Properties

Label 224.3.v.a.125.1
Level 224
Weight 3
Character 224.125
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 125.1
Root \(-0.581861 + 1.28897i\) of \(x^{8} + x^{4} + 16\)
Character \(\chi\) \(=\) 224.125
Dual form 224.3.v.a.181.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.125246 - 1.99607i) q^{2} +(-3.96863 - 0.500000i) q^{4} +(-4.94975 + 4.94975i) q^{7} +(-1.49509 + 7.85905i) q^{8} +(6.36396 + 6.36396i) q^{9} +O(q^{10})\) \(q+(0.125246 - 1.99607i) q^{2} +(-3.96863 - 0.500000i) q^{4} +(-4.94975 + 4.94975i) q^{7} +(-1.49509 + 7.85905i) q^{8} +(6.36396 + 6.36396i) q^{9} +(-15.9450 + 6.60464i) q^{11} +(9.26013 + 10.5000i) q^{14} +(15.5000 + 3.96863i) q^{16} +(13.5000 - 11.9059i) q^{18} +(11.1863 + 32.6546i) q^{22} +(12.1660 + 12.1660i) q^{23} +(-17.6777 + 17.6777i) q^{25} +(22.1186 - 17.1688i) q^{28} +(-1.02556 - 0.424802i) q^{29} +(9.86299 - 30.4421i) q^{32} +(-22.0742 - 28.4382i) q^{36} +(4.13596 + 9.98508i) q^{37} +(-71.9560 + 29.8052i) q^{43} +(66.5821 - 18.2388i) q^{44} +(25.8080 - 22.7605i) q^{46} -49.0000i q^{49} +(33.0719 + 37.5000i) q^{50} +(42.5379 - 17.6198i) q^{53} +(-31.5000 - 46.3006i) q^{56} +(-0.976384 + 1.99390i) q^{58} -63.0000 q^{63} +(-59.5294 - 23.5000i) q^{64} +(-78.2694 - 32.4202i) q^{67} +(-59.8665 + 59.8665i) q^{71} +(-59.5294 + 40.5000i) q^{72} +(20.4490 - 7.00509i) q^{74} +(46.2324 - 111.615i) q^{77} +23.3317i q^{79} +81.0000i q^{81} +(50.4811 + 147.363i) q^{86} +(-28.0669 - 135.187i) q^{88} +(-42.1994 - 54.3654i) q^{92} +(-97.8077 - 6.13705i) q^{98} +(-143.505 - 59.4417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 124q^{16} + 108q^{18} + 148q^{22} - 72q^{23} - 232q^{43} + 324q^{44} + 24q^{53} - 252q^{56} - 504q^{63} - 472q^{67} - 108q^{74} - 168q^{77} - 708q^{92} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.125246 1.99607i 0.0626229 0.998037i
\(3\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(4\) −3.96863 0.500000i −0.992157 0.125000i
\(5\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(6\) 0 0
\(7\) −4.94975 + 4.94975i −0.707107 + 0.707107i
\(8\) −1.49509 + 7.85905i −0.186886 + 0.982382i
\(9\) 6.36396 + 6.36396i 0.707107 + 0.707107i
\(10\) 0 0
\(11\) −15.9450 + 6.60464i −1.44955 + 0.600421i −0.962091 0.272727i \(-0.912074\pi\)
−0.487454 + 0.873149i \(0.662074\pi\)
\(12\) 0 0
\(13\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(14\) 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 \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 11.1863 + 32.6546i 0.508468 + 1.48430i
\(23\) 12.1660 + 12.1660i 0.528957 + 0.528957i 0.920261 0.391304i \(-0.127976\pi\)
−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
\(28\) 22.1186 17.1688i 0.789949 0.613172i
\(29\) −1.02556 0.424802i −0.0353642 0.0146483i 0.364931 0.931034i \(-0.381093\pi\)
−0.400295 + 0.916386i \(0.631093\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 9.86299 30.4421i 0.308218 0.951316i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −22.0742 28.4382i −0.613172 0.789949i
\(37\) 4.13596 + 9.98508i 0.111783 + 0.269867i 0.969864 0.243646i \(-0.0783436\pi\)
−0.858082 + 0.513514i \(0.828344\pi\)
\(38\) 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
\(43\) −71.9560 + 29.8052i −1.67340 + 0.693143i −0.998978 0.0452058i \(-0.985606\pi\)
−0.674419 + 0.738349i \(0.735606\pi\)
\(44\) 66.5821 18.2388i 1.51323 0.414519i
\(45\) 0 0
