Properties

Label 1900.2.l.b.1557.4
Level $1900$
Weight $2$
Character 1900.1557
Analytic conductor $15.172$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 4 x^{11} + 28 x^{10} - 64 x^{9} + 236 x^{8} - 420 x^{7} + 946 x^{6} - 1216 x^{5} + 1896 x^{4} - 1564 x^{3} + 2284 x^{2} - 1088 x + 1370\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1557.4
Root \(0.344446 - 1.84020i\) of defining polynomial
Character \(\chi\) \(=\) 1900.1557
Dual form 1900.2.l.b.493.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.49576 + 1.49576i) q^{3} +(-0.311108 - 0.311108i) q^{7} +1.47457i q^{9} +O(q^{10})\) \(q+(1.49576 + 1.49576i) q^{3} +(-0.311108 - 0.311108i) q^{7} +1.47457i q^{9} +2.90321 q^{11} +(2.84674 + 2.84674i) q^{13} +(2.52543 + 2.52543i) q^{17} +(-4.34250 + 0.377784i) q^{19} -0.930683i q^{21} +(4.11753 - 4.11753i) q^{23} +(2.28167 - 2.28167i) q^{27} +2.99151 q^{29} -0.930683i q^{31} +(4.34250 + 4.34250i) q^{33} +(-8.11992 + 8.11992i) q^{37} +8.51606i q^{39} +2.06083i q^{41} +(-2.11753 + 2.11753i) q^{43} +(2.73975 + 2.73975i) q^{47} -6.80642i q^{49} +7.55485i q^{51} +(0.565073 + 0.565073i) q^{53} +(-7.06039 - 5.93024i) q^{57} +9.32613 q^{59} +3.52543 q^{61} +(0.458751 - 0.458751i) q^{63} +(0.144771 - 0.144771i) q^{67} +12.3176 q^{69} +9.61568i q^{71} +(4.09679 - 4.09679i) q^{73} +(-0.903212 - 0.903212i) q^{77} +12.6072 q^{79} +11.2494 q^{81} +(-9.21432 + 9.21432i) q^{83} +(4.47457 + 4.47457i) q^{87} -7.55485 q^{89} -1.77129i q^{91} +(1.39207 - 1.39207i) q^{93} +(-12.0421 + 12.0421i) q^{97} +4.28100i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{7} + O(q^{10}) \) \( 12q - 4q^{7} + 8q^{11} + 4q^{17} - 4q^{23} + 28q^{43} - 20q^{47} - 24q^{57} + 16q^{61} - 20q^{63} + 76q^{73} + 16q^{77} + 4q^{81} - 84q^{83} + 80q^{87} - 8q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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
\(3\) 1.49576 + 1.49576i 0.863575 + 0.863575i 0.991751 0.128176i \(-0.0409123\pi\)
−0.128176 + 0.991751i \(0.540912\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.311108 0.311108i −0.117588 0.117588i 0.645864 0.763452i \(-0.276497\pi\)
−0.763452 + 0.645864i \(0.776497\pi\)
\(8\) 0 0
\(9\) 1.47457i 0.491524i
\(10\) 0 0
\(11\) 2.90321 0.875351 0.437676 0.899133i \(-0.355802\pi\)
0.437676 + 0.899133i \(0.355802\pi\)
\(12\) 0 0
\(13\) 2.84674 + 2.84674i 0.789544 + 0.789544i 0.981419 0.191875i \(-0.0614570\pi\)
−0.191875 + 0.981419i \(0.561457\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.52543 + 2.52543i 0.612506 + 0.612506i 0.943598 0.331092i \(-0.107417\pi\)
−0.331092 + 0.943598i \(0.607417\pi\)
\(18\) 0 0
\(19\) −4.34250 + 0.377784i −0.996237 + 0.0866697i
\(20\) 0 0
\(21\) 0.930683i 0.203092i
\(22\) 0 0
\(23\) 4.11753 4.11753i 0.858565 0.858565i −0.132604 0.991169i \(-0.542334\pi\)
0.991169 + 0.132604i \(0.0423340\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2.28167 2.28167i 0.439107 0.439107i
\(28\) 0 0
\(29\) 2.99151 0.555510 0.277755 0.960652i \(-0.410410\pi\)
0.277755 + 0.960652i \(0.410410\pi\)
\(30\) 0 0
\(31\) 0.930683i 0.167156i −0.996501 0.0835778i \(-0.973365\pi\)
0.996501 0.0835778i \(-0.0266347\pi\)
\(32\) 0 0
\(33\) 4.34250 + 4.34250i 0.755932 + 0.755932i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.11992 + 8.11992i −1.33491 + 1.33491i −0.433988 + 0.900919i \(0.642894\pi\)
−0.900919 + 0.433988i \(0.857106\pi\)
\(38\) 0 0
\(39\) 8.51606i 1.36366i
\(40\) 0 0
\(41\) 2.06083i 0.321847i 0.986967 + 0.160924i \(0.0514473\pi\)
−0.986967 + 0.160924i \(0.948553\pi\)
\(42\) 0 0
\(43\) −2.11753 + 2.11753i −0.322921 + 0.322921i −0.849886 0.526966i \(-0.823330\pi\)
0.526966 + 0.849886i \(0.323330\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.73975 + 2.73975i 0.399633 + 0.399633i 0.878104 0.478470i \(-0.158809\pi\)
−0.478470 + 0.878104i \(0.658809\pi\)
