Properties

Label 224.3.v.a.13.1
Level 224
Weight 3
Character 224.13
Analytic conductor 6.104
Analytic rank 0
Dimension 8
CM discriminant -7
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.v (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{8})\)
Coefficient field: 8.0.157351936.1
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{8}]$

Embedding invariants

Embedding label 13.1
Root \(-1.28897 + 0.581861i\) of \(x^{8} + x^{4} + 16\)
Character \(\chi\) \(=\) 224.13
Dual form 224.3.v.a.69.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.99607 + 0.125246i) q^{2} +(3.96863 - 0.500000i) q^{4} +(4.94975 - 4.94975i) q^{7} +(-7.85905 + 1.49509i) q^{8} +(-6.36396 - 6.36396i) q^{9} +O(q^{10})\) \(q+(-1.99607 + 0.125246i) q^{2} +(3.96863 - 0.500000i) q^{4} +(4.94975 - 4.94975i) q^{7} +(-7.85905 + 1.49509i) q^{8} +(-6.36396 - 6.36396i) q^{9} +(0.978370 + 2.36199i) q^{11} +(-9.26013 + 10.5000i) q^{14} +(15.5000 - 3.96863i) q^{16} +(13.5000 + 11.9059i) q^{18} +(-2.24873 - 4.59218i) q^{22} +(-30.1660 - 30.1660i) q^{23} +(17.6777 - 17.6777i) q^{25} +(17.1688 - 22.1186i) q^{28} +(15.9922 - 38.6086i) q^{29} +(-30.4421 + 9.86299i) q^{32} +(-28.4382 - 22.0742i) q^{36} +(40.7639 - 16.8850i) q^{37} +(-30.9438 - 74.7051i) q^{43} +(5.06378 + 8.88469i) q^{44} +(63.9918 + 56.4354i) q^{46} -49.0000i q^{49} +(-33.0719 + 37.5000i) q^{50} +(38.2953 + 92.4529i) q^{53} +(-31.5000 + 46.3006i) q^{56} +(-27.0860 + 79.0685i) q^{58} -63.0000 q^{63} +(59.5294 - 23.5000i) q^{64} +(5.16924 - 12.4797i) q^{67} +(-59.8665 + 59.8665i) q^{71} +(59.5294 + 40.5000i) q^{72} +(-79.2531 + 38.8092i) q^{74} +(16.5340 + 6.84859i) q^{77} +156.268i q^{79} +81.0000i q^{81} +(71.1227 + 145.241i) q^{86} +(-11.2205 - 17.1003i) q^{88} +(-134.801 - 104.635i) q^{92} +(6.13705 + 97.8077i) q^{98} +(8.80533 - 21.2579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 124q^{16} + 108q^{18} + 148q^{22} - 72q^{23} - 232q^{43} + 324q^{44} + 24q^{53} - 252q^{56} - 504q^{63} - 472q^{67} - 108q^{74} - 168q^{77} - 708q^{92} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{7}{8}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99607 + 0.125246i −0.998037 + 0.0626229i
\(3\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(4\) 3.96863 0.500000i 0.992157 0.125000i
\(5\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(6\) 0 0
\(7\) 4.94975 4.94975i 0.707107 0.707107i
\(8\) −7.85905 + 1.49509i −0.982382 + 0.186886i
\(9\) −6.36396 6.36396i −0.707107 0.707107i
\(10\) 0 0
\(11\) 0.978370 + 2.36199i 0.0889427 + 0.214727i 0.962091 0.272727i \(-0.0879257\pi\)
−0.873149 + 0.487454i \(0.837926\pi\)
\(12\) 0 0
\(13\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(14\) −9.26013 + 10.5000i −0.661438 + 0.750000i
\(15\) 0 0
\(16\) 15.5000 3.96863i 0.968750 0.248039i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 13.5000 + 11.9059i 0.750000 + 0.661438i
\(19\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.24873 4.59218i −0.102215 0.208735i
\(23\) −30.1660 30.1660i −1.31157 1.31157i −0.920261 0.391304i \(-0.872024\pi\)
−0.391304 0.920261i \(-0.627976\pi\)
\(24\) 0 0
\(25\) 17.6777 17.6777i 0.707107 0.707107i
\(26\) 0 0
\(27\) 0 0
\(28\) 17.1688 22.1186i 0.613172 0.789949i
\(29\) 15.9922 38.6086i 0.551455 1.33133i −0.364931 0.931034i \(-0.618907\pi\)
0.916386 0.400295i \(-0.131093\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) −30.4421 + 9.86299i −0.951316 + 0.308218i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −28.4382 22.0742i −0.789949 0.613172i
\(37\) 40.7639 16.8850i 1.10173 0.456351i 0.243646 0.969864i \(-0.421656\pi\)
0.858082 + 0.513514i \(0.171656\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(42\) 0 0
