Properties

Label 1344.2.q.m.961.1
Level $1344$
Weight $2$
Character 1344.961
Analytic conductor $10.732$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1344.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.7318940317\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1344.961
Dual form 1344.2.q.m.193.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{11} -1.00000 q^{13} -2.00000 q^{15} +(0.500000 - 0.866025i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -4.00000 q^{29} +(-4.50000 - 7.79423i) q^{31} +(1.00000 - 1.73205i) q^{33} +(1.00000 - 5.19615i) q^{35} +(1.50000 - 2.59808i) q^{37} +(-0.500000 - 0.866025i) q^{39} -10.0000 q^{41} -5.00000 q^{43} +(-1.00000 - 1.73205i) q^{45} +(3.00000 - 5.19615i) q^{47} +(5.50000 - 4.33013i) q^{49} +(6.00000 + 10.3923i) q^{53} +4.00000 q^{55} +1.00000 q^{57} +(-6.00000 - 10.3923i) q^{59} +(5.00000 - 8.66025i) q^{61} +(0.500000 - 2.59808i) q^{63} +(1.00000 - 1.73205i) q^{65} +(-2.50000 - 4.33013i) q^{67} -6.00000 q^{71} +(1.50000 + 2.59808i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(4.00000 + 3.46410i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} -6.00000 q^{83} +(-2.00000 - 3.46410i) q^{87} +(-8.00000 + 13.8564i) q^{89} +(2.50000 - 0.866025i) q^{91} +(4.50000 - 7.79423i) q^{93} +(1.00000 + 1.73205i) q^{95} -6.00000 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} - 2q^{5} - 5q^{7} - q^{9} + O(q^{10}) \) \( 2q + q^{3} - 2q^{5} - 5q^{7} - q^{9} - 2q^{11} - 2q^{13} - 4q^{15} + q^{19} - 4q^{21} + q^{25} - 2q^{27} - 8q^{29} - 9q^{31} + 2q^{33} + 2q^{35} + 3q^{37} - q^{39} - 20q^{41} - 10q^{43} - 2q^{45} + 6q^{47} + 11q^{49} + 12q^{53} + 8q^{55} + 2q^{57} - 12q^{59} + 10q^{61} + q^{63} + 2q^{65} - 5q^{67} - 12q^{71} + 3q^{73} - q^{75} + 8q^{77} + q^{79} - q^{81} - 12q^{83} - 4q^{87} - 16q^{89} + 5q^{91} + 9q^{93} + 2q^{95} - 12q^{97} + 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(449\) \(577\) \(1093\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(4\) 0 0
\(5\) −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) 0 0
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 0 0
\(15\) −2.00000 −0.516398
\(16\) 0 0
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) −2.00000 1.73205i −0.436436 0.377964i
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) −4.50000 7.79423i −0.808224 1.39988i −0.914093 0.405505i \(-0.867096\pi\)
0.105869 0.994380i \(-0.466238\pi\)
\(32\) 0 0
\(33\) 1.00000 1.73205i 0.174078 0.301511i
\(34\) 0 0
\(35\) 1.00000 5.19615i 0.169031 0.878310i
\(36\) 0 0
\(37\) 1.50000 2.59808i 0.246598 0.427121i −0.715981 0.698119i \(-0.754020\pi\)
0.962580 + 0.270998i \(0.0873538\pi\)
\(38\) 0 0
\(39\) −0.500000 0.866025i −0.0800641 0.138675i
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) −5.00000 −0.762493 −0.381246 0.924473i \(-0.624505\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 0 0
\(45\) −1.00000 1.73205i −0.149071 0.258199i
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.00000 + 10.3923i 0.824163 + 1.42749i 0.902557 + 0.430570i \(0.141688\pi\)
−0.0783936 + 0.996922i \(0.524979\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 1.00000 0.132453
\(58\) 0 0
\(59\) −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i \(-0.881308\pi\)
0.150148 0.988663i \(-0.452025\pi\)
\(60\) 0 0
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) 0 0
\(63\) 0.500000 2.59808i 0.0629941 0.327327i
\(64\) 0 0
\(65\) 1.00000 1.73205i 0.124035 0.214834i
\(66\) 0 0
