Properties

Label 756.2.ck.a.5.9
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 5.9
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.573178 - 1.63446i) q^{3} +(-0.0962103 + 0.545636i) q^{5} +(2.05240 - 1.66962i) q^{7} +(-2.34293 + 1.87368i) q^{9} +O(q^{10})\) \(q+(-0.573178 - 1.63446i) q^{3} +(-0.0962103 + 0.545636i) q^{5} +(2.05240 - 1.66962i) q^{7} +(-2.34293 + 1.87368i) q^{9} +(4.15140 - 0.732003i) q^{11} +(0.321641 - 0.383316i) q^{13} +(0.946967 - 0.155495i) q^{15} -0.634761 q^{17} -3.87297i q^{19} +(-3.90533 - 2.39759i) q^{21} +(0.0380538 - 0.0453508i) q^{23} +(4.41000 + 1.60511i) q^{25} +(4.40537 + 2.75548i) q^{27} +(0.935412 + 1.11478i) q^{29} +(-1.96410 - 5.39632i) q^{31} +(-3.57592 - 6.36573i) q^{33} +(0.713543 + 1.28050i) q^{35} +(-4.65406 - 8.06107i) q^{37} +(-0.810873 - 0.306001i) q^{39} +(-3.38733 - 2.84230i) q^{41} +(-2.15999 - 0.786173i) q^{43} +(-0.796931 - 1.45866i) q^{45} +(-1.12989 - 0.411247i) q^{47} +(1.42472 - 6.85348i) q^{49} +(0.363831 + 1.03749i) q^{51} +(1.86398 - 1.07617i) q^{53} +2.33558i q^{55} +(-6.33022 + 2.21990i) q^{57} +(6.19145 + 5.19525i) q^{59} +(1.28793 - 3.53855i) q^{61} +(-1.68031 + 7.75735i) q^{63} +(0.178206 + 0.212378i) q^{65} +(0.512180 - 2.90472i) q^{67} +(-0.0959358 - 0.0362035i) q^{69} +(4.37928 + 2.52838i) q^{71} +(-9.70247 - 5.60172i) q^{73} +(0.0957728 - 8.12799i) q^{75} +(7.29817 - 8.43363i) q^{77} +(1.31483 + 7.45679i) q^{79} +(1.97867 - 8.77980i) q^{81} +(-8.98967 + 7.54323i) q^{83} +(0.0610706 - 0.346349i) q^{85} +(1.28591 - 2.16786i) q^{87} -12.2440 q^{89} +(0.0201431 - 1.32374i) q^{91} +(-7.69431 + 6.30331i) q^{93} +(2.11323 + 0.372620i) q^{95} +(-0.237892 + 0.653602i) q^{97} +(-8.35491 + 9.49341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

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
\(3\) −0.573178 1.63446i −0.330925 0.943657i
\(4\) 0 0
\(5\) −0.0962103 + 0.545636i −0.0430266 + 0.244016i −0.998734 0.0503025i \(-0.983981\pi\)
0.955707 + 0.294318i \(0.0950926\pi\)
\(6\) 0 0
\(7\) 2.05240 1.66962i 0.775736 0.631058i
\(8\) 0 0
\(9\) −2.34293 + 1.87368i −0.780978 + 0.624559i
\(10\) 0 0
\(11\) 4.15140 0.732003i 1.25169 0.220707i 0.491773 0.870724i \(-0.336349\pi\)
0.759920 + 0.650016i \(0.225238\pi\)
\(12\) 0 0
\(13\) 0.321641 0.383316i 0.0892070 0.106313i −0.719594 0.694395i \(-0.755672\pi\)
0.808801 + 0.588082i \(0.200117\pi\)
\(14\) 0 0
\(15\) 0.946967 0.155495i 0.244506 0.0401485i
\(16\) 0 0
\(17\) −0.634761 −0.153952 −0.0769761 0.997033i \(-0.524527\pi\)
−0.0769761 + 0.997033i \(0.524527\pi\)
\(18\) 0 0
\(19\) 3.87297i 0.888520i −0.895898 0.444260i \(-0.853467\pi\)
0.895898 0.444260i \(-0.146533\pi\)
\(20\) 0 0
\(21\) −3.90533 2.39759i −0.852212 0.523196i
\(22\) 0 0
\(23\) 0.0380538 0.0453508i 0.00793477 0.00945630i −0.762062 0.647504i \(-0.775813\pi\)
0.769997 + 0.638047i \(0.220258\pi\)
\(24\) 0 0
\(25\) 4.41000 + 1.60511i 0.882000 + 0.321022i
\(26\) 0 0
\(27\) 4.40537 + 2.75548i 0.847814 + 0.530293i
\(28\) 0 0
\(29\) 0.935412 + 1.11478i 0.173702 + 0.207009i 0.845870 0.533388i \(-0.179082\pi\)
−0.672169 + 0.740398i \(0.734637\pi\)
\(30\) 0 0
\(31\) −1.96410 5.39632i −0.352763 0.969208i −0.981478 0.191573i \(-0.938641\pi\)
0.628715 0.777635i \(-0.283581\pi\)
\(32\) 0 0
\(33\) −3.57592 6.36573i −0.622488 1.10813i
\(34\) 0 0
\(35\) 0.713543 + 1.28050i 0.120611 + 0.216444i
\(36\) 0 0
\(37\) −4.65406 8.06107i −0.765122 1.32523i −0.940182 0.340673i \(-0.889345\pi\)
0.175059 0.984558i \(-0.443988\pi\)
\(38\) 0 0
\(39\) −0.810873 0.306001i −0.129844 0.0489993i
\(40\) 0 0
\(41\) −3.38733 2.84230i −0.529012 0.443893i 0.338748 0.940877i \(-0.389996\pi\)
−0.867760 + 0.496984i \(0.834441\pi\)
\(42\) 0 0
\(43\) −2.15999 0.786173i −0.329396 0.119890i 0.172028 0.985092i \(-0.444968\pi\)
−0.501424 + 0.865202i \(0.667190\pi\)
\(44\) 0 0
\(45\) −0.796931 1.45866i −0.118799 0.217444i
\(46\) 0 0
\(47\) −1.12989 0.411247i −0.164812 0.0599866i 0.258297 0.966066i \(-0.416839\pi\)
−0.423108 + 0.906079i \(0.639061\pi\)
\(48\) 0 0
\(49\) 1.42472 6.85348i 0.203532 0.979068i
\(50\) 0 0
\(51\) 0.363831 + 1.03749i 0.0509466 + 0.145278i
\(52\) 0 0
\(53\) 1.86398 1.07617i 0.256037 0.147823i −0.366488 0.930423i \(-0.619440\pi\)
0.622526 + 0.782599i \(0.286107\pi\)
\(54\) 0 0
\(55\) 2.33558i 0.314929i
\(56\) 0 0
\(57\) −6.33022 + 2.21990i −0.838459 + 0.294033i
