Properties

Label 546.2.o.b.265.2
Level $546$
Weight $2$
Character 546.265
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.836829184.2
Defining polynomial: \(x^{8} + 14 x^{6} + 61 x^{4} + 84 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 265.2
Root \(1.65222i\) of defining polynomial
Character \(\chi\) \(=\) 546.265
Dual form 546.2.o.b.307.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(0.461191 + 0.461191i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.62949 - 0.292893i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(0.461191 + 0.461191i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-2.62949 - 0.292893i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -0.652223 q^{10} +(1.60525 + 1.60525i) q^{11} -1.00000 q^{12} +(2.51608 + 2.58251i) q^{13} +(2.06644 - 1.65222i) q^{14} +(0.461191 - 0.461191i) q^{15} -1.00000 q^{16} +6.40303 q^{17} +(0.707107 - 0.707107i) q^{18} +(2.52763 + 2.52763i) q^{19} +(0.461191 - 0.461191i) q^{20} +(-0.292893 + 2.62949i) q^{21} -2.27016 q^{22} -8.51280i q^{23} +(0.707107 - 0.707107i) q^{24} -4.57461i q^{25} +(-3.60525 - 0.0469777i) q^{26} +1.00000i q^{27} +(-0.292893 + 2.62949i) q^{28} +7.91120 q^{29} +0.652223i q^{30} +(0.922382 + 0.922382i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.60525 - 1.60525i) q^{33} +(-4.52763 + 4.52763i) q^{34} +(-1.07762 - 1.34778i) q^{35} +1.00000i q^{36} +(-0.953022 - 0.953022i) q^{37} -3.57461 q^{38} +(2.58251 - 2.51608i) q^{39} +0.652223i q^{40} +(-3.89486 - 3.89486i) q^{41} +(-1.65222 - 2.06644i) q^{42} +4.17620i q^{43} +(1.60525 - 1.60525i) q^{44} +(-0.461191 - 0.461191i) q^{45} +(6.01946 + 6.01946i) q^{46} +(1.41421 - 1.41421i) q^{47} +1.00000i q^{48} +(6.82843 + 1.54032i) q^{49} +(3.23473 + 3.23473i) q^{50} -6.40303i q^{51} +(2.58251 - 2.51608i) q^{52} +9.10072 q^{53} +(-0.707107 - 0.707107i) q^{54} +1.48065i q^{55} +(-1.65222 - 2.06644i) q^{56} +(2.52763 - 2.52763i) q^{57} +(-5.59406 + 5.59406i) q^{58} +(1.17834 - 1.17834i) q^{59} +(-0.461191 - 0.461191i) q^{60} +14.4874i q^{61} -1.30445 q^{62} +(2.62949 + 0.292893i) q^{63} +1.00000i q^{64} +(-0.0306399 + 2.35142i) q^{65} +2.27016i q^{66} +(3.47602 - 3.47602i) q^{67} -6.40303i q^{68} -8.51280 q^{69} +(1.71501 + 0.191032i) q^{70} +(-8.29326 + 8.29326i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(-5.89851 + 5.89851i) q^{73} +1.34778 q^{74} -4.57461 q^{75} +(2.52763 - 2.52763i) q^{76} +(-3.75081 - 4.69114i) q^{77} +(-0.0469777 + 3.60525i) q^{78} -9.18813 q^{79} +(-0.461191 - 0.461191i) q^{80} +1.00000 q^{81} +5.50817 q^{82} +(9.98882 + 9.98882i) q^{83} +(2.62949 + 0.292893i) q^{84} +(2.95302 + 2.95302i) q^{85} +(-2.95302 - 2.95302i) q^{86} -7.91120i q^{87} +2.27016i q^{88} +(8.54709 - 8.54709i) q^{89} +0.652223 q^{90} +(-5.85959 - 7.52763i) q^{91} -8.51280 q^{92} +(0.922382 - 0.922382i) q^{93} +2.00000i q^{94} +2.33144i q^{95} +(-0.707107 - 0.707107i) q^{96} +(0.272296 + 0.272296i) q^{97} +(-5.91760 + 3.73926i) q^{98} +(-1.60525 - 1.60525i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{5} - 8q^{9} + O(q^{10}) \) \( 8q - 4q^{5} - 8q^{9} + 4q^{10} - 8q^{12} + 16q^{13} - 4q^{14} - 4q^{15} - 8q^{16} + 4q^{17} - 8q^{19} - 4q^{20} - 8q^{21} - 12q^{22} - 16q^{26} - 8q^{28} + 12q^{29} - 8q^{31} - 8q^{34} - 24q^{35} - 4q^{37} - 4q^{38} - 4q^{39} + 12q^{41} - 4q^{42} + 4q^{45} + 24q^{46} + 32q^{49} - 8q^{50} - 4q^{52} + 40q^{53} - 4q^{56} - 8q^{57} + 4q^{58} - 8q^{59} + 4q^{60} + 8q^{62} - 12q^{65} + 32q^{67} - 28q^{69} + 8q^{70} - 12q^{71} + 20q^{73} + 20q^{74} - 12q^{75} - 8q^{76} + 8q^{77} - 4q^{78} + 24q^{79} + 4q^{80} + 8q^{81} + 40q^{82} + 44q^{83} + 20q^{85} - 20q^{86} + 16q^{89} - 4q^{90} - 28q^{91} - 28q^{92} - 8q^{93} - 8q^{97} - 16q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 1.00000i 0.577350i
\(4\) 1.00000i 0.500000i
\(5\) 0.461191 + 0.461191i 0.206251 + 0.206251i 0.802672 0.596421i \(-0.203411\pi\)
−0.596421 + 0.802672i \(0.703411\pi\)
\(6\) 0.707107 + 0.707107i 0.288675 + 0.288675i
\(7\) −2.62949 0.292893i −0.993854 0.110703i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −1.00000 −0.333333
\(10\) −0.652223 −0.206251
\(11\) 1.60525 + 1.60525i 0.484000 + 0.484000i 0.906406 0.422407i \(-0.138815\pi\)
−0.422407 + 0.906406i \(0.638815\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.51608 + 2.58251i 0.697834 + 0.716260i
\(14\) 2.06644 1.65222i 0.552278 0.441575i
\(15\) 0.461191 0.461191i 0.119079 0.119079i
\(16\) −1.00000 −0.250000
\(17\) 6.40303 1.55296 0.776482 0.630140i \(-0.217002\pi\)
0.776482 + 0.630140i \(0.217002\pi\)
\(18\) 0.707107 0.707107i 0.166667 0.166667i
\(19\) 2.52763 + 2.52763i 0.579878 + 0.579878i 0.934869 0.354992i \(-0.115516\pi\)
−0.354992 + 0.934869i \(0.615516\pi\)
\(20\) 0.461191 0.461191i 0.103125 0.103125i
\(21\) −0.292893 + 2.62949i −0.0639145 + 0.573802i
\(22\) −2.27016 −0.484000
\(23\) 8.51280i 1.77504i −0.460768 0.887521i \(-0.652426\pi\)
0.460768 0.887521i \(-0.347574\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) 4.57461i 0.914921i
\(26\) −3.60525 0.0469777i −0.707047 0.00921308i
\(27\) 1.00000i 0.192450i
\(28\) −0.292893 + 2.62949i −0.0553516 + 0.496927i
\(29\) 7.91120 1.46907 0.734537 0.678569i \(-0.237400\pi\)
0.734537 + 0.678569i \(0.237400\pi\)
\(30\) 0.652223i 0.119079i
\(31\) 0.922382 + 0.922382i 0.165665 + 0.165665i 0.785071 0.619406i \(-0.212627\pi\)
−0.619406 + 0.785071i \(0.712627\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 1.60525 1.60525i 0.279437 0.279437i
\(34\) −4.52763 + 4.52763i −0.776482 + 0.776482i
\(35\) −1.07762 1.34778i −0.182151 0.227816i
