Properties

Label 756.2.ck.a.605.2
Level 756
Weight 2
Character 756.605
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 \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 605.2
Character \(\chi\) \(=\) 756.605
Dual form 756.2.ck.a.5.2

$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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 −0.995876 0.0907245i \(-0.971082\pi\)
0.904788 0.425863i \(-0.140029\pi\)
\(6\) 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 0.627192 0.778865i \(-0.284204\pi\)
0.322980 + 0.946406i \(0.395315\pi\)
\(12\) 0 0
\(13\) −1.12364 1.33911i −0.311643 0.371401i 0.587374 0.809316i \(-0.300162\pi\)
−0.899017 + 0.437914i \(0.855717\pi\)
\(14\) 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 \(0.276494\pi\)
−0.645873 + 0.763445i \(0.723506\pi\)
\(20\) 0 0
\(21\) −4.05827 + 2.12849i −0.885586 + 0.464475i
\(22\) 0 0
\(23\) −3.65594 4.35698i −0.762315 0.908492i 0.235677 0.971832i \(-0.424269\pi\)
−0.997992 + 0.0633394i \(0.979825\pi\)
\(24\) 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 −0.279300 0.960204i \(-0.590102\pi\)
0.994116 + 0.108319i \(0.0345467\pi\)
\(30\) 0 0
\(31\) 1.52309 4.18464i 0.273554 0.751584i −0.724502 0.689272i \(-0.757930\pi\)
0.998057 0.0623119i \(-0.0198474\pi\)
\(32\) 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 −0.149898 0.988702i \(-0.547894\pi\)
0.931189 0.364535i \(-0.118772\pi\)
\(38\) 0 0
\(39\) 1.40059 + 2.68434i 0.224273 + 0.429839i
\(40\) 0 0
\(41\) 7.74888 6.50209i 1.21017 1.01546i 0.210893 0.977509i \(-0.432363\pi\)
0.999280 0.0379460i \(-0.0120815\pi\)
\(42\) 0 0
\(43\) 3.80179 1.38374i 0.579768 0.211018i −0.0354555 0.999371i \(-0.511288\pi\)
0.615223 + 0.788353i \(0.289066\pi\)
\(44\) 0 0
\(45\) 0.904355 3.40063i 0.134813 0.506937i
\(46\) 0 0
\(47\) −7.95967 + 2.89708i −1.16104 + 0.422583i −0.849468 0.527641i \(-0.823077\pi\)
−0.311569 + 0.950224i \(0.600855\pi\)
\(48\) 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 −0.988347 0.152215i \(-0.951359\pi\)
−0.625996 0.779826i \(-0.715307\pi\)
\(54\) 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 −0.996964 0.0778642i \(-0.975190\pi\)
−0.0964398 + 0.995339i \(0.530746\pi\)
\(60\) 0 0
\(61\) −0.888063 2.43993i −0.113705 0.312402i 0.869767 0.493463i \(-0.164269\pi\)
−0.983472 + 0.181061i \(0.942047\pi\)
\(62\) 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 0.505039 + 0.863096i \(0.331478\pi\)
−0.179385 + 0.983779i \(0.557411\pi\)
\(68\) 0 0
\(69\) 4.55701 + 8.73390i 0.548600 + 1.05144i
\(70\) 0 0
\(71\) 2.08522 1.20391i 0.247471 0.142877i −0.371135 0.928579i \(-0.621031\pi\)
0.618606 + 0.785702i \(0.287698\pi\)
\(72\) 0 0
\(73\) 1.01078 0.583575i 0.118303 0.0683023i −0.439681 0.898154i \(-0.644908\pi\)
0.557984 + 0.829852i \(0.311575\pi\)
\(74\) 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 −0.714851 0.699277i \(-0.753505\pi\)
0.910907 0.412612i \(-0.135384\pi\)
\(80\) 0 0
\(81\) 5.81095 + 6.87262i 0.645661 + 0.763624i
\(82\) 0 0
\(83\) −5.29556 4.44350i −0.581263 0.487738i 0.304098 0.952641i \(-0.401645\pi\)
−0.885362 + 0.464903i \(0.846089\pi\)
\(84\) 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 0.936146 0.351611i \(-0.114366\pi\)
