Properties

Label 450.2.h.b.91.1
Level $450$
Weight $2$
Character 450.91
Analytic conductor $3.593$
Analytic rank $0$
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: \(0\)
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 150)
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.b.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.690983 + 2.12663i) q^{5} +2.00000 q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})\) \(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.690983 + 2.12663i) q^{5} +2.00000 q^{7} +(0.309017 - 0.951057i) q^{8} +(1.80902 - 1.31433i) q^{10} +(-0.618034 - 0.449028i) q^{11} +(-1.50000 + 1.08981i) q^{13} +(-1.61803 - 1.17557i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-0.354102 + 1.08981i) q^{17} +(-2.23607 + 6.88191i) q^{19} -2.23607 q^{20} +(0.236068 + 0.726543i) q^{22} +(4.85410 + 3.52671i) q^{23} +(-4.04508 - 2.93893i) q^{25} +1.85410 q^{26} +(0.618034 + 1.90211i) q^{28} +(1.11803 + 3.44095i) q^{29} +(-3.00000 + 9.23305i) q^{31} +1.00000 q^{32} +(0.927051 - 0.673542i) q^{34} +(-1.38197 + 4.25325i) q^{35} +(7.16312 - 5.20431i) q^{37} +(5.85410 - 4.25325i) q^{38} +(1.80902 + 1.31433i) q^{40} +(4.11803 - 2.99193i) q^{41} +3.23607 q^{43} +(0.236068 - 0.726543i) q^{44} +(-1.85410 - 5.70634i) q^{46} +(-2.85410 - 8.78402i) q^{47} -3.00000 q^{49} +(1.54508 + 4.75528i) q^{50} +(-1.50000 - 1.08981i) q^{52} +(3.57295 + 10.9964i) q^{53} +(1.38197 - 1.00406i) q^{55} +(0.618034 - 1.90211i) q^{56} +(1.11803 - 3.44095i) q^{58} +(-7.23607 + 5.25731i) q^{59} +(1.73607 + 1.26133i) q^{61} +(7.85410 - 5.70634i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(-1.28115 - 3.94298i) q^{65} +(1.14590 - 3.52671i) q^{67} -1.14590 q^{68} +(3.61803 - 2.62866i) q^{70} +(-2.52786 - 7.77997i) q^{71} +(7.97214 + 5.79210i) q^{73} -8.85410 q^{74} -7.23607 q^{76} +(-1.23607 - 0.898056i) q^{77} +(-0.690983 - 2.12663i) q^{80} -5.09017 q^{82} +(-1.85410 + 5.70634i) q^{83} +(-2.07295 - 1.50609i) q^{85} +(-2.61803 - 1.90211i) q^{86} +(-0.618034 + 0.449028i) q^{88} +(2.92705 + 2.12663i) q^{89} +(-3.00000 + 2.17963i) q^{91} +(-1.85410 + 5.70634i) q^{92} +(-2.85410 + 8.78402i) q^{94} +(-13.0902 - 9.51057i) q^{95} +(-2.20820 - 6.79615i) q^{97} +(2.42705 + 1.76336i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - q^{2} - q^{4} - 5q^{5} + 8q^{7} - q^{8} + O(q^{10}) \) \( 4q - q^{2} - q^{4} - 5q^{5} + 8q^{7} - q^{8} + 5q^{10} + 2q^{11} - 6q^{13} - 2q^{14} - q^{16} + 12q^{17} - 8q^{22} + 6q^{23} - 5q^{25} - 6q^{26} - 2q^{28} - 12q^{31} + 4q^{32} - 3q^{34} - 10q^{35} + 13q^{37} + 10q^{38} + 5q^{40} + 12q^{41} + 4q^{43} - 8q^{44} + 6q^{46} + 2q^{47} - 12q^{49} - 5q^{50} - 6q^{52} + 21q^{53} + 10q^{55} - 2q^{56} - 20q^{59} - 2q^{61} + 18q^{62} - q^{64} + 15q^{65} + 18q^{67} - 18q^{68} + 10q^{70} - 28q^{71} + 14q^{73} - 22q^{74} - 20q^{76} + 4q^{77} - 5q^{80} + 2q^{82} + 6q^{83} - 15q^{85} - 6q^{86} + 2q^{88} + 5q^{89} - 12q^{91} + 6q^{92} + 2q^{94} - 30q^{95} + 18q^{97} + 3q^{98} + O(q^{100}) \)

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
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 0.309017 0.951057i 0.109254 0.336249i
\(9\) 0 0
\(10\) 1.80902 1.31433i 0.572061 0.415627i
\(11\) −0.618034 0.449028i −0.186344 0.135387i 0.490702 0.871327i \(-0.336740\pi\)
−0.677046 + 0.735940i \(0.736740\pi\)
\(12\) 0 0
\(13\) −1.50000 + 1.08981i −0.416025 + 0.302260i −0.776037 0.630688i \(-0.782773\pi\)
0.360011 + 0.932948i \(0.382773\pi\)
\(14\) −1.61803 1.17557i −0.432438 0.314184i
\(15\) 0 0
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) −0.354102 + 1.08981i −0.0858823 + 0.264319i −0.984770 0.173860i \(-0.944376\pi\)
0.898888 + 0.438178i \(0.144376\pi\)
\(18\) 0 0
\(19\) −2.23607 + 6.88191i −0.512989 + 1.57882i 0.273922 + 0.961752i \(0.411679\pi\)
−0.786911 + 0.617066i \(0.788321\pi\)
\(20\) −2.23607 −0.500000
\(21\) 0 0
\(22\) 0.236068 + 0.726543i 0.0503299 + 0.154899i
\(23\) 4.85410 + 3.52671i 1.01215 + 0.735370i 0.964659 0.263501i \(-0.0848774\pi\)
0.0474912 + 0.998872i \(0.484877\pi\)
\(24\) 0 0
\(25\) −4.04508 2.93893i −0.809017 0.587785i
\(26\) 1.85410 0.363619
\(27\) 0 0
\(28\) 0.618034 + 1.90211i 0.116797 + 0.359466i
\(29\) 1.11803 + 3.44095i 0.207614 + 0.638969i 0.999596 + 0.0284251i \(0.00904922\pi\)
−0.791982 + 0.610544i \(0.790951\pi\)
\(30\) 0 0
\(31\) −3.00000 + 9.23305i −0.538816 + 1.65830i 0.196440 + 0.980516i \(0.437062\pi\)
−0.735256 + 0.677789i \(0.762938\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 0.927051 0.673542i 0.158988 0.115511i
\(35\) −1.38197 + 4.25325i −0.233595 + 0.718931i
\(36\) 0 0
\(37\) 7.16312 5.20431i 1.17761 0.855583i 0.185710 0.982605i \(-0.440542\pi\)
0.991900 + 0.127021i \(0.0405417\pi\)
\(38\) 5.85410 4.25325i 0.949661 0.689969i
\(39\) 0 0
\(40\) 1.80902 + 1.31433i 0.286031 + 0.207813i
\(41\) 4.11803 2.99193i 0.643129 0.467260i −0.217795 0.975995i \(-0.569886\pi\)
