Properties

Label 300.2.j.d.43.6
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 43.6
Root \(1.41127 + 0.0912546i\) of defining polynomial
Character \(\chi\) \(=\) 300.43
Dual form 300.2.j.d.7.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.41127 + 0.0912546i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.98335 + 0.257569i) q^{4} +(1.06244 - 0.933389i) q^{6} +(-1.86678 - 1.86678i) q^{7} +(2.77552 + 0.544488i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(1.41127 + 0.0912546i) 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} +(2.77552 + 0.544488i) q^{8} -1.00000i q^{9} -0.728515i q^{11} +(1.58457 - 1.22031i) 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} +(0.0912546 - 1.41127i) q^{18} -3.73356 q^{19} -2.64002 q^{21} +(0.0664803 - 1.02813i) 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} +(-3.22164 - 4.18329i) q^{28} +2.64002i q^{29} -6.01008i q^{31} +(5.36458 + 1.79480i) 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} +(-5.26904 - 0.340704i) q^{38} +4.41926 q^{39} -4.24977 q^{41} +(-3.72578 - 0.240914i) 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} +(3.45705 - 2.01216i) q^{48} -0.0302761i q^{49} +1.59083i q^{51} +(5.39285 + 7.00260i) 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} +(-0.240914 + 3.72578i) q^{58} -4.92834 q^{59} +2.31032 q^{61} +(0.548448 - 8.48183i) 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} +(-2.52077 + 1.94130i) q^{68} +8.24977i q^{69} +13.1240i q^{71} +(0.544488 - 2.77552i) 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} +(6.23675 + 0.403277i) q^{78} +7.11388 q^{79} -1.00000 q^{81} +(-5.99756 - 0.387811i) 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} +(0.396668 - 2.02201i) q^{88} +1.03028i q^{89} -11.6669i q^{91} +(-13.0723 + 10.0673i) 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} +(0.00276283 - 0.0427276i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41127 + 0.0912546i 0.997916 + 0.0645267i
\(3\) 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 0.260026 0.965602i \(-0.416269\pi\)
−0.965602 + 0.260026i \(0.916269\pi\)
\(8\) 2.77552 + 0.544488i 0.981296 + 0.192506i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 0.728515i 0.219656i −0.993951 0.109828i \(-0.964970\pi\)
0.993951 0.109828i \(-0.0350299\pi\)
\(12\) 1.58457 1.22031i 0.457425 0.352273i
\(13\) 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 \(0.311795\pi\)
\(18\) 0.0912546 1.41127i 0.0215089 0.332639i
\(19\) −3.73356 −0.856537 −0.428268 0.903652i \(-0.640876\pi\)
−0.428268 + 0.903652i \(0.640876\pi\)
\(20\) 0 0
\(21\) −2.64002 −0.576100
\(22\) 0.0664803 1.02813i 0.0141737 0.219198i
\(23\) −5.83347 + 5.83347i −1.21636 + 1.21636i −0.247466 + 0.968897i \(0.579598\pi\)
−0.968897 + 0.247466i \(0.920402\pi\)
\(24\) 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
\(28\) −3.22164 4.18329i −0.608833 0.790568i
\(29\) 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 \(-0.818530\pi\)
0.841844 0.539721i \(-0.181470\pi\)
\(32\) 5.36458 + 1.79480i 0.948333 + 0.317278i
\(33\) −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 \(0.368337\pi\)
\(38\) −5.26904 0.340704i −0.854752 0.0552695i
\(39\) 4.41926 0.707647
\(40\) 0 0
\(41\) −4.24977 −0.663703 −0.331851 0.943332i \(-0.607673\pi\)
−0.331851 + 0.943332i \(0.607673\pi\)
\(42\) −3.72578 0.240914i −0.574900 0.0371739i