\(67\) −2.50000 4.33013i −0.305424 0.529009i 0.671932 0.740613i \(-0.265465\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) 1.50000 + 2.59808i 0.175562 + 0.304082i 0.940356 0.340193i \(-0.110493\pi\)
−0.764794 + 0.644275i \(0.777159\pi\)
\(74\) 0 0
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) 0 0
\(77\) 4.00000 + 3.46410i 0.455842 + 0.394771i
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −2.00000 3.46410i −0.214423 0.371391i
\(88\) 0 0
\(89\) −8.00000 + 13.8564i −0.847998 + 1.46878i 0.0349934 + 0.999388i \(0.488859\pi\)
−0.882992 + 0.469389i \(0.844474\pi\)
\(90\) 0 0
\(91\) 2.50000 0.866025i 0.262071 0.0907841i
\(92\) 0 0
\(93\) 4.50000 7.79423i 0.466628 0.808224i
\(94\) 0 0
\(95\) 1.00000 + 1.73205i 0.102598 + 0.177705i
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) 1.00000 + 1.73205i 0.0995037 + 0.172345i 0.911479 0.411346i \(-0.134941\pi\)
−0.811976 + 0.583691i \(0.801608\pi\)
\(102\) 0 0
\(103\) 3.50000 6.06218i 0.344865 0.597324i −0.640464 0.767988i \(-0.721258\pi\)
0.985329 + 0.170664i \(0.0545913\pi\)
\(104\) 0 0
\(105\) 5.00000 1.73205i 0.487950 0.169031i
\(106\) 0 0
\(107\) −4.00000 + 6.92820i −0.386695 + 0.669775i −0.992003 0.126217i \(-0.959717\pi\)
0.605308 + 0.795991i \(0.293050\pi\)
\(108\) 0 0
\(109\) 4.50000 + 7.79423i 0.431022 + 0.746552i 0.996962 0.0778949i \(-0.0248199\pi\)
−0.565940 + 0.824447i \(0.691487\pi\)
\(110\) 0 0
\(111\) 3.00000 0.284747
\(112\) 0 0
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.500000 0.866025i 0.0462250 0.0800641i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 0 0
\(123\) −5.00000 8.66025i −0.450835 0.780869i
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −15.0000 −1.33103 −0.665517 0.746382i \(-0.731789\pi\)
−0.665517 + 0.746382i \(0.731789\pi\)
\(128\) 0 0
\(129\) −2.50000 4.33013i −0.220113 0.381246i
\(130\) 0 0
\(131\) −7.00000 + 12.1244i −0.611593 + 1.05931i 0.379379 + 0.925241i \(0.376138\pi\)
−0.990972 + 0.134069i \(0.957196\pi\)
\(132\) 0 0
\(133\) −0.500000 + 2.59808i −0.0433555 + 0.225282i
\(134\) 0 0
\(135\) 1.00000 1.73205i 0.0860663 0.149071i
\(136\) 0 0
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 0 0
\(139\) 3.00000 0.254457 0.127228 0.991873i \(-0.459392\pi\)
0.127228 + 0.991873i \(0.459392\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) 1.00000 + 1.73205i 0.0836242 + 0.144841i
\(144\) 0 0
\(145\) 4.00000 6.92820i 0.332182 0.575356i
\(146\) 0 0
\(147\) 6.50000 + 2.59808i 0.536111 + 0.214286i
\(148\) 0 0
\(149\) −6.00000 + 10.3923i −0.491539 + 0.851371i −0.999953 0.00974235i \(-0.996899\pi\)
0.508413 + 0.861113i \(0.330232\pi\)
\(150\) 0 0
\(151\) 8.00000 + 13.8564i 0.651031 + 1.12762i 0.982873 + 0.184284i \(0.0589965\pi\)
−0.331842 + 0.943335i \(0.607670\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 18.0000 1.44579
\(156\) 0 0
\(157\) −7.00000 12.1244i −0.558661 0.967629i −0.997609 0.0691164i \(-0.977982\pi\)
0.438948 0.898513i \(-0.355351\pi\)
\(158\) 0 0
\(159\) −6.00000 + 10.3923i −0.475831 + 0.824163i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 0 0
\(165\) 2.00000 + 3.46410i 0.155700 + 0.269680i
\(166\) 0 0
\(167\) −14.0000 −1.08335 −0.541676 0.840587i \(-0.682210\pi\)
−0.541676 + 0.840587i \(0.682210\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0.500000 + 0.866025i 0.0382360 + 0.0662266i
\(172\) 0 0
\(173\) 4.00000 6.92820i 0.304114 0.526742i −0.672949 0.739689i \(-0.734973\pi\)
0.977064 + 0.212947i \(0.0683062\pi\)
\(174\) 0 0
\(175\) −2.00000 1.73205i −0.151186 0.130931i
