Properties

Label 1148.2.k.b.337.7
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 337.7
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.b.729.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.796852 - 0.796852i) q^{3} -1.53973i q^{5} +(0.707107 + 0.707107i) q^{7} -1.73005i q^{9} +O(q^{10})\) \(q+(-0.796852 - 0.796852i) q^{3} -1.53973i q^{5} +(0.707107 + 0.707107i) q^{7} -1.73005i q^{9} +(2.10815 + 2.10815i) q^{11} +(3.47617 + 3.47617i) q^{13} +(-1.22694 + 1.22694i) q^{15} +(1.03340 - 1.03340i) q^{17} +(2.78503 - 2.78503i) q^{19} -1.12692i q^{21} -4.78666 q^{23} +2.62923 q^{25} +(-3.76915 + 3.76915i) q^{27} +(1.87396 + 1.87396i) q^{29} +1.64355 q^{31} -3.35977i q^{33} +(1.08875 - 1.08875i) q^{35} +7.76973 q^{37} -5.53999i q^{39} +(-5.27426 - 3.63073i) q^{41} -7.65515i q^{43} -2.66381 q^{45} +(6.34706 - 6.34706i) q^{47} +1.00000i q^{49} -1.64693 q^{51} +(-3.97278 - 3.97278i) q^{53} +(3.24598 - 3.24598i) q^{55} -4.43852 q^{57} -4.91766 q^{59} -14.5639i q^{61} +(1.22333 - 1.22333i) q^{63} +(5.35237 - 5.35237i) q^{65} +(-11.3876 + 11.3876i) q^{67} +(3.81426 + 3.81426i) q^{69} +(6.65860 + 6.65860i) q^{71} -12.2332i q^{73} +(-2.09511 - 2.09511i) q^{75} +2.98137i q^{77} +(2.18320 + 2.18320i) q^{79} +0.816762 q^{81} +10.0315 q^{83} +(-1.59115 - 1.59115i) q^{85} -2.98653i q^{87} +(11.2796 + 11.2796i) q^{89} +4.91605i q^{91} +(-1.30967 - 1.30967i) q^{93} +(-4.28820 - 4.28820i) q^{95} +(12.3703 - 12.3703i) q^{97} +(3.64721 - 3.64721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

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
\(3\) −0.796852 0.796852i −0.460063 0.460063i 0.438613 0.898676i \(-0.355470\pi\)
−0.898676 + 0.438613i \(0.855470\pi\)
\(4\) 0 0
\(5\) 1.53973i 0.688588i −0.938862 0.344294i \(-0.888118\pi\)
0.938862 0.344294i \(-0.111882\pi\)
\(6\) 0 0
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) 0 0
\(9\) 1.73005i 0.576684i
\(10\) 0 0
\(11\) 2.10815 + 2.10815i 0.635630 + 0.635630i 0.949475 0.313844i \(-0.101617\pi\)
−0.313844 + 0.949475i \(0.601617\pi\)
\(12\) 0 0
\(13\) 3.47617 + 3.47617i 0.964117 + 0.964117i 0.999378 0.0352612i \(-0.0112263\pi\)
−0.0352612 + 0.999378i \(0.511226\pi\)
\(14\) 0 0
\(15\) −1.22694 + 1.22694i −0.316794 + 0.316794i
\(16\) 0 0
\(17\) 1.03340 1.03340i 0.250635 0.250635i −0.570596 0.821231i \(-0.693288\pi\)
0.821231 + 0.570596i \(0.193288\pi\)
\(18\) 0 0
\(19\) 2.78503 2.78503i 0.638930 0.638930i −0.311361 0.950292i \(-0.600785\pi\)
0.950292 + 0.311361i \(0.100785\pi\)
\(20\) 0 0
\(21\) 1.12692i 0.245914i
\(22\) 0 0
\(23\) −4.78666 −0.998087 −0.499043 0.866577i \(-0.666315\pi\)
−0.499043 + 0.866577i \(0.666315\pi\)
\(24\) 0 0
\(25\) 2.62923 0.525846
\(26\) 0 0
\(27\) −3.76915 + 3.76915i −0.725374 + 0.725374i
\(28\) 0 0
\(29\) 1.87396 + 1.87396i 0.347985 + 0.347985i 0.859358 0.511374i \(-0.170863\pi\)
−0.511374 + 0.859358i \(0.670863\pi\)
\(30\) 0 0
\(31\) 1.64355 0.295190 0.147595 0.989048i \(-0.452847\pi\)
0.147595 + 0.989048i \(0.452847\pi\)
\(32\) 0 0
\(33\) 3.35977i 0.584860i
\(34\) 0 0
\(35\) 1.08875 1.08875i 0.184033 0.184033i
\(36\) 0 0
\(37\) 7.76973 1.27734 0.638668 0.769483i \(-0.279486\pi\)
0.638668 + 0.769483i \(0.279486\pi\)
\(38\) 0 0
\(39\) 5.53999i 0.887109i
\(40\) 0 0
\(41\) −5.27426 3.63073i −0.823701 0.567025i
\(42\) 0 0
\(43\) 7.65515i 1.16740i −0.811970 0.583700i \(-0.801604\pi\)
0.811970 0.583700i \(-0.198396\pi\)
\(44\) 0 0
\(45\) −2.66381 −0.397098
\(46\) 0 0
\(47\) 6.34706 6.34706i 0.925813 0.925813i −0.0716188 0.997432i \(-0.522817\pi\)
0.997432 + 0.0716188i \(0.0228165\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −1.64693 −0.230616
\(52\) 0 0
\(53\) −3.97278 3.97278i −0.545704 0.545704i 0.379492 0.925195i \(-0.376099\pi\)
−0.925195 + 0.379492i \(0.876099\pi\)
\(54\) 0 0
\(55\) 3.24598 3.24598i 0.437688 0.437688i
\(56\) 0 0
\(57\) −4.43852 −0.587896
\(58\) 0 0
\(59\) −4.91766 −0.640225 −0.320113 0.947379i \(-0.603721\pi\)
