Properties

Label 731.2.e.a.307.2
Level 731
Weight 2
Character 731.307
Analytic conductor 5.837
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 307.2
Character \(\chi\) = 731.307
Dual form 731.2.e.a.681.2

$q$-expansion

\(f(q)\) \(=\) \(q-2.66184 q^{2} +(-1.22526 + 2.12222i) q^{3} +5.08540 q^{4} +(-0.351592 + 0.608975i) q^{5} +(3.26146 - 5.64901i) q^{6} +(-1.71463 - 2.96983i) q^{7} -8.21285 q^{8} +(-1.50254 - 2.60247i) q^{9} +O(q^{10})\) \(q-2.66184 q^{2} +(-1.22526 + 2.12222i) q^{3} +5.08540 q^{4} +(-0.351592 + 0.608975i) q^{5} +(3.26146 - 5.64901i) q^{6} +(-1.71463 - 2.96983i) q^{7} -8.21285 q^{8} +(-1.50254 - 2.60247i) q^{9} +(0.935881 - 1.62099i) q^{10} -2.92598 q^{11} +(-6.23095 + 10.7923i) q^{12} +(-0.158863 - 0.275158i) q^{13} +(4.56408 + 7.90521i) q^{14} +(-0.861584 - 1.49231i) q^{15} +11.6905 q^{16} +(0.500000 + 0.866025i) q^{17} +(3.99952 + 6.92737i) q^{18} +(1.88935 - 3.27246i) q^{19} +(-1.78798 + 3.09688i) q^{20} +8.40349 q^{21} +7.78849 q^{22} +(0.112918 - 0.195579i) q^{23} +(10.0629 - 17.4295i) q^{24} +(2.25277 + 3.90191i) q^{25} +(0.422867 + 0.732428i) q^{26} +0.0124367 q^{27} +(-8.71959 - 15.1028i) q^{28} +(-1.31084 - 2.27043i) q^{29} +(2.29340 + 3.97229i) q^{30} +(2.45321 - 4.24908i) q^{31} -14.6926 q^{32} +(3.58509 - 6.20956i) q^{33} +(-1.33092 - 2.30522i) q^{34} +2.41140 q^{35} +(-7.64101 - 13.2346i) q^{36} +(-3.33013 + 5.76795i) q^{37} +(-5.02916 + 8.71077i) q^{38} +0.778594 q^{39} +(2.88757 - 5.00142i) q^{40} +8.73268 q^{41} -22.3688 q^{42} +(4.71201 - 4.56036i) q^{43} -14.8798 q^{44} +2.11312 q^{45} +(-0.300569 + 0.520601i) q^{46} +0.129653 q^{47} +(-14.3239 + 24.8098i) q^{48} +(-2.37992 + 4.12214i) q^{49} +(-5.99651 - 10.3863i) q^{50} -2.45053 q^{51} +(-0.807880 - 1.39929i) q^{52} +(-5.43802 + 9.41893i) q^{53} -0.0331044 q^{54} +(1.02875 - 1.78185i) q^{55} +(14.0820 + 24.3908i) q^{56} +(4.62991 + 8.01924i) q^{57} +(3.48924 + 6.04353i) q^{58} +8.37738 q^{59} +(-4.38150 - 7.58898i) q^{60} +(-0.201600 - 0.349182i) q^{61} +(-6.53006 + 11.3104i) q^{62} +(-5.15259 + 8.92456i) q^{63} +15.7283 q^{64} +0.223419 q^{65} +(-9.54295 + 16.5289i) q^{66} +(5.79001 - 10.0286i) q^{67} +(2.54270 + 4.40409i) q^{68} +(0.276708 + 0.479272i) q^{69} -6.41876 q^{70} +(1.66521 + 2.88422i) q^{71} +(12.3401 + 21.3737i) q^{72} +(2.18343 + 3.78181i) q^{73} +(8.86428 - 15.3534i) q^{74} -11.0409 q^{75} +(9.60813 - 16.6418i) q^{76} +(5.01698 + 8.68966i) q^{77} -2.07249 q^{78} +(8.40824 + 14.5635i) q^{79} +(-4.11028 + 7.11922i) q^{80} +(4.49237 - 7.78102i) q^{81} -23.2450 q^{82} +(-0.983722 + 1.70386i) q^{83} +42.7351 q^{84} -0.703183 q^{85} +(-12.5426 + 12.1390i) q^{86} +6.42447 q^{87} +24.0306 q^{88} +(-4.27897 + 7.41139i) q^{89} -5.62479 q^{90} +(-0.544782 + 0.943589i) q^{91} +(0.574232 - 0.994600i) q^{92} +(6.01165 + 10.4125i) q^{93} -0.345116 q^{94} +(1.32856 + 2.30114i) q^{95} +(18.0023 - 31.1808i) q^{96} -18.3370 q^{97} +(6.33497 - 10.9725i) q^{98} +(4.39639 + 7.61478i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + O(q^{10}) \) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + 4q^{10} + 16q^{11} + 12q^{12} + 2q^{13} - 11q^{14} + 7q^{15} + 30q^{16} + 29q^{17} + 8q^{18} + 8q^{19} - 33q^{20} - 26q^{21} - 22q^{22} - 5q^{23} + 12q^{24} - 36q^{25} - 12q^{27} + 15q^{28} + 2q^{29} + 11q^{30} + 3q^{31} - 40q^{32} + 17q^{33} - 3q^{34} + 38q^{35} - 7q^{36} + 2q^{37} + q^{38} - 54q^{39} + 5q^{40} + 14q^{41} - 112q^{42} + 31q^{43} - 24q^{44} - 46q^{45} - 13q^{46} - 28q^{47} - 28q^{49} - 13q^{50} + 6q^{51} + 85q^{52} - 10q^{53} + 34q^{54} + 36q^{55} - 54q^{56} - 23q^{57} + 3q^{58} + 12q^{59} + 2q^{60} - q^{61} - q^{62} - 14q^{63} + 28q^{64} + 80q^{65} - 74q^{66} + 11q^{67} + 27q^{68} - 11q^{69} + 2q^{70} + 16q^{71} + 21q^{72} + 14q^{73} + 21q^{74} - 54q^{75} + 44q^{76} + 25q^{77} + 88q^{78} - 4q^{79} - 112q^{80} + 11q^{81} - 176q^{82} - 3q^{83} + 100q^{84} - 2q^{85} + 44q^{86} + 8q^{87} - 106q^{88} + 82q^{89} + 54q^{90} - 15q^{91} + 42q^{92} + 88q^{94} + 29q^{95} + 20q^{96} + 20q^{97} + 44q^{98} - 54q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66184 −1.88221 −0.941103 0.338120i \(-0.890209\pi\)
−0.941103 + 0.338120i \(0.890209\pi\)
\(3\) −1.22526 + 2.12222i −0.707406 + 1.22526i 0.258411 + 0.966035i \(0.416801\pi\)
−0.965816 + 0.259228i \(0.916532\pi\)
\(4\) 5.08540 2.54270
\(5\) −0.351592 + 0.608975i −0.157237 + 0.272342i −0.933871 0.357610i \(-0.883592\pi\)
0.776635 + 0.629951i \(0.216925\pi\)
\(6\) 3.26146 5.64901i 1.33148 2.30620i
\(7\) −1.71463 2.96983i −0.648070 1.12249i −0.983583 0.180454i \(-0.942243\pi\)
0.335514 0.942035i \(-0.391090\pi\)
\(8\) −8.21285 −2.90368
\(9\) −1.50254 2.60247i −0.500846 0.867490i
\(10\) 0.935881 1.62099i 0.295952 0.512603i
\(11\) −2.92598 −0.882216 −0.441108 0.897454i \(-0.645414\pi\)
−0.441108 + 0.897454i \(0.645414\pi\)
\(12\) −6.23095 + 10.7923i −1.79872 + 3.11548i
\(13\) −0.158863 0.275158i −0.0440606 0.0763151i 0.843154 0.537672i \(-0.180696\pi\)
−0.887215 + 0.461357i \(0.847363\pi\)
\(14\) 4.56408 + 7.90521i 1.21980 + 2.11276i
\(15\) −0.861584 1.49231i −0.222460 0.385312i
\(16\) 11.6905 2.92263
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) 3.99952 + 6.92737i 0.942695 + 1.63280i
\(19\) 1.88935 3.27246i 0.433448 0.750753i −0.563720 0.825966i \(-0.690630\pi\)
0.997168 + 0.0752127i \(0.0239636\pi\)
\(20\) −1.78798 + 3.09688i −0.399806 + 0.692484i
\(21\) 8.40349 1.83379
\(22\) 7.78849 1.66051
\(23\) 0.112918 0.195579i 0.0235450 0.0407811i −0.854013 0.520252i \(-0.825838\pi\)
0.877558 + 0.479471i \(0.159171\pi\)
\(24\) 10.0629 17.4295i 2.05408 3.55777i
\(25\) 2.25277 + 3.90191i 0.450553 + 0.780381i
