Properties

Label 245.2.e.g.116.1
Level $245$
Weight $2$
Character 245.116
Analytic conductor $1.956$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 245.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.95633484952\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 116.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 245.116
Dual form 245.2.e.g.226.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 1.22474i) q^{2} +(1.20711 - 2.09077i) q^{3} +(0.500000 + 0.866025i) q^{5} -3.41421 q^{6} -2.82843 q^{8} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 1.22474i) q^{2} +(1.20711 - 2.09077i) q^{3} +(0.500000 + 0.866025i) q^{5} -3.41421 q^{6} -2.82843 q^{8} +(-1.41421 - 2.44949i) q^{9} +(0.707107 - 1.22474i) q^{10} +(2.91421 - 5.04757i) q^{11} -1.58579 q^{13} +2.41421 q^{15} +(2.00000 + 3.46410i) q^{16} +(-2.62132 + 4.54026i) q^{17} +(-2.00000 + 3.46410i) q^{18} +(3.00000 + 5.19615i) q^{19} -8.24264 q^{22} +(-2.29289 - 3.97141i) q^{23} +(-3.41421 + 5.91359i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.12132 + 1.94218i) q^{26} +0.414214 q^{27} +2.65685 q^{29} +(-1.70711 - 2.95680i) q^{30} +(0.878680 - 1.52192i) q^{31} +(-7.03553 - 12.1859i) q^{33} +7.41421 q^{34} +(3.12132 + 5.40629i) q^{37} +(4.24264 - 7.34847i) q^{38} +(-1.91421 + 3.31552i) q^{39} +(-1.41421 - 2.44949i) q^{40} -2.24264 q^{41} +2.00000 q^{43} +(1.41421 - 2.44949i) q^{45} +(-3.24264 + 5.61642i) q^{46} +(0.621320 + 1.07616i) q^{47} +9.65685 q^{48} +1.41421 q^{50} +(6.32843 + 10.9612i) q^{51} +(2.12132 - 3.67423i) q^{53} +(-0.292893 - 0.507306i) q^{54} +5.82843 q^{55} +14.4853 q^{57} +(-1.87868 - 3.25397i) q^{58} +(3.12132 - 5.40629i) q^{59} +(1.41421 + 2.44949i) q^{61} -2.48528 q^{62} +8.00000 q^{64} +(-0.792893 - 1.37333i) q^{65} +(-9.94975 + 17.2335i) q^{66} +(-0.121320 + 0.210133i) q^{67} -11.0711 q^{69} -8.82843 q^{71} +(4.00000 + 6.92820i) q^{72} +(4.24264 - 7.34847i) q^{73} +(4.41421 - 7.64564i) q^{74} +(1.20711 + 2.09077i) q^{75} +5.41421 q^{78} +(7.74264 + 13.4106i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(4.74264 - 8.21449i) q^{81} +(1.58579 + 2.74666i) q^{82} -5.24264 q^{85} +(-1.41421 - 2.44949i) q^{86} +(3.20711 - 5.55487i) q^{87} +(-8.24264 + 14.2767i) q^{88} +(-4.00000 - 6.92820i) q^{89} -4.00000 q^{90} +(-2.12132 - 3.67423i) q^{93} +(0.878680 - 1.52192i) q^{94} +(-3.00000 + 5.19615i) q^{95} -4.75736 q^{97} -16.4853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} + 2q^{5} - 8q^{6} + O(q^{10}) \) \( 4q + 2q^{3} + 2q^{5} - 8q^{6} + 6q^{11} - 12q^{13} + 4q^{15} + 8q^{16} - 2q^{17} - 8q^{18} + 12q^{19} - 16q^{22} - 12q^{23} - 8q^{24} - 2q^{25} - 4q^{26} - 4q^{27} - 12q^{29} - 4q^{30} + 12q^{31} - 14q^{33} + 24q^{34} + 4q^{37} - 2q^{39} + 8q^{41} + 8q^{43} + 4q^{46} - 6q^{47} + 16q^{48} + 14q^{51} - 4q^{54} + 12q^{55} + 24q^{57} - 16q^{58} + 4q^{59} + 24q^{62} + 32q^{64} - 6q^{65} - 20q^{66} + 8q^{67} - 16q^{69} - 24q^{71} + 16q^{72} + 12q^{74} + 2q^{75} + 16q^{78} + 14q^{79} - 8q^{80} + 2q^{81} + 12q^{82} - 4q^{85} + 10q^{87} - 16q^{88} - 16q^{89} - 16q^{90} + 12q^{94} - 12q^{95} - 36q^{97} - 32q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 1.22474i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(3\) 1.20711 2.09077i 0.696923 1.20711i −0.272605 0.962126i \(-0.587885\pi\)
0.969528 0.244981i \(-0.0787816\pi\)
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) −3.41421 −1.39385
\(7\) 0 0
\(8\) −2.82843 −1.00000
\(9\) −1.41421 2.44949i −0.471405 0.816497i
\(10\) 0.707107 1.22474i 0.223607 0.387298i
\(11\) 2.91421 5.04757i 0.878668 1.52190i 0.0258656 0.999665i \(-0.491766\pi\)
0.852803 0.522233i \(-0.174901\pi\)
\(12\) 0 0
\(13\) −1.58579 −0.439818 −0.219909 0.975520i \(-0.570576\pi\)
−0.219909 + 0.975520i \(0.570576\pi\)
\(14\) 0 0
\(15\) 2.41421 0.623347
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −2.62132 + 4.54026i −0.635764 + 1.10117i 0.350589 + 0.936529i \(0.385981\pi\)
−0.986353 + 0.164645i \(0.947352\pi\)
\(18\) −2.00000 + 3.46410i −0.471405 + 0.816497i
\(19\) 3.00000 + 5.19615i 0.688247 + 1.19208i 0.972404 + 0.233301i \(0.0749529\pi\)
−0.284157 + 0.958778i \(0.591714\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −8.24264 −1.75734
\(23\) −2.29289 3.97141i −0.478101 0.828096i 0.521584 0.853200i \(-0.325341\pi\)
−0.999685 + 0.0251045i \(0.992008\pi\)
\(24\) −3.41421 + 5.91359i −0.696923 + 1.20711i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 1.12132 + 1.94218i 0.219909 + 0.380894i
\(27\) 0.414214 0.0797154
\(28\) 0 0
\(29\) 2.65685 0.493365 0.246683 0.969096i \(-0.420659\pi\)
0.246683 + 0.969096i \(0.420659\pi\)
\(30\) −1.70711 2.95680i −0.311674 0.539835i
\(31\) 0.878680 1.52192i 0.157816 0.273345i −0.776265 0.630407i \(-0.782888\pi\)
0.934081 + 0.357062i \(0.116222\pi\)
\(32\) 0 0
\(33\) −7.03553 12.1859i −1.22473 2.12129i
\(34\) 7.41421 1.27153
\(35\) 0 0
\(36\) 0 0
