Properties

Label 980.2.c.e.979.22
Level $980$
Weight $2$
Character 980.979
Analytic conductor $7.825$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 979.22
Character \(\chi\) \(=\) 980.979
Dual form 980.2.c.e.979.23

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.255919 - 1.39086i) q^{2} +3.18626i q^{3} +(-1.86901 + 0.711898i) q^{4} +(1.80715 + 1.31689i) q^{5} +(4.43165 - 0.815425i) q^{6} +(1.46847 + 2.41735i) q^{8} -7.15223 q^{9} +O(q^{10})\) \(q+(-0.255919 - 1.39086i) q^{2} +3.18626i q^{3} +(-1.86901 + 0.711898i) q^{4} +(1.80715 + 1.31689i) q^{5} +(4.43165 - 0.815425i) q^{6} +(1.46847 + 2.41735i) q^{8} -7.15223 q^{9} +(1.36913 - 2.85052i) q^{10} +4.51680i q^{11} +(-2.26829 - 5.95515i) q^{12} -2.22528 q^{13} +(-4.19595 + 5.75805i) q^{15} +(2.98640 - 2.66109i) q^{16} -2.52865 q^{17} +(1.83040 + 9.94779i) q^{18} +5.21241 q^{19} +(-4.31508 - 1.17477i) q^{20} +(6.28226 - 1.15594i) q^{22} -1.71481 q^{23} +(-7.70231 + 4.67892i) q^{24} +(1.53160 + 4.75964i) q^{25} +(0.569493 + 3.09507i) q^{26} -13.2301i q^{27} -2.31039 q^{29} +(9.08250 + 4.36240i) q^{30} +4.62540 q^{31} +(-4.46550 - 3.47266i) q^{32} -14.3917 q^{33} +(0.647131 + 3.51701i) q^{34} +(13.3676 - 5.09167i) q^{36} -0.336766i q^{37} +(-1.33396 - 7.24976i) q^{38} -7.09032i q^{39} +(-0.529635 + 6.30234i) q^{40} -3.28064i q^{41} -6.66354 q^{43} +(-3.21551 - 8.44195i) q^{44} +(-12.9252 - 9.41870i) q^{45} +(0.438852 + 2.38506i) q^{46} +1.44644i q^{47} +(8.47892 + 9.51544i) q^{48} +(6.22805 - 3.34834i) q^{50} -8.05693i q^{51} +(4.15908 - 1.58418i) q^{52} -10.0769i q^{53} +(-18.4013 + 3.38584i) q^{54} +(-5.94813 + 8.16255i) q^{55} +16.6081i q^{57} +(0.591274 + 3.21344i) q^{58} +3.20322 q^{59} +(3.74312 - 13.7490i) q^{60} -6.05175i q^{61} +(-1.18373 - 6.43331i) q^{62} +(-3.68719 + 7.09962i) q^{64} +(-4.02143 - 2.93045i) q^{65} +(3.68311 + 20.0169i) q^{66} -11.1495 q^{67} +(4.72608 - 1.80014i) q^{68} -5.46381i q^{69} +9.15549i q^{71} +(-10.5028 - 17.2895i) q^{72} +3.24011 q^{73} +(-0.468396 + 0.0861849i) q^{74} +(-15.1654 + 4.88008i) q^{75} +(-9.74205 + 3.71071i) q^{76} +(-9.86168 + 1.81455i) q^{78} +14.2700i q^{79} +(8.90125 - 0.876239i) q^{80} +20.6978 q^{81} +(-4.56292 + 0.839579i) q^{82} +11.3059i q^{83} +(-4.56966 - 3.32995i) q^{85} +(1.70533 + 9.26808i) q^{86} -7.36150i q^{87} +(-10.9187 + 6.63279i) q^{88} +15.2152i q^{89} +(-9.79234 + 20.3876i) q^{90} +(3.20499 - 1.22077i) q^{92} +14.7377i q^{93} +(2.01181 - 0.370173i) q^{94} +(9.41962 + 6.86417i) q^{95} +(11.0648 - 14.2282i) q^{96} -4.49303 q^{97} -32.3052i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 16 q^{4} - 64 q^{9} + O(q^{10}) \) \( 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.255919 1.39086i −0.180962 0.983490i
\(3\) 3.18626i 1.83959i 0.392403 + 0.919793i \(0.371644\pi\)
−0.392403 + 0.919793i \(0.628356\pi\)
\(4\) −1.86901 + 0.711898i −0.934505 + 0.355949i
\(5\) 1.80715 + 1.31689i 0.808183 + 0.588931i
\(6\) 4.43165 0.815425i 1.80921 0.332896i
\(7\) 0 0
\(8\) 1.46847 + 2.41735i 0.519183 + 0.854663i
\(9\) −7.15223 −2.38408
\(10\) 1.36913 2.85052i 0.432957 0.901415i
\(11\) 4.51680i 1.36187i 0.732345 + 0.680934i \(0.238426\pi\)
−0.732345 + 0.680934i \(0.761574\pi\)
\(12\) −2.26829 5.95515i −0.654799 1.71910i
\(13\) −2.22528 −0.617182 −0.308591 0.951195i \(-0.599858\pi\)
−0.308591 + 0.951195i \(0.599858\pi\)
\(14\) 0 0
\(15\) −4.19595 + 5.75805i −1.08339 + 1.48672i
\(16\) 2.98640 2.66109i 0.746600 0.665273i
\(17\) −2.52865 −0.613288 −0.306644 0.951824i \(-0.599206\pi\)
−0.306644 + 0.951824i \(0.599206\pi\)
\(18\) 1.83040 + 9.94779i 0.431428 + 2.34472i
\(19\) 5.21241 1.19581 0.597904 0.801568i \(-0.296000\pi\)
0.597904 + 0.801568i \(0.296000\pi\)
\(20\) −4.31508 1.17477i −0.964881 0.262687i
\(21\) 0 0
\(22\) 6.28226 1.15594i 1.33938 0.246447i
\(23\) −1.71481 −0.357562 −0.178781 0.983889i \(-0.557215\pi\)
−0.178781 + 0.983889i \(0.557215\pi\)
\(24\) −7.70231 + 4.67892i −1.57223 + 0.955082i
\(25\) 1.53160 + 4.75964i 0.306321 + 0.951928i
\(26\) 0.569493 + 3.09507i 0.111687 + 0.606993i
\(27\) 13.2301i 2.54613i
\(28\) 0 0
\(29\) −2.31039 −0.429029 −0.214514 0.976721i \(-0.568817\pi\)
−0.214514 + 0.976721i \(0.568817\pi\)
\(30\) 9.08250 + 4.36240i 1.65823 + 0.796462i
\(31\) 4.62540 0.830747 0.415373 0.909651i \(-0.363651\pi\)
0.415373 + 0.909651i \(0.363651\pi\)
\(32\) −4.46550 3.47266i −0.789396 0.613885i
\(33\) −14.3917 −2.50527
\(34\) 0.647131 + 3.51701i 0.110982 + 0.603163i
\(35\) 0 0
\(36\) 13.3676 5.09167i 2.22793 0.848611i
\(37\) 0.336766i 0.0553640i −0.999617 0.0276820i \(-0.991187\pi\)
0.999617 0.0276820i \(-0.00881258\pi\)
\(38\) −1.33396 7.24976i −0.216396 1.17607i
\(39\) 7.09032i 1.13536i
\(40\) −0.529635 + 6.30234i −0.0837427 + 0.996487i
\(41\) 3.28064i 0.512350i −0.966630 0.256175i \(-0.917538\pi\)
0.966630 0.256175i \(-0.0824623\pi\)
\(42\) 0 0
\(43\) −6.66354 −1.01618 −0.508090 0.861304i \(-0.669648\pi\)
−0.508090 + 0.861304i \(0.669648\pi\)
\(44\) −3.21551 8.44195i −0.484756 1.27267i
\(45\) −12.9252 9.41870i −1.92677 1.40406i
