Properties

Label 384.2.c.b.383.1
Level $384$
Weight $2$
Character 384.383
Analytic conductor $3.066$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.06625543762\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 383.1
Root \(-0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 384.383
Dual form 384.2.c.b.383.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.61803 - 0.618034i) q^{3} +1.23607i q^{5} -3.23607i q^{7} +(2.23607 + 2.00000i) q^{9} +O(q^{10})\) \(q+(-1.61803 - 0.618034i) q^{3} +1.23607i q^{5} -3.23607i q^{7} +(2.23607 + 2.00000i) q^{9} +0.763932 q^{11} -4.47214 q^{13} +(0.763932 - 2.00000i) q^{15} -6.47214i q^{17} -5.23607i q^{19} +(-2.00000 + 5.23607i) q^{21} -6.47214 q^{23} +3.47214 q^{25} +(-2.38197 - 4.61803i) q^{27} -9.23607i q^{29} +0.763932i q^{31} +(-1.23607 - 0.472136i) q^{33} +4.00000 q^{35} +0.472136 q^{37} +(7.23607 + 2.76393i) q^{39} +2.47214i q^{41} +2.76393i q^{43} +(-2.47214 + 2.76393i) q^{45} -8.00000 q^{47} -3.47214 q^{49} +(-4.00000 + 10.4721i) q^{51} +1.23607i q^{53} +0.944272i q^{55} +(-3.23607 + 8.47214i) q^{57} +3.23607 q^{59} +8.47214 q^{61} +(6.47214 - 7.23607i) q^{63} -5.52786i q^{65} +3.70820i q^{67} +(10.4721 + 4.00000i) q^{69} +11.4164 q^{71} -2.00000 q^{73} +(-5.61803 - 2.14590i) q^{75} -2.47214i q^{77} +13.7082i q^{79} +(1.00000 + 8.94427i) q^{81} +7.23607 q^{83} +8.00000 q^{85} +(-5.70820 + 14.9443i) q^{87} -4.00000i q^{89} +14.4721i q^{91} +(0.472136 - 1.23607i) q^{93} +6.47214 q^{95} -8.47214 q^{97} +(1.70820 + 1.52786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} + O(q^{10}) \) \( 4q - 2q^{3} + 12q^{11} + 12q^{15} - 8q^{21} - 8q^{23} - 4q^{25} - 14q^{27} + 4q^{33} + 16q^{35} - 16q^{37} + 20q^{39} + 8q^{45} - 32q^{47} + 4q^{49} - 16q^{51} - 4q^{57} + 4q^{59} + 16q^{61} + 8q^{63} + 24q^{69} - 8q^{71} - 8q^{73} - 18q^{75} + 4q^{81} + 20q^{83} + 32q^{85} + 4q^{87} - 16q^{93} + 8q^{95} - 16q^{97} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.61803 0.618034i −0.934172 0.356822i
\(4\) 0 0
\(5\) 1.23607i 0.552786i 0.961045 + 0.276393i \(0.0891392\pi\)
−0.961045 + 0.276393i \(0.910861\pi\)
\(6\) 0 0
\(7\) 3.23607i 1.22312i −0.791199 0.611559i \(-0.790543\pi\)
0.791199 0.611559i \(-0.209457\pi\)
\(8\) 0 0
\(9\) 2.23607 + 2.00000i 0.745356 + 0.666667i
\(10\) 0 0
\(11\) 0.763932 0.230334 0.115167 0.993346i \(-0.463260\pi\)
0.115167 + 0.993346i \(0.463260\pi\)
\(12\) 0 0
\(13\) −4.47214 −1.24035 −0.620174 0.784465i \(-0.712938\pi\)
−0.620174 + 0.784465i \(0.712938\pi\)
\(14\) 0 0
\(15\) 0.763932 2.00000i 0.197246 0.516398i
\(16\) 0 0
\(17\) 6.47214i 1.56972i −0.619671 0.784862i \(-0.712734\pi\)
0.619671 0.784862i \(-0.287266\pi\)
\(18\) 0 0
\(19\) 5.23607i 1.20124i −0.799536 0.600618i \(-0.794921\pi\)
0.799536 0.600618i \(-0.205079\pi\)
\(20\) 0 0
\(21\) −2.00000 + 5.23607i −0.436436 + 1.14260i
\(22\) 0 0
\(23\) −6.47214 −1.34953 −0.674767 0.738031i \(-0.735756\pi\)
−0.674767 + 0.738031i \(0.735756\pi\)
\(24\) 0 0
\(25\) 3.47214 0.694427
\(26\) 0 0
\(27\) −2.38197 4.61803i −0.458410 0.888741i
\(28\) 0 0
\(29\) 9.23607i 1.71509i −0.514405 0.857547i \(-0.671987\pi\)
0.514405 0.857547i \(-0.328013\pi\)
\(30\) 0 0
\(31\) 0.763932i 0.137206i 0.997644 + 0.0686031i \(0.0218542\pi\)
−0.997644 + 0.0686031i \(0.978146\pi\)
\(32\) 0 0
\(33\) −1.23607 0.472136i −0.215172 0.0821883i
\(34\) 0 0
\(35\) 4.00000 0.676123
\(36\) 0 0
\(37\) 0.472136 0.0776187 0.0388093 0.999247i \(-0.487644\pi\)
0.0388093 + 0.999247i \(0.487644\pi\)
\(38\) 0 0
\(39\) 7.23607 + 2.76393i 1.15870 + 0.442583i
\(40\) 0 0
\(41\) 2.47214i 0.386083i 0.981191 + 0.193041i \(0.0618352\pi\)
−0.981191 + 0.193041i \(0.938165\pi\)
\(42\) 0 0
\(43\) 2.76393i 0.421496i 0.977540 + 0.210748i \(0.0675899\pi\)
−0.977540 + 0.210748i \(0.932410\pi\)
