Properties

Label 768.2.o.b.287.5
Level 768
Weight 2
Character 768.287
Analytic conductor 6.133
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.o (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 287.5
Character \(\chi\) \(=\) 768.287
Dual form 768.2.o.b.479.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.684042 - 1.59125i) q^{3} +(0.296199 - 0.715088i) q^{5} +(2.77714 - 2.77714i) q^{7} +(-2.06417 + 2.17697i) q^{9} +O(q^{10})\) \(q+(-0.684042 - 1.59125i) q^{3} +(0.296199 - 0.715088i) q^{5} +(2.77714 - 2.77714i) q^{7} +(-2.06417 + 2.17697i) q^{9} +(0.829014 - 2.00142i) q^{11} +(3.73669 - 1.54779i) q^{13} +(-1.34050 + 0.0178227i) q^{15} -5.19928 q^{17} +(0.814726 + 1.96692i) q^{19} +(-6.31881 - 2.51945i) q^{21} +(4.13184 - 4.13184i) q^{23} +(3.11192 + 3.11192i) q^{25} +(4.87609 + 1.79548i) q^{27} +(-3.45738 + 1.43209i) q^{29} -0.343074i q^{31} +(-3.75184 + 0.0498828i) q^{33} +(-1.16331 - 2.80849i) q^{35} +(-4.31781 - 1.78850i) q^{37} +(-5.01898 - 4.88727i) q^{39} +(-3.37894 - 3.37894i) q^{41} +(-9.15044 - 3.79024i) q^{43} +(0.945319 + 2.12088i) q^{45} -4.84842i q^{47} -8.42499i q^{49} +(3.55653 + 8.27337i) q^{51} +(4.15435 + 1.72079i) q^{53} +(-1.18564 - 1.18564i) q^{55} +(2.57256 - 2.64189i) q^{57} +(-8.08629 - 3.34945i) q^{59} +(2.47236 + 5.96880i) q^{61} +(0.313252 + 11.7782i) q^{63} -3.13052i q^{65} +(5.45025 - 2.25757i) q^{67} +(-9.40117 - 3.74845i) q^{69} +(6.23395 + 6.23395i) q^{71} +(-1.44956 + 1.44956i) q^{73} +(2.82316 - 7.08053i) q^{75} +(-3.25592 - 7.86050i) q^{77} -13.2460 q^{79} +(-0.478386 - 8.98728i) q^{81} +(6.19358 - 2.56547i) q^{83} +(-1.54002 + 3.71795i) q^{85} +(4.64382 + 4.52195i) q^{87} +(-9.26892 + 9.26892i) q^{89} +(6.07889 - 14.6757i) q^{91} +(-0.545918 + 0.234677i) q^{93} +1.64784 q^{95} +9.56950 q^{97} +(2.64579 + 5.93600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + O(q^{10}) \) \( 56q + 4q^{3} - 8q^{7} - 4q^{9} + 8q^{13} - 8q^{15} + 8q^{19} + 4q^{21} - 8q^{25} + 28q^{27} - 8q^{33} + 8q^{37} - 28q^{39} + 8q^{43} + 4q^{45} + 16q^{51} + 24q^{55} - 4q^{57} + 40q^{61} - 56q^{67} + 4q^{69} - 8q^{73} - 16q^{75} + 16q^{79} + 48q^{85} + 52q^{87} - 40q^{91} - 8q^{93} - 16q^{97} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{8}\right)\)

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
\(3\) −0.684042 1.59125i −0.394932 0.918710i
\(4\) 0 0
\(5\) 0.296199 0.715088i 0.132464 0.319797i −0.843705 0.536807i \(-0.819630\pi\)
0.976169 + 0.217010i \(0.0696303\pi\)
\(6\) 0 0
\(7\) 2.77714 2.77714i 1.04966 1.04966i 0.0509588 0.998701i \(-0.483772\pi\)
0.998701 0.0509588i \(-0.0162277\pi\)
\(8\) 0 0
\(9\) −2.06417 + 2.17697i −0.688057 + 0.725656i
\(10\) 0 0
\(11\) 0.829014 2.00142i 0.249957 0.603450i −0.748243 0.663425i \(-0.769102\pi\)
0.998200 + 0.0599753i \(0.0191022\pi\)
\(12\) 0 0
\(13\) 3.73669 1.54779i 1.03637 0.429279i 0.201363 0.979517i \(-0.435463\pi\)
0.835008 + 0.550237i \(0.185463\pi\)
\(14\) 0 0
\(15\) −1.34050 + 0.0178227i −0.346115 + 0.00460179i
\(16\) 0 0
\(17\) −5.19928 −1.26101 −0.630506 0.776185i \(-0.717152\pi\)
−0.630506 + 0.776185i \(0.717152\pi\)
\(18\) 0 0
\(19\) 0.814726 + 1.96692i 0.186911 + 0.451243i 0.989362 0.145475i \(-0.0464711\pi\)
−0.802451 + 0.596718i \(0.796471\pi\)
\(20\) 0 0
\(21\) −6.31881 2.51945i −1.37888 0.549789i
\(22\) 0 0
\(23\) 4.13184 4.13184i 0.861549 0.861549i −0.129969 0.991518i \(-0.541488\pi\)
0.991518 + 0.129969i \(0.0414878\pi\)
\(24\) 0 0
\(25\) 3.11192 + 3.11192i 0.622383 + 0.622383i
\(26\) 0 0
\(27\) 4.87609 + 1.79548i 0.938404 + 0.345541i
\(28\) 0 0
\(29\) −3.45738 + 1.43209i −0.642019 + 0.265933i −0.679850 0.733351i \(-0.737955\pi\)
0.0378308 + 0.999284i \(0.487955\pi\)
\(30\) 0 0
\(31\) 0.343074i 0.0616180i −0.999525 0.0308090i \(-0.990192\pi\)
0.999525 0.0308090i \(-0.00980836\pi\)
\(32\) 0 0
\(33\) −3.75184 + 0.0498828i −0.653112 + 0.00868348i
\(34\) 0 0
\(35\) −1.16331 2.80849i −0.196636 0.474721i
\(36\) 0 0
\(37\) −4.31781 1.78850i −0.709844 0.294027i −0.00160386 0.999999i \(-0.500511\pi\)
−0.708240 + 0.705972i \(0.750511\pi\)
\(38\) 0 0
\(39\) −5.01898 4.88727i −0.803680 0.782589i
\(40\) 0 0
\(41\) −3.37894 3.37894i −0.527702 0.527702i 0.392184 0.919887i \(-0.371720\pi\)
−0.919887 + 0.392184i \(0.871720\pi\)
\(42\) 0 0
\(43\) −9.15044 3.79024i −1.39543 0.578005i −0.446868 0.894600i \(-0.647461\pi\)
