Properties

Label 450.2.h.b.181.1
Level $450$
Weight $2$
Character 450.181
Analytic conductor $3.593$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 181.1
Root \(-0.309017 + 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 450.181
Dual form 450.2.h.b.271.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-1.80902 - 1.31433i) q^{5} +2.00000 q^{7} +(-0.809017 - 0.587785i) q^{8} +O(q^{10})\) \(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-1.80902 - 1.31433i) q^{5} +2.00000 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.690983 - 2.12663i) q^{10} +(1.61803 + 4.97980i) q^{11} +(-1.50000 + 4.61653i) q^{13} +(0.618034 + 1.90211i) q^{14} +(0.309017 - 0.951057i) q^{16} +(6.35410 + 4.61653i) q^{17} +(2.23607 + 1.62460i) q^{19} +2.23607 q^{20} +(-4.23607 + 3.07768i) q^{22} +(-1.85410 - 5.70634i) q^{23} +(1.54508 + 4.75528i) q^{25} -4.85410 q^{26} +(-1.61803 + 1.17557i) q^{28} +(-1.11803 + 0.812299i) q^{29} +(-3.00000 - 2.17963i) q^{31} +1.00000 q^{32} +(-2.42705 + 7.46969i) q^{34} +(-3.61803 - 2.62866i) q^{35} +(-0.663119 + 2.04087i) q^{37} +(-0.854102 + 2.62866i) q^{38} +(0.690983 + 2.12663i) q^{40} +(1.88197 - 5.79210i) q^{41} -1.23607 q^{43} +(-4.23607 - 3.07768i) q^{44} +(4.85410 - 3.52671i) q^{46} +(3.85410 - 2.80017i) q^{47} -3.00000 q^{49} +(-4.04508 + 2.93893i) q^{50} +(-1.50000 - 4.61653i) q^{52} +(6.92705 - 5.03280i) q^{53} +(3.61803 - 11.1352i) q^{55} +(-1.61803 - 1.17557i) q^{56} +(-1.11803 - 0.812299i) q^{58} +(-2.76393 + 8.50651i) q^{59} +(-2.73607 - 8.42075i) q^{61} +(1.14590 - 3.52671i) q^{62} +(0.309017 + 0.951057i) q^{64} +(8.78115 - 6.37988i) q^{65} +(7.85410 + 5.70634i) q^{67} -7.85410 q^{68} +(1.38197 - 4.25325i) q^{70} +(-11.4721 + 8.33499i) q^{71} +(-0.972136 - 2.99193i) q^{73} -2.14590 q^{74} -2.76393 q^{76} +(3.23607 + 9.95959i) q^{77} +(-1.80902 + 1.31433i) q^{80} +6.09017 q^{82} +(4.85410 + 3.52671i) q^{83} +(-5.42705 - 16.7027i) q^{85} +(-0.381966 - 1.17557i) q^{86} +(1.61803 - 4.97980i) q^{88} +(-0.427051 - 1.31433i) q^{89} +(-3.00000 + 9.23305i) q^{91} +(4.85410 + 3.52671i) q^{92} +(3.85410 + 2.80017i) q^{94} +(-1.90983 - 5.87785i) q^{95} +(11.2082 - 8.14324i) q^{97} +(-0.927051 - 2.85317i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - q^{2} - q^{4} - 5q^{5} + 8q^{7} - q^{8} + O(q^{10}) \) \( 4q - q^{2} - q^{4} - 5q^{5} + 8q^{7} - q^{8} + 5q^{10} + 2q^{11} - 6q^{13} - 2q^{14} - q^{16} + 12q^{17} - 8q^{22} + 6q^{23} - 5q^{25} - 6q^{26} - 2q^{28} - 12q^{31} + 4q^{32} - 3q^{34} - 10q^{35} + 13q^{37} + 10q^{38} + 5q^{40} + 12q^{41} + 4q^{43} - 8q^{44} + 6q^{46} + 2q^{47} - 12q^{49} - 5q^{50} - 6q^{52} + 21q^{53} + 10q^{55} - 2q^{56} - 20q^{59} - 2q^{61} + 18q^{62} - q^{64} + 15q^{65} + 18q^{67} - 18q^{68} + 10q^{70} - 28q^{71} + 14q^{73} - 22q^{74} - 20q^{76} + 4q^{77} - 5q^{80} + 2q^{82} + 6q^{83} - 15q^{85} - 6q^{86} + 2q^{88} + 5q^{89} - 12q^{91} + 6q^{92} + 2q^{94} - 30q^{95} + 18q^{97} + 3q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 + 0.951057i 0.218508 + 0.672499i
\(3\) 0 0
\(4\) −0.809017 + 0.587785i −0.404508 + 0.293893i
\(5\) −1.80902 1.31433i −0.809017 0.587785i
\(6\) 0 0
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) −0.809017 0.587785i −0.286031 0.207813i
\(9\) 0 0
\(10\) 0.690983 2.12663i 0.218508 0.672499i
\(11\) 1.61803 + 4.97980i 0.487856 + 1.50147i 0.827802 + 0.561020i \(0.189591\pi\)
−0.339946 + 0.940445i \(0.610409\pi\)
\(12\) 0 0
\(13\) −1.50000 + 4.61653i −0.416025 + 1.28039i 0.495306 + 0.868719i \(0.335056\pi\)
−0.911331 + 0.411675i \(0.864944\pi\)
\(14\) 0.618034 + 1.90211i 0.165177 + 0.508361i
\(15\) 0 0
\(16\) 0.309017 0.951057i 0.0772542 0.237764i
\(17\) 6.35410 + 4.61653i 1.54110 + 1.11967i 0.949644 + 0.313332i \(0.101445\pi\)
0.591452 + 0.806340i \(0.298555\pi\)
\(18\) 0 0
\(19\) 2.23607 + 1.62460i 0.512989 + 0.372708i 0.813956 0.580926i \(-0.197309\pi\)
−0.300967 + 0.953635i \(0.597309\pi\)
\(20\) 2.23607 0.500000
\(21\) 0 0
\(22\) −4.23607 + 3.07768i −0.903133 + 0.656164i
\(23\) −1.85410 5.70634i −0.386607 1.18985i −0.935308 0.353835i \(-0.884877\pi\)
0.548701 0.836019i \(-0.315123\pi\)
\(24\) 0 0
\(25\) 1.54508 + 4.75528i 0.309017 + 0.951057i
\(26\) −4.85410 −0.951968
\(27\) 0 0
\(28\) −1.61803 + 1.17557i −0.305780 + 0.222162i
\(29\) −1.11803 + 0.812299i −0.207614 + 0.150840i −0.686733 0.726909i \(-0.740956\pi\)
0.479120 + 0.877750i \(0.340956\pi\)
\(30\) 0 0
\(31\) −3.00000 2.17963i −0.538816 0.391473i 0.284829 0.958578i \(-0.408063\pi\)
−0.823645 + 0.567106i \(0.808063\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −2.42705 + 7.46969i −0.416236 + 1.28104i
\(35\) −3.61803 2.62866i −0.611559 0.444324i
\(36\) 0 0
\(37\) −0.663119 + 2.04087i −0.109016 + 0.335517i −0.990652 0.136413i \(-0.956443\pi\)
0.881636 + 0.471930i \(0.156443\pi\)
\(38\) −0.854102 + 2.62866i −0.138554 + 0.426424i
\(39\) 0 0
