Properties

Label 300.2.j.d.43.4
Level $300$
Weight $2$
Character 300.43
Analytic conductor $2.396$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.426337261060096.1
Defining polynomial: \(x^{12} - 4 x^{9} - 3 x^{8} + 4 x^{7} + 8 x^{6} + 8 x^{5} - 12 x^{4} - 32 x^{3} + 64\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.4
Root \(-0.0912546 - 1.41127i\) of defining polynomial
Character \(\chi\) \(=\) 300.43
Dual form 300.2.j.d.7.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0912546 - 1.41127i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.98335 + 0.257569i) q^{4} +(1.06244 + 0.933389i) q^{6} +(1.86678 + 1.86678i) q^{7} +(0.544488 + 2.77552i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.0912546 - 1.41127i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.98335 + 0.257569i) q^{4} +(1.06244 + 0.933389i) q^{6} +(1.86678 + 1.86678i) q^{7} +(0.544488 + 2.77552i) q^{8} -1.00000i q^{9} +0.728515i q^{11} +(1.22031 - 1.58457i) q^{12} +(3.12489 + 3.12489i) q^{13} +(2.46417 - 2.80487i) q^{14} +(3.86732 - 1.02170i) q^{16} +(-1.12489 + 1.12489i) q^{17} +(-1.41127 + 0.0912546i) q^{18} +3.73356 q^{19} -2.64002 q^{21} +(1.02813 - 0.0664803i) q^{22} +(5.83347 - 5.83347i) q^{23} +(-2.34760 - 1.57758i) q^{24} +(4.12489 - 4.69521i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-4.18329 - 3.22164i) q^{28} +2.64002i q^{29} +6.01008i q^{31} +(-1.79480 - 5.36458i) q^{32} +(-0.515138 - 0.515138i) q^{33} +(1.69016 + 1.48486i) q^{34} +(0.257569 + 1.98335i) q^{36} +(-3.12489 + 3.12489i) q^{37} +(-0.340704 - 5.26904i) q^{38} -4.41926 q^{39} -4.24977 q^{41} +(0.240914 + 3.72578i) q^{42} +(-5.10495 + 5.10495i) q^{43} +(-0.187643 - 1.44490i) q^{44} +(-8.76491 - 7.70025i) q^{46} +(-2.09991 - 2.09991i) q^{47} +(-2.01216 + 3.45705i) q^{48} -0.0302761i q^{49} -1.59083i q^{51} +(-7.00260 - 5.39285i) q^{52} +(-0.484862 - 0.484862i) q^{53} +(0.933389 - 1.06244i) q^{54} +(-4.16485 + 6.19773i) q^{56} +(-2.64002 + 2.64002i) q^{57} +(3.72578 - 0.240914i) q^{58} +4.92834 q^{59} +2.31032 q^{61} +(8.48183 - 0.548448i) q^{62} +(1.86678 - 1.86678i) q^{63} +(-7.40707 + 3.02248i) q^{64} +(-0.679988 + 0.774006i) q^{66} +(5.10495 + 5.10495i) q^{67} +(1.94130 - 2.52077i) q^{68} +8.24977i q^{69} -13.1240i q^{71} +(2.77552 - 0.544488i) q^{72} +(-3.96972 - 3.96972i) q^{73} +(4.69521 + 4.12489i) q^{74} +(-7.40493 + 0.961649i) q^{76} +(-1.35998 + 1.35998i) q^{77} +(0.403277 + 6.23675i) q^{78} -7.11388 q^{79} -1.00000 q^{81} +(0.387811 + 5.99756i) q^{82} +(-3.55694 + 3.55694i) q^{83} +(5.23608 - 0.679988i) q^{84} +(7.67030 + 6.73860i) q^{86} +(-1.86678 - 1.86678i) q^{87} +(-2.02201 + 0.396668i) q^{88} +1.03028i q^{89} +11.6669i q^{91} +(-10.0673 + 13.0723i) q^{92} +(-4.24977 - 4.24977i) q^{93} +(-2.77191 + 3.15516i) q^{94} +(5.06244 + 2.52422i) q^{96} +(12.5298 - 12.5298i) q^{97} +(-0.0427276 + 0.00276283i) q^{98} +0.728515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{6} + 12q^{8} + O(q^{10}) \) \( 12q - 4q^{6} + 12q^{8} + 8q^{12} + 4q^{13} + 12q^{16} + 20q^{17} - 12q^{22} + 16q^{26} + 4q^{28} - 20q^{32} - 8q^{33} + 4q^{36} - 4q^{37} - 16q^{38} + 16q^{41} - 20q^{42} - 40q^{46} - 16q^{48} + 8q^{52} - 4q^{53} - 64q^{56} + 20q^{58} - 32q^{61} + 56q^{62} - 24q^{66} + 16q^{68} + 12q^{72} - 44q^{73} + 8q^{76} - 48q^{77} + 24q^{78} - 12q^{81} - 16q^{82} + 64q^{86} - 60q^{88} - 56q^{92} + 16q^{93} + 44q^{96} + 20q^{97} - 24q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0912546 1.41127i −0.0645267 0.997916i
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) −1.98335 + 0.257569i −0.991673 + 0.128785i
\(5\) 0 0
\(6\) 1.06244 + 0.933389i 0.433740 + 0.381055i
\(7\) 1.86678 + 1.86678i 0.705576 + 0.705576i 0.965602 0.260026i \(-0.0837311\pi\)
−0.260026 + 0.965602i \(0.583731\pi\)
\(8\) 0.544488 + 2.77552i 0.192506 + 0.981296i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 0.728515i 0.219656i 0.993951 + 0.109828i \(0.0350299\pi\)
−0.993951 + 0.109828i \(0.964970\pi\)
\(12\) 1.22031 1.58457i 0.352273 0.457425i
\(13\) 3.12489 + 3.12489i 0.866687 + 0.866687i 0.992104 0.125417i \(-0.0400268\pi\)
−0.125417 + 0.992104i \(0.540027\pi\)
\(14\) 2.46417 2.80487i 0.658577 0.749634i
\(15\) 0 0
\(16\) 3.86732 1.02170i 0.966829 0.255424i
\(17\) −1.12489 + 1.12489i −0.272825 + 0.272825i −0.830236 0.557412i \(-0.811795\pi\)
0.557412 + 0.830236i \(0.311795\pi\)
\(18\) −1.41127 + 0.0912546i −0.332639 + 0.0215089i
\(19\) 3.73356 0.856537 0.428268 0.903652i \(-0.359124\pi\)
0.428268 + 0.903652i \(0.359124\pi\)
\(20\) 0 0
\(21\) −2.64002 −0.576100
\(22\) 1.02813 0.0664803i 0.219198 0.0141737i
\(23\) 5.83347 5.83347i 1.21636 1.21636i 0.247466 0.968897i \(-0.420402\pi\)
0.968897 0.247466i \(-0.0795978\pi\)
\(24\) −2.34760 1.57758i −0.479202 0.322022i
\(25\) 0 0
\(26\) 4.12489 4.69521i 0.808957 0.920806i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −4.18329 3.22164i −0.790568 0.608833i
\(29\) 2.64002i 0.490240i 0.969493 + 0.245120i \(0.0788274\pi\)
−0.969493 + 0.245120i \(0.921173\pi\)
\(30\) 0 0
\(31\) 6.01008i 1.07944i 0.841844 + 0.539721i \(0.181470\pi\)
−0.841844 + 0.539721i \(0.818530\pi\)
\(32\) −1.79480 5.36458i −0.317278 0.948333i
\(33\) −0.515138 0.515138i −0.0896740 0.0896740i
\(34\) 1.69016 + 1.48486i 0.289861 + 0.254652i
\(35\) 0 0