\(46\) 25.8080 22.7605i 0.561044 0.494794i
\(47\) 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
\(53\) 42.5379 17.6198i 0.802602 0.332449i 0.0566038 0.998397i \(-0.481973\pi\)
0.745998 + 0.665948i \(0.231973\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −31.5000 46.3006i −0.562500 0.826797i
\(57\) 0 0
\(58\) −0.976384 + 1.99390i −0.0168342 + 0.0343775i
\(59\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(60\) 0 0
\(61\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(62\) 0 0
\(63\) −63.0000 −1.00000
\(64\) −59.5294 23.5000i −0.930147 0.367188i
\(65\) 0 0
\(66\) 0 0
\(67\) −78.2694 32.4202i −1.16820 0.483884i −0.287602 0.957750i \(-0.592858\pi\)
−0.880597 + 0.473866i \(0.842858\pi\)
\(68\) 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 \(0.250000\pi\)
\(74\) 20.4490 7.00509i 0.276338 0.0946634i
\(75\) 0 0
\(76\) 0 0
\(77\) 46.2324 111.615i 0.600421 1.44955i
\(78\) 0 0
\(79\) 23.3317i 0.295338i 0.989037 + 0.147669i \(0.0471771\pi\)
−0.989037 + 0.147669i \(0.952823\pi\)
\(80\) 0 0
\(81\) 81.0000i 1.00000i
\(82\) 0 0
\(83\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 50.4811 + 147.363i 0.586990 + 1.71352i
\(87\) 0 0
\(88\) −28.0669 135.187i −0.318943 1.53622i
\(89\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −42.1994 54.3654i −0.458689 0.590928i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −97.8077 6.13705i −0.998037 0.0626229i
\(99\) −143.505 59.4417i −1.44955 0.600421i
\(100\) 78.9949 61.3172i 0.789949 0.613172i
\(101\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(102\) 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
\(106\) −29.8427 87.1156i −0.281535 0.821845i
\(107\) 121.344 50.2625i 1.13406 0.469743i 0.264901 0.964276i \(-0.414661\pi\)
0.869159 + 0.494533i \(0.164661\pi\)
\(108\) 0 0
\(109\) 82.8732 200.074i 0.760304 1.83554i 0.274066 0.961711i \(-0.411631\pi\)
0.486239 0.873826i \(-0.338369\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −96.3648 + 57.0774i −0.860400 + 0.509620i
\(113\) 186.911i 1.65408i 0.562144 + 0.827040i \(0.309977\pi\)
−0.562144 + 0.827040i \(0.690023\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 3.85768 + 2.19866i 0.0332558 + 0.0189540i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 125.062 125.062i 1.03357 1.03357i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −7.89049 + 125.753i −0.0626229 + 0.998037i
\(127\) 253.992 1.99994 0.999969 0.00787402i \(-0.00250640\pi\)
0.999969 + 0.00787402i \(0.00250640\pi\)
\(128\) −54.3636 + 115.882i −0.424715 + 0.905327i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −74.5161 + 152.171i −0.556090 + 1.13560i
\(135\) 0 0
\(136\) 0 0
\(137\) 192.830 + 192.830i 1.40752 + 1.40752i 0.772482 + 0.635036i \(0.219015\pi\)
0.635036 + 0.772482i \(0.280985\pi\)
\(138\) 0 0
\(139\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 112.000 + 126.996i 0.788732 + 0.894338i
\(143\) 0 0
\(144\) 73.3852 + 123.898i 0.509620 + 0.860400i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −11.4215 41.6951i −0.0771725 0.281723i
\(149\) 241.077 99.8575i 1.61797 0.670185i 0.624161 0.781296i \(-0.285441\pi\)
0.993808 + 0.111111i \(0.0354409\pi\)
\(150\) 0 0
\(151\) 200.498 + 200.498i 1.32780 + 1.32780i 0.907285 + 0.420517i \(0.138151\pi\)
0.420517 + 0.907285i \(0.361849\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −217.001 106.263i −1.40910 0.690018i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(158\) 46.5719 + 2.92220i 0.294759 + 0.0184950i
