Properties

Label 912.2.bn.b.449.1
Level $912$
Weight $2$
Character 912.449
Analytic conductor $7.282$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bn (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 449.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 912.449
Dual form 912.2.bn.b.65.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.73205i q^{3} +(3.00000 - 1.73205i) q^{5} +2.00000 q^{7} -3.00000 q^{9} +O(q^{10})\) \(q-1.73205i q^{3} +(3.00000 - 1.73205i) q^{5} +2.00000 q^{7} -3.00000 q^{9} -1.73205i q^{11} +(-3.00000 - 1.73205i) q^{13} +(-3.00000 - 5.19615i) q^{15} +(6.00000 - 3.46410i) q^{17} +(-0.500000 + 4.33013i) q^{19} -3.46410i q^{21} +(3.50000 - 6.06218i) q^{25} +5.19615i q^{27} +(-3.00000 + 5.19615i) q^{29} -6.92820i q^{31} -3.00000 q^{33} +(6.00000 - 3.46410i) q^{35} +6.92820i q^{37} +(-3.00000 + 5.19615i) q^{39} +(-1.50000 - 2.59808i) q^{41} +(4.00000 + 6.92820i) q^{43} +(-9.00000 + 5.19615i) q^{45} +(3.00000 + 1.73205i) q^{47} -3.00000 q^{49} +(-6.00000 - 10.3923i) q^{51} +(3.00000 - 5.19615i) q^{53} +(-3.00000 - 5.19615i) q^{55} +(7.50000 + 0.866025i) q^{57} +(-1.50000 - 2.59808i) q^{59} +(-5.00000 + 8.66025i) q^{61} -6.00000 q^{63} -12.0000 q^{65} +(-4.50000 - 2.59808i) q^{67} +(-3.00000 - 5.19615i) q^{71} +(-2.50000 - 4.33013i) q^{73} +(-10.5000 - 6.06218i) q^{75} -3.46410i q^{77} +(12.0000 - 6.92820i) q^{79} +9.00000 q^{81} -5.19615i q^{83} +(12.0000 - 20.7846i) q^{85} +(9.00000 + 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{89} +(-6.00000 - 3.46410i) q^{91} -12.0000 q^{93} +(6.00000 + 13.8564i) q^{95} +(7.50000 - 4.33013i) q^{97} +5.19615i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 6 q^{5} + 4 q^{7} - 6 q^{9} - 6 q^{13} - 6 q^{15} + 12 q^{17} - q^{19} + 7 q^{25} - 6 q^{29} - 6 q^{33} + 12 q^{35} - 6 q^{39} - 3 q^{41} + 8 q^{43} - 18 q^{45} + 6 q^{47} - 6 q^{49} - 12 q^{51} + 6 q^{53} - 6 q^{55} + 15 q^{57} - 3 q^{59} - 10 q^{61} - 12 q^{63} - 24 q^{65} - 9 q^{67} - 6 q^{71} - 5 q^{73} - 21 q^{75} + 24 q^{79} + 18 q^{81} + 24 q^{85} + 18 q^{87} - 6 q^{89} - 12 q^{91} - 24 q^{93} + 12 q^{95} + 15 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.73205i 1.00000i
\(4\) 0 0
\(5\) 3.00000 1.73205i 1.34164 0.774597i 0.354593 0.935021i \(-0.384620\pi\)
0.987048 + 0.160424i \(0.0512862\pi\)
\(6\) 0 0
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 1.73205i 0.522233i −0.965307 0.261116i \(-0.915909\pi\)
0.965307 0.261116i \(-0.0840907\pi\)
\(12\) 0 0
\(13\) −3.00000 1.73205i −0.832050 0.480384i 0.0225039 0.999747i \(-0.492836\pi\)
−0.854554 + 0.519362i \(0.826170\pi\)
\(14\) 0 0
\(15\) −3.00000 5.19615i −0.774597 1.34164i
\(16\) 0 0
\(17\) 6.00000 3.46410i 1.45521 0.840168i 0.456444 0.889752i \(-0.349123\pi\)
0.998770 + 0.0495842i \(0.0157896\pi\)
\(18\) 0 0
\(19\) −0.500000 + 4.33013i −0.114708 + 0.993399i
\(20\) 0 0
\(21\) 3.46410i 0.755929i
\(22\) 0 0
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 0 0
\(25\) 3.50000 6.06218i 0.700000 1.21244i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 0 0
\(31\) 6.92820i 1.24434i −0.782881 0.622171i \(-0.786251\pi\)
0.782881 0.622171i \(-0.213749\pi\)
\(32\) 0 0
\(33\) −3.00000 −0.522233
\(34\) 0 0
\(35\) 6.00000 3.46410i 1.01419 0.585540i
\(36\) 0 0
\(37\) 6.92820i 1.13899i 0.821995 + 0.569495i \(0.192861\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) −3.00000 + 5.19615i −0.480384 + 0.832050i
\(40\) 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
\(43\) 4.00000 + 6.92820i 0.609994 + 1.05654i 0.991241 + 0.132068i \(0.0421616\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 0 0
\(45\) −9.00000 + 5.19615i −1.34164 + 0.774597i
\(46\) 0 0
\(47\) 3.00000 + 1.73205i 0.437595 + 0.252646i 0.702577 0.711608i \(-0.252033\pi\)
−0.264982 + 0.964253i \(0.585366\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) −6.00000 10.3923i −0.840168 1.45521i
