Properties

Label 384.2.c.a.383.3
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 383.3
Root \(-1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 384.383
Dual form 384.2.c.a.383.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.618034 - 1.61803i) q^{3} -3.23607i q^{5} +1.23607i q^{7} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})\) \(q+(0.618034 - 1.61803i) q^{3} -3.23607i q^{5} +1.23607i q^{7} +(-2.23607 - 2.00000i) q^{9} +5.23607 q^{11} -4.47214 q^{13} +(-5.23607 - 2.00000i) q^{15} -2.47214i q^{17} +0.763932i q^{19} +(2.00000 + 0.763932i) q^{21} -2.47214 q^{23} -5.47214 q^{25} +(-4.61803 + 2.38197i) q^{27} -4.76393i q^{29} +5.23607i q^{31} +(3.23607 - 8.47214i) q^{33} +4.00000 q^{35} +8.47214 q^{37} +(-2.76393 + 7.23607i) q^{39} +6.47214i q^{41} -7.23607i q^{43} +(-6.47214 + 7.23607i) q^{45} +8.00000 q^{47} +5.47214 q^{49} +(-4.00000 - 1.52786i) q^{51} -3.23607i q^{53} -16.9443i q^{55} +(1.23607 + 0.472136i) q^{57} -1.23607 q^{59} +0.472136 q^{61} +(2.47214 - 2.76393i) q^{63} +14.4721i q^{65} +9.70820i q^{67} +(-1.52786 + 4.00000i) q^{69} +15.4164 q^{71} -2.00000 q^{73} +(-3.38197 + 8.85410i) q^{75} +6.47214i q^{77} +0.291796i q^{79} +(1.00000 + 8.94427i) q^{81} +2.76393 q^{83} -8.00000 q^{85} +(-7.70820 - 2.94427i) q^{87} +4.00000i q^{89} -5.52786i q^{91} +(8.47214 + 3.23607i) q^{93} +2.47214 q^{95} +0.472136 q^{97} +(-11.7082 - 10.4721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} + O(q^{10}) \) \( 4q - 2q^{3} + 12q^{11} - 12q^{15} + 8q^{21} + 8q^{23} - 4q^{25} - 14q^{27} + 4q^{33} + 16q^{35} + 16q^{37} - 20q^{39} - 8q^{45} + 32q^{47} + 4q^{49} - 16q^{51} - 4q^{57} + 4q^{59} - 16q^{61} - 8q^{63} - 24q^{69} + 8q^{71} - 8q^{73} - 18q^{75} + 4q^{81} + 20q^{83} - 32q^{85} - 4q^{87} + 16q^{93} - 8q^{95} - 16q^{97} - 20q^{99} + O(q^{100}) \)

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
\(3\) 0.618034 1.61803i 0.356822 0.934172i
\(4\) 0 0
\(5\) 3.23607i 1.44721i −0.690212 0.723607i \(-0.742483\pi\)
0.690212 0.723607i \(-0.257517\pi\)
\(6\) 0 0
\(7\) 1.23607i 0.467190i 0.972334 + 0.233595i \(0.0750489\pi\)
−0.972334 + 0.233595i \(0.924951\pi\)
\(8\) 0 0
\(9\) −2.23607 2.00000i −0.745356 0.666667i
\(10\) 0 0
\(11\) 5.23607 1.57873 0.789367 0.613922i \(-0.210409\pi\)
0.789367 + 0.613922i \(0.210409\pi\)
\(12\) 0 0
\(13\) −4.47214 −1.24035 −0.620174 0.784465i \(-0.712938\pi\)
−0.620174 + 0.784465i \(0.712938\pi\)
\(14\) 0 0
\(15\) −5.23607 2.00000i −1.35195 0.516398i
\(16\) 0 0
\(17\) 2.47214i 0.599581i −0.954005 0.299791i \(-0.903083\pi\)
0.954005 0.299791i \(-0.0969168\pi\)
\(18\) 0 0
\(19\) 0.763932i 0.175258i 0.996153 + 0.0876290i \(0.0279290\pi\)
−0.996153 + 0.0876290i \(0.972071\pi\)
\(20\) 0 0
\(21\) 2.00000 + 0.763932i 0.436436 + 0.166704i
\(22\) 0 0
\(23\) −2.47214 −0.515476 −0.257738 0.966215i \(-0.582977\pi\)
−0.257738 + 0.966215i \(0.582977\pi\)
\(24\) 0 0
\(25\) −5.47214 −1.09443
\(26\) 0 0
\(27\) −4.61803 + 2.38197i −0.888741 + 0.458410i
\(28\) 0 0
\(29\) 4.76393i 0.884640i −0.896857 0.442320i \(-0.854156\pi\)
0.896857 0.442320i \(-0.145844\pi\)
\(30\) 0 0
\(31\) 5.23607i 0.940426i 0.882553 + 0.470213i \(0.155823\pi\)
−0.882553 + 0.470213i \(0.844177\pi\)
\(32\) 0 0
\(33\) 3.23607 8.47214i 0.563327 1.47481i
\(34\) 0 0
\(35\) 4.00000 0.676123
\(36\) 0 0
\(37\) 8.47214 1.39281 0.696405 0.717649i \(-0.254782\pi\)
0.696405 + 0.717649i \(0.254782\pi\)
\(38\) 0 0
\(39\) −2.76393 + 7.23607i −0.442583 + 1.15870i
\(40\) 0 0
\(41\) 6.47214i 1.01078i 0.862892 + 0.505389i \(0.168651\pi\)
−0.862892 + 0.505389i \(0.831349\pi\)
\(42\) 0 0
\(43\) 7.23607i 1.10349i −0.834013 0.551745i \(-0.813962\pi\)
0.834013 0.551745i \(-0.186038\pi\)
\(44\) 0 0
\(45\) −6.47214 + 7.23607i −0.964809 + 1.07869i
\(46\) 0 0
