Properties

Label 912.2.bb.f.31.2
Level $912$
Weight $2$
Character 912.31
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.954288.1
Defining polynomial: \(x^{6} - x^{5} - 2 x^{4} + 3 x^{3} - 6 x^{2} - 9 x + 27\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.2
Root \(1.71903 + 0.211943i\) of defining polynomial
Character \(\chi\) \(=\) 912.31
Dual form 912.2.bb.f.559.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(-0.675970 - 1.17081i) q^{5} -1.45735i q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(-0.675970 - 1.17081i) q^{5} -1.45735i q^{7} +(-0.500000 + 0.866025i) q^{9} -3.18940i q^{11} +(-2.23419 - 1.28991i) q^{13} +(0.675970 - 1.17081i) q^{15} +(2.08613 + 3.61328i) q^{17} +(-2.43807 - 3.61328i) q^{19} +(1.26210 - 0.728674i) q^{21} +(-6.49629 - 3.75064i) q^{23} +(1.58613 - 2.74726i) q^{25} -1.00000 q^{27} +(-0.734191 - 0.423885i) q^{29} +0.351939 q^{31} +(2.76210 - 1.59470i) q^{33} +(-1.70628 + 0.985122i) q^{35} -6.89169i q^{37} -2.57982i q^{39} +(-4.05582 + 2.34163i) q^{41} +(6.52791 - 3.76889i) q^{43} +1.35194 q^{45} +(-8.04840 - 4.64675i) q^{47} +4.87614 q^{49} +(-2.08613 + 3.61328i) q^{51} +(8.76210 + 5.05880i) q^{53} +(-3.73419 + 2.15594i) q^{55} +(1.91016 - 3.91807i) q^{57} +(-0.675970 - 1.17081i) q^{59} +(4.29001 - 7.43051i) q^{61} +(1.26210 + 0.728674i) q^{63} +3.48776i q^{65} +(-1.08984 + 1.88766i) q^{67} -7.50127i q^{69} +(-0.438069 - 0.758758i) q^{71} +(6.67226 + 11.5567i) q^{73} +3.17226 q^{75} -4.64806 q^{77} +(-2.52791 - 4.37847i) q^{79} +(-0.500000 - 0.866025i) q^{81} -7.22657i q^{83} +(2.82032 - 4.88494i) q^{85} -0.847771i q^{87} +(-3.81792 - 2.20428i) q^{89} +(-1.87985 + 3.25599i) q^{91} +(0.175970 + 0.304788i) q^{93} +(-2.58242 + 5.29699i) q^{95} +(-7.79001 + 4.49756i) q^{97} +(2.76210 + 1.59470i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{3} - 2q^{5} - 3q^{9} + O(q^{10}) \) \( 6q + 3q^{3} - 2q^{5} - 3q^{9} - 3q^{13} + 2q^{15} - 2q^{17} + 4q^{19} - 9q^{21} - 12q^{23} - 5q^{25} - 6q^{27} + 6q^{29} - 2q^{31} - 6q^{35} - 12q^{41} + 33q^{43} + 4q^{45} + 18q^{47} - 8q^{49} + 2q^{51} + 36q^{53} - 12q^{55} - q^{57} - 2q^{59} + 3q^{61} - 9q^{63} - 19q^{67} + 16q^{71} + 11q^{73} - 10q^{75} - 32q^{77} - 9q^{79} - 3q^{81} - 8q^{85} + 6q^{89} - q^{91} - q^{93} + 26q^{95} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\) \(-1\)

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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) −0.675970 1.17081i −0.302303 0.523604i 0.674354 0.738408i \(-0.264422\pi\)
−0.976657 + 0.214804i \(0.931089\pi\)
\(6\) 0 0
\(7\) 1.45735i 0.550826i −0.961326 0.275413i \(-0.911185\pi\)
0.961326 0.275413i \(-0.0888145\pi\)
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 3.18940i 0.961640i −0.876819 0.480820i \(-0.840339\pi\)
0.876819 0.480820i \(-0.159661\pi\)
\(12\) 0 0
\(13\) −2.23419 1.28991i −0.619653 0.357757i 0.157081 0.987586i \(-0.449792\pi\)
−0.776734 + 0.629829i \(0.783125\pi\)
\(14\) 0 0
\(15\) 0.675970 1.17081i 0.174535 0.302303i
\(16\) 0 0
\(17\) 2.08613 + 3.61328i 0.505961 + 0.876350i 0.999976 + 0.00689678i \(0.00219533\pi\)
−0.494015 + 0.869453i \(0.664471\pi\)
\(18\) 0 0
\(19\) −2.43807 3.61328i −0.559331 0.828944i
\(20\) 0 0
\(21\) 1.26210 0.728674i 0.275413 0.159010i
\(22\) 0 0
\(23\) −6.49629 3.75064i −1.35457 0.782062i −0.365685 0.930739i \(-0.619165\pi\)
−0.988886 + 0.148677i \(0.952498\pi\)
\(24\) 0 0
\(25\) 1.58613 2.74726i 0.317226 0.549452i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −0.734191 0.423885i −0.136336 0.0787135i 0.430281 0.902695i \(-0.358415\pi\)
−0.566617 + 0.823982i \(0.691748\pi\)
\(30\) 0 0
\(31\) 0.351939 0.0632101 0.0316051 0.999500i \(-0.489938\pi\)
0.0316051 + 0.999500i \(0.489938\pi\)
\(32\) 0 0
\(33\) 2.76210 1.59470i 0.480820 0.277601i
\(34\) 0 0
\(35\) −1.70628 + 0.985122i −0.288414 + 0.166516i
\(36\) 0 0
\(37\) 6.89169i 1.13299i −0.824066 0.566494i \(-0.808300\pi\)
0.824066 0.566494i \(-0.191700\pi\)
\(38\) 0 0
\(39\) 2.57982i 0.413102i
\(40\) 0 0
\(41\) −4.05582 + 2.34163i −0.633412 + 0.365701i −0.782072 0.623188i \(-0.785837\pi\)
0.148660 + 0.988888i \(0.452504\pi\)
\(42\) 0 0
\(43\) 6.52791 3.76889i 0.995497 0.574750i 0.0885840 0.996069i \(-0.471766\pi\)
