Properties

Label 120.3.l.a.41.8
Level $120$
Weight $3$
Character 120.41
Analytic conductor $3.270$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 120.l (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.26976317232\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.681615360000.5
Defining polynomial: \(x^{8} - 4 x^{7} - 2 x^{6} + 20 x^{5} + 49 x^{4} - 136 x^{3} + 168 x^{2} - 96 x + 864\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{5}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 41.8
Root \(1.54294 + 1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 120.41
Dual form 120.3.l.a.41.7

$q$-expansion

\(f(q)\) \(=\) \(q+(2.98254 + 0.323191i) q^{3} -2.23607i q^{5} +4.72640 q^{7} +(8.79110 + 1.92786i) q^{9} +O(q^{10})\) \(q+(2.98254 + 0.323191i) q^{3} -2.23607i q^{5} +4.72640 q^{7} +(8.79110 + 1.92786i) q^{9} -4.76442i q^{11} -1.06692 q^{13} +(0.722676 - 6.66916i) q^{15} +26.7847i q^{17} -8.12938 q^{19} +(14.0967 + 1.52753i) q^{21} -40.0468i q^{23} -5.00000 q^{25} +(25.5967 + 8.59112i) q^{27} +20.8744i q^{29} -33.7860 q^{31} +(1.53982 - 14.2101i) q^{33} -10.5686i q^{35} -60.4351 q^{37} +(-3.18213 - 0.344819i) q^{39} +59.2611i q^{41} -56.4424 q^{43} +(4.31082 - 19.6575i) q^{45} -9.68942i q^{47} -26.6611 q^{49} +(-8.65657 + 79.8864i) q^{51} -93.1378i q^{53} -10.6536 q^{55} +(-24.2462 - 2.62734i) q^{57} +17.4907i q^{59} +57.7400 q^{61} +(41.5503 + 9.11184i) q^{63} +2.38570i q^{65} +101.531 q^{67} +(12.9428 - 119.441i) q^{69} +90.1745i q^{71} +40.0700 q^{73} +(-14.9127 - 1.61595i) q^{75} -22.5186i q^{77} +65.3727 q^{79} +(73.5667 + 33.8960i) q^{81} -117.888i q^{83} +59.8924 q^{85} +(-6.74641 + 62.2587i) q^{87} +119.679i q^{89} -5.04269 q^{91} +(-100.768 - 10.9193i) q^{93} +18.1779i q^{95} -15.2522 q^{97} +(9.18513 - 41.8845i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{3} + 16 q^{7} + 20 q^{9} + O(q^{10}) \) \( 8 q - 4 q^{3} + 16 q^{7} + 20 q^{9} - 8 q^{13} - 8 q^{19} + 28 q^{21} - 40 q^{25} + 20 q^{27} + 120 q^{31} - 112 q^{33} + 8 q^{37} - 72 q^{39} - 328 q^{43} - 60 q^{45} + 64 q^{49} + 64 q^{51} - 40 q^{55} + 72 q^{57} + 8 q^{61} + 88 q^{63} + 152 q^{67} + 100 q^{69} + 32 q^{73} + 20 q^{75} + 88 q^{79} + 224 q^{81} - 152 q^{87} + 560 q^{91} - 368 q^{93} + 144 q^{97} + 32 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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
\(3\) 2.98254 + 0.323191i 0.994180 + 0.107730i
\(4\) 0 0
\(5\) 2.23607i 0.447214i
\(6\) 0 0
\(7\) 4.72640 0.675201 0.337600 0.941290i \(-0.390385\pi\)
0.337600 + 0.941290i \(0.390385\pi\)
\(8\) 0 0
\(9\) 8.79110 + 1.92786i 0.976788 + 0.214207i
\(10\) 0 0
\(11\) 4.76442i 0.433129i −0.976268 0.216565i \(-0.930515\pi\)
0.976268 0.216565i \(-0.0694852\pi\)
\(12\) 0 0
\(13\) −1.06692 −0.0820707 −0.0410354 0.999158i \(-0.513066\pi\)
−0.0410354 + 0.999158i \(0.513066\pi\)
\(14\) 0 0
\(15\) 0.722676 6.66916i 0.0481784 0.444611i
\(16\) 0 0
\(17\) 26.7847i 1.57557i 0.615950 + 0.787785i \(0.288772\pi\)
−0.615950 + 0.787785i \(0.711228\pi\)
\(18\) 0 0
\(19\) −8.12938 −0.427862 −0.213931 0.976849i \(-0.568627\pi\)
−0.213931 + 0.976849i \(0.568627\pi\)
\(20\) 0 0
\(21\) 14.0967 + 1.52753i 0.671271 + 0.0727395i
\(22\) 0 0
\(23\) 40.0468i 1.74117i −0.492021 0.870583i \(-0.663742\pi\)
0.492021 0.870583i \(-0.336258\pi\)
\(24\) 0 0
\(25\) −5.00000 −0.200000
\(26\) 0 0
\(27\) 25.5967 + 8.59112i 0.948027 + 0.318190i
\(28\) 0 0
\(29\) 20.8744i 0.719807i 0.932990 + 0.359903i \(0.117190\pi\)
−0.932990 + 0.359903i \(0.882810\pi\)
\(30\) 0 0
\(31\) −33.7860 −1.08987 −0.544936 0.838478i \(-0.683446\pi\)
−0.544936 + 0.838478i \(0.683446\pi\)
\(32\) 0 0
\(33\) 1.53982 14.2101i 0.0466611 0.430608i
\(34\) 0 0
\(35\) 10.5686i 0.301959i
\(36\) 0 0
\(37\) −60.4351 −1.63338 −0.816691 0.577075i \(-0.804194\pi\)
−0.816691 + 0.577075i \(0.804194\pi\)
\(38\) 0 0
