Properties

Label 756.2.ck.a.5.17
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 5.17
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.17

$q$-expansion

\(f(q)\) \(=\) \(q+(1.06196 - 1.36830i) q^{3} +(0.449866 - 2.55131i) q^{5} +(-2.53584 - 0.754675i) q^{7} +(-0.744465 - 2.90616i) q^{9} +O(q^{10})\) \(q+(1.06196 - 1.36830i) q^{3} +(0.449866 - 2.55131i) q^{5} +(-2.53584 - 0.754675i) q^{7} +(-0.744465 - 2.90616i) q^{9} +(3.32853 - 0.586909i) q^{11} +(-0.718420 + 0.856180i) q^{13} +(-3.01321 - 3.32495i) q^{15} -2.35421 q^{17} -0.116725i q^{19} +(-3.72559 + 2.66833i) q^{21} +(-0.0811022 + 0.0966538i) q^{23} +(-1.60836 - 0.585397i) q^{25} +(-4.76708 - 2.06759i) q^{27} +(-1.74633 - 2.08119i) q^{29} +(0.400779 + 1.10113i) q^{31} +(2.73171 - 5.17769i) q^{33} +(-3.06620 + 6.13021i) q^{35} +(-5.12795 - 8.88188i) q^{37} +(0.408570 + 1.89224i) q^{39} +(2.53395 + 2.12623i) q^{41} +(-2.39884 - 0.873106i) q^{43} +(-7.74944 + 0.591981i) q^{45} +(7.71339 + 2.80744i) q^{47} +(5.86093 + 3.82747i) q^{49} +(-2.50009 + 3.22126i) q^{51} +(-8.17694 + 4.72096i) q^{53} -8.75615i q^{55} +(-0.159715 - 0.123958i) q^{57} +(6.49318 + 5.44842i) q^{59} +(1.60136 - 4.39971i) q^{61} +(-0.305368 + 7.93138i) q^{63} +(1.86119 + 2.21808i) q^{65} +(1.57661 - 8.94138i) q^{67} +(0.0461234 + 0.213615i) q^{69} +(7.05686 + 4.07428i) q^{71} +(9.72113 + 5.61250i) q^{73} +(-2.50902 + 1.57905i) q^{75} +(-8.88353 - 1.02365i) q^{77} +(-2.45450 - 13.9202i) q^{79} +(-7.89155 + 4.32707i) q^{81} +(9.54729 - 8.01113i) q^{83} +(-1.05908 + 6.00634i) q^{85} +(-4.70223 + 0.179341i) q^{87} -0.407850 q^{89} +(2.46793 - 1.62896i) q^{91} +(1.93229 + 0.620978i) q^{93} +(-0.297803 - 0.0525107i) q^{95} +(2.76618 - 7.60002i) q^{97} +(-4.18362 - 9.23631i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

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
\(3\) 1.06196 1.36830i 0.613125 0.789986i
\(4\) 0 0
\(5\) 0.449866 2.55131i 0.201186 1.14098i −0.702144 0.712035i \(-0.747774\pi\)
0.903330 0.428947i \(-0.141115\pi\)
\(6\) 0 0
\(7\) −2.53584 0.754675i −0.958456 0.285240i
\(8\) 0 0
\(9\) −0.744465 2.90616i −0.248155 0.968720i
\(10\) 0 0
\(11\) 3.32853 0.586909i 1.00359 0.176960i 0.352379 0.935857i \(-0.385373\pi\)
0.651210 + 0.758898i \(0.274262\pi\)
\(12\) 0 0
\(13\) −0.718420 + 0.856180i −0.199254 + 0.237462i −0.856414 0.516289i \(-0.827313\pi\)
0.657160 + 0.753751i \(0.271757\pi\)
\(14\) 0 0
\(15\) −3.01321 3.32495i −0.778008 0.858499i
\(16\) 0 0
\(17\) −2.35421 −0.570981 −0.285490 0.958382i \(-0.592156\pi\)
−0.285490 + 0.958382i \(0.592156\pi\)
\(18\) 0 0
\(19\) 0.116725i 0.0267786i −0.999910 0.0133893i \(-0.995738\pi\)
0.999910 0.0133893i \(-0.00426208\pi\)
\(20\) 0 0
\(21\) −3.72559 + 2.66833i −0.812989 + 0.582278i
\(22\) 0 0
\(23\) −0.0811022 + 0.0966538i −0.0169110 + 0.0201537i −0.774434 0.632655i \(-0.781965\pi\)
0.757523 + 0.652809i \(0.226410\pi\)
\(24\) 0 0
\(25\) −1.60836 0.585397i −0.321673 0.117079i
\(26\) 0 0
\(27\) −4.76708 2.06759i −0.917425 0.397908i
\(28\) 0 0
\(29\) −1.74633 2.08119i −0.324285 0.386468i 0.579130 0.815235i \(-0.303392\pi\)
−0.903415 + 0.428767i \(0.858948\pi\)
\(30\) 0 0
\(31\) 0.400779 + 1.10113i 0.0719821 + 0.197769i 0.970466 0.241237i \(-0.0775530\pi\)
−0.898484 + 0.439006i \(0.855331\pi\)
\(32\) 0 0
\(33\) 2.73171 5.17769i 0.475530 0.901319i
\(34\) 0 0
\(35\) −3.06620 + 6.13021i −0.518282 + 1.03620i
\(36\) 0 0
\(37\) −5.12795 8.88188i −0.843031 1.46017i −0.887321 0.461153i \(-0.847436\pi\)
0.0442901 0.999019i \(-0.485897\pi\)
\(38\) 0 0
\(39\) 0.408570 + 1.89224i 0.0654236 + 0.303001i
\(40\) 0 0
\(41\) 2.53395 + 2.12623i 0.395736 + 0.332062i 0.818843 0.574018i \(-0.194616\pi\)
−0.423107 + 0.906080i \(0.639060\pi\)
\(42\) 0 0
\(43\) −2.39884 0.873106i −0.365819 0.133147i 0.152569 0.988293i \(-0.451245\pi\)
−0.518388 + 0.855146i \(0.673468\pi\)
\(44\) 0 0
\(45\) −7.74944 + 0.591981i −1.15522 + 0.0882474i
\(46\) 0 0
\(47\) 7.71339 + 2.80744i 1.12511 + 0.409508i 0.836516 0.547943i \(-0.184589\pi\)
0.288597 + 0.957451i \(0.406811\pi\)
\(48\) 0 0
\(49\) 5.86093 + 3.82747i 0.837276 + 0.546781i
\(50\) 0 0
\(51\) −2.50009 + 3.22126i −0.350083 + 0.451067i
\(52\) 0 0
\(53\) −8.17694 + 4.72096i −1.12319 + 0.648473i −0.942213 0.335014i \(-0.891259\pi\)
−0.180976 + 0.983488i \(0.557925\pi\)
\(54\) 0 0
\(55\) 8.75615i 1.18068i
