Properties

Label 756.2.ck.a.5.2
Level 756
Weight 2
Character 756.5
Analytic conductor 6.037
Analytic rank 0
Dimension 144
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.ck (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.2
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.69135 + 0.373296i) q^{3} +(-0.203680 + 1.15512i) q^{5} +(2.02312 + 1.70498i) q^{7} +(2.72130 - 1.26275i) q^{9} +O(q^{10})\) \(q+(-1.69135 + 0.373296i) q^{3} +(-0.203680 + 1.15512i) q^{5} +(2.02312 + 1.70498i) q^{7} +(2.72130 - 1.26275i) q^{9} +(3.15137 - 0.555671i) q^{11} +(-1.12364 + 1.33911i) q^{13} +(-0.0867108 - 2.02975i) q^{15} -3.16451 q^{17} -6.65556i q^{19} +(-4.05827 - 2.12849i) q^{21} +(-3.65594 + 4.35698i) q^{23} +(3.40564 + 1.23955i) q^{25} +(-4.13128 + 3.15159i) q^{27} +(3.84940 + 4.58754i) q^{29} +(1.52309 + 4.18464i) q^{31} +(-5.12262 + 2.11622i) q^{33} +(-2.38154 + 1.98969i) q^{35} +(4.75241 + 8.23142i) q^{37} +(1.40059 - 2.68434i) q^{39} +(7.74888 + 6.50209i) q^{41} +(3.80179 + 1.38374i) q^{43} +(0.904355 + 3.40063i) q^{45} +(-7.95967 - 2.89708i) q^{47} +(1.18606 + 6.89879i) q^{49} +(5.35228 - 1.18130i) q^{51} +(-11.7526 + 6.78537i) q^{53} +3.75340i q^{55} +(2.48449 + 11.2568i) q^{57} +(-8.39859 - 7.04726i) q^{59} +(-0.888063 + 2.43993i) q^{61} +(7.65849 + 2.08508i) q^{63} +(-1.31797 - 1.57070i) q^{65} +(2.66559 - 15.1173i) q^{67} +(4.55701 - 8.73390i) q^{69} +(2.08522 + 1.20391i) q^{71} +(1.01078 + 0.583575i) q^{73} +(-6.22283 - 0.825197i) q^{75} +(7.32301 + 4.24883i) q^{77} +(1.74259 + 9.88269i) q^{79} +(5.81095 - 6.87262i) q^{81} +(-5.29556 + 4.44350i) q^{83} +(0.644546 - 3.65540i) q^{85} +(-8.22318 - 6.32215i) q^{87} +11.4908 q^{89} +(-4.55643 + 0.793385i) q^{91} +(-4.13817 - 6.50912i) q^{93} +(7.68800 + 1.35560i) q^{95} +(-0.0688894 + 0.189272i) q^{97} +(7.87414 - 5.49152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.69135 + 0.373296i −0.976499 + 0.215523i
\(4\) 0 0
\(5\) −0.203680 + 1.15512i −0.0910883 + 0.516587i 0.904788 + 0.425863i \(0.140029\pi\)
−0.995876 + 0.0907245i \(0.971082\pi\)
\(6\) 0 0
\(7\) 2.02312 + 1.70498i 0.764669 + 0.644423i
\(8\) 0 0
\(9\) 2.72130 1.26275i 0.907100 0.420915i
\(10\) 0 0
\(11\) 3.15137 0.555671i 0.950172 0.167541i 0.322980 0.946406i \(-0.395315\pi\)
0.627192 + 0.778865i \(0.284204\pi\)
\(12\) 0 0
\(13\) −1.12364 + 1.33911i −0.311643 + 0.371401i −0.899017 0.437914i \(-0.855717\pi\)
0.587374 + 0.809316i \(0.300162\pi\)
\(14\) 0 0
\(15\) −0.0867108 2.02975i −0.0223886 0.524078i
\(16\) 0 0
\(17\) −3.16451 −0.767506 −0.383753 0.923436i \(-0.625369\pi\)
−0.383753 + 0.923436i \(0.625369\pi\)
\(18\) 0 0
\(19\) 6.65556i 1.52689i −0.645873 0.763445i \(-0.723506\pi\)
0.645873 0.763445i \(-0.276494\pi\)
\(20\) 0 0
\(21\) −4.05827 2.12849i −0.885586 0.464475i
\(22\) 0 0
\(23\) −3.65594 + 4.35698i −0.762315 + 0.908492i −0.997992 0.0633394i \(-0.979825\pi\)
0.235677 + 0.971832i \(0.424269\pi\)
\(24\) 0 0
\(25\) 3.40564 + 1.23955i 0.681127 + 0.247910i
\(26\) 0 0
\(27\) −4.13128 + 3.15159i −0.795065 + 0.606524i
\(28\) 0 0
\(29\) 3.84940 + 4.58754i 0.714816 + 0.851885i 0.994116 0.108319i \(-0.0345467\pi\)
−0.279300 + 0.960204i \(0.590102\pi\)
\(30\) 0 0
\(31\) 1.52309 + 4.18464i 0.273554 + 0.751584i 0.998057 + 0.0623119i \(0.0198474\pi\)
−0.724502 + 0.689272i \(0.757930\pi\)
\(32\) 0 0
\(33\) −5.12262 + 2.11622i −0.891733 + 0.368387i
\(34\) 0 0
\(35\) −2.38154 + 1.98969i −0.402553 + 0.336319i
\(36\) 0 0
\(37\) 4.75241 + 8.23142i 0.781292 + 1.35324i 0.931189 + 0.364535i \(0.118772\pi\)
−0.149898 + 0.988702i \(0.547894\pi\)
\(38\) 0 0
\(39\) 1.40059 2.68434i 0.224273 0.429839i
\(40\) 0 0
\(41\) 7.74888 + 6.50209i 1.21017 + 1.01546i 0.999280 + 0.0379460i \(0.0120815\pi\)
0.210893 + 0.977509i \(0.432363\pi\)
\(42\) 0 0
\(43\) 3.80179 + 1.38374i 0.579768 + 0.211018i 0.615223 0.788353i \(-0.289066\pi\)
−0.0354555 + 0.999371i \(0.511288\pi\)
\(44\) 0 0
\(45\) 0.904355 + 3.40063i 0.134813 + 0.506937i
\(46\) 0 0
\(47\) −7.95967 2.89708i −1.16104 0.422583i −0.311569 0.950224i \(-0.600855\pi\)
−0.849468 + 0.527641i \(0.823077\pi\)
\(48\) 0 0
\(49\) 1.18606 + 6.89879i 0.169438 + 0.985541i
\(50\) 0 0
\(51\) 5.35228 1.18130i 0.749469 0.165415i
\(52\) 0 0
\(53\) −11.7526 + 6.78537i −1.61434 + 0.932042i −0.625996 + 0.779826i \(0.715307\pi\)
−0.988347 + 0.152215i \(0.951359\pi\)