\(52\) 0 0
\(53\) 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) 0 0
\(55\) −3.00000 5.19615i −0.404520 0.700649i
\(56\) 0 0
\(57\) 7.50000 + 0.866025i 0.993399 + 0.114708i
\(58\) 0 0
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) 0 0
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) 0 0
\(63\) −6.00000 −0.755929
\(64\) 0 0
\(65\) −12.0000 −1.48842
\(66\) 0 0
\(67\) −4.50000 2.59808i −0.549762 0.317406i 0.199264 0.979946i \(-0.436145\pi\)
−0.749026 + 0.662540i \(0.769478\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i \(-0.282538\pi\)
−0.987294 + 0.158901i \(0.949205\pi\)
\(72\) 0 0
\(73\) −2.50000 4.33013i −0.292603 0.506803i 0.681822 0.731519i \(-0.261188\pi\)
−0.974424 + 0.224716i \(0.927855\pi\)
\(74\) 0 0
\(75\) −10.5000 6.06218i −1.21244 0.700000i
\(76\) 0 0
\(77\) 3.46410i 0.394771i
\(78\) 0 0
\(79\) 12.0000 6.92820i 1.35011 0.779484i 0.361842 0.932240i \(-0.382148\pi\)
0.988264 + 0.152756i \(0.0488148\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 5.19615i 0.570352i −0.958475 0.285176i \(-0.907948\pi\)
0.958475 0.285176i \(-0.0920520\pi\)
\(84\) 0 0
\(85\) 12.0000 20.7846i 1.30158 2.25441i
\(86\) 0 0
\(87\) 9.00000 + 5.19615i 0.964901 + 0.557086i
\(88\) 0 0
\(89\) −3.00000 + 5.19615i −0.317999 + 0.550791i −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) 0 0
\(91\) −6.00000 3.46410i −0.628971 0.363137i
\(92\) 0 0
\(93\) −12.0000 −1.24434
\(94\) 0 0
\(95\) 6.00000 + 13.8564i 0.615587 + 1.42164i
\(96\) 0 0
\(97\) 7.50000 4.33013i 0.761510 0.439658i −0.0683279 0.997663i \(-0.521766\pi\)
0.829837 + 0.558005i \(0.188433\pi\)
\(98\) 0 0
\(99\) 5.19615i 0.522233i
\(100\) 0 0
\(101\) 9.00000 + 5.19615i 0.895533 + 0.517036i 0.875748 0.482768i \(-0.160368\pi\)
0.0197851 + 0.999804i \(0.493702\pi\)
\(102\) 0 0
\(103\) 10.3923i 1.02398i 0.858990 + 0.511992i \(0.171092\pi\)
−0.858990 + 0.511992i \(0.828908\pi\)
\(104\) 0 0
\(105\) −6.00000 10.3923i −0.585540 1.01419i
\(106\) 0 0
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0 0
\(111\) 12.0000 1.13899
\(112\) 0 0
\(113\) −15.0000 −1.41108 −0.705541 0.708669i \(-0.749296\pi\)
−0.705541 + 0.708669i \(0.749296\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 9.00000 + 5.19615i 0.832050 + 0.480384i
\(118\) 0 0
\(119\) 12.0000 6.92820i 1.10004 0.635107i
\(120\) 0 0
\(121\) 8.00000 0.727273
\(122\) 0 0
\(123\) −4.50000 + 2.59808i −0.405751 + 0.234261i
\(124\) 0 0
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) 9.00000 + 5.19615i 0.798621 + 0.461084i 0.842989 0.537931i \(-0.180794\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 0 0
\(129\) 12.0000 6.92820i 1.05654 0.609994i
\(130\) 0 0
\(131\) −16.5000 + 9.52628i −1.44161 + 0.832315i −0.997957 0.0638831i \(-0.979652\pi\)
−0.443654 + 0.896198i \(0.646318\pi\)
\(132\) 0 0
\(133\) −1.00000 + 8.66025i −0.0867110 + 0.750939i
\(134\) 0 0
\(135\) 9.00000 + 15.5885i 0.774597 + 1.34164i
\(136\) 0 0
\(137\) 1.50000 + 0.866025i 0.128154 + 0.0739895i 0.562706 0.826657i \(-0.309760\pi\)
−0.434553 + 0.900646i \(0.643094\pi\)
\(138\) 0 0
\(139\) 0.500000 0.866025i 0.0424094 0.0734553i −0.844042 0.536278i \(-0.819830\pi\)
0.886451 + 0.462822i \(0.153163\pi\)
\(140\) 0 0
\(141\) 3.00000 5.19615i 0.252646 0.437595i
\(142\) 0 0
\(143\) −3.00000 + 5.19615i −0.250873 + 0.434524i
\(144\) 0 0
\(145\) 20.7846i 1.72607i
\(146\) 0 0
\(147\) 5.19615i 0.428571i
\(148\) 0 0
\(149\) 6.00000 3.46410i 0.491539 0.283790i −0.233674 0.972315i \(-0.575075\pi\)
0.725213 + 0.688525i \(0.241741\pi\)
\(150\) 0 0
\(151\) 6.92820i 0.563809i 0.959442 + 0.281905i \(0.0909662\pi\)
−0.959442 + 0.281905i \(0.909034\pi\)
\(152\) 0 0
\(153\) −18.0000 + 10.3923i −1.45521 + 0.840168i
\(154\) 0 0
\(155\) −12.0000 20.7846i −0.963863 1.66946i
\(156\) 0 0
\(157\) 10.0000 + 17.3205i 0.798087 + 1.38233i 0.920860 + 0.389892i \(0.127488\pi\)
−0.122774 + 0.992435i \(0.539179\pi\)
