Properties

Label 605.2.g.l.366.2
Level $605$
Weight $2$
Character 605.366
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: \(x^{8} + 2 x^{6} + 4 x^{4} + 8 x^{2} + 16\)
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 366.2
Root \(-0.437016 - 1.34500i\) of defining polynomial
Character \(\chi\) \(=\) 605.366
Dual form 605.2.g.l.81.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.95314 - 1.41904i) q^{2} +(-0.874032 - 2.68999i) q^{3} +(1.18305 - 3.64105i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-5.52431 - 4.01365i) q^{6} +(0.618034 - 1.90211i) q^{7} +(-1.36407 - 4.19817i) q^{8} +(-4.04508 + 2.93893i) q^{9} +O(q^{10})\) \(q+(1.95314 - 1.41904i) q^{2} +(-0.874032 - 2.68999i) q^{3} +(1.18305 - 3.64105i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-5.52431 - 4.01365i) q^{6} +(0.618034 - 1.90211i) q^{7} +(-1.36407 - 4.19817i) q^{8} +(-4.04508 + 2.93893i) q^{9} +2.41421 q^{10} -10.8284 q^{12} +(-0.947822 + 0.688633i) q^{13} +(-1.49207 - 4.59211i) q^{14} +(0.874032 - 2.68999i) q^{15} +(-2.42705 - 1.76336i) q^{16} +(5.52431 + 4.01365i) q^{17} +(-3.73017 + 11.4803i) q^{18} +(3.09726 - 2.25029i) q^{20} -5.65685 q^{21} -2.82843 q^{23} +(-10.1008 + 7.33866i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.874032 + 2.68999i) q^{26} +(4.57649 + 3.32502i) q^{27} +(-6.19453 - 4.50059i) q^{28} +(1.13003 - 3.47788i) q^{29} +(-2.11010 - 6.49422i) q^{30} +1.58579 q^{32} +16.4853 q^{34} +(1.61803 - 1.17557i) q^{35} +(5.91525 + 18.2053i) q^{36} +(-2.36610 + 7.28210i) q^{37} +(2.68085 + 1.94775i) q^{39} +(1.36407 - 4.19817i) q^{40} +(-1.85410 - 5.70634i) q^{41} +(-11.0486 + 8.02730i) q^{42} +6.00000 q^{43} -5.00000 q^{45} +(-5.52431 + 4.01365i) q^{46} +(0.874032 + 2.68999i) q^{47} +(-2.62210 + 8.06998i) q^{48} +(2.42705 + 1.76336i) q^{49} +(1.95314 + 1.41904i) q^{50} +(5.96826 - 18.3684i) q^{51} +(1.38603 + 4.26576i) q^{52} +(-9.43059 + 6.85173i) q^{53} +13.6569 q^{54} -8.82843 q^{56} +(-2.72813 - 8.39633i) q^{58} +(0.511996 - 1.57576i) q^{59} +(-8.76038 - 6.36479i) q^{60} +(-7.53495 - 5.47446i) q^{61} +(3.09017 + 9.51057i) q^{63} +(7.95136 - 5.77700i) q^{64} -1.17157 q^{65} +12.4853 q^{67} +(21.1494 - 15.3660i) q^{68} +(2.47214 + 7.60845i) q^{69} +(1.49207 - 4.59211i) q^{70} +(-9.15298 - 6.65003i) q^{71} +(17.8559 + 12.9730i) q^{72} +(0.362036 - 1.11423i) q^{73} +(5.71227 + 17.5805i) q^{74} +(2.28825 - 1.66251i) q^{75} +8.00000 q^{78} +(3.23607 - 2.35114i) q^{79} +(-0.927051 - 2.85317i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-11.7188 - 8.51423i) q^{82} +(-4.85410 - 3.52671i) q^{83} +(-6.69234 + 20.5969i) q^{84} +(2.11010 + 6.49422i) q^{85} +(11.7188 - 8.51423i) q^{86} -10.3431 q^{87} -13.3137 q^{89} +(-9.76570 + 7.09520i) q^{90} +(0.724072 + 2.22846i) q^{91} +(-3.34617 + 10.2984i) q^{92} +(5.52431 + 4.01365i) q^{94} +(-1.38603 - 4.26576i) q^{96} +(-2.95846 + 2.14944i) q^{97} +7.24264 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9} + O(q^{10}) \) \( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9} + 8 q^{10} - 64 q^{12} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 8 q^{17} + 10 q^{18} + 2 q^{20} - 8 q^{24} - 2 q^{25} - 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{32} + 64 q^{34} + 4 q^{35} - 10 q^{36} + 4 q^{37} - 16 q^{39} - 6 q^{40} + 12 q^{41} - 16 q^{42} + 48 q^{43} - 40 q^{45} - 8 q^{46} + 6 q^{49} + 2 q^{50} - 16 q^{51} + 8 q^{52} - 12 q^{53} + 64 q^{54} - 48 q^{56} + 12 q^{58} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 20 q^{63} + 14 q^{64} - 32 q^{65} + 32 q^{67} + 24 q^{68} - 16 q^{69} - 4 q^{70} + 30 q^{72} - 8 q^{73} - 20 q^{74} + 64 q^{78} + 8 q^{79} + 6 q^{80} - 2 q^{81} - 12 q^{82} - 12 q^{83} + 32 q^{84} - 8 q^{85} + 12 q^{86} - 128 q^{87} - 16 q^{89} - 10 q^{90} - 16 q^{91} + 16 q^{92} + 8 q^{94} - 8 q^{96} + 4 q^{97} + 24 q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.95314 1.41904i 1.38108 1.00341i 0.384300 0.923208i \(-0.374443\pi\)
0.996778 0.0802039i \(-0.0255571\pi\)
\(3\) −0.874032 2.68999i −0.504623 1.55307i −0.801404 0.598123i \(-0.795913\pi\)
0.296781 0.954945i \(-0.404087\pi\)
\(4\) 1.18305 3.64105i 0.591525 1.82053i
\(5\) 0.809017 + 0.587785i 0.361803 + 0.262866i
\(6\) −5.52431 4.01365i −2.25529 1.63857i
\(7\) 0.618034 1.90211i 0.233595 0.718931i −0.763710 0.645560i \(-0.776624\pi\)
0.997305 0.0733714i \(-0.0233759\pi\)
\(8\) −1.36407 4.19817i −0.482271 1.48428i
\(9\) −4.04508 + 2.93893i −1.34836 + 0.979642i
\(10\) 2.41421 0.763441
\(11\) 0 0
\(12\) −10.8284 −3.12590
\(13\) −0.947822 + 0.688633i −0.262879 + 0.190993i −0.711415 0.702772i \(-0.751945\pi\)
0.448537 + 0.893765i \(0.351945\pi\)
\(14\) −1.49207 4.59211i −0.398771 1.22729i
\(15\) 0.874032 2.68999i 0.225674 0.694553i
\(16\) −2.42705 1.76336i −0.606763 0.440839i
\(17\) 5.52431 + 4.01365i 1.33984 + 0.973453i 0.999450 + 0.0331696i \(0.0105601\pi\)
0.340393 + 0.940283i \(0.389440\pi\)
\(18\) −3.73017 + 11.4803i −0.879208 + 2.70593i
\(19\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(20\) 3.09726 2.25029i 0.692569 0.503181i
\(21\) −5.65685 −1.23443
\(22\) 0 0
\(23\) −2.82843 −0.589768 −0.294884 0.955533i \(-0.595281\pi\)
−0.294884 + 0.955533i \(0.595281\pi\)
\(24\) −10.1008 + 7.33866i −2.06182 + 1.49800i
\(25\) 0.309017 + 0.951057i 0.0618034 + 0.190211i
\(26\) −0.874032 + 2.68999i −0.171412 + 0.527551i
\(27\) 4.57649 + 3.32502i 0.880746 + 0.639900i
\(28\) −6.19453 4.50059i −1.17066 0.850531i
