Properties

Label 605.2.g.l.251.2
Level $605$
Weight $2$
Character 605.251
Analytic conductor $4.831$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.64000000.2
Defining polynomial: \( x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 \) 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 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 251.2
Root \(-1.14412 + 0.831254i\) of defining polynomial
Character \(\chi\) \(=\) 605.251
Dual form 605.2.g.l.511.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.127999 - 0.393941i) q^{2} +(-2.28825 + 1.66251i) q^{3} +(1.47923 + 1.07472i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.362036 + 1.11423i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(1.28293 - 0.932102i) q^{8} +(1.54508 - 4.75528i) q^{9} +O(q^{10})\) \(q+(0.127999 - 0.393941i) q^{2} +(-2.28825 + 1.66251i) q^{3} +(1.47923 + 1.07472i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.362036 + 1.11423i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(1.28293 - 0.932102i) q^{8} +(1.54508 - 4.75528i) q^{9} -0.414214 q^{10} -5.17157 q^{12} +(2.11010 - 6.49422i) q^{13} +(-0.670212 + 0.486937i) q^{14} +(2.28825 + 1.66251i) q^{15} +(0.927051 + 2.85317i) q^{16} +(-0.362036 - 1.11423i) q^{17} +(-1.67553 - 1.21734i) q^{18} +(0.565015 - 1.73894i) q^{20} +5.65685 q^{21} +2.82843 q^{23} +(-1.38603 + 4.26576i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-2.28825 - 1.66251i) q^{26} +(1.74806 + 5.37999i) q^{27} +(-1.13003 - 3.47788i) q^{28} +(6.19453 + 4.50059i) q^{29} +(0.947822 - 0.688633i) q^{30} +4.41421 q^{32} -0.485281 q^{34} +(-0.618034 + 1.90211i) q^{35} +(7.39614 - 5.37361i) q^{36} +(-2.95846 - 2.14944i) q^{37} +(5.96826 + 18.3684i) q^{39} +(-1.28293 - 0.932102i) q^{40} +(4.85410 - 3.52671i) q^{41} +(0.724072 - 2.22846i) q^{42} +6.00000 q^{43} -5.00000 q^{45} +(0.362036 - 1.11423i) q^{46} +(2.28825 - 1.66251i) q^{47} +(-6.86474 - 4.98752i) q^{48} +(-0.927051 - 2.85317i) q^{49} +(0.127999 + 0.393941i) q^{50} +(2.68085 + 1.94775i) q^{51} +(10.1008 - 7.33866i) q^{52} +(0.106038 - 0.326351i) q^{53} +2.34315 q^{54} -3.17157 q^{56} +(2.56586 - 1.86420i) q^{58} +(7.81256 + 5.67616i) q^{59} +(1.59810 + 4.91846i) q^{60} +(-4.11416 - 12.6621i) q^{61} +(-8.09017 + 5.87785i) q^{63} +(-1.28909 + 3.96740i) q^{64} -6.82843 q^{65} -4.48528 q^{67} +(0.661956 - 2.03729i) q^{68} +(-6.47214 + 4.70228i) q^{69} +(0.670212 + 0.486937i) q^{70} +(-3.49613 - 10.7600i) q^{71} +(-2.45017 - 7.54086i) q^{72} +(-5.52431 - 4.01365i) q^{73} +(-1.22543 + 0.890329i) q^{74} +(0.874032 - 2.68999i) q^{75} +8.00000 q^{78} +(-1.23607 + 3.80423i) q^{79} +(2.42705 - 1.76336i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.767994 - 2.36364i) q^{82} +(1.85410 + 5.70634i) q^{83} +(8.36778 + 6.07955i) q^{84} +(-0.947822 + 0.688633i) q^{85} +(0.767994 - 2.36364i) q^{86} -21.6569 q^{87} +9.31371 q^{89} +(-0.639995 + 1.96970i) q^{90} +(-11.0486 + 8.02730i) q^{91} +(4.18389 + 3.03977i) q^{92} +(-0.362036 - 1.11423i) q^{94} +(-10.1008 + 7.33866i) q^{96} +(-2.36610 + 7.28210i) q^{97} -1.24264 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9} + 8 q^{10} - 64 q^{12} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 8 q^{17} + 10 q^{18} + 2 q^{20} - 8 q^{24} - 2 q^{25} - 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{32} + 64 q^{34} + 4 q^{35} - 10 q^{36} + 4 q^{37} - 16 q^{39} - 6 q^{40} + 12 q^{41} - 16 q^{42} + 48 q^{43} - 40 q^{45} - 8 q^{46} + 6 q^{49} + 2 q^{50} - 16 q^{51} + 8 q^{52} - 12 q^{53} + 64 q^{54} - 48 q^{56} + 12 q^{58} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 20 q^{63} + 14 q^{64} - 32 q^{65} + 32 q^{67} + 24 q^{68} - 16 q^{69} - 4 q^{70} + 30 q^{72} - 8 q^{73} - 20 q^{74} + 64 q^{78} + 8 q^{79} + 6 q^{80} - 2 q^{81} - 12 q^{82} - 12 q^{83} + 32 q^{84} - 8 q^{85} + 12 q^{86} - 128 q^{87} - 16 q^{89} - 10 q^{90} - 16 q^{91} + 16 q^{92} + 8 q^{94} - 8 q^{96} + 4 q^{97} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.127999 0.393941i 0.0905090 0.278558i −0.895548 0.444964i \(-0.853216\pi\)
0.986057 + 0.166406i \(0.0532163\pi\)
\(3\) −2.28825 + 1.66251i −1.32112 + 0.959849i −0.321202 + 0.947011i \(0.604087\pi\)
−0.999918 + 0.0128385i \(0.995913\pi\)
\(4\) 1.47923 + 1.07472i 0.739614 + 0.537361i
\(5\) −0.309017 0.951057i −0.138197 0.425325i
\(6\) 0.362036 + 1.11423i 0.147801 + 0.454883i
\(7\) −1.61803 1.17557i −0.611559 0.444324i 0.238404 0.971166i \(-0.423376\pi\)
−0.849963 + 0.526842i \(0.823376\pi\)
\(8\) 1.28293 0.932102i 0.453584 0.329548i
\(9\) 1.54508 4.75528i 0.515028 1.58509i
\(10\) −0.414214 −0.130986
\(11\) 0 0
\(12\) −5.17157 −1.49290
\(13\) 2.11010 6.49422i 0.585236 1.80117i −0.0130823 0.999914i \(-0.504164\pi\)
0.598319 0.801258i \(-0.295836\pi\)
\(14\) −0.670212 + 0.486937i −0.179122 + 0.130139i
\(15\) 2.28825 + 1.66251i 0.590822 + 0.429258i
\(16\) 0.927051 + 2.85317i 0.231763 + 0.713292i
\(17\) −0.362036 1.11423i −0.0878066 0.270241i 0.897506 0.441003i \(-0.145377\pi\)
−0.985312 + 0.170762i \(0.945377\pi\)
\(18\) −1.67553 1.21734i −0.394926 0.286931i
\(19\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(20\) 0.565015 1.73894i 0.126341 0.388838i
\(21\) 5.65685 1.23443
\(22\) 0 0
\(23\) 2.82843 0.589768 0.294884 0.955533i \(-0.404719\pi\)
0.294884 + 0.955533i \(0.404719\pi\)
\(24\) −1.38603 + 4.26576i −0.282922 + 0.870744i
\(25\) −0.809017 + 0.587785i −0.161803 + 0.117557i
\(26\) −2.28825 1.66251i −0.448762 0.326045i
\(27\) 1.74806 + 5.37999i 0.336415 + 1.03538i
