Properties

Label 448.2.p.a.255.1
Level $448$
Weight $2$
Character 448.255
Analytic conductor $3.577$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 448.p (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.57729801055\)
Analytic rank: \(1\)
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: no (minimal twist has level 112)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 255.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 448.255
Dual form 448.2.p.a.383.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 + 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 + 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-1.50000 - 0.866025i) q^{11} -1.73205i q^{15} +(-4.50000 - 2.59808i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(2.50000 - 0.866025i) q^{21} +(-7.50000 + 4.33013i) q^{23} +(-1.00000 + 1.73205i) q^{25} -5.00000 q^{27} +6.00000 q^{29} +(2.50000 - 4.33013i) q^{31} +(1.50000 - 0.866025i) q^{33} +(4.50000 + 0.866025i) q^{35} +(-2.50000 - 4.33013i) q^{37} -6.92820i q^{41} +3.46410i q^{43} +(-3.00000 - 1.73205i) q^{45} +(1.50000 + 2.59808i) q^{47} +(1.00000 + 6.92820i) q^{49} +(4.50000 - 2.59808i) q^{51} +(-4.50000 + 7.79423i) q^{53} +3.00000 q^{55} +7.00000 q^{57} +(-4.50000 + 7.79423i) q^{59} +(-7.50000 + 4.33013i) q^{61} +(1.00000 - 5.19615i) q^{63} +(4.50000 + 2.59808i) q^{67} -8.66025i q^{69} +3.46410i q^{71} +(1.50000 + 0.866025i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(1.50000 + 4.33013i) q^{77} +(4.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} +9.00000 q^{85} +(-3.00000 + 5.19615i) q^{87} +(-10.5000 + 6.06218i) q^{89} +(2.50000 + 4.33013i) q^{93} +(10.5000 + 6.06218i) q^{95} -6.92820i q^{97} -3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} - 3q^{5} - 4q^{7} + 2q^{9} + O(q^{10}) \) \( 2q - q^{3} - 3q^{5} - 4q^{7} + 2q^{9} - 3q^{11} - 9q^{17} - 7q^{19} + 5q^{21} - 15q^{23} - 2q^{25} - 10q^{27} + 12q^{29} + 5q^{31} + 3q^{33} + 9q^{35} - 5q^{37} - 6q^{45} + 3q^{47} + 2q^{49} + 9q^{51} - 9q^{53} + 6q^{55} + 14q^{57} - 9q^{59} - 15q^{61} + 2q^{63} + 9q^{67} + 3q^{73} - 2q^{75} + 3q^{77} + 9q^{79} - q^{81} + 24q^{83} + 18q^{85} - 6q^{87} - 21q^{89} + 5q^{93} + 21q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) 0 0
\(5\) −1.50000 + 0.866025i −0.670820 + 0.387298i −0.796387 0.604787i \(-0.793258\pi\)
0.125567 + 0.992085i \(0.459925\pi\)
\(6\) 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
\(11\) −1.50000 0.866025i −0.452267 0.261116i 0.256520 0.966539i \(-0.417424\pi\)
−0.708787 + 0.705422i \(0.750757\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 1.73205i 0.447214i
\(16\) 0 0
\(17\) −4.50000 2.59808i −1.09141 0.630126i −0.157459 0.987526i \(-0.550330\pi\)
−0.933952 + 0.357400i \(0.883663\pi\)
\(18\) 0 0
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(1.53659\pi\)
\(20\) 0 0
\(21\) 2.50000 0.866025i 0.545545 0.188982i
\(22\) 0 0
\(23\) −7.50000 + 4.33013i −1.56386 + 0.902894i −0.566997 + 0.823720i \(0.691895\pi\)
−0.996861 + 0.0791743i \(0.974772\pi\)
\(24\) 0 0
\(25\) −1.00000 + 1.73205i −0.200000 + 0.346410i
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 2.50000 4.33013i 0.449013 0.777714i −0.549309 0.835619i \(-0.685109\pi\)
0.998322 + 0.0579057i \(0.0184423\pi\)
\(32\) 0 0
\(33\) 1.50000 0.866025i 0.261116 0.150756i
\(34\) 0 0
\(35\) 4.50000 + 0.866025i 0.760639 + 0.146385i
\(36\) 0 0
\(37\) −2.50000 4.33013i −0.410997 0.711868i 0.584002 0.811752i \(-0.301486\pi\)
−0.994999 + 0.0998840i \(0.968153\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.92820i 1.08200i −0.841021 0.541002i \(-0.818045\pi\)
0.841021 0.541002i \(-0.181955\pi\)
\(42\) 0 0
\(43\) 3.46410i 0.528271i 0.964486 + 0.264135i \(0.0850865\pi\)
−0.964486 + 0.264135i \(0.914913\pi\)
\(44\) 0 0
\(45\) −3.00000 1.73205i −0.447214 0.258199i
\(46\) 0 0
