Properties

Label 819.2.et.c.145.3
Level $819$
Weight $2$
Character 819.145
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.et (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 145.3
Character \(\chi\) \(=\) 819.145
Dual form 819.2.et.c.514.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.698661 + 0.698661i) q^{2} +1.02375i q^{4} +(0.912136 - 0.244406i) q^{5} +(2.61412 - 0.407922i) q^{7} +(-2.11257 - 2.11257i) q^{8} +O(q^{10})\) \(q+(-0.698661 + 0.698661i) q^{2} +1.02375i q^{4} +(0.912136 - 0.244406i) q^{5} +(2.61412 - 0.407922i) q^{7} +(-2.11257 - 2.11257i) q^{8} +(-0.466517 + 0.808031i) q^{10} +(-6.35142 + 1.70186i) q^{11} +(-3.43957 - 1.08136i) q^{13} +(-1.54138 + 2.11138i) q^{14} +0.904452 q^{16} -3.73354 q^{17} +(-0.325628 + 1.21526i) q^{19} +(0.250210 + 0.933796i) q^{20} +(3.24847 - 5.62651i) q^{22} +0.233411i q^{23} +(-3.55787 + 2.05414i) q^{25} +(3.15860 - 1.64759i) q^{26} +(0.417609 + 2.67619i) q^{28} +(2.32457 + 4.02628i) q^{29} +(-1.96967 + 7.35090i) q^{31} +(3.59324 - 3.59324i) q^{32} +(2.60848 - 2.60848i) q^{34} +(2.28473 - 1.01099i) q^{35} +(3.55684 + 3.55684i) q^{37} +(-0.621551 - 1.07656i) q^{38} +(-2.44328 - 1.41063i) q^{40} +(-2.49056 + 9.29490i) q^{41} +(-10.4062 - 6.00801i) q^{43} +(-1.74227 - 6.50224i) q^{44} +(-0.163075 - 0.163075i) q^{46} +(0.563747 + 2.10393i) q^{47} +(6.66720 - 2.13271i) q^{49} +(1.05060 - 3.92089i) q^{50} +(1.10703 - 3.52125i) q^{52} +(-2.04084 - 3.53484i) q^{53} +(-5.37742 + 3.10465i) q^{55} +(-6.38428 - 4.66074i) q^{56} +(-4.43709 - 1.18891i) q^{58} +(5.27715 - 5.27715i) q^{59} +(-2.12633 + 1.22764i) q^{61} +(-3.75966 - 6.51191i) q^{62} +6.82982i q^{64} +(-3.40165 - 0.145692i) q^{65} +(-2.63222 - 9.82360i) q^{67} -3.82220i q^{68} +(-0.889915 + 2.30259i) q^{70} +(-0.433350 - 1.61728i) q^{71} +(-7.85180 - 2.10388i) q^{73} -4.97005 q^{74} +(-1.24412 - 0.333360i) q^{76} +(-15.9091 + 7.03974i) q^{77} +(-0.942160 + 1.63187i) q^{79} +(0.824984 - 0.221054i) q^{80} +(-4.75393 - 8.23404i) q^{82} +(9.95023 + 9.95023i) q^{83} +(-3.40550 + 0.912500i) q^{85} +(11.4680 - 3.07283i) q^{86} +(17.0131 + 9.82254i) q^{88} +(2.88517 - 2.88517i) q^{89} +(-9.43255 - 1.42371i) q^{91} -0.238954 q^{92} +(-1.86380 - 1.07607i) q^{94} +1.18807i q^{95} +(2.41702 - 0.647638i) q^{97} +(-3.16807 + 6.14815i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.698661 + 0.698661i −0.494028 + 0.494028i −0.909573 0.415545i \(-0.863591\pi\)
0.415545 + 0.909573i \(0.363591\pi\)
\(3\) 0 0
\(4\) 1.02375i 0.511873i
\(5\) 0.912136 0.244406i 0.407920 0.109302i −0.0490235 0.998798i \(-0.515611\pi\)
0.456943 + 0.889496i \(0.348944\pi\)
\(6\) 0 0
\(7\) 2.61412 0.407922i 0.988043 0.154180i
\(8\) −2.11257 2.11257i −0.746907 0.746907i
\(9\) 0 0
\(10\) −0.466517 + 0.808031i −0.147526 + 0.255522i
\(11\) −6.35142 + 1.70186i −1.91503 + 0.513130i −0.923427 + 0.383774i \(0.874624\pi\)
−0.991598 + 0.129356i \(0.958709\pi\)
\(12\) 0 0
\(13\) −3.43957 1.08136i −0.953966 0.299914i
\(14\) −1.54138 + 2.11138i −0.411951 + 0.564290i
\(15\) 0 0
\(16\) 0.904452 0.226113
\(17\) −3.73354 −0.905516 −0.452758 0.891633i \(-0.649560\pi\)
−0.452758 + 0.891633i \(0.649560\pi\)
\(18\) 0 0
\(19\) −0.325628 + 1.21526i −0.0747041 + 0.278800i −0.993166 0.116710i \(-0.962765\pi\)
0.918462 + 0.395509i \(0.129432\pi\)
\(20\) 0.250210 + 0.933796i 0.0559486 + 0.208803i
\(21\) 0 0
\(22\) 3.24847 5.62651i 0.692576 1.19958i
\(23\) 0.233411i 0.0486696i 0.999704 + 0.0243348i \(0.00774678\pi\)
−0.999704 + 0.0243348i \(0.992253\pi\)
\(24\) 0 0
\(25\) −3.55787 + 2.05414i −0.711574 + 0.410827i
\(26\) 3.15860 1.64759i 0.619452 0.323120i
\(27\) 0 0
\(28\) 0.417609 + 2.67619i 0.0789207 + 0.505752i
\(29\) 2.32457 + 4.02628i 0.431662 + 0.747661i 0.997017 0.0771873i \(-0.0245939\pi\)
−0.565354 + 0.824848i \(0.691261\pi\)
\(30\) 0 0
\(31\) −1.96967 + 7.35090i −0.353763 + 1.32026i 0.528272 + 0.849075i \(0.322840\pi\)
−0.882034 + 0.471185i \(0.843826\pi\)
\(32\) 3.59324 3.59324i 0.635201 0.635201i
\(33\) 0 0
\(34\) 2.60848 2.60848i 0.447350 0.447350i
\(35\) 2.28473 1.01099i 0.386190 0.170888i
\(36\) 0 0
\(37\) 3.55684 + 3.55684i 0.584741 + 0.584741i 0.936202 0.351461i \(-0.114315\pi\)
−0.351461 + 0.936202i \(0.614315\pi\)
\(38\) −0.621551 1.07656i −0.100829 0.174641i
\(39\) 0 0
\(40\) −2.44328 1.41063i −0.386317 0.223040i
\(41\) −2.49056 + 9.29490i −0.388960 + 1.45162i 0.442868 + 0.896587i \(0.353961\pi\)
−0.831828 + 0.555033i \(0.812706\pi\)
\(42\) 0 0
\(43\) −10.4062 6.00801i −1.58693 0.916213i −0.993809 0.111099i \(-0.964563\pi\)
−0.593119 0.805115i \(-0.702104\pi\)
\(44\) −1.74227 6.50224i −0.262657 0.980250i
\(45\) 0 0
\(46\) −0.163075 0.163075i −0.0240442 0.0240442i
\(47\) 0.563747 + 2.10393i 0.0822309 + 0.306890i 0.994775 0.102087i \(-0.0325521\pi\)
−0.912545 + 0.408977i \(0.865885\pi\)
\(48\) 0 0
\(49\) 6.66720 2.13271i 0.952457 0.304673i
\(50\) 1.05060 3.92089i 0.148577 0.554497i
\(51\) 0 0
\(52\) 1.10703 3.52125i 0.153518 0.488309i