\(26\) 0.422867 + 0.732428i 0.0829311 + 0.143641i
\(27\) 0.0124367 0.00239344
\(28\) −8.71959 15.1028i −1.64785 2.85415i
\(29\) −1.31084 2.27043i −0.243416 0.421609i 0.718269 0.695765i \(-0.244935\pi\)
−0.961685 + 0.274157i \(0.911601\pi\)
\(30\) 2.29340 + 3.97229i 0.418716 + 0.725237i
\(31\) 2.45321 4.24908i 0.440610 0.763158i −0.557125 0.830428i \(-0.688096\pi\)
0.997735 + 0.0672703i \(0.0214290\pi\)
\(32\) −14.6926 −2.59730
\(33\) 3.58509 6.20956i 0.624085 1.08095i
\(34\) −1.33092 2.30522i −0.228251 0.395342i
\(35\) 2.41140 0.407601
\(36\) −7.64101 13.2346i −1.27350 2.20577i
\(37\) −3.33013 + 5.76795i −0.547470 + 0.948246i 0.450977 + 0.892536i \(0.351076\pi\)
−0.998447 + 0.0557103i \(0.982258\pi\)
\(38\) −5.02916 + 8.71077i −0.815838 + 1.41307i
\(39\) 0.778594 0.124675
\(40\) 2.88757 5.00142i 0.456565 0.790794i
\(41\) 8.73268 1.36382 0.681908 0.731438i \(-0.261150\pi\)
0.681908 + 0.731438i \(0.261150\pi\)
\(42\) −22.3688 −3.45158
\(43\) 4.71201 4.56036i 0.718576 0.695449i
\(44\) −14.8798 −2.24321
\(45\) 2.11312 0.315005
\(46\) −0.300569 + 0.520601i −0.0443165 + 0.0767585i
\(47\) 0.129653 0.0189119 0.00945594 0.999955i \(-0.496990\pi\)
0.00945594 + 0.999955i \(0.496990\pi\)
\(48\) −14.3239 + 24.8098i −2.06748 + 3.58099i
\(49\) −2.37992 + 4.12214i −0.339988 + 0.588877i
\(50\) −5.99651 10.3863i −0.848034 1.46884i
\(51\) −2.45053 −0.343142
\(52\) −0.807880 1.39929i −0.112033 0.194047i
\(53\) −5.43802 + 9.41893i −0.746970 + 1.29379i 0.202299 + 0.979324i \(0.435159\pi\)
−0.949269 + 0.314466i \(0.898175\pi\)
\(54\) −0.0331044 −0.00450494
\(55\) 1.02875 1.78185i 0.138717 0.240264i
\(56\) 14.0820 + 24.3908i 1.88179 + 3.25935i
\(57\) 4.62991 + 8.01924i 0.613247 + 1.06217i
\(58\) 3.48924 + 6.04353i 0.458159 + 0.793555i
\(59\) 8.37738 1.09064 0.545321 0.838227i \(-0.316408\pi\)
0.545321 + 0.838227i \(0.316408\pi\)
\(60\) −4.38150 7.58898i −0.565650 0.979734i
\(61\) −0.201600 0.349182i −0.0258123 0.0447082i 0.852831 0.522187i \(-0.174884\pi\)
−0.878643 + 0.477479i \(0.841551\pi\)
\(62\) −6.53006 + 11.3104i −0.829318 + 1.43642i
\(63\) −5.15259 + 8.92456i −0.649166 + 1.12439i
\(64\) 15.7283 1.96604
\(65\) 0.223419 0.0277117
\(66\) −9.54295 + 16.5289i −1.17466 + 2.03456i
\(67\) 5.79001 10.0286i 0.707362 1.22519i −0.258470 0.966019i \(-0.583218\pi\)
0.965832 0.259168i \(-0.0834483\pi\)
\(68\) 2.54270 + 4.40409i 0.308348 + 0.534074i
\(69\) 0.276708 + 0.479272i 0.0333117 + 0.0576976i
\(70\) −6.41876 −0.767189
\(71\) 1.66521 + 2.88422i 0.197624 + 0.342294i 0.947757 0.318992i \(-0.103344\pi\)
−0.750134 + 0.661286i \(0.770011\pi\)
\(72\) 12.3401 + 21.3737i 1.45430 + 2.51892i
\(73\) 2.18343 + 3.78181i 0.255551 + 0.442627i 0.965045 0.262084i \(-0.0844099\pi\)
−0.709494 + 0.704711i \(0.751077\pi\)
\(74\) 8.86428 15.3534i 1.03045 1.78479i
\(75\) −11.0409 −1.27490
\(76\) 9.60813 16.6418i 1.10213 1.90894i
\(77\) 5.01698 + 8.68966i 0.571737 + 0.990278i
\(78\) −2.07249 −0.234664
\(79\) 8.40824 + 14.5635i 0.946000 + 1.63852i 0.753736 + 0.657178i \(0.228250\pi\)
0.192265 + 0.981343i \(0.438417\pi\)
\(80\) −4.11028 + 7.11922i −0.459544 + 0.795953i
\(81\) 4.49237 7.78102i 0.499153 0.864558i
\(82\) −23.2450 −2.56698
\(83\) −0.983722 + 1.70386i −0.107977 + 0.187023i −0.914951 0.403565i \(-0.867771\pi\)
0.806973 + 0.590588i \(0.201104\pi\)
\(84\) 42.7351 4.66279
\(85\) −0.703183 −0.0762709
\(86\) −12.5426 + 12.1390i −1.35251 + 1.30898i
\(87\) 6.42447 0.688776
\(88\) 24.0306 2.56167
\(89\) −4.27897 + 7.41139i −0.453570 + 0.785605i −0.998605 0.0528077i \(-0.983183\pi\)
0.545035 + 0.838413i \(0.316516\pi\)
\(90\) −5.62479 −0.592905
\(91\) −0.544782 + 0.943589i −0.0571086 + 0.0989150i
\(92\) 0.574232 0.994600i 0.0598679 0.103694i
\(93\) 6.01165 + 10.4125i 0.623380 + 1.07972i
\(94\) −0.345116 −0.0355960
\(95\) 1.32856 + 2.30114i 0.136308 + 0.236092i
\(96\) 18.0023 31.1808i 1.83735 3.18238i
\(97\) −18.3370 −1.86184 −0.930922 0.365218i \(-0.880994\pi\)
−0.930922 + 0.365218i \(0.880994\pi\)
\(98\) 6.33497 10.9725i 0.639928 1.10839i
\(99\) 4.39639 + 7.61478i 0.441854 + 0.765314i
\(100\) 11.4562 + 19.8428i 1.14562 + 1.98428i
\(101\) 6.97043 + 12.0731i 0.693583 + 1.20132i 0.970656 + 0.240472i \(0.0773024\pi\)
−0.277073 + 0.960849i \(0.589364\pi\)
\(102\) 6.52291 0.645864
\(103\) 2.77074 + 4.79906i 0.273009 + 0.472865i 0.969631 0.244573i \(-0.0786478\pi\)
−0.696622 + 0.717438i \(0.745314\pi\)
\(104\) 1.30472 + 2.25983i 0.127938 + 0.221595i
\(105\) −2.95460 + 5.11751i −0.288339 + 0.499418i
\(106\) 14.4752 25.0717i 1.40595 2.43518i
\(107\) −3.70336 −0.358017 −0.179009 0.983847i \(-0.557289\pi\)
−0.179009 + 0.983847i \(0.557289\pi\)
\(108\) 0.0632454 0.00608579
\(109\) −0.186327 + 0.322727i −0.0178469 + 0.0309117i −0.874811 0.484465i \(-0.839014\pi\)
0.856964 + 0.515376i \(0.172348\pi\)
\(110\) −2.73837 + 4.74300i −0.261093 + 0.452227i
\(111\) −8.16057 14.1345i −0.774567 1.34159i
\(112\) −20.0449 34.7188i −1.89407 3.28062i
\(113\) 15.6535 1.47255 0.736277 0.676681i \(-0.236582\pi\)
0.736277 + 0.676681i \(0.236582\pi\)
\(114\) −12.3241 21.3460i −1.15426 1.99923i
\(115\) 0.0794019 + 0.137528i 0.00740427 + 0.0128246i
\(116\) −6.66612 11.5461i −0.618934 1.07203i
\(117\) −0.477394 + 0.826871i −0.0441351 + 0.0764442i
\(118\) −22.2993 −2.05281
\(119\) 1.71463 2.96983i 0.157180 0.272244i
\(120\) 7.07606 + 12.2561i 0.645953 + 1.11882i
\(121\) −2.43864 −0.221695
\(122\) 0.536628 + 0.929467i 0.0485840 + 0.0841500i
\(123\) −10.6998 + 18.5326i −0.964771 + 1.67103i
\(124\) 12.4756 21.6083i 1.12034 1.94048i
\(125\) −6.68413 −0.597847
\(126\) 13.7154 23.7558i 1.22186 2.11633i
\(127\) 17.4681 1.55004 0.775019 0.631937i \(-0.217740\pi\)
0.775019 + 0.631937i \(0.217740\pi\)
