Properties

Label 1323.2.g.h.667.8
Level $1323$
Weight $2$
Character 1323.667
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.g (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 667.8
Character \(\chi\) \(=\) 1323.667
Dual form 1323.2.g.h.361.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0341870 + 0.0592136i) q^{2} +(0.997662 - 1.72800i) q^{4} +2.66379 q^{5} +0.273176 q^{8} +O(q^{10})\) \(q+(0.0341870 + 0.0592136i) q^{2} +(0.997662 - 1.72800i) q^{4} +2.66379 q^{5} +0.273176 q^{8} +(0.0910670 + 0.157733i) q^{10} +1.59913 q^{11} +(-2.62690 - 4.54992i) q^{13} +(-1.98599 - 3.43983i) q^{16} +(-3.27360 - 5.67005i) q^{17} +(-0.950968 + 1.64713i) q^{19} +(2.65756 - 4.60304i) q^{20} +(0.0546693 + 0.0946900i) q^{22} +3.06837 q^{23} +2.09578 q^{25} +(0.179612 - 0.311096i) q^{26} +(3.19452 - 5.53306i) q^{29} +(-3.35961 + 5.81902i) q^{31} +(0.408966 - 0.708350i) q^{32} +(0.223829 - 0.387684i) q^{34} +(-2.11477 + 3.66290i) q^{37} -0.130043 q^{38} +0.727684 q^{40} +(3.69648 + 6.40249i) q^{41} +(5.63176 - 9.75450i) q^{43} +(1.59539 - 2.76329i) q^{44} +(0.104898 + 0.181689i) q^{46} +(1.89959 + 3.29018i) q^{47} +(0.0716485 + 0.124099i) q^{50} -10.4830 q^{52} +(4.44931 + 7.70643i) q^{53} +4.25974 q^{55} +0.436843 q^{58} +(-5.44639 + 9.43343i) q^{59} +(-1.35693 - 2.35027i) q^{61} -0.459420 q^{62} -7.88802 q^{64} +(-6.99751 - 12.1200i) q^{65} +(1.66267 - 2.87982i) q^{67} -13.0638 q^{68} +12.3890 q^{71} +(-1.09932 - 1.90407i) q^{73} -0.289191 q^{74} +(1.89749 + 3.28655i) q^{76} +(-0.406778 - 0.704560i) q^{79} +(-5.29025 - 9.16298i) q^{80} +(-0.252743 + 0.437764i) q^{82} +(3.41842 - 5.92088i) q^{83} +(-8.72020 - 15.1038i) q^{85} +0.770132 q^{86} +0.436843 q^{88} +(0.235286 - 0.407527i) q^{89} +(3.06120 - 5.30216i) q^{92} +(-0.129882 + 0.224963i) q^{94} +(-2.53318 + 4.38760i) q^{95} +(2.57623 - 4.46216i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 4q^{2} - 12q^{4} + 24q^{8} + O(q^{10}) \) \( 24q - 4q^{2} - 12q^{4} + 24q^{8} + 40q^{11} - 12q^{16} + 64q^{23} + 24q^{25} - 16q^{29} - 48q^{32} - 12q^{37} - 56q^{44} + 24q^{46} + 4q^{50} - 32q^{53} + 96q^{64} - 60q^{65} - 12q^{67} + 112q^{71} + 136q^{74} + 12q^{79} + 12q^{85} + 152q^{86} - 16q^{92} - 64q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0341870 + 0.0592136i 0.0241739 + 0.0418703i 0.877859 0.478919i \(-0.158971\pi\)
−0.853685 + 0.520789i \(0.825638\pi\)
\(3\) 0 0
\(4\) 0.997662 1.72800i 0.498831 0.864001i
\(5\) 2.66379 1.19128 0.595642 0.803250i \(-0.296898\pi\)
0.595642 + 0.803250i \(0.296898\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0.273176 0.0965824
\(9\) 0 0
\(10\) 0.0910670 + 0.157733i 0.0287979 + 0.0498794i
\(11\) 1.59913 0.482155 0.241077 0.970506i \(-0.422499\pi\)
0.241077 + 0.970506i \(0.422499\pi\)
\(12\) 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
\(16\) −1.98599 3.43983i −0.496496 0.859957i
\(17\) −3.27360 5.67005i −0.793966 1.37519i −0.923494 0.383613i \(-0.874680\pi\)
0.129528 0.991576i \(-0.458654\pi\)
\(18\) 0 0
\(19\) −0.950968 + 1.64713i −0.218167 + 0.377877i −0.954248 0.299017i \(-0.903341\pi\)
0.736081 + 0.676894i \(0.236674\pi\)
\(20\) 2.65756 4.60304i 0.594249 1.02927i
\(21\) 0 0
\(22\) 0.0546693 + 0.0946900i 0.0116555 + 0.0201880i
\(23\) 3.06837 0.639800 0.319900 0.947451i \(-0.396351\pi\)
0.319900 + 0.947451i \(0.396351\pi\)
\(24\) 0 0
\(25\) 2.09578 0.419157
\(26\) 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
