Properties

Label 320.2.o.e.287.3
Level $320$
Weight $2$
Character 320.287
Analytic conductor $2.555$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.55521286468\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.49787136.1
Defining polynomial: \(x^{8} + 3 x^{6} + 5 x^{4} + 12 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 287.3
Root \(-0.228425 - 1.39564i\) of defining polynomial
Character \(\chi\) \(=\) 320.287
Dual form 320.2.o.e.223.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.456850 - 0.456850i) q^{3} +(-2.18890 + 0.456850i) q^{5} +(-2.79129 + 2.79129i) q^{7} +2.58258i q^{9} +O(q^{10})\) \(q+(0.456850 - 0.456850i) q^{3} +(-2.18890 + 0.456850i) q^{5} +(-2.79129 + 2.79129i) q^{7} +2.58258i q^{9} -4.37780 q^{11} +(1.73205 + 1.73205i) q^{13} +(-0.791288 + 1.20871i) q^{15} +(3.00000 + 3.00000i) q^{17} -3.46410i q^{19} +2.55040i q^{21} +(-0.791288 - 0.791288i) q^{23} +(4.58258 - 2.00000i) q^{25} +(2.55040 + 2.55040i) q^{27} -5.29150 q^{29} +1.58258i q^{31} +(-2.00000 + 2.00000i) q^{33} +(4.83465 - 7.38505i) q^{35} +(5.19615 - 5.19615i) q^{37} +1.58258 q^{39} -7.58258 q^{41} +(-8.29875 + 8.29875i) q^{43} +(-1.17985 - 5.65300i) q^{45} +(0.791288 - 0.791288i) q^{47} -8.58258i q^{49} +2.74110 q^{51} +(2.64575 + 2.64575i) q^{53} +(9.58258 - 2.00000i) q^{55} +(-1.58258 - 1.58258i) q^{57} +5.29150i q^{59} +9.66930i q^{61} +(-7.20871 - 7.20871i) q^{63} +(-4.58258 - 3.00000i) q^{65} +(8.29875 + 8.29875i) q^{67} -0.723000 q^{69} -13.5826i q^{71} +(0.582576 - 0.582576i) q^{73} +(1.17985 - 3.00725i) q^{75} +(12.2197 - 12.2197i) q^{77} +12.0000 q^{79} -5.41742 q^{81} +(4.83465 - 4.83465i) q^{83} +(-7.93725 - 5.19615i) q^{85} +(-2.41742 + 2.41742i) q^{87} -3.16515i q^{89} -9.66930 q^{91} +(0.723000 + 0.723000i) q^{93} +(1.58258 + 7.58258i) q^{95} +(0.582576 + 0.582576i) q^{97} -11.3060i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{7} + O(q^{10}) \) \( 8 q - 4 q^{7} + 12 q^{15} + 24 q^{17} + 12 q^{23} - 16 q^{33} - 24 q^{39} - 24 q^{41} - 12 q^{47} + 40 q^{55} + 24 q^{57} - 76 q^{63} - 32 q^{73} + 96 q^{79} - 80 q^{81} - 56 q^{87} - 24 q^{95} - 32 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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
\(3\) 0.456850 0.456850i 0.263763 0.263763i −0.562818 0.826581i \(-0.690283\pi\)
0.826581 + 0.562818i \(0.190283\pi\)
\(4\) 0 0
\(5\) −2.18890 + 0.456850i −0.978906 + 0.204310i
\(6\) 0 0
\(7\) −2.79129 + 2.79129i −1.05501 + 1.05501i −0.0566113 + 0.998396i \(0.518030\pi\)
−0.998396 + 0.0566113i \(0.981970\pi\)
\(8\) 0 0
\(9\) 2.58258i 0.860859i
\(10\) 0 0
\(11\) −4.37780 −1.31996 −0.659979 0.751284i \(-0.729435\pi\)
−0.659979 + 0.751284i \(0.729435\pi\)
\(12\) 0 0
\(13\) 1.73205 + 1.73205i 0.480384 + 0.480384i 0.905254 0.424870i \(-0.139680\pi\)
−0.424870 + 0.905254i \(0.639680\pi\)
\(14\) 0 0
\(15\) −0.791288 + 1.20871i −0.204310 + 0.312088i
\(16\) 0 0
\(17\) 3.00000 + 3.00000i 0.727607 + 0.727607i 0.970143 0.242536i \(-0.0779791\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 3.46410i 0.794719i −0.917663 0.397360i \(-0.869927\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 0 0
\(21\) 2.55040i 0.556543i
\(22\) 0 0
\(23\) −0.791288 0.791288i −0.164995 0.164995i 0.619780 0.784775i \(-0.287222\pi\)
−0.784775 + 0.619780i \(0.787222\pi\)
\(24\) 0 0
\(25\) 4.58258 2.00000i 0.916515 0.400000i
\(26\) 0 0
\(27\) 2.55040 + 2.55040i 0.490825 + 0.490825i
\(28\) 0 0
\(29\) −5.29150 −0.982607 −0.491304 0.870988i \(-0.663479\pi\)
−0.491304 + 0.870988i \(0.663479\pi\)
\(30\) 0 0
\(31\) 1.58258i 0.284239i 0.989850 + 0.142119i \(0.0453917\pi\)
−0.989850 + 0.142119i \(0.954608\pi\)
\(32\) 0 0
\(33\) −2.00000 + 2.00000i −0.348155 + 0.348155i
\(34\) 0 0
\(35\) 4.83465 7.38505i 0.817205 1.24830i
\(36\) 0 0
\(37\) 5.19615 5.19615i 0.854242 0.854242i −0.136410 0.990652i \(-0.543557\pi\)
0.990652 + 0.136410i \(0.0435565\pi\)
\(38\) 0 0
\(39\) 1.58258 0.253415
\(40\) 0 0
\(41\) −7.58258 −1.18420 −0.592100 0.805865i \(-0.701701\pi\)
−0.592100 + 0.805865i \(0.701701\pi\)
\(42\) 0 0
