Properties

Label 1900.2.i.d.201.2
Level $1900$
Weight $2$
Character 1900.201
Analytic conductor $15.172$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} + 9 x^{6} + 2 x^{5} + 65 x^{4} - 20 x^{3} + 25 x^{2} + 6 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.2
Root \(-0.176725 + 0.306096i\) of defining polynomial
Character \(\chi\) \(=\) 1900.201
Dual form 1900.2.i.d.501.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.176725 + 0.306096i) q^{3} +4.30507 q^{7} +(1.43754 + 2.48989i) q^{9} +O(q^{10})\) \(q+(-0.176725 + 0.306096i) q^{3} +4.30507 q^{7} +(1.43754 + 2.48989i) q^{9} +6.01196 q^{11} +(-2.97581 - 5.15425i) q^{13} +(1.93754 - 3.35591i) q^{17} +(4.19835 + 1.17212i) q^{19} +(-0.760812 + 1.31776i) q^{21} +(0.391721 + 0.678480i) q^{23} -2.07654 q^{27} +(-3.98179 - 6.89666i) q^{29} -4.49034 q^{31} +(-1.06246 + 1.84024i) q^{33} +0.988035 q^{37} +2.10360 q^{39} +(-3.15253 + 5.46035i) q^{41} +(-0.785004 + 1.35967i) q^{43} +(-0.630909 - 1.09277i) q^{47} +11.5336 q^{49} +(0.684822 + 1.18615i) q^{51} +(-4.07443 - 7.05712i) q^{53} +(-1.10073 + 1.07796i) q^{57} +(-2.62834 + 4.55242i) q^{59} +(-2.80507 - 4.85852i) q^{61} +(6.18869 + 10.7191i) q^{63} +(3.52162 + 6.09963i) q^{67} -0.276907 q^{69} +(2.90736 - 5.03570i) q^{71} +(-4.62024 + 8.00250i) q^{73} +25.8819 q^{77} +(6.99743 - 12.1199i) q^{79} +(-3.94563 + 6.83404i) q^{81} -6.58197 q^{83} +2.81472 q^{87} +(1.69237 + 2.93126i) q^{89} +(-12.8110 - 22.1894i) q^{91} +(0.793555 - 1.37448i) q^{93} +(-3.69835 + 6.40573i) q^{97} +(8.64242 + 14.9691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{3} - 5 q^{9} + O(q^{10}) \) \( 8 q + q^{3} - 5 q^{9} + 4 q^{11} - 9 q^{13} - q^{17} + 3 q^{19} + 8 q^{21} - 20 q^{27} + 5 q^{29} - 20 q^{31} - 25 q^{33} + 52 q^{37} - 54 q^{39} - 8 q^{41} - 7 q^{43} - 16 q^{47} + 20 q^{49} + 12 q^{51} - 5 q^{53} - 27 q^{57} + 11 q^{59} + 12 q^{61} + 3 q^{63} + 6 q^{69} + 14 q^{71} + 4 q^{73} + 44 q^{77} + 13 q^{79} - 24 q^{81} - 10 q^{83} + 4 q^{87} + 5 q^{89} - 46 q^{91} + 28 q^{93} + q^{97} + 24 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) −0.176725 + 0.306096i −0.102032 + 0.176725i −0.912522 0.409028i \(-0.865868\pi\)
0.810490 + 0.585753i \(0.199201\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.30507 1.62716 0.813581 0.581452i \(-0.197515\pi\)
0.813581 + 0.581452i \(0.197515\pi\)
\(8\) 0 0
\(9\) 1.43754 + 2.48989i 0.479179 + 0.829962i
\(10\) 0 0
\(11\) 6.01196 1.81268 0.906338 0.422554i \(-0.138866\pi\)
0.906338 + 0.422554i \(0.138866\pi\)
\(12\) 0 0
\(13\) −2.97581 5.15425i −0.825341 1.42953i −0.901659 0.432448i \(-0.857650\pi\)
0.0763181 0.997084i \(-0.475684\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.93754 3.35591i 0.469922 0.813928i −0.529487 0.848318i \(-0.677615\pi\)
0.999408 + 0.0343900i \(0.0109488\pi\)
\(18\) 0 0
\(19\) 4.19835 + 1.17212i 0.963167 + 0.268903i
\(20\) 0 0
\(21\) −0.760812 + 1.31776i −0.166023 + 0.287560i
\(22\) 0 0
\(23\) 0.391721 + 0.678480i 0.0816794 + 0.141473i 0.903971 0.427593i \(-0.140638\pi\)
−0.822292 + 0.569066i \(0.807305\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2.07654 −0.399631
\(28\) 0 0
\(29\) −3.98179 6.89666i −0.739400 1.28068i −0.952766 0.303706i \(-0.901776\pi\)
0.213366 0.976972i \(-0.431557\pi\)
\(30\) 0 0
\(31\) −4.49034 −0.806489 −0.403245 0.915092i \(-0.632118\pi\)
−0.403245 + 0.915092i \(0.632118\pi\)
\(32\) 0 0
\(33\) −1.06246 + 1.84024i −0.184951 + 0.320345i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.988035 0.162432 0.0812160 0.996697i \(-0.474120\pi\)
0.0812160 + 0.996697i \(0.474120\pi\)
\(38\) 0 0
\(39\) 2.10360 0.336845
\(40\) 0 0
\(41\) −3.15253 + 5.46035i −0.492343 + 0.852763i −0.999961 0.00881921i \(-0.997193\pi\)
0.507618 + 0.861582i \(0.330526\pi\)
\(42\) 0 0
\(43\) −0.785004 + 1.35967i −0.119712 + 0.207347i −0.919654 0.392731i \(-0.871530\pi\)
0.799942 + 0.600078i \(0.204864\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.630909 1.09277i −0.0920275 0.159396i 0.816337 0.577576i \(-0.196001\pi\)
