Properties

Label 1148.2.k.b.337.3
Level $1148$
Weight $2$
Character 1148.337
Analytic conductor $9.167$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 337.3
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.b.729.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.89621 - 1.89621i) q^{3} -1.39357i q^{5} +(-0.707107 - 0.707107i) q^{7} +4.19121i q^{9} +O(q^{10})\) \(q+(-1.89621 - 1.89621i) q^{3} -1.39357i q^{5} +(-0.707107 - 0.707107i) q^{7} +4.19121i q^{9} +(-0.00674500 - 0.00674500i) q^{11} +(-3.61779 - 3.61779i) q^{13} +(-2.64249 + 2.64249i) q^{15} +(-2.98892 + 2.98892i) q^{17} +(3.03265 - 3.03265i) q^{19} +2.68164i q^{21} -6.42985 q^{23} +3.05797 q^{25} +(2.25878 - 2.25878i) q^{27} +(6.04055 + 6.04055i) q^{29} -9.06781 q^{31} +0.0255799i q^{33} +(-0.985400 + 0.985400i) q^{35} -2.92526 q^{37} +13.7202i q^{39} +(-3.12241 - 5.59022i) q^{41} -7.31038i q^{43} +5.84073 q^{45} +(3.23183 - 3.23183i) q^{47} +1.00000i q^{49} +11.3352 q^{51} +(9.80407 + 9.80407i) q^{53} +(-0.00939961 + 0.00939961i) q^{55} -11.5011 q^{57} +8.32596 q^{59} +12.1771i q^{61} +(2.96363 - 2.96363i) q^{63} +(-5.04163 + 5.04163i) q^{65} +(-7.17560 + 7.17560i) q^{67} +(12.1923 + 12.1923i) q^{69} +(-0.0715608 - 0.0715608i) q^{71} +15.1426i q^{73} +(-5.79855 - 5.79855i) q^{75} +0.00953888i q^{77} +(7.11491 + 7.11491i) q^{79} +4.00739 q^{81} +0.354618 q^{83} +(4.16525 + 4.16525i) q^{85} -22.9083i q^{87} +(-2.66353 - 2.66353i) q^{89} +5.11633i q^{91} +(17.1944 + 17.1944i) q^{93} +(-4.22621 - 4.22621i) q^{95} +(3.41973 - 3.41973i) q^{97} +(0.0282697 - 0.0282697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.89621 1.89621i −1.09478 1.09478i −0.995011 0.0997652i \(-0.968191\pi\)
−0.0997652 0.995011i \(-0.531809\pi\)
\(4\) 0 0
\(5\) 1.39357i 0.623222i −0.950210 0.311611i \(-0.899131\pi\)
0.950210 0.311611i \(-0.100869\pi\)
\(6\) 0 0
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) 0 0
\(9\) 4.19121i 1.39707i
\(10\) 0 0
\(11\) −0.00674500 0.00674500i −0.00203370 0.00203370i 0.706089 0.708123i \(-0.250458\pi\)
−0.708123 + 0.706089i \(0.750458\pi\)
\(12\) 0 0
\(13\) −3.61779 3.61779i −1.00339 1.00339i −0.999994 0.00340044i \(-0.998918\pi\)
−0.00340044 0.999994i \(-0.501082\pi\)
\(14\) 0 0
\(15\) −2.64249 + 2.64249i −0.682289 + 0.682289i
\(16\) 0 0
\(17\) −2.98892 + 2.98892i −0.724918 + 0.724918i −0.969603 0.244684i \(-0.921316\pi\)
0.244684 + 0.969603i \(0.421316\pi\)
\(18\) 0 0
\(19\) 3.03265 3.03265i 0.695739 0.695739i −0.267750 0.963488i \(-0.586280\pi\)
0.963488 + 0.267750i \(0.0862801\pi\)
\(20\) 0 0
\(21\) 2.68164i 0.585182i
\(22\) 0 0
\(23\) −6.42985 −1.34072 −0.670359 0.742037i \(-0.733860\pi\)
−0.670359 + 0.742037i \(0.733860\pi\)
\(24\) 0 0
\(25\) 3.05797 0.611594
\(26\) 0 0
\(27\) 2.25878 2.25878i 0.434702 0.434702i
\(28\) 0 0
\(29\) 6.04055 + 6.04055i 1.12170 + 1.12170i 0.991486 + 0.130216i \(0.0415671\pi\)
0.130216 + 0.991486i \(0.458433\pi\)
\(30\) 0 0
\(31\) −9.06781 −1.62863 −0.814313 0.580426i \(-0.802886\pi\)
−0.814313 + 0.580426i \(0.802886\pi\)
\(32\) 0 0
\(33\) 0.0255799i 0.00445288i
\(34\) 0 0
\(35\) −0.985400 + 0.985400i −0.166563 + 0.166563i
\(36\) 0 0
\(37\) −2.92526 −0.480910 −0.240455 0.970660i \(-0.577297\pi\)
−0.240455 + 0.970660i \(0.577297\pi\)
\(38\) 0 0
\(39\) 13.7202i 2.19699i
\(40\) 0 0
\(41\) −3.12241 5.59022i −0.487639 0.873045i
\(42\) 0 0
\(43\) 7.31038i 1.11482i −0.830236 0.557411i \(-0.811795\pi\)
0.830236 0.557411i \(-0.188205\pi\)
\(44\) 0 0
\(45\) 5.84073 0.870685
\(46\) 0 0
\(47\) 3.23183 3.23183i 0.471412 0.471412i −0.430960 0.902371i \(-0.641825\pi\)
0.902371 + 0.430960i \(0.141825\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 11.3352 1.58725
\(52\) 0 0
\(53\) 9.80407 + 9.80407i 1.34669 + 1.34669i 0.889228 + 0.457464i \(0.151242\pi\)
0.457464 + 0.889228i \(0.348758\pi\)
\(54\) 0 0
\(55\) −0.00939961 + 0.00939961i −0.00126744 + 0.00126744i
\(56\) 0 0
\(57\) −11.5011 −1.52336
\(58\) 0 0