\(36\) 0.257569 + 1.98335i 0.0429282 + 0.330558i
\(37\) −3.12489 + 3.12489i −0.513728 + 0.513728i −0.915667 0.401939i \(-0.868337\pi\)
0.401939 + 0.915667i \(0.368337\pi\)
\(38\) −0.340704 5.26904i −0.0552695 0.854752i
\(39\) −4.41926 −0.707647
\(40\) 0 0
\(41\) −4.24977 −0.663703 −0.331851 0.943332i \(-0.607673\pi\)
−0.331851 + 0.943332i \(0.607673\pi\)
\(42\) 0.240914 + 3.72578i 0.0371739 + 0.574900i
\(43\) −5.10495 + 5.10495i −0.778498 + 0.778498i −0.979575 0.201077i \(-0.935556\pi\)
0.201077 + 0.979575i \(0.435556\pi\)
\(44\) −0.187643 1.44490i −0.0282882 0.217826i
\(45\) 0 0
\(46\) −8.76491 7.70025i −1.29232 1.13534i
\(47\) −2.09991 2.09991i −0.306304 0.306304i 0.537170 0.843474i \(-0.319493\pi\)
−0.843474 + 0.537170i \(0.819493\pi\)
\(48\) −2.01216 + 3.45705i −0.290430 + 0.498983i
\(49\) 0.0302761i 0.00432516i
\(50\) 0 0
\(51\) 1.59083i 0.222761i
\(52\) −7.00260 5.39285i −0.971086 0.747854i
\(53\) −0.484862 0.484862i −0.0666009 0.0666009i 0.673022 0.739623i \(-0.264996\pi\)
−0.739623 + 0.673022i \(0.764996\pi\)
\(54\) 0.933389 1.06244i 0.127018 0.144580i
\(55\) 0 0
\(56\) −4.16485 + 6.19773i −0.556552 + 0.828206i
\(57\) −2.64002 + 2.64002i −0.349680 + 0.349680i
\(58\) 3.72578 0.240914i 0.489218 0.0316336i
\(59\) 4.92834 0.641615 0.320808 0.947144i \(-0.396046\pi\)
0.320808 + 0.947144i \(0.396046\pi\)
\(60\) 0 0
\(61\) 2.31032 0.295807 0.147903 0.989002i \(-0.452748\pi\)
0.147903 + 0.989002i \(0.452748\pi\)
\(62\) 8.48183 0.548448i 1.07719 0.0696529i
\(63\) 1.86678 1.86678i 0.235192 0.235192i
\(64\) −7.40707 + 3.02248i −0.925883 + 0.377810i
\(65\) 0 0
\(66\) −0.679988 + 0.774006i −0.0837008 + 0.0952735i
\(67\) 5.10495 + 5.10495i 0.623669 + 0.623669i 0.946468 0.322798i \(-0.104624\pi\)
−0.322798 + 0.946468i \(0.604624\pi\)
\(68\) 1.94130 2.52077i 0.235417 0.305688i
\(69\) 8.24977i 0.993156i
\(70\) 0 0
\(71\) 13.1240i 1.55753i −0.627317 0.778764i \(-0.715847\pi\)
0.627317 0.778764i \(-0.284153\pi\)
\(72\) 2.77552 0.544488i 0.327099 0.0641685i
\(73\) −3.96972 3.96972i −0.464621 0.464621i 0.435546 0.900167i \(-0.356555\pi\)
−0.900167 + 0.435546i \(0.856555\pi\)
\(74\) 4.69521 + 4.12489i 0.545807 + 0.479508i
\(75\) 0 0
\(76\) −7.40493 + 0.961649i −0.849404 + 0.110309i
\(77\) −1.35998 + 1.35998i −0.154984 + 0.154984i
\(78\) 0.403277 + 6.23675i 0.0456622 + 0.706172i
\(79\) −7.11388 −0.800375 −0.400187 0.916433i \(-0.631055\pi\)
−0.400187 + 0.916433i \(0.631055\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0.387811 + 5.99756i 0.0428266 + 0.662320i
\(83\) −3.55694 + 3.55694i −0.390425 + 0.390425i −0.874839 0.484414i \(-0.839033\pi\)
0.484414 + 0.874839i \(0.339033\pi\)
\(84\) 5.23608 0.679988i 0.571303 0.0741928i
\(85\) 0 0
\(86\) 7.67030 + 6.73860i 0.827110 + 0.726642i
\(87\) −1.86678 1.86678i −0.200140 0.200140i
\(88\) −2.02201 + 0.396668i −0.215547 + 0.0422849i
\(89\) 1.03028i 0.109209i 0.998508 + 0.0546045i \(0.0173898\pi\)
−0.998508 + 0.0546045i \(0.982610\pi\)
\(90\) 0 0
\(91\) 11.6669i 1.22303i
\(92\) −10.0673 + 13.0723i −1.04958 + 1.36288i
\(93\) −4.24977 4.24977i −0.440681 0.440681i
\(94\) −2.77191 + 3.15516i −0.285901 + 0.325430i
\(95\) 0 0
\(96\) 5.06244 + 2.52422i 0.516683 + 0.257627i
\(97\) 12.5298 12.5298i 1.27221 1.27221i 0.327284 0.944926i \(-0.393867\pi\)
0.944926 0.327284i \(-0.106133\pi\)
\(98\) −0.0427276 + 0.00276283i −0.00431614 + 0.000279088i
\(99\) 0.728515 0.0732185
\(100\) 0 0
\(101\) −5.67030 −0.564216 −0.282108 0.959383i \(-0.591034\pi\)
−0.282108 + 0.959383i \(0.591034\pi\)
\(102\) −2.24508 + 0.145170i −0.222296 + 0.0143740i
\(103\) 0.0565188 0.0565188i 0.00556896 0.00556896i −0.704317 0.709886i \(-0.748747\pi\)
0.709886 + 0.704317i \(0.248747\pi\)
\(104\) −6.97173 + 10.3747i −0.683635 + 1.01732i
\(105\) 0 0
\(106\) −0.640023 + 0.728515i −0.0621646 + 0.0707597i
\(107\) −3.91017 3.91017i −0.378011 0.378011i 0.492373 0.870384i \(-0.336129\pi\)
−0.870384 + 0.492373i \(0.836129\pi\)
\(108\) −1.58457 1.22031i −0.152475 0.117424i
\(109\) 15.7796i 1.51141i −0.654912 0.755705i \(-0.727294\pi\)
0.654912 0.755705i \(-0.272706\pi\)
\(110\) 0 0
\(111\) 4.41926i 0.419457i
\(112\) 9.12670 + 5.31214i 0.862392 + 0.501950i
\(113\) 1.84484 + 1.84484i 0.173548 + 0.173548i 0.788536 0.614988i \(-0.210839\pi\)
−0.614988 + 0.788536i \(0.710839\pi\)
\(114\) 3.96669 + 3.48486i 0.371515 + 0.326387i
\(115\) 0 0
\(116\) −0.679988 5.23608i −0.0631353 0.486158i
\(117\) 3.12489 3.12489i 0.288896 0.288896i
\(118\) −0.449733 6.95520i −0.0414013 0.640278i
\(119\) −4.19982 −0.384997
\(120\) 0 0
\(121\) 10.4693 0.951751
\(122\) −0.210828 3.26048i −0.0190874 0.295190i
\(123\) 3.00504 3.00504i 0.270955 0.270955i
\(124\) −1.54801 11.9201i −0.139016 1.07045i
\(125\) 0 0
\(126\) −2.80487 2.46417i −0.249878 0.219526i
\(127\) −11.2572 11.2572i −0.998914 0.998914i 0.00108535 0.999999i \(-0.499655\pi\)
−0.999999 + 0.00108535i \(0.999655\pi\)
\(128\) 4.94145 + 10.1775i 0.436767 + 0.899575i
\(129\) 7.21949i 0.635641i
\(130\) 0 0
\(131\) 4.57511i 0.399729i 0.979824 + 0.199865i \(0.0640502\pi\)
−0.979824 + 0.199865i \(0.935950\pi\)
\(132\) 1.15438 + 0.889013i 0.100476 + 0.0773786i
\(133\) 6.96972 + 6.96972i 0.604352 + 0.604352i
\(134\) 6.73860 7.67030i 0.582126 0.662613i
\(135\) 0 0
\(136\) −3.73463 2.50966i −0.320242 0.215202i
