Properties

Label 1512.2.c.e.757.11
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 20
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.11
Root \(0.328272 - 1.37559i\)
Character \(\chi\) = 1512.757
Dual form 1512.2.c.e.757.12

$q$-expansion

\(f(q)\) \(=\) \(q+(0.328272 - 1.37559i) q^{2} +(-1.78447 - 0.903134i) q^{4} -0.512447i q^{5} -1.00000 q^{7} +(-1.82813 + 2.15822i) q^{8} +O(q^{10})\) \(q+(0.328272 - 1.37559i) q^{2} +(-1.78447 - 0.903134i) q^{4} -0.512447i q^{5} -1.00000 q^{7} +(-1.82813 + 2.15822i) q^{8} +(-0.704915 - 0.168222i) q^{10} +1.82890i q^{11} +1.80627i q^{13} +(-0.328272 + 1.37559i) q^{14} +(2.36870 + 3.22324i) q^{16} +8.11456 q^{17} +3.43946i q^{19} +(-0.462808 + 0.914448i) q^{20} +(2.51580 + 0.600376i) q^{22} -3.65626 q^{23} +4.73740 q^{25} +(2.48468 + 0.592948i) q^{26} +(1.78447 + 0.903134i) q^{28} +7.98990i q^{29} -1.56895 q^{31} +(5.21142 - 2.20025i) q^{32} +(2.66378 - 11.1623i) q^{34} +0.512447i q^{35} -8.44370i q^{37} +(4.73127 + 1.12908i) q^{38} +(1.10598 + 0.936820i) q^{40} -2.30828 q^{41} -10.7778i q^{43} +(1.65174 - 3.26362i) q^{44} +(-1.20025 + 5.02951i) q^{46} +11.3833 q^{47} +1.00000 q^{49} +(1.55516 - 6.51670i) q^{50} +(1.63130 - 3.22324i) q^{52} +8.87795i q^{53} +0.937212 q^{55} +(1.82813 - 2.15822i) q^{56} +(10.9908 + 2.62286i) q^{58} +2.50234i q^{59} -5.31310i q^{61} +(-0.515043 + 2.15822i) q^{62} +(-1.31587 - 7.89104i) q^{64} +0.925616 q^{65} +6.44648i q^{67} +(-14.4802 - 7.32853i) q^{68} +(0.704915 + 0.168222i) q^{70} +9.10975 q^{71} +9.24419 q^{73} +(-11.6150 - 2.77183i) q^{74} +(3.10629 - 6.13762i) q^{76} -1.82890i q^{77} +3.64300 q^{79} +(1.65174 - 1.21383i) q^{80} +(-0.757745 + 3.17524i) q^{82} +4.53105i q^{83} -4.15828i q^{85} +(-14.8258 - 3.53806i) q^{86} +(-3.94717 - 3.34346i) q^{88} -11.7359 q^{89} -1.80627i q^{91} +(6.52451 + 3.30209i) q^{92} +(3.73684 - 15.6588i) q^{94} +1.76254 q^{95} +15.2323 q^{97} +(0.328272 - 1.37559i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 2q^{4} - 20q^{7} + O(q^{10}) \) \( 20q - 2q^{4} - 20q^{7} - 12q^{10} - 14q^{16} + 8q^{22} - 28q^{25} + 2q^{28} + 36q^{31} - 6q^{34} - 16q^{40} - 18q^{46} + 20q^{49} + 94q^{52} + 48q^{55} + 66q^{58} + 22q^{64} + 12q^{70} + 12q^{76} + 64q^{79} - 92q^{88} - 24q^{94} + 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.328272 1.37559i 0.232124 0.972686i
\(3\) 0 0
\(4\) −1.78447 0.903134i −0.892237 0.451567i
\(5\) 0.512447i 0.229173i −0.993413 0.114587i \(-0.963446\pi\)
0.993413 0.114587i \(-0.0365543\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −1.82813 + 2.15822i −0.646342 + 0.763048i
\(9\) 0 0
\(10\) −0.704915 0.168222i −0.222914 0.0531965i
\(11\) 1.82890i 0.551433i 0.961239 + 0.275716i \(0.0889151\pi\)
−0.961239 + 0.275716i \(0.911085\pi\)
\(12\) 0 0
\(13\) 1.80627i 0.500968i 0.968121 + 0.250484i \(0.0805898\pi\)
−0.968121 + 0.250484i \(0.919410\pi\)
\(14\) −0.328272 + 1.37559i −0.0877345 + 0.367641i
\(15\) 0 0
\(16\) 2.36870 + 3.22324i 0.592175 + 0.805810i
\(17\) 8.11456 1.96807 0.984035 0.177977i \(-0.0569552\pi\)
0.984035 + 0.177977i \(0.0569552\pi\)
\(18\) 0 0
\(19\) 3.43946i 0.789066i 0.918882 + 0.394533i \(0.129094\pi\)
−0.918882 + 0.394533i \(0.870906\pi\)
\(20\) −0.462808 + 0.914448i −0.103487 + 0.204477i
\(21\) 0 0
\(22\) 2.51580 + 0.600376i 0.536371 + 0.128001i
\(23\) −3.65626 −0.762384 −0.381192 0.924496i \(-0.624486\pi\)
−0.381192 + 0.924496i \(0.624486\pi\)
\(24\) 0 0
\(25\) 4.73740 0.947480
\(26\) 2.48468 + 0.592948i 0.487285 + 0.116287i
\(27\) 0 0
\(28\) 1.78447 + 0.903134i 0.337234 + 0.170676i
\(29\) 7.98990i 1.48369i 0.670573 + 0.741843i \(0.266048\pi\)
−0.670573 + 0.741843i \(0.733952\pi\)
\(30\) 0 0
\(31\) −1.56895 −0.281792 −0.140896 0.990024i \(-0.544998\pi\)
−0.140896 + 0.990024i \(0.544998\pi\)
\(32\) 5.21142 2.20025i 0.921258 0.388953i
\(33\) 0 0
\(34\) 2.66378 11.1623i 0.456835 1.91431i
\(35\) 0.512447i 0.0866193i
\(36\) 0 0
\(37\) 8.44370i 1.38814i −0.719909 0.694068i \(-0.755817\pi\)
0.719909 0.694068i \(-0.244183\pi\)
\(38\) 4.73127 + 1.12908i 0.767513 + 0.183161i
\(39\) 0 0
\(40\) 1.10598 + 0.936820i 0.174870 + 0.148124i
\(41\) −2.30828 −0.360493 −0.180247 0.983621i \(-0.557690\pi\)
−0.180247 + 0.983621i \(0.557690\pi\)
\(42\) 0 0
\(43\) 10.7778i 1.64360i −0.569773 0.821802i \(-0.692969\pi\)
0.569773 0.821802i \(-0.307031\pi\)
\(44\) 1.65174 3.26362i 0.249009 0.492009i
\(45\) 0 0
