Properties

Label 1323.2.h.h.802.6
Level $1323$
Weight $2$
Character 1323.802
Analytic conductor $10.564$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 802.6
Character \(\chi\) \(=\) 1323.802
Dual form 1323.2.h.h.226.6

$q$-expansion

\(f(q)\) \(=\) \(q-0.0683740 q^{2} -1.99532 q^{4} +(-1.33190 + 2.30691i) q^{5} +0.273176 q^{8} +O(q^{10})\) \(q-0.0683740 q^{2} -1.99532 q^{4} +(-1.33190 + 2.30691i) q^{5} +0.273176 q^{8} +(0.0910670 - 0.157733i) q^{10} +(-0.799563 - 1.38488i) q^{11} +(-2.62690 - 4.54992i) q^{13} +3.97197 q^{16} +(-3.27360 + 5.67005i) q^{17} +(-0.950968 - 1.64713i) q^{19} +(2.65756 - 4.60304i) q^{20} +(0.0546693 + 0.0946900i) q^{22} +(-1.53419 + 2.65729i) q^{23} +(-1.04789 - 1.81500i) q^{25} +(0.179612 + 0.311096i) q^{26} +(3.19452 - 5.53306i) q^{29} +6.71923 q^{31} -0.817932 q^{32} +(0.223829 - 0.387684i) q^{34} +(-2.11477 - 3.66290i) q^{37} +(0.0650215 + 0.112621i) q^{38} +(-0.363842 + 0.630193i) q^{40} +(3.69648 + 6.40249i) q^{41} +(5.63176 - 9.75450i) q^{43} +(1.59539 + 2.76329i) q^{44} +(0.104898 - 0.181689i) q^{46} -3.79918 q^{47} +(0.0716485 + 0.124099i) q^{50} +(5.24152 + 9.07858i) q^{52} +(4.44931 - 7.70643i) q^{53} +4.25974 q^{55} +(-0.218422 + 0.378317i) q^{58} +10.8928 q^{59} +2.71386 q^{61} -0.459420 q^{62} -7.88802 q^{64} +13.9950 q^{65} -3.32533 q^{67} +(6.53190 - 11.3136i) q^{68} +12.3890 q^{71} +(-1.09932 + 1.90407i) q^{73} +(0.144596 + 0.250447i) q^{74} +(1.89749 + 3.28655i) q^{76} +0.813556 q^{79} +(-5.29025 + 9.16298i) q^{80} +(-0.252743 - 0.437764i) q^{82} +(3.41842 - 5.92088i) q^{83} +(-8.72020 - 15.1038i) q^{85} +(-0.385066 + 0.666954i) q^{86} +(-0.218422 - 0.378317i) q^{88} +(0.235286 + 0.407527i) q^{89} +(3.06120 - 5.30216i) q^{92} +0.259765 q^{94} +5.06636 q^{95} +(2.57623 - 4.46216i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{4} + 24q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{4} + 24q^{8} - 20q^{11} + 24q^{16} - 32q^{23} - 12q^{25} - 16q^{29} + 96q^{32} - 12q^{37} - 56q^{44} + 24q^{46} + 4q^{50} - 32q^{53} + 96q^{64} + 120q^{65} + 24q^{67} + 112q^{71} - 68q^{74} - 24q^{79} + 12q^{85} - 76q^{86} - 16q^{92} + 128q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0683740 −0.0483477 −0.0241739 0.999708i \(-0.507696\pi\)
−0.0241739 + 0.999708i \(0.507696\pi\)
\(3\) 0 0
\(4\) −1.99532 −0.997662
\(5\) −1.33190 + 2.30691i −0.595642 + 1.03168i 0.397814 + 0.917466i \(0.369769\pi\)
−0.993456 + 0.114216i \(0.963564\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0.273176 0.0965824
\(9\) 0 0
\(10\) 0.0910670 0.157733i 0.0287979 0.0498794i
\(11\) −0.799563 1.38488i −0.241077 0.417558i 0.719944 0.694032i \(-0.244167\pi\)
−0.961021 + 0.276474i \(0.910834\pi\)
\(12\) 0 0
\(13\) −2.62690 4.54992i −0.728571 1.26192i −0.957487 0.288476i \(-0.906852\pi\)
0.228916 0.973446i \(-0.426482\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 3.97197 0.992993
\(17\) −3.27360 + 5.67005i −0.793966 + 1.37519i 0.129528 + 0.991576i \(0.458654\pi\)
−0.923494 + 0.383613i \(0.874680\pi\)
\(18\) 0 0
\(19\) −0.950968 1.64713i −0.218167 0.377877i 0.736081 0.676894i \(-0.236674\pi\)
−0.954248 + 0.299017i \(0.903341\pi\)
\(20\) 2.65756 4.60304i 0.594249 1.02927i
\(21\) 0 0
\(22\) 0.0546693 + 0.0946900i 0.0116555 + 0.0201880i
\(23\) −1.53419 + 2.65729i −0.319900 + 0.554083i −0.980467 0.196684i \(-0.936983\pi\)
0.660567 + 0.750767i \(0.270316\pi\)
\(24\) 0 0
\(25\) −1.04789 1.81500i −0.209578 0.363000i
\(26\) 0.179612 + 0.311096i 0.0352247 + 0.0610110i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.19452 5.53306i 0.593207 1.02746i −0.400591 0.916257i \(-0.631195\pi\)
0.993797 0.111207i \(-0.0354716\pi\)
\(30\) 0 0
\(31\) 6.71923 1.20681 0.603405 0.797435i \(-0.293810\pi\)
0.603405 + 0.797435i \(0.293810\pi\)
\(32\) −0.817932 −0.144591
\(33\) 0 0
\(34\) 0.223829 0.387684i 0.0383864 0.0664872i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.11477 3.66290i −0.347667 0.602176i 0.638168 0.769897i \(-0.279693\pi\)
−0.985835 + 0.167721i \(0.946359\pi\)
\(38\) 0.0650215 + 0.112621i 0.0105479 + 0.0182695i
\(39\) 0 0
\(40\) −0.363842 + 0.630193i −0.0575285 + 0.0996423i
\(41\) 3.69648 + 6.40249i 0.577293 + 0.999901i 0.995788 + 0.0916820i \(0.0292243\pi\)
−0.418495 + 0.908219i \(0.637442\pi\)
\(42\) 0 0
\(43\) 5.63176 9.75450i 0.858836 1.48755i −0.0142043 0.999899i \(-0.504522\pi\)
0.873040 0.487648i \(-0.162145\pi\)
\(44\) 1.59539 + 2.76329i 0.240514 + 0.416582i
\(45\) 0 0
