\pi\)
0.999687 0.0250330i \(-0.00796907\pi\)
\(104\) 0 0
\(105\) 0.428986 + 0.375134i 0.0418647 + 0.0366093i
\(106\) 0 0
\(107\) 15.5574 1.50399 0.751993 0.659171i \(-0.229093\pi\)
0.751993 + 0.659171i \(0.229093\pi\)
\(108\) 0 0
\(109\) −14.3574 −1.37519 −0.687595 0.726094i \(-0.741334\pi\)
−0.687595 + 0.726094i \(0.741334\pi\)
\(110\) 0 0
\(111\) 0.428986 + 0.375134i 0.0407175 + 0.0356061i
\(112\) 0 0
\(113\) 1.94966 3.37691i 0.183409 0.317673i −0.759630 0.650355i \(-0.774620\pi\)
0.943039 + 0.332682i \(0.107954\pi\)
\(114\) 0 0
\(115\) −1.09997 1.90520i −0.102573 0.177661i
\(116\) 0 0
\(117\) −8.54315 3.51028i −0.789815 0.324525i
\(118\) 0 0
\(119\) −3.67871 6.37171i −0.337226 0.584093i
\(120\) 0 0
\(121\) 4.61686 7.99663i 0.419714 0.726967i
\(122\) 0 0
\(123\) −0.444430 + 0.151568i −0.0400729 + 0.0136665i
\(124\) 0 0
\(125\) −3.25454 −0.291095
\(126\) 0 0
\(127\) 7.00787 0.621848 0.310924 0.950435i \(-0.399362\pi\)
0.310924 + 0.950435i \(0.399362\pi\)
\(128\) 0 0
\(129\) 3.67871 18.6324i 0.323892 1.64049i
\(130\) 0 0
\(131\) 3.33280 5.77258i 0.291188 0.504353i −0.682903 0.730509i \(-0.739283\pi\)
0.974091 + 0.226156i \(0.0726161\pi\)
\(132\) 0 0
\(133\) −1.46835 2.54326i −0.127322 0.220529i
\(134\) 0 0
\(135\) −0.762673 1.53007i −0.0656405 0.131688i
\(136\) 0 0
\(137\) 8.41926 + 14.5826i 0.719306 + 1.24587i 0.961275 + 0.275591i \(0.0888734\pi\)
−0.241969 + 0.970284i \(0.577793\pi\)
\(138\) 0 0
\(139\) −7.81032 + 13.5279i −0.662463 + 1.14742i 0.317504 + 0.948257i \(0.397155\pi\)
−0.979967 + 0.199162i \(0.936178\pi\)
\(140\) 0 0
\(141\) −0.383141 + 1.94059i −0.0322663 + 0.163427i
\(142\) 0 0
\(143\) 4.09169 0.342164
\(144\) 0 0
\(145\) −2.55486 −0.212170
\(146\) 0 0
\(147\) −1.63934 + 0.559079i −0.135210 + 0.0461121i
\(148\) 0 0
\(149\) 7.53233 13.0464i 0.617073 1.06880i −0.372944 0.927854i \(-0.621652\pi\)
0.990017 0.140948i \(-0.0450149\pi\)
\(150\) 0 0
\(151\) −3.86714 6.69808i −0.314703 0.545082i 0.664671 0.747136i \(-0.268572\pi\)
−0.979374 + 0.202054i \(0.935238\pi\)
\(152\) 0 0
\(153\) 2.94318 + 21.8751i 0.237942 + 1.76850i
\(154\) 0 0
\(155\) −0.538122 0.932055i −0.0432230 0.0748645i
\(156\) 0 0
\(157\) 4.35812 7.54849i 0.347816 0.602435i −0.638045 0.769999i \(-0.720257\pi\)
0.985861 + 0.167564i \(0.0535901\pi\)
\(158\) 0 0
\(159\) 8.38149 + 7.32932i 0.664695 + 0.581253i
\(160\) 0 0
\(161\) 6.68643 0.526964
\(162\) 0 0
\(163\) −13.4513 −1.05359 −0.526793 0.849993i \(-0.676606\pi\)
−0.526793 + 0.849993i \(0.676606\pi\)
\(164\) 0 0
\(165\) 0.570129 + 0.498558i 0.0443845 + 0.0388127i
\(166\) 0 0
\(167\) −5.81804 + 10.0771i −0.450214 + 0.779793i −0.998399 0.0565638i \(-0.981986\pi\)
0.548185 + 0.836357i \(0.315319\pi\)
\(168\) 0 0
\(169\) 1.76069 + 3.04961i 0.135438 + 0.234585i
\(170\) 0 0
\(171\) 1.17477 + 8.73145i 0.0898370 + 0.667711i
\(172\) 0 0
\(173\) −0.885831 1.53430i −0.0673485 0.116651i 0.830385 0.557190i \(-0.188121\pi\)
−0.897733 + 0.440539i \(0.854787\pi\)
\(174\) 0 0
\(175\) 2.44587 4.23638i 0.184891 0.320240i
\(176\) 0 0
\(177\) 1.22023 0.416146i 0.0917178 0.0312794i
\(178\) 0 0
\(179\) 6.73139 0.503128 0.251564 0.967841i \(-0.419055\pi\)
0.251564 + 0.967841i \(0.419055\pi\)
\(180\) 0 0
\(181\) −13.2711 −0.986433 −0.493217 0.869906i \(-0.664179\pi\)
−0.493217 + 0.869906i \(0.664179\pi\)
\(182\) 0 0
\(183\) 2.96706 15.0280i 0.219331 1.11090i
\(184\) 0 0
\(185\) −0.0541257 + 0.0937484i −0.00397940 + 0.00689252i
\(186\) 0 0