−0.908364 + 0.418180i \(0.862668\pi\)
\(48\) 0 0
\(49\) 11.5336 1.64766
\(50\) 0 0
\(51\) 0.684822 + 1.18615i 0.0958942 + 0.166094i
\(52\) 0 0
\(53\) −4.07443 7.05712i −0.559666 0.969369i −0.997524 0.0703255i \(-0.977596\pi\)
0.437858 0.899044i \(-0.355737\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.10073 + 1.07796i −0.145796 + 0.142779i
\(58\) 0 0
\(59\) −2.62834 + 4.55242i −0.342181 + 0.592675i −0.984837 0.173480i \(-0.944499\pi\)
0.642657 + 0.766154i \(0.277832\pi\)
\(60\) 0 0
\(61\) −2.80507 4.85852i −0.359152 0.622069i 0.628668 0.777674i \(-0.283601\pi\)
−0.987819 + 0.155605i \(0.950267\pi\)
\(62\) 0 0
\(63\) 6.18869 + 10.7191i 0.779702 + 1.35048i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 3.52162 + 6.09963i 0.430235 + 0.745189i 0.996893 0.0787642i \(-0.0250974\pi\)
−0.566658 + 0.823953i \(0.691764\pi\)
\(68\) 0 0
\(69\) −0.276907 −0.0333357
\(70\) 0 0
\(71\) 2.90736 5.03570i 0.345040 0.597628i −0.640321 0.768108i \(-0.721199\pi\)
0.985361 + 0.170480i \(0.0545319\pi\)
\(72\) 0 0
\(73\) −4.62024 + 8.00250i −0.540759 + 0.936621i 0.458102 + 0.888900i \(0.348529\pi\)
−0.998861 + 0.0477218i \(0.984804\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 25.8819 2.94952
\(78\) 0 0
\(79\) 6.99743 12.1199i 0.787273 1.36360i −0.140359 0.990101i \(-0.544826\pi\)
0.927632 0.373495i \(-0.121841\pi\)
\(80\) 0 0
\(81\) −3.94563 + 6.83404i −0.438404 + 0.759338i
\(82\) 0 0
\(83\) −6.58197 −0.722465 −0.361233 0.932476i \(-0.617644\pi\)
−0.361233 + 0.932476i \(0.617644\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 2.81472 0.301770
\(88\) 0 0
\(89\) 1.69237 + 2.93126i 0.179390 + 0.310713i 0.941672 0.336532i \(-0.109254\pi\)
−0.762281 + 0.647246i \(0.775921\pi\)
\(90\) 0 0
\(91\) −12.8110 22.1894i −1.34296 2.32608i
\(92\) 0 0
\(93\) 0.793555 1.37448i 0.0822878 0.142527i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −3.69835 + 6.40573i −0.375510 + 0.650403i −0.990403 0.138208i \(-0.955866\pi\)
0.614893 + 0.788611i \(0.289199\pi\)
\(98\) 0 0
\(99\) 8.64242 + 14.9691i 0.868596 + 1.50445i
\(100\) 0 0
\(101\) 4.90369 + 8.49343i 0.487935 + 0.845128i 0.999904 0.0138759i \(-0.00441699\pi\)
−0.511969 + 0.859004i \(0.671084\pi\)
\(102\) 0 0
\(103\) −14.4368 −1.42250 −0.711251 0.702938i \(-0.751871\pi\)
−0.711251 + 0.702938i \(0.751871\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.49034 0.917466 0.458733 0.888574i \(-0.348303\pi\)
0.458733 + 0.888574i \(0.348303\pi\)
\(108\) 0 0
\(109\) 1.30920 2.26759i 0.125398 0.217196i −0.796490 0.604651i \(-0.793312\pi\)
0.921889 + 0.387455i \(0.126646\pi\)
\(110\) 0 0
\(111\) −0.174610 + 0.302434i −0.0165733 + 0.0287058i
\(112\) 0 0
\(113\) 13.6705 1.28601 0.643005 0.765862i \(-0.277687\pi\)
0.643005 + 0.765862i \(0.277687\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 8.55567 14.8188i 0.790972 1.37000i
\(118\) 0 0
\(119\) 8.34122 14.4474i 0.764639 1.32439i
\(120\) 0 0
\(121\) 25.1437 2.28579
\(122\) 0 0
\(123\) −1.11426 1.92996i −0.100470 0.174018i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 6.53359 + 11.3165i 0.579762 + 1.00418i 0.995506 + 0.0946960i \(0.0301879\pi\)
−0.415744 + 0.909482i \(0.636479\pi\)
\(128\) 0 0
\(129\) −0.277459 0.480574i −0.0244289 0.0423122i
\(130\) 0 0
\(131\) 3.75070 6.49640i 0.327700 0.567593i −0.654355 0.756188i \(-0.727060\pi\)
0.982055 + 0.188594i \(0.0603931\pi\)
\(132\) 0 0
\(133\) 18.0742 + 5.04606i 1.56723 + 0.437549i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.21500 7.30059i −0.360111 0.623731i 0.627867 0.778320i \(-0.283928\pi\)
−0.987979 + 0.154589i \(0.950595\pi\)
\(138\) 0 0
\(139\) −4.38961 7.60302i −0.372322 0.644880i 0.617601 0.786492i \(-0.288105\pi\)
−0.989922 + 0.141612i \(0.954771\pi\)
\(140\) 0 0
\(141\) 0.445989 0.0375591
\(142\) 0 0
\(143\) −17.8905 30.9872i −1.49607 2.59128i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −2.03827 + 3.53039i −0.168114 + 0.291182i
