Properties

Label 400.2.l.f.101.3
Level $400$
Weight $2$
Character 400.101
Analytic conductor $3.194$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.19401608085\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.4767670494822400.1
Defining polynomial: \(x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 101.3
Root \(0.719139 - 1.21772i\) of defining polynomial
Character \(\chi\) \(=\) 400.101
Dual form 400.2.l.f.301.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.719139 + 1.21772i) q^{2} +(1.66783 - 1.66783i) q^{3} +(-0.965679 - 1.75142i) q^{4} +(0.831547 + 3.23035i) q^{6} -1.87372i q^{7} +(2.82719 + 0.0835873i) q^{8} -2.56332i q^{9} +O(q^{10})\) \(q+(-0.719139 + 1.21772i) q^{2} +(1.66783 - 1.66783i) q^{3} +(-0.965679 - 1.75142i) q^{4} +(0.831547 + 3.23035i) q^{6} -1.87372i q^{7} +(2.82719 + 0.0835873i) q^{8} -2.56332i q^{9} +(-3.29695 - 3.29695i) q^{11} +(-4.53166 - 1.31048i) q^{12} +(1.90022 - 1.90022i) q^{13} +(2.28166 + 1.34746i) q^{14} +(-2.13493 + 3.38261i) q^{16} +2.57148 q^{17} +(3.12140 + 1.84338i) q^{18} +(-5.76636 + 5.76636i) q^{19} +(-3.12504 - 3.12504i) q^{21} +(6.38572 - 1.64379i) q^{22} -7.58574i q^{23} +(4.85469 - 4.57587i) q^{24} +(0.947414 + 3.68046i) q^{26} +(0.728312 + 0.728312i) q^{27} +(-3.28166 + 1.80941i) q^{28} +(6.45786 - 6.45786i) q^{29} -0.799135 q^{31} +(-2.58376 - 5.03231i) q^{32} -10.9975 q^{33} +(-1.84925 + 3.13134i) q^{34} +(-4.48944 + 2.47534i) q^{36} +(2.69652 + 2.69652i) q^{37} +(-2.87499 - 11.1686i) q^{38} -6.33850i q^{39} +0.946984i q^{41} +(6.05276 - 1.55808i) q^{42} +(0.829986 + 0.829986i) q^{43} +(-2.59054 + 8.95813i) q^{44} +(9.23730 + 5.45520i) q^{46} +1.52421 q^{47} +(2.08093 + 9.20233i) q^{48} +3.48919 q^{49} +(4.28879 - 4.28879i) q^{51} +(-5.16309 - 1.49308i) q^{52} +(6.97225 + 6.97225i) q^{53} +(-1.41064 + 0.363122i) q^{54} +(0.156619 - 5.29735i) q^{56} +19.2346i q^{57} +(3.21976 + 12.5080i) q^{58} +(6.84418 + 6.84418i) q^{59} +(-6.87247 + 6.87247i) q^{61} +(0.574689 - 0.973121i) q^{62} -4.80293 q^{63} +(7.98603 + 0.472635i) q^{64} +(7.90874 - 13.3919i) q^{66} +(-3.73647 + 3.73647i) q^{67} +(-2.48322 - 4.50373i) q^{68} +(-12.6517 - 12.6517i) q^{69} -9.34417i q^{71} +(0.214261 - 7.24699i) q^{72} -0.886316i q^{73} +(-5.22277 + 1.34443i) q^{74} +(15.6678 + 4.53086i) q^{76} +(-6.17755 + 6.17755i) q^{77} +(7.71851 + 4.55826i) q^{78} +3.07575 q^{79} +10.1194 q^{81} +(-1.15316 - 0.681013i) q^{82} +(-0.989393 + 0.989393i) q^{83} +(-2.45547 + 8.49104i) q^{84} +(-1.60756 + 0.413814i) q^{86} -21.5412i q^{87} +(-9.04553 - 9.59670i) q^{88} +10.0942i q^{89} +(-3.56048 - 3.56048i) q^{91} +(-13.2858 + 7.32539i) q^{92} +(-1.33282 + 1.33282i) q^{93} +(-1.09612 + 1.85606i) q^{94} +(-12.7023 - 4.08377i) q^{96} -7.16829 q^{97} +(-2.50921 + 4.24885i) q^{98} +(-8.45113 + 8.45113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} - 2q^{3} + 2q^{4} + 6q^{6} + 8q^{8} + O(q^{10}) \) \( 12q - 4q^{2} - 2q^{3} + 2q^{4} + 6q^{6} + 8q^{8} - 2q^{11} - 8q^{12} + 4q^{13} + 14q^{14} + 2q^{16} + 8q^{17} - 18q^{18} - 14q^{19} - 20q^{21} - 2q^{22} - 14q^{24} - 16q^{26} + 10q^{27} - 26q^{28} - 4q^{31} + 16q^{32} - 28q^{33} - 6q^{34} + 2q^{36} - 8q^{37} - 10q^{38} - 10q^{42} - 44q^{44} - 10q^{46} - 8q^{47} + 28q^{48} + 4q^{49} + 10q^{51} + 12q^{52} + 16q^{53} + 10q^{54} + 6q^{56} + 60q^{58} + 20q^{59} + 4q^{61} + 18q^{62} + 8q^{63} + 38q^{64} + 32q^{66} - 50q^{67} + 60q^{68} + 14q^{72} + 10q^{74} + 60q^{76} + 8q^{77} - 4q^{78} + 12q^{79} - 8q^{81} - 42q^{82} + 2q^{83} + 34q^{84} + 6q^{86} - 30q^{88} + 2q^{92} + 44q^{93} + 32q^{94} - 34q^{96} - 64q^{98} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.719139 + 1.21772i −0.508508 + 0.861057i
\(3\) 1.66783 1.66783i 0.962922 0.962922i −0.0364144 0.999337i \(-0.511594\pi\)
0.999337 + 0.0364144i \(0.0115936\pi\)
\(4\) −0.965679 1.75142i −0.482839 0.875709i
\(5\) 0 0
\(6\) 0.831547 + 3.23035i 0.339478 + 1.31879i
\(7\) 1.87372i 0.708198i −0.935208 0.354099i \(-0.884788\pi\)
0.935208 0.354099i \(-0.115212\pi\)
\(8\) 2.82719 + 0.0835873i 0.999563 + 0.0295526i
\(9\) 2.56332i 0.854439i
\(10\) 0 0
\(11\) −3.29695 3.29695i −0.994068 0.994068i 0.00591443 0.999983i \(-0.498117\pi\)
−0.999983 + 0.00591443i \(0.998117\pi\)
\(12\) −4.53166 1.31048i −1.30818 0.378303i
\(13\) 1.90022 1.90022i 0.527027 0.527027i −0.392658 0.919685i \(-0.628444\pi\)
0.919685 + 0.392658i \(0.128444\pi\)
\(14\) 2.28166 + 1.34746i 0.609799 + 0.360124i
\(15\) 0 0
\(16\) −2.13493 + 3.38261i −0.533732 + 0.845653i
\(17\) 2.57148 0.623675 0.311838 0.950135i \(-0.399056\pi\)
0.311838 + 0.950135i \(0.399056\pi\)
\(18\) 3.12140 + 1.84338i 0.735721 + 0.434489i
\(19\) −5.76636 + 5.76636i −1.32289 + 1.32289i −0.411472 + 0.911422i \(0.634985\pi\)
−0.911422 + 0.411472i \(0.865015\pi\)
\(20\) 0 0
\(21\) −3.12504 3.12504i −0.681940 0.681940i
\(22\) 6.38572 1.64379i 1.36144 0.350458i
\(23\) 7.58574i 1.58174i −0.611987 0.790868i \(-0.709629\pi\)
0.611987 0.790868i \(-0.290371\pi\)
\(24\) 4.85469 4.57587i 0.990959 0.934045i
\(25\) 0 0
\(26\) 0.947414 + 3.68046i 0.185803 + 0.721798i
\(27\) 0.728312 + 0.728312i 0.140164 + 0.140164i
\(28\) −3.28166 + 1.80941i −0.620175 + 0.341946i
\(29\) 6.45786 6.45786i 1.19919 1.19919i 0.224787 0.974408i \(-0.427831\pi\)
0.974408 0.224787i \(-0.0721685\pi\)
