Properties

Label 171.3.p.f.145.1
Level $171$
Weight $3$
Character 171.145
Analytic conductor $4.659$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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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: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.19163381760000.1
Defining polynomial: \( x^{8} - 14x^{6} + 177x^{4} - 266x^{2} + 361 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 145.1
Root \(-3.05907 + 1.76616i\) of defining polynomial
Character \(\chi\) \(=\) 171.145
Dual form 171.3.p.f.46.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.05907 + 1.76616i) q^{2} +(4.23861 - 7.34149i) q^{4} +(0.533068 + 0.923301i) q^{5} +0.477226 q^{7} +15.8150i q^{8} +O(q^{10})\) \(q+(-3.05907 + 1.76616i) q^{2} +(4.23861 - 7.34149i) q^{4} +(0.533068 + 0.923301i) q^{5} +0.477226 q^{7} +15.8150i q^{8} +(-3.26139 - 1.88296i) q^{10} -11.1702 q^{11} +(-12.9772 - 7.49240i) q^{13} +(-1.45987 + 0.842855i) q^{14} +(-10.9772 - 19.0131i) q^{16} +(-6.11814 - 10.5969i) q^{17} +(-6.52277 + 17.8453i) q^{19} +9.03788 q^{20} +(34.1703 - 19.7282i) q^{22} +(20.7411 - 35.9246i) q^{23} +(11.9317 - 20.6663i) q^{25} +52.9310 q^{26} +(2.02277 - 3.50355i) q^{28} +(-30.5907 - 17.6616i) q^{29} -15.8903i q^{31} +(12.3756 + 7.14507i) q^{32} +(37.4317 + 21.6112i) q^{34} +(0.254394 + 0.440623i) q^{35} +24.3276i q^{37} +(-11.5639 - 66.1102i) q^{38} +(-14.6020 + 8.43045i) q^{40} +(-5.83947 + 3.37142i) q^{41} +(-31.6703 - 54.8546i) q^{43} +(-47.3459 + 82.0056i) q^{44} +146.528i q^{46} +(20.2080 - 35.0013i) q^{47} -48.7723 q^{49} +84.2928i q^{50} +(-110.011 + 63.5148i) q^{52} +(26.3505 + 15.2134i) q^{53} +(-5.95445 - 10.3134i) q^{55} +7.54730i q^{56} +124.772 q^{58} +(-69.1775 + 39.9396i) q^{59} +(-35.8861 + 62.1566i) q^{61} +(28.0647 + 48.6095i) q^{62} +37.3406 q^{64} -15.9758i q^{65} +(7.62474 + 4.40215i) q^{67} -103.730 q^{68} +(-1.55642 - 0.898598i) q^{70} +(-42.2697 + 24.4044i) q^{71} +(-56.7950 - 98.3719i) q^{73} +(-42.9663 - 74.4199i) q^{74} +(103.363 + 123.526i) q^{76} -5.33068 q^{77} +(104.534 - 60.3525i) q^{79} +(11.7032 - 20.2706i) q^{80} +(11.9089 - 20.6268i) q^{82} +65.4460 q^{83} +(6.52277 - 11.2978i) q^{85} +(193.763 + 111.869i) q^{86} -176.655i q^{88} +(133.279 + 76.9484i) q^{89} +(-6.19306 - 3.57557i) q^{91} +(-175.827 - 304.541i) q^{92} +142.762i q^{94} +(-19.9536 + 3.49026i) q^{95} +(-83.0911 + 47.9727i) q^{97} +(149.198 - 86.1394i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 12 q^{4} - 40 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 12 q^{4} - 40 q^{7} - 48 q^{10} - 60 q^{13} - 44 q^{16} - 96 q^{19} + 120 q^{22} - 36 q^{25} + 60 q^{28} + 168 q^{34} + 168 q^{40} - 100 q^{43} + 48 q^{49} - 420 q^{52} + 40 q^{55} + 560 q^{58} - 68 q^{61} - 8 q^{64} - 180 q^{67} + 360 q^{70} - 60 q^{73} + 564 q^{76} + 420 q^{79} - 80 q^{82} + 96 q^{85} + 60 q^{91} - 840 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(20\) \(154\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.05907 + 1.76616i −1.52954 + 0.883078i −0.530155 + 0.847901i \(0.677866\pi\)
−0.999381 + 0.0351770i \(0.988801\pi\)
\(3\) 0 0
\(4\) 4.23861 7.34149i 1.05965 1.83537i
\(5\) 0.533068 + 0.923301i 0.106614 + 0.184660i 0.914396 0.404820i \(-0.132666\pi\)
−0.807783 + 0.589480i \(0.799333\pi\)
\(6\) 0 0
\(7\) 0.477226 0.0681751 0.0340875 0.999419i \(-0.489147\pi\)
0.0340875 + 0.999419i \(0.489147\pi\)
\(8\) 15.8150i 1.97687i
\(9\) 0 0
\(10\) −3.26139 1.88296i −0.326139 0.188296i
\(11\) −11.1702 −1.01547 −0.507734 0.861514i \(-0.669517\pi\)
−0.507734 + 0.861514i \(0.669517\pi\)
\(12\) 0 0
\(13\) −12.9772 7.49240i −0.998248 0.576339i −0.0905186 0.995895i \(-0.528852\pi\)
−0.907729 + 0.419556i \(0.862186\pi\)
\(14\) −1.45987 + 0.842855i −0.104276 + 0.0602039i
\(15\) 0 0
\(16\) −10.9772 19.0131i −0.686077 1.18832i
\(17\) −6.11814 10.5969i −0.359891 0.623349i 0.628051 0.778172i \(-0.283853\pi\)
−0.987942 + 0.154823i \(0.950519\pi\)
\(18\) 0 0
\(19\) −6.52277 + 17.8453i −0.343304 + 0.939224i
\(20\) 9.03788 0.451894
\(21\) 0 0
\(22\) 34.1703 19.7282i 1.55319 0.896738i
\(23\) 20.7411 35.9246i 0.901787 1.56194i 0.0766135 0.997061i \(-0.475589\pi\)
0.825173 0.564880i \(-0.191077\pi\)
\(24\) 0 0
\(25\) 11.9317 20.6663i 0.477267 0.826651i
\(26\) 52.9310 2.03581
\(27\) 0 0
\(28\) 2.02277 3.50355i 0.0722419 0.125127i
\(29\) −30.5907 17.6616i −1.05485 0.609019i −0.130848 0.991402i \(-0.541770\pi\)
−0.924004 + 0.382383i \(0.875103\pi\)
\(30\) 0 0
\(31\) 15.8903i 0.512590i −0.966599 0.256295i \(-0.917498\pi\)
0.966599 0.256295i \(-0.0825018\pi\)
\(32\) 12.3756 + 7.14507i 0.386738 + 0.223283i
\(33\) 0 0
\(34\) 37.4317 + 21.6112i 1.10093 + 0.635623i
