Properties

Label 605.2.g.a.511.1
Level $605$
Weight $2$
Character 605.511
Analytic conductor $4.831$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 511.1
Root \(-0.309017 + 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 605.511
Dual form 605.2.g.a.251.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(2.42705 + 1.76336i) q^{8} +(-0.927051 - 2.85317i) q^{9} +O(q^{10})\) \(q+(0.309017 + 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(2.42705 + 1.76336i) q^{8} +(-0.927051 - 2.85317i) q^{9} +1.00000 q^{10} +(0.618034 + 1.90211i) q^{13} +(-0.309017 + 0.951057i) q^{16} +(1.85410 - 5.70634i) q^{17} +(2.42705 - 1.76336i) q^{18} +(3.23607 + 2.35114i) q^{19} +(-0.309017 - 0.951057i) q^{20} +4.00000 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-1.61803 + 1.17557i) q^{26} +(-4.85410 + 3.52671i) q^{29} +(-2.47214 - 7.60845i) q^{31} +5.00000 q^{32} +6.00000 q^{34} +(-2.42705 - 1.76336i) q^{36} +(1.61803 - 1.17557i) q^{37} +(-1.23607 + 3.80423i) q^{38} +(2.42705 - 1.76336i) q^{40} +(-1.61803 - 1.17557i) q^{41} +4.00000 q^{43} -3.00000 q^{45} +(1.23607 + 3.80423i) q^{46} +(9.70820 + 7.05342i) q^{47} +(-2.16312 + 6.65740i) q^{49} +(0.309017 - 0.951057i) q^{50} +(1.61803 + 1.17557i) q^{52} +(-0.618034 - 1.90211i) q^{53} +(-4.85410 - 3.52671i) q^{58} +(-3.23607 + 2.35114i) q^{59} +(-3.09017 + 9.51057i) q^{61} +(6.47214 - 4.70228i) q^{62} +(2.16312 + 6.65740i) q^{64} +2.00000 q^{65} -16.0000 q^{67} +(-1.85410 - 5.70634i) q^{68} +(2.47214 - 7.60845i) q^{71} +(2.78115 - 8.55951i) q^{72} +(-11.3262 + 8.22899i) q^{73} +(1.61803 + 1.17557i) q^{74} +4.00000 q^{76} +(2.47214 + 7.60845i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(0.618034 - 1.90211i) q^{82} +(-1.23607 + 3.80423i) q^{83} +(-4.85410 - 3.52671i) q^{85} +(1.23607 + 3.80423i) q^{86} +10.0000 q^{89} +(-0.927051 - 2.85317i) q^{90} +(3.23607 - 2.35114i) q^{92} +(-3.70820 + 11.4127i) q^{94} +(3.23607 - 2.35114i) q^{95} +(3.09017 + 9.51057i) q^{97} -7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} + q^{4} - q^{5} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 + 0.951057i 0.218508 + 0.672499i 0.998886 + 0.0471903i \(0.0150267\pi\)
−0.780378 + 0.625308i \(0.784973\pi\)
\(3\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(4\) 0.809017 0.587785i 0.404508 0.293893i
\(5\) 0.309017 0.951057i 0.138197 0.425325i
\(6\) 0 0
\(7\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(8\) 2.42705 + 1.76336i 0.858092 + 0.623440i
\(9\) −0.927051 2.85317i −0.309017 0.951057i
\(10\) 1.00000 0.316228
\(11\) 0 0
\(12\) 0 0
\(13\) 0.618034 + 1.90211i 0.171412 + 0.527551i 0.999451 0.0331183i \(-0.0105438\pi\)
−0.828040 + 0.560670i \(0.810544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) 1.85410 5.70634i 0.449686 1.38399i −0.427576 0.903979i \(-0.640633\pi\)
0.877262 0.480011i \(-0.159367\pi\)
\(18\) 2.42705 1.76336i 0.572061 0.415627i
\(19\) 3.23607 + 2.35114i 0.742405 + 0.539389i 0.893463 0.449136i \(-0.148268\pi\)
−0.151058 + 0.988525i \(0.548268\pi\)
\(20\) −0.309017 0.951057i −0.0690983 0.212663i
\(21\) 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
\(25\) −0.809017 0.587785i −0.161803 0.117557i
\(26\) −1.61803 + 1.17557i −0.317323 + 0.230548i
\(27\) 0 0
\(28\) 0 0
\(29\) −4.85410 + 3.52671i −0.901384 + 0.654894i −0.938821 0.344405i \(-0.888081\pi\)
0.0374370 + 0.999299i \(0.488081\pi\)
\(30\) 0 0
\(31\) −2.47214 7.60845i −0.444009 1.36652i −0.883567 0.468304i \(-0.844865\pi\)
0.439558 0.898214i \(-0.355135\pi\)
\(32\) 5.00000 0.883883
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) −2.42705 1.76336i −0.404508 0.293893i
\(37\) 1.61803 1.17557i 0.266003 0.193263i −0.446786 0.894641i \(-0.647432\pi\)
0.712789 + 0.701378i \(0.247432\pi\)
\(38\) −1.23607 + 3.80423i −0.200517 + 0.617127i
\(39\) 0 0
\(40\) 2.42705 1.76336i 0.383750 0.278811i
\(41\) −1.61803 1.17557i −0.252694 0.183593i 0.454226 0.890887i \(-0.349916\pi\)
−0.706920 + 0.707293i \(0.749916\pi\)
\(42\) 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
\(46\) 1.23607 + 3.80423i 0.182248 + 0.560903i
\(47\) 9.70820 + 7.05342i 1.41609 + 1.02885i 0.992402 + 0.123038i \(0.0392637\pi\)
0.423685 + 0.905810i \(0.360736\pi\)
\(48\) 0 0
\(49\) −2.16312 + 6.65740i −0.309017 + 0.951057i
\(50\) 0.309017 0.951057i 0.0437016 0.134500i
\(51\) 0 0
