Properties

Label 576.2.i.e.385.1
Level $576$
Weight $2$
Character 576.385
Analytic conductor $4.599$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 385.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 576.385
Dual form 576.2.i.e.193.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.73205i q^{3} +(1.50000 + 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} -3.00000 q^{9} +O(q^{10})\) \(q+1.73205i q^{3} +(1.50000 + 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} -3.00000 q^{9} +(-1.50000 + 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-4.50000 + 2.59808i) q^{15} +6.00000 q^{17} -4.00000 q^{19} +(-1.50000 - 0.866025i) q^{21} +(-1.50000 - 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} -5.19615i q^{27} +(1.50000 - 2.59808i) q^{29} +(2.50000 + 4.33013i) q^{31} +(-4.50000 - 2.59808i) q^{33} -3.00000 q^{35} -2.00000 q^{37} +(1.50000 - 0.866025i) q^{39} +(-1.50000 - 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-4.50000 - 7.79423i) q^{45} +(-4.50000 + 7.79423i) q^{47} +(3.00000 + 5.19615i) q^{49} +10.3923i q^{51} +6.00000 q^{53} -9.00000 q^{55} -6.92820i q^{57} +(1.50000 + 2.59808i) q^{59} +(-6.50000 + 11.2583i) q^{61} +(1.50000 - 2.59808i) q^{63} +(1.50000 - 2.59808i) q^{65} +(3.50000 + 6.06218i) q^{67} +(4.50000 - 2.59808i) q^{69} +12.0000 q^{71} -10.0000 q^{73} +(-6.00000 - 3.46410i) q^{75} +(-1.50000 - 2.59808i) q^{77} +(5.50000 - 9.52628i) q^{79} +9.00000 q^{81} +(4.50000 - 7.79423i) q^{83} +(9.00000 + 15.5885i) q^{85} +(4.50000 + 2.59808i) q^{87} +6.00000 q^{89} +1.00000 q^{91} +(-7.50000 + 4.33013i) q^{93} +(-6.00000 - 10.3923i) q^{95} +(-5.50000 + 9.52628i) q^{97} +(4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{5} - q^{7} - 6q^{9} + O(q^{10}) \) \( 2q + 3q^{5} - q^{7} - 6q^{9} - 3q^{11} - q^{13} - 9q^{15} + 12q^{17} - 8q^{19} - 3q^{21} - 3q^{23} - 4q^{25} + 3q^{29} + 5q^{31} - 9q^{33} - 6q^{35} - 4q^{37} + 3q^{39} - 3q^{41} + q^{43} - 9q^{45} - 9q^{47} + 6q^{49} + 12q^{53} - 18q^{55} + 3q^{59} - 13q^{61} + 3q^{63} + 3q^{65} + 7q^{67} + 9q^{69} + 24q^{71} - 20q^{73} - 12q^{75} - 3q^{77} + 11q^{79} + 18q^{81} + 9q^{83} + 18q^{85} + 9q^{87} + 12q^{89} + 2q^{91} - 15q^{93} - 12q^{95} - 11q^{97} + 9q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(3\) 1.73205i 1.00000i
\(4\) 0 0
\(5\) 1.50000 + 2.59808i 0.670820 + 1.16190i 0.977672 + 0.210138i \(0.0673912\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i −0.944911 0.327327i \(-0.893852\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) −4.50000 + 2.59808i −1.16190 + 0.670820i
\(16\) 0 0
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) −1.50000 0.866025i −0.327327 0.188982i
\(22\) 0 0
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) 0 0
\(31\) 2.50000 + 4.33013i 0.449013 + 0.777714i 0.998322 0.0579057i \(-0.0184423\pi\)
−0.549309 + 0.835619i \(0.685109\pi\)
\(32\) 0 0
\(33\) −4.50000 2.59808i −0.783349 0.452267i
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 1.50000 0.866025i 0.240192 0.138675i
\(40\) 0 0
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 0 0
\(45\) −4.50000 7.79423i −0.670820 1.16190i
\(46\) 0 0
\(47\) −4.50000 + 7.79423i −0.656392 + 1.13691i 0.325150 + 0.945662i \(0.394585\pi\)
−0.981543 + 0.191243i \(0.938748\pi\)
\(48\) 0 0
\(49\) 3.00000 + 5.19615i 0.428571 + 0.742307i
\(50\) 0 0
\(51\) 10.3923i 1.45521i
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) −9.00000 −1.21356
\(56\) 0 0
\(57\) 6.92820i 0.917663i
\(58\) 0 0
\(59\) 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i \(-0.104104\pi\)
−0.751710 + 0.659494i \(0.770771\pi\)
\(60\) 0 0
