Properties

Label 441.2.e.e.226.1
Level $441$
Weight $2$
Character 441.226
Analytic conductor $3.521$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.2.e.e.361.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(3\) 0 0
\(4\) −1.00000 1.73205i −0.500000 0.866025i
\(5\) 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) −2.00000 3.46410i −0.632456 1.09545i
\(11\) −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
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 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 \(0.130073\pi\)
\(20\) −4.00000 −0.894427
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) 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
\(26\) −1.00000 + 1.73205i −0.196116 + 0.339683i
\(27\) 0 0
\(28\) 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 \(0.132904\pi\)
−0.105869 + 0.994380i \(0.533762\pi\)
\(32\) −4.00000 6.92820i −0.707107 1.22474i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) −1.00000 1.73205i −0.162221 0.280976i
\(39\) 0 0
\(40\) 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 \(-0.375495\pi\)
0.381246 + 0.924473i \(0.375495\pi\)
\(44\) −2.00000 + 3.46410i −0.301511 + 0.522233i
\(45\) 0 0
\(46\) 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
\(49\) 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 0.902557 + 0.430570i \(0.141688\pi\)
−0.0783936 + 0.996922i \(0.524979\pi\)
\(54\) 0 0
\(55\) −4.00000 −0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) −4.00000 + 6.92820i −0.525226 + 0.909718i
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 0 0
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) 18.0000 2.28600
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −1.00000 + 1.73205i −0.124035 + 0.214834i
\(66\) 0 0
\(67\) 2.50000 + 4.33013i 0.305424 + 0.529009i 0.977356 0.211604i \(-0.0678686\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) −1.50000 2.59808i −0.175562 0.304082i 0.764794 0.644275i \(-0.222841\pi\)
−0.940356 + 0.340193i \(0.889507\pi\)
\(74\) 3.00000 + 5.19615i 0.348743 + 0.604040i
\(75\) 0 0
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) −4.00000 6.92820i −0.447214 0.774597i
\(81\) 0 0
\(82\) −10.0000 + 17.3205i −1.10432 + 1.91273i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 5.00000 8.66025i 0.539164 0.933859i
\(87\) 0 0
\(88\) 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
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) −6.00000 10.3923i −0.618853 1.07188i
\(95\) −1.00000 1.73205i −0.102598 0.177705i
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000 1.73205i 0.100000 0.173205i
\(101\) −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i \(-0.198392\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) 0 0
\(103\) −3.50000 + 6.06218i −0.344865 + 0.597324i −0.985329 0.170664i \(-0.945409\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 24.0000 2.33109
\(107\) −4.00000 + 6.92820i −0.386695 + 0.669775i −0.992003 0.126217i \(-0.959717\pi\)
0.605308 + 0.795991i \(0.293050\pi\)
\(108\) 0 0
\(109\) −4.50000 7.79423i −0.431022 0.746552i 0.565940 0.824447i \(-0.308513\pi\)
−0.996962 + 0.0778949i \(0.975180\pi\)
\(110\) −4.00000 + 6.92820i −0.381385 + 0.660578i
\(111\) 0 0
\(112\) 0 0
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 4.00000 + 6.92820i 0.371391 + 0.643268i
\(117\) 0 0
\(118\) 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
\(123\) 0 0
\(124\) 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
\(129\) 0 0
\(130\) 2.00000 + 3.46410i 0.175412 + 0.303822i
\(131\) 7.00000 12.1244i 0.611593 1.05931i −0.379379 0.925241i \(-0.623862\pi\)
