Properties

Label 605.2.g.f.81.1
Level $605$
Weight $2$
Character 605.81
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 81.1
Root \(0.437016 + 1.34500i\) of defining polynomial
Character \(\chi\) \(=\) 605.81
Dual form 605.2.g.f.366.1

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

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

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 −0.996778 0.0802039i \(-0.974443\pi\)
−0.384300 0.923208i \(-0.625557\pi\)
\(3\) −0.874032 + 2.68999i −0.504623 + 1.55307i 0.296781 + 0.954945i \(0.404087\pi\)
−0.801404 + 0.598123i \(0.795913\pi\)
\(4\) 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 −0.997305 0.0733714i \(-0.976624\pi\)
0.763710 0.645560i \(-0.223376\pi\)
\(8\) 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 \(-0.248055\pi\)
−0.448537 + 0.893765i \(0.648055\pi\)
\(14\) −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 −0.340393 + 0.940283i \(0.610560\pi\)
−0.999450 + 0.0331696i \(0.989440\pi\)
\(18\) 3.73017 + 11.4803i 0.879208 + 2.70593i
\(19\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(20\) 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 −0.999480 0.0322527i \(-0.989732\pi\)
0.789638 0.613572i \(-0.210268\pi\)
\(30\) 2.11010 6.49422i 0.385250 1.18568i
\(31\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(32\) −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 −0.933549 0.358451i \(-0.883305\pi\)
0.544564 0.838719i \(-0.316695\pi\)
\(38\) 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 −0.695432 0.718592i \(-0.744787\pi\)
0.984994 0.172588i \(-0.0552131\pi\)
\(42\) −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 −0.866856 0.498559i \(-0.833863\pi\)
0.994347 + 0.106183i \(0.0338628\pi\)
\(48\) −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 −0.295492 0.955345i \(-0.595484\pi\)
−0.999899 + 0.0141880i \(0.995484\pi\)
\(54\) −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 0.978837 0.204641i \(-0.0656027\pi\)
−0.912181 + 0.409788i \(0.865603\pi\)
\(60\) −8.76038 + 6.36479i −1.13096 + 0.821691i
\(61\) 7.53495 5.47446i 0.964751 0.700933i 0.0105019 0.999945i \(-0.496657\pi\)
0.954249 + 0.299012i \(0.0966571\pi\)
\(62\) 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 −0.978764 0.204992i \(-0.934283\pi\)
−0.107496 + 0.994206i \(0.534283\pi\)
\(72\) −17.8559 + 12.9730i −2.10433 + 1.52889i
\(73\) −0.362036 1.11423i −0.0423731 0.130411i 0.927632 0.373495i \(-0.121841\pi\)
−0.970005 + 0.243084i \(0.921841\pi\)
\(74\) −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 \(-0.372244\pi\)
−0.754754 + 0.656007i \(0.772244\pi\)
\(80\) −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 \(-0.593190\pi\)
0.821407 + 0.570343i \(0.193190\pi\)
\(84\) 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 0.427374 0.904075i \(-0.359439\pi\)
−0.727760 + 0.685832i \(0.759439\pi\)
\(98\) −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 \(-0.453361\pi\)
−0.895751 + 0.444556i \(0.853361\pi\)
\(102\) −14.4087 + 44.3453i −1.42667 + 4.39084i
\(103\) 2.11010 + 6.49422i 0.207914 + 0.639895i 0.999581 + 0.0289414i \(0.00921362\pi\)
−0.791667 + 0.610953i \(0.790786\pi\)
\(104\) 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 −0.769151 0.639067i \(-0.779321\pi\)
0.997890 0.0649203i \(-0.0206793\pi\)
\(108\) 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 −0.0766284 0.997060i \(-0.524416\pi\)
0.648051 0.761597i \(-0.275584\pi\)
\(114\) 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 \(-0.761723\pi\)
0.420875 + 0.907119i \(0.361723\pi\)
\(128\) −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 −0.140106 0.990136i \(-0.544744\pi\)
0.898381 + 0.439218i \(0.144744\pi\)
\(138\) −15.6251 + 11.3523i −1.33010 + 0.966373i
\(139\) −1.23607 3.80423i −0.104842 0.322670i 0.884851 0.465873i \(-0.154260\pi\)
