Properties

Label 370.2.h.e.253.2
Level $370$
Weight $2$
Character 370.253
Analytic conductor $2.954$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.h (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} - 7362 x^{11} + 13826 x^{10} + 4848 x^{9} + 13544 x^{8} - 44248 x^{7} + 76384 x^{6} + 24512 x^{5} + 28432 x^{4} - 61952 x^{3} + 61952 x^{2} - 5632 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.2
Root \(-1.28900 - 1.28900i\) of defining polynomial
Character \(\chi\) \(=\) 370.253
Dual form 370.2.h.e.117.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-1.28900 + 1.28900i) q^{3} +1.00000 q^{4} +(1.63786 + 1.52231i) q^{5} +(1.28900 - 1.28900i) q^{6} +(-3.01566 + 3.01566i) q^{7} -1.00000 q^{8} -0.323040i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-1.28900 + 1.28900i) q^{3} +1.00000 q^{4} +(1.63786 + 1.52231i) q^{5} +(1.28900 - 1.28900i) q^{6} +(-3.01566 + 3.01566i) q^{7} -1.00000 q^{8} -0.323040i q^{9} +(-1.63786 - 1.52231i) q^{10} -2.38854i q^{11} +(-1.28900 + 1.28900i) q^{12} +1.44800 q^{13} +(3.01566 - 3.01566i) q^{14} +(-4.07345 + 0.148945i) q^{15} +1.00000 q^{16} +2.09597i q^{17} +0.323040i q^{18} +(-2.46518 - 2.46518i) q^{19} +(1.63786 + 1.52231i) q^{20} -7.77437i q^{21} +2.38854i q^{22} -0.168727 q^{23} +(1.28900 - 1.28900i) q^{24} +(0.365159 + 4.98665i) q^{25} -1.44800 q^{26} +(-3.45060 - 3.45060i) q^{27} +(-3.01566 + 3.01566i) q^{28} +(-4.74797 + 4.74797i) q^{29} +(4.07345 - 0.148945i) q^{30} +(-3.34342 - 3.34342i) q^{31} -1.00000 q^{32} +(3.07882 + 3.07882i) q^{33} -2.09597i q^{34} +(-9.52998 + 0.348461i) q^{35} -0.323040i q^{36} +(-1.89339 - 5.78058i) q^{37} +(2.46518 + 2.46518i) q^{38} +(-1.86647 + 1.86647i) q^{39} +(-1.63786 - 1.52231i) q^{40} +6.22969i q^{41} +7.77437i q^{42} -3.07893 q^{43} -2.38854i q^{44} +(0.491767 - 0.529094i) q^{45} +0.168727 q^{46} +(-4.67540 + 4.67540i) q^{47} +(-1.28900 + 1.28900i) q^{48} -11.1884i q^{49} +(-0.365159 - 4.98665i) q^{50} +(-2.70170 - 2.70170i) q^{51} +1.44800 q^{52} +(-2.87955 - 2.87955i) q^{53} +(3.45060 + 3.45060i) q^{54} +(3.63609 - 3.91208i) q^{55} +(3.01566 - 3.01566i) q^{56} +6.35524 q^{57} +(4.74797 - 4.74797i) q^{58} +(6.78438 + 6.78438i) q^{59} +(-4.07345 + 0.148945i) q^{60} +(6.94487 + 6.94487i) q^{61} +(3.34342 + 3.34342i) q^{62} +(0.974180 + 0.974180i) q^{63} +1.00000 q^{64} +(2.37161 + 2.20430i) q^{65} +(-3.07882 - 3.07882i) q^{66} +(7.89993 + 7.89993i) q^{67} +2.09597i q^{68} +(0.217489 - 0.217489i) q^{69} +(9.52998 - 0.348461i) q^{70} +12.6621 q^{71} +0.323040i q^{72} +(4.83010 - 4.83010i) q^{73} +(1.89339 + 5.78058i) q^{74} +(-6.89848 - 5.95710i) q^{75} +(-2.46518 - 2.46518i) q^{76} +(7.20301 + 7.20301i) q^{77} +(1.86647 - 1.86647i) q^{78} +(-5.31500 - 5.31500i) q^{79} +(1.63786 + 1.52231i) q^{80} +9.86477 q^{81} -6.22969i q^{82} +(8.43313 + 8.43313i) q^{83} -7.77437i q^{84} +(-3.19071 + 3.43290i) q^{85} +3.07893 q^{86} -12.2403i q^{87} +2.38854i q^{88} +(-11.6295 + 11.6295i) q^{89} +(-0.491767 + 0.529094i) q^{90} +(-4.36667 + 4.36667i) q^{91} -0.168727 q^{92} +8.61934 q^{93} +(4.67540 - 4.67540i) q^{94} +(-0.284853 - 7.79038i) q^{95} +(1.28900 - 1.28900i) q^{96} -5.04296i q^{97} +11.1884i q^{98} -0.771593 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + O(q^{10}) \) \( 20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + 4q^{10} + 4q^{12} + 2q^{14} - 4q^{15} + 20q^{16} + 6q^{19} - 4q^{20} - 4q^{23} - 4q^{24} + 10q^{25} - 20q^{27} - 2q^{28} + 18q^{29} + 4q^{30} + 12q^{31} - 20q^{32} + 4q^{33} - 12q^{35} - 32q^{37} - 6q^{38} + 6q^{39} + 4q^{40} + 16q^{43} + 22q^{45} + 4q^{46} - 22q^{47} + 4q^{48} - 10q^{50} + 8q^{51} - 4q^{53} + 20q^{54} + 16q^{55} + 2q^{56} + 24q^{57} - 18q^{58} - 10q^{59} - 4q^{60} + 10q^{61} - 12q^{62} - 2q^{63} + 20q^{64} + 20q^{65} - 4q^{66} + 8q^{67} - 34q^{69} + 12q^{70} + 16q^{71} - 6q^{73} + 32q^{74} - 26q^{75} + 6q^{76} - 4q^{77} - 6q^{78} + 12q^{79} - 4q^{80} - 28q^{81} + 6q^{83} + 10q^{85} - 16q^{86} - 44q^{89} - 22q^{90} - 40q^{91} - 4q^{92} - 40q^{93} + 22q^{94} + 50q^{95} - 4q^{96} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.28900 + 1.28900i −0.744204 + 0.744204i −0.973384 0.229180i \(-0.926396\pi\)
0.229180 + 0.973384i \(0.426396\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.63786 + 1.52231i 0.732472 + 0.680797i
\(6\) 1.28900 1.28900i 0.526232 0.526232i
\(7\) −3.01566 + 3.01566i −1.13981 + 1.13981i −0.151328 + 0.988484i \(0.548355\pi\)
−0.988484 + 0.151328i \(0.951645\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.323040i 0.107680i
\(10\) −1.63786 1.52231i −0.517936 0.481396i
\(11\) 2.38854i 0.720171i −0.932919 0.360085i \(-0.882748\pi\)
0.932919 0.360085i \(-0.117252\pi\)
\(12\) −1.28900 + 1.28900i −0.372102 + 0.372102i
\(13\) 1.44800 0.401602 0.200801 0.979632i \(-0.435646\pi\)
0.200801 + 0.979632i \(0.435646\pi\)
\(14\) 3.01566 3.01566i 0.805969 0.805969i
\(15\) −4.07345 + 0.148945i −1.05176 + 0.0384573i
\(16\) 1.00000 0.250000
\(17\) 2.09597i 0.508347i 0.967159 + 0.254173i \(0.0818034\pi\)
−0.967159 + 0.254173i \(0.918197\pi\)
\(18\) 0.323040i 0.0761413i
\(19\) −2.46518 2.46518i −0.565551 0.565551i 0.365328 0.930879i \(-0.380957\pi\)
−0.930879 + 0.365328i \(0.880957\pi\)
\(20\) 1.63786 + 1.52231i 0.366236 + 0.340398i
\(21\) 7.77437i 1.69651i
\(22\) 2.38854i 0.509238i
\(23\) −0.168727 −0.0351820 −0.0175910 0.999845i \(-0.505600\pi\)
−0.0175910 + 0.999845i \(0.505600\pi\)
\(24\) 1.28900 1.28900i 0.263116 0.263116i
\(25\) 0.365159 + 4.98665i 0.0730318 + 0.997330i
\(26\) −1.44800 −0.283976
\(27\) −3.45060 3.45060i −0.664068 0.664068i
\(28\) −3.01566 + 3.01566i −0.569906 + 0.569906i