\(187\) −4.88906 8.46810i −0.357523 0.619249i
\(188\) 0 0
\(189\) 5.18643 + 0.317738i 0.377257 + 0.0231121i
\(190\) 0 0
\(191\) 10.4083 + 18.0277i 0.753117 + 1.30444i 0.946305 + 0.323276i \(0.104784\pi\)
−0.193187 + 0.981162i \(0.561883\pi\)
\(192\) 0 0
\(193\) 10.2585 17.7683i 0.738426 1.27899i −0.214778 0.976663i \(-0.568903\pi\)
0.953204 0.302328i \(-0.0977638\pi\)
\(194\) 0 0
\(195\) 0.339838 1.72126i 0.0243363 0.123262i
\(196\) 0 0
\(197\) 7.20781 0.513535 0.256768 0.966473i \(-0.417342\pi\)
0.256768 + 0.966473i \(0.417342\pi\)
\(198\) 0 0
\(199\) 14.3276 1.01566 0.507828 0.861458i \(-0.330448\pi\)
0.507828 + 0.861458i \(0.330448\pi\)
\(200\) 0 0
\(201\) 14.0537 4.79288i 0.991273 0.338063i
\(202\) 0 0
\(203\) 3.88258 6.72483i 0.272504 0.471991i
\(204\) 0 0
\(205\) −0.0445987 0.0772471i −0.00311491 0.00539517i
\(206\) 0 0
\(207\) −18.5541 7.62366i −1.28960 0.529881i
\(208\) 0 0
\(209\) −1.95147 3.38004i −0.134986 0.233802i
\(210\) 0 0
\(211\) −3.68897 + 6.38948i −0.253959 + 0.439870i −0.964612 0.263672i \(-0.915066\pi\)
0.710653 + 0.703543i \(0.248400\pi\)
\(212\) 0 0
\(213\) −2.09618 1.83304i −0.143628 0.125598i
\(214\) 0 0
\(215\) 3.60769 0.246043
\(216\) 0 0
\(217\) 3.27110 0.222057
\(218\) 0 0
\(219\) −17.5942 15.3855i −1.18890 1.03966i
\(220\) 0 0
\(221\) −11.3258 + 19.6168i −0.761854 + 1.31957i
\(222\) 0 0
\(223\) −13.3549 23.1313i −0.894308 1.54899i −0.834658 0.550768i \(-0.814335\pi\)
−0.0596502 0.998219i \(-0.518999\pi\)
\(224\) 0 0
\(225\) −11.6172 + 8.96678i −0.774481 + 0.597785i
\(226\) 0 0
\(227\) −8.46386 14.6598i −0.561766 0.973007i −0.997342 0.0728556i \(-0.976789\pi\)
0.435576 0.900152i \(-0.356545\pi\)
\(228\) 0 0
\(229\) 8.22580 14.2475i 0.543576 0.941501i −0.455119 0.890431i \(-0.650403\pi\)
0.998695 0.0510706i \(-0.0162633\pi\)
\(230\) 0 0
\(231\) −2.17871 + 0.743025i −0.143348 + 0.0488875i
\(232\) 0 0
\(233\) 4.10855 0.269160 0.134580 0.990903i \(-0.457031\pi\)
0.134580 + 0.990903i \(0.457031\pi\)
\(234\) 0 0
\(235\) −0.375745 −0.0245109
\(236\) 0 0
\(237\) 0.422000 2.13740i 0.0274118 0.138839i
\(238\) 0 0
\(239\) 10.4182 18.0448i 0.673895 1.16722i −0.302896 0.953024i \(-0.597953\pi\)
0.976791 0.214197i \(-0.0687133\pi\)
\(240\) 0 0
\(241\) −11.3477 19.6548i −0.730969 1.26608i −0.956470 0.291832i \(-0.905735\pi\)
0.225501 0.974243i \(-0.427598\pi\)
\(242\) 0 0
\(243\) −14.0295 6.79509i −0.899992 0.435905i
\(244\) 0 0
\(245\) −0.164508 0.284936i −0.0105100 0.0182039i
\(246\) 0 0
\(247\) −4.52067 + 7.83004i −0.287644 + 0.498213i
\(248\) 0 0
\(249\) 0.0212339 0.107549i 0.00134564 0.00681561i
\(250\) 0 0
\(251\) −4.00030 −0.252497 −0.126248 0.991999i \(-0.540294\pi\)
−0.126248 + 0.991999i \(0.540294\pi\)
\(252\) 0 0
\(253\) 8.88637 0.558681
\(254\) 0 0
\(255\) −3.96835 + 1.35337i −0.248508 + 0.0847511i
\(256\) 0 0
\(257\) −0.254753 + 0.441245i −0.0158911 + 0.0275241i −0.873862 0.486175i \(-0.838392\pi\)
0.857971 + 0.513699i \(0.171725\pi\)
\(258\) 0 0
\(259\) −0.164508 0.284936i −0.0102220 0.0177051i
\(260\) 0 0
\(261\) −18.4412 + 14.2339i −1.14148 + 0.881054i
\(262\) 0 0
\(263\) −1.56344 2.70796i −0.0964059 0.166980i 0.813789 0.581161i \(-0.197401\pi\)
−0.910194 + 0.414181i \(0.864068\pi\)
\(264\) 0 0
\(265\) −1.05750 + 1.83165i −0.0649619 + 0.112517i
\(266\) 0 0
\(267\) 14.7427 + 12.8920i 0.902238 + 0.788976i
\(268\) 0 0
\(269\) −4.16505 −0.253947 −0.126974 0.991906i \(-0.540526\pi\)
−0.126974 + 0.991906i \(0.540526\pi\)
\(270\) 0 0
