Properties

Label 450.2.h.a.91.1
Level $450$
Weight $2$
Character 450.91
Analytic conductor $3.593$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 50)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 450.91
Dual form 450.2.h.a.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} -3.00000 q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})\) \(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.690983 - 2.12663i) q^{5} -3.00000 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.690983 + 2.12663i) q^{10} +(-0.190983 - 0.138757i) q^{11} +(-0.809017 + 0.587785i) q^{13} +(2.42705 + 1.76336i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-2.42705 + 7.46969i) q^{17} +(-0.263932 + 0.812299i) q^{19} +(1.80902 - 1.31433i) q^{20} +(0.0729490 + 0.224514i) q^{22} +(-5.04508 - 3.66547i) q^{23} +(-4.04508 + 2.93893i) q^{25} +1.00000 q^{26} +(-0.927051 - 2.85317i) q^{28} +(0.163119 + 0.502029i) q^{29} +(1.30902 - 4.02874i) q^{31} +1.00000 q^{32} +(6.35410 - 4.61653i) q^{34} +(2.07295 + 6.37988i) q^{35} +(-5.92705 + 4.30625i) q^{37} +(0.690983 - 0.502029i) q^{38} -2.23607 q^{40} +(-6.04508 + 4.39201i) q^{41} -1.76393 q^{43} +(0.0729490 - 0.224514i) q^{44} +(1.92705 + 5.93085i) q^{46} +(-1.83688 - 5.65334i) q^{47} +2.00000 q^{49} +5.00000 q^{50} +(-0.809017 - 0.587785i) q^{52} +(-0.472136 - 1.45309i) q^{53} +(-0.163119 + 0.502029i) q^{55} +(-0.927051 + 2.85317i) q^{56} +(0.163119 - 0.502029i) q^{58} +(3.61803 - 2.62866i) q^{59} +(1.73607 + 1.26133i) q^{61} +(-3.42705 + 2.48990i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(1.80902 + 1.31433i) q^{65} +(-1.78115 + 5.48183i) q^{67} -7.85410 q^{68} +(2.07295 - 6.37988i) q^{70} +(0.927051 + 2.85317i) q^{71} +(4.61803 + 3.35520i) q^{73} +7.32624 q^{74} -0.854102 q^{76} +(0.572949 + 0.416272i) q^{77} +(-0.854102 - 2.62866i) q^{79} +(1.80902 + 1.31433i) q^{80} +7.47214 q^{82} +(4.16312 - 12.8128i) q^{83} +17.5623 q^{85} +(1.42705 + 1.03681i) q^{86} +(-0.190983 + 0.138757i) q^{88} +(-3.61803 - 2.62866i) q^{89} +(2.42705 - 1.76336i) q^{91} +(1.92705 - 5.93085i) q^{92} +(-1.83688 + 5.65334i) q^{94} +1.90983 q^{95} +(-3.26393 - 10.0453i) q^{97} +(-1.61803 - 1.17557i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - q^{2} - q^{4} - 5q^{5} - 12q^{7} - q^{8} + O(q^{10}) \) \( 4q - q^{2} - q^{4} - 5q^{5} - 12q^{7} - q^{8} - 5q^{10} - 3q^{11} - q^{13} + 3q^{14} - q^{16} - 3q^{17} - 10q^{19} + 5q^{20} + 7q^{22} - 9q^{23} - 5q^{25} + 4q^{26} + 3q^{28} - 15q^{29} + 3q^{31} + 4q^{32} + 12q^{34} + 15q^{35} - 17q^{37} + 5q^{38} - 13q^{41} - 16q^{43} + 7q^{44} + q^{46} - 23q^{47} + 8q^{49} + 20q^{50} - q^{52} + 16q^{53} + 15q^{55} + 3q^{56} - 15q^{58} + 10q^{59} - 2q^{61} - 7q^{62} - q^{64} + 5q^{65} + 13q^{67} - 18q^{68} + 15q^{70} - 3q^{71} + 14q^{73} - 2q^{74} + 10q^{76} + 9q^{77} + 10q^{79} + 5q^{80} + 12q^{82} + q^{83} + 30q^{85} - q^{86} - 3q^{88} - 10q^{89} + 3q^{91} + q^{92} - 23q^{94} + 30q^{95} - 22q^{97} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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
\(3\) 0 0
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) −0.690983 2.12663i −0.309017 0.951057i
\(6\) 0 0
\(7\) −3.00000 −1.13389 −0.566947 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) 0.309017 0.951057i 0.109254 0.336249i
\(9\) 0 0
\(10\) −0.690983 + 2.12663i −0.218508 + 0.672499i
\(11\) −0.190983 0.138757i −0.0575835 0.0418369i 0.558621 0.829423i \(-0.311331\pi\)
−0.616205 + 0.787586i \(0.711331\pi\)
\(12\) 0 0
\(13\) −0.809017 + 0.587785i −0.224381 + 0.163022i −0.694297 0.719689i \(-0.744284\pi\)
0.469916 + 0.882711i \(0.344284\pi\)
\(14\) 2.42705 + 1.76336i 0.648657 + 0.471277i
\(15\) 0 0
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) −2.42705 + 7.46969i −0.588646 + 1.81167i −0.00454037 + 0.999990i \(0.501445\pi\)
−0.584106 + 0.811677i \(0.698555\pi\)
\(18\) 0 0
\(19\) −0.263932 + 0.812299i −0.0605502 + 0.186354i −0.976756 0.214353i \(-0.931236\pi\)
0.916206 + 0.400707i \(0.131236\pi\)
\(20\) 1.80902 1.31433i 0.404508 0.293893i
\(21\) 0 0
\(22\) 0.0729490 + 0.224514i 0.0155528 + 0.0478665i
\(23\) −5.04508 3.66547i −1.05197 0.764303i −0.0793863 0.996844i \(-0.525296\pi\)
−0.972587 + 0.232541i \(0.925296\pi\)
\(24\) 0 0
\(25\) −4.04508 + 2.93893i −0.809017 + 0.587785i
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) −0.927051 2.85317i −0.175196 0.539198i
\(29\) 0.163119 + 0.502029i 0.0302904 + 0.0932244i 0.965059 0.262033i \(-0.0843931\pi\)
−0.934768 + 0.355258i \(0.884393\pi\)
\(30\) 0 0
\(31\) 1.30902 4.02874i 0.235106 0.723583i −0.762001 0.647576i \(-0.775783\pi\)
0.997107 0.0760071i \(-0.0242172\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 6.35410 4.61653i 1.08972 0.791728i
\(35\) 2.07295 + 6.37988i 0.350392 + 1.07840i
\(36\) 0 0
\(37\) −5.92705 + 4.30625i −0.974401 + 0.707944i −0.956450 0.291895i \(-0.905714\pi\)
−0.0179508 + 0.999839i \(0.505714\pi\)