\(128\) −12.4811 −1.10318
\(129\) 3.90463 + 15.5876i 0.343783 + 1.37241i
\(130\) −0.594706 −0.0521592
\(131\) −11.1527 −0.974417 −0.487208 0.873286i \(-0.661985\pi\)
−0.487208 + 0.873286i \(0.661985\pi\)
\(132\) 18.2316 31.5781i 1.58686 2.74852i
\(133\) −12.9582 −1.12362
\(134\) −15.4121 + 26.6945i −1.33140 + 2.30606i
\(135\) −0.00437262 + 0.00757361i −0.000376336 + 0.000651832i
\(136\) −4.10643 7.11254i −0.352123 0.609895i
\(137\) −18.8214 −1.60802 −0.804012 0.594614i \(-0.797305\pi\)
−0.804012 + 0.594614i \(0.797305\pi\)
\(138\) −0.736553 1.27575i −0.0626995 0.108599i
\(139\) −6.55596 + 11.3553i −0.556069 + 0.963140i 0.441750 + 0.897138i \(0.354358\pi\)
−0.997819 + 0.0660021i \(0.978976\pi\)
\(140\) 12.2629 1.03641
\(141\) −0.158859 + 0.275152i −0.0133784 + 0.0231720i
\(142\) −4.43252 7.67735i −0.371969 0.644269i
\(143\) 0.464829 + 0.805107i 0.0388709 + 0.0673264i
\(144\) −17.5654 30.4242i −1.46379 2.53535i
\(145\) 1.84352 0.153096
\(146\) −5.81194 10.0666i −0.480999 0.833115i
\(147\) −5.83205 10.1014i −0.481019 0.833150i
\(148\) −16.9350 + 29.3324i −1.39205 + 2.41111i
\(149\) 9.32239 16.1469i 0.763720 1.32280i −0.177200 0.984175i \(-0.556704\pi\)
0.940921 0.338627i \(-0.109963\pi\)
\(150\) 29.3892 2.39962
\(151\) 5.61810 0.457195 0.228597 0.973521i \(-0.426586\pi\)
0.228597 + 0.973521i \(0.426586\pi\)
\(152\) −15.5170 + 26.8762i −1.25859 + 2.17995i
\(153\) 1.50254 2.60247i 0.121473 0.210397i
\(154\) −13.3544 23.1305i −1.07613 1.86391i
\(155\) 1.72506 + 2.98789i 0.138560 + 0.239993i
\(156\) 3.95946 0.317011
\(157\) 2.23349 + 3.86853i 0.178252 + 0.308742i 0.941282 0.337621i \(-0.109622\pi\)
−0.763030 + 0.646363i \(0.776289\pi\)
\(158\) −22.3814 38.7657i −1.78057 3.08403i
\(159\) −13.3260 23.0813i −1.05682 1.83047i
\(160\) 5.16579 8.94741i 0.408391 0.707354i
\(161\) −0.774450 −0.0610352
\(162\) −11.9580 + 20.7118i −0.939508 + 1.62728i
\(163\) 6.87124 + 11.9013i 0.538197 + 0.932184i 0.999001 + 0.0446826i \(0.0142277\pi\)
−0.460804 + 0.887502i \(0.652439\pi\)
\(164\) 44.4092 3.46778
\(165\) 2.52098 + 4.36646i 0.196258 + 0.339929i
\(166\) 2.61851 4.53540i 0.203236 0.352015i
\(167\) 10.5790 18.3234i 0.818629 1.41791i −0.0880631 0.996115i \(-0.528068\pi\)
0.906692 0.421793i \(-0.138599\pi\)
\(168\) −69.0166 −5.32475
\(169\) 6.44953 11.1709i 0.496117 0.859300i
\(170\) 1.87176 0.143558
\(171\) −11.3553 −0.868362
\(172\) 23.9625 23.1913i 1.82712 1.76832i
\(173\) −3.09221 −0.235096 −0.117548 0.993067i \(-0.537503\pi\)
−0.117548 + 0.993067i \(0.537503\pi\)
\(174\) −17.1009 −1.29642
\(175\) 7.72533 13.3807i 0.583980 1.01148i
\(176\) −34.2062 −2.57839
\(177\) −10.2645 + 17.7786i −0.771526 + 1.33632i
\(178\) 11.3899 19.7279i 0.853711 1.47867i
\(179\) 8.00272 + 13.8611i 0.598152 + 1.03603i 0.993094 + 0.117323i \(0.0374313\pi\)
−0.394942 + 0.918706i \(0.629235\pi\)
\(180\) 10.7461 0.800964
\(181\) −3.95342 6.84752i −0.293855 0.508972i 0.680863 0.732411i \(-0.261605\pi\)
−0.974718 + 0.223439i \(0.928272\pi\)
\(182\) 1.45012 2.51169i 0.107490 0.186179i
\(183\) 0.988053 0.0730390
\(184\) −0.927377 + 1.60626i −0.0683672 + 0.118415i
\(185\) −2.34169 4.05593i −0.172165 0.298198i
\(186\) −16.0021 27.7164i −1.17333 2.03227i
\(187\) −1.46299 2.53397i −0.106984 0.185302i
\(188\) 0.659339 0.0480872
\(189\) −0.0213243 0.0369347i −0.00155111 0.00268661i
\(190\) −3.53642 6.12527i −0.256559 0.444373i
\(191\) 7.55464 13.0850i 0.546635 0.946799i −0.451867 0.892085i \(-0.649242\pi\)
0.998502 0.0547138i \(-0.0174246\pi\)
\(192\) −19.2713 + 33.3789i −1.39079 + 2.40891i
\(193\) 20.6195 1.48423 0.742114 0.670274i \(-0.233823\pi\)
0.742114 + 0.670274i \(0.233823\pi\)
\(194\) 48.8103 3.50437
\(195\) −0.273747 + 0.474144i −0.0196034 + 0.0339542i
\(196\) −12.1028 + 20.9627i −0.864488 + 1.49734i
\(197\) −3.77914 6.54565i −0.269252 0.466359i 0.699417 0.714714i \(-0.253443\pi\)
−0.968669 + 0.248356i \(0.920110\pi\)
\(198\) −11.7025 20.2693i −0.831661 1.44048i
\(199\) 18.2105 1.29091 0.645455 0.763799i \(-0.276668\pi\)
0.645455 + 0.763799i \(0.276668\pi\)
\(200\) −18.5016 32.0458i −1.30826 2.26598i
\(201\) 14.1886 + 24.5753i 1.00078 + 1.73341i
\(202\) −18.5542 32.1368i −1.30547 2.26113i
\(203\) −4.49520 + 7.78591i −0.315501 + 0.546464i
\(204\) −12.4619 −0.872508
\(205\) −3.07034 + 5.31798i −0.214442 + 0.371424i
\(206\) −7.37527 12.7743i −0.513859 0.890030i
\(207\) −0.678653 −0.0471696
\(208\) −1.85718 3.21674i −0.128773 0.223041i
\(209\) −5.52821 + 9.57515i −0.382394 + 0.662327i
\(210\) 7.86467 13.6220i 0.542714 0.940008i
\(211\) −19.5051 −1.34279 −0.671393 0.741101i \(-0.734304\pi\)
−0.671393 + 0.741101i \(0.734304\pi\)
\(212\) −27.6545 + 47.8990i −1.89932 + 3.28972i
\(213\) −8.16127 −0.559201
\(214\) 9.85776 0.673863
\(215\) 1.12044 + 4.47288i 0.0764134 + 0.305048i
\(216\) −0.102140 −0.00694977
\(217\) −16.8254 −1.14218
\(218\) 0.495972 0.859049i 0.0335915 0.0581821i
\(219\) −10.7011 −0.723112
\(220\) 5.23161 9.06141i 0.352715 0.610920i
\(221\) 0.158863 0.275158i 0.0106863 0.0185091i
\(222\) 21.7221 + 37.6239i 1.45789 + 2.52515i
\(223\) 15.6232 1.04621 0.523104 0.852269i \(-0.324774\pi\)
0.523104 + 0.852269i \(0.324774\pi\)
\(224\) 25.1923 + 43.6344i 1.68323 + 2.91545i
\(225\) 6.76973 11.7255i 0.451316 0.781701i
\(226\) −41.6670 −2.77165
\(227\) 9.89831 17.1444i 0.656974 1.13791i −0.324421 0.945913i \(-0.605169\pi\)
0.981395 0.192000i \(-0.0614973\pi\)
\(228\) 23.5450 + 40.7811i 1.55930 + 2.70079i
\(229\) 9.87030 + 17.0959i 0.652248 + 1.12973i 0.982576 + 0.185860i \(0.0595072\pi\)
−0.330328 + 0.943866i \(0.607159\pi\)
\(230\) −0.211355 0.366078i −0.0139364 0.0241385i
\(231\) −24.5885 −1.61780