\(39\) −3.18213 0.344819i −0.0815931 0.00884150i
\(40\) 0 0
\(41\) 59.2611i 1.44539i 0.691166 + 0.722696i \(0.257097\pi\)
−0.691166 + 0.722696i \(0.742903\pi\)
\(42\) 0 0
\(43\) −56.4424 −1.31261 −0.656307 0.754494i \(-0.727883\pi\)
−0.656307 + 0.754494i \(0.727883\pi\)
\(44\) 0 0
\(45\) 4.31082 19.6575i 0.0957961 0.436833i
\(46\) 0 0
\(47\) 9.68942i 0.206158i −0.994673 0.103079i \(-0.967131\pi\)
0.994673 0.103079i \(-0.0328694\pi\)
\(48\) 0 0
\(49\) −26.6611 −0.544104
\(50\) 0 0
\(51\) −8.65657 + 79.8864i −0.169737 + 1.56640i
\(52\) 0 0
\(53\) 93.1378i 1.75732i −0.477451 0.878659i \(-0.658439\pi\)
0.477451 0.878659i \(-0.341561\pi\)
\(54\) 0 0
\(55\) −10.6536 −0.193701
\(56\) 0 0
\(57\) −24.2462 2.62734i −0.425372 0.0460937i
\(58\) 0 0
\(59\) 17.4907i 0.296453i 0.988953 + 0.148227i \(0.0473565\pi\)
−0.988953 + 0.148227i \(0.952643\pi\)
\(60\) 0 0
\(61\) 57.7400 0.946558 0.473279 0.880913i \(-0.343070\pi\)
0.473279 + 0.880913i \(0.343070\pi\)
\(62\) 0 0
\(63\) 41.5503 + 9.11184i 0.659528 + 0.144632i
\(64\) 0 0
\(65\) 2.38570i 0.0367032i
\(66\) 0 0
\(67\) 101.531 1.51539 0.757695 0.652609i \(-0.226325\pi\)
0.757695 + 0.652609i \(0.226325\pi\)
\(68\) 0 0
\(69\) 12.9428 119.441i 0.187576 1.73103i
\(70\) 0 0
\(71\) 90.1745i 1.27006i 0.772486 + 0.635032i \(0.219013\pi\)
−0.772486 + 0.635032i \(0.780987\pi\)
\(72\) 0 0
\(73\) 40.0700 0.548904 0.274452 0.961601i \(-0.411504\pi\)
0.274452 + 0.961601i \(0.411504\pi\)
\(74\) 0 0
\(75\) −14.9127 1.61595i −0.198836 0.0215460i
\(76\) 0 0
\(77\) 22.5186i 0.292449i
\(78\) 0 0
\(79\) 65.3727 0.827502 0.413751 0.910390i \(-0.364218\pi\)
0.413751 + 0.910390i \(0.364218\pi\)
\(80\) 0 0
\(81\) 73.5667 + 33.8960i 0.908231 + 0.418469i
\(82\) 0 0
\(83\) 117.888i 1.42033i −0.704034 0.710166i \(-0.748620\pi\)
0.704034 0.710166i \(-0.251380\pi\)
\(84\) 0 0
\(85\) 59.8924 0.704617
\(86\) 0 0
\(87\) −6.74641 + 62.2587i −0.0775450 + 0.715618i
\(88\) 0 0
\(89\) 119.679i 1.34471i 0.740228 + 0.672356i \(0.234718\pi\)
−0.740228 + 0.672356i \(0.765282\pi\)
\(90\) 0 0
\(91\) −5.04269 −0.0554142
\(92\) 0 0
\(93\) −100.768 10.9193i −1.08353 0.117412i
\(94\) 0 0
\(95\) 18.1779i 0.191346i
\(96\) 0 0
\(97\) −15.2522 −0.157239 −0.0786196 0.996905i \(-0.525051\pi\)
−0.0786196 + 0.996905i \(0.525051\pi\)
\(98\) 0 0
\(99\) 9.18513 41.8845i 0.0927791 0.423075i
\(100\) 0 0
\(101\) 72.0047i 0.712918i −0.934311 0.356459i \(-0.883984\pi\)
0.934311 0.356459i \(-0.116016\pi\)
\(102\) 0 0
\(103\) 110.950 1.07718 0.538591 0.842567i \(-0.318957\pi\)
0.538591 + 0.842567i \(0.318957\pi\)
\(104\) 0 0
\(105\) 3.41566 31.5212i 0.0325301 0.300202i
\(106\) 0 0
\(107\) 30.6020i 0.286000i −0.989723 0.143000i \(-0.954325\pi\)
0.989723 0.143000i \(-0.0456748\pi\)
\(108\) 0 0
\(109\) −17.3694 −0.159353 −0.0796763 0.996821i \(-0.525389\pi\)
−0.0796763 + 0.996821i \(0.525389\pi\)
\(110\) 0 0
\(111\) −180.250 19.5321i −1.62388 0.175965i
\(112\) 0 0
\(113\) 4.71526i 0.0417280i 0.999782 + 0.0208640i \(0.00664170\pi\)
−0.999782 + 0.0208640i \(0.993358\pi\)
\(114\) 0 0
\(115\) −89.5474 −0.778673
\(116\) 0 0
\(117\) −9.37939 2.05687i −0.0801657 0.0175801i
\(118\) 0 0
\(119\) 126.595i 1.06383i
\(120\) 0 0
\(121\) 98.3003 0.812399
\(122\) 0 0
\(123\) −19.1526 + 176.749i −0.155712 + 1.43698i
\(124\) 0 0
\(125\) 11.1803i 0.0894427i
\(126\) 0 0
\(127\) −1.39528 −0.0109865 −0.00549325 0.999985i \(-0.501749\pi\)
−0.00549325 + 0.999985i \(0.501749\pi\)
\(128\) 0 0
\(129\) −168.342 18.2417i −1.30498 0.141408i
\(130\) 0 0
\(131\) 226.220i 1.72687i −0.504460 0.863435i \(-0.668308\pi\)
0.504460 0.863435i \(-0.331692\pi\)
\(132\) 0 0
\(133\) −38.4227 −0.288893
\(134\) 0 0
\(135\) 19.2103 57.2360i 0.142299 0.423971i
\(136\) 0 0
\(137\) 76.2589i 0.556634i 0.960489 + 0.278317i \(0.0897766\pi\)
−0.960489 + 0.278317i \(0.910223\pi\)
\(138\) 0 0
\(139\) 127.660 0.918417 0.459208 0.888329i \(-0.348133\pi\)