\(46\) −1.20025 + 5.02951i −0.176967 + 0.741560i
\(47\) 11.3833 1.66043 0.830216 0.557442i \(-0.188217\pi\)
0.830216 + 0.557442i \(0.188217\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 1.55516 6.51670i 0.219932 0.921600i
\(51\) 0 0
\(52\) 1.63130 3.22324i 0.226221 0.446983i
\(53\) 8.87795i 1.21948i 0.792601 + 0.609740i \(0.208726\pi\)
−0.792601 + 0.609740i \(0.791274\pi\)
\(54\) 0 0
\(55\) 0.937212 0.126374
\(56\) 1.82813 2.15822i 0.244294 0.288405i
\(57\) 0 0
\(58\) 10.9908 + 2.62286i 1.44316 + 0.344399i
\(59\) 2.50234i 0.325778i 0.986644 + 0.162889i \(0.0520812\pi\)
−0.986644 + 0.162889i \(0.947919\pi\)
\(60\) 0 0
\(61\) 5.31310i 0.680272i −0.940376 0.340136i \(-0.889527\pi\)
0.940376 0.340136i \(-0.110473\pi\)
\(62\) −0.515043 + 2.15822i −0.0654105 + 0.274095i
\(63\) 0 0
\(64\) −1.31587 7.89104i −0.164484 0.986380i
\(65\) 0.925616 0.114809
\(66\) 0 0
\(67\) 6.44648i 0.787562i 0.919204 + 0.393781i \(0.128833\pi\)
−0.919204 + 0.393781i \(0.871167\pi\)
\(68\) −14.4802 7.32853i −1.75598 0.888715i
\(69\) 0 0
\(70\) 0.704915 + 0.168222i 0.0842534 + 0.0201064i
\(71\) 9.10975 1.08113 0.540564 0.841303i \(-0.318211\pi\)
0.540564 + 0.841303i \(0.318211\pi\)
\(72\) 0 0
\(73\) 9.24419 1.08195 0.540975 0.841039i \(-0.318055\pi\)
0.540975 + 0.841039i \(0.318055\pi\)
\(74\) −11.6150 2.77183i −1.35022 0.322219i
\(75\) 0 0
\(76\) 3.10629 6.13762i 0.356316 0.704034i
\(77\) 1.82890i 0.208422i
\(78\) 0 0
\(79\) 3.64300 0.409870 0.204935 0.978776i \(-0.434302\pi\)
0.204935 + 0.978776i \(0.434302\pi\)
\(80\) 1.65174 1.21383i 0.184670 0.135711i
\(81\) 0 0
\(82\) −0.757745 + 3.17524i −0.0836790 + 0.350647i
\(83\) 4.53105i 0.497348i 0.968587 + 0.248674i \(0.0799948\pi\)
−0.968587 + 0.248674i \(0.920005\pi\)
\(84\) 0 0
\(85\) 4.15828i 0.451029i
\(86\) −14.8258 3.53806i −1.59871 0.381519i
\(87\) 0 0
\(88\) −3.94717 3.34346i −0.420770 0.356414i
\(89\) −11.7359 −1.24401 −0.622003 0.783015i \(-0.713681\pi\)
−0.622003 + 0.783015i \(0.713681\pi\)
\(90\) 0 0
\(91\) 1.80627i 0.189348i
\(92\) 6.52451 + 3.30209i 0.680227 + 0.344267i
\(93\) 0 0
\(94\) 3.73684 15.6588i 0.385425 1.61508i
\(95\) 1.76254 0.180833
\(96\) 0 0
\(97\) 15.2323 1.54661 0.773303 0.634037i \(-0.218603\pi\)
0.773303 + 0.634037i \(0.218603\pi\)
\(98\) 0.328272 1.37559i 0.0331605 0.138955i
\(99\) 0 0
\(100\) −8.45377 4.27850i −0.845377 0.427850i
\(101\) 8.13524i 0.809487i 0.914430 + 0.404744i \(0.132639\pi\)
−0.914430 + 0.404744i \(0.867361\pi\)
\(102\) 0 0
\(103\) −15.9816 −1.57471 −0.787356 0.616498i \(-0.788551\pi\)
−0.787356 + 0.616498i \(0.788551\pi\)
\(104\) −3.89833 3.30209i −0.382263 0.323797i
\(105\) 0 0
\(106\) 12.2124 + 2.91439i 1.18617 + 0.283070i
\(107\) 12.1695i 1.17647i 0.808690 + 0.588235i \(0.200177\pi\)
−0.808690 + 0.588235i \(0.799823\pi\)
\(108\) 0 0
\(109\) 10.8452i 1.03878i 0.854537 + 0.519391i \(0.173841\pi\)
−0.854537 + 0.519391i \(0.826159\pi\)
\(110\) 0.307661 1.28922i 0.0293343 0.122922i
\(111\) 0 0
\(112\) −2.36870 3.22324i −0.223821 0.304567i
\(113\) 3.07563 0.289331 0.144665 0.989481i \(-0.453789\pi\)
0.144665 + 0.989481i \(0.453789\pi\)
\(114\) 0 0
\(115\) 1.87364i 0.174718i
\(116\) 7.21595 14.2578i 0.669984 1.32380i
\(117\) 0 0
\(118\) 3.44219 + 0.821450i 0.316879 + 0.0756206i
\(119\) −8.11456 −0.743860
\(120\) 0 0
\(121\) 7.65514 0.695922
\(122\) −7.30862 1.74414i −0.661692 0.157907i
\(123\) 0 0
\(124\) 2.79975 + 1.41697i 0.251425 + 0.127248i
\(125\) 4.98990i 0.446310i
\(126\) 0 0
\(127\) 6.67524 0.592332 0.296166 0.955137i \(-0.404292\pi\)
0.296166 + 0.955137i \(0.404292\pi\)
\(128\) −11.2868 0.780319i −0.997619 0.0689711i
\(129\) 0 0
\(130\) 0.303854 1.27326i 0.0266498 0.111673i
\(131\) 1.26995i 0.110956i 0.998460 + 0.0554778i \(0.0176682\pi\)
−0.998460 + 0.0554778i \(0.982332\pi\)
\(132\) 0 0
\(133\) 3.43946i 0.298239i
\(134\) 8.86768 + 2.11620i 0.766051 + 0.182812i
\(135\) 0 0
\(136\) −14.8345 + 17.5130i −1.27205 + 1.50173i
\(137\) 19.8507 1.69596 0.847980 0.530029i \(-0.177819\pi\)
0.847980 + 0.530029i \(0.177819\pi\)
\(138\) 0 0
\(139\) 13.9758i 1.18541i −0.805419 0.592706i \(-0.798059\pi\)
0.805419 0.592706i \(-0.201941\pi\)
\(140\) 0.462808 0.914448i 0.0391144 0.0772850i
\(141\) 0 0
\(142\) 2.99048 12.5312i 0.250955 1.05160i
\(143\) −3.30348 −0.276251
\(144\) 0 0
\(145\) 4.09440 0.340021
\(146\) 3.03461 12.7162i 0.251146 1.05240i
\(147\) 0 0