\(43\) −8.29875 + 8.29875i −1.26555 + 1.26555i −0.317184 + 0.948364i \(0.602737\pi\)
−0.948364 + 0.317184i \(0.897263\pi\)
\(44\) 0 0
\(45\) −1.17985 5.65300i −0.175882 0.842700i
\(46\) 0 0
\(47\) 0.791288 0.791288i 0.115421 0.115421i −0.647037 0.762458i \(-0.723992\pi\)
0.762458 + 0.647037i \(0.223992\pi\)
\(48\) 0 0
\(49\) 8.58258i 1.22608i
\(50\) 0 0
\(51\) 2.74110 0.383831
\(52\) 0 0
\(53\) 2.64575 + 2.64575i 0.363422 + 0.363422i 0.865071 0.501649i \(-0.167273\pi\)
−0.501649 + 0.865071i \(0.667273\pi\)
\(54\) 0 0
\(55\) 9.58258 2.00000i 1.29211 0.269680i
\(56\) 0 0
\(57\) −1.58258 1.58258i −0.209617 0.209617i
\(58\) 0 0
\(59\) 5.29150i 0.688895i 0.938806 + 0.344447i \(0.111934\pi\)
−0.938806 + 0.344447i \(0.888066\pi\)
\(60\) 0 0
\(61\) 9.66930i 1.23803i 0.785380 + 0.619014i \(0.212468\pi\)
−0.785380 + 0.619014i \(0.787532\pi\)
\(62\) 0 0
\(63\) −7.20871 7.20871i −0.908212 0.908212i
\(64\) 0 0
\(65\) −4.58258 3.00000i −0.568399 0.372104i
\(66\) 0 0
\(67\) 8.29875 + 8.29875i 1.01385 + 1.01385i 0.999903 + 0.0139515i \(0.00444104\pi\)
0.0139515 + 0.999903i \(0.495559\pi\)
\(68\) 0 0
\(69\) −0.723000 −0.0870390
\(70\) 0 0
\(71\) 13.5826i 1.61196i −0.591946 0.805978i \(-0.701640\pi\)
0.591946 0.805978i \(-0.298360\pi\)
\(72\) 0 0
\(73\) 0.582576 0.582576i 0.0681853 0.0681853i −0.672192 0.740377i \(-0.734647\pi\)
0.740377 + 0.672192i \(0.234647\pi\)
\(74\) 0 0
\(75\) 1.17985 3.00725i 0.136237 0.347247i
\(76\) 0 0
\(77\) 12.2197 12.2197i 1.39256 1.39256i
\(78\) 0 0
\(79\) 12.0000 1.35011 0.675053 0.737769i \(-0.264121\pi\)
0.675053 + 0.737769i \(0.264121\pi\)
\(80\) 0 0
\(81\) −5.41742 −0.601936
\(82\) 0 0
\(83\) 4.83465 4.83465i 0.530672 0.530672i −0.390100 0.920772i \(-0.627560\pi\)
0.920772 + 0.390100i \(0.127560\pi\)
\(84\) 0 0
\(85\) −7.93725 5.19615i −0.860916 0.563602i
\(86\) 0 0
\(87\) −2.41742 + 2.41742i −0.259175 + 0.259175i
\(88\) 0 0
\(89\) 3.16515i 0.335505i −0.985829 0.167753i \(-0.946349\pi\)
0.985829 0.167753i \(-0.0536510\pi\)
\(90\) 0 0
\(91\) −9.66930 −1.01362
\(92\) 0 0
\(93\) 0.723000 + 0.723000i 0.0749716 + 0.0749716i
\(94\) 0 0
\(95\) 1.58258 + 7.58258i 0.162369 + 0.777956i
\(96\) 0 0
\(97\) 0.582576 + 0.582576i 0.0591516 + 0.0591516i 0.736064 0.676912i \(-0.236682\pi\)
−0.676912 + 0.736064i \(0.736682\pi\)
\(98\) 0 0
\(99\) 11.3060i 1.13630i
\(100\) 0 0
\(101\) 3.65480i 0.363666i −0.983329 0.181833i \(-0.941797\pi\)
0.983329 0.181833i \(-0.0582031\pi\)
\(102\) 0 0
\(103\) 10.3739 + 10.3739i 1.02217 + 1.02217i 0.999749 + 0.0224185i \(0.00713662\pi\)
0.0224185 + 0.999749i \(0.492863\pi\)
\(104\) 0 0
\(105\) −1.16515 5.58258i −0.113707 0.544804i
\(106\) 0 0
\(107\) 8.29875 + 8.29875i 0.802271 + 0.802271i 0.983450 0.181179i \(-0.0579914\pi\)
−0.181179 + 0.983450i \(0.557991\pi\)
\(108\) 0 0
\(109\) 6.20520 0.594351 0.297175 0.954823i \(-0.403955\pi\)
0.297175 + 0.954823i \(0.403955\pi\)
\(110\) 0 0
\(111\) 4.74773i 0.450634i
\(112\) 0 0
\(113\) −4.58258 + 4.58258i −0.431092 + 0.431092i −0.889000 0.457907i \(-0.848599\pi\)
0.457907 + 0.889000i \(0.348599\pi\)
\(114\) 0 0
\(115\) 2.09355 + 1.37055i 0.195225 + 0.127805i
\(116\) 0 0
\(117\) −4.47315 + 4.47315i −0.413543 + 0.413543i
\(118\) 0 0
\(119\) −16.7477 −1.53526
\(120\) 0 0
\(121\) 8.16515 0.742286
\(122\) 0 0
\(123\) −3.46410 + 3.46410i −0.312348 + 0.312348i
\(124\) 0 0
\(125\) −9.11710 + 6.47135i −0.815459 + 0.578815i
\(126\) 0 0
\(127\) 1.20871 1.20871i 0.107256 0.107256i −0.651442 0.758698i \(-0.725836\pi\)
0.758698 + 0.651442i \(0.225836\pi\)
\(128\) 0 0
\(129\) 7.58258i 0.667609i
\(130\) 0 0
\(131\) −11.3060 −0.987810 −0.493905 0.869516i \(-0.664431\pi\)
−0.493905 + 0.869516i \(0.664431\pi\)
\(132\) 0 0
\(133\) 9.66930 + 9.66930i 0.838435 + 0.838435i
\(134\) 0 0
\(135\) −6.74773 4.41742i −0.580752 0.380191i
\(136\) 0 0
\(137\) 12.1652 + 12.1652i 1.03934 + 1.03934i 0.999194 + 0.0401452i \(0.0127820\pi\)
0.0401452 + 0.999194i \(0.487218\pi\)
\(138\) 0 0
\(139\) 8.94630i 0.758816i −0.925230 0.379408i \(-0.876128\pi\)
0.925230 0.379408i \(-0.123872\pi\)
\(140\) 0 0
\(141\) 0.723000i 0.0608876i
\(142\) 0 0
\(143\) −7.58258 7.58258i −0.634087 0.634087i
