Properties

Label 768.2.n.b.289.4
Level $768$
Weight $2$
Character 768.289
Analytic conductor $6.133$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 289.4
Character \(\chi\) \(=\) 768.289
Dual form 768.2.n.b.481.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.382683 + 0.923880i) q^{3} +(3.09318 - 1.28124i) q^{5} +(1.73503 - 1.73503i) q^{7} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\) \(q+(-0.382683 + 0.923880i) q^{3} +(3.09318 - 1.28124i) q^{5} +(1.73503 - 1.73503i) q^{7} +(-0.707107 - 0.707107i) q^{9} +(2.39923 + 5.79225i) q^{11} +(-0.0173304 - 0.00717850i) q^{13} +3.34804i q^{15} -5.57978i q^{17} +(-1.03052 - 0.426856i) q^{19} +(0.938989 + 2.26692i) q^{21} +(-2.01868 - 2.01868i) q^{23} +(4.39068 - 4.39068i) q^{25} +(0.923880 - 0.382683i) q^{27} +(0.706079 - 1.70463i) q^{29} -1.38048 q^{31} -6.26948 q^{33} +(3.14377 - 7.58973i) q^{35} +(2.87315 - 1.19010i) q^{37} +(0.0132641 - 0.0132641i) q^{39} +(6.97897 + 6.97897i) q^{41} +(1.67010 + 4.03197i) q^{43} +(-3.09318 - 1.28124i) q^{45} -1.15993i q^{47} +0.979375i q^{49} +(5.15504 + 2.13529i) q^{51} +(-2.56680 - 6.19681i) q^{53} +(14.8425 + 14.8425i) q^{55} +(0.788727 - 0.788727i) q^{57} +(-0.735935 + 0.304834i) q^{59} +(-4.82262 + 11.6428i) q^{61} -2.45370 q^{63} -0.0628036 q^{65} +(-2.05899 + 4.97085i) q^{67} +(2.63753 - 1.09250i) q^{69} +(1.78298 - 1.78298i) q^{71} +(1.67500 + 1.67500i) q^{73} +(2.37622 + 5.73670i) q^{75} +(14.2124 + 5.88697i) q^{77} +2.67236i q^{79} +1.00000i q^{81} +(-6.91877 - 2.86585i) q^{83} +(-7.14903 - 17.2593i) q^{85} +(1.30466 + 1.30466i) q^{87} +(6.73869 - 6.73869i) q^{89} +(-0.0425236 + 0.0176139i) q^{91} +(0.528286 - 1.27540i) q^{93} -3.73450 q^{95} -1.75001 q^{97} +(2.39923 - 5.79225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + O(q^{10}) \) \( 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91} + O(q^{100}) \)

Character values

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

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\)

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
\(3\) −0.382683 + 0.923880i −0.220942 + 0.533402i
\(4\) 0 0
\(5\) 3.09318 1.28124i 1.38331 0.572987i 0.437949 0.899000i \(-0.355705\pi\)
0.945365 + 0.326013i \(0.105705\pi\)
\(6\) 0 0
\(7\) 1.73503 1.73503i 0.655778 0.655778i −0.298600 0.954378i \(-0.596520\pi\)
0.954378 + 0.298600i \(0.0965198\pi\)
\(8\) 0 0
\(9\) −0.707107 0.707107i −0.235702 0.235702i
\(10\) 0 0
\(11\) 2.39923 + 5.79225i 0.723394 + 1.74643i 0.663443 + 0.748227i \(0.269095\pi\)
0.0599515 + 0.998201i \(0.480905\pi\)
\(12\) 0 0
\(13\) −0.0173304 0.00717850i −0.00480660 0.00199096i 0.380279 0.924872i \(-0.375828\pi\)
−0.385085 + 0.922881i \(0.625828\pi\)
\(14\) 0 0
\(15\) 3.34804i 0.864460i
\(16\) 0 0
\(17\) 5.57978i 1.35329i −0.736307 0.676647i \(-0.763432\pi\)
0.736307 0.676647i \(-0.236568\pi\)
\(18\) 0 0
\(19\) −1.03052 0.426856i −0.236418 0.0979274i 0.261329 0.965250i \(-0.415839\pi\)
−0.497747 + 0.867322i \(0.665839\pi\)
\(20\) 0 0
\(21\) 0.938989 + 2.26692i 0.204904 + 0.494682i
\(22\) 0 0
\(23\) −2.01868 2.01868i −0.420923 0.420923i 0.464598 0.885522i \(-0.346199\pi\)
−0.885522 + 0.464598i \(0.846199\pi\)
\(24\) 0 0
\(25\) 4.39068 4.39068i 0.878136 0.878136i
\(26\) 0 0
\(27\) 0.923880 0.382683i 0.177801 0.0736475i
\(28\) 0 0
\(29\) 0.706079 1.70463i 0.131116 0.316541i −0.844664 0.535297i \(-0.820200\pi\)
0.975780 + 0.218756i \(0.0701998\pi\)
\(30\) 0 0
\(31\) −1.38048 −0.247941 −0.123971 0.992286i \(-0.539563\pi\)
−0.123971 + 0.992286i \(0.539563\pi\)
\(32\) 0 0
\(33\) −6.26948 −1.09138
\(34\) 0 0
\(35\) 3.14377 7.58973i 0.531394 1.28290i
\(36\) 0 0
\(37\) 2.87315 1.19010i 0.472342 0.195651i −0.133797 0.991009i \(-0.542717\pi\)
0.606140 + 0.795358i \(0.292717\pi\)
\(38\) 0 0
\(39\) 0.0132641 0.0132641i 0.00212396 0.00212396i
\(40\) 0 0
\(41\) 6.97897 + 6.97897i 1.08993 + 1.08993i 0.995535 + 0.0943974i \(0.0300924\pi\)
0.0943974 + 0.995535i \(0.469908\pi\)
\(42\) 0 0
\(43\) 1.67010 + 4.03197i 0.254687 + 0.614869i 0.998571 0.0534396i \(-0.0170184\pi\)
−0.743884 + 0.668309i \(0.767018\pi\)
\(44\) 0 0
\(45\) −3.09318 1.28124i −0.461105 0.190996i
\(46\) 0 0
\(47\) 1.15993i 0.169193i −0.996415 0.0845966i \(-0.973040\pi\)
0.996415 0.0845966i \(-0.0269601\pi\)
\(48\) 0 0
\(49\) 0.979375i 0.139911i
