Properties

Label 731.2.m.c.87.4
Level 731
Weight 2
Character 731.87
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.m (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 87.4
Character \(\chi\) = 731.87
Dual form 731.2.m.c.689.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.56129 - 1.56129i) q^{2} +(-2.36310 + 0.978828i) q^{3} +2.87526i q^{4} +(1.21177 + 2.92548i) q^{5} +(5.21772 + 2.16125i) q^{6} +(1.72340 - 4.16065i) q^{7} +(1.36654 - 1.36654i) q^{8} +(2.50481 - 2.50481i) q^{9} +O(q^{10})\) \(q+(-1.56129 - 1.56129i) q^{2} +(-2.36310 + 0.978828i) q^{3} +2.87526i q^{4} +(1.21177 + 2.92548i) q^{5} +(5.21772 + 2.16125i) q^{6} +(1.72340 - 4.16065i) q^{7} +(1.36654 - 1.36654i) q^{8} +(2.50481 - 2.50481i) q^{9} +(2.67560 - 6.45946i) q^{10} +(2.87243 + 1.18980i) q^{11} +(-2.81439 - 6.79453i) q^{12} +1.03249i q^{13} +(-9.18672 + 3.80527i) q^{14} +(-5.72708 - 5.72708i) q^{15} +1.48338 q^{16} +(-4.07859 - 0.604236i) q^{17} -7.82149 q^{18} +(-0.211276 - 0.211276i) q^{19} +(-8.41153 + 3.48417i) q^{20} +11.5189i q^{21} +(-2.62708 - 6.34234i) q^{22} +(-3.32590 - 1.37763i) q^{23} +(-1.89167 + 4.56689i) q^{24} +(-3.55451 + 3.55451i) q^{25} +(1.61202 - 1.61202i) q^{26} +(-0.530857 + 1.28160i) q^{27} +(11.9630 + 4.95523i) q^{28} +(1.75074 + 4.22665i) q^{29} +17.8833i q^{30} +(4.62662 - 1.91641i) q^{31} +(-5.04908 - 5.04908i) q^{32} -7.95246 q^{33} +(5.42448 + 7.31126i) q^{34} +14.2603 q^{35} +(7.20200 + 7.20200i) q^{36} +(6.56065 - 2.71751i) q^{37} +0.659726i q^{38} +(-1.01063 - 2.43987i) q^{39} +(5.65374 + 2.34185i) q^{40} +(0.389323 - 0.939910i) q^{41} +(17.9844 - 17.9844i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(-3.42099 + 8.25901i) q^{44} +(10.3630 + 4.29251i) q^{45} +(3.04181 + 7.34358i) q^{46} +3.37242i q^{47} +(-3.50538 + 1.45198i) q^{48} +(-9.39119 - 9.39119i) q^{49} +11.0993 q^{50} +(10.2296 - 2.56437i) q^{51} -2.96868 q^{52} +(9.44775 + 9.44775i) q^{53} +(2.82978 - 1.17213i) q^{54} +9.84502i q^{55} +(-3.33061 - 8.04081i) q^{56} +(0.706068 + 0.292463i) q^{57} +(3.86563 - 9.33245i) q^{58} +(5.23580 - 5.23580i) q^{59} +(16.4669 - 16.4669i) q^{60} +(-2.69928 + 6.51664i) q^{61} +(-10.2156 - 4.23143i) q^{62} +(-6.10487 - 14.7384i) q^{63} +12.7994i q^{64} +(-3.02053 + 1.25114i) q^{65} +(12.4161 + 12.4161i) q^{66} -7.74847 q^{67} +(1.73734 - 11.7270i) q^{68} +9.20788 q^{69} +(-22.2645 - 22.2645i) q^{70} +(8.36432 - 3.46461i) q^{71} -6.84587i q^{72} +(-4.57810 - 11.0525i) q^{73} +(-14.4859 - 6.00026i) q^{74} +(4.92040 - 11.8789i) q^{75} +(0.607474 - 0.607474i) q^{76} +(9.90070 - 9.90070i) q^{77} +(-2.23147 + 5.38724i) q^{78} +(13.6896 + 5.67041i) q^{79} +(1.79753 + 4.33961i) q^{80} +7.07885i q^{81} +(-2.07532 + 0.859626i) q^{82} +(9.21094 + 9.21094i) q^{83} -33.1200 q^{84} +(-3.17465 - 12.6640i) q^{85} +2.20800 q^{86} +(-8.27433 - 8.27433i) q^{87} +(5.55122 - 2.29939i) q^{88} +0.648155i q^{89} +(-9.47787 - 22.8816i) q^{90} +(4.29583 + 1.77939i) q^{91} +(3.96105 - 9.56283i) q^{92} +(-9.05732 + 9.05732i) q^{93} +(5.26533 - 5.26533i) q^{94} +(0.362065 - 0.874102i) q^{95} +(16.8737 + 6.98930i) q^{96} +(3.19206 + 7.70631i) q^{97} +29.3248i q^{98} +(10.1751 - 4.21468i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} + O(q^{10}) \) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} - 8q^{10} - 4q^{11} + 12q^{12} + 12q^{14} - 12q^{15} - 144q^{16} - 12q^{17} + 64q^{18} - 28q^{19} - 8q^{20} - 12q^{22} + 16q^{23} - 16q^{24} - 20q^{25} + 16q^{26} - 8q^{27} + 20q^{28} + 12q^{31} - 4q^{32} - 104q^{33} + 20q^{34} + 32q^{35} - 96q^{36} - 12q^{37} + 8q^{39} + 216q^{40} + 24q^{41} - 4q^{42} + 24q^{44} - 28q^{45} - 48q^{46} + 28q^{48} - 80q^{50} - 20q^{51} + 56q^{52} - 36q^{53} - 12q^{54} - 8q^{56} + 72q^{57} - 32q^{58} + 48q^{59} - 40q^{60} - 76q^{61} - 44q^{62} + 36q^{65} - 68q^{66} - 48q^{67} + 32q^{68} + 216q^{69} - 196q^{70} + 4q^{71} + 20q^{73} + 88q^{74} + 80q^{75} + 72q^{76} + 28q^{77} - 120q^{78} + 68q^{79} - 68q^{80} + 28q^{82} - 36q^{83} - 152q^{84} + 28q^{85} - 24q^{86} - 56q^{87} + 20q^{88} - 112q^{90} + 96q^{91} - 28q^{92} + 24q^{93} - 36q^{94} - 108q^{95} + 272q^{96} + 8q^{97} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.56129 1.56129i −1.10400 1.10400i −0.993923 0.110077i \(-0.964890\pi\)
−0.110077 0.993923i \(-0.535110\pi\)
\(3\) −2.36310 + 0.978828i −1.36434 + 0.565126i −0.940247 0.340494i \(-0.889406\pi\)
−0.424089 + 0.905620i \(0.639406\pi\)
\(4\) 2.87526i 1.43763i
\(5\) 1.21177 + 2.92548i 0.541922 + 1.30831i 0.923365 + 0.383923i \(0.125427\pi\)
−0.381444 + 0.924392i \(0.624573\pi\)
\(6\) 5.21772 + 2.16125i 2.13013 + 0.882327i
\(7\) 1.72340 4.16065i 0.651384 1.57258i −0.159388 0.987216i \(-0.550952\pi\)
0.810771 0.585363i \(-0.199048\pi\)
\(8\) 1.36654 1.36654i 0.483146 0.483146i
\(9\) 2.50481 2.50481i 0.834937 0.834937i
\(10\) 2.67560 6.45946i 0.846098 2.04266i
\(11\) 2.87243 + 1.18980i 0.866072 + 0.358739i 0.771079 0.636739i \(-0.219717\pi\)
0.0949925 + 0.995478i \(0.469717\pi\)
\(12\) −2.81439 6.79453i −0.812444 1.96141i
\(13\) 1.03249i 0.286361i 0.989697 + 0.143180i \(0.0457329\pi\)
−0.989697 + 0.143180i \(0.954267\pi\)
\(14\) −9.18672 + 3.80527i −2.45526 + 1.01700i
\(15\) −5.72708 5.72708i −1.47873 1.47873i
\(16\) 1.48338 0.370846
\(17\) −4.07859 0.604236i −0.989203 0.146549i
\(18\) −7.82149 −1.84354
\(19\) −0.211276 0.211276i −0.0484700 0.0484700i 0.682456 0.730926i \(-0.260912\pi\)
−0.730926 + 0.682456i \(0.760912\pi\)
\(20\) −8.41153 + 3.48417i −1.88088 + 0.779084i
\(21\) 11.5189i 2.51364i
\(22\) −2.62708 6.34234i −0.560096 1.35219i
\(23\) −3.32590 1.37763i −0.693497 0.287256i 0.00795922 0.999968i \(-0.497466\pi\)
−0.701456 + 0.712712i \(0.747466\pi\)
\(24\) −1.89167 + 4.56689i −0.386135 + 0.932212i
\(25\) −3.55451 + 3.55451i −0.710902 + 0.710902i
\(26\) 1.61202 1.61202i 0.316142 0.316142i