0.459208 + 0.888329i \(0.348133\pi\)
\(140\) 0 0
\(141\) 3.13153 28.8991i 0.0222094 0.204958i
\(142\) 0 0
\(143\) 5.08325i 0.0355472i
\(144\) 0 0
\(145\) 46.6766 0.321907
\(146\) 0 0
\(147\) −79.5178 8.61662i −0.540938 0.0586165i
\(148\) 0 0
\(149\) 63.3790i 0.425362i 0.977122 + 0.212681i \(0.0682195\pi\)
−0.977122 + 0.212681i \(0.931780\pi\)
\(150\) 0 0
\(151\) −115.233 −0.763134 −0.381567 0.924341i \(-0.624615\pi\)
−0.381567 + 0.924341i \(0.624615\pi\)
\(152\) 0 0
\(153\) −51.6371 + 235.467i −0.337498 + 1.53900i
\(154\) 0 0
\(155\) 75.5479i 0.487406i
\(156\) 0 0
\(157\) −18.3695 −0.117003 −0.0585017 0.998287i \(-0.518632\pi\)
−0.0585017 + 0.998287i \(0.518632\pi\)
\(158\) 0 0
\(159\) 30.1013 277.787i 0.189316 1.74709i
\(160\) 0 0
\(161\) 189.278i 1.17564i
\(162\) 0 0
\(163\) −163.693 −1.00425 −0.502126 0.864794i \(-0.667449\pi\)
−0.502126 + 0.864794i \(0.667449\pi\)
\(164\) 0 0
\(165\) −31.7747 3.44313i −0.192574 0.0208675i
\(166\) 0 0
\(167\) 48.7025i 0.291632i 0.989312 + 0.145816i \(0.0465807\pi\)
−0.989312 + 0.145816i \(0.953419\pi\)
\(168\) 0 0
\(169\) −167.862 −0.993264
\(170\) 0 0
\(171\) −71.4662 15.6723i −0.417931 0.0916509i
\(172\) 0 0
\(173\) 140.785i 0.813787i 0.913476 + 0.406894i \(0.133388\pi\)
−0.913476 + 0.406894i \(0.866612\pi\)
\(174\) 0 0
\(175\) −23.6320 −0.135040
\(176\) 0 0
\(177\) −5.65285 + 52.1669i −0.0319370 + 0.294728i
\(178\) 0 0
\(179\) 11.1350i 0.0622065i 0.999516 + 0.0311033i \(0.00990207\pi\)
−0.999516 + 0.0311033i \(0.990098\pi\)
\(180\) 0 0
\(181\) −150.235 −0.830028 −0.415014 0.909815i \(-0.636223\pi\)
−0.415014 + 0.909815i \(0.636223\pi\)
\(182\) 0 0
\(183\) 172.212 + 18.6610i 0.941049 + 0.101973i
\(184\) 0 0
\(185\) 135.137i 0.730471i
\(186\) 0 0
\(187\) 127.614 0.682425
\(188\) 0 0
\(189\) 120.981 + 40.6051i 0.640108 + 0.214842i
\(190\) 0 0
\(191\) 168.060i 0.879895i −0.898023 0.439948i \(-0.854997\pi\)
0.898023 0.439948i \(-0.145003\pi\)
\(192\) 0 0
\(193\) 312.926 1.62138 0.810688 0.585479i \(-0.199093\pi\)
0.810688 + 0.585479i \(0.199093\pi\)
\(194\) 0 0
\(195\) −0.771038 + 7.11546i −0.00395404 + 0.0364895i
\(196\) 0 0
\(197\) 166.150i 0.843400i −0.906735 0.421700i \(-0.861434\pi\)
0.906735 0.421700i \(-0.138566\pi\)
\(198\) 0 0
\(199\) −105.535 −0.530327 −0.265163 0.964204i \(-0.585426\pi\)
−0.265163 + 0.964204i \(0.585426\pi\)
\(200\) 0 0
\(201\) 302.821 + 32.8139i 1.50657 + 0.163253i
\(202\) 0 0
\(203\) 98.6608i 0.486014i
\(204\) 0 0
\(205\) 132.512 0.646399
\(206\) 0 0
\(207\) 77.2046 352.056i 0.372969 1.70075i
\(208\) 0 0
\(209\) 38.7318i 0.185320i
\(210\) 0 0
\(211\) 283.373 1.34300 0.671500 0.741004i \(-0.265650\pi\)
0.671500 + 0.741004i \(0.265650\pi\)
\(212\) 0 0
\(213\) −29.1436 + 268.949i −0.136824 + 1.26267i
\(214\) 0 0
\(215\) 126.209i 0.587019i
\(216\) 0 0
\(217\) −159.686 −0.735882
\(218\) 0 0
\(219\) 119.510 + 12.9503i 0.545710 + 0.0591336i
\(220\) 0 0
\(221\) 28.5771i 0.129308i
\(222\) 0 0
\(223\) −100.108 −0.448915 −0.224458 0.974484i \(-0.572061\pi\)
−0.224458 + 0.974484i \(0.572061\pi\)
\(224\) 0 0
\(225\) −43.9555 9.63929i −0.195358 0.0428413i
\(226\) 0 0
\(227\) 239.794i 1.05636i −0.849132 0.528181i \(-0.822874\pi\)
0.849132 0.528181i \(-0.177126\pi\)
\(228\) 0 0
\(229\) 393.036 1.71632 0.858158 0.513386i \(-0.171609\pi\)
0.858158 + 0.513386i \(0.171609\pi\)
\(230\) 0 0
\(231\) 7.27779 67.1626i 0.0315056 0.290747i
\(232\) 0 0
\(233\) 278.691i 1.19610i −0.801459 0.598050i \(-0.795942\pi\)
0.801459 0.598050i \(-0.204058\pi\)
\(234\) 0 0
\(235\) −21.6662 −0.0921966
\(236\) 0 0
\(237\) 194.977 + 21.1278i 0.822686 + 0.0891470i
\(238\) 0 0
\(239\) 196.594i 0.822570i 0.911507 + 0.411285i \(0.134920\pi\)
−0.911507 + 0.411285i \(0.865080\pi\)
\(240\) 0 0
\(241\) −231.153 −0.959139 −0.479570 0.877504i \(-0.659207\pi\)
−0.479570 + 0.877504i \(0.659207\pi\)
\(242\) 0 0