0.906913 + 0.421318i \(0.138433\pi\)
\(44\) 0 0
\(45\) 1.35194 0.201535
\(46\) 0 0
\(47\) −8.04840 4.64675i −1.17398 0.677797i −0.219366 0.975643i \(-0.570399\pi\)
−0.954614 + 0.297845i \(0.903732\pi\)
\(48\) 0 0
\(49\) 4.87614 0.696591
\(50\) 0 0
\(51\) −2.08613 + 3.61328i −0.292117 + 0.505961i
\(52\) 0 0
\(53\) 8.76210 + 5.05880i 1.20357 + 0.694880i 0.961346 0.275342i \(-0.0887909\pi\)
0.242220 + 0.970221i \(0.422124\pi\)
\(54\) 0 0
\(55\) −3.73419 + 2.15594i −0.503518 + 0.290706i
\(56\) 0 0
\(57\) 1.91016 3.91807i 0.253007 0.518961i
\(58\) 0 0
\(59\) −0.675970 1.17081i −0.0880037 0.152427i 0.818663 0.574274i \(-0.194715\pi\)
−0.906667 + 0.421847i \(0.861382\pi\)
\(60\) 0 0
\(61\) 4.29001 7.43051i 0.549279 0.951380i −0.449045 0.893509i \(-0.648236\pi\)
0.998324 0.0578704i \(-0.0184310\pi\)
\(62\) 0 0
\(63\) 1.26210 + 0.728674i 0.159010 + 0.0918043i
\(64\) 0 0
\(65\) 3.48776i 0.432604i
\(66\) 0 0
\(67\) −1.08984 + 1.88766i −0.133145 + 0.230614i −0.924887 0.380241i \(-0.875841\pi\)
0.791742 + 0.610855i \(0.209174\pi\)
\(68\) 0 0
\(69\) 7.50127i 0.903047i
\(70\) 0 0
\(71\) −0.438069 0.758758i −0.0519893 0.0900481i 0.838860 0.544348i \(-0.183223\pi\)
−0.890849 + 0.454300i \(0.849889\pi\)
\(72\) 0 0
\(73\) 6.67226 + 11.5567i 0.780929 + 1.35261i 0.931401 + 0.363994i \(0.118587\pi\)
−0.150472 + 0.988614i \(0.548079\pi\)
\(74\) 0 0
\(75\) 3.17226 0.366301
\(76\) 0 0
\(77\) −4.64806 −0.529696
\(78\) 0 0
\(79\) −2.52791 4.37847i −0.284412 0.492616i 0.688054 0.725659i \(-0.258465\pi\)
−0.972466 + 0.233043i \(0.925132\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 7.22657i 0.793219i −0.917987 0.396609i \(-0.870187\pi\)
0.917987 0.396609i \(-0.129813\pi\)
\(84\) 0 0
\(85\) 2.82032 4.88494i 0.305907 0.529846i
\(86\) 0 0
\(87\) 0.847771i 0.0908906i
\(88\) 0 0
\(89\) −3.81792 2.20428i −0.404698 0.233653i 0.283811 0.958880i \(-0.408401\pi\)
−0.688509 + 0.725228i \(0.741735\pi\)
\(90\) 0 0
\(91\) −1.87985 + 3.25599i −0.197062 + 0.341321i
\(92\) 0 0
\(93\) 0.175970 + 0.304788i 0.0182472 + 0.0316051i
\(94\) 0 0
\(95\) −2.58242 + 5.29699i −0.264951 + 0.543460i
\(96\) 0 0
\(97\) −7.79001 + 4.49756i −0.790956 + 0.456658i −0.840299 0.542123i \(-0.817620\pi\)
0.0493433 + 0.998782i \(0.484287\pi\)
\(98\) 0 0
\(99\) 2.76210 + 1.59470i 0.277601 + 0.160273i
\(100\) 0 0
\(101\) −3.73419 + 6.46781i −0.371566 + 0.643571i −0.989807 0.142418i \(-0.954512\pi\)
0.618241 + 0.785989i \(0.287846\pi\)
\(102\) 0 0
\(103\) 11.5726 1.14028 0.570141 0.821547i \(-0.306889\pi\)
0.570141 + 0.821547i \(0.306889\pi\)
\(104\) 0 0
\(105\) −1.70628 0.985122i −0.166516 0.0961381i
\(106\) 0 0
\(107\) 10.1723 0.983390 0.491695 0.870768i \(-0.336378\pi\)
0.491695 + 0.870768i \(0.336378\pi\)
\(108\) 0 0
\(109\) 7.31421 4.22286i 0.700574 0.404477i −0.106987 0.994260i \(-0.534120\pi\)
0.807561 + 0.589784i \(0.200787\pi\)
\(110\) 0 0
\(111\) 5.96838 3.44585i 0.566494 0.327065i
\(112\) 0 0
\(113\) 12.4829i 1.17429i 0.809481 + 0.587146i \(0.199748\pi\)
−0.809481 + 0.587146i \(0.800252\pi\)
\(114\) 0 0
\(115\) 10.1413i 0.945678i
\(116\) 0 0
\(117\) 2.23419 1.28991i 0.206551 0.119252i
\(118\) 0 0
\(119\) 5.26581 3.04022i 0.482716 0.278696i
\(120\) 0 0
\(121\) 0.827740 0.0752491
\(122\) 0 0
\(123\) −4.05582 2.34163i −0.365701 0.211137i
\(124\) 0 0
\(125\) −11.0484 −0.988199
\(126\) 0 0
\(127\) −3.52420 + 6.10409i −0.312722 + 0.541651i −0.978951 0.204097i \(-0.934574\pi\)
0.666229 + 0.745748i \(0.267908\pi\)
\(128\) 0 0
\(129\) 6.52791 + 3.76889i 0.574750 + 0.331832i
\(130\) 0 0
\(131\) −2.74161 + 1.58287i −0.239536 + 0.138296i −0.614963 0.788556i \(-0.710829\pi\)
0.375428 + 0.926852i \(0.377496\pi\)
\(132\) 0 0
\(133\) −5.26581 + 3.55311i −0.456604 + 0.308094i
\(134\) 0 0
\(135\) 0.675970 + 1.17081i 0.0581782 + 0.100768i
\(136\) 0 0
\(137\) −3.25839 + 5.64370i −0.278383 + 0.482174i −0.970983 0.239148i \(-0.923132\pi\)
0.692600 + 0.721322i \(0.256465\pi\)
\(138\) 0 0
\(139\) −12.4647 7.19648i −1.05724 0.610398i −0.132572 0.991173i \(-0.542324\pi\)
−0.924667 + 0.380776i \(0.875657\pi\)
\(140\) 0 0
\(141\) 9.29349i 0.782653i
\(142\) 0 0
\(143\) −4.11404 + 7.12572i −0.344033 + 0.595883i
\(144\) 0 0
\(145\) 1.14613i 0.0951813i
\(146\) 0 0