\(52\) 1.61803 + 1.17557i 0.224381 + 0.163022i
\(53\) −0.618034 1.90211i −0.0848935 0.261275i 0.899595 0.436726i \(-0.143862\pi\)
−0.984488 + 0.175450i \(0.943862\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −4.85410 3.52671i −0.637375 0.463080i
\(59\) −3.23607 + 2.35114i −0.421300 + 0.306092i −0.778161 0.628065i \(-0.783847\pi\)
0.356861 + 0.934158i \(0.383847\pi\)
\(60\) 0 0
\(61\) −3.09017 + 9.51057i −0.395656 + 1.21770i 0.532794 + 0.846245i \(0.321142\pi\)
−0.928450 + 0.371458i \(0.878858\pi\)
\(62\) 6.47214 4.70228i 0.821962 0.597190i
\(63\) 0 0
\(64\) 2.16312 + 6.65740i 0.270390 + 0.832174i
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) −16.0000 −1.95471 −0.977356 0.211604i \(-0.932131\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) −1.85410 5.70634i −0.224843 0.691995i
\(69\) 0 0
\(70\) 0 0
\(71\) 2.47214 7.60845i 0.293389 0.902957i −0.690369 0.723457i \(-0.742552\pi\)
0.983758 0.179500i \(-0.0574480\pi\)
\(72\) 2.78115 8.55951i 0.327762 1.00875i
\(73\) −11.3262 + 8.22899i −1.32564 + 0.963131i −0.325792 + 0.945441i \(0.605631\pi\)
−0.999844 + 0.0176895i \(0.994369\pi\)
\(74\) 1.61803 + 1.17557i 0.188093 + 0.136657i
\(75\) 0 0
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 0 0
\(79\) 2.47214 + 7.60845i 0.278137 + 0.856018i 0.988372 + 0.152053i \(0.0485886\pi\)
−0.710235 + 0.703964i \(0.751411\pi\)
\(80\) 0.809017 + 0.587785i 0.0904508 + 0.0657164i
\(81\) −7.28115 + 5.29007i −0.809017 + 0.587785i
\(82\) 0.618034 1.90211i 0.0682504 0.210053i
\(83\) −1.23607 + 3.80423i −0.135676 + 0.417568i −0.995695 0.0926948i \(-0.970452\pi\)
0.860018 + 0.510263i \(0.170452\pi\)
\(84\) 0 0
\(85\) −4.85410 3.52671i −0.526501 0.382526i
\(86\) 1.23607 + 3.80423i 0.133289 + 0.410220i
\(87\) 0 0
\(88\) 0 0
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) −0.927051 2.85317i −0.0977198 0.300750i
\(91\) 0 0
\(92\) 3.23607 2.35114i 0.337383 0.245123i
\(93\) 0 0
\(94\) −3.70820 + 11.4127i −0.382472 + 1.17713i
\(95\) 3.23607 2.35114i 0.332014 0.241222i
\(96\) 0 0
\(97\) 3.09017 + 9.51057i 0.313759 + 0.965652i 0.976262 + 0.216592i \(0.0694942\pi\)
−0.662503 + 0.749059i \(0.730506\pi\)
\(98\) −7.00000 −0.707107
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −3.09017 9.51057i −0.307483 0.946337i −0.978739 0.205110i \(-0.934245\pi\)
0.671255 0.741226i \(-0.265755\pi\)
\(102\) 0 0
\(103\) 3.23607 2.35114i 0.318859 0.231665i −0.416829 0.908985i \(-0.636859\pi\)
0.735689 + 0.677320i \(0.236859\pi\)
\(104\) −1.85410 + 5.70634i −0.181810 + 0.559553i
\(105\) 0 0
\(106\) 1.61803 1.17557i 0.157157 0.114182i
\(107\) −9.70820 7.05342i −0.938527 0.681880i 0.00953827 0.999955i \(-0.496964\pi\)
−0.948066 + 0.318074i \(0.896964\pi\)
\(108\) 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
\(113\) 4.85410 + 3.52671i 0.456636 + 0.331765i 0.792210 0.610249i \(-0.208930\pi\)
−0.335575 + 0.942014i \(0.608930\pi\)
\(114\) 0 0
\(115\) 1.23607 3.80423i 0.115264 0.354746i
\(116\) −1.85410 + 5.70634i −0.172149 + 0.529820i
\(117\) 4.85410 3.52671i 0.448762 0.326045i
\(118\) −3.23607 2.35114i −0.297904 0.216440i
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) −10.0000 −0.905357
\(123\) 0 0
\(124\) −6.47214 4.70228i −0.581215 0.422277i
\(125\) −0.809017 + 0.587785i −0.0723607 + 0.0525731i
\(126\) 0 0
\(127\) 4.94427 15.2169i 0.438733 1.35028i −0.450479 0.892787i \(-0.648747\pi\)
0.889212 0.457495i \(-0.151253\pi\)
\(128\) 2.42705 1.76336i 0.214523 0.155860i
\(129\) 0 0
\(130\) 0.618034 + 1.90211i 0.0542052 + 0.166826i
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −4.94427 15.2169i −0.427120 1.31454i
\(135\) 0 0
\(136\) 14.5623 10.5801i 1.24871 0.907239i
\(137\) 5.56231 17.1190i 0.475220 1.46258i −0.370441 0.928856i \(-0.620793\pi\)
0.845661 0.533720i \(-0.179207\pi\)
\(138\) 0 0
\(139\) −9.70820 + 7.05342i −0.823439 + 0.598264i −0.917696 0.397284i \(-0.869953\pi\)
0.0942564 + 0.995548i \(0.469953\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 8.00000 0.671345
\(143\) 0 0
\(144\) 3.00000 0.250000
\(145\) 1.85410 + 5.70634i 0.153975 + 0.473886i
\(146\) −11.3262 8.22899i −0.937366 0.681036i
\(147\) 0 0
\(148\) 0.618034 1.90211i 0.0508021 0.156353i
\(149\) −3.09017 + 9.51057i −0.253157 + 0.779136i 0.741031 + 0.671471i \(0.234337\pi\)
−0.994187 + 0.107665i \(0.965663\pi\)
\(150\) 0 0