\(61\) −6.50000 + 11.2583i −0.832240 + 1.44148i 0.0640184 + 0.997949i \(0.479608\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 0 0
\(63\) 1.50000 2.59808i 0.188982 0.327327i
\(64\) 0 0
\(65\) 1.50000 2.59808i 0.186052 0.322252i
\(66\) 0 0
\(67\) 3.50000 + 6.06218i 0.427593 + 0.740613i 0.996659 0.0816792i \(-0.0260283\pi\)
−0.569066 + 0.822292i \(0.692695\pi\)
\(68\) 0 0
\(69\) 4.50000 2.59808i 0.541736 0.312772i
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 0 0
\(75\) −6.00000 3.46410i −0.692820 0.400000i
\(76\) 0 0
\(77\) −1.50000 2.59808i −0.170941 0.296078i
\(78\) 0 0
\(79\) 5.50000 9.52628i 0.618798 1.07179i −0.370907 0.928670i \(-0.620953\pi\)
0.989705 0.143120i \(-0.0457135\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 4.50000 7.79423i 0.493939 0.855528i −0.506036 0.862512i \(-0.668890\pi\)
0.999976 + 0.00698436i \(0.00222321\pi\)
\(84\) 0 0
\(85\) 9.00000 + 15.5885i 0.976187 + 1.69081i
\(86\) 0 0
\(87\) 4.50000 + 2.59808i 0.482451 + 0.278543i
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −7.50000 + 4.33013i −0.777714 + 0.449013i
\(94\) 0 0
\(95\) −6.00000 10.3923i −0.615587 1.06623i
\(96\) 0 0
\(97\) −5.50000 + 9.52628i −0.558440 + 0.967247i 0.439187 + 0.898396i \(0.355267\pi\)
−0.997627 + 0.0688512i \(0.978067\pi\)
\(98\) 0 0
\(99\) 4.50000 7.79423i 0.452267 0.783349i
\(100\) 0 0
\(101\) 7.50000 12.9904i 0.746278 1.29259i −0.203317 0.979113i \(-0.565172\pi\)
0.949595 0.313478i \(-0.101494\pi\)
\(102\) 0 0
\(103\) −3.50000 6.06218i −0.344865 0.597324i 0.640464 0.767988i \(-0.278742\pi\)
−0.985329 + 0.170664i \(0.945409\pi\)
\(104\) 0 0
\(105\) 5.19615i 0.507093i
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 0 0
\(111\) 3.46410i 0.328798i
\(112\) 0 0
\(113\) 4.50000 + 7.79423i 0.423324 + 0.733219i 0.996262 0.0863794i \(-0.0275297\pi\)
−0.572938 + 0.819599i \(0.694196\pi\)
\(114\) 0 0
\(115\) 4.50000 7.79423i 0.419627 0.726816i
\(116\) 0 0
\(117\) 1.50000 + 2.59808i 0.138675 + 0.240192i
\(118\) 0 0
\(119\) −3.00000 + 5.19615i −0.275010 + 0.476331i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 4.50000 2.59808i 0.405751 0.234261i
\(124\) 0 0
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 0 0
\(129\) 1.50000 + 0.866025i 0.132068 + 0.0762493i
\(130\) 0 0
\(131\) −10.5000 18.1865i −0.917389 1.58896i −0.803365 0.595487i \(-0.796959\pi\)
−0.114024 0.993478i \(-0.536374\pi\)
\(132\) 0 0
\(133\) 2.00000 3.46410i 0.173422 0.300376i
\(134\) 0 0
\(135\) 13.5000 7.79423i 1.16190 0.670820i
\(136\) 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
\(139\) −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i \(-0.234680\pi\)
−0.952355 + 0.304991i \(0.901346\pi\)
\(140\) 0 0
\(141\) −13.5000 7.79423i −1.13691 0.656392i
\(142\) 0 0
\(143\) 3.00000 0.250873
\(144\) 0 0
\(145\) 9.00000 0.747409
\(146\) 0 0
\(147\) −9.00000 + 5.19615i −0.742307 + 0.428571i
\(148\) 0 0
\(149\) 7.50000 + 12.9904i 0.614424 + 1.06421i 0.990485 + 0.137619i \(0.0439449\pi\)
−0.376061 + 0.926595i \(0.622722\pi\)
\(150\) 0 0
\(151\) −6.50000 + 11.2583i −0.528962 + 0.916190i 0.470467 + 0.882418i \(0.344085\pi\)
−0.999430 + 0.0337724i \(0.989248\pi\)
\(152\) 0 0
\(153\) −18.0000 −1.45521
\(154\) 0 0
\(155\) −7.50000 + 12.9904i −0.602414 + 1.04341i
\(156\) 0 0
\(157\) −6.50000 11.2583i −0.518756 0.898513i −0.999762 0.0217953i \(-0.993062\pi\)
0.481006 0.876717i \(-0.340272\pi\)
\(158\) 0 0
\(159\) 10.3923i 0.824163i
\(160\) 0 0
\(161\) 3.00000 0.236433
\(162\) 0 0
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 0 0
\(165\) 15.5885i 1.21356i
\(166\) 0 0
\(167\) 4.50000 + 7.79423i 0.348220 + 0.603136i 0.985933 0.167139i \(-0.0534527\pi\)
