Properties

Label 864.2.w.a.107.18
Level $864$
Weight $2$
Character 864.107
Analytic conductor $6.899$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 107.18
Character \(\chi\) \(=\) 864.107
Dual form 864.2.w.a.323.18

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0811033 + 1.41189i) q^{2} +(-1.98684 + 0.229017i) q^{4} +(-1.02313 - 0.423795i) q^{5} +(-0.549738 + 0.549738i) q^{7} +(-0.484486 - 2.78662i) q^{8} +O(q^{10})\) \(q+(0.0811033 + 1.41189i) q^{2} +(-1.98684 + 0.229017i) q^{4} +(-1.02313 - 0.423795i) q^{5} +(-0.549738 + 0.549738i) q^{7} +(-0.484486 - 2.78662i) q^{8} +(0.515371 - 1.47892i) q^{10} +(2.44818 + 1.01407i) q^{11} +(-2.24462 - 5.41899i) q^{13} +(-0.820752 - 0.731581i) q^{14} +(3.89510 - 0.910043i) q^{16} -0.515040 q^{17} +(2.66603 - 1.10431i) q^{19} +(2.12986 + 0.607700i) q^{20} +(-1.23320 + 3.53880i) q^{22} +(3.26913 - 3.26913i) q^{23} +(-2.66834 - 2.66834i) q^{25} +(7.46894 - 3.60864i) q^{26} +(0.966344 - 1.21814i) q^{28} +(2.83677 + 6.84857i) q^{29} -5.60227i q^{31} +(1.60078 + 5.42563i) q^{32} +(-0.0417714 - 0.727177i) q^{34} +(0.795430 - 0.329478i) q^{35} +(2.58718 - 6.24599i) q^{37} +(1.77538 + 3.67457i) q^{38} +(-0.685265 + 3.05641i) q^{40} +(8.45953 + 8.45953i) q^{41} +(1.31637 - 3.17800i) q^{43} +(-5.09640 - 1.45412i) q^{44} +(4.88078 + 4.35051i) q^{46} -2.34853i q^{47} +6.39558i q^{49} +(3.55098 - 3.98380i) q^{50} +(5.70075 + 10.2526i) q^{52} +(3.08254 - 7.44190i) q^{53} +(-2.07506 - 2.07506i) q^{55} +(1.79825 + 1.26557i) q^{56} +(-9.43932 + 4.56064i) q^{58} +(2.96161 - 7.14996i) q^{59} +(5.36346 - 2.22162i) q^{61} +(7.90977 - 0.454363i) q^{62} +(-7.53055 + 2.70016i) q^{64} +6.49559i q^{65} +(0.398752 + 0.962673i) q^{67} +(1.02330 - 0.117953i) q^{68} +(0.529697 + 1.09634i) q^{70} +(-5.43150 - 5.43150i) q^{71} +(2.98447 - 2.98447i) q^{73} +(9.02846 + 3.14623i) q^{74} +(-5.04409 + 2.80466i) q^{76} +(-1.90333 + 0.788386i) q^{77} -6.13141 q^{79} +(-4.37088 - 0.719631i) q^{80} +(-11.2578 + 12.6300i) q^{82} +(-1.05703 - 2.55189i) q^{83} +(0.526954 + 0.218271i) q^{85} +(4.59374 + 1.60082i) q^{86} +(1.63972 - 7.31347i) q^{88} +(0.656796 - 0.656796i) q^{89} +(4.21297 + 1.74507i) q^{91} +(-5.74657 + 7.24395i) q^{92} +(3.31586 - 0.190474i) q^{94} -3.19570 q^{95} -10.9570 q^{97} +(-9.02983 + 0.518703i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0811033 + 1.41189i 0.0573487 + 0.998354i
\(3\) 0 0
\(4\) −1.98684 + 0.229017i −0.993422 + 0.114509i
\(5\) −1.02313 0.423795i −0.457559 0.189527i 0.141985 0.989869i \(-0.454651\pi\)
−0.599544 + 0.800342i \(0.704651\pi\)
\(6\) 0 0
\(7\) −0.549738 + 0.549738i −0.207781 + 0.207781i −0.803324 0.595543i \(-0.796937\pi\)
0.595543 + 0.803324i \(0.296937\pi\)
\(8\) −0.484486 2.78662i −0.171292 0.985220i
\(9\) 0 0
\(10\) 0.515371 1.47892i 0.162975 0.467675i
\(11\) 2.44818 + 1.01407i 0.738155 + 0.305754i 0.719898 0.694080i \(-0.244188\pi\)
0.0182567 + 0.999833i \(0.494188\pi\)
\(12\) 0 0
\(13\) −2.24462 5.41899i −0.622545 1.50296i −0.848705 0.528866i \(-0.822617\pi\)
0.226161 0.974090i \(-0.427383\pi\)
\(14\) −0.820752 0.731581i −0.219355 0.195523i
\(15\) 0 0
\(16\) 3.89510 0.910043i 0.973776 0.227511i
\(17\) −0.515040 −0.124915 −0.0624577 0.998048i \(-0.519894\pi\)
−0.0624577 + 0.998048i \(0.519894\pi\)
\(18\) 0 0
\(19\) 2.66603 1.10431i 0.611630 0.253346i −0.0552952 0.998470i \(-0.517610\pi\)
0.666925 + 0.745125i \(0.267610\pi\)
\(20\) 2.12986 + 0.607700i 0.476251 + 0.135886i
\(21\) 0 0
\(22\) −1.23320 + 3.53880i −0.262918 + 0.754475i
\(23\) 3.26913 3.26913i 0.681661 0.681661i −0.278713 0.960374i \(-0.589908\pi\)
0.960374 + 0.278713i \(0.0899079\pi\)
\(24\) 0 0
\(25\) −2.66834 2.66834i −0.533667 0.533667i
\(26\) 7.46894 3.60864i 1.46478 0.707713i
\(27\) 0 0
\(28\) 0.966344 1.21814i 0.182622 0.230207i
\(29\) 2.83677 + 6.84857i 0.526775 + 1.27175i 0.933625 + 0.358252i \(0.116627\pi\)
−0.406850 + 0.913495i \(0.633373\pi\)
\(30\) 0 0
\(31\) 5.60227i 1.00620i −0.864229 0.503099i \(-0.832193\pi\)
0.864229 0.503099i \(-0.167807\pi\)
\(32\) 1.60078 + 5.42563i 0.282981 + 0.959125i
\(33\) 0 0
\(34\) −0.0417714 0.727177i −0.00716374 0.124710i
\(35\) 0.795430 0.329478i 0.134452 0.0556919i
\(36\) 0 0
\(37\) 2.58718 6.24599i 0.425329 1.02684i −0.555421 0.831569i \(-0.687443\pi\)
0.980750 0.195266i \(-0.0625570\pi\)
\(38\) 1.77538 + 3.67457i 0.288005 + 0.596095i
\(39\) 0 0
\(40\) −0.685265 + 3.05641i −0.108350 + 0.483260i
\(41\) 8.45953 + 8.45953i 1.32116 + 1.32116i 0.912841 + 0.408316i \(0.133884\pi\)
0.408316 + 0.912841i \(0.366116\pi\)
\(42\) 0 0
\(43\) 1.31637 3.17800i 0.200745 0.484640i −0.791162 0.611606i \(-0.790524\pi\)
0.991907 + 0.126966i \(0.0405238\pi\)
\(44\) −5.09640 1.45412i −0.768311 0.219218i
\(45\) 0 0
\(46\) 4.88078 + 4.35051i 0.719632 + 0.641447i
\(47\) 2.34853i 0.342569i −0.985222 0.171284i \(-0.945208\pi\)
0.985222 0.171284i \(-0.0547917\pi\)
\(48\) 0 0
\(49\) 6.39558i 0.913654i
\(50\) 3.55098 3.98380i 0.502184 0.563394i
