Properties

Label 512.2.e.j.385.2
Level $512$
Weight $2$
Character 512.385
Analytic conductor $4.088$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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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 385.2
Root \(0.923880 - 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 512.385
Dual form 512.2.e.j.129.2

$q$-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 \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).

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

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 \(-0.851153\pi\)
0.450760 + 0.892645i \(0.351153\pi\)
\(4\) 0 0
\(5\) −0.414214 0.414214i −0.185242 0.185242i 0.608394 0.793635i \(-0.291814\pi\)
−0.793635 + 0.608394i \(0.791814\pi\)
\(6\) 0 0
\(7\) 3.69552i 1.39677i −0.715720 0.698387i \(-0.753901\pi\)
0.715720 0.698387i \(-0.246099\pi\)
\(8\) 0 0
\(9\) 1.82843i 0.609476i
\(10\) 0 0
\(11\) −2.93015 2.93015i −0.883474 0.883474i 0.110412 0.993886i \(-0.464783\pi\)
−0.993886 + 0.110412i \(0.964783\pi\)
\(12\) 0 0
\(13\) −2.41421 + 2.41421i −0.669582 + 0.669582i −0.957619 0.288037i \(-0.906997\pi\)
0.288037 + 0.957619i \(0.406997\pi\)
\(14\) 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 −0.0236776 + 0.999720i \(0.507538\pi\)
−0.999720 + 0.0236776i \(0.992462\pi\)
\(20\) 0 0
\(21\) 2.82843 + 2.82843i 0.617213 + 0.617213i
\(22\) 0 0
\(23\) 6.75699i 1.40893i −0.709739 0.704464i \(-0.751187\pi\)
0.709739 0.704464i \(-0.248813\pi\)
\(24\) 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 \(-0.508317\pi\)
0.999659 + 0.0261248i \(0.00831671\pi\)
\(30\) 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 −0.998427 0.0560630i \(-0.982145\pi\)
−0.0560630 0.998427i \(-0.517855\pi\)
\(38\) 0 0
\(39\) 3.69552i 0.591756i
\(40\) 0 0
\(41\) 4.00000i 0.624695i 0.949968 + 0.312348i \(0.101115\pi\)
−0.949968 + 0.312348i \(0.898885\pi\)
\(42\) 0 0
\(43\) 0.765367 + 0.765367i 0.116717 + 0.116717i 0.763053 0.646336i \(-0.223699\pi\)
−0.646336 + 0.763053i \(0.723699\pi\)
\(44\) 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 \(-0.148011\pi\)
−0.448415 + 0.893826i \(0.648011\pi\)
\(54\) 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 \(-0.227554\pi\)
−0.655528 + 0.755171i \(0.727554\pi\)
\(60\) 0 0
\(61\) −0.757359 + 0.757359i −0.0969699 + 0.0969699i −0.753928 0.656958i \(-0.771843\pi\)
0.656958 + 0.753928i \(0.271843\pi\)
\(62\) 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 \(-0.788575\pi\)
0.616438 + 0.787404i \(0.288575\pi\)
\(68\) 0 0
\(69\) 5.17157 + 5.17157i 0.622584 + 0.622584i
\(70\) 0 0
\(71\) 8.02509i 0.952403i 0.879336 + 0.476201i \(0.157987\pi\)
−0.879336 + 0.476201i \(0.842013\pi\)
\(72\) 0 0
\(73\) 6.48528i 0.759045i 0.925183 + 0.379522i \(0.123912\pi\)
−0.925183 + 0.379522i \(0.876088\pi\)
\(74\) 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 0.0654452 0.997856i \(-0.479153\pi\)
0.997856 0.0654452i \(-0.0208468\pi\)
\(84\) 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 \(0.0823738\pi\)
−0.966702 + 0.255906i \(0.917626\pi\)
\(90\) 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 −0.973827 0.227289i \(-0.927014\pi\)
−0.227289 0.973827i \(-0.572986\pi\)
\(102\) 0 0
\(103\) 14.1480i 1.39405i 0.717049 + 0.697023i \(0.245492\pi\)
−0.717049 + 0.697023i \(0.754508\pi\)
\(104\) 0 0
\(105\) 2.34315i 0.228668i
\(106\) 0 0
\(107\) 1.39942 + 1.39942i 0.135287 + 0.135287i 0.771507 0.636220i \(-0.219503\pi\)
−0.636220 + 0.771507i \(0.719503\pi\)
\(108\) 0 0
\(109\) 9.24264 9.24264i 0.885284 0.885284i −0.108781 0.994066i \(-0.534695\pi\)