\(35\) 0.254394 + 0.440623i 0.00726839 + 0.0125892i
\(36\) 0 0
\(37\) 24.3276i 0.657503i 0.944416 + 0.328751i \(0.106628\pi\)
−0.944416 + 0.328751i \(0.893372\pi\)
\(38\) −11.5639 66.1102i −0.304313 1.73974i
\(39\) 0 0
\(40\) −14.6020 + 8.43045i −0.365049 + 0.210761i
\(41\) −5.83947 + 3.37142i −0.142426 + 0.0822297i −0.569520 0.821978i \(-0.692871\pi\)
0.427094 + 0.904207i \(0.359537\pi\)
\(42\) 0 0
\(43\) −31.6703 54.8546i −0.736518 1.27569i −0.954054 0.299635i \(-0.903135\pi\)
0.217536 0.976052i \(-0.430198\pi\)
\(44\) −47.3459 + 82.0056i −1.07604 + 1.86376i
\(45\) 0 0
\(46\) 146.528i 3.18539i
\(47\) 20.2080 35.0013i 0.429958 0.744709i −0.566911 0.823779i \(-0.691862\pi\)
0.996869 + 0.0790699i \(0.0251950\pi\)
\(48\) 0 0
\(49\) −48.7723 −0.995352
\(50\) 84.2928i 1.68586i
\(51\) 0 0
\(52\) −110.011 + 63.5148i −2.11559 + 1.22144i
\(53\) 26.3505 + 15.2134i 0.497178 + 0.287046i 0.727548 0.686057i \(-0.240660\pi\)
−0.230369 + 0.973103i \(0.573993\pi\)
\(54\) 0 0
\(55\) −5.95445 10.3134i −0.108263 0.187517i
\(56\) 7.54730i 0.134773i
\(57\) 0 0
\(58\) 124.772 2.15125
\(59\) −69.1775 + 39.9396i −1.17250 + 0.676943i −0.954267 0.298954i \(-0.903362\pi\)
−0.218232 + 0.975897i \(0.570029\pi\)
\(60\) 0 0
\(61\) −35.8861 + 62.1566i −0.588297 + 1.01896i 0.406158 + 0.913803i \(0.366868\pi\)
−0.994456 + 0.105158i \(0.966465\pi\)
\(62\) 28.0647 + 48.6095i 0.452657 + 0.784024i
\(63\) 0 0
\(64\) 37.3406 0.583447
\(65\) 15.9758i 0.245782i
\(66\) 0 0
\(67\) 7.62474 + 4.40215i 0.113802 + 0.0657037i 0.555821 0.831302i \(-0.312404\pi\)
−0.442019 + 0.897006i \(0.645737\pi\)
\(68\) −103.730 −1.52544
\(69\) 0 0
\(70\) −1.55642 0.898598i −0.0222345 0.0128371i
\(71\) −42.2697 + 24.4044i −0.595347 + 0.343724i −0.767209 0.641397i \(-0.778355\pi\)
0.171862 + 0.985121i \(0.445022\pi\)
\(72\) 0 0
\(73\) −56.7950 98.3719i −0.778014 1.34756i −0.933085 0.359657i \(-0.882894\pi\)
0.155071 0.987903i \(-0.450439\pi\)
\(74\) −42.9663 74.4199i −0.580626 1.00567i
\(75\) 0 0
\(76\) 103.363 + 123.526i 1.36004 + 1.62534i
\(77\) −5.33068 −0.0692296
\(78\) 0 0
\(79\) 104.534 60.3525i 1.32321 0.763956i 0.338971 0.940797i \(-0.389921\pi\)
0.984239 + 0.176841i \(0.0565877\pi\)
\(80\) 11.7032 20.2706i 0.146290 0.253382i
\(81\) 0 0
\(82\) 11.9089 20.6268i 0.145231 0.251547i
\(83\) 65.4460 0.788506 0.394253 0.919002i \(-0.371003\pi\)
0.394253 + 0.919002i \(0.371003\pi\)
\(84\) 0 0
\(85\) 6.52277 11.2978i 0.0767385 0.132915i
\(86\) 193.763 + 111.869i 2.25306 + 1.30081i
\(87\) 0 0
\(88\) 176.655i 2.00745i
\(89\) 133.279 + 76.9484i 1.49751 + 0.864589i 0.999996 0.00286509i \(-0.000911989\pi\)
0.497517 + 0.867454i \(0.334245\pi\)
\(90\) 0 0
\(91\) −6.19306 3.57557i −0.0680556 0.0392919i
\(92\) −175.827 304.541i −1.91116 3.31023i
\(93\) 0 0
\(94\) 142.762i 1.51875i
\(95\) −19.9536 + 3.49026i −0.210038 + 0.0367395i
\(96\) 0 0
\(97\) −83.0911 + 47.9727i −0.856609 + 0.494564i −0.862875 0.505417i \(-0.831339\pi\)
0.00626610 + 0.999980i \(0.498005\pi\)
\(98\) 149.198 86.1394i 1.52243 0.878974i
\(99\) 0 0
\(100\) −101.148 175.193i −1.01148 1.75193i
\(101\) −13.5811 + 23.5232i −0.134466 + 0.232902i −0.925393 0.379008i \(-0.876265\pi\)
0.790927 + 0.611910i \(0.209599\pi\)
\(102\) 0 0
\(103\) 43.4453i 0.421799i 0.977508 + 0.210900i \(0.0676393\pi\)
−0.977508 + 0.210900i \(0.932361\pi\)
\(104\) 118.492 205.234i 1.13935 1.97341i
\(105\) 0 0
\(106\) −107.477 −1.01394
\(107\) 35.9667i 0.336137i 0.985775 + 0.168069i \(0.0537530\pi\)
−0.985775 + 0.168069i \(0.946247\pi\)
\(108\) 0 0
\(109\) −70.0455 + 40.4408i −0.642620 + 0.371017i −0.785623 0.618706i \(-0.787657\pi\)
0.143003 + 0.989722i \(0.454324\pi\)
\(110\) 36.4302 + 21.0330i 0.331184 + 0.191209i
\(111\) 0 0
\(112\) −5.23861 9.07354i −0.0467733 0.0810138i
\(113\) 19.9908i 0.176910i −0.996080 0.0884550i \(-0.971807\pi\)
0.996080 0.0884550i \(-0.0281930\pi\)
\(114\) 0 0
\(115\) 44.2257 0.384571
\(116\) −259.324 + 149.721i −2.23556 + 1.29070i
\(117\) 0 0
\(118\) 141.079 244.356i 1.19559 2.07082i
\(119\) −2.91973 5.05713i −0.0245356 0.0424969i
\(120\) 0 0
\(121\) 3.77226 0.0311757
\(122\) 253.522i 2.07805i
\(123\) 0 0
\(124\) −116.658 67.3527i −0.940793 0.543167i
\(125\) 52.0950 0.416760
\(126\) 0 0
\(127\) −35.7267 20.6268i −0.281313 0.162416i 0.352705 0.935735i \(-0.385262\pi\)
−0.634018 + 0.773319i \(0.718595\pi\)
\(128\) −163.730 + 94.5296i −1.27914 + 0.738512i
\(129\) 0 0
\(130\) 28.2158 + 48.8713i 0.217045 + 0.375933i
\(131\) 102.942 + 178.301i 0.785819 + 1.36108i 0.928509 + 0.371311i \(0.121092\pi\)
−0.142689 + 0.989768i \(0.545575\pi\)
\(132\) 0 0
\(133\) −3.11283 + 8.51622i −0.0234048 + 0.0640317i
\(134\) −31.0995 −0.232086
\(135\) 0 0
\(136\) 167.590 96.7582i 1.23228 0.711457i