\(38\) 0.690983 0.502029i 0.112092 0.0814398i
\(39\) 0 0
\(40\) −2.23607 −0.353553
\(41\) −6.04508 + 4.39201i −0.944084 + 0.685917i −0.949400 0.314069i \(-0.898308\pi\)
0.00531652 + 0.999986i \(0.498308\pi\)
\(42\) 0 0
\(43\) −1.76393 −0.268997 −0.134499 0.990914i \(-0.542942\pi\)
−0.134499 + 0.990914i \(0.542942\pi\)
\(44\) 0.0729490 0.224514i 0.0109975 0.0338468i
\(45\) 0 0
\(46\) 1.92705 + 5.93085i 0.284128 + 0.874457i
\(47\) −1.83688 5.65334i −0.267937 0.824624i −0.991002 0.133845i \(-0.957268\pi\)
0.723066 0.690779i \(-0.242732\pi\)
\(48\) 0 0
\(49\) 2.00000 0.285714
\(50\) 5.00000 0.707107
\(51\) 0 0
\(52\) −0.809017 0.587785i −0.112190 0.0815111i
\(53\) −0.472136 1.45309i −0.0648529 0.199597i 0.913379 0.407109i \(-0.133463\pi\)
−0.978232 + 0.207513i \(0.933463\pi\)
\(54\) 0 0
\(55\) −0.163119 + 0.502029i −0.0219950 + 0.0676935i
\(56\) −0.927051 + 2.85317i −0.123882 + 0.381271i
\(57\) 0 0
\(58\) 0.163119 0.502029i 0.0214186 0.0659196i
\(59\) 3.61803 2.62866i 0.471028 0.342222i −0.326814 0.945089i \(-0.605975\pi\)
0.797842 + 0.602867i \(0.205975\pi\)
\(60\) 0 0
\(61\) 1.73607 + 1.26133i 0.222281 + 0.161496i 0.693353 0.720598i \(-0.256133\pi\)
−0.471072 + 0.882095i \(0.656133\pi\)
\(62\) −3.42705 + 2.48990i −0.435236 + 0.316217i
\(63\) 0 0
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) 1.80902 + 1.31433i 0.224381 + 0.163022i
\(66\) 0 0
\(67\) −1.78115 + 5.48183i −0.217602 + 0.669712i 0.781356 + 0.624085i \(0.214528\pi\)
−0.998959 + 0.0456261i \(0.985472\pi\)
\(68\) −7.85410 −0.952450
\(69\) 0 0
\(70\) 2.07295 6.37988i 0.247765 0.762542i
\(71\) 0.927051 + 2.85317i 0.110021 + 0.338609i 0.990876 0.134777i \(-0.0430317\pi\)
−0.880855 + 0.473386i \(0.843032\pi\)
\(72\) 0 0
\(73\) 4.61803 + 3.35520i 0.540500 + 0.392696i 0.824271 0.566196i \(-0.191585\pi\)
−0.283771 + 0.958892i \(0.591585\pi\)
\(74\) 7.32624 0.851658
\(75\) 0 0
\(76\) −0.854102 −0.0979722
\(77\) 0.572949 + 0.416272i 0.0652936 + 0.0474386i
\(78\) 0 0
\(79\) −0.854102 2.62866i −0.0960940 0.295747i 0.891443 0.453132i \(-0.149693\pi\)
−0.987537 + 0.157385i \(0.949693\pi\)
\(80\) 1.80902 + 1.31433i 0.202254 + 0.146946i
\(81\) 0 0
\(82\) 7.47214 0.825159
\(83\) 4.16312 12.8128i 0.456962 1.40638i −0.411855 0.911249i \(-0.635119\pi\)
0.868817 0.495134i \(-0.164881\pi\)
\(84\) 0 0
\(85\) 17.5623 1.90490
\(86\) 1.42705 + 1.03681i 0.153883 + 0.111802i
\(87\) 0 0
\(88\) −0.190983 + 0.138757i −0.0203589 + 0.0147916i
\(89\) −3.61803 2.62866i −0.383511 0.278637i 0.379280 0.925282i \(-0.376172\pi\)
−0.762791 + 0.646645i \(0.776172\pi\)
\(90\) 0 0
\(91\) 2.42705 1.76336i 0.254424 0.184850i
\(92\) 1.92705 5.93085i 0.200909 0.618334i
\(93\) 0 0
\(94\) −1.83688 + 5.65334i −0.189460 + 0.583097i
\(95\) 1.90983 0.195944
\(96\) 0 0
\(97\) −3.26393 10.0453i −0.331402 1.01995i −0.968467 0.249141i \(-0.919852\pi\)
0.637065 0.770810i \(-0.280148\pi\)
\(98\) −1.61803 1.17557i −0.163446 0.118751i
\(99\) 0 0
\(100\) −4.04508 2.93893i −0.404508 0.293893i
\(101\) 1.61803 0.161000 0.0805002 0.996755i \(-0.474348\pi\)
0.0805002 + 0.996755i \(0.474348\pi\)
\(102\) 0 0
\(103\) −6.13525 18.8824i −0.604525 1.86054i −0.500026 0.866010i \(-0.666676\pi\)
−0.104499 0.994525i \(-0.533324\pi\)
\(104\) 0.309017 + 0.951057i 0.0303016 + 0.0932588i
\(105\) 0 0
\(106\) −0.472136 + 1.45309i −0.0458579 + 0.141136i
\(107\) −10.0902 −0.975454 −0.487727 0.872996i \(-0.662174\pi\)
−0.487727 + 0.872996i \(0.662174\pi\)
\(108\) 0 0
\(109\) 12.1353 8.81678i 1.16235 0.844494i 0.172274 0.985049i \(-0.444889\pi\)
0.990073 + 0.140555i \(0.0448886\pi\)
\(110\) 0.427051 0.310271i 0.0407177 0.0295832i
\(111\) 0 0
\(112\) 2.42705 1.76336i 0.229335 0.166621i
\(113\) 6.66312 4.84104i 0.626814 0.455407i −0.228481 0.973548i \(-0.573376\pi\)
0.855295 + 0.518142i \(0.173376\pi\)
\(114\) 0 0
\(115\) −4.30902 + 13.2618i −0.401818 + 1.23667i
\(116\) −0.427051 + 0.310271i −0.0396507 + 0.0288079i
\(117\) 0 0
\(118\) −4.47214 −0.411693
\(119\) 7.28115 22.4091i 0.667462 2.05424i
\(120\) 0 0
\(121\) −3.38197 10.4086i −0.307451 0.946238i
\(122\) −0.663119 2.04087i −0.0600360 0.184772i
\(123\) 0 0
\(124\) 4.23607 0.380410
\(125\) 9.04508 + 6.57164i 0.809017 + 0.587785i
\(126\) 0 0
\(127\) 10.0902 + 7.33094i 0.895358 + 0.650516i 0.937269 0.348606i \(-0.113345\pi\)
−0.0419116 + 0.999121i \(0.513345\pi\)
\(128\) 0.309017 + 0.951057i 0.0273135 + 0.0840623i
\(129\) 0 0
\(130\) −0.690983 2.12663i −0.0606032 0.186518i
\(131\) −3.21885 + 9.90659i −0.281232 + 0.865543i 0.706271 + 0.707942i \(0.250376\pi\)
−0.987503 + 0.157601i \(0.949624\pi\)
\(132\) 0 0
\(133\) 0.791796 2.43690i 0.0686574 0.211306i
\(134\) 4.66312 3.38795i 0.402832 0.292675i
\(135\) 0 0
\(136\) 6.35410 + 4.61653i 0.544860 + 0.395864i
\(137\) −4.92705 + 3.57971i −0.420946 + 0.305835i −0.778018 0.628241i \(-0.783775\pi\)
0.357072 + 0.934077i \(0.383775\pi\)
\(138\) 0 0
\(139\) −8.35410 6.06961i −0.708586 0.514818i 0.174131 0.984722i \(-0.444288\pi\)