\(158\) 0 0
\(159\) −9.00000 5.19615i −0.713746 0.412082i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 17.0000 1.33154 0.665771 0.746156i \(-0.268103\pi\)
0.665771 + 0.746156i \(0.268103\pi\)
\(164\) 0 0
\(165\) −9.00000 + 5.19615i −0.700649 + 0.404520i
\(166\) 0 0
\(167\) −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 0 0
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 0 0
\(171\) 1.50000 12.9904i 0.114708 0.993399i
\(172\) 0 0
\(173\) 9.00000 + 15.5885i 0.684257 + 1.18517i 0.973670 + 0.227964i \(0.0732068\pi\)
−0.289412 + 0.957205i \(0.593460\pi\)
\(174\) 0 0
\(175\) 7.00000 12.1244i 0.529150 0.916515i
\(176\) 0 0
\(177\) −4.50000 + 2.59808i −0.338241 + 0.195283i
\(178\) 0 0
\(179\) 3.00000 0.224231 0.112115 0.993695i \(-0.464237\pi\)
0.112115 + 0.993695i \(0.464237\pi\)
\(180\) 0 0
\(181\) 6.00000 + 3.46410i 0.445976 + 0.257485i 0.706129 0.708083i \(-0.250440\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 15.0000 + 8.66025i 1.10883 + 0.640184i
\(184\) 0 0
\(185\) 12.0000 + 20.7846i 0.882258 + 1.52811i
\(186\) 0 0
\(187\) −6.00000 10.3923i −0.438763 0.759961i
\(188\) 0 0
\(189\) 10.3923i 0.755929i
\(190\) 0 0
\(191\) 6.92820i 0.501307i 0.968077 + 0.250654i \(0.0806455\pi\)
−0.968077 + 0.250654i \(0.919354\pi\)
\(192\) 0 0
\(193\) 18.0000 10.3923i 1.29567 0.748054i 0.316016 0.948754i \(-0.397655\pi\)
0.979653 + 0.200700i \(0.0643215\pi\)
\(194\) 0 0
\(195\) 20.7846i 1.48842i
\(196\) 0 0
\(197\) 20.7846i 1.48084i −0.672143 0.740421i \(-0.734626\pi\)
0.672143 0.740421i \(-0.265374\pi\)
\(198\) 0 0
\(199\) 7.00000 12.1244i 0.496217 0.859473i −0.503774 0.863836i \(-0.668055\pi\)
0.999990 + 0.00436292i \(0.00138876\pi\)
\(200\) 0 0
\(201\) −4.50000 + 7.79423i −0.317406 + 0.549762i
\(202\) 0 0
\(203\) −6.00000 + 10.3923i −0.421117 + 0.729397i
\(204\) 0 0
\(205\) −9.00000 5.19615i −0.628587 0.362915i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 7.50000 + 0.866025i 0.518786 + 0.0599042i
\(210\) 0 0
\(211\) −9.00000 + 5.19615i −0.619586 + 0.357718i −0.776708 0.629861i \(-0.783112\pi\)
0.157122 + 0.987579i \(0.449778\pi\)
\(212\) 0 0
\(213\) −9.00000 + 5.19615i −0.616670 + 0.356034i
\(214\) 0 0
\(215\) 24.0000 + 13.8564i 1.63679 + 0.944999i
\(216\) 0 0
\(217\) 13.8564i 0.940634i
\(218\) 0 0
\(219\) −7.50000 + 4.33013i −0.506803 + 0.292603i
\(220\) 0 0
\(221\) −24.0000 −1.61441
\(222\) 0 0
\(223\) −12.0000 + 6.92820i −0.803579 + 0.463947i −0.844721 0.535207i \(-0.820234\pi\)
0.0411418 + 0.999153i \(0.486900\pi\)
\(224\) 0 0
\(225\) −10.5000 + 18.1865i −0.700000 + 1.21244i
\(226\) 0 0
\(227\) 21.0000 1.39382 0.696909 0.717159i \(-0.254558\pi\)
0.696909 + 0.717159i \(0.254558\pi\)
\(228\) 0 0
\(229\) 4.00000 0.264327 0.132164 0.991228i \(-0.457808\pi\)
0.132164 + 0.991228i \(0.457808\pi\)
\(230\) 0 0
\(231\) −6.00000 −0.394771
\(232\) 0 0
\(233\) 1.50000 0.866025i 0.0982683 0.0567352i −0.450060 0.892998i \(-0.648598\pi\)
0.548329 + 0.836263i \(0.315264\pi\)
\(234\) 0 0
\(235\) 12.0000 0.782794
\(236\) 0 0
\(237\) −12.0000 20.7846i −0.779484 1.35011i
\(238\) 0 0
\(239\) 6.92820i 0.448148i 0.974572 + 0.224074i \(0.0719358\pi\)
−0.974572 + 0.224074i \(0.928064\pi\)
\(240\) 0 0
\(241\) 4.50000 + 2.59808i 0.289870 + 0.167357i 0.637883 0.770133i \(-0.279810\pi\)
−0.348013 + 0.937490i \(0.613143\pi\)
\(242\) 0 0
\(243\) 15.5885i 1.00000i
\(244\) 0 0
\(245\) −9.00000 + 5.19615i −0.574989 + 0.331970i
\(246\) 0 0
\(247\) 9.00000 12.1244i 0.572656 0.771454i
\(248\) 0 0
\(249\) −9.00000 −0.570352
\(250\) 0 0
\(251\) −7.50000 4.33013i −0.473396 0.273315i 0.244264 0.969709i \(-0.421454\pi\)
−0.717660 + 0.696393i \(0.754787\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −36.0000 20.7846i −2.25441 1.30158i
\(256\) 0 0
\(257\) −7.50000 + 12.9904i −0.467837 + 0.810318i −0.999325 0.0367485i \(-0.988300\pi\)
0.531487 + 0.847066i \(0.321633\pi\)