\(243\) 208.461 + 124.872i 0.857864 + 0.513877i
\(244\) 0 0
\(245\) 59.6160i 0.243331i
\(246\) 0 0
\(247\) 8.67340 0.0351150
\(248\) 0 0
\(249\) 38.1002 351.604i 0.153013 1.41207i
\(250\) 0 0
\(251\) 243.442i 0.969887i 0.874545 + 0.484944i \(0.161160\pi\)
−0.874545 + 0.484944i \(0.838840\pi\)
\(252\) 0 0
\(253\) −190.800 −0.754150
\(254\) 0 0
\(255\) 178.632 + 19.3567i 0.700516 + 0.0759085i
\(256\) 0 0
\(257\) 358.482i 1.39487i −0.716646 0.697437i \(-0.754324\pi\)
0.716646 0.697437i \(-0.245676\pi\)
\(258\) 0 0
\(259\) −285.641 −1.10286
\(260\) 0 0
\(261\) −40.2429 + 183.509i −0.154187 + 0.703099i
\(262\) 0 0
\(263\) 330.913i 1.25823i 0.777314 + 0.629113i \(0.216582\pi\)
−0.777314 + 0.629113i \(0.783418\pi\)
\(264\) 0 0
\(265\) −208.262 −0.785896
\(266\) 0 0
\(267\) −38.6793 + 356.949i −0.144866 + 1.33689i
\(268\) 0 0
\(269\) 97.0354i 0.360727i −0.983600 0.180363i \(-0.942273\pi\)
0.983600 0.180363i \(-0.0577273\pi\)
\(270\) 0 0
\(271\) 67.1851 0.247915 0.123958 0.992288i \(-0.460441\pi\)
0.123958 + 0.992288i \(0.460441\pi\)
\(272\) 0 0
\(273\) −15.0400 1.62975i −0.0550917 0.00596979i
\(274\) 0 0
\(275\) 23.8221i 0.0866258i
\(276\) 0 0
\(277\) −361.801 −1.30614 −0.653070 0.757298i \(-0.726519\pi\)
−0.653070 + 0.757298i \(0.726519\pi\)
\(278\) 0 0
\(279\) −297.016 65.1347i −1.06457 0.233458i
\(280\) 0 0
\(281\) 288.193i 1.02560i −0.858509 0.512798i \(-0.828609\pi\)
0.858509 0.512798i \(-0.171391\pi\)
\(282\) 0 0
\(283\) −272.474 −0.962805 −0.481402 0.876500i \(-0.659872\pi\)
−0.481402 + 0.876500i \(0.659872\pi\)
\(284\) 0 0
\(285\) −5.87491 + 54.2162i −0.0206137 + 0.190232i
\(286\) 0 0
\(287\) 280.092i 0.975930i
\(288\) 0 0
\(289\) −428.420 −1.48242
\(290\) 0 0
\(291\) −45.4903 4.92937i −0.156324 0.0169394i
\(292\) 0 0
\(293\) 70.5674i 0.240845i −0.992723 0.120422i \(-0.961575\pi\)
0.992723 0.120422i \(-0.0384248\pi\)
\(294\) 0 0
\(295\) 39.1105 0.132578
\(296\) 0 0
\(297\) 40.9317 121.954i 0.137817 0.410618i
\(298\) 0 0
\(299\) 42.7267i 0.142899i
\(300\) 0 0
\(301\) −266.770 −0.886278
\(302\) 0 0
\(303\) 23.2713 214.757i 0.0768028 0.708769i
\(304\) 0 0
\(305\) 129.111i 0.423313i
\(306\) 0 0
\(307\) −124.274 −0.404801 −0.202401 0.979303i \(-0.564874\pi\)
−0.202401 + 0.979303i \(0.564874\pi\)
\(308\) 0 0
\(309\) 330.912 + 35.8580i 1.07091 + 0.116045i
\(310\) 0 0
\(311\) 229.006i 0.736353i 0.929756 + 0.368176i \(0.120018\pi\)
−0.929756 + 0.368176i \(0.879982\pi\)
\(312\) 0 0
\(313\) 465.490 1.48719 0.743594 0.668631i \(-0.233120\pi\)
0.743594 + 0.668631i \(0.233120\pi\)
\(314\) 0 0
\(315\) 20.3747 92.9092i 0.0646816 0.294950i
\(316\) 0 0
\(317\) 405.458i 1.27905i 0.768771 + 0.639524i \(0.220869\pi\)
−0.768771 + 0.639524i \(0.779131\pi\)
\(318\) 0 0
\(319\) 99.4544 0.311769
\(320\) 0 0
\(321\) 9.89027 91.2716i 0.0308108 0.284335i
\(322\) 0 0
\(323\) 217.743i 0.674127i
\(324\) 0 0
\(325\) 5.33460 0.0164141
\(326\) 0 0
\(327\) −51.8051 5.61364i −0.158425 0.0171671i
\(328\) 0 0
\(329\) 45.7961i 0.139198i
\(330\) 0 0
\(331\) 45.9271 0.138753 0.0693763 0.997591i \(-0.477899\pi\)
0.0693763 + 0.997591i \(0.477899\pi\)
\(332\) 0 0
\(333\) −531.291 116.510i −1.59547 0.349881i
\(334\) 0 0
\(335\) 227.031i 0.677703i
\(336\) 0 0
\(337\) 516.924 1.53390 0.766950 0.641707i \(-0.221774\pi\)
0.766950 + 0.641707i \(0.221774\pi\)
\(338\) 0 0
\(339\) −1.52393 + 14.0635i −0.00449537 + 0.0414852i
\(340\) 0 0
\(341\) 160.971i 0.472055i
\(342\) 0 0
\(343\) −357.605 −1.04258
\(344\) 0 0
\(345\) −267.079 28.9409i −0.774142 0.0838867i
\(346\) 0 0
\(347\) 5.39280i 0.0155412i −0.999970 0.00777061i \(-0.997527\pi\)
0.999970 0.00777061i \(-0.00247349\pi\)
\(348\) 0 0
\(349\) 284.894 0.816315 0.408157 0.912912i \(-0.366171\pi\)
0.408157 + 0.912912i \(0.366171\pi\)
\(350\) 0 0
\(351\) −27.3097 9.16603i −0.0778053 0.0261141i
\(352\) 0 0
\(353\) 73.2882i 0.207615i −0.994597 0.103808i \(-0.966897\pi\)