\(30\) 0 0
\(31\) −0.799135 −0.143529 −0.0717644 0.997422i \(-0.522863\pi\)
−0.0717644 + 0.997422i \(0.522863\pi\)
\(32\) −2.58376 5.03231i −0.456749 0.889596i
\(33\) −10.9975 −1.91442
\(34\) −1.84925 + 3.13134i −0.317144 + 0.537020i
\(35\) 0 0
\(36\) −4.48944 + 2.47534i −0.748240 + 0.412557i
\(37\) 2.69652 + 2.69652i 0.443305 + 0.443305i 0.893121 0.449816i \(-0.148511\pi\)
−0.449816 + 0.893121i \(0.648511\pi\)
\(38\) −2.87499 11.1686i −0.466386 1.81179i
\(39\) 6.33850i 1.01497i
\(40\) 0 0
\(41\) 0.946984i 0.147894i 0.997262 + 0.0739471i \(0.0235596\pi\)
−0.997262 + 0.0739471i \(0.976440\pi\)
\(42\) 6.05276 1.55808i 0.933961 0.240417i
\(43\) 0.829986 + 0.829986i 0.126572 + 0.126572i 0.767555 0.640983i \(-0.221473\pi\)
−0.640983 + 0.767555i \(0.721473\pi\)
\(44\) −2.59054 + 8.95813i −0.390539 + 1.35049i
\(45\) 0 0
\(46\) 9.23730 + 5.45520i 1.36197 + 0.804325i
\(47\) 1.52421 0.222329 0.111165 0.993802i \(-0.464542\pi\)
0.111165 + 0.993802i \(0.464542\pi\)
\(48\) 2.08093 + 9.20233i 0.300356 + 1.32824i
\(49\) 3.48919 0.498456
\(50\) 0 0
\(51\) 4.28879 4.28879i 0.600551 0.600551i
\(52\) −5.16309 1.49308i −0.715992 0.207053i
\(53\) 6.97225 + 6.97225i 0.957712 + 0.957712i 0.999141 0.0414296i \(-0.0131912\pi\)
−0.0414296 + 0.999141i \(0.513191\pi\)
\(54\) −1.41064 + 0.363122i −0.191963 + 0.0494147i
\(55\) 0 0
\(56\) 0.156619 5.29735i 0.0209291 0.707889i
\(57\) 19.2346i 2.54769i
\(58\) 3.21976 + 12.5080i 0.422775 + 1.64238i
\(59\) 6.84418 + 6.84418i 0.891036 + 0.891036i 0.994621 0.103585i \(-0.0330313\pi\)
−0.103585 + 0.994621i \(0.533031\pi\)
\(60\) 0 0
\(61\) −6.87247 + 6.87247i −0.879930 + 0.879930i −0.993527 0.113597i \(-0.963763\pi\)
0.113597 + 0.993527i \(0.463763\pi\)
\(62\) 0.574689 0.973121i 0.0729856 0.123587i
\(63\) −4.80293 −0.605112
\(64\) 7.98603 + 0.472635i 0.998253 + 0.0590793i
\(65\) 0 0
\(66\) 7.90874 13.3919i 0.973498 1.64843i
\(67\) −3.73647 + 3.73647i −0.456483 + 0.456483i −0.897499 0.441016i \(-0.854618\pi\)
0.441016 + 0.897499i \(0.354618\pi\)
\(68\) −2.48322 4.50373i −0.301135 0.546158i
\(69\) −12.6517 12.6517i −1.52309 1.52309i
\(70\) 0 0
\(71\) 9.34417i 1.10895i −0.832201 0.554475i \(-0.812919\pi\)
0.832201 0.554475i \(-0.187081\pi\)
\(72\) 0.214261 7.24699i 0.0252509 0.854066i
\(73\) 0.886316i 0.103735i −0.998654 0.0518677i \(-0.983483\pi\)
0.998654 0.0518677i \(-0.0165174\pi\)
\(74\) −5.22277 + 1.34443i −0.607135 + 0.156287i
\(75\) 0 0
\(76\) 15.6678 + 4.53086i 1.79722 + 0.519725i
\(77\) −6.17755 + 6.17755i −0.703997 + 0.703997i
\(78\) 7.71851 + 4.55826i 0.873949 + 0.516122i
\(79\) 3.07575 0.346049 0.173024 0.984918i \(-0.444646\pi\)
0.173024 + 0.984918i \(0.444646\pi\)
\(80\) 0 0
\(81\) 10.1194 1.12437
\(82\) −1.15316 0.681013i −0.127345 0.0752053i
\(83\) −0.989393 + 0.989393i −0.108600 + 0.108600i −0.759319 0.650719i \(-0.774468\pi\)
0.650719 + 0.759319i \(0.274468\pi\)
\(84\) −2.45547 + 8.49104i −0.267913 + 0.926448i
\(85\) 0 0
\(86\) −1.60756 + 0.413814i −0.173348 + 0.0446227i
\(87\) 21.5412i 2.30946i
\(88\) −9.04553 9.59670i −0.964257 1.02301i
\(89\) 10.0942i 1.06998i 0.844859 + 0.534990i \(0.179684\pi\)
−0.844859 + 0.534990i \(0.820316\pi\)
\(90\) 0 0
\(91\) −3.56048 3.56048i −0.373239 0.373239i
\(92\) −13.2858 + 7.32539i −1.38514 + 0.763725i
\(93\) −1.33282 + 1.33282i −0.138207 + 0.138207i
\(94\) −1.09612 + 1.85606i −0.113056 + 0.191438i
\(95\) 0 0
\(96\) −12.7023 4.08377i −1.29643 0.416798i
\(97\) −7.16829 −0.727830 −0.363915 0.931432i \(-0.618560\pi\)
−0.363915 + 0.931432i \(0.618560\pi\)
\(98\) −2.50921 + 4.24885i −0.253469 + 0.429199i
\(99\) −8.45113 + 8.45113i −0.849371 + 0.849371i
\(100\) 0 0
\(101\) −1.05091 1.05091i −0.104570 0.104570i 0.652886 0.757456i \(-0.273558\pi\)
−0.757456 + 0.652886i \(0.773558\pi\)
\(102\) 2.13831 + 8.30678i 0.211724 + 0.822493i
\(103\) 8.20690i 0.808649i 0.914616 + 0.404325i \(0.132493\pi\)
−0.914616 + 0.404325i \(0.867507\pi\)
\(104\) 5.53113 5.21346i 0.542372 0.511222i
\(105\) 0 0
\(106\) −13.5043 + 3.47622i −1.31165 + 0.337641i
\(107\) −2.85743 2.85743i −0.276238 0.276238i 0.555367 0.831605i \(-0.312578\pi\)
−0.831605 + 0.555367i \(0.812578\pi\)
\(108\) 0.572264 1.97889i 0.0550661 0.190419i
\(109\) −11.3735 + 11.3735i −1.08939 + 1.08939i −0.0937940 + 0.995592i \(0.529900\pi\)
−0.995592 + 0.0937940i \(0.970100\pi\)
\(110\) 0 0
\(111\) 8.99467 0.853736
\(112\) 6.33806 + 4.00025i 0.598890 + 0.377988i
\(113\) −3.54221 −0.333223 −0.166611 0.986023i \(-0.553283\pi\)
−0.166611 + 0.986023i \(0.553283\pi\)
\(114\) −23.4224 13.8324i −2.19371 1.29552i
\(115\) 0 0
\(116\) −17.5466 5.07419i −1.62916 0.471127i
\(117\) −4.87088 4.87088i −0.450313 0.450313i
\(118\) −13.2562 + 3.41237i −1.22033 + 0.314134i
\(119\) 4.81822i 0.441685i
\(120\) 0 0
\(121\) 10.7398i 0.976343i
\(122\) −3.42648 13.3110i −0.310219 1.20512i
\(123\) 1.57941 + 1.57941i 0.142411 + 0.142411i
\(124\) 0.771707 + 1.39962i 0.0693014 + 0.125689i
\(125\) 0 0
\(126\) 3.45397 5.84862i 0.307704 0.521036i
\(127\) 18.0693 1.60339 0.801693 0.597735i \(-0.203933\pi\)
0.801693 + 0.597735i \(0.203933\pi\)
\(128\) −6.31860 + 9.38485i −0.558490 + 0.829511i
\(129\) 2.76855 0.243757
\(130\) 0 0
\(131\) −6.39614 + 6.39614i −0.558834 + 0.558834i −0.928975 0.370142i \(-0.879309\pi\)
0.370142 + 0.928975i \(0.379309\pi\)