\(36\) 1.00000i 0.166667i
\(37\) −0.953022 0.953022i −0.156676 0.156676i 0.624416 0.781092i \(-0.285337\pi\)
−0.781092 + 0.624416i \(0.785337\pi\)
\(38\) −3.57461 −0.579878
\(39\) 2.58251 2.51608i 0.413533 0.402894i
\(40\) 0.652223i 0.103125i
\(41\) −3.89486 3.89486i −0.608275 0.608275i 0.334220 0.942495i \(-0.391527\pi\)
−0.942495 + 0.334220i \(0.891527\pi\)
\(42\) −1.65222 2.06644i −0.254944 0.318858i
\(43\) 4.17620i 0.636865i 0.947946 + 0.318433i \(0.103156\pi\)
−0.947946 + 0.318433i \(0.896844\pi\)
\(44\) 1.60525 1.60525i 0.242000 0.242000i
\(45\) −0.461191 0.461191i −0.0687503 0.0687503i
\(46\) 6.01946 + 6.01946i 0.887521 + 0.887521i
\(47\) 1.41421 1.41421i 0.206284 0.206284i −0.596402 0.802686i \(-0.703403\pi\)
0.802686 + 0.596402i \(0.203403\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 6.82843 + 1.54032i 0.975490 + 0.220046i
\(50\) 3.23473 + 3.23473i 0.457461 + 0.457461i
\(51\) 6.40303i 0.896604i
\(52\) 2.58251 2.51608i 0.358130 0.348917i
\(53\) 9.10072 1.25008 0.625040 0.780593i \(-0.285083\pi\)
0.625040 + 0.780593i \(0.285083\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) 1.48065i 0.199651i
\(56\) −1.65222 2.06644i −0.220788 0.276139i
\(57\) 2.52763 2.52763i 0.334792 0.334792i
\(58\) −5.59406 + 5.59406i −0.734537 + 0.734537i
\(59\) 1.17834 1.17834i 0.153407 0.153407i −0.626231 0.779638i \(-0.715403\pi\)
0.779638 + 0.626231i \(0.215403\pi\)
\(60\) −0.461191 0.461191i −0.0595395 0.0595395i
\(61\) 14.4874i 1.85492i 0.373918 + 0.927462i \(0.378014\pi\)
−0.373918 + 0.927462i \(0.621986\pi\)
\(62\) −1.30445 −0.165665
\(63\) 2.62949 + 0.292893i 0.331285 + 0.0369011i
\(64\) 1.00000i 0.125000i
\(65\) −0.0306399 + 2.35142i −0.00380041 + 0.291658i
\(66\) 2.27016i 0.279437i
\(67\) 3.47602 3.47602i 0.424663 0.424663i −0.462142 0.886806i \(-0.652919\pi\)
0.886806 + 0.462142i \(0.152919\pi\)
\(68\) 6.40303i 0.776482i
\(69\) −8.51280 −1.02482
\(70\) 1.71501 + 0.191032i 0.204983 + 0.0228327i
\(71\) −8.29326 + 8.29326i −0.984229 + 0.984229i −0.999878 0.0156481i \(-0.995019\pi\)
0.0156481 + 0.999878i \(0.495019\pi\)
\(72\) −0.707107 0.707107i −0.0833333 0.0833333i
\(73\) −5.89851 + 5.89851i −0.690368 + 0.690368i −0.962313 0.271945i \(-0.912333\pi\)
0.271945 + 0.962313i \(0.412333\pi\)
\(74\) 1.34778 0.156676
\(75\) −4.57461 −0.528230
\(76\) 2.52763 2.52763i 0.289939 0.289939i
\(77\) −3.75081 4.69114i −0.427444 0.534605i
\(78\) −0.0469777 + 3.60525i −0.00531917 + 0.408214i
\(79\) −9.18813 −1.03375 −0.516873 0.856062i \(-0.672904\pi\)
−0.516873 + 0.856062i \(0.672904\pi\)
\(80\) −0.461191 0.461191i −0.0515627 0.0515627i
\(81\) 1.00000 0.111111
\(82\) 5.50817 0.608275
\(83\) 9.98882 + 9.98882i 1.09642 + 1.09642i 0.994826 + 0.101589i \(0.0323926\pi\)
0.101589 + 0.994826i \(0.467607\pi\)
\(84\) 2.62949 + 0.292893i 0.286901 + 0.0319573i
\(85\) 2.95302 + 2.95302i 0.320300 + 0.320300i
\(86\) −2.95302 2.95302i −0.318433 0.318433i
\(87\) 7.91120i 0.848170i
\(88\) 2.27016i 0.242000i
\(89\) 8.54709 8.54709i 0.905989 0.905989i −0.0899564 0.995946i \(-0.528673\pi\)
0.995946 + 0.0899564i \(0.0286728\pi\)
\(90\) 0.652223 0.0687503
\(91\) −5.85959 7.52763i −0.614252 0.789110i
\(92\) −8.51280 −0.887521
\(93\) 0.922382 0.922382i 0.0956466 0.0956466i
\(94\) 2.00000i 0.206284i
\(95\) 2.33144i 0.239201i
\(96\) −0.707107 0.707107i −0.0721688 0.0721688i
\(97\) 0.272296 + 0.272296i 0.0276474 + 0.0276474i 0.720795 0.693148i \(-0.243777\pi\)
−0.693148 + 0.720795i \(0.743777\pi\)
\(98\) −5.91760 + 3.73926i −0.597768 + 0.377722i
\(99\) −1.60525 1.60525i −0.161333 0.161333i
\(100\) −4.57461 −0.457461
\(101\) −8.03892 −0.799902 −0.399951 0.916536i \(-0.630973\pi\)
−0.399951 + 0.916536i \(0.630973\pi\)
\(102\) 4.52763 + 4.52763i 0.448302 + 0.448302i
\(103\) −7.62934 −0.751741 −0.375870 0.926672i \(-0.622656\pi\)
−0.375870 + 0.926672i \(0.622656\pi\)
\(104\) −0.0469777 + 3.60525i −0.00460654 + 0.353523i
\(105\) −1.34778 + 1.07762i −0.131530 + 0.105165i
\(106\) −6.43518 + 6.43518i −0.625040 + 0.625040i
\(107\) −14.3986 −1.39197 −0.695984 0.718058i \(-0.745031\pi\)
−0.695984 + 0.718058i \(0.745031\pi\)
\(108\) 1.00000 0.0962250
\(109\) −10.6815 + 10.6815i −1.02310 + 1.02310i −0.0233724 + 0.999727i \(0.507440\pi\)
−0.999727 + 0.0233724i \(0.992560\pi\)
\(110\) −1.04698 1.04698i −0.0998254 0.0998254i
\(111\) −0.953022 + 0.953022i −0.0904569 + 0.0904569i
\(112\) 2.62949 + 0.292893i 0.248463 + 0.0276758i
\(113\) 15.0256 1.41349 0.706745 0.707469i \(-0.250163\pi\)
0.706745 + 0.707469i \(0.250163\pi\)
\(114\) 3.57461i 0.334792i
\(115\) 3.92603 3.92603i 0.366104 0.366104i
\(116\) 7.91120i 0.734537i
\(117\) −2.51608 2.58251i −0.232611 0.238753i
\(118\) 1.66642i 0.153407i
\(119\) −16.8367 1.87540i −1.54342 0.171918i
\(120\) 0.652223 0.0595395
\(121\) 5.84638i 0.531489i
\(122\) −10.2442 10.2442i −0.927462 0.927462i
\(123\) −3.89486 + 3.89486i −0.351188 + 0.351188i
\(124\) 0.922382 0.922382i 0.0828324 0.0828324i
\(125\) 4.41572 4.41572i 0.394954 0.394954i
\(126\) −2.06644 + 1.65222i −0.184093 + 0.147192i
\(127\) 15.7970i 1.40176i −0.713280 0.700879i \(-0.752791\pi\)
0.713280 0.700879i \(-0.247209\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 4.17620 0.367694
\(130\) −1.64104 1.68437i −0.143929 0.147729i
\(131\) 1.75522i 0.153355i 0.997056 + 0.0766773i \(0.0244311\pi\)
−0.997056 + 0.0766773i \(0.975569\pi\)
\(132\) −1.60525 1.60525i −0.139719 0.139719i
\(133\) −5.90604 7.38669i −0.512119 0.640508i
\(134\) 4.91583i 0.424663i
\(135\) −0.461191 + 0.461191i −0.0396930 + 0.0396930i
\(136\) 4.52763 + 4.52763i 0.388241 + 0.388241i