\(148\) 0 0
\(149\) 0.915913 1.58641i 0.0750345 0.129964i −0.826067 0.563572i \(-0.809427\pi\)
0.901101 + 0.433609i \(0.142760\pi\)
\(150\) 0 0
\(151\) −0.389869 −0.0317271 −0.0158635 0.999874i \(-0.505050\pi\)
−0.0158635 + 0.999874i \(0.505050\pi\)
\(152\) 0 0
\(153\) 11.1411 0.900706
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.37608 + 2.38344i −0.109823 + 0.190219i −0.915698 0.401866i \(-0.868362\pi\)
0.805875 + 0.592085i \(0.201695\pi\)
\(158\) 0 0
\(159\) 2.88021 0.228416
\(160\) 0 0
\(161\) 1.68638 + 2.92090i 0.132906 + 0.230199i
\(162\) 0 0
\(163\) 15.0953 1.18236 0.591179 0.806540i \(-0.298663\pi\)
0.591179 + 0.806540i \(0.298663\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.49402 + 2.58771i 0.115611 + 0.200243i 0.918024 0.396526i \(-0.129784\pi\)
−0.802413 + 0.596769i \(0.796451\pi\)
\(168\) 0 0
\(169\) −11.2109 + 19.4178i −0.862374 + 1.49368i
\(170\) 0 0
\(171\) 3.11683 + 12.1384i 0.238350 + 0.928245i
\(172\) 0 0
\(173\) −11.5945 + 20.0822i −0.881513 + 1.52682i −0.0318535 + 0.999493i \(0.510141\pi\)
−0.849659 + 0.527332i \(0.823192\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −0.928986 1.60905i −0.0698269 0.120944i
\(178\) 0 0
\(179\) −13.5091 −1.00972 −0.504860 0.863201i \(-0.668456\pi\)
−0.504860 + 0.863201i \(0.668456\pi\)
\(180\) 0 0
\(181\) 10.1559 + 17.5906i 0.754886 + 1.30750i 0.945431 + 0.325822i \(0.105641\pi\)
−0.190546 + 0.981678i \(0.561026\pi\)
\(182\) 0 0
\(183\) 1.98290 0.146580
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 11.6484 20.1756i 0.851816 1.47539i
\(188\) 0 0
\(189\) −8.93965 −0.650264
\(190\) 0 0
\(191\) −7.04838 −0.510003 −0.255002 0.966941i \(-0.582076\pi\)
−0.255002 + 0.966941i \(0.582076\pi\)
\(192\) 0 0
\(193\) −11.8892 + 20.5926i −0.855800 + 1.48229i 0.0201010 + 0.999798i \(0.493601\pi\)
−0.875901 + 0.482491i \(0.839732\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −23.7428 −1.69160 −0.845802 0.533497i \(-0.820878\pi\)
−0.845802 + 0.533497i \(0.820878\pi\)
\(198\) 0 0
\(199\) 11.4893 + 19.9001i 0.814457 + 1.41068i 0.909717 + 0.415229i \(0.136299\pi\)
−0.0952595 + 0.995452i \(0.530368\pi\)
\(200\) 0 0
\(201\) −2.48943 −0.175591
\(202\) 0 0
\(203\) −17.1419 29.6906i −1.20312 2.08387i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.12623 + 1.95068i −0.0782781 + 0.135582i
\(208\) 0 0
\(209\) 25.2403 + 7.04675i 1.74591 + 0.487434i
\(210\) 0 0
\(211\) 0.692366 1.19921i 0.0476645 0.0825573i −0.841209 0.540710i \(-0.818156\pi\)
0.888873 + 0.458153i \(0.151489\pi\)
\(212\) 0 0
\(213\) 1.02761 + 1.77987i 0.0704104 + 0.121954i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −19.3312 −1.31229
\(218\) 0 0
\(219\) −1.63302 2.82848i −0.110349 0.191131i
\(220\) 0 0
\(221\) −23.0629 −1.55138
\(222\) 0 0
\(223\) −11.6500 + 20.1783i −0.780139 + 1.35124i 0.151721 + 0.988423i \(0.451519\pi\)
−0.931860 + 0.362818i \(0.881815\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4.48943 0.297974 0.148987 0.988839i \(-0.452399\pi\)
0.148987 + 0.988839i \(0.452399\pi\)
\(228\) 0 0
\(229\) 9.20830 0.608501 0.304251 0.952592i \(-0.401594\pi\)
0.304251 + 0.952592i \(0.401594\pi\)
\(230\) 0 0
\(231\) −4.57397 + 7.92236i −0.300945 + 0.521253i
\(232\) 0 0
\(233\) −2.16265 + 3.74581i −0.141680 + 0.245396i −0.928129 0.372258i \(-0.878584\pi\)
0.786450 + 0.617654i \(0.211917\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 2.47324 + 4.28378i 0.160654 + 0.278261i
\(238\) 0 0
\(239\) −14.8267 −0.959059 −0.479529 0.877526i \(-0.659193\pi\)
−0.479529 + 0.877526i \(0.659193\pi\)
\(240\) 0 0
\(241\) −1.44453 2.50199i −0.0930500 0.161167i 0.815743 0.578414i \(-0.196328\pi\)
−0.908793 + 0.417247i \(0.862995\pi\)
\(242\) 0 0
\(243\) −4.50940 7.81050i −0.289278 0.501044i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.45207 25.1273i −0.410535 1.59881i
\(248\) 0 0
\(249\) 1.16320 2.01472i 0.0737147 0.127678i
\(250\) 0 0
\(251\) −7.65253 13.2546i −0.483024 0.836621i 0.516786 0.856114i \(-0.327128\pi\)
