Properties

Label 224.3.v.a.13.2
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 13.2
Root \(0.581861 - 1.28897i\) of \(x^{8} + x^{4} + 16\)
Character \(\chi\) \(=\) 224.13
Dual form 224.3.v.a.69.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.125246 + 1.99607i) q^{2} +(-3.96863 - 0.500000i) q^{4} +(4.94975 - 4.94975i) q^{7} +(1.49509 - 7.85905i) q^{8} +(-6.36396 - 6.36396i) q^{9} +O(q^{10})\) \(q+(-0.125246 + 1.99607i) q^{2} +(-3.96863 - 0.500000i) q^{4} +(4.94975 - 4.94975i) q^{7} +(1.49509 - 7.85905i) q^{8} +(-6.36396 - 6.36396i) q^{9} +(-5.22101 - 12.6046i) q^{11} +(9.26013 + 10.5000i) q^{14} +(15.5000 + 3.96863i) q^{16} +(13.5000 - 11.9059i) q^{18} +(25.8137 - 8.84285i) q^{22} +(12.1660 + 12.1660i) q^{23} +(17.6777 - 17.6777i) q^{25} +(-22.1186 + 17.1688i) q^{28} +(22.1916 - 53.5752i) q^{29} +(-9.86299 + 30.4421i) q^{32} +(22.0742 + 28.4382i) q^{36} +(-67.6340 + 28.0149i) q^{37} +(13.9560 + 33.6929i) q^{43} +(14.4179 + 52.6336i) q^{44} +(-25.8080 + 22.7605i) q^{46} -49.0000i q^{49} +(33.0719 + 37.5000i) q^{50} +(-36.5379 - 88.2103i) q^{53} +(-31.5000 - 46.3006i) q^{56} +(104.161 + 51.0061i) q^{58} -63.0000 q^{63} +(-59.5294 - 23.5000i) q^{64} +(-39.7306 + 95.9183i) q^{67} +(59.8665 - 59.8665i) q^{71} +(-59.5294 + 40.5000i) q^{72} +(-47.4490 - 138.511i) q^{74} +(-88.2324 - 36.5471i) q^{77} -23.3317i q^{79} +81.0000i q^{81} +(-69.0014 + 23.6374i) q^{86} +(-106.866 + 22.1871i) q^{88} +(-42.1994 - 54.3654i) q^{92} +(97.8077 + 6.13705i) q^{98} +(-46.9891 + 113.442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 124q^{16} + 108q^{18} + 148q^{22} - 72q^{23} - 232q^{43} + 324q^{44} + 24q^{53} - 252q^{56} - 504q^{63} - 472q^{67} - 108q^{74} - 168q^{77} - 708q^{92} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.125246 + 1.99607i −0.0626229 + 0.998037i
\(3\) 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
\(8\) 1.49509 7.85905i 0.186886 0.982382i
\(9\) −6.36396 6.36396i −0.707107 0.707107i
\(10\) 0 0
\(11\) −5.22101 12.6046i −0.474637 1.14588i −0.962091 0.272727i \(-0.912074\pi\)
0.487454 0.873149i \(-0.337926\pi\)
\(12\) 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
\(22\) 25.8137 8.84285i 1.17335 0.401948i
\(23\) 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
\(29\) 22.1916 53.5752i 0.765227 1.84742i 0.364931 0.931034i \(-0.381093\pi\)
0.400295 0.916386i \(-0.368907\pi\)
\(30\) 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
\(37\) −67.6340 + 28.0149i −1.82795 + 0.757160i −0.858082 + 0.513514i \(0.828344\pi\)
−0.969864 + 0.243646i \(0.921656\pi\)
\(38\) 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
\(43\) 13.9560 + 33.6929i 0.324559 + 0.783555i 0.998978 + 0.0452058i \(0.0143943\pi\)
−0.674419 + 0.738349i \(0.735606\pi\)
\(44\) 14.4179 + 52.6336i 0.327680 + 1.19622i
\(45\) 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
\(53\) −36.5379 88.2103i −0.689394 1.66434i −0.745998 0.665948i \(-0.768027\pi\)
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
\(58\) 104.161 + 51.0061i 1.79587 + 0.879416i
\(59\) 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
\(67\) −39.7306 + 95.9183i −0.592995 + 1.43162i 0.287602 + 0.957750i \(0.407142\pi\)
−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 −0.146082 0.989272i \(-0.546666\pi\)
0.989272 + 0.146082i \(0.0466664\pi\)
\(72\) −59.5294 + 40.5000i −0.826797 + 0.562500i
\(73\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(74\) −47.4490 138.511i −0.641202 1.87177i
\(75\) 0 0
\(76\) 0 0
\(77\) −88.2324 36.5471i −1.14588 0.474637i
\(78\) 0 0
\(79\) 23.3317i 0.295338i −0.989037 0.147669i \(-0.952823\pi\)
0.989037 0.147669i \(-0.0471771\pi\)
\(80\) 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
\(86\) −69.0014 + 23.6374i −0.802342 + 0.274854i
\(87\) 0 0
\(88\) −106.866 + 22.1871i −1.21439 + 0.252126i
\(89\) 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