\(37\) 3.12132 + 5.40629i 0.513142 + 0.888788i 0.999884 + 0.0152420i \(0.00485188\pi\)
−0.486742 + 0.873546i \(0.661815\pi\)
\(38\) 4.24264 7.34847i 0.688247 1.19208i
\(39\) −1.91421 + 3.31552i −0.306519 + 0.530907i
\(40\) −1.41421 2.44949i −0.223607 0.387298i
\(41\) −2.24264 −0.350242 −0.175121 0.984547i \(-0.556032\pi\)
−0.175121 + 0.984547i \(0.556032\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 0 0
\(45\) 1.41421 2.44949i 0.210819 0.365148i
\(46\) −3.24264 + 5.61642i −0.478101 + 0.828096i
\(47\) 0.621320 + 1.07616i 0.0906289 + 0.156974i 0.907776 0.419455i \(-0.137779\pi\)
−0.817147 + 0.576429i \(0.804446\pi\)
\(48\) 9.65685 1.39385
\(49\) 0 0
\(50\) 1.41421 0.200000
\(51\) 6.32843 + 10.9612i 0.886157 + 1.53487i
\(52\) 0 0
\(53\) 2.12132 3.67423i 0.291386 0.504695i −0.682752 0.730650i \(-0.739217\pi\)
0.974138 + 0.225955i \(0.0725503\pi\)
\(54\) −0.292893 0.507306i −0.0398577 0.0690356i
\(55\) 5.82843 0.785905
\(56\) 0 0
\(57\) 14.4853 1.91862
\(58\) −1.87868 3.25397i −0.246683 0.427267i
\(59\) 3.12132 5.40629i 0.406361 0.703838i −0.588118 0.808775i \(-0.700131\pi\)
0.994479 + 0.104937i \(0.0334641\pi\)
\(60\) 0 0
\(61\) 1.41421 + 2.44949i 0.181071 + 0.313625i 0.942246 0.334922i \(-0.108710\pi\)
−0.761174 + 0.648547i \(0.775377\pi\)
\(62\) −2.48528 −0.315631
\(63\) 0 0
\(64\) 8.00000 1.00000
\(65\) −0.792893 1.37333i −0.0983463 0.170341i
\(66\) −9.94975 + 17.2335i −1.22473 + 2.12129i
\(67\) −0.121320 + 0.210133i −0.0148216 + 0.0256718i −0.873341 0.487109i \(-0.838051\pi\)
0.858519 + 0.512781i \(0.171385\pi\)
\(68\) 0 0
\(69\) −11.0711 −1.33280
\(70\) 0 0
\(71\) −8.82843 −1.04774 −0.523871 0.851798i \(-0.675513\pi\)
−0.523871 + 0.851798i \(0.675513\pi\)
\(72\) 4.00000 + 6.92820i 0.471405 + 0.816497i
\(73\) 4.24264 7.34847i 0.496564 0.860073i −0.503429 0.864037i \(-0.667928\pi\)
0.999992 + 0.00396356i \(0.00126164\pi\)
\(74\) 4.41421 7.64564i 0.513142 0.888788i
\(75\) 1.20711 + 2.09077i 0.139385 + 0.241421i
\(76\) 0 0
\(77\) 0 0
\(78\) 5.41421 0.613039
\(79\) 7.74264 + 13.4106i 0.871115 + 1.50882i 0.860844 + 0.508868i \(0.169936\pi\)
0.0102708 + 0.999947i \(0.496731\pi\)
\(80\) −2.00000 + 3.46410i −0.223607 + 0.387298i
\(81\) 4.74264 8.21449i 0.526960 0.912722i
\(82\) 1.58579 + 2.74666i 0.175121 + 0.303318i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −5.24264 −0.568644
\(86\) −1.41421 2.44949i −0.152499 0.264135i
\(87\) 3.20711 5.55487i 0.343838 0.595545i
\(88\) −8.24264 + 14.2767i −0.878668 + 1.52190i
\(89\) −4.00000 6.92820i −0.423999 0.734388i 0.572327 0.820025i \(-0.306041\pi\)
−0.996326 + 0.0856373i \(0.972707\pi\)
\(90\) −4.00000 −0.421637
\(91\) 0 0
\(92\) 0 0
\(93\) −2.12132 3.67423i −0.219971 0.381000i
\(94\) 0.878680 1.52192i 0.0906289 0.156974i
\(95\) −3.00000 + 5.19615i −0.307794 + 0.533114i
\(96\) 0 0
\(97\) −4.75736 −0.483037 −0.241518 0.970396i \(-0.577645\pi\)
−0.241518 + 0.970396i \(0.577645\pi\)
\(98\) 0 0
\(99\) −16.4853 −1.65683
\(100\) 0 0
\(101\) −7.24264 + 12.5446i −0.720670 + 1.24824i 0.240062 + 0.970758i \(0.422832\pi\)
−0.960732 + 0.277479i \(0.910501\pi\)
\(102\) 8.94975 15.5014i 0.886157 1.53487i
\(103\) 5.37868 + 9.31615i 0.529977 + 0.917947i 0.999388 + 0.0349676i \(0.0111328\pi\)
−0.469411 + 0.882980i \(0.655534\pi\)
\(104\) 4.48528 0.439818
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −7.24264 12.5446i −0.700173 1.21273i −0.968406 0.249380i \(-0.919773\pi\)
0.268233 0.963354i \(-0.413560\pi\)
\(108\) 0 0
\(109\) −2.50000 + 4.33013i −0.239457 + 0.414751i −0.960558 0.278078i \(-0.910303\pi\)
0.721102 + 0.692829i \(0.243636\pi\)
\(110\) −4.12132 7.13834i −0.392952 0.680614i
\(111\) 15.0711 1.43048
\(112\) 0 0
\(113\) 1.07107 0.100758 0.0503788 0.998730i \(-0.483957\pi\)
0.0503788 + 0.998730i \(0.483957\pi\)
\(114\) −10.2426 17.7408i −0.959311 1.66158i
\(115\) 2.29289 3.97141i 0.213813 0.370336i
\(116\) 0 0
\(117\) 2.24264 + 3.88437i 0.207332 + 0.359110i
\(118\) −8.82843 −0.812723
\(119\) 0 0
\(120\) −6.82843 −0.623347
\(121\) −11.4853 19.8931i −1.04412 1.80846i
\(122\) 2.00000 3.46410i 0.181071 0.313625i
\(123\) −2.70711 + 4.68885i −0.244092 + 0.422779i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −0.242641 −0.0215309 −0.0107654 0.999942i \(-0.503427\pi\)
−0.0107654 + 0.999942i \(0.503427\pi\)
\(128\) −5.65685 9.79796i −0.500000 0.866025i
\(129\) 2.41421 4.18154i 0.212560 0.368164i
\(130\) −1.12132 + 1.94218i −0.0983463 + 0.170341i
\(131\) 1.87868 + 3.25397i 0.164141 + 0.284301i 0.936350 0.351068i \(-0.114181\pi\)
−0.772209 + 0.635369i \(0.780848\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.343146 0.0296433
\(135\) 0.207107 + 0.358719i 0.0178249 + 0.0308737i
\(136\) 7.41421 12.8418i 0.635764 1.10117i
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 7.82843 + 13.5592i 0.666400 + 1.15424i
\(139\) −16.2426 −1.37768 −0.688841 0.724912i \(-0.741880\pi\)