\(47\) 1.50000 + 2.59808i 0.218797 + 0.378968i 0.954441 0.298401i \(-0.0964533\pi\)
−0.735643 + 0.677369i \(0.763120\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) 4.50000 2.59808i 0.630126 0.363803i
\(52\) 0 0
\(53\) −4.50000 + 7.79423i −0.618123 + 1.07062i 0.371706 + 0.928351i \(0.378773\pi\)
−0.989828 + 0.142269i \(0.954560\pi\)
\(54\) 0 0
\(55\) 3.00000 0.404520
\(56\) 0 0
\(57\) 7.00000 0.927173
\(58\) 0 0
\(59\) −4.50000 + 7.79423i −0.585850 + 1.01472i 0.408919 + 0.912571i \(0.365906\pi\)
−0.994769 + 0.102151i \(0.967427\pi\)
\(60\) 0 0
\(61\) −7.50000 + 4.33013i −0.960277 + 0.554416i −0.896258 0.443533i \(-0.853725\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) 0 0
\(63\) 1.00000 5.19615i 0.125988 0.654654i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.50000 + 2.59808i 0.549762 + 0.317406i 0.749026 0.662540i \(-0.230522\pi\)
−0.199264 + 0.979946i \(0.563855\pi\)
\(68\) 0 0
\(69\) 8.66025i 1.04257i
\(70\) 0 0
\(71\) 3.46410i 0.411113i 0.978645 + 0.205557i \(0.0659005\pi\)
−0.978645 + 0.205557i \(0.934100\pi\)
\(72\) 0 0
\(73\) 1.50000 + 0.866025i 0.175562 + 0.101361i 0.585206 0.810885i \(-0.301014\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) 0 0
\(75\) −1.00000 1.73205i −0.115470 0.200000i
\(76\) 0 0
\(77\) 1.50000 + 4.33013i 0.170941 + 0.493464i
\(78\) 0 0
\(79\) 4.50000 2.59808i 0.506290 0.292306i −0.225018 0.974355i \(-0.572244\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 9.00000 0.976187
\(86\) 0 0
\(87\) −3.00000 + 5.19615i −0.321634 + 0.557086i
\(88\) 0 0
\(89\) −10.5000 + 6.06218i −1.11300 + 0.642590i −0.939604 0.342263i \(-0.888807\pi\)
−0.173394 + 0.984853i \(0.555473\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 2.50000 + 4.33013i 0.259238 + 0.449013i
\(94\) 0 0
\(95\) 10.5000 + 6.06218i 1.07728 + 0.621966i
\(96\) 0 0
\(97\) 6.92820i 0.703452i −0.936103 0.351726i \(-0.885595\pi\)
0.936103 0.351726i \(-0.114405\pi\)
\(98\) 0 0
\(99\) 3.46410i 0.348155i
\(100\) 0 0
\(101\) 4.50000 + 2.59808i 0.447767 + 0.258518i 0.706887 0.707327i \(-0.250099\pi\)
−0.259120 + 0.965845i \(0.583432\pi\)
\(102\) 0 0
\(103\) −0.500000 0.866025i −0.0492665 0.0853320i 0.840341 0.542059i \(-0.182355\pi\)
−0.889607 + 0.456727i \(0.849022\pi\)
\(104\) 0 0
\(105\) −3.00000 + 3.46410i −0.292770 + 0.338062i
\(106\) 0 0
\(107\) −4.50000 + 2.59808i −0.435031 + 0.251166i −0.701488 0.712681i \(-0.747481\pi\)
0.266456 + 0.963847i \(0.414147\pi\)
\(108\) 0 0
\(109\) 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i \(-0.656723\pi\)
0.999512 0.0312328i \(-0.00994332\pi\)
\(110\) 0 0
\(111\) 5.00000 0.474579
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 7.50000 12.9904i 0.699379 1.21136i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.50000 + 12.9904i 0.412514 + 1.19083i
\(120\) 0 0
\(121\) −4.00000 6.92820i −0.363636 0.629837i
\(122\) 0 0
\(123\) 6.00000 + 3.46410i 0.541002 + 0.312348i
\(124\) 0 0
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 3.46410i 0.307389i 0.988118 + 0.153695i \(0.0491172\pi\)
−0.988118 + 0.153695i \(0.950883\pi\)
\(128\) 0 0
\(129\) −3.00000 1.73205i −0.264135 0.152499i
\(130\) 0 0
\(131\) 10.5000 + 18.1865i 0.917389 + 1.58896i 0.803365 + 0.595487i \(0.203041\pi\)
0.114024 + 0.993478i \(0.463626\pi\)
\(132\) 0 0
\(133\) −3.50000 + 18.1865i −0.303488 + 1.57697i
\(134\) 0 0
\(135\) 7.50000 4.33013i 0.645497 0.372678i
\(136\) 0 0
\(137\) −1.50000 + 2.59808i −0.128154 + 0.221969i −0.922961 0.384893i \(-0.874238\pi\)
0.794808 + 0.606861i \(0.207572\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −9.00000 + 5.19615i −0.747409 + 0.431517i
\(146\) 0 0
\(147\) −6.50000 2.59808i −0.536111 0.214286i
\(148\) 0 0
\(149\) −4.50000 7.79423i −0.368654 0.638528i 0.620701 0.784047i \(-0.286848\pi\)
−0.989355 + 0.145519i \(0.953515\pi\)
\(150\) 0 0