\(99\) −46.9891 + 113.442i −0.474637 + 1.14588i
\(100\) −78.9949 + 61.3172i −0.789949 + 0.613172i
\(101\) 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
\(106\) 180.651 61.8844i 1.70425 0.583815i
\(107\) 64.6556 + 156.093i 0.604258 + 1.45881i 0.869159 + 0.494533i \(0.164661\pi\)
−0.264901 + 0.964276i \(0.585339\pi\)
\(108\) 0 0
\(109\) 23.1268 + 9.57945i 0.212173 + 0.0878848i 0.486239 0.873826i \(-0.338369\pi\)
−0.274066 + 0.961711i \(0.588369\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 96.3648 57.0774i 0.860400 0.509620i
\(113\) 186.911i 1.65408i −0.562144 0.827040i \(-0.690023\pi\)
0.562144 0.827040i \(-0.309977\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −114.858 + 201.524i −0.990152 + 1.73728i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −46.0580 + 46.0580i −0.380644 + 0.380644i
\(122\) 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 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −186.484 91.3187i −1.39167 0.681483i
\(135\) 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 −0.382683 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
\(144\) −73.3852 123.898i −0.509620 0.860400i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 282.422 77.3638i 1.90825 0.522728i
\(149\) −55.0774 132.969i −0.369647 0.892407i −0.993808 0.111111i \(-0.964559\pi\)
0.624161 0.781296i \(-0.285441\pi\)
\(150\) 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
\(154\) 84.0014 171.541i 0.545464 1.11390i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(158\) 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
\(163\) −72.6583 + 175.413i −0.445756 + 1.07615i 0.528140 + 0.849158i \(0.322890\pi\)
−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
\(172\) −38.5399 140.692i −0.224069 0.817979i
\(173\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(174\) 0 0
\(175\) 175.000i 1.00000i
\(176\) −30.9026 216.092i −0.175583 1.22780i
\(177\) 0 0
\(178\) 0 0
\(179\) 30.5837 + 12.6682i 0.170858 + 0.0707719i 0.466473 0.884535i \(-0.345524\pi\)
−0.295615 + 0.955307i \(0.595524\pi\)
\(180\) 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
\(184\) 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 \(-0.936931\pi\)
−0.980435 + 0.196842i \(0.936931\pi\)
\(192\) 0 0
\(193\) 313.240 1.62300 0.811502 0.584349i \(-0.198650\pi\)
0.811502 + 0.584349i \(0.198650\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −24.5000 + 194.463i −0.125000 + 0.992157i
\(197\) −334.564 + 138.581i −1.69830 + 0.703457i −0.999925 0.0122790i \(-0.996091\pi\)
−0.698371 + 0.715736i \(0.746091\pi\)
\(198\) −220.553 108.002i −1.11390 0.545464i
\(199\) 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
\(203\) −155.341 375.026i −0.765227 1.84742i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 154.848i 0.748058i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 125.038 + 51.7925i 0.592598 + 0.245462i 0.658768 0.752346i \(-0.271078\pi\)
−0.0661700 + 0.997808i \(0.521078\pi\)
\(212\) 100.900 + 368.343i 0.475944 + 1.73747i
\(213\) 0 0
\(214\) −319.670 + 109.508i −1.49379 + 0.511717i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −22.0178 + 44.9631i −0.100999 + 0.206253i
\(219\) 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 0.382683 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
\(232\) −387.872 254.505i −1.67186 1.09700i
\(233\) 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 \(0.5\pi\)
\(242\) −86.1665 97.7037i −0.356060 0.403734i
\(243\) 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
\(253\) 89.8293 216.867i 0.355056 0.857182i
\(254\) −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
\(259\) −196.104 + 473.438i −0.757160 + 1.82795i
\(260\) 0 0
\(261\) −482.177 + 199.724i −1.84742 + 0.765227i
\(262\) 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
\(268\) 205.635 360.798i 0.767296 1.34626i