\(46\) 0.438852 + 2.38506i 0.0647052 + 0.351659i
\(47\) 1.44644i 0.210985i 0.994420 + 0.105493i \(0.0336420\pi\)
−0.994420 + 0.105493i \(0.966358\pi\)
\(48\) 8.47892 + 9.51544i 1.22383 + 1.37344i
\(49\) 0 0
\(50\) 6.22805 3.34834i 0.880780 0.473527i
\(51\) 8.05693i 1.12820i
\(52\) 4.15908 1.58418i 0.576760 0.219686i
\(53\) 10.0769i 1.38416i −0.721819 0.692082i \(-0.756694\pi\)
0.721819 0.692082i \(-0.243306\pi\)
\(54\) −18.4013 + 3.38584i −2.50410 + 0.460754i
\(55\) −5.94813 + 8.16255i −0.802046 + 1.10064i
\(56\) 0 0
\(57\) 16.6081i 2.19979i
\(58\) 0.591274 + 3.21344i 0.0776380 + 0.421945i
\(59\) 3.20322 0.417023 0.208512 0.978020i \(-0.433138\pi\)
0.208512 + 0.978020i \(0.433138\pi\)
\(60\) 3.74312 13.7490i 0.483235 1.77498i
\(61\) 6.05175i 0.774847i −0.921902 0.387424i \(-0.873365\pi\)
0.921902 0.387424i \(-0.126635\pi\)
\(62\) −1.18373 6.43331i −0.150334 0.817031i
\(63\) 0 0
\(64\) −3.68719 + 7.09962i −0.460899 + 0.887453i
\(65\) −4.02143 2.93045i −0.498797 0.363478i
\(66\) 3.68311 + 20.0169i 0.453360 + 2.46391i
\(67\) −11.1495 −1.36213 −0.681067 0.732221i \(-0.738484\pi\)
−0.681067 + 0.732221i \(0.738484\pi\)
\(68\) 4.72608 1.80014i 0.573121 0.218299i
\(69\) 5.46381i 0.657766i
\(70\) 0 0
\(71\) 9.15549i 1.08656i 0.839553 + 0.543278i \(0.182817\pi\)
−0.839553 + 0.543278i \(0.817183\pi\)
\(72\) −10.5028 17.2895i −1.23777 2.03758i
\(73\) 3.24011 0.379226 0.189613 0.981859i \(-0.439277\pi\)
0.189613 + 0.981859i \(0.439277\pi\)
\(74\) −0.468396 + 0.0861849i −0.0544499 + 0.0100188i
\(75\) −15.1654 + 4.88008i −1.75115 + 0.563504i
\(76\) −9.74205 + 3.71071i −1.11749 + 0.425647i
\(77\) 0 0
\(78\) −9.86168 + 1.81455i −1.11662 + 0.205457i
\(79\) 14.2700i 1.60550i 0.596318 + 0.802748i \(0.296630\pi\)
−0.596318 + 0.802748i \(0.703370\pi\)
\(80\) 8.90125 0.876239i 0.995190 0.0979666i
\(81\) 20.6978 2.29975
\(82\) −4.56292 + 0.839579i −0.503891 + 0.0927160i
\(83\) 11.3059i 1.24099i 0.784212 + 0.620493i \(0.213067\pi\)
−0.784212 + 0.620493i \(0.786933\pi\)
\(84\) 0 0
\(85\) −4.56966 3.32995i −0.495649 0.361184i
\(86\) 1.70533 + 9.26808i 0.183890 + 0.999403i
\(87\) 7.36150i 0.789235i
\(88\) −10.9187 + 6.63279i −1.16394 + 0.707058i
\(89\) 15.2152i 1.61281i 0.591364 + 0.806405i \(0.298590\pi\)
−0.591364 + 0.806405i \(0.701410\pi\)
\(90\) −9.79234 + 20.3876i −1.03220 + 2.14904i
\(91\) 0 0
\(92\) 3.20499 1.22077i 0.334143 0.127274i
\(93\) 14.7377i 1.52823i
\(94\) 2.01181 0.370173i 0.207502 0.0381804i
\(95\) 9.41962 + 6.86417i 0.966433 + 0.704249i
\(96\) 11.0648 14.2282i 1.12929 1.45216i
\(97\) −4.49303 −0.456198 −0.228099 0.973638i \(-0.573251\pi\)
−0.228099 + 0.973638i \(0.573251\pi\)
\(98\) 0 0
\(99\) 32.3052i 3.24680i
\(100\) −6.25097 7.80547i −0.625097 0.780547i
\(101\) 0.734445i 0.0730800i −0.999332 0.0365400i \(-0.988366\pi\)
0.999332 0.0365400i \(-0.0116336\pi\)
\(102\) −11.2061 + 2.06193i −1.10957 + 0.204161i
\(103\) 11.8422i 1.16685i −0.812167 0.583424i \(-0.801712\pi\)
0.812167 0.583424i \(-0.198288\pi\)
\(104\) −3.26776 5.37929i −0.320430 0.527483i
\(105\) 0 0
\(106\) −14.0155 + 2.57886i −1.36131 + 0.250481i
\(107\) −4.98954 −0.482357 −0.241179 0.970481i \(-0.577534\pi\)
−0.241179 + 0.970481i \(0.577534\pi\)
\(108\) 9.41848 + 24.7272i 0.906294 + 2.37937i
\(109\) 11.3159 1.08386 0.541931 0.840423i \(-0.317693\pi\)
0.541931 + 0.840423i \(0.317693\pi\)
\(110\) 12.8753 + 6.18409i 1.22761 + 0.589630i
\(111\) 1.07302 0.101847
\(112\) 0 0
\(113\) 1.57514i 0.148177i −0.997252 0.0740883i \(-0.976395\pi\)
0.997252 0.0740883i \(-0.0236047\pi\)
\(114\) 23.0996 4.25033i 2.16347 0.398080i
\(115\) −3.09892 2.25821i −0.288976 0.210579i
\(116\) 4.31814 1.64476i 0.400930 0.152712i
\(117\) 15.9157 1.47141
\(118\) −0.819765 4.45524i −0.0754655 0.410138i
\(119\) 0 0
\(120\) −20.0809 1.68755i −1.83312 0.154052i
\(121\) −9.40151 −0.854683
\(122\) −8.41717 + 1.54876i −0.762054 + 0.140218i
\(123\) 10.4530 0.942511
\(124\) −8.64493 + 3.29282i −0.776337 + 0.295704i
\(125\) −3.50008 + 10.6184i −0.313057 + 0.949734i
\(126\) 0 0
\(127\) 17.0124 1.50960 0.754801 0.655954i \(-0.227733\pi\)
0.754801 + 0.655954i \(0.227733\pi\)
\(128\) 10.8182 + 3.31145i 0.956206 + 0.292694i
\(129\) 21.2317i 1.86935i
\(130\) −3.04670 + 6.34322i −0.267213 + 0.556337i
\(131\) −8.95868 −0.782723 −0.391362 0.920237i \(-0.627996\pi\)
−0.391362 + 0.920237i \(0.627996\pi\)
\(132\) 26.8982 10.2454i 2.34119 0.891750i
\(133\) 0 0
\(134\) 2.85339 + 15.5075i 0.246495 + 1.33965i
\(135\) 17.4226 23.9088i 1.49950 2.05774i
\(136\) −3.71325 6.11264i −0.318409 0.524155i
\(137\) 8.32232i 0.711023i −0.934672 0.355512i \(-0.884307\pi\)
0.934672 0.355512i \(-0.115693\pi\)
\(138\) −7.59943 + 1.39830i −0.646906 + 0.119031i
\(139\) 15.5985 1.32305 0.661524 0.749924i \(-0.269910\pi\)
0.661524 + 0.749924i \(0.269910\pi\)
\(140\) 0 0
\(141\) −4.60874 −0.388126
\(142\) 12.7341 2.34307i 1.06862 0.196626i
\(143\) 10.0512i 0.840521i
\(144\) −21.3594 + 19.0328i −1.77995 + 1.58606i
\(145\) −4.17523 3.04253i −0.346734 0.252668i
\(146\) −0.829206 4.50655i −0.0686256 0.372965i
\(147\) 0 0
