Properties

Label 726.2.e.b.487.1
Level $726$
Weight $2$
Character 726.487
Analytic conductor $5.797$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 726.e (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.79713918674\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 66)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 487.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 726.487
Dual form 726.2.e.b.565.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.00000 q^{12} +(-3.23607 + 2.35114i) q^{13} +(-0.618034 - 1.90211i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-4.85410 - 3.52671i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.23607 + 3.80423i) q^{19} -2.00000 q^{21} +6.00000 q^{23} +(-0.809017 + 0.587785i) q^{24} +(-1.54508 - 4.75528i) q^{25} +(1.23607 - 3.80423i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(1.61803 + 1.17557i) q^{28} +(-1.85410 + 5.70634i) q^{29} +(-6.47214 + 4.70228i) q^{31} +1.00000 q^{32} +6.00000 q^{34} +(0.309017 + 0.951057i) q^{36} +(-3.09017 + 9.51057i) q^{37} +(-3.23607 - 2.35114i) q^{38} +(-3.23607 - 2.35114i) q^{39} +(-1.85410 - 5.70634i) q^{41} +(1.61803 - 1.17557i) q^{42} -8.00000 q^{43} +(-4.85410 + 3.52671i) q^{46} +(-1.85410 - 5.70634i) q^{47} +(0.309017 - 0.951057i) q^{48} +(2.42705 + 1.76336i) q^{49} +(4.04508 + 2.93893i) q^{50} +(1.85410 - 5.70634i) q^{51} +(1.23607 + 3.80423i) q^{52} +1.00000 q^{54} -2.00000 q^{56} +(-3.23607 + 2.35114i) q^{57} +(-1.85410 - 5.70634i) q^{58} +(6.47214 + 4.70228i) q^{61} +(2.47214 - 7.60845i) q^{62} +(-0.618034 - 1.90211i) q^{63} +(-0.809017 + 0.587785i) q^{64} -4.00000 q^{67} +(-4.85410 + 3.52671i) q^{68} +(1.85410 + 5.70634i) q^{69} +(-4.85410 - 3.52671i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-0.618034 + 1.90211i) q^{73} +(-3.09017 - 9.51057i) q^{74} +(4.04508 - 2.93893i) q^{75} +4.00000 q^{76} +4.00000 q^{78} +(11.3262 - 8.22899i) q^{79} +(0.309017 - 0.951057i) q^{81} +(4.85410 + 3.52671i) q^{82} +(-9.70820 - 7.05342i) q^{83} +(-0.618034 + 1.90211i) q^{84} +(6.47214 - 4.70228i) q^{86} -6.00000 q^{87} -6.00000 q^{89} +(-2.47214 - 7.60845i) q^{91} +(1.85410 - 5.70634i) q^{92} +(-6.47214 - 4.70228i) q^{93} +(4.85410 + 3.52671i) q^{94} +(0.309017 + 0.951057i) q^{96} +(-11.3262 + 8.22899i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - q^{3} - q^{4} - q^{6} + 2 q^{7} - q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} - q^{3} - q^{4} - q^{6} + 2 q^{7} - q^{8} - q^{9} + 4 q^{12} - 4 q^{13} + 2 q^{14} - q^{16} - 6 q^{17} - q^{18} - 4 q^{19} - 8 q^{21} + 24 q^{23} - q^{24} + 5 q^{25} - 4 q^{26} - q^{27} + 2 q^{28} + 6 q^{29} - 8 q^{31} + 4 q^{32} + 24 q^{34} - q^{36} + 10 q^{37} - 4 q^{38} - 4 q^{39} + 6 q^{41} + 2 q^{42} - 32 q^{43} - 6 q^{46} + 6 q^{47} - q^{48} + 3 q^{49} + 5 q^{50} - 6 q^{51} - 4 q^{52} + 4 q^{54} - 8 q^{56} - 4 q^{57} + 6 q^{58} + 8 q^{61} - 8 q^{62} + 2 q^{63} - q^{64} - 16 q^{67} - 6 q^{68} - 6 q^{69} - 6 q^{71} - q^{72} + 2 q^{73} + 10 q^{74} + 5 q^{75} + 16 q^{76} + 16 q^{78} + 14 q^{79} - q^{81} + 6 q^{82} - 12 q^{83} + 2 q^{84} + 8 q^{86} - 24 q^{87} - 24 q^{89} + 8 q^{91} - 6 q^{92} - 8 q^{93} + 6 q^{94} - q^{96} - 14 q^{97} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/726\mathbb{Z}\right)^\times\).

\(n\) \(485\) \(607\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.809017 + 0.587785i −0.572061 + 0.415627i
\(3\) 0.309017 + 0.951057i 0.178411 + 0.549093i
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(6\) −0.809017 0.587785i −0.330280 0.239962i
\(7\) −0.618034 + 1.90211i −0.233595 + 0.718931i 0.763710 + 0.645560i \(0.223376\pi\)
−0.997305 + 0.0733714i \(0.976624\pi\)
\(8\) 0.309017 + 0.951057i 0.109254 + 0.336249i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) 0 0
\(11\) 0 0
\(12\) 1.00000 0.288675
\(13\) −3.23607 + 2.35114i −0.897524 + 0.652089i −0.937829 0.347098i \(-0.887167\pi\)
0.0403050 + 0.999187i \(0.487167\pi\)
\(14\) −0.618034 1.90211i −0.165177 0.508361i
\(15\) 0 0
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) −4.85410 3.52671i −1.17729 0.855353i −0.185429 0.982658i \(-0.559367\pi\)
−0.991864 + 0.127304i \(0.959367\pi\)
\(18\) 0.309017 0.951057i 0.0728360 0.224166i
\(19\) 1.23607 + 3.80423i 0.283573 + 0.872749i 0.986823 + 0.161806i \(0.0517318\pi\)
−0.703249 + 0.710943i \(0.748268\pi\)
\(20\) 0 0
\(21\) −2.00000 −0.436436
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) −0.809017 + 0.587785i −0.165140 + 0.119981i
\(25\) −1.54508 4.75528i −0.309017 0.951057i
\(26\) 1.23607 3.80423i 0.242413 0.746070i
\(27\) −0.809017 0.587785i −0.155695 0.113119i
\(28\) 1.61803 + 1.17557i 0.305780 + 0.222162i
\(29\) −1.85410 + 5.70634i −0.344298 + 1.05964i 0.617660 + 0.786445i \(0.288081\pi\)
−0.961958 + 0.273196i \(0.911919\pi\)
\(30\) 0 0
