Properties

Label 605.2.g.a.81.1
Level $605$
Weight $2$
Character 605.81
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 81.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 605.81
Dual form 605.2.g.a.366.1

$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

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

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 \(-0.415027\pi\)
−0.835853 + 0.548953i \(0.815027\pi\)
\(3\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(4\) −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 \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(8\) −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 \(-0.389456\pi\)
−0.789107 + 0.614256i \(0.789456\pi\)
\(14\) 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 \(-0.959367\pi\)
−0.185429 + 0.982658i \(0.559367\pi\)
\(18\) −0.927051 2.85317i −0.218508 0.672499i
\(19\) −1.23607 + 3.80423i −0.283573 + 0.872749i 0.703249 + 0.710943i \(0.251732\pi\)
−0.986823 + 0.161806i \(0.948268\pi\)
\(20\) 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 0.961958 + 0.273196i \(0.0880806\pi\)
−0.617660 + 0.786445i \(0.711919\pi\)
\(30\) 0 0
\(31\) 6.47214 + 4.70228i 1.16243 + 0.844555i 0.990083 0.140482i \(-0.0448651\pi\)
0.172347 + 0.985036i \(0.444865\pi\)
\(32\) 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 0.887314 0.461165i \(-0.152568\pi\)
−0.988918 + 0.148460i \(0.952568\pi\)
\(38\) 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 \(-0.850084\pi\)
0.987647 + 0.156695i \(0.0500840\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 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 0.189653 + 0.981851i \(0.439264\pi\)
−0.730550 + 0.682859i \(0.760736\pi\)
\(48\) 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 0.693341 0.720610i \(-0.256138\pi\)
−0.471087 + 0.882087i \(0.656138\pi\)
\(54\) 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 0.998713 0.0507240i \(-0.0161529\pi\)
−0.837790 + 0.545992i \(0.816153\pi\)
\(60\) 0 0
\(61\) 8.09017 5.87785i 1.03584 0.752582i 0.0663709 0.997795i \(-0.478858\pi\)
0.969469 + 0.245213i \(0.0788579\pi\)
\(62\) −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 −0.901384 0.433020i \(-0.857448\pi\)
0.133283 + 0.991078i \(0.457448\pi\)
\(72\) −7.28115 + 5.29007i −0.858092 + 0.623440i
\(73\) 4.32624 + 13.3148i 0.506348 + 1.55838i 0.798493 + 0.602004i \(0.205631\pi\)
−0.292145 + 0.956374i \(0.594369\pi\)
\(74\) −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 \(-0.448589\pi\)
−0.888985 + 0.457937i \(0.848589\pi\)
\(80\) −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 \(-0.629548\pi\)
0.751049 + 0.660246i \(0.229548\pi\)
\(84\) 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 0.0956901 0.995411i \(-0.469494\pi\)
−0.917122 + 0.398606i \(0.869494\pi\)
\(98\) −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 \(-0.134245\pi\)
−0.107375 + 0.994219i \(0.534245\pi\)
\(102\) 0 0
\(103\) −1.23607 3.80423i −0.121793 0.374842i 0.871510 0.490378i \(-0.163141\pi\)
−0.993303 + 0.115536i \(0.963141\pi\)
\(104\) 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 −0.595475 0.803374i \(-0.703036\pi\)
0.953961 0.299932i \(-0.0969638\pi\)
\(108\) 0 0
\(109\) −18.0000 −1.72409 −0.862044 0.506834i \(-0.830816\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.85410 + 5.70634i −0.174419 + 0.536807i −0.999606 0.0280521i \(-0.991070\pi\)
0.825187 + 0.564859i \(0.191070\pi\)
\(114\) 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 \(-0.951253\pi\)
−0.160322 + 0.987065i \(0.551253\pi\)
\(128\) −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 \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 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 −0.997867 0.0652782i \(-0.979207\pi\)
−0.246275 + 0.969200i \(0.579207\pi\)
\(138\) 0 0
\(139\) 3.70820 + 11.4127i 0.314526 + 0.968011i 0.975949 + 0.217998i \(0.0699526\pi\)
−0.661423 + 0.750013i \(0.730047\pi\)
\(140\) 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 \(-0.565663\pi\)
0.867598 + 0.497266i \(0.165663\pi\)