\(27\) −0.530857 + 1.28160i −0.102163 + 0.246645i
\(28\) 11.9630 + 4.95523i 2.26079 + 0.936450i
\(29\) 1.75074 + 4.22665i 0.325104 + 0.784870i 0.998942 + 0.0459908i \(0.0146445\pi\)
−0.673838 + 0.738879i \(0.735355\pi\)
\(30\) 17.8833i 3.26503i
\(31\) 4.62662 1.91641i 0.830965 0.344197i 0.0736805 0.997282i \(-0.476526\pi\)
0.757285 + 0.653085i \(0.226526\pi\)
\(32\) −5.04908 5.04908i −0.892560 0.892560i
\(33\) −7.95246 −1.38435
\(34\) 5.42448 + 7.31126i 0.930291 + 1.25387i
\(35\) 14.2603 2.41043
\(36\) 7.20200 + 7.20200i 1.20033 + 1.20033i
\(37\) 6.56065 2.71751i 1.07856 0.446756i 0.228559 0.973530i \(-0.426599\pi\)
0.850005 + 0.526774i \(0.176599\pi\)
\(38\) 0.659726i 0.107022i
\(39\) −1.01063 2.43987i −0.161830 0.390692i
\(40\) 5.65374 + 2.34185i 0.893934 + 0.370280i
\(41\) 0.389323 0.939910i 0.0608021 0.146789i −0.890559 0.454869i \(-0.849686\pi\)
0.951361 + 0.308079i \(0.0996862\pi\)
\(42\) 17.9844 17.9844i 2.77506 2.77506i
\(43\) −0.707107 + 0.707107i −0.107833 + 0.107833i
\(44\) −3.42099 + 8.25901i −0.515734 + 1.24509i
\(45\) 10.3630 + 4.29251i 1.54483 + 0.639890i
\(46\) 3.04181 + 7.34358i 0.448490 + 1.08275i
\(47\) 3.37242i 0.491918i 0.969280 + 0.245959i \(0.0791028\pi\)
−0.969280 + 0.245959i \(0.920897\pi\)
\(48\) −3.50538 + 1.45198i −0.505958 + 0.209575i
\(49\) −9.39119 9.39119i −1.34160 1.34160i
\(50\) 11.0993 1.56967
\(51\) 10.2296 2.56437i 1.43242 0.359083i
\(52\) −2.96868 −0.411681
\(53\) 9.44775 + 9.44775i 1.29775 + 1.29775i 0.929877 + 0.367871i \(0.119913\pi\)
0.367871 + 0.929877i \(0.380087\pi\)
\(54\) 2.82978 1.17213i 0.385084 0.159507i
\(55\) 9.84502i 1.32750i
\(56\) −3.33061 8.04081i −0.445072 1.07450i
\(57\) 0.706068 + 0.292463i 0.0935210 + 0.0387377i
\(58\) 3.86563 9.33245i 0.507582 1.22541i
\(59\) 5.23580 5.23580i 0.681643 0.681643i −0.278727 0.960370i \(-0.589913\pi\)
0.960370 + 0.278727i \(0.0899126\pi\)
\(60\) 16.4669 16.4669i 2.12586 2.12586i
\(61\) −2.69928 + 6.51664i −0.345607 + 0.834370i 0.651520 + 0.758631i \(0.274132\pi\)
−0.997128 + 0.0757389i \(0.975868\pi\)
\(62\) −10.2156 4.23143i −1.29738 0.537392i
\(63\) −6.10487 14.7384i −0.769141 1.85687i
\(64\) 12.7994i 1.59993i
\(65\) −3.02053 + 1.25114i −0.374650 + 0.155185i
\(66\) 12.4161 + 12.4161i 1.52832 + 1.52832i
\(67\) −7.74847 −0.946627 −0.473313 0.880894i \(-0.656942\pi\)
−0.473313 + 0.880894i \(0.656942\pi\)
\(68\) 1.73734 11.7270i 0.210683 1.42211i
\(69\) 9.20788 1.10850
\(70\) −22.2645 22.2645i −2.66111 2.66111i
\(71\) 8.36432 3.46461i 0.992662 0.411174i 0.173561 0.984823i \(-0.444473\pi\)
0.819101 + 0.573649i \(0.194473\pi\)
\(72\) 6.84587i 0.806793i
\(73\) −4.57810 11.0525i −0.535826 1.29360i −0.927613 0.373542i \(-0.878143\pi\)
0.391787 0.920056i \(-0.371857\pi\)
\(74\) −14.4859 6.00026i −1.68395 0.697517i
\(75\) 4.92040 11.8789i 0.568159 1.37166i
\(76\) 0.607474 0.607474i 0.0696820 0.0696820i
\(77\) 9.90070 9.90070i 1.12829 1.12829i
\(78\) −2.23147 + 5.38724i −0.252664 + 0.609985i
\(79\) 13.6896 + 5.67041i 1.54020 + 0.637971i 0.981511 0.191407i \(-0.0613050\pi\)
0.558688 + 0.829378i \(0.311305\pi\)
\(80\) 1.79753 + 4.33961i 0.200969 + 0.485183i
\(81\) 7.07885i 0.786539i
\(82\) −2.07532 + 0.859626i −0.229181 + 0.0949298i
\(83\) 9.21094 + 9.21094i 1.01103 + 1.01103i 0.999938 + 0.0110933i \(0.00353117\pi\)
0.0110933 + 0.999938i \(0.496469\pi\)
\(84\) −33.1200 −3.61369
\(85\) −3.17465 12.6640i −0.344339 1.37361i
\(86\) 2.20800 0.238095
\(87\) −8.27433 8.27433i −0.887101 0.887101i
\(88\) 5.55122 2.29939i 0.591762 0.245116i
\(89\) 0.648155i 0.0687043i 0.999410 + 0.0343521i \(0.0109368\pi\)
−0.999410 + 0.0343521i \(0.989063\pi\)
\(90\) −9.47787 22.8816i −0.999056 2.41193i
\(91\) 4.29583 + 1.77939i 0.450325 + 0.186531i
\(92\) 3.96105 9.56283i 0.412968 0.996994i
\(93\) −9.05732 + 9.05732i −0.939201 + 0.939201i
\(94\) 5.26533 5.26533i 0.543077 0.543077i
\(95\) 0.362065 0.874102i 0.0371471 0.0896810i
\(96\) 16.8737 + 6.98930i 1.72216 + 0.713342i
\(97\) 3.19206 + 7.70631i 0.324105 + 0.782458i 0.999007 + 0.0445508i \(0.0141857\pi\)
−0.674903 + 0.737907i \(0.735814\pi\)
\(98\) 29.3248i 2.96225i
\(99\) 10.1751 4.21468i 1.02264 0.423591i
\(100\) −10.2202 10.2202i −1.02202 1.02202i
\(101\) −2.47902 −0.246672 −0.123336 0.992365i \(-0.539359\pi\)
−0.123336 + 0.992365i \(0.539359\pi\)
\(102\) −19.9750 11.9676i −1.97782 1.18497i
\(103\) 19.3793 1.90950 0.954749 0.297411i \(-0.0961233\pi\)
0.954749 + 0.297411i \(0.0961233\pi\)
\(104\) 1.41094 + 1.41094i 0.138354 + 0.138354i
\(105\) −33.6985 + 13.9584i −3.28863 + 1.36220i
\(106\) 29.5014i 2.86543i
\(107\) 5.91420 + 14.2781i 0.571747 + 1.38032i 0.900066 + 0.435753i \(0.143518\pi\)
−0.328319 + 0.944567i \(0.606482\pi\)
\(108\) −3.68495 1.52635i −0.354584 0.146874i
\(109\) −3.12465 + 7.54356i −0.299287 + 0.722542i 0.700672 + 0.713483i \(0.252884\pi\)
−0.999959 + 0.00905877i \(0.997116\pi\)
\(110\) 15.3710 15.3710i 1.46556 1.46556i
\(111\) −12.8435 + 12.8435i −1.21905 + 1.21905i
\(112\) 2.55646 6.17185i 0.241563 0.583185i
\(113\) −8.89575 3.68474i −0.836842 0.346631i −0.0772342 0.997013i \(-0.524609\pi\)
−0.759607 + 0.650382i \(0.774609\pi\)
\(114\) −0.645759 1.55900i −0.0604808 0.146014i
\(115\) 11.3992i 1.06298i
\(116\) −12.1527 + 5.03383i −1.12835 + 0.467380i
\(117\) 2.58619 + 2.58619i 0.239093 + 0.239093i
\(118\) −16.3492 −1.50507
\(119\) −9.54305 + 15.9283i −0.874810 + 1.46014i
\(120\) −15.6526 −1.42888
\(121\) −0.942922 0.942922i −0.0857202 0.0857202i
\(122\) 14.3887 5.96001i 1.30270 0.539594i
\(123\) 2.60218i 0.234631i
\(124\) 5.51018 + 13.3028i 0.494829 + 1.19462i
\(125\) −0.0785031 0.0325171i −0.00702153 0.00290841i
\(126\) −13.4795 + 32.5425i −1.20085 + 2.89912i
\(127\) 3.04865 3.04865i 0.270524 0.270524i −0.558787 0.829311i \(-0.688733\pi\)
0.829311 + 0.558787i \(0.188733\pi\)