\(148\) −7.62579 + 15.0676i −0.626836 + 1.23855i
\(149\) 11.8561i 0.971286i −0.874157 0.485643i \(-0.838585\pi\)
0.874157 0.485643i \(-0.161415\pi\)
\(150\) 0 0
\(151\) −13.4949 −1.09820 −0.549100 0.835757i \(-0.685029\pi\)
−0.549100 + 0.835757i \(0.685029\pi\)
\(152\) −7.42312 6.28778i −0.602095 0.510006i
\(153\) 0 0
\(154\) −2.51580 0.600376i −0.202729 0.0483797i
\(155\) 0.804003i 0.0645791i
\(156\) 0 0
\(157\) 9.88593i 0.788983i −0.918900 0.394492i \(-0.870921\pi\)
0.918900 0.394492i \(-0.129079\pi\)
\(158\) 1.19590 5.01126i 0.0951404 0.398675i
\(159\) 0 0
\(160\) −1.12751 2.67058i −0.0891376 0.211128i
\(161\) 3.65626 0.288154
\(162\) 0 0
\(163\) 4.43706i 0.347537i −0.984786 0.173769i \(-0.944405\pi\)
0.984786 0.173769i \(-0.0555945\pi\)
\(164\) 4.11907 + 2.08469i 0.321645 + 0.162787i
\(165\) 0 0
\(166\) 6.23286 + 1.48742i 0.483763 + 0.115446i
\(167\) −5.38391 −0.416619 −0.208310 0.978063i \(-0.566796\pi\)
−0.208310 + 0.978063i \(0.566796\pi\)
\(168\) 0 0
\(169\) 9.73740 0.749031
\(170\) −5.72007 1.36505i −0.438709 0.104694i
\(171\) 0 0
\(172\) −9.73382 + 19.2328i −0.742197 + 1.46648i
\(173\) 17.9611i 1.36556i 0.730624 + 0.682780i \(0.239229\pi\)
−0.730624 + 0.682780i \(0.760771\pi\)
\(174\) 0 0
\(175\) −4.73740 −0.358114
\(176\) −5.89497 + 4.33211i −0.444350 + 0.326545i
\(177\) 0 0
\(178\) −3.85258 + 16.1438i −0.288763 + 1.21003i
\(179\) 16.0482i 1.19950i 0.800188 + 0.599749i \(0.204733\pi\)
−0.800188 + 0.599749i \(0.795267\pi\)
\(180\) 0 0
\(181\) 5.91861i 0.439927i −0.975508 0.219964i \(-0.929406\pi\)
0.975508 0.219964i \(-0.0705938\pi\)
\(182\) −2.48468 0.592948i −0.184176 0.0439522i
\(183\) 0 0
\(184\) 6.68413 7.89104i 0.492761 0.581735i
\(185\) −4.32695 −0.318123
\(186\) 0 0
\(187\) 14.8407i 1.08526i
\(188\) −20.3133 10.2807i −1.48150 0.749796i
\(189\) 0 0
\(190\) 0.578593 2.42452i 0.0419755 0.175893i
\(191\) 0.0697837 0.00504937 0.00252469 0.999997i \(-0.499196\pi\)
0.00252469 + 0.999997i \(0.499196\pi\)
\(192\) 0 0
\(193\) −8.24356 −0.593384 −0.296692 0.954973i \(-0.595884\pi\)
−0.296692 + 0.954973i \(0.595884\pi\)
\(194\) 5.00034 20.9533i 0.359004 1.50436i
\(195\) 0 0
\(196\) −1.78447 0.903134i −0.127462 0.0645095i
\(197\) 1.91295i 0.136292i −0.997675 0.0681459i \(-0.978292\pi\)
0.997675 0.0681459i \(-0.0217083\pi\)
\(198\) 0 0
\(199\) −3.70579 −0.262696 −0.131348 0.991336i \(-0.541931\pi\)
−0.131348 + 0.991336i \(0.541931\pi\)
\(200\) −8.66059 + 10.2244i −0.612396 + 0.722972i
\(201\) 0 0
\(202\) 11.1907 + 2.67058i 0.787377 + 0.187901i
\(203\) 7.98990i 0.560781i
\(204\) 0 0
\(205\) 1.18287i 0.0826153i
\(206\) −5.24631 + 21.9840i −0.365528 + 1.53170i
\(207\) 0 0
\(208\) −5.82203 + 4.27850i −0.403685 + 0.296661i
\(209\) −6.29041 −0.435117
\(210\) 0 0
\(211\) 25.6006i 1.76242i 0.472724 + 0.881210i \(0.343271\pi\)
−0.472724 + 0.881210i \(0.656729\pi\)
\(212\) 8.01798 15.8425i 0.550677 1.08807i
\(213\) 0 0
\(214\) 16.7402 + 3.99491i 1.14434 + 0.273087i
\(215\) −5.52307 −0.376670
\(216\) 0 0
\(217\) 1.56895 0.106507
\(218\) 14.9185 + 3.56018i 1.01041 + 0.241126i
\(219\) 0 0
\(220\) −1.67243 0.846428i −0.112755 0.0570661i
\(221\) 14.6571i 0.985941i
\(222\) 0 0
\(223\) −14.2639 −0.955182 −0.477591 0.878582i \(-0.658490\pi\)
−0.477591 + 0.878582i \(0.658490\pi\)
\(224\) −5.21142 + 2.20025i −0.348203 + 0.147010i
\(225\) 0 0
\(226\) 1.00964 4.23079i 0.0671605 0.281428i
\(227\) 2.58553i 0.171608i −0.996312 0.0858039i \(-0.972654\pi\)
0.996312 0.0858039i \(-0.0273458\pi\)
\(228\) 0 0
\(229\) 27.5800i 1.82254i 0.411813 + 0.911268i \(0.364896\pi\)
−0.411813 + 0.911268i \(0.635104\pi\)
\(230\) 2.57735 + 0.615064i 0.169946 + 0.0405561i
\(231\) 0 0
\(232\) −17.2440 14.6066i −1.13212 0.958969i
\(233\) 5.61196 0.367652 0.183826 0.982959i \(-0.441152\pi\)
0.183826 + 0.982959i \(0.441152\pi\)
\(234\) 0 0
\(235\) 5.83336i 0.380526i
\(236\) 2.25995 4.46537i 0.147110 0.290671i
\(237\) 0 0
\(238\) −2.66378 + 11.1623i −0.172668 + 0.723543i
\(239\) 1.69275 0.109495 0.0547476 0.998500i \(-0.482565\pi\)
0.0547476 + 0.998500i \(0.482565\pi\)
\(240\) 0 0
\(241\) −22.6246 −1.45738 −0.728689 0.684845i \(-0.759870\pi\)
−0.728689 + 0.684845i \(0.759870\pi\)
\(242\) 2.51297 10.5303i 0.161540 0.676913i
\(243\) 0 0
\(244\) −4.79844 + 9.48109i −0.307188 + 0.606964i
\(245\) 0.512447i 0.0327390i
\(246\) 0 0
\(247\) −6.21258 −0.395297
\(248\) 2.86825 3.38615i 0.182134 0.215020i
\(249\) 0 0