\(132\) 10.6201 + 19.2612i 0.924358 + 1.67648i
\(133\) 10.8045 + 10.8045i 0.936871 + 0.936871i
\(134\) −1.86293 7.23702i −0.160933 0.625183i
\(135\) 0 0
\(136\) 7.27006 + 0.214943i 0.623403 + 0.0184312i
\(137\) 10.7357i 0.917212i −0.888640 0.458606i \(-0.848349\pi\)
0.888640 0.458606i \(-0.151651\pi\)
\(138\) 24.5046 6.30790i 2.08597 0.536964i
\(139\) −2.31086 2.31086i −0.196005 0.196005i 0.602280 0.798285i \(-0.294259\pi\)
−0.798285 + 0.602280i \(0.794259\pi\)
\(140\) 0 0
\(141\) 2.54213 2.54213i 0.214086 0.214086i
\(142\) 11.3786 + 6.71976i 0.954869 + 0.563909i
\(143\) −12.5299 −1.04780
\(144\) 8.67071 + 5.47250i 0.722559 + 0.456042i
\(145\) 0 0
\(146\) 1.07928 + 0.637384i 0.0893221 + 0.0527503i
\(147\) 5.81938 5.81938i 0.479974 0.479974i
\(148\) 2.11876 7.32670i 0.174161 0.602251i
\(149\) 1.38743 + 1.38743i 0.113663 + 0.113663i 0.761651 0.647988i \(-0.224389\pi\)
−0.647988 + 0.761651i \(0.724389\pi\)
\(150\) 0 0
\(151\) 5.68590i 0.462712i −0.972869 0.231356i \(-0.925684\pi\)
0.972869 0.231356i \(-0.0743163\pi\)
\(152\) −16.7846 + 15.8206i −1.36141 + 1.28322i
\(153\) 6.59152i 0.532892i
\(154\) −3.08000 11.9650i −0.248194 0.964170i
\(155\) 0 0
\(156\) −11.1014 + 6.12096i −0.888820 + 0.490069i
\(157\) −2.48874 + 2.48874i −0.198623 + 0.198623i −0.799409 0.600787i \(-0.794854\pi\)
0.600787 + 0.799409i \(0.294854\pi\)
\(158\) −2.21189 + 3.74540i −0.175969 + 0.297968i
\(159\) 23.2571 1.84440
\(160\) 0 0
\(161\) −14.2135 −1.12018
\(162\) −7.27722 + 12.3225i −0.571753 + 0.968149i
\(163\) 12.7091 12.7091i 0.995451 0.995451i −0.00453842 0.999990i \(-0.501445\pi\)
0.999990 + 0.00453842i \(0.00144463\pi\)
\(164\) 1.65857 0.914483i 0.129512 0.0714091i
\(165\) 0 0
\(166\) −0.493292 1.91631i −0.0382868 0.148735i
\(167\) 5.00982i 0.387672i −0.981034 0.193836i \(-0.937907\pi\)
0.981034 0.193836i \(-0.0620929\pi\)
\(168\) −8.57387 9.09630i −0.661489 0.701795i
\(169\) 5.77830i 0.444485i
\(170\) 0 0
\(171\) 14.7810 + 14.7810i 1.13033 + 1.13033i
\(172\) 0.652152 2.25515i 0.0497261 0.171954i
\(173\) 6.19546 6.19546i 0.471032 0.471032i −0.431216 0.902249i \(-0.641915\pi\)
0.902249 + 0.431216i \(0.141915\pi\)
\(174\) 26.2312 + 15.4911i 1.98858 + 1.17438i
\(175\) 0 0
\(176\) 18.1911 4.11356i 1.37120 0.310071i
\(177\) 22.8299 1.71600
\(178\) −12.2919 7.25911i −0.921313 0.544093i
\(179\) −5.51628 + 5.51628i −0.412306 + 0.412306i −0.882541 0.470235i \(-0.844169\pi\)
0.470235 + 0.882541i \(0.344169\pi\)
\(180\) 0 0
\(181\) 11.8993 + 11.8993i 0.884470 + 0.884470i 0.993985 0.109515i \(-0.0349298\pi\)
−0.109515 + 0.993985i \(0.534930\pi\)
\(182\) 6.89614 1.77518i 0.511176 0.131585i
\(183\) 22.9242i 1.69461i
\(184\) 0.634072 21.4463i 0.0467444 1.58105i
\(185\) 0 0
\(186\) −0.664518 2.58149i −0.0487248 0.189284i
\(187\) −8.47804 8.47804i −0.619976 0.619976i
\(188\) −1.47190 2.66954i −0.107349 0.194696i
\(189\) 1.36465 1.36465i 0.0992637 0.0992637i
\(190\) 0 0
\(191\) 11.1278 0.805180 0.402590 0.915380i \(-0.368110\pi\)
0.402590 + 0.915380i \(0.368110\pi\)
\(192\) 14.1076 12.5311i 1.01813 0.904352i
\(193\) 20.7821 1.49593 0.747965 0.663738i \(-0.231031\pi\)
0.747965 + 0.663738i \(0.231031\pi\)
\(194\) 5.15500 8.72896i 0.370107 0.626703i
\(195\) 0 0
\(196\) −3.36944 6.11103i −0.240674 0.436502i
\(197\) −14.0309 14.0309i −0.999663 0.999663i 0.000337236 1.00000i \(-0.499893\pi\)
−1.00000 0.000337236i \(0.999893\pi\)
\(198\) −4.21357 16.3686i −0.299445 1.16327i
\(199\) 3.24727i 0.230193i −0.993354 0.115096i \(-0.963282\pi\)
0.993354 0.115096i \(-0.0367177\pi\)
\(200\) 0 0
\(201\) 12.4636i 0.879115i
\(202\) 2.03547 0.523964i 0.143215 0.0368660i
\(203\) −12.1002 12.1002i −0.849267 0.849267i
\(204\) −11.6531 3.36987i −0.815877 0.235938i
\(205\) 0 0
\(206\) −9.99369 5.90190i −0.696294 0.411205i
\(207\) −19.4447 −1.35150
\(208\) 2.37088 + 10.4846i 0.164391 + 0.726974i
\(209\) 38.0228 2.63009
\(210\) 0 0
\(211\) −10.1821 + 10.1821i −0.700964 + 0.700964i −0.964617 0.263654i \(-0.915072\pi\)
0.263654 + 0.964617i \(0.415072\pi\)
\(212\) 5.47837 18.9443i 0.376256 1.30110i
\(213\) −15.5845 15.5845i −1.06783 1.06783i
\(214\) 5.53443 1.42466i 0.378326 0.0973876i
\(215\) 0 0
\(216\) 1.99820 + 2.11996i 0.135960 + 0.144245i
\(217\) 1.49735i 0.101647i
\(218\) −5.67061 22.0289i −0.384062 1.49198i
\(219\) −1.47822 1.47822i −0.0998892 0.0998892i
\(220\) 0 0
\(221\) 4.88638 4.88638i 0.328694 0.328694i
\(222\) −6.46842 + 10.9530i −0.434132 + 0.735116i
\(223\) 24.0469 1.61030 0.805151 0.593070i \(-0.202084\pi\)
0.805151 + 0.593070i \(0.202084\pi\)
\(224\) −9.42912 + 4.84124i −0.630010 + 0.323469i
\(225\) 0 0
\(226\) 2.54734 4.31341i 0.169446 0.286924i
\(227\) −11.9863 + 11.9863i −0.795562 + 0.795562i −0.982392 0.186830i \(-0.940179\pi\)
0.186830 + 0.982392i \(0.440179\pi\)
\(228\) 33.6879 18.5745i 2.23103 1.23012i
\(229\) −20.1972 20.1972i −1.33467 1.33467i −0.901140 0.433529i \(-0.857268\pi\)
−0.433529 0.901140i \(-0.642732\pi\)
\(230\) 0 0
\(231\) 20.6062i 1.35579i
\(232\) 18.7974 17.7178i 1.23411 1.16323i
\(233\) 10.0655i 0.659410i 0.944084 + 0.329705i \(0.106949\pi\)
−0.944084 + 0.329705i \(0.893051\pi\)
\(234\) 9.43419 2.42852i 0.616733 0.158757i
\(235\) 0 0
\(236\) 5.37774 18.5963i 0.350061 1.21052i
\(237\) 5.12983 5.12983i 0.333218 0.333218i
