Properties

Label 605.2.g.c.366.1
Level $605$
Weight $2$
Character 605.366
Analytic conductor $4.831$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.83094932229\)
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 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 366.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 605.366
Dual form 605.2.g.c.81.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.927051 + 2.85317i) q^{8} +(2.42705 - 1.76336i) q^{9} +O(q^{10})\) \(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.927051 + 2.85317i) q^{8} +(2.42705 - 1.76336i) q^{9} -1.00000 q^{10} +(1.61803 - 1.17557i) q^{13} +(0.809017 + 0.587785i) q^{16} +(4.85410 + 3.52671i) q^{17} +(0.927051 - 2.85317i) q^{18} +(1.23607 + 3.80423i) q^{19} +(0.809017 - 0.587785i) q^{20} +4.00000 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.618034 - 1.90211i) q^{26} +(-1.85410 + 5.70634i) q^{29} +(6.47214 - 4.70228i) q^{31} -5.00000 q^{32} +6.00000 q^{34} +(0.927051 + 2.85317i) q^{36} +(-0.618034 + 1.90211i) q^{37} +(3.23607 + 2.35114i) q^{38} +(0.927051 - 2.85317i) q^{40} +(-0.618034 - 1.90211i) q^{41} -4.00000 q^{43} -3.00000 q^{45} +(3.23607 - 2.35114i) q^{46} +(-3.70820 - 11.4127i) q^{47} +(5.66312 + 4.11450i) q^{49} +(0.809017 + 0.587785i) q^{50} +(0.618034 + 1.90211i) q^{52} +(1.61803 - 1.17557i) q^{53} +(1.85410 + 5.70634i) q^{58} +(1.23607 - 3.80423i) q^{59} +(-8.09017 - 5.87785i) q^{61} +(2.47214 - 7.60845i) q^{62} +(-5.66312 + 4.11450i) q^{64} -2.00000 q^{65} -16.0000 q^{67} +(-4.85410 + 3.52671i) q^{68} +(-6.47214 - 4.70228i) q^{71} +(7.28115 + 5.29007i) q^{72} +(-4.32624 + 13.3148i) q^{73} +(0.618034 + 1.90211i) q^{74} -4.00000 q^{76} +(6.47214 - 4.70228i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(2.78115 - 8.55951i) q^{81} +(-1.61803 - 1.17557i) q^{82} +(-3.23607 - 2.35114i) q^{83} +(-1.85410 - 5.70634i) q^{85} +(-3.23607 + 2.35114i) q^{86} +10.0000 q^{89} +(-2.42705 + 1.76336i) q^{90} +(-1.23607 + 3.80423i) q^{92} +(-9.70820 - 7.05342i) q^{94} +(1.23607 - 3.80423i) q^{95} +(-8.09017 + 5.87785i) q^{97} +7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} + q^{4} - q^{5} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} + q^{4} - q^{5} - 3 q^{8} + 3 q^{9} - 4 q^{10} + 2 q^{13} + q^{16} + 6 q^{17} - 3 q^{18} - 4 q^{19} + q^{20} + 16 q^{23} - q^{25} - 2 q^{26} + 6 q^{29} + 8 q^{31} - 20 q^{32} + 24 q^{34} - 3 q^{36} + 2 q^{37} + 4 q^{38} - 3 q^{40} + 2 q^{41} - 16 q^{43} - 12 q^{45} + 4 q^{46} + 12 q^{47} + 7 q^{49} + q^{50} - 2 q^{52} + 2 q^{53} - 6 q^{58} - 4 q^{59} - 10 q^{61} - 8 q^{62} - 7 q^{64} - 8 q^{65} - 64 q^{67} - 6 q^{68} - 8 q^{71} + 9 q^{72} + 14 q^{73} - 2 q^{74} - 16 q^{76} + 8 q^{79} + q^{80} - 9 q^{81} - 2 q^{82} - 4 q^{83} + 6 q^{85} - 4 q^{86} + 40 q^{89} - 3 q^{90} + 4 q^{92} - 12 q^{94} - 4 q^{95} - 10 q^{97} + 28 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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 −0.263792 0.964580i \(-0.584973\pi\)
0.835853 + 0.548953i \(0.184973\pi\)
\(3\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(4\) −0.309017 + 0.951057i −0.154508 + 0.475528i
\(5\) −0.809017 0.587785i −0.361803 0.262866i
\(6\) 0 0
\(7\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(8\) 0.927051 + 2.85317i 0.327762 + 1.00875i
\(9\) 2.42705 1.76336i 0.809017 0.587785i
\(10\) −1.00000 −0.316228
\(11\) 0 0
\(12\) 0 0
\(13\) 1.61803 1.17557i 0.448762 0.326045i −0.340345 0.940301i \(-0.610544\pi\)
0.789107 + 0.614256i \(0.210544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.809017 + 0.587785i 0.202254 + 0.146946i
\(17\) 4.85410 + 3.52671i 1.17729 + 0.855353i 0.991864 0.127304i \(-0.0406325\pi\)
0.185429 + 0.982658i \(0.440633\pi\)
\(18\) 0.927051 2.85317i 0.218508 0.672499i
\(19\) 1.23607 + 3.80423i 0.283573 + 0.872749i 0.986823 + 0.161806i \(0.0517318\pi\)
−0.703249 + 0.710943i \(0.748268\pi\)
\(20\) 0.809017 0.587785i 0.180902 0.131433i
\(21\) 0 0
\(22\) 0 0
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0 0
\(25\) 0.309017 + 0.951057i 0.0618034 + 0.190211i
\(26\) 0.618034 1.90211i 0.121206 0.373035i
\(27\) 0 0
\(28\) 0 0
\(29\) −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 0.172347 0.985036i \(-0.444865\pi\)
0.990083 + 0.140482i \(0.0448651\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 0.927051 + 2.85317i 0.154508 + 0.475528i
\(37\) −0.618034 + 1.90211i −0.101604 + 0.312705i −0.988918 0.148460i \(-0.952568\pi\)
0.887314 + 0.461165i \(0.152568\pi\)
\(38\) 3.23607 + 2.35114i 0.524960 + 0.381405i
\(39\) 0 0