−0.882717 + 0.469905i \(0.844288\pi\)
\(140\) −5.42705 + 3.94298i −0.458670 + 0.333243i
\(141\) 0 0
\(142\) 0.927051 2.85317i 0.0777964 0.239433i
\(143\) 0.236068 0.0197410
\(144\) 0 0
\(145\) 0.954915 0.693786i 0.0793014 0.0576158i
\(146\) −1.76393 5.42882i −0.145984 0.449293i
\(147\) 0 0
\(148\) −5.92705 4.30625i −0.487201 0.353972i
\(149\) 2.23607 0.183186 0.0915929 0.995797i \(-0.470804\pi\)
0.0915929 + 0.995797i \(0.470804\pi\)
\(150\) 0 0
\(151\) 3.70820 0.301769 0.150885 0.988551i \(-0.451788\pi\)
0.150885 + 0.988551i \(0.451788\pi\)
\(152\) 0.690983 + 0.502029i 0.0560461 + 0.0407199i
\(153\) 0 0
\(154\) −0.218847 0.673542i −0.0176352 0.0542756i
\(155\) −9.47214 −0.760820
\(156\) 0 0
\(157\) −15.5623 −1.24201 −0.621004 0.783808i \(-0.713275\pi\)
−0.621004 + 0.783808i \(0.713275\pi\)
\(158\) −0.854102 + 2.62866i −0.0679487 + 0.209125i
\(159\) 0 0
\(160\) −0.690983 2.12663i −0.0546270 0.168125i
\(161\) 15.1353 + 10.9964i 1.19283 + 0.866638i
\(162\) 0 0
\(163\) 3.92705 2.85317i 0.307590 0.223477i −0.423271 0.906003i \(-0.639118\pi\)
0.730862 + 0.682525i \(0.239118\pi\)
\(164\) −6.04508 4.39201i −0.472042 0.342958i
\(165\) 0 0
\(166\) −10.8992 + 7.91872i −0.845941 + 0.614612i
\(167\) −4.82624 + 14.8536i −0.373466 + 1.14941i 0.571043 + 0.820920i \(0.306539\pi\)
−0.944508 + 0.328488i \(0.893461\pi\)
\(168\) 0 0
\(169\) −3.70820 + 11.4127i −0.285246 + 0.877898i
\(170\) −14.2082 10.3229i −1.08972 0.791728i
\(171\) 0 0
\(172\) −0.545085 1.67760i −0.0415623 0.127916i
\(173\) 2.61803 + 1.90211i 0.199045 + 0.144615i 0.682843 0.730565i \(-0.260743\pi\)
−0.483798 + 0.875180i \(0.660743\pi\)
\(174\) 0 0
\(175\) 12.1353 8.81678i 0.917339 0.666486i
\(176\) 0.236068 0.0177943
\(177\) 0 0
\(178\) 1.38197 + 4.25325i 0.103583 + 0.318795i
\(179\) 3.45492 + 10.6331i 0.258232 + 0.794758i 0.993176 + 0.116629i \(0.0372089\pi\)
−0.734943 + 0.678129i \(0.762791\pi\)
\(180\) 0 0
\(181\) −6.61803 + 20.3682i −0.491915 + 1.51396i 0.329796 + 0.944052i \(0.393020\pi\)
−0.821710 + 0.569905i \(0.806980\pi\)
\(182\) −3.00000 −0.222375
\(183\) 0 0
\(184\) −5.04508 + 3.66547i −0.371929 + 0.270222i
\(185\) 13.2533 + 9.62908i 0.974401 + 0.707944i
\(186\) 0 0
\(187\) 1.50000 1.08981i 0.109691 0.0796951i
\(188\) 4.80902 3.49396i 0.350734 0.254823i
\(189\) 0 0
\(190\) −1.54508 1.12257i −0.112092 0.0814398i
\(191\) 14.2812 10.3759i 1.03335 0.750771i 0.0643719 0.997926i \(-0.479496\pi\)
0.968976 + 0.247155i \(0.0794956\pi\)
\(192\) 0 0
\(193\) 16.6525 1.19867 0.599336 0.800498i \(-0.295431\pi\)
0.599336 + 0.800498i \(0.295431\pi\)
\(194\) −3.26393 + 10.0453i −0.234337 + 0.721214i
\(195\) 0 0
\(196\) 0.618034 + 1.90211i 0.0441453 + 0.135865i
\(197\) −3.70820 11.4127i −0.264199 0.813120i −0.991877 0.127201i \(-0.959401\pi\)
0.727678 0.685919i \(-0.240599\pi\)
\(198\) 0 0
\(199\) −17.5623 −1.24496 −0.622479 0.782636i \(-0.713875\pi\)
−0.622479 + 0.782636i \(0.713875\pi\)
\(200\) 1.54508 + 4.75528i 0.109254 + 0.336249i
\(201\) 0 0
\(202\) −1.30902 0.951057i −0.0921021 0.0669161i
\(203\) −0.489357 1.50609i −0.0343461 0.105706i
\(204\) 0 0
\(205\) 13.5172 + 9.82084i 0.944084 + 0.685917i
\(206\) −6.13525 + 18.8824i −0.427463 + 1.31560i
\(207\) 0 0
\(208\) 0.309017 0.951057i 0.0214265 0.0659439i
\(209\) 0.163119 0.118513i 0.0112832 0.00819771i
\(210\) 0 0
\(211\) −9.11803 6.62464i −0.627711 0.456059i 0.227895 0.973686i \(-0.426816\pi\)
−0.855607 + 0.517627i \(0.826816\pi\)
\(212\) 1.23607 0.898056i 0.0848935 0.0616787i
\(213\) 0 0
\(214\) 8.16312 + 5.93085i 0.558019 + 0.405425i
\(215\) 1.21885 + 3.75123i 0.0831247 + 0.255831i
\(216\) 0 0
\(217\) −3.92705 + 12.0862i −0.266586 + 0.820466i
\(218\) −15.0000 −1.01593
\(219\) 0 0
\(220\) −0.527864 −0.0355886
\(221\) −2.42705 7.46969i −0.163261 0.502466i
\(222\) 0 0
\(223\) 7.28115 + 5.29007i 0.487582 + 0.354249i 0.804254 0.594286i \(-0.202565\pi\)
−0.316672 + 0.948535i \(0.602565\pi\)
\(224\) −3.00000 −0.200446
\(225\) 0 0
\(226\) −8.23607 −0.547855
\(227\) −12.4271 9.02878i −0.824812 0.599261i 0.0932746 0.995640i \(-0.470267\pi\)
−0.918087 + 0.396379i \(0.870267\pi\)
\(228\) 0 0
\(229\) 5.42705 + 16.7027i 0.358630 + 1.10375i 0.953875 + 0.300204i \(0.0970549\pi\)
−0.595245 + 0.803544i \(0.702945\pi\)
\(230\) 11.2812 8.19624i 0.743857 0.540444i
\(231\) 0 0
\(232\) 0.527864 0.0346560
\(233\) −8.56231 + 26.3521i −0.560935 + 1.72638i 0.118795 + 0.992919i \(0.462097\pi\)
−0.679730 + 0.733463i \(0.737903\pi\)
\(234\) 0 0
\(235\) −10.7533 + 7.81272i −0.701467 + 0.509646i
\(236\) 3.61803 + 2.62866i 0.235514 + 0.171111i
\(237\) 0 0
\(238\) −19.0623 + 13.8496i −1.23563 + 0.897735i
\(239\) −14.6353 10.6331i −0.946676 0.687800i 0.00334240 0.999994i \(-0.498936\pi\)
−0.950018 + 0.312194i \(0.898936\pi\)
\(240\) 0 0
\(241\) −10.8262 + 7.86572i −0.697379 + 0.506676i −0.879078 0.476679i \(-0.841841\pi\)
0.181698 + 0.983354i \(0.441841\pi\)