\(54\) 0 0
\(55\) 3.75340i 0.506108i
\(56\) 0 0
\(57\) 2.48449 + 11.2568i 0.329079 + 1.49101i
\(58\) 0 0
\(59\) −8.39859 7.04726i −1.09340 0.917475i −0.0964398 0.995339i \(-0.530746\pi\)
−0.996964 + 0.0778642i \(0.975190\pi\)
\(60\) 0 0
\(61\) −0.888063 + 2.43993i −0.113705 + 0.312402i −0.983472 0.181061i \(-0.942047\pi\)
0.869767 + 0.493463i \(0.164269\pi\)
\(62\) 0 0
\(63\) 7.65849 + 2.08508i 0.964879 + 0.262695i
\(64\) 0 0
\(65\) −1.31797 1.57070i −0.163474 0.194821i
\(66\) 0 0
\(67\) 2.66559 15.1173i 0.325654 1.84688i −0.179385 0.983779i \(-0.557411\pi\)
0.505039 0.863096i \(-0.331478\pi\)
\(68\) 0 0
\(69\) 4.55701 8.73390i 0.548600 1.05144i
\(70\) 0 0
\(71\) 2.08522 + 1.20391i 0.247471 + 0.142877i 0.618606 0.785702i \(-0.287698\pi\)
−0.371135 + 0.928579i \(0.621031\pi\)
\(72\) 0 0
\(73\) 1.01078 + 0.583575i 0.118303 + 0.0683023i 0.557984 0.829852i \(-0.311575\pi\)
−0.439681 + 0.898154i \(0.644908\pi\)
\(74\) 0 0
\(75\) −6.22283 0.825197i −0.718550 0.0952856i
\(76\) 0 0
\(77\) 7.32301 + 4.24883i 0.834535 + 0.484200i
\(78\) 0 0
\(79\) 1.74259 + 9.88269i 0.196056 + 1.11189i 0.910907 + 0.412612i \(0.135384\pi\)
−0.714851 + 0.699277i \(0.753505\pi\)
\(80\) 0 0
\(81\) 5.81095 6.87262i 0.645661 0.763624i
\(82\) 0 0
\(83\) −5.29556 + 4.44350i −0.581263 + 0.487738i −0.885362 0.464903i \(-0.846089\pi\)
0.304098 + 0.952641i \(0.401645\pi\)
\(84\) 0 0
\(85\) 0.644546 3.65540i 0.0699108 0.396484i
\(86\) 0 0
\(87\) −8.22318 6.32215i −0.881618 0.677806i
\(88\) 0 0
\(89\) 11.4908 1.21802 0.609011 0.793161i \(-0.291566\pi\)
0.609011 + 0.793161i \(0.291566\pi\)
\(90\) 0 0
\(91\) −4.55643 + 0.793385i −0.477643 + 0.0831693i
\(92\) 0 0
\(93\) −4.13817 6.50912i −0.429109 0.674964i
\(94\) 0 0
\(95\) 7.68800 + 1.35560i 0.788772 + 0.139082i
\(96\) 0 0
\(97\) −0.0688894 + 0.189272i −0.00699466 + 0.0192177i −0.943141 0.332393i \(-0.892144\pi\)
0.936146 + 0.351611i \(0.114366\pi\)
\(98\) 0 0
\(99\) 7.87414 5.49152i 0.791381 0.551918i
\(100\) 0 0
\(101\) −4.44873 + 3.73293i −0.442666 + 0.371441i −0.836706 0.547653i \(-0.815522\pi\)
0.394040 + 0.919093i \(0.371077\pi\)
\(102\) 0 0
\(103\) 5.21603 + 0.919726i 0.513950 + 0.0906233i 0.424607 0.905378i \(-0.360412\pi\)
0.0893431 + 0.996001i \(0.471523\pi\)
\(104\) 0 0
\(105\) 3.28526 4.25427i 0.320608 0.415174i
\(106\) 0 0
\(107\) −8.16755 4.71554i −0.789587 0.455868i 0.0502303 0.998738i \(-0.484004\pi\)
−0.839817 + 0.542870i \(0.817338\pi\)
\(108\) 0 0
\(109\) −8.19677 14.1972i −0.785108 1.35985i −0.928934 0.370244i \(-0.879274\pi\)
0.143826 0.989603i \(-0.454059\pi\)
\(110\) 0 0
\(111\) −11.1107 12.1481i −1.05458 1.15305i
\(112\) 0 0
\(113\) 2.80986 + 7.72002i 0.264329 + 0.726238i 0.998863 + 0.0476665i \(0.0151785\pi\)
−0.734534 + 0.678572i \(0.762599\pi\)
\(114\) 0 0
\(115\) −4.28821 5.11049i −0.399877 0.476555i
\(116\) 0 0
\(117\) −1.36682 + 5.06299i −0.126363 + 0.468073i
\(118\) 0 0
\(119\) −6.40220 5.39544i −0.586888 0.494599i
\(120\) 0 0
\(121\) −0.714285 + 0.259978i −0.0649350 + 0.0236344i
\(122\) 0 0
\(123\) −15.5332 8.10465i −1.40059 0.730771i
\(124\) 0 0
\(125\) −5.05785 + 8.76046i −0.452388 + 0.783559i
\(126\) 0 0
\(127\) 2.19382 + 3.79980i 0.194670 + 0.337178i 0.946792 0.321846i \(-0.104303\pi\)
−0.752123 + 0.659023i \(0.770970\pi\)
\(128\) 0 0
\(129\) −6.94668 0.921186i −0.611621 0.0811059i
\(130\) 0 0
\(131\) 7.95915 + 6.67852i 0.695395 + 0.583505i 0.920459 0.390839i \(-0.127815\pi\)
−0.225065 + 0.974344i \(0.572259\pi\)
\(132\) 0 0
\(133\) 11.3476 13.4650i 0.983963 1.16757i
\(134\) 0 0
\(135\) −2.79902 5.41406i −0.240901 0.465968i
\(136\) 0 0
\(137\) 2.88034 7.91366i 0.246084 0.676109i −0.753737 0.657176i \(-0.771751\pi\)
0.999821 0.0189333i \(-0.00602702\pi\)
\(138\) 0 0
\(139\) 17.3552 + 3.06020i 1.47205 + 0.259563i 0.851398 0.524521i \(-0.175755\pi\)
0.620655 + 0.784083i \(0.286867\pi\)
\(140\) 0 0
\(141\) 14.5440 + 1.92865i 1.22483 + 0.162422i
\(142\) 0 0
\(143\) −2.79691 + 4.84439i −0.233889 + 0.405108i
\(144\) 0 0
\(145\) −6.08323 + 3.51215i −0.505184 + 0.291668i
\(146\) 0 0
\(147\) −4.58133 11.2255i −0.377862 0.925862i
\(148\) 0 0
\(149\) −6.37048 17.5027i −0.521890 1.43388i −0.868414 0.495840i \(-0.834860\pi\)
0.346524 0.938041i \(-0.387362\pi\)
\(150\) 0 0
\(151\) 1.11679 + 6.33365i 0.0908834 + 0.515425i 0.995931 + 0.0901156i \(0.0287236\pi\)
