Properties

Label 112.2.p.a.47.1
Level $112$
Weight $2$
Character 112.47
Analytic conductor $0.894$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 112.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.894324502638\)
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: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 47.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 112.47
Dual form 112.2.p.a.31.1

$q$-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 \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\) \(85\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 0.684819 0.728714i \(-0.259881\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) 0 0
\(5\) 1.50000 + 0.866025i 0.670820 + 0.387298i 0.796387 0.604787i \(-0.206742\pi\)
−0.125567 + 0.992085i \(0.540075\pi\)
\(6\) 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 −0.708787 0.705422i \(-0.750757\pi\)
0.256520 + 0.966539i \(0.417424\pi\)
\(12\) 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 −0.933952 0.357400i \(-0.883663\pi\)
−0.157459 + 0.987526i \(0.550330\pi\)
\(18\) 0 0
\(19\) −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i \(0.463407\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 0 0
\(21\) −2.50000 0.866025i −0.545545 0.188982i
\(22\) 0 0
\(23\) 7.50000 + 4.33013i 1.56386 + 0.902894i 0.996861 + 0.0791743i \(0.0252284\pi\)
0.566997 + 0.823720i \(0.308105\pi\)
\(24\) 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 \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) 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 \(-0.698514\pi\)
0.994999 + 0.0998840i \(0.0318472\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.92820i 1.08200i 0.841021 + 0.541002i \(0.181955\pi\)
−0.841021 + 0.541002i \(0.818045\pi\)
\(42\) 0 0
\(43\) 3.46410i 0.528271i −0.964486 0.264135i \(-0.914913\pi\)
0.964486 0.264135i \(-0.0850865\pi\)
\(44\) 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 \(-0.903547\pi\)
0.735643 + 0.677369i \(0.236880\pi\)
\(48\) 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 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 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 −0.994769 0.102151i \(-0.967427\pi\)
0.408919 0.912571i \(1.63409\pi\)
\(60\) 0 0
\(61\) 7.50000 + 4.33013i 0.960277 + 0.554416i 0.896258 0.443533i \(-0.146275\pi\)
0.0640184 + 0.997949i \(0.479608\pi\)
\(62\) 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 −0.199264 0.979946i \(-0.563855\pi\)
0.749026 + 0.662540i \(0.230522\pi\)
\(68\) 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 −0.409644 0.912245i \(-0.634347\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 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 \(-0.427756\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 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 −0.173394 0.984853i \(-0.555473\pi\)
−0.939604 + 0.342263i \(0.888807\pi\)
\(90\) 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 \(0.114405\pi\)
−0.936103 + 0.351726i \(0.885595\pi\)
\(98\) 0 0
\(99\) 3.46410i 0.348155i
\(100\) 0 0
\(101\) −4.50000 + 2.59808i −0.447767 + 0.258518i −0.706887 0.707327i \(-0.749901\pi\)
0.259120 + 0.965845i \(0.416568\pi\)
\(102\) 0 0
\(103\) 0.500000 0.866025i 0.0492665 0.0853320i −0.840341 0.542059i \(-0.817645\pi\)
0.889607 + 0.456727i \(0.150978\pi\)
\(104\) 0 0
\(105\) −3.00000 3.46410i −0.292770 0.338062i
\(106\) 0 0
\(107\) −4.50000 2.59808i −0.435031 0.251166i 0.266456 0.963847i \(-0.414147\pi\)
−0.701488 + 0.712681i \(0.747481\pi\)
\(108\) 0 0
\(109\) −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i \(-0.990057\pi\)
0.472708 0.881219i \(-0.343277\pi\)
\(110\) 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 0.114024 0.993478i \(-0.463626\pi\)
0.803365 0.595487i \(-0.203041\pi\)