−0.948561 + 0.316595i \(0.897461\pi\)
\(44\) 0 0
\(45\) 0.945319 + 2.12088i 0.140920 + 0.316162i
\(46\) 0 0
\(47\) 4.84842i 0.707215i −0.935394 0.353608i \(-0.884955\pi\)
0.935394 0.353608i \(-0.115045\pi\)
\(48\) 0 0
\(49\) 8.42499i 1.20357i
\(50\) 0 0
\(51\) 3.55653 + 8.27337i 0.498014 + 1.15850i
\(52\) 0 0
\(53\) 4.15435 + 1.72079i 0.570644 + 0.236369i 0.649299 0.760533i \(-0.275062\pi\)
−0.0786546 + 0.996902i \(0.525062\pi\)
\(54\) 0 0
\(55\) −1.18564 1.18564i −0.159871 0.159871i
\(56\) 0 0
\(57\) 2.57256 2.64189i 0.340744 0.349927i
\(58\) 0 0
\(59\) −8.08629 3.34945i −1.05275 0.436062i −0.211875 0.977297i \(-0.567957\pi\)
−0.840871 + 0.541235i \(0.817957\pi\)
\(60\) 0 0
\(61\) 2.47236 + 5.96880i 0.316553 + 0.764227i 0.999432 + 0.0336954i \(0.0107276\pi\)
−0.682879 + 0.730531i \(0.739272\pi\)
\(62\) 0 0
\(63\) 0.313252 + 11.7782i 0.0394660 + 1.48392i
\(64\) 0 0
\(65\) 3.13052i 0.388293i
\(66\) 0 0
\(67\) 5.45025 2.25757i 0.665854 0.275806i −0.0240453 0.999711i \(-0.507655\pi\)
0.689900 + 0.723905i \(0.257655\pi\)
\(68\) 0 0
\(69\) −9.40117 3.74845i −1.13177 0.451261i
\(70\) 0 0
\(71\) 6.23395 + 6.23395i 0.739834 + 0.739834i 0.972546 0.232712i \(-0.0747598\pi\)
−0.232712 + 0.972546i \(0.574760\pi\)
\(72\) 0 0
\(73\) −1.44956 + 1.44956i −0.169658 + 0.169658i −0.786829 0.617171i \(-0.788279\pi\)
0.617171 + 0.786829i \(0.288279\pi\)
\(74\) 0 0
\(75\) 2.82316 7.08053i 0.325991 0.817589i
\(76\) 0 0
\(77\) −3.25592 7.86050i −0.371047 0.895787i
\(78\) 0 0
\(79\) −13.2460 −1.49029 −0.745144 0.666904i \(-0.767619\pi\)
−0.745144 + 0.666904i \(0.767619\pi\)
\(80\) 0 0
\(81\) −0.478386 8.98728i −0.0531540 0.998586i
\(82\) 0 0
\(83\) 6.19358 2.56547i 0.679834 0.281596i −0.0159235 0.999873i \(-0.505069\pi\)
0.695758 + 0.718277i \(0.255069\pi\)
\(84\) 0 0
\(85\) −1.54002 + 3.71795i −0.167039 + 0.403268i
\(86\) 0 0
\(87\) 4.64382 + 4.52195i 0.497870 + 0.484804i
\(88\) 0 0
\(89\) −9.26892 + 9.26892i −0.982503 + 0.982503i −0.999850 0.0173462i \(-0.994478\pi\)
0.0173462 + 0.999850i \(0.494478\pi\)
\(90\) 0 0
\(91\) 6.07889 14.6757i 0.637240 1.53843i
\(92\) 0 0
\(93\) −0.545918 + 0.234677i −0.0566091 + 0.0243349i
\(94\) 0 0
\(95\) 1.64784 0.169065
\(96\) 0 0
\(97\) 9.56950 0.971635 0.485818 0.874060i \(-0.338522\pi\)
0.485818 + 0.874060i \(0.338522\pi\)
\(98\) 0 0
\(99\) 2.64579 + 5.93600i 0.265912 + 0.596591i
\(100\) 0 0
\(101\) −1.02241 + 2.46831i −0.101733 + 0.245606i −0.966548 0.256485i \(-0.917436\pi\)
0.864815 + 0.502091i \(0.167436\pi\)
\(102\) 0 0
\(103\) 7.61434 7.61434i 0.750263 0.750263i −0.224265 0.974528i \(-0.571998\pi\)
0.974528 + 0.224265i \(0.0719982\pi\)
\(104\) 0 0
\(105\) −3.67326 + 3.77225i −0.358473 + 0.368134i
\(106\) 0 0
\(107\) −4.84555 + 11.6982i −0.468437 + 1.13091i 0.496409 + 0.868089i \(0.334652\pi\)
−0.964846 + 0.262817i \(0.915348\pi\)
\(108\) 0 0
\(109\) 13.7600 5.69956i 1.31796 0.545919i 0.390766 0.920490i \(-0.372210\pi\)
0.927198 + 0.374571i \(0.122210\pi\)
\(110\) 0 0
\(111\) 0.107616 + 8.09414i 0.0102145 + 0.768262i
\(112\) 0 0
\(113\) 15.8596 1.49195 0.745974 0.665975i \(-0.231984\pi\)
0.745974 + 0.665975i \(0.231984\pi\)
\(114\) 0 0
\(115\) −1.73078 4.17848i −0.161396 0.389645i
\(116\) 0 0
\(117\) −4.34369 + 11.3296i −0.401574 + 1.04742i
\(118\) 0 0
\(119\) −14.4391 + 14.4391i −1.32363 + 1.32363i
\(120\) 0 0
\(121\) 4.45977 + 4.45977i 0.405434 + 0.405434i
\(122\) 0 0
\(123\) −3.06541 + 7.68809i −0.276399 + 0.693212i
\(124\) 0 0
\(125\) 6.72248 2.78454i 0.601277 0.249057i
\(126\) 0 0
\(127\) 2.27121i 0.201537i 0.994910 + 0.100769i \(0.0321301\pi\)
−0.994910 + 0.100769i \(0.967870\pi\)
\(128\) 0 0
\(129\) 0.228063 + 17.1533i 0.0200798 + 1.51027i
\(130\) 0 0
\(131\) 2.57445 + 6.21528i 0.224931 + 0.543032i 0.995547 0.0942683i \(-0.0300512\pi\)
−0.770616 + 0.637300i \(0.780051\pi\)
\(132\) 0 0
\(133\) 7.72502 + 3.19981i 0.669844 + 0.277459i
\(134\) 0 0
\(135\) 2.72822 2.95501i 0.234808 0.254327i
\(136\) 0 0
\(137\) 8.23933 + 8.23933i 0.703934 + 0.703934i 0.965252 0.261319i \(-0.0841574\pi\)
−0.261319 + 0.965252i \(0.584157\pi\)
\(138\) 0 0
\(139\) 4.47443 + 1.85337i 0.379516 + 0.157201i 0.564283 0.825582i \(-0.309153\pi\)
−0.184766 + 0.982782i \(0.559153\pi\)
\(140\) 0 0
\(141\) −7.71507 + 3.31653i −0.649726 + 0.279302i
\(142\) 0 0