\(176\) 0 0
\(177\) 6.00000 10.3923i 0.450988 0.781133i
\(178\) 0 0
\(179\) 1.00000 + 1.73205i 0.0747435 + 0.129460i 0.900975 0.433872i \(-0.142853\pi\)
−0.826231 + 0.563331i \(0.809520\pi\)
\(180\) 0 0
\(181\) −13.0000 −0.966282 −0.483141 0.875542i \(-0.660504\pi\)
−0.483141 + 0.875542i \(0.660504\pi\)
\(182\) 0 0
\(183\) 10.0000 0.739221
\(184\) 0 0
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 2.50000 0.866025i 0.181848 0.0629941i
\(190\) 0 0
\(191\) −5.00000 + 8.66025i −0.361787 + 0.626634i −0.988255 0.152813i \(-0.951167\pi\)
0.626468 + 0.779447i \(0.284500\pi\)
\(192\) 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
\(195\) 2.00000 0.143223
\(196\) 0 0
\(197\) −16.0000 −1.13995 −0.569976 0.821661i \(-0.693048\pi\)
−0.569976 + 0.821661i \(0.693048\pi\)
\(198\) 0 0
\(199\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) 0 0
\(201\) 2.50000 4.33013i 0.176336 0.305424i
\(202\) 0 0
\(203\) 10.0000 3.46410i 0.701862 0.243132i
\(204\) 0 0
\(205\) 10.0000 17.3205i 0.698430 1.20972i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) −3.00000 5.19615i −0.205557 0.356034i
\(214\) 0 0
\(215\) 5.00000 8.66025i 0.340997 0.590624i
\(216\) 0 0
\(217\) 18.0000 + 15.5885i 1.22192 + 1.05821i
\(218\) 0 0
\(219\) −1.50000 + 2.59808i −0.101361 + 0.175562i
\(220\) 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
\(225\) −1.00000 −0.0666667
\(226\) 0 0
\(227\) 9.00000 + 15.5885i 0.597351 + 1.03464i 0.993210 + 0.116331i \(0.0371134\pi\)
−0.395860 + 0.918311i \(0.629553\pi\)
\(228\) 0 0
\(229\) −9.50000 + 16.4545i −0.627778 + 1.08734i 0.360219 + 0.932868i \(0.382702\pi\)
−0.987997 + 0.154475i \(0.950631\pi\)
\(230\) 0 0
\(231\) −1.00000 + 5.19615i −0.0657952 + 0.341882i
\(232\) 0 0
\(233\) −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) 0 0
\(235\) 6.00000 + 10.3923i 0.391397 + 0.677919i
\(236\) 0 0
\(237\) 1.00000 0.0649570
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i \(-0.315567\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 2.00000 + 13.8564i 0.127775 + 0.885253i
\(246\) 0 0
\(247\) −0.500000 + 0.866025i −0.0318142 + 0.0551039i
\(248\) 0 0
\(249\) −3.00000 5.19615i −0.190117 0.329293i
\(250\) 0 0
\(251\) 8.00000 0.504956 0.252478 0.967603i \(-0.418755\pi\)
0.252478 + 0.967603i \(0.418755\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −13.0000 + 22.5167i −0.810918 + 1.40455i 0.101305 + 0.994855i \(0.467698\pi\)
−0.912222 + 0.409695i \(0.865635\pi\)
\(258\) 0 0
\(259\) −1.50000 + 7.79423i −0.0932055 + 0.484310i
\(260\) 0 0
\(261\) 2.00000 3.46410i 0.123797 0.214423i
\(262\) 0 0
\(263\) −2.00000 3.46410i −0.123325 0.213606i 0.797752 0.602986i \(-0.206023\pi\)
−0.921077 + 0.389380i \(0.872689\pi\)
\(264\) 0 0
\(265\) −24.0000 −1.47431
\(266\) 0 0
\(267\) −16.0000 −0.979184
\(268\) 0 0
\(269\) 3.00000 + 5.19615i 0.182913 + 0.316815i 0.942871 0.333157i \(-0.108114\pi\)
−0.759958 + 0.649972i \(0.774781\pi\)
\(270\) 0 0
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) 0 0
\(273\) 2.00000 + 1.73205i 0.121046 + 0.104828i
\(274\) 0 0
\(275\) 1.00000 1.73205i 0.0603023 0.104447i
\(276\) 0 0
\(277\) 6.50000 + 11.2583i 0.390547 + 0.676448i 0.992522 0.122068i \(-0.0389525\pi\)
−0.601975 + 0.798515i \(0.705619\pi\)
\(278\) 0 0
\(279\) 9.00000 0.538816
\(280\) 0 0
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) 0 0
\(283\) −5.50000 9.52628i −0.326941 0.566279i 0.654962 0.755662i \(-0.272685\pi\)
−0.981903 + 0.189383i \(0.939351\pi\)
