Properties

Label 171.3.p.f.145.4
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 145.4
Root \(3.05907 - 1.76616i\) of defining polynomial
Character \(\chi\) \(=\) 171.145
Dual form 171.3.p.f.46.4

$q$-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 \(-0.322134\pi\)
0.999381 0.0351770i \(-0.0111995\pi\)
\(3\) 0 0
\(4\) 4.23861 7.34149i 1.05965 1.83537i
\(5\) −0.533068 0.923301i −0.106614 0.184660i 0.807783 0.589480i \(-0.200667\pi\)
−0.914396 + 0.404820i \(0.867334\pi\)
\(6\) 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 \(-0.330483\pi\)
0.507734 + 0.861514i \(0.330483\pi\)
\(12\) 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 0.987942 0.154823i \(-0.0494806\pi\)
−0.628051 + 0.778172i \(0.716147\pi\)
\(18\) 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 \(0.524411\pi\)
−0.825173 + 0.564880i \(0.808923\pi\)
\(24\) 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 0.924004 0.382383i \(-0.124897\pi\)
0.130848 + 0.991402i \(0.458230\pi\)
\(30\) 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 −0.427094 0.904207i \(-0.640463\pi\)
0.569520 + 0.821978i \(0.307129\pi\)
\(42\) 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 −0.996869 0.0790699i \(-0.974805\pi\)
0.566911 + 0.823779i \(0.308138\pi\)
\(48\) 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 0.230369 0.973103i \(-0.426007\pi\)
−0.727548 + 0.686057i \(0.759340\pi\)
\(54\) 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 0.218232 0.975897i \(-0.429971\pi\)
0.954267 + 0.298954i \(0.0966378\pi\)
\(60\) 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 −0.171862 0.985121i \(-0.554978\pi\)
0.767209 + 0.641397i \(0.221645\pi\)
\(72\) 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 \(-0.628997\pi\)
−0.394253 + 0.919002i \(0.628997\pi\)
\(84\) 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 −0.497517 0.867454i \(-0.665755\pi\)
−0.999996 + 0.00286509i \(0.999088\pi\)
\(90\) 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 −0.790927 0.611910i \(-0.790401\pi\)
0.925393 + 0.379008i \(0.123735\pi\)
\(102\) 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 \(-0.946247\pi\)
0.985775 0.168069i \(-0.0537530\pi\)
\(108\) 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 \(0.0281930\pi\)
−0.996080 + 0.0884550i \(0.971807\pi\)
\(114\) 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 \(-0.878908\pi\)
0.142689 0.989768i \(-0.454425\pi\)
\(132\) 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 \(-0.604728\pi\)
0.981128 0.193361i \(-0.0619389\pi\)
\(138\) 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 \(0.0946464\pi\)
−0.224333 + 0.974513i \(0.572020\pi\)
\(150\) 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 0.901640 0.432487i \(-0.142364\pi\)
0.0762758 + 0.997087i \(0.475697\pi\)
\(168\) 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 0.0753332 0.997158i \(-0.475998\pi\)
0.901231 + 0.433339i \(0.142665\pi\)
\(174\) 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 \(0.158264\pi\)
−0.878921 + 0.476966i \(0.841736\pi\)
\(180\) 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 \(-0.489843\pi\)
0.0319050 + 0.999491i \(0.489843\pi\)
\(192\) 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 \(-0.784209\pi\)
−0.778874 + 0.627181i \(0.784209\pi\)
\(198\) 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 \(0.268218\pi\)
−0.665501 + 0.746397i \(0.731782\pi\)
\(228\) 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 \(0.000476716\pi\)
−0.498702 + 0.866773i \(0.666190\pi\)
\(234\) 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 \(-0.263903\pi\)
0.675558 + 0.737307i \(0.263903\pi\)
\(240\) 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 \(0.345990\pi\)
−0.999210 + 0.0397521i \(0.987343\pi\)
\(252\) 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 \(0.0480133\pi\)
0.624458 + 0.781059i \(0.285320\pi\)
\(258\) 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 \(-0.996760\pi\)
0.491158 0.871070i \(-0.336574\pi\)
\(264\) 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 −0.468533 0.883446i \(-0.655217\pi\)
0.530820 + 0.847485i \(0.321884\pi\)
\(270\) 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 −0.318513 0.947919i \(-0.603183\pi\)
−0.980178 + 0.198119i \(0.936517\pi\)
\(282\) 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 \(0.176437\pi\)
−0.850272 + 0.526344i \(0.823563\pi\)
\(294\) 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 \(-0.657137\pi\)
−0.473854 + 0.880604i \(0.657137\pi\)
\(312\) 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 0.564877 0.825175i \(-0.308924\pi\)