\(137\) −90.1487 + 156.142i −0.658019 + 1.13972i 0.323108 + 0.946362i \(0.395272\pi\)
−0.981128 + 0.193361i \(0.938061\pi\)
\(138\) 0 0
\(139\) 35.8525 62.0983i 0.257932 0.446751i −0.707756 0.706457i \(-0.750292\pi\)
0.965688 + 0.259706i \(0.0836258\pi\)
\(140\) 4.31311 0.0308079
\(141\) 0 0
\(142\) 86.2039 149.310i 0.607070 1.05148i
\(143\) 144.958 + 83.6913i 1.01369 + 0.585254i
\(144\) 0 0
\(145\) 37.6593i 0.259719i
\(146\) 347.480 + 200.618i 2.38000 + 1.37409i
\(147\) 0 0
\(148\) 178.601 + 103.115i 1.20676 + 0.696725i
\(149\) −109.036 188.856i −0.731786 1.26749i −0.956119 0.292978i \(-0.905354\pi\)
0.224333 0.974513i \(-0.427980\pi\)
\(150\) 0 0
\(151\) 26.1899i 0.173443i −0.996233 0.0867217i \(-0.972361\pi\)
0.996233 0.0867217i \(-0.0276391\pi\)
\(152\) −282.222 103.157i −1.85672 0.678667i
\(153\) 0 0
\(154\) 16.3069 9.41481i 0.105889 0.0611352i
\(155\) 14.6715 8.47060i 0.0946549 0.0546490i
\(156\) 0 0
\(157\) 59.8861 + 103.726i 0.381440 + 0.660674i 0.991268 0.131860i \(-0.0420948\pi\)
−0.609828 + 0.792534i \(0.708762\pi\)
\(158\) −213.184 + 369.245i −1.34927 + 2.33700i
\(159\) 0 0
\(160\) 15.2352i 0.0952202i
\(161\) 9.89818 17.1442i 0.0614794 0.106485i
\(162\) 0 0
\(163\) 252.885 1.55144 0.775721 0.631076i \(-0.217386\pi\)
0.775721 + 0.631076i \(0.217386\pi\)
\(164\) 57.1606i 0.348540i
\(165\) 0 0
\(166\) −200.204 + 115.588i −1.20605 + 0.696312i
\(167\) −163.312 94.2882i −0.977916 0.564600i −0.0762758 0.997087i \(-0.524303\pi\)
−0.901640 + 0.432487i \(0.857636\pi\)
\(168\) 0 0
\(169\) 27.7723 + 48.1030i 0.164333 + 0.284633i
\(170\) 46.0809i 0.271064i
\(171\) 0 0
\(172\) −536.952 −3.12182
\(173\) −168.946 + 97.5408i −0.976564 + 0.563820i −0.901231 0.433339i \(-0.857335\pi\)
−0.0753332 + 0.997158i \(0.524002\pi\)
\(174\) 0 0
\(175\) 5.69410 9.86247i 0.0325377 0.0563570i
\(176\) 122.617 + 212.379i 0.696689 + 1.20670i
\(177\) 0 0
\(178\) −543.612 −3.05400
\(179\) 170.754i 0.953933i −0.878921 0.476966i \(-0.841736\pi\)
0.878921 0.476966i \(-0.158264\pi\)
\(180\) 0 0
\(181\) 1.70497 + 0.984365i 0.00941972 + 0.00543848i 0.504702 0.863293i \(-0.331602\pi\)
−0.495283 + 0.868732i \(0.664936\pi\)
\(182\) 25.2600 0.138791
\(183\) 0 0
\(184\) 568.146 + 328.020i 3.08775 + 1.78271i
\(185\) −22.4617 + 12.9683i −0.121415 + 0.0700988i
\(186\) 0 0
\(187\) 68.3406 + 118.369i 0.365458 + 0.632991i
\(188\) −171.308 296.714i −0.911213 1.57827i
\(189\) 0 0
\(190\) 54.8753 45.9182i 0.288817 0.241675i
\(191\) −12.1877 −0.0638101 −0.0319050 0.999491i \(-0.510157\pi\)
−0.0319050 + 0.999491i \(0.510157\pi\)
\(192\) 0 0
\(193\) −245.884 + 141.961i −1.27401 + 0.735550i −0.975740 0.218931i \(-0.929743\pi\)
−0.298270 + 0.954481i \(0.596410\pi\)
\(194\) 169.454 293.504i 0.873476 1.51291i
\(195\) 0 0
\(196\) −206.727 + 358.061i −1.05473 + 1.82684i
\(197\) 306.876 1.55775 0.778874 0.627181i \(-0.215791\pi\)
0.778874 + 0.627181i \(0.215791\pi\)
\(198\) 0 0
\(199\) −76.7376 + 132.913i −0.385616 + 0.667906i −0.991854 0.127376i \(-0.959344\pi\)
0.606238 + 0.795283i \(0.292678\pi\)
\(200\) 326.836 + 188.699i 1.63418 + 0.943495i
\(201\) 0 0
\(202\) 95.9453i 0.474977i
\(203\) −14.5987 8.42855i −0.0719146 0.0415199i
\(204\) 0 0
\(205\) −6.22567 3.59439i −0.0303691 0.0175336i
\(206\) −76.7312 132.902i −0.372481 0.645157i
\(207\) 0 0
\(208\) 328.983i 1.58165i
\(209\) 72.8604 199.334i 0.348614 0.953752i
\(210\) 0 0
\(211\) 238.078 137.454i 1.12833 0.651443i 0.184817 0.982773i \(-0.440831\pi\)
0.943515 + 0.331330i \(0.107497\pi\)
\(212\) 223.379 128.968i 1.05367 0.608339i
\(213\) 0 0
\(214\) −63.5228 110.025i −0.296835 0.514134i
\(215\) 33.7648 58.4824i 0.157046 0.272011i
\(216\) 0 0
\(217\) 7.58325i 0.0349458i
\(218\) 142.850 247.423i 0.655273 1.13497i
\(219\) 0 0
\(220\) −100.954 −0.458884
\(221\) 183.358i 0.829676i
\(222\) 0 0
\(223\) 347.646 200.714i 1.55895 0.900062i 0.561595 0.827412i \(-0.310188\pi\)
0.997358 0.0726498i \(-0.0231455\pi\)
\(224\) 5.90596 + 3.40981i 0.0263659 + 0.0152224i
\(225\) 0 0
\(226\) 35.3069 + 61.1534i 0.156225 + 0.270590i
\(227\) 338.864i 1.49279i −0.665501 0.746397i \(-0.731782\pi\)
0.665501 0.746397i \(-0.268218\pi\)
\(228\) 0 0
\(229\) −222.453 −0.971412 −0.485706 0.874122i \(-0.661437\pi\)
−0.485706 + 0.874122i \(0.661437\pi\)
\(230\) −135.289 + 78.1094i −0.588215 + 0.339606i
\(231\) 0 0
\(232\) 279.317 483.791i 1.20395 2.08531i
\(233\) −116.802 202.307i −0.501296 0.868271i −0.999999 0.00149765i \(-0.999523\pi\)
0.498702 0.866773i \(-0.333810\pi\)
\(234\) 0 0
\(235\) 43.0890 0.183358
\(236\) 677.154i 2.86930i
\(237\) 0 0
\(238\) 17.8634 + 10.3134i 0.0750561 + 0.0433337i
\(239\) −322.917 −1.35112 −0.675558 0.737307i \(-0.736097\pi\)
−0.675558 + 0.737307i \(0.736097\pi\)
\(240\) 0 0
