Properties

Label 354.2.c.a.353.2
Level 354
Weight 2
Character 354.353
Analytic conductor 2.827
Analytic rank 0
Dimension 10
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 354.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(2.82670423155\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: 10.0.41542366334681088.1
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 353.2
Root \(1.65530 + 0.509894i\)
Character \(\chi\) = 354.353
Dual form 354.2.c.a.353.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-1.65530 + 0.509894i) q^{3} +1.00000 q^{4} -2.90260i q^{5} +(1.65530 - 0.509894i) q^{6} -3.06916 q^{7} -1.00000 q^{8} +(2.48002 - 1.68805i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-1.65530 + 0.509894i) q^{3} +1.00000 q^{4} -2.90260i q^{5} +(1.65530 - 0.509894i) q^{6} -3.06916 q^{7} -1.00000 q^{8} +(2.48002 - 1.68805i) q^{9} +2.90260i q^{10} +1.35591 q^{11} +(-1.65530 + 0.509894i) q^{12} +7.06097i q^{13} +3.06916 q^{14} +(1.48002 + 4.80466i) q^{15} +1.00000 q^{16} -0.568263i q^{17} +(-2.48002 + 1.68805i) q^{18} -4.42507 q^{19} -2.90260i q^{20} +(5.08036 - 1.56494i) q^{21} -1.35591 q^{22} -7.20070 q^{23} +(1.65530 - 0.509894i) q^{24} -3.42507 q^{25} -7.06097i q^{26} +(-3.24444 + 4.05877i) q^{27} -3.06916 q^{28} +2.41581i q^{29} +(-1.48002 - 4.80466i) q^{30} +6.44875i q^{31} -1.00000 q^{32} +(-2.24444 + 0.691371i) q^{33} +0.568263i q^{34} +8.90852i q^{35} +(2.48002 - 1.68805i) q^{36} +1.74257i q^{37} +4.42507 q^{38} +(-3.60035 - 11.6880i) q^{39} +2.90260i q^{40} +8.09404i q^{41} +(-5.08036 + 1.56494i) q^{42} +0.770515i q^{43} +1.35591 q^{44} +(-4.89973 - 7.19849i) q^{45} +7.20070 q^{46} -4.48887 q^{47} +(-1.65530 + 0.509894i) q^{48} +2.41972 q^{49} +3.42507 q^{50} +(0.289754 + 0.940644i) q^{51} +7.06097i q^{52} +1.03307i q^{53} +(3.24444 - 4.05877i) q^{54} -3.93566i q^{55} +3.06916 q^{56} +(7.32480 - 2.25631i) q^{57} -2.41581i q^{58} +(-3.07451 - 7.03899i) q^{59} +(1.48002 + 4.80466i) q^{60} -10.6746i q^{61} -6.44875i q^{62} +(-7.61156 + 5.18089i) q^{63} +1.00000 q^{64} +20.4952 q^{65} +(2.24444 - 0.691371i) q^{66} +1.09256i q^{67} -0.568263i q^{68} +(11.9193 - 3.67159i) q^{69} -8.90852i q^{70} +11.0406i q^{71} +(-2.48002 + 1.68805i) q^{72} -5.96044i q^{73} -1.74257i q^{74} +(5.66950 - 1.74642i) q^{75} -4.42507 q^{76} -4.16150 q^{77} +(3.60035 + 11.6880i) q^{78} +8.62041 q^{79} -2.90260i q^{80} +(3.30096 - 8.37279i) q^{81} -8.09404i q^{82} +14.6504 q^{83} +(5.08036 - 1.56494i) q^{84} -1.64944 q^{85} -0.770515i q^{86} +(-1.23181 - 3.99888i) q^{87} -1.35591 q^{88} -11.5174 q^{89} +(4.89973 + 7.19849i) q^{90} -21.6712i q^{91} -7.20070 q^{92} +(-3.28818 - 10.6746i) q^{93} +4.48887 q^{94} +12.8442i q^{95} +(1.65530 - 0.509894i) q^{96} +8.16151i q^{97} -2.41972 q^{98} +(3.36268 - 2.28885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} - q^{3} + 10q^{4} + q^{6} - 2q^{7} - 10q^{8} + 3q^{9} + O(q^{10}) \) \( 10q - 10q^{2} - q^{3} + 10q^{4} + q^{6} - 2q^{7} - 10q^{8} + 3q^{9} + 4q^{11} - q^{12} + 2q^{14} - 7q^{15} + 10q^{16} - 3q^{18} - 6q^{19} - 3q^{21} - 4q^{22} - 8q^{23} + q^{24} + 4q^{25} - 10q^{27} - 2q^{28} + 7q^{30} - 10q^{32} + 3q^{36} + 6q^{38} - 4q^{39} + 3q^{42} + 4q^{44} - 11q^{45} + 8q^{46} - q^{48} + 8q^{49} - 4q^{50} + 2q^{51} + 10q^{54} + 2q^{56} - 3q^{57} + 20q^{59} - 7q^{60} - 19q^{63} + 10q^{64} + 16q^{65} + 14q^{69} - 3q^{72} - 4q^{75} - 6q^{76} + 48q^{77} + 4q^{78} + 6q^{79} + 7q^{81} + 12q^{83} - 3q^{84} - 4q^{85} - 15q^{87} - 4q^{88} - 16q^{89} + 11q^{90} - 8q^{92} - 52q^{93} + q^{96} - 8q^{98} + 2q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

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
\(3\) −1.65530 + 0.509894i −0.955686 + 0.294387i
\(4\) 1.00000 0.500000
\(5\) 2.90260i 1.29808i −0.760754 0.649040i \(-0.775171\pi\)
0.760754 0.649040i \(-0.224829\pi\)
\(6\) 1.65530 0.509894i 0.675772 0.208163i
\(7\) −3.06916 −1.16003 −0.580016 0.814605i \(-0.696954\pi\)
−0.580016 + 0.814605i \(0.696954\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.48002 1.68805i 0.826672 0.562684i
\(10\) 2.90260i 0.917882i
\(11\) 1.35591 0.408823 0.204411 0.978885i \(-0.434472\pi\)
0.204411 + 0.978885i \(0.434472\pi\)
\(12\) −1.65530 + 0.509894i −0.477843 + 0.147194i
\(13\) 7.06097i 1.95836i 0.202989 + 0.979181i \(0.434934\pi\)
−0.202989 + 0.979181i \(0.565066\pi\)
\(14\) 3.06916 0.820266
\(15\) 1.48002 + 4.80466i 0.382139 + 1.24056i
\(16\) 1.00000 0.250000
\(17\) 0.568263i 0.137824i −0.997623 0.0689120i \(-0.978047\pi\)
0.997623 0.0689120i \(-0.0219528\pi\)
\(18\) −2.48002 + 1.68805i −0.584545 + 0.397878i
\(19\) −4.42507 −1.01518 −0.507590 0.861599i \(-0.669464\pi\)
−0.507590 + 0.861599i \(0.669464\pi\)
\(20\) 2.90260i 0.649040i
\(21\) 5.08036 1.56494i 1.10863 0.341499i
\(22\) −1.35591 −0.289081
\(23\) −7.20070 −1.50145 −0.750724 0.660615i \(-0.770295\pi\)
−0.750724 + 0.660615i \(0.770295\pi\)
\(24\) 1.65530 0.509894i 0.337886 0.104082i
\(25\) −3.42507 −0.685013
\(26\) 7.06097i 1.38477i
\(27\) −3.24444 + 4.05877i −0.624392 + 0.781111i