\(144\) 0 0
\(145\) 11.5826 2.41742i 0.961881 0.200756i
\(146\) 0 0
\(147\) −3.92095 3.92095i −0.323395 0.323395i
\(148\) 0 0
\(149\) −4.37780 −0.358644 −0.179322 0.983790i \(-0.557390\pi\)
−0.179322 + 0.983790i \(0.557390\pi\)
\(150\) 0 0
\(151\) 12.7477i 1.03740i 0.854958 + 0.518698i \(0.173583\pi\)
−0.854958 + 0.518698i \(0.826417\pi\)
\(152\) 0 0
\(153\) −7.74773 + 7.74773i −0.626367 + 0.626367i
\(154\) 0 0
\(155\) −0.723000 3.46410i −0.0580728 0.278243i
\(156\) 0 0
\(157\) −11.4014 + 11.4014i −0.909927 + 0.909927i −0.996266 0.0863386i \(-0.972483\pi\)
0.0863386 + 0.996266i \(0.472483\pi\)
\(158\) 0 0
\(159\) 2.41742 0.191714
\(160\) 0 0
\(161\) 4.41742 0.348142
\(162\) 0 0
\(163\) −8.29875 + 8.29875i −0.650009 + 0.650009i −0.952995 0.302986i \(-0.902016\pi\)
0.302986 + 0.952995i \(0.402016\pi\)
\(164\) 0 0
\(165\) 3.46410 5.29150i 0.269680 0.411943i
\(166\) 0 0
\(167\) −11.2087 + 11.2087i −0.867356 + 0.867356i −0.992179 0.124823i \(-0.960164\pi\)
0.124823 + 0.992179i \(0.460164\pi\)
\(168\) 0 0
\(169\) 7.00000i 0.538462i
\(170\) 0 0
\(171\) 8.94630 0.684141
\(172\) 0 0
\(173\) −8.66025 8.66025i −0.658427 0.658427i 0.296581 0.955008i \(-0.404154\pi\)
−0.955008 + 0.296581i \(0.904154\pi\)
\(174\) 0 0
\(175\) −7.20871 + 18.3739i −0.544927 + 1.38893i
\(176\) 0 0
\(177\) 2.41742 + 2.41742i 0.181705 + 0.181705i
\(178\) 0 0
\(179\) 8.56490i 0.640171i 0.947389 + 0.320085i \(0.103712\pi\)
−0.947389 + 0.320085i \(0.896288\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i 0.966282 + 0.257485i \(0.0828937\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 0 0
\(183\) 4.41742 + 4.41742i 0.326545 + 0.326545i
\(184\) 0 0
\(185\) −9.00000 + 13.7477i −0.661693 + 1.01075i
\(186\) 0 0
\(187\) −13.1334 13.1334i −0.960410 0.960410i
\(188\) 0 0
\(189\) −14.2378 −1.03565
\(190\) 0 0
\(191\) 13.5826i 0.982801i 0.870934 + 0.491400i \(0.163515\pi\)
−0.870934 + 0.491400i \(0.836485\pi\)
\(192\) 0 0
\(193\) 14.1652 14.1652i 1.01963 1.01963i 0.0198265 0.999803i \(-0.493689\pi\)
0.999803 0.0198265i \(-0.00631138\pi\)
\(194\) 0 0
\(195\) −3.46410 + 0.723000i −0.248069 + 0.0517751i
\(196\) 0 0
\(197\) 2.64575 2.64575i 0.188502 0.188502i −0.606546 0.795048i \(-0.707446\pi\)
0.795048 + 0.606546i \(0.207446\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 0 0
\(201\) 7.58258 0.534834
\(202\) 0 0
\(203\) 14.7701 14.7701i 1.03666 1.03666i
\(204\) 0 0
\(205\) 16.5975 3.46410i 1.15922 0.241943i
\(206\) 0 0
\(207\) 2.04356 2.04356i 0.142037 0.142037i
\(208\) 0 0
\(209\) 15.1652i 1.04900i
\(210\) 0 0
\(211\) 7.65120 0.526731 0.263365 0.964696i \(-0.415168\pi\)
0.263365 + 0.964696i \(0.415168\pi\)
\(212\) 0 0
\(213\) −6.20520 6.20520i −0.425174 0.425174i
\(214\) 0 0
\(215\) 14.3739 21.9564i 0.980289 1.49742i
\(216\) 0 0
\(217\) −4.41742 4.41742i −0.299874 0.299874i
\(218\) 0 0
\(219\) 0.532300i 0.0359695i
\(220\) 0 0
\(221\) 10.3923i 0.699062i
\(222\) 0 0
\(223\) −12.3739 12.3739i −0.828615 0.828615i 0.158710 0.987325i \(-0.449266\pi\)
−0.987325 + 0.158710i \(0.949266\pi\)
\(224\) 0 0
\(225\) 5.16515 + 11.8348i 0.344343 + 0.788990i
\(226\) 0 0
\(227\) −6.66205 6.66205i −0.442176 0.442176i 0.450567 0.892743i \(-0.351222\pi\)
−0.892743 + 0.450567i \(0.851222\pi\)
\(228\) 0 0
\(229\) 3.46410 0.228914 0.114457 0.993428i \(-0.463487\pi\)
0.114457 + 0.993428i \(0.463487\pi\)
\(230\) 0 0
\(231\) 11.1652i 0.734613i
\(232\) 0 0
\(233\) 6.16515 6.16515i 0.403892 0.403892i −0.475710 0.879602i \(-0.657809\pi\)
0.879602 + 0.475710i \(0.157809\pi\)
\(234\) 0 0
\(235\) −1.37055 + 2.09355i −0.0894049 + 0.136568i
\(236\) 0 0
\(237\) 5.48220 5.48220i 0.356107 0.356107i
\(238\) 0 0
\(239\) 3.16515 0.204737 0.102368 0.994747i \(-0.467358\pi\)
0.102368 + 0.994747i \(0.467358\pi\)
\(240\) 0 0
\(241\) −10.7477 −0.692322 −0.346161 0.938175i \(-0.612515\pi\)
−0.346161 + 0.938175i \(0.612515\pi\)
\(242\) 0 0
\(243\) −10.1262 + 10.1262i −0.649593 + 0.649593i
\(244\) 0 0
\(245\) 3.92095 + 18.7864i 0.250500 + 1.20022i
\(246\) 0 0
\(247\) 6.00000 6.00000i 0.381771 0.381771i
\(248\) 0 0