\(58\) 0 0
\(59\) 6.19145 + 5.19525i 0.806058 + 0.676363i 0.949664 0.313272i \(-0.101425\pi\)
−0.143605 + 0.989635i \(0.545870\pi\)
\(60\) 0 0
\(61\) 1.28793 3.53855i 0.164902 0.453065i −0.829528 0.558466i \(-0.811390\pi\)
0.994430 + 0.105400i \(0.0336124\pi\)
\(62\) 0 0
\(63\) −1.68031 + 7.75735i −0.211700 + 0.977335i
\(64\) 0 0
\(65\) 0.178206 + 0.212378i 0.0221037 + 0.0263422i
\(66\) 0 0
\(67\) 0.512180 2.90472i 0.0625728 0.354868i −0.937405 0.348240i \(-0.886779\pi\)
0.999978 0.00662750i \(-0.00210961\pi\)
\(68\) 0 0
\(69\) −0.0959358 0.0362035i −0.0115493 0.00435838i
\(70\) 0 0
\(71\) 4.37928 + 2.52838i 0.519724 + 0.300063i 0.736822 0.676087i \(-0.236326\pi\)
−0.217098 + 0.976150i \(0.569659\pi\)
\(72\) 0 0
\(73\) −9.70247 5.60172i −1.13559 0.655632i −0.190254 0.981735i \(-0.560931\pi\)
−0.945334 + 0.326103i \(0.894264\pi\)
\(74\) 0 0
\(75\) 0.0957728 8.12799i 0.0110589 0.938540i
\(76\) 0 0
\(77\) 7.29817 8.43363i 0.831704 0.961101i
\(78\) 0 0
\(79\) 1.31483 + 7.45679i 0.147930 + 0.838954i 0.964968 + 0.262369i \(0.0845038\pi\)
−0.817037 + 0.576585i \(0.804385\pi\)
\(80\) 0 0
\(81\) 1.97867 8.77980i 0.219852 0.975533i
\(82\) 0 0
\(83\) −8.98967 + 7.54323i −0.986745 + 0.827977i −0.985093 0.172021i \(-0.944970\pi\)
−0.00165153 + 0.999999i \(0.500526\pi\)
\(84\) 0 0
\(85\) 0.0610706 0.346349i 0.00662404 0.0375668i
\(86\) 0 0
\(87\) 1.28591 2.16786i 0.137864 0.232419i
\(88\) 0 0
\(89\) −12.2440 −1.29786 −0.648930 0.760848i \(-0.724783\pi\)
−0.648930 + 0.760848i \(0.724783\pi\)
\(90\) 0 0
\(91\) 0.0201431 1.32374i 0.00211157 0.138765i
\(92\) 0 0
\(93\) −7.69431 + 6.30331i −0.797862 + 0.653622i
\(94\) 0 0
\(95\) 2.11323 + 0.372620i 0.216813 + 0.0382300i
\(96\) 0 0
\(97\) −0.237892 + 0.653602i −0.0241542 + 0.0663632i −0.951184 0.308625i \(-0.900131\pi\)
0.927029 + 0.374988i \(0.122353\pi\)
\(98\) 0 0
\(99\) −8.35491 + 9.49341i −0.839700 + 0.954124i
\(100\) 0 0
\(101\) 14.9463 12.5414i 1.48721 1.24792i 0.589168 0.808011i \(-0.299456\pi\)
0.898043 0.439907i \(-0.144989\pi\)
\(102\) 0 0
\(103\) 10.0086 + 1.76479i 0.986180 + 0.173890i 0.643404 0.765527i \(-0.277522\pi\)
0.342776 + 0.939417i \(0.388633\pi\)
\(104\) 0 0
\(105\) 1.68394 1.90021i 0.164336 0.185442i
\(106\) 0 0
\(107\) 10.0981 + 5.83016i 0.976223 + 0.563622i 0.901128 0.433554i \(-0.142741\pi\)
0.0750950 + 0.997176i \(0.476074\pi\)
\(108\) 0 0
\(109\) 7.58999 + 13.1462i 0.726989 + 1.25918i 0.958150 + 0.286266i \(0.0924142\pi\)
−0.231161 + 0.972916i \(0.574252\pi\)
\(110\) 0 0
\(111\) −10.5079 + 12.2273i −0.997366 + 1.16056i
\(112\) 0 0
\(113\) 4.91686 + 13.5090i 0.462539 + 1.27082i 0.923569 + 0.383431i \(0.125258\pi\)
−0.461030 + 0.887384i \(0.652520\pi\)
\(114\) 0 0
\(115\) 0.0210839 + 0.0251268i 0.00196608 + 0.00234308i
\(116\) 0 0
\(117\) −0.0353715 + 1.50073i −0.00327009 + 0.138743i
\(118\) 0 0
\(119\) −1.30279 + 1.05981i −0.119426 + 0.0971527i
\(120\) 0 0
\(121\) 6.36164 2.31545i 0.578331 0.210495i
\(122\) 0 0
\(123\) −2.70410 + 7.16561i −0.243820 + 0.646101i
\(124\) 0 0
\(125\) −2.68523 + 4.65095i −0.240174 + 0.415993i
\(126\) 0 0
\(127\) −3.46904 6.00855i −0.307827 0.533173i 0.670059 0.742307i \(-0.266269\pi\)
−0.977887 + 0.209135i \(0.932935\pi\)
\(128\) 0 0
\(129\) −0.0469089 + 3.98104i −0.00413010 + 0.350511i
\(130\) 0 0
\(131\) 11.6409 + 9.76784i 1.01707 + 0.853420i 0.989256 0.146193i \(-0.0467021\pi\)
0.0278105 + 0.999613i \(0.491147\pi\)
\(132\) 0 0
\(133\) −6.46640 7.94890i −0.560708 0.689257i
\(134\) 0 0
\(135\) −1.92733 + 2.13862i −0.165878 + 0.184063i
\(136\) 0 0
\(137\) 0.0437366 0.120165i 0.00373667 0.0102664i −0.937810 0.347148i \(-0.887150\pi\)
0.941547 + 0.336882i \(0.109372\pi\)
\(138\) 0 0
\(139\) 0.0959082 + 0.0169112i 0.00813482 + 0.00143439i 0.177714 0.984082i \(-0.443130\pi\)
−0.169579 + 0.985517i \(0.554241\pi\)
\(140\) 0 0
\(141\) −0.0245381 + 2.08248i −0.00206648 + 0.175377i
\(142\) 0 0
\(143\) 1.05467 1.82674i 0.0881958 0.152760i
\(144\) 0 0
\(145\) −0.698260 + 0.403141i −0.0579874 + 0.0334790i
\(146\) 0 0
\(147\) −12.0184 + 1.59961i −0.991259 + 0.131933i
\(148\) 0 0
\(149\) 6.80797 + 18.7047i 0.557731 + 1.53235i 0.822921 + 0.568156i \(0.192343\pi\)
−0.265190 + 0.964196i \(0.585435\pi\)
\(150\) 0 0
\(151\) 1.05185 + 5.96535i 0.0855986 + 0.485454i 0.997226 + 0.0744357i \(0.0237155\pi\)
−0.911627 + 0.411018i \(0.865173\pi\)
\(152\) 0 0