−0.943141 + 0.332393i \(0.892144\pi\)
\(98\) 0 0
\(99\) 7.87414 + 5.49152i 0.791381 + 0.551918i
\(100\) 0 0
\(101\) −4.44873 3.73293i −0.442666 0.371441i 0.394040 0.919093i \(-0.371077\pi\)
−0.836706 + 0.547653i \(0.815522\pi\)
\(102\) 0 0
\(103\) 5.21603 0.919726i 0.513950 0.0906233i 0.0893431 0.996001i \(-0.471523\pi\)
0.424607 + 0.905378i \(0.360412\pi\)
\(104\) 0 0
\(105\) 3.28526 + 4.25427i 0.320608 + 0.415174i
\(106\) 0 0
\(107\) −8.16755 + 4.71554i −0.789587 + 0.455868i −0.839817 0.542870i \(-0.817338\pi\)
0.0502303 + 0.998738i \(0.484004\pi\)
\(108\) 0 0
\(109\) −8.19677 + 14.1972i −0.785108 + 1.35985i 0.143826 + 0.989603i \(0.454059\pi\)
−0.928934 + 0.370244i \(0.879274\pi\)
\(110\) 0 0
\(111\) −11.1107 + 12.1481i −1.05458 + 1.15305i
\(112\) 0 0
\(113\) 2.80986 7.72002i 0.264329 0.726238i −0.734534 0.678572i \(-0.762599\pi\)
0.998863 0.0476665i \(-0.0151785\pi\)
\(114\) 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 −0.752123 0.659023i \(-0.770970\pi\)
0.946792 + 0.321846i \(0.104303\pi\)
\(128\) 0 0
\(129\) −6.94668 + 0.921186i −0.611621 + 0.0811059i
\(130\) 0 0
\(131\) 7.95915 6.67852i 0.695395 0.583505i −0.225065 0.974344i \(-0.572259\pi\)
0.920459 + 0.390839i \(0.127815\pi\)
\(132\) 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 0.999821 + 0.0189333i \(0.00602702\pi\)
−0.753737 + 0.657176i \(0.771751\pi\)
\(138\) 0 0
\(139\) 17.3552 3.06020i 1.47205 0.259563i 0.620655 0.784083i \(-0.286867\pi\)
0.851398 + 0.524521i \(0.175755\pi\)
\(140\) 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 0.346524 + 0.938041i \(0.387362\pi\)
−0.868414 + 0.495840i \(0.834860\pi\)
\(150\) 0 0
\(151\) 1.11679 6.33365i 0.0908834 0.515425i −0.905048 0.425310i \(-0.860165\pi\)
0.995931 0.0901156i \(-0.0287236\pi\)
\(152\) 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 0.857503 0.514480i \(-0.172015\pi\)
−0.655567 + 0.755137i \(0.727570\pi\)
\(158\) 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 0.732336 + 0.680944i \(0.238430\pi\)
0.223547 + 0.974693i \(0.428237\pi\)
\(164\) 0 0
\(165\) −1.40113 + 6.34829i −0.109078 + 0.494214i
\(166\) 0 0
\(167\) 3.10807 + 1.13125i 0.240510 + 0.0875384i 0.459463 0.888197i \(-0.348042\pi\)
−0.218953 + 0.975735i \(0.570264\pi\)
\(168\) 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 0.816404 0.577482i \(-0.195964\pi\)
−0.426941 + 0.904279i \(0.640409\pi\)
\(174\) 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 \(0.0749856\pi\)
−0.972380 + 0.233401i \(0.925014\pi\)
\(180\) 0 0
\(181\) 0.630501 + 0.364020i 0.0468648 + 0.0270574i 0.523249 0.852180i \(-0.324720\pi\)
−0.476385 + 0.879237i \(0.658053\pi\)
\(182\) 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 0.0844574 0.996427i \(-0.473084\pi\)
−0.261434 + 0.965221i \(0.584195\pi\)
\(192\) 0 0
\(193\) 16.7694 + 6.10356i 1.20709 + 0.439344i 0.865693 0.500576i \(-0.166878\pi\)
0.341395 + 0.939920i \(0.389101\pi\)
\(194\) 0 0
\(195\) 2.81548 2.16460i 0.201621 0.155010i
\(196\) 0 0
\(197\) −4.49176 2.59332i −0.320025 0.184766i 0.331379 0.943498i \(-0.392486\pi\)
−0.651404 + 0.758731i \(0.725820\pi\)
\(198\) 0 0
