Properties

Label 512.2.e.i.129.3
Level $512$
Weight $2$
Character 512.129
Analytic conductor $4.088$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 512 = 2^{9} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 512.e (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.08834058349\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{16})\)
Defining polynomial: \(x^{8} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 129.3
Root \(-0.923880 - 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 512.129
Dual form 512.2.e.i.385.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.765367 + 0.765367i) q^{3} +(0.414214 - 0.414214i) q^{5} +3.69552i q^{7} -1.82843i q^{9} +O(q^{10})\) \(q+(0.765367 + 0.765367i) q^{3} +(0.414214 - 0.414214i) q^{5} +3.69552i q^{7} -1.82843i q^{9} +(2.93015 - 2.93015i) q^{11} +(2.41421 + 2.41421i) q^{13} +0.634051 q^{15} -2.82843 q^{17} +(4.46088 + 4.46088i) q^{19} +(-2.82843 + 2.82843i) q^{21} +6.75699i q^{23} +4.65685i q^{25} +(3.69552 - 3.69552i) q^{27} +(-5.24264 - 5.24264i) q^{29} -3.06147 q^{31} +4.48528 q^{33} +(1.53073 + 1.53073i) q^{35} +(6.41421 - 6.41421i) q^{37} +3.69552i q^{39} -4.00000i q^{41} +(-0.765367 + 0.765367i) q^{43} +(-0.757359 - 0.757359i) q^{45} +3.06147 q^{47} -6.65685 q^{49} +(-2.16478 - 2.16478i) q^{51} +(-3.24264 + 3.24264i) q^{53} -2.42742i q^{55} +6.82843i q^{57} +(-0.765367 + 0.765367i) q^{59} +(0.757359 + 0.757359i) q^{61} +6.75699 q^{63} +2.00000 q^{65} +(1.39942 + 1.39942i) q^{67} +(-5.17157 + 5.17157i) q^{69} -8.02509i q^{71} -6.48528i q^{73} +(-3.56420 + 3.56420i) q^{75} +(10.8284 + 10.8284i) q^{77} -14.7821 q^{79} +0.171573 q^{81} +(-9.68714 - 9.68714i) q^{83} +(-1.17157 + 1.17157i) q^{85} -8.02509i q^{87} -4.82843i q^{89} +(-8.92177 + 8.92177i) q^{91} +(-2.34315 - 2.34315i) q^{93} +3.69552 q^{95} +5.17157 q^{97} +(-5.35757 - 5.35757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{5} + O(q^{10}) \) \( 8 q - 8 q^{5} + 8 q^{13} - 8 q^{29} - 32 q^{33} + 40 q^{37} - 40 q^{45} - 8 q^{49} + 8 q^{53} + 40 q^{61} + 16 q^{65} - 64 q^{69} + 64 q^{77} + 24 q^{81} - 32 q^{85} - 64 q^{93} + 64 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.765367 + 0.765367i 0.441885 + 0.441885i 0.892645 0.450760i \(-0.148847\pi\)
−0.450760 + 0.892645i \(0.648847\pi\)
\(4\) 0 0
\(5\) 0.414214 0.414214i 0.185242 0.185242i −0.608394 0.793635i \(-0.708186\pi\)
0.793635 + 0.608394i \(0.208186\pi\)
\(6\) 0 0
\(7\) 3.69552i 1.39677i 0.715720 + 0.698387i \(0.246099\pi\)
−0.715720 + 0.698387i \(0.753901\pi\)
\(8\) 0 0
\(9\) 1.82843i 0.609476i
\(10\) 0 0
\(11\) 2.93015 2.93015i 0.883474 0.883474i −0.110412 0.993886i \(-0.535217\pi\)
0.993886 + 0.110412i \(0.0352171\pi\)
\(12\) 0 0
\(13\) 2.41421 + 2.41421i 0.669582 + 0.669582i 0.957619 0.288037i \(-0.0930026\pi\)
−0.288037 + 0.957619i \(0.593003\pi\)
\(14\) 0 0
\(15\) 0.634051 0.163711
\(16\) 0 0
\(17\) −2.82843 −0.685994 −0.342997 0.939336i \(-0.611442\pi\)
−0.342997 + 0.939336i \(0.611442\pi\)
\(18\) 0 0
\(19\) 4.46088 + 4.46088i 1.02340 + 1.02340i 0.999720 + 0.0236776i \(0.00753751\pi\)
0.0236776 + 0.999720i \(0.492462\pi\)
\(20\) 0 0
\(21\) −2.82843 + 2.82843i −0.617213 + 0.617213i
\(22\) 0 0
\(23\) 6.75699i 1.40893i 0.709739 + 0.704464i \(0.248813\pi\)
−0.709739 + 0.704464i \(0.751187\pi\)
\(24\) 0 0
\(25\) 4.65685i 0.931371i
\(26\) 0 0
\(27\) 3.69552 3.69552i 0.711203 0.711203i
\(28\) 0 0
\(29\) −5.24264 5.24264i −0.973534 0.973534i 0.0261248 0.999659i \(-0.491683\pi\)
−0.999659 + 0.0261248i \(0.991683\pi\)
\(30\) 0 0
\(31\) −3.06147 −0.549856 −0.274928 0.961465i \(-0.588654\pi\)
−0.274928 + 0.961465i \(0.588654\pi\)
\(32\) 0 0
\(33\) 4.48528 0.780787
\(34\) 0 0
\(35\) 1.53073 + 1.53073i 0.258741 + 0.258741i
\(36\) 0 0
\(37\) 6.41421 6.41421i 1.05449 1.05449i 0.0560630 0.998427i \(-0.482145\pi\)
0.998427 0.0560630i \(-0.0178548\pi\)
\(38\) 0 0
\(39\) 3.69552i 0.591756i
\(40\) 0 0
\(41\) 4.00000i 0.624695i −0.949968 0.312348i \(-0.898885\pi\)
0.949968 0.312348i \(-0.101115\pi\)