\(51\) 0 0
\(52\) 5.70075 + 10.2526i 0.790551 + 1.42178i
\(53\) 3.08254 7.44190i 0.423419 1.02222i −0.557913 0.829900i \(-0.688398\pi\)
0.981331 0.192324i \(-0.0616024\pi\)
\(54\) 0 0
\(55\) −2.07506 2.07506i −0.279801 0.279801i
\(56\) 1.79825 + 1.26557i 0.240302 + 0.169119i
\(57\) 0 0
\(58\) −9.43932 + 4.56064i −1.23944 + 0.598841i
\(59\) 2.96161 7.14996i 0.385569 0.930846i −0.605298 0.795999i \(-0.706946\pi\)
0.990867 0.134846i \(-0.0430541\pi\)
\(60\) 0 0
\(61\) 5.36346 2.22162i 0.686721 0.284449i −0.0119123 0.999929i \(-0.503792\pi\)
0.698633 + 0.715480i \(0.253792\pi\)
\(62\) 7.90977 0.454363i 1.00454 0.0577041i
\(63\) 0 0
\(64\) −7.53055 + 2.70016i −0.941318 + 0.337520i
\(65\) 6.49559i 0.805679i
\(66\) 0 0
\(67\) 0.398752 + 0.962673i 0.0487153 + 0.117609i 0.946364 0.323103i \(-0.104726\pi\)
−0.897649 + 0.440712i \(0.854726\pi\)
\(68\) 1.02330 0.117953i 0.124094 0.0143039i
\(69\) 0 0
\(70\) 0.529697 + 1.09634i 0.0633110 + 0.131037i
\(71\) −5.43150 5.43150i −0.644601 0.644601i 0.307082 0.951683i \(-0.400647\pi\)
−0.951683 + 0.307082i \(0.900647\pi\)
\(72\) 0 0
\(73\) 2.98447 2.98447i 0.349306 0.349306i −0.510545 0.859851i \(-0.670556\pi\)
0.859851 + 0.510545i \(0.170556\pi\)
\(74\) 9.02846 + 3.14623i 1.04954 + 0.365741i
\(75\) 0 0
\(76\) −5.04409 + 2.80466i −0.578597 + 0.321716i
\(77\) −1.90333 + 0.788386i −0.216905 + 0.0898449i
\(78\) 0 0
\(79\) −6.13141 −0.689838 −0.344919 0.938632i \(-0.612094\pi\)
−0.344919 + 0.938632i \(0.612094\pi\)
\(80\) −4.37088 0.719631i −0.488679 0.0804572i
\(81\) 0 0
\(82\) −11.2578 + 12.6300i −1.24322 + 1.39475i
\(83\) −1.05703 2.55189i −0.116024 0.280106i 0.855190 0.518314i \(-0.173440\pi\)
−0.971214 + 0.238208i \(0.923440\pi\)
\(84\) 0 0
\(85\) 0.526954 + 0.218271i 0.0571561 + 0.0236749i
\(86\) 4.59374 + 1.60082i 0.495355 + 0.172621i
\(87\) 0 0
\(88\) 1.63972 7.31347i 0.174795 0.779618i
\(89\) 0.656796 0.656796i 0.0696202 0.0696202i −0.671439 0.741060i \(-0.734324\pi\)
0.741060 + 0.671439i \(0.234324\pi\)
\(90\) 0 0
\(91\) 4.21297 + 1.74507i 0.441639 + 0.182933i
\(92\) −5.74657 + 7.24395i −0.599121 + 0.755234i
\(93\) 0 0
\(94\) 3.31586 0.190474i 0.342005 0.0196459i
\(95\) −3.19570 −0.327872
\(96\) 0 0
\(97\) −10.9570 −1.11251 −0.556256 0.831011i \(-0.687763\pi\)
−0.556256 + 0.831011i \(0.687763\pi\)
\(98\) −9.02983 + 0.518703i −0.912150 + 0.0523969i
\(99\) 0 0
\(100\) 5.91267 + 4.69048i 0.591267 + 0.469048i
\(101\) 1.68484 + 0.697884i 0.167648 + 0.0694420i 0.464929 0.885348i \(-0.346080\pi\)
−0.297281 + 0.954790i \(0.596080\pi\)
\(102\) 0 0
\(103\) 2.98561 2.98561i 0.294181 0.294181i −0.544548 0.838729i \(-0.683299\pi\)
0.838729 + 0.544548i \(0.183299\pi\)
\(104\) −14.0132 + 8.88033i −1.37411 + 0.870788i
\(105\) 0 0
\(106\) 10.7571 + 3.74863i 1.04482 + 0.364099i
\(107\) −5.79461 2.40021i −0.560186 0.232037i 0.0845799 0.996417i \(-0.473045\pi\)
−0.644766 + 0.764380i \(0.723045\pi\)
\(108\) 0 0
\(109\) 1.10348 + 2.66404i 0.105694 + 0.255169i 0.967875 0.251432i \(-0.0809016\pi\)
−0.862180 + 0.506601i \(0.830902\pi\)
\(110\) 2.76145 3.09804i 0.263294 0.295386i
\(111\) 0 0
\(112\) −1.64100 + 2.64157i −0.155060 + 0.249605i
\(113\) −17.4090 −1.63770 −0.818850 0.574008i \(-0.805388\pi\)
−0.818850 + 0.574008i \(0.805388\pi\)
\(114\) 0 0
\(115\) −4.73020 + 1.95931i −0.441093 + 0.182707i
\(116\) −7.20466 12.9574i −0.668936 1.20306i
\(117\) 0 0
\(118\) 10.3351 + 3.60157i 0.951425 + 0.331551i
\(119\) 0.283137 0.283137i 0.0259551 0.0259551i
\(120\) 0 0
\(121\) −2.81291 2.81291i −0.255719 0.255719i
\(122\) 3.57167 + 7.39242i 0.323364 + 0.669278i
\(123\) 0 0
\(124\) 1.28302 + 11.1308i 0.115218 + 0.999579i
\(125\) 3.71821 + 8.97655i 0.332567 + 0.802887i
\(126\) 0 0
\(127\) 16.8370i 1.49404i −0.664801 0.747020i \(-0.731484\pi\)
0.664801 0.747020i \(-0.268516\pi\)
\(128\) −4.42307 10.4133i −0.390948 0.920413i
\(129\) 0 0
\(130\) −9.17104 + 0.526814i −0.804353 + 0.0462047i
\(131\) 7.92259 3.28164i 0.692200 0.286718i −0.00871665 0.999962i \(-0.502775\pi\)
0.700916 + 0.713244i \(0.252775\pi\)
\(132\) 0 0
\(133\) −0.858540 + 2.07270i −0.0744449 + 0.179726i
\(134\) −1.32684 + 0.641068i −0.114622 + 0.0553799i
\(135\) 0 0
\(136\) 0.249530 + 1.43522i 0.0213970 + 0.123069i
\(137\) −1.62791 1.62791i −0.139082 0.139082i 0.634138 0.773220i \(-0.281355\pi\)
−0.773220 + 0.634138i \(0.781355\pi\)
\(138\) 0 0
\(139\) −0.595578 + 1.43785i −0.0505163 + 0.121957i −0.947123 0.320870i \(-0.896025\pi\)
0.896607 + 0.442828i \(0.146025\pi\)
\(140\) −1.50494 + 0.836789i −0.127191 + 0.0707216i
\(141\) 0 0
\(142\) 7.22815 8.10918i 0.606573 0.680507i
\(143\) 15.5429i 1.29976i
\(144\) 0 0
\(145\) 8.20920i 0.681737i
\(146\) 4.45579 + 3.97169i 0.368764 + 0.328699i
\(147\) 0 0
\(148\) −3.70988 + 13.0023i −0.304950 + 1.06878i
\(149\) −7.63812 + 18.4401i −0.625739 + 1.51067i 0.219130 + 0.975696i \(0.429678\pi\)
−0.844869 + 0.534973i \(0.820322\pi\)
\(150\) 0 0