\(43\) −30.9438 74.7051i −0.719624 1.73733i −0.674419 0.738349i \(-0.735606\pi\)
−0.0452058 0.998978i \(-0.514394\pi\)
\(44\) 5.06378 + 8.88469i 0.115086 + 0.201925i
\(45\) 0 0
\(46\) 63.9918 + 56.4354i 1.39113 + 1.22686i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 49.0000i 1.00000i
\(50\) −33.0719 + 37.5000i −0.661438 + 0.750000i
\(51\) 0 0
\(52\) 0 0
\(53\) 38.2953 + 92.4529i 0.722552 + 1.74439i 0.665948 + 0.745998i \(0.268027\pi\)
0.0566038 + 0.998397i \(0.481973\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −31.5000 + 46.3006i −0.562500 + 0.826797i
\(57\) 0 0
\(58\) −27.0860 + 79.0685i −0.467001 + 1.36325i
\(59\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(60\) 0 0
\(61\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(62\) 0 0
\(63\) −63.0000 −1.00000
\(64\) 59.5294 23.5000i 0.930147 0.367188i
\(65\) 0 0
\(66\) 0 0
\(67\) 5.16924 12.4797i 0.0771529 0.186264i −0.880597 0.473866i \(-0.842858\pi\)
0.957750 + 0.287602i \(0.0928581\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −59.8665 + 59.8665i −0.843190 + 0.843190i −0.989272 0.146082i \(-0.953334\pi\)
0.146082 + 0.989272i \(0.453334\pi\)
\(72\) 59.5294 + 40.5000i 0.826797 + 0.562500i
\(73\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(74\) −79.2531 + 38.8092i −1.07099 + 0.524448i
\(75\) 0 0
\(76\) 0 0
\(77\) 16.5340 + 6.84859i 0.214727 + 0.0889427i
\(78\) 0 0
\(79\) 156.268i 1.97807i 0.147669 + 0.989037i \(0.452823\pi\)
−0.147669 + 0.989037i \(0.547177\pi\)
\(80\) 0 0
\(81\) 81.0000i 1.00000i
\(82\) 0 0
\(83\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 71.1227 + 145.241i 0.827008 + 1.68885i
\(87\) 0 0
\(88\) −11.2205 17.1003i −0.127505 0.194321i
\(89\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −134.801 104.635i −1.46522 1.13733i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 6.13705 + 97.8077i 0.0626229 + 0.998037i
\(99\) 8.80533 21.2579i 0.0889427 0.214727i
\(100\) 61.3172 78.9949i 0.613172 0.789949i
\(101\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(102\) 0 0
\(103\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −88.0195 179.747i −0.830373 1.69572i
\(107\) −10.1775 24.5707i −0.0951169 0.229632i 0.869159 0.494533i \(-0.164661\pi\)
−0.964276 + 0.264901i \(0.914661\pi\)
\(108\) 0 0
\(109\) 157.826 + 65.3739i 1.44795 + 0.599760i 0.961711 0.274066i \(-0.0883686\pi\)
0.486239 + 0.873826i \(0.338369\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 57.0774 96.3648i 0.509620 0.860400i
\(113\) 127.044i 1.12429i −0.827040 0.562144i \(-0.809977\pi\)
0.827040 0.562144i \(-0.190023\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 44.1628 161.219i 0.380713 1.38982i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 80.9381 80.9381i 0.668910 0.668910i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 125.753 7.89049i 0.998037 0.0626229i
\(127\) −253.992 −1.99994 −0.999969 0.00787402i \(-0.997494\pi\)
−0.999969 + 0.00787402i \(0.997494\pi\)
\(128\) −115.882 + 54.3636i −0.905327 + 0.424715i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −8.75517 + 25.5578i −0.0653371 + 0.190730i
\(135\) 0 0
\(136\) 0 0
\(137\) −18.8301 18.8301i −0.137446 0.137446i 0.635036 0.772482i \(-0.280985\pi\)
−0.772482 + 0.635036i \(0.780985\pi\)
\(138\) 0 0
\(139\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 112.000 126.996i 0.788732 0.894338i
\(143\) 0 0
\(144\) −123.898 73.3852i −0.860400 0.509620i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 153.334 87.3921i 1.03604 0.590487i
\(149\) 109.556 + 264.490i 0.735272 + 1.77510i 0.624161 + 0.781296i \(0.285441\pi\)
0.111111 + 0.993808i \(0.464559\pi\)
\(150\) 0 0
\(151\) 73.5020 + 73.5020i 0.486768 + 0.486768i 0.907285 0.420517i \(-0.138151\pi\)