\(284\) 0 0
\(285\) −1.00000 + 1.73205i −0.0592349 + 0.102598i
\(286\) 0 0
\(287\) 25.0000 8.66025i 1.47570 0.511199i
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 0 0
\(291\) −3.00000 5.19615i −0.175863 0.304604i
\(292\) 0 0
\(293\) −8.00000 −0.467365 −0.233682 0.972313i \(-0.575078\pi\)
−0.233682 + 0.972313i \(0.575078\pi\)
\(294\) 0 0
\(295\) 24.0000 1.39733
\(296\) 0 0
\(297\) 1.00000 + 1.73205i 0.0580259 + 0.100504i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 12.5000 4.33013i 0.720488 0.249584i
\(302\) 0 0
\(303\) −1.00000 + 1.73205i −0.0574485 + 0.0995037i
\(304\) 0 0
\(305\) 10.0000 + 17.3205i 0.572598 + 0.991769i
\(306\) 0 0
\(307\) 17.0000 0.970241 0.485121 0.874447i \(-0.338776\pi\)
0.485121 + 0.874447i \(0.338776\pi\)
\(308\) 0 0
\(309\) 7.00000 0.398216
\(310\) 0 0
\(311\) 3.00000 + 5.19615i 0.170114 + 0.294647i 0.938460 0.345389i \(-0.112253\pi\)
−0.768345 + 0.640036i \(0.778920\pi\)
\(312\) 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
\(315\) 4.00000 + 3.46410i 0.225374 + 0.195180i
\(316\) 0 0
\(317\) 12.0000 20.7846i 0.673987 1.16738i −0.302777 0.953062i \(-0.597914\pi\)
0.976764 0.214318i \(-0.0687530\pi\)
\(318\) 0 0
\(319\) 4.00000 + 6.92820i 0.223957 + 0.387905i
\(320\) 0 0
\(321\) −8.00000 −0.446516
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −0.500000 0.866025i −0.0277350 0.0480384i
\(326\) 0 0
\(327\) −4.50000 + 7.79423i −0.248851 + 0.431022i
\(328\) 0 0
\(329\) −3.00000 + 15.5885i −0.165395 + 0.859419i
\(330\) 0 0
\(331\) −12.5000 + 21.6506i −0.687062 + 1.19003i 0.285722 + 0.958313i \(0.407767\pi\)
−0.972784 + 0.231714i \(0.925567\pi\)
\(332\) 0 0
\(333\) 1.50000 + 2.59808i 0.0821995 + 0.142374i
\(334\) 0 0
\(335\) 10.0000 0.546358
\(336\) 0 0
\(337\) 13.0000 0.708155 0.354078 0.935216i \(-0.384795\pi\)
0.354078 + 0.935216i \(0.384795\pi\)
\(338\) 0 0
\(339\) 5.00000 + 8.66025i 0.271563 + 0.470360i
\(340\) 0 0
\(341\) −9.00000 + 15.5885i −0.487377 + 0.844162i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 16.0000 + 27.7128i 0.858925 + 1.48770i 0.872955 + 0.487800i \(0.162201\pi\)
−0.0140303 + 0.999902i \(0.504466\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) −17.0000 29.4449i −0.904819 1.56719i −0.821160 0.570697i \(-0.806673\pi\)
−0.0836583 0.996495i \(-0.526660\pi\)
\(354\) 0 0
\(355\) 6.00000 10.3923i 0.318447 0.551566i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10.0000 + 17.3205i −0.527780 + 0.914141i 0.471696 + 0.881761i \(0.343642\pi\)
−0.999476 + 0.0323801i \(0.989691\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 0 0
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) 4.50000 + 7.79423i 0.234898 + 0.406855i 0.959243 0.282582i \(-0.0911910\pi\)
−0.724345 + 0.689438i \(0.757858\pi\)
\(368\) 0 0
\(369\) 5.00000 8.66025i 0.260290 0.450835i
\(370\) 0 0
\(371\) −24.0000 20.7846i −1.24602 1.07908i
\(372\) 0 0
\(373\) 11.5000 19.9186i 0.595447 1.03135i −0.398036 0.917370i \(-0.630308\pi\)
0.993484 0.113975i \(-0.0363585\pi\)
\(374\) 0 0
\(375\) −6.00000 10.3923i −0.309839 0.536656i
\(376\) 0 0
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) −3.00000 −0.154100 −0.0770498 0.997027i \(-0.524550\pi\)
−0.0770498 + 0.997027i \(0.524550\pi\)
\(380\) 0 0
\(381\) −7.50000 12.9904i −0.384237 0.665517i
\(382\) 0 0
\(383\) 6.00000 10.3923i 0.306586 0.531022i −0.671027 0.741433i \(-0.734147\pi\)
0.977613 + 0.210411i \(0.0674801\pi\)
\(384\) 0 0
\(385\) −10.0000 + 3.46410i −0.509647 + 0.176547i
\(386\) 0 0