\(40\) 0.690983 + 2.12663i 0.109254 + 0.336249i
\(41\) 1.88197 5.79210i 0.293914 0.904573i −0.689670 0.724123i \(-0.742245\pi\)
0.983584 0.180450i \(-0.0577554\pi\)
\(42\) 0 0
\(43\) −1.23607 −0.188499 −0.0942493 0.995549i \(-0.530045\pi\)
−0.0942493 + 0.995549i \(0.530045\pi\)
\(44\) −4.23607 3.07768i −0.638611 0.463978i
\(45\) 0 0
\(46\) 4.85410 3.52671i 0.715698 0.519985i
\(47\) 3.85410 2.80017i 0.562179 0.408447i −0.270077 0.962839i \(-0.587049\pi\)
0.832256 + 0.554392i \(0.187049\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) −4.04508 + 2.93893i −0.572061 + 0.415627i
\(51\) 0 0
\(52\) −1.50000 4.61653i −0.208013 0.640197i
\(53\) 6.92705 5.03280i 0.951504 0.691308i 0.000341607 1.00000i \(-0.499891\pi\)
0.951162 + 0.308692i \(0.0998913\pi\)
\(54\) 0 0
\(55\) 3.61803 11.1352i 0.487856 1.50147i
\(56\) −1.61803 1.17557i −0.216219 0.157092i
\(57\) 0 0
\(58\) −1.11803 0.812299i −0.146805 0.106660i
\(59\) −2.76393 + 8.50651i −0.359833 + 1.10745i 0.593320 + 0.804966i \(0.297817\pi\)
−0.953154 + 0.302487i \(0.902183\pi\)
\(60\) 0 0
\(61\) −2.73607 8.42075i −0.350318 1.07817i −0.958675 0.284504i \(-0.908171\pi\)
0.608357 0.793663i \(-0.291829\pi\)
\(62\) 1.14590 3.52671i 0.145529 0.447893i
\(63\) 0 0
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) 8.78115 6.37988i 1.08917 0.791327i
\(66\) 0 0
\(67\) 7.85410 + 5.70634i 0.959531 + 0.697140i 0.953042 0.302839i \(-0.0979343\pi\)
0.00648944 + 0.999979i \(0.497934\pi\)
\(68\) −7.85410 −0.952450
\(69\) 0 0
\(70\) 1.38197 4.25325i 0.165177 0.508361i
\(71\) −11.4721 + 8.33499i −1.36149 + 0.989182i −0.363144 + 0.931733i \(0.618297\pi\)
−0.998348 + 0.0574487i \(0.981703\pi\)
\(72\) 0 0
\(73\) −0.972136 2.99193i −0.113780 0.350179i 0.877911 0.478824i \(-0.158937\pi\)
−0.991691 + 0.128646i \(0.958937\pi\)
\(74\) −2.14590 −0.249456
\(75\) 0 0
\(76\) −2.76393 −0.317045
\(77\) 3.23607 + 9.95959i 0.368784 + 1.13500i
\(78\) 0 0
\(79\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(80\) −1.80902 + 1.31433i −0.202254 + 0.146946i
\(81\) 0 0
\(82\) 6.09017 0.672547
\(83\) 4.85410 + 3.52671i 0.532807 + 0.387107i 0.821407 0.570343i \(-0.193190\pi\)
−0.288600 + 0.957450i \(0.593190\pi\)
\(84\) 0 0
\(85\) −5.42705 16.7027i −0.588646 1.81167i
\(86\) −0.381966 1.17557i −0.0411885 0.126765i
\(87\) 0 0
\(88\) 1.61803 4.97980i 0.172483 0.530848i
\(89\) −0.427051 1.31433i −0.0452673 0.139318i 0.925868 0.377846i \(-0.123335\pi\)
−0.971136 + 0.238528i \(0.923335\pi\)
\(90\) 0 0
\(91\) −3.00000 + 9.23305i −0.314485 + 0.967887i
\(92\) 4.85410 + 3.52671i 0.506075 + 0.367685i
\(93\) 0 0
\(94\) 3.85410 + 2.80017i 0.397520 + 0.288815i
\(95\) −1.90983 5.87785i −0.195944 0.603055i
\(96\) 0 0
\(97\) 11.2082 8.14324i 1.13802 0.826820i 0.151178 0.988506i \(-0.451693\pi\)
0.986842 + 0.161686i \(0.0516932\pi\)
\(98\) −0.927051 2.85317i −0.0936463 0.288214i
\(99\) 0 0
\(100\) −4.04508 2.93893i −0.404508 0.293893i
\(101\) −1.67376 −0.166546 −0.0832728 0.996527i \(-0.526537\pi\)
−0.0832728 + 0.996527i \(0.526537\pi\)
\(102\) 0 0
\(103\) 1.85410 1.34708i 0.182690 0.132732i −0.492682 0.870210i \(-0.663983\pi\)
0.675372 + 0.737478i \(0.263983\pi\)
\(104\) 3.92705 2.85317i 0.385079 0.279776i
\(105\) 0 0
\(106\) 6.92705 + 5.03280i 0.672815 + 0.488828i
\(107\) −10.9443 −1.05802 −0.529011 0.848615i \(-0.677437\pi\)
−0.529011 + 0.848615i \(0.677437\pi\)
\(108\) 0 0
\(109\) 0.791796 2.43690i 0.0758403 0.233412i −0.905949 0.423388i \(-0.860841\pi\)
0.981789 + 0.189975i \(0.0608408\pi\)
\(110\) 11.7082 1.11633
\(111\) 0 0
\(112\) 0.618034 1.90211i 0.0583987 0.179733i
\(113\) 3.57295 10.9964i 0.336115 1.03445i −0.630056 0.776550i \(-0.716968\pi\)
0.966170 0.257905i \(-0.0830321\pi\)
\(114\) 0 0
\(115\) −4.14590 + 12.7598i −0.386607 + 1.18985i
\(116\) 0.427051 1.31433i 0.0396507 0.122032i
\(117\) 0 0
\(118\) −8.94427 −0.823387
\(119\) 12.7082 + 9.23305i 1.16496 + 0.846392i
\(120\) 0 0
\(121\) −13.2812 + 9.64932i −1.20738 + 0.877211i
\(122\) 7.16312 5.20431i 0.648518 0.471176i
\(123\) 0 0
\(124\) 3.70820 0.333007
\(125\) 3.45492 10.6331i 0.309017 0.951057i
\(126\) 0 0
\(127\) 0.0901699 + 0.277515i 0.00800129 + 0.0246254i 0.954977 0.296678i \(-0.0958789\pi\)
−0.946976 + 0.321304i \(0.895879\pi\)
\(128\) −0.809017 + 0.587785i −0.0715077 + 0.0519534i
\(129\) 0 0
\(130\) 8.78115 + 6.37988i 0.770158 + 0.559553i
\(131\) −0.618034 0.449028i −0.0539979 0.0392318i 0.560459 0.828182i \(-0.310625\pi\)
−0.614457 + 0.788950i \(0.710625\pi\)
\(132\) 0 0
\(133\) 4.47214 + 3.24920i 0.387783 + 0.281741i
\(134\) −3.00000 + 9.23305i −0.259161 + 0.797614i
\(135\) 0 0
\(136\) −2.42705 7.46969i −0.208118 0.640521i
\(137\) 4.64590 14.2986i 0.396926 1.22161i −0.530526 0.847669i \(-0.678005\pi\)
0.927452 0.373943i \(-0.121995\pi\)
\(138\) 0 0
\(139\) −4.14590 12.7598i −0.351650 1.08227i −0.957926 0.287014i \(-0.907337\pi\)
0.606276 0.795254i \(-0.292663\pi\)