\(147\) 2.43807 + 4.22286i 0.201089 + 0.348296i
\(148\) 0 0
\(149\) −3.20017 5.54286i −0.262168 0.454088i 0.704650 0.709555i \(-0.251104\pi\)
−0.966818 + 0.255467i \(0.917771\pi\)
\(150\) 0 0
\(151\) 9.64064 0.784544 0.392272 0.919849i \(-0.371689\pi\)
0.392272 + 0.919849i \(0.371689\pi\)
\(152\) 0 0
\(153\) −4.17226 −0.337307
\(154\) 0 0
\(155\) −0.237900 0.412055i −0.0191086 0.0330971i
\(156\) 0 0
\(157\) −11.7281 20.3136i −0.936003 1.62120i −0.772836 0.634605i \(-0.781163\pi\)
−0.163166 0.986599i \(-0.552171\pi\)
\(158\) 0 0
\(159\) 10.1176i 0.802378i
\(160\) 0 0
\(161\) −5.46598 + 9.46735i −0.430779 + 0.746132i
\(162\) 0 0
\(163\) 3.15289i 0.246953i 0.992347 + 0.123477i \(0.0394044\pi\)
−0.992347 + 0.123477i \(0.960596\pi\)
\(164\) 0 0
\(165\) −3.73419 2.15594i −0.290706 0.167839i
\(166\) 0 0
\(167\) −3.49629 + 6.05575i −0.270551 + 0.468608i −0.969003 0.247049i \(-0.920539\pi\)
0.698452 + 0.715657i \(0.253873\pi\)
\(168\) 0 0
\(169\) −3.17226 5.49452i −0.244020 0.422655i
\(170\) 0 0
\(171\) 4.34823 0.304788i 0.332517 0.0233077i
\(172\) 0 0
\(173\) −17.3068 + 9.99208i −1.31581 + 0.759684i −0.983052 0.183328i \(-0.941313\pi\)
−0.332759 + 0.943012i \(0.607980\pi\)
\(174\) 0 0
\(175\) −4.00371 2.31154i −0.302652 0.174736i
\(176\) 0 0
\(177\) 0.675970 1.17081i 0.0508090 0.0880037i
\(178\) 0 0
\(179\) −15.6965 −1.17321 −0.586604 0.809874i \(-0.699536\pi\)
−0.586604 + 0.809874i \(0.699536\pi\)
\(180\) 0 0
\(181\) 13.3142 + 7.68696i 0.989637 + 0.571367i 0.905166 0.425059i \(-0.139746\pi\)
0.0844714 + 0.996426i \(0.473080\pi\)
\(182\) 0 0
\(183\) 8.58002 0.634253
\(184\) 0 0
\(185\) −8.06889 + 4.65858i −0.593237 + 0.342505i
\(186\) 0 0
\(187\) 11.5242 6.65350i 0.842733 0.486552i
\(188\) 0 0
\(189\) 1.45735i 0.106006i
\(190\) 0 0
\(191\) 3.85914i 0.279238i 0.990205 + 0.139619i \(0.0445878\pi\)
−0.990205 + 0.139619i \(0.955412\pi\)
\(192\) 0 0
\(193\) −11.8142 + 6.82094i −0.850405 + 0.490982i −0.860788 0.508964i \(-0.830028\pi\)
0.0103823 + 0.999946i \(0.496695\pi\)
\(194\) 0 0
\(195\) −3.02049 + 1.74388i −0.216302 + 0.124882i
\(196\) 0 0
\(197\) 23.7571 1.69262 0.846311 0.532689i \(-0.178818\pi\)
0.846311 + 0.532689i \(0.178818\pi\)
\(198\) 0 0
\(199\) 19.5205 + 11.2702i 1.38377 + 0.798920i 0.992604 0.121399i \(-0.0387381\pi\)
0.391167 + 0.920320i \(0.372071\pi\)
\(200\) 0 0
\(201\) −2.17968 −0.153743
\(202\) 0 0
\(203\) −0.617748 + 1.06997i −0.0433574 + 0.0750973i
\(204\) 0 0
\(205\) 5.48322 + 3.16574i 0.382965 + 0.221105i
\(206\) 0 0
\(207\) 6.49629 3.75064i 0.451523 0.260687i
\(208\) 0 0
\(209\) −11.5242 + 7.77597i −0.797146 + 0.537875i
\(210\) 0 0
\(211\) 11.0521 + 19.1428i 0.760859 + 1.31785i 0.942409 + 0.334464i \(0.108555\pi\)
−0.181550 + 0.983382i \(0.558111\pi\)
\(212\) 0 0
\(213\) 0.438069 0.758758i 0.0300160 0.0519893i
\(214\) 0 0
\(215\) −8.82534 5.09531i −0.601883 0.347497i
\(216\) 0 0
\(217\) 0.512898i 0.0348178i
\(218\) 0 0
\(219\) −6.67226 + 11.5567i −0.450870 + 0.780929i
\(220\) 0 0
\(221\) 10.7637i 0.724044i
\(222\) 0 0
\(223\) 2.87985 + 4.98804i 0.192849 + 0.334024i 0.946193 0.323602i \(-0.104894\pi\)
−0.753344 + 0.657626i \(0.771561\pi\)
\(224\) 0 0
\(225\) 1.58613 + 2.74726i 0.105742 + 0.183151i
\(226\) 0 0
\(227\) 23.5242 1.56136 0.780678 0.624934i \(-0.214874\pi\)
0.780678 + 0.624934i \(0.214874\pi\)
\(228\) 0 0
\(229\) −5.76450 −0.380929 −0.190465 0.981694i \(-0.560999\pi\)
−0.190465 + 0.981694i \(0.560999\pi\)
\(230\) 0 0
\(231\) −2.32403 4.02534i −0.152910 0.264848i
\(232\) 0 0
\(233\) −0.321627 0.557074i −0.0210705 0.0364951i 0.855298 0.518137i \(-0.173374\pi\)
−0.876368 + 0.481641i \(0.840041\pi\)
\(234\) 0 0
\(235\) 12.5642i 0.819600i
\(236\) 0 0
\(237\) 2.52791 4.37847i 0.164205 0.284412i
\(238\) 0 0
\(239\) 6.65350i 0.430379i −0.976572 0.215190i \(-0.930963\pi\)
0.976572 0.215190i \(-0.0690369\pi\)
\(240\) 0 0
\(241\) 0.548399 + 0.316618i 0.0353255 + 0.0203952i 0.517559 0.855648i \(-0.326841\pi\)
−0.482233 + 0.876043i \(0.660174\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) −3.29612 5.70905i −0.210581 0.364738i
\(246\) 0 0
\(247\) 0.786299 + 11.2177i 0.0500310 + 0.713762i
\(248\) 0 0
\(249\) 6.25839 3.61328i 0.396609 0.228983i
\(250\) 0 0
