Properties

Label 1900.2.s.b.349.2
Level $1900$
Weight $2$
Character 1900.349
Analytic conductor $15.172$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 349.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1900.349
Dual form 1900.2.s.b.49.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.73205 - 1.00000i) q^{3} +4.00000i q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.73205 - 1.00000i) q^{3} +4.00000i q^{7} +(0.500000 - 0.866025i) q^{9} -3.00000 q^{11} +(-5.19615 - 3.00000i) q^{13} +(-1.73205 + 1.00000i) q^{17} +(-3.50000 + 2.59808i) q^{19} +(4.00000 + 6.92820i) q^{21} +(-3.46410 - 2.00000i) q^{23} +4.00000i q^{27} +(0.500000 - 0.866025i) q^{29} -5.00000 q^{31} +(-5.19615 + 3.00000i) q^{33} +4.00000i q^{37} -12.0000 q^{39} +(-1.00000 - 1.73205i) q^{41} +(5.19615 + 3.00000i) q^{47} -9.00000 q^{49} +(-2.00000 + 3.46410i) q^{51} +(5.19615 + 3.00000i) q^{53} +(-3.46410 + 8.00000i) q^{57} +(-0.500000 - 0.866025i) q^{59} +(3.50000 - 6.06218i) q^{61} +(3.46410 + 2.00000i) q^{63} +(-12.1244 - 7.00000i) q^{67} -8.00000 q^{69} +(-7.50000 - 12.9904i) q^{71} +(10.3923 - 6.00000i) q^{73} -12.0000i q^{77} +(-0.500000 - 0.866025i) q^{79} +(5.50000 + 9.52628i) q^{81} +16.0000i q^{83} -2.00000i q^{87} +(8.50000 - 14.7224i) q^{89} +(12.0000 - 20.7846i) q^{91} +(-8.66025 + 5.00000i) q^{93} +(-10.3923 + 6.00000i) q^{97} +(-1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{9} - 12 q^{11} - 14 q^{19} + 16 q^{21} + 2 q^{29} - 20 q^{31} - 48 q^{39} - 4 q^{41} - 36 q^{49} - 8 q^{51} - 2 q^{59} + 14 q^{61} - 32 q^{69} - 30 q^{71} - 2 q^{79} + 22 q^{81} + 34 q^{89} + 48 q^{91} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 1.73205 1.00000i 1.00000 0.577350i 0.0917517 0.995782i \(-0.470753\pi\)
0.908248 + 0.418432i \(0.137420\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.00000i 1.51186i 0.654654 + 0.755929i \(0.272814\pi\)
−0.654654 + 0.755929i \(0.727186\pi\)
\(8\) 0 0
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 0 0
\(13\) −5.19615 3.00000i −1.44115 0.832050i −0.443227 0.896410i \(-0.646166\pi\)
−0.997927 + 0.0643593i \(0.979500\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.73205 + 1.00000i −0.420084 + 0.242536i −0.695113 0.718900i \(-0.744646\pi\)
0.275029 + 0.961436i \(0.411312\pi\)
\(18\) 0 0
\(19\) −3.50000 + 2.59808i −0.802955 + 0.596040i
\(20\) 0 0
\(21\) 4.00000 + 6.92820i 0.872872 + 1.51186i
\(22\) 0 0
\(23\) −3.46410 2.00000i −0.722315 0.417029i 0.0932891 0.995639i \(-0.470262\pi\)
−0.815604 + 0.578610i \(0.803595\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4.00000i 0.769800i
\(28\) 0 0
\(29\) 0.500000 0.866025i 0.0928477 0.160817i −0.815861 0.578249i \(-0.803736\pi\)
0.908708 + 0.417432i \(0.137070\pi\)
\(30\) 0 0
\(31\) −5.00000 −0.898027 −0.449013 0.893525i \(-0.648224\pi\)
−0.449013 + 0.893525i \(0.648224\pi\)
\(32\) 0 0
\(33\) −5.19615 + 3.00000i −0.904534 + 0.522233i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.00000i 0.657596i 0.944400 + 0.328798i \(0.106644\pi\)
−0.944400 + 0.328798i \(0.893356\pi\)
\(38\) 0 0
\(39\) −12.0000 −1.92154
\(40\) 0 0
\(41\) −1.00000 1.73205i −0.156174 0.270501i 0.777312 0.629115i \(-0.216583\pi\)
−0.933486 + 0.358614i \(0.883249\pi\)
\(42\) 0 0
\(43\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.19615 + 3.00000i 0.757937 + 0.437595i 0.828554 0.559908i \(-0.189164\pi\)
−0.0706177 + 0.997503i \(0.522497\pi\)
\(48\) 0 0
\(49\) −9.00000 −1.28571
\(50\) 0 0
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) 0 0
\(53\) 5.19615 + 3.00000i 0.713746 + 0.412082i 0.812447 0.583036i \(-0.198135\pi\)
−0.0987002 + 0.995117i \(0.531468\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −3.46410 + 8.00000i −0.458831 + 1.05963i
