Properties

Label 147.2.e.a.67.1
Level $147$
Weight $2$
Character 147.67
Analytic conductor $1.174$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.17380090971\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.2.e.a.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.00000 - 1.73205i) q^{5} -2.00000 q^{6} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.00000 - 1.73205i) q^{5} -2.00000 q^{6} +(-0.500000 - 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{10} +(1.00000 - 1.73205i) q^{11} +(1.00000 + 1.73205i) q^{12} -1.00000 q^{13} -2.00000 q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.00000 + 1.73205i) q^{18} +(0.500000 + 0.866025i) q^{19} +4.00000 q^{20} -4.00000 q^{22} +(0.500000 - 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} -1.00000 q^{27} +4.00000 q^{29} +(2.00000 + 3.46410i) q^{30} +(4.50000 - 7.79423i) q^{31} +(4.00000 - 6.92820i) q^{32} +(-1.00000 - 1.73205i) q^{33} +2.00000 q^{36} +(-1.50000 - 2.59808i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-0.500000 + 0.866025i) q^{39} +10.0000 q^{41} +5.00000 q^{43} +(2.00000 + 3.46410i) q^{44} +(-1.00000 + 1.73205i) q^{45} +(-3.00000 - 5.19615i) q^{47} +4.00000 q^{48} -2.00000 q^{50} +(1.00000 - 1.73205i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(1.00000 + 1.73205i) q^{54} -4.00000 q^{55} +1.00000 q^{57} +(-4.00000 - 6.92820i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(2.00000 - 3.46410i) q^{60} +(5.00000 + 8.66025i) q^{61} -18.0000 q^{62} -8.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(-2.00000 + 3.46410i) q^{66} +(2.50000 - 4.33013i) q^{67} -6.00000 q^{71} +(-1.50000 + 2.59808i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-0.500000 - 0.866025i) q^{75} -2.00000 q^{76} +2.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(4.00000 - 6.92820i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-10.0000 - 17.3205i) q^{82} -6.00000 q^{83} +(-5.00000 - 8.66025i) q^{86} +(2.00000 - 3.46410i) q^{87} +(8.00000 + 13.8564i) q^{89} +4.00000 q^{90} +(-4.50000 - 7.79423i) q^{93} +(-6.00000 + 10.3923i) q^{94} +(1.00000 - 1.73205i) q^{95} +(-4.00000 - 6.92820i) q^{96} +6.00000 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} + q^{3} - 2q^{4} - 2q^{5} - 4q^{6} - q^{9} + O(q^{10}) \) \( 2q - 2q^{2} + q^{3} - 2q^{4} - 2q^{5} - 4q^{6} - q^{9} - 4q^{10} + 2q^{11} + 2q^{12} - 2q^{13} - 4q^{15} + 4q^{16} - 2q^{18} + q^{19} + 8q^{20} - 8q^{22} + q^{25} + 2q^{26} - 2q^{27} + 8q^{29} + 4q^{30} + 9q^{31} + 8q^{32} - 2q^{33} + 4q^{36} - 3q^{37} + 2q^{38} - q^{39} + 20q^{41} + 10q^{43} + 4q^{44} - 2q^{45} - 6q^{47} + 8q^{48} - 4q^{50} + 2q^{52} - 12q^{53} + 2q^{54} - 8q^{55} + 2q^{57} - 8q^{58} - 12q^{59} + 4q^{60} + 10q^{61} - 36q^{62} - 16q^{64} + 2q^{65} - 4q^{66} + 5q^{67} - 12q^{71} - 3q^{73} - 6q^{74} - q^{75} - 4q^{76} + 4q^{78} + q^{79} + 8q^{80} - q^{81} - 20q^{82} - 12q^{83} - 10q^{86} + 4q^{87} + 16q^{89} + 8q^{90} - 9q^{93} - 12q^{94} + 2q^{95} - 8q^{96} + 12q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −1.00000 + 1.73205i −0.500000 + 0.866025i
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) −2.00000 −0.816497
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −2.00000 + 3.46410i −0.632456 + 1.09545i
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 1.00000 + 1.73205i 0.288675 + 0.500000i
\(13\) −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
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) −1.00000 + 1.73205i −0.235702 + 0.408248i
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 4.00000 0.894427
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 1.00000 + 1.73205i 0.196116 + 0.339683i
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 2.00000 + 3.46410i 0.365148 + 0.632456i
\(31\) 4.50000 7.79423i 0.808224 1.39988i −0.105869 0.994380i \(-0.533762\pi\)
0.914093 0.405505i \(-0.132904\pi\)
\(32\) 4.00000 6.92820i 0.707107 1.22474i
\(33\) −1.00000 1.73205i −0.174078 0.301511i
\(34\) 0 0
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) −1.50000 2.59808i −0.246598 0.427121i 0.715981 0.698119i \(-0.245980\pi\)
−0.962580 + 0.270998i \(0.912646\pi\)
\(38\) 1.00000 1.73205i 0.162221 0.280976i
\(39\) −0.500000 + 0.866025i −0.0800641 + 0.138675i
\(40\) 0 0