\(28\) −3.06916 −0.580016
\(29\) 2.41581i 0.448605i 0.974520 + 0.224302i \(0.0720103\pi\)
−0.974520 + 0.224302i \(0.927990\pi\)
\(30\) −1.48002 4.80466i −0.270213 0.877207i
\(31\) 6.44875i 1.15823i 0.815246 + 0.579115i \(0.196602\pi\)
−0.815246 + 0.579115i \(0.803398\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.24444 + 0.691371i −0.390706 + 0.120352i
\(34\) 0.568263i 0.0974563i
\(35\) 8.90852i 1.50581i
\(36\) 2.48002 1.68805i 0.413336 0.281342i
\(37\) 1.74257i 0.286476i 0.989688 + 0.143238i \(0.0457515\pi\)
−0.989688 + 0.143238i \(0.954248\pi\)
\(38\) 4.42507 0.717841
\(39\) −3.60035 11.6880i −0.576517 1.87158i
\(40\) 2.90260i 0.458941i
\(41\) 8.09404i 1.26408i 0.774937 + 0.632039i \(0.217782\pi\)
−0.774937 + 0.632039i \(0.782218\pi\)
\(42\) −5.08036 + 1.56494i −0.783917 + 0.241476i
\(43\) 0.770515i 0.117502i 0.998273 + 0.0587512i \(0.0187119\pi\)
−0.998273 + 0.0587512i \(0.981288\pi\)
\(44\) 1.35591 0.204411
\(45\) −4.89973 7.19849i −0.730409 1.07309i
\(46\) 7.20070 1.06168
\(47\) −4.48887 −0.654769 −0.327385 0.944891i \(-0.606167\pi\)
−0.327385 + 0.944891i \(0.606167\pi\)
\(48\) −1.65530 + 0.509894i −0.238922 + 0.0735968i
\(49\) 2.41972 0.345674
\(50\) 3.42507 0.484378
\(51\) 0.289754 + 0.940644i 0.0405737 + 0.131717i
\(52\) 7.06097i 0.979181i
\(53\) 1.03307i 0.141903i 0.997480 + 0.0709514i \(0.0226035\pi\)
−0.997480 + 0.0709514i \(0.977396\pi\)
\(54\) 3.24444 4.05877i 0.441512 0.552329i
\(55\) 3.93566i 0.530685i
\(56\) 3.06916 0.410133
\(57\) 7.32480 2.25631i 0.970194 0.298856i
\(58\) 2.41581i 0.317211i
\(59\) −3.07451 7.03899i −0.400267 0.916399i
\(60\) 1.48002 + 4.80466i 0.191069 + 0.620279i
\(61\) 10.6746i 1.36674i −0.730072 0.683371i \(-0.760513\pi\)
0.730072 0.683371i \(-0.239487\pi\)
\(62\) 6.44875i 0.818992i
\(63\) −7.61156 + 5.18089i −0.958966 + 0.652731i
\(64\) 1.00000 0.125000
\(65\) 20.4952 2.54211
\(66\) 2.24444 0.691371i 0.276271 0.0851019i
\(67\) 1.09256i 0.133478i 0.997770 + 0.0667388i \(0.0212594\pi\)
−0.997770 + 0.0667388i \(0.978741\pi\)
\(68\) 0.568263i 0.0689120i
\(69\) 11.9193 3.67159i 1.43491 0.442008i
\(70\) 8.90852i 1.06477i
\(71\) 11.0406i 1.31028i 0.755508 + 0.655139i \(0.227390\pi\)
−0.755508 + 0.655139i \(0.772610\pi\)
\(72\) −2.48002 + 1.68805i −0.292273 + 0.198939i
\(73\) 5.96044i 0.697617i −0.937194 0.348808i \(-0.886586\pi\)
0.937194 0.348808i \(-0.113414\pi\)
\(74\) 1.74257i 0.202569i
\(75\) 5.66950 1.74642i 0.654658 0.201659i
\(76\) −4.42507 −0.507590
\(77\) −4.16150 −0.474247
\(78\) 3.60035 + 11.6880i 0.407659 + 1.32341i
\(79\) 8.62041 0.969872 0.484936 0.874550i \(-0.338843\pi\)
0.484936 + 0.874550i \(0.338843\pi\)
\(80\) 2.90260i 0.324520i
\(81\) 3.30096 8.37279i 0.366774 0.930310i
\(82\) 8.09404i 0.893837i
\(83\) 14.6504 1.60809 0.804044 0.594570i \(-0.202678\pi\)
0.804044 + 0.594570i \(0.202678\pi\)
\(84\) 5.08036 1.56494i 0.554313 0.170749i
\(85\) −1.64944 −0.178907
\(86\) 0.770515i 0.0830867i
\(87\) −1.23181 3.99888i −0.132064 0.428725i
\(88\) −1.35591 −0.144541
\(89\) −11.5174 −1.22084 −0.610422 0.792077i \(-0.709000\pi\)
−0.610422 + 0.792077i \(0.709000\pi\)
\(90\) 4.89973 + 7.19849i 0.516477 + 0.758787i
\(91\) 21.6712i 2.27176i
\(92\) −7.20070 −0.750724
\(93\) −3.28818 10.6746i −0.340968 1.10690i
\(94\) 4.48887 0.462992
\(95\) 12.8442i 1.31779i
\(96\) 1.65530 0.509894i 0.168943 0.0520408i
\(97\) 8.16151i 0.828676i 0.910123 + 0.414338i \(0.135987\pi\)
−0.910123 + 0.414338i \(0.864013\pi\)
\(98\) −2.41972 −0.244428
\(99\) 3.36268 2.28885i 0.337962 0.230038i
\(100\) −3.42507 −0.342507
\(101\) −10.1615 −1.01111 −0.505554 0.862795i \(-0.668712\pi\)
−0.505554 + 0.862795i \(0.668712\pi\)
\(102\) −0.289754 0.940644i −0.0286899 0.0931377i
\(103\) 16.6350i 1.63910i 0.573009 + 0.819549i \(0.305776\pi\)
−0.573009 + 0.819549i \(0.694224\pi\)
\(104\) 7.06097i 0.692386i
\(105\) −4.54240 14.7462i −0.443293 1.43909i
\(106\) 1.03307i 0.100340i
\(107\) 19.5376i 1.88877i −0.328836 0.944387i \(-0.606656\pi\)
0.328836 0.944387i \(-0.393344\pi\)
\(108\) −3.24444 + 4.05877i −0.312196 + 0.390556i
\(109\) 1.42258i 0.136259i 0.997676 + 0.0681293i \(0.0217030\pi\)
−0.997676 + 0.0681293i \(0.978297\pi\)
\(110\) 3.93566i 0.375251i
\(111\) −0.888525 2.88447i −0.0843350 0.273782i
\(112\) −3.06916 −0.290008
\(113\) −16.6379 −1.56516 −0.782580 0.622550i \(-0.786097\pi\)
−0.782580 + 0.622550i \(0.786097\pi\)
\(114\) −7.32480 + 2.25631i −0.686030 + 0.211323i
\(115\) 20.9007i 1.94900i
\(116\) 2.41581i 0.224302i
\(117\) 11.9193 + 17.5113i 1.10194 + 1.61892i
\(118\) 3.07451 + 7.03899i 0.283031 + 0.647992i
\(119\) 1.74409i 0.159880i
\(120\) −1.48002 4.80466i −0.135106 0.438603i
\(121\) −9.16150 −0.832864
\(122\) 10.6746i 0.966432i
\(123\) −4.12710 13.3980i −0.372128 1.20806i
\(124\) 6.44875i 0.579115i
\(125\) 4.57139i 0.408878i
\(126\) 7.61156 5.18089i 0.678091 0.461551i
\(127\) 8.29304 0.735889 0.367944 0.929848i \(-0.380062\pi\)
0.367944 + 0.929848i \(0.380062\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.392881 1.27543i −0.0345912 0.112295i
\(130\) −20.4952 −1.79754