−0.320113 + 0.947379i \(0.603721\pi\)
\(60\) 0 0
\(61\) 14.5639i 1.86472i −0.361529 0.932361i \(-0.617745\pi\)
0.361529 0.932361i \(-0.382255\pi\)
\(62\) 0 0
\(63\) 1.22333 1.22333i 0.154125 0.154125i
\(64\) 0 0
\(65\) 5.35237 5.35237i 0.663879 0.663879i
\(66\) 0 0
\(67\) −11.3876 + 11.3876i −1.39122 + 1.39122i −0.568621 + 0.822600i \(0.692523\pi\)
−0.822600 + 0.568621i \(0.807477\pi\)
\(68\) 0 0
\(69\) 3.81426 + 3.81426i 0.459183 + 0.459183i
\(70\) 0 0
\(71\) 6.65860 + 6.65860i 0.790231 + 0.790231i 0.981531 0.191301i \(-0.0612706\pi\)
−0.191301 + 0.981531i \(0.561271\pi\)
\(72\) 0 0
\(73\) 12.2332i 1.43178i −0.698212 0.715891i \(-0.746021\pi\)
0.698212 0.715891i \(-0.253979\pi\)
\(74\) 0 0
\(75\) −2.09511 2.09511i −0.241922 0.241922i
\(76\) 0 0
\(77\) 2.98137i 0.339759i
\(78\) 0 0
\(79\) 2.18320 + 2.18320i 0.245629 + 0.245629i 0.819174 0.573545i \(-0.194432\pi\)
−0.573545 + 0.819174i \(0.694432\pi\)
\(80\) 0 0
\(81\) 0.816762 0.0907513
\(82\) 0 0
\(83\) 10.0315 1.10110 0.550551 0.834801i \(-0.314418\pi\)
0.550551 + 0.834801i \(0.314418\pi\)
\(84\) 0 0
\(85\) −1.59115 1.59115i −0.172585 0.172585i
\(86\) 0 0
\(87\) 2.98653i 0.320190i
\(88\) 0 0
\(89\) 11.2796 + 11.2796i 1.19564 + 1.19564i 0.975460 + 0.220178i \(0.0706638\pi\)
0.220178 + 0.975460i \(0.429336\pi\)
\(90\) 0 0
\(91\) 4.91605i 0.515342i
\(92\) 0 0
\(93\) −1.30967 1.30967i −0.135806 0.135806i
\(94\) 0 0
\(95\) −4.28820 4.28820i −0.439960 0.439960i
\(96\) 0 0
\(97\) 12.3703 12.3703i 1.25601 1.25601i 0.303031 0.952981i \(-0.402001\pi\)
0.952981 0.303031i \(-0.0979987\pi\)
\(98\) 0 0
\(99\) 3.64721 3.64721i 0.366558 0.366558i
\(100\) 0 0
\(101\) 2.57688 2.57688i 0.256409 0.256409i −0.567183 0.823592i \(-0.691967\pi\)
0.823592 + 0.567183i \(0.191967\pi\)
\(102\) 0 0
\(103\) 16.2949i 1.60558i 0.596259 + 0.802792i \(0.296653\pi\)
−0.596259 + 0.802792i \(0.703347\pi\)
\(104\) 0 0
\(105\) −1.73515 −0.169333
\(106\) 0 0
\(107\) −12.2066 −1.18005 −0.590027 0.807383i \(-0.700883\pi\)
−0.590027 + 0.807383i \(0.700883\pi\)
\(108\) 0 0
\(109\) 9.78183 9.78183i 0.936930 0.936930i −0.0611962 0.998126i \(-0.519492\pi\)
0.998126 + 0.0611962i \(0.0194915\pi\)
\(110\) 0 0
\(111\) −6.19133 6.19133i −0.587655 0.587655i
\(112\) 0 0
\(113\) −17.7307 −1.66796 −0.833982 0.551791i \(-0.813945\pi\)
−0.833982 + 0.551791i \(0.813945\pi\)
\(114\) 0 0
\(115\) 7.37016i 0.687271i
\(116\) 0 0
\(117\) 6.01396 6.01396i 0.555991 0.555991i
\(118\) 0 0
\(119\) 1.46144 0.133970
\(120\) 0 0
\(121\) 2.11143i 0.191948i
\(122\) 0 0
\(123\) 1.30965 + 7.09596i 0.118087 + 0.639821i
\(124\) 0 0
\(125\) 11.7470i 1.05068i
\(126\) 0 0
\(127\) −13.5312 −1.20070 −0.600349 0.799738i \(-0.704972\pi\)
−0.600349 + 0.799738i \(0.704972\pi\)
\(128\) 0 0
\(129\) −6.10003 + 6.10003i −0.537077 + 0.537077i
\(130\) 0 0
\(131\) 10.5159i 0.918783i −0.888234 0.459391i \(-0.848068\pi\)
0.888234 0.459391i \(-0.151932\pi\)
\(132\) 0 0
\(133\) 3.93863 0.341523
\(134\) 0 0
\(135\) 5.80348 + 5.80348i 0.499484 + 0.499484i
\(136\) 0 0
\(137\) −13.2794 + 13.2794i −1.13454 + 1.13454i −0.145126 + 0.989413i \(0.546359\pi\)
−0.989413 + 0.145126i \(0.953641\pi\)
\(138\) 0 0
\(139\) 13.0822 1.10962 0.554811 0.831977i \(-0.312791\pi\)
0.554811 + 0.831977i \(0.312791\pi\)
\(140\) 0 0
\(141\) −10.1153 −0.851865
\(142\) 0 0
\(143\) 14.6566i 1.22564i
\(144\) 0 0
\(145\) 2.88538 2.88538i 0.239618 0.239618i
\(146\) 0 0
\(147\) 0.796852 0.796852i 0.0657233 0.0657233i
\(148\) 0 0
\(149\) 0.00680408 0.00680408i 0.000557412 0.000557412i −0.706828 0.707385i \(-0.749875\pi\)
0.707385 + 0.706828i \(0.249875\pi\)
\(150\) 0 0
\(151\) 5.60095 + 5.60095i 0.455799 + 0.455799i 0.897274 0.441475i \(-0.145544\pi\)
−0.441475 + 0.897274i \(0.645544\pi\)
\(152\) 0 0
\(153\) −1.78783 1.78783i −0.144537 0.144537i
\(154\) 0 0
\(155\) 2.53062i 0.203265i
\(156\) 0 0
\(157\) −3.88536 3.88536i −0.310085 0.310085i 0.534857 0.844942i \(-0.320365\pi\)