\(48\) 0 0
\(49\) 6.80642i 0.972346i
\(50\) 0 0
\(51\) 7.55485i 1.05789i
\(52\) 0 0
\(53\) 0.565073 + 0.565073i 0.0776188 + 0.0776188i 0.744850 0.667232i \(-0.232521\pi\)
−0.667232 + 0.744850i \(0.732521\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −7.06039 5.93024i −0.935171 0.785480i
\(58\) 0 0
\(59\) 9.32613 1.21416 0.607080 0.794641i \(-0.292341\pi\)
0.607080 + 0.794641i \(0.292341\pi\)
\(60\) 0 0
\(61\) 3.52543 0.451385 0.225692 0.974199i \(-0.427536\pi\)
0.225692 + 0.974199i \(0.427536\pi\)
\(62\) 0 0
\(63\) 0.458751 0.458751i 0.0577972 0.0577972i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0.144771 0.144771i 0.0176866 0.0176866i −0.698208 0.715895i \(-0.746019\pi\)
0.715895 + 0.698208i \(0.246019\pi\)
\(68\) 0 0
\(69\) 12.3176 1.48287
\(70\) 0 0
\(71\) 9.61568i 1.14117i 0.821238 + 0.570585i \(0.193284\pi\)
−0.821238 + 0.570585i \(0.806716\pi\)
\(72\) 0 0
\(73\) 4.09679 4.09679i 0.479493 0.479493i −0.425477 0.904969i \(-0.639894\pi\)
0.904969 + 0.425477i \(0.139894\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.903212 0.903212i −0.102931 0.102931i
\(78\) 0 0
\(79\) 12.6072 1.41842 0.709210 0.704998i \(-0.249052\pi\)
0.709210 + 0.704998i \(0.249052\pi\)
\(80\) 0 0
\(81\) 11.2494 1.24993
\(82\) 0 0
\(83\) −9.21432 + 9.21432i −1.01140 + 1.01140i −0.0114688 + 0.999934i \(0.503651\pi\)
−0.999934 + 0.0114688i \(0.996349\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 4.47457 + 4.47457i 0.479725 + 0.479725i
\(88\) 0 0
\(89\) −7.55485 −0.800812 −0.400406 0.916338i \(-0.631131\pi\)
−0.400406 + 0.916338i \(0.631131\pi\)
\(90\) 0 0
\(91\) 1.77129i 0.185681i
\(92\) 0 0
\(93\) 1.39207 1.39207i 0.144351 0.144351i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −12.0421 + 12.0421i −1.22269 + 1.22269i −0.256020 + 0.966671i \(0.582411\pi\)
−0.966671 + 0.256020i \(0.917589\pi\)
\(98\) 0 0
\(99\) 4.28100i 0.430256i
\(100\) 0 0
\(101\) −8.76986 −0.872634 −0.436317 0.899793i \(-0.643717\pi\)
−0.436317 + 0.899793i \(0.643717\pi\)
\(102\) 0 0
\(103\) 8.54022 + 8.54022i 0.841493 + 0.841493i 0.989053 0.147560i \(-0.0471419\pi\)
−0.147560 + 0.989053i \(0.547142\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.77742 + 3.77742i −0.365177 + 0.365177i −0.865715 0.500538i \(-0.833136\pi\)
0.500538 + 0.865715i \(0.333136\pi\)
\(108\) 0 0
\(109\) 13.7373 1.31580 0.657899 0.753106i \(-0.271445\pi\)
0.657899 + 0.753106i \(0.271445\pi\)
\(110\) 0 0
\(111\) −24.2908 −2.30558
\(112\) 0 0
\(113\) −1.91606 1.91606i −0.180248 0.180248i 0.611216 0.791464i \(-0.290681\pi\)
−0.791464 + 0.611216i \(0.790681\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −4.19773 + 4.19773i −0.388080 + 0.388080i
\(118\) 0 0
\(119\) 1.57136i 0.144046i
\(120\) 0 0
\(121\) −2.57136 −0.233760
\(122\) 0 0
\(123\) −3.08250 + 3.08250i −0.277939 + 0.277939i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 5.12841 5.12841i 0.455073 0.455073i −0.441961 0.897034i \(-0.645717\pi\)
0.897034 + 0.441961i \(0.145717\pi\)
\(128\) 0 0
\(129\) −6.33462 −0.557732
\(130\) 0 0
\(131\) −10.3684 −0.905893 −0.452946 0.891538i \(-0.649627\pi\)
−0.452946 + 0.891538i \(0.649627\pi\)
\(132\) 0 0
\(133\) 1.46852 + 1.23345i 0.127337 + 0.106954i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.99063 7.99063i −0.682686 0.682686i 0.277919 0.960605i \(-0.410355\pi\)
−0.960605 + 0.277919i \(0.910355\pi\)
\(138\) 0 0
\(139\) 10.1891i 0.864231i −0.901818 0.432115i \(-0.857767\pi\)
0.901818 0.432115i \(-0.142233\pi\)
\(140\) 0 0
\(141\) 8.19599i 0.690227i
\(142\) 0 0
\(143\) 8.26469 + 8.26469i 0.691128 + 0.691128i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 10.1807 10.1807i 0.839694 0.839694i
\(148\) 0 0
\(149\) 18.0874i 1.48178i −0.671627 0.740890i \(-0.734404\pi\)
0.671627 0.740890i \(-0.265596\pi\)
\(150\) 0 0