\(151\) −6.02666 6.02666i −0.490443 0.490443i 0.418003 0.908446i \(-0.362730\pi\)
−0.908446 + 0.418003i \(0.862730\pi\)
\(152\) −4.36895 6.89421i −0.354368 0.559195i
\(153\) 0 0
\(154\) −1.26748 2.62335i −0.102136 0.211395i
\(155\) −2.37421 + 5.73186i −0.190701 + 0.460394i
\(156\) 0 0
\(157\) 13.9023 5.75854i 1.10953 0.459582i 0.248753 0.968567i \(-0.419979\pi\)
0.860775 + 0.508985i \(0.169979\pi\)
\(158\) −0.497278 8.65686i −0.0395613 0.688703i
\(159\) 0 0
\(160\) 0.661544 6.22954i 0.0522997 0.492489i
\(161\) 3.59433i 0.283273i
\(162\) 0 0
\(163\) 5.81643 + 14.0421i 0.455578 + 1.09986i 0.970169 + 0.242428i \(0.0779437\pi\)
−0.514591 + 0.857436i \(0.672056\pi\)
\(164\) −18.7452 14.8704i −1.46375 1.16118i
\(165\) 0 0
\(166\) 3.51725 1.69937i 0.272992 0.131897i
\(167\) 14.5368 + 14.5368i 1.12489 + 1.12489i 0.990995 + 0.133896i \(0.0427487\pi\)
0.133896 + 0.990995i \(0.457251\pi\)
\(168\) 0 0
\(169\) −15.1347 + 15.1347i −1.16421 + 1.16421i
\(170\) −0.265437 + 0.761701i −0.0203581 + 0.0584198i
\(171\) 0 0
\(172\) −1.88761 + 6.61566i −0.143929 + 0.504440i
\(173\) −4.13825 + 1.71412i −0.314626 + 0.130322i −0.534408 0.845227i \(-0.679465\pi\)
0.219782 + 0.975549i \(0.429465\pi\)
\(174\) 0 0
\(175\) 2.93377 0.221772
\(176\) 10.4588 + 1.72196i 0.788360 + 0.129797i
\(177\) 0 0
\(178\) 0.980589 + 0.874053i 0.0734983 + 0.0655130i
\(179\) −9.61242 23.2064i −0.718466 1.73453i −0.677673 0.735363i \(-0.737011\pi\)
−0.0407933 0.999168i \(-0.512989\pi\)
\(180\) 0 0
\(181\) 4.05011 + 1.67761i 0.301043 + 0.124696i 0.528092 0.849187i \(-0.322908\pi\)
−0.227049 + 0.973883i \(0.572908\pi\)
\(182\) −2.12215 + 6.08977i −0.157304 + 0.451403i
\(183\) 0 0
\(184\) −10.6937 7.52599i −0.788349 0.554824i
\(185\) −5.29404 + 5.29404i −0.389226 + 0.389226i
\(186\) 0 0
\(187\) −1.26091 0.522287i −0.0922070 0.0381934i
\(188\) 0.537855 + 4.66617i 0.0392271 + 0.340316i
\(189\) 0 0
\(190\) −0.259182 4.51197i −0.0188031 0.327333i
\(191\) −22.1321 −1.60142 −0.800710 0.599053i \(-0.795544\pi\)
−0.800710 + 0.599053i \(0.795544\pi\)
\(192\) 0 0
\(193\) 10.1418 0.730026 0.365013 0.931002i \(-0.381065\pi\)
0.365013 + 0.931002i \(0.381065\pi\)
\(194\) −0.888647 15.4700i −0.0638011 1.11068i
\(195\) 0 0
\(196\) −1.46470 12.7070i −0.104621 0.907644i
\(197\) −0.114773 0.0475406i −0.00817726 0.00338713i 0.378591 0.925564i \(-0.376409\pi\)
−0.386768 + 0.922177i \(0.626409\pi\)
\(198\) 0 0
\(199\) −5.93135 + 5.93135i −0.420462 + 0.420462i −0.885363 0.464901i \(-0.846090\pi\)
0.464901 + 0.885363i \(0.346090\pi\)
\(200\) −6.14288 + 8.72842i −0.434367 + 0.617193i
\(201\) 0 0
\(202\) −0.848686 + 2.43540i −0.0597133 + 0.171354i
\(203\) −5.32439 2.20544i −0.373699 0.154791i
\(204\) 0 0
\(205\) −5.07011 12.2403i −0.354112 0.854901i
\(206\) 4.45749 + 3.97320i 0.310568 + 0.276826i
\(207\) 0 0
\(208\) −13.6745 19.0648i −0.948158 1.32191i
\(209\) 7.64679 0.528939
\(210\) 0 0
\(211\) 22.0729 9.14290i 1.51956 0.629423i 0.542058 0.840341i \(-0.317645\pi\)
0.977504 + 0.210918i \(0.0676454\pi\)
\(212\) −4.42020 + 15.4919i −0.303580 + 1.06398i
\(213\) 0 0
\(214\) 2.91886 8.37599i 0.199529 0.572571i
\(215\) −2.69364 + 2.69364i −0.183705 + 0.183705i
\(216\) 0 0
\(217\) 3.07978 + 3.07978i 0.209069 + 0.209069i
\(218\) −3.67183 + 1.77405i −0.248688 + 0.120154i
\(219\) 0 0
\(220\) 4.59804 + 3.64759i 0.310000 + 0.245920i
\(221\) 1.15607 + 2.79099i 0.0777655 + 0.187742i
\(222\) 0 0
\(223\) 1.52014i 0.101796i −0.998704 0.0508979i \(-0.983792\pi\)
0.998704 0.0508979i \(-0.0162083\pi\)
\(224\) −3.86269 2.10266i −0.258087 0.140490i
\(225\) 0 0
\(226\) −1.41193 24.5795i −0.0939199 1.63500i
\(227\) 17.6896 7.32726i 1.17410 0.486328i 0.291553 0.956555i \(-0.405828\pi\)
0.882546 + 0.470227i \(0.155828\pi\)
\(228\) 0 0
\(229\) 9.31877 22.4975i 0.615801 1.48668i −0.240736 0.970591i \(-0.577389\pi\)
0.856537 0.516085i \(-0.172611\pi\)
\(230\) −3.14996 6.51959i −0.207702 0.429889i
\(231\) 0 0
\(232\) 17.7100 11.2230i 1.16272 0.736829i
\(233\) 6.47985 + 6.47985i 0.424509 + 0.424509i 0.886753 0.462244i \(-0.152956\pi\)
−0.462244 + 0.886753i \(0.652956\pi\)
\(234\) 0 0
\(235\) −0.995297 + 2.40286i −0.0649260 + 0.156745i
\(236\) −4.24680 + 14.8841i −0.276443 + 0.968874i
\(237\) 0 0
\(238\) 0.422720 + 0.376793i 0.0274009 + 0.0244239i
\(239\) 28.5450i 1.84642i −0.384291 0.923212i \(-0.625554\pi\)
0.384291 0.923212i \(-0.374446\pi\)
\(240\) 0 0
\(241\) 27.4173i 1.76610i 0.469278 + 0.883051i \(0.344514\pi\)
−0.469278 + 0.883051i \(0.655486\pi\)
\(242\) 3.74338 4.19965i 0.240633 0.269964i
\(243\) 0 0
\(244\) −10.1476 + 5.64234i −0.649632 + 0.361214i
\(245\) 2.71041 6.54352i 0.173162 0.418050i
\(246\) 0 0
\(247\) −11.9685 11.9685i −0.761534 0.761534i
\(248\) −15.6114 + 2.71422i −0.991326 + 0.172353i
\(249\) 0 0
\(250\) −12.3723 + 5.97771i −0.782493 + 0.378064i
\(251\) −7.40685 + 17.8817i −0.467516 + 1.12868i 0.497728 + 0.867333i \(0.334168\pi\)
−0.965244 + 0.261351i \(0.915832\pi\)
\(252\) 0 0