0.990972 0.134069i \(-0.0428042\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 10.0000 0.863868
\(135\) 0 0
\(136\) 0 0
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) 0 0
\(139\) 3.00000 0.254457 0.127228 0.991873i \(-0.459392\pi\)
0.127228 + 0.991873i \(0.459392\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.00000 10.3923i 0.503509 0.872103i
\(143\) 1.00000 + 1.73205i 0.0836242 + 0.144841i
\(144\) 0 0
\(145\) −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 \(-0.996899\pi\)
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 \(-0.355351\pi\)
\(158\) −1.00000 1.73205i −0.0795557 0.137795i
\(159\) 0 0
\(160\) −16.0000 −1.26491
\(161\) 0 0
\(162\) 0 0
\(163\) −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) 10.0000 + 17.3205i 0.780869 + 1.35250i
\(165\) 0 0
\(166\) 6.00000 10.3923i 0.465690 0.806599i
\(167\) −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 0
\(172\) −5.00000 8.66025i −0.381246 0.660338i
\(173\) −4.00000 + 6.92820i −0.304114 + 0.526742i −0.977064 0.212947i \(-0.931694\pi\)
0.672949 + 0.739689i \(0.265027\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −8.00000 −0.603023
\(177\) 0 0
\(178\) 16.0000 + 27.7128i 1.19925 + 2.07716i
\(179\) 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
\(183\) 0 0
\(184\) 0 0
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) 0 0
\(187\) 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 \(-0.715500\pi\)
0.988255 + 0.152813i \(0.0488333\pi\)
\(192\) 0 0
\(193\) −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i \(-0.296234\pi\)
−0.993215 + 0.116289i \(0.962900\pi\)
\(194\) 6.00000 10.3923i 0.430775 0.746124i
\(195\) 0 0
\(196\) 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
\(201\) 0 0
\(202\) −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
\(213\) 0 0
\(214\) 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
\(219\) 0 0
\(220\) 4.00000 + 6.92820i 0.269680 + 0.467099i
\(221\) 0 0
\(222\) 0 0
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −10.0000 + 17.3205i −0.665190 + 1.15214i
\(227\) −9.00000 15.5885i −0.597351 1.03464i −0.993210 0.116331i \(-0.962887\pi\)
0.395860 0.918311i \(-0.370447\pi\)
\(228\) 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
\(231\) 0 0
\(232\) 0 0
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) 0 0
\(235\) −6.00000 10.3923i −0.391397 0.677919i
\(236\) 12.0000 20.7846i 0.781133 1.35296i
\(237\) 0 0
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) 7.00000 + 12.1244i 0.450910 + 0.780998i 0.998443 0.0557856i \(-0.0177663\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) −7.00000 12.1244i −0.449977 0.779383i
\(243\) 0 0
\(244\) −20.0000 −1.28037
\(245\) 0 0
\(246\) 0 0
\(247\) −0.500000 + 0.866025i −0.0318142 + 0.0551039i
\(248\) 0 0
\(249\) 0 0
\(250\) 12.0000 20.7846i 0.758947 1.31453i
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 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 0.101305 + 0.994855i \(0.467698\pi\)
−0.912222 + 0.409695i \(0.865635\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 4.00000 0.248069
\(261\) 0 0
\(262\) −14.0000 24.2487i −0.864923 1.49809i
\(263\) 2.00000 + 3.46410i 0.123325 + 0.213606i 0.921077 0.389380i \(-0.127311\pi\)
−0.797752 + 0.602986i \(0.793977\pi\)
\(264\) 0 0
\(265\) 24.0000 1.47431
\(266\) 0 0
\(267\) 0 0
\(268\) 5.00000 8.66025i 0.305424 0.529009i
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) 0 0
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 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 0.601975 0.798515i \(-0.294381\pi\)