\(151\) 13.5379i 1.10170i −0.834605 0.550848i \(-0.814304\pi\)
0.834605 0.550848i \(-0.185696\pi\)
\(152\) 0 0
\(153\) −3.72393 + 3.72393i −0.301062 + 0.301062i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −15.1891 15.1891i −1.21222 1.21222i −0.970293 0.241931i \(-0.922219\pi\)
−0.241931 0.970293i \(-0.577781\pi\)
\(158\) 0 0
\(159\) 1.69042i 0.134059i
\(160\) 0 0
\(161\) −2.56199 −0.201913
\(162\) 0 0
\(163\) −5.44938 + 5.44938i −0.426829 + 0.426829i −0.887547 0.460718i \(-0.847592\pi\)
0.460718 + 0.887547i \(0.347592\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.42644 2.42644i 0.187763 0.187763i −0.606965 0.794729i \(-0.707613\pi\)
0.794729 + 0.606965i \(0.207613\pi\)
\(168\) 0 0
\(169\) 3.20787i 0.246759i
\(170\) 0 0
\(171\) −0.557070 6.40333i −0.0426002 0.489675i
\(172\) 0 0
\(173\) −5.83825 5.83825i −0.443874 0.443874i 0.449438 0.893312i \(-0.351624\pi\)
−0.893312 + 0.449438i \(0.851624\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 13.9496 + 13.9496i 1.04852 + 1.04852i
\(178\) 0 0
\(179\) −20.4516 −1.52862 −0.764311 0.644847i \(-0.776921\pi\)
−0.764311 + 0.644847i \(0.776921\pi\)
\(180\) 0 0
\(181\) 11.9660i 0.889429i 0.895672 + 0.444715i \(0.146695\pi\)
−0.895672 + 0.444715i \(0.853305\pi\)
\(182\) 0 0
\(183\) 5.27318 + 5.27318i 0.389805 + 0.389805i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 7.33185 + 7.33185i 0.536158 + 0.536158i
\(188\) 0 0
\(189\) −1.41969 −0.103267
\(190\) 0 0
\(191\) 23.0923 1.67090 0.835452 0.549564i \(-0.185206\pi\)
0.835452 + 0.549564i \(0.185206\pi\)
\(192\) 0 0
\(193\) 2.42644 + 2.42644i 0.174659 + 0.174659i 0.789023 0.614364i \(-0.210587\pi\)
−0.614364 + 0.789023i \(0.710587\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −13.0874 13.0874i −0.932440 0.932440i 0.0654179 0.997858i \(-0.479162\pi\)
−0.997858 + 0.0654179i \(0.979162\pi\)
\(198\) 0 0
\(199\) 10.2953i 0.729814i 0.931044 + 0.364907i \(0.118899\pi\)
−0.931044 + 0.364907i \(0.881101\pi\)
\(200\) 0 0
\(201\) 0.433085 0.0305475
\(202\) 0 0
\(203\) −0.930683 0.930683i −0.0653211 0.0653211i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 6.07160 + 6.07160i 0.422005 + 0.422005i
\(208\) 0 0
\(209\) −12.6072 + 1.09679i −0.872057 + 0.0758664i
\(210\) 0 0
\(211\) 14.9576i 1.02972i −0.857274 0.514860i \(-0.827844\pi\)
0.857274 0.514860i \(-0.172156\pi\)
\(212\) 0 0
\(213\) −14.3827 + 14.3827i −0.985487 + 0.985487i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −0.289543 + 0.289543i −0.0196554 + 0.0196554i
\(218\) 0 0
\(219\) 12.2556 0.828156
\(220\) 0 0
\(221\) 14.3785i 0.967201i
\(222\) 0 0
\(223\) 3.55659 + 3.55659i 0.238167 + 0.238167i 0.816091 0.577924i \(-0.196137\pi\)
−0.577924 + 0.816091i \(0.696137\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.83825 + 5.83825i −0.387498 + 0.387498i −0.873794 0.486296i \(-0.838348\pi\)
0.486296 + 0.873794i \(0.338348\pi\)
\(228\) 0 0
\(229\) 12.5763i 0.831064i −0.909579 0.415532i \(-0.863595\pi\)
0.909579 0.415532i \(-0.136405\pi\)
\(230\) 0 0
\(231\) 2.70197i 0.177777i
\(232\) 0 0
\(233\) 8.74620 8.74620i 0.572983 0.572983i −0.359978 0.932961i \(-0.617216\pi\)
0.932961 + 0.359978i \(0.117216\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 18.8573 + 18.8573i 1.22491 + 1.22491i
\(238\) 0 0
\(239\) 17.0923i 1.10561i 0.833310 + 0.552806i \(0.186443\pi\)
−0.833310 + 0.552806i \(0.813557\pi\)
\(240\) 0 0
\(241\) 25.8555i 1.66550i −0.553649 0.832750i \(-0.686765\pi\)
0.553649 0.832750i \(-0.313235\pi\)
\(242\) 0 0
\(243\) 9.98129 + 9.98129i 0.640300 + 0.640300i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −13.4374 11.2865i −0.855002 0.718143i
\(248\) 0 0
\(249\) −27.5647 −1.74685
\(250\) 0 0
\(251\) 5.37778 0.339443 0.169721 0.985492i \(-0.445713\pi\)
0.169721 + 0.985492i \(0.445713\pi\)
\(252\) 0 0