\(137\) 4.09461 4.09461i 0.349826 0.349826i −0.510219 0.860045i \(-0.670436\pi\)
0.860045 + 0.510219i \(0.170436\pi\)
\(138\) 11.6426 0.752829i 0.991086 0.0640851i
\(139\) 13.5902 1.15271 0.576354 0.817200i \(-0.304475\pi\)
0.576354 + 0.817200i \(0.304475\pi\)
\(140\) 0 0
\(141\) 2.96972 0.250096
\(142\) −18.5214 + 1.19762i −1.55428 + 0.100502i
\(143\) −2.27653 + 2.27653i −0.190373 + 0.190373i
\(144\) −1.02170 3.86732i −0.0851414 0.322276i
\(145\) 0 0
\(146\) −5.24008 + 5.96459i −0.433672 + 0.493633i
\(147\) 0.0214084 + 0.0214084i 0.00176574 + 0.00176574i
\(148\) 5.39285 7.00260i 0.443290 0.575610i
\(149\) 5.67030i 0.464529i −0.972653 0.232265i \(-0.925386\pi\)
0.972653 0.232265i \(-0.0746135\pi\)
\(150\) 0 0
\(151\) 19.2471i 1.56631i −0.621829 0.783153i \(-0.713610\pi\)
0.621829 0.783153i \(-0.286390\pi\)
\(152\) 2.03288 + 10.3626i 0.164888 + 0.840516i
\(153\) 1.12489 + 1.12489i 0.0909416 + 0.0909416i
\(154\) 2.04339 + 1.79518i 0.164661 + 0.144660i
\(155\) 0 0
\(156\) 8.76491 1.13826i 0.701754 0.0911340i
\(157\) 2.09461 2.09461i 0.167168 0.167168i −0.618565 0.785733i \(-0.712286\pi\)
0.785733 + 0.618565i \(0.212286\pi\)
\(158\) 0.649175 + 10.0396i 0.0516456 + 0.798707i
\(159\) 0.685698 0.0543794
\(160\) 0 0
\(161\) 21.7796 1.71647
\(162\) 0.0912546 + 1.41127i 0.00716964 + 0.110880i
\(163\) −4.28546 + 4.28546i −0.335663 + 0.335663i −0.854732 0.519069i \(-0.826279\pi\)
0.519069 + 0.854732i \(0.326279\pi\)
\(164\) 8.42876 1.09461i 0.658176 0.0854746i
\(165\) 0 0
\(166\) 5.34438 + 4.69521i 0.414804 + 0.364419i
\(167\) 4.37644 + 4.37644i 0.338659 + 0.338659i 0.855862 0.517203i \(-0.173027\pi\)
−0.517203 + 0.855862i \(0.673027\pi\)
\(168\) −1.43746 7.32745i −0.110902 0.565325i
\(169\) 6.52982i 0.502294i
\(170\) 0 0
\(171\) 3.73356i 0.285512i
\(172\) 8.81001 11.4398i 0.671757 0.872274i
\(173\) −16.4049 16.4049i −1.24724 1.24724i −0.956932 0.290312i \(-0.906241\pi\)
−0.290312 0.956932i \(-0.593759\pi\)
\(174\) −2.46417 + 2.80487i −0.186808 + 0.212637i
\(175\) 0 0
\(176\) 0.744321 + 2.81740i 0.0561053 + 0.212369i
\(177\) −3.48486 + 3.48486i −0.261938 + 0.261938i
\(178\) 1.45399 0.0940174i 0.108981 0.00704690i
\(179\) −24.4156 −1.82491 −0.912455 0.409178i \(-0.865815\pi\)
−0.912455 + 0.409178i \(0.865815\pi\)
\(180\) 0 0
\(181\) 11.2800 0.838439 0.419220 0.907885i \(-0.362304\pi\)
0.419220 + 0.907885i \(0.362304\pi\)
\(182\) 16.4652 1.06466i 1.22048 0.0789180i
\(183\) −1.63365 + 1.63365i −0.120763 + 0.120763i
\(184\) 19.3672 + 13.0147i 1.42777 + 0.959455i
\(185\) 0 0
\(186\) −5.60975 + 6.38537i −0.411327 + 0.468198i
\(187\) −0.819496 0.819496i −0.0599275 0.0599275i
\(188\) 4.70572 + 3.62398i 0.343200 + 0.264306i
\(189\) 2.64002i 0.192033i
\(190\) 0 0
\(191\) 3.26729i 0.236413i 0.992989 + 0.118206i \(0.0377144\pi\)
−0.992989 + 0.118206i \(0.962286\pi\)
\(192\) 3.10037 7.37480i 0.223750 0.532230i
\(193\) −0.939448 0.939448i −0.0676229 0.0676229i 0.672486 0.740109i \(-0.265226\pi\)
−0.740109 + 0.672486i \(0.765226\pi\)
\(194\) −18.8263 16.5395i −1.35165 1.18747i
\(195\) 0 0
\(196\) 0.00779818 + 0.0600479i 0.000557013 + 0.00428914i
\(197\) 1.45459 1.45459i 0.103635 0.103635i −0.653388 0.757023i \(-0.726653\pi\)
0.757023 + 0.653388i \(0.226653\pi\)
\(198\) −0.0664803 1.02813i −0.00472455 0.0730659i
\(199\) 5.19059 0.367951 0.183975 0.982931i \(-0.441103\pi\)
0.183975 + 0.982931i \(0.441103\pi\)
\(200\) 0 0
\(201\) −7.21949 −0.509224
\(202\) 0.517441 + 8.00230i 0.0364070 + 0.563040i
\(203\) −4.92834 + 4.92834i −0.345902 + 0.345902i
\(204\) 0.409748 + 3.15516i 0.0286881 + 0.220905i
\(205\) 0 0
\(206\) −0.0849206 0.0746054i −0.00591670 0.00519801i
\(207\) −5.83347 5.83347i −0.405454 0.405454i
\(208\) 15.2776 + 8.89224i 1.05931 + 0.616566i
\(209\) 2.71995i 0.188143i
\(210\) 0 0
\(211\) 11.7800i 0.810967i 0.914102 + 0.405483i \(0.132897\pi\)
−0.914102 + 0.405483i \(0.867103\pi\)
\(212\) 1.08653 + 0.836763i 0.0746235 + 0.0574691i
\(213\) 9.28005 + 9.28005i 0.635858 + 0.635858i
\(214\) −5.16147 + 5.87511i −0.352831 + 0.401615i
\(215\) 0 0
\(216\) −1.57758 + 2.34760i −0.107341 + 0.159734i
\(217\) −11.2195 + 11.2195i −0.761629 + 0.761629i
\(218\) −22.2692 + 1.43996i −1.50826 + 0.0975264i
\(219\) 5.61404 0.379361
\(220\) 0 0
\(221\) −7.03028 −0.472908
\(222\) −6.23675 + 0.403277i −0.418583 + 0.0270662i
\(223\) 3.32381 3.32381i 0.222579 0.222579i −0.587005 0.809583i \(-0.699693\pi\)
0.809583 + 0.587005i \(0.199693\pi\)
\(224\) 6.66399 13.3650i 0.445257 0.892984i
\(225\) 0 0
\(226\) 2.43521 2.77191i 0.161988 0.184385i
\(227\) 8.83851 + 8.83851i 0.586633 + 0.586633i 0.936718 0.350085i \(-0.113847\pi\)
−0.350085 + 0.936718i \(0.613847\pi\)
\(228\) 4.55609 5.91607i 0.301734 0.391801i
\(229\) 7.09083i 0.468575i 0.972167 + 0.234288i \(0.0752757\pi\)
−0.972167 + 0.234288i \(0.924724\pi\)
\(230\) 0 0
\(231\) 1.92330i 0.126544i
\(232\) −7.32745 + 1.43746i −0.481071 + 0.0943739i
\(233\) 15.3747 + 15.3747i 1.00723 + 1.00723i 0.999974 + 0.00725353i \(0.00230889\pi\)
0.00725353 + 0.999974i \(0.497691\pi\)
\(234\) −4.69521 4.12489i −0.306935 0.269652i
\(235\) 0 0
\(236\) −9.77460 + 1.26939i −0.636272 + 0.0826301i
\(237\) 5.03028 5.03028i 0.326752 0.326752i
\(238\) 0.383253 + 5.92707i 0.0248426 + 0.384195i
\(239\) 0.706459 0.0456970 0.0228485 0.999739i \(-0.492726\pi\)
