Properties

Label 605.2.g.l.511.2
Level $605$
Weight $2$
Character 605.511
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 511.2
Root \(-1.14412 - 0.831254i\) of defining polynomial
Character \(\chi\) \(=\) 605.511
Dual form 605.2.g.l.251.2

$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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 0.986057 0.166406i \(-0.0532163\pi\)
−0.895548 + 0.444964i \(0.853216\pi\)
\(3\) −2.28825 1.66251i −1.32112 0.959849i −0.999918 0.0128385i \(-0.995913\pi\)
−0.321202 0.947011i \(-0.604087\pi\)
\(4\) 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 −0.849963 0.526842i \(-0.823376\pi\)
0.238404 + 0.971166i \(0.423376\pi\)
\(8\) 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 0.598319 + 0.801258i \(0.295836\pi\)
−0.0130823 + 0.999914i \(0.504164\pi\)
\(14\) −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 −0.985312 0.170762i \(-0.945377\pi\)
0.897506 + 0.441003i \(0.145377\pi\)
\(18\) −1.67553 + 1.21734i −0.394926 + 0.286931i
\(19\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(20\) 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 0.161774 0.986828i \(-0.448278\pi\)
0.988520 + 0.151090i \(0.0482783\pi\)
\(30\) 0.947822 + 0.688633i 0.173048 + 0.125727i
\(31\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(32\) 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 −0.803786 0.594919i \(-0.797184\pi\)
0.317418 + 0.948286i \(0.397184\pi\)
\(38\) 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 0.898322 0.439338i \(-0.144787\pi\)
−0.140238 + 0.990118i \(0.544787\pi\)
\(42\) 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 0.742031 0.670366i \(-0.233863\pi\)
−0.408256 + 0.912868i \(0.633863\pi\)
\(48\) −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 0.958075 0.286517i \(-0.0924976\pi\)
−0.943510 + 0.331345i \(0.892498\pi\)
\(54\) 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 0.0514204 0.998677i \(-0.483625\pi\)
0.965688 + 0.259704i \(0.0836251\pi\)
\(60\) 1.59810 4.91846i 0.206314 0.634970i
\(61\) −4.11416 + 12.6621i −0.526764 + 1.62121i 0.234036 + 0.972228i \(0.424807\pi\)
−0.760800 + 0.648986i \(0.775193\pi\)
\(62\) 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 0.497414 + 0.867513i \(0.334283\pi\)
−0.912328 + 0.409461i \(0.865717\pi\)
\(72\) −2.45017 + 7.54086i −0.288756 + 0.888699i
\(73\) −5.52431 + 4.01365i −0.646572 + 0.469762i −0.862102 0.506735i \(-0.830852\pi\)
0.215530 + 0.976497i \(0.430852\pi\)
\(74\) −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 0.857132 0.515097i \(-0.172244\pi\)
−0.996201 + 0.0870877i \(0.972244\pi\)
\(80\) 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 −0.796257 0.604959i \(-0.793190\pi\)
0.999771 0.0213936i \(-0.00681031\pi\)
\(84\) 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 −0.996383 0.0849778i \(-0.972918\pi\)
0.756142 0.654408i \(-0.227082\pi\)
\(98\) −1.24264 −0.125526
\(99\) 0 0
\(100\) −1.82843 −0.182843
\(101\) 4.11416 + 12.6621i 0.409374 + 1.25992i 0.917187 + 0.398457i \(0.130454\pi\)
−0.507812 + 0.861468i \(0.669546\pi\)
\(102\) 1.11044 + 0.806784i 0.109950 + 0.0798835i
\(103\) −0.947822 + 0.688633i −0.0933917 + 0.0678531i −0.633501 0.773742i \(-0.718383\pi\)
0.540109 + 0.841595i \(0.318383\pi\)
\(104\) −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 0.435527 0.900175i \(-0.356562\pi\)
−0.721532 + 0.692381i \(0.756562\pi\)
\(108\) −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 0.223153 0.974783i \(-0.428365\pi\)
−0.858116 + 0.513456i \(0.828365\pi\)
\(114\) 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 0.469469 + 0.882949i \(0.344445\pi\)
−0.898793 + 0.438374i \(0.855555\pi\)
\(128\) 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 0.119937 0.992782i \(-0.461731\pi\)
0.486512 0.873674i \(-0.338269\pi\)
\(138\) 1.02399 3.15152i 0.0871680 0.268276i
\(139\) −3.23607 + 2.35114i −0.274480 + 0.199421i −0.716506 0.697581i \(-0.754260\pi\)
0.442026 + 0.897002i \(0.354260\pi\)