\(148\) 0.239743 + 0.629419i 0.0197068 + 0.0517379i
\(149\) 2.51385 0.205943 0.102971 0.994684i \(-0.467165\pi\)
0.102971 + 0.994684i \(0.467165\pi\)
\(150\) 10.6687 + 19.8442i 0.871093 + 1.62027i
\(151\) 12.7350i 1.03636i 0.855271 + 0.518181i \(0.173391\pi\)
−0.855271 + 0.518181i \(0.826609\pi\)
\(152\) 7.65427 + 12.6002i 0.620843 + 1.02201i
\(153\) 18.0855 1.46213
\(154\) 0 0
\(155\) 8.35881 + 6.09114i 0.671396 + 0.489253i
\(156\) 5.04759 + 13.2519i 0.404131 + 1.06100i
\(157\) 8.64749 0.690145 0.345073 0.938576i \(-0.387854\pi\)
0.345073 + 0.938576i \(0.387854\pi\)
\(158\) 19.8476 3.65196i 1.57899 0.290534i
\(159\) 32.1075 2.54629
\(160\) −3.49673 12.1562i −0.276441 0.961031i
\(161\) 0 0
\(162\) −5.29696 28.7878i −0.416168 2.26178i
\(163\) −3.41606 −0.267566 −0.133783 0.991011i \(-0.542713\pi\)
−0.133783 + 0.991011i \(0.542713\pi\)
\(164\) 2.33548 + 6.13155i 0.182370 + 0.478793i
\(165\) −26.0080 18.9523i −2.02472 1.47543i
\(166\) 15.7250 2.89340i 1.22050 0.224572i
\(167\) 11.6381i 0.900581i 0.892882 + 0.450290i \(0.148680\pi\)
−0.892882 + 0.450290i \(0.851320\pi\)
\(168\) 0 0
\(169\) −8.04812 −0.619086
\(170\) −3.46205 + 7.20798i −0.265527 + 0.552827i
\(171\) −37.2804 −2.85090
\(172\) 12.4542 4.74376i 0.949626 0.361708i
\(173\) 8.21670 0.624704 0.312352 0.949966i \(-0.398883\pi\)
0.312352 + 0.949966i \(0.398883\pi\)
\(174\) −10.2388 + 1.88395i −0.776205 + 0.142822i
\(175\) 0 0
\(176\) 12.0196 + 13.4890i 0.906013 + 1.01677i
\(177\) 10.2063i 0.767151i
\(178\) 21.1623 3.89387i 1.58618 0.291858i
\(179\) 15.5937i 1.16553i −0.812641 0.582764i \(-0.801971\pi\)
0.812641 0.582764i \(-0.198029\pi\)
\(180\) 30.8625 + 8.40224i 2.30035 + 0.626266i
\(181\) 15.8536i 1.17839i −0.807990 0.589196i \(-0.799445\pi\)
0.807990 0.589196i \(-0.200555\pi\)
\(182\) 0 0
\(183\) 19.2824 1.42540
\(184\) −2.51814 4.14529i −0.185640 0.305595i
\(185\) 0.443484 0.608588i 0.0326056 0.0447442i
\(186\) 20.4982 3.77167i 1.50300 0.276552i
\(187\) 11.4214i 0.835217i
\(188\) −1.02972 2.70342i −0.0751001 0.197167i
\(189\) 0 0
\(190\) 7.13647 14.8581i 0.517734 1.07792i
\(191\) 11.2516i 0.814137i 0.913398 + 0.407068i \(0.133449\pi\)
−0.913398 + 0.407068i \(0.866551\pi\)
\(192\) −22.6212 11.7483i −1.63255 0.847863i
\(193\) 24.8339i 1.78758i 0.448484 + 0.893791i \(0.351964\pi\)
−0.448484 + 0.893791i \(0.648036\pi\)
\(194\) 1.14985 + 6.24919i 0.0825546 + 0.448666i
\(195\) 9.33717 12.8133i 0.668649 0.917579i
\(196\) 0 0
\(197\) 13.9890i 0.996672i 0.866984 + 0.498336i \(0.166055\pi\)
−0.866984 + 0.498336i \(0.833945\pi\)
\(198\) −44.9322 + 8.26753i −3.19319 + 0.587548i
\(199\) 19.5440 1.38544 0.692719 0.721208i \(-0.256413\pi\)
0.692719 + 0.721208i \(0.256413\pi\)
\(200\) −9.25662 + 10.6918i −0.654542 + 0.756026i
\(201\) 35.5253i 2.50576i
\(202\) −1.02151 + 0.187959i −0.0718734 + 0.0132247i
\(203\) 0 0
\(204\) 5.73572 + 15.0585i 0.401581 + 1.05431i
\(205\) 4.32024 5.92862i 0.301739 0.414072i
\(206\) −16.4709 + 3.03065i −1.14758 + 0.211156i
\(207\) 12.2647 0.852455
\(208\) −6.64559 + 5.92168i −0.460789 + 0.410595i
\(209\) 23.5434i 1.62853i
\(210\) 0 0
\(211\) 3.60453i 0.248146i −0.992273 0.124073i \(-0.960404\pi\)
0.992273 0.124073i \(-0.0395957\pi\)
\(212\) 7.17370 + 18.8338i 0.492692 + 1.29351i
\(213\) −29.1717 −1.99882
\(214\) 1.27692 + 6.93978i 0.0872885 + 0.474394i
\(215\) −12.0420 8.77514i −0.821260 0.598460i
\(216\) 31.9818 19.4280i 2.17609 1.32191i
\(217\) 0 0
\(218\) −2.89595 15.7388i −0.196138 1.06597i
\(219\) 10.3238i 0.697619i
\(220\) 5.30621 19.4904i 0.357745 1.31404i
\(221\) 5.62696 0.378511
\(222\) −0.274607 1.49243i −0.0184304 0.100165i
\(223\) 1.51767i 0.101631i −0.998708 0.0508154i \(-0.983818\pi\)
0.998708 0.0508154i \(-0.0161820\pi\)
\(224\) 0 0
\(225\) −10.9544 34.0421i −0.730293 2.26947i
\(226\) −2.19080 + 0.403108i −0.145730 + 0.0268144i
\(227\) 15.5593i 1.03271i 0.856375 + 0.516354i \(0.172711\pi\)
−0.856375 + 0.516354i \(0.827289\pi\)
\(228\) −11.8233 31.0407i −0.783015 2.05572i
\(229\) 19.2013i 1.26885i −0.772982 0.634427i \(-0.781236\pi\)
0.772982 0.634427i \(-0.218764\pi\)
\(230\) −2.34779 + 4.88810i −0.154809 + 0.322311i
\(231\) 0 0
\(232\) −3.39274 5.58503i −0.222744 0.366675i
\(233\) 3.14543i 0.206064i 0.994678 + 0.103032i \(0.0328544\pi\)
−0.994678 + 0.103032i \(0.967146\pi\)
\(234\) −4.07315 22.1367i −0.266270 1.44712i
\(235\) −1.90481 + 2.61394i −0.124256 + 0.170515i
\(236\) −5.98685 + 2.28037i −0.389711 + 0.148439i
\(237\) −45.4678 −2.95345
\(238\) 0 0
\(239\) 3.75292i 0.242756i 0.992606 + 0.121378i \(0.0387314\pi\)
−0.992606 + 0.121378i \(0.961269\pi\)
\(240\) 2.79192 + 28.3617i 0.180218 + 1.83074i
\(241\) 7.43129i 0.478691i 0.970934 + 0.239346i \(0.0769329\pi\)
−0.970934 + 0.239346i \(0.923067\pi\)
\(242\) 2.40603 + 13.0762i 0.154665 + 0.840572i
\(243\) 26.2581i 1.68446i
\(244\) 4.30823 + 11.3108i 0.275806 + 0.724099i
\(245\) 0 0
\(246\) −2.67511 14.5387i −0.170559 0.926951i
\(247\) −11.5991 −0.738032
\(248\) 6.79227 + 11.1812i 0.431309 + 0.710009i
\(249\) −36.0236 −2.28290