\(53\) −2.04084 3.53484i −0.280331 0.485548i 0.691135 0.722726i \(-0.257111\pi\)
−0.971466 + 0.237178i \(0.923778\pi\)
\(54\) 0 0
\(55\) −5.37742 + 3.10465i −0.725091 + 0.418631i
\(56\) −6.38428 4.66074i −0.853135 0.622818i
\(57\) 0 0
\(58\) −4.43709 1.18891i −0.582618 0.156112i
\(59\) 5.27715 5.27715i 0.687026 0.687026i −0.274548 0.961573i \(-0.588528\pi\)
0.961573 + 0.274548i \(0.0885281\pi\)
\(60\) 0 0
\(61\) −2.12633 + 1.22764i −0.272248 + 0.157183i −0.629909 0.776669i \(-0.716908\pi\)
0.357661 + 0.933852i \(0.383574\pi\)
\(62\) −3.75966 6.51191i −0.477477 0.827014i
\(63\) 0 0
\(64\) 6.82982i 0.853727i
\(65\) −3.40165 0.145692i −0.421923 0.0180708i
\(66\) 0 0
\(67\) −2.63222 9.82360i −0.321577 1.20014i −0.917708 0.397256i \(-0.869963\pi\)
0.596131 0.802888i \(-0.296704\pi\)
\(68\) 3.82220i 0.463509i
\(69\) 0 0
\(70\) −0.889915 + 2.30259i −0.106365 + 0.275212i
\(71\) −0.433350 1.61728i −0.0514292 0.191936i 0.935432 0.353507i \(-0.115011\pi\)
−0.986861 + 0.161570i \(0.948344\pi\)
\(72\) 0 0
\(73\) −7.85180 2.10388i −0.918984 0.246241i −0.231833 0.972756i \(-0.574472\pi\)
−0.687151 + 0.726515i \(0.741139\pi\)
\(74\) −4.97005 −0.577757
\(75\) 0 0
\(76\) −1.24412 0.333360i −0.142710 0.0382390i
\(77\) −15.9091 + 7.03974i −1.81301 + 0.802253i
\(78\) 0 0
\(79\) −0.942160 + 1.63187i −0.106001 + 0.183600i −0.914147 0.405383i \(-0.867138\pi\)
0.808146 + 0.588983i \(0.200471\pi\)
\(80\) 0.824984 0.221054i 0.0922360 0.0247146i
\(81\) 0 0
\(82\) −4.75393 8.23404i −0.524983 0.909298i
\(83\) 9.95023 + 9.95023i 1.09218 + 1.09218i 0.995296 + 0.0968835i \(0.0308874\pi\)
0.0968835 + 0.995296i \(0.469113\pi\)
\(84\) 0 0
\(85\) −3.40550 + 0.912500i −0.369378 + 0.0989745i
\(86\) 11.4680 3.07283i 1.23662 0.331352i
\(87\) 0 0
\(88\) 17.0131 + 9.82254i 1.81361 + 1.04709i
\(89\) 2.88517 2.88517i 0.305827 0.305827i −0.537461 0.843288i \(-0.680617\pi\)
0.843288 + 0.537461i \(0.180617\pi\)
\(90\) 0 0
\(91\) −9.43255 1.42371i −0.988800 0.149246i
\(92\) −0.238954 −0.0249127
\(93\) 0 0
\(94\) −1.86380 1.07607i −0.192237 0.110988i
\(95\) 1.18807i 0.121893i
\(96\) 0 0
\(97\) 2.41702 0.647638i 0.245411 0.0657576i −0.134017 0.990979i \(-0.542788\pi\)
0.379428 + 0.925221i \(0.376121\pi\)
\(98\) −3.16807 + 6.14815i −0.320023 + 0.621057i
\(99\) 0 0
\(100\) −2.10291 3.64235i −0.210291 0.364235i
\(101\) −1.20221 + 2.08228i −0.119624 + 0.207195i −0.919619 0.392812i \(-0.871502\pi\)
0.799995 + 0.600007i \(0.204836\pi\)
\(102\) 0 0
\(103\) 1.45067 2.51263i 0.142938 0.247577i −0.785663 0.618654i \(-0.787678\pi\)
0.928602 + 0.371077i \(0.121012\pi\)
\(104\) 4.98191 + 9.55080i 0.488516 + 0.936533i
\(105\) 0 0
\(106\) 3.89551 + 1.04380i 0.378366 + 0.101383i
\(107\) 11.0841 1.07154 0.535770 0.844364i \(-0.320021\pi\)
0.535770 + 0.844364i \(0.320021\pi\)
\(108\) 0 0
\(109\) 7.01612 + 1.87996i 0.672023 + 0.180068i 0.578666 0.815565i \(-0.303574\pi\)
0.0933569 + 0.995633i \(0.470240\pi\)
\(110\) 1.58789 5.92609i 0.151399 0.565031i
\(111\) 0 0
\(112\) 2.36434 0.368946i 0.223409 0.0348621i
\(113\) 0.604359 1.04678i 0.0568533 0.0984728i −0.836198 0.548428i \(-0.815227\pi\)
0.893051 + 0.449955i \(0.148560\pi\)
\(114\) 0 0
\(115\) 0.0570472 + 0.212903i 0.00531968 + 0.0198533i
\(116\) −4.12188 + 2.37977i −0.382707 + 0.220956i
\(117\) 0 0
\(118\) 7.37387i 0.678820i
\(119\) −9.75990 + 1.52299i −0.894689 + 0.139613i
\(120\) 0 0
\(121\) 27.9179 16.1184i 2.53799 1.46531i
\(122\) 0.627881 2.34328i 0.0568457 0.212151i
\(123\) 0 0
\(124\) −7.52545 2.01644i −0.675806 0.181082i
\(125\) −6.08187 + 6.08187i −0.543979 + 0.543979i
\(126\) 0 0
\(127\) −8.44594 + 4.87627i −0.749456 + 0.432699i −0.825497 0.564406i \(-0.809105\pi\)
0.0760413 + 0.997105i \(0.475772\pi\)
\(128\) 2.41475 + 2.41475i 0.213436 + 0.213436i
\(129\) 0 0
\(130\) 2.47839 2.27481i 0.217369 0.199514i
\(131\) −14.7264 8.50232i −1.28666 0.742851i −0.308599 0.951192i \(-0.599860\pi\)
−0.978056 + 0.208341i \(0.933194\pi\)
\(132\) 0 0
\(133\) −0.355497 + 3.30966i −0.0308255 + 0.286984i
\(134\) 8.70239 + 5.02433i 0.751772 + 0.434036i
\(135\) 0 0
\(136\) 7.88737 + 7.88737i 0.676337 + 0.676337i
\(137\) 3.39152 + 3.39152i 0.289757 + 0.289757i 0.836984 0.547227i \(-0.184317\pi\)
−0.547227 + 0.836984i \(0.684317\pi\)
\(138\) 0 0
\(139\) −6.97771 4.02859i −0.591842 0.341700i 0.173984 0.984749i \(-0.444336\pi\)
−0.765826 + 0.643048i \(0.777669\pi\)
\(140\) 1.03499 + 2.33898i 0.0874729 + 0.197680i
\(141\) 0 0
\(142\) 1.43270 + 0.827168i 0.120229 + 0.0694144i
\(143\) 23.6865 + 1.01448i 1.98076 + 0.0848355i
\(144\) 0 0
\(145\) 3.10437 + 3.10437i 0.257804 + 0.257804i
\(146\) 6.95565 4.01584i 0.575653 0.332354i
\(147\) 0 0
\(148\) −3.64130 + 3.64130i −0.299313 + 0.299313i
\(149\) 14.8614 + 3.98209i 1.21749 + 0.326225i 0.809697 0.586849i \(-0.199632\pi\)
0.407793 + 0.913074i \(0.366298\pi\)
\(150\) 0 0
\(151\) −6.32512 + 23.6057i −0.514731 + 1.92100i −0.155142 + 0.987892i \(0.549584\pi\)