−0.688841 + 0.724912i \(0.741880\pi\)
\(140\) 0 0
\(141\) 3.00000 0.252646
\(142\) 6.24264 + 10.8126i 0.523871 + 0.907371i
\(143\) −4.62132 + 8.00436i −0.386454 + 0.669358i
\(144\) 5.65685 9.79796i 0.471405 0.816497i
\(145\) 1.32843 + 2.30090i 0.110320 + 0.191080i
\(146\) −12.0000 −0.993127
\(147\) 0 0
\(148\) 0 0
\(149\) 7.41421 + 12.8418i 0.607396 + 1.05204i 0.991668 + 0.128821i \(0.0411192\pi\)
−0.384272 + 0.923220i \(0.625547\pi\)
\(150\) 1.70711 2.95680i 0.139385 0.241421i
\(151\) −4.74264 + 8.21449i −0.385951 + 0.668486i −0.991901 0.127017i \(-0.959460\pi\)
0.605950 + 0.795503i \(0.292793\pi\)
\(152\) −8.48528 14.6969i −0.688247 1.19208i
\(153\) 14.8284 1.19881
\(154\) 0 0
\(155\) 1.75736 0.141154
\(156\) 0 0
\(157\) −10.4142 + 18.0379i −0.831145 + 1.43958i 0.0659864 + 0.997821i \(0.478981\pi\)
−0.897131 + 0.441764i \(0.854353\pi\)
\(158\) 10.9497 18.9655i 0.871115 1.50882i
\(159\) −5.12132 8.87039i −0.406147 0.703467i
\(160\) 0 0
\(161\) 0 0
\(162\) −13.4142 −1.05392
\(163\) 0.878680 + 1.52192i 0.0688235 + 0.119206i 0.898384 0.439212i \(-0.144742\pi\)
−0.829560 + 0.558417i \(0.811409\pi\)
\(164\) 0 0
\(165\) 7.03553 12.1859i 0.547716 0.948671i
\(166\) 0 0
\(167\) −9.24264 −0.715217 −0.357609 0.933872i \(-0.616408\pi\)
−0.357609 + 0.933872i \(0.616408\pi\)
\(168\) 0 0
\(169\) −10.4853 −0.806560
\(170\) 3.70711 + 6.42090i 0.284322 + 0.492460i
\(171\) 8.48528 14.6969i 0.648886 1.12390i
\(172\) 0 0
\(173\) 0.621320 + 1.07616i 0.0472381 + 0.0818188i 0.888678 0.458532i \(-0.151625\pi\)
−0.841440 + 0.540351i \(0.818291\pi\)
\(174\) −9.07107 −0.687676
\(175\) 0 0
\(176\) 23.3137 1.75734
\(177\) −7.53553 13.0519i −0.566405 0.981043i
\(178\) −5.65685 + 9.79796i −0.423999 + 0.734388i
\(179\) −1.24264 + 2.15232i −0.0928793 + 0.160872i −0.908722 0.417403i \(-0.862940\pi\)
0.815842 + 0.578275i \(0.196274\pi\)
\(180\) 0 0
\(181\) −6.72792 −0.500083 −0.250041 0.968235i \(-0.580444\pi\)
−0.250041 + 0.968235i \(0.580444\pi\)
\(182\) 0 0
\(183\) 6.82843 0.504772
\(184\) 6.48528 + 11.2328i 0.478101 + 0.828096i
\(185\) −3.12132 + 5.40629i −0.229484 + 0.397478i
\(186\) −3.00000 + 5.19615i −0.219971 + 0.381000i
\(187\) 15.2782 + 26.4626i 1.11725 + 1.93514i
\(188\) 0 0
\(189\) 0 0
\(190\) 8.48528 0.615587
\(191\) 9.98528 + 17.2950i 0.722510 + 1.25142i 0.959991 + 0.280031i \(0.0903448\pi\)
−0.237481 + 0.971392i \(0.576322\pi\)
\(192\) 9.65685 16.7262i 0.696923 1.20711i
\(193\) 8.00000 13.8564i 0.575853 0.997406i −0.420096 0.907480i \(-0.638004\pi\)
0.995948 0.0899262i \(-0.0286631\pi\)
\(194\) 3.36396 + 5.82655i 0.241518 + 0.418322i
\(195\) −3.82843 −0.274159
\(196\) 0 0
\(197\) 10.5858 0.754206 0.377103 0.926171i \(-0.376920\pi\)
0.377103 + 0.926171i \(0.376920\pi\)
\(198\) 11.6569 + 20.1903i 0.828417 + 1.43486i
\(199\) −2.29289 + 3.97141i −0.162539 + 0.281526i −0.935779 0.352588i \(-0.885302\pi\)
0.773240 + 0.634114i \(0.218635\pi\)
\(200\) 1.41421 2.44949i 0.100000 0.173205i
\(201\) 0.292893 + 0.507306i 0.0206591 + 0.0357826i
\(202\) 20.4853 1.44134
\(203\) 0 0
\(204\) 0 0
\(205\) −1.12132 1.94218i −0.0783164 0.135648i
\(206\) 7.60660 13.1750i 0.529977 0.917947i
\(207\) −6.48528 + 11.2328i −0.450758 + 0.780736i
\(208\) −3.17157 5.49333i −0.219909 0.380894i
\(209\) 34.9706 2.41896
\(210\) 0 0
\(211\) 9.00000 0.619586 0.309793 0.950804i \(-0.399740\pi\)
0.309793 + 0.950804i \(0.399740\pi\)
\(212\) 0 0
\(213\) −10.6569 + 18.4582i −0.730196 + 1.26474i
\(214\) −10.2426 + 17.7408i −0.700173 + 1.21273i
\(215\) 1.00000 + 1.73205i 0.0681994 + 0.118125i
\(216\) −1.17157 −0.0797154
\(217\) 0 0
\(218\) 7.07107 0.478913
\(219\) −10.2426 17.7408i −0.692134 1.19881i
\(220\) 0 0
\(221\) 4.15685 7.19988i 0.279620 0.484317i
\(222\) −10.6569 18.4582i −0.715241 1.23883i
\(223\) −18.2132 −1.21965 −0.609823 0.792538i \(-0.708760\pi\)
−0.609823 + 0.792538i \(0.708760\pi\)
\(224\) 0 0
\(225\) 2.82843 0.188562
\(226\) −0.757359 1.31178i −0.0503788 0.0872586i
\(227\) −4.86396 + 8.42463i −0.322832 + 0.559162i −0.981071 0.193647i \(-0.937968\pi\)
0.658239 + 0.752809i \(0.271302\pi\)
\(228\) 0 0
\(229\) −15.0208 26.0168i −0.992603 1.71924i −0.601439 0.798919i \(-0.705406\pi\)
−0.391164 0.920321i \(-0.627928\pi\)
\(230\) −6.48528 −0.427627
\(231\) 0 0
\(232\) −7.51472 −0.493365
\(233\) 7.41421 + 12.8418i 0.485721 + 0.841294i 0.999865 0.0164099i \(-0.00522367\pi\)
−0.514144 + 0.857704i \(0.671890\pi\)
\(234\) 3.17157 5.49333i 0.207332 0.359110i
\(235\) −0.621320 + 1.07616i −0.0405305 + 0.0702008i
\(236\) 0 0
\(237\) 37.3848 2.42840
\(238\) 0 0
\(239\) −0.514719 −0.0332944 −0.0166472 0.999861i \(-0.505299\pi\)
−0.0166472 + 0.999861i \(0.505299\pi\)
\(240\) 4.82843 + 8.36308i 0.311674 + 0.539835i
\(241\) 12.3640 21.4150i 0.796433 1.37946i −0.125493 0.992095i \(-0.540051\pi\)
0.921925 0.387367i \(-0.126616\pi\)
\(242\) −16.2426 + 28.1331i −1.04412 + 1.80846i