\(128\) 9.88545 9.88545i 0.873759 0.873759i
\(129\) 0.978828 2.36310i 0.0861810 0.208059i
\(130\) 6.66932 + 2.76252i 0.584938 + 0.242289i
\(131\) 4.22983 + 10.2117i 0.369562 + 0.892202i 0.993822 + 0.110985i \(0.0354007\pi\)
−0.624260 + 0.781217i \(0.714599\pi\)
\(132\) 22.8654i 1.99018i
\(133\) −1.24316 + 0.514933i −0.107795 + 0.0446504i
\(134\) 12.0976 + 12.0976i 1.04508 + 1.04508i
\(135\) −4.39258 −0.378053
\(136\) −6.39928 + 4.74786i −0.548734 + 0.407125i
\(137\) 16.2543 1.38870 0.694348 0.719639i \(-0.255693\pi\)
0.694348 + 0.719639i \(0.255693\pi\)
\(138\) −14.3762 14.3762i −1.22378 1.22378i
\(139\) −13.3405 + 5.52581i −1.13153 + 0.468693i −0.868299 0.496041i \(-0.834787\pi\)
−0.263226 + 0.964734i \(0.584787\pi\)
\(140\) 41.0021i 3.46531i
\(141\) −3.30102 7.96936i −0.277996 0.671141i
\(142\) −18.4684 7.64987i −1.54983 0.641963i
\(143\) −1.22846 + 2.96576i −0.102729 + 0.248009i
\(144\) 3.71560 3.71560i 0.309633 0.309633i
\(145\) −10.2435 + 10.2435i −0.850676 + 0.850676i
\(146\) −10.1084 + 24.4039i −0.836580 + 2.01968i
\(147\) 31.3847 + 12.9999i 2.58856 + 1.07222i
\(148\) 7.81356 + 18.8636i 0.642271 + 1.55058i
\(149\) 4.48722i 0.367607i 0.982963 + 0.183804i \(0.0588411\pi\)
−0.982963 + 0.183804i \(0.941159\pi\)
\(150\) −26.2286 + 10.8643i −2.14156 + 0.887063i
\(151\) 5.35678 + 5.35678i 0.435929 + 0.435929i 0.890639 0.454710i \(-0.150257\pi\)
−0.454710 + 0.890639i \(0.650257\pi\)
\(152\) −0.577435 −0.0468362
\(153\) −11.7296 + 8.70261i −0.948282 + 0.703564i
\(154\) −30.9158 −2.49126
\(155\) 11.2128 + 11.2128i 0.900636 + 0.900636i
\(156\) 7.01528 2.90582i 0.561672 0.232652i
\(157\) 14.8088i 1.18187i −0.806719 0.590936i \(-0.798759\pi\)
0.806719 0.590936i \(-0.201241\pi\)
\(158\) −12.5203 30.2266i −0.996059 2.40470i
\(159\) −31.5737 13.0782i −2.50396 1.03717i
\(160\) 8.65265 20.8893i 0.684052 1.65145i
\(161\) −11.4637 + 11.4637i −0.903465 + 0.903465i
\(162\) 11.0521 11.0521i 0.868339 0.868339i
\(163\) −2.81500 + 6.79601i −0.220488 + 0.532304i −0.994956 0.100308i \(-0.968017\pi\)
0.774469 + 0.632612i \(0.218017\pi\)
\(164\) 2.70249 + 1.11941i 0.211029 + 0.0874111i
\(165\) −9.63658 23.2648i −0.750207 1.81116i
\(166\) 28.7619i 2.23236i
\(167\) −18.0110 + 7.46040i −1.39373 + 0.577303i −0.948117 0.317921i \(-0.897015\pi\)
−0.445616 + 0.895224i \(0.647015\pi\)
\(168\) 15.7411 + 15.7411i 1.21445 + 1.21445i
\(169\) 11.9340 0.917997
\(170\) −14.8157 + 24.7288i −1.13631 + 1.89661i
\(171\) −1.05841 −0.0809388
\(172\) −2.03312 2.03312i −0.155024 0.155024i
\(173\) 9.80522 4.06146i 0.745477 0.308787i 0.0225826 0.999745i \(-0.492811\pi\)
0.722895 + 0.690958i \(0.242811\pi\)
\(174\) 25.8373i 1.95872i
\(175\) 8.66324 + 20.9149i 0.654880 + 1.58102i
\(176\) 4.26092 + 1.76493i 0.321179 + 0.133037i
\(177\) −7.24777 + 17.4977i −0.544775 + 1.31520i
\(178\) 1.01196 1.01196i 0.0758495 0.0758495i
\(179\) 11.2228 11.2228i 0.838829 0.838829i −0.149876 0.988705i \(-0.547887\pi\)
0.988705 + 0.149876i \(0.0478874\pi\)
\(180\) −12.3421 + 29.7965i −0.919927 + 2.22090i
\(181\) 4.43323 + 1.83630i 0.329519 + 0.136491i 0.541309 0.840824i \(-0.317929\pi\)
−0.211789 + 0.977315i \(0.567929\pi\)
\(182\) −3.92889 9.48519i −0.291229 0.703089i
\(183\) 18.0416i 1.33367i
\(184\) −6.42757 + 2.66239i −0.473847 + 0.196274i
\(185\) 15.9001 + 15.9001i 1.16900 + 1.16900i
\(186\) 28.2823 2.07376
\(187\) −10.9966 6.58834i −0.804148 0.481787i
\(188\) −9.69660 −0.707197
\(189\) 4.41742 + 4.41742i 0.321320 + 0.321320i
\(190\) −1.93002 + 0.799439i −0.140018 + 0.0579974i
\(191\) 7.78341i 0.563188i −0.959534 0.281594i \(-0.909137\pi\)
0.959534 0.281594i \(-0.0908631\pi\)
\(192\) −12.5284 30.2463i −0.904161 2.18284i
\(193\) 1.75426 + 0.726638i 0.126274 + 0.0523046i 0.444926 0.895567i \(-0.353230\pi\)
−0.318652 + 0.947872i \(0.603230\pi\)
\(194\) 7.04807 17.0155i 0.506022 1.22164i
\(195\) 5.91315 5.91315i 0.423449 0.423449i
\(196\) 27.0021 27.0021i 1.92872 1.92872i
\(197\) −8.02546 + 19.3752i −0.571791 + 1.38042i 0.328238 + 0.944595i \(0.393545\pi\)
−0.900029 + 0.435830i \(0.856455\pi\)
\(198\) −22.4667 9.30601i −1.59664 0.661350i
\(199\) 0.0611925 + 0.147732i 0.00433782 + 0.0104724i 0.926034 0.377441i \(-0.123196\pi\)
−0.921696 + 0.387914i \(0.873196\pi\)
\(200\) 9.71478i 0.686939i
\(201\) 18.3104 7.58442i 1.29152 0.534964i
\(202\) 3.87048 + 3.87048i 0.272326 + 0.272326i
\(203\) 20.6029 1.44604
\(204\) 7.37324 + 29.4127i 0.516230 + 2.05930i
\(205\) 3.22146 0.224997
\(206\) −30.2567 30.2567i −2.10809 2.10809i
\(207\) −11.7815 + 4.88004i −0.818868 + 0.339186i
\(208\) 1.53158i 0.106196i
\(209\) −0.355500 0.858252i −0.0245904 0.0593666i
\(210\) 74.4062 + 30.8201i 5.13452 + 2.12679i
\(211\) 8.42619 20.3426i 0.580083 1.40044i −0.312655 0.949867i \(-0.601218\pi\)
0.892738 0.450577i \(-0.148782\pi\)
\(212\) −27.1648 + 27.1648i −1.86568 + 1.86568i
\(213\) −16.3744 + 16.3744i −1.12196 + 1.12196i
\(214\) 13.0585 31.5261i 0.892664 2.15508i
\(215\) −2.92548 1.21177i −0.199516 0.0826423i
\(216\) 1.02593 + 2.47680i 0.0698054 + 0.168525i
\(217\) 22.5525i 1.53096i
\(218\) 16.6562 6.89922i 1.12810 0.467274i
\(219\) 21.6370 + 21.6370i 1.46209 + 1.46209i
\(220\) −28.3070 −1.90846
\(221\) 0.623866 4.21110i 0.0419658 0.283269i
\(222\) 40.1049 2.69166
\(223\) 1.50932 + 1.50932i 0.101071 + 0.101071i 0.755834 0.654763i \(-0.227232\pi\)
−0.654763 + 0.755834i \(0.727232\pi\)
\(224\) −29.7091 + 12.3059i −1.98502 + 0.822222i
\(225\) 17.8068i 1.18712i
\(226\) 8.13591 + 19.6418i 0.541192 + 1.30655i
\(227\) −8.40737 3.48245i −0.558017 0.231138i 0.0858073 0.996312i \(-0.472653\pi\)
−0.643824 + 0.765174i \(0.722653\pi\)
\(228\) −0.840909 + 2.03013i −0.0556905 + 0.134449i
\(229\) −6.38078 + 6.38078i −0.421654 + 0.421654i −0.885773 0.464119i \(-0.846371\pi\)
0.464119 + 0.885773i \(0.346371\pi\)
