Properties

Label 224.3.r.b.95.2
Level 224
Weight 3
Character 224.95
Analytic conductor 6.104
Analytic rank 0
Dimension 4
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.r (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 95.2
Root \(0.866025 + 0.500000i\) of \(x^{4} - x^{2} + 1\)
Character \(\chi\) \(=\) 224.95
Dual form 224.3.r.b.191.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{5} -7.00000i q^{7} +(-4.00000 - 6.92820i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{5} -7.00000i q^{7} +(-4.00000 - 6.92820i) q^{9} +(-14.7224 - 8.50000i) q^{11} +24.0000 q^{13} -1.00000i q^{15} +(-0.500000 + 0.866025i) q^{17} +(6.06218 - 3.50000i) q^{19} +(3.50000 - 6.06218i) q^{21} +(-6.06218 + 3.50000i) q^{23} +(12.0000 - 20.7846i) q^{25} -17.0000i q^{27} +24.0000 q^{29} +(-35.5070 - 20.5000i) q^{31} +(-8.50000 - 14.7224i) q^{33} +(-6.06218 + 3.50000i) q^{35} +(24.5000 + 42.4352i) q^{37} +(20.7846 + 12.0000i) q^{39} -48.0000 q^{41} +24.0000i q^{43} +(-4.00000 + 6.92820i) q^{45} +(47.6314 - 27.5000i) q^{47} -49.0000 q^{49} +(-0.866025 + 0.500000i) q^{51} +(12.5000 - 21.6506i) q^{53} +17.0000i q^{55} +7.00000 q^{57} +(14.7224 + 8.50000i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-48.4974 + 28.0000i) q^{63} +(-12.0000 - 20.7846i) q^{65} +(56.2917 + 32.5000i) q^{67} -7.00000 q^{69} +96.0000i q^{71} +(-47.5000 + 82.2724i) q^{73} +(20.7846 - 12.0000i) q^{75} +(-59.5000 + 103.057i) q^{77} +(35.5070 - 20.5000i) q^{79} +(-27.5000 + 47.6314i) q^{81} +72.0000i q^{83} +1.00000 q^{85} +(20.7846 + 12.0000i) q^{87} +(-47.5000 - 82.2724i) q^{89} -168.000i q^{91} +(-20.5000 - 35.5070i) q^{93} +(-6.06218 - 3.50000i) q^{95} +144.000 q^{97} +136.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{5} - 16q^{9} + O(q^{10}) \) \( 4q - 2q^{5} - 16q^{9} + 96q^{13} - 2q^{17} + 14q^{21} + 48q^{25} + 96q^{29} - 34q^{33} + 98q^{37} - 192q^{41} - 16q^{45} - 196q^{49} + 50q^{53} + 28q^{57} + 2q^{61} - 48q^{65} - 28q^{69} - 190q^{73} - 238q^{77} - 110q^{81} + 4q^{85} - 190q^{89} - 82q^{93} + 576q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.866025 + 0.500000i 0.288675 + 0.166667i 0.637344 0.770579i \(-0.280033\pi\)
−0.348669 + 0.937246i \(0.613366\pi\)
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.100000 0.173205i 0.811684 0.584096i \(-0.198551\pi\)
−0.911684 + 0.410891i \(0.865218\pi\)
\(6\) 0 0
\(7\) 7.00000i 1.00000i
\(8\) 0 0
\(9\) −4.00000 6.92820i −0.444444 0.769800i
\(10\) 0 0
\(11\) −14.7224 8.50000i −1.33840 0.772727i −0.351832 0.936063i \(-0.614441\pi\)
−0.986571 + 0.163336i \(0.947775\pi\)
\(12\) 0 0
\(13\) 24.0000 1.84615 0.923077 0.384615i \(-0.125666\pi\)
0.923077 + 0.384615i \(0.125666\pi\)
\(14\) 0 0
\(15\) 1.00000i 0.0666667i
\(16\) 0 0
\(17\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i −0.880357 0.474312i \(-0.842697\pi\)
0.850945 + 0.525255i \(0.176030\pi\)
\(18\) 0 0
\(19\) 6.06218 3.50000i 0.319062 0.184211i −0.331912 0.943310i \(-0.607694\pi\)
0.650974 + 0.759100i \(0.274361\pi\)
\(20\) 0 0
\(21\) 3.50000 6.06218i 0.166667 0.288675i
\(22\) 0 0
\(23\) −6.06218 + 3.50000i −0.263573 + 0.152174i −0.625963 0.779852i \(-0.715294\pi\)
0.362390 + 0.932026i \(0.381961\pi\)
\(24\) 0 0
\(25\) 12.0000 20.7846i 0.480000 0.831384i
\(26\) 0 0
\(27\) 17.0000i 0.629630i
\(28\) 0 0
\(29\) 24.0000 0.827586 0.413793 0.910371i \(-0.364204\pi\)
0.413793 + 0.910371i \(0.364204\pi\)
\(30\) 0 0
\(31\) −35.5070 20.5000i −1.14539 0.661290i −0.197629 0.980277i \(-0.563324\pi\)
−0.947759 + 0.318987i \(0.896658\pi\)
\(32\) 0 0
\(33\) −8.50000 14.7224i −0.257576 0.446134i
\(34\) 0 0
\(35\) −6.06218 + 3.50000i −0.173205 + 0.100000i
\(36\) 0 0
\(37\) 24.5000 + 42.4352i 0.662162 + 1.14690i 0.980046 + 0.198769i \(0.0636943\pi\)
−0.317884 + 0.948130i \(0.602972\pi\)
\(38\) 0 0
\(39\) 20.7846 + 12.0000i 0.532939 + 0.307692i
\(40\) 0 0
\(41\) −48.0000 −1.17073 −0.585366 0.810769i \(-0.699049\pi\)
−0.585366 + 0.810769i \(0.699049\pi\)
\(42\) 0 0
\(43\) 24.0000i 0.558140i 0.960271 + 0.279070i \(0.0900261\pi\)
−0.960271 + 0.279070i \(0.909974\pi\)
\(44\) 0 0
\(45\) −4.00000 + 6.92820i −0.0888889 + 0.153960i
\(46\) 0 0
