Properties

Label 171.3.p.c.46.2
Level $171$
Weight $3$
Character 171.46
Analytic conductor $4.659$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 171.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.65941252056\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.92607408.1
Defining polynomial: \( x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 57)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 46.2
Root \(0.500000 - 0.630453i\) of defining polynomial
Character \(\chi\) \(=\) 171.46
Dual form 171.3.p.c.145.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.204011 - 0.117786i) q^{2} +(-1.97225 - 3.41604i) q^{4} +(-2.88028 + 4.98878i) q^{5} +1.94451 q^{7} +1.87150i q^{8} +O(q^{10})\) \(q+(-0.204011 - 0.117786i) q^{2} +(-1.97225 - 3.41604i) q^{4} +(-2.88028 + 4.98878i) q^{5} +1.94451 q^{7} +1.87150i q^{8} +(1.17522 - 0.678513i) q^{10} -8.46561 q^{11} +(-16.7415 + 9.66573i) q^{13} +(-0.396701 - 0.229036i) q^{14} +(-7.66857 + 13.2824i) q^{16} +(-12.5365 + 21.7138i) q^{17} +(17.8181 + 6.59651i) q^{19} +22.7225 q^{20} +(1.72708 + 0.997131i) q^{22} +(-15.6408 - 27.0907i) q^{23} +(-4.09198 - 7.08751i) q^{25} +4.55395 q^{26} +(-3.83506 - 6.64251i) q^{28} +(-13.7071 + 7.91383i) q^{29} +14.4237i q^{31} +(9.61203 - 5.54951i) q^{32} +(5.11517 - 2.95325i) q^{34} +(-5.60071 + 9.70072i) q^{35} -41.6423i q^{37} +(-2.85813 - 3.44449i) q^{38} +(-9.33653 - 5.39045i) q^{40} +(-1.53439 - 0.885881i) q^{41} +(14.4358 - 25.0035i) q^{43} +(16.6963 + 28.9189i) q^{44} +7.36909i q^{46} +(-1.70506 - 2.95325i) q^{47} -45.2189 q^{49} +1.92791i q^{50} +(66.0371 + 38.1265i) q^{52} +(80.0952 - 46.2430i) q^{53} +(24.3833 - 42.2331i) q^{55} +3.63915i q^{56} +3.72855 q^{58} +(-4.27292 - 2.46697i) q^{59} +(7.45989 + 12.9209i) q^{61} +(1.69891 - 2.94259i) q^{62} +58.7340 q^{64} -111.360i q^{65} +(-70.4113 + 40.6520i) q^{67} +98.9005 q^{68} +(2.28522 - 1.31937i) q^{70} +(-52.9948 - 30.5966i) q^{71} +(-38.8299 + 67.2553i) q^{73} +(-4.90489 + 8.49551i) q^{74} +(-12.6079 - 73.8775i) q^{76} -16.4614 q^{77} +(84.0207 + 48.5094i) q^{79} +(-44.1752 - 76.5137i) q^{80} +(0.208689 + 0.361460i) q^{82} +102.323 q^{83} +(-72.2171 - 125.084i) q^{85} +(-5.89012 + 3.40067i) q^{86} -15.8434i q^{88} +(-103.596 + 59.8111i) q^{89} +(-32.5540 + 18.7951i) q^{91} +(-61.6953 + 106.859i) q^{92} +0.803328i q^{94} +(-84.2297 + 69.8911i) q^{95} +(-42.1438 - 24.3318i) q^{97} +(9.22517 + 5.32616i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7} + 54 q^{10} + 36 q^{11} - 3 q^{13} + 57 q^{14} - 23 q^{16} - 38 q^{17} - 10 q^{19} - 32 q^{20} + 36 q^{22} - 54 q^{23} - 21 q^{25} - 118 q^{26} - 101 q^{28} + 102 q^{29} + 63 q^{32} - 150 q^{34} + 24 q^{35} - 119 q^{38} + 30 q^{40} - 96 q^{41} + 107 q^{43} + 94 q^{44} + 50 q^{47} - 48 q^{49} + 399 q^{52} + 90 q^{53} + 148 q^{55} - 116 q^{58} + 27 q^{61} + 121 q^{62} + 46 q^{64} - 39 q^{67} + 388 q^{68} - 354 q^{70} - 84 q^{71} - 77 q^{73} - 219 q^{74} + 215 q^{76} - 260 q^{77} + 9 q^{79} - 312 q^{80} - 4 q^{82} + 348 q^{83} + 68 q^{85} - 249 q^{86} + 72 q^{89} - 393 q^{91} + 118 q^{92} - 104 q^{95} - 228 q^{97} - 540 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(154\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.204011 0.117786i −0.102006 0.0588930i 0.448129 0.893969i \(-0.352090\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(3\) 0 0
\(4\) −1.97225 3.41604i −0.493063 0.854011i
\(5\) −2.88028 + 4.98878i −0.576055 + 0.997757i 0.419871 + 0.907584i \(0.362075\pi\)
−0.995926 + 0.0901730i \(0.971258\pi\)
\(6\) 0 0
\(7\) 1.94451 0.277787 0.138893 0.990307i \(-0.455646\pi\)
0.138893 + 0.990307i \(0.455646\pi\)
\(8\) 1.87150i 0.233938i
\(9\) 0 0
\(10\) 1.17522 0.678513i 0.117522 0.0678513i
\(11\) −8.46561 −0.769601 −0.384800 0.923000i \(-0.625730\pi\)
−0.384800 + 0.923000i \(0.625730\pi\)
\(12\) 0 0
\(13\) −16.7415 + 9.66573i −1.28781 + 0.743518i −0.978263 0.207366i \(-0.933511\pi\)
−0.309547 + 0.950884i \(0.600178\pi\)
\(14\) −0.396701 0.229036i −0.0283358 0.0163597i
\(15\) 0 0
\(16\) −7.66857 + 13.2824i −0.479286 + 0.830148i
\(17\) −12.5365 + 21.7138i −0.737440 + 1.27728i 0.216204 + 0.976348i \(0.430632\pi\)
−0.953644 + 0.300936i \(0.902701\pi\)
\(18\) 0 0
\(19\) 17.8181 + 6.59651i 0.937797 + 0.347185i
\(20\) 22.7225 1.13613
\(21\) 0 0
\(22\) 1.72708 + 0.997131i 0.0785037 + 0.0453241i
\(23\) −15.6408 27.0907i −0.680036 1.17786i −0.974969 0.222339i \(-0.928631\pi\)
0.294933 0.955518i \(-0.404703\pi\)
\(24\) 0 0
\(25\) −4.09198 7.08751i −0.163679 0.283500i
\(26\) 4.55395 0.175152
\(27\) 0 0
\(28\) −3.83506 6.64251i −0.136966 0.237233i
\(29\) −13.7071 + 7.91383i −0.472660 + 0.272891i −0.717353 0.696710i \(-0.754646\pi\)
0.244692 + 0.969601i \(0.421313\pi\)
\(30\) 0 0
\(31\) 14.4237i 0.465280i 0.972563 + 0.232640i \(0.0747363\pi\)