0.860924 + 0.508734i \(0.169886\pi\)
\(42\) 0 0
\(43\) 3.23607 0.493496 0.246748 0.969080i \(-0.420638\pi\)
0.246748 + 0.969080i \(0.420638\pi\)
\(44\) 0.236068 0.726543i 0.0355886 0.109530i
\(45\) 0 0
\(46\) −1.85410 5.70634i −0.273372 0.841354i
\(47\) −2.85410 8.78402i −0.416314 1.28128i −0.911071 0.412250i \(-0.864743\pi\)
0.494757 0.869031i \(-0.335257\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) 1.54508 + 4.75528i 0.218508 + 0.672499i
\(51\) 0 0
\(52\) −1.50000 1.08981i −0.208013 0.151130i
\(53\) 3.57295 + 10.9964i 0.490782 + 1.51047i 0.823428 + 0.567421i \(0.192059\pi\)
−0.332646 + 0.943052i \(0.607941\pi\)
\(54\) 0 0
\(55\) 1.38197 1.00406i 0.186344 0.135387i
\(56\) 0.618034 1.90211i 0.0825883 0.254181i
\(57\) 0 0
\(58\) 1.11803 3.44095i 0.146805 0.451820i
\(59\) −7.23607 + 5.25731i −0.942056 + 0.684444i −0.948915 0.315533i \(-0.897817\pi\)
0.00685884 + 0.999976i \(0.497817\pi\)
\(60\) 0 0
\(61\) 1.73607 + 1.26133i 0.222281 + 0.161496i 0.693353 0.720598i \(-0.256133\pi\)
−0.471072 + 0.882095i \(0.656133\pi\)
\(62\) 7.85410 5.70634i 0.997472 0.724706i
\(63\) 0 0
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) −1.28115 3.94298i −0.158907 0.489067i
\(66\) 0 0
\(67\) 1.14590 3.52671i 0.139994 0.430856i −0.856340 0.516413i \(-0.827267\pi\)
0.996333 + 0.0855568i \(0.0272669\pi\)
\(68\) −1.14590 −0.138961
\(69\) 0 0
\(70\) 3.61803 2.62866i 0.432438 0.314184i
\(71\) −2.52786 7.77997i −0.300002 0.923312i −0.981495 0.191487i \(-0.938669\pi\)
0.681493 0.731825i \(-0.261331\pi\)
\(72\) 0 0
\(73\) 7.97214 + 5.79210i 0.933068 + 0.677914i 0.946742 0.321993i \(-0.104353\pi\)
−0.0136741 + 0.999907i \(0.504353\pi\)
\(74\) −8.85410 −1.02927
\(75\) 0 0
\(76\) −7.23607 −0.830034
\(77\) −1.23607 0.898056i −0.140863 0.102343i
\(78\) 0 0
\(79\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(80\) −0.690983 2.12663i −0.0772542 0.237764i
\(81\) 0 0
\(82\) −5.09017 −0.562115
\(83\) −1.85410 + 5.70634i −0.203514 + 0.626352i 0.796257 + 0.604959i \(0.206810\pi\)
−0.999771 + 0.0213936i \(0.993190\pi\)
\(84\) 0 0
\(85\) −2.07295 1.50609i −0.224843 0.163358i
\(86\) −2.61803 1.90211i −0.282310 0.205110i
\(87\) 0 0
\(88\) −0.618034 + 0.449028i −0.0658826 + 0.0478665i
\(89\) 2.92705 + 2.12663i 0.310267 + 0.225422i 0.732011 0.681293i \(-0.238582\pi\)
−0.421744 + 0.906715i \(0.638582\pi\)
\(90\) 0 0
\(91\) −3.00000 + 2.17963i −0.314485 + 0.228487i
\(92\) −1.85410 + 5.70634i −0.193303 + 0.594927i
\(93\) 0 0
\(94\) −2.85410 + 8.78402i −0.294378 + 0.906003i
\(95\) −13.0902 9.51057i −1.34302 0.975763i
\(96\) 0 0
\(97\) −2.20820 6.79615i −0.224209 0.690045i −0.998371 0.0570570i \(-0.981828\pi\)
0.774162 0.632988i \(-0.218172\pi\)
\(98\) 2.42705 + 1.76336i 0.245169 + 0.178126i
\(99\) 0 0
\(100\) 1.54508 4.75528i 0.154508 0.475528i
\(101\) −17.3262 −1.72403 −0.862013 0.506887i \(-0.830796\pi\)
−0.862013 + 0.506887i \(0.830796\pi\)
\(102\) 0 0
\(103\) −4.85410 14.9394i −0.478289 1.47202i −0.841470 0.540303i \(-0.818309\pi\)
0.363181 0.931718i \(-0.381691\pi\)
\(104\) 0.572949 + 1.76336i 0.0561823 + 0.172911i
\(105\) 0 0
\(106\) 3.57295 10.9964i 0.347035 1.06807i
\(107\) 6.94427 0.671328 0.335664 0.941982i \(-0.391039\pi\)
0.335664 + 0.941982i \(0.391039\pi\)
\(108\) 0 0
\(109\) 14.2082 10.3229i 1.36090 0.988751i 0.362512 0.931979i \(-0.381919\pi\)
0.998387 0.0567720i \(-0.0180808\pi\)
\(110\) −1.70820 −0.162871
\(111\) 0 0
\(112\) −1.61803 + 1.17557i −0.152890 + 0.111081i
\(113\) 6.92705 5.03280i 0.651642 0.473446i −0.212188 0.977229i \(-0.568059\pi\)
0.863830 + 0.503783i \(0.168059\pi\)
\(114\) 0 0
\(115\) −10.8541 + 7.88597i −1.01215 + 0.735370i
\(116\) −2.92705 + 2.12663i −0.271770 + 0.197452i
\(117\) 0 0
\(118\) 8.94427 0.823387
\(119\) −0.708204 + 2.17963i −0.0649209 + 0.199806i
\(120\) 0 0
\(121\) −3.21885 9.90659i −0.292622 0.900599i
\(122\) −0.663119 2.04087i −0.0600360 0.184772i
\(123\) 0 0
\(124\) −9.70820 −0.871822
\(125\) 9.04508 6.57164i 0.809017 0.587785i
\(126\) 0 0
\(127\) −11.0902 8.05748i −0.984093 0.714986i −0.0254737 0.999675i \(-0.508109\pi\)
−0.958620 + 0.284690i \(0.908109\pi\)
\(128\) 0.309017 + 0.951057i 0.0273135 + 0.0840623i
\(129\) 0 0
\(130\) −1.28115 + 3.94298i −0.112365 + 0.345823i
\(131\) 1.61803 4.97980i 0.141368 0.435087i −0.855158 0.518368i \(-0.826540\pi\)
0.996526 + 0.0832809i \(0.0265399\pi\)
\(132\) 0 0
\(133\) −4.47214 + 13.7638i −0.387783 + 1.19347i
\(134\) −3.00000 + 2.17963i −0.259161 + 0.188291i
\(135\) 0 0
\(136\) 0.927051 + 0.673542i 0.0794940 + 0.0577557i
\(137\) 11.3541 8.24924i 0.970046 0.704780i 0.0145842 0.999894i \(-0.495358\pi\)
0.955462 + 0.295114i \(0.0953575\pi\)
\(138\) 0 0
\(139\) −10.8541 7.88597i −0.920633 0.668879i 0.0230486 0.999734i \(-0.492663\pi\)
−0.943681 + 0.330855i \(0.892663\pi\)
\(140\) −4.47214 −0.377964
\(141\) 0 0