\(42\) 0 0
\(43\) −0.765367 + 0.765367i −0.116717 + 0.116717i −0.763053 0.646336i \(-0.776301\pi\)
0.646336 + 0.763053i \(0.276301\pi\)
\(44\) 0 0
\(45\) −0.757359 0.757359i −0.112900 0.112900i
\(46\) 0 0
\(47\) 3.06147 0.446561 0.223280 0.974754i \(-0.428323\pi\)
0.223280 + 0.974754i \(0.428323\pi\)
\(48\) 0 0
\(49\) −6.65685 −0.950979
\(50\) 0 0
\(51\) −2.16478 2.16478i −0.303130 0.303130i
\(52\) 0 0
\(53\) −3.24264 + 3.24264i −0.445411 + 0.445411i −0.893826 0.448415i \(-0.851989\pi\)
0.448415 + 0.893826i \(0.351989\pi\)
\(54\) 0 0
\(55\) 2.42742i 0.327313i
\(56\) 0 0
\(57\) 6.82843i 0.904447i
\(58\) 0 0
\(59\) −0.765367 + 0.765367i −0.0996423 + 0.0996423i −0.755171 0.655528i \(-0.772446\pi\)
0.655528 + 0.755171i \(0.272446\pi\)
\(60\) 0 0
\(61\) 0.757359 + 0.757359i 0.0969699 + 0.0969699i 0.753928 0.656958i \(-0.228157\pi\)
−0.656958 + 0.753928i \(0.728157\pi\)
\(62\) 0 0
\(63\) 6.75699 0.851300
\(64\) 0 0
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) 1.39942 + 1.39942i 0.170966 + 0.170966i 0.787404 0.616438i \(-0.211425\pi\)
−0.616438 + 0.787404i \(0.711425\pi\)
\(68\) 0 0
\(69\) −5.17157 + 5.17157i −0.622584 + 0.622584i
\(70\) 0 0
\(71\) 8.02509i 0.952403i −0.879336 0.476201i \(-0.842013\pi\)
0.879336 0.476201i \(-0.157987\pi\)
\(72\) 0 0
\(73\) 6.48528i 0.759045i −0.925183 0.379522i \(-0.876088\pi\)
0.925183 0.379522i \(-0.123912\pi\)
\(74\) 0 0
\(75\) −3.56420 + 3.56420i −0.411559 + 0.411559i
\(76\) 0 0
\(77\) 10.8284 + 10.8284i 1.23401 + 1.23401i
\(78\) 0 0
\(79\) −14.7821 −1.66311 −0.831557 0.555440i \(-0.812550\pi\)
−0.831557 + 0.555440i \(0.812550\pi\)
\(80\) 0 0
\(81\) 0.171573 0.0190637
\(82\) 0 0
\(83\) −9.68714 9.68714i −1.06330 1.06330i −0.997856 0.0654452i \(-0.979153\pi\)
−0.0654452 0.997856i \(-0.520847\pi\)
\(84\) 0 0
\(85\) −1.17157 + 1.17157i −0.127075 + 0.127075i
\(86\) 0 0
\(87\) 8.02509i 0.860380i
\(88\) 0 0
\(89\) 4.82843i 0.511812i −0.966702 0.255906i \(-0.917626\pi\)
0.966702 0.255906i \(-0.0823738\pi\)
\(90\) 0 0
\(91\) −8.92177 + 8.92177i −0.935256 + 0.935256i
\(92\) 0 0
\(93\) −2.34315 2.34315i −0.242973 0.242973i
\(94\) 0 0
\(95\) 3.69552 0.379152
\(96\) 0 0
\(97\) 5.17157 0.525094 0.262547 0.964919i \(-0.415438\pi\)
0.262547 + 0.964919i \(0.415438\pi\)
\(98\) 0 0
\(99\) −5.35757 5.35757i −0.538456 0.538456i
\(100\) 0 0
\(101\) 12.0711 12.0711i 1.20112 1.20112i 0.227289 0.973827i \(-0.427014\pi\)
0.973827 0.227289i \(-0.0729861\pi\)
\(102\) 0 0
\(103\) 14.1480i 1.39405i −0.717049 0.697023i \(-0.754508\pi\)
0.717049 0.697023i \(-0.245492\pi\)
\(104\) 0 0
\(105\) 2.34315i 0.228668i
\(106\) 0 0
\(107\) −1.39942 + 1.39942i −0.135287 + 0.135287i −0.771507 0.636220i \(-0.780497\pi\)
0.636220 + 0.771507i \(0.280497\pi\)
\(108\) 0 0
\(109\) −9.24264 9.24264i −0.885284 0.885284i 0.108781 0.994066i \(-0.465305\pi\)
−0.994066 + 0.108781i \(0.965305\pi\)
\(110\) 0 0
\(111\) 9.81845 0.931926
\(112\) 0 0
\(113\) 7.65685 0.720296 0.360148 0.932895i \(-0.382726\pi\)
0.360148 + 0.932895i \(0.382726\pi\)
\(114\) 0 0
\(115\) 2.79884 + 2.79884i 0.260993 + 0.260993i
\(116\) 0 0
\(117\) 4.41421 4.41421i 0.408094 0.408094i
\(118\) 0 0
\(119\) 10.4525i 0.958179i
\(120\) 0 0
\(121\) 6.17157i 0.561052i
\(122\) 0 0
\(123\) 3.06147 3.06147i 0.276043 0.276043i
\(124\) 0 0
\(125\) 4.00000 + 4.00000i 0.357771 + 0.357771i
\(126\) 0 0
\(127\) −11.7206 −1.04004 −0.520018 0.854155i \(-0.674075\pi\)
−0.520018 + 0.854155i \(0.674075\pi\)
\(128\) 0 0
\(129\) −1.17157 −0.103151
\(130\) 0 0
\(131\) −10.3212 10.3212i −0.901766 0.901766i 0.0938226 0.995589i \(-0.470091\pi\)
−0.995589 + 0.0938226i \(0.970091\pi\)
\(132\) 0 0
\(133\) −16.4853 + 16.4853i −1.42946 + 1.42946i
\(134\) 0 0
\(135\) 3.06147i 0.263489i
\(136\) 0 0
\(137\) 12.9706i 1.10815i 0.832467 + 0.554075i \(0.186928\pi\)
−0.832467 + 0.554075i \(0.813072\pi\)
\(138\) 0 0
\(139\) −14.2793 + 14.2793i −1.21116 + 1.21116i −0.240511 + 0.970646i \(0.577315\pi\)
−0.970646 + 0.240511i \(0.922685\pi\)
\(140\) 0 0
