Properties

Label 1148.2.i.b.165.1
Level $1148$
Weight $2$
Character 1148.165
Analytic conductor $9.167$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 165.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1148.165
Dual form 1148.2.i.b.821.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +(2.50000 - 4.33013i) q^{11} -2.00000 q^{13} +1.00000 q^{15} +(1.50000 - 2.59808i) q^{17} +(1.50000 + 2.59808i) q^{19} +(-2.50000 + 0.866025i) q^{21} +(0.500000 + 0.866025i) q^{23} +(2.00000 - 3.46410i) q^{25} +5.00000 q^{27} -10.0000 q^{29} +(5.50000 - 9.52628i) q^{31} +(-2.50000 - 4.33013i) q^{33} +(0.500000 - 2.59808i) q^{35} +(-3.50000 - 6.06218i) q^{37} +(-1.00000 + 1.73205i) q^{39} -1.00000 q^{41} +8.00000 q^{43} +(-1.00000 + 1.73205i) q^{45} +(3.50000 + 6.06218i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-1.50000 - 2.59808i) q^{51} +(5.50000 - 9.52628i) q^{53} +5.00000 q^{55} +3.00000 q^{57} +(3.50000 - 6.06218i) q^{59} +(0.500000 + 0.866025i) q^{61} +(1.00000 - 5.19615i) q^{63} +(-1.00000 - 1.73205i) q^{65} +(-3.50000 + 6.06218i) q^{67} +1.00000 q^{69} -12.0000 q^{71} +(2.50000 - 4.33013i) q^{73} +(-2.00000 - 3.46410i) q^{75} +(-12.5000 + 4.33013i) q^{77} +(-4.50000 - 7.79423i) q^{79} +(-0.500000 + 0.866025i) q^{81} +3.00000 q^{85} +(-5.00000 + 8.66025i) q^{87} +(1.50000 + 2.59808i) q^{89} +(4.00000 + 3.46410i) q^{91} +(-5.50000 - 9.52628i) q^{93} +(-1.50000 + 2.59808i) q^{95} +2.00000 q^{97} +10.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} + q^{5} - 4q^{7} + 2q^{9} + O(q^{10}) \) \( 2q + q^{3} + q^{5} - 4q^{7} + 2q^{9} + 5q^{11} - 4q^{13} + 2q^{15} + 3q^{17} + 3q^{19} - 5q^{21} + q^{23} + 4q^{25} + 10q^{27} - 20q^{29} + 11q^{31} - 5q^{33} + q^{35} - 7q^{37} - 2q^{39} - 2q^{41} + 16q^{43} - 2q^{45} + 7q^{47} + 2q^{49} - 3q^{51} + 11q^{53} + 10q^{55} + 6q^{57} + 7q^{59} + q^{61} + 2q^{63} - 2q^{65} - 7q^{67} + 2q^{69} - 24q^{71} + 5q^{73} - 4q^{75} - 25q^{77} - 9q^{79} - q^{81} + 6q^{85} - 10q^{87} + 3q^{89} + 8q^{91} - 11q^{93} - 3q^{95} + 4q^{97} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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 −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i 0.955901 0.293691i \(-0.0948835\pi\)
−0.732294 + 0.680989i \(0.761550\pi\)
\(6\) 0 0
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) 0 0
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) 2.50000 4.33013i 0.753778 1.30558i −0.192201 0.981356i \(-0.561563\pi\)
0.945979 0.324227i \(-0.105104\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) 0 0
\(19\) 1.50000 + 2.59808i 0.344124 + 0.596040i 0.985194 0.171442i \(-0.0548427\pi\)
−0.641071 + 0.767482i \(0.721509\pi\)
\(20\) 0 0
\(21\) −2.50000 + 0.866025i −0.545545 + 0.188982i
\(22\) 0 0
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i \(-0.133420\pi\)
−0.809177 + 0.587565i \(0.800087\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −10.0000 −1.85695 −0.928477 0.371391i \(-0.878881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 0 0
\(31\) 5.50000 9.52628i 0.987829 1.71097i 0.359211 0.933257i \(-0.383046\pi\)
0.628619 0.777714i \(-0.283621\pi\)
\(32\) 0 0
\(33\) −2.50000 4.33013i −0.435194 0.753778i
\(34\) 0 0
\(35\) 0.500000 2.59808i 0.0845154 0.439155i
\(36\) 0 0
\(37\) −3.50000 6.06218i −0.575396 0.996616i −0.995998 0.0893706i \(-0.971514\pi\)
0.420602 0.907245i \(-0.361819\pi\)
\(38\) 0 0
\(39\) −1.00000 + 1.73205i −0.160128 + 0.277350i
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) −1.00000 + 1.73205i −0.149071 + 0.258199i
\(46\) 0 0
\(47\) 3.50000 + 6.06218i 0.510527 + 0.884260i 0.999926 + 0.0121990i \(0.00388317\pi\)
−0.489398 + 0.872060i \(0.662783\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) −1.50000 2.59808i −0.210042 0.363803i
\(52\) 0 0