\(137\) −1.82994 1.82994i −0.156342 0.156342i 0.624602 0.780944i \(-0.285261\pi\)
−0.780944 + 0.624602i \(0.785261\pi\)
\(138\) 6.01946 6.01946i 0.512410 0.512410i
\(139\) 13.8448i 1.17430i −0.809479 0.587149i \(-0.800250\pi\)
0.809479 0.587149i \(-0.199750\pi\)
\(140\) −1.34778 + 1.07762i −0.113908 + 0.0910753i
\(141\) −1.41421 1.41421i −0.119098 0.119098i
\(142\) 11.7284i 0.984229i
\(143\) −0.106647 + 8.18448i −0.00891825 + 0.684421i
\(144\) 1.00000 0.0833333
\(145\) 3.64858 + 3.64858i 0.302998 + 0.302998i
\(146\) 8.34175i 0.690368i
\(147\) 1.54032 6.82843i 0.127043 0.563199i
\(148\) −0.953022 + 0.953022i −0.0783380 + 0.0783380i
\(149\) −3.12824 + 3.12824i −0.256276 + 0.256276i −0.823537 0.567262i \(-0.808003\pi\)
0.567262 + 0.823537i \(0.308003\pi\)
\(150\) 3.23473 3.23473i 0.264115 0.264115i
\(151\) 11.5502 + 11.5502i 0.939943 + 0.939943i 0.998296 0.0583534i \(-0.0185850\pi\)
−0.0583534 + 0.998296i \(0.518585\pi\)
\(152\) 3.57461i 0.289939i
\(153\) −6.40303 −0.517654
\(154\) 5.96936 + 0.664914i 0.481025 + 0.0535803i
\(155\) 0.850789i 0.0683370i
\(156\) −2.51608 2.58251i −0.201447 0.206766i
\(157\) 18.5294i 1.47880i −0.673264 0.739402i \(-0.735108\pi\)
0.673264 0.739402i \(-0.264892\pi\)
\(158\) 6.49699 6.49699i 0.516873 0.516873i
\(159\) 9.10072i 0.721734i
\(160\) 0.652223 0.0515627
\(161\) −2.49334 + 22.3843i −0.196503 + 1.76413i
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) −13.1032 13.1032i −1.02632 1.02632i −0.999644 0.0266792i \(-0.991507\pi\)
−0.0266792 0.999644i \(-0.508493\pi\)
\(164\) −3.89486 + 3.89486i −0.304138 + 0.304138i
\(165\) 1.48065 0.115268
\(166\) −14.1263 −1.09642
\(167\) 9.82552 9.82552i 0.760322 0.760322i −0.216059 0.976380i \(-0.569320\pi\)
0.976380 + 0.216059i \(0.0693202\pi\)
\(168\) −2.06644 + 1.65222i −0.159429 + 0.127472i
\(169\) −0.338732 + 12.9956i −0.0260563 + 0.999660i
\(170\) −4.17620 −0.320300
\(171\) −2.52763 2.52763i −0.193293 0.193293i
\(172\) 4.17620 0.318433
\(173\) −10.9940 −0.835856 −0.417928 0.908480i \(-0.637244\pi\)
−0.417928 + 0.908480i \(0.637244\pi\)
\(174\) 5.59406 + 5.59406i 0.424085 + 0.424085i
\(175\) −1.33987 + 12.0289i −0.101285 + 0.909298i
\(176\) −1.60525 1.60525i −0.121000 0.121000i
\(177\) −1.17834 1.17834i −0.0885695 0.0885695i
\(178\) 12.0874i 0.905989i
\(179\) 2.54656i 0.190339i 0.995461 + 0.0951695i \(0.0303393\pi\)
−0.995461 + 0.0951695i \(0.969661\pi\)
\(180\) −0.461191 + 0.461191i −0.0343752 + 0.0343752i
\(181\) −13.8933 −1.03268 −0.516339 0.856384i \(-0.672705\pi\)
−0.516339 + 0.856384i \(0.672705\pi\)
\(182\) 9.46619 + 1.17948i 0.701681 + 0.0874288i
\(183\) 14.4874 1.07094
\(184\) 6.01946 6.01946i 0.443760 0.443760i
\(185\) 0.879051i 0.0646291i
\(186\) 1.30445i 0.0956466i
\(187\) 10.2784 + 10.2784i 0.751634 + 0.751634i
\(188\) −1.41421 1.41421i −0.103142 0.103142i
\(189\) 0.292893 2.62949i 0.0213048 0.191267i
\(190\) −1.64858 1.64858i −0.119600 0.119600i
\(191\) −10.2290 −0.740142 −0.370071 0.929004i \(-0.620667\pi\)
−0.370071 + 0.929004i \(0.620667\pi\)
\(192\) 1.00000 0.0721688
\(193\) 12.3940 + 12.3940i 0.892139 + 0.892139i 0.994724 0.102585i \(-0.0327115\pi\)
−0.102585 + 0.994724i \(0.532712\pi\)
\(194\) −0.385084 −0.0276474
\(195\) 2.35142 + 0.0306399i 0.168389 + 0.00219417i
\(196\) 1.54032 6.82843i 0.110023 0.487745i
\(197\) 8.84638 8.84638i 0.630278 0.630278i −0.317860 0.948138i \(-0.602964\pi\)
0.948138 + 0.317860i \(0.102964\pi\)
\(198\) 2.27016 0.161333
\(199\) −7.40980 −0.525267 −0.262633 0.964896i \(-0.584591\pi\)
−0.262633 + 0.964896i \(0.584591\pi\)
\(200\) 3.23473 3.23473i 0.228730 0.228730i
\(201\) −3.47602 3.47602i −0.245179 0.245179i
\(202\) 5.68437 5.68437i 0.399951 0.399951i
\(203\) −20.8024 2.31714i −1.46004 0.162631i
\(204\) −6.40303 −0.448302
\(205\) 3.59255i 0.250915i
\(206\) 5.39475 5.39475i 0.375870 0.375870i
\(207\) 8.51280i 0.591681i
\(208\) −2.51608 2.58251i −0.174458 0.179065i
\(209\) 8.11492i 0.561321i
\(210\) 0.191032 1.71501i 0.0131824 0.118347i
\(211\) 14.6299 1.00716 0.503581 0.863948i \(-0.332016\pi\)
0.503581 + 0.863948i \(0.332016\pi\)
\(212\) 9.10072i 0.625040i
\(213\) 8.29326 + 8.29326i 0.568245 + 0.568245i
\(214\) 10.1814 10.1814i 0.695984 0.695984i
\(215\) −1.92603 + 1.92603i −0.131354 + 0.131354i
\(216\) −0.707107 + 0.707107i −0.0481125 + 0.0481125i
\(217\) −2.15524 2.69555i −0.146307 0.182986i
\(218\) 15.1059i 1.02310i
\(219\) 5.89851 + 5.89851i 0.398584 + 0.398584i
\(220\) 1.48065 0.0998254
\(221\) 16.1105 + 16.5359i 1.08371 + 1.11233i
\(222\) 1.34778i 0.0904569i
\(223\) −11.0574 11.0574i −0.740458 0.740458i 0.232208 0.972666i \(-0.425405\pi\)
−0.972666 + 0.232208i \(0.925405\pi\)
\(224\) −2.06644 + 1.65222i −0.138070 + 0.110394i
\(225\) 4.57461i 0.304974i
\(226\) −10.6247 + 10.6247i −0.706745 + 0.706745i
\(227\) 9.31423 + 9.31423i 0.618207 + 0.618207i 0.945071 0.326864i \(-0.105992\pi\)
−0.326864 + 0.945071i \(0.605992\pi\)
\(228\) −2.52763 2.52763i −0.167396 0.167396i
\(229\) −15.5860 + 15.5860i −1.02995 + 1.02995i −0.0304148 + 0.999537i \(0.509683\pi\)
−0.999537 + 0.0304148i \(0.990317\pi\)
\(230\) 5.55224i 0.366104i
\(231\) −4.69114 + 3.75081i −0.308654 + 0.246785i
\(232\) 5.59406 + 5.59406i 0.367268 + 0.367268i
\(233\) 14.4240i 0.944948i 0.881345 + 0.472474i \(0.156639\pi\)
−0.881345 + 0.472474i \(0.843361\pi\)
\(234\) 3.60525 + 0.0469777i 0.235682 + 0.00307103i
\(235\) 1.30445 0.0850927
\(236\) −1.17834 1.17834i −0.0767034 0.0767034i
\(237\) 9.18813i 0.596833i
\(238\) 13.2315 10.5792i 0.857668 0.685750i
\(239\) 3.83747 3.83747i 0.248225 0.248225i −0.572017 0.820242i \(-0.693839\pi\)
0.820242 + 0.572017i \(0.193839\pi\)