−0.637713 + 0.770274i \(0.720119\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 0 0
\(171\) 12.0000 0.917663
\(172\) 0 0
\(173\) −4.50000 + 7.79423i −0.342129 + 0.592584i −0.984828 0.173534i \(-0.944481\pi\)
0.642699 + 0.766119i \(0.277815\pi\)
\(174\) 0 0
\(175\) −2.00000 3.46410i −0.151186 0.261861i
\(176\) 0 0
\(177\) −4.50000 + 2.59808i −0.338241 + 0.195283i
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) −19.5000 11.2583i −1.44148 0.832240i
\(184\) 0 0
\(185\) −3.00000 5.19615i −0.220564 0.382029i
\(186\) 0 0
\(187\) −9.00000 + 15.5885i −0.658145 + 1.13994i
\(188\) 0 0
\(189\) 4.50000 + 2.59808i 0.327327 + 0.188982i
\(190\) 0 0
\(191\) 7.50000 12.9904i 0.542681 0.939951i −0.456068 0.889945i \(-0.650743\pi\)
0.998749 0.0500060i \(-0.0159241\pi\)
\(192\) 0 0
\(193\) −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i \(-0.296234\pi\)
−0.993215 + 0.116289i \(0.962900\pi\)
\(194\) 0 0
\(195\) 4.50000 + 2.59808i 0.322252 + 0.186052i
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 0 0
\(201\) −10.5000 + 6.06218i −0.740613 + 0.427593i
\(202\) 0 0
\(203\) 1.50000 + 2.59808i 0.105279 + 0.182349i
\(204\) 0 0
\(205\) 4.50000 7.79423i 0.314294 0.544373i
\(206\) 0 0
\(207\) 4.50000 + 7.79423i 0.312772 + 0.541736i
\(208\) 0 0
\(209\) 6.00000 10.3923i 0.415029 0.718851i
\(210\) 0 0
\(211\) −8.50000 14.7224i −0.585164 1.01353i −0.994855 0.101310i \(-0.967697\pi\)
0.409691 0.912224i \(-0.365637\pi\)
\(212\) 0 0
\(213\) 20.7846i 1.42414i
\(214\) 0 0
\(215\) 3.00000 0.204598
\(216\) 0 0
\(217\) −5.00000 −0.339422
\(218\) 0 0
\(219\) 17.3205i 1.17041i
\(220\) 0 0
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 0 0
\(223\) −0.500000 + 0.866025i −0.0334825 + 0.0579934i −0.882281 0.470723i \(-0.843993\pi\)
0.848799 + 0.528716i \(0.177326\pi\)
\(224\) 0 0
\(225\) 6.00000 10.3923i 0.400000 0.692820i
\(226\) 0 0
\(227\) −13.5000 + 23.3827i −0.896026 + 1.55196i −0.0634974 + 0.997982i \(0.520225\pi\)
−0.832529 + 0.553981i \(0.813108\pi\)
\(228\) 0 0
\(229\) −6.50000 11.2583i −0.429532 0.743971i 0.567300 0.823511i \(-0.307988\pi\)
−0.996832 + 0.0795401i \(0.974655\pi\)
\(230\) 0 0
\(231\) 4.50000 2.59808i 0.296078 0.170941i
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) −27.0000 −1.76129
\(236\) 0 0
\(237\) 16.5000 + 9.52628i 1.07179 + 0.618798i
\(238\) 0 0
\(239\) −13.5000 23.3827i −0.873242 1.51250i −0.858623 0.512607i \(-0.828680\pi\)
−0.0146191 0.999893i \(-0.504654\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) 0 0
\(243\) 15.5885i 1.00000i
\(244\) 0 0
\(245\) −9.00000 + 15.5885i −0.574989 + 0.995910i
\(246\) 0 0
\(247\) 2.00000 + 3.46410i 0.127257 + 0.220416i
\(248\) 0 0
\(249\) 13.5000 + 7.79423i 0.855528 + 0.493939i
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 9.00000 0.565825
\(254\) 0 0
\(255\) −27.0000 + 15.5885i −1.69081 + 0.976187i
\(256\) 0 0
\(257\) 4.50000 + 7.79423i 0.280702 + 0.486191i 0.971558 0.236802i \(-0.0760993\pi\)
−0.690856 + 0.722993i \(0.742766\pi\)
\(258\) 0 0
\(259\) 1.00000 1.73205i 0.0621370 0.107624i
\(260\) 0 0
\(261\) −4.50000 + 7.79423i −0.278543 + 0.482451i
\(262\) 0 0
\(263\) −10.5000 + 18.1865i −0.647458 + 1.12143i 0.336270 + 0.941766i \(0.390834\pi\)
−0.983728 + 0.179664i \(0.942499\pi\)
\(264\) 0 0
\(265\) 9.00000 + 15.5885i 0.552866 + 0.957591i
\(266\) 0 0
\(267\) 10.3923i 0.635999i
\(268\) 0 0
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 0 0
\(273\) 1.73205i 0.104828i
\(274\) 0 0
\(275\) −6.00000 10.3923i −0.361814 0.626680i
\(276\) 0 0
\(277\) −0.500000 + 0.866025i −0.0300421 + 0.0520344i −0.880656 0.473757i \(-0.842897\pi\)