\(132\) 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 0.794808 0.606861i \(-0.207572\pi\)
−0.922961 + 0.384893i \(0.874238\pi\)
\(138\) 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 \(-0.713152\pi\)
0.989355 + 0.145519i \(0.0464853\pi\)
\(150\) 0 0
\(151\) 10.5000 6.06218i 0.854478 0.493333i −0.00768132 0.999970i \(-0.502445\pi\)
0.862159 + 0.506637i \(0.169112\pi\)
\(152\) 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 \(-0.452968\pi\)
0.930199 + 0.367057i \(0.119635\pi\)
\(158\) 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 0.0288280 0.999584i \(-0.490822\pi\)
−0.851251 + 0.524758i \(0.824156\pi\)
\(164\) 0 0
\(165\) 1.50000 + 2.59808i 0.116775 + 0.202260i
\(166\) 0 0
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 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 \(-0.226550\pi\)
−0.187021 + 0.982356i \(0.559883\pi\)
\(174\) 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 −0.910910 0.412606i \(-0.864619\pi\)
−0.0981277 + 0.995174i \(0.531285\pi\)
\(180\) 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 \(-0.477874\pi\)
−0.829207 + 0.558941i \(0.811208\pi\)
\(192\) 0 0
\(193\) 2.50000 + 4.33013i 0.179954 + 0.311689i 0.941865 0.335993i \(-0.109072\pi\)
−0.761911 + 0.647682i \(0.775738\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) 5.50000 + 9.52628i 0.389885 + 0.675300i 0.992434 0.122782i \(-0.0391815\pi\)
−0.602549 + 0.798082i \(0.705848\pi\)
\(200\) 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 \(0.314345\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 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 \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) −4.00000 −0.266667
\(226\) 0 0
\(227\) −10.5000 18.1865i −0.696909 1.20708i −0.969533 0.244962i \(-0.921225\pi\)
0.272623 0.962121i \(1.58789\pi\)
\(228\) 0 0
\(229\) −10.5000 6.06218i −0.693860 0.400600i 0.111197 0.993798i \(-0.464532\pi\)
−0.805056 + 0.593198i \(0.797865\pi\)
\(230\) 0 0
\(231\) 4.50000 0.866025i 0.296078 0.0569803i
\(232\) 0 0
\(233\) −1.50000 + 2.59808i −0.0982683 + 0.170206i −0.910968 0.412477i \(-0.864664\pi\)
0.812700 + 0.582683i \(0.197997\pi\)
\(234\) 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 −0.798484 0.602016i \(-0.794364\pi\)
0.122119 + 0.992515i \(0.461031\pi\)
\(242\) 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 −0.112474 0.993655i \(-0.535878\pi\)
−0.916767 + 0.399422i \(0.869211\pi\)
\(258\) 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 \(-0.752701\pi\)
0.250612 + 0.968088i \(0.419368\pi\)
\(264\) 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 \(-0.649851\pi\)
0.545031 + 0.838416i \(0.316518\pi\)
\(270\) 0 0
\(271\) 0.500000 0.866025i 0.0303728 0.0526073i −0.850439 0.526073i \(-0.823664\pi\)
0.880812 + 0.473466i \(0.156997\pi\)
\(272\) 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 0.999923 + 0.0124177i \(0.00395278\pi\)
−0.489207 + 0.872167i \(0.662714\pi\)
\(278\) 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 0.981903 0.189383i \(-0.0606488\pi\)
−0.654962 + 0.755662i \(0.727315\pi\)
\(284\) 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 −0.773508 0.633786i \(-0.781500\pi\)
−0.162121 0.986771i \(1.44817\pi\)
\(312\) 0 0
\(313\) 25.5000 + 14.7224i 1.44135 + 0.832161i 0.997940 0.0641600i \(-0.0204368\pi\)
0.443406 + 0.896321i \(0.353770\pi\)
\(314\) 0 0
\(315\) 3.00000 8.66025i 0.169031 0.487950i
\(316\) 0 0
\(317\) 10.5000 18.1865i 0.589739 1.02146i −0.404528 0.914526i \(-0.632564\pi\)
0.994266 0.106932i \(-0.0341026\pi\)
\(318\) 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 0.994558 0.104188i \(-0.0332244\pi\)
0.407049 + 0.913406i \(0.366558\pi\)
\(332\) 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 −0.687614 0.726076i \(-0.741342\pi\)
0.284993 + 0.958530i \(0.408009\pi\)