\(58\) 0 0
\(59\) −0.500000 0.866025i −0.0650945 0.112747i 0.831641 0.555313i \(-0.187402\pi\)
−0.896736 + 0.442566i \(0.854068\pi\)
\(60\) 0 0
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) 0 0
\(63\) 3.46410 + 2.00000i 0.436436 + 0.251976i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −12.1244 7.00000i −1.48123 0.855186i −0.481452 0.876472i \(-0.659891\pi\)
−0.999773 + 0.0212861i \(0.993224\pi\)
\(68\) 0 0
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) −7.50000 12.9904i −0.890086 1.54167i −0.839771 0.542941i \(-0.817311\pi\)
−0.0503155 0.998733i \(-0.516023\pi\)
\(72\) 0 0
\(73\) 10.3923 6.00000i 1.21633 0.702247i 0.252197 0.967676i \(-0.418847\pi\)
0.964130 + 0.265429i \(0.0855136\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 12.0000i 1.36753i
\(78\) 0 0
\(79\) −0.500000 0.866025i −0.0562544 0.0974355i 0.836527 0.547926i \(-0.184582\pi\)
−0.892781 + 0.450490i \(0.851249\pi\)
\(80\) 0 0
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) 0 0
\(83\) 16.0000i 1.75623i 0.478451 + 0.878114i \(0.341198\pi\)
−0.478451 + 0.878114i \(0.658802\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 2.00000i 0.214423i
\(88\) 0 0
\(89\) 8.50000 14.7224i 0.900998 1.56057i 0.0747975 0.997199i \(-0.476169\pi\)
0.826201 0.563376i \(-0.190498\pi\)
\(90\) 0 0
\(91\) 12.0000 20.7846i 1.25794 2.17882i
\(92\) 0 0
\(93\) −8.66025 + 5.00000i −0.898027 + 0.518476i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −10.3923 + 6.00000i −1.05518 + 0.609208i −0.924095 0.382164i \(-0.875179\pi\)
−0.131084 + 0.991371i \(0.541846\pi\)
\(98\) 0 0
\(99\) −1.50000 + 2.59808i −0.150756 + 0.261116i
\(100\) 0 0
\(101\) −5.50000 + 9.52628i −0.547270 + 0.947900i 0.451190 + 0.892428i \(0.351000\pi\)
−0.998460 + 0.0554722i \(0.982334\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.0000i 1.16008i 0.814587 + 0.580042i \(0.196964\pi\)
−0.814587 + 0.580042i \(0.803036\pi\)
\(108\) 0 0
\(109\) 3.50000 + 6.06218i 0.335239 + 0.580651i 0.983531 0.180741i \(-0.0578495\pi\)
−0.648292 + 0.761392i \(0.724516\pi\)
\(110\) 0 0
\(111\) 4.00000 + 6.92820i 0.379663 + 0.657596i
\(112\) 0 0
\(113\) 14.0000i 1.31701i 0.752577 + 0.658505i \(0.228811\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −5.19615 + 3.00000i −0.480384 + 0.277350i
\(118\) 0 0
\(119\) −4.00000 6.92820i −0.366679 0.635107i
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) −3.46410 2.00000i −0.312348 0.180334i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 15.5885 + 9.00000i 1.38325 + 0.798621i 0.992543 0.121894i \(-0.0388966\pi\)
0.390709 + 0.920514i \(0.372230\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 10.0000 + 17.3205i 0.873704 + 1.51330i 0.858137 + 0.513421i \(0.171622\pi\)
0.0155672 + 0.999879i \(0.495045\pi\)
\(132\) 0 0
\(133\) −10.3923 14.0000i −0.901127 1.21395i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.3923 + 6.00000i 0.887875 + 0.512615i 0.873247 0.487278i \(-0.162010\pi\)
0.0146279 + 0.999893i \(0.495344\pi\)
\(138\) 0 0
\(139\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(140\) 0 0
\(141\) 12.0000 1.01058
\(142\) 0 0
\(143\) 15.5885 + 9.00000i 1.30357 + 0.752618i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −15.5885 + 9.00000i −1.28571 + 0.742307i
\(148\) 0 0
\(149\) −8.50000 14.7224i −0.696347 1.20611i −0.969724 0.244202i \(-0.921474\pi\)
0.273377 0.961907i \(-0.411859\pi\)
\(150\) 0 0
\(151\) 3.00000 0.244137 0.122068 0.992522i \(-0.461047\pi\)
0.122068 + 0.992522i \(0.461047\pi\)
\(152\) 0 0
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −15.5885 + 9.00000i −1.24409 + 0.718278i −0.969925 0.243403i \(-0.921736\pi\)
−0.274169 + 0.961681i \(0.588403\pi\)