\(250\) 15.6644 + 2.15070i 0.990706 + 0.136022i
\(251\) 5.77378 0.364438 0.182219 0.983258i \(-0.441672\pi\)
0.182219 + 0.983258i \(0.441672\pi\)
\(252\) 0 0
\(253\) 7.74544i 0.486952i
\(254\) −4.35379 23.6619i −0.273181 1.48468i
\(255\) 10.6101 14.5601i 0.664430 0.911790i
\(256\) 1.83718 15.8942i 0.114824 0.993386i
\(257\) 14.8503 0.926336 0.463168 0.886270i \(-0.346713\pi\)
0.463168 + 0.886270i \(0.346713\pi\)
\(258\) −29.5305 + 5.43361i −1.83849 + 0.338282i
\(259\) 0 0
\(260\) 9.60227 + 2.61420i 0.595508 + 0.162126i
\(261\) 16.5245 1.02284
\(262\) 2.29270 + 12.4603i 0.141643 + 0.769800i
\(263\) −25.0905 −1.54715 −0.773573 0.633707i \(-0.781533\pi\)
−0.773573 + 0.633707i \(0.781533\pi\)
\(264\) −21.1338 34.7898i −1.30069 2.14116i
\(265\) 13.2701 18.2104i 0.815176 1.11866i
\(266\) 0 0
\(267\) −48.4796 −2.96690
\(268\) 20.8386 7.93735i 1.27292 0.484851i
\(269\) 29.7861i 1.81609i 0.418871 + 0.908046i \(0.362426\pi\)
−0.418871 + 0.908046i \(0.637574\pi\)
\(270\) −37.7127 18.1137i −2.29512 1.10237i
\(271\) 1.90002 0.115418 0.0577091 0.998333i \(-0.481620\pi\)
0.0577091 + 0.998333i \(0.481620\pi\)
\(272\) −7.55157 + 6.72897i −0.457881 + 0.408004i
\(273\) 0 0
\(274\) −11.5752 + 2.12984i −0.699284 + 0.128668i
\(275\) −21.4984 + 6.91795i −1.29640 + 0.417168i
\(276\) 3.88968 + 10.2119i 0.234131 + 0.614686i
\(277\) 0.261529i 0.0157138i 0.999969 + 0.00785689i \(0.00250095\pi\)
−0.999969 + 0.00785689i \(0.997499\pi\)
\(278\) −3.99196 21.6954i −0.239422 1.30120i
\(279\) −33.0820 −1.98057
\(280\) 0 0
\(281\) 5.36553 0.320080 0.160040 0.987110i \(-0.448838\pi\)
0.160040 + 0.987110i \(0.448838\pi\)
\(282\) 1.17947 + 6.41013i 0.0702361 + 0.381718i
\(283\) 14.9849i 0.890757i 0.895342 + 0.445378i \(0.146931\pi\)
−0.895342 + 0.445378i \(0.853069\pi\)
\(284\) −6.51778 17.1117i −0.386759 1.01539i
\(285\) −21.8710 + 30.0133i −1.29553 + 1.77784i
\(286\) −13.9798 + 2.57229i −0.826644 + 0.152103i
\(287\) 0 0
\(288\) 31.9383 + 24.8372i 1.88198 + 1.46355i
\(289\) −10.6059 −0.623878
\(290\) −3.16322 + 6.58582i −0.185751 + 0.386733i
\(291\) 14.3159i 0.839215i
\(292\) −6.05579 + 2.30663i −0.354388 + 0.134985i
\(293\) 23.2770 1.35986 0.679928 0.733279i \(-0.262011\pi\)
0.679928 + 0.733279i \(0.262011\pi\)
\(294\) 0 0
\(295\) 5.78871 + 4.21828i 0.337031 + 0.245598i
\(296\) 0.814082 0.494531i 0.0473176 0.0287440i
\(297\) 59.7577 3.46749
\(298\) −0.643344 3.49643i −0.0372679 0.202543i
\(299\) 3.81593 0.220681
\(300\) 24.8702 19.9172i 1.43588 1.14992i
\(301\) 0 0
\(302\) 17.7127 3.25914i 1.01925 0.187542i
\(303\) 2.34013 0.134437
\(304\) 15.5663 13.8707i 0.892791 0.795539i
\(305\) 7.96948 10.9364i 0.456331 0.626219i
\(306\) −4.62843 25.1545i −0.264590 1.43799i
\(307\) 5.70758i 0.325749i 0.986647 + 0.162874i \(0.0520765\pi\)
−0.986647 + 0.162874i \(0.947923\pi\)
\(308\) 0 0
\(309\) 37.7324 2.14652
\(310\) 6.33278 13.1848i 0.359678 0.748847i
\(311\) 32.0916 1.81975 0.909873 0.414886i \(-0.136179\pi\)
0.909873 + 0.414886i \(0.136179\pi\)
\(312\) 17.1398 10.4119i 0.970351 0.589460i
\(313\) 28.1435 1.59077 0.795384 0.606106i \(-0.207269\pi\)
0.795384 + 0.606106i \(0.207269\pi\)
\(314\) −2.21306 12.0275i −0.124890 0.678751i
\(315\) 0 0
\(316\) −10.1588 26.6707i −0.571475 1.50034i
\(317\) 13.3985i 0.752533i 0.926511 + 0.376267i \(0.122792\pi\)
−0.926511 + 0.376267i \(0.877208\pi\)
\(318\) −8.21692 44.6571i −0.460782 2.50425i
\(319\) 10.4356i 0.584280i
\(320\) −16.0127 + 7.97449i −0.895139 + 0.445787i
\(321\) 15.8980i 0.887338i
\(322\) 0 0
\(323\) −13.1804 −0.733375
\(324\) −38.6843 + 14.7347i −2.14913 + 0.818595i
\(325\) −3.40825 10.5915i −0.189056 0.587513i
\(326\) 0.874236 + 4.75128i 0.0484194 + 0.263149i
\(327\) 36.0552i 1.99386i
\(328\) 7.93046 4.81752i 0.437886 0.266003i
\(329\) 0 0
\(330\) −19.7041 + 41.0239i −1.08468 + 2.25829i
\(331\) 22.7117i 1.24835i −0.781286 0.624173i \(-0.785436\pi\)
0.781286 0.624173i \(-0.214564\pi\)
\(332\) −8.04867 21.1309i −0.441728 1.15971i
\(333\) 2.40863i 0.131992i
\(334\) 16.1870 2.97841i 0.885712 0.162971i
\(335\) −20.1489 14.6827i −1.10085 0.802203i
\(336\) 0 0
\(337\) 8.84953i 0.482065i −0.970517 0.241032i \(-0.922514\pi\)
0.970517 0.241032i \(-0.0774860\pi\)
\(338\) 2.05967 + 11.1938i 0.112031 + 0.608865i
\(339\) 5.01880 0.272584
\(340\) 10.9113 + 2.97059i 0.591750 + 0.161103i
\(341\) 20.8920i 1.13137i
\(342\) 9.54077 + 51.8520i 0.515906 + 2.80383i
\(343\) 0 0
\(344\) −9.78521 16.1081i −0.527583 0.868492i
\(345\) 7.19524 9.87395i 0.387379 0.531596i
\(346\) −2.10281 11.4283i −0.113048 0.614390i
\(347\) 16.7339 0.898325 0.449163 0.893450i \(-0.351722\pi\)
0.449163 + 0.893450i \(0.351722\pi\)
\(348\) 5.24064 + 13.7587i 0.280928 + 0.737545i
\(349\) 3.86908i 0.207107i −0.994624 0.103554i \(-0.966979\pi\)
0.994624 0.103554i \(-0.0330213\pi\)
\(350\) 0 0
\(351\) 29.4407i 1.57143i
\(352\) 15.6853 20.1698i 0.836029 1.07505i
\(353\) 7.90229 0.420597 0.210298 0.977637i \(-0.432556\pi\)
0.210298 + 0.977637i \(0.432556\pi\)
\(354\) 14.1956 2.61198i 0.754485 0.138825i
\(355\) −12.0568 + 16.5454i −0.639907 + 0.878137i