\(29\) 1.13003 3.47788i 0.209841 0.645825i −0.789638 0.613572i \(-0.789732\pi\)
0.999480 0.0322527i \(-0.0102681\pi\)
\(30\) −2.11010 6.49422i −0.385250 1.18568i
\(31\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(32\) 1.58579 0.280330
\(33\) 0 0
\(34\) 16.4853 2.82720
\(35\) 1.61803 1.17557i 0.273498 0.198708i
\(36\) 5.91525 + 18.2053i 0.985874 + 3.03421i
\(37\) −2.36610 + 7.28210i −0.388984 + 1.19717i 0.544564 + 0.838719i \(0.316695\pi\)
−0.933549 + 0.358451i \(0.883305\pi\)
\(38\) 0 0
\(39\) 2.68085 + 1.94775i 0.429279 + 0.311889i
\(40\) 1.36407 4.19817i 0.215678 0.663788i
\(41\) −1.85410 5.70634i −0.289562 0.891180i −0.984994 0.172588i \(-0.944787\pi\)
0.695432 0.718592i \(-0.255213\pi\)
\(42\) −11.0486 + 8.02730i −1.70484 + 1.23864i
\(43\) 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
\(46\) −5.52431 + 4.01365i −0.814516 + 0.591780i
\(47\) 0.874032 + 2.68999i 0.127491 + 0.392376i 0.994347 0.106183i \(-0.0338628\pi\)
−0.866856 + 0.498559i \(0.833863\pi\)
\(48\) −2.62210 + 8.06998i −0.378467 + 1.16480i
\(49\) 2.42705 + 1.76336i 0.346722 + 0.251908i
\(50\) 1.95314 + 1.41904i 0.276216 + 0.200682i
\(51\) 5.96826 18.3684i 0.835724 2.57209i
\(52\) 1.38603 + 4.26576i 0.192208 + 0.591554i
\(53\) −9.43059 + 6.85173i −1.29539 + 0.941157i −0.999899 0.0141880i \(-0.995484\pi\)
−0.295492 + 0.955345i \(0.595484\pi\)
\(54\) 13.6569 1.85846
\(55\) 0 0
\(56\) −8.82843 −1.17975
\(57\) 0 0
\(58\) −2.72813 8.39633i −0.358222 1.10249i
\(59\) 0.511996 1.57576i 0.0666562 0.205147i −0.912181 0.409788i \(-0.865603\pi\)
0.978837 + 0.204641i \(0.0656027\pi\)
\(60\) −8.76038 6.36479i −1.13096 0.821691i
\(61\) −7.53495 5.47446i −0.964751 0.700933i −0.0105019 0.999945i \(-0.503343\pi\)
−0.954249 + 0.299012i \(0.903343\pi\)
\(62\) 0 0
\(63\) 3.09017 + 9.51057i 0.389325 + 1.19822i
\(64\) 7.95136 5.77700i 0.993921 0.722126i
\(65\) −1.17157 −0.145316
\(66\) 0 0
\(67\) 12.4853 1.52532 0.762660 0.646800i \(-0.223893\pi\)
0.762660 + 0.646800i \(0.223893\pi\)
\(68\) 21.1494 15.3660i 2.56475 1.86340i
\(69\) 2.47214 + 7.60845i 0.297610 + 0.915950i
\(70\) 1.49207 4.59211i 0.178336 0.548862i
\(71\) −9.15298 6.65003i −1.08626 0.789213i −0.107496 0.994206i \(-0.534283\pi\)
−0.978764 + 0.204992i \(0.934283\pi\)
\(72\) 17.8559 + 12.9730i 2.10433 + 1.52889i
\(73\) 0.362036 1.11423i 0.0423731 0.130411i −0.927632 0.373495i \(-0.878159\pi\)
0.970005 + 0.243084i \(0.0781592\pi\)
\(74\) 5.71227 + 17.5805i 0.664037 + 2.04370i
\(75\) 2.28825 1.66251i 0.264224 0.191970i
\(76\) 0 0
\(77\) 0 0
\(78\) 8.00000 0.905822
\(79\) 3.23607 2.35114i 0.364086 0.264524i −0.390668 0.920532i \(-0.627756\pi\)
0.754754 + 0.656007i \(0.227756\pi\)
\(80\) −0.927051 2.85317i −0.103647 0.318994i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) −11.7188 8.51423i −1.29413 0.940240i
\(83\) −4.85410 3.52671i −0.532807 0.387107i 0.288600 0.957450i \(-0.406810\pi\)
−0.821407 + 0.570343i \(0.806810\pi\)
\(84\) −6.69234 + 20.5969i −0.730194 + 2.24731i
\(85\) 2.11010 + 6.49422i 0.228872 + 0.704397i
\(86\) 11.7188 8.51423i 1.26367 0.918114i
\(87\) −10.3431 −1.10890
\(88\) 0 0
\(89\) −13.3137 −1.41125 −0.705625 0.708585i \(-0.749334\pi\)
−0.705625 + 0.708585i \(0.749334\pi\)
\(90\) −9.76570 + 7.09520i −1.02940 + 0.747899i
\(91\) 0.724072 + 2.22846i 0.0759034 + 0.233607i
\(92\) −3.34617 + 10.2984i −0.348862 + 1.07369i
\(93\) 0 0
\(94\) 5.52431 + 4.01365i 0.569789 + 0.413976i
\(95\) 0 0
\(96\) −1.38603 4.26576i −0.141461 0.435372i
\(97\) −2.95846 + 2.14944i −0.300386 + 0.218243i −0.727760 0.685832i \(-0.759439\pi\)
0.427374 + 0.904075i \(0.359439\pi\)
\(98\) 7.24264 0.731617
\(99\) 0 0
\(100\) 3.82843 0.382843
\(101\) 7.53495 5.47446i 0.749755 0.544729i −0.145996 0.989285i \(-0.546639\pi\)
0.895751 + 0.444556i \(0.146639\pi\)
\(102\) −14.4087 44.3453i −1.42667 4.39084i
\(103\) 2.11010 6.49422i 0.207914 0.639895i −0.791667 0.610953i \(-0.790786\pi\)
0.999581 0.0289414i \(-0.00921362\pi\)
\(104\) 4.18389 + 3.03977i 0.410264 + 0.298074i
\(105\) −4.57649 3.32502i −0.446620 0.324488i
\(106\) −8.69640 + 26.7648i −0.844669 + 2.59962i
\(107\) −2.36610 7.28210i −0.228739 0.703987i −0.997890 0.0649203i \(-0.979321\pi\)
0.769151 0.639067i \(-0.220679\pi\)
\(108\) 17.5208 12.7296i 1.68594 1.22490i
\(109\) 7.65685 0.733394 0.366697 0.930341i \(-0.380489\pi\)
0.366697 + 0.930341i \(0.380489\pi\)
\(110\) 0 0
\(111\) 21.6569 2.05558
\(112\) −4.85410 + 3.52671i −0.458670 + 0.333243i
\(113\) 6.07430 + 18.6948i 0.571422 + 1.75866i 0.648051 + 0.761597i \(0.275584\pi\)
−0.0766284 + 0.997060i \(0.524416\pi\)
\(114\) 0 0
\(115\) −2.28825 1.66251i −0.213380 0.155030i
\(116\) −11.3262 8.22899i −1.05161 0.764043i
\(117\) 1.81018 5.57116i 0.167351 0.515054i
\(118\) −1.23607 3.80423i −0.113789 0.350207i
\(119\) 11.0486 8.02730i 1.01283 0.735861i
\(120\) −12.4853 −1.13975
\(121\) 0 0
\(122\) −22.4853 −2.03572
\(123\) −13.7295 + 9.97505i −1.23794 + 0.899420i
\(124\) 0 0
\(125\) −0.309017 + 0.951057i −0.0276393 + 0.0850651i
\(126\) 19.5314 + 14.1904i 1.74000 + 1.26418i
\(127\) 3.51368 + 2.55284i 0.311789 + 0.226528i 0.732664 0.680591i \(-0.238277\pi\)
−0.420875 + 0.907119i \(0.638277\pi\)
\(128\) 6.35226 19.5502i 0.561466 1.72801i
\(129\) −5.24419 16.1400i −0.461725 1.42104i
\(130\) −2.28825 + 1.66251i −0.200692 + 0.145812i
\(131\) 11.3137 0.988483 0.494242 0.869325i \(-0.335446\pi\)
