Properties

Label 429.2.b.b.298.4
Level $429$
Weight $2$
Character 429.298
Analytic conductor $3.426$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} + \cdots)\)
Defining polynomial: \(x^{14} + 23 x^{12} + 201 x^{10} + 835 x^{8} + 1695 x^{6} + 1565 x^{4} + 511 x^{2} + 49\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 298.4
Root \(-1.42819i\) of defining polynomial
Character \(\chi\) \(=\) 429.298
Dual form 429.2.b.b.298.11

$q$-expansion

\(f(q)\) \(=\) \(q-1.42819i q^{2} +1.00000 q^{3} -0.0397381 q^{4} -0.0606573i q^{5} -1.42819i q^{6} -1.70646i q^{7} -2.79963i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.42819i q^{2} +1.00000 q^{3} -0.0397381 q^{4} -0.0606573i q^{5} -1.42819i q^{6} -1.70646i q^{7} -2.79963i q^{8} +1.00000 q^{9} -0.0866304 q^{10} +1.00000i q^{11} -0.0397381 q^{12} +(3.52912 + 0.738445i) q^{13} -2.43715 q^{14} -0.0606573i q^{15} -4.07790 q^{16} -3.75599 q^{17} -1.42819i q^{18} -2.02597i q^{19} +0.00241041i q^{20} -1.70646i q^{21} +1.42819 q^{22} -0.704722 q^{23} -2.79963i q^{24} +4.99632 q^{25} +(1.05464 - 5.04027i) q^{26} +1.00000 q^{27} +0.0678114i q^{28} -0.0346842 q^{29} -0.0866304 q^{30} -1.85987i q^{31} +0.224760i q^{32} +1.00000i q^{33} +5.36429i q^{34} -0.103509 q^{35} -0.0397381 q^{36} +8.82674i q^{37} -2.89348 q^{38} +(3.52912 + 0.738445i) q^{39} -0.169818 q^{40} -3.32960i q^{41} -2.43715 q^{42} -5.29022 q^{43} -0.0397381i q^{44} -0.0606573i q^{45} +1.00648i q^{46} +6.04622i q^{47} -4.07790 q^{48} +4.08800 q^{49} -7.13572i q^{50} -3.75599 q^{51} +(-0.140241 - 0.0293444i) q^{52} -10.6694 q^{53} -1.42819i q^{54} +0.0606573 q^{55} -4.77746 q^{56} -2.02597i q^{57} +0.0495358i q^{58} +3.34547i q^{59} +0.00241041i q^{60} +3.26757 q^{61} -2.65625 q^{62} -1.70646i q^{63} -7.83479 q^{64} +(0.0447920 - 0.214067i) q^{65} +1.42819 q^{66} +10.9701i q^{67} +0.149256 q^{68} -0.704722 q^{69} +0.147831i q^{70} -1.96928i q^{71} -2.79963i q^{72} +15.3057i q^{73} +12.6063 q^{74} +4.99632 q^{75} +0.0805084i q^{76} +1.70646 q^{77} +(1.05464 - 5.04027i) q^{78} +10.5938 q^{79} +0.247354i q^{80} +1.00000 q^{81} -4.75532 q^{82} -4.19820i q^{83} +0.0678114i q^{84} +0.227828i q^{85} +7.55546i q^{86} -0.0346842 q^{87} +2.79963 q^{88} +14.3643i q^{89} -0.0866304 q^{90} +(1.26012 - 6.02229i) q^{91} +0.0280043 q^{92} -1.85987i q^{93} +8.63517 q^{94} -0.122890 q^{95} +0.224760i q^{96} -5.86228i q^{97} -5.83846i q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 14q^{3} - 18q^{4} + 14q^{9} + O(q^{10}) \) \( 14q + 14q^{3} - 18q^{4} + 14q^{9} - 18q^{12} + 16q^{14} + 34q^{16} + 4q^{17} + 6q^{22} - 8q^{23} - 26q^{25} - 6q^{26} + 14q^{27} - 24q^{29} - 8q^{35} - 18q^{36} - 32q^{38} - 20q^{40} + 16q^{42} + 32q^{43} + 34q^{48} - 46q^{49} + 4q^{51} + 4q^{52} + 20q^{53} + 12q^{55} - 32q^{56} - 20q^{61} + 72q^{62} - 58q^{64} + 12q^{65} + 6q^{66} - 20q^{68} - 8q^{69} - 26q^{75} - 12q^{77} - 6q^{78} + 12q^{79} + 14q^{81} + 20q^{82} - 24q^{87} - 30q^{88} + 16q^{91} - 24q^{92} + 64q^{94} - 36q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.42819i 1.00989i −0.863153 0.504943i \(-0.831514\pi\)
0.863153 0.504943i \(-0.168486\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.0397381 −0.0198691
\(5\) 0.0606573i 0.0271268i −0.999908 0.0135634i \(-0.995683\pi\)
0.999908 0.0135634i \(-0.00431749\pi\)
\(6\) 1.42819i 0.583058i
\(7\) 1.70646i 0.644980i −0.946573 0.322490i \(-0.895480\pi\)
0.946573 0.322490i \(-0.104520\pi\)
\(8\) 2.79963i 0.989820i
\(9\) 1.00000 0.333333
\(10\) −0.0866304 −0.0273949
\(11\) 1.00000i 0.301511i
\(12\) −0.0397381 −0.0114714
\(13\) 3.52912 + 0.738445i 0.978802 + 0.204808i
\(14\) −2.43715 −0.651356
\(15\) 0.0606573i 0.0156616i
\(16\) −4.07790 −1.01947
\(17\) −3.75599 −0.910962 −0.455481 0.890246i \(-0.650533\pi\)
−0.455481 + 0.890246i \(0.650533\pi\)
\(18\) 1.42819i 0.336629i
\(19\) 2.02597i 0.464790i −0.972621 0.232395i \(-0.925344\pi\)
0.972621 0.232395i \(-0.0746562\pi\)
\(20\) 0.00241041i 0.000538983i
\(21\) 1.70646i 0.372379i
\(22\) 1.42819 0.304492
\(23\) −0.704722 −0.146945 −0.0734723 0.997297i \(-0.523408\pi\)
−0.0734723 + 0.997297i \(0.523408\pi\)
\(24\) 2.79963i 0.571473i
\(25\) 4.99632 0.999264
\(26\) 1.05464 5.04027i 0.206832 0.988478i
\(27\) 1.00000 0.192450
\(28\) 0.0678114i 0.0128151i
\(29\) −0.0346842 −0.00644069 −0.00322035 0.999995i \(-0.501025\pi\)
−0.00322035 + 0.999995i \(0.501025\pi\)
\(30\) −0.0866304 −0.0158165
\(31\) 1.85987i 0.334042i −0.985953 0.167021i \(-0.946585\pi\)
0.985953 0.167021i \(-0.0534148\pi\)
\(32\) 0.224760i 0.0397323i