\(150\) 0 0
\(151\) 2.47214 7.60845i 0.201180 0.619167i −0.798669 0.601770i \(-0.794462\pi\)
0.999849 0.0173966i \(-0.00553779\pi\)
\(152\) −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 −0.972685 0.232129i \(-0.925431\pi\)
0.923361 + 0.383934i \(0.125431\pi\)
\(158\) 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 −0.0488556 0.998806i \(-0.515557\pi\)
−0.965018 + 0.262184i \(0.915557\pi\)
\(164\) −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 \(-0.199829\pi\)
−0.308505 + 0.951223i \(0.599829\pi\)
\(168\) 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 \(-0.973247\pi\)
0.855505 + 0.517794i \(0.173247\pi\)
\(174\) 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 −0.894176 0.447715i \(-0.852238\pi\)
0.986564 + 0.163374i \(0.0522378\pi\)
\(180\) 0.927051 + 2.85317i 0.0690983 + 0.212663i
\(181\) 8.09017 5.87785i 0.601338 0.436897i −0.245016 0.969519i \(-0.578793\pi\)
0.846353 + 0.532622i \(0.178793\pi\)
\(182\) 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 0.999789 0.0205267i \(-0.00653431\pi\)
−0.820912 + 0.571055i \(0.806534\pi\)
\(192\) 0 0
\(193\) 21.0344 15.2824i 1.51409 1.10005i 0.549772 0.835315i \(-0.314715\pi\)
0.964321 0.264737i \(-0.0852853\pi\)
\(194\) 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 \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 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 \(-0.343966\pi\)
−0.693577 + 0.720382i \(0.743966\pi\)
\(212\) 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 −0.983875 0.178858i \(-0.942760\pi\)
0.901102 + 0.433608i \(0.142760\pi\)
\(224\) 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 −0.916471 0.400100i \(-0.868975\pi\)
0.506268 0.862376i \(-0.331025\pi\)
\(228\) 0 0
\(229\) 8.09017 + 5.87785i 0.534613 + 0.388419i 0.822081 0.569371i \(-0.192813\pi\)
−0.287467 + 0.957790i \(0.592813\pi\)
\(230\) 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 \(-0.362969\pi\)
−0.735323 + 0.677717i \(0.762969\pi\)
\(234\) −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 \(-0.816693\pi\)
0.998625 + 0.0524192i \(0.0166932\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 0 0
\(243\) 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 0.237614 0.971360i \(-0.423635\pi\)
−0.850391 + 0.526151i \(0.823635\pi\)
\(252\) 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 0.960522 + 0.278203i \(0.0897388\pi\)
−0.613555 + 0.789652i \(0.710261\pi\)
\(258\) 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 \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 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 −0.0474448 0.998874i \(-0.515108\pi\)
0.935324 + 0.353792i \(0.115108\pi\)
\(270\) 0 0
\(271\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(272\) −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 \(-0.397127\pi\)
−0.803679 + 0.595063i \(0.797127\pi\)
\(278\) 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 \(-0.880403\pi\)
0.0615273 + 0.998105i \(0.480403\pi\)
\(282\) 0 0
\(283\) 1.23607 3.80423i 0.0734766 0.226138i −0.907573 0.419894i \(-0.862067\pi\)
0.981050 + 0.193756i \(0.0620672\pi\)
\(284\) 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 \(-0.00564495\pi\)
−0.819313 + 0.573346i \(0.805645\pi\)
\(294\) 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 \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 6.47214 + 4.70228i 0.367593 + 0.267072i
\(311\) −7.41641 + 22.8254i −0.420546 + 1.29431i 0.486649 + 0.873597i \(0.338219\pi\)
−0.907195 + 0.420710i \(0.861781\pi\)
\(312\) 0 0
\(313\) 17.7984 12.9313i 1.00602 0.730919i 0.0426523 0.999090i \(-0.486419\pi\)
0.963371 + 0.268171i \(0.0864192\pi\)
\(314\) 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 0.916110 0.400926i \(-0.131312\pi\)
−0.0982098 + 0.995166i \(0.531312\pi\)
\(318\) 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 \(-0.0477473\pi\)
−0.887771 + 0.460285i \(0.847747\pi\)
\(338\) −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 \(-0.665758\pi\)
0.671248 + 0.741233i \(0.265758\pi\)
\(348\) 0 0