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 0 0
\(49\) 5.47214 0.781734
\(50\) 0 0
\(51\) −4.00000 1.52786i −0.560112 0.213944i
\(52\) 0 0
\(53\) 3.23607i 0.444508i −0.974989 0.222254i \(-0.928659\pi\)
0.974989 0.222254i \(-0.0713414\pi\)
\(54\) 0 0
\(55\) 16.9443i 2.28477i
\(56\) 0 0
\(57\) 1.23607 + 0.472136i 0.163721 + 0.0625359i
\(58\) 0 0
\(59\) −1.23607 −0.160922 −0.0804612 0.996758i \(-0.525639\pi\)
−0.0804612 + 0.996758i \(0.525639\pi\)
\(60\) 0 0
\(61\) 0.472136 0.0604508 0.0302254 0.999543i \(-0.490377\pi\)
0.0302254 + 0.999543i \(0.490377\pi\)
\(62\) 0 0
\(63\) 2.47214 2.76393i 0.311460 0.348223i
\(64\) 0 0
\(65\) 14.4721i 1.79505i
\(66\) 0 0
\(67\) 9.70820i 1.18605i 0.805186 + 0.593023i \(0.202066\pi\)
−0.805186 + 0.593023i \(0.797934\pi\)
\(68\) 0 0
\(69\) −1.52786 + 4.00000i −0.183933 + 0.481543i
\(70\) 0 0
\(71\) 15.4164 1.82959 0.914796 0.403917i \(-0.132352\pi\)
0.914796 + 0.403917i \(0.132352\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) −3.38197 + 8.85410i −0.390516 + 1.02238i
\(76\) 0 0
\(77\) 6.47214i 0.737568i
\(78\) 0 0
\(79\) 0.291796i 0.0328296i 0.999865 + 0.0164148i \(0.00522523\pi\)
−0.999865 + 0.0164148i \(0.994775\pi\)
\(80\) 0 0
\(81\) 1.00000 + 8.94427i 0.111111 + 0.993808i
\(82\) 0 0
\(83\) 2.76393 0.303381 0.151690 0.988428i \(-0.451528\pi\)
0.151690 + 0.988428i \(0.451528\pi\)
\(84\) 0 0
\(85\) −8.00000 −0.867722
\(86\) 0 0
\(87\) −7.70820 2.94427i −0.826406 0.315659i
\(88\) 0 0
\(89\) 4.00000i 0.423999i 0.977270 + 0.212000i \(0.0679975\pi\)
−0.977270 + 0.212000i \(0.932002\pi\)
\(90\) 0 0
\(91\) 5.52786i 0.579478i
\(92\) 0 0
\(93\) 8.47214 + 3.23607i 0.878520 + 0.335565i
\(94\) 0 0
\(95\) 2.47214 0.253636
\(96\) 0 0
\(97\) 0.472136 0.0479381 0.0239691 0.999713i \(-0.492370\pi\)
0.0239691 + 0.999713i \(0.492370\pi\)
\(98\) 0 0
\(99\) −11.7082 10.4721i −1.17672 1.05249i
\(100\) 0 0
\(101\) 1.70820i 0.169973i 0.996382 + 0.0849863i \(0.0270847\pi\)
−0.996382 + 0.0849863i \(0.972915\pi\)
\(102\) 0 0
\(103\) 14.1803i 1.39723i 0.715498 + 0.698615i \(0.246200\pi\)
−0.715498 + 0.698615i \(0.753800\pi\)
\(104\) 0 0
\(105\) 2.47214 6.47214i 0.241256 0.631616i
\(106\) 0 0
\(107\) −14.1803 −1.37087 −0.685433 0.728136i \(-0.740387\pi\)
−0.685433 + 0.728136i \(0.740387\pi\)
\(108\) 0 0
\(109\) 8.47214 0.811483 0.405742 0.913988i \(-0.367013\pi\)
0.405742 + 0.913988i \(0.367013\pi\)
\(110\) 0 0
\(111\) 5.23607 13.7082i 0.496986 1.30113i
\(112\) 0 0
\(113\) 8.00000i 0.752577i −0.926503 0.376288i \(-0.877200\pi\)
0.926503 0.376288i \(-0.122800\pi\)
\(114\) 0 0
\(115\) 8.00000i 0.746004i
\(116\) 0 0
\(117\) 10.0000 + 8.94427i 0.924500 + 0.826898i
\(118\) 0 0
\(119\) 3.05573 0.280118
\(120\) 0 0
\(121\) 16.4164 1.49240
\(122\) 0 0
\(123\) 10.4721 + 4.00000i 0.944241 + 0.360668i
\(124\) 0 0
\(125\) 1.52786i 0.136656i
\(126\) 0 0
\(127\) 13.2361i 1.17451i 0.809402 + 0.587256i \(0.199792\pi\)
−0.809402 + 0.587256i \(0.800208\pi\)
\(128\) 0 0
\(129\) −11.7082 4.47214i −1.03085 0.393750i
\(130\) 0 0
\(131\) −6.76393 −0.590967 −0.295484 0.955348i \(-0.595481\pi\)
−0.295484 + 0.955348i \(0.595481\pi\)
\(132\) 0 0
\(133\) −0.944272 −0.0818788
\(134\) 0 0
\(135\) 7.70820 + 14.9443i 0.663417 + 1.28620i
\(136\) 0 0
\(137\) 1.52786i 0.130534i 0.997868 + 0.0652671i \(0.0207899\pi\)
−0.997868 + 0.0652671i \(0.979210\pi\)
\(138\) 0 0
\(139\) 9.70820i 0.823439i 0.911311 + 0.411720i \(0.135072\pi\)
−0.911311 + 0.411720i \(0.864928\pi\)
\(140\) 0 0
\(141\) 4.94427 12.9443i 0.416383 1.09010i
\(142\) 0 0
\(143\) −23.4164 −1.95818
\(144\) 0 0
\(145\) −15.4164 −1.28026
\(146\) 0 0
\(147\) 3.38197 8.85410i 0.278940 0.730274i
\(148\) 0 0
\(149\) 9.70820i 0.795327i 0.917531 + 0.397664i \(0.130179\pi\)
−0.917531 + 0.397664i \(0.869821\pi\)