−0.432184 + 0.901786i \(0.642257\pi\)
\(318\) 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 0.921087 0.389357i \(-0.127303\pi\)
−0.797736 + 0.603006i \(0.793969\pi\)
\(348\) 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 \(-0.761567\pi\)
−0.732330 + 0.680949i \(0.761567\pi\)
\(354\) 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 0.666353 0.745636i \(-0.267854\pi\)
−0.978917 + 0.204261i \(0.934521\pi\)
\(360\) 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 −0.767734 0.640769i \(-0.778616\pi\)
0.171055 + 0.985261i \(0.445282\pi\)
\(384\) 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 −0.501409 0.865210i \(-0.667185\pi\)
0.999999 + 0.00162809i \(0.000518236\pi\)
\(390\) 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 0.0199812 0.999800i \(-0.493639\pi\)
0.875843 + 0.482596i \(0.160306\pi\)
\(402\) 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 \(-0.361651\pi\)
0.421081 + 0.907023i \(0.361651\pi\)
\(420\) 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 0.294872 0.955537i \(-0.404723\pi\)
−0.680083 + 0.733135i \(0.738056\pi\)
\(432\) 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 −0.998516 0.0544663i \(-0.982654\pi\)
0.546427 + 0.837507i \(0.315988\pi\)
\(444\) 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 \(-0.912506\pi\)
0.962460 0.271422i \(-0.0874939\pi\)
\(450\) 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 \(0.156559\pi\)
−0.0317484 + 0.999496i \(0.510108\pi\)
\(462\) 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 \(-0.658456\pi\)
−0.477498 + 0.878633i \(0.658456\pi\)
\(468\) 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 \(-0.604293\pi\)
0.980862 0.194702i \(-0.0623739\pi\)
\(480\) 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 0.788553 0.614967i \(-0.210831\pi\)
−0.926853 + 0.375424i \(0.877497\pi\)
\(492\) 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 \(-0.579942\pi\)
0.963113 0.269096i \(-0.0867249\pi\)
\(504\) 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 0.945606 0.325314i \(-0.105470\pi\)
0.191073 + 0.981576i \(0.438803\pi\)
\(510\) 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 \(0.265982\pi\)
−0.670727 + 0.741704i \(0.734018\pi\)
\(522\) 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 −0.973810 0.227364i \(-0.926989\pi\)
0.683808 + 0.729662i \(0.260323\pi\)
\(558\) 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 \(0.0942381\pi\)
−0.956494 + 0.291752i \(0.905762\pi\)
\(564\) 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 \(0.389373\pi\)
−0.340590 + 0.940212i \(0.610627\pi\)
\(570\) 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 0.723748 0.690065i \(-0.242418\pi\)
−0.959487 + 0.281752i \(0.909085\pi\)
\(588\) 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 −0.735253 0.677793i \(-0.762937\pi\)
0.954612 + 0.297851i \(0.0962699\pi\)
\(594\) 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 0.937061 0.349166i \(-0.113535\pi\)
0.166144 + 0.986102i \(0.446868\pi\)
\(600\) 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 −0.915197 0.403007i \(-0.867965\pi\)
0.806613 + 0.591081i \(0.201298\pi\)
\(618\) 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 −0.305972 0.952041i \(-0.598981\pi\)
0.671506 + 0.741000i \(0.265648\pi\)
\(642\) 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 \(-0.349036\pi\)
0.456686 + 0.889628i \(0.349036\pi\)
\(648\) 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 \(-0.774196\pi\)
−0.758763 + 0.651366i \(0.774196\pi\)
\(654\) 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 0.798958 0.601387i \(-0.205385\pi\)
−0.121338 + 0.992611i \(0.538718\pi\)
\(660\) 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 \(-0.765691\pi\)
0.741090 0.671406i \(-0.234309\pi\)
\(678\) 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 \(-0.980027\pi\)
0.998032 0.0627062i \(-0.0199731\pi\)
\(684\) 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 0.855988 0.516995i \(-0.172949\pi\)
−0.875725 + 0.482810i \(0.839616\pi\)
\(702\) 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 0.675643 0.737229i \(-0.263866\pi\)
−0.976281 + 0.216509i \(0.930533\pi\)
\(720\) 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 −0.431851 0.901945i \(-0.642139\pi\)
0.565182 + 0.824966i \(0.308806\pi\)
\(744\) 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 \(-0.721832\pi\)
−0.641847 + 0.766833i \(0.721832\pi\)
\(762\) 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 0.278248 0.960509i \(-0.410246\pi\)
−0.692702 + 0.721224i \(0.743580\pi\)
\(774\) 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