\(47\) 47.6314 27.5000i 1.01343 0.585106i 0.101239 0.994862i \(-0.467719\pi\)
0.912195 + 0.409756i \(0.134386\pi\)
\(48\) 0 0
\(49\) −49.0000 −1.00000
\(50\) 0 0
\(51\) −0.866025 + 0.500000i −0.0169809 + 0.00980392i
\(52\) 0 0
\(53\) 12.5000 21.6506i 0.235849 0.408503i −0.723670 0.690146i \(-0.757546\pi\)
0.959519 + 0.281644i \(0.0908796\pi\)
\(54\) 0 0
\(55\) 17.0000i 0.309091i
\(56\) 0 0
\(57\) 7.00000 0.122807
\(58\) 0 0
\(59\) 14.7224 + 8.50000i 0.249533 + 0.144068i 0.619550 0.784957i \(-0.287315\pi\)
−0.370018 + 0.929025i \(0.620648\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.00819672 + 0.0141971i 0.870095 0.492885i \(-0.164058\pi\)
−0.861898 + 0.507082i \(0.830724\pi\)
\(62\) 0 0
\(63\) −48.4974 + 28.0000i −0.769800 + 0.444444i
\(64\) 0 0
\(65\) −12.0000 20.7846i −0.184615 0.319763i
\(66\) 0 0
\(67\) 56.2917 + 32.5000i 0.840174 + 0.485075i 0.857323 0.514778i \(-0.172126\pi\)
−0.0171494 + 0.999853i \(0.505459\pi\)
\(68\) 0 0
\(69\) −7.00000 −0.101449
\(70\) 0 0
\(71\) 96.0000i 1.35211i 0.736850 + 0.676056i \(0.236312\pi\)
−0.736850 + 0.676056i \(0.763688\pi\)
\(72\) 0 0
\(73\) −47.5000 + 82.2724i −0.650685 + 1.12702i 0.332272 + 0.943184i \(0.392185\pi\)
−0.982957 + 0.183836i \(0.941149\pi\)
\(74\) 0 0
\(75\) 20.7846 12.0000i 0.277128 0.160000i
\(76\) 0 0
\(77\) −59.5000 + 103.057i −0.772727 + 1.33840i
\(78\) 0 0
\(79\) 35.5070 20.5000i 0.449456 0.259494i −0.258144 0.966106i \(-0.583111\pi\)
0.707601 + 0.706613i \(0.249778\pi\)
\(80\) 0 0
\(81\) −27.5000 + 47.6314i −0.339506 + 0.588042i
\(82\) 0 0
\(83\) 72.0000i 0.867470i 0.901041 + 0.433735i \(0.142805\pi\)
−0.901041 + 0.433735i \(0.857195\pi\)
\(84\) 0 0
\(85\) 1.00000 0.0117647
\(86\) 0 0
\(87\) 20.7846 + 12.0000i 0.238904 + 0.137931i
\(88\) 0 0
\(89\) −47.5000 82.2724i −0.533708 0.924409i −0.999225 0.0393701i \(-0.987465\pi\)
0.465517 0.885039i \(-0.345868\pi\)
\(90\) 0 0
\(91\) 168.000i 1.84615i
\(92\) 0 0
\(93\) −20.5000 35.5070i −0.220430 0.381796i
\(94\) 0 0
\(95\) −6.06218 3.50000i −0.0638124 0.0368421i
\(96\) 0 0
\(97\) 144.000 1.48454 0.742268 0.670103i \(-0.233750\pi\)
0.742268 + 0.670103i \(0.233750\pi\)
\(98\) 0 0
\(99\) 136.000i 1.37374i
\(100\) 0 0
\(101\) −36.5000 + 63.2199i −0.361386 + 0.625939i −0.988189 0.153239i \(-0.951030\pi\)
0.626803 + 0.779178i \(0.284363\pi\)
\(102\) 0 0
\(103\) 77.0763 44.5000i 0.748313 0.432039i −0.0767709 0.997049i \(-0.524461\pi\)
0.825084 + 0.565010i \(0.191128\pi\)
\(104\) 0 0
\(105\) −7.00000 −0.0666667
\(106\) 0 0
\(107\) −160.215 + 92.5000i −1.49733 + 0.864486i −0.999995 0.00307068i \(-0.999023\pi\)
−0.497338 + 0.867557i \(0.665689\pi\)
\(108\) 0 0
\(109\) 35.5000 61.4878i 0.325688 0.564108i −0.655963 0.754793i \(-0.727737\pi\)
0.981651 + 0.190684i \(0.0610707\pi\)
\(110\) 0 0
\(111\) 49.0000i 0.441441i
\(112\) 0 0
\(113\) 96.0000 0.849558 0.424779 0.905297i \(-0.360352\pi\)
0.424779 + 0.905297i \(0.360352\pi\)
\(114\) 0 0
\(115\) 6.06218 + 3.50000i 0.0527146 + 0.0304348i
\(116\) 0 0
\(117\) −96.0000 166.277i −0.820513 1.42117i
\(118\) 0 0
\(119\) 6.06218 + 3.50000i 0.0509427 + 0.0294118i
\(120\) 0 0
\(121\) 84.0000 + 145.492i 0.694215 + 1.20242i
\(122\) 0 0
\(123\) −41.5692 24.0000i −0.337961 0.195122i
\(124\) 0 0
\(125\) −49.0000 −0.392000
\(126\) 0 0
\(127\) 144.000i 1.13386i −0.823767 0.566929i \(-0.808131\pi\)
0.823767 0.566929i \(-0.191869\pi\)
\(128\) 0 0
\(129\) −12.0000 + 20.7846i −0.0930233 + 0.161121i
\(130\) 0 0
\(131\) 160.215 92.5000i 1.22301 0.706107i 0.257454 0.966291i \(-0.417116\pi\)
0.965559 + 0.260184i \(0.0837831\pi\)
\(132\) 0 0
\(133\) −24.5000 42.4352i −0.184211 0.319062i
\(134\) 0 0
\(135\) −14.7224 + 8.50000i −0.109055 + 0.0629630i
\(136\) 0 0
\(137\) 71.5000 123.842i 0.521898 0.903954i −0.477778 0.878481i \(-0.658558\pi\)
0.999676 0.0254728i \(-0.00810911\pi\)
\(138\) 0 0
\(139\) 216.000i 1.55396i −0.629527 0.776978i \(-0.716751\pi\)
0.629527 0.776978i \(-0.283249\pi\)
\(140\) 0 0
\(141\) 55.0000 0.390071
\(142\) 0 0
\(143\) −353.338 204.000i −2.47090 1.42657i
\(144\) 0 0
\(145\) −12.0000 20.7846i −0.0827586 0.143342i
\(146\) 0 0
\(147\) −42.4352 24.5000i −0.288675 0.166667i
\(148\) 0 0
\(149\) 23.5000 + 40.7032i 0.157718 + 0.273176i 0.934045 0.357154i \(-0.116253\pi\)