−0.992522 + 0.122068i \(0.961047\pi\)
\(278\) 3.00000 5.19615i 0.179928 0.311645i
\(279\) 0 0
\(280\) 0 0
\(281\) 4.00000 0.238620 0.119310 0.992857i \(-0.461932\pi\)
0.119310 + 0.992857i \(0.461932\pi\)
\(282\) 0 0
\(283\) −5.50000 9.52628i −0.326941 0.566279i 0.654962 0.755662i \(-0.272685\pi\)
−0.981903 + 0.189383i \(0.939351\pi\)
\(284\) −6.00000 10.3923i −0.356034 0.616670i
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 0 0
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 8.00000 + 13.8564i 0.469776 + 0.813676i
\(291\) 0 0
\(292\) −3.00000 + 5.19615i −0.175562 + 0.304082i
\(293\) 8.00000 0.467365 0.233682 0.972313i \(-0.424922\pi\)
0.233682 + 0.972313i \(0.424922\pi\)
\(294\) 0 0
\(295\) 24.0000 1.39733
\(296\) 0 0
\(297\) 0 0
\(298\) 12.0000 + 20.7846i 0.695141 + 1.20402i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 32.0000 1.84139
\(303\) 0 0
\(304\) −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
\(309\) 0 0
\(310\) 18.0000 31.1769i 1.02233 1.77073i
\(311\) 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 −0.879810 0.475325i \(-0.842331\pi\)
0.851549 + 0.524276i \(0.175664\pi\)
\(314\) −28.0000 −1.58013
\(315\) 0 0
\(316\) −2.00000 −0.112509
\(317\) 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
\(320\) −8.00000 + 13.8564i −0.447214 + 0.774597i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −0.500000 0.866025i −0.0277350 0.0480384i
\(326\) 4.00000 + 6.92820i 0.221540 + 0.383718i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 12.5000 21.6506i 0.687062 1.19003i −0.285722 0.958313i \(-0.592233\pi\)
0.972784 0.231714i \(-0.0744333\pi\)
\(332\) −6.00000 10.3923i −0.329293 0.570352i
\(333\) 0 0
\(334\) −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
\(339\) 0 0
\(340\) 0 0
\(341\) 9.00000 15.5885i 0.487377 0.844162i
\(342\) 0 0
\(343\) 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 0.872955 + 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
\(351\) 0 0
\(352\) −8.00000 + 13.8564i −0.426401 + 0.738549i
\(353\) −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
\(356\) 32.0000 1.69600
\(357\) 0 0
\(358\) 4.00000 0.211407
\(359\) 10.0000 17.3205i 0.527780 0.914141i −0.471696 0.881761i \(-0.656358\pi\)
0.999476 0.0323801i \(-0.0103087\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) −13.0000 + 22.5167i −0.683265 + 1.18345i
\(363\) 0 0
\(364\) 0 0
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) −4.50000 7.79423i −0.234898 0.406855i 0.724345 0.689438i \(-0.242142\pi\)
−0.959243 + 0.282582i \(0.908809\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 12.0000 0.623850
\(371\) 0 0
\(372\) 0 0
\(373\) −11.5000 + 19.9186i −0.595447 + 1.03135i 0.398036 + 0.917370i \(0.369692\pi\)
−0.993484 + 0.113975i \(0.963641\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 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
\(381\) 0 0
\(382\) −10.0000 17.3205i −0.511645 0.886194i
\(383\) 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
\(385\) 0 0
\(386\) −22.0000 −1.11977
\(387\) 0 0
\(388\) −6.00000 10.3923i −0.304604 0.527589i
\(389\) −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
\(393\) 0 0
\(394\) −16.0000 + 27.7128i −0.806068 + 1.39615i
\(395\) −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
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) −18.0000 + 31.1769i −0.898877 + 1.55690i −0.0699455 + 0.997551i \(0.522283\pi\)
−0.828932 + 0.559350i \(0.811051\pi\)
\(402\) 0 0
\(403\) −4.50000 7.79423i −0.224161 0.388258i
\(404\) −2.00000 + 3.46410i −0.0995037 + 0.172345i
