Properties

Label 605.2.g.c.251.1
Level $605$
Weight $2$
Character 605.251
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 251.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 605.251
Dual form 605.2.g.c.511.1

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

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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 0.780378 + 0.625308i \(0.215027\pi\)
−0.998886 + 0.0471903i \(0.984973\pi\)
\(3\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(4\) 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 \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(8\) −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 \(-0.989456\pi\)
0.828040 + 0.560670i \(0.189456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.309017 0.951057i −0.0772542 0.237764i
\(17\) −1.85410 5.70634i −0.449686 1.38399i −0.877262 0.480011i \(-0.840633\pi\)
0.427576 0.903979i \(-0.359367\pi\)
\(18\) −2.42705 1.76336i −0.572061 0.415627i
\(19\) −3.23607 + 2.35114i −0.742405 + 0.539389i −0.893463 0.449136i \(-0.851732\pi\)
0.151058 + 0.988525i \(0.451732\pi\)
\(20\) −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 \(-0.111919\pi\)
−0.0374370 + 0.999299i \(0.511919\pi\)
\(30\) 0 0
\(31\) −2.47214 + 7.60845i −0.444009 + 1.36652i 0.439558 + 0.898214i \(0.355135\pi\)
−0.883567 + 0.468304i \(0.844865\pi\)
\(32\) −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 0.712789 0.701378i \(-0.247432\pi\)
−0.446786 + 0.894641i \(0.647432\pi\)
\(38\) −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 \(-0.650084\pi\)
0.706920 + 0.707293i \(0.250084\pi\)
\(42\) 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
\(46\) −1.23607 + 3.80423i −0.182248 + 0.560903i
\(47\) 9.70820 7.05342i 1.41609 1.02885i 0.423685 0.905810i \(-0.360736\pi\)
0.992402 0.123038i \(-0.0392637\pi\)
\(48\) 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 −0.984488 0.175450i \(-0.943862\pi\)
0.899595 + 0.436726i \(0.143862\pi\)
\(54\) 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 0.356861 0.934158i \(-0.383847\pi\)
−0.778161 + 0.628065i \(0.783847\pi\)
\(60\) 0 0
\(61\) 3.09017 + 9.51057i 0.395656 + 1.21770i 0.928450 + 0.371458i \(0.121142\pi\)
−0.532794 + 0.846245i \(0.678858\pi\)
\(62\) −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 0.983758 + 0.179500i \(0.0574480\pi\)
−0.690369 + 0.723457i \(0.742552\pi\)
\(72\) −2.78115 8.55951i −0.327762 1.00875i
\(73\) 11.3262 + 8.22899i 1.32564 + 0.963131i 0.999844 + 0.0176895i \(0.00563103\pi\)
0.325792 + 0.945441i \(0.394369\pi\)
\(74\) −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 0.710235 + 0.703964i \(0.248589\pi\)
−0.988372 + 0.152053i \(0.951411\pi\)
\(80\) 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 \(-0.0295481\pi\)
−0.860018 + 0.510263i \(0.829548\pi\)
\(84\) 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 −0.662503 0.749059i \(-0.730506\pi\)
0.976262 0.216592i \(-0.0694942\pi\)
\(98\) 7.00000 0.707107
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) 3.09017 9.51057i 0.307483 0.946337i −0.671255 0.741226i \(-0.734245\pi\)
0.978739 0.205110i \(-0.0657554\pi\)
\(102\) 0 0
\(103\) 3.23607 + 2.35114i 0.318859 + 0.231665i 0.735689 0.677320i \(-0.236859\pi\)
−0.416829 + 0.908985i \(0.636859\pi\)
\(104\) −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 \(-0.503036\pi\)
0.948066 + 0.318074i \(0.103036\pi\)
\(108\) 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
\(113\) 4.85410 3.52671i 0.456636 0.331765i −0.335575 0.942014i \(-0.608930\pi\)
0.792210 + 0.610249i \(0.208930\pi\)
\(114\) 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 −0.889212 0.457495i \(-0.848747\pi\)
0.450479 0.892787i \(-0.351253\pi\)
\(128\) −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 \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 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 0.845661 + 0.533720i \(0.179207\pi\)
−0.370441 + 0.928856i \(0.620793\pi\)
\(138\) 0 0
\(139\) 9.70820 + 7.05342i 0.823439 + 0.598264i 0.917696 0.397284i \(-0.130047\pi\)
−0.0942564 + 0.995548i \(0.530047\pi\)
\(140\) 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 0.994187 + 0.107665i \(0.0343373\pi\)