\(33\) 1.00000i 0.174078i
\(34\) 5.36429i 0.919967i
\(35\) −0.103509 −0.0174962
\(36\) −0.0397381 −0.00662302
\(37\) 8.82674i 1.45111i 0.688166 + 0.725553i \(0.258416\pi\)
−0.688166 + 0.725553i \(0.741584\pi\)
\(38\) −2.89348 −0.469385
\(39\) 3.52912 + 0.738445i 0.565112 + 0.118246i
\(40\) −0.169818 −0.0268506
\(41\) 3.32960i 0.519996i −0.965609 0.259998i \(-0.916278\pi\)
0.965609 0.259998i \(-0.0837220\pi\)
\(42\) −2.43715 −0.376061
\(43\) −5.29022 −0.806751 −0.403376 0.915035i \(-0.632163\pi\)
−0.403376 + 0.915035i \(0.632163\pi\)
\(44\) 0.0397381i 0.00599075i
\(45\) 0.0606573i 0.00904225i
\(46\) 1.00648i 0.148397i
\(47\) 6.04622i 0.881931i 0.897524 + 0.440966i \(0.145364\pi\)
−0.897524 + 0.440966i \(0.854636\pi\)
\(48\) −4.07790 −0.588594
\(49\) 4.08800 0.584001
\(50\) 7.13572i 1.00914i
\(51\) −3.75599 −0.525944
\(52\) −0.140241 0.0293444i −0.0194479 0.00406934i
\(53\) −10.6694 −1.46555 −0.732775 0.680471i \(-0.761775\pi\)
−0.732775 + 0.680471i \(0.761775\pi\)
\(54\) 1.42819i 0.194353i
\(55\) 0.0606573 0.00817903
\(56\) −4.77746 −0.638414
\(57\) 2.02597i 0.268347i
\(58\) 0.0495358i 0.00650436i
\(59\) 3.34547i 0.435543i 0.976000 + 0.217771i \(0.0698787\pi\)
−0.976000 + 0.217771i \(0.930121\pi\)
\(60\) 0.00241041i 0.000311182i
\(61\) 3.26757 0.418369 0.209185 0.977876i \(-0.432919\pi\)
0.209185 + 0.977876i \(0.432919\pi\)
\(62\) −2.65625 −0.337344
\(63\) 1.70646i 0.214993i
\(64\) −7.83479 −0.979349
\(65\) 0.0447920 0.214067i 0.00555577 0.0265517i
\(66\) 1.42819 0.175799
\(67\) 10.9701i 1.34021i 0.742268 + 0.670103i \(0.233750\pi\)
−0.742268 + 0.670103i \(0.766250\pi\)
\(68\) 0.149256 0.0181000
\(69\) −0.704722 −0.0848385
\(70\) 0.147831i 0.0176692i
\(71\) 1.96928i 0.233711i −0.993149 0.116855i \(-0.962719\pi\)
0.993149 0.116855i \(-0.0372814\pi\)
\(72\) 2.79963i 0.329940i
\(73\) 15.3057i 1.79140i 0.444659 + 0.895700i \(0.353325\pi\)
−0.444659 + 0.895700i \(0.646675\pi\)
\(74\) 12.6063 1.46545
\(75\) 4.99632 0.576925
\(76\) 0.0805084i 0.00923494i
\(77\) 1.70646 0.194469
\(78\) 1.05464 5.04027i 0.119415 0.570698i
\(79\) 10.5938 1.19190 0.595951 0.803021i \(-0.296775\pi\)
0.595951 + 0.803021i \(0.296775\pi\)
\(80\) 0.247354i 0.0276550i
\(81\) 1.00000 0.111111
\(82\) −4.75532 −0.525137
\(83\) 4.19820i 0.460812i −0.973095 0.230406i \(-0.925994\pi\)
0.973095 0.230406i \(-0.0740055\pi\)
\(84\) 0.0678114i 0.00739883i
\(85\) 0.227828i 0.0247114i
\(86\) 7.55546i 0.814726i
\(87\) −0.0346842 −0.00371854
\(88\) 2.79963 0.298442
\(89\) 14.3643i 1.52261i 0.648393 + 0.761305i \(0.275441\pi\)
−0.648393 + 0.761305i \(0.724559\pi\)
\(90\) −0.0866304 −0.00913164
\(91\) 1.26012 6.02229i 0.132097 0.631308i
\(92\) 0.0280043 0.00291965
\(93\) 1.85987i 0.192859i
\(94\) 8.63517 0.890650
\(95\) −0.122890 −0.0126082
\(96\) 0.224760i 0.0229394i
\(97\) 5.86228i 0.595224i −0.954687 0.297612i \(-0.903810\pi\)
0.954687 0.297612i \(-0.0961902\pi\)
\(98\) 5.83846i 0.589774i
\(99\) 1.00000i 0.100504i
\(100\) −0.198544 −0.0198544
\(101\) 12.3706 1.23092 0.615460 0.788168i \(-0.288970\pi\)
0.615460 + 0.788168i \(0.288970\pi\)
\(102\) 5.36429i 0.531143i
\(103\) −10.0788 −0.993094 −0.496547 0.868010i \(-0.665399\pi\)
−0.496547 + 0.868010i \(0.665399\pi\)
\(104\) 2.06738 9.88025i 0.202723 0.968838i
\(105\) −0.103509 −0.0101014
\(106\) 15.2379i 1.48004i
\(107\) 6.17793 0.597243 0.298622 0.954372i \(-0.403473\pi\)
0.298622 + 0.954372i \(0.403473\pi\)
\(108\) −0.0397381 −0.00382380
\(109\) 4.64928i 0.445320i −0.974896 0.222660i \(-0.928526\pi\)
0.974896 0.222660i \(-0.0714740\pi\)
\(110\) 0.0866304i 0.00825988i
\(111\) 8.82674i 0.837797i
\(112\) 6.95876i 0.657541i
\(113\) 8.99146 0.845846 0.422923 0.906166i \(-0.361004\pi\)
0.422923 + 0.906166i \(0.361004\pi\)
\(114\) −2.89348 −0.270999
\(115\) 0.0427465i 0.00398613i
\(116\) 0.00137828 0.000127971
\(117\) 3.52912 + 0.738445i 0.326267 + 0.0682692i
\(118\) 4.77798 0.439848
\(119\) 6.40944i 0.587552i
\(120\) −0.169818 −0.0155022
\(121\) −1.00000 −0.0909091
\(122\) 4.66672i 0.422505i
\(123\) 3.32960i 0.300220i
\(124\) 0.0739076i 0.00663710i
\(125\) 0.606350i 0.0542336i
\(126\) −2.43715 −0.217119
\(127\) −1.74493 −0.154837 −0.0774187 0.996999i \(-0.524668\pi\)
−0.0774187 + 0.996999i \(0.524668\pi\)
\(128\) 11.6391i 1.02876i
\(129\) −5.29022 −0.465778
\(130\) −0.305729 0.0639717i −0.0268142 0.00561069i
\(131\) −13.8961 −1.21411 −0.607054 0.794661i \(-0.707649\pi\)
−0.607054 + 0.794661i \(0.707649\pi\)
\(132\) 0.0397381i 0.00345876i
\(133\) −3.45724 −0.299780
\(134\) 15.6674 1.35345
\(135\) 0.0606573i 0.00522055i
