Properties

Label 625.2.e.a.374.1
Level $625$
Weight $2$
Character 625.374
Analytic conductor $4.991$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 625 = 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 625.e (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.99065012633\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: 8.0.58140625.2
Defining polynomial: \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 374.1
Root \(-0.983224 - 0.644389i\) of defining polynomial
Character \(\chi\) \(=\) 625.374
Dual form 625.2.e.a.249.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22570 - 1.68703i) q^{2} +(-2.09089 - 0.679371i) q^{3} +(-0.725700 + 2.23347i) q^{4} +(1.41668 + 4.36010i) q^{6} -0.992398i q^{7} +(0.690983 - 0.224514i) q^{8} +(1.48322 + 1.07763i) q^{9} +O(q^{10})\) \(q+(-1.22570 - 1.68703i) q^{2} +(-2.09089 - 0.679371i) q^{3} +(-0.725700 + 2.23347i) q^{4} +(1.41668 + 4.36010i) q^{6} -0.992398i q^{7} +(0.690983 - 0.224514i) q^{8} +(1.48322 + 1.07763i) q^{9} +(-1.61803 + 1.17557i) q^{11} +(3.03472 - 4.17693i) q^{12} +(-1.98322 + 2.72967i) q^{13} +(-1.67421 + 1.21638i) q^{14} +(2.57411 + 1.87020i) q^{16} +(2.75284 - 0.894453i) q^{17} -3.82309i q^{18} +(0.798649 + 2.45799i) q^{19} +(-0.674207 + 2.07500i) q^{21} +(3.96645 + 1.28878i) q^{22} +(2.67421 + 3.68073i) q^{23} -1.59730 q^{24} +7.03588 q^{26} +(1.50757 + 2.07500i) q^{27} +(2.21650 + 0.720183i) q^{28} +(1.66384 - 5.12077i) q^{29} +(0.0421925 + 0.129855i) q^{31} -8.08800i q^{32} +(4.18178 - 1.35874i) q^{33} +(-4.88313 - 3.54780i) q^{34} +(-3.48322 + 2.53071i) q^{36} +(1.26321 - 1.73866i) q^{37} +(3.16780 - 4.36010i) q^{38} +(6.00116 - 4.36010i) q^{39} +(-6.98439 - 5.07446i) q^{41} +(4.32696 - 1.40591i) q^{42} +4.64398i q^{43} +(-1.45140 - 4.46695i) q^{44} +(2.93173 - 9.02294i) q^{46} +(-9.44047 - 3.06739i) q^{47} +(-4.11163 - 5.65917i) q^{48} +6.01515 q^{49} -6.36356 q^{51} +(-4.65743 - 6.41040i) q^{52} +(7.19494 + 2.33778i) q^{53} +(1.65275 - 5.08664i) q^{54} +(-0.222807 - 0.685730i) q^{56} -5.68196i q^{57} +(-10.6783 + 3.46958i) q^{58} +(3.97854 + 2.89058i) q^{59} +(2.24075 - 1.62800i) q^{61} +(0.167354 - 0.230343i) q^{62} +(1.06943 - 1.47195i) q^{63} +(-8.49648 + 6.17306i) q^{64} +(-7.41785 - 5.38938i) q^{66} +(2.07879 - 0.675441i) q^{67} +6.79751i q^{68} +(-3.09089 - 9.51278i) q^{69} +(2.97971 - 9.17060i) q^{71} +(1.26682 + 0.411616i) q^{72} +(-0.456080 - 0.627740i) q^{73} -4.48150 q^{74} -6.06943 q^{76} +(1.16663 + 1.60573i) q^{77} +(-14.7113 - 4.77998i) q^{78} +(-4.89818 + 15.0750i) q^{79} +(-3.44210 - 10.5937i) q^{81} +18.0026i q^{82} +(1.68442 - 0.547301i) q^{83} +(-4.14518 - 3.01165i) q^{84} +(7.83453 - 5.69212i) q^{86} +(-6.95781 + 9.57660i) q^{87} +(-0.854102 + 1.17557i) q^{88} +(11.7372 - 8.52760i) q^{89} +(2.70892 + 1.96815i) q^{91} +(-10.1615 + 3.30167i) q^{92} -0.300177i q^{93} +(6.39639 + 19.6861i) q^{94} +(-5.49476 + 16.9111i) q^{96} +(16.1956 + 5.26228i) q^{97} +(-7.37276 - 10.1477i) q^{98} -3.66673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9} - 4 q^{11} + 10 q^{12} - 5 q^{13} - 7 q^{14} - 2 q^{16} + 15 q^{17} + 10 q^{19} + q^{21} + 10 q^{22} + 15 q^{23} - 20 q^{24} + 6 q^{26} - 5 q^{27} - 20 q^{28} + 15 q^{29} + q^{31} + 10 q^{33} - 12 q^{34} - 17 q^{36} - 5 q^{37} + 12 q^{39} - 9 q^{41} + 5 q^{42} + 8 q^{44} + 16 q^{46} - 15 q^{47} - 5 q^{48} + 14 q^{49} - 4 q^{51} - 20 q^{52} + 35 q^{53} - 10 q^{54} - 15 q^{56} - 20 q^{58} + 15 q^{59} + 6 q^{61} + 45 q^{62} - 20 q^{63} - 26 q^{64} - 18 q^{66} - 13 q^{69} - 29 q^{71} + 5 q^{72} + 10 q^{73} - 12 q^{74} - 20 q^{76} + 20 q^{77} - 25 q^{78} - 10 q^{79} - 12 q^{81} + 15 q^{83} - 27 q^{84} + 16 q^{86} - 55 q^{87} + 20 q^{88} + 40 q^{89} + q^{91} - 5 q^{92} - 7 q^{94} + 11 q^{96} - 10 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22570 1.68703i −0.866701 1.19291i −0.979930 0.199342i \(-0.936119\pi\)
0.113229 0.993569i \(-0.463881\pi\)
\(3\) −2.09089 0.679371i −1.20718 0.392235i −0.364780 0.931094i \(-0.618856\pi\)
−0.842396 + 0.538859i \(0.818856\pi\)
\(4\) −0.725700 + 2.23347i −0.362850 + 1.11674i
\(5\) 0 0
\(6\) 1.41668 + 4.36010i 0.578358 + 1.78000i
\(7\) 0.992398i 0.375091i −0.982256 0.187546i \(-0.939947\pi\)
0.982256 0.187546i \(-0.0600533\pi\)
\(8\) 0.690983 0.224514i 0.244299 0.0793777i
\(9\) 1.48322 + 1.07763i 0.494408 + 0.359208i
\(10\) 0 0
\(11\) −1.61803 + 1.17557i −0.487856 + 0.354448i −0.804359 0.594144i \(-0.797491\pi\)
0.316503 + 0.948591i \(0.397491\pi\)
\(12\) 3.03472 4.17693i 0.876047 1.20578i
\(13\) −1.98322 + 2.72967i −0.550047 + 0.757075i −0.990019 0.140937i \(-0.954989\pi\)
0.439971 + 0.898012i \(0.354989\pi\)
\(14\) −1.67421 + 1.21638i −0.447451 + 0.325092i
\(15\) 0 0
\(16\) 2.57411 + 1.87020i 0.643528 + 0.467551i
\(17\) 2.75284 0.894453i 0.667663 0.216937i 0.0444767 0.999010i \(-0.485838\pi\)
0.623186 + 0.782074i \(0.285838\pi\)
\(18\) 3.82309i 0.901111i
\(19\) 0.798649 + 2.45799i 0.183223 + 0.563901i 0.999913 0.0131746i \(-0.00419372\pi\)
−0.816691 + 0.577076i \(0.804194\pi\)
\(20\) 0 0
\(21\) −0.674207 + 2.07500i −0.147124 + 0.452801i
\(22\) 3.96645 + 1.28878i 0.845650 + 0.274768i
\(23\) 2.67421 + 3.68073i 0.557611 + 0.767485i 0.991020 0.133712i \(-0.0426896\pi\)
−0.433410 + 0.901197i \(0.642690\pi\)
\(24\) −1.59730 −0.326047
\(25\) 0 0
\(26\) 7.03588 1.37985
\(27\) 1.50757 + 2.07500i 0.290132 + 0.399333i