−0.359589 + 0.933111i \(0.617083\pi\)
\(152\) 3.25524 1.87941i 0.264035 0.152440i
\(153\) 0 0
\(154\) 6.19669 16.0335i 0.499343 1.29201i
\(155\) 7.18642i 0.577227i
\(156\) 0 0
\(157\) 8.18219 4.72399i 0.653010 0.377015i −0.136599 0.990626i \(-0.543617\pi\)
0.789608 + 0.613611i \(0.210284\pi\)
\(158\) −0.481873 1.79837i −0.0383357 0.143071i
\(159\) 0 0
\(160\) 2.39932 4.15574i 0.189683 0.328540i
\(161\) 0.0952137 + 0.610164i 0.00750389 + 0.0480877i
\(162\) 0 0
\(163\) 4.87434 18.1913i 0.381788 1.42485i −0.461380 0.887203i \(-0.652646\pi\)
0.843168 0.537650i \(-0.180688\pi\)
\(164\) −9.51562 2.54970i −0.743045 0.199098i
\(165\) 0 0
\(166\) −13.9037 −1.07913
\(167\) −22.1608 5.93797i −1.71486 0.459494i −0.738249 0.674528i \(-0.764347\pi\)
−0.976606 + 0.215034i \(0.931014\pi\)
\(168\) 0 0
\(169\) 10.6613 + 7.43881i 0.820103 + 0.572216i
\(170\) 1.74176 3.01682i 0.133587 0.231379i
\(171\) 0 0
\(172\) 6.15068 10.6533i 0.468985 0.812306i
\(173\) −4.29402 7.43747i −0.326469 0.565460i 0.655340 0.755334i \(-0.272525\pi\)
−0.981808 + 0.189874i \(0.939192\pi\)
\(174\) 0 0
\(175\) −8.46275 + 6.82108i −0.639724 + 0.515625i
\(176\) −5.74456 + 1.53925i −0.433012 + 0.116025i
\(177\) 0 0
\(178\) 4.03150i 0.302174i
\(179\) −11.8098 6.81837i −0.882703 0.509629i −0.0111545 0.999938i \(-0.503551\pi\)
−0.871549 + 0.490309i \(0.836884\pi\)
\(180\) 0 0
\(181\) 11.2556 0.836622 0.418311 0.908304i \(-0.362622\pi\)
0.418311 + 0.908304i \(0.362622\pi\)
\(182\) 7.58485 5.59546i 0.562226 0.414763i
\(183\) 0 0
\(184\) 0.493099 0.493099i 0.0363517 0.0363517i
\(185\) 4.11364 + 2.37501i 0.302441 + 0.174614i
\(186\) 0 0
\(187\) 23.7133 6.35395i 1.73409 0.464647i
\(188\) −2.15389 + 0.577134i −0.157089 + 0.0420918i
\(189\) 0 0
\(190\) −0.830056 0.830056i −0.0602186 0.0602186i
\(191\) 5.69836 + 9.86984i 0.412319 + 0.714157i 0.995143 0.0984414i \(-0.0313857\pi\)
−0.582824 + 0.812598i \(0.698052\pi\)
\(192\) 0 0
\(193\) 2.39856 0.642692i 0.172652 0.0462620i −0.171457 0.985192i \(-0.554848\pi\)
0.344109 + 0.938930i \(0.388181\pi\)
\(194\) −1.23620 + 2.14115i −0.0887537 + 0.153726i
\(195\) 0 0
\(196\) 2.18336 + 6.82552i 0.155954 + 0.487537i
\(197\) 14.0826 + 3.77342i 1.00334 + 0.268845i 0.722846 0.691009i \(-0.242834\pi\)
0.280498 + 0.959854i \(0.409500\pi\)
\(198\) 0 0
\(199\) 5.22960 0.370716 0.185358 0.982671i \(-0.440655\pi\)
0.185358 + 0.982671i \(0.440655\pi\)
\(200\) 11.8558 + 3.17674i 0.838330 + 0.224630i
\(201\) 0 0
\(202\) −0.614874 2.29474i −0.0432624 0.161457i
\(203\) 7.71911 + 9.57691i 0.541775 + 0.672167i
\(204\) 0 0
\(205\) 9.08693i 0.634658i
\(206\) 0.741951 + 2.76900i 0.0516942 + 0.192925i
\(207\) 0 0
\(208\) −3.11093 0.978035i −0.215704 0.0678146i
\(209\) 8.27280i 0.572241i
\(210\) 0 0
\(211\) 5.55565 + 9.62266i 0.382466 + 0.662451i 0.991414 0.130759i \(-0.0417414\pi\)
−0.608948 + 0.793210i \(0.708408\pi\)
\(212\) 3.61878 2.08930i 0.248539 0.143494i
\(213\) 0 0
\(214\) −7.74402 + 7.74402i −0.529370 + 0.529370i
\(215\) −10.9603 2.93679i −0.747483 0.200288i
\(216\) 0 0
\(217\) −2.15034 + 20.0196i −0.145975 + 1.35902i
\(218\) −6.21535 + 3.58843i −0.420956 + 0.243039i
\(219\) 0 0
\(220\) −3.17838 5.50511i −0.214286 0.371154i
\(221\) 12.8418 + 4.03729i 0.863832 + 0.271577i
\(222\) 0 0
\(223\) −7.12168 + 26.5785i −0.476903 + 1.77983i 0.137137 + 0.990552i \(0.456210\pi\)
−0.614040 + 0.789275i \(0.710457\pi\)
\(224\) 7.92738 10.8589i 0.529671 0.725541i
\(225\) 0 0
\(226\) 0.309102 + 1.15359i 0.0205612 + 0.0767354i
\(227\) 8.30155 + 8.30155i 0.550993 + 0.550993i 0.926727 0.375734i \(-0.122610\pi\)
−0.375734 + 0.926727i \(0.622610\pi\)
\(228\) 0 0
\(229\) −3.62802 13.5399i −0.239746 0.894745i −0.975952 0.217987i \(-0.930051\pi\)
0.736206 0.676758i \(-0.236616\pi\)
\(230\) −0.188604 0.108890i −0.0124362 0.00718002i
\(231\) 0 0
\(232\) 3.59498 13.4166i 0.236022 0.880845i
\(233\) 5.26788 + 3.04141i 0.345110 + 0.199249i 0.662529 0.749036i \(-0.269483\pi\)
−0.317419 + 0.948285i \(0.602816\pi\)
\(234\) 0 0
\(235\) 1.02843 + 1.78129i 0.0670872 + 0.116199i
\(236\) 5.40246 + 5.40246i 0.351670 + 0.351670i
\(237\) 0 0
\(238\) 5.75481 7.88292i 0.373029 0.510974i
\(239\) 3.72605 3.72605i 0.241018 0.241018i −0.576253 0.817271i \(-0.695486\pi\)
0.817271 + 0.576253i \(0.195486\pi\)
\(240\) 0 0
\(241\) −18.9861 + 18.9861i −1.22300 + 1.22300i −0.256439 + 0.966560i \(0.582549\pi\)
−0.966560 + 0.256439i \(0.917451\pi\)
\(242\) −8.24386 + 30.7665i −0.529935 + 1.97775i
\(243\) 0 0
\(244\) −1.25679 2.17682i −0.0804576 0.139357i
\(245\) 5.56015 3.57483i 0.355225 0.228387i
\(246\) 0 0
\(247\) 2.43415 3.82785i 0.154881 0.243561i
\(248\) 19.6904 11.3682i 1.25034 0.721884i
\(249\) 0 0
\(250\) 8.49833i 0.537481i
\(251\) 6.48321 11.2292i 0.409217 0.708784i −0.585586 0.810611i \(-0.699135\pi\)
0.994802 + 0.101827i \(0.0324687\pi\)
\(252\) 0 0
\(253\) −0.397233 1.48249i −0.0249738 0.0932036i
\(254\) 2.49399 9.30771i 0.156487 0.584017i
\(255\) 0 0