\(29\) −4.74797 + 4.74797i −0.881676 + 0.881676i −0.993705 0.112029i \(-0.964265\pi\)
0.112029 + 0.993705i \(0.464265\pi\)
\(30\) 4.07345 0.148945i 0.743707 0.0271934i
\(31\) −3.34342 3.34342i −0.600496 0.600496i 0.339948 0.940444i \(-0.389590\pi\)
−0.940444 + 0.339948i \(0.889590\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.07882 + 3.07882i 0.535954 + 0.535954i
\(34\) 2.09597i 0.359456i
\(35\) −9.52998 + 0.348461i −1.61086 + 0.0589007i
\(36\) 0.323040i 0.0538401i
\(37\) −1.89339 5.78058i −0.311271 0.950321i
\(38\) 2.46518 + 2.46518i 0.399905 + 0.399905i
\(39\) −1.86647 + 1.86647i −0.298874 + 0.298874i
\(40\) −1.63786 1.52231i −0.258968 0.240698i
\(41\) 6.22969i 0.972913i 0.873705 + 0.486457i \(0.161711\pi\)
−0.873705 + 0.486457i \(0.838289\pi\)
\(42\) 7.77437i 1.19961i
\(43\) −3.07893 −0.469532 −0.234766 0.972052i \(-0.575432\pi\)
−0.234766 + 0.972052i \(0.575432\pi\)
\(44\) 2.38854i 0.360085i
\(45\) 0.491767 0.529094i 0.0733083 0.0788727i
\(46\) 0.168727 0.0248774
\(47\) −4.67540 + 4.67540i −0.681978 + 0.681978i −0.960446 0.278468i \(-0.910173\pi\)
0.278468 + 0.960446i \(0.410173\pi\)
\(48\) −1.28900 + 1.28900i −0.186051 + 0.186051i
\(49\) 11.1884i 1.59834i
\(50\) −0.365159 4.98665i −0.0516413 0.705219i
\(51\) −2.70170 2.70170i −0.378314 0.378314i
\(52\) 1.44800 0.200801
\(53\) −2.87955 2.87955i −0.395537 0.395537i 0.481119 0.876656i \(-0.340231\pi\)
−0.876656 + 0.481119i \(0.840231\pi\)
\(54\) 3.45060 + 3.45060i 0.469567 + 0.469567i
\(55\) 3.63609 3.91208i 0.490290 0.527505i
\(56\) 3.01566 3.01566i 0.402984 0.402984i
\(57\) 6.35524 0.841772
\(58\) 4.74797 4.74797i 0.623439 0.623439i
\(59\) 6.78438 + 6.78438i 0.883251 + 0.883251i 0.993864 0.110612i \(-0.0352812\pi\)
−0.110612 + 0.993864i \(0.535281\pi\)
\(60\) −4.07345 + 0.148945i −0.525880 + 0.0192287i
\(61\) 6.94487 + 6.94487i 0.889199 + 0.889199i 0.994446 0.105247i \(-0.0335634\pi\)
−0.105247 + 0.994446i \(0.533563\pi\)
\(62\) 3.34342 + 3.34342i 0.424615 + 0.424615i
\(63\) 0.974180 + 0.974180i 0.122735 + 0.122735i
\(64\) 1.00000 0.125000
\(65\) 2.37161 + 2.20430i 0.294162 + 0.273409i
\(66\) −3.07882 3.07882i −0.378977 0.378977i
\(67\) 7.89993 + 7.89993i 0.965130 + 0.965130i 0.999412 0.0342818i \(-0.0109144\pi\)
−0.0342818 + 0.999412i \(0.510914\pi\)
\(68\) 2.09597i 0.254173i
\(69\) 0.217489 0.217489i 0.0261826 0.0261826i
\(70\) 9.52998 0.348461i 1.13905 0.0416491i
\(71\) 12.6621 1.50272 0.751358 0.659895i \(-0.229399\pi\)
0.751358 + 0.659895i \(0.229399\pi\)
\(72\) 0.323040i 0.0380707i
\(73\) 4.83010 4.83010i 0.565321 0.565321i −0.365493 0.930814i \(-0.619100\pi\)
0.930814 + 0.365493i \(0.119100\pi\)
\(74\) 1.89339 + 5.78058i 0.220102 + 0.671978i
\(75\) −6.89848 5.95710i −0.796568 0.687866i
\(76\) −2.46518 2.46518i −0.282776 0.282776i
\(77\) 7.20301 + 7.20301i 0.820859 + 0.820859i
\(78\) 1.86647 1.86647i 0.211336 0.211336i
\(79\) −5.31500 5.31500i −0.597984 0.597984i 0.341792 0.939776i \(-0.388966\pi\)
−0.939776 + 0.341792i \(0.888966\pi\)
\(80\) 1.63786 + 1.52231i 0.183118 + 0.170199i
\(81\) 9.86477 1.09609
\(82\) 6.22969i 0.687954i
\(83\) 8.43313 + 8.43313i 0.925657 + 0.925657i 0.997422 0.0717648i \(-0.0228631\pi\)
−0.0717648 + 0.997422i \(0.522863\pi\)
\(84\) 7.77437i 0.848253i
\(85\) −3.19071 + 3.43290i −0.346081 + 0.372350i
\(86\) 3.07893 0.332009
\(87\) 12.2403i 1.31229i
\(88\) 2.38854i 0.254619i
\(89\) −11.6295 + 11.6295i −1.23273 + 1.23273i −0.269814 + 0.962912i \(0.586962\pi\)
−0.962912 + 0.269814i \(0.913038\pi\)
\(90\) −0.491767 + 0.529094i −0.0518368 + 0.0557714i
\(91\) −4.36667 + 4.36667i −0.457751 + 0.457751i
\(92\) −0.168727 −0.0175910
\(93\) 8.61934 0.893784
\(94\) 4.67540 4.67540i 0.482231 0.482231i
\(95\) −0.284853 7.79038i −0.0292253 0.799276i
\(96\) 1.28900 1.28900i 0.131558 0.131558i
\(97\) 5.04296i 0.512035i −0.966672 0.256018i \(-0.917589\pi\)
0.966672 0.256018i \(-0.0824105\pi\)
\(98\) 11.1884i 1.13020i
\(99\) −0.771593 −0.0775481
\(100\) 0.365159 + 4.98665i 0.0365159 + 0.498665i
\(101\) 11.7791i 1.17207i −0.810287 0.586033i \(-0.800689\pi\)
0.810287 0.586033i \(-0.199311\pi\)
\(102\) 2.70170 + 2.70170i 0.267508 + 0.267508i
\(103\) 6.35592i 0.626267i −0.949709 0.313134i \(-0.898621\pi\)
0.949709 0.313134i \(-0.101379\pi\)
\(104\) −1.44800 −0.141988
\(105\) 11.8350 12.7333i 1.15498 1.24264i
\(106\) 2.87955 + 2.87955i 0.279687 + 0.279687i
\(107\) −7.29845 + 7.29845i −0.705568 + 0.705568i −0.965600 0.260032i \(-0.916267\pi\)
0.260032 + 0.965600i \(0.416267\pi\)
\(108\) −3.45060 3.45060i −0.332034 0.332034i
\(109\) −7.27809 7.27809i −0.697114 0.697114i 0.266673 0.963787i \(-0.414076\pi\)
−0.963787 + 0.266673i \(0.914076\pi\)
\(110\) −3.63609 + 3.91208i −0.346687 + 0.373002i
\(111\) 9.89174 + 5.01058i 0.938883 + 0.475583i
\(112\) −3.01566 + 3.01566i −0.284953 + 0.284953i
\(113\) 5.37412i 0.505555i 0.967524 + 0.252777i \(0.0813440\pi\)
−0.967524 + 0.252777i \(0.918656\pi\)
\(114\) −6.35524 −0.595222
\(115\) −0.276350 0.256854i −0.0257698 0.0239518i
\(116\) −4.74797 + 4.74797i −0.440838 + 0.440838i
\(117\) 0.467761i 0.0432446i
\(118\) −6.78438 6.78438i −0.624553 0.624553i
\(119\) −6.32073 6.32073i −0.579420 0.579420i
\(120\) 4.07345 0.148945i 0.371854 0.0135967i
\(121\) 5.29490 0.481354
\(122\) −6.94487 6.94487i −0.628759 0.628759i
\(123\) −8.03006 8.03006i −0.724046 0.724046i
\(124\) −3.34342 3.34342i −0.300248 0.300248i
\(125\) −6.99313 + 8.72331i −0.625485 + 0.780236i
\(126\) −0.974180 0.974180i −0.0867868 0.0867868i
\(127\) −11.7621 + 11.7621i −1.04371 + 1.04371i −0.0447148 + 0.999000i \(0.514238\pi\)
−0.999000 + 0.0447148i \(0.985762\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 3.96873 3.96873i 0.349428 0.349428i