\(28\) −1.13003 3.47788i −0.213556 0.657257i
\(29\) 6.19453 + 4.50059i 1.15029 + 0.835738i 0.988520 0.151090i \(-0.0482783\pi\)
0.161774 + 0.986828i \(0.448278\pi\)
\(30\) 0.947822 0.688633i 0.173048 0.125727i
\(31\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(32\) 4.41421 0.780330
\(33\) 0 0
\(34\) −0.485281 −0.0832251
\(35\) −0.618034 + 1.90211i −0.104467 + 0.321516i
\(36\) 7.39614 5.37361i 1.23269 0.895602i
\(37\) −2.95846 2.14944i −0.486367 0.353367i 0.317418 0.948286i \(-0.397184\pi\)
−0.803786 + 0.594919i \(0.797184\pi\)
\(38\) 0 0
\(39\) 5.96826 + 18.3684i 0.955687 + 2.94130i
\(40\) −1.28293 0.932102i −0.202849 0.147378i
\(41\) 4.85410 3.52671i 0.758083 0.550780i −0.140238 0.990118i \(-0.544787\pi\)
0.898322 + 0.439338i \(0.144787\pi\)
\(42\) 0.724072 2.22846i 0.111727 0.343859i
\(43\) 6.00000 0.914991 0.457496 0.889212i \(-0.348747\pi\)
0.457496 + 0.889212i \(0.348747\pi\)
\(44\) 0 0
\(45\) −5.00000 −0.745356
\(46\) 0.362036 1.11423i 0.0533793 0.164285i
\(47\) 2.28825 1.66251i 0.333775 0.242502i −0.408256 0.912868i \(-0.633863\pi\)
0.742031 + 0.670366i \(0.233863\pi\)
\(48\) −6.86474 4.98752i −0.990839 0.719887i
\(49\) −0.927051 2.85317i −0.132436 0.407596i
\(50\) 0.127999 + 0.393941i 0.0181018 + 0.0557116i
\(51\) 2.68085 + 1.94775i 0.375394 + 0.272739i
\(52\) 10.1008 7.33866i 1.40073 1.01769i
\(53\) 0.106038 0.326351i 0.0145654 0.0448278i −0.943510 0.331345i \(-0.892498\pi\)
0.958075 + 0.286517i \(0.0924976\pi\)
\(54\) 2.34315 0.318862
\(55\) 0 0
\(56\) −3.17157 −0.423819
\(57\) 0 0
\(58\) 2.56586 1.86420i 0.336913 0.244782i
\(59\) 7.81256 + 5.67616i 1.01711 + 0.738973i 0.965688 0.259704i \(-0.0836251\pi\)
0.0514204 + 0.998677i \(0.483625\pi\)
\(60\) 1.59810 + 4.91846i 0.206314 + 0.634970i
\(61\) −4.11416 12.6621i −0.526764 1.62121i −0.760800 0.648986i \(-0.775193\pi\)
0.234036 0.972228i \(-0.424807\pi\)
\(62\) 0 0
\(63\) −8.09017 + 5.87785i −1.01927 + 0.740540i
\(64\) −1.28909 + 3.96740i −0.161136 + 0.495925i
\(65\) −6.82843 −0.846962
\(66\) 0 0
\(67\) −4.48528 −0.547964 −0.273982 0.961735i \(-0.588341\pi\)
−0.273982 + 0.961735i \(0.588341\pi\)
\(68\) 0.661956 2.03729i 0.0802740 0.247058i
\(69\) −6.47214 + 4.70228i −0.779154 + 0.566088i
\(70\) 0.670212 + 0.486937i 0.0801056 + 0.0582001i
\(71\) −3.49613 10.7600i −0.414914 1.27697i −0.912328 0.409461i \(-0.865717\pi\)
0.497414 0.867513i \(-0.334283\pi\)
\(72\) −2.45017 7.54086i −0.288756 0.888699i
\(73\) −5.52431 4.01365i −0.646572 0.469762i 0.215530 0.976497i \(-0.430852\pi\)
−0.862102 + 0.506735i \(0.830852\pi\)
\(74\) −1.22543 + 0.890329i −0.142454 + 0.103499i
\(75\) 0.874032 2.68999i 0.100925 0.310614i
\(76\) 0 0
\(77\) 0 0
\(78\) 8.00000 0.905822
\(79\) −1.23607 + 3.80423i −0.139069 + 0.428009i −0.996201 0.0870877i \(-0.972244\pi\)
0.857132 + 0.515097i \(0.172244\pi\)
\(80\) 2.42705 1.76336i 0.271353 0.197149i
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) −0.767994 2.36364i −0.0848108 0.261021i
\(83\) 1.85410 + 5.70634i 0.203514 + 0.626352i 0.999771 + 0.0213936i \(0.00681031\pi\)
−0.796257 + 0.604959i \(0.793190\pi\)
\(84\) 8.36778 + 6.07955i 0.913000 + 0.663333i
\(85\) −0.947822 + 0.688633i −0.102806 + 0.0746928i
\(86\) 0.767994 2.36364i 0.0828149 0.254878i
\(87\) −21.6569 −2.32186
\(88\) 0 0
\(89\) 9.31371 0.987251 0.493626 0.869675i \(-0.335671\pi\)
0.493626 + 0.869675i \(0.335671\pi\)
\(90\) −0.639995 + 1.96970i −0.0674614 + 0.207625i
\(91\) −11.0486 + 8.02730i −1.15821 + 0.841489i
\(92\) 4.18389 + 3.03977i 0.436201 + 0.316918i
\(93\) 0 0
\(94\) −0.362036 1.11423i −0.0373412 0.114924i
\(95\) 0 0
\(96\) −10.1008 + 7.33866i −1.03091 + 0.748999i
\(97\) −2.36610 + 7.28210i −0.240241 + 0.739385i 0.756142 + 0.654408i \(0.227082\pi\)
−0.996383 + 0.0849778i \(0.972918\pi\)
\(98\) −1.24264 −0.125526
\(99\) 0 0
\(100\) −1.82843 −0.182843
\(101\) 4.11416 12.6621i 0.409374 1.25992i −0.507812 0.861468i \(-0.669546\pi\)
0.917187 0.398457i \(-0.130454\pi\)
\(102\) 1.11044 0.806784i 0.109950 0.0798835i
\(103\) −0.947822 0.688633i −0.0933917 0.0678531i 0.540109 0.841595i \(-0.318383\pi\)
−0.633501 + 0.773742i \(0.718383\pi\)
\(104\) −3.34617 10.2984i −0.328119 1.00985i
\(105\) −1.74806 5.37999i −0.170594 0.525033i
\(106\) −0.114990 0.0835452i −0.0111688 0.00811463i
\(107\) −2.95846 + 2.14944i −0.286005 + 0.207795i −0.721532 0.692381i \(-0.756562\pi\)
0.435527 + 0.900175i \(0.356562\pi\)
\(108\) −3.19621 + 9.83692i −0.307555 + 0.946558i
\(109\) −3.65685 −0.350263 −0.175132 0.984545i \(-0.556035\pi\)
−0.175132 + 0.984545i \(0.556035\pi\)
\(110\) 0 0
\(111\) 10.3431 0.981728
\(112\) 1.85410 5.70634i 0.175196 0.539198i
\(113\) −6.74975 + 4.90398i −0.634963 + 0.461327i −0.858116 0.513456i \(-0.828365\pi\)
0.223153 + 0.974783i \(0.428365\pi\)
\(114\) 0 0
\(115\) −0.874032 2.68999i −0.0815039 0.250843i
\(116\) 4.32624 + 13.3148i 0.401681 + 1.23625i
\(117\) −27.6216 20.0682i −2.55361 1.85531i
\(118\) 3.23607 2.35114i 0.297904 0.216440i
\(119\) −0.724072 + 2.22846i −0.0663756 + 0.204283i
\(120\) 4.48528 0.409448
\(121\) 0 0
\(122\) −5.51472 −0.499279
\(123\) −5.24419 + 16.1400i −0.472853 + 1.45529i
\(124\) 0 0
\(125\) 0.809017 + 0.587785i 0.0723607 + 0.0525731i
\(126\) 1.27999 + 3.93941i 0.114031 + 0.350950i
\(127\) −4.83823 14.8906i −0.429324 1.32132i −0.898793 0.438374i \(-0.855555\pi\)
0.469469 0.882949i \(-0.344445\pi\)
\(128\) 8.54027 + 6.20487i 0.754860 + 0.548438i
\(129\) −13.7295 + 9.97505i −1.20881 + 0.878254i
\(130\) −0.874032 + 2.68999i −0.0766577 + 0.235928i