−0.905048 + 0.425310i \(0.860165\pi\)
\(152\) 0 0
\(153\) −8.61158 + 3.99597i −0.696205 + 0.323055i
\(154\) 0 0
\(155\) −5.14400 + 0.907027i −0.413176 + 0.0728541i
\(156\) 0 0
\(157\) 2.53024 3.01542i 0.201935 0.240657i −0.655567 0.755137i \(-0.727570\pi\)
0.857503 + 0.514480i \(0.172015\pi\)
\(158\) 0 0
\(159\) 17.3448 15.8636i 1.37553 1.25807i
\(160\) 0 0
\(161\) −14.8250 + 2.58139i −1.16837 + 0.203442i
\(162\) 0 0
\(163\) 12.2039 21.1378i 0.955882 1.65564i 0.223547 0.974693i \(-0.428237\pi\)
0.732336 0.680944i \(-0.238430\pi\)
\(164\) 0 0
\(165\) −1.40113 6.34829i −0.109078 0.494214i
\(166\) 0 0
\(167\) 3.10807 1.13125i 0.240510 0.0875384i −0.218953 0.975735i \(-0.570264\pi\)
0.459463 + 0.888197i \(0.348042\pi\)
\(168\) 0 0
\(169\) 1.72680 + 9.79314i 0.132830 + 0.753319i
\(170\) 0 0
\(171\) −8.40428 18.1118i −0.642691 1.38504i
\(172\) 0 0
\(173\) 5.12258 4.29835i 0.389462 0.326798i −0.426941 0.904279i \(-0.640409\pi\)
0.816404 + 0.577482i \(0.195964\pi\)
\(174\) 0 0
\(175\) 4.77661 + 8.31432i 0.361078 + 0.628503i
\(176\) 0 0
\(177\) 16.8356 + 8.78418i 1.26544 + 0.660260i
\(178\) 0 0
\(179\) 6.24539i 0.466803i −0.972380 0.233401i \(-0.925014\pi\)
0.972380 0.233401i \(-0.0749856\pi\)
\(180\) 0 0
\(181\) 0.630501 0.364020i 0.0468648 0.0270574i −0.476385 0.879237i \(-0.658053\pi\)
0.523249 + 0.852180i \(0.324720\pi\)
\(182\) 0 0
\(183\) 0.591204 4.45828i 0.0437031 0.329566i
\(184\) 0 0
\(185\) −10.4763 + 3.81305i −0.770231 + 0.280341i
\(186\) 0 0
\(187\) −9.97253 + 1.75843i −0.729263 + 0.128589i
\(188\) 0 0
\(189\) −13.7315 0.667708i −0.998820 0.0485686i
\(190\) 0 0
\(191\) −2.44587 + 0.431272i −0.176977 + 0.0312058i −0.261434 0.965221i \(-0.584195\pi\)
0.0844574 + 0.996427i \(0.473084\pi\)
\(192\) 0 0
\(193\) 16.7694 6.10356i 1.20709 0.439344i 0.341395 0.939920i \(-0.389101\pi\)
0.865693 + 0.500576i \(0.166878\pi\)
\(194\) 0 0
\(195\) 2.81548 + 2.16460i 0.201621 + 0.155010i
\(196\) 0 0
\(197\) −4.49176 + 2.59332i −0.320025 + 0.184766i −0.651404 0.758731i \(-0.725820\pi\)
0.331379 + 0.943498i \(0.392486\pi\)
\(198\) 0 0
\(199\) 21.3548i 1.51380i −0.653531 0.756900i \(-0.726713\pi\)
0.653531 0.756900i \(-0.273287\pi\)
\(200\) 0 0
\(201\) 1.13480 + 26.5637i 0.0800427 + 1.87366i
\(202\) 0 0
\(203\) −0.0338585 + 15.8443i −0.00237640 + 1.11205i
\(204\) 0 0
\(205\) −9.08901 + 7.62658i −0.634804 + 0.532664i
\(206\) 0 0
\(207\) −4.44715 + 16.4732i −0.309098 + 1.14496i
\(208\) 0 0
\(209\) −3.69830 20.9741i −0.255817 1.45081i
\(210\) 0 0
\(211\) 15.7930 5.74820i 1.08724 0.395722i 0.264641 0.964347i \(-0.414747\pi\)
0.822597 + 0.568625i \(0.192524\pi\)
\(212\) 0 0
\(213\) −3.97625 1.25781i −0.272448 0.0861839i
\(214\) 0 0
\(215\) −2.37274 + 4.10970i −0.161819 + 0.280279i
\(216\) 0 0
\(217\) −4.05336 + 11.0629i −0.275160 + 0.750998i
\(218\) 0 0
\(219\) −1.92743 0.609706i −0.130243 0.0412001i
\(220\) 0 0
\(221\) 3.55578 4.23762i 0.239188 0.285053i
\(222\) 0 0
\(223\) 0.0697119 0.0122921i 0.00466825 0.000823139i −0.171314 0.985217i \(-0.554801\pi\)
0.175982 + 0.984393i \(0.443690\pi\)
\(224\) 0 0
\(225\) 10.8330 0.927264i 0.722200 0.0618176i
\(226\) 0 0
\(227\) 1.52723 + 8.66137i 0.101366 + 0.574876i 0.992610 + 0.121351i \(0.0387226\pi\)
−0.891244 + 0.453525i \(0.850166\pi\)
\(228\) 0 0
\(229\) −7.04568 19.3578i −0.465591 1.27920i −0.921224 0.389034i \(-0.872809\pi\)
0.455632 0.890168i \(-0.349413\pi\)
\(230\) 0 0
\(231\) −13.9718 4.45260i −0.919278 0.292959i
\(232\) 0 0
\(233\) 9.43506 5.44734i 0.618111 0.356867i −0.158022 0.987436i \(-0.550512\pi\)
0.776133 + 0.630569i \(0.217178\pi\)
\(234\) 0 0
\(235\) 4.96771 8.60433i 0.324058 0.561284i
\(236\) 0 0
\(237\) −6.63648 16.0645i −0.431086 1.04350i
\(238\) 0 0
\(239\) 4.63739 + 0.817697i 0.299968 + 0.0528924i 0.321606 0.946873i \(-0.395777\pi\)
−0.0216386 + 0.999766i \(0.506888\pi\)
\(240\) 0 0
\(241\) −6.76085 + 18.5753i −0.435505 + 1.19654i 0.506882 + 0.862015i \(0.330798\pi\)
−0.942387 + 0.334524i \(0.891424\pi\)
\(242\) 0 0
\(243\) −7.26280 + 13.7932i −0.465909 + 0.884833i
\(244\) 0 0
\(245\) −8.21053 0.0350911i −0.524552 0.00224189i
\(246\) 0 0
\(247\) 8.91250 + 7.47848i 0.567089 + 0.475844i
\(248\) 0 0
\(249\) 7.29788 9.49231i 0.462484 0.601551i
\(250\) 0 0
\(251\) 4.08899 + 7.08234i 0.258095 + 0.447033i 0.965731 0.259543i \(-0.0835720\pi\)