\(238\) 5.86724 + 3.46497i 0.380316 + 0.224601i
\(239\) 0.992801 0.0642189 0.0321095 0.999484i \(-0.489777\pi\)
0.0321095 + 0.999484i \(0.489777\pi\)
\(240\) 0 0
\(241\) 14.1229 0.909738 0.454869 0.890558i \(-0.349686\pi\)
0.454869 + 0.890558i \(0.349686\pi\)
\(242\) −13.0780 7.72339i −0.840687 0.496478i
\(243\) 14.6924 14.6924i 0.942520 0.942520i
\(244\) 18.6732 + 5.39997i 1.19543 + 0.345698i
\(245\) 0 0
\(246\) −3.05909 + 0.787462i −0.195041 + 0.0502068i
\(247\) 21.9148i 1.39440i
\(248\) −2.25931 0.0667975i −0.143466 0.00424165i
\(249\) 3.30028i 0.209147i
\(250\) 0 0
\(251\) 1.56681 + 1.56681i 0.0988961 + 0.0988961i 0.754824 0.655928i \(-0.227722\pi\)
−0.655928 + 0.754824i \(0.727722\pi\)
\(252\) 4.63809 + 8.41193i 0.292172 + 0.529902i
\(253\) −25.0098 + 25.0098i −1.57235 + 1.57235i
\(254\) −12.9943 + 22.0033i −0.815335 + 1.38061i
\(255\) 0 0
\(256\) −6.88415 14.4433i −0.430260 0.902705i
\(257\) 10.2593 0.639960 0.319980 0.947424i \(-0.396324\pi\)
0.319980 + 0.947424i \(0.396324\pi\)
\(258\) −1.99097 + 3.37132i −0.123953 + 0.209889i
\(259\) 5.05251 5.05251i 0.313948 0.313948i
\(260\) 0 0
\(261\) −16.5535 16.5535i −1.02464 1.02464i
\(262\) −3.18899 12.3884i −0.197016 0.765359i
\(263\) 19.0630i 1.17548i 0.809051 + 0.587739i \(0.199982\pi\)
−0.809051 + 0.587739i \(0.800018\pi\)
\(264\) −31.0921 0.919252i −1.91358 0.0565761i
\(265\) 0 0
\(266\) −20.9268 + 5.38692i −1.28311 + 0.330293i
\(267\) 16.8354 + 16.8354i 1.03031 + 1.03031i
\(268\) 10.1524 + 2.93589i 0.620154 + 0.179338i
\(269\) 3.48459 3.48459i 0.212459 0.212459i −0.592852 0.805311i \(-0.701998\pi\)
0.805311 + 0.592852i \(0.201998\pi\)
\(270\) 0 0
\(271\) −30.0045 −1.82264 −0.911322 0.411695i \(-0.864937\pi\)
−0.911322 + 0.411695i \(0.864937\pi\)
\(272\) −5.48992 + 8.69832i −0.332876 + 0.527413i
\(273\) −11.8765 −0.718801
\(274\) 13.0731 + 7.72045i 0.789772 + 0.466409i
\(275\) 0 0
\(276\) −9.94096 + 34.3760i −0.598375 + 2.06919i
\(277\) −8.43732 8.43732i −0.506949 0.506949i 0.406639 0.913589i \(-0.366701\pi\)
−0.913589 + 0.406639i \(0.866701\pi\)
\(278\) 4.47581 1.15215i 0.268441 0.0691014i
\(279\) 2.04844i 0.122637i
\(280\) 0 0
\(281\) 6.44714i 0.384604i −0.981336 0.192302i \(-0.938405\pi\)
0.981336 0.192302i \(-0.0615954\pi\)
\(282\) 1.26746 + 4.92375i 0.0754759 + 0.293205i
\(283\) −2.61000 2.61000i −0.155148 0.155148i 0.625264 0.780413i \(-0.284991\pi\)
−0.780413 + 0.625264i \(0.784991\pi\)
\(284\) −16.3656 + 9.02347i −0.971117 + 0.535444i
\(285\) 0 0
\(286\) 9.01073 15.2579i 0.532815 0.902217i
\(287\) 1.77438 0.104738
\(288\) −12.8994 + 6.62300i −0.760105 + 0.390264i
\(289\) −10.3875 −0.611029
\(290\) 0 0
\(291\) −11.9555 + 11.9555i −0.700844 + 0.700844i
\(292\) −1.55231 + 0.855896i −0.0908420 + 0.0500875i
\(293\) 7.52428 + 7.52428i 0.439573 + 0.439573i 0.891868 0.452295i \(-0.149395\pi\)
−0.452295 + 0.891868i \(0.649395\pi\)
\(294\) 2.90143 + 11.2713i 0.169215 + 0.657356i
\(295\) 0 0
\(296\) 7.39818 + 7.84897i 0.430010 + 0.456212i
\(297\) 4.80242i 0.278665i
\(298\) −2.68726 + 0.691746i −0.155669 + 0.0400718i
\(299\) −14.4146 14.4146i −0.833618 0.833618i
\(300\) 0 0
\(301\) 1.55516 1.55516i 0.0896377 0.0896377i
\(302\) 6.92383 + 4.08895i 0.398422 + 0.235293i
\(303\) −3.50549 −0.201385
\(304\) −7.19460 31.8162i −0.412639 1.82478i
\(305\) 0 0
\(306\) 8.02661 + 4.74021i 0.458851 + 0.270980i
\(307\) −12.7130 + 12.7130i −0.725571 + 0.725571i −0.969734 0.244163i \(-0.921487\pi\)
0.244163 + 0.969734i \(0.421487\pi\)
\(308\) 16.7850 + 4.85394i 0.956414 + 0.276579i
\(309\) 13.6877 + 13.6877i 0.778667 + 0.778667i
\(310\) 0 0
\(311\) 11.9313i 0.676563i −0.941045 0.338281i \(-0.890154\pi\)
0.941045 0.338281i \(-0.109846\pi\)
\(312\) 0.529818 17.9202i 0.0299951 1.01453i
\(313\) 34.3458i 1.94134i −0.240414 0.970670i \(-0.577283\pi\)
0.240414 0.970670i \(-0.422717\pi\)
\(314\) −1.24083 4.82033i −0.0700244 0.272027i
\(315\) 0 0
\(316\) −2.97019 5.38692i −0.167086 0.303038i
\(317\) 17.1112 17.1112i 0.961060 0.961060i −0.0382097 0.999270i \(-0.512165\pi\)
0.999270 + 0.0382097i \(0.0121655\pi\)
\(318\) −16.7251 + 28.3206i −0.937894 + 1.58814i
\(319\) −42.5825 −2.38416
\(320\) 0 0
\(321\) −9.53141 −0.531992
\(322\) 10.2215 17.3081i 0.569622 0.964541i
\(323\) −14.8281 + 14.8281i −0.825056 + 0.825056i
\(324\) −9.77205 17.7232i −0.542891 0.984623i
\(325\) 0 0
\(326\) 6.33649 + 24.6157i 0.350946 + 1.36334i
\(327\) 37.9382i 2.09799i
\(328\) −0.0791559 + 2.67731i −0.00437065 + 0.147830i
\(329\) 2.85594i 0.157453i
\(330\) 0 0
\(331\) 9.80246 + 9.80246i 0.538792 + 0.538792i 0.923174 0.384382i \(-0.125585\pi\)
−0.384382 + 0.923174i \(0.625585\pi\)
\(332\) 2.68828 + 0.777405i 0.147538 + 0.0426656i
\(333\) 6.91203 6.91203i 0.378777 0.378777i
\(334\) 6.10056 + 3.60276i 0.333808 + 0.197134i
\(335\) 0 0
\(336\) 17.2425 3.89906i 0.940658 0.212711i
\(337\) −6.07501 −0.330927 −0.165463 0.986216i \(-0.552912\pi\)
−0.165463 + 0.986216i \(0.552912\pi\)
\(338\) −7.03635 4.15540i −0.382727 0.226024i
\(339\) −5.90780 + 5.90780i −0.320868 + 0.320868i
\(340\) 0 0
\(341\) 2.63471 + 2.63471i 0.142677 + 0.142677i
\(342\) −28.6287 + 7.36952i −1.54806 + 0.398498i
\(343\) 19.6538i 1.06120i
\(344\) 2.27715 + 2.41590i 0.122776 + 0.130257i
\(345\) 0 0
\(346\) 3.08894 + 11.9997i 0.166062 + 0.645110i
