Properties

Label 1323.2.h.h.802.5
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 802.5
Character \(\chi\) \(=\) 1323.802
Dual form 1323.2.h.h.226.5

$q$-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 \(-0.630231\pi\)
0.993456 0.114216i \(-0.0364355\pi\)
\(6\) 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 \(0.0931485\pi\)
−0.228916 + 0.973446i \(0.573518\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 3.97197 0.992993
\(17\) 3.27360 5.67005i 0.793966 1.37519i −0.129528 0.991576i \(-0.541346\pi\)
0.923494 0.383613i \(-0.125320\pi\)
\(18\) 0 0
\(19\) 0.950968 + 1.64713i 0.218167 + 0.377877i 0.954248 0.299017i \(-0.0966589\pi\)
−0.736081 + 0.676894i \(0.763326\pi\)
\(20\) −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 \(-0.706190\pi\)
−0.603405 + 0.797435i \(0.706190\pi\)
\(32\) −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 \(-0.970776\pi\)
0.418495 0.908219i \(-0.362558\pi\)
\(42\) 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 \(-0.410632\pi\)
0.277083 + 0.960846i \(0.410632\pi\)
\(48\) 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 \(-0.750880\pi\)
−0.709060 + 0.705148i \(0.750880\pi\)
\(60\) 0 0
\(61\) −2.71386 −0.347475 −0.173737 0.984792i \(-0.555584\pi\)
−0.173737 + 0.984792i \(0.555584\pi\)
\(62\) 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 −0.794494 0.607271i \(-0.792264\pi\)
0.923160 + 0.384417i \(0.125597\pi\)
\(74\) 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 −0.990360 0.138517i \(-0.955766\pi\)
0.615140 + 0.788418i \(0.289100\pi\)
\(84\) 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 0.853286 0.521443i \(-0.174606\pi\)
−0.878226 + 0.478246i \(0.841273\pi\)
\(90\) 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 −0.966661 0.256059i \(-0.917576\pi\)
0.705085 + 0.709123i \(0.250909\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.09088 + 3.62152i 0.209088 + 0.362152i
\(101\) 0.922440 + 1.59771i 0.0917862 + 0.158978i 0.908263 0.418400i \(-0.137409\pi\)
−0.816477 + 0.577379i \(0.804076\pi\)
\(102\) 0 0
\(103\) 2.58901 4.48430i 0.255103 0.441851i −0.709821 0.704383i \(-0.751224\pi\)
0.964923 + 0.262531i \(0.0845573\pi\)
\(104\) 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 −0.752204 0.658931i \(-0.771009\pi\)
0.946752 + 0.321962i \(0.104342\pi\)
\(132\) 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 0.916404 0.400256i \(-0.131079\pi\)
−0.804833 + 0.593501i \(0.797745\pi\)
\(140\) 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 \(-0.448035\pi\)
0.162528 + 0.986704i \(0.448035\pi\)
\(158\) −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 0.943805 0.330502i \(-0.107218\pi\)
−0.758126 + 0.652109i \(0.773885\pi\)
\(168\) 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 \(-0.438737\pi\)
0.191277 + 0.981536i \(0.438737\pi\)
\(174\) 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 \(-0.319763\pi\)
0.536454 + 0.843930i \(0.319763\pi\)
\(182\) 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 −0.994274 0.106858i \(-0.965921\pi\)
0.589679 + 0.807638i \(0.299254\pi\)
\(200\) −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 −0.720719 0.693228i \(-0.756188\pi\)
0.960712 + 0.277547i \(0.0895213\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −0.133463 0.231165i −0.00887784 0.0153769i
\(227\) 6.89434 + 11.9413i 0.457593 + 0.792575i 0.998833 0.0482933i \(-0.0153782\pi\)
−0.541240 + 0.840868i \(0.682045\pi\)
\(228\) 0 0
\(229\) −13.1972 + 22.8581i −0.872092 + 1.51051i −0.0122645 + 0.999925i \(0.503904\pi\)
−0.859828 + 0.510584i \(0.829429\pi\)
\(230\) −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 0.884401 0.466729i \(-0.154568\pi\)
−0.846399 + 0.532549i \(0.821234\pi\)
\(242\) −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 \(-0.443960\pi\)
0.175147 + 0.984542i \(0.443960\pi\)
\(252\) 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 −0.977619 0.210382i \(-0.932529\pi\)
0.671006 + 0.741452i \(0.265862\pi\)
\(258\) 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 \(0.533293\pi\)
−0.809092 + 0.587682i \(0.800041\pi\)
\(270\) 0 0
\(271\) −3.54825 6.14575i −0.215541 0.373328i 0.737899 0.674911i \(-0.235818\pi\)
−0.953440 + 0.301584i \(0.902485\pi\)
\(272\) 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 \(-0.471428\pi\)
0.0896399 + 0.995974i \(0.471428\pi\)
\(284\) −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 0.501721 0.865030i \(-0.332700\pi\)
−0.999998 + 0.00198814i \(0.999367\pi\)
\(294\) 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 \(-0.730527\pi\)
−0.662554 + 0.749014i \(0.730527\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.611900 1.05984i 0.0347536 0.0601950i
\(311\) 1.79093 0.101555 0.0507773 0.998710i \(-0.483830\pi\)