\(251\) 6.10422 + 3.52427i 0.385295 + 0.222450i 0.680119 0.733101i \(-0.261928\pi\)
−0.294825 + 0.955551i \(0.595261\pi\)
\(252\) 0 0
\(253\) −11.9623 + 20.7193i −0.752061 + 1.30261i
\(254\) 0 0
\(255\) 5.64064 0.353231
\(256\) 0 0
\(257\) 21.7547 + 12.5601i 1.35702 + 0.783476i 0.989221 0.146430i \(-0.0467782\pi\)
0.367799 + 0.929905i \(0.380112\pi\)
\(258\) 0 0
\(259\) −10.0436 −0.624078
\(260\) 0 0
\(261\) 0.734191 0.423885i 0.0454453 0.0262378i
\(262\) 0 0
\(263\) −12.3216 + 7.11389i −0.759784 + 0.438662i −0.829218 0.558925i \(-0.811214\pi\)
0.0694342 + 0.997587i \(0.477881\pi\)
\(264\) 0 0
\(265\) 13.6784i 0.840256i
\(266\) 0 0
\(267\) 4.40855i 0.269799i
\(268\) 0 0
\(269\) −1.18950 + 0.686759i −0.0725252 + 0.0418724i −0.535824 0.844330i \(-0.679999\pi\)
0.463299 + 0.886202i \(0.346666\pi\)
\(270\) 0 0
\(271\) 10.4684 6.04392i 0.635909 0.367142i −0.147128 0.989117i \(-0.547003\pi\)
0.783037 + 0.621975i \(0.213670\pi\)
\(272\) 0 0
\(273\) −3.75970 −0.227547
\(274\) 0 0
\(275\) −8.76210 5.05880i −0.528374 0.305057i
\(276\) 0 0
\(277\) 5.58002 0.335271 0.167635 0.985849i \(-0.446387\pi\)
0.167635 + 0.985849i \(0.446387\pi\)
\(278\) 0 0
\(279\) −0.175970 + 0.304788i −0.0105350 + 0.0182472i
\(280\) 0 0
\(281\) 11.6079 + 6.70184i 0.692471 + 0.399798i 0.804537 0.593903i \(-0.202414\pi\)
−0.112066 + 0.993701i \(0.535747\pi\)
\(282\) 0 0
\(283\) 7.88095 4.55007i 0.468474 0.270473i −0.247127 0.968983i \(-0.579486\pi\)
0.715601 + 0.698510i \(0.246153\pi\)
\(284\) 0 0
\(285\) −5.87854 + 0.412055i −0.348215 + 0.0244080i
\(286\) 0 0
\(287\) 3.41256 + 5.91073i 0.201437 + 0.348900i
\(288\) 0 0
\(289\) −0.203878 + 0.353128i −0.0119928 + 0.0207722i
\(290\) 0 0
\(291\) −7.79001 4.49756i −0.456658 0.263652i
\(292\) 0 0
\(293\) 5.70905i 0.333526i −0.985997 0.166763i \(-0.946668\pi\)
0.985997 0.166763i \(-0.0533315\pi\)
\(294\) 0 0
\(295\) −0.913870 + 1.58287i −0.0532076 + 0.0921582i
\(296\) 0 0
\(297\) 3.18940i 0.185068i
\(298\) 0 0
\(299\) 9.67597 + 16.7593i 0.559576 + 0.969214i
\(300\) 0 0
\(301\) −5.49258 9.51343i −0.316587 0.548345i
\(302\) 0 0
\(303\) −7.46838 −0.429047
\(304\) 0 0
\(305\) −11.5997 −0.664195
\(306\) 0 0
\(307\) −11.1419 19.2984i −0.635905 1.10142i −0.986323 0.164826i \(-0.947294\pi\)
0.350418 0.936593i \(-0.386039\pi\)
\(308\) 0 0
\(309\) 5.78630 + 10.0222i 0.329171 + 0.570141i
\(310\) 0 0
\(311\) 20.9286i 1.18675i 0.804925 + 0.593376i \(0.202205\pi\)
−0.804925 + 0.593376i \(0.797795\pi\)
\(312\) 0 0
\(313\) 0.561931 0.973292i 0.0317622 0.0550137i −0.849707 0.527255i \(-0.823221\pi\)
0.881470 + 0.472241i \(0.156555\pi\)
\(314\) 0 0
\(315\) 1.97024i 0.111011i
\(316\) 0 0
\(317\) −15.0205 8.67208i −0.843635 0.487073i 0.0148633 0.999890i \(-0.495269\pi\)
−0.858498 + 0.512817i \(0.828602\pi\)
\(318\) 0 0
\(319\) −1.35194 + 2.34163i −0.0756941 + 0.131106i
\(320\) 0 0
\(321\) 5.08613 + 8.80944i 0.283880 + 0.491695i
\(322\) 0 0
\(323\) 7.96969 16.3472i 0.443445 0.909583i
\(324\) 0 0
\(325\) −7.08744 + 4.09193i −0.393140 + 0.226980i
\(326\) 0 0
\(327\) 7.31421 + 4.22286i 0.404477 + 0.233525i
\(328\) 0 0
\(329\) −6.77192 + 11.7293i −0.373348 + 0.646658i
\(330\) 0 0
\(331\) −0.584825 −0.0321449 −0.0160724 0.999871i \(-0.505116\pi\)
−0.0160724 + 0.999871i \(0.505116\pi\)
\(332\) 0 0
\(333\) 5.96838 + 3.44585i 0.327065 + 0.188831i
\(334\) 0 0
\(335\) 2.94679 0.161001
\(336\) 0 0
\(337\) 23.8142 13.7491i 1.29724 0.748963i 0.317316 0.948320i \(-0.397219\pi\)
0.979927 + 0.199357i \(0.0638852\pi\)
\(338\) 0 0
\(339\) −10.8105 + 6.24144i −0.587146 + 0.338989i
\(340\) 0 0
\(341\) 1.12247i 0.0607854i
\(342\) 0 0
\(343\) 17.3077i 0.934526i
\(344\) 0 0
\(345\) −8.78259 + 5.07063i −0.472839 + 0.272994i
\(346\) 0 0
\(347\) 22.8105 13.1696i 1.22453 0.706984i 0.258651 0.965971i \(-0.416722\pi\)
0.965881 + 0.258987i \(0.0833887\pi\)
\(348\) 0 0
\(349\) 9.53162 0.510216 0.255108 0.966913i \(-0.417889\pi\)
0.255108 + 0.966913i \(0.417889\pi\)
\(350\) 0 0
\(351\) 2.23419 + 1.28991i 0.119252 + 0.0688503i
\(352\) 0 0
\(353\) 7.94418 0.422826 0.211413 0.977397i \(-0.432193\pi\)
0.211413 + 0.977397i \(0.432193\pi\)
\(354\) 0 0
\(355\) −0.592243 + 1.02580i −0.0314330 + 0.0544436i
\(356\) 0 0
\(357\) 5.26581 + 3.04022i 0.278696 + 0.160905i