\(249\) 4.41742i 0.279943i
\(250\) 0 0
\(251\) 18.2342 1.15093 0.575467 0.817825i \(-0.304821\pi\)
0.575467 + 0.817825i \(0.304821\pi\)
\(252\) 0 0
\(253\) 3.46410 + 3.46410i 0.217786 + 0.217786i
\(254\) 0 0
\(255\) −6.00000 + 1.25227i −0.375735 + 0.0784204i
\(256\) 0 0
\(257\) −19.7477 19.7477i −1.23183 1.23183i −0.963260 0.268569i \(-0.913449\pi\)
−0.268569 0.963260i \(-0.586551\pi\)
\(258\) 0 0
\(259\) 29.0079i 1.80246i
\(260\) 0 0
\(261\) 13.6657i 0.845886i
\(262\) 0 0
\(263\) 18.7913 + 18.7913i 1.15872 + 1.15872i 0.984751 + 0.173969i \(0.0556594\pi\)
0.173969 + 0.984751i \(0.444341\pi\)
\(264\) 0 0
\(265\) −7.00000 4.58258i −0.430007 0.281505i
\(266\) 0 0
\(267\) −1.44600 1.44600i −0.0884938 0.0884938i
\(268\) 0 0
\(269\) 23.7164 1.44602 0.723008 0.690840i \(-0.242759\pi\)
0.723008 + 0.690840i \(0.242759\pi\)
\(270\) 0 0
\(271\) 8.74773i 0.531387i 0.964058 + 0.265693i \(0.0856008\pi\)
−0.964058 + 0.265693i \(0.914399\pi\)
\(272\) 0 0
\(273\) −4.41742 + 4.41742i −0.267355 + 0.267355i
\(274\) 0 0
\(275\) −20.0616 + 8.75560i −1.20976 + 0.527983i
\(276\) 0 0
\(277\) −5.91915 + 5.91915i −0.355647 + 0.355647i −0.862206 0.506558i \(-0.830917\pi\)
0.506558 + 0.862206i \(0.330917\pi\)
\(278\) 0 0
\(279\) −4.08712 −0.244690
\(280\) 0 0
\(281\) −10.7477 −0.641156 −0.320578 0.947222i \(-0.603877\pi\)
−0.320578 + 0.947222i \(0.603877\pi\)
\(282\) 0 0
\(283\) 17.2451 17.2451i 1.02511 1.02511i 0.0254359 0.999676i \(-0.491903\pi\)
0.999676 0.0254359i \(-0.00809736\pi\)
\(284\) 0 0
\(285\) 4.18710 + 2.74110i 0.248023 + 0.162369i
\(286\) 0 0
\(287\) 21.1652 21.1652i 1.24934 1.24934i
\(288\) 0 0
\(289\) 1.00000i 0.0588235i
\(290\) 0 0
\(291\) 0.532300 0.0312040
\(292\) 0 0
\(293\) −23.4304 23.4304i −1.36882 1.36882i −0.862131 0.506685i \(-0.830871\pi\)
−0.506685 0.862131i \(-0.669129\pi\)
\(294\) 0 0
\(295\) −2.41742 11.5826i −0.140748 0.674364i
\(296\) 0 0
\(297\) −11.1652 11.1652i −0.647868 0.647868i
\(298\) 0 0
\(299\) 2.74110i 0.158522i
\(300\) 0 0
\(301\) 46.3284i 2.67033i
\(302\) 0 0
\(303\) −1.66970 1.66970i −0.0959216 0.0959216i
\(304\) 0 0
\(305\) −4.41742 21.1652i −0.252941 1.21191i
\(306\) 0 0
\(307\) 1.37055 + 1.37055i 0.0782215 + 0.0782215i 0.745135 0.666914i \(-0.232385\pi\)
−0.666914 + 0.745135i \(0.732385\pi\)
\(308\) 0 0
\(309\) 9.47860 0.539219
\(310\) 0 0
\(311\) 10.4174i 0.590718i −0.955386 0.295359i \(-0.904561\pi\)
0.955386 0.295359i \(-0.0954392\pi\)
\(312\) 0 0
\(313\) 2.58258 2.58258i 0.145976 0.145976i −0.630342 0.776318i \(-0.717085\pi\)
0.776318 + 0.630342i \(0.217085\pi\)
\(314\) 0 0
\(315\) 19.0725 + 12.4859i 1.07461 + 0.703498i
\(316\) 0 0
\(317\) −17.6066 + 17.6066i −0.988883 + 0.988883i −0.999939 0.0110560i \(-0.996481\pi\)
0.0110560 + 0.999939i \(0.496481\pi\)
\(318\) 0 0
\(319\) 23.1652 1.29700
\(320\) 0 0
\(321\) 7.58258 0.423218
\(322\) 0 0
\(323\) 10.3923 10.3923i 0.578243 0.578243i
\(324\) 0 0
\(325\) 11.4014 + 4.47315i 0.632433 + 0.248126i
\(326\) 0 0
\(327\) 2.83485 2.83485i 0.156767 0.156767i
\(328\) 0 0
\(329\) 4.41742i 0.243540i
\(330\) 0 0
\(331\) 6.20520 0.341069 0.170534 0.985352i \(-0.445451\pi\)
0.170534 + 0.985352i \(0.445451\pi\)
\(332\) 0 0
\(333\) 13.4195 + 13.4195i 0.735382 + 0.735382i
\(334\) 0 0
\(335\) −21.9564 14.3739i −1.19961 0.785328i
\(336\) 0 0
\(337\) 1.00000 + 1.00000i 0.0544735 + 0.0544735i 0.733819 0.679345i \(-0.237736\pi\)
−0.679345 + 0.733819i \(0.737736\pi\)
\(338\) 0 0
\(339\) 4.18710i 0.227412i
\(340\) 0 0
\(341\) 6.92820i 0.375183i
\(342\) 0 0
\(343\) 4.41742 + 4.41742i 0.238518 + 0.238518i
\(344\) 0 0
\(345\) 1.58258 0.330303i 0.0852030 0.0177829i
\(346\) 0 0
\(347\) 3.92095 + 3.92095i 0.210488 + 0.210488i 0.804475 0.593987i \(-0.202447\pi\)
−0.593987 + 0.804475i \(0.702447\pi\)
\(348\) 0 0
\(349\) −10.3923 −0.556287 −0.278144 0.960539i \(-0.589719\pi\)
−0.278144 + 0.960539i \(0.589719\pi\)
\(350\) 0 0
\(351\) 8.83485i 0.471569i
\(352\) 0 0
\(353\) 5.83485 5.83485i 0.310558 0.310558i −0.534568 0.845126i \(-0.679526\pi\)
0.845126 + 0.534568i \(0.179526\pi\)
\(354\) 0 0
\(355\) 6.20520 + 29.7309i 0.329338 + 1.57795i