\(46\) 0.104898 0.181689i 0.0154664 0.0267887i
\(47\) −3.79918 −0.554167 −0.277083 0.960846i \(-0.589368\pi\)
−0.277083 + 0.960846i \(0.589368\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.0716485 + 0.124099i 0.0101326 + 0.0175502i
\(51\) 0 0
\(52\) 5.24152 + 9.07858i 0.726868 + 1.25897i
\(53\) 4.44931 7.70643i 0.611160 1.05856i −0.379885 0.925034i \(-0.624037\pi\)
0.991045 0.133527i \(-0.0426301\pi\)
\(54\) 0 0
\(55\) 4.25974 0.574383
\(56\) 0 0
\(57\) 0 0
\(58\) −0.218422 + 0.378317i −0.0286802 + 0.0496755i
\(59\) 10.8928 1.41812 0.709060 0.705148i \(-0.249120\pi\)
0.709060 + 0.705148i \(0.249120\pi\)
\(60\) 0 0
\(61\) 2.71386 0.347475 0.173737 0.984792i \(-0.444416\pi\)
0.173737 + 0.984792i \(0.444416\pi\)
\(62\) −0.459420 −0.0583465
\(63\) 0 0
\(64\) −7.88802 −0.986002
\(65\) 13.9950 1.73587
\(66\) 0 0
\(67\) −3.32533 −0.406254 −0.203127 0.979152i \(-0.565110\pi\)
−0.203127 + 0.979152i \(0.565110\pi\)
\(68\) 6.53190 11.3136i 0.792110 1.37197i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.3890 1.47031 0.735154 0.677900i \(-0.237110\pi\)
0.735154 + 0.677900i \(0.237110\pi\)
\(72\) 0 0
\(73\) −1.09932 + 1.90407i −0.128665 + 0.222855i −0.923160 0.384417i \(-0.874403\pi\)
0.794494 + 0.607271i \(0.207736\pi\)
\(74\) 0.144596 + 0.250447i 0.0168089 + 0.0291138i
\(75\) 0 0
\(76\) 1.89749 + 3.28655i 0.217657 + 0.376993i
\(77\) 0 0
\(78\) 0 0
\(79\) 0.813556 0.0915322 0.0457661 0.998952i \(-0.485427\pi\)
0.0457661 + 0.998952i \(0.485427\pi\)
\(80\) −5.29025 + 9.16298i −0.591468 + 1.02445i
\(81\) 0 0
\(82\) −0.252743 0.437764i −0.0279108 0.0483429i
\(83\) 3.41842 5.92088i 0.375220 0.649901i −0.615140 0.788418i \(-0.710900\pi\)
0.990360 + 0.138517i \(0.0442337\pi\)
\(84\) 0 0
\(85\) −8.72020 15.1038i −0.945838 1.63824i
\(86\) −0.385066 + 0.666954i −0.0415227 + 0.0719195i
\(87\) 0 0
\(88\) −0.218422 0.378317i −0.0232838 0.0403288i
\(89\) 0.235286 + 0.407527i 0.0249403 + 0.0431978i 0.878226 0.478246i \(-0.158727\pi\)
−0.853286 + 0.521443i \(0.825394\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.06120 5.30216i 0.319152 0.552788i
\(93\) 0 0
\(94\) 0.259765 0.0267927
\(95\) 5.06636 0.519798
\(96\) 0 0
\(97\) 2.57623 4.46216i 0.261576 0.453064i −0.705085 0.709123i \(-0.749091\pi\)
0.966661 + 0.256059i \(0.0824243\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.09088 + 3.62152i 0.209088 + 0.362152i
\(101\) −0.922440 1.59771i −0.0917862 0.158978i 0.816477 0.577379i \(-0.195924\pi\)
−0.908263 + 0.418400i \(0.862591\pi\)
\(102\) 0 0
\(103\) −2.58901 + 4.48430i −0.255103 + 0.441851i −0.964923 0.262531i \(-0.915443\pi\)
0.709821 + 0.704383i \(0.248776\pi\)
\(104\) −0.717607 1.24293i −0.0703671 0.121879i
\(105\) 0 0
\(106\) −0.304217 + 0.526920i −0.0295482 + 0.0511790i
\(107\) −8.47445 14.6782i −0.819256 1.41899i −0.906231 0.422782i \(-0.861054\pi\)
0.0869755 0.996210i \(-0.472280\pi\)
\(108\) 0 0
\(109\) 4.24996 7.36115i 0.407073 0.705070i −0.587488 0.809233i \(-0.699883\pi\)
0.994560 + 0.104163i \(0.0332163\pi\)
\(110\) −0.291255 −0.0277701
\(111\) 0 0
\(112\) 0 0
\(113\) 1.95196 + 3.38089i 0.183625 + 0.318048i 0.943112 0.332474i \(-0.107884\pi\)
−0.759487 + 0.650522i \(0.774550\pi\)
\(114\) 0 0
\(115\) −4.08675 7.07847i −0.381092 0.660070i
\(116\) −6.37410 + 11.0403i −0.591820 + 1.02506i
\(117\) 0 0
\(118\) −0.744783 −0.0685628
\(119\) 0 0
\(120\) 0 0
\(121\) 4.22140 7.31167i 0.383763 0.664698i
\(122\) −0.185558 −0.0167996
\(123\) 0 0
\(124\) −13.4070 −1.20399
\(125\) −7.73623 −0.691949
\(126\) 0 0
\(127\) 10.9533 0.971946 0.485973 0.873974i \(-0.338465\pi\)
0.485973 + 0.873974i \(0.338465\pi\)
\(128\) 2.17520 0.192262
\(129\) 0 0
\(130\) −0.956896 −0.0839253
\(131\) −2.22671 + 3.85678i −0.194549 + 0.336968i −0.946752 0.321962i \(-0.895658\pi\)
0.752204 + 0.658931i \(0.228991\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.227366 0.0196414
\(135\) 0 0
\(136\) −0.894271 + 1.54892i −0.0766831 + 0.132819i
\(137\) −9.76800 16.9187i −0.834537 1.44546i −0.894407 0.447254i \(-0.852402\pi\)
0.0598699 0.998206i \(-0.480931\pi\)
\(138\) 0 0
\(139\) −1.31540 2.27833i −0.111570 0.193246i 0.804833 0.593501i \(-0.202255\pi\)
−0.916404 + 0.400256i \(0.868921\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.847087 −0.0710860
\(143\) −4.20075 + 7.27590i −0.351284 + 0.608442i
\(144\) 0 0
\(145\) 8.50952 + 14.7389i 0.706677 + 1.22400i
\(146\) 0.0751647 0.130189i 0.00622067 0.0107745i
\(147\) 0 0
\(148\) 4.21966 + 7.30867i 0.346854 + 0.600769i