\(358\) 0 0
\(359\) −15.9293 + 9.19681i −0.840719 + 0.485389i −0.857508 0.514470i \(-0.827989\pi\)
0.0167898 + 0.999859i \(0.494655\pi\)
\(360\) 0 0
\(361\) −7.11164 + 17.6189i −0.374297 + 0.927309i
\(362\) 0 0
\(363\) 0.413870 + 0.716844i 0.0217225 + 0.0376245i
\(364\) 0 0
\(365\) 9.02049 15.6239i 0.472154 0.817795i
\(366\) 0 0
\(367\) −7.41627 4.28179i −0.387126 0.223507i 0.293788 0.955871i \(-0.405084\pi\)
−0.680914 + 0.732363i \(0.738417\pi\)
\(368\) 0 0
\(369\) 4.68325i 0.243801i
\(370\) 0 0
\(371\) 7.37243 12.7694i 0.382757 0.662955i
\(372\) 0 0
\(373\) 25.0965i 1.29945i −0.760171 0.649723i \(-0.774885\pi\)
0.760171 0.649723i \(-0.225115\pi\)
\(374\) 0 0
\(375\) −5.52420 9.56819i −0.285268 0.494099i
\(376\) 0 0
\(377\) 1.09355 + 1.89408i 0.0563206 + 0.0975502i
\(378\) 0 0
\(379\) −34.6816 −1.78148 −0.890738 0.454518i \(-0.849812\pi\)
−0.890738 + 0.454518i \(0.849812\pi\)
\(380\) 0 0
\(381\) −7.04840 −0.361100
\(382\) 0 0
\(383\) 4.58984 + 7.94984i 0.234530 + 0.406218i 0.959136 0.282946i \(-0.0913116\pi\)
−0.724606 + 0.689163i \(0.757978\pi\)
\(384\) 0 0
\(385\) 3.14195 + 5.44201i 0.160128 + 0.277351i
\(386\) 0 0
\(387\) 7.53778i 0.383167i
\(388\) 0 0
\(389\) 11.4660 19.8597i 0.581348 1.00692i −0.413972 0.910290i \(-0.635859\pi\)
0.995320 0.0966348i \(-0.0308079\pi\)
\(390\) 0 0
\(391\) 31.2973i 1.58277i
\(392\) 0 0
\(393\) −2.74161 1.58287i −0.138296 0.0798452i
\(394\) 0 0
\(395\) −3.41758 + 5.91942i −0.171957 + 0.297838i
\(396\) 0 0
\(397\) −0.593549 1.02806i −0.0297894 0.0515967i 0.850746 0.525576i \(-0.176150\pi\)
−0.880536 + 0.473980i \(0.842817\pi\)
\(398\) 0 0
\(399\) −5.70999 2.78377i −0.285857 0.139363i
\(400\) 0 0
\(401\) 29.3273 16.9321i 1.46453 0.845549i 0.465319 0.885143i \(-0.345940\pi\)
0.999216 + 0.0395939i \(0.0126064\pi\)
\(402\) 0 0
\(403\) −0.786299 0.453970i −0.0391684 0.0226139i
\(404\) 0 0
\(405\) −0.675970 + 1.17081i −0.0335892 + 0.0581782i
\(406\) 0 0
\(407\) −21.9804 −1.08953
\(408\) 0 0
\(409\) −19.8310 11.4494i −0.980579 0.566138i −0.0781343 0.996943i \(-0.524896\pi\)
−0.902445 + 0.430805i \(0.858230\pi\)
\(410\) 0 0
\(411\) −6.51678 −0.321449
\(412\) 0 0
\(413\) −1.70628 + 0.985122i −0.0839607 + 0.0484747i
\(414\) 0 0
\(415\) −8.46096 + 4.88494i −0.415332 + 0.239792i
\(416\) 0 0
\(417\) 14.3930i 0.704826i
\(418\) 0 0
\(419\) 13.7020i 0.669389i −0.942327 0.334694i \(-0.891367\pi\)
0.942327 0.334694i \(-0.108633\pi\)
\(420\) 0 0
\(421\) 12.3216 7.11389i 0.600519 0.346710i −0.168727 0.985663i \(-0.553965\pi\)
0.769246 + 0.638953i \(0.220632\pi\)
\(422\) 0 0
\(423\) 8.04840 4.64675i 0.391327 0.225932i
\(424\) 0 0
\(425\) 13.2355 0.642016
\(426\) 0 0
\(427\) −10.8288 6.25203i −0.524044 0.302557i
\(428\) 0 0
\(429\) −8.22808 −0.397255
\(430\) 0 0
\(431\) 8.04840 13.9402i 0.387678 0.671478i −0.604459 0.796636i \(-0.706611\pi\)
0.992137 + 0.125159i \(0.0399440\pi\)
\(432\) 0 0
\(433\) 33.1635 + 19.1470i 1.59374 + 0.920145i 0.992658 + 0.120956i \(0.0385960\pi\)
0.601080 + 0.799189i \(0.294737\pi\)
\(434\) 0 0
\(435\) −0.992582 + 0.573067i −0.0475906 + 0.0274765i
\(436\) 0 0
\(437\) 2.28630 + 32.6172i 0.109369 + 1.56029i
\(438\) 0 0
\(439\) −6.95856 12.0526i −0.332114 0.575238i 0.650812 0.759239i \(-0.274429\pi\)
−0.982926 + 0.184001i \(0.941095\pi\)
\(440\) 0 0
\(441\) −2.43807 + 4.22286i −0.116099 + 0.201089i
\(442\) 0 0
\(443\) −2.16159 1.24800i −0.102700 0.0592941i 0.447770 0.894149i \(-0.352218\pi\)
−0.550470 + 0.834855i \(0.685552\pi\)
\(444\) 0 0
\(445\) 5.96009i 0.282536i
\(446\) 0 0
\(447\) 3.20017 5.54286i 0.151363 0.262168i
\(448\) 0 0
\(449\) 39.4766i 1.86302i −0.363721 0.931508i \(-0.618494\pi\)
0.363721 0.931508i \(-0.381506\pi\)
\(450\) 0 0
\(451\) 7.46838 + 12.9356i 0.351672 + 0.609114i
\(452\) 0 0
\(453\) 4.82032 + 8.34904i 0.226478 + 0.392272i
\(454\) 0 0
\(455\) 5.08288 0.238289
\(456\) 0 0
\(457\) −38.2207 −1.78789 −0.893944 0.448180i \(-0.852072\pi\)
−0.893944 + 0.448180i \(0.852072\pi\)
\(458\) 0 0
\(459\) −2.08613 3.61328i −0.0973722 0.168654i
\(460\) 0 0
\(461\) −13.3469 23.1176i −0.621628 1.07669i −0.989183 0.146690i \(-0.953138\pi\)
0.367554 0.930002i \(-0.380195\pi\)
\(462\) 0 0
\(463\) 4.96877i 0.230918i −0.993312 0.115459i \(-0.963166\pi\)