\(40\) 0.927051 2.85317i 0.146580 0.451126i
\(41\) −0.618034 1.90211i −0.0965207 0.297060i 0.891126 0.453755i \(-0.149916\pi\)
−0.987647 + 0.156695i \(0.949916\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) −3.00000 −0.447214
\(46\) 3.23607 2.35114i 0.477132 0.346657i
\(47\) −3.70820 11.4127i −0.540897 1.66471i −0.730550 0.682859i \(-0.760736\pi\)
0.189653 0.981851i \(-0.439264\pi\)
\(48\) 0 0
\(49\) 5.66312 + 4.11450i 0.809017 + 0.587785i
\(50\) 0.809017 + 0.587785i 0.114412 + 0.0831254i
\(51\) 0 0
\(52\) 0.618034 + 1.90211i 0.0857059 + 0.263776i
\(53\) 1.61803 1.17557i 0.222254 0.161477i −0.471087 0.882087i \(-0.656138\pi\)
0.693341 + 0.720610i \(0.256138\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 1.85410 + 5.70634i 0.243456 + 0.749279i
\(59\) 1.23607 3.80423i 0.160922 0.495268i −0.837790 0.545992i \(-0.816153\pi\)
0.998713 + 0.0507240i \(0.0161529\pi\)
\(60\) 0 0
\(61\) −8.09017 5.87785i −1.03584 0.752582i −0.0663709 0.997795i \(-0.521142\pi\)
−0.969469 + 0.245213i \(0.921142\pi\)
\(62\) 2.47214 7.60845i 0.313962 0.966274i
\(63\) 0 0
\(64\) −5.66312 + 4.11450i −0.707890 + 0.514312i
\(65\) −2.00000 −0.248069
\(66\) 0 0
\(67\) −16.0000 −1.95471 −0.977356 0.211604i \(-0.932131\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) −4.85410 + 3.52671i −0.588646 + 0.427677i
\(69\) 0 0
\(70\) 0 0
\(71\) −6.47214 4.70228i −0.768101 0.558058i 0.133283 0.991078i \(-0.457448\pi\)
−0.901384 + 0.433020i \(0.857448\pi\)
\(72\) 7.28115 + 5.29007i 0.858092 + 0.623440i
\(73\) −4.32624 + 13.3148i −0.506348 + 1.55838i 0.292145 + 0.956374i \(0.405631\pi\)
−0.798493 + 0.602004i \(0.794369\pi\)
\(74\) 0.618034 + 1.90211i 0.0718450 + 0.221116i
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 0 0
\(79\) 6.47214 4.70228i 0.728172 0.529048i −0.160813 0.986985i \(-0.551411\pi\)
0.888985 + 0.457937i \(0.151411\pi\)
\(80\) −0.309017 0.951057i −0.0345492 0.106331i
\(81\) 2.78115 8.55951i 0.309017 0.951057i
\(82\) −1.61803 1.17557i −0.178682 0.129820i
\(83\) −3.23607 2.35114i −0.355205 0.258071i 0.395845 0.918318i \(-0.370452\pi\)
−0.751049 + 0.660246i \(0.770452\pi\)
\(84\) 0 0
\(85\) −1.85410 5.70634i −0.201106 0.618939i
\(86\) −3.23607 + 2.35114i −0.348954 + 0.253530i
\(87\) 0 0
\(88\) 0 0
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) −2.42705 + 1.76336i −0.255834 + 0.185874i
\(91\) 0 0
\(92\) −1.23607 + 3.80423i −0.128869 + 0.396618i
\(93\) 0 0
\(94\) −9.70820 7.05342i −1.00132 0.727505i
\(95\) 1.23607 3.80423i 0.126818 0.390305i
\(96\) 0 0
\(97\) −8.09017 + 5.87785i −0.821432 + 0.596806i −0.917122 0.398606i \(-0.869494\pi\)
0.0956901 + 0.995411i \(0.469494\pi\)
\(98\) 7.00000 0.707107
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −8.09017 + 5.87785i −0.805002 + 0.584868i −0.912377 0.409350i \(-0.865755\pi\)
0.107375 + 0.994219i \(0.465755\pi\)
\(102\) 0 0
\(103\) −1.23607 + 3.80423i −0.121793 + 0.374842i −0.993303 0.115536i \(-0.963141\pi\)
0.871510 + 0.490378i \(0.163141\pi\)
\(104\) 4.85410 + 3.52671i 0.475984 + 0.345823i
\(105\) 0 0
\(106\) 0.618034 1.90211i 0.0600288 0.184750i
\(107\) −3.70820 11.4127i −0.358486 1.10331i −0.953961 0.299932i \(-0.903036\pi\)
0.595475 0.803374i \(-0.296964\pi\)
\(108\) 0 0
\(109\) 18.0000 1.72409 0.862044 0.506834i \(-0.169184\pi\)
0.862044 + 0.506834i \(0.169184\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.85410 5.70634i −0.174419 0.536807i 0.825187 0.564859i \(-0.191070\pi\)
−0.999606 + 0.0280521i \(0.991070\pi\)
\(114\) 0 0
\(115\) −3.23607 2.35114i −0.301765 0.219245i
\(116\) −4.85410 3.52671i −0.450692 0.327447i
\(117\) 1.85410 5.70634i 0.171412 0.527551i
\(118\) −1.23607 3.80423i −0.113789 0.350207i
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) −10.0000 −0.905357
\(123\) 0 0
\(124\) 2.47214 + 7.60845i 0.222004 + 0.683259i
\(125\) 0.309017 0.951057i 0.0276393 0.0850651i
\(126\) 0 0
\(127\) 12.9443 + 9.40456i 1.14862 + 0.834520i 0.988297 0.152545i \(-0.0487468\pi\)
0.160322 + 0.987065i \(0.448747\pi\)
\(128\) 0.927051 2.85317i 0.0819405 0.252187i
\(129\) 0 0
\(130\) −1.61803 + 1.17557i −0.141911 + 0.103104i
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −12.9443 + 9.40456i −1.11821 + 0.812431i
\(135\) 0 0
\(136\) −5.56231 + 17.1190i −0.476964 + 1.46794i
\(137\) −14.5623 10.5801i −1.24414 0.903922i −0.246275 0.969200i \(-0.579207\pi\)
−0.997867 + 0.0652782i \(0.979207\pi\)
\(138\) 0 0
\(139\) −3.70820 + 11.4127i −0.314526 + 0.968011i 0.661423 + 0.750013i \(0.269953\pi\)
