Properties

Label 390.2.f.a.259.4
Level $390$
Weight $2$
Character 390.259
Analytic conductor $3.114$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 259.4
Root \(-0.854638 + 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 390.259
Dual form 390.2.f.a.259.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.17009 - 0.539189i) q^{5} -1.00000i q^{6} -0.630898 q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(-2.17009 - 0.539189i) q^{5} -1.00000i q^{6} -0.630898 q^{7} -1.00000 q^{8} -1.00000 q^{9} +(2.17009 + 0.539189i) q^{10} -3.07838i q^{11} +1.00000i q^{12} +(2.87936 - 2.17009i) q^{13} +0.630898 q^{14} +(0.539189 - 2.17009i) q^{15} +1.00000 q^{16} -3.70928i q^{17} +1.00000 q^{18} -0.290725i q^{19} +(-2.17009 - 0.539189i) q^{20} -0.630898i q^{21} +3.07838i q^{22} -1.70928i q^{23} -1.00000i q^{24} +(4.41855 + 2.34017i) q^{25} +(-2.87936 + 2.17009i) q^{26} -1.00000i q^{27} -0.630898 q^{28} +0.447480 q^{29} +(-0.539189 + 2.17009i) q^{30} -6.68035i q^{31} -1.00000 q^{32} +3.07838 q^{33} +3.70928i q^{34} +(1.36910 + 0.340173i) q^{35} -1.00000 q^{36} +5.07838 q^{37} +0.290725i q^{38} +(2.17009 + 2.87936i) q^{39} +(2.17009 + 0.539189i) q^{40} -1.41855i q^{41} +0.630898i q^{42} -5.75872i q^{43} -3.07838i q^{44} +(2.17009 + 0.539189i) q^{45} +1.70928i q^{46} -2.73820 q^{47} +1.00000i q^{48} -6.60197 q^{49} +(-4.41855 - 2.34017i) q^{50} +3.70928 q^{51} +(2.87936 - 2.17009i) q^{52} -14.0989i q^{53} +1.00000i q^{54} +(-1.65983 + 6.68035i) q^{55} +0.630898 q^{56} +0.290725 q^{57} -0.447480 q^{58} +9.02052i q^{59} +(0.539189 - 2.17009i) q^{60} -3.26180 q^{61} +6.68035i q^{62} +0.630898 q^{63} +1.00000 q^{64} +(-7.41855 + 3.15676i) q^{65} -3.07838 q^{66} -7.75872 q^{67} -3.70928i q^{68} +1.70928 q^{69} +(-1.36910 - 0.340173i) q^{70} +1.65983i q^{71} +1.00000 q^{72} +15.3112 q^{73} -5.07838 q^{74} +(-2.34017 + 4.41855i) q^{75} -0.290725i q^{76} +1.94214i q^{77} +(-2.17009 - 2.87936i) q^{78} -10.6537 q^{79} +(-2.17009 - 0.539189i) q^{80} +1.00000 q^{81} +1.41855i q^{82} -3.23513 q^{83} -0.630898i q^{84} +(-2.00000 + 8.04945i) q^{85} +5.75872i q^{86} +0.447480i q^{87} +3.07838i q^{88} +12.3402i q^{89} +(-2.17009 - 0.539189i) q^{90} +(-1.81658 + 1.36910i) q^{91} -1.70928i q^{92} +6.68035 q^{93} +2.73820 q^{94} +(-0.156755 + 0.630898i) q^{95} -1.00000i q^{96} -8.20620 q^{97} +6.60197 q^{98} +3.07838i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9} + 2 q^{10} - 8 q^{13} - 4 q^{14} + 6 q^{16} + 6 q^{18} - 2 q^{20} - 2 q^{25} + 8 q^{26} + 4 q^{28} + 4 q^{29} - 6 q^{32} + 12 q^{33} + 16 q^{35} - 6 q^{36} + 24 q^{37} + 2 q^{39} + 2 q^{40} + 2 q^{45} - 32 q^{47} - 2 q^{49} + 2 q^{50} + 8 q^{51} - 8 q^{52} - 32 q^{55} - 4 q^{56} + 16 q^{57} - 4 q^{58} - 4 q^{61} - 4 q^{63} + 6 q^{64} - 16 q^{65} - 12 q^{66} + 4 q^{67} - 4 q^{69} - 16 q^{70} + 6 q^{72} + 40 q^{73} - 24 q^{74} + 8 q^{75} - 2 q^{78} - 16 q^{79} - 2 q^{80} + 6 q^{81} - 12 q^{85} - 2 q^{90} - 20 q^{91} - 4 q^{93} + 32 q^{94} + 12 q^{95} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000i 0.577350i
\(4\) 1.00000 0.500000
\(5\) −2.17009 0.539189i −0.970492 0.241133i
\(6\) 1.00000i 0.408248i
\(7\) −0.630898 −0.238457 −0.119228 0.992867i \(-0.538042\pi\)
−0.119228 + 0.992867i \(0.538042\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.00000 −0.333333
\(10\) 2.17009 + 0.539189i 0.686242 + 0.170506i
\(11\) 3.07838i 0.928166i −0.885792 0.464083i \(-0.846384\pi\)
0.885792 0.464083i \(-0.153616\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.87936 2.17009i 0.798591 0.601874i
\(14\) 0.630898 0.168614
\(15\) 0.539189 2.17009i 0.139218 0.560314i
\(16\) 1.00000 0.250000
\(17\) 3.70928i 0.899631i −0.893121 0.449816i \(-0.851490\pi\)
0.893121 0.449816i \(-0.148510\pi\)
\(18\) 1.00000 0.235702
\(19\) 0.290725i 0.0666968i −0.999444 0.0333484i \(-0.989383\pi\)
0.999444 0.0333484i \(-0.0106171\pi\)
\(20\) −2.17009 0.539189i −0.485246 0.120566i
\(21\) 0.630898i 0.137673i
\(22\) 3.07838i 0.656312i
\(23\) 1.70928i 0.356409i −0.983994 0.178204i \(-0.942971\pi\)
0.983994 0.178204i \(-0.0570288\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 4.41855 + 2.34017i 0.883710 + 0.468035i
\(26\) −2.87936 + 2.17009i −0.564689 + 0.425589i
\(27\) 1.00000i 0.192450i
\(28\) −0.630898 −0.119228
\(29\) 0.447480 0.0830950 0.0415475 0.999137i \(-0.486771\pi\)
0.0415475 + 0.999137i \(0.486771\pi\)
\(30\) −0.539189 + 2.17009i −0.0984420 + 0.396202i
\(31\) 6.68035i 1.19983i −0.800065 0.599913i \(-0.795202\pi\)
0.800065 0.599913i \(-0.204798\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.07838 0.535877
\(34\) 3.70928i 0.636135i
\(35\) 1.36910 + 0.340173i 0.231421 + 0.0574997i
\(36\) −1.00000 −0.166667
\(37\) 5.07838 0.834880 0.417440 0.908704i \(-0.362927\pi\)
0.417440 + 0.908704i \(0.362927\pi\)
\(38\) 0.290725i 0.0471618i