\(243\) −10.8284 18.7554i −0.694644 1.20316i
\(244\) 0 0
\(245\) 0 0
\(246\) 7.65685 0.488183
\(247\) −4.75736 8.23999i −0.302704 0.524298i
\(248\) −2.48528 + 4.30463i −0.157816 + 0.273345i
\(249\) 0 0
\(250\) 0.707107 + 1.22474i 0.0447214 + 0.0774597i
\(251\) 25.2132 1.59144 0.795722 0.605663i \(-0.207092\pi\)
0.795722 + 0.605663i \(0.207092\pi\)
\(252\) 0 0
\(253\) −26.7279 −1.68037
\(254\) 0.171573 + 0.297173i 0.0107654 + 0.0186463i
\(255\) −6.32843 + 10.9612i −0.396301 + 0.686414i
\(256\) 0 0
\(257\) −13.2426 22.9369i −0.826053 1.43077i −0.901112 0.433587i \(-0.857248\pi\)
0.0750585 0.997179i \(-0.476086\pi\)
\(258\) −6.82843 −0.425119
\(259\) 0 0
\(260\) 0 0
\(261\) −3.75736 6.50794i −0.232575 0.402831i
\(262\) 2.65685 4.60181i 0.164141 0.284301i
\(263\) −14.3137 + 24.7921i −0.882621 + 1.52874i −0.0342049 + 0.999415i \(0.510890\pi\)
−0.848416 + 0.529330i \(0.822443\pi\)
\(264\) 19.8995 + 34.4669i 1.22473 + 2.12129i
\(265\) 4.24264 0.260623
\(266\) 0 0
\(267\) −19.3137 −1.18198
\(268\) 0 0
\(269\) −3.87868 + 6.71807i −0.236487 + 0.409608i −0.959704 0.281013i \(-0.909329\pi\)
0.723217 + 0.690621i \(0.242663\pi\)
\(270\) 0.292893 0.507306i 0.0178249 0.0308737i
\(271\) −11.6569 20.1903i −0.708103 1.22647i −0.965560 0.260181i \(-0.916218\pi\)
0.257456 0.966290i \(-0.417116\pi\)
\(272\) −20.9706 −1.27153
\(273\) 0 0
\(274\) 16.9706 1.02523
\(275\) 2.91421 + 5.04757i 0.175734 + 0.304380i
\(276\) 0 0
\(277\) 13.6066 23.5673i 0.817541 1.41602i −0.0899471 0.995947i \(-0.528670\pi\)
0.907489 0.420077i \(-0.137997\pi\)
\(278\) 11.4853 + 19.8931i 0.688841 + 1.19311i
\(279\) −4.97056 −0.297580
\(280\) 0 0
\(281\) −20.3137 −1.21181 −0.605907 0.795535i \(-0.707190\pi\)
−0.605907 + 0.795535i \(0.707190\pi\)
\(282\) −2.12132 3.67423i −0.126323 0.218797i
\(283\) −3.27817 + 5.67796i −0.194867 + 0.337520i −0.946857 0.321655i \(-0.895761\pi\)
0.751990 + 0.659175i \(0.229094\pi\)
\(284\) 0 0
\(285\) 7.24264 + 12.5446i 0.429017 + 0.743079i
\(286\) 13.0711 0.772908
\(287\) 0 0
\(288\) 0 0
\(289\) −5.24264 9.08052i −0.308391 0.534148i
\(290\) 1.87868 3.25397i 0.110320 0.191080i
\(291\) −5.74264 + 9.94655i −0.336640 + 0.583077i
\(292\) 0 0
\(293\) −0.272078 −0.0158950 −0.00794748 0.999968i \(-0.502530\pi\)
−0.00794748 + 0.999968i \(0.502530\pi\)
\(294\) 0 0
\(295\) 6.24264 0.363461
\(296\) −8.82843 15.2913i −0.513142 0.888788i
\(297\) 1.20711 2.09077i 0.0700434 0.121319i
\(298\) 10.4853 18.1610i 0.607396 1.05204i
\(299\) 3.63604 + 6.29780i 0.210278 + 0.364211i
\(300\) 0 0
\(301\) 0 0
\(302\) 13.4142 0.771901
\(303\) 17.4853 + 30.2854i 1.00450 + 1.73985i
\(304\) −12.0000 + 20.7846i −0.688247 + 1.19208i
\(305\) −1.41421 + 2.44949i −0.0809776 + 0.140257i
\(306\) −10.4853 18.1610i −0.599404 1.03820i
\(307\) −11.1005 −0.633539 −0.316770 0.948503i \(-0.602598\pi\)
−0.316770 + 0.948503i \(0.602598\pi\)
\(308\) 0 0
\(309\) 25.9706 1.47741
\(310\) −1.24264 2.15232i −0.0705772 0.122243i
\(311\) −5.00000 + 8.66025i −0.283524 + 0.491078i −0.972250 0.233944i \(-0.924837\pi\)
0.688726 + 0.725022i \(0.258170\pi\)
\(312\) 5.41421 9.37769i 0.306519 0.530907i
\(313\) 12.1066 + 20.9692i 0.684306 + 1.18525i 0.973654 + 0.228028i \(0.0732279\pi\)
−0.289349 + 0.957224i \(0.593439\pi\)
\(314\) 29.4558 1.66229
\(315\) 0 0
\(316\) 0 0
\(317\) 5.82843 + 10.0951i 0.327357 + 0.566999i 0.981987 0.188951i \(-0.0605087\pi\)
−0.654629 + 0.755950i \(0.727175\pi\)
\(318\) −7.24264 + 12.5446i −0.406147 + 0.703467i
\(319\) 7.74264 13.4106i 0.433505 0.750852i
\(320\) 4.00000 + 6.92820i 0.223607 + 0.387298i
\(321\) −34.9706 −1.95187
\(322\) 0 0
\(323\) −31.4558 −1.75025
\(324\) 0 0
\(325\) 0.792893 1.37333i 0.0439818 0.0761787i
\(326\) 1.24264 2.15232i 0.0688235 0.119206i
\(327\) 6.03553 + 10.4539i 0.333766 + 0.578099i
\(328\) 6.34315 0.350242
\(329\) 0 0
\(330\) −19.8995 −1.09543
\(331\) −11.7279 20.3134i −0.644625 1.11652i −0.984388 0.176012i \(-0.943680\pi\)
0.339763 0.940511i \(-0.389653\pi\)
\(332\) 0 0
\(333\) 8.82843 15.2913i 0.483795 0.837957i
\(334\) 6.53553 + 11.3199i 0.357609 + 0.619396i
\(335\) −0.242641 −0.0132569
\(336\) 0 0
\(337\) 13.7574 0.749411 0.374706 0.927144i \(-0.377744\pi\)
0.374706 + 0.927144i \(0.377744\pi\)
\(338\) 7.41421 + 12.8418i 0.403280 + 0.698502i
\(339\) 1.29289 2.23936i 0.0702203 0.121625i
\(340\) 0 0
\(341\) −5.12132 8.87039i −0.277335 0.480358i
\(342\) −24.0000 −1.29777
\(343\) 0 0
\(344\) −5.65685 −0.304997
\(345\) −5.53553 9.58783i −0.298023 0.516191i
\(346\) 0.878680 1.52192i 0.0472381 0.0818188i
\(347\) 0.535534 0.927572i 0.0287490 0.0497947i −0.851293 0.524691i \(-0.824181\pi\)
0.880042 + 0.474896i \(0.157514\pi\)
\(348\) 0 0
\(349\) −22.9706 −1.22959 −0.614793 0.788688i \(-0.710760\pi\)
−0.614793 + 0.788688i \(0.710760\pi\)
\(350\) 0 0
\(351\) −0.656854 −0.0350603
\(352\) 0 0
\(353\) 18.1066 31.3616i 0.963717 1.66921i 0.250694 0.968066i \(-0.419341\pi\)