\(131\) −11.3137 −0.988483 −0.494242 0.869325i \(-0.664554\pi\)
−0.494242 + 0.869325i \(0.664554\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.574112 + 1.76693i −0.0495957 + 0.152640i
\(135\) 4.57649 3.32502i 0.393882 0.286172i
\(136\) −1.50304 1.09203i −0.128885 0.0936404i
\(137\) 7.09829 + 21.8463i 0.606448 + 1.86646i 0.486512 + 0.873674i \(0.338269\pi\)
0.119937 + 0.992782i \(0.461731\pi\)
\(138\) 1.02399 + 3.15152i 0.0871680 + 0.268276i
\(139\) −3.23607 2.35114i −0.274480 0.199421i 0.442026 0.897002i \(-0.354260\pi\)
−0.716506 + 0.697581i \(0.754260\pi\)
\(140\) −2.95846 + 2.14944i −0.250035 + 0.181661i
\(141\) −2.47214 + 7.60845i −0.208191 + 0.640747i
\(142\) −4.68629 −0.393265
\(143\) 0 0
\(144\) 15.0000 1.25000
\(145\) 2.36610 7.28210i 0.196494 0.604746i
\(146\) −2.28825 + 1.66251i −0.189377 + 0.137590i
\(147\) 6.86474 + 4.98752i 0.566194 + 0.411364i
\(148\) −2.06618 6.35904i −0.169839 0.522710i
\(149\) −3.60217 11.0863i −0.295101 0.908227i −0.983188 0.182599i \(-0.941549\pi\)
0.688087 0.725629i \(-0.258451\pi\)
\(150\) −0.947822 0.688633i −0.0773894 0.0562267i
\(151\) −9.70820 + 7.05342i −0.790042 + 0.573999i −0.907976 0.419022i \(-0.862373\pi\)
0.117934 + 0.993021i \(0.462373\pi\)
\(152\) 0 0
\(153\) −5.85786 −0.473580
\(154\) 0 0
\(155\) 0 0
\(156\) −10.9125 + 33.5853i −0.873702 + 2.68898i
\(157\) 11.3262 8.22899i 0.903932 0.656745i −0.0355408 0.999368i \(-0.511315\pi\)
0.939473 + 0.342623i \(0.111315\pi\)
\(158\) 1.34042 + 0.973874i 0.106638 + 0.0774773i
\(159\) 0.299920 + 0.923060i 0.0237852 + 0.0732034i
\(160\) −1.36407 4.19817i −0.107839 0.331894i
\(161\) −4.57649 3.32502i −0.360678 0.262048i
\(162\) −0.335106 + 0.243469i −0.0263284 + 0.0191287i
\(163\) −0.149960 + 0.461530i −0.0117458 + 0.0361498i −0.956758 0.290886i \(-0.906050\pi\)
0.945012 + 0.327036i \(0.106050\pi\)
\(164\) 10.9706 0.856657
\(165\) 0 0
\(166\) 2.48528 0.192895
\(167\) −3.39009 + 10.4336i −0.262333 + 0.807378i 0.729963 + 0.683487i \(0.239537\pi\)
−0.992296 + 0.123891i \(0.960463\pi\)
\(168\) 7.25734 5.27276i 0.559916 0.406803i
\(169\) −27.2052 19.7657i −2.09270 1.52044i
\(170\) 0.149960 + 0.461530i 0.0115014 + 0.0353977i
\(171\) 0 0
\(172\) 8.87537 + 6.44833i 0.676741 + 0.491681i
\(173\) 4.96909 3.61026i 0.377793 0.274483i −0.382642 0.923897i \(-0.624986\pi\)
0.760435 + 0.649414i \(0.224986\pi\)
\(174\) −2.77206 + 8.53151i −0.210149 + 0.646772i
\(175\) 2.00000 0.151186
\(176\) 0 0
\(177\) −27.3137 −2.05302
\(178\) 1.19215 3.66905i 0.0893551 0.275007i
\(179\) 1.34042 0.973874i 0.100188 0.0727908i −0.536563 0.843860i \(-0.680278\pi\)
0.636751 + 0.771069i \(0.280278\pi\)
\(180\) −7.39614 5.37361i −0.551276 0.400525i
\(181\) −0.405958 1.24941i −0.0301746 0.0928680i 0.934835 0.355082i \(-0.115547\pi\)
−0.965010 + 0.262214i \(0.915547\pi\)
\(182\) 1.74806 + 5.37999i 0.129575 + 0.398791i
\(183\) 30.4650 + 22.1341i 2.25204 + 1.63620i
\(184\) 3.62867 2.63638i 0.267509 0.194357i
\(185\) −1.13003 + 3.47788i −0.0830815 + 0.255698i
\(186\) 0 0
\(187\) 0 0
\(188\) 5.17157 0.377176
\(189\) 3.49613 10.7600i 0.254306 0.782673i
\(190\) 0 0
\(191\) 15.6251 + 11.3523i 1.13059 + 0.821425i 0.985781 0.168035i \(-0.0537420\pi\)
0.144813 + 0.989459i \(0.453742\pi\)
\(192\) −3.64609 11.2215i −0.263134 0.809842i
\(193\) 2.11010 + 6.49422i 0.151888 + 0.467464i 0.997832 0.0658075i \(-0.0209623\pi\)
−0.845944 + 0.533272i \(0.820962\pi\)
\(194\) 2.56586 + 1.86420i 0.184218 + 0.133842i
\(195\) 15.6251 11.3523i 1.11894 0.812956i
\(196\) 1.69505 5.21681i 0.121075 0.372629i
\(197\) 5.17157 0.368459 0.184230 0.982883i \(-0.441021\pi\)
0.184230 + 0.982883i \(0.441021\pi\)
\(198\) 0 0
\(199\) 21.6569 1.53521 0.767607 0.640921i \(-0.221447\pi\)
0.767607 + 0.640921i \(0.221447\pi\)
\(200\) −0.490035 + 1.50817i −0.0346507 + 0.106644i
\(201\) 10.2634 7.45682i 0.723926 0.525963i
\(202\) −4.46150 3.24147i −0.313910 0.228069i
\(203\) −4.73220 14.5642i −0.332135 1.02221i
\(204\) 1.87230 + 5.76233i 0.131087 + 0.403444i
\(205\) −4.85410 3.52671i −0.339025 0.246316i
\(206\) −0.392601 + 0.285241i −0.0273538 + 0.0198737i
\(207\) 4.37016 13.4500i 0.303747 0.934838i
\(208\) 20.4853 1.42040
\(209\) 0 0
\(210\) −2.34315 −0.161692
\(211\) 4.94427 15.2169i 0.340378 1.04757i −0.623634 0.781716i \(-0.714345\pi\)
0.964012 0.265859i \(-0.0856555\pi\)
\(212\) 0.507591 0.368786i 0.0348615 0.0253284i
\(213\) 25.8885 + 18.8091i 1.77385 + 1.28878i
\(214\) 0.468074 + 1.44058i 0.0319969 + 0.0984762i
\(215\) −1.85410 5.70634i −0.126449 0.389169i
\(216\) 7.25734 + 5.27276i 0.493799 + 0.358766i
\(217\) 0 0
\(218\) −0.468074 + 1.44058i −0.0317020 + 0.0975686i
\(219\) 19.3137 1.30510
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) 1.32391 4.07458i 0.0888552 0.273468i
\(223\) 4.18389 3.03977i 0.280174 0.203558i −0.438819 0.898575i \(-0.644603\pi\)
0.718993 + 0.695017i \(0.244603\pi\)
\(224\) −7.14235 5.18922i −0.477218 0.346719i
\(225\) 1.54508 + 4.75528i 0.103006 + 0.317019i
\(226\) 1.06791 + 3.28670i 0.0710366 + 0.218628i
\(227\) 2.17326 + 1.57896i 0.144244 + 0.104799i 0.657567 0.753396i \(-0.271586\pi\)
−0.513323 + 0.858196i \(0.671586\pi\)
\(228\) 0 0
\(229\) −6.58630 + 20.2705i −0.435235 + 1.33952i 0.457611 + 0.889153i \(0.348705\pi\)
−0.892846 + 0.450363i \(0.851295\pi\)
\(230\) −1.17157 −0.0772512
\(231\) 0 0
\(232\) 12.1421 0.797170
\(233\) −6.84230 + 21.0584i −0.448254 + 1.37958i 0.430622 + 0.902532i \(0.358294\pi\)
−0.878876 + 0.477051i \(0.841706\pi\)
\(234\) −11.4412 + 8.31254i −0.747936 + 0.543408i