\(143\) 8.76181i 0.732700i
\(144\) 0 0
\(145\) 2.89652i 0.240543i
\(146\) 0 0
\(147\) −13.4063 + 5.76305i −1.10573 + 0.475328i
\(148\) 0 0
\(149\) 14.7806 + 6.12233i 1.21087 + 0.501561i 0.894497 0.447073i \(-0.147534\pi\)
0.316377 + 0.948634i \(0.397534\pi\)
\(150\) 0 0
\(151\) −6.48300 6.48300i −0.527579 0.527579i 0.392271 0.919850i \(-0.371690\pi\)
−0.919850 + 0.392271i \(0.871690\pi\)
\(152\) 0 0
\(153\) 10.7322 11.3187i 0.867648 0.915061i
\(154\) 0 0
\(155\) −0.245328 0.101618i −0.0197053 0.00816218i
\(156\) 0 0
\(157\) −0.376399 0.908707i −0.0300399 0.0725227i 0.908148 0.418650i \(-0.137497\pi\)
−0.938188 + 0.346127i \(0.887497\pi\)
\(158\) 0 0
\(159\) −0.103542 7.78772i −0.00821142 0.617606i
\(160\) 0 0
\(161\) 22.9494i 1.80867i
\(162\) 0 0
\(163\) 1.44038 0.596624i 0.112819 0.0467312i −0.325560 0.945521i \(-0.605553\pi\)
0.438379 + 0.898790i \(0.355553\pi\)
\(164\) 0 0
\(165\) −1.07562 + 2.69767i −0.0837370 + 0.210013i
\(166\) 0 0
\(167\) 3.06006 + 3.06006i 0.236795 + 0.236795i 0.815522 0.578727i \(-0.196450\pi\)
−0.578727 + 0.815522i \(0.696450\pi\)
\(168\) 0 0
\(169\) 2.37482 2.37482i 0.182679 0.182679i
\(170\) 0 0
\(171\) −5.96366 2.28643i −0.456053 0.174848i
\(172\) 0 0
\(173\) 4.07676 + 9.84216i 0.309950 + 0.748286i 0.999706 + 0.0242438i \(0.00771779\pi\)
−0.689756 + 0.724042i \(0.742282\pi\)
\(174\) 0 0
\(175\) 17.2844 1.30658
\(176\) 0 0
\(177\) 0.201541 + 15.1585i 0.0151487 + 1.13938i
\(178\) 0 0
\(179\) 4.90033 2.02978i 0.366268 0.151713i −0.191956 0.981404i \(-0.561483\pi\)
0.558224 + 0.829690i \(0.311483\pi\)
\(180\) 0 0
\(181\) 7.21135 17.4097i 0.536016 1.29406i −0.391468 0.920192i \(-0.628033\pi\)
0.927483 0.373864i \(-0.121967\pi\)
\(182\) 0 0
\(183\) 7.80668 8.01706i 0.577086 0.592638i
\(184\) 0 0
\(185\) −2.55787 + 2.55787i −0.188058 + 0.188058i
\(186\) 0 0
\(187\) −4.31028 + 10.4059i −0.315199 + 0.760957i
\(188\) 0 0
\(189\) 18.5279 8.55527i 1.34770 0.622305i
\(190\) 0 0
\(191\) −5.45750 −0.394891 −0.197446 0.980314i \(-0.563265\pi\)
−0.197446 + 0.980314i \(0.563265\pi\)
\(192\) 0 0
\(193\) −10.5440 −0.758971 −0.379486 0.925198i \(-0.623899\pi\)
−0.379486 + 0.925198i \(0.623899\pi\)
\(194\) 0 0
\(195\) −4.98145 + 2.14141i −0.356729 + 0.153349i
\(196\) 0 0
\(197\) 0.0524216 0.126557i 0.00373489 0.00901681i −0.922001 0.387187i \(-0.873447\pi\)
0.925736 + 0.378170i \(0.123447\pi\)
\(198\) 0 0
\(199\) −6.64709 + 6.64709i −0.471200 + 0.471200i −0.902303 0.431103i \(-0.858125\pi\)
0.431103 + 0.902303i \(0.358125\pi\)
\(200\) 0 0
\(201\) −7.32057 7.12846i −0.516353 0.502803i
\(202\) 0 0
\(203\) −5.62450 + 13.5787i −0.394763 + 0.953041i
\(204\) 0 0
\(205\) −3.41708 + 1.41540i −0.238659 + 0.0988560i
\(206\) 0 0
\(207\) 0.466058 + 17.5237i 0.0323932 + 1.21798i
\(208\) 0 0
\(209\) 4.61205 0.319022
\(210\) 0 0
\(211\) 2.88401 + 6.96261i 0.198543 + 0.479326i 0.991524 0.129920i \(-0.0414722\pi\)
−0.792981 + 0.609246i \(0.791472\pi\)
\(212\) 0 0
\(213\) 5.65551 14.1841i 0.387509 0.971878i
\(214\) 0 0
\(215\) −5.42071 + 5.42071i −0.369689 + 0.369689i
\(216\) 0 0
\(217\) −0.952765 0.952765i −0.0646779 0.0646779i
\(218\) 0 0
\(219\) 3.29817 + 1.31505i 0.222870 + 0.0888632i
\(220\) 0 0
\(221\) −19.4281 + 8.04739i −1.30688 + 0.541326i
\(222\) 0 0
\(223\) 16.6352i 1.11398i −0.830520 0.556988i \(-0.811957\pi\)
0.830520 0.556988i \(-0.188043\pi\)
\(224\) 0 0
\(225\) −13.1981 + 0.351013i −0.879872 + 0.0234009i
\(226\) 0 0
\(227\) 1.09433 + 2.64195i 0.0726335 + 0.175353i 0.956027 0.293280i \(-0.0947468\pi\)
−0.883393 + 0.468633i \(0.844747\pi\)
\(228\) 0 0
\(229\) 1.48780 + 0.616268i 0.0983167 + 0.0407241i 0.431300 0.902209i \(-0.358055\pi\)
−0.332983 + 0.942933i \(0.608055\pi\)
\(230\) 0 0
\(231\) −10.2808 + 10.5579i −0.676430 + 0.694659i
\(232\) 0 0
\(233\) 14.1523 + 14.1523i 0.927150 + 0.927150i 0.997521 0.0703713i \(-0.0224184\pi\)
−0.0703713 + 0.997521i \(0.522418\pi\)
\(234\) 0 0
\(235\) −3.46705 1.43610i −0.226165 0.0936808i
\(236\) 0 0
\(237\) 9.06080 + 21.0777i 0.588562 + 1.36914i
\(238\) 0 0
\(239\) 5.75051i 0.371969i 0.982553 + 0.185985i \(0.0595475\pi\)
−0.982553 + 0.185985i \(0.940453\pi\)
\(240\) 0 0
\(241\) 0.404801i 0.0260755i 0.999915 + 0.0130378i \(0.00415016\pi\)
−0.999915 + 0.0130378i \(0.995850\pi\)
\(242\) 0 0
\(243\) −13.9738 + 6.90891i −0.896419 + 0.443207i