\(141\) 2.34315 + 2.34315i 0.197328 + 0.197328i
\(142\) 0 0
\(143\) 14.1480 1.18312
\(144\) 0 0
\(145\) −4.34315 −0.360679
\(146\) 0 0
\(147\) −5.09494 5.09494i −0.420223 0.420223i
\(148\) 0 0
\(149\) −1.24264 + 1.24264i −0.101801 + 0.101801i −0.756173 0.654372i \(-0.772933\pi\)
0.654372 + 0.756173i \(0.272933\pi\)
\(150\) 0 0
\(151\) 0.634051i 0.0515983i 0.999667 + 0.0257992i \(0.00821304\pi\)
−0.999667 + 0.0257992i \(0.991787\pi\)
\(152\) 0 0
\(153\) 5.17157i 0.418097i
\(154\) 0 0
\(155\) −1.26810 + 1.26810i −0.101856 + 0.101856i
\(156\) 0 0
\(157\) −1.58579 1.58579i −0.126560 0.126560i 0.640990 0.767549i \(-0.278524\pi\)
−0.767549 + 0.640990i \(0.778524\pi\)
\(158\) 0 0
\(159\) −4.96362 −0.393641
\(160\) 0 0
\(161\) −24.9706 −1.96796
\(162\) 0 0
\(163\) 3.82683 + 3.82683i 0.299741 + 0.299741i 0.840912 0.541171i \(-0.182019\pi\)
−0.541171 + 0.840912i \(0.682019\pi\)
\(164\) 0 0
\(165\) 1.85786 1.85786i 0.144635 0.144635i
\(166\) 0 0
\(167\) 3.69552i 0.285968i 0.989725 + 0.142984i \(0.0456697\pi\)
−0.989725 + 0.142984i \(0.954330\pi\)
\(168\) 0 0
\(169\) 1.34315i 0.103319i
\(170\) 0 0
\(171\) 8.15640 8.15640i 0.623736 0.623736i
\(172\) 0 0
\(173\) −13.5858 13.5858i −1.03291 1.03291i −0.999440 0.0334684i \(-0.989345\pi\)
−0.0334684 0.999440i \(-0.510655\pi\)
\(174\) 0 0
\(175\) −17.2095 −1.30092
\(176\) 0 0
\(177\) −1.17157 −0.0880608
\(178\) 0 0
\(179\) 8.15640 + 8.15640i 0.609638 + 0.609638i 0.942851 0.333213i \(-0.108133\pi\)
−0.333213 + 0.942851i \(0.608133\pi\)
\(180\) 0 0
\(181\) 10.0711 10.0711i 0.748577 0.748577i −0.225635 0.974212i \(-0.572446\pi\)
0.974212 + 0.225635i \(0.0724458\pi\)
\(182\) 0 0
\(183\) 1.15932i 0.0856991i
\(184\) 0 0
\(185\) 5.31371i 0.390672i
\(186\) 0 0
\(187\) −8.28772 + 8.28772i −0.606058 + 0.606058i
\(188\) 0 0
\(189\) 13.6569 + 13.6569i 0.993390 + 0.993390i
\(190\) 0 0
\(191\) 11.7206 0.848073 0.424037 0.905645i \(-0.360613\pi\)
0.424037 + 0.905645i \(0.360613\pi\)
\(192\) 0 0
\(193\) 0.485281 0.0349313 0.0174657 0.999847i \(-0.494440\pi\)
0.0174657 + 0.999847i \(0.494440\pi\)
\(194\) 0 0
\(195\) 1.53073 + 1.53073i 0.109618 + 0.109618i
\(196\) 0 0
\(197\) −7.58579 + 7.58579i −0.540465 + 0.540465i −0.923665 0.383200i \(-0.874822\pi\)
0.383200 + 0.923665i \(0.374822\pi\)
\(198\) 0 0
\(199\) 12.3547i 0.875798i 0.899024 + 0.437899i \(0.144277\pi\)
−0.899024 + 0.437899i \(0.855723\pi\)
\(200\) 0 0
\(201\) 2.14214i 0.151095i
\(202\) 0 0
\(203\) 19.3743 19.3743i 1.35981 1.35981i
\(204\) 0 0
\(205\) −1.65685 1.65685i −0.115720 0.115720i
\(206\) 0 0
\(207\) 12.3547 0.858708
\(208\) 0 0
\(209\) 26.1421 1.80829
\(210\) 0 0
\(211\) 9.42450 + 9.42450i 0.648810 + 0.648810i 0.952705 0.303896i \(-0.0982874\pi\)
−0.303896 + 0.952705i \(0.598287\pi\)
\(212\) 0 0
\(213\) 6.14214 6.14214i 0.420852 0.420852i
\(214\) 0 0
\(215\) 0.634051i 0.0432419i
\(216\) 0 0
\(217\) 11.3137i 0.768025i
\(218\) 0 0
\(219\) 4.96362 4.96362i 0.335410 0.335410i
\(220\) 0 0
\(221\) −6.82843 6.82843i −0.459330 0.459330i
\(222\) 0 0
\(223\) −3.06147 −0.205011 −0.102506 0.994732i \(-0.532686\pi\)
−0.102506 + 0.994732i \(0.532686\pi\)
\(224\) 0 0
\(225\) 8.51472 0.567648
\(226\) 0 0
\(227\) 0.765367 + 0.765367i 0.0507992 + 0.0507992i 0.732050 0.681251i \(-0.238564\pi\)
−0.681251 + 0.732050i \(0.738564\pi\)
\(228\) 0 0
\(229\) 2.75736 2.75736i 0.182211 0.182211i −0.610107 0.792319i \(-0.708874\pi\)
0.792319 + 0.610107i \(0.208874\pi\)
\(230\) 0 0
\(231\) 16.5754i 1.09058i
\(232\) 0 0
\(233\) 20.8284i 1.36452i 0.731112 + 0.682258i \(0.239002\pi\)
−0.731112 + 0.682258i \(0.760998\pi\)
\(234\) 0 0
\(235\) 1.26810 1.26810i 0.0827218 0.0827218i
\(236\) 0 0
\(237\) −11.3137 11.3137i −0.734904 0.734904i
\(238\) 0 0
\(239\) −12.2459 −0.792119 −0.396060 0.918225i \(-0.629623\pi\)
−0.396060 + 0.918225i \(0.629623\pi\)
\(240\) 0 0
\(241\) 13.1716 0.848456 0.424228 0.905556i \(-0.360546\pi\)
0.424228 + 0.905556i \(0.360546\pi\)
\(242\) 0 0
\(243\) −10.9552 10.9552i −0.702779 0.702779i
\(244\) 0 0