\(149\) −4.40640 + 7.63212i −0.360987 + 0.625247i −0.988124 0.153662i \(-0.950893\pi\)
0.627137 + 0.778909i \(0.284227\pi\)
\(150\) 0 0
\(151\) −2.33211 4.03933i −0.189784 0.328716i 0.755394 0.655271i \(-0.227446\pi\)
−0.945178 + 0.326555i \(0.894112\pi\)
\(152\) −0.259782 0.449956i −0.0210711 0.0364962i
\(153\) 0 0
\(154\) 0 0
\(155\) −8.94931 + 15.5007i −0.718826 + 1.24504i
\(156\) 0 0
\(157\) −4.07294 −0.325056 −0.162528 0.986704i \(-0.551965\pi\)
−0.162528 + 0.986704i \(0.551965\pi\)
\(158\) −0.0556261 −0.00442537
\(159\) 0 0
\(160\) 1.08940 1.88690i 0.0861246 0.149172i
\(161\) 0 0
\(162\) 0 0
\(163\) 6.06112 + 10.4982i 0.474744 + 0.822280i 0.999582 0.0289220i \(-0.00920745\pi\)
−0.524838 + 0.851202i \(0.675874\pi\)
\(164\) −7.37568 12.7750i −0.575944 0.997564i
\(165\) 0 0
\(166\) −0.233731 + 0.404834i −0.0181410 + 0.0314212i
\(167\) −2.39951 4.15608i −0.185680 0.321607i 0.758126 0.652109i \(-0.226115\pi\)
−0.943805 + 0.330502i \(0.892782\pi\)
\(168\) 0 0
\(169\) −7.30121 + 12.6461i −0.561631 + 0.972774i
\(170\) 0.596235 + 1.03271i 0.0457291 + 0.0792051i
\(171\) 0 0
\(172\) −11.2372 + 19.4634i −0.856828 + 1.48407i
\(173\) −5.03171 −0.382554 −0.191277 0.981536i \(-0.561263\pi\)
−0.191277 + 0.981536i \(0.561263\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3.17584 5.50072i −0.239388 0.414632i
\(177\) 0 0
\(178\) −0.0160874 0.0278642i −0.00120580 0.00208851i
\(179\) −8.19896 + 14.2010i −0.612819 + 1.06143i 0.377944 + 0.925828i \(0.376631\pi\)
−0.990763 + 0.135605i \(0.956702\pi\)
\(180\) 0 0
\(181\) −14.4345 −1.07291 −0.536454 0.843930i \(-0.680237\pi\)
−0.536454 + 0.843930i \(0.680237\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.419103 + 0.725908i −0.0308967 + 0.0535147i
\(185\) 11.2666 0.828339
\(186\) 0 0
\(187\) 10.4698 0.765629
\(188\) 7.58059 0.552871
\(189\) 0 0
\(190\) −0.346407 −0.0251310
\(191\) −2.84131 −0.205590 −0.102795 0.994703i \(-0.532779\pi\)
−0.102795 + 0.994703i \(0.532779\pi\)
\(192\) 0 0
\(193\) 8.82886 0.635515 0.317758 0.948172i \(-0.397070\pi\)
0.317758 + 0.948172i \(0.397070\pi\)
\(194\) −0.176147 + 0.305096i −0.0126466 + 0.0219046i
\(195\) 0 0
\(196\) 0 0
\(197\) −5.72354 −0.407785 −0.203893 0.978993i \(-0.565359\pi\)
−0.203893 + 0.978993i \(0.565359\pi\)
\(198\) 0 0
\(199\) 5.70752 9.88572i 0.404596 0.700780i −0.589679 0.807638i \(-0.700746\pi\)
0.994274 + 0.106858i \(0.0340789\pi\)
\(200\) −0.286259 0.495815i −0.0202416 0.0350594i
\(201\) 0 0
\(202\) 0.0630709 + 0.109242i 0.00443765 + 0.00768624i
\(203\) 0 0
\(204\) 0 0
\(205\) −19.6933 −1.37544
\(206\) 0.177021 0.306609i 0.0123336 0.0213625i
\(207\) 0 0
\(208\) −10.4340 18.0722i −0.723466 1.25308i
\(209\) −1.52072 + 2.63396i −0.105190 + 0.182195i
\(210\) 0 0
\(211\) 10.6919 + 18.5189i 0.736059 + 1.27489i 0.954257 + 0.298986i \(0.0966486\pi\)
−0.218199 + 0.975904i \(0.570018\pi\)
\(212\) −8.87782 + 15.3768i −0.609731 + 1.05609i
\(213\) 0 0
\(214\) 0.579432 + 1.00361i 0.0396091 + 0.0686050i
\(215\) 15.0018 + 25.9840i 1.02312 + 1.77209i
\(216\) 0 0
\(217\) 0 0
\(218\) −0.290587 + 0.503311i −0.0196810 + 0.0340885i
\(219\) 0 0
\(220\) −8.49956 −0.573041
\(221\) 34.3977 2.31384
\(222\) 0 0
\(223\) −3.58387 + 6.20744i −0.239994 + 0.415681i −0.960712 0.277547i \(-0.910479\pi\)
0.720719 + 0.693228i \(0.243812\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −0.133463 0.231165i −0.00887784 0.0153769i
\(227\) −6.89434 11.9413i −0.457593 0.792575i 0.541240 0.840868i \(-0.317955\pi\)
−0.998833 + 0.0482933i \(0.984622\pi\)
\(228\) 0 0
\(229\) 13.1972 22.8581i 0.872092 1.51051i 0.0122645 0.999925i \(-0.496096\pi\)
0.859828 0.510584i \(-0.170571\pi\)
\(230\) 0.279428 + 0.483983i 0.0184249 + 0.0319129i
\(231\) 0 0
\(232\) 0.872666 1.51150i 0.0572933 0.0992349i
\(233\) −6.32230 10.9505i −0.414187 0.717394i 0.581155 0.813793i \(-0.302601\pi\)
−0.995343 + 0.0963989i \(0.969268\pi\)
\(234\) 0 0
\(235\) 5.06010 8.76436i 0.330085 0.571724i
\(236\) −21.7346 −1.41481
\(237\) 0 0
\(238\) 0 0
\(239\) −7.71640 13.3652i −0.499133 0.864523i 0.500867 0.865524i \(-0.333015\pi\)
−0.999999 + 0.00100121i \(0.999681\pi\)
\(240\) 0 0
\(241\) −0.589942 1.02181i −0.0380015 0.0658205i 0.846399 0.532549i \(-0.178766\pi\)
−0.884401 + 0.466729i \(0.845432\pi\)
\(242\) −0.288634 + 0.499928i −0.0185541 + 0.0321366i
\(243\) 0 0
\(244\) −5.41504 −0.346662
\(245\) 0 0
\(246\) 0 0
\(247\) −4.99620 + 8.65367i −0.317900 + 0.550620i
\(248\) 1.83553 0.116557
\(249\) 0 0
\(250\) 0.528957 0.0334542