\(39\) 2.17009 + 2.87936i 0.347492 + 0.461067i
\(40\) 2.17009 + 0.539189i 0.343121 + 0.0852532i
\(41\) 1.41855i 0.221540i −0.993846 0.110770i \(-0.964668\pi\)
0.993846 0.110770i \(-0.0353318\pi\)
\(42\) 0.630898i 0.0973496i
\(43\) 5.75872i 0.878197i −0.898439 0.439099i \(-0.855298\pi\)
0.898439 0.439099i \(-0.144702\pi\)
\(44\) 3.07838i 0.464083i
\(45\) 2.17009 + 0.539189i 0.323497 + 0.0803775i
\(46\) 1.70928i 0.252019i
\(47\) −2.73820 −0.399408 −0.199704 0.979856i \(-0.563998\pi\)
−0.199704 + 0.979856i \(0.563998\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −6.60197 −0.943138
\(50\) −4.41855 2.34017i −0.624877 0.330950i
\(51\) 3.70928 0.519402
\(52\) 2.87936 2.17009i 0.399296 0.300937i
\(53\) 14.0989i 1.93663i −0.249727 0.968316i \(-0.580341\pi\)
0.249727 0.968316i \(-0.419659\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −1.65983 + 6.68035i −0.223811 + 0.900778i
\(56\) 0.630898 0.0843072
\(57\) 0.290725 0.0385074
\(58\) −0.447480 −0.0587570
\(59\) 9.02052i 1.17437i 0.809452 + 0.587186i \(0.199764\pi\)
−0.809452 + 0.587186i \(0.800236\pi\)
\(60\) 0.539189 2.17009i 0.0696090 0.280157i
\(61\) −3.26180 −0.417630 −0.208815 0.977955i \(-0.566961\pi\)
−0.208815 + 0.977955i \(0.566961\pi\)
\(62\) 6.68035i 0.848405i
\(63\) 0.630898 0.0794856
\(64\) 1.00000 0.125000
\(65\) −7.41855 + 3.15676i −0.920158 + 0.391547i
\(66\) −3.07838 −0.378922
\(67\) −7.75872 −0.947879 −0.473939 0.880557i \(-0.657168\pi\)
−0.473939 + 0.880557i \(0.657168\pi\)
\(68\) 3.70928i 0.449816i
\(69\) 1.70928 0.205773
\(70\) −1.36910 0.340173i −0.163639 0.0406584i
\(71\) 1.65983i 0.196985i 0.995138 + 0.0984926i \(0.0314021\pi\)
−0.995138 + 0.0984926i \(0.968598\pi\)
\(72\) 1.00000 0.117851
\(73\) 15.3112 1.79205 0.896023 0.444008i \(-0.146444\pi\)
0.896023 + 0.444008i \(0.146444\pi\)
\(74\) −5.07838 −0.590349
\(75\) −2.34017 + 4.41855i −0.270220 + 0.510210i
\(76\) 0.290725i 0.0333484i
\(77\) 1.94214i 0.221328i
\(78\) −2.17009 2.87936i −0.245714 0.326024i
\(79\) −10.6537 −1.19863 −0.599317 0.800512i \(-0.704561\pi\)
−0.599317 + 0.800512i \(0.704561\pi\)
\(80\) −2.17009 0.539189i −0.242623 0.0602831i
\(81\) 1.00000 0.111111
\(82\) 1.41855i 0.156653i
\(83\) −3.23513 −0.355102 −0.177551 0.984112i \(-0.556817\pi\)
−0.177551 + 0.984112i \(0.556817\pi\)
\(84\) 0.630898i 0.0688366i
\(85\) −2.00000 + 8.04945i −0.216930 + 0.873085i
\(86\) 5.75872i 0.620979i
\(87\) 0.447480i 0.0479749i
\(88\) 3.07838i 0.328156i
\(89\) 12.3402i 1.30806i 0.756470 + 0.654028i \(0.226922\pi\)
−0.756470 + 0.654028i \(0.773078\pi\)
\(90\) −2.17009 0.539189i −0.228747 0.0568355i
\(91\) −1.81658 + 1.36910i −0.190430 + 0.143521i
\(92\) 1.70928i 0.178204i
\(93\) 6.68035 0.692720
\(94\) 2.73820 0.282424
\(95\) −0.156755 + 0.630898i −0.0160828 + 0.0647287i
\(96\) 1.00000i 0.102062i
\(97\) −8.20620 −0.833214 −0.416607 0.909087i \(-0.636781\pi\)
−0.416607 + 0.909087i \(0.636781\pi\)
\(98\) 6.60197 0.666899
\(99\) 3.07838i 0.309389i
\(100\) 4.41855 + 2.34017i 0.441855 + 0.234017i
\(101\) 3.86603 0.384684 0.192342 0.981328i \(-0.438392\pi\)
0.192342 + 0.981328i \(0.438392\pi\)
\(102\) −3.70928 −0.367273
\(103\) 7.84324i 0.772818i 0.922328 + 0.386409i \(0.126285\pi\)
−0.922328 + 0.386409i \(0.873715\pi\)
\(104\) −2.87936 + 2.17009i −0.282345 + 0.212794i
\(105\) −0.340173 + 1.36910i −0.0331975 + 0.133611i
\(106\) 14.0989i 1.36941i
\(107\) 15.7321i 1.52088i 0.649411 + 0.760438i \(0.275016\pi\)
−0.649411 + 0.760438i \(0.724984\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 12.2329i 1.17170i −0.810421 0.585848i \(-0.800762\pi\)
0.810421 0.585848i \(-0.199238\pi\)
\(110\) 1.65983 6.68035i 0.158258 0.636946i
\(111\) 5.07838i 0.482018i
\(112\) −0.630898 −0.0596142
\(113\) 3.12783i 0.294241i −0.989119 0.147121i \(-0.952999\pi\)
0.989119 0.147121i \(-0.0470005\pi\)
\(114\) −0.290725 −0.0272289
\(115\) −0.921622 + 3.70928i −0.0859417 + 0.345892i
\(116\) 0.447480 0.0415475
\(117\) −2.87936 + 2.17009i −0.266197 + 0.200625i
\(118\) 9.02052i 0.830406i
\(119\) 2.34017i 0.214523i
\(120\) −0.539189 + 2.17009i −0.0492210 + 0.198101i
\(121\) 1.52359 0.138508
\(122\) 3.26180 0.295309
\(123\) 1.41855 0.127906
\(124\) 6.68035i 0.599913i
\(125\) −8.32684 7.46081i −0.744775 0.667315i
\(126\) −0.630898 −0.0562048
\(127\) 20.6225i 1.82995i 0.403511 + 0.914975i \(0.367790\pi\)
−0.403511 + 0.914975i \(0.632210\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 5.75872 0.507027
\(130\) 7.41855 3.15676i 0.650650 0.276866i
\(131\) 6.81432 0.595369 0.297685 0.954664i \(-0.403786\pi\)
0.297685 + 0.954664i \(0.403786\pi\)
\(132\) 3.07838 0.267938
\(133\) 0.183417i 0.0159043i
\(134\) 7.75872 0.670252
\(135\) −0.539189 + 2.17009i −0.0464060 + 0.186771i
\(136\) 3.70928i 0.318068i
\(137\) −0.424694 −0.0362840 −0.0181420 0.999835i \(-0.505775\pi\)
−0.0181420 + 0.999835i \(0.505775\pi\)