0.994597 0.103808i \(-0.0331026\pi\)
\(354\) 0 0
\(355\) 201.636 0.567990
\(356\) 0 0
\(357\) −40.9144 + 377.576i −0.114606 + 1.05763i
\(358\) 0 0
\(359\) 361.674i 1.00745i 0.863865 + 0.503724i \(0.168037\pi\)
−0.863865 + 0.503724i \(0.831963\pi\)
\(360\) 0 0
\(361\) −294.913 −0.816934
\(362\) 0 0
\(363\) 293.185 + 31.7697i 0.807671 + 0.0875200i
\(364\) 0 0
\(365\) 89.5992i 0.245477i
\(366\) 0 0
\(367\) −131.432 −0.358124 −0.179062 0.983838i \(-0.557306\pi\)
−0.179062 + 0.983838i \(0.557306\pi\)
\(368\) 0 0
\(369\) −114.247 + 520.970i −0.309612 + 1.41184i
\(370\) 0 0
\(371\) 440.207i 1.18654i
\(372\) 0 0
\(373\) 211.216 0.566262 0.283131 0.959081i \(-0.408627\pi\)
0.283131 + 0.959081i \(0.408627\pi\)
\(374\) 0 0
\(375\) −3.61338 + 33.3458i −0.00963569 + 0.0889222i
\(376\) 0 0
\(377\) 22.2713i 0.0590751i
\(378\) 0 0
\(379\) 47.4989 0.125327 0.0626635 0.998035i \(-0.480041\pi\)
0.0626635 + 0.998035i \(0.480041\pi\)
\(380\) 0 0
\(381\) −4.16149 0.450943i −0.0109226 0.00118358i
\(382\) 0 0
\(383\) 517.991i 1.35246i −0.736692 0.676228i \(-0.763613\pi\)
0.736692 0.676228i \(-0.236387\pi\)
\(384\) 0 0
\(385\) −50.3531 −0.130787
\(386\) 0 0
\(387\) −496.191 108.813i −1.28215 0.281171i
\(388\) 0 0
\(389\) 253.951i 0.652830i 0.945227 + 0.326415i \(0.105841\pi\)
−0.945227 + 0.326415i \(0.894159\pi\)
\(390\) 0 0
\(391\) 1072.64 2.74333
\(392\) 0 0
\(393\) 73.1122 674.710i 0.186036 1.71682i
\(394\) 0 0
\(395\) 146.178i 0.370070i
\(396\) 0 0
\(397\) 527.905 1.32974 0.664868 0.746961i \(-0.268488\pi\)
0.664868 + 0.746961i \(0.268488\pi\)
\(398\) 0 0
\(399\) −114.597 12.4179i −0.287212 0.0311225i
\(400\) 0 0
\(401\) 664.097i 1.65610i 0.560653 + 0.828051i \(0.310550\pi\)
−0.560653 + 0.828051i \(0.689450\pi\)
\(402\) 0 0
\(403\) 36.0470 0.0894466
\(404\) 0 0
\(405\) 75.7937 164.500i 0.187145 0.406173i
\(406\) 0 0
\(407\) 287.938i 0.707465i
\(408\) 0 0
\(409\) 79.2471 0.193758 0.0968791 0.995296i \(-0.469114\pi\)
0.0968791 + 0.995296i \(0.469114\pi\)
\(410\) 0 0
\(411\) −24.6462 + 227.445i −0.0599664 + 0.553395i
\(412\) 0 0
\(413\) 82.6683i 0.200165i
\(414\) 0 0
\(415\) −263.605 −0.635192
\(416\) 0 0
\(417\) 380.751 + 41.2585i 0.913072 + 0.0989413i
\(418\) 0 0
\(419\) 666.530i 1.59076i −0.606109 0.795381i \(-0.707271\pi\)
0.606109 0.795381i \(-0.292729\pi\)
\(420\) 0 0
\(421\) −306.220 −0.727364 −0.363682 0.931523i \(-0.618480\pi\)
−0.363682 + 0.931523i \(0.618480\pi\)
\(422\) 0 0
\(423\) 18.6798 85.1806i 0.0441604 0.201373i
\(424\) 0 0
\(425\) 133.923i 0.315114i
\(426\) 0 0
\(427\) 272.903 0.639116
\(428\) 0 0
\(429\) −1.64286 + 15.1610i −0.00382951 + 0.0353403i
\(430\) 0 0
\(431\) 254.551i 0.590605i 0.955404 + 0.295303i \(0.0954205\pi\)
−0.955404 + 0.295303i \(0.904579\pi\)
\(432\) 0 0
\(433\) 442.391 1.02169 0.510845 0.859673i \(-0.329333\pi\)
0.510845 + 0.859673i \(0.329333\pi\)
\(434\) 0 0
\(435\) 139.215 + 15.0854i 0.320034 + 0.0346792i
\(436\) 0 0
\(437\) 325.556i 0.744979i
\(438\) 0 0
\(439\) 561.568 1.27920 0.639599 0.768709i \(-0.279101\pi\)
0.639599 + 0.768709i \(0.279101\pi\)
\(440\) 0 0
\(441\) −234.380 51.3988i −0.531475 0.116551i
\(442\) 0 0
\(443\) 564.841i 1.27504i −0.770436 0.637518i \(-0.779961\pi\)
0.770436 0.637518i \(-0.220039\pi\)
\(444\) 0 0
\(445\) 267.611 0.601374
\(446\) 0 0
\(447\) −20.4835 + 189.030i −0.0458244 + 0.422887i
\(448\) 0 0
\(449\) 512.215i 1.14079i −0.821370 0.570396i \(-0.806790\pi\)
0.821370 0.570396i \(-0.193210\pi\)
\(450\) 0 0
\(451\) 282.345 0.626041
\(452\) 0 0
\(453\) −343.688 37.2423i −0.758692 0.0822126i
\(454\) 0 0
\(455\) 11.2758i 0.0247820i
\(456\) 0 0
\(457\) 52.5358 0.114958 0.0574790 0.998347i \(-0.481694\pi\)
0.0574790 + 0.998347i \(0.481694\pi\)
\(458\) 0 0
\(459\) −230.110 + 685.601i −0.501330 + 1.49368i
\(460\) 0 0
\(461\) 625.737i 1.35735i 0.734441 + 0.678673i \(0.237445\pi\)
−0.734441 + 0.678673i \(0.762555\pi\)