\(150\) 0 0
\(151\) 19.7082i 1.60383i −0.597438 0.801915i \(-0.703814\pi\)
0.597438 0.801915i \(-0.296186\pi\)
\(152\) 0 0
\(153\) −4.94427 + 5.52786i −0.399721 + 0.446901i
\(154\) 0 0
\(155\) 16.9443 1.36100
\(156\) 0 0
\(157\) −4.47214 −0.356915 −0.178458 0.983948i \(-0.557111\pi\)
−0.178458 + 0.983948i \(0.557111\pi\)
\(158\) 0 0
\(159\) −5.23607 2.00000i −0.415247 0.158610i
\(160\) 0 0
\(161\) 3.05573i 0.240825i
\(162\) 0 0
\(163\) 4.18034i 0.327429i −0.986508 0.163715i \(-0.947652\pi\)
0.986508 0.163715i \(-0.0523477\pi\)
\(164\) 0 0
\(165\) −27.4164 10.4721i −2.13436 0.815255i
\(166\) 0 0
\(167\) −13.5279 −1.04682 −0.523409 0.852082i \(-0.675340\pi\)
−0.523409 + 0.852082i \(0.675340\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) 0 0
\(171\) 1.52786 1.70820i 0.116839 0.130630i
\(172\) 0 0
\(173\) 22.6525i 1.72224i −0.508405 0.861118i \(-0.669765\pi\)
0.508405 0.861118i \(-0.330235\pi\)
\(174\) 0 0
\(175\) 6.76393i 0.511305i
\(176\) 0 0
\(177\) −0.763932 + 2.00000i −0.0574206 + 0.150329i
\(178\) 0 0
\(179\) 6.18034 0.461940 0.230970 0.972961i \(-0.425810\pi\)
0.230970 + 0.972961i \(0.425810\pi\)
\(180\) 0 0
\(181\) −20.4721 −1.52168 −0.760841 0.648938i \(-0.775213\pi\)
−0.760841 + 0.648938i \(0.775213\pi\)
\(182\) 0 0
\(183\) 0.291796 0.763932i 0.0215702 0.0564715i
\(184\) 0 0
\(185\) 27.4164i 2.01569i
\(186\) 0 0
\(187\) 12.9443i 0.946579i
\(188\) 0 0
\(189\) −2.94427 5.70820i −0.214164 0.415211i
\(190\) 0 0
\(191\) 12.9443 0.936615 0.468307 0.883566i \(-0.344864\pi\)
0.468307 + 0.883566i \(0.344864\pi\)
\(192\) 0 0
\(193\) −11.8885 −0.855756 −0.427878 0.903836i \(-0.640739\pi\)
−0.427878 + 0.903836i \(0.640739\pi\)
\(194\) 0 0
\(195\) 23.4164 + 8.94427i 1.67688 + 0.640513i
\(196\) 0 0
\(197\) 4.76393i 0.339416i 0.985494 + 0.169708i \(0.0542825\pi\)
−0.985494 + 0.169708i \(0.945718\pi\)
\(198\) 0 0
\(199\) 6.18034i 0.438113i 0.975712 + 0.219056i \(0.0702979\pi\)
−0.975712 + 0.219056i \(0.929702\pi\)
\(200\) 0 0
\(201\) 15.7082 + 6.00000i 1.10797 + 0.423207i
\(202\) 0 0
\(203\) 5.88854 0.413295
\(204\) 0 0
\(205\) 20.9443 1.46281
\(206\) 0 0
\(207\) 5.52786 + 4.94427i 0.384213 + 0.343651i
\(208\) 0 0
\(209\) 4.00000i 0.276686i
\(210\) 0 0
\(211\) 11.2361i 0.773523i −0.922180 0.386761i \(-0.873594\pi\)
0.922180 0.386761i \(-0.126406\pi\)
\(212\) 0 0
\(213\) 9.52786 24.9443i 0.652838 1.70915i
\(214\) 0 0
\(215\) −23.4164 −1.59699
\(216\) 0 0
\(217\) −6.47214 −0.439357
\(218\) 0 0
\(219\) −1.23607 + 3.23607i −0.0835257 + 0.218673i
\(220\) 0 0
\(221\) 11.0557i 0.743689i
\(222\) 0 0
\(223\) 10.1803i 0.681726i 0.940113 + 0.340863i \(0.110719\pi\)
−0.940113 + 0.340863i \(0.889281\pi\)
\(224\) 0 0
\(225\) 12.2361 + 10.9443i 0.815738 + 0.729618i
\(226\) 0 0
\(227\) −2.18034 −0.144714 −0.0723571 0.997379i \(-0.523052\pi\)
−0.0723571 + 0.997379i \(0.523052\pi\)
\(228\) 0 0
\(229\) 11.5279 0.761783 0.380891 0.924620i \(-0.375617\pi\)
0.380891 + 0.924620i \(0.375617\pi\)
\(230\) 0 0
\(231\) 10.4721 + 4.00000i 0.689016 + 0.263181i
\(232\) 0 0
\(233\) 24.9443i 1.63415i −0.576529 0.817077i \(-0.695593\pi\)
0.576529 0.817077i \(-0.304407\pi\)
\(234\) 0 0
\(235\) 25.8885i 1.68878i
\(236\) 0 0
\(237\) 0.472136 + 0.180340i 0.0306685 + 0.0117143i
\(238\) 0 0
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 0 0
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 0 0
\(243\) 15.0902 + 3.90983i 0.968035 + 0.250816i
\(244\) 0 0
\(245\) 17.7082i 1.13134i
\(246\) 0 0
\(247\) 3.41641i 0.217381i
\(248\) 0 0
\(249\) 1.70820 4.47214i 0.108253 0.283410i
\(250\) 0 0
\(251\) −23.7082 −1.49645 −0.748224 0.663446i \(-0.769093\pi\)
−0.748224 + 0.663446i \(0.769093\pi\)
\(252\) 0 0
\(253\) −12.9443 −0.813799
\(254\) 0 0
\(255\) −4.94427 + 12.9443i −0.309622 + 0.810602i