\(245\) −2.75736 + 2.75736i −0.176161 + 0.176161i
\(246\) 0 0
\(247\) 21.5391i 1.37050i
\(248\) 0 0
\(249\) 14.8284i 0.939713i
\(250\) 0 0
\(251\) 12.7486 12.7486i 0.804685 0.804685i −0.179139 0.983824i \(-0.557331\pi\)
0.983824 + 0.179139i \(0.0573312\pi\)
\(252\) 0 0
\(253\) 19.7990 + 19.7990i 1.24475 + 1.24475i
\(254\) 0 0
\(255\) −1.79337 −0.112305
\(256\) 0 0
\(257\) −14.9706 −0.933838 −0.466919 0.884300i \(-0.654636\pi\)
−0.466919 + 0.884300i \(0.654636\pi\)
\(258\) 0 0
\(259\) 23.7038 + 23.7038i 1.47289 + 1.47289i
\(260\) 0 0
\(261\) −9.58579 + 9.58579i −0.593345 + 0.593345i
\(262\) 0 0
\(263\) 12.8799i 0.794210i 0.917773 + 0.397105i \(0.129985\pi\)
−0.917773 + 0.397105i \(0.870015\pi\)
\(264\) 0 0
\(265\) 2.68629i 0.165018i
\(266\) 0 0
\(267\) 3.69552 3.69552i 0.226162 0.226162i
\(268\) 0 0
\(269\) 18.0711 + 18.0711i 1.10181 + 1.10181i 0.994192 + 0.107620i \(0.0343231\pi\)
0.107620 + 0.994192i \(0.465677\pi\)
\(270\) 0 0
\(271\) −5.59767 −0.340034 −0.170017 0.985441i \(-0.554382\pi\)
−0.170017 + 0.985441i \(0.554382\pi\)
\(272\) 0 0
\(273\) −13.6569 −0.826550
\(274\) 0 0
\(275\) 13.6453 + 13.6453i 0.822842 + 0.822842i
\(276\) 0 0
\(277\) 2.41421 2.41421i 0.145056 0.145056i −0.630849 0.775905i \(-0.717293\pi\)
0.775905 + 0.630849i \(0.217293\pi\)
\(278\) 0 0
\(279\) 5.59767i 0.335124i
\(280\) 0 0
\(281\) 17.7990i 1.06180i −0.847435 0.530899i \(-0.821854\pi\)
0.847435 0.530899i \(-0.178146\pi\)
\(282\) 0 0
\(283\) 10.3212 10.3212i 0.613531 0.613531i −0.330333 0.943864i \(-0.607161\pi\)
0.943864 + 0.330333i \(0.107161\pi\)
\(284\) 0 0
\(285\) 2.82843 + 2.82843i 0.167542 + 0.167542i
\(286\) 0 0
\(287\) 14.7821 0.872558
\(288\) 0 0
\(289\) −9.00000 −0.529412
\(290\) 0 0
\(291\) 3.95815 + 3.95815i 0.232031 + 0.232031i
\(292\) 0 0
\(293\) 0.414214 0.414214i 0.0241986 0.0241986i −0.694904 0.719103i \(-0.744553\pi\)
0.719103 + 0.694904i \(0.244553\pi\)
\(294\) 0 0
\(295\) 0.634051i 0.0369159i
\(296\) 0 0
\(297\) 21.6569i 1.25666i
\(298\) 0 0
\(299\) −16.3128 + 16.3128i −0.943394 + 0.943394i
\(300\) 0 0
\(301\) −2.82843 2.82843i −0.163028 0.163028i
\(302\) 0 0
\(303\) 18.4776 1.06151
\(304\) 0 0
\(305\) 0.627417 0.0359258
\(306\) 0 0
\(307\) 3.19278 + 3.19278i 0.182222 + 0.182222i 0.792323 0.610101i \(-0.208871\pi\)
−0.610101 + 0.792323i \(0.708871\pi\)
\(308\) 0 0
\(309\) 10.8284 10.8284i 0.616008 0.616008i
\(310\) 0 0
\(311\) 24.6005i 1.39497i 0.716600 + 0.697484i \(0.245697\pi\)
−0.716600 + 0.697484i \(0.754303\pi\)
\(312\) 0 0
\(313\) 31.3137i 1.76996i 0.465633 + 0.884978i \(0.345827\pi\)
−0.465633 + 0.884978i \(0.654173\pi\)
\(314\) 0 0
\(315\) 2.79884 2.79884i 0.157696 0.157696i
\(316\) 0 0
\(317\) −10.8995 10.8995i −0.612177 0.612177i 0.331336 0.943513i \(-0.392501\pi\)
−0.943513 + 0.331336i \(0.892501\pi\)
\(318\) 0 0
\(319\) −30.7235 −1.72018
\(320\) 0 0
\(321\) −2.14214 −0.119562
\(322\) 0 0
\(323\) −12.6173 12.6173i −0.702045 0.702045i
\(324\) 0 0
\(325\) −11.2426 + 11.2426i −0.623629 + 0.623629i
\(326\) 0 0
\(327\) 14.1480i 0.782387i
\(328\) 0 0
\(329\) 11.3137i 0.623745i
\(330\) 0 0
\(331\) 5.99162 5.99162i 0.329329 0.329329i −0.523002 0.852331i \(-0.675188\pi\)
0.852331 + 0.523002i \(0.175188\pi\)
\(332\) 0 0
\(333\) −11.7279 11.7279i −0.642686 0.642686i
\(334\) 0 0
\(335\) 1.15932 0.0633402
\(336\) 0 0
\(337\) 6.00000 0.326841 0.163420 0.986557i \(-0.447747\pi\)
0.163420 + 0.986557i \(0.447747\pi\)
\(338\) 0 0
\(339\) 5.86030 + 5.86030i 0.318288 + 0.318288i
\(340\) 0 0
\(341\) −8.97056 + 8.97056i −0.485783 + 0.485783i
\(342\) 0 0
\(343\) 1.26810i 0.0684710i
\(344\) 0 0
\(345\) 4.28427i 0.230657i
\(346\) 0 0
\(347\) 10.9552 10.9552i 0.588108 0.588108i −0.349011 0.937119i \(-0.613482\pi\)
0.937119 + 0.349011i \(0.113482\pi\)
\(348\) 0 0
\(349\) −1.92893 1.92893i −0.103253 0.103253i 0.653593 0.756846i \(-0.273261\pi\)
−0.756846 + 0.653593i \(0.773261\pi\)
\(350\) 0 0
\(351\) 17.8435 0.952418
\(352\) 0 0
\(353\) 22.9706 1.22260 0.611300 0.791399i \(-0.290647\pi\)