\(59\) 8.32596 1.08395 0.541974 0.840396i \(-0.317677\pi\)
0.541974 + 0.840396i \(0.317677\pi\)
\(60\) 0 0
\(61\) 12.1771i 1.55911i 0.626333 + 0.779556i \(0.284555\pi\)
−0.626333 + 0.779556i \(0.715445\pi\)
\(62\) 0 0
\(63\) 2.96363 2.96363i 0.373383 0.373383i
\(64\) 0 0
\(65\) −5.04163 + 5.04163i −0.625338 + 0.625338i
\(66\) 0 0
\(67\) −7.17560 + 7.17560i −0.876639 + 0.876639i −0.993185 0.116546i \(-0.962818\pi\)
0.116546 + 0.993185i \(0.462818\pi\)
\(68\) 0 0
\(69\) 12.1923 + 12.1923i 1.46779 + 1.46779i
\(70\) 0 0
\(71\) −0.0715608 0.0715608i −0.00849271 0.00849271i 0.702848 0.711340i \(-0.251912\pi\)
−0.711340 + 0.702848i \(0.751912\pi\)
\(72\) 0 0
\(73\) 15.1426i 1.77230i 0.463394 + 0.886152i \(0.346632\pi\)
−0.463394 + 0.886152i \(0.653368\pi\)
\(74\) 0 0
\(75\) −5.79855 5.79855i −0.669559 0.669559i
\(76\) 0 0
\(77\) 0.00953888i 0.00108706i
\(78\) 0 0
\(79\) 7.11491 + 7.11491i 0.800490 + 0.800490i 0.983172 0.182682i \(-0.0584779\pi\)
−0.182682 + 0.983172i \(0.558478\pi\)
\(80\) 0 0
\(81\) 4.00739 0.445266
\(82\) 0 0
\(83\) 0.354618 0.0389243 0.0194622 0.999811i \(-0.493805\pi\)
0.0194622 + 0.999811i \(0.493805\pi\)
\(84\) 0 0
\(85\) 4.16525 + 4.16525i 0.451785 + 0.451785i
\(86\) 0 0
\(87\) 22.9083i 2.45602i
\(88\) 0 0
\(89\) −2.66353 2.66353i −0.282333 0.282333i 0.551706 0.834039i \(-0.313977\pi\)
−0.834039 + 0.551706i \(0.813977\pi\)
\(90\) 0 0
\(91\) 5.11633i 0.536337i
\(92\) 0 0
\(93\) 17.1944 + 17.1944i 1.78298 + 1.78298i
\(94\) 0 0
\(95\) −4.22621 4.22621i −0.433600 0.433600i
\(96\) 0 0
\(97\) 3.41973 3.41973i 0.347221 0.347221i −0.511853 0.859073i \(-0.671041\pi\)
0.859073 + 0.511853i \(0.171041\pi\)
\(98\) 0 0
\(99\) 0.0282697 0.0282697i 0.00284121 0.00284121i
\(100\) 0 0
\(101\) −10.8891 + 10.8891i −1.08351 + 1.08351i −0.0873257 + 0.996180i \(0.527832\pi\)
−0.996180 + 0.0873257i \(0.972168\pi\)
\(102\) 0 0
\(103\) 12.7483i 1.25613i −0.778163 0.628063i \(-0.783848\pi\)
0.778163 0.628063i \(-0.216152\pi\)
\(104\) 0 0
\(105\) 3.73705 0.364699
\(106\) 0 0
\(107\) −11.9150 −1.15187 −0.575936 0.817495i \(-0.695362\pi\)
−0.575936 + 0.817495i \(0.695362\pi\)
\(108\) 0 0
\(109\) −6.77678 + 6.77678i −0.649098 + 0.649098i −0.952775 0.303677i \(-0.901785\pi\)
0.303677 + 0.952775i \(0.401785\pi\)
\(110\) 0 0
\(111\) 5.54690 + 5.54690i 0.526489 + 0.526489i
\(112\) 0 0
\(113\) −7.61496 −0.716355 −0.358177 0.933654i \(-0.616602\pi\)
−0.358177 + 0.933654i \(0.616602\pi\)
\(114\) 0 0
\(115\) 8.96043i 0.835565i
\(116\) 0 0
\(117\) 15.1629 15.1629i 1.40181 1.40181i
\(118\) 0 0
\(119\) 4.22696 0.387485
\(120\) 0 0
\(121\) 10.9999i 0.999992i
\(122\) 0 0
\(123\) −4.67947 + 16.5210i −0.421934 + 1.48964i
\(124\) 0 0
\(125\) 11.2293i 1.00438i
\(126\) 0 0
\(127\) −17.1559 −1.52234 −0.761171 0.648551i \(-0.775375\pi\)
−0.761171 + 0.648551i \(0.775375\pi\)
\(128\) 0 0
\(129\) −13.8620 + 13.8620i −1.22048 + 1.22048i
\(130\) 0 0
\(131\) 18.2459i 1.59416i −0.603877 0.797078i \(-0.706378\pi\)
0.603877 0.797078i \(-0.293622\pi\)
\(132\) 0 0
\(133\) −4.28882 −0.371888
\(134\) 0 0
\(135\) −3.14776 3.14776i −0.270916 0.270916i
\(136\) 0 0
\(137\) −3.70202 + 3.70202i −0.316285 + 0.316285i −0.847338 0.531054i \(-0.821796\pi\)
0.531054 + 0.847338i \(0.321796\pi\)
\(138\) 0 0
\(139\) 0.532554 0.0451707 0.0225853 0.999745i \(-0.492810\pi\)
0.0225853 + 0.999745i \(0.492810\pi\)
\(140\) 0 0
\(141\) −12.2565 −1.03218
\(142\) 0 0
\(143\) 0.0488040i 0.00408120i
\(144\) 0 0
\(145\) 8.41791 8.41791i 0.699069 0.699069i
\(146\) 0 0
\(147\) 1.89621 1.89621i 0.156397 0.156397i
\(148\) 0 0
\(149\) 13.3321 13.3321i 1.09221 1.09221i 0.0969123 0.995293i \(-0.469103\pi\)
0.995293 0.0969123i \(-0.0308966\pi\)
\(150\) 0 0
\(151\) 1.25214 + 1.25214i 0.101898 + 0.101898i 0.756218 0.654320i \(-0.227045\pi\)
−0.654320 + 0.756218i \(0.727045\pi\)
\(152\) 0 0
\(153\) −12.5272 12.5272i −1.01276 1.01276i
\(154\) 0 0
\(155\) 12.6366i 1.01500i
\(156\) 0 0
\(157\) −1.93133 1.93133i −0.154137 0.154137i 0.625826 0.779963i \(-0.284762\pi\)