−0.707637 + 0.706576i \(0.750239\pi\)
\(252\) 0 0
\(253\) −9.10015 + 15.7619i −0.572121 + 0.990943i
\(254\) 0 0
\(255\) 0.274397 + 6.42315i 0.0171834 + 0.402234i
\(256\) 0 0
\(257\) 18.2251 6.63338i 1.13685 0.413779i 0.296074 0.955165i \(-0.404323\pi\)
0.840774 + 0.541387i \(0.182100\pi\)
\(258\) 0 0
\(259\) −4.41971 + 24.7560i −0.274628 + 1.53826i
\(260\) 0 0
\(261\) 16.2683 + 7.62326i 1.00698 + 0.471868i
\(262\) 0 0
\(263\) −6.79618 8.09938i −0.419071 0.499429i 0.514665 0.857391i \(-0.327916\pi\)
−0.933736 + 0.357962i \(0.883472\pi\)
\(264\) 0 0
\(265\) −5.44418 14.9577i −0.334433 0.918847i
\(266\) 0 0
\(267\) −19.4349 + 4.28947i −1.18940 + 0.262511i
\(268\) 0 0
\(269\) 1.21301 + 2.10099i 0.0739585 + 0.128100i 0.900633 0.434581i \(-0.143103\pi\)
−0.826674 + 0.562681i \(0.809770\pi\)
\(270\) 0 0
\(271\) −13.7260 7.92468i −0.833792 0.481390i 0.0213570 0.999772i \(-0.493201\pi\)
−0.855149 + 0.518382i \(0.826535\pi\)
\(272\) 0 0
\(273\) 7.41032 3.04278i 0.448493 0.184158i
\(274\) 0 0
\(275\) 11.4212 + 2.01386i 0.688724 + 0.121441i
\(276\) 0 0
\(277\) −5.08767 + 4.26906i −0.305688 + 0.256503i −0.782707 0.622390i \(-0.786162\pi\)
0.477019 + 0.878893i \(0.341717\pi\)
\(278\) 0 0
\(279\) 9.42891 + 9.46440i 0.564494 + 0.566619i
\(280\) 0 0
\(281\) 5.25557 14.4396i 0.313521 0.861392i −0.678418 0.734676i \(-0.737334\pi\)
0.991939 0.126716i \(-0.0404436\pi\)
\(282\) 0 0
\(283\) −2.48443 0.438073i −0.147684 0.0260407i 0.0993172 0.995056i \(-0.468334\pi\)
−0.247001 + 0.969015i \(0.579445\pi\)
\(284\) 0 0
\(285\) −13.5091 + 0.577109i −0.800210 + 0.0341850i
\(286\) 0 0
\(287\) 4.59101 + 26.3662i 0.270999 + 1.55635i
\(288\) 0 0
\(289\) −6.98588 −0.410934
\(290\) 0 0
\(291\) 0.0458612 0.345840i 0.00268843 0.0202735i
\(292\) 0 0
\(293\) 0.425049 2.41057i 0.0248316 0.140827i −0.969871 0.243617i \(-0.921666\pi\)
0.994703 + 0.102790i \(0.0327770\pi\)
\(294\) 0 0
\(295\) 9.85108 8.26604i 0.573552 0.481267i
\(296\) 0 0
\(297\) −11.2679 + 12.2274i −0.653832 + 0.709508i
\(298\) 0 0
\(299\) −1.72648 9.79138i −0.0998451 0.566250i
\(300\) 0 0
\(301\) 5.33224 + 9.28146i 0.307345 + 0.534975i
\(302\) 0 0
\(303\) 6.13086 7.97437i 0.352209 0.458116i
\(304\) 0 0
\(305\) −2.63755 1.52279i −0.151025 0.0871946i
\(306\) 0 0
\(307\) −16.1947 9.34999i −0.924278 0.533632i −0.0392804 0.999228i \(-0.512507\pi\)
−0.884997 + 0.465596i \(0.845840\pi\)
\(308\) 0 0
\(309\) −9.16544 + 0.391548i −0.521403 + 0.0222744i
\(310\) 0 0
\(311\) −0.0875069 + 0.496276i −0.00496206 + 0.0281413i −0.987188 0.159560i \(-0.948993\pi\)
0.982226 + 0.187701i \(0.0601036\pi\)
\(312\) 0 0
\(313\) 12.0362 + 14.3442i 0.680327 + 0.810782i 0.990150 0.140012i \(-0.0447142\pi\)
−0.309823 + 0.950794i \(0.600270\pi\)
\(314\) 0 0
\(315\) −3.96840 + 8.42182i −0.223594 + 0.474516i
\(316\) 0 0
\(317\) 8.95841 24.6130i 0.503155 1.38241i −0.385023 0.922907i \(-0.625807\pi\)
0.888178 0.459499i \(-0.151971\pi\)
\(318\) 0 0
\(319\) 14.6800 + 12.3180i 0.821925 + 0.689677i
\(320\) 0 0
\(321\) 15.5744 + 4.92669i 0.869280 + 0.274981i
\(322\) 0 0
\(323\) 21.0616i 1.17190i
\(324\) 0 0
\(325\) −5.48661 + 3.16770i −0.304342 + 0.175712i
\(326\) 0 0
\(327\) 19.1633 + 20.9526i 1.05973 + 1.15868i
\(328\) 0 0
\(329\) −11.1639 19.4323i −0.615487 1.07133i
\(330\) 0 0
\(331\) −14.3667 5.22905i −0.789666 0.287415i −0.0844686 0.996426i \(-0.526919\pi\)
−0.705197 + 0.709011i \(0.749141\pi\)
\(332\) 0 0
\(333\) 23.3269 + 16.3991i 1.27831 + 0.898664i
\(334\) 0 0
\(335\) 16.9195 + 6.15818i 0.924409 + 0.336457i
\(336\) 0 0
\(337\) −10.5844 8.88138i −0.576570 0.483800i 0.307249 0.951629i \(-0.400592\pi\)
−0.883819 + 0.467830i \(0.845036\pi\)
\(338\) 0 0
\(339\) −7.63429 12.0083i −0.414638 0.652202i
\(340\) 0 0
\(341\) 7.12508 + 12.3410i 0.385845 + 0.668303i
\(342\) 0 0
\(343\) −9.36276 + 15.9793i −0.505542 + 0.862802i
\(344\) 0 0
\(345\) 9.16057 + 7.04283i 0.493188 + 0.379173i
\(346\) 0 0
\(347\) −5.65264 15.5305i −0.303450 0.833721i −0.993894 0.110336i \(-0.964807\pi\)
0.690445 0.723385i \(-0.257415\pi\)
\(348\) 0 0
\(349\) −4.58698 5.46655i −0.245535 0.292618i 0.629175 0.777264i \(-0.283393\pi\)
−0.874710 + 0.484646i \(0.838948\pi\)
\(350\) 0 0
\(351\) 0.421774 9.07349i 0.0225126 0.484307i
\(352\) 0 0
\(353\) 13.7755 + 5.01387i 0.733195 + 0.266861i 0.681517 0.731803i \(-0.261321\pi\)