\(356\) −10.8317 28.4374i −0.574079 1.50718i
\(357\) 0 0
\(358\) −21.6887 + 3.99073i −1.14629 + 0.210917i
\(359\) 4.16127i 0.219623i 0.993952 + 0.109812i \(0.0350248\pi\)
−0.993952 + 0.109812i \(0.964975\pi\)
\(360\) 3.78808 45.0758i 0.199649 2.37570i
\(361\) 8.16920 0.429958
\(362\) −22.0503 + 4.05725i −1.15894 + 0.213244i
\(363\) 29.9556i 1.57226i
\(364\) 0 0
\(365\) 5.85537 + 4.26686i 0.306484 + 0.223338i
\(366\) −4.93475 26.8193i −0.257943 1.40186i
\(367\) 27.3777i 1.42910i 0.699583 + 0.714551i \(0.253369\pi\)
−0.699583 + 0.714551i \(0.746631\pi\)
\(368\) −5.12110 + 4.56326i −0.266956 + 0.237876i
\(369\) 23.4639i 1.22148i
\(370\) −0.959959 0.461076i −0.0499059 0.0239702i
\(371\) 0 0
\(372\) −10.4918 27.5450i −0.543973 1.42814i
\(373\) 29.3085i 1.51754i −0.651360 0.758768i \(-0.725801\pi\)
0.651360 0.758768i \(-0.274199\pi\)
\(374\) −15.8857 + 2.92296i −0.821428 + 0.151143i
\(375\) −33.8328 11.1522i −1.74712 0.575895i
\(376\) −3.49656 + 2.12406i −0.180321 + 0.109540i
\(377\) 5.14127 0.264789
\(378\) 0 0
\(379\) 21.4131i 1.09992i 0.835192 + 0.549958i \(0.185356\pi\)
−0.835192 + 0.549958i \(0.814644\pi\)
\(380\) −22.4920 6.12339i −1.15381 0.314123i
\(381\) 54.2057i 2.77704i
\(382\) 15.6494 2.87950i 0.800695 0.147328i
\(383\) 19.2892i 0.985633i −0.870133 0.492817i \(-0.835967\pi\)
0.870133 0.492817i \(-0.164033\pi\)
\(384\) −10.5511 + 34.4697i −0.538435 + 1.75902i
\(385\) 0 0
\(386\) 34.5406 6.35547i 1.75807 0.323485i
\(387\) 47.6592 2.42265
\(388\) 8.39751 3.19858i 0.426319 0.162383i
\(389\) 15.5064 0.786203 0.393102 0.919495i \(-0.371402\pi\)
0.393102 + 0.919495i \(0.371402\pi\)
\(390\) −20.2111 9.70758i −1.02343 0.491562i
\(391\) 4.33615 0.219288
\(392\) 0 0
\(393\) 28.5446i 1.43989i
\(394\) 19.4567 3.58004i 0.980217 0.180360i
\(395\) −18.7920 + 25.7880i −0.945526 + 1.29754i
\(396\) 22.9980 + 60.3788i 1.15570 + 3.03415i
\(397\) −23.0690 −1.15780 −0.578899 0.815399i \(-0.696518\pi\)
−0.578899 + 0.815399i \(0.696518\pi\)
\(398\) −5.00169 27.1831i −0.250712 1.36256i
\(399\) 0 0
\(400\) 17.2398 + 10.1385i 0.861991 + 0.506923i
\(401\) 36.6133 1.82838 0.914191 0.405283i \(-0.132827\pi\)
0.914191 + 0.405283i \(0.132827\pi\)
\(402\) −49.4109 + 9.09162i −2.46439 + 0.453449i
\(403\) −10.2928 −0.512722
\(404\) 0.522850 + 1.37268i 0.0260128 + 0.0682936i
\(405\) 37.4040 + 27.2567i 1.85862 + 1.35439i
\(406\) 0 0
\(407\) 1.52111 0.0753984
\(408\) 19.4764 11.8314i 0.964228 0.585740i
\(409\) 30.9997i 1.53284i −0.642341 0.766419i \(-0.722037\pi\)
0.642341 0.766419i \(-0.277963\pi\)
\(410\) −9.35154 4.49162i −0.461839 0.221825i
\(411\) 26.5170 1.30799
\(412\) 8.43046 + 22.1332i 0.415339 + 1.09043i
\(413\) 0 0
\(414\) −3.13877 17.0585i −0.154262 0.838381i
\(415\) −14.8886 + 20.4315i −0.730855 + 1.00294i
\(416\) 9.93699 + 7.72764i 0.487201 + 0.378879i
\(417\) 49.7008i 2.43386i
\(418\) 32.7457 6.02522i 1.60165 0.294703i
\(419\) 11.9532 0.583953 0.291977 0.956425i \(-0.405687\pi\)
0.291977 + 0.956425i \(0.405687\pi\)
\(420\) 0 0
\(421\) 13.5052 0.658205 0.329103 0.944294i \(-0.393254\pi\)
0.329103 + 0.944294i \(0.393254\pi\)
\(422\) −5.01341 + 0.922469i −0.244049 + 0.0449051i
\(423\) 10.3453i 0.503006i
\(424\) 24.3593 14.7976i 1.18299 0.718634i
\(425\) −3.87289 12.0355i −0.187863 0.583806i
\(426\) 7.46561 + 40.5740i 0.361710 + 1.96581i
\(427\) 0 0
\(428\) 9.32551 3.55205i 0.450765 0.171695i
\(429\) 32.0256 1.54621
\(430\) −9.12325 + 18.9946i −0.439962 + 0.915999i
\(431\) 35.5892i 1.71427i 0.515090 + 0.857136i \(0.327758\pi\)
−0.515090 + 0.857136i \(0.672242\pi\)
\(432\) −35.2065 39.5103i −1.69387 1.90094i
\(433\) −16.8799 −0.811199 −0.405599 0.914051i \(-0.632937\pi\)
−0.405599 + 0.914051i \(0.632937\pi\)
\(434\) 0 0
\(435\) 9.69428 13.3034i 0.464805 0.637847i
\(436\) −21.1495 + 8.05574i −1.01288 + 0.385800i
\(437\) −8.93827 −0.427576
\(438\) 14.3590 2.64206i 0.686101 0.126243i
\(439\) −23.5676 −1.12482 −0.562410 0.826858i \(-0.690126\pi\)
−0.562410 + 0.826858i \(0.690126\pi\)
\(440\) −28.4664 2.39226i −1.35708 0.114046i
\(441\) 0 0
\(442\) −1.44005 7.82635i −0.0684962 0.372261i
\(443\) −8.93347 −0.424442 −0.212221 0.977222i \(-0.568070\pi\)
−0.212221 + 0.977222i \(0.568070\pi\)
\(444\) −2.00549 + 0.763883i −0.0951764 + 0.0362523i
\(445\) −20.0368 + 27.4962i −0.949834 + 1.30345i
\(446\) −2.11087 + 0.388401i −0.0999528 + 0.0183913i
\(447\) 8.00978i 0.378850i
\(448\) 0 0
\(449\) −33.1350 −1.56374 −0.781868 0.623445i \(-0.785733\pi\)
−0.781868 + 0.623445i \(0.785733\pi\)
\(450\) −44.5445 + 23.9481i −2.09985 + 1.12892i
\(451\) 14.8180 0.697752
\(452\) 1.12134 + 2.94395i 0.0527433 + 0.138472i
\(453\) −40.5771 −1.90648
\(454\) 21.6409 3.98193i 1.01566 0.186881i
\(455\) 0 0
\(456\) −40.1476 + 24.3885i −1.88008 + 1.14209i
\(457\) 24.6492i 1.15304i −0.817082 0.576521i \(-0.804410\pi\)
0.817082 0.576521i \(-0.195590\pi\)
\(458\) −26.7064 + 4.91397i −1.24791 + 0.229615i
\(459\) 33.4543i 1.56151i
\(460\) 7.39953 + 2.01450i 0.345005 + 0.0939268i
\(461\) 38.2341i 1.78074i 0.455239 + 0.890369i \(0.349554\pi\)
