Properties

Label 1200.3.bg.f.193.1
Level $1200$
Weight $3$
Character 1200.193
Analytic conductor $32.698$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1200.bg (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.6976317232\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 600)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 193.1
Root \(-1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1200.193
Dual form 1200.3.bg.f.1057.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 1.22474i) q^{3} +(-0.775255 + 0.775255i) q^{7} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.22474 - 1.22474i) q^{3} +(-0.775255 + 0.775255i) q^{7} +3.00000i q^{9} -2.89898 q^{11} +(5.87628 + 5.87628i) q^{13} +(4.44949 - 4.44949i) q^{17} +0.101021i q^{19} +1.89898 q^{21} +(-25.3485 - 25.3485i) q^{23} +(3.67423 - 3.67423i) q^{27} +32.2929i q^{29} +3.69694 q^{31} +(3.55051 + 3.55051i) q^{33} +(42.6969 - 42.6969i) q^{37} -14.3939i q^{39} -12.8990 q^{41} +(-49.2702 - 49.2702i) q^{43} +(-2.85357 + 2.85357i) q^{47} +47.7980i q^{49} -10.8990 q^{51} +(-13.1918 - 13.1918i) q^{53} +(0.123724 - 0.123724i) q^{57} -76.3837i q^{59} -103.788 q^{61} +(-2.32577 - 2.32577i) q^{63} +(-47.6288 + 47.6288i) q^{67} +62.0908i q^{69} -29.7071 q^{71} +(3.50510 + 3.50510i) q^{73} +(2.24745 - 2.24745i) q^{77} +87.7980i q^{79} -9.00000 q^{81} +(-81.7321 - 81.7321i) q^{83} +(39.5505 - 39.5505i) q^{87} +96.5857i q^{89} -9.11123 q^{91} +(-4.52781 - 4.52781i) q^{93} +(54.2804 - 54.2804i) q^{97} -8.69694i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{7} + O(q^{10}) \) \( 4 q - 8 q^{7} + 8 q^{11} + 48 q^{13} + 8 q^{17} - 12 q^{21} - 72 q^{23} - 44 q^{31} + 24 q^{33} + 112 q^{37} - 32 q^{41} - 104 q^{43} - 80 q^{47} - 24 q^{51} + 104 q^{53} - 24 q^{57} - 180 q^{61} - 24 q^{63} - 264 q^{67} - 256 q^{71} + 112 q^{73} - 40 q^{77} - 36 q^{81} + 16 q^{83} + 168 q^{87} - 252 q^{91} - 72 q^{93} + 320 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).

\(n\) \(401\) \(577\) \(751\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.22474 1.22474i −0.408248 0.408248i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.775255 + 0.775255i −0.110751 + 0.110751i −0.760311 0.649560i \(-0.774953\pi\)
0.649560 + 0.760311i \(0.274953\pi\)
\(8\) 0 0
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) −2.89898 −0.263544 −0.131772 0.991280i \(-0.542067\pi\)
−0.131772 + 0.991280i \(0.542067\pi\)
\(12\) 0 0
\(13\) 5.87628 + 5.87628i 0.452021 + 0.452021i 0.896025 0.444004i \(-0.146442\pi\)
−0.444004 + 0.896025i \(0.646442\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.44949 4.44949i 0.261735 0.261735i −0.564024 0.825759i \(-0.690747\pi\)
0.825759 + 0.564024i \(0.190747\pi\)
\(18\) 0 0
\(19\) 0.101021i 0.00531687i 0.999996 + 0.00265843i \(0.000846207\pi\)
−0.999996 + 0.00265843i \(0.999154\pi\)
\(20\) 0 0
\(21\) 1.89898 0.0904276
\(22\) 0 0
\(23\) −25.3485 25.3485i −1.10211 1.10211i −0.994156 0.107951i \(-0.965571\pi\)
−0.107951 0.994156i \(-0.534429\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) 0 0
\(29\) 32.2929i 1.11355i 0.830664 + 0.556773i \(0.187961\pi\)
−0.830664 + 0.556773i \(0.812039\pi\)
\(30\) 0 0
\(31\) 3.69694 0.119256 0.0596280 0.998221i \(-0.481009\pi\)
0.0596280 + 0.998221i \(0.481009\pi\)
\(32\) 0 0
\(33\) 3.55051 + 3.55051i 0.107591 + 0.107591i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 42.6969 42.6969i 1.15397 1.15397i 0.168222 0.985749i \(-0.446197\pi\)
0.985749 0.168222i \(-0.0538026\pi\)
\(38\) 0 0
\(39\) 14.3939i 0.369074i
\(40\) 0 0
\(41\) −12.8990 −0.314609 −0.157305 0.987550i \(-0.550280\pi\)
−0.157305 + 0.987550i \(0.550280\pi\)
\(42\) 0 0
\(43\) −49.2702 49.2702i −1.14582 1.14582i −0.987367 0.158451i \(-0.949350\pi\)