\(235\) −2.28825 1.66251i −0.149269 0.108450i
\(236\) 5.45627 + 16.7927i 0.355173 + 1.09311i
\(237\) −3.49613 10.7600i −0.227098 0.698936i
\(238\) 0.785202 + 0.570482i 0.0508971 + 0.0369789i
\(239\) −0.555221 + 0.403392i −0.0359143 + 0.0260933i −0.605598 0.795771i \(-0.707066\pi\)
0.569683 + 0.821864i \(0.307066\pi\)
\(240\) −2.62210 + 8.06998i −0.169256 + 0.520915i
\(241\) −6.00000 −0.386494 −0.193247 0.981150i \(-0.561902\pi\)
−0.193247 + 0.981150i \(0.561902\pi\)
\(242\) 0 0
\(243\) −14.1421 −0.907218
\(244\) 7.52245 23.1517i 0.481575 1.48214i
\(245\) −2.42705 + 1.76336i −0.155059 + 0.112657i
\(246\) 5.68693 + 4.13180i 0.362586 + 0.263434i
\(247\) 0 0
\(248\) 0 0
\(249\) −13.7295 9.97505i −0.870070 0.632143i
\(250\) 0.335106 0.243469i 0.0211940 0.0153983i
\(251\) 3.70820 11.4127i 0.234060 0.720362i −0.763185 0.646180i \(-0.776365\pi\)
0.997245 0.0741818i \(-0.0236345\pi\)
\(252\) −18.2843 −1.15180
\(253\) 0 0
\(254\) −6.48528 −0.406923
\(255\) 1.02399 3.15152i 0.0641249 0.197356i
\(256\) −3.21225 + 2.33384i −0.200766 + 0.145865i
\(257\) −10.7710 7.82560i −0.671878 0.488148i 0.198776 0.980045i \(-0.436304\pi\)
−0.870653 + 0.491897i \(0.836304\pi\)
\(258\) 2.17222 + 6.68539i 0.135236 + 0.416214i
\(259\) 2.26006 + 6.95575i 0.140433 + 0.432209i
\(260\) −10.1008 7.33866i −0.626425 0.455125i
\(261\) 30.9726 22.5029i 1.91716 1.39290i
\(262\) −1.44814 + 4.45693i −0.0894666 + 0.275350i
\(263\) −22.9706 −1.41643 −0.708213 0.705999i \(-0.750498\pi\)
−0.708213 + 0.705999i \(0.750498\pi\)
\(264\) 0 0
\(265\) −0.343146 −0.0210793
\(266\) 0 0
\(267\) −21.3121 + 15.4841i −1.30428 + 0.947612i
\(268\) −6.63476 4.82043i −0.405282 0.294455i
\(269\) −1.64203 5.05364i −0.100116 0.308126i 0.888437 0.458998i \(-0.151792\pi\)
−0.988553 + 0.150873i \(0.951792\pi\)
\(270\) −0.724072 2.22846i −0.0440656 0.135620i
\(271\) −12.3891 9.00117i −0.752581 0.546782i 0.144045 0.989571i \(-0.453989\pi\)
−0.896626 + 0.442789i \(0.853989\pi\)
\(272\) 2.84347 2.06590i 0.172411 0.125264i
\(273\) 11.9365 36.7369i 0.722432 2.22342i
\(274\) 9.51472 0.574805
\(275\) 0 0
\(276\) −14.6274 −0.880467
\(277\) −0.362036 + 1.11423i −0.0217526 + 0.0669477i −0.961344 0.275352i \(-0.911206\pi\)
0.939591 + 0.342299i \(0.111206\pi\)
\(278\) −1.34042 + 0.973874i −0.0803932 + 0.0584091i
\(279\) 0 0
\(280\) 0.980070 + 3.01635i 0.0585704 + 0.180261i
\(281\) 1.64203 + 5.05364i 0.0979551 + 0.301475i 0.988013 0.154374i \(-0.0493359\pi\)
−0.890057 + 0.455848i \(0.849336\pi\)
\(282\) 2.68085 + 1.94775i 0.159642 + 0.115987i
\(283\) −10.2158 + 7.42221i −0.607266 + 0.441205i −0.848451 0.529275i \(-0.822464\pi\)
0.241185 + 0.970479i \(0.422464\pi\)
\(284\) 6.39242 19.6738i 0.379320 1.16743i
\(285\) 0 0
\(286\) 0 0
\(287\) −12.0000 −0.708338
\(288\) 6.82034 20.9908i 0.401892 1.23690i
\(289\) 12.6428 9.18557i 0.743697 0.540327i
\(290\) −2.56586 1.86420i −0.150672 0.109470i
\(291\) −6.69234 20.5969i −0.392312 1.20741i
\(292\) −3.85816 11.8742i −0.225782 0.694885i
\(293\) −11.9964 8.71593i −0.700840 0.509190i 0.179366 0.983782i \(-0.442595\pi\)
−0.880206 + 0.474592i \(0.842595\pi\)
\(294\) 2.84347 2.06590i 0.165834 0.120486i
\(295\) 2.98413 9.18421i 0.173743 0.534726i
\(296\) −5.79899 −0.337059
\(297\) 0 0
\(298\) −4.82843 −0.279703
\(299\) 5.96826 18.3684i 0.345154 1.06227i
\(300\) 4.18389 3.03977i 0.241557 0.175501i
\(301\) −9.70820 7.05342i −0.559572 0.406553i
\(302\) 1.53599 + 4.72729i 0.0883862 + 0.272025i
\(303\) 11.6366 + 35.8138i 0.668506 + 2.05745i
\(304\) 0 0
\(305\) −10.7710 + 7.82560i −0.616747 + 0.448093i
\(306\) −0.749801 + 2.30765i −0.0428633 + 0.131920i
\(307\) 27.6569 1.57846 0.789230 0.614098i \(-0.210480\pi\)
0.789230 + 0.614098i \(0.210480\pi\)
\(308\) 0 0
\(309\) 3.31371 0.188510
\(310\) 0 0
\(311\) −22.0973 + 16.0546i −1.25302 + 0.910373i −0.998393 0.0566667i \(-0.981953\pi\)
−0.254627 + 0.967039i \(0.581953\pi\)
\(312\) 24.7781 + 18.0023i 1.40278 + 1.01918i
\(313\) 6.58630 + 20.2705i 0.372280 + 1.14576i 0.945296 + 0.326215i \(0.105773\pi\)
−0.573016 + 0.819544i \(0.694227\pi\)
\(314\) −1.79199 5.51517i −0.101128 0.311239i
\(315\) 8.09017 + 5.87785i 0.455829 + 0.331179i
\(316\) −5.91691 + 4.29889i −0.332852 + 0.241831i
\(317\) 6.58630 20.2705i 0.369923 1.13851i −0.576917 0.816803i \(-0.695744\pi\)
0.946840 0.321704i \(-0.104256\pi\)
\(318\) 0.402020 0.0225442
\(319\) 0 0
\(320\) 4.17157 0.233198
\(321\) 3.19621 9.83692i 0.178395 0.549043i
\(322\) −1.89564 + 1.37727i −0.105640 + 0.0767521i
\(323\) 0 0
\(324\) −0.565015 1.73894i −0.0313897 0.0966076i
\(325\) 2.11010 + 6.49422i 0.117047 + 0.360235i
\(326\) 0.162621 + 0.118151i 0.00900672 + 0.00654377i
\(327\) 8.36778 6.07955i 0.462739 0.336200i
\(328\) 2.94021 9.04904i 0.162346 0.499649i
\(329\) −5.65685 −0.311872
\(330\) 0 0
\(331\) 15.3137 0.841718 0.420859 0.907126i \(-0.361729\pi\)
0.420859 + 0.907126i \(0.361729\pi\)
\(332\) −3.39009 + 10.4336i −0.186055 + 0.572620i
\(333\) −14.7923 + 10.7472i −0.810612 + 0.588944i
\(334\) 3.67630 + 2.67099i 0.201158 + 0.146150i
\(335\) 1.38603 + 4.26576i 0.0757268 + 0.233063i
\(336\) 5.24419 + 16.1400i 0.286094 + 0.880507i
\(337\) −2.84347 2.06590i −0.154894 0.112537i 0.507639 0.861570i \(-0.330518\pi\)
−0.662533 + 0.749033i \(0.730518\pi\)
\(338\) −11.2687 + 8.18722i −0.612939 + 0.445326i
\(339\) 7.29218 22.4430i 0.396057 1.21894i
\(340\) −2.14214 −0.116174
\(341\) 0 0
\(342\) 0 0
\(343\) −6.18034 + 19.0211i −0.333707 + 1.02704i
\(344\) 7.69757 5.59261i 0.415025 0.301533i