−0.844942 + 0.534857i \(0.820365\pi\)
\(158\) 0 0
\(159\) 6.33144i 0.502116i
\(160\) 0 0
\(161\) −3.38468 3.38468i −0.266750 0.266750i
\(162\) 0 0
\(163\) 12.6693 0.992338 0.496169 0.868226i \(-0.334740\pi\)
0.496169 + 0.868226i \(0.334740\pi\)
\(164\) 0 0
\(165\) −5.17313 −0.402728
\(166\) 0 0
\(167\) 15.0232 + 15.0232i 1.16253 + 1.16253i 0.983920 + 0.178611i \(0.0571603\pi\)
0.178611 + 0.983920i \(0.442840\pi\)
\(168\) 0 0
\(169\) 11.1676i 0.859043i
\(170\) 0 0
\(171\) −4.81825 4.81825i −0.368461 0.368461i
\(172\) 0 0
\(173\) 11.8997i 0.904715i −0.891837 0.452357i \(-0.850583\pi\)
0.891837 0.452357i \(-0.149417\pi\)
\(174\) 0 0
\(175\) 1.85915 + 1.85915i 0.140538 + 0.140538i
\(176\) 0 0
\(177\) 3.91865 + 3.91865i 0.294544 + 0.294544i
\(178\) 0 0
\(179\) −1.37511 + 1.37511i −0.102781 + 0.102781i −0.756627 0.653846i \(-0.773154\pi\)
0.653846 + 0.756627i \(0.273154\pi\)
\(180\) 0 0
\(181\) −2.45197 + 2.45197i −0.182254 + 0.182254i −0.792337 0.610083i \(-0.791136\pi\)
0.610083 + 0.792337i \(0.291136\pi\)
\(182\) 0 0
\(183\) −11.6053 + 11.6053i −0.857889 + 0.857889i
\(184\) 0 0
\(185\) 11.9633i 0.879558i
\(186\) 0 0
\(187\) 4.35710 0.318623
\(188\) 0 0
\(189\) −5.33039 −0.387729
\(190\) 0 0
\(191\) 2.90384 2.90384i 0.210114 0.210114i −0.594202 0.804316i \(-0.702532\pi\)
0.804316 + 0.594202i \(0.202532\pi\)
\(192\) 0 0
\(193\) 15.8483 + 15.8483i 1.14079 + 1.14079i 0.988306 + 0.152482i \(0.0487267\pi\)
0.152482 + 0.988306i \(0.451273\pi\)
\(194\) 0 0
\(195\) −8.53009 −0.610853
\(196\) 0 0
\(197\) 22.1165i 1.57574i 0.615842 + 0.787869i \(0.288816\pi\)
−0.615842 + 0.787869i \(0.711184\pi\)
\(198\) 0 0
\(199\) −19.5789 + 19.5789i −1.38791 + 1.38791i −0.558207 + 0.829702i \(0.688510\pi\)
−0.829702 + 0.558207i \(0.811490\pi\)
\(200\) 0 0
\(201\) 18.1485 1.28010
\(202\) 0 0
\(203\) 2.65017i 0.186006i
\(204\) 0 0
\(205\) −5.59035 + 8.12093i −0.390447 + 0.567190i
\(206\) 0 0
\(207\) 8.28117i 0.575581i
\(208\) 0 0
\(209\) 11.7425 0.812247
\(210\) 0 0
\(211\) 2.45388 2.45388i 0.168932 0.168932i −0.617578 0.786510i \(-0.711886\pi\)
0.786510 + 0.617578i \(0.211886\pi\)
\(212\) 0 0
\(213\) 10.6118i 0.727112i
\(214\) 0 0
\(215\) −11.7869 −0.803857
\(216\) 0 0
\(217\) 1.16217 + 1.16217i 0.0788930 + 0.0788930i
\(218\) 0 0
\(219\) −9.74802 + 9.74802i −0.658710 + 0.658710i
\(220\) 0 0
\(221\) 7.18453 0.483284
\(222\) 0 0
\(223\) −21.3444 −1.42933 −0.714664 0.699468i \(-0.753420\pi\)
−0.714664 + 0.699468i \(0.753420\pi\)
\(224\) 0 0
\(225\) 4.54871i 0.303247i
\(226\) 0 0
\(227\) −15.4739 + 15.4739i −1.02704 + 1.02704i −0.0274179 + 0.999624i \(0.508728\pi\)
−0.999624 + 0.0274179i \(0.991272\pi\)
\(228\) 0 0
\(229\) −8.90215 + 8.90215i −0.588271 + 0.588271i −0.937163 0.348892i \(-0.886558\pi\)
0.348892 + 0.937163i \(0.386558\pi\)
\(230\) 0 0
\(231\) 2.37571 2.37571i 0.156310 0.156310i
\(232\) 0 0
\(233\) −11.4969 11.4969i −0.753187 0.753187i 0.221886 0.975073i \(-0.428779\pi\)
−0.975073 + 0.221886i \(0.928779\pi\)
\(234\) 0 0
\(235\) −9.77275 9.77275i −0.637504 0.637504i
\(236\) 0 0
\(237\) 3.47937i 0.226010i
\(238\) 0 0
\(239\) −12.4710 12.4710i −0.806683 0.806683i 0.177447 0.984130i \(-0.443216\pi\)
−0.984130 + 0.177447i \(0.943216\pi\)
\(240\) 0 0
\(241\) 20.6633i 1.33104i 0.746380 + 0.665519i \(0.231790\pi\)
−0.746380 + 0.665519i \(0.768210\pi\)
\(242\) 0 0
\(243\) 10.6566 + 10.6566i 0.683623 + 0.683623i
\(244\) 0 0
\(245\) 1.53973 0.0983697
\(246\) 0 0
\(247\) 19.3625 1.23201
\(248\) 0 0
\(249\) −7.99364 7.99364i −0.506576 0.506576i
\(250\) 0 0
\(251\) 5.19670i 0.328013i −0.986459 0.164006i \(-0.947558\pi\)
0.986459 0.164006i \(-0.0524417\pi\)
\(252\) 0 0
\(253\) −10.0910 10.0910i −0.634414 0.634414i
\(254\) 0 0
\(255\) 2.53582i 0.158800i
\(256\) 0 0
\(257\) 9.69943 + 9.69943i 0.605034 + 0.605034i 0.941644 0.336610i \(-0.109280\pi\)
−0.336610 + 0.941644i \(0.609280\pi\)
\(258\) 0 0
\(259\) 5.49403 + 5.49403i 0.341382 + 0.341382i
\(260\) 0 0