\(387\) 2.50000 4.33013i 0.127082 0.220113i
\(388\) 0 0
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −14.0000 −0.706207
\(394\) 0 0
\(395\) 1.00000 + 1.73205i 0.0503155 + 0.0871489i
\(396\) 0 0
\(397\) −4.50000 + 7.79423i −0.225849 + 0.391181i −0.956574 0.291491i \(-0.905849\pi\)
0.730725 + 0.682672i \(0.239182\pi\)
\(398\) 0 0
\(399\) −2.50000 + 0.866025i −0.125157 + 0.0433555i
\(400\) 0 0
\(401\) 18.0000 31.1769i 0.898877 1.55690i 0.0699455 0.997551i \(-0.477717\pi\)
0.828932 0.559350i \(-0.188949\pi\)
\(402\) 0 0
\(403\) 4.50000 + 7.79423i 0.224161 + 0.388258i
\(404\) 0 0
\(405\) 2.00000 0.0993808
\(406\) 0 0
\(407\) −6.00000 −0.297409
\(408\) 0 0
\(409\) −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i \(-0.206116\pi\)
−0.921192 + 0.389109i \(0.872783\pi\)
\(410\) 0 0
\(411\) −6.00000 + 10.3923i −0.295958 + 0.512615i
\(412\) 0 0
\(413\) 24.0000 + 20.7846i 1.18096 + 1.02274i
\(414\) 0 0
\(415\) 6.00000 10.3923i 0.294528 0.510138i
\(416\) 0 0
\(417\) 1.50000 + 2.59808i 0.0734553 + 0.127228i
\(418\) 0 0
\(419\) −30.0000 −1.46560 −0.732798 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) 0 0
\(421\) 7.00000 0.341159 0.170580 0.985344i \(-0.445436\pi\)
0.170580 + 0.985344i \(0.445436\pi\)
\(422\) 0 0
\(423\) 3.00000 + 5.19615i 0.145865 + 0.252646i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −5.00000 + 25.9808i −0.241967 + 1.25730i
\(428\) 0 0
\(429\) −1.00000 + 1.73205i −0.0482805 + 0.0836242i
\(430\) 0 0
\(431\) 9.00000 + 15.5885i 0.433515 + 0.750870i 0.997173 0.0751385i \(-0.0239399\pi\)
−0.563658 + 0.826008i \(0.690607\pi\)
\(432\) 0 0
\(433\) 31.0000 1.48976 0.744882 0.667196i \(-0.232506\pi\)
0.744882 + 0.667196i \(0.232506\pi\)
\(434\) 0 0
\(435\) 8.00000 0.383571
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0 0
\(441\) 1.00000 + 6.92820i 0.0476190 + 0.329914i
\(442\) 0 0
\(443\) 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i \(-0.741317\pi\)
0.972626 + 0.232377i \(0.0746503\pi\)
\(444\) 0 0
\(445\) −16.0000 27.7128i −0.758473 1.31371i
\(446\) 0 0
\(447\) −12.0000 −0.567581
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) 10.0000 + 17.3205i 0.470882 + 0.815591i
\(452\) 0 0
\(453\) −8.00000 + 13.8564i −0.375873 + 0.651031i
\(454\) 0 0
\(455\) −1.00000 + 5.19615i −0.0468807 + 0.243599i
\(456\) 0 0
\(457\) 5.50000 9.52628i 0.257279 0.445621i −0.708233 0.705979i \(-0.750507\pi\)
0.965512 + 0.260358i \(0.0838407\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −20.0000 −0.931493 −0.465746 0.884918i \(-0.654214\pi\)
−0.465746 + 0.884918i \(0.654214\pi\)
\(462\) 0 0
\(463\) −17.0000 −0.790057 −0.395029 0.918669i \(-0.629265\pi\)
−0.395029 + 0.918669i \(0.629265\pi\)
\(464\) 0 0
\(465\) 9.00000 + 15.5885i 0.417365 + 0.722897i
\(466\) 0 0
\(467\) 3.00000 5.19615i 0.138823 0.240449i −0.788228 0.615383i \(-0.789001\pi\)
0.927052 + 0.374934i \(0.122335\pi\)
\(468\) 0 0
\(469\) 10.0000 + 8.66025i 0.461757 + 0.399893i
\(470\) 0 0
\(471\) 7.00000 12.1244i 0.322543 0.558661i
\(472\) 0 0
\(473\) 5.00000 + 8.66025i 0.229900 + 0.398199i
\(474\) 0 0
\(475\) 1.00000 0.0458831
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) 0 0
\(479\) 14.0000 + 24.2487i 0.639676 + 1.10795i 0.985504 + 0.169654i \(0.0542649\pi\)
−0.345827 + 0.938298i \(0.612402\pi\)
\(480\) 0 0
\(481\) −1.50000 + 2.59808i −0.0683941 + 0.118462i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 6.00000 10.3923i 0.272446 0.471890i
\(486\) 0 0
\(487\) −15.5000 26.8468i −0.702372 1.21654i −0.967632 0.252367i \(-0.918791\pi\)