\(158\) 0 0
\(159\) 12.0000 0.951662
\(160\) 0 0
\(161\) 8.00000 13.8564i 0.630488 1.09204i
\(162\) 0 0
\(163\) 18.0000i 1.40987i 0.709273 + 0.704934i \(0.249024\pi\)
−0.709273 + 0.704934i \(0.750976\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.92820 + 4.00000i 0.536120 + 0.309529i 0.743505 0.668730i \(-0.233162\pi\)
−0.207385 + 0.978259i \(0.566495\pi\)
\(168\) 0 0
\(169\) 11.5000 + 19.9186i 0.884615 + 1.53220i
\(170\) 0 0
\(171\) 0.500000 + 4.33013i 0.0382360 + 0.331133i
\(172\) 0 0
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1.73205 1.00000i −0.130189 0.0751646i
\(178\) 0 0
\(179\) 15.0000 1.12115 0.560576 0.828103i \(-0.310580\pi\)
0.560576 + 0.828103i \(0.310580\pi\)
\(180\) 0 0
\(181\) −1.00000 + 1.73205i −0.0743294 + 0.128742i −0.900794 0.434246i \(-0.857015\pi\)
0.826465 + 0.562988i \(0.190348\pi\)
\(182\) 0 0
\(183\) 14.0000i 1.03491i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 5.19615 3.00000i 0.379980 0.219382i
\(188\) 0 0
\(189\) −16.0000 −1.16383
\(190\) 0 0
\(191\) −13.0000 −0.940647 −0.470323 0.882494i \(-0.655863\pi\)
−0.470323 + 0.882494i \(0.655863\pi\)
\(192\) 0 0
\(193\) 13.8564 8.00000i 0.997406 0.575853i 0.0899262 0.995948i \(-0.471337\pi\)
0.907480 + 0.420096i \(0.138004\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.00000i 0.142494i −0.997459 0.0712470i \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) 0 0
\(199\) 11.5000 19.9186i 0.815213 1.41199i −0.0939612 0.995576i \(-0.529953\pi\)
0.909175 0.416415i \(-0.136714\pi\)
\(200\) 0 0
\(201\) −28.0000 −1.97497
\(202\) 0 0
\(203\) 3.46410 + 2.00000i 0.243132 + 0.140372i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −3.46410 + 2.00000i −0.240772 + 0.139010i
\(208\) 0 0
\(209\) 10.5000 7.79423i 0.726300 0.539138i
\(210\) 0 0
\(211\) 0.500000 + 0.866025i 0.0344214 + 0.0596196i 0.882723 0.469894i \(-0.155708\pi\)
−0.848301 + 0.529514i \(0.822374\pi\)
\(212\) 0 0
\(213\) −25.9808 15.0000i −1.78017 1.02778i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 20.0000i 1.35769i
\(218\) 0 0
\(219\) 12.0000 20.7846i 0.810885 1.40449i
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) 6.92820 4.00000i 0.463947 0.267860i −0.249756 0.968309i \(-0.580350\pi\)
0.713702 + 0.700449i \(0.247017\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4.00000i 0.265489i 0.991150 + 0.132745i \(0.0423790\pi\)
−0.991150 + 0.132745i \(0.957621\pi\)
\(228\) 0 0
\(229\) −21.0000 −1.38772 −0.693860 0.720110i \(-0.744091\pi\)
−0.693860 + 0.720110i \(0.744091\pi\)
\(230\) 0 0
\(231\) −12.0000 20.7846i −0.789542 1.36753i
\(232\) 0 0
\(233\) −8.66025 + 5.00000i −0.567352 + 0.327561i −0.756091 0.654466i \(-0.772893\pi\)
0.188739 + 0.982027i \(0.439560\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.73205 1.00000i −0.112509 0.0649570i
\(238\) 0 0
\(239\) −15.0000 −0.970269 −0.485135 0.874439i \(-0.661229\pi\)
−0.485135 + 0.874439i \(0.661229\pi\)
\(240\) 0 0
\(241\) −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i \(-0.884818\pi\)
0.774202 + 0.632938i \(0.218151\pi\)
\(242\) 0 0
\(243\) 8.66025 + 5.00000i 0.555556 + 0.320750i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 25.9808 3.00000i 1.65312 0.190885i
\(248\) 0 0
\(249\) 16.0000 + 27.7128i 1.01396 + 1.75623i
\(250\) 0 0
\(251\) −15.5000 + 26.8468i −0.978351 + 1.69455i −0.309951 + 0.950753i \(0.600313\pi\)
−0.668400 + 0.743802i \(0.733021\pi\)
\(252\) 0 0
\(253\) 10.3923 + 6.00000i 0.653359 + 0.377217i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 15.5885 + 9.00000i 0.972381 + 0.561405i 0.899961 0.435970i \(-0.143595\pi\)
0.0724199 + 0.997374i \(0.476928\pi\)
\(258\) 0 0
\(259\) −16.0000 −0.994192
\(260\) 0 0