\(31\) −3.35961 + 5.81902i −0.603405 + 1.04513i 0.388897 + 0.921281i \(0.372856\pi\)
−0.992301 + 0.123846i \(0.960477\pi\)
\(32\) 0.408966 0.708350i 0.0722957 0.125220i
\(33\) 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 −0.985835 0.167721i \(-0.946359\pi\)
0.638168 + 0.769897i \(0.279693\pi\)
\(38\) −0.130043 −0.0210958
\(39\) 0 0
\(40\) 0.727684 0.115057
\(41\) 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
\(47\) 1.89959 + 3.29018i 0.277083 + 0.479922i 0.970659 0.240462i \(-0.0772989\pi\)
−0.693575 + 0.720384i \(0.743966\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.0716485 + 0.124099i 0.0101326 + 0.0175502i
\(51\) 0 0
\(52\) −10.4830 −1.45374
\(53\) 4.44931 + 7.70643i 0.611160 + 1.05856i 0.991045 + 0.133527i \(0.0426301\pi\)
−0.379885 + 0.925034i \(0.624037\pi\)
\(54\) 0 0
\(55\) 4.25974 0.574383
\(56\) 0 0
\(57\) 0 0
\(58\) 0.436843 0.0573604
\(59\) −5.44639 + 9.43343i −0.709060 + 1.22813i 0.256146 + 0.966638i \(0.417547\pi\)
−0.965206 + 0.261490i \(0.915786\pi\)
\(60\) 0 0
\(61\) −1.35693 2.35027i −0.173737 0.300922i 0.765986 0.642857i \(-0.222251\pi\)
−0.939724 + 0.341935i \(0.888918\pi\)
\(62\) −0.459420 −0.0583465
\(63\) 0 0
\(64\) −7.88802 −0.986002
\(65\) −6.99751 12.1200i −0.867935 1.50331i
\(66\) 0 0
\(67\) 1.66267 2.87982i 0.203127 0.351826i −0.746407 0.665489i \(-0.768223\pi\)
0.949534 + 0.313663i \(0.101556\pi\)
\(68\) −13.0638 −1.58422
\(69\) 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 \(-0.207736\pi\)
−0.923160 + 0.384417i \(0.874403\pi\)
\(74\) −0.289191 −0.0336178
\(75\) 0 0
\(76\) 1.89749 + 3.28655i 0.217657 + 0.376993i
\(77\) 0 0
\(78\) 0 0
\(79\) −0.406778 0.704560i −0.0457661 0.0792692i 0.842235 0.539111i \(-0.181240\pi\)
−0.888001 + 0.459841i \(0.847906\pi\)
\(80\) −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
\(86\) 0.770132 0.0830455
\(87\) 0 0
\(88\) 0.436843 0.0465677
\(89\) 0.235286 0.407527i 0.0249403 0.0431978i −0.853286 0.521443i \(-0.825394\pi\)
0.878226 + 0.478246i \(0.158727\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.06120 5.30216i 0.319152 0.552788i
\(93\) 0 0
\(94\) −0.129882 + 0.224963i −0.0133963 + 0.0232031i
\(95\) −2.53318 + 4.38760i −0.259899 + 0.450158i
\(96\) 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
\(101\) 1.84488 0.183572 0.0917862 0.995779i \(-0.470742\pi\)
0.0917862 + 0.995779i \(0.470742\pi\)
\(102\) 0 0
\(103\) 5.17802 0.510206 0.255103 0.966914i \(-0.417891\pi\)
0.255103 + 0.966914i \(0.417891\pi\)
\(104\) −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 0.0869755 + 0.996210i \(0.472280\pi\)
−0.906231 + 0.422782i \(0.861054\pi\)
\(108\) 0 0
\(109\) 4.24996 + 7.36115i 0.407073 + 0.705070i 0.994560 0.104163i \(-0.0332163\pi\)
−0.587488 + 0.809233i \(0.699883\pi\)
\(110\) 0.145628 + 0.252235i 0.0138851 + 0.0240496i
\(111\) 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
\(115\) 8.17351 0.762183
\(116\) −6.37410 11.0403i −0.591820 1.02506i
\(117\) 0 0
\(118\) −0.744783 −0.0685628
\(119\) 0 0
\(120\) 0 0
\(121\) −8.44279 −0.767527
\(122\) 0.0927788 0.160698i 0.00839980 0.0145489i
\(123\) 0 0
\(124\) 6.70352 + 11.6108i 0.601994 + 1.04268i
\(125\) −7.73623 −0.691949
\(126\) 0 0
\(127\) 10.9533 0.971946 0.485973 0.873974i \(-0.338465\pi\)
0.485973 + 0.873974i \(0.338465\pi\)
\(128\) −1.08760 1.88378i −0.0961311 0.166504i
\(129\) 0 0
\(130\) 0.478448 0.828696i 0.0419626 0.0726814i
\(131\) 4.45342 0.389097 0.194549 0.980893i \(-0.437676\pi\)