\(44\) 0 0
\(45\) −2.47214 + 2.76393i −0.368524 + 0.412023i
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0 0
\(49\) −3.47214 −0.496019
\(50\) 0 0
\(51\) −4.00000 + 10.4721i −0.560112 + 1.46639i
\(52\) 0 0
\(53\) 1.23607i 0.169787i 0.996390 + 0.0848935i \(0.0270550\pi\)
−0.996390 + 0.0848935i \(0.972945\pi\)
\(54\) 0 0
\(55\) 0.944272i 0.127326i
\(56\) 0 0
\(57\) −3.23607 + 8.47214i −0.428628 + 1.12216i
\(58\) 0 0
\(59\) 3.23607 0.421300 0.210650 0.977562i \(-0.432442\pi\)
0.210650 + 0.977562i \(0.432442\pi\)
\(60\) 0 0
\(61\) 8.47214 1.08475 0.542373 0.840138i \(-0.317526\pi\)
0.542373 + 0.840138i \(0.317526\pi\)
\(62\) 0 0
\(63\) 6.47214 7.23607i 0.815412 0.911659i
\(64\) 0 0
\(65\) 5.52786i 0.685647i
\(66\) 0 0
\(67\) 3.70820i 0.453029i 0.974008 + 0.226515i \(0.0727331\pi\)
−0.974008 + 0.226515i \(0.927267\pi\)
\(68\) 0 0
\(69\) 10.4721 + 4.00000i 1.26070 + 0.481543i
\(70\) 0 0
\(71\) 11.4164 1.35488 0.677439 0.735579i \(-0.263090\pi\)
0.677439 + 0.735579i \(0.263090\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) −5.61803 2.14590i −0.648715 0.247787i
\(76\) 0 0
\(77\) 2.47214i 0.281726i
\(78\) 0 0
\(79\) 13.7082i 1.54229i 0.636657 + 0.771147i \(0.280317\pi\)
−0.636657 + 0.771147i \(0.719683\pi\)
\(80\) 0 0
\(81\) 1.00000 + 8.94427i 0.111111 + 0.993808i
\(82\) 0 0
\(83\) 7.23607 0.794262 0.397131 0.917762i \(-0.370006\pi\)
0.397131 + 0.917762i \(0.370006\pi\)
\(84\) 0 0
\(85\) 8.00000 0.867722
\(86\) 0 0
\(87\) −5.70820 + 14.9443i −0.611984 + 1.60219i
\(88\) 0 0
\(89\) 4.00000i 0.423999i −0.977270 0.212000i \(-0.932002\pi\)
0.977270 0.212000i \(-0.0679975\pi\)
\(90\) 0 0
\(91\) 14.4721i 1.51709i
\(92\) 0 0
\(93\) 0.472136 1.23607i 0.0489582 0.128174i
\(94\) 0 0
\(95\) 6.47214 0.664027
\(96\) 0 0
\(97\) −8.47214 −0.860215 −0.430108 0.902778i \(-0.641524\pi\)
−0.430108 + 0.902778i \(0.641524\pi\)
\(98\) 0 0
\(99\) 1.70820 + 1.52786i 0.171681 + 0.153556i
\(100\) 0 0
\(101\) 11.7082i 1.16501i −0.812827 0.582505i \(-0.802073\pi\)
0.812827 0.582505i \(-0.197927\pi\)
\(102\) 0 0
\(103\) 8.18034i 0.806033i −0.915193 0.403016i \(-0.867962\pi\)
0.915193 0.403016i \(-0.132038\pi\)
\(104\) 0 0
\(105\) −6.47214 2.47214i −0.631616 0.241256i
\(106\) 0 0
\(107\) 8.18034 0.790823 0.395412 0.918504i \(-0.370602\pi\)
0.395412 + 0.918504i \(0.370602\pi\)
\(108\) 0 0
\(109\) 0.472136 0.0452224 0.0226112 0.999744i \(-0.492802\pi\)
0.0226112 + 0.999744i \(0.492802\pi\)
\(110\) 0 0
\(111\) −0.763932 0.291796i −0.0725092 0.0276961i
\(112\) 0 0
\(113\) 8.00000i 0.752577i 0.926503 + 0.376288i \(0.122800\pi\)
−0.926503 + 0.376288i \(0.877200\pi\)
\(114\) 0 0
\(115\) 8.00000i 0.746004i
\(116\) 0 0
\(117\) −10.0000 8.94427i −0.924500 0.826898i
\(118\) 0 0
\(119\) −20.9443 −1.91996
\(120\) 0 0
\(121\) −10.4164 −0.946946
\(122\) 0 0
\(123\) 1.52786 4.00000i 0.137763 0.360668i
\(124\) 0 0
\(125\) 10.4721i 0.936656i
\(126\) 0 0
\(127\) 8.76393i 0.777673i 0.921307 + 0.388837i \(0.127123\pi\)
−0.921307 + 0.388837i \(0.872877\pi\)
\(128\) 0 0
\(129\) 1.70820 4.47214i 0.150399 0.393750i
\(130\) 0 0
\(131\) −11.2361 −0.981700 −0.490850 0.871244i \(-0.663314\pi\)
−0.490850 + 0.871244i \(0.663314\pi\)
\(132\) 0 0
\(133\) −16.9443 −1.46925
\(134\) 0 0
\(135\) 5.70820 2.94427i 0.491284 0.253403i
\(136\) 0 0
\(137\) 10.4721i 0.894695i −0.894360 0.447347i \(-0.852369\pi\)
0.894360 0.447347i \(-0.147631\pi\)
\(138\) 0 0
\(139\) 3.70820i 0.314526i 0.987557 + 0.157263i \(0.0502670\pi\)
−0.987557 + 0.157263i \(0.949733\pi\)
\(140\) 0 0
\(141\) 12.9443 + 4.94427i 1.09010 + 0.416383i
\(142\) 0 0
\(143\) −3.41641 −0.285694
\(144\) 0 0
\(145\) 11.4164 0.948081
\(146\) 0 0
\(147\) 5.61803 + 2.14590i 0.463368 + 0.176991i
\(148\) 0 0
\(149\) 3.70820i 0.303788i −0.988397 0.151894i \(-0.951463\pi\)