\(136\) 10.5154i 0.901689i
\(137\) 3.08818i 0.263841i 0.991260 + 0.131921i \(0.0421144\pi\)
−0.991260 + 0.131921i \(0.957886\pi\)
\(138\) 1.00648i 0.0856772i
\(139\) 1.92887 0.163605 0.0818023 0.996649i \(-0.473932\pi\)
0.0818023 + 0.996649i \(0.473932\pi\)
\(140\) 0.00411325 0.000347633
\(141\) 6.04622i 0.509183i
\(142\) −2.81252 −0.236021
\(143\) −0.738445 + 3.52912i −0.0617519 + 0.295120i
\(144\) −4.07790 −0.339825
\(145\) 0.00210385i 0.000174715i
\(146\) 21.8595 1.80911
\(147\) 4.08800 0.337173
\(148\) 0.350758i 0.0288321i
\(149\) 9.05192i 0.741563i −0.928720 0.370781i \(-0.879090\pi\)
0.928720 0.370781i \(-0.120910\pi\)
\(150\) 7.13572i 0.582629i
\(151\) 2.44462i 0.198940i 0.995041 + 0.0994702i \(0.0317148\pi\)
−0.995041 + 0.0994702i \(0.968285\pi\)
\(152\) −5.67198 −0.460059
\(153\) −3.75599 −0.303654
\(154\) 2.43715i 0.196391i
\(155\) −0.112814 −0.00906147
\(156\) −0.140241 0.0293444i −0.0112282 0.00234943i
\(157\) −8.42793 −0.672622 −0.336311 0.941751i \(-0.609179\pi\)
−0.336311 + 0.941751i \(0.609179\pi\)
\(158\) 15.1301i 1.20368i
\(159\) −10.6694 −0.846135
\(160\) 0.0136333 0.00107781
\(161\) 1.20258i 0.0947763i
\(162\) 1.42819i 0.112210i
\(163\) 17.3969i 1.36263i −0.731990 0.681316i \(-0.761408\pi\)
0.731990 0.681316i \(-0.238592\pi\)
\(164\) 0.132312i 0.0103318i
\(165\) 0.0606573 0.00472216
\(166\) −5.99585 −0.465368
\(167\) 1.05104i 0.0813320i 0.999173 + 0.0406660i \(0.0129480\pi\)
−0.999173 + 0.0406660i \(0.987052\pi\)
\(168\) −4.77746 −0.368589
\(169\) 11.9094 + 5.21212i 0.916108 + 0.400933i
\(170\) 0.325383 0.0249557
\(171\) 2.02597i 0.154930i
\(172\) 0.210223 0.0160294
\(173\) −18.6654 −1.41910 −0.709552 0.704653i \(-0.751103\pi\)
−0.709552 + 0.704653i \(0.751103\pi\)
\(174\) 0.0495358i 0.00375530i
\(175\) 8.52601i 0.644505i
\(176\) 4.07790i 0.307383i
\(177\) 3.34547i 0.251461i
\(178\) 20.5150 1.53766
\(179\) 24.2443 1.81210 0.906051 0.423168i \(-0.139082\pi\)
0.906051 + 0.423168i \(0.139082\pi\)
\(180\) 0.00241041i 0.000179661i
\(181\) −20.9251 −1.55535 −0.777675 0.628666i \(-0.783601\pi\)
−0.777675 + 0.628666i \(0.783601\pi\)
\(182\) −8.60100 1.79970i −0.637549 0.133403i
\(183\) 3.26757 0.241545
\(184\) 1.97296i 0.145449i
\(185\) 0.535406 0.0393638
\(186\) −2.65625 −0.194766
\(187\) 3.75599i 0.274665i
\(188\) 0.240265i 0.0175231i
\(189\) 1.70646i 0.124126i
\(190\) 0.175511i 0.0127329i
\(191\) 2.77108 0.200508 0.100254 0.994962i \(-0.468034\pi\)
0.100254 + 0.994962i \(0.468034\pi\)
\(192\) −7.83479 −0.565428
\(193\) 8.50742i 0.612378i −0.951971 0.306189i \(-0.900946\pi\)
0.951971 0.306189i \(-0.0990539\pi\)
\(194\) −8.37247 −0.601108
\(195\) 0.0447920 0.214067i 0.00320763 0.0153296i
\(196\) −0.162450 −0.0116035
\(197\) 14.4278i 1.02794i 0.857810 + 0.513968i \(0.171825\pi\)
−0.857810 + 0.513968i \(0.828175\pi\)
\(198\) 1.42819 0.101497
\(199\) −15.9351 −1.12961 −0.564806 0.825224i \(-0.691049\pi\)
−0.564806 + 0.825224i \(0.691049\pi\)
\(200\) 13.9879i 0.989092i
\(201\) 10.9701i 0.773768i
\(202\) 17.6676i 1.24309i
\(203\) 0.0591871i 0.00415412i
\(204\) 0.149256 0.0104500
\(205\) −0.201965 −0.0141058
\(206\) 14.3945i 1.00291i
\(207\) −0.704722 −0.0489815
\(208\) −14.3914 3.01130i −0.997864 0.208796i
\(209\) 2.02597 0.140139
\(210\) 0.147831i 0.0102013i
\(211\) −16.6404 −1.14557 −0.572786 0.819705i \(-0.694138\pi\)
−0.572786 + 0.819705i \(0.694138\pi\)
\(212\) 0.423980 0.0291191
\(213\) 1.96928i 0.134933i
\(214\) 8.82329i 0.603147i
\(215\) 0.320890i 0.0218845i
\(216\) 2.79963i 0.190491i
\(217\) −3.17378 −0.215450
\(218\) −6.64007 −0.449722
\(219\) 15.3057i 1.03427i
\(220\) −0.00241041 −0.000162510
\(221\) −13.2554 2.77359i −0.891652 0.186572i
\(222\) 12.6063 0.846079
\(223\) 29.6492i 1.98546i −0.120372 0.992729i \(-0.538409\pi\)
0.120372 0.992729i \(-0.461591\pi\)
\(224\) 0.383543 0.0256265
\(225\) 4.99632 0.333088
\(226\) 12.8416i 0.854208i
\(227\) 2.17847i 0.144590i 0.997383 + 0.0722951i \(0.0230323\pi\)
−0.997383 + 0.0722951i \(0.976968\pi\)
\(228\) 0.0805084i 0.00533180i
\(229\) 2.89071i 0.191024i −0.995428 0.0955118i \(-0.969551\pi\)
0.995428 0.0955118i \(-0.0304488\pi\)
\(230\) 0.0610503 0.00402554
\(231\) 1.70646 0.112277
\(232\) 0.0971031i 0.00637513i
\(233\) −8.88961 −0.582377 −0.291189 0.956666i \(-0.594051\pi\)
−0.291189 + 0.956666i \(0.594051\pi\)
\(234\) 1.05464 5.04027i 0.0689441 0.329493i
\(235\) 0.366747 0.0239239
\(236\) 0.132943i 0.00865382i
\(237\) 10.5938 0.688144
\(238\) 9.15392 0.593361
\(239\) 28.4940i 1.84313i −0.388229 0.921563i \(-0.626913\pi\)