\(269\) 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
\(274\) −409.054 + 360.752i −1.49290 + 1.31661i
\(275\) −315.116 130.525i −1.14588 0.474637i
\(276\) 0 0
\(277\) 114.018 + 275.264i 0.411617 + 0.993731i 0.984704 + 0.174237i \(0.0557457\pi\)
−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 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(284\) −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 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 119.052 + 573.424i 0.402202 + 1.93724i
\(297\) 0 0
\(298\) 272.313 93.2848i 0.913803 0.313036i
\(299\) 0 0
\(300\) 0 0
\(301\) 235.850 + 97.6923i 0.783555 + 0.324559i
\(302\) −425.321 + 375.097i −1.40835 + 1.24204i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(308\) 331.888 + 189.158i 1.07756 + 0.614149i
\(309\) 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
\(317\) 131.860 318.339i 0.415963 1.00422i −0.567543 0.823344i \(-0.692106\pi\)
0.983505 0.180879i \(-0.0578941\pi\)
\(318\) 0 0
\(319\) −791.158 −2.48012
\(320\) 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
\(326\) −341.037 167.001i −1.04612 0.512273i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −196.256 473.803i −0.592917 1.43143i −0.880673 0.473725i \(-0.842909\pi\)
0.287755 0.957704i \(-0.407091\pi\)
\(332\) 0 0
\(333\) 608.706 + 252.134i 1.82795 + 0.757160i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 608.805i 1.80654i −0.429069 0.903272i \(-0.641158\pi\)
0.429069 0.903272i \(-0.358842\pi\)
\(338\) −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
\(344\) 285.660 59.3074i 0.830406 0.172405i
\(345\) 0 0
\(346\) 0 0
\(347\) 526.326 218.011i 1.51679 0.628275i 0.539844 0.841765i \(-0.318483\pi\)
0.976945 + 0.213490i \(0.0684831\pi\)
\(348\) 0 0
\(349\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(350\) 349.313 + 21.9180i 0.998037 + 0.0626229i
\(351\) 0 0
\(352\) 435.206 34.6192i 1.23638 0.0983500i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −29.1171 + 59.4606i −0.0813326 + 0.166091i
\(359\) 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
\(371\) −617.472 255.765i −1.66434 0.689394i
\(372\) 0 0
\(373\) −194.921 470.580i −0.522576 1.26161i −0.936298 0.351206i \(-0.885772\pi\)
0.413722 0.910403i \(-0.364228\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 162.311 67.2314i 0.428261 0.177392i −0.158132 0.987418i \(-0.550547\pi\)
0.586393 + 0.810026i \(0.300547\pi\)
\(380\) 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
\(387\) 125.604 303.236i 0.324559 0.783555i
\(388\) 0 0
\(389\) 107.794 44.6495i 0.277104 0.114780i −0.239804 0.970821i \(-0.577083\pi\)
0.516908 + 0.856041i \(0.327083\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −385.094 73.2595i −0.982382 0.186886i
\(393\) 0 0
\(394\) −234.715 685.172i −0.595724 1.73901i
\(395\) 0 0
\(396\) 243.203 426.713i 0.614149 1.07756i
\(397\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 344.160 203.848i 0.860400 0.509620i
\(401\) 258.550i 0.644762i 0.946610 + 0.322381i \(0.104483\pi\)
−0.946610 + 0.322381i \(0.895517\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 768.036 263.102i 1.89172 0.648034i
\(407\) 706.236 + 706.236i 1.73522 + 1.73522i
\(408\) 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 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(420\) 0 0
\(421\) −150.159 + 62.1981i −0.356673 + 0.147739i −0.553823 0.832635i \(-0.686832\pi\)
0.197150 + 0.980373i \(0.436832\pi\)
\(422\) −119.042 + 243.099i −0.282090 + 0.576063i
\(423\) 0 0
\(424\) −747.877 + 155.271i −1.76386 + 0.366205i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −178.548 651.801i −0.417168 1.52290i
\(429\) 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
\(436\) −86.9920 49.5807i −0.199523 0.113717i
\(437\) 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
\(443\) 804.148 333.089i 1.81523 0.751894i 0.836129 0.548533i \(-0.184813\pi\)