\(153\) 1.48720 1.18934i 0.120233 0.0961522i
\(154\) 0 0
\(155\) 3.13339 0.552502i 0.251680 0.0443780i
\(156\) 0 0
\(157\) 6.10649 7.27743i 0.487351 0.580802i −0.465191 0.885211i \(-0.654014\pi\)
0.952542 + 0.304408i \(0.0984587\pi\)
\(158\) 0 0
\(159\) −2.82735 2.42977i −0.224224 0.192693i
\(160\) 0 0
\(161\) 0.00238316 0.156614i 0.000187819 0.0123429i
\(162\) 0 0
\(163\) 3.38072 5.85558i 0.264799 0.458644i −0.702712 0.711474i \(-0.748028\pi\)
0.967511 + 0.252830i \(0.0813612\pi\)
\(164\) 0 0
\(165\) 3.81741 1.33870i 0.297185 0.104218i
\(166\) 0 0
\(167\) 8.41037 3.06112i 0.650814 0.236877i 0.00454856 0.999990i \(-0.498552\pi\)
0.646265 + 0.763113i \(0.276330\pi\)
\(168\) 0 0
\(169\) 2.21395 + 12.5559i 0.170304 + 0.965840i
\(170\) 0 0
\(171\) 7.25670 + 9.07411i 0.554933 + 0.693915i
\(172\) 0 0
\(173\) −11.0188 + 9.24588i −0.837744 + 0.702951i −0.957055 0.289906i \(-0.906376\pi\)
0.119311 + 0.992857i \(0.461931\pi\)
\(174\) 0 0
\(175\) 11.7310 4.06870i 0.886782 0.307565i
\(176\) 0 0
\(177\) 4.94263 13.0975i 0.371510 0.984468i
\(178\) 0 0
\(179\) 21.7169i 1.62320i 0.584214 + 0.811600i \(0.301403\pi\)
−0.584214 + 0.811600i \(0.698597\pi\)
\(180\) 0 0
\(181\) −1.00514 + 0.580317i −0.0747114 + 0.0431346i −0.536890 0.843652i \(-0.680401\pi\)
0.462179 + 0.886787i \(0.347068\pi\)
\(182\) 0 0
\(183\) −6.52184 0.0768474i −0.482109 0.00568072i
\(184\) 0 0
\(185\) 4.84618 1.76386i 0.356298 0.129682i
\(186\) 0 0
\(187\) −2.63515 + 0.464647i −0.192701 + 0.0339784i
\(188\) 0 0
\(189\) 13.6422 1.69994i 0.992326 0.123652i
\(190\) 0 0
\(191\) −10.4123 + 1.83597i −0.753406 + 0.132846i −0.537145 0.843490i \(-0.680497\pi\)
−0.216261 + 0.976336i \(0.569386\pi\)
\(192\) 0 0
\(193\) 2.42583 0.882930i 0.174615 0.0635547i −0.253233 0.967405i \(-0.581494\pi\)
0.427848 + 0.903851i \(0.359272\pi\)
\(194\) 0 0
\(195\) 0.244979 0.413001i 0.0175433 0.0295756i
\(196\) 0 0
\(197\) −19.8716 + 11.4729i −1.41580 + 0.817410i −0.995926 0.0901747i \(-0.971257\pi\)
−0.419869 + 0.907585i \(0.637924\pi\)
\(198\) 0 0
\(199\) 19.0252i 1.34866i −0.738431 0.674329i \(-0.764433\pi\)
0.738431 0.674329i \(-0.235567\pi\)
\(200\) 0 0
\(201\) −5.04122 + 0.827783i −0.355581 + 0.0583873i
\(202\) 0 0
\(203\) 3.78110 + 0.726195i 0.265381 + 0.0509689i
\(204\) 0 0
\(205\) 1.87676 1.57479i 0.131079 0.109988i
\(206\) 0 0
\(207\) −0.00418486 + 0.177554i −0.000290868 + 0.0123409i
\(208\) 0 0
\(209\) −2.83503 16.0782i −0.196103 1.11215i
\(210\) 0 0
\(211\) −0.106878 + 0.0389005i −0.00735779 + 0.00267802i −0.345696 0.938346i \(-0.612357\pi\)
0.338339 + 0.941024i \(0.390135\pi\)
\(212\) 0 0
\(213\) 1.62243 8.60697i 0.111167 0.589740i
\(214\) 0 0
\(215\) 0.636778 1.10293i 0.0434279 0.0752193i
\(216\) 0 0
\(217\) −13.0410 7.79613i −0.885277 0.529236i
\(218\) 0 0
\(219\) −3.59456 + 19.0691i −0.242898 + 1.28857i
\(220\) 0 0
\(221\) −0.204165 + 0.243314i −0.0137336 + 0.0163671i
\(222\) 0 0
\(223\) −14.3012 + 2.52169i −0.957682 + 0.168865i −0.630580 0.776124i \(-0.717183\pi\)
−0.327101 + 0.944989i \(0.606072\pi\)
\(224\) 0 0
\(225\) −13.3398 + 4.50225i −0.889320 + 0.300150i
\(226\) 0 0
\(227\) −2.13748 12.1223i −0.141870 0.804582i −0.969828 0.243792i \(-0.921609\pi\)
0.827958 0.560790i \(-0.189503\pi\)
\(228\) 0 0
\(229\) 6.16134 + 16.9281i 0.407153 + 1.11864i 0.958680 + 0.284487i \(0.0918231\pi\)
−0.551527 + 0.834157i \(0.685955\pi\)
\(230\) 0 0
\(231\) −17.9676 7.09461i −1.18218 0.466791i
\(232\) 0 0
\(233\) −9.89657 + 5.71379i −0.648346 + 0.374323i −0.787822 0.615903i \(-0.788791\pi\)
0.139476 + 0.990225i \(0.455458\pi\)
\(234\) 0 0
\(235\) 0.333099 0.576944i 0.0217290 0.0376356i
\(236\) 0 0
\(237\) 11.4342 6.42311i 0.742731 0.417226i
\(238\) 0 0
\(239\) −0.643294 0.113430i −0.0416112 0.00733718i 0.152804 0.988257i \(-0.451170\pi\)
−0.194415 + 0.980919i \(0.562281\pi\)
\(240\) 0 0
\(241\) −6.67035 + 18.3266i −0.429675 + 1.18052i 0.516336 + 0.856386i \(0.327296\pi\)
−0.946011 + 0.324136i \(0.894927\pi\)
\(242\) 0 0
\(243\) −15.4844 + 1.79833i −0.993323 + 0.115363i
\(244\) 0 0
\(245\) 3.60243 + 1.43676i 0.230151 + 0.0917910i
\(246\) 0 0
\(247\) −1.48457 1.24570i −0.0944611 0.0792623i
\(248\) 0 0
\(249\) 17.4818 + 10.3697i 1.10786 + 0.657151i
\(250\) 0 0
\(251\) 8.03105 + 13.9102i 0.506916 + 0.878004i 0.999968 + 0.00800396i \(0.00254777\pi\)
−0.493052 + 0.870000i \(0.664119\pi\)
\(252\) 0 0