0.988397 0.151894i \(-0.0485372\pi\)
\(150\) 0 0
\(151\) 6.29180i 0.512019i −0.966674 0.256010i \(-0.917592\pi\)
0.966674 0.256010i \(-0.0824079\pi\)
\(152\) 0 0
\(153\) 12.9443 14.4721i 1.04648 1.17000i
\(154\) 0 0
\(155\) −0.944272 −0.0758457
\(156\) 0 0
\(157\) −4.47214 −0.356915 −0.178458 0.983948i \(-0.557111\pi\)
−0.178458 + 0.983948i \(0.557111\pi\)
\(158\) 0 0
\(159\) 0.763932 2.00000i 0.0605838 0.158610i
\(160\) 0 0
\(161\) 20.9443i 1.65064i
\(162\) 0 0
\(163\) 18.1803i 1.42399i −0.702182 0.711997i \(-0.747791\pi\)
0.702182 0.711997i \(-0.252209\pi\)
\(164\) 0 0
\(165\) 0.583592 1.52786i 0.0454326 0.118944i
\(166\) 0 0
\(167\) 22.4721 1.73895 0.869473 0.493980i \(-0.164459\pi\)
0.869473 + 0.493980i \(0.164459\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) 0 0
\(171\) 10.4721 11.7082i 0.800824 0.895349i
\(172\) 0 0
\(173\) 8.65248i 0.657836i 0.944359 + 0.328918i \(0.106684\pi\)
−0.944359 + 0.328918i \(0.893316\pi\)
\(174\) 0 0
\(175\) 11.2361i 0.849367i
\(176\) 0 0
\(177\) −5.23607 2.00000i −0.393567 0.150329i
\(178\) 0 0
\(179\) −16.1803 −1.20938 −0.604688 0.796463i \(-0.706702\pi\)
−0.604688 + 0.796463i \(0.706702\pi\)
\(180\) 0 0
\(181\) 11.5279 0.856859 0.428430 0.903575i \(-0.359067\pi\)
0.428430 + 0.903575i \(0.359067\pi\)
\(182\) 0 0
\(183\) −13.7082 5.23607i −1.01334 0.387061i
\(184\) 0 0
\(185\) 0.583592i 0.0429065i
\(186\) 0 0
\(187\) 4.94427i 0.361561i
\(188\) 0 0
\(189\) −14.9443 + 7.70820i −1.08704 + 0.560689i
\(190\) 0 0
\(191\) 4.94427 0.357755 0.178877 0.983871i \(-0.442753\pi\)
0.178877 + 0.983871i \(0.442753\pi\)
\(192\) 0 0
\(193\) 23.8885 1.71954 0.859768 0.510686i \(-0.170608\pi\)
0.859768 + 0.510686i \(0.170608\pi\)
\(194\) 0 0
\(195\) −3.41641 + 8.94427i −0.244654 + 0.640513i
\(196\) 0 0
\(197\) 9.23607i 0.658043i 0.944323 + 0.329021i \(0.106719\pi\)
−0.944323 + 0.329021i \(0.893281\pi\)
\(198\) 0 0
\(199\) 16.1803i 1.14699i −0.819208 0.573497i \(-0.805586\pi\)
0.819208 0.573497i \(-0.194414\pi\)
\(200\) 0 0
\(201\) 2.29180 6.00000i 0.161651 0.423207i
\(202\) 0 0
\(203\) −29.8885 −2.09776
\(204\) 0 0
\(205\) −3.05573 −0.213421
\(206\) 0 0
\(207\) −14.4721 12.9443i −1.00588 0.899689i
\(208\) 0 0
\(209\) 4.00000i 0.276686i
\(210\) 0 0
\(211\) 6.76393i 0.465648i 0.972519 + 0.232824i \(0.0747967\pi\)
−0.972519 + 0.232824i \(0.925203\pi\)
\(212\) 0 0
\(213\) −18.4721 7.05573i −1.26569 0.483451i
\(214\) 0 0
\(215\) −3.41641 −0.232997
\(216\) 0 0
\(217\) 2.47214 0.167820
\(218\) 0 0
\(219\) 3.23607 + 1.23607i 0.218673 + 0.0835257i
\(220\) 0 0
\(221\) 28.9443i 1.94700i
\(222\) 0 0
\(223\) 12.1803i 0.815656i −0.913059 0.407828i \(-0.866286\pi\)
0.913059 0.407828i \(-0.133714\pi\)
\(224\) 0 0
\(225\) 7.76393 + 6.94427i 0.517595 + 0.462951i
\(226\) 0 0
\(227\) 20.1803 1.33942 0.669708 0.742624i \(-0.266419\pi\)
0.669708 + 0.742624i \(0.266419\pi\)
\(228\) 0 0
\(229\) −20.4721 −1.35284 −0.676418 0.736518i \(-0.736469\pi\)
−0.676418 + 0.736518i \(0.736469\pi\)
\(230\) 0 0
\(231\) −1.52786 + 4.00000i −0.100526 + 0.263181i
\(232\) 0 0
\(233\) 7.05573i 0.462236i 0.972926 + 0.231118i \(0.0742384\pi\)
−0.972926 + 0.231118i \(0.925762\pi\)
\(234\) 0 0
\(235\) 9.88854i 0.645057i
\(236\) 0 0
\(237\) 8.47214 22.1803i 0.550324 1.44077i
\(238\) 0 0
\(239\) 8.00000 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 0 0
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 0 0
\(243\) 3.90983 15.0902i 0.250816 0.968035i
\(244\) 0 0
\(245\) 4.29180i 0.274193i
\(246\) 0 0
\(247\) 23.4164i 1.48995i
\(248\) 0 0
\(249\) −11.7082 4.47214i −0.741977 0.283410i
\(250\) 0 0
\(251\) −10.2918 −0.649612 −0.324806 0.945781i \(-0.605299\pi\)
−0.324806 + 0.945781i \(0.605299\pi\)
\(252\) 0 0
\(253\) −4.94427 −0.310844
\(254\) 0 0
\(255\) −12.9443 4.94427i −0.810602 0.309622i