−0.455239 + 0.890369i \(0.650446\pi\)
\(462\) 0 0
\(463\) −14.6319 −0.680004 −0.340002 0.940425i \(-0.610428\pi\)
−0.340002 + 0.940425i \(0.610428\pi\)
\(464\) −6.89975 + 6.14816i −0.320313 + 0.285421i
\(465\) −19.4080 + 26.6333i −0.900022 + 1.23509i
\(466\) 4.37487 0.804976i 0.202662 0.0372898i
\(467\) 8.52322i 0.394408i −0.980363 0.197204i \(-0.936814\pi\)
0.980363 0.197204i \(-0.0631861\pi\)
\(468\) −29.7467 + 11.3304i −1.37504 + 0.523748i
\(469\) 0 0
\(470\) 4.12312 + 1.98037i 0.190185 + 0.0913476i
\(471\) 27.5531i 1.26958i
\(472\) 4.70383 + 7.74331i 0.216511 + 0.356415i
\(473\) 30.0979i 1.38390i
\(474\) 11.6361 + 63.2395i 0.534463 + 2.90469i
\(475\) 7.98335 + 24.8092i 0.366301 + 1.13832i
\(476\) 0 0
\(477\) 72.0721i 3.29995i
\(478\) 5.21981 0.960446i 0.238748 0.0439298i
\(479\) −39.2249 −1.79223 −0.896115 0.443823i \(-0.853622\pi\)
−0.896115 + 0.443823i \(0.853622\pi\)
\(480\) 38.7327 11.1415i 1.76790 0.508537i
\(481\) 0.749400i 0.0341697i
\(482\) 10.3359 1.90181i 0.470788 0.0866251i
\(483\) 0 0
\(484\) 17.5715 6.69292i 0.798706 0.304224i
\(485\) −8.11959 5.91682i −0.368691 0.268669i
\(486\) 36.5215 6.71996i 1.65665 0.304824i
\(487\) 25.5876 1.15948 0.579742 0.814800i \(-0.303153\pi\)
0.579742 + 0.814800i \(0.303153\pi\)
\(488\) 14.6292 8.88682i 0.662233 0.402287i
\(489\) 10.8844i 0.492212i
\(490\) 0 0
\(491\) 40.7008i 1.83680i −0.395654 0.918400i \(-0.629482\pi\)
0.395654 0.918400i \(-0.370518\pi\)
\(492\) −19.5367 + 7.44144i −0.880782 + 0.335486i
\(493\) 5.84217 0.263118
\(494\) 2.96843 + 16.1328i 0.133556 + 0.725847i
\(495\) 42.5424 58.3805i 1.91214 2.62401i
\(496\) 13.8133 12.3086i 0.620236 0.552673i
\(497\) 0 0
\(498\) 9.21913 + 50.1039i 0.413119 + 2.24521i
\(499\) 15.9072i 0.712106i −0.934466 0.356053i \(-0.884122\pi\)
0.934466 0.356053i \(-0.115878\pi\)
\(500\) −1.01751 22.3375i −0.0455042 0.998964i
\(501\) −37.0819 −1.65670
\(502\) −1.47762 8.03055i −0.0659495 0.358421i
\(503\) 9.64379i 0.429995i 0.976615 + 0.214998i \(0.0689744\pi\)
−0.976615 + 0.214998i \(0.931026\pi\)
\(504\) 0 0
\(505\) 0.967182 1.32725i 0.0430391 0.0590620i
\(506\) −10.7729 + 1.98221i −0.478912 + 0.0881199i
\(507\) 25.6434i 1.13886i
\(508\) −31.7963 + 12.1111i −1.41073 + 0.537342i
\(509\) 3.77669i 0.167399i 0.996491 + 0.0836995i \(0.0266736\pi\)
−0.996491 + 0.0836995i \(0.973326\pi\)
\(510\) −22.9665 11.0310i −1.01697 0.488460i
\(511\) 0 0
\(512\) −22.5768 + 1.51235i −0.997764 + 0.0668372i
\(513\) 68.9606i 3.04469i
\(514\) −3.80048 20.6548i −0.167632 0.911043i
\(515\) 15.5949 21.4007i 0.687193 0.943028i
\(516\) 15.1148 + 39.6824i 0.665394 + 1.74692i
\(517\) −6.53330 −0.287334
\(518\) 0 0
\(519\) 26.1805i 1.14920i
\(520\) 1.17859 14.0245i 0.0516845 0.615015i
\(521\) 0.0914926i 0.00400837i −0.999998 0.00200418i \(-0.999362\pi\)
0.999998 0.00200418i \(-0.000637952\pi\)
\(522\) −4.22893 22.9833i −0.185095 1.00595i
\(523\) 15.0818i 0.659480i −0.944072 0.329740i \(-0.893039\pi\)
0.944072 0.329740i \(-0.106961\pi\)
\(524\) 16.7439 6.37767i 0.731459 0.278610i
\(525\) 0 0
\(526\) 6.42115 + 34.8975i 0.279975 + 1.52160i
\(527\) −11.6960 −0.509487
\(528\) −42.9794 + 38.2976i −1.87044 + 1.66669i
\(529\) −20.0594 −0.872150
\(530\) −28.7243 13.7965i −1.24770 0.599283i
\(531\) −22.9102 −0.994217
\(532\) 0 0
\(533\) 7.30035i 0.316213i
\(534\) 12.4069 + 67.4286i 0.536898 + 2.91792i
\(535\) −9.01687 6.57068i −0.389833 0.284075i
\(536\) −16.3728 26.9524i −0.707197 1.16417i
\(537\) 49.6855 2.14409
\(538\) 41.4285 7.62284i 1.78611 0.328644i
\(539\) 0 0
\(540\) −15.5423 + 57.0889i −0.668835 + 2.45671i
\(541\) −27.4738 −1.18119 −0.590596 0.806968i \(-0.701107\pi\)
−0.590596 + 0.806968i \(0.701107\pi\)
\(542\) −0.486253 2.64268i −0.0208864 0.113513i
\(543\) 50.5138 2.16775
\(544\) 11.2917 + 8.78114i 0.484127 + 0.376488i
\(545\) 20.4495 + 14.9017i 0.875960 + 0.638320i
\(546\) 0 0
\(547\) −18.3722 −0.785540 −0.392770 0.919637i \(-0.628483\pi\)
−0.392770 + 0.919637i \(0.628483\pi\)
\(548\) 5.92464 + 15.5545i 0.253088 + 0.664455i
\(549\) 43.2835i 1.84730i
\(550\) 15.1238 + 28.1309i 0.644880 + 1.19950i
\(551\) −12.0427 −0.513036
\(552\) 13.2080 8.02345i 0.562168 0.341501i
\(553\) 0 0
\(554\) 0.363752 0.0669304i 0.0154543 0.00284360i
\(555\) 1.93912 + 1.41305i 0.0823109 + 0.0599807i
\(556\) −29.1538 + 11.1045i −1.23640 + 0.470938i
\(557\) 13.9550i 0.591294i 0.955297 + 0.295647i \(0.0955351\pi\)
−0.955297 + 0.295647i \(0.904465\pi\)
\(558\) 8.46632 + 46.0126i 0.358408 + 1.94787i
\(559\) 14.8283 0.627168
\(560\) 0 0
\(561\) 36.3916 1.53645
\(562\) −1.37314 7.46272i −0.0579225 0.314796i
\(563\) 18.5730i 0.782760i −0.920229 0.391380i \(-0.871998\pi\)
0.920229 0.391380i \(-0.128002\pi\)
\(564\) 8.61378 3.28095i 0.362706 0.138153i
\(565\) 2.07428 2.84652i 0.0872657 0.119754i
\(566\) 20.8419 3.83491i 0.876051 0.161193i
\(567\) 0 0
\(568\) −22.1320 + 13.4446i −0.928640 + 0.564122i
\(569\) 8.08905 0.339111 0.169555 0.985521i \(-0.445767\pi\)
0.169555 + 0.985521i \(0.445767\pi\)
\(570\) 47.3417 + 22.7386i 1.98293 + 0.952416i