0.0516785 + 0.998664i \(0.483543\pi\)
\(354\) 0 0
\(355\) −1.81538 + 2.16348i −0.0963502 + 0.114826i
\(356\) 0 0
\(357\) 12.8424 + 6.73563i 0.679693 + 0.356488i
\(358\) 0 0
\(359\) 4.76141i 0.251298i −0.992075 0.125649i \(-0.959899\pi\)
0.992075 0.125649i \(-0.0401013\pi\)
\(360\) 0 0
\(361\) −25.2964 −1.33139
\(362\) 0 0
\(363\) 1.11105 0.706353i 0.0583152 0.0370739i
\(364\) 0 0
\(365\) −0.879977 + 1.04872i −0.0460601 + 0.0548923i
\(366\) 0 0
\(367\) 5.90362 1.04097i 0.308166 0.0543380i −0.0174264 0.999848i \(-0.505547\pi\)
0.325593 + 0.945510i \(0.394436\pi\)
\(368\) 0 0
\(369\) 29.2975 + 7.90926i 1.52517 + 0.411740i
\(370\) 0 0
\(371\) −35.3459 6.31035i −1.83507 0.327617i
\(372\) 0 0
\(373\) −5.93592 + 33.6643i −0.307350 + 1.74307i 0.304879 + 0.952391i \(0.401384\pi\)
−0.612230 + 0.790680i \(0.709727\pi\)
\(374\) 0 0
\(375\) 5.28433 16.7050i 0.272882 0.862644i
\(376\) 0 0
\(377\) −10.4686 −0.539159
\(378\) 0 0
\(379\) −8.62058 −0.442810 −0.221405 0.975182i \(-0.571064\pi\)
−0.221405 + 0.975182i \(0.571064\pi\)
\(380\) 0 0
\(381\) −5.12895 5.60783i −0.262764 0.287298i
\(382\) 0 0
\(383\) 2.43473 13.8080i 0.124409 0.705558i −0.857248 0.514903i \(-0.827828\pi\)
0.981657 0.190655i \(-0.0610611\pi\)
\(384\) 0 0
\(385\) −6.39948 + 7.59359i −0.326148 + 0.387005i
\(386\) 0 0
\(387\) 12.0931 1.03513i 0.614728 0.0526184i
\(388\) 0 0
\(389\) 32.0313 5.64799i 1.62405 0.286364i 0.713779 0.700371i \(-0.246982\pi\)
0.910274 + 0.414007i \(0.135871\pi\)
\(390\) 0 0
\(391\) 11.5692 13.7877i 0.585082 0.697274i
\(392\) 0 0
\(393\) −15.9547 8.32457i −0.804811 0.419919i
\(394\) 0 0
\(395\) −11.7707 −0.592246
\(396\) 0 0
\(397\) 1.96860i 0.0988013i −0.998779 0.0494007i \(-0.984269\pi\)
0.998779 0.0494007i \(-0.0157311\pi\)
\(398\) 0 0
\(399\) −14.1663 + 27.0100i −0.709202 + 1.35219i
\(400\) 0 0
\(401\) −15.9098 + 18.9605i −0.794495 + 0.946842i −0.999490 0.0319205i \(-0.989838\pi\)
0.204995 + 0.978763i \(0.434282\pi\)
\(402\) 0 0
\(403\) −7.31509 2.66247i −0.364390 0.132627i
\(404\) 0 0
\(405\) 6.75516 + 8.11218i 0.335666 + 0.403097i
\(406\) 0 0
\(407\) 19.5505 + 23.2994i 0.969085 + 1.15491i
\(408\) 0 0
\(409\) −10.8941 29.9314i −0.538680 1.48001i −0.848489 0.529213i \(-0.822487\pi\)
0.309809 0.950799i \(-0.399735\pi\)
\(410\) 0 0
\(411\) −1.91751 + 14.4599i −0.0945836 + 0.713257i
\(412\) 0 0
\(413\) −4.97594 28.5769i −0.244850 1.40618i
\(414\) 0 0
\(415\) −4.05420 7.02208i −0.199013 0.344700i
\(416\) 0 0
\(417\) −30.4961 + 1.30279i −1.49340 + 0.0637981i
\(418\) 0 0
\(419\) 28.8373 + 24.1974i 1.40879 + 1.18212i 0.957032 + 0.289981i \(0.0936491\pi\)
0.451763 + 0.892138i \(0.350795\pi\)
\(420\) 0 0
\(421\) 3.47410 + 1.26447i 0.169317 + 0.0616264i 0.425288 0.905058i \(-0.360173\pi\)
−0.255971 + 0.966685i \(0.582395\pi\)
\(422\) 0 0
\(423\) −25.3189 + 2.16720i −1.23105 + 0.105373i
\(424\) 0 0
\(425\) −10.7772 3.92257i −0.522770 0.190273i
\(426\) 0 0
\(427\) −5.95671 + 3.42216i −0.288265 + 0.165610i
\(428\) 0 0
\(429\) 2.92215 9.23761i 0.141083 0.445996i
\(430\) 0 0
\(431\) 4.28781 2.47557i 0.206536 0.119244i −0.393164 0.919468i \(-0.628620\pi\)
0.599701 + 0.800224i \(0.295286\pi\)
\(432\) 0 0
\(433\) 6.70918i 0.322423i −0.986920 0.161211i \(-0.948460\pi\)
0.986920 0.161211i \(-0.0515401\pi\)
\(434\) 0 0
\(435\) 8.97776 8.21111i 0.430451 0.393692i
\(436\) 0 0
\(437\) 28.9981 + 24.3323i 1.38717 + 1.16397i
\(438\) 0 0
\(439\) −0.129633 + 0.356163i −0.00618704 + 0.0169988i −0.942748 0.333507i \(-0.891768\pi\)
0.936561 + 0.350506i \(0.113990\pi\)
\(440\) 0 0
\(441\) 11.9390 + 17.2760i 0.568526 + 0.822665i
\(442\) 0 0
\(443\) −10.8964 12.9858i −0.517705 0.616976i 0.442332 0.896851i \(-0.354151\pi\)
−0.960036 + 0.279875i \(0.909707\pi\)
\(444\) 0 0
\(445\) −2.34044 + 13.2733i −0.110948 + 0.629215i
\(446\) 0 0
\(447\) 17.3084 + 27.2251i 0.818659 + 1.28770i
\(448\) 0 0
\(449\) −15.9872 9.23020i −0.754481 0.435600i 0.0728294 0.997344i \(-0.476797\pi\)
−0.827311 + 0.561744i \(0.810130\pi\)
\(450\) 0 0
\(451\) 28.0326 + 16.1846i 1.32000 + 0.762104i
\(452\) 0 0
\(453\) −4.25321 10.2955i −0.199833 0.483725i
\(454\) 0 0
\(455\) 0.0115926 5.42483i 0.000543469 0.254320i
\(456\) 0 0
\(457\) −0.345758 1.96089i −0.0161739 0.0917266i 0.975652 0.219323i \(-0.0703849\pi\)
−0.991826 + 0.127596i \(0.959274\pi\)
\(458\) 0 0
\(459\) 13.0735 9.97324i 0.610218 0.465511i
