Properties

Label 224.3.v.a.181.2
Level 224
Weight 3
Character 224.181
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 181.2
Root \(1.28897 + 0.581861i\) of \(x^{8} + x^{4} + 16\)
Character \(\chi\) \(=\) 224.181
Dual form 224.3.v.a.125.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.99607 + 0.125246i) q^{2} +(3.96863 + 0.500000i) q^{4} +(-4.94975 - 4.94975i) q^{7} +(7.85905 + 1.49509i) q^{8} +(6.36396 - 6.36396i) q^{9} +O(q^{10})\) \(q+(1.99607 + 0.125246i) q^{2} +(3.96863 + 0.500000i) q^{4} +(-4.94975 - 4.94975i) q^{7} +(7.85905 + 1.49509i) q^{8} +(6.36396 - 6.36396i) q^{9} +(20.1876 + 8.36199i) q^{11} +(-9.26013 - 10.5000i) q^{14} +(15.5000 + 3.96863i) q^{16} +(13.5000 - 11.9059i) q^{18} +(39.2487 + 19.2196i) q^{22} +(-30.1660 + 30.1660i) q^{23} +(-17.6777 - 17.6777i) q^{25} +(-17.1688 - 22.1186i) q^{28} +(-37.1582 + 15.3914i) q^{29} +(30.4421 + 9.86299i) q^{32} +(28.4382 - 22.0742i) q^{36} +(22.7341 - 54.8850i) q^{37} +(-27.0562 - 11.2070i) q^{43} +(75.9362 + 43.2795i) q^{44} +(-63.9918 + 56.4354i) q^{46} +49.0000i q^{49} +(-33.0719 - 37.5000i) q^{50} +(-32.2953 - 13.3771i) q^{53} +(-31.5000 - 46.3006i) q^{56} +(-76.0983 + 26.0685i) q^{58} -63.0000 q^{63} +(59.5294 + 23.5000i) q^{64} +(-123.169 + 51.0184i) q^{67} +(59.8665 + 59.8665i) q^{71} +(59.5294 - 40.5000i) q^{72} +(52.2531 - 106.707i) q^{74} +(-58.5340 - 141.313i) q^{77} +156.268i q^{79} -81.0000i q^{81} +(-52.6025 - 25.7587i) q^{86} +(146.154 + 95.8997i) q^{88} +(-134.801 + 104.635i) q^{92} +(-6.13705 + 97.8077i) q^{98} +(181.689 - 75.2579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 124q^{16} + 108q^{18} + 148q^{22} - 72q^{23} - 232q^{43} + 324q^{44} + 24q^{53} - 252q^{56} - 504q^{63} - 472q^{67} - 108q^{74} - 168q^{77} - 708q^{92} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{8}\right)\)

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 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(4\) 3.96863 + 0.500000i 0.992157 + 0.125000i
\(5\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(6\) 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
\(11\) 20.1876 + 8.36199i 1.83524 + 0.760181i 0.962091 + 0.272727i \(0.0879257\pi\)
0.873149 + 0.487454i \(0.162074\pi\)
\(12\) 0 0
\(13\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(14\) −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 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 39.2487 + 19.2196i 1.78403 + 0.873617i
\(23\) −30.1660 + 30.1660i −1.31157 + 1.31157i −0.391304 + 0.920261i \(0.627976\pi\)
−0.920261 + 0.391304i \(0.872024\pi\)
\(24\) 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
\(29\) −37.1582 + 15.3914i −1.28132 + 0.530739i −0.916386 0.400295i \(-0.868907\pi\)
−0.364931 + 0.931034i \(0.618907\pi\)
\(30\) 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
\(37\) 22.7341 54.8850i 0.614435 1.48338i −0.243646 0.969864i \(-0.578344\pi\)
0.858082 0.513514i \(-0.171656\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(42\) 0 0
\(43\) −27.0562 11.2070i −0.629213 0.260628i 0.0452058 0.998978i \(-0.485606\pi\)
−0.674419 + 0.738349i \(0.735606\pi\)
\(44\) 75.9362 + 43.2795i 1.72582 + 0.983624i
\(45\) 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
\(53\) −32.2953 13.3771i −0.609344 0.252399i 0.0566038 0.998397i \(-0.481973\pi\)
−0.665948 + 0.745998i \(0.731973\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −31.5000 46.3006i −0.562500 0.826797i
\(57\) 0 0
\(58\) −76.0983 + 26.0685i −1.31204 + 0.449457i
\(59\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(60\) 0 0
\(61\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(62\) 0 0
\(63\) −63.0000 −1.00000