\(232\) 10.7657 + 18.6467i 0.706803 + 1.22422i
\(233\) 7.66226 + 13.2714i 0.501972 + 0.869440i 0.999997 + 0.00227815i \(0.000725158\pi\)
−0.498026 + 0.867162i \(0.665942\pi\)
\(234\) 1.27075 2.20100i 0.0830714 0.143884i
\(235\) −0.0455850 + 0.0789555i −0.00297364 + 0.00515049i
\(236\) 42.6023 2.77318
\(237\) −41.2092 −2.67682
\(238\) −4.56408 + 7.90521i −0.295845 + 0.512419i
\(239\) 1.04026 1.80178i 0.0672886 0.116547i −0.830418 0.557140i \(-0.811899\pi\)
0.897707 + 0.440593i \(0.145232\pi\)
\(240\) −10.0724 17.4458i −0.650168 1.12612i
\(241\) 5.81674 + 10.0749i 0.374689 + 0.648981i 0.990280 0.139085i \(-0.0444161\pi\)
−0.615591 + 0.788066i \(0.711083\pi\)
\(242\) 6.49128 0.417275
\(243\) 11.0273 + 19.0999i 0.707404 + 1.22526i
\(244\) −1.02522 1.77573i −0.0656329 0.113679i
\(245\) −1.67352 2.89862i −0.106917 0.185186i
\(246\) 28.4813 49.3310i 1.81590 3.14523i
\(247\) −1.20059 −0.0763918
\(248\) −20.1478 + 34.8971i −1.27939 + 2.21597i
\(249\) −2.41064 4.17534i −0.152768 0.264602i
\(250\) 17.7921 1.12527
\(251\) −12.2201 21.1658i −0.771326 1.33598i −0.936837 0.349767i \(-0.886261\pi\)
0.165511 0.986208i \(-0.447073\pi\)
\(252\) −26.2030 + 45.3849i −1.65063 + 2.85898i
\(253\) −0.330395 + 0.572261i −0.0207718 + 0.0359778i
\(254\) −46.4972 −2.91749
\(255\) 0.861584 1.49231i 0.0539545 0.0934519i
\(256\) 1.76609 0.110381
\(257\) 8.35513 0.521179 0.260589 0.965450i \(-0.416083\pi\)
0.260589 + 0.965450i \(0.416083\pi\)
\(258\) −10.3935 41.4916i −0.647071 2.58316i
\(259\) 22.8398 1.41919
\(260\) 1.13618 0.0704626
\(261\) −3.93916 + 6.82282i −0.243828 + 0.422322i
\(262\) 29.6867 1.83405
\(263\) 5.35592 9.27673i 0.330260 0.572028i −0.652302 0.757959i \(-0.726197\pi\)
0.982563 + 0.185931i \(0.0595301\pi\)
\(264\) −29.4438 + 50.9982i −1.81214 + 3.13872i
\(265\) −3.82393 6.62324i −0.234902 0.406862i
\(266\) 34.4926 2.11488
\(267\) −10.4857 18.1618i −0.641715 1.11148i
\(268\) 29.4445 50.9994i 1.79861 3.11528i
\(269\) 5.36873 0.327337 0.163669 0.986515i \(-0.447667\pi\)
0.163669 + 0.986515i \(0.447667\pi\)
\(270\) 0.0116392 0.0201597i 0.000708341 0.00122688i
\(271\) 3.56136 + 6.16845i 0.216337 + 0.374707i 0.953685 0.300806i \(-0.0972557\pi\)
−0.737348 + 0.675513i \(0.763922\pi\)
\(272\) 5.84525 + 10.1243i 0.354421 + 0.613874i
\(273\) −1.33500 2.31229i −0.0807979 0.139946i
\(274\) 50.0997 3.02663
\(275\) −6.59155 11.4169i −0.397485 0.688465i
\(276\) 1.40717 + 2.43729i 0.0847018 + 0.146708i
\(277\) 8.64831 14.9793i 0.519626 0.900019i −0.480113 0.877206i \(-0.659404\pi\)
0.999740 0.0228129i \(-0.00726220\pi\)
\(278\) 17.4509 30.2259i 1.04664 1.81283i
\(279\) −14.7442 −0.882710
\(280\) −19.8045 −1.18354
\(281\) 4.63359 8.02561i 0.276417 0.478768i −0.694075 0.719903i \(-0.744186\pi\)
0.970492 + 0.241135i \(0.0775197\pi\)
\(282\) 0.422858 0.732412i 0.0251808 0.0436145i
\(283\) −1.99006 3.44688i −0.118297 0.204896i 0.800796 0.598937i \(-0.204410\pi\)
−0.919093 + 0.394041i \(0.871077\pi\)
\(284\) 8.46825 + 14.6674i 0.502498 + 0.870352i
\(285\) −6.51135 −0.385699
\(286\) −1.23730 2.14307i −0.0731631 0.126722i
\(287\) −14.9733 25.9346i −0.883847 1.53087i
\(288\) 22.0761 + 38.2370i 1.30085 + 2.25314i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) −4.90715 −0.288158
\(291\) 22.4677 38.9152i 1.31708 2.28125i
\(292\) 11.1036 + 19.2320i 0.649789 + 1.12547i
\(293\) 26.9318 1.57337 0.786687 0.617352i \(-0.211794\pi\)
0.786687 + 0.617352i \(0.211794\pi\)
\(294\) 15.5240 + 26.8883i 0.905378 + 1.56816i
\(295\) −2.94542 + 5.10161i −0.171489 + 0.297027i
\(296\) 27.3499 47.3713i 1.58968 2.75340i
\(297\) −0.0363894 −0.00211153
\(298\) −24.8147 + 42.9804i −1.43748 + 2.48979i
\(299\) −0.0717537 −0.00414962
\(300\) −56.1475 −3.24168
\(301\) −21.6229 6.17453i −1.24632 0.355894i
\(302\) −14.9545 −0.860535
\(303\) −34.1624 −1.96258
\(304\) 22.0875 38.2567i 1.26681 2.19417i
\(305\) 0.283524 0.0162345
\(306\) −3.99952 + 6.92737i −0.228637 + 0.396011i
\(307\) −5.60546 + 9.70894i −0.319921 + 0.554119i −0.980471 0.196663i \(-0.936990\pi\)
0.660551 + 0.750782i \(0.270323\pi\)
\(308\) 25.5133 + 44.1904i 1.45376 + 2.51798i
\(309\) −13.5795 −0.772512
\(310\) −4.59183 7.95328i −0.260798 0.451716i
\(311\) 4.26099 7.38025i 0.241618 0.418495i −0.719557 0.694433i \(-0.755655\pi\)
0.961175 + 0.275938i \(0.0889884\pi\)
\(312\) −6.39448 −0.362016
\(313\) 2.83823 4.91596i 0.160426 0.277867i −0.774595 0.632457i \(-0.782046\pi\)
0.935022 + 0.354591i \(0.115380\pi\)
\(314\) −5.94521 10.2974i −0.335508 0.581116i
\(315\) −3.62322 6.27560i −0.204145 0.353590i
\(316\) 42.7593 + 74.0612i 2.40540 + 4.16627i
\(317\) 26.4575 1.48600 0.743001 0.669290i \(-0.233402\pi\)
0.743001 + 0.669290i \(0.233402\pi\)
\(318\) 35.4717 + 61.4389i 1.98916 + 3.44532i
\(319\) 3.83548 + 6.64324i 0.214746 + 0.371950i
\(320\) −5.52994 + 9.57813i −0.309133 + 0.535434i
\(321\) 4.53759 7.85934i 0.253264 0.438665i
\(322\) 2.06146 0.114881
\(323\) 3.77871 0.210253
\(324\) 22.8455 39.5696i 1.26920 2.19831i
\(325\) 0.715761 1.23973i 0.0397033 0.0687681i
\(326\) −18.2901 31.6795i −1.01300 1.75456i
\(327\) −0.456598 0.790851i −0.0252499 0.0437342i
\(328\) −71.7202 −3.96009
\(329\) −0.222307 0.385048i −0.0122562 0.0212284i
\(330\) −6.71045 11.6228i −0.369398 0.639816i
\(331\) 12.5582 + 21.7515i 0.690261 + 1.19557i 0.971752 + 0.236004i \(0.0758378\pi\)
−0.281491 + 0.959564i \(0.590829\pi\)
\(332\) −5.00262 + 8.66479i −0.274554 + 0.475542i
\(333\) 20.0146 1.09679
\(334\) −28.1597 + 48.7740i −1.54083 + 2.66879i
\(335\) 4.07144 + 7.05194i 0.222446 + 0.385289i
\(336\) 98.2411 5.35949
\(337\) 6.61043 + 11.4496i 0.360093 + 0.623700i 0.987976 0.154608i \(-0.0494115\pi\)