−0.776327 + 0.630330i \(0.782920\pi\)
\(150\) 0 0
\(151\) 172.339 + 99.5000i 1.14132 + 0.658940i 0.946757 0.321950i \(-0.104338\pi\)
0.194562 + 0.980890i \(0.437672\pi\)
\(152\) 0 0
\(153\) 8.00000 0.0522876
\(154\) 0 0
\(155\) 41.0000i 0.264516i
\(156\) 0 0
\(157\) 36.5000 63.2199i 0.232484 0.402674i −0.726054 0.687637i \(-0.758648\pi\)
0.958539 + 0.284963i \(0.0919813\pi\)
\(158\) 0 0
\(159\) 21.6506 12.5000i 0.136168 0.0786164i
\(160\) 0 0
\(161\) 24.5000 + 42.4352i 0.152174 + 0.263573i
\(162\) 0 0
\(163\) −47.6314 + 27.5000i −0.292217 + 0.168712i −0.638941 0.769255i \(-0.720627\pi\)
0.346724 + 0.937967i \(0.387294\pi\)
\(164\) 0 0
\(165\) −8.50000 + 14.7224i −0.0515152 + 0.0892269i
\(166\) 0 0
\(167\) 206.000i 1.23353i 0.787146 + 0.616766i \(0.211558\pi\)
−0.787146 + 0.616766i \(0.788442\pi\)
\(168\) 0 0
\(169\) 407.000 2.40828
\(170\) 0 0
\(171\) −48.4974 28.0000i −0.283611 0.163743i
\(172\) 0 0
\(173\) −119.500 206.980i −0.690751 1.19642i −0.971592 0.236662i \(-0.923947\pi\)
0.280841 0.959754i \(-0.409387\pi\)
\(174\) 0 0
\(175\) −145.492 84.0000i −0.831384 0.480000i
\(176\) 0 0
\(177\) 8.50000 + 14.7224i 0.0480226 + 0.0831776i
\(178\) 0 0
\(179\) −14.7224 8.50000i −0.0822482 0.0474860i 0.458312 0.888791i \(-0.348454\pi\)
−0.540560 + 0.841305i \(0.681788\pi\)
\(180\) 0 0
\(181\) 70.0000 0.386740 0.193370 0.981126i \(-0.438058\pi\)
0.193370 + 0.981126i \(0.438058\pi\)
\(182\) 0 0
\(183\) 1.00000i 0.00546448i
\(184\) 0 0
\(185\) 24.5000 42.4352i 0.132432 0.229380i
\(186\) 0 0
\(187\) 14.7224 8.50000i 0.0787296 0.0454545i
\(188\) 0 0
\(189\) −119.000 −0.629630
\(190\) 0 0
\(191\) 172.339 99.5000i 0.902299 0.520942i 0.0243534 0.999703i \(-0.492247\pi\)
0.877945 + 0.478761i \(0.158914\pi\)
\(192\) 0 0
\(193\) 23.5000 40.7032i 0.121762 0.210897i −0.798701 0.601728i \(-0.794479\pi\)
0.920462 + 0.390831i \(0.127812\pi\)
\(194\) 0 0
\(195\) 24.0000i 0.123077i
\(196\) 0 0
\(197\) 24.0000 0.121827 0.0609137 0.998143i \(-0.480599\pi\)
0.0609137 + 0.998143i \(0.480599\pi\)
\(198\) 0 0
\(199\) −118.645 68.5000i −0.596208 0.344221i 0.171340 0.985212i \(-0.445190\pi\)
−0.767549 + 0.640991i \(0.778524\pi\)
\(200\) 0 0
\(201\) 32.5000 + 56.2917i 0.161692 + 0.280058i
\(202\) 0 0
\(203\) 168.000i 0.827586i
\(204\) 0 0
\(205\) 24.0000 + 41.5692i 0.117073 + 0.202777i
\(206\) 0 0
\(207\) 48.4974 + 28.0000i 0.234287 + 0.135266i
\(208\) 0 0
\(209\) −119.000 −0.569378
\(210\) 0 0
\(211\) 264.000i 1.25118i 0.780150 + 0.625592i \(0.215143\pi\)
−0.780150 + 0.625592i \(0.784857\pi\)
\(212\) 0 0
\(213\) −48.0000 + 83.1384i −0.225352 + 0.390321i
\(214\) 0 0
\(215\) 20.7846 12.0000i 0.0966726 0.0558140i
\(216\) 0 0
\(217\) −143.500 + 248.549i −0.661290 + 1.14539i
\(218\) 0 0
\(219\) −82.2724 + 47.5000i −0.375673 + 0.216895i
\(220\) 0 0
\(221\) −12.0000 + 20.7846i −0.0542986 + 0.0940480i
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) −192.000 −0.853333
\(226\) 0 0
\(227\) 359.401 + 207.500i 1.58326 + 0.914097i 0.994379 + 0.105879i \(0.0337656\pi\)
0.588883 + 0.808218i \(0.299568\pi\)
\(228\) 0 0
\(229\) 71.5000 + 123.842i 0.312227 + 0.540793i 0.978844 0.204607i \(-0.0655917\pi\)
−0.666617 + 0.745400i \(0.732258\pi\)
\(230\) 0 0
\(231\) −103.057 + 59.5000i −0.446134 + 0.257576i
\(232\) 0 0
\(233\) −144.500 250.281i −0.620172 1.07417i −0.989453 0.144851i \(-0.953730\pi\)
0.369282 0.929317i \(-0.379604\pi\)
\(234\) 0 0
\(235\) −47.6314 27.5000i −0.202687 0.117021i
\(236\) 0 0
\(237\) 41.0000 0.172996
\(238\) 0 0
\(239\) 226.000i 0.945607i 0.881168 + 0.472803i \(0.156758\pi\)
−0.881168 + 0.472803i \(0.843242\pi\)
\(240\) 0 0
\(241\) −47.5000 + 82.2724i −0.197095 + 0.341379i −0.947585 0.319502i \(-0.896484\pi\)
0.750490 + 0.660882i \(0.229818\pi\)
\(242\) 0 0
\(243\) −180.133 + 104.000i −0.741289 + 0.427984i
\(244\) 0 0
\(245\) 24.5000 + 42.4352i 0.100000 + 0.173205i
\(246\) 0 0
\(247\) 145.492 84.0000i 0.589038 0.340081i
\(248\) 0 0
\(249\) −36.0000 + 62.3538i −0.144578 + 0.250417i
\(250\) 0 0
\(251\) 38.0000i 0.151394i −0.997131 0.0756972i \(-0.975882\pi\)
0.997131 0.0756972i \(-0.0241182\pi\)
\(252\) 0 0
\(253\) 119.000 0.470356
\(254\) 0 0