0.850613 + 0.525792i \(0.176231\pi\)
\(278\) 0 0
\(279\) −7.50000 12.9904i −0.449013 0.777714i
\(280\) 0 0
\(281\) −1.50000 + 2.59808i −0.0894825 + 0.154988i −0.907293 0.420500i \(-0.861855\pi\)
0.817810 + 0.575488i \(0.195188\pi\)
\(282\) 0 0
\(283\) −2.50000 4.33013i −0.148610 0.257399i 0.782104 0.623148i \(-0.214146\pi\)
−0.930714 + 0.365748i \(0.880813\pi\)
\(284\) 0 0
\(285\) 18.0000 10.3923i 1.06623 0.615587i
\(286\) 0 0
\(287\) 3.00000 0.177084
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) −16.5000 9.52628i −0.967247 0.558440i
\(292\) 0 0
\(293\) −10.5000 18.1865i −0.613417 1.06247i −0.990660 0.136355i \(-0.956461\pi\)
0.377244 0.926114i \(-0.376872\pi\)
\(294\) 0 0
\(295\) −4.50000 + 7.79423i −0.262000 + 0.453798i
\(296\) 0 0
\(297\) 13.5000 + 7.79423i 0.783349 + 0.452267i
\(298\) 0 0
\(299\) −1.50000 + 2.59808i −0.0867472 + 0.150251i
\(300\) 0 0
\(301\) 0.500000 + 0.866025i 0.0288195 + 0.0499169i
\(302\) 0 0
\(303\) 22.5000 + 12.9904i 1.29259 + 0.746278i
\(304\) 0 0
\(305\) −39.0000 −2.23313
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) 10.5000 6.06218i 0.597324 0.344865i
\(310\) 0 0
\(311\) 10.5000 + 18.1865i 0.595400 + 1.03126i 0.993490 + 0.113917i \(0.0363399\pi\)
−0.398090 + 0.917346i \(0.630327\pi\)
\(312\) 0 0
\(313\) 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i \(-0.824336\pi\)
0.879810 + 0.475325i \(0.157669\pi\)
\(314\) 0 0
\(315\) 9.00000 0.507093
\(316\) 0 0
\(317\) −10.5000 + 18.1865i −0.589739 + 1.02146i 0.404528 + 0.914526i \(0.367436\pi\)
−0.994266 + 0.106932i \(0.965897\pi\)
\(318\) 0 0
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) 0 0
\(321\) 20.7846i 1.16008i
\(322\) 0 0
\(323\) −24.0000 −1.33540
\(324\) 0 0
\(325\) 4.00000 0.221880
\(326\) 0 0
\(327\) 3.46410i 0.191565i
\(328\) 0 0
\(329\) −4.50000 7.79423i −0.248093 0.429710i
\(330\) 0 0
\(331\) −5.50000 + 9.52628i −0.302307 + 0.523612i −0.976658 0.214799i \(-0.931090\pi\)
0.674351 + 0.738411i \(0.264424\pi\)
\(332\) 0 0
\(333\) 6.00000 0.328798
\(334\) 0 0
\(335\) −10.5000 + 18.1865i −0.573676 + 0.993636i
\(336\) 0 0
\(337\) −11.5000 19.9186i −0.626445 1.08503i −0.988260 0.152784i \(-0.951176\pi\)
0.361815 0.932250i \(-0.382157\pi\)
\(338\) 0 0
\(339\) −13.5000 + 7.79423i −0.733219 + 0.423324i
\(340\) 0 0
\(341\) −15.0000 −0.812296
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) 13.5000 + 7.79423i 0.726816 + 0.419627i
\(346\) 0 0
\(347\) −4.50000 7.79423i −0.241573 0.418416i 0.719590 0.694399i \(-0.244330\pi\)
−0.961162 + 0.275983i \(0.910997\pi\)
\(348\) 0 0
\(349\) −0.500000 + 0.866025i −0.0267644 + 0.0463573i −0.879097 0.476642i \(-0.841854\pi\)
0.852333 + 0.523000i \(0.175187\pi\)
\(350\) 0 0
\(351\) −4.50000 + 2.59808i −0.240192 + 0.138675i
\(352\) 0 0
\(353\) −1.50000 + 2.59808i −0.0798369 + 0.138282i −0.903179 0.429263i \(-0.858773\pi\)
0.823343 + 0.567545i \(0.192107\pi\)
\(354\) 0 0
\(355\) 18.0000 + 31.1769i 0.955341 + 1.65470i
\(356\) 0 0
\(357\) −9.00000 5.19615i −0.476331 0.275010i
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) −3.00000 + 1.73205i −0.157459 + 0.0909091i
\(364\) 0 0
\(365\) −15.0000 25.9808i −0.785136 1.35990i
\(366\) 0 0
\(367\) −6.50000 + 11.2583i −0.339297 + 0.587680i −0.984301 0.176500i \(-0.943523\pi\)
0.645003 + 0.764180i \(0.276856\pi\)
\(368\) 0 0
\(369\) 4.50000 + 7.79423i 0.234261 + 0.405751i
\(370\) 0 0
\(371\) −3.00000 + 5.19615i −0.155752 + 0.269771i
\(372\) 0 0
\(373\) −0.500000 0.866025i −0.0258890 0.0448411i 0.852791 0.522253i \(-0.174908\pi\)
−0.878680 + 0.477412i \(0.841575\pi\)
\(374\) 0 0
\(375\) 5.19615i 0.268328i
\(376\) 0 0
\(377\) −3.00000 −0.154508