0.494242 + 0.869325i \(0.335446\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 24.3855 17.7171i 2.10659 1.53052i
\(135\) 1.74806 + 5.37999i 0.150449 + 0.463036i
\(136\) 9.31443 28.6669i 0.798706 2.45816i
\(137\) 8.87537 + 6.44833i 0.758274 + 0.550918i 0.898381 0.439218i \(-0.144744\pi\)
−0.140106 + 0.990136i \(0.544744\pi\)
\(138\) 15.6251 + 11.3523i 1.33010 + 0.966373i
\(139\) 1.23607 3.80423i 0.104842 0.322670i −0.884851 0.465873i \(-0.845740\pi\)
0.989693 + 0.143203i \(0.0457402\pi\)
\(140\) −2.36610 7.28210i −0.199972 0.615450i
\(141\) 6.47214 4.70228i 0.545052 0.396004i
\(142\) −27.3137 −2.29212
\(143\) 0 0
\(144\) 15.0000 1.25000
\(145\) 2.95846 2.14944i 0.245687 0.178502i
\(146\) −0.874032 2.68999i −0.0723354 0.222625i
\(147\) 2.62210 8.06998i 0.216267 0.665601i
\(148\) 23.7153 + 17.2302i 1.94938 + 1.41631i
\(149\) 0.277611 + 0.201696i 0.0227428 + 0.0165236i 0.599099 0.800675i \(-0.295526\pi\)
−0.576356 + 0.817199i \(0.695526\pi\)
\(150\) 2.11010 6.49422i 0.172289 0.530251i
\(151\) 3.70820 + 11.4127i 0.301769 + 0.928751i 0.980863 + 0.194699i \(0.0623730\pi\)
−0.679094 + 0.734052i \(0.737627\pi\)
\(152\) 0 0
\(153\) −34.1421 −2.76023
\(154\) 0 0
\(155\) 0 0
\(156\) 10.2634 7.45682i 0.821732 0.597023i
\(157\) −4.32624 13.3148i −0.345271 1.06264i −0.961438 0.275020i \(-0.911315\pi\)
0.616167 0.787616i \(-0.288685\pi\)
\(158\) 2.98413 9.18421i 0.237405 0.730657i
\(159\) 26.6737 + 19.3796i 2.11537 + 1.53690i
\(160\) 1.28293 + 0.932102i 0.101424 + 0.0736891i
\(161\) −1.74806 + 5.37999i −0.137767 + 0.424002i
\(162\) −0.746033 2.29605i −0.0586139 0.180395i
\(163\) −13.3369 + 9.68981i −1.04462 + 0.758964i −0.971183 0.238335i \(-0.923398\pi\)
−0.0734416 + 0.997300i \(0.523398\pi\)
\(164\) −22.9706 −1.79370
\(165\) 0 0
\(166\) −14.4853 −1.12428
\(167\) −18.5836 + 13.5018i −1.43804 + 1.04480i −0.449593 + 0.893234i \(0.648431\pi\)
−0.988447 + 0.151564i \(0.951569\pi\)
\(168\) 7.71633 + 23.7484i 0.595328 + 1.83223i
\(169\) −3.59307 + 11.0583i −0.276390 + 0.850641i
\(170\) 13.3369 + 9.68981i 1.02289 + 0.743174i
\(171\) 0 0
\(172\) 7.09829 21.8463i 0.541240 1.66577i
\(173\) 6.84230 + 21.0584i 0.520210 + 1.60104i 0.773597 + 0.633677i \(0.218455\pi\)
−0.253387 + 0.967365i \(0.581545\pi\)
\(174\) −20.2016 + 14.6773i −1.53148 + 1.11269i
\(175\) 2.00000 0.151186
\(176\) 0 0
\(177\) −4.68629 −0.352243
\(178\) −26.0035 + 18.8927i −1.94905 + 1.41607i
\(179\) 2.98413 + 9.18421i 0.223045 + 0.686460i 0.998484 + 0.0550388i \(0.0175282\pi\)
−0.775440 + 0.631422i \(0.782472\pi\)
\(180\) −5.91525 + 18.2053i −0.440896 + 1.35694i
\(181\) −17.2432 12.5279i −1.28167 0.931190i −0.282071 0.959393i \(-0.591021\pi\)
−0.999602 + 0.0282032i \(0.991021\pi\)
\(182\) 4.57649 + 3.32502i 0.339232 + 0.246467i
\(183\) −8.14048 + 25.0538i −0.601762 + 1.85203i
\(184\) 3.85816 + 11.8742i 0.284428 + 0.875378i
\(185\) −6.19453 + 4.50059i −0.455431 + 0.330890i
\(186\) 0 0
\(187\) 0 0
\(188\) 10.8284 0.789744
\(189\) 9.15298 6.65003i 0.665782 0.483719i
\(190\) 0 0
\(191\) 1.02399 3.15152i 0.0740935 0.228036i −0.907150 0.420806i \(-0.861747\pi\)
0.981244 + 0.192770i \(0.0617472\pi\)
\(192\) −22.4899 16.3398i −1.62307 1.17923i
\(193\) −0.947822 0.688633i −0.0682257 0.0495689i 0.553150 0.833082i \(-0.313426\pi\)
−0.621375 + 0.783513i \(0.713426\pi\)
\(194\) −2.72813 + 8.39633i −0.195869 + 0.602822i
\(195\) 1.02399 + 3.15152i 0.0733296 + 0.225685i
\(196\) 9.29179 6.75088i 0.663699 0.482206i
\(197\) 10.8284 0.771493 0.385747 0.922605i \(-0.373944\pi\)
0.385747 + 0.922605i \(0.373944\pi\)
\(198\) 0 0
\(199\) 10.3431 0.733206 0.366603 0.930377i \(-0.380521\pi\)
0.366603 + 0.930377i \(0.380521\pi\)
\(200\) 3.57117 2.59461i 0.252520 0.183467i
\(201\) −10.9125 33.5853i −0.769711 2.36893i
\(202\) 6.94833 21.3848i 0.488883 1.50463i
\(203\) −5.91691 4.29889i −0.415286 0.301723i
\(204\) −59.8196 43.4615i −4.18821 3.04291i
\(205\) 1.85410 5.70634i 0.129496 0.398548i
\(206\) −5.09423 15.6784i −0.354932 1.09237i
\(207\) 11.4412 8.31254i 0.795220 0.577761i
\(208\) 3.51472 0.243702
\(209\) 0 0
\(210\) −13.6569 −0.942412
\(211\) −12.9443 + 9.40456i −0.891120 + 0.647437i −0.936170 0.351548i \(-0.885655\pi\)
0.0450495 + 0.998985i \(0.485655\pi\)
\(212\) 13.7906 + 42.4432i 0.947144 + 2.91501i
\(213\) −9.88854 + 30.4338i −0.677552 + 2.08529i
\(214\) −14.9549 10.8654i −1.02230 0.742742i
\(215\) 4.85410 + 3.52671i 0.331047 + 0.240520i
\(216\) 7.71633 23.7484i 0.525030 1.61588i
\(217\) 0 0
\(218\) 14.9549 10.8654i 1.01287 0.735896i
\(219\) −3.31371 −0.223920
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) 42.2989 30.7319i 2.83891 2.06259i
\(223\) −3.34617 10.2984i −0.224076 0.689635i −0.998384 0.0568262i \(-0.981902\pi\)
0.774308 0.632809i \(-0.218098\pi\)
\(224\) 0.980070 3.01635i 0.0654837 0.201538i
\(225\) −4.04508 2.93893i −0.269672 0.195928i
\(226\) 38.3926 + 27.8938i 2.55384 + 1.85547i
\(227\) −7.82237 + 24.0748i −0.519189 + 1.59790i 0.256340 + 0.966587i \(0.417483\pi\)
−0.775529 + 0.631312i \(0.782517\pi\)
\(228\) 0 0
\(229\) −1.06281 + 0.772178i −0.0702326 + 0.0510270i −0.622348 0.782741i \(-0.713821\pi\)
0.552115 + 0.833768i \(0.313821\pi\)
\(230\) −6.82843 −0.450253
\(231\) 0 0
\(232\) −16.1421 −1.05978
\(233\) −4.96909 + 3.61026i −0.325536 + 0.236516i −0.738534 0.674216i \(-0.764482\pi\)
0.412998 + 0.910732i \(0.364482\pi\)
\(234\) −4.37016 13.4500i −0.285686 0.879252i
\(235\) −0.874032 + 2.68999i −0.0570156 + 0.175476i