\(255\) 0.866025 + 0.500000i 0.00339618 + 0.00196078i
\(256\) 0 0
\(257\) −96.5000 167.143i −0.375486 0.650361i 0.614913 0.788595i \(-0.289191\pi\)
−0.990400 + 0.138233i \(0.955858\pi\)
\(258\) 0 0
\(259\) 297.047 171.500i 1.14690 0.662162i
\(260\) 0 0
\(261\) −96.0000 166.277i −0.367816 0.637076i
\(262\) 0 0
\(263\) 201.784 + 116.500i 0.767239 + 0.442966i 0.831889 0.554942i \(-0.187260\pi\)
−0.0646496 + 0.997908i \(0.520593\pi\)
\(264\) 0 0
\(265\) −25.0000 −0.0943396
\(266\) 0 0
\(267\) 95.0000i 0.355805i
\(268\) 0 0
\(269\) −227.500 + 394.042i −0.845725 + 1.46484i 0.0392653 + 0.999229i \(0.487498\pi\)
−0.884990 + 0.465610i \(0.845835\pi\)
\(270\) 0 0
\(271\) 368.061 212.500i 1.35816 0.784133i 0.368782 0.929516i \(-0.379775\pi\)
0.989375 + 0.145383i \(0.0464414\pi\)
\(272\) 0 0
\(273\) 84.0000 145.492i 0.307692 0.532939i
\(274\) 0 0
\(275\) −353.338 + 204.000i −1.28487 + 0.741818i
\(276\) 0 0
\(277\) −83.5000 + 144.626i −0.301444 + 0.522116i −0.976463 0.215684i \(-0.930802\pi\)
0.675019 + 0.737800i \(0.264135\pi\)
\(278\) 0 0
\(279\) 328.000i 1.17563i
\(280\) 0 0
\(281\) −432.000 −1.53737 −0.768683 0.639630i \(-0.779088\pi\)
−0.768683 + 0.639630i \(0.779088\pi\)
\(282\) 0 0
\(283\) 193.124 + 111.500i 0.682416 + 0.393993i 0.800765 0.598979i \(-0.204427\pi\)
−0.118349 + 0.992972i \(0.537760\pi\)
\(284\) 0 0
\(285\) −3.50000 6.06218i −0.0122807 0.0212708i
\(286\) 0 0
\(287\) 336.000i 1.17073i
\(288\) 0 0
\(289\) 144.000 + 249.415i 0.498270 + 0.863029i
\(290\) 0 0
\(291\) 124.708 + 72.0000i 0.428549 + 0.247423i
\(292\) 0 0
\(293\) 26.0000 0.0887372 0.0443686 0.999015i \(-0.485872\pi\)
0.0443686 + 0.999015i \(0.485872\pi\)
\(294\) 0 0
\(295\) 17.0000i 0.0576271i
\(296\) 0 0
\(297\) −144.500 + 250.281i −0.486532 + 0.842698i
\(298\) 0 0
\(299\) −145.492 + 84.0000i −0.486596 + 0.280936i
\(300\) 0 0
\(301\) 168.000 0.558140
\(302\) 0 0
\(303\) −63.2199 + 36.5000i −0.208646 + 0.120462i
\(304\) 0 0
\(305\) 0.500000 0.866025i 0.00163934 0.00283943i
\(306\) 0 0
\(307\) 264.000i 0.859935i −0.902844 0.429967i \(-0.858525\pi\)
0.902844 0.429967i \(-0.141475\pi\)
\(308\) 0 0
\(309\) 89.0000 0.288026
\(310\) 0 0
\(311\) −297.047 171.500i −0.955134 0.551447i −0.0604621 0.998170i \(-0.519257\pi\)
−0.894672 + 0.446724i \(0.852591\pi\)
\(312\) 0 0
\(313\) −167.500 290.119i −0.535144 0.926896i −0.999156 0.0410676i \(-0.986924\pi\)
0.464013 0.885829i \(-0.346409\pi\)
\(314\) 0 0
\(315\) 48.4974 + 28.0000i 0.153960 + 0.0888889i
\(316\) 0 0
\(317\) 264.500 + 458.127i 0.834385 + 1.44520i 0.894530 + 0.447007i \(0.147510\pi\)
−0.0601454 + 0.998190i \(0.519156\pi\)
\(318\) 0 0
\(319\) −353.338 204.000i −1.10764 0.639498i
\(320\) 0 0
\(321\) −185.000 −0.576324
\(322\) 0 0
\(323\) 7.00000i 0.0216718i
\(324\) 0 0
\(325\) 288.000 498.831i 0.886154 1.53486i
\(326\) 0 0
\(327\) 61.4878 35.5000i 0.188036 0.108563i
\(328\) 0 0
\(329\) −192.500 333.420i −0.585106 1.01343i
\(330\) 0 0
\(331\) −47.6314 + 27.5000i −0.143902 + 0.0830816i −0.570222 0.821491i \(-0.693143\pi\)
0.426321 + 0.904572i \(0.359810\pi\)
\(332\) 0 0
\(333\) 196.000 339.482i 0.588589 1.01947i
\(334\) 0 0
\(335\) 65.0000i 0.194030i
\(336\) 0 0
\(337\) −240.000 −0.712166 −0.356083 0.934454i \(-0.615888\pi\)
−0.356083 + 0.934454i \(0.615888\pi\)
\(338\) 0 0
\(339\) 83.1384 + 48.0000i 0.245246 + 0.141593i
\(340\) 0 0
\(341\) 348.500 + 603.620i 1.02199 + 1.77015i
\(342\) 0 0
\(343\) 343.000i 1.00000i
\(344\) 0 0
\(345\) 3.50000 + 6.06218i 0.0101449 + 0.0175715i
\(346\) 0 0
\(347\) −26.8468 15.5000i −0.0773683 0.0446686i 0.460817 0.887495i \(-0.347557\pi\)
−0.538185 + 0.842827i \(0.680890\pi\)
\(348\) 0 0
\(349\) −120.000 −0.343840 −0.171920 0.985111i \(-0.554997\pi\)
−0.171920 + 0.985111i \(0.554997\pi\)
\(350\) 0 0
\(351\) 408.000i 1.16239i
\(352\) 0 0
\(353\) 263.500 456.395i 0.746459 1.29290i −0.203051 0.979168i \(-0.565086\pi\)
0.949510 0.313737i \(-0.101581\pi\)
\(354\) 0 0
\(355\) 83.1384 48.0000i 0.234193 0.135211i
\(356\) 0 0
\(357\) 3.50000 + 6.06218i 0.00980392 + 0.0169809i
\(358\) 0 0
\(359\) 463.324 267.500i 1.29059 0.745125i 0.311835 0.950136i \(-0.399056\pi\)
0.978760 + 0.205011i \(0.0657230\pi\)
\(360\) 0 0