\(244\) 0 0
\(245\) −6.02461 2.49548i −0.384898 0.159430i
\(246\) 0 0
\(247\) 6.08876 + 6.08876i 0.387418 + 0.387418i
\(248\) 0 0
\(249\) −8.31898 8.10067i −0.527194 0.513359i
\(250\) 0 0
\(251\) 10.1825 + 4.21772i 0.642712 + 0.266220i 0.680143 0.733079i \(-0.261917\pi\)
−0.0374311 + 0.999299i \(0.511917\pi\)
\(252\) 0 0
\(253\) −4.84418 11.6949i −0.304551 0.735252i
\(254\) 0 0
\(255\) 6.96963 0.0926651i 0.436455 0.00580291i
\(256\) 0 0
\(257\) 27.0174i 1.68530i 0.538460 + 0.842651i \(0.319006\pi\)
−0.538460 + 0.842651i \(0.680994\pi\)
\(258\) 0 0
\(259\) −16.9581 + 7.02426i −1.05372 + 0.436466i
\(260\) 0 0
\(261\) 4.01901 10.4827i 0.248770 0.648863i
\(262\) 0 0
\(263\) −0.0909901 0.0909901i −0.00561069 0.00561069i 0.704296 0.709907i \(-0.251263\pi\)
−0.709907 + 0.704296i \(0.751263\pi\)
\(264\) 0 0
\(265\) 2.46103 2.46103i 0.151180 0.151180i
\(266\) 0 0
\(267\) 21.0895 + 8.40886i 1.29066 + 0.514614i
\(268\) 0 0
\(269\) −8.83071 21.3192i −0.538418 1.29986i −0.925827 0.377948i \(-0.876630\pi\)
0.387409 0.921908i \(1.62663\pi\)
\(270\) 0 0
\(271\) −2.82777 −0.171775 −0.0858874 0.996305i \(-0.527373\pi\)
−0.0858874 + 0.996305i \(0.527373\pi\)
\(272\) 0 0
\(273\) −27.5110 + 0.365774i −1.66504 + 0.0221377i
\(274\) 0 0
\(275\) 8.80806 3.64842i 0.531146 0.220008i
\(276\) 0 0
\(277\) −5.81789 + 14.0456i −0.349563 + 0.843920i 0.647108 + 0.762398i \(0.275978\pi\)
−0.996672 + 0.0815223i \(0.974022\pi\)
\(278\) 0 0
\(279\) 0.746862 + 0.708164i 0.0447135 + 0.0423967i
\(280\) 0 0
\(281\) 11.3239 11.3239i 0.675530 0.675530i −0.283455 0.958985i \(-0.591481\pi\)
0.958985 + 0.283455i \(0.0914808\pi\)
\(282\) 0 0
\(283\) −3.05059 + 7.36479i −0.181339 + 0.437791i −0.988243 0.152892i \(-0.951141\pi\)
0.806904 + 0.590683i \(0.201141\pi\)
\(284\) 0 0
\(285\) −1.12719 2.62214i −0.0667693 0.155322i
\(286\) 0 0
\(287\) −18.7676 −1.10782
\(288\) 0 0
\(289\) 10.0325 0.590149
\(290\) 0 0
\(291\) −6.54594 15.2275i −0.383730 0.892652i
\(292\) 0 0
\(293\) 4.77629 11.5310i 0.279034 0.673648i −0.720775 0.693169i \(-0.756214\pi\)
0.999809 + 0.0195210i \(0.00621412\pi\)
\(294\) 0 0
\(295\) −4.79031 + 4.79031i −0.278903 + 0.278903i
\(296\) 0 0
\(297\) 7.63585 8.27061i 0.443077 0.479909i
\(298\) 0 0
\(299\) 9.04421 21.8346i 0.523040 1.26273i
\(300\) 0 0
\(301\) −35.9380 + 14.8860i −2.07143 + 0.858016i
\(302\) 0 0
\(303\) 4.62708 0.0615196i 0.265819 0.00353421i
\(304\) 0 0
\(305\) 5.00053 0.286330
\(306\) 0 0
\(307\) −12.3306 29.7687i −0.703744 1.69899i −0.715071 0.699052i \(-0.753606\pi\)
0.0113269 0.999936i \(-0.496394\pi\)
\(308\) 0 0
\(309\) −17.3249 6.90781i −0.985577 0.392971i
\(310\) 0 0
\(311\) 22.2380 22.2380i 1.26100 1.26100i 0.310392 0.950609i \(-0.399540\pi\)
0.950609 0.310392i \(-0.100460\pi\)
\(312\) 0 0
\(313\) −13.4230 13.4230i −0.758713 0.758713i 0.217375 0.976088i \(-0.430250\pi\)
−0.976088 + 0.217375i \(0.930250\pi\)
\(314\) 0 0
\(315\) 8.51526 + 3.26470i 0.479781 + 0.183945i
\(316\) 0 0
\(317\) 0.947076 0.392292i 0.0531931 0.0220333i −0.355928 0.934513i \(-0.615835\pi\)
0.409121 + 0.912480i \(0.365835\pi\)
\(318\) 0 0
\(319\) 8.10688i 0.453898i
\(320\) 0 0
\(321\) 21.9293 0.291562i 1.22398 0.0162734i
\(322\) 0 0
\(323\) −4.23599 10.2266i −0.235697 0.569022i
\(324\) 0 0
\(325\) 16.4449 + 6.81168i 0.912197 + 0.377844i
\(326\) 0 0
\(327\) −18.4818 17.9968i −1.02205 0.995227i
\(328\) 0 0
\(329\) −13.4647 13.4647i −0.742335 0.742335i
\(330\) 0 0
\(331\) 20.7914 + 8.61208i 1.14280 + 0.473363i 0.872113 0.489305i \(-0.162749\pi\)
0.270686 + 0.962668i \(0.412749\pi\)
\(332\) 0 0
\(333\) 12.8062 5.70798i 0.701776 0.312795i
\(334\) 0 0
\(335\) 4.56610i 0.249473i
\(336\) 0 0
\(337\) 29.6373i 1.61444i 0.590248 + 0.807222i \(0.299030\pi\)
−0.590248 + 0.807222i \(0.700970\pi\)
\(338\) 0 0
\(339\) −10.8487 25.2367i −0.589218 1.37067i
\(340\) 0 0
\(341\) −0.686634 0.284413i −0.0371833 0.0154018i
\(342\) 0 0
\(343\) −3.95740 3.95740i −0.213680 0.213680i
\(344\) 0 0
\(345\) −5.46509 + 5.61237i −0.294231 + 0.302160i
\(346\) 0 0
\(347\) −21.8544 9.05241i −1.17321 0.485959i −0.290956 0.956736i \(-0.593973\pi\)
−0.882252 + 0.470778i \(0.843973\pi\)
\(348\) 0 0
\(349\) −0.170032 0.410493i −0.00910160 0.0219732i 0.919263 0.393643i \(-0.128785\pi\)
−0.928365 + 0.371670i \(0.878785\pi\)
\(350\) 0 0