\(151\) −10.5000 6.06218i −0.854478 0.493333i 0.00768132 0.999970i \(-0.497555\pi\)
−0.862159 + 0.506637i \(0.830888\pi\)
\(152\) 0 0
\(153\) 10.3923i 0.840168i
\(154\) 0 0
\(155\) 8.66025i 0.695608i
\(156\) 0 0
\(157\) −13.5000 7.79423i −1.07742 0.622047i −0.147219 0.989104i \(-0.547032\pi\)
−0.930199 + 0.367057i \(0.880365\pi\)
\(158\) 0 0
\(159\) −4.50000 7.79423i −0.356873 0.618123i
\(160\) 0 0
\(161\) 22.5000 + 4.33013i 1.77325 + 0.341262i
\(162\) 0 0
\(163\) −10.5000 + 6.06218i −0.822423 + 0.474826i −0.851251 0.524758i \(-0.824156\pi\)
0.0288280 + 0.999584i \(0.490822\pi\)
\(164\) 0 0
\(165\) −1.50000 + 2.59808i −0.116775 + 0.202260i
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) 7.00000 12.1244i 0.535303 0.927173i
\(172\) 0 0
\(173\) −7.50000 + 4.33013i −0.570214 + 0.329213i −0.757235 0.653143i \(-0.773450\pi\)
0.187021 + 0.982356i \(0.440117\pi\)
\(174\) 0 0
\(175\) 5.00000 1.73205i 0.377964 0.130931i
\(176\) 0 0
\(177\) −4.50000 7.79423i −0.338241 0.585850i
\(178\) 0 0
\(179\) −13.5000 7.79423i −1.00904 0.582568i −0.0981277 0.995174i \(-0.531285\pi\)
−0.910910 + 0.412606i \(0.864619\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i −0.966282 0.257485i \(-0.917106\pi\)
0.966282 0.257485i \(-0.0828937\pi\)
\(182\) 0 0
\(183\) 8.66025i 0.640184i
\(184\) 0 0
\(185\) 7.50000 + 4.33013i 0.551411 + 0.318357i
\(186\) 0 0
\(187\) 4.50000 + 7.79423i 0.329073 + 0.569970i
\(188\) 0 0
\(189\) 10.0000 + 8.66025i 0.727393 + 0.629941i
\(190\) 0 0
\(191\) 10.5000 6.06218i 0.759753 0.438644i −0.0694538 0.997585i \(-0.522126\pi\)
0.829207 + 0.558941i \(0.188792\pi\)
\(192\) 0 0
\(193\) 2.50000 4.33013i 0.179954 0.311689i −0.761911 0.647682i \(-0.775738\pi\)
0.941865 + 0.335993i \(0.109072\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) −5.50000 + 9.52628i −0.389885 + 0.675300i −0.992434 0.122782i \(-0.960818\pi\)
0.602549 + 0.798082i \(0.294152\pi\)
\(200\) 0 0
\(201\) −4.50000 + 2.59808i −0.317406 + 0.183254i
\(202\) 0 0
\(203\) −12.0000 10.3923i −0.842235 0.729397i
\(204\) 0 0
\(205\) 6.00000 + 10.3923i 0.419058 + 0.725830i
\(206\) 0 0
\(207\) −15.0000 8.66025i −1.04257 0.601929i
\(208\) 0 0
\(209\) 12.1244i 0.838659i
\(210\) 0 0
\(211\) 24.2487i 1.66935i −0.550743 0.834675i \(-0.685655\pi\)
0.550743 0.834675i \(-0.314345\pi\)
\(212\) 0 0
\(213\) −3.00000 1.73205i −0.205557 0.118678i
\(214\) 0 0
\(215\) −3.00000 5.19615i −0.204598 0.354375i
\(216\) 0 0
\(217\) −12.5000 + 4.33013i −0.848555 + 0.293948i
\(218\) 0 0
\(219\) −1.50000 + 0.866025i −0.101361 + 0.0585206i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 0 0
\(225\) −4.00000 −0.266667
\(226\) 0 0
\(227\) −10.5000 + 18.1865i −0.696909 + 1.20708i 0.272623 + 0.962121i \(0.412109\pi\)
−0.969533 + 0.244962i \(0.921225\pi\)
\(228\) 0 0
\(229\) 10.5000 6.06218i 0.693860 0.400600i −0.111197 0.993798i \(-0.535468\pi\)
0.805056 + 0.593198i \(0.202135\pi\)
\(230\) 0 0
\(231\) −4.50000 0.866025i −0.296078 0.0569803i
\(232\) 0 0
\(233\) −1.50000 2.59808i −0.0982683 0.170206i 0.812700 0.582683i \(-0.197997\pi\)
−0.910968 + 0.412477i \(0.864664\pi\)
\(234\) 0 0
\(235\) −4.50000 2.59808i −0.293548 0.169480i
\(236\) 0 0
\(237\) 5.19615i 0.337526i
\(238\) 0 0
\(239\) 10.3923i 0.672222i 0.941822 + 0.336111i \(0.109112\pi\)
−0.941822 + 0.336111i \(0.890888\pi\)
\(240\) 0 0
\(241\) −10.5000 6.06218i −0.676364 0.390499i 0.122119 0.992515i \(-0.461031\pi\)
−0.798484 + 0.602016i \(0.794364\pi\)
\(242\) 0 0
\(243\) −8.00000 13.8564i −0.513200 0.888889i
\(244\) 0 0
\(245\) −7.50000 9.52628i −0.479157 0.608612i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −6.00000 + 10.3923i −0.380235 + 0.658586i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 15.0000 0.943042
\(254\) 0 0
\(255\) −4.50000 + 7.79423i −0.281801 + 0.488094i
\(256\) 0 0