\(256\) 0 0
\(257\) 3.05573i 0.190611i 0.995448 + 0.0953055i \(0.0303828\pi\)
−0.995448 + 0.0953055i \(0.969617\pi\)
\(258\) 0 0
\(259\) 1.52786i 0.0949369i
\(260\) 0 0
\(261\) 18.4721 20.6525i 1.14340 1.27836i
\(262\) 0 0
\(263\) 1.52786 0.0942121 0.0471061 0.998890i \(-0.485000\pi\)
0.0471061 + 0.998890i \(0.485000\pi\)
\(264\) 0 0
\(265\) −1.52786 −0.0938559
\(266\) 0 0
\(267\) −2.47214 + 6.47214i −0.151292 + 0.396088i
\(268\) 0 0
\(269\) 6.18034i 0.376822i −0.982090 0.188411i \(-0.939666\pi\)
0.982090 0.188411i \(-0.0603337\pi\)
\(270\) 0 0
\(271\) 13.7082i 0.832714i 0.909201 + 0.416357i \(0.136693\pi\)
−0.909201 + 0.416357i \(0.863307\pi\)
\(272\) 0 0
\(273\) 8.94427 23.4164i 0.541332 1.41723i
\(274\) 0 0
\(275\) 2.65248 0.159950
\(276\) 0 0
\(277\) 16.4721 0.989715 0.494857 0.868974i \(-0.335220\pi\)
0.494857 + 0.868974i \(0.335220\pi\)
\(278\) 0 0
\(279\) −1.52786 + 1.70820i −0.0914708 + 0.102267i
\(280\) 0 0
\(281\) 7.05573i 0.420909i −0.977604 0.210455i \(-0.932506\pi\)
0.977604 0.210455i \(-0.0674945\pi\)
\(282\) 0 0
\(283\) 25.2361i 1.50013i −0.661365 0.750064i \(-0.730023\pi\)
0.661365 0.750064i \(-0.269977\pi\)
\(284\) 0 0
\(285\) −10.4721 4.00000i −0.620316 0.236940i
\(286\) 0 0
\(287\) 8.00000 0.472225
\(288\) 0 0
\(289\) −24.8885 −1.46403
\(290\) 0 0
\(291\) 13.7082 + 5.23607i 0.803589 + 0.306944i
\(292\) 0 0
\(293\) 25.2361i 1.47431i 0.675725 + 0.737153i \(0.263831\pi\)
−0.675725 + 0.737153i \(0.736169\pi\)
\(294\) 0 0
\(295\) 4.00000i 0.232889i
\(296\) 0 0
\(297\) −1.81966 3.52786i −0.105587 0.204707i
\(298\) 0 0
\(299\) 28.9443 1.67389
\(300\) 0 0
\(301\) 8.94427 0.515539
\(302\) 0 0
\(303\) −7.23607 + 18.9443i −0.415701 + 1.08832i
\(304\) 0 0
\(305\) 10.4721i 0.599633i
\(306\) 0 0
\(307\) 21.5967i 1.23259i 0.787515 + 0.616296i \(0.211367\pi\)
−0.787515 + 0.616296i \(0.788633\pi\)
\(308\) 0 0
\(309\) −5.05573 + 13.2361i −0.287610 + 0.752974i
\(310\) 0 0
\(311\) 14.4721 0.820640 0.410320 0.911942i \(-0.365417\pi\)
0.410320 + 0.911942i \(0.365417\pi\)
\(312\) 0 0
\(313\) 8.47214 0.478873 0.239437 0.970912i \(-0.423037\pi\)
0.239437 + 0.970912i \(0.423037\pi\)
\(314\) 0 0
\(315\) 8.94427 + 8.00000i 0.503953 + 0.450749i
\(316\) 0 0
\(317\) 27.1246i 1.52347i −0.647889 0.761735i \(-0.724348\pi\)
0.647889 0.761735i \(-0.275652\pi\)
\(318\) 0 0
\(319\) 7.05573i 0.395045i
\(320\) 0 0
\(321\) −13.2361 5.05573i −0.738765 0.282183i
\(322\) 0 0
\(323\) −33.8885 −1.88561
\(324\) 0 0
\(325\) −15.5279 −0.861331
\(326\) 0 0
\(327\) −0.763932 0.291796i −0.0422455 0.0161364i
\(328\) 0 0
\(329\) 25.8885i 1.42728i
\(330\) 0 0
\(331\) 34.5410i 1.89855i 0.314453 + 0.949273i \(0.398179\pi\)
−0.314453 + 0.949273i \(0.601821\pi\)
\(332\) 0 0
\(333\) 1.05573 + 0.944272i 0.0578535 + 0.0517458i
\(334\) 0 0
\(335\) −4.58359 −0.250428
\(336\) 0 0
\(337\) −22.3607 −1.21806 −0.609032 0.793146i \(-0.708442\pi\)
−0.609032 + 0.793146i \(0.708442\pi\)
\(338\) 0 0
\(339\) 4.94427 12.9443i 0.268536 0.703036i
\(340\) 0 0
\(341\) 0.583592i 0.0316033i
\(342\) 0 0
\(343\) 11.4164i 0.616428i
\(344\) 0 0
\(345\) −4.94427 + 12.9443i −0.266191 + 0.696896i
\(346\) 0 0
\(347\) −10.2918 −0.552493 −0.276246 0.961087i \(-0.589091\pi\)
−0.276246 + 0.961087i \(0.589091\pi\)
\(348\) 0 0
\(349\) 19.5279 1.04530 0.522651 0.852547i \(-0.324943\pi\)
0.522651 + 0.852547i \(0.324943\pi\)
\(350\) 0 0
\(351\) 10.6525 + 20.6525i 0.568587 + 1.10235i
\(352\) 0 0
\(353\) 25.8885i 1.37791i −0.724805 0.688954i \(-0.758070\pi\)
0.724805 0.688954i \(-0.241930\pi\)
\(354\) 0 0
\(355\) 14.1115i 0.748958i
\(356\) 0 0
\(357\) 33.8885 + 12.9443i 1.79357 + 0.685084i
\(358\) 0 0
\(359\) −4.58359 −0.241913 −0.120956 0.992658i \(-0.538596\pi\)
−0.120956 + 0.992658i \(0.538596\pi\)
\(360\) 0 0