\(130\) −2.37161 2.20430i −0.208004 0.193330i
\(131\) 15.5939 + 15.5939i 1.36245 + 1.36245i 0.870789 + 0.491657i \(0.163609\pi\)
0.491657 + 0.870789i \(0.336391\pi\)
\(132\) 3.07882 + 3.07882i 0.267977 + 0.267977i
\(133\) 14.8683 1.28924
\(134\) −7.89993 7.89993i −0.682450 0.682450i
\(135\) −0.398719 10.9045i −0.0343162 0.938507i
\(136\) 2.09597i 0.179728i
\(137\) 0.952787 0.952787i 0.0814020 0.0814020i −0.665233 0.746635i \(-0.731668\pi\)
0.746635 + 0.665233i \(0.231668\pi\)
\(138\) −0.217489 + 0.217489i −0.0185139 + 0.0185139i
\(139\) 8.19245 0.694874 0.347437 0.937703i \(-0.387052\pi\)
0.347437 + 0.937703i \(0.387052\pi\)
\(140\) −9.52998 + 0.348461i −0.805431 + 0.0294503i
\(141\) 12.0532i 1.01506i
\(142\) −12.6621 −1.06258
\(143\) 3.45859i 0.289222i
\(144\) 0.323040i 0.0269200i
\(145\) −15.0044 + 0.548631i −1.24605 + 0.0455613i
\(146\) −4.83010 + 4.83010i −0.399742 + 0.399742i
\(147\) 14.4218 + 14.4218i 1.18949 + 1.18949i
\(148\) −1.89339 5.78058i −0.155636 0.475161i
\(149\) 22.8722i 1.87377i 0.349641 + 0.936884i \(0.386303\pi\)
−0.349641 + 0.936884i \(0.613697\pi\)
\(150\) 6.89848 + 5.95710i 0.563258 + 0.486395i
\(151\) 16.6501i 1.35496i 0.735539 + 0.677482i \(0.236929\pi\)
−0.735539 + 0.677482i \(0.763071\pi\)
\(152\) 2.46518 + 2.46518i 0.199953 + 0.199953i
\(153\) 0.677082 0.0547389
\(154\) −7.20301 7.20301i −0.580435 0.580435i
\(155\) −0.386334 10.5658i −0.0310311 0.848663i
\(156\) −1.86647 + 1.86647i −0.149437 + 0.149437i
\(157\) 10.1100 10.1100i 0.806865 0.806865i −0.177293 0.984158i \(-0.556734\pi\)
0.984158 + 0.177293i \(0.0567341\pi\)
\(158\) 5.31500 + 5.31500i 0.422838 + 0.422838i
\(159\) 7.42348 0.588721
\(160\) −1.63786 1.52231i −0.129484 0.120349i
\(161\) 0.508822 0.508822i 0.0401008 0.0401008i
\(162\) −9.86477 −0.775049
\(163\) 1.81513i 0.142172i 0.997470 + 0.0710859i \(0.0226465\pi\)
−0.997470 + 0.0710859i \(0.977354\pi\)
\(164\) 6.22969i 0.486457i
\(165\) 0.355759 + 9.72959i 0.0276958 + 0.757447i
\(166\) −8.43313 8.43313i −0.654538 0.654538i
\(167\) 16.2469i 1.25722i 0.777721 + 0.628610i \(0.216376\pi\)
−0.777721 + 0.628610i \(0.783624\pi\)
\(168\) 7.77437i 0.599805i
\(169\) −10.9033 −0.838716
\(170\) 3.19071 3.43290i 0.244716 0.263291i
\(171\) −0.796353 + 0.796353i −0.0608986 + 0.0608986i
\(172\) −3.07893 −0.234766
\(173\) 12.0071 12.0071i 0.912885 0.912885i −0.0836133 0.996498i \(-0.526646\pi\)
0.996498 + 0.0836133i \(0.0266461\pi\)
\(174\) 12.2403i 0.927932i
\(175\) −16.1392 13.9368i −1.22001 1.05353i
\(176\) 2.38854i 0.180043i
\(177\) −17.4901 −1.31464
\(178\) 11.6295 11.6295i 0.871669 0.871669i
\(179\) 8.45867 8.45867i 0.632231 0.632231i −0.316396 0.948627i \(-0.602473\pi\)
0.948627 + 0.316396i \(0.102473\pi\)
\(180\) 0.491767 0.529094i 0.0366541 0.0394364i
\(181\) 0.961200 0.0714454 0.0357227 0.999362i \(-0.488627\pi\)
0.0357227 + 0.999362i \(0.488627\pi\)
\(182\) 4.36667 4.36667i 0.323679 0.323679i
\(183\) −17.9039 −1.32349
\(184\) 0.168727 0.0124387
\(185\) 5.69871 12.3501i 0.418978 0.907997i
\(186\) −8.61934 −0.632000
\(187\) 5.00630 0.366097
\(188\) −4.67540 + 4.67540i −0.340989 + 0.340989i
\(189\) 20.8117 1.51383
\(190\) 0.284853 + 7.79038i 0.0206654 + 0.565174i
\(191\) 0.355141 0.355141i 0.0256971 0.0256971i −0.694141 0.719839i \(-0.744216\pi\)
0.719839 + 0.694141i \(0.244216\pi\)
\(192\) −1.28900 + 1.28900i −0.0930255 + 0.0930255i
\(193\) −7.33106 −0.527701 −0.263851 0.964564i \(-0.584993\pi\)
−0.263851 + 0.964564i \(0.584993\pi\)
\(194\) 5.04296i 0.362064i
\(195\) −5.89835 + 0.215671i −0.422389 + 0.0154445i
\(196\) 11.1884i 0.799171i
\(197\) −8.20672 + 8.20672i −0.584704 + 0.584704i −0.936192 0.351488i \(-0.885676\pi\)
0.351488 + 0.936192i \(0.385676\pi\)
\(198\) 0.771593 0.0548348
\(199\) −0.480679 + 0.480679i −0.0340744 + 0.0340744i −0.723939 0.689864i \(-0.757670\pi\)
0.689864 + 0.723939i \(0.257670\pi\)
\(200\) −0.365159 4.98665i −0.0258206 0.352609i
\(201\) −20.3660 −1.43651
\(202\) 11.7791i 0.828776i
\(203\) 28.6365i 2.00989i
\(204\) −2.70170 2.70170i −0.189157 0.189157i
\(205\) −9.48350 + 10.2033i −0.662356 + 0.712632i
\(206\) 6.35592i 0.442838i
\(207\) 0.0545055i 0.00378840i
\(208\) 1.44800 0.100401
\(209\) −5.88817 + 5.88817i −0.407293 + 0.407293i
\(210\) −11.8350 + 12.7333i −0.816691 + 0.878682i
\(211\) −24.5328 −1.68891 −0.844453 0.535630i \(-0.820074\pi\)
−0.844453 + 0.535630i \(0.820074\pi\)
\(212\) −2.87955 2.87955i −0.197768 0.197768i
\(213\) −16.3215 + 16.3215i −1.11833 + 1.11833i
\(214\) 7.29845 7.29845i 0.498912 0.498912i
\(215\) −5.04284 4.68707i −0.343919 0.319656i
\(216\) 3.45060 + 3.45060i 0.234784 + 0.234784i
\(217\) 20.1652 1.36891
\(218\) 7.27809 + 7.27809i 0.492934 + 0.492934i
\(219\) 12.4520i 0.841429i
\(220\) 3.63609 3.91208i 0.245145 0.263753i
\(221\) 3.03496i 0.204153i
\(222\) −9.89174 5.01058i −0.663890 0.336288i
\(223\) 13.8026 + 13.8026i 0.924289 + 0.924289i 0.997329 0.0730404i \(-0.0232702\pi\)
−0.0730404 + 0.997329i \(0.523270\pi\)
\(224\) 3.01566 3.01566i 0.201492 0.201492i
\(225\) 1.61089 0.117961i 0.107393 0.00786407i
\(226\) 5.37412i 0.357481i
\(227\) 10.8328i 0.718995i −0.933146 0.359498i \(-0.882948\pi\)
0.933146 0.359498i \(-0.117052\pi\)
\(228\) 6.35524 0.420886
\(229\) 17.5884i 1.16227i 0.813806 + 0.581136i \(0.197392\pi\)
−0.813806 + 0.581136i \(0.802608\pi\)
\(230\) 0.276350 + 0.256854i 0.0182220 + 0.0169365i
\(231\) −18.5694 −1.22177
\(232\) 4.74797 4.74797i 0.311720 0.311720i
\(233\) −1.47378 + 1.47378i −0.0965505 + 0.0965505i −0.753732 0.657182i \(-0.771748\pi\)
0.657182 + 0.753732i \(0.271748\pi\)
\(234\) 0.467761i 0.0305785i
\(235\) −14.7750 + 0.540245i −0.963818 + 0.0352417i