\(31\) −6.47214 + 4.70228i −1.16243 + 0.844555i −0.990083 0.140482i \(-0.955135\pi\)
−0.172347 + 0.985036i \(0.555135\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 0.309017 + 0.951057i 0.0515028 + 0.158509i
\(37\) −3.09017 + 9.51057i −0.508021 + 1.56353i 0.287611 + 0.957747i \(0.407139\pi\)
−0.795632 + 0.605780i \(0.792861\pi\)
\(38\) −3.23607 2.35114i −0.524960 0.381405i
\(39\) −3.23607 2.35114i −0.518186 0.376484i
\(40\) 0 0
\(41\) −1.85410 5.70634i −0.289562 0.891180i −0.984994 0.172588i \(-0.944787\pi\)
0.695432 0.718592i \(-0.255213\pi\)
\(42\) 1.61803 1.17557i 0.249668 0.181394i
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −4.85410 + 3.52671i −0.715698 + 0.519985i
\(47\) −1.85410 5.70634i −0.270449 0.832355i −0.990388 0.138318i \(-0.955830\pi\)
0.719939 0.694037i \(-0.244170\pi\)
\(48\) 0.309017 0.951057i 0.0446028 0.137273i
\(49\) 2.42705 + 1.76336i 0.346722 + 0.251908i
\(50\) 4.04508 + 2.93893i 0.572061 + 0.415627i
\(51\) 1.85410 5.70634i 0.259626 0.799047i
\(52\) 1.23607 + 3.80423i 0.171412 + 0.527551i
\(53\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) −3.23607 + 2.35114i −0.428628 + 0.311416i
\(58\) −1.85410 5.70634i −0.243456 0.749279i
\(59\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(60\) 0 0
\(61\) 6.47214 + 4.70228i 0.828672 + 0.602066i 0.919183 0.393830i \(-0.128850\pi\)
−0.0905112 + 0.995895i \(0.528850\pi\)
\(62\) 2.47214 7.60845i 0.313962 0.966274i
\(63\) −0.618034 1.90211i −0.0778650 0.239644i
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −4.85410 + 3.52671i −0.588646 + 0.427677i
\(69\) 1.85410 + 5.70634i 0.223208 + 0.686963i
\(70\) 0 0
\(71\) −4.85410 3.52671i −0.576076 0.418544i 0.261231 0.965276i \(-0.415871\pi\)
−0.837307 + 0.546733i \(0.815871\pi\)
\(72\) −0.809017 0.587785i −0.0953436 0.0692712i
\(73\) −0.618034 + 1.90211i −0.0723354 + 0.222625i −0.980688 0.195580i \(-0.937341\pi\)
0.908352 + 0.418206i \(0.137341\pi\)
\(74\) −3.09017 9.51057i −0.359225 1.10558i
\(75\) 4.04508 2.93893i 0.467086 0.339358i
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 4.00000 0.452911
\(79\) 11.3262 8.22899i 1.27430 0.925834i 0.274936 0.961462i \(-0.411343\pi\)
0.999365 + 0.0356284i \(0.0113433\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 4.85410 + 3.52671i 0.536046 + 0.389460i
\(83\) −9.70820 7.05342i −1.06561 0.774214i −0.0904951 0.995897i \(-0.528845\pi\)
−0.975119 + 0.221683i \(0.928845\pi\)
\(84\) −0.618034 + 1.90211i −0.0674330 + 0.207538i
\(85\) 0 0
\(86\) 6.47214 4.70228i 0.697908 0.507060i
\(87\) −6.00000 −0.643268
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) −2.47214 7.60845i −0.259150 0.797582i
\(92\) 1.85410 5.70634i 0.193303 0.594927i
\(93\) −6.47214 4.70228i −0.671129 0.487604i
\(94\) 4.85410 + 3.52671i 0.500662 + 0.363753i
\(95\) 0 0
\(96\) 0.309017 + 0.951057i 0.0315389 + 0.0970668i
\(97\) −11.3262 + 8.22899i −1.15001 + 0.835528i −0.988482 0.151341i \(-0.951641\pi\)
−0.161524 + 0.986869i \(0.551641\pi\)
\(98\) −3.00000 −0.303046
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) 4.85410 3.52671i 0.483001 0.350921i −0.319485 0.947591i \(-0.603510\pi\)
0.802486 + 0.596670i \(0.203510\pi\)
\(102\) 1.85410 + 5.70634i 0.183583 + 0.565012i
\(103\) −1.23607 + 3.80423i −0.121793 + 0.374842i −0.993303 0.115536i \(-0.963141\pi\)
0.871510 + 0.490378i \(0.163141\pi\)
\(104\) −3.23607 2.35114i −0.317323 0.230548i
\(105\) 0 0
\(106\) 0 0
\(107\) 3.70820 + 11.4127i 0.358486 + 1.10331i 0.953961 + 0.299932i \(0.0969638\pi\)
−0.595475 + 0.803374i \(0.703036\pi\)
\(108\) −0.809017 + 0.587785i −0.0778477 + 0.0565597i
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) −10.0000 −0.949158
\(112\) 1.61803 1.17557i 0.152890 0.111081i
\(113\) 5.56231 + 17.1190i 0.523258 + 1.61042i 0.767736 + 0.640767i \(0.221383\pi\)
−0.244478 + 0.969655i \(0.578617\pi\)
\(114\) 1.23607 3.80423i 0.115768 0.356298i
\(115\) 0 0
\(116\) 4.85410 + 3.52671i 0.450692 + 0.327447i
\(117\) 1.23607 3.80423i 0.114275 0.351701i
\(118\) 0 0
\(119\) 9.70820 7.05342i 0.889950 0.646586i
\(120\) 0 0
\(121\) 0 0
\(122\) −8.00000 −0.724286
\(123\) 4.85410 3.52671i 0.437680 0.317993i
\(124\) 2.47214 + 7.60845i 0.222004 + 0.683259i
\(125\) 0 0
\(126\) 1.61803 + 1.17557i 0.144146 + 0.104728i
\(127\) 11.3262 + 8.22899i 1.00504 + 0.730205i 0.963163 0.268918i \(-0.0866659\pi\)
0.0418779 + 0.999123i \(0.486666\pi\)
\(128\) 0.309017 0.951057i 0.0273135 0.0840623i
\(129\) −2.47214 7.60845i −0.217659 0.669887i
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) −8.00000 −0.693688
\(134\) 3.23607 2.35114i 0.279554 0.203108i
\(135\) 0 0
\(136\) 1.85410 5.70634i 0.158988 0.489315i
\(137\) 14.5623 + 10.5801i 1.24414 + 0.903922i 0.997867 0.0652782i \(-0.0207935\pi\)
0.246275 + 0.969200i \(0.420793\pi\)
\(138\) −4.85410 3.52671i −0.413209 0.300214i