0.0228485 + 0.999739i \(0.492726\pi\)
\(240\) 0 0
\(241\) −24.9991 −1.61033 −0.805166 0.593049i \(-0.797924\pi\)
−0.805166 + 0.593049i \(0.797924\pi\)
\(242\) −0.955368 14.7749i −0.0614134 0.949768i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −4.58217 + 0.595068i −0.293343 + 0.0380953i
\(245\) 0 0
\(246\) −4.51514 3.96669i −0.287875 0.252907i
\(247\) 11.6669 + 11.6669i 0.742349 + 0.742349i
\(248\) −16.6811 + 3.27242i −1.05925 + 0.207799i
\(249\) 5.03028i 0.318781i
\(250\) 0 0
\(251\) 28.6154i 1.80619i 0.429440 + 0.903095i \(0.358711\pi\)
−0.429440 + 0.903095i \(0.641289\pi\)
\(252\) −3.22164 + 4.18329i −0.202944 + 0.263523i
\(253\) 4.24977 + 4.24977i 0.267181 + 0.267181i
\(254\) −14.8596 + 16.9142i −0.932376 + 1.06129i
\(255\) 0 0
\(256\) 13.9123 7.90245i 0.869517 0.493903i
\(257\) 3.90539 3.90539i 0.243612 0.243612i −0.574731 0.818342i \(-0.694893\pi\)
0.818342 + 0.574731i \(0.194893\pi\)
\(258\) −10.1886 + 0.658812i −0.634316 + 0.0410158i
\(259\) −11.6669 −0.724948
\(260\) 0 0
\(261\) 2.64002 0.163413
\(262\) 6.45670 0.417500i 0.398896 0.0257932i
\(263\) −0.176615 + 0.176615i −0.0108905 + 0.0108905i −0.712531 0.701641i \(-0.752451\pi\)
0.701641 + 0.712531i \(0.252451\pi\)
\(264\) 1.14929 1.71026i 0.0707340 0.105259i
\(265\) 0 0
\(266\) 9.20012 10.4722i 0.564095 0.642089i
\(267\) −0.728515 0.728515i −0.0445844 0.0445844i
\(268\) −11.4398 8.81001i −0.698795 0.538157i
\(269\) 5.38934i 0.328594i 0.986411 + 0.164297i \(0.0525355\pi\)
−0.986411 + 0.164297i \(0.947465\pi\)
\(270\) 0 0
\(271\) 15.4005i 0.935513i −0.883857 0.467757i \(-0.845062\pi\)
0.883857 0.467757i \(-0.154938\pi\)
\(272\) −3.20100 + 5.49958i −0.194089 + 0.333461i
\(273\) −8.24977 8.24977i −0.499299 0.499299i
\(274\) −6.15224 5.40493i −0.371670 0.326524i
\(275\) 0 0
\(276\) −2.12489 16.3621i −0.127903 0.984885i
\(277\) −8.59415 + 8.59415i −0.516372 + 0.516372i −0.916472 0.400099i \(-0.868976\pi\)
0.400099 + 0.916472i \(0.368976\pi\)
\(278\) −1.24017 19.1794i −0.0743805 1.15031i
\(279\) 6.01008 0.359814
\(280\) 0 0
\(281\) −20.7493 −1.23780 −0.618900 0.785470i \(-0.712421\pi\)
−0.618900 + 0.785470i \(0.712421\pi\)
\(282\) −0.271001 4.19107i −0.0161379 0.249575i
\(283\) 18.5822 18.5822i 1.10459 1.10459i 0.110745 0.993849i \(-0.464676\pi\)
0.993849 0.110745i \(-0.0353238\pi\)
\(284\) 3.38033 + 26.0294i 0.200586 + 1.54456i
\(285\) 0 0
\(286\) 3.42053 + 3.00504i 0.202260 + 0.177692i
\(287\) −7.93338 7.93338i −0.468293 0.468293i
\(288\) −5.36458 + 1.79480i −0.316111 + 0.105759i
\(289\) 14.4693i 0.851133i
\(290\) 0 0
\(291\) 17.7198i 1.03876i
\(292\) 8.89581 + 6.85085i 0.520588 + 0.400916i
\(293\) −6.23509 6.23509i −0.364258 0.364258i 0.501120 0.865378i \(-0.332922\pi\)
−0.865378 + 0.501120i \(0.832922\pi\)
\(294\) 0.0282594 0.0321666i 0.00164812 0.00187600i
\(295\) 0 0
\(296\) −10.3747 6.97173i −0.603015 0.405224i
\(297\) −0.515138 + 0.515138i −0.0298913 + 0.0298913i
\(298\) −8.00230 + 0.517441i −0.463561 + 0.0299745i
\(299\) 36.4578 2.10841
\(300\) 0 0
\(301\) −19.0596 −1.09858
\(302\) −27.1628 + 1.75639i −1.56304 + 0.101069i
\(303\) 4.00951 4.00951i 0.230340 0.230340i
\(304\) 14.4388 3.81456i 0.828125 0.218780i
\(305\) 0 0
\(306\) 1.48486 1.69016i 0.0848839 0.0966202i
\(307\) 0.905130 + 0.905130i 0.0516585 + 0.0516585i 0.732464 0.680806i \(-0.238370\pi\)
−0.680806 + 0.732464i \(0.738370\pi\)
\(308\) 2.34702 3.04759i 0.133734 0.173653i
\(309\) 0.0799296i 0.00454704i
\(310\) 0 0
\(311\) 24.4377i 1.38573i −0.721066 0.692867i \(-0.756347\pi\)
0.721066 0.692867i \(-0.243653\pi\)
\(312\) −2.40623 12.2657i −0.136226 0.694411i
\(313\) −18.5904 18.5904i −1.05079 1.05079i −0.998639 0.0521506i \(-0.983392\pi\)
−0.0521506 0.998639i \(-0.516608\pi\)
\(314\) −3.14719 2.76491i −0.177606 0.156033i
\(315\) 0 0
\(316\) 14.1093 1.83232i 0.793710 0.103076i
\(317\) −19.3141 + 19.3141i −1.08479 + 1.08479i −0.0887327 + 0.996055i \(0.528282\pi\)
−0.996055 + 0.0887327i \(0.971718\pi\)
\(318\) −0.0625731 0.967703i −0.00350893 0.0542661i
\(319\) −1.92330 −0.107684
\(320\) 0 0
\(321\) 5.52982 0.308644
\(322\) −1.98749 30.7368i −0.110758 1.71289i
\(323\) −4.19982 + 4.19982i −0.233684 + 0.233684i
\(324\) 1.98335 0.257569i 0.110186 0.0143094i
\(325\) 0 0
\(326\) 6.43899 + 5.65685i 0.356623 + 0.313304i
\(327\) 11.1579 + 11.1579i 0.617031 + 0.617031i
\(328\) −2.31395 11.7953i −0.127766 0.651289i
\(329\) 7.84014i 0.432241i
\(330\) 0 0
\(331\) 11.0294i 0.606231i −0.952954 0.303115i \(-0.901973\pi\)
0.952954 0.303115i \(-0.0980268\pi\)
\(332\) 6.13849 7.97080i 0.336893 0.437455i
\(333\) 3.12489 + 3.12489i 0.171243 + 0.171243i
\(334\) 5.77695 6.57569i 0.316101 0.359806i
\(335\) 0 0
\(336\) −10.2098 + 2.69730i −0.556991 + 0.147150i
\(337\) −13.6206 + 13.6206i −0.741964 + 0.741964i −0.972956 0.230992i \(-0.925803\pi\)
0.230992 + 0.972956i \(0.425803\pi\)
\(338\) 9.21531 0.595876i 0.501247 0.0324114i
\(339\) −2.60900 −0.141701
\(340\) 0 0
\(341\) −4.37844 −0.237106
\(342\) −5.26904 + 0.340704i −0.284917 + 0.0184232i
\(343\) 13.1240 13.1240i 0.708628 0.708628i
\(344\) −16.9485 11.3893i −0.913802 0.614072i
\(345\) 0 0
\(346\) −21.6547 + 24.6488i −1.16416 + 1.32513i
\(347\) 17.7627 + 17.7627i 0.953549 + 0.953549i 0.998968 0.0454187i \(-0.0144622\pi\)
−0.0454187 + 0.998968i \(0.514462\pi\)