\(28\) 2.21650 + 0.720183i 0.418878 + 0.136102i
\(29\) 1.66384 5.12077i 0.308967 0.950903i −0.669200 0.743082i \(-0.733363\pi\)
0.978167 0.207821i \(-0.0666370\pi\)
\(30\) 0 0
\(31\) 0.0421925 + 0.129855i 0.00757799 + 0.0233227i 0.954774 0.297332i \(-0.0960970\pi\)
−0.947196 + 0.320655i \(0.896097\pi\)
\(32\) 8.08800i 1.42977i
\(33\) 4.18178 1.35874i 0.727954 0.236527i
\(34\) −4.88313 3.54780i −0.837450 0.608443i
\(35\) 0 0
\(36\) −3.48322 + 2.53071i −0.580537 + 0.421785i
\(37\) 1.26321 1.73866i 0.207671 0.285834i −0.692458 0.721458i \(-0.743472\pi\)
0.900129 + 0.435624i \(0.143472\pi\)
\(38\) 3.16780 4.36010i 0.513885 0.707302i
\(39\) 6.00116 4.36010i 0.960955 0.698175i
\(40\) 0 0
\(41\) −6.98439 5.07446i −1.09078 0.792497i −0.111248 0.993793i \(-0.535485\pi\)
−0.979530 + 0.201296i \(0.935485\pi\)
\(42\) 4.32696 1.40591i 0.667664 0.216937i
\(43\) 4.64398i 0.708200i 0.935208 + 0.354100i \(0.115213\pi\)
−0.935208 + 0.354100i \(0.884787\pi\)
\(44\) −1.45140 4.46695i −0.218807 0.673418i
\(45\) 0 0
\(46\) 2.93173 9.02294i 0.432260 1.33036i
\(47\) −9.44047 3.06739i −1.37703 0.447425i −0.475341 0.879802i \(-0.657675\pi\)
−0.901693 + 0.432376i \(0.857675\pi\)
\(48\) −4.11163 5.65917i −0.593462 0.816831i
\(49\) 6.01515 0.859306
\(50\) 0 0
\(51\) −6.36356 −0.891077
\(52\) −4.65743 6.41040i −0.645869 0.888963i
\(53\) 7.19494 + 2.33778i 0.988301 + 0.321119i 0.758181 0.652044i \(-0.226088\pi\)
0.230120 + 0.973162i \(0.426088\pi\)
\(54\) 1.65275 5.08664i 0.224911 0.692205i
\(55\) 0 0
\(56\) −0.222807 0.685730i −0.0297739 0.0916346i
\(57\) 5.68196i 0.752594i
\(58\) −10.6783 + 3.46958i −1.40212 + 0.455578i
\(59\) 3.97854 + 2.89058i 0.517962 + 0.376322i 0.815836 0.578284i \(-0.196277\pi\)
−0.297873 + 0.954605i \(0.596277\pi\)
\(60\) 0 0
\(61\) 2.24075 1.62800i 0.286898 0.208444i −0.435022 0.900420i \(-0.643260\pi\)
0.721921 + 0.691976i \(0.243260\pi\)
\(62\) 0.167354 0.230343i 0.0212540 0.0292536i
\(63\) 1.06943 1.47195i 0.134736 0.185448i
\(64\) −8.49648 + 6.17306i −1.06206 + 0.771632i
\(65\) 0 0
\(66\) −7.41785 5.38938i −0.913074 0.663387i
\(67\) 2.07879 0.675441i 0.253965 0.0825183i −0.179268 0.983800i \(-0.557373\pi\)
0.433233 + 0.901282i \(0.357373\pi\)
\(68\) 6.79751i 0.824319i
\(69\) −3.09089 9.51278i −0.372099 1.14520i
\(70\) 0 0
\(71\) 2.97971 9.17060i 0.353626 1.08835i −0.603175 0.797609i \(-0.706098\pi\)
0.956802 0.290741i \(-0.0939019\pi\)
\(72\) 1.26682 + 0.411616i 0.149297 + 0.0485094i
\(73\) −0.456080 0.627740i −0.0533801 0.0734714i 0.781492 0.623915i \(-0.214459\pi\)
−0.834873 + 0.550443i \(0.814459\pi\)
\(74\) −4.48150 −0.520963
\(75\) 0 0
\(76\) −6.06943 −0.696212
\(77\) 1.16663 + 1.60573i 0.132950 + 0.182990i
\(78\) −14.7113 4.77998i −1.66572 0.541226i
\(79\) −4.89818 + 15.0750i −0.551088 + 1.69608i 0.154968 + 0.987919i \(0.450473\pi\)
−0.706056 + 0.708156i \(0.749527\pi\)
\(80\) 0 0
\(81\) −3.44210 10.5937i −0.382455 1.17708i
\(82\) 18.0026i 1.98806i
\(83\) 1.68442 0.547301i 0.184889 0.0600740i −0.215109 0.976590i \(-0.569011\pi\)
0.399998 + 0.916516i \(0.369011\pi\)
\(84\) −4.14518 3.01165i −0.452276 0.328598i
\(85\) 0 0
\(86\) 7.83453 5.69212i 0.844819 0.613797i
\(87\) −6.95781 + 9.57660i −0.745955 + 1.02672i
\(88\) −0.854102 + 1.17557i −0.0910476 + 0.125316i
\(89\) 11.7372 8.52760i 1.24414 0.903924i 0.246277 0.969200i \(-0.420793\pi\)
0.997867 + 0.0652758i \(0.0207927\pi\)
\(90\) 0 0
\(91\) 2.70892 + 1.96815i 0.283972 + 0.206318i
\(92\) −10.1615 + 3.30167i −1.05941 + 0.344223i
\(93\) 0.300177i 0.0311269i
\(94\) 6.39639 + 19.6861i 0.659737 + 2.03046i
\(95\) 0 0
\(96\) −5.49476 + 16.9111i −0.560806 + 1.72598i
\(97\) 16.1956 + 5.26228i 1.64442 + 0.534304i 0.977520 0.210844i \(-0.0676214\pi\)
0.666899 + 0.745148i \(0.267621\pi\)
\(98\) −7.37276 10.1477i −0.744761 1.02508i
\(99\) −3.66673 −0.368520
\(100\) 0 0
\(101\) −2.54716 −0.253452 −0.126726 0.991938i \(-0.540447\pi\)
−0.126726 + 0.991938i \(0.540447\pi\)
\(102\) 7.79981 + 10.7355i 0.772297 + 1.06298i
\(103\) 9.66790 + 3.14129i 0.952606 + 0.309520i 0.743774 0.668431i \(-0.233034\pi\)
0.208832 + 0.977952i \(0.433034\pi\)
\(104\) −0.757524 + 2.33142i −0.0742814 + 0.228615i
\(105\) 0 0
\(106\) −4.87494 15.0035i −0.473496 1.45727i
\(107\) 4.81720i 0.465697i 0.972513 + 0.232848i \(0.0748046\pi\)
−0.972513 + 0.232848i \(0.925195\pi\)
\(108\) −5.72850 + 1.86130i −0.551225 + 0.179104i
\(109\) 13.1662 + 9.56578i 1.26109 + 0.916236i 0.998811 0.0487563i \(-0.0155258\pi\)
0.262280 + 0.964992i \(0.415526\pi\)
\(110\) 0 0
\(111\) −3.82243 + 2.77716i −0.362809 + 0.263596i
\(112\) 1.85599 2.55455i 0.175374 0.241382i
\(113\) 3.97169 5.46656i 0.373625 0.514251i −0.580256 0.814434i \(-0.697048\pi\)
0.953882 + 0.300183i \(0.0970477\pi\)
\(114\) −9.58565 + 6.96438i −0.897778 + 0.652274i
\(115\) 0 0
\(116\) 10.2297 + 7.43228i 0.949800 + 0.690070i
\(117\) −5.88313 + 1.91155i −0.543896 + 0.176722i
\(118\) 10.2549i 0.944041i
\(119\) −0.887654 2.73192i −0.0813711 0.250435i
\(120\) 0 0
\(121\) −2.16312 + 6.65740i −0.196647 + 0.605218i
\(122\) −5.49297 1.78477i −0.497310 0.161586i
\(123\) 11.1561 + 15.3551i 1.00592 + 1.38452i
\(124\) −0.320647 −0.0287950
\(125\) 0 0
\(126\) −3.79403 −0.337999
\(127\) −0.876278 1.20609i −0.0777571 0.107023i 0.768367 0.640010i \(-0.221070\pi\)
−0.846124 + 0.532986i \(0.821070\pi\)
\(128\) 5.44398 + 1.76886i 0.481185 + 0.156346i
\(129\) 3.15498 9.71004i 0.277781 0.854921i