−0.999810 + 0.0194930i \(0.993795\pi\)
\(252\) 0 0
\(253\) 2.35501 + 4.07900i 0.148058 + 0.256445i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.54214 + 11.3313i 0.408087 + 0.706828i 0.994675 0.103057i \(-0.0328625\pi\)
−0.586588 + 0.809886i \(0.699529\pi\)
\(258\) 0 0
\(259\) 4.25356 0.264303
\(260\) 0 0
\(261\) 11.4479 19.8284i 0.708610 1.22735i
\(262\) 0 0
\(263\) 9.68980 16.7832i 0.597499 1.03490i −0.395691 0.918384i \(-0.629495\pi\)
0.993189 0.116514i \(-0.0371720\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −1.19633 −0.0732144
\(268\) 0 0
\(269\) 0.728523 1.26184i 0.0444188 0.0769357i −0.842961 0.537974i \(-0.819190\pi\)
0.887380 + 0.461039i \(0.152523\pi\)
\(270\) 0 0
\(271\) −6.28133 + 10.8796i −0.381563 + 0.660887i −0.991286 0.131728i \(-0.957948\pi\)
0.609722 + 0.792615i \(0.291281\pi\)
\(272\) 0 0
\(273\) 9.05612 0.548101
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 4.39448 0.264039 0.132019 0.991247i \(-0.457854\pi\)
0.132019 + 0.991247i \(0.457854\pi\)
\(278\) 0 0
\(279\) −6.45503 11.1804i −0.386453 0.669355i
\(280\) 0 0
\(281\) −2.16265 3.74581i −0.129013 0.223456i 0.794282 0.607550i \(-0.207847\pi\)
−0.923294 + 0.384093i \(0.874514\pi\)
\(282\) 0 0
\(283\) 3.74885 6.49319i 0.222846 0.385980i −0.732825 0.680417i \(-0.761799\pi\)
0.955671 + 0.294437i \(0.0951320\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −13.5719 + 23.5072i −0.801122 + 1.38758i
\(288\) 0 0
\(289\) 0.991903 + 1.71803i 0.0583472 + 0.101060i
\(290\) 0 0
\(291\) −1.30718 2.26410i −0.0766282 0.132724i
\(292\) 0 0
\(293\) 22.2837 1.30183 0.650915 0.759151i \(-0.274385\pi\)
0.650915 + 0.759151i \(0.274385\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −12.4841 −0.724401
\(298\) 0 0
\(299\) 2.33137 4.03805i 0.134827 0.233527i
\(300\) 0 0
\(301\) −3.37949 + 5.85345i −0.194791 + 0.337387i
\(302\) 0 0
\(303\) −3.46641 −0.199140
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −15.1403 + 26.2238i −0.864103 + 1.49667i 0.00383236 + 0.999993i \(0.498780\pi\)
−0.867935 + 0.496677i \(0.834553\pi\)
\(308\) 0 0
\(309\) 2.55134 4.41906i 0.145141 0.251391i
\(310\) 0 0
\(311\) −5.37224 −0.304632 −0.152316 0.988332i \(-0.548673\pi\)
−0.152316 + 0.988332i \(0.548673\pi\)
\(312\) 0 0
\(313\) −2.40369 4.16331i −0.135864 0.235324i 0.790063 0.613026i \(-0.210048\pi\)
−0.925927 + 0.377702i \(0.876714\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −14.8855 25.7824i −0.836052 1.44808i −0.893171 0.449717i \(-0.851525\pi\)
0.0571197 0.998367i \(-0.481808\pi\)
\(318\) 0 0
\(319\) −23.9384 41.4625i −1.34029 2.32145i
\(320\) 0 0
\(321\) −1.67718 + 2.90496i −0.0936110 + 0.162139i
\(322\) 0 0
\(323\) 12.0680 11.8183i 0.671481 0.657586i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0.462735 + 0.801480i 0.0255893 + 0.0443220i
\(328\) 0 0
\(329\) −2.71610 4.70443i −0.149744 0.259364i
\(330\) 0 0
\(331\) 30.8042 1.69315 0.846577 0.532266i \(-0.178659\pi\)
0.846577 + 0.532266i \(0.178659\pi\)
\(332\) 0 0
\(333\) 1.42034 + 2.46010i 0.0778340 + 0.134812i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −3.32529 + 5.75957i −0.181140 + 0.313744i −0.942269 0.334857i \(-0.891312\pi\)
0.761129 + 0.648601i \(0.224645\pi\)
\(338\) 0 0
\(339\) −2.41591 + 4.18448i −0.131214 + 0.227270i
\(340\) 0 0
\(341\) −26.9958 −1.46190
\(342\) 0 0
\(343\) 19.5174 1.05384
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.70534 13.3460i 0.413644 0.716453i −0.581641 0.813446i \(-0.697589\pi\)
0.995285 + 0.0969930i \(0.0309224\pi\)
\(348\) 0 0
\(349\) −27.0157 −1.44612 −0.723058 0.690788i \(-0.757264\pi\)
−0.723058 + 0.690788i \(0.757264\pi\)
\(350\) 0 0
\(351\) 6.17939 + 10.7030i 0.329832 + 0.571285i
\(352\) 0 0
\(353\) −19.7783 −1.05269 −0.526346 0.850270i \(-0.676439\pi\)
−0.526346 + 0.850270i \(0.676439\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 2.94820 + 5.10644i 0.156035 + 0.270261i
\(358\) 0 0
