Properties

Label 900.3.c.j.451.1
Level $900$
Weight $3$
Character 900.451
Analytic conductor $24.523$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.5232237924\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 451.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 900.451
Dual form 900.3.c.j.451.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} -10.3923i q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} -10.3923i q^{7} -8.00000 q^{8} -10.3923i q^{11} -18.0000 q^{13} +(-18.0000 - 10.3923i) q^{14} +(-8.00000 + 13.8564i) q^{16} +10.0000 q^{17} +13.8564i q^{19} +(-18.0000 - 10.3923i) q^{22} +6.92820i q^{23} +(-18.0000 + 31.1769i) q^{26} +(-36.0000 + 20.7846i) q^{28} +36.0000 q^{29} -6.92820i q^{31} +(16.0000 + 27.7128i) q^{32} +(10.0000 - 17.3205i) q^{34} -54.0000 q^{37} +(24.0000 + 13.8564i) q^{38} -18.0000 q^{41} -20.7846i q^{43} +(-36.0000 + 20.7846i) q^{44} +(12.0000 + 6.92820i) q^{46} -59.0000 q^{49} +(36.0000 + 62.3538i) q^{52} -26.0000 q^{53} +83.1384i q^{56} +(36.0000 - 62.3538i) q^{58} +31.1769i q^{59} -74.0000 q^{61} +(-12.0000 - 6.92820i) q^{62} +64.0000 q^{64} -41.5692i q^{67} +(-20.0000 - 34.6410i) q^{68} +103.923i q^{71} -36.0000 q^{73} +(-54.0000 + 93.5307i) q^{74} +(48.0000 - 27.7128i) q^{76} -108.000 q^{77} +90.0666i q^{79} +(-18.0000 + 31.1769i) q^{82} -90.0666i q^{83} +(-36.0000 - 20.7846i) q^{86} +83.1384i q^{88} +18.0000 q^{89} +187.061i q^{91} +(24.0000 - 13.8564i) q^{92} +72.0000 q^{97} +(-59.0000 + 102.191i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 4q^{4} - 16q^{8} + O(q^{10}) \) \( 2q + 2q^{2} - 4q^{4} - 16q^{8} - 36q^{13} - 36q^{14} - 16q^{16} + 20q^{17} - 36q^{22} - 36q^{26} - 72q^{28} + 72q^{29} + 32q^{32} + 20q^{34} - 108q^{37} + 48q^{38} - 36q^{41} - 72q^{44} + 24q^{46} - 118q^{49} + 72q^{52} - 52q^{53} + 72q^{58} - 148q^{61} - 24q^{62} + 128q^{64} - 40q^{68} - 72q^{73} - 108q^{74} + 96q^{76} - 216q^{77} - 36q^{82} - 72q^{86} + 36q^{89} + 48q^{92} + 144q^{97} - 118q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(451\) \(577\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.500000 0.866025i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.500000 0.866025i
\(5\) 0 0
\(6\) 0 0
\(7\) 10.3923i 1.48461i −0.670059 0.742307i \(-0.733731\pi\)
0.670059 0.742307i \(-0.266269\pi\)
\(8\) −8.00000 −1.00000
\(9\) 0 0
\(10\) 0 0
\(11\) 10.3923i 0.944755i −0.881396 0.472377i \(-0.843396\pi\)
0.881396 0.472377i \(-0.156604\pi\)
\(12\) 0 0
\(13\) −18.0000 −1.38462 −0.692308 0.721602i \(-0.743406\pi\)
−0.692308 + 0.721602i \(0.743406\pi\)
\(14\) −18.0000 10.3923i −1.28571 0.742307i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(17\) 10.0000 0.588235 0.294118 0.955769i \(-0.404974\pi\)
0.294118 + 0.955769i \(0.404974\pi\)
\(18\) 0 0
\(19\) 13.8564i 0.729285i 0.931148 + 0.364642i \(0.118809\pi\)
−0.931148 + 0.364642i \(0.881191\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −18.0000 10.3923i −0.818182 0.472377i
\(23\) 6.92820i 0.301226i 0.988593 + 0.150613i \(0.0481248\pi\)
−0.988593 + 0.150613i \(0.951875\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −18.0000 + 31.1769i −0.692308 + 1.19911i
\(27\) 0 0
\(28\) −36.0000 + 20.7846i −1.28571 + 0.742307i
\(29\) 36.0000 1.24138 0.620690 0.784056i \(-0.286853\pi\)
0.620690 + 0.784056i \(0.286853\pi\)
\(30\) 0 0
\(31\) 6.92820i 0.223490i −0.993737 0.111745i \(-0.964356\pi\)
0.993737 0.111745i \(-0.0356441\pi\)
\(32\) 16.0000 + 27.7128i 0.500000 + 0.866025i
\(33\) 0 0
\(34\) 10.0000 17.3205i 0.294118 0.509427i
\(35\) 0 0
\(36\) 0 0
\(37\) −54.0000 −1.45946 −0.729730 0.683736i \(-0.760354\pi\)
−0.729730 + 0.683736i \(0.760354\pi\)
\(38\) 24.0000 + 13.8564i 0.631579 + 0.364642i
\(39\) 0 0
\(40\) 0 0
\(41\) −18.0000 −0.439024 −0.219512 0.975610i \(-0.570447\pi\)
−0.219512 + 0.975610i \(0.570447\pi\)
\(42\) 0 0
\(43\) 20.7846i 0.483363i −0.970356 0.241682i \(-0.922301\pi\)
0.970356 0.241682i \(-0.0776989\pi\)
\(44\) −36.0000 + 20.7846i −0.818182 + 0.472377i
\(45\) 0 0