\(242\) −3.38197 + 10.4086i −0.217401 + 0.669092i
\(243\) 0 0
\(244\) −0.663119 + 2.04087i −0.0424518 + 0.130653i
\(245\) −1.38197 4.25325i −0.0882906 0.271730i
\(246\) 0 0
\(247\) −0.263932 0.812299i −0.0167936 0.0516854i
\(248\) −3.42705 2.48990i −0.217618 0.158109i
\(249\) 0 0
\(250\) −3.45492 10.6331i −0.218508 0.672499i
\(251\) −23.1803 −1.46313 −0.731565 0.681772i \(-0.761210\pi\)
−0.731565 + 0.681772i \(0.761210\pi\)
\(252\) 0 0
\(253\) 0.454915 + 1.40008i 0.0286003 + 0.0880226i
\(254\) −3.85410 11.8617i −0.241828 0.744270i
\(255\) 0 0
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 16.7426 1.04438 0.522189 0.852830i \(-0.325116\pi\)
0.522189 + 0.852830i \(0.325116\pi\)
\(258\) 0 0
\(259\) 17.7812 12.9188i 1.10487 0.802733i
\(260\) −0.690983 + 2.12663i −0.0428529 + 0.131888i
\(261\) 0 0
\(262\) 8.42705 6.12261i 0.520625 0.378256i
\(263\) 1.92705 1.40008i 0.118827 0.0863329i −0.526785 0.849999i \(-0.676603\pi\)
0.645612 + 0.763666i \(0.276603\pi\)
\(264\) 0 0
\(265\) −2.76393 + 2.00811i −0.169787 + 0.123357i
\(266\) −2.07295 + 1.50609i −0.127101 + 0.0923440i
\(267\) 0 0
\(268\) −5.76393 −0.352088
\(269\) −4.04508 + 12.4495i −0.246633 + 0.759059i 0.748730 + 0.662875i \(0.230664\pi\)
−0.995364 + 0.0961842i \(0.969336\pi\)
\(270\) 0 0
\(271\) −2.93769 9.04129i −0.178452 0.549219i 0.821322 0.570465i \(-0.193237\pi\)
−0.999774 + 0.0212453i \(0.993237\pi\)
\(272\) −2.42705 7.46969i −0.147162 0.452917i
\(273\) 0 0
\(274\) 6.09017 0.367921
\(275\) 1.18034 0.0711772
\(276\) 0 0
\(277\) −11.0902 8.05748i −0.666344 0.484127i 0.202456 0.979291i \(-0.435108\pi\)
−0.868799 + 0.495164i \(0.835108\pi\)
\(278\) 3.19098 + 9.82084i 0.191382 + 0.589015i
\(279\) 0 0
\(280\) 6.70820 0.400892
\(281\) 5.92705 18.2416i 0.353578 1.08820i −0.603251 0.797551i \(-0.706128\pi\)
0.956829 0.290651i \(-0.0938717\pi\)
\(282\) 0 0
\(283\) −7.94427 + 24.4500i −0.472238 + 1.45340i 0.377409 + 0.926047i \(0.376815\pi\)
−0.849647 + 0.527352i \(0.823185\pi\)
\(284\) −2.42705 + 1.76336i −0.144019 + 0.104636i
\(285\) 0 0
\(286\) −0.190983 0.138757i −0.0112931 0.00820489i
\(287\) 18.1353 13.1760i 1.07049 0.777757i
\(288\) 0 0
\(289\) −36.1525 26.2663i −2.12662 1.54508i
\(290\) −1.18034 −0.0693119
\(291\) 0 0
\(292\) −1.76393 + 5.42882i −0.103226 + 0.317698i
\(293\) 11.5623 0.675477 0.337739 0.941240i \(-0.390338\pi\)
0.337739 + 0.941240i \(0.390338\pi\)
\(294\) 0 0
\(295\) −8.09017 5.87785i −0.471028 0.342222i
\(296\) 2.26393 + 6.96767i 0.131588 + 0.404987i
\(297\) 0 0
\(298\) −1.80902 1.31433i −0.104794 0.0761370i
\(299\) 6.23607 0.360641
\(300\) 0 0
\(301\) 5.29180 0.305014
\(302\) −3.00000 2.17963i −0.172631 0.125423i
\(303\) 0 0
\(304\) −0.263932 0.812299i −0.0151375 0.0465886i
\(305\) 1.48278 4.56352i 0.0849037 0.261307i
\(306\) 0 0
\(307\) 17.1246 0.977353 0.488677 0.872465i \(-0.337480\pi\)
0.488677 + 0.872465i \(0.337480\pi\)
\(308\) −0.218847 + 0.673542i −0.0124700 + 0.0383786i
\(309\) 0 0
\(310\) 7.66312 + 5.56758i 0.435236 + 0.316217i
\(311\) −17.0623 12.3965i −0.967515 0.702941i −0.0126308 0.999920i \(-0.504021\pi\)
−0.954884 + 0.296980i \(0.904021\pi\)
\(312\) 0 0
\(313\) −2.88197 + 2.09387i −0.162898 + 0.118353i −0.666248 0.745730i \(-0.732101\pi\)
0.503350 + 0.864083i \(0.332101\pi\)
\(314\) 12.5902 + 9.14729i 0.710504 + 0.516212i
\(315\) 0 0
\(316\) 2.23607 1.62460i 0.125789 0.0913908i
\(317\) −3.28115 + 10.0984i −0.184288 + 0.567180i −0.999935 0.0113694i \(-0.996381\pi\)
0.815647 + 0.578549i \(0.196381\pi\)
\(318\) 0 0
\(319\) 0.0385072 0.118513i 0.00215599 0.00663545i
\(320\) −0.690983 + 2.12663i −0.0386271 + 0.118882i
\(321\) 0 0
\(322\) −5.78115 17.7926i −0.322171 0.991541i
\(323\) −5.42705 3.94298i −0.301969 0.219393i
\(324\) 0 0
\(325\) 1.54508 4.75528i 0.0857059 0.263776i
\(326\) −4.85410 −0.268844
\(327\) 0 0
\(328\) 2.30902 + 7.10642i 0.127494 + 0.392387i
\(329\) 5.51064 + 16.9600i 0.303812 + 0.935036i
\(330\) 0 0
\(331\) 1.40983 4.33901i 0.0774913 0.238494i −0.904805 0.425825i \(-0.859984\pi\)
0.982297 + 0.187332i \(0.0599839\pi\)
\(332\) 13.4721 0.739380
\(333\) 0 0
\(334\) 12.6353 9.18005i 0.691370 0.502310i
\(335\) 12.8885 0.704176
\(336\) 0 0
\(337\) 25.4164 18.4661i 1.38452 1.00591i 0.388078 0.921626i \(-0.373139\pi\)
0.996442 0.0842863i \(-0.0268610\pi\)
\(338\) 9.70820 7.05342i 0.528057 0.383656i
\(339\) 0 0
\(340\) 5.42705 + 16.7027i 0.294323 + 0.905834i
\(341\) −0.809017 + 0.587785i −0.0438107 + 0.0318304i
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) −0.545085 + 1.67760i −0.0293890 + 0.0904501i
\(345\) 0 0
\(346\) −1.00000 3.07768i −0.0537603 0.165457i
\(347\) 3.06231 + 9.42481i 0.164393 + 0.505950i 0.998991 0.0449095i \(-0.0142999\pi\)
−0.834598 + 0.550860i \(0.814300\pi\)
\(348\) 0 0
\(349\) −22.2361 −1.19027 −0.595135 0.803626i \(-0.702901\pi\)
−0.595135 + 0.803626i \(0.702901\pi\)
\(350\) −15.0000 −0.801784
\(351\) 0 0
\(352\) −0.190983 0.138757i −0.0101794 0.00739579i