\(361\) −8.41641 −0.442969
\(362\) 0 0
\(363\) 16.8541 + 6.43769i 0.884611 + 0.337891i
\(364\) 0 0
\(365\) 2.47214i 0.129398i
\(366\) 0 0
\(367\) 0.763932i 0.0398769i 0.999801 + 0.0199385i \(0.00634703\pi\)
−0.999801 + 0.0199385i \(0.993653\pi\)
\(368\) 0 0
\(369\) −4.94427 + 5.52786i −0.257389 + 0.287769i
\(370\) 0 0
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) 29.4164 1.52312 0.761562 0.648092i \(-0.224433\pi\)
0.761562 + 0.648092i \(0.224433\pi\)
\(374\) 0 0
\(375\) 6.47214 16.9443i 0.334220 0.874998i
\(376\) 0 0
\(377\) 41.3050i 2.12731i
\(378\) 0 0
\(379\) 20.6525i 1.06085i 0.847733 + 0.530423i \(0.177967\pi\)
−0.847733 + 0.530423i \(0.822033\pi\)
\(380\) 0 0
\(381\) 5.41641 14.1803i 0.277491 0.726481i
\(382\) 0 0
\(383\) 11.0557 0.564921 0.282461 0.959279i \(-0.408849\pi\)
0.282461 + 0.959279i \(0.408849\pi\)
\(384\) 0 0
\(385\) 3.05573 0.155734
\(386\) 0 0
\(387\) −5.52786 + 6.18034i −0.280997 + 0.314164i
\(388\) 0 0
\(389\) 9.81966i 0.497877i −0.968519 0.248938i \(-0.919918\pi\)
0.968519 0.248938i \(-0.0800816\pi\)
\(390\) 0 0
\(391\) 41.8885i 2.11839i
\(392\) 0 0
\(393\) 18.1803 + 6.94427i 0.917077 + 0.350292i
\(394\) 0 0
\(395\) −16.9443 −0.852559
\(396\) 0 0
\(397\) −9.41641 −0.472596 −0.236298 0.971681i \(-0.575934\pi\)
−0.236298 + 0.971681i \(0.575934\pi\)
\(398\) 0 0
\(399\) 27.4164 + 10.4721i 1.37254 + 0.524263i
\(400\) 0 0
\(401\) 16.3607i 0.817013i 0.912755 + 0.408507i \(0.133950\pi\)
−0.912755 + 0.408507i \(0.866050\pi\)
\(402\) 0 0
\(403\) 3.41641i 0.170183i
\(404\) 0 0
\(405\) −11.0557 + 1.23607i −0.549364 + 0.0614207i
\(406\) 0 0
\(407\) 0.360680 0.0178782
\(408\) 0 0
\(409\) 3.88854 0.192276 0.0961381 0.995368i \(-0.469351\pi\)
0.0961381 + 0.995368i \(0.469351\pi\)
\(410\) 0 0
\(411\) −6.47214 + 16.9443i −0.319247 + 0.835799i
\(412\) 0 0
\(413\) 10.4721i 0.515300i
\(414\) 0 0
\(415\) 8.94427i 0.439057i
\(416\) 0 0
\(417\) 2.29180 6.00000i 0.112230 0.293821i
\(418\) 0 0
\(419\) 12.1803 0.595049 0.297524 0.954714i \(-0.403839\pi\)
0.297524 + 0.954714i \(0.403839\pi\)
\(420\) 0 0
\(421\) 5.41641 0.263980 0.131990 0.991251i \(-0.457863\pi\)
0.131990 + 0.991251i \(0.457863\pi\)
\(422\) 0 0
\(423\) −17.8885 16.0000i −0.869771 0.777947i
\(424\) 0 0
\(425\) 22.4721i 1.09006i
\(426\) 0 0
\(427\) 27.4164i 1.32677i
\(428\) 0 0
\(429\) 5.52786 + 2.11146i 0.266888 + 0.101942i
\(430\) 0 0
\(431\) 8.00000 0.385346 0.192673 0.981263i \(-0.438284\pi\)
0.192673 + 0.981263i \(0.438284\pi\)
\(432\) 0 0
\(433\) 7.52786 0.361766 0.180883 0.983505i \(-0.442104\pi\)
0.180883 + 0.983505i \(0.442104\pi\)
\(434\) 0 0
\(435\) −18.4721 7.05573i −0.885671 0.338296i
\(436\) 0 0
\(437\) 33.8885i 1.62111i
\(438\) 0 0
\(439\) 0.180340i 0.00860715i −0.999991 0.00430358i \(-0.998630\pi\)
0.999991 0.00430358i \(-0.00136988\pi\)
\(440\) 0 0
\(441\) −7.76393 6.94427i −0.369711 0.330680i
\(442\) 0 0
\(443\) 29.7082 1.41148 0.705740 0.708471i \(-0.250615\pi\)
0.705740 + 0.708471i \(0.250615\pi\)
\(444\) 0 0
\(445\) 4.94427 0.234381
\(446\) 0 0
\(447\) −2.29180 + 6.00000i −0.108398 + 0.283790i
\(448\) 0 0
\(449\) 27.4164i 1.29386i −0.762549 0.646930i \(-0.776053\pi\)
0.762549 0.646930i \(-0.223947\pi\)
\(450\) 0 0
\(451\) 1.88854i 0.0889281i
\(452\) 0 0
\(453\) −3.88854 + 10.1803i −0.182700 + 0.478314i
\(454\) 0 0
\(455\) −17.8885 −0.838628
\(456\) 0 0
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 0 0
\(459\) −29.8885 + 15.4164i −1.39508 + 0.719576i
\(460\) 0 0
\(461\) 14.1803i 0.660444i −0.943903 0.330222i \(-0.892876\pi\)
0.943903 0.330222i \(-0.107124\pi\)
\(462\) 0 0
\(463\) 39.2361i 1.82345i −0.410796 0.911727i \(-0.634749\pi\)
0.410796 0.911727i \(-0.365251\pi\)
\(464\) 0 0
\(465\) 1.52786 + 0.583592i 0.0708530 + 0.0270634i
\(466\) 0 0