0.713023 0.701141i \(-0.247326\pi\)
\(354\) −10.6569 + 18.4582i −0.566405 + 0.981043i
\(355\) −4.41421 7.64564i −0.234282 0.405789i
\(356\) 0 0
\(357\) 0 0
\(358\) 3.51472 0.185759
\(359\) −5.65685 9.79796i −0.298557 0.517116i 0.677249 0.735754i \(-0.263172\pi\)
−0.975806 + 0.218638i \(0.929839\pi\)
\(360\) −4.00000 + 6.92820i −0.210819 + 0.365148i
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) 4.75736 + 8.23999i 0.250041 + 0.433084i
\(363\) −55.4558 −2.91068
\(364\) 0 0
\(365\) 8.48528 0.444140
\(366\) −4.82843 8.36308i −0.252386 0.437145i
\(367\) 14.9350 25.8682i 0.779602 1.35031i −0.152569 0.988293i \(-0.548755\pi\)
0.932171 0.362018i \(-0.117912\pi\)
\(368\) 9.17157 15.8856i 0.478101 0.828096i
\(369\) 3.17157 + 5.49333i 0.165105 + 0.285971i
\(370\) 8.82843 0.458968
\(371\) 0 0
\(372\) 0 0
\(373\) −0.242641 0.420266i −0.0125635 0.0217605i 0.859675 0.510841i \(-0.170666\pi\)
−0.872239 + 0.489080i \(0.837333\pi\)
\(374\) 21.6066 37.4237i 1.11725 1.93514i
\(375\) −1.20711 + 2.09077i −0.0623347 + 0.107967i
\(376\) −1.75736 3.04384i −0.0906289 0.156974i
\(377\) −4.21320 −0.216991
\(378\) 0 0
\(379\) 2.00000 0.102733 0.0513665 0.998680i \(-0.483642\pi\)
0.0513665 + 0.998680i \(0.483642\pi\)
\(380\) 0 0
\(381\) −0.292893 + 0.507306i −0.0150054 + 0.0259901i
\(382\) 14.1213 24.4588i 0.722510 1.25142i
\(383\) −6.24264 10.8126i −0.318984 0.552497i 0.661292 0.750128i \(-0.270008\pi\)
−0.980276 + 0.197632i \(0.936675\pi\)
\(384\) −27.3137 −1.39385
\(385\) 0 0
\(386\) −22.6274 −1.15171
\(387\) −2.82843 4.89898i −0.143777 0.249029i
\(388\) 0 0
\(389\) 17.5711 30.4340i 0.890889 1.54306i 0.0520764 0.998643i \(-0.483416\pi\)
0.838812 0.544421i \(-0.183251\pi\)
\(390\) 2.70711 + 4.68885i 0.137080 + 0.237429i
\(391\) 24.0416 1.21584
\(392\) 0 0
\(393\) 9.07107 0.457575
\(394\) −7.48528 12.9649i −0.377103 0.653162i
\(395\) −7.74264 + 13.4106i −0.389575 + 0.674763i
\(396\) 0 0
\(397\) 2.20711 + 3.82282i 0.110772 + 0.191862i 0.916082 0.400992i \(-0.131334\pi\)
−0.805310 + 0.592854i \(0.798001\pi\)
\(398\) 6.48528 0.325078
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) −3.08579 5.34474i −0.154097 0.266904i 0.778633 0.627480i \(-0.215913\pi\)
−0.932730 + 0.360576i \(0.882580\pi\)
\(402\) 0.414214 0.717439i 0.0206591 0.0357826i
\(403\) −1.39340 + 2.41344i −0.0694101 + 0.120222i
\(404\) 0 0
\(405\) 9.48528 0.471327
\(406\) 0 0
\(407\) 36.3848 1.80353
\(408\) −17.8995 31.0028i −0.886157 1.53487i
\(409\) −7.24264 + 12.5446i −0.358126 + 0.620292i −0.987648 0.156691i \(-0.949917\pi\)
0.629522 + 0.776983i \(0.283251\pi\)
\(410\) −1.58579 + 2.74666i −0.0783164 + 0.135648i
\(411\) 14.4853 + 25.0892i 0.714506 + 1.23756i
\(412\) 0 0
\(413\) 0 0
\(414\) 18.3431 0.901516
\(415\) 0 0
\(416\) 0 0
\(417\) −19.6066 + 33.9596i −0.960139 + 1.66301i
\(418\) −24.7279 42.8300i −1.20948 2.09488i
\(419\) 6.72792 0.328681 0.164340 0.986404i \(-0.447450\pi\)
0.164340 + 0.986404i \(0.447450\pi\)
\(420\) 0 0
\(421\) −19.0000 −0.926003 −0.463002 0.886357i \(-0.653228\pi\)
−0.463002 + 0.886357i \(0.653228\pi\)
\(422\) −6.36396 11.0227i −0.309793 0.536577i
\(423\) 1.75736 3.04384i 0.0854457 0.147996i
\(424\) −6.00000 + 10.3923i −0.291386 + 0.504695i
\(425\) −2.62132 4.54026i −0.127153 0.220235i
\(426\) 30.1421 1.46039
\(427\) 0 0
\(428\) 0 0
\(429\) 11.1569 + 19.3242i 0.538658 + 0.932983i
\(430\) 1.41421 2.44949i 0.0681994 0.118125i
\(431\) −5.39949 + 9.35220i −0.260085 + 0.450480i −0.966264 0.257553i \(-0.917084\pi\)
0.706180 + 0.708033i \(0.250417\pi\)
\(432\) 0.828427 + 1.43488i 0.0398577 + 0.0690356i
\(433\) 22.9706 1.10389 0.551947 0.833879i \(-0.313885\pi\)
0.551947 + 0.833879i \(0.313885\pi\)
\(434\) 0 0
\(435\) 6.41421 0.307538
\(436\) 0 0
\(437\) 13.7574 23.8284i 0.658104 1.13987i
\(438\) −14.4853 + 25.0892i −0.692134 + 1.19881i
\(439\) 3.19239 + 5.52938i 0.152364 + 0.263903i 0.932096 0.362211i \(-0.117978\pi\)
−0.779732 + 0.626114i \(0.784645\pi\)
\(440\) −16.4853 −0.785905
\(441\) 0 0
\(442\) −11.7574 −0.559241
\(443\) −10.4142 18.0379i −0.494794 0.857009i 0.505188 0.863009i \(-0.331423\pi\)
−0.999982 + 0.00600072i \(0.998090\pi\)
\(444\) 0 0
\(445\) 4.00000 6.92820i 0.189618 0.328428i
\(446\) 12.8787 + 22.3065i 0.609823 + 1.05624i
\(447\) 35.7990 1.69323
\(448\) 0 0
\(449\) −29.8284 −1.40769 −0.703845 0.710353i \(-0.748535\pi\)
−0.703845 + 0.710353i \(0.748535\pi\)
\(450\) −2.00000 3.46410i −0.0942809 0.163299i
\(451\) −6.53553 + 11.3199i −0.307746 + 0.533032i
\(452\) 0 0
\(453\) 11.4497 + 19.8315i 0.537956 + 0.931767i
\(454\) 13.7574 0.645665
\(455\) 0 0
\(456\) −40.9706 −1.91862
\(457\) 10.1213 + 17.5306i 0.473455 + 0.820049i 0.999538 0.0303845i \(-0.00967317\pi\)
−0.526083 + 0.850433i \(0.676340\pi\)
\(458\) −21.2426 + 36.7933i −0.992603 + 1.71924i
\(459\) −1.08579 + 1.88064i −0.0506802 + 0.0877806i
\(460\) 0 0