−0.420517 + 0.907285i \(0.638151\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −33.8608 11.5995i −0.219875 0.0753214i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(158\) −19.5719 311.922i −0.123873 1.97419i
\(159\) 0 0
\(160\) 0 0
\(161\) −298.628 −1.85483
\(162\) −10.1449 161.682i −0.0626229 0.998037i
\(163\) 20.3324 49.0868i 0.124739 0.301146i −0.849158 0.528140i \(-0.822890\pi\)
0.973896 + 0.226994i \(0.0728897\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(168\) 0 0
\(169\) 119.501 + 119.501i 0.707107 + 0.707107i
\(170\) 0 0
\(171\) 0 0
\(172\) −160.157 281.005i −0.931146 1.63375i
\(173\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(174\) 0 0
\(175\) 175.000i 1.00000i
\(176\) 24.5386 + 32.7281i 0.139424 + 0.185955i
\(177\) 0 0
\(178\) 0 0
\(179\) 211.247 + 87.5013i 1.18015 + 0.488834i 0.884535 0.466473i \(-0.154476\pi\)
0.295615 + 0.955307i \(0.404476\pi\)
\(180\) 0 0
\(181\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 282.177 + 191.975i 1.53357 + 1.04334i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −75.1937 −0.393684 −0.196842 0.980435i \(-0.563069\pi\)
−0.196842 + 0.980435i \(0.563069\pi\)
\(192\) 0 0
\(193\) −225.559 −1.16870 −0.584349 0.811502i \(-0.698650\pi\)
−0.584349 + 0.811502i \(0.698650\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −24.5000 194.463i −0.125000 0.992157i
\(197\) 135.160 55.9851i 0.686092 0.284189i −0.0122790 0.999925i \(-0.503909\pi\)
0.698371 + 0.715736i \(0.253909\pi\)
\(198\) −14.9136 + 43.5353i −0.0753214 + 0.219875i
\(199\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(200\) −112.500 + 165.359i −0.562500 + 0.826797i
\(201\) 0 0
\(202\) 0 0
\(203\) −111.945 270.260i −0.551455 1.33133i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 383.951i 1.85483i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 349.538 + 144.783i 1.65658 + 0.686176i 0.997808 0.0661700i \(-0.0210780\pi\)
0.658768 + 0.752346i \(0.271078\pi\)
\(212\) 198.206 + 347.764i 0.934934 + 1.64039i
\(213\) 0 0
\(214\) 23.3924 + 47.7702i 0.109310 + 0.223225i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −323.221 110.724i −1.48267 0.507908i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) −101.861 + 199.500i −0.454739 + 0.890625i
\(225\) −225.000 −1.00000
\(226\) 15.9118 + 253.590i 0.0704061 + 1.12208i
\(227\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(228\) 0 0
\(229\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −67.9601 + 327.337i −0.292932 + 1.41093i
\(233\) −223.826 223.826i −0.960627 0.960627i 0.0386266 0.999254i \(-0.487702\pi\)
−0.999254 + 0.0386266i \(0.987702\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 423.320i 1.77121i 0.464435 + 0.885607i \(0.346257\pi\)
−0.464435 + 0.885607i \(0.653743\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) −151.421 + 171.696i −0.625708 + 0.709486i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(252\) −250.023 + 31.5000i −0.992157 + 0.125000i
\(253\) 41.7384 100.765i 0.164974 0.398282i
\(254\) 506.987 31.8115i 1.99601 0.125242i
\(255\) 0 0
\(256\) 224.500 123.027i 0.876953 0.480576i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 118.195 285.348i 0.456351 1.10173i
\(260\) 0 0
\(261\) −347.477 + 143.930i −1.33133 + 0.551455i
\(262\) 0 0
\(263\) 352.139 352.139i 1.33893 1.33893i 0.441837 0.897095i \(-0.354327\pi\)
0.897095 0.441837i \(-0.145673\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 14.2750 52.1117i 0.0532648 0.194447i
\(269\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 39.9446 + 35.2278i 0.145783 + 0.128569i
\(275\) 59.0499 + 24.4593i 0.214727 + 0.0889427i
\(276\) 0 0