−0.158451 0.987367i \(-0.550650\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.85357 + 2.85357i −0.0607143 + 0.0607143i −0.736812 0.676098i \(-0.763670\pi\)
0.676098 + 0.736812i \(0.263670\pi\)
\(48\) 0 0
\(49\) 47.7980i 0.975469i
\(50\) 0 0
\(51\) −10.8990 −0.213705
\(52\) 0 0
\(53\) −13.1918 13.1918i −0.248903 0.248903i 0.571618 0.820520i \(-0.306316\pi\)
−0.820520 + 0.571618i \(0.806316\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.123724 0.123724i 0.00217060 0.00217060i
\(58\) 0 0
\(59\) 76.3837i 1.29464i −0.762219 0.647319i \(-0.775890\pi\)
0.762219 0.647319i \(-0.224110\pi\)
\(60\) 0 0
\(61\) −103.788 −1.70144 −0.850719 0.525620i \(-0.823833\pi\)
−0.850719 + 0.525620i \(0.823833\pi\)
\(62\) 0 0
\(63\) −2.32577 2.32577i −0.0369169 0.0369169i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −47.6288 + 47.6288i −0.710878 + 0.710878i −0.966719 0.255841i \(-0.917648\pi\)
0.255841 + 0.966719i \(0.417648\pi\)
\(68\) 0 0
\(69\) 62.0908i 0.899867i
\(70\) 0 0
\(71\) −29.7071 −0.418410 −0.209205 0.977872i \(-0.567088\pi\)
−0.209205 + 0.977872i \(0.567088\pi\)
\(72\) 0 0
\(73\) 3.50510 + 3.50510i 0.0480151 + 0.0480151i 0.730707 0.682692i \(-0.239191\pi\)
−0.682692 + 0.730707i \(0.739191\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.24745 2.24745i 0.0291876 0.0291876i
\(78\) 0 0
\(79\) 87.7980i 1.11137i 0.831394 + 0.555683i \(0.187543\pi\)
−0.831394 + 0.555683i \(0.812457\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) −81.7321 81.7321i −0.984725 0.984725i 0.0151605 0.999885i \(-0.495174\pi\)
−0.999885 + 0.0151605i \(0.995174\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 39.5505 39.5505i 0.454604 0.454604i
\(88\) 0 0
\(89\) 96.5857i 1.08523i 0.839981 + 0.542616i \(0.182566\pi\)
−0.839981 + 0.542616i \(0.817434\pi\)
\(90\) 0 0
\(91\) −9.11123 −0.100123
\(92\) 0 0
\(93\) −4.52781 4.52781i −0.0486861 0.0486861i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 54.2804 54.2804i 0.559591 0.559591i −0.369600 0.929191i \(-0.620505\pi\)
0.929191 + 0.369600i \(0.120505\pi\)
\(98\) 0 0
\(99\) 8.69694i 0.0878479i
\(100\) 0 0
\(101\) −50.5153 −0.500152 −0.250076 0.968226i \(-0.580456\pi\)
−0.250076 + 0.968226i \(0.580456\pi\)
\(102\) 0 0
\(103\) −26.2020 26.2020i −0.254389 0.254389i 0.568378 0.822767i \(-0.307571\pi\)
−0.822767 + 0.568378i \(0.807571\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.48469 + 7.48469i −0.0699504 + 0.0699504i −0.741216 0.671266i \(-0.765751\pi\)
0.671266 + 0.741216i \(0.265751\pi\)
\(108\) 0 0
\(109\) 94.5755i 0.867665i −0.900993 0.433833i \(-0.857161\pi\)
0.900993 0.433833i \(-0.142839\pi\)
\(110\) 0 0
\(111\) −104.586 −0.942214
\(112\) 0 0
\(113\) −89.9796 89.9796i −0.796280 0.796280i 0.186227 0.982507i \(-0.440374\pi\)
−0.982507 + 0.186227i \(0.940374\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −17.6288 + 17.6288i −0.150674 + 0.150674i
\(118\) 0 0
\(119\) 6.89898i 0.0579746i
\(120\) 0 0
\(121\) −112.596 −0.930545
\(122\) 0 0
\(123\) 15.7980 + 15.7980i 0.128439 + 0.128439i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −37.3031 + 37.3031i −0.293725 + 0.293725i −0.838550 0.544825i \(-0.816596\pi\)
0.544825 + 0.838550i \(0.316596\pi\)
\(128\) 0 0
\(129\) 120.687i 0.935556i
\(130\) 0 0
\(131\) −192.677 −1.47081 −0.735407 0.677626i \(-0.763009\pi\)
−0.735407 + 0.677626i \(0.763009\pi\)
\(132\) 0 0
\(133\) −0.0783167 0.0783167i −0.000588847 0.000588847i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −165.328 + 165.328i −1.20677 + 1.20677i −0.234708 + 0.972066i \(0.575413\pi\)
−0.972066 + 0.234708i \(0.924587\pi\)
\(138\) 0 0
\(139\) 256.747i 1.84710i 0.383478 + 0.923550i \(0.374726\pi\)
−0.383478 + 0.923550i \(0.625274\pi\)
\(140\) 0 0
\(141\) 6.98979 0.0495730
\(142\) 0 0
\(143\) −17.0352 17.0352i −0.119127 0.119127i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 58.5403 58.5403i 0.398233 0.398233i