\(140\) −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 0.688087 + 0.725629i \(0.258451\pi\)
−0.983188 + 0.182599i \(0.941549\pi\)
\(150\) −0.947822 + 0.688633i −0.0773894 + 0.0562267i
\(151\) −9.70820 7.05342i −0.790042 0.573999i 0.117934 0.993021i \(-0.462373\pi\)
−0.907976 + 0.419022i \(0.862373\pi\)
\(152\) 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 0.939473 0.342623i \(-0.111315\pi\)
−0.0355408 + 0.999368i \(0.511315\pi\)
\(158\) 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 0.945012 0.327036i \(-0.106050\pi\)
−0.956758 + 0.290886i \(0.906050\pi\)
\(164\) 10.9706 0.856657
\(165\) 0 0
\(166\) 2.48528 0.192895
\(167\) −3.39009 10.4336i −0.262333 0.807378i −0.992296 0.123891i \(-0.960463\pi\)
0.729963 0.683487i \(-0.239537\pi\)
\(168\) 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 0.760435 0.649414i \(-0.224986\pi\)
−0.382642 + 0.923897i \(0.624986\pi\)
\(174\) −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 0.636751 0.771069i \(-0.280278\pi\)
−0.536563 + 0.843860i \(0.680278\pi\)
\(180\) −7.39614 + 5.37361i −0.551276 + 0.400525i
\(181\) −0.405958 + 1.24941i −0.0301746 + 0.0928680i −0.965010 0.262214i \(-0.915547\pi\)
0.934835 + 0.355082i \(0.115547\pi\)
\(182\) 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 0.144813 0.989459i \(-0.453742\pi\)
0.985781 + 0.168035i \(0.0537420\pi\)
\(192\) −3.64609 + 11.2215i −0.263134 + 0.809842i
\(193\) 2.11010 6.49422i 0.151888 0.467464i −0.845944 0.533272i \(-0.820962\pi\)
0.997832 + 0.0658075i \(0.0209623\pi\)
\(194\) 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 0.964012 + 0.265859i \(0.0856555\pi\)
−0.623634 + 0.781716i \(0.714345\pi\)
\(212\) 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 0.718993 0.695017i \(-0.244603\pi\)
−0.438819 + 0.898575i \(0.644603\pi\)
\(224\) −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 −0.513323 0.858196i \(-0.671586\pi\)
0.657567 + 0.753396i \(0.271586\pi\)
\(228\) 0 0
\(229\) −6.58630 20.2705i −0.435235 1.33952i −0.892846 0.450363i \(-0.851295\pi\)
0.457611 0.889153i \(-0.348705\pi\)
\(230\) −1.17157 −0.0772512
\(231\) 0 0
\(232\) 12.1421 0.797170
\(233\) −6.84230 21.0584i −0.448254 1.37958i −0.878876 0.477051i \(-0.841706\pi\)
0.430622 0.902532i \(-0.358294\pi\)
\(234\) −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 0.569683 0.821864i \(-0.307066\pi\)
−0.605598 + 0.795771i \(0.707066\pi\)
\(240\) −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 0.997245 + 0.0741818i \(0.0236345\pi\)
−0.763185 + 0.646180i \(0.776365\pi\)
\(252\) −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 −0.870653 0.491897i \(-0.836304\pi\)
0.198776 + 0.980045i \(0.436304\pi\)
\(258\) 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 −0.988553 0.150873i \(-0.951792\pi\)
0.888437 + 0.458998i \(0.151792\pi\)
\(270\) −0.724072 + 2.22846i −0.0440656 + 0.135620i
\(271\) −12.3891 + 9.00117i −0.752581 + 0.546782i −0.896626 0.442789i \(-0.853989\pi\)
0.144045 + 0.989571i \(0.453989\pi\)
\(272\) 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 0.939591 0.342299i \(-0.111206\pi\)
−0.961344 + 0.275352i \(0.911206\pi\)
\(278\) −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 −0.890057 0.455848i \(-0.849336\pi\)
0.988013 + 0.154374i \(0.0493359\pi\)
\(282\) 2.68085 1.94775i 0.159642 0.115987i
\(283\) −10.2158 7.42221i −0.607266 0.441205i 0.241185 0.970479i \(-0.422464\pi\)
−0.848451 + 0.529275i \(0.822464\pi\)
\(284\) 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 −0.880206 0.474592i \(-0.842595\pi\)
0.179366 + 0.983782i \(0.442595\pi\)
\(294\) 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 −0.254627 0.967039i \(-0.581953\pi\)
−0.998393 + 0.0566667i \(0.981953\pi\)
\(312\) 24.7781 18.0023i 1.40278 1.01918i
\(313\) 6.58630 20.2705i 0.372280 1.14576i −0.573016 0.819544i \(-0.694227\pi\)
0.945296 0.326215i \(-0.105773\pi\)
\(314\) −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 0.946840 + 0.321704i \(0.104256\pi\)