\(139\) 1.23607 3.80423i 0.104842 0.322670i −0.884851 0.465873i \(-0.845740\pi\)
0.989693 + 0.143203i \(0.0457402\pi\)
\(140\) 0 0
\(141\) 4.85410 3.52671i 0.408789 0.297003i
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −0.618034 1.90211i −0.0511489 0.157420i
\(147\) −0.927051 + 2.85317i −0.0764619 + 0.235325i
\(148\) 8.09017 + 5.87785i 0.665008 + 0.483157i
\(149\) −4.85410 3.52671i −0.397664 0.288919i 0.370925 0.928663i \(-0.379041\pi\)
−0.768589 + 0.639743i \(0.779041\pi\)
\(150\) −1.54508 + 4.75528i −0.126156 + 0.388267i
\(151\) 3.09017 + 9.51057i 0.251474 + 0.773959i 0.994504 + 0.104700i \(0.0333882\pi\)
−0.743029 + 0.669259i \(0.766612\pi\)
\(152\) −3.23607 + 2.35114i −0.262480 + 0.190703i
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) −3.23607 + 2.35114i −0.259093 + 0.188242i
\(157\) 0.618034 + 1.90211i 0.0493245 + 0.151805i 0.972685 0.232129i \(-0.0745691\pi\)
−0.923361 + 0.383934i \(0.874569\pi\)
\(158\) −4.32624 + 13.3148i −0.344177 + 1.05927i
\(159\) 0 0
\(160\) 0 0
\(161\) −3.70820 + 11.4127i −0.292247 + 0.899445i
\(162\) 0.309017 + 0.951057i 0.0242787 + 0.0747221i
\(163\) 3.23607 2.35114i 0.253468 0.184156i −0.453794 0.891107i \(-0.649930\pi\)
0.707263 + 0.706951i \(0.249930\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) 9.70820 7.05342i 0.751243 0.545810i −0.144969 0.989436i \(-0.546308\pi\)
0.896212 + 0.443626i \(0.146308\pi\)
\(168\) −0.618034 1.90211i −0.0476824 0.146751i
\(169\) 0.927051 2.85317i 0.0713116 0.219475i
\(170\) 0 0
\(171\) −3.23607 2.35114i −0.247468 0.179796i
\(172\) −2.47214 + 7.60845i −0.188499 + 0.580139i
\(173\) −1.85410 5.70634i −0.140965 0.433845i 0.855505 0.517794i \(-0.173247\pi\)
−0.996470 + 0.0839492i \(0.973247\pi\)
\(174\) 4.85410 3.52671i 0.367989 0.267359i
\(175\) 10.0000 0.755929
\(176\) 0 0
\(177\) 0 0
\(178\) 4.85410 3.52671i 0.363830 0.264338i
\(179\) 7.41641 + 22.8254i 0.554328 + 1.70605i 0.697710 + 0.716380i \(0.254202\pi\)
−0.143382 + 0.989667i \(0.545798\pi\)
\(180\) 0 0
\(181\) 17.7984 + 12.9313i 1.32294 + 0.961174i 0.999891 + 0.0147930i \(0.00470892\pi\)
0.323052 + 0.946381i \(0.395291\pi\)
\(182\) 6.47214 + 4.70228i 0.479747 + 0.348556i
\(183\) −2.47214 + 7.60845i −0.182746 + 0.562433i
\(184\) 1.85410 + 5.70634i 0.136686 + 0.420677i
\(185\) 0 0
\(186\) 8.00000 0.586588
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) 1.61803 1.17557i 0.117695 0.0855102i
\(190\) 0 0
\(191\) 5.56231 17.1190i 0.402474 1.23869i −0.520511 0.853855i \(-0.674259\pi\)
0.922986 0.384834i \(-0.125741\pi\)
\(192\) −0.809017 0.587785i −0.0583858 0.0424197i
\(193\) 11.3262 + 8.22899i 0.815280 + 0.592336i 0.915357 0.402644i \(-0.131909\pi\)
−0.100076 + 0.994980i \(0.531909\pi\)
\(194\) 4.32624 13.3148i 0.310606 0.955946i
\(195\) 0 0
\(196\) 2.42705 1.76336i 0.173361 0.125954i
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 4.04508 2.93893i 0.286031 0.207813i
\(201\) −1.23607 3.80423i −0.0871855 0.268329i
\(202\) −1.85410 + 5.70634i −0.130454 + 0.401497i
\(203\) −9.70820 7.05342i −0.681382 0.495053i
\(204\) −4.85410 3.52671i −0.339855 0.246919i
\(205\) 0 0
\(206\) −1.23607 3.80423i −0.0861209 0.265053i
\(207\) −4.85410 + 3.52671i −0.337383 + 0.245123i
\(208\) 4.00000 0.277350
\(209\) 0 0
\(210\) 0 0
\(211\) 6.47214 4.70228i 0.445560 0.323718i −0.342280 0.939598i \(-0.611199\pi\)
0.787840 + 0.615880i \(0.211199\pi\)
\(212\) 0 0
\(213\) 1.85410 5.70634i 0.127041 0.390992i
\(214\) −9.70820 7.05342i −0.663639 0.482162i
\(215\) 0 0
\(216\) 0.309017 0.951057i 0.0210259 0.0647112i
\(217\) −4.94427 15.2169i −0.335639 1.03299i
\(218\) −3.23607 + 2.35114i −0.219174 + 0.159239i
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) 24.0000 1.61441
\(222\) 8.09017 5.87785i 0.542977 0.394496i
\(223\) −4.94427 15.2169i −0.331093 1.01900i −0.968615 0.248567i \(-0.920040\pi\)
0.637522 0.770432i \(-0.279960\pi\)
\(224\) −0.618034 + 1.90211i −0.0412941 + 0.127090i
\(225\) 4.04508 + 2.93893i 0.269672 + 0.195928i
\(226\) −14.5623 10.5801i −0.968670 0.703780i
\(227\) 3.70820 11.4127i 0.246122 0.757486i −0.749328 0.662199i \(-0.769623\pi\)
0.995450 0.0952867i \(-0.0303768\pi\)
\(228\) 1.23607 + 3.80423i 0.0818606 + 0.251941i
\(229\) 17.7984 12.9313i 1.17615 0.854523i 0.184418 0.982848i \(-0.440960\pi\)
0.991732 + 0.128325i \(0.0409601\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −14.5623 + 10.5801i −0.954008 + 0.693128i −0.951752 0.306870i \(-0.900718\pi\)
−0.00225687 + 0.999997i \(0.500718\pi\)
\(234\) 1.23607 + 3.80423i 0.0808043 + 0.248690i
\(235\) 0 0
\(236\) 0 0
\(237\) 11.3262 + 8.22899i 0.735718 + 0.534531i
\(238\) −3.70820 + 11.4127i −0.240367 + 0.739774i
\(239\) 3.70820 + 11.4127i 0.239864 + 0.738225i 0.996439 + 0.0843180i \(0.0268712\pi\)