−0.741031 + 0.671471i \(0.765663\pi\)
\(150\) 0 0
\(151\) 6.47214 4.70228i 0.526695 0.382666i −0.292425 0.956288i \(-0.594462\pi\)
0.819120 + 0.573622i \(0.194462\pi\)
\(152\) 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 −0.521344 0.853347i \(-0.674569\pi\)
0.650477 + 0.759526i \(0.274569\pi\)
\(158\) −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 −0.547558 0.836768i \(-0.684443\pi\)
0.934824 0.355112i \(-0.115557\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) −4.00000 −0.310460
\(167\) 2.47214 7.60845i 0.191300 0.588760i −0.808700 0.588221i \(-0.799829\pi\)
1.00000 0.000538710i \(-0.000171477\pi\)
\(168\) 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 \(-0.773247\pi\)
0.387767 + 0.921758i \(0.373247\pi\)
\(174\) 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 −0.702118 0.712060i \(-0.747762\pi\)
0.460243 + 0.887793i \(0.347762\pi\)
\(180\) −2.42705 1.76336i −0.180902 0.131433i
\(181\) −3.09017 9.51057i −0.229691 0.706915i −0.997781 0.0665740i \(-0.978793\pi\)
0.768091 0.640341i \(-0.221207\pi\)
\(182\) 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 0.328474 0.944513i \(-0.393466\pi\)
−0.796781 + 0.604268i \(0.793466\pi\)
\(192\) 0 0
\(193\) 8.03444 + 24.7275i 0.578332 + 1.77992i 0.624543 + 0.780991i \(0.285285\pi\)
−0.0462111 + 0.998932i \(0.514715\pi\)
\(194\) 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 \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 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 \(-0.943966\pi\)
0.899451 + 0.437021i \(0.143966\pi\)
\(212\) −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 −0.474138 0.880450i \(-0.657240\pi\)
0.690841 + 0.723006i \(0.257240\pi\)
\(224\) 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 \(-0.531025\pi\)
−0.976614 + 0.215000i \(0.931025\pi\)
\(228\) 0 0
\(229\) −3.09017 + 9.51057i −0.204204 + 0.628476i 0.795541 + 0.605900i \(0.207187\pi\)
−0.999745 + 0.0225760i \(0.992813\pi\)
\(230\) −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 \(-0.962969\pi\)
0.871774 + 0.489907i \(0.162969\pi\)
\(234\) 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 \(-0.616693\pi\)
0.777093 + 0.629385i \(0.216693\pi\)
\(240\) 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
\(244\) −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 −0.763185 0.646180i \(-0.776365\pi\)
0.997245 0.0741818i \(-0.0236345\pi\)
\(252\) 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 0.0322308 0.999480i \(-0.489739\pi\)
−0.940603 + 0.339510i \(0.889739\pi\)
\(258\) 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 \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 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 −0.964647 0.263546i \(-0.915108\pi\)
0.625507 0.780219i \(-0.284892\pi\)
\(270\) 0 0
\(271\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(272\) −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 \(-0.997127\pi\)
0.814289 + 0.580460i \(0.197127\pi\)
\(278\) −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 −0.968268 0.249916i \(-0.919597\pi\)
0.636448 0.771319i \(-0.280403\pi\)
\(282\) 0 0
\(283\) 3.23607 2.35114i 0.192364 0.139761i −0.487434 0.873160i \(-0.662067\pi\)
0.679799 + 0.733399i \(0.262067\pi\)
\(284\) −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 \(-0.205645\pi\)
−0.325834 + 0.945427i \(0.605645\pi\)
\(294\) 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 \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 2.47214 7.60845i 0.140408 0.432131i
\(311\) 19.4164 14.1068i 1.10100 0.799926i 0.119780 0.992800i \(-0.461781\pi\)
0.981223 + 0.192875i \(0.0617811\pi\)
\(312\) 0 0
\(313\) −6.79837 20.9232i −0.384267 1.18265i −0.937011 0.349300i \(-0.886419\pi\)
0.552744 0.833351i \(-0.313581\pi\)
\(314\) 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 0.664397 + 0.747380i \(0.268688\pi\)
−0.976807 + 0.214120i \(0.931312\pi\)
\(318\) 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 \(-0.247747\pi\)
−0.447673 + 0.894197i \(0.647747\pi\)
\(338\) −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 \(-0.0657585\pi\)
−0.912381 + 0.409342i \(0.865758\pi\)