\(50\) 0 0
\(51\) 5.15504 + 2.13529i 0.721850 + 0.299000i
\(52\) 0 0
\(53\) −2.56680 6.19681i −0.352577 0.851197i −0.996300 0.0859383i \(-0.972611\pi\)
0.643723 0.765258i \(-0.277389\pi\)
\(54\) 0 0
\(55\) 14.8425 + 14.8425i 2.00136 + 2.00136i
\(56\) 0 0
\(57\) 0.788727 0.788727i 0.104469 0.104469i
\(58\) 0 0
\(59\) −0.735935 + 0.304834i −0.0958106 + 0.0396860i −0.430074 0.902794i \(-0.641513\pi\)
0.334263 + 0.942480i \(0.391513\pi\)
\(60\) 0 0
\(61\) −4.82262 + 11.6428i −0.617473 + 1.49071i 0.237156 + 0.971472i \(0.423785\pi\)
−0.854629 + 0.519240i \(0.826215\pi\)
\(62\) 0 0
\(63\) −2.45370 −0.309137
\(64\) 0 0
\(65\) −0.0628036 −0.00778983
\(66\) 0 0
\(67\) −2.05899 + 4.97085i −0.251546 + 0.607286i −0.998329 0.0577816i \(-0.981597\pi\)
0.746783 + 0.665068i \(0.231597\pi\)
\(68\) 0 0
\(69\) 2.63753 1.09250i 0.317521 0.131522i
\(70\) 0 0
\(71\) 1.78298 1.78298i 0.211600 0.211600i −0.593347 0.804947i \(-0.702194\pi\)
0.804947 + 0.593347i \(0.202194\pi\)
\(72\) 0 0
\(73\) 1.67500 + 1.67500i 0.196044 + 0.196044i 0.798302 0.602258i \(-0.205732\pi\)
−0.602258 + 0.798302i \(0.705732\pi\)
\(74\) 0 0
\(75\) 2.37622 + 5.73670i 0.274382 + 0.662417i
\(76\) 0 0
\(77\) 14.2124 + 5.88697i 1.61965 + 0.670883i
\(78\) 0 0
\(79\) 2.67236i 0.300664i 0.988636 + 0.150332i \(0.0480343\pi\)
−0.988636 + 0.150332i \(0.951966\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) −6.91877 2.86585i −0.759433 0.314568i −0.0308494 0.999524i \(-0.509821\pi\)
−0.728584 + 0.684956i \(0.759821\pi\)
\(84\) 0 0
\(85\) −7.14903 17.2593i −0.775421 1.87203i
\(86\) 0 0
\(87\) 1.30466 + 1.30466i 0.139875 + 0.139875i
\(88\) 0 0
\(89\) 6.73869 6.73869i 0.714300 0.714300i −0.253132 0.967432i \(-0.581461\pi\)
0.967432 + 0.253132i \(0.0814607\pi\)
\(90\) 0 0
\(91\) −0.0425236 + 0.0176139i −0.00445769 + 0.00184643i
\(92\) 0 0
\(93\) 0.528286 1.27540i 0.0547807 0.132252i
\(94\) 0 0
\(95\) −3.73450 −0.383151
\(96\) 0 0
\(97\) −1.75001 −0.177686 −0.0888431 0.996046i \(-0.528317\pi\)
−0.0888431 + 0.996046i \(0.528317\pi\)
\(98\) 0 0
\(99\) 2.39923 5.79225i 0.241131 0.582143i
\(100\) 0 0
\(101\) 7.71200 3.19442i 0.767373 0.317856i 0.0355651 0.999367i \(-0.488677\pi\)
0.731808 + 0.681511i \(0.238677\pi\)
\(102\) 0 0
\(103\) 3.90293 3.90293i 0.384567 0.384567i −0.488177 0.872744i \(-0.662338\pi\)
0.872744 + 0.488177i \(0.162338\pi\)
\(104\) 0 0
\(105\) 5.80893 + 5.80893i 0.566894 + 0.566894i
\(106\) 0 0
\(107\) −5.55747 13.4169i −0.537261 1.29706i −0.926628 0.375981i \(-0.877306\pi\)
0.389366 0.921083i \(-0.372694\pi\)
\(108\) 0 0
\(109\) −14.8488 6.15056i −1.42225 0.589117i −0.466828 0.884348i \(-0.654603\pi\)
−0.955426 + 0.295231i \(0.904603\pi\)
\(110\) 0 0
\(111\) 3.10987i 0.295176i
\(112\) 0 0
\(113\) 2.72924i 0.256745i 0.991726 + 0.128373i \(0.0409753\pi\)
−0.991726 + 0.128373i \(0.959025\pi\)
\(114\) 0 0
\(115\) −8.83055 3.65773i −0.823453 0.341085i
\(116\) 0 0
\(117\) 0.00717850 + 0.0173304i 0.000663652 + 0.00160220i
\(118\) 0 0
\(119\) −9.68106 9.68106i −0.887461 0.887461i
\(120\) 0 0
\(121\) −20.0157 + 20.0157i −1.81961 + 1.81961i
\(122\) 0 0
\(123\) −9.11846 + 3.77699i −0.822184 + 0.340560i
\(124\) 0 0
\(125\) 1.54948 3.74078i 0.138590 0.334585i
\(126\) 0 0
\(127\) −15.3336 −1.36064 −0.680319 0.732916i \(-0.738159\pi\)
−0.680319 + 0.732916i \(0.738159\pi\)
\(128\) 0 0
\(129\) −4.36417 −0.384244
\(130\) 0 0
\(131\) 5.70595 13.7754i 0.498531 1.20356i −0.451744 0.892148i \(-0.649198\pi\)
0.950275 0.311412i \(-0.100802\pi\)
\(132\) 0 0
\(133\) −2.52859 + 1.04737i −0.219256 + 0.0908189i
\(134\) 0 0
\(135\) 2.36742 2.36742i 0.203755 0.203755i
\(136\) 0 0
\(137\) −3.06155 3.06155i −0.261566 0.261566i 0.564124 0.825690i \(-0.309214\pi\)
−0.825690 + 0.564124i \(0.809214\pi\)
\(138\) 0 0
\(139\) 0.621401 + 1.50020i 0.0527066 + 0.127245i 0.948040 0.318152i \(-0.103062\pi\)
−0.895333 + 0.445397i \(0.853062\pi\)
\(140\) 0 0
\(141\) 1.07164 + 0.443886i 0.0902480 + 0.0373819i
\(142\) 0 0
\(143\) 0.117605i 0.00983462i
\(144\) 0 0
\(145\) 6.17738i 0.513003i
\(146\) 0 0
\(147\) −0.904825 0.374791i −0.0746287 0.0309122i
\(148\) 0 0
\(149\) 8.53959 + 20.6164i 0.699591 + 1.68896i 0.724503 + 0.689272i \(0.242070\pi\)
−0.0249118 + 0.999690i \(0.507930\pi\)
\(150\) 0 0