\(130\) 0 0
\(131\) 4.36167 + 13.4239i 0.381081 + 1.17285i 0.939283 + 0.343143i \(0.111491\pi\)
−0.558202 + 0.829705i \(0.688509\pi\)
\(132\) 10.3259i 0.898757i
\(133\) 2.43930 0.792578i 0.211514 0.0687252i
\(134\) −3.68747 2.67910i −0.318549 0.231439i
\(135\) 0 0
\(136\) 1.70135 1.23610i 0.145890 0.105995i
\(137\) 0.405247 0.557775i 0.0346226 0.0476539i −0.791355 0.611357i \(-0.790624\pi\)
0.825977 + 0.563703i \(0.190624\pi\)
\(138\) −12.2599 + 16.8742i −1.04363 + 1.43643i
\(139\) −13.4069 + 9.74070i −1.13716 + 0.826195i −0.986721 0.162424i \(-0.948069\pi\)
−0.150439 + 0.988619i \(0.548069\pi\)
\(140\) 0 0
\(141\) 17.6551 + 12.8272i 1.48683 + 1.08024i
\(142\) −19.1233 + 6.21354i −1.60479 + 0.521429i
\(143\) 6.74812i 0.564307i
\(144\) 1.80261 + 5.54786i 0.150217 + 0.462322i
\(145\) 0 0
\(146\) −0.500000 + 1.53884i −0.0413803 + 0.127355i
\(147\) −12.5770 4.08652i −1.03733 0.337050i
\(148\) 2.96655 + 4.08310i 0.243849 + 0.335629i
\(149\) −3.21156 −0.263101 −0.131551 0.991309i \(-0.541996\pi\)
−0.131551 + 0.991309i \(0.541996\pi\)
\(150\) 0 0
\(151\) 17.6863 1.43929 0.719647 0.694340i \(-0.244304\pi\)
0.719647 + 0.694340i \(0.244304\pi\)
\(152\) 1.10371 + 1.51912i 0.0895223 + 0.123217i
\(153\) 5.04697 + 1.63986i 0.408023 + 0.132575i
\(154\) 1.27898 3.93630i 0.103063 0.317196i
\(155\) 0 0
\(156\) 5.38313 + 16.5676i 0.430995 + 1.32647i
\(157\) 1.65512i 0.132093i −0.997817 0.0660465i \(-0.978961\pi\)
0.997817 0.0660465i \(-0.0210386\pi\)
\(158\) 31.4358 10.2141i 2.50090 0.812590i
\(159\) −13.4556 9.77608i −1.06710 0.775293i
\(160\) 0 0
\(161\) 3.65275 2.65388i 0.287877 0.209155i
\(162\) −13.6529 + 18.7916i −1.07267 + 1.47641i
\(163\) 0.524854 0.722399i 0.0411097 0.0565827i −0.787967 0.615717i \(-0.788866\pi\)
0.829077 + 0.559134i \(0.188866\pi\)
\(164\) 16.4022 11.9169i 1.28080 0.930555i
\(165\) 0 0
\(166\) −2.98790 2.17084i −0.231906 0.168490i
\(167\) 4.94129 1.60552i 0.382368 0.124239i −0.111525 0.993762i \(-0.535573\pi\)
0.493893 + 0.869523i \(0.335573\pi\)
\(168\) 1.58516i 0.122297i
\(169\) 0.499280 + 1.53663i 0.0384062 + 0.118202i
\(170\) 0 0
\(171\) −1.46422 + 4.50639i −0.111971 + 0.344612i
\(172\) −10.3722 3.37013i −0.790873 0.256970i
\(173\) 3.38837 + 4.66370i 0.257613 + 0.354574i 0.918159 0.396211i \(-0.129675\pi\)
−0.660546 + 0.750785i \(0.729675\pi\)
\(174\) 24.6842 1.87130
\(175\) 0 0
\(176\) −6.36356 −0.479671
\(177\) −6.35492 8.74680i −0.477665 0.657449i
\(178\) −28.7726 9.34880i −2.15660 0.700722i
\(179\) −2.67883 + 8.24458i −0.200225 + 0.616229i 0.799651 + 0.600465i \(0.205018\pi\)
−0.999876 + 0.0157637i \(0.994982\pi\)
\(180\) 0 0
\(181\) 4.41612 + 13.5914i 0.328248 + 1.01024i 0.969953 + 0.243291i \(0.0782271\pi\)
−0.641706 + 0.766951i \(0.721773\pi\)
\(182\) 6.98240i 0.517570i
\(183\) −5.79117 + 1.88167i −0.428096 + 0.139097i
\(184\) 2.67421 + 1.94293i 0.197145 + 0.143234i
\(185\) 0 0
\(186\) −0.506408 + 0.367927i −0.0371316 + 0.0269777i
\(187\) −3.40270 + 4.68342i −0.248830 + 0.342485i
\(188\) 13.7019 18.8590i 0.999313 1.37544i
\(189\) 2.05922 1.49611i 0.149786 0.108826i
\(190\) 0 0
\(191\) 1.02451 + 0.744347i 0.0741306 + 0.0538591i 0.624233 0.781238i \(-0.285411\pi\)
−0.550103 + 0.835097i \(0.685411\pi\)
\(192\) 21.9590 7.13492i 1.58476 0.514918i
\(193\) 21.1730i 1.52406i 0.647540 + 0.762031i \(0.275798\pi\)
−0.647540 + 0.762031i \(0.724202\pi\)
\(194\) −10.9734 33.7725i −0.787841 2.42473i
\(195\) 0 0
\(196\) −4.36519 + 13.4347i −0.311799 + 0.959620i
\(197\) 11.6042 + 3.77042i 0.826761 + 0.268631i 0.691681 0.722203i \(-0.256871\pi\)
0.135081 + 0.990835i \(0.456871\pi\)
\(198\) 4.49431 + 6.18589i 0.319397 + 0.439612i
\(199\) −10.4065 −0.737695 −0.368848 0.929490i \(-0.620248\pi\)
−0.368848 + 0.929490i \(0.620248\pi\)
\(200\) 0 0
\(201\) −4.80540 −0.338947
\(202\) 3.12205 + 4.29714i 0.219667 + 0.302346i
\(203\) −5.08184 1.65119i −0.356675 0.115891i
\(204\) 4.61803 14.2128i 0.323327 0.995098i
\(205\) 0 0
\(206\) −6.55049 20.1603i −0.456394 1.40464i
\(207\) 8.34114i 0.579749i
\(208\) −10.2101 + 3.31746i −0.707942 + 0.230024i
\(209\) −4.18178 3.03824i −0.289260 0.210160i
\(210\) 0 0
\(211\) 7.00421 5.08886i 0.482190 0.350332i −0.319983 0.947423i \(-0.603677\pi\)
0.802173 + 0.597092i \(0.203677\pi\)
\(212\) −10.4427 + 14.3732i −0.717210 + 0.987155i
\(213\) −12.4605 + 17.1504i −0.853778 + 1.17513i
\(214\) 8.12677 5.90445i 0.555535 0.403620i
\(215\) 0 0
\(216\) 1.50757 + 1.09532i 0.102577 + 0.0745268i
\(217\) 0.128868 0.0418717i 0.00874813 0.00284244i
\(218\) 33.9365i 2.29847i
\(219\) 0.527144 + 1.62238i 0.0356211 + 0.109630i
\(220\) 0 0
\(221\) −3.01794 + 9.28827i −0.203009 + 0.624796i
\(222\) 9.37032 + 3.04460i 0.628894 + 0.204340i
\(223\) −16.6598 22.9303i −1.11562 1.53552i −0.812860 0.582459i \(-0.802091\pi\)
−0.302764 0.953065i \(-0.597909\pi\)
\(224\) −8.02652 −0.536295
\(225\) 0 0
\(226\) −14.0904 −0.937277
\(227\) 13.0732 + 17.9937i 0.867699 + 1.19429i 0.979678 + 0.200575i \(0.0642809\pi\)
−0.111979 + 0.993711i \(0.535719\pi\)
\(228\) 12.6905 + 4.12340i 0.840450 + 0.273079i
\(229\) −0.765000 + 2.35443i −0.0505526 + 0.155585i −0.973146 0.230189i \(-0.926066\pi\)
0.922593 + 0.385774i \(0.126066\pi\)
\(230\) 0 0
\(231\) −1.34841 4.14999i −0.0887191 0.273049i
\(232\) 3.91192i 0.256830i
\(233\) −5.66454 + 1.84052i −0.371096 + 0.120576i −0.488627 0.872493i \(-0.662502\pi\)