\(142\) −2.52786 + 7.77997i −0.212134 + 0.652880i
\(143\) 1.41641 0.118446
\(144\) 0 0
\(145\) −8.09017 −0.671852
\(146\) −3.04508 9.37181i −0.252013 0.775616i
\(147\) 0 0
\(148\) 7.16312 + 5.20431i 0.588805 + 0.427792i
\(149\) 22.0344 1.80513 0.902566 0.430552i \(-0.141681\pi\)
0.902566 + 0.430552i \(0.141681\pi\)
\(150\) 0 0
\(151\) 10.9443 0.890632 0.445316 0.895373i \(-0.353091\pi\)
0.445316 + 0.895373i \(0.353091\pi\)
\(152\) 5.85410 + 4.25325i 0.474830 + 0.344984i
\(153\) 0 0
\(154\) 0.472136 + 1.45309i 0.0380458 + 0.117093i
\(155\) −17.5623 12.7598i −1.41064 1.02489i
\(156\) 0 0
\(157\) 11.1459 0.889540 0.444770 0.895645i \(-0.353286\pi\)
0.444770 + 0.895645i \(0.353286\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.690983 + 2.12663i −0.0546270 + 0.168125i
\(161\) 9.70820 + 7.05342i 0.765114 + 0.555888i
\(162\) 0 0
\(163\) −9.32624 + 6.77591i −0.730487 + 0.530730i −0.889718 0.456511i \(-0.849099\pi\)
0.159230 + 0.987241i \(0.449099\pi\)
\(164\) 4.11803 + 2.99193i 0.321564 + 0.233630i
\(165\) 0 0
\(166\) 4.85410 3.52671i 0.376751 0.273726i
\(167\) 0.763932 2.35114i 0.0591148 0.181937i −0.917139 0.398569i \(-0.869507\pi\)
0.976253 + 0.216632i \(0.0695071\pi\)
\(168\) 0 0
\(169\) −2.95492 + 9.09429i −0.227301 + 0.699561i
\(170\) 0.791796 + 2.43690i 0.0607280 + 0.186902i
\(171\) 0 0
\(172\) 1.00000 + 3.07768i 0.0762493 + 0.234671i
\(173\) −17.8713 12.9843i −1.35873 0.987176i −0.998524 0.0543039i \(-0.982706\pi\)
−0.360207 0.932872i \(-0.617294\pi\)
\(174\) 0 0
\(175\) −8.09017 5.87785i −0.611559 0.444324i
\(176\) 0.763932 0.0575835
\(177\) 0 0
\(178\) −1.11803 3.44095i −0.0838002 0.257910i
\(179\) 8.09017 + 24.8990i 0.604688 + 1.86104i 0.498923 + 0.866646i \(0.333729\pi\)
0.105764 + 0.994391i \(0.466271\pi\)
\(180\) 0 0
\(181\) 2.79180 8.59226i 0.207513 0.638658i −0.792088 0.610407i \(-0.791006\pi\)
0.999601 0.0282515i \(-0.00899392\pi\)
\(182\) 3.70820 0.274870
\(183\) 0 0
\(184\) 4.85410 3.52671i 0.357849 0.259993i
\(185\) 6.11803 + 18.8294i 0.449807 + 1.38436i
\(186\) 0 0
\(187\) 0.708204 0.514540i 0.0517890 0.0376269i
\(188\) 7.47214 5.42882i 0.544962 0.395938i
\(189\) 0 0
\(190\) 5.00000 + 15.3884i 0.362738 + 1.11639i
\(191\) −4.23607 + 3.07768i −0.306511 + 0.222693i −0.730398 0.683022i \(-0.760665\pi\)
0.423887 + 0.905715i \(0.360665\pi\)
\(192\) 0 0
\(193\) 4.61803 0.332413 0.166207 0.986091i \(-0.446848\pi\)
0.166207 + 0.986091i \(0.446848\pi\)
\(194\) −2.20820 + 6.79615i −0.158540 + 0.487935i
\(195\) 0 0
\(196\) −0.927051 2.85317i −0.0662179 0.203798i
\(197\) −0.718847 2.21238i −0.0512157 0.157626i 0.922177 0.386767i \(-0.126408\pi\)
−0.973393 + 0.229141i \(0.926408\pi\)
\(198\) 0 0
\(199\) 16.1803 1.14699 0.573497 0.819208i \(-0.305586\pi\)
0.573497 + 0.819208i \(0.305586\pi\)
\(200\) −4.04508 + 2.93893i −0.286031 + 0.207813i
\(201\) 0 0
\(202\) 14.0172 + 10.1841i 0.986248 + 0.716551i
\(203\) 2.23607 + 6.88191i 0.156941 + 0.483015i
\(204\) 0 0
\(205\) 3.51722 + 10.8249i 0.245653 + 0.756043i
\(206\) −4.85410 + 14.9394i −0.338201 + 1.04088i
\(207\) 0 0
\(208\) 0.572949 1.76336i 0.0397269 0.122267i
\(209\) 4.47214 3.24920i 0.309344 0.224752i
\(210\) 0 0
\(211\) 6.47214 + 4.70228i 0.445560 + 0.323718i 0.787840 0.615880i \(-0.211199\pi\)
−0.342280 + 0.939598i \(0.611199\pi\)
\(212\) −9.35410 + 6.79615i −0.642442 + 0.466762i
\(213\) 0 0
\(214\) −5.61803 4.08174i −0.384041 0.279022i
\(215\) −2.23607 + 6.88191i −0.152499 + 0.469342i
\(216\) 0 0
\(217\) −6.00000 + 18.4661i −0.407307 + 1.25356i
\(218\) −17.5623 −1.18947
\(219\) 0 0
\(220\) 1.38197 + 1.00406i 0.0931721 + 0.0676935i
\(221\) −0.656541 2.02063i −0.0441637 0.135922i
\(222\) 0 0
\(223\) 12.7082 + 9.23305i 0.851004 + 0.618291i 0.925423 0.378936i \(-0.123710\pi\)
−0.0744185 + 0.997227i \(0.523710\pi\)
\(224\) 2.00000 0.133631
\(225\) 0 0
\(226\) −8.56231 −0.569556
\(227\) 0.763932 + 0.555029i 0.0507039 + 0.0368386i 0.612849 0.790200i \(-0.290024\pi\)
−0.562145 + 0.827039i \(0.690024\pi\)
\(228\) 0 0
\(229\) 2.86475 + 8.81678i 0.189308 + 0.582629i 0.999996 0.00284891i \(-0.000906837\pi\)
−0.810688 + 0.585478i \(0.800907\pi\)
\(230\) 13.4164 0.884652
\(231\) 0 0
\(232\) 3.61803 0.237536
\(233\) 3.37132 10.3759i 0.220863 0.679746i −0.777823 0.628484i \(-0.783676\pi\)
0.998685 0.0512616i \(-0.0163242\pi\)
\(234\) 0 0
\(235\) 20.6525 1.34722
\(236\) −7.23607 5.25731i −0.471028 0.342222i
\(237\) 0 0
\(238\) 1.85410 1.34708i 0.120184 0.0873185i
\(239\) −21.7082 15.7719i −1.40419 1.02020i −0.994136 0.108139i \(-0.965511\pi\)
−0.410051 0.912063i \(-0.634489\pi\)
\(240\) 0 0
\(241\) 5.78115 4.20025i 0.372397 0.270562i −0.385807 0.922579i \(-0.626077\pi\)
0.758204 + 0.652017i \(0.226077\pi\)
\(242\) −3.21885 + 9.90659i −0.206915 + 0.636820i
\(243\) 0 0
\(244\) −0.663119 + 2.04087i −0.0424518 + 0.130653i
\(245\) 2.07295 6.37988i 0.132436 0.407596i
\(246\) 0 0