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) 5.00000 0.762493 0.381246 0.924473i \(-0.375495\pi\)
0.381246 + 0.924473i \(0.375495\pi\)
\(44\) 2.00000 + 3.46410i 0.301511 + 0.522233i
\(45\) −1.00000 + 1.73205i −0.149071 + 0.258199i
\(46\) 0 0
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 4.00000 0.577350
\(49\) 0 0
\(50\) −2.00000 −0.282843
\(51\) 0 0
\(52\) 1.00000 1.73205i 0.138675 0.240192i
\(53\) −6.00000 + 10.3923i −0.824163 + 1.42749i 0.0783936 + 0.996922i \(0.475021\pi\)
−0.902557 + 0.430570i \(0.858312\pi\)
\(54\) 1.00000 + 1.73205i 0.136083 + 0.235702i
\(55\) −4.00000 −0.539360
\(56\) 0 0
\(57\) 1.00000 0.132453
\(58\) −4.00000 6.92820i −0.525226 0.909718i
\(59\) −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) 2.00000 3.46410i 0.258199 0.447214i
\(61\) 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i \(0.0544754\pi\)
−0.345207 + 0.938527i \(0.612191\pi\)
\(62\) −18.0000 −2.28600
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 1.00000 + 1.73205i 0.124035 + 0.214834i
\(66\) −2.00000 + 3.46410i −0.246183 + 0.426401i
\(67\) 2.50000 4.33013i 0.305424 0.529009i −0.671932 0.740613i \(-0.734535\pi\)
0.977356 + 0.211604i \(0.0678686\pi\)
\(68\) 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 \(-0.889507\pi\)
0.764794 + 0.644275i \(0.222841\pi\)
\(74\) −3.00000 + 5.19615i −0.348743 + 0.604040i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 2.00000 0.226455
\(79\) 0.500000 + 0.866025i 0.0562544 + 0.0974355i 0.892781 0.450490i \(-0.148751\pi\)
−0.836527 + 0.547926i \(0.815418\pi\)
\(80\) 4.00000 6.92820i 0.447214 0.774597i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −10.0000 17.3205i −1.10432 1.91273i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −5.00000 8.66025i −0.539164 0.933859i
\(87\) 2.00000 3.46410i 0.214423 0.371391i
\(88\) 0 0
\(89\) 8.00000 + 13.8564i 0.847998 + 1.46878i 0.882992 + 0.469389i \(0.155526\pi\)
−0.0349934 + 0.999388i \(0.511141\pi\)
\(90\) 4.00000 0.421637
\(91\) 0 0
\(92\) 0 0
\(93\) −4.50000 7.79423i −0.466628 0.808224i
\(94\) −6.00000 + 10.3923i −0.618853 + 1.07188i
\(95\) 1.00000 1.73205i 0.102598 0.177705i
\(96\) −4.00000 6.92820i −0.408248 0.707107i
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) 1.00000 1.73205i 0.0995037 0.172345i −0.811976 0.583691i \(-0.801608\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) 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
\(105\) 0 0
\(106\) 24.0000 2.33109
\(107\) 4.00000 + 6.92820i 0.386695 + 0.669775i 0.992003 0.126217i \(-0.0402834\pi\)
−0.605308 + 0.795991i \(0.706950\pi\)
\(108\) 1.00000 1.73205i 0.0962250 0.166667i
\(109\) −4.50000 + 7.79423i −0.431022 + 0.746552i −0.996962 0.0778949i \(-0.975180\pi\)
0.565940 + 0.824447i \(0.308513\pi\)
\(110\) 4.00000 + 6.92820i 0.381385 + 0.660578i
\(111\) −3.00000 −0.284747
\(112\) 0 0
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) −1.00000 1.73205i −0.0936586 0.162221i
\(115\) 0 0
\(116\) −4.00000 + 6.92820i −0.371391 + 0.643268i
\(117\) 0.500000 + 0.866025i 0.0462250 + 0.0800641i
\(118\) 24.0000 2.20938
\(119\) 0 0
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 10.0000 17.3205i 0.905357 1.56813i
\(123\) 5.00000 8.66025i 0.450835 0.780869i
\(124\) 9.00000 + 15.5885i 0.808224 + 1.39988i
\(125\) −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
\(130\) 2.00000 3.46410i 0.175412 0.303822i
\(131\) −7.00000 12.1244i −0.611593 1.05931i −0.990972 0.134069i \(-0.957196\pi\)
0.379379 0.925241i \(-0.376138\pi\)
\(132\) 4.00000 0.348155
\(133\) 0 0
\(134\) −10.0000 −0.863868
\(135\) 1.00000 + 1.73205i 0.0860663 + 0.149071i
\(136\) 0 0
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 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
\(142\) 6.00000 + 10.3923i 0.503509 + 0.872103i
\(143\) −1.00000 + 1.73205i −0.0836242 + 0.144841i
\(144\) 2.00000 3.46410i 0.166667 0.288675i
\(145\) −4.00000 6.92820i −0.332182 0.575356i
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) 6.00000 0.493197
\(149\) 6.00000 + 10.3923i 0.491539 + 0.851371i 0.999953 0.00974235i \(-0.00310113\pi\)
−0.508413 + 0.861113i \(0.669768\pi\)
\(150\) −1.00000 + 1.73205i −0.0816497 + 0.141421i
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −18.0000 −1.44579