\(199\) 21.3548i 1.51380i 0.653531 + 0.756900i \(0.273287\pi\)
−0.653531 + 0.756900i \(0.726713\pi\)
\(200\) 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 0.822597 0.568625i \(-0.192524\pi\)
0.264641 + 0.964347i \(0.414747\pi\)
\(212\) 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 0.175982 0.984393i \(-0.443690\pi\)
−0.171314 + 0.985217i \(0.554801\pi\)
\(224\) 0 0
\(225\) 10.8330 + 0.927264i 0.722200 + 0.0618176i
\(226\) 0 0
\(227\) 1.52723 8.66137i 0.101366 0.574876i −0.891244 0.453525i \(-0.850166\pi\)
0.992610 0.121351i \(-0.0387226\pi\)
\(228\) 0 0
\(229\) −7.04568 + 19.3578i −0.465591 + 1.27920i 0.455632 + 0.890168i \(0.349413\pi\)
−0.921224 + 0.389034i \(0.872809\pi\)
\(230\) 0 0
\(231\) −13.9718 + 4.45260i −0.919278 + 0.292959i
\(232\) 0 0
\(233\) 9.43506 + 5.44734i 0.618111 + 0.356867i 0.776133 0.630569i \(-0.217178\pi\)
−0.158022 + 0.987436i \(0.550512\pi\)
\(234\) 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 −0.0216386 0.999766i \(-0.506888\pi\)
0.321606 + 0.946873i \(0.395777\pi\)
\(240\) 0 0
\(241\) −6.76085 18.5753i −0.435505 1.19654i −0.942387 0.334524i \(-0.891424\pi\)
0.506882 0.862015i \(-0.330798\pi\)
\(242\) 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 −0.707637 0.706576i \(-0.750239\pi\)
0.965731 + 0.259543i \(0.0835720\pi\)
\(252\) 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 0.840774 0.541387i \(-0.182100\pi\)
0.296074 + 0.955165i \(0.404323\pi\)
\(258\) 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 −0.933736 0.357962i \(-0.883472\pi\)
0.514665 + 0.857391i \(0.327916\pi\)
\(264\) 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 −0.826674 0.562681i \(-0.809770\pi\)
0.900633 + 0.434581i \(0.143103\pi\)
\(270\) 0 0
\(271\) −13.7260 + 7.92468i −0.833792 + 0.481390i −0.855149 0.518382i \(-0.826535\pi\)
0.0213570 + 0.999772i \(0.493201\pi\)
\(272\) 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 0.477019 0.878893i \(-0.341717\pi\)
−0.782707 + 0.622390i \(0.786162\pi\)
\(278\) 0 0
\(279\) 9.42891 9.46440i 0.564494 0.566619i
\(280\) 0 0
\(281\) 5.25557 + 14.4396i 0.313521 + 0.861392i 0.991939 + 0.126716i \(0.0404436\pi\)
−0.678418 + 0.734676i \(0.737334\pi\)
\(282\) 0 0
\(283\) −2.48443 + 0.438073i −0.147684 + 0.0260407i −0.247001 0.969015i \(-0.579445\pi\)
0.0993172 + 0.995056i \(0.468334\pi\)
\(284\) 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 0.994703 0.102790i \(-0.0327770\pi\)
−0.969871 + 0.243617i \(0.921666\pi\)
\(294\) 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 −0.884997 0.465596i \(-0.845840\pi\)
−0.0392804 + 0.999228i \(0.512507\pi\)
\(308\) 0 0
\(309\) −9.16544 0.391548i −0.521403 0.0222744i
\(310\) 0 0
\(311\) −0.0875069 0.496276i −0.00496206 0.0281413i 0.982226 0.187701i \(-0.0601036\pi\)
−0.987188 + 0.159560i \(0.948993\pi\)
\(312\) 0 0
\(313\) 12.0362 14.3442i 0.680327 0.810782i −0.309823 0.950794i \(-0.600270\pi\)
0.990150 + 0.140012i \(0.0447142\pi\)
\(314\) 0 0
\(315\) −3.96840 8.42182i −0.223594 0.474516i
\(316\) 0 0
\(317\) 8.95841 + 24.6130i 0.503155 + 1.38241i 0.888178 + 0.459499i \(0.151971\pi\)
−0.385023 + 0.922907i \(0.625807\pi\)