\(361\) −156.000 + 270.200i −0.432133 + 0.748476i
\(362\) 0 0
\(363\) 168.000i 0.462810i
\(364\) 0 0
\(365\) 95.0000 0.260274
\(366\) 0 0
\(367\) 77.0763 + 44.5000i 0.210017 + 0.121253i 0.601319 0.799009i \(-0.294642\pi\)
−0.391302 + 0.920262i \(0.627975\pi\)
\(368\) 0 0
\(369\) 192.000 + 332.554i 0.520325 + 0.901230i
\(370\) 0 0
\(371\) −151.554 87.5000i −0.408503 0.235849i
\(372\) 0 0
\(373\) −167.500 290.119i −0.449062 0.777798i 0.549264 0.835649i \(-0.314908\pi\)
−0.998325 + 0.0578516i \(0.981575\pi\)
\(374\) 0 0
\(375\) −42.4352 24.5000i −0.113161 0.0653333i
\(376\) 0 0
\(377\) 576.000 1.52785
\(378\) 0 0
\(379\) 38.0000i 0.100264i 0.998743 + 0.0501319i \(0.0159642\pi\)
−0.998743 + 0.0501319i \(0.984036\pi\)
\(380\) 0 0
\(381\) 72.0000 124.708i 0.188976 0.327317i
\(382\) 0 0
\(383\) −575.907 + 332.500i −1.50367 + 0.868146i −0.503682 + 0.863889i \(0.668022\pi\)
−0.999991 + 0.00425732i \(0.998645\pi\)
\(384\) 0 0
\(385\) 119.000 0.309091
\(386\) 0 0
\(387\) 166.277 96.0000i 0.429656 0.248062i
\(388\) 0 0
\(389\) −36.5000 + 63.2199i −0.0938303 + 0.162519i −0.909120 0.416535i \(-0.863244\pi\)
0.815290 + 0.579054i \(0.196578\pi\)
\(390\) 0 0
\(391\) 7.00000i 0.0179028i
\(392\) 0 0
\(393\) 185.000 0.470738
\(394\) 0 0
\(395\) −35.5070 20.5000i −0.0898912 0.0518987i
\(396\) 0 0
\(397\) −0.500000 0.866025i −0.00125945 0.00218142i 0.865395 0.501090i \(-0.167068\pi\)
−0.866654 + 0.498909i \(0.833734\pi\)
\(398\) 0 0
\(399\) 49.0000i 0.122807i
\(400\) 0 0
\(401\) −168.500 291.851i −0.420200 0.727807i 0.575759 0.817619i \(-0.304707\pi\)
−0.995959 + 0.0898124i \(0.971373\pi\)
\(402\) 0 0
\(403\) −852.169 492.000i −2.11456 1.22084i
\(404\) 0 0
\(405\) 55.0000 0.135802
\(406\) 0 0
\(407\) 833.000i 2.04668i
\(408\) 0 0
\(409\) 239.500 414.826i 0.585575 1.01424i −0.409229 0.912432i \(-0.634202\pi\)
0.994804 0.101813i \(-0.0324644\pi\)
\(410\) 0 0
\(411\) 123.842 71.5000i 0.301318 0.173966i
\(412\) 0 0
\(413\) 59.5000 103.057i 0.144068 0.249533i
\(414\) 0 0
\(415\) 62.3538 36.0000i 0.150250 0.0867470i
\(416\) 0 0
\(417\) 108.000 187.061i 0.258993 0.448589i
\(418\) 0 0
\(419\) 552.000i 1.31742i −0.752396 0.658711i \(-0.771102\pi\)
0.752396 0.658711i \(-0.228898\pi\)
\(420\) 0 0
\(421\) −216.000 −0.513064 −0.256532 0.966536i \(-0.582580\pi\)
−0.256532 + 0.966536i \(0.582580\pi\)
\(422\) 0 0
\(423\) −381.051 220.000i −0.900830 0.520095i
\(424\) 0 0
\(425\) 12.0000 + 20.7846i 0.0282353 + 0.0489050i
\(426\) 0 0
\(427\) 6.06218 3.50000i 0.0141971 0.00819672i
\(428\) 0 0
\(429\) −204.000 353.338i −0.475524 0.823633i
\(430\) 0 0
\(431\) 380.185 + 219.500i 0.882100 + 0.509281i 0.871350 0.490661i \(-0.163245\pi\)
0.0107498 + 0.999942i \(0.496578\pi\)
\(432\) 0 0
\(433\) −288.000 −0.665127 −0.332564 0.943081i \(-0.607914\pi\)
−0.332564 + 0.943081i \(0.607914\pi\)
\(434\) 0 0
\(435\) 24.0000i 0.0551724i
\(436\) 0 0
\(437\) −24.5000 + 42.4352i −0.0560641 + 0.0971058i
\(438\) 0 0
\(439\) −534.338 + 308.500i −1.21717 + 0.702733i −0.964312 0.264770i \(-0.914704\pi\)
−0.252858 + 0.967503i \(0.581371\pi\)
\(440\) 0 0
\(441\) 196.000 + 339.482i 0.444444 + 0.769800i
\(442\) 0 0
\(443\) 213.908 123.500i 0.482863 0.278781i −0.238746 0.971082i \(-0.576736\pi\)
0.721609 + 0.692301i \(0.243403\pi\)
\(444\) 0 0
\(445\) −47.5000 + 82.2724i −0.106742 + 0.184882i
\(446\) 0 0
\(447\) 47.0000i 0.105145i
\(448\) 0 0
\(449\) −288.000 −0.641425 −0.320713 0.947177i \(-0.603922\pi\)
−0.320713 + 0.947177i \(0.603922\pi\)
\(450\) 0 0
\(451\) 706.677 + 408.000i 1.56691 + 0.904656i
\(452\) 0 0
\(453\) 99.5000 + 172.339i 0.219647 + 0.380439i
\(454\) 0 0
\(455\) −145.492 + 84.0000i −0.319763 + 0.184615i
\(456\) 0 0
\(457\) 48.5000 + 84.0045i 0.106127 + 0.183817i 0.914198 0.405268i \(-0.132822\pi\)
−0.808071 + 0.589085i \(0.799488\pi\)
\(458\) 0 0
\(459\) 14.7224 + 8.50000i 0.0320750 + 0.0185185i
\(460\) 0 0
\(461\) 312.000 0.676790 0.338395 0.941004i \(-0.390116\pi\)
0.338395 + 0.941004i \(0.390116\pi\)
\(462\) 0 0
\(463\) 192.000i 0.414687i 0.978268 + 0.207343i \(0.0664817\pi\)
−0.978268 + 0.207343i \(0.933518\pi\)
\(464\) 0 0
\(465\) −20.5000 + 35.5070i −0.0440860 + 0.0763592i
\(466\) 0 0