\(140\) 4.47214 0.377964
\(141\) 0 0
\(142\) −11.4721 8.33499i −0.962720 0.699457i
\(143\) −25.4164 −2.12543
\(144\) 0 0
\(145\) 3.09017 0.256625
\(146\) 2.54508 1.84911i 0.210633 0.153034i
\(147\) 0 0
\(148\) −0.663119 2.04087i −0.0545080 0.167759i
\(149\) −7.03444 −0.576284 −0.288142 0.957588i \(-0.593038\pi\)
−0.288142 + 0.957588i \(0.593038\pi\)
\(150\) 0 0
\(151\) −6.94427 −0.565117 −0.282558 0.959250i \(-0.591183\pi\)
−0.282558 + 0.959250i \(0.591183\pi\)
\(152\) −0.854102 2.62866i −0.0692768 0.213212i
\(153\) 0 0
\(154\) −8.47214 + 6.15537i −0.682704 + 0.496014i
\(155\) 2.56231 + 7.88597i 0.205809 + 0.633416i
\(156\) 0 0
\(157\) 17.8541 1.42491 0.712456 0.701717i \(-0.247583\pi\)
0.712456 + 0.701717i \(0.247583\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −1.80902 1.31433i −0.143015 0.103907i
\(161\) −3.70820 11.4127i −0.292247 0.899445i
\(162\) 0 0
\(163\) 6.32624 19.4702i 0.495509 1.52502i −0.320652 0.947197i \(-0.603902\pi\)
0.816162 0.577824i \(-0.196098\pi\)
\(164\) 1.88197 + 5.79210i 0.146957 + 0.452287i
\(165\) 0 0
\(166\) −1.85410 + 5.70634i −0.143906 + 0.442898i
\(167\) 5.23607 + 3.80423i 0.405179 + 0.294380i 0.771647 0.636051i \(-0.219433\pi\)
−0.366468 + 0.930431i \(0.619433\pi\)
\(168\) 0 0
\(169\) −8.54508 6.20837i −0.657314 0.477567i
\(170\) 14.2082 10.3229i 1.08972 0.791728i
\(171\) 0 0
\(172\) 1.00000 0.726543i 0.0762493 0.0553983i
\(173\) 3.37132 + 10.3759i 0.256317 + 0.788862i 0.993567 + 0.113243i \(0.0361238\pi\)
−0.737250 + 0.675620i \(0.763876\pi\)
\(174\) 0 0
\(175\) 3.09017 + 9.51057i 0.233595 + 0.718931i
\(176\) 5.23607 0.394683
\(177\) 0 0
\(178\) 1.11803 0.812299i 0.0838002 0.0608844i
\(179\) −3.09017 + 2.24514i −0.230970 + 0.167810i −0.697251 0.716827i \(-0.745594\pi\)
0.466281 + 0.884637i \(0.345594\pi\)
\(180\) 0 0
\(181\) 16.2082 + 11.7759i 1.20475 + 0.875299i 0.994743 0.102401i \(-0.0326526\pi\)
0.210003 + 0.977701i \(0.432653\pi\)
\(182\) −9.70820 −0.719620
\(183\) 0 0
\(184\) −1.85410 + 5.70634i −0.136686 + 0.420677i
\(185\) 3.88197 2.82041i 0.285408 0.207361i
\(186\) 0 0
\(187\) −12.7082 + 39.1118i −0.929316 + 2.86014i
\(188\) −1.47214 + 4.53077i −0.107367 + 0.330440i
\(189\) 0 0
\(190\) 5.00000 3.63271i 0.362738 0.263545i
\(191\) 0.236068 0.726543i 0.0170813 0.0525708i −0.942153 0.335184i \(-0.891201\pi\)
0.959234 + 0.282614i \(0.0912014\pi\)
\(192\) 0 0
\(193\) 2.38197 0.171458 0.0857288 0.996319i \(-0.472678\pi\)
0.0857288 + 0.996319i \(0.472678\pi\)
\(194\) 11.2082 + 8.14324i 0.804702 + 0.584650i
\(195\) 0 0
\(196\) 2.42705 1.76336i 0.173361 0.125954i
\(197\) −10.7812 + 7.83297i −0.768125 + 0.558076i −0.901392 0.433005i \(-0.857453\pi\)
0.133266 + 0.991080i \(0.457453\pi\)
\(198\) 0 0
\(199\) −6.18034 −0.438113 −0.219056 0.975712i \(-0.570298\pi\)
−0.219056 + 0.975712i \(0.570298\pi\)
\(200\) 1.54508 4.75528i 0.109254 0.336249i
\(201\) 0 0
\(202\) −0.517221 1.59184i −0.0363915 0.112002i
\(203\) −2.23607 + 1.62460i −0.156941 + 0.114024i
\(204\) 0 0
\(205\) −11.0172 + 8.00448i −0.769476 + 0.559057i
\(206\) 1.85410 + 1.34708i 0.129181 + 0.0938558i
\(207\) 0 0
\(208\) 3.92705 + 2.85317i 0.272292 + 0.197832i
\(209\) −4.47214 + 13.7638i −0.309344 + 0.952063i
\(210\) 0 0
\(211\) −2.47214 7.60845i −0.170189 0.523787i 0.829192 0.558963i \(-0.188801\pi\)
−0.999381 + 0.0351760i \(0.988801\pi\)
\(212\) −2.64590 + 8.14324i −0.181721 + 0.559280i
\(213\) 0 0
\(214\) −3.38197 10.4086i −0.231186 0.711519i
\(215\) 2.23607 + 1.62460i 0.152499 + 0.110797i
\(216\) 0 0
\(217\) −6.00000 4.35926i −0.407307 0.295926i
\(218\) 2.56231 0.173541
\(219\) 0 0
\(220\) 3.61803 + 11.1352i 0.243928 + 0.750733i
\(221\) −30.8435 + 22.4091i −2.07476 + 1.50740i
\(222\) 0 0
\(223\) −0.708204 2.17963i −0.0474248 0.145959i 0.924540 0.381085i \(-0.124450\pi\)
−0.971965 + 0.235127i \(0.924450\pi\)
\(224\) 2.00000 0.133631
\(225\) 0 0
\(226\) 11.5623 0.769113
\(227\) 5.23607 + 16.1150i 0.347530 + 1.06959i 0.960215 + 0.279261i \(0.0900893\pi\)
−0.612685 + 0.790327i \(0.709911\pi\)
\(228\) 0 0
\(229\) 19.6353 14.2658i 1.29753 0.942714i 0.297606 0.954689i \(-0.403812\pi\)
0.999928 + 0.0119751i \(0.00381187\pi\)
\(230\) −13.4164 −0.884652
\(231\) 0 0
\(232\) 1.38197 0.0907305
\(233\) −17.8713 12.9843i −1.17079 0.850628i −0.179686 0.983724i \(-0.557508\pi\)
−0.991103 + 0.133096i \(0.957508\pi\)
\(234\) 0 0
\(235\) −10.6525 −0.694891
\(236\) −2.76393 8.50651i −0.179917 0.553727i
\(237\) 0 0
\(238\) −4.85410 + 14.9394i −0.314645 + 0.968377i
\(239\) −8.29180 25.5195i −0.536352 1.65072i −0.740710 0.671825i \(-0.765511\pi\)
0.204358 0.978896i \(-0.434489\pi\)
\(240\) 0 0
\(241\) −4.28115 + 13.1760i −0.275773 + 0.848743i 0.713240 + 0.700919i \(0.247227\pi\)
−0.989014 + 0.147824i \(0.952773\pi\)
\(242\) −13.2812 9.64932i −0.853745 0.620282i
\(243\) 0 0
\(244\) 7.16312 + 5.20431i 0.458572 + 0.333172i