\(247\) −4.14590 12.7598i −0.263797 0.811884i
\(248\) 7.85410 + 5.70634i 0.498736 + 0.362353i
\(249\) 0 0
\(250\) −11.1803 −0.707107
\(251\) 3.52786 0.222677 0.111338 0.993783i \(-0.464486\pi\)
0.111338 + 0.993783i \(0.464486\pi\)
\(252\) 0 0
\(253\) −1.41641 4.35926i −0.0890488 0.274064i
\(254\) 4.23607 + 13.0373i 0.265795 + 0.818031i
\(255\) 0 0
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 9.38197 0.585231 0.292615 0.956230i \(-0.405474\pi\)
0.292615 + 0.956230i \(0.405474\pi\)
\(258\) 0 0
\(259\) 14.3262 10.4086i 0.890189 0.646760i
\(260\) 3.35410 2.43690i 0.208013 0.151130i
\(261\) 0 0
\(262\) −4.23607 + 3.07768i −0.261705 + 0.190140i
\(263\) −6.85410 + 4.97980i −0.422642 + 0.307067i −0.778700 0.627396i \(-0.784121\pi\)
0.356058 + 0.934464i \(0.384121\pi\)
\(264\) 0 0
\(265\) −25.8541 −1.58820
\(266\) 11.7082 8.50651i 0.717876 0.521567i
\(267\) 0 0
\(268\) 3.70820 0.226515
\(269\) 4.04508 12.4495i 0.246633 0.759059i −0.748730 0.662875i \(-0.769336\pi\)
0.995364 0.0961842i \(-0.0306638\pi\)
\(270\) 0 0
\(271\) 1.79837 + 5.53483i 0.109243 + 0.336217i 0.990703 0.136043i \(-0.0434385\pi\)
−0.881460 + 0.472260i \(0.843438\pi\)
\(272\) −0.354102 1.08981i −0.0214706 0.0660797i
\(273\) 0 0
\(274\) −14.0344 −0.847852
\(275\) 1.18034 + 3.63271i 0.0711772 + 0.219061i
\(276\) 0 0
\(277\) 23.3435 + 16.9600i 1.40257 + 1.01903i 0.994351 + 0.106146i \(0.0338510\pi\)
0.408222 + 0.912883i \(0.366149\pi\)
\(278\) 4.14590 + 12.7598i 0.248654 + 0.765280i
\(279\) 0 0
\(280\) 3.61803 + 2.62866i 0.216219 + 0.157092i
\(281\) −1.57295 + 4.84104i −0.0938343 + 0.288792i −0.986948 0.161038i \(-0.948516\pi\)
0.893114 + 0.449831i \(0.148516\pi\)
\(282\) 0 0
\(283\) −0.381966 + 1.17557i −0.0227055 + 0.0698804i −0.961767 0.273868i \(-0.911697\pi\)
0.939062 + 0.343749i \(0.111697\pi\)
\(284\) 6.61803 4.80828i 0.392708 0.285319i
\(285\) 0 0
\(286\) −1.14590 0.832544i −0.0677584 0.0492293i
\(287\) 8.23607 5.98385i 0.486160 0.353216i
\(288\) 0 0
\(289\) 12.6910 + 9.22054i 0.746528 + 0.542385i
\(290\) 6.54508 + 4.75528i 0.384341 + 0.279240i
\(291\) 0 0
\(292\) −3.04508 + 9.37181i −0.178200 + 0.548444i
\(293\) 4.20163 0.245462 0.122731 0.992440i \(-0.460835\pi\)
0.122731 + 0.992440i \(0.460835\pi\)
\(294\) 0 0
\(295\) −6.18034 19.0211i −0.359833 1.10745i
\(296\) −2.73607 8.42075i −0.159031 0.489446i
\(297\) 0 0
\(298\) −17.8262 12.9515i −1.03265 0.750261i
\(299\) −11.1246 −0.643353
\(300\) 0 0
\(301\) 6.47214 0.373048
\(302\) −8.85410 6.43288i −0.509496 0.370171i
\(303\) 0 0
\(304\) −2.23607 6.88191i −0.128247 0.394705i
\(305\) −3.88197 + 2.82041i −0.222281 + 0.161496i
\(306\) 0 0
\(307\) −29.7082 −1.69554 −0.847768 0.530367i \(-0.822054\pi\)
−0.847768 + 0.530367i \(0.822054\pi\)
\(308\) 0.472136 1.45309i 0.0269024 0.0827972i
\(309\) 0 0
\(310\) 6.70820 + 20.6457i 0.381000 + 1.17260i
\(311\) 10.2361 + 7.43694i 0.580434 + 0.421710i 0.838881 0.544315i \(-0.183211\pi\)
−0.258446 + 0.966026i \(0.583211\pi\)
\(312\) 0 0
\(313\) −14.8541 + 10.7921i −0.839603 + 0.610008i −0.922260 0.386570i \(-0.873660\pi\)
0.0826564 + 0.996578i \(0.473660\pi\)
\(314\) −9.01722 6.55139i −0.508871 0.369717i
\(315\) 0 0
\(316\) 0 0
\(317\) −3.38197 + 10.4086i −0.189950 + 0.584606i −0.999998 0.00175672i \(-0.999441\pi\)
0.810048 + 0.586363i \(0.199441\pi\)
\(318\) 0 0
\(319\) 0.854102 2.62866i 0.0478205 0.147176i
\(320\) 1.80902 1.31433i 0.101127 0.0734732i
\(321\) 0 0
\(322\) −3.70820 11.4127i −0.206650 0.636004i
\(323\) −6.70820 4.87380i −0.373254 0.271185i
\(324\) 0 0
\(325\) 9.27051 0.514235
\(326\) 11.5279 0.638469
\(327\) 0 0
\(328\) −1.57295 4.84104i −0.0868516 0.267302i
\(329\) −5.70820 17.5680i −0.314703 0.968558i
\(330\) 0 0
\(331\) −7.27051 + 22.3763i −0.399623 + 1.22991i 0.525679 + 0.850683i \(0.323811\pi\)
−0.925302 + 0.379231i \(0.876189\pi\)
\(332\) −6.00000 −0.329293
\(333\) 0 0
\(334\) −2.00000 + 1.45309i −0.109435 + 0.0795093i
\(335\) 6.70820 + 4.87380i 0.366508 + 0.266284i
\(336\) 0 0
\(337\) 20.0902 14.5964i 1.09438 0.795115i 0.114248 0.993452i \(-0.463554\pi\)
0.980134 + 0.198338i \(0.0635543\pi\)
\(338\) 7.73607 5.62058i 0.420787 0.305719i
\(339\) 0 0
\(340\) 0.791796 2.43690i 0.0429412 0.132159i
\(341\) 6.00000 4.35926i 0.324918 0.236067i
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 1.00000 3.07768i 0.0539164 0.165938i
\(345\) 0 0
\(346\) 6.82624 + 21.0090i 0.366981 + 1.12945i
\(347\) 0.236068 + 0.726543i 0.0126728 + 0.0390028i 0.957193 0.289451i \(-0.0934726\pi\)
−0.944520 + 0.328453i \(0.893473\pi\)
\(348\) 0 0
\(349\) −9.79837 −0.524495 −0.262247 0.965001i \(-0.584464\pi\)
−0.262247 + 0.965001i \(0.584464\pi\)
\(350\) 3.09017 + 9.51057i 0.165177 + 0.508361i
\(351\) 0 0
\(352\) −0.618034 0.449028i −0.0329413 0.0239333i
\(353\) −3.56231 10.9637i −0.189602 0.583536i 0.810395 0.585884i \(-0.199253\pi\)
−0.999997 + 0.00234791i \(0.999253\pi\)