\(467\) −255.477 + 147.500i −0.547061 + 0.315846i −0.747936 0.663771i \(-0.768955\pi\)
0.200875 + 0.979617i \(0.435622\pi\)
\(468\) 0 0
\(469\) 227.500 394.042i 0.485075 0.840174i
\(470\) 0 0
\(471\) 63.2199 36.5000i 0.134225 0.0774947i
\(472\) 0 0
\(473\) 204.000 353.338i 0.431290 0.747016i
\(474\) 0 0
\(475\) 168.000i 0.353684i
\(476\) 0 0
\(477\) −200.000 −0.419287
\(478\) 0 0
\(479\) 534.338 + 308.500i 1.11553 + 0.644050i 0.940255 0.340470i \(-0.110586\pi\)
0.175272 + 0.984520i \(0.443919\pi\)
\(480\) 0 0
\(481\) 588.000 + 1018.45i 1.22245 + 2.11735i
\(482\) 0 0
\(483\) 49.0000i 0.101449i
\(484\) 0 0
\(485\) −72.0000 124.708i −0.148454 0.257129i
\(486\) 0 0
\(487\) −213.908 123.500i −0.439237 0.253593i 0.264037 0.964513i \(-0.414946\pi\)
−0.703274 + 0.710919i \(0.748279\pi\)
\(488\) 0 0
\(489\) −55.0000 −0.112474
\(490\) 0 0
\(491\) 134.000i 0.272912i 0.990646 + 0.136456i \(0.0435713\pi\)
−0.990646 + 0.136456i \(0.956429\pi\)
\(492\) 0 0
\(493\) −12.0000 + 20.7846i −0.0243408 + 0.0421595i
\(494\) 0 0
\(495\) 117.779 68.0000i 0.237938 0.137374i
\(496\) 0 0
\(497\) 672.000 1.35211
\(498\) 0 0
\(499\) −629.600 + 363.500i −1.26172 + 0.728457i −0.973408 0.229078i \(-0.926429\pi\)
−0.288316 + 0.957535i \(0.593095\pi\)
\(500\) 0 0
\(501\) −103.000 + 178.401i −0.205589 + 0.356090i
\(502\) 0 0
\(503\) 432.000i 0.858847i −0.903103 0.429423i \(-0.858717\pi\)
0.903103 0.429423i \(-0.141283\pi\)
\(504\) 0 0
\(505\) 73.0000 0.144554
\(506\) 0 0
\(507\) 352.472 + 203.500i 0.695212 + 0.401381i
\(508\) 0 0
\(509\) −216.500 374.989i −0.425344 0.736717i 0.571109 0.820874i \(-0.306513\pi\)
−0.996452 + 0.0841574i \(0.973180\pi\)
\(510\) 0 0
\(511\) 575.907 + 332.500i 1.12702 + 0.650685i
\(512\) 0 0
\(513\) −59.5000 103.057i −0.115984 0.200891i
\(514\) 0 0
\(515\) −77.0763 44.5000i −0.149663 0.0864078i
\(516\) 0 0
\(517\) −935.000 −1.80851
\(518\) 0 0
\(519\) 239.000i 0.460501i
\(520\) 0 0
\(521\) −239.500 + 414.826i −0.459693 + 0.796211i −0.998945 0.0459332i \(-0.985374\pi\)
0.539252 + 0.842145i \(0.318707\pi\)
\(522\) 0 0
\(523\) −783.753 + 452.500i −1.49857 + 0.865201i −0.999999 0.00164693i \(-0.999476\pi\)
−0.498573 + 0.866848i \(0.666142\pi\)
\(524\) 0 0
\(525\) −84.0000 145.492i −0.160000 0.277128i
\(526\) 0 0
\(527\) 35.5070 20.5000i 0.0673758 0.0388994i
\(528\) 0 0
\(529\) −240.000 + 415.692i −0.453686 + 0.785808i
\(530\) 0 0
\(531\) 136.000i 0.256121i
\(532\) 0 0
\(533\) −1152.00 −2.16135
\(534\) 0 0
\(535\) 160.215 + 92.5000i 0.299467 + 0.172897i
\(536\) 0 0
\(537\) −8.50000 14.7224i −0.0158287 0.0274161i
\(538\) 0 0
\(539\) 721.399 + 416.500i 1.33840 + 0.772727i
\(540\) 0 0
\(541\) 95.5000 + 165.411i 0.176525 + 0.305750i 0.940688 0.339273i \(-0.110181\pi\)
−0.764163 + 0.645023i \(0.776848\pi\)
\(542\) 0 0
\(543\) 60.6218 + 35.0000i 0.111642 + 0.0644567i
\(544\) 0 0
\(545\) −71.0000 −0.130275
\(546\) 0 0
\(547\) 374.000i 0.683729i −0.939749 0.341865i \(-0.888942\pi\)
0.939749 0.341865i \(-0.111058\pi\)
\(548\) 0 0
\(549\) 4.00000 6.92820i 0.00728597 0.0126197i
\(550\) 0 0
\(551\) 145.492 84.0000i 0.264051 0.152450i
\(552\) 0 0
\(553\) −143.500 248.549i −0.259494 0.449456i
\(554\) 0 0
\(555\) 42.4352 24.5000i 0.0764599 0.0441441i
\(556\) 0 0
\(557\) −468.500 + 811.466i −0.841113 + 1.45685i 0.0478413 + 0.998855i \(0.484766\pi\)
−0.888954 + 0.457996i \(0.848568\pi\)
\(558\) 0 0
\(559\) 576.000i 1.03041i
\(560\) 0 0
\(561\) 17.0000 0.0303030
\(562\) 0 0
\(563\) −691.954 399.500i −1.22905 0.709591i −0.262218 0.965009i \(-0.584454\pi\)
−0.966831 + 0.255417i \(0.917787\pi\)
\(564\) 0 0
\(565\) −48.0000 83.1384i −0.0849558 0.147148i
\(566\) 0 0
\(567\) 333.420 + 192.500i 0.588042 + 0.339506i
\(568\) 0 0
\(569\) 264.500 + 458.127i 0.464851 + 0.805145i 0.999195 0.0401221i \(-0.0127747\pi\)
−0.534344 + 0.845267i \(0.679441\pi\)
\(570\) 0 0
\(571\) 899.800 + 519.500i 1.57583 + 0.909807i 0.995432 + 0.0954765i \(0.0304375\pi\)
0.580401 + 0.814331i \(0.302896\pi\)
\(572\) 0 0
\(573\) 199.000 0.347295
\(574\) 0 0
\(575\) 168.000i 0.292174i
\(576\) 0 0
\(577\) 264.500 458.127i 0.458406 0.793982i −0.540471 0.841362i \(-0.681754\pi\)
0.998877 + 0.0473807i \(0.0150874\pi\)
\(578\) 0 0