\(348\) 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 −0.870067 0.492934i \(-0.835924\pi\)
−0.00813978 + 0.999967i \(0.502591\pi\)
\(354\) 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 \(-0.198386\pi\)
−0.0994843 + 0.995039i \(0.531719\pi\)
\(360\) 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 \(-0.174975\pi\)
−0.878780 + 0.477227i \(0.841642\pi\)
\(368\) 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 \(-0.724071\pi\)
0.983783 + 0.179364i \(0.0574041\pi\)
\(374\) 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 \(-0.913998\pi\)
0.963722 0.266908i \(-0.0860021\pi\)
\(380\) 0 0
\(381\) 3.00000 1.73205i 0.153695 0.0887357i
\(382\) 0 0
\(383\) −13.5000 + 23.3827i −0.689818 + 1.19480i 0.282079 + 0.959391i \(0.408976\pi\)
−0.971897 + 0.235408i \(0.924357\pi\)
\(384\) 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 0.999286 + 0.0377914i \(0.0120322\pi\)
−0.466915 + 0.884302i \(0.654634\pi\)
\(390\) 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 \(-0.431740\pi\)
−0.739786 + 0.672843i \(0.765073\pi\)
\(398\) 0 0
\(399\) 14.0000 12.1244i 0.700877 0.606977i
\(400\) 0 0
\(401\) −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) 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 −0.607112 0.794616i \(-0.707672\pi\)
0.384602 + 0.923083i \(0.374339\pi\)
\(410\) 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 \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 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 \(-0.917590\pi\)
−0.261619 + 0.965171i \(0.584257\pi\)
\(432\) 0 0
\(433\) 34.6410i 1.66474i −0.554220 0.832370i \(-0.686983\pi\)
0.554220 0.832370i \(-0.313017\pi\)
\(434\) 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 \(-0.983126\pi\)
0.545185 + 0.838316i \(0.316459\pi\)
\(440\) 0 0
\(441\) −11.0000 8.66025i −0.523810 0.412393i
\(442\) 0 0
\(443\) 19.5000 + 11.2583i 0.926473 + 0.534899i 0.885694 0.464269i \(-0.153683\pi\)
0.0407786 + 0.999168i \(0.487016\pi\)
\(444\) 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 −0.854094 0.520119i \(-0.825888\pi\)
0.877483 + 0.479608i \(0.159221\pi\)
\(458\) 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 −0.898642 0.438682i \(-0.855446\pi\)
0.829231 + 0.558906i \(0.188779\pi\)
\(468\) 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 \(-0.232585\pi\)
−0.950327 + 0.311253i \(0.899251\pi\)
\(480\) 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 \(-0.729532\pi\)
0.320352 + 0.947299i \(0.396199\pi\)
\(488\) 0 0
\(489\) 12.1244i 0.548282i
\(490\) 0 0
\(491\) 17.3205i 0.781664i 0.920462 + 0.390832i \(0.127813\pi\)
−0.920462 + 0.390832i \(0.872187\pi\)
\(492\) 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 0.246214 0.969216i \(-0.420813\pi\)
−0.716258 + 0.697835i \(0.754147\pi\)
\(500\) 0 0
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) 0 0
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 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 \(-0.221052\pi\)
−0.170026 + 0.985440i \(0.554385\pi\)
\(510\) 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 0.176497 0.984301i \(-0.443523\pi\)
0.940678 + 0.339300i \(0.110190\pi\)
\(522\) 0 0
\(523\) −11.5000 + 19.9186i −0.502860 + 0.870979i 0.497135 + 0.867673i \(0.334385\pi\)
−0.999995 + 0.00330547i \(0.998948\pi\)
\(524\) 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 \(-0.881414\pi\)
0.780926 + 0.624623i \(0.214748\pi\)
\(542\) 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 \(-0.826528\pi\)
0.855138 0.518400i \(-0.173472\pi\)
\(548\) 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 \(-0.186911\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(558\) 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 0.979668 0.200625i \(-0.0642974\pi\)
−0.663581 + 0.748105i \(0.730964\pi\)