\(148\) 0 0
\(149\) 192.788i 1.29388i −0.762542 0.646939i \(-0.776049\pi\)
0.762542 0.646939i \(-0.223951\pi\)
\(150\) 0 0
\(151\) −98.9092 −0.655028 −0.327514 0.944846i \(-0.606211\pi\)
−0.327514 + 0.944846i \(0.606211\pi\)
\(152\) 0 0
\(153\) 13.3485 + 13.3485i 0.0872449 + 0.0872449i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 103.452 103.452i 0.658929 0.658929i −0.296198 0.955127i \(-0.595719\pi\)
0.955127 + 0.296198i \(0.0957188\pi\)
\(158\) 0 0
\(159\) 32.3133i 0.203228i
\(160\) 0 0
\(161\) 39.3031 0.244118
\(162\) 0 0
\(163\) 19.1339 + 19.1339i 0.117386 + 0.117386i 0.763360 0.645974i \(-0.223548\pi\)
−0.645974 + 0.763360i \(0.723548\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 96.6969 96.6969i 0.579024 0.579024i −0.355611 0.934634i \(-0.615727\pi\)
0.934634 + 0.355611i \(0.115727\pi\)
\(168\) 0 0
\(169\) 99.9388i 0.591354i
\(170\) 0 0
\(171\) −0.303062 −0.00177229
\(172\) 0 0
\(173\) −180.136 180.136i −1.04125 1.04125i −0.999112 0.0421380i \(-0.986583\pi\)
−0.0421380 0.999112i \(-0.513417\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −93.5505 + 93.5505i −0.528534 + 0.528534i
\(178\) 0 0
\(179\) 134.000i 0.748603i −0.927307 0.374302i \(-0.877882\pi\)
0.927307 0.374302i \(-0.122118\pi\)
\(180\) 0 0
\(181\) −171.586 −0.947987 −0.473994 0.880528i \(-0.657188\pi\)
−0.473994 + 0.880528i \(0.657188\pi\)
\(182\) 0 0
\(183\) 127.114 + 127.114i 0.694609 + 0.694609i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −12.8990 + 12.8990i −0.0689785 + 0.0689785i
\(188\) 0 0
\(189\) 5.69694i 0.0301425i
\(190\) 0 0
\(191\) −26.2724 −0.137552 −0.0687760 0.997632i \(-0.521909\pi\)
−0.0687760 + 0.997632i \(0.521909\pi\)
\(192\) 0 0
\(193\) −74.1237 74.1237i −0.384061 0.384061i 0.488502 0.872563i \(-0.337543\pi\)
−0.872563 + 0.488502i \(0.837543\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −47.7526 + 47.7526i −0.242399 + 0.242399i −0.817842 0.575443i \(-0.804830\pi\)
0.575443 + 0.817842i \(0.304830\pi\)
\(198\) 0 0
\(199\) 355.454i 1.78620i 0.449857 + 0.893101i \(0.351475\pi\)
−0.449857 + 0.893101i \(0.648525\pi\)
\(200\) 0 0
\(201\) 116.666 0.580429
\(202\) 0 0
\(203\) −25.0352 25.0352i −0.123326 0.123326i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 76.0454 76.0454i 0.367369 0.367369i
\(208\) 0 0
\(209\) 0.292856i 0.00140123i
\(210\) 0 0
\(211\) 145.474 0.689453 0.344726 0.938703i \(-0.387972\pi\)
0.344726 + 0.938703i \(0.387972\pi\)
\(212\) 0 0
\(213\) 36.3837 + 36.3837i 0.170815 + 0.170815i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −2.86607 + 2.86607i −0.0132077 + 0.0132077i
\(218\) 0 0
\(219\) 8.58571i 0.0392042i
\(220\) 0 0
\(221\) 52.2929 0.236619
\(222\) 0 0
\(223\) 230.351 + 230.351i 1.03296 + 1.03296i 0.999438 + 0.0335252i \(0.0106734\pi\)
0.0335252 + 0.999438i \(0.489327\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −40.4745 + 40.4745i −0.178302 + 0.178302i −0.790615 0.612313i \(-0.790239\pi\)
0.612313 + 0.790615i \(0.290239\pi\)
\(228\) 0 0
\(229\) 210.192i 0.917868i −0.888470 0.458934i \(-0.848231\pi\)
0.888470 0.458934i \(-0.151769\pi\)
\(230\) 0 0
\(231\) −5.50510 −0.0238316
\(232\) 0 0
\(233\) −296.384 296.384i −1.27203 1.27203i −0.945020 0.327013i \(-0.893958\pi\)
−0.327013 0.945020i \(-0.606042\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 107.530 107.530i 0.453714 0.453714i
\(238\) 0 0
\(239\) 89.3031i 0.373653i −0.982393 0.186826i \(-0.940180\pi\)
0.982393 0.186826i \(-0.0598202\pi\)
\(240\) 0 0
\(241\) 120.616 0.500483 0.250241 0.968183i \(-0.419490\pi\)
0.250241 + 0.968183i \(0.419490\pi\)
\(242\) 0 0
\(243\) 11.0227 + 11.0227i 0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −0.593624 + 0.593624i −0.00240334 + 0.00240334i
\(248\) 0 0
\(249\) 200.202i 0.804024i
\(250\) 0 0
\(251\) 197.576 0.787153 0.393577 0.919292i \(-0.371238\pi\)