\(245\) 5.42705 + 3.94298i 0.346722 + 0.251908i
\(246\) 0 0
\(247\) −10.8541 + 7.88597i −0.690630 + 0.501772i
\(248\) 1.14590 + 3.52671i 0.0727646 + 0.223946i
\(249\) 0 0
\(250\) 11.1803 0.707107
\(251\) 12.4721 0.787234 0.393617 0.919274i \(-0.371224\pi\)
0.393617 + 0.919274i \(0.371224\pi\)
\(252\) 0 0
\(253\) 25.4164 18.4661i 1.59792 1.16095i
\(254\) −0.236068 + 0.171513i −0.0148122 + 0.0107617i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 11.6180 0.724713 0.362357 0.932040i \(-0.381972\pi\)
0.362357 + 0.932040i \(0.381972\pi\)
\(258\) 0 0
\(259\) −1.32624 + 4.08174i −0.0824084 + 0.253627i
\(260\) −3.35410 + 10.3229i −0.208013 + 0.640197i
\(261\) 0 0
\(262\) 0.236068 0.726543i 0.0145843 0.0448859i
\(263\) −0.145898 + 0.449028i −0.00899646 + 0.0276883i −0.955454 0.295140i \(-0.904634\pi\)
0.946458 + 0.322828i \(0.104634\pi\)
\(264\) 0 0
\(265\) −19.1459 −1.17612
\(266\) −1.70820 + 5.25731i −0.104737 + 0.322346i
\(267\) 0 0
\(268\) −9.70820 −0.593023
\(269\) −1.54508 1.12257i −0.0942055 0.0684443i 0.539685 0.841867i \(-0.318543\pi\)
−0.633891 + 0.773422i \(0.718543\pi\)
\(270\) 0 0
\(271\) −22.7984 + 16.5640i −1.38490 + 1.00619i −0.388500 + 0.921449i \(0.627007\pi\)
−0.996403 + 0.0847417i \(0.972993\pi\)
\(272\) 6.35410 4.61653i 0.385274 0.279918i
\(273\) 0 0
\(274\) 15.0344 0.908264
\(275\) −21.1803 + 15.3884i −1.27722 + 0.927957i
\(276\) 0 0
\(277\) −6.84346 21.0620i −0.411184 1.26549i −0.915620 0.402044i \(-0.868300\pi\)
0.504437 0.863449i \(-0.331700\pi\)
\(278\) 10.8541 7.88597i 0.650986 0.472969i
\(279\) 0 0
\(280\) 1.38197 + 4.25325i 0.0825883 + 0.254181i
\(281\) −4.92705 3.57971i −0.293923 0.213548i 0.431044 0.902331i \(-0.358145\pi\)
−0.724968 + 0.688783i \(0.758145\pi\)
\(282\) 0 0
\(283\) −2.61803 1.90211i −0.155626 0.113069i 0.507247 0.861801i \(-0.330663\pi\)
−0.662873 + 0.748732i \(0.730663\pi\)
\(284\) 4.38197 13.4863i 0.260022 0.800265i
\(285\) 0 0
\(286\) −7.85410 24.1724i −0.464423 1.42935i
\(287\) 3.76393 11.5842i 0.222178 0.683793i
\(288\) 0 0
\(289\) 13.8090 + 42.4998i 0.812295 + 2.49999i
\(290\) 0.954915 + 2.93893i 0.0560745 + 0.172580i
\(291\) 0 0
\(292\) 2.54508 + 1.84911i 0.148940 + 0.108211i
\(293\) 28.7984 1.68242 0.841209 0.540709i \(-0.181844\pi\)
0.841209 + 0.540709i \(0.181844\pi\)
\(294\) 0 0
\(295\) 16.1803 11.7557i 0.942056 0.684444i
\(296\) 1.73607 1.26133i 0.100907 0.0733132i
\(297\) 0 0
\(298\) −2.17376 6.69015i −0.125923 0.387550i
\(299\) 29.1246 1.68432
\(300\) 0 0
\(301\) −2.47214 −0.142492
\(302\) −2.14590 6.60440i −0.123483 0.380040i
\(303\) 0 0
\(304\) 2.23607 1.62460i 0.128247 0.0931771i
\(305\) −6.11803 + 18.8294i −0.350318 + 1.07817i
\(306\) 0 0
\(307\) −16.2918 −0.929822 −0.464911 0.885357i \(-0.653914\pi\)
−0.464911 + 0.885357i \(0.653914\pi\)
\(308\) −8.47214 6.15537i −0.482745 0.350735i
\(309\) 0 0
\(310\) −6.70820 + 4.87380i −0.381000 + 0.276813i
\(311\) 5.76393 + 17.7396i 0.326843 + 1.00592i 0.970602 + 0.240690i \(0.0773738\pi\)
−0.643759 + 0.765228i \(0.722626\pi\)
\(312\) 0 0
\(313\) −8.14590 + 25.0705i −0.460433 + 1.41707i 0.404203 + 0.914669i \(0.367549\pi\)
−0.864636 + 0.502399i \(0.832451\pi\)
\(314\) 5.51722 + 16.9803i 0.311355 + 0.958252i
\(315\) 0 0
\(316\) 0 0
\(317\) −5.61803 4.08174i −0.315540 0.229253i 0.418730 0.908111i \(-0.362475\pi\)
−0.734270 + 0.678857i \(0.762475\pi\)
\(318\) 0 0
\(319\) −5.85410 4.25325i −0.327767 0.238137i
\(320\) 0.690983 2.12663i 0.0386271 0.118882i
\(321\) 0 0
\(322\) 9.70820 7.05342i 0.541017 0.393072i
\(323\) 6.70820 + 20.6457i 0.373254 + 1.14876i
\(324\) 0 0
\(325\) −24.2705 −1.34629
\(326\) 20.4721 1.13385
\(327\) 0 0
\(328\) −4.92705 + 3.57971i −0.272051 + 0.197657i
\(329\) 7.70820 5.60034i 0.424967 0.308757i
\(330\) 0 0
\(331\) 26.2705 + 19.0866i 1.44396 + 1.04910i 0.987197 + 0.159507i \(0.0509906\pi\)
0.456761 + 0.889589i \(0.349009\pi\)
\(332\) −6.00000 −0.329293
\(333\) 0 0
\(334\) −2.00000 + 6.15537i −0.109435 + 0.336807i
\(335\) −6.70820 20.6457i −0.366508 1.12800i
\(336\) 0 0
\(337\) 8.90983 27.4216i 0.485349 1.49375i −0.346125 0.938188i \(-0.612503\pi\)
0.831474 0.555563i \(-0.187497\pi\)
\(338\) 3.26393 10.0453i 0.177534 0.546395i
\(339\) 0 0
\(340\) 14.2082 + 10.3229i 0.770548 + 0.559836i
\(341\) 6.00000 18.4661i 0.324918 0.999995i
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 1.00000 + 0.726543i 0.0539164 + 0.0391725i
\(345\) 0 0
\(346\) −8.82624 + 6.41264i −0.474501 + 0.344746i
\(347\) −4.23607 + 3.07768i −0.227404 + 0.165219i −0.695653 0.718378i \(-0.744885\pi\)
0.468249 + 0.883596i \(0.344885\pi\)
\(348\) 0 0
\(349\) 14.7984 0.792139 0.396069 0.918221i \(-0.370374\pi\)
0.396069 + 0.918221i \(0.370374\pi\)
\(350\) −8.09017 + 5.87785i −0.432438 + 0.314184i
\(351\) 0 0
\(352\) 1.61803 + 4.97980i 0.0862415 + 0.265424i
\(353\) 16.5623 12.0332i 0.881523 0.640464i −0.0521313 0.998640i \(-0.516601\pi\)