\(236\) −5.13171 3.72841i −0.334046 0.242699i
\(237\) −9.15298 6.65003i −0.594550 0.431966i
\(238\) 10.1885 31.3569i 0.660420 2.03256i
\(239\) 7.20433 + 22.1727i 0.466010 + 1.43423i 0.857708 + 0.514136i \(0.171887\pi\)
−0.391699 + 0.920093i \(0.628113\pi\)
\(240\) −6.86474 + 4.98752i −0.443117 + 0.321943i
\(241\) −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
\(244\) −28.8470 + 20.9586i −1.84674 + 1.34174i
\(245\) 0.927051 + 2.85317i 0.0592271 + 0.182282i
\(246\) −12.6606 + 38.9653i −0.807210 + 2.48434i
\(247\) 0 0
\(248\) 0 0
\(249\) −5.24419 + 16.1400i −0.332337 + 1.02283i
\(250\) 0.746033 + 2.29605i 0.0471833 + 0.145215i
\(251\) −9.70820 + 7.05342i −0.612776 + 0.445208i −0.850391 0.526151i \(-0.823635\pi\)
0.237614 + 0.971360i \(0.423635\pi\)
\(252\) 38.2843 2.41168
\(253\) 0 0
\(254\) 10.4853 0.657905
\(255\) 15.6251 11.3523i 0.978483 0.710909i
\(256\) −9.26141 28.5037i −0.578838 1.78148i
\(257\) −2.87809 + 8.85786i −0.179531 + 0.552538i −0.999811 0.0194227i \(-0.993817\pi\)
0.820281 + 0.571961i \(0.193817\pi\)
\(258\) −33.1459 24.0819i −2.06357 1.49927i
\(259\) 12.3891 + 9.00117i 0.769818 + 0.559306i
\(260\) −1.38603 + 4.26576i −0.0859578 + 0.264551i
\(261\) 5.65015 + 17.3894i 0.349736 + 1.07638i
\(262\) 22.0973 16.0546i 1.36517 0.991856i
\(263\) 10.9706 0.676474 0.338237 0.941061i \(-0.390169\pi\)
0.338237 + 0.941061i \(0.390169\pi\)
\(264\) 0 0
\(265\) −11.6569 −0.716075
\(266\) 0 0
\(267\) 11.6366 + 35.8138i 0.712149 + 2.19177i
\(268\) 14.7707 45.4595i 0.902264 2.77688i
\(269\) −14.0071 10.1767i −0.854027 0.620487i 0.0722264 0.997388i \(-0.476990\pi\)
−0.926253 + 0.376901i \(0.876990\pi\)
\(270\) 11.0486 + 8.02730i 0.672398 + 0.488526i
\(271\) −2.26006 + 6.95575i −0.137289 + 0.422532i −0.995939 0.0900304i \(-0.971304\pi\)
0.858650 + 0.512562i \(0.171304\pi\)
\(272\) −6.33030 19.4827i −0.383831 1.18131i
\(273\) 5.36169 3.89550i 0.324504 0.235766i
\(274\) 26.4853 1.60003
\(275\) 0 0
\(276\) 30.6274 1.84355
\(277\) 5.52431 4.01365i 0.331924 0.241157i −0.409323 0.912390i \(-0.634235\pi\)
0.741247 + 0.671233i \(0.234235\pi\)
\(278\) −2.98413 9.18421i −0.178976 0.550833i
\(279\) 0 0
\(280\) −7.14235 5.18922i −0.426837 0.310115i
\(281\) 14.0071 + 10.1767i 0.835593 + 0.607094i 0.921136 0.389241i \(-0.127263\pi\)
−0.0855434 + 0.996334i \(0.527263\pi\)
\(282\) 5.96826 18.3684i 0.355405 1.09382i
\(283\) −10.0824 31.0305i −0.599338 1.84457i −0.531825 0.846854i \(-0.678493\pi\)
−0.0675133 0.997718i \(-0.521507\pi\)
\(284\) −35.0415 + 25.4592i −2.07933 + 1.51072i
\(285\) 0 0
\(286\) 0 0
\(287\) −12.0000 −0.708338
\(288\) −6.41464 + 4.66051i −0.377986 + 0.274623i
\(289\) 9.15538 + 28.1773i 0.538551 + 1.65749i
\(290\) 2.72813 8.39633i 0.160202 0.493050i
\(291\) 8.36778 + 6.07955i 0.490528 + 0.356389i
\(292\) −3.62867 2.63638i −0.212352 0.154283i
\(293\) 2.83417 8.72268i 0.165574 0.509585i −0.833504 0.552513i \(-0.813669\pi\)
0.999078 + 0.0429287i \(0.0136688\pi\)
\(294\) −6.33030 19.4827i −0.369191 1.13625i
\(295\) 1.34042 0.973874i 0.0780425 0.0567012i
\(296\) 33.7990 1.96453
\(297\) 0 0
\(298\) 0.828427 0.0479895
\(299\) 2.68085 1.94775i 0.155037 0.112641i
\(300\) −3.34617 10.2984i −0.193191 0.594581i
\(301\) 3.70820 11.4127i 0.213737 0.657816i
\(302\) 23.4377 + 17.0285i 1.34869 + 0.979878i
\(303\) −21.3121 15.4841i −1.22435 0.889539i
\(304\) 0 0
\(305\) −2.87809 8.85786i −0.164799 0.507200i
\(306\) −66.6844 + 48.4490i −3.81209 + 2.76965i
\(307\) 16.3431 0.932753 0.466376 0.884586i \(-0.345559\pi\)
0.466376 + 0.884586i \(0.345559\pi\)
\(308\) 0 0
\(309\) −19.3137 −1.09872
\(310\) 0 0
\(311\) 1.44814 + 4.45693i 0.0821167 + 0.252729i 0.983683 0.179913i \(-0.0575815\pi\)
−0.901566 + 0.432642i \(0.857581\pi\)
\(312\) 4.52012 13.9115i 0.255901 0.787584i
\(313\) 1.06281 + 0.772178i 0.0600737 + 0.0436461i 0.617417 0.786636i \(-0.288179\pi\)
−0.557343 + 0.830282i \(0.688179\pi\)
\(314\) −27.3440 19.8665i −1.54311 1.12113i
\(315\) −3.09017 + 9.51057i −0.174111 + 0.535860i
\(316\) −4.73220 14.5642i −0.266207 0.819300i
\(317\) 1.06281 0.772178i 0.0596935 0.0433699i −0.557538 0.830151i \(-0.688254\pi\)
0.617232 + 0.786781i \(0.288254\pi\)
\(318\) 79.5980 4.46363
\(319\) 0 0
\(320\) 9.82843 0.549426
\(321\) −17.5208 + 12.7296i −0.977914 + 0.710496i
\(322\) 4.22020 + 12.9884i 0.235183 + 0.723817i
\(323\) 0 0
\(324\) −3.09726 2.25029i −0.172070 0.125016i
\(325\) −0.947822 0.688633i −0.0525757 0.0381985i
\(326\) −12.2986 + 37.8511i −0.681154 + 2.09638i
\(327\) −6.69234 20.5969i −0.370087 1.13901i
\(328\) −21.4270 + 15.5677i −1.18311 + 0.859580i
\(329\) 5.65685 0.311872
\(330\) 0 0
\(331\) −7.31371 −0.401998 −0.200999 0.979591i \(-0.564419\pi\)
−0.200999 + 0.979591i \(0.564419\pi\)
\(332\) −18.5836 + 13.5018i −1.01991 + 0.741005i
\(333\) −11.8305 36.4105i −0.648307 1.99528i
\(334\) −17.1368 + 52.7416i −0.937684 + 2.88589i
\(335\) 10.1008 + 7.33866i 0.551866 + 0.400954i
\(336\) 13.7295 + 9.97505i 0.749004 + 0.544183i
\(337\) 6.33030 19.4827i 0.344833 1.06129i −0.616840 0.787089i \(-0.711587\pi\)
0.961673 0.274199i \(-0.0884128\pi\)
\(338\) 8.67444 + 26.6972i 0.471827 + 1.45213i
\(339\) 44.9797 32.6797i 2.44296 1.77492i
\(340\) 26.1421 1.41776
\(341\) 0 0
\(342\) 0 0
\(343\) 16.1803 11.7557i 0.873656 0.634748i
\(344\) −8.18440 25.1890i −0.441273 1.35810i
\(345\) −2.47214 + 7.60845i −0.133095 + 0.409625i
\(346\) 43.2467 + 31.4206i 2.32496 + 1.68918i