0.388229 0.921563i \(-0.373087\pi\)
\(240\) 0.247354i 0.0159666i
\(241\) 15.6266i 1.00660i −0.864112 0.503299i \(-0.832119\pi\)
0.864112 0.503299i \(-0.167881\pi\)
\(242\) 1.42819i 0.0918078i
\(243\) 1.00000 0.0641500
\(244\) −0.129847 −0.00831260
\(245\) 0.247967i 0.0158420i
\(246\) −4.75532 −0.303188
\(247\) 1.49607 7.14991i 0.0951926 0.454938i
\(248\) −5.20695 −0.330641
\(249\) 4.19820i 0.266050i
\(250\) −0.865985 −0.0547697
\(251\) −20.7286 −1.30838 −0.654189 0.756331i \(-0.726990\pi\)
−0.654189 + 0.756331i \(0.726990\pi\)
\(252\) 0.0678114i 0.00427172i
\(253\) 0.704722i 0.0443055i
\(254\) 2.49210i 0.156368i
\(255\) 0.227828i 0.0142672i
\(256\) 0.953341 0.0595838
\(257\) 1.38511 0.0864008 0.0432004 0.999066i \(-0.486245\pi\)
0.0432004 + 0.999066i \(0.486245\pi\)
\(258\) 7.55546i 0.470383i
\(259\) 15.0624 0.935935
\(260\) −0.00177995 + 0.00850662i −0.000110388 + 0.000527558i
\(261\) −0.0346842 −0.00214690
\(262\) 19.8463i 1.22611i
\(263\) −17.4668 −1.07705 −0.538524 0.842610i \(-0.681018\pi\)
−0.538524 + 0.842610i \(0.681018\pi\)
\(264\) 2.79963 0.172306
\(265\) 0.647174i 0.0397556i
\(266\) 4.93760i 0.302744i
\(267\) 14.3643i 0.879080i
\(268\) 0.435929i 0.0266286i
\(269\) 0.559556 0.0341167 0.0170584 0.999854i \(-0.494570\pi\)
0.0170584 + 0.999854i \(0.494570\pi\)
\(270\) −0.0866304 −0.00527216
\(271\) 13.2324i 0.803810i −0.915681 0.401905i \(-0.868348\pi\)
0.915681 0.401905i \(-0.131652\pi\)
\(272\) 15.3166 0.928702
\(273\) 1.26012 6.02229i 0.0762662 0.364486i
\(274\) 4.41053 0.266450
\(275\) 4.99632i 0.301289i
\(276\) 0.0280043 0.00168566
\(277\) 18.4921 1.11108 0.555541 0.831489i \(-0.312511\pi\)
0.555541 + 0.831489i \(0.312511\pi\)
\(278\) 2.75480i 0.165222i
\(279\) 1.85987i 0.111347i
\(280\) 0.289787i 0.0173181i
\(281\) 25.8276i 1.54075i 0.637593 + 0.770373i \(0.279930\pi\)
−0.637593 + 0.770373i \(0.720070\pi\)
\(282\) 8.63517 0.514217
\(283\) −6.19965 −0.368531 −0.184265 0.982877i \(-0.558991\pi\)
−0.184265 + 0.982877i \(0.558991\pi\)
\(284\) 0.0782556i 0.00464362i
\(285\) −0.122890 −0.00727938
\(286\) 5.04027 + 1.05464i 0.298037 + 0.0623623i
\(287\) −5.68182 −0.335387
\(288\) 0.224760i 0.0132441i
\(289\) −2.89252 −0.170148
\(290\) 0.00300470 0.000176442
\(291\) 5.86228i 0.343653i
\(292\) 0.608221i 0.0355934i
\(293\) 8.49366i 0.496205i −0.968734 0.248102i \(-0.920193\pi\)
0.968734 0.248102i \(-0.0798070\pi\)
\(294\) 5.83846i 0.340506i
\(295\) 0.202927 0.0118149
\(296\) 24.7116 1.43633
\(297\) 1.00000i 0.0580259i
\(298\) −12.9279 −0.748893
\(299\) −2.48705 0.520398i −0.143830 0.0300954i
\(300\) −0.198544 −0.0114630
\(301\) 9.02753i 0.520338i
\(302\) 3.49139 0.200907
\(303\) 12.3706 0.710672
\(304\) 8.26171i 0.473842i
\(305\) 0.198202i 0.0113490i
\(306\) 5.36429i 0.306656i
\(307\) 10.6196i 0.606095i −0.952976 0.303047i \(-0.901996\pi\)
0.952976 0.303047i \(-0.0980040\pi\)
\(308\) −0.0678114 −0.00386391
\(309\) −10.0788 −0.573363
\(310\) 0.161121i 0.00915105i
\(311\) 27.5052 1.55968 0.779838 0.625981i \(-0.215301\pi\)
0.779838 + 0.625981i \(0.215301\pi\)
\(312\) 2.06738 9.88025i 0.117042 0.559359i
\(313\) 0.791246 0.0447239 0.0223619 0.999750i \(-0.492881\pi\)
0.0223619 + 0.999750i \(0.492881\pi\)
\(314\) 12.0367i 0.679271i
\(315\) −0.103509 −0.00583207
\(316\) −0.420980 −0.0236820
\(317\) 10.4687i 0.587983i 0.955808 + 0.293991i \(0.0949837\pi\)
−0.955808 + 0.293991i \(0.905016\pi\)
\(318\) 15.2379i 0.854500i
\(319\) 0.0346842i 0.00194194i
\(320\) 0.475237i 0.0265666i
\(321\) 6.17793 0.344819
\(322\) 1.71751 0.0957133
\(323\) 7.60954i 0.423406i
\(324\) −0.0397381 −0.00220767
\(325\) 17.6326 + 3.68951i 0.978082 + 0.204657i
\(326\) −24.8462 −1.37610
\(327\) 4.64928i 0.257106i
\(328\) −9.32167 −0.514703
\(329\) 10.3176 0.568828
\(330\) 0.0866304i 0.00476884i
\(331\) 21.1531i 1.16268i −0.813661 0.581339i \(-0.802529\pi\)
0.813661 0.581339i \(-0.197471\pi\)
\(332\) 0.166829i 0.00915591i
\(333\) 8.82674i 0.483702i
\(334\) 1.50109 0.0821361
\(335\) 0.665414 0.0363554
\(336\) 6.95876i 0.379631i
\(337\) 4.33688 0.236245 0.118123 0.992999i \(-0.462312\pi\)
0.118123 + 0.992999i \(0.462312\pi\)
\(338\) 7.44392 17.0089i 0.404896 0.925164i
\(339\) 8.99146 0.488349
\(340\) 0.00905347i 0.000490993i
\(341\) 1.85987 0.100717
\(342\) −2.89348 −0.156462
\(343\) 18.9212i 1.02165i
\(344\) 14.8107i 0.798539i
\(345\) 0.0427465i 0.00230139i
\(346\) 26.6578i 1.43313i
\(347\) −10.5906 −0.568532 −0.284266 0.958745i \(-0.591750\pi\)
−0.284266 + 0.958745i \(0.591750\pi\)
\(348\) 0.00137828 7.38838e−5
\(349\) 24.3761i 1.30482i 0.757864 + 0.652412i \(0.226243\pi\)