\(258\) 0 0
\(259\) 13.8564i 0.860995i
\(260\) 0 0
\(261\) 9.00000 15.5885i 0.557086 0.964901i
\(262\) 0 0
\(263\) 3.00000 1.73205i 0.184988 0.106803i −0.404646 0.914473i \(-0.632605\pi\)
0.589634 + 0.807671i \(0.299272\pi\)
\(264\) 0 0
\(265\) 20.7846i 1.27679i
\(266\) 0 0
\(267\) 9.00000 + 5.19615i 0.550791 + 0.317999i
\(268\) 0 0
\(269\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 0 0
\(271\) 13.0000 + 22.5167i 0.789694 + 1.36779i 0.926155 + 0.377144i \(0.123094\pi\)
−0.136461 + 0.990645i \(0.543573\pi\)
\(272\) 0 0
\(273\) −6.00000 + 10.3923i −0.363137 + 0.628971i
\(274\) 0 0
\(275\) −10.5000 6.06218i −0.633174 0.365563i
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 0 0
\(279\) 20.7846i 1.24434i
\(280\) 0 0
\(281\) 7.50000 12.9904i 0.447412 0.774941i −0.550804 0.834634i \(-0.685679\pi\)
0.998217 + 0.0596933i \(0.0190123\pi\)
\(282\) 0 0
\(283\) −0.500000 0.866025i −0.0297219 0.0514799i 0.850782 0.525519i \(-0.176129\pi\)
−0.880504 + 0.474039i \(0.842796\pi\)
\(284\) 0 0
\(285\) 24.0000 10.3923i 1.42164 0.615587i
\(286\) 0 0
\(287\) −3.00000 5.19615i −0.177084 0.306719i
\(288\) 0 0
\(289\) 15.5000 26.8468i 0.911765 1.57922i
\(290\) 0 0
\(291\) −7.50000 12.9904i −0.439658 0.761510i
\(292\) 0 0
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) −9.00000 5.19615i −0.524000 0.302532i
\(296\) 0 0
\(297\) 9.00000 0.522233
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 8.00000 + 13.8564i 0.461112 + 0.798670i
\(302\) 0 0
\(303\) 9.00000 15.5885i 0.517036 0.895533i
\(304\) 0 0
\(305\) 34.6410i 1.98354i
\(306\) 0 0
\(307\) 4.50000 2.59808i 0.256829 0.148280i −0.366058 0.930592i \(-0.619293\pi\)
0.622887 + 0.782312i \(0.285960\pi\)
\(308\) 0 0
\(309\) 18.0000 1.02398
\(310\) 0 0
\(311\) 13.8564i 0.785725i −0.919597 0.392862i \(-0.871485\pi\)
0.919597 0.392862i \(-0.128515\pi\)
\(312\) 0 0
\(313\) −15.5000 + 26.8468i −0.876112 + 1.51747i −0.0205381 + 0.999789i \(0.506538\pi\)
−0.855574 + 0.517681i \(0.826795\pi\)
\(314\) 0 0
\(315\) −18.0000 + 10.3923i −1.01419 + 0.585540i
\(316\) 0 0
\(317\) −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i \(-0.887225\pi\)
0.769395 + 0.638774i \(0.220558\pi\)
\(318\) 0 0
\(319\) 9.00000 + 5.19615i 0.503903 + 0.290929i
\(320\) 0 0
\(321\) 20.7846i 1.16008i
\(322\) 0 0
\(323\) 12.0000 + 27.7128i 0.667698 + 1.54198i
\(324\) 0 0
\(325\) −21.0000 + 12.1244i −1.16487 + 0.672538i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6.00000 + 3.46410i 0.330791 + 0.190982i
\(330\) 0 0
\(331\) 8.66025i 0.476011i −0.971264 0.238005i \(-0.923506\pi\)
0.971264 0.238005i \(-0.0764936\pi\)
\(332\) 0 0
\(333\) 20.7846i 1.13899i
\(334\) 0 0
\(335\) −18.0000 −0.983445
\(336\) 0 0
\(337\) −22.5000 + 12.9904i −1.22565 + 0.707631i −0.966118 0.258102i \(-0.916903\pi\)
−0.259536 + 0.965734i \(0.583569\pi\)
\(338\) 0 0
\(339\) 25.9808i 1.41108i
\(340\) 0 0
\(341\) −12.0000 −0.649836
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 0 0
\(345\) 0 0
\(346\) 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
\(349\) 8.00000 0.428230 0.214115 0.976808i \(-0.431313\pi\)
0.214115 + 0.976808i \(0.431313\pi\)
\(350\) 0 0
\(351\) 9.00000 15.5885i 0.480384 0.832050i
\(352\) 0 0
\(353\) 25.9808i 1.38282i −0.722464 0.691408i \(-0.756991\pi\)
0.722464 0.691408i \(-0.243009\pi\)
\(354\) 0 0
\(355\) −18.0000 10.3923i −0.955341 0.551566i
\(356\) 0 0
\(357\) −12.0000 20.7846i −0.635107 1.10004i
\(358\) 0 0
\(359\) 6.00000 3.46410i 0.316668 0.182828i −0.333238 0.942843i \(-0.608141\pi\)
0.649906 + 0.760014i \(0.274808\pi\)
\(360\) 0 0
\(361\) −18.5000 4.33013i −0.973684 0.227901i
\(362\) 0 0
\(363\) 13.8564i 0.727273i
\(364\) 0 0
\(365\) −15.0000 8.66025i −0.785136 0.453298i
\(366\) 0 0
\(367\) −2.00000 + 3.46410i −0.104399 + 0.180825i −0.913493 0.406855i \(-0.866625\pi\)
0.809093 + 0.587680i \(0.199959\pi\)
\(368\) 0 0