0.611300 + 0.791399i \(0.290647\pi\)
\(354\) 0 0
\(355\) −3.32410 3.32410i −0.176425 0.176425i
\(356\) 0 0
\(357\) 8.00000 8.00000i 0.423405 0.423405i
\(358\) 0 0
\(359\) 0.634051i 0.0334639i 0.999860 + 0.0167320i \(0.00532620\pi\)
−0.999860 + 0.0167320i \(0.994674\pi\)
\(360\) 0 0
\(361\) 20.7990i 1.09468i
\(362\) 0 0
\(363\) 4.72352 4.72352i 0.247920 0.247920i
\(364\) 0 0
\(365\) −2.68629 2.68629i −0.140607 0.140607i
\(366\) 0 0
\(367\) −9.18440 −0.479422 −0.239711 0.970844i \(-0.577053\pi\)
−0.239711 + 0.970844i \(0.577053\pi\)
\(368\) 0 0
\(369\) −7.31371 −0.380736
\(370\) 0 0
\(371\) −11.9832 11.9832i −0.622139 0.622139i
\(372\) 0 0
\(373\) 4.75736 4.75736i 0.246327 0.246327i −0.573135 0.819461i \(-0.694273\pi\)
0.819461 + 0.573135i \(0.194273\pi\)
\(374\) 0 0
\(375\) 6.12293i 0.316187i
\(376\) 0 0
\(377\) 25.3137i 1.30372i
\(378\) 0 0
\(379\) −18.6089 + 18.6089i −0.955875 + 0.955875i −0.999067 0.0431915i \(-0.986247\pi\)
0.0431915 + 0.999067i \(0.486247\pi\)
\(380\) 0 0
\(381\) −8.97056 8.97056i −0.459576 0.459576i
\(382\) 0 0
\(383\) 20.9050 1.06820 0.534098 0.845423i \(-0.320651\pi\)
0.534098 + 0.845423i \(0.320651\pi\)
\(384\) 0 0
\(385\) 8.97056 0.457182
\(386\) 0 0
\(387\) 1.39942 + 1.39942i 0.0711364 + 0.0711364i
\(388\) 0 0
\(389\) 14.4142 14.4142i 0.730830 0.730830i −0.239954 0.970784i \(-0.577133\pi\)
0.970784 + 0.239954i \(0.0771325\pi\)
\(390\) 0 0
\(391\) 19.1116i 0.966517i
\(392\) 0 0
\(393\) 15.7990i 0.796954i
\(394\) 0 0
\(395\) −6.12293 + 6.12293i −0.308078 + 0.308078i
\(396\) 0 0
\(397\) −3.58579 3.58579i −0.179965 0.179965i 0.611375 0.791341i \(-0.290617\pi\)
−0.791341 + 0.611375i \(0.790617\pi\)
\(398\) 0 0
\(399\) −25.2346 −1.26331
\(400\) 0 0
\(401\) −7.51472 −0.375267 −0.187634 0.982239i \(-0.560082\pi\)
−0.187634 + 0.982239i \(0.560082\pi\)
\(402\) 0 0
\(403\) −7.39104 7.39104i −0.368174 0.368174i
\(404\) 0 0
\(405\) 0.0710678 0.0710678i 0.00353139 0.00353139i
\(406\) 0 0
\(407\) 37.5892i 1.86323i
\(408\) 0 0
\(409\) 31.3137i 1.54836i 0.632964 + 0.774182i \(0.281838\pi\)
−0.632964 + 0.774182i \(0.718162\pi\)
\(410\) 0 0
\(411\) −9.92724 + 9.92724i −0.489675 + 0.489675i
\(412\) 0 0
\(413\) −2.82843 2.82843i −0.139178 0.139178i
\(414\) 0 0
\(415\) −8.02509 −0.393936
\(416\) 0 0
\(417\) −21.8579 −1.07038
\(418\) 0 0
\(419\) 8.79045 + 8.79045i 0.429442 + 0.429442i 0.888438 0.458996i \(-0.151791\pi\)
−0.458996 + 0.888438i \(0.651791\pi\)
\(420\) 0 0
\(421\) 6.07107 6.07107i 0.295886 0.295886i −0.543514 0.839400i \(-0.682907\pi\)
0.839400 + 0.543514i \(0.182907\pi\)
\(422\) 0 0
\(423\) 5.59767i 0.272168i
\(424\) 0 0
\(425\) 13.1716i 0.638915i
\(426\) 0 0
\(427\) −2.79884 + 2.79884i −0.135445 + 0.135445i
\(428\) 0 0
\(429\) 10.8284 + 10.8284i 0.522801 + 0.522801i
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) −25.4558 −1.22333 −0.611665 0.791117i \(-0.709500\pi\)
−0.611665 + 0.791117i \(0.709500\pi\)
\(434\) 0 0
\(435\) −3.32410 3.32410i −0.159378 0.159378i
\(436\) 0 0
\(437\) −30.1421 + 30.1421i −1.44189 + 1.44189i
\(438\) 0 0
\(439\) 38.1145i 1.81911i −0.415588 0.909553i \(-0.636424\pi\)
0.415588 0.909553i \(-0.363576\pi\)
\(440\) 0 0
\(441\) 12.1716i 0.579599i
\(442\) 0 0
\(443\) −1.39942 + 1.39942i −0.0664883 + 0.0664883i −0.739569 0.673081i \(-0.764971\pi\)
0.673081 + 0.739569i \(0.264971\pi\)
\(444\) 0 0
\(445\) −2.00000 2.00000i −0.0948091 0.0948091i
\(446\) 0 0
\(447\) −1.90215 −0.0899687
\(448\) 0 0
\(449\) −6.14214 −0.289865 −0.144933 0.989442i \(-0.546297\pi\)
−0.144933 + 0.989442i \(0.546297\pi\)
\(450\) 0 0
\(451\) −11.7206 11.7206i −0.551902 0.551902i
\(452\) 0 0
\(453\) −0.485281 + 0.485281i −0.0228005 + 0.0228005i
\(454\) 0 0
\(455\) 7.39104i 0.346497i
\(456\) 0 0
\(457\) 26.6274i 1.24558i −0.782390 0.622789i \(-0.785999\pi\)
0.782390 0.622789i \(-0.214001\pi\)
\(458\) 0 0
\(459\) −10.4525 + 10.4525i −0.487881 + 0.487881i
\(460\) 0 0
\(461\) 27.0416 + 27.0416i 1.25945 + 1.25945i 0.951354 + 0.308100i \(0.0996933\pi\)
0.308100 + 0.951354i \(0.400307\pi\)