−0.779963 + 0.625826i \(0.784762\pi\)
\(158\) 0 0
\(159\) 37.1811i 2.94865i
\(160\) 0 0
\(161\) 4.54659 + 4.54659i 0.358322 + 0.358322i
\(162\) 0 0
\(163\) −3.13101 −0.245239 −0.122620 0.992454i \(-0.539130\pi\)
−0.122620 + 0.992454i \(0.539130\pi\)
\(164\) 0 0
\(165\) 0.0356472 0.00277513
\(166\) 0 0
\(167\) 11.0777 + 11.0777i 0.857217 + 0.857217i 0.991009 0.133792i \(-0.0427155\pi\)
−0.133792 + 0.991009i \(0.542715\pi\)
\(168\) 0 0
\(169\) 13.1768i 1.01360i
\(170\) 0 0
\(171\) 12.7105 + 12.7105i 0.971995 + 0.971995i
\(172\) 0 0
\(173\) 3.43858i 0.261430i 0.991420 + 0.130715i \(0.0417273\pi\)
−0.991420 + 0.130715i \(0.958273\pi\)
\(174\) 0 0
\(175\) −2.16231 2.16231i −0.163455 0.163455i
\(176\) 0 0
\(177\) −15.7877 15.7877i −1.18668 1.18668i
\(178\) 0 0
\(179\) 1.39953 1.39953i 0.104606 0.104606i −0.652867 0.757473i \(-0.726434\pi\)
0.757473 + 0.652867i \(0.226434\pi\)
\(180\) 0 0
\(181\) −10.6180 + 10.6180i −0.789232 + 0.789232i −0.981368 0.192136i \(-0.938459\pi\)
0.192136 + 0.981368i \(0.438459\pi\)
\(182\) 0 0
\(183\) 23.0902 23.0902i 1.70688 1.70688i
\(184\) 0 0
\(185\) 4.07654i 0.299714i
\(186\) 0 0
\(187\) 0.0403205 0.00294853
\(188\) 0 0
\(189\) −3.19440 −0.232358
\(190\) 0 0
\(191\) −5.08849 + 5.08849i −0.368190 + 0.368190i −0.866817 0.498627i \(-0.833838\pi\)
0.498627 + 0.866817i \(0.333838\pi\)
\(192\) 0 0
\(193\) −18.5213 18.5213i −1.33319 1.33319i −0.902498 0.430694i \(-0.858269\pi\)
−0.430694 0.902498i \(-0.641731\pi\)
\(194\) 0 0
\(195\) 19.1200 1.36921
\(196\) 0 0
\(197\) 19.5976i 1.39627i −0.715966 0.698135i \(-0.754014\pi\)
0.715966 0.698135i \(-0.245986\pi\)
\(198\) 0 0
\(199\) −11.9830 + 11.9830i −0.849450 + 0.849450i −0.990064 0.140614i \(-0.955092\pi\)
0.140614 + 0.990064i \(0.455092\pi\)
\(200\) 0 0
\(201\) 27.2129 1.91945
\(202\) 0 0
\(203\) 8.54263i 0.599575i
\(204\) 0 0
\(205\) −7.79034 + 4.35129i −0.544101 + 0.303907i
\(206\) 0 0
\(207\) 26.9489i 1.87308i
\(208\) 0 0
\(209\) −0.0409105 −0.00282984
\(210\) 0 0
\(211\) −10.7095 + 10.7095i −0.737271 + 0.737271i −0.972049 0.234778i \(-0.924564\pi\)
0.234778 + 0.972049i \(0.424564\pi\)
\(212\) 0 0
\(213\) 0.271388i 0.0185952i
\(214\) 0 0
\(215\) −10.1875 −0.694782
\(216\) 0 0
\(217\) 6.41191 + 6.41191i 0.435269 + 0.435269i
\(218\) 0 0
\(219\) 28.7135 28.7135i 1.94028 1.94028i
\(220\) 0 0
\(221\) 21.6265 1.45476
\(222\) 0 0
\(223\) 1.13400 0.0759381 0.0379691 0.999279i \(-0.487911\pi\)
0.0379691 + 0.999279i \(0.487911\pi\)
\(224\) 0 0
\(225\) 12.8166i 0.854440i
\(226\) 0 0
\(227\) 0.320841 0.320841i 0.0212950 0.0212950i −0.696379 0.717674i \(-0.745207\pi\)
0.717674 + 0.696379i \(0.245207\pi\)
\(228\) 0 0
\(229\) −1.15816 + 1.15816i −0.0765336 + 0.0765336i −0.744337 0.667804i \(-0.767235\pi\)
0.667804 + 0.744337i \(0.267235\pi\)
\(230\) 0 0
\(231\) 0.0180877 0.0180877i 0.00119008 0.00119008i
\(232\) 0 0
\(233\) 7.26218 + 7.26218i 0.475762 + 0.475762i 0.903773 0.428012i \(-0.140786\pi\)
−0.428012 + 0.903773i \(0.640786\pi\)
\(234\) 0 0
\(235\) −4.50378 4.50378i −0.293794 0.293794i
\(236\) 0 0
\(237\) 26.9827i 1.75271i
\(238\) 0 0
\(239\) −13.4710 13.4710i −0.871364 0.871364i 0.121257 0.992621i \(-0.461307\pi\)
−0.992621 + 0.121257i \(0.961307\pi\)
\(240\) 0 0
\(241\) 26.7671i 1.72422i −0.506718 0.862112i \(-0.669141\pi\)
0.506718 0.862112i \(-0.330859\pi\)
\(242\) 0 0
\(243\) −14.3752 14.3752i −0.922169 0.922169i
\(244\) 0 0
\(245\) 1.39357 0.0890317
\(246\) 0 0
\(247\) −21.9430 −1.39620
\(248\) 0 0
\(249\) −0.672429 0.672429i −0.0426134 0.0426134i
\(250\) 0 0
\(251\) 4.39407i 0.277351i −0.990338 0.138676i \(-0.955715\pi\)
0.990338 0.138676i \(-0.0442845\pi\)
\(252\) 0 0
\(253\) 0.0433694 + 0.0433694i 0.00272661 + 0.00272661i
\(254\) 0 0
\(255\) 15.7964i 0.989207i
\(256\) 0 0
\(257\) −11.0972 11.0972i −0.692225 0.692225i 0.270496 0.962721i \(-0.412812\pi\)
−0.962721 + 0.270496i \(0.912812\pi\)
\(258\) 0 0
\(259\) 2.06847 + 2.06847i 0.128529 + 0.128529i