0.979104 0.203361i \(-0.0651866\pi\)
\(444\) 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 0.482757 0.875754i \(-0.339635\pi\)
−0.875754 + 0.482757i \(0.839635\pi\)
\(458\) 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
\(463\) 925.589i 1.99911i 0.0297960 + 0.999556i \(0.490514\pi\)
−0.0297960 + 0.999556i \(0.509486\pi\)
\(464\) 556.589 742.345i 1.19955 1.59988i
\(465\) 0 0
\(466\) −512.991 + 452.415i −1.10084 + 0.970848i
\(467\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(468\) 0 0
\(469\) 278.115 + 671.428i 0.592995 + 1.43162i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 351.822 351.822i 0.743809 0.743809i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −328.841 + 793.893i −0.689394 + 1.66434i
\(478\) 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
\(484\) 205.816 159.758i 0.425239 0.330078i
\(485\) 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
\(491\) 57.3936 + 138.560i 0.116891 + 0.282200i 0.971487 0.237094i \(-0.0761949\pi\)
−0.854596 + 0.519294i \(0.826195\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 592.648i 1.19245i
\(498\) 0 0
\(499\) 918.343 + 380.390i 1.84037 + 0.762305i 0.954379 + 0.298597i \(0.0965187\pi\)
0.885988 + 0.463708i \(0.153481\pi\)
\(500\) 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
\(506\) 421.632 + 206.468i 0.833265 + 0.408039i
\(507\) 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
\(512\) −273.690 + 432.710i −0.534550 + 0.845137i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −920.456 450.735i −1.77694 0.870145i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(522\) −338.274 987.475i −0.648034 1.89172i
\(523\) 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
\(529\) 232.976i 0.440409i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 694.426 + 455.652i 1.29557 + 0.850097i
\(537\) 0 0
\(538\) 0 0
\(539\) −617.627 + 255.830i −1.14588 + 0.474637i
\(540\) 0 0
\(541\) 370.812 895.219i 0.685420 1.65475i −0.0683919 0.997659i \(-0.521787\pi\)
0.753811 0.657091i \(-0.228213\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −195.402 + 471.743i −0.357225 + 0.862418i 0.638463 + 0.769653i \(0.279571\pi\)
−0.995688 + 0.0927652i \(0.970429\pi\)
\(548\) −668.856 861.686i −1.22054 1.57242i
\(549\) 0 0
\(550\) 300.005 612.647i 0.545464 1.11390i
\(551\) 0 0
\(552\) 0 0
\(553\) −115.486 115.486i −0.208836 0.208836i
\(554\) −563.727 + 193.113i −1.01756 + 0.348579i
\(555\) 0 0
\(556\) 0 0
\(557\) 1027.38 + 425.553i 1.84448 + 0.764010i 0.945021 + 0.327009i \(0.106041\pi\)
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 −0.923880 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 \(0.555122\pi\)
−0.985044 + 0.172306i \(0.944878\pi\)
\(570\) 0 0
\(571\) −1028.45 + 425.998i −1.80114 + 0.746057i −0.815151 + 0.579249i \(0.803346\pi\)
−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
\(583\) −921.094 + 921.094i −1.57992 + 1.57992i
\(584\) 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
\(592\) −1159.51 + 165.817i −1.95863 + 0.280096i
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 152.097 + 555.241i 0.255197 + 0.931613i
\(597\) 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 \(0.750000\pi\)
\(602\) −224.540 + 458.539i −0.372991 + 0.761692i
\(603\) 863.264 357.576i 1.43162 0.592995i
\(604\) −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
\(613\) 240.474 99.6077i 0.392291 0.162492i −0.177814 0.984064i \(-0.556903\pi\)
0.570105 + 0.821572i \(0.306903\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −419.141 + 638.782i −0.680424 + 1.03698i
\(617\) −778.265 778.265i −1.26137 1.26137i −0.950430 0.310939i \(-0.899356\pi\)
−0.310939 0.950430i \(-0.600644\pi\)
\(618\) 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 0.990609 0.136728i \(-0.0436586\pi\)
−0.136728 + 0.990609i \(0.543659\pi\)
\(632\) −183.365 34.8831i −0.290135 0.0551947i