\(253\) 11.3186 4.68830i 0.711592 0.294751i
\(254\) 23.7719 1.36554i 1.49158 0.0856813i
\(255\) 0 0
\(256\) 14.3436 7.08942i 0.896478 0.443089i
\(257\) 13.2444i 0.826160i 0.910695 + 0.413080i \(0.135547\pi\)
−0.910695 + 0.413080i \(0.864453\pi\)
\(258\) 0 0
\(259\) 2.01139 + 4.85593i 0.124982 + 0.301733i
\(260\) −1.48760 12.9057i −0.0922573 0.800380i
\(261\) 0 0
\(262\) 5.27585 + 10.9196i 0.325943 + 0.674618i
\(263\) 6.63410 + 6.63410i 0.409076 + 0.409076i 0.881416 0.472340i \(-0.156591\pi\)
−0.472340 + 0.881416i \(0.656591\pi\)
\(264\) 0 0
\(265\) −6.30768 + 6.30768i −0.387478 + 0.387478i
\(266\) −2.99604 1.04406i −0.183699 0.0640153i
\(267\) 0 0
\(268\) −1.01273 1.82136i −0.0618621 0.111257i
\(269\) −3.41644 + 1.41514i −0.208304 + 0.0862824i −0.484396 0.874849i \(-0.660961\pi\)
0.276092 + 0.961131i \(0.410961\pi\)
\(270\) 0 0
\(271\) −29.3563 −1.78327 −0.891635 0.452754i \(-0.850441\pi\)
−0.891635 + 0.452754i \(0.850441\pi\)
\(272\) −2.00613 + 0.468709i −0.121640 + 0.0284196i
\(273\) 0 0
\(274\) 2.16640 2.43046i 0.130877 0.146829i
\(275\) −3.82670 9.23846i −0.230758 0.557100i
\(276\) 0 0
\(277\) −15.8026 6.54564i −0.949484 0.393289i −0.146447 0.989218i \(-0.546784\pi\)
−0.803037 + 0.595929i \(0.796784\pi\)
\(278\) −2.07839 0.724274i −0.124653 0.0434391i
\(279\) 0 0
\(280\) −1.30351 2.05694i −0.0778994 0.122926i
\(281\) 4.81127 4.81127i 0.287016 0.287016i −0.548883 0.835899i \(-0.684947\pi\)
0.835899 + 0.548883i \(0.184947\pi\)
\(282\) 0 0
\(283\) 15.2722 + 6.32597i 0.907841 + 0.376040i 0.787230 0.616660i \(-0.211515\pi\)
0.120611 + 0.992700i \(0.461515\pi\)
\(284\) 12.0355 + 9.54764i 0.714173 + 0.566548i
\(285\) 0 0
\(286\) 21.9448 1.26058i 1.29762 0.0745396i
\(287\) −9.30104 −0.549023
\(288\) 0 0
\(289\) −16.7347 −0.984396
\(290\) 11.5904 0.665793i 0.680615 0.0390967i
\(291\) 0 0
\(292\) −5.24619 + 6.61318i −0.307010 + 0.387007i
\(293\) −20.9184 8.66470i −1.22207 0.506197i −0.324001 0.946057i \(-0.605028\pi\)
−0.898067 + 0.439860i \(0.855028\pi\)
\(294\) 0 0
\(295\) −6.06024 + 6.06024i −0.352841 + 0.352841i
\(296\) −18.6587 4.18339i −1.08451 0.243155i
\(297\) 0 0
\(298\) −26.6547 9.28861i −1.54407 0.538075i
\(299\) −25.0533 10.3774i −1.44887 0.600142i
\(300\) 0 0
\(301\) 1.02341 + 2.47072i 0.0589882 + 0.142410i
\(302\) 8.02018 8.99774i 0.461509 0.517762i
\(303\) 0 0
\(304\) 9.37951 6.72760i 0.537952 0.385854i
\(305\) −6.42904 −0.368126
\(306\) 0 0
\(307\) 23.9065 9.90242i 1.36442 0.565161i 0.424149 0.905592i \(-0.360573\pi\)
0.940269 + 0.340432i \(0.110573\pi\)
\(308\) 3.60107 2.00230i 0.205190 0.114091i
\(309\) 0 0
\(310\) −8.28529 2.88725i −0.470573 0.163985i
\(311\) 13.5439 13.5439i 0.768007 0.768007i −0.209749 0.977755i \(-0.567265\pi\)
0.977755 + 0.209749i \(0.0672646\pi\)
\(312\) 0 0
\(313\) 4.30307 + 4.30307i 0.243224 + 0.243224i 0.818183 0.574959i \(-0.194982\pi\)
−0.574959 + 0.818183i \(0.694982\pi\)
\(314\) 9.25793 + 19.1615i 0.522455 + 1.08135i
\(315\) 0 0
\(316\) 12.1822 1.40420i 0.685300 0.0789924i
\(317\) 12.0099 + 28.9944i 0.674541 + 1.62849i 0.773804 + 0.633425i \(0.218351\pi\)
−0.0992630 + 0.995061i \(0.531649\pi\)
\(318\) 0 0
\(319\) 19.6432i 1.09981i
\(320\) 8.84906 + 0.428788i 0.494677 + 0.0239700i
\(321\) 0 0
\(322\) −5.07479 + 0.291512i −0.282807 + 0.0162453i
\(323\) −1.37311 + 0.568762i −0.0764021 + 0.0316468i
\(324\) 0 0
\(325\) −8.47028 + 20.4491i −0.469847 + 1.13431i
\(326\) −19.3541 + 9.35100i −1.07193 + 0.517904i
\(327\) 0 0
\(328\) 19.4750 27.6721i 1.07533 1.52793i
\(329\) 1.29108 + 1.29108i 0.0711794 + 0.0711794i
\(330\) 0 0
\(331\) −12.6627 + 30.5704i −0.696003 + 1.68030i 0.0363165 + 0.999340i \(0.488438\pi\)
−0.732320 + 0.680961i \(0.761562\pi\)
\(332\) 2.68458 + 4.82813i 0.147335 + 0.264978i
\(333\) 0 0
\(334\) −19.3453 + 21.7033i −1.05853 + 1.18755i
\(335\) 1.15393i 0.0630459i
\(336\) 0 0
\(337\) 17.6737i 0.962748i 0.876515 + 0.481374i \(0.159862\pi\)
−0.876515 + 0.481374i \(0.840138\pi\)
\(338\) −22.5960 20.1410i −1.22906 1.09553i
\(339\) 0 0
\(340\) −1.09696 0.312990i −0.0594912 0.0169743i
\(341\) 5.68110 13.7154i 0.307649 0.742729i
\(342\) 0 0
\(343\) −7.36405 7.36405i −0.397621 0.397621i
\(344\) −9.49365 2.12853i −0.511864 0.114763i
\(345\) 0 0
\(346\) −2.75577 5.70372i −0.148151 0.306634i
\(347\) −7.92952 + 19.1436i −0.425679 + 1.02768i 0.554964 + 0.831875i \(0.312732\pi\)
−0.980643 + 0.195806i \(0.937268\pi\)
\(348\) 0 0
\(349\) −1.37363 + 0.568978i −0.0735289 + 0.0304567i −0.419145 0.907919i \(-0.637670\pi\)
0.345616 + 0.938376i \(0.387670\pi\)
\(350\) 0.237939 + 4.14215i 0.0127183 + 0.221407i
\(351\) 0 0
\(352\) −1.58296 + 14.9063i −0.0843723 + 0.794506i
\(353\) 2.64701i 0.140886i −0.997516 0.0704431i \(-0.977559\pi\)
0.997516 0.0704431i \(-0.0224413\pi\)
\(354\) 0 0
\(355\) 3.25530 + 7.85899i 0.172773 + 0.417112i
\(356\) −1.15453 + 1.45537i −0.0611902 + 0.0771344i
\(357\) 0 0
\(358\) 31.9853 15.4538i 1.69047 0.816757i