\(241\) 201.841 + 116.533i 0.837513 + 0.483538i 0.856418 0.516283i \(-0.172685\pi\)
−0.0189052 + 0.999821i \(0.506018\pi\)
\(242\) −11.5396 + 6.66239i −0.0476843 + 0.0275305i
\(243\) 0 0
\(244\) 304.215 + 526.915i 1.24678 + 2.15949i
\(245\) −25.9989 45.0315i −0.106118 0.183802i
\(246\) 0 0
\(247\) 218.351 182.711i 0.884014 0.739720i
\(248\) 251.304 1.01332
\(249\) 0 0
\(250\) −159.362 + 92.0079i −0.637449 + 0.368032i
\(251\) 134.042 232.167i 0.534031 0.924969i −0.465178 0.885217i \(-0.654010\pi\)
0.999210 0.0397521i \(-0.0126568\pi\)
\(252\) 0 0
\(253\) −231.681 + 401.284i −0.915736 + 1.58610i
\(254\) 145.721 0.573704
\(255\) 0 0
\(256\) 259.227 448.994i 1.01260 1.75388i
\(257\) −414.568 239.351i −1.61310 0.931326i −0.988645 0.150267i \(-0.951987\pi\)
−0.624458 0.781059i \(-0.714680\pi\)
\(258\) 0 0
\(259\) 11.6098i 0.0448253i
\(260\) −117.287 67.7154i −0.451102 0.260444i
\(261\) 0 0
\(262\) −629.816 363.624i −2.40388 1.38788i
\(263\) 133.812 + 231.769i 0.508790 + 0.881250i 0.999948 + 0.0101794i \(0.00324025\pi\)
−0.491158 + 0.871070i \(0.663426\pi\)
\(264\) 0 0
\(265\) 32.4392i 0.122412i
\(266\) −5.51858 31.5495i −0.0207465 0.118607i
\(267\) 0 0
\(268\) 64.6366 37.3180i 0.241182 0.139246i
\(269\) −16.7552 + 9.67363i −0.0622871 + 0.0359615i −0.530820 0.847485i \(-0.678116\pi\)
0.468533 + 0.883446i \(0.344783\pi\)
\(270\) 0 0
\(271\) 117.499 + 203.514i 0.433576 + 0.750975i 0.997178 0.0750712i \(-0.0239184\pi\)
−0.563603 + 0.826046i \(0.690585\pi\)
\(272\) −134.320 + 232.650i −0.493825 + 0.855330i
\(273\) 0 0
\(274\) 636.866i 2.32433i
\(275\) −133.279 + 230.845i −0.484650 + 0.839438i
\(276\) 0 0
\(277\) −107.636 −0.388576 −0.194288 0.980945i \(-0.562240\pi\)
−0.194288 + 0.980945i \(0.562240\pi\)
\(278\) 253.284i 0.911095i
\(279\) 0 0
\(280\) −6.96843 + 4.02323i −0.0248873 + 0.0143687i
\(281\) 364.932 + 210.694i 1.29869 + 0.749799i 0.980178 0.198119i \(-0.0634833\pi\)
0.318513 + 0.947919i \(0.396817\pi\)
\(282\) 0 0
\(283\) −10.4772 18.1471i −0.0370220 0.0641240i 0.846921 0.531719i \(-0.178454\pi\)
−0.883943 + 0.467595i \(0.845120\pi\)
\(284\) 413.763i 1.45691i
\(285\) 0 0
\(286\) −591.247 −2.06730
\(287\) −2.78674 + 1.60893i −0.00970991 + 0.00560602i
\(288\) 0 0
\(289\) 69.6366 120.614i 0.240957 0.417350i
\(290\) 66.5121 + 115.202i 0.229352 + 0.397250i
\(291\) 0 0
\(292\) −962.929 −3.29770
\(293\) 308.437i 1.05269i −0.850272 0.526344i \(-0.823563\pi\)
0.850272 0.526344i \(-0.176437\pi\)
\(294\) 0 0
\(295\) −73.7526 42.5811i −0.250009 0.144343i
\(296\) −384.740 −1.29980
\(297\) 0 0
\(298\) 667.099 + 385.150i 2.23859 + 1.29245i
\(299\) −538.324 + 310.801i −1.80041 + 1.03947i
\(300\) 0 0
\(301\) −15.1139 26.1780i −0.0502122 0.0869701i
\(302\) 46.2555 + 80.1169i 0.153164 + 0.265288i
\(303\) 0 0
\(304\) 410.896 71.8732i 1.35163 0.236425i
\(305\) −76.5190 −0.250882
\(306\) 0 0
\(307\) −17.8634 + 10.3134i −0.0581868 + 0.0335942i −0.528811 0.848739i \(-0.677362\pi\)
0.470624 + 0.882334i \(0.344029\pi\)
\(308\) −22.5947 + 39.1352i −0.0733594 + 0.127062i
\(309\) 0 0
\(310\) −29.9208 + 51.8244i −0.0965187 + 0.167175i
\(311\) 294.737 0.947707 0.473854 0.880604i \(-0.342863\pi\)
0.473854 + 0.880604i \(0.342863\pi\)
\(312\) 0 0
\(313\) 25.7267 44.5600i 0.0821940 0.142364i −0.821998 0.569490i \(-0.807141\pi\)
0.904192 + 0.427126i \(0.140474\pi\)
\(314\) −366.392 211.536i −1.16685 0.673683i
\(315\) 0 0
\(316\) 1023.24i 3.23811i
\(317\) −42.0638 24.2856i −0.132693 0.0766106i 0.432184 0.901786i \(-0.357743\pi\)
−0.564877 + 0.825175i \(0.691076\pi\)
\(318\) 0 0
\(319\) 341.703 + 197.282i 1.07117 + 0.618440i
\(320\) 19.9051 + 34.4766i 0.0622034 + 0.107739i
\(321\) 0 0
\(322\) 69.9269i 0.217164i
\(323\) 229.012 40.0585i 0.709017 0.124020i
\(324\) 0 0
\(325\) −309.680 + 178.794i −0.952862 + 0.550135i
\(326\) −773.594 + 446.634i −2.37299 + 1.37004i
\(327\) 0 0
\(328\) −53.3188 92.3509i −0.162557 0.281558i
\(329\) 9.64379 16.7035i 0.0293124 0.0507706i
\(330\) 0 0
\(331\) 351.908i 1.06317i −0.847006 0.531583i \(-0.821597\pi\)
0.847006 0.531583i \(-0.178403\pi\)
\(332\) 277.400 480.471i 0.835543 1.44720i
\(333\) 0 0
\(334\) 666.111 1.99434
\(335\) 9.38658i 0.0280196i
\(336\) 0 0
\(337\) 85.1791 49.1782i 0.252757 0.145929i −0.368269 0.929719i \(-0.620049\pi\)
0.621026 + 0.783790i \(0.286716\pi\)
\(338\) −169.915 98.1003i −0.502706 0.290237i
\(339\) 0 0
\(340\) −55.2950 95.7738i −0.162632 0.281688i
\(341\) 177.497i 0.520519i
\(342\) 0 0
\(343\) −46.6594 −0.136033
\(344\) 867.522 500.864i 2.52187 1.45600i
\(345\) 0 0
\(346\) 344.545 596.769i 0.995793 1.72476i
\(347\) −42.8027 74.1365i −0.123351 0.213650i 0.797736 0.603006i \(-0.206031\pi\)
−0.921087 + 0.389357i \(0.872697\pi\)
\(348\) 0 0