\(151\) −9.42348 9.42348i −0.766872 0.766872i 0.210683 0.977555i \(-0.432431\pi\)
−0.977555 + 0.210683i \(0.932431\pi\)
\(152\) 0 0
\(153\) −3.94550 + 3.94550i −0.318975 + 0.318975i
\(154\) 0 0
\(155\) −4.27007 + 1.76872i −0.342981 + 0.142067i
\(156\) 0 0
\(157\) −7.53965 + 18.2023i −0.601729 + 1.45270i 0.270070 + 0.962841i \(0.412953\pi\)
−0.871800 + 0.489863i \(0.837047\pi\)
\(158\) 0 0
\(159\) 6.70737 0.531929
\(160\) 0 0
\(161\) −7.00491 −0.552064
\(162\) 0 0
\(163\) −6.01448 + 14.5202i −0.471090 + 1.13731i 0.492592 + 0.870260i \(0.336050\pi\)
−0.963682 + 0.267052i \(0.913950\pi\)
\(164\) 0 0
\(165\) −19.3927 + 8.03271i −1.50972 + 0.625345i
\(166\) 0 0
\(167\) 11.8392 11.8392i 0.916142 0.916142i −0.0806038 0.996746i \(-0.525685\pi\)
0.996746 + 0.0806038i \(0.0256848\pi\)
\(168\) 0 0
\(169\) −9.19214 9.19214i −0.707088 0.707088i
\(170\) 0 0
\(171\) 0.426856 + 1.03052i 0.0326425 + 0.0788059i
\(172\) 0 0
\(173\) −21.0615 8.72397i −1.60128 0.663271i −0.609683 0.792645i \(-0.708703\pi\)
−0.991596 + 0.129374i \(0.958703\pi\)
\(174\) 0 0
\(175\) 15.2359i 1.15172i
\(176\) 0 0
\(177\) 0.796570i 0.0598739i
\(178\) 0 0
\(179\) −4.75826 1.97094i −0.355649 0.147315i 0.197703 0.980262i \(-0.436652\pi\)
−0.553353 + 0.832947i \(0.686652\pi\)
\(180\) 0 0
\(181\) 3.71100 + 8.95914i 0.275836 + 0.665928i 0.999712 0.0240027i \(-0.00764102\pi\)
−0.723876 + 0.689931i \(0.757641\pi\)
\(182\) 0 0
\(183\) −8.91104 8.91104i −0.658723 0.658723i
\(184\) 0 0
\(185\) 7.36237 7.36237i 0.541293 0.541293i
\(186\) 0 0
\(187\) 32.3195 13.3872i 2.36343 0.978966i
\(188\) 0 0
\(189\) 0.938989 2.26692i 0.0683014 0.164894i
\(190\) 0 0
\(191\) −11.4844 −0.830980 −0.415490 0.909598i \(-0.636390\pi\)
−0.415490 + 0.909598i \(0.636390\pi\)
\(192\) 0 0
\(193\) 19.2681 1.38695 0.693474 0.720482i \(-0.256079\pi\)
0.693474 + 0.720482i \(0.256079\pi\)
\(194\) 0 0
\(195\) 0.0240339 0.0580229i 0.00172110 0.00415511i
\(196\) 0 0
\(197\) −6.48659 + 2.68683i −0.462151 + 0.191429i −0.601596 0.798801i \(-0.705468\pi\)
0.139445 + 0.990230i \(0.455468\pi\)
\(198\) 0 0
\(199\) −14.6525 + 14.6525i −1.03868 + 1.03868i −0.0394638 + 0.999221i \(0.512565\pi\)
−0.999221 + 0.0394638i \(0.987435\pi\)
\(200\) 0 0
\(201\) −3.80452 3.80452i −0.268350 0.268350i
\(202\) 0 0
\(203\) −1.73250 4.18263i −0.121598 0.293563i
\(204\) 0 0
\(205\) 30.5290 + 12.6455i 2.13224 + 0.883201i
\(206\) 0 0
\(207\) 2.85484i 0.198425i
\(208\) 0 0
\(209\) 6.99316i 0.483727i
\(210\) 0 0
\(211\) −2.80379 1.16137i −0.193021 0.0799519i 0.284079 0.958801i \(-0.408312\pi\)
−0.477100 + 0.878849i \(0.658312\pi\)
\(212\) 0 0
\(213\) 0.964940 + 2.32957i 0.0661166 + 0.159620i
\(214\) 0 0
\(215\) 10.3318 + 10.3318i 0.704625 + 0.704625i
\(216\) 0 0
\(217\) −2.39517 + 2.39517i −0.162594 + 0.162594i
\(218\) 0 0
\(219\) −2.18850 + 0.906505i −0.147885 + 0.0612559i
\(220\) 0 0
\(221\) −0.0400544 + 0.0966999i −0.00269435 + 0.00650474i
\(222\) 0 0
\(223\) 6.12103 0.409894 0.204947 0.978773i \(-0.434298\pi\)
0.204947 + 0.978773i \(0.434298\pi\)
\(224\) 0 0
\(225\) −6.20936 −0.413957
\(226\) 0 0
\(227\) −6.52469 + 15.7520i −0.433059 + 1.04550i 0.545237 + 0.838282i \(0.316440\pi\)
−0.978296 + 0.207214i \(0.933560\pi\)
\(228\) 0 0
\(229\) 8.60895 3.56595i 0.568896 0.235644i −0.0796463 0.996823i \(-0.525379\pi\)
0.648542 + 0.761179i \(0.275379\pi\)
\(230\) 0 0
\(231\) −10.8777 + 10.8777i −0.715701 + 0.715701i
\(232\) 0 0
\(233\) 7.99720 + 7.99720i 0.523914 + 0.523914i 0.918751 0.394837i \(-0.129199\pi\)
−0.394837 + 0.918751i \(0.629199\pi\)
\(234\) 0 0
\(235\) −1.48615 3.58788i −0.0969456 0.234047i
\(236\) 0 0
\(237\) −2.46894 1.02267i −0.160375 0.0664295i
\(238\) 0 0
\(239\) 6.26707i 0.405383i −0.979243 0.202692i \(-0.935031\pi\)
0.979243 0.202692i \(-0.0649689\pi\)
\(240\) 0 0
\(241\) 15.7602i 1.01520i 0.861592 + 0.507601i \(0.169468\pi\)
−0.861592 + 0.507601i \(0.830532\pi\)
\(242\) 0 0
\(243\) −0.923880 0.382683i −0.0592669 0.0245492i
\(244\) 0 0
\(245\) 1.25481 + 3.02939i 0.0801671 + 0.193541i
\(246\) 0 0
\(247\) 0.0147952 + 0.0147952i 0.000941395 + 0.000941395i
\(248\) 0 0
\(249\) 5.29540 5.29540i 0.335582 0.335582i
\(250\) 0 0
\(251\) −19.0196 + 7.87816i −1.20050 + 0.497265i −0.891162 0.453686i \(-0.850109\pi\)
−0.309342 + 0.950951i \(0.600109\pi\)
\(252\) 0 0
\(253\) 6.84941 16.5359i 0.430619 1.03961i