0.194549 + 0.980893i \(0.437676\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.227366 0.0196414
\(135\) 0 0
\(136\) −0.894271 1.54892i −0.0766831 0.132819i
\(137\) 19.5360 1.66907 0.834537 0.550952i \(-0.185735\pi\)
0.834537 + 0.550952i \(0.185735\pi\)
\(138\) 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
\(142\) 0.423544 + 0.733599i 0.0355430 + 0.0615623i
\(143\) −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
\(149\) 8.81281 0.721973 0.360987 0.932571i \(-0.382440\pi\)
0.360987 + 0.932571i \(0.382440\pi\)
\(150\) 0 0
\(151\) 4.66422 0.379569 0.189784 0.981826i \(-0.439221\pi\)
0.189784 + 0.981826i \(0.439221\pi\)
\(152\) −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
\(157\) 2.03647 3.52727i 0.162528 0.281506i −0.773247 0.634105i \(-0.781369\pi\)
0.935775 + 0.352599i \(0.114702\pi\)
\(158\) 0.0278130 0.0481736i 0.00221269 0.00383249i
\(159\) 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 −0.524838 0.851202i \(-0.675874\pi\)
0.999582 + 0.0289220i \(0.00920745\pi\)
\(164\) 14.7514 1.15189
\(165\) 0 0
\(166\) 0.467462 0.0362821
\(167\) −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
\(173\) 2.51585 + 4.35759i 0.191277 + 0.331301i 0.945674 0.325118i \(-0.105404\pi\)
−0.754397 + 0.656419i \(0.772071\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3.17584 5.50072i −0.239388 0.414632i
\(177\) 0 0
\(178\) 0.0321749 0.00241161
\(179\) −8.19896 14.2010i −0.612819 1.06143i −0.990763 0.135605i \(-0.956702\pi\)
0.377944 0.925828i \(-0.376631\pi\)
\(180\) 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
\(184\) 0.838207 0.0617934
\(185\) −5.63332 + 9.75719i −0.414170 + 0.717363i
\(186\) 0 0
\(187\) −5.23491 9.06713i −0.382814 0.663054i
\(188\) 7.58059 0.552871
\(189\) 0 0
\(190\) −0.346407 −0.0251310
\(191\) 1.42066 + 2.46065i 0.102795 + 0.178046i 0.912835 0.408328i \(-0.133888\pi\)
−0.810040 + 0.586374i \(0.800555\pi\)
\(192\) 0 0
\(193\) −4.41443 + 7.64601i −0.317758 + 0.550372i −0.980020 0.198900i \(-0.936263\pi\)
0.662262 + 0.749272i \(0.269596\pi\)
\(194\) 0.352294 0.0252932
\(195\) 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 \(-0.0340789\pi\)
−0.589679 + 0.807638i \(0.700746\pi\)
\(200\) 0.572518 0.0404832
\(201\) 0 0
\(202\) 0.0630709 + 0.109242i 0.00443765 + 0.00768624i
\(203\) 0 0
\(204\) 0 0
\(205\) 9.84665 + 17.0549i 0.687720 + 1.19117i
\(206\) 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 \(0.570018\pi\)
\(212\) 17.7556 1.21946
\(213\) 0 0
\(214\) −1.15886 −0.0792183
\(215\) 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
\(220\) 4.24978 7.36084i 0.286520 0.496268i
\(221\) −17.1989 + 29.7893i −1.15692 + 2.00385i
\(222\) 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
\(227\) 13.7887 0.915187 0.457593 0.889162i \(-0.348712\pi\)
0.457593 + 0.889162i \(0.348712\pi\)
\(228\) 0 0
\(229\) −26.3943 −1.74418 −0.872092 0.489341i \(-0.837237\pi\)
−0.872092 + 0.489341i \(0.837237\pi\)
\(230\) 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 −0.995343 0.0963989i \(-0.969268\pi\)
0.581155 + 0.813793i \(0.302601\pi\)
\(234\) 0 0
\(235\) 5.06010 + 8.76436i 0.330085 + 0.571724i
\(236\) 10.8673 + 18.8228i 0.707403 + 1.22526i
\(237\) 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
\(241\) 1.17988 0.0760029 0.0380015 0.999278i \(-0.487901\pi\)
0.0380015 + 0.999278i \(0.487901\pi\)
\(242\) −0.288634 0.499928i −0.0185541 0.0321366i
\(243\) 0 0