\(138\) −1.70928 −0.145503
\(139\) −14.2557 −1.20915 −0.604574 0.796549i \(-0.706657\pi\)
−0.604574 + 0.796549i \(0.706657\pi\)
\(140\) 1.36910 + 0.340173i 0.115710 + 0.0287499i
\(141\) 2.73820i 0.230598i
\(142\) 1.65983i 0.139290i
\(143\) −6.68035 8.86376i −0.558639 0.741225i
\(144\) −1.00000 −0.0833333
\(145\) −0.971071 0.241276i −0.0806430 0.0200369i
\(146\) −15.3112 −1.26717
\(147\) 6.60197i 0.544521i
\(148\) 5.07838 0.417440
\(149\) 11.0205i 0.902836i −0.892313 0.451418i \(-0.850918\pi\)
0.892313 0.451418i \(-0.149082\pi\)
\(150\) 2.34017 4.41855i 0.191074 0.360773i
\(151\) 13.7321i 1.11750i −0.829336 0.558750i \(-0.811281\pi\)
0.829336 0.558750i \(-0.188719\pi\)
\(152\) 0.290725i 0.0235809i
\(153\) 3.70928i 0.299877i
\(154\) 1.94214i 0.156502i
\(155\) −3.60197 + 14.4969i −0.289317 + 1.16442i
\(156\) 2.17009 + 2.87936i 0.173746 + 0.230533i
\(157\) 20.8371i 1.66298i −0.555538 0.831491i \(-0.687488\pi\)
0.555538 0.831491i \(-0.312512\pi\)
\(158\) 10.6537 0.847562
\(159\) 14.0989 1.11812
\(160\) 2.17009 + 0.539189i 0.171560 + 0.0426266i
\(161\) 1.07838i 0.0849881i
\(162\) −1.00000 −0.0785674
\(163\) 5.23513 0.410047 0.205024 0.978757i \(-0.434273\pi\)
0.205024 + 0.978757i \(0.434273\pi\)
\(164\) 1.41855i 0.110770i
\(165\) −6.68035 1.65983i −0.520064 0.129217i
\(166\) 3.23513 0.251095
\(167\) 3.41855 0.264535 0.132268 0.991214i \(-0.457774\pi\)
0.132268 + 0.991214i \(0.457774\pi\)
\(168\) 0.630898i 0.0486748i
\(169\) 3.58145 12.4969i 0.275496 0.961302i
\(170\) 2.00000 8.04945i 0.153393 0.617365i
\(171\) 0.290725i 0.0222323i
\(172\) 5.75872i 0.439099i
\(173\) 8.83710i 0.671872i −0.941885 0.335936i \(-0.890947\pi\)
0.941885 0.335936i \(-0.109053\pi\)
\(174\) 0.447480i 0.0339234i
\(175\) −2.78765 1.47641i −0.210727 0.111606i
\(176\) 3.07838i 0.232041i
\(177\) −9.02052 −0.678024
\(178\) 12.3402i 0.924935i
\(179\) 21.3835 1.59828 0.799138 0.601147i \(-0.205290\pi\)
0.799138 + 0.601147i \(0.205290\pi\)
\(180\) 2.17009 + 0.539189i 0.161749 + 0.0401888i
\(181\) 10.9939 0.817167 0.408583 0.912721i \(-0.366023\pi\)
0.408583 + 0.912721i \(0.366023\pi\)
\(182\) 1.81658 1.36910i 0.134654 0.101485i
\(183\) 3.26180i 0.241119i
\(184\) 1.70928i 0.126009i
\(185\) −11.0205 2.73820i −0.810245 0.201317i
\(186\) −6.68035 −0.489827
\(187\) −11.4186 −0.835007
\(188\) −2.73820 −0.199704
\(189\) 0.630898i 0.0458910i
\(190\) 0.156755 0.630898i 0.0113722 0.0457701i
\(191\) 13.9421 1.00882 0.504409 0.863465i \(-0.331710\pi\)
0.504409 + 0.863465i \(0.331710\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) −3.79380 −0.273083 −0.136542 0.990634i \(-0.543599\pi\)
−0.136542 + 0.990634i \(0.543599\pi\)
\(194\) 8.20620 0.589171
\(195\) −3.15676 7.41855i −0.226060 0.531253i
\(196\) −6.60197 −0.471569
\(197\) 21.5174 1.53305 0.766527 0.642212i \(-0.221983\pi\)
0.766527 + 0.642212i \(0.221983\pi\)
\(198\) 3.07838i 0.218771i
\(199\) −17.8576 −1.26589 −0.632947 0.774195i \(-0.718155\pi\)
−0.632947 + 0.774195i \(0.718155\pi\)
\(200\) −4.41855 2.34017i −0.312439 0.165475i
\(201\) 7.75872i 0.547258i
\(202\) −3.86603 −0.272013
\(203\) −0.282314 −0.0198146
\(204\) 3.70928 0.259701
\(205\) −0.764867 + 3.07838i −0.0534206 + 0.215003i
\(206\) 7.84324i 0.546465i
\(207\) 1.70928i 0.118803i
\(208\) 2.87936 2.17009i 0.199648 0.150468i
\(209\) −0.894960 −0.0619057
\(210\) 0.340173 1.36910i 0.0234742 0.0944770i
\(211\) 16.7792 1.15513 0.577565 0.816344i \(-0.304003\pi\)
0.577565 + 0.816344i \(0.304003\pi\)
\(212\) 14.0989i 0.968316i
\(213\) −1.65983 −0.113729
\(214\) 15.7321i 1.07542i
\(215\) −3.10504 + 12.4969i −0.211762 + 0.852283i
\(216\) 1.00000i 0.0680414i
\(217\) 4.21461i 0.286107i
\(218\) 12.2329i 0.828514i
\(219\) 15.3112i 1.03464i
\(220\) −1.65983 + 6.68035i −0.111906 + 0.450389i
\(221\) −8.04945 10.6803i −0.541464 0.718438i
\(222\) 5.07838i 0.340838i
\(223\) −20.3630 −1.36360 −0.681802 0.731536i \(-0.738804\pi\)
−0.681802 + 0.731536i \(0.738804\pi\)
\(224\) 0.630898 0.0421536
\(225\) −4.41855 2.34017i −0.294570 0.156012i
\(226\) 3.12783i 0.208060i
\(227\) 14.8371 0.984773 0.492387 0.870377i \(-0.336125\pi\)
0.492387 + 0.870377i \(0.336125\pi\)
\(228\) 0.290725 0.0192537
\(229\) 12.6453i 0.835623i −0.908534 0.417812i \(-0.862797\pi\)
0.908534 0.417812i \(-0.137203\pi\)
\(230\) 0.921622 3.70928i 0.0607700 0.244582i
\(231\) −1.94214 −0.127784
\(232\) −0.447480 −0.0293785
\(233\) 25.3835i 1.66293i 0.555579 + 0.831463i \(0.312496\pi\)
−0.555579 + 0.831463i \(0.687504\pi\)
\(234\) 2.87936 2.17009i 0.188230 0.141863i
\(235\) 5.94214 + 1.47641i 0.387623 + 0.0963103i
\(236\) 9.02052i 0.587186i
\(237\) 10.6537i 0.692031i
\(238\) 2.34017i 0.151691i
\(239\) 9.84324i 0.636707i −0.947972 0.318353i \(-0.896870\pi\)
0.947972 0.318353i \(-0.103130\pi\)
\(240\) 0.539189 2.17009i 0.0348045 0.140078i