\(253\) 11.9541 11.9541i 0.751546 0.751546i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.48727 4.48727i 0.279908 0.279908i −0.553164 0.833072i \(-0.686580\pi\)
0.833072 + 0.553164i \(0.186580\pi\)
\(258\) 0 0
\(259\) 5.05234 0.313937
\(260\) 0 0
\(261\) 4.41120i 0.273047i
\(262\) 0 0
\(263\) 11.8365 11.8365i 0.729872 0.729872i −0.240722 0.970594i \(-0.577384\pi\)
0.970594 + 0.240722i \(0.0773842\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −11.3002 11.3002i −0.691562 0.691562i
\(268\) 0 0
\(269\) −6.33462 −0.386229 −0.193114 0.981176i \(-0.561859\pi\)
−0.193114 + 0.981176i \(0.561859\pi\)
\(270\) 0 0
\(271\) 13.5669 0.824131 0.412066 0.911154i \(-0.364807\pi\)
0.412066 + 0.911154i \(0.364807\pi\)
\(272\) 0 0
\(273\) 2.64941 2.64941i 0.160350 0.160350i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 11.9032 + 11.9032i 0.715195 + 0.715195i 0.967617 0.252422i \(-0.0812273\pi\)
−0.252422 + 0.967617i \(0.581227\pi\)
\(278\) 0 0
\(279\) 1.37236 0.0821610
\(280\) 0 0
\(281\) 26.6961i 1.59256i 0.604930 + 0.796279i \(0.293201\pi\)
−0.604930 + 0.796279i \(0.706799\pi\)
\(282\) 0 0
\(283\) 13.1684 13.1684i 0.782779 0.782779i −0.197520 0.980299i \(-0.563289\pi\)
0.980299 + 0.197520i \(0.0632886\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.641140 0.641140i 0.0378453 0.0378453i
\(288\) 0 0
\(289\) 4.24443i 0.249672i
\(290\) 0 0
\(291\) −36.0241 −2.11177
\(292\) 0 0
\(293\) −22.7879 22.7879i −1.33129 1.33129i −0.904221 0.427064i \(-0.859548\pi\)
−0.427064 0.904221i \(-0.640452\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 6.62416 6.62416i 0.384373 0.384373i
\(298\) 0 0
\(299\) 23.4431 1.35575
\(300\) 0 0
\(301\) 1.31756 0.0759430
\(302\) 0 0
\(303\) −13.1176 13.1176i −0.753585 0.753585i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 19.5756 19.5756i 1.11724 1.11724i 0.125093 0.992145i \(-0.460077\pi\)
0.992145 0.125093i \(-0.0399229\pi\)
\(308\) 0 0
\(309\) 25.5482i 1.45339i
\(310\) 0 0
\(311\) 30.1289 1.70845 0.854227 0.519901i \(-0.174031\pi\)
0.854227 + 0.519901i \(0.174031\pi\)
\(312\) 0 0
\(313\) −11.5620 + 11.5620i −0.653522 + 0.653522i −0.953839 0.300317i \(-0.902908\pi\)
0.300317 + 0.953839i \(0.402908\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10.6011 + 10.6011i −0.595414 + 0.595414i −0.939089 0.343674i \(-0.888328\pi\)
0.343674 + 0.939089i \(0.388328\pi\)
\(318\) 0 0
\(319\) 8.68499 0.486266
\(320\) 0 0
\(321\) −11.3002 −0.630716
\(322\) 0 0
\(323\) −11.9207 10.0126i −0.663287 0.557116i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 20.5477 + 20.5477i 1.13629 + 1.13629i
\(328\) 0 0
\(329\) 1.70471i 0.0939839i
\(330\) 0 0
\(331\) 26.7862i 1.47230i −0.676817 0.736151i \(-0.736641\pi\)
0.676817 0.736151i \(-0.263359\pi\)
\(332\) 0 0
\(333\) −11.9734 11.9734i −0.656139 0.656139i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 10.0500 10.0500i 0.547458 0.547458i −0.378247 0.925705i \(-0.623473\pi\)
0.925705 + 0.378247i \(0.123473\pi\)
\(338\) 0 0
\(339\) 5.73191i 0.311315i
\(340\) 0 0
\(341\) 2.70197i 0.146320i
\(342\) 0 0
\(343\) −4.29529 + 4.29529i −0.231924 + 0.231924i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −18.0573 18.0573i −0.969367 0.969367i 0.0301774 0.999545i \(-0.490393\pi\)
−0.999545 + 0.0301774i \(0.990393\pi\)
\(348\) 0 0
\(349\) 29.1941i 1.56272i 0.624079 + 0.781361i \(0.285474\pi\)
−0.624079 + 0.781361i \(0.714526\pi\)
\(350\) 0 0
\(351\) 12.9906 0.693389
\(352\) 0 0
\(353\) 8.89384 8.89384i 0.473372 0.473372i −0.429632 0.903004i \(-0.641357\pi\)
0.903004 + 0.429632i \(0.141357\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 2.35037 2.35037i 0.124395 0.124395i
\(358\) 0 0
\(359\) 27.9037i 1.47270i −0.676601 0.736350i \(-0.736548\pi\)
0.676601 0.736350i \(-0.263452\pi\)
\(360\) 0 0
\(361\) 18.7146 3.28105i 0.984977 0.172687i
\(362\) 0 0