0.117531 + 0.993069i \(0.462502\pi\)
\(234\) 10.4358 + 7.58204i 0.682209 + 0.495654i
\(235\) 0 0
\(236\) −9.34327 + 6.78828i −0.608195 + 0.441879i
\(237\) 20.4831 28.1926i 1.33052 1.83130i
\(238\) −3.52083 + 4.84601i −0.228222 + 0.314120i
\(239\) −5.68935 + 4.13356i −0.368014 + 0.267378i −0.756387 0.654125i \(-0.773037\pi\)
0.388373 + 0.921502i \(0.373037\pi\)
\(240\) 0 0
\(241\) −0.954449 0.693448i −0.0614815 0.0446689i 0.556620 0.830767i \(-0.312098\pi\)
−0.618102 + 0.786098i \(0.712098\pi\)
\(242\) 13.8826 4.51072i 0.892405 0.289960i
\(243\) 16.7942i 1.07735i
\(244\) 2.00998 + 6.18609i 0.128676 + 0.396024i
\(245\) 0 0
\(246\) 12.2305 37.6415i 0.779787 2.39994i
\(247\) −8.29341 2.69469i −0.527697 0.171459i
\(248\) 0.0583086 + 0.0802548i 0.00370260 + 0.00509619i
\(249\) −3.89375 −0.246757
\(250\) 0 0
\(251\) 4.60867 0.290897 0.145448 0.989366i \(-0.453538\pi\)
0.145448 + 0.989366i \(0.453538\pi\)
\(252\) 2.51147 + 3.45675i 0.158208 + 0.217755i
\(253\) −8.65392 2.81183i −0.544067 0.176778i
\(254\) −0.960663 + 2.95662i −0.0602774 + 0.185515i
\(255\) 0 0
\(256\) 2.80216 + 8.62417i 0.175135 + 0.539011i
\(257\) 9.75542i 0.608526i 0.952588 + 0.304263i \(0.0984102\pi\)
−0.952588 + 0.304263i \(0.901590\pi\)
\(258\) −20.2482 + 6.57904i −1.26060 + 0.409593i
\(259\) −1.72545 1.25361i −0.107214 0.0778955i
\(260\) 0 0
\(261\) 7.98612 5.80225i 0.494328 0.359150i
\(262\) 17.3004 23.8119i 1.06882 1.47110i
\(263\) 0.585333 0.805641i 0.0360932 0.0496780i −0.790589 0.612347i \(-0.790225\pi\)
0.826682 + 0.562669i \(0.190225\pi\)
\(264\) 2.58448 1.87774i 0.159064 0.115567i
\(265\) 0 0
\(266\) −4.32696 3.14372i −0.265303 0.192754i
\(267\) −30.3347 + 9.85633i −1.85645 + 0.603198i
\(268\) 5.13310i 0.313554i
\(269\) 1.01621 + 3.12758i 0.0619596 + 0.190692i 0.977245 0.212114i \(-0.0680349\pi\)
−0.915285 + 0.402806i \(0.868035\pi\)
\(270\) 0 0
\(271\) 3.75457 11.5554i 0.228074 0.701940i −0.769891 0.638175i \(-0.779689\pi\)
0.997965 0.0637642i \(-0.0203105\pi\)
\(272\) 8.75894 + 2.84595i 0.531089 + 0.172561i
\(273\) −4.32696 5.95555i −0.261879 0.360446i
\(274\) −1.43769 −0.0868543
\(275\) 0 0
\(276\) 23.4896 1.41391
\(277\) −6.97499 9.60025i −0.419087 0.576823i 0.546319 0.837577i \(-0.316029\pi\)
−0.965405 + 0.260754i \(0.916029\pi\)
\(278\) 32.8657 + 10.6787i 1.97115 + 0.640467i
\(279\) −0.0773542 + 0.238072i −0.00463108 + 0.0142530i
\(280\) 0 0
\(281\) −7.61468 23.4356i −0.454253 1.39805i −0.872009 0.489489i \(-0.837183\pi\)
0.417756 0.908559i \(-0.362817\pi\)
\(282\) 45.5069i 2.70990i
\(283\) 3.19881 1.03936i 0.190150 0.0617833i −0.212394 0.977184i \(-0.568126\pi\)
0.402544 + 0.915401i \(0.368126\pi\)
\(284\) 18.3199 + 13.3102i 1.08709 + 0.789815i
\(285\) 0 0
\(286\) −11.3843 + 8.27117i −0.673168 + 0.489085i
\(287\) −5.03588 + 6.93130i −0.297259 + 0.409141i
\(288\) 8.71584 11.9963i 0.513586 0.706890i
\(289\) −6.97519 + 5.06777i −0.410305 + 0.298104i
\(290\) 0 0
\(291\) −30.2883 22.0057i −1.77553 1.29000i
\(292\) 1.73302 0.563092i 0.101417 0.0329525i
\(293\) 8.96340i 0.523647i −0.965116 0.261824i \(-0.915676\pi\)
0.965116 0.261824i \(-0.0843239\pi\)
\(294\) 8.52155 + 26.2266i 0.496987 + 1.52957i
\(295\) 0 0
\(296\) 0.482504 1.48499i 0.0280450 0.0863136i
\(297\) −4.87861 1.58516i −0.283086 0.0919801i
\(298\) 3.93641 + 5.41801i 0.228030 + 0.313857i
\(299\) −15.3507 −0.887756
\(300\) 0 0
\(301\) 4.60867 0.265640
\(302\) −21.6781 29.8374i −1.24744 1.71695i
\(303\) 5.32583 + 1.73047i 0.305961 + 0.0994128i
\(304\) −2.54112 + 7.82078i −0.145743 + 0.448552i
\(305\) 0 0
\(306\) −3.41958 10.5244i −0.195484 0.601638i
\(307\) 9.48133i 0.541128i −0.962702 0.270564i \(-0.912790\pi\)
0.962702 0.270564i \(-0.0872102\pi\)
\(308\) −4.43299 + 1.44037i −0.252593 + 0.0820725i
\(309\) −18.0804 13.1362i −1.02856 0.747291i
\(310\) 0 0
\(311\) −23.7301 + 17.2409i −1.34561 + 0.977643i −0.346393 + 0.938089i \(0.612594\pi\)
−0.999217 + 0.0395541i \(0.987406\pi\)
\(312\) 3.16780 4.36010i 0.179341 0.246842i
\(313\) 11.1033 15.2824i 0.627596 0.863811i −0.370283 0.928919i \(-0.620739\pi\)
0.997878 + 0.0651079i \(0.0207392\pi\)
\(314\) −2.79224 + 2.02868i −0.157575 + 0.114485i
\(315\) 0 0
\(316\) −30.1151 21.8799i −1.69411 1.23084i
\(317\) 21.6739 7.04229i 1.21733 0.395534i 0.371221 0.928545i \(-0.378939\pi\)
0.846109 + 0.533010i \(0.178939\pi\)
\(318\) 34.6826i 1.94490i
\(319\) 3.32768 + 10.2415i 0.186314 + 0.573416i
\(320\) 0 0
\(321\) 3.27267 10.0722i 0.182663 0.562178i
\(322\) −8.95435 2.90945i −0.499007 0.162137i
\(323\) 4.39711 + 6.05210i 0.244662 + 0.336748i
\(324\) 26.1587 1.45326
\(325\) 0 0
\(326\) −1.86202 −0.103128
\(327\) −21.0303 28.9457i −1.16298 1.60070i
\(328\) −5.96538 1.93827i −0.329383 0.107023i
\(329\) −3.04408 + 9.36871i −0.167825 + 0.516513i
\(330\) 0 0
\(331\) 0.915615 + 2.81797i 0.0503268 + 0.154890i 0.973061 0.230546i \(-0.0740512\pi\)
−0.922735 + 0.385436i \(0.874051\pi\)
\(332\) 4.15928i 0.228270i
\(333\) 3.74725 1.21756i 0.205348 0.0667217i
\(334\) −8.76510 6.36822i −0.479605 0.348453i
\(335\) 0 0
\(336\) −5.61615 + 4.08037i −0.306386 + 0.222603i
\(337\) 11.0576 15.2195i 0.602345 0.829057i −0.393575 0.919292i \(-0.628762\pi\)
0.995920 + 0.0902353i \(0.0287619\pi\)
\(338\) 1.98037 2.72574i 0.107718 0.148261i
\(339\) −12.0182 + 8.73173i −0.652739 + 0.474242i
\(340\) 0 0
\(341\) −0.220923 0.160510i −0.0119636 0.00869209i
\(342\) 9.39711 3.05331i 0.508138 0.165104i