\(56\) 0 0
\(57\) −0.159715 0.123958i −0.0211547 0.0164187i
\(58\) 0 0
\(59\) 6.49318 + 5.44842i 0.845340 + 0.709324i 0.958758 0.284223i \(-0.0917357\pi\)
−0.113419 + 0.993547i \(0.536180\pi\)
\(60\) 0 0
\(61\) 1.60136 4.39971i 0.205033 0.563325i −0.793970 0.607957i \(-0.791989\pi\)
0.999003 + 0.0446321i \(0.0142115\pi\)
\(62\) 0 0
\(63\) −0.305368 + 7.93138i −0.0384728 + 0.999260i
\(64\) 0 0
\(65\) 1.86119 + 2.21808i 0.230852 + 0.275119i
\(66\) 0 0
\(67\) 1.57661 8.94138i 0.192613 1.09236i −0.723164 0.690677i \(-0.757313\pi\)
0.915777 0.401687i \(-0.131576\pi\)
\(68\) 0 0
\(69\) 0.0461234 + 0.213615i 0.00555260 + 0.0257162i
\(70\) 0 0
\(71\) 7.05686 + 4.07428i 0.837495 + 0.483528i 0.856412 0.516293i \(-0.172688\pi\)
−0.0189167 + 0.999821i \(0.506022\pi\)
\(72\) 0 0
\(73\) 9.72113 + 5.61250i 1.13777 + 0.656893i 0.945878 0.324523i \(-0.105204\pi\)
0.191894 + 0.981416i \(0.438537\pi\)
\(74\) 0 0
\(75\) −2.50902 + 1.57905i −0.289717 + 0.182333i
\(76\) 0 0
\(77\) −8.88353 1.02365i −1.01237 0.116656i
\(78\) 0 0
\(79\) −2.45450 13.9202i −0.276153 1.56614i −0.735275 0.677769i \(-0.762947\pi\)
0.459122 0.888373i \(-0.348164\pi\)
\(80\) 0 0
\(81\) −7.89155 + 4.32707i −0.876838 + 0.480785i
\(82\) 0 0
\(83\) 9.54729 8.01113i 1.04795 0.879336i 0.0550746 0.998482i \(-0.482460\pi\)
0.992877 + 0.119147i \(0.0380159\pi\)
\(84\) 0 0
\(85\) −1.05908 + 6.00634i −0.114873 + 0.651479i
\(86\) 0 0
\(87\) −4.70223 + 0.179341i −0.504132 + 0.0192273i
\(88\) 0 0
\(89\) −0.407850 −0.0432321 −0.0216160 0.999766i \(-0.506881\pi\)
−0.0216160 + 0.999766i \(0.506881\pi\)
\(90\) 0 0
\(91\) 2.46793 1.62896i 0.258710 0.170761i
\(92\) 0 0
\(93\) 1.93229 + 0.620978i 0.200369 + 0.0643925i
\(94\) 0 0
\(95\) −0.297803 0.0525107i −0.0305540 0.00538749i
\(96\) 0 0
\(97\) 2.76618 7.60002i 0.280863 0.771665i −0.716397 0.697693i \(-0.754210\pi\)
0.997260 0.0739724i \(-0.0235677\pi\)
\(98\) 0 0
\(99\) −4.18362 9.23631i −0.420470 0.928284i
\(100\) 0 0
\(101\) −8.69458 + 7.29562i −0.865143 + 0.725941i −0.963070 0.269252i \(-0.913223\pi\)
0.0979265 + 0.995194i \(0.468779\pi\)
\(102\) 0 0
\(103\) 15.4152 + 2.71812i 1.51891 + 0.267824i 0.870003 0.493047i \(-0.164117\pi\)
0.648903 + 0.760871i \(0.275228\pi\)
\(104\) 0 0
\(105\) 5.13175 + 10.7055i 0.500807 + 1.04475i
\(106\) 0 0
\(107\) −6.44745 3.72244i −0.623298 0.359862i 0.154854 0.987937i \(-0.450509\pi\)
−0.778152 + 0.628076i \(0.783843\pi\)
\(108\) 0 0
\(109\) −8.47513 14.6794i −0.811770 1.40603i −0.911624 0.411025i \(-0.865171\pi\)
0.0998542 0.995002i \(-0.468162\pi\)
\(110\) 0 0
\(111\) −17.5987 2.41568i −1.67040 0.229286i
\(112\) 0 0
\(113\) 0.327903 + 0.900905i 0.0308465 + 0.0847500i 0.954160 0.299297i \(-0.0967522\pi\)
−0.923313 + 0.384047i \(0.874530\pi\)
\(114\) 0 0
\(115\) 0.210109 + 0.250398i 0.0195928 + 0.0233498i
\(116\) 0 0
\(117\) 3.02303 + 1.45045i 0.279480 + 0.134094i
\(118\) 0 0
\(119\) 5.96990 + 1.77667i 0.547260 + 0.162867i
\(120\) 0 0
\(121\) 0.398017 0.144866i 0.0361834 0.0131697i
\(122\) 0 0
\(123\) 5.60028 1.20920i 0.504960 0.109030i
\(124\) 0 0
\(125\) 4.25960 7.37785i 0.380990 0.659895i
\(126\) 0 0
\(127\) 2.30393 + 3.99052i 0.204441 + 0.354102i 0.949954 0.312389i \(-0.101129\pi\)
−0.745514 + 0.666490i \(0.767796\pi\)
\(128\) 0 0
\(129\) −3.74215 + 2.35511i −0.329478 + 0.207356i
\(130\) 0 0
\(131\) 15.6483 + 13.1305i 1.36720 + 1.14721i 0.973686 + 0.227895i \(0.0731843\pi\)
0.393512 + 0.919320i \(0.371260\pi\)
\(132\) 0 0
\(133\) −0.0880897 + 0.295996i −0.00763835 + 0.0256661i
\(134\) 0 0
\(135\) −7.41962 + 11.2322i −0.638579 + 0.966713i
\(136\) 0 0
\(137\) 4.84629 13.3151i 0.414046 1.13758i −0.540973 0.841040i \(-0.681944\pi\)
0.955019 0.296543i \(-0.0958339\pi\)
\(138\) 0 0
\(139\) 18.1091 + 3.19312i 1.53599 + 0.270837i 0.876696 0.481045i \(-0.159743\pi\)
0.659298 + 0.751882i \(0.270854\pi\)
\(140\) 0 0
\(141\) 12.0327 7.57279i 1.01334 0.637744i
\(142\) 0 0
\(143\) −1.88878 + 3.27147i −0.157948 + 0.273574i
\(144\) 0 0
\(145\) −6.09539 + 3.51918i −0.506195 + 0.292252i
\(146\) 0 0
\(147\) 11.4612 3.95485i 0.945304 0.326191i
\(148\) 0 0
\(149\) 6.37358 + 17.5113i 0.522144 + 1.43458i 0.868129 + 0.496338i \(0.165322\pi\)
−0.345985 + 0.938240i \(0.612455\pi\)
\(150\) 0 0
\(151\) 1.85223 + 10.5045i 0.150733 + 0.854847i 0.962584 + 0.270983i \(0.0873487\pi\)