\(253\) 0.124780 0.216125i 0.00784483 0.0135876i
\(254\) 0 0
\(255\) −0.601098 + 0.0987019i −0.0376422 + 0.00618095i
\(256\) 0 0
\(257\) −20.3727 + 7.41506i −1.27081 + 0.462539i −0.887384 0.461031i \(-0.847480\pi\)
−0.383431 + 0.923570i \(0.625257\pi\)
\(258\) 0 0
\(259\) −23.0109 8.77405i −1.42983 0.545193i
\(260\) 0 0
\(261\) −4.28034 0.859196i −0.264947 0.0531829i
\(262\) 0 0
\(263\) −3.05565 3.64158i −0.188420 0.224550i 0.663562 0.748121i \(-0.269044\pi\)
−0.851982 + 0.523571i \(0.824599\pi\)
\(264\) 0 0
\(265\) 0.407863 + 1.12059i 0.0250548 + 0.0688375i
\(266\) 0 0
\(267\) 7.01799 + 20.0123i 0.429494 + 1.22474i
\(268\) 0 0
\(269\) −4.02474 6.97105i −0.245393 0.425033i 0.716849 0.697228i \(-0.245584\pi\)
−0.962242 + 0.272196i \(0.912250\pi\)
\(270\) 0 0
\(271\) −4.48964 2.59210i −0.272726 0.157459i 0.357400 0.933952i \(-0.383663\pi\)
−0.630126 + 0.776493i \(0.716997\pi\)
\(272\) 0 0
\(273\) −2.17515 + 0.725815i −0.131646 + 0.0439283i
\(274\) 0 0
\(275\) 19.4826 + 3.43531i 1.17485 + 0.207157i
\(276\) 0 0
\(277\) 5.66410 4.75274i 0.340323 0.285565i −0.456568 0.889689i \(-0.650921\pi\)
0.796890 + 0.604124i \(0.206477\pi\)
\(278\) 0 0
\(279\) 14.7127 + 8.96313i 0.880828 + 0.536609i
\(280\) 0 0
\(281\) 9.61797 26.4251i 0.573760 1.57639i −0.224754 0.974416i \(-0.572158\pi\)
0.798514 0.601976i \(-0.205620\pi\)
\(282\) 0 0
\(283\) 14.1402 + 2.49330i 0.840548 + 0.148211i 0.577316 0.816521i \(-0.304100\pi\)
0.263233 + 0.964732i \(0.415211\pi\)
\(284\) 0 0
\(285\) −0.602226 3.66758i −0.0356728 0.217248i
\(286\) 0 0
\(287\) −11.6977 0.178002i −0.690496 0.0105071i
\(288\) 0 0
\(289\) −16.5971 −0.976299
\(290\) 0 0
\(291\) 1.20464 + 0.0141944i 0.0706174 + 0.000832090i
\(292\) 0 0
\(293\) 5.28738 29.9862i 0.308892 1.75181i −0.295703 0.955280i \(-0.595554\pi\)
0.604595 0.796533i \(-0.293335\pi\)
\(294\) 0 0
\(295\) −3.43039 + 2.87844i −0.199725 + 0.167589i
\(296\) 0 0
\(297\) 20.3055 + 8.21436i 1.17824 + 0.476646i
\(298\) 0 0
\(299\) −0.00514404 0.0291733i −0.000297488 0.00168714i
\(300\) 0 0
\(301\) −5.74579 + 1.99283i −0.331182 + 0.114865i
\(302\) 0 0
\(303\) −29.0654 17.2407i −1.66976 0.990450i
\(304\) 0 0
\(305\) 1.80685 + 1.04319i 0.103460 + 0.0597326i
\(306\) 0 0
\(307\) 11.2817 + 6.51348i 0.643879 + 0.371744i 0.786107 0.618090i \(-0.212093\pi\)
−0.142228 + 0.989834i \(0.545427\pi\)
\(308\) 0 0
\(309\) −2.85225 17.3703i −0.162259 0.988160i
\(310\) 0 0
\(311\) 5.36781 30.4424i 0.304381 1.72623i −0.322025 0.946731i \(-0.604364\pi\)
0.626406 0.779497i \(-0.284525\pi\)
\(312\) 0 0
\(313\) 13.8278 + 16.4793i 0.781592 + 0.931465i 0.999004 0.0446148i \(-0.0142061\pi\)
−0.217412 + 0.976080i \(0.569762\pi\)
\(314\) 0 0
\(315\) −4.07103 1.66318i −0.229376 0.0937094i
\(316\) 0 0
\(317\) 6.44736 17.7140i 0.362120 0.994916i −0.616159 0.787622i \(-0.711312\pi\)
0.978279 0.207294i \(-0.0664657\pi\)
\(318\) 0 0
\(319\) 4.69929 + 3.94317i 0.263110 + 0.220775i
\(320\) 0 0
\(321\) 3.74114 19.8467i 0.208810 1.10774i
\(322\) 0 0
\(323\) 2.45841i 0.136790i
\(324\) 0 0
\(325\) 2.03370 1.17416i 0.112809 0.0651305i
\(326\) 0 0
\(327\) 17.1366 19.9407i 0.947657 1.10272i
\(328\) 0 0
\(329\) −3.00562 + 1.04245i −0.165705 + 0.0574720i
\(330\) 0 0
\(331\) 29.9532 + 10.9021i 1.64638 + 0.599232i 0.988137 0.153576i \(-0.0490790\pi\)
0.658240 + 0.752808i \(0.271301\pi\)
\(332\) 0 0
\(333\) 26.0080 + 10.1663i 1.42523 + 0.557112i
\(334\) 0 0
\(335\) 1.53564 + 0.558928i 0.0839011 + 0.0305375i
\(336\) 0 0
\(337\) −11.8444 9.93861i −0.645204 0.541391i 0.260407 0.965499i \(-0.416143\pi\)
−0.905611 + 0.424108i \(0.860588\pi\)
\(338\) 0 0
\(339\) 19.2616 15.7795i 1.04615 0.857023i
\(340\) 0 0
\(341\) −12.1039 20.9645i −0.655462 1.13529i
\(342\) 0 0
\(343\) −8.51861 16.4449i −0.459962 0.887939i
\(344\) 0 0
\(345\) 0.0289839 0.0488629i 0.00156044 0.00263069i
\(346\) 0 0
\(347\) 2.37448 + 6.52382i 0.127469 + 0.350217i 0.986967 0.160921i \(-0.0514464\pi\)
−0.859499 + 0.511138i \(0.829224\pi\)
\(348\) 0 0
\(349\) 16.9744 + 20.2294i 0.908621 + 1.08285i 0.996235 + 0.0866979i \(0.0276315\pi\)
−0.0876135 + 0.996155i \(0.527924\pi\)
\(350\) 0 0
\(351\) 2.47317 0.802375i 0.132008 0.0428276i
\(352\) 0 0
\(353\) −26.6523 9.70066i −1.41856 0.516314i −0.484931 0.874552i \(-0.661155\pi\)
−0.933630 + 0.358238i \(0.883377\pi\)
\(354\) 0 0
\(355\) −1.80090 + 2.14623i −0.0955821 + 0.113910i