\(53\) 5.50000 9.52628i 0.755483 1.30854i −0.189651 0.981852i \(-0.560736\pi\)
0.945134 0.326683i \(-0.105931\pi\)
\(54\) 0 0
\(55\) 5.00000 0.674200
\(56\) 0 0
\(57\) 3.00000 0.397360
\(58\) 0 0
\(59\) 3.50000 6.06218i 0.455661 0.789228i −0.543065 0.839691i \(-0.682736\pi\)
0.998726 + 0.0504625i \(0.0160695\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 0 0
\(63\) 1.00000 5.19615i 0.125988 0.654654i
\(64\) 0 0
\(65\) −1.00000 1.73205i −0.124035 0.214834i
\(66\) 0 0
\(67\) −3.50000 + 6.06218i −0.427593 + 0.740613i −0.996659 0.0816792i \(-0.973972\pi\)
0.569066 + 0.822292i \(0.307305\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 2.50000 4.33013i 0.292603 0.506803i −0.681822 0.731519i \(-0.738812\pi\)
0.974424 + 0.224716i \(0.0721453\pi\)
\(74\) 0 0
\(75\) −2.00000 3.46410i −0.230940 0.400000i
\(76\) 0 0
\(77\) −12.5000 + 4.33013i −1.42451 + 0.493464i
\(78\) 0 0
\(79\) −4.50000 7.79423i −0.506290 0.876919i −0.999974 0.00727784i \(-0.997683\pi\)
0.493684 0.869641i \(-0.335650\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 3.00000 0.325396
\(86\) 0 0
\(87\) −5.00000 + 8.66025i −0.536056 + 0.928477i
\(88\) 0 0
\(89\) 1.50000 + 2.59808i 0.159000 + 0.275396i 0.934508 0.355942i \(-0.115840\pi\)
−0.775509 + 0.631337i \(0.782506\pi\)
\(90\) 0 0
\(91\) 4.00000 + 3.46410i 0.419314 + 0.363137i
\(92\) 0 0
\(93\) −5.50000 9.52628i −0.570323 0.987829i
\(94\) 0 0
\(95\) −1.50000 + 2.59808i −0.153897 + 0.266557i
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) 10.0000 1.00504
\(100\) 0 0
\(101\) 5.50000 9.52628i 0.547270 0.947900i −0.451190 0.892428i \(-0.649000\pi\)
0.998460 0.0554722i \(-0.0176664\pi\)
\(102\) 0 0
\(103\) 0.500000 + 0.866025i 0.0492665 + 0.0853320i 0.889607 0.456727i \(-0.150978\pi\)
−0.840341 + 0.542059i \(0.817645\pi\)
\(104\) 0 0
\(105\) −2.00000 1.73205i −0.195180 0.169031i
\(106\) 0 0
\(107\) 6.50000 + 11.2583i 0.628379 + 1.08838i 0.987877 + 0.155238i \(0.0496145\pi\)
−0.359498 + 0.933146i \(0.617052\pi\)
\(108\) 0 0
\(109\) −8.50000 + 14.7224i −0.814152 + 1.41015i 0.0957826 + 0.995402i \(0.469465\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(110\) 0 0
\(111\) −7.00000 −0.664411
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) −0.500000 + 0.866025i −0.0466252 + 0.0807573i
\(116\) 0 0
\(117\) −2.00000 3.46410i −0.184900 0.320256i
\(118\) 0 0
\(119\) −7.50000 + 2.59808i −0.687524 + 0.238165i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 0 0
\(123\) −0.500000 + 0.866025i −0.0450835 + 0.0780869i
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) 0 0
\(129\) 4.00000 6.92820i 0.352180 0.609994i
\(130\) 0 0
\(131\) −1.50000 2.59808i −0.131056 0.226995i 0.793028 0.609185i \(-0.208503\pi\)
−0.924084 + 0.382190i \(0.875170\pi\)
\(132\) 0 0
\(133\) 1.50000 7.79423i 0.130066 0.675845i
\(134\) 0 0
\(135\) 2.50000 + 4.33013i 0.215166 + 0.372678i
\(136\) 0 0
\(137\) −4.50000 + 7.79423i −0.384461 + 0.665906i −0.991694 0.128618i \(-0.958946\pi\)
0.607233 + 0.794524i \(0.292279\pi\)
\(138\) 0 0
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 7.00000 0.589506
\(142\) 0 0
\(143\) −5.00000 + 8.66025i −0.418121 + 0.724207i
\(144\) 0 0
\(145\) −5.00000 8.66025i −0.415227 0.719195i
\(146\) 0 0
\(147\) 6.50000 + 2.59808i 0.536111 + 0.214286i
\(148\) 0 0
\(149\) 3.50000 + 6.06218i 0.286731 + 0.496633i 0.973028 0.230689i \(-0.0740980\pi\)
−0.686296 + 0.727322i \(0.740765\pi\)
\(150\) 0 0
\(151\) 2.50000 4.33013i 0.203447 0.352381i −0.746190 0.665733i \(-0.768119\pi\)
0.949637 + 0.313353i \(0.101452\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 11.0000 0.883541
\(156\) 0 0
\(157\) 1.50000 2.59808i 0.119713 0.207349i −0.799941 0.600079i \(-0.795136\pi\)
0.919654 + 0.392730i \(0.128469\pi\)
\(158\) 0 0
\(159\) −5.50000 9.52628i −0.436178 0.755483i
\(160\) 0 0
\(161\) 0.500000 2.59808i 0.0394055 0.204757i
