Properties

Label 1148.2.ba.a.113.6
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.6
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.15

$q$-expansion

\(f(q)\) \(=\) \(q-1.80180i q^{3} +(-0.0346732 - 0.106713i) q^{5} +(-0.587785 - 0.809017i) q^{7} -0.246466 q^{9} +O(q^{10})\) \(q-1.80180i q^{3} +(-0.0346732 - 0.106713i) q^{5} +(-0.587785 - 0.809017i) q^{7} -0.246466 q^{9} +(-1.80145 - 0.585326i) q^{11} +(1.57378 - 2.16612i) q^{13} +(-0.192275 + 0.0624741i) q^{15} +(-6.98358 - 2.26910i) q^{17} +(2.32100 + 3.19459i) q^{19} +(-1.45768 + 1.05907i) q^{21} +(-5.14309 - 3.73667i) q^{23} +(4.03490 - 2.93153i) q^{25} -4.96130i q^{27} +(-1.26529 + 0.411117i) q^{29} +(-0.816782 + 2.51380i) q^{31} +(-1.05464 + 3.24584i) q^{33} +(-0.0659524 + 0.0907757i) q^{35} +(0.133382 + 0.410509i) q^{37} +(-3.90291 - 2.83563i) q^{39} +(1.09345 + 6.30907i) q^{41} +(-7.59057 - 5.51487i) q^{43} +(0.00854578 + 0.0263012i) q^{45} +(4.38148 - 6.03059i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-4.08846 + 12.5830i) q^{51} +(-7.51371 + 2.44135i) q^{53} +0.212534i q^{55} +(5.75599 - 4.18197i) q^{57} +(-10.7411 - 7.80386i) q^{59} +(4.91011 - 3.56741i) q^{61} +(0.144869 + 0.199395i) q^{63} +(-0.285722 - 0.0928368i) q^{65} +(-10.3008 + 3.34693i) q^{67} +(-6.73272 + 9.26680i) q^{69} +(-1.62924 - 0.529371i) q^{71} +14.0323 q^{73} +(-5.28201 - 7.27006i) q^{75} +(0.585326 + 1.80145i) q^{77} +4.58413i q^{79} -9.67865 q^{81} +7.57146 q^{83} +0.823918i q^{85} +(0.740749 + 2.27979i) q^{87} +(6.75087 + 9.29178i) q^{89} -2.67748 q^{91} +(4.52935 + 1.47167i) q^{93} +(0.260428 - 0.358449i) q^{95} +(-10.6517 + 3.46094i) q^{97} +(0.443996 + 0.144263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.80180i 1.04027i −0.854085 0.520133i \(-0.825882\pi\)
0.854085 0.520133i \(-0.174118\pi\)
\(4\) 0 0
\(5\) −0.0346732 0.106713i −0.0155063 0.0477236i 0.943004 0.332782i \(-0.107987\pi\)
−0.958510 + 0.285058i \(0.907987\pi\)
\(6\) 0 0
\(7\) −0.587785 0.809017i −0.222162 0.305780i
\(8\) 0 0
\(9\) −0.246466 −0.0821554
\(10\) 0 0
\(11\) −1.80145 0.585326i −0.543157 0.176483i 0.0245716 0.999698i \(-0.492178\pi\)
−0.567729 + 0.823216i \(0.692178\pi\)
\(12\) 0 0
\(13\) 1.57378 2.16612i 0.436488 0.600775i −0.532939 0.846154i \(-0.678912\pi\)
0.969427 + 0.245379i \(0.0789124\pi\)
\(14\) 0 0
\(15\) −0.192275 + 0.0624741i −0.0496453 + 0.0161307i
\(16\) 0 0
\(17\) −6.98358 2.26910i −1.69377 0.550339i −0.706266 0.707946i \(-0.749622\pi\)
−0.987502 + 0.157608i \(0.949622\pi\)
\(18\) 0 0
\(19\) 2.32100 + 3.19459i 0.532475 + 0.732889i 0.987505 0.157587i \(-0.0503716\pi\)
−0.455030 + 0.890476i \(0.650372\pi\)
\(20\) 0 0
\(21\) −1.45768 + 1.05907i −0.318093 + 0.231108i
\(22\) 0 0
\(23\) −5.14309 3.73667i −1.07241 0.779150i −0.0960648 0.995375i \(-0.530626\pi\)
−0.976344 + 0.216225i \(0.930626\pi\)
\(24\) 0 0
\(25\) 4.03490 2.93153i 0.806980 0.586305i
\(26\) 0 0
\(27\) 4.96130i 0.954803i
\(28\) 0 0
\(29\) −1.26529 + 0.411117i −0.234958 + 0.0763426i −0.424130 0.905602i \(-0.639420\pi\)
0.189171 + 0.981944i \(0.439420\pi\)
\(30\) 0 0
\(31\) −0.816782 + 2.51380i −0.146698 + 0.451491i −0.997225 0.0744399i \(-0.976283\pi\)
0.850527 + 0.525931i \(0.176283\pi\)
\(32\) 0 0
\(33\) −1.05464 + 3.24584i −0.183589 + 0.565029i
\(34\) 0 0
\(35\) −0.0659524 + 0.0907757i −0.0111480 + 0.0153439i
\(36\) 0 0
\(37\) 0.133382 + 0.410509i 0.0219279 + 0.0674872i 0.961422 0.275079i \(-0.0887040\pi\)
−0.939494 + 0.342566i \(0.888704\pi\)
\(38\) 0 0
\(39\) −3.90291 2.83563i −0.624966 0.454065i
\(40\) 0 0
\(41\) 1.09345 + 6.30907i 0.170769 + 0.985311i
\(42\) 0 0
\(43\) −7.59057 5.51487i −1.15755 0.841010i −0.168084 0.985773i \(-0.553758\pi\)
−0.989466 + 0.144763i \(0.953758\pi\)
\(44\) 0 0
\(45\) 0.00854578 + 0.0263012i 0.00127393 + 0.00392075i
\(46\) 0 0
\(47\) 4.38148 6.03059i 0.639105 0.879652i −0.359463 0.933159i \(-0.617040\pi\)
0.998567 + 0.0535071i \(0.0170400\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) −4.08846 + 12.5830i −0.572499 + 1.76197i
\(52\) 0 0
\(53\) −7.51371 + 2.44135i −1.03209 + 0.335346i −0.775615 0.631206i \(-0.782560\pi\)
−0.256473 + 0.966551i \(0.582560\pi\)
\(54\) 0 0
\(55\) 0.212534i 0.0286580i
\(56\) 0 0
\(57\) 5.75599 4.18197i 0.762400 0.553916i
\(58\) 0 0
\(59\) −10.7411 7.80386i −1.39837 1.01598i −0.994888 0.100989i \(-0.967799\pi\)