\(256\) 0 0
\(257\) 20.9443i 1.30647i −0.757156 0.653234i \(-0.773412\pi\)
0.757156 0.653234i \(-0.226588\pi\)
\(258\) 0 0
\(259\) 10.4721i 0.650707i
\(260\) 0 0
\(261\) −9.52786 + 10.6525i −0.589760 + 0.659372i
\(262\) 0 0
\(263\) −10.4721 −0.645740 −0.322870 0.946443i \(-0.604648\pi\)
−0.322870 + 0.946443i \(0.604648\pi\)
\(264\) 0 0
\(265\) −10.4721 −0.643298
\(266\) 0 0
\(267\) 6.47214 + 2.47214i 0.396088 + 0.151292i
\(268\) 0 0
\(269\) 16.1803i 0.986533i 0.869878 + 0.493266i \(0.164197\pi\)
−0.869878 + 0.493266i \(0.835803\pi\)
\(270\) 0 0
\(271\) 0.291796i 0.0177253i 0.999961 + 0.00886267i \(0.00282111\pi\)
−0.999961 + 0.00886267i \(0.997179\pi\)
\(272\) 0 0
\(273\) −8.94427 3.41641i −0.541332 0.206770i
\(274\) 0 0
\(275\) −28.6525 −1.72781
\(276\) 0 0
\(277\) −7.52786 −0.452306 −0.226153 0.974092i \(-0.572615\pi\)
−0.226153 + 0.974092i \(0.572615\pi\)
\(278\) 0 0
\(279\) 10.4721 11.7082i 0.626950 0.700952i
\(280\) 0 0
\(281\) 24.9443i 1.48805i 0.668151 + 0.744025i \(0.267086\pi\)
−0.668151 + 0.744025i \(0.732914\pi\)
\(282\) 0 0
\(283\) 20.7639i 1.23429i 0.786850 + 0.617144i \(0.211710\pi\)
−0.786850 + 0.617144i \(0.788290\pi\)
\(284\) 0 0
\(285\) 1.52786 4.00000i 0.0905029 0.236940i
\(286\) 0 0
\(287\) −8.00000 −0.472225
\(288\) 0 0
\(289\) 10.8885 0.640503
\(290\) 0 0
\(291\) 0.291796 0.763932i 0.0171054 0.0447825i
\(292\) 0 0
\(293\) 20.7639i 1.21304i 0.795068 + 0.606521i \(0.207435\pi\)
−0.795068 + 0.606521i \(0.792565\pi\)
\(294\) 0 0
\(295\) 4.00000i 0.232889i
\(296\) 0 0
\(297\) −24.1803 + 12.4721i −1.40309 + 0.723707i
\(298\) 0 0
\(299\) 11.0557 0.639369
\(300\) 0 0
\(301\) 8.94427 0.515539
\(302\) 0 0
\(303\) 2.76393 + 1.05573i 0.158784 + 0.0606500i
\(304\) 0 0
\(305\) 1.52786i 0.0874852i
\(306\) 0 0
\(307\) 27.5967i 1.57503i 0.616296 + 0.787515i \(0.288633\pi\)
−0.616296 + 0.787515i \(0.711367\pi\)
\(308\) 0 0
\(309\) 22.9443 + 8.76393i 1.30525 + 0.498563i
\(310\) 0 0
\(311\) −5.52786 −0.313456 −0.156728 0.987642i \(-0.550095\pi\)
−0.156728 + 0.987642i \(0.550095\pi\)
\(312\) 0 0
\(313\) −0.472136 −0.0266867 −0.0133434 0.999911i \(-0.504247\pi\)
−0.0133434 + 0.999911i \(0.504247\pi\)
\(314\) 0 0
\(315\) −8.94427 8.00000i −0.503953 0.450749i
\(316\) 0 0
\(317\) 13.1246i 0.737152i 0.929598 + 0.368576i \(0.120155\pi\)
−0.929598 + 0.368576i \(0.879845\pi\)
\(318\) 0 0
\(319\) 24.9443i 1.39661i
\(320\) 0 0
\(321\) −8.76393 + 22.9443i −0.489155 + 1.28062i
\(322\) 0 0
\(323\) 1.88854 0.105081
\(324\) 0 0
\(325\) 24.4721 1.35747
\(326\) 0 0
\(327\) 5.23607 13.7082i 0.289555 0.758065i
\(328\) 0 0
\(329\) 9.88854i 0.545173i
\(330\) 0 0
\(331\) 32.5410i 1.78862i 0.447452 + 0.894308i \(0.352332\pi\)
−0.447452 + 0.894308i \(0.647668\pi\)
\(332\) 0 0
\(333\) −18.9443 16.9443i −1.03814 0.928540i
\(334\) 0 0
\(335\) 31.4164 1.71646
\(336\) 0 0
\(337\) 22.3607 1.21806 0.609032 0.793146i \(-0.291558\pi\)
0.609032 + 0.793146i \(0.291558\pi\)
\(338\) 0 0
\(339\) −12.9443 4.94427i −0.703036 0.268536i
\(340\) 0 0
\(341\) 27.4164i 1.48468i
\(342\) 0 0
\(343\) 15.4164i 0.832408i
\(344\) 0 0
\(345\) 12.9443 + 4.94427i 0.696896 + 0.266191i
\(346\) 0 0
\(347\) −23.7082 −1.27272 −0.636362 0.771391i \(-0.719561\pi\)
−0.636362 + 0.771391i \(0.719561\pi\)
\(348\) 0 0
\(349\) −28.4721 −1.52408 −0.762039 0.647531i \(-0.775802\pi\)
−0.762039 + 0.647531i \(0.775802\pi\)
\(350\) 0 0
\(351\) 20.6525 10.6525i 1.10235 0.568587i
\(352\) 0 0
\(353\) 9.88854i 0.526314i −0.964753 0.263157i \(-0.915236\pi\)
0.964753 0.263157i \(-0.0847637\pi\)
\(354\) 0 0
\(355\) 49.8885i 2.64781i
\(356\) 0 0
\(357\) 1.88854 4.94427i 0.0999523 0.261679i
\(358\) 0 0
\(359\) 31.4164 1.65809 0.829047 0.559178i \(-0.188883\pi\)
0.829047 + 0.559178i \(0.188883\pi\)