\(363\) −3.84613 3.84613i −0.201869 0.201869i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −1.89676 1.89676i −0.0990100 0.0990100i 0.655867 0.754877i \(-0.272303\pi\)
−0.754877 + 0.655867i \(0.772303\pi\)
\(368\) 0 0
\(369\) −3.03884 −0.158196
\(370\) 0 0
\(371\) 0.351597i 0.0182540i
\(372\) 0 0
\(373\) −6.05909 6.05909i −0.313728 0.313728i 0.532624 0.846352i \(-0.321206\pi\)
−0.846352 + 0.532624i \(0.821206\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.51606 + 8.51606i 0.438599 + 0.438599i
\(378\) 0 0
\(379\) −25.2144 −1.29518 −0.647588 0.761991i \(-0.724222\pi\)
−0.647588 + 0.761991i \(0.724222\pi\)
\(380\) 0 0
\(381\) 15.3417 0.785979
\(382\) 0 0
\(383\) −11.3323 11.3323i −0.579052 0.579052i 0.355590 0.934642i \(-0.384280\pi\)
−0.934642 + 0.355590i \(0.884280\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3.12245 3.12245i −0.158723 0.158723i
\(388\) 0 0
\(389\) 19.1338i 0.970124i −0.874480 0.485062i \(-0.838797\pi\)
0.874480 0.485062i \(-0.161203\pi\)
\(390\) 0 0
\(391\) 20.7971 1.05175
\(392\) 0 0
\(393\) −15.5086 15.5086i −0.782306 0.782306i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 6.71900 + 6.71900i 0.337217 + 0.337217i 0.855319 0.518102i \(-0.173361\pi\)
−0.518102 + 0.855319i \(0.673361\pi\)
\(398\) 0 0
\(399\) 0.351597 + 4.04149i 0.0176019 + 0.202327i
\(400\) 0 0
\(401\) 4.56334i 0.227882i 0.993488 + 0.113941i \(0.0363475\pi\)
−0.993488 + 0.113941i \(0.963653\pi\)
\(402\) 0 0
\(403\) 2.64941 2.64941i 0.131977 0.131977i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −23.5738 + 23.5738i −1.16851 + 1.16851i
\(408\) 0 0
\(409\) 21.5817 1.06715 0.533574 0.845754i \(-0.320849\pi\)
0.533574 + 0.845754i \(0.320849\pi\)
\(410\) 0 0
\(411\) 23.9041i 1.17910i
\(412\) 0 0
\(413\) −2.90143 2.90143i −0.142770 0.142770i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 15.2405 15.2405i 0.746328 0.746328i
\(418\) 0 0
\(419\) 7.58120i 0.370366i 0.982704 + 0.185183i \(0.0592878\pi\)
−0.982704 + 0.185183i \(0.940712\pi\)
\(420\) 0 0
\(421\) 25.0149i 1.21915i 0.792728 + 0.609576i \(0.208660\pi\)
−0.792728 + 0.609576i \(0.791340\pi\)
\(422\) 0 0
\(423\) −4.03996 + 4.03996i −0.196429 + 0.196429i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.09679 1.09679i −0.0530773 0.0530773i
\(428\) 0 0
\(429\) 24.7239i 1.19368i
\(430\) 0 0
\(431\) 21.2021i 1.02127i 0.859798 + 0.510635i \(0.170590\pi\)
−0.859798 + 0.510635i \(0.829410\pi\)
\(432\) 0 0
\(433\) −19.0866 19.0866i −0.917243 0.917243i 0.0795855 0.996828i \(-0.474640\pi\)
−0.996828 + 0.0795855i \(0.974640\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −16.3248 + 19.4359i −0.780922 + 0.929746i
\(438\) 0 0
\(439\) −38.6622 −1.84524 −0.922622 0.385705i \(-0.873958\pi\)
−0.922622 + 0.385705i \(0.873958\pi\)
\(440\) 0 0
\(441\) 10.0366 0.477932
\(442\) 0 0
\(443\) −0.725457 + 0.725457i −0.0344675 + 0.0344675i −0.724130 0.689663i \(-0.757759\pi\)
0.689663 + 0.724130i \(0.257759\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 27.0544 27.0544i 1.27963 1.27963i
\(448\) 0 0
\(449\) −41.0746 −1.93843 −0.969215 0.246216i \(-0.920813\pi\)
−0.969215 + 0.246216i \(0.920813\pi\)
\(450\) 0 0
\(451\) 5.98302i 0.281730i
\(452\) 0 0
\(453\) 20.2494 20.2494i 0.951398 0.951398i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −15.3684 15.3684i −0.718904 0.718904i 0.249477 0.968381i \(-0.419741\pi\)
−0.968381 + 0.249477i \(0.919741\pi\)
\(458\) 0 0
\(459\) 11.5244 0.537912
\(460\) 0 0
\(461\) −16.9304 −0.788528 −0.394264 0.918997i \(-0.629000\pi\)
−0.394264 + 0.918997i \(0.629000\pi\)
\(462\) 0 0
\(463\) 1.49532 1.49532i 0.0694932 0.0694932i −0.671506 0.740999i \(-0.734352\pi\)
0.740999 + 0.671506i \(0.234352\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 20.2192 + 20.2192i 0.935635 + 0.935635i 0.998050 0.0624153i \(-0.0198803\pi\)