\(260\) 0 0
\(261\) −25.3172 + 25.3172i −1.56710 + 1.56710i
\(262\) 0 0
\(263\) −6.60565 + 6.60565i −0.407322 + 0.407322i −0.880804 0.473482i \(-0.842997\pi\)
0.473482 + 0.880804i \(0.342997\pi\)
\(264\) 0 0
\(265\) 13.6626 13.6626i 0.839288 0.839288i
\(266\) 0 0
\(267\) 10.1012i 0.618184i
\(268\) 0 0
\(269\) 18.7014 1.14025 0.570123 0.821560i \(-0.306896\pi\)
0.570123 + 0.821560i \(0.306896\pi\)
\(270\) 0 0
\(271\) −15.7181 −0.954804 −0.477402 0.878685i \(-0.658421\pi\)
−0.477402 + 0.878685i \(0.658421\pi\)
\(272\) 0 0
\(273\) 9.70162 9.70162i 0.587169 0.587169i
\(274\) 0 0
\(275\) −0.0206260 0.0206260i −0.00124380 0.00124380i
\(276\) 0 0
\(277\) −29.2099 −1.75505 −0.877526 0.479529i \(-0.840808\pi\)
−0.877526 + 0.479529i \(0.840808\pi\)
\(278\) 0 0
\(279\) 38.0051i 2.27530i
\(280\) 0 0
\(281\) 0.718430 0.718430i 0.0428579 0.0428579i −0.685353 0.728211i \(-0.740352\pi\)
0.728211 + 0.685353i \(0.240352\pi\)
\(282\) 0 0
\(283\) −12.0991 −0.719218 −0.359609 0.933103i \(-0.617090\pi\)
−0.359609 + 0.933103i \(0.617090\pi\)
\(284\) 0 0
\(285\) 16.0275i 0.949389i
\(286\) 0 0
\(287\) −1.74500 + 6.16076i −0.103004 + 0.363658i
\(288\) 0 0
\(289\) 0.867231i 0.0510136i
\(290\) 0 0
\(291\) −12.9690 −0.760258
\(292\) 0 0
\(293\) −0.807697 + 0.807697i −0.0471861 + 0.0471861i −0.730306 0.683120i \(-0.760623\pi\)
0.683120 + 0.730306i \(0.260623\pi\)
\(294\) 0 0
\(295\) 11.6028i 0.675540i
\(296\) 0 0
\(297\) −0.0304710 −0.00176810
\(298\) 0 0
\(299\) 23.2619 + 23.2619i 1.34527 + 1.34527i
\(300\) 0 0
\(301\) −5.16922 + 5.16922i −0.297949 + 0.297949i
\(302\) 0 0
\(303\) 41.2960 2.37239
\(304\) 0 0
\(305\) 16.9695 0.971673
\(306\) 0 0
\(307\) 0.961340i 0.0548666i 0.999624 + 0.0274333i \(0.00873338\pi\)
−0.999624 + 0.0274333i \(0.991267\pi\)
\(308\) 0 0
\(309\) −24.1734 + 24.1734i −1.37518 + 1.37518i
\(310\) 0 0
\(311\) −23.9158 + 23.9158i −1.35614 + 1.35614i −0.477516 + 0.878623i \(0.658463\pi\)
−0.878623 + 0.477516i \(0.841537\pi\)
\(312\) 0 0
\(313\) 2.11859 2.11859i 0.119750 0.119750i −0.644692 0.764442i \(-0.723015\pi\)
0.764442 + 0.644692i \(0.223015\pi\)
\(314\) 0 0
\(315\) −4.13002 4.13002i −0.232700 0.232700i
\(316\) 0 0
\(317\) 14.0222 + 14.0222i 0.787566 + 0.787566i 0.981095 0.193528i \(-0.0619931\pi\)
−0.193528 + 0.981095i \(0.561993\pi\)
\(318\) 0 0
\(319\) 0.0814871i 0.00456240i
\(320\) 0 0
\(321\) 22.5934 + 22.5934i 1.26104 + 1.26104i
\(322\) 0 0
\(323\) 18.1287i 1.00871i
\(324\) 0 0
\(325\) −11.0631 11.0631i −0.613671 0.613671i
\(326\) 0 0
\(327\) 25.7004 1.42123
\(328\) 0 0
\(329\) −4.57050 −0.251980
\(330\) 0 0
\(331\) −13.7087 13.7087i −0.753498 0.753498i 0.221632 0.975130i \(-0.428862\pi\)
−0.975130 + 0.221632i \(0.928862\pi\)
\(332\) 0 0
\(333\) 12.2604i 0.671865i
\(334\) 0 0
\(335\) 9.99968 + 9.99968i 0.546341 + 0.546341i
\(336\) 0 0
\(337\) 13.5539i 0.738328i 0.929364 + 0.369164i \(0.120356\pi\)
−0.929364 + 0.369164i \(0.879644\pi\)
\(338\) 0 0
\(339\) 14.4395 + 14.4395i 0.784248 + 0.784248i
\(340\) 0 0
\(341\) 0.0611624 + 0.0611624i 0.00331213 + 0.00331213i
\(342\) 0 0
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 0 0
\(345\) 16.9908 16.9908i 0.914756 0.914756i
\(346\) 0 0
\(347\) 10.3180 10.3180i 0.553901 0.553901i −0.373663 0.927564i \(-0.621898\pi\)
0.927564 + 0.373663i \(0.121898\pi\)
\(348\) 0 0
\(349\) 9.62802i 0.515376i −0.966228 0.257688i \(-0.917039\pi\)
0.966228 0.257688i \(-0.0829607\pi\)
\(350\) 0 0
\(351\) −16.3436 −0.872356
\(352\) 0 0
\(353\) −0.263588 −0.0140293 −0.00701467 0.999975i \(-0.502233\pi\)
−0.00701467 + 0.999975i \(0.502233\pi\)
\(354\) 0 0
\(355\) −0.0997248 + 0.0997248i −0.00529284 + 0.00529284i
\(356\) 0 0
\(357\) −8.01520 8.01520i −0.424210 0.424210i
\(358\) 0 0
\(359\) 21.8699 1.15425 0.577125 0.816656i \(-0.304175\pi\)
0.577125 + 0.816656i \(0.304175\pi\)
\(360\) 0 0
\(361\) 0.606016i 0.0318956i
\(362\) 0 0
\(363\) −20.8581 + 20.8581i −1.09477 + 1.09477i
\(364\) 0 0
\(365\) 21.1022 1.10454
\(366\) 0 0