\(356\) 0 0
\(357\) 2.47895 + 1.52189i 0.131200 + 0.0805472i
\(358\) 0 0
\(359\) 21.8568i 1.15356i 0.816900 + 0.576779i \(0.195691\pi\)
−0.816900 + 0.576779i \(0.804309\pi\)
\(360\) 0 0
\(361\) 4.00010 0.210531
\(362\) 0 0
\(363\) −7.43087 9.07070i −0.390019 0.476088i
\(364\) 0 0
\(365\) 3.98998 4.75507i 0.208845 0.248892i
\(366\) 0 0
\(367\) −2.29250 + 0.404230i −0.119668 + 0.0211007i −0.233161 0.972438i \(-0.574907\pi\)
0.113494 + 0.993539i \(0.463796\pi\)
\(368\) 0 0
\(369\) 13.2618 + 0.312574i 0.690384 + 0.0162719i
\(370\) 0 0
\(371\) 2.02884 5.32088i 0.105332 0.276246i
\(372\) 0 0
\(373\) 4.27168 24.2259i 0.221179 1.25437i −0.648676 0.761064i \(-0.724677\pi\)
0.869856 0.493306i \(-0.164212\pi\)
\(374\) 0 0
\(375\) 9.14091 + 1.72308i 0.472035 + 0.0889793i
\(376\) 0 0
\(377\) 0.728180 0.0375032
\(378\) 0 0
\(379\) −26.3042 −1.35115 −0.675577 0.737289i \(-0.736105\pi\)
−0.675577 + 0.737289i \(0.736105\pi\)
\(380\) 0 0
\(381\) −7.83237 + 9.11398i −0.401265 + 0.466924i
\(382\) 0 0
\(383\) 0.938875 5.32463i 0.0479743 0.272076i −0.951379 0.308021i \(-0.900333\pi\)
0.999354 + 0.0359456i \(0.0114443\pi\)
\(384\) 0 0
\(385\) 3.89953 + 4.79355i 0.198738 + 0.244302i
\(386\) 0 0
\(387\) 6.53375 2.20518i 0.332129 0.112095i
\(388\) 0 0
\(389\) 17.0349 3.00370i 0.863701 0.152294i 0.275789 0.961218i \(-0.411061\pi\)
0.587913 + 0.808924i \(0.299950\pi\)
\(390\) 0 0
\(391\) −0.0241551 + 0.0287869i −0.00122158 + 0.00145582i
\(392\) 0 0
\(393\) 9.29288 24.6253i 0.468764 1.24218i
\(394\) 0 0
\(395\) −4.19519 −0.211083
\(396\) 0 0
\(397\) 35.6021i 1.78682i 0.449244 + 0.893409i \(0.351693\pi\)
−0.449244 + 0.893409i \(0.648307\pi\)
\(398\) 0 0
\(399\) −9.28578 + 15.1252i −0.464870 + 0.757208i
\(400\) 0 0
\(401\) −14.5463 + 17.3356i −0.726407 + 0.865698i −0.995237 0.0974895i \(-0.968919\pi\)
0.268829 + 0.963188i \(0.413363\pi\)
\(402\) 0 0
\(403\) −2.70023 0.982805i −0.134508 0.0489570i
\(404\) 0 0
\(405\) 4.60020 + 1.92434i 0.228586 + 0.0956213i
\(406\) 0 0
\(407\) −25.2216 30.0579i −1.25019 1.48991i
\(408\) 0 0
\(409\) 5.24708 + 14.4162i 0.259452 + 0.712837i 0.999201 + 0.0399554i \(0.0127216\pi\)
−0.739750 + 0.672882i \(0.765056\pi\)
\(410\) 0 0
\(411\) −0.221475 0.00260965i −0.0109245 0.000128725i
\(412\) 0 0
\(413\) 21.3815 + 0.325358i 1.05211 + 0.0160098i
\(414\) 0 0
\(415\) −3.25096 5.63082i −0.159583 0.276406i
\(416\) 0 0
\(417\) −0.0273318 0.166451i −0.00133844 0.00815116i
\(418\) 0 0
\(419\) 9.50477 + 7.97545i 0.464338 + 0.389626i 0.844724 0.535202i \(-0.179764\pi\)
−0.380386 + 0.924828i \(0.624209\pi\)
\(420\) 0 0
\(421\) −23.2648 8.46771i −1.13386 0.412691i −0.294167 0.955754i \(-0.595042\pi\)
−0.839692 + 0.543063i \(0.817264\pi\)
\(422\) 0 0
\(423\) 3.41781 1.15353i 0.166179 0.0560865i
\(424\) 0 0
\(425\) −2.79930 1.01886i −0.135786 0.0494220i
\(426\) 0 0
\(427\) −3.26470 9.41289i −0.157990 0.455522i
\(428\) 0 0
\(429\) −3.59025 0.676768i −0.173339 0.0326747i
\(430\) 0 0
\(431\) −3.52219 + 2.03354i −0.169658 + 0.0979520i −0.582424 0.812885i \(-0.697896\pi\)
0.412767 + 0.910837i \(0.364562\pi\)
\(432\) 0 0
\(433\) 15.1591i 0.728499i 0.931301 + 0.364249i \(0.118674\pi\)
−0.931301 + 0.364249i \(0.881326\pi\)
\(434\) 0 0
\(435\) 1.05915 + 0.910209i 0.0507822 + 0.0436412i
\(436\) 0 0
\(437\) −0.175642 0.147381i −0.00840211 0.00705021i
\(438\) 0 0
\(439\) 1.75309 4.81657i 0.0836703 0.229882i −0.890801 0.454393i \(-0.849856\pi\)
0.974472 + 0.224511i \(0.0720784\pi\)
\(440\) 0 0
\(441\) 9.50317 + 18.7267i 0.452532 + 0.891748i
\(442\) 0 0
\(443\) 22.7817 + 27.1502i 1.08239 + 1.28995i 0.954517 + 0.298155i \(0.0963714\pi\)
0.127876 + 0.991790i \(0.459184\pi\)
\(444\) 0 0
\(445\) 1.17800 6.68076i 0.0558425 0.316698i
\(446\) 0 0
\(447\) 26.6700 21.8485i 1.26145 1.03340i
\(448\) 0 0
\(449\) −30.4940 17.6057i −1.43910 0.830866i −0.441315 0.897352i \(-0.645488\pi\)
−0.997787 + 0.0664866i \(0.978821\pi\)
\(450\) 0 0
\(451\) −16.1427 9.32000i −0.760131 0.438862i
\(452\) 0 0
\(453\) 9.14725 5.13843i 0.429775 0.241424i
\(454\) 0 0
\(455\) 0.720341 + 0.138348i 0.0337701 + 0.00648586i
\(456\) 0 0
\(457\) 3.27561 + 18.5769i 0.153226 + 0.868991i 0.960389 + 0.278662i \(0.0898908\pi\)
−0.807163 + 0.590329i \(0.798998\pi\)
\(458\) 0 0
\(459\) −2.79636 1.74907i −0.130523 0.0816398i
\(460\) 0 0
\(461\) −28.9553 + 24.2964i −1.34858 + 1.13159i −0.369252 + 0.929329i \(0.620386\pi\)