\(318\) 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 −0.705197 0.709011i \(-0.749141\pi\)
−0.0844686 + 0.996426i \(0.526919\pi\)
\(332\) 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 −0.883819 0.467830i \(-0.845036\pi\)
0.307249 + 0.951629i \(0.400592\pi\)
\(338\) 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 0.690445 + 0.723385i \(0.257415\pi\)
−0.993894 + 0.110336i \(0.964807\pi\)
\(348\) 0 0
\(349\) −4.58698 + 5.46655i −0.245535 + 0.292618i −0.874710 0.484646i \(-0.838948\pi\)
0.629175 + 0.777264i \(0.283393\pi\)
\(350\) 0 0
\(351\) 0.421774 + 9.07349i 0.0225126 + 0.484307i
\(352\) 0 0
\(353\) 13.7755 5.01387i 0.733195 0.266861i 0.0516785 0.998664i \(-0.483543\pi\)
0.681517 + 0.731803i \(0.261321\pi\)
\(354\) 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 \(0.0401013\pi\)
−0.992075 + 0.125649i \(0.959899\pi\)
\(360\) 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 0.325593 0.945510i \(-0.394436\pi\)
−0.0174264 + 0.999848i \(0.505547\pi\)
\(368\) 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 −0.612230 0.790680i \(-0.709727\pi\)
0.304879 0.952391i \(-0.401384\pi\)
\(374\) 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 0.981657 + 0.190655i \(0.0610611\pi\)
−0.857248 + 0.514903i \(0.827828\pi\)
\(384\) 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 0.910274 0.414007i \(-0.135871\pi\)
0.713779 + 0.700371i \(0.246982\pi\)
\(390\) 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 \(0.0157311\pi\)
−0.998779 + 0.0494007i \(0.984269\pi\)
\(398\) 0 0
\(399\) −14.1663 27.0100i −0.709202 1.35219i
\(400\) 0 0
\(401\) −15.9098 18.9605i −0.794495 0.946842i 0.204995 0.978763i \(-0.434282\pi\)
−0.999490 + 0.0319205i \(0.989838\pi\)
\(402\) 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 0.309809 + 0.950799i \(0.399735\pi\)
−0.848489 + 0.529213i \(0.822487\pi\)
\(410\) 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 0.451763 0.892138i \(-0.350795\pi\)
0.957032 0.289981i \(-0.0936491\pi\)
\(420\) 0 0
\(421\) 3.47410 1.26447i 0.169317 0.0616264i −0.255971 0.966685i \(-0.582395\pi\)
0.425288 + 0.905058i \(0.360173\pi\)
\(422\) 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 0.599701 0.800224i \(-0.295286\pi\)
−0.393164 + 0.919468i \(0.628620\pi\)
\(432\) 0 0
\(433\) 6.70918i 0.322423i 0.986920 + 0.161211i \(0.0515401\pi\)
−0.986920 + 0.161211i \(0.948460\pi\)
\(434\) 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 0.936561 0.350506i \(-0.113990\pi\)
−0.942748 + 0.333507i \(0.891768\pi\)
\(440\) 0 0
\(441\) 11.9390 17.2760i 0.568526 0.822665i
\(442\) 0 0
\(443\) −10.8964 + 12.9858i −0.517705 + 0.616976i −0.960036 0.279875i \(-0.909707\pi\)
0.442332 + 0.896851i \(0.354151\pi\)
\(444\) 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 −0.827311 0.561744i \(-0.810130\pi\)
0.0728294 + 0.997344i \(0.476797\pi\)
\(450\) 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 −0.991826 0.127596i \(-0.959274\pi\)
0.975652 + 0.219323i \(0.0703849\pi\)
\(458\) 0 0
\(459\) 13.0735 + 9.97324i 0.610218 + 0.465511i
\(460\) 0 0
\(461\) 23.4896 + 19.7101i 1.09402 + 0.917992i 0.997009 0.0772911i \(-0.0246271\pi\)
0.0970119 + 0.995283i \(0.469072\pi\)
\(462\) 0 0