\(156\) −1.00000 1.73205i −0.0800641 0.138675i
\(157\) −7.00000 + 12.1244i −0.558661 + 0.967629i 0.438948 + 0.898513i \(0.355351\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) 1.00000 1.73205i 0.0795557 0.137795i
\(159\) 6.00000 + 10.3923i 0.475831 + 0.824163i
\(160\) −16.0000 −1.26491
\(161\) 0 0
\(162\) 2.00000 0.157135
\(163\) −2.00000 3.46410i −0.156652 0.271329i 0.777007 0.629492i \(-0.216737\pi\)
−0.933659 + 0.358162i \(0.883403\pi\)
\(164\) −10.0000 + 17.3205i −0.780869 + 1.35250i
\(165\) −2.00000 + 3.46410i −0.155700 + 0.269680i
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) 14.0000 1.08335 0.541676 0.840587i \(-0.317790\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0.500000 0.866025i 0.0382360 0.0662266i
\(172\) −5.00000 + 8.66025i −0.381246 + 0.660338i
\(173\) 4.00000 + 6.92820i 0.304114 + 0.526742i 0.977064 0.212947i \(-0.0683062\pi\)
−0.672949 + 0.739689i \(0.734973\pi\)
\(174\) −8.00000 −0.606478
\(175\) 0 0
\(176\) 8.00000 0.603023
\(177\) 6.00000 + 10.3923i 0.450988 + 0.781133i
\(178\) 16.0000 27.7128i 1.19925 2.07716i
\(179\) −1.00000 + 1.73205i −0.0747435 + 0.129460i −0.900975 0.433872i \(-0.857147\pi\)
0.826231 + 0.563331i \(0.190480\pi\)
\(180\) −2.00000 3.46410i −0.149071 0.258199i
\(181\) −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
\(186\) −9.00000 + 15.5885i −0.659912 + 1.14300i
\(187\) 0 0
\(188\) 12.0000 0.875190
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) −5.00000 8.66025i −0.361787 0.626634i 0.626468 0.779447i \(-0.284500\pi\)
−0.988255 + 0.152813i \(0.951167\pi\)
\(192\) −4.00000 + 6.92820i −0.288675 + 0.500000i
\(193\) −5.50000 + 9.52628i −0.395899 + 0.685717i −0.993215 0.116289i \(-0.962900\pi\)
0.597317 + 0.802005i \(0.296234\pi\)
\(194\) −6.00000 10.3923i −0.430775 0.746124i
\(195\) 2.00000 0.143223
\(196\) 0 0
\(197\) 16.0000 1.13995 0.569976 0.821661i \(-0.306952\pi\)
0.569976 + 0.821661i \(0.306952\pi\)
\(198\) 2.00000 + 3.46410i 0.142134 + 0.246183i
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 0 0
\(201\) −2.50000 4.33013i −0.176336 0.305424i
\(202\) −4.00000 −0.281439
\(203\) 0 0
\(204\) 0 0
\(205\) −10.0000 17.3205i −0.698430 1.20972i
\(206\) −7.00000 + 12.1244i −0.487713 + 0.844744i
\(207\) 0 0
\(208\) −2.00000 3.46410i −0.138675 0.240192i
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −12.0000 20.7846i −0.824163 1.42749i
\(213\) −3.00000 + 5.19615i −0.205557 + 0.356034i
\(214\) 8.00000 13.8564i 0.546869 0.947204i
\(215\) −5.00000 8.66025i −0.340997 0.590624i
\(216\) 0 0
\(217\) 0 0
\(218\) 18.0000 1.21911
\(219\) 1.50000 + 2.59808i 0.101361 + 0.175562i
\(220\) 4.00000 6.92820i 0.269680 0.467099i
\(221\) 0 0
\(222\) 3.00000 + 5.19615i 0.201347 + 0.348743i
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 0 0
\(225\) −1.00000 −0.0666667
\(226\) −10.0000 17.3205i −0.665190 1.15214i
\(227\) 9.00000 15.5885i 0.597351 1.03464i −0.395860 0.918311i \(-0.629553\pi\)
0.993210 0.116331i \(-0.0371134\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) −9.50000 16.4545i −0.627778 1.08734i −0.987997 0.154475i \(-0.950631\pi\)
0.360219 0.932868i \(-0.382702\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.00000 5.19615i −0.196537 0.340411i 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) 1.00000 1.73205i 0.0653720 0.113228i
\(235\) −6.00000 + 10.3923i −0.391397 + 0.677919i
\(236\) −12.0000 20.7846i −0.781133 1.35296i
\(237\) 1.00000 0.0649570
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) −4.00000 6.92820i −0.258199 0.447214i
\(241\) 7.00000 12.1244i 0.450910 0.780998i −0.547533 0.836784i \(-0.684433\pi\)
0.998443 + 0.0557856i \(0.0177663\pi\)
\(242\) 7.00000 12.1244i 0.449977 0.779383i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −20.0000 −1.28037
\(245\) 0 0
\(246\) −20.0000 −1.27515
\(247\) −0.500000 0.866025i −0.0318142 0.0551039i
\(248\) 0 0
\(249\) −3.00000 + 5.19615i −0.190117 + 0.329293i
\(250\) 12.0000 + 20.7846i 0.758947 + 1.31453i
\(251\) 8.00000 0.504956 0.252478 0.967603i \(-0.418755\pi\)
0.252478 + 0.967603i \(0.418755\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 15.0000 + 25.9808i 0.941184 + 1.63018i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 13.0000 + 22.5167i 0.810918 + 1.40455i 0.912222 + 0.409695i \(0.134365\pi\)