\(162\) 0 0
\(163\) 8.50000 + 14.7224i 0.665771 + 1.15315i 0.979076 + 0.203497i \(0.0652307\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) 0 0
\(165\) 2.50000 4.33013i 0.194625 0.337100i
\(166\) 0 0
\(167\) 16.0000 1.23812 0.619059 0.785345i \(-0.287514\pi\)
0.619059 + 0.785345i \(0.287514\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −3.00000 + 5.19615i −0.229416 + 0.397360i
\(172\) 0 0
\(173\) 10.5000 + 18.1865i 0.798300 + 1.38270i 0.920722 + 0.390218i \(0.127601\pi\)
−0.122422 + 0.992478i \(0.539066\pi\)
\(174\) 0 0
\(175\) −10.0000 + 3.46410i −0.755929 + 0.261861i
\(176\) 0 0
\(177\) −3.50000 6.06218i −0.263076 0.455661i
\(178\) 0 0
\(179\) −3.50000 + 6.06218i −0.261602 + 0.453108i −0.966668 0.256034i \(-0.917584\pi\)
0.705066 + 0.709142i \(0.250918\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) 1.00000 0.0739221
\(184\) 0 0
\(185\) 3.50000 6.06218i 0.257325 0.445700i
\(186\) 0 0
\(187\) −7.50000 12.9904i −0.548454 0.949951i
\(188\) 0 0
\(189\) −10.0000 8.66025i −0.727393 0.629941i
\(190\) 0 0
\(191\) −0.500000 0.866025i −0.0361787 0.0626634i 0.847369 0.531004i \(-0.178185\pi\)
−0.883548 + 0.468341i \(0.844852\pi\)
\(192\) 0 0
\(193\) −8.50000 + 14.7224i −0.611843 + 1.05974i 0.379086 + 0.925361i \(0.376238\pi\)
−0.990930 + 0.134382i \(0.957095\pi\)
\(194\) 0 0
\(195\) −2.00000 −0.143223
\(196\) 0 0
\(197\) 26.0000 1.85242 0.926212 0.377004i \(-0.123046\pi\)
0.926212 + 0.377004i \(0.123046\pi\)
\(198\) 0 0
\(199\) 10.5000 18.1865i 0.744325 1.28921i −0.206184 0.978513i \(-0.566105\pi\)
0.950509 0.310696i \(-0.100562\pi\)
\(200\) 0 0
\(201\) 3.50000 + 6.06218i 0.246871 + 0.427593i
\(202\) 0 0
\(203\) 20.0000 + 17.3205i 1.40372 + 1.21566i
\(204\) 0 0
\(205\) −0.500000 0.866025i −0.0349215 0.0604858i
\(206\) 0 0
\(207\) −1.00000 + 1.73205i −0.0695048 + 0.120386i
\(208\) 0 0
\(209\) 15.0000 1.03757
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 0 0
\(213\) −6.00000 + 10.3923i −0.411113 + 0.712069i
\(214\) 0 0
\(215\) 4.00000 + 6.92820i 0.272798 + 0.472500i
\(216\) 0 0
\(217\) −27.5000 + 9.52628i −1.86682 + 0.646686i
\(218\) 0 0
\(219\) −2.50000 4.33013i −0.168934 0.292603i
\(220\) 0 0
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) 0 0
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 0 0
\(225\) 8.00000 0.533333
\(226\) 0 0
\(227\) 4.50000 7.79423i 0.298675 0.517321i −0.677158 0.735838i \(-0.736789\pi\)
0.975833 + 0.218517i \(0.0701218\pi\)
\(228\) 0 0
\(229\) 13.5000 + 23.3827i 0.892105 + 1.54517i 0.837347 + 0.546672i \(0.184105\pi\)
0.0547581 + 0.998500i \(0.482561\pi\)
\(230\) 0 0
\(231\) −2.50000 + 12.9904i −0.164488 + 0.854704i
\(232\) 0 0
\(233\) −6.50000 11.2583i −0.425829 0.737558i 0.570668 0.821181i \(-0.306684\pi\)
−0.996497 + 0.0836229i \(0.973351\pi\)
\(234\) 0 0
\(235\) −3.50000 + 6.06218i −0.228315 + 0.395453i
\(236\) 0 0
\(237\) −9.00000 −0.584613
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) −9.50000 + 16.4545i −0.611949 + 1.05993i 0.378963 + 0.925412i \(0.376281\pi\)
−0.990912 + 0.134515i \(0.957053\pi\)
\(242\) 0 0
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 0 0
\(245\) −5.50000 + 4.33013i −0.351382 + 0.276642i
\(246\) 0 0
\(247\) −3.00000 5.19615i −0.190885 0.330623i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 5.00000 0.314347
\(254\) 0 0
\(255\) 1.50000 2.59808i 0.0939336 0.162698i
\(256\) 0 0
\(257\) 3.50000 + 6.06218i 0.218324 + 0.378148i 0.954296 0.298864i \(-0.0966077\pi\)
−0.735972 + 0.677012i \(0.763274\pi\)
\(258\) 0 0
\(259\) −3.50000 + 18.1865i −0.217479 + 1.13006i
\(260\) 0 0
\(261\) −10.0000 17.3205i −0.618984 1.07211i
\(262\) 0 0
\(263\) −9.50000 + 16.4545i −0.585795 + 1.01463i 0.408981 + 0.912543i \(0.365884\pi\)
−0.994776 + 0.102084i \(0.967449\pi\)
\(264\) 0 0
\(265\) 11.0000 0.675725
\(266\) 0 0