−0.975949 + 0.217998i \(0.930047\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −8.00000 −0.671345
\(143\) 0 0
\(144\) 3.00000 0.250000
\(145\) 4.85410 3.52671i 0.403111 0.292877i
\(146\) 4.32624 + 13.3148i 0.358042 + 1.10194i
\(147\) 0 0
\(148\) −1.61803 1.17557i −0.133002 0.0966313i
\(149\) −8.09017 5.87785i −0.662773 0.481532i 0.204826 0.978798i \(-0.434337\pi\)
−0.867598 + 0.497266i \(0.834337\pi\)
\(150\) 0 0
\(151\) −2.47214 7.60845i −0.201180 0.619167i −0.999849 0.0173966i \(-0.994462\pi\)
0.798669 0.601770i \(-0.205538\pi\)
\(152\) −9.70820 + 7.05342i −0.787439 + 0.572108i
\(153\) 18.0000 1.45521
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) −0.618034 1.90211i −0.0493245 0.151805i 0.923361 0.383934i \(-0.125431\pi\)
−0.972685 + 0.232129i \(0.925431\pi\)
\(158\) 2.47214 7.60845i 0.196673 0.605296i
\(159\) 0 0
\(160\) 4.04508 + 2.93893i 0.319792 + 0.232343i
\(161\) 0 0
\(162\) −2.78115 8.55951i −0.218508 0.672499i
\(163\) −12.9443 + 9.40456i −1.01387 + 0.736622i −0.965018 0.262184i \(-0.915557\pi\)
−0.0488556 + 0.998806i \(0.515557\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) −4.00000 −0.310460
\(167\) −6.47214 + 4.70228i −0.500829 + 0.363874i −0.809334 0.587349i \(-0.800171\pi\)
0.308505 + 0.951223i \(0.400171\pi\)
\(168\) 0 0
\(169\) −2.78115 + 8.55951i −0.213935 + 0.658424i
\(170\) −4.85410 3.52671i −0.372293 0.270486i
\(171\) 9.70820 + 7.05342i 0.742405 + 0.539389i
\(172\) 1.23607 3.80423i 0.0942493 0.290070i
\(173\) 1.85410 + 5.70634i 0.140965 + 0.433845i 0.996470 0.0839492i \(-0.0267533\pi\)
−0.855505 + 0.517794i \(0.826753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 8.09017 5.87785i 0.606384 0.440564i
\(179\) 1.23607 + 3.80423i 0.0923881 + 0.284341i 0.986564 0.163374i \(-0.0522378\pi\)
−0.894176 + 0.447715i \(0.852238\pi\)
\(180\) 0.927051 2.85317i 0.0690983 0.212663i
\(181\) 8.09017 + 5.87785i 0.601338 + 0.436897i 0.846353 0.532622i \(-0.178793\pi\)
−0.245016 + 0.969519i \(0.578793\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 3.70820 + 11.4127i 0.273372 + 0.841354i
\(185\) 1.61803 1.17557i 0.118960 0.0864297i
\(186\) 0 0
\(187\) 0 0
\(188\) 12.0000 0.875190
\(189\) 0 0
\(190\) −1.23607 3.80423i −0.0896738 0.275988i
\(191\) 2.47214 7.60845i 0.178877 0.550528i −0.820912 0.571055i \(-0.806534\pi\)
0.999789 + 0.0205267i \(0.00653431\pi\)
\(192\) 0 0
\(193\) −21.0344 15.2824i −1.51409 1.10005i −0.964321 0.264737i \(-0.914715\pi\)
−0.549772 0.835315i \(-0.685285\pi\)
\(194\) −3.09017 + 9.51057i −0.221861 + 0.682819i
\(195\) 0 0
\(196\) −5.66312 + 4.11450i −0.404508 + 0.293893i
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) −2.42705 + 1.76336i −0.171618 + 0.124688i
\(201\) 0 0
\(202\) −3.09017 + 9.51057i −0.217424 + 0.669161i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.618034 + 1.90211i −0.0431654 + 0.132849i
\(206\) 1.23607 + 3.80423i 0.0861209 + 0.265053i
\(207\) 9.70820 7.05342i 0.674767 0.490247i
\(208\) 2.00000 0.138675
\(209\) 0 0
\(210\) 0 0
\(211\) 3.23607 2.35114i 0.222780 0.161859i −0.470797 0.882242i \(-0.656034\pi\)
0.693577 + 0.720382i \(0.256034\pi\)
\(212\) 0.618034 + 1.90211i 0.0424467 + 0.130638i
\(213\) 0 0
\(214\) −9.70820 7.05342i −0.663639 0.482162i
\(215\) 3.23607 + 2.35114i 0.220698 + 0.160346i
\(216\) 0 0
\(217\) 0 0
\(218\) 14.5623 10.5801i 0.986284 0.716577i
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) −1.23607 3.80423i −0.0827732 0.254750i 0.901102 0.433608i \(-0.142760\pi\)
−0.983875 + 0.178858i \(0.942760\pi\)
\(224\) 0 0
\(225\) 2.42705 + 1.76336i 0.161803 + 0.117557i
\(226\) −4.85410 3.52671i −0.322890 0.234593i
\(227\) 6.18034 19.0211i 0.410204 1.26248i −0.506268 0.862376i \(-0.668975\pi\)
0.916471 0.400100i \(-0.131025\pi\)
\(228\) 0 0
\(229\) 8.09017 5.87785i 0.534613 0.388419i −0.287467 0.957790i \(-0.592813\pi\)
0.822081 + 0.569371i \(0.192813\pi\)
\(230\) −4.00000 −0.263752
\(231\) 0 0
\(232\) −18.0000 −1.18176
\(233\) 4.85410 3.52671i 0.318003 0.231043i −0.417320 0.908760i \(-0.637031\pi\)
0.735323 + 0.677717i \(0.237031\pi\)
\(234\) −1.85410 5.70634i −0.121206 0.373035i
\(235\) −3.70820 + 11.4127i −0.241897 + 0.744481i
\(236\) 3.23607 + 2.35114i 0.210650 + 0.153046i
\(237\) 0 0
\(238\) 0 0
\(239\) −2.47214 7.60845i −0.159909 0.492150i 0.838716 0.544569i \(-0.183307\pi\)
−0.998625 + 0.0524192i \(0.983307\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 8.09017 5.87785i 0.517920 0.376291i
\(245\) −2.16312 6.65740i −0.138197 0.425325i
\(246\) 0 0
\(247\) 6.47214 + 4.70228i 0.411812 + 0.299199i
\(248\) 19.4164 + 14.1068i 1.23294 + 0.895786i