\(236\) 6.78438 + 6.78438i 0.441626 + 0.441626i
\(237\) 13.7021 0.890044
\(238\) 6.32073 + 6.32073i 0.409712 + 0.409712i
\(239\) −0.869275 0.869275i −0.0562288 0.0562288i 0.678433 0.734662i \(-0.262659\pi\)
−0.734662 + 0.678433i \(0.762659\pi\)
\(240\) −4.07345 + 0.148945i −0.262940 + 0.00961433i
\(241\) 7.39427 7.39427i 0.476307 0.476307i −0.427642 0.903948i \(-0.640655\pi\)
0.903948 + 0.427642i \(0.140655\pi\)
\(242\) −5.29490 −0.340369
\(243\) −2.36388 + 2.36388i −0.151643 + 0.151643i
\(244\) 6.94487 + 6.94487i 0.444599 + 0.444599i
\(245\) 17.0322 18.3250i 1.08815 1.17074i
\(246\) 8.03006 + 8.03006i 0.511978 + 0.511978i
\(247\) −3.56958 3.56958i −0.227127 0.227127i
\(248\) 3.34342 + 3.34342i 0.212307 + 0.212307i
\(249\) −21.7406 −1.37776
\(250\) 6.99313 8.72331i 0.442285 0.551710i
\(251\) 15.8249 + 15.8249i 0.998857 + 0.998857i 0.999999 0.00114211i \(-0.000363545\pi\)
−0.00114211 + 0.999999i \(0.500364\pi\)
\(252\) 0.974180 + 0.974180i 0.0613675 + 0.0613675i
\(253\) 0.403010i 0.0253370i
\(254\) 11.7621 11.7621i 0.738018 0.738018i
\(255\) −0.312183 8.53783i −0.0195497 0.534660i
\(256\) 1.00000 0.0625000
\(257\) 23.1629i 1.44486i −0.691443 0.722431i \(-0.743025\pi\)
0.691443 0.722431i \(-0.256975\pi\)
\(258\) −3.96873 + 3.96873i −0.247083 + 0.247083i
\(259\) 23.1421 + 11.7224i 1.43798 + 0.728396i
\(260\) 2.37161 + 2.20430i 0.147081 + 0.136705i
\(261\) 1.53379 + 1.53379i 0.0949390 + 0.0949390i
\(262\) −15.5939 15.5939i −0.963395 0.963395i
\(263\) −12.7777 + 12.7777i −0.787909 + 0.787909i −0.981151 0.193242i \(-0.938100\pi\)
0.193242 + 0.981151i \(0.438100\pi\)
\(264\) −3.07882 3.07882i −0.189488 0.189488i
\(265\) −0.332734 9.09986i −0.0204397 0.559000i
\(266\) −14.8683 −0.911634
\(267\) 29.9809i 1.83480i
\(268\) 7.89993 + 7.89993i 0.482565 + 0.482565i
\(269\) 5.62728i 0.343101i −0.985175 0.171551i \(-0.945122\pi\)
0.985175 0.171551i \(-0.0548777\pi\)
\(270\) 0.398719 + 10.9045i 0.0242652 + 0.663625i
\(271\) −21.2992 −1.29384 −0.646919 0.762559i \(-0.723943\pi\)
−0.646919 + 0.762559i \(0.723943\pi\)
\(272\) 2.09597i 0.127087i
\(273\) 11.2573i 0.681320i
\(274\) −0.952787 + 0.952787i −0.0575599 + 0.0575599i
\(275\) 11.9108 0.872195i 0.718247 0.0525953i
\(276\) 0.217489 0.217489i 0.0130913 0.0130913i
\(277\) 24.8652 1.49401 0.747003 0.664821i \(-0.231492\pi\)
0.747003 + 0.664821i \(0.231492\pi\)
\(278\) −8.19245 −0.491350
\(279\) −1.08006 + 1.08006i −0.0646615 + 0.0646615i
\(280\) 9.52998 0.348461i 0.569525 0.0208245i
\(281\) 0.925329 0.925329i 0.0552005 0.0552005i −0.678968 0.734168i \(-0.737572\pi\)
0.734168 + 0.678968i \(0.237572\pi\)
\(282\) 12.0532i 0.717757i
\(283\) 0.300587i 0.0178681i −0.999960 0.00893403i \(-0.997156\pi\)
0.999960 0.00893403i \(-0.00284383\pi\)
\(284\) 12.6621 0.751358
\(285\) 10.4090 + 9.67462i 0.616574 + 0.573075i
\(286\) 3.45859i 0.204511i
\(287\) −18.7866 18.7866i −1.10894 1.10894i
\(288\) 0.323040i 0.0190353i
\(289\) 12.6069 0.741583
\(290\) 15.0044 0.548631i 0.881087 0.0322167i
\(291\) 6.50038 + 6.50038i 0.381059 + 0.381059i
\(292\) 4.83010 4.83010i 0.282660 0.282660i
\(293\) −22.4364 22.4364i −1.31075 1.31075i −0.920865 0.389881i \(-0.872516\pi\)
−0.389881 0.920865i \(-0.627484\pi\)
\(294\) −14.4218 14.4218i −0.841099 0.841099i
\(295\) 0.783939 + 21.4398i 0.0456427 + 1.24827i
\(296\) 1.89339 + 5.78058i 0.110051 + 0.335989i
\(297\) −8.24188 + 8.24188i −0.478242 + 0.478242i
\(298\) 22.8722i 1.32495i
\(299\) −0.244316 −0.0141291
\(300\) −6.89848 5.95710i −0.398284 0.343933i
\(301\) 9.28499 9.28499i 0.535178 0.535178i
\(302\) 16.6501i 0.958104i
\(303\) 15.1833 + 15.1833i 0.872257 + 0.872257i
\(304\) −2.46518 2.46518i −0.141388 0.141388i
\(305\) 0.802483 + 21.9469i 0.0459500 + 1.25668i
\(306\) −0.677082 −0.0387062
\(307\) −2.94724 2.94724i −0.168208 0.168208i 0.617983 0.786191i \(-0.287950\pi\)
−0.786191 + 0.617983i \(0.787950\pi\)
\(308\) 7.20301 + 7.20301i 0.410430 + 0.410430i
\(309\) 8.19278 + 8.19278i 0.466071 + 0.466071i
\(310\) 0.386334 + 10.5658i 0.0219423 + 0.600095i
\(311\) −12.0863 12.0863i −0.685353 0.685353i 0.275848 0.961201i \(-0.411041\pi\)
−0.961201 + 0.275848i \(0.911041\pi\)
\(312\) 1.86647 1.86647i 0.105668 0.105668i
\(313\) 2.00477 0.113316 0.0566582 0.998394i \(-0.481955\pi\)
0.0566582 + 0.998394i \(0.481955\pi\)
\(314\) −10.1100 + 10.1100i −0.570540 + 0.570540i
\(315\) 0.112567 + 3.07857i 0.00634243 + 0.173458i
\(316\) −5.31500 5.31500i −0.298992 0.298992i
\(317\) −7.28840 7.28840i −0.409357 0.409357i 0.472157 0.881514i \(-0.343475\pi\)
−0.881514 + 0.472157i \(0.843475\pi\)
\(318\) −7.42348 −0.416288
\(319\) 11.3407 + 11.3407i 0.634957 + 0.634957i
\(320\) 1.63786 + 1.52231i 0.0915591 + 0.0850996i
\(321\) 18.8154i 1.05017i
\(322\) −0.508822 + 0.508822i −0.0283556 + 0.0283556i
\(323\) 5.16694 5.16694i 0.287496 0.287496i
\(324\) 9.86477 0.548043
\(325\) 0.528749 + 7.22065i 0.0293297 + 0.400530i
\(326\) 1.81513i 0.100531i
\(327\) 18.7629 1.03759
\(328\) 6.22969i 0.343977i
\(329\) 28.1988i 1.55465i
\(330\) −0.355759 9.72959i −0.0195839 0.535596i
\(331\) −0.839383 + 0.839383i −0.0461367 + 0.0461367i −0.729799 0.683662i \(-0.760386\pi\)
0.683662 + 0.729799i \(0.260386\pi\)
\(332\) 8.43313 + 8.43313i 0.462828 + 0.462828i
\(333\) −1.86736 + 0.611642i −0.102331 + 0.0335178i
\(334\) 16.2469i 0.888988i
\(335\) 0.912841 + 24.9651i 0.0498739 + 1.36399i
\(336\) 7.77437i 0.424127i
\(337\) 7.69155 + 7.69155i 0.418986 + 0.418986i 0.884854 0.465868i \(-0.154258\pi\)
−0.465868 + 0.884854i \(0.654258\pi\)
\(338\) 10.9033 0.593062
\(339\) −6.92724 6.92724i −0.376236 0.376236i
\(340\) −3.19071 + 3.43290i −0.173040 + 0.186175i