\(349\) 146.137 0.418730 0.209365 0.977838i \(-0.432860\pi\)
0.209365 + 0.977838i \(0.432860\pi\)
\(350\) 40.2267i 0.114933i
\(351\) 0 0
\(352\) −138.238 79.8115i −0.392720 0.226737i
\(353\) 517.025 1.46466 0.732330 0.680949i \(-0.238433\pi\)
0.732330 + 0.680949i \(0.238433\pi\)
\(354\) 0 0
\(355\) −45.0652 26.0184i −0.126944 0.0732913i
\(356\) 1129.83 652.309i 3.17369 1.83233i
\(357\) 0 0
\(358\) 301.578 + 522.349i 0.842397 + 1.45907i
\(359\) 112.210 + 194.354i 0.312563 + 0.541376i 0.978917 0.204261i \(-0.0654790\pi\)
−0.666353 + 0.745636i \(0.732146\pi\)
\(360\) 0 0
\(361\) −275.907 232.801i −0.764285 0.644879i
\(362\) −6.95417 −0.0192104
\(363\) 0 0
\(364\) −52.5000 + 30.3109i −0.144231 + 0.0832717i
\(365\) 60.5512 104.878i 0.165894 0.287337i
\(366\) 0 0
\(367\) 171.714 297.417i 0.467885 0.810400i −0.531442 0.847095i \(-0.678350\pi\)
0.999327 + 0.0366945i \(0.0116828\pi\)
\(368\) −910.719 −2.47478
\(369\) 0 0
\(370\) 45.8080 79.3417i 0.123805 0.214437i
\(371\) 12.5751 + 7.26024i 0.0338952 + 0.0195694i
\(372\) 0 0
\(373\) 497.699i 1.33431i 0.744918 + 0.667156i \(0.232489\pi\)
−0.744918 + 0.667156i \(0.767511\pi\)
\(374\) −418.117 241.400i −1.11796 0.645455i
\(375\) 0 0
\(376\) 553.545 + 319.589i 1.47219 + 0.849971i
\(377\) 264.655 + 458.396i 0.702003 + 1.21590i
\(378\) 0 0
\(379\) 73.4149i 0.193707i 0.995299 + 0.0968535i \(0.0308778\pi\)
−0.995299 + 0.0968535i \(0.969122\pi\)
\(380\) −58.9520 + 161.283i −0.155137 + 0.424430i
\(381\) 0 0
\(382\) 37.2831 21.5254i 0.0975998 0.0563493i
\(383\) 228.528 131.941i 0.596678 0.344492i −0.171055 0.985261i \(-0.554718\pi\)
0.767734 + 0.640769i \(0.221384\pi\)
\(384\) 0 0
\(385\) −2.84162 4.92182i −0.00738082 0.0127840i
\(386\) 501.451 868.539i 1.29910 2.25010i
\(387\) 0 0
\(388\) 813.350i 2.09626i
\(389\) −193.951 + 335.933i −0.498589 + 0.863582i −0.999999 0.00162809i \(-0.999482\pi\)
0.501409 + 0.865210i \(0.332815\pi\)
\(390\) 0 0
\(391\) −507.588 −1.29818
\(392\) 771.331i 1.96768i
\(393\) 0 0
\(394\) −938.756 + 541.991i −2.38263 + 1.37561i
\(395\) 111.447 + 64.3440i 0.282145 + 0.162896i
\(396\) 0 0
\(397\) −207.294 359.044i −0.522151 0.904392i −0.999668 0.0257696i \(-0.991796\pi\)
0.477517 0.878623i \(-0.341537\pi\)
\(398\) 542.122i 1.36212i
\(399\) 0 0
\(400\) −523.907 −1.30977
\(401\) −359.226 + 207.399i −0.895824 + 0.517204i −0.875843 0.482596i \(-0.839694\pi\)
−0.0199812 + 0.999800i \(0.506361\pi\)
\(402\) 0 0
\(403\) −119.056 + 206.212i −0.295425 + 0.511692i
\(404\) 115.130 + 199.411i 0.284975 + 0.493592i
\(405\) 0 0
\(406\) 59.5445 0.146661
\(407\) 271.743i 0.667673i
\(408\) 0 0
\(409\) −385.954 222.831i −0.943654 0.544819i −0.0525501 0.998618i \(-0.516735\pi\)
−0.891104 + 0.453799i \(0.850068\pi\)
\(410\) 25.3930 0.0619342
\(411\) 0 0
\(412\) 318.953 + 184.148i 0.774159 + 0.446961i
\(413\) −33.0133 + 19.0602i −0.0799352 + 0.0461506i
\(414\) 0 0
\(415\) 34.8872 + 60.4263i 0.0840655 + 0.145606i
\(416\) −107.068 185.446i −0.257374 0.445785i
\(417\) 0 0
\(418\) 129.170 + 738.461i 0.309020 + 1.76665i
\(419\) −352.866 −0.842162 −0.421081 0.907023i \(-0.638349\pi\)
−0.421081 + 0.907023i \(0.638349\pi\)
\(420\) 0 0
\(421\) 281.887 162.748i 0.669566 0.386574i −0.126346 0.991986i \(-0.540325\pi\)
0.795912 + 0.605412i \(0.206992\pi\)
\(422\) −485.532 + 840.966i −1.15055 + 1.99281i
\(423\) 0 0
\(424\) −240.600 + 416.731i −0.567453 + 0.982857i
\(425\) −291.999 −0.687056
\(426\) 0 0
\(427\) −17.1258 + 29.6627i −0.0401072 + 0.0694677i
\(428\) 264.049 + 152.449i 0.616937 + 0.356189i
\(429\) 0 0
\(430\) 238.536i 0.554735i
\(431\) 166.026 + 95.8551i 0.385211 + 0.222402i 0.680083 0.733135i \(-0.261944\pi\)
−0.294872 + 0.955537i \(0.595277\pi\)
\(432\) 0 0
\(433\) −253.975 146.633i −0.586548 0.338643i 0.177184 0.984178i \(-0.443301\pi\)
−0.763731 + 0.645534i \(0.776635\pi\)
\(434\) 13.3932 + 23.1977i 0.0308599 + 0.0534509i
\(435\) 0 0
\(436\) 685.652i 1.57260i
\(437\) 505.795 + 604.459i 1.15743 + 1.38320i
\(438\) 0 0
\(439\) 202.351 116.828i 0.460937 0.266122i −0.251501 0.967857i \(-0.580924\pi\)
0.712438 + 0.701735i \(0.247591\pi\)
\(440\) 163.106 94.1694i 0.370696 0.214021i
\(441\) 0 0
\(442\) −323.840 560.907i −0.732669 1.26902i
\(443\) 200.275 346.887i 0.452089 0.783040i −0.546427 0.837507i \(-0.684012\pi\)
0.998516 + 0.0544663i \(0.0173458\pi\)
\(444\) 0 0
\(445\) 164.075i 0.368708i
\(446\) −708.984 + 1228.00i −1.58965 + 2.75335i
\(447\) 0 0
\(448\) 17.8199 0.0397765
\(449\) 243.737i 0.542844i 0.962460 + 0.271422i \(0.0874939\pi\)
−0.962460 + 0.271422i \(0.912506\pi\)
\(450\) 0 0
\(451\) 65.2277 37.6593i 0.144629 0.0835017i
\(452\) −146.763 84.7334i −0.324696 0.187463i
\(453\) 0 0
\(454\) 598.487 + 1036.61i 1.31825 + 2.28328i
\(455\) 7.62408i 0.0167562i