−0.403483 0.914987i \(-0.632201\pi\)
\(60\) 0 0
\(61\) 4.91011 3.56741i 0.628676 0.456760i −0.227266 0.973833i \(-0.572979\pi\)
0.855941 + 0.517073i \(0.172979\pi\)
\(62\) 0 0
\(63\) 0.144869 + 0.199395i 0.0182518 + 0.0251214i
\(64\) 0 0
\(65\) −0.285722 0.0928368i −0.0354395 0.0115150i
\(66\) 0 0
\(67\) −10.3008 + 3.34693i −1.25844 + 0.408893i −0.860939 0.508708i \(-0.830123\pi\)
−0.397503 + 0.917601i \(0.630123\pi\)
\(68\) 0 0
\(69\) −6.73272 + 9.26680i −0.810524 + 1.11559i
\(70\) 0 0
\(71\) −1.62924 0.529371i −0.193355 0.0628248i 0.210739 0.977542i \(-0.432413\pi\)
−0.404094 + 0.914718i \(0.632413\pi\)
\(72\) 0 0
\(73\) 14.0323 1.64236 0.821181 0.570668i \(-0.193316\pi\)
0.821181 + 0.570668i \(0.193316\pi\)
\(74\) 0 0
\(75\) −5.28201 7.27006i −0.609914 0.839475i
\(76\) 0 0
\(77\) 0.585326 + 1.80145i 0.0667041 + 0.205294i
\(78\) 0 0
\(79\) 4.58413i 0.515755i 0.966178 + 0.257877i \(0.0830231\pi\)
−0.966178 + 0.257877i \(0.916977\pi\)
\(80\) 0 0
\(81\) −9.67865 −1.07541
\(82\) 0 0
\(83\) 7.57146 0.831075 0.415538 0.909576i \(-0.363593\pi\)
0.415538 + 0.909576i \(0.363593\pi\)
\(84\) 0 0
\(85\) 0.823918i 0.0893665i
\(86\) 0 0
\(87\) 0.740749 + 2.27979i 0.0794167 + 0.244419i
\(88\) 0 0
\(89\) 6.75087 + 9.29178i 0.715591 + 0.984927i 0.999659 + 0.0261223i \(0.00831593\pi\)
−0.284068 + 0.958804i \(0.591684\pi\)
\(90\) 0 0
\(91\) −2.67748 −0.280676
\(92\) 0 0
\(93\) 4.52935 + 1.47167i 0.469672 + 0.152606i
\(94\) 0 0
\(95\) 0.260428 0.358449i 0.0267194 0.0367760i
\(96\) 0 0
\(97\) −10.6517 + 3.46094i −1.08151 + 0.351405i −0.794961 0.606660i \(-0.792509\pi\)
−0.286551 + 0.958065i \(0.592509\pi\)
\(98\) 0 0
\(99\) 0.443996 + 0.144263i 0.0446233 + 0.0144990i
\(100\) 0 0
\(101\) 0.591389 + 0.813978i 0.0588454 + 0.0809938i 0.837426 0.546551i \(-0.184060\pi\)
−0.778580 + 0.627545i \(0.784060\pi\)
\(102\) 0 0
\(103\) −4.08508 + 2.96798i −0.402515 + 0.292444i −0.770564 0.637362i \(-0.780026\pi\)
0.368050 + 0.929806i \(0.380026\pi\)
\(104\) 0 0
\(105\) 0.163559 + 0.118833i 0.0159617 + 0.0115969i
\(106\) 0 0
\(107\) −4.15426 + 3.01825i −0.401608 + 0.291785i −0.770196 0.637808i \(-0.779841\pi\)
0.368588 + 0.929593i \(0.379841\pi\)
\(108\) 0 0
\(109\) 10.8078i 1.03520i 0.855622 + 0.517601i \(0.173175\pi\)
−0.855622 + 0.517601i \(0.826825\pi\)
\(110\) 0 0
\(111\) 0.739653 0.240328i 0.0702047 0.0228109i
\(112\) 0 0
\(113\) 4.55865 14.0301i 0.428842 1.31984i −0.470425 0.882440i \(-0.655899\pi\)
0.899267 0.437400i \(-0.144101\pi\)
\(114\) 0 0
\(115\) −0.220425 + 0.678398i −0.0205547 + 0.0632610i
\(116\) 0 0
\(117\) −0.387884 + 0.533876i −0.0358599 + 0.0493569i
\(118\) 0 0
\(119\) 2.26910 + 6.98358i 0.208008 + 0.640184i
\(120\) 0 0
\(121\) −5.99657 4.35677i −0.545143 0.396070i
\(122\) 0 0
\(123\) 11.3677 1.97018i 1.02499 0.177645i
\(124\) 0 0
\(125\) −0.906614 0.658694i −0.0810901 0.0589154i
\(126\) 0 0
\(127\) −3.72182 11.4546i −0.330258 1.01643i −0.969011 0.247018i \(-0.920549\pi\)
0.638753 0.769412i \(-0.279451\pi\)
\(128\) 0 0
\(129\) −9.93667 + 13.6767i −0.874875 + 1.20416i
\(130\) 0 0
\(131\) 5.40587 16.6376i 0.472313 1.45363i −0.377234 0.926118i \(-0.623125\pi\)
0.849547 0.527513i \(-0.176875\pi\)
\(132\) 0 0
\(133\) 1.22022 3.75546i 0.105807 0.325640i
\(134\) 0 0
\(135\) −0.529437 + 0.172024i −0.0455667 + 0.0148055i
\(136\) 0 0
\(137\) 6.05678i 0.517466i −0.965949 0.258733i \(-0.916695\pi\)
0.965949 0.258733i \(-0.0833050\pi\)
\(138\) 0 0
\(139\) 11.8192 8.58716i 1.00249 0.728354i 0.0398717 0.999205i \(-0.487305\pi\)
0.962621 + 0.270851i \(0.0873051\pi\)
\(140\) 0 0
\(141\) −10.8659 7.89453i −0.915073 0.664840i
\(142\) 0 0
\(143\) −4.10298 + 2.98099i −0.343108 + 0.249283i
\(144\) 0 0
\(145\) 0.0877434 + 0.120768i 0.00728669 + 0.0100293i
\(146\) 0 0
\(147\) 1.71361 + 0.556785i 0.141336 + 0.0459229i
\(148\) 0 0
\(149\) 18.2099 5.91675i 1.49181 0.484719i 0.554195 0.832387i \(-0.313026\pi\)
0.937618 + 0.347668i \(0.113026\pi\)
\(150\) 0 0
\(151\) −2.43892 + 3.35688i −0.198476 + 0.273179i −0.896641 0.442758i \(-0.854000\pi\)
0.698165 + 0.715937i \(0.254000\pi\)
\(152\) 0 0
\(153\) 1.72122 + 0.559257i 0.139152 + 0.0452133i
\(154\) 0 0
\(155\) 0.296576 0.0238216
\(156\) 0 0
\(157\) −4.40420 6.06187i −0.351494 0.483790i 0.596260 0.802791i \(-0.296653\pi\)