\(633\) 0 0
\(634\) 618.912 + 303.073i 0.976203 + 0.478033i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 99.0893 1579.21i 0.155312 2.47525i
\(639\) −761.976 −1.19245
\(640\) 0 0
\(641\) −1278.19 −1.99406 −0.997030 0.0770186i \(-0.975460\pi\)
−0.997030 + 0.0770186i \(0.975460\pi\)
\(642\) 0 0
\(643\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(644\) −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
\(652\) 376.060 659.818i 0.576779 1.01199i
\(653\) −832.060 344.650i −1.27421 0.527796i −0.359969 0.932964i \(-0.617213\pi\)
−0.914242 + 0.405169i \(0.867213\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 939.078 + 388.979i 1.42501 + 0.590256i 0.956113 0.292999i \(-0.0946533\pi\)
0.468892 + 0.883255i \(0.344653\pi\)
\(660\) 0 0
\(661\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(662\) 970.326 332.399i 1.46575 0.502113i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −579.517 + 1183.44i −0.870145 + 1.77694i
\(667\) 921.779 381.814i 1.38198 0.572434i
\(668\) 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 0.923880 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
\(683\) −293.229 707.917i −0.429325 1.03648i −0.979502 0.201433i \(-0.935440\pi\)
0.550178 0.835048i \(-0.314560\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 514.500 453.746i 0.750000 0.661438i
\(687\) 0 0
\(688\) 82.6042 + 577.626i 0.120064 + 0.839572i
\(689\) 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
\(693\) 328.924 + 794.092i 0.474637 + 1.14588i
\(694\) 369.247 + 1077.89i 0.532056 + 1.55316i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −87.5000 + 694.510i −0.125000 + 0.992157i
\(701\) 167.316 403.936i 0.238682 0.576228i −0.758465 0.651713i \(-0.774051\pi\)
0.997147 + 0.0754851i \(0.0240505\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 14.5947 + 873.040i 0.0207312 + 1.24011i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1067.36 442.115i 1.50545 0.623576i 0.530834 0.847476i \(-0.321879\pi\)
0.974612 + 0.223900i \(0.0718789\pi\)
\(710\) 0 0
\(711\) −148.482 + 148.482i −0.208836 + 0.208836i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −115.041 65.5671i −0.160672 0.0915741i
\(717\) 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
\(725\) −554.789 1339.38i −0.765227 1.84742i
\(726\) 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
\(736\) −490.352 + 250.366i −0.666239 + 0.340171i
\(737\) 1416.45 1.92191
\(738\) 0 0
\(739\) 554.344 1338.31i 0.750128 1.81097i 0.191620 0.981469i \(-0.438626\pi\)
0.558508 0.829499i \(-0.311374\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 587.862 1200.49i 0.792267 1.61791i
\(743\) 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
\(746\) 963.727 330.138i 1.29186 0.442544i
\(747\) 0 0
\(748\) 0 0
\(749\) 1092.65 + 452.590i 1.45881 + 0.604258i
\(750\) 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
\(757\) −3.26865 7.89121i −0.00431790 0.0104243i 0.921706 0.387890i \(-0.126796\pi\)
−0.926024 + 0.377465i \(0.876796\pi\)
\(758\) 113.870 + 332.405i 0.150224 + 0.438529i
\(759\) 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
\(763\) 161.888 67.0561i 0.212173 0.0878848i
\(764\) 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 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(774\) 589.550 + 288.695i 0.761692 + 0.372991i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 75.6231 + 220.756i 0.0972020 + 0.283748i
\(779\) 0 0
\(780\) 0 0
\(781\) −1067.16 442.032i −1.36640 0.565982i
\(782\) 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 \(0.125000\pi\)
\(788\) 1397.05 382.694i 1.77291 0.485653i
\(789\) 0 0
\(790\) 0 0
\(791\) −925.162 925.162i −1.16961 1.16961i
\(792\) 821.291 + 538.895i 1.03698 + 0.680424i
\(793\) 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
\(802\) −516.084 32.3823i −0.643497 0.0403769i
\(803\) 0 0
\(804\) 0