\(369\) 4.50000 + 7.79423i 0.234261 + 0.405751i
\(370\) 0 0
\(371\) 6.00000 10.3923i 0.311504 0.539542i
\(372\) 0 0
\(373\) 6.92820i 0.358729i −0.983783 0.179364i \(-0.942596\pi\)
0.983783 0.179364i \(-0.0574041\pi\)
\(374\) 0 0
\(375\) −12.0000 −0.619677
\(376\) 0 0
\(377\) 18.0000 10.3923i 0.927047 0.535231i
\(378\) 0 0
\(379\) 10.3923i 0.533817i 0.963722 + 0.266908i \(0.0860021\pi\)
−0.963722 + 0.266908i \(0.913998\pi\)
\(380\) 0 0
\(381\) 9.00000 15.5885i 0.461084 0.798621i
\(382\) 0 0
\(383\) 9.00000 + 15.5885i 0.459879 + 0.796533i 0.998954 0.0457244i \(-0.0145596\pi\)
−0.539076 + 0.842257i \(0.681226\pi\)
\(384\) 0 0
\(385\) −6.00000 10.3923i −0.305788 0.529641i
\(386\) 0 0
\(387\) −12.0000 20.7846i −0.609994 1.05654i
\(388\) 0 0
\(389\) 30.0000 + 17.3205i 1.52106 + 0.878185i 0.999691 + 0.0248535i \(0.00791191\pi\)
0.521369 + 0.853331i \(0.325421\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 16.5000 + 28.5788i 0.832315 + 1.44161i
\(394\) 0 0
\(395\) 24.0000 41.5692i 1.20757 2.09157i
\(396\) 0 0
\(397\) −10.0000 17.3205i −0.501886 0.869291i −0.999998 0.00217869i \(-0.999307\pi\)
0.498112 0.867113i \(-0.334027\pi\)
\(398\) 0 0
\(399\) 15.0000 + 1.73205i 0.750939 + 0.0867110i
\(400\) 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
\(403\) −12.0000 + 20.7846i −0.597763 + 1.03536i
\(404\) 0 0
\(405\) 27.0000 15.5885i 1.34164 0.774597i
\(406\) 0 0
\(407\) 12.0000 0.594818
\(408\) 0 0
\(409\) −16.5000 9.52628i −0.815872 0.471044i 0.0331186 0.999451i \(-0.489456\pi\)
−0.848991 + 0.528407i \(0.822789\pi\)
\(410\) 0 0
\(411\) 1.50000 2.59808i 0.0739895 0.128154i
\(412\) 0 0
\(413\) −3.00000 5.19615i −0.147620 0.255686i
\(414\) 0 0
\(415\) −9.00000 15.5885i −0.441793 0.765207i
\(416\) 0 0
\(417\) −1.50000 0.866025i −0.0734553 0.0424094i
\(418\) 0 0
\(419\) 10.3923i 0.507697i 0.967244 + 0.253849i \(0.0816965\pi\)
−0.967244 + 0.253849i \(0.918303\pi\)
\(420\) 0 0
\(421\) −12.0000 + 6.92820i −0.584844 + 0.337660i −0.763056 0.646332i \(-0.776302\pi\)
0.178212 + 0.983992i \(0.442969\pi\)
\(422\) 0 0
\(423\) −9.00000 5.19615i −0.437595 0.252646i
\(424\) 0 0
\(425\) 48.4974i 2.35247i
\(426\) 0 0
\(427\) −10.0000 + 17.3205i −0.483934 + 0.838198i
\(428\) 0 0
\(429\) 9.00000 + 5.19615i 0.434524 + 0.250873i
\(430\) 0 0
\(431\) 3.00000 5.19615i 0.144505 0.250290i −0.784683 0.619897i \(-0.787174\pi\)
0.929188 + 0.369607i \(0.120508\pi\)
\(432\) 0 0
\(433\) −12.0000 6.92820i −0.576683 0.332948i 0.183131 0.983089i \(-0.441377\pi\)
−0.759814 + 0.650140i \(0.774710\pi\)
\(434\) 0 0
\(435\) 36.0000 1.72607
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 12.0000 6.92820i 0.572729 0.330665i −0.185510 0.982642i \(-0.559394\pi\)
0.758238 + 0.651977i \(0.226060\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 0 0
\(443\) −10.5000 6.06218i −0.498870 0.288023i 0.229377 0.973338i \(-0.426331\pi\)
−0.728247 + 0.685315i \(0.759665\pi\)
\(444\) 0 0
\(445\) 20.7846i 0.985285i
\(446\) 0 0
\(447\) −6.00000 10.3923i −0.283790 0.491539i
\(448\) 0 0
\(449\) −3.00000 −0.141579 −0.0707894 0.997491i \(-0.522552\pi\)
−0.0707894 + 0.997491i \(0.522552\pi\)
\(450\) 0 0
\(451\) −4.50000 + 2.59808i −0.211897 + 0.122339i
\(452\) 0 0
\(453\) 12.0000 0.563809
\(454\) 0 0
\(455\) −24.0000 −1.12514
\(456\) 0 0
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) 0 0
\(459\) 18.0000 + 31.1769i 0.840168 + 1.45521i
\(460\) 0 0
\(461\) −21.0000 + 12.1244i −0.978068 + 0.564688i −0.901686 0.432391i \(-0.857670\pi\)
−0.0763814 + 0.997079i \(0.524337\pi\)
\(462\) 0 0
\(463\) −14.0000 −0.650635 −0.325318 0.945605i \(-0.605471\pi\)
−0.325318 + 0.945605i \(0.605471\pi\)
\(464\) 0 0
\(465\) −36.0000 + 20.7846i −1.66946 + 0.963863i
\(466\) 0 0
\(467\) 12.1244i 0.561048i −0.959847 0.280524i \(-0.909492\pi\)
0.959847 0.280524i \(-0.0905083\pi\)
\(468\) 0 0
\(469\) −9.00000 5.19615i −0.415581 0.239936i
\(470\) 0 0