\(348\) 4.18329 + 3.22164i 0.224248 + 0.172698i
\(349\) 14.6888i 0.786271i 0.919480 + 0.393136i \(0.128610\pi\)
−0.919480 + 0.393136i \(0.871390\pi\)
\(350\) 0 0
\(351\) 4.41926i 0.235882i
\(352\) 3.90818 1.30754i 0.208307 0.0696919i
\(353\) 18.4049 + 18.4049i 0.979596 + 0.979596i 0.999796 0.0202002i \(-0.00643038\pi\)
−0.0202002 + 0.999796i \(0.506430\pi\)
\(354\) 5.23608 + 4.60006i 0.278294 + 0.244490i
\(355\) 0 0
\(356\) −0.265367 2.04339i −0.0140644 0.108300i
\(357\) 2.96972 2.96972i 0.157174 0.157174i
\(358\) 2.22804 + 34.4569i 0.117755 + 1.82111i
\(359\) −9.63060 −0.508284 −0.254142 0.967167i \(-0.581793\pi\)
−0.254142 + 0.967167i \(0.581793\pi\)
\(360\) 0 0
\(361\) −5.06055 −0.266345
\(362\) −1.02936 15.9192i −0.0541017 0.836692i
\(363\) −7.40289 + 7.40289i −0.388551 + 0.388551i
\(364\) −3.00504 23.1396i −0.157507 1.21284i
\(365\) 0 0
\(366\) 2.45459 + 2.15643i 0.128303 + 0.112718i
\(367\) −15.4570 15.4570i −0.806850 0.806850i 0.177306 0.984156i \(-0.443262\pi\)
−0.984156 + 0.177306i \(0.943262\pi\)
\(368\) 16.5998 28.5199i 0.865326 1.48670i
\(369\) 4.24977i 0.221234i
\(370\) 0 0
\(371\) 1.81026i 0.0939840i
\(372\) 9.52337 + 7.33415i 0.493764 + 0.380258i
\(373\) −3.37466 3.37466i −0.174733 0.174733i 0.614322 0.789055i \(-0.289430\pi\)
−0.789055 + 0.614322i \(0.789430\pi\)
\(374\) −1.08174 + 1.23131i −0.0559357 + 0.0636695i
\(375\) 0 0
\(376\) 4.68498 6.97173i 0.241609 0.359540i
\(377\) −8.24977 + 8.24977i −0.424885 + 0.424885i
\(378\) 3.72578 0.240914i 0.191633 0.0123913i
\(379\) −5.89705 −0.302911 −0.151455 0.988464i \(-0.548396\pi\)
−0.151455 + 0.988464i \(0.548396\pi\)
\(380\) 0 0
\(381\) 15.9201 0.815610
\(382\) 4.61102 0.298155i 0.235920 0.0152549i
\(383\) 0.642881 0.642881i 0.0328497 0.0328497i −0.690491 0.723341i \(-0.742606\pi\)
0.723341 + 0.690491i \(0.242606\pi\)
\(384\) −10.6907 3.70247i −0.545559 0.188941i
\(385\) 0 0
\(386\) −1.24008 + 1.41154i −0.0631185 + 0.0718455i
\(387\) 5.10495 + 5.10495i 0.259499 + 0.259499i
\(388\) −21.6237 + 28.0782i −1.09778 + 1.42546i
\(389\) 18.8292i 0.954680i −0.878719 0.477340i \(-0.841601\pi\)
0.878719 0.477340i \(-0.158399\pi\)
\(390\) 0 0
\(391\) 13.1240i 0.663708i
\(392\) 0.0840320 0.0164850i 0.00424426 0.000832616i
\(393\) −3.23509 3.23509i −0.163189 0.163189i
\(394\) −2.18555 1.92007i −0.110106 0.0967317i
\(395\) 0 0
\(396\) −1.44490 + 0.187643i −0.0726088 + 0.00942941i
\(397\) 24.3444 24.3444i 1.22181 1.22181i 0.254821 0.966988i \(-0.417983\pi\)
0.966988 0.254821i \(-0.0820166\pi\)
\(398\) −0.473665 7.32530i −0.0237427 0.367184i
\(399\) −9.85668 −0.493451
\(400\) 0 0
\(401\) 15.9394 0.795978 0.397989 0.917390i \(-0.369708\pi\)
0.397989 + 0.917390i \(0.369708\pi\)
\(402\) 0.658812 + 10.1886i 0.0328586 + 0.508163i
\(403\) −18.7808 + 18.7808i −0.935539 + 0.935539i
\(404\) 11.2462 1.46049i 0.559517 0.0726623i
\(405\) 0 0
\(406\) 7.40493 + 6.50547i 0.367501 + 0.322861i
\(407\) −2.27653 2.27653i −0.112843 0.112843i
\(408\) 4.41538 0.866187i 0.218594 0.0428826i
\(409\) 23.4087i 1.15749i −0.815510 0.578743i \(-0.803543\pi\)
0.815510 0.578743i \(-0.196457\pi\)
\(410\) 0 0
\(411\) 5.79065i 0.285632i
\(412\) −0.0975387 + 0.126654i −0.00480539 + 0.00623978i
\(413\) 9.20012 + 9.20012i 0.452708 + 0.452708i
\(414\) −7.70025 + 8.76491i −0.378447 + 0.430772i
\(415\) 0 0
\(416\) 11.1552 22.3722i 0.546927 1.09689i
\(417\) −9.60975 + 9.60975i −0.470591 + 0.470591i
\(418\) 3.83858 0.248208i 0.187751 0.0121403i
\(419\) 28.0361 1.36966 0.684828 0.728705i \(-0.259878\pi\)
0.684828 + 0.728705i \(0.259878\pi\)
\(420\) 0 0
\(421\) 17.4087 0.848449 0.424224 0.905557i \(-0.360547\pi\)
0.424224 + 0.905557i \(0.360547\pi\)
\(422\) 16.6247 1.07498i 0.809277 0.0523290i
\(423\) −2.09991 + 2.09991i −0.102101 + 0.102101i
\(424\) 1.08174 1.60975i 0.0525342 0.0781762i
\(425\) 0 0
\(426\) 12.2498 13.9435i 0.593503 0.675563i
\(427\) 4.31286 + 4.31286i 0.208714 + 0.208714i
\(428\) 8.76236 + 6.74808i 0.423545 + 0.326181i
\(429\) 3.21949i 0.155439i
\(430\) 0 0
\(431\) 31.1542i 1.50065i 0.661071 + 0.750323i \(0.270102\pi\)
−0.661071 + 0.750323i \(0.729898\pi\)
\(432\) 3.45705 + 2.01216i 0.166328 + 0.0968100i
\(433\) 12.1589 + 12.1589i 0.584321 + 0.584321i 0.936088 0.351766i \(-0.114419\pi\)
−0.351766 + 0.936088i \(0.614419\pi\)
\(434\) 16.8575 + 14.8099i 0.809187 + 0.710896i
\(435\) 0 0
\(436\) 4.06433 + 31.2964i 0.194646 + 1.49882i
\(437\) 21.7796 21.7796i 1.04186 1.04186i
\(438\) −0.512307 7.92290i −0.0244790 0.378571i
\(439\) −14.2967 −0.682344 −0.341172 0.940001i \(-0.610824\pi\)
−0.341172 + 0.940001i \(0.610824\pi\)
\(440\) 0 0
\(441\) −0.0302761 −0.00144172
\(442\) 0.641545 + 9.92159i 0.0305152 + 0.471922i
\(443\) 7.02825 7.02825i 0.333922 0.333922i −0.520152 0.854074i \(-0.674125\pi\)
0.854074 + 0.520152i \(0.174125\pi\)
\(444\) 1.13826 + 8.76491i 0.0540196 + 0.415964i
\(445\) 0 0
\(446\) −4.99409 4.38747i −0.236477 0.207753i
\(447\) 4.00951 + 4.00951i 0.189643 + 0.189643i
\(448\) −19.4696 8.18505i −0.919854 0.386707i
\(449\) 38.4608i 1.81508i 0.419969 + 0.907538i \(0.362041\pi\)
−0.419969 + 0.907538i \(0.637959\pi\)
\(450\) 0 0
\(451\) 3.09602i 0.145786i
\(452\) −4.13412 3.18378i −0.194453 0.149752i
\(453\) 13.6097 + 13.6097i 0.639442 + 0.639442i
\(454\) 11.6669 13.2800i 0.547557 0.623263i
\(455\) 0 0