\(256\) −17.0338 −1.06461
\(257\) −18.5733 −1.15857 −0.579284 0.815126i \(-0.696668\pi\)
−0.579284 + 0.815126i \(0.696668\pi\)
\(258\) 0 0
\(259\) 10.7489 + 7.84708i 0.667905 + 0.487594i
\(260\) 0.149151 3.48243i 0.00924996 0.215971i
\(261\) 0 0
\(262\) 16.2290 4.34855i 1.00263 0.268655i
\(263\) −4.33110 + 7.50169i −0.267067 + 0.462574i −0.968103 0.250552i \(-0.919388\pi\)
0.701036 + 0.713126i \(0.252721\pi\)
\(264\) 0 0
\(265\) −2.72546 2.72546i −0.167424 0.167424i
\(266\) −2.06396 2.56070i −0.126549 0.157007i
\(267\) 0 0
\(268\) 10.0569 2.69473i 0.614321 0.164607i
\(269\) 7.28972i 0.444462i −0.974994 0.222231i \(-0.928666\pi\)
0.974994 0.222231i \(-0.0713339\pi\)
\(270\) 0 0
\(271\) −16.6156 + 16.6156i −1.00933 + 1.00933i −0.00937188 + 0.999956i \(0.502983\pi\)
−0.999956 + 0.00937188i \(0.997017\pi\)
\(272\) −3.37681 −0.204749
\(273\) 0 0
\(274\) −4.73904 −0.286296
\(275\) 19.1017 19.1017i 1.15187 1.15187i
\(276\) 0 0
\(277\) 2.45156i 0.147300i −0.997284 0.0736499i \(-0.976535\pi\)
0.997284 0.0736499i \(-0.0234647\pi\)
\(278\) 7.68967 2.06044i 0.461196 0.123577i
\(279\) 0 0
\(280\) −6.96244 2.69088i −0.416086 0.160811i
\(281\) 9.26224 + 9.26224i 0.552539 + 0.552539i 0.927173 0.374634i \(-0.122232\pi\)
−0.374634 + 0.927173i \(0.622232\pi\)
\(282\) 0 0
\(283\) 0.287880 0.498622i 0.0171127 0.0296400i −0.857342 0.514747i \(-0.827886\pi\)
0.874455 + 0.485107i \(0.161219\pi\)
\(284\) 1.65569 0.443640i 0.0982470 0.0263252i
\(285\) 0 0
\(286\) −17.2576 + 15.8400i −1.02046 + 0.936642i
\(287\) −2.71902 + 25.3139i −0.160498 + 1.49423i
\(288\) 0 0
\(289\) −3.06068 −0.180040
\(290\) −4.33781 −0.254725
\(291\) 0 0
\(292\) 2.15384 8.03825i 0.126044 0.470403i
\(293\) 4.53613 + 16.9291i 0.265004 + 0.989007i 0.962248 + 0.272174i \(0.0877425\pi\)
−0.697245 + 0.716833i \(0.745591\pi\)
\(294\) 0 0
\(295\) 3.52371 6.10324i 0.205158 0.355345i
\(296\) 15.0282i 0.873495i
\(297\) 0 0
\(298\) −13.1652 + 7.60092i −0.762638 + 0.440310i
\(299\) 0.252401 0.802836i 0.0145967 0.0464292i
\(300\) 0 0
\(301\) −29.6538 11.4607i −1.70921 0.660585i
\(302\) −12.0732 20.9115i −0.694737 1.20332i
\(303\) 0 0
\(304\) −0.294515 + 1.09914i −0.0168916 + 0.0630402i
\(305\) −1.63946 + 1.63946i −0.0938752 + 0.0938752i
\(306\) 0 0
\(307\) −10.3888 + 10.3888i −0.592923 + 0.592923i −0.938420 0.345497i \(-0.887710\pi\)
0.345497 + 0.938420i \(0.387710\pi\)
\(308\) −7.20691 16.2869i −0.410652 0.928032i
\(309\) 0 0
\(310\) −5.02087 5.02087i −0.285166 0.285166i
\(311\) −6.38744 11.0634i −0.362199 0.627346i 0.626124 0.779724i \(-0.284640\pi\)
−0.988322 + 0.152377i \(0.951307\pi\)
\(312\) 0 0
\(313\) 12.3070 + 7.10546i 0.695633 + 0.401624i 0.805719 0.592298i \(-0.201779\pi\)
−0.110086 + 0.993922i \(0.535112\pi\)
\(314\) −2.41611 + 9.01704i −0.136349 + 0.508861i
\(315\) 0 0
\(316\) −1.67062 0.964532i −0.0939797 0.0542592i
\(317\) 4.84186 + 18.0701i 0.271946 + 1.01492i 0.957860 + 0.287234i \(0.0927358\pi\)
−0.685914 + 0.727682i \(0.740598\pi\)
\(318\) 0 0
\(319\) −21.6165 21.6165i −1.21029 1.21029i
\(320\) 1.66925 + 6.22973i 0.0933139 + 0.348252i
\(321\) 0 0
\(322\) −0.492820 0.359776i −0.0274638 0.0200495i
\(323\) 1.21574 4.53722i 0.0676458 0.252458i
\(324\) 0 0
\(325\) 14.4588 3.21803i 0.802030 0.178504i
\(326\) 9.30403 + 16.1151i 0.515303 + 0.892531i
\(327\) 0 0
\(328\) 24.8976 14.3747i 1.37474 0.793708i
\(329\) 2.33194 + 5.26996i 0.128564 + 0.290542i
\(330\) 0 0
\(331\) 3.81375 + 1.02189i 0.209623 + 0.0561682i 0.362102 0.932138i \(-0.382059\pi\)
−0.152480 + 0.988307i \(0.548726\pi\)
\(332\) −10.1865 + 10.1865i −0.559057 + 0.559057i
\(333\) 0 0
\(334\) 19.6315 11.3343i 1.07419 0.620183i
\(335\) −4.80190 8.31713i −0.262356 0.454413i
\(336\) 0 0
\(337\) 15.1443i 0.824962i −0.910966 0.412481i \(-0.864662\pi\)
0.910966 0.412481i \(-0.135338\pi\)
\(338\) −12.6459 + 2.25145i −0.687844 + 0.122463i
\(339\) 0 0
\(340\) −0.934168 3.48636i −0.0506624 0.189075i
\(341\) 50.0407i 2.70986i
\(342\) 0 0
\(343\) 16.5588 8.29486i 0.894094 0.447880i
\(344\) 9.29146 + 34.6762i 0.500962 + 1.86961i
\(345\) 0 0
\(346\) 8.19633 + 2.19620i 0.440638 + 0.118069i
\(347\) −6.79449 −0.364747 −0.182374 0.983229i \(-0.558378\pi\)
−0.182374 + 0.983229i \(0.558378\pi\)
\(348\) 0 0
\(349\) 0.378000 + 0.101285i 0.0202339 + 0.00542165i 0.268922 0.963162i \(-0.413333\pi\)
−0.248688 + 0.968584i \(0.579999\pi\)
\(350\) 1.14697 10.6782i 0.0613081 0.570775i
\(351\) 0 0
\(352\) −16.7070 + 28.9374i −0.890486 + 1.54237i
\(353\) −19.2883 + 5.16829i −1.02661 + 0.275081i −0.732556 0.680707i \(-0.761673\pi\)
−0.294059 + 0.955787i \(0.595006\pi\)
\(354\) 0 0
\(355\) −0.790548 1.36927i −0.0419579 0.0726733i
\(356\) 2.95368 + 2.95368i 0.156545 + 0.156545i
\(357\) 0 0
\(358\) 13.0147 3.48729i 0.687851 0.184309i
\(359\) −26.7736 + 7.17397i −1.41306 + 0.378628i −0.883016 0.469344i \(-0.844491\pi\)
−0.530042 + 0.847971i \(0.677824\pi\)
\(360\) 0 0
\(361\) 15.0837 + 8.70856i 0.793877 + 0.458345i