\(46\) 12.0000 + 6.92820i 0.260870 + 0.150613i
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) −59.0000 −1.20408
\(50\) 0 0
\(51\) 0 0
\(52\) 36.0000 + 62.3538i 0.692308 + 1.19911i
\(53\) −26.0000 −0.490566 −0.245283 0.969452i \(-0.578881\pi\)
−0.245283 + 0.969452i \(0.578881\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 83.1384i 1.48461i
\(57\) 0 0
\(58\) 36.0000 62.3538i 0.620690 1.07507i
\(59\) 31.1769i 0.528422i 0.964465 + 0.264211i \(0.0851116\pi\)
−0.964465 + 0.264211i \(0.914888\pi\)
\(60\) 0 0
\(61\) −74.0000 −1.21311 −0.606557 0.795040i \(-0.707450\pi\)
−0.606557 + 0.795040i \(0.707450\pi\)
\(62\) −12.0000 6.92820i −0.193548 0.111745i
\(63\) 0 0
\(64\) 64.0000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 41.5692i 0.620436i −0.950665 0.310218i \(-0.899598\pi\)
0.950665 0.310218i \(-0.100402\pi\)
\(68\) −20.0000 34.6410i −0.294118 0.509427i
\(69\) 0 0
\(70\) 0 0
\(71\) 103.923i 1.46370i 0.681463 + 0.731852i \(0.261344\pi\)
−0.681463 + 0.731852i \(0.738656\pi\)
\(72\) 0 0
\(73\) −36.0000 −0.493151 −0.246575 0.969124i \(-0.579305\pi\)
−0.246575 + 0.969124i \(0.579305\pi\)
\(74\) −54.0000 + 93.5307i −0.729730 + 1.26393i
\(75\) 0 0
\(76\) 48.0000 27.7128i 0.631579 0.364642i
\(77\) −108.000 −1.40260
\(78\) 0 0
\(79\) 90.0666i 1.14008i 0.821616 + 0.570042i \(0.193073\pi\)
−0.821616 + 0.570042i \(0.806927\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −18.0000 + 31.1769i −0.219512 + 0.380206i
\(83\) 90.0666i 1.08514i −0.840011 0.542570i \(-0.817451\pi\)
0.840011 0.542570i \(-0.182549\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −36.0000 20.7846i −0.418605 0.241682i
\(87\) 0 0
\(88\) 83.1384i 0.944755i
\(89\) 18.0000 0.202247 0.101124 0.994874i \(-0.467756\pi\)
0.101124 + 0.994874i \(0.467756\pi\)
\(90\) 0 0
\(91\) 187.061i 2.05562i
\(92\) 24.0000 13.8564i 0.260870 0.150613i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 72.0000 0.742268 0.371134 0.928579i \(-0.378969\pi\)
0.371134 + 0.928579i \(0.378969\pi\)
\(98\) −59.0000 + 102.191i −0.602041 + 1.04277i
\(99\) 0 0
\(100\) 0 0
\(101\) −36.0000 −0.356436 −0.178218 0.983991i \(-0.557033\pi\)
−0.178218 + 0.983991i \(0.557033\pi\)
\(102\) 0 0
\(103\) 10.3923i 0.100896i −0.998727 0.0504481i \(-0.983935\pi\)
0.998727 0.0504481i \(-0.0160649\pi\)
\(104\) 144.000 1.38462
\(105\) 0 0
\(106\) −26.0000 + 45.0333i −0.245283 + 0.424843i
\(107\) 187.061i 1.74824i −0.485712 0.874119i \(-0.661439\pi\)
0.485712 0.874119i \(-0.338561\pi\)
\(108\) 0 0
\(109\) −26.0000 −0.238532 −0.119266 0.992862i \(-0.538054\pi\)
−0.119266 + 0.992862i \(0.538054\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 144.000 + 83.1384i 1.28571 + 0.742307i
\(113\) −10.0000 −0.0884956 −0.0442478 0.999021i \(-0.514089\pi\)
−0.0442478 + 0.999021i \(0.514089\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −72.0000 124.708i −0.620690 1.07507i
\(117\) 0 0
\(118\) 54.0000 + 31.1769i 0.457627 + 0.264211i
\(119\) 103.923i 0.873303i
\(120\) 0 0
\(121\) 13.0000 0.107438
\(122\) −74.0000 + 128.172i −0.606557 + 1.05059i
\(123\) 0 0
\(124\) −24.0000 + 13.8564i −0.193548 + 0.111745i
\(125\) 0 0
\(126\) 0 0
\(127\) 218.238i 1.71841i −0.511629 0.859206i \(-0.670958\pi\)
0.511629 0.859206i \(-0.329042\pi\)
\(128\) 64.0000 110.851i 0.500000 0.866025i
\(129\) 0 0
\(130\) 0 0
\(131\) 135.100i 1.03130i 0.856800 + 0.515649i \(0.172449\pi\)
−0.856800 + 0.515649i \(0.827551\pi\)
\(132\) 0 0
\(133\) 144.000 1.08271
\(134\) −72.0000 41.5692i −0.537313 0.310218i
\(135\) 0 0
\(136\) −80.0000 −0.588235
\(137\) 110.000 0.802920 0.401460 0.915877i \(-0.368503\pi\)
0.401460 + 0.915877i \(0.368503\pi\)
\(138\) 0 0
\(139\) 187.061i 1.34577i −0.739749 0.672883i \(-0.765056\pi\)
0.739749 0.672883i \(-0.234944\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 180.000 + 103.923i 1.26761 + 0.731852i
\(143\) 187.061i 1.30812i
\(144\) 0 0
\(145\) 0 0
\(146\) −36.0000 + 62.3538i −0.246575 + 0.427081i
\(147\) 0 0
\(148\) 108.000 + 187.061i 0.729730 + 1.26393i