\(249\) 0 0
\(250\) −0.309017 0.951057i −0.0195440 0.0601501i
\(251\) −9.70820 + 7.05342i −0.612776 + 0.445208i −0.850391 0.526151i \(-0.823635\pi\)
0.237614 + 0.971360i \(0.423635\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 16.0000 1.00393
\(255\) 0 0
\(256\) −5.25329 16.1680i −0.328331 1.01050i
\(257\) 5.56231 17.1190i 0.346967 1.06785i −0.613555 0.789652i \(-0.710261\pi\)
0.960522 0.278203i \(-0.0897388\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0.618034 1.90211i 0.0383288 0.117964i
\(261\) 5.56231 + 17.1190i 0.344298 + 1.05964i
\(262\) 9.70820 7.05342i 0.599775 0.435762i
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 0 0
\(265\) −2.00000 −0.122859
\(266\) 0 0
\(267\) 0 0
\(268\) 4.94427 15.2169i 0.302019 0.929520i
\(269\) 14.5623 + 10.5801i 0.887879 + 0.645082i 0.935324 0.353792i \(-0.115108\pi\)
−0.0474448 + 0.998874i \(0.515108\pi\)
\(270\) 0 0
\(271\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(272\) 1.85410 + 5.70634i 0.112421 + 0.345998i
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) 0 0
\(277\) 8.09017 5.87785i 0.486091 0.353166i −0.317588 0.948229i \(-0.602873\pi\)
0.803679 + 0.595063i \(0.202873\pi\)
\(278\) 3.70820 + 11.4127i 0.222403 + 0.684487i
\(279\) 7.41641 22.8254i 0.444009 1.36652i
\(280\) 0 0
\(281\) 14.5623 + 10.5801i 0.868714 + 0.631158i 0.930242 0.366947i \(-0.119597\pi\)
−0.0615273 + 0.998105i \(0.519597\pi\)
\(282\) 0 0
\(283\) −1.23607 3.80423i −0.0734766 0.226138i 0.907573 0.419894i \(-0.137933\pi\)
−0.981050 + 0.193756i \(0.937933\pi\)
\(284\) 6.47214 4.70228i 0.384051 0.279029i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −12.1353 + 8.81678i −0.715077 + 0.519534i
\(289\) 5.87132 + 18.0701i 0.345372 + 1.06295i
\(290\) 1.85410 5.70634i 0.108877 0.335088i
\(291\) 0 0
\(292\) −11.3262 8.22899i −0.662818 0.481565i
\(293\) −3.09017 + 9.51057i −0.180530 + 0.555613i −0.999843 0.0177332i \(-0.994355\pi\)
0.819313 + 0.573346i \(0.194355\pi\)
\(294\) 0 0
\(295\) −3.23607 + 2.35114i −0.188411 + 0.136889i
\(296\) −6.00000 −0.348743
\(297\) 0 0
\(298\) −10.0000 −0.579284
\(299\) 6.47214 4.70228i 0.374293 0.271940i
\(300\) 0 0
\(301\) 0 0
\(302\) −6.47214 4.70228i −0.372430 0.270586i
\(303\) 0 0
\(304\) −1.23607 + 3.80423i −0.0708934 + 0.218187i
\(305\) 3.09017 + 9.51057i 0.176943 + 0.544573i
\(306\) 14.5623 10.5801i 0.832472 0.604826i
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −6.47214 + 4.70228i −0.367593 + 0.267072i
\(311\) −7.41641 22.8254i −0.420546 1.29431i −0.907195 0.420710i \(-0.861781\pi\)
0.486649 0.873597i \(-0.338219\pi\)
\(312\) 0 0
\(313\) 17.7984 + 12.9313i 1.00602 + 0.730919i 0.963371 0.268171i \(-0.0864192\pi\)
0.0426523 + 0.999090i \(0.486419\pi\)
\(314\) −1.61803 1.17557i −0.0913109 0.0663413i
\(315\) 0 0
\(316\) 2.47214 + 7.60845i 0.139069 + 0.428009i
\(317\) 14.5623 10.5801i 0.817901 0.594240i −0.0982098 0.995166i \(-0.531312\pi\)
0.916110 + 0.400926i \(0.131312\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 7.00000 0.391312
\(321\) 0 0
\(322\) 0 0
\(323\) −7.41641 + 22.8254i −0.412660 + 1.27004i
\(324\) 7.28115 + 5.29007i 0.404508 + 0.293893i
\(325\) 1.61803 + 1.17557i 0.0897524 + 0.0652089i
\(326\) −4.94427 + 15.2169i −0.273838 + 0.842786i
\(327\) 0 0
\(328\) 4.85410 3.52671i 0.268023 0.194730i
\(329\) 0 0
\(330\) 0 0
\(331\) 4.00000 0.219860 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) 3.23607 2.35114i 0.177602 0.129036i
\(333\) 1.85410 + 5.70634i 0.101604 + 0.312705i
\(334\) −2.47214 + 7.60845i −0.135269 + 0.416316i
\(335\) 12.9443 + 9.40456i 0.707221 + 0.513826i
\(336\) 0 0
\(337\) −1.85410 + 5.70634i −0.100999 + 0.310844i −0.988771 0.149441i \(-0.952253\pi\)
0.887771 + 0.460285i \(0.152253\pi\)
\(338\) 2.78115 + 8.55951i 0.151275 + 0.465576i
\(339\) 0 0
\(340\) 6.00000 0.325396
\(341\) 0 0
\(342\) 12.0000 0.648886
\(343\) 0 0
\(344\) −3.70820 11.4127i −0.199933 0.615330i
\(345\) 0 0
\(346\) 4.85410 + 3.52671i 0.260958 + 0.189597i
\(347\) −3.23607 2.35114i −0.173721 0.126216i 0.497527 0.867448i \(-0.334242\pi\)
−0.671248 + 0.741233i \(0.734242\pi\)
\(348\) 0 0
\(349\) 3.09017 + 9.51057i 0.165413 + 0.509089i 0.999066 0.0431990i \(-0.0137549\pi\)
−0.833653 + 0.552288i \(0.813755\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 0 0
\(355\) 2.47214 + 7.60845i 0.131207 + 0.403815i
\(356\) −3.09017 + 9.51057i −0.163779 + 0.504059i
\(357\) 0 0
\(358\) 3.23607 + 2.35114i 0.171032 + 0.124262i
\(359\) 9.88854 30.4338i 0.521897 1.60623i −0.248473 0.968639i \(-0.579929\pi\)
0.770371 0.637596i \(-0.220071\pi\)