\(151\) −6.47214 4.70228i −0.526695 0.382666i 0.292425 0.956288i \(-0.405538\pi\)
−0.819120 + 0.573622i \(0.805538\pi\)
\(152\) 3.70820 + 11.4127i 0.300775 + 0.925690i
\(153\) −18.0000 −1.45521
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) 1.61803 + 1.17557i 0.129133 + 0.0938207i 0.650477 0.759526i \(-0.274569\pi\)
−0.521344 + 0.853347i \(0.674569\pi\)
\(158\) −6.47214 + 4.70228i −0.514895 + 0.374093i
\(159\) 0 0
\(160\) 1.54508 4.75528i 0.122150 0.375938i
\(161\) 0 0
\(162\) −7.28115 5.29007i −0.572061 0.415627i
\(163\) 4.94427 + 15.2169i 0.387265 + 1.19188i 0.934824 + 0.355112i \(0.115557\pi\)
−0.547558 + 0.836768i \(0.684443\pi\)
\(164\) −2.00000 −0.156174
\(165\) 0 0
\(166\) −4.00000 −0.310460
\(167\) −2.47214 7.60845i −0.191300 0.588760i −1.00000 0.000538710i \(-0.999829\pi\)
0.808700 0.588221i \(-0.200171\pi\)
\(168\) 0 0
\(169\) 7.28115 5.29007i 0.560089 0.406928i
\(170\) 1.85410 5.70634i 0.142203 0.437656i
\(171\) 3.70820 11.4127i 0.283573 0.872749i
\(172\) 3.23607 2.35114i 0.246748 0.179273i
\(173\) 4.85410 + 3.52671i 0.369051 + 0.268131i 0.756817 0.653627i \(-0.226753\pi\)
−0.387767 + 0.921758i \(0.626753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 3.09017 + 9.51057i 0.231618 + 0.712847i
\(179\) −3.23607 2.35114i −0.241875 0.175733i 0.460243 0.887793i \(-0.347762\pi\)
−0.702118 + 0.712060i \(0.747762\pi\)
\(180\) −2.42705 + 1.76336i −0.180902 + 0.131433i
\(181\) −3.09017 + 9.51057i −0.229691 + 0.706915i 0.768091 + 0.640341i \(0.221207\pi\)
−0.997781 + 0.0665740i \(0.978793\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 9.70820 + 7.05342i 0.715698 + 0.519985i
\(185\) −0.618034 1.90211i −0.0454388 0.139846i
\(186\) 0 0
\(187\) 0 0
\(188\) 12.0000 0.875190
\(189\) 0 0
\(190\) 3.23607 + 2.35114i 0.234769 + 0.170570i
\(191\) −6.47214 + 4.70228i −0.468307 + 0.340245i −0.796781 0.604268i \(-0.793466\pi\)
0.328474 + 0.944513i \(0.393466\pi\)
\(192\) 0 0
\(193\) −8.03444 + 24.7275i −0.578332 + 1.77992i 0.0462111 + 0.998932i \(0.485285\pi\)
−0.624543 + 0.780991i \(0.714715\pi\)
\(194\) −8.09017 + 5.87785i −0.580840 + 0.422005i
\(195\) 0 0
\(196\) 2.16312 + 6.65740i 0.154508 + 0.475528i
\(197\) 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 \(0.5\pi\)
\(200\) −0.927051 2.85317i −0.0655524 0.201750i
\(201\) 0 0
\(202\) 8.09017 5.87785i 0.569222 0.413564i
\(203\) 0 0
\(204\) 0 0
\(205\) −1.61803 + 1.17557i −0.113008 + 0.0821054i
\(206\) 3.23607 + 2.35114i 0.225468 + 0.163812i
\(207\) −3.70820 11.4127i −0.257738 0.793236i
\(208\) −2.00000 −0.138675
\(209\) 0 0
\(210\) 0 0
\(211\) 1.23607 + 3.80423i 0.0850944 + 0.261894i 0.984546 0.175127i \(-0.0560336\pi\)
−0.899451 + 0.437021i \(0.856034\pi\)
\(212\) −1.61803 1.17557i −0.111127 0.0807385i
\(213\) 0 0
\(214\) 3.70820 11.4127i 0.253488 0.780155i
\(215\) 1.23607 3.80423i 0.0842991 0.259446i
\(216\) 0 0
\(217\) 0 0
\(218\) −5.56231 17.1190i −0.376727 1.15945i
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) 3.23607 + 2.35114i 0.216703 + 0.157444i 0.690841 0.723006i \(-0.257240\pi\)
−0.474138 + 0.880450i \(0.657240\pi\)
\(224\) 0 0
\(225\) −0.927051 + 2.85317i −0.0618034 + 0.190211i
\(226\) −1.85410 + 5.70634i −0.123333 + 0.379580i
\(227\) 16.1803 11.7557i 1.07393 0.780254i 0.0973129 0.995254i \(-0.468975\pi\)
0.976614 + 0.215000i \(0.0689752\pi\)
\(228\) 0 0
\(229\) −3.09017 9.51057i −0.204204 0.628476i −0.999745 0.0225760i \(-0.992813\pi\)
0.795541 0.605900i \(-0.207187\pi\)
\(230\) 4.00000 0.263752
\(231\) 0 0
\(232\) −18.0000 −1.18176
\(233\) 1.85410 + 5.70634i 0.121466 + 0.373835i 0.993241 0.116073i \(-0.0370306\pi\)
−0.871774 + 0.489907i \(0.837031\pi\)
\(234\) 4.85410 + 3.52671i 0.317323 + 0.230548i
\(235\) 9.70820 7.05342i 0.633293 0.460115i
\(236\) −1.23607 + 3.80423i −0.0804612 + 0.247634i
\(237\) 0 0
\(238\) 0 0
\(239\) −6.47214 4.70228i −0.418648 0.304165i 0.358446 0.933551i \(-0.383307\pi\)
−0.777093 + 0.629385i \(0.783307\pi\)
\(240\) 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
\(244\) 3.09017 + 9.51057i 0.197828 + 0.608852i
\(245\) 5.66312 + 4.11450i 0.361803 + 0.262866i
\(246\) 0 0
\(247\) −2.47214 + 7.60845i −0.157298 + 0.484114i
\(248\) 7.41641 22.8254i 0.470942 1.44941i
\(249\) 0 0
\(250\) −0.809017 0.587785i −0.0511667 0.0371748i
\(251\) 3.70820 + 11.4127i 0.234060 + 0.720362i 0.997245 + 0.0741818i \(0.0236345\pi\)