0.933654 + 0.358177i \(0.116601\pi\)
\(354\) 0 0
\(355\) 31.7082 1.68290
\(356\) 1.11803 + 0.812299i 0.0592557 + 0.0430518i
\(357\) 0 0
\(358\) −3.09017 2.24514i −0.163321 0.118659i
\(359\) 8.61803 26.5236i 0.454842 1.39986i −0.416478 0.909146i \(-0.636736\pi\)
0.871320 0.490715i \(-0.163264\pi\)
\(360\) 0 0
\(361\) −3.51064 10.8046i −0.184771 0.568666i
\(362\) −6.19098 + 19.0539i −0.325391 + 1.00145i
\(363\) 0 0
\(364\) −3.00000 9.23305i −0.157243 0.483943i
\(365\) −2.17376 + 6.69015i −0.113780 + 0.350179i
\(366\) 0 0
\(367\) 10.0902 + 7.33094i 0.526703 + 0.382672i 0.819123 0.573618i \(-0.194461\pi\)
−0.292420 + 0.956290i \(0.594461\pi\)
\(368\) −6.00000 −0.312772
\(369\) 0 0
\(370\) 3.88197 + 2.82041i 0.201814 + 0.146626i
\(371\) 13.8541 10.0656i 0.719269 0.522580i
\(372\) 0 0
\(373\) 0.798374 + 2.45714i 0.0413382 + 0.127226i 0.969596 0.244712i \(-0.0786934\pi\)
−0.928258 + 0.371938i \(0.878693\pi\)
\(374\) −41.1246 −2.12650
\(375\) 0 0
\(376\) −4.76393 −0.245681
\(377\) −2.07295 6.37988i −0.106762 0.328581i
\(378\) 0 0
\(379\) 2.76393 2.00811i 0.141974 0.103150i −0.514531 0.857472i \(-0.672034\pi\)
0.656505 + 0.754322i \(0.272034\pi\)
\(380\) 5.00000 + 3.63271i 0.256495 + 0.186354i
\(381\) 0 0
\(382\) 0.763932 0.0390862
\(383\) 16.5623 + 12.0332i 0.846294 + 0.614869i 0.924122 0.382098i \(-0.124798\pi\)
−0.0778275 + 0.996967i \(0.524798\pi\)
\(384\) 0 0
\(385\) 7.23607 22.2703i 0.368784 1.13500i
\(386\) 0.736068 + 2.26538i 0.0374649 + 0.115305i
\(387\) 0 0
\(388\) −4.28115 + 13.1760i −0.217343 + 0.668912i
\(389\) −4.93769 15.1967i −0.250351 0.770501i −0.994710 0.102722i \(-0.967245\pi\)
0.744359 0.667780i \(-0.232755\pi\)
\(390\) 0 0
\(391\) 14.5623 44.8182i 0.736447 2.26655i
\(392\) 2.42705 + 1.76336i 0.122585 + 0.0890629i
\(393\) 0 0
\(394\) −10.7812 7.83297i −0.543147 0.394619i
\(395\) 0 0
\(396\) 0 0
\(397\) −23.3262 + 16.9475i −1.17071 + 0.850571i −0.991094 0.133166i \(-0.957486\pi\)
−0.179617 + 0.983737i \(0.557486\pi\)
\(398\) −1.90983 5.87785i −0.0957311 0.294630i
\(399\) 0 0
\(400\) 5.00000 0.250000
\(401\) 26.0902 1.30288 0.651440 0.758700i \(-0.274165\pi\)
0.651440 + 0.758700i \(0.274165\pi\)
\(402\) 0 0
\(403\) 14.5623 10.5801i 0.725400 0.527034i
\(404\) 1.35410 0.983813i 0.0673691 0.0489465i
\(405\) 0 0
\(406\) −2.23607 1.62460i −0.110974 0.0806275i
\(407\) −11.2361 −0.556951
\(408\) 0 0
\(409\) 6.48278 19.9519i 0.320553 0.986560i −0.652855 0.757483i \(-0.726429\pi\)
0.973408 0.229077i \(-0.0735709\pi\)
\(410\) −11.0172 8.00448i −0.544102 0.395313i
\(411\) 0 0
\(412\) −0.708204 + 2.17963i −0.0348907 + 0.107383i
\(413\) −5.52786 + 17.0130i −0.272008 + 0.837156i
\(414\) 0 0
\(415\) −4.14590 12.7598i −0.203514 0.626352i
\(416\) −1.50000 + 4.61653i −0.0735436 + 0.226344i
\(417\) 0 0
\(418\) −14.4721 −0.707855
\(419\) −30.6525 22.2703i −1.49747 1.08798i −0.971375 0.237552i \(-0.923655\pi\)
−0.526097 0.850425i \(-0.676345\pi\)
\(420\) 0 0
\(421\) 8.97214 6.51864i 0.437275 0.317699i −0.347276 0.937763i \(-0.612893\pi\)
0.784551 + 0.620064i \(0.212893\pi\)
\(422\) 6.47214 4.70228i 0.315059 0.228904i
\(423\) 0 0
\(424\) −8.56231 −0.415822
\(425\) −12.1353 + 37.3485i −0.588646 + 1.81167i
\(426\) 0 0
\(427\) −5.47214 16.8415i −0.264815 0.815017i
\(428\) 8.85410 6.43288i 0.427979 0.310945i
\(429\) 0 0
\(430\) −0.854102 + 2.62866i −0.0411885 + 0.126765i
\(431\) 3.00000 + 2.17963i 0.144505 + 0.104989i 0.657689 0.753290i \(-0.271534\pi\)
−0.513184 + 0.858279i \(0.671534\pi\)
\(432\) 0 0
\(433\) 18.7254 + 13.6048i 0.899886 + 0.653806i 0.938437 0.345451i \(-0.112274\pi\)
−0.0385504 + 0.999257i \(0.512274\pi\)
\(434\) 2.29180 7.05342i 0.110010 0.338575i
\(435\) 0 0
\(436\) 0.791796 + 2.43690i 0.0379202 + 0.116706i
\(437\) 5.12461 15.7719i 0.245143 0.754474i
\(438\) 0 0
\(439\) −7.76393 23.8949i −0.370552 1.14044i −0.946431 0.322907i \(-0.895340\pi\)
0.575878 0.817535i \(-0.304660\pi\)
\(440\) −9.47214 + 6.88191i −0.451566 + 0.328082i
\(441\) 0 0
\(442\) −30.8435 22.4091i −1.46707 1.06589i
\(443\) −30.0689 −1.42862 −0.714308 0.699832i \(-0.753258\pi\)
−0.714308 + 0.699832i \(0.753258\pi\)
\(444\) 0 0
\(445\) −0.954915 + 2.93893i −0.0452673 + 0.139318i
\(446\) 1.85410 1.34708i 0.0877943 0.0637863i
\(447\) 0 0
\(448\) 0.618034 + 1.90211i 0.0291994 + 0.0898664i
\(449\) −4.79837 −0.226449 −0.113225 0.993569i \(-0.536118\pi\)
−0.113225 + 0.993569i \(0.536118\pi\)
\(450\) 0 0
\(451\) 31.8885 1.50157
\(452\) 3.57295 + 10.9964i 0.168057 + 0.517227i
\(453\) 0 0
\(454\) −13.7082 + 9.95959i −0.643358 + 0.467427i
\(455\) 17.5623 12.7598i 0.823334 0.598187i
\(456\) 0 0
\(457\) −12.4721 −0.583422 −0.291711 0.956507i \(-0.594225\pi\)
−0.291711 + 0.956507i \(0.594225\pi\)
\(458\) 19.6353 + 14.2658i 0.917495 + 0.666599i
\(459\) 0 0
\(460\) −4.14590 12.7598i −0.193303 0.594927i
\(461\) −7.75329 23.8622i −0.361107 1.11137i −0.952383 0.304903i \(-0.901376\pi\)