−0.989693 + 0.143203i \(0.954260\pi\)
\(140\) 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 \(-0.704474\pi\)
0.576356 + 0.817199i \(0.304474\pi\)
\(150\) −2.11010 6.49422i −0.172289 0.530251i
\(151\) −3.70820 + 11.4127i −0.301769 + 0.928751i 0.679094 + 0.734052i \(0.262373\pi\)
−0.980863 + 0.194699i \(0.937627\pi\)
\(152\) 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 0.616167 + 0.787616i \(0.288685\pi\)
−0.961438 + 0.275020i \(0.911315\pi\)
\(158\) 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 −0.0734416 0.997300i \(-0.523398\pi\)
−0.971183 + 0.238335i \(0.923398\pi\)
\(164\) 22.9706 1.79370
\(165\) 0 0
\(166\) −14.4853 −1.12428
\(167\) 18.5836 + 13.5018i 1.43804 + 1.04480i 0.988447 + 0.151564i \(0.0484309\pi\)
0.449593 + 0.893234i \(0.351569\pi\)
\(168\) 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 0.253387 + 0.967365i \(0.418455\pi\)
−0.773597 + 0.633677i \(0.781545\pi\)
\(174\) −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 −0.775440 0.631422i \(-0.782472\pi\)
0.998484 0.0550388i \(-0.0175282\pi\)
\(180\) −5.91525 18.2053i −0.440896 1.35694i
\(181\) −17.2432 + 12.5279i −1.28167 + 0.931190i −0.999602 0.0282032i \(-0.991021\pi\)
−0.282071 + 0.959393i \(0.591021\pi\)
\(182\) −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 0.981244 0.192770i \(-0.0617472\pi\)
−0.907150 + 0.420806i \(0.861747\pi\)
\(192\) −22.4899 + 16.3398i −1.62307 + 1.17923i
\(193\) 0.947822 0.688633i 0.0682257 0.0495689i −0.553150 0.833082i \(-0.686574\pi\)
0.621375 + 0.783513i \(0.286574\pi\)
\(194\) 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 0.936170 0.351548i \(-0.114345\pi\)
−0.0450495 + 0.998985i \(0.514345\pi\)
\(212\) 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 0.774308 + 0.632809i \(0.218098\pi\)
−0.998384 + 0.0568262i \(0.981902\pi\)
\(224\) 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 0.775529 + 0.631312i \(0.217483\pi\)
−0.256340 + 0.966587i \(0.582517\pi\)
\(228\) 0 0
\(229\) −1.06281 0.772178i −0.0702326 0.0510270i 0.552115 0.833768i \(-0.313821\pi\)
−0.622348 + 0.782741i \(0.713821\pi\)
\(230\) 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 \(-0.235518\pi\)
−0.412998 + 0.910732i \(0.635518\pi\)
\(234\) −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 0.391699 + 0.920093i \(0.371887\pi\)
−0.857708 + 0.514136i \(0.828113\pi\)
\(240\) −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 0.237614 0.971360i \(-0.423635\pi\)
−0.850391 + 0.526151i \(0.823635\pi\)
\(252\) −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 0.820281 0.571961i \(-0.193817\pi\)
−0.999811 + 0.0194227i \(0.993817\pi\)
\(258\) −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 −0.926253 0.376901i \(-0.876990\pi\)
0.0722264 + 0.997388i \(0.476990\pi\)
\(270\) −11.0486 + 8.02730i −0.672398 + 0.488526i
\(271\) 2.26006 + 6.95575i 0.137289 + 0.422532i 0.995939 0.0900304i \(-0.0286964\pi\)
−0.858650 + 0.512562i \(0.828696\pi\)
\(272\) 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 \(-0.365765\pi\)
−0.741247 + 0.671233i \(0.765765\pi\)
\(278\) −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 \(-0.872737\pi\)
0.0855434 + 0.996334i \(0.472737\pi\)
\(282\) −5.96826 18.3684i −0.355405 1.09382i
\(283\) 10.0824 31.0305i 0.599338 1.84457i 0.0675133 0.997718i \(-0.478493\pi\)
0.531825 0.846854i \(-0.321507\pi\)
\(284\) −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 \(-0.186331\pi\)
−0.999078 + 0.0429287i \(0.986331\pi\)
\(294\) 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 −0.901566 0.432642i \(-0.857581\pi\)
0.983683 + 0.179913i \(0.0575815\pi\)
\(312\) 4.52012 + 13.9115i 0.255901 + 0.787584i
\(313\) 1.06281 0.772178i 0.0600737 0.0436461i −0.557343 0.830282i \(-0.688179\pi\)
0.617417 + 0.786636i \(0.288179\pi\)