−0.763185 + 0.646180i \(0.776365\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 16.0000 1.00393
\(255\) 0 0
\(256\) 13.7533 + 9.99235i 0.859581 + 0.624522i
\(257\) −14.5623 + 10.5801i −0.908372 + 0.659971i −0.940603 0.339510i \(-0.889739\pi\)
0.0322308 + 0.999480i \(0.489739\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.61803 1.17557i 0.100346 0.0729058i
\(261\) 14.5623 + 10.5801i 0.901384 + 0.654894i
\(262\) −3.70820 11.4127i −0.229094 0.705078i
\(263\) 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
\(268\) −12.9443 + 9.40456i −0.790697 + 0.574475i
\(269\) −5.56231 + 17.1190i −0.339140 + 1.04376i 0.625507 + 0.780219i \(0.284892\pi\)
−0.964647 + 0.263546i \(0.915108\pi\)
\(270\) 0 0
\(271\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(272\) 4.85410 + 3.52671i 0.294323 + 0.213838i
\(273\) 0 0
\(274\) 18.0000 1.08742
\(275\) 0 0
\(276\) 0 0
\(277\) 3.09017 + 9.51057i 0.185670 + 0.571434i 0.999959 0.00902525i \(-0.00287287\pi\)
−0.814289 + 0.580460i \(0.802873\pi\)
\(278\) −9.70820 7.05342i −0.582259 0.423036i
\(279\) −19.4164 + 14.1068i −1.16243 + 0.844555i
\(280\) 0 0
\(281\) 5.56231 17.1190i 0.331819 1.02123i −0.636448 0.771319i \(-0.719597\pi\)
0.968268 0.249916i \(-0.0804029\pi\)
\(282\) 0 0
\(283\) −3.23607 2.35114i −0.192364 0.139761i 0.487434 0.873160i \(-0.337933\pi\)
−0.679799 + 0.733399i \(0.737933\pi\)
\(284\) −2.47214 7.60845i −0.146694 0.451479i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −4.63525 14.2658i −0.273135 0.840623i
\(289\) −15.3713 11.1679i −0.904195 0.656936i
\(290\) −4.85410 + 3.52671i −0.285043 + 0.207096i
\(291\) 0 0
\(292\) −4.32624 + 13.3148i −0.253174 + 0.779189i
\(293\) −8.09017 + 5.87785i −0.472633 + 0.343388i −0.798466 0.602039i \(-0.794355\pi\)
0.325834 + 0.945427i \(0.394355\pi\)
\(294\) 0 0
\(295\) 1.23607 + 3.80423i 0.0719667 + 0.221491i
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) −10.0000 −0.579284
\(299\) 2.47214 + 7.60845i 0.142967 + 0.440008i
\(300\) 0 0
\(301\) 0 0
\(302\) 2.47214 7.60845i 0.142255 0.437817i
\(303\) 0 0
\(304\) −3.23607 + 2.35114i −0.185601 + 0.134847i
\(305\) 8.09017 + 5.87785i 0.463242 + 0.336565i
\(306\) −5.56231 17.1190i −0.317976 0.978629i
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −2.47214 7.60845i −0.140408 0.432131i
\(311\) 19.4164 + 14.1068i 1.10100 + 0.799926i 0.981223 0.192875i \(-0.0617811\pi\)
0.119780 + 0.992800i \(0.461781\pi\)
\(312\) 0 0
\(313\) −6.79837 + 20.9232i −0.384267 + 1.18265i 0.552744 + 0.833351i \(0.313581\pi\)
−0.937011 + 0.349300i \(0.886419\pi\)
\(314\) −0.618034 + 1.90211i −0.0348777 + 0.107342i
\(315\) 0 0
\(316\) 6.47214 + 4.70228i 0.364086 + 0.264524i
\(317\) −5.56231 17.1190i −0.312410 0.961500i −0.976807 0.214120i \(-0.931312\pi\)
0.664397 0.747380i \(-0.268688\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 7.00000 0.391312
\(321\) 0 0
\(322\) 0 0
\(323\) 19.4164 14.1068i 1.08036 0.784926i
\(324\) −2.78115 + 8.55951i −0.154508 + 0.475528i
\(325\) 0.618034 1.90211i 0.0342824 0.105510i
\(326\) −12.9443 + 9.40456i −0.716917 + 0.520871i
\(327\) 0 0
\(328\) −1.85410 5.70634i −0.102376 0.315080i
\(329\) 0 0
\(330\) 0 0
\(331\) 4.00000 0.219860 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) 1.23607 + 3.80423i 0.0678380 + 0.208784i
\(333\) −4.85410 3.52671i −0.266003 0.193263i
\(334\) 6.47214 4.70228i 0.354140 0.257297i
\(335\) −4.94427 + 15.2169i −0.270134 + 0.831388i
\(336\) 0 0
\(337\) −4.85410 + 3.52671i −0.264420 + 0.192112i −0.712093 0.702085i \(-0.752253\pi\)
0.447673 + 0.894197i \(0.352253\pi\)
\(338\) 7.28115 + 5.29007i 0.396043 + 0.287742i
\(339\) 0 0
\(340\) −6.00000 −0.325396
\(341\) 0 0
\(342\) 12.0000 0.648886
\(343\) 0 0
\(344\) 9.70820 + 7.05342i 0.523431 + 0.380295i
\(345\) 0 0
\(346\) −1.85410 + 5.70634i −0.0996771 + 0.306775i
\(347\) −1.23607 + 3.80423i −0.0663556 + 0.204222i −0.978737 0.205120i \(-0.934242\pi\)
0.912381 + 0.409342i \(0.134242\pi\)
\(348\) 0 0
\(349\) 8.09017 + 5.87785i 0.433057 + 0.314634i 0.782870 0.622185i \(-0.213755\pi\)
−0.349813 + 0.936819i \(0.613755\pi\)
\(350\) 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
\(355\) −6.47214 4.70228i −0.343505 0.249571i
\(356\) 8.09017 5.87785i 0.428778 0.311526i
\(357\) 0 0
\(358\) 1.23607 3.80423i 0.0653282 0.201060i
\(359\) 25.8885 18.8091i 1.36635 0.992708i 0.368332 0.929694i \(-0.379929\pi\)