\(261\) −0.500000 0.866025i −0.0309492 0.0536056i
\(262\) 0 0
\(263\) 8.66025 5.00000i 0.534014 0.308313i −0.208635 0.977993i \(-0.566902\pi\)
0.742650 + 0.669680i \(0.233569\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 34.0000i 2.08077i
\(268\) 0 0
\(269\) −0.500000 0.866025i −0.0304855 0.0528025i 0.850380 0.526169i \(-0.176372\pi\)
−0.880866 + 0.473366i \(0.843039\pi\)
\(270\) 0 0
\(271\) −8.50000 14.7224i −0.516338 0.894324i −0.999820 0.0189696i \(-0.993961\pi\)
0.483482 0.875354i \(-0.339372\pi\)
\(272\) 0 0
\(273\) 48.0000i 2.90509i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 16.0000i 0.961347i −0.876900 0.480673i \(-0.840392\pi\)
0.876900 0.480673i \(-0.159608\pi\)
\(278\) 0 0
\(279\) −2.50000 + 4.33013i −0.149671 + 0.259238i
\(280\) 0 0
\(281\) 13.0000 22.5167i 0.775515 1.34323i −0.158990 0.987280i \(-0.550824\pi\)
0.934505 0.355951i \(-0.115843\pi\)
\(282\) 0 0
\(283\) −22.5167 + 13.0000i −1.33848 + 0.772770i −0.986581 0.163270i \(-0.947796\pi\)
−0.351895 + 0.936039i \(0.614463\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.92820 4.00000i 0.408959 0.236113i
\(288\) 0 0
\(289\) −6.50000 + 11.2583i −0.382353 + 0.662255i
\(290\) 0 0
\(291\) −12.0000 + 20.7846i −0.703452 + 1.21842i
\(292\) 0 0
\(293\) 16.0000i 0.934730i 0.884064 + 0.467365i \(0.154797\pi\)
−0.884064 + 0.467365i \(0.845203\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 12.0000i 0.696311i
\(298\) 0 0
\(299\) 12.0000 + 20.7846i 0.693978 + 1.20201i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 22.0000i 1.26387i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 12.1244 7.00000i 0.691974 0.399511i −0.112377 0.993666i \(-0.535847\pi\)
0.804351 + 0.594154i \(0.202513\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −29.4449 17.0000i −1.66432 0.960897i −0.970614 0.240640i \(-0.922643\pi\)
−0.693708 0.720257i \(-0.744024\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10.3923 6.00000i −0.583690 0.336994i 0.178908 0.983866i \(-0.442743\pi\)
−0.762598 + 0.646872i \(0.776077\pi\)
\(318\) 0 0
\(319\) −1.50000 + 2.59808i −0.0839839 + 0.145464i
\(320\) 0 0
\(321\) 12.0000 + 20.7846i 0.669775 + 1.16008i
\(322\) 0 0
\(323\) 3.46410 8.00000i 0.192748 0.445132i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 12.1244 + 7.00000i 0.670478 + 0.387101i
\(328\) 0 0
\(329\) −12.0000 + 20.7846i −0.661581 + 1.14589i
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) 0 0
\(333\) 3.46410 + 2.00000i 0.189832 + 0.109599i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −3.46410 + 2.00000i −0.188702 + 0.108947i −0.591375 0.806397i \(-0.701415\pi\)
0.402673 + 0.915344i \(0.368081\pi\)
\(338\) 0 0
\(339\) 14.0000 + 24.2487i 0.760376 + 1.31701i
\(340\) 0 0
\(341\) 15.0000 0.812296
\(342\) 0 0
\(343\) 8.00000i 0.431959i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10.3923 + 6.00000i −0.557888 + 0.322097i −0.752297 0.658824i \(-0.771054\pi\)
0.194409 + 0.980921i \(0.437721\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) 12.0000 20.7846i 0.640513 1.10940i
\(352\) 0 0
\(353\) 36.0000i 1.91609i −0.286623 0.958043i \(-0.592533\pi\)
0.286623 0.958043i \(-0.407467\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −13.8564 8.00000i −0.733359 0.423405i
\(358\) 0 0
\(359\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(360\) 0 0
\(361\) 5.50000 18.1865i 0.289474 0.957186i
\(362\) 0 0
\(363\) −3.46410 + 2.00000i −0.181818 + 0.104973i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −24.2487 14.0000i −1.26577 0.730794i −0.291587 0.956544i \(-0.594183\pi\)
−0.974185 + 0.225750i \(0.927517\pi\)
\(368\) 0 0
\(369\) −2.00000 −0.104116
\(370\) 0 0
\(371\) −12.0000 + 20.7846i −0.623009 + 1.07908i