0.0507773 + 0.998710i \(0.483830\pi\)
\(312\) 0 0
\(313\) −4.60917 −0.260526 −0.130263 0.991480i \(-0.541582\pi\)
−0.130263 + 0.991480i \(0.541582\pi\)
\(314\) −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 \(-0.573017\pi\)
0.957032 0.289983i \(-0.0936496\pi\)
\(350\) 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 \(0.0559517\pi\)
−0.340850 + 0.940118i \(0.610715\pi\)
\(354\) 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 \(0.200737\pi\)
0.106831 + 0.994277i \(0.465930\pi\)
\(368\) −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 \(-0.632994\pi\)
0.994410 0.105588i \(-0.0336724\pi\)
\(384\) 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 0.995344 0.0963911i \(-0.0307300\pi\)
−0.581149 + 0.813797i \(0.697397\pi\)
\(398\) 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 \(-0.227226\pi\)
0.755846 + 0.654750i \(0.227226\pi\)
\(410\) 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 \(0.0103954\pi\)
−0.471456 + 0.881890i \(0.656271\pi\)
\(420\) 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 \(-0.526147\pi\)
−0.0820494 + 0.996628i \(0.526147\pi\)
\(434\) 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 \(-0.550254\pi\)
−0.157221 + 0.987563i \(0.550254\pi\)
\(440\) −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 \(0.357297\pi\)
−0.997168 + 0.0752117i \(0.976037\pi\)
\(462\) 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 \(0.0504379\pi\)
−0.357083 + 0.934073i \(0.616229\pi\)
\(468\) 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 0.530452 0.847715i \(-0.322022\pi\)
−0.999369 + 0.0355269i \(0.988689\pi\)
\(480\) 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 \(-0.618608\pi\)
−0.364055 + 0.931377i \(0.618608\pi\)
\(504\) 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 −0.677415 0.735601i \(-0.736900\pi\)
0.975757 + 0.218858i \(0.0702332\pi\)
\(510\) 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 −0.849982 0.526812i \(-0.823387\pi\)
0.881223 + 0.472700i \(0.156721\pi\)
\(522\) 0 0
\(523\) −3.85530 6.67758i −0.168581 0.291990i 0.769340 0.638839i \(-0.220585\pi\)
−0.937921 + 0.346849i \(0.887252\pi\)
\(524\) −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 \(-0.390347\pi\)
0.337712 + 0.941249i \(0.390347\pi\)
\(564\) 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 −0.979100 0.203381i \(-0.934807\pi\)
0.665683 + 0.746235i \(0.268140\pi\)
\(578\) 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 −0.882760 0.469823i \(-0.844318\pi\)
0.848259 + 0.529581i \(0.177651\pi\)
\(588\) 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 0.955448 0.295159i \(-0.0953726\pi\)
−0.733339 + 0.679863i \(0.762039\pi\)
\(594\) 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 \(0.343068\pi\)
−0.999532 + 0.0305765i \(0.990266\pi\)
\(602\) 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 \(0.445031\pi\)
−0.939061 + 0.343750i \(0.888303\pi\)
\(608\) −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 \(-0.934178\pi\)
0.311538 0.950234i \(-0.399156\pi\)
\(620\) 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 0.795983 0.605319i \(-0.206955\pi\)
−0.922213 + 0.386682i \(0.873621\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.851419 −0.0334986
\(647\) 1.94403 3.36716i 0.0764278 0.132377i −0.825278 0.564726i \(-0.808982\pi\)
0.901706 + 0.432349i \(0.142315\pi\)
\(648\) 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 \(-0.623272\pi\)
−0.377662 + 0.925944i \(0.623272\pi\)
\(662\) −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 \(-0.751612\pi\)
−0.710678 + 0.703518i \(0.751612\pi\)
\(678\) 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 \(-0.409380\pi\)
0.280860 + 0.959749i \(0.409380\pi\)
\(692\) −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 0.971291 0.237893i \(-0.0764567\pi\)
−0.691667 + 0.722217i \(0.743123\pi\)
\(720\) 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 −0.999833 0.0182642i \(-0.994186\pi\)
0.515734 + 0.856749i \(0.327519\pi\)
\(728\) 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 \(0.342287\pi\)
−0.999604 + 0.0281244i \(0.991047\pi\)
\(734\) −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 \(-0.628989\pi\)
0.993003 0.118091i \(-0.0376774\pi\)
\(762\) 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 0.841853 0.539707i \(-0.181465\pi\)
−0.888327 + 0.459212i \(0.848132\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −17.6164 −0.634030
\(773\) 3.36486 5.82811i 0.121026 0.209623i −0.799147 0.601136i \(-0.794715\pi\)
0.920172 + 0.391513i \(0.128048\pi\)
\(774\) 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 \(-0.329291\pi\)
0.510956 + 0.859607i \(0.329291\pi\)
\(788\) 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