\(159\) 0 0
\(160\) 0 0
\(161\) −120.437 −0.748058
\(162\) 161.682 + 10.1449i 0.998037 + 0.0626229i
\(163\) −244.832 101.413i −1.50204 0.622164i −0.528140 0.849158i \(-0.677110\pi\)
−0.973896 + 0.226994i \(0.927110\pi\)
\(164\) 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
\(172\) 300.469 82.3076i 1.74691 0.478532i
\(173\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(174\) 0 0
\(175\) 175.000i 1.00000i
\(176\) −273.359 + 39.0921i −1.55318 + 0.222114i
\(177\) 0 0
\(178\) 0 0
\(179\) −136.414 + 329.332i −0.762088 + 1.83984i −0.295615 + 0.955307i \(0.595524\pi\)
−0.466473 + 0.884535i \(0.654476\pi\)
\(180\) 0 0
\(181\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −113.803 + 77.4240i −0.618492 + 0.420783i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 374.526 1.96087 0.980435 0.196842i \(-0.0630686\pi\)
0.980435 + 0.196842i \(0.0630686\pi\)
\(192\) 0 0
\(193\) −313.240 −1.62300 −0.811502 0.584349i \(-0.801350\pi\)
−0.811502 + 0.584349i \(0.801350\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −24.5000 + 194.463i −0.125000 + 0.992157i
\(197\) 59.4061 + 143.419i 0.301554 + 0.728015i 0.999925 + 0.0122790i \(0.00390863\pi\)
−0.698371 + 0.715736i \(0.746091\pi\)
\(198\) −136.623 + 279.002i −0.690018 + 1.40910i
\(199\) 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
\(203\) 7.17894 2.97361i 0.0353642 0.0146483i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 154.848i 0.748058i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 152.962 369.283i 0.724938 1.75015i 0.0661700 0.997808i \(-0.478922\pi\)
0.658768 0.752346i \(-0.271078\pi\)
\(212\) −177.627 + 48.6574i −0.837863 + 0.229516i
\(213\) 0 0
\(214\) −85.1298 248.508i −0.397803 1.16125i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −388.982 190.479i −1.78432 0.873759i
\(219\) 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
\(226\) 373.088 + 23.4098i 1.65083 + 0.103583i
\(227\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(228\) 0 0
\(229\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.87185 7.42484i 0.0209994 0.0320036i
\(233\) 241.826 + 241.826i 1.03788 + 1.03788i 0.999254 + 0.0386266i \(0.0122983\pi\)
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 \(0.5\pi\)
\(242\) −233.969 265.296i −0.966816 1.09627i
\(243\) 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 \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(252\) 250.023 + 31.5000i 0.992157 + 0.125000i
\(253\) −274.339 113.635i −1.08434 0.449150i
\(254\) 31.8115 506.987i 0.125242 1.99601i
\(255\) 0 0
\(256\) 224.500 + 123.027i 0.876953 + 0.480576i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −69.8956 28.9517i −0.269867 0.111783i
\(260\) 0 0
\(261\) −3.82322 9.23007i −0.0146483 0.0353642i
\(262\) 0 0
\(263\) −352.139 + 352.139i −1.33893 + 1.33893i −0.441837 + 0.897095i \(0.645673\pi\)
−0.897095 + 0.441837i \(0.854327\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 294.412 + 167.798i 1.09855 + 0.626114i
\(269\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 409.054 360.752i 1.49290 1.31661i
\(275\) 165.116 398.625i 0.600421 1.44955i
\(276\) 0 0
\(277\) −431.508 + 178.736i −1.55779 + 0.645258i −0.984704 0.174237i \(-0.944254\pi\)
−0.573087 + 0.819495i \(0.694254\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −218.158 + 218.158i −0.776363 + 0.776363i −0.979210 0.202847i \(-0.934981\pi\)