0.998013 0.0630137i \(-0.0200712\pi\)
\(360\) −7.28115 5.29007i −0.383750 0.278811i
\(361\) −0.927051 2.85317i −0.0487922 0.150167i
\(362\) −10.0000 −0.525588
\(363\) 0 0
\(364\) 0 0
\(365\) 4.32624 + 13.3148i 0.226446 + 0.696928i
\(366\) 0 0
\(367\) −3.23607 + 2.35114i −0.168921 + 0.122729i −0.669034 0.743232i \(-0.733292\pi\)
0.500113 + 0.865960i \(0.333292\pi\)
\(368\) −1.23607 + 3.80423i −0.0644345 + 0.198309i
\(369\) −1.85410 + 5.70634i −0.0965207 + 0.297060i
\(370\) 1.61803 1.17557i 0.0841176 0.0611150i
\(371\) 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
\(376\) 11.1246 + 34.2380i 0.573708 + 1.76569i
\(377\) −9.70820 7.05342i −0.499998 0.363270i
\(378\) 0 0
\(379\) 6.18034 19.0211i 0.317463 0.977050i −0.657266 0.753659i \(-0.728287\pi\)
0.974729 0.223391i \(-0.0717128\pi\)
\(380\) 1.23607 3.80423i 0.0634089 0.195153i
\(381\) 0 0
\(382\) −6.47214 4.70228i −0.331143 0.240590i
\(383\) −3.70820 11.4127i −0.189480 0.583161i 0.810516 0.585716i \(-0.199187\pi\)
−0.999997 + 0.00255538i \(0.999187\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −26.0000 −1.32337
\(387\) −3.70820 11.4127i −0.188499 0.580139i
\(388\) 8.09017 + 5.87785i 0.410716 + 0.298403i
\(389\) −4.85410 + 3.52671i −0.246113 + 0.178811i −0.704002 0.710198i \(-0.748606\pi\)
0.457890 + 0.889009i \(0.348606\pi\)
\(390\) 0 0
\(391\) 7.41641 22.8254i 0.375064 1.15433i
\(392\) −16.9894 + 12.3435i −0.858092 + 0.623440i
\(393\) 0 0
\(394\) 0.618034 + 1.90211i 0.0311361 + 0.0958271i
\(395\) 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
\(400\) 0.809017 0.587785i 0.0404508 0.0293893i
\(401\) 0.618034 1.90211i 0.0308631 0.0949870i −0.934438 0.356125i \(-0.884098\pi\)
0.965301 + 0.261138i \(0.0840977\pi\)
\(402\) 0 0
\(403\) 12.9443 9.40456i 0.644800 0.468475i
\(404\) −8.09017 5.87785i −0.402501 0.292434i
\(405\) 2.78115 + 8.55951i 0.138197 + 0.425325i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.85410 5.70634i −0.0916794 0.282160i 0.894695 0.446678i \(-0.147393\pi\)
−0.986374 + 0.164518i \(0.947393\pi\)
\(410\) −1.61803 1.17557i −0.0799090 0.0580573i
\(411\) 0 0
\(412\) 1.23607 3.80423i 0.0608967 0.187421i
\(413\) 0 0
\(414\) 9.70820 7.05342i 0.477132 0.346657i
\(415\) 3.23607 + 2.35114i 0.158852 + 0.115413i
\(416\) 3.09017 + 9.51057i 0.151508 + 0.466294i
\(417\) 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
\(421\) −4.85410 3.52671i −0.236574 0.171881i 0.463181 0.886264i \(-0.346708\pi\)
−0.699756 + 0.714382i \(0.746708\pi\)
\(422\) −3.23607 + 2.35114i −0.157529 + 0.114452i
\(423\) 11.1246 34.2380i 0.540897 1.66471i
\(424\) 1.85410 5.70634i 0.0900432 0.277124i
\(425\) −4.85410 + 3.52671i −0.235459 + 0.171071i
\(426\) 0 0
\(427\) 0 0
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 4.00000 0.192897
\(431\) −7.41641 22.8254i −0.357236 1.09946i −0.954702 0.297564i \(-0.903826\pi\)
0.597466 0.801894i \(-0.296174\pi\)
\(432\) 0 0
\(433\) 17.7984 12.9313i 0.855335 0.621437i −0.0712766 0.997457i \(-0.522707\pi\)
0.926612 + 0.376019i \(0.122707\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −14.5623 + 10.5801i −0.697408 + 0.506697i
\(437\) 12.9443 + 9.40456i 0.619208 + 0.449881i
\(438\) 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
\(442\) 3.70820 + 11.4127i 0.176381 + 0.542846i
\(443\) −6.47214 4.70228i −0.307500 0.223412i 0.423323 0.905979i \(-0.360864\pi\)
−0.730823 + 0.682567i \(0.760864\pi\)
\(444\) 0 0
\(445\) 3.09017 9.51057i 0.146488 0.450844i
\(446\) −1.23607 + 3.80423i −0.0585295 + 0.180135i
\(447\) 0 0
\(448\) 0 0
\(449\) 0.618034 + 1.90211i 0.0291668 + 0.0897663i 0.964580 0.263790i \(-0.0849724\pi\)
−0.935413 + 0.353556i \(0.884972\pi\)
\(450\) −3.00000 −0.141421
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) 0 0
\(454\) 16.1803 + 11.7557i 0.759381 + 0.551723i
\(455\) 0 0
\(456\) 0 0
\(457\) −8.03444 + 24.7275i −0.375835 + 1.15670i 0.567078 + 0.823664i \(0.308074\pi\)
−0.942913 + 0.333038i \(0.891926\pi\)
\(458\) 8.09017 5.87785i 0.378029 0.274654i
\(459\) 0 0
\(460\) −1.23607 3.80423i −0.0576320 0.177373i
\(461\) −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 \(0.815420\pi\)
\(464\) −1.85410 5.70634i −0.0860745 0.264910i
\(465\) 0 0
\(466\) −4.85410 + 3.52671i −0.224862 + 0.163372i
\(467\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(468\) 1.85410 5.70634i 0.0857059 0.263776i
