Properties

Label 625.2.e.a.249.1
Level $625$
Weight $2$
Character 625.249
Analytic conductor $4.991$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 249.1
Root \(-0.983224 + 0.644389i\) of defining polynomial
Character \(\chi\) \(=\) 625.249
Dual form 625.2.e.a.374.1

$q$-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 \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\)

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 0.113229 + 0.993569i \(0.463881\pi\)
−0.979930 + 0.199342i \(0.936119\pi\)
\(3\) −2.09089 + 0.679371i −1.20718 + 0.392235i −0.842396 0.538859i \(-0.818856\pi\)
−0.364780 + 0.931094i \(0.618856\pi\)
\(4\) −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 \(0.0600533\pi\)
−0.982256 + 0.187546i \(0.939947\pi\)
\(8\) 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 0.316503 0.948591i \(-0.397491\pi\)
−0.804359 + 0.594144i \(0.797491\pi\)
\(12\) 3.03472 + 4.17693i 0.876047 + 1.20578i
\(13\) −1.98322 2.72967i −0.550047 0.757075i 0.439971 0.898012i \(-0.354989\pi\)
−0.990019 + 0.140937i \(0.954989\pi\)
\(14\) −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 0.623186 0.782074i \(-0.285838\pi\)
0.0444767 + 0.999010i \(0.485838\pi\)
\(18\) 3.82309i 0.901111i
\(19\) 0.798649 2.45799i 0.183223 0.563901i −0.816691 0.577076i \(-0.804194\pi\)
0.999913 + 0.0131746i \(0.00419372\pi\)
\(20\) 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 −0.433410 0.901197i \(-0.642690\pi\)
0.991020 + 0.133712i \(0.0426896\pi\)
\(24\) −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 0.978167 + 0.207821i \(0.0666370\pi\)
−0.669200 + 0.743082i \(0.733363\pi\)
\(30\) 0 0
\(31\) 0.0421925 0.129855i 0.00757799 0.0233227i −0.947196 0.320655i \(-0.896097\pi\)
0.954774 + 0.297332i \(0.0960970\pi\)
\(32\) 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 0.900129 0.435624i \(-0.143472\pi\)
−0.692458 + 0.721458i \(0.743472\pi\)
\(38\) 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 −0.979530 0.201296i \(-0.935485\pi\)
−0.111248 + 0.993793i \(0.535485\pi\)
\(42\) 4.32696 + 1.40591i 0.667664 + 0.216937i
\(43\) 4.64398i 0.708200i −0.935208 0.354100i \(-0.884787\pi\)
0.935208 0.354100i \(-0.115213\pi\)
\(44\) −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 −0.901693 0.432376i \(-0.857675\pi\)
−0.475341 + 0.879802i \(0.657675\pi\)
\(48\) −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 0.230120 0.973162i \(-0.426088\pi\)
0.758181 + 0.652044i \(0.226088\pi\)
\(54\) 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 −0.297873 0.954605i \(-0.596277\pi\)
0.815836 + 0.578284i \(0.196277\pi\)
\(60\) 0 0
\(61\) 2.24075 + 1.62800i 0.286898 + 0.208444i 0.721921 0.691976i \(-0.243260\pi\)
−0.435022 + 0.900420i \(0.643260\pi\)
\(62\) 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 0.433233 0.901282i \(-0.357373\pi\)
−0.179268 + 0.983800i \(0.557373\pi\)
\(68\) 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 0.956802 + 0.290741i \(0.0939019\pi\)
−0.603175 + 0.797609i \(0.706098\pi\)
\(72\) 1.26682 0.411616i 0.149297 0.0485094i
\(73\) −0.456080 + 0.627740i −0.0533801 + 0.0734714i −0.834873 0.550443i \(-0.814459\pi\)
0.781492 + 0.623915i \(0.214459\pi\)
\(74\) −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 −0.706056 0.708156i \(-0.749527\pi\)
0.154968 0.987919i \(-0.450473\pi\)
\(80\) 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 0.399998 0.916516i \(-0.369011\pi\)
−0.215109 + 0.976590i \(0.569011\pi\)
\(84\) −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 0.997867 0.0652758i \(-0.0207927\pi\)