\(347\) 8.87537 + 6.44833i 0.476455 + 0.346165i 0.799952 0.600065i \(-0.204858\pi\)
−0.323497 + 0.946229i \(0.604858\pi\)
\(348\) −12.2364 + 37.6599i −0.655943 + 2.01878i
\(349\) −8.33436 25.6505i −0.446128 1.37304i −0.881242 0.472666i \(-0.843292\pi\)
0.435114 0.900376i \(-0.356708\pi\)
\(350\) 3.90628 2.83808i 0.208799 0.151702i
\(351\) −6.62742 −0.353745
\(352\) 0 0
\(353\) 21.3137 1.13441 0.567207 0.823575i \(-0.308024\pi\)
0.567207 + 0.823575i \(0.308024\pi\)
\(354\) −9.15298 + 6.65003i −0.486476 + 0.353445i
\(355\) −3.49613 10.7600i −0.185555 0.571080i
\(356\) −15.7508 + 48.4759i −0.834789 + 2.56922i
\(357\) −31.2502 22.7046i −1.65394 1.20166i
\(358\) 18.8612 + 13.7035i 0.996845 + 0.724250i
\(359\) −0.212076 + 0.652702i −0.0111929 + 0.0344483i −0.956497 0.291742i \(-0.905765\pi\)
0.945304 + 0.326190i \(0.105765\pi\)
\(360\) 6.82034 + 20.9908i 0.359463 + 1.10631i
\(361\) 15.3713 11.1679i 0.809017 0.587785i
\(362\) −51.4558 −2.70446
\(363\) 0 0
\(364\) 8.97056 0.470185
\(365\) 0.947822 0.688633i 0.0496113 0.0360447i
\(366\) 19.6529 + 60.4853i 1.02727 + 3.16162i
\(367\) −2.62210 + 8.06998i −0.136872 + 0.421250i −0.995877 0.0907188i \(-0.971084\pi\)
0.859004 + 0.511968i \(0.171084\pi\)
\(368\) 6.86474 + 4.98752i 0.357849 + 0.259993i
\(369\) 24.2705 + 17.6336i 1.26347 + 0.917966i
\(370\) −5.71227 + 17.5805i −0.296967 + 0.913969i
\(371\) 7.20433 + 22.1727i 0.374030 + 1.15115i
\(372\) 0 0
\(373\) −35.7990 −1.85360 −0.926801 0.375554i \(-0.877453\pi\)
−0.926801 + 0.375554i \(0.877453\pi\)
\(374\) 0 0
\(375\) 2.82843 0.146059
\(376\) 10.1008 7.33866i 0.520909 0.378463i
\(377\) 1.32391 + 4.07458i 0.0681850 + 0.209852i
\(378\) 8.44040 25.9769i 0.434127 1.33611i
\(379\) −27.2290 19.7830i −1.39866 1.01618i −0.994852 0.101340i \(-0.967687\pi\)
−0.403806 0.914845i \(-0.632313\pi\)
\(380\) 0 0
\(381\) 3.79605 11.6830i 0.194477 0.598540i
\(382\) −2.47214 7.60845i −0.126485 0.389282i
\(383\) 4.73911 3.44317i 0.242157 0.175938i −0.460087 0.887874i \(-0.652182\pi\)
0.702244 + 0.711936i \(0.252182\pi\)
\(384\) −58.1421 −2.96705
\(385\) 0 0
\(386\) −2.82843 −0.143963
\(387\) −24.2705 + 17.6336i −1.23374 + 0.896364i
\(388\) 4.32624 + 13.3148i 0.219631 + 0.675956i
\(389\) 6.37422 19.6178i 0.323186 0.994664i −0.649067 0.760731i \(-0.724840\pi\)
0.972253 0.233933i \(-0.0751595\pi\)
\(390\) 6.47214 + 4.70228i 0.327729 + 0.238109i
\(391\) −15.6251 11.3523i −0.790196 0.574111i
\(392\) 4.09220 12.5945i 0.206687 0.636118i
\(393\) −9.88854 30.4338i −0.498811 1.53518i
\(394\) 21.1494 15.3660i 1.06549 0.774126i
\(395\) 4.00000 0.201262
\(396\) 0 0
\(397\) −9.31371 −0.467442 −0.233721 0.972304i \(-0.575090\pi\)
−0.233721 + 0.972304i \(0.575090\pi\)
\(398\) 20.2016 14.6773i 1.01262 0.735708i
\(399\) 0 0
\(400\) 0.927051 2.85317i 0.0463525 0.142658i
\(401\) 4.29888 + 3.12332i 0.214676 + 0.155971i 0.689927 0.723879i \(-0.257643\pi\)
−0.475251 + 0.879850i \(0.657643\pi\)
\(402\) −68.9726 50.1115i −3.44004 2.49934i
\(403\) 0 0
\(404\) −11.0186 33.9117i −0.548195 1.68717i
\(405\) 0.809017 0.587785i 0.0402004 0.0292073i
\(406\) −17.6569 −0.876295
\(407\) 0 0
\(408\) −85.2548 −4.22074
\(409\) 0.832832 0.605088i 0.0411809 0.0299197i −0.567004 0.823715i \(-0.691898\pi\)
0.608185 + 0.793795i \(0.291898\pi\)
\(410\) −4.47620 13.7763i −0.221064 0.680364i
\(411\) 9.58862 29.5107i 0.472972 1.45566i
\(412\) −21.1494 15.3660i −1.04196 0.757027i
\(413\) −2.68085 1.94775i −0.131916 0.0958425i
\(414\) 10.5505 32.4711i 0.518529 1.59587i
\(415\) −1.85410 5.70634i −0.0910143 0.280113i
\(416\) −1.50304 + 1.09203i −0.0736928 + 0.0535409i
\(417\) −11.3137 −0.554035
\(418\) 0 0
\(419\) −25.6569 −1.25342 −0.626710 0.779253i \(-0.715599\pi\)
−0.626710 + 0.779253i \(0.715599\pi\)
\(420\) −17.5208 + 12.7296i −0.854926 + 0.621140i
\(421\) −1.85410 5.70634i −0.0903634 0.278110i 0.895654 0.444751i \(-0.146708\pi\)
−0.986018 + 0.166641i \(0.946708\pi\)
\(422\) −11.9365 + 36.7369i −0.581061 + 1.78832i
\(423\) −11.4412 8.31254i −0.556292 0.404169i
\(424\) 41.6287 + 30.2450i 2.02167 + 1.46883i
\(425\) −2.11010 + 6.49422i −0.102355 + 0.315016i
\(426\) 23.8731 + 73.4737i 1.15665 + 3.55981i
\(427\) −15.0699 + 10.9489i −0.729283 + 0.529855i
\(428\) −29.3137 −1.41693
\(429\) 0 0
\(430\) 14.4853 0.698542
\(431\) −9.15298 + 6.65003i −0.440884 + 0.320321i −0.785986 0.618244i \(-0.787844\pi\)
0.345102 + 0.938565i \(0.387844\pi\)
\(432\) −5.24419 16.1400i −0.252311 0.776534i
\(433\) −2.36610 + 7.28210i −0.113707 + 0.349955i −0.991675 0.128764i \(-0.958899\pi\)
0.877968 + 0.478720i \(0.158899\pi\)
\(434\) 0 0
\(435\) −8.36778 6.07955i −0.401204 0.291492i
\(436\) 9.05843 27.8790i 0.433820 1.33516i
\(437\) 0 0
\(438\) −6.47214 + 4.70228i −0.309251 + 0.224684i
\(439\) 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
\(442\) −15.6251 + 11.3523i −0.743211 + 0.539974i
\(443\) −8.29044 25.5154i −0.393891 1.21227i −0.929822 0.368009i \(-0.880039\pi\)
0.535931 0.844262i \(-0.319961\pi\)
\(444\) 25.6211 78.8537i 1.21592 3.74223i
\(445\) −10.7710 7.82560i −0.510595 0.370969i
\(446\) −21.1494 15.3660i −1.00145 0.727599i
\(447\) 0.299920 0.923060i 0.0141857 0.0436592i
\(448\) −6.07430 18.6948i −0.286984 0.883245i
\(449\) −23.1601 + 16.8268i −1.09299 + 0.794105i −0.979902 0.199480i \(-0.936075\pi\)
−0.113089 + 0.993585i \(0.536075\pi\)
\(450\) −12.0711 −0.569036
\(451\) 0 0
\(452\) 75.2548 3.53969