\(469\) 0 0
\(470\) 9.70820 + 7.05342i 0.447806 + 0.325350i
\(471\) 0 0
\(472\) −12.0000 −0.552345
\(473\) 0 0
\(474\) 0 0
\(475\) −1.23607 3.80423i −0.0567147 0.174550i
\(476\) 0 0
\(477\) −4.85410 + 3.52671i −0.222254 + 0.161477i
\(478\) 2.47214 7.60845i 0.113073 0.348003i
\(479\) 7.41641 22.8254i 0.338864 1.04292i −0.625923 0.779885i \(-0.715277\pi\)
0.964787 0.263032i \(-0.0847225\pi\)
\(480\) 0 0
\(481\) 3.23607 + 2.35114i 0.147552 + 0.107203i
\(482\) 3.09017 + 9.51057i 0.140753 + 0.433194i
\(483\) 0 0
\(484\) 0 0
\(485\) 10.0000 0.454077
\(486\) 0 0
\(487\) −22.6525 16.4580i −1.02648 0.745783i −0.0588802 0.998265i \(-0.518753\pi\)
−0.967601 + 0.252482i \(0.918753\pi\)
\(488\) −24.2705 + 17.6336i −1.09867 + 0.798234i
\(489\) 0 0
\(490\) −2.16312 + 6.65740i −0.0977198 + 0.300750i
\(491\) 22.6525 16.4580i 1.02229 0.742739i 0.0555405 0.998456i \(-0.482312\pi\)
0.966751 + 0.255718i \(0.0823118\pi\)
\(492\) 0 0
\(493\) 11.1246 + 34.2380i 0.501027 + 1.54200i
\(494\) −8.00000 −0.359937
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) 0 0
\(499\) 29.1246 21.1603i 1.30380 0.947264i 0.303812 0.952732i \(-0.401741\pi\)
0.999985 + 0.00546838i \(0.00174065\pi\)
\(500\) −0.309017 + 0.951057i −0.0138197 + 0.0425325i
\(501\) 0 0
\(502\) −9.70820 + 7.05342i −0.433298 + 0.314810i
\(503\) 12.9443 + 9.40456i 0.577157 + 0.419329i 0.837698 0.546134i \(-0.183901\pi\)
−0.260541 + 0.965463i \(0.583901\pi\)
\(504\) 0 0
\(505\) −10.0000 −0.444994
\(506\) 0 0
\(507\) 0 0
\(508\) −4.94427 15.2169i −0.219367 0.675141i
\(509\) −11.3262 8.22899i −0.502027 0.364744i 0.307764 0.951463i \(-0.400419\pi\)
−0.809791 + 0.586719i \(0.800419\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −3.39919 + 10.4616i −0.150224 + 0.462343i
\(513\) 0 0
\(514\) −14.5623 10.5801i −0.642316 0.466670i
\(515\) −1.23607 3.80423i −0.0544677 0.167634i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 4.85410 + 3.52671i 0.212866 + 0.154657i
\(521\) 4.85410 3.52671i 0.212662 0.154508i −0.476355 0.879253i \(-0.658042\pi\)
0.689017 + 0.724745i \(0.258042\pi\)
\(522\) −5.56231 + 17.1190i −0.243456 + 0.749279i
\(523\) −6.18034 + 19.0211i −0.270247 + 0.831736i 0.720190 + 0.693776i \(0.244054\pi\)
−0.990438 + 0.137960i \(0.955946\pi\)
\(524\) −9.70820 + 7.05342i −0.424105 + 0.308130i
\(525\) 0 0
\(526\) 7.41641 + 22.8254i 0.323371 + 0.995233i
\(527\) −48.0000 −2.09091
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) −0.618034 1.90211i −0.0268457 0.0826225i
\(531\) 9.70820 + 7.05342i 0.421300 + 0.306092i
\(532\) 0 0
\(533\) 1.23607 3.80423i 0.0535400 0.164779i
\(534\) 0 0
\(535\) −9.70820 + 7.05342i −0.419722 + 0.304946i
\(536\) −38.8328 28.2137i −1.67732 1.21865i
\(537\) 0 0
\(538\) −18.0000 −0.776035
\(539\) 0 0
\(540\) 0 0
\(541\) −10.5066 32.3359i −0.451713 1.39023i −0.874951 0.484211i \(-0.839107\pi\)
0.423238 0.906019i \(-0.360893\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 9.27051 28.5317i 0.397470 1.22329i
\(545\) −5.56231 + 17.1190i −0.238263 + 0.733298i
\(546\) 0 0
\(547\) −9.70820 7.05342i −0.415093 0.301583i 0.360568 0.932733i \(-0.382583\pi\)
−0.775660 + 0.631151i \(0.782583\pi\)
\(548\) −5.56231 17.1190i −0.237610 0.731288i
\(549\) 30.0000 1.28037
\(550\) 0 0
\(551\) −24.0000 −1.02243
\(552\) 0 0
\(553\) 0 0
\(554\) −8.09017 + 5.87785i −0.343718 + 0.249726i
\(555\) 0 0
\(556\) −3.70820 + 11.4127i −0.157263 + 0.484005i
\(557\) −8.09017 + 5.87785i −0.342792 + 0.249053i −0.745839 0.666127i \(-0.767951\pi\)
0.403047 + 0.915179i \(0.367951\pi\)
\(558\) −19.4164 14.1068i −0.821962 0.597190i
\(559\) 2.47214 + 7.60845i 0.104560 + 0.321803i
\(560\) 0 0
\(561\) 0 0
\(562\) 18.0000 0.759284
\(563\) 11.1246 + 34.2380i 0.468846 + 1.44296i 0.854080 + 0.520142i \(0.174121\pi\)
−0.385233 + 0.922819i \(0.625879\pi\)
\(564\) 0 0
\(565\) 4.85410 3.52671i 0.204214 0.148370i
\(566\) 1.23607 3.80423i 0.0519558 0.159904i
\(567\) 0 0
\(568\) 19.4164 14.1068i 0.814694 0.591910i
\(569\) −21.0344 15.2824i −0.881810 0.640672i 0.0519200 0.998651i \(-0.483466\pi\)
−0.933730 + 0.357979i \(0.883466\pi\)
\(570\) 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
\(575\) −3.23607 2.35114i −0.134953 0.0980494i
\(576\) 16.9894 12.3435i 0.707890 0.514312i
\(577\) −6.79837 + 20.9232i −0.283020 + 0.871046i 0.703965 + 0.710235i \(0.251411\pi\)