0.246277 + 0.969200i \(0.420793\pi\)
\(90\) 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 0.666899 0.745148i \(-0.267621\pi\)
0.977520 + 0.210844i \(0.0676214\pi\)
\(98\) −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 0.208832 0.977952i \(-0.433034\pi\)
0.743774 + 0.668431i \(0.233034\pi\)
\(104\) −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 \(-0.925195\pi\)
0.972513 0.232848i \(-0.0748046\pi\)
\(108\) −5.72850 1.86130i −0.551225 0.179104i
\(109\) 13.1662 9.56578i 1.26109 0.916236i 0.262280 0.964992i \(-0.415526\pi\)
0.998811 + 0.0487563i \(0.0155258\pi\)
\(110\) 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 0.953882 0.300183i \(-0.0970477\pi\)
−0.580256 + 0.814434i \(0.697048\pi\)
\(114\) −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 −0.846124 0.532986i \(-0.821070\pi\)
0.768367 + 0.640010i \(0.221070\pi\)
\(128\) 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 −0.558202 0.829705i \(-0.688509\pi\)
0.939283 0.343143i \(-0.111491\pi\)
\(132\) 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 0.825977 0.563703i \(-0.190624\pi\)
−0.791355 + 0.611357i \(0.790624\pi\)
\(138\) −12.2599 16.8742i −1.04363 1.43643i
\(139\) −13.4069 9.74070i −1.13716 0.826195i −0.150439 0.988619i \(-0.548069\pi\)
−0.986721 + 0.162424i \(0.948069\pi\)
\(140\) 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 \(0.0210386\pi\)
−0.997817 + 0.0660465i \(0.978961\pi\)
\(158\) 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 0.829077 0.559134i \(-0.188866\pi\)
−0.787967 + 0.615717i \(0.788866\pi\)
\(164\) 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 0.493893 0.869523i \(-0.335573\pi\)
−0.111525 + 0.993762i \(0.535573\pi\)
\(168\) 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 −0.660546 0.750785i \(-0.729675\pi\)
0.918159 + 0.396211i \(0.129675\pi\)
\(174\) 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 −0.999876 0.0157637i \(-0.994982\pi\)
0.799651 0.600465i \(-0.205018\pi\)
\(180\) 0 0
\(181\) 4.41612 13.5914i 0.328248 1.01024i −0.641706 0.766951i \(-0.721773\pi\)
0.969953 0.243291i \(-0.0782271\pi\)
\(182\) 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 −0.550103 0.835097i \(-0.685411\pi\)
0.624233 + 0.781238i \(0.285411\pi\)
\(192\) 21.9590 + 7.13492i 1.58476 + 0.514918i
\(193\) 21.1730i 1.52406i −0.647540 0.762031i \(-0.724202\pi\)
0.647540 0.762031i \(-0.275798\pi\)
\(194\) −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 0.135081 0.990835i \(-0.456871\pi\)
0.691681 + 0.722203i \(0.256871\pi\)
\(198\) 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 0.802173 0.597092i \(-0.203677\pi\)
−0.319983 + 0.947423i \(0.603677\pi\)
\(212\) −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 −0.302764 + 0.953065i \(0.597909\pi\)
−0.812860 + 0.582459i \(0.802091\pi\)
\(224\) −8.02652 −0.536295
\(225\) 0 0
\(226\) −14.0904 −0.937277
\(227\) 13.0732 17.9937i 0.867699 1.19429i −0.111979 0.993711i \(-0.535719\pi\)
0.979678 0.200575i \(-0.0642809\pi\)
\(228\) 12.6905 4.12340i 0.840450 0.273079i
\(229\) −0.765000 2.35443i −0.0505526 0.155585i 0.922593 0.385774i \(-0.126066\pi\)
−0.973146 + 0.230189i \(0.926066\pi\)
\(230\) 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 0.117531 0.993069i \(-0.462502\pi\)
−0.488627 + 0.872493i \(0.662502\pi\)
\(234\) 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 0.388373 0.921502i \(-0.373037\pi\)
−0.756387 + 0.654125i \(0.773037\pi\)
\(240\) 0 0