−0.757864 + 0.652412i \(0.773757\pi\)
\(350\) −12.1768 −0.650877
\(351\) 3.52912 + 0.738445i 0.188371 + 0.0394153i
\(352\) −0.224760 −0.0119797
\(353\) 21.4564i 1.14201i 0.820947 + 0.571004i \(0.193446\pi\)
−0.820947 + 0.571004i \(0.806554\pi\)
\(354\) 4.77798 0.253947
\(355\) −0.119451 −0.00633982
\(356\) 0.570810i 0.0302528i
\(357\) 6.40944i 0.339224i
\(358\) 34.6255i 1.83002i
\(359\) 33.2863i 1.75679i −0.477939 0.878393i \(-0.658616\pi\)
0.477939 0.878393i \(-0.341384\pi\)
\(360\) −0.169818 −0.00895020
\(361\) 14.8954 0.783970
\(362\) 29.8851i 1.57073i
\(363\) −1.00000 −0.0524864
\(364\) −0.0500750 + 0.239315i −0.00262464 + 0.0125435i
\(365\) 0.928404 0.0485949
\(366\) 4.66672i 0.243933i
\(367\) 15.3463 0.801073 0.400536 0.916281i \(-0.368824\pi\)
0.400536 + 0.916281i \(0.368824\pi\)
\(368\) 2.87378 0.149806
\(369\) 3.32960i 0.173332i
\(370\) 0.764663i 0.0397529i
\(371\) 18.2068i 0.945250i
\(372\) 0.0739076i 0.00383193i
\(373\) −22.1576 −1.14728 −0.573638 0.819109i \(-0.694469\pi\)
−0.573638 + 0.819109i \(0.694469\pi\)
\(374\) −5.36429 −0.277381
\(375\) 0.606350i 0.0313118i
\(376\) 16.9272 0.872954
\(377\) −0.122405 0.0256124i −0.00630416 0.00131910i
\(378\) −2.43715 −0.125354
\(379\) 21.0884i 1.08324i 0.840624 + 0.541619i \(0.182188\pi\)
−0.840624 + 0.541619i \(0.817812\pi\)
\(380\) 0.00488342 0.000250514
\(381\) −1.74493 −0.0893955
\(382\) 3.95764i 0.202490i
\(383\) 6.90976i 0.353072i −0.984294 0.176536i \(-0.943511\pi\)
0.984294 0.176536i \(-0.0564892\pi\)
\(384\) 11.6391i 0.593957i
\(385\) 0.103509i 0.00527531i
\(386\) −12.1502 −0.618431
\(387\) −5.29022 −0.268917
\(388\) 0.232956i 0.0118265i
\(389\) 32.7232 1.65913 0.829565 0.558410i \(-0.188588\pi\)
0.829565 + 0.558410i \(0.188588\pi\)
\(390\) −0.305729 0.0639717i −0.0154812 0.00323933i
\(391\) 2.64693 0.133861
\(392\) 11.4449i 0.578056i
\(393\) −13.8961 −0.700966
\(394\) 20.6056 1.03810
\(395\) 0.642594i 0.0323324i
\(396\) 0.0397381i 0.00199692i
\(397\) 10.1016i 0.506987i −0.967337 0.253494i \(-0.918420\pi\)
0.967337 0.253494i \(-0.0815797\pi\)
\(398\) 22.7585i 1.14078i
\(399\) −3.45724 −0.173078
\(400\) −20.3745 −1.01872
\(401\) 18.3377i 0.915739i 0.889019 + 0.457870i \(0.151387\pi\)
−0.889019 + 0.457870i \(0.848613\pi\)
\(402\) 15.6674 0.781417
\(403\) 1.37341 6.56369i 0.0684144 0.326961i
\(404\) −0.491584 −0.0244572
\(405\) 0.0606573i 0.00301408i
\(406\) 0.0845306 0.00419518
\(407\) −8.82674 −0.437525
\(408\) 10.5154i 0.520590i
\(409\) 5.60283i 0.277042i 0.990359 + 0.138521i \(0.0442349\pi\)
−0.990359 + 0.138521i \(0.955765\pi\)
\(410\) 0.288445i 0.0142453i
\(411\) 3.08818i 0.152329i
\(412\) 0.400513 0.0197318
\(413\) 5.70890 0.280916
\(414\) 1.00648i 0.0494657i
\(415\) −0.254651 −0.0125003
\(416\) −0.165973 + 0.793204i −0.00813748 + 0.0388900i
\(417\) 1.92887 0.0944572
\(418\) 2.89348i 0.141525i
\(419\) −24.6413 −1.20380 −0.601902 0.798570i \(-0.705590\pi\)
−0.601902 + 0.798570i \(0.705590\pi\)
\(420\) 0.00411325 0.000200706
\(421\) 25.4002i 1.23793i −0.785419 0.618964i \(-0.787553\pi\)
0.785419 0.618964i \(-0.212447\pi\)
\(422\) 23.7657i 1.15690i
\(423\) 6.04622i 0.293977i
\(424\) 29.8703i 1.45063i
\(425\) −18.7661 −0.910292
\(426\) −2.81252 −0.136267
\(427\) 5.57596i 0.269840i
\(428\) −0.245499 −0.0118667
\(429\) −0.738445 + 3.52912i −0.0356525 + 0.170388i
\(430\) 0.458294 0.0221009
\(431\) 33.6254i 1.61968i −0.586653 0.809838i \(-0.699555\pi\)
0.586653 0.809838i \(-0.300445\pi\)
\(432\) −4.07790 −0.196198
\(433\) −9.72637 −0.467420 −0.233710 0.972306i \(-0.575087\pi\)
−0.233710 + 0.972306i \(0.575087\pi\)
\(434\) 4.53278i 0.217580i
\(435\) 0.00210385i 0.000100872i
\(436\) 0.184754i 0.00884809i
\(437\) 1.42775i 0.0682984i
\(438\) 21.8595 1.04449
\(439\) −17.0758 −0.814986 −0.407493 0.913208i \(-0.633597\pi\)
−0.407493 + 0.913208i \(0.633597\pi\)
\(440\) 0.169818i 0.00809576i
\(441\) 4.08800 0.194667
\(442\) −3.96123 + 18.9312i −0.188416 + 0.900466i
\(443\) 21.8637 1.03878 0.519389 0.854538i \(-0.326160\pi\)
0.519389 + 0.854538i \(0.326160\pi\)
\(444\) 0.350758i 0.0166462i
\(445\) 0.871298 0.0413035
\(446\) −42.3448 −2.00509
\(447\) 9.05192i 0.428141i
\(448\) 13.3697i 0.631661i
\(449\) 8.95803i 0.422755i −0.977404 0.211378i \(-0.932205\pi\)
0.977404 0.211378i \(-0.0677950\pi\)
\(450\) 7.13572i 0.336381i
\(451\) 3.32960 0.156785
\(452\) −0.357304 −0.0168062
\(453\) 2.44462i 0.114858i
\(454\) 3.11128 0.146020
\(455\) −0.365296 0.0764357i −0.0171253 0.00358336i
\(456\) −5.67198 −0.265615
\(457\) 37.7837i 1.76744i 0.468011 + 0.883722i \(0.344971\pi\)