\(359\) 13.3235 + 13.3235i 0.703189 + 0.703189i 0.965094 0.261904i \(-0.0843505\pi\)
−0.261904 + 0.965094i \(0.584351\pi\)
\(360\) 0 0
\(361\) −7.54679 + 7.54679i −0.397199 + 0.397199i
\(362\) −2.04012 + 5.85436i −0.107226 + 0.307698i
\(363\) 0 0
\(364\) −8.77017 2.50234i −0.459682 0.131158i
\(365\) −4.31832 + 1.78871i −0.226031 + 0.0936251i
\(366\) 0 0
\(367\) 2.91350 0.152083 0.0760417 0.997105i \(-0.475772\pi\)
0.0760417 + 0.997105i \(0.475772\pi\)
\(368\) 9.75855 15.7087i 0.508700 0.818870i
\(369\) 0 0
\(370\) −7.90395 7.04522i −0.410907 0.366264i
\(371\) 2.39651 + 5.78568i 0.124420 + 0.300377i
\(372\) 0 0
\(373\) 26.3018 + 10.8946i 1.36186 + 0.564100i 0.939568 0.342362i \(-0.111227\pi\)
0.422289 + 0.906461i \(0.361227\pi\)
\(374\) 0.635145 1.82262i 0.0328426 0.0942456i
\(375\) 0 0
\(376\) −6.54448 + 1.13783i −0.337506 + 0.0586792i
\(377\) 30.7448 30.7448i 1.58344 1.58344i
\(378\) 0 0
\(379\) 29.2228 + 12.1045i 1.50108 + 0.621766i 0.973693 0.227862i \(-0.0731737\pi\)
0.527382 + 0.849628i \(0.323174\pi\)
\(380\) 6.34937 0.731872i 0.325716 0.0375442i
\(381\) 0 0
\(382\) −1.79498 31.2479i −0.0918393 1.59878i
\(383\) 21.2542 1.08604 0.543018 0.839721i \(-0.317281\pi\)
0.543018 + 0.839721i \(0.317281\pi\)
\(384\) 0 0
\(385\) 2.28147 0.116275
\(386\) 0.822537 + 14.3191i 0.0418660 + 0.728824i
\(387\) 0 0
\(388\) 21.7698 2.50934i 1.10519 0.127392i
\(389\) −0.560211 0.232047i −0.0284038 0.0117652i 0.368436 0.929653i \(-0.379893\pi\)
−0.396840 + 0.917888i \(0.629893\pi\)
\(390\) 0 0
\(391\) −1.68373 + 1.68373i −0.0851501 + 0.0851501i
\(392\) 17.8221 3.09857i 0.900150 0.156501i
\(393\) 0 0
\(394\) 0.0578135 0.165902i 0.00291260 0.00835804i
\(395\) 6.27324 + 2.59846i 0.315641 + 0.130743i
\(396\) 0 0
\(397\) 6.50947 + 15.7153i 0.326701 + 0.788726i 0.998833 + 0.0482949i \(0.0153787\pi\)
−0.672132 + 0.740431i \(0.734621\pi\)
\(398\) −8.85544 7.89334i −0.443883 0.395657i
\(399\) 0 0
\(400\) −12.8217 7.96514i −0.641087 0.398257i
\(401\) −31.5480 −1.57543 −0.787717 0.616038i \(-0.788737\pi\)
−0.787717 + 0.616038i \(0.788737\pi\)
\(402\) 0 0
\(403\) −30.3586 + 12.5749i −1.51227 + 0.626403i
\(404\) −3.50734 1.00073i −0.174497 0.0497881i
\(405\) 0 0
\(406\) 2.68200 7.69630i 0.133105 0.381961i
\(407\) 12.6678 12.6678i 0.627918 0.627918i
\(408\) 0 0
\(409\) 7.70292 + 7.70292i 0.380885 + 0.380885i 0.871421 0.490536i \(-0.163199\pi\)
−0.490536 + 0.871421i \(0.663199\pi\)
\(410\) 16.8707 8.15115i 0.833186 0.402556i
\(411\) 0 0
\(412\) −5.24819 + 6.61570i −0.258560 + 0.325932i
\(413\) 2.30249 + 5.55871i 0.113298 + 0.273526i
\(414\) 0 0
\(415\) 3.05888i 0.150155i
\(416\) 25.8083 20.8531i 1.26535 1.02241i
\(417\) 0 0
\(418\) 0.620180 + 10.7964i 0.0303340 + 0.528069i
\(419\) 37.3177 15.4575i 1.82309 0.755149i 0.849223 0.528034i \(-0.177071\pi\)
0.973868 0.227116i \(-0.0729295\pi\)
\(420\) 0 0
\(421\) 10.7666 25.9930i 0.524734 1.26682i −0.410199 0.911996i \(-0.634541\pi\)
0.934933 0.354824i \(-0.115459\pi\)
\(422\) 14.6989 + 30.4229i 0.715532 + 1.48096i
\(423\) 0 0
\(424\) −22.2312 4.98437i −1.07964 0.242063i
\(425\) 1.37430 + 1.37430i 0.0666633 + 0.0666633i
\(426\) 0 0
\(427\) −1.72719 + 4.16981i −0.0835846 + 0.201791i
\(428\) 12.0627 + 3.44177i 0.583072 + 0.166364i
\(429\) 0 0
\(430\) −4.02158 3.58465i −0.193938 0.172867i
\(431\) 25.8873i 1.24695i 0.781844 + 0.623474i \(0.214279\pi\)
−0.781844 + 0.623474i \(0.785721\pi\)
\(432\) 0 0
\(433\) 14.8695i 0.714583i −0.933993 0.357292i \(-0.883700\pi\)
0.933993 0.357292i \(-0.116300\pi\)
\(434\) −4.09852 + 4.59808i −0.196735 + 0.220715i
\(435\) 0 0
\(436\) −2.80256 5.04032i −0.134218 0.241388i
\(437\) 5.10549 12.3257i 0.244229 0.589620i
\(438\) 0 0
\(439\) 4.49359 + 4.49359i 0.214467 + 0.214467i 0.806162 0.591695i \(-0.201541\pi\)
−0.591695 + 0.806162i \(0.701541\pi\)
\(440\) −4.77707 + 6.78774i −0.227738 + 0.323593i
\(441\) 0 0
\(442\) −3.84680 + 1.85859i −0.182974 + 0.0884043i
\(443\) −1.53078 + 3.69564i −0.0727297 + 0.175585i −0.956064 0.293159i \(-0.905293\pi\)
0.883334 + 0.468744i \(0.155293\pi\)
\(444\) 0 0
\(445\) −0.950336 + 0.393642i −0.0450502 + 0.0186604i
\(446\) 2.14626 0.123288i 0.101628 0.00583786i
\(447\) 0 0
\(448\) 2.65545 5.62420i 0.125458 0.265719i
\(449\) 7.05855i 0.333114i −0.986032 0.166557i \(-0.946735\pi\)
0.986032 0.166557i \(-0.0532649\pi\)
\(450\) 0 0
\(451\) 12.1319 + 29.2890i 0.571270 + 1.37917i
\(452\) 34.5889 3.98696i 1.62693 0.187531i
\(453\) 0 0
\(454\) 11.7799 + 24.3814i 0.552860 + 1.14428i
\(455\) −3.57087 3.57087i −0.167405 0.167405i
\(456\) 0 0
\(457\) −21.4531 + 21.4531i −1.00353 + 1.00353i −0.00353826 + 0.999994i \(0.501126\pi\)
−0.999994 + 0.00353826i \(0.998874\pi\)
\(458\) 32.5197 + 11.3324i 1.51954 + 0.529529i
\(459\) 0 0
\(460\) 8.94945 4.97614i 0.417270 0.232014i
\(461\) −14.0545 + 5.82154i −0.654581 + 0.271136i −0.685156 0.728396i \(-0.740266\pi\)
0.0305752 + 0.999532i \(0.490266\pi\)
\(462\) 0 0
\(463\) 23.0001 1.06890 0.534452 0.845199i \(-0.320518\pi\)