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) 27.7128i 1.41977i
\(382\) 0 0
\(383\) −7.50000 12.9904i −0.383232 0.663777i 0.608290 0.793715i \(-0.291856\pi\)
−0.991522 + 0.129937i \(0.958522\pi\)
\(384\) 0 0
\(385\) 4.50000 7.79423i 0.229341 0.397231i
\(386\) 0 0
\(387\) −1.50000 + 2.59808i −0.0762493 + 0.132068i
\(388\) 0 0
\(389\) 7.50000 12.9904i 0.380265 0.658638i −0.610835 0.791758i \(-0.709166\pi\)
0.991100 + 0.133120i \(0.0424994\pi\)
\(390\) 0 0
\(391\) −9.00000 15.5885i −0.455150 0.788342i
\(392\) 0 0
\(393\) 31.5000 18.1865i 1.58896 0.917389i
\(394\) 0 0
\(395\) 33.0000 1.66041
\(396\) 0 0
\(397\) −2.00000 −0.100377 −0.0501886 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) 0 0
\(399\) 6.00000 + 3.46410i 0.300376 + 0.173422i
\(400\) 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
\(403\) 2.50000 4.33013i 0.124534 0.215699i
\(404\) 0 0
\(405\) 13.5000 + 23.3827i 0.670820 + 1.16190i
\(406\) 0 0
\(407\) 3.00000 5.19615i 0.148704 0.257564i
\(408\) 0 0
\(409\) −11.5000 19.9186i −0.568638 0.984911i −0.996701 0.0811615i \(-0.974137\pi\)
0.428063 0.903749i \(-0.359196\pi\)
\(410\) 0 0
\(411\) −4.50000 2.59808i −0.221969 0.128154i
\(412\) 0 0
\(413\) −3.00000 −0.147620
\(414\) 0 0
\(415\) 27.0000 1.32538
\(416\) 0 0
\(417\) 7.50000 4.33013i 0.367277 0.212047i
\(418\) 0 0
\(419\) −4.50000 7.79423i −0.219839 0.380773i 0.734919 0.678155i \(-0.237220\pi\)
−0.954759 + 0.297382i \(0.903887\pi\)
\(420\) 0 0
\(421\) 17.5000 30.3109i 0.852898 1.47726i −0.0256838 0.999670i \(-0.508176\pi\)
0.878582 0.477592i \(-0.158490\pi\)
\(422\) 0 0
\(423\) 13.5000 23.3827i 0.656392 1.13691i
\(424\) 0 0
\(425\) −12.0000 + 20.7846i −0.582086 + 1.00820i
\(426\) 0 0
\(427\) −6.50000 11.2583i −0.314557 0.544829i
\(428\) 0 0
\(429\) 5.19615i 0.250873i
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 0 0
\(435\) 15.5885i 0.747409i
\(436\) 0 0
\(437\) 6.00000 + 10.3923i 0.287019 + 0.497131i
\(438\) 0 0
\(439\) 17.5000 30.3109i 0.835229 1.44666i −0.0586141 0.998281i \(-0.518668\pi\)
0.893843 0.448379i \(-0.147999\pi\)
\(440\) 0 0
\(441\) −9.00000 15.5885i −0.428571 0.742307i
\(442\) 0 0
\(443\) 4.50000 7.79423i 0.213801 0.370315i −0.739100 0.673596i \(-0.764749\pi\)
0.952901 + 0.303281i \(0.0980821\pi\)
\(444\) 0 0
\(445\) 9.00000 + 15.5885i 0.426641 + 0.738964i
\(446\) 0 0
\(447\) −22.5000 + 12.9904i −1.06421 + 0.614424i
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) 9.00000 0.423793
\(452\) 0 0
\(453\) −19.5000 11.2583i −0.916190 0.528962i
\(454\) 0 0
\(455\) 1.50000 + 2.59808i 0.0703211 + 0.121800i
\(456\) 0 0
\(457\) 18.5000 32.0429i 0.865393 1.49891i −0.00126243 0.999999i \(-0.500402\pi\)
0.866656 0.498906i \(-0.166265\pi\)
\(458\) 0 0
\(459\) 31.1769i 1.45521i
\(460\) 0 0
\(461\) 1.50000 2.59808i 0.0698620 0.121004i −0.828978 0.559281i \(-0.811077\pi\)
0.898840 + 0.438276i \(0.144411\pi\)
\(462\) 0 0
\(463\) −9.50000 16.4545i −0.441502 0.764705i 0.556299 0.830982i \(-0.312221\pi\)
−0.997801 + 0.0662777i \(0.978888\pi\)
\(464\) 0 0
\(465\) −22.5000 12.9904i −1.04341 0.602414i
\(466\) 0 0
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) −7.00000 −0.323230
\(470\) 0 0
\(471\) 19.5000 11.2583i 0.898513 0.518756i
\(472\) 0 0
\(473\) 1.50000 + 2.59808i 0.0689701 + 0.119460i
\(474\) 0 0
\(475\) 8.00000 13.8564i 0.367065 0.635776i
\(476\) 0 0
\(477\) −18.0000 −0.824163
\(478\) 0 0
\(479\) 13.5000 23.3827i 0.616831 1.06838i −0.373230 0.927739i \(-0.621750\pi\)
0.990060 0.140643i \(-0.0449170\pi\)
\(480\) 0 0
\(481\) 1.00000 + 1.73205i 0.0455961 + 0.0789747i
\(482\) 0 0
\(483\) 5.19615i 0.236433i
\(484\) 0 0
\(485\) −33.0000 −1.49845