\(354\) 0 0
\(355\) 18.2918 0.970828
\(356\) −1.11803 + 3.44095i −0.0592557 + 0.182370i
\(357\) 0 0
\(358\) 8.09017 24.8990i 0.427579 1.31595i
\(359\) 6.38197 4.63677i 0.336827 0.244719i −0.406495 0.913653i \(-0.633249\pi\)
0.743322 + 0.668934i \(0.233249\pi\)
\(360\) 0 0
\(361\) −26.9894 19.6089i −1.42049 1.03205i
\(362\) −7.30902 + 5.31031i −0.384153 + 0.279104i
\(363\) 0 0
\(364\) −3.00000 2.17963i −0.157243 0.114244i
\(365\) −17.8262 + 12.9515i −0.933068 + 0.677914i
\(366\) 0 0
\(367\) −1.09017 + 3.35520i −0.0569064 + 0.175140i −0.975470 0.220134i \(-0.929350\pi\)
0.918563 + 0.395274i \(0.129350\pi\)
\(368\) −6.00000 −0.312772
\(369\) 0 0
\(370\) 6.11803 18.8294i 0.318061 0.978892i
\(371\) 7.14590 + 21.9928i 0.370997 + 1.14181i
\(372\) 0 0
\(373\) −23.7984 17.2905i −1.23223 0.895270i −0.235178 0.971952i \(-0.575567\pi\)
−0.997056 + 0.0766827i \(0.975567\pi\)
\(374\) −0.875388 −0.0452652
\(375\) 0 0
\(376\) −9.23607 −0.476314
\(377\) −5.42705 3.94298i −0.279507 0.203074i
\(378\) 0 0
\(379\) 7.23607 + 22.2703i 0.371692 + 1.14395i 0.945684 + 0.325089i \(0.105394\pi\)
−0.573992 + 0.818861i \(0.694606\pi\)
\(380\) 5.00000 15.3884i 0.256495 0.789409i
\(381\) 0 0
\(382\) 5.23607 0.267901
\(383\) −3.56231 + 10.9637i −0.182025 + 0.560216i −0.999884 0.0152022i \(-0.995161\pi\)
0.817859 + 0.575419i \(0.195161\pi\)
\(384\) 0 0
\(385\) 2.76393 2.00811i 0.140863 0.102343i
\(386\) −3.73607 2.71441i −0.190161 0.138160i
\(387\) 0 0
\(388\) 5.78115 4.20025i 0.293494 0.213236i
\(389\) −25.0623 18.2088i −1.27071 0.923224i −0.271479 0.962444i \(-0.587513\pi\)
−0.999231 + 0.0392200i \(0.987513\pi\)
\(390\) 0 0
\(391\) −5.56231 + 4.04125i −0.281298 + 0.204375i
\(392\) −0.927051 + 2.85317i −0.0468231 + 0.144107i
\(393\) 0 0
\(394\) −0.718847 + 2.21238i −0.0362150 + 0.111458i
\(395\) 0 0
\(396\) 0 0
\(397\) −7.67376 23.6174i −0.385135 1.18532i −0.936382 0.350982i \(-0.885848\pi\)
0.551247 0.834342i \(-0.314152\pi\)
\(398\) −13.0902 9.51057i −0.656151 0.476722i
\(399\) 0 0
\(400\) 5.00000 0.250000
\(401\) 14.9098 0.744561 0.372281 0.928120i \(-0.378576\pi\)
0.372281 + 0.928120i \(0.378576\pi\)
\(402\) 0 0
\(403\) −5.56231 17.1190i −0.277078 0.852759i
\(404\) −5.35410 16.4782i −0.266377 0.819823i
\(405\) 0 0
\(406\) 2.23607 6.88191i 0.110974 0.341543i
\(407\) −6.76393 −0.335276
\(408\) 0 0
\(409\) 21.0172 15.2699i 1.03923 0.755048i 0.0690987 0.997610i \(-0.477988\pi\)
0.970136 + 0.242562i \(0.0779877\pi\)
\(410\) 3.51722 10.8249i 0.173703 0.534603i
\(411\) 0 0
\(412\) 12.7082 9.23305i 0.626088 0.454880i
\(413\) −14.4721 + 10.5146i −0.712127 + 0.517391i
\(414\) 0 0
\(415\) −10.8541 7.88597i −0.532807 0.387107i
\(416\) −1.50000 + 1.08981i −0.0735436 + 0.0534325i
\(417\) 0 0
\(418\) −5.52786 −0.270377
\(419\) 0.652476 2.00811i 0.0318755 0.0981028i −0.933853 0.357657i \(-0.883576\pi\)
0.965729 + 0.259554i \(0.0835757\pi\)
\(420\) 0 0
\(421\) 0.0278640 + 0.0857567i 0.00135801 + 0.00417953i 0.951733 0.306926i \(-0.0993006\pi\)
−0.950375 + 0.311106i \(0.899301\pi\)
\(422\) −2.47214 7.60845i −0.120342 0.370374i
\(423\) 0 0
\(424\) 11.5623 0.561515
\(425\) 4.63525 3.36771i 0.224843 0.163358i
\(426\) 0 0
\(427\) 3.47214 + 2.52265i 0.168028 + 0.122080i
\(428\) 2.14590 + 6.60440i 0.103726 + 0.319235i
\(429\) 0 0
\(430\) 5.85410 4.25325i 0.282310 0.205110i
\(431\) 3.00000 9.23305i 0.144505 0.444740i −0.852442 0.522822i \(-0.824879\pi\)
0.996947 + 0.0780813i \(0.0248794\pi\)
\(432\) 0 0
\(433\) −9.22542 + 28.3929i −0.443346 + 1.36448i 0.440942 + 0.897535i \(0.354644\pi\)
−0.884288 + 0.466942i \(0.845356\pi\)
\(434\) 15.7082 11.4127i 0.754018 0.547826i
\(435\) 0 0
\(436\) 14.2082 + 10.3229i 0.680450 + 0.494376i
\(437\) −35.1246 + 25.5195i −1.68024 + 1.22076i
\(438\) 0 0
\(439\) −12.2361 8.89002i −0.583996 0.424298i 0.256167 0.966633i \(-0.417540\pi\)
−0.840162 + 0.542335i \(0.817540\pi\)
\(440\) −0.527864 1.62460i −0.0251649 0.0774497i
\(441\) 0 0
\(442\) −0.656541 + 2.02063i −0.0312285 + 0.0961114i
\(443\) 28.0689 1.33359 0.666796 0.745240i \(-0.267665\pi\)
0.666796 + 0.745240i \(0.267665\pi\)
\(444\) 0 0
\(445\) −6.54508 + 4.75528i −0.310267 + 0.225422i
\(446\) −4.85410 14.9394i −0.229848 0.707401i
\(447\) 0 0
\(448\) −1.61803 1.17557i −0.0764449 0.0555405i
\(449\) 19.7984 0.934343 0.467172 0.884167i \(-0.345273\pi\)
0.467172 + 0.884167i \(0.345273\pi\)
\(450\) 0 0
\(451\) −3.88854 −0.183104
\(452\) 6.92705 + 5.03280i 0.325821 + 0.236723i
\(453\) 0 0
\(454\) −0.291796 0.898056i −0.0136947 0.0421479i
\(455\) −2.56231 7.88597i −0.120123 0.369700i
\(456\) 0 0
\(457\) −3.52786 −0.165027 −0.0825133 0.996590i \(-0.526295\pi\)
−0.0825133 + 0.996590i \(0.526295\pi\)
\(458\) 2.86475 8.81678i 0.133861 0.411981i
\(459\) 0 0
\(460\) −10.8541 7.88597i −0.506075 0.367685i
\(461\) 11.2533 + 8.17599i 0.524118 + 0.380794i 0.818153 0.575001i \(-0.194998\pi\)