\(261\) 3.24204 3.24204i 0.200677 0.200677i
\(262\) 0 0
\(263\) −12.8975 + 12.8975i −0.795291 + 0.795291i −0.982349 0.187058i \(-0.940105\pi\)
0.187058 + 0.982349i \(0.440105\pi\)
\(264\) 0 0
\(265\) −6.11701 + 6.11701i −0.375765 + 0.375765i
\(266\) 0 0
\(267\) 17.9764i 1.10014i
\(268\) 0 0
\(269\) −21.5268 −1.31252 −0.656258 0.754537i \(-0.727862\pi\)
−0.656258 + 0.754537i \(0.727862\pi\)
\(270\) 0 0
\(271\) 10.0928 0.613094 0.306547 0.951856i \(-0.400826\pi\)
0.306547 + 0.951856i \(0.400826\pi\)
\(272\) 0 0
\(273\) 3.91737 3.91737i 0.237090 0.237090i
\(274\) 0 0
\(275\) 5.54281 + 5.54281i 0.334244 + 0.334244i
\(276\) 0 0
\(277\) 19.5376 1.17390 0.586951 0.809623i \(-0.300328\pi\)
0.586951 + 0.809623i \(0.300328\pi\)
\(278\) 0 0
\(279\) 2.84343i 0.170232i
\(280\) 0 0
\(281\) −14.3739 + 14.3739i −0.857473 + 0.857473i −0.991040 0.133567i \(-0.957357\pi\)
0.133567 + 0.991040i \(0.457357\pi\)
\(282\) 0 0
\(283\) 10.7230 0.637415 0.318707 0.947853i \(-0.396751\pi\)
0.318707 + 0.947853i \(0.396751\pi\)
\(284\) 0 0
\(285\) 6.83412i 0.404818i
\(286\) 0 0
\(287\) −1.16215 6.29678i −0.0685994 0.371687i
\(288\) 0 0
\(289\) 14.8642i 0.874364i
\(290\) 0 0
\(291\) −19.7146 −1.15569
\(292\) 0 0
\(293\) 8.30625 8.30625i 0.485256 0.485256i −0.421549 0.906805i \(-0.638514\pi\)
0.906805 + 0.421549i \(0.138514\pi\)
\(294\) 0 0
\(295\) 7.57187i 0.440851i
\(296\) 0 0
\(297\) −15.8919 −0.922140
\(298\) 0 0
\(299\) −16.6392 16.6392i −0.962272 0.962272i
\(300\) 0 0
\(301\) 5.41301 5.41301i 0.312001 0.312001i
\(302\) 0 0
\(303\) −4.10678 −0.235929
\(304\) 0 0
\(305\) −22.4245 −1.28403
\(306\) 0 0
\(307\) 0.278293i 0.0158830i −0.999968 0.00794151i \(-0.997472\pi\)
0.999968 0.00794151i \(-0.00252789\pi\)
\(308\) 0 0
\(309\) 12.9846 12.9846i 0.738670 0.738670i
\(310\) 0 0
\(311\) 19.3892 19.3892i 1.09946 1.09946i 0.104989 0.994473i \(-0.466519\pi\)
0.994473 0.104989i \(-0.0334807\pi\)
\(312\) 0 0
\(313\) 13.2824 13.2824i 0.750767 0.750767i −0.223855 0.974622i \(-0.571864\pi\)
0.974622 + 0.223855i \(0.0718644\pi\)
\(314\) 0 0
\(315\) −1.88360 1.88360i −0.106129 0.106129i
\(316\) 0 0
\(317\) 1.98498 + 1.98498i 0.111487 + 0.111487i 0.760650 0.649162i \(-0.224880\pi\)
−0.649162 + 0.760650i \(0.724880\pi\)
\(318\) 0 0
\(319\) 7.90115i 0.442379i
\(320\) 0 0
\(321\) 9.72684 + 9.72684i 0.542900 + 0.542900i
\(322\) 0 0
\(323\) 5.75608i 0.320277i
\(324\) 0 0
\(325\) 9.13967 + 9.13967i 0.506977 + 0.506977i
\(326\) 0 0
\(327\) −15.5894 −0.862093
\(328\) 0 0
\(329\) 8.97609 0.494868
\(330\) 0 0
\(331\) −6.37823 6.37823i −0.350579 0.350579i 0.509746 0.860325i \(-0.329739\pi\)
−0.860325 + 0.509746i \(0.829739\pi\)
\(332\) 0 0
\(333\) 13.4420i 0.736619i
\(334\) 0 0
\(335\) 17.5339 + 17.5339i 0.957978 + 0.957978i
\(336\) 0 0
\(337\) 29.4522i 1.60437i 0.597079 + 0.802183i \(0.296328\pi\)
−0.597079 + 0.802183i \(0.703672\pi\)
\(338\) 0 0
\(339\) 14.1288 + 14.1288i 0.767369 + 0.767369i
\(340\) 0 0
\(341\) 3.46485 + 3.46485i 0.187632 + 0.187632i
\(342\) 0 0
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 0 0
\(345\) 5.87293 5.87293i 0.316188 0.316188i
\(346\) 0 0
\(347\) −11.1930 + 11.1930i −0.600871 + 0.600871i −0.940544 0.339673i \(-0.889684\pi\)
0.339673 + 0.940544i \(0.389684\pi\)
\(348\) 0 0
\(349\) 4.72869i 0.253121i −0.991959 0.126560i \(-0.959606\pi\)
0.991959 0.126560i \(-0.0403938\pi\)
\(350\) 0 0
\(351\) −26.2045 −1.39869
\(352\) 0 0
\(353\) 1.62589 0.0865376 0.0432688 0.999063i \(-0.486223\pi\)
0.0432688 + 0.999063i \(0.486223\pi\)
\(354\) 0 0
\(355\) 10.2524 10.2524i 0.544143 0.544143i
\(356\) 0 0
\(357\) −1.16455 1.16455i −0.0616348 0.0616348i
\(358\) 0 0
\(359\) 20.1493 1.06344 0.531720 0.846920i \(-0.321546\pi\)
0.531720 + 0.846920i \(0.321546\pi\)
\(360\) 0 0
\(361\) 3.48718i 0.183536i
\(362\) 0 0
\(363\) −1.68250 + 1.68250i −0.0883081 + 0.0883081i
\(364\) 0 0
\(365\) −18.8358 −0.985908
\(366\) 0 0
\(367\) 12.5103i 0.653031i 0.945192 + 0.326515i \(0.105874\pi\)