−0.576917 + 0.816803i \(0.695744\pi\)
\(318\) 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 −0.662533 0.749033i \(-0.730518\pi\)
0.507639 + 0.861570i \(0.330518\pi\)
\(338\) −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 −0.558244 0.829677i \(-0.688525\pi\)
0.939301 0.343095i \(-0.111475\pi\)
\(348\) −32.0354 + 23.2751i −1.71728 + 1.24768i
\(349\) −5.63930 4.09719i −0.301865 0.219318i 0.426533 0.904472i \(-0.359735\pi\)
−0.728398 + 0.685154i \(0.759735\pi\)
\(350\) 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 0.0343464 0.999410i \(-0.489065\pi\)
0.961109 + 0.276169i \(0.0890651\pi\)
\(360\) −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 −0.752358 0.658755i \(-0.771084\pi\)
0.394022 + 0.919101i \(0.371084\pi\)
\(368\) 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 −0.601553 0.798833i \(-0.705451\pi\)
0.956209 0.292685i \(-0.0945489\pi\)
\(380\) 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 −0.734607 0.678492i \(-0.762634\pi\)
0.195502 0.980703i \(-0.437366\pi\)
\(384\) −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 0.0459386 0.998944i \(-0.485372\pi\)
0.964248 + 0.265001i \(0.0853721\pi\)
\(390\) −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 −0.724006 0.689794i \(-0.757701\pi\)
0.991184 0.132495i \(-0.0422988\pi\)
\(402\) −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 −0.745056 0.667002i \(-0.767577\pi\)
0.210709 0.977549i \(-0.432423\pi\)
\(410\) −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 0.699756 0.714382i \(-0.253292\pi\)
−0.463181 + 0.886264i \(0.653292\pi\)
\(422\) −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 0.830868 0.556469i \(-0.187844\pi\)
−0.999271 + 0.0381792i \(0.987844\pi\)
\(432\) −13.7295 9.97505i −0.660560 0.479925i
\(433\) −2.95846 + 2.14944i −0.142174 + 0.103296i −0.656599 0.754240i \(-0.728006\pi\)
0.514425 + 0.857536i \(0.328006\pi\)
\(434\) 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 0.914925 0.403624i \(-0.132249\pi\)
−0.101142 + 0.994872i \(0.532249\pi\)
\(444\) 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 −0.996040 0.0889063i \(-0.971663\pi\)
0.753555 0.657384i \(-0.228337\pi\)
\(450\) 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 −0.758369 0.651826i \(-0.774003\pi\)
0.996667 0.0815803i \(-0.0259967\pi\)
\(458\) 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 −0.994971 0.100160i \(-0.968064\pi\)
0.863821 + 0.503798i \(0.168064\pi\)
\(468\) −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 −0.286861 0.957972i \(-0.592612\pi\)
0.795157 0.606403i \(-0.207388\pi\)
\(480\) 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 0.716948 0.697127i \(-0.245539\pi\)
−0.441458 + 0.897282i \(0.645539\pi\)
\(488\) −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 −0.925475 0.378809i \(-0.876334\pi\)
0.0742814 + 0.997237i \(0.476334\pi\)
\(492\) −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 −0.557378 0.830259i \(-0.688193\pi\)
0.617384 + 0.786662i \(0.288193\pi\)
\(500\) 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 −0.0638177 0.997962i \(-0.520328\pi\)
−0.968839 + 0.247693i \(0.920328\pi\)
\(504\) −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 0.408137 0.912921i \(-0.366179\pi\)
−0.742118 + 0.670269i \(0.766179\pi\)
\(510\) −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 −0.634373 0.773027i \(-0.718742\pi\)
0.539161 + 0.842203i \(0.318742\pi\)
\(522\) −4.90035 + 15.0817i −0.214482 + 0.660109i
\(523\) −11.6184 + 35.7578i −0.508038 + 1.56358i 0.287565 + 0.957761i \(0.407154\pi\)
−0.795603 + 0.605818i \(0.792846\pi\)
\(524\) −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 0.903255 0.429103i \(-0.141170\pi\)
−0.982970 + 0.183768i \(0.941170\pi\)
\(542\) −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 −0.184370 0.982857i \(-0.559025\pi\)
−0.991726 + 0.128373i \(0.959025\pi\)
\(548\) −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 0.307481 0.951554i \(-0.400514\pi\)