\(372\) 0 0
\(373\) 12.0000i 0.621336i −0.950518 0.310668i \(-0.899447\pi\)
0.950518 0.310668i \(-0.100553\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.19615 + 3.00000i −0.267615 + 0.154508i
\(378\) 0 0
\(379\) 19.0000 0.975964 0.487982 0.872854i \(-0.337733\pi\)
0.487982 + 0.872854i \(0.337733\pi\)
\(380\) 0 0
\(381\) 36.0000 1.84434
\(382\) 0 0
\(383\) −15.5885 + 9.00000i −0.796533 + 0.459879i −0.842257 0.539076i \(-0.818774\pi\)
0.0457244 + 0.998954i \(0.485440\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −10.5000 + 18.1865i −0.532371 + 0.922094i 0.466915 + 0.884302i \(0.345366\pi\)
−0.999286 + 0.0377914i \(0.987968\pi\)
\(390\) 0 0
\(391\) 8.00000 0.404577
\(392\) 0 0
\(393\) 34.6410 + 20.0000i 1.74741 + 1.00887i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 6.92820 4.00000i 0.347717 0.200754i −0.315963 0.948772i \(-0.602327\pi\)
0.663679 + 0.748017i \(0.268994\pi\)
\(398\) 0 0
\(399\) −32.0000 13.8564i −1.60200 0.693688i
\(400\) 0 0
\(401\) −7.50000 12.9904i −0.374532 0.648709i 0.615725 0.787961i \(-0.288863\pi\)
−0.990257 + 0.139253i \(0.955530\pi\)
\(402\) 0 0
\(403\) 25.9808 + 15.0000i 1.29419 + 0.747203i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 12.0000i 0.594818i
\(408\) 0 0
\(409\) −0.500000 + 0.866025i −0.0247234 + 0.0428222i −0.878122 0.478436i \(-0.841204\pi\)
0.853399 + 0.521258i \(0.174537\pi\)
\(410\) 0 0
\(411\) 24.0000 1.18383
\(412\) 0 0
\(413\) 3.46410 2.00000i 0.170457 0.0984136i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5.00000 0.244266 0.122133 0.992514i \(-0.461027\pi\)
0.122133 + 0.992514i \(0.461027\pi\)
\(420\) 0 0
\(421\) −12.5000 21.6506i −0.609213 1.05519i −0.991370 0.131090i \(-0.958152\pi\)
0.382158 0.924097i \(-0.375181\pi\)
\(422\) 0 0
\(423\) 5.19615 3.00000i 0.252646 0.145865i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 24.2487 + 14.0000i 1.17348 + 0.677507i
\(428\) 0 0
\(429\) 36.0000 1.73810
\(430\) 0 0
\(431\) −13.5000 + 23.3827i −0.650272 + 1.12630i 0.332785 + 0.943003i \(0.392012\pi\)
−0.983057 + 0.183301i \(0.941322\pi\)
\(432\) 0 0
\(433\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 17.3205 2.00000i 0.828552 0.0956730i
\(438\) 0 0
\(439\) 0.500000 + 0.866025i 0.0238637 + 0.0413331i 0.877711 0.479191i \(-0.159070\pi\)
−0.853847 + 0.520524i \(0.825737\pi\)
\(440\) 0 0
\(441\) −4.50000 + 7.79423i −0.214286 + 0.371154i
\(442\) 0 0
\(443\) 10.3923 + 6.00000i 0.493753 + 0.285069i 0.726130 0.687557i \(-0.241317\pi\)
−0.232377 + 0.972626i \(0.574650\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −29.4449 17.0000i −1.39269 0.804072i
\(448\) 0 0
\(449\) 1.00000 0.0471929 0.0235965 0.999722i \(-0.492488\pi\)
0.0235965 + 0.999722i \(0.492488\pi\)
\(450\) 0 0
\(451\) 3.00000 + 5.19615i 0.141264 + 0.244677i
\(452\) 0 0
\(453\) 5.19615 3.00000i 0.244137 0.140952i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 2.00000i 0.0935561i 0.998905 + 0.0467780i \(0.0148953\pi\)
−0.998905 + 0.0467780i \(0.985105\pi\)
\(458\) 0 0
\(459\) −4.00000 6.92820i −0.186704 0.323381i
\(460\) 0 0
\(461\) −17.5000 30.3109i −0.815056 1.41172i −0.909288 0.416169i \(-0.863373\pi\)
0.0942312 0.995550i \(-0.469961\pi\)
\(462\) 0 0
\(463\) 8.00000i 0.371792i −0.982569 0.185896i \(-0.940481\pi\)
0.982569 0.185896i \(-0.0595187\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 20.0000i 0.925490i 0.886492 + 0.462745i \(0.153135\pi\)
−0.886492 + 0.462745i \(0.846865\pi\)
\(468\) 0 0
\(469\) 28.0000 48.4974i 1.29292 2.23940i
\(470\) 0 0
\(471\) −18.0000 + 31.1769i −0.829396 + 1.43656i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 5.19615 3.00000i 0.237915 0.137361i
\(478\) 0 0