\(149\) −288.000 −1.93289 −0.966443 0.256881i \(-0.917305\pi\)
−0.966443 + 0.256881i \(0.917305\pi\)
\(150\) 0 0
\(151\) 187.061i 1.23882i −0.785069 0.619409i \(-0.787372\pi\)
0.785069 0.619409i \(-0.212628\pi\)
\(152\) 110.851i 0.729285i
\(153\) 0 0
\(154\) −108.000 + 187.061i −0.701299 + 1.21468i
\(155\) 0 0
\(156\) 0 0
\(157\) −234.000 −1.49045 −0.745223 0.666815i \(-0.767657\pi\)
−0.745223 + 0.666815i \(0.767657\pi\)
\(158\) 156.000 + 90.0666i 0.987342 + 0.570042i
\(159\) 0 0
\(160\) 0 0
\(161\) 72.0000 0.447205
\(162\) 0 0
\(163\) 124.708i 0.765078i −0.923939 0.382539i \(-0.875050\pi\)
0.923939 0.382539i \(-0.124950\pi\)
\(164\) 36.0000 + 62.3538i 0.219512 + 0.380206i
\(165\) 0 0
\(166\) −156.000 90.0666i −0.939759 0.542570i
\(167\) 131.636i 0.788239i 0.919059 + 0.394119i \(0.128950\pi\)
−0.919059 + 0.394119i \(0.871050\pi\)
\(168\) 0 0
\(169\) 155.000 0.917160
\(170\) 0 0
\(171\) 0 0
\(172\) −72.0000 + 41.5692i −0.418605 + 0.241682i
\(173\) 146.000 0.843931 0.421965 0.906612i \(-0.361340\pi\)
0.421965 + 0.906612i \(0.361340\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 144.000 + 83.1384i 0.818182 + 0.472377i
\(177\) 0 0
\(178\) 18.0000 31.1769i 0.101124 0.175151i
\(179\) 72.7461i 0.406403i 0.979137 + 0.203201i \(0.0651346\pi\)
−0.979137 + 0.203201i \(0.934865\pi\)
\(180\) 0 0
\(181\) 262.000 1.44751 0.723757 0.690055i \(-0.242414\pi\)
0.723757 + 0.690055i \(0.242414\pi\)
\(182\) 324.000 + 187.061i 1.78022 + 1.02781i
\(183\) 0 0
\(184\) 55.4256i 0.301226i
\(185\) 0 0
\(186\) 0 0
\(187\) 103.923i 0.555738i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 187.061i 0.979380i −0.871897 0.489690i \(-0.837110\pi\)
0.871897 0.489690i \(-0.162890\pi\)
\(192\) 0 0
\(193\) −180.000 −0.932642 −0.466321 0.884615i \(-0.654421\pi\)
−0.466321 + 0.884615i \(0.654421\pi\)
\(194\) 72.0000 124.708i 0.371134 0.642823i
\(195\) 0 0
\(196\) 118.000 + 204.382i 0.602041 + 1.04277i
\(197\) −154.000 −0.781726 −0.390863 0.920449i \(-0.627823\pi\)
−0.390863 + 0.920449i \(0.627823\pi\)
\(198\) 0 0
\(199\) 187.061i 0.940007i −0.882664 0.470004i \(-0.844253\pi\)
0.882664 0.470004i \(-0.155747\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −36.0000 + 62.3538i −0.178218 + 0.308682i
\(203\) 374.123i 1.84297i
\(204\) 0 0
\(205\) 0 0
\(206\) −18.0000 10.3923i −0.0873786 0.0504481i
\(207\) 0 0
\(208\) 144.000 249.415i 0.692308 1.19911i
\(209\) 144.000 0.688995
\(210\) 0 0
\(211\) 242.487i 1.14923i −0.818425 0.574614i \(-0.805152\pi\)
0.818425 0.574614i \(-0.194848\pi\)
\(212\) 52.0000 + 90.0666i 0.245283 + 0.424843i
\(213\) 0 0
\(214\) −324.000 187.061i −1.51402 0.874119i
\(215\) 0 0
\(216\) 0 0
\(217\) −72.0000 −0.331797
\(218\) −26.0000 + 45.0333i −0.119266 + 0.206575i
\(219\) 0 0
\(220\) 0 0
\(221\) −180.000 −0.814480
\(222\) 0 0
\(223\) 93.5307i 0.419420i −0.977764 0.209710i \(-0.932748\pi\)
0.977764 0.209710i \(-0.0672521\pi\)
\(224\) 288.000 166.277i 1.28571 0.742307i
\(225\) 0 0
\(226\) −10.0000 + 17.3205i −0.0442478 + 0.0766394i
\(227\) 214.774i 0.946142i −0.881024 0.473071i \(-0.843145\pi\)
0.881024 0.473071i \(-0.156855\pi\)
\(228\) 0 0
\(229\) 338.000 1.47598 0.737991 0.674810i \(-0.235775\pi\)
0.737991 + 0.674810i \(0.235775\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −288.000 −1.24138
\(233\) −182.000 −0.781116 −0.390558 0.920578i \(-0.627718\pi\)
−0.390558 + 0.920578i \(0.627718\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 108.000 62.3538i 0.457627 0.264211i
\(237\) 0 0
\(238\) −180.000 103.923i −0.756303 0.436651i
\(239\) 353.338i 1.47840i 0.673484 + 0.739202i \(0.264797\pi\)
−0.673484 + 0.739202i \(0.735203\pi\)
\(240\) 0 0
\(241\) −106.000 −0.439834 −0.219917 0.975519i \(-0.570579\pi\)
−0.219917 + 0.975519i \(0.570579\pi\)
\(242\) 13.0000 22.5167i 0.0537190 0.0930441i
\(243\) 0 0
\(244\) 148.000 + 256.344i 0.606557 + 1.05059i
\(245\) 0 0
\(246\) 0 0
\(247\) 249.415i 1.00978i
\(248\) 55.4256i 0.223490i
\(249\) 0 0
\(250\) 0 0
\(251\) 322.161i 1.28351i −0.766909 0.641756i \(-0.778206\pi\)