0.202847 + 0.979210i \(0.434981\pi\)
\(282\) 0 0
\(283\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(284\) 267.521 207.655i 0.941976 0.731178i
\(285\) 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 \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −84.6569 + 17.5761i −0.286003 + 0.0593787i
\(297\) 0 0
\(298\) −169.129 493.715i −0.567547 1.65676i
\(299\) 0 0
\(300\) 0 0
\(301\) 208.636 503.692i 0.693143 1.67340i
\(302\) 425.321 375.097i 1.40835 1.24204i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(308\) −239.287 + 419.842i −0.776905 + 1.36312i
\(309\) 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
\(316\) 11.6659 92.5950i 0.0369173 0.293022i
\(317\) −491.682 203.661i −1.55105 0.642465i −0.567543 0.823344i \(-0.692106\pi\)
−0.983505 + 0.180879i \(0.942106\pi\)
\(318\) 0 0
\(319\) 19.1583 0.0600573
\(320\) 0 0
\(321\) 0 0
\(322\) −15.0843 + 240.402i −0.0468456 + 0.746590i
\(323\) 0 0
\(324\) 40.5000 321.459i 0.125000 0.992157i
\(325\) 0 0
\(326\) −233.091 + 476.001i −0.715004 + 1.46013i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 386.750 160.197i 1.16843 0.483979i 0.287755 0.957704i \(-0.407091\pi\)
0.880673 + 0.473725i \(0.157091\pi\)
\(332\) 0 0
\(333\) −37.2236 + 89.8658i −0.111783 + 0.269867i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 608.805i 1.80654i 0.429069 + 0.903272i \(0.358842\pi\)
−0.429069 + 0.903272i \(0.641158\pi\)
\(338\) −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
\(344\) −126.660 610.068i −0.368196 1.77345i
\(345\) 0 0
\(346\) 0 0
\(347\) 151.674 + 366.173i 0.437101 + 1.05525i 0.976945 + 0.213490i \(0.0684831\pi\)
−0.539844 + 0.841765i \(0.681517\pi\)
\(348\) 0 0
\(349\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(350\) −349.313 21.9180i −0.998037 0.0626229i
\(351\) 0 0
\(352\) 43.7937 + 550.541i 0.124414 + 1.56404i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 640.286 + 313.539i 1.78851 + 0.875808i
\(359\) 178.838 178.838i 0.498156 0.498156i −0.412708 0.910864i \(-0.635417\pi\)
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 \(0.5\pi\)
\(368\) 140.291 + 236.856i 0.381225 + 0.643629i
\(369\) 0 0
\(370\) 0 0
\(371\) −123.338 + 297.765i −0.332449 + 0.802602i
\(372\) 0 0
\(373\) −503.558 + 208.580i −1.35002 + 0.559197i −0.936298 0.351206i \(-0.885772\pi\)
−0.413722 + 0.910403i \(0.635772\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 282.175 + 681.231i 0.744526 + 1.79744i 0.586393 + 0.810026i \(0.300547\pi\)
0.158132 + 0.987418i \(0.449453\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 46.9078 747.582i 0.122795 1.95702i
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −39.2320 + 625.250i −0.101637 + 1.61982i
\(387\) −647.604 268.247i −1.67340 0.693143i
\(388\) 0 0
\(389\) 294.361 + 710.650i 0.756711 + 1.82686i 0.516908 + 0.856041i \(0.327083\pi\)
0.239804 + 0.970821i \(0.422917\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 385.094 + 73.2595i 0.982382 + 0.186886i
\(393\) 0 0
\(394\) 293.715 100.616i 0.745470 0.255371i
\(395\) 0 0
\(396\) 539.797 + 307.654i 1.36312 + 0.776905i
\(397\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −344.160 + 203.848i −0.860400 + 0.509620i
\(401\) 258.550i 0.644762i −0.946610 0.322381i \(-0.895517\pi\)
0.946610 0.322381i \(-0.104483\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) −5.03642 14.7021i −0.0124050 0.0362122i