\(271\) 13.0230 0.791092 0.395546 0.918446i \(-0.370555\pi\)
0.395546 + 0.918446i \(0.370555\pi\)
\(272\) 0 0
\(273\) 4.01420 + 3.51028i 0.242950 + 0.212452i
\(274\) 0 0
\(275\) 3.25061 5.63021i 0.196019 0.339515i
\(276\) 0 0
\(277\) 0.347709 + 0.602250i 0.0208918 + 0.0361857i 0.876282 0.481798i \(-0.160016\pi\)
−0.855390 + 0.517984i \(0.826683\pi\)
\(278\) 0 0
\(279\) −9.07695 3.72961i −0.543423 0.223286i
\(280\) 0 0
\(281\) −16.1488 27.9706i −0.963359 1.66859i −0.713960 0.700186i \(-0.753100\pi\)
−0.249399 0.968401i \(-0.580233\pi\)
\(282\) 0 0
\(283\) −7.06383 + 12.2349i −0.419901 + 0.727290i −0.995929 0.0901399i \(-0.971269\pi\)
0.576028 + 0.817430i \(0.304602\pi\)
\(284\) 0 0
\(285\) −1.58397 + 0.540196i −0.0938261 + 0.0319984i
\(286\) 0 0
\(287\) 0.271104 0.0160027
\(288\) 0 0
\(289\) 37.1315 2.18421
\(290\) 0 0
\(291\) −3.69994 + 18.7400i −0.216894 + 1.09856i
\(292\) 0 0
\(293\) −8.33818 + 14.4422i −0.487122 + 0.843720i −0.999890 0.0148072i \(-0.995287\pi\)
0.512769 + 0.858527i \(0.328620\pi\)
\(294\) 0 0
\(295\) 0.122450 + 0.212090i 0.00712931 + 0.0123483i
\(296\) 0 0
\(297\) 6.89285 + 0.422279i 0.399963 + 0.0245031i
\(298\) 0 0
\(299\) −10.2929 17.8278i −0.595252 1.03101i
\(300\) 0 0
\(301\) −5.48255 + 9.49606i −0.316009 + 0.547344i
\(302\) 0 0
\(303\) 4.77794 24.2000i 0.274486 1.39025i
\(304\) 0 0
\(305\) 2.90978 0.166614
\(306\) 0 0
\(307\) −27.0345 −1.54294 −0.771469 0.636267i \(-0.780478\pi\)
−0.771469 + 0.636267i \(0.780478\pi\)
\(308\) 0 0
\(309\) 17.3536 5.91828i 0.987213 0.336679i
\(310\) 0 0
\(311\) −11.7377 + 20.3302i −0.665581 + 1.15282i 0.313546 + 0.949573i \(0.398483\pi\)
−0.979127 + 0.203248i \(0.934850\pi\)
\(312\) 0 0
\(313\) 0.364597 + 0.631501i 0.0206083 + 0.0356946i 0.876146 0.482047i \(-0.160106\pi\)
−0.855537 + 0.517741i \(0.826773\pi\)
\(314\) 0 0
\(315\) 0.131616 + 0.978233i 0.00741573 + 0.0551172i
\(316\) 0 0
\(317\) −16.7398 28.9943i −0.940203 1.62848i −0.765082 0.643933i \(-0.777301\pi\)
−0.175122 0.984547i \(-0.556032\pi\)
\(318\) 0 0
\(319\) 5.16001 8.93741i 0.288905 0.500399i
\(320\) 0 0
\(321\) 20.2844 + 17.7380i 1.13216 + 0.990039i
\(322\) 0 0
\(323\) 21.6066 1.20222
\(324\) 0 0
\(325\) −15.0604 −0.835401
\(326\) 0 0
\(327\) −18.7199 16.3699i −1.03521 0.905256i
\(328\) 0 0
\(329\) 0.571014 0.989025i 0.0314810 0.0545267i
\(330\) 0 0
\(331\) −4.92051 8.52257i −0.270456 0.468443i 0.698523 0.715588i \(-0.253841\pi\)
−0.968979 + 0.247145i \(0.920508\pi\)
\(332\) 0 0
\(333\) 0.131616 + 0.978233i 0.00721252 + 0.0536068i
\(334\) 0 0
\(335\) 1.41029 + 2.44270i 0.0770525 + 0.133459i
\(336\) 0 0
\(337\) 3.93490 6.81545i 0.214348 0.371261i −0.738723 0.674009i \(-0.764571\pi\)
0.953071 + 0.302748i \(0.0979041\pi\)
\(338\) 0 0
\(339\) 6.39231 2.18003i 0.347182 0.118403i
\(340\) 0 0
\(341\) 4.34735 0.235422
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0.738063 3.73825i 0.0397360 0.201260i
\(346\) 0 0
\(347\) −8.14721 + 14.1114i −0.437365 + 0.757539i −0.997485 0.0708727i \(-0.977422\pi\)
0.560120 + 0.828411i \(0.310755\pi\)
\(348\) 0 0
\(349\) 1.79219 + 3.10416i 0.0959336 + 0.166162i 0.909998 0.414613i \(-0.136083\pi\)
−0.814064 + 0.580775i \(0.802750\pi\)
\(350\) 0 0
\(351\) −7.13665 14.3175i −0.380926 0.764212i
\(352\) 0 0
\(353\) 9.80329 + 16.9798i 0.521776 + 0.903743i 0.999679 + 0.0253304i \(0.00806378\pi\)
−0.477903 + 0.878413i \(0.658603\pi\)
\(354\) 0 0
\(355\) 0.264478 0.458089i 0.0140370 0.0243129i
\(356\) 0 0
\(357\) 2.46835 12.5021i 0.130639 0.661680i