−0.972563 + 0.232640i \(0.925264\pi\)
\(32\) 9.61203 5.54951i 0.300376 0.173422i
\(33\) 0 0
\(34\) 5.11517 2.95325i 0.150446 0.0868602i
\(35\) −5.60071 + 9.70072i −0.160020 + 0.277163i
\(36\) 0 0
\(37\) 41.6423i 1.12547i −0.826638 0.562734i \(-0.809749\pi\)
0.826638 0.562734i \(-0.190251\pi\)
\(38\) −2.85813 3.44449i −0.0752139 0.0906445i
\(39\) 0 0
\(40\) −9.33653 5.39045i −0.233413 0.134761i
\(41\) −1.53439 0.885881i −0.0374242 0.0216069i 0.481171 0.876627i \(-0.340212\pi\)
−0.518595 + 0.855020i \(0.673545\pi\)
\(42\) 0 0
\(43\) 14.4358 25.0035i 0.335716 0.581476i −0.647906 0.761720i \(-0.724355\pi\)
0.983622 + 0.180243i \(0.0576886\pi\)
\(44\) 16.6963 + 28.9189i 0.379462 + 0.657247i
\(45\) 0 0
\(46\) 7.36909i 0.160198i
\(47\) −1.70506 2.95325i −0.0362778 0.0628350i 0.847316 0.531088i \(-0.178217\pi\)
−0.883594 + 0.468253i \(0.844883\pi\)
\(48\) 0 0
\(49\) −45.2189 −0.922835
\(50\) 1.92791i 0.0385582i
\(51\) 0 0
\(52\) 66.0371 + 38.1265i 1.26994 + 0.733203i
\(53\) 80.0952 46.2430i 1.51123 0.872510i 0.511317 0.859392i \(-0.329158\pi\)
0.999914 0.0131174i \(-0.00417552\pi\)
\(54\) 0 0
\(55\) 24.3833 42.2331i 0.443333 0.767874i
\(56\) 3.63915i 0.0649848i
\(57\) 0 0
\(58\) 3.72855 0.0642854
\(59\) −4.27292 2.46697i −0.0724224 0.0418131i 0.463352 0.886175i \(-0.346647\pi\)
−0.535774 + 0.844361i \(0.679980\pi\)
\(60\) 0 0
\(61\) 7.45989 + 12.9209i 0.122293 + 0.211818i 0.920672 0.390338i \(-0.127642\pi\)
−0.798378 + 0.602156i \(0.794309\pi\)
\(62\) 1.69891 2.94259i 0.0274017 0.0474612i
\(63\) 0 0
\(64\) 58.7340 0.917718
\(65\) 111.360i 1.71323i
\(66\) 0 0
\(67\) −70.4113 + 40.6520i −1.05091 + 0.606746i −0.922905 0.385027i \(-0.874192\pi\)
−0.128009 + 0.991773i \(0.540859\pi\)
\(68\) 98.9005 1.45442
\(69\) 0 0
\(70\) 2.28522 1.31937i 0.0326460 0.0188482i
\(71\) −52.9948 30.5966i −0.746406 0.430938i 0.0779878 0.996954i \(-0.475150\pi\)
−0.824394 + 0.566017i \(0.808484\pi\)
\(72\) 0 0
\(73\) −38.8299 + 67.2553i −0.531916 + 0.921306i 0.467390 + 0.884051i \(0.345195\pi\)
−0.999306 + 0.0372545i \(0.988139\pi\)
\(74\) −4.90489 + 8.49551i −0.0662822 + 0.114804i
\(75\) 0 0
\(76\) −12.6079 73.8775i −0.165894 0.972072i
\(77\) −16.4614 −0.213785
\(78\) 0 0
\(79\) 84.0207 + 48.5094i 1.06355 + 0.614043i 0.926413 0.376509i \(-0.122875\pi\)
0.137140 + 0.990552i \(0.456209\pi\)
\(80\) −44.1752 76.5137i −0.552190 0.956422i
\(81\) 0 0
\(82\) 0.208689 + 0.361460i 0.00254499 + 0.00440805i
\(83\) 102.323 1.23280 0.616401 0.787432i \(-0.288590\pi\)
0.616401 + 0.787432i \(0.288590\pi\)
\(84\) 0 0
\(85\) −72.2171 125.084i −0.849612 1.47157i
\(86\) −5.89012 + 3.40067i −0.0684898 + 0.0395426i
\(87\) 0 0
\(88\) 15.8434i 0.180039i
\(89\) −103.596 + 59.8111i −1.16400 + 0.672034i −0.952259 0.305292i \(-0.901246\pi\)
−0.211739 + 0.977326i \(0.567913\pi\)
\(90\) 0 0
\(91\) −32.5540 + 18.7951i −0.357737 + 0.206539i
\(92\) −61.6953 + 106.859i −0.670601 + 1.16152i
\(93\) 0 0
\(94\) 0.803328i 0.00854604i
\(95\) −84.2297 + 69.8911i −0.886629 + 0.735695i
\(96\) 0 0
\(97\) −42.1438 24.3318i −0.434473 0.250843i 0.266778 0.963758i \(-0.414041\pi\)
−0.701250 + 0.712915i \(0.747374\pi\)
\(98\) 9.22517 + 5.32616i 0.0941344 + 0.0543485i
\(99\) 0 0
\(100\) −16.1408 + 27.9567i −0.161408 + 0.279567i
\(101\) 81.5540 + 141.256i 0.807465 + 1.39857i 0.914614 + 0.404327i \(0.132494\pi\)
−0.107149 + 0.994243i \(0.534172\pi\)
\(102\) 0 0
\(103\) 18.2732i 0.177410i 0.996058 + 0.0887050i \(0.0282728\pi\)
−0.996058 + 0.0887050i \(0.971727\pi\)
\(104\) −18.0895 31.3319i −0.173937 0.301268i
\(105\) 0 0
\(106\) −21.7871 −0.205539
\(107\) 55.4789i 0.518494i −0.965811 0.259247i \(-0.916526\pi\)
0.965811 0.259247i \(-0.0834744\pi\)
\(108\) 0 0
\(109\) 96.4369 + 55.6779i 0.884743 + 0.510806i 0.872219 0.489115i \(-0.162680\pi\)
0.0125234 + 0.999922i \(0.496014\pi\)
\(110\) −9.94894 + 5.74402i −0.0904449 + 0.0522184i
\(111\) 0 0
\(112\) −14.9116 + 25.8276i −0.133139 + 0.230604i
\(113\) 110.968i 0.982019i 0.871154 + 0.491010i \(0.163372\pi\)
−0.871154 + 0.491010i \(0.836628\pi\)
\(114\) 0 0
\(115\) 180.200 1.56695
\(116\) 54.0679 + 31.2161i 0.466103 + 0.269105i
\(117\) 0 0
\(118\) 0.581150 + 1.00658i 0.00492500 + 0.00853034i
\(119\) −24.3773 + 42.2227i −0.204851 + 0.354812i
\(120\) 0 0
\(121\) −49.3335 −0.407715
\(122\) 3.51468i 0.0288089i
\(123\) 0 0
\(124\) 49.2719 28.4471i 0.397354 0.229412i
\(125\) −96.8697 −0.774958
\(126\) 0 0
\(127\) −209.627 + 121.028i −1.65061 + 0.952979i −0.673785 + 0.738927i \(0.735333\pi\)
−0.976822 + 0.214052i \(0.931334\pi\)
\(128\) −50.4305 29.1161i −0.393989 0.227469i
\(129\) 0 0
\(130\) −13.1166 + 22.7187i −0.100897 + 0.174759i
\(131\) −78.7288 + 136.362i −0.600983 + 1.04093i 0.391689 + 0.920098i \(0.371891\pi\)