\(240\) −0.461191 + 0.461191i −0.0297698 + 0.0297698i
\(241\) −14.2110 + 14.2110i −0.915412 + 0.915412i −0.996691 0.0812794i \(-0.974099\pi\)
0.0812794 + 0.996691i \(0.474099\pi\)
\(242\) 4.13401 + 4.13401i 0.265744 + 0.265744i
\(243\) 1.00000i 0.0641500i
\(244\) 14.4874 0.927462
\(245\) 2.43883 + 3.85959i 0.155811 + 0.246580i
\(246\) 5.50817i 0.351188i
\(247\) −0.167927 + 12.8873i −0.0106849 + 0.820001i
\(248\) 1.30445i 0.0828324i
\(249\) 9.98882 9.98882i 0.633016 0.633016i
\(250\) 6.24478i 0.394954i
\(251\) −5.39399 −0.340465 −0.170233 0.985404i \(-0.554452\pi\)
−0.170233 + 0.985404i \(0.554452\pi\)
\(252\) 0.292893 2.62949i 0.0184505 0.165642i
\(253\) 13.6651 13.6651i 0.859119 0.859119i
\(254\) 11.1702 + 11.1702i 0.700879 + 0.700879i
\(255\) 2.95302 2.95302i 0.184925 0.184925i
\(256\) 1.00000 0.0625000
\(257\) 4.38508 0.273534 0.136767 0.990603i \(-0.456329\pi\)
0.136767 + 0.990603i \(0.456329\pi\)
\(258\) −2.95302 + 2.95302i −0.183847 + 0.183847i
\(259\) 2.22683 + 2.78510i 0.138368 + 0.173057i
\(260\) 2.35142 + 0.0306399i 0.145829 + 0.00190021i
\(261\) −7.91120 −0.489691
\(262\) −1.24113 1.24113i −0.0766773 0.0766773i
\(263\) −12.4336 −0.766687 −0.383343 0.923606i \(-0.625227\pi\)
−0.383343 + 0.923606i \(0.625227\pi\)
\(264\) 2.27016 0.139719
\(265\) 4.19717 + 4.19717i 0.257830 + 0.257830i
\(266\) 9.39939 + 1.04698i 0.576313 + 0.0641943i
\(267\) −8.54709 8.54709i −0.523073 0.523073i
\(268\) −3.47602 3.47602i −0.212332 0.212332i
\(269\) 29.7839i 1.81596i 0.419016 + 0.907979i \(0.362375\pi\)
−0.419016 + 0.907979i \(0.637625\pi\)
\(270\) 0.652223i 0.0396930i
\(271\) 14.7173 14.7173i 0.894010 0.894010i −0.100888 0.994898i \(-0.532168\pi\)
0.994898 + 0.100888i \(0.0321682\pi\)
\(272\) −6.40303 −0.388241
\(273\) −7.52763 + 5.85959i −0.455593 + 0.354639i
\(274\) 2.58792 0.156342
\(275\) 7.34336 7.34336i 0.442821 0.442821i
\(276\) 8.51280i 0.512410i
\(277\) 24.1271i 1.44965i −0.688930 0.724827i \(-0.741919\pi\)
0.688930 0.724827i \(-0.258081\pi\)
\(278\) 9.78973 + 9.78973i 0.587149 + 0.587149i
\(279\) −0.922382 0.922382i −0.0552216 0.0552216i
\(280\) 0.191032 1.71501i 0.0114163 0.102492i
\(281\) −7.70534 7.70534i −0.459662 0.459662i 0.438882 0.898545i \(-0.355374\pi\)
−0.898545 + 0.438882i \(0.855374\pi\)
\(282\) 2.00000 0.119098
\(283\) −6.39133 −0.379925 −0.189962 0.981791i \(-0.560837\pi\)
−0.189962 + 0.981791i \(0.560837\pi\)
\(284\) 8.29326 + 8.29326i 0.492115 + 0.492115i
\(285\) 2.33144 0.138103
\(286\) −5.71189 5.86271i −0.337751 0.346670i
\(287\) 9.10072 + 11.3823i 0.537199 + 0.671875i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) 23.9988 1.41170
\(290\) −5.15987 −0.302998
\(291\) 0.272296 0.272296i 0.0159622 0.0159622i
\(292\) 5.89851 + 5.89851i 0.345184 + 0.345184i
\(293\) 8.93819 8.93819i 0.522175 0.522175i −0.396053 0.918228i \(-0.629620\pi\)
0.918228 + 0.396053i \(0.129620\pi\)
\(294\) 3.73926 + 5.91760i 0.218078 + 0.345121i
\(295\) 1.08688 0.0632806
\(296\) 1.34778i 0.0783380i
\(297\) −1.60525 + 1.60525i −0.0931458 + 0.0931458i
\(298\) 4.42400i 0.256276i
\(299\) 21.9844 21.4188i 1.27139 1.23868i
\(300\) 4.57461i 0.264115i
\(301\) 1.22318 10.9813i 0.0705030 0.632951i
\(302\) −16.3345 −0.939943
\(303\) 8.03892i 0.461824i
\(304\) −2.52763 2.52763i −0.144969 0.144969i
\(305\) −6.68147 + 6.68147i −0.382580 + 0.382580i
\(306\) 4.52763 4.52763i 0.258827 0.258827i
\(307\) 1.27177 1.27177i 0.0725838 0.0725838i −0.669883 0.742467i \(-0.733656\pi\)
0.742467 + 0.669883i \(0.233656\pi\)
\(308\) −4.69114 + 3.75081i −0.267303 + 0.213722i
\(309\) 7.62934i 0.434018i
\(310\) −0.601599 0.601599i −0.0341685 0.0341685i
\(311\) −1.52201 −0.0863053 −0.0431527 0.999068i \(-0.513740\pi\)
−0.0431527 + 0.999068i \(0.513740\pi\)
\(312\) 3.60525 + 0.0469777i 0.204107 + 0.00265959i
\(313\) 3.48506i 0.196987i 0.995138 + 0.0984937i \(0.0314024\pi\)
−0.995138 + 0.0984937i \(0.968598\pi\)
\(314\) 13.1022 + 13.1022i 0.739402 + 0.739402i
\(315\) 1.07762 + 1.34778i 0.0607169 + 0.0759386i
\(316\) 9.18813i 0.516873i
\(317\) 3.61566 3.61566i 0.203076 0.203076i −0.598241 0.801316i \(-0.704133\pi\)
0.801316 + 0.598241i \(0.204133\pi\)
\(318\) 6.43518 + 6.43518i 0.360867 + 0.360867i
\(319\) 12.6994 + 12.6994i 0.711031 + 0.711031i
\(320\) −0.461191 + 0.461191i −0.0257814 + 0.0257814i
\(321\) 14.3986i 0.803653i
\(322\) −14.0650 17.5912i −0.783814 0.980317i
\(323\) 16.1845 + 16.1845i 0.900529 + 0.900529i
\(324\) 1.00000i 0.0555556i
\(325\) 11.8140 11.5101i 0.655321 0.638463i
\(326\) 18.5307 1.02632
\(327\) 10.6815 + 10.6815i 0.590687 + 0.590687i
\(328\) 5.50817i 0.304138i
\(329\) −4.13287 + 3.30445i −0.227853 + 0.182180i
\(330\) −1.04698 + 1.04698i −0.0576342 + 0.0576342i
\(331\) 4.50162 4.50162i 0.247431 0.247431i −0.572484 0.819916i \(-0.694020\pi\)
0.819916 + 0.572484i \(0.194020\pi\)
\(332\) 9.98882 9.98882i 0.548208 0.548208i
\(333\) 0.953022 + 0.953022i 0.0522253 + 0.0522253i
\(334\) 13.8954i 0.760322i
\(335\) 3.20622 0.175174
\(336\) 0.292893 2.62949i 0.0159786 0.143450i
\(337\) 20.7331i 1.12940i −0.825295 0.564701i \(-0.808991\pi\)
0.825295 0.564701i \(-0.191009\pi\)
\(338\) −8.94975 9.42879i −0.486802 0.512858i
\(339\) 15.0256i 0.816079i
\(340\) 2.95302 2.95302i 0.160150 0.160150i
\(341\) 2.96130i 0.160363i
\(342\) 3.57461 0.193293
\(343\) −17.5041 6.05025i −0.945134 0.326683i
\(344\) −2.95302 + 2.95302i −0.159216 + 0.159216i
\(345\) −3.92603 3.92603i −0.211370 0.211370i
\(346\) 7.77391 7.77391i 0.417928 0.417928i
\(347\) 0.161276 0.00865778 0.00432889 0.999991i \(-0.498622\pi\)
0.00432889 + 0.999991i \(0.498622\pi\)