\(241\) 15.7854i 1.01683i 0.861113 + 0.508413i \(0.169768\pi\)
−0.861113 + 0.508413i \(0.830232\pi\)
\(242\) −1.52359 −0.0979401
\(243\) 1.00000i 0.0641500i
\(244\) −3.26180 −0.208815
\(245\) 14.3268 + 3.55971i 0.915308 + 0.227421i
\(246\) −1.41855 −0.0904435
\(247\) −0.630898 0.837101i −0.0401431 0.0532635i
\(248\) 6.68035i 0.424202i
\(249\) 3.23513i 0.205018i
\(250\) 8.32684 + 7.46081i 0.526636 + 0.471863i
\(251\) 10.1340 0.639650 0.319825 0.947477i \(-0.396376\pi\)
0.319825 + 0.947477i \(0.396376\pi\)
\(252\) 0.630898 0.0397428
\(253\) −5.26180 −0.330806
\(254\) 20.6225i 1.29397i
\(255\) −8.04945 2.00000i −0.504076 0.125245i
\(256\) 1.00000 0.0625000
\(257\) 28.7565i 1.79378i 0.442255 + 0.896889i \(0.354179\pi\)
−0.442255 + 0.896889i \(0.645821\pi\)
\(258\) −5.75872 −0.358522
\(259\) −3.20394 −0.199083
\(260\) −7.41855 + 3.15676i −0.460079 + 0.195774i
\(261\) −0.447480 −0.0276983
\(262\) −6.81432 −0.420990
\(263\) 7.28458i 0.449187i 0.974453 + 0.224593i \(0.0721053\pi\)
−0.974453 + 0.224593i \(0.927895\pi\)
\(264\) −3.07838 −0.189461
\(265\) −7.60197 + 30.5958i −0.466985 + 1.87949i
\(266\) 0.183417i 0.0112460i
\(267\) −12.3402 −0.755206
\(268\) −7.75872 −0.473939
\(269\) 21.9071 1.33570 0.667849 0.744297i \(-0.267215\pi\)
0.667849 + 0.744297i \(0.267215\pi\)
\(270\) 0.539189 2.17009i 0.0328140 0.132067i
\(271\) 9.10504i 0.553092i −0.961001 0.276546i \(-0.910810\pi\)
0.961001 0.276546i \(-0.0891898\pi\)
\(272\) 3.70928i 0.224908i
\(273\) −1.36910 1.81658i −0.0828618 0.109945i
\(274\) 0.424694 0.0256567
\(275\) 7.20394 13.6020i 0.434414 0.820230i
\(276\) 1.70928 0.102886
\(277\) 25.2039i 1.51436i −0.653208 0.757179i \(-0.726577\pi\)
0.653208 0.757179i \(-0.273423\pi\)
\(278\) 14.2557 0.854997
\(279\) 6.68035i 0.399942i
\(280\) −1.36910 0.340173i −0.0818195 0.0203292i
\(281\) 15.5441i 0.927284i −0.886023 0.463642i \(-0.846542\pi\)
0.886023 0.463642i \(-0.153458\pi\)
\(282\) 2.73820i 0.163058i
\(283\) 13.2762i 0.789186i 0.918856 + 0.394593i \(0.129114\pi\)
−0.918856 + 0.394593i \(0.870886\pi\)
\(284\) 1.65983i 0.0984926i
\(285\) −0.630898 0.156755i −0.0373711 0.00928539i
\(286\) 6.68035 + 8.86376i 0.395017 + 0.524125i
\(287\) 0.894960i 0.0528278i
\(288\) 1.00000 0.0589256
\(289\) 3.24128 0.190663
\(290\) 0.971071 + 0.241276i 0.0570232 + 0.0141682i
\(291\) 8.20620i 0.481056i
\(292\) 15.3112 0.896023
\(293\) 9.31965 0.544460 0.272230 0.962232i \(-0.412239\pi\)
0.272230 + 0.962232i \(0.412239\pi\)
\(294\) 6.60197i 0.385035i
\(295\) 4.86376 19.5753i 0.283179 1.13972i
\(296\) −5.07838 −0.295175
\(297\) −3.07838 −0.178626
\(298\) 11.0205i 0.638402i
\(299\) −3.70928 4.92162i −0.214513 0.284625i
\(300\) −2.34017 + 4.41855i −0.135110 + 0.255105i
\(301\) 3.63317i 0.209412i
\(302\) 13.7321i 0.790191i
\(303\) 3.86603i 0.222098i
\(304\) 0.290725i 0.0166742i
\(305\) 7.07838 + 1.75872i 0.405307 + 0.100704i
\(306\) 3.70928i 0.212045i
\(307\) 7.54411 0.430565 0.215283 0.976552i \(-0.430933\pi\)
0.215283 + 0.976552i \(0.430933\pi\)
\(308\) 1.94214i 0.110664i
\(309\) −7.84324 −0.446187
\(310\) 3.60197 14.4969i 0.204578 0.823370i
\(311\) −29.9421 −1.69786 −0.848932 0.528503i \(-0.822754\pi\)
−0.848932 + 0.528503i \(0.822754\pi\)
\(312\) −2.17009 2.87936i −0.122857 0.163012i
\(313\) 6.52359i 0.368735i −0.982857 0.184368i \(-0.940976\pi\)
0.982857 0.184368i \(-0.0590237\pi\)
\(314\) 20.8371i 1.17591i
\(315\) −1.36910 0.340173i −0.0771402 0.0191666i
\(316\) −10.6537 −0.599317
\(317\) 6.49693 0.364904 0.182452 0.983215i \(-0.441597\pi\)
0.182452 + 0.983215i \(0.441597\pi\)
\(318\) −14.0989 −0.790627
\(319\) 1.37751i 0.0771259i
\(320\) −2.17009 0.539189i −0.121312 0.0301416i
\(321\) −15.7321 −0.878078
\(322\) 1.07838i 0.0600956i
\(323\) −1.07838 −0.0600025
\(324\) 1.00000 0.0555556
\(325\) 17.8010 2.85043i 0.987421 0.158114i
\(326\) −5.23513 −0.289947
\(327\) 12.2329 0.676479
\(328\) 1.41855i 0.0783264i
\(329\) 1.72753 0.0952416
\(330\) 6.68035 + 1.65983i 0.367741 + 0.0913705i
\(331\) 14.8143i 0.814268i 0.913368 + 0.407134i \(0.133472\pi\)
−0.913368 + 0.407134i \(0.866528\pi\)
\(332\) −3.23513 −0.177551
\(333\) −5.07838 −0.278293
\(334\) −3.41855 −0.187055
\(335\) 16.8371 + 4.18342i 0.919909 + 0.228565i
\(336\) 0.630898i 0.0344183i
\(337\) 6.25565i 0.340767i 0.985378 + 0.170384i \(0.0545007\pi\)
−0.985378 + 0.170384i \(0.945499\pi\)
\(338\) −3.58145 + 12.4969i −0.194805 + 0.679743i
\(339\) 3.12783 0.169880
\(340\) −2.00000 + 8.04945i −0.108465 + 0.436543i
\(341\) −20.5646 −1.11364
\(342\) 0.290725i 0.0157206i
\(343\) 8.58145 0.463355
\(344\) 5.75872i 0.310490i
\(345\) −3.70928 0.921622i −0.199701 0.0496185i
\(346\) 8.83710i 0.475086i
\(347\) 8.41241i 0.451602i −0.974173 0.225801i \(-0.927500\pi\)
0.974173 0.225801i \(-0.0724999\pi\)
\(348\) 0.447480i 0.0239875i
\(349\) 23.5525i 1.26074i 0.776296 + 0.630369i \(0.217096\pi\)