\(267\) 3.00000 0.183597
\(268\) 0 0
\(269\) −5.50000 + 9.52628i −0.335341 + 0.580828i −0.983550 0.180635i \(-0.942185\pi\)
0.648209 + 0.761462i \(0.275518\pi\)
\(270\) 0 0
\(271\) 12.5000 + 21.6506i 0.759321 + 1.31518i 0.943197 + 0.332233i \(0.107802\pi\)
−0.183876 + 0.982949i \(0.558865\pi\)
\(272\) 0 0
\(273\) 5.00000 1.73205i 0.302614 0.104828i
\(274\) 0 0
\(275\) −10.0000 17.3205i −0.603023 1.04447i
\(276\) 0 0
\(277\) −11.5000 + 19.9186i −0.690968 + 1.19679i 0.280553 + 0.959839i \(0.409482\pi\)
−0.971521 + 0.236953i \(0.923851\pi\)
\(278\) 0 0
\(279\) 22.0000 1.31711
\(280\) 0 0
\(281\) −14.0000 −0.835170 −0.417585 0.908638i \(-0.637123\pi\)
−0.417585 + 0.908638i \(0.637123\pi\)
\(282\) 0 0
\(283\) −8.50000 + 14.7224i −0.505273 + 0.875158i 0.494709 + 0.869059i \(0.335275\pi\)
−0.999981 + 0.00609896i \(0.998059\pi\)
\(284\) 0 0
\(285\) 1.50000 + 2.59808i 0.0888523 + 0.153897i
\(286\) 0 0
\(287\) 2.00000 + 1.73205i 0.118056 + 0.102240i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) 1.00000 1.73205i 0.0586210 0.101535i
\(292\) 0 0
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 0 0
\(295\) 7.00000 0.407556
\(296\) 0 0
\(297\) 12.5000 21.6506i 0.725324 1.25630i
\(298\) 0 0
\(299\) −1.00000 1.73205i −0.0578315 0.100167i
\(300\) 0 0
\(301\) −16.0000 13.8564i −0.922225 0.798670i
\(302\) 0 0
\(303\) −5.50000 9.52628i −0.315967 0.547270i
\(304\) 0 0
\(305\) −0.500000 + 0.866025i −0.0286299 + 0.0495885i
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) 1.00000 0.0568880
\(310\) 0 0
\(311\) 0.500000 0.866025i 0.0283524 0.0491078i −0.851501 0.524353i \(-0.824307\pi\)
0.879853 + 0.475245i \(0.157641\pi\)
\(312\) 0 0
\(313\) 5.50000 + 9.52628i 0.310878 + 0.538457i 0.978553 0.205996i \(-0.0660435\pi\)
−0.667674 + 0.744453i \(0.732710\pi\)
\(314\) 0 0
\(315\) 5.00000 1.73205i 0.281718 0.0975900i
\(316\) 0 0
\(317\) −8.50000 14.7224i −0.477408 0.826894i 0.522257 0.852788i \(-0.325090\pi\)
−0.999665 + 0.0258939i \(0.991757\pi\)
\(318\) 0 0
\(319\) −25.0000 + 43.3013i −1.39973 + 2.42441i
\(320\) 0 0
\(321\) 13.0000 0.725589
\(322\) 0 0
\(323\) 9.00000 0.500773
\(324\) 0 0
\(325\) −4.00000 + 6.92820i −0.221880 + 0.384308i
\(326\) 0 0
\(327\) 8.50000 + 14.7224i 0.470051 + 0.814152i
\(328\) 0 0
\(329\) 3.50000 18.1865i 0.192961 1.00266i
\(330\) 0 0
\(331\) 1.50000 + 2.59808i 0.0824475 + 0.142803i 0.904301 0.426896i \(-0.140393\pi\)
−0.821853 + 0.569699i \(0.807060\pi\)
\(332\) 0 0
\(333\) 7.00000 12.1244i 0.383598 0.664411i
\(334\) 0 0
\(335\) −7.00000 −0.382451
\(336\) 0 0
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) 0 0
\(339\) 3.00000 5.19615i 0.162938 0.282216i
\(340\) 0 0
\(341\) −27.5000 47.6314i −1.48921 2.57938i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 0.500000 + 0.866025i 0.0269191 + 0.0466252i
\(346\) 0 0
\(347\) 4.50000 7.79423i 0.241573 0.418416i −0.719590 0.694399i \(-0.755670\pi\)
0.961162 + 0.275983i \(0.0890035\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) −10.0000 −0.533761
\(352\) 0 0
\(353\) 4.50000 7.79423i 0.239511 0.414845i −0.721063 0.692869i \(-0.756346\pi\)
0.960574 + 0.278024i \(0.0896796\pi\)
\(354\) 0 0
\(355\) −6.00000 10.3923i −0.318447 0.551566i
\(356\) 0 0
\(357\) −1.50000 + 7.79423i −0.0793884 + 0.412514i
\(358\) 0 0
\(359\) 14.5000 + 25.1147i 0.765281 + 1.32551i 0.940098 + 0.340904i \(0.110733\pi\)
−0.174817 + 0.984601i \(0.555933\pi\)
\(360\) 0 0
\(361\) 5.00000 8.66025i 0.263158 0.455803i
\(362\) 0 0
\(363\) −14.0000 −0.734809
\(364\) 0 0
\(365\) 5.00000 0.261712
\(366\) 0 0
\(367\) 7.50000 12.9904i 0.391497 0.678092i −0.601150 0.799136i \(-0.705291\pi\)
0.992647 + 0.121044i \(0.0386241\pi\)
\(368\) 0 0
\(369\) −1.00000 1.73205i −0.0520579 0.0901670i
\(370\) 0 0
\(371\) −27.5000 + 9.52628i −1.42773 + 0.494580i
\(372\) 0 0