0.591277 0.806469i \(-0.298624\pi\)
\(462\) 0 0
\(463\) −3.79837 + 11.6902i −0.176525 + 0.543289i −0.999700 0.0244992i \(-0.992201\pi\)
0.823174 + 0.567789i \(0.192201\pi\)
\(464\) 0.427051 + 1.31433i 0.0198253 + 0.0610161i
\(465\) 0 0
\(466\) 6.82624 21.0090i 0.316219 0.973223i
\(467\) 12.7984 + 9.29856i 0.592238 + 0.430286i 0.843115 0.537733i \(-0.180719\pi\)
−0.250877 + 0.968019i \(0.580719\pi\)
\(468\) 0 0
\(469\) 15.7082 + 11.4127i 0.725337 + 0.526989i
\(470\) −3.29180 10.1311i −0.151839 0.467313i
\(471\) 0 0
\(472\) 7.23607 5.25731i 0.333067 0.241987i
\(473\) −2.00000 6.15537i −0.0919601 0.283024i
\(474\) 0 0
\(475\) −4.27051 + 13.1433i −0.195944 + 0.603055i
\(476\) −15.7082 −0.719984
\(477\) 0 0
\(478\) 21.7082 15.7719i 0.992910 0.721391i
\(479\) 3.61803 2.62866i 0.165312 0.120106i −0.502053 0.864837i \(-0.667422\pi\)
0.667366 + 0.744730i \(0.267422\pi\)
\(480\) 0 0
\(481\) −8.42705 6.12261i −0.384240 0.279167i
\(482\) −13.8541 −0.631037
\(483\) 0 0
\(484\) 5.07295 15.6129i 0.230589 0.709679i
\(485\) −30.9787 −1.40667
\(486\) 0 0
\(487\) 3.18034 9.78808i 0.144115 0.443540i −0.852781 0.522268i \(-0.825086\pi\)
0.996896 + 0.0787282i \(0.0250859\pi\)
\(488\) −2.73607 + 8.42075i −0.123856 + 0.381190i
\(489\) 0 0
\(490\) −2.07295 + 6.37988i −0.0936463 + 0.288214i
\(491\) −9.23607 + 28.4257i −0.416818 + 1.28283i 0.493797 + 0.869577i \(0.335609\pi\)
−0.910615 + 0.413256i \(0.864391\pi\)
\(492\) 0 0
\(493\) −10.8541 −0.488844
\(494\) −10.8541 7.88597i −0.488349 0.354806i
\(495\) 0 0
\(496\) −3.00000 + 2.17963i −0.134704 + 0.0978682i
\(497\) −22.9443 + 16.6700i −1.02919 + 0.747751i
\(498\) 0 0
\(499\) −33.4164 −1.49592 −0.747962 0.663742i \(-0.768967\pi\)
−0.747962 + 0.663742i \(0.768967\pi\)
\(500\) 3.45492 + 10.6331i 0.154508 + 0.475528i
\(501\) 0 0
\(502\) 3.85410 + 11.8617i 0.172017 + 0.529414i
\(503\) 17.4164 12.6538i 0.776559 0.564203i −0.127385 0.991853i \(-0.540658\pi\)
0.903944 + 0.427650i \(0.140658\pi\)
\(504\) 0 0
\(505\) 3.02786 + 2.19987i 0.134738 + 0.0978930i
\(506\) 25.4164 + 18.4661i 1.12990 + 0.820918i
\(507\) 0 0
\(508\) −0.236068 0.171513i −0.0104738 0.00760968i
\(509\) 4.24671 13.0700i 0.188232 0.579319i −0.811757 0.583995i \(-0.801489\pi\)
0.999989 + 0.00467647i \(0.00148857\pi\)
\(510\) 0 0
\(511\) −1.94427 5.98385i −0.0860095 0.264710i
\(512\) 0.309017 0.951057i 0.0136568 0.0420312i
\(513\) 0 0
\(514\) 3.59017 + 11.0494i 0.158356 + 0.487368i
\(515\) −5.12461 −0.225817
\(516\) 0 0
\(517\) 20.1803 + 14.6619i 0.887530 + 0.644829i
\(518\) −4.29180 −0.188571
\(519\) 0 0
\(520\) −10.8541 −0.475984
\(521\) 5.07295 3.68571i 0.222250 0.161474i −0.471089 0.882086i \(-0.656139\pi\)
0.693339 + 0.720612i \(0.256139\pi\)
\(522\) 0 0
\(523\) −0.708204 2.17963i −0.0309676 0.0953085i 0.934378 0.356283i \(-0.115956\pi\)
−0.965346 + 0.260975i \(0.915956\pi\)
\(524\) 0.763932 0.0333725
\(525\) 0 0
\(526\) −0.472136 −0.0205861
\(527\) −9.00000 27.6992i −0.392046 1.20659i
\(528\) 0 0
\(529\) −10.5172 + 7.64121i −0.457270 + 0.332226i
\(530\) −5.91641 18.2088i −0.256992 0.790941i
\(531\) 0 0
\(532\) −5.52786 −0.239663
\(533\) 23.9164 + 17.3763i 1.03593 + 0.752651i
\(534\) 0 0
\(535\) 19.7984 + 14.3844i 0.855958 + 0.621890i
\(536\) −3.00000 9.23305i −0.129580 0.398807i
\(537\) 0 0
\(538\) 0.590170 1.81636i 0.0254440 0.0783087i
\(539\) −4.85410 14.9394i −0.209081 0.643485i
\(540\) 0 0
\(541\) 6.57295 20.2295i 0.282593 0.869732i −0.704517 0.709688i \(-0.748836\pi\)
0.987110 0.160045i \(-0.0511639\pi\)
\(542\) −22.7984 16.5640i −0.979274 0.711484i
\(543\) 0 0
\(544\) 6.35410 + 4.61653i 0.272430 + 0.197932i
\(545\) −4.63525 + 3.36771i −0.198553 + 0.144257i
\(546\) 0 0
\(547\) −1.61803 + 1.17557i −0.0691821 + 0.0502638i −0.621839 0.783145i \(-0.713614\pi\)
0.552657 + 0.833409i \(0.313614\pi\)
\(548\) 4.64590 + 14.2986i 0.198463 + 0.610806i
\(549\) 0 0
\(550\) −21.1803 15.3884i −0.903133 0.656164i
\(551\) −3.81966 −0.162723
\(552\) 0 0
\(553\) 0 0
\(554\) 17.9164 13.0170i 0.761195 0.553041i
\(555\) 0 0
\(556\) 10.8541 + 7.88597i 0.460316 + 0.334439i
\(557\) 27.2705 1.15549 0.577744 0.816218i \(-0.303933\pi\)
0.577744 + 0.816218i \(0.303933\pi\)
\(558\) 0 0
\(559\) 1.85410 5.70634i 0.0784202 0.241352i
\(560\) −3.61803 + 2.62866i −0.152890 + 0.111081i
\(561\) 0 0
\(562\) 1.88197 5.79210i 0.0793859 0.244325i
\(563\) −3.23607 + 9.95959i −0.136384 + 0.419747i −0.995803 0.0915256i \(-0.970826\pi\)
0.859419 + 0.511272i \(0.170826\pi\)
\(564\) 0 0
\(565\) −20.9164 + 15.1967i −0.879960 + 0.639328i
\(566\) 1.00000 3.07768i 0.0420331 0.129365i
\(567\) 0 0
\(568\) 14.1803 0.594994
\(569\) 17.2984 + 12.5680i 0.725186 + 0.526878i 0.888037 0.459772i \(-0.152069\pi\)
−0.162851 + 0.986651i \(0.552069\pi\)
\(570\) 0 0
\(571\) −27.2705 + 19.8132i −1.14124 + 0.829156i −0.987291 0.158924i \(-0.949198\pi\)