−0.947754 + 0.319001i \(0.896653\pi\)
\(158\) 0 0
\(159\) 4.39882 + 13.5382i 0.348849 + 1.07365i
\(160\) 0 0
\(161\) 6.35721i 0.501018i
\(162\) 0 0
\(163\) −0.0928394 −0.00727174 −0.00363587 0.999993i \(-0.501157\pi\)
−0.00363587 + 0.999993i \(0.501157\pi\)
\(164\) 0 0
\(165\) 0.382942 0.0298120
\(166\) 0 0
\(167\) 11.6428i 0.900945i 0.892790 + 0.450472i \(0.148744\pi\)
−0.892790 + 0.450472i \(0.851256\pi\)
\(168\) 0 0
\(169\) 1.80191 + 5.54572i 0.138609 + 0.426594i
\(170\) 0 0
\(171\) −0.572049 0.787358i −0.0437457 0.0602107i
\(172\) 0 0
\(173\) 21.2662 1.61684 0.808420 0.588607i \(-0.200323\pi\)
0.808420 + 0.588607i \(0.200323\pi\)
\(174\) 0 0
\(175\) −4.74331 1.54119i −0.358560 0.116503i
\(176\) 0 0
\(177\) −14.0610 + 19.3532i −1.05689 + 1.45468i
\(178\) 0 0
\(179\) 6.05628 1.96780i 0.452667 0.147081i −0.0738051 0.997273i \(-0.523514\pi\)
0.526473 + 0.850192i \(0.323514\pi\)
\(180\) 0 0
\(181\) 6.50244 + 2.11277i 0.483322 + 0.157041i 0.540536 0.841321i \(-0.318222\pi\)
−0.0572135 + 0.998362i \(0.518222\pi\)
\(182\) 0 0
\(183\) −6.42774 8.84702i −0.475152 0.653990i
\(184\) 0 0
\(185\) 0.0391819 0.0284673i 0.00288071 0.00209296i
\(186\) 0 0
\(187\) 11.2524 + 8.17535i 0.822857 + 0.597841i
\(188\) 0 0
\(189\) −4.01378 + 2.91618i −0.291959 + 0.212121i
\(190\) 0 0
\(191\) 14.8683i 1.07583i −0.842998 0.537916i \(-0.819212\pi\)
0.842998 0.537916i \(-0.180788\pi\)
\(192\) 0 0
\(193\) 14.1221 4.58853i 1.01653 0.330290i 0.247077 0.968996i \(-0.420530\pi\)
0.769451 + 0.638706i \(0.220530\pi\)
\(194\) 0 0
\(195\) −0.167273 + 0.514813i −0.0119787 + 0.0368665i
\(196\) 0 0
\(197\) 4.82211 14.8409i 0.343561 1.05737i −0.618788 0.785558i \(-0.712376\pi\)
0.962349 0.271815i \(-0.0876240\pi\)
\(198\) 0 0
\(199\) 13.9894 19.2548i 0.991684 1.36494i 0.0613926 0.998114i \(-0.480446\pi\)
0.930291 0.366822i \(-0.119554\pi\)
\(200\) 0 0
\(201\) 6.03048 + 18.5599i 0.425358 + 1.30912i
\(202\) 0 0
\(203\) 1.07632 + 0.781992i 0.0755428 + 0.0548851i
\(204\) 0 0
\(205\) 0.635348 0.335442i 0.0443746 0.0234283i
\(206\) 0 0
\(207\) 1.26760 + 0.920964i 0.0881041 + 0.0640114i
\(208\) 0 0
\(209\) −2.31129 7.11343i −0.159876 0.492046i
\(210\) 0 0
\(211\) 14.0888 19.3916i 0.969913 1.33497i 0.0278225 0.999613i \(-0.491143\pi\)
0.942091 0.335358i \(-0.108857\pi\)
\(212\) 0 0
\(213\) −0.953819 + 2.93555i −0.0653546 + 0.201141i
\(214\) 0 0
\(215\) −0.325320 + 1.00123i −0.0221867 + 0.0682835i
\(216\) 0 0
\(217\) 2.51380 0.816782i 0.170648 0.0554468i
\(218\) 0 0
\(219\) 25.2834i 1.70849i
\(220\) 0 0
\(221\) −15.9058 + 11.5562i −1.06994 + 0.777357i
\(222\) 0 0
\(223\) 21.6525 + 15.7314i 1.44996 + 1.05346i 0.985841 + 0.167680i \(0.0536276\pi\)
0.464115 + 0.885775i \(0.346372\pi\)
\(224\) 0 0
\(225\) −0.994466 + 0.722522i −0.0662977 + 0.0481681i
\(226\) 0 0
\(227\) −14.6011 20.0967i −0.969110 1.33387i −0.942495 0.334220i \(-0.891527\pi\)
−0.0266150 0.999646i \(-0.508473\pi\)
\(228\) 0 0
\(229\) 28.0376 + 9.10996i 1.85277 + 0.602003i 0.996313 + 0.0857923i \(0.0273422\pi\)
0.856462 + 0.516211i \(0.172658\pi\)
\(230\) 0 0
\(231\) 3.24584 1.05464i 0.213561 0.0693901i
\(232\) 0 0
\(233\) −16.8196 + 23.1502i −1.10189 + 1.51662i −0.269033 + 0.963131i \(0.586704\pi\)
−0.832856 + 0.553489i \(0.813296\pi\)
\(234\) 0 0
\(235\) −0.795464 0.258462i −0.0518904 0.0168602i
\(236\) 0 0
\(237\) 8.25966 0.536523
\(238\) 0 0
\(239\) 2.08036 + 2.86337i 0.134567 + 0.185216i 0.870983 0.491314i \(-0.163483\pi\)
−0.736415 + 0.676530i \(0.763483\pi\)
\(240\) 0 0
\(241\) −4.68866 14.4302i −0.302023 0.929532i −0.980771 0.195161i \(-0.937477\pi\)
0.678748 0.734371i \(-0.262523\pi\)
\(242\) 0 0
\(243\) 2.55504i 0.163906i
\(244\) 0 0
\(245\) 0.112205 0.00716851
\(246\) 0 0
\(247\) 10.5726 0.672720
\(248\) 0 0
\(249\) 13.6422i 0.864540i
\(250\) 0 0
\(251\) 1.25912 + 3.87517i 0.0794750 + 0.244599i 0.982898 0.184152i \(-0.0589539\pi\)
−0.903423 + 0.428751i \(0.858954\pi\)
\(252\) 0 0
\(253\) 7.07784 + 9.74181i 0.444980 + 0.612463i
\(254\) 0 0
\(255\) 1.48453 0.0929650
\(256\) 0 0
\(257\) −0.778836 0.253059i −0.0485824 0.0157854i 0.284625 0.958639i \(-0.408131\pi\)
−0.333207 + 0.942854i \(0.608131\pi\)
\(258\) 0 0
\(259\) 0.253708 0.349200i 0.0157647 0.0216982i
\(260\) 0 0
\(261\) 0.311851 0.101327i 0.0193031 0.00627195i
\(262\) 0 0