0.393577 + 0.919292i \(0.371238\pi\)
\(252\) 0 0
\(253\) 73.4847 + 73.4847i 0.290453 + 0.290453i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −223.868 + 223.868i −0.871083 + 0.871083i −0.992591 0.121507i \(-0.961227\pi\)
0.121507 + 0.992591i \(0.461227\pi\)
\(258\) 0 0
\(259\) 66.2020i 0.255606i
\(260\) 0 0
\(261\) −96.8786 −0.371182
\(262\) 0 0
\(263\) −90.7673 90.7673i −0.345123 0.345123i 0.513166 0.858289i \(-0.328472\pi\)
−0.858289 + 0.513166i \(0.828472\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 118.293 118.293i 0.443044 0.443044i
\(268\) 0 0
\(269\) 361.909i 1.34539i −0.739921 0.672694i \(-0.765137\pi\)
0.739921 0.672694i \(-0.234863\pi\)
\(270\) 0 0
\(271\) 216.788 0.799955 0.399977 0.916525i \(-0.369018\pi\)
0.399977 + 0.916525i \(0.369018\pi\)
\(272\) 0 0
\(273\) 11.1589 + 11.1589i 0.0408752 + 0.0408752i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 205.406 205.406i 0.741539 0.741539i −0.231335 0.972874i \(-0.574309\pi\)
0.972874 + 0.231335i \(0.0743093\pi\)
\(278\) 0 0
\(279\) 11.0908i 0.0397520i
\(280\) 0 0
\(281\) 334.899 1.19181 0.595906 0.803054i \(-0.296793\pi\)
0.595906 + 0.803054i \(0.296793\pi\)
\(282\) 0 0
\(283\) 74.3508 + 74.3508i 0.262724 + 0.262724i 0.826160 0.563436i \(-0.190521\pi\)
−0.563436 + 0.826160i \(0.690521\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10.0000 10.0000i 0.0348432 0.0348432i
\(288\) 0 0
\(289\) 249.404i 0.862990i
\(290\) 0 0
\(291\) −132.959 −0.456904
\(292\) 0 0
\(293\) 116.874 + 116.874i 0.398887 + 0.398887i 0.877840 0.478953i \(-0.158984\pi\)
−0.478953 + 0.877840i \(0.658984\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −10.6515 + 10.6515i −0.0358637 + 0.0358637i
\(298\) 0 0
\(299\) 297.909i 0.996352i
\(300\) 0 0
\(301\) 76.3939 0.253800
\(302\) 0 0
\(303\) 61.8684 + 61.8684i 0.204186 + 0.204186i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 135.250 135.250i 0.440553 0.440553i −0.451645 0.892198i \(-0.649163\pi\)
0.892198 + 0.451645i \(0.149163\pi\)
\(308\) 0 0
\(309\) 64.1816i 0.207708i
\(310\) 0 0
\(311\) 239.212 0.769171 0.384586 0.923089i \(-0.374344\pi\)
0.384586 + 0.923089i \(0.374344\pi\)
\(312\) 0 0
\(313\) 271.386 + 271.386i 0.867048 + 0.867048i 0.992145 0.125097i \(-0.0399241\pi\)
−0.125097 + 0.992145i \(0.539924\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 175.060 175.060i 0.552240 0.552240i −0.374847 0.927087i \(-0.622305\pi\)
0.927087 + 0.374847i \(0.122305\pi\)
\(318\) 0 0
\(319\) 93.6163i 0.293468i
\(320\) 0 0
\(321\) 18.3337 0.0571143
\(322\) 0 0
\(323\) 0.449490 + 0.449490i 0.00139161 + 0.00139161i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −115.831 + 115.831i −0.354223 + 0.354223i
\(328\) 0 0
\(329\) 4.42449i 0.0134483i
\(330\) 0 0
\(331\) 134.445 0.406178 0.203089 0.979160i \(-0.434902\pi\)
0.203089 + 0.979160i \(0.434902\pi\)
\(332\) 0 0
\(333\) 128.091 + 128.091i 0.384657 + 0.384657i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −137.654 + 137.654i −0.408468 + 0.408468i −0.881204 0.472736i \(-0.843266\pi\)
0.472736 + 0.881204i \(0.343266\pi\)
\(338\) 0 0
\(339\) 220.404i 0.650160i
\(340\) 0 0
\(341\) −10.7173 −0.0314292
\(342\) 0 0
\(343\) −75.0431 75.0431i −0.218785 0.218785i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −365.823 + 365.823i −1.05424 + 1.05424i −0.0558030 + 0.998442i \(0.517772\pi\)
−0.998442 + 0.0558030i \(0.982228\pi\)
\(348\) 0 0
\(349\) 140.020i 0.401205i −0.979673 0.200602i \(-0.935710\pi\)
0.979673 0.200602i \(-0.0642899\pi\)
\(350\) 0 0
\(351\) 43.1816 0.123025
\(352\) 0 0
\(353\) 208.672 + 208.672i 0.591139 + 0.591139i 0.937939 0.346800i \(-0.112732\pi\)
−0.346800 + 0.937939i \(0.612732\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 8.44949 8.44949i 0.0236680 0.0236680i
\(358\) 0 0