\(407\) −131.896 131.896i −0.324068 0.324068i
\(408\) 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
\(414\) 309.088 + 19.3941i 0.746590 + 0.0468456i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(420\) 0 0
\(421\) 316.159 + 763.276i 0.750972 + 1.81301i 0.553823 + 0.832635i \(0.313168\pi\)
0.197150 + 0.980373i \(0.436832\pi\)
\(422\) −717.958 351.574i −1.70132 0.833115i
\(423\) 0 0
\(424\) 74.8767 + 360.651i 0.176596 + 0.850591i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −506.702 + 138.801i −1.18388 + 0.324301i
\(429\) 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
\(436\) −428.929 + 752.581i −0.983783 + 1.72610i
\(437\) 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
\(443\) −63.3378 152.911i −0.142975 0.345171i 0.836129 0.548533i \(-0.184813\pi\)
−0.979104 + 0.203361i \(0.934813\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 410.975 178.336i 0.917354 0.398072i
\(449\) −84.6640 −0.188561 −0.0942807 0.995546i \(-0.530055\pi\)
−0.0942807 + 0.995546i \(0.530055\pi\)
\(450\) −28.1803 + 449.117i −0.0626229 + 0.998037i
\(451\) 0 0
\(452\) 93.4555 741.780i 0.206760 1.64111i
\(453\) 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 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(462\) 0 0
\(463\) 925.589i 1.99911i −0.0297960 0.999556i \(-0.509486\pi\)
0.0297960 0.999556i \(-0.490514\pi\)
\(464\) −14.2103 10.6545i −0.0306257 0.0229623i
\(465\) 0 0
\(466\) 512.991 452.415i 1.10084 0.970848i
\(467\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(468\) 0 0
\(469\) 547.885 226.942i 1.16820 0.483884i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 950.487 950.487i 2.00949 2.00949i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 382.841 + 158.578i 0.802602 + 0.332449i
\(478\) −844.979 53.0191i −1.76774 0.110919i
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −558.855 + 433.793i −1.15466 + 0.896267i
\(485\) 0 0
\(486\) 0 0
\(487\) −643.486 + 643.486i −1.32133 + 1.32133i −0.408624 + 0.912703i \(0.633991\pi\)
−0.912703 + 0.408624i \(0.866009\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 896.606 371.387i 1.82608 0.756388i 0.854596 0.519294i \(-0.173805\pi\)
0.971487 0.237094i \(-0.0761949\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 592.648i 1.19245i
\(498\) 0 0
\(499\) 34.1272 82.3903i 0.0683911 0.165111i −0.885988 0.463708i \(-0.846519\pi\)
0.954379 + 0.298597i \(0.0965187\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(504\) 94.1907 495.120i 0.186886 0.982382i
\(505\) 0 0
\(506\) −261.184 + 533.369i −0.516173 + 1.05409i
\(507\) 0 0
\(508\) −1008.00 126.996i −1.98425 0.249992i
\(509\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 273.690 432.710i 0.534550 0.845137i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −66.5439 + 135.891i −0.128463 + 0.262337i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(522\) −18.9027 + 6.47540i −0.0362122 + 0.0124050i
\(523\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 658.792 + 747.000i 1.25246 + 1.42015i
\(527\) 0 0
\(528\) 0 0
\(529\) 232.976i 0.440409i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 371.812 566.652i 0.693679 1.05719i
\(537\) 0 0
\(538\) 0 0
\(539\) 323.627 + 781.305i 0.600421 + 1.44955i
\(540\) 0 0
\(541\) −444.812 184.247i −0.822203 0.340568i −0.0683919 0.997659i \(-0.521787\pi\)