\(351\) 20.9995 0.837993i 1.12087 0.0447288i
\(352\) 0 0
\(353\) 23.1851i 1.23402i −0.786956 0.617010i \(-0.788344\pi\)
0.786956 0.617010i \(-0.211656\pi\)
\(354\) 0 0
\(355\) 6.30432 2.61133i 0.334599 0.138595i
\(356\) 0 0
\(357\) 32.8533 + 13.0993i 1.73878 + 0.693290i
\(358\) 0 0
\(359\) 7.59655 + 7.59655i 0.400930 + 0.400930i 0.878561 0.477630i \(-0.158504\pi\)
−0.477630 + 0.878561i \(0.658504\pi\)
\(360\) 0 0
\(361\) 10.2300 10.2300i 0.538422 0.538422i
\(362\) 0 0
\(363\) 4.04595 10.1473i 0.212357 0.532595i
\(364\) 0 0
\(365\) 0.607204 + 1.46592i 0.0317825 + 0.0767298i
\(366\) 0 0
\(367\) 14.4269 0.753079 0.376540 0.926401i \(-0.377114\pi\)
0.376540 + 0.926401i \(0.377114\pi\)
\(368\) 0 0
\(369\) 14.3306 0.381133i 0.746020 0.0198410i
\(370\) 0 0
\(371\) 16.3161 6.75834i 0.847089 0.350876i
\(372\) 0 0
\(373\) −4.38447 + 10.5851i −0.227019 + 0.548073i −0.995812 0.0914248i \(-0.970858\pi\)
0.768793 + 0.639498i \(0.220858\pi\)
\(374\) 0 0
\(375\) −9.02938 8.79243i −0.466275 0.454039i
\(376\) 0 0
\(377\) −10.7026 + 10.7026i −0.551211 + 0.551211i
\(378\) 0 0
\(379\) −1.10789 + 2.67468i −0.0569084 + 0.137389i −0.949776 0.312930i \(-0.898690\pi\)
0.892868 + 0.450319i \(0.148690\pi\)
\(380\) 0 0
\(381\) 3.61406 1.55360i 0.185154 0.0795934i
\(382\) 0 0
\(383\) −3.50037 −0.178861 −0.0894304 0.995993i \(-0.528505\pi\)
−0.0894304 + 0.995993i \(0.528505\pi\)
\(384\) 0 0
\(385\) −6.58535 −0.335621
\(386\) 0 0
\(387\) 27.1393 12.0965i 1.37957 0.614901i
\(388\) 0 0
\(389\) −10.6893 + 25.8063i −0.541969 + 1.30843i 0.381362 + 0.924426i \(0.375455\pi\)
−0.923332 + 0.384004i \(0.874545\pi\)
\(390\) 0 0
\(391\) −21.4826 + 21.4826i −1.08642 + 1.08642i
\(392\) 0 0
\(393\) 8.12905 8.34813i 0.410056 0.421107i
\(394\) 0 0
\(395\) −3.92344 + 9.47203i −0.197410 + 0.476590i
\(396\) 0 0
\(397\) −11.8148 + 4.89383i −0.592966 + 0.245614i −0.658926 0.752208i \(-0.728989\pi\)
0.0659602 + 0.997822i \(0.478989\pi\)
\(398\) 0 0
\(399\) −0.192536 14.4813i −0.00963887 0.724970i
\(400\) 0 0
\(401\) −37.4682 −1.87107 −0.935537 0.353229i \(-0.885084\pi\)
−0.935537 + 0.353229i \(0.885084\pi\)
\(402\) 0 0
\(403\) −0.531006 1.28196i −0.0264513 0.0638591i
\(404\) 0 0
\(405\) −6.56839 2.31994i −0.326386 0.115279i
\(406\) 0 0
\(407\) −7.15905 + 7.15905i −0.354861 + 0.354861i
\(408\) 0 0
\(409\) −9.85216 9.85216i −0.487158 0.487158i 0.420250 0.907408i \(-0.361942\pi\)
−0.907408 + 0.420250i \(0.861942\pi\)
\(410\) 0 0
\(411\) 7.47481 18.7469i 0.368705 0.924717i
\(412\) 0 0
\(413\) −31.7586 + 13.1549i −1.56274 + 0.647308i
\(414\) 0 0
\(415\) 5.18885i 0.254710i
\(416\) 0 0
\(417\) −0.111520 8.38774i −0.00546114 0.410749i
\(418\) 0 0
\(419\) 5.45030 + 13.1582i 0.266264 + 0.642819i 0.999302 0.0373695i \(-0.0118979\pi\)
−0.733037 + 0.680189i \(0.761898\pi\)
\(420\) 0 0
\(421\) −13.4081 5.55381i −0.653470 0.270676i 0.0312176 0.999513i \(-0.490062\pi\)
−0.684688 + 0.728836i \(0.740062\pi\)
\(422\) 0 0
\(423\) 10.5549 + 10.0080i 0.513195 + 0.486605i
\(424\) 0 0
\(425\) −16.1797 16.1797i −0.784832 0.784832i
\(426\) 0 0
\(427\) 23.4423 + 9.71011i 1.13445 + 0.469905i
\(428\) 0 0
\(429\) −13.9423 + 5.99345i −0.673139 + 0.289367i
\(430\) 0 0
\(431\) 37.0767i 1.78592i −0.450133 0.892962i \(-0.648623\pi\)
0.450133 0.892962i \(-0.351377\pi\)
\(432\) 0 0
\(433\) 0.656469i 0.0315479i −0.999876 0.0157739i \(-0.994979\pi\)
0.999876 0.0157739i \(-0.00502121\pi\)
\(434\) 0 0
\(435\) 4.60909 1.98134i 0.220989 0.0949980i
\(436\) 0 0
\(437\) 11.4933 + 4.76069i 0.549801 + 0.227735i
\(438\) 0 0
\(439\) 14.8613 + 14.8613i 0.709293 + 0.709293i 0.966387 0.257093i \(-0.0827648\pi\)
−0.257093 + 0.966387i \(0.582765\pi\)
\(440\) 0 0
\(441\) 18.3409 + 17.3906i 0.873378 + 0.828125i
\(442\) 0 0
\(443\) 5.86331 + 2.42866i 0.278574 + 0.115389i 0.517596 0.855625i \(-0.326827\pi\)
−0.239022 + 0.971014i \(0.576827\pi\)
\(444\) 0 0
\(445\) 3.88265 + 9.37354i 0.184055 + 0.444348i
\(446\) 0 0
\(447\) −0.368388 27.7076i −0.0174241 1.31053i
\(448\) 0 0
\(449\) 0.964596i 0.0455221i −0.999741 0.0227611i \(-0.992754\pi\)
0.999741 0.0227611i \(-0.00724569\pi\)
\(450\) 0 0
\(451\) −9.56386 + 3.96148i −0.450345 + 0.186539i
\(452\) 0 0
\(453\) −5.88145 + 14.7507i −0.276334 + 0.693050i
\(454\) 0 0
\(455\) −8.69388 8.69388i −0.407575 0.407575i
\(456\) 0 0