\(367\) 5.62891i 0.293827i −0.989149 0.146913i \(-0.953066\pi\)
0.989149 0.146913i \(-0.0469339\pi\)
\(368\) 0 0
\(369\) 23.4298 13.0867i 1.21971 0.681265i
\(370\) 0 0
\(371\) 13.8650i 0.719837i
\(372\) 0 0
\(373\) −26.6675 −1.38079 −0.690396 0.723432i \(-0.742564\pi\)
−0.690396 + 0.723432i \(0.742564\pi\)
\(374\) 0 0
\(375\) −21.2931 + 21.2931i −1.09957 + 1.09957i
\(376\) 0 0
\(377\) 43.7069i 2.25102i
\(378\) 0 0
\(379\) 26.5049 1.36147 0.680733 0.732531i \(-0.261661\pi\)
0.680733 + 0.732531i \(0.261661\pi\)
\(380\) 0 0
\(381\) 32.5312 + 32.5312i 1.66662 + 1.66662i
\(382\) 0 0
\(383\) −9.81104 + 9.81104i −0.501321 + 0.501321i −0.911848 0.410528i \(-0.865345\pi\)
0.410528 + 0.911848i \(0.365345\pi\)
\(384\) 0 0
\(385\) 0.0132931 0.000677477
\(386\) 0 0
\(387\) 30.6393 1.55749
\(388\) 0 0
\(389\) 21.2251i 1.07616i −0.842895 0.538078i \(-0.819151\pi\)
0.842895 0.538078i \(-0.180849\pi\)
\(390\) 0 0
\(391\) 19.2183 19.2183i 0.971911 0.971911i
\(392\) 0 0
\(393\) −34.5981 + 34.5981i −1.74524 + 1.74524i
\(394\) 0 0
\(395\) 9.91510 9.91510i 0.498883 0.498883i
\(396\) 0 0
\(397\) 17.9977 + 17.9977i 0.903280 + 0.903280i 0.995718 0.0924383i \(-0.0294661\pi\)
−0.0924383 + 0.995718i \(0.529466\pi\)
\(398\) 0 0
\(399\) 8.13250 + 8.13250i 0.407134 + 0.407134i
\(400\) 0 0
\(401\) 1.49738i 0.0747756i −0.999301 0.0373878i \(-0.988096\pi\)
0.999301 0.0373878i \(-0.0119037\pi\)
\(402\) 0 0
\(403\) 32.8054 + 32.8054i 1.63415 + 1.63415i
\(404\) 0 0
\(405\) 5.58457i 0.277499i
\(406\) 0 0
\(407\) 0.0197309 + 0.0197309i 0.000978024 + 0.000978024i
\(408\) 0 0
\(409\) −1.12242 −0.0554999 −0.0277500 0.999615i \(-0.508834\pi\)
−0.0277500 + 0.999615i \(0.508834\pi\)
\(410\) 0 0
\(411\) 14.0396 0.692522
\(412\) 0 0
\(413\) −5.88734 5.88734i −0.289697 0.289697i
\(414\) 0 0
\(415\) 0.494183i 0.0242585i
\(416\) 0 0
\(417\) −1.00983 1.00983i −0.0494518 0.0494518i
\(418\) 0 0
\(419\) 1.10985i 0.0542197i 0.999632 + 0.0271098i \(0.00863039\pi\)
−0.999632 + 0.0271098i \(0.991370\pi\)
\(420\) 0 0
\(421\) −17.8911 17.8911i −0.871961 0.871961i 0.120725 0.992686i \(-0.461478\pi\)
−0.992686 + 0.120725i \(0.961478\pi\)
\(422\) 0 0
\(423\) 13.5453 + 13.5453i 0.658595 + 0.658595i
\(424\) 0 0
\(425\) −9.14002 + 9.14002i −0.443356 + 0.443356i
\(426\) 0 0
\(427\) 8.61048 8.61048i 0.416690 0.416690i
\(428\) 0 0
\(429\) 0.0925426 0.0925426i 0.00446800 0.00446800i
\(430\) 0 0
\(431\) 24.2929i 1.17015i 0.810980 + 0.585074i \(0.198934\pi\)
−0.810980 + 0.585074i \(0.801066\pi\)
\(432\) 0 0
\(433\) −27.6018 −1.32646 −0.663229 0.748417i \(-0.730814\pi\)
−0.663229 + 0.748417i \(0.730814\pi\)
\(434\) 0 0
\(435\) −31.9242 −1.53065
\(436\) 0 0
\(437\) −19.4995 + 19.4995i −0.932789 + 0.932789i
\(438\) 0 0
\(439\) 8.39852 + 8.39852i 0.400839 + 0.400839i 0.878529 0.477689i \(-0.158526\pi\)
−0.477689 + 0.878529i \(0.658526\pi\)
\(440\) 0 0
\(441\) −4.19121 −0.199581
\(442\) 0 0
\(443\) 9.52893i 0.452733i 0.974042 + 0.226367i \(0.0726848\pi\)
−0.974042 + 0.226367i \(0.927315\pi\)
\(444\) 0 0
\(445\) −3.71180 + 3.71180i −0.175956 + 0.175956i
\(446\) 0 0
\(447\) −50.5607 −2.39144
\(448\) 0 0
\(449\) 9.07784i 0.428410i 0.976789 + 0.214205i \(0.0687160\pi\)
−0.976789 + 0.214205i \(0.931284\pi\)
\(450\) 0 0
\(451\) −0.0166454 + 0.0587667i −0.000783800 + 0.00276722i
\(452\) 0 0
\(453\) 4.74863i 0.223110i
\(454\) 0 0
\(455\) 7.12995 0.334257
\(456\) 0 0
\(457\) −8.30624 + 8.30624i −0.388550 + 0.388550i −0.874170 0.485620i \(-0.838594\pi\)
0.485620 + 0.874170i \(0.338594\pi\)
\(458\) 0 0
\(459\) 13.5026i 0.630248i
\(460\) 0 0
\(461\) 20.0754 0.935004 0.467502 0.883992i \(-0.345154\pi\)
0.467502 + 0.883992i \(0.345154\pi\)
\(462\) 0 0
\(463\) −9.44582 9.44582i −0.438985 0.438985i 0.452686 0.891670i \(-0.350466\pi\)
−0.891670 + 0.452686i \(0.850466\pi\)
\(464\) 0 0
\(465\) 23.9616 23.9616i 1.11119 1.11119i
\(466\) 0 0
\(467\) −29.8969 −1.38346 −0.691731 0.722155i \(-0.743152\pi\)
−0.691731 + 0.722155i \(0.743152\pi\)