\(456\) −8.76491 5.88999i −0.410454 0.275824i
\(457\) −4.93945 + 4.93945i −0.231058 + 0.231058i −0.813134 0.582076i \(-0.802240\pi\)
0.582076 + 0.813134i \(0.302240\pi\)
\(458\) 10.0070 0.647071i 0.467599 0.0302356i
\(459\) −1.59083 −0.0742535
\(460\) 0 0
\(461\) 27.1689 1.26538 0.632691 0.774404i \(-0.281950\pi\)
0.632691 + 0.774404i \(0.281950\pi\)
\(462\) −2.71428 + 0.175510i −0.126280 + 0.00816545i
\(463\) 4.96280 4.96280i 0.230641 0.230641i −0.582319 0.812960i \(-0.697855\pi\)
0.812960 + 0.582319i \(0.197855\pi\)
\(464\) 2.69730 + 10.2098i 0.125219 + 0.473978i
\(465\) 0 0
\(466\) 20.2947 23.1007i 0.940135 1.07012i
\(467\) −21.2340 21.2340i −0.982591 0.982591i 0.0172604 0.999851i \(-0.494506\pi\)
−0.999851 + 0.0172604i \(0.994506\pi\)
\(468\) −5.39285 + 7.00260i −0.249285 + 0.323695i
\(469\) 19.0596i 0.880092i
\(470\) 0 0
\(471\) 2.96222i 0.136492i
\(472\) 2.68342 + 13.6787i 0.123514 + 0.629614i
\(473\) −3.71904 3.71904i −0.171001 0.171001i
\(474\) −7.55809 6.64002i −0.347155 0.304986i
\(475\) 0 0
\(476\) 8.32970 1.08174i 0.381791 0.0495817i
\(477\) −0.484862 + 0.484862i −0.0222003 + 0.0222003i
\(478\) −0.0644676 0.997001i −0.00294868 0.0456018i
\(479\) −18.7808 −0.858118 −0.429059 0.903277i \(-0.641155\pi\)
−0.429059 + 0.903277i \(0.641155\pi\)
\(480\) 0 0
\(481\) −19.5298 −0.890483
\(482\) 2.28128 + 35.2804i 0.103909 + 1.60698i
\(483\) −15.4005 + 15.4005i −0.700747 + 0.700747i
\(484\) −20.7642 + 2.69656i −0.943826 + 0.122571i
\(485\) 0 0
\(486\) −1.06244 0.933389i −0.0481934 0.0423394i
\(487\) 2.97058 + 2.97058i 0.134610 + 0.134610i 0.771201 0.636591i \(-0.219656\pi\)
−0.636591 + 0.771201i \(0.719656\pi\)
\(488\) 1.25794 + 6.41236i 0.0569444 + 0.290274i
\(489\) 6.06055i 0.274068i
\(490\) 0 0
\(491\) 29.5480i 1.33348i −0.745290 0.666741i \(-0.767689\pi\)
0.745290 0.666741i \(-0.232311\pi\)
\(492\) −5.18603 + 6.73404i −0.233804 + 0.303594i
\(493\) −2.96972 2.96972i −0.133750 0.133750i
\(494\) 15.4005 17.5298i 0.692901 0.788704i
\(495\) 0 0
\(496\) 6.14048 + 23.2429i 0.275716 + 1.04364i
\(497\) 24.4995 24.4995i 1.09895 1.09895i
\(498\) −7.09906 + 0.459036i −0.318116 + 0.0205699i
\(499\) −15.0473 −0.673608 −0.336804 0.941575i \(-0.609346\pi\)
−0.336804 + 0.941575i \(0.609346\pi\)
\(500\) 0 0
\(501\) −6.18922 −0.276514
\(502\) 40.3840 2.61129i 1.80243 0.116548i
\(503\) 13.4136 13.4136i 0.598084 0.598084i −0.341719 0.939802i \(-0.611009\pi\)
0.939802 + 0.341719i \(0.111009\pi\)
\(504\) 6.19773 + 4.16485i 0.276069 + 0.185517i
\(505\) 0 0
\(506\) 5.60975 6.38537i 0.249384 0.283864i
\(507\) −4.61728 4.61728i −0.205061 0.205061i
\(508\) 25.2264 + 19.4274i 1.11924 + 0.861951i
\(509\) 41.4187i 1.83585i −0.396752 0.917926i \(-0.629863\pi\)
0.396752 0.917926i \(-0.370137\pi\)
\(510\) 0 0
\(511\) 14.8212i 0.655651i
\(512\) −12.4220 18.9128i −0.548981 0.835835i
\(513\) 2.64002 + 2.64002i 0.116560 + 0.116560i
\(514\) −5.86793 5.15516i −0.258823 0.227384i
\(515\) 0 0
\(516\) 1.85952 + 14.3188i 0.0818607 + 0.630348i
\(517\) 1.52982 1.52982i 0.0672813 0.0672813i
\(518\) 1.06466 + 16.4652i 0.0467785 + 0.723437i
\(519\) 23.2001 1.01837
\(520\) 0 0
\(521\) 30.8392 1.35109 0.675545 0.737318i \(-0.263908\pi\)
0.675545 + 0.737318i \(0.263908\pi\)
\(522\) −0.240914 3.72578i −0.0105445 0.163073i
\(523\) −17.1251 + 17.1251i −0.748829 + 0.748829i −0.974259 0.225430i \(-0.927621\pi\)
0.225430 + 0.974259i \(0.427621\pi\)
\(524\) −1.17841 9.07402i −0.0514789 0.396400i
\(525\) 0 0
\(526\) 0.265367 + 0.233133i 0.0115706 + 0.0101651i
\(527\) −6.76066 6.76066i −0.294499 0.294499i
\(528\) −2.51852 1.46589i −0.109604 0.0637945i
\(529\) 45.0587i 1.95907i
\(530\) 0 0
\(531\) 4.92834i 0.213872i
\(532\) −15.6186 12.0282i −0.677150 0.521488i
\(533\) −13.2800 13.2800i −0.575223 0.575223i
\(534\) −0.961649 + 1.09461i −0.0416146 + 0.0473684i
\(535\) 0 0
\(536\) −11.3893 + 16.9485i −0.491944 + 0.732064i
\(537\) 17.2645 17.2645i 0.745016 0.745016i
\(538\) 7.60579 0.491802i 0.327909 0.0212031i
\(539\) 0.0220566 0.000950045
\(540\) 0 0
\(541\) −22.3397 −0.960458 −0.480229 0.877143i \(-0.659446\pi\)
−0.480229 + 0.877143i \(0.659446\pi\)
\(542\) −21.7342 + 1.40537i −0.933564 + 0.0603656i
\(543\) −7.97620 + 7.97620i −0.342291 + 0.342291i
\(544\) 8.05348 + 4.01560i 0.345290 + 0.172167i
\(545\) 0 0
\(546\) −10.8898 + 12.3955i −0.466040 + 0.530476i
\(547\) −25.3428 25.3428i −1.08358 1.08358i −0.996173 0.0874075i \(-0.972142\pi\)
−0.0874075 0.996173i \(-0.527858\pi\)
\(548\) −7.06638 + 9.17567i −0.301861 + 0.391965i
\(549\) 2.31032i 0.0986022i
\(550\) 0 0
\(551\) 9.85668i 0.419909i
\(552\) −22.8974 + 4.49190i −0.974580 + 0.191188i
\(553\) −13.2800 13.2800i −0.564725 0.564725i
\(554\) 12.9129 + 11.3444i 0.548616 + 0.481977i
\(555\) 0 0
\(556\) −26.9541 + 3.50042i −1.14311 + 0.148451i
\(557\) −21.1055 + 21.1055i −0.894269 + 0.894269i −0.994922 0.100653i \(-0.967907\pi\)
0.100653 + 0.994922i \(0.467907\pi\)
\(558\) −0.548448 8.48183i −0.0232176 0.359064i
\(559\) −31.9048 −1.34943
\(560\) 0 0
\(561\) 1.15894 0.0489306
\(562\) 1.89347 + 29.2828i 0.0798712 + 1.23522i
\(563\) 10.2955 10.2955i 0.433905 0.433905i −0.456049 0.889955i \(-0.650736\pi\)
0.889955 + 0.456049i \(0.150736\pi\)
\(564\) −5.88999 + 0.764909i −0.248013 + 0.0322085i
\(565\) 0 0
\(566\) −27.9201 24.5287i −1.17357 1.03102i