\(64\) 59.5294 + 23.5000i 0.930147 + 0.367188i
\(65\) 0 0
\(66\) 0 0
\(67\) −123.169 + 51.0184i −1.83835 + 0.761468i −0.880597 + 0.473866i \(0.842858\pi\)
−0.957750 + 0.287602i \(0.907142\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 59.8665 + 59.8665i 0.843190 + 0.843190i 0.989272 0.146082i \(-0.0466664\pi\)
−0.146082 + 0.989272i \(0.546666\pi\)
\(72\) 59.5294 40.5000i 0.826797 0.562500i
\(73\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(74\) 52.2531 106.707i 0.706123 1.44199i
\(75\) 0 0
\(76\) 0 0
\(77\) −58.5340 141.313i −0.760181 1.83524i
\(78\) 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 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −52.6025 25.7587i −0.611657 0.299520i
\(87\) 0 0
\(88\) 146.154 + 95.8997i 1.66084 + 1.08977i
\(89\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(90\) 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
\(99\) 181.689 75.2579i 1.83524 0.760181i
\(100\) −61.3172 78.9949i −0.613172 0.789949i
\(101\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −62.7883 30.7466i −0.592342 0.290062i
\(107\) 196.178 + 81.2594i 1.83343 + 0.759433i 0.964276 + 0.264901i \(0.0853391\pi\)
0.869159 + 0.494533i \(0.164661\pi\)
\(108\) 0 0
\(109\) −51.8265 125.120i −0.475472 1.14789i −0.961711 0.274066i \(-0.911631\pi\)
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
\(116\) −155.163 + 42.5037i −1.33761 + 0.366412i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 252.058 + 252.058i 2.08312 + 2.08312i
\(122\) 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 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −252.245 + 86.4100i −1.88242 + 0.644851i
\(135\) 0 0
\(136\) 0 0
\(137\) −18.8301 + 18.8301i −0.137446 + 0.137446i −0.772482 0.635036i \(-0.780985\pi\)
0.635036 + 0.772482i \(0.280985\pi\)
\(138\) 0 0
\(139\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(140\) 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
\(148\) 117.666 206.451i 0.795038 1.39494i
\(149\) 76.4445 + 31.6643i 0.513050 + 0.212512i 0.624161 0.781296i \(-0.285441\pi\)
−0.111111 + 0.993808i \(0.535441\pi\)
\(150\) 0 0
\(151\) 73.5020 73.5020i 0.486768 0.486768i −0.420517 0.907285i \(-0.638151\pi\)
0.907285 + 0.420517i \(0.138151\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −99.1392 289.403i −0.643761 1.87924i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(158\) −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
\(163\) 297.158 123.087i 1.82305 0.755134i 0.849158 0.528140i \(-0.177110\pi\)
0.973896 0.226994i \(-0.0728897\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(168\) 0 0
\(169\) −119.501 + 119.501i −0.707107 + 0.707107i
\(170\) 0 0
\(171\) 0 0
\(172\) −101.772 58.0046i −0.591699 0.337236i
\(173\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(174\) 0 0
\(175\) 175.000i 1.00000i
\(176\) 279.723 + 209.728i 1.58933 + 1.19164i
\(177\) 0 0
\(178\) 0 0
\(179\) −105.417 254.499i −0.588921 1.42178i −0.884535 0.466473i \(-0.845524\pi\)
0.295615 0.955307i \(-0.404476\pi\)
\(180\) 0 0
\(181\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(182\) 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 \(-0.436931\pi\)
0.196842 + 0.980435i \(0.436931\pi\)
\(192\) 0 0
\(193\) 225.559 1.16870 0.584349 0.811502i \(-0.301350\pi\)
0.584349 + 0.811502i \(0.301350\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −24.5000 + 194.463i −0.125000 + 0.992157i
\(197\) 139.998 337.985i 0.710650 1.71566i 0.0122790 0.999925i \(-0.496091\pi\)
0.698371 0.715736i \(-0.253909\pi\)
\(198\) 372.090 127.465i 1.87924 0.643761i
\(199\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(200\) −112.500 165.359i −0.562500 0.826797i