\(359\) 583.019i 1.62401i −0.583651 0.812005i \(-0.698376\pi\)
0.583651 0.812005i \(-0.301624\pi\)
\(360\) 0 0
\(361\) 360.990 0.999972
\(362\) 0 0
\(363\) 137.901 + 137.901i 0.379893 + 0.379893i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −123.341 + 123.341i −0.336078 + 0.336078i −0.854889 0.518811i \(-0.826375\pi\)
0.518811 + 0.854889i \(0.326375\pi\)
\(368\) 0 0
\(369\) 38.6969i 0.104870i
\(370\) 0 0
\(371\) 20.4541 0.0551323
\(372\) 0 0
\(373\) 345.052 + 345.052i 0.925073 + 0.925073i 0.997382 0.0723091i \(-0.0230368\pi\)
−0.0723091 + 0.997382i \(0.523037\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −189.762 + 189.762i −0.503347 + 0.503347i
\(378\) 0 0
\(379\) 421.393i 1.11185i −0.831231 0.555927i \(-0.812363\pi\)
0.831231 0.555927i \(-0.187637\pi\)
\(380\) 0 0
\(381\) 91.3735 0.239825
\(382\) 0 0
\(383\) −344.586 344.586i −0.899702 0.899702i 0.0957079 0.995409i \(-0.469489\pi\)
−0.995409 + 0.0957079i \(0.969489\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 147.810 147.810i 0.381939 0.381939i
\(388\) 0 0
\(389\) 486.111i 1.24964i −0.780768 0.624822i \(-0.785172\pi\)
0.780768 0.624822i \(-0.214828\pi\)
\(390\) 0 0
\(391\) −225.576 −0.576919
\(392\) 0 0
\(393\) 235.980 + 235.980i 0.600457 + 0.600457i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 312.062 312.062i 0.786052 0.786052i −0.194793 0.980844i \(-0.562403\pi\)
0.980844 + 0.194793i \(0.0624034\pi\)
\(398\) 0 0
\(399\) 0.191836i 0.000480792i
\(400\) 0 0
\(401\) 590.252 1.47195 0.735975 0.677009i \(-0.236724\pi\)
0.735975 + 0.677009i \(0.236724\pi\)
\(402\) 0 0
\(403\) 21.7242 + 21.7242i 0.0539063 + 0.0539063i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −123.778 + 123.778i −0.304122 + 0.304122i
\(408\) 0 0
\(409\) 736.696i 1.80121i 0.434636 + 0.900606i \(0.356877\pi\)
−0.434636 + 0.900606i \(0.643123\pi\)
\(410\) 0 0
\(411\) 404.969 0.985327
\(412\) 0 0
\(413\) 59.2168 + 59.2168i 0.143382 + 0.143382i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 314.449 314.449i 0.754076 0.754076i
\(418\) 0 0
\(419\) 38.0296i 0.0907627i 0.998970 + 0.0453814i \(0.0144503\pi\)
−0.998970 + 0.0453814i \(0.985550\pi\)
\(420\) 0 0
\(421\) −331.394 −0.787159 −0.393579 0.919291i \(-0.628763\pi\)
−0.393579 + 0.919291i \(0.628763\pi\)
\(422\) 0 0
\(423\) −8.56072 8.56072i −0.0202381 0.0202381i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 80.4620 80.4620i 0.188436 0.188436i
\(428\) 0 0
\(429\) 41.7276i 0.0972670i
\(430\) 0 0
\(431\) 843.040 1.95601 0.978004 0.208584i \(-0.0668856\pi\)
0.978004 + 0.208584i \(0.0668856\pi\)
\(432\) 0 0
\(433\) 149.381 + 149.381i 0.344992 + 0.344992i 0.858240 0.513248i \(-0.171558\pi\)
−0.513248 + 0.858240i \(0.671558\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.56072 2.56072i 0.00585976 0.00585976i
\(438\) 0 0
\(439\) 545.999i 1.24373i −0.783123 0.621867i \(-0.786375\pi\)
0.783123 0.621867i \(-0.213625\pi\)
\(440\) 0 0
\(441\) −143.394 −0.325156
\(442\) 0 0
\(443\) 45.0398 + 45.0398i 0.101670 + 0.101670i 0.756112 0.654442i \(-0.227096\pi\)
−0.654442 + 0.756112i \(0.727096\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −236.116 + 236.116i −0.528223 + 0.528223i
\(448\) 0 0
\(449\) 320.767i 0.714404i 0.934027 + 0.357202i \(0.116269\pi\)
−0.934027 + 0.357202i \(0.883731\pi\)
\(450\) 0 0
\(451\) 37.3939 0.0829133
\(452\) 0 0
\(453\) 121.139 + 121.139i 0.267414 + 0.267414i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −599.918 + 599.918i −1.31273 + 1.31273i −0.393337 + 0.919394i \(0.628680\pi\)
−0.919394 + 0.393337i \(0.871320\pi\)
\(458\) 0 0
\(459\) 32.6969i 0.0712352i
\(460\) 0 0
\(461\) −376.595 −0.816909 −0.408454 0.912779i \(-0.633932\pi\)
−0.408454 + 0.912779i \(0.633932\pi\)
\(462\) 0 0
\(463\) 214.838 + 214.838i 0.464012 + 0.464012i 0.899968 0.435956i \(-0.143590\pi\)