\(356\) 0 0
\(357\) −7.65120 + 7.65120i −0.404945 + 0.404945i
\(358\) 0 0
\(359\) −8.83485 −0.466285 −0.233143 0.972443i \(-0.574901\pi\)
−0.233143 + 0.972443i \(0.574901\pi\)
\(360\) 0 0
\(361\) 7.00000 0.368421
\(362\) 0 0
\(363\) 3.73025 3.73025i 0.195787 0.195787i
\(364\) 0 0
\(365\) −1.00905 + 1.54135i −0.0528161 + 0.0806780i
\(366\) 0 0
\(367\) 15.5390 15.5390i 0.811130 0.811130i −0.173673 0.984803i \(-0.555564\pi\)
0.984803 + 0.173673i \(0.0555637\pi\)
\(368\) 0 0
\(369\) 19.5826i 1.01943i
\(370\) 0 0
\(371\) −14.7701 −0.766826
\(372\) 0 0
\(373\) 5.19615 + 5.19615i 0.269047 + 0.269047i 0.828716 0.559669i \(-0.189072\pi\)
−0.559669 + 0.828716i \(0.689072\pi\)
\(374\) 0 0
\(375\) −1.20871 + 7.12159i −0.0624176 + 0.367757i
\(376\) 0 0
\(377\) −9.16515 9.16515i −0.472029 0.472029i
\(378\) 0 0
\(379\) 10.3923i 0.533817i −0.963722 0.266908i \(-0.913998\pi\)
0.963722 0.266908i \(-0.0860021\pi\)
\(380\) 0 0
\(381\) 1.10440i 0.0565802i
\(382\) 0 0
\(383\) 3.62614 + 3.62614i 0.185287 + 0.185287i 0.793655 0.608368i \(-0.208176\pi\)
−0.608368 + 0.793655i \(0.708176\pi\)
\(384\) 0 0
\(385\) −21.1652 + 32.3303i −1.07868 + 1.64770i
\(386\) 0 0
\(387\) −21.4322 21.4322i −1.08946 1.08946i
\(388\) 0 0
\(389\) 30.2632 1.53441 0.767203 0.641404i \(-0.221648\pi\)
0.767203 + 0.641404i \(0.221648\pi\)
\(390\) 0 0
\(391\) 4.74773i 0.240103i
\(392\) 0 0
\(393\) −5.16515 + 5.16515i −0.260547 + 0.260547i
\(394\) 0 0
\(395\) −26.2668 + 5.48220i −1.32163 + 0.275840i
\(396\) 0 0
\(397\) −7.93725 + 7.93725i −0.398359 + 0.398359i −0.877654 0.479295i \(-0.840893\pi\)
0.479295 + 0.877654i \(0.340893\pi\)
\(398\) 0 0
\(399\) 8.83485 0.442296
\(400\) 0 0
\(401\) 12.3303 0.615746 0.307873 0.951427i \(-0.400383\pi\)
0.307873 + 0.951427i \(0.400383\pi\)
\(402\) 0 0
\(403\) −2.74110 + 2.74110i −0.136544 + 0.136544i
\(404\) 0 0
\(405\) 11.8582 2.47495i 0.589239 0.122981i
\(406\) 0 0
\(407\) −22.7477 + 22.7477i −1.12756 + 1.12756i
\(408\) 0 0
\(409\) 25.5826i 1.26498i 0.774570 + 0.632488i \(0.217966\pi\)
−0.774570 + 0.632488i \(0.782034\pi\)
\(410\) 0 0
\(411\) 11.1153 0.548278
\(412\) 0 0
\(413\) −14.7701 14.7701i −0.726789 0.726789i
\(414\) 0 0
\(415\) −8.37386 + 12.7913i −0.411057 + 0.627900i
\(416\) 0 0
\(417\) −4.08712 4.08712i −0.200147 0.200147i
\(418\) 0 0
\(419\) 0.190700i 0.00931632i −0.999989 0.00465816i \(-0.998517\pi\)
0.999989 0.00465816i \(-0.00148274\pi\)
\(420\) 0 0
\(421\) 2.74110i 0.133593i 0.997767 + 0.0667966i \(0.0212778\pi\)
−0.997767 + 0.0667966i \(0.978722\pi\)
\(422\) 0 0
\(423\) 2.04356 + 2.04356i 0.0993613 + 0.0993613i
\(424\) 0 0
\(425\) 19.7477 + 7.74773i 0.957905 + 0.375820i
\(426\) 0 0
\(427\) −26.9898 26.9898i −1.30613 1.30613i
\(428\) 0 0
\(429\) −6.92820 −0.334497
\(430\) 0 0
\(431\) 16.7477i 0.806710i 0.915044 + 0.403355i \(0.132156\pi\)
−0.915044 + 0.403355i \(0.867844\pi\)
\(432\) 0 0
\(433\) −14.5826 + 14.5826i −0.700794 + 0.700794i −0.964581 0.263787i \(-0.915028\pi\)
0.263787 + 0.964581i \(0.415028\pi\)
\(434\) 0 0
\(435\) 4.18710 6.39590i 0.200756 0.306660i
\(436\) 0 0
\(437\) −2.74110 + 2.74110i −0.131125 + 0.131125i
\(438\) 0 0
\(439\) −29.4955 −1.40774 −0.703871 0.710328i \(-0.748547\pi\)
−0.703871 + 0.710328i \(0.748547\pi\)
\(440\) 0 0
\(441\) 22.1652 1.05548
\(442\) 0 0
\(443\) 1.17985 1.17985i 0.0560564 0.0560564i −0.678523 0.734579i \(-0.737380\pi\)
0.734579 + 0.678523i \(0.237380\pi\)
\(444\) 0 0
\(445\) 1.44600 + 6.92820i 0.0685470 + 0.328428i
\(446\) 0 0
\(447\) −2.00000 + 2.00000i −0.0945968 + 0.0945968i
\(448\) 0 0
\(449\) 10.4174i 0.491629i 0.969317 + 0.245814i \(0.0790553\pi\)
−0.969317 + 0.245814i \(0.920945\pi\)
\(450\) 0 0
\(451\) 33.1950 1.56309
\(452\) 0 0
\(453\) 5.82380 + 5.82380i 0.273626 + 0.273626i
\(454\) 0 0
\(455\) 21.1652 4.41742i 0.992238 0.207092i
\(456\) 0 0
\(457\) 3.41742 + 3.41742i 0.159860 + 0.159860i 0.782505 0.622644i \(-0.213942\pi\)
−0.622644 + 0.782505i \(0.713942\pi\)
\(458\) 0 0
\(459\) 15.3024i 0.714255i
\(460\) 0 0
\(461\) 17.5112i 0.815578i 0.913076 + 0.407789i \(0.133700\pi\)
−0.913076 + 0.407789i \(0.866300\pi\)