\(345\) 6.47214 + 4.70228i 0.348448 + 0.253162i
\(346\) −0.786187 2.41964i −0.0422657 0.130080i
\(347\) 7.09829 + 21.8463i 0.381056 + 1.17277i 0.939301 + 0.343095i \(0.111475\pi\)
−0.558244 + 0.829677i \(0.688525\pi\)
\(348\) −32.0354 23.2751i −1.71728 1.24768i
\(349\) −5.63930 + 4.09719i −0.301865 + 0.219318i −0.728398 0.685154i \(-0.759735\pi\)
0.426533 + 0.904472i \(0.359735\pi\)
\(350\) 0.255998 0.787881i 0.0136837 0.0421140i
\(351\) 38.6274 2.06178
\(352\) 0 0
\(353\) −1.31371 −0.0699216 −0.0349608 0.999389i \(-0.511131\pi\)
−0.0349608 + 0.999389i \(0.511131\pi\)
\(354\) −3.49613 + 10.7600i −0.185817 + 0.571886i
\(355\) −9.15298 + 6.65003i −0.485790 + 0.352947i
\(356\) 13.7771 + 10.0097i 0.730185 + 0.530510i
\(357\) −2.04798 6.30305i −0.108391 0.333593i
\(358\) −0.212076 0.652702i −0.0112086 0.0344964i
\(359\) 18.8612 + 13.7035i 0.995455 + 0.723241i 0.961109 0.276169i \(-0.0890651\pi\)
0.0343464 + 0.999410i \(0.489065\pi\)
\(360\) −6.41464 + 4.66051i −0.338081 + 0.245630i
\(361\) −5.87132 + 18.0701i −0.309017 + 0.951057i
\(362\) −0.544156 −0.0286002
\(363\) 0 0
\(364\) −24.9706 −1.30881
\(365\) −2.11010 + 6.49422i −0.110448 + 0.339923i
\(366\) 12.6190 9.16826i 0.659607 0.479233i
\(367\) −6.86474 4.98752i −0.358336 0.260347i 0.394022 0.919101i \(-0.371084\pi\)
−0.752358 + 0.658755i \(0.771084\pi\)
\(368\) 2.62210 + 8.06998i 0.136686 + 0.420677i
\(369\) −9.27051 28.5317i −0.482603 1.48530i
\(370\) 1.22543 + 0.890329i 0.0637072 + 0.0462860i
\(371\) −0.555221 + 0.403392i −0.0288257 + 0.0209431i
\(372\) 0 0
\(373\) 3.79899 0.196704 0.0983521 0.995152i \(-0.468643\pi\)
0.0983521 + 0.995152i \(0.468643\pi\)
\(374\) 0 0
\(375\) −2.82843 −0.146059
\(376\) 1.38603 4.26576i 0.0714789 0.219990i
\(377\) 42.2989 30.7319i 2.17850 1.58277i
\(378\) −3.79129 2.75453i −0.195003 0.141678i
\(379\) 6.90441 + 21.2496i 0.354656 + 1.09152i 0.956209 + 0.292685i \(0.0945489\pi\)
−0.601553 + 0.798833i \(0.705451\pi\)
\(380\) 0 0
\(381\) 35.8267 + 26.0296i 1.83546 + 1.33354i
\(382\) 6.47214 4.70228i 0.331143 0.240590i
\(383\) −10.5505 + 32.4711i −0.539105 + 1.65920i 0.195502 + 0.980703i \(0.437366\pi\)
−0.734607 + 0.678492i \(0.762634\pi\)
\(384\) −29.8579 −1.52368
\(385\) 0 0
\(386\) 2.82843 0.143963
\(387\) 9.27051 28.5317i 0.471246 1.45035i
\(388\) −11.3262 + 8.22899i −0.575003 + 0.417764i
\(389\) 19.9240 + 14.4756i 1.01019 + 0.733944i 0.964248 0.265001i \(-0.0853721\pi\)
0.0459386 + 0.998944i \(0.485372\pi\)
\(390\) −2.47214 7.60845i −0.125181 0.385269i
\(391\) −1.02399 3.15152i −0.0517855 0.159379i
\(392\) −3.84878 2.79631i −0.194393 0.141235i
\(393\) 25.8885 18.8091i 1.30590 0.948795i
\(394\) 0.661956 2.03729i 0.0333489 0.102637i
\(395\) 4.00000 0.201262
\(396\) 0 0
\(397\) 13.3137 0.668196 0.334098 0.942538i \(-0.391568\pi\)
0.334098 + 0.942538i \(0.391568\pi\)
\(398\) 2.77206 8.53151i 0.138951 0.427646i
\(399\) 0 0
\(400\) −2.42705 1.76336i −0.121353 0.0881678i
\(401\) 5.35023 + 16.4663i 0.267178 + 0.822289i 0.991184 + 0.132495i \(0.0422988\pi\)
−0.724006 + 0.689794i \(0.757701\pi\)
\(402\) −1.62383 4.99764i −0.0809894 0.249260i
\(403\) 0 0
\(404\) 19.6940 14.3085i 0.979814 0.711877i
\(405\) −0.309017 + 0.951057i −0.0153552 + 0.0472584i
\(406\) −6.34315 −0.314805
\(407\) 0 0
\(408\) 5.25483 0.260153
\(409\) −10.8065 + 33.2590i −0.534347 + 1.64455i 0.210709 + 0.977549i \(0.432423\pi\)
−0.745056 + 0.667002i \(0.767577\pi\)
\(410\) −2.01063 + 1.46081i −0.0992982 + 0.0721443i
\(411\) −52.5623 38.1887i −2.59271 1.88371i
\(412\) −0.661956 2.03729i −0.0326122 0.100370i
\(413\) −5.96826 18.3684i −0.293679 0.903851i
\(414\) −4.73911 3.44317i −0.232915 0.169222i
\(415\) 4.85410 3.52671i 0.238278 0.173119i
\(416\) 9.31443 28.6669i 0.456678 1.40551i
\(417\) 11.3137 0.554035
\(418\) 0 0
\(419\) −14.3431 −0.700709 −0.350354 0.936617i \(-0.613939\pi\)
−0.350354 + 0.936617i \(0.613939\pi\)
\(420\) 3.19621 9.83692i 0.155959 0.479992i
\(421\) 4.85410 3.52671i 0.236574 0.171881i −0.463181 0.886264i \(-0.653292\pi\)
0.699756 + 0.714382i \(0.253292\pi\)
\(422\) −5.36169 3.89550i −0.261003 0.189630i
\(423\) −4.37016 13.4500i −0.212484 0.653960i
\(424\) −0.168153 0.517523i −0.00816625 0.0251331i
\(425\) 0.947822 + 0.688633i 0.0459761 + 0.0334036i
\(426\) 10.7234 7.79100i 0.519550 0.377475i
\(427\) −8.22832 + 25.3242i −0.398197 + 1.22552i
\(428\) −6.68629 −0.323194
\(429\) 0 0
\(430\) −2.48528 −0.119851
\(431\) −3.49613 + 10.7600i −0.168403 + 0.518290i −0.999271 0.0381792i \(-0.987844\pi\)
0.830868 + 0.556469i \(0.187844\pi\)
\(432\) −13.7295 + 9.97505i −0.660560 + 0.479925i
\(433\) −2.95846 2.14944i −0.142174 0.103296i 0.514425 0.857536i \(-0.328006\pi\)
−0.656599 + 0.754240i \(0.728006\pi\)
\(434\) 0 0
\(435\) 6.69234 + 20.5969i 0.320873 + 0.987545i
\(436\) −5.40932 3.93010i −0.259060 0.188218i
\(437\) 0 0
\(438\) 2.47214 7.60845i 0.118123 0.363546i
\(439\) 16.0000 0.763638 0.381819 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 0 0
\(441\) −15.0000 −0.714286
\(442\) −1.02399 + 3.15152i −0.0487063 + 0.149903i
\(443\) 17.1282 12.4443i 0.813784 0.591248i −0.101142 0.994872i \(-0.532249\pi\)
0.914925 + 0.403624i \(0.132249\pi\)
\(444\) 15.2999 + 11.1160i 0.726100 + 0.527543i
\(445\) −2.87809 8.85786i −0.136435 0.419903i
\(446\) −0.661956 2.03729i −0.0313445 0.0964686i
\(447\) 26.6737 + 19.3796i 1.26162 + 0.916624i
\(448\) 6.74975 4.90398i 0.318896 0.231691i
\(449\) −5.13815 + 15.8136i −0.242484 + 0.746291i 0.753555 + 0.657384i \(0.228337\pi\)