\(343\) 12.9162i 0.697410i
\(344\) 1.04264 + 3.20891i 0.0562152 + 0.173013i
\(345\) 0 0
\(346\) 3.71467 11.4326i 0.199702 0.614620i
\(347\) 21.6253 + 7.02649i 1.16091 + 0.377201i 0.825242 0.564780i \(-0.191039\pi\)
0.335665 + 0.941981i \(0.391039\pi\)
\(348\) −16.3398 22.4898i −0.875906 1.20558i
\(349\) −1.93849 −0.103765 −0.0518824 0.998653i \(-0.516522\pi\)
−0.0518824 + 0.998653i \(0.516522\pi\)
\(350\) 0 0
\(351\) −8.65392 −0.461912
\(352\) 9.50802 + 13.0867i 0.506779 + 0.697522i
\(353\) 4.99252 + 1.62217i 0.265725 + 0.0863394i 0.438849 0.898561i \(-0.355386\pi\)
−0.173124 + 0.984900i \(0.555386\pi\)
\(354\) −6.96689 + 21.4419i −0.370286 + 1.13962i
\(355\) 0 0
\(356\) 10.5285 + 32.4033i 0.558008 + 1.71737i
\(357\) 6.31519i 0.334235i
\(358\) 17.1923 5.58612i 0.908642 0.295236i
\(359\) 18.2787 + 13.2803i 0.964713 + 0.700905i 0.954241 0.299040i \(-0.0966664\pi\)
0.0104726 + 0.999945i \(0.496666\pi\)
\(360\) 0 0
\(361\) 9.96746 7.24178i 0.524603 0.381146i
\(362\) 17.5163 24.1091i 0.920637 1.26715i
\(363\) 9.04569 12.4503i 0.474775 0.653472i
\(364\) −6.36167 + 4.62203i −0.333442 + 0.242260i
\(365\) 0 0
\(366\) 10.2727 + 7.46353i 0.536961 + 0.390125i
\(367\) −6.94150 + 2.25543i −0.362343 + 0.117732i −0.484530 0.874775i \(-0.661009\pi\)
0.122187 + 0.992507i \(0.461009\pi\)
\(368\) 14.4759i 0.754610i
\(369\) −4.89105 15.0531i −0.254618 0.783634i
\(370\) 0 0
\(371\) 2.32001 7.14025i 0.120449 0.370703i
\(372\) 0.670438 + 0.217838i 0.0347606 + 0.0112944i
\(373\) 13.1119 + 18.0470i 0.678911 + 0.934440i 0.999920 0.0126358i \(-0.00402219\pi\)
−0.321010 + 0.947076i \(0.604022\pi\)
\(374\) 12.0718 0.624216
\(375\) 0 0
\(376\) −7.21188 −0.371924
\(377\) 10.6783 + 14.6974i 0.549959 + 0.756953i
\(378\) −5.04798 1.64019i −0.259640 0.0843621i
\(379\) 10.1811 31.3341i 0.522966 1.60952i −0.245337 0.969438i \(-0.578899\pi\)
0.768303 0.640086i \(-0.221101\pi\)
\(380\) 0 0
\(381\) 1.01282 + 3.11713i 0.0518881 + 0.159695i
\(382\) 2.64072i 0.135111i
\(383\) 19.6871 6.39671i 1.00596 0.326857i 0.240716 0.970595i \(-0.422618\pi\)
0.765245 + 0.643739i \(0.222618\pi\)
\(384\) −10.1811 7.39697i −0.519550 0.377475i
\(385\) 0 0
\(386\) 35.7194 25.9517i 1.81807 1.32091i
\(387\) −5.00447 + 6.88806i −0.254391 + 0.350140i
\(388\) −23.5063 + 32.3537i −1.19335 + 1.64251i
\(389\) −0.925886 + 0.672696i −0.0469443 + 0.0341070i −0.611010 0.791623i \(-0.709236\pi\)
0.564066 + 0.825730i \(0.309236\pi\)
\(390\) 0 0
\(391\) 10.6539 + 7.74052i 0.538792 + 0.391455i
\(392\) 4.15636 1.35048i 0.209928 0.0682098i
\(393\) 31.0310i 1.56531i
\(394\) −7.86239 24.1980i −0.396102 1.21908i
\(395\) 0 0
\(396\) 2.66095 8.18955i 0.133718 0.411540i
\(397\) 4.45583 + 1.44779i 0.223631 + 0.0726623i 0.418690 0.908129i \(-0.362490\pi\)
−0.195058 + 0.980792i \(0.562490\pi\)
\(398\) 12.7552 + 17.5560i 0.639361 + 0.880005i
\(399\) −5.63877 −0.282292
\(400\) 0 0
\(401\) −24.0851 −1.20275 −0.601376 0.798966i \(-0.705381\pi\)
−0.601376 + 0.798966i \(0.705381\pi\)
\(402\) 5.88998 + 8.10687i 0.293766 + 0.404334i
\(403\) −0.438139 0.142360i −0.0218253 0.00709146i
\(404\) 1.84847 5.68902i 0.0919650 0.283039i
\(405\) 0 0
\(406\) 3.44320 + 10.5971i 0.170883 + 0.525925i
\(407\) 4.29821i 0.213054i
\(408\) −4.39711 + 1.42871i −0.217689 + 0.0707316i
\(409\) −1.53660 1.11641i −0.0759801 0.0552027i 0.549147 0.835726i \(-0.314953\pi\)
−0.625127 + 0.780523i \(0.714953\pi\)
\(410\) 0 0
\(411\) −1.22626 + 0.890932i −0.0604871 + 0.0439464i
\(412\) −14.0320 + 19.3134i −0.691306 + 0.951501i
\(413\) 2.86861 3.94830i 0.141155 0.194283i
\(414\) 14.0718 10.2237i 0.691589 0.502469i
\(415\) 0 0
\(416\) 22.0776 + 16.0403i 1.08244 + 0.786441i
\(417\) 34.6499 11.2584i 1.69681 0.551328i
\(418\) 10.7788i 0.527207i
\(419\) 0.719410 + 2.21412i 0.0351455 + 0.108167i 0.967090 0.254434i \(-0.0818890\pi\)
−0.931945 + 0.362600i \(0.881889\pi\)
\(420\) 0 0
\(421\) −7.40097 + 22.7779i −0.360701 + 1.11012i 0.591928 + 0.805991i \(0.298367\pi\)
−0.952629 + 0.304134i \(0.901633\pi\)
\(422\) −17.1701 5.57891i −0.835829 0.271577i
\(423\) −10.6968 14.7229i −0.520098 0.715853i
\(424\) 5.49645 0.266931
\(425\) 0 0
\(426\) 44.2060 2.14179
\(427\) −1.61562 2.22371i −0.0781855 0.107613i
\(428\) −10.7591 3.49584i −0.520061 0.168978i
\(429\) −4.58448 + 14.1096i −0.221341 + 0.681217i
\(430\) 0 0
\(431\) 0.368430 + 1.13391i 0.0177467 + 0.0546186i 0.959538 0.281580i \(-0.0908586\pi\)
−0.941791 + 0.336199i \(0.890859\pi\)
\(432\) 8.16074i 0.392634i
\(433\) −24.3602 + 7.91511i −1.17068 + 0.380376i −0.828895 0.559404i \(-0.811030\pi\)
−0.341781 + 0.939780i \(0.611030\pi\)
\(434\) −0.228592 0.166082i −0.0109728 0.00797219i
\(435\) 0 0
\(436\) −30.9196 + 22.4644i −1.48078 + 1.07585i
\(437\) −6.91144 + 9.51278i −0.330619 + 0.455058i
\(438\) 2.09089 2.87786i 0.0999066 0.137510i
\(439\) 15.6740 11.3878i 0.748079 0.543511i −0.147152 0.989114i \(-0.547011\pi\)
0.895231 + 0.445603i \(0.147011\pi\)
\(440\) 0 0
\(441\) 8.92181 + 6.48207i 0.424848 + 0.308670i
\(442\) 19.3687 6.29327i 0.921274 0.299340i
\(443\) 2.46263i 0.117003i −0.998287 0.0585016i \(-0.981368\pi\)
0.998287 0.0585016i \(-0.0186323\pi\)
\(444\) −3.42878 10.5527i −0.162723 0.500809i
\(445\) 0 0
\(446\) −18.2641 + 56.2113i −0.864833 + 2.66168i
\(447\) 6.71502 + 2.18184i 0.317610 + 0.103198i
\(448\) 6.12613 + 8.43190i 0.289433 + 0.398370i
\(449\) 14.3585 0.677618 0.338809 0.940855i \(-0.389976\pi\)