−0.294035 + 0.955795i \(0.594998\pi\)
\(462\) 0 0
\(463\) 20.7984 15.1109i 0.966582 0.702263i 0.0119123 0.999929i \(-0.496208\pi\)
0.954670 + 0.297666i \(0.0962081\pi\)
\(464\) −2.92705 2.12663i −0.135885 0.0987262i
\(465\) 0 0
\(466\) −8.82624 + 6.41264i −0.408868 + 0.297060i
\(467\) −11.7984 + 36.3117i −0.545964 + 1.68030i 0.172724 + 0.984970i \(0.444743\pi\)
−0.718688 + 0.695333i \(0.755257\pi\)
\(468\) 0 0
\(469\) 2.29180 7.05342i 0.105825 0.325697i
\(470\) −16.7082 12.1392i −0.770692 0.559940i
\(471\) 0 0
\(472\) 2.76393 + 8.50651i 0.127220 + 0.391544i
\(473\) −2.00000 1.45309i −0.0919601 0.0668129i
\(474\) 0 0
\(475\) 29.2705 21.2663i 1.34302 0.975763i
\(476\) −2.29180 −0.105044
\(477\) 0 0
\(478\) 8.29180 + 25.5195i 0.379258 + 1.16724i
\(479\) 1.38197 + 4.25325i 0.0631436 + 0.194336i 0.977652 0.210232i \(-0.0674219\pi\)
−0.914508 + 0.404568i \(0.867422\pi\)
\(480\) 0 0
\(481\) −5.07295 + 15.6129i −0.231307 + 0.711888i
\(482\) −7.14590 −0.325487
\(483\) 0 0
\(484\) 8.42705 6.12261i 0.383048 0.278300i
\(485\) 15.9787 0.725556
\(486\) 0 0
\(487\) −19.1803 + 13.9353i −0.869144 + 0.631470i −0.930357 0.366655i \(-0.880503\pi\)
0.0612130 + 0.998125i \(0.480503\pi\)
\(488\) 1.73607 1.26133i 0.0785881 0.0570976i
\(489\) 0 0
\(490\) −5.42705 + 3.94298i −0.245169 + 0.178126i
\(491\) −4.76393 + 3.46120i −0.214993 + 0.156202i −0.690070 0.723743i \(-0.742420\pi\)
0.475077 + 0.879944i \(0.342420\pi\)
\(492\) 0 0
\(493\) −4.14590 −0.186722
\(494\) −4.14590 + 12.7598i −0.186533 + 0.574089i
\(495\) 0 0
\(496\) −3.00000 9.23305i −0.134704 0.414576i
\(497\) −5.05573 15.5599i −0.226780 0.697958i
\(498\) 0 0
\(499\) −6.58359 −0.294722 −0.147361 0.989083i \(-0.547078\pi\)
−0.147361 + 0.989083i \(0.547078\pi\)
\(500\) 9.04508 + 6.57164i 0.404508 + 0.293893i
\(501\) 0 0
\(502\) −2.85410 2.07363i −0.127385 0.0925505i
\(503\) −9.41641 28.9807i −0.419857 1.29219i −0.907834 0.419330i \(-0.862265\pi\)
0.487977 0.872857i \(-0.337735\pi\)
\(504\) 0 0
\(505\) 11.9721 36.8464i 0.532753 1.63965i
\(506\) −1.41641 + 4.35926i −0.0629670 + 0.193793i
\(507\) 0 0
\(508\) 4.23607 13.0373i 0.187945 0.578436i
\(509\) 23.2533 16.8945i 1.03068 0.748836i 0.0622385 0.998061i \(-0.480176\pi\)
0.968445 + 0.249226i \(0.0801761\pi\)
\(510\) 0 0
\(511\) 15.9443 + 11.5842i 0.705333 + 0.512454i
\(512\) −0.809017 + 0.587785i −0.0357538 + 0.0259767i
\(513\) 0 0
\(514\) −7.59017 5.51458i −0.334788 0.243238i
\(515\) 35.1246 1.54778
\(516\) 0 0
\(517\) −2.18034 + 6.71040i −0.0958912 + 0.295123i
\(518\) −17.7082 −0.778054
\(519\) 0 0
\(520\) −4.14590 −0.181810
\(521\) 8.42705 + 25.9358i 0.369196 + 1.13627i 0.947312 + 0.320313i \(0.103788\pi\)
−0.578116 + 0.815955i \(0.696212\pi\)
\(522\) 0 0
\(523\) 12.7082 + 9.23305i 0.555691 + 0.403733i 0.829879 0.557943i \(-0.188409\pi\)
−0.274188 + 0.961676i \(0.588409\pi\)
\(524\) 5.23607 0.228739
\(525\) 0 0
\(526\) 8.47214 0.369403
\(527\) −9.00000 6.53888i −0.392046 0.284838i
\(528\) 0 0
\(529\) 4.01722 + 12.3637i 0.174662 + 0.537554i
\(530\) 20.9164 + 15.1967i 0.908551 + 0.660101i
\(531\) 0 0
\(532\) −14.4721 −0.627447
\(533\) −2.91641 + 8.97578i −0.126324 + 0.388784i
\(534\) 0 0
\(535\) −4.79837 + 14.7679i −0.207452 + 0.638471i
\(536\) −3.00000 2.17963i −0.129580 0.0941456i
\(537\) 0 0
\(538\) −10.5902 + 7.69421i −0.456575 + 0.331721i
\(539\) 1.85410 + 1.34708i 0.0798618 + 0.0580230i
\(540\) 0 0
\(541\) 9.92705 7.21242i 0.426797 0.310086i −0.353570 0.935408i \(-0.615032\pi\)
0.780367 + 0.625322i \(0.215032\pi\)
\(542\) 1.79837 5.53483i 0.0772468 0.237741i
\(543\) 0 0
\(544\) −0.354102 + 1.08981i −0.0151820 + 0.0467254i
\(545\) 12.1353 + 37.3485i 0.519817 + 1.59983i
\(546\) 0 0
\(547\) 0.618034 + 1.90211i 0.0264252 + 0.0813285i 0.963399 0.268070i \(-0.0863859\pi\)
−0.936974 + 0.349399i \(0.886386\pi\)
\(548\) 11.3541 + 8.24924i 0.485023 + 0.352390i
\(549\) 0 0
\(550\) 1.18034 3.63271i 0.0503299 0.154899i
\(551\) −26.1803 −1.11532
\(552\) 0 0
\(553\) 0 0
\(554\) −8.91641 27.4419i −0.378822 1.16589i
\(555\) 0 0
\(556\) 4.14590 12.7598i 0.175825 0.541134i
\(557\) −6.27051 −0.265690 −0.132845 0.991137i \(-0.542411\pi\)
−0.132845 + 0.991137i \(0.542411\pi\)
\(558\) 0 0
\(559\) −4.85410 + 3.52671i −0.205307 + 0.149164i
\(560\) −1.38197 4.25325i −0.0583987 0.179733i
\(561\) 0 0
\(562\) 4.11803 2.99193i 0.173709 0.126207i
\(563\) 1.23607 0.898056i 0.0520941 0.0378485i −0.561434 0.827522i \(-0.689750\pi\)
0.613528 + 0.789673i \(0.289750\pi\)
\(564\) 0 0
\(565\) 5.91641 + 18.2088i 0.248905 + 0.766051i
\(566\) 1.00000 0.726543i 0.0420331 0.0305389i
\(567\) 0 0
\(568\) −8.18034 −0.343239
\(569\) −7.29837 + 22.4621i −0.305964 + 0.941660i 0.673352 + 0.739322i \(0.264854\pi\)
−0.979316 + 0.202338i \(0.935146\pi\)
\(570\) 0 0
\(571\) 6.27051 + 19.2986i 0.262413 + 0.807623i 0.992278 + 0.124032i \(0.0395827\pi\)