−0.811852 + 0.583864i \(0.801540\pi\)
\(152\) 0 0
\(153\) 1.75263 + 6.84172i 0.141692 + 0.553121i
\(154\) 0 0
\(155\) 2.98963 0.527153i 0.240133 0.0423419i
\(156\) 0 0
\(157\) 3.30641 3.94043i 0.263881 0.314481i −0.617793 0.786341i \(-0.711973\pi\)
0.881673 + 0.471860i \(0.156417\pi\)
\(158\) 0 0
\(159\) −2.22395 + 16.2020i −0.176371 + 1.28490i
\(160\) 0 0
\(161\) 0.278604 0.183892i 0.0219571 0.0144928i
\(162\) 0 0
\(163\) 1.26560 2.19209i 0.0991296 0.171697i −0.812195 0.583386i \(-0.801727\pi\)
0.911325 + 0.411689i \(0.135061\pi\)
\(164\) 0 0
\(165\) −11.9810 9.29872i −0.932720 0.723904i
\(166\) 0 0
\(167\) −6.21832 + 2.26328i −0.481188 + 0.175138i −0.571214 0.820801i \(-0.693527\pi\)
0.0900259 + 0.995939i \(0.471305\pi\)
\(168\) 0 0
\(169\) 2.04051 + 11.5723i 0.156962 + 0.890177i
\(170\) 0 0
\(171\) −0.339223 + 0.0868979i −0.0259410 + 0.00664525i
\(172\) 0 0
\(173\) −8.20343 + 6.88349i −0.623695 + 0.523342i −0.898963 0.438025i \(-0.855678\pi\)
0.275267 + 0.961368i \(0.411234\pi\)
\(174\) 0 0
\(175\) 3.63676 + 2.69826i 0.274914 + 0.203970i
\(176\) 0 0
\(177\) 14.3506 3.09855i 1.07866 0.232902i
\(178\) 0 0
\(179\) 4.62241i 0.345495i 0.984966 + 0.172748i \(0.0552645\pi\)
−0.984966 + 0.172748i \(0.944735\pi\)
\(180\) 0 0
\(181\) 9.48331 5.47519i 0.704889 0.406968i −0.104277 0.994548i \(-0.533253\pi\)
0.809166 + 0.587580i \(0.199919\pi\)
\(182\) 0 0
\(183\) −4.31951 6.86347i −0.319307 0.507362i
\(184\) 0 0
\(185\) −24.9674 + 9.08737i −1.83564 + 0.668117i
\(186\) 0 0
\(187\) −7.83607 + 1.38171i −0.573030 + 0.101041i
\(188\) 0 0
\(189\) 10.5282 + 8.84067i 0.765812 + 0.643064i
\(190\) 0 0
\(191\) 19.4111 3.42270i 1.40454 0.247658i 0.580532 0.814237i \(-0.302845\pi\)
0.824007 + 0.566579i \(0.191733\pi\)
\(192\) 0 0
\(193\) −20.8024 + 7.57147i −1.49739 + 0.545006i −0.955384 0.295367i \(-0.904558\pi\)
−0.542008 + 0.840373i \(0.682336\pi\)
\(194\) 0 0
\(195\) 5.01151 0.191137i 0.358882 0.0136876i
\(196\) 0 0
\(197\) 1.74551 1.00777i 0.124363 0.0718008i −0.436528 0.899691i \(-0.643792\pi\)
0.560891 + 0.827890i \(0.310459\pi\)
\(198\) 0 0
\(199\) 3.72542i 0.264088i 0.991244 + 0.132044i \(0.0421540\pi\)
−0.991244 + 0.132044i \(0.957846\pi\)
\(200\) 0 0
\(201\) −10.5602 11.6527i −0.744856 0.821917i
\(202\) 0 0
\(203\) 2.85778 + 6.59548i 0.200577 + 0.462912i
\(204\) 0 0
\(205\) 6.56463 5.50838i 0.458493 0.384722i
\(206\) 0 0
\(207\) 0.341269 + 0.163741i 0.0237199 + 0.0113808i
\(208\) 0 0
\(209\) −0.0685072 0.388524i −0.00473874 0.0268747i
\(210\) 0 0
\(211\) 4.81139 1.75120i 0.331229 0.120558i −0.171052 0.985262i \(-0.554717\pi\)
0.502281 + 0.864704i \(0.332494\pi\)
\(212\) 0 0
\(213\) 13.0690 5.32913i 0.895470 0.365146i
\(214\) 0 0
\(215\) −3.30672 + 5.72741i −0.225517 + 0.390606i
\(216\) 0 0
\(217\) −0.185313 3.09475i −0.0125799 0.210085i
\(218\) 0 0
\(219\) 18.0030 7.34111i 1.21653 0.496066i
\(220\) 0 0
\(221\) 1.69131 2.01563i 0.113770 0.135586i
\(222\) 0 0
\(223\) −23.3657 + 4.12001i −1.56468 + 0.275896i −0.887812 0.460205i \(-0.847776\pi\)
−0.676871 + 0.736101i \(0.736665\pi\)
\(224\) 0 0
\(225\) −0.503887 + 5.10997i −0.0335925 + 0.340665i
\(226\) 0 0
\(227\) 3.55971 + 20.1881i 0.236266 + 1.33993i 0.839931 + 0.542693i \(0.182595\pi\)
−0.603665 + 0.797238i \(0.706294\pi\)
\(228\) 0 0
\(229\) −6.76544 18.5879i −0.447073 1.22832i −0.934752 0.355300i \(-0.884379\pi\)
0.487679 0.873023i \(-0.337844\pi\)
\(230\) 0 0
\(231\) −10.8346 + 11.0682i −0.712867 + 0.728235i
\(232\) 0 0
\(233\) 15.2011 8.77638i 0.995859 0.574959i 0.0888386 0.996046i \(-0.471684\pi\)
0.907020 + 0.421087i \(0.138351\pi\)
\(234\) 0 0
\(235\) 10.6327 18.4163i 0.693598 1.20135i
\(236\) 0 0
\(237\) −21.6535 11.4242i −1.40655 0.742084i
\(238\) 0 0
\(239\) 17.9853 + 3.17130i 1.16337 + 0.205134i 0.721807 0.692095i \(-0.243312\pi\)
0.441566 + 0.897229i \(0.354423\pi\)
\(240\) 0 0
\(241\) −5.56206 + 15.2816i −0.358284 + 0.984377i 0.621341 + 0.783541i \(0.286588\pi\)
−0.979625 + 0.200837i \(0.935634\pi\)
\(242\) 0 0
\(243\) −2.45983 + 15.3932i −0.157798 + 0.987471i
\(244\) 0 0
\(245\) 12.4017 13.2312i 0.792316 0.845312i
\(246\) 0 0
\(247\) 0.0999379 + 0.0838578i 0.00635890 + 0.00533575i
\(248\) 0 0
\(249\) −0.822710 21.5710i −0.0521371 1.36701i
\(250\) 0 0
\(251\) −3.28698 5.69321i −0.207472 0.359352i 0.743445 0.668797i \(-0.233190\pi\)
−0.950918 + 0.309444i \(0.899857\pi\)