\(457\) 8.65709 8.65709i 0.404962 0.404962i −0.475016 0.879977i \(-0.657558\pi\)
0.879977 + 0.475016i \(0.157558\pi\)
\(458\) 0 0
\(459\) −25.3522 9.33521i −1.18334 0.435730i
\(460\) 0 0
\(461\) −12.4022 29.9416i −0.577628 1.39452i −0.894936 0.446195i \(-0.852779\pi\)
0.317308 0.948323i \(1.60278\pi\)
\(462\) 0 0
\(463\) 18.0597 0.839306 0.419653 0.907685i \(-0.362152\pi\)
0.419653 + 0.907685i \(0.362152\pi\)
\(464\) 0 0
\(465\) 0.00611450 + 0.459891i 0.000283553 + 0.0213269i
\(466\) 0 0
\(467\) −3.41999 + 1.41660i −0.158258 + 0.0655526i −0.460406 0.887708i \(-0.652296\pi\)
0.302148 + 0.953261i \(0.402296\pi\)
\(468\) 0 0
\(469\) 8.86653 21.4057i 0.409418 0.988423i
\(470\) 0 0
\(471\) −1.18851 + 1.22054i −0.0547636 + 0.0562395i
\(472\) 0 0
\(473\) −15.1717 + 15.1717i −0.697594 + 0.697594i
\(474\) 0 0
\(475\) −3.58554 + 8.65625i −0.164516 + 0.397176i
\(476\) 0 0
\(477\) −12.3214 + 5.49189i −0.564158 + 0.251456i
\(478\) 0 0
\(479\) 22.0035 1.00537 0.502684 0.864470i \(-0.332346\pi\)
0.502684 + 0.864470i \(0.332346\pi\)
\(480\) 0 0
\(481\) −18.9025 −0.861882
\(482\) 0 0
\(483\) −36.5183 + 15.6984i −1.66164 + 0.714300i
\(484\) 0 0
\(485\) 2.83448 6.84304i 0.128707 0.310726i
\(486\) 0 0
\(487\) −4.12841 + 4.12841i −0.187076 + 0.187076i −0.794431 0.607355i \(-0.792231\pi\)
0.607355 + 0.794431i \(0.292231\pi\)
\(488\) 0 0
\(489\) −1.93466 1.88389i −0.0874882 0.0851924i
\(490\) 0 0
\(491\) 5.44901 13.1551i 0.245911 0.593681i −0.751939 0.659233i \(-0.770881\pi\)
0.997849 + 0.0655526i \(0.0208810\pi\)
\(492\) 0 0
\(493\) 17.9759 7.44586i 0.809594 0.335345i
\(494\) 0 0
\(495\) 5.02845 0.133736i 0.226012 0.00601097i
\(496\) 0 0
\(497\) 34.6251 1.55315
\(498\) 0 0
\(499\) 14.4361 + 34.8519i 0.646250 + 1.56018i 0.818109 + 0.575063i \(0.195022\pi\)
−0.171860 + 0.985121i \(0.554978\pi\)
\(500\) 0 0
\(501\) 2.77612 6.96255i 0.124028 0.311064i
\(502\) 0 0
\(503\) −2.95140 + 2.95140i −0.131596 + 0.131596i −0.769837 0.638241i \(-0.779662\pi\)
0.638241 + 0.769837i \(0.279662\pi\)
\(504\) 0 0
\(505\) 1.46222 + 1.46222i 0.0650681 + 0.0650681i
\(506\) 0 0
\(507\) −5.40343 2.15447i −0.239975 0.0956832i
\(508\) 0 0
\(509\) 40.0107 16.5730i 1.77344 0.734584i 0.779281 0.626675i \(-0.215585\pi\)
0.994161 0.107909i \(-0.0344154\pi\)
\(510\) 0 0
\(511\) 8.05125i 0.356166i
\(512\) 0 0
\(513\) 0.441103 + 11.0537i 0.0194752 + 0.488033i
\(514\) 0 0
\(515\) −3.18956 7.70028i −0.140549 0.339315i
\(516\) 0 0
\(517\) −9.70371 4.01941i −0.426769 0.176773i
\(518\) 0 0
\(519\) 12.8727 13.2196i 0.565049 0.580276i
\(520\) 0 0
\(521\) 9.10873 + 9.10873i 0.399061 + 0.399061i 0.877902 0.478841i \(-0.158943\pi\)
−0.478841 + 0.877902i \(0.658943\pi\)
\(522\) 0 0
\(523\) −18.7797 7.77882i −0.821181 0.340144i −0.0677753 0.997701i \(-0.521590\pi\)
−0.753405 + 0.657556i \(0.771590\pi\)
\(524\) 0 0
\(525\) −11.8233 27.5039i −0.516011 1.20037i
\(526\) 0 0
\(527\) 1.78374i 0.0777009i
\(528\) 0 0
\(529\) 11.1443i 0.484534i
\(530\) 0 0
\(531\) 23.9832 10.6898i 1.04078 0.463896i
\(532\) 0 0
\(533\) −17.8560 7.39618i −0.773427 0.320364i
\(534\) 0 0
\(535\) 6.92999 + 6.92999i 0.299609 + 0.299609i
\(536\) 0 0
\(537\) −6.58194 6.40921i −0.284032 0.276578i
\(538\) 0 0
\(539\) −16.8619 6.98443i −0.726294 0.300841i
\(540\) 0 0
\(541\) −4.91944 11.8766i −0.211503 0.510614i 0.782151 0.623088i \(-0.214122\pi\)
−0.993655 + 0.112475i \(0.964122\pi\)
\(542\) 0 0
\(543\) −32.6362 + 0.433916i −1.40055 + 0.0186211i
\(544\) 0 0
\(545\) 11.5278i 0.493796i
\(546\) 0 0
\(547\) 19.4330 8.04942i 0.830896 0.344168i 0.0736387 0.997285i \(-0.476539\pi\)
0.757257 + 0.653117i \(0.226539\pi\)
\(548\) 0 0
\(549\) −18.0973 6.93839i −0.772373 0.296123i
\(550\) 0 0
\(551\) −5.63363 5.63363i −0.240001 0.240001i
\(552\) 0 0
\(553\) −36.7859 + 36.7859i −1.56429 + 1.56429i
\(554\) 0 0
\(555\) 5.81990 + 2.32052i 0.247041 + 0.0985007i
\(556\) 0 0
\(557\) 14.3258 + 34.5854i 0.607002 + 1.46543i 0.866245 + 0.499620i \(0.166527\pi\)
−0.259243 + 0.965812i \(0.583473\pi\)
\(558\) 0 0
\(559\) −40.0588 −1.69431
\(560\) 0 0
\(561\) 19.5069 0.259355i 0.823581 0.0109500i
\(562\) 0 0
\(563\) −14.4215 + 5.97357i −0.607793 + 0.251756i −0.665284 0.746590i \(-0.731690\pi\)
0.0574918 + 0.998346i \(0.481690\pi\)
\(564\) 0 0
\(565\) 4.69761 11.3410i 0.197630 0.477121i
\(566\) 0 0
\(567\) −26.2875 23.6304i −1.10397 0.992382i