−0.468011 + 0.883722i \(0.655029\pi\)
\(458\) −4.12850 −0.192912
\(459\) −3.75599 −0.175315
\(460\) 0.00169867i 7.92007e-5i
\(461\) 6.10348i 0.284268i 0.989847 + 0.142134i \(0.0453963\pi\)
−0.989847 + 0.142134i \(0.954604\pi\)
\(462\) 2.43715i 0.113387i
\(463\) 37.1501i 1.72651i −0.504768 0.863255i \(-0.668422\pi\)
0.504768 0.863255i \(-0.331578\pi\)
\(464\) 0.141439 0.00656612
\(465\) −0.112814 −0.00523164
\(466\) 12.6961i 0.588135i
\(467\) 10.3642 0.479598 0.239799 0.970823i \(-0.422919\pi\)
0.239799 + 0.970823i \(0.422919\pi\)
\(468\) −0.140241 0.0293444i −0.00648263 0.00135645i
\(469\) 18.7199 0.864406
\(470\) 0.523786i 0.0241604i
\(471\) −8.42793 −0.388338
\(472\) 9.36608 0.431109
\(473\) 5.29022i 0.243245i
\(474\) 15.1301i 0.694947i
\(475\) 10.1224i 0.464448i
\(476\) 0.254699i 0.0116741i
\(477\) −10.6694 −0.488516
\(478\) −40.6950 −1.86135
\(479\) 20.4038i 0.932273i 0.884713 + 0.466136i \(0.154354\pi\)
−0.884713 + 0.466136i \(0.845646\pi\)
\(480\) 0.0136333 0.000622273
\(481\) −6.51806 + 31.1506i −0.297198 + 1.42035i
\(482\) −22.3178 −1.01655
\(483\) 1.20258i 0.0547191i
\(484\) 0.0397381 0.00180628
\(485\) −0.355590 −0.0161465
\(486\) 1.42819i 0.0647842i
\(487\) 18.1762i 0.823644i −0.911264 0.411822i \(-0.864893\pi\)
0.911264 0.411822i \(-0.135107\pi\)
\(488\) 9.14799i 0.414110i
\(489\) 17.3969i 0.786716i
\(490\) −0.354145 −0.0159987
\(491\) 19.2029 0.866613 0.433307 0.901247i \(-0.357347\pi\)
0.433307 + 0.901247i \(0.357347\pi\)
\(492\) 0.132312i 0.00596509i
\(493\) 0.130274 0.00586723
\(494\) −10.2115 2.13668i −0.459435 0.0961337i
\(495\) 0.0606573 0.00272634
\(496\) 7.58434i 0.340547i
\(497\) −3.36050 −0.150739
\(498\) −5.99585 −0.268680
\(499\) 6.46441i 0.289387i 0.989477 + 0.144693i \(0.0462196\pi\)
−0.989477 + 0.144693i \(0.953780\pi\)
\(500\) 0.0240952i 0.00107757i
\(501\) 1.05104i 0.0469571i
\(502\) 29.6045i 1.32131i
\(503\) −23.6756 −1.05564 −0.527821 0.849355i \(-0.676991\pi\)
−0.527821 + 0.849355i \(0.676991\pi\)
\(504\) −4.77746 −0.212805
\(505\) 0.750367i 0.0333909i
\(506\) −1.00648 −0.0447435
\(507\) 11.9094 + 5.21212i 0.528915 + 0.231479i
\(508\) 0.0693402 0.00307648
\(509\) 29.5632i 1.31037i −0.755470 0.655183i \(-0.772591\pi\)
0.755470 0.655183i \(-0.227409\pi\)
\(510\) 0.325383 0.0144082
\(511\) 26.1186 1.15542
\(512\) 21.9167i 0.968590i
\(513\) 2.02597i 0.0894489i
\(514\) 1.97821i 0.0872550i
\(515\) 0.611353i 0.0269394i
\(516\) 0.210223 0.00925457
\(517\) −6.04622 −0.265912
\(518\) 21.5121i 0.945187i
\(519\) −18.6654 −0.819320
\(520\) −0.599309 0.125401i −0.0262814 0.00549921i
\(521\) 35.0790 1.53684 0.768420 0.639946i \(-0.221043\pi\)
0.768420 + 0.639946i \(0.221043\pi\)
\(522\) 0.0495358i 0.00216812i
\(523\) 12.7792 0.558797 0.279399 0.960175i \(-0.409865\pi\)
0.279399 + 0.960175i \(0.409865\pi\)
\(524\) 0.552205 0.0241232
\(525\) 8.52601i 0.372105i
\(526\) 24.9459i 1.08769i
\(527\) 6.98564i 0.304299i
\(528\) 4.07790i 0.177468i
\(529\) −22.5034 −0.978407
\(530\) 0.924290 0.0401486
\(531\) 3.34547i 0.145181i
\(532\) 0.137384 0.00595635
\(533\) 2.45873 11.7506i 0.106499 0.508974i
\(534\) 20.5150 0.887770
\(535\) 0.374737i 0.0162013i
\(536\) 30.7121 1.32656
\(537\) 24.2443 1.04622
\(538\) 0.799155i 0.0344540i
\(539\) 4.08800i 0.176083i
\(540\) 0.00241041i 0.000103727i
\(541\) 16.4144i 0.705711i 0.935678 + 0.352856i \(0.114789\pi\)
−0.935678 + 0.352856i \(0.885211\pi\)
\(542\) −18.8984 −0.811756
\(543\) −20.9251 −0.897982
\(544\) 0.844196i 0.0361946i
\(545\) −0.282013 −0.0120801
\(546\) −8.60100 1.79970i −0.368089 0.0770201i
\(547\) −30.0865 −1.28640 −0.643202 0.765696i \(-0.722395\pi\)
−0.643202 + 0.765696i \(0.722395\pi\)
\(548\) 0.122719i 0.00524228i
\(549\) 3.26757 0.139456
\(550\) 7.13572 0.304268
\(551\) 0.0702692i 0.00299357i
\(552\) 1.97296i 0.0839749i
\(553\) 18.0779i 0.768753i
\(554\) 26.4103i 1.12207i
\(555\) 0.535406 0.0227267
\(556\) −0.0766497 −0.00325067
\(557\) 9.18200i 0.389054i −0.980897 0.194527i \(-0.937683\pi\)
0.980897 0.194527i \(-0.0623171\pi\)
\(558\) −2.65625 −0.112448
\(559\) −18.6698 3.90654i −0.789650 0.165229i
\(560\) 0.422099 0.0178369
\(561\) 3.75599i 0.158578i
\(562\) 36.8868 1.55598
\(563\) 15.8217 0.666804 0.333402 0.942785i \(-0.391803\pi\)
0.333402 + 0.942785i \(0.391803\pi\)
\(564\) 0.240265i 0.0101170i
\(565\) 0.545398i 0.0229451i
\(566\) 8.85430i 0.372174i
\(567\) 1.70646i 0.0716645i
\(568\) −5.51327 −0.231332
\(569\) 35.8645 1.50352 0.751760 0.659437i \(-0.229205\pi\)
0.751760 + 0.659437i \(0.229205\pi\)