\(257\) −16.5000 + 9.52628i −1.02924 + 0.594233i −0.916767 0.399422i \(-0.869211\pi\)
−0.112474 + 0.993655i \(0.535878\pi\)
\(258\) 0 0
\(259\) −2.50000 + 12.9904i −0.155342 + 0.807183i
\(260\) 0 0
\(261\) 6.00000 + 10.3923i 0.371391 + 0.643268i
\(262\) 0 0
\(263\) 7.50000 + 4.33013i 0.462470 + 0.267007i 0.713082 0.701080i \(-0.247299\pi\)
−0.250612 + 0.968088i \(0.580632\pi\)
\(264\) 0 0
\(265\) 15.5885i 0.957591i
\(266\) 0 0
\(267\) 12.1244i 0.741999i
\(268\) 0 0
\(269\) −1.50000 0.866025i −0.0914566 0.0528025i 0.453574 0.891219i \(-0.350149\pi\)
−0.545031 + 0.838416i \(0.683482\pi\)
\(270\) 0 0
\(271\) −0.500000 0.866025i −0.0303728 0.0526073i 0.850439 0.526073i \(-0.176336\pi\)
−0.880812 + 0.473466i \(0.843003\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.00000 1.73205i 0.180907 0.104447i
\(276\) 0 0
\(277\) −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i \(0.337286\pi\)
−0.999923 + 0.0124177i \(0.996047\pi\)
\(278\) 0 0
\(279\) 10.0000 0.598684
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 5.50000 9.52628i 0.326941 0.566279i −0.654962 0.755662i \(-0.727315\pi\)
0.981903 + 0.189383i \(0.0606488\pi\)
\(284\) 0 0
\(285\) −10.5000 + 6.06218i −0.621966 + 0.359092i
\(286\) 0 0
\(287\) −12.0000 + 13.8564i −0.708338 + 0.817918i
\(288\) 0 0
\(289\) 5.00000 + 8.66025i 0.294118 + 0.509427i
\(290\) 0 0
\(291\) 6.00000 + 3.46410i 0.351726 + 0.203069i
\(292\) 0 0
\(293\) 20.7846i 1.21425i −0.794606 0.607125i \(-0.792323\pi\)
0.794606 0.607125i \(-0.207677\pi\)
\(294\) 0 0
\(295\) 15.5885i 0.907595i
\(296\) 0 0
\(297\) 7.50000 + 4.33013i 0.435194 + 0.251259i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 6.00000 6.92820i 0.345834 0.399335i
\(302\) 0 0
\(303\) −4.50000 + 2.59808i −0.258518 + 0.149256i
\(304\) 0 0
\(305\) 7.50000 12.9904i 0.429449 0.743827i
\(306\) 0 0
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) 1.00000 0.0568880
\(310\) 0 0
\(311\) 16.5000 28.5788i 0.935629 1.62056i 0.162121 0.986771i \(-0.448167\pi\)
0.773508 0.633786i \(-0.218500\pi\)
\(312\) 0 0
\(313\) 25.5000 14.7224i 1.44135 0.832161i 0.443406 0.896321i \(-0.353770\pi\)
0.997940 + 0.0641600i \(0.0204368\pi\)
\(314\) 0 0
\(315\) 3.00000 + 8.66025i 0.169031 + 0.487950i
\(316\) 0 0
\(317\) −10.5000 18.1865i −0.589739 1.02146i −0.994266 0.106932i \(-0.965897\pi\)
0.404528 0.914526i \(-0.367436\pi\)
\(318\) 0 0
\(319\) −9.00000 5.19615i −0.503903 0.290929i
\(320\) 0 0
\(321\) 5.19615i 0.290021i
\(322\) 0 0
\(323\) 36.3731i 2.02385i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 5.50000 + 9.52628i 0.304151 + 0.526804i
\(328\) 0 0
\(329\) 1.50000 7.79423i 0.0826977 0.429710i
\(330\) 0 0
\(331\) 25.5000 14.7224i 1.40161 0.809218i 0.407049 0.913406i \(-0.366558\pi\)
0.994558 + 0.104188i \(0.0332244\pi\)
\(332\) 0 0
\(333\) 5.00000 8.66025i 0.273998 0.474579i
\(334\) 0 0
\(335\) −9.00000 −0.491723
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) 0 0
\(341\) −7.50000 + 4.33013i −0.406148 + 0.234490i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 7.50000 + 12.9904i 0.403786 + 0.699379i
\(346\) 0 0
\(347\) −7.50000 4.33013i −0.402621 0.232453i 0.284993 0.958530i \(-0.408009\pi\)
−0.687614 + 0.726076i \(0.741342\pi\)
\(348\) 0 0
\(349\) 27.7128i 1.48343i 0.670714 + 0.741716i \(0.265988\pi\)
−0.670714 + 0.741716i \(0.734012\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −16.5000 9.52628i −0.878206 0.507033i −0.00813978 0.999967i \(-0.502591\pi\)
−0.870067 + 0.492934i \(0.835924\pi\)
\(354\) 0 0
\(355\) −3.00000 5.19615i −0.159223 0.275783i
\(356\) 0 0
\(357\) −13.5000 2.59808i −0.714496 0.137505i
\(358\) 0 0
\(359\) −13.5000 + 7.79423i −0.712503 + 0.411364i −0.811987 0.583675i \(-0.801614\pi\)
0.0994843 + 0.995039i \(0.468281\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) 0 0
\(363\) 8.00000 0.419891
\(364\) 0 0