0.338809 + 0.940855i \(0.389976\pi\)
\(450\) 0 0
\(451\) 17.2664 0.813041
\(452\) 9.32717 + 12.8378i 0.438713 + 0.603837i
\(453\) −36.9802 12.0156i −1.73748 0.564542i
\(454\) 14.3321 44.1098i 0.672641 2.07018i
\(455\) 0 0
\(456\) −1.27568 3.92614i −0.0597392 0.183858i
\(457\) 25.1964i 1.17864i −0.807901 0.589319i \(-0.799396\pi\)
0.807901 0.589319i \(-0.200604\pi\)
\(458\) 4.90965 1.59524i 0.229413 0.0745408i
\(459\) 6.00610 + 4.36369i 0.280341 + 0.203679i
\(460\) 0 0
\(461\) −23.3203 + 16.9432i −1.08614 + 0.789124i −0.978743 0.205092i \(-0.934251\pi\)
−0.107394 + 0.994217i \(0.534251\pi\)
\(462\) −5.34841 + 7.36146i −0.248831 + 0.342486i
\(463\) −18.7384 + 25.7911i −0.870846 + 1.19862i 0.108028 + 0.994148i \(0.465547\pi\)
−0.978873 + 0.204468i \(0.934453\pi\)
\(464\) 13.8598 10.0697i 0.643425 0.467475i
\(465\) 0 0
\(466\) 10.0480 + 7.30033i 0.465466 + 0.338181i
\(467\) −40.9902 + 13.3185i −1.89680 + 0.616307i −0.925314 + 0.379201i \(0.876199\pi\)
−0.971484 + 0.237106i \(0.923801\pi\)
\(468\) 14.5270i 0.671512i
\(469\) −0.670307 2.06299i −0.0309519 0.0952601i
\(470\) 0 0
\(471\) −1.12444 + 3.46068i −0.0518115 + 0.159460i
\(472\) 3.39808 + 1.10410i 0.156409 + 0.0508205i
\(473\) −5.45932 7.51411i −0.251020 0.345499i
\(474\) −72.6679 −3.33775
\(475\) 0 0
\(476\) 6.74584 0.309195
\(477\) 8.15246 + 11.2209i 0.373276 + 0.513770i
\(478\) 13.9469 + 4.53161i 0.637915 + 0.207271i
\(479\) −6.49749 + 19.9972i −0.296878 + 0.913697i 0.685706 + 0.727878i \(0.259494\pi\)
−0.982584 + 0.185818i \(0.940506\pi\)
\(480\) 0 0
\(481\) 2.24075 + 6.89631i 0.102169 + 0.314445i
\(482\) 2.46014i 0.112057i
\(483\) −9.44047 + 3.06739i −0.429556 + 0.139571i
\(484\) −13.2993 9.66254i −0.604516 0.439206i
\(485\) 0 0
\(486\) 28.3323 20.5846i 1.28518 0.933739i
\(487\) −16.4104 + 22.5869i −0.743625 + 1.02351i 0.254777 + 0.967000i \(0.417998\pi\)
−0.998402 + 0.0565121i \(0.982002\pi\)
\(488\) 1.18281 1.62800i 0.0535433 0.0736960i
\(489\) −1.58819 + 1.15389i −0.0718204 + 0.0521805i
\(490\) 0 0
\(491\) −12.1037 8.79389i −0.546234 0.396862i 0.280161 0.959953i \(-0.409612\pi\)
−0.826395 + 0.563091i \(0.809612\pi\)
\(492\) −42.3913 + 13.7738i −1.91115 + 0.620969i
\(493\) 15.5849i 0.701909i
\(494\) 5.61920 + 17.2941i 0.252820 + 0.778099i
\(495\) 0 0
\(496\) −0.134247 + 0.413170i −0.00602787 + 0.0185519i
\(497\) −9.10089 2.95706i −0.408231 0.132642i
\(498\) 4.77257 + 6.56888i 0.213864 + 0.294359i
\(499\) 44.3253 1.98427 0.992137 0.125160i \(-0.0399443\pi\)
0.992137 + 0.125160i \(0.0399443\pi\)
\(500\) 0 0
\(501\) −11.4224 −0.510316
\(502\) −5.64885 7.77498i −0.252121 0.347014i
\(503\) −22.4651 7.29936i −1.00167 0.325462i −0.238137 0.971232i \(-0.576537\pi\)
−0.763532 + 0.645769i \(0.776537\pi\)
\(504\) 0.408487 1.25719i 0.0181955 0.0559999i
\(505\) 0 0
\(506\) 5.86346 + 18.0459i 0.260663 + 0.802237i
\(507\) 3.55211i 0.157755i
\(508\) 3.32969 1.08188i 0.147731 0.0480008i
\(509\) −21.6132 15.7029i −0.957990 0.696020i −0.00530682 0.999986i \(-0.501689\pi\)
−0.952683 + 0.303966i \(0.901689\pi\)
\(510\) 0 0
\(511\) −0.622968 + 0.452613i −0.0275585 + 0.0200224i
\(512\) 17.8438 24.5598i 0.788591 1.08540i
\(513\) −3.89629 + 5.36279i −0.172026 + 0.236773i
\(514\) 16.4577 11.9572i 0.725918 0.527410i
\(515\) 0 0
\(516\) 19.3976 + 14.0931i 0.853930 + 0.620416i
\(517\) 18.8809 6.13479i 0.830383 0.269808i
\(518\) 4.44743i 0.195409i
\(519\) −3.91633 12.0532i −0.171908 0.529078i
\(520\) 0 0
\(521\) 10.1071 31.1065i 0.442800 1.36280i −0.442078 0.896977i \(-0.645759\pi\)
0.884878 0.465822i \(-0.154241\pi\)
\(522\) −19.5772 6.36101i −0.856869 0.278414i
\(523\) −0.138697 0.190901i −0.00606481 0.00834750i 0.805974 0.591951i \(-0.201642\pi\)
−0.812039 + 0.583604i \(0.801642\pi\)
\(524\) −33.1471 −1.44804
\(525\) 0 0
\(526\) −2.07658 −0.0905434
\(527\) 0.232299 + 0.319732i 0.0101191 + 0.0139277i
\(528\) 13.3055 + 4.32322i 0.579048 + 0.188144i
\(529\) 0.710999 2.18823i 0.0309130 0.0951405i
\(530\) 0 0
\(531\) 2.78611 + 8.57476i 0.120907 + 0.372113i
\(532\) 6.02330i 0.261143i
\(533\) 27.7032 9.00132i 1.19996 0.389890i
\(534\) 53.8091 + 39.0946i 2.32855 + 1.69179i
\(535\) 0 0
\(536\) 1.28477 0.933437i 0.0554934 0.0403183i
\(537\) 11.2023 15.4186i 0.483413 0.665361i
\(538\) 4.03076 5.54786i 0.173778 0.239185i
\(539\) −9.73271 + 7.07123i −0.419217 + 0.304579i
\(540\) 0 0
\(541\) 27.1484 + 19.7244i 1.16720 + 0.848020i 0.990671 0.136276i \(-0.0435133\pi\)
0.176528 + 0.984296i \(0.443513\pi\)
\(542\) −24.0963 + 7.82935i −1.03502 + 0.336299i
\(543\) 31.4183i 1.34829i
\(544\) −7.23434 22.2650i −0.310170 0.954604i
\(545\) 0 0
\(546\) −4.74364 + 14.5994i −0.203009 + 0.624798i
\(547\) −36.6276 11.9010i −1.56608 0.508851i −0.607658 0.794199i \(-0.707891\pi\)
−0.958424 + 0.285348i \(0.907891\pi\)
\(548\) 0.951688 + 1.30989i 0.0406541 + 0.0559555i
\(549\) 5.07790 0.216720
\(550\) 0 0
\(551\) 13.9156 0.592825
\(552\) −4.27150 5.87922i −0.181807 0.250236i
\(553\) 14.9605 + 4.86095i 0.636183 + 0.206708i
\(554\) −7.64668 + 23.5341i −0.324876 + 0.999866i
\(555\) 0 0
\(556\) −12.0262 37.0128i −0.510024 1.56969i
\(557\) 4.33445i 0.183657i −0.995775 0.0918283i \(-0.970729\pi\)
0.995775 0.0918283i \(-0.0292711\pi\)
\(558\) 0.496448 0.161306i 0.0210163 0.00682861i
\(559\) −12.6765 9.21004i −0.536160 0.389543i
\(560\) 0 0
\(561\) 10.2965 7.48081i 0.434717 0.315840i