\(358\) 0 0
\(359\) 16.8040 0.886882 0.443441 0.896303i \(-0.353757\pi\)
0.443441 + 0.896303i \(0.353757\pi\)
\(360\) 0 0
\(361\) −10.3757 −0.546092
\(362\) 0 0
\(363\) 15.1372 5.16238i 0.794496 0.270955i
\(364\) 0 0
\(365\) 2.21988 3.84494i 0.116194 0.201254i
\(366\) 0 0
\(367\) 16.8160 + 29.1262i 0.877790 + 1.52038i 0.853760 + 0.520666i \(0.174316\pi\)
0.0240298 + 0.999711i \(0.492350\pi\)
\(368\) 0 0
\(369\) −0.752282 0.309104i −0.0391623 0.0160913i
\(370\) 0 0
\(371\) −3.21414 5.56705i −0.166870 0.289027i
\(372\) 0 0
\(373\) 17.2159 29.8189i 0.891407 1.54396i 0.0532169 0.998583i \(-0.483053\pi\)
0.838190 0.545379i \(-0.183614\pi\)
\(374\) 0 0
\(375\) −4.24342 3.71073i −0.219129 0.191621i
\(376\) 0 0
\(377\) −23.9069 −1.23127
\(378\) 0 0
\(379\) −18.0913 −0.929287 −0.464644 0.885498i \(-0.653818\pi\)
−0.464644 + 0.885498i \(0.653818\pi\)
\(380\) 0 0
\(381\) 9.13719 + 7.99016i 0.468112 + 0.409348i
\(382\) 0 0
\(383\) −5.03792 + 8.72594i −0.257426 + 0.445875i −0.965552 0.260212i \(-0.916208\pi\)
0.708126 + 0.706086i \(0.249541\pi\)
\(384\) 0 0
\(385\) −0.218634 0.378684i −0.0111426 0.0192995i
\(386\) 0 0
\(387\) 26.0406 20.0995i 1.32372 1.02171i
\(388\) 0 0
\(389\) 0.715236 + 1.23882i 0.0362639 + 0.0628109i 0.883588 0.468266i \(-0.155121\pi\)
−0.847324 + 0.531077i \(0.821788\pi\)
\(390\) 0 0
\(391\) −24.5974 + 42.6040i −1.24394 + 2.15457i
\(392\) 0 0
\(393\) 10.9272 3.72660i 0.551203 0.187982i
\(394\) 0 0
\(395\) 0.413853 0.0208232
\(396\) 0 0
\(397\) −10.5433 −0.529152 −0.264576 0.964365i \(-0.585232\pi\)
−0.264576 + 0.964365i \(0.585232\pi\)
\(398\) 0 0
\(399\) 0.985242 4.99020i 0.0493238 0.249822i
\(400\) 0 0
\(401\) −0.804044 + 1.39265i −0.0401521 + 0.0695454i −0.885403 0.464824i \(-0.846118\pi\)
0.845251 + 0.534369i \(0.179451\pi\)
\(402\) 0 0
\(403\) −5.03543 8.72162i −0.250833 0.434455i
\(404\) 0 0
\(405\) 0.750130 2.86455i 0.0372743 0.142341i
\(406\) 0 0
\(407\) −0.218634 0.378684i −0.0108373 0.0187707i
\(408\) 0 0
\(409\) −13.0174 + 22.5468i −0.643670 + 1.11487i 0.340937 + 0.940086i \(0.389256\pi\)
−0.984607 + 0.174783i \(0.944077\pi\)
\(410\) 0 0
\(411\) −5.64919 + 28.6128i −0.278654 + 1.41137i
\(412\) 0 0
\(413\) −0.744341 −0.0366266
\(414\) 0 0
\(415\) 0.0208240 0.00102221
\(416\) 0 0
\(417\) −25.6075 + 8.73318i −1.25401 + 0.427666i
\(418\) 0 0
\(419\) 2.00882 3.47938i 0.0981372 0.169979i −0.812776 0.582576i \(-0.802045\pi\)
0.910914 + 0.412597i \(0.135378\pi\)
\(420\) 0 0
\(421\) −2.63431 4.56275i −0.128388 0.222375i 0.794664 0.607049i \(-0.207647\pi\)
−0.923052 + 0.384675i \(0.874314\pi\)
\(422\) 0 0
\(423\) −2.71216 + 2.09338i −0.131870 + 0.101784i
\(424\) 0 0
\(425\) 17.9953 + 31.1688i 0.872901 + 1.51191i
\(426\) 0 0
\(427\) −4.42195 + 7.65904i −0.213993 + 0.370647i
\(428\) 0 0
\(429\) 5.33493 + 4.66522i 0.257573 + 0.225239i
\(430\) 0 0
\(431\) 17.7343 0.854230 0.427115 0.904197i \(-0.359530\pi\)
0.427115 + 0.904197i \(0.359530\pi\)
\(432\) 0 0
\(433\) −4.76835 −0.229152 −0.114576 0.993414i \(-0.536551\pi\)
−0.114576 + 0.993414i \(0.536551\pi\)
\(434\) 0 0
\(435\) −3.33115 2.91297i −0.159716 0.139666i
\(436\) 0 0
\(437\) −9.81804 + 17.0054i −0.469661 + 0.813476i
\(438\) 0 0
\(439\) 18.1134 + 31.3733i 0.864506 + 1.49737i 0.867537 + 0.497373i \(0.165702\pi\)
−0.00303091 + 0.999995i \(0.500965\pi\)
\(440\) 0 0
\(441\) −2.77489 1.14017i −0.132138 0.0542938i
\(442\) 0 0
\(443\) 7.81211 + 13.5310i 0.371164 + 0.642876i 0.989745 0.142846i \(-0.0456253\pi\)