\(568\) 0 0
\(569\) 3.11604 3.11604i 0.130631 0.130631i −0.638768 0.769399i \(-0.720556\pi\)
0.769399 + 0.638768i \(0.220556\pi\)
\(570\) 0 0
\(571\) −4.75950 + 11.4904i −0.199179 + 0.480860i −0.991636 0.129068i \(-0.958802\pi\)
0.792457 + 0.609928i \(0.208802\pi\)
\(572\) 0 0
\(573\) 3.73316 + 8.68427i 0.155955 + 0.362791i
\(574\) 0 0
\(575\) 25.7159 1.07243
\(576\) 0 0
\(577\) −18.4677 −0.768820 −0.384410 0.923163i \(-0.625595\pi\)
−0.384410 + 0.923163i \(0.625595\pi\)
\(578\) 0 0
\(579\) 7.21252 + 16.7781i 0.299742 + 0.697275i
\(580\) 0 0
\(581\) 10.0758 24.3251i 0.418014 1.00917i
\(582\) 0 0
\(583\) 6.88803 6.88803i 0.285273 0.285273i
\(584\) 0 0
\(585\) 6.81504 + 6.46193i 0.281767 + 0.267168i
\(586\) 0 0
\(587\) 2.04862 4.94582i 0.0845558 0.204136i −0.875946 0.482409i \(-0.839762\pi\)
0.960502 + 0.278273i \(0.0897620\pi\)
\(588\) 0 0
\(589\) 0.674800 0.279511i 0.0278047 0.0115171i
\(590\) 0 0
\(591\) −0.237243 + 0.00315427i −0.00975886 + 0.000129749i
\(592\) 0 0
\(593\) −26.6090 −1.09270 −0.546351 0.837556i \(-0.683984\pi\)
−0.546351 + 0.837556i \(0.683984\pi\)
\(594\) 0 0
\(595\) 6.04839 + 14.6021i 0.247960 + 0.598628i
\(596\) 0 0
\(597\) 15.1241 + 6.03031i 0.618988 + 0.246804i
\(598\) 0 0
\(599\) −12.7251 + 12.7251i −0.519933 + 0.519933i −0.917551 0.397618i \(-0.869837\pi\)
0.397618 + 0.917551i \(0.369837\pi\)
\(600\) 0 0
\(601\) −6.45474 6.45474i −0.263294 0.263294i 0.563097 0.826391i \(-0.309610\pi\)
−0.826391 + 0.563097i \(0.809610\pi\)
\(602\) 0 0
\(603\) −6.33560 + 16.5250i −0.258006 + 0.672952i
\(604\) 0 0
\(605\) 4.51011 1.86815i 0.183362 0.0759511i
\(606\) 0 0
\(607\) 30.2504i 1.22783i 0.789373 + 0.613914i \(0.210406\pi\)
−0.789373 + 0.613914i \(0.789594\pi\)
\(608\) 0 0
\(609\) 25.4546 0.338433i 1.03147 0.0137140i
\(610\) 0 0
\(611\) −7.50433 18.1171i −0.303593 0.732938i
\(612\) 0 0
\(613\) 2.29750 + 0.951656i 0.0927952 + 0.0384370i 0.428598 0.903495i \(-0.359008\pi\)
−0.335803 + 0.941932i \(0.609008\pi\)
\(614\) 0 0
\(615\) 4.58969 + 4.46925i 0.185074 + 0.180217i
\(616\) 0 0
\(617\) 3.87504 + 3.87504i 0.156003 + 0.156003i 0.780793 0.624790i \(-0.214815\pi\)
−0.624790 + 0.780793i \(0.714815\pi\)
\(618\) 0 0
\(619\) −7.55208 3.12818i −0.303544 0.125732i 0.225712 0.974194i \(-0.427529\pi\)
−0.529256 + 0.848462i \(0.677529\pi\)
\(620\) 0 0
\(621\) 27.5659 12.7286i 1.10618 0.510781i
\(622\) 0 0
\(623\) 51.4821i 2.06259i
\(624\) 0 0
\(625\) 16.3726i 0.654905i
\(626\) 0 0
\(627\) −3.15484 7.33894i −0.125992 0.293089i
\(628\) 0 0
\(629\) 22.4495 + 9.29889i 0.895121 + 0.370771i
\(630\) 0 0
\(631\) −3.02275 3.02275i −0.120334 0.120334i 0.644375 0.764709i \(-0.277117\pi\)
−0.764709 + 0.644375i \(0.777117\pi\)
\(632\) 0 0
\(633\) 9.10648 9.35190i 0.361950 0.371705i
\(634\) 0 0
\(635\) 1.62411 + 0.672730i 0.0644510 + 0.0266965i
\(636\) 0 0
\(637\) −13.0401 31.4816i −0.516668 1.24735i
\(638\) 0 0
\(639\) −26.4391 + 0.703168i −1.04591 + 0.0278169i
\(640\) 0 0
\(641\) 30.4562i 1.20295i 0.798893 + 0.601473i \(0.205419\pi\)
−0.798893 + 0.601473i \(0.794581\pi\)
\(642\) 0 0
\(643\) −18.0821 + 7.48986i −0.713089 + 0.295371i −0.709582 0.704623i \(-0.751116\pi\)
−0.00350703 + 0.999994i \(0.501116\pi\)
\(644\) 0 0
\(645\) 12.3337 + 4.91772i 0.485639 + 0.193635i
\(646\) 0 0
\(647\) 28.1003 + 28.1003i 1.10474 + 1.10474i 0.993831 + 0.110905i \(0.0353748\pi\)
0.110905 + 0.993831i \(0.464625\pi\)
\(648\) 0 0
\(649\) −13.4073 + 13.4073i −0.526282 + 0.526282i
\(650\) 0 0
\(651\) −0.864358 + 2.16782i −0.0338769 + 0.0849636i
\(652\) 0 0
\(653\) 6.44946 + 15.5704i 0.252387 + 0.609316i 0.998396 0.0566202i \(-0.0180324\pi\)
−0.746009 + 0.665936i \(0.768032\pi\)
\(654\) 0 0
\(655\) 5.20703 0.203455
\(656\) 0 0
\(657\) −0.163505 6.14778i −0.00637894 0.239848i
\(658\) 0 0
\(659\) −30.0479 + 12.4463i −1.17050 + 0.484838i −0.881358 0.472448i \(-0.843370\pi\)
−0.289143 + 0.957286i \(0.593370\pi\)
\(660\) 0 0
\(661\) −16.0509 + 38.7503i −0.624308 + 1.50721i 0.222290 + 0.974981i \(0.428647\pi\)
−0.846598 + 0.532233i \(0.821353\pi\)
\(662\) 0 0
\(663\) 26.0951 + 25.4103i 1.01345 + 0.986854i
\(664\) 0 0
\(665\) 4.57629 4.57629i 0.177461 0.177461i
\(666\) 0 0
\(667\) −8.36817 + 20.2025i −0.324017 + 0.782246i
\(668\) 0 0
\(669\) −26.4708 + 11.3792i −1.02342 + 0.439945i
\(670\) 0 0
\(671\) 13.9957 0.540297