\(462\) 0 0
\(463\) 35.6871 1.65852 0.829260 0.558864i \(-0.188762\pi\)
0.829260 + 0.558864i \(0.188762\pi\)
\(464\) 0 0
\(465\) −1.94113 −0.0900175
\(466\) 0 0
\(467\) −26.8966 26.8966i −1.24463 1.24463i −0.958060 0.286567i \(-0.907486\pi\)
−0.286567 0.958060i \(-0.592514\pi\)
\(468\) 0 0
\(469\) −5.17157 + 5.17157i −0.238801 + 0.238801i
\(470\) 0 0
\(471\) 2.42742i 0.111849i
\(472\) 0 0
\(473\) 4.48528i 0.206233i
\(474\) 0 0
\(475\) −20.7737 + 20.7737i −0.953162 + 0.953162i
\(476\) 0 0
\(477\) 5.92893 + 5.92893i 0.271467 + 0.271467i
\(478\) 0 0
\(479\) −35.1618 −1.60658 −0.803292 0.595585i \(-0.796920\pi\)
−0.803292 + 0.595585i \(0.796920\pi\)
\(480\) 0 0
\(481\) 30.9706 1.41214
\(482\) 0 0
\(483\) −19.1116 19.1116i −0.869610 0.869610i
\(484\) 0 0
\(485\) 2.14214 2.14214i 0.0972694 0.0972694i
\(486\) 0 0
\(487\) 6.23172i 0.282386i 0.989982 + 0.141193i \(0.0450938\pi\)
−0.989982 + 0.141193i \(0.954906\pi\)
\(488\) 0 0
\(489\) 5.85786i 0.264902i
\(490\) 0 0
\(491\) 3.56420 3.56420i 0.160850 0.160850i −0.622093 0.782943i \(-0.713717\pi\)
0.782943 + 0.622093i \(0.213717\pi\)
\(492\) 0 0
\(493\) 14.8284 + 14.8284i 0.667839 + 0.667839i
\(494\) 0 0
\(495\) −4.43835 −0.199489
\(496\) 0 0
\(497\) 29.6569 1.33029
\(498\) 0 0
\(499\) 12.4860 + 12.4860i 0.558949 + 0.558949i 0.929008 0.370059i \(-0.120663\pi\)
−0.370059 + 0.929008i \(0.620663\pi\)
\(500\) 0 0
\(501\) −2.82843 + 2.82843i −0.126365 + 0.126365i
\(502\) 0 0
\(503\) 22.8072i 1.01692i −0.861085 0.508460i \(-0.830215\pi\)
0.861085 0.508460i \(-0.169785\pi\)
\(504\) 0 0
\(505\) 10.0000i 0.444994i
\(506\) 0 0
\(507\) 1.02800 1.02800i 0.0456550 0.0456550i
\(508\) 0 0
\(509\) −18.5563 18.5563i −0.822496 0.822496i 0.163970 0.986465i \(-0.447570\pi\)
−0.986465 + 0.163970i \(0.947570\pi\)
\(510\) 0 0
\(511\) 23.9665 1.06021
\(512\) 0 0
\(513\) 32.9706 1.45569
\(514\) 0 0
\(515\) −5.86030 5.86030i −0.258236 0.258236i
\(516\) 0 0
\(517\) 8.97056 8.97056i 0.394525 0.394525i
\(518\) 0 0
\(519\) 20.7962i 0.912853i
\(520\) 0 0
\(521\) 6.34315i 0.277898i 0.990300 + 0.138949i \(0.0443725\pi\)
−0.990300 + 0.138949i \(0.955628\pi\)
\(522\) 0 0
\(523\) −10.0586 + 10.0586i −0.439830 + 0.439830i −0.891955 0.452125i \(-0.850666\pi\)
0.452125 + 0.891955i \(0.350666\pi\)
\(524\) 0 0
\(525\) −13.1716 13.1716i −0.574855 0.574855i
\(526\) 0 0
\(527\) 8.65914 0.377198
\(528\) 0 0
\(529\) −22.6569 −0.985081
\(530\) 0 0
\(531\) 1.39942 + 1.39942i 0.0607295 + 0.0607295i
\(532\) 0 0
\(533\) 9.65685 9.65685i 0.418285 0.418285i
\(534\) 0 0
\(535\) 1.15932i 0.0501216i
\(536\) 0 0
\(537\) 12.4853i 0.538780i
\(538\) 0 0
\(539\) −19.5056 + 19.5056i −0.840165 + 0.840165i
\(540\) 0 0
\(541\) −7.24264 7.24264i −0.311385 0.311385i 0.534061 0.845446i \(-0.320665\pi\)
−0.845446 + 0.534061i \(0.820665\pi\)
\(542\) 0 0
\(543\) 15.4161 0.661569
\(544\) 0 0
\(545\) −7.65685 −0.327984
\(546\) 0 0
\(547\) −13.3827 13.3827i −0.572201 0.572201i 0.360542 0.932743i \(-0.382592\pi\)
−0.932743 + 0.360542i \(0.882592\pi\)
\(548\) 0 0
\(549\) 1.38478 1.38478i 0.0591008 0.0591008i
\(550\) 0 0
\(551\) 46.7736i 1.99262i
\(552\) 0 0
\(553\) 54.6274i 2.32299i
\(554\) 0 0
\(555\) 4.06694 4.06694i 0.172632 0.172632i
\(556\) 0 0
\(557\) 8.07107 + 8.07107i 0.341982 + 0.341982i 0.857112 0.515130i \(-0.172256\pi\)
−0.515130 + 0.857112i \(0.672256\pi\)
\(558\) 0 0
\(559\) −3.69552 −0.156304
\(560\) 0 0
\(561\) −12.6863 −0.535616
\(562\) 0 0
\(563\) 10.5838 + 10.5838i 0.446055 + 0.446055i 0.894041 0.447986i \(-0.147859\pi\)
−0.447986 + 0.894041i \(0.647859\pi\)
\(564\) 0 0
\(565\) 3.17157 3.17157i 0.133429 0.133429i
\(566\) 0 0
\(567\) 0.634051i 0.0266276i
\(568\) 0 0
\(569\) 25.6569i 1.07559i 0.843075 + 0.537796i \(0.180743\pi\)
−0.843075 + 0.537796i \(0.819257\pi\)
\(570\) 0 0
\(571\) 19.5056 19.5056i 0.816284 0.816284i −0.169284 0.985567i \(-0.554145\pi\)
0.985567 + 0.169284i \(0.0541455\pi\)
\(572\) 0 0
\(573\) 8.97056 + 8.97056i 0.374751 + 0.374751i
\(574\) 0 0