\(254\) 0 0
\(255\) 18.6813 1.16987
\(256\) 0 0
\(257\) −5.22771 −0.326096 −0.163048 0.986618i \(-0.552132\pi\)
−0.163048 + 0.986618i \(0.552132\pi\)
\(258\) 0 0
\(259\) 2.92013 7.04983i 0.181448 0.438055i
\(260\) 0 0
\(261\) −1.70463 + 0.706079i −0.105514 + 0.0437052i
\(262\) 0 0
\(263\) −5.59065 + 5.59065i −0.344734 + 0.344734i −0.858144 0.513410i \(-0.828382\pi\)
0.513410 + 0.858144i \(0.328382\pi\)
\(264\) 0 0
\(265\) −15.8792 15.8792i −0.975450 0.975450i
\(266\) 0 0
\(267\) 3.64695 + 8.80452i 0.223190 + 0.538828i
\(268\) 0 0
\(269\) −9.92617 4.11155i −0.605209 0.250686i 0.0589693 0.998260i \(-0.481219\pi\)
−0.664179 + 0.747574i \(0.731219\pi\)
\(270\) 0 0
\(271\) 15.4368i 0.937717i −0.883273 0.468858i \(-0.844665\pi\)
0.883273 0.468858i \(-0.155335\pi\)
\(272\) 0 0
\(273\) 0.0460272i 0.00278569i
\(274\) 0 0
\(275\) 35.9662 + 14.8977i 2.16884 + 0.898363i
\(276\) 0 0
\(277\) −1.79136 4.32473i −0.107633 0.259848i 0.860882 0.508804i \(-0.169912\pi\)
−0.968515 + 0.248956i \(0.919912\pi\)
\(278\) 0 0
\(279\) 0.976146 + 0.976146i 0.0584403 + 0.0584403i
\(280\) 0 0
\(281\) −3.70347 + 3.70347i −0.220931 + 0.220931i −0.808890 0.587960i \(-0.799931\pi\)
0.587960 + 0.808890i \(0.299931\pi\)
\(282\) 0 0
\(283\) −16.1605 + 6.69389i −0.960641 + 0.397910i −0.807220 0.590250i \(-0.799029\pi\)
−0.153421 + 0.988161i \(0.549029\pi\)
\(284\) 0 0
\(285\) 1.42913 3.45022i 0.0846543 0.204374i
\(286\) 0 0
\(287\) 24.2174 1.42951
\(288\) 0 0
\(289\) −14.1339 −0.831407
\(290\) 0 0
\(291\) 0.669698 1.61679i 0.0392584 0.0947782i
\(292\) 0 0
\(293\) −13.5656 + 5.61904i −0.792509 + 0.328268i −0.741952 0.670453i \(-0.766100\pi\)
−0.0505573 + 0.998721i \(0.516100\pi\)
\(294\) 0 0
\(295\) −1.88582 + 1.88582i −0.109796 + 0.109796i
\(296\) 0 0
\(297\) 4.43319 + 4.43319i 0.257240 + 0.257240i
\(298\) 0 0
\(299\) 0.0204935 + 0.0494756i 0.00118517 + 0.00286125i
\(300\) 0 0
\(301\) 9.89322 + 4.09791i 0.570236 + 0.236199i
\(302\) 0 0
\(303\) 8.34741i 0.479546i
\(304\) 0 0
\(305\) 42.1923i 2.41593i
\(306\) 0 0
\(307\) 15.6321 + 6.47504i 0.892173 + 0.369550i 0.781206 0.624274i \(-0.214605\pi\)
0.110968 + 0.993824i \(0.464605\pi\)
\(308\) 0 0
\(309\) 2.11225 + 5.09942i 0.120162 + 0.290096i
\(310\) 0 0
\(311\) −22.8167 22.8167i −1.29381 1.29381i −0.932408 0.361407i \(-0.882297\pi\)
−0.361407 0.932408i \(-0.617703\pi\)
\(312\) 0 0
\(313\) 7.52178 7.52178i 0.425156 0.425156i −0.461819 0.886974i \(-0.652803\pi\)
0.886974 + 0.461819i \(0.152803\pi\)
\(314\) 0 0
\(315\) −7.58973 + 3.14377i −0.427633 + 0.177131i
\(316\) 0 0
\(317\) 9.98241 24.0997i 0.560668 1.35357i −0.348565 0.937285i \(-0.613331\pi\)
0.909233 0.416288i \(-0.136669\pi\)
\(318\) 0 0
\(319\) 11.5677 0.647665
\(320\) 0 0
\(321\) 14.5224 0.810560
\(322\) 0 0
\(323\) −2.38176 + 5.75008i −0.132525 + 0.319943i
\(324\) 0 0
\(325\) −0.107611 + 0.0445739i −0.00596918 + 0.00247251i
\(326\) 0 0
\(327\) 11.3648 11.3648i 0.628472 0.628472i
\(328\) 0 0
\(329\) −2.01251 2.01251i −0.110953 0.110953i
\(330\) 0 0
\(331\) −12.9034 31.1516i −0.709235 1.71225i −0.701903 0.712272i \(-0.747666\pi\)
−0.00733222 0.999973i \(-0.502334\pi\)
\(332\) 0 0
\(333\) −2.87315 1.19010i −0.157447 0.0652169i
\(334\) 0 0
\(335\) 18.0138i 0.984200i
\(336\) 0 0
\(337\) 0.925243i 0.0504012i −0.999682 0.0252006i \(-0.991978\pi\)
0.999682 0.0252006i \(-0.00802245\pi\)
\(338\) 0 0
\(339\) −2.52149 1.04443i −0.136948 0.0567259i
\(340\) 0 0
\(341\) −3.31208 7.99607i −0.179359 0.433012i
\(342\) 0 0
\(343\) 13.8444 + 13.8444i 0.747528 + 0.747528i
\(344\) 0 0
\(345\) 6.75861 6.75861i 0.363871 0.363871i
\(346\) 0 0
\(347\) 8.68292 3.59658i 0.466123 0.193075i −0.137245 0.990537i \(-0.543825\pi\)
0.603369 + 0.797462i \(0.293825\pi\)
\(348\) 0 0
\(349\) −0.586633 + 1.41626i −0.0314017 + 0.0758105i −0.938802 0.344456i \(-0.888063\pi\)
0.907401 + 0.420266i \(0.138063\pi\)
\(350\) 0 0
\(351\) −0.0187583 −0.00100125
\(352\) 0 0
\(353\) 10.8550 0.577751 0.288876 0.957367i \(-0.406719\pi\)
0.288876 + 0.957367i \(0.406719\pi\)
\(354\) 0 0
\(355\) 3.23066 7.79949i 0.171465 0.413954i
\(356\) 0 0
\(357\) 12.6489 5.23935i 0.669451 0.277296i
\(358\) 0 0
\(359\) −21.6767 + 21.6767i −1.14406 + 1.14406i −0.156354 + 0.987701i \(0.549974\pi\)
−0.987701 + 0.156354i \(0.950026\pi\)
\(360\) 0 0