\(405\) 0 0
\(406\) 0 0
\(407\) 6.00000 0.297409
\(408\) 0 0
\(409\) 2.50000 + 4.33013i 0.123617 + 0.214111i 0.921192 0.389109i \(-0.127217\pi\)
−0.797574 + 0.603220i \(0.793884\pi\)
\(410\) 20.0000 + 34.6410i 0.987730 + 1.71080i
\(411\) 0 0
\(412\) 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
\(417\) 0 0
\(418\) −2.00000 + 3.46410i −0.0978232 + 0.169435i
\(419\) 30.0000 1.46560 0.732798 0.680446i \(-0.238214\pi\)
0.732798 + 0.680446i \(0.238214\pi\)
\(420\) 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
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 16.0000 0.773389
\(429\) 0 0
\(430\) −10.0000 17.3205i −0.482243 0.835269i
\(431\) −9.00000 15.5885i −0.433515 0.750870i 0.563658 0.826008i \(-0.309393\pi\)
−0.997173 + 0.0751385i \(0.976060\pi\)
\(432\) 0 0
\(433\) −31.0000 −1.48976 −0.744882 0.667196i \(-0.767494\pi\)
−0.744882 + 0.667196i \(0.767494\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −9.00000 + 15.5885i −0.431022 + 0.746552i
\(437\) 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
\(441\) 0 0
\(442\) 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
\(446\) −16.0000 + 27.7128i −0.757622 + 1.31224i
\(447\) 0 0
\(448\) 0 0
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 0 0
\(451\) 10.0000 + 17.3205i 0.470882 + 0.815591i
\(452\) 10.0000 + 17.3205i 0.470360 + 0.814688i
\(453\) 0 0
\(454\) −36.0000 −1.68956
\(455\) 0 0
\(456\) 0 0
\(457\) 5.50000 9.52628i 0.257279 0.445621i −0.708233 0.705979i \(-0.750507\pi\)
0.965512 + 0.260358i \(0.0838407\pi\)
\(458\) 19.0000 + 32.9090i 0.887812 + 1.53773i
\(459\) 0 0
\(460\) 0 0
\(461\) 20.0000 0.931493 0.465746 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(462\) 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
\(465\) 0 0
\(466\) −6.00000 10.3923i −0.277945 0.481414i
\(467\) −3.00000 + 5.19615i −0.138823 + 0.240449i −0.927052 0.374934i \(-0.877665\pi\)
0.788228 + 0.615383i \(0.210999\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −24.0000 −1.10704
\(471\) 0 0
\(472\) 0 0
\(473\) −5.00000 8.66025i −0.229900 0.398199i
\(474\) 0 0
\(475\) 1.00000 0.0458831
\(476\) 0 0
\(477\) 0 0
\(478\) −6.00000 + 10.3923i −0.274434 + 0.475333i
\(479\) 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
\(482\) 28.0000 1.27537
\(483\) 0 0
\(484\) −14.0000 −0.636364
\(485\) 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
\(489\) 0 0
\(490\) 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
\(494\) 1.00000 + 1.73205i 0.0449921 + 0.0779287i
\(495\) 0 0
\(496\) 36.0000 1.61645
\(497\) 0 0
\(498\) 0 0
\(499\) −18.5000 + 32.0429i −0.828174 + 1.43444i 0.0712957 + 0.997455i \(0.477287\pi\)
−0.899469 + 0.436984i \(0.856047\pi\)
\(500\) −12.0000 20.7846i −0.536656 0.929516i
\(501\) 0 0
\(502\) −8.00000 + 13.8564i −0.357057 + 0.618442i
\(503\) −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
\(507\) 0 0
\(508\) 15.0000 + 25.9808i 0.665517 + 1.15271i
\(509\) −1.00000 + 1.73205i −0.0443242 + 0.0767718i −0.887336 0.461123i \(-0.847447\pi\)
0.843012 + 0.537895i \(0.180780\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −32.0000 −1.41421
\(513\) 0 0
\(514\) 26.0000 + 45.0333i 1.14681 + 1.98633i
\(515\) 7.00000 + 12.1244i 0.308457 + 0.534263i
\(516\) 0 0
\(517\) −12.0000 −0.527759
\(518\) 0 0
\(519\) 0 0
\(520\) 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 \(-0.0703858\pi\)
\(524\) −28.0000 −1.22319
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 0 0
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 24.0000 41.5692i 1.04249 1.80565i
\(531\) 0 0
\(532\) 0 0