0.766909 0.641756i \(-0.221794\pi\)
\(252\) 0 0
\(253\) 72.0000 0.284585
\(254\) −378.000 218.238i −1.48819 0.859206i
\(255\) 0 0
\(256\) −128.000 221.703i −0.500000 0.866025i
\(257\) 14.0000 0.0544747 0.0272374 0.999629i \(-0.491329\pi\)
0.0272374 + 0.999629i \(0.491329\pi\)
\(258\) 0 0
\(259\) 561.184i 2.16674i
\(260\) 0 0
\(261\) 0 0
\(262\) 234.000 + 135.100i 0.893130 + 0.515649i
\(263\) 187.061i 0.711260i 0.934627 + 0.355630i \(0.115734\pi\)
−0.934627 + 0.355630i \(0.884266\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 144.000 249.415i 0.541353 0.937652i
\(267\) 0 0
\(268\) −144.000 + 83.1384i −0.537313 + 0.310218i
\(269\) 108.000 0.401487 0.200743 0.979644i \(-0.435664\pi\)
0.200743 + 0.979644i \(0.435664\pi\)
\(270\) 0 0
\(271\) 325.626i 1.20157i 0.799411 + 0.600785i \(0.205145\pi\)
−0.799411 + 0.600785i \(0.794855\pi\)
\(272\) −80.0000 + 138.564i −0.294118 + 0.509427i
\(273\) 0 0
\(274\) 110.000 190.526i 0.401460 0.695349i
\(275\) 0 0
\(276\) 0 0
\(277\) −270.000 −0.974729 −0.487365 0.873199i \(-0.662042\pi\)
−0.487365 + 0.873199i \(0.662042\pi\)
\(278\) −324.000 187.061i −1.16547 0.672883i
\(279\) 0 0
\(280\) 0 0
\(281\) 234.000 0.832740 0.416370 0.909195i \(-0.363302\pi\)
0.416370 + 0.909195i \(0.363302\pi\)
\(282\) 0 0
\(283\) 83.1384i 0.293775i 0.989153 + 0.146888i \(0.0469256\pi\)
−0.989153 + 0.146888i \(0.953074\pi\)
\(284\) 360.000 207.846i 1.26761 0.731852i
\(285\) 0 0
\(286\) 324.000 + 187.061i 1.13287 + 0.654061i
\(287\) 187.061i 0.651782i
\(288\) 0 0
\(289\) −189.000 −0.653979
\(290\) 0 0
\(291\) 0 0
\(292\) 72.0000 + 124.708i 0.246575 + 0.427081i
\(293\) −58.0000 −0.197952 −0.0989761 0.995090i \(-0.531557\pi\)
−0.0989761 + 0.995090i \(0.531557\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 432.000 1.45946
\(297\) 0 0
\(298\) −288.000 + 498.831i −0.966443 + 1.67393i
\(299\) 124.708i 0.417082i
\(300\) 0 0
\(301\) −216.000 −0.717608
\(302\) −324.000 187.061i −1.07285 0.619409i
\(303\) 0 0
\(304\) −192.000 110.851i −0.631579 0.364642i
\(305\) 0 0
\(306\) 0 0
\(307\) 270.200i 0.880130i 0.897966 + 0.440065i \(0.145045\pi\)
−0.897966 + 0.440065i \(0.854955\pi\)
\(308\) 216.000 + 374.123i 0.701299 + 1.21468i
\(309\) 0 0
\(310\) 0 0
\(311\) 270.200i 0.868810i −0.900718 0.434405i \(-0.856959\pi\)
0.900718 0.434405i \(-0.143041\pi\)
\(312\) 0 0
\(313\) −468.000 −1.49521 −0.747604 0.664145i \(-0.768796\pi\)
−0.747604 + 0.664145i \(0.768796\pi\)
\(314\) −234.000 + 405.300i −0.745223 + 1.29076i
\(315\) 0 0
\(316\) 312.000 180.133i 0.987342 0.570042i
\(317\) 250.000 0.788644 0.394322 0.918972i \(-0.370980\pi\)
0.394322 + 0.918972i \(0.370980\pi\)
\(318\) 0 0
\(319\) 374.123i 1.17280i
\(320\) 0 0
\(321\) 0 0
\(322\) 72.0000 124.708i 0.223602 0.387291i
\(323\) 138.564i 0.428991i
\(324\) 0 0
\(325\) 0 0
\(326\) −216.000 124.708i −0.662577 0.382539i
\(327\) 0 0
\(328\) 144.000 0.439024
\(329\) 0 0
\(330\) 0 0
\(331\) 374.123i 1.13028i −0.824995 0.565140i \(-0.808822\pi\)
0.824995 0.565140i \(-0.191178\pi\)
\(332\) −312.000 + 180.133i −0.939759 + 0.542570i
\(333\) 0 0
\(334\) 228.000 + 131.636i 0.682635 + 0.394119i
\(335\) 0 0
\(336\) 0 0
\(337\) 468.000 1.38872 0.694362 0.719626i \(-0.255687\pi\)
0.694362 + 0.719626i \(0.255687\pi\)
\(338\) 155.000 268.468i 0.458580 0.794284i
\(339\) 0 0
\(340\) 0 0
\(341\) −72.0000 −0.211144
\(342\) 0 0
\(343\) 103.923i 0.302983i
\(344\) 166.277i 0.483363i
\(345\) 0 0
\(346\) 146.000 252.879i 0.421965 0.730865i
\(347\) 561.184i 1.61725i −0.588327 0.808623i \(-0.700213\pi\)
0.588327 0.808623i \(-0.299787\pi\)
\(348\) 0 0
\(349\) −434.000 −1.24355 −0.621777 0.783195i \(-0.713589\pi\)
−0.621777 + 0.783195i \(0.713589\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 288.000 166.277i 0.818182 0.472377i
\(353\) −158.000 −0.447592 −0.223796 0.974636i \(-0.571845\pi\)
−0.223796 + 0.974636i \(0.571845\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −36.0000 62.3538i −0.101124 0.175151i
\(357\) 0 0
\(358\) 126.000 + 72.7461i 0.351955 + 0.203201i