−0.756575 + 0.653907i \(0.773129\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 6.47214 4.70228i 0.414336 0.301033i
\(245\) 0 0
\(246\) −1.85410 + 5.70634i −0.118213 + 0.363823i
\(247\) −12.9443 9.40456i −0.823624 0.598398i
\(248\) −6.47214 4.70228i −0.410981 0.298595i
\(249\) 3.70820 11.4127i 0.234998 0.723249i
\(250\) 0 0
\(251\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(252\) −2.00000 −0.125988
\(253\) 0 0
\(254\) −14.0000 −0.878438
\(255\) 0 0
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) −9.27051 + 28.5317i −0.578279 + 1.77976i 0.0464552 + 0.998920i \(0.485208\pi\)
−0.624734 + 0.780838i \(0.714792\pi\)
\(258\) 6.47214 + 4.70228i 0.402938 + 0.292751i
\(259\) −16.1803 11.7557i −1.00540 0.730464i
\(260\) 0 0
\(261\) −1.85410 5.70634i −0.114766 0.353214i
\(262\) −9.70820 + 7.05342i −0.599775 + 0.435762i
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 6.47214 4.70228i 0.396832 0.288315i
\(267\) −1.85410 5.70634i −0.113469 0.349222i
\(268\) −1.23607 + 3.80423i −0.0755049 + 0.232380i
\(269\) 19.4164 + 14.1068i 1.18384 + 0.860110i 0.992600 0.121434i \(-0.0387492\pi\)
0.191240 + 0.981543i \(0.438749\pi\)
\(270\) 0 0
\(271\) −0.618034 + 1.90211i −0.0375429 + 0.115545i −0.968072 0.250674i \(-0.919348\pi\)
0.930529 + 0.366219i \(0.119348\pi\)
\(272\) 1.85410 + 5.70634i 0.112421 + 0.345998i
\(273\) 6.47214 4.70228i 0.391711 0.284595i
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) 6.00000 0.361158
\(277\) −12.9443 + 9.40456i −0.777746 + 0.565065i −0.904302 0.426894i \(-0.859608\pi\)
0.126556 + 0.991959i \(0.459608\pi\)
\(278\) 1.23607 + 3.80423i 0.0741344 + 0.228162i
\(279\) 2.47214 7.60845i 0.148003 0.455506i
\(280\) 0 0
\(281\) −4.85410 3.52671i −0.289571 0.210386i 0.433510 0.901149i \(-0.357275\pi\)
−0.723081 + 0.690763i \(0.757275\pi\)
\(282\) −1.85410 + 5.70634i −0.110410 + 0.339808i
\(283\) −2.47214 7.60845i −0.146953 0.452276i 0.850304 0.526292i \(-0.176418\pi\)
−0.997257 + 0.0740167i \(0.976418\pi\)
\(284\) −4.85410 + 3.52671i −0.288038 + 0.209272i
\(285\) 0 0
\(286\) 0 0
\(287\) 12.0000 0.708338
\(288\) −0.809017 + 0.587785i −0.0476718 + 0.0346356i
\(289\) 5.87132 + 18.0701i 0.345372 + 1.06295i
\(290\) 0 0
\(291\) −11.3262 8.22899i −0.663956 0.482392i
\(292\) 1.61803 + 1.17557i 0.0946883 + 0.0687951i
\(293\) 1.85410 5.70634i 0.108318 0.333368i −0.882177 0.470918i \(-0.843923\pi\)
0.990495 + 0.137550i \(0.0439228\pi\)
\(294\) −0.927051 2.85317i −0.0540667 0.166400i
\(295\) 0 0
\(296\) −10.0000 −0.581238
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) −19.4164 + 14.1068i −1.12288 + 0.815820i
\(300\) −1.54508 4.75528i −0.0892055 0.274546i
\(301\) 4.94427 15.2169i 0.284983 0.877088i
\(302\) −8.09017 5.87785i −0.465537 0.338232i
\(303\) 4.85410 + 3.52671i 0.278861 + 0.202604i
\(304\) 1.23607 3.80423i 0.0708934 0.218187i
\(305\) 0 0
\(306\) −4.85410 + 3.52671i −0.277491 + 0.201609i
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) −5.56231 17.1190i −0.315409 0.970730i −0.975586 0.219620i \(-0.929518\pi\)
0.660176 0.751111i \(-0.270482\pi\)
\(312\) 1.23607 3.80423i 0.0699786 0.215372i
\(313\) −21.0344 15.2824i −1.18894 0.863813i −0.195785 0.980647i \(-0.562726\pi\)
−0.993152 + 0.116834i \(0.962726\pi\)
\(314\) −1.61803 1.17557i −0.0913109 0.0663413i
\(315\) 0 0
\(316\) −4.32624 13.3148i −0.243370 0.749016i
\(317\) −9.70820 + 7.05342i −0.545267 + 0.396160i −0.826037 0.563615i \(-0.809410\pi\)
0.280770 + 0.959775i \(0.409410\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −9.70820 + 7.05342i −0.541859 + 0.393684i
\(322\) −3.70820 11.4127i −0.206650 0.636004i
\(323\) 7.41641 22.8254i 0.412660 1.27004i
\(324\) −0.809017 0.587785i −0.0449454 0.0326547i
\(325\) 16.1803 + 11.7557i 0.897524 + 0.652089i
\(326\) −1.23607 + 3.80423i −0.0684595 + 0.210697i
\(327\) 1.23607 + 3.80423i 0.0683547 + 0.210374i
\(328\) 4.85410 3.52671i 0.268023 0.194730i
\(329\) 12.0000 0.661581
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) −9.70820 + 7.05342i −0.532807 + 0.387107i
\(333\) −3.09017 9.51057i −0.169340 0.521176i
\(334\) −3.70820 + 11.4127i −0.202904 + 0.624474i
\(335\) 0 0
\(336\) 1.61803 + 1.17557i 0.0882710 + 0.0641326i
\(337\) −0.618034 + 1.90211i −0.0336665 + 0.103615i −0.966478 0.256751i \(-0.917348\pi\)
0.932811 + 0.360366i \(0.117348\pi\)
\(338\) 0.927051 + 2.85317i 0.0504249 + 0.155192i
\(339\) −14.5623 + 10.5801i −0.790916 + 0.574634i
\(340\) 0 0
\(341\) 0 0
\(342\) 4.00000 0.216295
\(343\) −16.1803 + 11.7557i −0.873656 + 0.634748i
\(344\) −2.47214 7.60845i −0.133289 0.410220i
\(345\) 0 0
\(346\) 4.85410 + 3.52671i 0.260958 + 0.189597i
\(347\) 29.1246 + 21.1603i 1.56349 + 1.13594i 0.933073 + 0.359687i \(0.117117\pi\)
0.630418 + 0.776256i \(0.282883\pi\)
\(348\) −1.85410 + 5.70634i −0.0993903 + 0.305892i
\(349\) 1.23607 + 3.80423i 0.0661652 + 0.203636i 0.978673 0.205423i \(-0.0658571\pi\)