\(479\) −1.50000 + 2.59808i −0.0685367 + 0.118709i −0.898257 0.439470i \(-0.855166\pi\)
0.829721 + 0.558179i \(0.188500\pi\)
\(480\) 0 0
\(481\) 12.0000 20.7846i 0.547153 0.947697i
\(482\) 0 0
\(483\) 32.0000i 1.45605i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 34.0000i 1.54069i −0.637629 0.770344i \(-0.720085\pi\)
0.637629 0.770344i \(-0.279915\pi\)
\(488\) 0 0
\(489\) 18.0000 + 31.1769i 0.813988 + 1.40987i
\(490\) 0 0
\(491\) 12.5000 + 21.6506i 0.564117 + 0.977079i 0.997131 + 0.0756923i \(0.0241167\pi\)
−0.433014 + 0.901387i \(0.642550\pi\)
\(492\) 0 0
\(493\) 2.00000i 0.0900755i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 51.9615 30.0000i 2.33079 1.34568i
\(498\) 0 0
\(499\) 18.0000 + 31.1769i 0.805791 + 1.39567i 0.915756 + 0.401735i \(0.131593\pi\)
−0.109965 + 0.993935i \(0.535074\pi\)
\(500\) 0 0
\(501\) 16.0000 0.714827
\(502\) 0 0
\(503\) −19.0526 11.0000i −0.849512 0.490466i 0.0109744 0.999940i \(-0.496507\pi\)
−0.860486 + 0.509474i \(0.829840\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 39.8372 + 23.0000i 1.76923 + 1.02147i
\(508\) 0 0
\(509\) 15.0000 25.9808i 0.664863 1.15158i −0.314459 0.949271i \(-0.601823\pi\)
0.979322 0.202306i \(-0.0648436\pi\)
\(510\) 0 0
\(511\) 24.0000 + 41.5692i 1.06170 + 1.83891i
\(512\) 0 0
\(513\) −10.3923 14.0000i −0.458831 0.618115i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −15.5885 9.00000i −0.685580 0.395820i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −45.0000 −1.97149 −0.985743 0.168259i \(-0.946186\pi\)
−0.985743 + 0.168259i \(0.946186\pi\)
\(522\) 0 0
\(523\) 8.66025 + 5.00000i 0.378686 + 0.218635i 0.677247 0.735756i \(-0.263173\pi\)
−0.298560 + 0.954391i \(0.596506\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.66025 5.00000i 0.377247 0.217803i
\(528\) 0 0
\(529\) −3.50000 6.06218i −0.152174 0.263573i
\(530\) 0 0
\(531\) −1.00000 −0.0433963
\(532\) 0 0
\(533\) 12.0000i 0.519778i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 25.9808 15.0000i 1.12115 0.647298i
\(538\) 0 0
\(539\) 27.0000 1.16297
\(540\) 0 0
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) 0 0
\(543\) 4.00000i 0.171656i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −6.92820 4.00000i −0.296229 0.171028i 0.344519 0.938779i \(-0.388042\pi\)
−0.640747 + 0.767752i \(0.721375\pi\)
\(548\) 0 0
\(549\) −3.50000 6.06218i −0.149376 0.258727i
\(550\) 0 0
\(551\) 0.500000 + 4.33013i 0.0213007 + 0.184470i
\(552\) 0 0
\(553\) 3.46410 2.00000i 0.147309 0.0850487i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −34.6410 20.0000i −1.46779 0.847427i −0.468438 0.883497i \(-0.655183\pi\)
−0.999349 + 0.0360693i \(0.988516\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 6.00000 10.3923i 0.253320 0.438763i
\(562\) 0 0
\(563\) 10.0000i 0.421450i 0.977545 + 0.210725i \(0.0675824\pi\)
−0.977545 + 0.210725i \(0.932418\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −38.1051 + 22.0000i −1.60026 + 0.923913i
\(568\) 0 0
\(569\) 17.0000 0.712677 0.356339 0.934357i \(-0.384025\pi\)
0.356339 + 0.934357i \(0.384025\pi\)
\(570\) 0 0
\(571\) −17.0000 −0.711428 −0.355714 0.934595i \(-0.615762\pi\)
−0.355714 + 0.934595i \(0.615762\pi\)
\(572\) 0 0
\(573\) −22.5167 + 13.0000i −0.940647 + 0.543083i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 20.0000i 0.832611i 0.909225 + 0.416305i \(0.136675\pi\)
−0.909225 + 0.416305i \(0.863325\pi\)
\(578\) 0 0
\(579\) 16.0000 27.7128i 0.664937 1.15171i
\(580\) 0 0
\(581\) −64.0000 −2.65517
\(582\) 0 0
\(583\) −15.5885 9.00000i −0.645608 0.372742i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 10.3923 6.00000i 0.428936 0.247647i −0.269957 0.962872i \(-0.587010\pi\)
0.698893 + 0.715226i \(0.253676\pi\)
\(588\) 0 0