\(251\) −5.54970 −0.350294 −0.175147 0.984542i \(-0.556040\pi\)
−0.175147 + 0.984542i \(0.556040\pi\)
\(252\) 0 0
\(253\) 4.90672 0.308483
\(254\) −0.748919 −0.0469913
\(255\) 0 0
\(256\) 15.6273 0.976707
\(257\) 4.91538 8.51369i 0.306613 0.531069i −0.671006 0.741452i \(-0.734138\pi\)
0.977619 + 0.210382i \(0.0674709\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −27.9246 −1.73181
\(261\) 0 0
\(262\) 0.152249 0.263703i 0.00940598 0.0162916i
\(263\) 5.96612 + 10.3336i 0.367887 + 0.637199i 0.989235 0.146336i \(-0.0467480\pi\)
−0.621348 + 0.783535i \(0.713415\pi\)
\(264\) 0 0
\(265\) 11.8520 + 20.5283i 0.728065 + 1.26105i
\(266\) 0 0
\(267\) 0 0
\(268\) 6.63512 0.405304
\(269\) 14.9824 25.9503i 0.913494 1.58222i 0.104401 0.994535i \(-0.466707\pi\)
0.809092 0.587682i \(-0.199959\pi\)
\(270\) 0 0
\(271\) 3.54825 + 6.14575i 0.215541 + 0.373328i 0.953440 0.301584i \(-0.0975152\pi\)
−0.737899 + 0.674911i \(0.764182\pi\)
\(272\) −13.0027 + 22.5213i −0.788402 + 1.36555i
\(273\) 0 0
\(274\) 0.667877 + 1.15680i 0.0403479 + 0.0698847i
\(275\) −1.67571 + 2.90242i −0.101049 + 0.175022i
\(276\) 0 0
\(277\) 4.91175 + 8.50741i 0.295119 + 0.511161i 0.975013 0.222150i \(-0.0713075\pi\)
−0.679894 + 0.733311i \(0.737974\pi\)
\(278\) 0.0899388 + 0.155779i 0.00539417 + 0.00934298i
\(279\) 0 0
\(280\) 0 0
\(281\) −11.9389 + 20.6787i −0.712213 + 1.23359i 0.251812 + 0.967776i \(0.418974\pi\)
−0.964025 + 0.265813i \(0.914360\pi\)
\(282\) 0 0
\(283\) −3.01595 −0.179280 −0.0896399 0.995974i \(-0.528572\pi\)
−0.0896399 + 0.995974i \(0.528572\pi\)
\(284\) −24.7201 −1.46687
\(285\) 0 0
\(286\) 0.287222 0.497483i 0.0169838 0.0294168i
\(287\) 0 0
\(288\) 0 0
\(289\) −12.9330 22.4006i −0.760763 1.31768i
\(290\) −0.581830 1.00776i −0.0341662 0.0591776i
\(291\) 0 0
\(292\) 2.19350 3.79925i 0.128365 0.222334i
\(293\) 8.52913 + 14.7729i 0.498277 + 0.863041i 0.999998 0.00198814i \(-0.000632845\pi\)
−0.501721 + 0.865030i \(0.667300\pi\)
\(294\) 0 0
\(295\) −14.5081 + 25.1287i −0.844692 + 1.46305i
\(296\) −0.577706 1.00062i −0.0335785 0.0581596i
\(297\) 0 0
\(298\) 0.301283 0.521838i 0.0174529 0.0302293i
\(299\) 16.1206 0.932280
\(300\) 0 0
\(301\) 0 0
\(302\) 0.159456 + 0.276185i 0.00917564 + 0.0158927i
\(303\) 0 0
\(304\) −3.77722 6.54234i −0.216638 0.375229i
\(305\) −3.61458 + 6.26064i −0.206970 + 0.358483i
\(306\) 0 0
\(307\) 23.2178 1.32511 0.662554 0.749014i \(-0.269473\pi\)
0.662554 + 0.749014i \(0.269473\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.611900 1.05984i 0.0347536 0.0601950i
\(311\) −1.79093 −0.101555 −0.0507773 0.998710i \(-0.516170\pi\)
−0.0507773 + 0.998710i \(0.516170\pi\)
\(312\) 0 0
\(313\) 4.60917 0.260526 0.130263 0.991480i \(-0.458418\pi\)
0.130263 + 0.991480i \(0.458418\pi\)
\(314\) 0.278483 0.0157157
\(315\) 0 0
\(316\) −1.62331 −0.0913183
\(317\) 25.8841 1.45380 0.726898 0.686745i \(-0.240961\pi\)
0.726898 + 0.686745i \(0.240961\pi\)
\(318\) 0 0
\(319\) −10.2169 −0.572035
\(320\) 10.5060 18.1970i 0.587304 1.01724i
\(321\) 0 0
\(322\) 0 0
\(323\) 12.4524 0.692869
\(324\) 0 0
\(325\) −5.50541 + 9.53566i −0.305385 + 0.528943i
\(326\) −0.414423 0.717802i −0.0229528 0.0397554i
\(327\) 0 0
\(328\) 1.00979 + 1.74901i 0.0557563 + 0.0965728i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.161323 0.00886714 0.00443357 0.999990i \(-0.498589\pi\)
0.00443357 + 0.999990i \(0.498589\pi\)
\(332\) −6.82086 + 11.8141i −0.374343 + 0.648382i
\(333\) 0 0
\(334\) 0.164064 + 0.284168i 0.00897719 + 0.0155490i
\(335\) 4.42899 7.67124i 0.241982 0.419125i
\(336\) 0 0
\(337\) 4.52675 + 7.84057i 0.246588 + 0.427103i 0.962577 0.271009i \(-0.0873572\pi\)
−0.715989 + 0.698112i \(0.754024\pi\)
\(338\) 0.499213 0.864662i 0.0271536 0.0470314i
\(339\) 0 0
\(340\) 17.3996 + 30.1370i 0.943627 + 1.63441i
\(341\) −5.37245 9.30535i −0.290934 0.503913i
\(342\) 0 0
\(343\) 0 0
\(344\) 1.53846 2.66470i 0.0829484 0.143671i
\(345\) 0 0
\(346\) 0.344038 0.0184956
\(347\) 5.81968 0.312417 0.156208 0.987724i \(-0.450073\pi\)
0.156208 + 0.987724i \(0.450073\pi\)
\(348\) 0 0
\(349\) −13.6310 + 23.6095i −0.729648 + 1.26379i 0.227384 + 0.973805i \(0.426983\pi\)
−0.957032 + 0.289983i \(0.906350\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.653988 + 1.13274i 0.0348577 + 0.0603753i
\(353\) −12.0948 20.9488i −0.643741 1.11499i −0.984591 0.174874i \(-0.944048\pi\)
0.340850 0.940118i \(-0.389285\pi\)
\(354\) 0 0
\(355\) −16.5009 + 28.5804i −0.875777 + 1.51689i