\(456\) 0 0
\(457\) 4.08902 0.00894753 0.00447377 0.999990i \(-0.498576\pi\)
0.00447377 + 0.999990i \(0.498576\pi\)
\(458\) 680.501 392.887i 1.48581 0.857833i
\(459\) 0 0
\(460\) 187.455 324.682i 0.407512 0.705831i
\(461\) −391.718 678.476i −0.849715 1.47175i −0.881463 0.472253i \(-0.843441\pi\)
0.0317484 0.999496i \(-0.489892\pi\)
\(462\) 0 0
\(463\) −219.978 −0.475115 −0.237558 0.971373i \(-0.576347\pi\)
−0.237558 + 0.971373i \(0.576347\pi\)
\(464\) 775.500i 1.67134i
\(465\) 0 0
\(466\) 714.612 + 412.581i 1.53350 + 0.885368i
\(467\) 445.983 0.954995 0.477498 0.878633i \(-0.341544\pi\)
0.477498 + 0.878633i \(0.341544\pi\)
\(468\) 0 0
\(469\) 3.63872 + 2.10082i 0.00775847 + 0.00447935i
\(470\) −131.812 + 76.1019i −0.280452 + 0.161919i
\(471\) 0 0
\(472\) −631.643 1094.04i −1.33823 2.31788i
\(473\) 353.762 + 612.734i 0.747911 + 1.29542i
\(474\) 0 0
\(475\) 290.967 + 347.725i 0.612563 + 0.732053i
\(476\) −49.5025 −0.103997
\(477\) 0 0
\(478\) 987.826 570.321i 2.06658 1.19314i
\(479\) −315.684 + 546.781i −0.659048 + 1.14150i 0.321815 + 0.946803i \(0.395707\pi\)
−0.980862 + 0.194702i \(0.937626\pi\)
\(480\) 0 0
\(481\) 182.272 315.705i 0.378944 0.656351i
\(482\) −823.260 −1.70801
\(483\) 0 0
\(484\) 15.9891 27.6940i 0.0330354 0.0572190i
\(485\) −88.5864 51.1454i −0.182652 0.105454i
\(486\) 0 0
\(487\) 792.723i 1.62777i −0.581027 0.813884i \(-0.697349\pi\)
0.581027 0.813884i \(-0.302651\pi\)
\(488\) −983.004 567.538i −2.01435 1.16299i
\(489\) 0 0
\(490\) 159.065 + 91.8363i 0.324623 + 0.187421i
\(491\) 67.9055 + 117.616i 0.138300 + 0.239543i 0.926853 0.375424i \(-0.122503\pi\)
−0.788553 + 0.614967i \(0.789169\pi\)
\(492\) 0 0
\(493\) 432.224i 0.876722i
\(494\) −345.257 + 944.568i −0.698901 + 1.91208i
\(495\) 0 0
\(496\) −302.124 + 174.431i −0.609120 + 0.351676i
\(497\) −20.1722 + 11.6464i −0.0405878 + 0.0234334i
\(498\) 0 0
\(499\) −236.577 409.764i −0.474102 0.821170i 0.525458 0.850820i \(-0.323894\pi\)
−0.999560 + 0.0296501i \(0.990561\pi\)
\(500\) 220.811 382.455i 0.441621 0.764910i
\(501\) 0 0
\(502\) 946.955i 1.88636i
\(503\) −359.444 + 622.575i −0.714601 + 1.23772i 0.248513 + 0.968629i \(0.420058\pi\)
−0.963113 + 0.269096i \(0.913275\pi\)
\(504\) 0 0
\(505\) −28.9586 −0.0573438
\(506\) 1636.74i 3.23466i
\(507\) 0 0
\(508\) −302.863 + 174.858i −0.596188 + 0.344209i
\(509\) −578.570 334.037i −1.13668 0.656262i −0.191073 0.981576i \(-0.561197\pi\)
−0.945606 + 0.325314i \(0.894530\pi\)
\(510\) 0 0
\(511\) −27.1040 46.9456i −0.0530412 0.0918700i
\(512\) 1075.10i 2.09981i
\(513\) 0 0
\(514\) 1690.92 3.28973
\(515\) −40.1131 + 23.1593i −0.0778895 + 0.0449695i
\(516\) 0 0
\(517\) −225.727 + 390.970i −0.436609 + 0.756228i
\(518\) −20.5046 35.5151i −0.0395842 0.0685619i
\(519\) 0 0
\(520\) 252.657 0.485880
\(521\) 772.856i 1.48341i −0.670727 0.741704i \(-0.734018\pi\)
0.670727 0.741704i \(-0.265982\pi\)
\(522\) 0 0
\(523\) −599.415 346.072i −1.14611 0.661706i −0.198172 0.980167i \(-0.563501\pi\)
−0.947936 + 0.318461i \(0.896834\pi\)
\(524\) 1745.33 3.33078
\(525\) 0 0
\(526\) −818.679 472.665i −1.55642 0.898602i
\(527\) −168.388 + 97.2190i −0.319522 + 0.184476i
\(528\) 0 0
\(529\) −595.886 1032.11i −1.12644 1.95105i
\(530\) −57.2927 99.2338i −0.108099 0.187234i
\(531\) 0 0
\(532\) 49.3276 + 58.9498i 0.0927211 + 0.110808i
\(533\) 101.040 0.189569
\(534\) 0 0
\(535\) −33.2081 + 19.1727i −0.0620712 + 0.0358368i
\(536\) −69.6197 + 120.585i −0.129888 + 0.224972i
\(537\) 0 0
\(538\) 34.1703 59.1847i 0.0635135 0.110009i
\(539\) 544.793 1.01075
\(540\) 0 0
\(541\) −488.635 + 846.340i −0.903206 + 1.56440i −0.0798991 + 0.996803i \(0.525460\pi\)
−0.823307 + 0.567596i \(0.807874\pi\)
\(542\) −718.875 415.043i −1.32634 0.765762i
\(543\) 0 0
\(544\) 174.858i 0.321431i
\(545\) −74.6781 43.1154i −0.137024 0.0791109i
\(546\) 0 0
\(547\) 166.215 + 95.9642i 0.303866 + 0.175437i 0.644178 0.764875i \(-0.277199\pi\)
−0.340312 + 0.940312i \(0.610533\pi\)
\(548\) 764.211 + 1323.65i 1.39454 + 2.41542i
\(549\) 0 0
\(550\) 941.563i 1.71193i
\(551\) 514.711 430.697i 0.934141 0.781664i
\(552\) 0 0
\(553\) 49.8861 28.8018i 0.0902100 0.0520828i
\(554\) 329.265 190.101i 0.594341 0.343143i
\(555\) 0 0
\(556\) −303.930 526.422i −0.546636 0.946801i
\(557\) 161.531 279.780i 0.290002 0.502299i −0.683808 0.729662i \(-0.739677\pi\)
0.973810 + 0.227364i \(0.0730106\pi\)
\(558\) 0 0
\(559\) 949.147i 1.69794i
\(560\) 5.58508 9.67363i 0.00997335 0.0172743i
\(561\) 0 0
\(562\) −1488.47 −2.64852
\(563\) 328.512i 0.583503i −0.956494 0.291752i \(-0.905762\pi\)
0.956494 0.291752i \(-0.0942381\pi\)
\(564\) 0 0
\(565\) 18.4576 10.6565i 0.0326683 0.0188610i
\(566\) 64.1012 + 37.0088i 0.113253 + 0.0653866i
\(567\) 0 0