\(360\) −2.78115 8.55951i −0.146580 0.451126i
\(361\) 2.42705 1.76336i 0.127740 0.0928082i
\(362\) 10.0000 0.525588
\(363\) 0 0
\(364\) 0 0
\(365\) 11.3262 8.22899i 0.592842 0.430725i
\(366\) 0 0
\(367\) 1.23607 3.80423i 0.0645222 0.198579i −0.913598 0.406618i \(-0.866708\pi\)
0.978121 + 0.208039i \(0.0667081\pi\)
\(368\) 3.23607 + 2.35114i 0.168692 + 0.122562i
\(369\) −4.85410 3.52671i −0.252694 0.183593i
\(370\) 0.618034 1.90211i 0.0321301 0.0988861i
\(371\) 0 0
\(372\) 0 0
\(373\) −18.0000 −0.932005 −0.466002 0.884783i \(-0.654306\pi\)
−0.466002 + 0.884783i \(0.654306\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 29.1246 21.1603i 1.50199 1.09126i
\(377\) 3.70820 + 11.4127i 0.190982 + 0.587783i
\(378\) 0 0
\(379\) −16.1803 11.7557i −0.831128 0.603850i 0.0887501 0.996054i \(-0.471713\pi\)
−0.919878 + 0.392204i \(0.871713\pi\)
\(380\) 3.23607 + 2.35114i 0.166007 + 0.120611i
\(381\) 0 0
\(382\) −2.47214 7.60845i −0.126485 0.389282i
\(383\) 9.70820 7.05342i 0.496066 0.360413i −0.311446 0.950264i \(-0.600813\pi\)
0.807512 + 0.589851i \(0.200813\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −26.0000 −1.32337
\(387\) −9.70820 + 7.05342i −0.493496 + 0.358546i
\(388\) −3.09017 9.51057i −0.156880 0.482826i
\(389\) 1.85410 5.70634i 0.0940067 0.289323i −0.892987 0.450083i \(-0.851394\pi\)
0.986994 + 0.160760i \(0.0513945\pi\)
\(390\) 0 0
\(391\) 19.4164 + 14.1068i 0.981930 + 0.713414i
\(392\) −6.48936 + 19.9722i −0.327762 + 1.00875i
\(393\) 0 0
\(394\) −1.61803 + 1.17557i −0.0815154 + 0.0592244i
\(395\) −8.00000 −0.402524
\(396\) 0 0
\(397\) 30.0000 1.50566 0.752828 0.658217i \(-0.228689\pi\)
0.752828 + 0.658217i \(0.228689\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.309017 + 0.951057i −0.0154508 + 0.0475528i
\(401\) −1.61803 1.17557i −0.0808008 0.0587052i 0.546652 0.837360i \(-0.315902\pi\)
−0.627452 + 0.778655i \(0.715902\pi\)
\(402\) 0 0
\(403\) 4.94427 15.2169i 0.246292 0.758008i
\(404\) −3.09017 9.51057i −0.153742 0.473168i
\(405\) −7.28115 + 5.29007i −0.361803 + 0.262866i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −4.85410 + 3.52671i −0.240020 + 0.174385i −0.701292 0.712874i \(-0.747393\pi\)
0.461272 + 0.887259i \(0.347393\pi\)
\(410\) 0.618034 + 1.90211i 0.0305225 + 0.0939387i
\(411\) 0 0
\(412\) −3.23607 2.35114i −0.159430 0.115832i
\(413\) 0 0
\(414\) 3.70820 11.4127i 0.182248 0.560903i
\(415\) 1.23607 + 3.80423i 0.0606762 + 0.186742i
\(416\) −8.09017 + 5.87785i −0.396653 + 0.288185i
\(417\) 0 0
\(418\) 0 0
\(419\) −28.0000 −1.36789 −0.683945 0.729534i \(-0.739737\pi\)
−0.683945 + 0.729534i \(0.739737\pi\)
\(420\) 0 0
\(421\) 1.85410 + 5.70634i 0.0903634 + 0.278110i 0.986018 0.166641i \(-0.0532921\pi\)
−0.895654 + 0.444751i \(0.853292\pi\)
\(422\) 1.23607 3.80423i 0.0601708 0.185187i
\(423\) −29.1246 21.1603i −1.41609 1.02885i
\(424\) 4.85410 + 3.52671i 0.235736 + 0.171272i
\(425\) −1.85410 + 5.70634i −0.0899372 + 0.276798i
\(426\) 0 0
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 4.00000 0.192897
\(431\) −19.4164 + 14.1068i −0.935255 + 0.679503i −0.947274 0.320425i \(-0.896174\pi\)
0.0120185 + 0.999928i \(0.496174\pi\)
\(432\) 0 0
\(433\) −6.79837 + 20.9232i −0.326709 + 1.00551i 0.643954 + 0.765064i \(0.277293\pi\)
−0.970663 + 0.240443i \(0.922707\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −5.56231 + 17.1190i −0.266386 + 0.819852i
\(437\) 4.94427 + 15.2169i 0.236517 + 0.727923i
\(438\) 0 0
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 0 0
\(441\) 21.0000 1.00000
\(442\) 9.70820 7.05342i 0.461772 0.335497i
\(443\) 2.47214 + 7.60845i 0.117455 + 0.361488i 0.992451 0.122641i \(-0.0391364\pi\)
−0.874996 + 0.484129i \(0.839136\pi\)
\(444\) 0 0
\(445\) −8.09017 5.87785i −0.383511 0.278637i
\(446\) −3.23607 2.35114i −0.153232 0.111330i
\(447\) 0 0
\(448\) 0 0
\(449\) −1.61803 + 1.17557i −0.0763597 + 0.0554786i −0.625310 0.780376i \(-0.715028\pi\)
0.548950 + 0.835855i \(0.315028\pi\)
\(450\) 3.00000 0.141421
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) 0 0
\(454\) −6.18034 19.0211i −0.290058 0.892706i
\(455\) 0 0
\(456\) 0 0
\(457\) −21.0344 15.2824i −0.983950 0.714881i −0.0253618 0.999678i \(-0.508074\pi\)
−0.958588 + 0.284797i \(0.908074\pi\)
\(458\) 3.09017 9.51057i 0.144394 0.444400i
\(459\) 0 0
\(460\) 3.23607 2.35114i 0.150882 0.109623i
\(461\) 34.0000 1.58354 0.791769 0.610821i \(-0.209160\pi\)
0.791769 + 0.610821i \(0.209160\pi\)
\(462\) 0 0
\(463\) −36.0000 −1.67306 −0.836531 0.547920i \(-0.815420\pi\)