\(241\) −0.954449 + 0.693448i −0.0614815 + 0.0446689i −0.618102 0.786098i \(-0.712098\pi\)
0.556620 + 0.830767i \(0.312098\pi\)
\(242\) 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 \(-0.901590\pi\)
0.952588 0.304263i \(-0.0984102\pi\)
\(258\) −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 0.826682 0.562669i \(-0.190225\pi\)
−0.790589 + 0.612347i \(0.790225\pi\)
\(264\) 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 −0.915285 0.402806i \(-0.868035\pi\)
0.977245 + 0.212114i \(0.0680349\pi\)
\(270\) 0 0
\(271\) 3.75457 + 11.5554i 0.228074 + 0.701940i 0.997965 + 0.0637642i \(0.0203105\pi\)
−0.769891 + 0.638175i \(0.779689\pi\)
\(272\) 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 −0.965405 0.260754i \(-0.916029\pi\)
0.546319 + 0.837577i \(0.316029\pi\)
\(278\) 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 0.417756 + 0.908559i \(0.362817\pi\)
−0.872009 + 0.489489i \(0.837183\pi\)
\(282\) 45.5069i 2.70990i
\(283\) 3.19881 + 1.03936i 0.190150 + 0.0617833i 0.402544 0.915401i \(-0.368126\pi\)
−0.212394 + 0.977184i \(0.568126\pi\)
\(284\) 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 \(0.0843239\pi\)
−0.965116 + 0.261824i \(0.915676\pi\)
\(294\) 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 \(0.0872102\pi\)
−0.962702 + 0.270564i \(0.912790\pi\)
\(308\) −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 −0.999217 0.0395541i \(-0.987406\pi\)
−0.346393 0.938089i \(-0.612594\pi\)
\(312\) 3.16780 + 4.36010i 0.179341 + 0.246842i
\(313\) 11.1033 + 15.2824i 0.627596 + 0.863811i 0.997878 0.0651079i \(-0.0207392\pi\)
−0.370283 + 0.928919i \(0.620739\pi\)
\(314\) −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 0.846109 0.533010i \(-0.178939\pi\)
0.371221 + 0.928545i \(0.378939\pi\)
\(318\) 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 −0.922735 0.385436i \(-0.874051\pi\)
0.973061 + 0.230546i \(0.0740512\pi\)
\(332\) 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 0.995920 0.0902353i \(-0.0287619\pi\)
−0.393575 + 0.919292i \(0.628762\pi\)
\(338\) 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 0.335665 0.941981i \(-0.391039\pi\)
0.825242 + 0.564780i \(0.191039\pi\)
\(348\) −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 −0.173124 0.984900i \(-0.555386\pi\)
0.438849 + 0.898561i \(0.355386\pi\)
\(354\) −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 0.0104726 0.999945i \(-0.496666\pi\)
0.954241 + 0.299040i \(0.0966664\pi\)
\(360\) 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 0.122187 0.992507i \(-0.461009\pi\)
−0.484530 + 0.874775i \(0.661009\pi\)
\(368\) 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 −0.321010 0.947076i \(-0.604022\pi\)
0.999920 + 0.0126358i \(0.00402219\pi\)
\(374\) 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 0.768303 + 0.640086i \(0.221101\pi\)
−0.245337 + 0.969438i \(0.578899\pi\)
\(380\) 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 0.765245 0.643739i \(-0.222618\pi\)
0.240716 + 0.970595i \(0.422618\pi\)
\(384\) −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 0.564066 0.825730i \(-0.309236\pi\)
−0.611010 + 0.791623i \(0.709236\pi\)
\(390\) 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 −0.195058 0.980792i \(-0.562490\pi\)
0.418690 + 0.908129i \(0.362490\pi\)
\(398\) 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 −0.625127 0.780523i \(-0.714953\pi\)
0.549147 + 0.835726i \(0.314953\pi\)
\(410\) 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 −0.931945 0.362600i \(-0.881889\pi\)