\(314\) 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 0.617232 0.786781i \(-0.288254\pi\)
−0.557538 + 0.830151i \(0.688254\pi\)
\(318\) −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 −0.961673 0.274199i \(-0.911587\pi\)
0.616840 0.787089i \(-0.288413\pi\)
\(338\) −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 \(-0.795142\pi\)
0.323497 + 0.946229i \(0.395142\pi\)
\(348\) 12.2364 + 37.6599i 0.655943 + 2.01878i
\(349\) 8.33436 25.6505i 0.446128 1.37304i −0.435114 0.900376i \(-0.643292\pi\)
0.881242 0.472666i \(-0.156708\pi\)
\(350\) 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 \(-0.0942349\pi\)
−0.945304 + 0.326190i \(0.894235\pi\)
\(360\) −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 0.859004 0.511968i \(-0.171084\pi\)
−0.995877 + 0.0907188i \(0.971084\pi\)
\(368\) 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 −0.403806 + 0.914845i \(0.632313\pi\)
−0.994852 + 0.101340i \(0.967687\pi\)
\(380\) 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 0.702244 0.711936i \(-0.252182\pi\)
−0.460087 + 0.887874i \(0.652182\pi\)
\(384\) 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 0.972253 + 0.233933i \(0.0751595\pi\)
−0.649067 + 0.760731i \(0.724840\pi\)
\(390\) 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 −0.475251 0.879850i \(-0.657643\pi\)
0.689927 + 0.723879i \(0.257643\pi\)
\(402\) 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 \(-0.308102\pi\)
−0.608185 + 0.793795i \(0.708102\pi\)
\(410\) −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 −0.986018 0.166641i \(-0.946708\pi\)
0.895654 + 0.444751i \(0.146708\pi\)
\(422\) −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 \(-0.212156\pi\)
−0.345102 + 0.938565i \(0.612156\pi\)
\(432\) −5.24419 + 16.1400i −0.252311 + 0.776534i
\(433\) −2.36610 7.28210i −0.113707 0.349955i 0.877968 0.478720i \(-0.158899\pi\)
−0.991675 + 0.128764i \(0.958899\pi\)
\(434\) 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 0.535931 + 0.844262i \(0.319961\pi\)
−0.929822 + 0.368009i \(0.880039\pi\)
\(444\) 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 −0.113089 0.993585i \(-0.536075\pi\)
−0.979902 + 0.199480i \(0.936075\pi\)
\(450\) 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 \(-0.703613\pi\)
0.578565 + 0.815636i \(0.303613\pi\)
\(458\) 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 −0.274544 0.961575i \(-0.588527\pi\)
0.829673 + 0.558249i \(0.188527\pi\)
\(468\) 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 0.331007 0.943628i \(-0.392612\pi\)
0.999731 0.0232090i \(-0.00738832\pi\)
\(480\) −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 0.619852 + 0.784719i \(0.287193\pi\)
−0.962717 + 0.270511i \(0.912807\pi\)
\(488\) −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 \(-0.104930\pi\)
−0.955728 + 0.294252i \(0.904930\pi\)
\(492\) −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 0.995368 0.0961409i \(-0.0306500\pi\)
−0.861780 + 0.507283i \(0.830650\pi\)
\(500\) 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 −0.768751 0.639549i \(-0.779121\pi\)
0.997850 0.0655455i \(-0.0208787\pi\)
\(504\) 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 −0.999893 0.0146406i \(-0.995340\pi\)
0.817536 + 0.575878i \(0.195340\pi\)
\(510\) 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 0.962801 + 0.270210i \(0.0870931\pi\)
−0.620097 + 0.784525i \(0.712907\pi\)
\(522\) 35.7117 25.9461i 1.56306 1.13563i
\(523\) 33.6535 24.4507i 1.47156 1.06915i 0.491407 0.870930i \(-0.336483\pi\)
0.980157 0.198223i \(-0.0635171\pi\)
\(524\) −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 \(-0.341170\pi\)
−0.687223 + 0.726447i \(0.741170\pi\)
\(542\) 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 0.428550 + 0.903518i \(0.359025\pi\)
−0.877779 + 0.479066i \(0.840975\pi\)
\(548\) 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 \(-0.0330294\pi\)