\(356\) −0.469472 0.813149i −0.0248820 0.0430968i
\(357\) 0 0
\(358\) 0.560595 0.970979i 0.0296284 0.0513179i
\(359\) −10.5188 18.2191i −0.555161 0.961567i −0.997891 0.0649124i \(-0.979323\pi\)
0.442730 0.896655i \(-0.354010\pi\)
\(360\) 0 0
\(361\) 7.69132 13.3218i 0.404806 0.701145i
\(362\) 0.986944 0.0518726
\(363\) 0 0
\(364\) 0 0
\(365\) −2.92835 5.07205i −0.153277 0.265483i
\(366\) 0 0
\(367\) −17.5190 30.3438i −0.914485 1.58393i −0.807654 0.589657i \(-0.799263\pi\)
−0.106831 0.994277i \(-0.534070\pi\)
\(368\) −6.09375 + 10.5547i −0.317659 + 0.550201i
\(369\) 0 0
\(370\) −0.770345 −0.0400483
\(371\) 0 0
\(372\) 0 0
\(373\) −0.564310 + 0.977414i −0.0292189 + 0.0506086i −0.880265 0.474482i \(-0.842635\pi\)
0.851046 + 0.525091i \(0.175969\pi\)
\(374\) −0.715863 −0.0370164
\(375\) 0 0
\(376\) −1.03784 −0.0535227
\(377\) −33.5667 −1.72877
\(378\) 0 0
\(379\) −21.9619 −1.12811 −0.564054 0.825738i \(-0.690759\pi\)
−0.564054 + 0.825738i \(0.690759\pi\)
\(380\) −10.1090 −0.518583
\(381\) 0 0
\(382\) 0.194272 0.00993981
\(383\) −11.5200 + 19.9533i −0.588647 + 1.01957i 0.405763 + 0.913978i \(0.367006\pi\)
−0.994410 + 0.105588i \(0.966328\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.603664 −0.0307257
\(387\) 0 0
\(388\) −5.14042 + 8.90346i −0.260965 + 0.452005i
\(389\) 7.88753 + 13.6616i 0.399914 + 0.692671i 0.993715 0.111941i \(-0.0357067\pi\)
−0.593801 + 0.804612i \(0.702373\pi\)
\(390\) 0 0
\(391\) −10.0446 17.3978i −0.507979 0.879846i
\(392\) 0 0
\(393\) 0 0
\(394\) 0.391341 0.0197155
\(395\) −1.08357 + 1.87680i −0.0545204 + 0.0944321i
\(396\) 0 0
\(397\) −8.25277 14.2942i −0.414195 0.717406i 0.581149 0.813797i \(-0.302603\pi\)
−0.995344 + 0.0963911i \(0.969270\pi\)
\(398\) −0.390246 + 0.675926i −0.0195613 + 0.0338811i
\(399\) 0 0
\(400\) −4.16220 7.20914i −0.208110 0.360457i
\(401\) 10.8300 18.7581i 0.540823 0.936733i −0.458034 0.888935i \(-0.651446\pi\)
0.998857 0.0477986i \(-0.0152206\pi\)
\(402\) 0 0
\(403\) −17.6507 30.5720i −0.879246 1.52290i
\(404\) 1.84057 + 3.18796i 0.0915716 + 0.158607i
\(405\) 0 0
\(406\) 0 0
\(407\) −3.38179 + 5.85743i −0.167629 + 0.290342i
\(408\) 0 0
\(409\) −30.5721 −1.51169 −0.755846 0.654750i \(-0.772774\pi\)
−0.755846 + 0.654750i \(0.772774\pi\)
\(410\) 1.34651 0.0664993
\(411\) 0 0
\(412\) 5.16592 8.94763i 0.254507 0.440818i
\(413\) 0 0
\(414\) 0 0
\(415\) 9.10596 + 15.7720i 0.446994 + 0.774216i
\(416\) 2.14863 + 3.72153i 0.105345 + 0.182463i
\(417\) 0 0
\(418\) 0.103978 0.180094i 0.00508571 0.00880871i
\(419\) −10.8081 18.7202i −0.528011 0.914542i −0.999467 0.0326524i \(-0.989605\pi\)
0.471456 0.881890i \(-0.343729\pi\)
\(420\) 0 0
\(421\) 13.6217 23.5935i 0.663881 1.14988i −0.315706 0.948857i \(-0.602241\pi\)
0.979587 0.201019i \(-0.0644252\pi\)
\(422\) −0.731046 1.26621i −0.0355867 0.0616380i
\(423\) 0 0
\(424\) 1.21545 2.10521i 0.0590273 0.102238i
\(425\) 13.7215 0.665592
\(426\) 0 0
\(427\) 0 0
\(428\) 16.9093 + 29.2877i 0.817341 + 1.41568i
\(429\) 0 0
\(430\) −1.02574 1.77663i −0.0494654 0.0856765i
\(431\) 4.09843 7.09869i 0.197415 0.341932i −0.750275 0.661126i \(-0.770079\pi\)
0.947689 + 0.319194i \(0.103412\pi\)
\(432\) 0 0
\(433\) 3.41468 0.164099 0.0820494 0.996628i \(-0.473853\pi\)
0.0820494 + 0.996628i \(0.473853\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −8.48005 + 14.6879i −0.406121 + 0.703422i
\(437\) 5.83585 0.279167
\(438\) 0 0
\(439\) 6.58831 0.314443 0.157221 0.987563i \(-0.449746\pi\)
0.157221 + 0.987563i \(0.449746\pi\)
\(440\) 1.16366 0.0554753
\(441\) 0 0
\(442\) −2.35191 −0.111869
\(443\) −28.6912 −1.36316 −0.681581 0.731743i \(-0.738707\pi\)
−0.681581 + 0.731743i \(0.738707\pi\)
\(444\) 0 0
\(445\) −1.25350 −0.0594218
\(446\) 0.245043 0.424428i 0.0116031 0.0200972i
\(447\) 0 0
\(448\) 0 0
\(449\) −0.457724 −0.0216013 −0.0108007 0.999942i \(-0.503438\pi\)
−0.0108007 + 0.999942i \(0.503438\pi\)
\(450\) 0 0
\(451\) 5.91114 10.2384i 0.278345 0.482107i
\(452\) −3.89479 6.74598i −0.183196 0.317304i
\(453\) 0 0
\(454\) 0.471393 + 0.816477i 0.0221236 + 0.0383192i
\(455\) 0 0
\(456\) 0 0
\(457\) 20.2210 0.945900 0.472950 0.881089i \(-0.343189\pi\)
0.472950 + 0.881089i \(0.343189\pi\)
\(458\) −0.902342 + 1.56290i −0.0421637 + 0.0730296i
\(459\) 0 0
\(460\) 8.15440 + 14.1238i 0.380201 + 0.658527i
\(461\) 12.1036 20.9640i 0.563719 0.976390i −0.433449 0.901178i \(-0.642703\pi\)
0.997168 0.0752117i \(-0.0239633\pi\)
\(462\) 0 0
\(463\) 2.40242 + 4.16111i 0.111650 + 0.193383i 0.916436 0.400182i \(-0.131053\pi\)