\(230\) −17.7975 + 17.7975i −1.17353 + 1.17353i
\(231\) −13.7053 + 33.0874i −0.901740 + 2.17699i
\(232\) 8.16836 + 3.38345i 0.536279 + 0.222134i
\(233\) −11.5654 27.9213i −0.757673 1.82919i −0.509504 0.860468i \(-0.670171\pi\)
−0.248169 0.968717i \(-0.579829\pi\)
\(234\) 8.07559i 0.527918i
\(235\) −9.86595 + 4.08661i −0.643583 + 0.266581i
\(236\) 15.0543 + 15.0543i 0.979952 + 0.979952i
\(237\) −37.9002 −2.46188
\(238\) 39.7682 9.96917i 2.57779 0.646206i
\(239\) −3.13654 −0.202886 −0.101443 0.994841i \(-0.532346\pi\)
−0.101443 + 0.994841i \(0.532346\pi\)
\(240\) −8.49546 8.49546i −0.548380 0.548380i
\(241\) −15.7579 + 6.52712i −1.01505 + 0.420449i −0.827296 0.561767i \(-0.810122\pi\)
−0.187757 + 0.982215i \(0.560122\pi\)
\(242\) 2.94435i 0.189270i
\(243\) −8.52154 20.5728i −0.546657 1.31975i
\(244\) −18.7371 7.76114i −1.19952 0.496856i
\(245\) 16.0937 38.8537i 1.02819 2.48227i
\(246\) 4.06276 4.06276i 0.259032 0.259032i
\(247\) 0.218140 0.218140i 0.0138799 0.0138799i
\(248\) 3.70362 8.94133i 0.235180 0.567775i
\(249\) −30.7823 12.7504i −1.95075 0.808026i
\(250\) 0.0717977 + 0.173335i 0.00454088 + 0.0109627i
\(251\) 11.6656i 0.736326i −0.929761 0.368163i \(-0.879987\pi\)
0.929761 0.368163i \(-0.120013\pi\)
\(252\) 42.3769 17.5531i 2.66950 1.10574i
\(253\) −7.91431 7.91431i −0.497568 0.497568i
\(254\) −9.51967 −0.597317
\(255\) 19.8979 + 26.8189i 1.24606 + 1.67947i
\(256\) −5.26933 −0.329333
\(257\) 18.2096 + 18.2096i 1.13588 + 1.13588i 0.989180 + 0.146704i \(0.0468666\pi\)
0.146704 + 0.989180i \(0.453133\pi\)
\(258\) −5.21772 + 2.16125i −0.324841 + 0.134554i
\(259\) 31.9800i 1.98714i
\(260\) −3.59737 8.68481i −0.223099 0.538609i
\(261\) 14.9722 + 6.20171i 0.926759 + 0.383876i
\(262\) 9.33947 22.5475i 0.576994 1.39299i
\(263\) 0.908644 0.908644i 0.0560294 0.0560294i −0.678537 0.734566i \(-0.737386\pi\)
0.734566 + 0.678537i \(0.237386\pi\)
\(264\) −10.8674 + 10.8674i −0.668841 + 0.668841i
\(265\) −16.1907 + 39.0877i −0.994585 + 2.40114i
\(266\) 2.74489 + 1.13697i 0.168300 + 0.0697122i
\(267\) −0.634432 1.53165i −0.0388266 0.0937357i
\(268\) 22.2789i 1.36090i
\(269\) −22.5557 + 9.34288i −1.37525 + 0.569646i −0.943206 0.332209i \(-0.892206\pi\)
−0.432040 + 0.901854i \(0.642206\pi\)
\(270\) 6.85810 + 6.85810i 0.417371 + 0.417371i
\(271\) 3.42702 0.208177 0.104088 0.994568i \(-0.466808\pi\)
0.104088 + 0.994568i \(0.466808\pi\)
\(272\) −6.05011 0.896313i −0.366842 0.0543470i
\(273\) −11.8932 −0.719808
\(274\) −25.3777 25.3777i −1.53312 1.53312i
\(275\) −14.4393 + 5.98093i −0.870720 + 0.360664i
\(276\) 26.4751i 1.59361i
\(277\) −0.933522 2.25372i −0.0560899 0.135413i 0.893350 0.449361i \(-0.148348\pi\)
−0.949440 + 0.313948i \(0.898348\pi\)
\(278\) 29.4558 + 12.2010i 1.76664 + 0.731767i
\(279\) 6.78857 16.3891i 0.406421 0.981187i
\(280\) 19.4873 19.4873i 1.16459 1.16459i
\(281\) −19.4656 + 19.4656i −1.16122 + 1.16122i −0.177009 + 0.984209i \(0.556642\pi\)
−0.984209 + 0.177009i \(0.943358\pi\)
\(282\) −7.28865 + 17.5963i −0.434032 + 1.04785i
\(283\) −23.6803 9.80869i −1.40765 0.583066i −0.455921 0.890020i \(-0.650690\pi\)
−0.951724 + 0.306954i \(0.900690\pi\)
\(284\) 9.96168 + 24.0496i 0.591117 + 1.42708i
\(285\) 2.41999i 0.143348i
\(286\) 6.54839 2.71243i 0.387214 0.160389i
\(287\) −3.23968 3.23968i −0.191232 0.191232i
\(288\) −25.2940 −1.49046
\(289\) 16.2698 + 4.92886i 0.957047 + 0.289933i
\(290\) 31.9862 1.87829
\(291\) −15.0863 15.0863i −0.884375 0.884375i
\(292\) 31.7789 13.1632i 1.85972 0.770320i
\(293\) 32.4619i 1.89645i −0.317607 0.948223i \(-0.602879\pi\)
0.317607 0.948223i \(-0.397121\pi\)
\(294\) −28.7039 69.2973i −1.67404 4.04150i
\(295\) 21.6618 + 8.97263i 1.26120 + 0.522406i
\(296\) 5.25182 12.6790i 0.305256 0.736952i
\(297\) −3.04970 + 3.04970i −0.176962 + 0.176962i
\(298\) 7.00586 7.00586i 0.405838 0.405838i
\(299\) 1.42239 3.43395i 0.0822588 0.198590i
\(300\) 34.1550 + 14.1475i 1.97194 + 0.816804i
\(301\) 1.72340 + 4.16065i 0.0993351 + 0.239816i
\(302\) 16.7270i 0.962531i
\(303\) 5.85818 2.42654i 0.336544 0.139401i
\(304\) −0.313403 0.313403i −0.0179749 0.0179749i
\(305\) −22.3352 −1.27891
\(306\) 31.9006 + 4.72602i 1.82364 + 0.270169i
\(307\) −10.6281 −0.606575 −0.303288 0.952899i \(-0.598084\pi\)
−0.303288 + 0.952899i \(0.598084\pi\)
\(308\) 28.4671 + 28.4671i 1.62207 + 1.62207i
\(309\) −45.7952 + 18.9690i −2.60520 + 1.07911i
\(310\) 35.0130i 1.98860i
\(311\) 3.61462 + 8.72647i 0.204966 + 0.494833i 0.992617 0.121289i \(-0.0387029\pi\)
−0.787651 + 0.616122i \(0.788703\pi\)
\(312\) −4.71526 1.95312i −0.266949 0.110574i
\(313\) −10.6299 + 25.6630i −0.600840 + 1.45056i 0.271878 + 0.962332i \(0.412355\pi\)
−0.872718 + 0.488224i \(0.837645\pi\)
\(314\) −23.1209 + 23.1209i −1.30479 + 1.30479i
\(315\) 35.7193 35.7193i 2.01256 2.01256i
\(316\) −16.3039 + 39.3612i −0.917168 + 2.21424i
\(317\) 29.0241 + 12.0222i 1.63016 + 0.675233i 0.995250 0.0973552i \(-0.0310383\pi\)
0.634907 + 0.772588i \(0.281038\pi\)
\(318\) 28.8768 + 69.7147i 1.61933 + 3.90941i
\(319\) 14.2238i 0.796381i
\(320\) −37.4444 + 15.5100i −2.09321 + 0.867035i
\(321\) −27.9517 27.9517i −1.56011 1.56011i
\(322\) 35.7963 1.99485
\(323\) 0.734047 + 0.989368i 0.0408435 + 0.0550499i
\(324\) −20.3536 −1.13075
\(325\) −3.66999 3.66999i −0.203574 0.203574i
\(326\) 15.0056 6.21552i 0.831082 0.344246i
\(327\) 20.8847i 1.15492i
\(328\) −0.752400 1.81645i −0.0415443 0.100297i
\(329\) 14.0315 + 5.81202i 0.773580 + 0.320427i
\(330\) −21.2776 + 51.3686i −1.17129 + 2.82775i
\(331\) 8.67152 8.67152i 0.476630 0.476630i −0.427422 0.904052i \(-0.640578\pi\)
0.904052 + 0.427422i \(0.140578\pi\)
\(332\) −26.4839 + 26.4839i −1.45349 + 1.45349i
\(333\) 9.62635 23.2401i 0.527521 1.27355i
\(334\) 39.7683 + 16.4726i 2.17602 + 0.901338i
\(335\) −9.38940 22.6680i −0.512998 1.23849i