\(471\) 30.0000 17.3205i 1.38233 0.798087i
\(472\) 0 0
\(473\) 12.0000 6.92820i 0.551761 0.318559i
\(474\) 0 0
\(475\) 24.5000 + 18.1865i 1.12414 + 0.834455i
\(476\) 0 0
\(477\) −9.00000 + 15.5885i −0.412082 + 0.713746i
\(478\) 0 0
\(479\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) 0 0
\(481\) 12.0000 20.7846i 0.547153 0.947697i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 15.0000 25.9808i 0.681115 1.17973i
\(486\) 0 0
\(487\) 6.92820i 0.313947i 0.987603 + 0.156973i \(0.0501737\pi\)
−0.987603 + 0.156973i \(0.949826\pi\)
\(488\) 0 0
\(489\) 29.4449i 1.33154i
\(490\) 0 0
\(491\) 27.0000 15.5885i 1.21849 0.703497i 0.253897 0.967231i \(-0.418287\pi\)
0.964595 + 0.263734i \(0.0849541\pi\)
\(492\) 0 0
\(493\) 41.5692i 1.87218i
\(494\) 0 0
\(495\) 9.00000 + 15.5885i 0.404520 + 0.700649i
\(496\) 0 0
\(497\) −6.00000 10.3923i −0.269137 0.466159i
\(498\) 0 0
\(499\) −20.5000 35.5070i −0.917706 1.58951i −0.802890 0.596127i \(-0.796706\pi\)
−0.114816 0.993387i \(-0.536628\pi\)
\(500\) 0 0
\(501\) 18.0000 + 10.3923i 0.804181 + 0.464294i
\(502\) 0 0
\(503\) −18.0000 10.3923i −0.802580 0.463370i 0.0417923 0.999126i \(-0.486693\pi\)
−0.844373 + 0.535756i \(0.820027\pi\)
\(504\) 0 0
\(505\) 36.0000 1.60198
\(506\) 0 0
\(507\) −1.50000 + 0.866025i −0.0666173 + 0.0384615i
\(508\) 0 0
\(509\) −12.0000 + 20.7846i −0.531891 + 0.921262i 0.467416 + 0.884037i \(0.345185\pi\)
−0.999307 + 0.0372243i \(0.988148\pi\)
\(510\) 0 0
\(511\) −5.00000 8.66025i −0.221187 0.383107i
\(512\) 0 0
\(513\) −22.5000 2.59808i −0.993399 0.114708i
\(514\) 0 0
\(515\) 18.0000 + 31.1769i 0.793175 + 1.37382i
\(516\) 0 0
\(517\) 3.00000 5.19615i 0.131940 0.228527i
\(518\) 0 0
\(519\) 27.0000 15.5885i 1.18517 0.684257i
\(520\) 0 0
\(521\) 21.0000 0.920027 0.460013 0.887912i \(-0.347845\pi\)
0.460013 + 0.887912i \(0.347845\pi\)
\(522\) 0 0
\(523\) −15.0000 8.66025i −0.655904 0.378686i 0.134810 0.990871i \(-0.456957\pi\)
−0.790715 + 0.612185i \(0.790291\pi\)
\(524\) 0 0
\(525\) −21.0000 12.1244i −0.916515 0.529150i
\(526\) 0 0
\(527\) −24.0000 41.5692i −1.04546 1.81078i
\(528\) 0 0
\(529\) −11.5000 19.9186i −0.500000 0.866025i
\(530\) 0 0
\(531\) 4.50000 + 7.79423i 0.195283 + 0.338241i
\(532\) 0 0
\(533\) 10.3923i 0.450141i
\(534\) 0 0
\(535\) −36.0000 + 20.7846i −1.55642 + 0.898597i
\(536\) 0 0
\(537\) 5.19615i 0.224231i
\(538\) 0 0
\(539\) 5.19615i 0.223814i
\(540\) 0 0
\(541\) −10.0000 + 17.3205i −0.429934 + 0.744667i −0.996867 0.0790969i \(-0.974796\pi\)
0.566933 + 0.823764i \(0.308130\pi\)
\(542\) 0 0
\(543\) 6.00000 10.3923i 0.257485 0.445976i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 21.0000 + 12.1244i 0.897895 + 0.518400i 0.876517 0.481371i \(-0.159861\pi\)
0.0213785 + 0.999771i \(0.493195\pi\)
\(548\) 0 0
\(549\) 15.0000 25.9808i 0.640184 1.10883i
\(550\) 0 0
\(551\) −21.0000 15.5885i −0.894630 0.664091i
\(552\) 0 0
\(553\) 24.0000 13.8564i 1.02058 0.589234i
\(554\) 0 0
\(555\) 36.0000 20.7846i 1.52811 0.882258i
\(556\) 0 0
\(557\) −12.0000 6.92820i −0.508456 0.293557i 0.223743 0.974648i \(-0.428173\pi\)
−0.732199 + 0.681091i \(0.761506\pi\)
\(558\) 0 0
\(559\) 27.7128i 1.17213i
\(560\) 0 0
\(561\) −18.0000 + 10.3923i −0.759961 + 0.438763i
\(562\) 0 0
\(563\) −21.0000 −0.885044 −0.442522 0.896758i \(-0.645916\pi\)
−0.442522 + 0.896758i \(0.645916\pi\)
\(564\) 0 0
\(565\) −45.0000 + 25.9808i −1.89316 + 1.09302i
\(566\) 0 0
\(567\) 18.0000 0.755929
\(568\) 0 0
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) 43.0000 1.79949 0.899747 0.436412i \(-0.143751\pi\)
0.899747 + 0.436412i \(0.143751\pi\)
\(572\) 0 0
\(573\) 12.0000 0.501307
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −29.0000 −1.20729 −0.603643 0.797255i \(-0.706285\pi\)
−0.603643 + 0.797255i \(0.706285\pi\)
\(578\) 0 0
\(579\) −18.0000 31.1769i −0.748054 1.29567i
\(580\) 0 0
\(581\) 10.3923i 0.431145i
\(582\) 0 0