\(568\) −385.954 668.493i −0.679497 1.17692i
\(569\) 1069.96i 1.88042i −0.340590 0.940212i \(-0.610627\pi\)
0.340590 0.940212i \(-0.389373\pi\)
\(570\) 0 0
\(571\) 226.109 0.395987 0.197994 0.980203i \(-0.436557\pi\)
0.197994 + 0.980203i \(0.436557\pi\)
\(572\) 1228.84 709.470i 2.14832 1.24033i
\(573\) 0 0
\(574\) 5.68323 9.84365i 0.00990110 0.0171492i
\(575\) −494.952 857.282i −0.860786 1.49093i
\(576\) 0 0
\(577\) 563.905 0.977305 0.488652 0.872479i \(-0.337489\pi\)
0.488652 + 0.872479i \(0.337489\pi\)
\(578\) 491.957i 0.851136i
\(579\) 0 0
\(580\) −276.475 159.623i −0.476681 0.275212i
\(581\) 31.2325 0.0537564
\(582\) 0 0
\(583\) −294.339 169.936i −0.504869 0.291486i
\(584\) 1555.75 898.211i 2.66395 1.53803i
\(585\) 0 0
\(586\) 544.748 + 943.532i 0.929605 + 1.61012i
\(587\) 138.379 + 239.680i 0.235740 + 0.408313i 0.959487 0.281752i \(-0.0909154\pi\)
−0.723748 + 0.690065i \(0.757582\pi\)
\(588\) 0 0
\(589\) 283.566 + 103.649i 0.481437 + 0.175974i
\(590\) 300.819 0.509863
\(591\) 0 0
\(592\) 462.543 267.050i 0.781323 0.451097i
\(593\) −130.080 + 225.306i −0.219360 + 0.379942i −0.954612 0.297851i \(-0.903730\pi\)
0.735253 + 0.677793i \(0.237063\pi\)
\(594\) 0 0
\(595\) 3.11283 5.39159i 0.00523166 0.00906149i
\(596\) −1848.65 −3.10176
\(597\) 0 0
\(598\) 1097.85 1901.53i 1.83587 3.17981i
\(599\) −660.820 381.524i −1.10320 0.636936i −0.166144 0.986102i \(-0.553132\pi\)
−0.937061 + 0.349166i \(0.886465\pi\)
\(600\) 0 0
\(601\) 628.679i 1.04606i −0.852316 0.523028i \(-0.824802\pi\)
0.852316 0.523028i \(-0.175198\pi\)
\(602\) 92.4688 + 53.3869i 0.153603 + 0.0886826i
\(603\) 0 0
\(604\) −192.273 111.009i −0.318333 0.183790i
\(605\) 2.01087 + 3.48293i 0.00332375 + 0.00575691i
\(606\) 0 0
\(607\) 56.3825i 0.0928871i 0.998921 + 0.0464436i \(0.0147888\pi\)
−0.998921 + 0.0464436i \(0.985211\pi\)
\(608\) −208.229 + 174.241i −0.342482 + 0.286580i
\(609\) 0 0
\(610\) 234.077 135.144i 0.383733 0.221548i
\(611\) −524.488 + 302.813i −0.858410 + 0.495603i
\(612\) 0 0
\(613\) 14.0673 + 24.3653i 0.0229483 + 0.0397476i 0.877271 0.479995i \(-0.159361\pi\)
−0.854323 + 0.519742i \(0.826028\pi\)
\(614\) 36.4302 63.0989i 0.0593325 0.102767i
\(615\) 0 0
\(616\) 84.3045i 0.136858i
\(617\) 66.9966 116.042i 0.108584 0.188074i −0.806613 0.591081i \(-0.798702\pi\)
0.915197 + 0.403007i \(0.132035\pi\)
\(618\) 0 0
\(619\) 586.929 0.948188 0.474094 0.880474i \(-0.342776\pi\)
0.474094 + 0.880474i \(0.342776\pi\)
\(620\) 143.614i 0.231636i
\(621\) 0 0
\(622\) −901.622 + 520.551i −1.44955 + 0.836900i
\(623\) 63.6040 + 36.7218i 0.102093 + 0.0589434i
\(624\) 0 0
\(625\) −270.522 468.557i −0.432835 0.749692i
\(626\) 181.749i 0.290335i
\(627\) 0 0
\(628\) 1015.34 1.61678
\(629\) 257.798 148.840i 0.409854 0.236629i
\(630\) 0 0
\(631\) −163.649 + 283.448i −0.259348 + 0.449204i −0.966067 0.258290i \(-0.916841\pi\)
0.706719 + 0.707494i \(0.250174\pi\)
\(632\) 954.473 + 1653.19i 1.51024 + 2.61581i
\(633\) 0 0
\(634\) 171.568 0.270612
\(635\) 43.9820i 0.0692630i
\(636\) 0 0
\(637\) 632.929 + 365.421i 0.993608 + 0.573660i
\(638\) −1393.72 −2.18452
\(639\) 0 0
\(640\) −174.558 100.781i −0.272748 0.157471i
\(641\) −234.307 + 135.277i −0.365534 + 0.211041i −0.671506 0.741000i \(-0.734352\pi\)
0.305972 + 0.952041i \(0.401019\pi\)
\(642\) 0 0
\(643\) −402.896 697.836i −0.626588 1.08528i −0.988232 0.152966i \(-0.951118\pi\)
0.361644 0.932316i \(-0.382216\pi\)
\(644\) −83.9091 145.335i −0.130294 0.225675i
\(645\) 0 0
\(646\) −629.816 + 527.013i −0.974947 + 0.815810i
\(647\) −590.952 −0.913372 −0.456686 0.889628i \(-0.650964\pi\)
−0.456686 + 0.889628i \(0.650964\pi\)
\(648\) 0 0
\(649\) 772.723 446.132i 1.19064 0.687414i
\(650\) 631.556 1093.89i 0.971624 1.68290i
\(651\) 0 0
\(652\) 1071.88 1856.55i 1.64399 2.84748i
\(653\) 990.945 1.51753 0.758763 0.651366i \(-0.225804\pi\)
0.758763 + 0.651366i \(0.225804\pi\)
\(654\) 0 0
\(655\) −109.751 + 190.093i −0.167558 + 0.290219i
\(656\) 128.202 + 74.0177i 0.195430 + 0.112832i
\(657\) 0 0
\(658\) 68.1297i 0.103541i
\(659\) −446.552 257.817i −0.677620 0.391224i 0.121338 0.992611i \(-0.461282\pi\)
−0.798958 + 0.601387i \(0.794615\pi\)
\(660\) 0 0
\(661\) 1142.22 + 659.462i 1.72802 + 0.997673i 0.898100 + 0.439791i \(0.144948\pi\)
0.829921 + 0.557882i \(0.188386\pi\)
\(662\) 621.525 + 1076.51i 0.938859 + 1.62615i
\(663\) 0 0
\(664\) 1035.03i 1.55877i
\(665\) −9.52238 + 1.66564i −0.0143194 + 0.00250472i
\(666\) 0 0
\(667\) −1268.97 + 732.640i −1.90250 + 1.09841i
\(668\) −1384.43 + 799.303i −2.07250 + 1.19656i
\(669\) 0 0
\(670\) −16.5782 28.7142i −0.0247435 0.0428570i
\(671\) 400.853 694.299i 0.597397 1.03472i
\(672\) 0 0
\(673\) 569.028i 0.845510i −0.906244 0.422755i \(-0.861063\pi\)