\(462\) 0 0
\(463\) −16.7913 16.7913i −0.780357 0.780357i 0.199534 0.979891i \(-0.436057\pi\)
−0.979891 + 0.199534i \(0.936057\pi\)
\(464\) 0 0
\(465\) −1.91288 1.25227i −0.0887076 0.0580728i
\(466\) 0 0
\(467\) 7.57575 + 7.57575i 0.350564 + 0.350564i 0.860319 0.509755i \(-0.170264\pi\)
−0.509755 + 0.860319i \(0.670264\pi\)
\(468\) 0 0
\(469\) −46.3284 −2.13925
\(470\) 0 0
\(471\) 10.4174i 0.480010i
\(472\) 0 0
\(473\) 36.3303 36.3303i 1.67047 1.67047i
\(474\) 0 0
\(475\) −6.92820 15.8745i −0.317888 0.728372i
\(476\) 0 0
\(477\) −6.83285 + 6.83285i −0.312855 + 0.312855i
\(478\) 0 0
\(479\) −21.4955 −0.982152 −0.491076 0.871117i \(-0.663396\pi\)
−0.491076 + 0.871117i \(0.663396\pi\)
\(480\) 0 0
\(481\) 18.0000 0.820729
\(482\) 0 0
\(483\) 2.01810 2.01810i 0.0918268 0.0918268i
\(484\) 0 0
\(485\) −1.54135 1.00905i −0.0699891 0.0458186i
\(486\) 0 0
\(487\) 0.373864 0.373864i 0.0169414 0.0169414i −0.698585 0.715527i \(-0.746187\pi\)
0.715527 + 0.698585i \(0.246187\pi\)
\(488\) 0 0
\(489\) 7.58258i 0.342896i
\(490\) 0 0
\(491\) 9.86001 0.444976 0.222488 0.974935i \(-0.428582\pi\)
0.222488 + 0.974935i \(0.428582\pi\)
\(492\) 0 0
\(493\) −15.8745 15.8745i −0.714952 0.714952i
\(494\) 0 0
\(495\) 5.16515 + 24.7477i 0.232156 + 1.11233i
\(496\) 0 0
\(497\) 37.9129 + 37.9129i 1.70063 + 1.70063i
\(498\) 0 0
\(499\) 24.2487i 1.08552i −0.839887 0.542761i \(-0.817379\pi\)
0.839887 0.542761i \(-0.182621\pi\)
\(500\) 0 0
\(501\) 10.2414i 0.457552i
\(502\) 0 0
\(503\) 17.5390 + 17.5390i 0.782026 + 0.782026i 0.980172 0.198146i \(-0.0634922\pi\)
−0.198146 + 0.980172i \(0.563492\pi\)
\(504\) 0 0
\(505\) 1.66970 + 8.00000i 0.0743006 + 0.355995i
\(506\) 0 0
\(507\) −3.19795 3.19795i −0.142026 0.142026i
\(508\) 0 0
\(509\) 38.4865 1.70588 0.852942 0.522005i \(-0.174816\pi\)
0.852942 + 0.522005i \(0.174816\pi\)
\(510\) 0 0
\(511\) 3.25227i 0.143872i
\(512\) 0 0
\(513\) 8.83485 8.83485i 0.390068 0.390068i
\(514\) 0 0
\(515\) −27.4467 17.9681i −1.20944 0.791767i
\(516\) 0 0
\(517\) −3.46410 + 3.46410i −0.152351 + 0.152351i
\(518\) 0 0
\(519\) −7.91288 −0.347337
\(520\) 0 0
\(521\) −33.1652 −1.45299 −0.726496 0.687171i \(-0.758852\pi\)
−0.726496 + 0.687171i \(0.758852\pi\)
\(522\) 0 0
\(523\) −15.9500 + 15.9500i −0.697443 + 0.697443i −0.963858 0.266415i \(-0.914161\pi\)
0.266415 + 0.963858i \(0.414161\pi\)
\(524\) 0 0
\(525\) 5.10080 + 11.6874i 0.222617 + 0.510080i
\(526\) 0 0
\(527\) −4.74773 + 4.74773i −0.206814 + 0.206814i
\(528\) 0 0
\(529\) 21.7477i 0.945553i
\(530\) 0 0
\(531\) −13.6657 −0.593041
\(532\) 0 0
\(533\) −13.1334 13.1334i −0.568871 0.568871i
\(534\) 0 0
\(535\) −21.9564 14.3739i −0.949260 0.621436i
\(536\) 0 0
\(537\) 3.91288 + 3.91288i 0.168853 + 0.168853i
\(538\) 0 0
\(539\) 37.5728i 1.61838i
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 3.16515 + 3.16515i 0.135830 + 0.135830i
\(544\) 0 0
\(545\) −13.5826 + 2.83485i −0.581814 + 0.121432i
\(546\) 0 0
\(547\) 0.647551 + 0.647551i 0.0276873 + 0.0276873i 0.720815 0.693128i \(-0.243768\pi\)
−0.693128 + 0.720815i \(0.743768\pi\)
\(548\) 0 0
\(549\) −24.9717 −1.06577
\(550\) 0 0
\(551\) 18.3303i 0.780897i
\(552\) 0 0
\(553\) −33.4955 + 33.4955i −1.42437 + 1.42437i
\(554\) 0 0
\(555\) 2.16900 + 10.3923i 0.0920689 + 0.441129i
\(556\) 0 0
\(557\) 10.2970 10.2970i 0.436296 0.436296i −0.454467 0.890763i \(-0.650170\pi\)
0.890763 + 0.454467i \(0.150170\pi\)
\(558\) 0 0
\(559\) −28.7477 −1.21590
\(560\) 0 0
\(561\) −12.0000 −0.506640
\(562\) 0 0
\(563\) 14.3133 14.3133i 0.603232 0.603232i −0.337937 0.941169i \(-0.609729\pi\)
0.941169 + 0.337937i \(0.109729\pi\)
\(564\) 0 0
\(565\) 7.93725 12.1244i 0.333923 0.510075i
\(566\) 0 0
\(567\) 15.1216 15.1216i 0.635047 0.635047i
\(568\) 0 0
\(569\) 4.74773i 0.199035i 0.995036 + 0.0995175i \(0.0317299\pi\)
−0.995036 + 0.0995175i \(0.968270\pi\)
\(570\) 0 0
\(571\) −39.4002 −1.64885 −0.824424 0.565973i \(-0.808501\pi\)
−0.824424 + 0.565973i \(0.808501\pi\)
\(572\) 0 0
\(573\) 6.20520 + 6.20520i 0.259226 + 0.259226i
\(574\) 0 0
\(575\) −5.20871 2.04356i −0.217218 0.0852224i
\(576\) 0 0