−0.992672 + 0.120836i \(0.961443\pi\)
\(132\) 0 0
\(133\) 34.6475 + 12.8270i 0.260507 + 0.0964433i
\(134\) 19.1529 0.142932
\(135\) 0 0
\(136\) −40.6375 23.4621i −0.298805 0.172515i
\(137\) −121.173 209.877i −0.884473 1.53195i −0.846317 0.532680i \(-0.821185\pi\)
−0.0381558 0.999272i \(-0.512148\pi\)
\(138\) 0 0
\(139\) −65.0431 112.658i −0.467936 0.810489i 0.531392 0.847126i \(-0.321669\pi\)
−0.999329 + 0.0366365i \(0.988336\pi\)
\(140\) 44.1841 0.315601
\(141\) 0 0
\(142\) 7.20770 + 12.4841i 0.0507585 + 0.0879162i
\(143\) 141.727 81.8263i 0.991100 0.572212i
\(144\) 0 0
\(145\) 91.1760i 0.628800i
\(146\) 15.8435 9.14724i 0.108517 0.0626523i
\(147\) 0 0
\(148\) −142.252 + 82.1292i −0.961162 + 0.554927i
\(149\) 102.368 177.306i 0.687030 1.18997i −0.285764 0.958300i \(-0.592247\pi\)
0.972794 0.231672i \(-0.0744195\pi\)
\(150\) 0 0
\(151\) 234.305i 1.55169i 0.630924 + 0.775845i \(0.282676\pi\)
−0.630924 + 0.775845i \(0.717324\pi\)
\(152\) −12.3454 + 33.3467i −0.0812197 + 0.219386i
\(153\) 0 0
\(154\) 3.35832 + 1.93893i 0.0218073 + 0.0125904i
\(155\) −71.9566 41.5441i −0.464236 0.268027i
\(156\) 0 0
\(157\) 44.2955 76.7220i 0.282137 0.488675i −0.689774 0.724025i \(-0.742290\pi\)
0.971911 + 0.235349i \(0.0756234\pi\)
\(158\) −11.4275 19.7929i −0.0723257 0.125272i
\(159\) 0 0
\(160\) 63.9365i 0.399603i
\(161\) −30.4137 52.6780i −0.188905 0.327193i
\(162\) 0 0
\(163\) 115.918 0.711153 0.355576 0.934647i \(-0.384285\pi\)
0.355576 + 0.934647i \(0.384285\pi\)
\(164\) 6.98873i 0.0426142i
\(165\) 0 0
\(166\) −20.8750 12.0522i −0.125753 0.0726035i
\(167\) −78.0426 + 45.0579i −0.467321 + 0.269808i −0.715118 0.699004i \(-0.753627\pi\)
0.247797 + 0.968812i \(0.420293\pi\)
\(168\) 0 0
\(169\) 102.353 177.280i 0.605638 1.04900i
\(170\) 34.0247i 0.200145i
\(171\) 0 0
\(172\) −113.884 −0.662116
\(173\) 38.5739 + 22.2707i 0.222971 + 0.128732i 0.607325 0.794454i \(-0.292243\pi\)
−0.384354 + 0.923186i \(0.625576\pi\)
\(174\) 0 0
\(175\) −7.95687 13.7817i −0.0454678 0.0787526i
\(176\) 64.9192 112.443i 0.368859 0.638882i
\(177\) 0 0
\(178\) 28.1796 0.158313
\(179\) 229.632i 1.28286i 0.767181 + 0.641431i \(0.221659\pi\)
−0.767181 + 0.641431i \(0.778341\pi\)
\(180\) 0 0
\(181\) 157.070 90.6845i 0.867791 0.501019i 0.00117734 0.999999i \(-0.499625\pi\)
0.866613 + 0.498980i \(0.166292\pi\)
\(182\) 8.85519 0.0486549
\(183\) 0 0
\(184\) 50.7004 29.2719i 0.275545 0.159086i
\(185\) 207.745 + 119.941i 1.12294 + 0.648332i
\(186\) 0 0
\(187\) 106.129 183.821i 0.567535 0.982999i
\(188\) −6.72561 + 11.6491i −0.0357745 + 0.0619633i
\(189\) 0 0
\(190\) 25.4160 4.33749i 0.133769 0.0228289i
\(191\) 278.704 1.45918 0.729592 0.683882i \(-0.239710\pi\)
0.729592 + 0.683882i \(0.239710\pi\)
\(192\) 0 0
\(193\) −167.512 96.7133i −0.867939 0.501105i −0.00127645 0.999999i \(-0.500406\pi\)
−0.866663 + 0.498894i \(0.833740\pi\)
\(194\) 5.73188 + 9.92791i 0.0295458 + 0.0511748i
\(195\) 0 0
\(196\) 89.1831 + 154.470i 0.455016 + 0.788111i
\(197\) 96.9300 0.492030 0.246015 0.969266i \(-0.420879\pi\)
0.246015 + 0.969266i \(0.420879\pi\)
\(198\) 0 0
\(199\) 172.893 + 299.460i 0.868811 + 1.50482i 0.863213 + 0.504840i \(0.168449\pi\)
0.00559823 + 0.999984i \(0.498218\pi\)
\(200\) 13.2643 7.65815i 0.0663215 0.0382908i
\(201\) 0 0
\(202\) 38.4237i 0.190216i
\(203\) −26.6536 + 15.3885i −0.131299 + 0.0758053i
\(204\) 0 0
\(205\) 8.83894 5.10316i 0.0431168 0.0248935i
\(206\) 2.15233 3.72795i 0.0104482 0.0180968i
\(207\) 0 0
\(208\) 296.490i 1.42543i
\(209\) −150.841 55.8435i −0.721729 0.267194i
\(210\) 0 0
\(211\) −11.1758 6.45233i −0.0529657 0.0305798i 0.473283 0.880910i \(-0.343069\pi\)
−0.526249 + 0.850330i \(0.676402\pi\)
\(212\) −315.936 182.406i −1.49026 0.860405i
\(213\) 0 0
\(214\) −6.53464 + 11.3183i −0.0305357 + 0.0528894i
\(215\) 83.1580 + 144.034i 0.386781 + 0.669925i
\(216\) 0 0
\(217\) 28.0469i 0.129248i
\(218\) −13.1162 22.7179i −0.0601659 0.104210i
\(219\) 0 0
\(220\) −192.360 −0.874364
\(221\) 484.697i 2.19320i
\(222\) 0 0
\(223\) −80.3821 46.4086i −0.360458 0.208110i 0.308824 0.951119i \(-0.400065\pi\)
−0.669282 + 0.743009i \(0.733398\pi\)
\(224\) 18.6907 10.7911i 0.0834404 0.0481744i
\(225\) 0 0
\(226\) 13.0705 22.6388i 0.0578341 0.100172i
\(227\) 280.870i 1.23731i 0.785662 + 0.618656i \(0.212323\pi\)
−0.785662 + 0.618656i \(0.787677\pi\)
\(228\) 0 0
\(229\) 137.541 0.600615 0.300308 0.953842i \(-0.402911\pi\)
0.300308 + 0.953842i \(0.402911\pi\)
\(230\) −36.7628 21.2250i −0.159838 0.0922826i
\(231\) 0 0
\(232\) −14.8108 25.6530i −0.0638395 0.110573i
\(233\) 183.683 318.148i 0.788339 1.36544i −0.138645 0.990342i \(-0.544275\pi\)
0.926984 0.375101i \(-0.122392\pi\)
\(234\) 0 0
\(235\) 19.6441 0.0835921
\(236\) 19.4620i 0.0824659i
\(237\) 0 0
\(238\) 9.94648 5.74260i 0.0417919 0.0241286i