\(486\) 0 0
\(487\) −32.0000 −1.45006 −0.725029 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(488\) 0 0
\(489\) 34.6410i 1.56652i
\(490\) 0 0
\(491\) 1.50000 + 2.59808i 0.0676941 + 0.117250i 0.897886 0.440228i \(-0.145102\pi\)
−0.830192 + 0.557478i \(0.811769\pi\)
\(492\) 0 0
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) 0 0
\(495\) 27.0000 1.21356
\(496\) 0 0
\(497\) −6.00000 + 10.3923i −0.269137 + 0.466159i
\(498\) 0 0
\(499\) −2.50000 4.33013i −0.111915 0.193843i 0.804627 0.593780i \(-0.202365\pi\)
−0.916542 + 0.399937i \(0.869032\pi\)
\(500\) 0 0
\(501\) −13.5000 + 7.79423i −0.603136 + 0.348220i
\(502\) 0 0
\(503\) 36.0000 1.60516 0.802580 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) 0 0
\(505\) 45.0000 2.00247
\(506\) 0 0
\(507\) 18.0000 + 10.3923i 0.799408 + 0.461538i
\(508\) 0 0
\(509\) 19.5000 + 33.7750i 0.864322 + 1.49705i 0.867719 + 0.497056i \(0.165586\pi\)
−0.00339621 + 0.999994i \(0.501081\pi\)
\(510\) 0 0
\(511\) 5.00000 8.66025i 0.221187 0.383107i
\(512\) 0 0
\(513\) 20.7846i 0.917663i
\(514\) 0 0
\(515\) 10.5000 18.1865i 0.462685 0.801394i
\(516\) 0 0
\(517\) −13.5000 23.3827i −0.593729 1.02837i
\(518\) 0 0
\(519\) −13.5000 7.79423i −0.592584 0.342129i
\(520\) 0 0
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) 0 0
\(523\) 8.00000 0.349816 0.174908 0.984585i \(-0.444037\pi\)
0.174908 + 0.984585i \(0.444037\pi\)
\(524\) 0 0
\(525\) 6.00000 3.46410i 0.261861 0.151186i
\(526\) 0 0
\(527\) 15.0000 + 25.9808i 0.653410 + 1.13174i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) −4.50000 7.79423i −0.195283 0.338241i
\(532\) 0 0
\(533\) −1.50000 + 2.59808i −0.0649722 + 0.112535i
\(534\) 0 0
\(535\) 18.0000 + 31.1769i 0.778208 + 1.34790i
\(536\) 0 0
\(537\) 20.7846i 0.896922i
\(538\) 0 0
\(539\) −18.0000 −0.775315
\(540\) 0 0
\(541\) 34.0000 1.46177 0.730887 0.682498i \(-0.239107\pi\)
0.730887 + 0.682498i \(0.239107\pi\)
\(542\) 0 0
\(543\) 3.46410i 0.148659i
\(544\) 0 0
\(545\) −3.00000 5.19615i −0.128506 0.222579i
\(546\) 0 0
\(547\) 6.50000 11.2583i 0.277920 0.481371i −0.692948 0.720988i \(-0.743688\pi\)
0.970868 + 0.239616i \(0.0770217\pi\)
\(548\) 0 0
\(549\) 19.5000 33.7750i 0.832240 1.44148i
\(550\) 0 0
\(551\) −6.00000 + 10.3923i −0.255609 + 0.442727i
\(552\) 0 0
\(553\) 5.50000 + 9.52628i 0.233884 + 0.405099i
\(554\) 0 0
\(555\) 9.00000 5.19615i 0.382029 0.220564i
\(556\) 0 0
\(557\) 30.0000 1.27114 0.635570 0.772043i \(-0.280765\pi\)
0.635570 + 0.772043i \(0.280765\pi\)
\(558\) 0 0
\(559\) −1.00000 −0.0422955
\(560\) 0 0
\(561\) −27.0000 15.5885i −1.13994 0.658145i
\(562\) 0 0
\(563\) −4.50000 7.79423i −0.189652 0.328488i 0.755482 0.655169i \(-0.227403\pi\)
−0.945134 + 0.326682i \(0.894069\pi\)
\(564\) 0 0
\(565\) −13.5000 + 23.3827i −0.567949 + 0.983717i
\(566\) 0 0
\(567\) −4.50000 + 7.79423i −0.188982 + 0.327327i
\(568\) 0 0
\(569\) −7.50000 + 12.9904i −0.314416 + 0.544585i −0.979313 0.202350i \(-0.935142\pi\)
0.664897 + 0.746935i \(0.268475\pi\)
\(570\) 0 0
\(571\) 15.5000 + 26.8468i 0.648655 + 1.12350i 0.983444 + 0.181210i \(0.0580014\pi\)
−0.334790 + 0.942293i \(0.608665\pi\)
\(572\) 0 0
\(573\) 22.5000 + 12.9904i 0.939951 + 0.542681i
\(574\) 0 0
\(575\) 12.0000 0.500435
\(576\) 0 0
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) 0 0
\(579\) 16.5000 9.52628i 0.685717 0.395899i
\(580\) 0 0
\(581\) 4.50000 + 7.79423i 0.186691 + 0.323359i
\(582\) 0 0
\(583\) −9.00000 + 15.5885i −0.372742 + 0.645608i
\(584\) 0 0
\(585\) −4.50000 + 7.79423i −0.186052 + 0.322252i
\(586\) 0 0
\(587\) −7.50000 + 12.9904i −0.309558 + 0.536170i −0.978266 0.207355i \(-0.933514\pi\)