\(577\) −11.7477 11.7477i −0.489064 0.489064i 0.418947 0.908011i \(-0.362399\pi\)
−0.908011 + 0.418947i \(0.862399\pi\)
\(578\) 0 0
\(579\) 12.9427i 0.537881i
\(580\) 0 0
\(581\) 26.9898i 1.11973i
\(582\) 0 0
\(583\) −11.5826 11.5826i −0.479701 0.479701i
\(584\) 0 0
\(585\) 7.74773 11.8348i 0.320329 0.489311i
\(586\) 0 0
\(587\) 28.3604 + 28.3604i 1.17056 + 1.17056i 0.982077 + 0.188481i \(0.0603562\pi\)
0.188481 + 0.982077i \(0.439644\pi\)
\(588\) 0 0
\(589\) 5.48220 0.225890
\(590\) 0 0
\(591\) 2.41742i 0.0994395i
\(592\) 0 0
\(593\) 0.165151 0.165151i 0.00678195 0.00678195i −0.703708 0.710490i \(-0.748474\pi\)
0.710490 + 0.703708i \(0.248474\pi\)
\(594\) 0 0
\(595\) 36.6591 7.65120i 1.50288 0.313669i
\(596\) 0 0
\(597\) −1.82740 + 1.82740i −0.0747905 + 0.0747905i
\(598\) 0 0
\(599\) 42.3303 1.72957 0.864785 0.502143i \(-0.167455\pi\)
0.864785 + 0.502143i \(0.167455\pi\)
\(600\) 0 0
\(601\) −2.74773 −0.112082 −0.0560411 0.998428i \(-0.517848\pi\)
−0.0560411 + 0.998428i \(0.517848\pi\)
\(602\) 0 0
\(603\) −21.4322 + 21.4322i −0.872785 + 0.872785i
\(604\) 0 0
\(605\) −17.8727 + 3.73025i −0.726629 + 0.151656i
\(606\) 0 0
\(607\) −6.37386 + 6.37386i −0.258707 + 0.258707i −0.824528 0.565821i \(-0.808559\pi\)
0.565821 + 0.824528i \(0.308559\pi\)
\(608\) 0 0
\(609\) 13.4955i 0.546863i
\(610\) 0 0
\(611\) 2.74110 0.110893
\(612\) 0 0
\(613\) 8.66025 + 8.66025i 0.349784 + 0.349784i 0.860029 0.510245i \(-0.170445\pi\)
−0.510245 + 0.860029i \(0.670445\pi\)
\(614\) 0 0
\(615\) 6.00000 9.16515i 0.241943 0.369575i
\(616\) 0 0
\(617\) 3.00000 + 3.00000i 0.120775 + 0.120775i 0.764911 0.644136i \(-0.222783\pi\)
−0.644136 + 0.764911i \(0.722783\pi\)
\(618\) 0 0
\(619\) 29.7309i 1.19499i −0.801874 0.597493i \(-0.796164\pi\)
0.801874 0.597493i \(-0.203836\pi\)
\(620\) 0 0
\(621\) 4.03620i 0.161967i
\(622\) 0 0
\(623\) 8.83485 + 8.83485i 0.353961 + 0.353961i
\(624\) 0 0
\(625\) 17.0000 18.3303i 0.680000 0.733212i
\(626\) 0 0
\(627\) 6.92820 + 6.92820i 0.276686 + 0.276686i
\(628\) 0 0
\(629\) 31.1769 1.24310
\(630\) 0 0
\(631\) 47.0780i 1.87415i −0.349132 0.937073i \(-0.613524\pi\)
0.349132 0.937073i \(-0.386476\pi\)
\(632\) 0 0
\(633\) 3.49545 3.49545i 0.138932 0.138932i
\(634\) 0 0
\(635\) −2.09355 + 3.19795i −0.0830800 + 0.126907i
\(636\) 0 0
\(637\) 14.8655 14.8655i 0.588991 0.588991i
\(638\) 0 0
\(639\) 35.0780 1.38767
\(640\) 0 0
\(641\) 25.9129 1.02350 0.511749 0.859135i \(-0.328998\pi\)
0.511749 + 0.859135i \(0.328998\pi\)
\(642\) 0 0
\(643\) 18.6911 18.6911i 0.737103 0.737103i −0.234913 0.972016i \(-0.575481\pi\)
0.972016 + 0.234913i \(0.0754805\pi\)
\(644\) 0 0
\(645\) −3.46410 16.5975i −0.136399 0.653526i
\(646\) 0 0
\(647\) −0.460985 + 0.460985i −0.0181232 + 0.0181232i −0.716110 0.697987i \(-0.754079\pi\)
0.697987 + 0.716110i \(0.254079\pi\)
\(648\) 0 0
\(649\) 23.1652i 0.909312i
\(650\) 0 0
\(651\) −4.03620 −0.158191
\(652\) 0 0
\(653\) 11.4014 + 11.4014i 0.446170 + 0.446170i 0.894079 0.447909i \(-0.147831\pi\)
−0.447909 + 0.894079i \(0.647831\pi\)
\(654\) 0 0
\(655\) 24.7477 5.16515i 0.966974 0.201819i
\(656\) 0 0
\(657\) 1.50455 + 1.50455i 0.0586979 + 0.0586979i
\(658\) 0 0
\(659\) 3.84550i 0.149800i −0.997191 0.0748998i \(-0.976136\pi\)
0.997191 0.0748998i \(-0.0238637\pi\)
\(660\) 0 0
\(661\) 41.4183i 1.61099i −0.592605 0.805493i \(-0.701901\pi\)
0.592605 0.805493i \(-0.298099\pi\)
\(662\) 0 0
\(663\) 4.74773 + 4.74773i 0.184386 + 0.184386i
\(664\) 0 0
\(665\) −25.5826 16.7477i −0.992050 0.649449i
\(666\) 0 0
\(667\) 4.18710 + 4.18710i 0.162125 + 0.162125i
\(668\) 0 0
\(669\) −11.3060 −0.437115
\(670\) 0 0
\(671\) 42.3303i 1.63414i
\(672\) 0 0
\(673\) −18.5826 + 18.5826i −0.716306 + 0.716306i −0.967847 0.251541i \(-0.919063\pi\)
0.251541 + 0.967847i \(0.419063\pi\)
\(674\) 0 0
\(675\) 16.7882 + 6.58660i 0.646178 + 0.253519i
\(676\) 0 0
\(677\) 18.3296 18.3296i 0.704462 0.704462i −0.260903 0.965365i \(-0.584020\pi\)
0.965365 + 0.260903i \(0.0840202\pi\)
\(678\) 0 0
\(679\) −3.25227 −0.124811
\(680\) 0 0
\(681\) −6.08712 −0.233259
\(682\) 0 0