−0.912508 + 0.409059i \(0.865857\pi\)
\(350\) −8.09017 + 5.87785i −0.432438 + 0.314184i
\(351\) 4.00000 0.213504
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.85410 + 5.70634i −0.0982672 + 0.302435i
\(357\) 9.70820 + 7.05342i 0.513813 + 0.373307i
\(358\) −19.4164 14.1068i −1.02619 0.745570i
\(359\) 3.70820 11.4127i 0.195712 0.602338i −0.804256 0.594283i \(-0.797436\pi\)
0.999968 0.00805517i \(-0.00256407\pi\)
\(360\) 0 0
\(361\) 2.42705 1.76336i 0.127740 0.0928082i
\(362\) −22.0000 −1.15629
\(363\) 0 0
\(364\) −8.00000 −0.419314
\(365\) 0 0
\(366\) −2.47214 7.60845i −0.129221 0.397700i
\(367\) 2.47214 7.60845i 0.129044 0.397158i −0.865572 0.500785i \(-0.833045\pi\)
0.994616 + 0.103627i \(0.0330448\pi\)
\(368\) −4.85410 3.52671i −0.253038 0.183843i
\(369\) 4.85410 + 3.52671i 0.252694 + 0.183593i
\(370\) 0 0
\(371\) 0 0
\(372\) −6.47214 + 4.70228i −0.335565 + 0.243802i
\(373\) −20.0000 −1.03556 −0.517780 0.855514i \(-0.673242\pi\)
−0.517780 + 0.855514i \(0.673242\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 4.85410 3.52671i 0.250331 0.181876i
\(377\) −7.41641 22.8254i −0.381964 1.17557i
\(378\) −0.618034 + 1.90211i −0.0317882 + 0.0978341i
\(379\) −16.1803 11.7557i −0.831128 0.603850i 0.0887501 0.996054i \(-0.471713\pi\)
−0.919878 + 0.392204i \(0.871713\pi\)
\(380\) 0 0
\(381\) −4.32624 + 13.3148i −0.221640 + 0.682137i
\(382\) 5.56231 + 17.1190i 0.284592 + 0.875885i
\(383\) −4.85410 + 3.52671i −0.248033 + 0.180207i −0.704855 0.709352i \(-0.748988\pi\)
0.456822 + 0.889558i \(0.348988\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) 6.47214 4.70228i 0.328997 0.239030i
\(388\) 4.32624 + 13.3148i 0.219631 + 0.675956i
\(389\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(390\) 0 0
\(391\) −29.1246 21.1603i −1.47289 1.07012i
\(392\) −0.927051 + 2.85317i −0.0468231 + 0.144107i
\(393\) 3.70820 + 11.4127i 0.187054 + 0.575693i
\(394\) 4.85410 3.52671i 0.244546 0.177673i
\(395\) 0 0
\(396\) 0 0
\(397\) 26.0000 1.30490 0.652451 0.757831i \(-0.273741\pi\)
0.652451 + 0.757831i \(0.273741\pi\)
\(398\) 3.23607 2.35114i 0.162209 0.117852i
\(399\) −2.47214 7.60845i −0.123762 0.380899i
\(400\) −1.54508 + 4.75528i −0.0772542 + 0.237764i
\(401\) −24.2705 17.6336i −1.21201 0.880578i −0.216600 0.976261i \(-0.569497\pi\)
−0.995412 + 0.0956827i \(0.969497\pi\)
\(402\) 3.23607 + 2.35114i 0.161400 + 0.117264i
\(403\) 9.88854 30.4338i 0.492583 1.51602i
\(404\) −1.85410 5.70634i −0.0922450 0.283901i
\(405\) 0 0
\(406\) 12.0000 0.595550
\(407\) 0 0
\(408\) 6.00000 0.297044
\(409\) −27.5066 + 19.9847i −1.36011 + 0.988180i −0.361675 + 0.932304i \(0.617795\pi\)
−0.998438 + 0.0558755i \(0.982205\pi\)
\(410\) 0 0
\(411\) −5.56231 + 17.1190i −0.274368 + 0.844419i
\(412\) 3.23607 + 2.35114i 0.159430 + 0.115832i
\(413\) 0 0
\(414\) 1.85410 5.70634i 0.0911241 0.280451i
\(415\) 0 0
\(416\) −3.23607 + 2.35114i −0.158661 + 0.115274i
\(417\) 4.00000 0.195881
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) −3.09017 9.51057i −0.150606 0.463517i 0.847084 0.531460i \(-0.178356\pi\)
−0.997689 + 0.0679432i \(0.978356\pi\)
\(422\) −2.47214 + 7.60845i −0.120342 + 0.370374i
\(423\) 4.85410 + 3.52671i 0.236015 + 0.171475i
\(424\) 0 0
\(425\) −9.27051 + 28.5317i −0.449686 + 1.38399i
\(426\) 1.85410 + 5.70634i 0.0898315 + 0.276473i
\(427\) −12.9443 + 9.40456i −0.626417 + 0.455119i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(432\) 0.309017 + 0.951057i 0.0148676 + 0.0457577i
\(433\) 8.03444 24.7275i 0.386111 1.18833i −0.549561 0.835454i \(-0.685205\pi\)
0.935671 0.352873i \(-0.114795\pi\)
\(434\) 12.9443 + 9.40456i 0.621345 + 0.451434i
\(435\) 0 0
\(436\) 1.23607 3.80423i 0.0591969 0.182189i
\(437\) 7.41641 + 22.8254i 0.354775 + 1.09188i
\(438\) 1.61803 1.17557i 0.0773127 0.0561709i
\(439\) 10.0000 0.477274 0.238637 0.971109i \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) −19.4164 + 14.1068i −0.923544 + 0.670994i
\(443\) −7.41641 22.8254i −0.352364 1.08447i −0.957522 0.288360i \(-0.906890\pi\)
0.605158 0.796105i \(-0.293110\pi\)
\(444\) −3.09017 + 9.51057i −0.146653 + 0.451351i
\(445\) 0 0
\(446\) 12.9443 + 9.40456i 0.612929 + 0.445319i
\(447\) 1.85410 5.70634i 0.0876960 0.269901i
\(448\) −0.618034 1.90211i −0.0291994 0.0898664i
\(449\) −4.85410 + 3.52671i −0.229079 + 0.166436i −0.696404 0.717650i \(-0.745218\pi\)
0.467325 + 0.884086i \(0.345218\pi\)
\(450\) −5.00000 −0.235702
\(451\) 0 0
\(452\) 18.0000 0.846649
\(453\) −8.09017 + 5.87785i −0.380109 + 0.276166i
\(454\) 3.70820 + 11.4127i 0.174035 + 0.535624i
\(455\) 0 0
\(456\) −3.23607 2.35114i −0.151543 0.110102i
\(457\) −8.09017 5.87785i −0.378442 0.274954i 0.382261 0.924054i \(-0.375146\pi\)
−0.760703 + 0.649100i \(0.775146\pi\)
\(458\) −6.79837 + 20.9232i −0.317667 + 0.977679i