\(277\) 207.009 + 499.763i 0.747323 + 1.80420i 0.573087 + 0.819495i \(0.305746\pi\)
0.174237 + 0.984704i \(0.444254\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 332.158 332.158i 1.18206 1.18206i 0.202847 0.979210i \(-0.434981\pi\)
0.979210 0.202847i \(-0.0650194\pi\)
\(282\) 0 0
\(283\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(284\) −207.655 + 267.521i −0.731178 + 0.941976i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 256.500 + 130.965i 0.890625 + 0.454739i
\(289\) −289.000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −295.121 + 193.646i −0.997031 + 0.654208i
\(297\) 0 0
\(298\) −251.807 514.221i −0.844991 1.72557i
\(299\) 0 0
\(300\) 0 0
\(301\) −522.935 216.607i −1.73733 0.719624i
\(302\) −155.921 137.510i −0.516295 0.455330i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(308\) 69.0414 + 18.9125i 0.224160 + 0.0614043i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(312\) 0 0
\(313\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 78.1339 + 620.169i 0.247259 + 1.96256i
\(317\) 237.250 572.771i 0.748421 1.80685i 0.180879 0.983505i \(-0.442106\pi\)
0.567543 0.823344i \(-0.307894\pi\)
\(318\) 0 0
\(319\) 106.840 0.334920
\(320\) 0 0
\(321\) 0 0
\(322\) 596.084 37.4019i 1.85119 0.116155i
\(323\) 0 0
\(324\) 40.5000 + 321.459i 0.125000 + 0.992157i
\(325\) 0 0
\(326\) −34.4371 + 100.527i −0.105635 + 0.308366i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −252.050 608.503i −0.761481 1.83838i −0.473725 0.880673i \(-0.657091\pi\)
−0.287755 0.957704i \(-0.592909\pi\)
\(332\) 0 0
\(333\) −366.875 151.965i −1.10173 0.456351i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 289.193i 0.858139i 0.903272 + 0.429069i \(0.141158\pi\)
−0.903272 + 0.429069i \(0.858842\pi\)
\(338\) −253.500 223.566i −0.750000 0.661438i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −242.538 242.538i −0.707107 0.707107i
\(344\) 354.880 + 540.847i 1.03163 + 1.57223i
\(345\) 0 0
\(346\) 0 0
\(347\) 631.092 261.407i 1.81871 0.753334i 0.841765 0.539844i \(-0.181517\pi\)
0.976945 0.213490i \(-0.0684831\pi\)
\(348\) 0 0
\(349\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(350\) 21.9180 + 349.313i 0.0626229 + 0.998037i
\(351\) 0 0
\(352\) −53.0800 62.2544i −0.150795 0.176859i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −432.624 148.201i −1.20845 0.413970i
\(359\) 475.162 475.162i 1.32357 1.32357i 0.412708 0.910864i \(-0.364583\pi\)
0.910864 0.412708i \(-0.135417\pi\)
\(360\) 0 0
\(361\) 255.266 + 255.266i 0.707107 + 0.707107i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) −587.291 347.856i −1.59590 0.945260i
\(369\) 0 0
\(370\) 0 0
\(371\) 647.170 + 268.067i 1.74439 + 0.722552i
\(372\) 0 0
\(373\) 9.65880 + 23.3184i 0.0258949 + 0.0625158i 0.936298 0.351206i \(-0.114228\pi\)
−0.910403 + 0.413722i \(0.864228\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −596.475 + 247.068i −1.57381 + 0.651894i −0.987418 0.158132i \(-0.949453\pi\)
−0.586393 + 0.810026i \(0.699453\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 150.092 9.41769i 0.392911 0.0246536i
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 450.232 28.2503i 1.16640 0.0731873i
\(387\) −278.495 + 672.346i −0.719624 + 1.73733i
\(388\) 0 0
\(389\) −578.727 + 239.716i −1.48773 + 0.616238i −0.970821 0.239804i \(-0.922917\pi\)
−0.516908 + 0.856041i \(0.672917\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 73.2595 + 385.094i 0.186886 + 0.982382i
\(393\) 0 0
\(394\) −262.778 + 128.679i −0.666949 + 0.326596i
\(395\) 0 0
\(396\) 24.3161 88.7675i 0.0614043 0.224160i
\(397\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 203.848 344.160i 0.509620 0.860400i
\(401\) 759.181i 1.89322i −0.322381 0.946610i \(-0.604483\pi\)