\(353\) 5.18034 + 15.9434i 0.275722 + 0.848584i 0.989028 + 0.147731i \(0.0471970\pi\)
−0.713306 + 0.700853i \(0.752803\pi\)
\(354\) 0 0
\(355\) 5.42705 3.94298i 0.288038 0.209272i
\(356\) 1.38197 4.25325i 0.0732441 0.225422i
\(357\) 0 0
\(358\) 3.45492 10.6331i 0.182598 0.561979i
\(359\) 2.50000 1.81636i 0.131945 0.0958636i −0.519855 0.854254i \(-0.674014\pi\)
0.651800 + 0.758391i \(0.274014\pi\)
\(360\) 0 0
\(361\) 14.7812 + 10.7391i 0.777955 + 0.565218i
\(362\) 17.3262 12.5882i 0.910647 0.661624i
\(363\) 0 0
\(364\) 2.42705 + 1.76336i 0.127212 + 0.0924250i
\(365\) 3.94427 12.1392i 0.206453 0.635396i
\(366\) 0 0
\(367\) −9.74671 + 29.9973i −0.508774 + 1.56585i 0.285557 + 0.958362i \(0.407821\pi\)
−0.794332 + 0.607484i \(0.792179\pi\)
\(368\) 6.23607 0.325078
\(369\) 0 0
\(370\) −5.06231 15.5802i −0.263177 0.809975i
\(371\) 1.41641 + 4.35926i 0.0735362 + 0.226321i
\(372\) 0 0
\(373\) 13.1353 + 9.54332i 0.680118 + 0.494134i 0.873397 0.487009i \(-0.161912\pi\)
−0.193279 + 0.981144i \(0.561912\pi\)
\(374\) −1.85410 −0.0958733
\(375\) 0 0
\(376\) −5.94427 −0.306552
\(377\) −0.427051 0.310271i −0.0219942 0.0159798i
\(378\) 0 0
\(379\) 0.163119 + 0.502029i 0.00837886 + 0.0257875i 0.955159 0.296095i \(-0.0956845\pi\)
−0.946780 + 0.321882i \(0.895684\pi\)
\(380\) 0.590170 + 1.81636i 0.0302751 + 0.0931771i
\(381\) 0 0
\(382\) −17.6525 −0.903179
\(383\) 1.33688 4.11450i 0.0683114 0.210241i −0.911073 0.412244i \(-0.864745\pi\)
0.979385 + 0.202003i \(0.0647451\pi\)
\(384\) 0 0
\(385\) 0.489357 1.50609i 0.0249399 0.0767572i
\(386\) −13.4721 9.78808i −0.685714 0.498200i
\(387\) 0 0
\(388\) 8.54508 6.20837i 0.433811 0.315182i
\(389\) −26.8713 19.5232i −1.36243 0.989863i −0.998286 0.0585208i \(-0.981362\pi\)
−0.364144 0.931343i \(-0.618638\pi\)
\(390\) 0 0
\(391\) 39.6246 28.7890i 2.00390 1.45592i
\(392\) 0.618034 1.90211i 0.0312154 0.0960712i
\(393\) 0 0
\(394\) −3.70820 + 11.4127i −0.186817 + 0.574962i
\(395\) −5.00000 + 3.63271i −0.251577 + 0.182782i
\(396\) 0 0
\(397\) −1.78115 5.48183i −0.0893935 0.275125i 0.896359 0.443330i \(-0.146203\pi\)
−0.985752 + 0.168205i \(0.946203\pi\)
\(398\) 14.2082 + 10.3229i 0.712193 + 0.517438i
\(399\) 0 0
\(400\) 1.54508 4.75528i 0.0772542 0.237764i
\(401\) −8.18034 −0.408507 −0.204253 0.978918i \(-0.565477\pi\)
−0.204253 + 0.978918i \(0.565477\pi\)
\(402\) 0 0
\(403\) 1.30902 + 4.02874i 0.0652068 + 0.200686i
\(404\) 0.500000 + 1.53884i 0.0248759 + 0.0765602i
\(405\) 0 0
\(406\) −0.489357 + 1.50609i −0.0242864 + 0.0747458i
\(407\) 1.72949 0.0857276
\(408\) 0 0
\(409\) −5.42705 + 3.94298i −0.268350 + 0.194968i −0.713820 0.700329i \(-0.753037\pi\)
0.445470 + 0.895297i \(0.353037\pi\)
\(410\) −5.16312 15.8904i −0.254988 0.784773i
\(411\) 0 0
\(412\) 16.0623 11.6699i 0.791333 0.574937i
\(413\) −10.8541 + 7.88597i −0.534095 + 0.388043i
\(414\) 0 0
\(415\) −30.1246 −1.47876
\(416\) −0.809017 + 0.587785i −0.0396653 + 0.0288185i
\(417\) 0 0
\(418\) −0.201626 −0.00986186
\(419\) −8.41641 + 25.9030i −0.411168 + 1.26545i 0.504465 + 0.863432i \(0.331690\pi\)
−0.915633 + 0.402014i \(0.868310\pi\)
\(420\) 0 0
\(421\) −3.79180 11.6699i −0.184801 0.568758i 0.815144 0.579258i \(-0.196658\pi\)
−0.999945 + 0.0104998i \(0.996658\pi\)
\(422\) 3.48278 + 10.7189i 0.169539 + 0.521787i
\(423\) 0 0
\(424\) −1.52786 −0.0741996
\(425\) −12.1353 37.3485i −0.588646 1.81167i
\(426\) 0 0
\(427\) −5.20820 3.78398i −0.252043 0.183120i
\(428\) −3.11803 9.59632i −0.150716 0.463856i
\(429\) 0 0
\(430\) 1.21885 3.75123i 0.0587780 0.180900i
\(431\) 9.90983 30.4993i 0.477340 1.46910i −0.365436 0.930836i \(-0.619080\pi\)
0.842776 0.538264i \(-0.180920\pi\)
\(432\) 0 0
\(433\) 7.21885 22.2173i 0.346916 1.06770i −0.613635 0.789590i \(-0.710293\pi\)
0.960550 0.278106i \(-0.0897068\pi\)
\(434\) 10.2812 7.46969i 0.493511 0.358557i
\(435\) 0 0
\(436\) 12.1353 + 8.81678i 0.581173 + 0.422247i
\(437\) 4.30902 3.13068i 0.206128 0.149761i
\(438\) 0 0
\(439\) 4.57295 + 3.32244i 0.218255 + 0.158572i 0.691541 0.722337i \(-0.256932\pi\)
−0.473286 + 0.880909i \(0.656932\pi\)
\(440\) 0.427051 + 0.310271i 0.0203589 + 0.0147916i
\(441\) 0 0
\(442\) −2.42705 + 7.46969i −0.115443 + 0.355297i
\(443\) 7.41641 0.352364 0.176182 0.984358i \(-0.443625\pi\)
0.176182 + 0.984358i \(0.443625\pi\)
\(444\) 0 0
\(445\) −3.09017 + 9.51057i −0.146488 + 0.450844i
\(446\) −2.78115 8.55951i −0.131691 0.405304i
\(447\) 0 0
\(448\) 2.42705 + 1.76336i 0.114667 + 0.0833107i
\(449\) −13.9443 −0.658071 −0.329035 0.944318i \(-0.606724\pi\)
−0.329035 + 0.944318i \(0.606724\pi\)
\(450\) 0 0
\(451\) 1.76393 0.0830603
\(452\) 6.66312 + 4.84104i 0.313407 + 0.227703i
\(453\) 0 0
\(454\) 4.74671 + 14.6089i 0.222774 + 0.685628i
\(455\) −5.42705 3.94298i −0.254424 0.184850i
\(456\) 0 0
\(457\) −11.2148 −0.524605 −0.262303 0.964986i \(-0.584482\pi\)
−0.262303 + 0.964986i \(0.584482\pi\)
\(458\) 5.42705 16.7027i 0.253589 0.780468i
\(459\) 0 0