\(571\) 0.840877i 0.0351896i −0.999845 0.0175948i \(-0.994399\pi\)
0.999845 0.0175948i \(-0.00560089\pi\)
\(572\) 7.15541 + 18.7857i 0.299183 + 0.785471i
\(573\) −35.8505 −1.49767
\(574\) 0 0
\(575\) −2.62640 8.16186i −0.109529 0.340373i
\(576\) 26.3716 50.7782i 1.09882 2.11576i
\(577\) 46.1975 1.92323 0.961614 0.274404i \(-0.0884807\pi\)
0.961614 + 0.274404i \(0.0884807\pi\)
\(578\) 2.71426 + 14.7514i 0.112898 + 0.613578i
\(579\) −79.1271 −3.28841
\(580\) 9.96952 + 2.71418i 0.413962 + 0.112700i
\(581\) 0 0
\(582\) −19.9115 + 3.66373i −0.825360 + 0.151866i
\(583\) 45.5152 1.88505
\(584\) 4.75800 + 7.83248i 0.196887 + 0.324110i
\(585\) 28.7622 + 20.9593i 1.18917 + 0.866560i
\(586\) −5.95703 32.3751i −0.246083 1.33740i
\(587\) 2.72072i 0.112296i 0.998422 + 0.0561482i \(0.0178819\pi\)
−0.998422 + 0.0561482i \(0.982118\pi\)
\(588\) 0 0
\(589\) 24.1095 0.993414
\(590\) 4.38562 9.13085i 0.180553 0.375911i
\(591\) −44.5724 −1.83346
\(592\) −0.896165 1.00572i −0.0368322 0.0413348i
\(593\) −34.7891 −1.42862 −0.714308 0.699831i \(-0.753259\pi\)
−0.714308 + 0.699831i \(0.753259\pi\)
\(594\) −15.2932 83.1149i −0.627486 3.41025i
\(595\) 0 0
\(596\) −4.69842 + 1.78961i −0.192455 + 0.0733052i
\(597\) 62.2722i 2.54863i
\(598\) −0.976570 5.30744i −0.0399349 0.217037i
\(599\) 11.7189i 0.478821i 0.970918 + 0.239411i \(0.0769542\pi\)
−0.970918 + 0.239411i \(0.923046\pi\)
\(600\) −34.0669 29.4940i −1.39078 1.20409i
\(601\) 17.1738i 0.700532i 0.936650 + 0.350266i \(0.113909\pi\)
−0.936650 + 0.350266i \(0.886091\pi\)
\(602\) 0 0
\(603\) 79.7442 3.24743
\(604\) −9.06605 23.8019i −0.368892 0.968485i
\(605\) −16.9900 12.3808i −0.690740 0.503349i
\(606\) −0.598884 3.25480i −0.0243280 0.132217i
\(607\) 16.6117i 0.674247i 0.941460 + 0.337123i \(0.109454\pi\)
−0.941460 + 0.337123i \(0.890546\pi\)
\(608\) −23.2760 18.1009i −0.943966 0.734088i
\(609\) 0 0
\(610\) −17.2507 8.28563i −0.698458 0.335475i
\(611\) 3.21874i 0.130216i
\(612\) −33.8020 + 12.8750i −1.36637 + 0.520443i
\(613\) 32.9900i 1.33245i −0.745750 0.666226i \(-0.767908\pi\)
0.745750 0.666226i \(-0.232092\pi\)
\(614\) 7.93847 1.46068i 0.320371 0.0589483i
\(615\) 18.8901 + 13.7654i 0.761722 + 0.555074i
\(616\) 0 0
\(617\) 23.9885i 0.965739i 0.875692 + 0.482870i \(0.160405\pi\)
−0.875692 + 0.482870i \(0.839595\pi\)
\(618\) −9.65644 52.4806i −0.388439 2.11108i
\(619\) −31.3184 −1.25879 −0.629396 0.777085i \(-0.716698\pi\)
−0.629396 + 0.777085i \(0.716698\pi\)
\(620\) −19.9590 5.43379i −0.801572 0.218226i
\(621\) 22.6870i 0.910400i
\(622\) −8.21286 44.6351i −0.329306 1.78970i
\(623\) 0 0
\(624\) −18.8680 21.1746i −0.755325 0.847660i
\(625\) −20.3084 + 14.5798i −0.812335 + 0.583191i
\(626\) −7.20248 39.1439i −0.287869 1.56450i
\(627\) −75.0154 −2.99583
\(628\) −16.1623 + 6.15614i −0.644944 + 0.245657i
\(629\) 0.851564i 0.0339541i
\(630\) 0 0
\(631\) 37.4842i 1.49222i −0.665821 0.746112i \(-0.731919\pi\)
0.665821 0.746112i \(-0.268081\pi\)
\(632\) −34.4955 + 20.9550i −1.37216 + 0.833546i
\(633\) 11.4850 0.456486
\(634\) 18.6355 3.42893i 0.740109 0.136180i
\(635\) 30.7439 + 22.4034i 1.22004 + 0.889051i
\(636\) −60.0092 + 22.8573i −2.37952 + 0.906349i
\(637\) 0 0
\(638\) −14.5145 + 2.67067i −0.574634 + 0.105733i
\(639\) 65.4822i 2.59044i
\(640\) 15.1894 + 20.2307i 0.600414 + 0.799690i
\(641\) 35.6213 1.40696 0.703479 0.710716i \(-0.251629\pi\)
0.703479 + 0.710716i \(0.251629\pi\)
\(642\) −22.1119 + 4.06860i −0.872688 + 0.160575i
\(643\) 2.55684i 0.100832i 0.998728 + 0.0504159i \(0.0160547\pi\)
−0.998728 + 0.0504159i \(0.983945\pi\)
\(644\) 0 0
\(645\) 27.9599 38.3690i 1.10092 1.51078i
\(646\) 3.37311 + 18.3321i 0.132713 + 0.721267i
\(647\) 17.7876i 0.699301i −0.936880 0.349651i \(-0.886300\pi\)
0.936880 0.349651i \(-0.113700\pi\)
\(648\) 30.3940 + 50.0338i 1.19399 + 1.96551i
\(649\) 14.4683i 0.567931i
\(650\) −13.8592 + 7.45100i −0.543602 + 0.292252i
\(651\) 0 0
\(652\) 6.38465 2.43189i 0.250042 0.0952401i
\(653\) 13.0090i 0.509081i 0.967062 + 0.254541i \(0.0819242\pi\)
−0.967062 + 0.254541i \(0.918076\pi\)
\(654\) 50.1480 9.22723i 1.96094 0.360813i
\(655\) −16.1897 11.7976i −0.632584 0.460970i
\(656\) −8.73008 9.79730i −0.340852 0.382520i
\(657\) −23.1740 −0.904104
\(658\) 0 0
\(659\) 5.68280i 0.221370i 0.993856 + 0.110685i \(0.0353045\pi\)
−0.993856 + 0.110685i \(0.964695\pi\)
\(660\) 62.1013 + 16.9069i 2.41729 + 0.658102i
\(661\) 16.1645i 0.628727i −0.949303 0.314364i \(-0.898209\pi\)
0.949303 0.314364i \(-0.101791\pi\)
\(662\) −31.5889 + 5.81235i −1.22774 + 0.225904i
\(663\) 17.9290i 0.696303i
\(664\) −27.3304 + 16.6024i −1.06063 + 0.644299i
\(665\) 0 0
\(666\) 3.35008 0.616415i 0.129813 0.0238856i
\(667\) 3.96187 0.153404
\(668\) −8.28512 21.7517i −0.320561 0.841597i
\(669\) 4.83569 0.186959
\(670\) −15.2652 + 31.7820i −0.589745 + 1.22785i
\(671\) 27.3346 1.05524
\(672\) 0 0
\(673\) 32.4901i 1.25240i −0.779662 0.626200i \(-0.784609\pi\)
0.779662 0.626200i \(-0.215391\pi\)
\(674\) −12.3085 + 2.26477i −0.474106 + 0.0872355i
\(675\) 62.9705 20.2633i 2.42373 0.779933i