\(43\) 5.10495 5.10495i 0.778498 0.778498i −0.201077 0.979575i \(-0.564444\pi\)
0.979575 + 0.201077i \(0.0644442\pi\)
\(44\) 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 0.843474 0.537170i \(-0.180507\pi\)
−0.537170 + 0.843474i \(0.680507\pi\)
\(48\) 3.45705 2.01216i 0.498983 0.290430i
\(49\) 0.0302761i 0.00432516i
\(50\) 0 0
\(51\) 1.59083i 0.222761i
\(52\) 5.39285 + 7.00260i 0.747854 + 0.971086i
\(53\) −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
\(58\) −0.240914 + 3.72578i −0.0316336 + 0.489218i
\(59\) −4.92834 −0.641615 −0.320808 0.947144i \(-0.603954\pi\)
−0.320808 + 0.947144i \(0.603954\pi\)
\(60\) 0 0
\(61\) 2.31032 0.295807 0.147903 0.989002i \(-0.452748\pi\)
0.147903 + 0.989002i \(0.452748\pi\)
\(62\) 0.548448 8.48183i 0.0696529 1.07719i
\(63\) −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 0.322798 0.946468i \(-0.395376\pi\)
−0.946468 + 0.322798i \(0.895376\pi\)
\(68\) −2.52077 + 1.94130i −0.305688 + 0.235417i
\(69\) 8.24977i 0.993156i
\(70\) 0 0
\(71\) 13.1240i 1.55753i 0.627317 + 0.778764i \(0.284153\pi\)
−0.627317 + 0.778764i \(0.715847\pi\)
\(72\) 0.544488 2.77552i 0.0641685 0.327099i
\(73\) −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
\(78\) 6.23675 + 0.403277i 0.706172 + 0.0456622i
\(79\) 7.11388 0.800375 0.400187 0.916433i \(-0.368945\pi\)
0.400187 + 0.916433i \(0.368945\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) −5.99756 0.387811i −0.662320 0.0428266i
\(83\) 3.55694 3.55694i 0.390425 0.390425i −0.484414 0.874839i \(-0.660967\pi\)
0.874839 + 0.484414i \(0.160967\pi\)
\(84\) −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
\(88\) 0.396668 2.02201i 0.0422849 0.215547i
\(89\) 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
\(92\) −13.0723 + 10.0673i −1.36288 + 1.04958i
\(93\) −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 \(-0.106133\pi\)
\(98\) 0.00276283 0.0427276i 0.000279088 0.00431614i
\(99\) −0.728515 −0.0732185
\(100\) 0 0
\(101\) −5.67030 −0.564216 −0.282108 0.959383i \(-0.591034\pi\)
−0.282108 + 0.959383i \(0.591034\pi\)
\(102\) −0.145170 + 2.24508i −0.0143740 + 0.222296i
\(103\) −0.0565188 + 0.0565188i −0.00556896 + 0.00556896i −0.709886 0.704317i \(-0.751253\pi\)
0.704317 + 0.709886i \(0.251253\pi\)
\(104\) 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 0.870384 0.492373i \(-0.163871\pi\)
−0.492373 + 0.870384i \(0.663871\pi\)
\(108\) −1.22031 1.58457i −0.117424 0.152475i
\(109\) 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
\(112\) −5.31214 9.12670i −0.501950 0.862392i
\(113\) 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
\(118\) −6.95520 0.449733i −0.640278 0.0414013i
\(119\) 4.19982 0.384997
\(120\) 0 0
\(121\) 10.4693 0.951751
\(122\) 3.26048 + 0.210828i 0.295190 + 0.0190874i
\(123\) −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 0.999999 0.00108535i \(-0.000345478\pi\)
−0.00108535 + 0.999999i \(0.500345\pi\)
\(128\) 10.1775 + 4.94145i 0.899575 + 0.436767i
\(129\) 7.21949i 0.635641i
\(130\) 0 0
\(131\) 4.57511i 0.399729i −0.979824 0.199865i \(-0.935950\pi\)
0.979824 0.199865i \(-0.0640502\pi\)
\(132\) −0.889013 1.15438i −0.0773786 0.100476i
\(133\) 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 \(0.170436\pi\)
\(138\) −0.752829 + 11.6426i −0.0640851 + 0.991086i
\(139\) −13.5902 −1.15271 −0.576354 0.817200i \(-0.695525\pi\)
−0.576354 + 0.817200i \(0.695525\pi\)