\(348\) −7.91120 −0.424085
\(349\) 7.17995 7.17995i 0.384334 0.384334i −0.488327 0.872661i \(-0.662393\pi\)
0.872661 + 0.488327i \(0.162393\pi\)
\(350\) −7.55827 9.45313i −0.404006 0.505291i
\(351\) −2.58251 + 2.51608i −0.137844 + 0.134298i
\(352\) 2.27016 0.121000
\(353\) −9.44711 9.44711i −0.502819 0.502819i 0.409494 0.912313i \(-0.365705\pi\)
−0.912313 + 0.409494i \(0.865705\pi\)
\(354\) 1.66642 0.0885695
\(355\) −7.64956 −0.405997
\(356\) −8.54709 8.54709i −0.452995 0.452995i
\(357\) −1.87540 + 16.8367i −0.0992569 + 0.891093i
\(358\) −1.80069 1.80069i −0.0951695 0.0951695i
\(359\) −19.1933 19.1933i −1.01298 1.01298i −0.999915 0.0130682i \(-0.995840\pi\)
−0.0130682 0.999915i \(-0.504160\pi\)
\(360\) 0.652223i 0.0343752i
\(361\) 6.22220i 0.327484i
\(362\) 9.82401 9.82401i 0.516339 0.516339i
\(363\) −5.84638 −0.306855
\(364\) −7.52763 + 5.85959i −0.394555 + 0.307126i
\(365\) −5.44068 −0.284778
\(366\) −10.2442 + 10.2442i −0.535470 + 0.535470i
\(367\) 24.3142i 1.26919i 0.772844 + 0.634596i \(0.218834\pi\)
−0.772844 + 0.634596i \(0.781166\pi\)
\(368\) 8.51280i 0.443760i
\(369\) 3.89486 + 3.89486i 0.202758 + 0.202758i
\(370\) 0.621583 + 0.621583i 0.0323146 + 0.0323146i
\(371\) −23.9303 2.66554i −1.24240 0.138388i
\(372\) −0.922382 0.922382i −0.0478233 0.0478233i
\(373\) 9.74654 0.504657 0.252328 0.967642i \(-0.418804\pi\)
0.252328 + 0.967642i \(0.418804\pi\)
\(374\) −14.5359 −0.751634
\(375\) −4.41572 4.41572i −0.228027 0.228027i
\(376\) 2.00000 0.103142
\(377\) 19.9052 + 20.4308i 1.02517 + 1.05224i
\(378\) 1.65222 + 2.06644i 0.0849812 + 0.106286i
\(379\) 14.5776 14.5776i 0.748802 0.748802i −0.225452 0.974254i \(-0.572386\pi\)
0.974254 + 0.225452i \(0.0723859\pi\)
\(380\) 2.33144 0.119600
\(381\) −15.7970 −0.809306
\(382\) 7.23297 7.23297i 0.370071 0.370071i
\(383\) −20.8642 20.8642i −1.06611 1.06611i −0.997654 0.0684580i \(-0.978192\pi\)
−0.0684580 0.997654i \(-0.521808\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) 0.433672 3.89335i 0.0221020 0.198424i
\(386\) −17.5277 −0.892139
\(387\) 4.17620i 0.212288i
\(388\) 0.272296 0.272296i 0.0138237 0.0138237i
\(389\) 6.09321i 0.308938i −0.987998 0.154469i \(-0.950633\pi\)
0.987998 0.154469i \(-0.0493667\pi\)
\(390\) −1.68437 + 1.64104i −0.0852915 + 0.0830974i
\(391\) 54.5077i 2.75657i
\(392\) 3.73926 + 5.91760i 0.188861 + 0.298884i
\(393\) 1.75522 0.0885393
\(394\) 12.5107i 0.630278i
\(395\) −4.23748 4.23748i −0.213211 0.213211i
\(396\) −1.60525 + 1.60525i −0.0806666 + 0.0806666i
\(397\) −26.9792 + 26.9792i −1.35405 + 1.35405i −0.472972 + 0.881077i \(0.656819\pi\)
−0.881077 + 0.472972i \(0.843181\pi\)
\(398\) 5.23952 5.23952i 0.262633 0.262633i
\(399\) −7.38669 + 5.90604i −0.369797 + 0.295672i
\(400\) 4.57461i 0.228730i
\(401\) 21.4604 + 21.4604i 1.07168 + 1.07168i 0.997224 + 0.0744583i \(0.0237228\pi\)
0.0744583 + 0.997224i \(0.476277\pi\)
\(402\) 4.91583 0.245179
\(403\) −0.0612798 + 4.70285i −0.00305256 + 0.234265i
\(404\) 8.03892i 0.399951i
\(405\) 0.461191 + 0.461191i 0.0229168 + 0.0229168i
\(406\) 16.3480 13.0711i 0.811337 0.648706i
\(407\) 3.05967i 0.151662i
\(408\) 4.52763 4.52763i 0.224151 0.224151i
\(409\) 4.20898 + 4.20898i 0.208121 + 0.208121i 0.803468 0.595348i \(-0.202986\pi\)
−0.595348 + 0.803468i \(0.702986\pi\)
\(410\) 2.54032 + 2.54032i 0.125457 + 0.125457i
\(411\) −1.82994 + 1.82994i −0.0902642 + 0.0902642i
\(412\) 7.62934i 0.375870i
\(413\) −3.44356 + 2.75330i −0.169447 + 0.135481i
\(414\) −6.01946 6.01946i −0.295840 0.295840i
\(415\) 9.21351i 0.452273i
\(416\) 3.60525 + 0.0469777i 0.176762 + 0.00230327i
\(417\) −13.8448 −0.677981
\(418\) −5.73812 5.73812i −0.280661 0.280661i
\(419\) 3.78685i 0.185000i 0.995713 + 0.0924998i \(0.0294858\pi\)
−0.995713 + 0.0924998i \(0.970514\pi\)
\(420\) 1.07762 + 1.34778i 0.0525824 + 0.0657648i
\(421\) −16.2730 + 16.2730i −0.793099 + 0.793099i −0.981997 0.188897i \(-0.939509\pi\)
0.188897 + 0.981997i \(0.439509\pi\)
\(422\) −10.3449 + 10.3449i −0.503581 + 0.503581i
\(423\) −1.41421 + 1.41421i −0.0687614 + 0.0687614i
\(424\) 6.43518 + 6.43518i 0.312520 + 0.312520i
\(425\) 29.2913i 1.42084i
\(426\) −11.7284 −0.568245
\(427\) 4.24327 38.0945i 0.205346 1.84352i
\(428\) 14.3986i 0.695984i
\(429\) 8.18448 + 0.106647i 0.395151 + 0.00514895i
\(430\) 2.72382i 0.131354i
\(431\) −17.7084 + 17.7084i −0.852982 + 0.852982i −0.990499 0.137518i \(-0.956088\pi\)
0.137518 + 0.990499i \(0.456088\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −13.2092 −0.634796 −0.317398 0.948292i \(-0.602809\pi\)
−0.317398 + 0.948292i \(0.602809\pi\)
\(434\) 3.43003 + 0.382063i 0.164647 + 0.0183396i
\(435\) 3.64858 3.64858i 0.174936 0.174936i
\(436\) 10.6815 + 10.6815i 0.511550 + 0.511550i
\(437\) 21.5172 21.5172i 1.02931 1.02931i
\(438\) −8.34175 −0.398584
\(439\) −27.2638 −1.30123 −0.650616 0.759407i \(-0.725489\pi\)
−0.650616 + 0.759407i \(0.725489\pi\)
\(440\) −1.04698 + 1.04698i −0.0499127 + 0.0499127i
\(441\) −6.82843 1.54032i −0.325163 0.0733485i
\(442\) −23.0845 0.300799i −1.09802 0.0143076i
\(443\) 22.3627 1.06248 0.531242 0.847220i \(-0.321725\pi\)
0.531242 + 0.847220i \(0.321725\pi\)
\(444\) 0.953022 + 0.953022i 0.0452284 + 0.0452284i
\(445\) 7.88368 0.373722
\(446\) 15.6375 0.740458
\(447\) 3.12824 + 3.12824i 0.147961 + 0.147961i
\(448\) 0.292893 2.62949i 0.0138379 0.124232i
\(449\) 3.36702 + 3.36702i 0.158899 + 0.158899i 0.782079 0.623179i \(-0.214159\pi\)
−0.623179 + 0.782079i \(0.714159\pi\)
\(450\) −3.23473 3.23473i −0.152487 0.152487i
\(451\) 12.5044i 0.588810i
\(452\) 15.0256i 0.706745i