−0.986985 + 0.160811i \(0.948589\pi\)
\(578\) 5.87132 18.0701i 0.244215 0.751616i
\(579\) 0 0
\(580\) 4.85410 + 3.52671i 0.201556 + 0.146439i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −42.0000 −1.73797
\(585\) −1.85410 5.70634i −0.0766577 0.235928i
\(586\) −8.09017 5.87785i −0.334202 0.242812i
\(587\) 19.4164 14.1068i 0.801401 0.582252i −0.109924 0.993940i \(-0.535061\pi\)
0.911325 + 0.411688i \(0.135061\pi\)
\(588\) 0 0
\(589\) 9.88854 30.4338i 0.407450 1.25400i
\(590\) −3.23607 + 2.35114i −0.133227 + 0.0967949i
\(591\) 0 0
\(592\) 0.618034 + 1.90211i 0.0254010 + 0.0781764i
\(593\) 22.0000 0.903432 0.451716 0.892162i \(-0.350812\pi\)
0.451716 + 0.892162i \(0.350812\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3.09017 + 9.51057i 0.126578 + 0.389568i
\(597\) 0 0
\(598\) −6.47214 + 4.70228i −0.264665 + 0.192291i
\(599\) 7.41641 22.8254i 0.303026 0.932619i −0.677380 0.735633i \(-0.736885\pi\)
0.980406 0.196986i \(-0.0631152\pi\)
\(600\) 0 0
\(601\) −1.61803 + 1.17557i −0.0660010 + 0.0479525i −0.620297 0.784367i \(-0.712988\pi\)
0.554296 + 0.832320i \(0.312988\pi\)
\(602\) 0 0
\(603\) 14.8328 + 45.6507i 0.604039 + 1.85904i
\(604\) −8.00000 −0.325515
\(605\) 0 0
\(606\) 0 0
\(607\) −9.88854 30.4338i −0.401364 1.23527i −0.923894 0.382649i \(-0.875012\pi\)
0.522530 0.852621i \(-0.324988\pi\)
\(608\) 16.1803 + 11.7557i 0.656199 + 0.476757i
\(609\) 0 0
\(610\) −3.09017 + 9.51057i −0.125117 + 0.385072i
\(611\) −7.41641 + 22.8254i −0.300036 + 0.923415i
\(612\) −14.5623 + 10.5801i −0.588646 + 0.427677i
\(613\) −27.5066 19.9847i −1.11098 0.807174i −0.128162 0.991753i \(-0.540908\pi\)
−0.982818 + 0.184579i \(0.940908\pi\)
\(614\) 6.18034 + 19.0211i 0.249418 + 0.767630i
\(615\) 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
\(619\) 16.1803 + 11.7557i 0.650343 + 0.472502i 0.863388 0.504541i \(-0.168338\pi\)
−0.213045 + 0.977042i \(0.568338\pi\)
\(620\) −6.47214 + 4.70228i −0.259927 + 0.188848i
\(621\) 0 0
\(622\) −7.41641 + 22.8254i −0.297371 + 0.915213i
\(623\) 0 0
\(624\) 0 0
\(625\) 0.309017 + 0.951057i 0.0123607 + 0.0380423i
\(626\) −22.0000 −0.879297
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) −3.70820 11.4127i −0.147856 0.455053i
\(630\) 0 0
\(631\) −32.3607 + 23.5114i −1.28826 + 0.935974i −0.999769 0.0215086i \(-0.993153\pi\)
−0.288490 + 0.957483i \(0.593153\pi\)
\(632\) −7.41641 + 22.8254i −0.295009 + 0.907944i
\(633\) 0 0
\(634\) 14.5623 10.5801i 0.578343 0.420191i
\(635\) −12.9443 9.40456i −0.513678 0.373209i
\(636\) 0 0
\(637\) −14.0000 −0.554700
\(638\) 0 0
\(639\) −24.0000 −0.949425
\(640\) −0.927051 2.85317i −0.0366449 0.112781i
\(641\) −27.5066 19.9847i −1.08644 0.789348i −0.107649 0.994189i \(-0.534332\pi\)
−0.978795 + 0.204841i \(0.934332\pi\)
\(642\) 0 0
\(643\) −4.94427 + 15.2169i −0.194983 + 0.600096i 0.804994 + 0.593283i \(0.202169\pi\)
−0.999977 + 0.00681282i \(0.997831\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 19.4164 + 14.1068i 0.763928 + 0.555026i
\(647\) 6.18034 + 19.0211i 0.242974 + 0.747798i 0.995963 + 0.0897645i \(0.0286114\pi\)
−0.752989 + 0.658033i \(0.771389\pi\)
\(648\) −27.0000 −1.06066
\(649\) 0 0
\(650\) 2.00000 0.0784465
\(651\) 0 0
\(652\) 12.9443 + 9.40456i 0.506937 + 0.368311i
\(653\) 8.09017 5.87785i 0.316593 0.230018i −0.418127 0.908388i \(-0.637313\pi\)
0.734720 + 0.678370i \(0.237313\pi\)
\(654\) 0 0
\(655\) −3.70820 + 11.4127i −0.144892 + 0.445930i
\(656\) 1.61803 1.17557i 0.0631736 0.0458983i
\(657\) 33.9787 + 24.6870i 1.32564 + 0.963131i
\(658\) 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 \(0.562301\pi\)
\(662\) 1.23607 + 3.80423i 0.0480411 + 0.147855i
\(663\) 0 0
\(664\) −9.70820 + 7.05342i −0.376751 + 0.273726i
\(665\) 0 0
\(666\) 1.85410 5.70634i 0.0718450 0.221116i
\(667\) −19.4164 + 14.1068i −0.751806 + 0.546219i
\(668\) −6.47214 4.70228i −0.250414 0.181937i
\(669\) 0 0
\(670\) −16.0000 −0.618134
\(671\) 0 0
\(672\) 0 0
\(673\) −8.03444 24.7275i −0.309705 0.953174i −0.977879 0.209169i \(-0.932924\pi\)
0.668174 0.744005i \(-0.267076\pi\)
\(674\) −4.85410 3.52671i −0.186973 0.135844i
\(675\) 0 0
\(676\) 2.78115 8.55951i 0.106967 0.329212i
\(677\) −11.7426 + 36.1401i −0.451307 + 1.38898i 0.424111 + 0.905610i \(0.360587\pi\)