−0.101305 + 0.994855i \(0.532302\pi\)
\(258\) −10.0000 −0.622573
\(259\) 0 0
\(260\) −4.00000 −0.248069
\(261\) −2.00000 3.46410i −0.123797 0.214423i
\(262\) −14.0000 + 24.2487i −0.864923 + 1.49809i
\(263\) −2.00000 + 3.46410i −0.123325 + 0.213606i −0.921077 0.389380i \(-0.872689\pi\)
0.797752 + 0.602986i \(0.206023\pi\)
\(264\) 0 0
\(265\) 24.0000 1.47431
\(266\) 0 0
\(267\) 16.0000 0.979184
\(268\) 5.00000 + 8.66025i 0.305424 + 0.529009i
\(269\) 3.00000 5.19615i 0.182913 0.316815i −0.759958 0.649972i \(-0.774781\pi\)
0.942871 + 0.333157i \(0.108114\pi\)
\(270\) 2.00000 3.46410i 0.121716 0.210819i
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −24.0000 −1.44989
\(275\) −1.00000 1.73205i −0.0603023 0.104447i
\(276\) 0 0
\(277\) −6.50000 + 11.2583i −0.390547 + 0.676448i −0.992522 0.122068i \(-0.961047\pi\)
0.601975 + 0.798515i \(0.294381\pi\)
\(278\) −3.00000 5.19615i −0.179928 0.311645i
\(279\) −9.00000 −0.538816
\(280\) 0 0
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) 6.00000 + 10.3923i 0.357295 + 0.618853i
\(283\) −5.50000 + 9.52628i −0.326941 + 0.566279i −0.981903 0.189383i \(-0.939351\pi\)
0.654962 + 0.755662i \(0.272685\pi\)
\(284\) 6.00000 10.3923i 0.356034 0.616670i
\(285\) −1.00000 1.73205i −0.0592349 0.102598i
\(286\) 4.00000 0.236525
\(287\) 0 0
\(288\) −8.00000 −0.471405
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −8.00000 + 13.8564i −0.469776 + 0.813676i
\(291\) 3.00000 5.19615i 0.175863 0.304604i
\(292\) −3.00000 5.19615i −0.175562 0.304082i
\(293\) −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
\(298\) 12.0000 20.7846i 0.695141 1.20402i
\(299\) 0 0
\(300\) 2.00000 0.115470
\(301\) 0 0
\(302\) −32.0000 −1.84139
\(303\) −1.00000 1.73205i −0.0574485 0.0995037i
\(304\) −2.00000 + 3.46410i −0.114708 + 0.198680i
\(305\) 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
\(310\) 18.0000 + 31.1769i 1.02233 + 1.77073i
\(311\) −3.00000 + 5.19615i −0.170114 + 0.294647i −0.938460 0.345389i \(-0.887747\pi\)
0.768345 + 0.640036i \(0.221080\pi\)
\(312\) 0 0
\(313\) −0.500000 0.866025i −0.0282617 0.0489506i 0.851549 0.524276i \(-0.175664\pi\)
−0.879810 + 0.475325i \(0.842331\pi\)
\(314\) 28.0000 1.58013
\(315\) 0 0
\(316\) −2.00000 −0.112509
\(317\) −12.0000 20.7846i −0.673987 1.16738i −0.976764 0.214318i \(-0.931247\pi\)
0.302777 0.953062i \(-0.402086\pi\)
\(318\) 12.0000 20.7846i 0.672927 1.16554i
\(319\) 4.00000 6.92820i 0.223957 0.387905i
\(320\) 8.00000 + 13.8564i 0.447214 + 0.774597i
\(321\) 8.00000 0.446516
\(322\) 0 0
\(323\) 0 0
\(324\) −1.00000 1.73205i −0.0555556 0.0962250i
\(325\) −0.500000 + 0.866025i −0.0277350 + 0.0480384i
\(326\) −4.00000 + 6.92820i −0.221540 + 0.383718i
\(327\) 4.50000 + 7.79423i 0.248851 + 0.431022i
\(328\) 0 0
\(329\) 0 0
\(330\) 8.00000 0.440386
\(331\) 12.5000 + 21.6506i 0.687062 + 1.19003i 0.972784 + 0.231714i \(0.0744333\pi\)
−0.285722 + 0.958313i \(0.592233\pi\)
\(332\) 6.00000 10.3923i 0.329293 0.570352i
\(333\) −1.50000 + 2.59808i −0.0821995 + 0.142374i
\(334\) −14.0000 24.2487i −0.766046 1.32683i
\(335\) −10.0000 −0.546358
\(336\) 0 0
\(337\) 13.0000 0.708155 0.354078 0.935216i \(-0.384795\pi\)
0.354078 + 0.935216i \(0.384795\pi\)
\(338\) 12.0000 + 20.7846i 0.652714 + 1.13053i
\(339\) 5.00000 8.66025i 0.271563 0.470360i
\(340\) 0 0
\(341\) −9.00000 15.5885i −0.487377 0.844162i
\(342\) −2.00000 −0.108148
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 8.00000 13.8564i 0.430083 0.744925i
\(347\) −16.0000 + 27.7128i −0.858925 + 1.48770i 0.0140303 + 0.999902i \(0.495534\pi\)
−0.872955 + 0.487800i \(0.837799\pi\)
\(348\) 4.00000 + 6.92820i 0.214423 + 0.371391i
\(349\) 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
\(352\) −8.00000 13.8564i −0.426401 0.738549i
\(353\) 17.0000 29.4449i 0.904819 1.56719i 0.0836583 0.996495i \(-0.473340\pi\)
0.821160 0.570697i \(-0.193327\pi\)
\(354\) 12.0000 20.7846i 0.637793 1.10469i
\(355\) 6.00000 + 10.3923i 0.318447 + 0.551566i
\(356\) −32.0000 −1.69600
\(357\) 0 0
\(358\) 4.00000 0.211407
\(359\) −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i \(-0.989691\pi\)
0.471696 0.881761i \(-0.343642\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 13.0000 + 22.5167i 0.683265 + 1.18345i