−0.979331 + 0.202265i \(0.935170\pi\)
\(462\) 0 0
\(463\) −1.15887 + 6.57229i −0.0538574 + 0.305440i −0.999823 0.0188273i \(-0.994007\pi\)
0.945965 + 0.324268i \(0.105118\pi\)
\(464\) 0 0
\(465\) −2.69904 4.80473i −0.125165 0.222814i
\(466\) 0 0
\(467\) −14.7392 −0.682050 −0.341025 0.940054i \(-0.610774\pi\)
−0.341025 + 0.940054i \(0.610774\pi\)
\(468\) 0 0
\(469\) −3.79858 6.81681i −0.175402 0.314771i
\(470\) 0 0
\(471\) −15.3948 5.80956i −0.709355 0.267690i
\(472\) 0 0
\(473\) −9.54247 1.68259i −0.438763 0.0773658i
\(474\) 0 0
\(475\) 6.21654 17.0798i 0.285234 0.783675i
\(476\) 0 0
\(477\) −2.35079 + 6.01389i −0.107635 + 0.275357i
\(478\) 0 0
\(479\) 23.1775 19.4482i 1.05901 0.888612i 0.0649944 0.997886i \(-0.479297\pi\)
0.994012 + 0.109274i \(0.0348526\pi\)
\(480\) 0 0
\(481\) −4.58687 0.808789i −0.209143 0.0368776i
\(482\) 0 0
\(483\) −0.257345 + 0.0858724i −0.0117096 + 0.00390733i
\(484\) 0 0
\(485\) −0.333741 0.192686i −0.0151544 0.00874940i
\(486\) 0 0
\(487\) −10.1186 17.5260i −0.458519 0.794177i 0.540364 0.841431i \(-0.318286\pi\)
−0.998883 + 0.0472537i \(0.984953\pi\)
\(488\) 0 0
\(489\) −11.5085 2.16937i −0.520432 0.0981022i
\(490\) 0 0
\(491\) −3.07553 8.44994i −0.138797 0.381340i 0.850747 0.525576i \(-0.176150\pi\)
−0.989543 + 0.144235i \(0.953928\pi\)
\(492\) 0 0
\(493\) −0.593763 0.707619i −0.0267417 0.0318696i
\(494\) 0 0
\(495\) −4.37612 5.47210i −0.196692 0.245953i
\(496\) 0 0
\(497\) 13.2095 2.12249i 0.592526 0.0952065i
\(498\) 0 0
\(499\) 40.8211 14.8576i 1.82740 0.665120i 0.833815 0.552044i \(-0.186152\pi\)
0.993586 0.113075i \(-0.0360702\pi\)
\(500\) 0 0
\(501\) −9.82393 11.9919i −0.438901 0.535757i
\(502\) 0 0
\(503\) 4.11258 7.12321i 0.183371 0.317608i −0.759655 0.650326i \(-0.774632\pi\)
0.943026 + 0.332718i \(0.107966\pi\)
\(504\) 0 0
\(505\) 5.40506 + 9.36184i 0.240522 + 0.416597i
\(506\) 0 0
\(507\) 19.2532 10.8154i 0.855064 0.480329i
\(508\) 0 0
\(509\) −14.5922 12.2443i −0.646790 0.542721i 0.259305 0.965795i \(-0.416506\pi\)
−0.906095 + 0.423074i \(0.860951\pi\)
\(510\) 0 0
\(511\) −29.2661 + 4.70245i −1.29466 + 0.208024i
\(512\) 0 0
\(513\) 10.6719 17.0619i 0.471176 0.753300i
\(514\) 0 0
\(515\) −1.92587 + 5.29128i −0.0848639 + 0.233162i
\(516\) 0 0
\(517\) −4.99166 0.880165i −0.219533 0.0387096i
\(518\) 0 0
\(519\) 21.4278 + 12.7103i 0.940575 + 0.557920i
\(520\) 0 0
\(521\) 1.31024 2.26940i 0.0574027 0.0994244i −0.835896 0.548888i \(-0.815051\pi\)
0.893299 + 0.449463i \(0.148385\pi\)
\(522\) 0 0
\(523\) 11.2694 6.50639i 0.492776 0.284505i −0.232949 0.972489i \(-0.574838\pi\)
0.725726 + 0.687984i \(0.241504\pi\)
\(524\) 0 0
\(525\) −13.3741 16.8418i −0.583694 0.735038i
\(526\) 0 0
\(527\) 1.24674 + 3.42538i 0.0543086 + 0.149212i
\(528\) 0 0
\(529\) 3.99330 + 22.6471i 0.173622 + 0.984658i
\(530\) 0 0
\(531\) −24.2404 0.571331i −1.05194 0.0247937i
\(532\) 0 0
\(533\) −2.17900 + 0.384217i −0.0943831 + 0.0166423i
\(534\) 0 0
\(535\) −4.15269 + 4.94898i −0.179536 + 0.213963i
\(536\) 0 0
\(537\) 35.4955 12.4477i 1.53174 0.537157i
\(538\) 0 0
\(539\) 0.897829 29.4944i 0.0386722 1.27041i
\(540\) 0 0
\(541\) 3.26613 5.65710i 0.140422 0.243218i −0.787234 0.616655i \(-0.788487\pi\)
0.927655 + 0.373437i \(0.121821\pi\)
\(542\) 0 0
\(543\) 1.52463 + 1.31024i 0.0654281 + 0.0562276i
\(544\) 0 0
\(545\) −7.90330 + 2.87657i −0.338540 + 0.123219i
\(546\) 0 0
\(547\) 4.30486 + 24.4141i 0.184063 + 1.04387i 0.927154 + 0.374681i \(0.122248\pi\)
−0.743091 + 0.669190i \(0.766641\pi\)
\(548\) 0 0
\(549\) 3.61258 + 10.7038i 0.154181 + 0.456825i
\(550\) 0 0
\(551\) 4.31751 3.62282i 0.183932 0.154337i
\(552\) 0 0
\(553\) 15.1486 + 13.1091i 0.644183 + 0.557454i
\(554\) 0 0
\(555\) −5.66069 6.90988i −0.240283 0.293308i
\(556\) 0 0
\(557\) 39.4427i 1.67124i −0.549308 0.835620i \(-0.685109\pi\)
0.549308 0.835620i \(-0.314891\pi\)
\(558\) 0 0
\(559\) −0.996094 + 0.575095i −0.0421303 + 0.0243239i
\(560\) 0 0
\(561\) 2.26986 + 4.04072i 0.0958334 + 0.170599i
\(562\) 0 0
\(563\) −2.37268 + 0.863585i −0.0999965 + 0.0363958i −0.391534 0.920164i \(-0.628055\pi\)
0.291537 + 0.956559i \(0.405833\pi\)
\(564\) 0 0
\(565\) −7.84403 + 1.38311i −0.330001 + 0.0581880i
\(566\) 0 0
\(567\) −10.5979 21.3233i −0.445071 0.895496i
\(568\) 0 0
\(569\) −32.9897 + 5.81697i −1.38300 + 0.243860i −0.815139 0.579266i \(-0.803339\pi\)