\(348\) 0 0
\(349\) −8.09017 + 5.87785i −0.433057 + 0.314634i −0.782870 0.622185i \(-0.786245\pi\)
0.349813 + 0.936819i \(0.386245\pi\)
\(350\) 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 −0.998013 0.0630137i \(-0.979929\pi\)
−0.368332 0.929694i \(-0.620071\pi\)
\(360\) 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 0.500113 0.865960i \(-0.333292\pi\)
−0.669034 + 0.743232i \(0.733292\pi\)
\(368\) −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 \(-0.654306\pi\)
−0.466002 + 0.884783i \(0.654306\pi\)
\(374\) 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 0.974729 + 0.223391i \(0.0717128\pi\)
−0.657266 + 0.753659i \(0.728287\pi\)
\(380\) −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 −0.999997 0.00255538i \(-0.999187\pi\)
0.810516 + 0.585716i \(0.199187\pi\)
\(384\) 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 0.457890 0.889009i \(-0.348606\pi\)
−0.704002 + 0.710198i \(0.748606\pi\)
\(390\) 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 0.965301 0.261138i \(-0.0840977\pi\)
−0.934438 + 0.356125i \(0.884098\pi\)
\(402\) 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 \(-0.852607\pi\)
0.986374 + 0.164518i \(0.0526069\pi\)
\(410\) −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 −0.699756 0.714382i \(-0.746708\pi\)
0.463181 + 0.886264i \(0.346708\pi\)
\(422\) −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 −0.597466 0.801894i \(-0.703826\pi\)
0.954702 0.297564i \(-0.0961743\pi\)
\(432\) 0 0
\(433\) 17.7984 + 12.9313i 0.855335 + 0.621437i 0.926612 0.376019i \(-0.122707\pi\)
−0.0712766 + 0.997457i \(0.522707\pi\)
\(434\) 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 \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 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 −0.730823 0.682567i \(-0.760864\pi\)
0.423323 + 0.905979i \(0.360864\pi\)
\(444\) 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 −0.935413 0.353556i \(-0.884972\pi\)
0.964580 + 0.263790i \(0.0849724\pi\)
\(450\) 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 0.942913 + 0.333038i \(0.108074\pi\)
−0.567078 + 0.823664i \(0.691926\pi\)
\(458\) −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 \(-0.209160\pi\)
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 \(0.815420\pi\)
\(464\) 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 \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(468\) −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 −0.964787 0.263032i \(-0.915277\pi\)
0.625923 0.779885i \(-0.284723\pi\)
\(480\) 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 −0.967601 0.252482i \(-0.918753\pi\)
−0.0588802 + 0.998265i \(0.518753\pi\)
\(488\) −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 \(-0.517688\pi\)
−0.966751 + 0.255718i \(0.917688\pi\)
\(492\) 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 0.999985 0.00546838i \(-0.00174065\pi\)
0.303812 + 0.952732i \(0.401741\pi\)
\(500\) −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 \(-0.816099\pi\)
0.260541 + 0.965463i \(0.416099\pi\)
\(504\) 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 −0.809791 0.586719i \(-0.800419\pi\)
0.307764 + 0.951463i \(0.400419\pi\)
\(510\) 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 0.689017 0.724745i \(-0.258042\pi\)
−0.476355 + 0.879253i \(0.658042\pi\)
\(522\) −5.56231 17.1190i −0.243456 0.749279i
\(523\) 6.18034 + 19.0211i 0.270247 + 0.831736i 0.990438 + 0.137960i \(0.0440544\pi\)
−0.720190 + 0.693776i \(0.755946\pi\)
\(524\) 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 −0.423238 0.906019i \(-0.639107\pi\)
0.874951 0.484211i \(-0.160893\pi\)
\(542\) 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 \(-0.617417\pi\)
0.775660 + 0.631151i \(0.217417\pi\)
\(548\) −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 \(-0.232049\pi\)
−0.403047 + 0.915179i \(0.632049\pi\)
\(558\) 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 0.385233 + 0.922819i \(0.374121\pi\)
−0.854080 + 0.520142i \(0.825879\pi\)
\(564\) 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 \(-0.516534\pi\)
0.933730 + 0.357979i \(0.116534\pi\)