−0.618581 + 0.785721i \(0.712292\pi\)
\(444\) 0 0
\(445\) −1.86010 + 3.22179i −0.0881773 + 0.152728i
\(446\) 0 0
\(447\) 24.6961 8.42235i 1.16808 0.398363i
\(448\) 0 0
\(449\) −15.4142 −0.727441 −0.363721 0.931508i \(-0.618494\pi\)
−0.363721 + 0.931508i \(0.618494\pi\)
\(450\) 0 0
\(451\) 0.360301 0.0169659
\(452\) 0 0
\(453\) 2.59479 13.1425i 0.121914 0.617486i
\(454\) 0 0
\(455\) −0.506476 + 0.877243i −0.0237440 + 0.0411258i
\(456\) 0 0
\(457\) 4.71214 + 8.16166i 0.220424 + 0.381786i 0.954937 0.296809i \(-0.0959224\pi\)
−0.734512 + 0.678595i \(0.762589\pi\)
\(458\) 0 0
\(459\) −21.1039 + 31.8775i −0.985045 + 1.48792i
\(460\) 0 0
\(461\) −20.0406 34.7113i −0.933383 1.61667i −0.777491 0.628893i \(-0.783508\pi\)
−0.155892 0.987774i \(-0.549825\pi\)
\(462\) 0 0
\(463\) 10.9717 19.0036i 0.509900 0.883172i −0.490035 0.871703i \(-0.663016\pi\)
0.999934 0.0114690i \(-0.00365078\pi\)
\(464\) 0 0
\(465\) 0.361072 1.82881i 0.0167443 0.0848089i
\(466\) 0 0
\(467\) 20.9808 0.970878 0.485439 0.874271i \(-0.338660\pi\)
0.485439 + 0.874271i \(0.338660\pi\)
\(468\) 0 0
\(469\) −8.57280 −0.395855
\(470\) 0 0
\(471\) 14.2889 4.87307i 0.658396 0.224539i
\(472\) 0 0
\(473\) −7.28640 + 12.6204i −0.335029 + 0.580287i
\(474\) 0 0
\(475\) 7.18282 + 12.4410i 0.329570 + 0.570833i
\(476\) 0 0
\(477\) 2.57150 + 19.1126i 0.117741 + 0.875107i
\(478\) 0 0
\(479\) −6.65194 11.5215i −0.303935 0.526431i 0.673089 0.739562i \(-0.264967\pi\)
−0.977024 + 0.213131i \(0.931634\pi\)
\(480\) 0 0
\(481\) −0.506476 + 0.877243i −0.0230933 + 0.0399988i
\(482\) 0 0
\(483\) 8.71807 + 7.62366i 0.396686 + 0.346888i
\(484\) 0 0
\(485\) −3.62852 −0.164762
\(486\) 0 0
\(487\) 38.5519 1.74695 0.873477 0.486865i \(-0.161860\pi\)
0.873477 + 0.486865i \(0.161860\pi\)
\(488\) 0 0
\(489\) −17.5384 15.3367i −0.793115 0.693552i
\(490\) 0 0
\(491\) −3.25959 + 5.64578i −0.147103 + 0.254791i −0.930156 0.367165i \(-0.880328\pi\)
0.783052 + 0.621956i \(0.213662\pi\)
\(492\) 0 0
\(493\) 28.5658 + 49.4774i 1.28654 + 2.22835i
\(494\) 0 0
\(495\) 0.174920 + 1.30009i 0.00786206 + 0.0584346i
\(496\) 0 0
\(497\) 0.803846 + 1.39230i 0.0360574 + 0.0624533i
\(498\) 0 0
\(499\) 14.3259 24.8132i 0.641316 1.11079i −0.343823 0.939034i \(-0.611722\pi\)
0.985139 0.171758i \(-0.0549446\pi\)
\(500\) 0 0
\(501\) −19.0755 + 6.50550i −0.852230 + 0.290644i
\(502\) 0 0
\(503\) −16.2801 −0.725892 −0.362946 0.931810i \(-0.618229\pi\)
−0.362946 + 0.931810i \(0.618229\pi\)
\(504\) 0 0
\(505\) 4.68571 0.208511
\(506\) 0 0
\(507\) −1.18140 + 5.98370i −0.0524676 + 0.265746i
\(508\) 0 0
\(509\) −13.2296 + 22.9143i −0.586391 + 1.01566i 0.408309 + 0.912844i \(0.366118\pi\)
−0.994700 + 0.102815i \(0.967215\pi\)
\(510\) 0 0
\(511\) 6.74703 + 11.6862i 0.298471 + 0.516967i
\(512\) 0 0
\(513\) −8.42361 + 12.7239i −0.371911 + 0.561774i
\(514\) 0 0
\(515\) 1.74144 + 3.01626i 0.0767370 + 0.132912i
\(516\) 0 0
\(517\) 0.758887 1.31443i 0.0333758 0.0578086i
\(518\) 0 0
\(519\) 0.594379 3.01049i 0.0260903 0.132146i
\(520\) 0 0
\(521\) −7.72559 −0.338464 −0.169232 0.985576i \(-0.554129\pi\)
−0.169232 + 0.985576i \(0.554129\pi\)
\(522\) 0 0
\(523\) 16.9546 0.741375 0.370687 0.928758i \(-0.379122\pi\)
0.370687 + 0.928758i \(0.379122\pi\)
\(524\) 0 0
\(525\) 8.01923 2.73488i 0.349988 0.119360i
\(526\) 0 0
\(527\) −12.0334 + 20.8425i −0.524184 + 0.907914i
\(528\) 0 0
\(529\) −10.8542 18.8000i −0.471920 0.817390i
\(530\) 0 0
\(531\) 2.06546 + 0.848674i 0.0896335 + 0.0368293i