\(589\) 17.5000 12.9904i 0.721075 0.535259i
\(590\) 0 0
\(591\) −2.00000 3.46410i −0.0822690 0.142494i
\(592\) 0 0
\(593\) 3.46410 + 2.00000i 0.142254 + 0.0821302i 0.569438 0.822035i \(-0.307161\pi\)
−0.427184 + 0.904165i \(0.640494\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 46.0000i 1.88265i
\(598\) 0 0
\(599\) −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i \(-0.996449\pi\)
0.509631 + 0.860393i \(0.329782\pi\)
\(600\) 0 0
\(601\) 17.0000 0.693444 0.346722 0.937968i \(-0.387295\pi\)
0.346722 + 0.937968i \(0.387295\pi\)
\(602\) 0 0
\(603\) −12.1244 + 7.00000i −0.493742 + 0.285062i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 14.0000i 0.568242i 0.958788 + 0.284121i \(0.0917018\pi\)
−0.958788 + 0.284121i \(0.908298\pi\)
\(608\) 0 0
\(609\) 8.00000 0.324176
\(610\) 0 0
\(611\) −18.0000 31.1769i −0.728202 1.26128i
\(612\) 0 0
\(613\) −19.0526 + 11.0000i −0.769526 + 0.444286i −0.832705 0.553716i \(-0.813209\pi\)
0.0631797 + 0.998002i \(0.479876\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −6.92820 4.00000i −0.278919 0.161034i 0.354015 0.935240i \(-0.384816\pi\)
−0.632934 + 0.774206i \(0.718150\pi\)
\(618\) 0 0
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) 8.00000 13.8564i 0.321029 0.556038i
\(622\) 0 0
\(623\) 58.8897 + 34.0000i 2.35937 + 1.36218i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 10.3923 24.0000i 0.415029 0.958468i
\(628\) 0 0
\(629\) −4.00000 6.92820i −0.159490 0.276246i
\(630\) 0 0
\(631\) 16.5000 28.5788i 0.656855 1.13771i −0.324571 0.945861i \(-0.605220\pi\)
0.981425 0.191844i \(-0.0614468\pi\)
\(632\) 0 0
\(633\) 1.73205 + 1.00000i 0.0688428 + 0.0397464i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 46.7654 + 27.0000i 1.85291 + 1.06978i
\(638\) 0 0
\(639\) −15.0000 −0.593391
\(640\) 0 0
\(641\) −4.50000 7.79423i −0.177739 0.307854i 0.763367 0.645966i \(-0.223545\pi\)
−0.941106 + 0.338112i \(0.890212\pi\)
\(642\) 0 0
\(643\) −1.73205 + 1.00000i −0.0683054 + 0.0394362i −0.533764 0.845634i \(-0.679223\pi\)
0.465458 + 0.885070i \(0.345890\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 30.0000i 1.17942i 0.807614 + 0.589711i \(0.200758\pi\)
−0.807614 + 0.589711i \(0.799242\pi\)
\(648\) 0 0
\(649\) 1.50000 + 2.59808i 0.0588802 + 0.101983i
\(650\) 0 0
\(651\) −20.0000 34.6410i −0.783862 1.35769i
\(652\) 0 0
\(653\) 12.0000i 0.469596i 0.972044 + 0.234798i \(0.0754429\pi\)
−0.972044 + 0.234798i \(0.924557\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 12.0000i 0.468165i
\(658\) 0 0
\(659\) −18.0000 + 31.1769i −0.701180 + 1.21448i 0.266872 + 0.963732i \(0.414010\pi\)
−0.968052 + 0.250748i \(0.919323\pi\)
\(660\) 0 0
\(661\) −20.5000 + 35.5070i −0.797358 + 1.38106i 0.123974 + 0.992286i \(0.460436\pi\)
−0.921331 + 0.388778i \(0.872897\pi\)
\(662\) 0 0
\(663\) 20.7846 12.0000i 0.807207 0.466041i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −3.46410 + 2.00000i −0.134131 + 0.0774403i
\(668\) 0 0
\(669\) 8.00000 13.8564i 0.309298 0.535720i
\(670\) 0 0
\(671\) −10.5000 + 18.1865i −0.405348 + 0.702083i
\(672\) 0 0
\(673\) 28.0000i 1.07932i −0.841883 0.539660i \(-0.818553\pi\)
0.841883 0.539660i \(-0.181447\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 32.0000i 1.22986i 0.788582 + 0.614930i \(0.210816\pi\)
−0.788582 + 0.614930i \(0.789184\pi\)
\(678\) 0 0
\(679\) −24.0000 41.5692i −0.921035 1.59528i
\(680\) 0 0
\(681\) 4.00000 + 6.92820i 0.153280 + 0.265489i
\(682\) 0 0
\(683\) 6.00000i 0.229584i 0.993390 + 0.114792i \(0.0366201\pi\)
−0.993390 + 0.114792i \(0.963380\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −36.3731 + 21.0000i −1.38772 + 0.801200i
\(688\) 0 0
\(689\) −18.0000 31.1769i −0.685745 1.18775i