\(360\) 0 0
\(361\) 18.4164 0.969285
\(362\) 0 0
\(363\) 10.1459 26.5623i 0.532522 1.39416i
\(364\) 0 0
\(365\) 6.47214i 0.338767i
\(366\) 0 0
\(367\) 5.23607i 0.273321i 0.990618 + 0.136660i \(0.0436369\pi\)
−0.990618 + 0.136660i \(0.956363\pi\)
\(368\) 0 0
\(369\) 12.9443 14.4721i 0.673852 0.753389i
\(370\) 0 0
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) −2.58359 −0.133773 −0.0668867 0.997761i \(-0.521307\pi\)
−0.0668867 + 0.997761i \(0.521307\pi\)
\(374\) 0 0
\(375\) 2.47214 + 0.944272i 0.127661 + 0.0487620i
\(376\) 0 0
\(377\) 21.3050i 1.09726i
\(378\) 0 0
\(379\) 10.6525i 0.547181i 0.961846 + 0.273590i \(0.0882113\pi\)
−0.961846 + 0.273590i \(0.911789\pi\)
\(380\) 0 0
\(381\) 21.4164 + 8.18034i 1.09720 + 0.419092i
\(382\) 0 0
\(383\) −28.9443 −1.47898 −0.739492 0.673166i \(-0.764934\pi\)
−0.739492 + 0.673166i \(0.764934\pi\)
\(384\) 0 0
\(385\) 20.9443 1.06742
\(386\) 0 0
\(387\) −14.4721 + 16.1803i −0.735660 + 0.822493i
\(388\) 0 0
\(389\) 32.1803i 1.63161i −0.578328 0.815804i \(-0.696295\pi\)
0.578328 0.815804i \(-0.303705\pi\)
\(390\) 0 0
\(391\) 6.11146i 0.309070i
\(392\) 0 0
\(393\) −4.18034 + 10.9443i −0.210870 + 0.552065i
\(394\) 0 0
\(395\) 0.944272 0.0475115
\(396\) 0 0
\(397\) −17.4164 −0.874104 −0.437052 0.899436i \(-0.643978\pi\)
−0.437052 + 0.899436i \(0.643978\pi\)
\(398\) 0 0
\(399\) −0.583592 + 1.52786i −0.0292161 + 0.0764889i
\(400\) 0 0
\(401\) 28.3607i 1.41626i 0.706080 + 0.708132i \(0.250462\pi\)
−0.706080 + 0.708132i \(0.749538\pi\)
\(402\) 0 0
\(403\) 23.4164i 1.16645i
\(404\) 0 0
\(405\) 28.9443 3.23607i 1.43825 0.160802i
\(406\) 0 0
\(407\) 44.3607 2.19888
\(408\) 0 0
\(409\) −31.8885 −1.57679 −0.788394 0.615171i \(-0.789087\pi\)
−0.788394 + 0.615171i \(0.789087\pi\)
\(410\) 0 0
\(411\) 2.47214 + 0.944272i 0.121941 + 0.0465775i
\(412\) 0 0
\(413\) 1.52786i 0.0751813i
\(414\) 0 0
\(415\) 8.94427i 0.439057i
\(416\) 0 0
\(417\) 15.7082 + 6.00000i 0.769234 + 0.293821i
\(418\) 0 0
\(419\) −10.1803 −0.497342 −0.248671 0.968588i \(-0.579994\pi\)
−0.248671 + 0.968588i \(0.579994\pi\)
\(420\) 0 0
\(421\) 21.4164 1.04377 0.521886 0.853015i \(-0.325229\pi\)
0.521886 + 0.853015i \(0.325229\pi\)
\(422\) 0 0
\(423\) −17.8885 16.0000i −0.869771 0.777947i
\(424\) 0 0
\(425\) 13.5279i 0.656198i
\(426\) 0 0
\(427\) 0.583592i 0.0282420i
\(428\) 0 0
\(429\) −14.4721 + 37.8885i −0.698721 + 1.82928i
\(430\) 0 0
\(431\) −8.00000 −0.385346 −0.192673 0.981263i \(-0.561716\pi\)
−0.192673 + 0.981263i \(0.561716\pi\)
\(432\) 0 0
\(433\) 16.4721 0.791600 0.395800 0.918337i \(-0.370467\pi\)
0.395800 + 0.918337i \(0.370467\pi\)
\(434\) 0 0
\(435\) −9.52786 + 24.9443i −0.456826 + 1.19599i
\(436\) 0 0
\(437\) 1.88854i 0.0903413i
\(438\) 0 0
\(439\) 22.1803i 1.05861i 0.848432 + 0.529305i \(0.177547\pi\)
−0.848432 + 0.529305i \(0.822453\pi\)
\(440\) 0 0
\(441\) −12.2361 10.9443i −0.582670 0.521156i
\(442\) 0 0
\(443\) 16.2918 0.774047 0.387023 0.922070i \(-0.373503\pi\)
0.387023 + 0.922070i \(0.373503\pi\)
\(444\) 0 0
\(445\) 12.9443 0.613617
\(446\) 0 0
\(447\) 15.7082 + 6.00000i 0.742973 + 0.283790i
\(448\) 0 0
\(449\) 0.583592i 0.0275414i 0.999905 + 0.0137707i \(0.00438349\pi\)
−0.999905 + 0.0137707i \(0.995617\pi\)
\(450\) 0 0
\(451\) 33.8885i 1.59575i
\(452\) 0 0
\(453\) −31.8885 12.1803i −1.49825 0.572282i
\(454\) 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
\(459\) 5.88854 + 11.4164i 0.274854 + 0.532872i
\(460\) 0 0
\(461\) 8.18034i 0.380996i 0.981688 + 0.190498i \(0.0610103\pi\)
−0.981688 + 0.190498i \(0.938990\pi\)
\(462\) 0 0
\(463\) 34.7639i 1.61562i −0.589445 0.807808i \(-0.700654\pi\)
0.589445 0.807808i \(-0.299346\pi\)
\(464\) 0 0
\(465\) 10.4721 27.4164i 0.485634 1.27141i
\(466\) 0 0