\(131\) −10.0063 −0.874253 −0.437127 0.899400i \(-0.644004\pi\)
−0.437127 + 0.899400i \(0.644004\pi\)
\(132\) −2.24444 + 0.691371i −0.195353 + 0.0601761i
\(133\) 13.5812 1.17764
\(134\) 1.09256i 0.0943830i
\(135\) 11.7810 + 9.41729i 1.01395 + 0.810511i
\(136\) 0.568263i 0.0487282i
\(137\) 12.8067i 1.09415i −0.837084 0.547074i \(-0.815742\pi\)
0.837084 0.547074i \(-0.184258\pi\)
\(138\) −11.9193 + 3.67159i −1.01464 + 0.312547i
\(139\) 8.09377 0.686505 0.343252 0.939243i \(-0.388471\pi\)
0.343252 + 0.939243i \(0.388471\pi\)
\(140\) 8.90852i 0.752907i
\(141\) 7.43042 2.28885i 0.625754 0.192756i
\(142\) 11.0406i 0.926507i
\(143\) 9.57406i 0.800623i
\(144\) 2.48002 1.68805i 0.206668 0.140671i
\(145\) 7.01212 0.582325
\(146\) 5.96044i 0.493290i
\(147\) −4.00535 + 1.23380i −0.330356 + 0.101762i
\(148\) 1.74257i 0.143238i
\(149\) 12.4139 1.01698 0.508492 0.861066i \(-0.330203\pi\)
0.508492 + 0.861066i \(0.330203\pi\)
\(150\) −5.66950 + 1.74642i −0.462913 + 0.142595i
\(151\) 6.74099i 0.548574i −0.961648 0.274287i \(-0.911558\pi\)
0.961648 0.274287i \(-0.0884418\pi\)
\(152\) 4.42507 0.358920
\(153\) −0.959258 1.40930i −0.0775514 0.113935i
\(154\) 4.16150 0.335344
\(155\) 18.7181 1.50347
\(156\) −3.60035 11.6880i −0.288259 0.935790i
\(157\) 4.18807i 0.334244i 0.985936 + 0.167122i \(0.0534474\pi\)
−0.985936 + 0.167122i \(0.946553\pi\)
\(158\) −8.62041 −0.685803
\(159\) −0.526755 1.71003i −0.0417744 0.135615i
\(160\) 2.90260i 0.229470i
\(161\) 22.1001 1.74173
\(162\) −3.30096 + 8.37279i −0.259348 + 0.657829i
\(163\) −1.85728 −0.145473 −0.0727365 0.997351i \(-0.523173\pi\)
−0.0727365 + 0.997351i \(0.523173\pi\)
\(164\) 8.09404i 0.632039i
\(165\) 2.00677 + 6.51469i 0.156227 + 0.507168i
\(166\) −14.6504 −1.13709
\(167\) 7.28369i 0.563629i 0.959469 + 0.281814i \(0.0909362\pi\)
−0.959469 + 0.281814i \(0.909064\pi\)
\(168\) −5.08036 + 1.56494i −0.391959 + 0.120738i
\(169\) −36.8574 −2.83518
\(170\) 1.64944 0.126506
\(171\) −10.9742 + 7.46974i −0.839221 + 0.571225i
\(172\) 0.770515i 0.0587512i
\(173\) −21.8511 −1.66131 −0.830653 0.556790i \(-0.812033\pi\)
−0.830653 + 0.556790i \(0.812033\pi\)
\(174\) 1.23181 + 3.99888i 0.0933830 + 0.303155i
\(175\) 10.5121 0.794637
\(176\) 1.35591 0.102206
\(177\) 8.67836 + 10.0840i 0.652305 + 0.757956i
\(178\) 11.5174 0.863267
\(179\) −17.9386 −1.34079 −0.670395 0.742004i \(-0.733875\pi\)
−0.670395 + 0.742004i \(0.733875\pi\)
\(180\) −4.89973 7.19849i −0.365205 0.536544i
\(181\) 1.63018 0.121170 0.0605850 0.998163i \(-0.480703\pi\)
0.0605850 + 0.998163i \(0.480703\pi\)
\(182\) 21.6712i 1.60638i
\(183\) 5.44291 + 17.6696i 0.402351 + 1.30618i
\(184\) 7.20070 0.530842
\(185\) 5.05797 0.371869
\(186\) 3.28818 + 10.6746i 0.241101 + 0.782699i
\(187\) 0.770515i 0.0563456i
\(188\) −4.48887 −0.327385
\(189\) 9.95768 12.4570i 0.724315 0.906114i
\(190\) 12.8442i 0.931815i
\(191\) 4.94832 0.358048 0.179024 0.983845i \(-0.442706\pi\)
0.179024 + 0.983845i \(0.442706\pi\)
\(192\) −1.65530 + 0.509894i −0.119461 + 0.0367984i
\(193\) −7.55803 −0.544039 −0.272019 0.962292i \(-0.587691\pi\)
−0.272019 + 0.962292i \(0.587691\pi\)
\(194\) 8.16151i 0.585962i
\(195\) −33.9256 + 10.4504i −2.42946 + 0.748366i
\(196\) 2.41972 0.172837
\(197\) 6.53668i 0.465719i −0.972510 0.232859i \(-0.925192\pi\)
0.972510 0.232859i \(-0.0748082\pi\)
\(198\) −3.36268 + 2.28885i −0.238975 + 0.162661i
\(199\) −16.9942 −1.20468 −0.602342 0.798238i \(-0.705766\pi\)
−0.602342 + 0.798238i \(0.705766\pi\)
\(200\) 3.42507 0.242189
\(201\) −0.557091 1.80851i −0.0392941 0.127563i
\(202\) 10.1615 0.714961
\(203\) 7.41450i 0.520396i
\(204\) 0.289754 + 0.940644i 0.0202868 + 0.0658583i
\(205\) 23.4937 1.64087
\(206\) 16.6350i 1.15902i
\(207\) −17.8578 + 12.1551i −1.24121 + 0.844841i
\(208\) 7.06097i 0.489590i
\(209\) −6.00000 −0.415029
\(210\) 4.54240 + 14.7462i 0.313455 + 1.01759i
\(211\) 27.9219i 1.92222i −0.276167 0.961110i \(-0.589064\pi\)
0.276167 0.961110i \(-0.410936\pi\)
\(212\) 1.03307i 0.0709514i
\(213\) −5.62954 18.2755i −0.385729 1.25222i
\(214\) 19.5376i 1.33556i
\(215\) 2.23649 0.152528
\(216\) 3.24444 4.05877i 0.220756 0.276164i
\(217\) 19.7922i 1.34358i
\(218\) 1.42258i 0.0963494i
\(219\) 3.03919 + 9.86630i 0.205370 + 0.666703i
\(220\) 3.93566i 0.265342i
\(221\) 4.01249 0.269909
\(222\) 0.888525 + 2.88447i 0.0596339 + 0.193593i
\(223\) −21.6281 −1.44833 −0.724163 0.689629i \(-0.757774\pi\)
−0.724163 + 0.689629i \(0.757774\pi\)
\(224\) 3.06916 0.205067
\(225\) −8.49422 + 5.78169i −0.566282 + 0.385446i
\(226\) 16.6379 1.10674
\(227\) 0.476381 0.0316185 0.0158093 0.999875i \(-0.494968\pi\)
0.0158093 + 0.999875i \(0.494968\pi\)
\(228\) 7.32480 2.25631i 0.485097 0.149428i
\(229\) 18.0656i 1.19381i 0.802313 + 0.596904i \(0.203603\pi\)
−0.802313 + 0.596904i \(0.796397\pi\)
\(230\) 20.9007i 1.37815i
\(231\) 6.88852 2.12193i 0.453232 0.139612i
\(232\) 2.41581i 0.158606i
\(233\) 7.83229 0.513111 0.256555 0.966530i \(-0.417412\pi\)
0.256555 + 0.966530i \(0.417412\pi\)
\(234\) −11.9193 17.5113i −0.779188 1.14475i