\(349\) −3.09017 + 9.51057i −0.165413 + 0.509089i −0.999066 0.0431990i \(-0.986245\pi\)
0.833653 + 0.552288i \(0.186245\pi\)
\(350\) 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 −0.770371 0.637596i \(-0.779929\pi\)
0.248473 0.968639i \(-0.420071\pi\)
\(360\) 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 0.978121 0.208039i \(-0.0667081\pi\)
−0.913598 + 0.406618i \(0.866708\pi\)
\(368\) 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 \(-0.345694\pi\)
0.466002 + 0.884783i \(0.345694\pi\)
\(374\) 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 −0.919878 0.392204i \(-0.871713\pi\)
0.0887501 + 0.996054i \(0.471713\pi\)
\(380\) −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 0.807512 0.589851i \(-0.200813\pi\)
−0.311446 + 0.950264i \(0.600813\pi\)
\(384\) 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 0.986994 0.160760i \(-0.0513945\pi\)
−0.892987 + 0.450083i \(0.851394\pi\)
\(390\) 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 −0.627452 0.778655i \(-0.715902\pi\)
0.546652 + 0.837360i \(0.315902\pi\)
\(402\) 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 \(-0.252607\pi\)
−0.461272 + 0.887259i \(0.652607\pi\)
\(410\) 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 −0.895654 0.444751i \(-0.853292\pi\)
0.986018 + 0.166641i \(0.0532921\pi\)
\(422\) 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 \(-0.103826\pi\)
−0.0120185 + 0.999928i \(0.503826\pi\)
\(432\) 0 0
\(433\) −6.79837 20.9232i −0.326709 1.00551i −0.970663 0.240443i \(-0.922707\pi\)
0.643954 0.765064i \(-0.277293\pi\)
\(434\) 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 \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 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 −0.874996 0.484129i \(-0.839136\pi\)
0.992451 + 0.122641i \(0.0391364\pi\)
\(444\) 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 0.548950 0.835855i \(-0.315028\pi\)
−0.625310 + 0.780376i \(0.715028\pi\)
\(450\) −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 \(-0.491926\pi\)
0.958588 + 0.284797i \(0.0919262\pi\)
\(458\) −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 \(-0.790840\pi\)
−0.791769 + 0.610821i \(0.790840\pi\)
\(462\) 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 \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(468\) −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 \(-0.884723\pi\)
0.0479772 + 0.998848i \(0.484723\pi\)
\(480\) 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 −0.539130 0.842222i \(-0.681247\pi\)
0.931212 0.364479i \(-0.118753\pi\)
\(488\) 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 −0.932426 0.361362i \(-0.882312\pi\)
0.541945 0.840414i \(-0.317688\pi\)
\(492\) 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 −0.812219 0.583352i \(-0.801741\pi\)
0.314213 0.949352i \(-0.398259\pi\)
\(500\) 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 0.778267 + 0.627933i \(0.216099\pi\)
−0.998721 + 0.0505549i \(0.983901\pi\)
\(504\) 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 −0.808242 0.588850i \(-0.799581\pi\)
0.999999 0.00131729i \(-0.000419307\pi\)
\(510\) 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 0.902191 0.431336i \(-0.141958\pi\)
−0.983421 + 0.181337i \(0.941958\pi\)
\(522\) 14.5623 10.5801i 0.637375 0.463080i
\(523\) 16.1803 11.7557i 0.707517 0.514041i −0.174855 0.984594i \(-0.555946\pi\)
0.882372 + 0.470553i \(0.155946\pi\)
\(524\) 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 \(-0.0391066\pi\)
0.190138 + 0.981757i \(0.439107\pi\)
\(542\) 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 \(-0.817417\pi\)
0.998503 + 0.0546898i \(0.0174170\pi\)
\(548\) 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 \(-0.0320490\pi\)
−0.864001 + 0.503490i \(0.832049\pi\)
\(558\) 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 \(-0.574121\pi\)
−0.996697 + 0.0812119i \(0.974121\pi\)
\(564\) 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 −0.628997 0.777408i \(-0.716534\pi\)
0.965818 0.259221i \(-0.0834659\pi\)
\(570\) 0 0