\(140\) 0 0
\(141\) 2.96972 0.250096
\(142\) −1.19762 + 18.5214i −0.100502 + 1.55428i
\(143\) 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
\(148\) −7.00260 + 5.39285i −0.575610 + 0.443290i
\(149\) 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 \(0.286390\pi\)
−0.621829 + 0.783153i \(0.713610\pi\)
\(152\) −10.3626 2.03288i −0.840516 0.164888i
\(153\) 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 \(0.212286\pi\)
\(158\) 10.0396 + 0.649175i 0.798707 + 0.0516456i
\(159\) −0.685698 −0.0543794
\(160\) 0 0
\(161\) 21.7796 1.71647
\(162\) −1.41127 0.0912546i −0.110880 0.00716964i
\(163\) 4.28546 4.28546i 0.335663 0.335663i −0.519069 0.854732i \(-0.673721\pi\)
0.854732 + 0.519069i \(0.173721\pi\)
\(164\) −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 0.517203 0.855862i \(-0.326973\pi\)
−0.855862 + 0.517203i \(0.826973\pi\)
\(168\) −7.32745 1.43746i −0.565325 0.110902i
\(169\) 6.52982i 0.502294i
\(170\) 0 0
\(171\) 3.73356i 0.285512i
\(172\) 11.4398 8.81001i 0.872274 0.671757i
\(173\) −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
\(178\) −0.0940174 + 1.45399i −0.00704690 + 0.108981i
\(179\) 24.4156 1.82491 0.912455 0.409178i \(-0.134185\pi\)
0.912455 + 0.409178i \(0.134185\pi\)
\(180\) 0 0
\(181\) 11.2800 0.838439 0.419220 0.907885i \(-0.362304\pi\)
0.419220 + 0.907885i \(0.362304\pi\)
\(182\) 1.06466 16.4652i 0.0789180 1.22048i
\(183\) 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
\(188\) 3.62398 + 4.70572i 0.264306 + 0.343200i
\(189\) 2.64002i 0.192033i
\(190\) 0 0
\(191\) 3.26729i 0.236413i −0.992989 0.118206i \(-0.962286\pi\)
0.992989 0.118206i \(-0.0377144\pi\)
\(192\) 7.37480 3.10037i 0.532230 0.223750i
\(193\) −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 \(0.226653\pi\)
\(198\) −1.02813 0.0664803i −0.0730659 0.00472455i
\(199\) −5.19059 −0.367951 −0.183975 0.982931i \(-0.558897\pi\)
−0.183975 + 0.982931i \(0.558897\pi\)
\(200\) 0 0
\(201\) −7.21949 −0.509224
\(202\) −8.00230 0.517441i −0.563040 0.0364070i
\(203\) 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
\(208\) 8.89224 + 15.2776i 0.616566 + 1.05931i
\(209\) 2.71995i 0.188143i
\(210\) 0 0
\(211\) 11.7800i 0.810967i −0.914102 0.405483i \(-0.867103\pi\)
0.914102 0.405483i \(-0.132897\pi\)
\(212\) −0.836763 1.08653i −0.0574691 0.0746235i
\(213\) 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
\(218\) 1.43996 22.2692i 0.0975264 1.50826i
\(219\) −5.61404 −0.379361
\(220\) 0 0
\(221\) −7.03028 −0.472908
\(222\) −0.403277 + 6.23675i −0.0270662 + 0.418583i
\(223\) −3.32381 + 3.32381i −0.222579 + 0.222579i −0.809583 0.587005i \(-0.800307\pi\)
0.587005 + 0.809583i \(0.300307\pi\)
\(224\) −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 0.350085 0.936718i \(-0.386153\pi\)
−0.936718 + 0.350085i \(0.886153\pi\)
\(228\) −5.91607 + 4.55609i −0.391801 + 0.301734i
\(229\) 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
\(232\) −1.43746 + 7.32745i −0.0943739 + 0.481071i
\(233\) 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
\(238\) 5.92707 + 0.383253i 0.384195 + 0.0248426i
\(239\) −0.706459 −0.0456970 −0.0228485 0.999739i \(-0.507274\pi\)
−0.0228485 + 0.999739i \(0.507274\pi\)
\(240\) 0 0
\(241\) −24.9991 −1.61033 −0.805166 0.593049i \(-0.797924\pi\)
−0.805166 + 0.593049i \(0.797924\pi\)
\(242\) 14.7749 + 0.955368i 0.949768 + 0.0614134i