\(459\) 1.85410 + 5.70634i 0.0865421 + 0.266349i
\(460\) 0 0
\(461\) −42.0000 −1.95614 −0.978068 0.208288i \(-0.933211\pi\)
−0.978068 + 0.208288i \(0.933211\pi\)
\(462\) 0 0
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 4.85410 3.52671i 0.225346 0.163723i
\(465\) 0 0
\(466\) 5.56231 17.1190i 0.257669 0.793023i
\(467\) 9.70820 + 7.05342i 0.449242 + 0.326393i 0.789296 0.614012i \(-0.210445\pi\)
−0.340054 + 0.940406i \(0.610445\pi\)
\(468\) −3.23607 2.35114i −0.149587 0.108682i
\(469\) 2.47214 7.60845i 0.114153 0.351326i
\(470\) 0 0
\(471\) −1.61803 + 1.17557i −0.0745551 + 0.0541674i
\(472\) 0 0
\(473\) 0 0
\(474\) −14.0000 −0.643041
\(475\) 16.1803 11.7557i 0.742405 0.539389i
\(476\) −3.70820 11.4127i −0.169965 0.523099i
\(477\) 0 0
\(478\) −9.70820 7.05342i −0.444043 0.322616i
\(479\) −19.4164 14.1068i −0.887158 0.644558i 0.0479772 0.998848i \(-0.484723\pi\)
−0.935136 + 0.354290i \(0.884723\pi\)
\(480\) 0 0
\(481\) −12.3607 38.0423i −0.563598 1.73458i
\(482\) −8.09017 + 5.87785i −0.368497 + 0.267729i
\(483\) −12.0000 −0.546019
\(484\) 0 0
\(485\) 0 0
\(486\) −0.809017 + 0.587785i −0.0366978 + 0.0266625i
\(487\) 6.18034 + 19.0211i 0.280058 + 0.861930i 0.987837 + 0.155495i \(0.0496974\pi\)
−0.707779 + 0.706434i \(0.750303\pi\)
\(488\) −2.47214 + 7.60845i −0.111908 + 0.344418i
\(489\) 3.23607 + 2.35114i 0.146340 + 0.106322i
\(490\) 0 0
\(491\) −3.70820 + 11.4127i −0.167349 + 0.515047i −0.999202 0.0399494i \(-0.987280\pi\)
0.831853 + 0.554996i \(0.187280\pi\)
\(492\) −1.85410 5.70634i −0.0835894 0.257262i
\(493\) 29.1246 21.1603i 1.31171 0.953011i
\(494\) 16.0000 0.719874
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 9.70820 7.05342i 0.435472 0.316389i
\(498\) 3.70820 + 11.4127i 0.166169 + 0.511414i
\(499\) −1.23607 + 3.80423i −0.0553340 + 0.170301i −0.974904 0.222626i \(-0.928537\pi\)
0.919570 + 0.392926i \(0.128537\pi\)
\(500\) 0 0
\(501\) 9.70820 + 7.05342i 0.433731 + 0.315124i
\(502\) 0 0
\(503\) −3.70820 11.4127i −0.165341 0.508866i 0.833721 0.552187i \(-0.186206\pi\)
−0.999061 + 0.0433204i \(0.986206\pi\)
\(504\) 1.61803 1.17557i 0.0720730 0.0523641i
\(505\) 0 0
\(506\) 0 0
\(507\) 3.00000 0.133235
\(508\) 11.3262 8.22899i 0.502521 0.365103i
\(509\) 7.41641 + 22.8254i 0.328726 + 1.01172i 0.969730 + 0.244178i \(0.0785183\pi\)
−0.641004 + 0.767538i \(0.721482\pi\)
\(510\) 0 0
\(511\) −3.23607 2.35114i −0.143155 0.104008i
\(512\) −0.809017 0.587785i −0.0357538 0.0259767i
\(513\) 1.23607 3.80423i 0.0545737 0.167961i
\(514\) −9.27051 28.5317i −0.408905 1.25848i
\(515\) 0 0
\(516\) −8.00000 −0.352180
\(517\) 0 0
\(518\) 20.0000 0.878750
\(519\) 4.85410 3.52671i 0.213071 0.154805i
\(520\) 0 0
\(521\) −5.56231 + 17.1190i −0.243689 + 0.749998i 0.752160 + 0.658980i \(0.229012\pi\)
−0.995849 + 0.0910175i \(0.970988\pi\)
\(522\) 4.85410 + 3.52671i 0.212458 + 0.154360i
\(523\) −12.9443 9.40456i −0.566013 0.411233i 0.267641 0.963519i \(-0.413756\pi\)
−0.833655 + 0.552286i \(0.813756\pi\)
\(524\) 3.70820 11.4127i 0.161994 0.498565i
\(525\) 3.09017 + 9.51057i 0.134866 + 0.415075i
\(526\) 0 0
\(527\) 48.0000 2.09091
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) −2.47214 + 7.60845i −0.107181 + 0.329868i
\(533\) 19.4164 + 14.1068i 0.841018 + 0.611035i
\(534\) 4.85410 + 3.52671i 0.210058 + 0.152616i
\(535\) 0 0
\(536\) −1.23607 3.80423i −0.0533900 0.164318i
\(537\) −19.4164 + 14.1068i −0.837880 + 0.608755i
\(538\) −24.0000 −1.03471
\(539\) 0 0
\(540\) 0 0
\(541\) 16.1803 11.7557i 0.695647 0.505417i −0.182865 0.983138i \(-0.558537\pi\)
0.878512 + 0.477721i \(0.158537\pi\)
\(542\) −0.618034 1.90211i −0.0265468 0.0817028i
\(543\) −6.79837 + 20.9232i −0.291746 + 0.897902i
\(544\) −4.85410 3.52671i −0.208118 0.151207i
\(545\) 0 0
\(546\) −2.47214 + 7.60845i −0.105798 + 0.325612i
\(547\) 8.65248 + 26.6296i 0.369953 + 1.13860i 0.946821 + 0.321761i \(0.104275\pi\)
−0.576868 + 0.816838i \(0.695725\pi\)
\(548\) 14.5623 10.5801i 0.622071 0.451961i
\(549\) −8.00000 −0.341432
\(550\) 0 0
\(551\) −24.0000 −1.02243
\(552\) −4.85410 + 3.52671i −0.206604 + 0.150107i
\(553\) 8.65248 + 26.6296i 0.367941 + 1.13241i
\(554\) 4.94427 15.2169i 0.210062 0.646504i
\(555\) 0 0
\(556\) −3.23607 2.35114i −0.137240 0.0997106i
\(557\) −5.56231 + 17.1190i −0.235682 + 0.725356i 0.761348 + 0.648344i \(0.224538\pi\)
−0.997030 + 0.0770122i \(0.975462\pi\)
\(558\) 2.47214 + 7.60845i 0.104654 + 0.322091i
\(559\) 25.8885 18.8091i 1.09497 0.795541i
\(560\) 0 0
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) −9.70820 + 7.05342i −0.409152 + 0.297266i −0.773258 0.634091i \(-0.781374\pi\)
0.364106 + 0.931357i \(0.381374\pi\)
\(564\) −1.85410 5.70634i −0.0780718 0.240280i
\(565\) 0 0
\(566\) 6.47214 + 4.70228i 0.272044 + 0.197652i
\(567\) 1.61803 + 1.17557i 0.0679510 + 0.0493693i