\(235\) 13.0294i 0.849943i
\(236\) −3.07451 7.03899i −0.200133 0.458199i
\(237\) −14.2693 + 4.39550i −0.926893 + 0.285518i
\(238\) 1.74409i 0.113052i
\(239\) 13.1302i 0.849325i 0.905352 + 0.424662i \(0.139607\pi\)
−0.905352 + 0.424662i \(0.860393\pi\)
\(240\) 1.48002 + 4.80466i 0.0955346 + 0.310139i
\(241\) 12.0024 0.773140 0.386570 0.922260i \(-0.373660\pi\)
0.386570 + 0.922260i \(0.373660\pi\)
\(242\) 9.16150 0.588924
\(243\) −1.19484 + 15.5426i −0.0766489 + 0.997058i
\(244\) 10.6746i 0.683371i
\(245\) 7.02346i 0.448713i
\(246\) 4.12710 + 13.3980i 0.263134 + 0.854228i
\(247\) 31.2453i 1.98809i
\(248\) 6.44875i 0.409496i
\(249\) −24.2507 + 7.47014i −1.53683 + 0.473401i
\(250\) 4.57139i 0.289120i
\(251\) 2.86482i 0.180826i −0.995904 0.0904129i \(-0.971181\pi\)
0.995904 0.0904129i \(-0.0288187\pi\)
\(252\) −7.61156 + 5.18089i −0.479483 + 0.326366i
\(253\) −9.76351 −0.613826
\(254\) −8.29304 −0.520352
\(255\) 2.73031 0.841039i 0.170979 0.0526679i
\(256\) 1.00000 0.0625000
\(257\) 11.8361i 0.738318i 0.929366 + 0.369159i \(0.120354\pi\)
−0.929366 + 0.369159i \(0.879646\pi\)
\(258\) 0.392881 + 1.27543i 0.0244597 + 0.0794048i
\(259\) 5.34821i 0.332322i
\(260\) 20.4952 1.27106
\(261\) 4.07801 + 5.99125i 0.252423 + 0.370849i
\(262\) 10.0063 0.618191
\(263\) 15.9639i 0.984373i −0.870490 0.492187i \(-0.836198\pi\)
0.870490 0.492187i \(-0.163802\pi\)
\(264\) 2.24444 0.691371i 0.138136 0.0425509i
\(265\) 2.99858 0.184201
\(266\) −13.5812 −0.832718
\(267\) 19.0647 5.87266i 1.16674 0.359401i
\(268\) 1.09256i 0.0667388i
\(269\) 19.1392 1.16694 0.583470 0.812134i \(-0.301694\pi\)
0.583470 + 0.812134i \(0.301694\pi\)
\(270\) −11.7810 9.41729i −0.716968 0.573118i
\(271\) 16.9434 1.02924 0.514620 0.857419i \(-0.327933\pi\)
0.514620 + 0.857419i \(0.327933\pi\)
\(272\) 0.568263i 0.0344560i
\(273\) 11.0500 + 35.8723i 0.668778 + 2.17109i
\(274\) 12.8067i 0.773679i
\(275\) −4.64409 −0.280049
\(276\) 11.9193 3.67159i 0.717457 0.221004i
\(277\) 17.8471 1.07233 0.536165 0.844113i \(-0.319872\pi\)
0.536165 + 0.844113i \(0.319872\pi\)
\(278\) −8.09377 −0.485432
\(279\) 10.8858 + 15.9930i 0.651717 + 0.957476i
\(280\) 8.90852i 0.532386i
\(281\) 29.1267i 1.73755i 0.495207 + 0.868775i \(0.335092\pi\)
−0.495207 + 0.868775i \(0.664908\pi\)
\(282\) −7.43042 + 2.28885i −0.442475 + 0.136299i
\(283\) 6.45672i 0.383812i 0.981413 + 0.191906i \(0.0614669\pi\)
−0.981413 + 0.191906i \(0.938533\pi\)
\(284\) 11.0406i 0.655139i
\(285\) −6.54917 21.2609i −0.387939 1.25939i
\(286\) 9.57406i 0.566126i
\(287\) 24.8419i 1.46637i
\(288\) −2.48002 + 1.68805i −0.146136 + 0.0994694i
\(289\) 16.6771 0.981005
\(290\) −7.01212 −0.411766
\(291\) −4.16150 13.5097i −0.243952 0.791954i
\(292\) 5.96044i 0.348808i
\(293\) 28.9847i 1.69331i 0.532146 + 0.846653i \(0.321386\pi\)
−0.532146 + 0.846653i \(0.678614\pi\)
\(294\) 4.00535 1.23380i 0.233597 0.0719566i
\(295\) −20.4314 + 8.92405i −1.18956 + 0.519578i
\(296\) 1.74257i 0.101285i
\(297\) −4.39917 + 5.50334i −0.255266 + 0.319336i
\(298\) −12.4139 −0.719117
\(299\) 50.8439i 2.94038i
\(300\) 5.66950 1.74642i 0.327329 0.100830i
\(301\) 2.36483i 0.136306i
\(302\) 6.74099i 0.387900i
\(303\) 16.8203 5.18129i 0.966301 0.297657i
\(304\) −4.42507 −0.253795
\(305\) −30.9840 −1.77414
\(306\) 0.959258 + 1.40930i 0.0548371 + 0.0805644i
\(307\) 5.63646 0.321690 0.160845 0.986980i \(-0.448578\pi\)
0.160845 + 0.986980i \(0.448578\pi\)
\(308\) −4.16150 −0.237124
\(309\) −8.48210 27.5359i −0.482530 1.56646i
\(310\) −18.7181 −1.06312
\(311\) 11.9919i 0.680000i 0.940425 + 0.340000i \(0.110427\pi\)
−0.940425 + 0.340000i \(0.889573\pi\)
\(312\) 3.60035 + 11.6880i 0.203830 + 0.661703i
\(313\) 8.31980i 0.470263i −0.971964 0.235131i \(-0.924448\pi\)
0.971964 0.235131i \(-0.0755520\pi\)
\(314\) 4.18807i 0.236346i
\(315\) 15.0380 + 22.0933i 0.847298 + 1.24482i
\(316\) 8.62041 0.484936
\(317\) 26.2936i 1.47680i −0.674365 0.738398i \(-0.735583\pi\)
0.674365 0.738398i \(-0.264417\pi\)
\(318\) 0.526755 + 1.71003i 0.0295390 + 0.0958939i
\(319\) 3.27562i 0.183400i
\(320\) 2.90260i 0.162260i
\(321\) 9.96212 + 32.3406i 0.556031 + 1.80508i
\(322\) −22.1001 −1.23159
\(323\) 2.51460i 0.139916i
\(324\) 3.30096 8.37279i 0.183387 0.465155i
\(325\) 24.1843i 1.34150i
\(326\) 1.85728 0.102865
\(327\) −0.725366 2.35480i −0.0401128 0.130220i
\(328\) 8.09404i 0.446919i
\(329\) 13.7770 0.759553
\(330\) −2.00677 6.51469i −0.110469 0.358622i
\(331\) −20.2592 −1.11355 −0.556773 0.830665i \(-0.687961\pi\)
−0.556773 + 0.830665i \(0.687961\pi\)
\(332\) 14.6504 0.804044
\(333\) 2.94154 + 4.32160i 0.161196 + 0.236822i
\(334\) 7.28369i 0.398546i
\(335\) 3.17127 0.173265
\(336\) 5.08036 1.56494i 0.277157 0.0853747i
\(337\) 33.0786i 1.80190i −0.433919 0.900952i \(-0.642870\pi\)
0.433919 0.900952i \(-0.357130\pi\)
\(338\) 36.8574 2.00478
\(339\) 27.5406 8.48356i 1.49580 0.460764i
\(340\) −1.64944 −0.0894534
\(341\) 8.74393i 0.473510i
\(342\) 10.9742 7.46974i 0.593419 0.403917i
\(343\) 14.0576 0.759039
\(344\) 0.770515i 0.0415434i
\(345\) −10.6571 34.5969i −0.573762 1.86263i