\(373\) −9.50000 16.4545i −0.491891 0.851981i 0.508065 0.861319i \(-0.330361\pi\)
−0.999956 + 0.00933789i \(0.997028\pi\)
\(374\) 0 0
\(375\) 4.50000 7.79423i 0.232379 0.402492i
\(376\) 0 0
\(377\) 20.0000 1.03005
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) 2.00000 3.46410i 0.102463 0.177471i
\(382\) 0 0
\(383\) 13.5000 + 23.3827i 0.689818 + 1.19480i 0.971897 + 0.235408i \(0.0756427\pi\)
−0.282079 + 0.959391i \(0.591024\pi\)
\(384\) 0 0
\(385\) −10.0000 8.66025i −0.509647 0.441367i
\(386\) 0 0
\(387\) 8.00000 + 13.8564i 0.406663 + 0.704361i
\(388\) 0 0
\(389\) −1.50000 + 2.59808i −0.0760530 + 0.131728i −0.901544 0.432688i \(-0.857565\pi\)
0.825491 + 0.564416i \(0.190898\pi\)
\(390\) 0 0
\(391\) 3.00000 0.151717
\(392\) 0 0
\(393\) −3.00000 −0.151330
\(394\) 0 0
\(395\) 4.50000 7.79423i 0.226420 0.392170i
\(396\) 0 0
\(397\) −14.5000 25.1147i −0.727734 1.26047i −0.957839 0.287307i \(-0.907240\pi\)
0.230105 0.973166i \(-0.426093\pi\)
\(398\) 0 0
\(399\) −6.00000 5.19615i −0.300376 0.260133i
\(400\) 0 0
\(401\) 6.50000 + 11.2583i 0.324595 + 0.562214i 0.981430 0.191820i \(-0.0614388\pi\)
−0.656836 + 0.754034i \(0.728105\pi\)
\(402\) 0 0
\(403\) −11.0000 + 19.0526i −0.547949 + 0.949076i
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −35.0000 −1.73489
\(408\) 0 0
\(409\) −17.5000 + 30.3109i −0.865319 + 1.49878i 0.00141047 + 0.999999i \(0.499551\pi\)
−0.866730 + 0.498778i \(0.833782\pi\)
\(410\) 0 0
\(411\) 4.50000 + 7.79423i 0.221969 + 0.384461i
\(412\) 0 0
\(413\) −17.5000 + 6.06218i −0.861119 + 0.298300i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −10.0000 + 17.3205i −0.489702 + 0.848189i
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −18.0000 −0.877266 −0.438633 0.898666i \(-0.644537\pi\)
−0.438633 + 0.898666i \(0.644537\pi\)
\(422\) 0 0
\(423\) −7.00000 + 12.1244i −0.340352 + 0.589506i
\(424\) 0 0
\(425\) −6.00000 10.3923i −0.291043 0.504101i
\(426\) 0 0
\(427\) 0.500000 2.59808i 0.0241967 0.125730i
\(428\) 0 0
\(429\) 5.00000 + 8.66025i 0.241402 + 0.418121i
\(430\) 0 0
\(431\) 17.5000 30.3109i 0.842945 1.46002i −0.0444483 0.999012i \(-0.514153\pi\)
0.887394 0.461012i \(-0.152514\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) −10.0000 −0.479463
\(436\) 0 0
\(437\) −1.50000 + 2.59808i −0.0717547 + 0.124283i
\(438\) 0 0
\(439\) 3.50000 + 6.06218i 0.167046 + 0.289332i 0.937380 0.348309i \(-0.113244\pi\)
−0.770334 + 0.637641i \(0.779911\pi\)
\(440\) 0 0
\(441\) −11.0000 + 8.66025i −0.523810 + 0.412393i
\(442\) 0 0
\(443\) −19.5000 33.7750i −0.926473 1.60470i −0.789175 0.614168i \(-0.789492\pi\)
−0.137298 0.990530i \(-0.543842\pi\)
\(444\) 0 0
\(445\) −1.50000 + 2.59808i −0.0711068 + 0.123161i
\(446\) 0 0
\(447\) 7.00000 0.331089
\(448\) 0 0
\(449\) 22.0000 1.03824 0.519122 0.854700i \(-0.326259\pi\)
0.519122 + 0.854700i \(0.326259\pi\)
\(450\) 0 0
\(451\) −2.50000 + 4.33013i −0.117720 + 0.203898i
\(452\) 0 0
\(453\) −2.50000 4.33013i −0.117460 0.203447i
\(454\) 0 0
\(455\) −1.00000 + 5.19615i −0.0468807 + 0.243599i
\(456\) 0 0
\(457\) −2.50000 4.33013i −0.116945 0.202555i 0.801611 0.597847i \(-0.203977\pi\)
−0.918556 + 0.395292i \(0.870643\pi\)
\(458\) 0 0
\(459\) 7.50000 12.9904i 0.350070 0.606339i
\(460\) 0 0
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 0 0
\(465\) 5.50000 9.52628i 0.255056 0.441771i
\(466\) 0 0
\(467\) 16.5000 + 28.5788i 0.763529 + 1.32247i 0.941021 + 0.338349i \(0.109868\pi\)
−0.177492 + 0.984122i \(0.556798\pi\)
\(468\) 0 0
\(469\) 17.5000 6.06218i 0.808075 0.279925i
\(470\) 0 0
\(471\) −1.50000 2.59808i −0.0691164 0.119713i
\(472\) 0 0
\(473\) 20.0000 34.6410i 0.919601 1.59280i
\(474\) 0 0
\(475\) 12.0000 0.550598
\(476\) 0 0
\(477\) 22.0000 1.00731
\(478\) 0 0
\(479\) 8.50000 14.7224i 0.388375 0.672685i −0.603856 0.797093i \(-0.706370\pi\)