−0.776296 + 0.630369i \(0.782904\pi\)
\(350\) 2.78765 + 1.47641i 0.149006 + 0.0789174i
\(351\) −2.17009 2.87936i −0.115831 0.153689i
\(352\) 3.07838i 0.164078i
\(353\) −14.4124 −0.767095 −0.383548 0.923521i \(-0.625298\pi\)
−0.383548 + 0.923521i \(0.625298\pi\)
\(354\) 9.02052 0.479435
\(355\) 0.894960 3.60197i 0.0474996 0.191173i
\(356\) 12.3402i 0.654028i
\(357\) −2.34017 −0.123855
\(358\) −21.3835 −1.13015
\(359\) 31.3340i 1.65375i 0.562388 + 0.826873i \(0.309883\pi\)
−0.562388 + 0.826873i \(0.690117\pi\)
\(360\) −2.17009 0.539189i −0.114374 0.0284177i
\(361\) 18.9155 0.995552
\(362\) −10.9939 −0.577824
\(363\) 1.52359i 0.0799678i
\(364\) −1.81658 + 1.36910i −0.0952148 + 0.0717605i
\(365\) −33.2267 8.25565i −1.73917 0.432121i
\(366\) 3.26180i 0.170497i
\(367\) 5.05172i 0.263697i −0.991270 0.131849i \(-0.957909\pi\)
0.991270 0.131849i \(-0.0420913\pi\)
\(368\) 1.70928i 0.0891021i
\(369\) 1.41855i 0.0738468i
\(370\) 11.0205 + 2.73820i 0.572929 + 0.142352i
\(371\) 8.89496i 0.461803i
\(372\) 6.68035 0.346360
\(373\) 13.5174i 0.699907i 0.936767 + 0.349953i \(0.113803\pi\)
−0.936767 + 0.349953i \(0.886197\pi\)
\(374\) 11.4186 0.590439
\(375\) 7.46081 8.32684i 0.385275 0.429996i
\(376\) 2.73820 0.141212
\(377\) 1.28846 0.971071i 0.0663589 0.0500127i
\(378\) 0.630898i 0.0324499i
\(379\) 6.59970i 0.339004i −0.985530 0.169502i \(-0.945784\pi\)
0.985530 0.169502i \(-0.0542159\pi\)
\(380\) −0.156755 + 0.630898i −0.00804139 + 0.0323644i
\(381\) −20.6225 −1.05652
\(382\) −13.9421 −0.713342
\(383\) −25.9421 −1.32558 −0.662791 0.748805i \(-0.730628\pi\)
−0.662791 + 0.748805i \(0.730628\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 1.04718 4.21461i 0.0533693 0.214797i
\(386\) 3.79380 0.193099
\(387\) 5.75872i 0.292732i
\(388\) −8.20620 −0.416607
\(389\) −6.75646 −0.342566 −0.171283 0.985222i \(-0.554791\pi\)
−0.171283 + 0.985222i \(0.554791\pi\)
\(390\) 3.15676 + 7.41855i 0.159849 + 0.375653i
\(391\) −6.34017 −0.320636
\(392\) 6.60197 0.333450
\(393\) 6.81432i 0.343737i
\(394\) −21.5174 −1.08403
\(395\) 23.1194 + 5.74435i 1.16326 + 0.289030i
\(396\) 3.07838i 0.154694i
\(397\) 33.1773 1.66512 0.832560 0.553935i \(-0.186874\pi\)
0.832560 + 0.553935i \(0.186874\pi\)
\(398\) 17.8576 0.895122
\(399\) −0.183417 −0.00918236
\(400\) 4.41855 + 2.34017i 0.220928 + 0.117009i
\(401\) 10.8950i 0.544068i −0.962288 0.272034i \(-0.912304\pi\)
0.962288 0.272034i \(-0.0876964\pi\)
\(402\) 7.75872i 0.386970i
\(403\) −14.4969 19.2351i −0.722143 0.958170i
\(404\) 3.86603 0.192342
\(405\) −2.17009 0.539189i −0.107832 0.0267925i
\(406\) 0.282314 0.0140110
\(407\) 15.6332i 0.774907i
\(408\) −3.70928 −0.183636
\(409\) 5.78992i 0.286293i 0.989701 + 0.143147i \(0.0457220\pi\)
−0.989701 + 0.143147i \(0.954278\pi\)
\(410\) 0.764867 3.07838i 0.0377741 0.152030i
\(411\) 0.424694i 0.0209486i
\(412\) 7.84324i 0.386409i
\(413\) 5.69102i 0.280037i
\(414\) 1.70928i 0.0840063i
\(415\) 7.02052 + 1.74435i 0.344624 + 0.0856267i
\(416\) −2.87936 + 2.17009i −0.141172 + 0.106397i
\(417\) 14.2557i 0.698102i
\(418\) 0.894960 0.0437739
\(419\) −40.4885 −1.97799 −0.988997 0.147937i \(-0.952737\pi\)
−0.988997 + 0.147937i \(0.952737\pi\)
\(420\) −0.340173 + 1.36910i −0.0165987 + 0.0668054i
\(421\) 24.3318i 1.18586i 0.805255 + 0.592929i \(0.202028\pi\)
−0.805255 + 0.592929i \(0.797972\pi\)
\(422\) −16.7792 −0.816801
\(423\) 2.73820 0.133136
\(424\) 14.0989i 0.684703i
\(425\) 8.68035 16.3896i 0.421059 0.795013i
\(426\) 1.65983 0.0804189
\(427\) 2.05786 0.0995868
\(428\) 15.7321i 0.760438i
\(429\) 8.86376 6.68035i 0.427947 0.322530i
\(430\) 3.10504 12.4969i 0.149738 0.602655i
\(431\) 32.8781i 1.58368i −0.610726 0.791842i \(-0.709122\pi\)
0.610726 0.791842i \(-0.290878\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 33.4063i 1.60540i 0.596381 + 0.802701i \(0.296605\pi\)
−0.596381 + 0.802701i \(0.703395\pi\)
\(434\) 4.21461i 0.202308i
\(435\) 0.241276 0.971071i 0.0115683 0.0465593i
\(436\) 12.2329i 0.585848i
\(437\) −0.496928 −0.0237713
\(438\) 15.3112i 0.731600i
\(439\) −30.0410 −1.43378 −0.716890 0.697186i \(-0.754435\pi\)
−0.716890 + 0.697186i \(0.754435\pi\)
\(440\) 1.65983 6.68035i 0.0791291 0.318473i
\(441\) 6.60197 0.314379
\(442\) 8.04945 + 10.6803i 0.382873 + 0.508012i
\(443\) 4.58145i 0.217671i −0.994060 0.108836i \(-0.965288\pi\)
0.994060 0.108836i \(-0.0347122\pi\)
\(444\) 5.07838i 0.241009i
\(445\) 6.65368 26.7792i 0.315415 1.26946i
\(446\) 20.3630 0.964214
\(447\) 11.0205 0.521253
\(448\) −0.630898 −0.0298071
\(449\) 13.8166i 0.652045i −0.945362 0.326022i \(-0.894292\pi\)
0.945362 0.326022i \(-0.105708\pi\)
\(450\) 4.41855 + 2.34017i 0.208292 + 0.110317i
\(451\) −4.36683 −0.205626
\(452\) 3.12783i 0.147121i
\(453\) 13.7321 0.645189
\(454\) −14.8371 −0.696340
\(455\) 4.68035 1.99159i 0.219418 0.0933672i
\(456\) −0.290725 −0.0136144