\(365\) −3.00000 −0.157027
\(366\) 0 0
\(367\) 0.500000 0.866025i 0.0260998 0.0452062i −0.852680 0.522433i \(-0.825025\pi\)
0.878780 + 0.477227i \(0.158358\pi\)
\(368\) 0 0
\(369\) 12.0000 6.92820i 0.624695 0.360668i
\(370\) 0 0
\(371\) 22.5000 7.79423i 1.16814 0.404656i
\(372\) 0 0
\(373\) −6.50000 11.2583i −0.336557 0.582934i 0.647225 0.762299i \(-0.275929\pi\)
−0.983783 + 0.179364i \(0.942596\pi\)
\(374\) 0 0
\(375\) 10.5000 + 6.06218i 0.542218 + 0.313050i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 10.3923i 0.533817i 0.963722 + 0.266908i \(0.0860021\pi\)
−0.963722 + 0.266908i \(0.913998\pi\)
\(380\) 0 0
\(381\) −3.00000 1.73205i −0.153695 0.0887357i
\(382\) 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
\(385\) −6.00000 5.19615i −0.305788 0.264820i
\(386\) 0 0
\(387\) −6.00000 + 3.46410i −0.304997 + 0.176090i
\(388\) 0 0
\(389\) −10.5000 + 18.1865i −0.532371 + 0.922094i 0.466915 + 0.884302i \(0.345366\pi\)
−0.999286 + 0.0377914i \(0.987968\pi\)
\(390\) 0 0
\(391\) 45.0000 2.27575
\(392\) 0 0
\(393\) −21.0000 −1.05931
\(394\) 0 0
\(395\) −4.50000 + 7.79423i −0.226420 + 0.392170i
\(396\) 0 0
\(397\) 10.5000 6.06218i 0.526980 0.304252i −0.212806 0.977095i \(-0.568260\pi\)
0.739786 + 0.672843i \(0.234927\pi\)
\(398\) 0 0
\(399\) −14.0000 12.1244i −0.700877 0.606977i
\(400\) 0 0
\(401\) −1.50000 2.59808i −0.0749064 0.129742i 0.826139 0.563466i \(-0.190532\pi\)
−0.901046 + 0.433724i \(0.857199\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.73205i 0.0860663i
\(406\) 0 0
\(407\) 8.66025i 0.429273i
\(408\) 0 0
\(409\) −4.50000 2.59808i −0.222511 0.128467i 0.384602 0.923083i \(-0.374339\pi\)
−0.607112 + 0.794616i \(0.707672\pi\)
\(410\) 0 0
\(411\) −1.50000 2.59808i −0.0739895 0.128154i
\(412\) 0 0
\(413\) 22.5000 7.79423i 1.10715 0.383529i
\(414\) 0 0
\(415\) −18.0000 + 10.3923i −0.883585 + 0.510138i
\(416\) 0 0
\(417\) 2.00000 3.46410i 0.0979404 0.169638i
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 0 0
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) 9.00000 5.19615i 0.436564 0.252050i
\(426\) 0 0
\(427\) 22.5000 + 4.33013i 1.08885 + 0.209550i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 25.5000 + 14.7224i 1.22829 + 0.709155i 0.966672 0.256017i \(-0.0824102\pi\)
0.261619 + 0.965171i \(0.415743\pi\)
\(432\) 0 0
\(433\) 34.6410i 1.66474i 0.554220 + 0.832370i \(0.313017\pi\)
−0.554220 + 0.832370i \(0.686983\pi\)
\(434\) 0 0
\(435\) 10.3923i 0.498273i
\(436\) 0 0
\(437\) 52.5000 + 30.3109i 2.51142 + 1.44997i
\(438\) 0 0
\(439\) 9.50000 + 16.4545i 0.453410 + 0.785330i 0.998595 0.0529862i \(-0.0168739\pi\)
−0.545185 + 0.838316i \(0.683541\pi\)
\(440\) 0 0
\(441\) −11.0000 + 8.66025i −0.523810 + 0.412393i
\(442\) 0 0
\(443\) 19.5000 11.2583i 0.926473 0.534899i 0.0407786 0.999168i \(-0.487016\pi\)
0.885694 + 0.464269i \(0.153683\pi\)
\(444\) 0 0
\(445\) 10.5000 18.1865i 0.497748 0.862124i
\(446\) 0 0
\(447\) 9.00000 0.425685
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) −6.00000 + 10.3923i −0.282529 + 0.489355i
\(452\) 0 0
\(453\) 10.5000 6.06218i 0.493333 0.284826i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.500000 + 0.866025i 0.0233890 + 0.0405110i 0.877483 0.479608i \(-0.159221\pi\)
−0.854094 + 0.520119i \(0.825888\pi\)
\(458\) 0 0
\(459\) 22.5000 + 12.9904i 1.05021 + 0.606339i
\(460\) 0 0
\(461\) 27.7128i 1.29071i 0.763881 + 0.645357i \(0.223291\pi\)
−0.763881 + 0.645357i \(0.776709\pi\)
\(462\) 0 0
\(463\) 3.46410i 0.160990i 0.996755 + 0.0804952i \(0.0256502\pi\)
−0.996755 + 0.0804952i \(0.974350\pi\)
\(464\) 0 0
\(465\) −7.50000 4.33013i −0.347804 0.200805i
\(466\) 0 0
\(467\) −1.50000 2.59808i −0.0694117 0.120225i 0.829231 0.558906i \(-0.188779\pi\)
−0.898642 + 0.438682i \(0.855446\pi\)
\(468\) 0 0
\(469\) −4.50000 12.9904i −0.207791 0.599840i
\(470\) 0 0