\(336\) 17.0870i 0.932173i
\(337\) 15.4110 6.38343i 0.839488 0.347727i 0.0788366 0.996888i \(-0.474879\pi\)
0.760652 + 0.649160i \(0.224879\pi\)
\(338\) −18.6324 18.6324i −1.01347 1.01347i
\(339\) 24.6283 1.33762
\(340\) 36.4124 9.12796i 1.97474 0.495033i
\(341\) 15.5698 0.843152
\(342\) 1.65249 + 1.65249i 0.0893565 + 0.0893565i
\(343\) −26.1337 + 10.8249i −1.41108 + 0.584490i
\(344\) 1.93258i 0.104198i
\(345\) 11.1579 + 26.9375i 0.600720 + 1.45027i
\(346\) −21.6499 8.96770i −1.16391 0.482106i
\(347\) 6.88925 16.6321i 0.369834 0.892859i −0.623943 0.781470i \(-0.714470\pi\)
0.993777 0.111389i \(-0.0355298\pi\)
\(348\) 23.7909 23.7909i 1.27533 1.27533i
\(349\) 3.14299 3.14299i 0.168241 0.168241i −0.617965 0.786206i \(-0.712043\pi\)
0.786206 + 0.617965i \(0.212043\pi\)
\(350\) 19.1284 46.1801i 1.02246 2.46843i
\(351\) −1.32324 0.548104i −0.0706293 0.0292556i
\(352\) −8.49575 20.5106i −0.452825 1.09322i
\(353\) 25.9443i 1.38088i −0.723392 0.690438i \(-0.757418\pi\)
0.723392 0.690438i \(-0.242582\pi\)
\(354\) 38.6348 16.0031i 2.05342 0.850554i
\(355\) 20.2713 + 20.2713i 1.07589 + 1.07589i
\(356\) −1.86362 −0.0987715
\(357\) 6.96016 46.9811i 0.368371 2.48650i
\(358\) −35.0440 −1.85213
\(359\) 9.05355 + 9.05355i 0.477828 + 0.477828i 0.904436 0.426609i \(-0.140292\pi\)
−0.426609 + 0.904436i \(0.640292\pi\)
\(360\) 20.0275 8.29564i 1.05554 0.437219i
\(361\) 18.9107i 0.995301i
\(362\) −4.05456 9.78857i −0.213103 0.514476i
\(363\) 3.15118 + 1.30526i 0.165394 + 0.0685084i
\(364\) −5.11622 + 12.3516i −0.268163 + 0.647402i
\(365\) 26.7863 26.7863i 1.40206 1.40206i
\(366\) −28.1682 + 28.1682i −1.47237 + 1.47237i
\(367\) −2.15269 + 5.19704i −0.112369 + 0.271283i −0.970053 0.242895i \(-0.921903\pi\)
0.857683 + 0.514178i \(0.171903\pi\)
\(368\) −4.93358 2.04356i −0.257181 0.106528i
\(369\) −1.37912 3.32948i −0.0717939 0.173326i
\(370\) 49.6492i 2.58114i
\(371\) 55.5910 23.0266i 2.88614 1.19548i
\(372\) −26.0422 26.0422i −1.35023 1.35023i
\(373\) 14.5728 0.754550 0.377275 0.926101i \(-0.376861\pi\)
0.377275 + 0.926101i \(0.376861\pi\)
\(374\) 6.88252 + 27.4552i 0.355887 + 1.41967i
\(375\) 0.217339 0.0112234
\(376\) 4.60856 + 4.60856i 0.237668 + 0.237668i
\(377\) −4.36397 + 1.80762i −0.224756 + 0.0930970i
\(378\) 13.7938i 0.709475i
\(379\) 0.496843 + 1.19948i 0.0255211 + 0.0616134i 0.936126 0.351664i \(-0.114384\pi\)
−0.910605 + 0.413277i \(0.864384\pi\)
\(380\) 2.51327 + 1.04103i 0.128928 + 0.0534038i
\(381\) −4.22016 + 10.1884i −0.216205 + 0.521966i
\(382\) −12.1522 + 12.1522i −0.621760 + 0.621760i
\(383\) 10.2049 10.2049i 0.521445 0.521445i −0.396563 0.918008i \(-0.629797\pi\)
0.918008 + 0.396563i \(0.129797\pi\)
\(384\) −13.6841 + 33.0365i −0.698316 + 1.68588i
\(385\) 40.9617 + 16.9669i 2.08760 + 0.864713i
\(386\) −1.60442 3.87341i −0.0816627 0.197151i
\(387\) 3.54234i 0.180067i
\(388\) −22.1577 + 9.17802i −1.12489 + 0.465943i
\(389\) −19.8049 19.8049i −1.00415 1.00415i −0.999991 0.00415819i \(-0.998676\pi\)
−0.00415819 0.999991i \(-0.501324\pi\)
\(390\) −18.4643 −0.934976
\(391\) 12.7326 + 7.62842i 0.643913 + 0.385786i
\(392\) −25.6669 −1.29638
\(393\) −19.9910 19.9910i −1.00841 1.00841i
\(394\) 42.7804 17.7202i 2.15525 0.892732i
\(395\) 46.9199i 2.36080i
\(396\) 12.1183 + 29.2562i 0.608969 + 1.47018i
\(397\) 20.9853 + 8.69241i 1.05322 + 0.436259i 0.841041 0.540971i \(-0.181943\pi\)
0.212182 + 0.977230i \(0.431943\pi\)
\(398\) 0.135113 0.326192i 0.00677261 0.0163505i
\(399\) 2.43368 2.43368i 0.121836 0.121836i
\(400\) −5.27270 + 5.27270i −0.263635 + 0.263635i
\(401\) −4.86218 + 11.7383i −0.242806 + 0.586184i −0.997559 0.0698237i \(-0.977756\pi\)
0.754754 + 0.656008i \(0.227756\pi\)
\(402\) −40.4294 16.7464i −2.01643 0.835235i
\(403\) 1.97867 + 4.77693i 0.0985645 + 0.237956i
\(404\) 7.12785i 0.354624i
\(405\) −20.7090 + 8.57796i −1.02904 + 0.426242i
\(406\) −32.1671 32.1671i −1.59643 1.59643i
\(407\) 22.0783 1.09438
\(408\) 10.4748 17.4834i 0.518580 0.865560i
\(409\) −7.15006 −0.353548 −0.176774 0.984252i \(-0.556566\pi\)
−0.176774 + 0.984252i \(0.556566\pi\)
\(410\) −5.02964 5.02964i −0.248396 0.248396i
\(411\) −38.4105 + 15.9101i −1.89465 + 0.784789i
\(412\) 55.7206i 2.74516i
\(413\) −12.7610 30.8077i −0.627927 1.51595i
\(414\) 26.0134 + 10.7751i 1.27849 + 0.529568i
\(415\) −15.7848 + 38.1080i −0.774848 + 1.87065i
\(416\) 5.21312 5.21312i 0.255594 0.255594i
\(417\) 26.1161 26.1161i 1.27891 1.27891i
\(418\) −0.784943 + 1.89502i −0.0383928 + 0.0926885i
\(419\) −3.62351 1.50091i −0.177020 0.0733241i 0.292413 0.956292i \(-0.405542\pi\)
−0.469433 + 0.882968i \(0.655542\pi\)
\(420\) −40.1340 96.8920i −1.95834 4.72784i
\(421\) 32.2725i 1.57287i 0.617676 + 0.786433i \(0.288074\pi\)
−0.617676 + 0.786433i \(0.711926\pi\)
\(422\) −44.9165 + 18.6050i −2.18650 + 0.905678i
\(423\) 8.44728 + 8.44728i 0.410721 + 0.410721i
\(424\) 25.8215 1.25400
\(425\) 16.6451 12.3496i 0.807408 0.599045i
\(426\) 51.1306 2.47728
\(427\) 22.4615 + 22.4615i 1.08699 + 1.08699i
\(428\) −41.0534 + 17.0049i −1.98439 + 0.821962i
\(429\) 8.21082i 0.396422i
\(430\) 2.67560 + 6.45946i 0.129029 + 0.311503i
\(431\) 4.98703 + 2.06569i 0.240217 + 0.0995010i 0.499544 0.866288i \(-0.333501\pi\)
−0.259327 + 0.965789i \(0.583501\pi\)
\(432\) −0.787465 + 1.90111i −0.0378869 + 0.0914671i
\(433\) −2.89931 + 2.89931i −0.139332 + 0.139332i −0.773333 0.634000i \(-0.781412\pi\)
0.634000 + 0.773333i \(0.281412\pi\)
\(434\) −35.2110 + 35.2110i −1.69018 + 1.69018i
\(435\) 14.1798 34.2330i 0.679868 1.64135i
\(436\) −21.6897 8.98418i −1.03875 0.430264i
\(437\) 0.411621 + 0.993742i 0.0196905 + 0.0475371i
\(438\) 67.5633i 3.22830i
\(439\) 20.9200 8.66533i 0.998455 0.413574i 0.177225 0.984170i \(-0.443288\pi\)
0.821230 + 0.570597i \(0.193288\pi\)