\(460\) −13.9443 −0.650155
\(461\) 22.7984 + 16.5640i 1.06183 + 0.771462i 0.974425 0.224711i \(-0.0721439\pi\)
0.0874008 + 0.996173i \(0.472144\pi\)
\(462\) 0 0
\(463\) −9.69098 + 7.04091i −0.450378 + 0.327219i −0.789745 0.613435i \(-0.789787\pi\)
0.339367 + 0.940654i \(0.389787\pi\)
\(464\) −0.427051 0.310271i −0.0198253 0.0144040i
\(465\) 0 0
\(466\) 22.4164 16.2865i 1.03842 0.754456i
\(467\) −0.982779 + 3.02468i −0.0454776 + 0.139966i −0.971217 0.238196i \(-0.923444\pi\)
0.925739 + 0.378162i \(0.123444\pi\)
\(468\) 0 0
\(469\) 5.34346 16.4455i 0.246738 0.759381i
\(470\) 13.2918 0.613105
\(471\) 0 0
\(472\) −1.38197 4.25325i −0.0636101 0.195772i
\(473\) 0.336881 + 0.244758i 0.0154898 + 0.0112540i
\(474\) 0 0
\(475\) −1.31966 4.06150i −0.0605502 0.186354i
\(476\) 23.5623 1.07998
\(477\) 0 0
\(478\) 5.59017 + 17.2048i 0.255688 + 0.786928i
\(479\) 12.2984 + 37.8505i 0.561927 + 1.72943i 0.676910 + 0.736066i \(0.263319\pi\)
−0.114983 + 0.993368i \(0.536681\pi\)
\(480\) 0 0
\(481\) 2.26393 6.96767i 0.103226 0.317698i
\(482\) 13.3820 0.609532
\(483\) 0 0
\(484\) 8.85410 6.43288i 0.402459 0.292404i
\(485\) −19.1074 + 13.8823i −0.867622 + 0.630364i
\(486\) 0 0
\(487\) 14.6631 10.6534i 0.664449 0.482751i −0.203713 0.979031i \(-0.565301\pi\)
0.868163 + 0.496280i \(0.165301\pi\)
\(488\) 1.73607 1.26133i 0.0785881 0.0570976i
\(489\) 0 0
\(490\) −1.38197 + 4.25325i −0.0624309 + 0.192142i
\(491\) 11.9443 8.67802i 0.539037 0.391634i −0.284690 0.958620i \(-0.591891\pi\)
0.823727 + 0.566986i \(0.191891\pi\)
\(492\) 0 0
\(493\) −4.14590 −0.186722
\(494\) −0.263932 + 0.812299i −0.0118749 + 0.0365471i
\(495\) 0 0
\(496\) 1.30902 + 4.02874i 0.0587766 + 0.180896i
\(497\) −2.78115 8.55951i −0.124752 0.383946i
\(498\) 0 0
\(499\) 40.8541 1.82888 0.914440 0.404721i \(-0.132631\pi\)
0.914440 + 0.404721i \(0.132631\pi\)
\(500\) −3.45492 + 10.6331i −0.154508 + 0.475528i
\(501\) 0 0
\(502\) 18.7533 + 13.6251i 0.837000 + 0.608116i
\(503\) −2.31966 7.13918i −0.103429 0.318320i 0.885930 0.463819i \(-0.153521\pi\)
−0.989358 + 0.145499i \(0.953521\pi\)
\(504\) 0 0
\(505\) −1.11803 3.44095i −0.0497519 0.153120i
\(506\) 0.454915 1.40008i 0.0202234 0.0622413i
\(507\) 0 0
\(508\) −3.85410 + 11.8617i −0.170998 + 0.526278i
\(509\) −10.5902 + 7.69421i −0.469401 + 0.341040i −0.797208 0.603705i \(-0.793690\pi\)
0.327807 + 0.944745i \(0.393690\pi\)
\(510\) 0 0
\(511\) −13.8541 10.0656i −0.612869 0.445276i
\(512\) −0.809017 + 0.587785i −0.0357538 + 0.0259767i
\(513\) 0 0
\(514\) −13.5451 9.84108i −0.597448 0.434071i
\(515\) −35.9164 + 26.0948i −1.58267 + 1.14987i
\(516\) 0 0
\(517\) −0.433629 + 1.33457i −0.0190710 + 0.0586944i
\(518\) −21.9787 −0.965689
\(519\) 0 0
\(520\) 1.80902 1.31433i 0.0793306 0.0576371i
\(521\) −10.0279 30.8626i −0.439329 1.35211i −0.888585 0.458712i \(-0.848311\pi\)
0.449256 0.893403i \(-0.351689\pi\)
\(522\) 0 0
\(523\) −21.5623 15.6659i −0.942854 0.685023i 0.00625211 0.999980i \(-0.498010\pi\)
−0.949106 + 0.314957i \(0.898010\pi\)
\(524\) −10.4164 −0.455043
\(525\) 0 0
\(526\) −2.38197 −0.103859
\(527\) 26.9164 + 19.5559i 1.17250 + 0.851869i
\(528\) 0 0
\(529\) 4.90983 + 15.1109i 0.213471 + 0.656996i
\(530\) 3.41641 0.148399
\(531\) 0 0
\(532\) 2.56231 0.111090
\(533\) 2.30902 7.10642i 0.100015 0.307813i
\(534\) 0 0
\(535\) 6.97214 + 21.4580i 0.301432 + 0.927711i
\(536\) 4.66312 + 3.38795i 0.201416 + 0.146337i
\(537\) 0 0
\(538\) 10.5902 7.69421i 0.456575 0.331721i
\(539\) −0.381966 0.277515i −0.0164524 0.0119534i
\(540\) 0 0
\(541\) −23.2254 + 16.8743i −0.998539 + 0.725481i −0.961774 0.273843i \(-0.911705\pi\)
−0.0367646 + 0.999324i \(0.511705\pi\)
\(542\) −2.93769 + 9.04129i −0.126185 + 0.388357i
\(543\) 0 0
\(544\) −2.42705 + 7.46969i −0.104059 + 0.320261i
\(545\) −27.1353 19.7149i −1.16235 0.844494i
\(546\) 0 0
\(547\) 3.28115 + 10.0984i 0.140292 + 0.431774i 0.996376 0.0850631i \(-0.0271092\pi\)
−0.856084 + 0.516837i \(0.827109\pi\)
\(548\) −4.92705 3.57971i −0.210473 0.152918i
\(549\) 0 0
\(550\) −0.954915 0.693786i −0.0407177 0.0295832i
\(551\) −0.450850 −0.0192068
\(552\) 0 0
\(553\) 2.56231 + 7.88597i 0.108960 + 0.335345i
\(554\) 4.23607 + 13.0373i 0.179973 + 0.553901i
\(555\) 0 0
\(556\) 3.19098 9.82084i 0.135328 0.416496i
\(557\) 10.8885 0.461362 0.230681 0.973029i \(-0.425905\pi\)
0.230681 + 0.973029i \(0.425905\pi\)
\(558\) 0 0
\(559\) 1.42705 1.03681i 0.0603578 0.0438525i
\(560\) −5.42705 3.94298i −0.229335 0.166621i
\(561\) 0 0
\(562\) −15.5172 + 11.2739i −0.654554 + 0.475562i
\(563\) −28.1976 + 20.4867i −1.18839 + 0.863413i −0.993093 0.117332i \(-0.962566\pi\)
−0.195293 + 0.980745i \(0.562566\pi\)
\(564\) 0 0
\(565\) −14.8992 10.8249i −0.626814 0.455407i
\(566\) 20.7984 15.1109i 0.874221 0.635159i
\(567\) 0 0
\(568\) 3.00000 0.125877
\(569\) −6.87132 + 21.1478i −0.288061 + 0.886560i 0.697404 + 0.716679i \(0.254339\pi\)
−0.985464 + 0.169882i \(0.945661\pi\)
\(570\) 0 0