−0.567859 + 0.823126i \(0.692228\pi\)
\(570\) 0 0
\(571\) 7.98320 2.90565i 0.334087 0.121598i −0.169530 0.985525i \(-0.554225\pi\)
0.503616 + 0.863928i \(0.332003\pi\)
\(572\) 0 0
\(573\) 8.96891 + 15.9661i 0.374682 + 0.666995i
\(574\) 0 0
\(575\) 0.240610 0.138917i 0.0100341 0.00579322i
\(576\) 0 0
\(577\) 16.3727i 0.681606i 0.940135 + 0.340803i \(0.110699\pi\)
−0.940135 + 0.340803i \(0.889301\pi\)
\(578\) 0 0
\(579\) −2.83355 3.45885i −0.117758 0.143745i
\(580\) 0 0
\(581\) −5.85610 + 30.4911i −0.242952 + 1.26498i
\(582\) 0 0
\(583\) 6.95036 5.83205i 0.287855 0.241539i
\(584\) 0 0
\(585\) −0.815452 0.163686i −0.0337148 0.00676759i
\(586\) 0 0
\(587\) −5.51445 31.2740i −0.227606 1.29082i −0.857641 0.514249i \(-0.828071\pi\)
0.630035 0.776567i \(-0.283041\pi\)
\(588\) 0 0
\(589\) −20.8998 + 7.60691i −0.861162 + 0.313437i
\(590\) 0 0
\(591\) 30.1420 + 25.9034i 1.23988 + 1.06552i
\(592\) 0 0
\(593\) −15.2689 + 26.4465i −0.627019 + 1.08603i 0.361127 + 0.932517i \(0.382392\pi\)
−0.988147 + 0.153513i \(0.950941\pi\)
\(594\) 0 0
\(595\) −0.452930 0.812812i −0.0185683 0.0333220i
\(596\) 0 0
\(597\) −31.0959 + 10.9048i −1.27267 + 0.446304i
\(598\) 0 0
\(599\) −6.67755 + 7.95800i −0.272837 + 0.325155i −0.885012 0.465567i \(-0.845850\pi\)
0.612175 + 0.790722i \(0.290295\pi\)
\(600\) 0 0
\(601\) −0.660314 + 0.116431i −0.0269348 + 0.00474933i −0.187099 0.982341i \(-0.559909\pi\)
0.160165 + 0.987090i \(0.448798\pi\)
\(602\) 0 0
\(603\) 4.24250 + 7.76522i 0.172768 + 0.316224i
\(604\) 0 0
\(605\) 0.651336 + 3.69391i 0.0264806 + 0.150179i
\(606\) 0 0
\(607\) −1.11798 3.07164i −0.0453776 0.124674i 0.914934 0.403604i \(-0.132243\pi\)
−0.960311 + 0.278930i \(0.910020\pi\)
\(608\) 0 0
\(609\) −0.980308 6.59631i −0.0397241 0.267296i
\(610\) 0 0
\(611\) −0.521057 + 0.300832i −0.0210797 + 0.0121704i
\(612\) 0 0
\(613\) −17.2368 + 29.8550i −0.696187 + 1.20583i 0.273592 + 0.961846i \(0.411788\pi\)
−0.969779 + 0.243985i \(0.921545\pi\)
\(614\) 0 0
\(615\) −3.64965 2.16486i −0.147168 0.0872955i
\(616\) 0 0
\(617\) 37.9055 + 6.68375i 1.52602 + 0.269078i 0.872794 0.488089i \(-0.162306\pi\)
0.653222 + 0.757166i \(0.273417\pi\)
\(618\) 0 0
\(619\) −12.1028 + 33.2522i −0.486453 + 1.33652i 0.417419 + 0.908714i \(0.362935\pi\)
−0.903872 + 0.427804i \(0.859287\pi\)
\(620\) 0 0
\(621\) 0.292605 0.0949304i 0.0117418 0.00380943i
\(622\) 0 0
\(623\) −25.1296 + 20.4428i −1.00680 + 0.819025i
\(624\) 0 0
\(625\) 15.6960 + 13.1705i 0.627838 + 0.526819i
\(626\) 0 0
\(627\) −24.6543 + 13.8494i −0.984598 + 0.553093i
\(628\) 0 0
\(629\) 2.95422 + 5.11685i 0.117792 + 0.204022i
\(630\) 0 0
\(631\) −12.0125 + 20.8062i −0.478208 + 0.828281i −0.999688 0.0249829i \(-0.992047\pi\)
0.521480 + 0.853264i \(0.325380\pi\)
\(632\) 0 0
\(633\) 0.124842 + 0.152391i 0.00496201 + 0.00605701i
\(634\) 0 0
\(635\) 3.61224 1.31475i 0.143347 0.0521742i
\(636\) 0 0
\(637\) −2.16880 2.75048i −0.0859310 0.108978i
\(638\) 0 0
\(639\) −14.9977 + 2.28153i −0.593300 + 0.0902560i
\(640\) 0 0
\(641\) −8.90313 10.6103i −0.351653 0.419083i 0.561002 0.827814i \(-0.310416\pi\)
−0.912655 + 0.408731i \(0.865971\pi\)
\(642\) 0 0
\(643\) 1.97788 + 5.43418i 0.0780000 + 0.214303i 0.972563 0.232638i \(-0.0747356\pi\)
−0.894563 + 0.446941i \(0.852513\pi\)
\(644\) 0 0
\(645\) −2.16769 0.408613i −0.0853526 0.0160891i
\(646\) 0 0
\(647\) −4.57324 7.92108i −0.179793 0.311410i 0.762017 0.647557i \(-0.224209\pi\)
−0.941809 + 0.336147i \(0.890876\pi\)
\(648\) 0 0
\(649\) 29.5061 + 17.0354i 1.15822 + 0.668696i
\(650\) 0 0
\(651\) −5.26769 + 25.7835i −0.206457 + 1.01054i
\(652\) 0 0
\(653\) −1.55734 0.274601i −0.0609433 0.0107460i 0.143093 0.989709i \(-0.454295\pi\)
−0.204037 + 0.978963i \(0.565406\pi\)
\(654\) 0 0
\(655\) −6.44966 + 5.41190i −0.252009 + 0.211461i
\(656\) 0 0
\(657\) 33.2280 5.05483i 1.29635 0.197208i
\(658\) 0 0
\(659\) −3.88785 + 10.6818i −0.151449 + 0.416103i −0.992096 0.125481i \(-0.959953\pi\)
0.840647 + 0.541583i \(0.182175\pi\)
\(660\) 0 0
\(661\) −26.9919 4.75940i −1.04986 0.185119i −0.378008 0.925802i \(-0.623391\pi\)
−0.671854 + 0.740683i \(0.734502\pi\)
\(662\) 0 0
\(663\) 0.514711 + 0.194237i 0.0199897 + 0.00754355i
\(664\) 0 0
\(665\) 4.95934 2.76353i 0.192315 0.107165i
\(666\) 0 0
\(667\) 0.0861522 0.00333583
\(668\) 0 0
\(669\) 12.3188 + 21.9294i 0.476271 + 0.847842i