\(347\) −5.77231 5.77231i −0.309874 0.309874i 0.534987 0.844860i \(-0.320317\pi\)
−0.844860 + 0.534987i \(0.820317\pi\)
\(348\) −37.7277 + 20.8019i −2.02242 + 1.11510i
\(349\) −7.58851 + 7.58851i −0.406203 + 0.406203i −0.880412 0.474209i \(-0.842734\pi\)
0.474209 + 0.880412i \(0.342734\pi\)
\(350\) 0 0
\(351\) 2.76791 0.147740
\(352\) −8.07275 + 25.1098i −0.430279 + 1.33836i
\(353\) 16.2285 0.863753 0.431877 0.901933i \(-0.357852\pi\)
0.431877 + 0.901933i \(0.357852\pi\)
\(354\) −16.4178 + 27.8003i −0.872598 + 1.47757i
\(355\) 0 0
\(356\) 17.6791 9.74772i 0.936990 0.516628i
\(357\) −8.03597 8.03597i −0.425309 0.425309i
\(358\) −2.75031 10.6843i −0.145358 0.564680i
\(359\) 6.77298i 0.357464i −0.983898 0.178732i \(-0.942800\pi\)
0.983898 0.178732i \(-0.0571996\pi\)
\(360\) 0 0
\(361\) 47.5019i 2.50010i
\(362\) −23.0473 + 5.93277i −1.21134 + 0.311819i
\(363\) 17.9121 + 17.9121i 0.940142 + 0.940142i
\(364\) −2.79761 + 9.67416i −0.146634 + 0.507064i
\(365\) 0 0
\(366\) −27.9153 16.4857i −1.45915 0.861722i
\(367\) 6.35705 0.331835 0.165918 0.986140i \(-0.446941\pi\)
0.165918 + 0.986140i \(0.446941\pi\)
\(368\) 25.6596 + 16.1950i 1.33760 + 0.844224i
\(369\) 2.42742 0.126367
\(370\) 0 0
\(371\) 13.0640 13.0640i 0.678250 0.678250i
\(372\) 3.62140 + 1.04725i 0.187761 + 0.0542974i
\(373\) −9.20937 9.20937i −0.476843 0.476843i 0.427278 0.904121i \(-0.359473\pi\)
−0.904121 + 0.427278i \(0.859473\pi\)
\(374\) 16.4208 4.22698i 0.849097 0.218572i
\(375\) 0 0
\(376\) 4.30925 + 0.127405i 0.222232 + 0.00657041i
\(377\) 24.5428i 1.26402i
\(378\) 0.680387 + 2.64313i 0.0349954 + 0.135948i
\(379\) 5.41600 + 5.41600i 0.278201 + 0.278201i 0.832391 0.554189i \(-0.186972\pi\)
−0.554189 + 0.832391i \(0.686972\pi\)
\(380\) 0 0
\(381\) 30.1365 30.1365i 1.54394 1.54394i
\(382\) −8.00244 + 13.5505i −0.409440 + 0.693306i
\(383\) −28.1626 −1.43904 −0.719520 0.694472i \(-0.755638\pi\)
−0.719520 + 0.694472i \(0.755638\pi\)
\(384\) 5.11398 + 26.1907i 0.260972 + 1.33654i
\(385\) 0 0
\(386\) −14.9452 + 25.3068i −0.760693 + 1.28808i
\(387\) 2.12752 2.12752i 0.108148 0.108148i
\(388\) 6.92227 + 12.5547i 0.351425 + 0.637367i
\(389\) 9.59783 + 9.59783i 0.486629 + 0.486629i 0.907241 0.420611i \(-0.138184\pi\)
−0.420611 + 0.907241i \(0.638184\pi\)
\(390\) 0 0
\(391\) 19.5066i 0.986490i
\(392\) 9.86461 + 0.291652i 0.498238 + 0.0147307i
\(393\) 21.3354i 1.07623i
\(394\) 27.1759 6.99554i 1.36910 0.352430i
\(395\) 0 0
\(396\) 22.9625 + 6.64039i 1.15391 + 0.333692i
\(397\) −10.4884 + 10.4884i −0.526399 + 0.526399i −0.919497 0.393098i \(-0.871403\pi\)
0.393098 + 0.919497i \(0.371403\pi\)
\(398\) 3.95426 + 2.33524i 0.198209 + 0.117055i
\(399\) 36.0402 1.80427
\(400\) 0 0
\(401\) −2.44221 −0.121958 −0.0609791 0.998139i \(-0.519422\pi\)
−0.0609791 + 0.998139i \(0.519422\pi\)
\(402\) −15.1772 8.96306i −0.756969 0.447037i
\(403\) −1.51853 + 1.51853i −0.0756436 + 0.0756436i
\(404\) −0.825743 + 2.85543i −0.0410823 + 0.142063i
\(405\) 0 0
\(406\) 23.4364 6.03292i 1.16313 0.299409i
\(407\) 17.7806i 0.881350i
\(408\) 12.4837 11.7667i 0.618036 0.582541i
\(409\) 24.6628i 1.21950i 0.792596 + 0.609748i \(0.208729\pi\)
−0.792596 + 0.609748i \(0.791271\pi\)
\(410\) 0 0
\(411\) −17.9053 17.9053i −0.883204 0.883204i
\(412\) 14.3737 7.92522i 0.708142 0.390448i
\(413\) 12.8240 12.8240i 0.631030 0.631030i
\(414\) 13.9834 23.6781i 0.687247 1.16372i
\(415\) 0 0
\(416\) −14.4722 4.65279i −0.709560 0.228122i
\(417\) −7.70826 −0.377475
\(418\) −27.3437 + 46.3011i −1.33742 + 2.26466i
\(419\) 19.1661 19.1661i 0.936326 0.936326i −0.0617649 0.998091i \(-0.519673\pi\)
0.998091 + 0.0617649i \(0.0196729\pi\)
\(420\) 0 0
\(421\) −7.43469 7.43469i −0.362345 0.362345i 0.502331 0.864676i \(-0.332476\pi\)
−0.864676 + 0.502331i \(0.832476\pi\)
\(422\) −5.07659 19.7213i −0.247124 0.960016i
\(423\) 3.90704i 0.189967i
\(424\) 19.1291 + 20.2947i 0.928991 + 0.985596i
\(425\) 0 0
\(426\) 30.1850 7.77012i 1.46247 0.376464i
\(427\) 12.8771 + 12.8771i 0.623164 + 0.623164i
\(428\) −2.24519 + 7.76391i −0.108526 + 0.375283i
\(429\) −20.8977 + 20.8977i −1.00895 + 1.00895i
\(430\) 0 0
\(431\) 22.5647 1.08690 0.543451 0.839441i \(-0.317117\pi\)
0.543451 + 0.839441i \(0.317117\pi\)
\(432\) −4.01849 + 0.908704i −0.193340 + 0.0437201i
\(433\) −26.4811 −1.27260 −0.636301 0.771441i \(-0.719536\pi\)
−0.636301 + 0.771441i \(0.719536\pi\)
\(434\) −1.82335 1.07680i −0.0875237 0.0516882i
\(435\) 0 0
\(436\) 30.9030 + 8.93662i 1.47998 + 0.427986i
\(437\) 43.7421 + 43.7421i 2.09247 + 2.09247i
\(438\) 2.86311 0.737013i 0.136805 0.0352159i
\(439\) 0.765288i 0.0365252i 0.999833 + 0.0182626i \(0.00581349\pi\)
−0.999833 + 0.0182626i \(0.994187\pi\)
\(440\) 0 0
\(441\) 8.94390i 0.425900i
\(442\) 2.43625 + 9.46423i 0.115881 + 0.450167i
\(443\) −20.2685 20.2685i −0.962985 0.962985i 0.0363537 0.999339i \(-0.488426\pi\)
−0.999339 + 0.0363537i \(0.988426\pi\)
\(444\) −8.68596 15.7534i −0.412218 0.747625i
\(445\) 0 0
\(446\) −17.2931 + 29.2824i −0.818851 + 1.38656i
\(447\) 4.62800 0.218897
\(448\) 0.885583 14.9635i 0.0418399 0.706961i
\(449\) −35.2717 −1.66457 −0.832287 0.554345i \(-0.812969\pi\)
−0.832287 + 0.554345i \(0.812969\pi\)
\(450\) 0 0
\(451\) 3.12216 3.12216i 0.147017 0.147017i
\(452\) 3.42063 + 6.20388i 0.160893 + 0.291806i