0.265260 0.964177i \(-0.414542\pi\)
\(488\) 0 0
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) 28.0000 1.26362 0.631811 0.775122i \(-0.282312\pi\)
0.631811 + 0.775122i \(0.282312\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −2.00000 + 3.46410i −0.0898933 + 0.155700i
\(496\) 0 0
\(497\) 15.0000 5.19615i 0.672842 0.233079i
\(498\) 0 0
\(499\) 18.5000 32.0429i 0.828174 1.43444i −0.0712957 0.997455i \(-0.522713\pi\)
0.899469 0.436984i \(-0.143953\pi\)
\(500\) 0 0
\(501\) −7.00000 12.1244i −0.312737 0.541676i
\(502\) 0 0
\(503\) −42.0000 −1.87269 −0.936344 0.351085i \(-0.885813\pi\)
−0.936344 + 0.351085i \(0.885813\pi\)
\(504\) 0 0
\(505\) −4.00000 −0.177998
\(506\) 0 0
\(507\) −6.00000 10.3923i −0.266469 0.461538i
\(508\) 0 0
\(509\) 1.00000 1.73205i 0.0443242 0.0767718i −0.843012 0.537895i \(-0.819220\pi\)
0.887336 + 0.461123i \(0.152553\pi\)
\(510\) 0 0
\(511\) −6.00000 5.19615i −0.265424 0.229864i
\(512\) 0 0
\(513\) −0.500000 + 0.866025i −0.0220755 + 0.0382360i
\(514\) 0 0
\(515\) 7.00000 + 12.1244i 0.308457 + 0.534263i
\(516\) 0 0
\(517\) −12.0000 −0.527759
\(518\) 0 0
\(519\) 8.00000 0.351161
\(520\) 0 0
\(521\) −6.00000 10.3923i −0.262865 0.455295i 0.704137 0.710064i \(-0.251334\pi\)
−0.967002 + 0.254769i \(0.918001\pi\)
\(522\) 0 0
\(523\) 15.5000 26.8468i 0.677768 1.17393i −0.297884 0.954602i \(-0.596281\pi\)
0.975652 0.219326i \(-0.0703858\pi\)
\(524\) 0 0
\(525\) 0.500000 2.59808i 0.0218218 0.113389i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) 10.0000 0.433148
\(534\) 0 0
\(535\) −8.00000 13.8564i −0.345870 0.599065i
\(536\) 0 0
\(537\) −1.00000 + 1.73205i −0.0431532 + 0.0747435i
\(538\) 0 0
\(539\) −13.0000 5.19615i −0.559950 0.223814i
\(540\) 0 0
\(541\) −9.50000 + 16.4545i −0.408437 + 0.707433i −0.994715 0.102677i \(-0.967259\pi\)
0.586278 + 0.810110i \(0.300593\pi\)
\(542\) 0 0
\(543\) −6.50000 11.2583i −0.278942 0.483141i
\(544\) 0 0
\(545\) −18.0000 −0.771035
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) 5.00000 + 8.66025i 0.213395 + 0.369611i
\(550\) 0 0
\(551\) −2.00000 + 3.46410i −0.0852029 + 0.147576i
\(552\) 0 0
\(553\) −0.500000 + 2.59808i −0.0212622 + 0.110481i
\(554\) 0 0
\(555\) −3.00000 + 5.19615i −0.127343 + 0.220564i
\(556\) 0 0
\(557\) −1.00000 1.73205i −0.0423714 0.0733893i 0.844062 0.536246i \(-0.180158\pi\)
−0.886433 + 0.462856i \(0.846825\pi\)
\(558\) 0 0
\(559\) 5.00000 0.211477
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −13.0000 22.5167i −0.547885 0.948964i −0.998419 0.0562051i \(-0.982100\pi\)
0.450535 0.892759i \(-0.351233\pi\)
\(564\) 0 0
\(565\) −10.0000 + 17.3205i −0.420703 + 0.728679i
\(566\) 0 0
\(567\) 2.00000 + 1.73205i 0.0839921 + 0.0727393i
\(568\) 0 0
\(569\) 13.0000 22.5167i 0.544988 0.943948i −0.453619 0.891196i \(-0.649867\pi\)
0.998608 0.0527519i \(-0.0167993\pi\)
\(570\) 0 0
\(571\) −9.50000 16.4545i −0.397563 0.688599i 0.595862 0.803087i \(-0.296811\pi\)
−0.993425 + 0.114488i \(0.963477\pi\)
\(572\) 0 0
\(573\) −10.0000 −0.417756
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 8.50000 + 14.7224i 0.353860 + 0.612903i 0.986922 0.161198i \(-0.0515357\pi\)
−0.633062 + 0.774101i \(0.718202\pi\)
\(578\) 0 0
\(579\) 5.50000 9.52628i 0.228572 0.395899i
\(580\) 0 0
\(581\) 15.0000 5.19615i 0.622305 0.215573i
\(582\) 0 0
\(583\) 12.0000 20.7846i 0.496989 0.860811i
\(584\) 0 0
\(585\) 1.00000 + 1.73205i 0.0413449 + 0.0716115i
\(586\) 0 0
\(587\) −16.0000 −0.660391 −0.330195 0.943913i \(-0.607115\pi\)