−0.875417 + 0.483368i \(0.839413\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −5.56231 17.1190i −0.213305 0.656484i
\(681\) 0 0
\(682\) 0 0
\(683\) −16.0000 −0.612223 −0.306111 0.951996i \(-0.599028\pi\)
−0.306111 + 0.951996i \(0.599028\pi\)
\(684\) −3.70820 11.4127i −0.141787 0.436375i
\(685\) −14.5623 10.5801i −0.556397 0.404246i
\(686\) 0 0
\(687\) 0 0
\(688\) −1.23607 + 3.80423i −0.0471246 + 0.145035i
\(689\) 3.23607 2.35114i 0.123284 0.0895713i
\(690\) 0 0
\(691\) −8.65248 26.6296i −0.329156 1.01304i −0.969530 0.244974i \(-0.921221\pi\)
0.640374 0.768063i \(-0.278779\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −4.00000 −0.151838
\(695\) 3.70820 + 11.4127i 0.140660 + 0.432908i
\(696\) 0 0
\(697\) −9.70820 + 7.05342i −0.367724 + 0.267167i
\(698\) −3.09017 + 9.51057i −0.116965 + 0.359980i
\(699\) 0 0
\(700\) 0 0
\(701\) −17.7984 12.9313i −0.672235 0.488408i 0.198537 0.980093i \(-0.436381\pi\)
−0.870773 + 0.491686i \(0.836381\pi\)
\(702\) 0 0
\(703\) 8.00000 0.301726
\(704\) 0 0
\(705\) 0 0
\(706\) 5.56231 + 17.1190i 0.209340 + 0.644283i
\(707\) 0 0
\(708\) 0 0
\(709\) −3.09017 + 9.51057i −0.116054 + 0.357177i −0.992165 0.124932i \(-0.960129\pi\)
0.876112 + 0.482108i \(0.160129\pi\)
\(710\) 2.47214 7.60845i 0.0927776 0.285540i
\(711\) 19.4164 14.1068i 0.728172 0.529048i
\(712\) 24.2705 + 17.6336i 0.909576 + 0.660846i
\(713\) −9.88854 30.4338i −0.370329 1.13976i
\(714\) 0 0
\(715\) 0 0
\(716\) −4.00000 −0.149487
\(717\) 0 0
\(718\) 25.8885 + 18.8091i 0.966152 + 0.701950i
\(719\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(720\) 0.927051 2.85317i 0.0345492 0.106331i
\(721\) 0 0
\(722\) 2.42705 1.76336i 0.0903255 0.0656253i
\(723\) 0 0
\(724\) 3.09017 + 9.51057i 0.114845 + 0.353457i
\(725\) 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
\(729\) 21.8435 + 15.8702i 0.809017 + 0.587785i
\(730\) −11.3262 + 8.22899i −0.419203 + 0.304569i
\(731\) 7.41641 22.8254i 0.274306 0.844226i
\(732\) 0 0
\(733\) −33.9787 + 24.6870i −1.25503 + 0.911834i −0.998503 0.0547019i \(-0.982579\pi\)
−0.256530 + 0.966536i \(0.582579\pi\)
\(734\) −3.23607 2.35114i −0.119445 0.0867822i
\(735\) 0 0
\(736\) 20.0000 0.737210
\(737\) 0 0
\(738\) −6.00000 −0.220863
\(739\) 1.23607 + 3.80423i 0.0454695 + 0.139941i 0.971214 0.238209i \(-0.0765604\pi\)
−0.925744 + 0.378150i \(0.876560\pi\)
\(740\) −1.61803 1.17557i −0.0594801 0.0432148i
\(741\) 0 0
\(742\) 0 0
\(743\) 12.3607 38.0423i 0.453469 1.39564i −0.419453 0.907777i \(-0.637778\pi\)
0.872923 0.487858i \(-0.162222\pi\)
\(744\) 0 0
\(745\) 8.09017 + 5.87785i 0.296401 + 0.215348i
\(746\) 5.56231 + 17.1190i 0.203650 + 0.626772i
\(747\) 12.0000 0.439057
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −12.9443 9.40456i −0.472343 0.343177i 0.326011 0.945366i \(-0.394295\pi\)
−0.798354 + 0.602189i \(0.794295\pi\)
\(752\) −9.70820 + 7.05342i −0.354022 + 0.257212i
\(753\) 0 0
\(754\) 3.70820 11.4127i 0.135045 0.415625i
\(755\) −6.47214 + 4.70228i −0.235545 + 0.171134i
\(756\) 0 0
\(757\) 1.85410 + 5.70634i 0.0673885 + 0.207400i 0.979080 0.203474i \(-0.0652233\pi\)
−0.911692 + 0.410875i \(0.865223\pi\)
\(758\) 20.0000 0.726433
\(759\) 0 0
\(760\) 12.0000 0.435286
\(761\) 3.09017 + 9.51057i 0.112019 + 0.344758i 0.991314 0.131520i \(-0.0419857\pi\)
−0.879295 + 0.476278i \(0.841986\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −2.47214 + 7.60845i −0.0894387 + 0.275264i
\(765\) −5.56231 + 17.1190i −0.201106 + 0.618939i
\(766\) 9.70820 7.05342i 0.350772 0.254851i
\(767\) −6.47214 4.70228i −0.233695 0.169790i
\(768\) 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
\(772\) 8.03444 + 24.7275i 0.289166 + 0.889961i
\(773\) −11.3262 8.22899i −0.407376 0.295976i 0.365162 0.930944i \(-0.381013\pi\)
−0.772539 + 0.634968i \(0.781013\pi\)
\(774\) 9.70820 7.05342i 0.348954 0.253530i
\(775\) −2.47214 + 7.60845i −0.0888017 + 0.273304i
\(776\) −9.27051 + 28.5317i −0.332792 + 1.02423i
\(777\) 0 0
\(778\) −4.85410 3.52671i −0.174028 0.126439i
\(779\) −2.47214 7.60845i −0.0885735 0.272601i
\(780\) 0 0
\(781\) 0 0
\(782\) 24.0000 0.858238
\(783\) 0 0
\(784\) −5.66312 4.11450i −0.202254 0.146946i
\(785\) 1.61803 1.17557i 0.0577501 0.0419579i
\(786\) 0 0
\(787\) 16.0689 49.4549i 0.572794 1.76288i −0.0707776 0.997492i \(-0.522548\pi\)
0.643571 0.765386i \(-0.277452\pi\)
\(788\) 1.61803 1.17557i 0.0576401 0.0418780i
\(789\) 0 0