\(453\) 11.5502 11.5502i 0.542676 0.542676i
\(454\) −13.1723 −0.618207
\(455\) 0.769283 6.17407i 0.0360646 0.289445i
\(456\) 3.57461 0.167396
\(457\) −12.5030 + 12.5030i −0.584866 + 0.584866i −0.936237 0.351370i \(-0.885716\pi\)
0.351370 + 0.936237i \(0.385716\pi\)
\(458\) 22.0419i 1.02995i
\(459\) 6.40303i 0.298868i
\(460\) −3.92603 3.92603i −0.183052 0.183052i
\(461\) 4.03719 + 4.03719i 0.188031 + 0.188031i 0.794844 0.606814i \(-0.207553\pi\)
−0.606814 + 0.794844i \(0.707553\pi\)
\(462\) 0.664914 5.96936i 0.0309346 0.277720i
\(463\) −12.8250 12.8250i −0.596028 0.596028i 0.343225 0.939253i \(-0.388481\pi\)
−0.939253 + 0.343225i \(0.888481\pi\)
\(464\) −7.91120 −0.367268
\(465\) 0.850789 0.0394544
\(466\) −10.1993 10.1993i −0.472474 0.472474i
\(467\) 17.0280 0.787964 0.393982 0.919118i \(-0.371097\pi\)
0.393982 + 0.919118i \(0.371097\pi\)
\(468\) −2.58251 + 2.51608i −0.119377 + 0.116306i
\(469\) −10.1583 + 8.12205i −0.469065 + 0.375041i
\(470\) −0.922382 + 0.922382i −0.0425463 + 0.0425463i
\(471\) −18.5294 −0.853788
\(472\) 1.66642 0.0767034
\(473\) −6.70383 + 6.70383i −0.308243 + 0.308243i
\(474\) −6.49699 6.49699i −0.298417 0.298417i
\(475\) 11.5629 11.5629i 0.530542 0.530542i
\(476\) −1.87540 + 16.8367i −0.0859590 + 0.771709i
\(477\) −9.10072 −0.416693
\(478\) 5.42701i 0.248225i
\(479\) −22.7406 + 22.7406i −1.03905 + 1.03905i −0.0398390 + 0.999206i \(0.512685\pi\)
−0.999206 + 0.0398390i \(0.987315\pi\)
\(480\) 0.652223i 0.0297698i
\(481\) 0.0633154 4.85907i 0.00288693 0.221554i
\(482\) 20.0974i 0.915412i
\(483\) 22.3843 + 2.49334i 1.01852 + 0.113451i
\(484\) −5.84638 −0.265744
\(485\) 0.251161i 0.0114046i
\(486\) 0.707107 + 0.707107i 0.0320750 + 0.0320750i
\(487\) −8.40745 + 8.40745i −0.380978 + 0.380978i −0.871454 0.490477i \(-0.836823\pi\)
0.490477 + 0.871454i \(0.336823\pi\)
\(488\) −10.2442 + 10.2442i −0.463731 + 0.463731i
\(489\) −13.1032 + 13.1032i −0.592548 + 0.592548i
\(490\) −4.45366 1.00463i −0.201196 0.0453846i
\(491\) 12.3150i 0.555767i −0.960615 0.277884i \(-0.910367\pi\)
0.960615 0.277884i \(-0.0896329\pi\)
\(492\) 3.89486 + 3.89486i 0.175594 + 0.175594i
\(493\) 50.6557 2.28142
\(494\) −8.99398 9.23146i −0.404658 0.415343i
\(495\) 1.48065i 0.0665503i
\(496\) −0.922382 0.922382i −0.0414162 0.0414162i
\(497\) 24.2361 19.3780i 1.08714 0.869222i
\(498\) 14.1263i 0.633016i
\(499\) 4.13266 4.13266i 0.185003 0.185003i −0.608529 0.793532i \(-0.708240\pi\)
0.793532 + 0.608529i \(0.208240\pi\)
\(500\) −4.41572 4.41572i −0.197477 0.197477i
\(501\) −9.82552 9.82552i −0.438972 0.438972i
\(502\) 3.81412 3.81412i 0.170233 0.170233i
\(503\) 32.1557i 1.43375i 0.697201 + 0.716875i \(0.254428\pi\)
−0.697201 + 0.716875i \(0.745572\pi\)
\(504\) 1.65222 + 2.06644i 0.0735959 + 0.0920464i
\(505\) −3.70748 3.70748i −0.164981 0.164981i
\(506\) 19.3254i 0.859119i
\(507\) 12.9956 + 0.338732i 0.577154 + 0.0150436i
\(508\) −15.7970 −0.700879
\(509\) −25.9435 25.9435i −1.14992 1.14992i −0.986567 0.163357i \(-0.947768\pi\)
−0.163357 0.986567i \(-0.552232\pi\)
\(510\) 4.17620i 0.184925i
\(511\) 17.2377 13.7824i 0.762551 0.609699i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −2.52763 + 2.52763i −0.111597 + 0.111597i
\(514\) −3.10072 + 3.10072i −0.136767 + 0.136767i
\(515\) −3.51858 3.51858i −0.155047 0.155047i
\(516\) 4.17620i 0.183847i
\(517\) 4.54032 0.199683
\(518\) −3.54397 0.394755i −0.155713 0.0173445i
\(519\) 10.9940i 0.482582i
\(520\) −1.68437 + 1.64104i −0.0738646 + 0.0719644i
\(521\) 3.85949i 0.169087i 0.996420 + 0.0845437i \(0.0269433\pi\)
−0.996420 + 0.0845437i \(0.973057\pi\)
\(522\) 5.59406 5.59406i 0.244846 0.244846i
\(523\) 36.3670i 1.59022i 0.606467 + 0.795109i \(0.292586\pi\)
−0.606467 + 0.795109i \(0.707414\pi\)
\(524\) 1.75522 0.0766773
\(525\) 12.0289 + 1.33987i 0.524983 + 0.0584768i
\(526\) 8.79186 8.79186i 0.383343 0.383343i
\(527\) 5.90604 + 5.90604i 0.257271 + 0.257271i
\(528\) −1.60525 + 1.60525i −0.0698593 + 0.0698593i
\(529\) −49.4678 −2.15077
\(530\) −5.93570 −0.257830
\(531\) −1.17834 + 1.17834i −0.0511356 + 0.0511356i
\(532\) −7.38669 + 5.90604i −0.320254 + 0.256060i
\(533\) 0.258761 19.8583i 0.0112082 0.860158i
\(534\) 12.0874 0.523073
\(535\) −6.64052 6.64052i −0.287095 0.287095i
\(536\) 4.91583 0.212332
\(537\) 2.54656 0.109892
\(538\) −21.0604 21.0604i −0.907979 0.907979i
\(539\) 8.48871 + 13.4339i 0.365635 + 0.578639i
\(540\) 0.461191 + 0.461191i 0.0198465 + 0.0198465i
\(541\) 18.4800 + 18.4800i 0.794518 + 0.794518i 0.982225 0.187707i \(-0.0601055\pi\)
−0.187707 + 0.982225i \(0.560105\pi\)
\(542\) 20.8134i 0.894010i
\(543\) 13.8933i 0.596217i
\(544\) 4.52763 4.52763i 0.194120 0.194120i
\(545\) −9.85240 −0.422030
\(546\) 1.17948 9.46619i 0.0504770 0.405116i
\(547\) 3.22661 0.137960 0.0689800 0.997618i \(-0.478026\pi\)
0.0689800 + 0.997618i \(0.478026\pi\)
\(548\) −1.82994 + 1.82994i −0.0781711 + 0.0781711i
\(549\) 14.4874i 0.618308i
\(550\) 10.3851i 0.442821i
\(551\) 19.9966 + 19.9966i 0.851883 + 0.851883i
\(552\) −6.01946 6.01946i −0.256205 0.256205i
\(553\) 24.1601 + 2.69114i 1.02739 + 0.114439i
\(554\) 17.0604 + 17.0604i 0.724827 + 0.724827i
\(555\) −0.879051 −0.0373136
\(556\) −13.8448 −0.587149
\(557\) −27.1310 27.1310i −1.14958 1.14958i −0.986636 0.162939i \(-0.947903\pi\)
−0.162939 0.986636i \(-0.552097\pi\)
\(558\) 1.30445 0.0552216
\(559\) −10.7851 + 10.5076i −0.456161 + 0.444426i
\(560\) 1.07762 + 1.34778i 0.0455377 + 0.0569540i
\(561\) 10.2784 10.2784i 0.433956 0.433956i
\(562\) 10.8970 0.459662
\(563\) 2.30304 0.0970614 0.0485307 0.998822i \(-0.484546\pi\)
0.0485307 + 0.998822i \(0.484546\pi\)