\(676\) 15.0420 5.72944i 0.578539 0.220363i
\(677\) 18.1326 0.696891 0.348446 0.937329i \(-0.386710\pi\)
0.348446 + 0.937329i \(0.386710\pi\)
\(678\) −1.28441 6.98047i −0.0493273 0.268083i
\(679\) 0 0
\(680\) 1.33926 15.9364i 0.0513584 0.611134i
\(681\) −49.5760 −1.89976
\(682\) 29.0580 5.34668i 1.11269 0.204735i
\(683\) −8.81555 −0.337318 −0.168659 0.985674i \(-0.553944\pi\)
−0.168659 + 0.985674i \(0.553944\pi\)
\(684\) 69.6774 26.5398i 2.66418 1.01478i
\(685\) 10.9596 15.0397i 0.418744 0.574637i
\(686\) 0 0
\(687\) 61.1801 2.33417
\(688\) −19.9000 + 17.7323i −0.758680 + 0.676037i
\(689\) 22.4239i 0.854281i
\(690\) −15.5747 7.48067i −0.592920 0.284784i
\(691\) 9.13188 0.347393 0.173697 0.984799i \(-0.444429\pi\)
0.173697 + 0.984799i \(0.444429\pi\)
\(692\) −15.3571 + 5.84945i −0.583789 + 0.222363i
\(693\) 0 0
\(694\) −4.28254 23.2747i −0.162563 0.883494i
\(695\) 28.1889 + 20.5415i 1.06927 + 0.779184i
\(696\) 17.7953 10.8101i 0.674530 0.409757i
\(697\) 8.29559i 0.314218i
\(698\) −5.38137 + 0.990173i −0.203688 + 0.0374786i
\(699\) −10.0221 −0.379072
\(700\) 0 0
\(701\) −23.3178 −0.880700 −0.440350 0.897826i \(-0.645146\pi\)
−0.440350 + 0.897826i \(0.645146\pi\)
\(702\) 40.9480 7.53444i 1.54548 0.284369i
\(703\) 1.75536i 0.0662047i
\(704\) −32.0676 16.6543i −1.20859 0.627683i
\(705\) −8.32870 6.06920i −0.313677 0.228579i
\(706\) −2.02235 10.9910i −0.0761121 0.413653i
\(707\) 0 0
\(708\) −7.26583 19.0756i −0.273067 0.716906i
\(709\) 0.346485 0.0130125 0.00650625 0.999979i \(-0.497929\pi\)
0.00650625 + 0.999979i \(0.497929\pi\)
\(710\) 26.0979 + 12.5351i 0.979438 + 0.470432i
\(711\) 102.062i 3.82763i
\(712\) −36.7806 + 22.3431i −1.37841 + 0.837343i
\(713\) −7.93167 −0.297043
\(714\) 0 0
\(715\) 13.2363 18.1640i 0.495009 0.679295i
\(716\) 11.1011 + 29.1448i 0.414869 + 1.08919i
\(717\) −11.9578 −0.446571
\(718\) 5.78776 1.06495i 0.215997 0.0397436i
\(719\) −40.3315 −1.50411 −0.752056 0.659099i \(-0.770938\pi\)
−0.752056 + 0.659099i \(0.770938\pi\)
\(720\) −63.6638 + 6.26707i −2.37261 + 0.233560i
\(721\) 0 0
\(722\) −2.09066 11.3623i −0.0778062 0.422859i
\(723\) −23.6780 −0.880594
\(724\) 11.2862 + 29.6306i 0.419448 + 1.10121i
\(725\) −3.53860 10.9966i −0.131420 0.408405i
\(726\) −41.6642 + 7.66623i −1.54630 + 0.284520i
\(727\) 19.5590i 0.725402i −0.931906 0.362701i \(-0.881855\pi\)
0.931906 0.362701i \(-0.118145\pi\)
\(728\) 0 0
\(729\) −21.5718 −0.798957
\(730\) 4.43613 9.23600i 0.164188 0.341840i
\(731\) 16.8498 0.623211
\(732\) −36.0391 + 13.7271i −1.33204 + 0.507369i
\(733\) 19.6314 0.725101 0.362550 0.931964i \(-0.381906\pi\)
0.362550 + 0.931964i \(0.381906\pi\)
\(734\) 38.0786 7.00647i 1.40551 0.258614i
\(735\) 0 0
\(736\) 7.65746 + 5.95493i 0.282258 + 0.219502i
\(737\) 50.3603i 1.85505i
\(738\) 32.6351 6.00486i 1.20131 0.221042i
\(739\) 0.386471i 0.0142166i 0.999975 + 0.00710828i \(0.00226265\pi\)
−0.999975 + 0.00710828i \(0.997737\pi\)
\(740\) −0.395623 + 1.45317i −0.0145434 + 0.0534197i
\(741\) 36.9577i 1.35767i
\(742\) 0 0
\(743\) −51.2724 −1.88100 −0.940502 0.339789i \(-0.889644\pi\)
−0.940502 + 0.339789i \(0.889644\pi\)
\(744\) −35.6263 + 21.6419i −1.30612 + 0.793431i
\(745\) 4.54292 + 3.31047i 0.166440 + 0.121286i
\(746\) −40.7642 + 7.50061i −1.49248 + 0.274617i
\(747\) 80.8626i 2.95861i
\(748\) 8.13089 + 21.3468i 0.297295 + 0.780515i
\(749\) 0 0
\(750\) −6.85267 + 49.9109i −0.250224 + 1.82249i
\(751\) 6.96844i 0.254282i −0.991885 0.127141i \(-0.959420\pi\)
0.991885 0.127141i \(-0.0405801\pi\)
\(752\) 3.84912 + 4.31966i 0.140363 + 0.157522i
\(753\) 18.3967i 0.670415i
\(754\) −1.31575 7.15082i −0.0479168 0.260417i
\(755\) −16.7706 + 23.0141i −0.610345 + 0.837570i
\(756\) 0 0
\(757\) 15.8945i 0.577696i −0.957375 0.288848i \(-0.906728\pi\)
0.957375 0.288848i \(-0.0932722\pi\)
\(758\) 29.7827 5.48003i 1.08176 0.199044i
\(759\) 24.6790 0.895790
\(760\) −2.76068 + 32.8504i −0.100140 + 1.19161i
\(761\) 15.2848i 0.554074i −0.960859 0.277037i \(-0.910648\pi\)
0.960859 0.277037i \(-0.0893524\pi\)
\(762\) 75.3929 13.8723i 2.73120 0.502540i
\(763\) 0 0
\(764\) −8.00999 21.0293i −0.289791 0.760815i
\(765\) 32.6833 + 23.8166i 1.18167 + 0.861092i
\(766\) −26.8287 + 4.93649i −0.969360 + 0.178362i
\(767\) −7.12807 −0.257380
\(768\) 50.6429 + 5.85374i 1.82742 + 0.211229i
\(769\) 7.67597i 0.276803i −0.990376 0.138401i \(-0.955804\pi\)
0.990376 0.138401i \(-0.0441964\pi\)
\(770\) 0 0
\(771\) 47.3169i 1.70408i
\(772\) −17.6792 46.4148i −0.636288 1.67050i
\(773\) −18.7437 −0.674162 −0.337081 0.941476i \(-0.609440\pi\)
−0.337081 + 0.941476i \(0.609440\pi\)
\(774\) −12.1969 66.2875i −0.438409 2.38265i
\(775\) 7.08429 + 22.0153i 0.254475 + 0.790812i
\(776\) −6.59788 10.8612i −0.236850 0.389895i
\(777\) 0 0
\(778\) −3.96837 21.5672i −0.142273 0.773223i
\(779\) 17.1000i 0.612672i
\(780\) −8.32951 + 30.5953i −0.298244 + 1.09549i
\(781\) −41.3535 −1.47975
\(782\) −1.10970 6.03100i −0.0396829 0.215668i
\(783\) 30.5667i 1.09236i
\(784\) 0 0
\(785\) 15.6273 + 11.3878i 0.557764 + 0.406448i
\(786\) −39.7017 + 7.30513i −1.41611