−0.0624153 + 0.998050i \(0.519880\pi\)
\(468\) 0 0
\(469\) −0.0900790 −0.00415946
\(470\) 0 0
\(471\) 45.4385i 2.09369i
\(472\) 0 0
\(473\) −6.14764 + 6.14764i −0.282669 + 0.282669i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.833241 + 0.833241i −0.0381515 + 0.0381515i
\(478\) 0 0
\(479\) 11.2587i 0.514424i 0.966355 + 0.257212i \(0.0828039\pi\)
−0.966355 + 0.257212i \(0.917196\pi\)
\(480\) 0 0
\(481\) −46.2306 −2.10793
\(482\) 0 0
\(483\) −3.83212 3.83212i −0.174367 0.174367i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 15.4539 15.4539i 0.700284 0.700284i −0.264187 0.964471i \(-0.585104\pi\)
0.964471 + 0.264187i \(0.0851036\pi\)
\(488\) 0 0
\(489\) −16.3019 −0.737197
\(490\) 0 0
\(491\) −20.9906 −0.947294 −0.473647 0.880715i \(-0.657063\pi\)
−0.473647 + 0.880715i \(0.657063\pi\)
\(492\) 0 0
\(493\) 7.55485 + 7.55485i 0.340253 + 0.340253i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.99151 2.99151i 0.134188 0.134188i
\(498\) 0 0
\(499\) 24.6780i 1.10474i −0.833599 0.552369i \(-0.813724\pi\)
0.833599 0.552369i \(-0.186276\pi\)
\(500\) 0 0
\(501\) 7.25872 0.324296
\(502\) 0 0
\(503\) 15.0065 15.0065i 0.669105 0.669105i −0.288404 0.957509i \(-0.593125\pi\)
0.957509 + 0.288404i \(0.0931246\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −4.79819 + 4.79819i −0.213095 + 0.213095i
\(508\) 0 0
\(509\) 34.6306 1.53497 0.767487 0.641065i \(-0.221507\pi\)
0.767487 + 0.641065i \(0.221507\pi\)
\(510\) 0 0
\(511\) −2.54909 −0.112765
\(512\) 0 0
\(513\) −9.04616 + 10.7701i −0.399398 + 0.475512i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 7.95407 + 7.95407i 0.349819 + 0.349819i
\(518\) 0 0
\(519\) 17.4652i 0.766637i
\(520\) 0 0
\(521\) 39.0418i 1.71045i −0.518255 0.855226i \(-0.673418\pi\)
0.518255 0.855226i \(-0.326582\pi\)
\(522\) 0 0
\(523\) 25.2904 + 25.2904i 1.10587 + 1.10587i 0.993687 + 0.112187i \(0.0357855\pi\)
0.112187 + 0.993687i \(0.464215\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.35037 2.35037i 0.102384 0.102384i
\(528\) 0 0
\(529\) 10.9081i 0.474267i
\(530\) 0 0
\(531\) 13.7521i 0.596789i
\(532\) 0 0
\(533\) −5.86665 + 5.86665i −0.254113 + 0.254113i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −30.5906 30.5906i −1.32008 1.32008i
\(538\) 0 0
\(539\) 19.7605i 0.851145i
\(540\) 0 0
\(541\) −8.85283 −0.380613 −0.190307 0.981725i \(-0.560948\pi\)
−0.190307 + 0.981725i \(0.560948\pi\)
\(542\) 0 0
\(543\) −17.8983 + 17.8983i −0.768089 + 0.768089i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 11.9520 11.9520i 0.511032 0.511032i −0.403810 0.914843i \(-0.632314\pi\)
0.914843 + 0.403810i \(0.132314\pi\)
\(548\) 0 0
\(549\) 5.19850i 0.221867i
\(550\) 0 0
\(551\) −12.9906 + 1.13015i −0.553420 + 0.0481459i
\(552\) 0 0
\(553\) −3.92219 3.92219i −0.166789 0.166789i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −19.8430 19.8430i −0.840774 0.840774i 0.148185 0.988960i \(-0.452657\pi\)
−0.988960 + 0.148185i \(0.952657\pi\)
\(558\) 0 0
\(559\) −12.0561 −0.509920
\(560\) 0 0
\(561\) 21.9333i 0.926026i
\(562\) 0 0
\(563\) −10.4703 10.4703i −0.441270 0.441270i 0.451169 0.892439i \(-0.351007\pi\)
−0.892439 + 0.451169i \(0.851007\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −3.49976 3.49976i −0.146976 0.146976i
\(568\) 0 0
\(569\) −42.6744 −1.78901 −0.894503 0.447062i \(-0.852470\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(570\) 0 0
\(571\) −23.2815 −0.974299 −0.487150 0.873319i \(-0.661963\pi\)
−0.487150 + 0.873319i \(0.661963\pi\)
\(572\) 0 0
\(573\) 34.5405 + 34.5405i 1.44295 + 1.44295i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 14.5526 + 14.5526i 0.605834 + 0.605834i 0.941855 0.336021i \(-0.109081\pi\)
−0.336021 + 0.941855i \(0.609081\pi\)
\(578\) 0 0
\(579\) 7.25872i 0.301662i
\(580\) 0 0
\(581\) 5.73329 0.237857
\(582\) 0 0