\(252\) 0 0
\(253\) −0.213224 + 0.369315i −0.0134053 + 0.0232186i
\(254\) 0 0
\(255\) 7.09374 + 7.82765i 0.444227 + 0.490187i
\(256\) 0 0
\(257\) 15.3134 5.57362i 0.955224 0.347673i 0.183064 0.983101i \(-0.441398\pi\)
0.772160 + 0.635428i \(0.219176\pi\)
\(258\) 0 0
\(259\) 6.30072 + 26.3929i 0.391508 + 1.63998i
\(260\) 0 0
\(261\) −4.74820 + 6.62449i −0.293906 + 0.410046i
\(262\) 0 0
\(263\) 3.67048 + 4.37430i 0.226331 + 0.269731i 0.867245 0.497882i \(-0.165889\pi\)
−0.640914 + 0.767613i \(0.721444\pi\)
\(264\) 0 0
\(265\) 8.36612 + 22.9857i 0.513927 + 1.41200i
\(266\) 0 0
\(267\) −0.433122 + 0.558060i −0.0265067 + 0.0341527i
\(268\) 0 0
\(269\) −12.6846 21.9703i −0.773392 1.33955i −0.935694 0.352813i \(-0.885225\pi\)
0.162302 0.986741i \(-0.448108\pi\)
\(270\) 0 0
\(271\) 2.95607 + 1.70669i 0.179568 + 0.103674i 0.587090 0.809522i \(-0.300274\pi\)
−0.407521 + 0.913196i \(0.633607\pi\)
\(272\) 0 0
\(273\) 0.391962 5.10676i 0.0237226 0.309075i
\(274\) 0 0
\(275\) −5.69706 1.00455i −0.343546 0.0605764i
\(276\) 0 0
\(277\) −16.4067 + 13.7669i −0.985784 + 0.827171i −0.984952 0.172829i \(-0.944709\pi\)
−0.000832089 1.00000i \(0.500265\pi\)
\(278\) 0 0
\(279\) 2.90170 1.98448i 0.173720 0.118808i
\(280\) 0 0
\(281\) −2.04388 + 5.61551i −0.121928 + 0.334993i −0.985608 0.169046i \(-0.945931\pi\)
0.863680 + 0.504040i \(0.168153\pi\)
\(282\) 0 0
\(283\) −5.29351 0.933388i −0.314666 0.0554842i 0.0140846 0.999901i \(-0.495517\pi\)
−0.328751 + 0.944417i \(0.606628\pi\)
\(284\) 0 0
\(285\) −0.388106 + 0.351718i −0.0229894 + 0.0208340i
\(286\) 0 0
\(287\) −4.82106 7.30409i −0.284578 0.431147i
\(288\) 0 0
\(289\) −11.4577 −0.673981
\(290\) 0 0
\(291\) −7.46149 11.8559i −0.437400 0.695005i
\(292\) 0 0
\(293\) −4.55335 + 25.8233i −0.266010 + 1.50862i 0.500135 + 0.865948i \(0.333284\pi\)
−0.766144 + 0.642668i \(0.777827\pi\)
\(294\) 0 0
\(295\) 16.8217 14.1151i 0.979397 0.821812i
\(296\) 0 0
\(297\) −17.0809 4.08419i −0.991132 0.236989i
\(298\) 0 0
\(299\) −0.0244876 0.138876i −0.00141615 0.00803141i
\(300\) 0 0
\(301\) 5.42415 + 4.02440i 0.312643 + 0.231962i
\(302\) 0 0
\(303\) 0.749230 + 19.6444i 0.0430421 + 1.12854i
\(304\) 0 0
\(305\) −10.5046 6.06486i −0.601494 0.347273i
\(306\) 0 0
\(307\) 10.1398 + 5.85419i 0.578707 + 0.334116i 0.760619 0.649198i \(-0.224895\pi\)
−0.181913 + 0.983315i \(0.558229\pi\)
\(308\) 0 0
\(309\) 20.0896 18.2060i 1.14286 1.03570i
\(310\) 0 0
\(311\) −1.85672 + 10.5300i −0.105285 + 0.597100i 0.885821 + 0.464027i \(0.153596\pi\)
−0.991106 + 0.133074i \(0.957515\pi\)
\(312\) 0 0
\(313\) 1.63919 + 1.95351i 0.0926523 + 0.110419i 0.810379 0.585907i \(-0.199262\pi\)
−0.717726 + 0.696325i \(0.754817\pi\)
\(314\) 0 0
\(315\) 20.0981 + 4.34714i 1.13240 + 0.244934i
\(316\) 0 0
\(317\) 5.30604 14.5782i 0.298017 0.818795i −0.696814 0.717252i \(-0.745400\pi\)
0.994831 0.101543i \(-0.0323780\pi\)
\(318\) 0 0
\(319\) −7.03418 5.90237i −0.393838 0.330470i
\(320\) 0 0
\(321\) −11.9404 + 4.86892i −0.666446 + 0.271757i
\(322\) 0 0
\(323\) 0.274796i 0.0152901i
\(324\) 0 0
\(325\) 1.65669 0.956488i 0.0918964 0.0530564i
\(326\) 0 0
\(327\) −29.0860 3.99247i −1.60846 0.220784i
\(328\) 0 0
\(329\) −17.4412 12.9403i −0.961563 0.713423i
\(330\) 0 0
\(331\) −22.6410 8.24065i −1.24446 0.452947i −0.365936 0.930640i \(-0.619251\pi\)
−0.878527 + 0.477693i \(0.841473\pi\)
\(332\) 0 0
\(333\) −21.9946 + 21.5149i −1.20530 + 1.17901i
\(334\) 0 0
\(335\) −22.1030 8.04484i −1.20762 0.439537i
\(336\) 0 0
\(337\) −10.1610 8.52606i −0.553503 0.464444i 0.322622 0.946528i \(-0.395436\pi\)
−0.876125 + 0.482084i \(0.839880\pi\)
\(338\) 0 0
\(339\) 1.58092 + 0.508061i 0.0858641 + 0.0275941i
\(340\) 0 0
\(341\) 1.98027 + 3.42993i 0.107238 + 0.185741i
\(342\) 0 0
\(343\) −11.9739 14.1289i −0.646528 0.762890i
\(344\) 0 0
\(345\) 0.565747 0.0215773i 0.0304588 0.00116169i
\(346\) 0 0
\(347\) 2.30205 + 6.32484i 0.123581 + 0.339535i 0.986020 0.166625i \(-0.0532868\pi\)
−0.862440 + 0.506160i \(0.831065\pi\)
\(348\) 0 0
\(349\) −1.49276 1.77900i −0.0799055 0.0952277i 0.724611 0.689159i \(-0.242020\pi\)
−0.804516 + 0.593931i \(0.797575\pi\)
\(350\) 0 0
\(351\) 5.19500 2.59608i 0.277288 0.138568i
\(352\) 0 0
\(353\) −10.1311 3.68740i −0.539221 0.196261i 0.0580297 0.998315i \(-0.481518\pi\)
−0.597251 + 0.802054i \(0.703740\pi\)
\(354\) 0 0