0.967090 + 0.254434i \(0.0818890\pi\)
\(420\) 0 0
\(421\) −7.40097 22.7779i −0.360701 1.11012i −0.952629 0.304134i \(-0.901633\pi\)
0.591928 0.805991i \(-0.298367\pi\)
\(422\) −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 −0.941791 0.336199i \(-0.890859\pi\)
0.959538 + 0.281580i \(0.0908586\pi\)
\(432\) 8.16074i 0.392634i
\(433\) −24.3602 7.91511i −1.17068 0.380376i −0.341781 0.939780i \(-0.611030\pi\)
−0.828895 + 0.559404i \(0.811030\pi\)
\(434\) −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 0.895231 0.445603i \(-0.147011\pi\)
−0.147152 + 0.989114i \(0.547011\pi\)
\(440\) 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 \(0.0186323\pi\)
−0.998287 + 0.0585016i \(0.981368\pi\)
\(444\) −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 \(0.200604\pi\)
−0.807901 + 0.589319i \(0.799396\pi\)
\(458\) 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 −0.107394 0.994217i \(-0.534251\pi\)
−0.978743 + 0.205092i \(0.934251\pi\)
\(462\) −5.34841 7.36146i −0.248831 0.342486i
\(463\) −18.7384 25.7911i −0.870846 1.19862i −0.978873 0.204468i \(-0.934453\pi\)
0.108028 0.994148i \(-0.465547\pi\)
\(464\) 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 −0.971484 0.237106i \(-0.923801\pi\)
−0.925314 0.379201i \(-0.876199\pi\)
\(468\) 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 −0.982584 0.185818i \(-0.940506\pi\)
0.685706 0.727878i \(-0.259494\pi\)
\(480\) 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 −0.998402 0.0565121i \(-0.982002\pi\)
0.254777 0.967000i \(-0.417998\pi\)
\(488\) 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 −0.826395 0.563091i \(-0.809612\pi\)
0.280161 + 0.959953i \(0.409612\pi\)
\(492\) −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 −0.763532 0.645769i \(-0.776537\pi\)
−0.238137 + 0.971232i \(0.576537\pi\)
\(504\) 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 −0.952683 0.303966i \(-0.901689\pi\)
−0.00530682 + 0.999986i \(0.501689\pi\)
\(510\) 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 0.884878 + 0.465822i \(0.154241\pi\)
−0.442078 + 0.896977i \(0.645759\pi\)
\(522\) −19.5772 + 6.36101i −0.856869 + 0.278414i
\(523\) −0.138697 + 0.190901i −0.00606481 + 0.00834750i −0.812039 0.583604i \(-0.801642\pi\)
0.805974 + 0.591951i \(0.201642\pi\)
\(524\) −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 0.176528 0.984296i \(-0.443513\pi\)
0.990671 + 0.136276i \(0.0435133\pi\)
\(542\) −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 −0.958424 0.285348i \(-0.907891\pi\)
−0.607658 + 0.794199i \(0.707891\pi\)
\(548\) 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 \(0.0292711\pi\)
−0.995775 + 0.0918283i \(0.970729\pi\)
\(558\) 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 −0.980454 0.196747i \(-0.936962\pi\)
0.115860 0.993266i \(-0.463038\pi\)
\(564\) −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 −0.180571 0.983562i \(-0.557795\pi\)
0.724208 0.689581i \(-0.242205\pi\)
\(570\) 0 0
\(571\) −4.27469 13.1561i −0.178890 0.550567i 0.820900 0.571072i \(-0.193472\pi\)
−0.999790 + 0.0205055i \(0.993472\pi\)
\(572\) 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 −0.623516 0.781810i \(-0.714296\pi\)
0.936223 + 0.351407i \(0.114296\pi\)
\(578\) 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 0.635181 0.772363i \(-0.280925\pi\)
−0.930843 + 0.365420i \(0.880925\pi\)
\(588\) 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 \(-0.778185\pi\)
0.766866 0.641807i \(-0.221815\pi\)