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) −10.0000 17.3205i −0.522708 0.905357i
\(367\) −4.50000 + 7.79423i −0.234898 + 0.406855i −0.959243 0.282582i \(-0.908809\pi\)
0.724345 + 0.689438i \(0.242142\pi\)
\(368\) 0 0
\(369\) −5.00000 8.66025i −0.260290 0.450835i
\(370\) 12.0000 0.623850
\(371\) 0 0
\(372\) 18.0000 0.933257
\(373\) −11.5000 19.9186i −0.595447 1.03135i −0.993484 0.113975i \(-0.963641\pi\)
0.398036 0.917370i \(-0.369692\pi\)
\(374\) 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 \(-0.475450\pi\)
0.0770498 + 0.997027i \(0.475450\pi\)
\(380\) 2.00000 + 3.46410i 0.102598 + 0.177705i
\(381\) −7.50000 + 12.9904i −0.384237 + 0.665517i
\(382\) −10.0000 + 17.3205i −0.511645 + 0.886194i
\(383\) −6.00000 10.3923i −0.306586 0.531022i 0.671027 0.741433i \(-0.265853\pi\)
−0.977613 + 0.210411i \(0.932520\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 22.0000 1.11977
\(387\) −2.50000 4.33013i −0.127082 0.220113i
\(388\) −6.00000 + 10.3923i −0.304604 + 0.527589i
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) −2.00000 3.46410i −0.101274 0.175412i
\(391\) 0 0
\(392\) 0 0
\(393\) −14.0000 −0.706207
\(394\) −16.0000 27.7128i −0.806068 1.39615i
\(395\) 1.00000 1.73205i 0.0503155 0.0871489i
\(396\) 2.00000 3.46410i 0.100504 0.174078i
\(397\) −4.50000 7.79423i −0.225849 0.391181i 0.730725 0.682672i \(-0.239182\pi\)
−0.956574 + 0.291491i \(0.905849\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) 18.0000 + 31.1769i 0.898877 + 1.55690i 0.828932 + 0.559350i \(0.188949\pi\)
0.0699455 + 0.997551i \(0.477717\pi\)
\(402\) −5.00000 + 8.66025i −0.249377 + 0.431934i
\(403\) −4.50000 + 7.79423i −0.224161 + 0.388258i
\(404\) 2.00000 + 3.46410i 0.0995037 + 0.172345i
\(405\) 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 \(-0.793884\pi\)
0.921192 + 0.389109i \(0.127217\pi\)
\(410\) −20.0000 + 34.6410i −0.987730 + 1.71080i
\(411\) −6.00000 10.3923i −0.295958 0.512615i
\(412\) 14.0000 0.689730
\(413\) 0 0
\(414\) 0 0
\(415\) 6.00000 + 10.3923i 0.294528 + 0.510138i
\(416\) −4.00000 + 6.92820i −0.196116 + 0.339683i
\(417\) 1.50000 2.59808i 0.0734553 0.127228i
\(418\) −2.00000 3.46410i −0.0978232 0.169435i
\(419\) −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 \(-0.554564\pi\)
−0.170580 + 0.985344i \(0.554564\pi\)
\(422\) −4.00000 6.92820i −0.194717 0.337260i
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) 0 0
\(426\) 12.0000 0.581402
\(427\) 0 0
\(428\) −16.0000 −0.773389
\(429\) 1.00000 + 1.73205i 0.0482805 + 0.0836242i
\(430\) −10.0000 + 17.3205i −0.482243 + 0.835269i
\(431\) 9.00000 15.5885i 0.433515 0.750870i −0.563658 0.826008i \(-0.690607\pi\)
0.997173 + 0.0751385i \(0.0239399\pi\)
\(432\) −2.00000 3.46410i −0.0962250 0.166667i
\(433\) −31.0000 −1.48976 −0.744882 0.667196i \(-0.767494\pi\)
−0.744882 + 0.667196i \(0.767494\pi\)
\(434\) 0 0
\(435\) −8.00000 −0.383571
\(436\) −9.00000 15.5885i −0.431022 0.746552i
\(437\) 0 0
\(438\) 3.00000 5.19615i 0.143346 0.248282i
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i \(-0.258683\pi\)
−0.972626 + 0.232377i \(0.925350\pi\)
\(444\) 3.00000 5.19615i 0.142374 0.246598i
\(445\) 16.0000 27.7128i 0.758473 1.31371i
\(446\) 16.0000 + 27.7128i 0.757622 + 1.31224i
\(447\) 12.0000 0.567581
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 1.00000 + 1.73205i 0.0471405 + 0.0816497i
\(451\) 10.0000 17.3205i 0.470882 0.815591i
\(452\) −10.0000 + 17.3205i −0.470360 + 0.814688i
\(453\) −8.00000 13.8564i −0.375873 0.651031i
\(454\) −36.0000 −1.68956
\(455\) 0 0
\(456\) 0 0
\(457\) 5.50000 + 9.52628i 0.257279 + 0.445621i 0.965512 0.260358i \(-0.0838407\pi\)
−0.708233 + 0.705979i \(0.750507\pi\)
\(458\) −19.0000 + 32.9090i −0.887812 + 1.53773i
\(459\) 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 \(0.629265\pi\)
\(464\) 8.00000 + 13.8564i 0.371391 + 0.643268i
\(465\) −9.00000 + 15.5885i −0.417365 + 0.722897i
\(466\) −6.00000 + 10.3923i −0.277945 + 0.481414i
\(467\) 3.00000 + 5.19615i 0.138823 + 0.240449i 0.927052 0.374934i \(-0.122335\pi\)
−0.788228 + 0.615383i \(0.789001\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) 24.0000 1.10704
\(471\) 7.00000 + 12.1244i 0.322543 + 0.558661i