0.992231 + 0.124408i \(0.0397032\pi\)
\(480\) 0 0
\(481\) 7.00000 + 12.1244i 0.319173 + 0.552823i
\(482\) 0 0
\(483\) −2.00000 1.73205i −0.0910032 0.0788110i
\(484\) 0 0
\(485\) 1.00000 + 1.73205i 0.0454077 + 0.0786484i
\(486\) 0 0
\(487\) 17.5000 30.3109i 0.793001 1.37352i −0.131100 0.991369i \(-0.541851\pi\)
0.924101 0.382148i \(-0.124816\pi\)
\(488\) 0 0
\(489\) 17.0000 0.768767
\(490\) 0 0
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) 0 0
\(493\) −15.0000 + 25.9808i −0.675566 + 1.17011i
\(494\) 0 0
\(495\) 5.00000 + 8.66025i 0.224733 + 0.389249i
\(496\) 0 0
\(497\) 24.0000 + 20.7846i 1.07655 + 0.932317i
\(498\) 0 0
\(499\) 1.50000 + 2.59808i 0.0671492 + 0.116306i 0.897645 0.440719i \(-0.145276\pi\)
−0.830496 + 0.557024i \(0.811943\pi\)
\(500\) 0 0
\(501\) 8.00000 13.8564i 0.357414 0.619059i
\(502\) 0 0
\(503\) 40.0000 1.78351 0.891756 0.452517i \(-0.149474\pi\)
0.891756 + 0.452517i \(0.149474\pi\)
\(504\) 0 0
\(505\) 11.0000 0.489494
\(506\) 0 0
\(507\) −4.50000 + 7.79423i −0.199852 + 0.346154i
\(508\) 0 0
\(509\) −2.50000 4.33013i −0.110811 0.191930i 0.805287 0.592886i \(-0.202011\pi\)
−0.916097 + 0.400956i \(0.868678\pi\)
\(510\) 0 0
\(511\) −12.5000 + 4.33013i −0.552967 + 0.191554i
\(512\) 0 0
\(513\) 7.50000 + 12.9904i 0.331133 + 0.573539i
\(514\) 0 0
\(515\) −0.500000 + 0.866025i −0.0220326 + 0.0381616i
\(516\) 0 0
\(517\) 35.0000 1.53930
\(518\) 0 0
\(519\) 21.0000 0.921798
\(520\) 0 0
\(521\) 13.5000 23.3827i 0.591446 1.02441i −0.402592 0.915379i \(-0.631891\pi\)
0.994038 0.109035i \(-0.0347759\pi\)
\(522\) 0 0
\(523\) −19.5000 33.7750i −0.852675 1.47688i −0.878785 0.477218i \(-0.841645\pi\)
0.0261094 0.999659i \(-0.491688\pi\)
\(524\) 0 0
\(525\) −2.00000 + 10.3923i −0.0872872 + 0.453557i
\(526\) 0 0
\(527\) −16.5000 28.5788i −0.718751 1.24491i
\(528\) 0 0
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) 0 0
\(531\) 14.0000 0.607548
\(532\) 0 0
\(533\) 2.00000 0.0866296
\(534\) 0 0
\(535\) −6.50000 + 11.2583i −0.281020 + 0.486740i
\(536\) 0 0
\(537\) 3.50000 + 6.06218i 0.151036 + 0.261602i
\(538\) 0 0
\(539\) 32.5000 + 12.9904i 1.39987 + 0.559535i
\(540\) 0 0
\(541\) −5.50000 9.52628i −0.236463 0.409567i 0.723234 0.690604i \(-0.242655\pi\)
−0.959697 + 0.281037i \(0.909322\pi\)
\(542\) 0 0
\(543\) −11.0000 + 19.0526i −0.472055 + 0.817624i
\(544\) 0 0
\(545\) −17.0000 −0.728200
\(546\) 0 0
\(547\) −4.00000 −0.171028 −0.0855138 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(548\) 0 0
\(549\) −1.00000 + 1.73205i −0.0426790 + 0.0739221i
\(550\) 0 0
\(551\) −15.0000 25.9808i −0.639021 1.10682i
\(552\) 0 0
\(553\) −4.50000 + 23.3827i −0.191359 + 0.994333i
\(554\) 0 0
\(555\) −3.50000 6.06218i −0.148567 0.257325i
\(556\) 0 0
\(557\) −16.5000 + 28.5788i −0.699127 + 1.21092i 0.269642 + 0.962961i \(0.413095\pi\)
−0.968769 + 0.247964i \(0.920239\pi\)
\(558\) 0 0
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) −15.0000 −0.633300
\(562\) 0 0
\(563\) 12.5000 21.6506i 0.526812 0.912465i −0.472700 0.881224i \(-0.656720\pi\)
0.999512 0.0312419i \(-0.00994622\pi\)
\(564\) 0 0
\(565\) 3.00000 + 5.19615i 0.126211 + 0.218604i
\(566\) 0 0
\(567\) 2.50000 0.866025i 0.104990 0.0363696i
\(568\) 0 0
\(569\) −7.50000 12.9904i −0.314416 0.544585i 0.664897 0.746935i \(-0.268475\pi\)
−0.979313 + 0.202350i \(0.935142\pi\)
\(570\) 0 0
\(571\) −7.50000 + 12.9904i −0.313865 + 0.543631i −0.979196 0.202919i \(-0.934957\pi\)
0.665330 + 0.746549i \(0.268291\pi\)
\(572\) 0 0
\(573\) −1.00000 −0.0417756
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) 0 0
\(577\) 19.5000 33.7750i 0.811796 1.40607i −0.0998105 0.995006i \(-0.531824\pi\)
0.911606 0.411065i \(-0.134843\pi\)
\(578\) 0 0
\(579\) 8.50000 + 14.7224i 0.353248 + 0.611843i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −27.5000 47.6314i −1.13893 1.97269i