−0.836531 + 0.547920i \(0.815420\pi\)
\(464\) −4.85410 + 3.52671i −0.225346 + 0.163723i
\(465\) 0 0
\(466\) 1.85410 5.70634i 0.0858896 0.264341i
\(467\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(468\) 4.85410 + 3.52671i 0.224381 + 0.163022i
\(469\) 0 0
\(470\) 3.70820 + 11.4127i 0.171047 + 0.526428i
\(471\) 0 0
\(472\) 12.0000 0.552345
\(473\) 0 0
\(474\) 0 0
\(475\) −3.23607 + 2.35114i −0.148481 + 0.107878i
\(476\) 0 0
\(477\) 1.85410 5.70634i 0.0848935 0.261275i
\(478\) −6.47214 4.70228i −0.296029 0.215077i
\(479\) 19.4164 + 14.1068i 0.887158 + 0.644558i 0.935136 0.354290i \(-0.115277\pi\)
−0.0479772 + 0.998848i \(0.515277\pi\)
\(480\) 0 0
\(481\) 1.23607 + 3.80423i 0.0563598 + 0.173458i
\(482\) −8.09017 + 5.87785i −0.368497 + 0.267729i
\(483\) 0 0
\(484\) 0 0
\(485\) 10.0000 0.454077
\(486\) 0 0
\(487\) 8.65248 + 26.6296i 0.392081 + 1.20670i 0.931212 + 0.364479i \(0.118753\pi\)
−0.539130 + 0.842222i \(0.681247\pi\)
\(488\) 9.27051 28.5317i 0.419656 1.29157i
\(489\) 0 0
\(490\) −5.66312 4.11450i −0.255834 0.185874i
\(491\) 8.65248 26.6296i 0.390481 1.20178i −0.541945 0.840414i \(-0.682312\pi\)
0.932426 0.361362i \(-0.117688\pi\)
\(492\) 0 0
\(493\) −29.1246 + 21.1603i −1.31171 + 0.953011i
\(494\) 8.00000 0.359937
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) 0 0
\(499\) −11.1246 + 34.2380i −0.498006 + 1.53270i 0.314213 + 0.949352i \(0.398259\pi\)
−0.812219 + 0.583352i \(0.801741\pi\)
\(500\) 0.809017 + 0.587785i 0.0361803 + 0.0262866i
\(501\) 0 0
\(502\) −3.70820 + 11.4127i −0.165505 + 0.509373i
\(503\) 4.94427 + 15.2169i 0.220454 + 0.678488i 0.998721 + 0.0505549i \(0.0160990\pi\)
−0.778267 + 0.627933i \(0.783901\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) 0 0
\(507\) 0 0
\(508\) −12.9443 + 9.40456i −0.574309 + 0.417260i
\(509\) 4.32624 + 13.3148i 0.191757 + 0.590168i 0.999999 + 0.00131729i \(0.000419307\pi\)
−0.808242 + 0.588850i \(0.799581\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −8.89919 6.46564i −0.393292 0.285744i
\(513\) 0 0
\(514\) −5.56231 17.1190i −0.245343 0.755087i
\(515\) 3.23607 2.35114i 0.142598 0.103604i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −1.85410 5.70634i −0.0813077 0.250240i
\(521\) −1.85410 + 5.70634i −0.0812297 + 0.249999i −0.983421 0.181337i \(-0.941958\pi\)
0.902191 + 0.431336i \(0.141958\pi\)
\(522\) 14.5623 + 10.5801i 0.637375 + 0.463080i
\(523\) −16.1803 11.7557i −0.707517 0.514041i 0.174855 0.984594i \(-0.444054\pi\)
−0.882372 + 0.470553i \(0.844054\pi\)
\(524\) −3.70820 + 11.4127i −0.161994 + 0.498565i
\(525\) 0 0
\(526\) −19.4164 + 14.1068i −0.846596 + 0.615088i
\(527\) 48.0000 2.09091
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) −1.61803 + 1.17557i −0.0702829 + 0.0510635i
\(531\) −3.70820 11.4127i −0.160922 0.495268i
\(532\) 0 0
\(533\) −3.23607 2.35114i −0.140170 0.101839i
\(534\) 0 0
\(535\) −3.70820 + 11.4127i −0.160320 + 0.493413i
\(536\) −14.8328 45.6507i −0.640680 1.97181i
\(537\) 0 0
\(538\) 18.0000 0.776035
\(539\) 0 0
\(540\) 0 0
\(541\) −27.5066 + 19.9847i −1.18260 + 0.859209i −0.992463 0.122548i \(-0.960893\pi\)
−0.190138 + 0.981757i \(0.560893\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −24.2705 17.6336i −1.04059 0.756033i
\(545\) −14.5623 10.5801i −0.623781 0.453203i
\(546\) 0 0
\(547\) −3.70820 11.4127i −0.158551 0.487971i 0.839952 0.542661i \(-0.182583\pi\)
−0.998503 + 0.0546898i \(0.982583\pi\)
\(548\) 14.5623 10.5801i 0.622071 0.451961i
\(549\) −30.0000 −1.28037
\(550\) 0 0
\(551\) −24.0000 −1.02243
\(552\) 0 0
\(553\) 0 0
\(554\) 3.09017 9.51057i 0.131289 0.404065i
\(555\) 0 0
\(556\) −9.70820 7.05342i −0.411720 0.299132i
\(557\) −3.09017 + 9.51057i −0.130935 + 0.402976i −0.994936 0.100515i \(-0.967951\pi\)
0.864001 + 0.503490i \(0.167951\pi\)
\(558\) −7.41641 22.8254i −0.313962 0.966274i
\(559\) −6.47214 + 4.70228i −0.273742 + 0.198885i
\(560\) 0 0
\(561\) 0 0
\(562\) 18.0000 0.759284
\(563\) 29.1246 21.1603i 1.22746 0.891799i 0.230759 0.973011i \(-0.425879\pi\)
0.996697 + 0.0812119i \(0.0258790\pi\)
\(564\) 0 0
\(565\) −1.85410 + 5.70634i −0.0780027 + 0.240067i
\(566\) −3.23607 2.35114i −0.136022 0.0988258i
\(567\) 0 0
\(568\) 7.41641 22.8254i 0.311186 0.957731i
\(569\) −8.03444 24.7275i −0.336821 1.03663i −0.965818 0.259221i \(-0.916534\pi\)
0.628997 0.777408i \(-0.283466\pi\)
\(570\) 0 0
\(571\) −36.0000 −1.50655 −0.753277 0.657704i \(-0.771528\pi\)
−0.753277 + 0.657704i \(0.771528\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.23607 + 3.80423i 0.0515476 + 0.158647i