\(453\) −9.48312 9.48312i −0.445556 0.445556i
\(454\) −5.97615 23.2158i −0.280475 1.08957i
\(455\) 0 0
\(456\) −1.60777 + 54.3800i −0.0752908 + 2.54658i
\(457\) 9.01188i 0.421558i −0.977534 0.210779i \(-0.932400\pi\)
0.977534 0.210779i \(-0.0676000\pi\)
\(458\) 39.1191 10.0699i 1.82792 0.470537i
\(459\) 1.87284 + 1.87284i 0.0874167 + 0.0874167i
\(460\) 0 0
\(461\) −22.8247 + 22.8247i −1.06305 + 1.06305i −0.0651807 + 0.997873i \(0.520762\pi\)
−0.997873 + 0.0651807i \(0.979238\pi\)
\(462\) −25.0926 14.8187i −1.16741 0.689429i
\(463\) −3.72721 −0.173218 −0.0866090 0.996242i \(-0.527603\pi\)
−0.0866090 + 0.996242i \(0.527603\pi\)
\(464\) 8.05738 + 35.6315i 0.374054 + 1.65415i
\(465\) 0 0
\(466\) −12.2569 7.23846i −0.567790 0.335315i
\(467\) 3.23477 3.23477i 0.149687 0.149687i −0.628291 0.777978i \(-0.716245\pi\)
0.777978 + 0.628291i \(0.216245\pi\)
\(468\) −3.82724 + 13.2346i −0.176914 + 0.611771i
\(469\) 7.00109 + 7.00109i 0.323280 + 0.323280i
\(470\) 0 0
\(471\) 8.30158i 0.382517i
\(472\) 18.7777 + 19.9219i 0.864314 + 0.916979i
\(473\) 5.47284i 0.251642i
\(474\) 2.55763 + 9.93575i 0.117476 + 0.456364i
\(475\) 0 0
\(476\) −8.43871 + 4.65285i −0.386788 + 0.213263i
\(477\) 17.8721 17.8721i 0.818307 0.818307i
\(478\) −0.713961 + 1.20895i −0.0326558 + 0.0552962i
\(479\) −11.0636 −0.505508 −0.252754 0.967531i \(-0.581336\pi\)
−0.252754 + 0.967531i \(0.581336\pi\)
\(480\) 0 0
\(481\) 10.2480 0.467267
\(482\) −10.1563 + 17.1978i −0.462609 + 0.783336i
\(483\) −23.7057 + 23.7057i −1.07865 + 1.07865i
\(484\) 18.8098 10.3712i 0.854992 0.471417i
\(485\) 0 0
\(486\) 7.32536 + 28.4572i 0.332285 + 1.29084i
\(487\) 6.68176i 0.302779i 0.988474 + 0.151390i \(0.0483748\pi\)
−0.988474 + 0.151390i \(0.951625\pi\)
\(488\) −20.0042 + 18.8553i −0.905550 + 0.853541i
\(489\) 42.3932i 1.91708i
\(490\) 0 0
\(491\) −18.4274 18.4274i −0.831618 0.831618i 0.156120 0.987738i \(-0.450101\pi\)
−0.987738 + 0.156120i \(0.950101\pi\)
\(492\) 1.24100 4.29141i 0.0559488 0.193472i
\(493\) 16.6063 16.6063i 0.747908 0.747908i
\(494\) −26.6860 15.7597i −1.20066 0.709065i
\(495\) 0 0
\(496\) 1.70610 2.70316i 0.0766060 0.121376i
\(497\) −17.5083 −0.785356
\(498\) −4.01881 2.37336i −0.180087 0.106353i
\(499\) 8.84615 8.84615i 0.396008 0.396008i −0.480814 0.876822i \(-0.659659\pi\)
0.876822 + 0.480814i \(0.159659\pi\)
\(500\) 0 0
\(501\) −8.35554 8.35554i −0.373298 0.373298i
\(502\) −3.03469 + 0.781180i −0.135445 + 0.0348658i
\(503\) 16.8746i 0.752401i −0.926538 0.376201i \(-0.877230\pi\)
0.926538 0.376201i \(-0.122770\pi\)
\(504\) −13.5788 0.401464i −0.604848 0.0178826i
\(505\) 0 0
\(506\) −12.4694 48.4405i −0.554332 2.15344i
\(507\) 9.63723 + 9.63723i 0.428004 + 0.428004i
\(508\) −17.4491 31.6468i −0.774178 1.40410i
\(509\) 20.5691 20.5691i 0.911707 0.911707i −0.0846994 0.996407i \(-0.526993\pi\)
0.996407 + 0.0846994i \(0.0269930\pi\)
\(510\) 0 0
\(511\) −1.66070 −0.0734652
\(512\) 22.5385 + 2.00376i 0.996071 + 0.0885545i
\(513\) −8.39943 −0.370844
\(514\) −7.37788 + 12.4930i −0.325425 + 0.551042i
\(515\) 0 0
\(516\) −2.67353 4.84889i −0.117696 0.213460i
\(517\) −5.02526 5.02526i −0.221011 0.221011i
\(518\) 2.51908 + 9.78599i 0.110682 + 0.429972i
\(519\) 20.6660i 0.907135i
\(520\) 0 0
\(521\) 12.6708i 0.555118i 0.960709 + 0.277559i \(0.0895253\pi\)
−0.960709 + 0.277559i \(0.910475\pi\)
\(522\) 32.0619 8.25327i 1.40331 0.361236i
\(523\) 27.8509 + 27.8509i 1.21784 + 1.21784i 0.968388 + 0.249448i \(0.0802491\pi\)
0.249448 + 0.968388i \(0.419751\pi\)
\(524\) 17.3789 + 5.02570i 0.759202 + 0.219549i
\(525\) 0 0
\(526\) −23.2134 13.7090i −1.01215 0.597740i
\(527\) −2.05496 −0.0895154
\(528\) 23.4789 37.2003i 1.02179 1.61894i
\(529\) −34.5435 −1.50189
\(530\) 0 0
\(531\) 17.5438 17.5438i 0.761336 0.761336i
\(532\) 8.48954 29.3569i 0.368068 1.27278i
\(533\) 1.79948 + 1.79948i 0.0779442 + 0.0779442i
\(534\) −32.6077 + 8.39377i −1.41107 + 0.363234i
\(535\) 0 0
\(536\) −10.8760 + 10.2514i −0.469774 + 0.442793i
\(537\) 18.4005i 0.794038i
\(538\) 1.73734 + 6.74915i 0.0749023 + 0.290976i
\(539\) −11.5037 11.5037i −0.495499 0.495499i
\(540\) 0 0
\(541\) −23.4122 + 23.4122i −1.00657 + 1.00657i −0.00659048 + 0.999978i \(0.502098\pi\)
−0.999978 + 0.00659048i \(0.997902\pi\)
\(542\) 21.5774 36.5370i 0.926829 1.56940i
\(543\) 39.6921 1.70335
\(544\) −6.64409 12.9405i −0.284863 0.554819i
\(545\) 0 0
\(546\) 8.54089 14.4623i 0.365516 0.618929i
\(547\) −17.3745 + 17.3745i −0.742878 + 0.742878i −0.973131 0.230253i \(-0.926045\pi\)
0.230253 + 0.973131i \(0.426045\pi\)
\(548\) −18.8027 + 10.3672i −0.803211 + 0.442866i
\(549\) 17.6163 + 17.6163i 0.751846 + 0.751846i
\(550\) 0 0
\(551\) 74.4767i 3.17282i
\(552\) −34.7113 36.8264i −1.47741 1.56744i
\(553\) 5.76308i 0.245071i
\(554\) 16.3419 4.20668i 0.694300 0.178725i
\(555\) 0 0
\(556\) −1.81574 + 6.27884i −0.0770043 + 0.266282i
\(557\) −22.8889 + 22.8889i −0.969832 + 0.969832i −0.999558 0.0297261i \(-0.990536\pi\)
0.0297261 + 0.999558i \(0.490536\pi\)
\(558\) −2.49442 1.47311i −0.105597 0.0623617i
\(559\) 3.15432 0.133413
\(560\) 0 0
\(561\) −28.2799 −1.19398
\(562\) 7.85081 + 4.63639i 0.331166 + 0.195574i
\(563\) −19.2489 + 19.2489i −0.811246 + 0.811246i −0.984821 0.173574i \(-0.944468\pi\)
0.173574 + 0.984821i \(0.444468\pi\)
\(564\) −6.90721 1.99745i −0.290846 0.0841079i