\(359\) −17.8408 + 30.9011i −0.941600 + 1.63090i −0.179179 + 0.983816i \(0.557344\pi\)
−0.762420 + 0.647082i \(0.775989\pi\)
\(360\) 0 0
\(361\) 16.2523 + 9.84195i 0.855382 + 0.517997i
\(362\) 0 0
\(363\) −4.44352 + 7.69640i −0.233224 + 0.403956i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −1.05235 1.82272i −0.0549322 0.0951454i 0.837252 0.546818i \(-0.184161\pi\)
−0.892184 + 0.451672i \(0.850828\pi\)
\(368\) 0 0
\(369\) −18.1275 −0.943681
\(370\) 0 0
\(371\) −17.5407 30.3813i −0.910667 1.57732i
\(372\) 0 0
\(373\) 32.0208 1.65797 0.828987 0.559268i \(-0.188918\pi\)
0.828987 + 0.559268i \(0.188918\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −23.6981 + 41.0463i −1.22051 + 2.11399i
\(378\) 0 0
\(379\) −2.24784 −0.115464 −0.0577319 0.998332i \(-0.518387\pi\)
−0.0577319 + 0.998332i \(0.518387\pi\)
\(380\) 0 0
\(381\) −4.61859 −0.236617
\(382\) 0 0
\(383\) 1.33479 2.31192i 0.0682044 0.118133i −0.829907 0.557902i \(-0.811606\pi\)
0.898111 + 0.439769i \(0.144940\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −4.51389 −0.229454
\(388\) 0 0
\(389\) −7.76036 13.4413i −0.393466 0.681503i 0.599438 0.800421i \(-0.295391\pi\)
−0.992904 + 0.118918i \(0.962057\pi\)
\(390\) 0 0
\(391\) 3.03589 0.153532
\(392\) 0 0
\(393\) 1.32568 + 2.29615i 0.0668719 + 0.115825i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1.24839 2.16228i 0.0626551 0.108522i −0.832996 0.553278i \(-0.813377\pi\)
0.895651 + 0.444757i \(0.146710\pi\)
\(398\) 0 0
\(399\) −4.73873 + 4.64067i −0.237233 + 0.232324i
\(400\) 0 0
\(401\) 10.8590 18.8083i 0.542271 0.939242i −0.456502 0.889723i \(-0.650898\pi\)
0.998773 0.0495192i \(-0.0157689\pi\)
\(402\) 0 0
\(403\) 13.3624 + 23.1443i 0.665628 + 1.15290i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.94003 0.294437
\(408\) 0 0
\(409\) −12.1200 20.9924i −0.599294 1.03801i −0.992925 0.118740i \(-0.962115\pi\)
0.393631 0.919269i \(-0.371219\pi\)
\(410\) 0 0
\(411\) 2.97958 0.146972
\(412\) 0 0
\(413\) −11.3152 + 19.5985i −0.556784 + 0.964377i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 3.10301 0.151955
\(418\) 0 0
\(419\) −37.6543 −1.83953 −0.919766 0.392467i \(-0.871622\pi\)
−0.919766 + 0.392467i \(0.871622\pi\)
\(420\) 0 0
\(421\) 18.6884 32.3693i 0.910818 1.57758i 0.0979071 0.995196i \(-0.468785\pi\)
0.812911 0.582388i \(-0.197881\pi\)
\(422\) 0 0
\(423\) 1.81391 3.14178i 0.0881953 0.152759i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −12.0760 20.9162i −0.584398 1.01221i
\(428\) 0 0
\(429\) 12.6467 0.610591
\(430\) 0 0
\(431\) −5.41491 9.37889i −0.260827 0.451765i 0.705635 0.708576i \(-0.250662\pi\)
−0.966462 + 0.256810i \(0.917329\pi\)
\(432\) 0 0
\(433\) 5.71031 + 9.89055i 0.274420 + 0.475310i 0.969989 0.243150i \(-0.0781808\pi\)
−0.695569 + 0.718460i \(0.744847\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.849319 + 3.30764i 0.0406284 + 0.158226i
\(438\) 0 0
\(439\) −15.0612 + 26.0868i −0.718832 + 1.24505i 0.242631 + 0.970119i \(0.421989\pi\)
−0.961463 + 0.274934i \(0.911344\pi\)
\(440\) 0 0
\(441\) 16.5800 + 28.7173i 0.789522 + 1.36749i
\(442\) 0 0
\(443\) −10.3045 17.8479i −0.489582 0.847981i 0.510346 0.859969i \(-0.329517\pi\)
−0.999928 + 0.0119880i \(0.996184\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0.323729 + 0.560715i 0.0153119 + 0.0265209i
\(448\) 0 0
\(449\) −3.61436 −0.170572 −0.0852861 0.996357i \(-0.527180\pi\)
−0.0852861 + 0.996357i \(0.527180\pi\)
\(450\) 0 0
\(451\) −18.9529 + 32.8274i −0.892458 + 1.54578i
\(452\) 0 0
\(453\) 0.0688995 0.119338i 0.00323718 0.00560697i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5.50452 −0.257491 −0.128745 0.991678i \(-0.541095\pi\)
−0.128745 + 0.991678i \(0.541095\pi\)
\(458\) 0 0
\(459\) −4.02338 + 6.96869i −0.187795 + 0.325271i
\(460\) 0 0
\(461\) −9.66053 + 16.7325i −0.449936 + 0.779312i −0.998381 0.0568746i \(-0.981886\pi\)
0.548446 + 0.836186i \(0.315220\pi\)
\(462\) 0 0
\(463\) −1.05722 −0.0491334 −0.0245667 0.999698i \(-0.507821\pi\)