\(263\) −21.1218 6.86289i −1.30243 0.423184i −0.426001 0.904723i \(-0.640078\pi\)
−0.876425 + 0.481539i \(0.840078\pi\)
\(264\) 0 0
\(265\) 0.521050 + 0.717163i 0.0320078 + 0.0440550i
\(266\) 0 0
\(267\) 16.7419 12.1637i 1.02459 0.744406i
\(268\) 0 0
\(269\) 0.115013 + 0.0835620i 0.00701248 + 0.00509487i 0.591286 0.806462i \(-0.298620\pi\)
−0.584273 + 0.811557i \(0.698620\pi\)
\(270\) 0 0
\(271\) 1.24281 0.902953i 0.0754952 0.0548505i −0.549397 0.835561i \(-0.685143\pi\)
0.624893 + 0.780711i \(0.285143\pi\)
\(272\) 0 0
\(273\) 4.82427i 0.291978i
\(274\) 0 0
\(275\) −8.98457 + 2.91926i −0.541790 + 0.176038i
\(276\) 0 0
\(277\) 9.06136 27.8880i 0.544444 1.67563i −0.177864 0.984055i \(-0.556919\pi\)
0.722308 0.691572i \(-0.243081\pi\)
\(278\) 0 0
\(279\) 0.201309 0.619566i 0.0120521 0.0370924i
\(280\) 0 0
\(281\) −13.2555 + 18.2447i −0.790759 + 1.08839i 0.203255 + 0.979126i \(0.434848\pi\)
−0.994013 + 0.109260i \(0.965152\pi\)
\(282\) 0 0
\(283\) 1.39713 + 4.29993i 0.0830509 + 0.255604i 0.983956 0.178412i \(-0.0570960\pi\)
−0.900905 + 0.434016i \(0.857096\pi\)
\(284\) 0 0
\(285\) −0.645851 0.469238i −0.0382569 0.0277953i
\(286\) 0 0
\(287\) 4.46143 4.59300i 0.263350 0.271116i
\(288\) 0 0
\(289\) 29.8683 + 21.7006i 1.75696 + 1.27651i
\(290\) 0 0
\(291\) 6.23590 + 19.1921i 0.365555 + 1.12506i
\(292\) 0 0
\(293\) −7.85594 + 10.8128i −0.458949 + 0.631689i −0.974290 0.225296i \(-0.927665\pi\)
0.515341 + 0.856985i \(0.327665\pi\)
\(294\) 0 0
\(295\) −0.460347 + 1.41680i −0.0268024 + 0.0824894i
\(296\) 0 0
\(297\) −2.90398 + 8.93754i −0.168506 + 0.518609i
\(298\) 0 0
\(299\) −16.1882 + 5.25986i −0.936188 + 0.304186i
\(300\) 0 0
\(301\) 9.38246i 0.540796i
\(302\) 0 0
\(303\) 1.46662 1.06556i 0.0842552 0.0612150i
\(304\) 0 0
\(305\) −0.550939 0.400281i −0.0315467 0.0229200i
\(306\) 0 0
\(307\) −0.431601 + 0.313576i −0.0246328 + 0.0178968i −0.600034 0.799975i \(-0.704846\pi\)
0.575401 + 0.817872i \(0.304846\pi\)
\(308\) 0 0
\(309\) 5.34770 + 7.36047i 0.304220 + 0.418723i
\(310\) 0 0
\(311\) 31.2633 + 10.1581i 1.77278 + 0.576011i 0.998391 0.0566994i \(-0.0180577\pi\)
0.774388 + 0.632710i \(0.218058\pi\)
\(312\) 0 0
\(313\) −21.9912 + 7.14538i −1.24302 + 0.403880i −0.855413 0.517946i \(-0.826697\pi\)
−0.387603 + 0.921826i \(0.626697\pi\)
\(314\) 0 0
\(315\) 0.0162550 0.0223731i 0.000915868 0.00126058i
\(316\) 0 0
\(317\) 19.0339 + 6.18448i 1.06905 + 0.347355i 0.790117 0.612956i \(-0.210020\pi\)
0.278931 + 0.960311i \(0.410020\pi\)
\(318\) 0 0
\(319\) 2.51999 0.141092
\(320\) 0 0
\(321\) 5.43827 + 7.48513i 0.303534 + 0.417779i
\(322\) 0 0
\(323\) −8.96007 27.5763i −0.498552 1.53438i
\(324\) 0 0
\(325\) 13.3537i 0.740729i
\(326\) 0 0
\(327\) 19.4735 1.07689
\(328\) 0 0
\(329\) −7.45422 −0.410965
\(330\) 0 0
\(331\) 6.20469i 0.341041i 0.985354 + 0.170520i \(0.0545448\pi\)
−0.985354 + 0.170520i \(0.945455\pi\)
\(332\) 0 0
\(333\) −0.0328742 0.101177i −0.00180150 0.00554444i
\(334\) 0 0
\(335\) 0.714324 + 0.983182i 0.0390277 + 0.0537170i
\(336\) 0 0
\(337\) −0.239221 −0.0130312 −0.00651560 0.999979i \(-0.502074\pi\)
−0.00651560 + 0.999979i \(0.502074\pi\)
\(338\) 0 0
\(339\) −25.2794 8.21376i −1.37299 0.446110i
\(340\) 0 0
\(341\) 2.94278 4.05039i 0.159361 0.219341i
\(342\) 0 0
\(343\) 0.951057 0.309017i 0.0513522 0.0166853i
\(344\) 0 0
\(345\) 1.22234 + 0.397161i 0.0658083 + 0.0213824i
\(346\) 0 0
\(347\) −4.09662 5.63851i −0.219918 0.302691i 0.684776 0.728754i \(-0.259900\pi\)
−0.904694 + 0.426063i \(0.859900\pi\)
\(348\) 0 0
\(349\) 0.117288 0.0852148i 0.00627829 0.00456144i −0.584642 0.811292i \(-0.698765\pi\)
0.590920 + 0.806730i \(0.298765\pi\)
\(350\) 0 0
\(351\) −10.7468 7.80801i −0.573622 0.416761i
\(352\) 0 0
\(353\) 6.51049 4.73015i 0.346518 0.251760i −0.400889 0.916127i \(-0.631299\pi\)
0.747407 + 0.664366i \(0.231299\pi\)
\(354\) 0 0
\(355\) 0.192216i 0.0102018i
\(356\) 0 0
\(357\) 12.5830 4.08846i 0.665962 0.216384i
\(358\) 0 0
\(359\) −1.66872 + 5.13578i −0.0880715 + 0.271056i −0.985386 0.170335i \(-0.945515\pi\)
0.897315 + 0.441391i \(0.145515\pi\)
\(360\) 0 0
\(361\) 1.05299 3.24078i 0.0554206 0.170567i
\(362\) 0 0
\(363\) −7.85000 + 10.8046i −0.412018 + 0.567094i
\(364\) 0 0
\(365\) −0.486547 1.49744i −0.0254670 0.0783795i
\(366\) 0 0
