Properties

Label 605.2.g.f.366.1
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 366.1
Root \(0.437016 - 1.34500i\) of defining polynomial
Character \(\chi\) \(=\) 605.366
Dual form 605.2.g.f.81.1

$q$-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 \(0.625557\pi\)
−0.996778 + 0.0802039i \(0.974443\pi\)
\(3\) −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 \(0.223376\pi\)
−0.997305 + 0.0733714i \(0.976624\pi\)
\(8\) 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 −0.448537 0.893765i \(-0.648055\pi\)
0.711415 + 0.702772i \(0.248055\pi\)
\(14\) −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 \(-0.989440\pi\)
−0.340393 0.940283i \(-0.610560\pi\)
\(18\) 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 \(0.210268\pi\)
−0.999480 + 0.0322527i \(0.989732\pi\)
\(30\) 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 \(0.0552131\pi\)
−0.695432 + 0.718592i \(0.744787\pi\)
\(42\) −11.0486 + 8.02730i −1.70484 + 1.23864i
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 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 0.954249 0.299012i \(-0.0966571\pi\)
0.0105019 + 0.999945i \(0.496657\pi\)
\(62\) 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 −0.970005 0.243084i \(-0.921841\pi\)
0.927632 + 0.373495i \(0.121841\pi\)
\(74\) −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 −0.754754 0.656007i \(-0.772244\pi\)
0.390668 + 0.920532i \(0.372244\pi\)
\(80\) −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 0.821407 0.570343i \(-0.193190\pi\)
−0.288600 + 0.957450i \(0.593190\pi\)
\(84\) 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 −0.895751 0.444556i \(-0.853361\pi\)
0.145996 + 0.989285i \(0.453361\pi\)
\(102\) −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 \(0.0206793\pi\)
−0.769151 + 0.639067i \(0.779321\pi\)
\(108\) 17.5208 12.7296i 1.68594 1.22490i
\(109\) −7.65685 −0.733394 −0.366697 0.930341i \(-0.619511\pi\)
−0.366697 + 0.930341i \(0.619511\pi\)
\(110\) 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 0.420875 0.907119i \(-0.361723\pi\)
−0.732664 + 0.680591i \(0.761723\pi\)
\(128\) −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 \(-0.664554\pi\)
−0.494242 + 0.869325i \(0.664554\pi\)
\(132\) 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 −0.989693 0.143203i \(-0.954260\pi\)
0.884851 + 0.465873i \(0.154260\pi\)
\(140\) 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 0.576356 0.817199i \(-0.304474\pi\)
−0.599099 + 0.800675i \(0.704474\pi\)
\(150\) −2.11010 + 6.49422i −0.172289 + 0.530251i
\(151\) −3.70820 11.4127i −0.301769 0.928751i −0.980863 0.194699i \(-0.937627\pi\)
0.679094 0.734052i \(-0.262373\pi\)
\(152\) 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 \(-0.351569\pi\)
0.988447 0.151564i \(-0.0484309\pi\)
\(168\) 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 \(-0.781545\pi\)
0.253387 0.967365i \(-0.418455\pi\)
\(174\) −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 0.621375 0.783513i \(-0.286574\pi\)
−0.553150 + 0.833082i \(0.686574\pi\)
\(194\) 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 \(-0.626056\pi\)
−0.385747 + 0.922605i \(0.626056\pi\)
\(198\) 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 −0.0450495 0.998985i \(-0.514345\pi\)
0.936170 + 0.351548i \(0.114345\pi\)
\(212\) 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 \(-0.582517\pi\)
0.775529 0.631312i \(-0.217483\pi\)
\(228\) 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 −0.412998 0.910732i \(-0.635518\pi\)
0.738534 + 0.674216i \(0.235518\pi\)
\(234\) −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 \(-0.828113\pi\)
0.391699 0.920093i \(-0.371887\pi\)
\(240\) −6.86474 + 4.98752i −0.443117 + 0.321943i
\(241\) 6.00000 0.386494 0.193247 0.981150i \(-0.438098\pi\)
0.193247 + 0.981150i \(0.438098\pi\)
\(242\) 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 \(-0.609831\pi\)
−0.338237 + 0.941061i \(0.609831\pi\)
\(264\) 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 −0.858650 0.512562i \(-0.828696\pi\)
0.995939 + 0.0900304i \(0.0286964\pi\)
\(272\) 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 −0.741247 0.671233i \(-0.765765\pi\)
0.409323 + 0.912390i \(0.365765\pi\)
\(278\) −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 0.0855434 0.996334i \(-0.472737\pi\)
−0.921136 + 0.389241i \(0.872737\pi\)
\(282\) −5.96826 + 18.3684i −0.355405 + 1.09382i
\(283\) 10.0824 + 31.0305i 0.599338 + 1.84457i 0.531825 + 0.846854i \(0.321507\pi\)
0.0675133 + 0.997718i \(0.478493\pi\)