\(244\) −5.41504 −0.346662
\(245\) 0 0
\(246\) 0 0
\(247\) 9.99240 0.635801
\(248\) −0.917767 + 1.58962i −0.0582783 + 0.100941i
\(249\) 0 0
\(250\) −0.264478 0.458090i −0.0167271 0.0289721i
\(251\) −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
\(254\) 0.374459 + 0.648583i 0.0234957 + 0.0406957i
\(255\) 0 0
\(256\) −7.81365 + 13.5336i −0.488353 + 0.845853i
\(257\) −9.83076 −0.613226 −0.306613 0.951834i \(-0.599196\pi\)
−0.306613 + 0.951834i \(0.599196\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −27.9246 −1.73181
\(261\) 0 0
\(262\) 0.152249 + 0.263703i 0.00940598 + 0.0162916i
\(263\) −11.9322 −0.735774 −0.367887 0.929870i \(-0.619919\pi\)
−0.367887 + 0.929870i \(0.619919\pi\)
\(264\) 0 0
\(265\) 11.8520 + 20.5283i 0.728065 + 1.26105i
\(266\) 0 0
\(267\) 0 0
\(268\) −3.31756 5.74618i −0.202652 0.351004i
\(269\) 14.9824 + 25.9503i 0.913494 + 1.58222i 0.809092 + 0.587682i \(0.199959\pi\)
0.104401 + 0.994535i \(0.466707\pi\)
\(270\) 0 0
\(271\) 3.54825 6.14575i 0.215541 0.373328i −0.737899 0.674911i \(-0.764182\pi\)
0.953440 + 0.301584i \(0.0975152\pi\)
\(272\) −13.0027 + 22.5213i −0.788402 + 1.36555i
\(273\) 0 0
\(274\) 0.667877 + 1.15680i 0.0403479 + 0.0698847i
\(275\) 3.35142 0.202098
\(276\) 0 0
\(277\) −9.82351 −0.590237 −0.295119 0.955461i \(-0.595359\pi\)
−0.295119 + 0.955461i \(0.595359\pi\)
\(278\) 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
\(283\) 1.50798 2.61189i 0.0896399 0.155261i −0.817719 0.575618i \(-0.804762\pi\)
0.907359 + 0.420357i \(0.138095\pi\)
\(284\) 12.3601 21.4083i 0.733435 1.27035i
\(285\) 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
\(290\) 1.16366 0.0683324
\(291\) 0 0
\(292\) −4.38699 −0.256729
\(293\) 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
\(299\) −8.06031 13.9609i −0.466140 0.807378i
\(300\) 0 0
\(301\) 0 0
\(302\) 0.159456 + 0.276185i 0.00917564 + 0.0158927i
\(303\) 0 0
\(304\) 7.55444 0.433277
\(305\) −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
\(310\) −1.22380 −0.0695072
\(311\) 0.895467 1.55100i 0.0507773 0.0879489i −0.839520 0.543329i \(-0.817163\pi\)
0.890297 + 0.455381i \(0.150497\pi\)
\(312\) 0 0
\(313\) −2.30458 3.99166i −0.130263 0.225622i 0.793515 0.608551i \(-0.208249\pi\)
−0.923778 + 0.382929i \(0.874915\pi\)
\(314\) 0.278483 0.0157157
\(315\) 0 0
\(316\) −1.62331 −0.0913183
\(317\) −12.9421 22.4163i −0.726898 1.25902i −0.958188 0.286140i \(-0.907628\pi\)
0.231290 0.972885i \(-0.425705\pi\)
\(318\) 0 0
\(319\) 5.10843 8.84807i 0.286017 0.495397i
\(320\) −21.0120 −1.17461
\(321\) 0 0
\(322\) 0 0
\(323\) 12.4524 0.692869
\(324\) 0 0
\(325\) −5.50541 9.53566i −0.305385 0.528943i
\(326\) 0.828846 0.0459055
\(327\) 0 0
\(328\) 1.00979 + 1.74901i 0.0557563 + 0.0965728i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.0806617 0.139710i −0.00443357 0.00767917i 0.863800 0.503835i \(-0.168078\pi\)
−0.868234 + 0.496156i \(0.834745\pi\)
\(332\) −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 \(0.754024\pi\)
\(338\) −0.998425 −0.0543072
\(339\) 0 0
\(340\) −34.7993 −1.88725
\(341\) −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
\(346\) −0.172019 + 0.297945i −0.00924779 + 0.0160176i
\(347\) −2.90984 + 5.03999i −0.156208 + 0.270561i −0.933498 0.358582i \(-0.883260\pi\)
0.777290 + 0.629142i \(0.216594\pi\)
\(348\) 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
\(353\) 24.1896 1.28748 0.643741 0.765244i \(-0.277382\pi\)