0.534452 + 0.845199i \(0.320518\pi\)
\(464\) 17.2820 + 24.0943i 0.802297 + 1.11855i
\(465\) 0 0
\(466\) −8.62327 + 9.67435i −0.399465 + 0.448155i
\(467\) 5.98019 + 14.4375i 0.276730 + 0.668086i 0.999741 0.0227507i \(-0.00724239\pi\)
−0.723011 + 0.690837i \(0.757242\pi\)
\(468\) 0 0
\(469\) −0.748426 0.310008i −0.0345591 0.0143149i
\(470\) −3.47329 1.21037i −0.160211 0.0558300i
\(471\) 0 0
\(472\) −21.3591 4.78884i −0.983133 0.220424i
\(473\) 6.44543 6.44543i 0.296361 0.296361i
\(474\) 0 0
\(475\) −10.0605 4.16721i −0.461609 0.191205i
\(476\) −0.497705 + 0.627392i −0.0228123 + 0.0287565i
\(477\) 0 0
\(478\) 40.3023 2.31510i 1.84339 0.105890i
\(479\) −21.2145 −0.969314 −0.484657 0.874704i \(-0.661056\pi\)
−0.484657 + 0.874704i \(0.661056\pi\)
\(480\) 0 0
\(481\) −39.6542 −1.80807
\(482\) −38.7101 + 2.22363i −1.76319 + 0.101284i
\(483\) 0 0
\(484\) 6.23303 + 4.94462i 0.283319 + 0.224755i
\(485\) 11.2104 + 4.64351i 0.509039 + 0.210851i
\(486\) 0 0
\(487\) 3.68805 3.68805i 0.167121 0.167121i −0.618591 0.785713i \(-0.712296\pi\)
0.785713 + 0.618591i \(0.212296\pi\)
\(488\) −8.78934 13.8696i −0.397875 0.627848i
\(489\) 0 0
\(490\) 9.45853 + 3.29610i 0.427293 + 0.148902i
\(491\) 36.8386 + 15.2590i 1.66250 + 0.688631i 0.998264 0.0588902i \(-0.0187562\pi\)
0.664238 + 0.747521i \(0.268756\pi\)
\(492\) 0 0
\(493\) −1.46105 3.52728i −0.0658023 0.158861i
\(494\) 15.9274 17.8688i 0.716608 0.803954i
\(495\) 0 0
\(496\) −5.09831 21.8214i −0.228921 0.979810i
\(497\) 5.97180 0.267872
\(498\) 0 0
\(499\) −30.4487 + 12.6123i −1.36307 + 0.564603i −0.939901 0.341447i \(-0.889083\pi\)
−0.423171 + 0.906050i \(0.639083\pi\)
\(500\) −9.44329 16.9835i −0.422317 0.759524i
\(501\) 0 0
\(502\) −25.8477 9.00736i −1.15364 0.402018i
\(503\) −20.2577 + 20.2577i −0.903248 + 0.903248i −0.995716 0.0924678i \(-0.970524\pi\)
0.0924678 + 0.995716i \(0.470524\pi\)
\(504\) 0 0
\(505\) −1.42805 1.42805i −0.0635476 0.0635476i
\(506\) 7.53732 + 15.6003i 0.335075 + 0.693518i
\(507\) 0 0
\(508\) 3.85596 + 33.4525i 0.171081 + 1.48421i
\(509\) 5.53680 + 13.3670i 0.245414 + 0.592483i 0.997804 0.0662355i \(-0.0210988\pi\)
−0.752390 + 0.658718i \(0.771099\pi\)
\(510\) 0 0
\(511\) 3.28136i 0.145159i
\(512\) 11.1728 + 19.6766i 0.493772 + 0.869592i
\(513\) 0 0
\(514\) −18.6995 + 1.07416i −0.824801 + 0.0473792i
\(515\) −4.31996 + 1.78939i −0.190360 + 0.0788498i
\(516\) 0 0
\(517\) 2.38158 5.74964i 0.104742 0.252869i
\(518\) −6.69288 + 3.23369i −0.294068 + 0.142080i
\(519\) 0 0
\(520\) 18.1008 3.14702i 0.793772 0.138006i
\(521\) 31.1921 + 31.1921i 1.36655 + 1.36655i 0.865306 + 0.501244i \(0.167124\pi\)
0.501244 + 0.865306i \(0.332876\pi\)
\(522\) 0 0
\(523\) 6.74337 16.2799i 0.294867 0.711872i −0.705129 0.709079i \(-0.749111\pi\)
0.999996 0.00279304i \(-0.000889052\pi\)
\(524\) −14.9894 + 8.33452i −0.654815 + 0.364095i
\(525\) 0 0
\(526\) −8.82855 + 9.90465i −0.384943 + 0.431863i
\(527\) 2.88539i 0.125690i
\(528\) 0 0
\(529\) 1.62554i 0.0706757i
\(530\) −9.41730 8.39416i −0.409062 0.364619i
\(531\) 0 0
\(532\) 1.23110 4.31475i 0.0533750 0.187068i
\(533\) 26.8537 64.8305i 1.16316 2.80812i
\(534\) 0 0
\(535\) 4.91145 + 4.91145i 0.212341 + 0.212341i
\(536\) 2.48942 1.57757i 0.107526 0.0681408i
\(537\) 0 0
\(538\) −2.27510 4.70885i −0.0980863 0.203013i
\(539\) −6.48557 + 15.6575i −0.279353 + 0.674418i
\(540\) 0 0
\(541\) −18.2188 + 7.54647i −0.783287 + 0.324448i −0.738241 0.674537i \(-0.764343\pi\)
−0.0450459 + 0.998985i \(0.514343\pi\)
\(542\) −2.38090 41.4478i −0.102268 1.78034i
\(543\) 0 0
\(544\) −0.824467 2.79442i −0.0353487 0.119810i
\(545\) 3.19332i 0.136787i
\(546\) 0 0
\(547\) 1.49915 + 3.61926i 0.0640988 + 0.154748i 0.952683 0.303965i \(-0.0983105\pi\)
−0.888584 + 0.458713i \(0.848311\pi\)
\(548\) 3.60723 + 2.86159i 0.154093 + 0.122241i
\(549\) 0 0
\(550\) 12.7333 6.15213i 0.542950 0.262328i
\(551\) 15.1258 + 15.1258i 0.644383 + 0.644383i
\(552\) 0 0
\(553\) 3.37067 3.37067i 0.143335 0.143335i
\(554\) 7.96005 22.8423i 0.338190 0.970476i
\(555\) 0 0
\(556\) 0.854028 2.99319i 0.0362189 0.126939i
\(557\) 22.8281 9.45572i 0.967259 0.400652i 0.157568 0.987508i \(-0.449635\pi\)
0.809691 + 0.586856i \(0.199635\pi\)
\(558\) 0 0
\(559\) −20.1763 −0.853366
\(560\) 2.79844 2.00723i 0.118256 0.0848208i
\(561\) 0 0
\(562\) 7.18317 + 6.40275i 0.303004 + 0.270084i
\(563\) −13.1864 31.8347i −0.555740 1.34167i −0.913111 0.407712i \(-0.866327\pi\)
0.357371 0.933963i \(-0.383673\pi\)
\(564\) 0 0
\(565\) 17.8117 + 7.37784i 0.749343 + 0.310388i
\(566\) −7.69292 + 22.0757i −0.323358 + 0.927912i
\(567\) 0 0
\(568\) −12.5041 + 17.7670i −0.524659 + 0.745488i
\(569\) 10.7413 10.7413i 0.450298 0.450298i −0.445155 0.895454i \(-0.646851\pi\)
0.895454 + 0.445155i \(0.146851\pi\)
\(570\) 0 0
\(571\) −4.73710 1.96217i −0.198241 0.0821143i 0.281354 0.959604i \(-0.409217\pi\)
−0.479595 + 0.877490i \(0.659217\pi\)
\(572\) 3.55959 + 30.8813i 0.148834 + 1.29121i
\(573\) 0 0