0.994066 + 0.108781i \(0.0346948\pi\)
\(110\) 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 \(-0.529909\pi\)
0.995589 + 0.0938226i \(0.0299086\pi\)
\(132\) 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 \(-0.813072\pi\)
0.832467 0.554075i \(-0.186928\pi\)
\(138\) 0 0
\(139\) 14.2793 + 14.2793i 1.21116 + 1.21116i 0.970646 + 0.240511i \(0.0773151\pi\)
0.240511 + 0.970646i \(0.422685\pi\)
\(140\) 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 \(-0.227067\pi\)
−0.654372 + 0.756173i \(0.727067\pi\)
\(150\) 0 0
\(151\) 0.634051i 0.0515983i −0.999667 0.0257992i \(-0.991787\pi\)
0.999667 0.0257992i \(-0.00821304\pi\)
\(152\) 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 \(-0.721476\pi\)
0.767549 + 0.640990i \(0.221476\pi\)
\(158\) 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 \(-0.817981\pi\)
0.541171 + 0.840912i \(0.317981\pi\)
\(164\) 0 0
\(165\) −1.85786 1.85786i −0.144635 0.144635i
\(166\) 0 0
\(167\) 3.69552i 0.285968i −0.989725 0.142984i \(-0.954330\pi\)
0.989725 0.142984i \(-0.0456697\pi\)
\(168\) 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 0.0334684 0.999440i \(-0.489345\pi\)
0.999440 0.0334684i \(-0.0106553\pi\)
\(174\) 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 \(-0.891867\pi\)
0.333213 + 0.942851i \(0.391867\pi\)
\(180\) 0 0
\(181\) −10.0711 10.0711i −0.748577 0.748577i 0.225635 0.974212i \(-0.427554\pi\)
−0.974212 + 0.225635i \(0.927554\pi\)
\(182\) 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 \(-0.125178\pi\)
−0.383200 + 0.923665i \(0.625178\pi\)
\(198\) 0 0
\(199\) 12.3547i 0.875798i −0.899024 0.437899i \(-0.855723\pi\)
0.899024 0.437899i \(-0.144277\pi\)
\(200\) 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 \(-0.901713\pi\)
0.303896 + 0.952705i \(0.401713\pi\)
\(212\) 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 \(-0.761436\pi\)
0.681251 + 0.732050i \(0.261436\pi\)
\(228\) 0 0
\(229\) −2.75736 2.75736i −0.182211 0.182211i 0.610107 0.792319i \(-0.291126\pi\)
−0.792319 + 0.610107i \(0.791126\pi\)
\(230\) 0 0
\(231\) 16.5754i 1.09058i
\(232\) 0 0
\(233\) 20.8284i 1.36452i −0.731112 0.682258i \(-0.760998\pi\)
0.731112 0.682258i \(-0.239002\pi\)
\(234\) 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 \(-0.442669\pi\)
−0.983824 + 0.179139i \(0.942669\pi\)
\(252\) 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 \(-0.870015\pi\)
0.917773 0.397105i \(-0.129985\pi\)
\(264\) 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 −0.107620 + 0.994192i \(0.534323\pi\)
−0.994192 + 0.107620i \(0.965677\pi\)
\(270\) 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 \(-0.282707\pi\)
−0.775905 + 0.630849i \(0.782707\pi\)
\(278\) 0 0
\(279\) 5.59767i 0.335124i
\(280\) 0 0
\(281\) 17.7990i 1.06180i 0.847435 + 0.530899i \(0.178146\pi\)
−0.847435 + 0.530899i \(0.821854\pi\)
\(282\) 0 0
\(283\) −10.3212 10.3212i −0.613531 0.613531i 0.330333 0.943864i \(-0.392839\pi\)
−0.943864 + 0.330333i \(0.892839\pi\)
\(284\) 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 \(-0.255447\pi\)
−0.719103 + 0.694904i \(0.755447\pi\)
\(294\) 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 \(-0.791129\pi\)
0.610101 + 0.792323i \(0.291129\pi\)
\(308\) 0 0
\(309\) −10.8284 10.8284i −0.616008 0.616008i
\(310\) 0 0
\(311\) 24.6005i 1.39497i −0.716600 0.697484i \(-0.754303\pi\)
0.716600 0.697484i \(-0.245697\pi\)
\(312\) 0 0
\(313\) 31.3137i 1.76996i −0.465633 0.884978i \(-0.654173\pi\)
0.465633 0.884978i \(-0.345827\pi\)
\(314\) 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 \(-0.607499\pi\)