\(460\) 0 0
\(461\) 23.4896 19.7101i 1.09402 0.917992i 0.0970119 0.995283i \(-0.469072\pi\)
0.997009 + 0.0772911i \(0.0246271\pi\)
\(462\) 0 0
\(463\) 1.76880 10.0313i 0.0822029 0.466196i −0.915722 0.401812i \(-0.868381\pi\)
0.997925 0.0643841i \(-0.0205083\pi\)
\(464\) 0 0
\(465\) 8.36170 3.45433i 0.387764 0.160191i
\(466\) 0 0
\(467\) −12.6759 −0.586569 −0.293285 0.956025i \(-0.594748\pi\)
−0.293285 + 0.956025i \(0.594748\pi\)
\(468\) 0 0
\(469\) 31.1676 26.0394i 1.43919 1.20239i
\(470\) 0 0
\(471\) −3.15387 + 6.04465i −0.145322 + 0.278523i
\(472\) 0 0
\(473\) 12.7497 + 2.24812i 0.586233 + 0.103369i
\(474\) 0 0
\(475\) 8.24990 22.6664i 0.378531 1.04001i
\(476\) 0 0
\(477\) −23.4142 + 33.3056i −1.07206 + 1.52496i
\(478\) 0 0
\(479\) −26.8830 + 22.5575i −1.22831 + 1.03068i −0.229968 + 0.973198i \(0.573862\pi\)
−0.998347 + 0.0574804i \(0.981693\pi\)
\(480\) 0 0
\(481\) −16.3628 2.88520i −0.746078 0.131554i
\(482\) 0 0
\(483\) 24.1105 9.90013i 1.09707 0.450472i
\(484\) 0 0
\(485\) −0.204601 0.118127i −0.00929046 0.00536385i
\(486\) 0 0
\(487\) −2.49812 4.32688i −0.113201 0.196070i 0.803858 0.594821i \(-0.202777\pi\)
−0.917059 + 0.398751i \(0.869444\pi\)
\(488\) 0 0
\(489\) −12.7504 + 40.3069i −0.576591 + 1.82274i
\(490\) 0 0
\(491\) 4.65547 + 12.7908i 0.210098 + 0.577241i 0.999320 0.0368676i \(-0.0117380\pi\)
−0.789222 + 0.614108i \(0.789516\pi\)
\(492\) 0 0
\(493\) −12.1815 14.5173i −0.548626 0.653827i
\(494\) 0 0
\(495\) 4.73958 + 10.2141i 0.213029 + 0.459091i
\(496\) 0 0
\(497\) 2.16603 + 5.99092i 0.0971598 + 0.268730i
\(498\) 0 0
\(499\) 15.5283 5.65183i 0.695141 0.253011i 0.0298062 0.999556i \(-0.490511\pi\)
0.665335 + 0.746545i \(0.268289\pi\)
\(500\) 0 0
\(501\) −4.83453 + 3.07356i −0.215991 + 0.137316i
\(502\) 0 0
\(503\) 4.71614 8.16859i 0.210282 0.364219i −0.741521 0.670930i \(-0.765895\pi\)
0.951803 + 0.306711i \(0.0992284\pi\)
\(504\) 0 0
\(505\) −3.40588 5.89916i −0.151560 0.262509i
\(506\) 0 0
\(507\) −6.57635 15.9190i −0.292066 0.706987i
\(508\) 0 0
\(509\) 25.2080 + 21.1520i 1.11733 + 0.937547i 0.998466 0.0553640i \(-0.0176319\pi\)
0.118859 + 0.992911i \(0.462076\pi\)
\(510\) 0 0
\(511\) 1.04995 + 2.90401i 0.0464471 + 0.128466i
\(512\) 0 0
\(513\) 20.9756 + 27.4960i 0.926095 + 1.21398i
\(514\) 0 0
\(515\) −2.12480 + 5.83783i −0.0936297 + 0.257246i
\(516\) 0 0
\(517\) −26.6936 4.70681i −1.17399 0.207005i
\(518\) 0 0
\(519\) −7.05949 + 9.18224i −0.309877 + 0.403056i
\(520\) 0 0
\(521\) 2.24316 3.88526i 0.0982745 0.170216i −0.812696 0.582688i \(-0.802001\pi\)
0.910971 + 0.412471i \(0.135334\pi\)
\(522\) 0 0
\(523\) −29.1689 + 16.8407i −1.27547 + 0.736391i −0.976011 0.217719i \(-0.930138\pi\)
−0.299455 + 0.954110i \(0.596805\pi\)
\(524\) 0 0
\(525\) −11.1826 12.2793i −0.488049 0.535912i
\(526\) 0 0
\(527\) −4.81982 13.2423i −0.209955 0.576846i
\(528\) 0 0
\(529\) −1.62346 9.20707i −0.0705850 0.400307i
\(530\) 0 0
\(531\) −31.7540 8.57241i −1.37801 0.372011i
\(532\) 0 0
\(533\) −17.4140 + 3.07055i −0.754283 + 0.133000i
\(534\) 0 0
\(535\) 7.11059 8.47407i 0.307418 0.366366i
\(536\) 0 0
\(537\) 2.33138 + 10.5631i 0.100607 + 0.455832i
\(538\) 0 0
\(539\) 7.57117 + 21.0815i 0.326114 + 0.908046i
\(540\) 0 0
\(541\) −13.5046 + 23.3907i −0.580610 + 1.00565i 0.414797 + 0.909914i \(0.363853\pi\)
−0.995407 + 0.0957324i \(0.969481\pi\)
\(542\) 0 0
\(543\) −0.930509 + 0.851048i −0.0399319 + 0.0365220i
\(544\) 0 0
\(545\) 18.0691 6.57660i 0.773994 0.281711i
\(546\) 0 0
\(547\) 7.54588 + 42.7948i 0.322638 + 1.82977i 0.525775 + 0.850623i \(0.323775\pi\)
−0.203137 + 0.979150i \(0.565114\pi\)
\(548\) 0 0
\(549\) 0.664329 + 7.76119i 0.0283529 + 0.331240i
\(550\) 0 0
\(551\) 30.5326 25.6199i 1.30073 1.09145i
\(552\) 0 0
\(553\) −13.3244 + 22.9650i −0.566609 + 0.976571i
\(554\) 0 0
\(555\) 16.2956 10.3599i 0.691710 0.439755i
\(556\) 0 0
\(557\) 13.7719i 0.583536i 0.956489 + 0.291768i \(0.0942436\pi\)
−0.956489 + 0.291768i \(0.905756\pi\)
\(558\) 0 0
\(559\) −6.12483 + 3.53617i −0.259053 + 0.149564i
\(560\) 0 0
\(561\) 16.2106 6.69681i 0.684411 0.282740i
\(562\) 0 0
\(563\) 17.8735 6.50544i 0.753280 0.274172i 0.0632947 0.997995i \(-0.479839\pi\)
0.689985 + 0.723823i \(0.257617\pi\)
\(564\) 0 0
\(565\) −9.48989 + 1.67332i −0.399243 + 0.0703972i
\(566\) 0 0
\(567\) 23.4740 3.99659i 0.985814 0.167841i