\(575\) −31.4663 −1.31224
\(576\) 0 0
\(577\) 17.3137 0.720779 0.360390 0.932802i \(-0.382644\pi\)
0.360390 + 0.932802i \(0.382644\pi\)
\(578\) 0 0
\(579\) 0.371418 + 0.371418i 0.0154356 + 0.0154356i
\(580\) 0 0
\(581\) 35.7990 35.7990i 1.48519 1.48519i
\(582\) 0 0
\(583\) 19.0029i 0.787018i
\(584\) 0 0
\(585\) 3.65685i 0.151192i
\(586\) 0 0
\(587\) −13.1200 + 13.1200i −0.541521 + 0.541521i −0.923975 0.382453i \(-0.875079\pi\)
0.382453 + 0.923975i \(0.375079\pi\)
\(588\) 0 0
\(589\) −13.6569 13.6569i −0.562721 0.562721i
\(590\) 0 0
\(591\) −11.6118 −0.477646
\(592\) 0 0
\(593\) −9.31371 −0.382468 −0.191234 0.981544i \(-0.561249\pi\)
−0.191234 + 0.981544i \(0.561249\pi\)
\(594\) 0 0
\(595\) −4.32957 4.32957i −0.177495 0.177495i
\(596\) 0 0
\(597\) −9.45584 + 9.45584i −0.387002 + 0.387002i
\(598\) 0 0
\(599\) 45.5055i 1.85931i 0.368437 + 0.929653i \(0.379893\pi\)
−0.368437 + 0.929653i \(0.620107\pi\)
\(600\) 0 0
\(601\) 20.8284i 0.849609i −0.905285 0.424805i \(-0.860343\pi\)
0.905285 0.424805i \(-0.139657\pi\)
\(602\) 0 0
\(603\) 2.55873 2.55873i 0.104200 0.104200i
\(604\) 0 0
\(605\) −2.55635 2.55635i −0.103930 0.103930i
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 29.6569 1.20176
\(610\) 0 0
\(611\) 7.39104 + 7.39104i 0.299009 + 0.299009i
\(612\) 0 0
\(613\) −27.8701 + 27.8701i −1.12566 + 1.12566i −0.134786 + 0.990875i \(0.543035\pi\)
−0.990875 + 0.134786i \(0.956965\pi\)
\(614\) 0 0
\(615\) 2.53620i 0.102270i
\(616\) 0 0
\(617\) 38.4853i 1.54936i 0.632354 + 0.774680i \(0.282089\pi\)
−0.632354 + 0.774680i \(0.717911\pi\)
\(618\) 0 0
\(619\) 2.93015 2.93015i 0.117773 0.117773i −0.645764 0.763537i \(-0.723461\pi\)
0.763537 + 0.645764i \(0.223461\pi\)
\(620\) 0 0
\(621\) 24.9706 + 24.9706i 1.00203 + 1.00203i
\(622\) 0 0
\(623\) 17.8435 0.714886
\(624\) 0 0
\(625\) −19.9706 −0.798823
\(626\) 0 0
\(627\) 20.0083 + 20.0083i 0.799056 + 0.799056i
\(628\) 0 0
\(629\) −18.1421 + 18.1421i −0.723374 + 0.723374i
\(630\) 0 0
\(631\) 14.1480i 0.563224i −0.959528 0.281612i \(-0.909131\pi\)
0.959528 0.281612i \(-0.0908691\pi\)
\(632\) 0 0
\(633\) 14.4264i 0.573398i
\(634\) 0 0
\(635\) −4.85483 + 4.85483i −0.192658 + 0.192658i
\(636\) 0 0
\(637\) −16.0711 16.0711i −0.636759 0.636759i
\(638\) 0 0
\(639\) −14.6733 −0.580466
\(640\) 0 0
\(641\) −38.1421 −1.50652 −0.753262 0.657721i \(-0.771521\pi\)
−0.753262 + 0.657721i \(0.771521\pi\)
\(642\) 0 0
\(643\) −13.3827 13.3827i −0.527760 0.527760i 0.392144 0.919904i \(-0.371734\pi\)
−0.919904 + 0.392144i \(0.871734\pi\)
\(644\) 0 0
\(645\) −0.485281 + 0.485281i −0.0191079 + 0.0191079i
\(646\) 0 0
\(647\) 21.5391i 0.846788i 0.905946 + 0.423394i \(0.139161\pi\)
−0.905946 + 0.423394i \(0.860839\pi\)
\(648\) 0 0
\(649\) 4.48528i 0.176063i
\(650\) 0 0
\(651\) 8.65914 8.65914i 0.339378 0.339378i
\(652\) 0 0
\(653\) −4.55635 4.55635i −0.178304 0.178304i 0.612312 0.790616i \(-0.290240\pi\)
−0.790616 + 0.612312i \(0.790240\pi\)
\(654\) 0 0
\(655\) −8.55035 −0.334090
\(656\) 0 0
\(657\) −11.8579 −0.462619
\(658\) 0 0
\(659\) −1.02800 1.02800i −0.0400452 0.0400452i 0.686801 0.726846i \(-0.259015\pi\)
−0.726846 + 0.686801i \(0.759015\pi\)
\(660\) 0 0
\(661\) −20.5563 + 20.5563i −0.799549 + 0.799549i −0.983024 0.183475i \(-0.941265\pi\)
0.183475 + 0.983024i \(0.441265\pi\)
\(662\) 0 0
\(663\) 10.4525i 0.405942i
\(664\) 0 0
\(665\) 13.6569i 0.529590i
\(666\) 0 0
\(667\) 35.4244 35.4244i 1.37164 1.37164i
\(668\) 0 0
\(669\) −2.34315 2.34315i −0.0905912 0.0905912i
\(670\) 0 0
\(671\) 4.43835 0.171341
\(672\) 0 0
\(673\) −26.8284 −1.03416 −0.517080 0.855937i \(-0.672981\pi\)
−0.517080 + 0.855937i \(0.672981\pi\)
\(674\) 0 0
\(675\) 17.2095 + 17.2095i 0.662394 + 0.662394i
\(676\) 0 0
\(677\) −9.58579 + 9.58579i −0.368412 + 0.368412i −0.866898 0.498486i \(-0.833890\pi\)
0.498486 + 0.866898i \(0.333890\pi\)
\(678\) 0 0
\(679\) 19.1116i 0.733437i
\(680\) 0 0
\(681\) 1.17157i 0.0448948i
\(682\) 0 0
\(683\) 23.2011 23.2011i 0.887766 0.887766i −0.106542 0.994308i \(-0.533978\pi\)