0.643741 + 0.765244i \(0.277382\pi\)
\(354\) 0 0
\(355\) 33.0018 1.75155
\(356\) −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 0.442730 + 0.896655i \(0.354010\pi\)
−0.997891 + 0.0649124i \(0.979323\pi\)
\(360\) 0 0
\(361\) 7.69132 + 13.3218i 0.404806 + 0.701145i
\(362\) −0.493472 0.854719i −0.0259363 0.0449230i
\(363\) 0 0
\(364\) 0 0
\(365\) −2.92835 5.07205i −0.153277 0.265483i
\(366\) 0 0
\(367\) 35.0380 1.82897 0.914485 0.404620i \(-0.132596\pi\)
0.914485 + 0.404620i \(0.132596\pi\)
\(368\) −6.09375 10.5547i −0.317659 0.550201i
\(369\) 0 0
\(370\) −0.770345 −0.0400483
\(371\) 0 0
\(372\) 0 0
\(373\) 1.12862 0.0584377 0.0292189 0.999573i \(-0.490698\pi\)
0.0292189 + 0.999573i \(0.490698\pi\)
\(374\) 0.357931 0.619955i 0.0185082 0.0320571i
\(375\) 0 0
\(376\) 0.518922 + 0.898800i 0.0267614 + 0.0463521i
\(377\) −33.5667 −1.72877
\(378\) 0 0
\(379\) −21.9619 −1.12811 −0.564054 0.825738i \(-0.690759\pi\)
−0.564054 + 0.825738i \(0.690759\pi\)
\(380\) 5.05452 + 8.75468i 0.259291 + 0.449106i
\(381\) 0 0
\(382\) −0.0971359 + 0.168244i −0.00496991 + 0.00860813i
\(383\) 23.0401 1.17729 0.588647 0.808390i \(-0.299661\pi\)
0.588647 + 0.808390i \(0.299661\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.603664 −0.0307257
\(387\) 0 0
\(388\) −5.14042 8.90346i −0.260965 0.452005i
\(389\) −15.7751 −0.799828 −0.399914 0.916553i \(-0.630960\pi\)
−0.399914 + 0.916553i \(0.630960\pi\)
\(390\) 0 0
\(391\) −10.0446 17.3978i −0.507979 0.879846i
\(392\) 0 0
\(393\) 0 0
\(394\) −0.195671 0.338912i −0.00985774 0.0170741i
\(395\) −1.08357 1.87680i −0.0545204 0.0944321i
\(396\) 0 0
\(397\) −8.25277 + 14.2942i −0.414195 + 0.717406i −0.995344 0.0963911i \(-0.969270\pi\)
0.581149 + 0.813797i \(0.302603\pi\)
\(398\) −0.390246 + 0.675926i −0.0195613 + 0.0338811i
\(399\) 0 0
\(400\) −4.16220 7.20914i −0.208110 0.360457i
\(401\) −21.6600 −1.08165 −0.540823 0.841136i \(-0.681887\pi\)
−0.540823 + 0.841136i \(0.681887\pi\)
\(402\) 0 0
\(403\) 35.3015 1.75849
\(404\) 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
\(409\) 15.2860 26.4762i 0.755846 1.30916i −0.189107 0.981956i \(-0.560559\pi\)
0.944953 0.327207i \(-0.106107\pi\)
\(410\) −0.673255 + 1.16611i −0.0332497 + 0.0575901i
\(411\) 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
\(416\) −4.29725 −0.210690
\(417\) 0 0
\(418\) −0.207955 −0.0101714
\(419\) −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
\(425\) −6.86077 11.8832i −0.332796 0.576420i
\(426\) 0 0
\(427\) 0 0
\(428\) 16.9093 + 29.2877i 0.817341 + 1.41568i
\(429\) 0 0
\(430\) 2.05147 0.0989307
\(431\) 4.09843 + 7.09869i 0.197415 + 0.341932i 0.947689 0.319194i \(-0.103412\pi\)
−0.750275 + 0.661126i \(0.770079\pi\)
\(432\) 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
\(436\) 16.9601 0.812242
\(437\) −2.91793 + 5.05400i −0.139583 + 0.241765i
\(438\) 0 0
\(439\) −3.29416 5.70564i −0.157221 0.272316i 0.776644 0.629939i \(-0.216920\pi\)
−0.933866 + 0.357624i \(0.883587\pi\)
\(440\) 1.16366 0.0554753
\(441\) 0 0
\(442\) −2.35191 −0.111869
\(443\) 14.3456 + 24.8473i 0.681581 + 1.18053i 0.974498 + 0.224395i \(0.0720407\pi\)
−0.292917 + 0.956138i \(0.594626\pi\)
\(444\) 0 0
\(445\) 0.626752 1.08557i 0.0297109 0.0514608i
\(446\) −0.490087 −0.0232063
\(447\) 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
\(452\) 7.78958 0.366391
\(453\) 0 0
\(454\) 0.471393 + 0.816477i 0.0221236 + 0.0383192i
\(455\) 0 0
\(456\) 0 0