\(467\) 10.7639 0.498095 0.249048 0.968491i \(-0.419882\pi\)
0.249048 + 0.968491i \(0.419882\pi\)
\(468\) 0 0
\(469\) −12.0000 −0.554109
\(470\) 0 0
\(471\) −2.76393 + 7.23607i −0.127355 + 0.333420i
\(472\) 0 0
\(473\) 37.8885i 1.74212i
\(474\) 0 0
\(475\) 4.18034i 0.191807i
\(476\) 0 0
\(477\) −6.47214 + 7.23607i −0.296339 + 0.331317i
\(478\) 0 0
\(479\) 6.11146 0.279240 0.139620 0.990205i \(-0.455412\pi\)
0.139620 + 0.990205i \(0.455412\pi\)
\(480\) 0 0
\(481\) −37.8885 −1.72757
\(482\) 0 0
\(483\) −4.94427 1.88854i −0.224972 0.0859317i
\(484\) 0 0
\(485\) 1.52786i 0.0693767i
\(486\) 0 0
\(487\) 32.6525i 1.47962i −0.672813 0.739812i \(-0.734914\pi\)
0.672813 0.739812i \(-0.265086\pi\)
\(488\) 0 0
\(489\) −6.76393 2.58359i −0.305876 0.116834i
\(490\) 0 0
\(491\) −32.0689 −1.44725 −0.723624 0.690194i \(-0.757525\pi\)
−0.723624 + 0.690194i \(0.757525\pi\)
\(492\) 0 0
\(493\) −11.7771 −0.530413
\(494\) 0 0
\(495\) −33.8885 + 37.8885i −1.52318 + 1.70296i
\(496\) 0 0
\(497\) 19.0557i 0.854766i
\(498\) 0 0
\(499\) 27.2361i 1.21925i −0.792688 0.609627i \(-0.791319\pi\)
0.792688 0.609627i \(-0.208681\pi\)
\(500\) 0 0
\(501\) −8.36068 + 21.8885i −0.373528 + 0.977908i
\(502\) 0 0
\(503\) −21.5279 −0.959880 −0.479940 0.877301i \(-0.659342\pi\)
−0.479940 + 0.877301i \(0.659342\pi\)
\(504\) 0 0
\(505\) 5.52786 0.245987
\(506\) 0 0
\(507\) 4.32624 11.3262i 0.192135 0.503016i
\(508\) 0 0
\(509\) 25.7082i 1.13950i −0.821819 0.569748i \(-0.807041\pi\)
0.821819 0.569748i \(-0.192959\pi\)
\(510\) 0 0
\(511\) 2.47214i 0.109361i
\(512\) 0 0
\(513\) −1.81966 3.52786i −0.0803400 0.155759i
\(514\) 0 0
\(515\) 45.8885 2.02209
\(516\) 0 0
\(517\) 41.8885 1.84226
\(518\) 0 0
\(519\) −36.6525 14.0000i −1.60887 0.614532i
\(520\) 0 0
\(521\) 24.3607i 1.06726i −0.845718 0.533630i \(-0.820827\pi\)
0.845718 0.533630i \(-0.179173\pi\)
\(522\) 0 0
\(523\) 11.8197i 0.516838i 0.966033 + 0.258419i \(0.0832015\pi\)
−0.966033 + 0.258419i \(0.916799\pi\)
\(524\) 0 0
\(525\) −10.9443 4.18034i −0.477647 0.182445i
\(526\) 0 0
\(527\) 12.9443 0.563861
\(528\) 0 0
\(529\) −16.8885 −0.734285
\(530\) 0 0
\(531\) 2.76393 + 2.47214i 0.119944 + 0.107282i
\(532\) 0 0
\(533\) 28.9443i 1.25372i
\(534\) 0 0
\(535\) 45.8885i 1.98393i
\(536\) 0 0
\(537\) 3.81966 10.0000i 0.164831 0.431532i
\(538\) 0 0
\(539\) 28.6525 1.23415
\(540\) 0 0
\(541\) 26.3607 1.13333 0.566667 0.823947i \(-0.308233\pi\)
0.566667 + 0.823947i \(0.308233\pi\)
\(542\) 0 0
\(543\) −12.6525 + 33.1246i −0.542970 + 1.42151i
\(544\) 0 0
\(545\) 27.4164i 1.17439i
\(546\) 0 0
\(547\) 7.23607i 0.309392i −0.987962 0.154696i \(-0.950560\pi\)
0.987962 0.154696i \(-0.0494398\pi\)
\(548\) 0 0
\(549\) −1.05573 0.944272i −0.0450574 0.0403005i
\(550\) 0 0
\(551\) 3.63932 0.155040
\(552\) 0 0
\(553\) −0.360680 −0.0153377
\(554\) 0 0
\(555\) −44.3607 16.9443i −1.88301 0.719244i
\(556\) 0 0
\(557\) 14.6525i 0.620845i −0.950599 0.310423i \(-0.899529\pi\)
0.950599 0.310423i \(-0.100471\pi\)
\(558\) 0 0
\(559\) 32.3607i 1.36871i
\(560\) 0 0
\(561\) −20.9443 8.00000i −0.884268 0.337760i
\(562\) 0 0
\(563\) 30.5410 1.28715 0.643575 0.765383i \(-0.277450\pi\)
0.643575 + 0.765383i \(0.277450\pi\)
\(564\) 0 0
\(565\) −25.8885 −1.08914
\(566\) 0 0
\(567\) −11.0557 + 1.23607i −0.464297 + 0.0519100i
\(568\) 0 0
\(569\) 46.4721i 1.94821i 0.226089 + 0.974107i \(0.427406\pi\)
−0.226089 + 0.974107i \(0.572594\pi\)
\(570\) 0 0
\(571\) 5.12461i 0.214458i −0.994234 0.107229i \(-0.965802\pi\)
0.994234 0.107229i \(-0.0341979\pi\)
\(572\) 0 0
\(573\) 8.00000 20.9443i 0.334205 0.874960i
\(574\) 0 0
\(575\) 13.5279 0.564151
\(576\) 0 0
\(577\) 28.4721 1.18531 0.592655 0.805456i \(-0.298080\pi\)
0.592655 + 0.805456i \(0.298080\pi\)
\(578\) 0 0
\(579\) −7.34752 + 19.2361i −0.305353 + 0.799424i