\(359\) 457.261i 1.27371i −0.770984 0.636854i \(-0.780235\pi\)
0.770984 0.636854i \(-0.219765\pi\)
\(360\) 0 0
\(361\) 169.000 0.468144
\(362\) 262.000 453.797i 0.723757 1.25358i
\(363\) 0 0
\(364\) 648.000 374.123i 1.78022 1.02781i
\(365\) 0 0
\(366\) 0 0
\(367\) 218.238i 0.594655i −0.954776 0.297328i \(-0.903905\pi\)
0.954776 0.297328i \(-0.0960953\pi\)
\(368\) −96.0000 55.4256i −0.260870 0.150613i
\(369\) 0 0
\(370\) 0 0
\(371\) 270.200i 0.728302i
\(372\) 0 0
\(373\) 270.000 0.723861 0.361930 0.932205i \(-0.382118\pi\)
0.361930 + 0.932205i \(0.382118\pi\)
\(374\) −180.000 103.923i −0.481283 0.277869i
\(375\) 0 0
\(376\) 0 0
\(377\) −648.000 −1.71883
\(378\) 0 0
\(379\) 325.626i 0.859170i −0.903026 0.429585i \(-0.858660\pi\)
0.903026 0.429585i \(-0.141340\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −324.000 187.061i −0.848168 0.489690i
\(383\) 55.4256i 0.144714i −0.997379 0.0723572i \(-0.976948\pi\)
0.997379 0.0723572i \(-0.0230522\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −180.000 + 311.769i −0.466321 + 0.807692i
\(387\) 0 0
\(388\) −144.000 249.415i −0.371134 0.642823i
\(389\) 288.000 0.740360 0.370180 0.928960i \(-0.379296\pi\)
0.370180 + 0.928960i \(0.379296\pi\)
\(390\) 0 0
\(391\) 69.2820i 0.177192i
\(392\) 472.000 1.20408
\(393\) 0 0
\(394\) −154.000 + 266.736i −0.390863 + 0.676994i
\(395\) 0 0
\(396\) 0 0
\(397\) 306.000 0.770781 0.385390 0.922754i \(-0.374067\pi\)
0.385390 + 0.922754i \(0.374067\pi\)
\(398\) −324.000 187.061i −0.814070 0.470004i
\(399\) 0 0
\(400\) 0 0
\(401\) 450.000 1.12219 0.561097 0.827750i \(-0.310379\pi\)
0.561097 + 0.827750i \(0.310379\pi\)
\(402\) 0 0
\(403\) 124.708i 0.309448i
\(404\) 72.0000 + 124.708i 0.178218 + 0.308682i
\(405\) 0 0
\(406\) −648.000 374.123i −1.59606 0.921485i
\(407\) 561.184i 1.37883i
\(408\) 0 0
\(409\) −50.0000 −0.122249 −0.0611247 0.998130i \(-0.519469\pi\)
−0.0611247 + 0.998130i \(0.519469\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −36.0000 + 20.7846i −0.0873786 + 0.0504481i
\(413\) 324.000 0.784504
\(414\) 0 0
\(415\) 0 0
\(416\) −288.000 498.831i −0.692308 1.19911i
\(417\) 0 0
\(418\) 144.000 249.415i 0.344498 0.596687i
\(419\) 737.854i 1.76099i −0.474058 0.880494i \(-0.657211\pi\)
0.474058 0.880494i \(-0.342789\pi\)
\(420\) 0 0
\(421\) −286.000 −0.679335 −0.339667 0.940546i \(-0.610315\pi\)
−0.339667 + 0.940546i \(0.610315\pi\)
\(422\) −420.000 242.487i −0.995261 0.574614i
\(423\) 0 0
\(424\) 208.000 0.490566
\(425\) 0 0
\(426\) 0 0
\(427\) 769.031i 1.80101i
\(428\) −648.000 + 374.123i −1.51402 + 0.874119i
\(429\) 0 0
\(430\) 0 0
\(431\) 124.708i 0.289345i 0.989480 + 0.144672i \(0.0462128\pi\)
−0.989480 + 0.144672i \(0.953787\pi\)
\(432\) 0 0
\(433\) 36.0000 0.0831409 0.0415704 0.999136i \(-0.486764\pi\)
0.0415704 + 0.999136i \(0.486764\pi\)
\(434\) −72.0000 + 124.708i −0.165899 + 0.287345i
\(435\) 0 0
\(436\) 52.0000 + 90.0666i 0.119266 + 0.206575i
\(437\) −96.0000 −0.219680
\(438\) 0 0
\(439\) 782.887i 1.78334i 0.452684 + 0.891671i \(0.350466\pi\)
−0.452684 + 0.891671i \(0.649534\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −180.000 + 311.769i −0.407240 + 0.705360i
\(443\) 214.774i 0.484818i −0.970174 0.242409i \(-0.922062\pi\)
0.970174 0.242409i \(-0.0779376\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −162.000 93.5307i −0.363229 0.209710i
\(447\) 0 0
\(448\) 665.108i 1.48461i
\(449\) −54.0000 −0.120267 −0.0601336 0.998190i \(-0.519153\pi\)
−0.0601336 + 0.998190i \(0.519153\pi\)
\(450\) 0 0
\(451\) 187.061i 0.414770i
\(452\) 20.0000 + 34.6410i 0.0442478 + 0.0766394i
\(453\) 0 0
\(454\) −372.000 214.774i −0.819383 0.473071i
\(455\) 0 0
\(456\) 0 0
\(457\) −288.000 −0.630197 −0.315098 0.949059i \(-0.602038\pi\)
−0.315098 + 0.949059i \(0.602038\pi\)
\(458\) 338.000 585.433i 0.737991 1.27824i
\(459\) 0 0
\(460\) 0 0
\(461\) 288.000 0.624729 0.312364 0.949962i \(-0.398879\pi\)
0.312364 + 0.949962i \(0.398879\pi\)
\(462\) 0 0
\(463\) 405.300i 0.875378i −0.899126 0.437689i \(-0.855797\pi\)