\(341\) −7.98588 + 7.98588i −0.432460 + 0.432460i
\(342\) 0.796353 0.796353i 0.0430618 0.0430618i
\(343\) 12.6308 + 12.6308i 0.681998 + 0.681998i
\(344\) 3.07893 0.166005
\(345\) 0.687300 0.0251309i 0.0370030 0.00135300i
\(346\) −12.0071 + 12.0071i −0.645507 + 0.645507i
\(347\) 21.8436 1.17263 0.586313 0.810085i \(-0.300579\pi\)
0.586313 + 0.810085i \(0.300579\pi\)
\(348\) 12.2403i 0.656147i
\(349\) 4.00432i 0.214346i −0.994240 0.107173i \(-0.965820\pi\)
0.994240 0.107173i \(-0.0341799\pi\)
\(350\) 16.1392 + 13.9368i 0.862678 + 0.744955i
\(351\) −4.99646 4.99646i −0.266691 0.266691i
\(352\) 2.38854i 0.127309i
\(353\) 11.1747i 0.594769i −0.954758 0.297384i \(-0.903886\pi\)
0.954758 0.297384i \(-0.0961143\pi\)
\(354\) 17.4901 0.929590
\(355\) 20.7387 + 19.2756i 1.10070 + 1.02304i
\(356\) −11.6295 + 11.6295i −0.616363 + 0.616363i
\(357\) 16.2948 0.862414
\(358\) −8.45867 + 8.45867i −0.447055 + 0.447055i
\(359\) 19.4341i 1.02570i 0.858480 + 0.512848i \(0.171409\pi\)
−0.858480 + 0.512848i \(0.828591\pi\)
\(360\) −0.491767 + 0.529094i −0.0259184 + 0.0278857i
\(361\) 6.84576i 0.360303i
\(362\) −0.961200 −0.0505196
\(363\) −6.82512 + 6.82512i −0.358226 + 0.358226i
\(364\) −4.36667 + 4.36667i −0.228875 + 0.228875i
\(365\) 15.2639 0.558121i 0.798951 0.0292134i
\(366\) 17.9039 0.935850
\(367\) 10.2957 10.2957i 0.537430 0.537430i −0.385343 0.922773i \(-0.625917\pi\)
0.922773 + 0.385343i \(0.125917\pi\)
\(368\) −0.168727 −0.00879549
\(369\) 2.01244 0.104763
\(370\) −5.69871 + 12.3501i −0.296262 + 0.642051i
\(371\) 17.3675 0.901675
\(372\) 8.61934 0.446892
\(373\) −23.2626 + 23.2626i −1.20449 + 1.20449i −0.231704 + 0.972786i \(0.574430\pi\)
−0.972786 + 0.231704i \(0.925570\pi\)
\(374\) −5.00630 −0.258869
\(375\) −2.23019 20.2585i −0.115167 1.04614i
\(376\) 4.67540 4.67540i 0.241115 0.241115i
\(377\) −6.87505 + 6.87505i −0.354083 + 0.354083i
\(378\) −20.8117 −1.07044
\(379\) 11.6263i 0.597203i −0.954378 0.298602i \(-0.903480\pi\)
0.954378 0.298602i \(-0.0965202\pi\)
\(380\) −0.284853 7.79038i −0.0146127 0.399638i
\(381\) 30.3226i 1.55347i
\(382\) −0.355141 + 0.355141i −0.0181706 + 0.0181706i
\(383\) 8.97694 0.458700 0.229350 0.973344i \(-0.426340\pi\)
0.229350 + 0.973344i \(0.426340\pi\)
\(384\) 1.28900 1.28900i 0.0657790 0.0657790i
\(385\) 0.832312 + 22.7627i 0.0424185 + 1.16009i
\(386\) 7.33106 0.373141
\(387\) 0.994617i 0.0505592i
\(388\) 5.04296i 0.256018i
\(389\) 14.6826 + 14.6826i 0.744440 + 0.744440i 0.973429 0.228989i \(-0.0735420\pi\)
−0.228989 + 0.973429i \(0.573542\pi\)
\(390\) 5.89835 0.215671i 0.298674 0.0109209i
\(391\) 0.353646i 0.0178846i
\(392\) 11.1884i 0.565100i
\(393\) −40.2011 −2.02788
\(394\) 8.20672 8.20672i 0.413448 0.413448i
\(395\) −0.614151 16.7963i −0.0309013 0.845112i
\(396\) −0.771593 −0.0387740
\(397\) 0.327150 + 0.327150i 0.0164192 + 0.0164192i 0.715269 0.698850i \(-0.246304\pi\)
−0.698850 + 0.715269i \(0.746304\pi\)
\(398\) 0.480679 0.480679i 0.0240943 0.0240943i
\(399\) −19.1652 + 19.1652i −0.959461 + 0.959461i
\(400\) 0.365159 + 4.98665i 0.0182579 + 0.249332i
\(401\) 19.1836 + 19.1836i 0.957985 + 0.957985i 0.999152 0.0411677i \(-0.0131078\pi\)
−0.0411677 + 0.999152i \(0.513108\pi\)
\(402\) 20.3660 1.01576
\(403\) −4.84126 4.84126i −0.241161 0.241161i
\(404\) 11.7791i 0.586033i
\(405\) 16.1571 + 15.0172i 0.802852 + 0.746211i
\(406\) 28.6365i 1.42121i
\(407\) −13.8071 + 4.52243i −0.684393 + 0.224169i
\(408\) 2.70170 + 2.70170i 0.133754 + 0.133754i
\(409\) 9.30031 9.30031i 0.459871 0.459871i −0.438742 0.898613i \(-0.644576\pi\)
0.898613 + 0.438742i \(0.144576\pi\)
\(410\) 9.48350 10.2033i 0.468357 0.503907i
\(411\) 2.45628i 0.121160i
\(412\) 6.35592i 0.313134i
\(413\) −40.9188 −2.01348
\(414\) 0.0545055i 0.00267880i
\(415\) 0.974453 + 26.6501i 0.0478340 + 1.30820i
\(416\) −1.44800 −0.0709939
\(417\) −10.5601 + 10.5601i −0.517128 + 0.517128i
\(418\) 5.88817 5.88817i 0.288000 0.288000i
\(419\) 11.9651i 0.584532i 0.956337 + 0.292266i \(0.0944093\pi\)
−0.956337 + 0.292266i \(0.905591\pi\)
\(420\) 11.8350 12.7333i 0.577488 0.621322i
\(421\) 17.5941 + 17.5941i 0.857482 + 0.857482i 0.991041 0.133559i \(-0.0426405\pi\)
−0.133559 + 0.991041i \(0.542641\pi\)
\(422\) 24.5328 1.19424
\(423\) 1.51034 + 1.51034i 0.0734354 + 0.0734354i
\(424\) 2.87955 + 2.87955i 0.139843 + 0.139843i
\(425\) −10.4519 + 0.765361i −0.506990 + 0.0371255i
\(426\) 16.3215 16.3215i 0.790777 0.790777i
\(427\) −41.8867 −2.02704
\(428\) −7.29845 + 7.29845i −0.352784 + 0.352784i
\(429\) 4.45812 + 4.45812i 0.215240 + 0.215240i
\(430\) 5.04284 + 4.68707i 0.243187 + 0.226031i
\(431\) −9.36769 9.36769i −0.451226 0.451226i 0.444536 0.895761i \(-0.353369\pi\)
−0.895761 + 0.444536i \(0.853369\pi\)
\(432\) −3.45060 3.45060i −0.166017 0.166017i
\(433\) 11.6303 + 11.6303i 0.558916 + 0.558916i 0.928999 0.370083i \(-0.120671\pi\)
−0.370083 + 0.928999i \(0.620671\pi\)
\(434\) −20.1652 −0.967962
\(435\) 18.6335 20.0478i 0.893406 0.961219i
\(436\) −7.27809 7.27809i −0.348557 0.348557i
\(437\) 0.415942 + 0.415942i 0.0198972 + 0.0198972i
\(438\) 12.4520i 0.594980i
\(439\) 16.3753 16.3753i 0.781552 0.781552i −0.198540 0.980093i \(-0.563620\pi\)
0.980093 + 0.198540i \(0.0636201\pi\)
\(440\) −3.63609 + 3.91208i −0.173344 + 0.186501i
\(441\) −3.61430 −0.172110
\(442\) 3.03496i 0.144358i
\(443\) 18.4976 18.4976i 0.878850 0.878850i −0.114566 0.993416i \(-0.536548\pi\)
0.993416 + 0.114566i \(0.0365477\pi\)
\(444\) 9.89174 + 5.01058i 0.469441 + 0.237792i
\(445\) −36.7512 + 1.34380i −1.74217 + 0.0637021i
\(446\) −13.8026 13.8026i −0.653571 0.653571i
\(447\) −29.4823 29.4823i −1.39447 1.39447i