\(471\) 13.5000 7.79423i 0.622047 0.359139i
\(472\) 0 0
\(473\) 3.00000 5.19615i 0.137940 0.238919i
\(474\) 0 0
\(475\) 14.0000 0.642364
\(476\) 0 0
\(477\) −18.0000 −0.824163
\(478\) 0 0
\(479\) 4.50000 7.79423i 0.205610 0.356127i −0.744717 0.667381i \(-0.767415\pi\)
0.950327 + 0.311253i \(0.100749\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −15.0000 + 17.3205i −0.682524 + 0.788110i
\(484\) 0 0
\(485\) 6.00000 + 10.3923i 0.272446 + 0.471890i
\(486\) 0 0
\(487\) 7.50000 + 4.33013i 0.339857 + 0.196217i 0.660209 0.751082i \(-0.270468\pi\)
−0.320352 + 0.947299i \(0.603801\pi\)
\(488\) 0 0
\(489\) 12.1244i 0.548282i
\(490\) 0 0
\(491\) 17.3205i 0.781664i −0.920462 0.390832i \(-0.872187\pi\)
0.920462 0.390832i \(-0.127813\pi\)
\(492\) 0 0
\(493\) −27.0000 15.5885i −1.21602 0.702069i
\(494\) 0 0
\(495\) 3.00000 + 5.19615i 0.134840 + 0.233550i
\(496\) 0 0
\(497\) 6.00000 6.92820i 0.269137 0.310772i
\(498\) 0 0
\(499\) −10.5000 + 6.06218i −0.470045 + 0.271380i −0.716258 0.697835i \(-0.754147\pi\)
0.246214 + 0.969216i \(0.420813\pi\)
\(500\) 0 0
\(501\) 6.00000 10.3923i 0.268060 0.464294i
\(502\) 0 0
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) −9.00000 −0.400495
\(506\) 0 0
\(507\) −6.50000 + 11.2583i −0.288675 + 0.500000i
\(508\) 0 0
\(509\) −13.5000 + 7.79423i −0.598377 + 0.345473i −0.768403 0.639966i \(-0.778948\pi\)
0.170026 + 0.985440i \(0.445615\pi\)
\(510\) 0 0
\(511\) −1.50000 4.33013i −0.0663561 0.191554i
\(512\) 0 0
\(513\) 17.5000 + 30.3109i 0.772644 + 1.33826i
\(514\) 0 0
\(515\) 1.50000 + 0.866025i 0.0660979 + 0.0381616i
\(516\) 0 0
\(517\) 5.19615i 0.228527i
\(518\) 0 0
\(519\) 8.66025i 0.380143i
\(520\) 0 0
\(521\) 25.5000 + 14.7224i 1.11718 + 0.645001i 0.940678 0.339300i \(-0.110190\pi\)
0.176497 + 0.984301i \(0.443523\pi\)
\(522\) 0 0
\(523\) −11.5000 19.9186i −0.502860 0.870979i −0.999995 0.00330547i \(-0.998948\pi\)
0.497135 0.867673i \(1.66561\pi\)
\(524\) 0 0
\(525\) −1.00000 + 5.19615i −0.0436436 + 0.226779i
\(526\) 0 0
\(527\) −22.5000 + 12.9904i −0.980115 + 0.565870i
\(528\) 0 0
\(529\) 26.0000 45.0333i 1.13043 1.95797i
\(530\) 0 0
\(531\) −18.0000 −0.781133
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 4.50000 7.79423i 0.194552 0.336974i
\(536\) 0 0
\(537\) 13.5000 7.79423i 0.582568 0.336346i
\(538\) 0 0
\(539\) 4.50000 11.2583i 0.193829 0.484931i
\(540\) 0 0
\(541\) 3.50000 + 6.06218i 0.150477 + 0.260633i 0.931403 0.363990i \(-0.118586\pi\)
−0.780926 + 0.624623i \(0.785252\pi\)
\(542\) 0 0
\(543\) 6.00000 + 3.46410i 0.257485 + 0.148659i
\(544\) 0 0
\(545\) 19.0526i 0.816122i
\(546\) 0 0
\(547\) 24.2487i 1.03680i 0.855138 + 0.518400i \(0.173472\pi\)
−0.855138 + 0.518400i \(0.826528\pi\)
\(548\) 0 0
\(549\) −15.0000 8.66025i −0.640184 0.369611i
\(550\) 0 0
\(551\) −21.0000 36.3731i −0.894630 1.54954i
\(552\) 0 0
\(553\) −13.5000 2.59808i −0.574078 0.110481i
\(554\) 0 0
\(555\) −7.50000 + 4.33013i −0.318357 + 0.183804i
\(556\) 0 0
\(557\) 1.50000 2.59808i 0.0635570 0.110084i −0.832496 0.554031i \(-0.813089\pi\)
0.896053 + 0.443947i \(0.146422\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −9.00000 −0.379980
\(562\) 0 0
\(563\) 7.50000 12.9904i 0.316087 0.547479i −0.663581 0.748105i \(-0.730964\pi\)
0.979668 + 0.200625i \(0.0642974\pi\)
\(564\) 0 0
\(565\) −9.00000 + 5.19615i −0.378633 + 0.218604i
\(566\) 0 0
\(567\) 2.50000 0.866025i 0.104990 0.0363696i
\(568\) 0 0
\(569\) −19.5000 33.7750i −0.817483 1.41592i −0.907532 0.419984i \(-0.862036\pi\)
0.0900490 0.995937i \(-0.471298\pi\)
\(570\) 0 0
\(571\) 10.5000 + 6.06218i 0.439411 + 0.253694i 0.703348 0.710846i \(-0.251688\pi\)
−0.263937 + 0.964540i \(0.585021\pi\)
\(572\) 0 0
\(573\) 12.1244i 0.506502i
\(574\) 0 0
\(575\) 17.3205i 0.722315i
\(576\) 0 0
\(577\) 13.5000 + 7.79423i 0.562012 + 0.324478i 0.753953 0.656929i \(-0.228145\pi\)