\(239\) 196.388 0.821707 0.410854 0.911701i \(-0.365231\pi\)
0.410854 + 0.911701i \(0.365231\pi\)
\(240\) 0 0
\(241\) −118.225 + 68.2572i −0.490560 + 0.283225i −0.724807 0.688952i \(-0.758071\pi\)
0.234247 + 0.972177i \(0.424738\pi\)
\(242\) 10.0646 + 5.81079i 0.0415892 + 0.0240115i
\(243\) 0 0
\(244\) 29.4256 50.9666i 0.120597 0.208879i
\(245\) 130.243 225.587i 0.531604 0.920765i
\(246\) 0 0
\(247\) −362.063 + 61.7896i −1.46584 + 0.250160i
\(248\) −26.9940 −0.108847
\(249\) 0 0
\(250\) 19.7625 + 11.4099i 0.0790501 + 0.0456396i
\(251\) 23.3322 + 40.4126i 0.0929571 + 0.161006i 0.908754 0.417332i \(-0.137035\pi\)
−0.815797 + 0.578338i \(0.803701\pi\)
\(252\) 0 0
\(253\) 132.409 + 229.339i 0.523356 + 0.906480i
\(254\) 57.0218 0.224495
\(255\) 0 0
\(256\) −110.609 191.580i −0.432066 0.748361i
\(257\) −4.73878 + 2.73593i −0.0184388 + 0.0106457i −0.509191 0.860653i \(-0.670055\pi\)
0.490752 + 0.871299i \(0.336722\pi\)
\(258\) 0 0
\(259\) 80.9737i 0.312640i
\(260\) −380.410 + 219.630i −1.46312 + 0.844730i
\(261\) 0 0
\(262\) 32.1232 18.5463i 0.122607 0.0707874i
\(263\) −37.1071 + 64.2713i −0.141091 + 0.244378i −0.927908 0.372809i \(-0.878394\pi\)
0.786816 + 0.617187i \(0.211728\pi\)
\(264\) 0 0
\(265\) 532.770i 2.01045i
\(266\) −5.55764 6.69784i −0.0208934 0.0251798i
\(267\) 0 0
\(268\) 277.738 + 160.352i 1.03633 + 0.598328i
\(269\) 64.2197 + 37.0772i 0.238735 + 0.137834i 0.614595 0.788843i \(-0.289319\pi\)
−0.375860 + 0.926676i \(0.622653\pi\)
\(270\) 0 0
\(271\) 48.0380 83.2043i 0.177262 0.307027i −0.763680 0.645595i \(-0.776609\pi\)
0.940942 + 0.338568i \(0.109943\pi\)
\(272\) −192.274 333.028i −0.706889 1.22437i
\(273\) 0 0
\(274\) 57.0898i 0.208357i
\(275\) 34.6411 + 60.0001i 0.125968 + 0.218182i
\(276\) 0 0
\(277\) 123.007 0.444068 0.222034 0.975039i \(-0.428730\pi\)
0.222034 + 0.975039i \(0.428730\pi\)
\(278\) 30.6447i 0.110233i
\(279\) 0 0
\(280\) −18.1549 10.4818i −0.0648391 0.0374348i
\(281\) −352.110 + 203.291i −1.25306 + 0.723454i −0.971716 0.236153i \(-0.924113\pi\)
−0.281344 + 0.959607i \(0.590780\pi\)
\(282\) 0 0
\(283\) −92.7689 + 160.680i −0.327805 + 0.567776i −0.982076 0.188485i \(-0.939642\pi\)
0.654271 + 0.756260i \(0.272976\pi\)
\(284\) 241.377i 0.849918i
\(285\) 0 0
\(286\) −38.5520 −0.134797
\(287\) −2.98363 1.72260i −0.0103959 0.00600209i
\(288\) 0 0
\(289\) −169.827 294.149i −0.587636 1.01782i
\(290\) −10.7393 + 18.6009i −0.0370319 + 0.0641412i
\(291\) 0 0
\(292\) 306.329 1.04907
\(293\) 360.407i 1.23006i 0.788505 + 0.615028i \(0.210855\pi\)
−0.788505 + 0.615028i \(0.789145\pi\)
\(294\) 0 0
\(295\) 24.6144 14.2111i 0.0834385 0.0481733i
\(296\) 77.9338 0.263290
\(297\) 0 0
\(298\) −41.7683 + 24.1149i −0.140162 + 0.0809226i
\(299\) 523.703 + 302.360i 1.75152 + 1.01124i
\(300\) 0 0
\(301\) 28.0704 48.6194i 0.0932573 0.161526i
\(302\) 27.5979 47.8009i 0.0913837 0.158281i
\(303\) 0 0
\(304\) −224.257 + 186.081i −0.737687 + 0.612109i
\(305\) −85.9461 −0.281791
\(306\) 0 0
\(307\) −233.152 134.610i −0.759453 0.438470i 0.0696463 0.997572i \(-0.477813\pi\)
−0.829099 + 0.559101i \(0.811146\pi\)
\(308\) 32.4661 + 56.2329i 0.105409 + 0.182574i
\(309\) 0 0
\(310\) 9.78664 + 16.9510i 0.0315698 + 0.0546805i
\(311\) −53.4530 −0.171874 −0.0859372 0.996301i \(-0.527388\pi\)
−0.0859372 + 0.996301i \(0.527388\pi\)
\(312\) 0 0
\(313\) −119.760 207.430i −0.382618 0.662715i 0.608817 0.793310i \(-0.291644\pi\)
−0.991436 + 0.130596i \(0.958311\pi\)
\(314\) −18.0736 + 10.4348i −0.0575592 + 0.0332318i
\(315\) 0 0
\(316\) 382.691i 1.21105i
\(317\) −391.754 + 226.179i −1.23582 + 0.713499i −0.968236 0.250036i \(-0.919557\pi\)
−0.267580 + 0.963536i \(0.586224\pi\)
\(318\) 0 0
\(319\) 116.039 66.9954i 0.363760 0.210017i
\(320\) −169.170 + 293.011i −0.528656 + 0.915660i
\(321\) 0 0
\(322\) 14.3292i 0.0445007i
\(323\) −366.612 + 304.203i −1.13502 + 0.941805i
\(324\) 0 0
\(325\) 137.012 + 79.1039i 0.421575 + 0.243397i
\(326\) −23.6486 13.6535i −0.0725417 0.0418820i
\(327\) 0 0
\(328\) 1.65793 2.87162i 0.00505467 0.00875494i
\(329\) −3.31549 5.74260i −0.0100775 0.0174547i
\(330\) 0 0
\(331\) 95.4707i 0.288431i −0.989546 0.144216i \(-0.953934\pi\)
0.989546 0.144216i \(-0.0460659\pi\)
\(332\) −201.806 349.538i −0.607850 1.05283i
\(333\) 0 0
\(334\) 21.2288 0.0635592
\(335\) 468.356i 1.39808i
\(336\) 0 0
\(337\) −82.2367 47.4794i −0.244026 0.140888i 0.373000 0.927831i \(-0.378329\pi\)
−0.617026 + 0.786943i \(0.711663\pi\)
\(338\) −41.7623 + 24.1115i −0.123557 + 0.0713357i
\(339\) 0 0
\(340\) −284.861 + 493.393i −0.837825 + 1.45116i
\(341\) 122.105i 0.358080i
\(342\) 0 0
\(343\) −183.209 −0.534138
\(344\) 46.7941 + 27.0166i 0.136029 + 0.0785366i
\(345\) 0 0
\(346\) −5.24635 9.08694i −0.0151628 0.0262628i