−0.804786 + 0.593565i \(0.797720\pi\)
\(464\) 12.6885 21.9772i 0.589050 1.02026i
\(465\) 0 0
\(466\) 0.432281 + 0.748732i 0.0200250 + 0.0346843i
\(467\) −13.6228 23.5954i −0.630389 1.09187i −0.987472 0.157793i \(-0.949562\pi\)
0.357083 0.934073i \(-0.383771\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −0.345979 + 0.599254i −0.0159588 + 0.0276415i
\(471\) 0 0
\(472\) 2.97565 0.136965
\(473\) −18.0118 −0.828184
\(474\) 0 0
\(475\) −1.99302 + 3.45202i −0.0914462 + 0.158389i
\(476\) 0 0
\(477\) 0 0
\(478\) 0.527601 + 0.913832i 0.0241319 + 0.0417977i
\(479\) 10.2628 + 17.7756i 0.468917 + 0.812188i 0.999369 0.0355269i \(-0.0113109\pi\)
−0.530452 + 0.847715i \(0.677978\pi\)
\(480\) 0 0
\(481\) −11.1106 + 19.2441i −0.506600 + 0.877457i
\(482\) 0.0403366 + 0.0698651i 0.00183728 + 0.00318227i
\(483\) 0 0
\(484\) −8.42306 + 14.5892i −0.382866 + 0.663144i
\(485\) 6.86254 + 11.8863i 0.311612 + 0.539727i
\(486\) 0 0
\(487\) −12.9224 + 22.3823i −0.585571 + 1.01424i 0.409233 + 0.912430i \(0.365796\pi\)
−0.994804 + 0.101809i \(0.967537\pi\)
\(488\) 0.741363 0.0335599
\(489\) 0 0
\(490\) 0 0
\(491\) 7.80775 + 13.5234i 0.352359 + 0.610303i 0.986662 0.162781i \(-0.0520463\pi\)
−0.634303 + 0.773084i \(0.718713\pi\)
\(492\) 0 0
\(493\) 20.9152 + 36.2261i 0.941971 + 1.63154i
\(494\) 0.341610 0.591686i 0.0153698 0.0266212i
\(495\) 0 0
\(496\) 26.6886 1.19835
\(497\) 0 0
\(498\) 0 0
\(499\) −10.6345 + 18.4195i −0.476066 + 0.824571i −0.999624 0.0274192i \(-0.991271\pi\)
0.523558 + 0.851990i \(0.324604\pi\)
\(500\) 15.4363 0.690332
\(501\) 0 0
\(502\) 0.379455 0.0169359
\(503\) 16.3298 0.728110 0.364055 0.931377i \(-0.381392\pi\)
0.364055 + 0.931377i \(0.381392\pi\)
\(504\) 0 0
\(505\) 4.91437 0.218687
\(506\) −0.335492 −0.0149144
\(507\) 0 0
\(508\) −21.8553 −0.969674
\(509\) −6.73089 + 11.6582i −0.298342 + 0.516743i −0.975757 0.218858i \(-0.929767\pi\)
0.677415 + 0.735601i \(0.263100\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −5.41890 −0.239484
\(513\) 0 0
\(514\) −0.336084 + 0.582115i −0.0148240 + 0.0256760i
\(515\) −6.89659 11.9452i −0.303900 0.526370i
\(516\) 0 0
\(517\) 3.03768 + 5.26142i 0.133597 + 0.231397i
\(518\) 0 0
\(519\) 0 0
\(520\) 3.82311 0.167654
\(521\) −0.713095 + 1.23512i −0.0312413 + 0.0541115i −0.881223 0.472700i \(-0.843279\pi\)
0.849982 + 0.526812i \(0.176613\pi\)
\(522\) 0 0
\(523\) 3.85530 + 6.67758i 0.168581 + 0.291990i 0.937921 0.346849i \(-0.112748\pi\)
−0.769340 + 0.638839i \(0.779415\pi\)
\(524\) 4.44301 7.69553i 0.194094 0.336181i
\(525\) 0 0
\(526\) −0.407928 0.706551i −0.0177865 0.0308071i
\(527\) −21.9961 + 38.0984i −0.958165 + 1.65959i
\(528\) 0 0
\(529\) 6.79254 + 11.7650i 0.295328 + 0.511523i
\(530\) −0.810371 1.40360i −0.0352003 0.0609686i
\(531\) 0 0
\(532\) 0 0
\(533\) 19.4206 33.6374i 0.841198 1.45700i
\(534\) 0 0
\(535\) 45.1483 1.95193
\(536\) −0.908402 −0.0392370
\(537\) 0 0
\(538\) −1.02441 + 1.77432i −0.0441653 + 0.0764966i
\(539\) 0 0
\(540\) 0 0
\(541\) −14.0228 24.2882i −0.602886 1.04423i −0.992382 0.123201i \(-0.960684\pi\)
0.389495 0.921028i \(-0.372649\pi\)
\(542\) −0.242608 0.420209i −0.0104209 0.0180495i
\(543\) 0 0
\(544\) 2.67759 4.63771i 0.114801 0.198840i
\(545\) 11.3210 + 19.6086i 0.484939 + 0.839939i
\(546\) 0 0
\(547\) 17.7305 30.7101i 0.758101 1.31307i −0.185717 0.982603i \(-0.559461\pi\)
0.943818 0.330466i \(-0.107206\pi\)
\(548\) 19.4903 + 33.7583i 0.832586 + 1.44208i
\(549\) 0 0
\(550\) 0.114575 0.198450i 0.00488550 0.00846193i
\(551\) −12.1515 −0.517673
\(552\) 0 0
\(553\) 0 0
\(554\) −0.335836 0.581685i −0.0142683 0.0247134i
\(555\) 0 0
\(556\) 2.62464 + 4.54601i 0.111310 + 0.192794i
\(557\) 17.5209 30.3472i 0.742386 1.28585i −0.209019 0.977911i \(-0.567027\pi\)
0.951406 0.307940i \(-0.0996395\pi\)
\(558\) 0 0
\(559\) −59.1763 −2.50289
\(560\) 0 0
\(561\) 0 0
\(562\) 0.816308 1.41389i 0.0344339 0.0596412i
\(563\) −16.0262 −0.675425 −0.337712 0.941249i \(-0.609653\pi\)
−0.337712 + 0.941249i \(0.609653\pi\)
\(564\) 0 0
\(565\) −10.3992 −0.437499
\(566\) 0.206213 0.00866776
\(567\) 0 0
\(568\) 3.38439 0.142006
\(569\) −0.371302 −0.0155658 −0.00778290 0.999970i \(-0.502477\pi\)
−0.00778290 + 0.999970i \(0.502477\pi\)
\(570\) 0 0
\(571\) 29.2304 1.22325 0.611626 0.791147i \(-0.290516\pi\)
0.611626 + 0.791147i \(0.290516\pi\)
\(572\) 8.38185 14.5178i 0.350463 0.607019i
\(573\) 0 0
\(574\) 0 0
\(575\) 6.43065 0.268177
\(576\) 0 0