\(462\) 0 0
\(463\) −49.8782 −0.107728 −0.0538641 0.998548i \(-0.517154\pi\)
−0.0538641 + 0.998548i \(0.517154\pi\)
\(464\) 0 0
\(465\) −24.4164 + 225.325i −0.0525083 + 0.484569i
\(466\) 0 0
\(467\) 64.6312i 0.138397i 0.997603 + 0.0691983i \(0.0220441\pi\)
−0.997603 + 0.0691983i \(0.977956\pi\)
\(468\) 0 0
\(469\) 479.877 1.02319
\(470\) 0 0
\(471\) −54.7879 5.93686i −0.116322 0.0126048i
\(472\) 0 0
\(473\) 268.915i 0.568532i
\(474\) 0 0
\(475\) 40.6469 0.0855724
\(476\) 0 0
\(477\) 179.557 818.783i 0.376429 1.71653i
\(478\) 0 0
\(479\) 872.673i 1.82186i −0.412556 0.910932i \(-0.635364\pi\)
0.412556 0.910932i \(-0.364636\pi\)
\(480\) 0 0
\(481\) 64.4794 0.134053
\(482\) 0 0
\(483\) 61.1727 564.528i 0.126652 1.16879i
\(484\) 0 0
\(485\) 34.1050i 0.0703195i
\(486\) 0 0
\(487\) −883.613 −1.81440 −0.907201 0.420698i \(-0.861785\pi\)
−0.907201 + 0.420698i \(0.861785\pi\)
\(488\) 0 0
\(489\) −488.221 52.9041i −0.998408 0.108188i
\(490\) 0 0
\(491\) 596.247i 1.21435i 0.794567 + 0.607177i \(0.207698\pi\)
−0.794567 + 0.607177i \(0.792302\pi\)
\(492\) 0 0
\(493\) −559.114 −1.13411
\(494\) 0 0
\(495\) −93.6565 20.5386i −0.189205 0.0414921i
\(496\) 0 0
\(497\) 426.201i 0.857548i
\(498\) 0 0
\(499\) −560.109 −1.12246 −0.561231 0.827659i \(-0.689672\pi\)
−0.561231 + 0.827659i \(0.689672\pi\)
\(500\) 0 0
\(501\) −15.7402 + 145.257i −0.0314175 + 0.289934i
\(502\) 0 0
\(503\) 505.038i 1.00405i 0.864853 + 0.502026i \(0.167412\pi\)
−0.864853 + 0.502026i \(0.832588\pi\)
\(504\) 0 0
\(505\) −161.007 −0.318827
\(506\) 0 0
\(507\) −500.654 54.2513i −0.987484 0.107005i
\(508\) 0 0
\(509\) 13.3027i 0.0261350i 0.999915 + 0.0130675i \(0.00415963\pi\)
−0.999915 + 0.0130675i \(0.995840\pi\)
\(510\) 0 0
\(511\) 189.387 0.370620
\(512\) 0 0
\(513\) −208.086 69.8405i −0.405625 0.136141i
\(514\) 0 0
\(515\) 248.091i 0.481731i
\(516\) 0 0
\(517\) −46.1645 −0.0892930
\(518\) 0 0
\(519\) −45.5005 + 419.898i −0.0876695 + 0.809051i
\(520\) 0 0
\(521\) 267.898i 0.514200i 0.966385 + 0.257100i \(0.0827670\pi\)
−0.966385 + 0.257100i \(0.917233\pi\)
\(522\) 0 0
\(523\) 176.493 0.337463 0.168731 0.985662i \(-0.446033\pi\)
0.168731 + 0.985662i \(0.446033\pi\)
\(524\) 0 0
\(525\) −70.4835 7.63765i −0.134254 0.0145479i
\(526\) 0 0
\(527\) 904.949i 1.71717i
\(528\) 0 0
\(529\) −1074.75 −2.03166
\(530\) 0 0
\(531\) −33.7197 + 153.763i −0.0635022 + 0.289572i
\(532\) 0 0
\(533\) 63.2268i 0.118624i
\(534\) 0 0
\(535\) −68.4281 −0.127903
\(536\) 0 0
\(537\) −3.59872 + 33.2105i −0.00670152 + 0.0618445i
\(538\) 0 0
\(539\) 127.025i 0.235667i
\(540\) 0 0
\(541\) −790.757 −1.46166 −0.730829 0.682561i \(-0.760866\pi\)
−0.730829 + 0.682561i \(0.760866\pi\)
\(542\) 0 0
\(543\) −448.082 48.5546i −0.825198 0.0894191i
\(544\) 0 0
\(545\) 38.8392i 0.0712647i
\(546\) 0 0
\(547\) −44.1668 −0.0807436 −0.0403718 0.999185i \(-0.512854\pi\)
−0.0403718 + 0.999185i \(0.512854\pi\)
\(548\) 0 0
\(549\) 507.598 + 111.315i 0.924587 + 0.202759i
\(550\) 0 0
\(551\) 169.696i 0.307978i
\(552\) 0 0
\(553\) 308.978 0.558730
\(554\) 0 0
\(555\) −43.6751 + 403.052i −0.0786938 + 0.726219i
\(556\) 0 0
\(557\) 753.685i 1.35312i −0.736390 0.676558i \(-0.763471\pi\)
0.736390 0.676558i \(-0.236529\pi\)
\(558\) 0 0
\(559\) 60.2195 0.107727
\(560\) 0 0
\(561\) 380.613 + 41.2435i 0.678454 + 0.0735179i
\(562\) 0 0
\(563\) 609.590i 1.08275i 0.840780 + 0.541376i \(0.182097\pi\)
−0.840780 + 0.541376i \(0.817903\pi\)
\(564\) 0 0
\(565\) 10.5437 0.0186613
\(566\) 0 0
\(567\) 347.706 + 160.206i 0.613238 + 0.282550i
\(568\) 0 0
\(569\) 528.082i 0.928088i 0.885812 + 0.464044i \(0.153602\pi\)
−0.885812 + 0.464044i \(0.846398\pi\)
\(570\) 0 0
\(571\) −708.097 −1.24010 −0.620050 0.784562i \(-0.712888\pi\)
−0.620050 + 0.784562i \(0.712888\pi\)
\(572\) 0 0
\(573\) 54.3154 501.246i 0.0947913 0.874774i
\(574\) 0 0
\(575\) 200.234i 0.348233i