\(472\) 0 0
\(473\) 5.00000 8.66025i 0.229900 0.398199i
\(474\) −1.00000 1.73205i −0.0459315 0.0795557i
\(475\) 1.00000 0.0458831
\(476\) 0 0
\(477\) 12.0000 0.549442
\(478\) −6.00000 10.3923i −0.274434 0.475333i
\(479\) −14.0000 + 24.2487i −0.639676 + 1.10795i 0.345827 + 0.938298i \(0.387598\pi\)
−0.985504 + 0.169654i \(0.945735\pi\)
\(480\) −8.00000 + 13.8564i −0.365148 + 0.632456i
\(481\) 1.50000 + 2.59808i 0.0683941 + 0.118462i
\(482\) −28.0000 −1.27537
\(483\) 0 0
\(484\) −14.0000 −0.636364
\(485\) −6.00000 10.3923i −0.272446 0.471890i
\(486\) 1.00000 1.73205i 0.0453609 0.0785674i
\(487\) −15.5000 + 26.8468i −0.702372 + 1.21654i 0.265260 + 0.964177i \(0.414542\pi\)
−0.967632 + 0.252367i \(0.918791\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) −28.0000 −1.26362 −0.631811 0.775122i \(-0.717688\pi\)
−0.631811 + 0.775122i \(0.717688\pi\)
\(492\) 10.0000 + 17.3205i 0.450835 + 0.780869i
\(493\) 0 0
\(494\) −1.00000 + 1.73205i −0.0449921 + 0.0779287i
\(495\) 2.00000 + 3.46410i 0.0898933 + 0.155700i
\(496\) 36.0000 1.61645
\(497\) 0 0
\(498\) 12.0000 0.537733
\(499\) −18.5000 32.0429i −0.828174 1.43444i −0.899469 0.436984i \(-0.856047\pi\)
0.0712957 0.997455i \(-0.477287\pi\)
\(500\) 12.0000 20.7846i 0.536656 0.929516i
\(501\) 7.00000 12.1244i 0.312737 0.541676i
\(502\) −8.00000 13.8564i −0.357057 0.618442i
\(503\) 42.0000 1.87269 0.936344 0.351085i \(-0.114187\pi\)
0.936344 + 0.351085i \(0.114187\pi\)
\(504\) 0 0
\(505\) −4.00000 −0.177998
\(506\) 0 0
\(507\) −6.00000 + 10.3923i −0.266469 + 0.461538i
\(508\) 15.0000 25.9808i 0.665517 1.15271i
\(509\) 1.00000 + 1.73205i 0.0443242 + 0.0767718i 0.887336 0.461123i \(-0.152553\pi\)
−0.843012 + 0.537895i \(0.819220\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 32.0000 1.41421
\(513\) −0.500000 0.866025i −0.0220755 0.0382360i
\(514\) 26.0000 45.0333i 1.14681 1.98633i
\(515\) −7.00000 + 12.1244i −0.308457 + 0.534263i
\(516\) 5.00000 + 8.66025i 0.220113 + 0.381246i
\(517\) −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 \(-0.748666\pi\)
0.967002 + 0.254769i \(0.0819994\pi\)
\(522\) −4.00000 + 6.92820i −0.175075 + 0.303239i
\(523\) 15.5000 + 26.8468i 0.677768 + 1.17393i 0.975652 + 0.219326i \(0.0703858\pi\)
−0.297884 + 0.954602i \(0.596281\pi\)
\(524\) 28.0000 1.22319
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 0 0
\(528\) 4.00000 6.92820i 0.174078 0.301511i
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) −24.0000 41.5692i −1.04249 1.80565i
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) −10.0000 −0.433148
\(534\) −16.0000 27.7128i −0.692388 1.19925i
\(535\) 8.00000 13.8564i 0.345870 0.599065i
\(536\) 0 0
\(537\) 1.00000 + 1.73205i 0.0431532 + 0.0747435i
\(538\) −12.0000 −0.517357
\(539\) 0 0
\(540\) −4.00000 −0.172133
\(541\) 9.50000 + 16.4545i 0.408437 + 0.707433i 0.994715 0.102677i \(-0.0327407\pi\)
−0.586278 + 0.810110i \(0.699407\pi\)
\(542\) 16.0000 27.7128i 0.687259 1.19037i
\(543\) −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 \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 12.0000 + 20.7846i 0.512615 + 0.887875i
\(549\) 5.00000 8.66025i 0.213395 0.369611i
\(550\) −2.00000 + 3.46410i −0.0852803 + 0.147710i
\(551\) 2.00000 + 3.46410i 0.0852029 + 0.147576i
\(552\) 0 0
\(553\) 0 0
\(554\) 26.0000 1.10463
\(555\) 3.00000 + 5.19615i 0.127343 + 0.220564i
\(556\) −3.00000 + 5.19615i −0.127228 + 0.220366i
\(557\) 1.00000 1.73205i 0.0423714 0.0733893i −0.844062 0.536246i \(-0.819842\pi\)
0.886433 + 0.462856i \(0.153175\pi\)
\(558\) 9.00000 + 15.5885i 0.381000 + 0.659912i
\(559\) −5.00000 −0.211477
\(560\) 0 0
\(561\) 0 0
\(562\) 4.00000 + 6.92820i 0.168730 + 0.292249i
\(563\) −13.0000 + 22.5167i −0.547885 + 0.948964i 0.450535 + 0.892759i \(0.351233\pi\)
−0.998419 + 0.0562051i \(0.982100\pi\)
\(564\) 6.00000 10.3923i 0.252646 0.437595i
\(565\) −10.0000 17.3205i −0.420703 0.728679i
\(566\) 22.0000 0.924729
\(567\) 0 0
\(568\) 0 0
\(569\) 13.0000 + 22.5167i 0.544988 + 0.943948i 0.998608 + 0.0527519i \(0.0167993\pi\)
−0.453619 + 0.891196i \(0.649867\pi\)
\(570\) −2.00000 + 3.46410i −0.0837708 + 0.145095i
\(571\) 9.50000 16.4545i 0.397563 0.688599i −0.595862 0.803087i \(-0.703189\pi\)
0.993425 + 0.114488i \(0.0365228\pi\)