\(457\) −10.1105 17.5119i −0.472950 0.819173i 0.526571 0.850131i \(-0.323477\pi\)
−0.999521 + 0.0309581i \(0.990144\pi\)
\(458\) −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 \(0.797720\pi\)
\(464\) −25.3770 −1.17810
\(465\) 0 0
\(466\) −0.864561 −0.0400500
\(467\) −13.6228 + 23.5954i −0.630389 + 1.09187i 0.357083 + 0.934073i \(0.383771\pi\)
−0.987472 + 0.157793i \(0.949562\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −0.345979 + 0.599254i −0.0159588 + 0.0276415i
\(471\) 0 0
\(472\) −1.48783 + 2.57699i −0.0684827 + 0.118616i
\(473\) 9.00590 15.5987i 0.414092 0.717228i
\(474\) 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
\(479\) −20.5255 −0.937834 −0.468917 0.883242i \(-0.655356\pi\)
−0.468917 + 0.883242i \(0.655356\pi\)
\(480\) 0 0
\(481\) 22.2212 1.01320
\(482\) 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 −0.994804 0.101809i \(-0.967537\pi\)
0.409233 0.912430i \(-0.365796\pi\)
\(488\) −0.370682 0.642039i −0.0167800 0.0290638i
\(489\) 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
\(493\) −41.8303 −1.88394
\(494\) 0.341610 + 0.591686i 0.0153698 + 0.0266212i
\(495\) 0 0
\(496\) 26.6886 1.19835
\(497\) 0 0
\(498\) 0 0
\(499\) 21.2690 0.952133 0.476066 0.879409i \(-0.342062\pi\)
0.476066 + 0.879409i \(0.342062\pi\)
\(500\) −7.71814 + 13.3682i −0.345166 + 0.597845i
\(501\) 0 0
\(502\) −0.189728 0.328618i −0.00846795 0.0146669i
\(503\) 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
\(506\) 0.167746 + 0.290544i 0.00745722 + 0.0129163i
\(507\) 0 0
\(508\) 10.9277 18.9273i 0.484837 0.839762i
\(509\) 13.4618 0.596683 0.298342 0.954459i \(-0.403567\pi\)
0.298342 + 0.954459i \(0.403567\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −5.41890 −0.239484
\(513\) 0 0
\(514\) −0.336084 0.582115i −0.0148240 0.0256760i
\(515\) 13.7932 0.607800
\(516\) 0 0
\(517\) 3.03768 + 5.26142i 0.133597 + 0.231397i
\(518\) 0 0
\(519\) 0 0
\(520\) −1.91155 3.31091i −0.0838272 0.145193i
\(521\) −0.713095 1.23512i −0.0312413 0.0541115i 0.849982 0.526812i \(-0.176613\pi\)
−0.881223 + 0.472700i \(0.843279\pi\)
\(522\) 0 0
\(523\) 3.85530 6.67758i 0.168581 0.291990i −0.769340 0.638839i \(-0.779415\pi\)
0.937921 + 0.346849i \(0.112748\pi\)
\(524\) 4.44301 7.69553i 0.194094 0.336181i
\(525\) 0 0
\(526\) −0.407928 0.706551i −0.0177865 0.0308071i
\(527\) 43.9922 1.91633
\(528\) 0 0
\(529\) −13.5851 −0.590656
\(530\) −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
\(535\) −22.5742 + 39.0996i −0.975966 + 1.69042i
\(536\) 0.454201 0.786699i 0.0196185 0.0339802i
\(537\) 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 0.389495 + 0.921028i \(0.372649\pi\)
−0.992382 + 0.123201i \(0.960684\pi\)
\(542\) 0.485216 0.0208418
\(543\) 0 0
\(544\) −5.35517 −0.229601
\(545\) 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
\(551\) 6.07577 + 10.5235i 0.258836 + 0.448318i
\(552\) 0 0
\(553\) 0 0
\(554\) −0.335836 0.581685i −0.0142683 0.0247134i
\(555\) 0 0
\(556\) −5.24928 −0.222619
\(557\) 17.5209 + 30.3472i 0.742386 + 1.28585i 0.951406 + 0.307940i \(0.0996395\pi\)
−0.209019 + 0.977911i \(0.567027\pi\)
\(558\) 0 0
\(559\) −59.1763 −2.50289
\(560\) 0 0
\(561\) 0 0
\(562\) −1.63262 −0.0688677
\(563\) 8.01311 13.8791i 0.337712 0.584935i −0.646290 0.763092i \(-0.723680\pi\)
0.984002 + 0.178157i \(0.0570135\pi\)
\(564\) 0 0
\(565\) 5.19961 + 9.00599i 0.218749 + 0.378885i
\(566\) 0.206213 0.00866776
\(567\) 0 0
\(568\) 3.38439 0.142006