\(347\) −115.221 + 199.568i −0.332048 + 0.575124i −0.982913 0.184069i \(-0.941073\pi\)
0.650865 + 0.759193i \(0.274406\pi\)
\(348\) 0 0
\(349\) −209.160 −0.599312 −0.299656 0.954047i \(-0.596872\pi\)
−0.299656 + 0.954047i \(0.596872\pi\)
\(350\) 3.74884i 0.0107110i
\(351\) 0 0
\(352\) −81.3717 + 46.9800i −0.231170 + 0.133466i
\(353\) −326.125 −0.923866 −0.461933 0.886915i \(-0.652844\pi\)
−0.461933 + 0.886915i \(0.652844\pi\)
\(354\) 0 0
\(355\) 305.279 176.253i 0.859942 0.496488i
\(356\) 408.634 + 235.925i 1.14785 + 0.662711i
\(357\) 0 0
\(358\) 27.0475 46.8476i 0.0755516 0.130859i
\(359\) 268.735 465.463i 0.748566 1.29655i −0.199945 0.979807i \(-0.564076\pi\)
0.948510 0.316747i \(-0.102590\pi\)
\(360\) 0 0
\(361\) 273.972 + 235.075i 0.758925 + 0.651178i
\(362\) −42.7255 −0.118026
\(363\) 0 0
\(364\) 128.410 + 74.1373i 0.352773 + 0.203674i
\(365\) −223.682 387.428i −0.612826 1.06145i
\(366\) 0 0
\(367\) −181.274 313.976i −0.493935 0.855520i 0.506041 0.862509i \(-0.331108\pi\)
−0.999976 + 0.00698970i \(0.997775\pi\)
\(368\) 479.771 1.30373
\(369\) 0 0
\(370\) −28.2548 48.9388i −0.0763644 0.132267i
\(371\) 155.746 89.9198i 0.419800 0.242371i
\(372\) 0 0
\(373\) 336.486i 0.902108i 0.892497 + 0.451054i \(0.148952\pi\)
−0.892497 + 0.451054i \(0.851048\pi\)
\(374\) −43.3030 + 25.0010i −0.115784 + 0.0668477i
\(375\) 0 0
\(376\) 5.52701 3.19102i 0.0146995 0.00848676i
\(377\) 152.986 264.979i 0.405798 0.702863i
\(378\) 0 0
\(379\) 336.744i 0.888507i 0.895901 + 0.444253i \(0.146531\pi\)
−0.895901 + 0.444253i \(0.853469\pi\)
\(380\) 404.873 + 149.889i 1.06546 + 0.394446i
\(381\) 0 0
\(382\) −56.8589 32.8275i −0.148845 0.0859358i
\(383\) 193.755 + 111.865i 0.505888 + 0.292075i 0.731142 0.682226i \(-0.238988\pi\)
−0.225254 + 0.974300i \(0.572321\pi\)
\(384\) 0 0
\(385\) 47.4134 82.1225i 0.123152 0.213305i
\(386\) 22.7830 + 39.4612i 0.0590232 + 0.102231i
\(387\) 0 0
\(388\) 191.954i 0.494726i
\(389\) −100.458 173.998i −0.258246 0.447295i 0.707526 0.706687i \(-0.249811\pi\)
−0.965772 + 0.259392i \(0.916478\pi\)
\(390\) 0 0
\(391\) 784.324 2.00594
\(392\) 84.6274i 0.215886i
\(393\) 0 0
\(394\) −19.7748 11.4170i −0.0501899 0.0289772i
\(395\) −484.006 + 279.441i −1.22533 + 0.707445i
\(396\) 0 0
\(397\) −53.1506 + 92.0595i −0.133880 + 0.231888i −0.925169 0.379555i \(-0.876077\pi\)
0.791289 + 0.611443i \(0.209410\pi\)
\(398\) 81.4577i 0.204668i
\(399\) 0 0
\(400\) 125.519 0.313796
\(401\) −185.008 106.815i −0.461368 0.266371i 0.251252 0.967922i \(-0.419158\pi\)
−0.712619 + 0.701551i \(0.752491\pi\)
\(402\) 0 0
\(403\) −139.415 241.474i −0.345944 0.599192i
\(404\) 321.690 557.184i 0.796262 1.37917i
\(405\) 0 0
\(406\) 7.25019 0.0178576
\(407\) 352.528i 0.866161i
\(408\) 0 0
\(409\) −46.6112 + 26.9110i −0.113964 + 0.0657970i −0.555898 0.831250i \(-0.687626\pi\)
0.441935 + 0.897047i \(0.354292\pi\)
\(410\) −2.40433 −0.00586421
\(411\) 0 0
\(412\) 62.4221 36.0394i 0.151510 0.0874744i
\(413\) −8.30872 4.79704i −0.0201180 0.0116151i
\(414\) 0 0
\(415\) −294.717 + 510.465i −0.710162 + 1.23004i
\(416\) −107.280 + 185.815i −0.257885 + 0.446670i
\(417\) 0 0
\(418\) 24.1958 + 29.1597i 0.0578846 + 0.0697601i
\(419\) 808.890 1.93052 0.965262 0.261282i \(-0.0841454\pi\)
0.965262 + 0.261282i \(0.0841454\pi\)
\(420\) 0 0
\(421\) −309.086 178.451i −0.734171 0.423874i 0.0857753 0.996315i \(-0.472663\pi\)
−0.819946 + 0.572441i \(0.805997\pi\)
\(422\) 1.51999 + 2.63270i 0.00360187 + 0.00623863i
\(423\) 0 0
\(424\) 86.5440 + 149.899i 0.204113 + 0.353534i
\(425\) 205.196 0.482814
\(426\) 0 0
\(427\) 14.5058 + 25.1248i 0.0339714 + 0.0588402i
\(428\) −189.518 + 109.418i −0.442800 + 0.255651i
\(429\) 0 0
\(430\) 39.1794i 0.0911149i
\(431\) 36.3673 20.9967i 0.0843789 0.0487162i −0.457217 0.889355i \(-0.651154\pi\)
0.541596 + 0.840639i \(0.317820\pi\)
\(432\) 0 0
\(433\) 533.602 308.075i 1.23234 0.711491i 0.264821 0.964298i \(-0.414687\pi\)
0.967517 + 0.252807i \(0.0813538\pi\)
\(434\) 3.30353 5.72189i 0.00761183 0.0131841i
\(435\) 0 0
\(436\) 439.244i 1.00744i
\(437\) −99.9862 585.881i −0.228801 1.34069i
\(438\) 0 0
\(439\) −408.012 235.566i −0.929413 0.536597i −0.0427870 0.999084i \(-0.513624\pi\)
−0.886626 + 0.462487i \(0.846957\pi\)
\(440\) 79.0394 + 45.6334i 0.179635 + 0.103712i
\(441\) 0 0
\(442\) −57.0906 + 98.8838i −0.129164 + 0.223719i
\(443\) −52.2697 90.5338i −0.117990 0.204365i 0.800981 0.598690i \(-0.204312\pi\)
−0.918971 + 0.394325i \(0.870979\pi\)
\(444\) 0 0
\(445\) 689.089i 1.54852i
\(446\) 10.9326 + 18.9358i 0.0245125 + 0.0424569i
\(447\) 0 0
\(448\) 114.209 0.254930
\(449\) 713.259i 1.58855i 0.607559 + 0.794275i \(0.292149\pi\)
−0.607559 + 0.794275i \(0.707851\pi\)
\(450\) 0 0
\(451\) 12.9896 + 7.49952i 0.0288017 + 0.0166287i
\(452\) 379.072 218.857i 0.838655 0.484198i