\(361\) −12.5553 12.5553i −0.660803 0.660803i
\(362\) 0 0
\(363\) −10.8324 26.1517i −0.568553 1.37261i
\(364\) 0 0
\(365\) 7.32717 + 3.03501i 0.383521 + 0.158860i
\(366\) 0 0
\(367\) 0.154514i 0.00806555i 0.999992 + 0.00403277i \(0.00128367\pi\)
−0.999992 + 0.00403277i \(0.998716\pi\)
\(368\) 0 0
\(369\) 9.86975i 0.513799i
\(370\) 0 0
\(371\) −15.2051 6.29815i −0.789408 0.326984i
\(372\) 0 0
\(373\) −5.40842 13.0571i −0.280037 0.676070i 0.719799 0.694183i \(-0.244234\pi\)
−0.999836 + 0.0181131i \(0.994234\pi\)
\(374\) 0 0
\(375\) 2.86307 + 2.86307i 0.147848 + 0.147848i
\(376\) 0 0
\(377\) −0.0244733 + 0.0244733i −0.00126044 + 0.00126044i
\(378\) 0 0
\(379\) 17.4888 7.24410i 0.898340 0.372105i 0.114758 0.993393i \(-0.463391\pi\)
0.783582 + 0.621289i \(0.213391\pi\)
\(380\) 0 0
\(381\) 5.86792 14.1664i 0.300623 0.725767i
\(382\) 0 0
\(383\) 30.0898 1.53752 0.768759 0.639538i \(-0.220874\pi\)
0.768759 + 0.639538i \(0.220874\pi\)
\(384\) 0 0
\(385\) 51.5042 2.62490
\(386\) 0 0
\(387\) 1.67010 4.03197i 0.0848957 0.204956i
\(388\) 0 0
\(389\) −11.7666 + 4.87387i −0.596589 + 0.247115i −0.660482 0.750842i \(-0.729648\pi\)
0.0638936 + 0.997957i \(0.479648\pi\)
\(390\) 0 0
\(391\) −11.2638 + 11.2638i −0.569633 + 0.569633i
\(392\) 0 0
\(393\) 10.5432 + 10.5432i 0.531835 + 0.531835i
\(394\) 0 0
\(395\) 3.42394 + 8.26611i 0.172277 + 0.415913i
\(396\) 0 0
\(397\) −15.2331 6.30976i −0.764527 0.316678i −0.0338739 0.999426i \(-0.510784\pi\)
−0.730653 + 0.682749i \(0.760784\pi\)
\(398\) 0 0
\(399\) 2.73692i 0.137017i
\(400\) 0 0
\(401\) 35.7766i 1.78660i −0.449463 0.893299i \(-0.648385\pi\)
0.449463 0.893299i \(-0.351615\pi\)
\(402\) 0 0
\(403\) 0.0239243 + 0.00990976i 0.00119175 + 0.000493641i
\(404\) 0 0
\(405\) 1.28124 + 3.09318i 0.0636653 + 0.153702i
\(406\) 0 0
\(407\) 13.7867 + 13.7867i 0.683380 + 0.683380i
\(408\) 0 0
\(409\) −4.31657 + 4.31657i −0.213440 + 0.213440i −0.805727 0.592287i \(-0.798225\pi\)
0.592287 + 0.805727i \(0.298225\pi\)
\(410\) 0 0
\(411\) 4.00011 1.65690i 0.197311 0.0817289i
\(412\) 0 0
\(413\) −0.747970 + 1.80576i −0.0368052 + 0.0888557i
\(414\) 0 0
\(415\) −25.0729 −1.23078
\(416\) 0 0
\(417\) −1.62380 −0.0795178
\(418\) 0 0
\(419\) −7.37576 + 17.8067i −0.360330 + 0.869913i 0.634922 + 0.772576i \(0.281032\pi\)
−0.995252 + 0.0973364i \(0.968968\pi\)
\(420\) 0 0
\(421\) 5.03356 2.08497i 0.245321 0.101615i −0.256635 0.966508i \(-0.582614\pi\)
0.501956 + 0.864893i \(0.332614\pi\)
\(422\) 0 0
\(423\) −0.820194 + 0.820194i −0.0398792 + 0.0398792i
\(424\) 0 0
\(425\) −24.4990 24.4990i −1.18838 1.18838i
\(426\) 0 0
\(427\) 11.8332 + 28.5680i 0.572651 + 1.38250i
\(428\) 0 0
\(429\) 0.108653 + 0.0450055i 0.00524581 + 0.00217288i
\(430\) 0 0
\(431\) 18.4128i 0.886914i 0.896296 + 0.443457i \(0.146248\pi\)
−0.896296 + 0.443457i \(0.853752\pi\)
\(432\) 0 0
\(433\) 0.227663i 0.0109408i 0.999985 + 0.00547038i \(0.00174129\pi\)
−0.999985 + 0.00547038i \(0.998259\pi\)
\(434\) 0 0
\(435\) 5.70715 + 2.36398i 0.273637 + 0.113344i
\(436\) 0 0
\(437\) 1.21860 + 2.94197i 0.0582938 + 0.140734i
\(438\) 0 0
\(439\) 19.0619 + 19.0619i 0.909774 + 0.909774i 0.996254 0.0864799i \(-0.0275618\pi\)
−0.0864799 + 0.996254i \(0.527562\pi\)
\(440\) 0 0
\(441\) 0.692523 0.692523i 0.0329773 0.0329773i
\(442\) 0 0
\(443\) 28.0493 11.6184i 1.33266 0.552008i 0.401250 0.915968i \(-0.368576\pi\)
0.931414 + 0.363961i \(0.118576\pi\)
\(444\) 0 0
\(445\) 12.2101 29.4779i 0.578816 1.39739i
\(446\) 0 0
\(447\) −22.3150 −1.05546
\(448\) 0 0
\(449\) 33.0005 1.55739 0.778696 0.627401i \(-0.215881\pi\)
0.778696 + 0.627401i \(0.215881\pi\)
\(450\) 0 0
\(451\) −23.6798 + 57.1681i −1.11504 + 2.69194i
\(452\) 0 0
\(453\) 12.3124 5.09995i 0.578486 0.239617i
\(454\) 0 0
\(455\) −0.108966 + 0.108966i −0.00510839 + 0.00510839i
\(456\) 0 0
\(457\) 19.3344 + 19.3344i 0.904423 + 0.904423i 0.995815 0.0913920i \(-0.0291316\pi\)
−0.0913920 + 0.995815i \(0.529132\pi\)
\(458\) 0 0
\(459\) −2.13529 5.15504i −0.0996667 0.240617i
\(460\) 0 0
\(461\) 19.0532 + 7.89211i 0.887398 + 0.367572i 0.779361 0.626575i \(-0.215544\pi\)
0.108037 + 0.994147i \(0.465544\pi\)
\(462\) 0 0
\(463\) 18.6664i 0.867499i 0.901034 + 0.433749i \(0.142810\pi\)
−0.901034 + 0.433749i \(0.857190\pi\)
\(464\) 0 0
\(465\) 4.62190i 0.214335i
\(466\) 0 0