\(362\) −7.86384 + 7.86384i −0.413314 + 0.413314i
\(363\) 0 0
\(364\) 1.45752 9.65654i 0.0763948 0.506140i
\(365\) −7.67612 −0.401786
\(366\) 0 0
\(367\) −5.78423 3.33953i −0.301934 0.174322i 0.341377 0.939926i \(-0.389107\pi\)
−0.643312 + 0.765605i \(0.722440\pi\)
\(368\) 0.211109i 0.0110048i
\(369\) 0 0
\(370\) −4.53337 + 1.21471i −0.235678 + 0.0631499i
\(371\) −6.77694 8.40798i −0.351841 0.436520i
\(372\) 0 0
\(373\) −0.503050 0.871308i −0.0260469 0.0451146i 0.852708 0.522388i \(-0.174959\pi\)
−0.878755 + 0.477273i \(0.841625\pi\)
\(374\) −12.1283 + 21.0068i −0.627138 + 1.08624i
\(375\) 0 0
\(376\) 3.25375 5.63567i 0.167800 0.290637i
\(377\) −3.64170 16.3624i −0.187557 0.842705i
\(378\) 0 0
\(379\) −20.6414 5.53086i −1.06028 0.284101i −0.313786 0.949494i \(-0.601597\pi\)
−0.746493 + 0.665393i \(0.768264\pi\)
\(380\) −1.21628 −0.0623938
\(381\) 0 0
\(382\) −10.8769 2.91445i −0.556510 0.149116i
\(383\) 5.91371 22.0703i 0.302177 1.12774i −0.633172 0.774011i \(-0.718247\pi\)
0.935349 0.353727i \(-0.115086\pi\)
\(384\) 0 0
\(385\) −12.7907 + 10.3095i −0.651876 + 0.525420i
\(386\) −1.22676 + 2.12480i −0.0624402 + 0.108150i
\(387\) 0 0
\(388\) 0.663016 + 2.47441i 0.0336596 + 0.125619i
\(389\) −17.3058 + 9.99148i −0.877437 + 0.506588i −0.869812 0.493383i \(-0.835760\pi\)
−0.00762436 + 0.999971i \(0.502427\pi\)
\(390\) 0 0
\(391\) 0.871451i 0.0440712i
\(392\) −18.5905 9.57943i −0.938960 0.483834i
\(393\) 0 0
\(394\) −12.4753 + 7.20262i −0.628497 + 0.362863i
\(395\) −0.460539 + 1.71876i −0.0231723 + 0.0864800i
\(396\) 0 0
\(397\) 24.1600 + 6.47366i 1.21256 + 0.324904i 0.807765 0.589505i \(-0.200677\pi\)
0.404793 + 0.914408i \(0.367344\pi\)
\(398\) −3.65372 + 3.65372i −0.183144 + 0.183144i
\(399\) 0 0
\(400\) −3.21792 + 1.85787i −0.160896 + 0.0928934i
\(401\) −0.994403 0.994403i −0.0496581 0.0496581i 0.681842 0.731500i \(-0.261179\pi\)
−0.731500 + 0.681842i \(0.761179\pi\)
\(402\) 0 0
\(403\) 14.7238 23.1540i 0.733443 1.15339i
\(404\) −2.13173 1.23075i −0.106057 0.0612322i
\(405\) 0 0
\(406\) −12.0840 1.29797i −0.599721 0.0644173i
\(407\) −28.6442 16.5378i −1.41984 0.819746i
\(408\) 0 0
\(409\) 1.96094 + 1.96094i 0.0969623 + 0.0969623i 0.753924 0.656962i \(-0.228159\pi\)
−0.656962 + 0.753924i \(0.728159\pi\)
\(410\) −6.34868 6.34868i −0.313539 0.313539i
\(411\) 0 0
\(412\) 2.57229 + 1.48511i 0.126728 + 0.0731663i
\(413\) 11.6424 15.9477i 0.572885 0.784737i
\(414\) 0 0
\(415\) 11.5079 + 6.64407i 0.564899 + 0.326144i
\(416\) −16.2448 + 8.47364i −0.796466 + 0.415454i
\(417\) 0 0
\(418\) 5.77988 + 5.77988i 0.282703 + 0.282703i
\(419\) −16.7456 + 9.66807i −0.818075 + 0.472316i −0.849752 0.527182i \(-0.823249\pi\)
0.0316770 + 0.999498i \(0.489915\pi\)
\(420\) 0 0
\(421\) 2.40433 2.40433i 0.117180 0.117180i −0.646085 0.763265i \(-0.723595\pi\)
0.763265 + 0.646085i \(0.223595\pi\)
\(422\) −10.6045 2.84146i −0.516218 0.138320i
\(423\) 0 0
\(424\) −3.15618 + 11.7790i −0.153278 + 0.572041i
\(425\) 13.2834 7.66920i 0.644342 0.372011i
\(426\) 0 0
\(427\) −5.05769 + 4.07656i −0.244759 + 0.197279i
\(428\) 11.3473i 0.548492i
\(429\) 0 0
\(430\) 9.70932 5.60568i 0.468225 0.270330i
\(431\) 0.179529 + 0.670011i 0.00864760 + 0.0322733i 0.970115 0.242646i \(-0.0780154\pi\)
−0.961467 + 0.274920i \(0.911349\pi\)
\(432\) 0 0
\(433\) 10.5144 18.2115i 0.505290 0.875188i −0.494691 0.869069i \(-0.664719\pi\)
0.999981 0.00611893i \(-0.00194773\pi\)
\(434\) −12.4845 15.4892i −0.599277 0.743508i
\(435\) 0 0
\(436\) −1.92461 + 7.18273i −0.0921719 + 0.343990i
\(437\) −0.283655 0.0760052i −0.0135691 0.00363582i
\(438\) 0 0
\(439\) −22.8237 −1.08932 −0.544659 0.838658i \(-0.683341\pi\)
−0.544659 + 0.838658i \(0.683341\pi\)
\(440\) 17.9190 + 4.80138i 0.854255 + 0.228897i
\(441\) 0 0
\(442\) −11.7927 + 6.15136i −0.560924 + 0.292590i
\(443\) 8.38733 14.5273i 0.398494 0.690212i −0.595046 0.803691i \(-0.702866\pi\)
0.993540 + 0.113480i \(0.0361997\pi\)
\(444\) 0 0
\(445\) 1.92651 3.33682i 0.0913254 0.158180i
\(446\) −13.5937 23.5450i −0.643681 1.11489i
\(447\) 0 0
\(448\) 2.78604 + 17.8539i 0.131628 + 0.843519i
\(449\) −14.8030 + 3.96646i −0.698599 + 0.187189i −0.590603 0.806962i \(-0.701110\pi\)
−0.107996 + 0.994151i \(0.534443\pi\)
\(450\) 0 0
\(451\) 63.2744i 2.97948i
\(452\) 1.07164 + 0.618710i 0.0504055 + 0.0291017i
\(453\) 0 0
\(454\) −11.5999 −0.544412
\(455\) −8.95174 + 1.00675i −0.419664 + 0.0471974i
\(456\) 0 0
\(457\) −9.84760 + 9.84760i −0.460651 + 0.460651i −0.898869 0.438218i \(-0.855610\pi\)
0.438218 + 0.898869i \(0.355610\pi\)
\(458\) 11.9946 + 6.92507i 0.560470 + 0.323587i
\(459\) 0 0
\(460\) −0.217959 + 0.0584018i −0.0101624 + 0.00272300i
\(461\) −15.2937 + 4.09793i −0.712298 + 0.190860i −0.596733 0.802440i \(-0.703535\pi\)
−0.115565 + 0.993300i \(0.536868\pi\)
\(462\) 0 0
\(463\) 26.2699 + 26.2699i 1.22086 + 1.22086i 0.967325 + 0.253538i \(0.0815943\pi\)
0.253538 + 0.967325i \(0.418406\pi\)