\(440\) 13.4536 + 13.4536i 0.641377 + 0.641377i
\(441\) −47.0463 −2.24030
\(442\) −7.54879 + 5.60072i −0.359059 + 0.266399i
\(443\) −4.94708 −0.235043 −0.117521 0.993070i \(-0.537495\pi\)
−0.117521 + 0.993070i \(0.537495\pi\)
\(444\) −36.9284 36.9284i −1.75255 1.75255i
\(445\) −1.89616 + 0.785417i −0.0898868 + 0.0372323i
\(446\) 4.71297i 0.223166i
\(447\) −4.39221 10.6037i −0.207745 0.501540i
\(448\) 53.2539 + 22.0585i 2.51601 + 1.04217i
\(449\) 1.68781 4.07473i 0.0796526 0.192298i −0.879036 0.476755i \(-0.841813\pi\)
0.958689 + 0.284456i \(0.0918131\pi\)
\(450\) 27.8015 27.8015i 1.31058 1.31058i
\(451\) 2.23661 2.23661i 0.105318 0.105318i
\(452\) 10.5946 25.5776i 0.498328 1.20307i
\(453\) −17.9020 7.41524i −0.841108 0.348398i
\(454\) 7.68924 + 18.5635i 0.360874 + 0.871227i
\(455\) 14.7236i 0.690252i
\(456\) 1.36454 0.565209i 0.0639003 0.0264684i
\(457\) 23.9409 + 23.9409i 1.11991 + 1.11991i 0.991754 + 0.128154i \(0.0409052\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(458\) 19.9245 0.931011
\(459\) 2.93954 4.90637i 0.137206 0.229010i
\(460\) 32.7758 1.52818
\(461\) −9.82111 9.82111i −0.457415 0.457415i 0.440391 0.897806i \(-0.354840\pi\)
−0.897806 + 0.440391i \(0.854840\pi\)
\(462\) 73.0570 30.2612i 3.39892 1.40788i
\(463\) 34.8610i 1.62013i −0.586342 0.810064i \(-0.699432\pi\)
0.586342 0.810064i \(-0.300568\pi\)
\(464\) 2.59701 + 6.26975i 0.120563 + 0.291066i
\(465\) −37.4725 15.5216i −1.73774 0.719797i
\(466\) −25.5364 + 61.6502i −1.18295 + 2.85589i
\(467\) −7.99744 + 7.99744i −0.370077 + 0.370077i −0.867505 0.497428i \(-0.834278\pi\)
0.497428 + 0.867505i \(0.334278\pi\)
\(468\) −7.43598 + 7.43598i −0.343728 + 0.343728i
\(469\) −13.3537 + 32.2387i −0.616617 + 1.48865i
\(470\) 21.7840 + 9.02323i 1.00482 + 0.416211i
\(471\) 14.4953 + 34.9947i 0.667907 + 1.61247i
\(472\) 14.3099i 0.658666i
\(473\) −2.87243 + 1.18980i −0.132075 + 0.0547071i
\(474\) 59.1733 + 59.1733i 2.71792 + 2.71792i
\(475\) 1.50196 0.0689148
\(476\) −45.7980 27.4388i −2.09915 1.25766i
\(477\) 47.3297 2.16708
\(478\) 4.89705 + 4.89705i 0.223986 + 0.223986i
\(479\) 9.27306 3.84103i 0.423697 0.175501i −0.160638 0.987013i \(-0.551355\pi\)
0.584335 + 0.811512i \(0.301355\pi\)
\(480\) 57.8330i 2.63970i
\(481\) 2.80580 + 6.77380i 0.127933 + 0.308859i
\(482\) 34.7933 + 14.4119i 1.58479 + 0.656443i
\(483\) 15.8689 38.3108i 0.722058 1.74320i
\(484\) 2.71115 2.71115i 0.123234 0.123234i
\(485\) −18.6766 + 18.6766i −0.848062 + 0.848062i
\(486\) −18.8156 + 45.4248i −0.853492 + 2.06051i
\(487\) 19.9107 + 8.24729i 0.902240 + 0.373720i 0.785081 0.619393i \(-0.212621\pi\)
0.117159 + 0.993113i \(0.462621\pi\)
\(488\) 5.21658 + 12.5939i 0.236144 + 0.570101i
\(489\) 18.8150i 0.850845i
\(490\) −85.7890 + 35.5350i −3.87555 + 1.60531i
\(491\) −15.8274 15.8274i −0.714279 0.714279i 0.253149 0.967427i \(-0.418534\pi\)
−0.967427 + 0.253149i \(0.918534\pi\)
\(492\) −7.48196 −0.337313
\(493\) −4.58665 18.2966i −0.206572 0.824039i
\(494\) −0.681160 −0.0306468
\(495\) 24.6599 + 24.6599i 1.10838 + 1.10838i
\(496\) 6.86305 2.84277i 0.308160 0.127644i
\(497\) 40.7719i 1.82887i
\(498\) 28.1530 + 67.9673i 1.26156 + 3.04569i
\(499\) −13.3268 5.52013i −0.596589 0.247115i 0.0638936 0.997957i \(-0.479648\pi\)
−0.660482 + 0.750842i \(0.729648\pi\)
\(500\) 0.0934952 0.225717i 0.00418123 0.0100944i
\(501\) 35.2593 35.2593i 1.57527 1.57527i
\(502\) −18.2134 + 18.2134i −0.812903 + 0.812903i
\(503\) −2.35434 + 5.68389i −0.104975 + 0.253432i −0.967636 0.252351i \(-0.918796\pi\)
0.862661 + 0.505783i \(0.168796\pi\)
\(504\) −28.4833 11.7982i −1.26875 0.525532i
\(505\) −3.00402 7.25234i −0.133677 0.322725i
\(506\) 24.7131i 1.09863i
\(507\) −28.2011 + 11.6813i −1.25246 + 0.518785i
\(508\) 8.76568 + 8.76568i 0.388914 + 0.388914i
\(509\) −28.7701 −1.27521 −0.637605 0.770363i \(-0.720075\pi\)
−0.637605 + 0.770363i \(0.720075\pi\)
\(510\) 10.8057 72.9386i 0.478485 3.22978i
\(511\) −53.8755 −2.38331
\(512\) −11.5439 11.5439i −0.510175 0.510175i
\(513\) 0.382929 0.158614i 0.0169067 0.00700299i
\(514\) 56.8611i 2.50803i
\(515\) 23.4833 + 56.6938i 1.03480 + 2.49823i
\(516\) 6.79453 + 2.81439i 0.299113 + 0.123897i
\(517\) −4.01251 + 9.68705i −0.176470 + 0.426036i
\(518\) −49.9300 + 49.9300i −2.19380 + 2.19380i
\(519\) −19.1952 + 19.1952i −0.842578 + 0.842578i
\(520\) −2.41794 + 5.83742i −0.106034 + 0.255988i
\(521\) −9.07837 3.76039i −0.397731 0.164745i 0.174848 0.984596i \(-0.444057\pi\)
−0.572578 + 0.819850i \(0.694057\pi\)
\(522\) −13.6934 33.0587i −0.599342 1.44694i
\(523\) 11.5287i 0.504115i 0.967712 + 0.252058i \(0.0811073\pi\)
−0.967712 + 0.252058i \(0.918893\pi\)
\(524\) −29.3614 + 12.1619i −1.28266 + 0.531295i
\(525\) −40.9442 40.9442i −1.78695 1.78695i
\(526\) −2.83732 −0.123713
\(527\) −20.0280 + 5.02068i −0.872435 + 0.218704i
\(528\) −11.7965 −0.513379
\(529\) −7.09974 7.09974i −0.308684 0.308684i
\(530\) 86.3057 35.7490i 3.74888 1.55284i
\(531\) 26.2294i 1.13826i
\(532\) −1.48057 3.57441i −0.0641908 0.154970i
\(533\) 0.970446 + 0.401972i 0.0420347 + 0.0174113i
\(534\) −1.40083 + 3.38189i −0.0606196 + 0.146349i
\(535\) −34.6037 + 34.6037i −1.49605 + 1.49605i
\(536\) −10.5886 + 10.5886i −0.457359 + 0.457359i
\(537\) −15.5354 + 37.5057i −0.670400 + 1.61849i
\(538\) 49.8030 + 20.6291i 2.14716 + 0.889383i
\(539\) −15.8019 38.1492i −0.680637 1.64320i
\(540\) 12.6298i 0.543502i
\(541\) 25.5810 10.5960i 1.09981 0.455558i 0.242396 0.970177i \(-0.422067\pi\)
0.857419 + 0.514619i \(0.172067\pi\)
\(542\) −5.35058 5.35058i −0.229827 0.229827i
\(543\) −12.2736 −0.526710
\(544\) 17.5423 + 23.6440i 0.752120 + 1.01373i
\(545\) −25.8549 −1.10750
\(546\) 18.5687 + 18.5687i 0.794668 + 0.794668i
\(547\) 7.46051 3.09024i 0.318988 0.132129i −0.217444 0.976073i \(-0.569772\pi\)
0.536432 + 0.843944i \(0.319772\pi\)