−0.627883 + 0.778308i \(0.716078\pi\)
\(338\) −17.1676 + 29.7352i −0.933795 + 1.61738i
\(339\) −19.1796 + 33.2200i −1.04169 + 1.80426i
\(340\) −3.57597 −0.193934
\(341\) −7.17804 + 12.4327i −0.388713 + 0.673270i
\(342\) 30.2260 1.63444
\(343\) −7.68211 −0.414795
\(344\) −38.6991 + 37.4536i −2.08651 + 2.01936i
\(345\) −0.389153 −0.0209513
\(346\) 8.23098 0.442500
\(347\) −8.37594 + 14.5076i −0.449644 + 0.778807i −0.998363 0.0572005i \(-0.981783\pi\)
0.548718 + 0.836007i \(0.315116\pi\)
\(348\) 32.6710 1.75135
\(349\) −3.67932 + 6.37276i −0.196949 + 0.341126i −0.947538 0.319644i \(-0.896437\pi\)
0.750588 + 0.660770i \(0.229770\pi\)
\(350\) −20.5636 + 35.6172i −1.09917 + 1.90382i
\(351\) −0.00197572 0.00342205i −0.000105456 0.000182655i
\(352\) 42.9902 2.29138
\(353\) 6.14561 + 10.6445i 0.327098 + 0.566550i 0.981935 0.189220i \(-0.0605959\pi\)
−0.654837 + 0.755770i \(0.727263\pi\)
\(354\) 27.3225 47.3239i 1.45217 2.51524i
\(355\) −2.34189 −0.124295
\(356\) −21.7603 + 37.6899i −1.15329 + 1.99756i
\(357\) 4.20175 + 7.27764i 0.222380 + 0.385173i
\(358\) −21.3020 36.8961i −1.12584 1.95002i
\(359\) −16.5754 28.7094i −0.874814 1.51522i −0.856960 0.515382i \(-0.827650\pi\)
−0.0178541 0.999841i \(-0.505683\pi\)
\(360\) −17.3547 −0.914674
\(361\) 2.36068 + 4.08882i 0.124246 + 0.215201i
\(362\) 10.5234 + 18.2270i 0.553096 + 0.957991i
\(363\) 2.98798 5.17533i 0.156828 0.271634i
\(364\) −2.77043 + 4.79853i −0.145210 + 0.251511i
\(365\) −3.07070 −0.160728
\(366\) −2.63004 −0.137474
\(367\) 0.423423 0.733390i 0.0221025 0.0382827i −0.854763 0.519019i \(-0.826297\pi\)
0.876865 + 0.480737i \(0.159631\pi\)
\(368\) 1.32007 2.28642i 0.0688132 0.119188i
\(369\) −13.1212 22.7266i −0.683061 1.18310i
\(370\) 6.23321 + 10.7962i 0.324049 + 0.561270i
\(371\) 37.2968 1.93635
\(372\) 30.5717 + 52.9517i 1.58507 + 2.74542i
\(373\) 1.49305 + 2.58603i 0.0773070 + 0.133900i 0.902087 0.431554i \(-0.142034\pi\)
−0.824780 + 0.565454i \(0.808701\pi\)
\(374\) 3.89425 + 6.74503i 0.201367 + 0.348777i
\(375\) 8.18982 14.1852i 0.422920 0.732520i
\(376\) −1.06482 −0.0549140
\(377\) −0.416486 + 0.721374i −0.0214501 + 0.0371527i
\(378\) 0.0567618 + 0.0983144i 0.00291951 + 0.00505675i
\(379\) −32.7797 −1.68378 −0.841890 0.539649i \(-0.818557\pi\)
−0.841890 + 0.539649i \(0.818557\pi\)
\(380\) 6.75627 + 11.7022i 0.346590 + 0.600311i
\(381\) −21.4030 + 37.0710i −1.09651 + 1.89920i
\(382\) −20.1093 + 34.8303i −1.02888 + 1.78207i
\(383\) 33.3246 1.70281 0.851403 0.524512i \(-0.175752\pi\)
0.851403 + 0.524512i \(0.175752\pi\)
\(384\) 15.2926 26.4876i 0.780398 1.35169i
\(385\) −7.05571 −0.359592
\(386\) −54.8860 −2.79362
\(387\) −18.9482 5.41077i −0.963191 0.275045i
\(388\) −93.2512 −4.73411
\(389\) 14.7578 0.748248 0.374124 0.927379i \(-0.377943\pi\)
0.374124 + 0.927379i \(0.377943\pi\)
\(390\) 0.728672 1.26210i 0.0368977 0.0639087i
\(391\) 0.225836 0.0114210
\(392\) 19.5459 33.8545i 0.987218 1.70991i
\(393\) 13.6650 23.6685i 0.689308 1.19392i
\(394\) 10.0595 + 17.4235i 0.506788 + 0.877783i
\(395\) −11.8251 −0.594983
\(396\) 22.3574 + 38.7242i 1.12350 + 1.94596i
\(397\) 6.87590 11.9094i 0.345092 0.597716i −0.640279 0.768143i \(-0.721181\pi\)
0.985370 + 0.170426i \(0.0545145\pi\)
\(398\) −48.4735 −2.42976
\(399\) 15.8772 27.5001i 0.794853 1.37673i
\(400\) 26.3360 + 45.6153i 1.31680 + 2.28076i
\(401\) −17.8172 30.8604i −0.889751 1.54109i −0.840170 0.542324i \(-0.817545\pi\)
−0.0495811 0.998770i \(-0.515789\pi\)
\(402\) −37.7677 65.4156i −1.88368 3.26263i
\(403\) −1.55889 −0.0776540
\(404\) 35.4474 + 61.3967i 1.76357 + 3.05460i
\(405\) 3.15896 + 5.47148i 0.156970 + 0.271880i
\(406\) 11.9655 20.7249i 0.593838 1.02856i
\(407\) 9.74389 16.8769i 0.482987 0.836558i
\(408\) 20.1258 0.996376
\(409\) 36.1870 1.78933 0.894667 0.446734i \(-0.147413\pi\)
0.894667 + 0.446734i \(0.147413\pi\)
\(410\) 8.17275 14.1556i 0.403624 0.699096i
\(411\) 23.0612 39.9432i 1.13752 1.97025i
\(412\) 14.0903 + 24.4051i 0.694180 + 1.20235i
\(413\) −14.3641 24.8794i −0.706812 1.22423i
\(414\) 1.80647 0.0887830
\(415\) −0.691737 1.19812i −0.0339560 0.0588136i
\(416\) 2.33410 + 4.04278i 0.114439 + 0.198214i
\(417\) −16.0655 27.8263i −0.786733 1.36266i
\(418\) 14.7152 25.4875i 0.719745 1.24664i
\(419\) −32.9566 −1.61003 −0.805017 0.593252i \(-0.797844\pi\)
−0.805017 + 0.593252i \(0.797844\pi\)
\(420\) −15.0253 + 26.0246i −0.733160 + 1.26987i
\(421\) 6.60220 + 11.4353i 0.321772 + 0.557325i 0.980854 0.194746i \(-0.0623883\pi\)
−0.659082 + 0.752071i \(0.729055\pi\)
\(422\) 51.9195 2.52740
\(423\) −0.194809 0.337419i −0.00947193 0.0164059i
\(424\) 44.6617 77.3563i 2.16896 3.75675i
\(425\) −2.25277 + 3.90191i −0.109275 + 0.189270i
\(426\) 21.7240 1.05253
\(427\) −0.691340 + 1.19744i −0.0334563 + 0.0579480i
\(428\) −18.8331 −0.910331
\(429\) −2.27815 −0.109990
\(430\) −2.98244 11.9061i −0.143826 0.574163i
\(431\) 17.1406 0.825633 0.412817 0.910814i \(-0.364545\pi\)
0.412817 + 0.910814i \(0.364545\pi\)
\(432\) 0.145391 0.00699512
\(433\) −9.73627 + 16.8637i −0.467895 + 0.810419i −0.999327 0.0366826i \(-0.988321\pi\)
0.531432 + 0.847101i \(0.321654\pi\)
\(434\) 44.7866 2.14982
\(435\) −2.25879 + 3.91234i −0.108301 + 0.187582i
\(436\) −0.947546 + 1.64120i −0.0453792 + 0.0785991i
\(437\) −0.426684 0.739038i −0.0204110 0.0353530i
\(438\) 28.4846 1.36105
\(439\) −7.11030 12.3154i −0.339356 0.587782i 0.644956 0.764220i \(-0.276876\pi\)
−0.984312 + 0.176438i \(0.943542\pi\)
\(440\) −8.44897 + 14.6340i −0.402789 + 0.697651i
\(441\) 14.3037 0.681127
\(442\) −0.422867 + 0.732428i −0.0201137 + 0.0348380i
\(443\) −11.2184 19.4308i −0.533002 0.923187i −0.999257 0.0385364i \(-0.987730\pi\)