\(346\) 21.8511 1.17472
\(347\) 20.5577 1.10359 0.551796 0.833979i \(-0.313943\pi\)
0.551796 + 0.833979i \(0.313943\pi\)
\(348\) −1.23181 3.99888i −0.0660318 0.214363i
\(349\) 26.3694i 1.41152i 0.708449 + 0.705762i \(0.249395\pi\)
−0.708449 + 0.705762i \(0.750605\pi\)
\(350\) −10.5121 −0.561894
\(351\) −28.6589 22.9089i −1.52970 1.22279i
\(352\) −1.35591 −0.0722703
\(353\) −16.1784 −0.861092 −0.430546 0.902569i \(-0.641679\pi\)
−0.430546 + 0.902569i \(0.641679\pi\)
\(354\) −8.67836 10.0840i −0.461250 0.535956i
\(355\) 32.0464 1.70085
\(356\) −11.5174 −0.610422
\(357\) −0.889300 2.88698i −0.0470667 0.152795i
\(358\) 17.9386 0.948082
\(359\) 19.3351i 1.02047i 0.860036 + 0.510234i \(0.170441\pi\)
−0.860036 + 0.510234i \(0.829559\pi\)
\(360\) 4.89973 + 7.19849i 0.258239 + 0.379394i
\(361\) 0.581221 0.0305906
\(362\) −1.63018 −0.0856801
\(363\) 15.1650 4.67140i 0.795957 0.245185i
\(364\) 21.6712i 1.13588i
\(365\) −17.3008 −0.905563
\(366\) −5.44291 17.6696i −0.284505 0.923606i
\(367\) 7.18946i 0.375287i −0.982237 0.187643i \(-0.939915\pi\)
0.982237 0.187643i \(-0.0600849\pi\)
\(368\) −7.20070 −0.375362
\(369\) 13.6632 + 20.0734i 0.711276 + 1.04498i
\(370\) −5.05797 −0.262951
\(371\) 3.17065i 0.164612i
\(372\) −3.28818 10.6746i −0.170484 0.553452i
\(373\) 20.0865 1.04004 0.520020 0.854154i \(-0.325924\pi\)
0.520020 + 0.854154i \(0.325924\pi\)
\(374\) 0.770515i 0.0398424i
\(375\) 2.33093 + 7.56702i 0.120369 + 0.390759i
\(376\) 4.48887 0.231496
\(377\) −17.0580 −0.878530
\(378\) −9.95768 + 12.4570i −0.512168 + 0.640719i
\(379\) 2.68186 0.137758 0.0688789 0.997625i \(-0.478058\pi\)
0.0688789 + 0.997625i \(0.478058\pi\)
\(380\) 12.8442i 0.658893i
\(381\) −13.7275 + 4.22857i −0.703279 + 0.216636i
\(382\) −4.94832 −0.253178
\(383\) 22.1048i 1.12950i 0.825261 + 0.564752i \(0.191028\pi\)
−0.825261 + 0.564752i \(0.808972\pi\)
\(384\) 1.65530 0.509894i 0.0844715 0.0260204i
\(385\) 12.0792i 0.615611i
\(386\) 7.55803 0.384694
\(387\) 1.30067 + 1.91089i 0.0661167 + 0.0971359i
\(388\) 8.16151i 0.414338i
\(389\) 1.33259i 0.0675651i 0.999429 + 0.0337825i \(0.0107554\pi\)
−0.999429 + 0.0337825i \(0.989245\pi\)
\(390\) 33.9256 10.4504i 1.71789 0.529174i
\(391\) 4.09189i 0.206936i
\(392\) −2.41972 −0.122214
\(393\) 16.5634 5.10215i 0.835512 0.257369i
\(394\) 6.53668i 0.329313i
\(395\) 25.0216i 1.25897i
\(396\) 3.36268 2.28885i 0.168981 0.115019i
\(397\) 25.3810i 1.27384i −0.770931 0.636919i \(-0.780209\pi\)
0.770931 0.636919i \(-0.219791\pi\)
\(398\) 16.9942 0.851841
\(399\) −22.4810 + 6.92498i −1.12546 + 0.346683i
\(400\) −3.42507 −0.171253
\(401\) 14.2292 0.710574 0.355287 0.934757i \(-0.384383\pi\)
0.355287 + 0.934757i \(0.384383\pi\)
\(402\) 0.557091 + 1.80851i 0.0277852 + 0.0902005i
\(403\) −45.5344 −2.26823
\(404\) −10.1615 −0.505554
\(405\) −24.3028 9.58136i −1.20762 0.476102i
\(406\) 7.41450i 0.367975i
\(407\) 2.36277i 0.117118i
\(408\) −0.289754 0.940644i −0.0143450 0.0465688i
\(409\) 15.8746i 0.784946i 0.919764 + 0.392473i \(0.128380\pi\)
−0.919764 + 0.392473i \(0.871620\pi\)
\(410\) −23.4937 −1.16027
\(411\) 6.53004 + 21.1988i 0.322103 + 1.04566i
\(412\) 16.6350i 0.819549i
\(413\) 9.43614 + 21.6038i 0.464322 + 1.06305i
\(414\) 17.8578 12.1551i 0.877665 0.597393i
\(415\) 42.5241i 2.08743i
\(416\) 7.06097i 0.346193i
\(417\) −13.3976 + 4.12696i −0.656083 + 0.202098i
\(418\) 6.00000 0.293470
\(419\) 16.8244 0.821924 0.410962 0.911652i \(-0.365193\pi\)
0.410962 + 0.911652i \(0.365193\pi\)
\(420\) −4.54240 14.7462i −0.221646 0.719543i
\(421\) 4.37616i 0.213281i 0.994298 + 0.106640i \(0.0340094\pi\)
−0.994298 + 0.106640i \(0.965991\pi\)
\(422\) 27.9219i 1.35921i
\(423\) −11.1325 + 7.57745i −0.541280 + 0.368428i
\(424\) 1.03307i 0.0501702i
\(425\) 1.94634i 0.0944113i
\(426\) 5.62954 + 18.2755i 0.272752 + 0.885450i
\(427\) 32.7620i 1.58546i
\(428\) 19.5376i 0.944387i
\(429\) −4.88175 15.8479i −0.235693 0.765144i
\(430\) −2.23649 −0.107853
\(431\) 2.04895 0.0986947 0.0493473 0.998782i \(-0.484286\pi\)
0.0493473 + 0.998782i \(0.484286\pi\)
\(432\) −3.24444 + 4.05877i −0.156098 + 0.195278i
\(433\) −29.6427 −1.42454 −0.712269 0.701907i \(-0.752332\pi\)
−0.712269 + 0.701907i \(0.752332\pi\)
\(434\) 19.7922i 0.950056i
\(435\) −11.6071 + 3.57544i −0.556520 + 0.171429i
\(436\) 1.42258i 0.0681293i
\(437\) 31.8636 1.52424
\(438\) −3.03919 9.86630i −0.145218 0.471430i
\(439\) −22.0490 −1.05234 −0.526172 0.850378i \(-0.676373\pi\)
−0.526172 + 0.850378i \(0.676373\pi\)
\(440\) 3.93566i 0.187625i
\(441\) 6.00094 4.08461i 0.285759 0.194505i
\(442\) −4.01249 −0.190855
\(443\) −8.23544 −0.391278 −0.195639 0.980676i \(-0.562678\pi\)
−0.195639 + 0.980676i \(0.562678\pi\)
\(444\) −0.888525 2.88447i −0.0421675 0.136891i
\(445\) 33.4304i 1.58475i
\(446\) 21.6281 1.02412
\(447\) −20.5487 + 6.32976i −0.971918 + 0.299388i
\(448\) −3.06916 −0.145004
\(449\) 1.44717i 0.0682961i 0.999417 + 0.0341481i \(0.0108718\pi\)
−0.999417 + 0.0341481i \(0.989128\pi\)
\(450\) 8.49422 5.78169i 0.400422 0.272552i
\(451\) 10.9748i 0.516783i