\(565\) 0 0
\(566\) 5.05520 1.30129i 0.212486 0.0546975i
\(567\) 18.9608i 0.796278i
\(568\) 0.781054 26.4178i 0.0327723 1.10846i
\(569\) 34.4274i 1.44327i 0.692273 + 0.721635i \(0.256609\pi\)
−0.692273 + 0.721635i \(0.743391\pi\)
\(570\) 0 0
\(571\) 5.85059 + 5.85059i 0.244840 + 0.244840i 0.818849 0.574009i \(-0.194613\pi\)
−0.574009 + 0.818849i \(0.694613\pi\)
\(572\) 12.0998 + 21.9451i 0.505920 + 0.917569i
\(573\) 18.5593 18.5593i 0.775326 0.775326i
\(574\) −1.27603 + 2.16070i −0.0532603 + 0.0901857i
\(575\) 0 0
\(576\) 1.21151 20.4707i 0.0504797 0.852947i
\(577\) −32.5042 −1.35317 −0.676585 0.736365i \(-0.736541\pi\)
−0.676585 + 0.736365i \(0.736541\pi\)
\(578\) 7.47005 12.6491i 0.310713 0.526131i
\(579\) 34.6611 34.6611i 1.44047 1.44047i
\(580\) 0 0
\(581\) 1.85384 + 1.85384i 0.0769103 + 0.0769103i
\(582\) −5.96077 23.1561i −0.247082 0.959851i
\(583\) 45.9743i 1.90406i
\(584\) 0.0740848 2.50578i 0.00306565 0.103690i
\(585\) 0 0
\(586\) −14.5735 + 3.75146i −0.602024 + 0.154971i
\(587\) 14.7519 + 14.7519i 0.608875 + 0.608875i 0.942652 0.333777i \(-0.108323\pi\)
−0.333777 + 0.942652i \(0.608323\pi\)
\(588\) −15.8118 4.57251i −0.652068 0.188567i
\(589\) 4.60810 4.60810i 0.189873 0.189873i
\(590\) 0 0
\(591\) −46.8024 −1.92520
\(592\) −14.8782 + 3.36440i −0.611488 + 0.138276i
\(593\) 20.5310 0.843108 0.421554 0.906803i \(-0.361485\pi\)
0.421554 + 0.906803i \(0.361485\pi\)
\(594\) 5.84800 + 3.45361i 0.239946 + 0.141703i
\(595\) 0 0
\(596\) 1.09016 3.76979i 0.0446547 0.154416i
\(597\) −5.41590 5.41590i −0.221658 0.221658i
\(598\) 27.9190 7.18683i 1.14169 0.293891i
\(599\) 12.3998i 0.506644i 0.967382 + 0.253322i \(0.0815232\pi\)
−0.967382 + 0.253322i \(0.918477\pi\)
\(600\) 0 0
\(601\) 12.3980i 0.505723i 0.967502 + 0.252862i \(0.0813718\pi\)
−0.967502 + 0.252862i \(0.918628\pi\)
\(602\) 0.775370 + 3.01212i 0.0316017 + 0.122765i
\(603\) 9.57777 + 9.57777i 0.390037 + 0.390037i
\(604\) −9.95839 + 5.49076i −0.405201 + 0.223416i
\(605\) 0 0
\(606\) 2.52093 4.26870i 0.102406 0.173404i
\(607\) −4.90398 −0.199046 −0.0995232 0.995035i \(-0.531732\pi\)
−0.0995232 + 0.995035i \(0.531732\pi\)
\(608\) 43.9171 + 14.1192i 1.78107 + 0.572610i
\(609\) −40.3621 −1.63556
\(610\) 0 0
\(611\) 2.89635 2.89635i 0.117174 0.117174i
\(612\) −11.5445 + 6.36529i −0.466659 + 0.257301i
\(613\) 0.408547 + 0.408547i 0.0165011 + 0.0165011i 0.715309 0.698808i \(-0.246286\pi\)
−0.698808 + 0.715309i \(0.746286\pi\)
\(614\) −6.33846 24.6233i −0.255800 0.993717i
\(615\) 0 0
\(616\) −17.9815 + 16.9487i −0.724494 + 0.682884i
\(617\) 6.17186i 0.248470i 0.992253 + 0.124235i \(0.0396476\pi\)
−0.992253 + 0.124235i \(0.960352\pi\)
\(618\) −26.5111 + 6.82442i −1.06643 + 0.274518i
\(619\) 18.5138 + 18.5138i 0.744132 + 0.744132i 0.973370 0.229238i \(-0.0736234\pi\)
−0.229238 + 0.973370i \(0.573623\pi\)
\(620\) 0 0
\(621\) 5.52479 5.52479i 0.221702 0.221702i
\(622\) 14.5290 + 8.58027i 0.582559 + 0.344037i
\(623\) 18.9136 0.757757
\(624\) 21.4407 + 13.5323i 0.858315 + 0.541724i
\(625\) 0 0
\(626\) 41.8236 + 24.6994i 1.67161 + 0.987187i
\(627\) 63.4156 63.4156i 2.53258 2.53258i
\(628\) 6.76214 + 1.95550i 0.269839 + 0.0780329i
\(629\) 6.93404 + 6.93404i 0.276478 + 0.276478i
\(630\) 0 0
\(631\) 20.7940i 0.827795i −0.910323 0.413897i \(-0.864167\pi\)
0.910323 0.413897i \(-0.135833\pi\)
\(632\) 8.69574 + 0.257094i 0.345898 + 0.0102266i
\(633\) 33.9640i 1.34995i
\(634\) 8.53130 + 33.1419i 0.338821 + 1.31623i
\(635\) 0 0
\(636\) −22.4588 40.7328i −0.890551 1.61516i
\(637\) 6.63024 6.63024i 0.262700 0.262700i
\(638\) 30.6227 51.8535i 1.21237 2.05290i
\(639\) −23.9521 −0.947530
\(640\) 0 0
\(641\) 16.1179 0.636620 0.318310 0.947987i \(-0.396885\pi\)
0.318310 + 0.947987i \(0.396885\pi\)
\(642\) 6.85441 11.6066i 0.270522 0.458075i
\(643\) −10.3733 + 10.3733i −0.409082 + 0.409082i −0.881419 0.472336i \(-0.843411\pi\)
0.472336 + 0.881419i \(0.343411\pi\)
\(644\) 13.7257 + 24.8938i 0.540868 + 0.980954i
\(645\) 0 0
\(646\) −7.39298 28.7199i −0.290873 1.12997i
\(647\) 32.5724i 1.28055i 0.768145 + 0.640276i \(0.221180\pi\)
−0.768145 + 0.640276i \(0.778820\pi\)
\(648\) 28.6094 + 0.845850i 1.12388 + 0.0332281i
\(649\) 45.1298i 1.77150i
\(650\) 0 0
\(651\) 2.49733 + 2.49733i 0.0978780 + 0.0978780i
\(652\) −34.5318 9.98601i −1.35237 0.391083i
\(653\) −4.31962 + 4.31962i −0.169040 + 0.169040i −0.786557 0.617517i \(-0.788139\pi\)
0.617517 + 0.786557i \(0.288139\pi\)
\(654\) −46.1981 27.2828i −1.80649 1.06684i
\(655\) 0 0
\(656\) −3.20328 2.02174i −0.125067 0.0789359i
\(657\) −2.27191 −0.0886356
\(658\) 3.47774 + 2.05382i 0.135576 + 0.0800662i
\(659\) −4.19711 + 4.19711i −0.163496 + 0.163496i −0.784114 0.620617i \(-0.786882\pi\)
0.620617 + 0.784114i \(0.286882\pi\)
\(660\) 0 0
\(661\) 21.2310 + 21.2310i 0.825790 + 0.825790i 0.986931 0.161141i \(-0.0515175\pi\)
−0.161141 + 0.986931i \(0.551518\pi\)
\(662\) −18.9860 + 4.88731i −0.737911 + 0.189951i
\(663\) 16.2993i 0.633013i
\(664\) −2.87990 + 2.71450i −0.111762 + 0.105343i
\(665\) 0 0
\(666\) 3.44620 + 13.3876i 0.133538 + 0.518760i
\(667\) −48.9877 48.9877i −1.89681 1.89681i
\(668\) −8.77429 + 4.83788i −0.339488 + 0.187183i
\(669\) 40.1062 40.1062i 1.55060 1.55060i
\(670\) 0 0
\(671\) 45.3164 1.74942