\(577\) 7.52852 13.0398i 0.313417 0.542853i −0.665683 0.746235i \(-0.731860\pi\)
0.979100 + 0.203381i \(0.0651930\pi\)
\(578\) 0.884279 + 1.53162i 0.0367811 + 0.0637068i
\(579\) 0 0
\(580\) −16.9793 29.4089i −0.705025 1.22114i
\(581\) 0 0
\(582\) 0 0
\(583\) −14.2300 −0.589347
\(584\) −0.300307 + 0.520148i −0.0124268 + 0.0215239i
\(585\) 0 0
\(586\) −0.583171 1.01008i −0.0240906 0.0417261i
\(587\) 0.835901 1.44782i 0.0345013 0.0597580i −0.848259 0.529581i \(-0.822349\pi\)
0.882760 + 0.469823i \(0.155682\pi\)
\(588\) 0 0
\(589\) −6.38977 11.0674i −0.263286 0.456025i
\(590\) 0.991973 1.71815i 0.0408389 0.0707350i
\(591\) 0 0
\(592\) −8.39982 14.5489i −0.345231 0.597957i
\(593\) −5.40871 9.36816i −0.222109 0.384704i 0.733339 0.679863i \(-0.237961\pi\)
−0.955448 + 0.295159i \(0.904627\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 8.79221 15.2286i 0.360143 0.623786i
\(597\) 0 0
\(598\) −1.10223 −0.0450736
\(599\) −16.6401 −0.679898 −0.339949 0.940444i \(-0.610410\pi\)
−0.339949 + 0.940444i \(0.610410\pi\)
\(600\) 0 0
\(601\) 12.9011 22.3453i 0.526246 0.911485i −0.473286 0.880909i \(-0.656932\pi\)
0.999532 0.0305765i \(-0.00973432\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4.65332 + 8.05978i 0.189341 + 0.327948i
\(605\) 11.2449 + 19.4768i 0.457171 + 0.791843i
\(606\) 0 0
\(607\) 18.9025 32.7400i 0.767227 1.32888i −0.171834 0.985126i \(-0.554969\pi\)
0.939061 0.343750i \(-0.111697\pi\)
\(608\) 0.777828 + 1.34724i 0.0315451 + 0.0546377i
\(609\) 0 0
\(610\) 0.247143 0.428065i 0.0100065 0.0173318i
\(611\) 9.98005 + 17.2860i 0.403750 + 0.699315i
\(612\) 0 0
\(613\) 6.47719 11.2188i 0.261611 0.453124i −0.705059 0.709149i \(-0.749080\pi\)
0.966670 + 0.256025i \(0.0824129\pi\)
\(614\) −1.58749 −0.0640659
\(615\) 0 0
\(616\) 0 0
\(617\) −16.2202 28.0941i −0.652999 1.13103i −0.982391 0.186834i \(-0.940177\pi\)
0.329393 0.944193i \(-0.393156\pi\)
\(618\) 0 0
\(619\) 16.5987 + 28.7498i 0.667157 + 1.15555i 0.978696 + 0.205317i \(0.0658224\pi\)
−0.311538 + 0.950234i \(0.600844\pi\)
\(620\) 17.8568 30.9289i 0.717146 1.24213i
\(621\) 0 0
\(622\) 0.122453 0.00490993
\(623\) 0 0
\(624\) 0 0
\(625\) 15.5433 26.9218i 0.621732 1.07687i
\(626\) −0.315147 −0.0125958
\(627\) 0 0
\(628\) 8.12683 0.324296
\(629\) 27.6917 1.10414
\(630\) 0 0
\(631\) 32.2773 1.28494 0.642470 0.766311i \(-0.277910\pi\)
0.642470 + 0.766311i \(0.277910\pi\)
\(632\) 0.222244 0.00884040
\(633\) 0 0
\(634\) −1.76980 −0.0702877
\(635\) −14.5886 + 25.2682i −0.578931 + 1.00274i
\(636\) 0 0
\(637\) 0 0
\(638\) 0.698568 0.0276566
\(639\) 0 0
\(640\) −2.89714 + 5.01799i −0.114519 + 0.198353i
\(641\) 21.5407 + 37.3096i 0.850806 + 1.47364i 0.880482 + 0.474079i \(0.157219\pi\)
−0.0296762 + 0.999560i \(0.509448\pi\)
\(642\) 0 0
\(643\) 3.20088 + 5.54409i 0.126230 + 0.218638i 0.922213 0.386682i \(-0.126379\pi\)
−0.795983 + 0.605319i \(0.793045\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.851419 −0.0334986
\(647\) −1.94403 + 3.36716i −0.0764278 + 0.132377i −0.901706 0.432349i \(-0.857685\pi\)
0.825278 + 0.564726i \(0.191018\pi\)
\(648\) 0 0
\(649\) −8.70947 15.0852i −0.341877 0.592148i
\(650\) 0.376427 0.651991i 0.0147647 0.0255732i
\(651\) 0 0
\(652\) −12.0939 20.9473i −0.473634 0.820358i
\(653\) 7.55174 13.0800i 0.295522 0.511860i −0.679584 0.733598i \(-0.737840\pi\)
0.975106 + 0.221738i \(0.0711730\pi\)
\(654\) 0 0
\(655\) −5.93150 10.2737i −0.231763 0.401425i
\(656\) 14.6823 + 25.4305i 0.573248 + 0.992895i
\(657\) 0 0
\(658\) 0 0
\(659\) 7.13002 12.3496i 0.277746 0.481070i −0.693078 0.720862i \(-0.743746\pi\)
0.970824 + 0.239792i \(0.0770793\pi\)
\(660\) 0 0
\(661\) 19.4193 0.755323 0.377662 0.925944i \(-0.376728\pi\)
0.377662 + 0.925944i \(0.376728\pi\)
\(662\) −0.0110303 −0.000428706
\(663\) 0 0
\(664\) 0.933832 1.61744i 0.0362397 0.0627690i
\(665\) 0 0
\(666\) 0 0
\(667\) 9.80197 + 16.9775i 0.379534 + 0.657372i
\(668\) 4.78781 + 8.29273i 0.185246 + 0.320855i
\(669\) 0 0
\(670\) −0.302828 + 0.524513i −0.0116993 + 0.0202637i
\(671\) −2.16991 3.75839i −0.0837683 0.145091i
\(672\) 0 0
\(673\) −2.96563 + 5.13663i −0.114317 + 0.198002i −0.917506 0.397721i \(-0.869801\pi\)
0.803190 + 0.595723i \(0.203135\pi\)
\(674\) −0.309512 0.536091i −0.0119220 0.0206494i
\(675\) 0 0
\(676\) 14.5683 25.2330i 0.560318 0.970500i
\(677\) 36.9826 1.42136 0.710678 0.703518i \(-0.248388\pi\)
0.710678 + 0.703518i \(0.248388\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −2.38215 4.12601i −0.0913513 0.158225i