−0.996040 + 0.0889063i \(0.971663\pi\)
\(450\) 2.07107 0.0976311
\(451\) 0 0
\(452\) −15.2548 −0.717527
\(453\) 10.4884 32.2799i 0.492787 1.51664i
\(454\) 0.900192 0.654028i 0.0422481 0.0306950i
\(455\) 11.0486 + 8.02730i 0.517968 + 0.376326i
\(456\) 0 0
\(457\) 5.09423 + 15.6784i 0.238298 + 0.733406i 0.996667 + 0.0815803i \(0.0259967\pi\)
−0.758369 + 0.651826i \(0.774003\pi\)
\(458\) 7.14235 + 5.18922i 0.333740 + 0.242476i
\(459\) 5.36169 3.89550i 0.250262 0.181826i
\(460\) 1.59810 4.91846i 0.0745120 0.229324i
\(461\) 32.6274 1.51961 0.759805 0.650151i \(-0.225294\pi\)
0.759805 + 0.650151i \(0.225294\pi\)
\(462\) 0 0
\(463\) 22.1421 1.02903 0.514516 0.857481i \(-0.327972\pi\)
0.514516 + 0.857481i \(0.327972\pi\)
\(464\) −7.09829 + 21.8463i −0.329530 + 1.01419i
\(465\) 0 0
\(466\) 7.41996 + 5.39092i 0.343723 + 0.249729i
\(467\) −2.83417 8.72268i −0.131150 0.403638i 0.863821 0.503798i \(-0.168064\pi\)
−0.994971 + 0.100160i \(0.968064\pi\)
\(468\) −19.2908 59.3710i −0.891718 2.74443i
\(469\) 7.25734 + 5.27276i 0.335113 + 0.243474i
\(470\) −0.947822 + 0.688633i −0.0437198 + 0.0317643i
\(471\) −12.2364 + 37.6599i −0.563826 + 1.73528i
\(472\) 15.3137 0.704871
\(473\) 0 0
\(474\) −4.68629 −0.215248
\(475\) 0 0
\(476\) −3.46605 + 2.51823i −0.158866 + 0.115423i
\(477\) −1.38805 1.00848i −0.0635546 0.0461751i
\(478\) 0.0878446 + 0.270358i 0.00401792 + 0.0123659i
\(479\) 11.1246 + 34.2380i 0.508296 + 1.56438i 0.795157 + 0.606403i \(0.207388\pi\)
−0.286861 + 0.957972i \(0.592612\pi\)
\(480\) 10.1008 + 7.33866i 0.461037 + 0.334963i
\(481\) −20.2016 + 14.6773i −0.921114 + 0.669229i
\(482\) −0.767994 + 2.36364i −0.0349812 + 0.107661i
\(483\) 16.0000 0.728025
\(484\) 0 0
\(485\) 7.65685 0.347680
\(486\) −1.81018 + 5.57116i −0.0821114 + 0.252713i
\(487\) 6.07954 4.41704i 0.275490 0.200155i −0.441458 0.897282i \(-0.645539\pi\)
0.716948 + 0.697127i \(0.245539\pi\)
\(488\) −17.0805 12.4097i −0.773199 0.561762i
\(489\) −0.424151 1.30540i −0.0191808 0.0590324i
\(490\) 0.383997 + 1.18182i 0.0173472 + 0.0533893i
\(491\) −18.8612 13.7035i −0.851193 0.618428i 0.0742814 0.997237i \(-0.476334\pi\)
−0.925475 + 0.378809i \(0.876334\pi\)
\(492\) −25.1033 + 18.2386i −1.13175 + 0.822262i
\(493\) 2.77206 8.53151i 0.124847 0.384240i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6.99226 + 21.5200i −0.313646 + 0.965302i
\(498\) −5.68693 + 4.13180i −0.254838 + 0.185150i
\(499\) 1.34042 + 0.973874i 0.0600056 + 0.0435966i 0.617384 0.786662i \(-0.288193\pi\)
−0.557378 + 0.830259i \(0.688193\pi\)
\(500\) 0.565015 + 1.73894i 0.0252682 + 0.0777677i
\(501\) −9.58862 29.5107i −0.428388 1.31844i
\(502\) −4.02127 2.92162i −0.179478 0.130398i
\(503\) −23.1601 + 16.8268i −1.03266 + 0.750269i −0.968839 0.247693i \(-0.920328\pi\)
−0.0638177 + 0.997962i \(0.520328\pi\)
\(504\) −4.90035 + 15.0817i −0.218279 + 0.671793i
\(505\) −13.3137 −0.592452
\(506\) 0 0
\(507\) 95.1127 4.22410
\(508\) 8.84636 27.2263i 0.392494 1.20797i
\(509\) −7.53495 + 5.47446i −0.333981 + 0.242651i −0.742118 0.670269i \(-0.766179\pi\)
0.408137 + 0.912921i \(0.366179\pi\)
\(510\) −1.11044 0.806784i −0.0491712 0.0357250i
\(511\) 4.22020 + 12.9884i 0.186691 + 0.574575i
\(512\) 7.03241 + 21.6435i 0.310792 + 0.956518i
\(513\) 0 0
\(514\) −4.46150 + 3.24147i −0.196788 + 0.142975i
\(515\) −0.362036 + 1.11423i −0.0159532 + 0.0490989i
\(516\) −31.0294 −1.36599
\(517\) 0 0
\(518\) 3.02944 0.133106
\(519\) −5.36842 + 16.5223i −0.235648 + 0.725249i
\(520\) −8.76038 + 6.36479i −0.384168 + 0.279114i
\(521\) −2.17326 1.57896i −0.0952121 0.0691756i 0.539161 0.842203i \(-0.318742\pi\)
−0.634373 + 0.773027i \(0.718742\pi\)
\(522\) −4.90035 15.0817i −0.214482 0.660109i
\(523\) −11.6184 35.7578i −0.508038 1.56358i −0.795603 0.605818i \(-0.792846\pi\)
0.287565 0.957761i \(-0.407154\pi\)
\(524\) −16.7356 12.1591i −0.731096 0.531173i
\(525\) −4.57649 + 3.32502i −0.199734 + 0.145116i
\(526\) −2.94021 + 9.04904i −0.128199 + 0.394557i
\(527\) 0 0
\(528\) 0 0
\(529\) −15.0000 −0.652174
\(530\) −0.0439223 + 0.135179i −0.00190786 + 0.00587180i
\(531\) 39.0628 28.3808i 1.69518 1.23162i
\(532\) 0 0
\(533\) −12.6606 38.9653i −0.548391 1.68778i
\(534\) 3.37190 + 10.3776i 0.145916 + 0.449084i
\(535\) 2.95846 + 2.14944i 0.127905 + 0.0929286i
\(536\) −5.75429 + 4.18074i −0.248548 + 0.180580i
\(537\) −1.44814 + 4.45693i −0.0624920 + 0.192331i
\(538\) −2.20101 −0.0948923
\(539\) 0 0
\(540\) 10.3431 0.445098
\(541\) −1.85410 + 5.70634i −0.0797141 + 0.245335i −0.982970 0.183768i \(-0.941170\pi\)
0.903255 + 0.429103i \(0.141170\pi\)
\(542\) −5.13171 + 3.72841i −0.220426 + 0.160149i
\(543\) 3.00609 + 2.18405i 0.129004 + 0.0937266i
\(544\) −1.59810 4.91846i −0.0685181 0.210877i
\(545\) 1.13003 + 3.47788i 0.0484052 + 0.148976i
\(546\) −12.9443 9.40456i −0.553964 0.402478i
\(547\) −27.5066 + 19.9847i −1.17610 + 0.854484i −0.991726 0.128373i \(-0.959025\pi\)
−0.184370 + 0.982857i \(0.559025\pi\)
\(548\) −12.9787 + 39.9444i −0.554423 + 1.70634i
\(549\) −66.5685 −2.84108
\(550\) 0 0
\(551\) 0 0
\(552\) −3.92028 + 12.0654i −0.166858 + 0.513537i
\(553\) 6.47214 4.70228i 0.275223 0.199961i
\(554\) 0.392601 + 0.285241i 0.0166800 + 0.0121187i
\(555\) −3.19621 9.83692i −0.135671 0.417554i
\(556\) −2.26006 6.95575i −0.0958479 0.294990i
\(557\) 30.8576 + 22.4194i 1.30748 + 0.949940i 0.999999 0.00161430i \(-0.000513849\pi\)
0.307481 + 0.951554i \(0.400514\pi\)
\(558\) 0 0
\(559\) 12.6606 38.9653i 0.535486 1.64806i
\(560\) −6.00000 −0.253546