\(568\) 1.85410 5.70634i 0.0777964 0.239433i
\(569\) −5.56231 17.1190i −0.233184 0.717667i −0.997357 0.0726553i \(-0.976853\pi\)
0.764173 0.645011i \(-0.223147\pi\)
\(570\) 0 0
\(571\) 28.0000 1.17176 0.585882 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) 0 0
\(573\) 18.0000 0.751961
\(574\) −9.70820 + 7.05342i −0.405213 + 0.294404i
\(575\) −9.27051 28.5317i −0.386607 1.18985i
\(576\) 0.309017 0.951057i 0.0128757 0.0396274i
\(577\) 27.5066 + 19.9847i 1.14511 + 0.831974i 0.987824 0.155579i \(-0.0497242\pi\)
0.157290 + 0.987552i \(0.449724\pi\)
\(578\) −15.3713 11.1679i −0.639363 0.464524i
\(579\) −4.32624 + 13.3148i −0.179792 + 0.553344i
\(580\) 0 0
\(581\) 19.4164 14.1068i 0.805528 0.585251i
\(582\) 14.0000 0.580319
\(583\) 0 0
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) 1.85410 + 5.70634i 0.0765922 + 0.235727i
\(587\) 7.41641 22.8254i 0.306108 0.942103i −0.673154 0.739503i \(-0.735061\pi\)
0.979261 0.202601i \(-0.0649393\pi\)
\(588\) 2.42705 + 1.76336i 0.100090 + 0.0727196i
\(589\) −25.8885 18.8091i −1.06672 0.775017i
\(590\) 0 0
\(591\) −1.85410 5.70634i −0.0762676 0.234727i
\(592\) 8.09017 5.87785i 0.332504 0.241578i
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −4.85410 + 3.52671i −0.198832 + 0.144460i
\(597\) −1.23607 3.80423i −0.0505889 0.155697i
\(598\) 7.41641 22.8254i 0.303279 0.933398i
\(599\) −24.2705 17.6336i −0.991666 0.720488i −0.0313808 0.999508i \(-0.509990\pi\)
−0.960285 + 0.279020i \(0.909990\pi\)
\(600\) 4.04508 + 2.93893i 0.165140 + 0.119981i
\(601\) 6.79837 20.9232i 0.277311 0.853477i −0.711287 0.702902i \(-0.751887\pi\)
0.988599 0.150575i \(-0.0481126\pi\)
\(602\) 4.94427 + 15.2169i 0.201513 + 0.620195i
\(603\) 3.23607 2.35114i 0.131783 0.0957459i
\(604\) 10.0000 0.406894
\(605\) 0 0
\(606\) −6.00000 −0.243733
\(607\) 11.3262 8.22899i 0.459718 0.334005i −0.333703 0.942678i \(-0.608298\pi\)
0.793421 + 0.608674i \(0.208298\pi\)
\(608\) 1.23607 + 3.80423i 0.0501292 + 0.154282i
\(609\) 3.70820 11.4127i 0.150264 0.462465i
\(610\) 0 0
\(611\) 19.4164 + 14.1068i 0.785504 + 0.570702i
\(612\) 1.85410 5.70634i 0.0749476 0.230665i
\(613\) 4.94427 + 15.2169i 0.199697 + 0.614605i 0.999890 + 0.0148615i \(0.00473072\pi\)
−0.800192 + 0.599744i \(0.795269\pi\)
\(614\) 16.1803 11.7557i 0.652985 0.474422i
\(615\) 0 0
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 3.23607 2.35114i 0.130174 0.0945768i
\(619\) 13.5967 + 41.8465i 0.546499 + 1.68195i 0.717398 + 0.696664i \(0.245333\pi\)
−0.170898 + 0.985289i \(0.554667\pi\)
\(620\) 0 0
\(621\) −4.85410 3.52671i −0.194788 0.141522i
\(622\) 14.5623 + 10.5801i 0.583895 + 0.424225i
\(623\) 3.70820 11.4127i 0.148566 0.457239i
\(624\) 1.23607 + 3.80423i 0.0494823 + 0.152291i
\(625\) −20.2254 + 14.6946i −0.809017 + 0.587785i
\(626\) 26.0000 1.03917
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) 48.5410 35.2671i 1.93546 1.40619i
\(630\) 0 0
\(631\) −4.94427 + 15.2169i −0.196828 + 0.605775i 0.803122 + 0.595815i \(0.203171\pi\)
−0.999950 + 0.00996082i \(0.996829\pi\)
\(632\) 11.3262 + 8.22899i 0.450534 + 0.327332i
\(633\) 6.47214 + 4.70228i 0.257244 + 0.186899i
\(634\) 3.70820 11.4127i 0.147272 0.453255i
\(635\) 0 0
\(636\) 0 0
\(637\) −12.0000 −0.475457
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) 1.85410 + 5.70634i 0.0732326 + 0.225387i 0.980973 0.194147i \(-0.0621937\pi\)
−0.907740 + 0.419533i \(0.862194\pi\)
\(642\) 3.70820 11.4127i 0.146351 0.450422i
\(643\) 3.23607 + 2.35114i 0.127618 + 0.0927200i 0.649763 0.760137i \(-0.274868\pi\)
−0.522145 + 0.852857i \(0.674868\pi\)
\(644\) 9.70820 + 7.05342i 0.382557 + 0.277944i
\(645\) 0 0
\(646\) 7.41641 + 22.8254i 0.291795 + 0.898052i
\(647\) −4.85410 + 3.52671i −0.190834 + 0.138649i −0.679100 0.734046i \(-0.737630\pi\)
0.488266 + 0.872695i \(0.337630\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) −20.0000 −0.784465
\(651\) 12.9443 9.40456i 0.507326 0.368594i
\(652\) −1.23607 3.80423i −0.0484082 0.148985i
\(653\) −11.1246 + 34.2380i −0.435340 + 1.33984i 0.457398 + 0.889262i \(0.348781\pi\)
−0.892738 + 0.450576i \(0.851219\pi\)
\(654\) −3.23607 2.35114i −0.126540 0.0919369i
\(655\) 0 0
\(656\) −1.85410 + 5.70634i −0.0723905 + 0.222795i
\(657\) −0.618034 1.90211i −0.0241118 0.0742085i
\(658\) −9.70820 + 7.05342i −0.378465 + 0.274971i
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −22.0000 −0.855701 −0.427850 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) 3.23607 2.35114i 0.125773 0.0913797i
\(663\) 7.41641 + 22.8254i 0.288029 + 0.886463i
\(664\) 3.70820 11.4127i 0.143906 0.442898i
\(665\) 0 0
\(666\) 8.09017 + 5.87785i 0.313488 + 0.227762i
\(667\) −11.1246 + 34.2380i −0.430747 + 1.32570i
\(668\) −3.70820 11.4127i −0.143475 0.441570i
\(669\) 12.9443 9.40456i 0.500454 0.363601i