\(464\) 2.10246 + 3.64157i 0.0976044 + 0.169056i
\(465\) 0 0
\(466\) −5.80537 + 1.55555i −0.268929 + 0.0720592i
\(467\) −16.6813 + 28.8928i −0.771917 + 1.33700i 0.164595 + 0.986361i \(0.447368\pi\)
−0.936511 + 0.350637i \(0.885965\pi\)
\(468\) 0 0
\(469\) −10.8882 24.6063i −0.502771 1.13621i
\(470\) −1.96304 0.525995i −0.0905483 0.0242623i
\(471\) 0 0
\(472\) −22.2967 −1.02629
\(473\) 76.3188 + 20.4496i 3.50914 + 0.940272i
\(474\) 0 0
\(475\) −1.33777 4.99262i −0.0613810 0.229077i
\(476\) −1.55916 9.99166i −0.0714639 0.457967i
\(477\) 0 0
\(478\) 5.20650i 0.238140i
\(479\) 1.37572 + 5.13427i 0.0628584 + 0.234591i 0.990207 0.139608i \(-0.0445844\pi\)
−0.927348 + 0.374199i \(0.877918\pi\)
\(480\) 0 0
\(481\) −8.38781 16.0802i −0.382451 0.733196i
\(482\) 26.5296i 1.20839i
\(483\) 0 0
\(484\) 16.5012 + 28.5809i 0.750054 + 1.29913i
\(485\) 2.04636 1.18147i 0.0929205 0.0536477i
\(486\) 0 0
\(487\) 9.83431 9.83431i 0.445635 0.445635i −0.448265 0.893900i \(-0.647958\pi\)
0.893900 + 0.448265i \(0.147958\pi\)
\(488\) 7.08549 + 1.89855i 0.320745 + 0.0859434i
\(489\) 0 0
\(490\) −1.38706 + 6.38225i −0.0626611 + 0.288321i
\(491\) 6.73956 3.89109i 0.304152 0.175602i −0.340155 0.940370i \(-0.610479\pi\)
0.644307 + 0.764767i \(0.277146\pi\)
\(492\) 0 0
\(493\) −8.67888 15.0323i −0.390877 0.677019i
\(494\) 0.973727 + 4.37502i 0.0438101 + 0.196841i
\(495\) 0 0
\(496\) −1.78147 + 6.64854i −0.0799904 + 0.298528i
\(497\) −1.79255 4.05099i −0.0804070 0.181712i
\(498\) 0 0
\(499\) −3.34017 12.4657i −0.149527 0.558041i −0.999512 0.0312347i \(-0.990056\pi\)
0.849985 0.526806i \(-0.176611\pi\)
\(500\) −6.22629 6.22629i −0.278448 0.278448i
\(501\) 0 0
\(502\) 3.31587 + 12.3750i 0.147995 + 0.552323i
\(503\) 0.631010 + 0.364314i 0.0281354 + 0.0162440i 0.514002 0.857789i \(-0.328162\pi\)
−0.485866 + 0.874033i \(0.661496\pi\)
\(504\) 0 0
\(505\) −0.587653 + 2.19315i −0.0261502 + 0.0975939i
\(506\) 1.31329 + 0.758229i 0.0583829 + 0.0337074i
\(507\) 0 0
\(508\) −4.99206 8.64650i −0.221487 0.383626i
\(509\) 10.5628 + 10.5628i 0.468188 + 0.468188i 0.901327 0.433139i \(-0.142594\pi\)
−0.433139 + 0.901327i \(0.642594\pi\)
\(510\) 0 0
\(511\) −21.3837 2.29687i −0.945961 0.101608i
\(512\) 7.07136 7.07136i 0.312513 0.312513i
\(513\) 0 0
\(514\) 12.9764 12.9764i 0.572365 0.572365i
\(515\) 0.709104 2.64641i 0.0312469 0.116615i
\(516\) 0 0
\(517\) −7.16119 12.4035i −0.314949 0.545507i
\(518\) −12.9923 + 2.02740i −0.570849 + 0.0890787i
\(519\) 0 0
\(520\) 6.87845 + 7.49402i 0.301640 + 0.328635i
\(521\) −26.7816 + 15.4624i −1.17332 + 0.677419i −0.954461 0.298336i \(-0.903568\pi\)
−0.218864 + 0.975755i \(0.570235\pi\)
\(522\) 0 0
\(523\) 19.8628i 0.868538i −0.900783 0.434269i \(-0.857007\pi\)
0.900783 0.434269i \(-0.142993\pi\)
\(524\) 8.70421 15.0761i 0.380245 0.658604i
\(525\) 0 0
\(526\) −2.21517 8.26711i −0.0965858 0.360463i
\(527\) 7.35383 27.4449i 0.320338 1.19552i
\(528\) 0 0
\(529\) 22.9455 0.997631
\(530\) 3.80835 0.165424
\(531\) 0 0
\(532\) −3.38825 0.363939i −0.146899 0.0157787i
\(533\) 18.6176 29.2773i 0.806417 1.26814i
\(534\) 0 0
\(535\) 10.1102 2.70902i 0.437102 0.117121i
\(536\) −15.1923 + 26.3138i −0.656207 + 1.13658i
\(537\) 0 0
\(538\) 5.09304 + 5.09304i 0.219577 + 0.219577i
\(539\) −38.7166 + 24.8924i −1.66764 + 1.07219i
\(540\) 0 0
\(541\) 9.59205 2.57018i 0.412395 0.110501i −0.0466559 0.998911i \(-0.514856\pi\)
0.459050 + 0.888410i \(0.348190\pi\)
\(542\) 23.2174i 0.997272i
\(543\) 0 0
\(544\) −13.4155 + 13.4155i −0.575185 + 0.575185i
\(545\) 6.85914 0.293813
\(546\) 0 0
\(547\) −5.37266 −0.229718 −0.114859 0.993382i \(-0.536642\pi\)
−0.114859 + 0.993382i \(0.536642\pi\)
\(548\) −3.47205 + 3.47205i −0.148319 + 0.148319i
\(549\) 0 0
\(550\) 26.6912i 1.13812i
\(551\) −5.64992 + 1.51389i −0.240694 + 0.0644939i
\(552\) 0 0
\(553\) −1.79724 + 4.65022i −0.0764264 + 0.197748i
\(554\) 1.71281 + 1.71281i 0.0727702 + 0.0727702i
\(555\) 0 0
\(556\) 4.12425 7.14341i 0.174907 0.302948i
\(557\) 12.4110 3.32551i 0.525869 0.140906i 0.0138891 0.999904i \(-0.495579\pi\)
0.511980 + 0.858997i \(0.328912\pi\)
\(558\) 0 0
\(559\) 29.2960 + 31.9178i 1.23909 + 1.34998i
\(560\) 2.06643 0.914389i 0.0873226 0.0386400i
\(561\) 0 0
\(562\) −12.9423 −0.545939
\(563\) −6.31884 −0.266307 −0.133154 0.991095i \(-0.542510\pi\)
−0.133154 + 0.991095i \(0.542510\pi\)
\(564\) 0 0
\(565\) 0.295418 1.10252i 0.0124283 0.0463832i
\(566\) 0.147238 + 0.549498i 0.00618886 + 0.0230971i
\(567\) 0 0
\(568\) −2.50115 + 4.33211i −0.104946 + 0.181771i
\(569\) 5.11436i 0.214405i 0.994237 + 0.107203i \(0.0341893\pi\)
−0.994237 + 0.107203i \(0.965811\pi\)
\(570\) 0 0
\(571\) −24.2776 + 14.0167i −1.01599 + 0.586580i −0.912939 0.408097i \(-0.866193\pi\)
−0.103047 + 0.994676i \(0.532859\pi\)
\(572\) −1.03857 + 24.2490i −0.0434250 + 1.01390i
\(573\) 0 0
\(574\) −15.7862 19.5855i −0.658902 0.817483i
\(575\) −0.479459 0.830447i −0.0199948 0.0346320i
\(576\) 0 0