\(367\) 24.7454 + 17.9786i 1.29170 + 0.938476i 0.999838 0.0179839i \(-0.00572478\pi\)
0.291863 + 0.956460i \(0.405725\pi\)
\(368\) 0 0
\(369\) −0.269499 1.55497i −0.0140296 0.0809486i
\(370\) 0 0
\(371\) 6.39155 + 4.64373i 0.331833 + 0.241090i
\(372\) 0 0
\(373\) 9.98945 + 30.7444i 0.517234 + 1.59188i 0.779180 + 0.626800i \(0.215636\pi\)
−0.261946 + 0.965083i \(0.584364\pi\)
\(374\) 0 0
\(375\) −1.18683 + 1.63353i −0.0612877 + 0.0843553i
\(376\) 0 0
\(377\) −1.10076 + 3.38778i −0.0566919 + 0.174480i
\(378\) 0 0
\(379\) 1.36775 4.20951i 0.0702568 0.216228i −0.909763 0.415128i \(-0.863737\pi\)
0.980020 + 0.198900i \(0.0637368\pi\)
\(380\) 0 0
\(381\) −20.6388 + 6.70596i −1.05736 + 0.343557i
\(382\) 0 0
\(383\) 30.8518i 1.57645i 0.615386 + 0.788226i \(0.289000\pi\)
−0.615386 + 0.788226i \(0.711000\pi\)
\(384\) 0 0
\(385\) 0.171943 0.124924i 0.00876304 0.00636672i
\(386\) 0 0
\(387\) 1.87082 + 1.35923i 0.0950990 + 0.0690935i
\(388\) 0 0
\(389\) 20.6252 14.9851i 1.04574 0.759776i 0.0743433 0.997233i \(-0.476314\pi\)
0.971398 + 0.237457i \(0.0763140\pi\)
\(390\) 0 0
\(391\) 27.4383 + 37.7656i 1.38761 + 1.90989i
\(392\) 0 0
\(393\) −29.9775 9.74027i −1.51216 0.491332i
\(394\) 0 0
\(395\) 0.489187 0.158947i 0.0246137 0.00799747i
\(396\) 0 0
\(397\) 2.71913 3.74256i 0.136469 0.187834i −0.735313 0.677728i \(-0.762965\pi\)
0.871782 + 0.489894i \(0.162965\pi\)
\(398\) 0 0
\(399\) −6.76657 2.19859i −0.338752 0.110067i
\(400\) 0 0
\(401\) −27.3210 −1.36435 −0.682173 0.731190i \(-0.738965\pi\)
−0.682173 + 0.731190i \(0.738965\pi\)
\(402\) 0 0
\(403\) 4.15976 + 5.72542i 0.207212 + 0.285203i
\(404\) 0 0
\(405\) 0.335590 + 1.03284i 0.0166756 + 0.0513223i
\(406\) 0 0
\(407\) 0.817583i 0.0405261i
\(408\) 0 0
\(409\) −10.7717 −0.532628 −0.266314 0.963886i \(-0.585806\pi\)
−0.266314 + 0.963886i \(0.585806\pi\)
\(410\) 0 0
\(411\) −10.9131 −0.538303
\(412\) 0 0
\(413\) 13.2767i 0.653304i
\(414\) 0 0
\(415\) −0.262527 0.807975i −0.0128869 0.0396619i
\(416\) 0 0
\(417\) −15.4723 21.2958i −0.757682 1.04286i
\(418\) 0 0
\(419\) 22.4032 1.09447 0.547233 0.836980i \(-0.315681\pi\)
0.547233 + 0.836980i \(0.315681\pi\)
\(420\) 0 0
\(421\) −32.9383 10.7023i −1.60531 0.521598i −0.636899 0.770947i \(-0.719783\pi\)
−0.968414 + 0.249349i \(0.919783\pi\)
\(422\) 0 0
\(423\) −1.07989 + 1.48634i −0.0525059 + 0.0722682i
\(424\) 0 0
\(425\) −34.8300 + 11.3170i −1.68950 + 0.548953i
\(426\) 0 0
\(427\) −5.77218 1.87550i −0.279336 0.0907616i
\(428\) 0 0
\(429\) 5.37113 + 7.39272i 0.259321 + 0.356924i
\(430\) 0 0
\(431\) 6.58772 4.78626i 0.317319 0.230546i −0.417712 0.908580i \(-0.637168\pi\)
0.735031 + 0.678034i \(0.237168\pi\)
\(432\) 0 0
\(433\) −20.7560 15.0801i −0.997472 0.724706i −0.0359272 0.999354i \(-0.511438\pi\)
−0.961545 + 0.274649i \(0.911438\pi\)
\(434\) 0 0
\(435\) 0.217600 0.158096i 0.0104331 0.00758010i
\(436\) 0 0
\(437\) 25.1029i 1.20083i
\(438\) 0 0
\(439\) −18.8988 + 6.14058i −0.901989 + 0.293074i −0.723058 0.690788i \(-0.757264\pi\)
−0.178931 + 0.983862i \(0.557264\pi\)
\(440\) 0 0
\(441\) 0.0761622 0.234403i 0.00362677 0.0111621i
\(442\) 0 0
\(443\) 5.83350 17.9537i 0.277158 0.853004i −0.711482 0.702704i \(-0.751976\pi\)
0.988640 0.150300i \(-0.0480241\pi\)
\(444\) 0 0
\(445\) 0.757481 1.04258i 0.0359081 0.0494232i
\(446\) 0 0
\(447\) −10.6608 32.8105i −0.504237 1.55188i
\(448\) 0 0
\(449\) −16.0443 11.6569i −0.757177 0.550121i 0.140866 0.990029i \(-0.455011\pi\)
−0.898043 + 0.439908i \(0.855011\pi\)
\(450\) 0 0
\(451\) 1.72307 12.0055i 0.0811360 0.565317i
\(452\) 0 0
\(453\) 6.04842 + 4.39443i 0.284179 + 0.206468i
\(454\) 0 0
\(455\) 0.0928368 + 0.285722i 0.00435226 + 0.0133949i
\(456\) 0 0
\(457\) 15.5693 21.4293i 0.728302 1.00242i −0.270905 0.962606i \(-0.587323\pi\)
0.999207 0.0398152i \(-0.0126769\pi\)
\(458\) 0 0
\(459\) −11.2577 + 34.6477i −0.525465 + 1.61722i
\(460\) 0 0
\(461\) 2.36995 7.29396i 0.110380 0.339714i −0.880576 0.473906i \(-0.842844\pi\)
0.990955 + 0.134192i \(0.0428438\pi\)
\(462\) 0 0
\(463\) 6.76522 2.19815i 0.314406 0.102157i −0.147563 0.989053i \(-0.547143\pi\)
0.461969 + 0.886896i \(0.347143\pi\)
\(464\) 0 0
\(465\) 0.534369i 0.0247808i
\(466\) 0 0
\(467\) −18.9820 + 13.7912i −0.878382 + 0.638182i −0.932823 0.360335i \(-0.882662\pi\)
0.0544407 + 0.998517i \(0.482662\pi\)