−0.330195 + 0.943913i \(0.607115\pi\)
\(588\) 0 0
\(589\) −9.00000 −0.370839
\(590\) 0 0
\(591\) −8.00000 13.8564i −0.329076 0.569976i
\(592\) 0 0
\(593\) 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i \(-0.794019\pi\)
0.921026 + 0.389501i \(0.127353\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i \(-0.245505\pi\)
−0.962175 + 0.272433i \(0.912172\pi\)
\(600\) 0 0
\(601\) −9.00000 −0.367118 −0.183559 0.983009i \(-0.558762\pi\)
−0.183559 + 0.983009i \(0.558762\pi\)
\(602\) 0 0
\(603\) 5.00000 0.203616
\(604\) 0 0
\(605\) 7.00000 + 12.1244i 0.284590 + 0.492925i
\(606\) 0 0
\(607\) −11.5000 + 19.9186i −0.466771 + 0.808470i −0.999279 0.0379540i \(-0.987916\pi\)
0.532509 + 0.846424i \(0.321249\pi\)
\(608\) 0 0
\(609\) 8.00000 + 6.92820i 0.324176 + 0.280745i
\(610\) 0 0
\(611\) −3.00000 + 5.19615i −0.121367 + 0.210214i
\(612\) 0 0
\(613\) 17.0000 + 29.4449i 0.686624 + 1.18927i 0.972924 + 0.231127i \(0.0742412\pi\)
−0.286300 + 0.958140i \(0.592425\pi\)
\(614\) 0 0
\(615\) 20.0000 0.806478
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 0 0
\(619\) −14.5000 25.1147i −0.582804 1.00945i −0.995145 0.0984169i \(-0.968622\pi\)
0.412341 0.911030i \(-0.364711\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 8.00000 41.5692i 0.320513 1.66544i
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 0 0
\(627\) −1.00000 1.73205i −0.0399362 0.0691714i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) −2.00000 3.46410i −0.0794929 0.137686i
\(634\) 0 0
\(635\) 15.0000 25.9808i 0.595257 1.03102i
\(636\) 0 0
\(637\) −5.50000 + 4.33013i −0.217918 + 0.171566i
\(638\) 0 0
\(639\) 3.00000 5.19615i 0.118678 0.205557i
\(640\) 0 0
\(641\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(642\) 0 0
\(643\) 19.0000 0.749287 0.374643 0.927169i \(-0.377765\pi\)
0.374643 + 0.927169i \(0.377765\pi\)
\(644\) 0 0
\(645\) 10.0000 0.393750
\(646\) 0 0
\(647\) −1.00000 1.73205i −0.0393141 0.0680939i 0.845699 0.533660i \(-0.179184\pi\)
−0.885013 + 0.465566i \(0.845851\pi\)
\(648\) 0 0
\(649\) −12.0000 + 20.7846i −0.471041 + 0.815867i
\(650\) 0 0
\(651\) −4.50000 + 23.3827i −0.176369 + 0.916440i
\(652\) 0 0
\(653\) 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) 0 0
\(655\) −14.0000 24.2487i −0.547025 0.947476i
\(656\) 0 0
\(657\) −3.00000 −0.117041
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −20.5000 35.5070i −0.797358 1.38106i −0.921331 0.388778i \(-0.872897\pi\)
0.123974 0.992286i \(-0.460436\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.00000 3.46410i −0.155113 0.134332i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 8.00000 + 13.8564i 0.309298 + 0.535720i
\(670\) 0 0
\(671\) −20.0000 −0.772091
\(672\) 0 0
\(673\) −41.0000 −1.58043 −0.790217 0.612827i \(-0.790032\pi\)
−0.790217 + 0.612827i \(0.790032\pi\)
\(674\) 0 0
\(675\) −0.500000 0.866025i −0.0192450 0.0333333i
\(676\) 0 0
\(677\) 6.00000 10.3923i 0.230599 0.399409i −0.727386 0.686229i \(-0.759265\pi\)
0.957984 + 0.286820i \(0.0925982\pi\)
\(678\) 0 0
\(679\) 15.0000 5.19615i 0.575647 0.199410i
\(680\) 0 0
\(681\) −9.00000 + 15.5885i −0.344881 + 0.597351i
\(682\) 0 0
\(683\) −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) 0 0
\(685\) −24.0000 −0.916993
\(686\) 0 0
\(687\) −19.0000 −0.724895
\(688\) 0 0
\(689\) −6.00000 10.3923i −0.228582 0.395915i
\(690\) 0 0
\(691\) −18.5000 + 32.0429i −0.703773 + 1.21897i 0.263359 + 0.964698i \(0.415170\pi\)
−0.967132 + 0.254273i \(0.918164\pi\)
\(692\) 0 0