\(569\) 0.185651 + 0.321557i 0.00778290 + 0.0134804i 0.869891 0.493245i \(-0.164189\pi\)
−0.862108 + 0.506725i \(0.830856\pi\)
\(570\) 0 0
\(571\) −14.6152 + 25.3142i −0.611626 + 1.05937i 0.379340 + 0.925257i \(0.376151\pi\)
−0.990966 + 0.134110i \(0.957182\pi\)
\(572\) −16.7637 −0.700926
\(573\) 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 \(-0.0651930\pi\)
−0.665683 + 0.746235i \(0.731860\pi\)
\(578\) −1.76856 −0.0735623
\(579\) 0 0
\(580\) −16.9793 29.4089i −0.705025 1.22114i
\(581\) 0 0
\(582\) 0 0
\(583\) 7.11501 + 12.3236i 0.294674 + 0.510390i
\(584\) −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
\(590\) −1.98395 −0.0816778
\(591\) 0 0
\(592\) 16.7996 0.690461
\(593\) −5.40871 + 9.36816i −0.222109 + 0.384704i −0.955448 0.295159i \(-0.904627\pi\)
0.733339 + 0.679863i \(0.237961\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 8.79221 15.2286i 0.360143 0.623786i
\(597\) 0 0
\(598\) 0.551116 0.954560i 0.0225368 0.0390349i
\(599\) 8.32007 14.4108i 0.339949 0.588809i −0.644474 0.764626i \(-0.722924\pi\)
0.984423 + 0.175817i \(0.0562568\pi\)
\(600\) 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
\(605\) −22.4898 −0.914342
\(606\) 0 0
\(607\) −37.8049 −1.53445 −0.767227 0.641376i \(-0.778364\pi\)
−0.767227 + 0.641376i \(0.778364\pi\)
\(608\) 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 0.966670 0.256025i \(-0.0824129\pi\)
−0.705059 + 0.709149i \(0.749080\pi\)
\(614\) 0.793745 + 1.37481i 0.0320330 + 0.0554827i
\(615\) 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
\(619\) −33.1974 −1.33431 −0.667157 0.744917i \(-0.732489\pi\)
−0.667157 + 0.744917i \(0.732489\pi\)
\(620\) 17.8568 + 30.9289i 0.717146 + 1.24213i
\(621\) 0 0
\(622\) 0.122453 0.00490993
\(623\) 0 0
\(624\) 0 0
\(625\) −31.0866 −1.24346
\(626\) 0.157574 0.272925i 0.00629791 0.0109083i
\(627\) 0 0
\(628\) −4.06342 7.03804i −0.162148 0.280848i
\(629\) 27.6917 1.10414
\(630\) 0 0
\(631\) 32.2773 1.28494 0.642470 0.766311i \(-0.277910\pi\)
0.642470 + 0.766311i \(0.277910\pi\)
\(632\) −0.111122 0.192469i −0.00442020 0.00765601i
\(633\) 0 0
\(634\) 0.884900 1.53269i 0.0351439 0.0608709i
\(635\) 29.1772 1.15786
\(636\) 0 0
\(637\) 0 0
\(638\) 0.698568 0.0276566
\(639\) 0 0
\(640\) −2.89714 5.01799i −0.114519 0.198353i
\(641\) −43.0814 −1.70161 −0.850806 0.525480i \(-0.823886\pi\)
−0.850806 + 0.525480i \(0.823886\pi\)
\(642\) 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
\(646\) 0.425709 + 0.737350i 0.0167493 + 0.0290107i
\(647\) −1.94403 3.36716i −0.0764278 0.132377i 0.825278 0.564726i \(-0.191018\pi\)
−0.901706 + 0.432349i \(0.857685\pi\)
\(648\) 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
\(653\) −15.1035 −0.591044 −0.295522 0.955336i \(-0.595494\pi\)
−0.295522 + 0.955336i \(0.595494\pi\)
\(654\) 0 0
\(655\) 11.8630 0.463525
\(656\) 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
\(661\) −9.70965 + 16.8176i −0.377662 + 0.654129i −0.990722 0.135907i \(-0.956605\pi\)
0.613060 + 0.790036i \(0.289938\pi\)
\(662\) 0.00551516 0.00955254i 0.000214353 0.000371270i
\(663\) 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
\(668\) −9.57561 −0.370492
\(669\) 0 0
\(670\) 0.605656 0.0233985
\(671\) −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
\(677\) −18.4913 32.0278i −0.710678 1.23093i −0.964603 0.263706i \(-0.915055\pi\)
0.253925 0.967224i \(-0.418278\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −2.38215 4.12601i −0.0913513 0.158225i