\(672\) 0 0
\(673\) 1.07753 0.0415357 0.0207678 0.999784i \(-0.493389\pi\)
0.0207678 + 0.999784i \(0.493389\pi\)
\(674\) 0 0
\(675\) 9.58659 + 20.7614i 0.368988 + 0.799106i
\(676\) 0 0
\(677\) −12.6041 + 30.4289i −0.484414 + 1.16948i 0.473078 + 0.881021i \(0.343143\pi\)
−0.957492 + 0.288459i \(0.906857\pi\)
\(678\) 0 0
\(679\) 26.5758 26.5758i 1.01989 1.01989i
\(680\) 0 0
\(681\) 3.45545 3.54857i 0.132413 0.135981i
\(682\) 0 0
\(683\) −19.7550 + 47.6928i −0.755904 + 1.82491i −0.233120 + 0.972448i \(0.574893\pi\)
−0.522784 + 0.852465i \(0.675107\pi\)
\(684\) 0 0
\(685\) 8.33233 3.45136i 0.318362 0.131870i
\(686\) 0 0
\(687\) −0.0370816 2.78902i −0.00141475 0.106408i
\(688\) 0 0
\(689\) 18.1870 0.692868
\(690\) 0 0
\(691\) −4.23089 10.2143i −0.160951 0.388569i 0.822745 0.568411i \(-0.192441\pi\)
−0.983696 + 0.179842i \(0.942441\pi\)
\(692\) 0 0
\(693\) 23.8328 + 9.13737i 0.905335 + 0.347100i
\(694\) 0 0
\(695\) 2.65065 2.65065i 0.100545 0.100545i
\(696\) 0 0
\(697\) 17.5681 + 17.5681i 0.665438 + 0.665438i
\(698\) 0 0
\(699\) 12.8391 32.2007i 0.485621 1.21794i
\(700\) 0 0
\(701\) 22.1122 9.15919i 0.835168 0.345938i 0.0762214 0.997091i \(-0.475714\pi\)
0.758946 + 0.651153i \(0.225714\pi\)
\(702\) 0 0
\(703\) 9.94993i 0.375269i
\(704\) 0 0
\(705\) 0.0864119 + 6.49931i 0.00325446 + 0.244778i
\(706\) 0 0
\(707\) 4.01547 + 9.69421i 0.151017 + 0.364588i
\(708\) 0 0
\(709\) −28.2667 11.7085i −1.06158 0.439721i −0.217568 0.976045i \(-0.569812\pi\)
−0.844012 + 0.536325i \(0.819812\pi\)
\(710\) 0 0
\(711\) 27.3419 28.8360i 1.02540 1.08144i
\(712\) 0 0
\(713\) −1.41753 1.41753i −0.0530869 0.0530869i
\(714\) 0 0
\(715\) −6.26547 2.59524i −0.234315 0.0970566i
\(716\) 0 0
\(717\) 9.15051 3.93359i 0.341732 0.146903i
\(718\) 0 0
\(719\) 19.8341i 0.739687i 0.929094 + 0.369843i \(0.120589\pi\)
−0.929094 + 0.369843i \(0.879411\pi\)
\(720\) 0 0
\(721\) 42.2921i 1.57504i
\(722\) 0 0
\(723\) 0.644140 0.276901i 0.0239558 0.0102981i
\(724\) 0 0
\(725\) −15.2156 6.30252i −0.565095 0.234070i
\(726\) 0 0
\(727\) −21.1914 21.1914i −0.785946 0.785946i 0.194881 0.980827i \(-0.437568\pi\)
−0.980827 + 0.194881i \(0.937568\pi\)
\(728\) 0 0
\(729\) 20.5525 + 17.5099i 0.761203 + 0.648513i
\(730\) 0 0
\(731\) 47.5757 + 19.7065i 1.75965 + 0.728871i
\(732\) 0 0
\(733\) 18.2396 + 44.0342i 0.673694 + 1.62644i 0.775283 + 0.631614i \(0.217607\pi\)
−0.101589 + 0.994826i \(0.532393\pi\)
\(734\) 0 0
\(735\) 0.150156 + 11.2937i 0.00553858 + 0.416574i
\(736\) 0 0
\(737\) 12.7798i 0.470749i
\(738\) 0 0
\(739\) 14.9807 6.20519i 0.551073 0.228262i −0.0897317 0.995966i \(-0.528601\pi\)
0.640804 + 0.767704i \(0.278601\pi\)
\(740\) 0 0
\(741\) 5.52378 13.8537i 0.202921 0.508929i
\(742\) 0 0
\(743\) −22.8633 22.8633i −0.838773 0.838773i 0.149925 0.988697i \(-0.452097\pi\)
−0.988697 + 0.149925i \(0.952097\pi\)
\(744\) 0 0
\(745\) 8.75601 8.75601i 0.320795 0.320795i
\(746\) 0 0
\(747\) −7.19968 + 18.7788i −0.263423 + 0.687080i
\(748\) 0 0
\(749\) 19.0307 + 45.9442i 0.695367 + 1.67877i
\(750\) 0 0
\(751\) −25.4070 −0.927116 −0.463558 0.886067i \(-0.653427\pi\)
−0.463558 + 0.886067i \(0.653427\pi\)
\(752\) 0 0
\(753\) −0.253785 19.0880i −0.00924845 0.695605i
\(754\) 0 0
\(755\) −6.55618 + 2.71566i −0.238604 + 0.0988329i
\(756\) 0 0
\(757\) −12.3294 + 29.7658i −0.448120 + 1.08186i 0.524906 + 0.851160i \(0.324101\pi\)
−0.973026 + 0.230697i \(0.925899\pi\)
\(758\) 0 0
\(759\) −15.2959 + 15.7081i −0.555206 + 0.570169i
\(760\) 0 0
\(761\) 23.7667 23.7667i 0.861542 0.861542i −0.129975 0.991517i \(-0.541490\pi\)
0.991517 + 0.129975i \(0.0414898\pi\)
\(762\) 0 0
\(763\) 22.3848 54.0418i 0.810385 1.95644i
\(764\) 0 0
\(765\) −4.91498 11.0271i −0.177701 0.398684i
\(766\) 0 0
\(767\) −35.4002 −1.27823
\(768\) 0 0
\(769\) 20.4960 0.739104 0.369552 0.929210i \(-0.379511\pi\)
0.369552 + 0.929210i \(0.379511\pi\)
\(770\) 0 0
\(771\) 42.9916 18.4811i 1.54830 0.665580i
\(772\) 0 0
\(773\) 17.8280 43.0405i 0.641228 1.54806i −0.183797 0.982964i \(-0.558839\pi\)
0.825025 0.565097i \(-0.191161\pi\)
\(774\) 0 0
\(775\) 1.06762 1.06762i 0.0383500 0.0383500i
\(776\) 0 0
\(777\) 22.7774 + 22.1797i 0.817135 + 0.795691i
\(778\) 0 0
\(779\) 3.89320 9.39903i 0.139489 0.336755i
\(780\) 0 0
\(781\) 17.6448 7.30870i 0.631380 0.261526i
\(782\) 0 0
\(783\) −19.4298 +