\(584\) 0 0
\(585\) 2.00000 3.46410i 0.0826898 0.143223i
\(586\) 0 0
\(587\) 36.0000 1.48588 0.742940 0.669359i \(-0.233431\pi\)
0.742940 + 0.669359i \(0.233431\pi\)
\(588\) 0 0
\(589\) 33.0000 1.35974
\(590\) 0 0
\(591\) 13.0000 22.5167i 0.534749 0.926212i
\(592\) 0 0
\(593\) −2.50000 4.33013i −0.102663 0.177817i 0.810118 0.586267i \(-0.199403\pi\)
−0.912781 + 0.408450i \(0.866070\pi\)
\(594\) 0 0
\(595\) −6.00000 5.19615i −0.245976 0.213021i
\(596\) 0 0
\(597\) −10.5000 18.1865i −0.429736 0.744325i
\(598\) 0 0
\(599\) −4.50000 + 7.79423i −0.183865 + 0.318464i −0.943193 0.332244i \(-0.892194\pi\)
0.759328 + 0.650708i \(0.225528\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) −14.0000 −0.570124
\(604\) 0 0
\(605\) 7.00000 12.1244i 0.284590 0.492925i
\(606\) 0 0
\(607\) −17.5000 30.3109i −0.710303 1.23028i −0.964743 0.263193i \(-0.915225\pi\)
0.254440 0.967088i \(-0.418109\pi\)
\(608\) 0 0
\(609\) 25.0000 8.66025i 1.01305 0.350931i
\(610\) 0 0
\(611\) −7.00000 12.1244i −0.283190 0.490499i
\(612\) 0 0
\(613\) −13.5000 + 23.3827i −0.545260 + 0.944418i 0.453331 + 0.891342i \(0.350236\pi\)
−0.998591 + 0.0530754i \(0.983098\pi\)
\(614\) 0 0
\(615\) −1.00000 −0.0403239
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 0 0
\(619\) 5.50000 9.52628i 0.221064 0.382893i −0.734068 0.679076i \(-0.762380\pi\)
0.955131 + 0.296183i \(0.0957138\pi\)
\(620\) 0 0
\(621\) 2.50000 + 4.33013i 0.100322 + 0.173762i
\(622\) 0 0
\(623\) 1.50000 7.79423i 0.0600962 0.312269i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 0 0
\(627\) 7.50000 12.9904i 0.299521 0.518786i
\(628\) 0 0
\(629\) −21.0000 −0.837325
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) −6.00000 + 10.3923i −0.238479 + 0.413057i
\(634\) 0 0
\(635\) 2.00000 + 3.46410i 0.0793676 + 0.137469i
\(636\) 0 0
\(637\) −2.00000 13.8564i −0.0792429 0.549011i
\(638\) 0 0
\(639\) −12.0000 20.7846i −0.474713 0.822226i
\(640\) 0 0
\(641\) 7.50000 12.9904i 0.296232 0.513089i −0.679039 0.734103i \(-0.737603\pi\)
0.975271 + 0.221013i \(0.0709364\pi\)
\(642\) 0 0
\(643\) −36.0000 −1.41970 −0.709851 0.704352i \(-0.751238\pi\)
−0.709851 + 0.704352i \(0.751238\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) 0 0
\(647\) 9.50000 16.4545i 0.373484 0.646892i −0.616615 0.787265i \(-0.711497\pi\)
0.990099 + 0.140372i \(0.0448299\pi\)
\(648\) 0 0
\(649\) −17.5000 30.3109i −0.686935 1.18981i
\(650\) 0 0
\(651\) −5.50000 + 28.5788i −0.215562 + 1.12009i
\(652\) 0 0
\(653\) −4.50000 7.79423i −0.176099 0.305012i 0.764442 0.644692i \(-0.223014\pi\)
−0.940541 + 0.339680i \(0.889681\pi\)
\(654\) 0 0
\(655\) 1.50000 2.59808i 0.0586098 0.101515i
\(656\) 0 0
\(657\) 10.0000 0.390137
\(658\) 0 0
\(659\) −4.00000 −0.155818 −0.0779089 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 0 0
\(661\) −25.5000 + 44.1673i −0.991835 + 1.71791i −0.385476 + 0.922718i \(0.625963\pi\)
−0.606359 + 0.795191i \(0.707371\pi\)
\(662\) 0 0
\(663\) 3.00000 + 5.19615i 0.116510 + 0.201802i
\(664\) 0 0
\(665\) 7.50000 2.59808i 0.290838 0.100749i
\(666\) 0 0
\(667\) −5.00000 8.66025i −0.193601 0.335326i
\(668\) 0 0
\(669\) 4.00000 6.92820i 0.154649 0.267860i
\(670\) 0 0
\(671\) 5.00000 0.193023
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 0 0
\(675\) 10.0000 17.3205i 0.384900 0.666667i
\(676\) 0 0
\(677\) −7.50000 12.9904i −0.288248 0.499261i 0.685143 0.728408i \(-0.259740\pi\)
−0.973392 + 0.229147i \(0.926406\pi\)
\(678\) 0 0
\(679\) −4.00000 3.46410i −0.153506 0.132940i
\(680\) 0 0
\(681\) −4.50000 7.79423i −0.172440 0.298675i
\(682\) 0 0
\(683\) −15.5000 + 26.8468i −0.593091 + 1.02726i 0.400722 + 0.916200i \(0.368759\pi\)
−0.993813 + 0.111064i \(0.964574\pi\)
\(684\) 0 0
\(685\) −9.00000 −0.343872
\(686\) 0 0
\(687\) 27.0000 1.03011
\(688\) 0 0
\(689\) −11.0000 + 19.0526i −0.419067 + 0.725845i