\(533\) 10.0000 0.433148
\(534\) 0 0
\(535\) 8.00000 + 13.8564i 0.345870 + 0.599065i
\(536\) 0 0
\(537\) 0 0
\(538\) −12.0000 −0.517357
\(539\) 0 0
\(540\) 0 0
\(541\) 9.50000 16.4545i 0.408437 0.707433i −0.586278 0.810110i \(-0.699407\pi\)
0.994715 + 0.102677i \(0.0327407\pi\)
\(542\) −16.0000 27.7128i −0.687259 1.19037i
\(543\) 0 0
\(544\) 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
\(549\) 0 0
\(550\) −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
\(555\) 0 0
\(556\) −3.00000 5.19615i −0.127228 0.220366i
\(557\) −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
\(562\) 4.00000 6.92820i 0.168730 0.292249i
\(563\) 13.0000 + 22.5167i 0.547885 + 0.948964i 0.998419 + 0.0562051i \(0.0179001\pi\)
−0.450535 + 0.892759i \(0.648767\pi\)
\(564\) 0 0
\(565\) −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 0.453619 + 0.891196i \(0.350133\pi\)
−0.998608 + 0.0527519i \(0.983201\pi\)
\(570\) 0 0
\(571\) 9.50000 + 16.4545i 0.397563 + 0.688599i 0.993425 0.114488i \(-0.0365228\pi\)
−0.595862 + 0.803087i \(0.703189\pi\)
\(572\) 2.00000 3.46410i 0.0836242 0.144841i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −8.50000 14.7224i −0.353860 0.612903i 0.633062 0.774101i \(-0.281798\pi\)
−0.986922 + 0.161198i \(0.948464\pi\)
\(578\) −17.0000 29.4449i −0.707107 1.22474i
\(579\) 0 0
\(580\) 16.0000 0.664364
\(581\) 0 0
\(582\) 0 0
\(583\) 12.0000 20.7846i 0.496989 0.860811i
\(584\) 0 0
\(585\) 0 0
\(586\) 8.00000 13.8564i 0.330477 0.572403i
\(587\) 16.0000 0.660391 0.330195 0.943913i \(-0.392885\pi\)
0.330195 + 0.943913i \(0.392885\pi\)
\(588\) 0 0
\(589\) 9.00000 0.370839
\(590\) 24.0000 41.5692i 0.988064 1.71138i
\(591\) 0 0
\(592\) 6.00000 + 10.3923i 0.246598 + 0.427121i
\(593\) 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
\(596\) 24.0000 0.983078
\(597\) 0 0
\(598\) 0 0
\(599\) 6.00000 + 10.3923i 0.245153 + 0.424618i 0.962175 0.272433i \(-0.0878284\pi\)
−0.717021 + 0.697051i \(0.754495\pi\)
\(600\) 0 0
\(601\) 9.00000 0.367118 0.183559 0.983009i \(-0.441238\pi\)
0.183559 + 0.983009i \(0.441238\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 16.0000 27.7128i 0.651031 1.12762i
\(605\) −7.00000 12.1244i −0.284590 0.492925i
\(606\) 0 0
\(607\) 11.5000 19.9186i 0.466771 0.808470i −0.532509 0.846424i \(-0.678751\pi\)
0.999279 + 0.0379540i \(0.0120840\pi\)
\(608\) −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 −0.972924 0.231127i \(-0.925759\pi\)
0.286300 0.958140i \(-0.407575\pi\)
\(614\) 17.0000 29.4449i 0.686064 1.18830i
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) −14.5000 25.1147i −0.582804 1.00945i −0.995145 0.0984169i \(-0.968622\pi\)
0.412341 0.911030i \(-0.364711\pi\)
\(620\) −18.0000 31.1769i −0.722897 1.25210i
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) 0 0
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 1.00000 + 1.73205i 0.0399680 + 0.0692267i
\(627\) 0 0
\(628\) −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
\(633\) 0 0
\(634\) −24.0000 41.5692i −0.953162 1.65092i
\(635\) −15.0000 + 25.9808i −0.595257 + 1.03102i
\(636\) 0 0
\(637\) 0 0
\(638\) 16.0000 0.633446
\(639\) 0 0
\(640\) 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
\(645\) 0 0
\(646\) 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
\(650\) −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 \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) 0 0
\(655\) −14.0000 24.2487i −0.547025 0.947476i
\(656\) −20.0000 + 34.6410i −0.780869 + 1.35250i
\(657\) 0 0
\(658\) 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 \(-0.460436\pi\)