\(579\) 40.7032 23.5000i 0.0702991 0.0405872i
\(580\) 0 0
\(581\) 504.000 0.867470
\(582\) 0 0
\(583\) −368.061 + 212.500i −0.631322 + 0.364494i
\(584\) 0 0
\(585\) −96.0000 + 166.277i −0.164103 + 0.284234i
\(586\) 0 0
\(587\) 840.000i 1.43101i 0.698610 + 0.715503i \(0.253802\pi\)
−0.698610 + 0.715503i \(0.746198\pi\)
\(588\) 0 0
\(589\) −287.000 −0.487267
\(590\) 0 0
\(591\) 20.7846 + 12.0000i 0.0351685 + 0.0203046i
\(592\) 0 0
\(593\) 191.500 + 331.688i 0.322934 + 0.559338i 0.981092 0.193541i \(-0.0619974\pi\)
−0.658158 + 0.752880i \(0.728664\pi\)
\(594\) 0 0
\(595\) 7.00000i 0.0117647i
\(596\) 0 0
\(597\) −68.5000 118.645i −0.114740 0.198736i
\(598\) 0 0
\(599\) −297.047 171.500i −0.495904 0.286311i 0.231116 0.972926i \(-0.425762\pi\)
−0.727021 + 0.686616i \(0.759096\pi\)
\(600\) 0 0
\(601\) −624.000 −1.03827 −0.519135 0.854692i \(-0.673746\pi\)
−0.519135 + 0.854692i \(0.673746\pi\)
\(602\) 0 0
\(603\) 520.000i 0.862355i
\(604\) 0 0
\(605\) 84.0000 145.492i 0.138843 0.240483i
\(606\) 0 0
\(607\) −118.645 + 68.5000i −0.195462 + 0.112850i −0.594537 0.804068i \(-0.702665\pi\)
0.399075 + 0.916918i \(0.369331\pi\)
\(608\) 0 0
\(609\) 84.0000 145.492i 0.137931 0.238904i
\(610\) 0 0
\(611\) 1143.15 660.000i 1.87096 1.08020i
\(612\) 0 0
\(613\) 35.5000 61.4878i 0.0579119 0.100306i −0.835616 0.549314i \(-0.814889\pi\)
0.893528 + 0.449008i \(0.148222\pi\)
\(614\) 0 0
\(615\) 48.0000i 0.0780488i
\(616\) 0 0
\(617\) 384.000 0.622366 0.311183 0.950350i \(-0.399275\pi\)
0.311183 + 0.950350i \(0.399275\pi\)
\(618\) 0 0
\(619\) 513.553 + 296.500i 0.829650 + 0.478998i 0.853733 0.520712i \(-0.174333\pi\)
−0.0240831 + 0.999710i \(0.507667\pi\)
\(620\) 0 0
\(621\) 59.5000 + 103.057i 0.0958132 + 0.165953i
\(622\) 0 0
\(623\) −575.907 + 332.500i −0.924409 + 0.533708i
\(624\) 0 0
\(625\) −275.500 477.180i −0.440800 0.763488i
\(626\) 0 0
\(627\) −103.057 59.5000i −0.164365 0.0948963i
\(628\) 0 0
\(629\) −49.0000 −0.0779014
\(630\) 0 0
\(631\) 384.000i 0.608558i 0.952583 + 0.304279i \(0.0984155\pi\)
−0.952583 + 0.304279i \(0.901585\pi\)
\(632\) 0 0
\(633\) −132.000 + 228.631i −0.208531 + 0.361186i
\(634\) 0 0
\(635\) −124.708 + 72.0000i −0.196390 + 0.113386i
\(636\) 0 0
\(637\) −1176.00 −1.84615
\(638\) 0 0
\(639\) 665.108 384.000i 1.04086 0.600939i
\(640\) 0 0
\(641\) −383.500 + 664.241i −0.598284 + 1.03626i 0.394790 + 0.918771i \(0.370817\pi\)
−0.993074 + 0.117487i \(0.962516\pi\)
\(642\) 0 0
\(643\) 456.000i 0.709176i 0.935023 + 0.354588i \(0.115379\pi\)
−0.935023 + 0.354588i \(0.884621\pi\)
\(644\) 0 0
\(645\) 24.0000 0.0372093
\(646\) 0 0
\(647\) 77.0763 + 44.5000i 0.119129 + 0.0687790i 0.558380 0.829585i \(-0.311423\pi\)
−0.439252 + 0.898364i \(0.644756\pi\)
\(648\) 0 0
\(649\) −144.500 250.281i −0.222650 0.385642i
\(650\) 0 0
\(651\) −248.549 + 143.500i −0.381796 + 0.220430i
\(652\) 0 0
\(653\) −263.500 456.395i −0.403522 0.698921i 0.590626 0.806945i \(-0.298881\pi\)
−0.994148 + 0.108024i \(0.965548\pi\)
\(654\) 0 0
\(655\) −160.215 92.5000i −0.244603 0.141221i
\(656\) 0 0
\(657\) 760.000 1.15677
\(658\) 0 0
\(659\) 936.000i 1.42033i −0.704033 0.710167i \(-0.748619\pi\)
0.704033 0.710167i \(-0.251381\pi\)
\(660\) 0 0
\(661\) 372.500 645.189i 0.563540 0.976080i −0.433644 0.901084i \(-0.642772\pi\)
0.997184 0.0749957i \(-0.0238943\pi\)
\(662\) 0 0
\(663\) −20.7846 + 12.0000i −0.0313493 + 0.0180995i
\(664\) 0 0
\(665\) −24.5000 + 42.4352i −0.0368421 + 0.0638124i
\(666\) 0 0
\(667\) −145.492 + 84.0000i −0.218129 + 0.125937i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 17.0000i 0.0253353i
\(672\) 0 0
\(673\) −720.000 −1.06984 −0.534918 0.844904i \(-0.679658\pi\)
−0.534918 + 0.844904i \(0.679658\pi\)
\(674\) 0 0
\(675\) −353.338 204.000i −0.523464 0.302222i
\(676\) 0 0
\(677\) 575.500 + 996.795i 0.850074 + 1.47237i 0.881141 + 0.472854i \(0.156776\pi\)
−0.0310670 + 0.999517i \(0.509891\pi\)
\(678\) 0 0
\(679\) 1008.00i 1.48454i
\(680\) 0 0
\(681\) 207.500 + 359.401i 0.304699 + 0.527754i
\(682\) 0 0
\(683\) −638.261 368.500i −0.934496 0.539531i −0.0462653 0.998929i \(-0.514732\pi\)
−0.888231 + 0.459398i \(0.848065\pi\)
\(684\) 0 0
\(685\) −143.000 −0.208759
\(686\) 0 0