\(457\) −28.2062 −1.31943 −0.659715 0.751516i \(-0.729323\pi\)
−0.659715 + 0.751516i \(0.729323\pi\)
\(458\) 12.6453i 0.590875i
\(459\) −3.70928 −0.173134
\(460\) −0.921622 + 3.70928i −0.0429709 + 0.172946i
\(461\) 28.3812i 1.32184i 0.750454 + 0.660922i \(0.229835\pi\)
−0.750454 + 0.660922i \(0.770165\pi\)
\(462\) 1.94214 0.0903566
\(463\) 39.5669 1.83883 0.919415 0.393289i \(-0.128663\pi\)
0.919415 + 0.393289i \(0.128663\pi\)
\(464\) 0.447480 0.0207737
\(465\) −14.4969 3.60197i −0.672279 0.167037i
\(466\) 25.3835i 1.17587i
\(467\) 36.0989i 1.67046i −0.549902 0.835229i \(-0.685335\pi\)
0.549902 0.835229i \(-0.314665\pi\)
\(468\) −2.87936 + 2.17009i −0.133099 + 0.100312i
\(469\) 4.89496 0.226028
\(470\) −5.94214 1.47641i −0.274091 0.0681017i
\(471\) 20.8371 0.960123
\(472\) 9.02052i 0.415203i
\(473\) −17.7275 −0.815113
\(474\) 10.6537i 0.489340i
\(475\) 0.680346 1.28458i 0.0312164 0.0589406i
\(476\) 2.34017i 0.107262i
\(477\) 14.0989i 0.645544i
\(478\) 9.84324i 0.450220i
\(479\) 37.3607i 1.70705i 0.521049 + 0.853527i \(0.325541\pi\)
−0.521049 + 0.853527i \(0.674459\pi\)
\(480\) −0.539189 + 2.17009i −0.0246105 + 0.0990504i
\(481\) 14.6225 11.0205i 0.666728 0.502492i
\(482\) 15.7854i 0.719005i
\(483\) −1.07838 −0.0490679
\(484\) 1.52359 0.0692541
\(485\) 17.8082 + 4.42469i 0.808627 + 0.200915i
\(486\) 1.00000i 0.0453609i
\(487\) 32.0950 1.45436 0.727182 0.686445i \(-0.240830\pi\)
0.727182 + 0.686445i \(0.240830\pi\)
\(488\) 3.26180 0.147655
\(489\) 5.23513i 0.236741i
\(490\) −14.3268 3.55971i −0.647221 0.160811i
\(491\) 20.5874 0.929097 0.464549 0.885548i \(-0.346217\pi\)
0.464549 + 0.885548i \(0.346217\pi\)
\(492\) 1.41855 0.0639532
\(493\) 1.65983i 0.0747548i
\(494\) 0.630898 + 0.837101i 0.0283854 + 0.0376630i
\(495\) 1.65983 6.68035i 0.0746037 0.300259i
\(496\) 6.68035i 0.299956i
\(497\) 1.04718i 0.0469725i
\(498\) 3.23513i 0.144970i
\(499\) 31.7093i 1.41950i −0.704453 0.709751i \(-0.748807\pi\)
0.704453 0.709751i \(-0.251193\pi\)
\(500\) −8.32684 7.46081i −0.372388 0.333658i
\(501\) 3.41855i 0.152730i
\(502\) −10.1340 −0.452301
\(503\) 1.70928i 0.0762128i −0.999274 0.0381064i \(-0.987867\pi\)
0.999274 0.0381064i \(-0.0121326\pi\)
\(504\) −0.630898 −0.0281024
\(505\) −8.38962 2.08452i −0.373333 0.0927600i
\(506\) 5.26180 0.233915
\(507\) 12.4969 + 3.58145i 0.555008 + 0.159058i
\(508\) 20.6225i 0.914975i
\(509\) 15.6475i 0.693565i −0.937946 0.346783i \(-0.887274\pi\)
0.937946 0.346783i \(-0.112726\pi\)
\(510\) 8.04945 + 2.00000i 0.356436 + 0.0885615i
\(511\) −9.65983 −0.427326
\(512\) −1.00000 −0.0441942
\(513\) −0.290725 −0.0128358
\(514\) 28.7565i 1.26839i
\(515\) 4.22899 17.0205i 0.186352 0.750014i
\(516\) 5.75872 0.253514
\(517\) 8.42923i 0.370717i
\(518\) 3.20394 0.140773
\(519\) 8.83710 0.387906
\(520\) 7.41855 3.15676i 0.325325 0.138433i
\(521\) −3.67420 −0.160970 −0.0804849 0.996756i \(-0.525647\pi\)
−0.0804849 + 0.996756i \(0.525647\pi\)
\(522\) 0.447480 0.0195857
\(523\) 20.6803i 0.904288i 0.891945 + 0.452144i \(0.149341\pi\)
−0.891945 + 0.452144i \(0.850659\pi\)
\(524\) 6.81432 0.297685
\(525\) 1.47641 2.78765i 0.0644358 0.121663i
\(526\) 7.28458i 0.317623i
\(527\) −24.7792 −1.07940
\(528\) 3.07838 0.133969
\(529\) 20.0784 0.872973
\(530\) 7.60197 30.5958i 0.330208 1.32900i
\(531\) 9.02052i 0.391457i
\(532\) 0.183417i 0.00795216i
\(533\) −3.07838 4.08452i −0.133339 0.176920i
\(534\) 12.3402 0.534012
\(535\) 8.48255 34.1399i 0.366733 1.47600i
\(536\) 7.75872 0.335126
\(537\) 21.3835i 0.922765i
\(538\) −21.9071 −0.944481
\(539\) 20.3234i 0.875389i
\(540\) −0.539189 + 2.17009i −0.0232030 + 0.0933857i
\(541\) 8.13397i 0.349707i −0.984594 0.174853i \(-0.944055\pi\)
0.984594 0.174853i \(-0.0559451\pi\)
\(542\) 9.10504i 0.391095i
\(543\) 10.9939i 0.471792i
\(544\) 3.70928i 0.159034i
\(545\) −6.59583 + 26.5464i −0.282534 + 1.13712i
\(546\) 1.36910 + 1.81658i 0.0585922 + 0.0777426i
\(547\) 10.8371i 0.463361i −0.972792 0.231680i \(-0.925578\pi\)
0.972792 0.231680i \(-0.0744224\pi\)
\(548\) −0.424694 −0.0181420
\(549\) 3.26180 0.139210
\(550\) −7.20394 + 13.6020i −0.307177 + 0.579990i
\(551\) 0.130094i 0.00554217i
\(552\) −1.70928 −0.0727516
\(553\) 6.72138 0.285822
\(554\) 25.2039i 1.07081i
\(555\) 2.73820 11.0205i 0.116230 0.467795i
\(556\) −14.2557 −0.604574
\(557\) −1.18956 −0.0504033 −0.0252016 0.999682i \(-0.508023\pi\)
−0.0252016 + 0.999682i \(0.508023\pi\)
\(558\) 6.68035i 0.282802i
\(559\) −12.4969 16.5814i −0.528564 0.701321i
\(560\) 1.36910 + 0.340173i 0.0578551 + 0.0143749i
\(561\) 11.4186i 0.482092i
\(562\) 15.5441i 0.655689i
\(563\) 7.47187i 0.314902i 0.987527 + 0.157451i \(0.0503276\pi\)
−0.987527 + 0.157451i \(0.949672\pi\)
\(564\) 2.73820i 0.115299i
\(565\) −1.68649 + 6.78765i −0.0709511 + 0.285559i
\(566\) 13.2762i 0.558039i
\(567\) −0.630898 −0.0264952