0.899126 0.437689i \(-0.144203\pi\)
\(464\) −288.000 + 498.831i −0.620690 + 1.07507i
\(465\) 0 0
\(466\) −182.000 + 315.233i −0.390558 + 0.676466i
\(467\) 575.041i 1.23135i 0.788000 + 0.615675i \(0.211117\pi\)
−0.788000 + 0.615675i \(0.788883\pi\)
\(468\) 0 0
\(469\) −432.000 −0.921109
\(470\) 0 0
\(471\) 0 0
\(472\) 249.415i 0.528422i
\(473\) −216.000 −0.456660
\(474\) 0 0
\(475\) 0 0
\(476\) −360.000 + 207.846i −0.756303 + 0.436651i
\(477\) 0 0
\(478\) 612.000 + 353.338i 1.28033 + 0.739202i
\(479\) 145.492i 0.303742i 0.988400 + 0.151871i \(0.0485298\pi\)
−0.988400 + 0.151871i \(0.951470\pi\)
\(480\) 0 0
\(481\) 972.000 2.02079
\(482\) −106.000 + 183.597i −0.219917 + 0.380907i
\(483\) 0 0
\(484\) −26.0000 45.0333i −0.0537190 0.0930441i
\(485\) 0 0
\(486\) 0 0
\(487\) 259.808i 0.533486i 0.963768 + 0.266743i \(0.0859475\pi\)
−0.963768 + 0.266743i \(0.914053\pi\)
\(488\) 592.000 1.21311
\(489\) 0 0
\(490\) 0 0
\(491\) 72.7461i 0.148159i −0.997252 0.0740796i \(-0.976398\pi\)
0.997252 0.0740796i \(-0.0236019\pi\)
\(492\) 0 0
\(493\) 360.000 0.730223
\(494\) −432.000 249.415i −0.874494 0.504889i
\(495\) 0 0
\(496\) 96.0000 + 55.4256i 0.193548 + 0.111745i
\(497\) 1080.00 2.17304
\(498\) 0 0
\(499\) 443.405i 0.888587i −0.895881 0.444294i \(-0.853455\pi\)
0.895881 0.444294i \(-0.146545\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −558.000 322.161i −1.11155 0.641756i
\(503\) 110.851i 0.220380i 0.993911 + 0.110190i \(0.0351460\pi\)
−0.993911 + 0.110190i \(0.964854\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 72.0000 124.708i 0.142292 0.246458i
\(507\) 0 0
\(508\) −756.000 + 436.477i −1.48819 + 0.859206i
\(509\) 252.000 0.495088 0.247544 0.968877i \(-0.420376\pi\)
0.247544 + 0.968877i \(0.420376\pi\)
\(510\) 0 0
\(511\) 374.123i 0.732139i
\(512\) −512.000 −1.00000
\(513\) 0 0
\(514\) 14.0000 24.2487i 0.0272374 0.0471765i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 972.000 + 561.184i 1.87645 + 1.08337i
\(519\) 0 0
\(520\) 0 0
\(521\) −54.0000 −0.103647 −0.0518234 0.998656i \(-0.516503\pi\)
−0.0518234 + 0.998656i \(0.516503\pi\)
\(522\) 0 0
\(523\) 623.538i 1.19223i 0.802898 + 0.596117i \(0.203291\pi\)
−0.802898 + 0.596117i \(0.796709\pi\)
\(524\) 468.000 270.200i 0.893130 0.515649i
\(525\) 0 0
\(526\) 324.000 + 187.061i 0.615970 + 0.355630i
\(527\) 69.2820i 0.131465i
\(528\) 0 0
\(529\) 481.000 0.909263
\(530\) 0 0
\(531\) 0 0
\(532\) −288.000 498.831i −0.541353 0.937652i
\(533\) 324.000 0.607880
\(534\) 0 0
\(535\) 0 0
\(536\) 332.554i 0.620436i
\(537\) 0 0
\(538\) 108.000 187.061i 0.200743 0.347698i
\(539\) 613.146i 1.13756i
\(540\) 0 0
\(541\) −650.000 −1.20148 −0.600739 0.799445i \(-0.705127\pi\)
−0.600739 + 0.799445i \(0.705127\pi\)
\(542\) 564.000 + 325.626i 1.04059 + 0.600785i
\(543\) 0 0
\(544\) 160.000 + 277.128i 0.294118 + 0.509427i
\(545\) 0 0
\(546\) 0 0
\(547\) 685.892i 1.25392i 0.779053 + 0.626958i \(0.215700\pi\)
−0.779053 + 0.626958i \(0.784300\pi\)
\(548\) −220.000 381.051i −0.401460 0.695349i
\(549\) 0 0
\(550\) 0 0
\(551\) 498.831i 0.905319i
\(552\) 0 0
\(553\) 936.000 1.69259
\(554\) −270.000 + 467.654i −0.487365 + 0.844140i
\(555\) 0 0
\(556\) −648.000 + 374.123i −1.16547 + 0.672883i
\(557\) 574.000 1.03052 0.515260 0.857034i \(-0.327695\pi\)
0.515260 + 0.857034i \(0.327695\pi\)
\(558\) 0 0
\(559\) 374.123i 0.669272i
\(560\) 0 0
\(561\) 0 0
\(562\) 234.000 405.300i 0.416370 0.721174i
\(563\) 561.184i 0.996775i 0.866954 + 0.498388i \(0.166074\pi\)
−0.866954 + 0.498388i \(0.833926\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 144.000 + 83.1384i 0.254417 + 0.146888i
\(567\) 0 0
\(568\) 831.384i 1.46370i
\(569\) −198.000 −0.347979 −0.173989 0.984748i \(-0.555666\pi\)
−0.173989 + 0.984748i \(0.555666\pi\)
\(570\) 0 0
\(571\) 180.133i 0.315470i 0.987481 + 0.157735i \(0.0504192\pi\)
−0.987481 + 0.157735i \(0.949581\pi\)
\(572\) 648.000 374.123i 1.13287 0.654061i
\(573\) 0 0
\(574\) 324.000 + 187.061i 0.564460 + 0.325891i