\(467\) −1.38748 0.574712i −0.0642048 0.0265945i 0.350350 0.936619i \(-0.386063\pi\)
−0.414555 + 0.910024i \(0.636063\pi\)
\(468\) 0 0
\(469\) 5.05214 + 12.1970i 0.233286 + 0.563203i
\(470\) 0 0
\(471\) −13.9315 13.9315i −0.641927 0.641927i
\(472\) 0 0
\(473\) −19.3472 + 19.3472i −0.889586 + 0.889586i
\(474\) 0 0
\(475\) −6.39888 + 2.65050i −0.293601 + 0.121613i
\(476\) 0 0
\(477\) −2.56680 + 6.19681i −0.117526 + 0.283732i
\(478\) 0 0
\(479\) 20.1621 0.921229 0.460615 0.887600i \(-0.347629\pi\)
0.460615 + 0.887600i \(0.347629\pi\)
\(480\) 0 0
\(481\) −0.0583360 −0.00265989
\(482\) 0 0
\(483\) 2.68066 6.47169i 0.121974 0.294472i
\(484\) 0 0
\(485\) −5.41309 + 2.24218i −0.245796 + 0.101812i
\(486\) 0 0
\(487\) 14.3589 14.3589i 0.650665 0.650665i −0.302488 0.953153i \(-0.597817\pi\)
0.953153 + 0.302488i \(0.0978173\pi\)
\(488\) 0 0
\(489\) −11.1133 11.1133i −0.502561 0.502561i
\(490\) 0 0
\(491\) 7.84066 + 18.9290i 0.353844 + 0.854255i 0.996138 + 0.0877968i \(0.0279826\pi\)
−0.642294 + 0.766458i \(0.722017\pi\)
\(492\) 0 0
\(493\) −9.51144 3.93977i −0.428374 0.177438i
\(494\) 0 0
\(495\) 20.9905i 0.943452i
\(496\) 0 0
\(497\) 6.18702i 0.277526i
\(498\) 0 0
\(499\) 11.1249 + 4.60809i 0.498020 + 0.206286i 0.617531 0.786546i \(-0.288133\pi\)
−0.119512 + 0.992833i \(0.538133\pi\)
\(500\) 0 0
\(501\) 6.40731 + 15.4686i 0.286258 + 0.691087i
\(502\) 0 0
\(503\) 10.7388 + 10.7388i 0.478820 + 0.478820i 0.904754 0.425934i \(-0.140054\pi\)
−0.425934 + 0.904754i \(0.640054\pi\)
\(504\) 0 0
\(505\) 19.7618 19.7618i 0.879390 0.879390i
\(506\) 0 0
\(507\) 12.0101 4.97475i 0.533388 0.220936i
\(508\) 0 0
\(509\) 7.73386 18.6712i 0.342797 0.827586i −0.654633 0.755947i \(-0.727177\pi\)
0.997431 0.0716392i \(-0.0228230\pi\)
\(510\) 0 0
\(511\) 5.81234 0.257123
\(512\) 0 0
\(513\) −1.11543 −0.0492473
\(514\) 0 0
\(515\) 7.07189 17.0731i 0.311625 0.752329i
\(516\) 0 0
\(517\) 6.71860 2.78294i 0.295484 0.122393i
\(518\) 0 0
\(519\) 16.1198 16.1198i 0.707581 0.707581i
\(520\) 0 0
\(521\) 13.6485 + 13.6485i 0.597953 + 0.597953i 0.939767 0.341815i \(-0.111042\pi\)
−0.341815 + 0.939767i \(0.611042\pi\)
\(522\) 0 0
\(523\) −6.91544 16.6954i −0.302391 0.730037i −0.999909 0.0134697i \(-0.995712\pi\)
0.697518 0.716567i \(-0.254288\pi\)
\(524\) 0 0
\(525\) 14.0761 + 5.83052i 0.614332 + 0.254465i
\(526\) 0 0
\(527\) 7.70276i 0.335538i
\(528\) 0 0
\(529\) 14.8499i 0.645647i
\(530\) 0 0
\(531\) 0.735935 + 0.304834i 0.0319369 + 0.0132287i
\(532\) 0 0
\(533\) −0.0708500 0.171047i −0.00306885 0.00740887i
\(534\) 0 0
\(535\) −34.3806 34.3806i −1.48640 1.48640i
\(536\) 0 0
\(537\) 3.64182 3.64182i 0.157156 0.157156i
\(538\) 0 0
\(539\) −5.67279 + 2.34974i −0.244344 + 0.101211i
\(540\) 0 0
\(541\) −9.51555 + 22.9726i −0.409106 + 0.987668i 0.576268 + 0.817261i \(0.304508\pi\)
−0.985374 + 0.170407i \(0.945492\pi\)
\(542\) 0 0
\(543\) −9.69731 −0.416151
\(544\) 0 0
\(545\) −53.8103 −2.30498
\(546\) 0 0
\(547\) 11.3958 27.5119i 0.487250 1.17633i −0.468848 0.883279i \(-0.655331\pi\)
0.956098 0.293046i \(-0.0946690\pi\)
\(548\) 0 0
\(549\) 11.6428 4.82262i 0.496904 0.205824i
\(550\) 0 0
\(551\) −1.45526 + 1.45526i −0.0619961 + 0.0619961i
\(552\) 0 0
\(553\) 4.63662 + 4.63662i 0.197169 + 0.197169i
\(554\) 0 0
\(555\) 3.98449 + 9.61941i 0.169132 + 0.408321i
\(556\) 0 0
\(557\) −1.70939 0.708053i −0.0724292 0.0300012i 0.346175 0.938170i \(-0.387480\pi\)
−0.418604 + 0.908169i \(0.637480\pi\)
\(558\) 0 0
\(559\) 0.0818645i 0.00346250i
\(560\) 0 0
\(561\) 34.9823i 1.47695i
\(562\) 0 0
\(563\) 19.1605 + 7.93652i 0.807517 + 0.334485i 0.747963 0.663741i \(-0.231032\pi\)
0.0595542 + 0.998225i \(0.481032\pi\)
\(564\) 0 0
\(565\) 3.49681 + 8.44204i 0.147112 + 0.355159i
\(566\) 0 0
\(567\) 1.73503 + 1.73503i 0.0728642 + 0.0728642i
\(568\) 0 0
\(569\) −15.1289 + 15.1289i −0.634235 + 0.634235i −0.949127 0.314892i \(-0.898032\pi\)
0.314892 + 0.949127i \(0.398032\pi\)
\(570\) 0 0
\(571\) −12.1094 + 5.01587i −0.506761 + 0.209907i −0.621391 0.783501i \(-0.713432\pi\)
0.114629 + 0.993408i \(0.463432\pi\)
\(572\) 0 0
\(573\) 4.39488 10.6102i 0.183599 0.443246i
\(574\) 0 0
\(575\) −17.7267 −0.739256
\(576\) 0 0
\(577\) −35.7790 −1.48950 −0.744749 0.667344i \(-0.767431\pi\)
−0.744749 + 0.667344i \(0.767431\pi\)
\(578\) 0 0