−0.753811 + 0.657091i \(0.771787\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 893.881 + 370.257i 1.63415 + 0.676887i 0.995688 0.0927652i \(-0.0295706\pi\)
0.638463 + 0.769653i \(0.279571\pi\)
\(548\) −668.856 861.686i −1.22054 1.57242i
\(549\) 0 0
\(550\) −775.005 379.510i −1.40910 0.690018i
\(551\) 0 0
\(552\) 0 0
\(553\) −115.486 115.486i −0.208836 0.208836i
\(554\) 302.727 + 883.708i 0.546438 + 1.59514i
\(555\) 0 0
\(556\) 0 0
\(557\) −25.3767 + 61.2649i −0.0455597 + 0.109991i −0.945021 0.327009i \(-0.893959\pi\)
0.899461 + 0.437000i \(0.143959\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 408.137 + 462.783i 0.726222 + 0.823458i
\(563\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(564\) 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
\(571\) −97.5490 235.504i −0.170839 0.412442i 0.815151 0.579249i \(-0.196654\pi\)
−0.985989 + 0.166807i \(0.946654\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −430.133 −0.748058
\(576\) −229.290 528.396i −0.398072 0.917354i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −36.1960 + 576.866i −0.0626229 + 0.998037i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −561.895 + 561.895i −0.963799 + 0.963799i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 24.4803 + 171.183i 0.0413518 + 0.289160i
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1006.68 + 275.759i −1.68905 + 0.462682i
\(597\) 0 0
\(598\) 0 0
\(599\) −123.037 123.037i −0.205403 0.205403i 0.596907 0.802310i \(-0.296396\pi\)
−0.802310 + 0.596907i \(0.796396\pi\)
\(600\) 0 0
\(601\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(602\) −979.277 479.539i −1.62671 0.796576i
\(603\) −291.782 704.424i −0.483884 1.16820i
\(604\) −695.453 895.951i −1.15141 1.48336i
\(605\) 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
\(613\) −458.474 1106.85i −0.747919 1.80564i −0.570105 0.821572i \(-0.693097\pi\)
−0.177814 0.984064i \(-0.556903\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 808.066 + 530.218i 1.31180 + 0.860743i
\(617\) 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 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(620\) 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 \(0.956341\pi\)
\(632\) −183.365 34.8831i −0.290135 0.0551947i
\(633\) 0 0
\(634\) −468.105 + 955.927i −0.738335 + 1.50777i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 2.39949 38.2413i 0.00376096 0.0599394i
\(639\) −761.976 −1.19245
\(640\) 0 0
\(641\) 1278.19 1.99406 0.997030 0.0770186i \(-0.0245401\pi\)
0.997030 + 0.0770186i \(0.0245401\pi\)
\(642\) 0 0
\(643\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(644\) 477.971 + 60.2187i 0.742191 + 0.0935073i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(648\) −636.583 121.102i −0.982382 0.186886i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 920.940 + 524.885i 1.41248 + 0.805038i
\(653\) −361.940 + 873.801i −0.554273 + 1.33813i 0.359969 + 0.932964i \(0.382787\pi\)
−0.914242 + 0.405169i \(0.867213\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −321.078 + 775.152i −0.487220 + 1.17625i 0.468892 + 0.883255i \(0.344653\pi\)
−0.956113 + 0.292999i \(0.905347\pi\)
\(660\) 0 0
\(661\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(662\) −271.326 792.045i −0.409859 1.19644i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 174.717 + 85.5564i 0.262337 + 0.128463i