\(243\) −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
\(248\) 3.27242 16.6811i 0.207799 1.05925i
\(249\) 5.03028i 0.318781i
\(250\) 0 0
\(251\) 28.6154i 1.80619i −0.429440 0.903095i \(-0.641289\pi\)
0.429440 0.903095i \(-0.358711\pi\)
\(252\) −4.18329 + 3.22164i −0.263523 + 0.202944i
\(253\) 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 \(0.194893\pi\)
\(258\) 0.658812 10.1886i 0.0410158 0.634316i
\(259\) 11.6669 0.724948
\(260\) 0 0
\(261\) 2.64002 0.163413
\(262\) 0.417500 6.45670i 0.0257932 0.398896i
\(263\) 0.176615 0.176615i 0.0108905 0.0108905i −0.701641 0.712531i \(-0.747549\pi\)
0.712531 + 0.701641i \(0.247549\pi\)
\(264\) −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
\(268\) −8.81001 11.4398i −0.538157 0.698795i
\(269\) 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 \(0.154938\pi\)
−0.883857 + 0.467757i \(0.845062\pi\)
\(272\) −5.49958 + 3.20100i −0.333461 + 0.194089i
\(273\) −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 \(0.368976\pi\)
\(278\) −19.1794 1.24017i −1.15031 0.0743805i
\(279\) −6.01008 −0.359814
\(280\) 0 0
\(281\) −20.7493 −1.23780 −0.618900 0.785470i \(-0.712421\pi\)
−0.618900 + 0.785470i \(0.712421\pi\)
\(282\) 4.19107 + 0.271001i 0.249575 + 0.0161379i
\(283\) −18.5822 + 18.5822i −1.10459 + 1.10459i −0.110745 + 0.993849i \(0.535324\pi\)
−0.993849 + 0.110745i \(0.964676\pi\)
\(284\) −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
\(288\) 1.79480 5.36458i 0.105759 0.316111i
\(289\) 14.4693i 0.851133i
\(290\) 0 0
\(291\) 17.7198i 1.03876i
\(292\) −6.85085 8.89581i −0.400916 0.520588i
\(293\) −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
\(298\) 0.517441 8.00230i 0.0299745 0.463561i
\(299\) −36.4578 −2.10841
\(300\) 0 0
\(301\) −19.0596 −1.09858
\(302\) −1.75639 + 27.1628i −0.101069 + 1.56304i
\(303\) −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 0.680806 0.732464i \(-0.261630\pi\)
−0.732464 + 0.680806i \(0.761630\pi\)
\(308\) −3.04759 + 2.34702i −0.173653 + 0.133734i
\(309\) 0.0799296i 0.00454704i
\(310\) 0 0
\(311\) 24.4377i 1.38573i 0.721066 + 0.692867i \(0.243653\pi\)
−0.721066 + 0.692867i \(0.756347\pi\)
\(312\) 12.2657 + 2.40623i 0.694411 + 0.136226i
\(313\) −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 \(0.971718\pi\)
\(318\) −0.967703 0.0625731i −0.0542661 0.00350893i
\(319\) 1.92330 0.107684
\(320\) 0 0
\(321\) 5.52982 0.308644
\(322\) 30.7368 + 1.98749i 1.71289 + 0.110758i
\(323\) 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
\(328\) −11.7953 2.31395i −0.651289 0.127766i
\(329\) 7.84014i 0.432241i
\(330\) 0 0
\(331\) 11.0294i 0.606231i 0.952954 + 0.303115i \(0.0980268\pi\)
−0.952954 + 0.303115i \(0.901973\pi\)
\(332\) 7.97080 6.13849i 0.437455 0.336893i
\(333\) 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 \(0.425803\pi\)
\(338\) −0.595876 + 9.21531i −0.0324114 + 0.501247i
\(339\) 2.60900 0.141701
\(340\) 0 0
\(341\) −4.37844 −0.237106
\(342\) −0.340704 + 5.26904i −0.0184232 + 0.284917i
\(343\) −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 0.0454187 0.998968i \(-0.485538\pi\)
−0.998968 + 0.0454187i \(0.985538\pi\)
\(348\) 3.22164 + 4.18329i 0.172698 + 0.224248i
\(349\) 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
\(352\) 1.30754 3.90818i 0.0696919 0.208307i
\(353\) 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