\(683\) −6.85275 + 6.85275i −0.262213 + 0.262213i −0.825953 0.563739i \(-0.809362\pi\)
0.563739 + 0.825953i \(0.309362\pi\)
\(684\) 0 0
\(685\) −32.1860 21.0707i −1.22976 0.805069i
\(686\) 0 0
\(687\) 1.58258 1.58258i 0.0603790 0.0603790i
\(688\) 0 0
\(689\) 9.16515i 0.349164i
\(690\) 0 0
\(691\) 32.4720 1.23529 0.617647 0.786456i \(-0.288086\pi\)
0.617647 + 0.786456i \(0.288086\pi\)
\(692\) 0 0
\(693\) 31.5583 + 31.5583i 1.19880 + 1.19880i
\(694\) 0 0
\(695\) 4.08712 + 19.5826i 0.155033 + 0.742809i
\(696\) 0 0
\(697\) −22.7477 22.7477i −0.861632 0.861632i
\(698\) 0 0
\(699\) 5.63310i 0.213063i
\(700\) 0 0
\(701\) 19.8709i 0.750514i −0.926921 0.375257i \(-0.877554\pi\)
0.926921 0.375257i \(-0.122446\pi\)
\(702\) 0 0
\(703\) −18.0000 18.0000i −0.678883 0.678883i
\(704\) 0 0
\(705\) 0.330303 + 1.58258i 0.0124399 + 0.0596032i
\(706\) 0 0
\(707\) 10.2016 + 10.2016i 0.383671 + 0.383671i
\(708\) 0 0
\(709\) 4.91010 0.184403 0.0922014 0.995740i \(-0.470610\pi\)
0.0922014 + 0.995740i \(0.470610\pi\)
\(710\) 0 0
\(711\) 30.9909i 1.16225i
\(712\) 0 0
\(713\) 1.25227 1.25227i 0.0468980 0.0468980i
\(714\) 0 0
\(715\) 20.0616 + 13.1334i 0.750262 + 0.491162i
\(716\) 0 0
\(717\) 1.44600 1.44600i 0.0540019 0.0540019i
\(718\) 0 0
\(719\) 39.8258 1.48525 0.742625 0.669707i \(-0.233580\pi\)
0.742625 + 0.669707i \(0.233580\pi\)
\(720\) 0 0
\(721\) −57.9129 −2.15679
\(722\) 0 0
\(723\) −4.91010 + 4.91010i −0.182609 + 0.182609i
\(724\) 0 0
\(725\) −24.2487 + 10.5830i −0.900575 + 0.393043i
\(726\) 0 0
\(727\) −5.95644 + 5.95644i −0.220912 + 0.220912i −0.808882 0.587970i \(-0.799927\pi\)
0.587970 + 0.808882i \(0.299927\pi\)
\(728\) 0 0
\(729\) 7.00000i 0.259259i
\(730\) 0 0
\(731\) −49.7925 −1.84164
\(732\) 0 0
\(733\) 17.6066 + 17.6066i 0.650313 + 0.650313i 0.953068 0.302755i \(-0.0979065\pi\)
−0.302755 + 0.953068i \(0.597906\pi\)
\(734\) 0 0
\(735\) 10.3739 + 6.79129i 0.382646 + 0.250500i
\(736\) 0 0
\(737\) −36.3303 36.3303i −1.33824 1.33824i
\(738\) 0 0
\(739\) 2.01810i 0.0742371i 0.999311 + 0.0371185i \(0.0118179\pi\)
−0.999311 + 0.0371185i \(0.988182\pi\)
\(740\) 0 0
\(741\) 5.48220i 0.201394i
\(742\) 0 0
\(743\) −17.2087 17.2087i −0.631326 0.631326i 0.317074 0.948401i \(-0.397300\pi\)
−0.948401 + 0.317074i \(0.897300\pi\)
\(744\) 0 0
\(745\) 9.58258 2.00000i 0.351078 0.0732743i
\(746\) 0 0
\(747\) 12.4859 + 12.4859i 0.456834 + 0.456834i
\(748\) 0 0
\(749\) −46.3284 −1.69280
\(750\) 0 0
\(751\) 23.0780i 0.842129i −0.907031 0.421065i \(-0.861657\pi\)
0.907031 0.421065i \(-0.138343\pi\)
\(752\) 0 0
\(753\) 8.33030 8.33030i 0.303573 0.303573i
\(754\) 0 0
\(755\) −5.82380 27.9035i −0.211950 1.01551i
\(756\) 0 0
\(757\) 20.3477 20.3477i 0.739548 0.739548i −0.232942 0.972491i \(-0.574835\pi\)
0.972491 + 0.232942i \(0.0748353\pi\)
\(758\) 0 0
\(759\) 3.16515 0.114888
\(760\) 0 0
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 0 0
\(763\) −17.3205 + 17.3205i −0.627044 + 0.627044i
\(764\) 0 0
\(765\) 13.4195 20.4986i 0.485181 0.741127i
\(766\) 0 0
\(767\) −9.16515 + 9.16515i −0.330934 + 0.330934i
\(768\) 0 0
\(769\) 37.4955i 1.35212i 0.736846 + 0.676060i \(0.236314\pi\)
−0.736846 + 0.676060i \(0.763686\pi\)
\(770\) 0 0
\(771\) −18.0435 −0.649821
\(772\) 0 0
\(773\) 0.286051 + 0.286051i 0.0102885 + 0.0102885i 0.712232 0.701944i \(-0.247684\pi\)
−0.701944 + 0.712232i \(0.747684\pi\)
\(774\) 0 0
\(775\) 3.16515 + 7.25227i 0.113696 + 0.260509i
\(776\) 0 0
\(777\) 13.2523 + 13.2523i 0.475423 + 0.475423i
\(778\) 0 0
\(779\) 26.2668i 0.941106i
\(780\) 0 0
\(781\) 59.4618i 2.12771i
\(782\) 0 0
\(783\) −13.4955 13.4955i −0.482288 0.482288i
\(784\) 0 0
\(785\) 19.7477 30.1652i 0.704827 1.07664i
\(786\) 0 0
\(787\) 20.7092 + 20.7092i 0.738202 + 0.738202i 0.972230 0.234028i \(-0.0751907\pi\)
−0.234028 + 0.972230i \(0.575191\pi\)
\(788\) 0 0
\(789\) 17.1696 0.611254
\(790\) 0 0
\(791\) 25.5826i 0.909612i
\(792\) 0 0
\(793\) −16.7477 + 16.7477i −0.594729 + 0.594729i
\(794\) 0 0
\(795\) −5.29150 + 1.10440i −0.187670 + 0.0391691i
\(796\) 0 0
\(797\) 34.9271 34.9271i 1.23718 1.23718i 0.276032 0.961149i \(-0.410981\pi\)
0.961149 0.276032i