\(355\) 13.5694 16.1714i 0.720190 0.858289i
\(356\) 0 0
\(357\) 8.77083 6.28183i 0.464201 0.332470i
\(358\) 0 0
\(359\) 27.3379i 1.44284i −0.692497 0.721421i \(-0.743489\pi\)
0.692497 0.721421i \(-0.256511\pi\)
\(360\) 0 0
\(361\) 18.9864 0.999283
\(362\) 0 0
\(363\) 0.224460 0.698448i 0.0117811 0.0366590i
\(364\) 0 0
\(365\) 18.6924 22.2768i 0.978407 1.16602i
\(366\) 0 0
\(367\) −28.5523 + 5.03454i −1.49042 + 0.262801i −0.858732 0.512424i \(-0.828748\pi\)
−0.631685 + 0.775225i \(0.717636\pi\)
\(368\) 0 0
\(369\) 4.29274 8.94696i 0.223471 0.465760i
\(370\) 0 0
\(371\) 24.2982 5.80064i 1.26150 0.301154i
\(372\) 0 0
\(373\) −3.02012 + 17.1280i −0.156376 + 0.886852i 0.801141 + 0.598476i \(0.204227\pi\)
−0.957517 + 0.288377i \(0.906884\pi\)
\(374\) 0 0
\(375\) −5.57153 13.6634i −0.287713 0.705575i
\(376\) 0 0
\(377\) 3.03647 0.156386
\(378\) 0 0
\(379\) 19.8221 1.01819 0.509097 0.860709i \(-0.329980\pi\)
0.509097 + 0.860709i \(0.329980\pi\)
\(380\) 0 0
\(381\) 7.90690 + 1.08534i 0.405083 + 0.0556034i
\(382\) 0 0
\(383\) −2.13848 + 12.1279i −0.109271 + 0.619707i 0.880157 + 0.474683i \(0.157437\pi\)
−0.989428 + 0.145024i \(0.953674\pi\)
\(384\) 0 0
\(385\) −6.60805 + 22.2042i −0.336778 + 1.13163i
\(386\) 0 0
\(387\) −0.751536 + 7.62141i −0.0382027 + 0.387418i
\(388\) 0 0
\(389\) −10.0836 + 1.77801i −0.511257 + 0.0901484i −0.423325 0.905978i \(-0.639137\pi\)
−0.0879325 + 0.996126i \(0.528026\pi\)
\(390\) 0 0
\(391\) 0.190932 0.227544i 0.00965584 0.0115074i
\(392\) 0 0
\(393\) 34.5843 7.46739i 1.74455 0.376680i
\(394\) 0 0
\(395\) −36.6189 −1.84250
\(396\) 0 0
\(397\) 33.0450i 1.65848i −0.558892 0.829240i \(-0.688773\pi\)
0.558892 0.829240i \(-0.311227\pi\)
\(398\) 0 0
\(399\) 0.311462 + 0.434870i 0.0155926 + 0.0217707i
\(400\) 0 0
\(401\) 1.12919 1.34572i 0.0563892 0.0672020i −0.737113 0.675770i \(-0.763811\pi\)
0.793502 + 0.608568i \(0.208256\pi\)
\(402\) 0 0
\(403\) −1.23070 0.447936i −0.0613053 0.0223133i
\(404\) 0 0
\(405\) 7.48958 + 22.0804i 0.372160 + 1.09718i
\(406\) 0 0
\(407\) −22.2814 26.5539i −1.10445 1.31623i
\(408\) 0 0
\(409\) 3.23082 + 8.87661i 0.159754 + 0.438920i 0.993583 0.113102i \(-0.0360786\pi\)
−0.833829 + 0.552022i \(0.813856\pi\)
\(410\) 0 0
\(411\) −13.0724 20.7713i −0.644812 1.02457i
\(412\) 0 0
\(413\) −12.3538 18.7165i −0.607893 0.920981i
\(414\) 0 0
\(415\) −16.1439 27.9621i −0.792473 1.37260i
\(416\) 0 0
\(417\) 23.6004 21.3876i 1.15571 1.04736i
\(418\) 0 0
\(419\) −5.84407 4.90375i −0.285501 0.239564i 0.488778 0.872408i \(-0.337443\pi\)
−0.774279 + 0.632844i \(0.781887\pi\)
\(420\) 0 0
\(421\) −7.26865 2.64557i −0.354252 0.128937i 0.158763 0.987317i \(-0.449249\pi\)
−0.513015 + 0.858379i \(0.671472\pi\)
\(422\) 0 0
\(423\) 2.41654 24.5064i 0.117496 1.19154i
\(424\) 0 0
\(425\) 3.78643 + 1.37815i 0.183669 + 0.0668501i
\(426\) 0 0
\(427\) −7.38114 + 9.94843i −0.357199 + 0.481438i
\(428\) 0 0
\(429\) 2.47051 + 6.05859i 0.119277 + 0.292511i
\(430\) 0 0
\(431\) −32.2999 + 18.6484i −1.55583 + 0.898260i −0.558183 + 0.829718i \(0.688501\pi\)
−0.997648 + 0.0685418i \(0.978165\pi\)
\(432\) 0 0
\(433\) 11.0883i 0.532870i −0.963853 0.266435i \(-0.914154\pi\)
0.963853 0.266435i \(-0.0858458\pi\)
\(434\) 0 0
\(435\) −1.65782 + 12.0775i −0.0794862 + 0.579074i
\(436\) 0 0
\(437\) 0.0112819 + 0.00946668i 0.000539689 + 0.000452853i
\(438\) 0 0
\(439\) 9.22473 25.3447i 0.440272 1.20964i −0.499041 0.866578i \(-0.666314\pi\)
0.939313 0.343060i \(-0.111464\pi\)
\(440\) 0 0
\(441\) 6.75998 19.8822i 0.321904 0.946772i
\(442\) 0 0
\(443\) −25.6317 30.5467i −1.21780 1.45132i −0.854346 0.519705i \(-0.826042\pi\)
−0.363454 0.931612i \(-0.618403\pi\)
\(444\) 0 0
\(445\) −0.183478 + 1.04055i −0.00869768 + 0.0493270i
\(446\) 0 0
\(447\) 30.7291 + 9.87539i 1.45344 + 0.467090i
\(448\) 0 0
\(449\) −1.95937 1.13124i −0.0924682 0.0533865i 0.453053 0.891484i \(-0.350335\pi\)
−0.545521 + 0.838097i \(0.683668\pi\)
\(450\) 0 0
\(451\) 9.68222 + 5.59003i 0.455918 + 0.263224i
\(452\) 0 0
\(453\) 16.3403 + 8.62104i 0.767735 + 0.405052i
\(454\) 0 0
\(455\) −3.04575 7.02929i −0.142787 0.329538i
\(456\) 0 0
\(457\) 3.51406 + 19.9292i 0.164381 + 0.932250i 0.949700 + 0.313160i \(0.101388\pi\)
−0.785320 + 0.619091i \(0.787501\pi\)
\(458\) 0 0
\(459\) 11.2227 + 4.86755i 0.523832 + 0.227198i
\(460\) 0 0