\(453\) 27.4589 19.9501i 1.29013 0.937337i
\(454\) 18.8849 + 58.1216i 0.886311 + 2.72778i
\(455\) −0.724072 + 2.22846i −0.0339450 + 0.104472i
\(456\) 0 0
\(457\) 0.392601 + 0.285241i 0.0183651 + 0.0133430i 0.596930 0.802293i \(-0.296387\pi\)
−0.578565 + 0.815636i \(0.696387\pi\)
\(458\) −0.980070 + 3.01635i −0.0457957 + 0.140945i
\(459\) 11.9365 + 36.7369i 0.557149 + 1.71473i
\(460\) −8.76038 + 6.36479i −0.408455 + 0.296760i
\(461\) −12.6274 −0.588117 −0.294059 0.955787i \(-0.595006\pi\)
−0.294059 + 0.955787i \(0.595006\pi\)
\(462\) 0 0
\(463\) −6.14214 −0.285449 −0.142725 0.989762i \(-0.545586\pi\)
−0.142725 + 0.989762i \(0.545586\pi\)
\(464\) −8.87537 + 6.44833i −0.412029 + 0.299356i
\(465\) 0 0
\(466\) −4.58224 + 14.1027i −0.212268 + 0.653294i
\(467\) 11.9964 + 8.71593i 0.555129 + 0.403325i 0.829673 0.558249i \(-0.188527\pi\)
−0.274544 + 0.961575i \(0.588527\pi\)
\(468\) −18.1433 13.1819i −0.838676 0.609334i
\(469\) 7.71633 23.7484i 0.356307 1.09660i
\(470\) 2.11010 + 6.49422i 0.0973317 + 0.299556i
\(471\) −32.0354 + 23.2751i −1.47612 + 1.07246i
\(472\) −7.31371 −0.336641
\(473\) 0 0
\(474\) −27.3137 −1.25456
\(475\) 0 0
\(476\) −16.1567 49.7253i −0.740542 2.27916i
\(477\) 18.0108 55.4316i 0.824659 2.53804i
\(478\) 45.5349 + 33.0831i 2.08272 + 1.51318i
\(479\) −29.1246 21.1603i −1.33074 0.966837i −0.999731 0.0232090i \(-0.992612\pi\)
−0.331007 0.943628i \(-0.607388\pi\)
\(480\) 1.38603 4.26576i 0.0632632 0.194704i
\(481\) −2.77206 8.53151i −0.126395 0.389003i
\(482\) −11.7188 + 8.51423i −0.533778 + 0.387813i
\(483\) 16.0000 0.728025
\(484\) 0 0
\(485\) −3.65685 −0.166049
\(486\) 27.6216 20.0682i 1.25294 0.910314i
\(487\) −7.56637 23.2869i −0.342865 1.05523i −0.962717 0.270511i \(-0.912807\pi\)
0.619852 0.784719i \(-0.287193\pi\)
\(488\) −12.7045 + 39.1005i −0.575107 + 1.77000i
\(489\) 37.7224 + 27.4069i 1.70586 + 1.23938i
\(490\) 5.85942 + 4.25712i 0.264702 + 0.192317i
\(491\) 0.212076 0.652702i 0.00957084 0.0294560i −0.946157 0.323708i \(-0.895070\pi\)
0.955728 + 0.294252i \(0.0950705\pi\)
\(492\) 20.0770 + 61.7907i 0.905141 + 2.78574i
\(493\) 20.2016 14.6773i 0.909835 0.661034i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −18.3060 + 13.3001i −0.821135 + 0.596589i
\(498\) 12.6606 + 38.9653i 0.567335 + 1.74608i
\(499\) 2.98413 9.18421i 0.133588 0.411142i −0.861780 0.507283i \(-0.830650\pi\)
0.995368 + 0.0961409i \(0.0306500\pi\)
\(500\) 3.09726 + 2.25029i 0.138514 + 0.100636i
\(501\) 52.5623 + 38.1887i 2.34831 + 1.70615i
\(502\) −8.95240 + 27.5526i −0.399565 + 1.22973i
\(503\) −5.13815 15.8136i −0.229099 0.705094i −0.997850 0.0655455i \(-0.979121\pi\)
0.768751 0.639549i \(-0.220879\pi\)
\(504\) 35.7117 25.9461i 1.59073 1.15573i
\(505\) 9.31371 0.414455
\(506\) 0 0
\(507\) 32.8873 1.46058
\(508\) 13.4519 9.77335i 0.596830 0.433622i
\(509\) −4.11416 12.6621i −0.182357 0.561237i 0.817536 0.575878i \(-0.195340\pi\)
−0.999893 + 0.0146406i \(0.995340\pi\)
\(510\) 14.4087 44.3453i 0.638026 1.96364i
\(511\) −1.89564 1.37727i −0.0838584 0.0609267i
\(512\) −25.2758 18.3640i −1.11704 0.811580i
\(513\) 0 0
\(514\) 6.94833 + 21.3848i 0.306478 + 0.943242i
\(515\) 5.52431 4.01365i 0.243430 0.176862i
\(516\) −64.9706 −2.86017
\(517\) 0 0
\(518\) 36.9706 1.62439
\(519\) 50.6666 36.8115i 2.22402 1.61584i
\(520\) 1.59810 + 4.91846i 0.0700815 + 0.215689i
\(521\) 7.82237 24.0748i 0.342704 1.05473i −0.620097 0.784525i \(-0.712907\pi\)
0.962801 0.270210i \(-0.0870931\pi\)
\(522\) 35.7117 + 25.9461i 1.56306 + 1.13563i
\(523\) −33.6535 24.4507i −1.47156 1.06915i −0.980157 0.198223i \(-0.936483\pi\)
−0.491407 0.870930i \(-0.663517\pi\)
\(524\) 13.3847 41.1938i 0.584712 1.79956i
\(525\) −1.74806 5.37999i −0.0762918 0.234802i
\(526\) 21.4270 15.5677i 0.934263 0.678782i
\(527\) 0 0
\(528\) 0 0
\(529\) −15.0000 −0.652174
\(530\) −22.7675 + 16.5415i −0.988956 + 0.718518i
\(531\) 2.55998 + 7.87881i 0.111094 + 0.341911i
\(532\) 0 0
\(533\) 5.68693 + 4.13180i 0.246328 + 0.178968i
\(534\) 73.5491 + 53.4365i 3.18278 + 2.31243i
\(535\) 2.36610 7.28210i 0.102295 0.314833i
\(536\) −17.0308 52.4153i −0.735617 2.26400i
\(537\) 22.0973 16.0546i 0.953567 0.692807i
\(538\) −41.7990 −1.80208
\(539\) 0 0
\(540\) 21.6569 0.931963
\(541\) 4.85410 3.52671i 0.208694 0.151625i −0.478529 0.878072i \(-0.658830\pi\)
0.687223 + 0.726447i \(0.258830\pi\)
\(542\) 5.45627 + 16.7927i 0.234367 + 0.721307i
\(543\) −18.6289 + 57.3337i −0.799441 + 2.46043i
\(544\) 8.76038 + 6.36479i 0.375598 + 0.272888i
\(545\) 6.19453 + 4.50059i 0.265344 + 0.192784i
\(546\) 4.94427 15.2169i 0.211595 0.651223i
\(547\) 10.5066 + 32.3359i 0.449229 + 1.38258i 0.877779 + 0.479066i \(0.159025\pi\)
−0.428550 + 0.903518i \(0.640975\pi\)
\(548\) 33.9787 24.6870i 1.45150 1.05458i
\(549\) 46.5685 1.98750
\(550\) 0 0
\(551\) 0 0
\(552\) 28.5694 20.7569i 1.21599 0.883471i
\(553\) −2.47214 7.60845i −0.105126 0.323544i
\(554\) 5.09423 15.6784i 0.216433 0.666113i
\(555\) 17.5208 + 12.7296i 0.743715 + 0.540341i
\(556\) −12.3891 9.00117i −0.525413 0.381735i
\(557\) −3.04625 + 9.37539i −0.129074 + 0.397248i −0.994621 0.103579i \(-0.966971\pi\)
0.865548 + 0.500827i \(0.166971\pi\)
\(558\) 0 0
\(559\) −5.68693 + 4.13180i −0.240532 + 0.174757i
\(560\) −6.00000 −0.253546
\(561\) 0 0
\(562\) 41.7990 1.76318
\(563\) 0.277611 0.201696i 0.0116999 0.00850047i −0.581920 0.813246i \(-0.697698\pi\)
0.593620 + 0.804746i \(0.297698\pi\)