\(453\) 0 0
\(454\) 33.0826 57.3007i 0.0728691 0.126213i
\(455\) 216.540i 0.475912i
\(456\) 0 0
\(457\) −5.29457 −0.0115855 −0.00579275 0.999983i \(-0.501844\pi\)
−0.00579275 + 0.999983i \(0.501844\pi\)
\(458\) −28.0599 16.2004i −0.0612662 0.0353721i
\(459\) 0 0
\(460\) −355.399 615.569i −0.772607 1.33819i
\(461\) 93.4120 161.794i 0.202629 0.350964i −0.746746 0.665110i \(-0.768385\pi\)
0.949375 + 0.314146i \(0.101718\pi\)
\(462\) 0 0
\(463\) 718.582 1.55201 0.776007 0.630725i \(-0.217242\pi\)
0.776007 + 0.630725i \(0.217242\pi\)
\(464\) 242.751i 0.523170i
\(465\) 0 0
\(466\) −74.9468 + 43.2706i −0.160830 + 0.0928553i
\(467\) −864.548 −1.85128 −0.925641 0.378404i \(-0.876473\pi\)
−0.925641 + 0.378404i \(0.876473\pi\)
\(468\) 0 0
\(469\) −136.915 + 79.0480i −0.291930 + 0.168546i
\(470\) −4.00763 2.31381i −0.00852687 0.00492299i
\(471\) 0 0
\(472\) 4.61695 7.99679i 0.00978167 0.0169423i
\(473\) −122.208 + 211.670i −0.258367 + 0.447505i
\(474\) 0 0
\(475\) −26.1585 153.279i −0.0550706 0.322693i
\(476\) 192.313 0.404018
\(477\) 0 0
\(478\) −40.0654 23.1318i −0.0838189 0.0483928i
\(479\) −63.1395 109.361i −0.131815 0.228311i 0.792561 0.609793i \(-0.208747\pi\)
−0.924376 + 0.381482i \(0.875414\pi\)
\(480\) 0 0
\(481\) 402.504 + 697.157i 0.836806 + 1.44939i
\(482\) 32.1590 0.0667199
\(483\) 0 0
\(484\) 97.2981 + 168.525i 0.201029 + 0.348193i
\(485\) 242.772 140.164i 0.500560 0.288999i
\(486\) 0 0
\(487\) 12.1199i 0.0248868i −0.999923 0.0124434i \(-0.996039\pi\)
0.999923 0.0124434i \(-0.00396097\pi\)
\(488\) −24.1815 + 13.9612i −0.0495523 + 0.0286090i
\(489\) 0 0
\(490\) −53.1421 + 30.6816i −0.108453 + 0.0626155i
\(491\) −246.271 + 426.554i −0.501570 + 0.868745i 0.498428 + 0.866931i \(0.333911\pi\)
−0.999998 + 0.00181372i \(0.999423\pi\)
\(492\) 0 0
\(493\) 396.846i 0.804962i
\(494\) 81.1430 + 30.0402i 0.164257 + 0.0608102i
\(495\) 0 0
\(496\) −191.580 110.609i −0.386251 0.223002i
\(497\) −103.049 59.4952i −0.207342 0.119709i
\(498\) 0 0
\(499\) 173.134 299.877i 0.346962 0.600956i −0.638746 0.769417i \(-0.720547\pi\)
0.985708 + 0.168462i \(0.0538800\pi\)
\(500\) 191.052 + 330.911i 0.382103 + 0.661822i
\(501\) 0 0
\(502\) 10.9928i 0.0218981i
\(503\) −166.249 287.952i −0.330516 0.572470i 0.652098 0.758135i \(-0.273889\pi\)
−0.982613 + 0.185665i \(0.940556\pi\)
\(504\) 0 0
\(505\) −939.592 −1.86058
\(506\) 62.3838i 0.123288i
\(507\) 0 0
\(508\) 826.876 + 477.397i 1.62771 + 0.939758i
\(509\) 461.493 266.443i 0.906666 0.523464i 0.0273090 0.999627i \(-0.491306\pi\)
0.879357 + 0.476163i \(0.157973\pi\)
\(510\) 0 0
\(511\) −75.5049 + 130.778i −0.147759 + 0.255926i
\(512\) 285.041i 0.556722i
\(513\) 0 0
\(514\) 1.28902 0.00250782
\(515\) −91.1612 52.6319i −0.177012 0.102198i
\(516\) 0 0
\(517\) 14.4343 + 25.0010i 0.0279194 + 0.0483579i
\(518\) −9.53758 + 16.5196i −0.0184123 + 0.0318911i
\(519\) 0 0
\(520\) 208.411 0.400789
\(521\) 74.3056i 0.142621i −0.997454 0.0713106i \(-0.977282\pi\)
0.997454 0.0713106i \(-0.0227181\pi\)
\(522\) 0 0
\(523\) 25.3191 14.6180i 0.0484113 0.0279503i −0.475599 0.879662i \(-0.657769\pi\)
0.524010 + 0.851712i \(0.324435\pi\)
\(524\) 621.092 1.18529
\(525\) 0 0
\(526\) 15.1405 8.74139i 0.0287843 0.0166186i
\(527\) −313.193 180.822i −0.594294 0.343116i
\(528\) 0 0
\(529\) −224.771 + 389.315i −0.424898 + 0.735945i
\(530\) 62.7529 108.691i 0.118402 0.205078i
\(531\) 0 0
\(532\) −24.5162 143.655i −0.0460830 0.270029i
\(533\) 34.2508 0.0642603
\(534\) 0 0
\(535\) 276.772 + 159.795i 0.517331 + 0.298681i
\(536\) −76.0803 131.775i −0.141941 0.245849i
\(537\) 0 0
\(538\) −8.73436 15.1284i −0.0162349 0.0281196i
\(539\) 382.805 0.710214
\(540\) 0 0
\(541\) 109.055 + 188.889i 0.201580 + 0.349147i 0.949038 0.315163i \(-0.102059\pi\)
−0.747458 + 0.664310i \(0.768726\pi\)
\(542\) −19.6006 + 11.3164i −0.0361635 + 0.0208790i
\(543\) 0 0
\(544\) 278.285i 0.511554i
\(545\) −555.530 + 320.735i −1.01932 + 0.588505i
\(546\) 0 0
\(547\) −465.237 + 268.605i −0.850525 + 0.491051i −0.860828 0.508896i \(-0.830054\pi\)
0.0103027 + 0.999947i \(0.496721\pi\)
\(548\) −477.967 + 827.863i −0.872202 + 1.51070i
\(549\) 0 0
\(550\) 16.3209i 0.0296744i
\(551\) −296.440 + 50.5903i −0.538003 + 0.0918154i
\(552\) 0 0
\(553\) 163.379 + 94.3268i 0.295441 + 0.170573i
\(554\) −25.0948 14.4885i −0.0452975 0.0261525i
\(555\) 0 0
\(556\) −256.563 + 444.380i −0.461444 + 0.799245i
\(557\) 158.164 + 273.947i 0.283956 + 0.491826i 0.972355 0.233505i \(-0.0750197\pi\)
−0.688399 + 0.725332i \(0.741686\pi\)
\(558\) 0 0
\(559\) 558.129i 0.998442i
\(560\) −85.8990 148.781i −0.153391 0.265681i
\(561\) 0 0
\(562\) 95.7792 0.170426
\(563\) 595.272i 1.05732i −0.848833 0.528661i \(-0.822694\pi\)
0.848833 0.528661i \(-0.177306\pi\)
\(564\) 0 0