\(580\) 0 0
\(581\) 3.41641i 0.141736i
\(582\) 0 0
\(583\) 16.9443i 0.701760i
\(584\) 0 0
\(585\) 28.9443 32.3607i 1.19670 1.33795i
\(586\) 0 0
\(587\) 21.5967 0.891393 0.445697 0.895184i \(-0.352956\pi\)
0.445697 + 0.895184i \(0.352956\pi\)
\(588\) 0 0
\(589\) −4.00000 −0.164817
\(590\) 0 0
\(591\) 7.70820 + 2.94427i 0.317073 + 0.121111i
\(592\) 0 0
\(593\) 28.9443i 1.18860i −0.804244 0.594299i \(-0.797429\pi\)
0.804244 0.594299i \(-0.202571\pi\)
\(594\) 0 0
\(595\) 9.88854i 0.405391i
\(596\) 0 0
\(597\) 10.0000 + 3.81966i 0.409273 + 0.156328i
\(598\) 0 0
\(599\) 7.41641 0.303026 0.151513 0.988455i \(-0.451585\pi\)
0.151513 + 0.988455i \(0.451585\pi\)
\(600\) 0 0
\(601\) 33.7771 1.37780 0.688898 0.724858i \(-0.258095\pi\)
0.688898 + 0.724858i \(0.258095\pi\)
\(602\) 0 0
\(603\) 19.4164 21.7082i 0.790697 0.884026i
\(604\) 0 0
\(605\) 53.1246i 2.15982i
\(606\) 0 0
\(607\) 34.7639i 1.41102i −0.708698 0.705512i \(-0.750717\pi\)
0.708698 0.705512i \(-0.249283\pi\)
\(608\) 0 0
\(609\) 3.63932 9.52786i 0.147473 0.386089i
\(610\) 0 0
\(611\) −35.7771 −1.44739
\(612\) 0 0
\(613\) −19.3050 −0.779720 −0.389860 0.920874i \(-0.627477\pi\)
−0.389860 + 0.920874i \(0.627477\pi\)
\(614\) 0 0
\(615\) 12.9443 33.8885i 0.521963 1.36652i
\(616\) 0 0
\(617\) 21.8885i 0.881200i 0.897704 + 0.440600i \(0.145234\pi\)
−0.897704 + 0.440600i \(0.854766\pi\)
\(618\) 0 0
\(619\) 29.1246i 1.17062i −0.810811 0.585308i \(-0.800973\pi\)
0.810811 0.585308i \(-0.199027\pi\)
\(620\) 0 0
\(621\) 11.4164 5.88854i 0.458125 0.236299i
\(622\) 0 0
\(623\) −4.94427 −0.198088
\(624\) 0 0
\(625\) −22.4164 −0.896656
\(626\) 0 0
\(627\) 6.47214 + 2.47214i 0.258472 + 0.0987276i
\(628\) 0 0
\(629\) 20.9443i 0.835103i
\(630\) 0 0
\(631\) 19.1246i 0.761339i 0.924711 + 0.380669i \(0.124306\pi\)
−0.924711 + 0.380669i \(0.875694\pi\)
\(632\) 0 0
\(633\) −18.1803 6.94427i −0.722604 0.276010i
\(634\) 0 0
\(635\) 42.8328 1.69977
\(636\) 0 0
\(637\) −24.4721 −0.969621
\(638\) 0 0
\(639\) −34.4721 30.8328i −1.36370 1.21973i
\(640\) 0 0
\(641\) 25.3050i 0.999485i 0.866174 + 0.499743i \(0.166572\pi\)
−0.866174 + 0.499743i \(0.833428\pi\)
\(642\) 0 0
\(643\) 13.3475i 0.526375i −0.964745 0.263187i \(-0.915226\pi\)
0.964745 0.263187i \(-0.0847738\pi\)
\(644\) 0 0
\(645\) −14.4721 + 37.8885i −0.569840 + 1.49186i
\(646\) 0 0
\(647\) −33.3050 −1.30935 −0.654676 0.755909i \(-0.727195\pi\)
−0.654676 + 0.755909i \(0.727195\pi\)
\(648\) 0 0
\(649\) −6.47214 −0.254054
\(650\) 0 0
\(651\) −4.00000 + 10.4721i −0.156772 + 0.410435i
\(652\) 0 0
\(653\) 14.2918i 0.559281i 0.960105 + 0.279641i \(0.0902153\pi\)
−0.960105 + 0.279641i \(0.909785\pi\)
\(654\) 0 0
\(655\) 21.8885i 0.855256i
\(656\) 0 0
\(657\) 4.47214 + 4.00000i 0.174475 + 0.156055i
\(658\) 0 0
\(659\) 28.2918 1.10209 0.551046 0.834475i \(-0.314229\pi\)
0.551046 + 0.834475i \(0.314229\pi\)
\(660\) 0 0
\(661\) −51.3050 −1.99553 −0.997766 0.0668107i \(-0.978718\pi\)
−0.997766 + 0.0668107i \(0.978718\pi\)
\(662\) 0 0
\(663\) 17.8885 + 6.83282i 0.694733 + 0.265365i
\(664\) 0 0
\(665\) 3.05573i 0.118496i
\(666\) 0 0
\(667\) 11.7771i 0.456011i
\(668\) 0 0
\(669\) 16.4721 + 6.29180i 0.636850 + 0.243255i
\(670\) 0 0
\(671\) 2.47214 0.0954358
\(672\) 0 0
\(673\) −25.4164 −0.979731 −0.489865 0.871798i \(-0.662954\pi\)
−0.489865 + 0.871798i \(0.662954\pi\)
\(674\) 0 0
\(675\) 25.2705 13.0344i 0.972662 0.501696i
\(676\) 0 0
\(677\) 14.2918i 0.549278i −0.961547 0.274639i \(-0.911442\pi\)
0.961547 0.274639i \(-0.0885584\pi\)
\(678\) 0 0
\(679\) 0.583592i 0.0223962i
\(680\) 0 0
\(681\) −1.34752 + 3.52786i −0.0516372 + 0.135188i
\(682\) 0 0
\(683\) 13.2361 0.506464 0.253232 0.967406i \(-0.418506\pi\)
0.253232 + 0.967406i \(0.418506\pi\)
\(684\) 0 0
\(685\) 4.94427 0.188911