\(693\) −5.00000 + 1.73205i −0.189934 + 0.0657952i
\(694\) 0 0
\(695\) −3.00000 + 5.19615i −0.113796 + 0.197101i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) −1.50000 2.59808i −0.0565736 0.0979883i
\(704\) 0 0
\(705\) −6.00000 + 10.3923i −0.225973 + 0.391397i
\(706\) 0 0
\(707\) −4.00000 3.46410i −0.150435 0.130281i
\(708\) 0 0
\(709\) 15.0000 25.9808i 0.563337 0.975728i −0.433865 0.900978i \(-0.642851\pi\)
0.997202 0.0747503i \(-0.0238160\pi\)
\(710\) 0 0
\(711\) 0.500000 + 0.866025i 0.0187515 + 0.0324785i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −4.00000 −0.149592
\(716\) 0 0
\(717\) 3.00000 + 5.19615i 0.112037 + 0.194054i
\(718\) 0 0
\(719\) 9.00000 15.5885i 0.335643 0.581351i −0.647965 0.761670i \(-0.724380\pi\)
0.983608 + 0.180319i \(0.0577130\pi\)
\(720\) 0 0
\(721\) −3.50000 + 18.1865i −0.130347 + 0.677302i
\(722\) 0 0
\(723\) 7.00000 12.1244i 0.260333 0.450910i
\(724\) 0 0
\(725\) −2.00000 3.46410i −0.0742781 0.128654i
\(726\) 0 0
\(727\) −13.0000 −0.482143 −0.241072 0.970507i \(-0.577499\pi\)
−0.241072 + 0.970507i \(0.577499\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −7.50000 + 12.9904i −0.277019 + 0.479811i −0.970642 0.240527i \(-0.922680\pi\)
0.693624 + 0.720338i \(0.256013\pi\)
\(734\) 0 0
\(735\) −11.0000 + 8.66025i −0.405741 + 0.319438i
\(736\) 0 0
\(737\) −5.00000 + 8.66025i −0.184177 + 0.319005i
\(738\) 0 0
\(739\) −7.50000 12.9904i −0.275892 0.477859i 0.694468 0.719524i \(-0.255640\pi\)
−0.970360 + 0.241665i \(0.922307\pi\)
\(740\) 0 0
\(741\) −1.00000 −0.0367359
\(742\) 0 0
\(743\) 42.0000 1.54083 0.770415 0.637542i \(-0.220049\pi\)
0.770415 + 0.637542i \(0.220049\pi\)
\(744\) 0 0
\(745\) −12.0000 20.7846i −0.439646 0.761489i
\(746\) 0 0
\(747\) 3.00000 5.19615i 0.109764 0.190117i
\(748\) 0 0
\(749\) 4.00000 20.7846i 0.146157 0.759453i
\(750\) 0 0
\(751\) −6.50000 + 11.2583i −0.237188 + 0.410822i −0.959906 0.280321i \(-0.909559\pi\)
0.722718 + 0.691143i \(0.242893\pi\)
\(752\) 0 0
\(753\) 4.00000 + 6.92820i 0.145768 + 0.252478i
\(754\) 0 0
\(755\) −32.0000 −1.16460
\(756\) 0 0
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 24.0000 41.5692i 0.869999 1.50688i 0.00800331 0.999968i \(-0.497452\pi\)
0.861996 0.506915i \(-0.169214\pi\)
\(762\) 0 0
\(763\) −18.0000 15.5885i −0.651644 0.564340i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6.00000 + 10.3923i 0.216647 + 0.375244i
\(768\) 0 0
\(769\) −49.0000 −1.76699 −0.883493 0.468445i \(-0.844814\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 0 0
\(771\) −26.0000 −0.936367
\(772\) 0 0
\(773\) −17.0000 29.4449i −0.611448 1.05906i −0.990997 0.133887i \(-0.957254\pi\)
0.379549 0.925172i \(-0.376079\pi\)
\(774\) 0 0
\(775\) 4.50000 7.79423i 0.161645 0.279977i
\(776\) 0 0
\(777\) −7.50000 + 2.59808i −0.269061 + 0.0932055i
\(778\) 0 0
\(779\) −5.00000 + 8.66025i −0.179144 + 0.310286i
\(780\) 0 0
\(781\) 6.00000 + 10.3923i 0.214697 + 0.371866i
\(782\) 0 0
\(783\) 4.00000 0.142948
\(784\) 0 0
\(785\) 28.0000 0.999363
\(786\) 0 0
\(787\) 20.0000 + 34.6410i 0.712923 + 1.23482i 0.963755 + 0.266788i \(0.0859624\pi\)
−0.250832 + 0.968031i \(0.580704\pi\)
\(788\) 0 0
\(789\) 2.00000 3.46410i 0.0712019 0.123325i
\(790\) 0 0
\(791\) −25.0000 + 8.66025i −0.888898 + 0.307923i
\(792\) 0 0
\(793\) −5.00000 + 8.66025i −0.177555 + 0.307535i
\(794\) 0 0
\(795\) −12.0000 20.7846i −0.425596 0.737154i
\(796\) 0 0
\(797\) 8.00000 0.283375 0.141687 0.989911i \(-0.454747\pi\)
0.141687 + 0.989911i \(0.454747\pi\)