\(358\) 34.4569 + 2.22804i 1.82111 + 0.117755i
\(359\) 9.63060 0.508284 0.254142 0.967167i \(-0.418207\pi\)
0.254142 + 0.967167i \(0.418207\pi\)
\(360\) 0 0
\(361\) −5.06055 −0.266345
\(362\) 15.9192 + 1.02936i 0.836692 + 0.0541017i
\(363\) 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 0.984156 0.177306i \(-0.0567383\pi\)
−0.177306 + 0.984156i \(0.556738\pi\)
\(368\) −28.5199 + 16.5998i −1.48670 + 0.865326i
\(369\) 4.24977i 0.221234i
\(370\) 0 0
\(371\) 1.81026i 0.0939840i
\(372\) −7.33415 9.52337i −0.380258 0.493764i
\(373\) −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
\(378\) −0.240914 + 3.72578i −0.0123913 + 0.191633i
\(379\) 5.89705 0.302911 0.151455 0.988464i \(-0.451604\pi\)
0.151455 + 0.988464i \(0.451604\pi\)
\(380\) 0 0
\(381\) 15.9201 0.815610
\(382\) 0.298155 4.61102i 0.0152549 0.235920i
\(383\) −0.642881 + 0.642881i −0.0328497 + 0.0328497i −0.723341 0.690491i \(-0.757394\pi\)
0.690491 + 0.723341i \(0.257394\pi\)
\(384\) 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
\(388\) 28.0782 21.6237i 1.42546 1.09778i
\(389\) 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
\(392\) 0.0164850 0.0840320i 0.000832616 0.00424426i
\(393\) −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 \(-0.0820166\pi\)
\(398\) −7.32530 0.473665i −0.367184 0.0237427i
\(399\) 9.85668 0.493451
\(400\) 0 0
\(401\) 15.9394 0.795978 0.397989 0.917390i \(-0.369708\pi\)
0.397989 + 0.917390i \(0.369708\pi\)
\(402\) −10.1886 0.658812i −0.508163 0.0328586i
\(403\) 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
\(408\) −0.866187 + 4.41538i −0.0428826 + 0.218594i
\(409\) 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
\(412\) −0.126654 + 0.0975387i −0.00623978 + 0.00480539i
\(413\) 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
\(418\) −0.248208 + 3.83858i −0.0121403 + 0.187751i
\(419\) −28.0361 −1.36966 −0.684828 0.728705i \(-0.740122\pi\)
−0.684828 + 0.728705i \(0.740122\pi\)
\(420\) 0 0
\(421\) 17.4087 0.848449 0.424224 0.905557i \(-0.360547\pi\)
0.424224 + 0.905557i \(0.360547\pi\)
\(422\) 1.07498 16.6247i 0.0523290 0.809277i
\(423\) 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
\(428\) 6.74808 + 8.76236i 0.326181 + 0.423545i
\(429\) 3.21949i 0.155439i
\(430\) 0 0
\(431\) 31.1542i 1.50065i −0.661071 0.750323i \(-0.729898\pi\)
0.661071 0.750323i \(-0.270102\pi\)
\(432\) −2.01216 3.45705i −0.0968100 0.166328i
\(433\) 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
\(438\) −7.92290 0.512307i −0.378571 0.0244790i
\(439\) 14.2967 0.682344 0.341172 0.940001i \(-0.389176\pi\)
0.341172 + 0.940001i \(0.389176\pi\)
\(440\) 0 0
\(441\) −0.0302761 −0.00144172
\(442\) −9.92159 0.641545i −0.471922 0.0305152i
\(443\) −7.02825 + 7.02825i −0.333922 + 0.333922i −0.854074 0.520152i \(-0.825875\pi\)
0.520152 + 0.854074i \(0.325875\pi\)
\(444\) −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
\(448\) −8.18505 19.4696i −0.386707 0.919854i
\(449\) 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
\(452\) 3.18378 + 4.13412i 0.149752 + 0.194453i
\(453\) 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 \(0.302240\pi\)
\(458\) −0.647071 + 10.0070i −0.0302356 + 0.467599i
\(459\) 1.59083 0.0742535
\(460\) 0 0
\(461\) 27.1689 1.26538 0.632691 0.774404i \(-0.281950\pi\)
0.632691 + 0.774404i \(0.281950\pi\)
\(462\) −0.175510 + 2.71428i −0.00816545 + 0.126280i