\(548\) 46.7353i 1.99644i
\(549\) 9.56177 + 23.0841i 0.408086 + 0.985207i
\(550\) 31.8819 + 13.2059i 1.35945 + 0.563102i
\(551\) 0.523101 1.26288i 0.0222849 0.0538004i
\(552\) 12.5830 12.5830i 0.535567 0.535567i
\(553\) 47.1852 47.1852i 2.00652 2.00652i
\(554\) −2.06122 + 4.97622i −0.0875727 + 0.211419i
\(555\) −53.1368 22.0100i −2.25553 0.934272i
\(556\) −15.8882 38.3574i −0.673808 1.62672i
\(557\) 46.6793i 1.97787i 0.148362 + 0.988933i \(0.452600\pi\)
−0.148362 + 0.988933i \(0.547400\pi\)
\(558\) −36.1870 + 14.9892i −1.53192 + 0.634542i
\(559\) −0.730080 0.730080i −0.0308791 0.0308791i
\(560\) 21.1535 0.893897
\(561\) 32.4348 + 4.80516i 1.36940 + 0.202874i
\(562\) 60.7829 2.56397
\(563\) −6.15039 6.15039i −0.259208 0.259208i 0.565524 0.824732i \(-0.308674\pi\)
−0.824732 + 0.565524i \(0.808674\pi\)
\(564\) 22.9140 9.49130i 0.964854 0.399656i
\(565\) 30.4894i 1.28270i
\(566\) 21.6576 + 52.2860i 0.910336 + 2.19775i
\(567\) 29.4526 + 12.1997i 1.23689 + 0.512338i
\(568\) 6.69566 16.1647i 0.280943 0.678257i
\(569\) 11.4552 11.4552i 0.480229 0.480229i −0.424976 0.905205i \(-0.639717\pi\)
0.905205 + 0.424976i \(0.139717\pi\)
\(570\) 3.77831 3.77831i 0.158256 0.158256i
\(571\) 12.2475 29.5680i 0.512541 1.23738i −0.429860 0.902896i \(-0.641437\pi\)
0.942400 0.334487i \(-0.108563\pi\)
\(572\) −8.52733 3.53214i −0.356546 0.147686i
\(573\) 7.61862 + 18.3930i 0.318272 + 0.768378i
\(574\) 10.1162i 0.422241i
\(575\) 16.7187 6.92512i 0.697219 0.288798i
\(576\) 32.0601 + 32.0601i 1.33584 + 1.33584i
\(577\) −25.8407 −1.07576 −0.537881 0.843021i \(-0.680775\pi\)
−0.537881 + 0.843021i \(0.680775\pi\)
\(578\) −17.7065 33.0973i −0.736494 1.37667i
\(579\) −4.85674 −0.201839
\(580\) −29.4528 29.4528i −1.22296 1.22296i
\(581\) 54.1976 22.4494i 2.24850 0.931358i
\(582\) 47.1083i 1.95270i
\(583\) 15.8971 + 38.3790i 0.658390 + 1.58949i
\(584\) −21.3599 8.84756i −0.883879 0.366115i
\(585\) −4.43197 + 10.6997i −0.183239 + 0.442379i
\(586\) −50.6825 + 50.6825i −2.09368 + 2.09368i
\(587\) 6.44529 6.44529i 0.266026 0.266026i −0.561471 0.827496i \(-0.689764\pi\)
0.827496 + 0.561471i \(0.189764\pi\)
\(588\) −37.3783 + 90.2392i −1.54145 + 3.72140i
\(589\) −1.38238 0.572602i −0.0569601 0.0235937i
\(590\) −19.8116 47.8293i −0.815629 1.96910i
\(591\) 53.6410i 2.20650i
\(592\) 9.73196 4.03111i 0.399981 0.165678i
\(593\) 14.9549 + 14.9549i 0.614123 + 0.614123i 0.944018 0.329895i \(-0.107013\pi\)
−0.329895 + 0.944018i \(0.607013\pi\)
\(594\) 9.52296 0.390732
\(595\) −58.1618 8.61657i −2.38440 0.353245i
\(596\) −12.9019 −0.528484
\(597\) −0.289208 0.289208i −0.0118365 0.0118365i
\(598\) −7.58216 + 3.14063i −0.310058 + 0.128430i
\(599\) 13.0569i 0.533490i 0.963767 + 0.266745i \(0.0859481\pi\)
−0.963767 + 0.266745i \(0.914052\pi\)
\(600\) −9.50909 22.9570i −0.388207 0.937215i
\(601\) −3.71887 1.54041i −0.151696 0.0628345i 0.305544 0.952178i \(-0.401162\pi\)
−0.457240 + 0.889344i \(0.651162\pi\)
\(602\) 3.80527 9.18672i 0.155091 0.374423i
\(603\) −19.4085 + 19.4085i −0.790374 + 0.790374i
\(604\) −15.4022 + 15.4022i −0.626705 + 0.626705i
\(605\) 1.61589 3.90111i 0.0656954 0.158603i
\(606\) −12.9349 5.35780i −0.525443 0.217646i
\(607\) −10.6487 25.7083i −0.432219 1.04347i −0.978570 0.205912i \(-0.933984\pi\)
0.546352 0.837556i \(-0.316016\pi\)
\(608\) 2.13350i 0.0865248i
\(609\) −48.6866 + 20.1666i −1.97288 + 0.817194i
\(610\) 34.8718 + 34.8718i 1.41192 + 1.41192i
\(611\) −3.48198 −0.140866
\(612\) −25.0223 33.7257i −1.01147 1.36328i
\(613\) 0.584613 0.0236123 0.0118061 0.999930i \(-0.496242\pi\)
0.0118061 + 0.999930i \(0.496242\pi\)
\(614\) 16.5935 + 16.5935i 0.669659 + 0.669659i
\(615\) −7.61263 + 3.15325i −0.306971 + 0.127151i
\(616\) 27.0595i 1.09026i
\(617\) −16.8921 40.7812i −0.680051 1.64179i −0.763919 0.645312i \(-0.776727\pi\)
0.0838674 0.996477i \(-0.473273\pi\)
\(618\) 101.116 + 41.8835i 4.06747 + 1.68480i
\(619\) −2.52394 + 6.09332i −0.101446 + 0.244911i −0.966451 0.256851i \(-0.917315\pi\)
0.865005 + 0.501763i \(0.167315\pi\)
\(620\) −32.2399 + 32.2399i −1.29478 + 1.29478i
\(621\) 3.53115 3.53115i 0.141700 0.141700i
\(622\) 7.98108 19.2680i 0.320012 0.772578i
\(623\) 2.69675 + 1.11703i 0.108043 + 0.0447528i
\(624\) −1.49915 3.61927i −0.0600140 0.144887i
\(625\) 24.8651i 0.994604i
\(626\) 56.6638 23.4709i 2.26474 0.938086i
\(627\) 1.68016 + 1.68016i 0.0670992 + 0.0670992i
\(628\) 42.5792 1.69910
\(629\) −28.4002 + 7.11943i −1.13239 + 0.283870i
\(630\) −111.537 −4.44372
\(631\) −8.11252 8.11252i −0.322954 0.322954i 0.526945 0.849899i \(-0.323337\pi\)
−0.849899 + 0.526945i \(0.823337\pi\)
\(632\) 26.4563 10.9585i 1.05237 0.435908i
\(633\) 56.3194i 2.23850i
\(634\) −26.5450 64.0853i −1.05424 2.54515i
\(635\) 12.6130 + 5.22449i 0.500533 + 0.207328i
\(636\) 37.6034 90.7827i 1.49107 3.59977i
\(637\) 9.69629 9.69629i 0.384181 0.384181i
\(638\) 22.2075 22.2075i 0.879204 0.879204i
\(639\) 12.2728 29.6293i 0.485506 1.17212i
\(640\) 40.8986 + 16.9408i 1.61666 + 0.669643i
\(641\) −4.86844 11.7534i −0.192292 0.464233i 0.798100 0.602525i \(-0.205839\pi\)
−0.990392 + 0.138292i \(0.955839\pi\)
\(642\) 87.2814i 3.44472i
\(643\) −32.7679 + 13.5729i −1.29224 + 0.535263i −0.919652 0.392734i \(-0.871529\pi\)
−0.372587 + 0.927997i \(0.621529\pi\)
\(644\) −32.9611 32.9611i −1.29885 1.29885i
\(645\) 8.09932 0.318910
\(646\) 0.398630 2.69075i 0.0156839 0.105866i
\(647\) −0.956215 −0.0375927 −0.0187963 0.999823i \(-0.505983\pi\)
−0.0187963 + 0.999823i \(0.505983\pi\)
\(648\) 9.67355 + 9.67355i 0.380013 + 0.380013i
\(649\) 21.2691 8.80993i 0.834883 0.345820i
\(650\) 11.4598i 0.449492i
\(651\) 22.0750 + 53.2938i 0.865188 + 2.08875i
\(652\) −19.5403 8.09386i −0.765258 0.316980i
\(653\) 0.112945 0.272673i 0.00441988 0.0106705i −0.921654 0.388012i \(-0.873162\pi\)