\(452\) −16.6379 −0.782580
\(453\) 3.43719 + 11.1583i 0.161493 + 0.524264i
\(454\) −0.476381 −0.0223577
\(455\) −62.9028 −2.94893
\(456\) −7.32480 + 2.25631i −0.343015 + 0.105662i
\(457\) 22.1516i 1.03621i 0.855318 + 0.518103i \(0.173362\pi\)
−0.855318 + 0.518103i \(0.826638\pi\)
\(458\) 18.0656i 0.844149i
\(459\) 2.30645 + 1.84369i 0.107656 + 0.0860563i
\(460\) 20.9007i 0.974501i
\(461\) 17.2878i 0.805174i 0.915382 + 0.402587i \(0.131889\pi\)
−0.915382 + 0.402587i \(0.868111\pi\)
\(462\) −6.88852 + 2.12193i −0.320483 + 0.0987209i
\(463\) 14.3744i 0.668033i 0.942567 + 0.334016i \(0.108404\pi\)
−0.942567 + 0.334016i \(0.891596\pi\)
\(464\) 2.41581i 0.112151i
\(465\) −30.9840 + 9.54425i −1.43685 + 0.442604i
\(466\) −7.83229 −0.362824
\(467\) 23.6209 1.09304 0.546522 0.837445i \(-0.315952\pi\)
0.546522 + 0.837445i \(0.315952\pi\)
\(468\) 11.9193 + 17.5113i 0.550969 + 0.809462i
\(469\) 3.35324i 0.154838i
\(470\) 13.0294i 0.601001i
\(471\) −2.13547 6.93249i −0.0983972 0.319432i
\(472\) 3.07451 + 7.03899i 0.141516 + 0.323996i
\(473\) 1.04475i 0.0480376i
\(474\) 14.2693 4.39550i 0.655413 0.201892i
\(475\) 15.1562 0.695412
\(476\) 1.74409i 0.0799401i
\(477\) 1.74387 + 2.56202i 0.0798464 + 0.117307i
\(478\) 13.1302i 0.600563i
\(479\) 10.4744i 0.478588i −0.970947 0.239294i \(-0.923084\pi\)
0.970947 0.239294i \(-0.0769159\pi\)
\(480\) −1.48002 4.80466i −0.0675532 0.219302i
\(481\) −12.3042 −0.561024
\(482\) −12.0024 −0.546692
\(483\) −36.5822 + 11.2687i −1.66455 + 0.512743i
\(484\) −9.16150 −0.416432
\(485\) 23.6896 1.07569
\(486\) 1.19484 15.5426i 0.0541989 0.705027i
\(487\) 8.93084 0.404695 0.202348 0.979314i \(-0.435143\pi\)
0.202348 + 0.979314i \(0.435143\pi\)
\(488\) 10.6746i 0.483216i
\(489\) 3.07434 0.947014i 0.139027 0.0428254i
\(490\) 7.02346i 0.317288i
\(491\) 17.9966i 0.812175i −0.913834 0.406088i \(-0.866893\pi\)
0.913834 0.406088i \(-0.133107\pi\)
\(492\) −4.12710 13.3980i −0.186064 0.604030i
\(493\) 1.37282 0.0618285
\(494\) 31.2453i 1.40579i
\(495\) −6.64361 9.76051i −0.298608 0.438702i
\(496\) 6.44875i 0.289557i
\(497\) 33.8853i 1.51996i
\(498\) 24.2507 7.47014i 1.08670 0.334745i
\(499\) 22.6464 1.01379 0.506897 0.862007i \(-0.330792\pi\)
0.506897 + 0.862007i \(0.330792\pi\)
\(500\) 4.57139i 0.204439i
\(501\) −3.71391 12.0567i −0.165925 0.538652i
\(502\) 2.86482i 0.127863i
\(503\) −24.9528 −1.11259 −0.556294 0.830985i \(-0.687777\pi\)
−0.556294 + 0.830985i \(0.687777\pi\)
\(504\) 7.61156 5.18089i 0.339046 0.230775i
\(505\) 29.4947i 1.31250i
\(506\) 9.76351 0.434041
\(507\) 61.0099 18.7933i 2.70954 0.834642i
\(508\) 8.29304 0.367944
\(509\) 8.75035 0.387852 0.193926 0.981016i \(-0.437878\pi\)
0.193926 + 0.981016i \(0.437878\pi\)
\(510\) −2.73031 + 0.841039i −0.120900 + 0.0372418i
\(511\) 18.2935i 0.809258i
\(512\) −1.00000 −0.0441942
\(513\) 14.3568 17.9603i 0.633870 0.792968i
\(514\) 11.8361i 0.522070i
\(515\) 48.2848 2.12768
\(516\) −0.392881 1.27543i −0.0172956 0.0561477i
\(517\) −6.08651 −0.267685
\(518\) 5.34821i 0.234987i
\(519\) 36.1700 11.1417i 1.58769 0.489068i
\(520\) −20.4952 −0.898772
\(521\) 6.33855i 0.277697i −0.990314 0.138848i \(-0.955660\pi\)
0.990314 0.138848i \(-0.0443401\pi\)
\(522\) −4.07801 5.99125i −0.178490 0.262230i
\(523\) 2.35554 0.103001 0.0515003 0.998673i \(-0.483600\pi\)
0.0515003 + 0.998673i \(0.483600\pi\)
\(524\) −10.0063 −0.437127
\(525\) −17.4006 + 5.36004i −0.759424 + 0.233931i
\(526\) 15.9639i 0.696057i
\(527\) 3.66459 0.159632
\(528\) −2.24444 + 0.691371i −0.0976766 + 0.0300881i
\(529\) 28.8500 1.25435
\(530\) −2.99858 −0.130250
\(531\) −19.5070 12.2669i −0.846532 0.532338i
\(532\) 13.5812 0.588821
\(533\) −57.1518 −2.47552
\(534\) −19.0647 + 5.87266i −0.825012 + 0.254135i
\(535\) −56.7099 −2.45178
\(536\) 1.09256i 0.0471915i
\(537\) 29.6936 9.14676i 1.28137 0.394712i
\(538\) −19.1392 −0.825152
\(539\) 3.28092 0.141319
\(540\) 11.7810 + 9.41729i 0.506973 + 0.405256i
\(541\) 38.4666i 1.65381i −0.562343 0.826904i \(-0.690100\pi\)
0.562343 0.826904i \(-0.309900\pi\)
\(542\) −16.9434 −0.727782
\(543\) −2.69843 + 0.831217i −0.115801 + 0.0356709i
\(544\) 0.568263i 0.0243641i
\(545\) 4.12918 0.176875
\(546\) −11.0500 35.8723i −0.472898 1.53519i
\(547\) 13.2301 0.565679 0.282840 0.959167i \(-0.408724\pi\)
0.282840 + 0.959167i \(0.408724\pi\)
\(548\) 12.8067i 0.547074i
\(549\) −18.0193 26.4732i −0.769043 1.12985i
\(550\) 4.64409 0.198025
\(551\) 10.6901i 0.455414i
\(552\) −11.9193 + 3.67159i −0.507319 + 0.156273i
\(553\) −26.4574 −1.12508
\(554\) −17.8471 −0.758252
\(555\) −8.37245 + 2.57903i −0.355391 + 0.109474i
\(556\) 8.09377 0.343252
\(557\) 26.6677i 1.12995i 0.825109 + 0.564974i \(0.191114\pi\)
−0.825109 + 0.564974i \(0.808886\pi\)
\(558\) −10.8858 15.9930i −0.460833 0.677038i
\(559\) −5.44058 −0.230112
\(560\) 8.90852i 0.376454i
\(561\) 0.392881 + 1.27543i 0.0165874 + 0.0538487i
\(562\) 29.1267i 1.22863i
\(563\) 22.5381 0.949869 0.474935 0.880021i \(-0.342472\pi\)
0.474935 + 0.880021i \(0.342472\pi\)
\(564\) 7.43042 2.28885i 0.312877 0.0963779i