\(565\) −553.596 319.619i −0.979816 0.565697i
\(566\) 37.8518 21.8538i 0.0668760 0.0386109i
\(567\) 0 0
\(568\) 57.2616 99.1800i 0.100813 0.174613i
\(569\) 536.213i 0.942377i 0.882032 + 0.471189i \(0.156175\pi\)
−0.882032 + 0.471189i \(0.843825\pi\)
\(570\) 0 0
\(571\) −84.5912 −0.148146 −0.0740729 0.997253i \(-0.523600\pi\)
−0.0740729 + 0.997253i \(0.523600\pi\)
\(572\) −559.044 322.764i −0.977350 0.564273i
\(573\) 0 0
\(574\) 0.405797 + 0.702861i 0.000706963 + 0.00122450i
\(575\) −128.004 + 221.709i −0.222615 + 0.385581i
\(576\) 0 0
\(577\) −850.008 −1.47315 −0.736575 0.676356i \(-0.763558\pi\)
−0.736575 + 0.676356i \(0.763558\pi\)
\(578\) 80.0129i 0.138431i
\(579\) 0 0
\(580\) −311.461 + 179.822i −0.537002 + 0.310038i
\(581\) 198.967 0.342456
\(582\) 0 0
\(583\) −678.055 + 391.475i −1.16304 + 0.671484i
\(584\) −125.869 72.6703i −0.215528 0.124435i
\(585\) 0 0
\(586\) 42.4509 73.5271i 0.0724417 0.125473i
\(587\) −229.370 + 397.281i −0.390750 + 0.676798i −0.992549 0.121849i \(-0.961117\pi\)
0.601799 + 0.798648i \(0.294451\pi\)
\(588\) 0 0
\(589\) −95.1459 + 257.003i −0.161538 + 0.436338i
\(590\) −6.69548 −0.0113483
\(591\) 0 0
\(592\) 553.108 + 319.337i 0.934305 + 0.539421i
\(593\) 51.3293 + 88.9049i 0.0865586 + 0.149924i 0.906054 0.423161i \(-0.139080\pi\)
−0.819496 + 0.573085i \(0.805746\pi\)
\(594\) 0 0
\(595\) −140.426 243.226i −0.236011 0.408783i
\(596\) −807.579 −1.35500
\(597\) 0 0
\(598\) −71.2276 123.370i −0.119110 0.206304i
\(599\) −322.250 + 186.051i −0.537980 + 0.310603i −0.744260 0.667890i \(-0.767198\pi\)
0.206280 + 0.978493i \(0.433864\pi\)
\(600\) 0 0
\(601\) 850.837i 1.41570i −0.706362 0.707851i \(-0.749665\pi\)
0.706362 0.707851i \(-0.250335\pi\)
\(602\) −11.4534 + 6.61261i −0.0190256 + 0.0109844i
\(603\) 0 0
\(604\) 800.396 462.109i 1.32516 0.765081i
\(605\) 142.094 246.114i 0.234866 0.406800i
\(606\) 0 0
\(607\) 314.498i 0.518119i 0.965861 + 0.259060i \(0.0834126\pi\)
−0.965861 + 0.259060i \(0.916587\pi\)
\(608\) 207.876 35.4760i 0.341901 0.0583488i
\(609\) 0 0
\(610\) 17.5340 + 10.1233i 0.0287442 + 0.0165955i
\(611\) 57.0906 + 32.9613i 0.0934379 + 0.0539464i
\(612\) 0 0
\(613\) 146.198 253.222i 0.238495 0.413086i −0.721787 0.692115i \(-0.756679\pi\)
0.960283 + 0.279029i \(0.0900125\pi\)
\(614\) 31.7105 + 54.9241i 0.0516457 + 0.0894530i
\(615\) 0 0
\(616\) 30.8076i 0.0500124i
\(617\) 438.183 + 758.955i 0.710183 + 1.23007i 0.964788 + 0.263028i \(0.0847212\pi\)
−0.254605 + 0.967045i \(0.581945\pi\)
\(618\) 0 0
\(619\) −166.847 −0.269542 −0.134771 0.990877i \(-0.543030\pi\)
−0.134771 + 0.990877i \(0.543030\pi\)
\(620\) 327.742i 0.528617i
\(621\) 0 0
\(622\) 10.9050 + 6.29601i 0.0175322 + 0.0101222i
\(623\) −201.443 + 116.303i −0.323343 + 0.186682i
\(624\) 0 0
\(625\) 381.311 660.450i 0.610097 1.05672i
\(626\) 56.4240i 0.0901342i
\(627\) 0 0
\(628\) −349.448 −0.556445
\(629\) 904.214 + 522.048i 1.43754 + 0.829965i
\(630\) 0 0
\(631\) 464.592 + 804.698i 0.736280 + 1.27527i 0.954160 + 0.299298i \(0.0967525\pi\)
−0.217880 + 0.975976i \(0.569914\pi\)
\(632\) −90.7855 + 157.245i −0.143648 + 0.248806i
\(633\) 0 0
\(634\) 106.563 0.168080
\(635\) 1394.38i 2.19587i
\(636\) 0 0
\(637\) 757.034 437.074i 1.18844 0.686144i
\(638\) −31.5645 −0.0494741
\(639\) 0 0
\(640\) 290.508 167.725i 0.453918 0.262070i
\(641\) −425.692 245.773i −0.664106 0.383422i 0.129734 0.991549i \(-0.458588\pi\)
−0.793840 + 0.608127i \(0.791921\pi\)
\(642\) 0 0
\(643\) 175.770 304.442i 0.273359 0.473472i −0.696361 0.717692i \(-0.745199\pi\)
0.969720 + 0.244220i \(0.0785319\pi\)
\(644\) −119.967 + 207.789i −0.186284 + 0.322653i
\(645\) 0 0
\(646\) 110.624 18.8790i 0.171245 0.0292245i
\(647\) −767.027 −1.18551 −0.592757 0.805381i \(-0.701961\pi\)
−0.592757 + 0.805381i \(0.701961\pi\)
\(648\) 0 0
\(649\) 36.1729 + 20.8844i 0.0557363 + 0.0321794i
\(650\) −18.6347 32.2762i −0.0286687 0.0496557i
\(651\) 0 0
\(652\) −228.619 395.981i −0.350643 0.607332i
\(653\) 254.877 0.390317 0.195159 0.980772i \(-0.437478\pi\)
0.195159 + 0.980772i \(0.437478\pi\)
\(654\) 0 0
\(655\) −453.521 785.522i −0.692399 1.19927i
\(656\) 23.5332 13.5869i 0.0358738 0.0207117i
\(657\) 0 0
\(658\) 1.56208i 0.00237398i
\(659\) 427.502 246.818i 0.648713 0.374535i −0.139250 0.990257i \(-0.544469\pi\)
0.787963 + 0.615723i \(0.211136\pi\)
\(660\) 0 0
\(661\) −1110.75 + 641.292i −1.68041 + 0.970185i −0.719021 + 0.694988i \(0.755410\pi\)
−0.961388 + 0.275197i \(0.911257\pi\)
\(662\) −11.2451 + 19.4771i −0.0169866 + 0.0294216i
\(663\) 0 0
\(664\) 191.497i 0.288399i
\(665\) −163.785 + 135.904i −0.246294 + 0.204366i
\(666\) 0 0
\(667\) 428.782 + 247.558i 0.642852 + 0.371151i
\(668\) 307.839 + 177.731i 0.460837 + 0.266065i
\(669\) 0 0
\(670\) −55.1658 + 95.5499i −0.0823370 + 0.142612i