\(561\) 0 0
\(562\) 2.20101 0.0928440
\(563\) −3.60217 + 11.0863i −0.151813 + 0.467233i −0.997824 0.0659327i \(-0.978998\pi\)
0.846011 + 0.533166i \(0.178998\pi\)
\(564\) −11.8338 + 8.59778i −0.498294 + 0.362032i
\(565\) 6.74975 + 4.90398i 0.283964 + 0.206312i
\(566\) 1.61630 + 4.97445i 0.0679380 + 0.209092i
\(567\) 0.618034 + 1.90211i 0.0259550 + 0.0798812i
\(568\) −14.5147 10.5455i −0.609022 0.442481i
\(569\) 16.4580 11.9574i 0.689953 0.501280i −0.186692 0.982419i \(-0.559776\pi\)
0.876645 + 0.481138i \(0.159776\pi\)
\(570\) 0 0
\(571\) −45.9411 −1.92258 −0.961288 0.275545i \(-0.911142\pi\)
−0.961288 + 0.275545i \(0.911142\pi\)
\(572\) 0 0
\(573\) −54.6274 −2.28209
\(574\) −1.53599 + 4.72729i −0.0641109 + 0.197313i
\(575\) −2.28825 + 1.66251i −0.0954264 + 0.0693314i
\(576\) 16.8744 + 12.2599i 0.703099 + 0.510831i
\(577\) 2.15402 + 6.62940i 0.0896731 + 0.275985i 0.985829 0.167754i \(-0.0536515\pi\)
−0.896156 + 0.443740i \(0.853651\pi\)
\(578\) −2.00029 6.15627i −0.0832013 0.256067i
\(579\) −15.6251 11.3523i −0.649358 0.471786i
\(580\) 11.3262 8.22899i 0.470296 0.341690i
\(581\) 3.70820 11.4127i 0.153842 0.473478i
\(582\) −8.97056 −0.371842
\(583\) 0 0
\(584\) −10.8284 −0.448084
\(585\) −10.5505 + 32.4711i −0.436209 + 1.34251i
\(586\) −4.96909 + 3.61026i −0.205271 + 0.149138i
\(587\) −21.1494 15.3660i −0.872930 0.634221i 0.0584412 0.998291i \(-0.481387\pi\)
−0.931372 + 0.364070i \(0.881387\pi\)
\(588\) 4.79431 + 14.7554i 0.197714 + 0.608501i
\(589\) 0 0
\(590\) −3.23607 2.35114i −0.133227 0.0967949i
\(591\) −11.8338 + 8.59778i −0.486779 + 0.353665i
\(592\) 3.39009 10.4336i 0.139332 0.428819i
\(593\) −20.4853 −0.841230 −0.420615 0.907239i \(-0.638186\pi\)
−0.420615 + 0.907239i \(0.638186\pi\)
\(594\) 0 0
\(595\) 2.34315 0.0960596
\(596\) 6.58630 20.2705i 0.269785 0.830314i
\(597\) −49.5562 + 36.0047i −2.02820 + 1.47357i
\(598\) −6.47214 4.70228i −0.264665 0.192291i
\(599\) 1.74806 + 5.37999i 0.0714240 + 0.219820i 0.980396 0.197036i \(-0.0631317\pi\)
−0.908972 + 0.416857i \(0.863132\pi\)
\(600\) −1.38603 4.26576i −0.0565844 0.174149i
\(601\) −35.5491 25.8279i −1.45008 1.05354i −0.985813 0.167848i \(-0.946318\pi\)
−0.464266 0.885696i \(-0.653682\pi\)
\(602\) −4.02127 + 2.92162i −0.163895 + 0.119076i
\(603\) −6.93014 + 21.3288i −0.282217 + 0.868575i
\(604\) −21.9411 −0.892772
\(605\) 0 0
\(606\) 15.5980 0.633625
\(607\) 5.65015 17.3894i 0.229333 0.705813i −0.768490 0.639861i \(-0.778992\pi\)
0.997823 0.0659515i \(-0.0210083\pi\)
\(608\) 0 0
\(609\) 35.0415 + 25.4592i 1.41995 + 1.03166i
\(610\) 1.70414 + 5.24481i 0.0689987 + 0.212356i
\(611\) −5.96826 18.3684i −0.241450 0.743107i
\(612\) −8.66512 6.29558i −0.350267 0.254484i
\(613\) 20.5942 14.9626i 0.831792 0.604333i −0.0882735 0.996096i \(-0.528135\pi\)
0.920066 + 0.391764i \(0.128135\pi\)
\(614\) 3.54005 10.8952i 0.142865 0.439693i
\(615\) 16.9706 0.684319
\(616\) 0 0
\(617\) 11.6569 0.469287 0.234644 0.972081i \(-0.424608\pi\)
0.234644 + 0.972081i \(0.424608\pi\)
\(618\) 0.424151 1.30540i 0.0170619 0.0525111i
\(619\) 20.7568 15.0807i 0.834287 0.606145i −0.0864816 0.996253i \(-0.527562\pi\)
0.920769 + 0.390108i \(0.127562\pi\)
\(620\) 0 0
\(621\) 4.94427 + 15.2169i 0.198407 + 0.610633i
\(622\) 3.49613 + 10.7600i 0.140182 + 0.431436i
\(623\) −15.0699 10.9489i −0.603763 0.438659i
\(624\) −46.8754 + 34.0569i −1.87652 + 1.36337i
\(625\) 0.309017 0.951057i 0.0123607 0.0380423i
\(626\) 8.82843 0.352855
\(627\) 0 0
\(628\) 25.5980 1.02147
\(629\) −1.32391 + 4.07458i −0.0527879 + 0.162464i
\(630\) 3.35106 2.43469i 0.133509 0.0970002i
\(631\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(632\) 1.96014 + 6.03269i 0.0779702 + 0.239968i
\(633\) 13.9845 + 43.0399i 0.555834 + 1.71068i
\(634\) −7.14235 5.18922i −0.283659 0.206090i
\(635\) −12.6667 + 9.20287i −0.502661 + 0.365205i
\(636\) −0.548383 + 1.68775i −0.0217448 + 0.0669236i
\(637\) −20.4853 −0.811656
\(638\) 0 0
\(639\) −56.5685 −2.23782
\(640\) 3.26209 10.0397i 0.128945 0.396853i
\(641\) −24.2705 + 17.6336i −0.958628 + 0.696484i −0.952832 0.303500i \(-0.901845\pi\)
−0.00579592 + 0.999983i \(0.501845\pi\)
\(642\) −3.46605 2.51823i −0.136794 0.0993867i
\(643\) 15.2827 + 47.0353i 0.602691 + 1.85489i 0.511947 + 0.859017i \(0.328924\pi\)
0.0907436 + 0.995874i \(0.471076\pi\)
\(644\) −3.19621 9.83692i −0.125948 0.387629i
\(645\) 13.7295 + 9.97505i 0.540597 + 0.392767i
\(646\) 0 0
\(647\) −10.8504 + 33.3942i −0.426574 + 1.31286i 0.474905 + 0.880037i \(0.342482\pi\)
−0.901479 + 0.432823i \(0.857518\pi\)
\(648\) −1.58579 −0.0622956
\(649\) 0 0
\(650\) 2.82843 0.110940
\(651\) 0 0
\(652\) −0.717842 + 0.521543i −0.0281129 + 0.0204252i
\(653\) −0.277611 0.201696i −0.0108637 0.00789297i 0.582340 0.812945i \(-0.302137\pi\)
−0.593204 + 0.805052i \(0.702137\pi\)
\(654\) −1.32391 4.07458i −0.0517691 0.159329i
\(655\) 3.49613 + 10.7600i 0.136605 + 0.420427i
\(656\) 14.5623 + 10.5801i 0.568563 + 0.413085i
\(657\) −27.6216 + 20.0682i −1.07762 + 0.782937i
\(658\) −0.724072 + 2.22846i −0.0282273 + 0.0868746i
\(659\) 21.9411 0.854705 0.427352 0.904085i \(-0.359446\pi\)
0.427352 + 0.904085i \(0.359446\pi\)
\(660\) 0 0
\(661\) −0.627417 −0.0244037 −0.0122018 0.999926i \(-0.503884\pi\)
−0.0122018 + 0.999926i \(0.503884\pi\)
\(662\) 1.96014 6.03269i 0.0761830 0.234467i
\(663\) 18.3060 13.3001i 0.710945 0.516532i
\(664\) 7.69757 + 5.59261i 0.298724 + 0.217035i
\(665\) 0 0
\(666\) 2.34037 + 7.20292i 0.0906875 + 0.279107i
\(667\) 17.5208 + 12.7296i 0.678407 + 0.492891i