0.993312 0.115459i \(-0.0368339\pi\)
\(464\) 0 0
\(465\) 0.237900 0.412055i 0.0110324 0.0191086i
\(466\) 0 0
\(467\) 24.1757i 1.11872i −0.828926 0.559359i \(-0.811047\pi\)
0.828926 0.559359i \(-0.188953\pi\)
\(468\) 0 0
\(469\) 2.75097 + 1.58827i 0.127028 + 0.0733397i
\(470\) 0 0
\(471\) 11.7281 20.3136i 0.540401 0.936003i
\(472\) 0 0
\(473\) −12.0205 20.8201i −0.552703 0.957309i
\(474\) 0 0
\(475\) −13.7937 + 0.966868i −0.632899 + 0.0443629i
\(476\) 0 0
\(477\) −8.76210 + 5.05880i −0.401189 + 0.231627i
\(478\) 0 0
\(479\) −32.9500 19.0237i −1.50553 0.869216i −0.999979 0.00641641i \(-0.997958\pi\)
−0.505546 0.862799i \(-0.668709\pi\)
\(480\) 0 0
\(481\) −8.88967 + 15.3974i −0.405334 + 0.702059i
\(482\) 0 0
\(483\) −10.9320 −0.497421
\(484\) 0 0
\(485\) 10.5316 + 6.08043i 0.478216 + 0.276098i
\(486\) 0 0
\(487\) −0.344521 −0.0156117 −0.00780586 0.999970i \(-0.502485\pi\)
−0.00780586 + 0.999970i \(0.502485\pi\)
\(488\) 0 0
\(489\) −2.73048 + 1.57644i −0.123477 + 0.0712893i
\(490\) 0 0
\(491\) 0.838408 0.484055i 0.0378368 0.0218451i −0.480962 0.876741i \(-0.659713\pi\)
0.518799 + 0.854896i \(0.326379\pi\)
\(492\) 0 0
\(493\) 3.53712i 0.159304i
\(494\) 0 0
\(495\) 4.31187i 0.193804i
\(496\) 0 0
\(497\) −1.10577 + 0.638419i −0.0496008 + 0.0286370i
\(498\) 0 0
\(499\) 12.2695 7.08381i 0.549259 0.317115i −0.199564 0.979885i \(-0.563953\pi\)
0.748823 + 0.662770i \(0.230619\pi\)
\(500\) 0 0
\(501\) −6.99258 −0.312406
\(502\) 0 0
\(503\) 36.7752 + 21.2322i 1.63972 + 0.946695i 0.980928 + 0.194374i \(0.0622674\pi\)
0.658796 + 0.752321i \(0.271066\pi\)
\(504\) 0 0
\(505\) 10.0968 0.449302
\(506\) 0 0
\(507\) 3.17226 5.49452i 0.140885 0.244020i
\(508\) 0 0
\(509\) 15.4758 + 8.93496i 0.685953 + 0.396035i 0.802094 0.597198i \(-0.203719\pi\)
−0.116141 + 0.993233i \(0.537053\pi\)
\(510\) 0 0
\(511\) 16.8421 9.72380i 0.745051 0.430156i
\(512\) 0 0
\(513\) 2.43807 + 3.61328i 0.107643 + 0.159530i
\(514\) 0 0
\(515\) −7.82272 13.5494i −0.344710 0.597056i
\(516\) 0 0
\(517\) −14.8203 + 25.6695i −0.651797 + 1.12895i
\(518\) 0 0
\(519\) −17.3068 9.99208i −0.759684 0.438604i
\(520\) 0 0
\(521\) 11.0384i 0.483601i −0.970326 0.241800i \(-0.922262\pi\)
0.970326 0.241800i \(-0.0777379\pi\)
\(522\) 0 0
\(523\) −11.0824 + 19.1953i −0.484600 + 0.839353i −0.999843 0.0176915i \(-0.994368\pi\)
0.515243 + 0.857044i \(0.327702\pi\)
\(524\) 0 0
\(525\) 4.62309i 0.201768i
\(526\) 0 0
\(527\) 0.734191 + 1.27166i 0.0319819 + 0.0553942i
\(528\) 0 0
\(529\) 16.6345 + 28.8119i 0.723240 + 1.25269i
\(530\) 0 0
\(531\) 1.35194 0.0586692
\(532\) 0 0
\(533\) 12.0820 0.523328
\(534\) 0 0
\(535\) −6.87614 11.9098i −0.297281 0.514906i
\(536\) 0 0
\(537\) −7.84823 13.5935i −0.338676 0.586604i
\(538\) 0 0
\(539\) 15.5519i 0.669870i
\(540\) 0 0
\(541\) −12.4245 + 21.5199i −0.534173 + 0.925214i 0.465030 + 0.885295i \(0.346043\pi\)
−0.999203 + 0.0399193i \(0.987290\pi\)
\(542\) 0 0
\(543\) 15.3739i 0.659758i
\(544\) 0 0
\(545\) −9.88836 5.70905i −0.423571 0.244549i
\(546\) 0 0
\(547\) −15.8798 + 27.5047i −0.678973 + 1.17602i 0.296317 + 0.955090i \(0.404241\pi\)
−0.975290 + 0.220927i \(0.929092\pi\)
\(548\) 0 0
\(549\) 4.29001 + 7.43051i 0.183093 + 0.317127i
\(550\) 0 0
\(551\) 0.258391 + 3.68630i 0.0110078 + 0.157042i
\(552\) 0 0
\(553\) −6.38095 + 3.68404i −0.271345 + 0.156661i
\(554\) 0 0
\(555\) −8.06889 4.65858i −0.342505 0.197746i
\(556\) 0 0
\(557\) 4.72677 8.18701i 0.200280 0.346895i −0.748339 0.663317i \(-0.769148\pi\)
0.948619 + 0.316422i \(0.102482\pi\)
\(558\) 0 0
\(559\) −19.4461 −0.822484
\(560\) 0 0
\(561\) 11.5242 + 6.65350i 0.486552 + 0.280911i
\(562\) 0 0
\(563\) 43.5503 1.83543 0.917714 0.397242i \(-0.130032\pi\)
0.917714 + 0.397242i \(0.130032\pi\)
\(564\) 0 0
\(565\) 14.6151 8.43805i 0.614863 0.354992i
\(566\) 0 0
\(567\) −1.26210 + 0.728674i −0.0530032 + 0.0306014i
\(568\) 0 0
\(569\) 46.3471i 1.94297i −0.237097 0.971486i \(-0.576196\pi\)
0.237097 0.971486i \(-0.423804\pi\)
\(570\) 0 0
\(571\) 38.0346i 1.59170i −0.605495 0.795849i \(-0.707025\pi\)
0.605495 0.795849i \(-0.292975\pi\)
\(572\) 0 0
\(573\) −3.34212 + 1.92957i −0.139619 + 0.0806090i
\(574\) 0 0
\(575\) −20.6079 + 11.8980i −0.859410 + 0.496181i