\(574\) −0.754346 13.1320i −0.0314858 0.548120i
\(575\) −17.4463 −0.727561
\(576\) 0 0
\(577\) 33.2804 1.38548 0.692740 0.721187i \(-0.256403\pi\)
0.692740 + 0.721187i \(0.256403\pi\)
\(578\) −1.35724 23.6275i −0.0564538 0.982776i
\(579\) 0 0
\(580\) 1.88005 + 16.3104i 0.0780647 + 0.677252i
\(581\) 1.98396 + 0.821782i 0.0823085 + 0.0340933i
\(582\) 0 0
\(583\) 15.0932 15.0932i 0.625098 0.625098i
\(584\) −9.76254 6.87067i −0.403977 0.284310i
\(585\) 0 0
\(586\) 10.5370 30.2372i 0.435280 1.24909i
\(587\) −20.7958 8.61391i −0.858335 0.355534i −0.0902789 0.995917i \(-0.528776\pi\)
−0.768056 + 0.640382i \(0.778776\pi\)
\(588\) 0 0
\(589\) −6.18663 14.9358i −0.254916 0.615421i
\(590\) −9.04787 8.06486i −0.372495 0.332025i
\(591\) 0 0
\(592\) 4.39319 26.6832i 0.180559 1.09667i
\(593\) −31.7996 −1.30585 −0.652927 0.757420i \(-0.726459\pi\)
−0.652927 + 0.757420i \(0.726459\pi\)
\(594\) 0 0
\(595\) −0.409678 + 0.169694i −0.0167952 + 0.00695679i
\(596\) 10.9527 38.3868i 0.448639 1.57238i
\(597\) 0 0
\(598\) 12.6198 36.2141i 0.516064 1.48090i
\(599\) −12.0277 + 12.0277i −0.491440 + 0.491440i −0.908760 0.417319i \(-0.862970\pi\)
0.417319 + 0.908760i \(0.362970\pi\)
\(600\) 0 0
\(601\) 13.1841 + 13.1841i 0.537791 + 0.537791i 0.922880 0.385089i \(-0.125829\pi\)
−0.385089 + 0.922880i \(0.625829\pi\)
\(602\) −3.40538 + 1.64532i −0.138793 + 0.0670582i
\(603\) 0 0
\(604\) 13.3542 + 10.5938i 0.543377 + 0.431057i
\(605\) 1.68588 + 4.07008i 0.0685409 + 0.165472i
\(606\) 0 0
\(607\) 29.6602i 1.20387i −0.798545 0.601935i \(-0.794397\pi\)
0.798545 0.601935i \(-0.205603\pi\)
\(608\) 10.2593 + 12.6972i 0.416070 + 0.514938i
\(609\) 0 0
\(610\) −0.521417 9.07707i −0.0211115 0.367520i
\(611\) −12.7267 + 5.27156i −0.514866 + 0.213264i
\(612\) 0 0
\(613\) −3.95354 + 9.54469i −0.159682 + 0.385507i −0.983389 0.181509i \(-0.941902\pi\)
0.823707 + 0.567015i \(0.191902\pi\)
\(614\) 15.9200 + 32.9502i 0.642478 + 1.32976i
\(615\) 0 0
\(616\) 3.11907 + 4.92191i 0.125671 + 0.198309i
\(617\) −3.41501 3.41501i −0.137483 0.137483i 0.635016 0.772499i \(-0.280994\pi\)
−0.772499 + 0.635016i \(0.780994\pi\)
\(618\) 0 0
\(619\) 10.1724 24.5583i 0.408863 0.987082i −0.576575 0.817044i \(-0.695611\pi\)
0.985438 0.170038i \(-0.0543890\pi\)
\(620\) 3.40450 11.9321i 0.136728 0.479203i
\(621\) 0 0
\(622\) 20.2210 + 18.0240i 0.810787 + 0.722698i
\(623\) 0.722131i 0.0289316i
\(624\) 0 0
\(625\) 8.10804i 0.324322i
\(626\) −5.72645 + 6.42444i −0.228875 + 0.256772i
\(627\) 0 0
\(628\) −26.3030 + 14.6252i −1.04960 + 0.583609i
\(629\) −1.33250 + 3.21694i −0.0531302 + 0.128268i
\(630\) 0 0
\(631\) −22.4300 22.4300i −0.892924 0.892924i 0.101874 0.994797i \(-0.467516\pi\)
−0.994797 + 0.101874i \(0.967516\pi\)
\(632\) 2.97058 + 17.0859i 0.118163 + 0.679642i
\(633\) 0 0
\(634\) −39.9627 + 19.3081i −1.58712 + 0.766823i
\(635\) −7.13543 + 17.2265i −0.283161 + 0.683611i
\(636\) 0 0
\(637\) 34.6575 14.3556i 1.37318 0.568790i
\(638\) −27.7340 + 1.59313i −1.09800 + 0.0630727i
\(639\) 0 0
\(640\) 0.112288 + 12.5286i 0.00443855 + 0.495238i
\(641\) 21.6739i 0.856067i −0.903763 0.428034i \(-0.859206\pi\)
0.903763 0.428034i \(-0.140794\pi\)
\(642\) 0 0
\(643\) −9.95208 24.0264i −0.392472 0.947511i −0.989400 0.145216i \(-0.953612\pi\)
0.596928 0.802295i \(-0.296388\pi\)
\(644\) −0.823164 7.14138i −0.0324372 0.281410i
\(645\) 0 0
\(646\) −0.914392 1.89255i −0.0359763 0.0744614i
\(647\) 17.5596 + 17.5596i 0.690340 + 0.690340i 0.962307 0.271967i \(-0.0876740\pi\)
−0.271967 + 0.962307i \(0.587674\pi\)
\(648\) 0 0
\(649\) 14.5011 14.5011i 0.569219 0.569219i
\(650\) −29.5587 10.3006i −1.15939 0.404022i
\(651\) 0 0
\(652\) −14.7722 26.5674i −0.578525 1.04046i
\(653\) −27.2736 + 11.2971i −1.06730 + 0.442089i −0.846036 0.533125i \(-0.821017\pi\)
−0.221261 + 0.975215i \(0.571017\pi\)
\(654\) 0 0
\(655\) −9.49660 −0.371063
\(656\) 40.6493 + 25.2522i 1.58709 + 0.985933i
\(657\) 0 0
\(658\) −1.71814 + 1.92756i −0.0669802 + 0.0751443i
\(659\) 9.50276 + 22.9417i 0.370175 + 0.893681i 0.993720 + 0.111894i \(0.0356917\pi\)
−0.623545 + 0.781787i \(0.714308\pi\)
\(660\) 0 0
\(661\) −12.4726 5.16632i −0.485128 0.200947i 0.126694 0.991942i \(-0.459563\pi\)
−0.611822 + 0.790995i \(0.709563\pi\)
\(662\) −44.1889 15.3989i −1.71745 0.598495i
\(663\) 0 0
\(664\) −6.59904 + 4.18189i −0.256093 + 0.162289i
\(665\) 1.75680 1.75680i 0.0681258 0.0681258i
\(666\) 0 0
\(667\) 31.6626 + 13.1151i 1.22598 + 0.507819i
\(668\) −32.2115 25.5532i −1.24630 0.988682i
\(669\) 0 0
\(670\) 1.62922 0.0935876i 0.0629422 0.00361560i
\(671\) 15.3836 0.593878
\(672\) 0 0
\(673\) −24.4439 −0.942245 −0.471122 0.882068i \(-0.656151\pi\)
−0.471122 + 0.882068i \(0.656151\pi\)
\(674\) −24.9532 + 1.43340i −0.961163 + 0.0552123i
\(675\) 0 0
\(676\) 26.6042 33.5364i 1.02324 1.28986i
\(677\) −29.4250 12.1882i −1.13089 0.468431i −0.262808 0.964848i \(-0.584649\pi\)
−0.868084 + 0.496417i \(0.834649\pi\)
\(678\) 0 0