0.668708 + 0.743525i \(0.266848\pi\)
\(588\) 0 0
\(589\) −10.0000 17.3205i −0.412043 0.713679i
\(590\) 0 0
\(591\) 10.3923i 0.427482i
\(592\) 0 0
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) −18.0000 −0.737928
\(596\) 0 0
\(597\) 6.92820i 0.283552i
\(598\) 0 0
\(599\) −19.5000 33.7750i −0.796748 1.38001i −0.921723 0.387849i \(-0.873218\pi\)
0.124975 0.992160i \(-0.460115\pi\)
\(600\) 0 0
\(601\) −17.5000 + 30.3109i −0.713840 + 1.23641i 0.249565 + 0.968358i \(0.419712\pi\)
−0.963405 + 0.268049i \(0.913621\pi\)
\(602\) 0 0
\(603\) −10.5000 18.1865i −0.427593 0.740613i
\(604\) 0 0
\(605\) −3.00000 + 5.19615i −0.121967 + 0.211254i
\(606\) 0 0
\(607\) 20.5000 + 35.5070i 0.832069 + 1.44119i 0.896394 + 0.443257i \(0.146177\pi\)
−0.0643251 + 0.997929i \(0.520489\pi\)
\(608\) 0 0
\(609\) −4.50000 + 2.59808i −0.182349 + 0.105279i
\(610\) 0 0
\(611\) 9.00000 0.364101
\(612\) 0 0
\(613\) −26.0000 −1.05013 −0.525065 0.851062i \(-0.675959\pi\)
−0.525065 + 0.851062i \(0.675959\pi\)
\(614\) 0 0
\(615\) 13.5000 + 7.79423i 0.544373 + 0.314294i
\(616\) 0 0
\(617\) −1.50000 2.59808i −0.0603877 0.104595i 0.834251 0.551385i \(-0.185900\pi\)
−0.894639 + 0.446790i \(0.852567\pi\)
\(618\) 0 0
\(619\) 6.50000 11.2583i 0.261257 0.452510i −0.705319 0.708890i \(-0.749196\pi\)
0.966576 + 0.256379i \(0.0825296\pi\)
\(620\) 0 0
\(621\) −13.5000 + 7.79423i −0.541736 + 0.312772i
\(622\) 0 0
\(623\) −3.00000 + 5.19615i −0.120192 + 0.208179i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 0 0
\(627\) 18.0000 + 10.3923i 0.718851 + 0.415029i
\(628\) 0 0
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 0 0
\(633\) 25.5000 14.7224i 1.01353 0.585164i
\(634\) 0 0
\(635\) 24.0000 + 41.5692i 0.952411 + 1.64962i
\(636\) 0 0
\(637\) 3.00000 5.19615i 0.118864 0.205879i
\(638\) 0 0
\(639\) −36.0000 −1.42414
\(640\) 0 0
\(641\) 16.5000 28.5788i 0.651711 1.12880i −0.330997 0.943632i \(-0.607385\pi\)
0.982708 0.185164i \(-0.0592817\pi\)
\(642\) 0 0
\(643\) −20.5000 35.5070i −0.808441 1.40026i −0.913943 0.405842i \(-0.866978\pi\)
0.105502 0.994419i \(-0.466355\pi\)
\(644\) 0 0
\(645\) 5.19615i 0.204598i
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) −9.00000 −0.353281
\(650\) 0 0
\(651\) 8.66025i 0.339422i
\(652\) 0 0
\(653\) −10.5000 18.1865i −0.410897 0.711694i 0.584091 0.811688i \(-0.301451\pi\)
−0.994988 + 0.0999939i \(0.968118\pi\)
\(654\) 0 0
\(655\) 31.5000 54.5596i 1.23081 2.13182i
\(656\) 0 0
\(657\) 30.0000 1.17041
\(658\) 0 0
\(659\) 10.5000 18.1865i 0.409022 0.708447i −0.585758 0.810486i \(-0.699203\pi\)
0.994780 + 0.102039i \(0.0325366\pi\)
\(660\) 0 0
\(661\) 5.50000 + 9.52628i 0.213925 + 0.370529i 0.952940 0.303160i \(-0.0980418\pi\)
−0.739014 + 0.673690i \(0.764708\pi\)
\(662\) 0 0
\(663\) 9.00000 5.19615i 0.349531 0.201802i
\(664\) 0 0
\(665\) 12.0000 0.465340
\(666\) 0 0
\(667\) −9.00000 −0.348481
\(668\) 0 0
\(669\) −1.50000 0.866025i −0.0579934 0.0334825i
\(670\) 0 0
\(671\) −19.5000 33.7750i −0.752789 1.30387i
\(672\) 0 0
\(673\) −5.50000 + 9.52628i −0.212009 + 0.367211i −0.952343 0.305028i \(-0.901334\pi\)
0.740334 + 0.672239i \(0.234667\pi\)
\(674\) 0 0
\(675\) 18.0000 + 10.3923i 0.692820 + 0.400000i
\(676\) 0 0
\(677\) 7.50000 12.9904i 0.288248 0.499261i −0.685143 0.728408i \(-0.740260\pi\)
0.973392 + 0.229147i \(0.0735938\pi\)
\(678\) 0 0
\(679\) −5.50000 9.52628i −0.211071 0.365585i
\(680\) 0 0
\(681\) −40.5000 23.3827i −1.55196 0.896026i
\(682\) 0 0
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0 0
\(685\) −9.00000 −0.343872
\(686\) 0 0
\(687\) 19.5000 11.2583i 0.743971 0.429532i
\(688\) 0 0
\(689\) −3.00000 5.19615i −0.114291 0.197958i