\(576\) 0 0
\(577\) 22.8761 0.952346 0.476173 0.879352i \(-0.342024\pi\)
0.476173 + 0.879352i \(0.342024\pi\)
\(578\) 0 0
\(579\) −11.8142 6.82094i −0.490982 0.283468i
\(580\) 0 0
\(581\) −10.5316 −0.436925
\(582\) 0 0
\(583\) 16.1345 27.9458i 0.668224 1.15740i
\(584\) 0 0
\(585\) −3.02049 1.74388i −0.124882 0.0721006i
\(586\) 0 0
\(587\) −17.6079 + 10.1659i −0.726757 + 0.419593i −0.817235 0.576305i \(-0.804494\pi\)
0.0904777 + 0.995898i \(0.471161\pi\)
\(588\) 0 0
\(589\) −0.858052 1.27166i −0.0353554 0.0523977i
\(590\) 0 0
\(591\) 11.8785 + 20.5742i 0.488618 + 0.846311i
\(592\) 0 0
\(593\) −3.81792 + 6.61283i −0.156783 + 0.271556i −0.933707 0.358038i \(-0.883446\pi\)
0.776924 + 0.629595i \(0.216779\pi\)
\(594\) 0 0
\(595\) −7.11905 4.11019i −0.291853 0.168501i
\(596\) 0 0
\(597\) 22.5403i 0.922514i
\(598\) 0 0
\(599\) 5.94178 10.2915i 0.242774 0.420498i −0.718729 0.695290i \(-0.755276\pi\)
0.961504 + 0.274792i \(0.0886092\pi\)
\(600\) 0 0
\(601\) 35.0962i 1.43161i −0.698303 0.715803i \(-0.746061\pi\)
0.698303 0.715803i \(-0.253939\pi\)
\(602\) 0 0
\(603\) −1.08984 1.88766i −0.0443817 0.0768713i
\(604\) 0 0
\(605\) −0.559527 0.969129i −0.0227480 0.0394007i
\(606\) 0 0
\(607\) 32.9293 1.33656 0.668280 0.743909i \(-0.267031\pi\)
0.668280 + 0.743909i \(0.267031\pi\)
\(608\) 0 0
\(609\) −1.23550 −0.0500648
\(610\) 0 0
\(611\) 11.9878 + 20.7634i 0.484973 + 0.839999i
\(612\) 0 0
\(613\) 14.8310 + 25.6880i 0.599018 + 1.03753i 0.992966 + 0.118397i \(0.0377756\pi\)
−0.393948 + 0.919133i \(0.628891\pi\)
\(614\) 0 0
\(615\) 6.33148i 0.255310i
\(616\) 0 0
\(617\) 13.2560 22.9600i 0.533666 0.924337i −0.465561 0.885016i \(-0.654147\pi\)
0.999227 0.0393206i \(-0.0125194\pi\)
\(618\) 0 0
\(619\) 19.8510i 0.797878i 0.916977 + 0.398939i \(0.130621\pi\)
−0.916977 + 0.398939i \(0.869379\pi\)
\(620\) 0 0
\(621\) 6.49629 + 3.75064i 0.260687 + 0.150508i
\(622\) 0 0
\(623\) −3.21240 + 5.56403i −0.128702 + 0.222918i
\(624\) 0 0
\(625\) −0.462269 0.800673i −0.0184908 0.0320269i
\(626\) 0 0
\(627\) −12.4963 6.09226i −0.499054 0.243302i
\(628\) 0 0
\(629\) 24.9016 14.3770i 0.992894 0.573247i
\(630\) 0 0
\(631\) −20.3179 11.7306i −0.808844 0.466986i 0.0377106 0.999289i \(-0.487994\pi\)
−0.846554 + 0.532303i \(0.821327\pi\)
\(632\) 0 0
\(633\) −11.0521 + 19.1428i −0.439282 + 0.760859i
\(634\) 0 0
\(635\) 9.52901 0.378147
\(636\) 0 0
\(637\) −10.8942 6.28978i −0.431645 0.249210i
\(638\) 0 0
\(639\) 0.876139 0.0346595
\(640\) 0 0
\(641\) 42.4535 24.5106i 1.67681 0.968109i 0.713143 0.701019i \(-0.247271\pi\)
0.963672 0.267090i \(-0.0860622\pi\)
\(642\) 0 0
\(643\) 12.8495 7.41868i 0.506736 0.292564i −0.224755 0.974415i \(-0.572158\pi\)
0.731491 + 0.681851i \(0.238825\pi\)
\(644\) 0 0
\(645\) 10.1906i 0.401255i
\(646\) 0 0
\(647\) 25.8135i 1.01484i 0.861700 + 0.507418i \(0.169400\pi\)
−0.861700 + 0.507418i \(0.830600\pi\)
\(648\) 0 0
\(649\) −3.73419 + 2.15594i −0.146580 + 0.0846279i
\(650\) 0 0
\(651\) 0.444182 0.256449i 0.0174089 0.0100510i
\(652\) 0 0
\(653\) 24.6433 0.964365 0.482183 0.876071i \(-0.339844\pi\)
0.482183 + 0.876071i \(0.339844\pi\)
\(654\) 0 0
\(655\) 3.70649 + 2.13994i 0.144825 + 0.0836145i
\(656\) 0 0
\(657\) −13.3445 −0.520619
\(658\) 0 0
\(659\) −0.0582214 + 0.100842i −0.00226798 + 0.00392826i −0.867157 0.498035i \(-0.834055\pi\)
0.864889 + 0.501963i \(0.167389\pi\)
\(660\) 0 0
\(661\) 5.35675 + 3.09272i 0.208353 + 0.120293i 0.600546 0.799590i \(-0.294950\pi\)
−0.392193 + 0.919883i \(0.628283\pi\)
\(662\) 0 0
\(663\) 9.32163 5.38184i 0.362022 0.209013i
\(664\) 0 0
\(665\) 7.71956 + 3.76348i 0.299352 + 0.145942i
\(666\) 0 0
\(667\) 3.17968 + 5.50737i 0.123118 + 0.213246i
\(668\) 0 0
\(669\) −2.87985 + 4.98804i −0.111341 + 0.192849i
\(670\) 0 0
\(671\) −23.6989 13.6825i −0.914884 0.528209i
\(672\) 0 0
\(673\) 18.6082i 0.717292i −0.933474 0.358646i \(-0.883239\pi\)
0.933474 0.358646i \(-0.116761\pi\)
\(674\) 0 0
\(675\) −1.58613 + 2.74726i −0.0610502 + 0.105742i
\(676\) 0 0
\(677\) 28.9793i 1.11376i 0.830591 + 0.556882i \(0.188003\pi\)
−0.830591 + 0.556882i \(0.811997\pi\)
\(678\) 0 0
\(679\) 6.55451 + 11.3527i 0.251539 + 0.435678i
\(680\) 0 0
\(681\) 11.7621 + 20.3726i 0.450725 + 0.780678i