\(571\) 0.517221 + 1.59184i 0.0216450 + 0.0666165i 0.961296 0.275519i \(-0.0888497\pi\)
−0.939651 + 0.342136i \(0.888850\pi\)
\(572\) 0.0729490 + 0.224514i 0.00305015 + 0.00938740i
\(573\) 0 0
\(574\) −22.4164 −0.935643
\(575\) 31.1803 1.30031
\(576\) 0 0
\(577\) 34.7877 + 25.2748i 1.44823 + 1.05220i 0.986240 + 0.165318i \(0.0528651\pi\)
0.461992 + 0.886884i \(0.347135\pi\)
\(578\) 13.8090 + 42.4998i 0.574379 + 1.76776i
\(579\) 0 0
\(580\) 0.954915 + 0.693786i 0.0396507 + 0.0288079i
\(581\) −12.4894 + 38.4383i −0.518146 + 1.59469i
\(582\) 0 0
\(583\) −0.111456 + 0.343027i −0.00461604 + 0.0142067i
\(584\) 4.61803 3.35520i 0.191096 0.138839i
\(585\) 0 0
\(586\) −9.35410 6.79615i −0.386414 0.280746i
\(587\) −9.56231 + 6.94742i −0.394679 + 0.286751i −0.767370 0.641205i \(-0.778435\pi\)
0.372691 + 0.927955i \(0.378435\pi\)
\(588\) 0 0
\(589\) 2.92705 + 2.12663i 0.120607 + 0.0876261i
\(590\) 3.09017 + 9.51057i 0.127220 + 0.391544i
\(591\) 0 0
\(592\) 2.26393 6.96767i 0.0930470 0.286369i
\(593\) 47.0132 1.93060 0.965299 0.261145i \(-0.0841002\pi\)
0.965299 + 0.261145i \(0.0841002\pi\)
\(594\) 0 0
\(595\) −52.6869 −2.15995
\(596\) 0.690983 + 2.12663i 0.0283038 + 0.0871100i
\(597\) 0 0
\(598\) −5.04508 3.66547i −0.206309 0.149892i
\(599\) 8.94427 0.365453 0.182727 0.983164i \(-0.441508\pi\)
0.182727 + 0.983164i \(0.441508\pi\)
\(600\) 0 0
\(601\) −14.8328 −0.605043 −0.302522 0.953143i \(-0.597828\pi\)
−0.302522 + 0.953143i \(0.597828\pi\)
\(602\) −4.28115 3.11044i −0.174487 0.126772i
\(603\) 0 0
\(604\) 1.14590 + 3.52671i 0.0466259 + 0.143500i
\(605\) −19.7984 + 14.3844i −0.804918 + 0.584807i
\(606\) 0 0
\(607\) −27.1459 −1.10182 −0.550909 0.834565i \(-0.685719\pi\)
−0.550909 + 0.834565i \(0.685719\pi\)
\(608\) −0.263932 + 0.812299i −0.0107039 + 0.0329431i
\(609\) 0 0
\(610\) −3.88197 + 2.82041i −0.157176 + 0.114195i
\(611\) 4.80902 + 3.49396i 0.194552 + 0.141350i
\(612\) 0 0
\(613\) 33.6246 24.4297i 1.35809 0.986707i 0.359521 0.933137i \(-0.382940\pi\)
0.998564 0.0535698i \(-0.0170600\pi\)
\(614\) −13.8541 10.0656i −0.559106 0.406214i
\(615\) 0 0
\(616\) 0.572949 0.416272i 0.0230848 0.0167721i
\(617\) 9.38197 28.8747i 0.377704 1.16245i −0.563933 0.825821i \(-0.690712\pi\)
0.941636 0.336632i \(-0.109288\pi\)
\(618\) 0 0
\(619\) −14.5106 + 44.6592i −0.583232 + 1.79500i 0.0230252 + 0.999735i \(0.492670\pi\)
−0.606257 + 0.795269i \(0.707330\pi\)
\(620\) −2.92705 9.00854i −0.117553 0.361792i
\(621\) 0 0
\(622\) 6.51722 + 20.0579i 0.261317 + 0.804250i
\(623\) 10.8541 + 7.88597i 0.434860 + 0.315945i
\(624\) 0 0
\(625\) 7.72542 23.7764i 0.309017 0.951057i
\(626\) 3.56231 0.142378
\(627\) 0 0
\(628\) −4.80902 14.8006i −0.191901 0.590610i
\(629\) −17.7812 54.7248i −0.708981 2.18202i
\(630\) 0 0
\(631\) 2.72949 8.40051i 0.108659 0.334419i −0.881913 0.471413i \(-0.843744\pi\)
0.990572 + 0.136994i \(0.0437441\pi\)
\(632\) −2.76393 −0.109943
\(633\) 0 0
\(634\) 8.59017 6.24112i 0.341159 0.247867i
\(635\) 8.61803 26.5236i 0.341996 1.05256i
\(636\) 0 0
\(637\) −1.61803 + 1.17557i −0.0641088 + 0.0465778i
\(638\) −0.100813 + 0.0732450i −0.00399123 + 0.00289980i
\(639\) 0 0
\(640\) 1.80902 1.31433i 0.0715077 0.0519534i
\(641\) 11.6180 8.44100i 0.458885 0.333399i −0.334209 0.942499i \(-0.608469\pi\)
0.793094 + 0.609100i \(0.208469\pi\)
\(642\) 0 0
\(643\) −36.2361 −1.42901 −0.714506 0.699630i \(-0.753348\pi\)
−0.714506 + 0.699630i \(0.753348\pi\)
\(644\) −5.78115 + 17.7926i −0.227809 + 0.701125i
\(645\) 0 0
\(646\) 2.07295 + 6.37988i 0.0815591 + 0.251013i
\(647\) −2.36475 7.27794i −0.0929677 0.286125i 0.893751 0.448563i \(-0.148064\pi\)
−0.986719 + 0.162438i \(0.948064\pi\)
\(648\) 0 0
\(649\) −1.05573 −0.0414410
\(650\) −4.04508 + 2.93893i −0.158661 + 0.115274i
\(651\) 0 0
\(652\) 3.92705 + 2.85317i 0.153795 + 0.111739i
\(653\) −12.5451 38.6098i −0.490927 1.51092i −0.823209 0.567738i \(-0.807819\pi\)
0.332282 0.943180i \(-0.392181\pi\)
\(654\) 0 0
\(655\) 23.2918 0.910086
\(656\) 2.30902 7.10642i 0.0901520 0.277459i
\(657\) 0 0
\(658\) 5.51064 16.9600i 0.214827 0.661170i
\(659\) 4.57295 3.32244i 0.178137 0.129424i −0.495144 0.868811i \(-0.664885\pi\)
0.673281 + 0.739387i \(0.264885\pi\)
\(660\) 0 0
\(661\) −5.07295 3.68571i −0.197315 0.143358i 0.484741 0.874658i \(-0.338914\pi\)
−0.682056 + 0.731300i \(0.738914\pi\)
\(662\) −3.69098 + 2.68166i −0.143454 + 0.104226i
\(663\) 0 0
\(664\) −10.8992 7.91872i −0.422970 0.307306i
\(665\) −5.72949 −0.222180
\(666\) 0 0
\(667\) 1.01722 3.13068i 0.0393870 0.121221i
\(668\) −15.6180 −0.604280
\(669\) 0 0
\(670\) −10.4271 7.57570i −0.402832 0.292675i
\(671\) −0.156541 0.481784i −0.00604320 0.0185991i
\(672\) 0 0
\(673\) 1.00000 + 0.726543i 0.0385472 + 0.0280062i 0.606892 0.794784i \(-0.292416\pi\)
−0.568345 + 0.822790i \(0.692416\pi\)
\(674\) −31.4164 −1.21011
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) 8.59017 + 6.24112i 0.330147 + 0.239866i 0.740493 0.672064i \(-0.234592\pi\)