\(250\) −6.86403 1.63805i −0.434120 0.103599i
\(251\) 18.1391i 1.14493i −0.819930 0.572464i \(-0.805988\pi\)
0.819930 0.572464i \(-0.194012\pi\)
\(252\) 0 0
\(253\) 6.68693i 0.420403i
\(254\) 2.19130 9.18237i 0.137494 0.576153i
\(255\) 0 0
\(256\) −4.77853 + 15.2698i −0.298658 + 0.954360i
\(257\) −8.62562 −0.538051 −0.269026 0.963133i \(-0.586702\pi\)
−0.269026 + 0.963133i \(0.586702\pi\)
\(258\) 0 0
\(259\) 8.44370i 0.524666i
\(260\) −1.65174 0.835955i −0.102436 0.0518437i
\(261\) 0 0
\(262\) 1.74692 + 0.416888i 0.107925 + 0.0257554i
\(263\) 2.79262 0.172201 0.0861003 0.996286i \(-0.472559\pi\)
0.0861003 + 0.996286i \(0.472559\pi\)
\(264\) 0 0
\(265\) 4.54948 0.279472
\(266\) −4.73127 1.12908i −0.290093 0.0692282i
\(267\) 0 0
\(268\) 5.82203 11.5036i 0.355637 0.702693i
\(269\) 17.8391i 1.08767i −0.839192 0.543836i \(-0.816971\pi\)
0.839192 0.543836i \(-0.183029\pi\)
\(270\) 0 0
\(271\) −22.5304 −1.36863 −0.684313 0.729188i \(-0.739898\pi\)
−0.684313 + 0.729188i \(0.739898\pi\)
\(272\) 19.2209 + 26.1552i 1.16544 + 1.58589i
\(273\) 0 0
\(274\) 6.51643 27.3063i 0.393672 1.64964i
\(275\) 8.66421i 0.522472i
\(276\) 0 0
\(277\) 2.18249i 0.131133i −0.997848 0.0655666i \(-0.979115\pi\)
0.997848 0.0655666i \(-0.0208855\pi\)
\(278\) −19.2249 4.58787i −1.15303 0.275162i
\(279\) 0 0
\(280\) −1.10598 0.936820i −0.0660947 0.0559857i
\(281\) 7.54152 0.449890 0.224945 0.974372i \(-0.427780\pi\)
0.224945 + 0.974372i \(0.427780\pi\)
\(282\) 0 0
\(283\) 11.5743i 0.688021i 0.938966 + 0.344011i \(0.111786\pi\)
−0.938966 + 0.344011i \(0.888214\pi\)
\(284\) −16.2561 8.22732i −0.964623 0.488202i
\(285\) 0 0
\(286\) −1.08444 + 4.54422i −0.0641243 + 0.268705i
\(287\) 2.30828 0.136254
\(288\) 0 0
\(289\) 48.8460 2.87330
\(290\) 1.34408 5.63220i 0.0789269 0.330734i
\(291\) 0 0
\(292\) −16.4960 8.34874i −0.965356 0.488573i
\(293\) 8.12045i 0.474402i −0.971461 0.237201i \(-0.923770\pi\)
0.971461 0.237201i \(-0.0762300\pi\)
\(294\) 0 0
\(295\) 1.28232 0.0746595
\(296\) 18.2234 + 15.4362i 1.05921 + 0.897211i
\(297\) 0 0
\(298\) −16.3090 3.89202i −0.944757 0.225458i
\(299\) 6.60419i 0.381930i
\(300\) 0 0
\(301\) 10.7778i 0.621224i
\(302\) −4.43000 + 18.5634i −0.254918 + 1.06820i
\(303\) 0 0
\(304\) −11.0862 + 8.14704i −0.635837 + 0.467265i
\(305\) −2.72268 −0.155900
\(306\) 0 0
\(307\) 2.73852i 0.156295i 0.996942 + 0.0781477i \(0.0249006\pi\)
−0.996942 + 0.0781477i \(0.975099\pi\)
\(308\) −1.65174 + 3.26362i −0.0941165 + 0.185962i
\(309\) 0 0
\(310\) 1.10598 + 0.263932i 0.0628152 + 0.0149903i
\(311\) 17.9488 1.01778 0.508891 0.860831i \(-0.330055\pi\)
0.508891 + 0.860831i \(0.330055\pi\)
\(312\) 0 0
\(313\) 5.95819 0.336777 0.168388 0.985721i \(-0.446144\pi\)
0.168388 + 0.985721i \(0.446144\pi\)
\(314\) −13.5990 3.24528i −0.767433 0.183142i
\(315\) 0 0
\(316\) −6.50084 3.29012i −0.365701 0.185084i
\(317\) 21.6033i 1.21336i 0.794945 + 0.606682i \(0.207500\pi\)
−0.794945 + 0.606682i \(0.792500\pi\)
\(318\) 0 0
\(319\) −14.6127 −0.818154
\(320\) −4.04374 + 0.674313i −0.226052 + 0.0376952i
\(321\) 0 0
\(322\) 1.20025 5.02951i 0.0668873 0.280283i
\(323\) 27.9097i 1.55294i
\(324\) 0 0
\(325\) 8.55701i 0.474657i
\(326\) −6.10356 1.45656i −0.338045 0.0806716i
\(327\) 0 0
\(328\) 4.21984 4.98179i 0.233002 0.275073i
\(329\) −11.3833 −0.627584
\(330\) 0 0
\(331\) 12.6066i 0.692920i 0.938065 + 0.346460i \(0.112616\pi\)
−0.938065 + 0.346460i \(0.887384\pi\)
\(332\) 4.09215 8.08555i 0.224586 0.443752i
\(333\) 0 0
\(334\) −1.76739 + 7.40603i −0.0967072 + 0.405240i
\(335\) 3.30348 0.180488
\(336\) 0 0
\(337\) −28.9818 −1.57874 −0.789370 0.613917i \(-0.789593\pi\)
−0.789370 + 0.613917i \(0.789593\pi\)
\(338\) 3.19652 13.3946i 0.173868 0.728572i
\(339\) 0 0
\(340\) −3.75548 + 7.42034i −0.203670 + 0.402425i
\(341\) 2.86945i 0.155389i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 23.2610 + 19.7033i 1.25415 + 1.06233i
\(345\) 0 0
\(346\) 24.7071 + 5.89614i 1.32826 + 0.316979i
\(347\) 12.2675i 0.658553i 0.944234 + 0.329277i \(0.106805\pi\)
−0.944234 + 0.329277i \(0.893195\pi\)
\(348\) 0 0
\(349\) 28.3289i 1.51641i −0.652016 0.758205i \(-0.726077\pi\)
0.652016 0.758205i \(-0.273923\pi\)
\(350\) −1.55516 + 6.51670i −0.0831266 + 0.348332i
\(351\) 0 0
\(352\) 4.02403 + 9.53115i 0.214481 + 0.508012i
\(353\) −1.40996 −0.0750444 −0.0375222 0.999296i \(-0.511946\pi\)
−0.0375222 + 0.999296i \(0.511946\pi\)