\(687\) 143.000i 0.208151i
\(688\) 0 0
\(689\) 300.000 519.615i 0.435414 0.754159i
\(690\) 0 0
\(691\) −879.016 + 507.500i −1.27209 + 0.734443i −0.975381 0.220525i \(-0.929223\pi\)
−0.296711 + 0.954967i \(0.595890\pi\)
\(692\) 0 0
\(693\) 952.000 1.37374
\(694\) 0 0
\(695\) −187.061 + 108.000i −0.269153 + 0.155396i
\(696\) 0 0
\(697\) 24.0000 41.5692i 0.0344333 0.0596402i
\(698\) 0 0
\(699\) 289.000i 0.413448i
\(700\) 0 0
\(701\) 1226.00 1.74893 0.874465 0.485089i \(-0.161213\pi\)
0.874465 + 0.485089i \(0.161213\pi\)
\(702\) 0 0
\(703\) 297.047 + 171.500i 0.422542 + 0.243954i
\(704\) 0 0
\(705\) −27.5000 47.6314i −0.0390071 0.0675623i
\(706\) 0 0
\(707\) 442.539 + 255.500i 0.625939 + 0.361386i
\(708\) 0 0
\(709\) 312.500 + 541.266i 0.440762 + 0.763422i 0.997746 0.0671013i \(-0.0213751\pi\)
−0.556985 + 0.830523i \(0.688042\pi\)
\(710\) 0 0
\(711\) −284.056 164.000i −0.399517 0.230661i
\(712\) 0 0
\(713\) 287.000 0.402525
\(714\) 0 0
\(715\) 408.000i 0.570629i
\(716\) 0 0
\(717\) −113.000 + 195.722i −0.157601 + 0.272973i
\(718\) 0 0
\(719\) 118.645 68.5000i 0.165015 0.0952712i −0.415218 0.909722i \(-0.636295\pi\)
0.580233 + 0.814451i \(0.302962\pi\)
\(720\) 0 0
\(721\) −311.500 539.534i −0.432039 0.748313i
\(722\) 0 0
\(723\) −82.2724 + 47.5000i −0.113793 + 0.0656985i
\(724\) 0 0
\(725\) 288.000 498.831i 0.397241 0.688042i
\(726\) 0 0
\(727\) 960.000i 1.32050i −0.751048 0.660248i \(-0.770451\pi\)
0.751048 0.660248i \(-0.229549\pi\)
\(728\) 0 0
\(729\) 287.000 0.393690
\(730\) 0 0
\(731\) −20.7846 12.0000i −0.0284331 0.0164159i
\(732\) 0 0
\(733\) −239.500 414.826i −0.326739 0.565929i 0.655123 0.755522i \(-0.272617\pi\)
−0.981863 + 0.189593i \(0.939283\pi\)
\(734\) 0 0
\(735\) 49.0000i 0.0666667i
\(736\) 0 0
\(737\) −552.500 956.958i −0.749661 1.29845i
\(738\) 0 0
\(739\) 442.539 + 255.500i 0.598835 + 0.345737i 0.768583 0.639750i \(-0.220962\pi\)
−0.169748 + 0.985487i \(0.554295\pi\)
\(740\) 0 0
\(741\) 168.000 0.226721
\(742\) 0 0
\(743\) 528.000i 0.710633i −0.934746 0.355316i \(-0.884373\pi\)
0.934746 0.355316i \(-0.115627\pi\)
\(744\) 0 0
\(745\) 23.5000 40.7032i 0.0315436 0.0546352i
\(746\) 0 0
\(747\) 498.831 288.000i 0.667779 0.385542i
\(748\) 0 0
\(749\) 647.500 + 1121.50i 0.864486 + 1.49733i
\(750\) 0 0
\(751\) −700.615 + 404.500i −0.932909 + 0.538615i −0.887730 0.460364i \(-0.847719\pi\)
−0.0451785 + 0.998979i \(0.514386\pi\)
\(752\) 0 0
\(753\) 19.0000 32.9090i 0.0252324 0.0437038i
\(754\) 0 0
\(755\) 199.000i 0.263576i
\(756\) 0 0
\(757\) −120.000 −0.158520 −0.0792602 0.996854i \(-0.525256\pi\)
−0.0792602 + 0.996854i \(0.525256\pi\)
\(758\) 0 0
\(759\) 103.057 + 59.5000i 0.135780 + 0.0783926i
\(760\) 0 0
\(761\) −384.500 665.974i −0.505256 0.875129i −0.999982 0.00608006i \(-0.998065\pi\)
0.494725 0.869049i \(-0.335269\pi\)
\(762\) 0 0
\(763\) −430.415 248.500i −0.564108 0.325688i
\(764\) 0 0
\(765\) −4.00000 6.92820i −0.00522876 0.00905647i
\(766\) 0 0
\(767\) 353.338 + 204.000i 0.460676 + 0.265971i
\(768\) 0 0
\(769\) −144.000 −0.187256 −0.0936281 0.995607i \(-0.529846\pi\)
−0.0936281 + 0.995607i \(0.529846\pi\)
\(770\) 0 0
\(771\) 193.000i 0.250324i
\(772\) 0 0
\(773\) 203.500 352.472i 0.263260 0.455980i −0.703846 0.710352i \(-0.748536\pi\)
0.967106 + 0.254373i \(0.0818690\pi\)
\(774\) 0 0
\(775\) −852.169 + 492.000i −1.09957 + 0.634839i
\(776\) 0 0
\(777\) 343.000 0.441441
\(778\) 0 0
\(779\) −290.985 + 168.000i −0.373536 + 0.215661i
\(780\) 0 0
\(781\) 816.000 1413.35i 1.04481 1.80967i
\(782\) 0 0
\(783\) 408.000i 0.521073i
\(784\) 0 0
\(785\) −73.0000 −0.0929936
\(786\) 0 0
\(787\) −982.939 567.500i −1.24897 0.721093i −0.278065 0.960562i \(-0.589693\pi\)
−0.970904 + 0.239469i \(0.923027\pi\)
\(788\) 0 0
\(789\) 116.500 + 201.784i 0.147655 + 0.255746i
\(790\) 0 0
\(791\) 672.000i 0.849558i
\(792\) 0 0
\(793\) 12.0000 + 20.7846i 0.0151324 + 0.0262101i
\(794\) 0 0
\(795\) −21.6506 12.5000i −0.0272335 0.0157233i
\(796\) 0 0
\(797\) 312.000 0.391468 0.195734 0.980657i \(-0.437291\pi\)
0.195734 + 0.980657i \(0.437291\pi\)
\(798\) 0 0
\(799\) 55.0000i 0.0688360i
\(800\) 0 0
\(801\) −380.000 + 658.179i −0.474407 + 0.821697i
\(802\) 0 0
\(803\)