\(467\) 15.2361 0.705041 0.352521 0.935804i \(-0.385325\pi\)
0.352521 + 0.935804i \(0.385325\pi\)
\(468\) 0 0
\(469\) 12.0000 0.554109
\(470\) 0 0
\(471\) 7.23607 + 2.76393i 0.333420 + 0.127355i
\(472\) 0 0
\(473\) 2.11146i 0.0970849i
\(474\) 0 0
\(475\) 18.1803i 0.834171i
\(476\) 0 0
\(477\) −2.47214 + 2.76393i −0.113191 + 0.126552i
\(478\) 0 0
\(479\) −41.8885 −1.91394 −0.956968 0.290193i \(-0.906281\pi\)
−0.956968 + 0.290193i \(0.906281\pi\)
\(480\) 0 0
\(481\) −2.11146 −0.0962741
\(482\) 0 0
\(483\) 12.9443 33.8885i 0.588985 1.54198i
\(484\) 0 0
\(485\) 10.4721i 0.475515i
\(486\) 0 0
\(487\) 1.34752i 0.0610621i −0.999534 0.0305311i \(-0.990280\pi\)
0.999534 0.0305311i \(-0.00971985\pi\)
\(488\) 0 0
\(489\) −11.2361 + 29.4164i −0.508113 + 1.33026i
\(490\) 0 0
\(491\) 26.0689 1.17647 0.588236 0.808689i \(-0.299823\pi\)
0.588236 + 0.808689i \(0.299823\pi\)
\(492\) 0 0
\(493\) −59.7771 −2.69222
\(494\) 0 0
\(495\) −1.88854 + 2.11146i −0.0848837 + 0.0949029i
\(496\) 0 0
\(497\) 36.9443i 1.65718i
\(498\) 0 0
\(499\) 22.7639i 1.01905i 0.860455 + 0.509527i \(0.170180\pi\)
−0.860455 + 0.509527i \(0.829820\pi\)
\(500\) 0 0
\(501\) −36.3607 13.8885i −1.62448 0.620494i
\(502\) 0 0
\(503\) 30.4721 1.35869 0.679343 0.733821i \(-0.262265\pi\)
0.679343 + 0.733821i \(0.262265\pi\)
\(504\) 0 0
\(505\) 14.4721 0.644002
\(506\) 0 0
\(507\) −11.3262 4.32624i −0.503016 0.192135i
\(508\) 0 0
\(509\) 12.2918i 0.544824i −0.962181 0.272412i \(-0.912179\pi\)
0.962181 0.272412i \(-0.0878214\pi\)
\(510\) 0 0
\(511\) 6.47214i 0.286310i
\(512\) 0 0
\(513\) −24.1803 + 12.4721i −1.06759 + 0.550658i
\(514\) 0 0
\(515\) 10.1115 0.445564
\(516\) 0 0
\(517\) −6.11146 −0.268782
\(518\) 0 0
\(519\) 5.34752 14.0000i 0.234730 0.614532i
\(520\) 0 0
\(521\) 20.3607i 0.892018i −0.895029 0.446009i \(-0.852845\pi\)
0.895029 0.446009i \(-0.147155\pi\)
\(522\) 0 0
\(523\) 34.1803i 1.49460i −0.664486 0.747301i \(-0.731349\pi\)
0.664486 0.747301i \(-0.268651\pi\)
\(524\) 0 0
\(525\) −6.94427 + 18.1803i −0.303073 + 0.793455i
\(526\) 0 0
\(527\) 4.94427 0.215376
\(528\) 0 0
\(529\) 18.8885 0.821241
\(530\) 0 0
\(531\) 7.23607 + 6.47214i 0.314019 + 0.280867i
\(532\) 0 0
\(533\) 11.0557i 0.478877i
\(534\) 0 0
\(535\) 10.1115i 0.437156i
\(536\) 0 0
\(537\) 26.1803 + 10.0000i 1.12977 + 0.431532i
\(538\) 0 0
\(539\) −2.65248 −0.114250
\(540\) 0 0
\(541\) 18.3607 0.789387 0.394694 0.918813i \(-0.370851\pi\)
0.394694 + 0.918813i \(0.370851\pi\)
\(542\) 0 0
\(543\) −18.6525 7.12461i −0.800454 0.305746i
\(544\) 0 0
\(545\) 0.583592i 0.0249983i
\(546\) 0 0
\(547\) 2.76393i 0.118177i 0.998253 + 0.0590886i \(0.0188194\pi\)
−0.998253 + 0.0590886i \(0.981181\pi\)
\(548\) 0 0
\(549\) 18.9443 + 16.9443i 0.808522 + 0.723164i
\(550\) 0 0
\(551\) −48.3607 −2.06023
\(552\) 0 0
\(553\) 44.3607 1.88641
\(554\) 0 0
\(555\) 0.360680 0.944272i 0.0153100 0.0400821i
\(556\) 0 0
\(557\) 16.6525i 0.705588i 0.935701 + 0.352794i \(0.114768\pi\)
−0.935701 + 0.352794i \(0.885232\pi\)
\(558\) 0 0
\(559\) 12.3607i 0.522801i
\(560\) 0 0
\(561\) −3.05573 + 8.00000i −0.129013 + 0.337760i
\(562\) 0 0
\(563\) −36.5410 −1.54002 −0.770010 0.638032i \(-0.779749\pi\)
−0.770010 + 0.638032i \(0.779749\pi\)
\(564\) 0 0
\(565\) −9.88854 −0.416014
\(566\) 0 0
\(567\) 28.9443 3.23607i 1.21555 0.135902i
\(568\) 0 0
\(569\) 37.5279i 1.57325i −0.617431 0.786625i \(-0.711827\pi\)
0.617431 0.786625i \(-0.288173\pi\)
\(570\) 0 0
\(571\) 35.1246i 1.46992i −0.678111 0.734960i \(-0.737201\pi\)
0.678111 0.734960i \(-0.262799\pi\)
\(572\) 0 0
\(573\) −8.00000 3.05573i −0.334205 0.127655i
\(574\) 0 0
\(575\) −22.4721 −0.937153
\(576\) 0 0
\(577\) 19.5279 0.812956 0.406478 0.913661i \(-0.366757\pi\)
0.406478 + 0.913661i \(0.366757\pi\)
\(578\) 0 0
\(579\) −38.6525 14.7639i −1.60634 0.613568i