\(568\) 0 0
\(569\) 15.2893 2.69591i 0.640959 0.113018i 0.156283 0.987712i \(-0.450049\pi\)
0.484676 + 0.874694i \(0.338938\pi\)
\(570\) 0 0
\(571\) −18.8715 + 6.86868i −0.789749 + 0.287445i −0.705232 0.708977i \(-0.749157\pi\)
−0.0845175 + 0.996422i \(0.526935\pi\)
\(572\) 0 0
\(573\) 3.97581 1.64246i 0.166092 0.0686149i
\(574\) 0 0
\(575\) −17.8515 + 10.3066i −0.744458 + 0.429813i
\(576\) 0 0
\(577\) 18.1983i 0.757606i 0.925477 + 0.378803i \(0.123664\pi\)
−0.925477 + 0.378803i \(0.876336\pi\)
\(578\) 0 0
\(579\) −26.0844 + 16.5832i −1.08403 + 0.689174i
\(580\) 0 0
\(581\) −18.2897 0.0390841i −0.758784 0.00162148i
\(582\) 0 0
\(583\) −33.2663 + 27.9137i −1.37775 + 1.15607i
\(584\) 0 0
\(585\) −5.56998 2.61007i −0.230291 0.107913i
\(586\) 0 0
\(587\) −7.53824 42.7515i −0.311136 1.76454i −0.593111 0.805121i \(-0.702100\pi\)
0.281974 0.959422i \(-0.409011\pi\)
\(588\) 0 0
\(589\) 27.8511 10.1370i 1.14759 0.417687i
\(590\) 0 0
\(591\) 6.62905 6.06296i 0.272683 0.249397i
\(592\) 0 0
\(593\) 19.1883 33.2351i 0.787970 1.36480i −0.139239 0.990259i \(-0.544466\pi\)
0.927209 0.374544i \(-0.122201\pi\)
\(594\) 0 0
\(595\) 7.53640 6.29639i 0.308962 0.258127i
\(596\) 0 0
\(597\) 7.97165 + 36.1183i 0.326258 + 1.47822i
\(598\) 0 0
\(599\) 6.15487 7.33509i 0.251481 0.299704i −0.625504 0.780221i \(-0.715107\pi\)
0.876985 + 0.480517i \(0.159551\pi\)
\(600\) 0 0
\(601\) −22.7261 + 4.00723i −0.927018 + 0.163458i −0.616721 0.787181i \(-0.711540\pi\)
−0.310297 + 0.950640i \(0.600428\pi\)
\(602\) 0 0
\(603\) −11.8355 44.5047i −0.481977 1.81237i
\(604\) 0 0
\(605\) −0.154822 0.878040i −0.00629442 0.0356974i
\(606\) 0 0
\(607\) 2.50667 + 6.88703i 0.101743 + 0.279536i 0.980111 0.198448i \(-0.0635900\pi\)
−0.878369 + 0.477984i \(0.841368\pi\)
\(608\) 0 0
\(609\) −5.85736 26.8109i −0.237352 1.08643i
\(610\) 0 0
\(611\) 12.8233 7.40355i 0.518776 0.299516i
\(612\) 0 0
\(613\) 9.67118 16.7510i 0.390615 0.676566i −0.601916 0.798560i \(-0.705596\pi\)
0.992531 + 0.121994i \(0.0389289\pi\)
\(614\) 0 0
\(615\) 12.5257 16.2921i 0.505084 0.656960i
\(616\) 0 0
\(617\) −18.4581 3.25466i −0.743094 0.131028i −0.210731 0.977544i \(-0.567585\pi\)
−0.532362 + 0.846517i \(0.678696\pi\)
\(618\) 0 0
\(619\) 12.5229 34.4065i 0.503339 1.38291i −0.384655 0.923060i \(-0.625680\pi\)
0.887995 0.459853i \(-0.152098\pi\)
\(620\) 0 0
\(621\) 1.37230 29.5219i 0.0550686 1.18467i
\(622\) 0 0
\(623\) 23.2473 + 19.5916i 0.931385 + 0.784922i
\(624\) 0 0
\(625\) 4.79227 + 4.02119i 0.191691 + 0.160848i
\(626\) 0 0
\(627\) 14.0846 + 34.0939i 0.562487 + 1.36158i
\(628\) 0 0
\(629\) −15.0391 26.0484i −0.599646 1.03862i
\(630\) 0 0
\(631\) 11.0792 19.1897i 0.441056 0.763931i −0.556712 0.830706i \(-0.687937\pi\)
0.997768 + 0.0667740i \(0.0212707\pi\)
\(632\) 0 0
\(633\) −24.5657 + 15.6177i −0.976399 + 0.620746i
\(634\) 0 0
\(635\) −4.83608 + 1.76019i −0.191914 + 0.0698509i
\(636\) 0 0
\(637\) −10.5709 6.16351i −0.418835 0.244207i
\(638\) 0 0
\(639\) 7.19475 + 0.643079i 0.284620 + 0.0254398i
\(640\) 0 0
\(641\) −30.2591 36.0614i −1.19516 1.42434i −0.879783 0.475376i \(-0.842312\pi\)
−0.315381 0.948965i \(-0.602132\pi\)
\(642\) 0 0
\(643\) −2.45049 6.73265i −0.0966377 0.265510i 0.881949 0.471345i \(-0.156231\pi\)
−0.978587 + 0.205835i \(0.934009\pi\)
\(644\) 0 0
\(645\) 2.47898 7.83666i 0.0976098 0.308568i
\(646\) 0 0
\(647\) 9.26911 + 16.0546i 0.364406 + 0.631170i 0.988681 0.150035i \(-0.0479386\pi\)
−0.624274 + 0.781205i \(0.714605\pi\)
\(648\) 0 0
\(649\) −30.3830 17.5416i −1.19264 0.688569i
\(650\) 0 0
\(651\) 2.72589 20.2243i 0.106836 0.792652i
\(652\) 0 0
\(653\) −43.2991 7.63480i −1.69442 0.298773i −0.758683 0.651460i \(-0.774157\pi\)
−0.935741 + 0.352687i \(0.885268\pi\)
\(654\) 0 0
\(655\) −9.33564 + 7.83353i −0.364774 + 0.306081i
\(656\) 0 0
\(657\) 3.48755 + 0.311723i 0.136062 + 0.0121615i
\(658\) 0 0
\(659\) 12.0098 32.9965i 0.467834 1.28536i −0.451636 0.892202i \(-0.649160\pi\)
0.919470 0.393160i \(-0.128618\pi\)
\(660\) 0 0
\(661\) 2.60599 + 0.459507i 0.101361 + 0.0178728i 0.224099 0.974566i \(-0.428056\pi\)
−0.122737 + 0.992439i \(0.539167\pi\)
\(662\) 0 0
\(663\) −4.43217 + 8.49463i −0.172131 + 0.329904i
\(664\) 0 0
\(665\) 13.2425 + 15.8505i 0.513522 + 0.614654i
\(666\) 0 0
\(667\) −34.0610 −1.31885
\(668\) 0 0