−0.191940 + 0.981407i \(0.561478\pi\)
\(578\) 0 0
\(579\) 2.50000 + 4.33013i 0.103896 + 0.179954i
\(580\) 0 0
\(581\) −24.0000 20.7846i −0.995688 0.862291i
\(582\) 0 0
\(583\) 13.5000 7.79423i 0.559113 0.322804i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) −35.0000 −1.44215
\(590\) 0 0
\(591\) −3.00000 + 5.19615i −0.123404 + 0.213741i
\(592\) 0 0
\(593\) −16.5000 + 9.52628i −0.677574 + 0.391197i −0.798940 0.601410i \(-0.794606\pi\)
0.121367 + 0.992608i \(0.461272\pi\)
\(594\) 0 0
\(595\) −18.0000 15.5885i −0.737928 0.639064i
\(596\) 0 0
\(597\) −5.50000 9.52628i −0.225100 0.389885i
\(598\) 0 0
\(599\) −28.5000 16.4545i −1.16448 0.672312i −0.212105 0.977247i \(-0.568032\pi\)
−0.952373 + 0.304935i \(0.901365\pi\)
\(600\) 0 0
\(601\) 6.92820i 0.282607i 0.989966 + 0.141304i \(0.0451294\pi\)
−0.989966 + 0.141304i \(0.954871\pi\)
\(602\) 0 0
\(603\) 10.3923i 0.423207i
\(604\) 0 0
\(605\) 12.0000 + 6.92820i 0.487869 + 0.281672i
\(606\) 0 0
\(607\) −14.5000 25.1147i −0.588537 1.01938i −0.994424 0.105453i \(-0.966371\pi\)
0.405887 0.913923i \(1.63304\pi\)
\(608\) 0 0
\(609\) 15.0000 5.19615i 0.607831 0.210559i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 5.50000 9.52628i 0.222143 0.384763i −0.733316 0.679888i \(-0.762028\pi\)
0.955458 + 0.295126i \(0.0953615\pi\)
\(614\) 0 0
\(615\) −12.0000 −0.483887
\(616\) 0 0
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 0 0
\(619\) 3.50000 6.06218i 0.140677 0.243659i −0.787075 0.616858i \(-0.788405\pi\)
0.927752 + 0.373198i \(0.121739\pi\)
\(620\) 0 0
\(621\) 37.5000 21.6506i 1.50482 0.868810i
\(622\) 0 0
\(623\) 31.5000 + 6.06218i 1.26202 + 0.242876i
\(624\) 0 0
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 0 0
\(627\) −10.5000 6.06218i −0.419330 0.242100i
\(628\) 0 0
\(629\) 25.9808i 1.03592i
\(630\) 0 0
\(631\) 45.0333i 1.79275i 0.443298 + 0.896374i \(0.353808\pi\)
−0.443298 + 0.896374i \(0.646192\pi\)
\(632\) 0 0
\(633\) 21.0000 + 12.1244i 0.834675 + 0.481900i
\(634\) 0 0
\(635\) −3.00000 5.19615i −0.119051 0.206203i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −6.00000 + 3.46410i −0.237356 + 0.137038i
\(640\) 0 0
\(641\) 4.50000 7.79423i 0.177739 0.307854i −0.763367 0.645966i \(-0.776455\pi\)
0.941106 + 0.338112i \(0.109788\pi\)
\(642\) 0 0
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) 6.00000 0.236250
\(646\) 0 0
\(647\) −7.50000 + 12.9904i −0.294855 + 0.510705i −0.974951 0.222419i \(-0.928605\pi\)
0.680096 + 0.733123i \(0.261938\pi\)
\(648\) 0 0
\(649\) 13.5000 7.79423i 0.529921 0.305950i
\(650\) 0 0
\(651\) 2.50000 12.9904i 0.0979827 0.509133i
\(652\) 0 0
\(653\) 1.50000 + 2.59808i 0.0586995 + 0.101671i 0.893882 0.448303i \(-0.147971\pi\)
−0.835182 + 0.549973i \(0.814638\pi\)
\(654\) 0 0
\(655\) −31.5000 18.1865i −1.23081 0.710607i
\(656\) 0 0
\(657\) 3.46410i 0.135147i
\(658\) 0 0
\(659\) 24.2487i 0.944596i −0.881439 0.472298i \(-0.843425\pi\)
0.881439 0.472298i \(-0.156575\pi\)
\(660\) 0 0
\(661\) 34.5000 + 19.9186i 1.34189 + 0.774743i 0.987085 0.160196i \(-0.0512125\pi\)
0.354809 + 0.934939i \(0.384546\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −10.5000 30.3109i −0.407173 1.17541i
\(666\) 0 0
\(667\) −45.0000 + 25.9808i −1.74241 + 1.00598i
\(668\) 0 0
\(669\) 8.00000 13.8564i 0.309298 0.535720i
\(670\) 0 0
\(671\) 15.0000 0.579069
\(672\) 0 0
\(673\) −50.0000 −1.92736 −0.963679 0.267063i \(-0.913947\pi\)
−0.963679 + 0.267063i \(0.913947\pi\)
\(674\) 0 0
\(675\) 5.00000 8.66025i 0.192450 0.333333i
\(676\) 0 0
\(677\) 34.5000 19.9186i 1.32594 0.765533i 0.341273 0.939964i \(-0.389142\pi\)
0.984669 + 0.174431i \(0.0558085\pi\)
\(678\) 0 0
\(679\) −12.0000 + 13.8564i −0.460518 + 0.531760i
\(680\) 0 0
\(681\) −10.5000 18.1865i −0.402361 0.696909i
\(682\) 0 0
\(683\) −37.5000 21.6506i −1.43490 0.828439i −0.437409 0.899263i \(-0.644104\pi\)