\(575\) 0 0
\(576\) 0 0
\(577\) 504.000 0.873484 0.436742 0.899587i \(-0.356132\pi\)
0.436742 + 0.899587i \(0.356132\pi\)
\(578\) −189.000 + 327.358i −0.326990 + 0.566363i
\(579\) 0 0
\(580\) 0 0
\(581\) −936.000 −1.61102
\(582\) 0 0
\(583\) 270.200i 0.463465i
\(584\) 288.000 0.493151
\(585\) 0 0
\(586\) −58.0000 + 100.459i −0.0989761 + 0.171432i
\(587\) 408.764i 0.696361i −0.937427 0.348181i \(-0.886800\pi\)
0.937427 0.348181i \(-0.113200\pi\)
\(588\) 0 0
\(589\) 96.0000 0.162988
\(590\) 0 0
\(591\) 0 0
\(592\) 432.000 748.246i 0.729730 1.26393i
\(593\) 998.000 1.68297 0.841484 0.540282i \(-0.181682\pi\)
0.841484 + 0.540282i \(0.181682\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 576.000 + 997.661i 0.966443 + 1.67393i
\(597\) 0 0
\(598\) −216.000 124.708i −0.361204 0.208541i
\(599\) 540.400i 0.902170i 0.892481 + 0.451085i \(0.148963\pi\)
−0.892481 + 0.451085i \(0.851037\pi\)
\(600\) 0 0
\(601\) −614.000 −1.02163 −0.510815 0.859690i \(-0.670656\pi\)
−0.510815 + 0.859690i \(0.670656\pi\)
\(602\) −216.000 + 374.123i −0.358804 + 0.621467i
\(603\) 0 0
\(604\) −648.000 + 374.123i −1.07285 + 0.619409i
\(605\) 0 0
\(606\) 0 0
\(607\) 654.715i 1.07861i −0.842111 0.539304i \(-0.818687\pi\)
0.842111 0.539304i \(-0.181313\pi\)
\(608\) −384.000 + 221.703i −0.631579 + 0.364642i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −414.000 −0.675367 −0.337684 0.941260i \(-0.609643\pi\)
−0.337684 + 0.941260i \(0.609643\pi\)
\(614\) 468.000 + 270.200i 0.762215 + 0.440065i
\(615\) 0 0
\(616\) 864.000 1.40260
\(617\) 58.0000 0.0940032 0.0470016 0.998895i \(-0.485033\pi\)
0.0470016 + 0.998895i \(0.485033\pi\)
\(618\) 0 0
\(619\) 187.061i 0.302199i 0.988519 + 0.151100i \(0.0482815\pi\)
−0.988519 + 0.151100i \(0.951719\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −468.000 270.200i −0.752412 0.434405i
\(623\) 187.061i 0.300259i
\(624\) 0 0
\(625\) 0 0
\(626\) −468.000 + 810.600i −0.747604 + 1.29489i
\(627\) 0 0
\(628\) 468.000 + 810.600i 0.745223 + 1.29076i
\(629\) −540.000 −0.858506
\(630\) 0 0
\(631\) 824.456i 1.30659i −0.757105 0.653293i \(-0.773387\pi\)
0.757105 0.653293i \(-0.226613\pi\)
\(632\) 720.533i 1.14008i
\(633\) 0 0
\(634\) 250.000 433.013i 0.394322 0.682985i
\(635\) 0 0
\(636\) 0 0
\(637\) 1062.00 1.66719
\(638\) −648.000 374.123i −1.01567 0.586400i
\(639\) 0 0
\(640\) 0 0
\(641\) −810.000 −1.26365 −0.631825 0.775111i \(-0.717694\pi\)
−0.631825 + 0.775111i \(0.717694\pi\)
\(642\) 0 0
\(643\) 415.692i 0.646489i 0.946316 + 0.323244i \(0.104774\pi\)
−0.946316 + 0.323244i \(0.895226\pi\)
\(644\) −144.000 249.415i −0.223602 0.387291i
\(645\) 0 0
\(646\) 240.000 + 138.564i 0.371517 + 0.214495i
\(647\) 983.805i 1.52056i 0.649593 + 0.760282i \(0.274939\pi\)
−0.649593 + 0.760282i \(0.725061\pi\)
\(648\) 0 0
\(649\) 324.000 0.499230
\(650\) 0 0
\(651\) 0 0
\(652\) −432.000 + 249.415i −0.662577 + 0.382539i
\(653\) −950.000 −1.45482 −0.727412 0.686201i \(-0.759277\pi\)
−0.727412 + 0.686201i \(0.759277\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 144.000 249.415i 0.219512 0.380206i
\(657\) 0 0
\(658\) 0 0
\(659\) 1132.76i 1.71891i 0.511212 + 0.859455i \(0.329197\pi\)
−0.511212 + 0.859455i \(0.670803\pi\)
\(660\) 0 0
\(661\) −242.000 −0.366112 −0.183056 0.983102i \(-0.558599\pi\)
−0.183056 + 0.983102i \(0.558599\pi\)
\(662\) −648.000 374.123i −0.978852 0.565140i
\(663\) 0 0
\(664\) 720.533i 1.08514i
\(665\) 0 0
\(666\) 0 0
\(667\) 249.415i 0.373936i
\(668\) 456.000 263.272i 0.682635 0.394119i
\(669\) 0 0
\(670\) 0 0
\(671\) 769.031i 1.14610i
\(672\) 0 0
\(673\) −324.000 −0.481426 −0.240713 0.970596i \(-0.577381\pi\)
−0.240713 + 0.970596i \(0.577381\pi\)
\(674\) 468.000 810.600i 0.694362 1.20267i
\(675\) 0 0
\(676\) −310.000 536.936i −0.458580 0.794284i
\(677\) −806.000 −1.19055 −0.595273 0.803523i \(-0.702956\pi\)
−0.595273 + 0.803523i \(0.702956\pi\)
\(678\) 0 0
\(679\) 748.246i 1.10198i
\(680\) 0 0
\(681\) 0 0
\(682\) −72.0000 + 124.708i −0.105572 + 0.182856i