0.943513 + 0.331336i \(0.107499\pi\)
\(318\) 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 \(-0.324812\pi\)
−0.852331 + 0.523002i \(0.824812\pi\)
\(332\) 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 \(-0.386518\pi\)
−0.937119 + 0.349011i \(0.886518\pi\)
\(348\) 0 0
\(349\) 1.92893 1.92893i 0.103253 0.103253i −0.653593 0.756846i \(-0.726739\pi\)
0.756846 + 0.653593i \(0.226739\pi\)
\(350\) 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 \(-0.994674\pi\)
0.999860 0.0167320i \(-0.00532620\pi\)
\(360\) 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 \(-0.305727\pi\)
−0.819461 + 0.573135i \(0.805727\pi\)
\(374\) 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 \(-0.0137526\pi\)
−0.0431915 + 0.999067i \(0.513753\pi\)
\(380\) 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 \(-0.422867\pi\)
−0.970784 + 0.239954i \(0.922867\pi\)
\(390\) 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 \(-0.709383\pi\)
0.791341 + 0.611375i \(0.209383\pi\)
\(398\) 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 \(-0.718162\pi\)
0.632964 0.774182i \(-0.281838\pi\)
\(410\) 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 \(-0.848209\pi\)
0.458996 + 0.888438i \(0.348209\pi\)
\(420\) 0 0
\(421\) −6.07107 6.07107i −0.295886 0.295886i 0.543514 0.839400i \(-0.317093\pi\)
−0.839400 + 0.543514i \(0.817093\pi\)
\(422\) 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 \(0.363576\pi\)
−0.415588 + 0.909553i \(0.636424\pi\)
\(440\) 0 0
\(441\) 12.1716i 0.579599i
\(442\) 0 0
\(443\) 1.39942 + 1.39942i 0.0664883 + 0.0664883i 0.739569 0.673081i \(-0.235029\pi\)
−0.673081 + 0.739569i \(0.735029\pi\)
\(444\) 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 \(0.214001\pi\)
−0.782390 + 0.622789i \(0.785999\pi\)
\(458\) 0 0
\(459\) 10.4525 + 10.4525i 0.487881 + 0.487881i
\(460\) 0 0
\(461\) −27.0416 + 27.0416i −1.25945 + 1.25945i −0.308100 + 0.951354i \(0.599693\pi\)
−0.951354 + 0.308100i \(0.900307\pi\)
\(462\) 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 0.286567 0.958060i \(-0.407486\pi\)
0.958060 0.286567i \(-0.0925142\pi\)
\(468\) 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 \(-0.954906\pi\)
0.989982 0.141193i \(-0.0450938\pi\)
\(488\) 0 0
\(489\) 5.85786i 0.264902i
\(490\) 0 0
\(491\) −3.56420 3.56420i −0.160850 0.160850i 0.622093 0.782943i \(-0.286283\pi\)
−0.782943 + 0.622093i \(0.786283\pi\)
\(492\) 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 \(-0.879337\pi\)
0.370059 + 0.929008i \(0.379337\pi\)
\(500\) 0 0
\(501\) 2.82843 + 2.82843i 0.126365 + 0.126365i
\(502\) 0 0
\(503\) 22.8072i 1.01692i 0.861085 + 0.508460i \(0.169785\pi\)
−0.861085 + 0.508460i \(0.830215\pi\)
\(504\) 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 \(-0.552430\pi\)
0.986465 + 0.163970i \(0.0524299\pi\)
\(510\) 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 \(-0.955628\pi\)
0.990300 0.138949i \(-0.0443725\pi\)
\(522\) 0 0
\(523\) 10.0586 + 10.0586i 0.439830 + 0.439830i 0.891955 0.452125i \(-0.149334\pi\)
−0.452125 + 0.891955i \(0.649334\pi\)
\(524\) 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 \(-0.679335\pi\)
0.845446 + 0.534061i \(0.179335\pi\)
\(542\) 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 \(-0.617408\pi\)
0.932743 + 0.360542i \(0.117408\pi\)
\(548\) 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 \(-0.827744\pi\)
0.515130 + 0.857112i \(0.327744\pi\)
\(558\) 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 \(-0.852141\pi\)
0.447986 + 0.894041i \(0.352141\pi\)
\(564\) 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 \(-0.819257\pi\)