\(201\) 0 0
\(202\) 0 0
\(203\) 260.107 + 107.740i 1.28132 + 0.530739i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 383.951i 1.85483i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −71.5376 172.707i −0.339041 0.818516i −0.997808 0.0661700i \(-0.978922\pi\)
0.658768 0.752346i \(-0.271078\pi\)
\(212\) −121.479 69.2365i −0.573015 0.326587i
\(213\) 0 0
\(214\) 381.408 + 186.770i 1.78228 + 0.872758i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −87.7788 256.240i −0.402655 1.17541i
\(219\) 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 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(228\) 0 0
\(229\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −315.040 + 65.4072i −1.35793 + 0.281927i
\(233\) −223.826 + 223.826i −0.960627 + 0.960627i −0.999254 0.0386266i \(-0.987702\pi\)
0.0386266 + 0.999254i \(0.487702\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 423.320i 1.77121i −0.464435 0.885607i \(-0.653743\pi\)
0.464435 0.885607i \(-0.346257\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 471.557 + 534.696i 1.94858 + 2.20949i
\(243\) 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 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(252\) −250.023 31.5000i −0.992157 0.125000i
\(253\) −861.229 + 356.733i −3.40407 + 1.41001i
\(254\) −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
\(259\) −384.195 + 159.139i −1.48338 + 0.614435i
\(260\) 0 0
\(261\) −138.523 + 334.424i −0.530739 + 1.28132i
\(262\) 0 0
\(263\) −352.139 352.139i −1.33893 1.33893i −0.897095 0.441837i \(-0.854327\pi\)
−0.441837 0.897095i \(-0.645673\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −514.322 + 140.888i −1.91911 + 0.525702i
\(269\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(270\) 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
\(275\) −209.050 504.691i −0.760181 1.83524i
\(276\) 0 0
\(277\) 110.482 + 45.7630i 0.398850 + 0.165209i 0.573087 0.819495i \(-0.305746\pi\)
−0.174237 + 0.984704i \(0.555746\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 332.158 + 332.158i 1.18206 + 1.18206i 0.979210 + 0.202847i \(0.0650194\pi\)
0.202847 + 0.979210i \(0.434981\pi\)
\(282\) 0 0
\(283\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(284\) 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 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 260.727 397.354i 0.880833 1.34241i
\(297\) 0 0
\(298\) 148.623 + 72.7787i 0.498735 + 0.244224i
\(299\) 0 0
\(300\) 0 0
\(301\) 78.4492 + 189.393i 0.260628 + 0.629213i
\(302\) 155.921 137.510i 0.516295 0.455330i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(308\) −161.643 590.087i −0.524814 1.91587i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(312\) 0 0
\(313\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −78.1339 + 620.169i −0.247259 + 1.96256i
\(317\) 122.573 50.7712i 0.386664 0.160162i −0.180879 0.983505i \(-0.557894\pi\)
0.567543 + 0.823344i \(0.307894\pi\)
\(318\) 0 0
\(319\) −878.840 −2.75498
\(320\) 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
\(326\) 608.565 208.473i 1.86676 0.639486i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 61.5560 + 25.4973i 0.185970 + 0.0770312i 0.473725 0.880673i \(-0.342909\pi\)
−0.287755 + 0.957704i \(0.592909\pi\)
\(332\) 0 0
\(333\) −204.607 493.965i −0.614435 1.48338i
\(334\) 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
\(344\) −195.880 128.528i −0.569419 0.373628i
\(345\) 0 0
\(346\) 0 0
\(347\) 46.9076 113.245i 0.135180 0.326354i −0.841765 0.539844i \(-0.818483\pi\)
0.976945 + 0.213490i \(0.0684831\pi\)
\(348\) 0 0
\(349\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(350\) −21.9180 + 349.313i −0.0626229 + 0.998037i