\(562\) −30.2032 + 41.5712i −1.27405 + 1.75357i
\(563\) −20.5148 + 28.2362i −0.864595 + 1.19001i 0.115860 + 0.993266i \(0.463038\pi\)
−0.980454 + 0.196747i \(0.936962\pi\)
\(564\) −41.4614 + 30.1235i −1.74584 + 1.26843i
\(565\) 0 0
\(566\) −5.67421 4.12255i −0.238505 0.173284i
\(567\) −10.5132 + 3.41593i −0.441511 + 0.143456i
\(568\) 7.00572i 0.293953i
\(569\) 12.9678 + 39.9107i 0.543637 + 1.67314i 0.724208 + 0.689581i \(0.242205\pi\)
−0.180571 + 0.983562i \(0.557795\pi\)
\(570\) 0 0
\(571\) −4.27469 + 13.1561i −0.178890 + 0.550567i −0.999790 0.0205055i \(-0.993472\pi\)
0.820900 + 0.571072i \(0.193472\pi\)
\(572\) 15.0718 + 4.89711i 0.630182 + 0.204759i
\(573\) −1.63644 2.25237i −0.0683633 0.0940940i
\(574\) 17.8658 0.745704
\(575\) 0 0
\(576\) −19.2544 −0.802268
\(577\) 7.51147 + 10.3387i 0.312707 + 0.430404i 0.936223 0.351407i \(-0.114296\pi\)
−0.623516 + 0.781810i \(0.714296\pi\)
\(578\) 17.0990 + 5.55579i 0.711223 + 0.231090i
\(579\) 14.3843 44.2703i 0.597791 1.83981i
\(580\) 0 0
\(581\) −0.543140 1.67161i −0.0225333 0.0693502i
\(582\) 78.0696i 3.23609i
\(583\) −14.3899 + 4.67556i −0.595968 + 0.193642i
\(584\) −0.456080 0.331361i −0.0188727 0.0137118i
\(585\) 0 0
\(586\) −15.1215 + 10.9864i −0.624665 + 0.453845i
\(587\) −7.16331 + 9.85945i −0.295661 + 0.406943i −0.930843 0.365420i \(-0.880925\pi\)
0.635181 + 0.772363i \(0.280925\pi\)
\(588\) 18.2543 25.1248i 0.752793 1.03613i
\(589\) −0.285485 + 0.207417i −0.0117632 + 0.00854648i
\(590\) 0 0
\(591\) −21.7015 15.7671i −0.892680 0.648570i
\(592\) 6.50330 2.11305i 0.267284 0.0868459i
\(593\) 31.2580i 1.28361i 0.766866 + 0.641807i \(0.221815\pi\)
−0.766866 + 0.641807i \(0.778185\pi\)
\(594\) 3.30550 + 10.1733i 0.135626 + 0.417415i
\(595\) 0 0
\(596\) 2.33063 7.17294i 0.0954663 0.293815i
\(597\) 21.7588 + 7.06986i 0.890528 + 0.289350i
\(598\) 18.8154 + 25.8972i 0.769419 + 1.05901i
\(599\) 33.3707 1.36349 0.681746 0.731589i \(-0.261221\pi\)
0.681746 + 0.731589i \(0.261221\pi\)
\(600\) 0 0
\(601\) −46.8052 −1.90922 −0.954611 0.297854i \(-0.903729\pi\)
−0.954611 + 0.297854i \(0.903729\pi\)
\(602\) −5.64885 7.77498i −0.230230 0.316884i
\(603\) 3.81119 + 1.23833i 0.155204 + 0.0504287i
\(604\) −12.8350 + 39.5020i −0.522248 + 1.60731i
\(605\) 0 0
\(606\) −3.60852 11.1059i −0.146586 0.451145i
\(607\) 30.7401i 1.24770i 0.781543 + 0.623851i \(0.214433\pi\)
−0.781543 + 0.623851i \(0.785567\pi\)
\(608\) 19.8802 6.45947i 0.806249 0.261966i
\(609\) 9.50380 + 6.90492i 0.385114 + 0.279801i
\(610\) 0 0
\(611\) 27.0955 19.6861i 1.09617 0.796413i
\(612\) −7.32517 + 10.0822i −0.296102 + 0.407550i
\(613\) 22.5060 30.9768i 0.909008 1.25114i −0.0584964 0.998288i \(-0.518631\pi\)
0.967504 0.252854i \(-0.0813694\pi\)
\(614\) −15.9953 + 11.6213i −0.645518 + 0.468996i
\(615\) 0 0
\(616\) 1.16663 + 0.847609i 0.0470050 + 0.0341512i
\(617\) −0.404490 + 0.131427i −0.0162842 + 0.00529104i −0.317148 0.948376i \(-0.602725\pi\)
0.300864 + 0.953667i \(0.402725\pi\)
\(618\) 46.6032i 1.87466i
\(619\) −2.32117 7.14384i −0.0932958 0.287135i 0.893510 0.449043i \(-0.148235\pi\)
−0.986806 + 0.161908i \(0.948235\pi\)
\(620\) 0 0
\(621\) −3.60594 + 11.0979i −0.144701 + 0.445345i
\(622\) 58.1720 + 18.9012i 2.33248 + 0.757870i
\(623\) −8.46278 11.6480i −0.339054 0.466668i
\(624\) 23.6020 0.944834
\(625\) 0 0
\(626\) −39.3912 −1.57439
\(627\) 6.67955 + 9.19361i 0.266755 + 0.367157i
\(628\) 3.69667 + 1.20112i 0.147513 + 0.0479300i
\(629\) 1.92227 5.91615i 0.0766461 0.235892i
\(630\) 0 0
\(631\) −3.48311 10.7199i −0.138660 0.426752i 0.857481 0.514515i \(-0.172028\pi\)
−0.996141 + 0.0877630i \(0.972028\pi\)
\(632\) 11.5163i 0.458094i
\(633\) −18.1023 + 5.88178i −0.719500 + 0.233780i
\(634\) −38.4463 27.9329i −1.52690 1.10936i
\(635\) 0 0
\(636\) 31.5994 22.9583i 1.25300 0.910355i
\(637\) −11.9294 + 16.4194i −0.472659 + 0.650560i
\(638\) 13.1991 18.1669i 0.522556 0.719236i
\(639\) 14.3020 10.3910i 0.565780 0.411063i
\(640\) 0 0
\(641\) −21.1012 15.3309i −0.833447 0.605535i 0.0870851 0.996201i \(-0.472245\pi\)
−0.920533 + 0.390666i \(0.872245\pi\)
\(642\) −21.0035 + 6.82445i −0.828942 + 0.269340i
\(643\) 31.9492i 1.25995i 0.776614 + 0.629977i \(0.216936\pi\)
−0.776614 + 0.629977i \(0.783064\pi\)
\(644\) 3.27657 + 10.0842i 0.129115 + 0.397375i
\(645\) 0 0
\(646\) 4.82055 14.8361i 0.189662 0.583720i
\(647\) −7.03243 2.28497i −0.276473 0.0898316i 0.167499 0.985872i \(-0.446431\pi\)
−0.443972 + 0.896041i \(0.646431\pi\)
\(648\) −4.75686 6.54726i −0.186867 0.257201i
\(649\) −9.83550 −0.386077
\(650\) 0 0
\(651\) −0.297895 −0.0116754
\(652\) 1.23257 + 1.69649i 0.0482713 + 0.0664398i
\(653\) −17.7708 5.77407i −0.695424 0.225957i −0.0600882 0.998193i \(-0.519138\pi\)
−0.635336 + 0.772236i \(0.719138\pi\)
\(654\) −23.0555 + 70.9575i −0.901541 + 2.77466i
\(655\) 0 0
\(656\) −8.48835 26.1245i −0.331414 1.01999i
\(657\) 1.42256i 0.0554994i
\(658\) 19.5364 6.34777i 0.761609 0.247462i
\(659\) 7.92963 + 5.76122i 0.308895 + 0.224425i 0.731422 0.681925i \(-0.238857\pi\)
−0.422527 + 0.906350i \(0.638857\pi\)
\(660\) 0 0
\(661\) 22.7807 16.5511i 0.886066 0.643765i −0.0487833 0.998809i \(-0.515534\pi\)
0.934849 + 0.355045i \(0.115534\pi\)
\(662\) 3.63174 4.99866i 0.141152 0.194278i
\(663\) 12.6204 17.3704i 0.490134 0.674612i
\(664\) 1.04103 0.756351i 0.0403997 0.0293521i
\(665\) 0 0
\(666\) −6.64706 4.82937i −0.257568 0.187134i