\(564\) −9.46439 29.1284i −0.398523 1.22653i
\(565\) −6.07430 + 18.6948i −0.255548 + 0.786495i
\(566\) −63.7259 46.2996i −2.67860 1.94612i
\(567\) −1.61803 1.17557i −0.0679510 0.0493693i
\(568\) −15.4327 + 47.4968i −0.647540 + 1.99292i
\(569\) −9.78251 30.1075i −0.410104 1.26217i −0.916557 0.399903i \(-0.869044\pi\)
0.506453 0.862267i \(-0.330956\pi\)
\(570\) 0 0
\(571\) 21.9411 0.918208 0.459104 0.888383i \(-0.348171\pi\)
0.459104 + 0.888383i \(0.348171\pi\)
\(572\) 0 0
\(573\) −9.37258 −0.391545
\(574\) −23.4377 + 17.0285i −0.978270 + 0.710755i
\(575\) −0.874032 2.68999i −0.0364497 0.112181i
\(576\) −15.1858 + 46.7369i −0.632740 + 1.94737i
\(577\) 21.8196 + 15.8529i 0.908364 + 0.659965i 0.940600 0.339515i \(-0.110263\pi\)
−0.0322368 + 0.999480i \(0.510263\pi\)
\(578\) 57.8665 + 42.0425i 2.40693 + 1.74874i
\(579\) −1.02399 + 3.15152i −0.0425557 + 0.130973i
\(580\) −4.32624 13.3148i −0.179637 0.552867i
\(581\) −9.70820 + 7.05342i −0.402764 + 0.292625i
\(582\) 24.9706 1.03506
\(583\) 0 0
\(584\) −5.17157 −0.214001
\(585\) 4.73911 3.44317i 0.195938 0.142357i
\(586\) −6.84230 21.0584i −0.282653 0.869915i
\(587\) −0.661956 + 2.03729i −0.0273219 + 0.0840880i −0.963788 0.266671i \(-0.914076\pi\)
0.936466 + 0.350759i \(0.114076\pi\)
\(588\) −26.2811 19.0944i −1.08382 0.787439i
\(589\) 0 0
\(590\) 1.23607 3.80423i 0.0508881 0.156618i
\(591\) −9.46439 29.1284i −0.389313 1.19818i
\(592\) 18.5836 13.5018i 0.763780 0.554919i
\(593\) −3.51472 −0.144332 −0.0721661 0.997393i \(-0.522991\pi\)
−0.0721661 + 0.997393i \(0.522991\pi\)
\(594\) 0 0
\(595\) 13.6569 0.559876
\(596\) 1.06281 0.772178i 0.0435345 0.0316297i
\(597\) −9.04024 27.8230i −0.369992 1.13872i
\(598\) 2.47214 7.60845i 0.101093 0.311133i
\(599\) 4.57649 + 3.32502i 0.186990 + 0.135856i 0.677342 0.735668i \(-0.263132\pi\)
−0.490352 + 0.871525i \(0.663132\pi\)
\(600\) −10.1008 7.33866i −0.412364 0.299600i
\(601\) −7.39821 + 22.7694i −0.301779 + 0.928782i 0.679080 + 0.734064i \(0.262379\pi\)
−0.980859 + 0.194717i \(0.937621\pi\)
\(602\) −8.95240 27.5526i −0.364872 1.12296i
\(603\) −50.5040 + 36.6933i −2.05668 + 1.49427i
\(604\) 45.9411 1.86932
\(605\) 0 0
\(606\) −63.5980 −2.58349
\(607\) 30.9726 22.5029i 1.25714 0.913366i 0.258526 0.966004i \(-0.416763\pi\)
0.998614 + 0.0526384i \(0.0167631\pi\)
\(608\) 0 0
\(609\) −6.39242 + 19.6738i −0.259034 + 0.797224i
\(610\) −18.1910 13.2165i −0.736531 0.535121i
\(611\) −2.68085 1.94775i −0.108455 0.0787975i
\(612\) −40.3918 + 124.313i −1.63274 + 5.02506i
\(613\) 7.86629 + 24.2099i 0.317716 + 0.977831i 0.974622 + 0.223858i \(0.0718650\pi\)
−0.656905 + 0.753973i \(0.728135\pi\)
\(614\) 31.9204 23.1916i 1.28820 0.935935i
\(615\) −16.9706 −0.684319
\(616\) 0 0
\(617\) 0.343146 0.0138145 0.00690726 0.999976i \(-0.497801\pi\)
0.00690726 + 0.999976i \(0.497801\pi\)
\(618\) −37.7224 + 27.4069i −1.51742 + 1.10247i
\(619\) −4.43228 13.6411i −0.178148 0.548284i 0.821615 0.570043i \(-0.193073\pi\)
−0.999763 + 0.0217589i \(0.993073\pi\)
\(620\) 0 0
\(621\) −12.9443 9.40456i −0.519436 0.377392i
\(622\) 9.15298 + 6.65003i 0.367001 + 0.266642i
\(623\) −8.22832 + 25.3242i −0.329661 + 1.01459i
\(624\) −3.07198 9.45457i −0.122977 0.378486i
\(625\) −0.809017 + 0.587785i −0.0323607 + 0.0235114i
\(626\) 3.17157 0.126762
\(627\) 0 0
\(628\) −53.5980 −2.13879
\(629\) −42.2989 + 30.7319i −1.68657 + 1.22536i
\(630\) 7.46033 + 22.9605i 0.297227 + 0.914770i
\(631\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(632\) −14.2847 10.3784i −0.568215 0.412832i
\(633\) 36.6119 + 26.6001i 1.45519 + 1.05726i
\(634\) 0.980070 3.01635i 0.0389235 0.119794i
\(635\) 1.34211 + 4.13058i 0.0532598 + 0.163917i
\(636\) 102.118 74.1934i 4.04926 2.94196i
\(637\) −3.51472 −0.139258
\(638\) 0 0
\(639\) 56.5685 2.23782
\(640\) 16.6304 12.0827i 0.657376 0.477611i
\(641\) 9.27051 + 28.5317i 0.366163 + 1.12693i 0.949250 + 0.314524i \(0.101845\pi\)
−0.583086 + 0.812410i \(0.698155\pi\)
\(642\) −16.1567 + 49.7253i −0.637655 + 1.96250i
\(643\) 1.17780 + 0.855724i 0.0464480 + 0.0337464i 0.610767 0.791810i \(-0.290861\pi\)
−0.564319 + 0.825557i \(0.690861\pi\)
\(644\) 17.5208 + 12.7296i 0.690415 + 0.501616i
\(645\) 5.24419 16.1400i 0.206490 0.635510i
\(646\) 0 0
\(647\) −21.9346 + 15.9364i −0.862339 + 0.626526i −0.928520 0.371281i \(-0.878919\pi\)
0.0661810 + 0.997808i \(0.478919\pi\)
\(648\) −4.41421 −0.173407
\(649\) 0 0
\(650\) −2.82843 −0.110940
\(651\) 0 0
\(652\) 19.5029 + 60.0237i 0.763792 + 2.35071i
\(653\) 3.60217 11.0863i 0.140964 0.433842i −0.855506 0.517793i \(-0.826754\pi\)
0.996470 + 0.0839510i \(0.0267539\pi\)
\(654\) −42.2989 30.7319i −1.65402 1.20171i
\(655\) 9.15298 + 6.65003i 0.357637 + 0.259838i
\(656\) −5.56231 + 17.1190i −0.217172 + 0.668385i
\(657\) 1.81018 + 5.57116i 0.0706218 + 0.217352i
\(658\) 11.0486 8.02730i 0.430720 0.312937i
\(659\) −45.9411 −1.78961 −0.894806 0.446455i \(-0.852686\pi\)
−0.894806 + 0.446455i \(0.852686\pi\)
\(660\) 0 0
\(661\) 44.6274 1.73581 0.867903 0.496734i \(-0.165468\pi\)
0.867903 + 0.496734i \(0.165468\pi\)
\(662\) −14.2847 + 10.3784i −0.555190 + 0.403369i
\(663\) 6.99226 + 21.5200i 0.271557 + 0.835766i
\(664\) −8.18440 + 25.1890i −0.317616 + 0.977523i
\(665\) 0 0
\(666\) −74.7745 54.3269i −2.89745 2.10512i
\(667\) −3.19621 + 9.83692i −0.123758 + 0.380887i
\(668\) 27.1753 + 83.6370i 1.05144 + 3.23601i
\(669\) −24.7781 + 18.0023i −0.957977 + 0.696011i