\(579\) −7.37358 + 17.8014i −0.306435 + 0.739801i
\(580\) 0 0
\(581\) −16.9766 + 7.03192i −0.704306 + 0.291733i
\(582\) 0 0
\(583\) 29.7351 29.7351i 1.23150 1.23150i
\(584\) 0 0
\(585\) 0.0444088 + 0.0444088i 0.00183608 + 0.00183608i
\(586\) 0 0
\(587\) 10.9958 + 26.5462i 0.453845 + 1.09568i 0.970848 + 0.239696i \(0.0770477\pi\)
−0.517003 + 0.855984i \(0.672952\pi\)
\(588\) 0 0
\(589\) 1.42261 + 0.589265i 0.0586177 + 0.0242803i
\(590\) 0 0
\(591\) 7.02104i 0.288807i
\(592\) 0 0
\(593\) 13.4778i 0.553469i −0.960946 0.276734i \(-0.910748\pi\)
0.960946 0.276734i \(-0.0892522\pi\)
\(594\) 0 0
\(595\) −42.3490 17.5415i −1.73614 0.719133i
\(596\) 0 0
\(597\) −7.92985 19.1444i −0.324547 0.783526i
\(598\) 0 0
\(599\) 11.7247 + 11.7247i 0.479059 + 0.479059i 0.904831 0.425771i \(-0.139997\pi\)
−0.425771 + 0.904831i \(0.639997\pi\)
\(600\) 0 0
\(601\) −14.2752 + 14.2752i −0.582299 + 0.582299i −0.935535 0.353235i \(-0.885082\pi\)
0.353235 + 0.935535i \(0.385082\pi\)
\(602\) 0 0
\(603\) 4.97085 2.05899i 0.202429 0.0838487i
\(604\) 0 0
\(605\) −36.2673 + 87.5570i −1.47447 + 3.55970i
\(606\) 0 0
\(607\) 30.9234 1.25514 0.627571 0.778559i \(-0.284049\pi\)
0.627571 + 0.778559i \(0.284049\pi\)
\(608\) 0 0
\(609\) 4.52725 0.183453
\(610\) 0 0
\(611\) −0.00832655 + 0.0201021i −0.000336856 + 0.000813243i
\(612\) 0 0
\(613\) −34.3535 + 14.2297i −1.38753 + 0.574732i −0.946483 0.322754i \(-0.895391\pi\)
−0.441043 + 0.897486i \(0.645391\pi\)
\(614\) 0 0
\(615\) −23.3659 + 23.3659i −0.942202 + 0.942202i
\(616\) 0 0
\(617\) −10.2583 10.2583i −0.412985 0.412985i 0.469792 0.882777i \(-0.344329\pi\)
−0.882777 + 0.469792i \(0.844329\pi\)
\(618\) 0 0
\(619\) −8.23548 19.8822i −0.331012 0.799133i −0.998512 0.0545238i \(-0.982636\pi\)
0.667501 0.744609i \(-0.267364\pi\)
\(620\) 0 0
\(621\) −2.63753 1.09250i −0.105840 0.0438405i
\(622\) 0 0
\(623\) 23.3836i 0.936844i
\(624\) 0 0
\(625\) 17.4906i 0.699626i
\(626\) 0 0
\(627\) 6.46083 + 2.67617i 0.258021 + 0.106876i
\(628\) 0 0
\(629\) −6.64047 16.0315i −0.264773 0.639219i
\(630\) 0 0
\(631\) −10.2772 10.2772i −0.409128 0.409128i 0.472307 0.881434i \(-0.343421\pi\)
−0.881434 + 0.472307i \(0.843421\pi\)
\(632\) 0 0
\(633\) 2.14593 2.14593i 0.0852930 0.0852930i
\(634\) 0 0
\(635\) −47.4297 + 19.6460i −1.88219 + 0.779629i
\(636\) 0 0
\(637\) 0.00703045 0.0169730i 0.000278556 0.000672495i
\(638\) 0 0
\(639\) −2.52151 −0.0997494
\(640\) 0 0
\(641\) −14.5702 −0.575489 −0.287745 0.957707i \(-0.592905\pi\)
−0.287745 + 0.957707i \(0.592905\pi\)
\(642\) 0 0
\(643\) 7.72635 18.6531i 0.304698 0.735605i −0.695162 0.718853i \(-0.744667\pi\)
0.999860 0.0167519i \(-0.00533255\pi\)
\(644\) 0 0
\(645\) −13.4992 + 5.59154i −0.531530 + 0.220167i
\(646\) 0 0
\(647\) −5.45944 + 5.45944i −0.214633 + 0.214633i −0.806232 0.591599i \(-0.798497\pi\)
0.591599 + 0.806232i \(0.298497\pi\)
\(648\) 0 0
\(649\) −3.53135 3.53135i −0.138618 0.138618i
\(650\) 0 0
\(651\) −1.29625 3.12943i −0.0508042 0.122652i
\(652\) 0 0
\(653\) 8.05307 + 3.33569i 0.315141 + 0.130536i 0.534647 0.845075i \(-0.320445\pi\)
−0.219506 + 0.975611i \(0.570445\pi\)
\(654\) 0 0
\(655\) 49.9204i 1.95055i
\(656\) 0 0
\(657\) 2.36881i 0.0924161i
\(658\) 0 0
\(659\) 11.5755 + 4.79474i 0.450919 + 0.186777i 0.596573 0.802559i \(-0.296529\pi\)
−0.145654 + 0.989336i \(0.546529\pi\)
\(660\) 0 0
\(661\) 4.73190 + 11.4238i 0.184049 + 0.444335i 0.988794 0.149287i \(-0.0476977\pi\)
−0.804745 + 0.593621i \(0.797698\pi\)
\(662\) 0 0
\(663\) −0.0740109 0.0740109i −0.00287435 0.00287435i
\(664\) 0 0
\(665\) −6.47944 + 6.47944i −0.251262 + 0.251262i
\(666\) 0 0
\(667\) −4.86643 + 2.01574i −0.188429 + 0.0780499i
\(668\) 0 0
\(669\) −2.34242 + 5.65509i −0.0905631 + 0.218639i
\(670\) 0 0
\(671\) −79.0087 −3.05010
\(672\) 0 0
\(673\) 11.7838 0.454233 0.227117 0.973868i \(-0.427070\pi\)
0.227117 + 0.973868i \(0.427070\pi\)
\(674\) 0 0
\(675\) 2.37622 5.73670i 0.0914607 0.220806i
\(676\) 0 0
\(677\) 31.1449 12.9006i 1.19700 0.495812i 0.306969 0.951719i \(-0.400685\pi\)
0.890027 + 0.455907i \(0.150685\pi\)
\(678\) 0 0
\(679\) −3.03630 + 3.03630i −0.116523 + 0.116523i
\(680\) 0 0
\(681\) −12.0560 12.0560i −0.461989 0.461989i
\(682\) 0 0
\(683\) −2.44866 5.91159i −0.0936954 0.226201i 0.870083 0.492905i \(-0.164065\pi\)