\(679\) 6.02346 6.02346i 0.231159 0.231159i
\(680\) 0.352939 1.57417i 0.0135346 0.0603667i
\(681\) 0 0
\(682\) 19.8253 + 6.90870i 0.759150 + 0.264548i
\(683\) −5.00090 2.07144i −0.191354 0.0792614i 0.284949 0.958543i \(-0.408023\pi\)
−0.476303 + 0.879281i \(0.658023\pi\)
\(684\) 0 0
\(685\) 0.975668 + 2.35547i 0.0372784 + 0.0899979i
\(686\) 9.79995 10.9945i 0.374164 0.419770i
\(687\) 0 0
\(688\) 2.23528 13.5766i 0.0852193 0.517603i
\(689\) −47.2467 −1.79995
\(690\) 0 0
\(691\) 29.6641 12.2873i 1.12848 0.467431i 0.261214 0.965281i \(-0.415877\pi\)
0.867263 + 0.497850i \(0.165877\pi\)
\(692\) 7.82950 4.35342i 0.297633 0.165492i
\(693\) 0 0
\(694\) −27.6716 9.64298i −1.05040 0.366042i
\(695\) 1.21871 1.21871i 0.0462283 0.0462283i
\(696\) 0 0
\(697\) −4.35699 4.35699i −0.165033 0.165033i
\(698\) −0.914738 1.89327i −0.0346233 0.0716613i
\(699\) 0 0
\(700\) −5.82895 + 0.671884i −0.220313 + 0.0253948i
\(701\) 3.53387 + 8.53152i 0.133472 + 0.322231i 0.976459 0.215704i \(-0.0692046\pi\)
−0.842986 + 0.537935i \(0.819205\pi\)
\(702\) 0 0
\(703\) 19.5091i 0.735799i
\(704\) −21.1743 1.02602i −0.798037 0.0386695i
\(705\) 0 0
\(706\) 3.73728 0.214681i 0.140654 0.00807964i
\(707\) −1.30987 + 0.542567i −0.0492628 + 0.0204053i
\(708\) 0 0
\(709\) 7.15181 17.2660i 0.268592 0.648438i −0.730826 0.682564i \(-0.760865\pi\)
0.999418 + 0.0341261i \(0.0108648\pi\)
\(710\) −10.8320 + 5.23350i −0.406517 + 0.196410i
\(711\) 0 0
\(712\) −2.14845 1.51203i −0.0805166 0.0566659i
\(713\) −18.3146 18.3146i −0.685886 0.685886i
\(714\) 0 0
\(715\) −6.58699 + 15.9024i −0.246340 + 0.594716i
\(716\) 24.4131 + 43.9062i 0.912359 + 1.64085i
\(717\) 0 0
\(718\) −17.7307 + 19.8919i −0.661705 + 0.742359i
\(719\) 14.3048i 0.533478i −0.963769 0.266739i \(-0.914054\pi\)
0.963769 0.266739i \(-0.0859462\pi\)
\(720\) 0 0
\(721\) 3.28261i 0.122251i
\(722\) −11.2673 10.0431i −0.419324 0.373767i
\(723\) 0 0
\(724\) −8.43115 2.40561i −0.313341 0.0894037i
\(725\) 10.7048 25.8437i 0.397567 0.959812i
\(726\) 0 0
\(727\) 22.6384 + 22.6384i 0.839610 + 0.839610i 0.988807 0.149197i \(-0.0476690\pi\)
−0.149197 + 0.988807i \(0.547669\pi\)
\(728\) 2.82173 12.5854i 0.104580 0.466447i
\(729\) 0 0
\(730\) −2.87568 5.95190i −0.106434 0.220290i
\(731\) −0.677983 + 1.63680i −0.0250761 + 0.0605391i
\(732\) 0 0
\(733\) −18.9242 + 7.83864i −0.698980 + 0.289527i −0.703736 0.710462i \(-0.748486\pi\)
0.00475595 + 0.999989i \(0.498486\pi\)
\(734\) 0.236294 + 4.11353i 0.00872178 + 0.151833i
\(735\) 0 0
\(736\) 22.9703 + 12.5039i 0.846696 + 0.460901i
\(737\) 2.76116i 0.101709i
\(738\) 0 0
\(739\) −13.0834 31.5861i −0.481281 1.16191i −0.959001 0.283403i \(-0.908537\pi\)
0.477720 0.878512i \(-0.341463\pi\)
\(740\) 9.30602 11.7309i 0.342096 0.431235i
\(741\) 0 0
\(742\) −7.97435 + 3.85283i −0.292748 + 0.141442i
\(743\) 6.99193 + 6.99193i 0.256509 + 0.256509i 0.823633 0.567124i \(-0.191944\pi\)
−0.567124 + 0.823633i \(0.691944\pi\)
\(744\) 0 0
\(745\) 15.6296 15.6296i 0.572625 0.572625i
\(746\) −13.2487 + 38.0188i −0.485071 + 1.39197i
\(747\) 0 0
\(748\) 2.62485 + 0.748932i 0.0959740 + 0.0273837i
\(749\) 4.50500 1.86603i 0.164609 0.0681833i
\(750\) 0 0
\(751\) −36.9772 −1.34932 −0.674658 0.738130i \(-0.735709\pi\)
−0.674658 + 0.738130i \(0.735709\pi\)
\(752\) −2.13727 9.14778i −0.0779381 0.333585i
\(753\) 0 0
\(754\) 45.9017 + 40.9147i 1.67164 + 1.49002i
\(755\) 3.61200 + 8.72014i 0.131454 + 0.317358i
\(756\) 0 0
\(757\) −0.561827 0.232716i −0.0204199 0.00845822i 0.372450 0.928052i \(-0.378518\pi\)
−0.392870 + 0.919594i \(0.628518\pi\)
\(758\) −14.7201 + 42.2410i −0.534658 + 1.53426i
\(759\) 0 0
\(760\) 1.54827 + 8.90523i 0.0561618 + 0.323027i
\(761\) 25.2794 25.2794i 0.916379 0.916379i −0.0803851 0.996764i \(-0.525615\pi\)
0.996764 + 0.0803851i \(0.0256150\pi\)
\(762\) 0 0
\(763\) −2.07115 0.857899i −0.0749807 0.0310580i
\(764\) 43.9729 5.06862i 1.59089 0.183376i
\(765\) 0 0
\(766\) 1.72378 + 30.0084i 0.0622828 + 1.08425i
\(767\) −45.3932 −1.63905
\(768\) 0 0
\(769\) 21.2233 0.765331 0.382666 0.923887i \(-0.375006\pi\)
0.382666 + 0.923887i \(0.375006\pi\)
\(770\) 0.185035 + 3.22118i 0.00666820 + 0.116083i
\(771\) 0 0
\(772\) −20.1503 + 2.32266i −0.725224 + 0.0835943i
\(773\) −37.9146 15.7047i −1.36369 0.564860i −0.423623 0.905839i \(-0.639242\pi\)
−0.940071 + 0.340978i \(0.889242\pi\)
\(774\) 0 0
\(775\) −14.9487 + 14.9487i −0.536975 + 0.536975i
\(776\) 5.30850 + 30.5330i 0.190564 + 1.09607i
\(777\) 0 0
\(778\) 0.282189 0.809773i 0.0101170 0.0290318i
\(779\) 31.8953 + 13.2115i 1.14277 + 0.473350i
\(780\) 0 0
\(781\) −7.78939 18.8052i −0.278726 0.672904i
\(782\) −2.51380 2.24068i −0.0898932 0.0801267i
\(783\) 0 0
\(784\) 5.82025 + 24.9114i 0.207866 + 0.889694i
\(785\) −16.6644 −0.594777
\(786\) 0 0
\(787\) 5.68394 2.35436i 0.202610 0.0839240i −0.279071 0.960271i \(-0.590026\pi\)
0.481681 + 0.876347i \(0.340026\pi\)
\(788\) 0.238924 + 0.0681708i 0.00851132 + 0.00242848i