\(576\) 0 0
\(577\) −55.0939 −0.0954834 −0.0477417 0.998860i \(-0.515202\pi\)
−0.0477417 + 0.998860i \(0.515202\pi\)
\(578\) 0 0
\(579\) 933.313 + 101.135i 1.61194 + 0.174671i
\(580\) 0 0
\(581\) 557.184i 0.959009i
\(582\) 0 0
\(583\) −443.748 −0.761145
\(584\) 0 0
\(585\) −4.59930 + 20.9730i −0.00786206 + 0.0358512i
\(586\) 0 0
\(587\) 596.377i 1.01598i 0.861364 + 0.507988i \(0.169610\pi\)
−0.861364 + 0.507988i \(0.830390\pi\)
\(588\) 0 0
\(589\) 274.660 0.466315
\(590\) 0 0
\(591\) 53.6981 495.549i 0.0908597 0.838492i
\(592\) 0 0
\(593\) 269.915i 0.455169i 0.973758 + 0.227584i \(0.0730828\pi\)
−0.973758 + 0.227584i \(0.926917\pi\)
\(594\) 0 0
\(595\) 283.076 0.475758
\(596\) 0 0
\(597\) −314.762 34.1079i −0.527240 0.0571322i
\(598\) 0 0
\(599\) 622.634i 1.03946i −0.854332 0.519728i \(-0.826033\pi\)
0.854332 0.519728i \(-0.173967\pi\)
\(600\) 0 0
\(601\) 865.760 1.44053 0.720266 0.693698i \(-0.244020\pi\)
0.720266 + 0.693698i \(0.244020\pi\)
\(602\) 0 0
\(603\) 892.570 + 195.738i 1.48022 + 0.324606i
\(604\) 0 0
\(605\) 219.806i 0.363316i
\(606\) 0 0
\(607\) 390.780 0.643790 0.321895 0.946775i \(-0.395680\pi\)
0.321895 + 0.946775i \(0.395680\pi\)
\(608\) 0 0
\(609\) −31.8863 + 294.260i −0.0523584 + 0.483185i
\(610\) 0 0
\(611\) 10.3378i 0.0169195i
\(612\) 0 0
\(613\) −398.441 −0.649985 −0.324993 0.945717i \(-0.605362\pi\)
−0.324993 + 0.945717i \(0.605362\pi\)
\(614\) 0 0
\(615\) 395.222 + 42.8266i 0.642637 + 0.0696367i
\(616\) 0 0
\(617\) 178.765i 0.289732i 0.989451 + 0.144866i \(0.0462752\pi\)
−0.989451 + 0.144866i \(0.953725\pi\)
\(618\) 0 0
\(619\) −224.867 −0.363274 −0.181637 0.983366i \(-0.558140\pi\)
−0.181637 + 0.983366i \(0.558140\pi\)
\(620\) 0 0
\(621\) 344.047 1025.07i 0.554021 1.65067i
\(622\) 0 0
\(623\) 565.653i 0.907950i
\(624\) 0 0
\(625\) 25.0000 0.0400000
\(626\) 0 0
\(627\) −12.5178 + 115.519i −0.0199645 + 0.184241i
\(628\) 0 0
\(629\) 1618.74i 2.57351i
\(630\) 0 0
\(631\) −9.36019 −0.0148339 −0.00741695 0.999972i \(-0.502361\pi\)
−0.00741695 + 0.999972i \(0.502361\pi\)
\(632\) 0 0
\(633\) 845.172 + 91.5836i 1.33518 + 0.144682i
\(634\) 0 0
\(635\) 3.11995i 0.00491331i
\(636\) 0 0
\(637\) 28.4453 0.0446550
\(638\) 0 0
\(639\) −173.844 + 792.733i −0.272056 + 1.24058i
\(640\) 0 0
\(641\) 785.281i 1.22509i −0.790437 0.612543i \(-0.790146\pi\)
0.790437 0.612543i \(-0.209854\pi\)
\(642\) 0 0
\(643\) 131.320 0.204230 0.102115 0.994773i \(-0.467439\pi\)
0.102115 + 0.994773i \(0.467439\pi\)
\(644\) 0 0
\(645\) −40.7896 + 376.424i −0.0632397 + 0.583603i
\(646\) 0 0
\(647\) 155.225i 0.239915i 0.992779 + 0.119958i \(0.0382759\pi\)
−0.992779 + 0.119958i \(0.961724\pi\)
\(648\) 0 0
\(649\) 83.3333 0.128403
\(650\) 0 0
\(651\) −476.271 51.6092i −0.731599 0.0792768i
\(652\) 0 0
\(653\) 668.464i 1.02368i 0.859080 + 0.511841i \(0.171036\pi\)
−0.859080 + 0.511841i \(0.828964\pi\)
\(654\) 0 0
\(655\) −505.843 −0.772280
\(656\) 0 0
\(657\) 352.259 + 77.2493i 0.536163 + 0.117579i
\(658\) 0 0
\(659\) 579.510i 0.879377i 0.898150 + 0.439689i \(0.144911\pi\)
−0.898150 + 0.439689i \(0.855089\pi\)
\(660\) 0 0
\(661\) −307.070 −0.464553 −0.232277 0.972650i \(-0.574617\pi\)
−0.232277 + 0.972650i \(0.574617\pi\)
\(662\) 0 0
\(663\) 9.23586 85.2324i 0.0139304 0.128556i
\(664\) 0 0
\(665\) 85.9159i 0.129197i
\(666\) 0 0
\(667\) 835.953 1.25330
\(668\) 0 0
\(669\) −298.576 32.3540i −0.446302 0.0483617i
\(670\) 0 0
\(671\) 275.098i 0.409982i
\(672\) 0 0
\(673\) 7.02018 0.0104312 0.00521559 0.999986i \(-0.498340\pi\)
0.00521559 + 0.999986i \(0.498340\pi\)
\(674\) 0 0
\(675\) −127.984 42.9556i −0.189605 0.0636379i
\(676\) 0 0
\(677\) 1.21742i 0.00179825i −1.00000 0.000899127i \(-0.999714\pi\)
1.00000 0.000899127i \(-0.000286201\pi\)
\(678\) 0 0
\(679\) −72.0881 −0.106168
\(680\) 0 0
\(681\) 77.4993 715.196i 0.113802 1.05021i
\(682\) 0 0