\(682\) 0 0
\(683\) 43.8687 1.67859 0.839295 0.543676i \(-0.182968\pi\)
0.839295 + 0.543676i \(0.182968\pi\)
\(684\) 0 0
\(685\) 8.81029 0.336624
\(686\) 0 0
\(687\) −2.88225 4.99221i −0.109965 0.190465i
\(688\) 0 0
\(689\) −13.0508 22.6047i −0.497196 0.861169i
\(690\) 0 0
\(691\) 27.2837i 1.03792i 0.854798 + 0.518961i \(0.173681\pi\)
−0.854798 + 0.518961i \(0.826319\pi\)
\(692\) 0 0
\(693\) 2.32403 4.02534i 0.0882826 0.152910i
\(694\) 0 0
\(695\) 19.4584i 0.738100i
\(696\) 0 0
\(697\) −16.9219 9.76988i −0.640964 0.370061i
\(698\) 0 0
\(699\) 0.321627 0.557074i 0.0121650 0.0210705i
\(700\) 0 0
\(701\) 5.44047 + 9.42318i 0.205484 + 0.355908i 0.950287 0.311376i \(-0.100790\pi\)
−0.744803 + 0.667284i \(0.767457\pi\)
\(702\) 0 0
\(703\) −24.9016 + 16.8024i −0.939183 + 0.633716i
\(704\) 0 0
\(705\) −10.8809 + 6.28212i −0.409800 + 0.236598i
\(706\) 0 0
\(707\) 9.42584 + 5.44201i 0.354495 + 0.204668i
\(708\) 0 0
\(709\) −24.8626 + 43.0633i −0.933735 + 1.61728i −0.156860 + 0.987621i \(0.550137\pi\)
−0.776875 + 0.629655i \(0.783196\pi\)
\(710\) 0 0
\(711\) 5.05582 0.189608
\(712\) 0 0
\(713\) −2.28630 1.32000i −0.0856226 0.0494342i
\(714\) 0 0
\(715\) 11.1239 0.416009
\(716\) 0 0
\(717\) 5.76210 3.32675i 0.215190 0.124240i
\(718\) 0 0
\(719\) −26.6079 + 15.3621i −0.992308 + 0.572909i −0.905963 0.423356i \(-0.860852\pi\)
−0.0863447 + 0.996265i \(0.527519\pi\)
\(720\) 0 0
\(721\) 16.8653i 0.628096i
\(722\) 0 0
\(723\) 0.633237i 0.0235503i
\(724\) 0 0
\(725\) −2.32905 + 1.34467i −0.0864986 + 0.0499400i
\(726\) 0 0
\(727\) −25.9963 + 15.0090i −0.964149 + 0.556652i −0.897448 0.441121i \(-0.854581\pi\)
−0.0667015 + 0.997773i \(0.521248\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 27.2361 + 15.7248i 1.00736 + 0.581602i
\(732\) 0 0
\(733\) −47.3026 −1.74716 −0.873581 0.486679i \(-0.838208\pi\)
−0.873581 + 0.486679i \(0.838208\pi\)
\(734\) 0 0
\(735\) 3.29612 5.70905i 0.121579 0.210581i
\(736\) 0 0
\(737\) 6.02049 + 3.47593i 0.221768 + 0.128038i
\(738\) 0 0
\(739\) −27.3515 + 15.7914i −1.00614 + 0.580895i −0.910059 0.414478i \(-0.863964\pi\)
−0.0960811 + 0.995374i \(0.530631\pi\)
\(740\) 0 0
\(741\) −9.32163 + 6.28978i −0.342439 + 0.231061i
\(742\) 0 0
\(743\) −16.7063 28.9361i −0.612894 1.06156i −0.990750 0.135699i \(-0.956672\pi\)
0.377856 0.925864i \(-0.376661\pi\)
\(744\) 0 0
\(745\) −4.32643 + 7.49360i −0.158508 + 0.274544i
\(746\) 0 0
\(747\) 6.25839 + 3.61328i 0.228983 + 0.132203i
\(748\) 0 0
\(749\) 14.8245i 0.541676i
\(750\) 0 0
\(751\) −9.84212 + 17.0470i −0.359144 + 0.622056i −0.987818 0.155613i \(-0.950265\pi\)
0.628674 + 0.777669i \(0.283598\pi\)
\(752\) 0 0
\(753\) 7.04854i 0.256863i
\(754\) 0 0
\(755\) −6.51678 11.2874i −0.237170 0.410790i
\(756\) 0 0
\(757\) 16.5181 + 28.6102i 0.600360 + 1.03985i 0.992766 + 0.120062i \(0.0383094\pi\)
−0.392406 + 0.919792i \(0.628357\pi\)
\(758\) 0 0
\(759\) −23.9245 −0.868406
\(760\) 0 0
\(761\) −46.5726 −1.68826 −0.844128 0.536142i \(-0.819881\pi\)
−0.844128 + 0.536142i \(0.819881\pi\)
\(762\) 0 0
\(763\) −6.15417 10.6593i −0.222796 0.385894i
\(764\) 0 0
\(765\) 2.82032 + 4.88494i 0.101969 + 0.176615i
\(766\) 0 0
\(767\) 3.48776i 0.125936i
\(768\) 0 0
\(769\) 15.9562 27.6369i 0.575394 0.996611i −0.420605 0.907244i \(-0.638182\pi\)
0.995999 0.0893673i \(-0.0284845\pi\)
\(770\) 0 0
\(771\) 25.1201i 0.904680i
\(772\) 0 0
\(773\) −13.0558 7.53778i −0.469585 0.271115i 0.246481 0.969148i \(-0.420726\pi\)
−0.716066 + 0.698033i \(0.754059\pi\)
\(774\) 0 0
\(775\) 0.558221 0.966868i 0.0200519 0.0347309i
\(776\) 0 0
\(777\) −5.02180 8.69801i −0.180156 0.312039i
\(778\) 0 0
\(779\) 18.3493 + 8.94577i 0.657433 + 0.320515i
\(780\) 0 0
\(781\) −2.41998 + 1.39718i −0.0865938 + 0.0499949i
\(782\) 0 0
\(783\) 0.734191 + 0.423885i 0.0262378 + 0.0151484i
\(784\) 0 0
\(785\) −15.8556 + 27.4628i −0.565912 + 0.980189i
\(786\) 0 0
\(787\) 37.9023 1.35107 0.675535 0.737328i \(-0.263913\pi\)
0.675535 + 0.737328i \(0.263913\pi\)
\(788\) 0 0
\(789\) −12.3216 7.11389i −0.438662 0.253261i
\(790\) 0 0
\(791\) 18.1919 0.646830
\(792\) 0 0
\(793\) −19.1694 + 11.0675i −0.680725 + 0.393017i
\(794\) 0 0
\(795\) 11.8458 6.83919i 0.420128 0.242561i
\(796\) 0 0
\(797\) 2.06692i 0.0732142i