\(448\) −3.01566 + 3.01566i −0.142477 + 0.142477i
\(449\) −28.1954 28.1954i −1.33062 1.33062i −0.904814 0.425808i \(-0.859990\pi\)
−0.425808 0.904814i \(-0.640010\pi\)
\(450\) −1.61089 + 0.117961i −0.0759380 + 0.00556074i
\(451\) 14.8798 0.700664
\(452\) 5.37412i 0.252777i
\(453\) −21.4619 21.4619i −1.00837 1.00837i
\(454\) 10.8328i 0.508406i
\(455\) −13.7994 + 0.504570i −0.646925 + 0.0236546i
\(456\) −6.35524 −0.297611
\(457\) 30.7275i 1.43737i −0.695334 0.718687i \(-0.744744\pi\)
0.695334 0.718687i \(-0.255256\pi\)
\(458\) 17.5884i 0.821851i
\(459\) 7.23235 7.23235i 0.337577 0.337577i
\(460\) −0.276350 0.256854i −0.0128849 0.0119759i
\(461\) −9.22827 + 9.22827i −0.429804 + 0.429804i −0.888561 0.458758i \(-0.848295\pi\)
0.458758 + 0.888561i \(0.348295\pi\)
\(462\) 18.5694 0.863925
\(463\) 13.6064 0.632343 0.316172 0.948702i \(-0.397602\pi\)
0.316172 + 0.948702i \(0.397602\pi\)
\(464\) −4.74797 + 4.74797i −0.220419 + 0.220419i
\(465\) 14.1173 + 13.1213i 0.654672 + 0.608485i
\(466\) 1.47378 1.47378i 0.0682715 0.0682715i
\(467\) 19.5369i 0.904059i 0.892003 + 0.452030i \(0.149300\pi\)
−0.892003 + 0.452030i \(0.850700\pi\)
\(468\) 0.467761i 0.0216223i
\(469\) −47.6470 −2.20013
\(470\) 14.7750 0.540245i 0.681522 0.0249197i
\(471\) 26.0635i 1.20094i
\(472\) −6.78438 6.78438i −0.312277 0.312277i
\(473\) 7.35412i 0.338143i
\(474\) −13.7021 −0.629356
\(475\) 11.3928 13.1932i 0.522738 0.605344i
\(476\) −6.32073 6.32073i −0.289710 0.289710i
\(477\) −0.930212 + 0.930212i −0.0425915 + 0.0425915i
\(478\) 0.869275 + 0.869275i 0.0397597 + 0.0397597i
\(479\) −25.1547 25.1547i −1.14935 1.14935i −0.986681 0.162667i \(-0.947990\pi\)
−0.162667 0.986681i \(-0.552010\pi\)
\(480\) 4.07345 0.148945i 0.185927 0.00679836i
\(481\) −2.74162 8.37026i −0.125007 0.381651i
\(482\) −7.39427 + 7.39427i −0.336800 + 0.336800i
\(483\) 1.31174i 0.0596864i
\(484\) 5.29490 0.240677
\(485\) 7.67694 8.25966i 0.348592 0.375052i
\(486\) 2.36388 2.36388i 0.107228 0.107228i
\(487\) 41.5088i 1.88094i −0.339873 0.940471i \(-0.610384\pi\)
0.339873 0.940471i \(-0.389616\pi\)
\(488\) −6.94487 6.94487i −0.314379 0.314379i
\(489\) −2.33970 2.33970i −0.105805 0.105805i
\(490\) −17.0322 + 18.3250i −0.769436 + 0.827840i
\(491\) −24.6515 −1.11250 −0.556252 0.831013i \(-0.687761\pi\)
−0.556252 + 0.831013i \(0.687761\pi\)
\(492\) −8.03006 8.03006i −0.362023 0.362023i
\(493\) −9.95160 9.95160i −0.448197 0.448197i
\(494\) 3.56958 + 3.56958i 0.160603 + 0.160603i
\(495\) −1.26376 1.17460i −0.0568018 0.0527945i
\(496\) −3.34342 3.34342i −0.150124 0.150124i
\(497\) −38.1846 + 38.1846i −1.71281 + 1.71281i
\(498\) 21.7406 0.974220
\(499\) −16.8585 + 16.8585i −0.754689 + 0.754689i −0.975350 0.220662i \(-0.929178\pi\)
0.220662 + 0.975350i \(0.429178\pi\)
\(500\) −6.99313 + 8.72331i −0.312742 + 0.390118i
\(501\) −20.9422 20.9422i −0.935628 0.935628i
\(502\) −15.8249 15.8249i −0.706299 0.706299i
\(503\) −14.5276 −0.647755 −0.323877 0.946099i \(-0.604987\pi\)
−0.323877 + 0.946099i \(0.604987\pi\)
\(504\) −0.974180 0.974180i −0.0433934 0.0433934i
\(505\) 17.9314 19.2925i 0.797939 0.858506i
\(506\) 0.403010i 0.0179160i
\(507\) 14.0544 14.0544i 0.624176 0.624176i
\(508\) −11.7621 + 11.7621i −0.521857 + 0.521857i
\(509\) 38.8001 1.71978 0.859892 0.510476i \(-0.170531\pi\)
0.859892 + 0.510476i \(0.170531\pi\)
\(510\) 0.312183 + 8.53783i 0.0138237 + 0.378061i
\(511\) 29.1319i 1.28872i
\(512\) −1.00000 −0.0441942
\(513\) 17.0127i 0.751129i
\(514\) 23.1629i 1.02167i
\(515\) 9.67567 10.4101i 0.426361 0.458724i
\(516\) 3.96873 3.96873i 0.174714 0.174714i
\(517\) 11.1674 + 11.1674i 0.491140 + 0.491140i
\(518\) −23.1421 11.7224i −1.01680 0.515054i
\(519\) 30.9544i 1.35875i
\(520\) −2.37161 2.20430i −0.104002 0.0966648i
\(521\) 1.46992i 0.0643983i −0.999481 0.0321991i \(-0.989749\pi\)
0.999481 0.0321991i \(-0.0102511\pi\)
\(522\) −1.53379 1.53379i −0.0671320 0.0671320i
\(523\) 37.4377 1.63704 0.818519 0.574479i \(-0.194795\pi\)
0.818519 + 0.574479i \(0.194795\pi\)
\(524\) 15.5939 + 15.5939i 0.681223 + 0.681223i
\(525\) 38.7680 2.83888i 1.69198 0.123899i
\(526\) 12.7777 12.7777i 0.557136 0.557136i
\(527\) 7.00770 7.00770i 0.305260 0.305260i
\(528\) 3.07882 + 3.07882i 0.133989 + 0.133989i
\(529\) −22.9715 −0.998762
\(530\) 0.332734 + 9.09986i 0.0144530 + 0.395273i
\(531\) 2.19163 2.19163i 0.0951086 0.0951086i
\(532\) 14.8683 0.644622
\(533\) 9.02057i 0.390724i
\(534\) 29.9809i 1.29740i
\(535\) −23.0643 + 0.843340i −0.997157 + 0.0364608i
\(536\) −7.89993 7.89993i −0.341225 0.341225i
\(537\) 21.8065i 0.941018i
\(538\) 5.62728i 0.242609i
\(539\) −26.7239 −1.15108
\(540\) −0.398719 10.9045i −0.0171581 0.469254i
\(541\) 1.13614 1.13614i 0.0488465 0.0488465i −0.682262 0.731108i \(-0.739003\pi\)
0.731108 + 0.682262i \(0.239003\pi\)
\(542\) 21.2992 0.914881
\(543\) −1.23899 + 1.23899i −0.0531700 + 0.0531700i
\(544\) 2.09597i 0.0898639i
\(545\) −0.840987 23.0000i −0.0360239 0.985210i
\(546\) 11.2573i 0.481766i
\(547\) 41.4457 1.77209 0.886045 0.463599i \(-0.153442\pi\)
0.886045 + 0.463599i \(0.153442\pi\)
\(548\) 0.952787 0.952787i 0.0407010 0.0407010i
\(549\) 2.24347 2.24347i 0.0957490 0.0957490i
\(550\) −11.9108 + 0.872195i −0.507878 + 0.0371905i
\(551\) 23.4092 0.997266
\(552\) −0.217489 + 0.217489i −0.00925694 + 0.00925694i
\(553\) 32.0564 1.36318
\(554\) −24.8652 −1.05642
\(555\) 8.57362 + 23.2649i 0.363930 + 0.987540i
\(556\) 8.19245 0.347437
\(557\) 24.9812 1.05849 0.529244 0.848470i \(-0.322476\pi\)
0.529244 + 0.848470i \(0.322476\pi\)
\(558\) 1.08006 1.08006i 0.0457226 0.0457226i
\(559\) −4.45827 −0.188565
\(560\) −9.52998 + 0.348461i −0.402715 + 0.0147252i