\(564\) −1.41421 + 1.41421i −0.0595491 + 0.0595491i
\(565\) 6.92968 + 6.92968i 0.291534 + 0.291534i
\(566\) 4.51935 4.51935i 0.189962 0.189962i
\(567\) −2.62949 0.292893i −0.110428 0.0123004i
\(568\) −11.7284 −0.492115
\(569\) 5.19115i 0.217624i 0.994062 + 0.108812i \(0.0347047\pi\)
−0.994062 + 0.108812i \(0.965295\pi\)
\(570\) −1.64858 + 1.64858i −0.0690513 + 0.0690513i
\(571\) 11.8508i 0.495941i 0.968768 + 0.247970i \(0.0797636\pi\)
−0.968768 + 0.247970i \(0.920236\pi\)
\(572\) 8.18448 + 0.106647i 0.342210 + 0.00445913i
\(573\) 10.2290i 0.427321i
\(574\) −14.4837 1.61331i −0.604537 0.0673381i
\(575\) −38.9427 −1.62402
\(576\) 1.00000i 0.0416667i
\(577\) −29.5340 29.5340i −1.22952 1.22952i −0.964147 0.265369i \(-0.914506\pi\)
−0.265369 0.964147i \(-0.585494\pi\)
\(578\) −16.9697 + 16.9697i −0.705848 + 0.705848i
\(579\) 12.3940 12.3940i 0.515077 0.515077i
\(580\) 3.64858 3.64858i 0.151499 0.151499i
\(581\) −23.3398 29.1911i −0.968299 1.21105i
\(582\) 0.385084i 0.0159622i
\(583\) 14.6089 + 14.6089i 0.605038 + 0.605038i
\(584\) −8.34175 −0.345184
\(585\) 0.0306399 2.35142i 0.00126680 0.0972194i
\(586\) 12.6405i 0.522175i
\(587\) −11.2384 11.2384i −0.463857 0.463857i 0.436060 0.899917i \(-0.356373\pi\)
−0.899917 + 0.436060i \(0.856373\pi\)
\(588\) −6.82843 1.54032i −0.281600 0.0635217i
\(589\) 4.66288i 0.192131i
\(590\) −0.768540 + 0.768540i −0.0316403 + 0.0316403i
\(591\) −8.84638 8.84638i −0.363891 0.363891i
\(592\) 0.953022 + 0.953022i 0.0391690 + 0.0391690i
\(593\) 7.99323 7.99323i 0.328243 0.328243i −0.523675 0.851918i \(-0.675439\pi\)
0.851918 + 0.523675i \(0.175439\pi\)
\(594\) 2.27016i 0.0931458i
\(595\) −6.90002 8.62986i −0.282873 0.353790i
\(596\) 3.12824 + 3.12824i 0.128138 + 0.128138i
\(597\) 7.40980i 0.303263i
\(598\) −0.399911 + 30.6907i −0.0163536 + 1.25504i
\(599\) 25.0503 1.02353 0.511764 0.859126i \(-0.328992\pi\)
0.511764 + 0.859126i \(0.328992\pi\)
\(600\) −3.23473 3.23473i −0.132057 0.132057i
\(601\) 11.5478i 0.471046i 0.971869 + 0.235523i \(0.0756803\pi\)
−0.971869 + 0.235523i \(0.924320\pi\)
\(602\) 6.90002 + 8.62986i 0.281224 + 0.351727i
\(603\) −3.47602 + 3.47602i −0.141554 + 0.141554i
\(604\) 11.5502 11.5502i 0.469971 0.469971i
\(605\) 2.69630 2.69630i 0.109620 0.109620i
\(606\) −5.68437 5.68437i −0.230912 0.230912i
\(607\) 15.2350i 0.618369i 0.951002 + 0.309185i \(0.100056\pi\)
−0.951002 + 0.309185i \(0.899944\pi\)
\(608\) 3.57461 0.144969
\(609\) −2.31714 + 20.8024i −0.0938951 + 0.842957i
\(610\) 9.44903i 0.382580i
\(611\) 7.21049 + 0.0939553i 0.291705 + 0.00380103i
\(612\) 6.40303i 0.258827i
\(613\) 11.5903 11.5903i 0.468129 0.468129i −0.433179 0.901308i \(-0.642608\pi\)
0.901308 + 0.433179i \(0.142608\pi\)
\(614\) 1.79855i 0.0725838i
\(615\) −3.59255 −0.144866
\(616\) 0.664914 5.96936i 0.0267902 0.240512i
\(617\) 14.5420 14.5420i 0.585441 0.585441i −0.350952 0.936393i \(-0.614142\pi\)
0.936393 + 0.350952i \(0.114142\pi\)
\(618\) −5.39475 5.39475i −0.217009 0.217009i
\(619\) −7.62482 + 7.62482i −0.306467 + 0.306467i −0.843538 0.537070i \(-0.819531\pi\)
0.537070 + 0.843538i \(0.319531\pi\)
\(620\) 0.850789 0.0341685
\(621\) 8.51280 0.341607
\(622\) 1.07622 1.07622i 0.0431527 0.0431527i
\(623\) −24.9779 + 19.9711i −1.00072 + 0.800125i
\(624\) −2.58251 + 2.51608i −0.103383 + 0.100724i
\(625\) −18.8000 −0.752002
\(626\) −2.46431 2.46431i −0.0984937 0.0984937i
\(627\) 8.11492 0.324079
\(628\) −18.5294 −0.739402
\(629\) −6.10223 6.10223i −0.243312 0.243312i
\(630\) −1.71501 0.191032i −0.0683278 0.00761088i
\(631\) 28.8742 + 28.8742i 1.14946 + 1.14946i 0.986658 + 0.162807i \(0.0520548\pi\)
0.162807 + 0.986658i \(0.447945\pi\)
\(632\) −6.49699 6.49699i −0.258436 0.258436i
\(633\) 14.6299i 0.581485i
\(634\) 5.11331i 0.203076i
\(635\) 7.28545 7.28545i 0.289114 0.289114i
\(636\) −9.10072 −0.360867
\(637\) 13.2029 + 21.5101i 0.523120 + 0.852259i
\(638\) −17.9597 −0.711031
\(639\) 8.29326 8.29326i 0.328076 0.328076i
\(640\) 0.652223i 0.0257814i
\(641\) 13.9110i 0.549453i −0.961522 0.274726i \(-0.911413\pi\)
0.961522 0.274726i \(-0.0885873\pi\)
\(642\) −10.1814 10.1814i −0.401826 0.401826i
\(643\) 31.6768 + 31.6768i 1.24921 + 1.24921i 0.956068 + 0.293144i \(0.0947017\pi\)
0.293144 + 0.956068i \(0.405298\pi\)
\(644\) 22.3843 + 2.49334i 0.882066 + 0.0982514i
\(645\) 1.92603 + 1.92603i 0.0758373 + 0.0758373i
\(646\) −22.8883 −0.900529
\(647\) 2.61086 0.102644 0.0513218 0.998682i \(-0.483657\pi\)
0.0513218 + 0.998682i \(0.483657\pi\)
\(648\) 0.707107 + 0.707107i 0.0277778 + 0.0277778i
\(649\) 3.78305 0.148498
\(650\) −0.214904 + 16.4926i −0.00842924 + 0.646892i
\(651\) −2.69555 + 2.15524i −0.105647 + 0.0844703i
\(652\) −13.1032 + 13.1032i −0.513162 + 0.513162i
\(653\) 2.35132 0.0920144 0.0460072 0.998941i \(-0.485350\pi\)
0.0460072 + 0.998941i \(0.485350\pi\)
\(654\) −15.1059 −0.590687
\(655\) −0.809494 + 0.809494i −0.0316295 + 0.0316295i
\(656\) 3.89486 + 3.89486i 0.152069 + 0.152069i
\(657\) 5.89851 5.89851i 0.230123 0.230123i
\(658\) 0.585786 5.25898i 0.0228363 0.205016i
\(659\) 13.1002 0.510312 0.255156 0.966900i \(-0.417873\pi\)
0.255156 + 0.966900i \(0.417873\pi\)
\(660\) 1.48065i 0.0576342i
\(661\) −12.5885 + 12.5885i −0.489636 + 0.489636i −0.908191 0.418555i \(-0.862537\pi\)
0.418555 + 0.908191i \(0.362537\pi\)
\(662\) 6.36625i 0.247431i
\(663\) 16.5359 16.1105i 0.642201 0.625680i
\(664\) 14.1263i 0.548208i
\(665\) 0.682863 6.13049i 0.0264803 0.237730i
\(666\) −1.34778 −0.0522253
\(667\) 67.3465i 2.60767i
\(668\) −9.82552 9.82552i −0.380161 0.380161i
\(669\) −11.0574 + 11.0574i −0.427503 + 0.427503i