0.466255 0.884650i \(-0.345603\pi\)
\(444\) −41.4998 71.8797i −1.96949 3.41126i
\(445\) −3.00890 5.21156i −0.142635 0.247052i
\(446\) −41.5866 −1.96918
\(447\) 22.8448 + 39.5683i 1.08052 + 1.87152i
\(448\) −26.9682 46.7103i −1.27413 2.20686i
\(449\) −13.7128 + 23.7513i −0.647149 + 1.12089i 0.336652 + 0.941629i \(0.390705\pi\)
−0.983801 + 0.179265i \(0.942628\pi\)
\(450\) −18.0200 + 31.2115i −0.849469 + 1.47132i
\(451\) −25.5516 −1.20318
\(452\) 79.6041 3.74426
\(453\) −6.88365 + 11.9228i −0.323422 + 0.560184i
\(454\) −26.3477 + 45.6356i −1.23656 + 2.14179i
\(455\) −0.383081 0.663516i −0.0179591 0.0311061i
\(456\) −38.0248 65.8608i −1.78067 3.08422i
\(457\) −14.3885 −0.673066 −0.336533 0.941672i \(-0.609254\pi\)
−0.336533 + 0.941672i \(0.609254\pi\)
\(458\) −26.2732 45.5065i −1.22766 2.12638i
\(459\) 0.00621833 + 0.0107705i 0.000290247 + 0.000502722i
\(460\) 0.403791 + 0.699386i 0.0188268 + 0.0326090i
\(461\) −2.24942 + 3.89611i −0.104766 + 0.181460i −0.913643 0.406519i \(-0.866743\pi\)
0.808877 + 0.587978i \(0.200076\pi\)
\(462\) 65.4506 3.04504
\(463\) 11.2886 19.5524i 0.524625 0.908677i −0.474964 0.880005i \(-0.657539\pi\)
0.999589 0.0286715i \(-0.00912769\pi\)
\(464\) −15.3243 26.5425i −0.711414 1.23221i
\(465\) −8.45459 −0.392072
\(466\) −20.3957 35.3265i −0.944814 1.63647i
\(467\) 6.12367 10.6065i 0.283370 0.490811i −0.688843 0.724911i \(-0.741881\pi\)
0.972212 + 0.234100i \(0.0752144\pi\)
\(468\) −2.42774 + 4.20497i −0.112222 + 0.194375i
\(469\) −39.7109 −1.83368
\(470\) 0.121340 0.210167i 0.00559700 0.00969429i
\(471\) −10.9465 −0.504387
\(472\) −68.8022 −3.16688
\(473\) −13.7873 + 13.3435i −0.633939 + 0.613536i
\(474\) 109.692 5.03834
\(475\) 17.0251 0.781165
\(476\) 8.71959 15.1028i 0.399662 0.692234i
\(477\) 32.6833 1.49647
\(478\) −2.76900 + 4.79605i −0.126651 + 0.219366i
\(479\) −16.3519 + 28.3224i −0.747139 + 1.29408i 0.202050 + 0.979375i \(0.435240\pi\)
−0.949189 + 0.314707i \(0.898094\pi\)
\(480\) 12.6589 + 21.9258i 0.577797 + 1.00077i
\(481\) 2.11613 0.0964874
\(482\) −15.4832 26.8178i −0.705242 1.22152i
\(483\) 0.948904 1.64355i 0.0431766 0.0747841i
\(484\) −12.4015 −0.563704
\(485\) 6.44715 11.1668i 0.292750 0.507058i
\(486\) −29.3530 50.8409i −1.33148 2.30619i
\(487\) −13.8728 24.0283i −0.628634 1.08883i −0.987826 0.155563i \(-0.950281\pi\)
0.359192 0.933264i \(-0.383052\pi\)
\(488\) 1.65571 + 2.86778i 0.0749506 + 0.129818i
\(489\) −33.6763 −1.52289
\(490\) 4.45464 + 7.71567i 0.201240 + 0.348558i
\(491\) −1.72602 2.98956i −0.0778943 0.134917i 0.824447 0.565939i \(-0.191486\pi\)
−0.902341 + 0.431022i \(0.858153\pi\)
\(492\) −54.4129 + 94.2460i −2.45312 + 4.24894i
\(493\) 1.31084 2.27043i 0.0590371 0.102255i
\(494\) 3.19578 0.143785
\(495\) −6.18294 −0.277903
\(496\) 28.6793 49.6740i 1.28774 2.23043i
\(497\) 5.71043 9.89076i 0.256148 0.443661i
\(498\) 6.41673 + 11.1141i 0.287541 + 0.498035i
\(499\) −0.993084 1.72007i −0.0444565 0.0770010i 0.842941 0.538006i \(-0.180822\pi\)
−0.887397 + 0.461005i \(0.847489\pi\)
\(500\) −33.9915 −1.52015
\(501\) 25.9242 + 44.9020i 1.15821 + 2.00607i
\(502\) 32.5280 + 56.3401i 1.45179 + 2.51458i
\(503\) 13.9002 + 24.0759i 0.619779 + 1.07349i 0.989526 + 0.144357i \(0.0461112\pi\)
−0.369746 + 0.929133i \(0.620555\pi\)
\(504\) 42.3175 73.2960i 1.88497 3.26487i
\(505\) −9.80297 −0.436227
\(506\) 0.879460 1.52327i 0.0390968 0.0677176i
\(507\) 15.8047 + 27.3746i 0.701913 + 1.21575i
\(508\) 88.8321 3.94129
\(509\) 0.630573 + 1.09219i 0.0279497 + 0.0484103i 0.879662 0.475600i \(-0.157769\pi\)
−0.851712 + 0.524010i \(0.824436\pi\)
\(510\) −2.29340 + 3.97229i −0.101554 + 0.175896i
\(511\) 7.48754 12.9688i 0.331229 0.573706i
\(512\) 20.2611 0.895424
\(513\) 0.0234973 0.0406984i 0.00103743 0.00179688i
\(514\) −22.2400 −0.980966
\(515\) −3.89667 −0.171708
\(516\) 19.8566 + 79.2690i 0.874138 + 3.48962i
\(517\) −0.379363 −0.0166844
\(518\) −60.7959 −2.67122
\(519\) 3.78877 6.56234i 0.166309 0.288055i
\(520\) −1.83491 −0.0804660
\(521\) 16.4658 28.5196i 0.721379 1.24946i −0.239068 0.971003i \(-0.576842\pi\)
0.960447 0.278462i \(-0.0898246\pi\)
\(522\) 10.4854 18.1613i 0.458934 0.794897i
\(523\) −6.49964 11.2577i −0.284209 0.492265i 0.688208 0.725514i \(-0.258398\pi\)
−0.972417 + 0.233248i \(0.925064\pi\)
\(524\) −56.7160 −2.47765
\(525\) 18.9311 + 32.7896i 0.826221 + 1.43106i
\(526\) −14.2566 + 24.6932i −0.621618 + 1.07667i
\(527\) 4.90642 0.213727
\(528\) 41.9116 72.5930i 1.82397 3.15920i
\(529\) 11.4745 + 19.8744i 0.498891 + 0.864105i
\(530\) 10.1787 + 17.6300i 0.442134 + 0.765798i
\(531\) −12.5873 21.8019i −0.546244 0.946122i
\(532\) −65.8976 −2.85702
\(533\) −1.38730 2.40287i −0.0600905 0.104080i
\(534\) 27.9113 + 48.3438i 1.20784 + 2.09204i
\(535\) 1.30207 2.25525i 0.0562934 0.0975031i
\(536\) −47.5525 + 82.3633i −2.05395 + 3.55755i
\(537\) −39.2218 −1.69254
\(538\) −14.2907 −0.616116
\(539\) 6.96359 12.0613i 0.299943 0.519517i
\(540\) −0.0222366 + 0.0385148i −0.000956909 + 0.00165741i
\(541\) −1.99732 3.45946i −0.0858714 0.148734i 0.819891 0.572520i \(-0.194034\pi\)
−0.905762 + 0.423786i \(0.860701\pi\)
\(542\) −9.47977 16.4194i −0.407191 0.705275i
\(543\) 19.3759 0.831500
\(544\) −7.34629 12.7241i −0.314969 0.545543i
\(545\) −0.131022 0.226936i −0.00561236 0.00972089i
\(546\) 3.55356 + 6.15495i 0.152078 + 0.263408i
\(547\) −7.25034 + 12.5580i −0.310002 + 0.536939i −0.978362 0.206898i \(-0.933663\pi\)
0.668360 + 0.743838i \(0.266996\pi\)
\(548\) −95.7145 −4.08872
\(549\) −0.605824 + 1.04932i −0.0258559 + 0.0447838i
\(550\) 17.5457 + 30.3900i 0.748150 + 1.29583i
\(551\) −9.90653 −0.422032
\(552\) −2.27256 3.93619i −0.0967266 0.167535i