−0.945192 + 0.326515i \(0.894126\pi\)
\(368\) 0 0
\(369\) −6.28136 + 9.12474i −0.326994 + 0.475015i
\(370\) 0 0
\(371\) 5.61836i 0.291691i
\(372\) 0 0
\(373\) 15.4653 0.800762 0.400381 0.916349i \(-0.368878\pi\)
0.400381 + 0.916349i \(0.368878\pi\)
\(374\) 0 0
\(375\) −9.36059 + 9.36059i −0.483379 + 0.483379i
\(376\) 0 0
\(377\) 13.0284i 0.670996i
\(378\) 0 0
\(379\) −14.2443 −0.731683 −0.365841 0.930677i \(-0.619219\pi\)
−0.365841 + 0.930677i \(0.619219\pi\)
\(380\) 0 0
\(381\) 10.7824 + 10.7824i 0.552397 + 0.552397i
\(382\) 0 0
\(383\) 9.84275 9.84275i 0.502941 0.502941i −0.409409 0.912351i \(-0.634265\pi\)
0.912351 + 0.409409i \(0.134265\pi\)
\(384\) 0 0
\(385\) 4.59051 0.233954
\(386\) 0 0
\(387\) −13.2438 −0.673221
\(388\) 0 0
\(389\) 28.6675i 1.45350i −0.686903 0.726749i \(-0.741030\pi\)
0.686903 0.726749i \(-0.258970\pi\)
\(390\) 0 0
\(391\) −4.94651 + 4.94651i −0.250156 + 0.250156i
\(392\) 0 0
\(393\) −8.37966 + 8.37966i −0.422698 + 0.422698i
\(394\) 0 0
\(395\) 3.36153 3.36153i 0.169137 0.169137i
\(396\) 0 0
\(397\) 9.40102 + 9.40102i 0.471824 + 0.471824i 0.902504 0.430681i \(-0.141727\pi\)
−0.430681 + 0.902504i \(0.641727\pi\)
\(398\) 0 0
\(399\) −3.13851 3.13851i −0.157122 0.157122i
\(400\) 0 0
\(401\) 20.9770i 1.04754i 0.851859 + 0.523771i \(0.175475\pi\)
−0.851859 + 0.523771i \(0.824525\pi\)
\(402\) 0 0
\(403\) 5.71327 + 5.71327i 0.284598 + 0.284598i
\(404\) 0 0
\(405\) 1.25759i 0.0624903i
\(406\) 0 0
\(407\) 16.3797 + 16.3797i 0.811913 + 0.811913i
\(408\) 0 0
\(409\) −5.84520 −0.289027 −0.144513 0.989503i \(-0.546162\pi\)
−0.144513 + 0.989503i \(0.546162\pi\)
\(410\) 0 0
\(411\) 21.1635 1.04392
\(412\) 0 0
\(413\) −3.47731 3.47731i −0.171107 0.171107i
\(414\) 0 0
\(415\) 15.4458i 0.758206i
\(416\) 0 0
\(417\) −10.4246 10.4246i −0.510496 0.510496i
\(418\) 0 0
\(419\) 9.78788i 0.478169i −0.970999 0.239085i \(-0.923153\pi\)
0.970999 0.239085i \(-0.0768474\pi\)
\(420\) 0 0
\(421\) −12.5522 12.5522i −0.611755 0.611755i 0.331648 0.943403i \(-0.392395\pi\)
−0.943403 + 0.331648i \(0.892395\pi\)
\(422\) 0 0
\(423\) −10.9807 10.9807i −0.533902 0.533902i
\(424\) 0 0
\(425\) 2.71704 2.71704i 0.131796 0.131796i
\(426\) 0 0
\(427\) 10.2983 10.2983i 0.498368 0.498368i
\(428\) 0 0
\(429\) 11.6791 11.6791i 0.563873 0.563873i
\(430\) 0 0
\(431\) 32.8471i 1.58219i −0.611693 0.791095i \(-0.709511\pi\)
0.611693 0.791095i \(-0.290489\pi\)
\(432\) 0 0
\(433\) 1.16476 0.0559750 0.0279875 0.999608i \(-0.491090\pi\)
0.0279875 + 0.999608i \(0.491090\pi\)
\(434\) 0 0
\(435\) −4.59845 −0.220479
\(436\) 0 0
\(437\) −13.3310 + 13.3310i −0.637708 + 0.637708i
\(438\) 0 0
\(439\) −7.71968 7.71968i −0.368440 0.368440i 0.498468 0.866908i \(-0.333896\pi\)
−0.866908 + 0.498468i \(0.833896\pi\)
\(440\) 0 0
\(441\) 1.73005 0.0823834
\(442\) 0 0
\(443\) 4.62164i 0.219581i −0.993955 0.109790i \(-0.964982\pi\)
0.993955 0.109790i \(-0.0350179\pi\)
\(444\) 0 0
\(445\) 17.3676 17.3676i 0.823302 0.823302i
\(446\) 0 0
\(447\) −0.0108437 −0.000512889
\(448\) 0 0
\(449\) 15.7864i 0.745006i −0.928031 0.372503i \(-0.878500\pi\)
0.928031 0.372503i \(-0.121500\pi\)
\(450\) 0 0
\(451\) −3.46480 18.7730i −0.163151 0.883988i
\(452\) 0 0
\(453\) 8.92627i 0.419393i
\(454\) 0 0
\(455\) 7.56939 0.354858
\(456\) 0 0
\(457\) 7.44056 7.44056i 0.348055 0.348055i −0.511330 0.859385i \(-0.670847\pi\)
0.859385 + 0.511330i \(0.170847\pi\)
\(458\) 0 0
\(459\) 7.79006i 0.363609i
\(460\) 0 0
\(461\) −0.885724 −0.0412523 −0.0206261 0.999787i \(-0.506566\pi\)
−0.0206261 + 0.999787i \(0.506566\pi\)
\(462\) 0 0
\(463\) 1.58178 + 1.58178i 0.0735117 + 0.0735117i 0.742907 0.669395i \(-0.233447\pi\)
−0.669395 + 0.742907i \(0.733447\pi\)
\(464\) 0 0
\(465\) −2.01653 + 2.01653i −0.0935145 + 0.0935145i
\(466\) 0 0
\(467\) −5.75929 −0.266508 −0.133254 0.991082i \(-0.542543\pi\)
−0.133254 + 0.991082i \(0.542543\pi\)
\(468\) 0 0
\(469\) −16.1045 −0.743639