0.906244 0.422755i \(-0.138937\pi\)
\(674\) −173.713 + 300.879i −0.257734 + 0.446408i
\(675\) 0 0
\(676\) 470.863 0.696543
\(677\) 909.084i 1.34281i 0.741090 + 0.671406i \(0.234309\pi\)
−0.741090 + 0.671406i \(0.765691\pi\)
\(678\) 0 0
\(679\) −39.6532 + 22.8938i −0.0583994 + 0.0337169i
\(680\) 178.674 + 103.157i 0.262756 + 0.151702i
\(681\) 0 0
\(682\) −313.487 542.976i −0.459658 0.796152i
\(683\) 85.6567i 0.125412i 0.998032 + 0.0627062i \(0.0199731\pi\)
−0.998032 + 0.0627062i \(0.980027\pi\)
\(684\) 0 0
\(685\) −192.222 −0.280615
\(686\) 142.735 82.4078i 0.208068 0.120128i
\(687\) 0 0
\(688\) −695.304 + 1204.30i −1.01062 + 1.75044i
\(689\) −227.971 394.856i −0.330872 0.573086i
\(690\) 0 0
\(691\) −12.0911 −0.0174980 −0.00874899 0.999962i \(-0.502785\pi\)
−0.00874899 + 0.999962i \(0.502785\pi\)
\(692\) 1653.75i 2.38981i
\(693\) 0 0
\(694\) 261.873 + 151.193i 0.377339 + 0.217857i
\(695\) 76.4473 0.109996
\(696\) 0 0
\(697\) 71.4534 + 41.2536i 0.102516 + 0.0591874i
\(698\) −447.042 + 258.100i −0.640462 + 0.369771i
\(699\) 0 0
\(700\) −48.2702 83.6064i −0.0689574 0.119438i
\(701\) 13.8355 + 23.9638i 0.0197368 + 0.0341851i 0.875725 0.482810i \(-0.160384\pi\)
−0.855988 + 0.516995i \(0.827051\pi\)
\(702\) 0 0
\(703\) −434.132 158.683i −0.617543 0.225723i
\(704\) −417.100 −0.592471
\(705\) 0 0
\(706\) −1581.62 + 913.147i −2.24025 + 1.29341i
\(707\) −6.48125 + 11.2258i −0.00916725 + 0.0158781i
\(708\) 0 0
\(709\) −330.042 + 571.650i −0.465504 + 0.806277i −0.999224 0.0393844i \(-0.987460\pi\)
0.533720 + 0.845661i \(0.320794\pi\)
\(710\) 183.810 0.258888
\(711\) 0 0
\(712\) −1216.94 + 2107.80i −1.70918 + 2.96039i
\(713\) −570.853 329.582i −0.800635 0.462247i
\(714\) 0 0
\(715\) 178.453i 0.249584i
\(716\) −1253.59 723.760i −1.75082 1.01084i
\(717\) 0 0
\(718\) −686.519 396.362i −0.956154 0.552036i
\(719\) 216.159 + 374.398i 0.300638 + 0.520720i 0.976281 0.216509i \(-0.0694671\pi\)
−0.675643 + 0.737229i \(0.736134\pi\)
\(720\) 0 0
\(721\) 20.7332i 0.0287562i
\(722\) 1255.18 + 224.861i 1.73848 + 0.311442i
\(723\) 0 0
\(724\) 14.4534 8.34468i 0.0199633 0.0115258i
\(725\) −729.997 + 421.464i −1.00689 + 0.581330i
\(726\) 0 0
\(727\) 517.896 + 897.022i 0.712374 + 1.23387i 0.963964 + 0.266034i \(0.0857134\pi\)
−0.251590 + 0.967834i \(0.580953\pi\)
\(728\) 56.5474 97.9430i 0.0776751 0.134537i
\(729\) 0 0
\(730\) 427.772i 0.585989i
\(731\) −387.527 + 671.216i −0.530132 + 0.918216i
\(732\) 0 0
\(733\) 416.182 0.567779 0.283890 0.958857i \(-0.408375\pi\)
0.283890 + 0.958857i \(0.408375\pi\)
\(734\) 1213.09i 1.65272i
\(735\) 0 0
\(736\) 513.368 296.393i 0.697511 0.402708i
\(737\) −85.1695 49.1726i −0.115562 0.0667200i
\(738\) 0 0
\(739\) 330.536 + 572.505i 0.447274 + 0.774702i 0.998208 0.0598475i \(-0.0190614\pi\)
−0.550933 + 0.834549i \(0.685728\pi\)
\(740\) 219.870i 0.297122i
\(741\) 0 0
\(742\) −51.2909 −0.0691252
\(743\) −99.0651 + 57.1953i −0.133331 + 0.0769788i −0.565182 0.824966i \(-0.691194\pi\)
0.431851 + 0.901945i \(0.357861\pi\)
\(744\) 0 0
\(745\) 116.247 201.346i 0.156037 0.270264i
\(746\) −879.013 1522.50i −1.17830 2.04088i
\(747\) 0 0
\(748\) 1158.68 1.54903
\(749\) 17.1642i 0.0229162i
\(750\) 0 0
\(751\) −118.013 68.1348i −0.157141 0.0907254i 0.419367 0.907817i \(-0.362252\pi\)
−0.576509 + 0.817091i \(0.695585\pi\)
\(752\) −887.312 −1.17994
\(753\) 0 0
\(754\) −1619.20 934.844i −2.14748 1.23985i
\(755\) 24.1812 13.9610i 0.0320281 0.0184914i
\(756\) 0 0
\(757\) 101.860 + 176.427i 0.134558 + 0.233061i 0.925428 0.378922i \(-0.123705\pi\)
−0.790871 + 0.611983i \(0.790372\pi\)
\(758\) −129.662 224.582i −0.171058 0.296282i
\(759\) 0 0
\(760\) −55.1983 315.566i −0.0726293 0.415218i
\(761\) 976.891 1.28369 0.641847 0.766833i \(-0.278168\pi\)
0.641847 + 0.766833i \(0.278168\pi\)
\(762\) 0 0
\(763\) −33.4275 + 19.2994i −0.0438107 + 0.0252941i
\(764\) −51.6590 + 89.4761i −0.0676166 + 0.117115i
\(765\) 0 0
\(766\) −466.055 + 807.232i −0.608427 + 1.05383i
\(767\) 1196.98 1.56059
\(768\) 0 0
\(769\) 357.908 619.915i 0.465420 0.806131i −0.533801 0.845610i \(-0.679237\pi\)
0.999220 + 0.0394796i \(0.0125700\pi\)
\(770\) 17.3854 + 10.0375i 0.0225785 + 0.0130357i
\(771\) 0 0
\(772\) 2406.87i 3.11771i
\(773\) 320.373 + 184.967i 0.414454 + 0.239285i 0.692702 0.721224i \(-0.256420\pi\)
−0.278248 + 0.960509i \(0.589754\pi\)
\(774\) 0 0
\(775\) −328.393 189.598i −0.423733 0.244642i
\(776\) −758.686 1314.08i −0.977688 1.69340i
\(777\) 0 0
\(778\) 1370.19i 1.76117i
\(779\) −22.0743 126.198i −0.0283367 0.162000i
\(780\) 0 0
\(781\) 472.158 272.601i 0.604556 0.349041i
\(782\) 1552.75 896.479i 1.98561 1.14639i
\(783\) 0 0
\(784\) 535.384 + 927.312i 0.682888 + 1.18280i
\(785\) −63.8468 + 110.586i −0.0813335 + 0.140874i