\(468\) 0 0
\(469\) 8.76238 + 6.36624i 0.404609 + 0.293966i
\(470\) 0 0
\(471\) −10.9222 + 7.93548i −0.503270 + 0.365647i
\(472\) 0 0
\(473\) 10.4460 + 14.3777i 0.480309 + 0.661088i
\(474\) 0 0
\(475\) 18.7300 + 6.08576i 0.859393 + 0.279234i
\(476\) 0 0
\(477\) 1.85188 0.601711i 0.0847916 0.0275505i
\(478\) 0 0
\(479\) 16.0295 22.0627i 0.732406 1.00807i −0.266613 0.963804i \(-0.585905\pi\)
0.999020 0.0442673i \(-0.0140953\pi\)
\(480\) 0 0
\(481\) 1.09913 + 0.357128i 0.0501159 + 0.0162836i
\(482\) 0 0
\(483\) 11.4544 0.521193
\(484\) 0 0
\(485\) 0.738655 + 1.01667i 0.0335406 + 0.0461647i
\(486\) 0 0
\(487\) −1.00109 3.08103i −0.0453636 0.139615i 0.925809 0.377991i \(-0.123385\pi\)
−0.971173 + 0.238376i \(0.923385\pi\)
\(488\) 0 0
\(489\) 0.167278i 0.00756456i
\(490\) 0 0
\(491\) −34.6834 −1.56524 −0.782620 0.622500i \(-0.786117\pi\)
−0.782620 + 0.622500i \(0.786117\pi\)
\(492\) 0 0
\(493\) 9.76912 0.439979
\(494\) 0 0
\(495\) 0.0523824i 0.00235441i
\(496\) 0 0
\(497\) 0.529371 + 1.62924i 0.0237456 + 0.0730813i
\(498\) 0 0
\(499\) 18.8491 + 25.9436i 0.843802 + 1.16139i 0.985195 + 0.171440i \(0.0548421\pi\)
−0.141392 + 0.989954i \(0.545158\pi\)
\(500\) 0 0
\(501\) 20.9779 0.937223
\(502\) 0 0
\(503\) −33.5728 10.9085i −1.49694 0.486385i −0.557815 0.829965i \(-0.688360\pi\)
−0.939123 + 0.343581i \(0.888360\pi\)
\(504\) 0 0
\(505\) 0.0663568 0.0913323i 0.00295284 0.00406424i
\(506\) 0 0
\(507\) 9.99226 3.24668i 0.443772 0.144190i
\(508\) 0 0
\(509\) −8.50159 2.76233i −0.376826 0.122438i 0.114479 0.993426i \(-0.463480\pi\)
−0.491305 + 0.870987i \(0.663480\pi\)
\(510\) 0 0
\(511\) −8.24801 11.3524i −0.364870 0.502201i
\(512\) 0 0
\(513\) 15.8493 11.5152i 0.699765 0.508409i
\(514\) 0 0
\(515\) 0.458366 + 0.333022i 0.0201980 + 0.0146747i
\(516\) 0 0
\(517\) −11.4229 + 8.29921i −0.502378 + 0.364999i
\(518\) 0 0
\(519\) 38.3173i 1.68194i
\(520\) 0 0
\(521\) −7.04866 + 2.29025i −0.308807 + 0.100338i −0.459321 0.888270i \(-0.651907\pi\)
0.150514 + 0.988608i \(0.451907\pi\)
\(522\) 0 0
\(523\) 5.16994 15.9114i 0.226066 0.695759i −0.772116 0.635482i \(-0.780802\pi\)
0.998182 0.0602773i \(-0.0191985\pi\)
\(524\) 0 0
\(525\) −2.77692 + 8.54647i −0.121195 + 0.372999i
\(526\) 0 0
\(527\) 11.4081 15.7020i 0.496946 0.683988i
\(528\) 0 0
\(529\) 5.38125 + 16.5618i 0.233968 + 0.720078i
\(530\) 0 0
\(531\) 2.64731 + 1.92339i 0.114884 + 0.0834679i
\(532\) 0 0
\(533\) 15.3871 + 7.56054i 0.666489 + 0.327483i
\(534\) 0 0
\(535\) 0.466129 + 0.338662i 0.0201525 + 0.0146417i
\(536\) 0 0
\(537\) −3.54558 10.9122i −0.153003 0.470895i
\(538\) 0 0
\(539\) 1.11336 1.53240i 0.0479557 0.0660053i
\(540\) 0 0
\(541\) −1.38701 + 4.26877i −0.0596321 + 0.183529i −0.976435 0.215811i \(-0.930761\pi\)
0.916803 + 0.399340i \(0.130761\pi\)
\(542\) 0 0
\(543\) 3.80678 11.7161i 0.163364 0.502784i
\(544\) 0 0
\(545\) 1.15334 0.374742i 0.0494036 0.0160522i
\(546\) 0 0
\(547\) 20.8598i 0.891903i −0.895057 0.445951i \(-0.852865\pi\)
0.895057 0.445951i \(-0.147135\pi\)
\(548\) 0 0
\(549\) −1.21018 + 0.879245i −0.0516491 + 0.0375253i
\(550\) 0 0
\(551\) −4.25009 3.08787i −0.181060 0.131548i
\(552\) 0 0
\(553\) 3.70864 2.69448i 0.157707 0.114581i
\(554\) 0 0
\(555\) −0.0512923 0.0705978i −0.00217724 0.00299671i
\(556\) 0 0
\(557\) 16.6524 + 5.41070i 0.705585 + 0.229259i 0.639762 0.768573i \(-0.279033\pi\)
0.0658230 + 0.997831i \(0.479033\pi\)
\(558\) 0 0
\(559\) −23.8918 + 7.76291i −1.01052 + 0.328336i
\(560\) 0 0
\(561\) 14.7303 20.2745i 0.621914 0.855991i
\(562\) 0 0
\(563\) −5.12592 1.66551i −0.216032 0.0701929i 0.199002 0.979999i \(-0.436230\pi\)
−0.415033 + 0.909806i \(0.636230\pi\)
\(564\) 0 0
\(565\) −1.65526 −0.0696373
\(566\) 0 0
\(567\) 5.68897 + 7.83019i 0.238914 + 0.328837i
\(568\) 0 0
\(569\) 1.14983 + 3.53882i 0.0482035 + 0.148355i 0.972261 0.233898i \(-0.0751482\pi\)
−0.924058 + 0.382253i \(0.875148\pi\)
\(570\) 0 0
\(571\) 28.4150i 1.18913i −0.804048 0.594565i \(-0.797324\pi\)
0.804048 0.594565i \(-0.202676\pi\)
\(572\) 0 0
\(573\) −26.7896 −1.11915
\(574\) 0 0
\(575\) −31.7060 −1.32223
\(576\) 0 0
\(577\) 36.1589i 1.50531i 0.658413 + 0.752657i \(0.271228\pi\)
−0.658413 + 0.752657i \(0.728772\pi\)
\(578\) 0 0
\(579\) −8.26760 25.4450i −0.343590 1.05746i
\(580\) 0 0
\(581\) −4.45039 6.12544i −0.184633 0.254126i