\(461\) −36.9706 −1.72189 −0.860945 0.508697i \(-0.830127\pi\)
−0.860945 + 0.508697i \(0.830127\pi\)
\(462\) 0 0
\(463\) 29.4558 1.36893 0.684465 0.729046i \(-0.260036\pi\)
0.684465 + 0.729046i \(0.260036\pi\)
\(464\) 5.31371 + 9.20361i 0.246683 + 0.427267i
\(465\) 2.12132 3.67423i 0.0983739 0.170389i
\(466\) 10.4853 18.1610i 0.485721 0.841294i
\(467\) 9.86396 + 17.0849i 0.456450 + 0.790594i 0.998770 0.0495776i \(-0.0157875\pi\)
−0.542321 + 0.840172i \(0.682454\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1.75736 0.0810609
\(471\) 25.1421 + 43.5475i 1.15849 + 2.00656i
\(472\) −8.82843 + 15.2913i −0.406361 + 0.703838i
\(473\) 5.82843 10.0951i 0.267991 0.464175i
\(474\) −26.4350 45.7868i −1.21420 2.10306i
\(475\) −6.00000 −0.275299
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) 0.363961 + 0.630399i 0.0166472 + 0.0288338i
\(479\) 10.1213 17.5306i 0.462455 0.800995i −0.536628 0.843819i \(-0.680302\pi\)
0.999083 + 0.0428237i \(0.0136354\pi\)
\(480\) 0 0
\(481\) −4.94975 8.57321i −0.225689 0.390905i
\(482\) −34.9706 −1.59287
\(483\) 0 0
\(484\) 0 0
\(485\) −2.37868 4.11999i −0.108010 0.187079i
\(486\) −15.3137 + 26.5241i −0.694644 + 1.20316i
\(487\) 15.8492 27.4517i 0.718198 1.24395i −0.243515 0.969897i \(-0.578301\pi\)
0.961713 0.274058i \(-0.0883660\pi\)
\(488\) −4.00000 6.92820i −0.181071 0.313625i
\(489\) 4.24264 0.191859
\(490\) 0 0
\(491\) 19.2843 0.870287 0.435143 0.900361i \(-0.356698\pi\)
0.435143 + 0.900361i \(0.356698\pi\)
\(492\) 0 0
\(493\) −6.96447 + 12.0628i −0.313664 + 0.543282i
\(494\) −6.72792 + 11.6531i −0.302704 + 0.524298i
\(495\) −8.24264 14.2767i −0.370479 0.641689i
\(496\) 7.02944 0.315631
\(497\) 0 0
\(498\) 0 0
\(499\) −1.50000 2.59808i −0.0671492 0.116306i 0.830496 0.557024i \(-0.188057\pi\)
−0.897645 + 0.440719i \(0.854724\pi\)
\(500\) 0 0
\(501\) −11.1569 + 19.3242i −0.498451 + 0.863343i
\(502\) −17.8284 30.8797i −0.795722 1.37823i
\(503\) 32.7574 1.46058 0.730289 0.683138i \(-0.239385\pi\)
0.730289 + 0.683138i \(0.239385\pi\)
\(504\) 0 0
\(505\) −14.4853 −0.644587
\(506\) 18.8995 + 32.7349i 0.840185 + 1.45524i
\(507\) −12.6569 + 21.9223i −0.562111 + 0.973604i
\(508\) 0 0
\(509\) 8.60660 + 14.9071i 0.381481 + 0.660744i 0.991274 0.131816i \(-0.0420809\pi\)
−0.609793 + 0.792561i \(0.708748\pi\)
\(510\) 17.8995 0.792603
\(511\) 0 0
\(512\) −22.6274 −1.00000
\(513\) 1.24264 + 2.15232i 0.0548639 + 0.0950271i
\(514\) −18.7279 + 32.4377i −0.826053 + 1.43077i
\(515\) −5.37868 + 9.31615i −0.237013 + 0.410518i
\(516\) 0 0
\(517\) 7.24264 0.318531
\(518\) 0 0
\(519\) 3.00000 0.131685
\(520\) 2.24264 + 3.88437i 0.0983463 + 0.170341i
\(521\) −9.48528 + 16.4290i −0.415558 + 0.719767i −0.995487 0.0948999i \(-0.969747\pi\)
0.579929 + 0.814667i \(0.303080\pi\)
\(522\) −5.31371 + 9.20361i −0.232575 + 0.402831i
\(523\) 7.75736 + 13.4361i 0.339206 + 0.587521i 0.984284 0.176595i \(-0.0565084\pi\)
−0.645078 + 0.764117i \(0.723175\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 40.4853 1.76524
\(527\) 4.60660 + 7.97887i 0.200667 + 0.347565i
\(528\) 28.1421 48.7436i 1.22473 2.12129i
\(529\) 0.985281 1.70656i 0.0428383 0.0741981i
\(530\) −3.00000 5.19615i −0.130312 0.225706i
\(531\) −17.6569 −0.766242
\(532\) 0 0
\(533\) 3.55635 0.154043
\(534\) 13.6569 + 23.6544i 0.590990 + 1.02362i
\(535\) 7.24264 12.5446i 0.313127 0.542351i
\(536\) 0.343146 0.594346i 0.0148216 0.0256718i
\(537\) 3.00000 + 5.19615i 0.129460 + 0.224231i
\(538\) 10.9706 0.472975
\(539\) 0 0
\(540\) 0 0
\(541\) −5.98528 10.3668i −0.257327 0.445704i 0.708198 0.706014i \(-0.249509\pi\)
−0.965525 + 0.260310i \(0.916175\pi\)
\(542\) −16.4853 + 28.5533i −0.708103 + 1.22647i
\(543\) −8.12132 + 14.0665i −0.348519 + 0.603653i
\(544\) 0 0
\(545\) −5.00000 −0.214176
\(546\) 0 0
\(547\) −7.51472 −0.321306 −0.160653 0.987011i \(-0.551360\pi\)
−0.160653 + 0.987011i \(0.551360\pi\)
\(548\) 0 0
\(549\) 4.00000 6.92820i 0.170716 0.295689i
\(550\) 4.12132 7.13834i 0.175734 0.304380i
\(551\) 7.97056 + 13.8054i 0.339557 + 0.588131i
\(552\) 31.3137 1.33280
\(553\) 0 0
\(554\) −38.4853 −1.63508
\(555\) 7.53553 + 13.0519i 0.319866 + 0.554023i
\(556\) 0 0
\(557\) −15.8995 + 27.5387i −0.673683 + 1.16685i 0.303169 + 0.952937i \(0.401955\pi\)
−0.976852 + 0.213917i \(0.931378\pi\)
\(558\) 3.51472 + 6.08767i 0.148790 + 0.257712i
\(559\) −3.17157 −0.134143
\(560\) 0 0
\(561\) 73.7696 3.11455
\(562\) 14.3640 + 24.8791i 0.605907 + 1.04946i
\(563\) 17.9706 31.1259i 0.757369 1.31180i −0.186819 0.982394i \(-0.559818\pi\)
0.944188 0.329407i \(-0.106849\pi\)
\(564\) 0 0
\(565\) 0.535534 + 0.927572i 0.0225301 + 0.0390232i
\(566\) 9.27208 0.389735
\(567\) 0 0
\(568\) 24.9706 1.04774
\(569\) 1.07107 + 1.85514i 0.0449015 + 0.0777717i 0.887603 0.460610i \(-0.152369\pi\)
−0.842701 + 0.538382i \(0.819036\pi\)
\(570\) 10.2426 17.7408i 0.429017 0.743079i
\(571\) 17.2426 29.8651i 0.721582 1.24982i −0.238783 0.971073i \(-0.576749\pi\)