\(570\) 0.175511i 0.00735134i
\(571\) −0.130007 −0.00544063 −0.00272032 0.999996i \(-0.500866\pi\)
−0.00272032 + 0.999996i \(0.500866\pi\)
\(572\) 0.0293444 0.140241i 0.00122695 0.00586376i
\(573\) 2.77108 0.115763
\(574\) 8.11474i 0.338703i
\(575\) −3.52101 −0.146836
\(576\) −7.83479 −0.326450
\(577\) 24.3812i 1.01500i 0.861650 + 0.507502i \(0.169431\pi\)
−0.861650 + 0.507502i \(0.830569\pi\)
\(578\) 4.13108i 0.171830i
\(579\) 8.50742i 0.353556i
\(580\) 0 8.36030e-5i 0 3.47143e-6i
\(581\) −7.16405 −0.297215
\(582\) −8.37247 −0.347050
\(583\) 10.6694i 0.441880i
\(584\) 42.8504 1.77316
\(585\) 0.0447920 0.214067i 0.00185192 0.00885058i
\(586\) −12.1306 −0.501110
\(587\) 6.61208i 0.272910i −0.990646 0.136455i \(-0.956429\pi\)
0.990646 0.136455i \(-0.0435709\pi\)
\(588\) −0.162450 −0.00669931
\(589\) −3.76804 −0.155259
\(590\) 0.289819i 0.0119317i
\(591\) 14.4278i 0.593479i
\(592\) 35.9945i 1.47937i
\(593\) 26.4128i 1.08464i −0.840170 0.542322i \(-0.817545\pi\)
0.840170 0.542322i \(-0.182455\pi\)
\(594\) 1.42819 0.0585995
\(595\) 0.388779 0.0159384
\(596\) 0.359706i 0.0147342i
\(597\) −15.9351 −0.652182
\(598\) −0.743229 + 3.55199i −0.0303929 + 0.145252i
\(599\) 21.4702 0.877248 0.438624 0.898671i \(-0.355466\pi\)
0.438624 + 0.898671i \(0.355466\pi\)
\(600\) 13.9879i 0.571052i
\(601\) −9.57861 −0.390720 −0.195360 0.980732i \(-0.562587\pi\)
−0.195360 + 0.980732i \(0.562587\pi\)
\(602\) 12.8931 0.525482
\(603\) 10.9701i 0.446735i
\(604\) 0.0971446i 0.00395276i
\(605\) 0.0606573i 0.00246607i
\(606\) 17.6676i 0.717698i
\(607\) −28.5549 −1.15901 −0.579504 0.814969i \(-0.696754\pi\)
−0.579504 + 0.814969i \(0.696754\pi\)
\(608\) 0.455357 0.0184672
\(609\) 0.0591871i 0.00239838i
\(610\) −0.283070 −0.0114612
\(611\) −4.46480 + 21.3378i −0.180626 + 0.863236i
\(612\) 0.149256 0.00603332
\(613\) 25.5390i 1.03151i 0.856736 + 0.515755i \(0.172488\pi\)
−0.856736 + 0.515755i \(0.827512\pi\)
\(614\) −15.1669 −0.612086
\(615\) −0.201965 −0.00814400
\(616\) 4.77746i 0.192489i
\(617\) 33.4193i 1.34541i −0.739910 0.672706i \(-0.765132\pi\)
0.739910 0.672706i \(-0.234868\pi\)
\(618\) 14.3945i 0.579031i
\(619\) 34.5887i 1.39024i 0.718895 + 0.695119i \(0.244648\pi\)
−0.718895 + 0.695119i \(0.755352\pi\)
\(620\) 0.00448303 0.000180043
\(621\) −0.704722 −0.0282795
\(622\) 39.2827i 1.57509i
\(623\) 24.5120 0.982054
\(624\) −14.3914 3.01130i −0.576117 0.120549i
\(625\) 24.9448 0.997793
\(626\) 1.13005i 0.0451660i
\(627\) 2.02597 0.0809096
\(628\) 0.334910 0.0133644
\(629\) 33.1532i 1.32190i
\(630\) 0.147831i 0.00588973i
\(631\) 12.7021i 0.505662i −0.967510 0.252831i \(-0.918638\pi\)
0.967510 0.252831i \(-0.0813617\pi\)
\(632\) 29.6589i 1.17977i
\(633\) −16.6404 −0.661397
\(634\) 14.9514 0.593796
\(635\) 0.105843i 0.00420024i
\(636\) 0.423980 0.0168119
\(637\) 14.4271 + 3.01877i 0.571621 + 0.119608i
\(638\) −0.0495358 −0.00196114
\(639\) 1.96928i 0.0779036i
\(640\) 0.705998 0.0279070
\(641\) 25.9825 1.02625 0.513124 0.858314i \(-0.328488\pi\)
0.513124 + 0.858314i \(0.328488\pi\)
\(642\) 8.82329i 0.348227i
\(643\) 32.8848i 1.29685i −0.761278 0.648425i \(-0.775428\pi\)
0.761278 0.648425i \(-0.224572\pi\)
\(644\) 0.0477881i 0.00188312i
\(645\) 0.320890i 0.0126350i
\(646\) 10.8679 0.427592
\(647\) −2.75086 −0.108148 −0.0540738 0.998537i \(-0.517221\pi\)
−0.0540738 + 0.998537i \(0.517221\pi\)
\(648\) 2.79963i 0.109980i
\(649\) −3.34547 −0.131321
\(650\) 5.26933 25.1828i 0.206680 0.987751i
\(651\) −3.17378 −0.124390
\(652\) 0.691321i 0.0270742i
\(653\) 27.4851 1.07557 0.537787 0.843081i \(-0.319260\pi\)
0.537787 + 0.843081i \(0.319260\pi\)
\(654\) −6.64007 −0.259647
\(655\) 0.842900i 0.0329348i
\(656\) 13.5778i 0.530123i
\(657\) 15.3057i 0.597133i
\(658\) 14.7355i 0.574451i
\(659\) 17.2631 0.672474 0.336237 0.941777i \(-0.390846\pi\)
0.336237 + 0.941777i \(0.390846\pi\)
\(660\) −0.00241041 −9.38249e−5
\(661\) 2.44386i 0.0950551i −0.998870 0.0475276i \(-0.984866\pi\)
0.998870 0.0475276i \(-0.0151342\pi\)
\(662\) −30.2107 −1.17417
\(663\) −13.2554 2.77359i −0.514795 0.107717i
\(664\) −11.7534 −0.456122
\(665\) 0.209706i 0.00813207i
\(666\) 12.6063 0.488484
\(667\) 0.0244427 0.000946425
\(668\) 0.0417664i 0.00161599i
\(669\) 29.6492i 1.14630i
\(670\) 0.950340i 0.0367148i
\(671\) 3.26757i 0.126143i
\(672\) 0.383543 0.0147955
\(673\) −26.7842 −1.03246 −0.516228 0.856451i \(-0.672664\pi\)
−0.516228 + 0.856451i \(0.672664\pi\)
\(674\) 6.19391i 0.238581i
\(675\) 4.99632 0.192308
\(676\) −0.473257 0.207120i −0.0182022 0.00796615i