\(468\) 0 0
\(469\) 10.1478 0.468583
\(470\) 0 0
\(471\) 7.32440i 0.337491i
\(472\) 0 0
\(473\) −0.0493086 + 0.0493086i −0.00226721 + 0.00226721i
\(474\) 0 0
\(475\) 9.27377 9.27377i 0.425510 0.425510i
\(476\) 0 0
\(477\) −41.0909 + 41.0909i −1.88142 + 1.88142i
\(478\) 0 0
\(479\) −14.1130 14.1130i −0.644838 0.644838i 0.306903 0.951741i \(-0.400707\pi\)
−0.951741 + 0.306903i \(0.900707\pi\)
\(480\) 0 0
\(481\) 10.5830 + 10.5830i 0.482542 + 0.482542i
\(482\) 0 0
\(483\) 17.2426i 0.784564i
\(484\) 0 0
\(485\) −4.76562 4.76562i −0.216395 0.216395i
\(486\) 0 0
\(487\) 5.15444i 0.233570i −0.993157 0.116785i \(-0.962741\pi\)
0.993157 0.116785i \(-0.0372588\pi\)
\(488\) 0 0
\(489\) 5.93704 + 5.93704i 0.268482 + 0.268482i
\(490\) 0 0
\(491\) −14.9946 −0.676698 −0.338349 0.941021i \(-0.609868\pi\)
−0.338349 + 0.941021i \(0.609868\pi\)
\(492\) 0 0
\(493\) −36.1094 −1.62628
\(494\) 0 0
\(495\) −0.0393957 0.0393957i −0.00177071 0.00177071i
\(496\) 0 0
\(497\) 0.101202i 0.00453954i
\(498\) 0 0
\(499\) −13.6146 13.6146i −0.609473 0.609473i 0.333335 0.942808i \(-0.391826\pi\)
−0.942808 + 0.333335i \(0.891826\pi\)
\(500\) 0 0
\(501\) 42.0112i 1.87692i
\(502\) 0 0
\(503\) 11.4796 + 11.4796i 0.511851 + 0.511851i 0.915093 0.403242i \(-0.132117\pi\)
−0.403242 + 0.915093i \(0.632117\pi\)
\(504\) 0 0
\(505\) 15.1747 + 15.1747i 0.675264 + 0.675264i
\(506\) 0 0
\(507\) 24.9860 24.9860i 1.10967 1.10967i
\(508\) 0 0
\(509\) −26.6021 + 26.6021i −1.17912 + 1.17912i −0.199147 + 0.979970i \(0.563817\pi\)
−0.979970 + 0.199147i \(0.936183\pi\)
\(510\) 0 0
\(511\) 10.7074 10.7074i 0.473668 0.473668i
\(512\) 0 0
\(513\) 13.7002i 0.604879i
\(514\) 0 0
\(515\) −17.7656 −0.782845
\(516\) 0 0
\(517\) −0.0435975 −0.00191742
\(518\) 0 0
\(519\) 6.52026 6.52026i 0.286208 0.286208i
\(520\) 0 0
\(521\) −12.6539 12.6539i −0.554377 0.554377i 0.373324 0.927701i \(-0.378218\pi\)
−0.927701 + 0.373324i \(0.878218\pi\)
\(522\) 0 0
\(523\) 29.1074 1.27278 0.636389 0.771368i \(-0.280427\pi\)
0.636389 + 0.771368i \(0.280427\pi\)
\(524\) 0 0
\(525\) 8.20039i 0.357894i
\(526\) 0 0
\(527\) 27.1029 27.1029i 1.18062 1.18062i
\(528\) 0 0
\(529\) 18.3430 0.797523
\(530\) 0 0
\(531\) 34.8958i 1.51435i
\(532\) 0 0
\(533\) −8.92801 + 31.5205i −0.386715 + 1.36530i
\(534\) 0 0
\(535\) 16.6044i 0.717871i
\(536\) 0 0
\(537\) −5.30760 −0.229040
\(538\) 0 0
\(539\) 0.00674500 0.00674500i 0.000290528 0.000290528i
\(540\) 0 0
\(541\) 36.5818i 1.57278i −0.617733 0.786388i \(-0.711949\pi\)
0.617733 0.786388i \(-0.288051\pi\)
\(542\) 0 0
\(543\) 40.2680 1.72807
\(544\) 0 0
\(545\) 9.44389 + 9.44389i 0.404532 + 0.404532i
\(546\) 0 0
\(547\) 18.3817 18.3817i 0.785944 0.785944i −0.194883 0.980827i \(-0.562433\pi\)
0.980827 + 0.194883i \(0.0624327\pi\)
\(548\) 0 0
\(549\) −51.0366 −2.17819
\(550\) 0 0
\(551\) 36.6378 1.56082
\(552\) 0 0
\(553\) 10.0620i 0.427880i
\(554\) 0 0
\(555\) 7.72998 7.72998i 0.328119 0.328119i
\(556\) 0 0
\(557\) 13.9573 13.9573i 0.591390 0.591390i −0.346617 0.938007i \(-0.612670\pi\)
0.938007 + 0.346617i \(0.112670\pi\)
\(558\) 0 0
\(559\) −26.4474 + 26.4474i −1.11861 + 1.11861i
\(560\) 0 0
\(561\) −0.0764560 0.0764560i −0.00322798 0.00322798i
\(562\) 0 0
\(563\) 1.09376 + 1.09376i 0.0460966 + 0.0460966i 0.729779 0.683683i \(-0.239623\pi\)
−0.683683 + 0.729779i \(0.739623\pi\)
\(564\) 0 0
\(565\) 10.6120i 0.446448i
\(566\) 0 0
\(567\) −2.83365 2.83365i −0.119002 0.119002i
\(568\) 0 0
\(569\) 1.32617i 0.0555959i −0.999614 0.0277980i \(-0.991150\pi\)
0.999614 0.0277980i \(-0.00884951\pi\)
\(570\) 0 0
\(571\) 16.4221 + 16.4221i 0.687244 + 0.687244i 0.961622 0.274378i \(-0.0884720\pi\)
−0.274378 + 0.961622i \(0.588472\pi\)
\(572\) 0 0
\(573\) 19.2977 0.806171
\(574\) 0 0
\(575\) −19.6623 −0.819975
\(576\) 0 0
\(577\) −29.2600 29.2600i −1.21811 1.21811i −0.968294 0.249815i \(-0.919630\pi\)
−0.249815 0.968294i \(-0.580370\pi\)
\(578\) 0 0
\(579\) 70.2405i 2.91909i
\(580\) 0 0