\(576\) −6.48936 + 19.9722i −0.270390 + 0.832174i
\(577\) 17.7984 + 12.9313i 0.740956 + 0.538336i 0.893010 0.450036i \(-0.148589\pi\)
−0.152054 + 0.988372i \(0.548589\pi\)
\(578\) 15.3713 + 11.1679i 0.639363 + 0.464524i
\(579\) 0 0
\(580\) 1.85410 + 5.70634i 0.0769874 + 0.236943i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −42.0000 −1.73797
\(585\) −4.85410 + 3.52671i −0.200692 + 0.145812i
\(586\) 3.09017 + 9.51057i 0.127654 + 0.392878i
\(587\) −7.41641 + 22.8254i −0.306108 + 0.942103i 0.673154 + 0.739503i \(0.264939\pi\)
−0.979261 + 0.202601i \(0.935061\pi\)
\(588\) 0 0
\(589\) 25.8885 + 18.8091i 1.06672 + 0.775017i
\(590\) −1.23607 + 3.80423i −0.0508881 + 0.156618i
\(591\) 0 0
\(592\) −1.61803 + 1.17557i −0.0665008 + 0.0483157i
\(593\) −22.0000 −0.903432 −0.451716 0.892162i \(-0.649188\pi\)
−0.451716 + 0.892162i \(0.649188\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 8.09017 5.87785i 0.331386 0.240766i
\(597\) 0 0
\(598\) 2.47214 7.60845i 0.101093 0.311133i
\(599\) −19.4164 14.1068i −0.793333 0.576390i 0.115618 0.993294i \(-0.463115\pi\)
−0.908951 + 0.416904i \(0.863115\pi\)
\(600\) 0 0
\(601\) −0.618034 + 1.90211i −0.0252101 + 0.0775888i −0.962870 0.269965i \(-0.912988\pi\)
0.937660 + 0.347554i \(0.112988\pi\)
\(602\) 0 0
\(603\) −38.8328 + 28.2137i −1.58139 + 1.14895i
\(604\) 8.00000 0.325515
\(605\) 0 0
\(606\) 0 0
\(607\) −25.8885 + 18.8091i −1.05078 + 0.763439i −0.972361 0.233481i \(-0.924988\pi\)
−0.0784223 + 0.996920i \(0.524988\pi\)
\(608\) −6.18034 19.0211i −0.250646 0.771409i
\(609\) 0 0
\(610\) 8.09017 + 5.87785i 0.327561 + 0.237987i
\(611\) −19.4164 14.1068i −0.785504 0.570702i
\(612\) −5.56231 + 17.1190i −0.224843 + 0.691995i
\(613\) −10.5066 32.3359i −0.424357 1.30604i −0.903609 0.428358i \(-0.859092\pi\)
0.479252 0.877677i \(-0.340908\pi\)
\(614\) −16.1803 + 11.7557i −0.652985 + 0.474422i
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000 0.0805170 0.0402585 0.999189i \(-0.487182\pi\)
0.0402585 + 0.999189i \(0.487182\pi\)
\(618\) 0 0
\(619\) −6.18034 19.0211i −0.248409 0.764524i −0.995057 0.0993047i \(-0.968338\pi\)
0.746648 0.665219i \(-0.231662\pi\)
\(620\) 2.47214 7.60845i 0.0992834 0.305563i
\(621\) 0 0
\(622\) −19.4164 14.1068i −0.778527 0.565633i
\(623\) 0 0
\(624\) 0 0
\(625\) −0.809017 + 0.587785i −0.0323607 + 0.0235114i
\(626\) 22.0000 0.879297
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) −9.70820 + 7.05342i −0.387091 + 0.281238i
\(630\) 0 0
\(631\) 12.3607 38.0423i 0.492071 1.51444i −0.329401 0.944190i \(-0.606847\pi\)
0.821472 0.570248i \(-0.193153\pi\)
\(632\) 19.4164 + 14.1068i 0.772343 + 0.561140i
\(633\) 0 0
\(634\) 5.56231 17.1190i 0.220907 0.679883i
\(635\) −4.94427 15.2169i −0.196207 0.603864i
\(636\) 0 0
\(637\) 14.0000 0.554700
\(638\) 0 0
\(639\) −24.0000 −0.949425
\(640\) −2.42705 + 1.76336i −0.0959376 + 0.0697028i
\(641\) 10.5066 + 32.3359i 0.414985 + 1.27719i 0.912264 + 0.409602i \(0.134332\pi\)
−0.497280 + 0.867590i \(0.665668\pi\)
\(642\) 0 0
\(643\) 12.9443 + 9.40456i 0.510472 + 0.370880i 0.813003 0.582260i \(-0.197831\pi\)
−0.302530 + 0.953140i \(0.597831\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 7.41641 + 22.8254i 0.291795 + 0.898052i
\(647\) −16.1803 + 11.7557i −0.636115 + 0.462164i −0.858513 0.512791i \(-0.828611\pi\)
0.222398 + 0.974956i \(0.428611\pi\)
\(648\) 27.0000 1.06066
\(649\) 0 0
\(650\) 2.00000 0.0784465
\(651\) 0 0
\(652\) −4.94427 15.2169i −0.193633 0.595940i
\(653\) −3.09017 + 9.51057i −0.120928 + 0.372177i −0.993137 0.116955i \(-0.962687\pi\)
0.872209 + 0.489133i \(0.162687\pi\)
\(654\) 0 0
\(655\) −9.70820 7.05342i −0.379331 0.275600i
\(656\) 0.618034 1.90211i 0.0241302 0.0742650i
\(657\) 12.9787 + 39.9444i 0.506348 + 1.55838i
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −10.0000 −0.388955 −0.194477 0.980907i \(-0.562301\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(662\) 3.23607 2.35114i 0.125773 0.0913797i
\(663\) 0 0
\(664\) 3.70820 11.4127i 0.143906 0.442898i
\(665\) 0 0
\(666\) 4.85410 + 3.52671i 0.188093 + 0.136657i
\(667\) −7.41641 + 22.8254i −0.287164 + 0.883801i
\(668\) −2.47214 7.60845i −0.0956498 0.294380i
\(669\) 0 0
\(670\) 16.0000 0.618134
\(671\) 0 0
\(672\) 0 0
\(673\) −21.0344 + 15.2824i −0.810818 + 0.589094i −0.914068 0.405562i \(-0.867076\pi\)
0.103250 + 0.994655i \(0.467076\pi\)
\(674\) 1.85410 + 5.70634i 0.0714173 + 0.219800i
\(675\) 0 0
\(676\) −7.28115 5.29007i −0.280044 0.203464i
\(677\) −30.7426 22.3358i −1.18154 0.858436i −0.189192 0.981940i \(-0.560587\pi\)