\(568\) 1.65983i 0.0696448i
\(569\) 31.0472 1.30157 0.650783 0.759264i \(-0.274441\pi\)
0.650783 + 0.759264i \(0.274441\pi\)
\(570\) 0.630898 + 0.156755i 0.0264254 + 0.00656577i
\(571\) 6.73820 0.281985 0.140993 0.990011i \(-0.454971\pi\)
0.140993 + 0.990011i \(0.454971\pi\)
\(572\) −6.68035 8.86376i −0.279319 0.370613i
\(573\) 13.9421i 0.582441i
\(574\) 0.894960i 0.0373549i
\(575\) 4.00000 7.55252i 0.166812 0.314962i
\(576\) −1.00000 −0.0416667
\(577\) −4.47414 −0.186261 −0.0931305 0.995654i \(-0.529687\pi\)
−0.0931305 + 0.995654i \(0.529687\pi\)
\(578\) −3.24128 −0.134819
\(579\) 3.79380i 0.157665i
\(580\) −0.971071 0.241276i −0.0403215 0.0100185i
\(581\) 2.04104 0.0846765
\(582\) 8.20620i 0.340158i
\(583\) −43.4017 −1.79752
\(584\) −15.3112 −0.633584
\(585\) 7.41855 3.15676i 0.306719 0.130516i
\(586\) −9.31965 −0.384991
\(587\) −36.0288 −1.48707 −0.743533 0.668699i \(-0.766851\pi\)
−0.743533 + 0.668699i \(0.766851\pi\)
\(588\) 6.60197i 0.272261i
\(589\) −1.94214 −0.0800245
\(590\) −4.86376 + 19.5753i −0.200238 + 0.805903i
\(591\) 21.5174i 0.885110i
\(592\) 5.07838 0.208720
\(593\) −39.1917 −1.60941 −0.804704 0.593676i \(-0.797676\pi\)
−0.804704 + 0.593676i \(0.797676\pi\)
\(594\) 3.07838 0.126307
\(595\) 1.26180 5.07838i 0.0517286 0.208193i
\(596\) 11.0205i 0.451418i
\(597\) 17.8576i 0.730864i
\(598\) 3.70928 + 4.92162i 0.151684 + 0.201260i
\(599\) 5.10957 0.208772 0.104386 0.994537i \(-0.466712\pi\)
0.104386 + 0.994537i \(0.466712\pi\)
\(600\) 2.34017 4.41855i 0.0955372 0.180387i
\(601\) 19.4452 0.793187 0.396593 0.917994i \(-0.370192\pi\)
0.396593 + 0.917994i \(0.370192\pi\)
\(602\) 3.63317i 0.148077i
\(603\) 7.75872 0.315960
\(604\) 13.7321i 0.558750i
\(605\) −3.30632 0.821503i −0.134421 0.0333988i
\(606\) 3.86603i 0.157047i
\(607\) 20.6225i 0.837041i 0.908207 + 0.418520i \(0.137451\pi\)
−0.908207 + 0.418520i \(0.862549\pi\)
\(608\) 0.290725i 0.0117904i
\(609\) 0.282314i 0.0114399i
\(610\) −7.07838 1.75872i −0.286595 0.0712086i
\(611\) −7.88428 + 5.94214i −0.318964 + 0.240393i
\(612\) 3.70928i 0.149939i
\(613\) 4.71154 0.190297 0.0951487 0.995463i \(-0.469667\pi\)
0.0951487 + 0.995463i \(0.469667\pi\)
\(614\) −7.54411 −0.304455
\(615\) −3.07838 0.764867i −0.124132 0.0308424i
\(616\) 1.94214i 0.0782511i
\(617\) −13.6332 −0.548851 −0.274425 0.961608i \(-0.588488\pi\)
−0.274425 + 0.961608i \(0.588488\pi\)
\(618\) 7.84324 0.315502
\(619\) 37.4368i 1.50471i 0.658757 + 0.752356i \(0.271083\pi\)
−0.658757 + 0.752356i \(0.728917\pi\)
\(620\) −3.60197 + 14.4969i −0.144659 + 0.582211i
\(621\) −1.70928 −0.0685909
\(622\) 29.9421 1.20057
\(623\) 7.78539i 0.311915i
\(624\) 2.17009 + 2.87936i 0.0868730 + 0.115267i
\(625\) 14.0472 + 20.6803i 0.561887 + 0.827214i
\(626\) 6.52359i 0.260735i
\(627\) 0.894960i 0.0357413i
\(628\) 20.8371i 0.831491i
\(629\) 18.8371i 0.751084i
\(630\) 1.36910 + 0.340173i 0.0545463 + 0.0135528i
\(631\) 8.05786i 0.320778i 0.987054 + 0.160389i \(0.0512749\pi\)
−0.987054 + 0.160389i \(0.948725\pi\)
\(632\) 10.6537 0.423781
\(633\) 16.7792i 0.666915i
\(634\) −6.49693 −0.258026
\(635\) 11.1194 44.7526i 0.441261 1.77595i
\(636\) 14.0989 0.559058
\(637\) −19.0095 + 14.3268i −0.753182 + 0.567650i
\(638\) 1.37751i 0.0545363i
\(639\) 1.65983i 0.0656617i
\(640\) 2.17009 + 0.539189i 0.0857802 + 0.0213133i
\(641\) 46.2967 1.82861 0.914305 0.405027i \(-0.132738\pi\)
0.914305 + 0.405027i \(0.132738\pi\)
\(642\) 15.7321 0.620895
\(643\) 21.4329 0.845232 0.422616 0.906309i \(-0.361112\pi\)
0.422616 + 0.906309i \(0.361112\pi\)
\(644\) 1.07838i 0.0424940i
\(645\) −12.4969 3.10504i −0.492066 0.122261i
\(646\) 1.07838 0.0424282
\(647\) 26.5874i 1.04526i −0.852560 0.522630i \(-0.824951\pi\)
0.852560 0.522630i \(-0.175049\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 27.7686 1.09001
\(650\) −17.8010 + 2.85043i −0.698212 + 0.111803i
\(651\) −4.21461 −0.165184
\(652\) 5.23513 0.205024
\(653\) 1.53427i 0.0600406i 0.999549 + 0.0300203i \(0.00955719\pi\)
−0.999549 + 0.0300203i \(0.990443\pi\)
\(654\) −12.2329 −0.478343
\(655\) −14.7877 3.67420i −0.577801 0.143563i
\(656\) 1.41855i 0.0553851i
\(657\) −15.3112 −0.597349
\(658\) −1.72753 −0.0673460
\(659\) −14.3318 −0.558286 −0.279143 0.960250i \(-0.590050\pi\)
−0.279143 + 0.960250i \(0.590050\pi\)
\(660\) −6.68035 1.65983i −0.260032 0.0646087i
\(661\) 38.1049i 1.48211i 0.671446 + 0.741054i \(0.265674\pi\)
−0.671446 + 0.741054i \(0.734326\pi\)
\(662\) 14.8143i 0.575775i
\(663\) 10.6803 8.04945i 0.414790 0.312615i
\(664\) 3.23513 0.125548
\(665\) 0.0988967 0.398032i 0.00383505 0.0154350i
\(666\) 5.07838 0.196783
\(667\) 0.764867i 0.0296158i
\(668\) 3.41855 0.132268
\(669\) 20.3630i 0.787277i
\(670\) −16.8371 4.18342i −0.650474 0.161620i
\(671\) 10.0410i 0.387630i
\(672\) 0.630898i 0.0243374i
\(673\) 28.4657i 1.09727i −0.836061 0.548637i \(-0.815147\pi\)