−0.0245667 + 0.999698i \(0.507821\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −21.9413 −1.01532 −0.507662 0.861556i \(-0.669490\pi\)
−0.507662 + 0.861556i \(0.669490\pi\)
\(468\) 0 0
\(469\) 15.1608 + 26.2593i 0.700062 + 1.21254i
\(470\) 0 0
\(471\) −0.486375 0.842426i −0.0224110 0.0388169i
\(472\) 0 0
\(473\) −4.71942 + 8.17427i −0.216999 + 0.375853i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 11.7143 20.2897i 0.536360 0.929003i
\(478\) 0 0
\(479\) 6.60203 + 11.4351i 0.301655 + 0.522481i 0.976511 0.215468i \(-0.0691277\pi\)
−0.674856 + 0.737949i \(0.735794\pi\)
\(480\) 0 0
\(481\) −2.94020 5.09258i −0.134062 0.232202i
\(482\) 0 0
\(483\) −1.19210 −0.0542426
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −15.5627 −0.705211 −0.352606 0.935772i \(-0.614704\pi\)
−0.352606 + 0.935772i \(0.614704\pi\)
\(488\) 0 0
\(489\) −2.66772 + 4.62063i −0.120638 + 0.208952i
\(490\) 0 0
\(491\) 14.7978 25.6306i 0.667816 1.15669i −0.310698 0.950509i \(-0.600563\pi\)
0.978514 0.206182i \(-0.0661040\pi\)
\(492\) 0 0
\(493\) −30.8595 −1.38984
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.5164 21.6790i 0.561437 0.972437i
\(498\) 0 0
\(499\) 2.92190 5.06087i 0.130802 0.226556i −0.793184 0.608982i \(-0.791578\pi\)
0.923986 + 0.382426i \(0.124911\pi\)
\(500\) 0 0
\(501\) −1.05612 −0.0471840
\(502\) 0 0
\(503\) 3.14544 + 5.44807i 0.140248 + 0.242917i 0.927590 0.373600i \(-0.121877\pi\)
−0.787342 + 0.616517i \(0.788543\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −3.96248 6.86321i −0.175980 0.304806i
\(508\) 0 0
\(509\) 1.84591 + 3.19720i 0.0818183 + 0.141713i 0.904031 0.427467i \(-0.140594\pi\)
−0.822213 + 0.569180i \(0.807261\pi\)
\(510\) 0 0
\(511\) −19.8905 + 34.4513i −0.879902 + 1.52403i
\(512\) 0 0
\(513\) −8.71805 2.43396i −0.384911 0.107462i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −3.79300 6.56967i −0.166816 0.288934i
\(518\) 0 0
\(519\) −4.09807 7.09806i −0.179885 0.311570i
\(520\) 0 0
\(521\) 29.0510 1.27275 0.636373 0.771381i \(-0.280434\pi\)
0.636373 + 0.771381i \(0.280434\pi\)
\(522\) 0 0
\(523\) 9.21685 + 15.9640i 0.403025 + 0.698059i 0.994089 0.108565i \(-0.0346256\pi\)
−0.591065 + 0.806624i \(0.701292\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.70020 + 15.0692i −0.378987 + 0.656424i
\(528\) 0 0
\(529\) 11.1931 19.3870i 0.486657 0.842915i
\(530\) 0 0
\(531\) −15.1133 −0.655863
\(532\) 0 0
\(533\) 37.5253 1.62540
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 2.38740 4.13510i 0.103024 0.178443i
\(538\) 0 0
\(539\) 69.3395 2.98666
\(540\) 0 0
\(541\) 21.0875 + 36.5246i 0.906622 + 1.57032i 0.818724 + 0.574187i \(0.194682\pi\)
0.0878981 + 0.996129i \(0.471985\pi\)
\(542\) 0 0
\(543\) −7.17923 −0.308090
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 7.87719 + 13.6437i 0.336804 + 0.583362i 0.983830 0.179106i \(-0.0573206\pi\)
−0.647025 + 0.762468i \(0.723987\pi\)
\(548\) 0 0
\(549\) 8.06477 13.9686i 0.344196 0.596165i
\(550\) 0 0
\(551\) −8.63321 33.6217i −0.367787 1.43233i
\(552\) 0 0
\(553\) 30.1244 52.1770i 1.28102 2.21879i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 11.5924 + 20.0786i 0.491185 + 0.850757i 0.999948 0.0101493i \(-0.00323068\pi\)
−0.508764 + 0.860906i \(0.669897\pi\)
\(558\) 0 0
\(559\) 9.34408 0.395213
\(560\) 0 0
\(561\) 4.11712 + 7.13107i 0.173825 + 0.301074i
\(562\) 0 0
\(563\) 0.970934 0.0409200 0.0204600 0.999791i \(-0.493487\pi\)
0.0204600 + 0.999791i \(0.493487\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −16.9862 + 29.4210i −0.713354 + 1.23556i
\(568\) 0 0
\(569\) −30.1395 −1.26351 −0.631757 0.775167i \(-0.717666\pi\)
−0.631757 + 0.775167i \(0.717666\pi\)
\(570\) 0 0
\(571\) −31.8976 −1.33487 −0.667436 0.744667i \(-0.732608\pi\)
−0.667436 + 0.744667i \(0.732608\pi\)
\(572\) 0 0
\(573\) 1.24562 2.15748i 0.0520367 0.0901302i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −23.2889 −0.969528 −0.484764 0.874645i \(-0.661095\pi\)
−0.484764 + 0.874645i \(0.661095\pi\)