\(582\) 0 0
\(583\) 14.9646 0.619769
\(584\) 0 0
\(585\) 0.0704209 + 0.0228811i 0.00291154 + 0.000946018i
\(586\) 0 0
\(587\) −12.5568 + 17.2829i −0.518274 + 0.713343i −0.985287 0.170907i \(-0.945330\pi\)
0.467013 + 0.884250i \(0.345330\pi\)
\(588\) 0 0
\(589\) −9.92630 + 3.22525i −0.409006 + 0.132894i
\(590\) 0 0
\(591\) −26.7403 8.68846i −1.09995 0.357396i
\(592\) 0 0
\(593\) −3.34572 4.60499i −0.137392 0.189104i 0.734776 0.678309i \(-0.237287\pi\)
−0.872169 + 0.489205i \(0.837287\pi\)
\(594\) 0 0
\(595\) 0.666564 0.484287i 0.0273265 0.0198538i
\(596\) 0 0
\(597\) −34.6932 25.2061i −1.41990 1.03162i
\(598\) 0 0
\(599\) −13.4135 + 9.74550i −0.548062 + 0.398190i −0.827070 0.562098i \(-0.809994\pi\)
0.279008 + 0.960289i \(0.409994\pi\)
\(600\) 0 0
\(601\) 14.6959i 0.599459i 0.954024 + 0.299729i \(0.0968964\pi\)
−0.954024 + 0.299729i \(0.903104\pi\)
\(602\) 0 0
\(603\) 2.53880 0.824905i 0.103388 0.0335927i
\(604\) 0 0
\(605\) −0.257004 + 0.790977i −0.0104487 + 0.0321578i
\(606\) 0 0
\(607\) −4.60137 + 14.1616i −0.186764 + 0.574801i −0.999974 0.00716942i \(-0.997718\pi\)
0.813210 + 0.581970i \(0.197718\pi\)
\(608\) 0 0
\(609\) 1.40899 1.93931i 0.0570951 0.0785847i
\(610\) 0 0
\(611\) −6.16752 18.9817i −0.249511 0.767916i
\(612\) 0 0
\(613\) −12.9339 9.39704i −0.522396 0.379543i 0.295110 0.955463i \(-0.404644\pi\)
−0.817506 + 0.575920i \(0.804644\pi\)
\(614\) 0 0
\(615\) −0.604397 1.14477i −0.0243717 0.0461615i
\(616\) 0 0
\(617\) 17.8526 + 12.9707i 0.718718 + 0.522179i 0.885974 0.463734i \(-0.153491\pi\)
−0.167257 + 0.985913i \(0.553491\pi\)
\(618\) 0 0
\(619\) −4.05308 12.4741i −0.162907 0.501376i 0.835969 0.548777i \(-0.184906\pi\)
−0.998876 + 0.0474005i \(0.984906\pi\)
\(620\) 0 0
\(621\) −18.5388 + 25.5164i −0.743935 + 1.02394i
\(622\) 0 0
\(623\) 3.54914 10.9231i 0.142193 0.437626i
\(624\) 0 0
\(625\) 7.66712 23.5970i 0.306685 0.943878i
\(626\) 0 0
\(627\) −12.8169 + 4.16448i −0.511860 + 0.166313i
\(628\) 0 0
\(629\) 3.16948i 0.126375i
\(630\) 0 0
\(631\) −22.2463 + 16.1629i −0.885611 + 0.643434i −0.934730 0.355359i \(-0.884359\pi\)
0.0491187 + 0.998793i \(0.484359\pi\)
\(632\) 0 0
\(633\) −34.9396 25.3851i −1.38873 1.00897i
\(634\) 0 0
\(635\) −1.09331 + 0.794335i −0.0433866 + 0.0315222i
\(636\) 0 0
\(637\) 1.57378 + 2.16612i 0.0623555 + 0.0858250i
\(638\) 0 0
\(639\) 0.401552 + 0.130472i 0.0158852 + 0.00516140i
\(640\) 0 0
\(641\) −17.5566 + 5.70450i −0.693445 + 0.225314i −0.634472 0.772945i \(-0.718783\pi\)
−0.0589730 + 0.998260i \(0.518783\pi\)
\(642\) 0 0
\(643\) −16.2188 + 22.3233i −0.639609 + 0.880346i −0.998595 0.0529968i \(-0.983123\pi\)
0.358986 + 0.933343i \(0.383123\pi\)
\(644\) 0 0
\(645\) 1.80402 + 0.586160i 0.0710331 + 0.0230800i
\(646\) 0 0
\(647\) −6.82820 −0.268444 −0.134222 0.990951i \(-0.542854\pi\)
−0.134222 + 0.990951i \(0.542854\pi\)
\(648\) 0 0
\(649\) 14.7817 + 20.3453i 0.580233 + 0.798623i
\(650\) 0 0
\(651\) −1.47167 4.52935i −0.0576795 0.177519i
\(652\) 0 0
\(653\) 25.7376i 1.00719i −0.863940 0.503594i \(-0.832011\pi\)
0.863940 0.503594i \(-0.167989\pi\)
\(654\) 0 0
\(655\) −1.96289 −0.0766964
\(656\) 0 0
\(657\) −3.45850 −0.134929
\(658\) 0 0
\(659\) 17.9999i 0.701177i 0.936530 + 0.350588i \(0.114018\pi\)
−0.936530 + 0.350588i \(0.885982\pi\)
\(660\) 0 0
\(661\) −13.3355 41.0424i −0.518690 1.59636i −0.776466 0.630159i \(-0.782990\pi\)
0.257777 0.966205i \(-0.417010\pi\)
\(662\) 0 0
\(663\) 20.8220 + 28.6590i 0.808659 + 1.11302i
\(664\) 0 0
\(665\) −0.443067 −0.0171814
\(666\) 0 0
\(667\) 8.04371 + 2.61356i 0.311454 + 0.101197i
\(668\) 0 0
\(669\) 28.3448 39.0133i 1.09587 1.50834i
\(670\) 0 0
\(671\) −10.9334 + 3.55248i −0.422080 + 0.137142i
\(672\) 0 0
\(673\) 18.4686 + 6.00083i 0.711914 + 0.231315i 0.642514 0.766274i \(-0.277892\pi\)
0.0694001 + 0.997589i \(0.477892\pi\)
\(674\) 0 0
\(675\) −14.5442 20.0184i −0.559806 0.770507i
\(676\) 0 0
\(677\) 11.7650 8.54776i 0.452165 0.328517i −0.338285 0.941044i \(-0.609847\pi\)
0.790450 + 0.612526i \(0.209847\pi\)
\(678\) 0 0
\(679\) 9.06085 + 6.58309i 0.347723 + 0.252636i
\(680\) 0 0
\(681\) −36.2102 + 26.3082i −1.38758 + 1.00813i
\(682\) 0 0
\(683\) 14.5045i 0.555001i −0.960725 0.277500i \(-0.910494\pi\)
0.960725 0.277500i \(-0.0895060\pi\)
\(684\) 0 0