\(577\) −5.18104 + 19.3359i −0.215689 + 0.804964i 0.770233 + 0.637762i \(0.220140\pi\)
−0.985923 + 0.167202i \(0.946527\pi\)
\(578\) 2.13838 2.13838i 0.0889449 0.0889449i
\(579\) 0 0
\(580\) −3.17809 + 3.17809i −0.131963 + 0.131963i
\(581\) 30.0700 + 21.9521i 1.24751 + 0.910727i
\(582\) 0 0
\(583\) 18.9780 + 18.9780i 0.785990 + 0.785990i
\(584\) 12.1429 + 21.0321i 0.502477 + 0.870315i
\(585\) 0 0
\(586\) −14.9969 8.65846i −0.619516 0.357678i
\(587\) −1.06109 + 3.96003i −0.0437957 + 0.163448i −0.984360 0.176167i \(-0.943630\pi\)
0.940565 + 0.339615i \(0.110297\pi\)
\(588\) 0 0
\(589\) −8.29187 4.78731i −0.341661 0.197258i
\(590\) 1.80222 + 6.72598i 0.0741962 + 0.276904i
\(591\) 0 0
\(592\) 3.21699 + 3.21699i 0.132218 + 0.132218i
\(593\) 4.49553 + 16.7775i 0.184609 + 0.688971i 0.994714 + 0.102686i \(0.0327435\pi\)
−0.810105 + 0.586285i \(0.800590\pi\)
\(594\) 0 0
\(595\) −8.53013 + 3.77456i −0.349701 + 0.154742i
\(596\) −4.07665 + 15.2143i −0.166986 + 0.623200i
\(597\) 0 0
\(598\) 0.384567 + 0.737253i 0.0157261 + 0.0301485i
\(599\) 7.18140 + 12.4386i 0.293424 + 0.508226i 0.974617 0.223878i \(-0.0718718\pi\)
−0.681193 + 0.732104i \(0.738539\pi\)
\(600\) 0 0
\(601\) 7.65598 4.42018i 0.312294 0.180303i −0.335659 0.941984i \(-0.608959\pi\)
0.647952 + 0.761681i \(0.275626\pi\)
\(602\) 28.7251 12.7108i 1.17075 0.518052i
\(603\) 0 0
\(604\) −24.1662 6.47532i −0.983310 0.263477i
\(605\) 21.5255 21.5255i 0.875137 0.875137i
\(606\) 0 0
\(607\) −23.5526 + 13.5981i −0.955971 + 0.551930i −0.894931 0.446205i \(-0.852775\pi\)
−0.0610406 + 0.998135i \(0.519442\pi\)
\(608\) 3.19666 + 5.53678i 0.129642 + 0.224546i
\(609\) 0 0
\(610\) 2.29085i 0.0927539i
\(611\) 0.336052 7.84624i 0.0135952 0.317425i
\(612\) 0 0
\(613\) 11.4723 + 42.8151i 0.463361 + 1.72929i 0.662267 + 0.749268i \(0.269594\pi\)
−0.198906 + 0.980019i \(0.563739\pi\)
\(614\) 14.5166i 0.585841i
\(615\) 0 0
\(616\) 48.4811 + 18.7372i 1.95336 + 0.754944i
\(617\) 7.15534 + 26.7041i 0.288063 + 1.07507i 0.946572 + 0.322493i \(0.104521\pi\)
−0.658509 + 0.752573i \(0.728812\pi\)
\(618\) 0 0
\(619\) −38.0315 10.1905i −1.52861 0.409591i −0.606047 0.795429i \(-0.707246\pi\)
−0.922567 + 0.385838i \(0.873912\pi\)
\(620\) −7.35707 −0.295467
\(621\) 0 0
\(622\) 12.1922 + 3.26689i 0.488863 + 0.130990i
\(623\) 6.36523 8.71908i 0.255018 0.349322i
\(624\) 0 0
\(625\) 6.20963 10.7554i 0.248385 0.430216i
\(626\) −13.5627 + 3.63412i −0.542076 + 0.145249i
\(627\) 0 0
\(628\) 4.83616 + 8.37648i 0.192984 + 0.334258i
\(629\) −13.2796 13.2796i −0.529493 0.529493i
\(630\) 0 0
\(631\) 7.08811 1.89925i 0.282173 0.0756081i −0.114957 0.993371i \(-0.536673\pi\)
0.397130 + 0.917762i \(0.370006\pi\)
\(632\) 5.43782 1.45706i 0.216305 0.0579588i
\(633\) 0 0
\(634\) −16.0077 9.24203i −0.635746 0.367048i
\(635\) −6.51206 + 6.51206i −0.258423 + 0.258423i
\(636\) 0 0
\(637\) −25.2385 + 0.126001i −0.999988 + 0.00499235i
\(638\) 30.2052 1.19583
\(639\) 0 0
\(640\) 2.79277 + 1.61240i 0.110394 + 0.0637359i
\(641\) 33.6134i 1.32765i −0.747887 0.663826i \(-0.768932\pi\)
0.747887 0.663826i \(-0.231068\pi\)
\(642\) 0 0
\(643\) 22.8004 6.10935i 0.899160 0.240929i 0.220504 0.975386i \(-0.429230\pi\)
0.678655 + 0.734457i \(0.262563\pi\)
\(644\) −0.624653 + 0.0974747i −0.0246148 + 0.00384104i
\(645\) 0 0
\(646\) 2.32058 + 4.01937i 0.0913022 + 0.158140i
\(647\) −0.513809 + 0.889943i −0.0201999 + 0.0349873i −0.875949 0.482404i \(-0.839764\pi\)
0.855749 + 0.517392i \(0.173097\pi\)
\(648\) 0 0
\(649\) −24.5364 + 42.4983i −0.963139 + 1.66821i
\(650\) −7.85349 + 12.3501i −0.308039 + 0.484411i
\(651\) 0 0
\(652\) 18.6233 + 4.99009i 0.729343 + 0.195427i
\(653\) −22.4684 −0.879256 −0.439628 0.898180i \(-0.644890\pi\)
−0.439628 + 0.898180i \(0.644890\pi\)
\(654\) 0 0
\(655\) −15.5105 4.15604i −0.606047 0.162390i
\(656\) −2.25259 + 8.40679i −0.0879490 + 0.328230i
\(657\) 0 0
\(658\) −5.31115 2.05268i −0.207050 0.0800217i
\(659\) 15.3326 26.5569i 0.597275 1.03451i −0.395947 0.918273i \(-0.629584\pi\)
0.993222 0.116237i \(-0.0370831\pi\)
\(660\) 0 0
\(661\) 8.93857 + 33.3592i 0.347670 + 1.29752i 0.889462 + 0.457010i \(0.151079\pi\)
−0.541792 + 0.840513i \(0.682254\pi\)
\(662\) −3.37847 + 1.95056i −0.131308 + 0.0758107i
\(663\) 0 0
\(664\) 42.0412i 1.63151i
\(665\) 0.484639 + 3.10575i 0.0187935 + 0.120436i
\(666\) 0 0
\(667\) −0.939779 + 0.542582i −0.0363884 + 0.0210088i
\(668\) 6.07898 22.6870i 0.235203 0.877788i
\(669\) 0 0
\(670\) 9.16575 + 2.45595i 0.354104 + 0.0948818i
\(671\) 11.4159 11.4159i 0.440708 0.440708i
\(672\) 0 0
\(673\) 27.9964 16.1637i 1.07918 0.623066i 0.148506 0.988912i \(-0.452554\pi\)
0.930675 + 0.365846i \(0.119220\pi\)
\(674\) 10.5807 + 10.5807i 0.407554 + 0.407554i
\(675\) 0 0
\(676\) −7.61545 + 10.9145i −0.292902 + 0.419788i
\(677\) 25.7232 + 14.8513i 0.988623 + 0.570782i 0.904862 0.425704i \(-0.139974\pi\)
0.0837606 + 0.996486i \(0.473307\pi\)
\(678\) 0 0
\(679\) 6.05417 2.67895i 0.232338 0.102809i