\(662\) −25.0000 43.3013i −0.971653 1.68295i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 14.0000 + 24.2487i 0.541676 + 0.938211i
\(669\) 0 0
\(670\) 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 0
\(676\) 12.0000 + 20.7846i 0.461538 + 0.799408i
\(677\) −6.00000 + 10.3923i −0.230599 + 0.399409i −0.957984 0.286820i \(-0.907402\pi\)
0.727386 + 0.686229i \(0.240735\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) −18.0000 31.1769i −0.689256 1.19383i
\(683\) −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
\(687\) 0 0
\(688\) 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 0.263359 + 0.964698i \(0.415170\pi\)
−0.967132 + 0.254273i \(0.918164\pi\)
\(692\) 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
\(699\) 0 0
\(700\) 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
\(704\) 8.00000 + 13.8564i 0.301511 + 0.522233i
\(705\) 0 0
\(706\) −68.0000 −2.55921
\(707\) 0 0
\(708\) 0 0
\(709\) −15.0000 + 25.9808i −0.563337 + 0.975728i 0.433865 + 0.900978i \(0.357149\pi\)
−0.997202 + 0.0747503i \(0.976184\pi\)
\(710\) −12.0000 20.7846i −0.450352 0.780033i
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 4.00000 0.149592
\(716\) 2.00000 3.46410i 0.0747435 0.129460i
\(717\) 0 0
\(718\) −20.0000 34.6410i −0.746393 1.29279i
\(719\) 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
\(721\) 0 0
\(722\) 36.0000 1.33978
\(723\) 0 0
\(724\) 13.0000 + 22.5167i 0.483141 + 0.836825i
\(725\) −2.00000 3.46410i −0.0742781 0.128654i
\(726\) 0 0
\(727\) 13.0000 0.482143 0.241072 0.970507i \(-0.422501\pi\)
0.241072 + 0.970507i \(0.422501\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −6.00000 + 10.3923i −0.222070 + 0.384636i
\(731\) 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 \(0.256013\pi\)
\(734\) −18.0000 −0.664392
\(735\) 0 0
\(736\) 0 0
\(737\) 5.00000 8.66025i 0.184177 0.319005i
\(738\) 0 0
\(739\) 7.50000 + 12.9904i 0.275892 + 0.477859i 0.970360 0.241665i \(-0.0776935\pi\)
−0.694468 + 0.719524i \(0.744360\pi\)
\(740\) 6.00000 10.3923i 0.220564 0.382029i
\(741\) 0 0
\(742\) 0 0
\(743\) −42.0000 −1.54083 −0.770415 0.637542i \(-0.779951\pi\)
−0.770415 + 0.637542i \(0.779951\pi\)
\(744\) 0 0
\(745\) 12.0000 + 20.7846i 0.439646 + 0.761489i
\(746\) 23.0000 + 39.8372i 0.842090 + 1.45854i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −6.50000 + 11.2583i −0.237188 + 0.410822i −0.959906 0.280321i \(-0.909559\pi\)
0.722718 + 0.691143i \(0.242893\pi\)
\(752\) −12.0000 20.7846i −0.437595 0.757937i
\(753\) 0 0
\(754\) 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 0.00800331 0.999968i \(-0.497452\pi\)
0.861996 0.506915i \(-0.169214\pi\)
\(762\) 0 0
\(763\) 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
\(768\) 0 0
\(769\) 49.0000 1.76699 0.883493 0.468445i \(-0.155186\pi\)
0.883493 + 0.468445i \(0.155186\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −11.0000 + 19.0526i −0.395899 + 0.685717i
\(773\) 17.0000 + 29.4449i 0.611448 + 1.05906i 0.990997 + 0.133887i \(0.0427458\pi\)
−0.379549 + 0.925172i \(0.623921\pi\)
\(774\) 0 0
\(775\) −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
\(780\) 0 0
\(781\) −6.00000 10.3923i −0.214697 0.371866i
\(782\) 0 0
\(783\) 0 0
\(784\) 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 \(0.580704\pi\)
\(788\) 16.0000 + 27.7128i 0.569976 + 0.987228i
\(789\) 0 0
\(790\) −4.00000 −0.142314
\(791\) 0 0
\(792\) 0 0
\(793\) −5.00000 + 8.66025i −0.177555 + 0.307535i
\(794\) 9.00000 + 15.5885i 0.319398 + 0.553214i
\(795\) 0 0
\(796\) 0 0
\(797\) −8.00000 −0.283375 −0.141687 0.989911i \(-0.545253\pi\)
&minus