0.322381 0.946610i \(-0.395517\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 257.300 + 525.438i 0.633744 + 1.29418i
\(407\) 79.7644 + 79.7644i 0.195981 + 0.195981i
\(408\) 0 0
\(409\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −48.0882 766.394i −0.116155 1.85119i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(420\) 0 0
\(421\) 433.539 179.578i 1.02978 0.426551i 0.197150 0.980373i \(-0.436832\pi\)
0.832635 + 0.553823i \(0.186832\pi\)
\(422\) −715.837 245.220i −1.69630 0.581090i
\(423\) 0 0
\(424\) −439.190 669.337i −1.03583 1.57863i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −52.6761 92.4231i −0.123075 0.215942i
\(429\) 0 0
\(430\) 0 0
\(431\) 162.000i 0.375870i −0.982181 0.187935i \(-0.939821\pi\)
0.982181 0.187935i \(-0.0601794\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 659.041 + 180.531i 1.51156 + 0.414063i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(440\) 0 0
\(441\) −311.834 + 311.834i −0.707107 + 0.707107i
\(442\) 0 0
\(443\) −460.494 + 190.743i −1.03949 + 0.430571i −0.836129 0.548533i \(-0.815187\pi\)
−0.203361 + 0.979104i \(0.565187\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 178.336 410.975i 0.398072 0.917354i
\(449\) 84.6640 0.188561 0.0942807 0.995546i \(-0.469945\pi\)
0.0942807 + 0.995546i \(0.469945\pi\)
\(450\) 449.117 28.1803i 0.998037 0.0626229i
\(451\) 0 0
\(452\) −63.5222 504.192i −0.140536 1.11547i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 179.600 + 179.600i 0.392997 + 0.392997i 0.875754 0.482757i \(-0.160365\pi\)
−0.482757 + 0.875754i \(0.660365\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(462\) 0 0
\(463\) 27.5911i 0.0595920i 0.999556 + 0.0297960i \(0.00948576\pi\)
−0.999556 + 0.0297960i \(0.990514\pi\)
\(464\) 94.6560 661.900i 0.204000 1.42651i
\(465\) 0 0
\(466\) 474.807 + 418.740i 1.01890 + 0.898584i
\(467\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(468\) 0 0
\(469\) −36.1847 87.3576i −0.0771529 0.186264i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 146.178 146.178i 0.309045 0.309045i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 344.657 832.076i 0.722552 1.74439i
\(478\) −53.0191 844.979i −0.110919 1.76774i
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 280.744 361.682i 0.580050 0.747277i
\(485\) 0 0
\(486\) 0 0
\(487\) 245.486 245.486i 0.504078 0.504078i −0.408624 0.912703i \(-0.633991\pi\)
0.912703 + 0.408624i \(0.133991\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 222.027 + 536.019i 0.452193 + 1.09169i 0.971487 + 0.237094i \(0.0761949\pi\)
−0.519294 + 0.854596i \(0.673805\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 592.648i 1.19245i
\(498\) 0 0
\(499\) −707.625 293.108i −1.41809 0.587391i −0.463708 0.885988i \(-0.653481\pi\)
−0.954379 + 0.298597i \(0.903481\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(504\) 495.120 94.1907i 0.982382 0.186886i
\(505\) 0 0
\(506\) −70.6926 + 206.363i −0.139709 + 0.407832i
\(507\) 0 0
\(508\) −1008.00 + 126.996i −1.98425 + 0.249992i
\(509\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −432.710 + 273.690i −0.845137 + 0.534550i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −200.187 + 584.378i −0.386462 + 1.12814i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(522\) 675.564 330.815i 1.29418 0.633744i
\(523\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −658.792 + 747.000i −1.25246 + 1.42015i
\(527\) 0 0
\(528\) 0 0
\(529\) 1290.98i 2.44041i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −21.9671 + 105.807i −0.0409835 + 0.197401i
\(537\) 0 0
\(538\) 0 0
\(539\) 115.738 47.9401i 0.214727 0.0889427i
\(540\) 0 0