−0.729866 + 0.683591i \(0.760417\pi\)
\(572\) 0.437694 + 1.34708i 0.0183009 + 0.0563244i
\(573\) 0 0
\(574\) −10.1803 −0.424919
\(575\) −9.27051 28.5317i −0.386607 1.18985i
\(576\) 0 0
\(577\) 20.0902 + 14.5964i 0.836365 + 0.607655i 0.921353 0.388727i \(-0.127085\pi\)
−0.0849881 + 0.996382i \(0.527085\pi\)
\(578\) −4.84752 14.9191i −0.201630 0.620555i
\(579\) 0 0
\(580\) −2.50000 7.69421i −0.103807 0.319485i
\(581\) −3.70820 + 11.4127i −0.153842 + 0.473478i
\(582\) 0 0
\(583\) 2.72949 8.40051i 0.113044 0.347913i
\(584\) 7.97214 5.79210i 0.329889 0.239679i
\(585\) 0 0
\(586\) −3.39919 2.46965i −0.140419 0.102020i
\(587\) 16.0902 11.6902i 0.664112 0.482506i −0.203937 0.978984i \(-0.565374\pi\)
0.868049 + 0.496478i \(0.165374\pi\)
\(588\) 0 0
\(589\) −56.8328 41.2915i −2.34176 1.70138i
\(590\) −6.18034 + 19.0211i −0.254441 + 0.783088i
\(591\) 0 0
\(592\) −2.73607 + 8.42075i −0.112452 + 0.346091i
\(593\) −23.0344 −0.945911 −0.472956 0.881086i \(-0.656813\pi\)
−0.472956 + 0.881086i \(0.656813\pi\)
\(594\) 0 0
\(595\) −4.14590 3.01217i −0.169965 0.123487i
\(596\) 6.80902 + 20.9560i 0.278908 + 0.858391i
\(597\) 0 0
\(598\) 9.00000 + 6.53888i 0.368037 + 0.267395i
\(599\) −18.9443 −0.774042 −0.387021 0.922071i \(-0.626496\pi\)
−0.387021 + 0.922071i \(0.626496\pi\)
\(600\) 0 0
\(601\) −8.32624 −0.339634 −0.169817 0.985476i \(-0.554318\pi\)
−0.169817 + 0.985476i \(0.554318\pi\)
\(602\) −5.23607 3.80423i −0.213406 0.155049i
\(603\) 0 0
\(604\) 3.38197 + 10.4086i 0.137610 + 0.423521i
\(605\) 23.2918 0.946946
\(606\) 0 0
\(607\) −24.1803 −0.981450 −0.490725 0.871315i \(-0.663268\pi\)
−0.490725 + 0.871315i \(0.663268\pi\)
\(608\) −2.23607 + 6.88191i −0.0906845 + 0.279098i
\(609\) 0 0
\(610\) 4.79837 0.194280
\(611\) 13.8541 + 10.0656i 0.560477 + 0.407210i
\(612\) 0 0
\(613\) 1.16312 0.845055i 0.0469779 0.0341315i −0.564048 0.825742i \(-0.690757\pi\)
0.611026 + 0.791610i \(0.290757\pi\)
\(614\) 24.0344 + 17.4620i 0.969951 + 0.704711i
\(615\) 0 0
\(616\) −1.23607 + 0.898056i −0.0498026 + 0.0361837i
\(617\) −3.28115 + 10.0984i −0.132094 + 0.406544i −0.995127 0.0986041i \(-0.968562\pi\)
0.863032 + 0.505148i \(0.168562\pi\)
\(618\) 0 0
\(619\) −7.23607 + 22.2703i −0.290842 + 0.895120i 0.693744 + 0.720221i \(0.255960\pi\)
−0.984586 + 0.174899i \(0.944040\pi\)
\(620\) 6.70820 20.6457i 0.269408 0.829152i
\(621\) 0 0
\(622\) −3.90983 12.0332i −0.156770 0.482488i
\(623\) 5.85410 + 4.25325i 0.234540 + 0.170403i
\(624\) 0 0
\(625\) 7.72542 + 23.7764i 0.309017 + 0.951057i
\(626\) 18.3607 0.733840
\(627\) 0 0
\(628\) 3.44427 + 10.6004i 0.137441 + 0.423001i
\(629\) 3.13525 + 9.64932i 0.125011 + 0.384744i
\(630\) 0 0
\(631\) −0.888544 + 2.73466i −0.0353724 + 0.108865i −0.967184 0.254078i \(-0.918228\pi\)
0.931811 + 0.362943i \(0.118228\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 8.85410 6.43288i 0.351641 0.255482i
\(635\) 24.7984 18.0171i 0.984093 0.714986i
\(636\) 0 0
\(637\) 4.50000 3.26944i 0.178296 0.129540i
\(638\) −2.23607 + 1.62460i −0.0885268 + 0.0643185i
\(639\) 0 0
\(640\) −2.23607 −0.0883883
\(641\) −7.32624 + 5.32282i −0.289369 + 0.210239i −0.722994 0.690855i \(-0.757234\pi\)
0.433625 + 0.901094i \(0.357234\pi\)
\(642\) 0 0
\(643\) 31.7771 1.25317 0.626583 0.779355i \(-0.284453\pi\)
0.626583 + 0.779355i \(0.284453\pi\)
\(644\) −3.70820 + 11.4127i −0.146124 + 0.449723i
\(645\) 0 0
\(646\) 2.56231 + 7.88597i 0.100813 + 0.310269i
\(647\) 0.0344419 + 0.106001i 0.00135405 + 0.00416733i 0.951731 0.306933i \(-0.0993026\pi\)
−0.950377 + 0.311100i \(0.899303\pi\)
\(648\) 0 0
\(649\) 6.83282 0.268211
\(650\) −7.50000 5.44907i −0.294174 0.213730i
\(651\) 0 0
\(652\) −9.32624 6.77591i −0.365244 0.265365i
\(653\) −5.93769 18.2743i −0.232360 0.715130i −0.997461 0.0712197i \(-0.977311\pi\)
0.765101 0.643911i \(-0.222689\pi\)
\(654\) 0 0
\(655\) 9.47214 + 6.88191i 0.370107 + 0.268898i
\(656\) −1.57295 + 4.84104i −0.0614133 + 0.189011i
\(657\) 0 0
\(658\) −5.70820 + 17.5680i −0.222529 + 0.684874i
\(659\) 17.0344 12.3762i 0.663568 0.482110i −0.204298 0.978909i \(-0.565491\pi\)
0.867866 + 0.496799i \(0.165491\pi\)
\(660\) 0 0
\(661\) 26.2705 + 19.0866i 1.02180 + 0.742384i 0.966652 0.256094i \(-0.0824355\pi\)
0.0551524 + 0.998478i \(0.482436\pi\)
\(662\) 19.0344 13.8293i 0.739795 0.537492i
\(663\) 0 0
\(664\) 4.85410 + 3.52671i 0.188376 + 0.136863i
\(665\) −26.1803 19.0211i −1.01523 0.737608i
\(666\) 0 0
\(667\) −6.70820 + 20.6457i −0.259743 + 0.799406i
\(668\) 2.47214 0.0956498
\(669\) 0 0
\(670\) −2.56231 7.88597i −0.0989905 0.304661i
\(671\) −0.506578 1.55909i −0.0195562 0.0601879i
\(672\) 0 0
\(673\) −4.69098 3.40820i −0.180824 0.131376i 0.493691 0.869637i \(-0.335647\pi\)
−0.674515 + 0.738261i \(0.735647\pi\)
\(674\) −24.8328 −0.956524
\(675\) 0 0
\(676\) −9.56231 −0.367781
\(677\) 22.2705 + 16.1805i 0.855925 + 0.621866i 0.926773 0.375621i \(-0.122571\pi\)