\(581\) −0.250752 0.250752i −0.0104030 0.0104030i
\(582\) 0 0
\(583\) 0.132257i 0.00547752i
\(584\) 0 0
\(585\) −21.1305 21.1305i −0.873640 0.873640i
\(586\) 0 0
\(587\) 18.1193 + 18.1193i 0.747863 + 0.747863i 0.974078 0.226214i \(-0.0726350\pi\)
−0.226214 + 0.974078i \(0.572635\pi\)
\(588\) 0 0
\(589\) −27.4995 + 27.4995i −1.13310 + 1.13310i
\(590\) 0 0
\(591\) −37.1611 + 37.1611i −1.52860 + 1.52860i
\(592\) 0 0
\(593\) 6.80967 6.80967i 0.279640 0.279640i −0.553325 0.832965i \(-0.686641\pi\)
0.832965 + 0.553325i \(0.186641\pi\)
\(594\) 0 0
\(595\) 5.89056i 0.241489i
\(596\) 0 0
\(597\) 45.4444 1.85992
\(598\) 0 0
\(599\) −35.5213 −1.45136 −0.725680 0.688032i \(-0.758475\pi\)
−0.725680 + 0.688032i \(0.758475\pi\)
\(600\) 0 0
\(601\) −17.3178 + 17.3178i −0.706408 + 0.706408i −0.965778 0.259370i \(-0.916485\pi\)
0.259370 + 0.965778i \(0.416485\pi\)
\(602\) 0 0
\(603\) −30.0744 30.0744i −1.22473 1.22473i
\(604\) 0 0
\(605\) −15.3291 −0.623217
\(606\) 0 0
\(607\) 1.58614i 0.0643795i 0.999482 + 0.0321897i \(0.0102481\pi\)
−0.999482 + 0.0321897i \(0.989752\pi\)
\(608\) 0 0
\(609\) −16.1986 + 16.1986i −0.656400 + 0.656400i
\(610\) 0 0
\(611\) −23.3842 −0.946024
\(612\) 0 0
\(613\) 5.57022i 0.224979i −0.993653 0.112489i \(-0.964118\pi\)
0.993653 0.112489i \(-0.0358825\pi\)
\(614\) 0 0
\(615\) 23.0231 + 6.52116i 0.928379 + 0.262959i
\(616\) 0 0
\(617\) 17.3638i 0.699039i −0.936929 0.349520i \(-0.886345\pi\)
0.936929 0.349520i \(-0.113655\pi\)
\(618\) 0 0
\(619\) 8.25046 0.331614 0.165807 0.986158i \(-0.446977\pi\)
0.165807 + 0.986158i \(0.446977\pi\)
\(620\) 0 0
\(621\) −14.5236 + 14.5236i −0.582813 + 0.582813i
\(622\) 0 0
\(623\) 3.76680i 0.150914i
\(624\) 0 0
\(625\) −0.358948 −0.0143579
\(626\) 0 0
\(627\) 0.0775749 + 0.0775749i 0.00309804 + 0.00309804i
\(628\) 0 0
\(629\) 8.74336 8.74336i 0.348620 0.348620i
\(630\) 0 0
\(631\) −8.58953 −0.341944 −0.170972 0.985276i \(-0.554691\pi\)
−0.170972 + 0.985276i \(0.554691\pi\)
\(632\) 0 0
\(633\) 40.6148 1.61429
\(634\) 0 0
\(635\) 23.9079i 0.948757i
\(636\) 0 0
\(637\) 3.61779 3.61779i 0.143342 0.143342i
\(638\) 0 0
\(639\) 0.299926 0.299926i 0.0118649 0.0118649i
\(640\) 0 0
\(641\) 12.8597 12.8597i 0.507928 0.507928i −0.405962 0.913890i \(-0.633063\pi\)
0.913890 + 0.405962i \(0.133063\pi\)
\(642\) 0 0
\(643\) 11.1854 + 11.1854i 0.441109 + 0.441109i 0.892385 0.451276i \(-0.149031\pi\)
−0.451276 + 0.892385i \(0.649031\pi\)
\(644\) 0 0
\(645\) 19.3176 + 19.3176i 0.760631 + 0.760631i
\(646\) 0 0
\(647\) 16.0824i 0.632262i −0.948715 0.316131i \(-0.897616\pi\)
0.948715 0.316131i \(-0.102384\pi\)
\(648\) 0 0
\(649\) −0.0561586 0.0561586i −0.00220442 0.00220442i
\(650\) 0 0
\(651\) 24.3166i 0.953043i
\(652\) 0 0
\(653\) 30.4749 + 30.4749i 1.19257 + 1.19257i 0.976342 + 0.216232i \(0.0693767\pi\)
0.216232 + 0.976342i \(0.430623\pi\)
\(654\) 0 0
\(655\) −25.4269 −0.993513
\(656\) 0 0
\(657\) −63.4657 −2.47603
\(658\) 0 0
\(659\) 28.5379 + 28.5379i 1.11168 + 1.11168i 0.992923 + 0.118757i \(0.0378910\pi\)
0.118757 + 0.992923i \(0.462109\pi\)
\(660\) 0 0
\(661\) 37.6558i 1.46464i 0.680960 + 0.732321i \(0.261563\pi\)
−0.680960 + 0.732321i \(0.738437\pi\)
\(662\) 0 0
\(663\) −41.0084 41.0084i −1.59264 1.59264i
\(664\) 0 0
\(665\) 5.97676i 0.231769i
\(666\) 0 0
\(667\) −38.8399 38.8399i −1.50389 1.50389i
\(668\) 0 0
\(669\) −2.15030 2.15030i −0.0831353 0.0831353i
\(670\) 0 0
\(671\) 0.0821343 0.0821343i 0.00317076 0.00317076i
\(672\) 0 0
\(673\) 11.5798 11.5798i 0.446367 0.446367i −0.447778 0.894145i \(-0.647784\pi\)
0.894145 + 0.447778i \(0.147784\pi\)
\(674\) 0 0
\(675\) 6.90729 6.90729i 0.265862 0.265862i
\(676\) 0 0
\(677\) 28.7742i 1.10588i −0.833220 0.552941i \(-0.813506\pi\)
0.833220 0.552941i \(-0.186494\pi\)
\(678\) 0 0
\(679\) −4.83622 −0.185597
\(680\) 0 0
\(681\) −1.21676 −0.0466264
\(682\) 0 0
\(683\) 13.3405 13.3405i 0.510461 0.510461i −0.404207 0.914668i \(-0.632452\pi\)
0.914668 + 0.404207i \(0.132452\pi\)
\(684\) 0 0