\(541\) −392.486 + 947.545i −0.725483 + 1.75147i −0.0683919 + 0.997659i \(0.521787\pi\)
−0.657091 + 0.753811i \(0.728213\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −399.982 + 965.641i −0.731228 + 1.76534i −0.0927652 + 0.995688i \(0.529571\pi\)
−0.638463 + 0.769653i \(0.720429\pi\)
\(548\) −84.1445 65.3144i −0.153548 0.119187i
\(549\) 0 0
\(550\) −120.931 41.4267i −0.219875 0.0753214i
\(551\) 0 0
\(552\) 0 0
\(553\) 773.486 + 773.486i 1.39871 + 1.39871i
\(554\) −475.798 971.637i −0.858841 1.75386i
\(555\) 0 0
\(556\) 0 0
\(557\) 683.144 + 282.968i 1.22647 + 0.508021i 0.899461 0.437000i \(-0.143959\pi\)
0.327009 + 0.945021i \(0.393959\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −621.411 + 704.614i −1.10571 + 1.25376i
\(563\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 400.930 + 400.930i 0.707107 + 0.707107i
\(568\) 380.988 560.000i 0.670754 0.985915i
\(569\) 658.532 658.532i 1.15735 1.15735i 0.172306 0.985044i \(-0.444878\pi\)
0.985044 0.172306i \(-0.0551217\pi\)
\(570\) 0 0
\(571\) −893.751 + 370.204i −1.56524 + 0.648343i −0.985989 0.166807i \(-0.946654\pi\)
−0.579249 + 0.815151i \(0.696654\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1066.53 −1.85483
\(576\) −528.396 229.290i −0.917354 0.398072i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 576.866 36.1960i 0.998037 0.0626229i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −180.906 + 180.906i −0.310302 + 0.310302i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 564.831 423.494i 0.954106 0.715361i
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 567.030 + 994.886i 0.951393 + 1.66927i
\(597\) 0 0
\(598\) 0 0
\(599\) 123.037 + 123.037i 0.205403 + 0.205403i 0.802310 0.596907i \(-0.203604\pi\)
−0.596907 + 0.802310i \(0.703604\pi\)
\(600\) 0 0
\(601\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(602\) 1070.95 + 366.868i 1.77898 + 0.609415i
\(603\) −112.317 + 46.5232i −0.186264 + 0.0771529i
\(604\) 328.453 + 254.951i 0.543796 + 0.422104i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −612.624 + 253.757i −0.999386 + 0.413959i −0.821572 0.570105i \(-0.806903\pi\)
−0.177814 + 0.984064i \(0.556903\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −140.181 29.1037i −0.227566 0.0472462i
\(617\) 778.265 + 778.265i 1.26137 + 1.26137i 0.950430 + 0.310939i \(0.100644\pi\)
0.310939 + 0.950430i \(0.399356\pi\)
\(618\) 0 0
\(619\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000i 1.00000i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −538.799 538.799i −0.853881 0.853881i 0.136728 0.990609i \(-0.456341\pi\)
−0.990609 + 0.136728i \(0.956341\pi\)
\(632\) −233.635 1228.12i −0.369675 1.94322i
\(633\) 0 0
\(634\) −401.831 + 1173.01i −0.633802 + 1.85017i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −213.260 + 13.3812i −0.334263 + 0.0209737i
\(639\) 761.976 1.19245
\(640\) 0 0
\(641\) 98.7379 0.154037 0.0770186 0.997030i \(-0.475460\pi\)
0.0770186 + 0.997030i \(0.475460\pi\)
\(642\) 0 0
\(643\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(644\) −1185.14 + 149.314i −1.84029 + 0.231854i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(648\) −121.102 636.583i −0.186886 0.982382i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 56.1484 204.973i 0.0861171 0.314376i
\(653\) −1206.23 499.635i −1.84721 0.765138i −0.932964 0.359969i \(-0.882787\pi\)
−0.914242 0.405169i \(-0.867213\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 115.914 + 48.0130i 0.175893 + 0.0728574i 0.468892 0.883255i \(-0.344653\pi\)
−0.292999 + 0.956113i \(0.594653\pi\)
\(660\) 0 0
\(661\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(662\) 579.323 + 1183.05i 0.875110 + 1.78708i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 751.344 + 257.383i 1.12814 + 0.386462i