\(354\) 0 0
\(355\) 4.66826i 0.247766i
\(356\) 20.9425 + 10.5991i 1.10995 + 0.561752i
\(357\) 0 0
\(358\) 22.0757 + 5.26818i 1.16674 + 0.278432i
\(359\) 17.0581 0.900290 0.450145 0.892955i \(-0.351372\pi\)
0.450145 + 0.892955i \(0.351372\pi\)
\(360\) 0 0
\(361\) 7.17014 0.377376
\(362\) −8.14156 1.94292i −0.427911 0.102117i
\(363\) 0 0
\(364\) −1.63130 + 3.22324i −0.0855034 + 0.168944i
\(365\) 4.73715i 0.247954i
\(366\) 0 0
\(367\) −25.4558 −1.32878 −0.664390 0.747386i \(-0.731308\pi\)
−0.664390 + 0.747386i \(0.731308\pi\)
\(368\) −8.66059 11.7850i −0.451464 0.614336i
\(369\) 0 0
\(370\) −1.42042 + 5.95209i −0.0738440 + 0.309434i
\(371\) 8.87795i 0.460920i
\(372\) 0 0
\(373\) 20.3176i 1.05201i −0.850483 0.526003i \(-0.823690\pi\)
0.850483 0.526003i \(-0.176310\pi\)
\(374\) 20.4146 + 4.87179i 1.05562 + 0.251914i
\(375\) 0 0
\(376\) −20.8103 + 24.5678i −1.07321 + 1.26699i
\(377\) −14.4319 −0.743280
\(378\) 0 0
\(379\) 11.8832i 0.610397i −0.952289 0.305198i \(-0.901277\pi\)
0.952289 0.305198i \(-0.0987228\pi\)
\(380\) −3.14521 1.59181i −0.161346 0.0816580i
\(381\) 0 0
\(382\) 0.0229081 0.0959935i 0.00117208 0.00491146i
\(383\) −18.6261 −0.951749 −0.475874 0.879513i \(-0.657868\pi\)
−0.475874 + 0.879513i \(0.657868\pi\)
\(384\) 0 0
\(385\) −0.937212 −0.0477647
\(386\) −2.70613 + 11.3397i −0.137739 + 0.577177i
\(387\) 0 0
\(388\) −27.1816 13.7568i −1.37994 0.698396i
\(389\) 20.7636i 1.05276i 0.850251 + 0.526378i \(0.176450\pi\)
−0.850251 + 0.526378i \(0.823550\pi\)
\(390\) 0 0
\(391\) −29.6690 −1.50042
\(392\) −1.82813 + 2.15822i −0.0923346 + 0.109007i
\(393\) 0 0
\(394\) −2.63142 0.627967i −0.132569 0.0316365i
\(395\) 1.86684i 0.0939311i
\(396\) 0 0
\(397\) 20.9726i 1.05259i −0.850303 0.526293i \(-0.823582\pi\)
0.850303 0.526293i \(-0.176418\pi\)
\(398\) −1.21651 + 5.09763i −0.0609780 + 0.255521i
\(399\) 0 0
\(400\) 11.2215 + 15.2698i 0.561074 + 0.763488i
\(401\) −0.476166 −0.0237786 −0.0118893 0.999929i \(-0.503785\pi\)
−0.0118893 + 0.999929i \(0.503785\pi\)
\(402\) 0 0
\(403\) 2.83394i 0.141169i
\(404\) 7.34721 14.5171i 0.365537 0.722255i
\(405\) 0 0
\(406\) −10.9908 2.62286i −0.545464 0.130170i
\(407\) 15.4427 0.765464
\(408\) 0 0
\(409\) −2.08700 −0.103196 −0.0515978 0.998668i \(-0.516431\pi\)
−0.0515978 + 0.998668i \(0.516431\pi\)
\(410\) 1.62714 + 0.388304i 0.0803588 + 0.0191770i
\(411\) 0 0
\(412\) 28.5187 + 14.4335i 1.40502 + 0.711088i
\(413\) 2.50234i 0.123132i
\(414\) 0 0
\(415\) 2.32192 0.113979
\(416\) 3.97424 + 9.41322i 0.194853 + 0.461521i
\(417\) 0 0
\(418\) −2.06497 + 8.65300i −0.101001 + 0.423232i
\(419\) 15.8104i 0.772388i −0.922418 0.386194i \(-0.873790\pi\)
0.922418 0.386194i \(-0.126210\pi\)
\(420\) 0 0
\(421\) 21.8824i 1.06648i 0.845963 + 0.533241i \(0.179026\pi\)
−0.845963 + 0.533241i \(0.820974\pi\)
\(422\) 35.2159 + 8.40398i 1.71428 + 0.409099i
\(423\) 0 0
\(424\) −19.1606 16.2301i −0.930522 0.788202i
\(425\) 38.4419 1.86471
\(426\) 0 0
\(427\) 5.31310i 0.257119i
\(428\) 10.9907 21.7162i 0.531255 1.04969i
\(429\) 0 0
\(430\) −1.81307 + 7.59745i −0.0874340 + 0.366382i
\(431\) 25.3231 1.21977 0.609885 0.792490i \(-0.291216\pi\)
0.609885 + 0.792490i \(0.291216\pi\)
\(432\) 0 0
\(433\) 30.9197 1.48590 0.742952 0.669344i \(-0.233425\pi\)
0.742952 + 0.669344i \(0.233425\pi\)
\(434\) 0.515043 2.15822i 0.0247228 0.103598i
\(435\) 0 0
\(436\) 9.79467 19.3530i 0.469080 0.926840i
\(437\) 12.5756i 0.601571i
\(438\) 0 0
\(439\) −8.75669 −0.417934 −0.208967 0.977923i \(-0.567010\pi\)
−0.208967 + 0.977923i \(0.567010\pi\)
\(440\) −1.71335 + 2.02271i −0.0816806 + 0.0964291i
\(441\) 0 0
\(442\) 20.1620 + 4.81151i 0.959011 + 0.228860i
\(443\) 27.6190i 1.31222i −0.754666 0.656109i \(-0.772201\pi\)
0.754666 0.656109i \(-0.227799\pi\)
\(444\) 0 0
\(445\) 6.01404i 0.285093i
\(446\) −4.68244 + 19.6212i −0.221720 + 0.929092i
\(447\) 0 0
\(448\) 1.31587 + 7.89104i 0.0621689 + 0.372817i
\(449\) 13.6994 0.646516 0.323258 0.946311i \(-0.395222\pi\)
0.323258 + 0.946311i \(0.395222\pi\)
\(450\) 0 0
\(451\) 4.22161i 0.198788i
\(452\) −5.48838 2.77770i −0.258152 0.130652i
\(453\) 0 0
\(454\) −3.55662 0.848758i −0.166920 0.0398342i
\(455\) −0.925616 −0.0433935
\(456\) 0 0
\(457\) 5.85452 0.273863 0.136931 0.990581i \(-0.456276\pi\)
0.136931 + 0.990581i \(0.456276\pi\)
\(458\) 37.9386 + 9.05374i 1.77276 + 0.423054i
\(459\) 0 0
\(460\) 1.69215 3.34346i 0.0788968 0.155890i