\(461\) 8.26907 6.93857i 0.385129 0.323162i −0.429583 0.903027i \(-0.641339\pi\)
0.814712 + 0.579866i \(0.196895\pi\)
\(462\) 0 0
\(463\) −3.86641 + 21.9275i −0.179687 + 1.01906i 0.752906 + 0.658128i \(0.228651\pi\)
−0.932593 + 0.360929i \(0.882460\pi\)
\(464\) 0 0
\(465\) 2.45358 4.65052i 0.113782 0.215663i
\(466\) 0 0
\(467\) −1.50943 −0.0698481 −0.0349241 0.999390i \(-0.511119\pi\)
−0.0349241 + 0.999390i \(0.511119\pi\)
\(468\) 0 0
\(469\) −10.7459 + 21.4841i −0.496198 + 0.992041i
\(470\) 0 0
\(471\) −1.88038 8.70875i −0.0866434 0.401278i
\(472\) 0 0
\(473\) −8.49703 1.49826i −0.390694 0.0688899i
\(474\) 0 0
\(475\) −0.0683306 + 0.187737i −0.00313523 + 0.00861396i
\(476\) 0 0
\(477\) 19.8073 + 20.2489i 0.906914 + 0.927134i
\(478\) 0 0
\(479\) −9.83065 + 8.24890i −0.449174 + 0.376902i −0.839129 0.543932i \(-0.816935\pi\)
0.389955 + 0.920834i \(0.372490\pi\)
\(480\) 0 0
\(481\) 11.2885 + 1.99047i 0.514712 + 0.0907576i
\(482\) 0 0
\(483\) 0.0442484 0.576500i 0.00201337 0.0262316i
\(484\) 0 0
\(485\) −18.1456 10.4764i −0.823951 0.475708i
\(486\) 0 0
\(487\) −11.2032 19.4046i −0.507667 0.879306i −0.999961 0.00887634i \(-0.997175\pi\)
0.492293 0.870429i \(-0.336159\pi\)
\(488\) 0 0
\(489\) −1.65540 4.05963i −0.0748597 0.183583i
\(490\) 0 0
\(491\) 1.86210 + 5.11607i 0.0840353 + 0.230885i 0.974592 0.223987i \(-0.0719073\pi\)
−0.890557 + 0.454872i \(0.849685\pi\)
\(492\) 0 0
\(493\) 4.11123 + 4.89957i 0.185161 + 0.220666i
\(494\) 0 0
\(495\) −25.4468 + 6.51864i −1.14375 + 0.292991i
\(496\) 0 0
\(497\) −14.8203 15.6573i −0.664781 0.702328i
\(498\) 0 0
\(499\) −14.3904 + 5.23768i −0.644203 + 0.234471i −0.643401 0.765529i \(-0.722477\pi\)
−0.000801335 1.00000i \(0.500255\pi\)
\(500\) 0 0
\(501\) −3.50679 + 10.9120i −0.156672 + 0.487513i
\(502\) 0 0
\(503\) −5.37147 + 9.30366i −0.239502 + 0.414830i −0.960572 0.278033i \(-0.910318\pi\)
0.721069 + 0.692863i \(0.243651\pi\)
\(504\) 0 0
\(505\) 14.7020 + 25.4647i 0.654232 + 1.13316i
\(506\) 0 0
\(507\) 18.0013 + 9.49735i 0.799465 + 0.421792i
\(508\) 0 0
\(509\) 10.4319 + 8.75343i 0.462387 + 0.387989i 0.844008 0.536330i \(-0.180190\pi\)
−0.381621 + 0.924319i \(0.624634\pi\)
\(510\) 0 0
\(511\) −20.4156 21.5687i −0.903132 0.954142i
\(512\) 0 0
\(513\) −0.241340 + 0.556439i −0.0106554 + 0.0245674i
\(514\) 0 0
\(515\) 13.8696 38.1063i 0.611165 1.67916i
\(516\) 0 0
\(517\) 27.3219 + 4.81759i 1.20162 + 0.211878i
\(518\) 0 0
\(519\) 0.706906 + 18.5347i 0.0310297 + 0.813585i
\(520\) 0 0
\(521\) 7.64859 13.2477i 0.335091 0.580394i −0.648412 0.761290i \(-0.724566\pi\)
0.983502 + 0.180896i \(0.0578997\pi\)
\(522\) 0 0
\(523\) −12.1121 + 6.99294i −0.529626 + 0.305780i −0.740864 0.671655i \(-0.765584\pi\)
0.211238 + 0.977435i \(0.432250\pi\)
\(524\) 0 0
\(525\) 7.55413 2.11071i 0.329689 0.0921189i
\(526\) 0 0
\(527\) −0.943520 2.59230i −0.0411004 0.112922i
\(528\) 0 0
\(529\) 3.99114 + 22.6349i 0.173528 + 0.984126i
\(530\) 0 0
\(531\) 11.0001 22.9264i 0.477362 0.994920i
\(532\) 0 0
\(533\) −3.64088 + 0.641985i −0.157704 + 0.0278074i
\(534\) 0 0
\(535\) −12.3976 + 14.7749i −0.535995 + 0.638774i
\(536\) 0 0
\(537\) 6.32483 + 4.90884i 0.272936 + 0.211832i
\(538\) 0 0
\(539\) 21.7546 + 9.29999i 0.937039 + 0.400579i
\(540\) 0 0
\(541\) −16.0626 + 27.8212i −0.690583 + 1.19613i 0.281064 + 0.959689i \(0.409313\pi\)
−0.971647 + 0.236436i \(0.924021\pi\)
\(542\) 0 0
\(543\) 2.57926 18.7904i 0.110686 0.806375i
\(544\) 0 0
\(545\) −41.2643 + 15.0190i −1.76757 + 0.643343i
\(546\) 0 0
\(547\) −4.13424 23.4464i −0.176767 1.00250i −0.936084 0.351776i \(-0.885578\pi\)
0.759317 0.650721i \(-0.225533\pi\)
\(548\) 0 0
\(549\) −13.9784 1.37839i −0.596584 0.0588283i
\(550\) 0 0
\(551\) −0.242928 + 0.203841i −0.0103491 + 0.00868391i
\(552\) 0 0
\(553\) −4.28100 + 37.1516i −0.182046 + 1.57985i
\(554\) 0 0
\(555\) −14.0802 + 43.8132i −0.597672 + 1.85977i
\(556\) 0 0
\(557\) 9.33194i 0.395407i 0.980262 + 0.197703i \(0.0633483\pi\)
−0.980262 + 0.197703i \(0.936652\pi\)
\(558\) 0 0
\(559\) 2.47091 1.42658i 0.104508 0.0603379i
\(560\) 0 0
\(561\) −6.43103 + 12.1894i −0.271518 + 0.514636i
\(562\) 0 0
\(563\) 30.5263 11.1107i 1.28653 0.468259i 0.393943 0.919135i \(-0.371111\pi\)
0.892586 + 0.450876i \(0.148888\pi\)
\(564\) 0 0
\(565\) 2.44600 0.431297i 0.102904 0.0181448i
\(566\) 0 0
\(567\) 23.2772 5.01718i 0.977550 0.210702i