−0.153944 + 0.988080i \(0.549198\pi\)
\(572\) 20.5623 14.9394i 0.859753 0.624647i
\(573\) 0 0
\(574\) 12.1803 0.508398
\(575\) 24.2705 17.6336i 1.01215 0.735370i
\(576\) 0 0
\(577\) 8.90983 + 27.4216i 0.370921 + 1.14158i 0.946190 + 0.323613i \(0.104898\pi\)
−0.575268 + 0.817965i \(0.695102\pi\)
\(578\) −36.1525 + 26.2663i −1.50374 + 1.09253i
\(579\) 0 0
\(580\) −2.50000 + 1.81636i −0.103807 + 0.0754201i
\(581\) 9.70820 + 7.05342i 0.402764 + 0.292625i
\(582\) 0 0
\(583\) 36.2705 + 26.3521i 1.50217 + 1.09139i
\(584\) −0.972136 + 2.99193i −0.0402273 + 0.123807i
\(585\) 0 0
\(586\) 8.89919 + 27.3889i 0.367622 + 1.13142i
\(587\) 4.90983 15.1109i 0.202650 0.623694i −0.797151 0.603780i \(-0.793661\pi\)
0.999802 0.0199141i \(-0.00633929\pi\)
\(588\) 0 0
\(589\) −3.16718 9.74759i −0.130502 0.401642i
\(590\) 16.1803 + 11.7557i 0.666134 + 0.483975i
\(591\) 0 0
\(592\) 1.73607 + 1.26133i 0.0713520 + 0.0518402i
\(593\) 6.03444 0.247805 0.123902 0.992294i \(-0.460459\pi\)
0.123902 + 0.992294i \(0.460459\pi\)
\(594\) 0 0
\(595\) −10.8541 33.4055i −0.444975 1.36949i
\(596\) 5.69098 4.13474i 0.233112 0.169366i
\(597\) 0 0
\(598\) 9.00000 + 27.6992i 0.368037 + 1.13270i
\(599\) −1.05573 −0.0431359 −0.0215679 0.999767i \(-0.506866\pi\)
−0.0215679 + 0.999767i \(0.506866\pi\)
\(600\) 0 0
\(601\) 7.32624 0.298843 0.149422 0.988774i \(-0.452259\pi\)
0.149422 + 0.988774i \(0.452259\pi\)
\(602\) −0.763932 2.35114i −0.0311355 0.0958254i
\(603\) 0 0
\(604\) 5.61803 4.08174i 0.228595 0.166084i
\(605\) 36.7082 1.49240
\(606\) 0 0
\(607\) −1.81966 −0.0738577 −0.0369289 0.999318i \(-0.511757\pi\)
−0.0369289 + 0.999318i \(0.511757\pi\)
\(608\) 2.23607 + 1.62460i 0.0906845 + 0.0658862i
\(609\) 0 0
\(610\) −19.7984 −0.801613
\(611\) 7.14590 + 21.9928i 0.289092 + 0.889734i
\(612\) 0 0
\(613\) −6.66312 + 20.5070i −0.269121 + 0.828269i 0.721594 + 0.692316i \(0.243410\pi\)
−0.990715 + 0.135953i \(0.956590\pi\)
\(614\) −5.03444 15.4944i −0.203174 0.625304i
\(615\) 0 0
\(616\) 3.23607 9.95959i 0.130385 0.401283i
\(617\) 6.78115 + 4.92680i 0.272999 + 0.198345i 0.715858 0.698246i \(-0.246036\pi\)
−0.442859 + 0.896591i \(0.646036\pi\)
\(618\) 0 0
\(619\) −2.76393 2.00811i −0.111092 0.0807129i 0.530852 0.847464i \(-0.321872\pi\)
−0.641944 + 0.766751i \(0.721872\pi\)
\(620\) −6.70820 4.87380i −0.269408 0.195736i
\(621\) 0 0
\(622\) −15.0902 + 10.9637i −0.605061 + 0.439602i
\(623\) −0.854102 2.62866i −0.0342189 0.105315i
\(624\) 0 0
\(625\) −20.2254 + 14.6946i −0.809017 + 0.587785i
\(626\) −26.3607 −1.05358
\(627\) 0 0
\(628\) −14.4443 + 10.4944i −0.576389 + 0.418771i
\(629\) −13.6353 + 9.90659i −0.543673 + 0.395002i
\(630\) 0 0
\(631\) 34.8885 + 25.3480i 1.38889 + 1.00909i 0.995986 + 0.0895093i \(0.0285299\pi\)
0.392905 + 0.919579i \(0.371470\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 2.14590 6.60440i 0.0852245 0.262294i
\(635\) 0.201626 0.620541i 0.00800129 0.0246254i
\(636\) 0 0
\(637\) 4.50000 13.8496i 0.178296 0.548740i
\(638\) 2.23607 6.88191i 0.0885268 0.272457i
\(639\) 0 0
\(640\) 2.23607 0.0883883
\(641\) 8.32624 25.6255i 0.328867 1.01215i −0.640798 0.767709i \(-0.721397\pi\)
0.969665 0.244438i \(-0.0786035\pi\)
\(642\) 0 0
\(643\) −39.7771 −1.56866 −0.784328 0.620347i \(-0.786992\pi\)
−0.784328 + 0.620347i \(0.786992\pi\)
\(644\) 9.70820 + 7.05342i 0.382557 + 0.277944i
\(645\) 0 0
\(646\) −17.5623 + 12.7598i −0.690980 + 0.502026i
\(647\) −29.0344 + 21.0948i −1.14146 + 0.829320i −0.987322 0.158729i \(-0.949261\pi\)
−0.154139 + 0.988049i \(0.549261\pi\)
\(648\) 0 0
\(649\) −46.8328 −1.83835
\(650\) −7.50000 23.0826i −0.294174 0.905375i
\(651\) 0 0
\(652\) 6.32624 + 19.4702i 0.247755 + 0.762510i
\(653\) −26.0623 + 18.9354i −1.01990 + 0.740998i −0.966262 0.257562i \(-0.917081\pi\)
−0.0536351 + 0.998561i \(0.517081\pi\)
\(654\) 0 0
\(655\) 0.527864 + 1.62460i 0.0206254 + 0.0634783i
\(656\) −4.92705 3.57971i −0.192369 0.139764i
\(657\) 0 0
\(658\) 7.70820 + 5.60034i 0.300497 + 0.218324i
\(659\) −12.0344 + 37.0382i −0.468795 + 1.44280i 0.385351 + 0.922770i \(0.374080\pi\)
−0.854146 + 0.520033i \(0.825920\pi\)
\(660\) 0 0
\(661\) −7.27051 22.3763i −0.282790 0.870338i −0.987052 0.160398i \(-0.948722\pi\)
0.704262 0.709940i \(-0.251278\pi\)
\(662\) −10.0344 + 30.8828i −0.390000 + 1.20030i
\(663\) 0 0
\(664\) −1.85410 5.70634i −0.0719531 0.221449i
\(665\) −3.81966 11.7557i −0.148120 0.455867i
\(666\) 0 0
\(667\) 6.70820 + 4.87380i 0.259743 + 0.188714i
\(668\) −6.47214 −0.250414
\(669\) 0 0
\(670\) 17.5623 12.7598i 0.678491 0.492953i
\(671\) 37.5066 27.2501i 1.44793 1.05198i
\(672\) 0 0
\(673\) −5.80902 17.8783i −0.223921 0.689158i −0.998399 0.0565578i \(-0.981987\pi\)
0.774478 0.632601i \(-0.218013\pi\)
\(674\) 28.8328 1.11060
\(675\) 0 0
\(676\) 10.5623 0.406243
\(677\) −11.2705 34.6871i −0.433161 1.33313i −0.894960 0.446147i \(-0.852796\pi\)