−0.0708481 + 0.997487i \(0.522571\pi\)
\(678\) 0 0
\(679\) −4.41641 13.5923i −0.169486 0.521625i
\(680\) −2.07295 + 1.50609i −0.0794940 + 0.0577557i
\(681\) 0 0
\(682\) −7.41641 −0.283989
\(683\) 2.29180 7.05342i 0.0876931 0.269892i −0.897588 0.440836i \(-0.854682\pi\)
0.985281 + 0.170945i \(0.0546819\pi\)
\(684\) 0 0
\(685\) 9.69756 + 29.8460i 0.370525 + 1.14036i
\(686\) 16.1803 + 11.7557i 0.617768 + 0.448835i
\(687\) 0 0
\(688\) −2.61803 + 1.90211i −0.0998116 + 0.0725174i
\(689\) −17.3435 12.6008i −0.660733 0.480051i
\(690\) 0 0
\(691\) 1.47214 1.06957i 0.0560027 0.0406883i −0.559432 0.828876i \(-0.688981\pi\)
0.615434 + 0.788188i \(0.288981\pi\)
\(692\) 6.82624 21.0090i 0.259495 0.798642i
\(693\) 0 0
\(694\) 0.236068 0.726543i 0.00896102 0.0275792i
\(695\) 24.2705 17.6336i 0.920633 0.668879i
\(696\) 0 0
\(697\) 1.80244 + 5.54734i 0.0682723 + 0.210120i
\(698\) 7.92705 + 5.75934i 0.300043 + 0.217994i
\(699\) 0 0
\(700\) 3.09017 9.51057i 0.116797 0.359466i
\(701\) −49.1591 −1.85671 −0.928356 0.371692i \(-0.878778\pi\)
−0.928356 + 0.371692i \(0.878778\pi\)
\(702\) 0 0
\(703\) 19.7984 + 60.9331i 0.746710 + 2.29814i
\(704\) 0.236068 + 0.726543i 0.00889715 + 0.0273826i
\(705\) 0 0
\(706\) −3.56231 + 10.9637i −0.134069 + 0.412622i
\(707\) −34.6525 −1.30324
\(708\) 0 0
\(709\) 4.20820 3.05744i 0.158042 0.114825i −0.505953 0.862561i \(-0.668859\pi\)
0.663996 + 0.747736i \(0.268859\pi\)
\(710\) −14.7984 10.7516i −0.555373 0.403502i
\(711\) 0 0
\(712\) 2.92705 2.12663i 0.109696 0.0796987i
\(713\) −47.1246 + 34.2380i −1.76483 + 1.28222i
\(714\) 0 0
\(715\) −0.978714 + 3.01217i −0.0366018 + 0.112649i
\(716\) −21.1803 + 15.3884i −0.791546 + 0.575092i
\(717\) 0 0
\(718\) −7.88854 −0.294398
\(719\) 6.90983 21.2663i 0.257693 0.793098i −0.735594 0.677423i \(-0.763097\pi\)
0.993287 0.115675i \(-0.0369032\pi\)
\(720\) 0 0
\(721\) −9.70820 29.8788i −0.361552 1.11274i
\(722\) 10.3090 + 31.7279i 0.383662 + 1.18079i
\(723\) 0 0
\(724\) 9.03444 0.335762
\(725\) 5.59017 17.2048i 0.207614 0.638969i
\(726\) 0 0
\(727\) −19.1803 13.9353i −0.711359 0.516833i 0.172253 0.985053i \(-0.444895\pi\)
−0.883612 + 0.468220i \(0.844895\pi\)
\(728\) 1.14590 + 3.52671i 0.0424698 + 0.130709i
\(729\) 0 0
\(730\) 22.0344 0.815531
\(731\) −1.14590 + 3.52671i −0.0423826 + 0.130440i
\(732\) 0 0
\(733\) 11.8541 36.4832i 0.437841 1.34754i −0.452306 0.891863i \(-0.649398\pi\)
0.890147 0.455674i \(-0.150602\pi\)
\(734\) 2.85410 2.07363i 0.105347 0.0765389i
\(735\) 0 0
\(736\) 4.85410 + 3.52671i 0.178925 + 0.129996i
\(737\) −2.29180 + 1.66509i −0.0844194 + 0.0613343i
\(738\) 0 0
\(739\) −17.5623 12.7598i −0.646040 0.469375i 0.215880 0.976420i \(-0.430738\pi\)
−0.861920 + 0.507044i \(0.830738\pi\)
\(740\) −16.0172 + 11.6372i −0.588805 + 0.427792i
\(741\) 0 0
\(742\) 7.14590 21.9928i 0.262334 0.807382i
\(743\) 24.6525 0.904412 0.452206 0.891914i \(-0.350637\pi\)
0.452206 + 0.891914i \(0.350637\pi\)
\(744\) 0 0
\(745\) −15.2254 + 46.8590i −0.557816 + 1.71678i
\(746\) 9.09017 + 27.9767i 0.332815 + 1.02430i
\(747\) 0 0
\(748\) 0.708204 + 0.514540i 0.0258945 + 0.0188135i
\(749\) 13.8885 0.507476
\(750\) 0 0
\(751\) 19.2361 0.701934 0.350967 0.936388i \(-0.385853\pi\)
0.350967 + 0.936388i \(0.385853\pi\)
\(752\) 7.47214 + 5.42882i 0.272481 + 0.197969i
\(753\) 0 0
\(754\) 2.07295 + 6.37988i 0.0754924 + 0.232342i
\(755\) −7.56231 + 23.2744i −0.275220 + 0.847042i
\(756\) 0 0
\(757\) −22.1459 −0.804906 −0.402453 0.915441i \(-0.631842\pi\)
−0.402453 + 0.915441i \(0.631842\pi\)
\(758\) 7.23607 22.2703i 0.262826 0.808895i
\(759\) 0 0
\(760\) −13.0902 + 9.51057i −0.474830 + 0.344984i
\(761\) −36.5344 26.5438i −1.32437 0.962213i −0.999867 0.0163292i \(-0.994802\pi\)
−0.324506 0.945884i \(-0.605198\pi\)
\(762\) 0 0
\(763\) 28.4164 20.6457i 1.02874 0.747426i
\(764\) −4.23607 3.07768i −0.153256 0.111347i
\(765\) 0 0
\(766\) 9.32624 6.77591i 0.336971 0.244824i
\(767\) 5.12461 15.7719i 0.185039 0.569492i
\(768\) 0 0
\(769\) 13.0902 40.2874i 0.472044 1.45280i −0.377860 0.925863i \(-0.623340\pi\)
0.849904 0.526938i \(-0.176660\pi\)
\(770\) −3.41641 −0.123119
\(771\) 0 0
\(772\) 1.42705 + 4.39201i 0.0513607 + 0.158072i
\(773\) 2.35410 + 1.71036i 0.0846712 + 0.0615172i 0.629315 0.777150i \(-0.283335\pi\)
−0.544644 + 0.838667i \(0.683335\pi\)
\(774\) 0 0
\(775\) 39.2705 28.5317i 1.41064 1.02489i
\(776\) −7.14590 −0.256523
\(777\) 0 0
\(778\) 9.57295 + 29.4625i 0.343207 + 1.05628i
\(779\) 11.3820 + 35.0301i 0.407801 + 1.25508i
\(780\) 0 0
\(781\) −1.93112 + 5.94336i −0.0691008 + 0.212670i
\(782\) 6.87539 0.245863
\(783\) 0 0
\(784\) 2.42705 1.76336i 0.0866804 0.0629770i
\(785\) −7.70163 + 23.7032i −0.274883 + 0.846002i
\(786\) 0 0
\(787\) 29.5623 21.4783i 1.05378 0.765618i 0.0808543 0.996726i \(-0.474235\pi\)
0.972928 + 0.231108i \(0.0742351\pi\)
\(788\) 1.88197 1.36733i