\(463\) −4.96280 + 4.96280i −0.230641 + 0.230641i −0.812960 0.582319i \(-0.802145\pi\)
0.582319 + 0.812960i \(0.302145\pi\)
\(464\) −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 0.999851 0.0172604i \(-0.00549442\pi\)
−0.0172604 + 0.999851i \(0.505494\pi\)
\(468\) 7.00260 5.39285i 0.323695 0.249285i
\(469\) 19.0596i 0.880092i
\(470\) 0 0
\(471\) 2.96222i 0.136492i
\(472\) −13.6787 2.68342i −0.629614 0.123514i
\(473\) −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
\(478\) −0.997001 0.0644676i −0.0456018 0.00294868i
\(479\) 18.7808 0.858118 0.429059 0.903277i \(-0.358845\pi\)
0.429059 + 0.903277i \(0.358845\pi\)
\(480\) 0 0
\(481\) −19.5298 −0.890483
\(482\) −35.2804 2.28128i −1.60698 0.103909i
\(483\) 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 0.636591 0.771201i \(-0.280344\pi\)
−0.771201 + 0.636591i \(0.780344\pi\)
\(488\) 6.41236 + 1.25794i 0.290274 + 0.0569444i
\(489\) 6.06055i 0.274068i
\(490\) 0 0
\(491\) 29.5480i 1.33348i 0.745290 + 0.666741i \(0.232311\pi\)
−0.745290 + 0.666741i \(0.767689\pi\)
\(492\) −6.73404 + 5.18603i −0.303594 + 0.233804i
\(493\) −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
\(498\) 0.459036 7.09906i 0.0205699 0.318116i
\(499\) 15.0473 0.673608 0.336804 0.941575i \(-0.390654\pi\)
0.336804 + 0.941575i \(0.390654\pi\)
\(500\) 0 0
\(501\) −6.18922 −0.276514
\(502\) 2.61129 40.3840i 0.116548 1.80243i
\(503\) −13.4136 + 13.4136i −0.598084 + 0.598084i −0.939802 0.341719i \(-0.888991\pi\)
0.341719 + 0.939802i \(0.388991\pi\)
\(504\) −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
\(508\) 19.4274 + 25.2264i 0.861951 + 1.11924i
\(509\) 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
\(512\) 18.9128 + 12.4220i 0.835835 + 0.548981i
\(513\) 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
\(518\) 16.4652 + 1.06466i 0.723437 + 0.0467785i
\(519\) −23.2001 −1.01837
\(520\) 0 0
\(521\) 30.8392 1.35109 0.675545 0.737318i \(-0.263908\pi\)
0.675545 + 0.737318i \(0.263908\pi\)
\(522\) 3.72578 + 0.240914i 0.163073 + 0.0105445i
\(523\) 17.1251 17.1251i 0.748829 0.748829i −0.225430 0.974259i \(-0.572379\pi\)
0.974259 + 0.225430i \(0.0723787\pi\)
\(524\) 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
\(528\) −1.46589 2.51852i −0.0637945 0.109604i
\(529\) 45.0587i 1.95907i
\(530\) 0 0
\(531\) 4.92834i 0.213872i
\(532\) 12.0282 + 15.6186i 0.521488 + 0.677150i
\(533\) −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
\(538\) −0.491802 + 7.60579i −0.0212031 + 0.327909i
\(539\) −0.0220566 −0.000950045
\(540\) 0 0
\(541\) −22.3397 −0.960458 −0.480229 0.877143i \(-0.659446\pi\)
−0.480229 + 0.877143i \(0.659446\pi\)
\(542\) −1.40537 + 21.7342i −0.0603656 + 0.933564i
\(543\) 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 \(0.0278582\pi\)
0.0874075 + 0.996173i \(0.472142\pi\)
\(548\) 9.17567 7.06638i 0.391965 0.301861i
\(549\) 2.31032i 0.0986022i
\(550\) 0 0
\(551\) 9.85668i 0.419909i
\(552\) −4.49190 + 22.8974i −0.191188 + 0.974580i
\(553\) −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 \(0.467907\pi\)
\(558\) −8.48183 0.548448i −0.359064 0.0232176i
\(559\) 31.9048 1.34943
\(560\) 0 0
\(561\) 1.15894 0.0489306
\(562\) −29.2828 1.89347i −1.23522 0.0798712i
\(563\) −10.2955 + 10.2955i −0.433905 + 0.433905i −0.889955 0.456049i \(-0.849264\pi\)
0.456049 + 0.889955i \(0.349264\pi\)