\(681\) 0 0
\(682\) −0.734671 −0.0281320
\(683\) 6.56800 + 11.3761i 0.251317 + 0.435294i 0.963889 0.266305i \(-0.0858029\pi\)
−0.712571 + 0.701600i \(0.752470\pi\)
\(684\) 0 0
\(685\) 52.0398 1.98834
\(686\) 0 0
\(687\) 0 0
\(688\) −44.7384 −1.70564
\(689\) 23.3758 40.4881i 0.890547 1.54247i
\(690\) 0 0
\(691\) 7.38292 + 12.7876i 0.280860 + 0.486463i 0.971597 0.236643i \(-0.0760472\pi\)
−0.690737 + 0.723106i \(0.742714\pi\)
\(692\) 10.0399 0.381659
\(693\) 0 0
\(694\) −0.397915 −0.0151046
\(695\) −3.50394 6.06900i −0.132912 0.230210i
\(696\) 0 0
\(697\) 24.2016 41.9184i 0.916702 1.58777i
\(698\) −1.86401 −0.0705536
\(699\) 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
\(704\) −12.6139 −0.475406
\(705\) 0 0
\(706\) 0.826969 + 1.43235i 0.0311234 + 0.0539073i
\(707\) 0 0
\(708\) 0 0
\(709\) −7.05152 12.2136i −0.264825 0.458691i 0.702693 0.711494i \(-0.251981\pi\)
−0.967518 + 0.252803i \(0.918648\pi\)
\(710\) 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
\(716\) −32.7192 −1.22277
\(717\) 0 0
\(718\) −1.43842 −0.0536815
\(719\) −7.49790 + 12.9867i −0.279624 + 0.484324i −0.971291 0.237893i \(-0.923543\pi\)
0.691667 + 0.722217i \(0.256877\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.525886 + 0.910861i −0.0195715 + 0.0338987i
\(723\) 0 0
\(724\) −14.4008 + 24.9429i −0.535200 + 0.926994i
\(725\) 6.69501 11.5961i 0.248646 0.430668i
\(726\) 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
\(731\) −73.7447 −2.72754
\(732\) 0 0
\(733\) −28.3821 −1.04832 −0.524159 0.851621i \(-0.675620\pi\)
−0.524159 + 0.851621i \(0.675620\pi\)
\(734\) 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 −0.874912 0.484282i \(-0.839081\pi\)
0.0180552 0.999837i \(-0.494253\pi\)
\(740\) 11.2403 + 19.4688i 0.413202 + 0.715686i
\(741\) 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
\(745\) 23.4755 0.860075
\(746\) 0.0385841 + 0.0668297i 0.00141267 + 0.00244681i
\(747\) 0 0
\(748\) −20.8907 −0.763839
\(749\) 0 0
\(750\) 0 0
\(751\) −36.3662 −1.32702 −0.663510 0.748168i \(-0.730934\pi\)
−0.663510 + 0.748168i \(0.730934\pi\)
\(752\) 7.54511 13.0685i 0.275142 0.476560i
\(753\) 0 0
\(754\) −1.14754 1.98760i −0.0417911 0.0723843i
\(755\) 12.4245 0.452174
\(756\) 0 0
\(757\) −27.4703 −0.998424 −0.499212 0.866480i \(-0.666377\pi\)
−0.499212 + 0.866480i \(0.666377\pi\)
\(758\) −0.750812 1.30044i −0.0272707 0.0472343i
\(759\) 0 0
\(760\) −0.692005 + 1.19859i −0.0251017 + 0.0434773i
\(761\) 33.0357 1.19754 0.598771 0.800920i \(-0.295656\pi\)
0.598771 + 0.800920i \(0.295656\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 5.66934 0.205110
\(765\) 0 0
\(766\) 0.787671 + 1.36429i 0.0284597 + 0.0492937i
\(767\) 57.2285 2.06640
\(768\) 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
\(772\) 8.80822 + 15.2563i 0.317015 + 0.549086i
\(773\) −3.36486 5.82811i −0.121026 0.209623i 0.799147 0.601136i \(-0.205285\pi\)
−0.920172 + 0.391513i \(0.871952\pi\)
\(774\) 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
\(779\) −14.0609 −0.503785
\(780\) 0 0
\(781\) 19.8116 0.708916
\(782\) 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
\(787\) 14.3341 24.8274i 0.510956 0.885003i −0.488963 0.872305i \(-0.662625\pi\)
0.999919 0.0126980i \(-0.00404201\pi\)
\(788\) −5.71016 + 9.89029i −0.203416 + 0.352327i
\(789\) 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
\(794\) −1.12855 −0.0400507
\(795\) 0 0
\(796\) 22.7767 0.807300