\(677\) −25.7769 −0.990687 −0.495343 0.868697i \(-0.664958\pi\)
−0.495343 + 0.868697i \(0.664958\pi\)
\(678\) 12.8416i 0.493177i
\(679\) −10.0037 −0.383908
\(680\) 0.637836 0.0244599
\(681\) 2.17847i 0.0834792i
\(682\) 2.65625i 0.101713i
\(683\) 12.8667i 0.492329i 0.969228 + 0.246165i \(0.0791704\pi\)
−0.969228 + 0.246165i \(0.920830\pi\)
\(684\) 0.0805084i 0.00307831i
\(685\) 0.187321 0.00715716
\(686\) −27.0231 −1.03175
\(687\) 2.89071i 0.110288i
\(688\) 21.5730 0.822462
\(689\) −37.6535 7.87873i −1.43448 0.300156i
\(690\) 0.0610503 0.00232414
\(691\) 33.9707i 1.29230i 0.763208 + 0.646152i \(0.223623\pi\)
−0.763208 + 0.646152i \(0.776377\pi\)
\(692\) 0.741728 0.0281963
\(693\) 1.70646 0.0648229
\(694\) 15.1254i 0.574152i
\(695\) 0.117000i 0.00443806i
\(696\) 0.0971031i 0.00368068i
\(697\) 12.5060i 0.473697i
\(698\) 34.8138 1.31772
\(699\) −8.88961 −0.336236
\(700\) 0.338807i 0.0128057i
\(701\) 18.4719 0.697675 0.348837 0.937183i \(-0.386577\pi\)
0.348837 + 0.937183i \(0.386577\pi\)
\(702\) 1.05464 5.04027i 0.0398049 0.190233i
\(703\) 17.8827 0.674460
\(704\) 7.83479i 0.295285i
\(705\) 0.366747 0.0138125
\(706\) 30.6439 1.15330
\(707\) 21.1099i 0.793919i
\(708\) 0.132943i 0.00499629i
\(709\) 33.8830i 1.27250i 0.771482 + 0.636251i \(0.219516\pi\)
−0.771482 + 0.636251i \(0.780484\pi\)
\(710\) 0.170600i 0.00640249i
\(711\) 10.5938 0.397300
\(712\) 40.2147 1.50711
\(713\) 1.31069i 0.0490856i
\(714\) 9.15392 0.342577
\(715\) 0.214067 + 0.0447920i 0.00800565 + 0.00167513i
\(716\) −0.963422 −0.0360048
\(717\) 28.4940i 1.06413i
\(718\) −47.5393 −1.77415
\(719\) −31.1501 −1.16170 −0.580851 0.814010i \(-0.697280\pi\)
−0.580851 + 0.814010i \(0.697280\pi\)
\(720\) 0.247354i 0.00921834i
\(721\) 17.1990i 0.640526i
\(722\) 21.2736i 0.791720i
\(723\) 15.6266i 0.581160i
\(724\) 0.831524 0.0309034
\(725\) −0.173293 −0.00643595
\(726\) 1.42819i 0.0530053i
\(727\) −1.50815 −0.0559341 −0.0279671 0.999609i \(-0.508903\pi\)
−0.0279671 + 0.999609i \(0.508903\pi\)
\(728\) −16.8602 3.52789i −0.624881 0.130752i
\(729\) 1.00000 0.0370370
\(730\) 1.32594i 0.0490753i
\(731\) 19.8700 0.734920
\(732\) −0.129847 −0.00479928
\(733\) 4.42002i 0.163257i 0.996663 + 0.0816285i \(0.0260121\pi\)
−0.996663 + 0.0816285i \(0.973988\pi\)
\(734\) 21.9176i 0.808992i
\(735\) 0.247967i 0.00914641i
\(736\) 0.158393i 0.00583844i
\(737\) −10.9701 −0.404087
\(738\) −4.75532 −0.175046
\(739\) 13.7640i 0.506317i −0.967425 0.253159i \(-0.918531\pi\)
0.967425 0.253159i \(-0.0814695\pi\)
\(740\) −0.0212760 −0.000782122
\(741\) 1.49607 7.14991i 0.0549595 0.262658i
\(742\) 26.0028 0.954594
\(743\) 52.1763i 1.91416i −0.289819 0.957081i \(-0.593595\pi\)
0.289819 0.957081i \(-0.406405\pi\)
\(744\) −5.20695 −0.190896
\(745\) −0.549065 −0.0201162
\(746\) 31.6453i 1.15862i
\(747\) 4.19820i 0.153604i
\(748\) 0.149256i 0.00545734i
\(749\) 10.5424i 0.385210i
\(750\) −0.865985 −0.0316213
\(751\) −13.4236 −0.489836 −0.244918 0.969544i \(-0.578761\pi\)
−0.244918 + 0.969544i \(0.578761\pi\)
\(752\) 24.6559i 0.899106i
\(753\) −20.7286 −0.755393
\(754\) −0.0365794 + 0.174818i −0.00133214 + 0.00636649i
\(755\) 0.148284 0.00539661
\(756\) 0.0678114i 0.00246628i
\(757\) 12.9431 0.470426 0.235213 0.971944i \(-0.424421\pi\)
0.235213 + 0.971944i \(0.424421\pi\)
\(758\) 30.1183 1.09395
\(759\) 0.704722i 0.0255798i
\(760\) 0.344047i 0.0124799i
\(761\) 24.5952i 0.891576i 0.895139 + 0.445788i \(0.147077\pi\)
−0.895139 + 0.445788i \(0.852923\pi\)
\(762\) 2.49210i 0.0902792i
\(763\) −7.93379 −0.287223
\(764\) −0.110117 −0.00398391
\(765\) 0.227828i 0.00823715i
\(766\) −9.86847 −0.356562
\(767\) −2.47044 + 11.8066i −0.0892025 + 0.426310i
\(768\) 0.953341 0.0344007
\(769\) 48.0101i 1.73129i 0.500660 + 0.865644i \(0.333091\pi\)
−0.500660 + 0.865644i \(0.666909\pi\)
\(770\) −0.147831 −0.00532746
\(771\) 1.38511 0.0498835
\(772\) 0.338069i 0.0121674i
\(773\) 20.9744i 0.754398i 0.926132 + 0.377199i \(0.123113\pi\)
−0.926132 + 0.377199i \(0.876887\pi\)
\(774\) 7.55546i 0.271575i
\(775\) 9.29249i 0.333796i
\(776\) −16.4122 −0.589165
\(777\) 15.0624 0.540362
\(778\) 46.7350i 1.67553i
\(779\) −6.74568 −0.241689
\(780\) −0.00177995 + 0.00850662i −6.37325e−5 + 0.000304586i
\(781\) 1.96928 0.0704665
\(782\) 3.78033i 0.135184i
\(783\) −0.0346842 −0.00123951
\(784\) −16.6705 −0.595374
\(785\) 0.511215i 0.0182460i
\(786\) 19.8463i 0.707895i
\(787\) 42.1206i 1.50144i 0.660622 + 0.750719i \(0.270293\pi\)
−0.660622 + 0.750719i \(0.729707\pi\)
\(788\) 0.573332i 0.0204241i
\(789\) −17.4668 −0.621834
\(790\) −0.917749 −0.0326520