\(532\) 0 0
\(533\) −0.417328 0.722833i −0.0180765 0.0313094i
\(534\) 0 0
\(535\) −2.55931 + 4.43285i −0.110648 + 0.191649i
\(536\) 0 0
\(537\) 8.77669 + 7.67492i 0.378742 + 0.331197i
\(538\) 0 0
\(539\) 1.32902 0.0572448
\(540\) 0 0
\(541\) 21.9353 0.943072 0.471536 0.881847i \(-0.343700\pi\)
0.471536 + 0.881847i \(0.343700\pi\)
\(542\) 0 0
\(543\) −17.3035 15.1313i −0.742563 0.649346i
\(544\) 0 0
\(545\) 2.36191 4.09094i 0.101173 0.175237i
\(546\) 0 0
\(547\) 21.4034 + 37.0718i 0.915144 + 1.58508i 0.806691 + 0.590974i \(0.201256\pi\)
0.108453 + 0.994102i \(0.465410\pi\)
\(548\) 0 0
\(549\) 21.0030 16.2112i 0.896387 0.691879i
\(550\) 0 0
\(551\) 11.4020 + 19.7489i 0.485742 + 0.841330i
\(552\) 0 0
\(553\) −0.628926 + 1.08933i −0.0267447 + 0.0463231i
\(554\) 0 0
\(555\) −0.177461 + 0.0605211i −0.00753278 + 0.00256898i
\(556\) 0 0
\(557\) 36.5498 1.54866 0.774332 0.632780i \(-0.218086\pi\)
0.774332 + 0.632780i \(0.218086\pi\)
\(558\) 0 0
\(559\) 33.7587 1.42784
\(560\) 0 0
\(561\) 3.28048 16.6155i 0.138502 0.701505i
\(562\) 0 0
\(563\) 19.8582 34.3955i 0.836925 1.44960i −0.0555277 0.998457i \(-0.517684\pi\)
0.892453 0.451140i \(-0.148983\pi\)
\(564\) 0 0
\(565\) 0.641469 + 1.11106i 0.0269868 + 0.0467425i
\(566\) 0 0
\(567\) 6.40003 + 6.32769i 0.268776 + 0.265738i
\(568\) 0 0
\(569\) −15.4173 26.7035i −0.646325 1.11947i −0.983994 0.178203i \(-0.942972\pi\)
0.337669 0.941265i \(-0.390362\pi\)
\(570\) 0 0
\(571\) −19.4009 + 33.6033i −0.811901 + 1.40625i 0.0996310 + 0.995024i \(0.468234\pi\)
−0.911532 + 0.411229i \(0.865100\pi\)
\(572\) 0 0
\(573\) −6.98380 + 35.3725i −0.291752 + 1.47771i
\(574\) 0 0
\(575\) −32.7083 −1.36403
\(576\) 0 0
\(577\) −2.10713 −0.0877211 −0.0438606 0.999038i \(-0.513966\pi\)
−0.0438606 + 0.999038i \(0.513966\pi\)
\(578\) 0 0
\(579\) 33.6344 11.4707i 1.39780 0.476705i
\(580\) 0 0
\(581\) −0.0316459 + 0.0548124i −0.00131289 + 0.00227400i
\(582\) 0 0
\(583\) −4.27164 7.39870i −0.176913 0.306423i
\(584\) 0 0
\(585\) 2.40562 1.85678i 0.0994602 0.0767686i
\(586\) 0 0
\(587\) 3.46457 + 6.00081i 0.142998 + 0.247680i 0.928624 0.371022i \(-0.120992\pi\)
−0.785626 + 0.618701i \(0.787659\pi\)
\(588\) 0 0
\(589\) −4.80314 + 8.31928i −0.197910 + 0.342790i
\(590\) 0 0
\(591\) 9.39788 + 8.21812i 0.386577 + 0.338048i
\(592\) 0 0
\(593\) −10.0323 −0.411977 −0.205989 0.978554i \(-0.566041\pi\)
−0.205989 + 0.978554i \(0.566041\pi\)
\(594\) 0 0
\(595\) 2.42070 0.0992392
\(596\) 0 0
\(597\) 18.6810 + 16.3359i 0.764562 + 0.668583i
\(598\) 0 0
\(599\) −21.6645 + 37.5240i −0.885187 + 1.53319i −0.0396877 + 0.999212i \(0.512636\pi\)
−0.845499 + 0.533977i \(0.820697\pi\)
\(600\) 0 0
\(601\) 23.2578 + 40.2837i 0.948707 + 1.64321i 0.748154 + 0.663525i \(0.230941\pi\)
0.200553 + 0.979683i \(0.435726\pi\)
\(602\) 0 0
\(603\) 23.7886 + 9.77444i 0.968746 + 0.398046i
\(604\) 0 0
\(605\) 1.51902 + 2.63102i 0.0617569 + 0.106966i
\(606\) 0 0
\(607\) 18.9227 32.7751i 0.768048 1.33030i −0.170572 0.985345i \(-0.554561\pi\)
0.938620 0.344953i \(-0.112105\pi\)
\(608\) 0 0
\(609\) 12.7297 4.34134i 0.515835 0.175920i
\(610\) 0 0
\(611\) −3.51600 −0.142242
\(612\) 0 0
\(613\) 30.2811 1.22304 0.611522 0.791228i \(-0.290558\pi\)
0.611522 + 0.791228i \(0.290558\pi\)
\(614\) 0 0
\(615\) 0.0299250 0.151568i 0.00120669 0.00611183i
\(616\) 0 0
\(617\) 8.08770 14.0083i 0.325599 0.563954i −0.656035 0.754731i \(-0.727767\pi\)
0.981633 + 0.190777i \(0.0611008\pi\)
\(618\) 0 0