−0.435956 + 0.899968i \(0.643590\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −463.419 + 463.419i −0.992332 + 0.992332i −0.999971 0.00763918i \(-0.997568\pi\)
0.00763918 + 0.999971i \(0.497568\pi\)
\(468\) 0 0
\(469\) 73.8490i 0.157461i
\(470\) 0 0
\(471\) −253.404 −0.538013
\(472\) 0 0
\(473\) 142.833 + 142.833i 0.301973 + 0.301973i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 39.5755 39.5755i 0.0829675 0.0829675i
\(478\) 0 0
\(479\) 415.394i 0.867211i −0.901103 0.433605i \(-0.857241\pi\)
0.901103 0.433605i \(-0.142759\pi\)
\(480\) 0 0
\(481\) 501.798 1.04324
\(482\) 0 0
\(483\) −48.1362 48.1362i −0.0996609 0.0996609i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −38.1033 + 38.1033i −0.0782409 + 0.0782409i −0.745144 0.666903i \(-0.767619\pi\)
0.666903 + 0.745144i \(0.267619\pi\)
\(488\) 0 0
\(489\) 46.8684i 0.0958453i
\(490\) 0 0
\(491\) −383.514 −0.781088 −0.390544 0.920584i \(-0.627713\pi\)
−0.390544 + 0.920584i \(0.627713\pi\)
\(492\) 0 0
\(493\) 143.687 + 143.687i 0.291454 + 0.291454i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 23.0306 23.0306i 0.0463393 0.0463393i
\(498\) 0 0
\(499\) 81.4133i 0.163153i −0.996667 0.0815764i \(-0.974005\pi\)
0.996667 0.0815764i \(-0.0259955\pi\)
\(500\) 0 0
\(501\) −236.858 −0.472771
\(502\) 0 0
\(503\) −171.626 171.626i −0.341204 0.341204i 0.515616 0.856820i \(-0.327563\pi\)
−0.856820 + 0.515616i \(0.827563\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −122.399 + 122.399i −0.241419 + 0.241419i
\(508\) 0 0
\(509\) 452.202i 0.888413i −0.895925 0.444206i \(-0.853486\pi\)
0.895925 0.444206i \(-0.146514\pi\)
\(510\) 0 0
\(511\) −5.43470 −0.0106354
\(512\) 0 0
\(513\) 0.371173 + 0.371173i 0.000723534 + 0.000723534i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 8.27245 8.27245i 0.0160009 0.0160009i
\(518\) 0 0
\(519\) 441.242i 0.850177i
\(520\) 0 0
\(521\) −773.928 −1.48547 −0.742733 0.669588i \(-0.766471\pi\)
−0.742733 + 0.669588i \(0.766471\pi\)
\(522\) 0 0
\(523\) 474.507 + 474.507i 0.907280 + 0.907280i 0.996052 0.0887721i \(-0.0282943\pi\)
−0.0887721 + 0.996052i \(0.528294\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 16.4495 16.4495i 0.0312135 0.0312135i
\(528\) 0 0
\(529\) 756.090i 1.42928i
\(530\) 0 0
\(531\) 229.151 0.431546
\(532\) 0 0
\(533\) −75.7980 75.7980i −0.142210 0.142210i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −164.116 + 164.116i −0.305616 + 0.305616i
\(538\) 0 0
\(539\) 138.565i 0.257078i
\(540\) 0 0
\(541\) 511.867 0.946150 0.473075 0.881022i \(-0.343144\pi\)
0.473075 + 0.881022i \(0.343144\pi\)
\(542\) 0 0
\(543\) 210.149 + 210.149i 0.387014 + 0.387014i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 373.980 373.980i 0.683692 0.683692i −0.277138 0.960830i \(-0.589386\pi\)
0.960830 + 0.277138i \(0.0893859\pi\)
\(548\) 0 0
\(549\) 311.363i 0.567146i
\(550\) 0 0
\(551\) −3.26224 −0.00592058
\(552\) 0 0
\(553\) −68.0658 68.0658i −0.123085 0.123085i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 421.015 421.015i 0.755861 0.755861i −0.219705 0.975566i \(-0.570509\pi\)
0.975566 + 0.219705i \(0.0705095\pi\)
\(558\) 0 0
\(559\) 579.050i 1.03587i
\(560\) 0 0
\(561\) 31.5959 0.0563207
\(562\) 0 0
\(563\) −7.77296 7.77296i −0.0138063 0.0138063i 0.700170 0.713976i \(-0.253108\pi\)
−0.713976 + 0.700170i \(0.753108\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 6.97730 6.97730i 0.0123056 0.0123056i
\(568\) 0 0
\(569\) 473.787i 0.832666i −0.909212 0.416333i \(-0.863315\pi\)
0.909212 0.416333i \(-0.136685\pi\)
\(570\) 0 0
\(571\) 120.344 0.210760 0.105380 0.994432i \(-0.466394\pi\)
0.105380 + 0.994432i \(0.466394\pi\)
\(572\) 0 0
\(573\) 32.1770 + 32.1770i 0.0561554 + 0.0561554i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −266.033 + 266.033i −0.461062 + 0.461062i −0.899004 0.437941i \(-0.855708\pi\)