\(583\) −9.00000 5.19615i −0.372742 0.215203i
\(584\) 0 0
\(585\) 36.0000 1.48842
\(586\) 0 0
\(587\) −33.0000 + 19.0526i −1.36206 + 0.786383i −0.989897 0.141786i \(-0.954716\pi\)
−0.372158 + 0.928169i \(0.621382\pi\)
\(588\) 0 0
\(589\) 30.0000 + 3.46410i 1.23613 + 0.142736i
\(590\) 0 0
\(591\) −36.0000 −1.48084
\(592\) 0 0
\(593\) −22.5000 12.9904i −0.923964 0.533451i −0.0390666 0.999237i \(-0.512438\pi\)
−0.884898 + 0.465786i \(0.845772\pi\)
\(594\) 0 0
\(595\) 24.0000 41.5692i 0.983904 1.70417i
\(596\) 0 0
\(597\) −21.0000 12.1244i −0.859473 0.496217i
\(598\) 0 0
\(599\) 18.0000 31.1769i 0.735460 1.27385i −0.219061 0.975711i \(-0.570299\pi\)
0.954521 0.298143i \(-0.0963673\pi\)
\(600\) 0 0
\(601\) 8.66025i 0.353259i 0.984277 + 0.176630i \(0.0565195\pi\)
−0.984277 + 0.176630i \(0.943481\pi\)
\(602\) 0 0
\(603\) 13.5000 + 7.79423i 0.549762 + 0.317406i
\(604\) 0 0
\(605\) 24.0000 13.8564i 0.975739 0.563343i
\(606\) 0 0
\(607\) 31.1769i 1.26543i 0.774384 + 0.632716i \(0.218060\pi\)
−0.774384 + 0.632716i \(0.781940\pi\)
\(608\) 0 0
\(609\) 18.0000 + 10.3923i 0.729397 + 0.421117i
\(610\) 0 0
\(611\) −6.00000 10.3923i −0.242734 0.420428i
\(612\) 0 0
\(613\) −17.0000 29.4449i −0.686624 1.18927i −0.972924 0.231127i \(-0.925759\pi\)
0.286300 0.958140i \(-0.407575\pi\)
\(614\) 0 0
\(615\) −9.00000 + 15.5885i −0.362915 + 0.628587i
\(616\) 0 0
\(617\) 1.50000 + 0.866025i 0.0603877 + 0.0348649i 0.529890 0.848066i \(-0.322233\pi\)
−0.469502 + 0.882931i \(0.655567\pi\)
\(618\) 0 0
\(619\) −40.0000 −1.60774 −0.803868 0.594808i \(-0.797228\pi\)
−0.803868 + 0.594808i \(0.797228\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −6.00000 + 10.3923i −0.240385 + 0.416359i
\(624\) 0 0
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 0 0
\(627\) 1.50000 12.9904i 0.0599042 0.518786i
\(628\) 0 0
\(629\) 24.0000 + 41.5692i 0.956943 + 1.65747i
\(630\) 0 0
\(631\) −1.00000 + 1.73205i −0.0398094 + 0.0689519i −0.885244 0.465128i \(-0.846008\pi\)
0.845434 + 0.534080i \(0.179342\pi\)
\(632\) 0 0
\(633\) 9.00000 + 15.5885i 0.357718 + 0.619586i
\(634\) 0 0
\(635\) 36.0000 1.42862
\(636\) 0 0
\(637\) 9.00000 + 5.19615i 0.356593 + 0.205879i
\(638\) 0 0
\(639\) 9.00000 + 15.5885i 0.356034 + 0.616670i
\(640\) 0 0
\(641\) −22.5000 38.9711i −0.888697 1.53927i −0.841417 0.540386i \(-0.818278\pi\)
−0.0472793 0.998882i \(-0.515055\pi\)
\(642\) 0 0
\(643\) −24.5000 42.4352i −0.966186 1.67348i −0.706395 0.707818i \(-0.749680\pi\)
−0.259791 0.965665i \(-0.583654\pi\)
\(644\) 0 0
\(645\) 24.0000 41.5692i 0.944999 1.63679i
\(646\) 0 0
\(647\) 24.2487i 0.953315i 0.879089 + 0.476658i \(0.158152\pi\)
−0.879089 + 0.476658i \(0.841848\pi\)
\(648\) 0 0
\(649\) −4.50000 + 2.59808i −0.176640 + 0.101983i
\(650\) 0 0
\(651\) −24.0000 −0.940634
\(652\) 0 0
\(653\) 6.92820i 0.271122i −0.990769 0.135561i \(-0.956716\pi\)
0.990769 0.135561i \(-0.0432836\pi\)
\(654\) 0 0
\(655\) −33.0000 + 57.1577i −1.28942 + 2.23334i
\(656\) 0 0
\(657\) 7.50000 + 12.9904i 0.292603 + 0.506803i
\(658\) 0 0
\(659\) −18.0000 + 31.1769i −0.701180 + 1.21448i 0.266872 + 0.963732i \(0.414010\pi\)
−0.968052 + 0.250748i \(0.919323\pi\)
\(660\) 0 0
\(661\) −33.0000 19.0526i −1.28355 0.741059i −0.306055 0.952014i \(-0.599009\pi\)
−0.977496 + 0.210955i \(0.932343\pi\)
\(662\) 0 0
\(663\) 41.5692i 1.61441i
\(664\) 0 0
\(665\) 12.0000 + 27.7128i 0.465340 + 1.07466i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 12.0000 + 20.7846i 0.463947 + 0.803579i
\(670\) 0 0
\(671\) 15.0000 + 8.66025i 0.579069 + 0.334325i
\(672\) 0 0
\(673\) 20.7846i 0.801188i 0.916256 + 0.400594i \(0.131196\pi\)
−0.916256 + 0.400594i \(0.868804\pi\)
\(674\) 0 0
\(675\) 31.5000 + 18.1865i 1.21244 + 0.700000i
\(676\) 0 0
\(677\) −42.0000 −1.61419 −0.807096 0.590421i \(-0.798962\pi\)
−0.807096 + 0.590421i \(0.798962\pi\)
\(678\) 0 0
\(679\) 15.0000 8.66025i 0.575647 0.332350i