\(567\) −1.86678 1.86678i −0.0783973 0.0783973i
\(568\) 36.4259 7.14584i 1.52840 0.299833i
\(569\) 28.3179i 1.18715i 0.804780 + 0.593574i \(0.202283\pi\)
−0.804780 + 0.593574i \(0.797717\pi\)
\(570\) 0 0
\(571\) 27.2387i 1.13990i −0.821678 0.569952i \(-0.806962\pi\)
0.821678 0.569952i \(-0.193038\pi\)
\(572\) 3.92878 5.10150i 0.164270 0.213304i
\(573\) −2.31032 2.31032i −0.0965151 0.0965151i
\(574\) −10.4722 + 11.9201i −0.437099 + 0.497534i
\(575\) 0 0
\(576\) 3.02248 + 7.40707i 0.125937 + 0.308628i
\(577\) −4.81078 + 4.81078i −0.200275 + 0.200275i −0.800118 0.599843i \(-0.795230\pi\)
0.599843 + 0.800118i \(0.295230\pi\)
\(578\) 20.4200 1.32039i 0.849359 0.0549208i
\(579\) 1.32858 0.0552139
\(580\) 0 0
\(581\) −13.2800 −0.550949
\(582\) 25.0074 1.61702i 1.03659 0.0670275i
\(583\) 0.353229 0.353229i 0.0146293 0.0146293i
\(584\) 8.85660 13.1795i 0.366489 0.545373i
\(585\) 0 0
\(586\) −8.23039 + 9.36835i −0.339994 + 0.387003i
\(587\) 4.84271 + 4.84271i 0.199880 + 0.199880i 0.799948 0.600069i \(-0.204860\pi\)
−0.600069 + 0.799948i \(0.704860\pi\)
\(588\) −0.0479745 0.0369462i −0.00197843 0.00152363i
\(589\) 22.4390i 0.924582i
\(590\) 0 0
\(591\) 2.05710i 0.0846176i
\(592\) −8.89224 + 15.2776i −0.365469 + 0.627906i
\(593\) −18.8439 18.8439i −0.773827 0.773827i 0.204946 0.978773i \(-0.434298\pi\)
−0.978773 + 0.204946i \(0.934298\pi\)
\(594\) 0.774006 + 0.679988i 0.0317578 + 0.0279003i
\(595\) 0 0
\(596\) 1.46049 + 11.2462i 0.0598241 + 0.460661i
\(597\) −3.67030 + 3.67030i −0.150215 + 0.150215i
\(598\) −3.32695 51.4517i −0.136049 2.10402i
\(599\) 30.2765 1.23706 0.618532 0.785760i \(-0.287728\pi\)
0.618532 + 0.785760i \(0.287728\pi\)
\(600\) 0 0
\(601\) 30.1505 1.22986 0.614932 0.788581i \(-0.289184\pi\)
0.614932 + 0.788581i \(0.289184\pi\)
\(602\) 1.73928 + 26.8982i 0.0708877 + 1.09629i
\(603\) 5.10495 5.10495i 0.207890 0.207890i
\(604\) 4.95745 + 38.1736i 0.201716 + 1.55326i
\(605\) 0 0
\(606\) −6.02437 5.29260i −0.244723 0.214997i
\(607\) 19.5438 + 19.5438i 0.793258 + 0.793258i 0.982022 0.188764i \(-0.0604482\pi\)
−0.188764 + 0.982022i \(0.560448\pi\)
\(608\) −6.70097 20.0290i −0.271760 0.812282i
\(609\) 6.96972i 0.282427i
\(610\) 0 0
\(611\) 13.1240i 0.530939i
\(612\) −2.52077 1.94130i −0.101896 0.0784724i
\(613\) −23.4040 23.4040i −0.945279 0.945279i 0.0532993 0.998579i \(-0.483026\pi\)
−0.998579 + 0.0532993i \(0.983026\pi\)
\(614\) 1.19478 1.35998i 0.0482175 0.0548842i
\(615\) 0 0
\(616\) −4.51514 3.03416i −0.181920 0.122250i
\(617\) 17.9348 17.9348i 0.722026 0.722026i −0.246992 0.969018i \(-0.579442\pi\)
0.969018 + 0.246992i \(0.0794421\pi\)
\(618\) 0.112802 0.00729394i 0.00453756 0.000293405i
\(619\) 38.9056 1.56375 0.781875 0.623435i \(-0.214264\pi\)
0.781875 + 0.623435i \(0.214264\pi\)
\(620\) 0 0
\(621\) 8.24977 0.331052
\(622\) −34.4881 + 2.23005i −1.38285 + 0.0894169i
\(623\) −1.92330 + 1.92330i −0.0770553 + 0.0770553i
\(624\) −17.0907 + 4.51514i −0.684174 + 0.180750i
\(625\) 0 0
\(626\) −24.5395 + 27.9324i −0.980796 + 1.11640i
\(627\) −1.92330 1.92330i −0.0768091 0.0768091i
\(628\) −3.61483 + 4.69384i −0.144247 + 0.187305i
\(629\) 7.03028i 0.280315i
\(630\) 0 0
\(631\) 12.7707i 0.508395i −0.967152 0.254198i \(-0.918189\pi\)
0.967152 0.254198i \(-0.0818113\pi\)
\(632\) −3.87342 19.7448i −0.154077 0.785404i
\(633\) −8.32970 8.32970i −0.331076 0.331076i
\(634\) 29.0198 + 25.4948i 1.15253 + 1.01253i
\(635\) 0 0
\(636\) −1.35998 + 0.176615i −0.0539266 + 0.00700323i
\(637\) 0.0946093 0.0946093i 0.00374856 0.00374856i
\(638\) 0.175510 + 2.71428i 0.00694849 + 0.107460i
\(639\) −13.1240 −0.519176
\(640\) 0 0
\(641\) −16.4683 −0.650461 −0.325230 0.945635i \(-0.605442\pi\)
−0.325230 + 0.945635i \(0.605442\pi\)
\(642\) −0.504621 7.80405i −0.0199158 0.308001i
\(643\) 5.74249 5.74249i 0.226462 0.226462i −0.584751 0.811213i \(-0.698808\pi\)
0.811213 + 0.584751i \(0.198808\pi\)
\(644\) −43.1964 + 5.60975i −1.70218 + 0.221055i
\(645\) 0 0
\(646\) 6.31032 + 5.54382i 0.248276 + 0.218119i
\(647\) −4.61663 4.61663i −0.181498 0.181498i 0.610510 0.792009i \(-0.290964\pi\)
−0.792009 + 0.610510i \(0.790964\pi\)
\(648\) −0.544488 2.77552i −0.0213895 0.109033i
\(649\) 3.59037i 0.140934i
\(650\) 0 0
\(651\) 15.8668i 0.621867i
\(652\) 7.39574 9.60334i 0.289640 0.376096i
\(653\) −14.4655 14.4655i −0.566078 0.566078i 0.364949 0.931027i \(-0.381086\pi\)
−0.931027 + 0.364949i \(0.881086\pi\)
\(654\) 14.7285 16.7649i 0.575930 0.655560i
\(655\) 0 0
\(656\) −16.4352 + 4.34198i −0.641687 + 0.169526i
\(657\) −3.96972 + 3.96972i −0.154874 + 0.154874i
\(658\) −11.0645 + 0.715449i −0.431340 + 0.0278911i
\(659\) −35.5474 −1.38473 −0.692364 0.721548i \(-0.743431\pi\)
−0.692364 + 0.721548i \(0.743431\pi\)
\(660\) 0 0
\(661\) 15.1883 0.590756 0.295378 0.955380i \(-0.404554\pi\)
0.295378 + 0.955380i \(0.404554\pi\)
\(662\) −15.5654 + 1.00648i −0.604967 + 0.0391181i
\(663\) 4.97116 4.97116i 0.193064 0.193064i
\(664\) −11.8091 7.93567i −0.458282 0.307964i
\(665\) 0 0
\(666\) 4.12489 4.69521i 0.159836 0.181936i
\(667\) 15.4005 + 15.4005i 0.596310 + 0.596310i
\(668\) −9.80722 7.55275i −0.379453 0.292225i
\(669\) 4.70058i 0.181735i
\(670\) 0 0
\(671\) 1.68311i 0.0649756i
\(672\) 4.73830 + 14.1626i 0.182784 + 0.546335i
\(673\) 20.3700 + 20.3700i 0.785204 + 0.785204i 0.980704 0.195500i \(-0.0626328\pi\)