\(685\) −0.646339 + 0.210008i −0.0246954 + 0.00802401i
\(686\) 0 0
\(687\) 16.4143 50.5180i 0.626244 1.92738i
\(688\) 0 0
\(689\) −6.53667 + 20.1178i −0.249027 + 0.766427i
\(690\) 0 0
\(691\) −20.6508 + 28.4234i −0.785593 + 1.08128i 0.209050 + 0.977905i \(0.432963\pi\)
−0.994643 + 0.103371i \(0.967037\pi\)
\(692\) 0 0
\(693\) −0.144263 0.443996i −0.00548010 0.0168660i
\(694\) 0 0
\(695\) −1.32617 0.963522i −0.0503047 0.0365485i
\(696\) 0 0
\(697\) 6.67972 46.5411i 0.253012 1.76287i
\(698\) 0 0
\(699\) 41.7119 + 30.3055i 1.57769 + 1.14626i
\(700\) 0 0
\(701\) −6.53588 20.1154i −0.246857 0.759747i −0.995326 0.0965767i \(-0.969211\pi\)
0.748469 0.663170i \(-0.230789\pi\)
\(702\) 0 0
\(703\) −1.00183 + 1.37889i −0.0377845 + 0.0520060i
\(704\) 0 0
\(705\) −0.465696 + 1.43326i −0.0175391 + 0.0539798i
\(706\) 0 0
\(707\) 0.310912 0.956888i 0.0116930 0.0359875i
\(708\) 0 0
\(709\) 12.5968 4.09294i 0.473082 0.153714i −0.0627658 0.998028i \(-0.519992\pi\)
0.535848 + 0.844315i \(0.319992\pi\)
\(710\) 0 0
\(711\) 1.12983i 0.0423720i
\(712\) 0 0
\(713\) 13.5940 9.87664i 0.509100 0.369883i
\(714\) 0 0
\(715\) 0.460374 + 0.334482i 0.0172170 + 0.0125089i
\(716\) 0 0
\(717\) 5.15920 3.74838i 0.192674 0.139986i
\(718\) 0 0
\(719\) 6.65804 + 9.16401i 0.248303 + 0.341760i 0.914916 0.403644i \(-0.132257\pi\)
−0.666613 + 0.745404i \(0.732257\pi\)
\(720\) 0 0
\(721\) 4.80230 + 1.56036i 0.178847 + 0.0581109i
\(722\) 0 0
\(723\) −26.0003 + 8.44801i −0.966962 + 0.314185i
\(724\) 0 0
\(725\) −3.90011 + 5.36805i −0.144847 + 0.199364i
\(726\) 0 0
\(727\) 33.1465 + 10.7700i 1.22934 + 0.399436i 0.850474 0.526017i \(-0.176315\pi\)
0.378863 + 0.925453i \(0.376315\pi\)
\(728\) 0 0
\(729\) −24.4323 −0.904900
\(730\) 0 0
\(731\) 40.4956 + 55.7374i 1.49778 + 2.06152i
\(732\) 0 0
\(733\) −2.47776 7.62576i −0.0915181 0.281664i 0.894813 0.446442i \(-0.147309\pi\)
−0.986331 + 0.164778i \(0.947309\pi\)
\(734\) 0 0
\(735\) 0.202170i 0.00745717i
\(736\) 0 0
\(737\) 20.5154 0.755695
\(738\) 0 0
\(739\) −12.4775 −0.458991 −0.229495 0.973310i \(-0.573708\pi\)
−0.229495 + 0.973310i \(0.573708\pi\)
\(740\) 0 0
\(741\) 19.0497i 0.699808i
\(742\) 0 0
\(743\) 8.05974 + 24.8053i 0.295683 + 0.910019i 0.982991 + 0.183653i \(0.0587923\pi\)
−0.687308 + 0.726366i \(0.741208\pi\)
\(744\) 0 0
\(745\) −1.26279 1.73808i −0.0462651 0.0636785i
\(746\) 0 0
\(747\) −1.86611 −0.0682773
\(748\) 0 0
\(749\) 4.88363 + 1.58679i 0.178444 + 0.0579799i
\(750\) 0 0
\(751\) −26.5361 + 36.5238i −0.968315 + 1.33277i −0.0254221 + 0.999677i \(0.508093\pi\)
−0.942893 + 0.333095i \(0.891907\pi\)
\(752\) 0 0
\(753\) 6.98227 2.26868i 0.254448 0.0826752i
\(754\) 0 0
\(755\) 0.442789 + 0.143871i 0.0161148 + 0.00523600i
\(756\) 0 0
\(757\) 17.9133 + 24.6555i 0.651070 + 0.896120i 0.999145 0.0413462i \(-0.0131647\pi\)
−0.348075 + 0.937467i \(0.613165\pi\)
\(758\) 0 0
\(759\) 17.5528 12.7528i 0.637125 0.462898i
\(760\) 0 0
\(761\) 13.3360 + 9.68919i 0.483431 + 0.351233i 0.802652 0.596447i \(-0.203421\pi\)
−0.319222 + 0.947680i \(0.603421\pi\)
\(762\) 0 0
\(763\) 8.74371 6.35268i 0.316544 0.229982i
\(764\) 0 0
\(765\) 0.203068i 0.00734194i
\(766\) 0 0
\(767\) −33.8083 + 10.9850i −1.22075 + 0.396644i
\(768\) 0 0
\(769\) 9.30295 28.6316i 0.335473 1.03248i −0.631015 0.775770i \(-0.717362\pi\)
0.966489 0.256710i \(-0.0826385\pi\)
\(770\) 0 0
\(771\) −0.455961 + 1.40330i −0.0164210 + 0.0505387i
\(772\) 0 0
\(773\) 4.95050 6.81378i 0.178057 0.245075i −0.710655 0.703541i \(-0.751601\pi\)
0.888712 + 0.458467i \(0.151601\pi\)
\(774\) 0 0
\(775\) 4.07363 + 12.5373i 0.146329 + 0.450354i
\(776\) 0 0
\(777\) −0.629186 0.457131i −0.0225719 0.0163995i
\(778\) 0 0
\(779\) −17.6170 + 18.1365i −0.631193 + 0.649808i
\(780\) 0 0
\(781\) 2.62513 + 1.90727i 0.0939347 + 0.0682475i
\(782\) 0 0
\(783\) 2.03968 + 6.27749i 0.0728922 + 0.224339i
\(784\) 0 0
\(785\) −0.494174 + 0.680172i −0.0176378 + 0.0242764i
\(786\) 0 0
\(787\) 7.78032 23.9454i 0.277338 0.853560i −0.711253 0.702936i \(-0.751872\pi\)
0.988591 0.150624i \(-0.0481282\pi\)
\(788\) 0 0
\(789\) −12.3655 + 38.0572i −0.440224 + 1.35487i
\(790\) 0 0
\(791\) −14.0301 + 4.55865i −0.498853 + 0.162087i
\(792\) 0 0
\(793\) 16.2502i 0.577063i
\(794\) 0 0
\(795\) 1.29218 0.938825i 0.0458290 0.0332967i
\(796\) 0 0
\(797\) −33.2386 24.1492i −1.17737