\(351\) 0 0
\(352\) 532.080 + 453.667i 1.51159 + 1.28883i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −178.545 521.201i −0.498729 1.45587i
\(359\) 475.162 + 475.162i 1.32357 + 1.32357i 0.910864 + 0.412708i \(0.135417\pi\)
0.412708 + 0.910864i \(0.364583\pi\)
\(360\) 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
\(371\) 93.6399 + 226.067i 0.252399 + 0.609344i
\(372\) 0 0
\(373\) 688.820 + 285.318i 1.84670 + 0.764929i 0.936298 + 0.351206i \(0.114228\pi\)
0.910403 + 0.413722i \(0.135772\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 151.988 366.932i 0.401024 0.968159i −0.586393 0.810026i \(-0.699453\pi\)
0.987418 0.158132i \(-0.0505473\pi\)
\(380\) 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
\(387\) −243.505 + 100.863i −0.629213 + 0.260628i
\(388\) 0 0
\(389\) 176.572 426.284i 0.453914 1.09584i −0.516908 0.856041i \(-0.672917\pi\)
0.970821 0.239804i \(-0.0770830\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −73.2595 + 385.094i −0.186886 + 0.982382i
\(393\) 0 0
\(394\) 321.778 657.109i 0.816695 1.66779i
\(395\) 0 0
\(396\) 758.684 207.826i 1.91587 0.524814i
\(397\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(398\) 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
\(406\) 505.700 + 247.634i 1.24557 + 0.609937i
\(407\) 917.896 917.896i 2.25527 2.25527i
\(408\) 0 0
\(409\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(410\) 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 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(420\) 0 0
\(421\) −267.539 + 645.897i −0.635485 + 1.53420i 0.197150 + 0.980373i \(0.436832\pi\)
−0.832635 + 0.553823i \(0.813168\pi\)
\(422\) −121.163 353.696i −0.287117 0.838142i
\(423\) 0 0
\(424\) −233.810 153.416i −0.551439 0.361830i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 737.926 + 420.577i 1.72413 + 0.982656i
\(429\) 0 0
\(430\) 0 0
\(431\) 162.000i 0.375870i 0.982181 + 0.187935i \(0.0601794\pi\)
−0.982181 + 0.187935i \(0.939821\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −143.120 522.469i −0.328257 1.19832i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(440\) 0 0
\(441\) 311.834 + 311.834i 0.707107 + 0.707107i
\(442\) 0 0
\(443\) −280.316 + 676.743i −0.632768 + 1.52764i 0.203361 + 0.979104i \(0.434813\pi\)
−0.836129 + 0.548533i \(0.815187\pi\)
\(444\) 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 \(-0.839635\pi\)
0.482757 + 0.875754i \(0.339635\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(462\) 0 0
\(463\) 27.5911i 0.0595920i 0.999556 + 0.0297960i \(0.00948576\pi\)
−0.999556 + 0.0297960i \(0.990514\pi\)
\(464\) −637.035 + 91.1001i −1.37292 + 0.196337i
\(465\) 0 0
\(466\) −474.807 + 418.740i −1.01890 + 0.898584i
\(467\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(468\) 0 0
\(469\) 862.185 + 357.129i 1.83835 + 0.761468i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −452.487 452.487i −0.956632 0.956632i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −290.657 + 120.394i −0.609344 + 0.252399i
\(478\) 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
\(484\) 874.295 + 1126.35i 1.80639 + 2.32718i
\(485\) 0 0
\(486\) 0 0
\(487\) 245.486 + 245.486i 0.504078 + 0.504078i 0.912703 0.408624i \(-0.133991\pi\)
−0.408624 + 0.912703i \(0.633991\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 731.973 + 303.193i 1.49078 + 0.617502i 0.971487 0.237094i \(-0.0761949\pi\)
0.519294 + 0.854596i \(0.326195\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 592.648i 1.19245i
\(498\) 0 0
\(499\) −244.845 591.108i −0.490671 1.18459i −0.954379 0.298597i \(-0.903481\pi\)