\(553\) 28.8340 49.9420i 1.22615 2.12375i
\(554\) −23.0204 + 39.8725i −0.978044 + 1.69402i
\(555\) 11.4768 0.487161
\(556\) −33.3397 + 57.7460i −1.41392 + 2.44898i
\(557\) −14.6700 −0.621589 −0.310795 0.950477i \(-0.600595\pi\)
−0.310795 + 0.950477i \(0.600595\pi\)
\(558\) 39.2466 1.66144
\(559\) −2.00338 0.572078i −0.0847341 0.0241963i
\(560\) 28.1905 1.19127
\(561\) 7.17019 0.302726
\(562\) −12.3339 + 21.3629i −0.520273 + 0.901139i
\(563\) −6.21691 −0.262011 −0.131006 0.991382i \(-0.541821\pi\)
−0.131006 + 0.991382i \(0.541821\pi\)
\(564\) −0.807863 + 1.39926i −0.0340172 + 0.0589195i
\(565\) −5.50362 + 9.53256i −0.231539 + 0.401038i
\(566\) 5.29722 + 9.17506i 0.222659 + 0.385656i
\(567\) −30.8111 −1.29394
\(568\) −13.6761 23.6877i −0.573836 0.993914i
\(569\) 4.31537 7.47444i 0.180910 0.313345i −0.761281 0.648422i \(-0.775429\pi\)
0.942191 + 0.335077i \(0.108762\pi\)
\(570\) 17.3322 0.725966
\(571\) −4.66111 + 8.07327i −0.195061 + 0.337856i −0.946921 0.321468i \(-0.895824\pi\)
0.751859 + 0.659323i \(0.229157\pi\)
\(572\) 2.36384 + 4.09429i 0.0988372 + 0.171191i
\(573\) 18.5128 + 32.0652i 0.773385 + 1.33954i
\(574\) 39.8566 + 69.0337i 1.66358 + 2.88141i
\(575\) 1.01751 0.0424331
\(576\) −23.6324 40.9324i −0.984682 1.70552i
\(577\) 4.36270 + 7.55642i 0.181622 + 0.314578i 0.942433 0.334395i \(-0.108532\pi\)
−0.760811 + 0.648973i \(0.775199\pi\)
\(578\) 1.33092 2.30522i 0.0553590 0.0958846i
\(579\) −25.2644 + 43.7591i −1.04995 + 1.81857i
\(580\) 9.37502 0.389276
\(581\) 6.74688 0.279908
\(582\) −59.8054 + 103.586i −2.47902 + 4.29378i
\(583\) 15.9115 27.5596i 0.658989 1.14140i
\(584\) −17.9322 31.0594i −0.742038 1.28525i
\(585\) −0.335696 0.581442i −0.0138793 0.0240397i
\(586\) −71.6883 −2.96142
\(587\) 12.5113 + 21.6702i 0.516398 + 0.894427i 0.999819 + 0.0190389i \(0.00606064\pi\)
−0.483421 + 0.875388i \(0.660606\pi\)
\(588\) −29.6583 51.3697i −1.22309 2.11845i
\(589\) −9.26997 16.0561i −0.381962 0.661578i
\(590\) 7.84023 13.5797i 0.322777 0.559067i
\(591\) 18.5217 0.761882
\(592\) −38.9309 + 67.4303i −1.60005 + 2.77137i
\(593\) −15.3787 26.6367i −0.631528 1.09384i −0.987240 0.159242i \(-0.949095\pi\)
0.355712 0.934596i \(-0.384238\pi\)
\(594\) 0.0968628 0.00397433
\(595\) 1.20570 + 2.08833i 0.0494289 + 0.0856133i
\(596\) 47.4081 82.1133i 1.94191 3.36349i
\(597\) −22.3127 + 38.6467i −0.913197 + 1.58170i
\(598\) 0.190997 0.00781045
\(599\) −7.11657 + 12.3263i −0.290775 + 0.503637i −0.973993 0.226577i \(-0.927247\pi\)
0.683218 + 0.730214i \(0.260580\pi\)
\(600\) 90.6775 3.70189
\(601\) 15.2760 0.623122 0.311561 0.950226i \(-0.399148\pi\)
0.311561 + 0.950226i \(0.399148\pi\)
\(602\) 57.5566 + 16.4356i 2.34583 + 0.669866i
\(603\) −34.7988 −1.41712
\(604\) 28.5703 1.16251
\(605\) 0.857407 1.48507i 0.0348585 0.0603767i
\(606\) 90.9349 3.69398
\(607\) 22.3753 38.7552i 0.908186 1.57302i 0.0916029 0.995796i \(-0.470801\pi\)
0.816583 0.577228i \(-0.195866\pi\)
\(608\) −27.7595 + 48.0808i −1.12580 + 1.94994i
\(609\) −11.0156 19.0796i −0.446374 0.773143i
\(610\) −0.754696 −0.0305567
\(611\) −0.0205971 0.0356752i −0.000833268 0.00144326i
\(612\) 7.64101 13.2346i 0.308869 0.534977i
\(613\) 34.9046 1.40978 0.704891 0.709316i \(-0.250996\pi\)
0.704891 + 0.709316i \(0.250996\pi\)
\(614\) 14.9209 25.8437i 0.602157 1.04297i
\(615\) −7.52394 13.0318i −0.303395 0.525495i
\(616\) −41.2037 71.3668i −1.66014 2.87545i
\(617\) −14.7279 25.5095i −0.592924 1.02698i −0.993836 0.110858i \(-0.964640\pi\)
0.400912 0.916117i \(-0.368693\pi\)
\(618\) 36.1466 1.45403
\(619\) 16.7430 + 28.9997i 0.672957 + 1.16560i 0.977062 + 0.212957i \(0.0683094\pi\)
−0.304105 + 0.952639i \(0.598357\pi\)
\(620\) 8.77261 + 15.1946i 0.352316 + 0.610230i
\(621\) 0.00140432 0.00243235i 5.63534e−5 9.76070e-5i
\(622\) −11.3421 + 19.6450i −0.454776 + 0.787695i
\(623\) 29.3474 1.17578
\(624\) 9.10216 0.364378
\(625\) −8.91375 + 15.4391i −0.356550 + 0.617563i
\(626\) −7.55492 + 13.0855i −0.301956 + 0.523002i
\(627\) −13.5470 23.4641i −0.541016 0.937067i
\(628\) 11.3582 + 19.6730i 0.453242 + 0.785038i
\(629\) −6.66026 −0.265562
\(630\) 9.64443 + 16.7047i 0.384243 + 0.665529i
\(631\) −11.6191 20.1249i −0.462549 0.801159i 0.536538 0.843876i \(-0.319732\pi\)
−0.999087 + 0.0427175i \(0.986398\pi\)
\(632\) −69.0556 119.608i −2.74688 4.75774i
\(633\) 23.8989 41.3941i 0.949895 1.64527i
\(634\) −70.4257 −2.79696
\(635\) −6.14162 + 10.6376i −0.243723 + 0.422140i
\(636\) −67.7681 117.378i −2.68718 4.65433i
\(637\) 1.51232 0.0599203
\(638\) −10.2094 17.6833i −0.404195 0.700087i
\(639\) 5.00407 8.66731i 0.197958 0.342873i
\(640\) 4.38825 7.60067i 0.173461 0.300443i
\(641\) −2.06861 −0.0817052 −0.0408526 0.999165i \(-0.513007\pi\)
−0.0408526 + 0.999165i \(0.513007\pi\)
\(642\) −12.0783 + 20.9203i −0.476694 + 0.825659i
\(643\) −13.1092 −0.516976 −0.258488 0.966014i \(-0.583224\pi\)
−0.258488 + 0.966014i \(0.583224\pi\)
\(644\) −3.93839 −0.155194
\(645\) −10.8653 3.10264i −0.427819 0.122166i
\(646\) −10.0583 −0.395740
\(647\) 7.35349 0.289095 0.144548 0.989498i \(-0.453827\pi\)
0.144548 + 0.989498i \(0.453827\pi\)
\(648\) −36.8952 + 63.9044i −1.44938 + 2.51040i
\(649\) −24.5120 −0.962182
\(650\) −1.90524 + 3.29998i −0.0747298 + 0.129436i
\(651\) 20.6155 35.7072i 0.807987 1.39947i
\(652\) 34.9430 + 60.5231i 1.36847 + 2.37027i
\(653\) −13.0903 −0.512261 −0.256131 0.966642i \(-0.582448\pi\)
−0.256131 + 0.966642i \(0.582448\pi\)
\(654\) 1.21539 + 2.10512i 0.0475256 + 0.0823167i
\(655\) 3.92120 6.79172i 0.153214 0.265374i
\(656\) 102.089 3.98592
\(657\) 6.56136 11.3646i 0.255983 0.443376i
\(658\) 0.591747 + 1.02494i 0.0230687 + 0.0399562i