\(670\) 30.1421 1.16449
\(671\) 0 0
\(672\) −8.97056 −0.346047
\(673\) −10.1008 + 7.33866i −0.389357 + 0.282885i −0.765192 0.643802i \(-0.777356\pi\)
0.375835 + 0.926687i \(0.377356\pi\)
\(674\) −15.2827 47.0353i −0.588667 1.81173i
\(675\) −1.74806 + 5.37999i −0.0672830 + 0.207076i
\(676\) 36.0132 + 26.1651i 1.38512 + 1.00635i
\(677\) 18.4686 + 13.4182i 0.709805 + 0.515704i 0.883111 0.469164i \(-0.155445\pi\)
−0.173305 + 0.984868i \(0.555445\pi\)
\(678\) 41.4779 127.656i 1.59295 4.90260i
\(679\) 2.26006 + 6.95575i 0.0867332 + 0.266937i
\(680\) 24.3855 17.7171i 0.935141 0.679420i
\(681\) 71.5980 2.74364
\(682\) 0 0
\(683\) −7.79899 −0.298420 −0.149210 0.988806i \(-0.547673\pi\)
−0.149210 + 0.988806i \(0.547673\pi\)
\(684\) 0 0
\(685\) 3.39009 + 10.4336i 0.129529 + 0.398648i
\(686\) 14.9207 45.9211i 0.569673 1.75327i
\(687\) 3.00609 + 2.18405i 0.114689 + 0.0833267i
\(688\) −14.5623 10.5801i −0.555183 0.403364i
\(689\) 4.22020 12.9884i 0.160777 0.494820i
\(690\) 5.96826 + 18.3684i 0.227208 + 0.699274i
\(691\) 31.8055 23.1080i 1.20994 0.879070i 0.214712 0.976677i \(-0.431119\pi\)
0.995225 + 0.0976071i \(0.0311188\pi\)
\(692\) 84.7696 3.22245
\(693\) 0 0
\(694\) 26.4853 1.00537
\(695\) 3.23607 2.35114i 0.122751 0.0891839i
\(696\) 14.1087 + 43.4222i 0.534791 + 1.64592i
\(697\) 12.6606 38.9653i 0.479554 1.47592i
\(698\) −52.6773 38.2723i −1.99386 1.44863i
\(699\) 14.0547 + 10.2113i 0.531598 + 0.386229i
\(700\) 2.36610 7.28210i 0.0894301 0.275238i
\(701\) 3.90209 + 12.0094i 0.147380 + 0.453588i 0.997309 0.0733080i \(-0.0233556\pi\)
−0.849930 + 0.526896i \(0.823356\pi\)
\(702\) −12.9443 + 9.40456i −0.488550 + 0.354952i
\(703\) 0 0
\(704\) 0 0
\(705\) 8.00000 0.301297
\(706\) 41.6287 30.2450i 1.56671 1.13829i
\(707\) −5.75619 17.7157i −0.216484 0.666268i
\(708\) −5.54411 + 17.0630i −0.208361 + 0.641268i
\(709\) −19.9240 14.4756i −0.748261 0.543644i 0.147026 0.989133i \(-0.453030\pi\)
−0.895287 + 0.445489i \(0.853030\pi\)
\(710\) −22.0973 16.0546i −0.829295 0.602518i
\(711\) −6.18034 + 19.0211i −0.231781 + 0.713348i
\(712\) 18.1608 + 55.8932i 0.680604 + 2.09468i
\(713\) 0 0
\(714\) −93.2548 −3.48997
\(715\) 0 0
\(716\) 36.9706 1.38165
\(717\) 53.3475 38.7592i 1.99230 1.44749i
\(718\) 0.511996 + 1.57576i 0.0191075 + 0.0588069i
\(719\) 5.66834 17.4454i 0.211394 0.650602i −0.787996 0.615680i \(-0.788882\pi\)
0.999390 0.0349227i \(-0.0111185\pi\)
\(720\) 12.1353 + 8.81678i 0.452254 + 0.328582i
\(721\) −11.0486 8.02730i −0.411472 0.298952i
\(722\) 14.1746 43.6250i 0.527525 1.62356i
\(723\) 5.24419 + 16.1400i 0.195034 + 0.600252i
\(724\) −66.0142 + 47.9621i −2.45340 + 1.78250i
\(725\) 3.65685 0.135812
\(726\) 0 0
\(727\) −19.5147 −0.723761 −0.361880 0.932225i \(-0.617865\pi\)
−0.361880 + 0.932225i \(0.617865\pi\)
\(728\) 8.36778 6.07955i 0.310131 0.225323i
\(729\) −13.2877 40.8954i −0.492138 1.51465i
\(730\) 0.874032 2.68999i 0.0323494 0.0995611i
\(731\) 33.1459 + 24.0819i 1.22594 + 0.890701i
\(732\) 81.5916 + 59.2798i 3.01571 + 2.19104i
\(733\) 5.39415 16.6015i 0.199238 0.613190i −0.800663 0.599114i \(-0.795519\pi\)
0.999901 0.0140757i \(-0.00448058\pi\)
\(734\) 6.33030 + 19.4827i 0.233656 + 0.719118i
\(735\) 6.86474 4.98752i 0.253210 0.183968i
\(736\) −4.48528 −0.165330
\(737\) 0 0
\(738\) 72.4264 2.66605
\(739\) 24.2229 17.5990i 0.891053 0.647388i −0.0450993 0.998983i \(-0.514360\pi\)
0.936152 + 0.351595i \(0.114360\pi\)
\(740\) 9.05843 + 27.8790i 0.332995 + 1.02485i
\(741\) 0 0
\(742\) 45.5349 + 33.0831i 1.67164 + 1.21452i
\(743\) −40.1256 29.1530i −1.47207 1.06952i −0.980009 0.198956i \(-0.936245\pi\)
−0.492057 0.870563i \(-0.663755\pi\)
\(744\) 0 0
\(745\) 0.106038 + 0.326351i 0.00388493 + 0.0119566i
\(746\) −69.9204 + 50.8002i −2.55997 + 1.85993i
\(747\) 30.0000 1.09764
\(748\) 0 0
\(749\) −15.3137 −0.559551
\(750\) 5.52431 4.01365i 0.201719 0.146558i
\(751\) −4.94427 15.2169i −0.180419 0.555273i 0.819420 0.573193i \(-0.194295\pi\)
−0.999839 + 0.0179203i \(0.994295\pi\)
\(752\) 2.62210 8.06998i 0.0956180 0.294282i
\(753\) 27.4589 + 19.9501i 1.00066 + 0.727022i
\(754\) 8.36778 + 6.07955i 0.304737 + 0.221404i
\(755\) −3.70820 + 11.4127i −0.134955 + 0.415350i
\(756\) −13.3847 41.1938i −0.486796 1.49820i
\(757\) −10.7710 + 7.82560i −0.391479 + 0.284426i −0.766061 0.642767i \(-0.777786\pi\)
0.374582 + 0.927194i \(0.377786\pi\)
\(758\) −81.2548 −2.95131
\(759\) 0 0
\(760\) 0 0
\(761\) −24.2705 + 17.6336i −0.879805 + 0.639216i −0.933200 0.359358i \(-0.882996\pi\)
0.0533947 + 0.998573i \(0.482996\pi\)
\(762\) −9.16447 28.2053i −0.331994 1.02177i
\(763\) 4.73220 14.5642i 0.171317 0.527260i
\(764\) −10.2634 7.45682i −0.371318 0.269778i
\(765\) −27.6216 20.0682i −0.998660 0.725569i
\(766\) 4.37016 13.4500i 0.157900 0.485967i
\(767\) 0.599841 + 1.84612i 0.0216590 + 0.0666595i
\(768\) −68.5800 + 49.8263i −2.47467 + 1.79795i
\(769\) 18.9706 0.684096 0.342048 0.939682i \(-0.388879\pi\)
0.342048 + 0.939682i \(0.388879\pi\)
\(770\) 0 0
\(771\) 26.3431 0.948725
\(772\) −3.62867 + 2.63638i −0.130599 + 0.0948855i
\(773\) 8.12229 + 24.9978i 0.292138 + 0.899109i 0.984168 + 0.177240i \(0.0567169\pi\)
−0.692029 + 0.721869i \(0.743283\pi\)
\(774\) −22.3810 + 68.8816i −0.804468 + 2.47590i
\(775\) 0 0
\(776\) 13.0593 + 9.48811i 0.468800 + 0.340603i
\(777\) 13.3847 41.1938i 0.480172 1.47782i
\(778\) −15.3887 47.3617i −0.551713 1.69800i
\(779\) 0 0
\(780\) 12.6863