\(690\) 0 0
\(691\) −4.50000 7.79423i −0.171188 0.296506i 0.767647 0.640872i \(-0.221427\pi\)
−0.938835 + 0.344366i \(0.888094\pi\)
\(692\) 0 0
\(693\) −20.0000 17.3205i −0.759737 0.657952i
\(694\) 0 0
\(695\) −10.0000 17.3205i −0.379322 0.657004i
\(696\) 0 0
\(697\) −1.50000 + 2.59808i −0.0568166 + 0.0984092i
\(698\) 0 0
\(699\) −13.0000 −0.491705
\(700\) 0 0
\(701\) 50.0000 1.88847 0.944237 0.329267i \(-0.106802\pi\)
0.944237 + 0.329267i \(0.106802\pi\)
\(702\) 0 0
\(703\) 10.5000 18.1865i 0.396015 0.685918i
\(704\) 0 0
\(705\) 3.50000 + 6.06218i 0.131818 + 0.228315i
\(706\) 0 0
\(707\) −27.5000 + 9.52628i −1.03424 + 0.358273i
\(708\) 0 0
\(709\) 9.50000 + 16.4545i 0.356780 + 0.617961i 0.987421 0.158114i \(-0.0505412\pi\)
−0.630641 + 0.776075i \(0.717208\pi\)
\(710\) 0 0
\(711\) 9.00000 15.5885i 0.337526 0.584613i
\(712\) 0 0
\(713\) 11.0000 0.411953
\(714\) 0 0
\(715\) −10.0000 −0.373979
\(716\) 0 0
\(717\) −8.00000 + 13.8564i −0.298765 + 0.517477i
\(718\) 0 0
\(719\) 5.50000 + 9.52628i 0.205115 + 0.355270i 0.950169 0.311734i \(-0.100910\pi\)
−0.745054 + 0.667004i \(0.767576\pi\)
\(720\) 0 0
\(721\) 0.500000 2.59808i 0.0186210 0.0967574i
\(722\) 0 0
\(723\) 9.50000 + 16.4545i 0.353309 + 0.611949i
\(724\) 0 0
\(725\) −20.0000 + 34.6410i −0.742781 + 1.28654i
\(726\) 0 0
\(727\) 32.0000 1.18681 0.593407 0.804902i \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) 0 0
\(733\) −1.50000 2.59808i −0.0554038 0.0959621i 0.836993 0.547213i \(-0.184311\pi\)
−0.892397 + 0.451251i \(0.850978\pi\)
\(734\) 0 0
\(735\) 1.00000 + 6.92820i 0.0368856 + 0.255551i
\(736\) 0 0
\(737\) 17.5000 + 30.3109i 0.644621 + 1.11652i
\(738\) 0 0
\(739\) 7.50000 12.9904i 0.275892 0.477859i −0.694468 0.719524i \(-0.744360\pi\)
0.970360 + 0.241665i \(0.0776935\pi\)
\(740\) 0 0
\(741\) −6.00000 −0.220416
\(742\) 0 0
\(743\) −48.0000 −1.76095 −0.880475 0.474093i \(-0.842776\pi\)
−0.880475 + 0.474093i \(0.842776\pi\)
\(744\) 0 0
\(745\) −3.50000 + 6.06218i −0.128230 + 0.222101i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.50000 33.7750i 0.237505 1.23411i
\(750\) 0 0
\(751\) 3.50000 + 6.06218i 0.127717 + 0.221212i 0.922792 0.385299i \(-0.125902\pi\)
−0.795075 + 0.606511i \(0.792568\pi\)
\(752\) 0 0
\(753\) 12.0000 20.7846i 0.437304 0.757433i
\(754\) 0 0
\(755\) 5.00000 0.181969
\(756\) 0 0
\(757\) −38.0000 −1.38113 −0.690567 0.723269i \(-0.742639\pi\)
−0.690567 + 0.723269i \(0.742639\pi\)
\(758\) 0 0
\(759\) 2.50000 4.33013i 0.0907443 0.157174i
\(760\) 0 0
\(761\) 24.5000 + 42.4352i 0.888124 + 1.53828i 0.842090 + 0.539337i \(0.181325\pi\)
0.0460340 + 0.998940i \(0.485342\pi\)
\(762\) 0 0
\(763\) 42.5000 14.7224i 1.53860 0.532988i
\(764\) 0 0
\(765\) 3.00000 + 5.19615i 0.108465 + 0.187867i
\(766\) 0 0
\(767\) −7.00000 + 12.1244i −0.252755 + 0.437785i
\(768\) 0 0
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) 7.00000 0.252099
\(772\) 0 0
\(773\) 9.50000 16.4545i 0.341691 0.591827i −0.643056 0.765819i \(-0.722334\pi\)
0.984747 + 0.173993i \(0.0556670\pi\)
\(774\) 0 0
\(775\) −22.0000 38.1051i −0.790263 1.36878i
\(776\) 0 0
\(777\) 14.0000 + 12.1244i 0.502247 + 0.434959i
\(778\) 0 0
\(779\) −1.50000 2.59808i −0.0537431 0.0930857i
\(780\) 0 0
\(781\) −30.0000 + 51.9615i −1.07348 + 1.85933i
\(782\) 0 0
\(783\) −50.0000 −1.78685
\(784\) 0 0
\(785\) 3.00000 0.107075
\(786\) 0 0
\(787\) 23.5000 40.7032i 0.837685 1.45091i −0.0541413 0.998533i \(-0.517242\pi\)
0.891826 0.452379i \(-0.149425\pi\)
\(788\) 0 0
\(789\) 9.50000 + 16.4545i 0.338209 + 0.585795i
\(790\) 0 0
\(791\) −12.0000 10.3923i −0.426671 0.369508i
\(792\) 0 0
\(793\) −1.00000 1.73205i −0.0355110 0.0615069i
\(794\) 0 0
\(795\) 5.50000 9.52628i 0.195065 0.337862i
\(796\) 0 0
\(797\) 2.00000 0.0708436 0.0354218 0.999372i \(-0.488723\pi\)
0.0354218