\(669\) −0.113318 + 0.0468133i −0.00438114 + 0.00180991i
\(670\) 0 0
\(671\) −1.44281 + 8.18259i −0.0556991 + 0.315886i
\(672\) 0 0
\(673\) 8.03878 6.74534i 0.309872 0.260014i −0.474567 0.880219i \(-0.657395\pi\)
0.784439 + 0.620206i \(0.212951\pi\)
\(674\) 0 0
\(675\) −17.9762 + 5.61224i −0.691904 + 0.216015i
\(676\) 0 0
\(677\) 7.64065 + 43.3323i 0.293654 + 1.66539i 0.672623 + 0.739985i \(0.265168\pi\)
−0.378969 + 0.925409i \(0.623721\pi\)
\(678\) 0 0
\(679\) −0.462077 + 0.265465i −0.0177329 + 0.0101876i
\(680\) 0 0
\(681\) −5.81634 14.0793i −0.222883 0.539519i
\(682\) 0 0
\(683\) 14.2133 + 8.20603i 0.543855 + 0.313995i 0.746640 0.665228i \(-0.231666\pi\)
−0.202785 + 0.979223i \(0.564999\pi\)
\(684\) 0 0
\(685\) 8.55459 + 4.93900i 0.326854 + 0.188709i
\(686\) 0 0
\(687\) 19.1429 + 30.1107i 0.730346 + 1.14879i
\(688\) 0 0
\(689\) 4.11941 23.3623i 0.156937 0.890033i
\(690\) 0 0
\(691\) 0.431926 + 0.514749i 0.0164312 + 0.0195820i 0.774197 0.632944i \(-0.218154\pi\)
−0.757766 + 0.652526i \(0.773709\pi\)
\(692\) 0 0
\(693\) 25.2933 + 2.31525i 0.960813 + 0.0879492i
\(694\) 0 0
\(695\) −7.06982 + 19.4242i −0.268174 + 0.736801i
\(696\) 0 0
\(697\) −24.5214 20.5759i −0.928815 0.779368i
\(698\) 0 0
\(699\) −13.9245 + 12.7354i −0.526672 + 0.481697i
\(700\) 0 0
\(701\) 51.7991i 1.95643i −0.207606 0.978213i \(-0.566567\pi\)
0.207606 0.978213i \(-0.433433\pi\)
\(702\) 0 0
\(703\) 54.7847 31.6300i 2.06624 1.19295i
\(704\) 0 0
\(705\) −5.19015 + 16.4073i −0.195472 + 0.617935i
\(706\) 0 0
\(707\) −15.3649 0.0328341i −0.577858 0.00123485i
\(708\) 0 0
\(709\) −16.4657 5.99302i −0.618382 0.225073i 0.0137846 0.999905i \(-0.495612\pi\)
−0.632167 + 0.774832i \(0.717834\pi\)
\(710\) 0 0
\(711\) 17.2214 + 24.6933i 0.645854 + 0.926072i
\(712\) 0 0
\(713\) −23.8007 8.66274i −0.891343 0.324422i
\(714\) 0 0
\(715\) −5.02620 4.21748i −0.187969 0.157725i
\(716\) 0 0
\(717\) −8.14867 + 0.348111i −0.304318 + 0.0130005i
\(718\) 0 0
\(719\) −8.95164 15.5047i −0.333840 0.578228i 0.649421 0.760429i \(-0.275011\pi\)
−0.983261 + 0.182201i \(0.941678\pi\)
\(720\) 0 0
\(721\) 8.98455 + 10.7540i 0.334602 + 0.400498i
\(722\) 0 0
\(723\) 4.50086 33.9410i 0.167389 1.26228i
\(724\) 0 0
\(725\) 7.42318 + 20.3950i 0.275690 + 0.757452i
\(726\) 0 0
\(727\) 20.1921 + 24.0641i 0.748885 + 0.892487i 0.997091 0.0762207i \(-0.0242854\pi\)
−0.248206 + 0.968707i \(0.579841\pi\)
\(728\) 0 0
\(729\) 7.13497 26.0402i 0.264258 0.964452i
\(730\) 0 0
\(731\) −12.0308 4.37885i −0.444975 0.161958i
\(732\) 0 0
\(733\) 27.6262 32.9236i 1.02040 1.21606i 0.0442345 0.999021i \(-0.485915\pi\)
0.976163 0.217041i \(-0.0696404\pi\)
\(734\) 0 0
\(735\) 13.8999 3.00561i 0.512707 0.110864i
\(736\) 0 0
\(737\) 49.1214i 1.80941i
\(738\) 0 0
\(739\) −18.4984 −0.680476 −0.340238 0.940339i \(-0.610508\pi\)
−0.340238 + 0.940339i \(0.610508\pi\)
\(740\) 0 0
\(741\) −17.8658 9.32169i −0.656317 0.342441i
\(742\) 0 0
\(743\) 2.62524 3.12864i 0.0963108 0.114779i −0.715736 0.698371i \(-0.753909\pi\)
0.812047 + 0.583592i \(0.198353\pi\)
\(744\) 0 0
\(745\) 21.5154 3.79374i 0.788262 0.138992i
\(746\) 0 0
\(747\) −8.79980 + 18.7790i −0.321968 + 0.687089i
\(748\) 0 0
\(749\) −8.48405 23.4657i −0.310001 0.857416i
\(750\) 0 0
\(751\) −2.26625 + 12.8525i −0.0826965 + 0.468995i 0.915133 + 0.403151i \(0.132085\pi\)
−0.997830 + 0.0658441i \(0.979026\pi\)
\(752\) 0 0
\(753\) −9.55970 10.4523i −0.348375 0.380902i
\(754\) 0 0
\(755\) −7.54362 −0.274540
\(756\) 0 0
\(757\) −13.3825 −0.486396 −0.243198 0.969977i \(-0.578196\pi\)
−0.243198 + 0.969977i \(0.578196\pi\)
\(758\) 0 0
\(759\) 9.50763 30.0559i 0.345105 1.09096i
\(760\) 0 0
\(761\) 8.32479 47.2122i 0.301773 1.71144i −0.336544 0.941668i \(-0.609258\pi\)
0.638317 0.769774i \(-0.279631\pi\)
\(762\) 0 0
\(763\) 7.62294 42.6981i 0.275969 1.54577i
\(764\) 0 0
\(765\) −2.86184 10.7613i −0.103470 0.389077i
\(766\) 0 0
\(767\) 18.8741 3.32800i 0.681503 0.120167i
\(768\) 0 0
\(769\) −3.11190 + 3.70862i −0.112218 + 0.133736i −0.819229 0.573466i \(-0.805599\pi\)
0.707011 + 0.707202i \(0.250043\pi\)
\(770\) 0 0
\(771\) −28.3486 + 18.0227i −1.02095 + 0.649071i
\(772\) 0 0
\(773\) 5.99893 0.215766 0.107883 0.994164i \(-0.465593\pi\)
0.107883 + 0.994164i \(0.465593\pi\)
\(774\) 0 0
\(775\) 16.1393i 0.579741i
\(776\) 0 0
\(777\) −1.76604 43.5208i −0.0633565 1.56130i