\(284\) −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 −0.999078 0.0429287i \(-0.986331\pi\)
0.833504 + 0.552513i \(0.186331\pi\)
\(294\) 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 \(-0.654441\pi\)
−0.466376 + 0.884586i \(0.654441\pi\)
\(308\) 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 \(0.288413\pi\)
−0.961673 + 0.274199i \(0.911587\pi\)
\(338\) −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 0.323497 0.946229i \(-0.395142\pi\)
−0.799952 + 0.600065i \(0.795142\pi\)
\(348\) 12.2364 37.6599i 0.655943 2.01878i
\(349\) 8.33436 + 25.6505i 0.446128 + 1.37304i 0.881242 + 0.472666i \(0.156708\pi\)
−0.435114 + 0.900376i \(0.643292\pi\)
\(350\) 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 −0.945304 0.326190i \(-0.894235\pi\)
0.956497 + 0.291742i \(0.0942349\pi\)
\(360\) −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 \(-0.122547\pi\)
0.926801 + 0.375554i \(0.122547\pi\)
\(374\) 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 −0.608185 0.793795i \(-0.708102\pi\)
0.567004 + 0.823715i \(0.308102\pi\)
\(410\) −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 −0.345102 0.938565i \(-0.612156\pi\)
0.785986 + 0.618244i \(0.212156\pi\)
\(432\) −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 \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) 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 0.578565 0.815636i \(-0.303613\pi\)
−0.596930 + 0.802293i \(0.703613\pi\)
\(458\) 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 \(-0.404994\pi\)
0.294059 + 0.955787i \(0.404994\pi\)
\(462\) 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 \(0.00738832\pi\)
0.331007 + 0.943628i \(0.392612\pi\)
\(480\) −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 −0.955728 0.294252i \(-0.904930\pi\)
0.946157 + 0.323708i \(0.104930\pi\)
\(492\) −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 \(0.0208787\pi\)
−0.768751 + 0.639549i \(0.779121\pi\)
\(504\) 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 \(0.0635171\pi\)
0.491407 + 0.870930i \(0.336483\pi\)
\(524\) −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 −0.687223 0.726447i \(-0.741170\pi\)
0.478529 + 0.878072i \(0.341170\pi\)
\(542\) 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 \(-0.840975\pi\)
0.428550 0.903518i \(-0.359025\pi\)
\(548\) 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 −0.865548 0.500827i \(-0.833029\pi\)
0.994621 + 0.103579i \(0.0330294\pi\)
\(558\) 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 −0.593620 0.804746i \(-0.702302\pi\)
0.581920 + 0.813246i \(0.302302\pi\)
\(564\) −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 \(0.130956\pi\)
−0.506453 + 0.862267i \(0.669044\pi\)
\(570\) 0 0
\(571\) −21.9411 −0.918208 −0.459104 0.888383i \(-0.651829\pi\)
−0.459104 + 0.888383i \(0.651829\pi\)
\(572\) 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 \(-0.477009\pi\)
0.0721661 + 0.997393i \(0.477009\pi\)
\(594\) 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 \(-0.737621\pi\)
0.980859 0.194717i \(-0.0623790\pi\)
\(602\) 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 −0.998614 0.0526384i \(-0.983237\pi\)
−0.258526 + 0.966004i \(0.583237\pi\)
\(608\) 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 \(-0.928135\pi\)
0.656905 0.753973i \(-0.271865\pi\)
\(614\) 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 \(-0.147314\pi\)
0.894806 + 0.446455i \(0.147314\pi\)
\(660\) 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 −0.375835 0.926687i \(-0.622644\pi\)
0.765192 + 0.643802i \(0.222644\pi\)
\(674\) −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 0.173305 0.984868i \(-0.444555\pi\)
−0.883111 + 0.469164i \(0.844555\pi\)
\(678\) −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 0.849930 0.526896i \(-0.176644\pi\)
−0.997309 + 0.0733080i \(0.976644\pi\)
\(702\) −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 \(0.204481\pi\)
−0.999901 + 0.0140757i \(0.995519\pi\)
\(734\) −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 −0.936152 0.351595i \(-0.885640\pi\)
0.0450993 + 0.998983i \(0.485640\pi\)
\(740\) 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 \(0.0637550\pi\)
0.492057 + 0.870563i \(0.336245\pi\)
\(744\) 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 −0.0533947 0.998573i \(-0.517004\pi\)
0.933200 + 0.359358i \(0.117004\pi\)
\(762\) −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 \(-0.611121\pi\)
−0.342048 + 0.939682i \(0.611121\pi\)
\(770\) 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