0.461799 0.886985i \(-0.347204\pi\)
\(678\) 0 0
\(679\) 22.4164 16.2865i 0.860263 0.625017i
\(680\) −5.42705 + 16.7027i −0.208118 + 0.640521i
\(681\) 0 0
\(682\) 19.4164 0.743493
\(683\) 15.7082 + 11.4127i 0.601058 + 0.436694i 0.846254 0.532779i \(-0.178852\pi\)
−0.245196 + 0.969473i \(0.578852\pi\)
\(684\) 0 0
\(685\) −27.1976 + 19.7602i −1.03917 + 0.754998i
\(686\) −6.18034 19.0211i −0.235966 0.726230i
\(687\) 0 0
\(688\) −0.381966 + 1.17557i −0.0145623 + 0.0448182i
\(689\) 12.8435 + 39.5281i 0.489297 + 1.50590i
\(690\) 0 0
\(691\) −7.47214 + 22.9969i −0.284253 + 0.874842i 0.702368 + 0.711814i \(0.252126\pi\)
−0.986621 + 0.163028i \(0.947874\pi\)
\(692\) −8.82624 6.41264i −0.335523 0.243772i
\(693\) 0 0
\(694\) −4.23607 3.07768i −0.160799 0.116827i
\(695\) −9.27051 + 28.5317i −0.351650 + 1.08227i
\(696\) 0 0
\(697\) 38.6976 28.1154i 1.46577 1.06495i
\(698\) 4.57295 + 14.0741i 0.173089 + 0.532712i
\(699\) 0 0
\(700\) −8.09017 5.87785i −0.305780 0.222162i
\(701\) 20.1591 0.761397 0.380698 0.924699i \(-0.375684\pi\)
0.380698 + 0.924699i \(0.375684\pi\)
\(702\) 0 0
\(703\) −4.79837 + 3.48622i −0.180974 + 0.131485i
\(704\) −4.23607 + 3.07768i −0.159653 + 0.115995i
\(705\) 0 0
\(706\) 16.5623 + 12.0332i 0.623331 + 0.452876i
\(707\) −3.34752 −0.125897
\(708\) 0 0
\(709\) −9.20820 + 28.3399i −0.345821 + 1.06433i 0.615321 + 0.788276i \(0.289026\pi\)
−0.961143 + 0.276052i \(0.910974\pi\)
\(710\) 9.79837 + 30.1563i 0.367726 + 1.13175i
\(711\) 0 0
\(712\) −0.427051 + 1.31433i −0.0160044 + 0.0492565i
\(713\) −6.87539 + 21.1603i −0.257485 + 0.792458i
\(714\) 0 0
\(715\) 45.9787 + 33.4055i 1.71951 + 1.24929i
\(716\) 1.18034 3.63271i 0.0441114 0.135761i
\(717\) 0 0
\(718\) 27.8885 1.04079
\(719\) 18.0902 + 13.1433i 0.674649 + 0.490162i 0.871578 0.490256i \(-0.163097\pi\)
−0.196929 + 0.980418i \(0.563097\pi\)
\(720\) 0 0
\(721\) 3.70820 2.69417i 0.138101 0.100336i
\(722\) 9.19098 6.67764i 0.342053 0.248516i
\(723\) 0 0
\(724\) −20.0344 −0.744574
\(725\) −5.59017 4.06150i −0.207614 0.150840i
\(726\) 0 0
\(727\) 3.18034 + 9.78808i 0.117952 + 0.363020i 0.992551 0.121827i \(-0.0388753\pi\)
−0.874599 + 0.484847i \(0.838875\pi\)
\(728\) 7.85410 5.70634i 0.291092 0.211491i
\(729\) 0 0
\(730\) −7.03444 −0.260356
\(731\) −7.85410 5.70634i −0.290494 0.211057i
\(732\) 0 0
\(733\) 5.14590 + 3.73871i 0.190068 + 0.138093i 0.678750 0.734370i \(-0.262522\pi\)
−0.488682 + 0.872462i \(0.662522\pi\)
\(734\) −3.85410 + 11.8617i −0.142257 + 0.437824i
\(735\) 0 0
\(736\) −1.85410 5.70634i −0.0683431 0.210338i
\(737\) −15.7082 + 48.3449i −0.578619 + 1.78081i
\(738\) 0 0
\(739\) 2.56231 + 7.88597i 0.0942559 + 0.290090i 0.987059 0.160357i \(-0.0512646\pi\)
−0.892803 + 0.450447i \(0.851265\pi\)
\(740\) −1.48278 + 4.56352i −0.0545080 + 0.167759i
\(741\) 0 0
\(742\) 13.8541 + 10.0656i 0.508600 + 0.369520i
\(743\) −6.65248 −0.244056 −0.122028 0.992527i \(-0.538940\pi\)
−0.122028 + 0.992527i \(0.538940\pi\)
\(744\) 0 0
\(745\) 12.7254 + 9.24556i 0.466223 + 0.338731i
\(746\) −2.09017 + 1.51860i −0.0765266 + 0.0555998i
\(747\) 0 0
\(748\) −12.7082 39.1118i −0.464658 1.43007i
\(749\) −21.8885 −0.799790
\(750\) 0 0
\(751\) 14.7639 0.538744 0.269372 0.963036i \(-0.413184\pi\)
0.269372 + 0.963036i \(0.413184\pi\)
\(752\) −1.47214 4.53077i −0.0536833 0.165220i
\(753\) 0 0
\(754\) 5.42705 3.94298i 0.197642 0.143595i
\(755\) 12.5623 + 9.12705i 0.457189 + 0.332167i
\(756\) 0 0
\(757\) −28.8541 −1.04872 −0.524360 0.851497i \(-0.675695\pi\)
−0.524360 + 0.851497i \(0.675695\pi\)
\(758\) 2.76393 + 2.00811i 0.100391 + 0.0729380i
\(759\) 0 0
\(760\) −1.90983 + 5.87785i −0.0692768 + 0.213212i
\(761\) −7.46556 22.9766i −0.270626 0.832902i −0.990344 0.138635i \(-0.955729\pi\)
0.719717 0.694267i \(-0.244271\pi\)
\(762\) 0 0
\(763\) 1.58359 4.87380i 0.0573299 0.176443i
\(764\) 0.236068 + 0.726543i 0.00854064 + 0.0262854i
\(765\) 0 0
\(766\) −6.32624 + 19.4702i −0.228576 + 0.703485i
\(767\) −35.1246 25.5195i −1.26828 0.921457i
\(768\) 0 0
\(769\) 1.90983 + 1.38757i 0.0688702 + 0.0500372i 0.621688 0.783265i \(-0.286447\pi\)
−0.552817 + 0.833302i \(0.686447\pi\)
\(770\) 23.4164 0.843869
\(771\) 0 0
\(772\) −1.92705 + 1.40008i −0.0693561 + 0.0503901i
\(773\) −4.35410 13.4005i −0.156606 0.481984i 0.841714 0.539924i \(-0.181547\pi\)
−0.998320 + 0.0579395i \(0.981547\pi\)
\(774\) 0 0
\(775\) 5.72949 17.6336i 0.205809 0.633416i
\(776\) −13.8541 −0.497333
\(777\) 0 0
\(778\) 12.9271 9.39205i 0.463457 0.336721i
\(779\) 13.6180 9.89408i 0.487917 0.354492i
\(780\) 0 0
\(781\) −60.0689 43.6426i −2.14943 1.56165i
\(782\) 47.1246 1.68517
\(783\) 0 0
\(784\) −0.927051 + 2.85317i −0.0331090 + 0.101899i
\(785\) −32.2984 23.4661i −1.15278 0.837543i
\(786\) 0 0
\(787\) 9.43769 29.0462i 0.336417 1.03539i −0.629602 0.776918i \(-0.716782\pi\)
0.966020 0.258469i \(-0.0832179\pi\)
\(788\) 4.11803