\(680\) 9.12208 + 5.26664i 0.349816 + 0.201966i
\(681\) 0 0
\(682\) 34.9615 + 34.9615i 1.33875 + 1.33875i
\(683\) −13.2049 13.2049i −0.505271 0.505271i 0.407800 0.913071i \(-0.366296\pi\)
−0.913071 + 0.407800i \(0.866296\pi\)
\(684\) 0 0
\(685\) 3.92244 + 2.26462i 0.149869 + 0.0865267i
\(686\) −5.77373 + 17.3643i −0.220442 + 0.662972i
\(687\) 0 0
\(688\) −9.41190 5.43396i −0.358825 0.207168i
\(689\) 3.19720 + 14.3652i 0.121804 + 0.547271i
\(690\) 0 0
\(691\) 7.85320 + 7.85320i 0.298750 + 0.298750i 0.840524 0.541774i \(-0.182247\pi\)
−0.541774 + 0.840524i \(0.682247\pi\)
\(692\) 7.61408 4.39599i 0.289444 0.167110i
\(693\) 0 0
\(694\) 4.74704 4.74704i 0.180195 0.180195i
\(695\) −7.34924 1.96922i −0.278772 0.0746969i
\(696\) 0 0
\(697\) 9.29861 34.7029i 0.352210 1.31447i
\(698\) −0.334858 + 0.193330i −0.0126746 + 0.00731766i
\(699\) 0 0
\(700\) −6.98306 8.66371i −0.263935 0.327457i
\(701\) 9.68156i 0.365668i 0.983144 + 0.182834i \(0.0585270\pi\)
−0.983144 + 0.182834i \(0.941473\pi\)
\(702\) 0 0
\(703\) −5.48069 + 3.16428i −0.206708 + 0.119343i
\(704\) −11.6234 43.3790i −0.438073 1.63491i
\(705\) 0 0
\(706\) 9.86512 17.0869i 0.371279 0.643074i
\(707\) −2.29329 + 5.93373i −0.0862482 + 0.223161i
\(708\) 0 0
\(709\) −0.391304 + 1.46036i −0.0146957 + 0.0548452i −0.972884 0.231292i \(-0.925705\pi\)
0.958189 + 0.286137i \(0.0923713\pi\)
\(710\) 1.50898 + 0.404330i 0.0566310 + 0.0151742i
\(711\) 0 0
\(712\) −12.1902 −0.456849
\(713\) −1.71578 0.459743i −0.0642566 0.0172175i
\(714\) 0 0
\(715\) 21.8533 4.86378i 0.817266 0.181895i
\(716\) 6.98028 12.0902i 0.260865 0.451832i
\(717\) 0 0
\(718\) 13.6935 23.7179i 0.511037 0.885142i
\(719\) −13.8587 24.0039i −0.516842 0.895196i −0.999809 0.0195576i \(-0.993774\pi\)
0.482967 0.875639i \(-0.339559\pi\)
\(720\) 0 0
\(721\) 2.76725 7.16006i 0.103058 0.266655i
\(722\) −16.6227 + 4.45404i −0.618632 + 0.165762i
\(723\) 0 0
\(724\) 11.5229i 0.428244i
\(725\) −16.5410 9.54997i −0.614319 0.354677i
\(726\) 0 0
\(727\) −29.0510 −1.07744 −0.538721 0.842484i \(-0.681092\pi\)
−0.538721 + 0.842484i \(0.681092\pi\)
\(728\) 16.9193 + 22.9347i 0.627069 + 0.850015i
\(729\) 0 0
\(730\) 5.36300 5.36300i 0.198494 0.198494i
\(731\) 38.8519 + 22.4312i 1.43699 + 0.829646i
\(732\) 0 0
\(733\) 32.8045 8.78993i 1.21166 0.324663i 0.404247 0.914650i \(-0.367534\pi\)
0.807413 + 0.589986i \(0.200867\pi\)
\(734\) 6.37441 1.70802i 0.235284 0.0630441i
\(735\) 0 0
\(736\) 0.838703 + 0.838703i 0.0309150 + 0.0309150i
\(737\) 33.4367 + 57.9141i 1.23166 + 2.13329i
\(738\) 0 0
\(739\) −13.2974 + 3.56302i −0.489152 + 0.131068i −0.494961 0.868915i \(-0.664818\pi\)
0.00580900 + 0.999983i \(0.498151\pi\)
\(740\) −2.43141 + 4.21132i −0.0893803 + 0.154811i
\(741\) 0 0
\(742\) 10.6091 + 1.13955i 0.389472 + 0.0418340i
\(743\) 30.3940 + 8.14404i 1.11505 + 0.298776i 0.768878 0.639396i \(-0.220816\pi\)
0.346169 + 0.938172i \(0.387482\pi\)
\(744\) 0 0
\(745\) 14.5288 0.532295
\(746\) 0.960210 + 0.257288i 0.0351558 + 0.00941997i
\(747\) 0 0
\(748\) 6.50483 + 24.2764i 0.237840 + 0.887632i
\(749\) 28.9751 4.52145i 1.05873 0.165210i
\(750\) 0 0
\(751\) 26.5309i 0.968127i −0.875033 0.484064i \(-0.839160\pi\)
0.875033 0.484064i \(-0.160840\pi\)
\(752\) 0.509882 + 1.90291i 0.0185935 + 0.0693918i
\(753\) 0 0
\(754\) 13.9761 + 8.88743i 0.508978 + 0.323661i
\(755\) 23.0775i 0.839876i
\(756\) 0 0
\(757\) 7.38184 + 12.7857i 0.268298 + 0.464705i 0.968422 0.249315i \(-0.0802056\pi\)
−0.700125 + 0.714021i \(0.746872\pi\)
\(758\) 18.2856 10.5572i 0.664161 0.383454i
\(759\) 0 0
\(760\) 2.50988 2.50988i 0.0910429 0.0910429i
\(761\) −31.6870 8.49051i −1.14865 0.307781i −0.366228 0.930525i \(-0.619351\pi\)
−0.782425 + 0.622744i \(0.786018\pi\)
\(762\) 0 0
\(763\) 19.1078 + 2.05241i 0.691750 + 0.0743023i
\(764\) −10.1042 + 5.83367i −0.365558 + 0.211055i
\(765\) 0 0
\(766\) 11.2880 + 19.5513i 0.407850 + 0.706418i
\(767\) −23.8576 + 12.4447i −0.861448 + 0.449350i
\(768\) 0 0
\(769\) −1.79577 + 6.70191i −0.0647572 + 0.241677i −0.990716 0.135947i \(-0.956592\pi\)
0.925959 + 0.377624i \(0.123259\pi\)
\(770\) 1.73355 16.1392i 0.0624727 0.581617i
\(771\) 0 0
\(772\) 0.657953 + 2.45551i 0.0236802 + 0.0883759i
\(773\) −0.711465 0.711465i −0.0255896 0.0255896i 0.694196 0.719786i \(-0.255760\pi\)
−0.719786 + 0.694196i \(0.755760\pi\)
\(774\) 0 0
\(775\) −8.09193 30.1995i −0.290671 1.08480i
\(776\) −6.47431 3.73794i −0.232414 0.134184i
\(777\) 0 0
\(778\) 5.11020 19.0715i 0.183209 0.683747i
\(779\) −10.4847 6.05336i −0.375654 0.216884i
\(780\) 0 0
\(781\) 5.50477 + 9.53455i 0.196976 + 0.341173i
\(782\) 0.608848 + 0.608848i 0.0217724 + 0.0217724i
\(783\) 0 0
\(784\) 6.03016 1.92894i 0.215363 0.0688906i
\(785\) 6.30870 6.30870i 0.225167 0.225167i
\(786\) 0 0
\(787\) −28.0302 + 28.0302i −0.999170 + 0.999170i −1.00000 0.000830028i \(-0.999736\pi\)
0.000830028 1.00000i \(0.499736\pi\)
\(788\) −3.86303 + 14.4170i −0.137615 + 0.513585i