\(668\) −16.2280 + 11.7903i −0.627879 + 0.456181i
\(669\) −4.52012 + 13.9115i −0.174758 + 0.537850i
\(670\) 1.85786 0.0717756
\(671\) 0 0
\(672\) 24.9706 0.963260
\(673\) −1.38603 + 4.26576i −0.0534275 + 0.164433i −0.974210 0.225644i \(-0.927551\pi\)
0.920782 + 0.390077i \(0.127551\pi\)
\(674\) −1.17780 + 0.855724i −0.0453673 + 0.0329612i
\(675\) −4.57649 3.32502i −0.176149 0.127980i
\(676\) −19.0000 58.4760i −0.730769 2.24908i
\(677\) −5.30631 16.3311i −0.203938 0.627657i −0.999755 0.0221198i \(-0.992958\pi\)
0.795817 0.605537i \(-0.207042\pi\)
\(678\) −7.90782 5.74537i −0.303698 0.220650i
\(679\) 12.3891 9.00117i 0.475448 0.345433i
\(680\) −0.574112 + 1.76693i −0.0220162 + 0.0677588i
\(681\) −7.59798 −0.291155
\(682\) 0 0
\(683\) 31.7990 1.21675 0.608377 0.793648i \(-0.291821\pi\)
0.608377 + 0.793648i \(0.291821\pi\)
\(684\) 0 0
\(685\) 18.5836 13.5018i 0.710042 0.515876i
\(686\) 6.70212 + 4.86937i 0.255888 + 0.185914i
\(687\) −18.6289 57.3337i −0.710736 2.18742i
\(688\) 5.56231 + 17.1190i 0.212061 + 0.652656i
\(689\) −1.89564 1.37727i −0.0722183 0.0524697i
\(690\) 2.68085 1.94775i 0.102058 0.0741495i
\(691\) −5.15635 + 15.8696i −0.196157 + 0.603708i 0.803804 + 0.594894i \(0.202806\pi\)
−0.999961 + 0.00881465i \(0.997194\pi\)
\(692\) 11.2304 0.426918
\(693\) 0 0
\(694\) 9.51472 0.361174
\(695\) −1.23607 + 3.80423i −0.0468867 + 0.144303i
\(696\) −27.7842 + 20.1864i −1.05316 + 0.765163i
\(697\) −5.68693 4.13180i −0.215408 0.156503i
\(698\) 0.892225 + 2.74599i 0.0337712 + 0.103937i
\(699\) −19.3529 59.5622i −0.731995 2.25285i
\(700\) 2.95846 + 2.14944i 0.111819 + 0.0812414i
\(701\) 26.3961 19.1779i 0.996968 0.724340i 0.0355322 0.999369i \(-0.488687\pi\)
0.961436 + 0.275029i \(0.0886874\pi\)
\(702\) 4.94427 15.2169i 0.186610 0.574325i
\(703\) 0 0
\(704\) 0 0
\(705\) 8.00000 0.301297
\(706\) −0.168153 + 0.517523i −0.00632854 + 0.0194772i
\(707\) −21.5420 + 15.6512i −0.810172 + 0.588624i
\(708\) −40.4032 29.3547i −1.51845 1.10322i
\(709\) −6.37422 19.6178i −0.239389 0.736763i −0.996509 0.0834875i \(-0.973394\pi\)
0.757120 0.653276i \(-0.226606\pi\)
\(710\) 1.44814 + 4.45693i 0.0543479 + 0.167266i
\(711\) 16.1803 + 11.7557i 0.606810 + 0.440873i
\(712\) 11.9488 8.68133i 0.447801 0.325346i
\(713\) 0 0
\(714\) −2.74517 −0.102735
\(715\) 0 0
\(716\) 3.02944 0.113215
\(717\) 0.599841 1.84612i 0.0224015 0.0689446i
\(718\) 7.81256 5.67616i 0.291562 0.211832i
\(719\) −23.9929 17.4319i −0.894784 0.650099i 0.0423368 0.999103i \(-0.486520\pi\)
−0.937121 + 0.349005i \(0.886520\pi\)
\(720\) −4.63525 14.2658i −0.172746 0.531657i
\(721\) 0.724072 + 2.22846i 0.0269658 + 0.0829923i
\(722\) 6.36701 + 4.62590i 0.236956 + 0.172158i
\(723\) 13.7295 9.97505i 0.510605 0.370976i
\(724\) 0.742265 2.28446i 0.0275861 0.0849012i
\(725\) −7.65685 −0.284368
\(726\) 0 0
\(727\) −36.4853 −1.35316 −0.676582 0.736367i \(-0.736540\pi\)
−0.676582 + 0.736367i \(0.736540\pi\)
\(728\) −6.69234 + 20.5969i −0.248034 + 0.763372i
\(729\) 34.7877 25.2748i 1.28843 0.936102i
\(730\) 2.28825 + 1.66251i 0.0846918 + 0.0615322i
\(731\) −2.17222 6.68539i −0.0803423 0.247268i
\(732\) 21.2767 + 65.4829i 0.786409 + 2.42032i
\(733\) 27.0663 + 19.6649i 0.999718 + 0.726338i 0.962028 0.272952i \(-0.0879999\pi\)
0.0376905 + 0.999289i \(0.488000\pi\)
\(734\) −2.84347 + 2.06590i −0.104954 + 0.0762538i
\(735\) 2.62210 8.06998i 0.0967175 0.297666i
\(736\) 12.4853 0.460214
\(737\) 0 0
\(738\) −12.4264 −0.457422
\(739\) 11.7245 36.0842i 0.431291 1.32738i −0.465549 0.885022i \(-0.654143\pi\)
0.896840 0.442355i \(-0.145857\pi\)
\(740\) −5.40932 + 3.93010i −0.198851 + 0.144473i
\(741\) 0 0
\(742\) 0.0878446 + 0.270358i 0.00322488 + 0.00992516i
\(743\) −9.14628 28.1494i −0.335544 1.03270i −0.966453 0.256843i \(-0.917318\pi\)
0.630909 0.775857i \(-0.282682\pi\)
\(744\) 0 0
\(745\) −9.43059 + 6.85173i −0.345510 + 0.251028i
\(746\) 0.486267 1.49658i 0.0178035 0.0547935i
\(747\) 30.0000 1.09764
\(748\) 0 0
\(749\) 7.31371 0.267237
\(750\) −0.362036 + 1.11423i −0.0132197 + 0.0406860i
\(751\) 12.9443 9.40456i 0.472343 0.343177i −0.326011 0.945366i \(-0.605705\pi\)
0.798354 + 0.602189i \(0.205705\pi\)
\(752\) 6.86474 + 4.98752i 0.250331 + 0.181876i
\(753\) 10.4884 + 32.2799i 0.382218 + 1.17635i
\(754\) −6.69234 20.5969i −0.243721 0.750095i
\(755\) 9.70820 + 7.05342i 0.353318 + 0.256700i
\(756\) 16.7356 12.1591i 0.608666 0.442222i
\(757\) −2.87809 + 8.85786i −0.104606 + 0.321945i −0.989638 0.143586i \(-0.954137\pi\)
0.885032 + 0.465531i \(0.154137\pi\)
\(758\) 9.25483 0.336151
\(759\) 0 0
\(760\) 0 0
\(761\) 9.27051 28.5317i 0.336056 1.03427i −0.630144 0.776478i \(-0.717004\pi\)
0.966200 0.257795i \(-0.0829959\pi\)
\(762\) 14.8399 10.7818i 0.537593 0.390585i
\(763\) 5.91691 + 4.29889i 0.214207 + 0.155630i
\(764\) 10.9125 + 33.5853i 0.394802 + 1.21507i
\(765\) 1.81018 + 5.57116i 0.0654472 + 0.201426i
\(766\) 11.4412 + 8.31254i 0.413388 + 0.300344i
\(767\) 53.3475 38.7592i 1.92627 1.39951i
\(768\) 3.47040 10.6808i 0.125227 0.385410i
\(769\) −14.9706 −0.539852 −0.269926 0.962881i \(-0.586999\pi\)
−0.269926 + 0.962881i \(0.586999\pi\)
\(770\) 0 0
\(771\) 37.6569 1.35618
\(772\) −3.85816 + 11.8742i −0.138858 + 0.427362i
\(773\) 24.5005 17.8006i 0.881221 0.640245i −0.0523529 0.998629i \(-0.516672\pi\)
0.933574 + 0.358384i \(0.116672\pi\)
\(774\) −10.0532 7.30406i −0.361354 0.262539i
\(775\) 0 0
\(776\) 3.75213 + 11.5479i 0.134693 + 0.414544i
\(777\) −16.7356 12.1591i −0.600385 0.436205i
\(778\)