\(667\) −1647.09 + 682.246i −2.46940 + 1.02286i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1269.96 1.88701 0.943507 0.331352i \(-0.107505\pi\)
0.943507 + 0.331352i \(0.107505\pi\)
\(674\) −36.2202 577.250i −0.0537391 0.856454i
\(675\) 0 0
\(676\) 534.006 + 414.505i 0.789949 + 0.613172i
\(677\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −98.6625 238.192i −0.144455 0.348744i 0.835048 0.550178i \(-0.185440\pi\)
−0.979502 + 0.201433i \(0.935440\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 514.500 + 453.746i 0.750000 + 0.661438i
\(687\) 0 0
\(688\) −776.106 1035.12i −1.12806 1.50454i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(692\) 0 0
\(693\) −61.6373 148.806i −0.0889427 0.214727i
\(694\) −1226.97 + 600.830i −1.76796 + 0.865749i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −87.5000 694.510i −0.125000 0.992157i
\(701\) 242.149 584.599i 0.345434 0.833950i −0.651713 0.758465i \(-0.725949\pi\)
0.997147 0.0754851i \(-0.0240505\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 113.749 + 117.616i 0.161575 + 0.167069i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1291.86 535.106i 1.82209 0.754734i 0.847476 0.530834i \(-0.178121\pi\)
0.974612 0.223900i \(-0.0718789\pi\)
\(710\) 0 0
\(711\) 994.482 994.482i 1.39871 1.39871i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 882.111 + 241.637i 1.23200 + 0.337481i
\(717\) 0 0
\(718\) −888.947 + 1007.97i −1.23809 + 1.40386i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −541.500 477.558i −0.750000 0.661438i
\(723\) 0 0
\(724\) 0 0
\(725\) −399.805 965.214i −0.551455 1.33133i
\(726\) 0 0
\(727\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(728\) 0 0
\(729\) 515.481 515.481i 0.707107 0.707107i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 1215.84 + 620.790i 1.65196 + 0.843464i
\(737\) 34.5343 0.0468580
\(738\) 0 0
\(739\) 312.569 754.607i 0.422961 1.02112i −0.558508 0.829499i \(-0.688626\pi\)
0.981469 0.191620i \(-0.0613741\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1325.37 454.026i −1.78622 0.611895i
\(743\) −683.810 + 683.810i −0.920337 + 0.920337i −0.997053 0.0767160i \(-0.975557\pi\)
0.0767160 + 0.997053i \(0.475557\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −22.2002 45.3355i −0.0297590 0.0607715i
\(747\) 0 0
\(748\) 0 0
\(749\) −171.995 71.2425i −0.229632 0.0951169i
\(750\) 0 0
\(751\) 1269.96i 1.69103i −0.533955 0.845513i \(-0.679295\pi\)
0.533955 0.845513i \(-0.320705\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −407.368 983.472i −0.538134 1.29917i −0.926024 0.377465i \(-0.876796\pi\)
0.387890 0.921706i \(-0.373204\pi\)
\(758\) 1159.66 567.872i 1.52990 0.749171i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(762\) 0 0
\(763\) 1104.79 457.617i 1.44795 0.599760i
\(764\) −298.416 + 37.5968i −0.390596 + 0.0492105i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −895.158 + 112.779i −1.15953 + 0.146087i
\(773\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(774\) 471.688 1376.93i 0.609415 1.77898i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 1125.16 550.975i 1.44622 0.708194i
\(779\) 0 0
\(780\) 0 0
\(781\) −199.976 82.8328i −0.256051 0.106060i
\(782\) 0 0
\(783\) 0 0
\(784\) −194.463 759.500i −0.248039 0.968750i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(788\) 508.407 289.764i 0.645187 0.367721i
\(789\) 0 0
\(790\) 0 0
\(791\) −628.838 628.838i −0.794991 0.794991i
\(792\) −37.4190 + 180.232i −0.0472462 + 0.227566i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −363.791 + 712.500i −0.454739 + 0.890625i
\(801\) 0 0
\(802\) 95.0843 + 1515.38i 0.118559 + 1.88950i
\(803\) 0 0
\(804\)