\(568\) 0 0
\(569\) 40.1659 7.08232i 1.68384 0.296906i 0.751835 0.659351i \(-0.229169\pi\)
0.932005 + 0.362445i \(0.118058\pi\)
\(570\) 0 0
\(571\) 31.1702 11.3450i 1.30443 0.474775i 0.405995 0.913875i \(-0.366925\pi\)
0.898438 + 0.439101i \(0.144703\pi\)
\(572\) 0 0
\(573\) 15.9306 30.1949i 0.665512 1.26141i
\(574\) 0 0
\(575\) 0.187023 0.107978i 0.00779939 0.00450298i
\(576\) 0 0
\(577\) 43.1437i 1.79609i 0.439899 + 0.898047i \(0.355014\pi\)
−0.439899 + 0.898047i \(0.644986\pi\)
\(578\) 0 0
\(579\) −11.7314 + 36.5045i −0.487542 + 1.51708i
\(580\) 0 0
\(581\) −30.2562 + 13.1098i −1.25524 + 0.543886i
\(582\) 0 0
\(583\) −24.4464 + 20.5130i −1.01247 + 0.849560i
\(584\) 0 0
\(585\) 5.06051 7.06021i 0.209226 0.291904i
\(586\) 0 0
\(587\) 7.44234 + 42.2076i 0.307178 + 1.74209i 0.613070 + 0.790028i \(0.289934\pi\)
−0.305892 + 0.952066i \(0.598955\pi\)
\(588\) 0 0
\(589\) 0.128530 0.0467811i 0.00529599 0.00192758i
\(590\) 0 0
\(591\) 0.474742 3.45859i 0.0195283 0.142268i
\(592\) 0 0
\(593\) 2.95663 5.12102i 0.121414 0.210295i −0.798911 0.601449i \(-0.794590\pi\)
0.920326 + 0.391153i \(0.127924\pi\)
\(594\) 0 0
\(595\) 7.21849 14.4318i 0.295929 0.591647i
\(596\) 0 0
\(597\) 5.09747 + 3.95626i 0.208626 + 0.161919i
\(598\) 0 0
\(599\) 16.5465 19.7193i 0.676070 0.805709i −0.313527 0.949579i \(-0.601511\pi\)
0.989596 + 0.143871i \(0.0459550\pi\)
\(600\) 0 0
\(601\) −19.3751 + 3.41635i −0.790325 + 0.139356i −0.554218 0.832371i \(-0.686983\pi\)
−0.236107 + 0.971727i \(0.575872\pi\)
\(602\) 0 0
\(603\) −27.1588 + 2.07467i −1.10599 + 0.0844870i
\(604\) 0 0
\(605\) −0.190546 1.08064i −0.00774678 0.0439342i
\(606\) 0 0
\(607\) 4.38614 + 12.0508i 0.178028 + 0.489128i 0.996324 0.0856697i \(-0.0273030\pi\)
−0.818296 + 0.574798i \(0.805081\pi\)
\(608\) 0 0
\(609\) 12.0594 + 3.09388i 0.488672 + 0.125370i
\(610\) 0 0
\(611\) −7.94513 + 4.58712i −0.321425 + 0.185575i
\(612\) 0 0
\(613\) −15.1423 + 26.2273i −0.611594 + 1.05931i 0.379378 + 0.925242i \(0.376138\pi\)
−0.990972 + 0.134070i \(0.957195\pi\)
\(614\) 0 0
\(615\) −0.565687 14.8320i −0.0228107 0.598086i
\(616\) 0 0
\(617\) −33.7970 5.95933i −1.36062 0.239913i −0.554753 0.832015i \(-0.687187\pi\)
−0.805863 + 0.592101i \(0.798298\pi\)
\(618\) 0 0
\(619\) −7.36707 + 20.2409i −0.296107 + 0.813548i 0.699034 + 0.715089i \(0.253614\pi\)
−0.995141 + 0.0984597i \(0.968608\pi\)
\(620\) 0 0
\(621\) 0.586461 0.293070i 0.0235339 0.0117605i
\(622\) 0 0
\(623\) 1.03424 + 0.307795i 0.0414360 + 0.0123315i
\(624\) 0 0
\(625\) −23.4627 19.6876i −0.938509 0.787502i
\(626\) 0 0
\(627\) −0.604367 0.318860i −0.0241361 0.0127340i
\(628\) 0 0
\(629\) 12.0723 + 20.9098i 0.481354 + 0.833730i
\(630\) 0 0
\(631\) 9.15885 15.8636i 0.364608 0.631520i −0.624105 0.781340i \(-0.714536\pi\)
0.988713 + 0.149821i \(0.0478697\pi\)
\(632\) 0 0
\(633\) 2.71336 8.44311i 0.107846 0.335583i
\(634\) 0 0
\(635\) 11.2175 4.08285i 0.445154 0.162023i
\(636\) 0 0
\(637\) −7.48761 + 2.26828i −0.296670 + 0.0898726i
\(638\) 0 0
\(639\) 6.58693 23.5415i 0.260575 0.931289i
\(640\) 0 0
\(641\) 26.4237 + 31.4905i 1.04367 + 1.24380i 0.969121 + 0.246584i \(0.0793080\pi\)
0.0745514 + 0.997217i \(0.476248\pi\)
\(642\) 0 0
\(643\) 14.5325 + 39.9277i 0.573105 + 1.57459i 0.799569 + 0.600574i \(0.205061\pi\)
−0.226464 + 0.974020i \(0.572716\pi\)
\(644\) 0 0
\(645\) 4.32517 + 10.6069i 0.170303 + 0.417645i
\(646\) 0 0
\(647\) 2.03413 + 3.52322i 0.0799700 + 0.138512i 0.903237 0.429143i \(-0.141184\pi\)
−0.823267 + 0.567655i \(0.807851\pi\)
\(648\) 0 0
\(649\) 24.8104 + 14.3243i 0.973895 + 0.562279i
\(650\) 0 0
\(651\) −4.43133 3.03295i −0.173677 0.118871i
\(652\) 0 0
\(653\) 30.6601 + 5.40620i 1.19982 + 0.211561i 0.737622 0.675214i \(-0.235949\pi\)
0.462201 + 0.886775i \(0.347060\pi\)
\(654\) 0 0
\(655\) 40.5396 34.0168i 1.58401 1.32914i
\(656\) 0 0
\(657\) 9.07378 32.4295i 0.354002 1.26519i
\(658\) 0 0
\(659\) −8.48007 + 23.2988i −0.330337 + 0.907593i 0.657687 + 0.753291i \(0.271535\pi\)
−0.988024 + 0.154302i \(0.950687\pi\)
\(660\) 0 0
\(661\) 30.1409 + 5.31465i 1.17234 + 0.206716i 0.725710 0.688001i \(-0.241511\pi\)
0.446634 + 0.894717i \(0.352623\pi\)
\(662\) 0 0
\(663\) −0.961862 4.45474i −0.0373556 0.173008i
\(664\) 0 0
\(665\) 0.715551 + 0.357903i 0.0277479 + 0.0138789i
\(666\) 0 0
\(667\) 0.342786 0.0132727
\(668\) 0 0