\(461\) 2.42544i 0.112964i 0.998404 + 0.0564821i \(0.0179884\pi\)
−0.998404 + 0.0564821i \(0.982012\pi\)
\(462\) 0 0
\(463\) −1.26366 −0.0587273 −0.0293636 0.999569i \(-0.509348\pi\)
−0.0293636 + 0.999569i \(0.509348\pi\)
\(464\) −25.7533 + 18.9257i −1.19557 + 0.878602i
\(465\) 0 0
\(466\) 1.84225 7.71974i 0.0853407 0.357610i
\(467\) 27.2456i 1.26078i 0.776280 + 0.630388i \(0.217104\pi\)
−0.776280 + 0.630388i \(0.782896\pi\)
\(468\) 0 0
\(469\) 6.44648i 0.297671i
\(470\) −8.02429 1.91493i −0.370133 0.0883291i
\(471\) 0 0
\(472\) −5.40062 4.57462i −0.248584 0.210564i
\(473\) 19.7115 0.906338
\(474\) 0 0
\(475\) 16.2941i 0.747624i
\(476\) 14.4802 + 7.32853i 0.663700 + 0.335903i
\(477\) 0 0
\(478\) 0.555684 2.32853i 0.0254164 0.106504i
\(479\) −27.4035 −1.25210 −0.626050 0.779783i \(-0.715329\pi\)
−0.626050 + 0.779783i \(0.715329\pi\)
\(480\) 0 0
\(481\) 15.2516 0.695412
\(482\) −7.42703 + 31.1221i −0.338292 + 1.41757i
\(483\) 0 0
\(484\) −13.6604 6.91361i −0.620927 0.314255i
\(485\) 7.80574i 0.354440i
\(486\) 0 0
\(487\) 27.0530 1.22589 0.612944 0.790126i \(-0.289985\pi\)
0.612944 + 0.790126i \(0.289985\pi\)
\(488\) 11.4669 + 9.71304i 0.519080 + 0.439689i
\(489\) 0 0
\(490\) −0.704915 0.168222i −0.0318448 0.00759950i
\(491\) 29.2739i 1.32111i −0.750776 0.660556i \(-0.770320\pi\)
0.750776 0.660556i \(-0.229680\pi\)
\(492\) 0 0
\(493\) 64.8345i 2.92000i
\(494\) −2.03942 + 8.54594i −0.0917577 + 0.384500i
\(495\) 0 0
\(496\) −3.71637 5.05710i −0.166870 0.227070i
\(497\) −9.10975 −0.408628
\(498\) 0 0
\(499\) 39.8348i 1.78325i −0.452775 0.891625i \(-0.649566\pi\)
0.452775 0.891625i \(-0.350434\pi\)
\(500\) −4.50654 + 8.90435i −0.201539 + 0.398214i
\(501\) 0 0
\(502\) −24.9518 5.95455i −1.11366 0.265765i
\(503\) −36.3079 −1.61889 −0.809444 0.587197i \(-0.800231\pi\)
−0.809444 + 0.587197i \(0.800231\pi\)
\(504\) 0 0
\(505\) 4.16888 0.185513
\(506\) −9.19844 2.19513i −0.408921 0.0975856i
\(507\) 0 0
\(508\) −11.9118 6.02863i −0.528500 0.267477i
\(509\) 22.2853i 0.987778i −0.869525 0.493889i \(-0.835575\pi\)
0.869525 0.493889i \(-0.164425\pi\)
\(510\) 0 0
\(511\) −9.24419 −0.408939
\(512\) 19.4362 + 11.5859i 0.858968 + 0.512030i
\(513\) 0 0
\(514\) −2.83155 + 11.8653i −0.124894 + 0.523355i
\(515\) 8.18971i 0.360882i
\(516\) 0 0
\(517\) 20.8190i 0.915617i
\(518\) 11.6150 + 2.77183i 0.510336 + 0.121787i
\(519\) 0 0
\(520\) −1.69215 + 1.99769i −0.0742056 + 0.0876044i
\(521\) −28.8909 −1.26573 −0.632866 0.774261i \(-0.718122\pi\)
−0.632866 + 0.774261i \(0.718122\pi\)
\(522\) 0 0
\(523\) 22.7284i 0.993842i 0.867796 + 0.496921i \(0.165536\pi\)
−0.867796 + 0.496921i \(0.834464\pi\)
\(524\) 1.14693 2.26619i 0.0501039 0.0989988i
\(525\) 0 0
\(526\) 0.916741 3.84149i 0.0399718 0.167497i
\(527\) −12.7313 −0.554585
\(528\) 0 0
\(529\) −9.63174 −0.418771
\(530\) 1.49347 6.25820i 0.0648721 0.271839i
\(531\) 0 0
\(532\) −3.10629 + 6.13762i −0.134675 + 0.266100i
\(533\) 4.16938i 0.180596i
\(534\) 0 0
\(535\) 6.23622 0.269615
\(536\) −13.9129 11.7850i −0.600948 0.509035i
\(537\) 0 0
\(538\) −24.5393 5.85610i −1.05796 0.252474i
\(539\) 1.82890i 0.0787761i
\(540\) 0 0
\(541\) 12.7291i 0.547268i −0.961834 0.273634i \(-0.911774\pi\)
0.961834 0.273634i \(-0.0882257\pi\)
\(542\) −7.39612 + 30.9926i −0.317690 + 1.33124i
\(543\) 0 0
\(544\) 42.2884 17.8541i 1.81310 0.765486i
\(545\) 5.55759 0.238061
\(546\) 0 0
\(547\) 28.7154i 1.22778i −0.789391 0.613890i \(-0.789604\pi\)
0.789391 0.613890i \(-0.210396\pi\)
\(548\) −35.4231 17.9278i −1.51320 0.765839i
\(549\) 0 0
\(550\) 11.9184 + 2.84422i 0.508201 + 0.121278i
\(551\) −27.4809 −1.17073
\(552\) 0 0
\(553\) −3.64300 −0.154916
\(554\) −3.00221 0.716452i −0.127552 0.0304391i
\(555\) 0 0
\(556\) −12.6220 + 24.9395i −0.535293 + 1.05767i
\(557\) 7.36295i 0.311978i −0.987759 0.155989i \(-0.950143\pi\)
0.987759 0.155989i \(-0.0498565\pi\)
\(558\) 0 0
\(559\) 19.4676 0.823394
\(560\) −1.65174 + 1.21383i −0.0697987 + 0.0512938i
\(561\) 0 0
\(562\) 2.47567 10.3740i 0.104430 0.437601i
\(563\) 15.9713i 0.673110i 0.941664 + 0.336555i \(0.109262\pi\)
−0.941664 + 0.336555i \(0.890738\pi\)
\(564\) 0 0
\(565\) 1.57610i 0.0663068i
\(566\) 15.9215 + 3.79952i 0.669229 + 0.159706i
\(567\) 0 0
\(568\) −16.6538 + 19.6609i −0.698779 + 0.824953i
\(569\) −26.9769 −1.13093 −0.565465 0.824772i \(-0.691303\pi\)
−0.565465 + 0.824772i \(0.691303\pi\)