−0.410346 + 0.911930i \(0.634592\pi\)
\(678\) 0 0
\(679\) 9.79180 + 30.1360i 0.375775 + 1.15652i
\(680\) 5.42705 16.7027i 0.208118 0.640521i
\(681\) 0 0
\(682\) 1.00000 0.0382920
\(683\) −10.3090 + 31.7279i −0.394464 + 1.21403i 0.534915 + 0.844906i \(0.320344\pi\)
−0.929379 + 0.369128i \(0.879656\pi\)
\(684\) 0 0
\(685\) 11.0172 + 8.00448i 0.420946 + 0.305835i
\(686\) −12.1353 8.81678i −0.463326 0.336626i
\(687\) 0 0
\(688\) 1.42705 1.03681i 0.0544058 0.0395281i
\(689\) 1.23607 + 0.898056i 0.0470904 + 0.0342132i
\(690\) 0 0
\(691\) −1.02786 + 0.746787i −0.0391018 + 0.0284091i −0.607164 0.794576i \(-0.707693\pi\)
0.568063 + 0.822985i \(0.307693\pi\)
\(692\) −1.00000 + 3.07768i −0.0380143 + 0.116996i
\(693\) 0 0
\(694\) 3.06231 9.42481i 0.116244 0.357761i
\(695\) −7.13525 + 21.9601i −0.270656 + 0.832992i
\(696\) 0 0
\(697\) −18.1353 55.8146i −0.686922 2.11413i
\(698\) 17.9894 + 13.0700i 0.680907 + 0.494708i
\(699\) 0 0
\(700\) 12.1353 + 8.81678i 0.458670 + 0.333243i
\(701\) 4.18034 0.157889 0.0789446 0.996879i \(-0.474845\pi\)
0.0789446 + 0.996879i \(0.474845\pi\)
\(702\) 0 0
\(703\) −1.93363 5.95110i −0.0729282 0.224450i
\(704\) 0.0729490 + 0.224514i 0.00274937 + 0.00846169i
\(705\) 0 0
\(706\) 5.18034 15.9434i 0.194965 0.600040i
\(707\) −4.85410 −0.182557
\(708\) 0 0
\(709\) −6.28115 + 4.56352i −0.235894 + 0.171387i −0.699452 0.714680i \(-0.746572\pi\)
0.463558 + 0.886066i \(0.346572\pi\)
\(710\) −6.70820 −0.251754
\(711\) 0 0
\(712\) −3.61803 + 2.62866i −0.135592 + 0.0985130i
\(713\) −21.3713 + 15.5272i −0.800362 + 0.581497i
\(714\) 0 0
\(715\) −0.163119 0.502029i −0.00610030 0.0187748i
\(716\) −9.04508 + 6.57164i −0.338031 + 0.245594i
\(717\) 0 0
\(718\) −3.09017 −0.115324
\(719\) 8.19098 25.2093i 0.305472 0.940147i −0.674028 0.738705i \(-0.735438\pi\)
0.979501 0.201441i \(-0.0645625\pi\)
\(720\) 0 0
\(721\) 18.4058 + 56.6471i 0.685466 + 2.10965i
\(722\) −5.64590 17.3763i −0.210119 0.646678i
\(723\) 0 0
\(724\) −21.4164 −0.795935
\(725\) −2.13525 1.55135i −0.0793014 0.0576158i
\(726\) 0 0
\(727\) 23.1803 + 16.8415i 0.859711 + 0.624617i 0.927806 0.373062i \(-0.121692\pi\)
−0.0680952 + 0.997679i \(0.521692\pi\)
\(728\) −0.927051 2.85317i −0.0343588 0.105745i
\(729\) 0 0
\(730\) −10.3262 + 7.50245i −0.382191 + 0.277678i
\(731\) 4.28115 13.1760i 0.158344 0.487333i
\(732\) 0 0
\(733\) −12.2918 + 37.8303i −0.454008 + 1.39729i 0.418288 + 0.908314i \(0.362630\pi\)
−0.872296 + 0.488978i \(0.837370\pi\)
\(734\) 25.5172 18.5393i 0.941858 0.684300i
\(735\) 0 0
\(736\) −5.04508 3.66547i −0.185964 0.135111i
\(737\) 1.10081 0.799788i 0.0405490 0.0294606i
\(738\) 0 0
\(739\) −24.2705 17.6336i −0.892805 0.648661i 0.0438028 0.999040i \(-0.486053\pi\)
−0.936608 + 0.350379i \(0.886053\pi\)
\(740\) −5.06231 + 15.5802i −0.186094 + 0.572739i
\(741\) 0 0
\(742\) 1.41641 4.35926i 0.0519980 0.160033i
\(743\) 18.2705 0.670280 0.335140 0.942168i \(-0.391216\pi\)
0.335140 + 0.942168i \(0.391216\pi\)
\(744\) 0 0
\(745\) −1.54508 4.75528i −0.0566075 0.174220i
\(746\) −5.01722 15.4414i −0.183694 0.565350i
\(747\) 0 0
\(748\) 1.50000 + 1.08981i 0.0548454 + 0.0398475i
\(749\) 30.2705 1.10606
\(750\) 0 0
\(751\) 1.14590 0.0418144 0.0209072 0.999781i \(-0.493345\pi\)
0.0209072 + 0.999781i \(0.493345\pi\)
\(752\) 4.80902 + 3.49396i 0.175367 + 0.127411i
\(753\) 0 0
\(754\) 0.163119 + 0.502029i 0.00594044 + 0.0182828i
\(755\) −2.56231 7.88597i −0.0932519 0.287000i
\(756\) 0 0
\(757\) 10.4164 0.378591 0.189295 0.981920i \(-0.439380\pi\)
0.189295 + 0.981920i \(0.439380\pi\)
\(758\) 0.163119 0.502029i 0.00592475 0.0182345i
\(759\) 0 0
\(760\) 0.590170 1.81636i 0.0214077 0.0658862i
\(761\) −30.6803 22.2906i −1.11216 0.808033i −0.129159 0.991624i \(-0.541228\pi\)
−0.983003 + 0.183591i \(0.941228\pi\)
\(762\) 0 0
\(763\) −36.4058 + 26.4503i −1.31798 + 0.957566i
\(764\) 14.2812 + 10.3759i 0.516674 + 0.375386i
\(765\) 0 0
\(766\) −3.50000 + 2.54290i −0.126460 + 0.0918787i
\(767\) −1.38197 + 4.25325i −0.0498999 + 0.153576i
\(768\) 0 0
\(769\) −7.23607 + 22.2703i −0.260939 + 0.803089i 0.731662 + 0.681668i \(0.238745\pi\)
−0.992601 + 0.121421i \(0.961255\pi\)
\(770\) −1.28115 + 0.930812i −0.0461695 + 0.0335441i
\(771\) 0 0
\(772\) 5.14590 + 15.8374i 0.185205 + 0.570002i
\(773\) 5.01722 + 3.64522i 0.180457 + 0.131110i 0.674347 0.738415i \(-0.264425\pi\)
−0.493890 + 0.869525i \(0.664425\pi\)
\(774\) 0 0
\(775\) 6.54508 + 20.1437i 0.235106 + 0.723583i
\(776\) −10.5623 −0.379165
\(777\) 0 0
\(778\) 10.2639 + 31.5891i 0.367980 + 1.13253i
\(779\) −1.97214 6.06961i −0.0706591 0.217466i
\(780\) 0 0
\(781\) 0.218847 0.673542i 0.00783096 0.0241012i
\(782\) −48.9787 −1.75148
\(783\) 0 0
\(784\) −1.61803 + 1.17557i −0.0577869 + 0.0419847i
\(785\) 10.7533 + 33.0952i 0.383801 + 1.18122i
\(786\) 0 0
\(787\) −12.4721 + 9.06154i −0.444584 + 0.323009i −0.787454 0.616374i \(-0.788601\pi\)
0.342870 </