\(580\) 0 0
\(581\) 23.4164i 0.971476i
\(582\) 0 0
\(583\) 0.944272i 0.0391077i
\(584\) 0 0
\(585\) 11.0557 12.3607i 0.457098 0.511051i
\(586\) 0 0
\(587\) −27.5967 −1.13904 −0.569520 0.821978i \(-0.692871\pi\)
−0.569520 + 0.821978i \(0.692871\pi\)
\(588\) 0 0
\(589\) 4.00000 0.164817
\(590\) 0 0
\(591\) 5.70820 14.9443i 0.234804 0.614725i
\(592\) 0 0
\(593\) 11.0557i 0.454004i 0.973894 + 0.227002i \(0.0728924\pi\)
−0.973894 + 0.227002i \(0.927108\pi\)
\(594\) 0 0
\(595\) 25.8885i 1.06133i
\(596\) 0 0
\(597\) −10.0000 + 26.1803i −0.409273 + 1.07149i
\(598\) 0 0
\(599\) 19.4164 0.793333 0.396666 0.917963i \(-0.370167\pi\)
0.396666 + 0.917963i \(0.370167\pi\)
\(600\) 0 0
\(601\) −37.7771 −1.54096 −0.770480 0.637464i \(-0.779983\pi\)
−0.770480 + 0.637464i \(0.779983\pi\)
\(602\) 0 0
\(603\) −7.41641 + 8.29180i −0.302019 + 0.337668i
\(604\) 0 0
\(605\) 12.8754i 0.523459i
\(606\) 0 0
\(607\) 39.2361i 1.59254i −0.604940 0.796271i \(-0.706803\pi\)
0.604940 0.796271i \(-0.293197\pi\)
\(608\) 0 0
\(609\) 48.3607 + 18.4721i 1.95967 + 0.748529i
\(610\) 0 0
\(611\) 35.7771 1.44739
\(612\) 0 0
\(613\) −43.3050 −1.74907 −0.874535 0.484962i \(-0.838833\pi\)
−0.874535 + 0.484962i \(0.838833\pi\)
\(614\) 0 0
\(615\) 4.94427 + 1.88854i 0.199372 + 0.0761534i
\(616\) 0 0
\(617\) 13.8885i 0.559132i 0.960127 + 0.279566i \(0.0901905\pi\)
−0.960127 + 0.279566i \(0.909809\pi\)
\(618\) 0 0
\(619\) 11.1246i 0.447136i −0.974688 0.223568i \(-0.928230\pi\)
0.974688 0.223568i \(-0.0717705\pi\)
\(620\) 0 0
\(621\) 15.4164 + 29.8885i 0.618639 + 1.19939i
\(622\) 0 0
\(623\) −12.9443 −0.518601
\(624\) 0 0
\(625\) 4.41641 0.176656
\(626\) 0 0
\(627\) −2.47214 + 6.47214i −0.0987276 + 0.258472i
\(628\) 0 0
\(629\) 3.05573i 0.121840i
\(630\) 0 0
\(631\) 21.1246i 0.840958i −0.907302 0.420479i \(-0.861862\pi\)
0.907302 0.420479i \(-0.138138\pi\)
\(632\) 0 0
\(633\) 4.18034 10.9443i 0.166154 0.434996i
\(634\) 0 0
\(635\) −10.8328 −0.429887
\(636\) 0 0
\(637\) 15.5279 0.615236
\(638\) 0 0
\(639\) 25.5279 + 22.8328i 1.00987 + 0.903252i
\(640\) 0 0
\(641\) 37.3050i 1.47346i 0.676189 + 0.736729i \(0.263630\pi\)
−0.676189 + 0.736729i \(0.736370\pi\)
\(642\) 0 0
\(643\) 44.6525i 1.76092i 0.474119 + 0.880461i \(0.342767\pi\)
−0.474119 + 0.880461i \(0.657233\pi\)
\(644\) 0 0
\(645\) 5.52786 + 2.11146i 0.217659 + 0.0831385i
\(646\) 0 0
\(647\) −29.3050 −1.15210 −0.576048 0.817416i \(-0.695406\pi\)
−0.576048 + 0.817416i \(0.695406\pi\)
\(648\) 0 0
\(649\) 2.47214 0.0970398
\(650\) 0 0
\(651\) −4.00000 1.52786i −0.156772 0.0598817i
\(652\) 0 0
\(653\) 27.7082i 1.08431i 0.840280 + 0.542153i \(0.182391\pi\)
−0.840280 + 0.542153i \(0.817609\pi\)
\(654\) 0 0
\(655\) 13.8885i 0.542670i
\(656\) 0 0
\(657\) −4.47214 4.00000i −0.174475 0.156055i
\(658\) 0 0
\(659\) 41.7082 1.62472 0.812360 0.583156i \(-0.198182\pi\)
0.812360 + 0.583156i \(0.198182\pi\)
\(660\) 0 0
\(661\) −11.3050 −0.439712 −0.219856 0.975532i \(-0.570559\pi\)
−0.219856 + 0.975532i \(0.570559\pi\)
\(662\) 0 0
\(663\) 17.8885 46.8328i 0.694733 1.81884i
\(664\) 0 0
\(665\) 20.9443i 0.812184i
\(666\) 0 0
\(667\) 59.7771i 2.31458i
\(668\) 0 0
\(669\) −7.52786 + 19.7082i −0.291044 + 0.761963i
\(670\) 0 0
\(671\) 6.47214 0.249854
\(672\) 0 0
\(673\) 1.41641 0.0545985 0.0272993 0.999627i \(-0.491309\pi\)
0.0272993 + 0.999627i \(0.491309\pi\)
\(674\) 0 0
\(675\) −8.27051 16.0344i −0.318332 0.617166i
\(676\) 0 0
\(677\) 27.7082i 1.06491i −0.846457 0.532456i \(-0.821269\pi\)
0.846457 0.532456i \(-0.178731\pi\)
\(678\) 0 0
\(679\) 27.4164i 1.05215i
\(680\) 0 0
\(681\) −32.6525 12.4721i −1.25125 0.477933i
\(682\) 0 0
\(683\) 8.76393 0.335343 0.167671 0.985843i \(-0.446375\pi\)
0.167671 + 0.985843i \(0.446375\pi\)
\(684\) 0 0
\(685\) 12.9443 0.494575