\(619\) −12.9377 22.4088i −0.520012 0.900687i −0.999729 0.0232638i \(-0.992594\pi\)
0.479718 0.877423i \(-0.340739\pi\)
\(620\) 0 0
\(621\) −15.4994 31.0949i −0.621971 1.24779i
\(622\) 0 0
\(623\) −5.65354 9.79221i −0.226504 0.392317i
\(624\) 0 0
\(625\) −11.6940 + 20.2546i −0.467759 + 0.810182i
\(626\) 0 0
\(627\) 1.30940 6.63205i 0.0522925 0.264859i
\(628\) 0 0
\(629\) 2.42070 0.0965198
\(630\) 0 0
\(631\) −29.2969 −1.16629 −0.583146 0.812368i \(-0.698178\pi\)
−0.583146 + 0.812368i \(0.698178\pi\)
\(632\) 0 0
\(633\) −12.0949 + 4.12485i −0.480731 + 0.163948i
\(634\) 0 0
\(635\) −1.15285 + 1.99679i −0.0457495 + 0.0792404i
\(636\) 0 0
\(637\) −1.53937 2.66626i −0.0609920 0.105641i
\(638\) 0 0
\(639\) −0.643125 4.78001i −0.0254416 0.189094i
\(640\) 0 0
\(641\) 8.82630 + 15.2876i 0.348618 + 0.603824i 0.986004 0.166720i \(-0.0533177\pi\)
−0.637386 + 0.770545i \(0.719984\pi\)
\(642\) 0 0
\(643\) −14.5426 + 25.1885i −0.573504 + 0.993338i 0.422698 + 0.906270i \(0.361083\pi\)
−0.996202 + 0.0870676i \(0.972250\pi\)
\(644\) 0 0
\(645\) 4.70388 + 4.11338i 0.185215 + 0.161964i
\(646\) 0 0
\(647\) −39.8747 −1.56764 −0.783819 0.620989i \(-0.786731\pi\)
−0.783819 + 0.620989i \(0.786731\pi\)
\(648\) 0 0
\(649\) −0.989241 −0.0388311
\(650\) 0 0
\(651\) 4.26502 + 3.72961i 0.167159 + 0.146175i
\(652\) 0 0
\(653\) −7.08986 + 12.2800i −0.277448 + 0.480553i −0.970750 0.240094i \(-0.922822\pi\)
0.693302 + 0.720647i \(0.256155\pi\)
\(654\) 0 0
\(655\) 1.09654 + 1.89927i 0.0428455 + 0.0742106i
\(656\) 0 0
\(657\) −5.39803 40.1207i −0.210597 1.56526i
\(658\) 0 0
\(659\) −11.3592 19.6747i −0.442491 0.766418i 0.555382 0.831595i \(-0.312572\pi\)
−0.997874 + 0.0651775i \(0.979239\pi\)
\(660\) 0 0
\(661\) −20.0052 + 34.6500i −0.778111 + 1.34773i 0.154919 + 0.987927i \(0.450488\pi\)
−0.933030 + 0.359800i \(0.882845\pi\)
\(662\) 0 0
\(663\) −37.1335 + 12.6640i −1.44215 + 0.491829i
\(664\) 0 0
\(665\) 0.966223 0.0374685
\(666\) 0 0
\(667\) −51.9212 −2.01040
\(668\) 0 0
\(669\) 8.96091 45.3865i 0.346449 1.75474i
\(670\) 0 0
\(671\) −5.87684 + 10.1790i −0.226873 + 0.392956i
\(672\) 0 0
\(673\) 0.913881 + 1.58289i 0.0352275 + 0.0610159i 0.883102 0.469182i \(-0.155451\pi\)
−0.847874 + 0.530198i \(0.822118\pi\)
\(674\) 0 0
\(675\) −25.3707 1.55430i −0.976519 0.0598249i
\(676\) 0 0
\(677\) 14.2246 + 24.6376i 0.546694 + 0.946902i 0.998498 + 0.0547845i \(0.0174472\pi\)
−0.451804 + 0.892117i \(0.649219\pi\)
\(678\) 0 0
\(679\) 5.51420 9.55087i 0.211616 0.366529i
\(680\) 0 0
\(681\) 5.67912 28.7644i 0.217624 1.10225i
\(682\) 0 0
\(683\) −0.868335 −0.0332259 −0.0166130 0.999862i \(-0.505288\pi\)
−0.0166130 + 0.999862i \(0.505288\pi\)
\(684\) 0 0
\(685\) −5.54014 −0.211678
\(686\) 0 0
\(687\) 26.9697 9.19775i 1.02896 0.350916i
\(688\) 0 0
\(689\) −9.89549 + 17.1395i −0.376988 + 0.652962i
\(690\) 0 0
\(691\) −8.71932 15.1023i −0.331699 0.574519i 0.651146 0.758952i \(-0.274288\pi\)
−0.982845 + 0.184433i \(0.940955\pi\)
\(692\) 0 0
\(693\) −3.68787 1.51530i −0.140091 0.0575616i
\(694\) 0 0
\(695\) −2.56972 4.45088i −0.0974750 0.168832i
\(696\) 0 0
\(697\) −0.997310 + 1.72739i −0.0377758 + 0.0654296i
\(698\) 0 0
\(699\) 5.35692 + 4.68444i 0.202617 + 0.177182i
\(700\) 0 0
\(701\) 9.23113 0.348655 0.174327 0.984688i \(-0.444225\pi\)
0.174327 + 0.984688i \(0.444225\pi\)
\(702\) 0 0
\(703\) 0.966223 0.0364418
\(704\) 0 0
\(705\) −0.489914 0.428413i −0.0184512 0.0161350i
\(706\) 0 0
\(707\) −7.12079 + 12.3336i −0.267805 + 0.463852i