\(670\) 0 0
\(671\) 2.75647 15.6327i 0.106412 0.603494i
\(672\) 0 0
\(673\) 30.5814 25.6609i 1.17883 0.989154i 0.178841 0.983878i \(-0.442765\pi\)
0.999986 0.00527559i \(-0.00167928\pi\)
\(674\) 0 0
\(675\) 15.0048 + 19.2228i 0.577537 + 0.739886i
\(676\) 0 0
\(677\) −0.621865 3.52677i −0.0239002 0.135545i 0.970523 0.241009i \(-0.0774783\pi\)
−0.994423 + 0.105464i \(0.966367\pi\)
\(678\) 0 0
\(679\) 0.603018 + 1.73864i 0.0231417 + 0.0667231i
\(680\) 0 0
\(681\) −18.5882 + 10.4418i −0.712302 + 0.400132i
\(682\) 0 0
\(683\) −6.44543 3.72127i −0.246627 0.142390i 0.371592 0.928396i \(-0.378812\pi\)
−0.618219 + 0.786006i \(0.712146\pi\)
\(684\) 0 0
\(685\) 0.0613587 + 0.0354254i 0.00234439 + 0.00135354i
\(686\) 0 0
\(687\) 24.1369 19.7733i 0.920879 0.754400i
\(688\) 0 0
\(689\) 0.187018 1.06063i 0.00712483 0.0404069i
\(690\) 0 0
\(691\) 16.2167 + 19.3264i 0.616914 + 0.735209i 0.980536 0.196337i \(-0.0629047\pi\)
−0.363623 + 0.931546i \(0.618460\pi\)
\(692\) 0 0
\(693\) −1.29724 + 33.4338i −0.0492780 + 1.27005i
\(694\) 0 0
\(695\) −0.0184547 + 0.0507039i −0.000700027 + 0.00192331i
\(696\) 0 0
\(697\) 2.15014 + 1.80418i 0.0814425 + 0.0683384i
\(698\) 0 0
\(699\) 15.0115 + 12.9006i 0.567786 + 0.487944i
\(700\) 0 0
\(701\) 26.7157i 1.00904i 0.863401 + 0.504518i \(0.168330\pi\)
−0.863401 + 0.504518i \(0.831670\pi\)
\(702\) 0 0
\(703\) −31.2203 + 18.0250i −1.17749 + 0.679827i
\(704\) 0 0
\(705\) −1.13392 0.213745i −0.0427058 0.00805011i
\(706\) 0 0
\(707\) 9.73638 50.6947i 0.366174 1.90657i
\(708\) 0 0
\(709\) −24.9988 9.09883i −0.938850 0.341714i −0.173139 0.984897i \(-0.555391\pi\)
−0.765712 + 0.643184i \(0.777613\pi\)
\(710\) 0 0
\(711\) −17.0522 15.0072i −0.639506 0.562813i
\(712\) 0 0
\(713\) −0.319469 0.116277i −0.0119642 0.00435462i
\(714\) 0 0
\(715\) 0.895265 + 0.751216i 0.0334810 + 0.0280939i
\(716\) 0 0
\(717\) 0.183325 + 1.11646i 0.00684640 + 0.0416948i
\(718\) 0 0
\(719\) 13.5495 + 23.4684i 0.505311 + 0.875225i 0.999981 + 0.00614379i \(0.00195564\pi\)
−0.494670 + 0.869081i \(0.664711\pi\)
\(720\) 0 0
\(721\) 23.4883 13.0886i 0.874750 0.487444i
\(722\) 0 0
\(723\) 33.7775 + 0.398003i 1.25620 + 0.0148019i
\(724\) 0 0
\(725\) 2.33582 + 6.41762i 0.0867503 + 0.238344i
\(726\) 0 0
\(727\) −18.8028 22.4084i −0.697359 0.831080i 0.294866 0.955539i \(-0.404725\pi\)
−0.992225 + 0.124459i \(0.960281\pi\)
\(728\) 0 0
\(729\) 11.8146 + 24.2779i 0.437578 + 0.899180i
\(730\) 0 0
\(731\) 1.37108 + 0.499032i 0.0507112 + 0.0184574i
\(732\) 0 0
\(733\) −14.5245 + 17.3096i −0.536473 + 0.639344i −0.964393 0.264473i \(-0.914802\pi\)
0.427920 + 0.903817i \(0.359247\pi\)
\(734\) 0 0
\(735\) 0.283489 6.71155i 0.0104566 0.247559i
\(736\) 0 0
\(737\) 12.4336i 0.457996i
\(738\) 0 0
\(739\) −28.0070 −1.03025 −0.515127 0.857114i \(-0.672255\pi\)
−0.515127 + 0.857114i \(0.672255\pi\)
\(740\) 0 0
\(741\) −1.18513 + 3.14049i −0.0435369 + 0.115369i
\(742\) 0 0
\(743\) 11.9061 14.1891i 0.436791 0.520547i −0.502078 0.864822i \(-0.667431\pi\)
0.938869 + 0.344275i \(0.111875\pi\)
\(744\) 0 0
\(745\) −10.8610 + 1.91508i −0.397915 + 0.0701632i
\(746\) 0 0
\(747\) 6.92862 34.5170i 0.253505 1.26291i
\(748\) 0 0
\(749\) 30.4596 4.89422i 1.11297 0.178831i
\(750\) 0 0
\(751\) 5.90033 33.4624i 0.215306 1.22106i −0.665068 0.746782i \(-0.731598\pi\)
0.880375 0.474279i \(-0.157291\pi\)
\(752\) 0 0
\(753\) 18.1325 21.0995i 0.660783 0.768908i
\(754\) 0 0
\(755\) −3.35611 −0.122141
\(756\) 0 0
\(757\) 27.8065 1.01064 0.505322 0.862931i \(-0.331374\pi\)
0.505322 + 0.862931i \(0.331374\pi\)
\(758\) 0 0
\(759\) −0.424769 0.0800696i −0.0154181 0.00290634i
\(760\) 0 0
\(761\) −7.09933 + 40.2623i −0.257351 + 1.45951i 0.532616 + 0.846357i \(0.321209\pi\)
−0.789966 + 0.613150i \(0.789902\pi\)
\(762\) 0 0
\(763\) 37.5270 + 14.3090i 1.35857 + 0.518020i
\(764\) 0 0
\(765\) 0.505861 + 0.925898i 0.0182894 + 0.0334759i
\(766\) 0 0
\(767\) 3.98284 0.702283i 0.143812 0.0253580i
\(768\) 0 0
\(769\) −32.0054 + 38.1425i −1.15414 + 1.37545i −0.239646 + 0.970860i \(0.577031\pi\)
−0.914497 + 0.404593i \(0.867413\pi\)
\(770\) 0 0
\(771\) 23.7968 + 29.0483i 0.857022 + 1.04615i
\(772\) 0 0
\(773\) −9.51135 −0.342099 −0.171050 0.985262i \(-0.554716\pi\)
−0.171050 + 0.985262i \(0.554716\pi\)
\(774\) 0 0
\(775\) 26.9504i 0.968087i
\(776\) 0 0
\(777\) −1.15147 + 42.6396i −0.0413088 + 1.52969i