−0.963778 + 0.266705i \(0.914065\pi\)
\(684\) 0 0
\(685\) −13.3925 5.54737i −0.511702 0.211954i
\(686\) 0 0
\(687\) 9.31826i 0.355514i
\(688\) 0 0
\(689\) 0.125819i 0.00479333i
\(690\) 0 0
\(691\) 6.81893 + 2.82449i 0.259404 + 0.107449i 0.508596 0.861005i \(-0.330165\pi\)
−0.249191 + 0.968454i \(0.580165\pi\)
\(692\) 0 0
\(693\) −5.88697 14.2124i −0.223628 0.539885i
\(694\) 0 0
\(695\) 3.84422 + 3.84422i 0.145819 + 0.145819i
\(696\) 0 0
\(697\) 38.9411 38.9411i 1.47500 1.47500i
\(698\) 0 0
\(699\) −10.4488 + 4.32805i −0.395212 + 0.163702i
\(700\) 0 0
\(701\) −2.75369 + 6.64799i −0.104005 + 0.251091i −0.967312 0.253588i \(-0.918389\pi\)
0.863307 + 0.504679i \(0.168389\pi\)
\(702\) 0 0
\(703\) −3.46884 −0.130830
\(704\) 0 0
\(705\) 3.88349 0.146261
\(706\) 0 0
\(707\) 7.83813 18.9229i 0.294783 0.711669i
\(708\) 0 0
\(709\) 46.0951 19.0932i 1.73114 0.717061i 0.731770 0.681552i \(-0.238695\pi\)
0.999369 0.0355098i \(-0.0113055\pi\)
\(710\) 0 0
\(711\) 1.88965 1.88965i 0.0708673 0.0708673i
\(712\) 0 0
\(713\) 2.78674 + 2.78674i 0.104364 + 0.104364i
\(714\) 0 0
\(715\) −0.150680 0.363774i −0.00563512 0.0136044i
\(716\) 0 0
\(717\) 5.79002 + 2.39830i 0.216232 + 0.0895663i
\(718\) 0 0
\(719\) 22.0801i 0.823447i −0.911309 0.411724i \(-0.864927\pi\)
0.911309 0.411724i \(-0.135073\pi\)
\(720\) 0 0
\(721\) 13.5434i 0.504381i
\(722\) 0 0
\(723\) −14.5605 6.03116i −0.541511 0.224301i
\(724\) 0 0
\(725\) −4.38430 10.5846i −0.162829 0.393104i
\(726\) 0 0
\(727\) −12.2216 12.2216i −0.453274 0.453274i 0.443166 0.896440i \(-0.353855\pi\)
−0.896440 + 0.443166i \(0.853855\pi\)
\(728\) 0 0
\(729\) 0.707107 0.707107i 0.0261891 0.0261891i
\(730\) 0 0
\(731\) 22.4975 9.31876i 0.832100 0.344667i
\(732\) 0 0
\(733\) −10.2112 + 24.6520i −0.377159 + 0.910541i 0.615337 + 0.788264i \(0.289020\pi\)
−0.992496 + 0.122278i \(0.960980\pi\)
\(734\) 0 0
\(735\) −3.27899 −0.120947
\(736\) 0 0
\(737\) −33.7324 −1.24255
\(738\) 0 0
\(739\) 12.9929 31.3677i 0.477953 1.15388i −0.482614 0.875833i \(-0.660313\pi\)
0.960567 0.278048i \(-0.0896874\pi\)
\(740\) 0 0
\(741\) −0.0193308 + 0.00800710i −0.000710136 + 0.000294148i
\(742\) 0 0
\(743\) 14.2568 14.2568i 0.523030 0.523030i −0.395455 0.918485i \(-0.629413\pi\)
0.918485 + 0.395455i \(0.129413\pi\)
\(744\) 0 0
\(745\) 52.8291 + 52.8291i 1.93551 + 1.93551i
\(746\) 0 0
\(747\) 2.86585 + 6.91877i 0.104856 + 0.253144i
\(748\) 0 0
\(749\) −32.9211 13.6364i −1.20291 0.498262i
\(750\) 0 0
\(751\) 37.4275i 1.36575i 0.730536 + 0.682874i \(0.239270\pi\)
−0.730536 + 0.682874i \(0.760730\pi\)
\(752\) 0 0
\(753\) 20.5866i 0.750218i
\(754\) 0 0
\(755\) −41.2223 17.0748i −1.50023 0.621417i
\(756\) 0 0
\(757\) −14.2534 34.4107i −0.518048 1.25068i −0.939100 0.343643i \(-0.888339\pi\)
0.421052 0.907036i \(-0.361661\pi\)
\(758\) 0 0
\(759\) 12.6561 + 12.6561i 0.459386 + 0.459386i
\(760\) 0 0
\(761\) 4.71958 4.71958i 0.171085 0.171085i −0.616371 0.787456i \(-0.711398\pi\)
0.787456 + 0.616371i \(0.211398\pi\)
\(762\) 0 0
\(763\) −36.4344 + 15.0916i −1.31901 + 0.546353i
\(764\) 0 0
\(765\) −7.14903 + 17.2593i −0.258474 + 0.624011i
\(766\) 0 0
\(767\) 0.0149423 0.000539536
\(768\) 0 0
\(769\) −0.848264 −0.0305892 −0.0152946 0.999883i \(-0.504869\pi\)
−0.0152946 + 0.999883i \(0.504869\pi\)
\(770\) 0 0
\(771\) 2.00056 4.82977i 0.0720483 0.173940i
\(772\) 0 0
\(773\) 7.34212 3.04121i 0.264078 0.109385i −0.246716 0.969088i \(-0.579352\pi\)
0.510794 + 0.859703i \(0.329352\pi\)
\(774\) 0 0
\(775\) −6.06124 + 6.06124i −0.217726 + 0.217726i
\(776\) 0 0
\(777\) 5.39571 + 5.39571i 0.193570 + 0.193570i
\(778\) 0 0
\(779\) −4.21296 10.1710i −0.150945 0.364413i
\(780\) 0 0
\(781\) 14.6052 + 6.04967i 0.522615 + 0.216474i
\(782\) 0 0
\(783\) 1.84507i 0.0659376i
\(784\) 0 0
\(785\) 65.9632i 2.35433i
\(786\) 0 0
\(787\) −19.1514 7.93278i −0.682674 0.282773i 0.0142701 0.999898i \(-0.495458\pi\)
−0.696944 + 0.717125i \(0.745458\pi\)
\(788\) 0 0
\(789\) −3.02564 7.30453i −0.107716 0.260048i
\(790\) 0 0
\(791\) 4.73530 + 4.73530i 0.168368 + 0.168368i
\(792\) 0 0
\(793\) 0.167156 0.167156i 0.00593589 0.00593589i
\(794\) 0 0
\(795\) 20.7471 8.59375i 0.735825 0.304789i
\(796\) 0 0
\(797\) 8.34929 20.1570i 0.295747 0.713997i −0.704245 0.709957i \(-0.748714\pi\)
0.999992 0.00403944i \(-0.00128580\pi\)