\(669\) −19.1762 + 36.3465i −0.741393 + 1.40524i
\(670\) 0 0
\(671\) 2.74795 15.5844i 0.106083 0.601629i
\(672\) 0 0
\(673\) 4.44436 3.72926i 0.171317 0.143752i −0.553098 0.833116i \(-0.686554\pi\)
0.724415 + 0.689364i \(0.242110\pi\)
\(674\) 0 0
\(675\) 6.45684 + 6.11608i 0.248524 + 0.235408i
\(676\) 0 0
\(677\) −6.28158 35.6246i −0.241421 1.36917i −0.828660 0.559752i \(-0.810896\pi\)
0.587239 0.809413i \(-0.300215\pi\)
\(678\) 0 0
\(679\) −12.7501 + 17.1848i −0.489305 + 0.659493i
\(680\) 0 0
\(681\) 31.4036 + 16.5683i 1.20339 + 0.634899i
\(682\) 0 0
\(683\) −23.1494 13.3653i −0.885788 0.511410i −0.0132254 0.999913i \(-0.504210\pi\)
−0.872562 + 0.488503i \(0.837543\pi\)
\(684\) 0 0
\(685\) −31.7908 18.3544i −1.21466 0.701286i
\(686\) 0 0
\(687\) −32.6184 10.4826i −1.24447 0.399935i
\(688\) 0 0
\(689\) 1.83249 10.3926i 0.0698122 0.395925i
\(690\) 0 0
\(691\) −16.7330 19.9416i −0.636553 0.758615i 0.347268 0.937766i \(-0.387109\pi\)
−0.983822 + 0.179151i \(0.942665\pi\)
\(692\) 0 0
\(693\) 3.63857 + 26.5790i 0.138218 + 1.00965i
\(694\) 0 0
\(695\) 16.2933 44.7655i 0.618041 1.69805i
\(696\) 0 0
\(697\) −5.96545 5.00561i −0.225958 0.189601i
\(698\) 0 0
\(699\) 4.13438 30.1198i 0.156377 1.13924i
\(700\) 0 0
\(701\) 22.3146i 0.842809i 0.906873 + 0.421405i \(0.138463\pi\)
−0.906873 + 0.421405i \(0.861537\pi\)
\(702\) 0 0
\(703\) −1.03674 + 0.598562i −0.0391014 + 0.0225752i
\(704\) 0 0
\(705\) −13.9074 34.1061i −0.523785 1.28451i
\(706\) 0 0
\(707\) 27.5539 11.9389i 1.03627 0.449009i
\(708\) 0 0
\(709\) 5.43860 + 1.97949i 0.204251 + 0.0743412i 0.442120 0.896956i \(-0.354227\pi\)
−0.237869 + 0.971297i \(0.576449\pi\)
\(710\) 0 0
\(711\) −38.6270 + 17.4963i −1.44862 + 0.656161i
\(712\) 0 0
\(713\) −0.138933 0.0505674i −0.00520307 0.00189376i
\(714\) 0 0
\(715\) 7.49684 + 6.29060i 0.280366 + 0.235255i
\(716\) 0 0
\(717\) 23.4390 21.2414i 0.875346 0.793275i
\(718\) 0 0
\(719\) 26.2658 + 45.4937i 0.979548 + 1.69663i 0.664026 + 0.747709i \(0.268846\pi\)
0.315522 + 0.948918i \(0.397820\pi\)
\(720\) 0 0
\(721\) −37.0392 18.5262i −1.37941 0.689951i
\(722\) 0 0
\(723\) 15.0031 + 23.8391i 0.557971 + 0.886586i
\(724\) 0 0
\(725\) 1.59041 + 4.36961i 0.0590663 + 0.162283i
\(726\) 0 0
\(727\) −12.3912 14.7672i −0.459563 0.547686i 0.485645 0.874156i \(-0.338585\pi\)
−0.945207 + 0.326471i \(0.894141\pi\)
\(728\) 0 0
\(729\) 18.4501 + 19.7128i 0.683338 + 0.730102i
\(730\) 0 0
\(731\) 5.64738 + 2.05548i 0.208876 + 0.0760246i
\(732\) 0 0
\(733\) 25.2536 30.0960i 0.932762 1.11162i −0.0607798 0.998151i \(-0.519359\pi\)
0.993541 0.113471i \(-0.0361968\pi\)
\(734\) 0 0
\(735\) −4.93407 31.0203i −0.181996 1.14420i
\(736\) 0 0
\(737\) 30.6870i 1.13037i
\(738\) 0 0
\(739\) 13.0679 0.480710 0.240355 0.970685i \(-0.422736\pi\)
0.240355 + 0.970685i \(0.422736\pi\)
\(740\) 0 0
\(741\) 0.220873 0.0476905i 0.00811396 0.00175196i
\(742\) 0 0
\(743\) −3.14402 + 3.74690i −0.115343 + 0.137460i −0.820626 0.571465i \(-0.806375\pi\)
0.705284 + 0.708925i \(0.250820\pi\)
\(744\) 0 0
\(745\) 47.5440 8.38329i 1.74188 0.307140i
\(746\) 0 0
\(747\) −30.3892 21.7820i −1.11188 0.796960i
\(748\) 0 0
\(749\) 13.5404 + 14.3052i 0.494757 + 0.522701i
\(750\) 0 0
\(751\) 3.51062 19.9097i 0.128104 0.726516i −0.851311 0.524661i \(-0.824192\pi\)
0.979415 0.201855i \(-0.0646969\pi\)
\(752\) 0 0
\(753\) −11.2806 1.54843i −0.411090 0.0564280i
\(754\) 0 0
\(755\) 27.6336 1.00569
\(756\) 0 0
\(757\) −38.4613 −1.39790 −0.698950 0.715171i \(-0.746349\pi\)
−0.698950 + 0.715171i \(0.746349\pi\)
\(758\) 0 0
\(759\) 0.278895 + 0.683952i 0.0101233 + 0.0248259i
\(760\) 0 0
\(761\) −6.92697 + 39.2848i −0.251102 + 1.42407i 0.554780 + 0.831997i \(0.312802\pi\)
−0.805883 + 0.592075i \(0.798309\pi\)
\(762\) 0 0
\(763\) 10.4134 + 43.6204i 0.376990 + 1.57916i
\(764\) 0 0
\(765\) 18.2438 1.39365i 0.659607 0.0503875i
\(766\) 0 0
\(767\) −9.32966 + 1.64507i −0.336874 + 0.0594000i
\(768\) 0 0
\(769\) −12.0209 + 14.3260i −0.433486 + 0.516609i −0.937925 0.346839i \(-0.887255\pi\)
0.504438 + 0.863448i \(0.331700\pi\)
\(770\) 0 0
\(771\) 8.63592 26.8723i 0.311015 0.967780i
\(772\) 0 0
\(773\) −8.57951 −0.308583 −0.154292 0.988025i \(-0.549310\pi\)
−0.154292 + 0.988025i \(0.549310\pi\)
\(774\) 0 0
\(775\) 2.00564i 0.0720446i
\(776\) 0 0
\(777\) 42.8045 + 19.4071i 1.53560 + 0.696226i
\(778\)