\(470\) 0 0
\(471\) 6.19211i 0.285317i
\(472\) 0 0
\(473\) 16.1382 16.1382i 0.742035 0.742035i
\(474\) 0 0
\(475\) 7.32250 7.32250i 0.335979 0.335979i
\(476\) 0 0
\(477\) −6.87312 + 6.87312i −0.314699 + 0.314699i
\(478\) 0 0
\(479\) −4.64839 4.64839i −0.212391 0.212391i 0.592892 0.805282i \(-0.297986\pi\)
−0.805282 + 0.592892i \(0.797986\pi\)
\(480\) 0 0
\(481\) 27.0089 + 27.0089i 1.23150 + 1.23150i
\(482\) 0 0
\(483\) 5.39418i 0.245444i
\(484\) 0 0
\(485\) −19.0469 19.0469i −0.864875 0.864875i
\(486\) 0 0
\(487\) 22.1042i 1.00164i 0.865552 + 0.500818i \(0.166968\pi\)
−0.865552 + 0.500818i \(0.833032\pi\)
\(488\) 0 0
\(489\) −10.0956 10.0956i −0.456538 0.456538i
\(490\) 0 0
\(491\) −28.6325 −1.29217 −0.646084 0.763266i \(-0.723595\pi\)
−0.646084 + 0.763266i \(0.723595\pi\)
\(492\) 0 0
\(493\) 3.87308 0.174435
\(494\) 0 0
\(495\) −5.61571 5.61571i −0.252407 0.252407i
\(496\) 0 0
\(497\) 9.41669i 0.422396i
\(498\) 0 0
\(499\) −3.11218 3.11218i −0.139320 0.139320i 0.634007 0.773327i \(-0.281409\pi\)
−0.773327 + 0.634007i \(0.781409\pi\)
\(500\) 0 0
\(501\) 23.9426i 1.06967i
\(502\) 0 0
\(503\) 2.93325 + 2.93325i 0.130787 + 0.130787i 0.769470 0.638683i \(-0.220520\pi\)
−0.638683 + 0.769470i \(0.720520\pi\)
\(504\) 0 0
\(505\) −3.96770 3.96770i −0.176560 0.176560i
\(506\) 0 0
\(507\) 8.89889 8.89889i 0.395214 0.395214i
\(508\) 0 0
\(509\) 13.8828 13.8828i 0.615344 0.615344i −0.328989 0.944334i \(-0.606708\pi\)
0.944334 + 0.328989i \(0.106708\pi\)
\(510\) 0 0
\(511\) 8.65015 8.65015i 0.382660 0.382660i
\(512\) 0 0
\(513\) 20.9944i 0.926927i
\(514\) 0 0
\(515\) 25.0897 1.10559
\(516\) 0 0
\(517\) 26.7611 1.17695
\(518\) 0 0
\(519\) −9.48228 + 9.48228i −0.416226 + 0.416226i
\(520\) 0 0
\(521\) 2.27330 + 2.27330i 0.0995951 + 0.0995951i 0.755149 0.655554i \(-0.227565\pi\)
−0.655554 + 0.755149i \(0.727565\pi\)
\(522\) 0 0
\(523\) −4.07618 −0.178239 −0.0891195 0.996021i \(-0.528405\pi\)
−0.0891195 + 0.996021i \(0.528405\pi\)
\(524\) 0 0
\(525\) 2.96293i 0.129313i
\(526\) 0 0
\(527\) 1.69844 1.69844i 0.0739852 0.0739852i
\(528\) 0 0
\(529\) −0.0879250 −0.00382283
\(530\) 0 0
\(531\) 8.50781i 0.369208i
\(532\) 0 0
\(533\) −5.71318 30.9553i −0.247465 1.34082i
\(534\) 0 0
\(535\) 18.7948i 0.812572i
\(536\) 0 0
\(537\) 2.19152 0.0945712
\(538\) 0 0
\(539\) −2.10815 + 2.10815i −0.0908043 + 0.0908043i
\(540\) 0 0
\(541\) 12.8281i 0.551523i −0.961226 0.275761i \(-0.911070\pi\)
0.961226 0.275761i \(-0.0889299\pi\)
\(542\) 0 0
\(543\) 3.90772 0.167696
\(544\) 0 0
\(545\) −15.0614 15.0614i −0.645159 0.645159i
\(546\) 0 0
\(547\) −30.3801 + 30.3801i −1.29896 + 1.29896i −0.369878 + 0.929080i \(0.620601\pi\)
−0.929080 + 0.369878i \(0.879399\pi\)
\(548\) 0 0
\(549\) −25.1964 −1.07536
\(550\) 0 0
\(551\) 10.4381 0.444676
\(552\) 0 0
\(553\) 3.08751i 0.131294i
\(554\) 0 0
\(555\) −9.53297 + 9.53297i −0.404652 + 0.404652i
\(556\) 0 0
\(557\) 26.7939 26.7939i 1.13530 1.13530i 0.146013 0.989283i \(-0.453356\pi\)
0.989283 0.146013i \(-0.0466440\pi\)
\(558\) 0 0
\(559\) 26.6106 26.6106i 1.12551 1.12551i
\(560\) 0 0
\(561\) −3.47197 3.47197i −0.146587 0.146587i
\(562\) 0 0
\(563\) −14.1972 14.1972i −0.598341 0.598341i 0.341530 0.939871i \(-0.389055\pi\)
−0.939871 + 0.341530i \(0.889055\pi\)
\(564\) 0 0
\(565\) 27.3005i 1.14854i
\(566\) 0 0
\(567\) 0.577538 + 0.577538i 0.0242543 + 0.0242543i
\(568\) 0 0
\(569\) 17.2476i 0.723059i 0.932361 + 0.361529i \(0.117745\pi\)
−0.932361 + 0.361529i \(0.882255\pi\)
\(570\) 0 0
\(571\) −11.2139 11.2139i −0.469286 0.469286i 0.432397 0.901683i \(-0.357668\pi\)
−0.901683 + 0.432397i \(0.857668\pi\)
\(572\) 0 0
\(573\) −4.62786 −0.193332
\(574\) 0 0
\(575\) −12.5852 −0.524840
\(576\) 0 0
\(577\) 1.19548 + 1.19548i 0.0497686 + 0.0497686i 0.731553 0.681785i \(-0.238796\pi\)
−0.681785 + 0.731553i \(0.738796\pi\)
\(578\) 0 0
\(579\) 25.2576i 1.04967i
\(580\) 0 0
\(581\) 7.09336 + 7.09336i 0.294282 + 0.294282i
\(582\) 0 0