\(686\) 0 0
\(687\) 7.12461 18.6525i 0.271821 0.711636i
\(688\) 0 0
\(689\) 14.4721i 0.551344i
\(690\) 0 0
\(691\) 29.7082i 1.13015i 0.825038 + 0.565077i \(0.191153\pi\)
−0.825038 + 0.565077i \(0.808847\pi\)
\(692\) 0 0
\(693\) 12.9443 14.4721i 0.491712 0.549751i
\(694\) 0 0
\(695\) 31.4164 1.19169
\(696\) 0 0
\(697\) 16.0000 0.606043
\(698\) 0 0
\(699\) −40.3607 15.4164i −1.52658 0.583102i
\(700\) 0 0
\(701\) 14.2918i 0.539794i 0.962889 + 0.269897i \(0.0869896\pi\)
−0.962889 + 0.269897i \(0.913010\pi\)
\(702\) 0 0
\(703\) 6.47214i 0.244101i
\(704\) 0 0
\(705\) −41.8885 16.0000i −1.57761 0.602595i
\(706\) 0 0
\(707\) −2.11146 −0.0794095
\(708\) 0 0
\(709\) −7.52786 −0.282715 −0.141357 0.989959i \(-0.545147\pi\)
−0.141357 + 0.989959i \(0.545147\pi\)
\(710\) 0 0
\(711\) 0.583592 0.652476i 0.0218864 0.0244698i
\(712\) 0 0
\(713\) 12.9443i 0.484767i
\(714\) 0 0
\(715\) 75.7771i 2.83390i
\(716\) 0 0
\(717\) −4.94427 + 12.9443i −0.184647 + 0.483413i
\(718\) 0 0
\(719\) 30.8328 1.14987 0.574935 0.818199i \(-0.305027\pi\)
0.574935 + 0.818199i \(0.305027\pi\)
\(720\) 0 0
\(721\) −17.5279 −0.652772
\(722\) 0 0
\(723\) −1.23607 + 3.23607i −0.0459699 + 0.120351i
\(724\) 0 0
\(725\) 26.0689i 0.968174i
\(726\) 0 0
\(727\) 14.1803i 0.525920i 0.964807 + 0.262960i \(0.0846987\pi\)
−0.964807 + 0.262960i \(0.915301\pi\)
\(728\) 0 0
\(729\) 15.6525 22.0000i 0.579721 0.814815i
\(730\) 0 0
\(731\) −17.8885 −0.661632
\(732\) 0 0
\(733\) 29.4164 1.08652 0.543260 0.839565i \(-0.317190\pi\)
0.543260 + 0.839565i \(0.317190\pi\)
\(734\) 0 0
\(735\) −28.6525 10.9443i −1.05686 0.403686i
\(736\) 0 0
\(737\) 50.8328i 1.87245i
\(738\) 0 0
\(739\) 13.1246i 0.482797i −0.970426 0.241398i \(-0.922394\pi\)
0.970426 0.241398i \(-0.0776060\pi\)
\(740\) 0 0
\(741\) −5.52786 2.11146i −0.203071 0.0775663i
\(742\) 0 0
\(743\) −7.41641 −0.272082 −0.136041 0.990703i \(-0.543438\pi\)
−0.136041 + 0.990703i \(0.543438\pi\)
\(744\) 0 0
\(745\) 31.4164 1.15101
\(746\) 0 0
\(747\) −6.18034 5.52786i −0.226127 0.202254i
\(748\) 0 0
\(749\) 17.5279i 0.640454i
\(750\) 0 0
\(751\) 17.5967i 0.642114i −0.947060 0.321057i \(-0.895962\pi\)
0.947060 0.321057i \(-0.104038\pi\)
\(752\) 0 0
\(753\) −14.6525 + 38.3607i −0.533966 + 1.39794i
\(754\) 0 0
\(755\) −63.7771 −2.32109
\(756\) 0 0
\(757\) 5.41641 0.196863 0.0984313 0.995144i \(-0.468618\pi\)
0.0984313 + 0.995144i \(0.468618\pi\)
\(758\) 0 0
\(759\) −8.00000 + 20.9443i −0.290382 + 0.760229i
\(760\) 0 0
\(761\) 42.2492i 1.53153i −0.643119 0.765767i \(-0.722360\pi\)
0.643119 0.765767i \(-0.277640\pi\)
\(762\) 0 0
\(763\) 10.4721i 0.379117i
\(764\) 0 0
\(765\) 17.8885 + 16.0000i 0.646762 + 0.578481i
\(766\) 0 0
\(767\) 5.52786 0.199600
\(768\) 0 0
\(769\) 49.7771 1.79501 0.897504 0.441007i \(-0.145378\pi\)
0.897504 + 0.441007i \(0.145378\pi\)
\(770\) 0 0
\(771\) −33.8885 12.9443i −1.22047 0.466177i
\(772\) 0 0
\(773\) 7.81966i 0.281254i 0.990063 + 0.140627i \(0.0449118\pi\)
−0.990063 + 0.140627i \(0.955088\pi\)
\(774\) 0 0
\(775\) 28.6525i 1.02923i
\(776\) 0 0
\(777\) 16.9443 + 6.47214i 0.607872 + 0.232187i
\(778\) 0 0
\(779\) −4.94427 −0.177147
\(780\) 0 0
\(781\) 80.7214 2.88844
\(782\) 0 0
\(783\) 11.3475 + 22.0000i 0.405527 + 0.786216i
\(784\) 0 0
\(785\) 14.4721i 0.516533i
\(786\) 0 0
\(787\) 28.1803i 1.00452i −0.864716 0.502260i \(-0.832502\pi\)
0.864716 0.502260i \(-0.167498\pi\)
\(788\) 0 0
\(789\) −6.47214 + 16.9443i −0.230414 + 0.603232i
\(790\) 0 0
\(791\) 9.88854 0.351596
\(792\) 0 0
\(793\) −2.11146 −0.0749800
\(794\) 0 0
\(795\) −6.47214 + 16.9443i −0.229543 + 0.600951i
\(796\) 0 0
\(797\) 50.0689i 1.77353i 0.462220 + 0.886765i \(0.347053\pi\)
−0.462220 + 0.886765i \(0.652947\pi\)
\(798\) 0 0
\(799\) 19.7771i 0.699663i
\(800\) 0 0