\(463\) 1.76880 + 10.0313i 0.0822029 + 0.466196i 0.997925 + 0.0643841i \(0.0205083\pi\)
−0.915722 + 0.401812i \(0.868381\pi\)
\(464\) 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 −0.998347 0.0574804i \(-0.981693\pi\)
−0.229968 0.973198i \(-0.573862\pi\)
\(480\) 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 −0.917059 0.398751i \(-0.869444\pi\)
0.803858 + 0.594821i \(0.202777\pi\)
\(488\) 0 0
\(489\) −12.7504 40.3069i −0.576591 1.82274i
\(490\) 0 0
\(491\) 4.65547 12.7908i 0.210098 0.577241i −0.789222 0.614108i \(-0.789516\pi\)
0.999320 + 0.0368676i \(0.0117380\pi\)
\(492\) 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 0.665335 0.746545i \(-0.268289\pi\)
0.0298062 + 0.999556i \(0.490511\pi\)
\(500\) 0 0
\(501\) −4.83453 3.07356i −0.215991 0.137316i
\(502\) 0 0
\(503\) 4.71614 + 8.16859i 0.210282 + 0.364219i 0.951803 0.306711i \(-0.0992284\pi\)
−0.741521 + 0.670930i \(0.765895\pi\)
\(504\) 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 0.118859 0.992911i \(-0.462076\pi\)
0.998466 + 0.0553640i \(0.0176319\pi\)
\(510\) 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 0.910971 0.412471i \(-0.135334\pi\)
−0.812696 + 0.582688i \(0.802001\pi\)
\(522\) 0 0
\(523\) −29.1689 16.8407i −1.27547 0.736391i −0.299455 0.954110i \(-0.596805\pi\)
−0.976011 + 0.217719i \(0.930138\pi\)
\(524\) 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 −0.995407 0.0957324i \(-0.969481\pi\)
0.414797 0.909914i \(-0.363853\pi\)
\(542\) 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 −0.203137 0.979150i \(-0.565114\pi\)
0.525775 0.850623i \(-0.323775\pi\)
\(548\) 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 \(-0.905756\pi\)
0.956489 0.291768i \(-0.0942436\pi\)
\(558\) 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 0.689985 0.723823i \(-0.257617\pi\)
0.0632947 + 0.997995i \(0.479839\pi\)
\(564\) 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 0.484676 0.874694i \(-0.338938\pi\)
0.156283 + 0.987712i \(0.450049\pi\)
\(570\) 0 0
\(571\) −18.8715 6.86868i −0.789749 0.287445i −0.0845175 0.996422i \(-0.526935\pi\)
−0.705232 + 0.708977i \(0.749157\pi\)
\(572\) 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 \(-0.876336\pi\)
0.925477 0.378803i \(-0.123664\pi\)
\(578\) 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 0.281974 + 0.959422i \(0.409011\pi\)
−0.593111 + 0.805121i \(0.702100\pi\)
\(588\) 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 0.927209 + 0.374544i \(0.122201\pi\)
−0.139239 + 0.990259i \(0.544466\pi\)
\(594\) 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 0.876985 0.480517i \(-0.159551\pi\)
−0.625504 + 0.780221i \(0.715107\pi\)
\(600\) 0 0
\(601\) −22.7261 4.00723i −0.927018 0.163458i −0.310297 0.950640i \(-0.600428\pi\)
−0.616721 + 0.787181i \(0.711540\pi\)
\(602\) 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 −0.878369 0.477984i \(-0.841368\pi\)
0.980111 + 0.198448i \(0.0635900\pi\)
\(608\) 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 0.992531 0.121994i \(-0.0389289\pi\)
−0.601916 + 0.798560i \(0.705596\pi\)
\(614\) 0 0
\(615\) 12.5257 + 16.2921i 0.505084 + 0.656960i
\(616\) 0 0