\(572\) −2.00000 3.46410i −0.0836242 0.144841i
\(573\) −10.0000 −0.417756
\(574\) 0 0
\(575\) 0 0
\(576\) 4.00000 + 6.92820i 0.166667 + 0.288675i
\(577\) −8.50000 + 14.7224i −0.353860 + 0.612903i −0.986922 0.161198i \(-0.948464\pi\)
0.633062 + 0.774101i \(0.281798\pi\)
\(578\) 17.0000 29.4449i 0.707107 1.22474i
\(579\) 5.50000 + 9.52628i 0.228572 + 0.395899i
\(580\) 16.0000 0.664364
\(581\) 0 0
\(582\) −12.0000 −0.497416
\(583\) 12.0000 + 20.7846i 0.496989 + 0.860811i
\(584\) 0 0
\(585\) 1.00000 1.73205i 0.0413449 0.0716115i
\(586\) 8.00000 + 13.8564i 0.330477 + 0.572403i
\(587\) −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
\(590\) −24.0000 41.5692i −0.988064 1.71138i
\(591\) 8.00000 13.8564i 0.329076 0.569976i
\(592\) 6.00000 10.3923i 0.246598 0.427121i
\(593\) −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i \(-0.205981\pi\)
−0.921026 + 0.389501i \(0.872647\pi\)
\(594\) 4.00000 0.164122
\(595\) 0 0
\(596\) −24.0000 −0.983078
\(597\) 0 0
\(598\) 0 0
\(599\) −6.00000 + 10.3923i −0.245153 + 0.424618i −0.962175 0.272433i \(-0.912172\pi\)
0.717021 + 0.697051i \(0.245505\pi\)
\(600\) 0 0
\(601\) 9.00000 0.367118 0.183559 0.983009i \(-0.441238\pi\)
0.183559 + 0.983009i \(0.441238\pi\)
\(602\) 0 0
\(603\) −5.00000 −0.203616
\(604\) 16.0000 + 27.7128i 0.651031 + 1.12762i
\(605\) 7.00000 12.1244i 0.284590 0.492925i
\(606\) −2.00000 + 3.46410i −0.0812444 + 0.140720i
\(607\) 11.5000 + 19.9186i 0.466771 + 0.808470i 0.999279 0.0379540i \(-0.0120840\pi\)
−0.532509 + 0.846424i \(0.678751\pi\)
\(608\) 8.00000 0.324443
\(609\) 0 0
\(610\) −40.0000 −1.61955
\(611\) 3.00000 + 5.19615i 0.121367 + 0.210214i
\(612\) 0 0
\(613\) −17.0000 + 29.4449i −0.686624 + 1.18927i 0.286300 + 0.958140i \(0.407575\pi\)
−0.972924 + 0.231127i \(0.925759\pi\)
\(614\) −17.0000 29.4449i −0.686064 1.18830i
\(615\) −20.0000 −0.806478
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 7.00000 + 12.1244i 0.281581 + 0.487713i
\(619\) −14.5000 + 25.1147i −0.582804 + 1.00945i 0.412341 + 0.911030i \(0.364711\pi\)
−0.995145 + 0.0984169i \(0.968622\pi\)
\(620\) 18.0000 31.1769i 0.722897 1.25210i
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) −1.00000 + 1.73205i −0.0399680 + 0.0692267i
\(627\) 1.00000 1.73205i 0.0399362 0.0691714i
\(628\) −14.0000 24.2487i −0.558661 0.967629i
\(629\) 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
\(634\) −24.0000 + 41.5692i −0.953162 + 1.65092i
\(635\) 15.0000 + 25.9808i 0.595257 + 1.03102i
\(636\) −24.0000 −0.951662
\(637\) 0 0
\(638\) −16.0000 −0.633446
\(639\) 3.00000 + 5.19615i 0.118678 + 0.205557i
\(640\) 0 0
\(641\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(642\) −8.00000 13.8564i −0.315735 0.546869i
\(643\) 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 \(-0.820816\pi\)
0.885013 + 0.465566i \(0.154149\pi\)
\(648\) 0 0
\(649\) 12.0000 + 20.7846i 0.471041 + 0.815867i
\(650\) 2.00000 0.0784465
\(651\) 0 0
\(652\) 8.00000 0.313304
\(653\) −9.00000 15.5885i −0.352197 0.610023i 0.634437 0.772975i \(-0.281232\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(654\) 9.00000 15.5885i 0.351928 0.609557i
\(655\) −14.0000 + 24.2487i −0.547025 + 0.947476i
\(656\) 20.0000 + 34.6410i 0.780869 + 1.35250i
\(657\) 3.00000 0.117041
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) −4.00000 6.92820i −0.155700 0.269680i
\(661\) −20.5000 + 35.5070i −0.797358 + 1.38106i 0.123974 + 0.992286i \(0.460436\pi\)
−0.921331 + 0.388778i \(0.872897\pi\)
\(662\) 25.0000 43.3013i 0.971653 1.68295i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 0 0
\(668\) −14.0000 + 24.2487i −0.541676 + 0.938211i
\(669\) −8.00000 + 13.8564i −0.309298 + 0.535720i
\(670\) 10.0000 + 17.3205i 0.386334 + 0.669150i
\(671\) 20.0000 0.772091
\(672\) 0 0
\(673\) −41.0000 −1.58043 −0.790217 0.612827i \(-0.790032\pi\)
−0.790217 + 0.612827i \(0.790032\pi\)
\(674\) −13.0000 22.5167i −0.500741 0.867309i
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) 12.0000 20.7846i 0.461538 0.799408i
\(677\) 6.00000 + 10.3923i 0.230599 + 0.399409i 0.957984 0.286820i \(-0.0925982\pi\)
−0.727386 + 0.686229i \(0.759265\pi\)
\(678\) −20.0000 −0.768095
\(679\) 0 0
\(680\) 0 0
\(681\) −9.00000 15.5885i −0.344881 0.597351i