0.960365 0.278744i \(-0.0899181\pi\)
\(572\) 0 0
\(573\) 48.2132 2.01414
\(574\) 0 0
\(575\) 4.58579 0.191241
\(576\) −11.3137 19.5959i −0.471405 0.816497i
\(577\) −4.86396 + 8.42463i −0.202489 + 0.350722i −0.949330 0.314281i \(-0.898236\pi\)
0.746841 + 0.665003i \(0.231570\pi\)
\(578\) −7.41421 + 12.8418i −0.308391 + 0.534148i
\(579\) −19.3137 33.4523i −0.802650 1.39023i
\(580\) 0 0
\(581\) 0 0
\(582\) 16.2426 0.673279
\(583\) −12.3640 21.4150i −0.512063 0.886919i
\(584\) −12.0000 + 20.7846i −0.496564 + 0.860073i
\(585\) −2.24264 + 3.88437i −0.0927218 + 0.160599i
\(586\) 0.192388 + 0.333226i 0.00794748 + 0.0137654i
\(587\) −13.4558 −0.555382 −0.277691 0.960670i \(-0.589569\pi\)
−0.277691 + 0.960670i \(0.589569\pi\)
\(588\) 0 0
\(589\) 10.5442 0.434464
\(590\) −4.41421 7.64564i −0.181730 0.314766i
\(591\) 12.7782 22.1324i 0.525624 0.910407i
\(592\) −12.4853 + 21.6251i −0.513142 + 0.888788i
\(593\) 5.37868 + 9.31615i 0.220876 + 0.382568i 0.955074 0.296367i \(-0.0957751\pi\)
−0.734198 + 0.678935i \(0.762442\pi\)
\(594\) −3.41421 −0.140087
\(595\) 0 0
\(596\) 0 0
\(597\) 5.53553 + 9.58783i 0.226554 + 0.392404i
\(598\) 5.14214 8.90644i 0.210278 0.364211i
\(599\) 6.08579 10.5409i 0.248658 0.430689i −0.714495 0.699640i \(-0.753344\pi\)
0.963154 + 0.268951i \(0.0866770\pi\)
\(600\) −3.41421 5.91359i −0.139385 0.241421i
\(601\) −22.9706 −0.936989 −0.468494 0.883466i \(-0.655203\pi\)
−0.468494 + 0.883466i \(0.655203\pi\)
\(602\) 0 0
\(603\) 0.686292 0.0279480
\(604\) 0 0
\(605\) 11.4853 19.8931i 0.466943 0.808769i
\(606\) 24.7279 42.8300i 1.00450 1.73985i
\(607\) −12.4497 21.5636i −0.505320 0.875239i −0.999981 0.00615355i \(-0.998041\pi\)
0.494661 0.869086i \(-0.335292\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 4.00000 0.161955
\(611\) −0.985281 1.70656i −0.0398602 0.0690399i
\(612\) 0 0
\(613\) −21.9706 + 38.0541i −0.887383 + 1.53699i −0.0444245 + 0.999013i \(0.514145\pi\)
−0.842958 + 0.537979i \(0.819188\pi\)
\(614\) 7.84924 + 13.5953i 0.316770 + 0.548661i
\(615\) −5.41421 −0.218322
\(616\) 0 0
\(617\) 7.41421 0.298485 0.149242 0.988801i \(-0.452316\pi\)
0.149242 + 0.988801i \(0.452316\pi\)
\(618\) −18.3640 31.8073i −0.738707 1.27948i
\(619\) 15.5355 26.9083i 0.624426 1.08154i −0.364226 0.931311i \(-0.618666\pi\)
0.988652 0.150227i \(-0.0480003\pi\)
\(620\) 0 0
\(621\) −0.949747 1.64501i −0.0381121 0.0660120i
\(622\) 14.1421 0.567048
\(623\) 0 0
\(624\) −15.3137 −0.613039
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 17.1213 29.6550i 0.684306 1.18525i
\(627\) 42.2132 73.1154i 1.68583 2.91995i
\(628\) 0 0
\(629\) −32.7279 −1.30495
\(630\) 0 0
\(631\) 8.45584 0.336622 0.168311 0.985734i \(-0.446169\pi\)
0.168311 + 0.985734i \(0.446169\pi\)
\(632\) −21.8995 37.9310i −0.871115 1.50882i
\(633\) 10.8640 18.8169i 0.431804 0.747906i
\(634\) 8.24264 14.2767i 0.327357 0.566999i
\(635\) −0.121320 0.210133i −0.00481445 0.00833887i
\(636\) 0 0
\(637\) 0 0
\(638\) −21.8995 −0.867009
\(639\) 12.4853 + 21.6251i 0.493910 + 0.855477i
\(640\) 5.65685 9.79796i 0.223607 0.387298i
\(641\) 0.343146 0.594346i 0.0135534 0.0234753i −0.859169 0.511692i \(-0.829019\pi\)
0.872723 + 0.488216i \(0.162352\pi\)
\(642\) 24.7279 + 42.8300i 0.975933 + 1.69037i
\(643\) −27.7279 −1.09348 −0.546741 0.837302i \(-0.684132\pi\)
−0.546741 + 0.837302i \(0.684132\pi\)
\(644\) 0 0
\(645\) 4.82843 0.190119
\(646\) 22.2426 + 38.5254i 0.875125 + 1.51576i
\(647\) −14.2426 + 24.6690i −0.559936 + 0.969838i 0.437565 + 0.899187i \(0.355841\pi\)
−0.997501 + 0.0706508i \(0.977492\pi\)
\(648\) −13.4142 + 23.2341i −0.526960 + 0.912722i
\(649\) −18.1924 31.5101i −0.714114 1.23688i
\(650\) −2.24264 −0.0879636
\(651\) 0 0
\(652\) 0 0
\(653\) −0.514719 0.891519i −0.0201425 0.0348878i 0.855778 0.517342i \(-0.173079\pi\)
−0.875921 + 0.482455i \(0.839745\pi\)
\(654\) 8.53553 14.7840i 0.333766 0.578099i
\(655\) −1.87868 + 3.25397i −0.0734061 + 0.127143i
\(656\) −4.48528 7.76874i −0.175121 0.303318i
\(657\) −24.0000 −0.936329
\(658\) 0 0
\(659\) −13.9706 −0.544216 −0.272108 0.962267i \(-0.587721\pi\)
−0.272108 + 0.962267i \(0.587721\pi\)
\(660\) 0 0
\(661\) −18.7279 + 32.4377i −0.728432 + 1.26168i 0.229114 + 0.973400i \(0.426417\pi\)
−0.957546 + 0.288281i \(0.906916\pi\)
\(662\) −16.5858 + 28.7274i −0.644625 + 1.11652i
\(663\) −10.0355 17.3821i −0.389748 0.675063i
\(664\) 0 0
\(665\) 0 0
\(666\) −24.9706 −0.967590
\(667\) −6.09188 10.5515i −0.235879 0.408554i
\(668\) 0 0
\(669\) −21.9853 + 38.0796i −0.850000 + 1.47224i
\(670\) 0.171573 + 0.297173i 0.00662844 + 0.0114808i
\(671\) 16.4853 0.636407
\(672\) 0 0
\(673\) 20.4853 0.789650 0.394825 0.918756i \(-0.370805\pi\)
0.394825 + 0.918756i \(0.370805\pi\)
\(674\) −9.72792 16.8493i −0.374706 0.649009i
\(675\) −0.207107 + 0.358719i −0.00797154 + 0.0138071i
\(676\) 0 0
\(677\) 0.893398 + 1.54741i 0.0343361 + 0.0594718i 0.882683 0.469969i \(-0.155735\pi\)