0.463708 0.885988i \(-0.346519\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(504\) −495.120 94.1907i −0.982382 0.186886i
\(505\) 0 0
\(506\) −1763.76 + 604.199i −3.48568 + 1.19407i
\(507\) 0 0
\(508\) −1008.00 126.996i −1.98425 0.249992i
\(509\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(510\) 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
\(518\) −786.813 + 269.534i −1.51894 + 0.520336i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(522\) −318.387 + 650.185i −0.609937 + 1.24557i
\(523\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(524\) 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
\(536\) −1044.27 + 216.807i −1.94827 + 0.404490i
\(537\) 0 0
\(538\) 0 0
\(539\) −409.738 + 989.194i −0.760181 + 1.83524i
\(540\) 0 0
\(541\) 318.486 131.921i 0.588699 0.243847i −0.0683919 0.997659i \(-0.521787\pi\)
0.657091 + 0.753811i \(0.271787\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −298.497 + 123.641i −0.545698 + 0.226035i −0.638463 0.769653i \(-0.720429\pi\)
0.0927652 + 0.995688i \(0.470429\pi\)
\(548\) −84.1445 + 65.3144i −0.153548 + 0.119187i
\(549\) 0 0
\(550\) −354.069 1033.58i −0.643761 1.87924i
\(551\) 0 0
\(552\) 0 0
\(553\) 773.486 773.486i 1.39871 1.39871i
\(554\) 214.798 + 105.184i 0.387722 + 0.189862i
\(555\) 0 0
\(556\) 0 0
\(557\) 318.856 + 769.786i 0.572452 + 1.38202i 0.899461 + 0.437000i \(0.143959\pi\)
−0.327009 + 0.945021i \(0.606041\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 621.411 + 704.614i 1.10571 + 1.25376i
\(563\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(564\) 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 −0.985044 0.172306i \(-0.944878\pi\)
−0.172306 0.985044i \(-0.555122\pi\)
\(570\) 0 0
\(571\) −232.249 + 560.698i −0.406740 + 0.981958i 0.579249 + 0.815151i \(0.303346\pi\)
−0.985989 + 0.166807i \(0.946654\pi\)
\(572\) 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
\(583\) −540.105 540.105i −0.926424 0.926424i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 570.197 760.494i 0.963170 1.28462i
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 287.547 + 163.886i 0.482462 + 0.274977i
\(597\) 0 0
\(598\) 0 0
\(599\) −123.037 + 123.037i −0.205403 + 0.205403i −0.802310 0.596907i \(-0.796396\pi\)
0.596907 + 0.802310i \(0.296396\pi\)
\(600\) 0 0
\(601\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(602\) 132.870 + 387.868i 0.220714 + 0.644299i
\(603\) −459.165 + 1108.52i −0.761468 + 1.83835i
\(604\) 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
\(613\) 394.624 952.706i 0.643758 1.55417i −0.177814 0.984064i \(-0.556903\pi\)
0.821572 0.570105i \(-0.193097\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −248.745 1198.10i −0.403807 1.94497i
\(617\) −778.265 + 778.265i −1.26137 + 1.26137i −0.310939 + 0.950430i \(0.600644\pi\)
−0.950430 + 0.310939i \(0.899356\pi\)
\(618\) 0 0
\(619\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(620\) 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 \(-0.543659\pi\)
0.990609 + 0.136728i \(0.0436586\pi\)
\(632\) −233.635 + 1228.12i −0.369675 + 1.94322i
\(633\) 0 0
\(634\) 251.023 85.9914i 0.395935 0.135633i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −1754.23 110.071i −2.74958 0.172525i
\(639\) 761.976 1.19245
\(640\) 0 0
\(641\) −98.7379 −0.154037 −0.0770186 0.997030i \(-0.524540\pi\)
−0.0770186 + 0.997030i \(0.524540\pi\)
\(642\) 0 0
\(643\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(644\) 1185.14 + 149.314i 1.84029 + 0.231854i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(648\) 121.102 636.583i 0.186886 0.982382i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 1240.85 339.907i 1.90315 0.521329i