\(564\) 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 0.0900490 + 0.995937i \(0.471298\pi\)
−0.907532 + 0.419984i \(0.862036\pi\)
\(570\) 0 0
\(571\) 10.5000 6.06218i 0.439411 0.253694i −0.263937 0.964540i \(-0.585021\pi\)
0.703348 + 0.710846i \(0.251688\pi\)
\(572\) 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 −0.191940 0.981407i \(-0.561478\pi\)
0.753953 + 0.656929i \(0.228145\pi\)
\(578\) 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 0.121367 0.992608i \(-0.461272\pi\)
−0.798940 + 0.601410i \(0.794606\pi\)
\(594\) 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 \(-0.431968\pi\)
0.952373 + 0.304935i \(0.0986347\pi\)
\(600\) 0 0
\(601\) 6.92820i 0.282607i −0.989966 0.141304i \(-0.954871\pi\)
0.989966 0.141304i \(-0.0451294\pi\)
\(602\) 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 −0.405887 0.913923i \(-0.633038\pi\)
0.994424 0.105453i \(-0.0336291\pi\)
\(608\) 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 \(-0.237972\pi\)
−0.955458 + 0.295126i \(0.904638\pi\)
\(614\) 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 0.927752 0.373198i \(-0.121739\pi\)
−0.787075 + 0.616858i \(0.788405\pi\)
\(620\) 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 0.941106 0.338112i \(-0.109788\pi\)
−0.763367 + 0.645966i \(0.776455\pi\)
\(642\) 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 \(-0.0713952\pi\)
−0.680096 + 0.733123i \(0.738062\pi\)
\(648\) 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 \(-0.852029\pi\)
0.835182 + 0.549973i \(0.185362\pi\)
\(654\) 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 \(0.156575\pi\)
−0.881439 + 0.472298i \(0.843425\pi\)
\(660\) 0 0
\(661\) −34.5000 + 19.9186i −1.34189 + 0.774743i −0.987085 0.160196i \(-0.948788\pi\)
−0.354809 + 0.934939i \(0.615454\pi\)
\(662\) 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 \(-0.610858\pi\)
−0.984669 + 0.174431i \(0.944191\pi\)
\(678\) 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 −0.997489 0.0708242i \(-0.977437\pi\)
−0.437409 + 0.899263i \(0.644104\pi\)
\(684\) 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 −0.715496 0.698617i \(-0.753799\pi\)
0.962768 + 0.270330i \(0.0871327\pi\)
\(692\) 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 \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 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 0.324104 + 0.946021i \(0.394937\pi\)
−0.981331 + 0.192328i \(0.938396\pi\)
\(710\) 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 −0.374978 0.927034i \(-0.622350\pi\)
0.990324 0.138777i \(-0.0443171\pi\)
\(720\) 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 \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 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 \(-0.447784\pi\)
−0.772747 + 0.634714i \(0.781118\pi\)
\(734\) 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 −0.527335 0.849657i \(-0.676809\pi\)
0.472157 + 0.881514i \(0.343476\pi\)
\(740\) 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 \(-0.592345\pi\)
−0.972865 + 0.231373i \(0.925678\pi\)
\(752\) 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 \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 0 0
\(759\) 7.50000 + 12.9904i 0.272233 + 0.471521i
\(760\) 0 0
\(761\) −4.50000 2.59808i −0.163125 0.0941802i 0.416215 0.909266i \(-0.363356\pi\)
−0.579340 + 0.815086i \(0.696690\pi\)
\(762\) 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 \(-0.960133\pi\)
0.992167 0.124919i \(-0.0398670\pi\)
\(770\) 0 0
\(771\) 19.0526i 0.686161i
\(772\) 0 0
\(773\) 7.50000 4.33013i 0.269756 0.155744i −0.359021 0.933330i \(-0.616889\pi\)
0.628777 + 0.777586i \(0.283556\pi\)
\(774\) 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 0.921640 0.388047i \(-0.126850\pi\)
−0.796878 + 0.604140i \(0.793517\pi\)
\(788\) 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
\(797\)