\(583\) 16.7504i 0.693732i
\(584\) 0 0
\(585\) −9.25987 9.25987i −0.382849 0.382849i
\(586\) 0 0
\(587\) 27.6662 + 27.6662i 1.14191 + 1.14191i 0.988101 + 0.153807i \(0.0491534\pi\)
0.153807 + 0.988101i \(0.450847\pi\)
\(588\) 0 0
\(589\) 4.57734 4.57734i 0.188606 0.188606i
\(590\) 0 0
\(591\) 17.6236 17.6236i 0.724939 0.724939i
\(592\) 0 0
\(593\) −31.1669 + 31.1669i −1.27987 + 1.27987i −0.339135 + 0.940738i \(0.610134\pi\)
−0.940738 + 0.339135i \(0.889866\pi\)
\(594\) 0 0
\(595\) 2.25023i 0.0922503i
\(596\) 0 0
\(597\) 31.2029 1.27705
\(598\) 0 0
\(599\) −19.5895 −0.800404 −0.400202 0.916427i \(-0.631060\pi\)
−0.400202 + 0.916427i \(0.631060\pi\)
\(600\) 0 0
\(601\) 20.2511 20.2511i 0.826060 0.826060i −0.160910 0.986969i \(-0.551443\pi\)
0.986969 + 0.160910i \(0.0514427\pi\)
\(602\) 0 0
\(603\) 19.7012 + 19.7012i 0.802295 + 0.802295i
\(604\) 0 0
\(605\) −3.25103 −0.132173
\(606\) 0 0
\(607\) 22.1875i 0.900564i 0.892886 + 0.450282i \(0.148677\pi\)
−0.892886 + 0.450282i \(0.851323\pi\)
\(608\) 0 0
\(609\) 2.11180 2.11180i 0.0855743 0.0855743i
\(610\) 0 0
\(611\) 44.1269 1.78518
\(612\) 0 0
\(613\) 42.4171i 1.71321i 0.515972 + 0.856605i \(0.327431\pi\)
−0.515972 + 0.856605i \(0.672569\pi\)
\(614\) 0 0
\(615\) 10.9259 2.01650i 0.440573 0.0813133i
\(616\) 0 0
\(617\) 24.3536i 0.980439i 0.871599 + 0.490219i \(0.163083\pi\)
−0.871599 + 0.490219i \(0.836917\pi\)
\(618\) 0 0
\(619\) 9.96324 0.400456 0.200228 0.979749i \(-0.435832\pi\)
0.200228 + 0.979749i \(0.435832\pi\)
\(620\) 0 0
\(621\) 18.0416 18.0416i 0.723986 0.723986i
\(622\) 0 0
\(623\) 15.9518i 0.639095i
\(624\) 0 0
\(625\) −4.94098 −0.197639
\(626\) 0 0
\(627\) −9.35706 9.35706i −0.373685 0.373685i
\(628\) 0 0
\(629\) 8.02921 8.02921i 0.320145 0.320145i
\(630\) 0 0
\(631\) 47.3991 1.88693 0.943465 0.331472i \(-0.107545\pi\)
0.943465 + 0.331472i \(0.107545\pi\)
\(632\) 0 0
\(633\) −3.91077 −0.155439
\(634\) 0 0
\(635\) 20.8344i 0.826787i
\(636\) 0 0
\(637\) −3.47617 + 3.47617i −0.137731 + 0.137731i
\(638\) 0 0
\(639\) 11.5197 11.5197i 0.455713 0.455713i
\(640\) 0 0
\(641\) 18.8876 18.8876i 0.746016 0.746016i −0.227713 0.973728i \(-0.573125\pi\)
0.973728 + 0.227713i \(0.0731247\pi\)
\(642\) 0 0
\(643\) −15.2009 15.2009i −0.599464 0.599464i 0.340706 0.940170i \(-0.389334\pi\)
−0.940170 + 0.340706i \(0.889334\pi\)
\(644\) 0 0
\(645\) 9.39239 + 9.39239i 0.369825 + 0.369825i
\(646\) 0 0
\(647\) 19.2251i 0.755817i −0.925843 0.377908i \(-0.876643\pi\)
0.925843 0.377908i \(-0.123357\pi\)
\(648\) 0 0
\(649\) −10.3672 10.3672i −0.406947 0.406947i
\(650\) 0 0
\(651\) 1.85215i 0.0725915i
\(652\) 0 0
\(653\) −14.3416 14.3416i −0.561231 0.561231i 0.368426 0.929657i \(-0.379897\pi\)
−0.929657 + 0.368426i \(0.879897\pi\)
\(654\) 0 0
\(655\) −16.1917 −0.632663
\(656\) 0 0
\(657\) −21.1640 −0.825686
\(658\) 0 0
\(659\) −22.8346 22.8346i −0.889509 0.889509i 0.104967 0.994476i \(-0.466526\pi\)
−0.994476 + 0.104967i \(0.966526\pi\)
\(660\) 0 0
\(661\) 10.9825i 0.427171i −0.976924 0.213586i \(-0.931486\pi\)
0.976924 0.213586i \(-0.0685143\pi\)
\(662\) 0 0
\(663\) −5.72501 5.72501i −0.222341 0.222341i
\(664\) 0 0
\(665\) 6.06443i 0.235168i
\(666\) 0 0
\(667\) −8.96998 8.96998i −0.347319 0.347319i
\(668\) 0 0
\(669\) 17.0083 + 17.0083i 0.657581 + 0.657581i
\(670\) 0 0
\(671\) 30.7029 30.7029i 1.18527 1.18527i
\(672\) 0 0
\(673\) −10.7203 + 10.7203i −0.413239 + 0.413239i −0.882865 0.469626i \(-0.844389\pi\)
0.469626 + 0.882865i \(0.344389\pi\)
\(674\) 0 0
\(675\) −9.90998 + 9.90998i −0.381435 + 0.381435i
\(676\) 0 0
\(677\) 0.0998855i 0.00383891i 0.999998 + 0.00191946i \(0.000610982\pi\)
−0.999998 + 0.00191946i \(0.999389\pi\)
\(678\) 0 0
\(679\) 17.4942 0.671367
\(680\) 0 0
\(681\) 24.6609 0.945008
\(682\) 0 0
\(683\) −18.4954 + 18.4954i −0.707705 + 0.707705i −0.966052 0.258347i \(-0.916822\pi\)
0.258347 + 0.966052i \(0.416822\pi\)
\(684\) 0 0
\(685\) 20.4468 + 20.4468i 0.781230 + 0.781230i