\(671\) −63.1525 109.383i −0.0941169 0.163015i
\(672\) 0 0
\(673\) 337.649i 0.501707i 0.968025 + 0.250853i \(0.0807112\pi\)
−0.968025 + 0.250853i \(0.919289\pi\)
\(674\) 11.1848 + 19.3727i 0.0165947 + 0.0287428i
\(675\) 0 0
\(676\) −807.462 −1.19447
\(677\) 394.197i 0.582270i −0.956682 0.291135i \(-0.905967\pi\)
0.956682 0.291135i \(-0.0940329\pi\)
\(678\) 0 0
\(679\) −81.9489 47.3132i −0.120691 0.0696808i
\(680\) 234.094 135.155i 0.344257 0.198757i
\(681\) 0 0
\(682\) −14.3823 + 24.9108i −0.0210884 + 0.0365262i
\(683\) 612.782i 0.897192i −0.893735 0.448596i \(-0.851924\pi\)
0.893735 0.448596i \(-0.148076\pi\)
\(684\) 0 0
\(685\) 1396.04 2.03802
\(686\) 37.3768 + 21.5795i 0.0544851 + 0.0314570i
\(687\) 0 0
\(688\) 221.404 + 383.482i 0.321807 + 0.557387i
\(689\) −893.945 + 1548.36i −1.29745 + 2.24725i
\(690\) 0 0
\(691\) 254.757 0.368678 0.184339 0.982863i \(-0.440986\pi\)
0.184339 + 0.982863i \(0.440986\pi\)
\(692\) 175.693i 0.253892i
\(693\) 0 0
\(694\) 47.0127 27.1428i 0.0677417 0.0391107i
\(695\) 749.369 1.07823
\(696\) 0 0
\(697\) 38.4717 22.2117i 0.0551962 0.0318675i
\(698\) 42.6710 + 24.6361i 0.0611333 + 0.0352953i
\(699\) 0 0
\(700\) −31.3859 + 54.3620i −0.0448370 + 0.0776600i
\(701\) 3.62864 6.28499i 0.00517638 0.00896576i −0.863426 0.504476i \(-0.831686\pi\)
0.868602 + 0.495510i \(0.165019\pi\)
\(702\) 0 0
\(703\) 274.694 741.989i 0.390746 1.05546i
\(704\) −497.219 −0.706277
\(705\) 0 0
\(706\) 66.5332 + 38.4130i 0.0942396 + 0.0544093i
\(707\) 158.582 + 274.672i 0.224303 + 0.388504i
\(708\) 0 0
\(709\) −522.280 904.615i −0.736643 1.27590i −0.953999 0.299810i \(-0.903077\pi\)
0.217356 0.976092i \(-0.430257\pi\)
\(710\) −83.0407 −0.116959
\(711\) 0 0
\(712\) −111.937 193.880i −0.157214 0.272303i
\(713\) 390.747 225.598i 0.548033 0.316407i
\(714\) 0 0
\(715\) 942.729i 1.31850i
\(716\) 784.433 452.893i 1.09558 0.632532i
\(717\) 0 0
\(718\) −109.650 + 63.3065i −0.152716 + 0.0881706i
\(719\) 658.810 1141.09i 0.916286 1.58705i 0.111279 0.993789i \(-0.464505\pi\)
0.805007 0.593265i \(-0.202161\pi\)
\(720\) 0 0
\(721\) 35.5324i 0.0492821i
\(722\) −28.2049 80.2281i −0.0390649 0.111119i
\(723\) 0 0
\(724\) −619.564 357.705i −0.855751 0.494068i
\(725\) 112.179 + 64.7664i 0.154729 + 0.0893330i
\(726\) 0 0
\(727\) −88.8280 + 153.855i −0.122184 + 0.211630i −0.920629 0.390439i \(-0.872323\pi\)
0.798444 + 0.602068i \(0.205657\pi\)
\(728\) −35.1751 60.9250i −0.0483174 0.0836882i
\(729\) 0 0
\(730\) 105.386i 0.144365i
\(731\) 361.948 + 626.912i 0.495140 + 0.857608i
\(732\) 0 0
\(733\) 321.795 0.439011 0.219505 0.975611i \(-0.429556\pi\)
0.219505 + 0.975611i \(0.429556\pi\)
\(734\) 85.4062i 0.116357i
\(735\) 0 0
\(736\) −300.680 173.598i −0.408533 0.235867i
\(737\) 596.074 344.144i 0.808785 0.466952i
\(738\) 0 0
\(739\) 85.7034 148.443i 0.115972 0.200870i −0.802196 0.597061i \(-0.796335\pi\)
0.918168 + 0.396191i \(0.129668\pi\)
\(740\) 946.219i 1.27867i
\(741\) 0 0
\(742\) −42.3652 −0.0570960
\(743\) 257.044 + 148.405i 0.345955 + 0.199737i 0.662902 0.748706i \(-0.269325\pi\)
−0.316947 + 0.948443i \(0.602658\pi\)
\(744\) 0 0
\(745\) 589.693 + 1021.38i 0.791535 + 1.37098i
\(746\) 39.6334 68.6471i 0.0531279 0.0920202i
\(747\) 0 0
\(748\) −837.253 −1.11932
\(749\) 107.879i 0.144031i
\(750\) 0 0
\(751\) −117.403 + 67.7829i −0.156329 + 0.0902568i −0.576124 0.817362i \(-0.695435\pi\)
0.419795 + 0.907619i \(0.362102\pi\)
\(752\) 52.3014 0.0695498
\(753\) 0 0
\(754\) −62.4217 + 36.0392i −0.0827874 + 0.0477974i
\(755\) −1168.90 674.864i −1.54821 0.893859i
\(756\) 0 0
\(757\) 4.71078 8.15931i 0.00622296 0.0107785i −0.862897 0.505380i \(-0.831352\pi\)
0.869120 + 0.494601i \(0.164686\pi\)
\(758\) 39.6637 68.6996i 0.0523268 0.0906327i
\(759\) 0 0
\(760\) −130.801 157.636i −0.172107 0.207416i
\(761\) 501.946 0.659587 0.329794 0.944053i \(-0.393021\pi\)
0.329794 + 0.944053i \(0.393021\pi\)
\(762\) 0 0
\(763\) 187.522 + 108.266i 0.245770 + 0.141895i
\(764\) −549.675 952.066i −0.719470 1.24616i
\(765\) 0 0
\(766\) −26.3522 45.6433i −0.0344023 0.0595866i
\(767\) 95.3803 0.124355
\(768\) 0 0
\(769\) 722.257 + 1250.99i 0.939216 + 1.62677i 0.766937 + 0.641722i \(0.221780\pi\)
0.172279 + 0.985048i \(0.444887\pi\)
\(770\) −19.3458 + 11.1693i −0.0251244 + 0.0145056i
\(771\) 0 0
\(772\) 762.972i 0.988306i
\(773\) 572.771 330.690i 0.740972 0.427800i −0.0814506 0.996677i \(-0.525955\pi\)
0.822423 + 0.568877i \(0.192622\pi\)
\(774\) 0 0
\(775\) 102.228 59.0213i 0.131907 0.0761565i
\(776\) 45.5370 78.8724i 0.0586817 0.101640i
\(777\) 0 0
\(778\) 47.3301i 0.0608356i
\(779\) −21.4963 25.9064i −0.0275947 0.0332559i
\(780\) 0 0
\(781\) 448.633 + 259.019i 0.574435 + 0.331650i
\(782\) −160.011 92.3824i −0.204618 0.118136i
\(783\) 0 0
\(784\) 346.764 600.614i 0.442302 0.766089i