\(564\) 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
\(568\) −7.14584 + 36.4259i −0.299833 + 1.52840i
\(569\) 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 \(0.193038\pi\)
−0.821678 + 0.569952i \(0.806962\pi\)
\(572\) 5.10150 3.92878i 0.213304 0.164270i
\(573\) −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 \(0.295230\pi\)
\(578\) −1.32039 + 20.4200i −0.0549208 + 0.849359i
\(579\) −1.32858 −0.0552139
\(580\) 0 0
\(581\) −13.2800 −0.550949
\(582\) 1.61702 25.0074i 0.0670275 1.03659i
\(583\) −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 0.600069 0.799948i \(-0.295140\pi\)
−0.799948 + 0.600069i \(0.795140\pi\)
\(588\) −0.0369462 0.0479745i −0.00152363 0.00197843i
\(589\) 22.4390i 0.924582i
\(590\) 0 0
\(591\) 2.05710i 0.0846176i
\(592\) −15.2776 + 8.89224i −0.627906 + 0.365469i
\(593\) −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
\(598\) −51.4517 3.32695i −2.10402 0.136049i
\(599\) −30.2765 −1.23706 −0.618532 0.785760i \(-0.712272\pi\)
−0.618532 + 0.785760i \(0.712272\pi\)
\(600\) 0 0
\(601\) 30.1505 1.22986 0.614932 0.788581i \(-0.289184\pi\)
0.614932 + 0.788581i \(0.289184\pi\)
\(602\) −26.8982 1.73928i −1.09629 0.0708877i
\(603\) −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 0.188764 0.982022i \(-0.439552\pi\)
−0.982022 + 0.188764i \(0.939552\pi\)
\(608\) −20.0290 6.70097i −0.812282 0.271760i
\(609\) 6.96972i 0.282427i
\(610\) 0 0
\(611\) 13.1240i 0.530939i
\(612\) 1.94130 + 2.52077i 0.0784724 + 0.101896i
\(613\) −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 \(0.0794421\pi\)
\(618\) −0.00729394 + 0.112802i −0.000293405 + 0.00453756i
\(619\) −38.9056 −1.56375 −0.781875 0.623435i \(-0.785736\pi\)
−0.781875 + 0.623435i \(0.785736\pi\)
\(620\) 0 0
\(621\) 8.24977 0.331052
\(622\) −2.23005 + 34.4881i −0.0894169 + 1.38285i
\(623\) 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
\(628\) 4.69384 3.61483i 0.187305 0.144247i
\(629\) 7.03028i 0.280315i
\(630\) 0 0
\(631\) 12.7707i 0.508395i 0.967152 + 0.254198i \(0.0818113\pi\)
−0.967152 + 0.254198i \(0.918189\pi\)
\(632\) 19.7448 + 3.87342i 0.785404 + 0.154077i
\(633\) −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
\(638\) 2.71428 + 0.175510i 0.107460 + 0.00694849i
\(639\) 13.1240 0.519176
\(640\) 0 0
\(641\) −16.4683 −0.650461 −0.325230 0.945635i \(-0.605442\pi\)
−0.325230 + 0.945635i \(0.605442\pi\)
\(642\) 7.80405 + 0.504621i 0.308001 + 0.0199158i
\(643\) −5.74249 + 5.74249i −0.226462 + 0.226462i −0.811213 0.584751i \(-0.801192\pi\)
0.584751 + 0.811213i \(0.301192\pi\)
\(644\) 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 0.792009 0.610510i \(-0.209036\pi\)
−0.610510 + 0.792009i \(0.709036\pi\)
\(648\) −2.77552 0.544488i −0.109033 0.0213895i
\(649\) 3.59037i 0.140934i
\(650\) 0 0
\(651\) 15.8668i 0.621867i
\(652\) 9.60334 7.39574i 0.376096 0.289640i
\(653\) −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
\(658\) 0.715449 11.0645i 0.0278911 0.431340i
\(659\) 35.5474 1.38473 0.692364 0.721548i \(-0.256569\pi\)
0.692364 + 0.721548i \(0.256569\pi\)
\(660\) 0 0
\(661\) 15.1883 0.590756 0.295378 0.955380i \(-0.404554\pi\)
0.295378 + 0.955380i \(0.404554\pi\)
\(662\) −1.00648 + 15.5654i −0.0391181 + 0.604967i
\(663\) −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
\(668\) −7.55275 9.80722i −0.292225 0.379453i
\(669\) 4.70058i 0.181735i
\(670\) 0 0
\(671\) 1.68311i 0.0649756i