\(680\) 0 0
\(681\) 36.3731i 1.39382i
\(682\) 0 0
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0 0
\(685\) 6.00000 0.229248
\(686\) 0 0
\(687\) 6.92820i 0.264327i
\(688\) 0 0
\(689\) −18.0000 + 10.3923i −0.685745 + 0.395915i
\(690\) 0 0
\(691\) −20.0000 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) 0 0
\(693\) 10.3923i 0.394771i
\(694\) 0 0
\(695\) 3.46410i 0.131401i
\(696\) 0 0
\(697\) −18.0000 10.3923i −0.681799 0.393637i
\(698\) 0 0
\(699\) −1.50000 2.59808i −0.0567352 0.0982683i
\(700\) 0 0
\(701\) −9.00000 + 5.19615i −0.339925 + 0.196256i −0.660239 0.751056i \(-0.729545\pi\)
0.320314 + 0.947312i \(0.396212\pi\)
\(702\) 0 0
\(703\) −30.0000 3.46410i −1.13147 0.130651i
\(704\) 0 0
\(705\) 20.7846i 0.782794i
\(706\) 0 0
\(707\) 18.0000 + 10.3923i 0.676960 + 0.390843i
\(708\) 0 0
\(709\) −4.00000 + 6.92820i −0.150223 + 0.260194i −0.931309 0.364229i \(-0.881333\pi\)
0.781086 + 0.624423i \(0.214666\pi\)
\(710\) 0 0
\(711\) −36.0000 + 20.7846i −1.35011 + 0.779484i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 20.7846i 0.777300i
\(716\) 0 0
\(717\) 12.0000 0.448148
\(718\) 0 0
\(719\) 3.00000 1.73205i 0.111881 0.0645946i −0.443015 0.896514i \(-0.646091\pi\)
0.554896 + 0.831919i \(0.312758\pi\)
\(720\) 0 0
\(721\) 20.7846i 0.774059i
\(722\) 0 0
\(723\) 4.50000 7.79423i 0.167357 0.289870i
\(724\) 0 0
\(725\) 21.0000 + 36.3731i 0.779920 + 1.35086i
\(726\) 0 0
\(727\) 4.00000 + 6.92820i 0.148352 + 0.256953i 0.930618 0.365991i \(-0.119270\pi\)
−0.782267 + 0.622944i \(0.785937\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 48.0000 + 27.7128i 1.77534 + 1.02500i
\(732\) 0 0
\(733\) −4.00000 −0.147743 −0.0738717 0.997268i \(-0.523536\pi\)
−0.0738717 + 0.997268i \(0.523536\pi\)
\(734\) 0 0
\(735\) 9.00000 + 15.5885i 0.331970 + 0.574989i
\(736\) 0 0
\(737\) −4.50000 + 7.79423i −0.165760 + 0.287104i
\(738\) 0 0
\(739\) −5.50000 9.52628i −0.202321 0.350430i 0.746955 0.664875i \(-0.231515\pi\)
−0.949276 + 0.314445i \(0.898182\pi\)
\(740\) 0 0
\(741\) −21.0000 15.5885i −0.771454 0.572656i
\(742\) 0 0
\(743\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0 0
\(745\) 12.0000 20.7846i 0.439646 0.761489i
\(746\) 0 0
\(747\) 15.5885i 0.570352i
\(748\) 0 0
\(749\) −24.0000 −0.876941
\(750\) 0 0
\(751\) 33.0000 + 19.0526i 1.20419 + 0.695238i 0.961483 0.274863i \(-0.0886324\pi\)
0.242704 + 0.970100i \(0.421966\pi\)
\(752\) 0 0
\(753\) −7.50000 + 12.9904i −0.273315 + 0.473396i
\(754\) 0 0
\(755\) 12.0000 + 20.7846i 0.436725 + 0.756429i
\(756\) 0 0
\(757\) 19.0000 + 32.9090i 0.690567 + 1.19610i 0.971652 + 0.236414i \(0.0759722\pi\)
−0.281086 + 0.959683i \(0.590695\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 8.66025i 0.313934i −0.987604 0.156967i \(-0.949828\pi\)
0.987604 0.156967i \(-0.0501716\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −36.0000 + 62.3538i −1.30158 + 2.25441i
\(766\) 0 0
\(767\) 10.3923i 0.375244i
\(768\) 0 0
\(769\) 7.00000 12.1244i 0.252426 0.437215i −0.711767 0.702416i \(-0.752105\pi\)
0.964193 + 0.265200i \(0.0854381\pi\)
\(770\) 0 0
\(771\) 22.5000 + 12.9904i 0.810318 + 0.467837i
\(772\) 0 0
\(773\) 3.00000 5.19615i 0.107903 0.186893i −0.807018 0.590527i \(-0.798920\pi\)
0.914920 + 0.403634i \(0.132253\pi\)
\(774\) 0 0
\(775\) −42.0000 24.2487i −1.50868 0.871039i
\(776\) 0 0
\(777\) 24.0000 0.860995
\(778\) 0 0
\(779\) 12.0000 5.19615i 0.429945 0.186171i
\(780\) 0 0
\(781\) −9.00000 + 5.19615i −0.322045 + 0.185933i
\(782\) 0 0
\(783\) −27.0000 15.5885i −0.964901 0.557086i
\(784\) 0 0
\(785\) 60.0000 + 34.6410i 2.14149 + 1.23639i
\(786\) 0 0
\(787\) 1.73205i 0.0617409i 0.999523 + 0.0308705i \(0.00982794\pi\)
−0.999523 + 0.0308705i \(0.990172\pi\)
\(788\) 0 0
\(789\) −3.00000 5.19615i −0.106803 0.184988i
\(790\) 0 0
\(791\) −30.0000 −1.06668
\(792\) 0 0
\(793\) 30.0000 17.3205i 1.06533 0.615069i
\(794\) 0 0