0.836061 0.548637i \(-0.184853\pi\)
\(674\) 6.25565i 0.240959i
\(675\) 2.34017 4.41855i 0.0900733 0.170070i
\(676\) 3.58145 12.4969i 0.137748 0.480651i
\(677\) 0.424694i 0.0163223i −0.999967 0.00816115i \(-0.997402\pi\)
0.999967 0.00816115i \(-0.00259780\pi\)
\(678\) −3.12783 −0.120123
\(679\) 5.17727 0.198686
\(680\) 2.00000 8.04945i 0.0766965 0.308682i
\(681\) 14.8371i 0.568559i
\(682\) 20.5646 0.787460
\(683\) −4.28231 −0.163858 −0.0819291 0.996638i \(-0.526108\pi\)
−0.0819291 + 0.996638i \(0.526108\pi\)
\(684\) 0.290725i 0.0111161i
\(685\) 0.921622 + 0.228990i 0.0352134 + 0.00874926i
\(686\) −8.58145 −0.327641
\(687\) 12.6453 0.482447
\(688\) 5.75872i 0.219549i
\(689\) −30.5958 40.5958i −1.16561 1.54658i
\(690\) 3.70928 + 0.921622i 0.141210 + 0.0350856i
\(691\) 38.5464i 1.46637i −0.680027 0.733187i \(-0.738032\pi\)
0.680027 0.733187i \(-0.261968\pi\)
\(692\) 8.83710i 0.335936i
\(693\) 1.94214i 0.0737758i
\(694\) 8.41241i 0.319331i
\(695\) 30.9360 + 7.68649i 1.17347 + 0.291565i
\(696\) 0.447480i 0.0169617i
\(697\) −5.26180 −0.199305
\(698\) 23.5525i 0.891476i
\(699\) −25.3835 −0.960091
\(700\) −2.78765 1.47641i −0.105363 0.0558030i
\(701\) −47.4824 −1.79338 −0.896692 0.442654i \(-0.854037\pi\)
−0.896692 + 0.442654i \(0.854037\pi\)
\(702\) 2.17009 + 2.87936i 0.0819046 + 0.108675i
\(703\) 1.47641i 0.0556838i
\(704\) 3.07838i 0.116021i
\(705\) −1.47641 + 5.94214i −0.0556048 + 0.223794i
\(706\) 14.4124 0.542418
\(707\) −2.43907 −0.0917307
\(708\) −9.02052 −0.339012
\(709\) 35.4824i 1.33257i −0.745698 0.666284i \(-0.767884\pi\)
0.745698 0.666284i \(-0.232116\pi\)
\(710\) −0.894960 + 3.60197i −0.0335873 + 0.135179i
\(711\) 10.6537 0.399544
\(712\) 12.3402i 0.462468i
\(713\) −11.4186 −0.427628
\(714\) 2.34017 0.0875788
\(715\) 9.71769 + 22.8371i 0.363421 + 0.854059i
\(716\) 21.3835 0.799138
\(717\) 9.84324 0.367603
\(718\) 31.3340i 1.16938i
\(719\) 32.8781 1.22615 0.613074 0.790026i \(-0.289933\pi\)
0.613074 + 0.790026i \(0.289933\pi\)
\(720\) 2.17009 + 0.539189i 0.0808743 + 0.0200944i
\(721\) 4.94828i 0.184284i
\(722\) −18.9155 −0.703961
\(723\) −15.7854 −0.587065
\(724\) 10.9939 0.408583
\(725\) 1.97721 + 1.04718i 0.0734319 + 0.0388913i
\(726\) 1.52359i 0.0565457i
\(727\) 26.9939i 1.00115i −0.865694 0.500573i \(-0.833123\pi\)
0.865694 0.500573i \(-0.166877\pi\)
\(728\) 1.81658 1.36910i 0.0673270 0.0507423i
\(729\) −1.00000 −0.0370370
\(730\) 33.2267 + 8.25565i 1.22978 + 0.305555i
\(731\) −21.3607 −0.790054
\(732\) 3.26180i 0.120559i
\(733\) 23.3340 0.861862 0.430931 0.902385i \(-0.358185\pi\)
0.430931 + 0.902385i \(0.358185\pi\)
\(734\) 5.05172i 0.186462i
\(735\) −3.55971 + 14.3268i −0.131302 + 0.528454i
\(736\) 1.70928i 0.0630047i
\(737\) 23.8843i 0.879789i
\(738\) 1.41855i 0.0522176i
\(739\) 45.3835i 1.66946i 0.550661 + 0.834729i \(0.314376\pi\)
−0.550661 + 0.834729i \(0.685624\pi\)
\(740\) −11.0205 2.73820i −0.405122 0.100658i
\(741\) 0.837101 0.630898i 0.0307517 0.0231766i
\(742\) 8.89496i 0.326544i
\(743\) 10.8904 0.399531 0.199765 0.979844i \(-0.435982\pi\)
0.199765 + 0.979844i \(0.435982\pi\)
\(744\) −6.68035 −0.244913
\(745\) −5.94214 + 23.9155i −0.217703 + 0.876195i
\(746\) 13.5174i 0.494909i
\(747\) 3.23513 0.118367
\(748\) −11.4186 −0.417504
\(749\) 9.92532i 0.362663i
\(750\) −7.46081 + 8.32684i −0.272430 + 0.304053i
\(751\) −33.1917 −1.21118 −0.605590 0.795777i \(-0.707063\pi\)
−0.605590 + 0.795777i \(0.707063\pi\)
\(752\) −2.73820 −0.0998521
\(753\) 10.1340i 0.369302i
\(754\) −1.28846 + 0.971071i −0.0469228 + 0.0353643i
\(755\) −7.40417 + 29.7998i −0.269466 + 1.08452i
\(756\) 0.630898i 0.0229455i
\(757\) 7.54411i 0.274195i 0.990558 + 0.137098i \(0.0437774\pi\)
−0.990558 + 0.137098i \(0.956223\pi\)
\(758\) 6.59970i 0.239712i
\(759\) 5.26180i 0.190991i
\(760\) 0.156755 0.630898i 0.00568612 0.0228851i
\(761\) 35.8264i 1.29871i 0.760487 + 0.649353i \(0.224960\pi\)
−0.760487 + 0.649353i \(0.775040\pi\)
\(762\) 20.6225 0.747074
\(763\) 7.71769i 0.279399i
\(764\) 13.9421 0.504409
\(765\) 2.00000 8.04945i 0.0723102 0.291028i
\(766\) 25.9421 0.937328
\(767\) 19.5753 + 25.9733i 0.706823 + 0.937843i
\(768\) 1.00000i 0.0360844i
\(769\) 36.3135i 1.30950i 0.755846 + 0.654749i \(0.227226\pi\)
−0.755846 + 0.654749i \(0.772774\pi\)
\(770\) −1.04718 + 4.21461i −0.0377378 + 0.151884i
\(771\) −28.7565 −1.03564
\(772\) −3.79380 −0.136542
\(773\) −2.99386 −0.107682 −0.0538408 0.998550i \(-0.517146\pi\)
−0.0538408 + 0.998550i \(0.517146\pi\)
\(774\) 5.75872i 0.206993i
\(775\) 15.6332 29.5174i 0.561560 1.06030i
\(776\) 8.20620 0.294586
\(777\) 3.20394i 0.114941i
\(778\) 6.75646 0.242231
\(779\) −0.412408 −0.0147760
\(780\) −3.15676 7.41855i −0.113030 0.265627i
\(781\) 5.10957 0.182835
\(782\) 6.34017 0.226724
\(783\) 0.447480i 0.0159916i
\(784\) −6.60197 −0.235785