\(667\) −7.30886 17.6452i −0.0109578 0.0264545i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1269.96 −1.88701 −0.943507 0.331352i \(-0.892495\pi\)
−0.943507 + 0.331352i \(0.892495\pi\)
\(674\) 1215.22 + 76.2503i 1.80300 + 0.113131i
\(675\) 0 0
\(676\) 414.505 + 534.006i 0.613172 + 0.789949i
\(677\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1044.77 + 432.758i −1.52968 + 0.633614i −0.979502 0.201433i \(-0.935440\pi\)
−0.550178 + 0.835048i \(0.685440\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 514.500 453.746i 0.750000 0.661438i
\(687\) 0 0
\(688\) −1233.60 + 176.413i −1.79303 + 0.256415i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(692\) 0 0
\(693\) 1004.53 416.092i 1.44955 0.600421i
\(694\) 749.906 256.891i 1.08056 0.370160i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −87.5000 + 694.510i −0.125000 + 0.992157i
\(701\) 1230.68 + 509.766i 1.75561 + 0.727198i 0.997147 + 0.0754851i \(0.0240505\pi\)
0.758465 + 0.651713i \(0.225949\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1104.41 18.4625i 1.56876 0.0262251i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 314.639 + 759.606i 0.443778 + 1.07138i 0.974612 + 0.223900i \(0.0718789\pi\)
−0.530834 + 0.847476i \(0.678121\pi\)
\(710\) 0 0
\(711\) −148.482 + 148.482i −0.208836 + 0.208836i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 706.041 1238.79i 0.986091 1.73015i
\(717\) 0 0
\(718\) −334.575 379.373i −0.465982 0.528374i
\(719\) 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
\(725\) 25.6391 10.6201i 0.0353642 0.0146483i
\(726\) 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 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 490.352 250.366i 0.666239 0.340171i
\(737\) 1462.13 1.98389
\(738\) 0 0
\(739\) 271.130 + 112.306i 0.366888 + 0.151970i 0.558508 0.829499i \(-0.311374\pi\)
−0.191620 + 0.981469i \(0.561374\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 578.914 + 283.487i 0.780208 + 0.382057i
\(743\) 797.810 797.810i 1.07377 1.07377i 0.0767160 0.997053i \(-0.475557\pi\)
0.997053 0.0767160i \(-0.0244435\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 353.273 + 1031.26i 0.473557 + 1.38239i
\(747\) 0 0
\(748\) 0 0
\(749\) −351.837 + 849.410i −0.469743 + 1.13406i
\(750\) 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
\(757\) −1398.73 + 579.373i −1.84773 + 0.765355i −0.921706 + 0.387890i \(0.873204\pi\)
−0.926024 + 0.377465i \(0.876796\pi\)
\(758\) 1395.13 477.922i 1.84054 0.630503i
\(759\) 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
\(763\) 580.112 + 1400.51i 0.760304 + 1.83554i
\(764\) −1486.35 187.263i −1.94549 0.245109i
\(765\) 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
\(772\) 1243.13 + 156.620i 1.61028 + 0.202876i
\(773\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(774\) −616.550 + 1259.07i −0.796576 + 1.62671i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 1455.38 498.560i 1.87066 0.640823i
\(779\) 0 0
\(780\) 0 0
\(781\) 559.175 1349.97i 0.715973 1.72851i
\(782\) 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 \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(788\) −164.051 598.879i −0.208187 0.759999i
\(789\) 0 0
\(790\) 0 0
\(791\) −925.162 925.162i −1.16961 1.16961i
\(792\) 681.709 1038.94i 0.860743 1.31180i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 363.791 + 712.500i 0.454739 + 0.890625i
\(801\) 0 0
\(802\) −516.084 32.3823i −0.643497 0.0403769i
\(803\) 0 0
\(804\)