\(659\) 20.3639 + 35.2713i 0.793265 + 1.37398i 0.923935 + 0.382549i \(0.124954\pi\)
−0.130670 + 0.991426i \(0.541713\pi\)
\(660\) 12.8202 + 22.2052i 0.499025 + 0.864337i
\(661\) −15.5594 −0.605190 −0.302595 0.953119i \(-0.597853\pi\)
−0.302595 + 0.953119i \(0.597853\pi\)
\(662\) −33.4280 57.8989i −1.29921 2.25031i
\(663\) 0.389297 + 0.674282i 0.0151190 + 0.0261869i
\(664\) 8.07916 13.9935i 0.313532 0.543054i
\(665\) 4.55599 7.89120i 0.176674 0.306008i
\(666\) −53.2757 −2.06439
\(667\) −0.592067 −0.0229249
\(668\) 53.7986 93.1819i 2.08153 3.60531i
\(669\) −19.1426 + 33.1559i −0.740094 + 1.28188i
\(670\) −10.8375 18.7711i −0.418690 0.725192i
\(671\) 0.589878 + 1.02170i 0.0227720 + 0.0394423i
\(672\) −123.469 −4.76292
\(673\) −5.31343 9.20314i −0.204818 0.354755i 0.745257 0.666777i \(-0.232327\pi\)
−0.950075 + 0.312023i \(0.898994\pi\)
\(674\) −17.5959 30.4770i −0.677770 1.17393i
\(675\) 0.0280169 + 0.0485267i 0.00107837 + 0.00186779i
\(676\) 32.7984 56.8085i 1.26148 2.18494i
\(677\) 23.4113 0.899770 0.449885 0.893087i \(-0.351465\pi\)
0.449885 + 0.893087i \(0.351465\pi\)
\(678\) 51.0531 88.4265i 1.96068 3.39600i
\(679\) 31.4413 + 54.4578i 1.20660 + 2.08990i
\(680\) 5.77514 0.221466
\(681\) 24.2561 + 42.0127i 0.929495 + 1.60993i
\(682\) 19.1068 33.0940i 0.731638 1.26723i
\(683\) −13.0234 + 22.5573i −0.498328 + 0.863130i −0.999998 0.00192947i \(-0.999386\pi\)
0.501670 + 0.865059i \(0.332719\pi\)
\(684\) −57.7463 −2.20798
\(685\) 6.61746 11.4618i 0.252840 0.437932i
\(686\) 20.4486 0.780730
\(687\) −48.3748 −1.84562
\(688\) 55.0858 53.3130i 2.10013 2.03254i
\(689\) 3.45559 0.131648
\(690\) 1.03586 0.0394346
\(691\) −17.4462 + 30.2177i −0.663684 + 1.14953i 0.315956 + 0.948774i \(0.397675\pi\)
−0.979640 + 0.200761i \(0.935659\pi\)
\(692\) −15.7251 −0.597780
\(693\) 15.0764 26.1131i 0.572705 0.991953i
\(694\) 22.2954 38.6168i 0.846323 1.46587i
\(695\) −4.61004 7.98483i −0.174869 0.302882i
\(696\) −52.7632 −1.99998
\(697\) 4.36634 + 7.56272i 0.165387 + 0.286459i
\(698\) 9.79376 16.9633i 0.370699 0.642070i
\(699\) −37.5531 −1.42039
\(700\) 39.2864 68.0460i 1.48489 2.57190i
\(701\) −7.58640 13.1400i −0.286534 0.496292i 0.686446 0.727181i \(-0.259170\pi\)
−0.972980 + 0.230889i \(0.925837\pi\)
\(702\) 0.00525905 + 0.00910895i 0.000198490 + 0.000343795i
\(703\) 12.5836 + 21.7954i 0.474599 + 0.822030i
\(704\) −46.0207 −1.73447
\(705\) −0.111707 0.193483i −0.00420714 0.00728698i
\(706\) −16.3587 28.3340i −0.615666 1.06636i
\(707\) 23.9034 41.4019i 0.898980 1.55708i
\(708\) −52.1991 + 90.4114i −1.96176 + 3.39787i
\(709\) 1.67241 0.0628086 0.0314043 0.999507i \(-0.490002\pi\)
0.0314043 + 0.999507i \(0.490002\pi\)
\(710\) 6.23375 0.233948
\(711\) 25.2674 43.7644i 0.947601 1.64129i
\(712\) 35.1425 60.8686i 1.31702 2.28115i
\(713\) −0.554022 0.959595i −0.0207483 0.0359371i
\(714\) −11.1844 19.3719i −0.418565 0.724976i
\(715\) −0.653720 −0.0244477
\(716\) 40.6971 + 70.4894i 1.52092 + 2.63431i
\(717\) 2.54918 + 4.41530i 0.0952007 + 0.164892i
\(718\) 44.1210 + 76.4198i 1.64658 + 2.85196i
\(719\) −0.467306 + 0.809398i −0.0174276 + 0.0301854i −0.874608 0.484831i \(-0.838881\pi\)
0.857180 + 0.515017i \(0.172214\pi\)
\(720\) 24.7034 0.920642
\(721\) 9.50158 16.4572i 0.353858 0.612899i
\(722\) −6.28375 10.8838i −0.233857 0.405052i
\(723\) −28.5081 −1.06023
\(724\) −20.1047 34.8224i −0.747186 1.29416i
\(725\) 5.90601 10.2295i 0.219344 0.379915i
\(726\) −7.95353 + 13.7759i −0.295183 + 0.511272i
\(727\) −45.5589 −1.68969 −0.844843 0.535014i \(-0.820306\pi\)
−0.844843 + 0.535014i \(0.820306\pi\)
\(728\) 4.47421 7.74956i 0.165825 0.287218i
\(729\) −27.0913 −1.00338
\(730\) 8.17371 0.302523
\(731\) 6.30540 + 1.80054i 0.233214 + 0.0665955i
\(732\) 5.02465 0.185716
\(733\) 42.1164 1.55560 0.777802 0.628509i \(-0.216334\pi\)
0.777802 + 0.628509i \(0.216334\pi\)
\(734\) −1.12709 + 1.95217i −0.0416015 + 0.0720559i
\(735\) 8.20200 0.302535
\(736\) −1.65905 + 2.87357i −0.0611535 + 0.105921i
\(737\) −16.9414 + 29.3435i −0.624046 + 1.08088i
\(738\) 34.9265 + 60.4945i 1.28566 + 2.22683i
\(739\) −48.0025 −1.76580 −0.882899 0.469562i \(-0.844412\pi\)
−0.882899 + 0.469562i \(0.844412\pi\)
\(740\) −11.9084 20.6260i −0.437763 0.758228i
\(741\) 1.47104 2.54792i 0.0540400 0.0936000i
\(742\) −99.2782 −3.64462
\(743\) 20.0402 34.7107i 0.735205 1.27341i −0.219428 0.975629i \(-0.570419\pi\)
0.954633 0.297784i \(-0.0962475\pi\)
\(744\) −49.3728 85.5162i −1.81010 3.13518i
\(745\) 6.55535 + 11.3542i 0.240170 + 0.415986i
\(746\) −3.97425 6.88361i −0.145508 0.252027i
\(747\) 5.91232 0.216320
\(748\) −7.43989 12.8863i −0.272029 0.471169i
\(749\) 6.34990 + 10.9983i 0.232020 + 0.401871i
\(750\) −21.8000 + 37.7587i −0.796023 + 1.37875i
\(751\) −6.32589 + 10.9568i −0.230835 + 0.399818i −0.958054 0.286588i \(-0.907479\pi\)
0.727219 + 0.686405i \(0.240812\pi\)
\(752\) 1.51571 0.0552723
\(753\) 59.8913 2.18256
\(754\) 1.10862 1.92018i 0.0403735 0.0699290i
\(755\) −1.97528 + 3.42128i −0.0718877 + 0.124513i
\(756\) −0.108442 0.187828i −0.00394402 0.00683124i
\(757\) 21.9092 + 37.9478i 0.796303 + 1.37924i 0.922008 + 0.387170i \(0.126547\pi\)
−0.125705 + 0.992068i \(0.540119\pi\)
\(758\) 87.2544 3.16922
\(759\) −0.809642 1.40234i −0.0293881 0.0509018i
\(760\) −10.9113 18.8989i −0.395794 0.685535i
\(761\) 10.3549 + 17.9352i 0.375365 + 0.650152i 0.990382 0.138362i \(-0.0441839\pi\)
−0.615016 + 0.788514i \(0.710851\pi\)
\(762\) 56.9713 98.6771i 2.06385 3.57470i
\(763\) 1.27793 0.0462640
\(764\) 38.4184 66.5426i 1.38993 2.40743i
\(765\) 1.05656 + 1.83001i 0.0382000 + 0.0661643i
\(766\) −88.7047 −3.20503
\(767\) −1.33085 2.30510i −0.0480543 0.0832325i
\(768\) −2.1639