\(672\) −14.1626 4.73830i −0.546335 0.182784i
\(673\) 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 \(0.329226\pi\)
\(678\) 3.68199 + 0.238083i 0.141406 + 0.00914351i
\(679\) −46.7808 −1.79528
\(680\) 0 0
\(681\) −12.4995 −0.478983
\(682\) −6.17914 0.399552i −0.236612 0.0152997i
\(683\) 24.8545 24.8545i 0.951030 0.951030i −0.0478253 0.998856i \(-0.515229\pi\)
0.998856 + 0.0478253i \(0.0152291\pi\)
\(684\) −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
\(688\) 24.9582 14.5268i 0.951522 0.553827i
\(689\) 3.03028i 0.115444i
\(690\) 0 0
\(691\) 40.8979i 1.55583i −0.628371 0.777914i \(-0.716278\pi\)
0.628371 0.777914i \(-0.283722\pi\)
\(692\) −28.3112 36.7620i −1.07623 1.39748i
\(693\) 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
\(698\) −1.34042 + 20.7298i −0.0507355 + 0.784633i
\(699\) 21.7430 0.822398
\(700\) 0 0
\(701\) −43.1396 −1.62936 −0.814679 0.579912i \(-0.803087\pi\)
−0.814679 + 0.579912i \(0.803087\pi\)
\(702\) 0.403277 6.23675i 0.0152207 0.235391i
\(703\) 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
\(708\) −7.80928 + 6.01409i −0.293491 + 0.226023i
\(709\) 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
\(712\) −0.560973 + 2.85956i −0.0210233 + 0.107166i
\(713\) 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
\(718\) 13.5913 + 0.878837i 0.507225 + 0.0327979i
\(719\) 33.3725 1.24458 0.622292 0.782785i \(-0.286201\pi\)
0.622292 + 0.782785i \(0.286201\pi\)
\(720\) 0 0
\(721\) 0.211016 0.00785865
\(722\) −7.14179 0.461799i −0.265790 0.0171864i
\(723\) −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 0.991721 0.128412i \(-0.0409879\pi\)
−0.128412 + 0.991721i \(0.540988\pi\)
\(728\) 6.35251 32.3819i 0.235440 1.20015i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 11.4850i 0.424787i
\(732\) 3.66086 2.81931i 0.135309 0.104205i
\(733\) 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
\(738\) −0.387811 + 5.99756i −0.0142755 + 0.220773i
\(739\) 14.3408 0.527535 0.263768 0.964586i \(-0.415035\pi\)
0.263768 + 0.964586i \(0.415035\pi\)
\(740\) 0 0
\(741\) −16.4995 −0.606126
\(742\) −0.165194 + 2.55476i −0.00606448 + 0.0937881i
\(743\) 11.6034 11.6034i 0.425686 0.425686i −0.461470 0.887156i \(-0.652678\pi\)
0.887156 + 0.461470i \(0.152678\pi\)
\(744\) −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
\(748\) 1.41427 + 1.83642i 0.0517107 + 0.0671462i
\(749\) 14.5988i 0.533430i
\(750\) 0 0
\(751\) 35.1721i 1.28345i −0.766936 0.641724i \(-0.778220\pi\)
0.766936 0.641724i \(-0.221780\pi\)
\(752\) 5.97555 + 10.2665i 0.217906 + 0.374381i
\(753\) −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 \(0.117389\pi\)
\(758\) 8.32230 + 0.538132i 0.302280 + 0.0195459i
\(759\) 6.01008 0.218152
\(760\) 0 0
\(761\) −24.4002 −0.884508 −0.442254 0.896890i \(-0.645821\pi\)
−0.442254 + 0.896890i \(0.645821\pi\)
\(762\) 22.4675 + 1.45278i 0.813910 + 0.0526286i
\(763\) −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
\(768\) 15.4253 4.24959i 0.556614 0.153344i
\(769\) 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
\(772\) −1.62128 2.10522i −0.0583510 0.0757686i
\(773\) 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
\(778\) 1.71825 26.5731i 0.0616024 0.952691i
\(779\) 15.8668 0.568486
\(780\) 0 0
\(781\) 9.56101 0.342120
\(782\) 1.19762 18.5214i 0.0428269 0.662324i
\(783\) 1.86678 1.86678i 0.0667132 0.0667132i