\(570\) 0 0
\(571\) 35.5632i 1.48827i 0.668027 + 0.744137i \(0.267139\pi\)
−0.668027 + 0.744137i \(0.732861\pi\)
\(572\) 5.89497 + 2.98348i 0.246481 + 0.124746i
\(573\) 0 0
\(574\) 0.757745 3.17524i 0.0316277 0.132532i
\(575\) −17.3212 −0.722343
\(576\) 0 0
\(577\) −23.4330 −0.975528 −0.487764 0.872976i \(-0.662187\pi\)
−0.487764 + 0.872976i \(0.662187\pi\)
\(578\) 16.0348 67.1919i 0.666960 2.79482i
\(579\) 0 0
\(580\) −7.30635 3.69779i −0.303380 0.153542i
\(581\) 4.53105i 0.187980i
\(582\) 0 0
\(583\) −16.2369 −0.672462
\(584\) −16.8996 + 19.9510i −0.699310 + 0.825580i
\(585\) 0 0
\(586\) −11.1704 2.66572i −0.461444 0.110120i
\(587\) 37.1113i 1.53175i −0.642991 0.765874i \(-0.722307\pi\)
0.642991 0.765874i \(-0.277693\pi\)
\(588\) 0 0
\(589\) 5.39633i 0.222352i
\(590\) 0.420950 1.76394i 0.0173302 0.0726202i
\(591\) 0 0
\(592\) 27.2161 20.0006i 1.11857 0.822019i
\(593\) 23.8317 0.978650 0.489325 0.872102i \(-0.337243\pi\)
0.489325 + 0.872102i \(0.337243\pi\)
\(594\) 0 0
\(595\) 4.15828i 0.170473i
\(596\) −10.7076 + 21.1568i −0.438601 + 0.866618i
\(597\) 0 0
\(598\) −9.08463 2.16797i −0.371498 0.0886550i
\(599\) 12.0955 0.494210 0.247105 0.968989i \(-0.420521\pi\)
0.247105 + 0.968989i \(0.420521\pi\)
\(600\) 0 0
\(601\) 20.4752 0.835202 0.417601 0.908631i \(-0.362871\pi\)
0.417601 + 0.908631i \(0.362871\pi\)
\(602\) 14.8258 + 3.53806i 0.604256 + 0.144201i
\(603\) 0 0
\(604\) 24.0813 + 12.1877i 0.979854 + 0.495910i
\(605\) 3.92285i 0.159487i
\(606\) 0 0
\(607\) −24.0329 −0.975466 −0.487733 0.872993i \(-0.662176\pi\)
−0.487733 + 0.872993i \(0.662176\pi\)
\(608\) 7.56767 + 17.9245i 0.306909 + 0.726933i
\(609\) 0 0
\(610\) −0.893780 + 3.74528i −0.0361881 + 0.151642i
\(611\) 20.5614i 0.831824i
\(612\) 0 0
\(613\) 45.2862i 1.82909i −0.404480 0.914547i \(-0.632548\pi\)
0.404480 0.914547i \(-0.367452\pi\)
\(614\) 3.76706 + 0.898979i 0.152026 + 0.0362798i
\(615\) 0 0
\(616\) 3.94717 + 3.34346i 0.159036 + 0.134712i
\(617\) −20.4393 −0.822855 −0.411428 0.911442i \(-0.634970\pi\)
−0.411428 + 0.911442i \(0.634970\pi\)
\(618\) 0 0
\(619\) 15.3328i 0.616277i 0.951342 + 0.308138i \(0.0997060\pi\)
−0.951342 + 0.308138i \(0.900294\pi\)
\(620\) 0.726122 1.43472i 0.0291618 0.0576199i
\(621\) 0 0
\(622\) 5.89209 24.6901i 0.236251 0.989983i
\(623\) 11.7359 0.470190
\(624\) 0 0
\(625\) 21.1299 0.845197
\(626\) 1.95591 8.19600i 0.0781738 0.327578i
\(627\) 0 0
\(628\) −8.92832 + 17.6412i −0.356279 + 0.703960i
\(629\) 68.5169i 2.73195i
\(630\) 0 0
\(631\) 20.4869 0.815572 0.407786 0.913078i \(-0.366301\pi\)
0.407786 + 0.913078i \(0.366301\pi\)
\(632\) −6.65989 + 7.86242i −0.264916 + 0.312750i
\(633\) 0 0
\(634\) 29.7172 + 7.09177i 1.18022 + 0.281650i
\(635\) 3.42070i 0.135747i
\(636\) 0 0
\(637\) 1.80627i 0.0715669i
\(638\) −4.79694 + 20.1010i −0.189913 + 0.795807i
\(639\) 0 0
\(640\) −0.399872 + 5.78387i −0.0158063 + 0.228627i
\(641\) −42.6868 −1.68603 −0.843013 0.537893i \(-0.819220\pi\)
−0.843013 + 0.537893i \(0.819220\pi\)
\(642\) 0 0
\(643\) 29.7804i 1.17442i 0.809434 + 0.587211i \(0.199774\pi\)
−0.809434 + 0.587211i \(0.800226\pi\)
\(644\) −6.52451 3.30209i −0.257102 0.130121i
\(645\) 0 0
\(646\) 38.3922 + 9.16197i 1.51052 + 0.360473i
\(647\) 6.63482 0.260842 0.130421 0.991459i \(-0.458367\pi\)
0.130421 + 0.991459i \(0.458367\pi\)
\(648\) 0 0
\(649\) −4.57653 −0.179644
\(650\) 11.7709 + 2.80903i 0.461693 + 0.110179i
\(651\) 0 0
\(652\) −4.00726 + 7.91782i −0.156936 + 0.310086i
\(653\) 4.48147i 0.175373i −0.996148 0.0876867i \(-0.972053\pi\)
0.996148 0.0876867i \(-0.0279474\pi\)
\(654\) 0 0
\(655\) 0.650779 0.0254281
\(656\) −5.46763 7.44014i −0.213475 0.290489i
\(657\) 0 0
\(658\) −3.73684 + 15.6588i −0.145677 + 0.610443i
\(659\) 49.4245i 1.92530i −0.270741 0.962652i \(-0.587269\pi\)
0.270741 0.962652i \(-0.412731\pi\)
\(660\) 0 0
\(661\) 12.5279i 0.487278i −0.969866 0.243639i \(-0.921659\pi\)
0.969866 0.243639i \(-0.0783413\pi\)
\(662\) 17.3414 + 4.13839i 0.673993 + 0.160843i
\(663\) 0 0
\(664\) −9.77903 8.28336i −0.379500 0.321457i
\(665\) −1.76254 −0.0683483
\(666\) 0 0
\(667\) 29.2132i 1.13114i
\(668\) 9.60745 + 4.86239i 0.371723 + 0.188132i
\(669\) 0 0
\(670\) 1.08444 4.54422i 0.0418956 0.175558i
\(671\) 9.71710 0.375125
\(672\) 0 0
\(673\) −26.3343 −1.01511 −0.507556 0.861619i \(-0.669451\pi\)
−0.507556 + 0.861619i \(0.669451\pi\)
\(674\) −9.51393 + 39.8670i −0.366463 + 1.53562i