−0.992344 + 0.123504i \(0.960587\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 14.5623 10.5801i 0.558439 0.405730i
\(681\) 0 0
\(682\) 0 0
\(683\) −16.0000 −0.612223 −0.306111 0.951996i \(-0.599028\pi\)
−0.306111 + 0.951996i \(0.599028\pi\)
\(684\) −9.70820 + 7.05342i −0.371202 + 0.269694i
\(685\) 5.56231 + 17.1190i 0.212525 + 0.654084i
\(686\) 0 0
\(687\) 0 0
\(688\) −3.23607 2.35114i −0.123374 0.0896364i
\(689\) 1.23607 3.80423i 0.0470904 0.144929i
\(690\) 0 0
\(691\) 22.6525 16.4580i 0.861741 0.626091i −0.0666172 0.997779i \(-0.521221\pi\)
0.928358 + 0.371687i \(0.121221\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −4.00000 −0.151838
\(695\) 9.70820 7.05342i 0.368253 0.267552i
\(696\) 0 0
\(697\) 3.70820 11.4127i 0.140458 0.432286i
\(698\) 8.09017 + 5.87785i 0.306217 + 0.222480i
\(699\) 0 0
\(700\) 0 0
\(701\) −6.79837 20.9232i −0.256771 0.790260i −0.993476 0.114045i \(-0.963619\pi\)
0.736705 0.676215i \(-0.236381\pi\)
\(702\) 0 0
\(703\) −8.00000 −0.301726
\(704\) 0 0
\(705\) 0 0
\(706\) 14.5623 10.5801i 0.548060 0.398189i
\(707\) 0 0
\(708\) 0 0
\(709\) 8.09017 + 5.87785i 0.303833 + 0.220747i 0.729246 0.684252i \(-0.239871\pi\)
−0.425413 + 0.904999i \(0.639871\pi\)
\(710\) 6.47214 + 4.70228i 0.242895 + 0.176473i
\(711\) 7.41641 22.8254i 0.278137 0.856018i
\(712\) 9.27051 + 28.5317i 0.347427 + 1.06927i
\(713\) 25.8885 18.8091i 0.969534 0.704407i
\(714\) 0 0
\(715\) 0 0
\(716\) −4.00000 −0.149487
\(717\) 0 0
\(718\) −9.88854 30.4338i −0.369037 1.13578i
\(719\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(720\) −2.42705 1.76336i −0.0904508 0.0657164i
\(721\) 0 0
\(722\) 0.927051 2.85317i 0.0345013 0.106184i
\(723\) 0 0
\(724\) −8.09017 + 5.87785i −0.300669 + 0.218449i
\(725\) −6.00000 −0.222834
\(726\) 0 0
\(727\) 52.0000 1.92857 0.964287 0.264861i \(-0.0853260\pi\)
0.964287 + 0.264861i \(0.0853260\pi\)
\(728\) 0 0
\(729\) −8.34346 25.6785i −0.309017 0.951057i
\(730\) 4.32624 13.3148i 0.160121 0.492803i
\(731\) −19.4164 14.1068i −0.718142 0.521761i
\(732\) 0 0
\(733\) −12.9787 + 39.9444i −0.479380 + 1.47538i 0.360579 + 0.932729i \(0.382579\pi\)
−0.839959 + 0.542650i \(0.817421\pi\)
\(734\) −1.23607 3.80423i −0.0456241 0.140417i
\(735\) 0 0
\(736\) −20.0000 −0.737210
\(737\) 0 0
\(738\) −6.00000 −0.220863
\(739\) 3.23607 2.35114i 0.119041 0.0864881i −0.526672 0.850069i \(-0.676560\pi\)
0.645713 + 0.763580i \(0.276560\pi\)
\(740\) 0.618034 + 1.90211i 0.0227194 + 0.0699231i
\(741\) 0 0
\(742\) 0 0
\(743\) 32.3607 + 23.5114i 1.18720 + 0.862550i 0.992965 0.118405i \(-0.0377783\pi\)
0.194233 + 0.980955i \(0.437778\pi\)
\(744\) 0 0
\(745\) 3.09017 + 9.51057i 0.113215 + 0.348440i
\(746\) −14.5623 + 10.5801i −0.533164 + 0.387366i
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 4.94427 + 15.2169i 0.180419 + 0.555273i 0.999839 0.0179203i \(-0.00570452\pi\)
−0.819420 + 0.573193i \(0.805705\pi\)
\(752\) 3.70820 11.4127i 0.135224 0.416178i
\(753\) 0 0
\(754\) 9.70820 + 7.05342i 0.353552 + 0.256871i
\(755\) −2.47214 + 7.60845i −0.0899702 + 0.276900i
\(756\) 0 0
\(757\) −4.85410 + 3.52671i −0.176425 + 0.128181i −0.672493 0.740103i \(-0.734777\pi\)
0.496068 + 0.868284i \(0.334777\pi\)
\(758\) −20.0000 −0.726433
\(759\) 0 0
\(760\) 12.0000 0.435286
\(761\) 8.09017 5.87785i 0.293268 0.213072i −0.431416 0.902153i \(-0.641986\pi\)
0.724684 + 0.689081i \(0.241986\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 6.47214 + 4.70228i 0.234154 + 0.170123i
\(765\) −14.5623 10.5801i −0.526501 0.382526i
\(766\) 3.70820 11.4127i 0.133983 0.412357i
\(767\) −2.47214 7.60845i −0.0892637 0.274725i
\(768\) 0 0
\(769\) 22.0000 0.793340 0.396670 0.917961i \(-0.370166\pi\)
0.396670 + 0.917961i \(0.370166\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 21.0344 15.2824i 0.757046 0.550026i
\(773\) 4.32624 + 13.3148i 0.155604 + 0.478900i 0.998222 0.0596126i \(-0.0189865\pi\)
−0.842618 + 0.538512i \(0.818987\pi\)
\(774\) −3.70820 + 11.4127i −0.133289 + 0.410220i
\(775\) 6.47214 + 4.70228i 0.232486 + 0.168911i
\(776\) −24.2705 17.6336i −0.871261 0.633008i
\(777\) 0 0
\(778\) −1.85410 5.70634i −0.0664728 0.204582i
\(779\) 6.47214 4.70228i 0.231888 0.168477i
\(780\) 0 0
\(781\) 0 0
\(782\) 24.0000 0.858238
\(783\) 0 0
\(784\) 2.16312 + 6.65740i 0.0772542 + 0.237764i
\(785\) −0.618034 + 1.90211i −0.0220586 + 0.0678893i
\(786\) 0 0
\(787\) 42.0689 + 30.5648i 1.49959 + 1.08952i 0.970543 + 0.240929i \(0.0774519\pi\)
0.529051 + 0.848590i \(0.322548\pi\)
\(788\) 0.618034 1.90211i 0.0220165 0.0677600i
\(789\) 0 0
\(790\) −6.47214 +