\(565\) 48.2931i 2.03170i
\(566\) 6.45672i 0.271396i
\(567\) −10.1312 + 25.6974i −0.425469 + 1.07919i
\(568\) 11.0406i 0.463253i
\(569\) −9.22568 −0.386761 −0.193380 0.981124i \(-0.561945\pi\)
−0.193380 + 0.981124i \(0.561945\pi\)
\(570\) 6.54917 + 21.2609i 0.274315 + 0.890523i
\(571\) 34.5742i 1.44689i 0.690385 + 0.723443i \(0.257441\pi\)
−0.690385 + 0.723443i \(0.742559\pi\)
\(572\) 9.57406i 0.400311i
\(573\) −8.19093 + 2.52312i −0.342181 + 0.105405i
\(574\) 24.8419i 1.03688i
\(575\) 24.6629 1.02851
\(576\) 2.48002 1.68805i 0.103334 0.0703355i
\(577\) 16.2878 0.678070 0.339035 0.940774i \(-0.389899\pi\)
0.339035 + 0.940774i \(0.389899\pi\)
\(578\) −16.6771 −0.693675
\(579\) 12.5108 3.85379i 0.519930 0.160158i
\(580\) 7.01212 0.291163
\(581\) −44.9643 −1.86543
\(582\) 4.16150 + 13.5097i 0.172500 + 0.559996i
\(583\) 1.40075i 0.0580131i
\(584\) 5.96044i 0.246645i
\(585\) 50.8283 34.5969i 2.10149 1.43041i
\(586\) 28.9847i 1.19735i
\(587\) −23.7823 −0.981600 −0.490800 0.871272i \(-0.663295\pi\)
−0.490800 + 0.871272i \(0.663295\pi\)
\(588\) −4.00535 + 1.23380i −0.165178 + 0.0508810i
\(589\) 28.5361i 1.17581i
\(590\) 20.4314 8.92405i 0.841146 0.367397i
\(591\) 3.33301 + 10.8201i 0.137102 + 0.445081i
\(592\) 1.74257i 0.0716191i
\(593\) 4.32008i 0.177404i 0.996058 + 0.0887021i \(0.0282719\pi\)
−0.996058 + 0.0887021i \(0.971728\pi\)
\(594\) 4.39917 5.50334i 0.180500 0.225805i
\(595\) 5.06238 0.207538
\(596\) 12.4139 0.508492
\(597\) 28.1304 8.66522i 1.15130 0.354644i
\(598\) 50.8439i 2.07916i
\(599\) 7.74067i 0.316275i −0.987417 0.158138i \(-0.949451\pi\)
0.987417 0.158138i \(-0.0505489\pi\)
\(600\) −5.66950 + 1.74642i −0.231457 + 0.0712973i
\(601\) 12.8711i 0.525023i 0.964929 + 0.262512i \(0.0845508\pi\)
−0.964929 + 0.262512i \(0.915449\pi\)
\(602\) 2.36483i 0.0963832i
\(603\) 1.84430 + 2.70957i 0.0751057 + 0.110342i
\(604\) 6.74099i 0.274287i
\(605\) 26.5922i 1.08112i
\(606\) −16.8203 + 5.18129i −0.683278 + 0.210475i
\(607\) −28.6668 −1.16355 −0.581775 0.813350i \(-0.697641\pi\)
−0.581775 + 0.813350i \(0.697641\pi\)
\(608\) 4.42507 0.179460
\(609\) 3.78061 + 12.2732i 0.153198 + 0.497335i
\(610\) 30.9840 1.25451
\(611\) 31.6958i 1.28228i
\(612\) −0.959258 1.40930i −0.0387757 0.0569677i
\(613\) 16.5246i 0.667421i 0.942676 + 0.333710i \(0.108301\pi\)
−0.942676 + 0.333710i \(0.891699\pi\)
\(614\) −5.63646 −0.227469
\(615\) −38.8891 + 11.9793i −1.56816 + 0.483053i
\(616\) 4.16150 0.167672
\(617\) 10.8626i 0.437310i −0.975802 0.218655i \(-0.929833\pi\)
0.975802 0.218655i \(-0.0701670\pi\)
\(618\) 8.48210 + 27.5359i 0.341200 + 1.10766i
\(619\) 25.8336 1.03834 0.519170 0.854671i \(-0.326241\pi\)
0.519170 + 0.854671i \(0.326241\pi\)
\(620\) 18.7181 0.751737
\(621\) 23.3622 29.2260i 0.937493 1.17280i
\(622\) 11.9919i 0.480833i
\(623\) 35.3487 1.41622
\(624\) −3.60035 11.6880i −0.144129 0.467895i
\(625\) −30.3943 −1.21577
\(626\) 8.31980i 0.332526i
\(627\) 9.93178 3.05936i 0.396637 0.122179i
\(628\) 4.18807i 0.167122i
\(629\) 0.990237 0.0394833
\(630\) −15.0380 22.0933i −0.599130 0.880217i
\(631\) 21.7636 0.866395 0.433197 0.901299i \(-0.357385\pi\)
0.433197 + 0.901299i \(0.357385\pi\)
\(632\) −8.62041 −0.342902
\(633\) 14.2372 + 46.2190i 0.565877 + 1.83704i
\(634\) 26.2936i 1.04425i
\(635\) 24.0714i 0.955243i
\(636\) −0.526755 1.71003i −0.0208872 0.0678073i
\(637\) 17.0856i 0.676955i
\(638\) 3.27562i 0.129683i
\(639\) 18.6371 + 27.3809i 0.737273 + 1.08317i
\(640\) 2.90260i 0.114735i
\(641\) 20.9447i 0.827265i 0.910444 + 0.413633i \(0.135740\pi\)
−0.910444 + 0.413633i \(0.864260\pi\)
\(642\) −9.96212 32.3406i −0.393173 1.27638i
\(643\) 2.51696 0.0992592 0.0496296 0.998768i \(-0.484196\pi\)
0.0496296 + 0.998768i \(0.484196\pi\)
\(644\) 22.1001 0.870864
\(645\) −3.70206 + 1.14037i −0.145768 + 0.0449022i
\(646\) 2.51460i 0.0989357i
\(647\) 2.74431i 0.107890i −0.998544 0.0539450i \(-0.982820\pi\)
0.998544 0.0539450i \(-0.0171796\pi\)
\(648\) −3.30096 + 8.37279i −0.129674 + 0.328914i
\(649\) −4.16876 9.54425i −0.163638 0.374645i
\(650\) 24.1843i 0.948587i
\(651\) 10.0919 + 32.7620i 0.395534 + 1.28404i
\(652\) −1.85728 −0.0727365
\(653\) 16.8300i 0.658609i 0.944224 + 0.329304i \(0.106814\pi\)
−0.944224 + 0.329304i \(0.893186\pi\)
\(654\) 0.725366 + 2.35480i 0.0283640 + 0.0920798i
\(655\) 29.0442i 1.13485i
\(656\) 8.09404i 0.316019i
\(657\) −10.0615 14.7820i −0.392538 0.576700i
\(658\) −13.7770 −0.537085
\(659\) −28.5754 −1.11314 −0.556570 0.830801i \(-0.687883\pi\)
−0.556570 + 0.830801i \(0.687883\pi\)
\(660\) 2.00677 + 6.51469i 0.0781135 + 0.253584i
\(661\) −5.84243 −0.227244 −0.113622 0.993524i \(-0.536245\pi\)
−0.113622 + 0.993524i \(0.536245\pi\)
\(662\) 20.2592 0.787396
\(663\) −6.64187 + 2.04595i −0.257949 + 0.0794579i
\(664\) −14.6504 −0.568545
\(665\) 39.4208i 1.52867i
\(666\) −2.94154 4.32160i −0.113983 0.167458i
\(667\) 17.3955i 0.673557i
\(668\) 7.28369i 0.281814i
\(669\) 35.8010 11.0280i 1.38415 0.426369i
\(670\) −3.17127 −0.122517
\(671\) 14.4738i 0.558755i
\(672\) −5.08036 + 1.56494i −0.195979 + 0.0603690i