\(561\) −6.45311 + 6.45311i −0.272451 + 0.272451i
\(562\) −0.925329 + 0.925329i −0.0390326 + 0.0390326i
\(563\) 36.8702 1.55389 0.776946 0.629567i \(-0.216768\pi\)
0.776946 + 0.629567i \(0.216768\pi\)
\(564\) 12.0532i 0.507531i
\(565\) −8.18106 + 8.80205i −0.344180 + 0.370305i
\(566\) 0.300587i 0.0126346i
\(567\) −29.7488 + 29.7488i −1.24933 + 1.24933i
\(568\) −12.6621 −0.531290
\(569\) −9.95317 + 9.95317i −0.417259 + 0.417259i −0.884258 0.466999i \(-0.845335\pi\)
0.466999 + 0.884258i \(0.345335\pi\)
\(570\) −10.4090 9.67462i −0.435984 0.405225i
\(571\) 13.1507 0.550340 0.275170 0.961396i \(-0.411266\pi\)
0.275170 + 0.961396i \(0.411266\pi\)
\(572\) 3.45859i 0.144611i
\(573\) 0.915554i 0.0382478i
\(574\) 18.7866 + 18.7866i 0.784138 + 0.784138i
\(575\) −0.0616121 0.841381i −0.00256940 0.0350880i
\(576\) 0.323040i 0.0134600i
\(577\) 4.76642i 0.198429i 0.995066 + 0.0992144i \(0.0316330\pi\)
−0.995066 + 0.0992144i \(0.968367\pi\)
\(578\) −12.6069 −0.524379
\(579\) 9.44973 9.44973i 0.392718 0.392718i
\(580\) −15.0044 + 0.548631i −0.623023 + 0.0227806i
\(581\) −50.8629 −2.11015
\(582\) −6.50038 6.50038i −0.269449 0.269449i
\(583\) −6.87791 + 6.87791i −0.284854 + 0.284854i
\(584\) −4.83010 + 4.83010i −0.199871 + 0.199871i
\(585\) 0.712077 0.766127i 0.0294408 0.0316755i
\(586\) 22.4364 + 22.4364i 0.926837 + 0.926837i
\(587\) −1.56926 −0.0647702 −0.0323851 0.999475i \(-0.510310\pi\)
−0.0323851 + 0.999475i \(0.510310\pi\)
\(588\) 14.4218 + 14.4218i 0.594747 + 0.594747i
\(589\) 16.4843i 0.679223i
\(590\) −0.783939 21.4398i −0.0322743 0.882661i
\(591\) 21.1569i 0.870279i
\(592\) −1.89339 5.78058i −0.0778179 0.237580i
\(593\) 9.67923 + 9.67923i 0.397478 + 0.397478i 0.877343 0.479864i \(-0.159314\pi\)
−0.479864 + 0.877343i \(0.659314\pi\)
\(594\) 8.24188 8.24188i 0.338168 0.338168i
\(595\) −0.730363 19.9745i −0.0299420 0.818876i
\(596\) 22.8722i 0.936884i
\(597\) 1.23919i 0.0507167i
\(598\) 0.244316 0.00999082
\(599\) 43.4898i 1.77694i −0.458931 0.888472i \(-0.651768\pi\)
0.458931 0.888472i \(-0.348232\pi\)
\(600\) 6.89848 + 5.95710i 0.281629 + 0.243198i
\(601\) −46.6191 −1.90163 −0.950817 0.309754i \(-0.899753\pi\)
−0.950817 + 0.309754i \(0.899753\pi\)
\(602\) −9.28499 + 9.28499i −0.378428 + 0.378428i
\(603\) 2.55200 2.55200i 0.103925 0.103925i
\(604\) 16.6501i 0.677482i
\(605\) 8.67229 + 8.06046i 0.352579 + 0.327704i
\(606\) −15.1833 15.1833i −0.616779 0.616779i
\(607\) −11.8472 −0.480862 −0.240431 0.970666i \(-0.577289\pi\)
−0.240431 + 0.970666i \(0.577289\pi\)
\(608\) 2.46518 + 2.46518i 0.0999763 + 0.0999763i
\(609\) 36.9125 + 36.9125i 1.49577 + 1.49577i
\(610\) −0.802483 21.9469i −0.0324916 0.888605i
\(611\) −6.76997 + 6.76997i −0.273884 + 0.273884i
\(612\) 0.677082 0.0273694
\(613\) −32.8563 + 32.8563i −1.32705 + 1.32705i −0.419122 + 0.907930i \(0.637662\pi\)
−0.907930 + 0.419122i \(0.862338\pi\)
\(614\) 2.94724 + 2.94724i 0.118941 + 0.118941i
\(615\) −0.927878 25.3763i −0.0374156 1.02327i
\(616\) −7.20301 7.20301i −0.290218 0.290218i
\(617\) 7.41696 + 7.41696i 0.298595 + 0.298595i 0.840464 0.541868i \(-0.182283\pi\)
−0.541868 + 0.840464i \(0.682283\pi\)
\(618\) −8.19278 8.19278i −0.329562 0.329562i
\(619\) −4.51948 −0.181653 −0.0908266 0.995867i \(-0.528951\pi\)
−0.0908266 + 0.995867i \(0.528951\pi\)
\(620\) −0.386334 10.5658i −0.0155155 0.424331i
\(621\) 0.582209 + 0.582209i 0.0233632 + 0.0233632i
\(622\) 12.0863 + 12.0863i 0.484618 + 0.484618i
\(623\) 70.1413i 2.81015i
\(624\) −1.86647 + 1.86647i −0.0747185 + 0.0747185i
\(625\) −24.7333 + 3.64184i −0.989333 + 0.145673i
\(626\) −2.00477 −0.0801267
\(627\) 15.1797i 0.606219i
\(628\) 10.1100 10.1100i 0.403432 0.403432i
\(629\) 12.1159 3.96849i 0.483093 0.158234i
\(630\) −0.112567 3.07857i −0.00448478 0.122653i
\(631\) −5.79579 5.79579i −0.230727 0.230727i 0.582269 0.812996i \(-0.302165\pi\)
−0.812996 + 0.582269i \(0.802165\pi\)
\(632\) 5.31500 + 5.31500i 0.211419 + 0.211419i
\(633\) 31.6227 31.6227i 1.25689 1.25689i
\(634\) 7.28840 + 7.28840i 0.289459 + 0.289459i
\(635\) −37.1701 + 1.35911i −1.47505 + 0.0539348i
\(636\) 7.42348 0.294360
\(637\) 16.2008i 0.641898i
\(638\) −11.3407 11.3407i −0.448983 0.448983i
\(639\) 4.09037i 0.161813i
\(640\) −1.63786 1.52231i −0.0647420 0.0601745i
\(641\) 34.7174 1.37125 0.685627 0.727953i \(-0.259528\pi\)
0.685627 + 0.727953i \(0.259528\pi\)
\(642\) 18.8154i 0.742585i
\(643\) 39.5100i 1.55812i −0.626949 0.779060i \(-0.715697\pi\)
0.626949 0.779060i \(-0.284303\pi\)
\(644\) 0.508822 0.508822i 0.0200504 0.0200504i
\(645\) 12.5419 0.458589i 0.493835 0.0180569i
\(646\) −5.16694 + 5.16694i −0.203291 + 0.203291i
\(647\) −4.05796 −0.159535 −0.0797675 0.996813i \(-0.525418\pi\)
−0.0797675 + 0.996813i \(0.525418\pi\)
\(648\) −9.86477 −0.387525
\(649\) 16.2047 16.2047i 0.636092 0.636092i
\(650\) −0.528749 7.22065i −0.0207392 0.283217i
\(651\) −25.9930 + 25.9930i −1.01875 + 1.01875i
\(652\) 1.81513i 0.0710859i
\(653\) 27.8245i 1.08886i 0.838807 + 0.544429i \(0.183253\pi\)
−0.838807 + 0.544429i \(0.816747\pi\)
\(654\) −18.7629 −0.733688
\(655\) 1.80188 + 49.2793i 0.0704054 + 1.92550i
\(656\) 6.22969i 0.243228i
\(657\) −1.56032 1.56032i −0.0608738 0.0608738i
\(658\) 28.1988i 1.09931i
\(659\) 34.5284 1.34503 0.672517 0.740082i \(-0.265213\pi\)
0.672517 + 0.740082i \(0.265213\pi\)
\(660\) 0.355759 + 9.72959i 0.0138479 + 0.378724i
\(661\) −28.4737 28.4737i −1.10750 1.10750i −0.993478 0.114022i \(-0.963627\pi\)
−0.114022 0.993478i \(-0.536373\pi\)
\(662\) 0.839383 0.839383i 0.0326236 0.0326236i
\(663\) −3.91206 3.91206i −0.151932 0.151932i
\(664\) −8.43313 8.43313i −0.327269 0.327269i
\(665\) 24.3522 + 22.6341i 0.944336 + 0.877713i