\(685\) 5.15901 + 5.15901i 0.197116 + 0.197116i
\(686\) 0 0
\(687\) 4.39224 0.167574
\(688\) 0 0
\(689\) 70.9381i 2.70253i
\(690\) 0 0
\(691\) −10.8623 + 10.8623i −0.413223 + 0.413223i −0.882860 0.469637i \(-0.844385\pi\)
0.469637 + 0.882860i \(0.344385\pi\)
\(692\) 0 0
\(693\) −0.0399794 −0.00151869
\(694\) 0 0
\(695\) 0.742150i 0.0281514i
\(696\) 0 0
\(697\) 26.0413 + 7.37607i 0.986385 + 0.279388i
\(698\) 0 0
\(699\) 27.5412i 1.04170i
\(700\) 0 0
\(701\) 38.5490 1.45597 0.727987 0.685590i \(-0.240456\pi\)
0.727987 + 0.685590i \(0.240456\pi\)
\(702\) 0 0
\(703\) −8.87130 + 8.87130i −0.334588 + 0.334588i
\(704\) 0 0
\(705\) 17.0802i 0.643277i
\(706\) 0 0
\(707\) 15.3995 0.579158
\(708\) 0 0
\(709\) −5.66884 5.66884i −0.212898 0.212898i 0.592599 0.805497i \(-0.298102\pi\)
−0.805497 + 0.592599i \(0.798102\pi\)
\(710\) 0 0
\(711\) −29.8201 + 29.8201i −1.11834 + 1.11834i
\(712\) 0 0
\(713\) 58.3047 2.18353
\(714\) 0 0
\(715\) 0.0680117 0.00254349
\(716\) 0 0
\(717\) 51.0875i 1.90790i
\(718\) 0 0
\(719\) −4.13342 + 4.13342i −0.154151 + 0.154151i −0.779969 0.625818i \(-0.784765\pi\)
0.625818 + 0.779969i \(0.284765\pi\)
\(720\) 0 0
\(721\) −9.01439 + 9.01439i −0.335714 + 0.335714i
\(722\) 0 0
\(723\) −50.7561 + 50.7561i −1.88764 + 1.88764i
\(724\) 0 0
\(725\) 18.4718 + 18.4718i 0.686027 + 0.686027i
\(726\) 0 0
\(727\) −22.2792 22.2792i −0.826290 0.826290i 0.160711 0.987001i \(-0.448621\pi\)
−0.987001 + 0.160711i \(0.948621\pi\)
\(728\) 0 0
\(729\) 42.4945i 1.57387i
\(730\) 0 0
\(731\) 21.8501 + 21.8501i 0.808156 + 0.808156i
\(732\) 0 0
\(733\) 2.65116i 0.0979227i 0.998801 + 0.0489613i \(0.0155911\pi\)
−0.998801 + 0.0489613i \(0.984409\pi\)
\(734\) 0 0
\(735\) −2.64249 2.64249i −0.0974698 0.0974698i
\(736\) 0 0
\(737\) 0.0967989 0.00356563
\(738\) 0 0
\(739\) −21.0698 −0.775063 −0.387532 0.921856i \(-0.626672\pi\)
−0.387532 + 0.921856i \(0.626672\pi\)
\(740\) 0 0
\(741\) 41.6085 + 41.6085i 1.52853 + 1.52853i
\(742\) 0 0
\(743\) 3.45220i 0.126649i −0.997993 0.0633244i \(-0.979830\pi\)
0.997993 0.0633244i \(-0.0201703\pi\)
\(744\) 0 0
\(745\) −18.5791 18.5791i −0.680686 0.680686i
\(746\) 0 0
\(747\) 1.48628i 0.0543800i
\(748\) 0 0
\(749\) 8.42521 + 8.42521i 0.307851 + 0.307851i
\(750\) 0 0
\(751\) −7.25122 7.25122i −0.264601 0.264601i 0.562319 0.826920i \(-0.309909\pi\)
−0.826920 + 0.562319i \(0.809909\pi\)
\(752\) 0 0
\(753\) −8.33206 + 8.33206i −0.303637 + 0.303637i
\(754\) 0 0
\(755\) 1.74494 1.74494i 0.0635048 0.0635048i
\(756\) 0 0
\(757\) 30.8552 30.8552i 1.12145 1.12145i 0.129930 0.991523i \(-0.458525\pi\)
0.991523 0.129930i \(-0.0414752\pi\)
\(758\) 0 0
\(759\) 0.164475i 0.00597006i
\(760\) 0 0
\(761\) 37.6284 1.36403 0.682015 0.731338i \(-0.261104\pi\)
0.682015 + 0.731338i \(0.261104\pi\)
\(762\) 0 0
\(763\) 9.58381 0.346957
\(764\) 0 0
\(765\) −17.4574 + 17.4574i −0.631175 + 0.631175i
\(766\) 0 0
\(767\) −30.1216 30.1216i −1.08763 1.08763i
\(768\) 0 0
\(769\) −41.8990 −1.51092 −0.755459 0.655196i \(-0.772586\pi\)
−0.755459 + 0.655196i \(0.772586\pi\)
\(770\) 0 0
\(771\) 42.0852i 1.51566i
\(772\) 0 0
\(773\) 35.1673 35.1673i 1.26488 1.26488i 0.316180 0.948699i \(-0.397600\pi\)
0.948699 0.316180i \(-0.102400\pi\)
\(774\) 0 0
\(775\) −27.7291 −0.996059
\(776\) 0 0
\(777\) 7.84450i 0.281420i
\(778\) 0 0
\(779\) −26.4224 7.48400i −0.946681 0.268142i
\(780\) 0 0
\(781\) 0 0.000965356i 0 3.45432e-5i
\(782\) 0 0
\(783\) 27.2885 0.975213
\(784\) 0 0
\(785\) −2.69144 + 2.69144i −0.0960615 + 0.0960615i
\(786\) 0 0
\(787\) 37.5717i 1.33929i 0.742683 + 0.669643i \(0.233553\pi\)
−0.742683 + 0.669643i \(0.766447\pi\)
\(788\) 0 0
\(789\) 25.0514 0.891852
\(790\) 0 0
\(791\) 5.38459 + 5.38459i 0.191454 + 0.191454i
\(792\) 0 0
\(793\) 44.0540 44.0540i 1.56440 1.56440i
\(794\) 0 0
\(795\) −51.8143 −1.83767
\(796\) 0 0
\(797\) 28.9887 1.02683 0.513417 0.858139i \(-0.328380\pi\)
0.513417 + 0.858139i \(0.328380\pi\)
\(798\) 0 0
\(799\) 19.3194i 0.683470i
\(800\) 0 0