\(681\) 0 0
\(682\) 0.367336 + 0.636244i 0.0140660 + 0.0243630i
\(683\) 6.56800 11.3761i 0.251317 0.435294i −0.712571 0.701600i \(-0.752470\pi\)
0.963889 + 0.266305i \(0.0858029\pi\)
\(684\) 0 0
\(685\) 52.0398 1.98834
\(686\) 0 0
\(687\) 0 0
\(688\) 22.3692 38.7446i 0.852818 1.47712i
\(689\) −46.7516 −1.78109
\(690\) 0 0
\(691\) −14.7658 −0.561719 −0.280860 0.959749i \(-0.590620\pi\)
−0.280860 + 0.959749i \(0.590620\pi\)
\(692\) 10.0399 0.381659
\(693\) 0 0
\(694\) −0.397915 −0.0151046
\(695\) 7.00788 0.265824
\(696\) 0 0
\(697\) −48.4032 −1.83340
\(698\) 0.932003 1.61428i 0.0352768 0.0611012i
\(699\) 0 0
\(700\) 0 0
\(701\) 30.4627 1.15056 0.575281 0.817956i \(-0.304893\pi\)
0.575281 + 0.817956i \(0.304893\pi\)
\(702\) 0 0
\(703\) −4.02217 + 6.96660i −0.151699 + 0.262750i
\(704\) 6.30697 + 10.9240i 0.237703 + 0.411713i
\(705\) 0 0
\(706\) 0.826969 + 1.43235i 0.0311234 + 0.0539073i
\(707\) 0 0
\(708\) 0 0
\(709\) 14.1030 0.529650 0.264825 0.964296i \(-0.414686\pi\)
0.264825 + 0.964296i \(0.414686\pi\)
\(710\) 1.12823 1.95415i 0.0423418 0.0733381i
\(711\) 0 0
\(712\) 0.0642745 + 0.111327i 0.00240879 + 0.00417215i
\(713\) −10.3086 + 17.8549i −0.386058 + 0.668673i
\(714\) 0 0
\(715\) −11.1899 19.3815i −0.418479 0.724827i
\(716\) 16.3596 28.3356i 0.611386 1.05895i
\(717\) 0 0
\(718\) 0.719212 + 1.24571i 0.0268408 + 0.0464896i
\(719\) −7.49790 12.9867i −0.279624 0.484324i 0.691667 0.722217i \(-0.256877\pi\)
−0.971291 + 0.237893i \(0.923543\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.525886 + 0.910861i −0.0195715 + 0.0338987i
\(723\) 0 0
\(724\) 28.8015 1.07040
\(725\) −13.3900 −0.497293
\(726\) 0 0
\(727\) 13.0527 22.6080i 0.484099 0.838485i −0.515734 0.856749i \(-0.672481\pi\)
0.999833 + 0.0182642i \(0.00581399\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0.200223 + 0.346796i 0.00741059 + 0.0128355i
\(731\) 36.8723 + 63.8648i 1.36377 + 2.36212i
\(732\) 0 0
\(733\) 14.1911 24.5796i 0.524159 0.907869i −0.475446 0.879745i \(-0.657713\pi\)
0.999604 0.0281244i \(-0.00895345\pi\)
\(734\) 1.19784 + 2.07473i 0.0442132 + 0.0765796i
\(735\) 0 0
\(736\) 1.25486 2.17348i 0.0462548 0.0801156i
\(737\) 2.65881 + 4.60520i 0.0979386 + 0.169635i
\(738\) 0 0
\(739\) −23.2933 + 40.3451i −0.856857 + 1.48412i 0.0180552 + 0.999837i \(0.494253\pi\)
−0.874912 + 0.484282i \(0.839081\pi\)
\(740\) −22.4806 −0.826403
\(741\) 0 0
\(742\) 0 0
\(743\) 0.169513 + 0.293606i 0.00621884 + 0.0107713i 0.869118 0.494605i \(-0.164687\pi\)
−0.862899 + 0.505376i \(0.831354\pi\)
\(744\) 0 0
\(745\) −11.7377 20.3304i −0.430038 0.744847i
\(746\) 0.0385841 0.0668297i 0.00141267 0.00244681i
\(747\) 0 0
\(748\) −20.8907 −0.763839
\(749\) 0 0
\(750\) 0 0
\(751\) 18.1831 31.4940i 0.663510 1.14923i −0.316177 0.948700i \(-0.602399\pi\)
0.979687 0.200533i \(-0.0642673\pi\)
\(752\) −15.0902 −0.550284
\(753\) 0 0
\(754\) 2.29509 0.0835822
\(755\) 12.4245 0.452174
\(756\) 0 0
\(757\) −27.4703 −0.998424 −0.499212 0.866480i \(-0.666377\pi\)
−0.499212 + 0.866480i \(0.666377\pi\)
\(758\) 1.50162 0.0545415
\(759\) 0 0
\(760\) 1.38401 0.0502033
\(761\) −16.5178 + 28.6097i −0.598771 + 1.03710i 0.394232 + 0.919011i \(0.371011\pi\)
−0.993003 + 0.118091i \(0.962323\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 5.66934 0.205110
\(765\) 0 0
\(766\) 0.787671 1.36429i 0.0284597 0.0492937i
\(767\) −28.6143 49.5614i −1.03320 1.78956i
\(768\) 0 0
\(769\) 1.28876 + 2.23219i 0.0464738 + 0.0804949i 0.888327 0.459212i \(-0.151868\pi\)
−0.841853 + 0.539707i \(0.818535\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −17.6164 −0.634030
\(773\) −3.36486 + 5.82811i −0.121026 + 0.209623i −0.920172 0.391513i \(-0.871952\pi\)
0.799147 + 0.601136i \(0.205285\pi\)
\(774\) 0 0
\(775\) −7.04102 12.1954i −0.252921 0.438072i
\(776\) 0.703765 1.21896i 0.0252637 0.0437580i
\(777\) 0 0
\(778\) −0.539302 0.934099i −0.0193349 0.0334891i
\(779\) 7.03047 12.1771i 0.251893 0.436291i
\(780\) 0 0
\(781\) −9.90581 17.1574i −0.354458 0.613939i
\(782\) 0.686792 + 1.18956i 0.0245596 + 0.0425385i
\(783\) 0 0
\(784\) 0 0
\(785\) 5.42473 9.39590i 0.193617 0.335354i
\(786\) 0 0
\(787\) −28.6683 −1.02191 −0.510956 0.859607i \(-0.670709\pi\)
−0.510956 + 0.859607i \(0.670709\pi\)
\(788\) 11.4203 0.406832
\(789\) 0 0
\(790\) 0.0740881 0.128324i 0.00263594 0.00456558i
\(791\) 0 0
\(792\) 0 0
\(793\) −7.12905 12.3479i −0.253160 0.438486i
\(794\) 0.564275 + 0.977352i 0.0200254 + 0.0346849i
\(795\) 0 0
\(796\)