\(675\) 0 0
\(676\) −17.3761 8.79417i −0.668313 0.338237i
\(677\) 14.4868i 0.556774i 0.960469 + 0.278387i \(0.0897998\pi\)
−0.960469 + 0.278387i \(0.910200\pi\)
\(678\) 0 0
\(679\) −15.2323 −0.584562
\(680\) 8.97450 + 7.60188i 0.344156 + 0.291519i
\(681\) 0 0
\(682\) −3.94717 0.941959i −0.151145 0.0360695i
\(683\) 0.0232069i 0.000887989i −1.00000 0.000443994i \(-0.999859\pi\)
1.00000 0.000443994i \(-0.000141328\pi\)
\(684\) 0 0
\(685\) 10.1724i 0.388668i
\(686\) −0.328272 + 1.37559i −0.0125335 + 0.0525201i
\(687\) 0 0
\(688\) 34.7395 25.5294i 1.32443 0.973301i
\(689\) −16.0360 −0.610921
\(690\) 0 0
\(691\) 17.2719i 0.657054i −0.944495 0.328527i \(-0.893448\pi\)
0.944495 0.328527i \(-0.106552\pi\)
\(692\) 16.2213 32.0512i 0.616642 1.21840i
\(693\) 0 0
\(694\) 16.8750 + 4.02708i 0.640566 + 0.152866i
\(695\) −7.16186 −0.271665
\(696\) 0 0
\(697\) −18.7307 −0.709476
\(698\) −38.9688 9.29958i −1.47499 0.351994i
\(699\) 0 0
\(700\) 8.45377 + 4.27850i 0.319522 + 0.161712i
\(701\) 23.9519i 0.904651i −0.891853 0.452326i \(-0.850595\pi\)
0.891853 0.452326i \(-0.149405\pi\)
\(702\) 0 0
\(703\) 29.0417 1.09533
\(704\) 14.4319 2.40659i 0.543922 0.0907017i
\(705\) 0 0
\(706\) −0.462850 + 1.93952i −0.0174196 + 0.0729947i
\(707\) 8.13524i 0.305957i
\(708\) 0 0
\(709\) 32.1099i 1.20591i −0.797774 0.602956i \(-0.793989\pi\)
0.797774 0.602956i \(-0.206011\pi\)
\(710\) −6.42160 1.53246i −0.240998 0.0575122i
\(711\) 0 0
\(712\) 21.4548 25.3288i 0.804054 0.949236i
\(713\) 5.73649 0.214833
\(714\) 0 0
\(715\) 1.69286i 0.0633092i
\(716\) 14.4937 28.6376i 0.541654 1.07024i
\(717\) 0 0
\(718\) 5.59969 23.4648i 0.208979 0.875700i
\(719\) 19.4708 0.726139 0.363070 0.931762i \(-0.381729\pi\)
0.363070 + 0.931762i \(0.381729\pi\)
\(720\) 0 0
\(721\) 15.9816 0.595185
\(722\) 2.35376 9.86314i 0.0875978 0.367068i
\(723\) 0 0
\(724\) −5.34530 + 10.5616i −0.198656 + 0.392519i
\(725\) 37.8513i 1.40576i
\(726\) 0 0
\(727\) 18.3066 0.678954 0.339477 0.940614i \(-0.389750\pi\)
0.339477 + 0.940614i \(0.389750\pi\)
\(728\) 3.89833 + 3.30209i 0.144482 + 0.122384i
\(729\) 0 0
\(730\) −6.51636 1.55508i −0.241181 0.0575560i
\(731\) 87.4573i 3.23473i
\(732\) 0 0
\(733\) 36.3167i 1.34139i −0.741735 0.670693i \(-0.765997\pi\)
0.741735 0.670693i \(-0.234003\pi\)
\(734\) −8.35642 + 35.0166i −0.308441 + 1.29249i
\(735\) 0 0
\(736\) −19.0543 + 8.04469i −0.702352 + 0.296531i
\(737\) −11.7899 −0.434288
\(738\) 0 0
\(739\) 15.6764i 0.576665i −0.957530 0.288332i \(-0.906899\pi\)
0.957530 0.288332i \(-0.0931008\pi\)
\(740\) 7.72133 + 3.90781i 0.283842 + 0.143654i
\(741\) 0 0
\(742\) −12.2124 2.91439i −0.448331 0.106990i
\(743\) −49.3578 −1.81076 −0.905381 0.424599i \(-0.860415\pi\)
−0.905381 + 0.424599i \(0.860415\pi\)
\(744\) 0 0
\(745\) −6.07560 −0.222593
\(746\) −27.9486 6.66971i −1.02327 0.244195i
\(747\) 0 0
\(748\) 13.4031 26.4828i 0.490067 0.968308i
\(749\) 12.1695i 0.444664i
\(750\) 0 0
\(751\) 29.7930 1.08716 0.543582 0.839356i \(-0.317068\pi\)
0.543582 + 0.839356i \(0.317068\pi\)
\(752\) 26.9637 + 36.6912i 0.983266 + 1.33799i
\(753\) 0 0
\(754\) −4.73759 + 19.8523i −0.172533 + 0.722979i
\(755\) 6.91542i 0.251678i
\(756\) 0 0
\(757\) 13.6736i 0.496974i 0.968635 + 0.248487i \(0.0799333\pi\)
−0.968635 + 0.248487i \(0.920067\pi\)
\(758\) −16.3463 3.90091i −0.593725 0.141687i
\(759\) 0 0
\(760\) −3.22215 + 3.80395i −0.116880 + 0.137984i
\(761\) 3.34618 0.121299 0.0606494 0.998159i \(-0.480683\pi\)
0.0606494 + 0.998159i \(0.480683\pi\)
\(762\) 0 0
\(763\) 10.8452i 0.392623i
\(764\) −0.124527 0.0630240i −0.00450524 0.00228013i
\(765\) 0 0
\(766\) −6.11443 + 25.6218i −0.220923 + 0.925753i
\(767\) −4.51990 −0.163204
\(768\) 0 0
\(769\) 10.2544 0.369783 0.184891 0.982759i \(-0.440807\pi\)
0.184891 + 0.982759i \(0.440807\pi\)
\(770\) −0.307661 + 1.28922i −0.0110873 + 0.0464601i
\(771\) 0 0
\(772\) 14.7104 + 7.44504i 0.529440 + 0.267953i
\(773\) 27.9261i 1.00443i −0.864742 0.502217i \(-0.832518\pi\)
0.864742 0.502217i \(-0.167482\pi\)
\(774\) 0 0
\(775\) −7.43274 −0.266992
\(776\) −27.8466 + 32.8747i −0.999636 + 1.18013i
\(777\) 0 0
\(778\) 28.5621 + 6.81611i 1.02400 + 0.244369i
\(779\) 7.93924i 0.284453i
\(780\) 0 0
\(781\) 16.6608i 0.596170i
\(782\) −9.73950 + 40.8122i −0.348284 + 1.45944i
\(783\) 0 0
\(784\) 2.36870 + 3.22324i 0.0845964 + 0.115116i
\(785\) −5.06601 −0.180814
\(786\) 0 0