−0.865548 + 0.500827i \(0.833029\pi\)
\(558\) 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 \(-0.302302\pi\)
−0.593620 + 0.804746i \(0.702302\pi\)
\(564\) −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 −0.506453 0.862267i \(-0.669044\pi\)
0.916557 0.399903i \(-0.130956\pi\)
\(570\) 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 −0.0322368 0.999480i \(-0.510263\pi\)
0.940600 + 0.339515i \(0.110263\pi\)
\(578\) −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 0.936466 0.350759i \(-0.114076\pi\)
−0.963788 + 0.266671i \(0.914076\pi\)
\(588\) −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 −0.490352 0.871525i \(-0.663132\pi\)
0.677342 + 0.735668i \(0.263132\pi\)
\(600\) 10.1008 7.33866i 0.412364 0.299600i
\(601\) 7.39821 + 22.7694i 0.301779 + 0.928782i 0.980859 + 0.194717i \(0.0623790\pi\)
−0.679080 + 0.734064i \(0.737621\pi\)
\(602\) 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 \(-0.583237\pi\)
−0.998614 + 0.0526384i \(0.983237\pi\)
\(608\) 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 0.656905 + 0.753973i \(0.271865\pi\)
−0.974622 + 0.223858i \(0.928135\pi\)
\(614\) 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 −0.999763 0.0217589i \(-0.993073\pi\)
0.821615 + 0.570043i \(0.193073\pi\)
\(620\) 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 \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(632\) −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 −0.583086 0.812410i \(-0.698155\pi\)
0.949250 0.314524i \(-0.101845\pi\)
\(642\) −16.1567 49.7253i −0.637655 1.96250i
\(643\) 1.17780 0.855724i 0.0464480 0.0337464i −0.564319 0.825557i \(-0.690861\pi\)
0.610767 + 0.791810i \(0.290861\pi\)
\(644\) −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 0.0661810 0.997808i \(-0.478919\pi\)
−0.928520 + 0.371281i \(0.878919\pi\)
\(648\) 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 0.996470 0.0839510i \(-0.0267539\pi\)
−0.855506 + 0.517793i \(0.826754\pi\)
\(654\) −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 0.765192 0.643802i \(-0.222644\pi\)
−0.375835 + 0.926687i \(0.622644\pi\)
\(674\) −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 \(-0.844555\pi\)
0.173305 + 0.984868i \(0.444555\pi\)
\(678\) −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 0.995225 0.0976071i \(-0.0311188\pi\)
0.214712 + 0.976677i \(0.431119\pi\)
\(692\) −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 \(-0.976644\pi\)
0.849930 + 0.526896i \(0.176644\pi\)
\(702\) −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 −0.895287 0.445489i \(-0.853030\pi\)
0.147026 + 0.989133i \(0.453030\pi\)
\(710\) 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 0.999390 + 0.0349227i \(0.0111185\pi\)
−0.787996 + 0.615680i \(0.788882\pi\)
\(720\) 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 −0.999901 0.0140757i \(-0.995519\pi\)
0.800663 0.599114i \(-0.204481\pi\)
\(734\) −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 \(-0.485640\pi\)
−0.936152 + 0.351595i \(0.885640\pi\)
\(740\) 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 0.492057 0.870563i \(-0.336245\pi\)
0.980009 0.198956i \(-0.0637550\pi\)
\(744\) 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 −0.999839 0.0179203i \(-0.994295\pi\)
0.819420 + 0.573193i \(0.194295\pi\)
\(752\) 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 0.374582 0.927194i \(-0.377786\pi\)
−0.766061 + 0.642767i \(0.777786\pi\)
\(758\) 81.2548 2.95131
\(759\) 0 0
\(760\) 0 0
\(761\) 24.2705 + 17.6336i 0.879805 + 0.639216i 0.933200 0.359358i \(-0.117004\pi\)
−0.0533947 + 0.998573i \(0.517004\pi\)
\(762\) −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 −0.692029 0.721869i \(-0.743283\pi\)
0.984168 0.177240i \(-0.0567169\pi\)
\(774\) −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