0.437941 + 0.899004i \(0.355708\pi\)
\(578\) 0 0
\(579\) 181.565i 0.313584i
\(580\) 0 0
\(581\) 126.727 0.218118
\(582\) 0 0
\(583\) 38.2429 + 38.2429i 0.0655967 + 0.0655967i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −114.141 + 114.141i −0.194448 + 0.194448i −0.797615 0.603167i \(-0.793905\pi\)
0.603167 + 0.797615i \(0.293905\pi\)
\(588\) 0 0
\(589\) 0.373467i 0.000634069i
\(590\) 0 0
\(591\) 116.969 0.197918
\(592\) 0 0
\(593\) −566.636 566.636i −0.955541 0.955541i 0.0435121 0.999053i \(-0.486145\pi\)
−0.999053 + 0.0435121i \(0.986145\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 435.341 435.341i 0.729214 0.729214i
\(598\) 0 0
\(599\) 1002.44i 1.67353i 0.547564 + 0.836764i \(0.315555\pi\)
−0.547564 + 0.836764i \(0.684445\pi\)
\(600\) 0 0
\(601\) −20.8796 −0.0347414 −0.0173707 0.999849i \(-0.505530\pi\)
−0.0173707 + 0.999849i \(0.505530\pi\)
\(602\) 0 0
\(603\) −142.886 142.886i −0.236959 0.236959i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 305.748 305.748i 0.503703 0.503703i −0.408883 0.912587i \(-0.634082\pi\)
0.912587 + 0.408883i \(0.134082\pi\)
\(608\) 0 0
\(609\) 61.3235i 0.100695i
\(610\) 0 0
\(611\) −33.5367 −0.0548883
\(612\) 0 0
\(613\) −153.303 153.303i −0.250087 0.250087i 0.570919 0.821006i \(-0.306587\pi\)
−0.821006 + 0.570919i \(0.806587\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −276.879 + 276.879i −0.448750 + 0.448750i −0.894939 0.446189i \(-0.852781\pi\)
0.446189 + 0.894939i \(0.352781\pi\)
\(618\) 0 0
\(619\) 389.352i 0.629002i 0.949257 + 0.314501i \(0.101837\pi\)
−0.949257 + 0.314501i \(0.898163\pi\)
\(620\) 0 0
\(621\) −186.272 −0.299956
\(622\) 0 0
\(623\) −74.8786 74.8786i −0.120190 0.120190i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −0.358674 + 0.358674i −0.000572048 + 0.000572048i
\(628\) 0 0
\(629\) 379.959i 0.604069i
\(630\) 0 0
\(631\) −576.201 −0.913155 −0.456578 0.889684i \(-0.650925\pi\)
−0.456578 + 0.889684i \(0.650925\pi\)
\(632\) 0 0
\(633\) −178.169 178.169i −0.281468 0.281468i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −280.874 + 280.874i −0.440932 + 0.440932i
\(638\) 0 0
\(639\) 89.1214i 0.139470i
\(640\) 0 0
\(641\) 780.827 1.21814 0.609069 0.793117i \(-0.291543\pi\)
0.609069 + 0.793117i \(0.291543\pi\)
\(642\) 0 0
\(643\) −403.787 403.787i −0.627973 0.627973i 0.319585 0.947558i \(-0.396457\pi\)
−0.947558 + 0.319585i \(0.896457\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 381.898 381.898i 0.590260 0.590260i −0.347442 0.937702i \(-0.612950\pi\)
0.937702 + 0.347442i \(0.112950\pi\)
\(648\) 0 0
\(649\) 221.435i 0.341194i
\(650\) 0 0
\(651\) 7.02041 0.0107840
\(652\) 0 0
\(653\) 149.864 + 149.864i 0.229500 + 0.229500i 0.812484 0.582984i \(-0.198115\pi\)
−0.582984 + 0.812484i \(0.698115\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −10.5153 + 10.5153i −0.0160050 + 0.0160050i
\(658\) 0 0
\(659\) 552.495i 0.838384i 0.907898 + 0.419192i \(0.137687\pi\)
−0.907898 + 0.419192i \(0.862313\pi\)
\(660\) 0 0
\(661\) −274.767 −0.415684 −0.207842 0.978162i \(-0.566644\pi\)
−0.207842 + 0.978162i \(0.566644\pi\)
\(662\) 0 0
\(663\) −64.0454 64.0454i −0.0965994 0.0965994i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 818.574 818.574i 1.22725 1.22725i
\(668\) 0 0
\(669\) 564.242i 0.843411i
\(670\) 0 0
\(671\) 300.879 0.448403
\(672\) 0 0
\(673\) −624.272 624.272i −0.927597 0.927597i 0.0699537 0.997550i \(-0.477715\pi\)
−0.997550 + 0.0699537i \(0.977715\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −4.04541 + 4.04541i −0.00597549 + 0.00597549i −0.710088 0.704113i \(-0.751345\pi\)
0.704113 + 0.710088i \(0.251345\pi\)
\(678\) 0 0
\(679\) 84.1623i 0.123950i
\(680\) 0 0
\(681\) 99.1418 0.145583
\(682\) 0 0
\(683\) 913.757 + 913.757i 1.33786 + 1.33786i 0.898132 + 0.439726i \(0.144925\pi\)