\(670\) 0 0
\(671\) 0 0
\(672\) −2.00000 −0.0771517
\(673\) 11.3262 8.22899i 0.436594 0.317204i −0.347686 0.937611i \(-0.613032\pi\)
0.784280 + 0.620407i \(0.213032\pi\)
\(674\) −0.618034 1.90211i −0.0238058 0.0732667i
\(675\) −1.54508 + 4.75528i −0.0594703 + 0.183031i
\(676\) −2.42705 1.76336i −0.0933481 0.0678214i
\(677\) 24.2705 + 17.6336i 0.932791 + 0.677713i 0.946675 0.322191i \(-0.104419\pi\)
−0.0138832 + 0.999904i \(0.504419\pi\)
\(678\) 5.56231 17.1190i 0.213619 0.657452i
\(679\) −8.65248 26.6296i −0.332052 1.02195i
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) −3.23607 + 2.35114i −0.123734 + 0.0898981i
\(685\) 0 0
\(686\) 6.18034 19.0211i 0.235966 0.726230i
\(687\) 17.7984 + 12.9313i 0.679050 + 0.493359i
\(688\) 6.47214 + 4.70228i 0.246748 + 0.179273i
\(689\) 0 0
\(690\) 0 0
\(691\) −16.1803 + 11.7557i −0.615529 + 0.447208i −0.851357 0.524587i \(-0.824220\pi\)
0.235828 + 0.971795i \(0.424220\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −36.0000 −1.36654
\(695\) 0 0
\(696\) −1.85410 5.70634i −0.0702796 0.216298i
\(697\) −11.1246 + 34.2380i −0.421375 + 1.29686i
\(698\) −3.23607 2.35114i −0.122487 0.0889920i
\(699\) −14.5623 10.5801i −0.550797 0.400177i
\(700\) 3.09017 9.51057i 0.116797 0.359466i
\(701\) 1.85410 + 5.70634i 0.0700285 + 0.215525i 0.979946 0.199264i \(-0.0638552\pi\)
−0.909917 + 0.414790i \(0.863855\pi\)
\(702\) −3.23607 + 2.35114i −0.122138 + 0.0887381i
\(703\) −40.0000 −1.50863
\(704\) 0 0
\(705\) 0 0
\(706\) 4.85410 3.52671i 0.182687 0.132730i
\(707\) 3.70820 + 11.4127i 0.139461 + 0.429218i
\(708\) 0 0
\(709\) −21.0344 15.2824i −0.789965 0.573943i 0.117988 0.993015i \(-0.462356\pi\)
−0.907953 + 0.419072i \(0.862356\pi\)
\(710\) 0 0
\(711\) −4.32624 + 13.3148i −0.162247 + 0.499344i
\(712\) −1.85410 5.70634i −0.0694854 0.213854i
\(713\) −38.8328 + 28.2137i −1.45430 + 1.05661i
\(714\) −12.0000 −0.449089
\(715\) 0 0
\(716\) 24.0000 0.896922
\(717\) −9.70820 + 7.05342i −0.362560 + 0.263415i
\(718\) 3.70820 + 11.4127i 0.138389 + 0.425917i
\(719\) 9.27051 28.5317i 0.345732 1.06405i −0.615459 0.788169i \(-0.711029\pi\)
0.961191 0.275884i \(-0.0889706\pi\)
\(720\) 0 0
\(721\) −6.47214 4.70228i −0.241035 0.175122i
\(722\) −0.927051 + 2.85317i −0.0345013 + 0.106184i
\(723\) 3.09017 + 9.51057i 0.114925 + 0.353702i
\(724\) 17.7984 12.9313i 0.661471 0.480587i
\(725\) 30.0000 1.11417
\(726\) 0 0
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 6.47214 4.70228i 0.239873 0.174278i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) 38.8328 + 28.2137i 1.43628 + 1.04352i
\(732\) 6.47214 + 4.70228i 0.239217 + 0.173801i
\(733\) 1.23607 3.80423i 0.0456552 0.140512i −0.925630 0.378429i \(-0.876464\pi\)
0.971286 + 0.237917i \(0.0764645\pi\)
\(734\) 2.47214 + 7.60845i 0.0912482 + 0.280833i
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 0 0
\(738\) −6.00000 −0.220863
\(739\) 6.47214 4.70228i 0.238081 0.172976i −0.462347 0.886699i \(-0.652992\pi\)
0.700428 + 0.713723i \(0.252992\pi\)
\(740\) 0 0
\(741\) 4.94427 15.2169i 0.181632 0.559007i
\(742\) 0 0
\(743\) 29.1246 + 21.1603i 1.06848 + 0.776295i 0.975638 0.219386i \(-0.0704054\pi\)
0.0928402 + 0.995681i \(0.470405\pi\)
\(744\) 2.47214 7.60845i 0.0906329 0.278939i
\(745\) 0 0
\(746\) 16.1803 11.7557i 0.592404 0.430407i
\(747\) 12.0000 0.439057
\(748\) 0 0
\(749\) −24.0000 −0.876941
\(750\) 0 0
\(751\) 2.47214 + 7.60845i 0.0902095 + 0.277636i 0.985976 0.166889i \(-0.0533723\pi\)
−0.895766 + 0.444526i \(0.853372\pi\)
\(752\) −1.85410 + 5.70634i −0.0676121 + 0.208089i
\(753\) 0 0
\(754\) 19.4164 + 14.1068i 0.707104 + 0.513741i
\(755\) 0 0
\(756\) −0.618034 1.90211i −0.0224777 0.0691792i
\(757\) 27.5066 19.9847i 0.999744 0.726356i 0.0377104 0.999289i \(-0.487994\pi\)
0.962033 + 0.272932i \(0.0879936\pi\)
\(758\) 20.0000 0.726433
\(759\) 0 0
\(760\) 0 0
\(761\) 14.5623 10.5801i 0.527883 0.383530i −0.291682 0.956515i \(-0.594215\pi\)
0.819565 + 0.572986i \(0.194215\pi\)
\(762\) −4.32624 13.3148i −0.156723 0.482344i
\(763\) −2.47214 + 7.60845i −0.0894973 + 0.275444i
\(764\) −14.5623 10.5801i −0.526846 0.382776i
\(765\) 0 0
\(766\) 1.85410 5.70634i 0.0669914 0.206178i
\(767\) 0 0
\(768\) −0.809017 + 0.587785i −0.0291929 + 0.0212099i
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) −30.0000 −1.08042
\(772\) 11.3262 8.22899i 0.407640 0.296168i
\(773\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(774\) −2.47214 + 7.60845i −0.0888591 + 0.273480i
\(775\) 32.3607 + 23.5114i 1.16243 + 0.844555i
\(776\) −11.3262 8.22899i −0.406588 0.295404i
\(777\) 6.18034 19.0211i 0.221718 0.682379i
\(778\) 0 0
\(779\) 19.4164 14.1068i 0.695665 0.505430i
\(780\) 0 0
\(781\) 0 0
\(782\) 36.0000 1.28736
\(783\) 4.85410 3.52671i 0.173471 0.126034i
\(784\) −0.927051 2.85317i −0.0331090 0.101899i