\(667\) 23.2976 7.56986i 0.902087 0.293106i
\(668\) 12.2014i 0.472085i
\(669\) 19.2557 + 59.2629i 0.744468 + 2.29124i
\(670\) 0 0
\(671\) −1.71178 + 5.26831i −0.0660825 + 0.203381i
\(672\) 16.7826 + 5.45299i 0.647402 + 0.210354i
\(673\) −22.9385 31.5721i −0.884214 1.21702i −0.975236 0.221168i \(-0.929013\pi\)
0.0910215 0.995849i \(-0.470987\pi\)
\(674\) −39.2290 −1.51104
\(675\) 0 0
\(676\) −3.79434 −0.145936
\(677\) −2.95969 4.07367i −0.113750 0.156564i 0.748346 0.663309i \(-0.230848\pi\)
−0.862096 + 0.506745i \(0.830848\pi\)
\(678\) 29.4614 + 9.57259i 1.13146 + 0.367633i
\(679\) 5.22228 16.0725i 0.200413 0.616807i
\(680\) 0 0
\(681\) −15.1102 46.5044i −0.579025 1.78205i
\(682\) 0.569440i 0.0218050i
\(683\) −28.8467 + 9.37285i −1.10379 + 0.358642i −0.803559 0.595225i \(-0.797063\pi\)
−0.300228 + 0.953867i \(0.597063\pi\)
\(684\) −9.00233 6.54058i −0.344213 0.250085i
\(685\) 0 0
\(686\) −21.7900 + 15.8314i −0.831948 + 0.604446i
\(687\) 3.19906 4.40313i 0.122052 0.167990i
\(688\) −8.68518 + 11.9541i −0.331119 + 0.455747i
\(689\) −20.6506 + 15.0035i −0.786724 + 0.571588i
\(690\) 0 0
\(691\) 17.1778 + 12.4804i 0.653474 + 0.474777i 0.864453 0.502714i \(-0.167665\pi\)
−0.210979 + 0.977491i \(0.567665\pi\)
\(692\) −12.8752 + 4.18340i −0.489441 + 0.159029i
\(693\) 3.63886i 0.138229i
\(694\) −14.6522 45.0949i −0.556191 1.71178i
\(695\) 0 0
\(696\) −2.65765 + 8.17939i −0.100738 + 0.310039i
\(697\) −23.7658 7.72198i −0.900194 0.292491i
\(698\) 2.37600 + 3.27029i 0.0899330 + 0.123782i
\(699\) 13.0943 0.495273
\(700\) 0 0
\(701\) 32.7698 1.23770 0.618849 0.785510i \(-0.287599\pi\)
0.618849 + 0.785510i \(0.287599\pi\)
\(702\) 10.6071 + 14.5994i 0.400339 + 0.551020i
\(703\) 5.28247 + 1.71638i 0.199232 + 0.0647345i
\(704\) 6.49074 19.9764i 0.244629 0.752890i
\(705\) 0 0
\(706\) −3.38269 10.4108i −0.127309 0.391817i
\(707\) 2.52780i 0.0950676i
\(708\) 24.1475 7.84600i 0.907519 0.294871i
\(709\) 16.0557 + 11.6652i 0.602985 + 0.438094i 0.846937 0.531693i \(-0.178444\pi\)
−0.243952 + 0.969787i \(0.578444\pi\)
\(710\) 0 0
\(711\) −23.5103 + 17.0813i −0.881707 + 0.640598i
\(712\) 6.19566 8.52760i 0.232192 0.319585i
\(713\) −0.365130 + 0.502558i −0.0136742 + 0.0188210i
\(714\) 10.6539 7.74052i 0.398713 0.289682i
\(715\) 0 0
\(716\) −16.4700 11.9662i −0.615514 0.447197i
\(717\) 14.7040 4.77763i 0.549132 0.178424i
\(718\) 47.1144i 1.75829i
\(719\) −7.48443 23.0347i −0.279122 0.859049i −0.988099 0.153818i \(-0.950843\pi\)
0.708977 0.705231i \(-0.249157\pi\)
\(720\) 0 0
\(721\) 3.11741 9.59440i 0.116098 0.357314i
\(722\) −24.4342 7.93916i −0.909347 0.295465i
\(723\) 1.52454 + 2.09835i 0.0566982 + 0.0780384i
\(724\) −33.5609 −1.24728
\(725\) 0 0
\(726\) −32.0914 −1.19102
\(727\) 3.44742 + 4.74496i 0.127858 + 0.175981i 0.868147 0.496308i \(-0.165311\pi\)
−0.740289 + 0.672289i \(0.765311\pi\)
\(728\) 2.31370 + 0.751766i 0.0857513 + 0.0278623i
\(729\) 1.08320 3.33374i 0.0401185 0.123472i
\(730\) 0 0
\(731\) 4.15382 + 12.7841i 0.153635 + 0.472838i
\(732\) 14.3000i 0.528542i
\(733\) −32.8129 + 10.6615i −1.21197 + 0.393793i −0.844152 0.536104i \(-0.819895\pi\)
−0.367819 + 0.929897i \(0.619895\pi\)
\(734\) 12.3132 + 8.94604i 0.454487 + 0.330204i
\(735\) 0 0
\(736\) 29.7698 21.6290i 1.09733 0.797255i
\(737\) −2.56953 + 3.53666i −0.0946499 + 0.130274i
\(738\) −19.4001 + 26.7019i −0.714128 + 0.982912i
\(739\) 32.0138 23.2594i 1.17765 0.855611i 0.185743 0.982598i \(-0.440531\pi\)
0.991904 + 0.126988i \(0.0405309\pi\)
\(740\) 0 0
\(741\) 15.5099 + 11.2686i 0.569770 + 0.413962i
\(742\) −14.8895 + 4.83788i −0.546609 + 0.177604i
\(743\) 29.7058i 1.08980i −0.838501 0.544900i \(-0.816567\pi\)
0.838501 0.544900i \(-0.183433\pi\)
\(744\) −0.0673939 0.207417i −0.00247078 0.00760428i
\(745\) 0 0
\(746\) 14.3746 44.2405i 0.526292 1.61976i
\(747\) 3.08815 + 1.00340i 0.112990 + 0.0367126i
\(748\) −7.99095 10.9986i −0.292178 0.402149i
\(749\) 4.78058 0.174679
\(750\) 0 0
\(751\) 26.8870 0.981122 0.490561 0.871407i \(-0.336792\pi\)
0.490561 + 0.871407i \(0.336792\pi\)
\(752\) −18.5642 25.5514i −0.676966 0.931764i
\(753\) −9.63623 3.13100i −0.351164 0.114100i
\(754\) 11.7066 36.0291i 0.426328 1.31210i
\(755\) 0 0
\(756\) 1.84715 + 5.68495i 0.0671803 + 0.206760i
\(757\) 44.6792i 1.62389i −0.583731 0.811947i \(-0.698408\pi\)
0.583731 0.811947i \(-0.301592\pi\)
\(758\) −65.3405 + 21.2304i −2.37327 + 0.771123i
\(759\) 16.1841 + 11.7584i 0.587446 + 0.426804i
\(760\) 0 0
\(761\) −16.4295 + 11.9367i −0.595568 + 0.432706i −0.844303 0.535866i \(-0.819985\pi\)
0.248735 + 0.968572i \(0.419985\pi\)
\(762\) 4.01728 5.52931i 0.145531 0.200306i
\(763\) 9.49307 13.0661i 0.343672 0.473024i
\(764\) −2.40596 + 1.74803i −0.0870447 + 0.0632417i
\(765\) 0 0
\(766\) −34.9219 25.3722i −1.26178 0.916736i
\(767\) −15.7807 + 5.12746i −0.569808 + 0.185142i
\(768\) 19.9359i 0.719375i
\(769\) −8.05227 24.7823i −0.290372 0.893674i −0.984737 0.174051i \(-0.944314\pi\)
0.694364 0.719624i \(-0.255686\pi\)
\(770\) 0 0
\(771\) 6.62755 20.3975i 0.238685 0.734598i
\(772\) −47.2892 15.3652i −1.70198 0.553006i
\(773\) −8.07058 11.1082i −0.290278 0.399534i 0.638826 0.769351i \(-0.279420\pi\)
−0.929105 + 0.369817i \(0.879420\pi\)
\(774\) 17.7543 0.638166
\(775\) 0 0
\(776\) 12.3724 0.444142
\(777\) 2.75605 + 3.79338i 0.0988728 + 0.136087i
\(778\) 2.26972 + 0.737476i 0.0813733 + 0.0264398i
\(779\) 6.89488 21.2203i