0.439726 + 0.898132i \(0.355075\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −257.431 + 257.431i −0.374718 + 0.374718i
\(688\) 0 0
\(689\) 155.038i 0.225018i
\(690\) 0 0
\(691\) −1286.24 −1.86142 −0.930710 0.365759i \(-0.880810\pi\)
−0.930710 + 0.365759i \(0.880810\pi\)
\(692\) 0 0
\(693\) 6.74235 + 6.74235i 0.00972922 + 0.00972922i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −57.3939 + 57.3939i −0.0823442 + 0.0823442i
\(698\) 0 0
\(699\) 725.989i 1.03861i
\(700\) 0 0
\(701\) −527.181 −0.752041 −0.376020 0.926611i \(-0.622708\pi\)
−0.376020 + 0.926611i \(0.622708\pi\)
\(702\) 0 0
\(703\) 4.31327 + 4.31327i 0.00613551 + 0.00613551i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 39.1623 39.1623i 0.0553922 0.0553922i
\(708\) 0 0
\(709\) 204.514i 0.288455i 0.989545 + 0.144227i \(0.0460696\pi\)
−0.989545 + 0.144227i \(0.953930\pi\)
\(710\) 0 0
\(711\) −263.394 −0.370456
\(712\) 0 0
\(713\) −93.7117 93.7117i −0.131433 0.131433i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −109.373 + 109.373i −0.152543 + 0.152543i
\(718\) 0 0
\(719\) 511.989i 0.712085i 0.934470 + 0.356042i \(0.115874\pi\)
−0.934470 + 0.356042i \(0.884126\pi\)
\(720\) 0 0
\(721\) 40.6265 0.0563475
\(722\) 0 0
\(723\) −147.724 147.724i −0.204321 0.204321i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −211.992 + 211.992i −0.291598 + 0.291598i −0.837712 0.546113i \(-0.816107\pi\)
0.546113 + 0.837712i \(0.316107\pi\)
\(728\) 0 0
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) −438.454 −0.599800
\(732\) 0 0
\(733\) −702.979 702.979i −0.959043 0.959043i 0.0401506 0.999194i \(-0.487216\pi\)
−0.999194 + 0.0401506i \(0.987216\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 138.075 138.075i 0.187347 0.187347i
\(738\) 0 0
\(739\) 838.586i 1.13476i 0.823457 + 0.567379i \(0.192042\pi\)
−0.823457 + 0.567379i \(0.807958\pi\)
\(740\) 0 0
\(741\) 1.45408 0.00196232
\(742\) 0 0
\(743\) −962.534 962.534i −1.29547 1.29547i −0.931354 0.364115i \(-0.881371\pi\)
−0.364115 0.931354i \(-0.618629\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 245.196 245.196i 0.328242 0.328242i
\(748\) 0 0
\(749\) 11.6051i 0.0154941i
\(750\) 0 0
\(751\) −594.241 −0.791266 −0.395633 0.918409i \(-0.629475\pi\)
−0.395633 + 0.918409i \(0.629475\pi\)
\(752\) 0 0
\(753\) −241.980 241.980i −0.321354 0.321354i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −399.402 + 399.402i −0.527611 + 0.527611i −0.919859 0.392248i \(-0.871697\pi\)
0.392248 + 0.919859i \(0.371697\pi\)
\(758\) 0 0
\(759\) 180.000i 0.237154i
\(760\) 0 0
\(761\) 127.292 0.167269 0.0836346 0.996496i \(-0.473347\pi\)
0.0836346 + 0.996496i \(0.473347\pi\)
\(762\) 0 0
\(763\) 73.3201 + 73.3201i 0.0960946 + 0.0960946i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 448.852 448.852i 0.585204 0.585204i
\(768\) 0 0
\(769\) 699.847i 0.910074i −0.890473 0.455037i \(-0.849626\pi\)
0.890473 0.455037i \(-0.150374\pi\)
\(770\) 0 0
\(771\) 548.363 0.711236
\(772\) 0 0
\(773\) −627.485 627.485i −0.811753 0.811753i 0.173144 0.984897i \(-0.444607\pi\)
−0.984897 + 0.173144i \(0.944607\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 81.0806 81.0806i 0.104351 0.104351i
\(778\) 0 0
\(779\) 1.30306i 0.00167274i
\(780\) 0 0
\(781\) 86.1204 0.110269
\(782\) 0 0
\(783\) 118.652 + 118.652i 0.151535 + 0.151535i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 363.992 363.992i 0.462506 0.462506i −0.436970 0.899476i \(-0.643948\pi\)
0.899476 + 0.436970i \(0.143948\pi\)
\(788\) 0 0
\(789\) 222.334i 0.281792i
\(790\) 0 0
\(791\) 139.514 0.176377
\(792\) 0 0
\(793\) −609.885 609.885i −0.769086 0.769086i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 506.080 506.080i 0.634981 0.634981i −0.314332 0.949313i \(-0.601781\pi\)
0.949313 + 0.314332i \(0.101781\pi\)
\(798\) 0 0
\(799\) 25.3939i