0.843075 0.537796i \(-0.180743\pi\)
\(570\) 0 0
\(571\) −19.5056 19.5056i −0.816284 0.816284i 0.169284 0.985567i \(-0.445855\pi\)
−0.985567 + 0.169284i \(0.945855\pi\)
\(572\) 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 \(-0.124921\pi\)
−0.382453 + 0.923975i \(0.624921\pi\)
\(588\) 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 \(-0.620107\pi\)
0.368437 0.929653i \(-0.379893\pi\)
\(600\) 0 0
\(601\) 20.8284i 0.849609i 0.905285 + 0.424805i \(0.139657\pi\)
−0.905285 + 0.424805i \(0.860343\pi\)
\(602\) 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 0.990875 + 0.134786i \(0.0430348\pi\)
0.134786 + 0.990875i \(0.456965\pi\)
\(614\) 0 0
\(615\) 2.53620i 0.102270i
\(616\) 0 0
\(617\) 38.4853i 1.54936i −0.632354 0.774680i \(-0.717911\pi\)
0.632354 0.774680i \(-0.282089\pi\)
\(618\) 0 0
\(619\) −2.93015 2.93015i −0.117773 0.117773i 0.645764 0.763537i \(-0.276539\pi\)
−0.763537 + 0.645764i \(0.776539\pi\)
\(620\) 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 \(0.0908691\pi\)
−0.959528 + 0.281612i \(0.909131\pi\)
\(632\) 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 \(-0.628266\pi\)
0.919904 + 0.392144i \(0.128266\pi\)
\(644\) 0 0
\(645\) 0.485281 + 0.485281i 0.0191079 + 0.0191079i
\(646\) 0 0
\(647\) 21.5391i 0.846788i −0.905946 0.423394i \(-0.860839\pi\)
0.905946 0.423394i \(-0.139161\pi\)
\(648\) 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 \(-0.709760\pi\)
0.790616 + 0.612312i \(0.209760\pi\)
\(654\) 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 \(-0.740985\pi\)
0.726846 + 0.686801i \(0.240985\pi\)
\(660\) 0 0
\(661\) 20.5563 + 20.5563i 0.799549 + 0.799549i 0.983024 0.183475i \(-0.0587347\pi\)
−0.183475 + 0.983024i \(0.558735\pi\)
\(662\) 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 \(-0.166110\pi\)
−0.498486 + 0.866898i \(0.666110\pi\)
\(678\) 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 \(-0.466022\pi\)
−0.994308 + 0.106542i \(0.966022\pi\)
\(684\) 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 0.100634 0.994924i \(-0.467913\pi\)
0.994924 0.100634i \(-0.0320870\pi\)
\(692\) 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 \(-0.594375\pi\)
0.956369 + 0.292163i \(0.0943749\pi\)
\(702\) 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 \(-0.396799\pi\)
−0.947901 + 0.318565i \(0.896799\pi\)
\(710\) 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 \(-0.865822\pi\)
0.912463 0.409160i \(-0.134178\pi\)
\(728\) 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 \(-0.861156\pi\)
0.422490 + 0.906368i \(0.361156\pi\)
\(734\) 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 −0.362162 + 0.932115i \(0.617961\pi\)
−0.932115 + 0.362162i \(0.882039\pi\)
\(740\) 0 0
\(741\) 16.4853 + 16.4853i 0.605602 + 0.605602i
\(742\) 0 0
\(743\) 27.1367i 0.995550i −0.867306 0.497775i \(-0.834151\pi\)
0.867306 0.497775i \(-0.165849\pi\)
\(744\) 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 \(-0.361779\pi\)
−0.907193 + 0.420715i \(0.861779\pi\)
\(758\) 0 0
\(759\) 30.3070i 1.10007i
\(760\) 0 0
\(761\) 34.6274i 1.25524i 0.778519 + 0.627621i \(0.215971\pi\)
−0.778519 + 0.627621i \(0.784029\pi\)
\(762\) 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 −0.999953 0.00969311i \(-0.996915\pi\)
−0.00969311 0.999953i \(-0.503085\pi\)
\(774\) 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 \(-0.795244\pi\)
0.599807 + 0.800145i \(0.295244\pi\)
\(788\) 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 \(-0.998200\pi\)
0.00565577 + 0.999984i \(0.498200\pi\)
\(798\) 0 0