0.999999 + 0.00161430i \(0.000513849\pi\)
\(558\) 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 0.846011 0.533166i \(-0.178998\pi\)
−0.997824 + 0.0659327i \(0.978998\pi\)
\(564\) −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 0.876645 0.481138i \(-0.159776\pi\)
−0.186692 + 0.982419i \(0.559776\pi\)
\(570\) 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 −0.896156 0.443740i \(-0.853651\pi\)
0.985829 + 0.167754i \(0.0536515\pi\)
\(578\) −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 −0.931372 0.364070i \(-0.881387\pi\)
0.0584412 + 0.998291i \(0.481387\pi\)
\(588\) 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 −0.908972 0.416857i \(-0.863132\pi\)
0.980396 + 0.197036i \(0.0631317\pi\)
\(600\) −1.38603 + 4.26576i −0.0565844 + 0.174149i
\(601\) −35.5491 + 25.8279i −1.45008 + 1.05354i −0.464266 + 0.885696i \(0.653682\pi\)
−0.985813 + 0.167848i \(0.946318\pi\)
\(602\) −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 0.997823 + 0.0659515i \(0.0210083\pi\)
−0.768490 + 0.639861i \(0.778992\pi\)
\(608\) 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 0.920066 0.391764i \(-0.128135\pi\)
−0.0882735 + 0.996096i \(0.528135\pi\)
\(614\) 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 0.920769 0.390108i \(-0.127562\pi\)
−0.0864816 + 0.996253i \(0.527562\pi\)
\(620\) 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 \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(632\) 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 −0.00579592 0.999983i \(-0.501845\pi\)
−0.952832 + 0.303500i \(0.901845\pi\)
\(642\) −3.46605 + 2.51823i −0.136794 + 0.0993867i
\(643\) 15.2827 47.0353i 0.602691 1.85489i 0.0907436 0.995874i \(-0.471076\pi\)
0.511947 0.859017i \(-0.328924\pi\)
\(644\) −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 −0.901479 0.432823i \(-0.857518\pi\)
0.474905 0.880037i \(-0.342482\pi\)
\(648\) −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 −0.593204 0.805052i \(-0.702137\pi\)
0.582340 + 0.812945i \(0.302137\pi\)
\(654\) −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 0.920782 0.390077i \(-0.127551\pi\)
−0.974210 + 0.225644i \(0.927551\pi\)
\(674\) −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 0.795817 + 0.605537i \(0.207042\pi\)
−0.999755 + 0.0221198i \(0.992958\pi\)
\(678\) −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 −0.999961 0.00881465i \(-0.997194\pi\)
0.803804 0.594894i \(-0.202806\pi\)
\(692\) 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 0.961436 0.275029i \(-0.0886874\pi\)
0.0355322 + 0.999369i \(0.488687\pi\)
\(702\) 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 0.757120 + 0.653276i \(0.226606\pi\)
−0.996509 + 0.0834875i \(0.973394\pi\)
\(710\) 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 −0.937121 0.349005i \(-0.886520\pi\)
0.0423368 + 0.999103i \(0.486520\pi\)
\(720\) −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 0.0376905 0.999289i \(-0.488000\pi\)
0.962028 + 0.272952i \(0.0879999\pi\)
\(734\) −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 0.896840 + 0.442355i \(0.145857\pi\)
−0.465549 + 0.885022i \(0.654143\pi\)
\(740\) −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 0.630909 + 0.775857i \(0.282682\pi\)
−0.966453 + 0.256843i \(0.917318\pi\)
\(744\) 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 0.798354 0.602189i \(-0.205705\pi\)
−0.326011 + 0.945366i \(0.605705\pi\)
\(752\) 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 0.885032 0.465531i \(-0.154137\pi\)
−0.989638 + 0.143586i \(0.954137\pi\)
\(758\) 9.25483 0.336151
\(759\) 0 0
\(760\) 0 0
\(761\) 9.27051 + 28.5317i 0.336056 + 1.03427i 0.966200 + 0.257795i \(0.0829959\pi\)
−0.630144 + 0.776478i \(0.717004\pi\)
\(762\) 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 0.933574 0.358384i \(-0.116672\pi\)
−0.0523529 + 0.998629i \(0.516672\pi\)
\(774\) −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