−0.195500 + 0.980704i \(0.562633\pi\)
\(674\) 20.4653 + 17.9794i 0.788294 + 0.692541i
\(675\) 0 0
\(676\) −1.68188 12.9509i −0.0646876 0.498111i
\(677\) −9.06433 + 9.06433i −0.348371 + 0.348371i −0.859502 0.511132i \(-0.829226\pi\)
0.511132 + 0.859502i \(0.329226\pi\)
\(678\) 0.238083 + 3.68199i 0.00914351 + 0.141406i
\(679\) 46.7808 1.79528
\(680\) 0 0
\(681\) −12.4995 −0.478983
\(682\) 0.399552 + 6.17914i 0.0152997 + 0.236612i
\(683\) −24.8545 + 24.8545i −0.951030 + 0.951030i −0.998856 0.0478253i \(-0.984771\pi\)
0.0478253 + 0.998856i \(0.484771\pi\)
\(684\) 0.961649 + 7.40493i 0.0367696 + 0.283135i
\(685\) 0 0
\(686\) −19.7190 17.3238i −0.752876 0.661425i
\(687\) −5.01397 5.01397i −0.191295 0.191295i
\(688\) −14.5268 + 24.9582i −0.553827 + 0.951522i
\(689\) 3.03028i 0.115444i
\(690\) 0 0
\(691\) 40.8979i 1.55583i 0.628371 + 0.777914i \(0.283722\pi\)
−0.628371 + 0.777914i \(0.716278\pi\)
\(692\) 36.7620 + 28.3112i 1.39748 + 1.07623i
\(693\) 1.35998 + 1.35998i 0.0516612 + 0.0516612i
\(694\) 23.4469 26.6888i 0.890033 1.01309i
\(695\) 0 0
\(696\) 4.16485 6.19773i 0.157868 0.234924i
\(697\) 4.78051 4.78051i 0.181075 0.181075i
\(698\) 20.7298 1.34042i 0.784633 0.0507355i
\(699\) −21.7430 −0.822398
\(700\) 0 0
\(701\) −43.1396 −1.62936 −0.814679 0.579912i \(-0.803087\pi\)
−0.814679 + 0.579912i \(0.803087\pi\)
\(702\) 6.23675 0.403277i 0.235391 0.0152207i
\(703\) −11.6669 + 11.6669i −0.440027 + 0.440027i
\(704\) −2.20192 5.39616i −0.0829880 0.203375i
\(705\) 0 0
\(706\) 24.2947 27.6538i 0.914344 1.04076i
\(707\) −10.5852 10.5852i −0.398097 0.398097i
\(708\) 6.01409 7.80928i 0.226023 0.293491i
\(709\) 18.4702i 0.693662i 0.937928 + 0.346831i \(0.112742\pi\)
−0.937928 + 0.346831i \(0.887258\pi\)
\(710\) 0 0
\(711\) 7.11388i 0.266792i
\(712\) −2.85956 + 0.560973i −0.107166 + 0.0210233i
\(713\) 35.0596 + 35.0596i 1.31299 + 1.31299i
\(714\) −4.46207 3.92007i −0.166989 0.146705i
\(715\) 0 0
\(716\) 48.4246 6.28871i 1.80971 0.235020i
\(717\) −0.499542 + 0.499542i −0.0186557 + 0.0186557i
\(718\) 0.878837 + 13.5913i 0.0327979 + 0.507225i
\(719\) −33.3725 −1.24458 −0.622292 0.782785i \(-0.713799\pi\)
−0.622292 + 0.782785i \(0.713799\pi\)
\(720\) 0 0
\(721\) 0.211016 0.00785865
\(722\) 0.461799 + 7.14179i 0.0171864 + 0.265790i
\(723\) 17.6770 17.6770i 0.657415 0.657415i
\(724\) −22.3722 + 2.90539i −0.831457 + 0.107978i
\(725\) 0 0
\(726\) 11.1230 + 9.77190i 0.412813 + 0.362669i
\(727\) −23.2774 23.2774i −0.863309 0.863309i 0.128412 0.991721i \(-0.459012\pi\)
−0.991721 + 0.128412i \(0.959012\pi\)
\(728\) −32.3819 + 6.35251i −1.20015 + 0.235440i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 11.4850i 0.424787i
\(732\) 2.81931 3.66086i 0.104205 0.135309i
\(733\) 16.2157 + 16.2157i 0.598941 + 0.598941i 0.940031 0.341090i \(-0.110796\pi\)
−0.341090 + 0.940031i \(0.610796\pi\)
\(734\) −20.4034 + 23.2245i −0.753105 + 0.857231i
\(735\) 0 0
\(736\) −41.7640 20.8242i −1.53944 0.767591i
\(737\) −3.71904 + 3.71904i −0.136992 + 0.136992i
\(738\) 5.99756 0.387811i 0.220773 0.0142755i
\(739\) −14.3408 −0.527535 −0.263768 0.964586i \(-0.584965\pi\)
−0.263768 + 0.964586i \(0.584965\pi\)
\(740\) 0 0
\(741\) −16.4995 −0.606126
\(742\) −2.55476 + 0.165194i −0.0937881 + 0.00606448i
\(743\) −11.6034 + 11.6034i −0.425686 + 0.425686i −0.887156 0.461470i \(-0.847322\pi\)
0.461470 + 0.887156i \(0.347322\pi\)
\(744\) 9.48139 14.1093i 0.347605 0.517272i
\(745\) 0 0
\(746\) −4.45459 + 5.07049i −0.163094 + 0.185644i
\(747\) 3.55694 + 3.55694i 0.130142 + 0.130142i
\(748\) 1.83642 + 1.41427i 0.0671462 + 0.0517107i
\(749\) 14.5988i 0.533430i
\(750\) 0 0
\(751\) 35.1721i 1.28345i 0.766936 + 0.641724i \(0.221780\pi\)
−0.766936 + 0.641724i \(0.778220\pi\)
\(752\) −10.2665 5.97555i −0.374381 0.217906i
\(753\) −20.2342 20.2342i −0.737374 0.737374i
\(754\) 12.3955 + 10.8898i 0.451416 + 0.396583i
\(755\) 0 0
\(756\) −0.679988 5.23608i −0.0247309 0.190434i
\(757\) 15.7455 15.7455i 0.572281 0.572281i −0.360484 0.932765i \(-0.617389\pi\)
0.932765 + 0.360484i \(0.117389\pi\)
\(758\) 0.538132 + 8.32230i 0.0195459 + 0.302280i
\(759\) −6.01008 −0.218152
\(760\) 0 0
\(761\) −24.4002 −0.884508 −0.442254 0.896890i \(-0.645821\pi\)
−0.442254 + 0.896890i \(0.645821\pi\)
\(762\) −1.45278 22.4675i −0.0526286 0.813910i
\(763\) 29.4570 29.4570i 1.06641 1.06641i
\(764\) −0.841553 6.48016i −0.0304463 0.234444i
\(765\) 0 0
\(766\) −0.965943 0.848611i −0.0349009 0.0306616i
\(767\) 15.4005 + 15.4005i 0.556080 + 0.556080i
\(768\) −4.24959 + 15.4253i −0.153344 + 0.556614i
\(769\) 15.9688i 0.575850i 0.957653 + 0.287925i \(0.0929654\pi\)
−0.957653 + 0.287925i \(0.907035\pi\)
\(770\) 0 0
\(771\) 5.52306i 0.198908i
\(772\) 2.10522 + 1.62128i 0.0757686 + 0.0583510i
\(773\) 2.84392 + 2.84392i 0.102289 + 0.102289i 0.756399 0.654110i \(-0.226957\pi\)
−0.654110 + 0.756399i \(0.726957\pi\)
\(774\) 6.73860 7.67030i 0.242214 0.275703i
\(775\) 0 0
\(776\) 41.5991 + 27.9545i 1.49332 + 1.00351i
\(777\) 8.24977 8.24977i 0.295959 0.295959i
\(778\) −26.5731 + 1.71825i −0.952691 + 0.0616024i
\(779\) −15.8668 −0.568486
\(780\) 0 0
\(781\) 9.56101 0.342120
\(782\) 18.5214 1.19762i 0.662324 0.0428269i
\(783\) −1.86678 + 1.86678i −0.0667132 + 0.0667132i
\(784\) −0.0309330 0.117087i