0.926074 + 0.377342i \(0.123162\pi\)
\(654\) −32.6071 + 32.6071i −1.27504 + 1.27504i
\(655\) −24.7486 + 24.7486i −0.967007 + 0.967007i
\(656\) 0.577516 1.39425i 0.0225482 0.0544362i
\(657\) −39.1517 16.2172i −1.52745 0.632692i
\(658\) −12.8329 30.9815i −0.500280 1.20778i
\(659\) 41.0073i 1.59742i −0.601719 0.798708i \(-0.705517\pi\)
0.601719 0.798708i \(-0.294483\pi\)
\(660\) 66.8923 27.7077i 2.60378 1.07852i
\(661\) 4.32848 + 4.32848i 0.168358 + 0.168358i 0.786257 0.617899i \(-0.212016\pi\)
−0.617899 + 0.786257i \(0.712016\pi\)
\(662\) −27.0775 −1.05240
\(663\) 2.64768 + 10.5619i 0.102827 + 0.410190i
\(664\) 25.1743 0.976952
\(665\) −3.01285 3.01285i −0.116833 0.116833i
\(666\) −51.3140 + 21.2550i −1.98838 + 0.823614i
\(667\) 16.4693i 0.637693i
\(668\) −21.4506 51.7864i −0.829949 2.00367i
\(669\) −5.04403 2.08931i −0.195013 0.0807772i
\(670\) −20.7318 + 50.0510i −0.800939 + 1.93364i
\(671\) −15.5070 + 15.5070i −0.598641 + 0.598641i
\(672\) 58.1601 58.1601i 2.24357 2.24357i
\(673\) −7.70629 + 18.6046i −0.297055 + 0.717155i 0.702927 + 0.711262i \(0.251876\pi\)
−0.999983 + 0.00589354i \(0.998124\pi\)
\(674\) −34.0274 14.0946i −1.31069 0.542904i
\(675\) −2.66853 6.44240i −0.102712 0.247968i
\(676\) 34.3133i 1.31974i
\(677\) −32.5693 + 13.4906i −1.25174 + 0.518487i −0.907364 0.420345i \(-0.861909\pi\)
−0.344374 + 0.938832i \(0.611909\pi\)
\(678\) −38.4519 38.4519i −1.47674 1.47674i
\(679\) 37.5645 1.44159
\(680\) −21.6442 12.9677i −0.830019 0.497287i
\(681\) 23.2762 0.891944
\(682\) −24.3090 24.3090i −0.930840 0.930840i
\(683\) −26.6272 + 11.0293i −1.01886 + 0.422026i −0.828680 0.559723i \(-0.810908\pi\)
−0.190181 + 0.981749i \(0.560908\pi\)
\(684\) 3.04322i 0.116360i
\(685\) 19.6965 + 47.5516i 0.752565 + 1.81685i
\(686\) 57.7031 + 23.9014i 2.20311 + 0.912560i
\(687\) 8.83273 21.3241i 0.336990 0.813565i
\(688\) −1.04891 + 1.04891i −0.0399893 + 0.0399893i
\(689\) −9.75469 + 9.75469i −0.371624 + 0.371624i
\(690\) 24.6366 59.4780i 0.937899 2.26429i
\(691\) 10.6352 + 4.40526i 0.404584 + 0.167584i 0.575689 0.817669i \(-0.304734\pi\)
−0.171105 + 0.985253i \(0.554734\pi\)
\(692\) 11.6778 + 28.1926i 0.443922 + 1.07172i
\(693\) 49.5988i 1.88410i
\(694\) −36.7237 + 15.2115i −1.39401 + 0.577419i
\(695\) −32.3313 32.3313i −1.22640 1.22640i
\(696\) −22.6145 −0.857199
\(697\) −2.15582 + 3.59826i −0.0816574 + 0.136294i
\(698\) −9.81426 −0.371475
\(699\) 54.6603 + 54.6603i 2.06744 + 2.06744i
\(700\) −60.1359 + 24.9091i −2.27292 + 0.941476i
\(701\) 39.1601i 1.47905i −0.673126 0.739527i \(-0.735049\pi\)
0.673126 0.739527i \(-0.264951\pi\)
\(702\) 1.21021 + 2.92171i 0.0456766 + 0.110273i
\(703\) −1.96025 0.811963i −0.0739323 0.0306238i
\(704\) −15.2288 + 36.7655i −0.573955 + 1.38565i
\(705\) 19.3141 19.3141i 0.727412 0.727412i
\(706\) −40.5066 + 40.5066i −1.52449 + 1.52449i
\(707\) −4.27235 + 10.3144i −0.160678 + 0.387912i
\(708\) −50.3104 20.8392i −1.89078 0.783187i
\(709\) 2.57992 + 6.22847i 0.0968908 + 0.233915i 0.964892 0.262647i \(-0.0845955\pi\)
−0.868001 + 0.496562i \(0.834595\pi\)
\(710\) 63.2989i 2.37557i
\(711\) 48.4932 20.0865i 1.81864 0.753304i
\(712\) 0.885731 + 0.885731i 0.0331942 + 0.0331942i
\(713\) −18.0278 −0.675145
\(714\) −84.2180 + 62.4843i −3.15178 + 2.33842i
\(715\) −10.1649 −0.380145
\(716\) 32.2684 + 32.2684i 1.20593 + 1.20593i
\(717\) 7.41195 3.07013i 0.276804 0.114656i
\(718\) 28.2705i 1.05504i
\(719\) 1.07944 + 2.60601i 0.0402565 + 0.0971877i 0.942729 0.333560i \(-0.108250\pi\)
−0.902472 + 0.430748i \(0.858250\pi\)
\(720\) 15.3724 + 6.36745i 0.572895 + 0.237301i
\(721\) 33.3983 80.6305i 1.24382 3.00284i
\(722\) −29.5252 + 29.5252i −1.09881 + 1.09881i
\(723\) 30.8484 30.8484i 1.14727 1.14727i
\(724\) −5.27986 + 12.7467i −0.196224 + 0.473728i
\(725\) −21.2467 8.80067i −0.789082 0.326849i
\(726\) −2.88201 6.95780i −0.106962 0.258228i
\(727\) 19.7635i 0.732988i −0.930420 0.366494i \(-0.880558\pi\)
0.930420 0.366494i \(-0.119442\pi\)
\(728\) 8.30205 3.43882i 0.307694 0.127451i
\(729\) 25.2580 + 25.2580i 0.935481 + 0.935481i
\(730\) −83.6424 −3.09574
\(731\) 3.31126 2.45674i 0.122471 0.0908658i
\(732\) 51.8743 1.91733
\(733\) −20.0771 20.0771i −0.741566 0.741566i 0.231313 0.972879i \(-0.425698\pi\)
−0.972879 + 0.231313i \(0.925698\pi\)
\(734\) 11.4751 4.75313i 0.423553 0.175441i
\(735\) 107.568i 3.96771i
\(736\) 9.83694 + 23.7485i 0.362595 + 0.875381i
\(737\) −22.2570 9.21915i −0.819847 0.339592i
\(738\) −3.04509 + 7.35149i −0.112091 + 0.270612i
\(739\) 21.3421 21.3421i 0.785080 0.785080i −0.195603 0.980683i \(-0.562666\pi\)
0.980683 + 0.195603i \(0.0626664\pi\)
\(740\) −45.7169 + 45.7169i −1.68058 + 1.68058i
\(741\) −0.301965 + 0.729007i −0.0110930 + 0.0267808i
\(742\) −122.745 50.8427i −4.50611 1.86649i
\(743\) 8.65078 + 20.8848i 0.317366 + 0.766190i 0.999392 + 0.0348620i \(0.0110992\pi\)
−0.682026 + 0.731328i \(0.738901\pi\)
\(744\) 24.7544i 0.907542i
\(745\) −13.1273 + 5.43749i −0.480946 + 0.199214i
\(746\) −22.7523 22.7523i −0.833023 0.833023i
\(747\) 46.1433 1.68830
\(748\) 18.9432 31.6180i 0.692633 1.15607i
\(749\) 69.5989 2.54309
\(750\) −0.339330 0.339330i −0.0123906 0.0123906i
\(751\) 9.28064 3.84417i 0.338656 0.140276i −0.206873 0.978368i \(-0.566329\pi\)
0.545529 + 0.838092i \(0.316329\pi\)
\(752\) 5.00259i 0.182426i
\(753\) 11.4186 + 27.5669i 0.416117 + 1.00460i
\(754\) 9.63565 + 3.99122i 0.350910 + 0.145352i
\(755\) −9.17996 + 22.1624i −0.334093 + 0.806572i
\(756\) −12.7013 + 12.7013i −0.461941 + 0.461941i
\(757\) −26.6178 + 26.6178i −0.967441 + 0.967441i −0.999486 0.0320455i \(-0.989798\pi\)
0.0320455 + 0.999486i \(0.489798\pi\)
\(758\) 1.09703 2.64846i 0.0398459 0.0961964i
\(759\) 26.4490 + 10.9556i 0.960039 + 0.397661i
\(760\) −0.699721 1.68928i −0.0253815 0.0612765i
\(761\) 15.6442i 0.567104i 0.958957 +