\(583\) 1.64053 + 1.64053i 0.0679437 + 0.0679437i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6.20495 + 6.20495i 0.256106 + 0.256106i 0.823468 0.567362i \(-0.192036\pi\)
−0.567362 + 0.823468i \(0.692036\pi\)
\(588\) 0 0
\(589\) 0.351597 + 4.04149i 0.0144873 + 0.166527i
\(590\) 0 0
\(591\) 39.1512i 1.61046i
\(592\) 0 0
\(593\) −32.5210 + 32.5210i −1.33548 + 1.33548i −0.435089 + 0.900387i \(0.643283\pi\)
−0.900387 + 0.435089i \(0.856717\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −15.3992 + 15.3992i −0.630249 + 0.630249i
\(598\) 0 0
\(599\) 20.8505 0.851929 0.425964 0.904740i \(-0.359935\pi\)
0.425964 + 0.904740i \(0.359935\pi\)
\(600\) 0 0
\(601\) 7.64493i 0.311843i 0.987769 + 0.155922i \(0.0498347\pi\)
−0.987769 + 0.155922i \(0.950165\pi\)
\(602\) 0 0
\(603\) 0.213476 + 0.213476i 0.00869341 + 0.00869341i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 16.0951 16.0951i 0.653279 0.653279i −0.300502 0.953781i \(-0.597154\pi\)
0.953781 + 0.300502i \(0.0971543\pi\)
\(608\) 0 0
\(609\) 2.78415i 0.112819i
\(610\) 0 0
\(611\) 15.5987i 0.631056i
\(612\) 0 0
\(613\) −9.69535 + 9.69535i −0.391591 + 0.391591i −0.875254 0.483663i \(-0.839306\pi\)
0.483663 + 0.875254i \(0.339306\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 26.3319 + 26.3319i 1.06008 + 1.06008i 0.998076 + 0.0620046i \(0.0197493\pi\)
0.0620046 + 0.998076i \(0.480251\pi\)
\(618\) 0 0
\(619\) 38.0054i 1.52757i −0.645473 0.763783i \(-0.723340\pi\)
0.645473 0.763783i \(-0.276660\pi\)
\(620\) 0 0
\(621\) 18.7897i 0.754004i
\(622\) 0 0
\(623\) 2.35037 + 2.35037i 0.0941657 + 0.0941657i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −20.4978 17.2168i −0.818604 0.687571i
\(628\) 0 0
\(629\) −41.0125 −1.63528
\(630\) 0 0
\(631\) 25.0968 0.999087 0.499544 0.866289i \(-0.333501\pi\)
0.499544 + 0.866289i \(0.333501\pi\)
\(632\) 0 0
\(633\) 22.3729 22.3729i 0.889241 0.889241i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 19.3761 19.3761i 0.767710 0.767710i
\(638\) 0 0
\(639\) −14.1790 −0.560913
\(640\) 0 0
\(641\) 10.1667i 0.401562i −0.979636 0.200781i \(-0.935652\pi\)
0.979636 0.200781i \(-0.0643480\pi\)
\(642\) 0 0
\(643\) −31.1082 + 31.1082i −1.22679 + 1.22679i −0.261614 + 0.965173i \(0.584255\pi\)
−0.965173 + 0.261614i \(0.915745\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −24.6336 24.6336i −0.968446 0.968446i 0.0310708 0.999517i \(-0.490108\pi\)
−0.999517 + 0.0310708i \(0.990108\pi\)
\(648\) 0 0
\(649\) 27.0757 1.06282
\(650\) 0 0
\(651\) −0.866170 −0.0339479
\(652\) 0 0
\(653\) −4.09234 + 4.09234i −0.160146 + 0.160146i −0.782631 0.622486i \(-0.786123\pi\)
0.622486 + 0.782631i \(0.286123\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 6.04101 + 6.04101i 0.235682 + 0.235682i
\(658\) 0 0
\(659\) −9.90522 −0.385853 −0.192926 0.981213i \(-0.561798\pi\)
−0.192926 + 0.981213i \(0.561798\pi\)
\(660\) 0 0
\(661\) 22.1328i 0.860866i 0.902623 + 0.430433i \(0.141639\pi\)
−0.902623 + 0.430433i \(0.858361\pi\)
\(662\) 0 0
\(663\) −21.5067 + 21.5067i −0.835251 + 0.835251i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 12.3176 12.3176i 0.476941 0.476941i
\(668\) 0 0
\(669\) 10.6396i 0.411349i
\(670\) 0 0
\(671\) 10.2351 0.395120
\(672\) 0 0
\(673\) −27.1304 27.1304i −1.04580 1.04580i −0.998899 0.0469019i \(-0.985065\pi\)
−0.0469019 0.998899i \(-0.514935\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −21.5677 + 21.5677i −0.828915 + 0.828915i −0.987367 0.158452i \(-0.949350\pi\)
0.158452 + 0.987367i \(0.449350\pi\)
\(678\) 0 0
\(679\) 7.49279 0.287547
\(680\) 0 0
\(681\) −17.4652 −0.669268
\(682\) 0 0
\(683\) 18.0872 + 18.0872i 0.692087 + 0.692087i 0.962691 0.270604i \(-0.0872233\pi\)
−0.270604 + 0.962691i \(0.587223\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 18.8111 18.8111i 0.717686 0.717686i