\(673\) 8.90428i 0.343235i −0.985164 0.171617i \(-0.945101\pi\)
0.985164 0.171617i \(-0.0548993\pi\)
\(674\) 33.0786i 1.27414i
\(675\) 11.1124 13.9016i 0.427717 0.535072i
\(676\) −36.8574 −1.41759
\(677\) 8.80973i 0.338585i 0.985566 + 0.169293i \(0.0541483\pi\)
−0.985566 + 0.169293i \(0.945852\pi\)
\(678\) −27.5406 + 8.48356i −1.05769 + 0.325809i
\(679\) 25.0489i 0.961290i
\(680\) 1.64944 0.0632531
\(681\) −0.788552 + 0.242904i −0.0302174 + 0.00930809i
\(682\) 8.74393i 0.334822i
\(683\) 24.8965 0.952637 0.476318 0.879273i \(-0.341971\pi\)
0.476318 + 0.879273i \(0.341971\pi\)
\(684\) −10.9742 + 7.46974i −0.419611 + 0.285613i
\(685\) −37.1726 −1.42029
\(686\) −14.0576 −0.536722
\(687\) −9.21153 29.9039i −0.351442 1.14091i
\(688\) 0.770515i 0.0293756i
\(689\) −7.29446 −0.277897
\(690\) 10.6571 + 34.5969i 0.405711 + 1.31708i
\(691\) 23.9319i 0.910413i −0.890386 0.455206i \(-0.849565\pi\)
0.890386 0.455206i \(-0.150435\pi\)
\(692\) −21.8511 −0.830653
\(693\) −10.3206 + 7.02483i −0.392047 + 0.266851i
\(694\) −20.5577 −0.780358
\(695\) 23.4929i 0.891138i
\(696\) 1.23181 + 3.99888i 0.0466915 + 0.151577i
\(697\) 4.59955 0.174220
\(698\) 26.3694i 0.998098i
\(699\) −12.9648 + 3.99364i −0.490373 + 0.151053i
\(700\) 10.5121 0.397319
\(701\) −25.7011 −0.970717 −0.485358 0.874315i \(-0.661311\pi\)
−0.485358 + 0.874315i \(0.661311\pi\)
\(702\) 28.6589 + 22.9089i 1.08166 + 0.864640i
\(703\) 7.71098i 0.290825i
\(704\) 1.35591 0.0511028
\(705\) −6.64361 21.5675i −0.250213 0.812279i
\(706\) 16.1784 0.608884
\(707\) 31.1872 1.17292
\(708\) 8.67836 + 10.0840i 0.326153 + 0.378978i
\(709\) −37.5287 −1.40942 −0.704710 0.709496i \(-0.748923\pi\)
−0.704710 + 0.709496i \(0.748923\pi\)
\(710\) −32.0464 −1.20268
\(711\) 21.3788 14.5517i 0.801766 0.545732i
\(712\) 11.5174 0.431633
\(713\) 46.4355i 1.73902i
\(714\) 0.889300 + 2.88698i 0.0332812 + 0.108043i
\(715\) 27.7896 1.03927
\(716\) −17.9386 −0.670395
\(717\) −6.69503 21.7344i −0.250030 0.811688i
\(718\) 19.3351i 0.721580i
\(719\) −35.0768 −1.30815 −0.654073 0.756432i \(-0.726941\pi\)
−0.654073 + 0.756432i \(0.726941\pi\)
\(720\) −4.89973 7.19849i −0.182602 0.268272i
\(721\) 51.0555i 1.90141i
\(722\) −0.581221 −0.0216308
\(723\) −19.8675 + 6.11993i −0.738879 + 0.227603i
\(724\) 1.63018 0.0605850
\(725\) 8.27431i 0.307300i
\(726\) −15.1650 + 4.67140i −0.562826 + 0.173372i
\(727\) 37.6281 1.39555 0.697775 0.716317i \(-0.254174\pi\)
0.697775 + 0.716317i \(0.254174\pi\)
\(728\) 21.6712i 0.803189i
\(729\) −5.94727 26.3369i −0.220269 0.975439i
\(730\) 17.3008 0.640330
\(731\) 0.437855 0.0161947
\(732\) 5.44291 + 17.6696i 0.201176 + 0.653088i
\(733\) −18.3230 −0.676776 −0.338388 0.941007i \(-0.609882\pi\)
−0.338388 + 0.941007i \(0.609882\pi\)
\(734\) 7.18946i 0.265368i
\(735\) 3.58122 + 11.6259i 0.132095 + 0.428828i
\(736\) 7.20070 0.265421
\(737\) 1.48142i 0.0545687i
\(738\) −13.6632 20.0734i −0.502948 0.738910i
\(739\) 37.2587i 1.37058i 0.728270 + 0.685291i \(0.240325\pi\)
−0.728270 + 0.685291i \(0.759675\pi\)
\(740\) 5.05797 0.185935
\(741\) 15.9318 + 51.7202i 0.585269 + 1.89999i
\(742\) 3.17065i 0.116398i
\(743\) 21.2235i 0.778614i 0.921108 + 0.389307i \(0.127285\pi\)
−0.921108 + 0.389307i \(0.872715\pi\)
\(744\) 3.28818 + 10.6746i 0.120550 + 0.391350i
\(745\) 36.0325i 1.32013i
\(746\) −20.0865 −0.735420
\(747\) 36.3332 24.7306i 1.32936 0.904845i
\(748\) 0.770515i 0.0281728i
\(749\) 59.9640i 2.19104i
\(750\) −2.33093 7.56702i −0.0851134 0.276308i
\(751\) 24.3301i 0.887817i 0.896072 + 0.443908i \(0.146408\pi\)
−0.896072 + 0.443908i \(0.853592\pi\)
\(752\) −4.48887 −0.163692
\(753\) 1.46075 + 4.74212i 0.0532328 + 0.172813i
\(754\) 17.0580 0.621215
\(755\) −19.5664 −0.712093
\(756\) 9.95768 12.4570i 0.362157 0.453057i
\(757\) 32.8729 1.19479 0.597393 0.801949i \(-0.296203\pi\)
0.597393 + 0.801949i \(0.296203\pi\)
\(758\) −2.68186 −0.0974095
\(759\) 16.1615 4.97835i 0.586625 0.180703i
\(760\) 12.8442i 0.465908i
\(761\) 15.2935i 0.554390i 0.960814 + 0.277195i \(0.0894048\pi\)
−0.960814 + 0.277195i \(0.910595\pi\)
\(762\) 13.7275 4.22857i 0.497293 0.153185i
\(763\) 4.36613i 0.158064i
\(764\) 4.94832 0.179024
\(765\) −4.09064 + 2.78434i −0.147897 + 0.100668i
\(766\) 22.1048i 0.798680i
\(767\) 49.7021 21.7090i 1.79464 0.783867i
\(768\) −1.65530 + 0.509894i −0.0597304 + 0.0183992i
\(769\) 11.7785i 0.424745i 0.977189 + 0.212372i \(0.0681190\pi\)
−0.977189 + 0.212372i \(0.931881\pi\)
\(770\) 12.0792i 0.435303i
\(771\) −6.03518 19.5923i −0.217352 0.705600i
\(772\) −7.55803 −0.272019
\(773\) −0.997271 −0.0358694 −0.0179347 0.999839i \(-0.505709\pi\)
−0.0179347 + 0.999839i \(0.505709\pi\)
\(774\) −1.30067 1.91089i −0.0467516 0.0686855i
\(775\) 22.0874i 0.793403i
\(776\) 8.16151i 0.292981i
\(777\) 2.72702 + 8.85288i 0.0978313 + 0.317595i
\(778\) 1.33259i 0.0477757i
\(779\) 35.8167i 1.28327i
\(780\) −33.9256 + 10.4504i −1.21473 + 0.374183i
\(781\) 14.9701i 0.535672i
\(782\) 4.09189i 0.146326i
\(783\) −9.80522 7.83794i −0.350410 0.280105i
\(784\) 2.41972 0.0864185