\(594\) 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 \(-0.785567\pi\)
0.781543 0.623851i \(-0.214433\pi\)
\(608\) 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 0.967504 + 0.252854i \(0.0813694\pi\)
−0.0584964 + 0.998288i \(0.518631\pi\)
\(614\) −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 0.300864 0.953667i \(-0.402725\pi\)
−0.317148 + 0.948376i \(0.602725\pi\)
\(618\) 46.6032i 1.87466i
\(619\) −2.32117 + 7.14384i −0.0932958 + 0.287135i −0.986806 0.161908i \(-0.948235\pi\)
0.893510 + 0.449043i \(0.148235\pi\)
\(620\) 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 −0.996141 0.0877630i \(-0.972028\pi\)
0.857481 + 0.514515i \(0.172028\pi\)
\(632\) 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 −0.920533 0.390666i \(-0.872245\pi\)
0.0870851 + 0.996201i \(0.472245\pi\)
\(642\) −21.0035 6.82445i −0.828942 0.269340i
\(643\) 31.9492i 1.25995i −0.776614 0.629977i \(-0.783064\pi\)
0.776614 0.629977i \(-0.216936\pi\)
\(644\) 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 −0.443972 0.896041i \(-0.646431\pi\)
0.167499 + 0.985872i \(0.446431\pi\)
\(648\) −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 −0.635336 0.772236i \(-0.719138\pi\)
−0.0600882 + 0.998193i \(0.519138\pi\)
\(654\) −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 −0.422527 0.906350i \(-0.638857\pi\)
0.731422 + 0.681925i \(0.238857\pi\)
\(660\) 0 0
\(661\) 22.7807 + 16.5511i 0.886066 + 0.643765i 0.934849 0.355045i \(-0.115534\pi\)
−0.0487833 + 0.998809i \(0.515534\pi\)
\(662\) 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 0.0910215 + 0.995849i \(0.470987\pi\)
−0.975236 + 0.221168i \(0.929013\pi\)
\(674\) −39.2290 −1.51104
\(675\) 0 0
\(676\) −3.79434 −0.145936
\(677\) −2.95969 + 4.07367i −0.113750 + 0.156564i −0.862096 0.506745i \(-0.830848\pi\)
0.748346 + 0.663309i \(0.230848\pi\)
\(678\) 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 −0.300228 0.953867i \(-0.597063\pi\)
−0.803559 + 0.595225i \(0.797063\pi\)
\(684\) −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 −0.210979 0.977491i \(-0.567665\pi\)
0.864453 + 0.502714i \(0.167665\pi\)
\(692\) −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 −0.243952 0.969787i \(-0.578444\pi\)
0.846937 + 0.531693i \(0.178444\pi\)
\(710\) 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 0.708977 + 0.705231i \(0.249157\pi\)
−0.988099 + 0.153818i \(0.950843\pi\)
\(720\) 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 −0.740289 0.672289i \(-0.765311\pi\)
0.868147 + 0.496308i \(0.165311\pi\)
\(728\) 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 −0.367819 0.929897i \(-0.619895\pi\)
−0.844152 + 0.536104i \(0.819895\pi\)
\(734\) 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 0.991904 0.126988i \(-0.0405309\pi\)
0.185743 + 0.982598i \(0.440531\pi\)
\(740\) 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 \(0.183433\pi\)
−0.838501 + 0.544900i \(0.816567\pi\)
\(744\) −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 \(0.301592\pi\)
−0.583731 + 0.811947i \(0.698408\pi\)
\(758\) −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 0.248735 0.968572i \(-0.419985\pi\)
−0.844303 + 0.535866i \(0.819985\pi\)
\(762\) 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 0.694364 + 0.719624i \(0.255686\pi\)
−0.984737 + 0.174051i \(0.944314\pi\)
\(770\) 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 −0.929105 0.369817i \(-0.879420\pi\)
0.638826 + 0.769351i \(0.279420\pi\)
\(774\) 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 +