−0.848347 + 0.529441i \(0.822402\pi\)
\(678\) −3.65685 −0.140441
\(679\) 0 0
\(680\) 14.8284 0.568644
\(681\) 11.7426 + 20.3389i 0.449979 + 0.779386i
\(682\) −7.24264 + 12.5446i −0.277335 + 0.480358i
\(683\) 3.89949 6.75412i 0.149210 0.258439i −0.781726 0.623622i \(-0.785660\pi\)
0.930936 + 0.365183i \(0.118994\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) −72.5269 −2.76707
\(688\) 4.00000 + 6.92820i 0.152499 + 0.264135i
\(689\) −3.36396 + 5.82655i −0.128157 + 0.221974i
\(690\) −7.82843 + 13.5592i −0.298023 + 0.516191i
\(691\) 4.58579 + 7.94282i 0.174452 + 0.302159i 0.939971 0.341253i \(-0.110851\pi\)
−0.765520 + 0.643412i \(0.777518\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1.51472 −0.0574979
\(695\) −8.12132 14.0665i −0.308059 0.533574i
\(696\) −9.07107 + 15.7116i −0.343838 + 0.595545i
\(697\) 5.87868 10.1822i 0.222671 0.385677i
\(698\) 16.2426 + 28.1331i 0.614793 + 1.06485i
\(699\) 35.7990 1.35404
\(700\) 0 0
\(701\) −4.45584 −0.168295 −0.0841475 0.996453i \(-0.526817\pi\)
−0.0841475 + 0.996453i \(0.526817\pi\)
\(702\) 0.464466 + 0.804479i 0.0175301 + 0.0303631i
\(703\) −18.7279 + 32.4377i −0.706337 + 1.22341i
\(704\) 23.3137 40.3805i 0.878668 1.52190i
\(705\) 1.50000 + 2.59808i 0.0564933 + 0.0978492i
\(706\) −51.2132 −1.92743
\(707\) 0 0
\(708\) 0 0
\(709\) −8.50000 14.7224i −0.319224 0.552913i 0.661102 0.750296i \(-0.270089\pi\)
−0.980326 + 0.197383i \(0.936756\pi\)
\(710\) −6.24264 + 10.8126i −0.234282 + 0.405789i
\(711\) 21.8995 37.9310i 0.821295 1.42253i
\(712\) 11.3137 + 19.5959i 0.423999 + 0.734388i
\(713\) −8.05887 −0.301807
\(714\) 0 0
\(715\) −9.24264 −0.345655
\(716\) 0 0
\(717\) −0.621320 + 1.07616i −0.0232036 + 0.0401899i
\(718\) −8.00000 + 13.8564i −0.298557 + 0.517116i
\(719\) 8.60660 + 14.9071i 0.320972 + 0.555940i 0.980689 0.195574i \(-0.0626571\pi\)
−0.659717 + 0.751514i \(0.729324\pi\)
\(720\) 11.3137 0.421637
\(721\) 0 0
\(722\) 24.0416 0.894737
\(723\) −29.8492 51.7004i −1.11011 1.92276i
\(724\) 0 0
\(725\) −1.32843 + 2.30090i −0.0493365 + 0.0854534i
\(726\) 39.2132 + 67.9193i 1.45534 + 2.52072i
\(727\) 29.3137 1.08719 0.543593 0.839349i \(-0.317064\pi\)
0.543593 + 0.839349i \(0.317064\pi\)
\(728\) 0 0
\(729\) −23.8284 −0.882534
\(730\) −6.00000 10.3923i −0.222070 0.384636i
\(731\) −5.24264 + 9.08052i −0.193906 + 0.335855i
\(732\) 0 0
\(733\) −22.3492 38.7100i −0.825488 1.42979i −0.901546 0.432684i \(-0.857567\pi\)
0.0760576 0.997103i \(-0.475767\pi\)
\(734\) −42.2426 −1.55920
\(735\) 0 0
\(736\) 0 0
\(737\) 0.707107 + 1.22474i 0.0260466 + 0.0451141i
\(738\) 4.48528 7.76874i 0.165105 0.285971i
\(739\) 1.98528 3.43861i 0.0730298 0.126491i −0.827198 0.561911i \(-0.810067\pi\)
0.900228 + 0.435419i \(0.143400\pi\)
\(740\) 0 0
\(741\) −22.9706 −0.843845
\(742\) 0 0
\(743\) 36.7279 1.34742 0.673708 0.738997i \(-0.264700\pi\)
0.673708 + 0.738997i \(0.264700\pi\)
\(744\) 6.00000 + 10.3923i 0.219971 + 0.381000i
\(745\) −7.41421 + 12.8418i −0.271636 + 0.470487i
\(746\) −0.343146 + 0.594346i −0.0125635 + 0.0217605i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 3.41421 0.124669
\(751\) −6.25736 10.8381i −0.228334 0.395487i 0.728980 0.684535i \(-0.239995\pi\)
−0.957315 + 0.289048i \(0.906661\pi\)
\(752\) −2.48528 + 4.30463i −0.0906289 + 0.156974i
\(753\) 30.4350 52.7150i 1.10911 1.92104i
\(754\) 2.97918 + 5.16010i 0.108496 + 0.187920i
\(755\) −9.48528 −0.345205
\(756\) 0 0
\(757\) −16.4853 −0.599168 −0.299584 0.954070i \(-0.596848\pi\)
−0.299584 + 0.954070i \(0.596848\pi\)
\(758\) −1.41421 2.44949i −0.0513665 0.0889695i
\(759\) −32.2635 + 55.8819i −1.17109 + 2.02839i
\(760\) 8.48528 14.6969i 0.307794 0.533114i
\(761\) 6.36396 + 11.0227i 0.230693 + 0.399573i 0.958012 0.286727i \(-0.0925672\pi\)
−0.727319 + 0.686300i \(0.759234\pi\)
\(762\) 0.828427 0.0300107
\(763\) 0 0
\(764\) 0 0
\(765\) 7.41421 + 12.8418i 0.268061 + 0.464296i
\(766\) −8.82843 + 15.2913i −0.318984 + 0.552497i
\(767\) −4.94975 + 8.57321i −0.178725 + 0.309561i
\(768\) 0 0
\(769\) 3.17157 0.114370 0.0571849 0.998364i \(-0.481788\pi\)
0.0571849 + 0.998364i \(0.481788\pi\)
\(770\) 0 0
\(771\) −63.9411 −2.30278
\(772\) 0 0
\(773\) 18.1066 31.3616i 0.651249 1.12800i −0.331571 0.943430i \(-0.607579\pi\)
0.982820 0.184566i \(-0.0590881\pi\)
\(774\) −4.00000 + 6.92820i −0.143777 + 0.249029i
\(775\) 0.878680 + 1.52192i 0.0315631 + 0.0546689i
\(776\) 13.4558 0.483037
\(777\) 0 0
\(778\) −49.6985 −1.78178
\(779\) −6.72792 11.6531i −0.241053 0.417516i
\(780\) 0 0
\(781\) −25.7279 + 44.5621i −0.920617 + 1.59456i
\(782\) −17.0000 29.4449i −0.607919 1.05295i
\(783\) 1.10051 0.0393288
\(784\) 0 0
\(785\) −20.8284 −0.743398
\(786\) −6.41421 11.1097i −0.228787 0.396271i
\(787\) 22.8640 39.6015i 0.815012 1.41164i −0.0943070 0.995543i \(-0.530064\pi\)
0.909319 0.416099i \(-0.136603\pi\)
\(788\) 0 0