\(688\) 0 0
\(689\) 3.21723i 0.122567i
\(690\) 0 0
\(691\) 9.09679 0.346058 0.173029 0.984917i \(-0.444645\pi\)
0.173029 + 0.984917i \(0.444645\pi\)
\(692\) 0 0
\(693\) 1.33185 1.33185i 0.0505929 0.0505929i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −5.20448 + 5.20448i −0.197134 + 0.197134i
\(698\) 0 0
\(699\) 26.1644 0.989627
\(700\) 0 0
\(701\) −14.0687 −0.531367 −0.265683 0.964060i \(-0.585598\pi\)
−0.265683 + 0.964060i \(0.585598\pi\)
\(702\) 0 0
\(703\) 32.1932 38.3283i 1.21419 1.44558i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.72837 + 2.72837i 0.102611 + 0.102611i
\(708\) 0 0
\(709\) 40.6035i 1.52490i −0.647050 0.762448i \(-0.723997\pi\)
0.647050 0.762448i \(-0.276003\pi\)
\(710\) 0 0
\(711\) 18.5902i 0.697187i
\(712\) 0 0
\(713\) −3.83212 3.83212i −0.143514 0.143514i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −25.5660 + 25.5660i −0.954779 + 0.954779i
\(718\) 0 0
\(719\) 33.5067i 1.24959i 0.780789 + 0.624794i \(0.214817\pi\)
−0.780789 + 0.624794i \(0.785183\pi\)
\(720\) 0 0
\(721\) 5.31386i 0.197898i
\(722\) 0 0
\(723\) 38.6735 38.6735i 1.43828 1.43828i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −2.59210 2.59210i −0.0961358 0.0961358i 0.657403 0.753539i \(-0.271655\pi\)
−0.753539 + 0.657403i \(0.771655\pi\)
\(728\) 0 0
\(729\) 3.88892i 0.144034i
\(730\) 0 0
\(731\) −10.6953 −0.395582
\(732\) 0 0
\(733\) −15.1334 + 15.1334i −0.558963 + 0.558963i −0.929012 0.370049i \(-0.879341\pi\)
0.370049 + 0.929012i \(0.379341\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.420302 0.420302i 0.0154820 0.0154820i
\(738\) 0 0
\(739\) 13.4291i 0.493998i 0.969016 + 0.246999i \(0.0794444\pi\)
−0.969016 + 0.246999i \(0.920556\pi\)
\(740\) 0 0
\(741\) −3.21723 36.9810i −0.118188 1.35853i
\(742\) 0 0
\(743\) −23.7186 23.7186i −0.870152 0.870152i 0.122337 0.992489i \(-0.460961\pi\)
−0.992489 + 0.122337i \(0.960961\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −13.5872 13.5872i −0.497129 0.497129i
\(748\) 0 0
\(749\) 2.35037 0.0858807
\(750\) 0 0
\(751\) 20.3615i 0.743002i 0.928433 + 0.371501i \(0.121157\pi\)
−0.928433 + 0.371501i \(0.878843\pi\)
\(752\) 0 0
\(753\) 8.04385 + 8.04385i 0.293134 + 0.293134i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 3.67799 + 3.67799i 0.133679 + 0.133679i 0.770780 0.637101i \(-0.219867\pi\)
−0.637101 + 0.770780i \(0.719867\pi\)
\(758\) 0 0
\(759\) 35.7607 1.29803
\(760\) 0 0
\(761\) −15.9126 −0.576831 −0.288415 0.957505i \(-0.593128\pi\)
−0.288415 + 0.957505i \(0.593128\pi\)
\(762\) 0 0
\(763\) −4.27379 4.27379i −0.154722 0.154722i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 26.5491 + 26.5491i 0.958632 + 0.958632i
\(768\) 0 0
\(769\) 27.0277i 0.974643i 0.873223 + 0.487321i \(0.162026\pi\)
−0.873223 + 0.487321i \(0.837974\pi\)
\(770\) 0 0
\(771\) 13.4237 0.483443
\(772\) 0 0
\(773\) 8.89182 + 8.89182i 0.319817 + 0.319817i 0.848697 0.528880i \(-0.177388\pi\)
−0.528880 + 0.848697i \(0.677388\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 7.55707 + 7.55707i 0.271108 + 0.271108i
\(778\) 0 0
\(779\) −0.778549 8.94914i −0.0278944 0.320636i
\(780\) 0 0
\(781\) 27.9163i 0.998925i
\(782\) 0 0
\(783\) 6.82564 6.82564i 0.243928 0.243928i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −20.9266 + 20.9266i −0.745952 + 0.745952i −0.973716 0.227764i \(-0.926858\pi\)
0.227764 + 0.973716i \(0.426858\pi\)
\(788\) 0 0
\(789\) 35.4091 1.26060
\(790\) 0 0
\(791\) 1.19220i 0.0423898i
\(792\) 0 0
\(793\) 10.0360 + 10.0360i 0.356388 + 0.356388i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −35.3951 + 35.3951i −1.25376 + 1.25376i −0.299738 + 0.954021i \(0.596899\pi\)
−0.954021 + 0.299738i \(0.903101\pi\)
\(798\) 0 0
\(799\) 13.8381i 0.489556i
\(800\) 0 0
\(801\) 11.1402i 0.393619i
\(802\) 0 0
\(803\) 11.8938 11.8938i 0.419725 &m