\(666\) 1.86736 0.611642i 0.0723587 0.0237006i
\(667\) 0.801110 0.801110i 0.0310191 0.0310191i
\(668\) 16.2469i 0.628610i
\(669\) −35.5830 −1.37572
\(670\) −0.912841 24.9651i −0.0352661 0.964486i
\(671\) 16.5881 16.5881i 0.640375 0.640375i
\(672\) 7.77437i 0.299903i
\(673\) 7.80123 + 7.80123i 0.300715 + 0.300715i 0.841294 0.540578i \(-0.181795\pi\)
−0.540578 + 0.841294i \(0.681795\pi\)
\(674\) −7.69155 7.69155i −0.296268 0.296268i
\(675\) 15.9469 18.4669i 0.613797 0.710793i
\(676\) −10.9033 −0.419358
\(677\) 27.1256 + 27.1256i 1.04252 + 1.04252i 0.999055 + 0.0434658i \(0.0138400\pi\)
0.0434658 + 0.999055i \(0.486160\pi\)
\(678\) 6.92724 + 6.92724i 0.266039 + 0.266039i
\(679\) 15.2079 + 15.2079i 0.583624 + 0.583624i
\(680\) 3.19071 3.43290i 0.122358 0.131646i
\(681\) 13.9634 + 13.9634i 0.535079 + 0.535079i
\(682\) 7.98588 7.98588i 0.305795 0.305795i
\(683\) −5.91525 −0.226341 −0.113170 0.993576i \(-0.536101\pi\)
−0.113170 + 0.993576i \(0.536101\pi\)
\(684\) −0.796353 + 0.796353i −0.0304493 + 0.0304493i
\(685\) 3.01096 0.110095i 0.115043 0.00420651i
\(686\) −12.6308 12.6308i −0.482246 0.482246i
\(687\) −22.6714 22.6714i −0.864968 0.864968i
\(688\) −3.07893 −0.117383
\(689\) −4.16958 4.16958i −0.158848 0.158848i
\(690\) −0.687300 + 0.0251309i −0.0261651 + 0.000956718i
\(691\) 8.32303i 0.316623i −0.987389 0.158312i \(-0.949395\pi\)
0.987389 0.158312i \(-0.0506050\pi\)
\(692\) 12.0071 12.0071i 0.456442 0.456442i
\(693\) 2.32686 2.32686i 0.0883902 0.0883902i
\(694\) −21.8436 −0.829171
\(695\) 13.4181 + 12.4714i 0.508976 + 0.473068i
\(696\) 12.2403i 0.463966i
\(697\) −13.0572 −0.494578
\(698\) 4.00432i 0.151566i
\(699\) 3.79940i 0.143707i
\(700\) −16.1392 13.9368i −0.610005 0.526763i
\(701\) 15.3758 15.3758i 0.580737 0.580737i −0.354369 0.935106i \(-0.615304\pi\)
0.935106 + 0.354369i \(0.115304\pi\)
\(702\) 4.99646 + 4.99646i 0.188579 + 0.188579i
\(703\) −9.58262 + 18.9177i −0.361415 + 0.713495i
\(704\) 2.38854i 0.0900213i
\(705\) 18.3487 19.7414i 0.691050 0.743504i
\(706\) 11.1747i 0.420565i
\(707\) 35.5218 + 35.5218i 1.33594 + 1.33594i
\(708\) −17.4901 −0.657319
\(709\) −18.0591 18.0591i −0.678223 0.678223i 0.281375 0.959598i \(-0.409210\pi\)
−0.959598 + 0.281375i \(0.909210\pi\)
\(710\) −20.7387 19.2756i −0.778311 0.723401i
\(711\) −1.71696 + 1.71696i −0.0643910 + 0.0643910i
\(712\) 11.6295 11.6295i 0.435835 0.435835i
\(713\) 0.564125 + 0.564125i 0.0211266 + 0.0211266i
\(714\) −16.2948 −0.609819
\(715\) 5.26504 5.66468i 0.196901 0.211847i
\(716\) 8.45867 8.45867i 0.316115 0.316115i
\(717\) 2.24099 0.0836914
\(718\) 19.4341i 0.725276i
\(719\) 18.4885i 0.689505i −0.938694 0.344752i \(-0.887963\pi\)
0.938694 0.344752i \(-0.112037\pi\)
\(720\) 0.491767 0.529094i 0.0183271 0.0197182i
\(721\) 19.1673 + 19.1673i 0.713827 + 0.713827i
\(722\) 6.84576i 0.254773i
\(723\) 19.0624i 0.708939i
\(724\) 0.961200 0.0357227
\(725\) −25.4102 21.9427i −0.943712 0.814931i
\(726\) 6.82512 6.82512i 0.253304 0.253304i
\(727\) −0.154078 −0.00571445 −0.00285722 0.999996i \(-0.500909\pi\)
−0.00285722 + 0.999996i \(0.500909\pi\)
\(728\) 4.36667 4.36667i 0.161839 0.161839i
\(729\) 23.5002i 0.870378i
\(730\) −15.2639 + 0.558121i −0.564943 + 0.0206570i
\(731\) 6.45333i 0.238685i
\(732\) −17.9039 −0.661746
\(733\) −26.0288 + 26.0288i −0.961397 + 0.961397i −0.999282 0.0378850i \(-0.987938\pi\)
0.0378850 + 0.999282i \(0.487938\pi\)
\(734\) −10.2957 + 10.2957i −0.380020 + 0.380020i
\(735\) 1.66645 + 45.5754i 0.0614680 + 1.68107i
\(736\) 0.168727 0.00621935
\(737\) 18.8693 18.8693i 0.695059 0.695059i
\(738\) −2.01244 −0.0740789
\(739\) 36.2429 1.33322 0.666608 0.745408i \(-0.267745\pi\)
0.666608 + 0.745408i \(0.267745\pi\)
\(740\) 5.69871 12.3501i 0.209489 0.453998i
\(741\) 9.20236 0.338057
\(742\) −17.3675 −0.637581
\(743\) −7.38988 + 7.38988i −0.271109 + 0.271109i −0.829546 0.558438i \(-0.811401\pi\)
0.558438 + 0.829546i \(0.311401\pi\)
\(744\) −8.61934 −0.316000
\(745\) −34.8186 + 37.4615i −1.27565 + 1.37248i
\(746\) 23.2626 23.2626i 0.851704 0.851704i
\(747\) 2.72424 2.72424i 0.0996748 0.0996748i
\(748\) 5.00630 0.183048
\(749\) 44.0193i 1.60843i
\(750\) 2.23019 + 20.2585i 0.0814351 + 0.739735i
\(751\) 18.3541i 0.669749i 0.942263 + 0.334874i \(0.108694\pi\)
−0.942263 + 0.334874i \(0.891306\pi\)
\(752\) −4.67540 + 4.67540i −0.170494 + 0.170494i
\(753\) −40.7965 −1.48671
\(754\) 6.87505 6.87505i 0.250374 0.250374i
\(755\) −25.3465 + 27.2705i −0.922455 + 0.992474i
\(756\) 20.8117 0.756913
\(757\) 7.26929i 0.264207i −0.991236 0.132104i \(-0.957827\pi\)
0.991236 0.132104i \(-0.0421731\pi\)
\(758\) 11.6263i 0.422287i
\(759\) −0.519480 0.519480i −0.0188559 0.0188559i
\(760\) 0.284853 + 7.79038i 0.0103327 + 0.282587i
\(761\) 19.7277i 0.715127i 0.933889 + 0.357564i \(0.116392\pi\)
−0.933889 + 0.357564i \(0.883608\pi\)
\(762\) 30.3226i 1.09847i
\(763\) 43.8965 1.58916
\(764\) 0.355141 0.355141i 0.0128486 0.0128486i
\(765\) 1.10896 + 1.03073i 0.0400947 + 0.0372660i
\(766\) −8.97694 −0.324350
\(767\) 9.82377 + 9.82377i 0.354716 + 0.354716i
\(768\) −1.28900 + 1.28900i −0.0465128 + 0.0465128i
\(769\) −22.1613 + 22.1613i −0.799158 + 0.799158i −0.982963 0.183805i \(-0.941159\pi\)
0.183805 + 0.982963i \(0.441159\pi\)
\(770\) −0.832312 22.7627i −0.0299944 0.820311i
\(771\) 29.8570 + 29.8570i 1.07527 + 1.07527i
\(772\) −7.33106 −0.263851
\(773\) −30.0504 30.0504i −1.08084 1.08084i −0.996432 0.0844052i \(-0.973101\pi\)
−0.0844052 0.996432i \(-0.526899\pi\)
\(774\) 0.994617i 0.0357508i
\(775\) 15.4516 17.8933i 0.555037 0.642748i
\(776\) 5.04296i 0.181032i
\(777\) −44.9403 + 14.7199i −1.61223 + 0.528074i