\(578\) 0 0
\(579\) −4.20222 7.27845i −0.174638 0.302482i
\(580\) 0 0
\(581\) −28.3358 −1.17557
\(582\) 0 0
\(583\) −24.4953 42.4271i −1.01449 1.75715i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.74059 8.21094i 0.195665 0.338902i −0.751453 0.659786i \(-0.770647\pi\)
0.947118 + 0.320885i \(0.103980\pi\)
\(588\) 0 0
\(589\) −18.8520 5.26323i −0.776784 0.216867i
\(590\) 0 0
\(591\) 4.19594 7.26758i 0.172598 0.298948i
\(592\) 0 0
\(593\) −21.2234 36.7600i −0.871540 1.50955i −0.860403 0.509614i \(-0.829788\pi\)
−0.0111366 0.999938i \(-0.503545\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −8.12180 −0.332403
\(598\) 0 0
\(599\) 12.8961 + 22.3368i 0.526922 + 0.912656i 0.999508 + 0.0313711i \(0.00998736\pi\)
−0.472586 + 0.881285i \(0.656679\pi\)
\(600\) 0 0
\(601\) 0.206080 0.00840619 0.00420310 0.999991i \(-0.498662\pi\)
0.00420310 + 0.999991i \(0.498662\pi\)
\(602\) 0 0
\(603\) −10.1249 + 17.5369i −0.412319 + 0.714157i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −0.100472 −0.00407802 −0.00203901 0.999998i \(-0.500649\pi\)
−0.00203901 + 0.999998i \(0.500649\pi\)
\(608\) 0 0
\(609\) 12.1176 0.491029
\(610\) 0 0
\(611\) −3.75493 + 6.50373i −0.151908 + 0.263113i
\(612\) 0 0
\(613\) −19.7400 + 34.1907i −0.797292 + 1.38095i 0.124081 + 0.992272i \(0.460402\pi\)
−0.921373 + 0.388679i \(0.872932\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −14.1658 24.5359i −0.570294 0.987777i −0.996536 0.0831682i \(-0.973496\pi\)
0.426242 0.904609i \(-0.359837\pi\)
\(618\) 0 0
\(619\) −1.39670 −0.0561380 −0.0280690 0.999606i \(-0.508936\pi\)
−0.0280690 + 0.999606i \(0.508936\pi\)
\(620\) 0 0
\(621\) −0.813425 1.40889i −0.0326416 0.0565369i
\(622\) 0 0
\(623\) 7.28575 + 12.6193i 0.291897 + 0.505581i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −6.61758 + 6.48063i −0.264281 + 0.258812i
\(628\) 0 0
\(629\) 1.91435 3.31576i 0.0763303 0.132208i
\(630\) 0 0
\(631\) −4.07397 7.05633i −0.162182 0.280908i 0.773469 0.633834i \(-0.218520\pi\)
−0.935651 + 0.352926i \(0.885187\pi\)
\(632\) 0 0
\(633\) 0.244717 + 0.423862i 0.00972661 + 0.0168470i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −34.3217 59.4470i −1.35988 2.35538i
\(638\) 0 0
\(639\) 16.7178 0.661344
\(640\) 0 0
\(641\) −9.76367 + 16.9112i −0.385642 + 0.667951i −0.991858 0.127349i \(-0.959353\pi\)
0.606216 + 0.795300i \(0.292687\pi\)
\(642\) 0 0
\(643\) 21.5945 37.4028i 0.851604 1.47502i −0.0281570 0.999604i \(-0.508964\pi\)
0.879761 0.475417i \(-0.157703\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −27.4390 −1.07874 −0.539370 0.842069i \(-0.681338\pi\)
−0.539370 + 0.842069i \(0.681338\pi\)
\(648\) 0 0
\(649\) −15.8015 + 27.3690i −0.620263 + 1.07433i
\(650\) 0 0
\(651\) 3.41630 5.91721i 0.133896 0.231914i
\(652\) 0 0
\(653\) 3.40515 0.133254 0.0666270 0.997778i \(-0.478776\pi\)
0.0666270 + 0.997778i \(0.478776\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −26.5671 −1.03648
\(658\) 0 0
\(659\) −6.09862 10.5631i −0.237569 0.411481i 0.722448 0.691426i \(-0.243017\pi\)
−0.960016 + 0.279945i \(0.909684\pi\)
\(660\) 0 0
\(661\) 19.0683 + 33.0272i 0.741670 + 1.28461i 0.951734 + 0.306923i \(0.0992994\pi\)
−0.210064 + 0.977688i \(0.567367\pi\)
\(662\) 0 0
\(663\) 4.07580 7.05948i 0.158291 0.274168i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 3.11950 5.40313i 0.120788 0.209210i
\(668\) 0 0
\(669\) −4.11768 7.13202i −0.159199 0.275740i
\(670\) 0 0
\(671\) −16.8640 29.2092i −0.651026 1.12761i
\(672\) 0 0
\(673\) 37.9505 1.46288 0.731442 0.681903i \(-0.238848\pi\)
0.731442 + 0.681903i \(0.238848\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 32.4499 1.24715 0.623575 0.781763i \(-0.285679\pi\)
0.623575 + 0.781763i \(0.285679\pi\)
\(678\) 0 0
\(679\) −15.9216 + 27.5771i −0.611016 + 1.05831i
\(680\) 0 0
\(681\) −0.793394 + 1.37420i −0.0304029 + 0.0526594i
\(682\) 0 0
\(683\) −40.5283 −1.55077 −0.775385 0.631488i \(-0.782444\pi\)