\(672\) −7.65182 + 23.8005i −0.295175 + 0.918126i
\(673\) 6.08317 0.234489 0.117244 0.993103i \(-0.462594\pi\)
0.117244 + 0.993103i \(0.462594\pi\)
\(674\) 4.36877 7.39765i 0.168279 0.284947i
\(675\) 0 0
\(676\) 10.1202 5.57998i 0.389239 0.214615i
\(677\) 8.42443 + 8.42443i 0.323777 + 0.323777i 0.850214 0.526437i \(-0.176472\pi\)
−0.526437 + 0.850214i \(0.676472\pi\)
\(678\) −2.94551 11.4426i −0.113122 0.439449i
\(679\) 13.4313i 0.515447i
\(680\) 0 0
\(681\) 39.9824i 1.53213i
\(682\) −5.10305 + 1.31361i −0.195406 + 0.0503008i
\(683\) −14.7609 14.7609i −0.564812 0.564812i 0.365859 0.930670i \(-0.380775\pi\)
−0.930670 + 0.365859i \(0.880775\pi\)
\(684\) 11.6140 40.1615i 0.444073 1.53561i
\(685\) 0 0
\(686\) 23.9328 + 14.1338i 0.913757 + 0.539630i
\(687\) −67.3710 −2.57036
\(688\) −4.57948 + 1.03556i −0.174591 + 0.0394804i
\(689\) 26.4977 1.00948
\(690\) 0 0
\(691\) −4.06268 + 4.06268i −0.154552 + 0.154552i −0.780147 0.625596i \(-0.784856\pi\)
0.625596 + 0.780147i \(0.284856\pi\)
\(692\) −16.8337 4.86802i −0.639920 0.185054i
\(693\) 15.8350 + 15.8350i 0.601523 + 0.601523i
\(694\) 11.1801 2.87796i 0.424392 0.109246i
\(695\) 0 0
\(696\) 1.80057 60.9012i 0.0682506 2.30845i
\(697\) 2.43515i 0.0922379i
\(698\) −3.78348 14.6979i −0.143207 0.556322i
\(699\) 16.7875 + 16.7875i 0.634961 + 0.634961i
\(700\) 0 0
\(701\) 11.1049 11.1049i 0.419428 0.419428i −0.465578 0.885007i \(-0.654154\pi\)
0.885007 + 0.465578i \(0.154154\pi\)
\(702\) −1.99051 + 3.37054i −0.0751271 + 0.127213i
\(703\) −31.0982 −1.17289
\(704\) −24.7713 27.8878i −0.933603 1.05106i
\(705\) 0 0
\(706\) −11.6705 + 19.7617i −0.439225 + 0.743741i
\(707\) −1.96911 + 1.96911i −0.0740561 + 0.0740561i
\(708\) −22.0463 39.9846i −0.828551 1.50271i
\(709\) 13.0114 + 13.0114i 0.488652 + 0.488652i 0.907881 0.419229i \(-0.137700\pi\)
−0.419229 + 0.907881i \(0.637700\pi\)
\(710\) 0 0
\(711\) 7.88412i 0.295678i
\(712\) −0.843744 + 28.5381i −0.0316206 + 1.06951i
\(713\) 6.06203i 0.227025i
\(714\) 15.5645 4.00658i 0.582488 0.149942i
\(715\) 0 0
\(716\) 14.9883 + 4.33436i 0.560138 + 0.161983i
\(717\) 1.65582 1.65582i 0.0618378 0.0618378i
\(718\) 8.24759 + 4.87071i 0.307797 + 0.181773i
\(719\) −50.0570 −1.86681 −0.933406 0.358821i \(-0.883179\pi\)
−0.933406 + 0.358821i \(0.883179\pi\)
\(720\) 0 0
\(721\) 15.3774 0.572684
\(722\) 57.8439 + 34.1604i 2.15273 + 1.27132i
\(723\) 23.5547 23.5547i 0.876007 0.876007i
\(724\) 9.34977 32.3316i 0.347481 1.20160i
\(725\) 0 0
\(726\) −34.6932 + 8.93062i −1.28759 + 0.331447i
\(727\) 27.7141i 1.02786i −0.857832 0.513930i \(-0.828189\pi\)
0.857832 0.513930i \(-0.171811\pi\)
\(728\) −9.76854 10.3638i −0.362046 0.384107i
\(729\) 18.6509i 0.690775i
\(730\) 0 0
\(731\) 2.13429 + 2.13429i 0.0789396 + 0.0789396i
\(732\) 40.1499 22.1374i 1.48398 0.818224i
\(733\) −16.8860 + 16.8860i −0.623698 + 0.623698i −0.946475 0.322777i \(-0.895384\pi\)
0.322777 + 0.946475i \(0.395384\pi\)
\(734\) −4.57160 + 7.74110i −0.168741 + 0.285729i
\(735\) 0 0
\(736\) −38.1738 + 19.5998i −1.40711 + 0.722457i
\(737\) 24.6379 0.907550
\(738\) −1.74565 + 2.95592i −0.0642584 + 0.108809i
\(739\) −23.6286 + 23.6286i −0.869193 + 0.869193i −0.992383 0.123190i \(-0.960688\pi\)
0.123190 + 0.992383i \(0.460688\pi\)
\(740\) 0 0
\(741\) 36.5501 + 36.5501i 1.34270 + 1.34270i
\(742\) 6.51345 + 25.3031i 0.239116 + 0.928907i
\(743\) 6.53356i 0.239693i 0.992792 + 0.119846i \(0.0382402\pi\)
−0.992792 + 0.119846i \(0.961760\pi\)
\(744\) −3.87955 + 3.65673i −0.142231 + 0.134062i
\(745\) 0 0
\(746\) 17.8372 4.59161i 0.653068 0.168111i
\(747\) 2.53613 + 2.53613i 0.0927921 + 0.0927921i
\(748\) −6.66153 + 23.0356i −0.243570 + 0.842267i
\(749\) −5.35401 + 5.35401i −0.195631 + 0.195631i
\(750\) 0 0
\(751\) −22.8483 −0.833746 −0.416873 0.908965i \(-0.636874\pi\)
−0.416873 + 0.908965i \(0.636874\pi\)
\(752\) −3.25409 + 5.15583i −0.118664 + 0.188014i
\(753\) 5.22634 0.190459
\(754\) 29.8862 + 17.6496i 1.08839 + 0.642762i
\(755\) 0 0
\(756\) −3.70789 1.07226i −0.134855 0.0389977i
\(757\) 24.0190 + 24.0190i 0.872985 + 0.872985i 0.992797 0.119811i \(-0.0382290\pi\)
−0.119811 + 0.992797i \(0.538229\pi\)
\(758\) −10.4900 + 2.70031i −0.381015 + 0.0980797i
\(759\) 83.4243i 3.02811i
\(760\) 0 0
\(761\) 5.51772i 0.200017i −0.994987 0.100009i \(-0.968113\pi\)
0.994987 0.100009i \(-0.0318871\pi\)
\(762\) 15.0254 + 58.3700i 0.544314 + 2.11452i
\(763\) 21.3107 + 21.3107i 0.771501 + 0.771501i
\(764\) −10.7459 19.4894i −0.388772 0.705103i
\(765\) 0 0
\(766\) 20.2528 34.2941i 0.731763 1.23910i
\(767\) 26.0109 0.939200
\(768\) −35.5706 12.6073i −1.28354 0.454928i
\(769\) 14.0124 0.505299 0.252649 0.967558i \(-0.418698\pi\)
0.252649 + 0.967558i \(0.418698\pi\)
\(770\) 0 0
\(771\) 17.1108 17.1108i 0.616231 0.616231i
\(772\) −20.0689 36.3982i −0.722294 1.31000i
\(773\) −0.753043 0.753043i −0.0270851 0.0270851i 0.693435 0.720520i \(-0.256097\pi\)
−0.720520 + 0.693435i \(0.756097\pi\)
\(774\) 1.06074 + 4.12070i 0.0381274 + 0.148115i
\(775\) 0 0
\(776\) −20.2661 0.599178i −0.727512 0.0215092i
\(777\) 16.8535i 0.604614i
\(778\) −18.5896 + 4.78529i −0.666471 + 0.171561i
\(779\) −5.46066 5.46066i −0.195648 0.195648i
\(780\) 0 0
\(781\) −30.8073 + 30.8073i −1.10237 + 1.10237i
\(782\) 23.7535 + 14.0279i 0.849424 + 0.501638i
\(783\) 9.40668 0.336167