\(690\) 0 0
\(691\) 37.0000 1.40755 0.703773 0.710425i \(-0.251497\pi\)
0.703773 + 0.710425i \(0.251497\pi\)
\(692\) 0 0
\(693\) −10.3923 6.00000i −0.394771 0.227921i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 3.46410 + 2.00000i 0.131212 + 0.0757554i
\(698\) 0 0
\(699\) −10.0000 + 17.3205i −0.378235 + 0.655122i
\(700\) 0 0
\(701\) 21.0000 + 36.3731i 0.793159 + 1.37379i 0.924002 + 0.382389i \(0.124898\pi\)
−0.130843 + 0.991403i \(0.541768\pi\)
\(702\) 0 0
\(703\) −10.3923 14.0000i −0.391953 0.528020i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −38.1051 22.0000i −1.43309 0.827395i
\(708\) 0 0
\(709\) 2.50000 4.33013i 0.0938895 0.162621i −0.815255 0.579102i \(-0.803403\pi\)
0.909145 + 0.416481i \(0.136737\pi\)
\(710\) 0 0
\(711\) −1.00000 −0.0375029
\(712\) 0 0
\(713\) 17.3205 + 10.0000i 0.648658 + 0.374503i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −25.9808 + 15.0000i −0.970269 + 0.560185i
\(718\) 0 0
\(719\) 14.5000 + 25.1147i 0.540759 + 0.936622i 0.998861 + 0.0477220i \(0.0151961\pi\)
−0.458102 + 0.888900i \(0.651471\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 10.0000i 0.371904i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −22.5167 + 13.0000i −0.835097 + 0.482143i −0.855595 0.517647i \(-0.826808\pi\)
0.0204978 + 0.999790i \(0.493475\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 12.0000i 0.443230i −0.975134 0.221615i \(-0.928867\pi\)
0.975134 0.221615i \(-0.0711328\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 36.3731 + 21.0000i 1.33982 + 0.773545i
\(738\) 0 0
\(739\) −9.50000 16.4545i −0.349463 0.605288i 0.636691 0.771119i \(-0.280303\pi\)
−0.986154 + 0.165831i \(0.946969\pi\)
\(740\) 0 0
\(741\) 42.0000 31.1769i 1.54291 1.14531i
\(742\) 0 0
\(743\) 45.0333 26.0000i 1.65211 0.953847i 0.675910 0.736984i \(-0.263751\pi\)
0.976202 0.216864i \(-0.0695827\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 13.8564 + 8.00000i 0.506979 + 0.292705i
\(748\) 0 0
\(749\) −48.0000 −1.75388
\(750\) 0 0
\(751\) −9.50000 + 16.4545i −0.346660 + 0.600433i −0.985654 0.168779i \(-0.946018\pi\)
0.638994 + 0.769212i \(0.279351\pi\)
\(752\) 0 0
\(753\) 62.0000i 2.25941i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 12.1244 7.00000i 0.440667 0.254419i −0.263213 0.964738i \(-0.584782\pi\)
0.703881 + 0.710318i \(0.251449\pi\)
\(758\) 0 0
\(759\) 24.0000 0.871145
\(760\) 0 0
\(761\) 54.0000 1.95750 0.978749 0.205061i \(-0.0657392\pi\)
0.978749 + 0.205061i \(0.0657392\pi\)
\(762\) 0 0
\(763\) −24.2487 + 14.0000i −0.877862 + 0.506834i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6.00000i 0.216647i
\(768\) 0 0
\(769\) 6.50000 11.2583i 0.234396 0.405986i −0.724701 0.689063i \(-0.758022\pi\)
0.959097 + 0.283078i \(0.0913554\pi\)
\(770\) 0 0
\(771\) 36.0000 1.29651
\(772\) 0 0
\(773\) 46.7654 + 27.0000i 1.68203 + 0.971123i 0.960307 + 0.278944i \(0.0899843\pi\)
0.721726 + 0.692179i \(0.243349\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −27.7128 + 16.0000i −0.994192 + 0.573997i
\(778\) 0 0
\(779\) 8.00000 + 3.46410i 0.286630 + 0.124114i
\(780\) 0 0
\(781\) 22.5000 + 38.9711i 0.805113 + 1.39450i
\(782\) 0 0
\(783\) 3.46410 + 2.00000i 0.123797 + 0.0714742i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 38.0000i 1.35455i −0.735728 0.677277i \(-0.763160\pi\)
0.735728 0.677277i \(-0.236840\pi\)
\(788\) 0 0
\(789\) 10.0000 17.3205i 0.356009 0.616626i
\(790\) 0 0
\(791\) −56.0000 −1.99113
\(792\) 0 0
\(793\) −36.3731 + 21.0000i −1.29165 + 0.745732i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 22.0000i 0.779280i 0.920967 + 0.389640i \(0.127401\pi\)
−0.920967 + 0.389640i \(0.872599\pi\)
\(798\) 0 0
\(799\) −12.0000 −0.424529