\(708\) 0 0
\(709\) −10.8231 18.7461i −0.406469 0.704025i 0.588022 0.808845i \(-0.299907\pi\)
−0.994491 + 0.104820i \(0.966573\pi\)
\(710\) 0 0
\(711\) 2.98722 2.30570i 0.112030 0.0864703i
\(712\) 0 0
\(713\) −10.9360 18.9417i −0.409556 0.709373i
\(714\) 0 0
\(715\) −0.673115 + 1.16587i −0.0251731 + 0.0436010i
\(716\) 0 0
\(717\) 34.1578 11.6492i 1.27565 0.435046i
\(718\) 0 0
\(719\) −48.6526 −1.81444 −0.907218 0.420661i \(-0.861798\pi\)
−0.907218 + 0.420661i \(0.861798\pi\)
\(720\) 0 0
\(721\) −10.5858 −0.394234
\(722\) 0 0
\(723\) 7.61412 38.5651i 0.283172 1.43425i
\(724\) 0 0
\(725\) −18.9926 + 32.8962i −0.705368 + 1.22173i
\(726\) 0 0
\(727\) 1.11417 + 1.92980i 0.0413222 + 0.0715722i 0.885947 0.463787i \(-0.153510\pi\)
−0.844625 + 0.535359i \(0.820176\pi\)
\(728\) 0 0
\(729\) −10.5447 24.8557i −0.390546 0.920583i
\(730\) 0 0
\(731\) −40.3374 69.8664i −1.49193 2.58410i
\(732\) 0 0
\(733\) −19.0129 + 32.9313i −0.702258 + 1.21635i 0.265415 + 0.964134i \(0.414491\pi\)
−0.967672 + 0.252211i \(0.918842\pi\)
\(734\) 0 0
\(735\) 0.110382 0.559079i 0.00407151 0.0206220i
\(736\) 0 0
\(737\) −11.3934 −0.419681
\(738\) 0 0
\(739\) 48.6048 1.78796 0.893978 0.448112i \(-0.147903\pi\)
0.893978 + 0.448112i \(0.147903\pi\)
\(740\) 0 0
\(741\) −14.8218 + 5.05483i −0.544494 + 0.185694i
\(742\) 0 0
\(743\) −21.2700 + 36.8408i −0.780322 + 1.35156i 0.151432 + 0.988468i \(0.451612\pi\)
−0.931754 + 0.363090i \(0.881722\pi\)
\(744\) 0 0
\(745\) 2.47826 + 4.29247i 0.0907963 + 0.157264i
\(746\) 0 0
\(747\) 0.150309 0.116017i 0.00549953 0.00424482i
\(748\) 0 0
\(749\) −7.77868 13.4731i −0.284227 0.492295i
\(750\) 0 0
\(751\) 4.62893 8.01754i 0.168912 0.292564i −0.769126 0.639098i \(-0.779308\pi\)
0.938038 + 0.346534i \(0.112641\pi\)
\(752\) 0 0
\(753\) −5.21577 4.56102i −0.190073 0.166213i
\(754\) 0 0
\(755\) 2.54470 0.0926111
\(756\) 0 0
\(757\) 41.0363 1.49149 0.745744 0.666232i \(-0.232094\pi\)
0.745744 + 0.666232i \(0.232094\pi\)
\(758\) 0 0
\(759\) 11.5865 + 10.1320i 0.420562 + 0.367767i
\(760\) 0 0
\(761\) 19.1859 33.2309i 0.695487 1.20462i −0.274529 0.961579i \(-0.588522\pi\)
0.970016 0.243040i \(-0.0781448\pi\)
\(762\) 0 0
\(763\) 7.17871 + 12.4339i 0.259887 + 0.450137i
\(764\) 0 0
\(765\) −6.71719 2.76001i −0.242861 0.0997885i
\(766\) 0 0
\(767\) 1.14581 + 1.98461i 0.0413730 + 0.0716601i
\(768\) 0 0
\(769\) 0.149772 0.259412i 0.00540090 0.00935463i −0.863312 0.504670i \(-0.831614\pi\)
0.868713 + 0.495315i \(0.164947\pi\)
\(770\) 0 0
\(771\) −0.835252 + 0.284854i −0.0300809 + 0.0102588i
\(772\) 0 0
\(773\) 40.2941 1.44928 0.724639 0.689128i \(-0.242006\pi\)
0.724639 + 0.689128i \(0.242006\pi\)
\(774\) 0 0
\(775\) −16.0014 −0.574788
\(776\) 0 0
\(777\) 0.110382 0.559079i 0.00395994 0.0200569i
\(778\) 0 0
\(779\) −0.398076 + 0.689488i −0.0142626 + 0.0247035i
\(780\) 0 0
\(781\) 1.06832 + 1.85039i 0.0382276 + 0.0662122i
\(782\) 0 0
\(783\) −40.2735 2.46729i −1.43926 0.0881738i
\(784\) 0 0
\(785\) 1.43389 + 2.48357i 0.0511777 + 0.0886425i
\(786\) 0 0
\(787\) 12.2565 21.2289i 0.436897 0.756728i −0.560551 0.828120i \(-0.689411\pi\)
0.997448 + 0.0713920i \(0.0227441\pi\)
\(788\) 0 0
\(789\) 1.04904 5.31335i 0.0373470 0.189160i
\(790\) 0 0
\(791\) −3.89932 −0.138644
\(792\) 0 0
\(793\) 27.2280 0.966896
\(794\) 0 0
\(795\) −3.46721 + 1.18246i −0.122969 + 0.0419374i
\(796\) 0 0
\(797\) 26.9140 46.6164i 0.953343 1.65124i 0.215228 0.976564i \(-0.430951\pi\)
0.738115 0.674675i \(-0.235716\pi\)