\(617\) −18.4581 + 3.25466i −0.743094 + 0.131028i −0.532362 0.846517i \(-0.678696\pi\)
−0.210731 + 0.977544i \(0.567585\pi\)
\(618\) 0 0
\(619\) 12.5229 + 34.4065i 0.503339 + 1.38291i 0.887995 + 0.459853i \(0.152098\pi\)
−0.384655 + 0.923060i \(0.625680\pi\)
\(620\) 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 0.997768 0.0667740i \(-0.0212707\pi\)
−0.556712 + 0.830706i \(0.687937\pi\)
\(632\) 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 −0.315381 + 0.948965i \(0.602132\pi\)
−0.879783 + 0.475376i \(0.842312\pi\)
\(642\) 0 0
\(643\) −2.45049 + 6.73265i −0.0966377 + 0.265510i −0.978587 0.205835i \(-0.934009\pi\)
0.881949 + 0.471345i \(0.156231\pi\)
\(644\) 0 0
\(645\) 2.47898 + 7.83666i 0.0976098 + 0.308568i
\(646\) 0 0
\(647\) 9.26911 16.0546i 0.364406 0.631170i −0.624274 0.781205i \(-0.714605\pi\)
0.988681 + 0.150035i \(0.0479386\pi\)
\(648\) 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 −0.935741 0.352687i \(-0.885268\pi\)
−0.758683 + 0.651460i \(0.774157\pi\)
\(654\) 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 0.919470 + 0.393160i \(0.128618\pi\)
−0.451636 + 0.892202i \(0.649160\pi\)
\(660\) 0 0
\(661\) 2.60599 0.459507i 0.101361 0.0178728i −0.122737 0.992439i \(-0.539167\pi\)
0.224099 + 0.974566i \(0.428056\pi\)
\(662\) 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 0.784439 0.620206i \(-0.212951\pi\)
−0.474567 + 0.880219i \(0.657395\pi\)
\(674\) 0 0
\(675\) −17.9762 5.61224i −0.691904 0.216015i
\(676\) 0 0
\(677\) 7.64065 43.3323i 0.293654 1.66539i −0.378969 0.925409i \(-0.623721\pi\)
0.672623 0.739985i \(-0.265168\pi\)
\(678\) 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 −0.202785 0.979223i \(-0.564999\pi\)
0.746640 + 0.665228i \(0.231666\pi\)
\(684\) 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 −0.757766 0.652526i \(-0.773709\pi\)
0.774197 + 0.632944i \(0.218154\pi\)
\(692\) 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 \(0.433433\pi\)
−0.207606 + 0.978213i \(0.566567\pi\)
\(702\) 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 −0.632167 0.774832i \(-0.717834\pi\)
0.0137846 + 0.999905i \(0.495612\pi\)
\(710\) 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 −0.983261 0.182201i \(-0.941678\pi\)
0.649421 + 0.760429i \(0.275011\pi\)
\(720\) 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 −0.248206 0.968707i \(-0.579841\pi\)
0.997091 + 0.0762207i \(0.0242854\pi\)
\(728\) 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 0.976163 + 0.217041i \(0.0696404\pi\)
0.0442345 + 0.999021i \(0.485915\pi\)
\(734\) 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 0.812047 0.583592i \(-0.198353\pi\)
−0.715736 + 0.698371i \(0.753909\pi\)
\(744\) 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 −0.997830 0.0658441i \(-0.979026\pi\)
0.915133 0.403151i \(-0.132085\pi\)
\(752\) 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 0.638317 + 0.769774i \(0.279631\pi\)
−0.336544 + 0.941668i \(0.609258\pi\)
\(762\) 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 0.707011 0.707202i \(-0.250043\pi\)
−0.819229 + 0.573466i \(0.805599\pi\)
\(770\) 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
\(778\)