\(686\) 0 0
\(687\) 14.1874 0.541283
\(688\) 0 0
\(689\) 27.6202i 1.05224i
\(690\) 0 0
\(691\) 4.26188 4.26188i 0.162129 0.162129i −0.621380 0.783509i \(-0.713428\pi\)
0.783509 + 0.621380i \(0.213428\pi\)
\(692\) 0 0
\(693\) 5.15793 0.195933
\(694\) 0 0
\(695\) 20.1431i 0.764072i
\(696\) 0 0
\(697\) −9.20238 + 1.69841i −0.348565 + 0.0643320i
\(698\) 0 0
\(699\) 18.3227i 0.693027i
\(700\) 0 0
\(701\) 33.5159 1.26588 0.632939 0.774202i \(-0.281848\pi\)
0.632939 + 0.774202i \(0.281848\pi\)
\(702\) 0 0
\(703\) 21.6389 21.6389i 0.816128 0.816128i
\(704\) 0 0
\(705\) 15.5749i 0.586584i
\(706\) 0 0
\(707\) 3.64426 0.137056
\(708\) 0 0
\(709\) −1.96607 1.96607i −0.0738374 0.0738374i 0.669224 0.743061i \(-0.266627\pi\)
−0.743061 + 0.669224i \(0.766627\pi\)
\(710\) 0 0
\(711\) 3.77705 3.77705i 0.141650 0.141650i
\(712\) 0 0
\(713\) −7.86711 −0.294626
\(714\) 0 0
\(715\) 22.5672 0.843964
\(716\) 0 0
\(717\) 19.8751i 0.742250i
\(718\) 0 0
\(719\) −18.4776 + 18.4776i −0.689099 + 0.689099i −0.962033 0.272934i \(-0.912006\pi\)
0.272934 + 0.962033i \(0.412006\pi\)
\(720\) 0 0
\(721\) −11.5222 + 11.5222i −0.429110 + 0.429110i
\(722\) 0 0
\(723\) 16.4656 16.4656i 0.612362 0.612362i
\(724\) 0 0
\(725\) 4.92706 + 4.92706i 0.182987 + 0.182987i
\(726\) 0 0
\(727\) −18.2309 18.2309i −0.676148 0.676148i 0.282978 0.959126i \(-0.408678\pi\)
−0.959126 + 0.282978i \(0.908678\pi\)
\(728\) 0 0
\(729\) 19.4338i 0.719770i
\(730\) 0 0
\(731\) −7.91080 7.91080i −0.292592 0.292592i
\(732\) 0 0
\(733\) 12.7998i 0.472773i 0.971659 + 0.236386i \(0.0759631\pi\)
−0.971659 + 0.236386i \(0.924037\pi\)
\(734\) 0 0
\(735\) −1.22694 1.22694i −0.0452563 0.0452563i
\(736\) 0 0
\(737\) −48.0136 −1.76860
\(738\) 0 0
\(739\) 33.1712 1.22022 0.610111 0.792316i \(-0.291125\pi\)
0.610111 + 0.792316i \(0.291125\pi\)
\(740\) 0 0
\(741\) −15.4291 15.4291i −0.566801 0.566801i
\(742\) 0 0
\(743\) 20.7424i 0.760965i 0.924788 + 0.380483i \(0.124242\pi\)
−0.924788 + 0.380483i \(0.875758\pi\)
\(744\) 0 0
\(745\) −0.0104764 0.0104764i −0.000383827 0.000383827i
\(746\) 0 0
\(747\) 17.3551i 0.634988i
\(748\) 0 0
\(749\) −8.63136 8.63136i −0.315383 0.315383i
\(750\) 0 0
\(751\) −11.5095 11.5095i −0.419988 0.419988i 0.465212 0.885199i \(-0.345978\pi\)
−0.885199 + 0.465212i \(0.845978\pi\)
\(752\) 0 0
\(753\) −4.14100 + 4.14100i −0.150906 + 0.150906i
\(754\) 0 0
\(755\) 8.62396 8.62396i 0.313858 0.313858i
\(756\) 0 0
\(757\) −37.3908 + 37.3908i −1.35899 + 1.35899i −0.483832 + 0.875161i \(0.660755\pi\)
−0.875161 + 0.483832i \(0.839245\pi\)
\(758\) 0 0
\(759\) 16.0820i 0.583741i
\(760\) 0 0
\(761\) −41.5281 −1.50539 −0.752696 0.658368i \(-0.771247\pi\)
−0.752696 + 0.658368i \(0.771247\pi\)
\(762\) 0 0
\(763\) 13.8336 0.500810
\(764\) 0 0
\(765\) −2.75277 + 2.75277i −0.0995268 + 0.0995268i
\(766\) 0 0
\(767\) −17.0946 17.0946i −0.617252 0.617252i
\(768\) 0 0
\(769\) −28.8257 −1.03948 −0.519740 0.854324i \(-0.673971\pi\)
−0.519740 + 0.854324i \(0.673971\pi\)
\(770\) 0 0
\(771\) 15.4580i 0.556707i
\(772\) 0 0
\(773\) −9.35719 + 9.35719i −0.336555 + 0.336555i −0.855069 0.518514i \(-0.826485\pi\)
0.518514 + 0.855069i \(0.326485\pi\)
\(774\) 0 0
\(775\) 4.32128 0.155225
\(776\) 0 0
\(777\) 8.75586i 0.314115i
\(778\) 0 0
\(779\) −24.8007 + 4.57727i −0.888577 + 0.163998i
\(780\) 0 0
\(781\) 28.0746i 1.00459i
\(782\) 0 0
\(783\) −14.1264 −0.504838
\(784\) 0 0
\(785\) −5.98240 + 5.98240i −0.213521 + 0.213521i
\(786\) 0 0
\(787\) 7.83827i 0.279404i 0.990194 + 0.139702i \(0.0446145\pi\)
−0.990194 + 0.139702i \(0.955385\pi\)
\(788\) 0 0
\(789\) 20.5547 0.731768
\(790\) 0 0
\(791\) −12.5375 12.5375i −0.445782 0.445782i
\(792\) 0 0
\(793\) 50.6268 50.6268i 1.79781 1.79781i
\(794\) 0 0
\(795\) 9.74871 0.345751
\(796\) 0 0
\(797\) −2.46476 −0.0873063 −0.0436531 0.999047i \(-0.513900\pi\)
−0.0436531 + 0.999047i \(0.513900\pi\)
\(798\) 0 0
\(799\) 13.1180i 0.464083i
\(800\) 0 0
\(801\)