\(682\) −18.0000 + 31.1769i −0.689256 + 1.19383i
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) 1.00000 + 1.73205i 0.0382360 + 0.0662266i
\(685\) −24.0000 −0.916993
\(686\) 0 0
\(687\) −19.0000 −0.724895
\(688\) 10.0000 + 17.3205i 0.381246 + 0.660338i
\(689\) 6.00000 10.3923i 0.228582 0.395915i
\(690\) 0 0
\(691\) −18.5000 32.0429i −0.703773 1.21897i −0.967132 0.254273i \(-0.918164\pi\)
0.263359 0.964698i \(-0.415170\pi\)
\(692\) −16.0000 −0.608229
\(693\) 0 0
\(694\) 64.0000 2.42941
\(695\) −3.00000 5.19615i −0.113796 0.197101i
\(696\) 0 0
\(697\) 0 0
\(698\) −14.0000 24.2487i −0.529908 0.917827i
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) −1.00000 1.73205i −0.0377426 0.0653720i
\(703\) 1.50000 2.59808i 0.0565736 0.0979883i
\(704\) −8.00000 + 13.8564i −0.301511 + 0.522233i
\(705\) 6.00000 + 10.3923i 0.225973 + 0.391397i
\(706\) −68.0000 −2.55921
\(707\) 0 0
\(708\) −24.0000 −0.901975
\(709\) −15.0000 25.9808i −0.563337 0.975728i −0.997202 0.0747503i \(-0.976184\pi\)
0.433865 0.900978i \(-0.357149\pi\)
\(710\) 12.0000 20.7846i 0.450352 0.780033i
\(711\) 0.500000 0.866025i 0.0187515 0.0324785i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 4.00000 0.149592
\(716\) −2.00000 3.46410i −0.0747435 0.129460i
\(717\) 3.00000 5.19615i 0.112037 0.194054i
\(718\) −20.0000 + 34.6410i −0.746393 + 1.29279i
\(719\) −9.00000 15.5885i −0.335643 0.581351i 0.647965 0.761670i \(-0.275620\pi\)
−0.983608 + 0.180319i \(0.942287\pi\)
\(720\) −8.00000 −0.298142
\(721\) 0 0
\(722\) −36.0000 −1.33978
\(723\) −7.00000 12.1244i −0.260333 0.450910i
\(724\) 13.0000 22.5167i 0.483141 0.836825i
\(725\) 2.00000 3.46410i 0.0742781 0.128654i
\(726\) −7.00000 12.1244i −0.259794 0.449977i
\(727\) 13.0000 0.482143 0.241072 0.970507i \(-0.422501\pi\)
0.241072 + 0.970507i \(0.422501\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −6.00000 10.3923i −0.222070 0.384636i
\(731\) 0 0
\(732\) −10.0000 + 17.3205i −0.369611 + 0.640184i
\(733\) −7.50000 12.9904i −0.277019 0.479811i 0.693624 0.720338i \(-0.256013\pi\)
−0.970642 + 0.240527i \(0.922680\pi\)
\(734\) 18.0000 0.664392
\(735\) 0 0
\(736\) 0 0
\(737\) −5.00000 8.66025i −0.184177 0.319005i
\(738\) −10.0000 + 17.3205i −0.368105 + 0.637577i
\(739\) 7.50000 12.9904i 0.275892 0.477859i −0.694468 0.719524i \(-0.744360\pi\)
0.970360 + 0.241665i \(0.0776935\pi\)
\(740\) −6.00000 10.3923i −0.220564 0.382029i
\(741\) −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
\(746\) −23.0000 + 39.8372i −0.842090 + 1.45854i
\(747\) 3.00000 + 5.19615i 0.109764 + 0.190117i
\(748\) 0 0
\(749\) 0 0
\(750\) 24.0000 0.876356
\(751\) −6.50000 11.2583i −0.237188 0.410822i 0.722718 0.691143i \(-0.242893\pi\)
−0.959906 + 0.280321i \(0.909559\pi\)
\(752\) 12.0000 20.7846i 0.437595 0.757937i
\(753\) 4.00000 6.92820i 0.145768 0.252478i
\(754\) 4.00000 + 6.92820i 0.145671 + 0.252310i
\(755\) −32.0000 −1.16460
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) −3.00000 5.19615i −0.108965 0.188733i
\(759\) 0 0
\(760\) 0 0
\(761\) −24.0000 41.5692i −0.869999 1.50688i −0.861996 0.506915i \(-0.830786\pi\)
−0.00800331 0.999968i \(-0.502548\pi\)
\(762\) 30.0000 1.08679
\(763\) 0 0
\(764\) 20.0000 0.723575
\(765\) 0 0
\(766\) −12.0000 + 20.7846i −0.433578 + 0.750978i
\(767\) 6.00000 10.3923i 0.216647 0.375244i
\(768\) 8.00000 + 13.8564i 0.288675 + 0.500000i
\(769\) 49.0000 1.76699 0.883493 0.468445i \(-0.155186\pi\)
0.883493 + 0.468445i \(0.155186\pi\)
\(770\) 0 0
\(771\) 26.0000 0.936367
\(772\) −11.0000 19.0526i −0.395899 0.685717i
\(773\) −17.0000 + 29.4449i −0.611448 + 1.05906i 0.379549 + 0.925172i \(0.376079\pi\)
−0.990997 + 0.133887i \(0.957254\pi\)
\(774\) −5.00000 + 8.66025i −0.179721 + 0.311286i
\(775\) −4.50000 7.79423i −0.161645 0.279977i
\(776\) 0 0
\(777\) 0 0
\(778\) −12.0000 −0.430221
\(779\) 5.00000 + 8.66025i 0.179144 + 0.310286i
\(780\) −2.00000 + 3.46410i −0.0716115 + 0.124035i
\(781\) −6.00000 + 10.3923i −0.214697 + 0.371866i
\(782\) 0 0
\(783\) −4.00000 −0.142948
\(784\) 0 0
\(785\) 28.0000 0.999363
\(786\) 14.0000 + 24.2487i 0.499363 + 0.864923i
\(787\) 20.0000 34.6410i 0.712923 1.23482i −0.250832 0.968031i \(-0.580704\pi\)
0.963755 0.266788i \(-0.0859624\pi\)
\(788\) −16.0000 + 27.7128i −0.569976 + 0.987228i