−0.997489 + 0.0708242i \(0.977437\pi\)
\(684\) 0 0
\(685\) 5.19615i 0.198535i
\(686\) 0 0
\(687\) 12.1244i 0.462573i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 6.50000 + 11.2583i 0.247272 + 0.428287i 0.962768 0.270330i \(-0.0871327\pi\)
−0.715496 + 0.698617i \(0.753799\pi\)
\(692\) 0 0
\(693\) −6.00000 + 6.92820i −0.227921 + 0.263181i
\(694\) 0 0
\(695\) 6.00000 3.46410i 0.227593 0.131401i
\(696\) 0 0
\(697\) −18.0000 + 31.1769i −0.681799 + 1.18091i
\(698\) 0 0
\(699\) 3.00000 0.113470
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) −17.5000 + 30.3109i −0.660025 + 1.14320i
\(704\) 0 0
\(705\) 4.50000 2.59808i 0.169480 0.0978492i
\(706\) 0 0
\(707\) −4.50000 12.9904i −0.169240 0.488554i
\(708\) 0 0
\(709\) 17.5000 + 30.3109i 0.657226 + 1.13835i 0.981331 + 0.192328i \(0.0616038\pi\)
−0.324104 + 0.946021i \(0.605063\pi\)
\(710\) 0 0
\(711\) 9.00000 + 5.19615i 0.337526 + 0.194871i
\(712\) 0 0
\(713\) 43.3013i 1.62165i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −9.00000 5.19615i −0.336111 0.194054i
\(718\) 0 0
\(719\) −16.5000 28.5788i −0.615346 1.06581i −0.990324 0.138777i \(-0.955683\pi\)
0.374978 0.927034i \(1.62235\pi\)
\(720\) 0 0
\(721\) −0.500000 + 2.59808i −0.0186210 + 0.0967574i
\(722\) 0 0
\(723\) 10.5000 6.06218i 0.390499 0.225455i
\(724\) 0 0
\(725\) −6.00000 + 10.3923i −0.222834 + 0.385961i
\(726\) 0 0
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 9.00000 15.5885i 0.332877 0.576560i
\(732\) 0 0
\(733\) 16.5000 9.52628i 0.609441 0.351861i −0.163305 0.986576i \(-0.552216\pi\)
0.772747 + 0.634714i \(0.218882\pi\)
\(734\) 0 0
\(735\) 12.0000 1.73205i 0.442627 0.0638877i
\(736\) 0 0
\(737\) −4.50000 7.79423i −0.165760 0.287104i
\(738\) 0 0
\(739\) −1.50000 0.866025i −0.0551784 0.0318573i 0.472157 0.881514i \(-0.343476\pi\)
−0.527335 + 0.849657i \(0.676809\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 38.1051i 1.39794i −0.715150 0.698971i \(-0.753642\pi\)
0.715150 0.698971i \(-0.246358\pi\)
\(744\) 0 0
\(745\) 13.5000 + 7.79423i 0.494602 + 0.285558i
\(746\) 0 0
\(747\) 12.0000 + 20.7846i 0.439057 + 0.760469i
\(748\) 0 0
\(749\) 13.5000 + 2.59808i 0.493279 + 0.0949316i
\(750\) 0 0
\(751\) 34.5000 19.9186i 1.25892 0.726839i 0.286058 0.958212i \(-0.407655\pi\)
0.972865 + 0.231373i \(0.0743217\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 21.0000 0.764268
\(756\) 0 0
\(757\) −26.0000 −0.944986 −0.472493 0.881334i \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) 0 0
\(759\) −7.50000 + 12.9904i −0.272233 + 0.471521i
\(760\) 0 0
\(761\) −4.50000 + 2.59808i −0.163125 + 0.0941802i −0.579340 0.815086i \(-0.696690\pi\)
0.416215 + 0.909266i \(0.363356\pi\)
\(762\) 0 0
\(763\) −27.5000 + 9.52628i −0.995567 + 0.344874i
\(764\) 0 0
\(765\) 9.00000 + 15.5885i 0.325396 + 0.563602i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 6.92820i 0.249837i 0.992167 + 0.124919i \(0.0398670\pi\)
−0.992167 + 0.124919i \(0.960133\pi\)
\(770\) 0 0
\(771\) 19.0526i 0.686161i
\(772\) 0 0
\(773\) −7.50000 4.33013i −0.269756 0.155744i 0.359021 0.933330i \(-0.383111\pi\)
−0.628777 + 0.777586i \(0.716444\pi\)
\(774\) 0 0
\(775\) 5.00000 + 8.66025i 0.179605 + 0.311086i
\(776\) 0 0
\(777\) −10.0000 8.66025i −0.358748 0.310685i
\(778\) 0 0
\(779\) −42.0000 + 24.2487i −1.50481 + 0.868800i
\(780\) 0 0
\(781\) 3.00000 5.19615i 0.107348 0.185933i
\(782\) 0 0
\(783\) −30.0000 −1.07211
\(784\) 0 0
\(785\) 27.0000 0.963671
\(786\) 0 0
\(787\) 3.50000 6.06218i 0.124762 0.216093i −0.796878 0.604140i \(-0.793517\pi\)
0.921640 + 0.388047i \(0.126850\pi\)
\(788\) 0 0
\(789\) −7.50000 + 4.33013i −0.267007 + 0.154157i
\(790\) 0 0
\(791\) −12.0000 10.3923i −0.426671 0.369508i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 13.5000 + 7.79423i 0.478796 + 0.276433i
\(796\) 0 0