−0.775385 + 0.631488i \(0.782444\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −1.62733 + 2.81863i −0.0620867 + 0.107537i
\(688\) 0 0
\(689\) −24.2494 + 42.0012i −0.923830 + 1.60012i
\(690\) 0 0
\(691\) 1.78657 0.0679642 0.0339821 0.999422i \(-0.489181\pi\)
0.0339821 + 0.999422i \(0.489181\pi\)
\(692\) 0 0
\(693\) 37.2062 + 64.4430i 1.41335 + 2.44799i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 12.2163 + 21.1592i 0.462725 + 0.801464i
\(698\) 0 0
\(699\) −0.764386 1.32396i −0.0289117 0.0500766i
\(700\) 0 0
\(701\) 21.8614 37.8650i 0.825693 1.43014i −0.0756952 0.997131i \(-0.524118\pi\)
0.901388 0.433011i \(-0.142549\pi\)
\(702\) 0 0
\(703\) 4.14812 + 1.15810i 0.156449 + 0.0436785i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 21.1107 + 36.5648i 0.793949 + 1.37516i
\(708\) 0 0
\(709\) −7.32015 12.6789i −0.274914 0.476165i 0.695199 0.718817i \(-0.255316\pi\)
−0.970113 + 0.242652i \(0.921983\pi\)
\(710\) 0 0
\(711\) 40.2363 1.50898
\(712\) 0 0
\(713\) −1.75896 3.04661i −0.0658736 0.114096i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 2.62024 4.53840i 0.0978548 0.169489i
\(718\) 0 0
\(719\) 11.1778 19.3606i 0.416863 0.722028i −0.578759 0.815499i \(-0.696463\pi\)
0.995622 + 0.0934709i \(0.0297962\pi\)
\(720\) 0 0
\(721\) −62.1515 −2.31464
\(722\) 0 0
\(723\) 1.02113 0.0379764
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 4.15042 7.18874i 0.153930 0.266615i −0.778739 0.627349i \(-0.784140\pi\)
0.932669 + 0.360733i \(0.117473\pi\)
\(728\) 0 0
\(729\) −20.4861 −0.758745
\(730\) 0 0
\(731\) 3.04195 + 5.26881i 0.112511 + 0.194874i
\(732\) 0 0
\(733\) −35.7912 −1.32198 −0.660989 0.750396i \(-0.729863\pi\)
−0.660989 + 0.750396i \(0.729863\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 21.1719 + 36.6708i 0.779876 + 1.35079i
\(738\) 0 0
\(739\) 16.6216 28.7895i 0.611437 1.05904i −0.379561 0.925167i \(-0.623925\pi\)
0.990998 0.133873i \(-0.0427415\pi\)
\(740\) 0 0
\(741\) 8.83163 + 2.46567i 0.324438 + 0.0905787i
\(742\) 0 0
\(743\) −9.27444 + 16.0638i −0.340246 + 0.589324i −0.984478 0.175506i \(-0.943844\pi\)
0.644232 + 0.764830i \(0.277177\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −9.46183 16.3884i −0.346190 0.599619i
\(748\) 0 0
\(749\) 40.8565 1.49287
\(750\) 0 0
\(751\) −21.5748 37.3687i −0.787276 1.36360i −0.927630 0.373501i \(-0.878157\pi\)
0.140353 0.990101i \(-0.455176\pi\)
\(752\) 0 0
\(753\) 5.40957 0.197136
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 4.77434 8.26940i 0.173526 0.300556i −0.766124 0.642693i \(-0.777817\pi\)
0.939650 + 0.342136i \(0.111151\pi\)
\(758\) 0 0
\(759\) −1.66476 −0.0604268
\(760\) 0 0
\(761\) 35.8512 1.29960 0.649802 0.760103i \(-0.274852\pi\)
0.649802 + 0.760103i \(0.274852\pi\)
\(762\) 0 0
\(763\) 5.63617 9.76214i 0.204043 0.353413i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 31.2857 1.12966
\(768\) 0 0
\(769\) 8.93698 + 15.4793i 0.322276 + 0.558198i 0.980957 0.194224i \(-0.0622188\pi\)
−0.658681 + 0.752422i \(0.728886\pi\)
\(770\) 0 0
\(771\) −4.62463 −0.166552
\(772\) 0 0
\(773\) 0.926769 + 1.60521i 0.0333336 + 0.0577354i 0.882211 0.470854i \(-0.156054\pi\)
−0.848877 + 0.528590i \(0.822721\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −0.751709 + 1.30200i −0.0269674 + 0.0467089i
\(778\) 0 0
\(779\) −19.6356 + 19.2293i −0.703519 + 0.688961i
\(780\) 0 0
\(781\) 17.4790 30.2744i 0.625446 1.08330i
\(782\) 0 0
\(783\) 8.26836 + 14.3212i 0.295487 + 0.511798i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 53.8501 1.91955 0.959774 0.280773i \(-0.0905907\pi\)
0.959774 + 0.280773i \(0.0905907\pi\)
\(788\) 0 0
\(789\) 3.42486 + 5.93202i 0.121928 + 0.211186i
\(790\) 0 0
\(791\) 58.8523 2.09255
\(792\) 0 0
\(793\) −16.6947 + 28.9160i −0.592845 + 1.02684i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 44.2766 1.56836 0.784179 0.620535i \(-0.213085\pi\)
0.784179 + 0.620535i \(0.213085\pi\)
\(798\) 0 0
\(799\) −4.88964 −0.172983
\(800\) 0 0
\(801\) −4.86568 + 8.42760i