\(670\) −2.26714 + 2.26714i −0.0875872 + 0.0875872i
\(671\) −23.2559 + 23.2559i −0.897782 + 0.897782i
\(672\) 1.65222 + 2.06644i 0.0637359 + 0.0797145i
\(673\) 7.32134i 0.282217i −0.989994 0.141109i \(-0.954933\pi\)
0.989994 0.141109i \(-0.0450667\pi\)
\(674\) 14.6605 + 14.6605i 0.564701 + 0.564701i
\(675\) 4.57461 0.176077
\(676\) 12.9956 + 0.338732i 0.499830 + 0.0130282i
\(677\) 27.2432i 1.04704i −0.852013 0.523520i \(-0.824619\pi\)
0.852013 0.523520i \(-0.175381\pi\)
\(678\) 10.6247 + 10.6247i 0.408039 + 0.408039i
\(679\) −0.636245 0.795752i −0.0244168 0.0305381i
\(680\) 4.17620i 0.160150i
\(681\) 9.31423 9.31423i 0.356922 0.356922i
\(682\) −2.09396 2.09396i −0.0801817 0.0801817i
\(683\) −3.89033 3.89033i −0.148859 0.148859i 0.628749 0.777608i \(-0.283567\pi\)
−0.777608 + 0.628749i \(0.783567\pi\)
\(684\) −2.52763 + 2.52763i −0.0966463 + 0.0966463i
\(685\) 1.68790i 0.0644914i
\(686\) 16.6555 8.09911i 0.635908 0.309226i
\(687\) 15.5860 + 15.5860i 0.594643 + 0.594643i
\(688\) 4.17620i 0.159216i
\(689\) 22.8981 + 23.5027i 0.872348 + 0.895382i
\(690\) 5.55224 0.211370
\(691\) 7.75081 + 7.75081i 0.294855 + 0.294855i 0.838995 0.544140i \(-0.183144\pi\)
−0.544140 + 0.838995i \(0.683144\pi\)
\(692\) 10.9940i 0.417928i
\(693\) 3.75081 + 4.69114i 0.142481 + 0.178202i
\(694\) −0.114040 + 0.114040i −0.00432889 + 0.00432889i
\(695\) 6.38508 6.38508i 0.242200 0.242200i
\(696\) 5.59406 5.59406i 0.212042 0.212042i
\(697\) −24.9389 24.9389i −0.944630 0.944630i
\(698\) 10.1540i 0.384334i
\(699\) 14.4240 0.545566
\(700\) 12.0289 + 1.33987i 0.454649 + 0.0506424i
\(701\) 5.02289i 0.189712i −0.995491 0.0948559i \(-0.969761\pi\)
0.995491 0.0948559i \(-0.0302390\pi\)
\(702\) 0.0469777 3.60525i 0.00177306 0.136071i
\(703\) 4.81777i 0.181706i
\(704\) −1.60525 + 1.60525i −0.0605000 + 0.0605000i
\(705\) 1.30445i 0.0491283i
\(706\) 13.3602 0.502819
\(707\) 21.1382 + 2.35454i 0.794986 + 0.0885518i
\(708\) −1.17834 + 1.17834i −0.0442847 + 0.0442847i
\(709\) 4.80002 + 4.80002i 0.180269 + 0.180269i 0.791473 0.611204i \(-0.209315\pi\)
−0.611204 + 0.791473i \(0.709315\pi\)
\(710\) 5.40906 5.40906i 0.202998 0.202998i
\(711\) 9.18813 0.344582
\(712\) 12.0874 0.452995
\(713\) 7.85206 7.85206i 0.294062 0.294062i
\(714\) −10.5792 13.2315i −0.395918 0.495175i
\(715\) −3.82380 + 3.72543i −0.143002 + 0.139323i
\(716\) 2.54656 0.0951695
\(717\) −3.83747 3.83747i −0.143313 0.143313i
\(718\) 27.1434 1.01298
\(719\) −23.2670 −0.867713 −0.433857 0.900982i \(-0.642848\pi\)
−0.433857 + 0.900982i \(0.642848\pi\)
\(720\) 0.461191 + 0.461191i 0.0171876 + 0.0171876i
\(721\) 20.0613 + 2.23458i 0.747120 + 0.0832201i
\(722\) 4.39976 + 4.39976i 0.163742 + 0.163742i
\(723\) 14.2110 + 14.2110i 0.528513 + 0.528513i
\(724\) 13.8933i 0.516339i
\(725\) 36.1906i 1.34409i
\(726\) 4.13401 4.13401i 0.153428 0.153428i
\(727\) 29.8368 1.10659 0.553293 0.832987i \(-0.313371\pi\)
0.553293 + 0.832987i \(0.313371\pi\)
\(728\) 1.17948 9.46619i 0.0437144 0.350840i
\(729\) −1.00000 −0.0370370
\(730\) 3.84714 3.84714i 0.142389 0.142389i
\(731\) 26.7404i 0.989028i
\(732\) 14.4874i 0.535470i
\(733\) 11.7443 + 11.7443i 0.433784 + 0.433784i 0.889913 0.456129i \(-0.150765\pi\)
−0.456129 + 0.889913i \(0.650765\pi\)
\(734\) −17.1928 17.1928i −0.634596 0.634596i
\(735\) 3.85959 2.43883i 0.142363 0.0899576i
\(736\) −6.01946 6.01946i −0.221880 0.221880i
\(737\) 11.1597 0.411074
\(738\) −5.50817 −0.202758
\(739\) −21.9136 21.9136i −0.806103 0.806103i 0.177938 0.984042i \(-0.443057\pi\)
−0.984042 + 0.177938i \(0.943057\pi\)
\(740\) −0.879051 −0.0323146
\(741\) 12.8873 + 0.167927i 0.473428 + 0.00616894i
\(742\) 18.8061 15.0364i 0.690392 0.552004i
\(743\) 8.70770 8.70770i 0.319454 0.319454i −0.529103 0.848558i \(-0.677472\pi\)
0.848558 + 0.529103i \(0.177472\pi\)
\(744\) 1.30445 0.0478233
\(745\) −2.88544 −0.105714
\(746\) −6.89184 + 6.89184i −0.252328 + 0.252328i
\(747\) −9.98882 9.98882i −0.365472 0.365472i
\(748\) 10.2784 10.2784i 0.375817 0.375817i
\(749\) 37.8610 + 4.21726i 1.38341 + 0.154095i
\(750\) 6.24478 0.228027
\(751\) 34.2765i 1.25077i 0.780318 + 0.625384i \(0.215057\pi\)
−0.780318 + 0.625384i \(0.784943\pi\)
\(752\) −1.41421 + 1.41421i −0.0515711 + 0.0515711i
\(753\) 5.39399i 0.196568i
\(754\) −28.5218 0.371650i −1.03870 0.0135347i
\(755\) 10.6537i 0.387728i
\(756\) −2.62949 0.292893i −0.0956336 0.0106524i
\(757\) −28.0153 −1.01823 −0.509117 0.860697i \(-0.670028\pi\)
−0.509117 + 0.860697i \(0.670028\pi\)
\(758\) 20.6159i 0.748802i
\(759\) −13.6651 13.6651i −0.496013 0.496013i
\(760\) −1.64858 + 1.64858i −0.0598002 + 0.0598002i
\(761\) −24.7400 + 24.7400i −0.896824 + 0.896824i −0.995154 0.0983300i \(-0.968650\pi\)
0.0983300 + 0.995154i \(0.468650\pi\)
\(762\) 11.1702 11.1702i 0.404653 0.404653i
\(763\) 31.2153 24.9583i 1.13007 0.903550i
\(764\) 10.2290i 0.370071i
\(765\) −2.95302 2.95302i −0.106767 0.106767i
\(766\) 29.5065 1.06611
\(767\) 6.00787 + 0.0782847i 0.216932 + 0.00282670i
\(768\) 1.00000i 0.0360844i
\(769\) −24.3745 24.3745i −0.878968 0.878968i 0.114460 0.993428i \(-0.463486\pi\)
−0.993428 + 0.114460i \(0.963486\pi\)
\(770\) 2.44636 + 3.05967i 0.0881608 + 0.110263i
\(771\) 4.38508i 0.157925i
\(772\) 12.3940 12.3940i 0.446069 0.446069i
\(773\) −21.0774 21.0774i −0.758100 0.758100i 0.217876 0.975976i \(-0.430087\pi\)
−0.975976 + 0.217876i \(0.930087\pi\)
\(774\) 2.95302 + 2.95302i 0.106144 + 0.106144i
\(775\) 4.21954 4.21954i 0.151570 0.151570i
\(776\) 0.385084i 0.0138237i
\(777\) 2.78510 2.22683i 0.0999148 0.0798870i
\(778\) 4.30855 + 4.30855i 0.154469 + 0.154469i