\(571\) 36.0000 1.50655 0.753277 0.657704i \(-0.228472\pi\)
0.753277 + 0.657704i \(0.228472\pi\)
\(572\) 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 −0.152054 0.988372i \(-0.548589\pi\)
0.893010 + 0.450036i \(0.148589\pi\)
\(578\) −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 −0.979261 0.202601i \(-0.935061\pi\)
0.673154 0.739503i \(-0.264939\pi\)
\(588\) 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 \(-0.350812\pi\)
0.451716 + 0.892162i \(0.350812\pi\)
\(594\) 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 −0.908951 0.416904i \(-0.863115\pi\)
0.115618 + 0.993294i \(0.463115\pi\)
\(600\) 0 0
\(601\) 0.618034 + 1.90211i 0.0252101 + 0.0775888i 0.962870 0.269965i \(-0.0870123\pi\)
−0.937660 + 0.347554i \(0.887012\pi\)
\(602\) 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 \(-0.0750118\pi\)
0.0784223 + 0.996920i \(0.475012\pi\)
\(608\) −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 −0.479252 0.877677i \(-0.659092\pi\)
0.903609 0.428358i \(-0.140908\pi\)
\(614\) −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 0.746648 + 0.665219i \(0.231662\pi\)
−0.995057 + 0.0993047i \(0.968338\pi\)
\(620\) 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 0.821472 + 0.570248i \(0.193153\pi\)
−0.329401 + 0.944190i \(0.606847\pi\)
\(632\) 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 −0.497280 0.867590i \(-0.665668\pi\)
0.912264 0.409602i \(-0.134332\pi\)
\(642\) 0 0
\(643\) 12.9443 9.40456i 0.510472 0.370880i −0.302530 0.953140i \(-0.597831\pi\)
0.813003 + 0.582260i \(0.197831\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −7.41641 + 22.8254i −0.291795 + 0.898052i
\(647\) −16.1803 11.7557i −0.636115 0.462164i 0.222398 0.974956i \(-0.428611\pi\)
−0.858513 + 0.512791i \(0.828611\pi\)
\(648\) −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 0.872209 0.489133i \(-0.162687\pi\)
−0.993137 + 0.116955i \(0.962687\pi\)
\(654\) 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 \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 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 \(-0.132924\pi\)
−0.103250 + 0.994655i \(0.532924\pi\)
\(674\) 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 \(-0.439413\pi\)
0.992344 + 0.123504i \(0.0394132\pi\)
\(678\) 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 0.928358 0.371687i \(-0.121221\pi\)
−0.0666172 + 0.997779i \(0.521221\pi\)
\(692\) 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 −0.736705 0.676215i \(-0.763619\pi\)
0.993476 0.114045i \(-0.0363809\pi\)
\(702\) 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 −0.425413 0.904999i \(-0.639871\pi\)
0.729246 + 0.684252i \(0.239871\pi\)
\(710\) −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 \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(720\) −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 0.839959 + 0.542650i \(0.182579\pi\)
−0.360579 + 0.932729i \(0.617421\pi\)
\(734\) 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 \(-0.323440\pi\)
−0.645713 + 0.763580i \(0.723440\pi\)
\(740\) 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 \(-0.962222\pi\)
−0.194233 + 0.980955i \(0.562222\pi\)
\(744\) 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 −0.819420 0.573193i \(-0.805705\pi\)
0.999839 + 0.0179203i \(0.00570452\pi\)
\(752\) 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 0.496068 0.868284i \(-0.334777\pi\)
−0.672493 + 0.740103i \(0.734777\pi\)
\(758\) 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 \(-0.358014\pi\)
−0.724684 + 0.689081i \(0.758014\pi\)
\(762\) 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 \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −21.0344 15.2824i −0.757046 0.550026i
\(773\) 4.32624 13.3148i 0.155604 0.478900i −0.842618 0.538512i \(-0.818987\pi\)
0.998222 + 0.0596126i \(0.0189865\pi\)
\(774\) −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 −0.529051 + 0.848590i \(0.677452\pi\)
−0.970543 + 0.240929i \(0.922548\pi\)
\(788\) −0.618034 1.90211i −0.0220165 0.0677600i
\(789\) 0 0