\(683\) 1261.23i 1.84661i 0.384067 + 0.923305i \(0.374523\pi\)
−0.384067 + 0.923305i \(0.625477\pi\)
\(684\) 0 0
\(685\) 170.520 0.248934
\(686\) 0 0
\(687\) 1172.25 + 127.026i 1.70633 + 0.184899i
\(688\) 0 0
\(689\) 99.3706i 0.144224i
\(690\) 0 0
\(691\) −158.177 −0.228910 −0.114455 0.993428i \(-0.536512\pi\)
−0.114455 + 0.993428i \(0.536512\pi\)
\(692\) 0 0
\(693\) 43.4126 197.963i 0.0626445 0.285661i
\(694\) 0 0
\(695\) 285.456i 0.410729i
\(696\) 0 0
\(697\) −1587.29 −2.27732
\(698\) 0 0
\(699\) 90.0705 831.208i 0.128856 1.18914i
\(700\) 0 0
\(701\) 331.746i 0.473247i −0.971601 0.236623i \(-0.923959\pi\)
0.971601 0.236623i \(-0.0760408\pi\)
\(702\) 0 0
\(703\) 491.300 0.698863
\(704\) 0 0
\(705\) −64.6203 7.00232i −0.0916600 0.00993236i
\(706\) 0 0
\(707\) 340.323i 0.481363i
\(708\) 0 0
\(709\) 854.366 1.20503 0.602515 0.798108i \(-0.294165\pi\)
0.602515 + 0.798108i \(0.294165\pi\)
\(710\) 0 0
\(711\) 574.697 + 126.029i 0.808295 + 0.177256i
\(712\) 0 0
\(713\) 1353.02i 1.89765i
\(714\) 0 0
\(715\) 11.3665 0.0158972
\(716\) 0 0
\(717\) −63.5374 + 586.350i −0.0886156 + 0.817782i
\(718\) 0 0
\(719\) 218.882i 0.304426i 0.988348 + 0.152213i \(0.0486400\pi\)
−0.988348 + 0.152213i \(0.951360\pi\)
\(720\) 0 0
\(721\) 524.394 0.727314
\(722\) 0 0
\(723\) −689.422 74.7064i −0.953557 0.103328i
\(724\) 0 0
\(725\) 104.372i 0.143961i
\(726\) 0 0
\(727\) 12.2420 0.0168391 0.00841954 0.999965i \(-0.497320\pi\)
0.00841954 + 0.999965i \(0.497320\pi\)
\(728\) 0 0
\(729\) 581.385 + 439.809i 0.797511 + 0.603305i
\(730\) 0 0
\(731\) 1511.79i 2.06812i
\(732\) 0 0
\(733\) 86.8331 0.118463 0.0592313 0.998244i \(-0.481135\pi\)
0.0592313 + 0.998244i \(0.481135\pi\)
\(734\) 0 0
\(735\) −19.2674 + 177.807i −0.0262141 + 0.241915i
\(736\) 0 0
\(737\) 483.737i 0.656360i
\(738\) 0 0
\(739\) −187.725 −0.254026 −0.127013 0.991901i \(-0.540539\pi\)
−0.127013 + 0.991901i \(0.540539\pi\)
\(740\) 0 0
\(741\) 25.8688 + 2.80316i 0.0349106 + 0.00378294i
\(742\) 0 0
\(743\) 178.264i 0.239925i −0.992778 0.119963i \(-0.961723\pi\)
0.992778 0.119963i \(-0.0382775\pi\)
\(744\) 0 0
\(745\) 141.720 0.190228
\(746\) 0 0
\(747\) 227.271 1036.36i 0.304244 1.38736i
\(748\) 0 0
\(749\) 144.637i 0.193107i
\(750\) 0 0
\(751\) −1328.32 −1.76874 −0.884370 0.466786i \(-0.845412\pi\)
−0.884370 + 0.466786i \(0.845412\pi\)
\(752\) 0 0
\(753\) −78.6781 + 726.075i −0.104486 + 0.964243i
\(754\) 0 0
\(755\) 257.669i 0.341284i
\(756\) 0 0
\(757\) −545.957 −0.721211 −0.360606 0.932718i \(-0.617430\pi\)
−0.360606 + 0.932718i \(0.617430\pi\)
\(758\) 0 0
\(759\) −569.068 61.6648i −0.749761 0.0812448i
\(760\) 0 0
\(761\) 828.655i 1.08890i 0.838793 + 0.544451i \(0.183262\pi\)
−0.838793 + 0.544451i \(0.816738\pi\)
\(762\) 0 0
\(763\) −82.0950 −0.107595
\(764\) 0 0
\(765\) 526.520 + 115.464i 0.688261 + 0.150933i
\(766\) 0 0
\(767\) 18.6612i 0.0243301i
\(768\) 0 0
\(769\) −303.757 −0.395002 −0.197501 0.980303i \(-0.563283\pi\)
−0.197501 + 0.980303i \(0.563283\pi\)
\(770\) 0 0
\(771\) 115.858 1069.19i 0.150270 1.38676i
\(772\) 0 0
\(773\) 59.2137i 0.0766025i 0.999266 + 0.0383013i \(0.0121947\pi\)
−0.999266 + 0.0383013i \(0.987805\pi\)
\(774\) 0 0
\(775\) 168.930 0.217974
\(776\) 0 0
\(777\) −851.936 92.3165i −1.09644 0.118811i
\(778\) 0 0
\(779\) 481.756i 0.618429i
\(780\) 0 0
\(781\) 429.629 0.550102
\(782\) 0 0
\(783\) −179.334 + 534.316i −0.229035 + 0.682396i
\(784\) 0 0
\(785\) 41.0755i 0.0523255i
\(786\) 0 0
\(787\) 214.281 0.272276 0.136138 0.990690i \(-0.456531\pi\)
0.136138 + 0.990690i \(0.456531\pi\)
\(788\) 0 0
\(789\) −106.948 + 986.963i −0.135549 + 1.25090i
\(790\) 0 0
\(791\) 22.2862i 0.0281748i
\(792\) 0 0
\(793\) −61.6040 −0.0776847
\(794\) 0 0
\(795\) −621.151 67.3085i −0.781322 0.0846648i
\(796\) 0 0
\(797\) 124.487i 0.156195i 0.996946 + 0.0780974i \(0.0248845\pi\)
−0.996946 + 0.0780974i \(0.975115\pi\)
\(798\) 0 0
\(799\)