\(570\) 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
\(575\) −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 −0.986985 0.160811i \(-0.948589\pi\)
0.703965 0.710235i \(-0.251411\pi\)
\(578\) −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 0.911325 0.411688i \(-0.135061\pi\)
−0.109924 + 0.993940i \(0.535061\pi\)
\(588\) 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 \(-0.649188\pi\)
−0.451716 + 0.892162i \(0.649188\pi\)
\(594\) 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 0.980406 + 0.196986i \(0.0631152\pi\)
−0.677380 + 0.735633i \(0.736885\pi\)
\(600\) 0 0
\(601\) 1.61803 + 1.17557i 0.0660010 + 0.0479525i 0.620297 0.784367i \(-0.287012\pi\)
−0.554296 + 0.832320i \(0.687012\pi\)
\(602\) 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 −0.522530 0.852621i \(-0.675012\pi\)
0.923894 0.382649i \(-0.124988\pi\)
\(608\) 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 \(-0.459092\pi\)
0.982818 + 0.184579i \(0.0590921\pi\)
\(614\) 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 −0.213045 0.977042i \(-0.568338\pi\)
0.863388 + 0.504541i \(0.168338\pi\)
\(620\) −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 −0.288490 0.957483i \(-0.593153\pi\)
−0.999769 + 0.0215086i \(0.993153\pi\)
\(632\) −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 −0.978795 0.204841i \(-0.934332\pi\)
−0.107649 + 0.994189i \(0.534332\pi\)
\(642\) 0 0
\(643\) −4.94427 15.2169i −0.194983 0.600096i −0.999977 0.00681282i \(-0.997831\pi\)
0.804994 0.593283i \(-0.202169\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −19.4164 + 14.1068i −0.763928 + 0.555026i
\(647\) 6.18034 19.0211i 0.242974 0.747798i −0.752989 0.658033i \(-0.771389\pi\)
0.995963 0.0897645i \(-0.0286114\pi\)
\(648\) 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 0.734720 0.678370i \(-0.237313\pi\)
−0.418127 + 0.908388i \(0.637313\pi\)
\(654\) 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 \(-0.747343\pi\)
−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 \(0.562301\pi\)
\(662\) −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 −0.668174 0.744005i \(-0.732924\pi\)
0.977879 0.209169i \(-0.0670760\pi\)
\(674\) −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 0.875417 + 0.483368i \(0.160587\pi\)
−0.424111 + 0.905610i \(0.639413\pi\)
\(678\) 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 0.640374 + 0.768063i \(0.278779\pi\)
−0.969530 + 0.244974i \(0.921221\pi\)
\(692\) −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 \(-0.563619\pi\)
0.870773 + 0.491686i \(0.163619\pi\)
\(702\) 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 0.876112 0.482108i \(-0.160129\pi\)
−0.992165 + 0.124932i \(0.960129\pi\)
\(710\) −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 \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(720\) 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 \(-0.0174209\pi\)
0.256530 + 0.966536i \(0.417421\pi\)
\(734\) 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 \(-0.923440\pi\)
0.925744 + 0.378150i \(0.123440\pi\)
\(740\) −1.61803 + 1.17557i −0.0594801 + 0.0432148i
\(741\) 0 0
\(742\) 0 0
\(743\) −12.3607 38.0423i −0.453469 1.39564i −0.872923 0.487858i \(-0.837778\pi\)
0.419453 0.907777i \(-0.362222\pi\)
\(744\) 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 −0.798354 0.602189i \(-0.794295\pi\)
0.326011 + 0.945366i \(0.394295\pi\)
\(752\) −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 −0.911692 0.410875i \(-0.865223\pi\)
0.979080 + 0.203474i \(0.0652233\pi\)
\(758\) −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 \(-0.958014\pi\)
0.879295 + 0.476278i \(0.158014\pi\)
\(762\) 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 \(-0.370166\pi\)
0.396670 + 0.917961i \(0.370166\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −8.03444 + 24.7275i −0.289166 + 0.889961i
\(773\) −11.3262 + 8.22899i −0.407376 + 0.295976i −0.772539 0.634968i \(-0.781013\pi\)
0.365162 + 0.930944i \(0.381013\pi\)
\(774\) 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 −0.643571 0.765386i \(-0.722548\pi\)
0.0707776 0.997492i \(-0.477452\pi\)
\(788\) −1.61803 1.17557i −0.0576401 0.0418780i
\(789\) 0 0
\(790\)