0.994308 + 0.106542i \(0.0339780\pi\)
\(684\) 0 0
\(685\) 5.37258 + 5.37258i 0.205276 + 0.205276i
\(686\) 0 0
\(687\) 4.22078 0.161033
\(688\) 0 0
\(689\) −15.6569 −0.596479
\(690\) 0 0
\(691\) −28.7988 28.7988i −1.09556 1.09556i −0.994924 0.100634i \(-0.967913\pi\)
−0.100634 0.994924i \(-0.532087\pi\)
\(692\) 0 0
\(693\) 19.7990 19.7990i 0.752101 0.752101i
\(694\) 0 0
\(695\) 11.8294i 0.448714i
\(696\) 0 0
\(697\) 11.3137i 0.428537i
\(698\) 0 0
\(699\) −15.9414 + 15.9414i −0.602959 + 0.602959i
\(700\) 0 0
\(701\) −17.5858 17.5858i −0.664206 0.664206i 0.292163 0.956369i \(-0.405625\pi\)
−0.956369 + 0.292163i \(0.905625\pi\)
\(702\) 0 0
\(703\) 57.2261 2.15832
\(704\) 0 0
\(705\) 1.94113 0.0731070
\(706\) 0 0
\(707\) 44.6088 + 44.6088i 1.67769 + 1.67769i
\(708\) 0 0
\(709\) 16.7574 16.7574i 0.629336 0.629336i −0.318565 0.947901i \(-0.603201\pi\)
0.947901 + 0.318565i \(0.103201\pi\)
\(710\) 0 0
\(711\) 27.0279i 1.01363i
\(712\) 0 0
\(713\) 20.6863i 0.774708i
\(714\) 0 0
\(715\) 5.86030 5.86030i 0.219163 0.219163i
\(716\) 0 0
\(717\) −9.37258 9.37258i −0.350026 0.350026i
\(718\) 0 0
\(719\) −29.5641 −1.10256 −0.551278 0.834321i \(-0.685860\pi\)
−0.551278 + 0.834321i \(0.685860\pi\)
\(720\) 0 0
\(721\) 52.2843 1.94717
\(722\) 0 0
\(723\) 10.0811 + 10.0811i 0.374920 + 0.374920i
\(724\) 0 0
\(725\) 24.4142 24.4142i 0.906721 0.906721i
\(726\) 0 0
\(727\) 22.0643i 0.818320i 0.912463 + 0.409160i \(0.134178\pi\)
−0.912463 + 0.409160i \(0.865822\pi\)
\(728\) 0 0
\(729\) 17.2843i 0.640158i
\(730\) 0 0
\(731\) 2.16478 2.16478i 0.0800674 0.0800674i
\(732\) 0 0
\(733\) 13.1005 + 13.1005i 0.483878 + 0.483878i 0.906368 0.422490i \(-0.138844\pi\)
−0.422490 + 0.906368i \(0.638844\pi\)
\(734\) 0 0
\(735\) −4.22078 −0.155686
\(736\) 0 0
\(737\) 8.20101 0.302088
\(738\) 0 0
\(739\) 35.1843 + 35.1843i 1.29428 + 1.29428i 0.932115 + 0.362162i \(0.117961\pi\)
0.362162 + 0.932115i \(0.382039\pi\)
\(740\) 0 0
\(741\) −16.4853 + 16.4853i −0.605602 + 0.605602i
\(742\) 0 0
\(743\) 27.1367i 0.995550i 0.867306 + 0.497775i \(0.165849\pi\)
−0.867306 + 0.497775i \(0.834151\pi\)
\(744\) 0 0
\(745\) 1.02944i 0.0377157i
\(746\) 0 0
\(747\) −17.7122 + 17.7122i −0.648056 + 0.648056i
\(748\) 0 0
\(749\) −5.17157 5.17157i −0.188965 0.188965i
\(750\) 0 0
\(751\) 14.7821 0.539405 0.269703 0.962944i \(-0.413075\pi\)
0.269703 + 0.962944i \(0.413075\pi\)
\(752\) 0 0
\(753\) 19.5147 0.711156
\(754\) 0 0
\(755\) 0.262632 + 0.262632i 0.00955817 + 0.00955817i
\(756\) 0 0
\(757\) 13.3848 13.3848i 0.486478 0.486478i −0.420715 0.907193i \(-0.638221\pi\)
0.907193 + 0.420715i \(0.138221\pi\)
\(758\) 0 0
\(759\) 30.3070i 1.10007i
\(760\) 0 0
\(761\) 34.6274i 1.25524i −0.778519 0.627621i \(-0.784029\pi\)
0.778519 0.627621i \(-0.215971\pi\)
\(762\) 0 0
\(763\) 34.1563 34.1563i 1.23654 1.23654i
\(764\) 0 0
\(765\) 2.14214 + 2.14214i 0.0774491 + 0.0774491i
\(766\) 0 0
\(767\) −3.69552 −0.133437
\(768\) 0 0
\(769\) 5.17157 0.186492 0.0932458 0.995643i \(-0.470276\pi\)
0.0932458 + 0.995643i \(0.470276\pi\)
\(770\) 0 0
\(771\) −11.4580 11.4580i −0.412649 0.412649i
\(772\) 0 0
\(773\) 28.0711 28.0711i 1.00965 1.00965i 0.00969311 0.999953i \(-0.496915\pi\)
0.999953 0.00969311i \(-0.00308546\pi\)
\(774\) 0 0
\(775\) 14.2568i 0.512120i
\(776\) 0 0
\(777\) 36.2843i 1.30169i
\(778\) 0 0
\(779\) 17.8435 17.8435i 0.639311 0.639311i
\(780\) 0 0
\(781\) −23.5147 23.5147i −0.841423 0.841423i
\(782\) 0 0
\(783\) −38.7485 −1.38476
\(784\) 0 0
\(785\) −1.31371 −0.0468883
\(786\) 0 0
\(787\) 5.62020 + 5.62020i 0.200339 + 0.200339i 0.800145 0.599807i \(-0.204756\pi\)
−0.599807 + 0.800145i \(0.704756\pi\)
\(788\) 0 0
\(789\) −9.85786 + 9.85786i −0.350949 + 0.350949i
\(790\) 0 0
\(791\) 28.2960i 1.00609i
\(792\) 0 0
\(793\) 3.65685i 0.129859i
\(794\) 0 0
\(795\) −2.05600 + 2.05600i −0.0729188 + 0.0729188i
\(796\) 0 0
\(797\) 28.0711 + 28.0711i 0.994328 + 0.994328i 0.999984 0.00565577i \(-0.00180030\pi\)
−0.00565577 + 0.999984i \(0.501800\pi\)
\(798\) 0 0