\(653\) 12.2256 + 29.5153i 0.0187222 + 0.0451995i 0.932964 0.359969i \(-0.117213\pi\)
−0.914242 + 0.405169i \(0.867213\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 502.086 + 1212.14i 0.761891 + 1.83937i 0.468892 + 0.883255i \(0.344653\pi\)
0.292999 + 0.956113i \(0.405347\pi\)
\(660\) 0 0
\(661\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(662\) 119.677 + 58.6042i 0.180781 + 0.0885259i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −346.544 1011.62i −0.520336 1.51894i
\(667\) 656.617 1585.21i 0.984433 2.37663i
\(668\) 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 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1239.34 513.350i −1.81455 0.751611i −0.979502 0.201433i \(-0.935440\pi\)
−0.835048 0.550178i \(-0.814560\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 514.500 453.746i 0.750000 0.661438i
\(687\) 0 0
\(688\) −374.894 281.085i −0.544904 0.408553i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(692\) 0 0
\(693\) −1271.82 526.806i −1.83524 0.760181i
\(694\) 107.815 220.170i 0.155352 0.317248i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −87.5000 + 694.510i −0.125000 + 0.992157i
\(701\) 1155.85 478.769i 1.64886 0.682980i 0.651713 0.758465i \(-0.274051\pi\)
0.997147 + 0.0754851i \(0.0240505\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1005.25 + 972.194i 1.42791 + 1.38096i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 90.1395 217.616i 0.127136 0.306934i −0.847476 0.530834i \(-0.821879\pi\)
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
\(716\) −291.111 1062.72i −0.406579 1.48424i
\(717\) 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
\(725\) 928.955 + 384.786i 1.28132 + 0.530739i
\(726\) 0 0
\(727\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(728\) 0 0
\(729\) −515.481 515.481i −0.707107 0.707107i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −1215.84 + 620.790i −1.65196 + 0.843464i
\(737\) −2913.11 −3.95266
\(738\) 0 0
\(739\) −1138.04 + 471.393i −1.53998 + 0.637879i −0.981469 0.191620i \(-0.938626\pi\)
−0.558508 + 0.829499i \(0.688626\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 158.598 + 462.974i 0.213744 + 0.623954i
\(743\) −683.810 683.810i −0.920337 0.920337i 0.0767160 0.997053i \(-0.475557\pi\)
−0.997053 + 0.0767160i \(0.975557\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1339.20 + 655.789i 1.79517 + 0.879073i
\(747\) 0 0
\(748\) 0 0
\(749\) −568.816 1373.24i −0.759433 1.83343i
\(750\) 0 0
\(751\) 1269.96i 1.69103i 0.533955 + 0.845513i \(0.320705\pi\)
−0.533955 + 0.845513i \(0.679295\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −994.632 411.990i −1.31391 0.544241i −0.387890 0.921706i \(-0.626796\pi\)
−0.926024 + 0.377465i \(0.876796\pi\)
\(758\) 349.337 713.388i 0.460866 0.941145i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(762\) 0 0
\(763\) −362.785 + 875.842i −0.475472 + 1.14789i
\(764\) 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 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(774\) −498.688 + 170.832i −0.644299 + 0.220714i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 405.842 828.779i 0.521648 1.06527i
\(779\) 0 0
\(780\) 0 0
\(781\) 707.960 + 1709.17i 0.906479 + 2.18843i
\(782\) 0 0
\(783\) 0 0
\(784\) −194.463 + 759.500i −0.248039 + 0.968750i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(788\) 724.593 1271.34i 0.919534 1.61337i
\(789\) 0 0
\(790\) 0 0
\(791\) −628.838 + 628.838i −0.794991 + 0.794991i
\(792\) 1540.42 319.815i 1.94497 0.403807i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(798\) 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
\(804\)