\(686\) 0 0
\(687\) 33.1246 + 12.6525i 1.26378 + 0.482722i
\(688\) 0 0
\(689\) 5.52786i 0.210595i
\(690\) 0 0
\(691\) 16.2918i 0.619769i −0.950774 0.309885i \(-0.899710\pi\)
0.950774 0.309885i \(-0.100290\pi\)
\(692\) 0 0
\(693\) 4.94427 5.52786i 0.187817 0.209986i
\(694\) 0 0
\(695\) −4.58359 −0.173866
\(696\) 0 0
\(697\) 16.0000 0.606043
\(698\) 0 0
\(699\) 4.36068 11.4164i 0.164936 0.431808i
\(700\) 0 0
\(701\) 27.7082i 1.04652i 0.852172 + 0.523262i \(0.175285\pi\)
−0.852172 + 0.523262i \(0.824715\pi\)
\(702\) 0 0
\(703\) 2.47214i 0.0932384i
\(704\) 0 0
\(705\) −6.11146 + 16.0000i −0.230171 + 0.602595i
\(706\) 0 0
\(707\) −37.8885 −1.42495
\(708\) 0 0
\(709\) 16.4721 0.618624 0.309312 0.950961i \(-0.399901\pi\)
0.309312 + 0.950961i \(0.399901\pi\)
\(710\) 0 0
\(711\) −27.4164 + 30.6525i −1.02820 + 1.14956i
\(712\) 0 0
\(713\) 4.94427i 0.185164i
\(714\) 0 0
\(715\) 4.22291i 0.157928i
\(716\) 0 0
\(717\) −12.9443 4.94427i −0.483413 0.184647i
\(718\) 0 0
\(719\) 22.8328 0.851520 0.425760 0.904836i \(-0.360007\pi\)
0.425760 + 0.904836i \(0.360007\pi\)
\(720\) 0 0
\(721\) −26.4721 −0.985874
\(722\) 0 0
\(723\) 3.23607 + 1.23607i 0.120351 + 0.0459699i
\(724\) 0 0
\(725\) 32.0689i 1.19101i
\(726\) 0 0
\(727\) 8.18034i 0.303392i −0.988427 0.151696i \(-0.951527\pi\)
0.988427 0.151696i \(-0.0484735\pi\)
\(728\) 0 0
\(729\) −15.6525 + 22.0000i −0.579721 + 0.814815i
\(730\) 0 0
\(731\) 17.8885 0.661632
\(732\) 0 0
\(733\) −2.58359 −0.0954272 −0.0477136 0.998861i \(-0.515193\pi\)
−0.0477136 + 0.998861i \(0.515193\pi\)
\(734\) 0 0
\(735\) −2.65248 + 6.94427i −0.0978380 + 0.256143i
\(736\) 0 0
\(737\) 2.83282i 0.104348i
\(738\) 0 0
\(739\) 27.1246i 0.997795i −0.866661 0.498897i \(-0.833738\pi\)
0.866661 0.498897i \(-0.166262\pi\)
\(740\) 0 0
\(741\) 14.4721 37.8885i 0.531647 1.39187i
\(742\) 0 0
\(743\) −19.4164 −0.712319 −0.356159 0.934425i \(-0.615914\pi\)
−0.356159 + 0.934425i \(0.615914\pi\)
\(744\) 0 0
\(745\) 4.58359 0.167930
\(746\) 0 0
\(747\) 16.1803 + 14.4721i 0.592008 + 0.529508i
\(748\) 0 0
\(749\) 26.4721i 0.967271i
\(750\) 0 0
\(751\) 31.5967i 1.15298i 0.817104 + 0.576491i \(0.195578\pi\)
−0.817104 + 0.576491i \(0.804422\pi\)
\(752\) 0 0
\(753\) 16.6525 + 6.36068i 0.606850 + 0.231796i
\(754\) 0 0
\(755\) 7.77709 0.283037
\(756\) 0 0
\(757\) 21.4164 0.778393 0.389196 0.921155i \(-0.372753\pi\)
0.389196 + 0.921155i \(0.372753\pi\)
\(758\) 0 0
\(759\) 8.00000 + 3.05573i 0.290382 + 0.110916i
\(760\) 0 0
\(761\) 38.2492i 1.38653i −0.720681 0.693267i \(-0.756171\pi\)
0.720681 0.693267i \(-0.243829\pi\)
\(762\) 0 0
\(763\) 1.52786i 0.0553124i
\(764\) 0 0
\(765\) 17.8885 + 16.0000i 0.646762 + 0.578481i
\(766\) 0 0
\(767\) −14.4721 −0.522559
\(768\) 0 0
\(769\) −21.7771 −0.785302 −0.392651 0.919688i \(-0.628442\pi\)
−0.392651 + 0.919688i \(0.628442\pi\)
\(770\) 0 0
\(771\) 1.88854 4.94427i 0.0680142 0.178064i
\(772\) 0 0
\(773\) 30.1803i 1.08551i 0.839891 + 0.542756i \(0.182619\pi\)
−0.839891 + 0.542756i \(0.817381\pi\)
\(774\) 0 0
\(775\) 2.65248i 0.0952797i
\(776\) 0 0
\(777\) −0.944272 + 2.47214i −0.0338756 + 0.0886874i
\(778\) 0 0
\(779\) 12.9443 0.463777
\(780\) 0 0
\(781\) 8.72136 0.312075
\(782\) 0 0
\(783\) −42.6525 + 22.0000i −1.52428 + 0.786216i
\(784\) 0 0
\(785\) 5.52786i 0.197298i
\(786\) 0 0
\(787\) 5.81966i 0.207448i 0.994606 + 0.103724i \(0.0330759\pi\)
−0.994606 + 0.103724i \(0.966924\pi\)
\(788\) 0 0
\(789\) −2.47214 0.944272i −0.0880104 0.0336170i
\(790\) 0 0
\(791\) 25.8885 0.920491
\(792\) 0 0
\(793\) −37.8885 −1.34546
\(794\) 0 0
\(795\) 2.47214 + 0.944272i 0.0876776 + 0.0334899i
\(796\) 0 0
\(797\) 8.06888i 0.285815i −0.989736 0.142907i \(-0.954355\pi\)
0.989736 0.142907i \(-0.0456451\pi\)
\(798\) 0 0
\(799\) 51.7771i 1.83174i
\(800\) 0 0