\(683\) 575.041i 0.841934i 0.907076 + 0.420967i \(0.138309\pi\)
−0.907076 + 0.420967i \(0.861691\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 180.000 + 103.923i 0.262391 + 0.151491i
\(687\) 0 0
\(688\) 288.000 + 166.277i 0.418605 + 0.241682i
\(689\) 468.000 0.679245
\(690\) 0 0
\(691\) 775.959i 1.12295i 0.827494 + 0.561475i \(0.189766\pi\)
−0.827494 + 0.561475i \(0.810234\pi\)
\(692\) −292.000 505.759i −0.421965 0.730865i
\(693\) 0 0
\(694\) −972.000 561.184i −1.40058 0.808623i
\(695\) 0 0
\(696\) 0 0
\(697\) −180.000 −0.258250
\(698\) −434.000 + 751.710i −0.621777 + 1.07695i
\(699\) 0 0
\(700\) 0 0
\(701\) −756.000 −1.07846 −0.539230 0.842159i \(-0.681285\pi\)
−0.539230 + 0.842159i \(0.681285\pi\)
\(702\) 0 0
\(703\) 748.246i 1.06436i
\(704\) 665.108i 0.944755i
\(705\) 0 0
\(706\) −158.000 + 273.664i −0.223796 + 0.387626i
\(707\) 374.123i 0.529170i
\(708\) 0 0
\(709\) −310.000 −0.437236 −0.218618 0.975811i \(-0.570155\pi\)
−0.218618 + 0.975811i \(0.570155\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −144.000 −0.202247
\(713\) 48.0000 0.0673212
\(714\) 0 0
\(715\) 0 0
\(716\) 252.000 145.492i 0.351955 0.203201i
\(717\) 0 0
\(718\) −792.000 457.261i −1.10306 0.636854i
\(719\) 83.1384i 0.115631i −0.998327 0.0578153i \(-0.981587\pi\)
0.998327 0.0578153i \(-0.0184135\pi\)
\(720\) 0 0
\(721\) −108.000 −0.149792
\(722\) 169.000 292.717i 0.234072 0.405425i
\(723\) 0 0
\(724\) −524.000 907.595i −0.723757 1.25358i
\(725\) 0 0
\(726\) 0 0
\(727\) 1091.19i 1.50095i 0.660898 + 0.750476i \(0.270176\pi\)
−0.660898 + 0.750476i \(0.729824\pi\)
\(728\) 1496.49i 2.05562i
\(729\) 0 0
\(730\) 0 0
\(731\) 207.846i 0.284331i
\(732\) 0 0
\(733\) −1206.00 −1.64529 −0.822647 0.568553i \(-0.807503\pi\)
−0.822647 + 0.568553i \(0.807503\pi\)
\(734\) −378.000 218.238i −0.514986 0.297328i
\(735\) 0 0
\(736\) −192.000 + 110.851i −0.260870 + 0.150613i
\(737\) −432.000 −0.586160
\(738\) 0 0
\(739\) 484.974i 0.656257i 0.944633 + 0.328129i \(0.106418\pi\)
−0.944633 + 0.328129i \(0.893582\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 468.000 + 270.200i 0.630728 + 0.364151i
\(743\) 1122.37i 1.51059i −0.655385 0.755295i \(-0.727493\pi\)
0.655385 0.755295i \(-0.272507\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 270.000 467.654i 0.361930 0.626882i
\(747\) 0 0
\(748\) −360.000 + 207.846i −0.481283 + 0.277869i
\(749\) −1944.00 −2.59546
\(750\) 0 0
\(751\) 242.487i 0.322886i −0.986882 0.161443i \(-0.948385\pi\)
0.986882 0.161443i \(-0.0516147\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −648.000 + 1122.37i −0.859416 + 1.48855i
\(755\) 0 0
\(756\) 0 0
\(757\) −846.000 −1.11757 −0.558785 0.829313i \(-0.688732\pi\)
−0.558785 + 0.829313i \(0.688732\pi\)
\(758\) −564.000 325.626i −0.744063 0.429585i
\(759\) 0 0
\(760\) 0 0
\(761\) 1458.00 1.91590 0.957950 0.286935i \(-0.0926364\pi\)
0.957950 + 0.286935i \(0.0926364\pi\)
\(762\) 0 0
\(763\) 270.200i 0.354128i
\(764\) −648.000 + 374.123i −0.848168 + 0.489690i
\(765\) 0 0
\(766\) −96.0000 55.4256i −0.125326 0.0723572i
\(767\) 561.184i 0.731662i
\(768\) 0 0
\(769\) 1282.00 1.66710 0.833550 0.552444i \(-0.186305\pi\)
0.833550 + 0.552444i \(0.186305\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 360.000 + 623.538i 0.466321 + 0.807692i
\(773\) −422.000 −0.545925 −0.272962 0.962025i \(-0.588003\pi\)
−0.272962 + 0.962025i \(0.588003\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −576.000 −0.742268
\(777\) 0 0
\(778\) 288.000 498.831i 0.370180 0.641170i
\(779\) 249.415i 0.320174i
\(780\) 0 0
\(781\) 1080.00 1.38284
\(782\) 120.000 + 69.2820i 0.153453 + 0.0885959i
\(783\) 0 0
\(784\) 472.000 817.528i 0.602041 1.04277i
\(785\) 0 0
\(786\) 0 0
\(787\) 1205.51i 1.53178i 0.642974 + 0.765888i \(0.277700\pi\)
−0.642974 + 0.765888i \(0.722300\pi\)
\(788\) 308.000 + 533.472i 0.390863 + 0.676994i
\(789\) 0 0
\(790\) 0 0
\(791\) 103.923i 0.131382i
\(792\) 0 0
\(793\) 1332.00 1.67970
\(794\) 306.000 530.008i 0.385390 0.667516i
\(795\) 0 0
\(796\) −648.000 + 374.123i