\(690\) 0 0
\(691\) 0.500000 0.866025i 0.0190209 0.0329452i −0.856358 0.516382i \(-0.827278\pi\)
0.875379 + 0.483437i \(0.160612\pi\)
\(692\) 0 0
\(693\) 4.50000 + 7.79423i 0.170941 + 0.296078i
\(694\) 0 0
\(695\) 7.50000 12.9904i 0.284491 0.492753i
\(696\) 0 0
\(697\) −9.00000 15.5885i −0.340899 0.590455i
\(698\) 0 0
\(699\) 10.3923i 0.393073i
\(700\) 0 0
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 0 0
\(703\) 8.00000 0.301726
\(704\) 0 0
\(705\) 46.7654i 1.76129i
\(706\) 0 0
\(707\) 7.50000 + 12.9904i 0.282067 + 0.488554i
\(708\) 0 0
\(709\) −12.5000 + 21.6506i −0.469447 + 0.813107i −0.999390 0.0349269i \(-0.988880\pi\)
0.529943 + 0.848034i \(0.322213\pi\)
\(710\) 0 0
\(711\) −16.5000 + 28.5788i −0.618798 + 1.07179i
\(712\) 0 0
\(713\) 7.50000 12.9904i 0.280877 0.486494i
\(714\) 0 0
\(715\) 4.50000 + 7.79423i 0.168290 + 0.291488i
\(716\) 0 0
\(717\) 40.5000 23.3827i 1.51250 0.873242i
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 7.00000 0.260694
\(722\) 0 0
\(723\) 1.50000 + 0.866025i 0.0557856 + 0.0322078i
\(724\) 0 0
\(725\) 6.00000 + 10.3923i 0.222834 + 0.385961i
\(726\) 0 0
\(727\) −18.5000 + 32.0429i −0.686127 + 1.18841i 0.286954 + 0.957944i \(0.407357\pi\)
−0.973081 + 0.230463i \(0.925976\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 3.00000 5.19615i 0.110959 0.192187i
\(732\) 0 0
\(733\) 11.5000 + 19.9186i 0.424762 + 0.735710i 0.996398 0.0847976i \(-0.0270244\pi\)
−0.571636 + 0.820507i \(0.693691\pi\)
\(734\) 0 0
\(735\) −27.0000 15.5885i −0.995910 0.574989i
\(736\) 0 0
\(737\) −21.0000 −0.773545
\(738\) 0 0
\(739\) −16.0000 −0.588570 −0.294285 0.955718i \(-0.595081\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 0 0
\(741\) −6.00000 + 3.46410i −0.220416 + 0.127257i
\(742\) 0 0
\(743\) 4.50000 + 7.79423i 0.165089 + 0.285943i 0.936687 0.350168i \(-0.113876\pi\)
−0.771598 + 0.636111i \(0.780542\pi\)
\(744\) 0 0
\(745\) −22.5000 + 38.9711i −0.824336 + 1.42779i
\(746\) 0 0
\(747\) −13.5000 + 23.3827i −0.493939 + 0.855528i
\(748\) 0 0
\(749\) −6.00000 + 10.3923i −0.219235 + 0.379727i
\(750\) 0 0
\(751\) −15.5000 26.8468i −0.565603 0.979653i −0.996993 0.0774878i \(-0.975310\pi\)
0.431390 0.902165i \(-0.358023\pi\)
\(752\) 0 0
\(753\) 20.7846i 0.757433i
\(754\) 0 0
\(755\) −39.0000 −1.41936
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 0 0
\(759\) 15.5885i 0.565825i
\(760\) 0 0
\(761\) −13.5000 23.3827i −0.489375 0.847622i 0.510551 0.859848i \(-0.329442\pi\)
−0.999925 + 0.0122260i \(0.996108\pi\)
\(762\) 0 0
\(763\) 1.00000 1.73205i 0.0362024 0.0627044i
\(764\) 0 0
\(765\) −27.0000 46.7654i −0.976187 1.69081i
\(766\) 0 0
\(767\) 1.50000 2.59808i 0.0541619 0.0938111i
\(768\) 0 0
\(769\) 0.500000 + 0.866025i 0.0180305 + 0.0312297i 0.874900 0.484304i \(-0.160927\pi\)
−0.856869 + 0.515534i \(0.827594\pi\)
\(770\) 0 0
\(771\) −13.5000 + 7.79423i −0.486191 + 0.280702i
\(772\) 0 0
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) 0 0
\(775\) −20.0000 −0.718421
\(776\) 0 0
\(777\) 3.00000 + 1.73205i 0.107624 + 0.0621370i
\(778\) 0 0
\(779\) 6.00000 + 10.3923i 0.214972 + 0.372343i
\(780\) 0 0
\(781\) −18.0000 + 31.1769i −0.644091 + 1.11560i
\(782\) 0 0
\(783\) −13.5000 7.79423i −0.482451 0.278543i
\(784\) 0 0
\(785\) 19.5000 33.7750i 0.695985 1.20548i
\(786\) 0 0
\(787\) 21.5000 + 37.2391i 0.766392 + 1.32743i 0.939507 + 0.342529i \(0.111283\pi\)
−0.173115 + 0.984902i \(0.555383\pi\)
\(788\) 0 0
\(789\) −31.5000 18.1865i −1.12143 0.647458i
\(790\) 0 0
\(791\) −9.00000 −0.320003
\(792\) 0 0
\(793\) 13.0000 0.461644
\(794\) 0 0
\(795\) −27.0000 + 15.5885i −0.957591 + 0.552866i
\(796\) 0