Properties

Label 177.2.d.c.176.3
Level $177$
Weight $2$
Character 177.176
Analytic conductor $1.413$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.41335211578\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.19298288.1
Defining polynomial: \(x^{6} - x^{5} + 3 x^{4} - 2 x^{3} + 9 x^{2} - 9 x + 27\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 176.3
Root \(-1.16170 + 1.28470i\) of defining polynomial
Character \(\chi\) \(=\) 177.176
Dual form 177.2.d.c.176.4

$q$-expansion

\(f(q)\) \(=\) \(q+1.46260 q^{2} +(1.16170 - 1.28470i) q^{3} +0.139194 q^{4} +0.594299i q^{5} +(1.69910 - 1.87900i) q^{6} +1.86081 q^{7} -2.72161 q^{8} +(-0.300896 - 2.98487i) q^{9} +O(q^{10})\) \(q+1.46260 q^{2} +(1.16170 - 1.28470i) q^{3} +0.139194 q^{4} +0.594299i q^{5} +(1.69910 - 1.87900i) q^{6} +1.86081 q^{7} -2.72161 q^{8} +(-0.300896 - 2.98487i) q^{9} +0.869221i q^{10} -0.676596 q^{11} +(0.161702 - 0.178822i) q^{12} +5.37545i q^{13} +2.72161 q^{14} +(0.763495 + 0.690399i) q^{15} -4.25901 q^{16} -1.70017i q^{17} +(-0.440090 - 4.36567i) q^{18} -2.25901 q^{19} +0.0827230i q^{20} +(2.16170 - 2.39057i) q^{21} -0.989588 q^{22} -4.86081 q^{23} +(-3.16170 + 3.49645i) q^{24} +4.64681 q^{25} +7.86212i q^{26} +(-4.18421 - 3.08097i) q^{27} +0.259013 q^{28} +6.24467i q^{29} +(1.11669 + 1.00978i) q^{30} +2.48667i q^{31} -0.786003 q^{32} +(-0.786003 + 0.869221i) q^{33} -2.48667i q^{34} +1.10588i q^{35} +(-0.0418830 - 0.415477i) q^{36} -7.86212i q^{37} -3.30403 q^{38} +(6.90582 + 6.24467i) q^{39} -1.61745i q^{40} +2.29447i q^{41} +(3.16170 - 3.49645i) q^{42} -7.11389i q^{43} -0.0941782 q^{44} +(1.77391 - 0.178822i) q^{45} -7.10941 q^{46} +8.46260 q^{47} +(-4.94770 + 5.47154i) q^{48} -3.53740 q^{49} +6.79641 q^{50} +(-2.18421 - 1.97510i) q^{51} +0.748230i q^{52} +5.73309i q^{53} +(-6.11982 - 4.50622i) q^{54} -0.402100i q^{55} -5.06439 q^{56} +(-2.62430 + 2.90215i) q^{57} +9.13344i q^{58} +(-1.93561 - 7.43326i) q^{59} +(0.106274 + 0.0960994i) q^{60} -10.0027i q^{61} +3.63700i q^{62} +(-0.559910 - 5.55427i) q^{63} +7.36842 q^{64} -3.19462 q^{65} +(-1.14961 + 1.27132i) q^{66} -5.37545i q^{67} -0.236654i q^{68} +(-5.64681 + 6.24467i) q^{69} +1.61745i q^{70} -5.92529i q^{71} +(0.818923 + 8.12366i) q^{72} +8.26422i q^{73} -11.4991i q^{74} +(5.39821 - 5.96974i) q^{75} -0.314441 q^{76} -1.25901 q^{77} +(10.1004 + 9.13344i) q^{78} +8.29362 q^{79} -2.53113i q^{80} +(-8.81892 + 1.79627i) q^{81} +3.35589i q^{82} -0.0941782 q^{83} +(0.300896 - 0.332754i) q^{84} +1.01041 q^{85} -10.4048i q^{86} +(8.02251 + 7.25444i) q^{87} +1.84143 q^{88} +10.9806 q^{89} +(2.59451 - 0.261545i) q^{90} +10.0027i q^{91} -0.676596 q^{92} +(3.19462 + 2.88877i) q^{93} +12.3774 q^{94} -1.34253i q^{95} +(-0.913101 + 1.00978i) q^{96} -17.8648i q^{97} -5.17380 q^{98} +(0.203585 + 2.01955i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 4q^{2} - q^{3} + 12q^{4} + 7q^{6} + 6q^{8} - 5q^{9} + O(q^{10}) \) \( 6q + 4q^{2} - q^{3} + 12q^{4} + 7q^{6} + 6q^{8} - 5q^{9} - 20q^{11} - 7q^{12} - 6q^{14} + 3q^{15} - 8q^{16} - 17q^{18} + 4q^{19} + 5q^{21} + 2q^{22} - 18q^{23} - 11q^{24} - 4q^{25} + 2q^{27} - 16q^{28} + 37q^{30} + 16q^{32} + 16q^{33} - 21q^{36} + 36q^{38} - 8q^{39} + 11q^{42} - 50q^{44} + 17q^{45} - 6q^{46} + 46q^{47} - q^{48} - 26q^{49} + 28q^{50} + 14q^{51} - 8q^{54} - 32q^{56} - 3q^{57} - 10q^{59} + 23q^{60} + 11q^{63} - 10q^{64} - 26q^{66} - 2q^{69} - 27q^{72} + 26q^{75} + 46q^{76} + 10q^{77} - 8q^{78} - 14q^{79} - 21q^{81} - 50q^{83} + 5q^{84} + 14q^{85} + 29q^{87} - 40q^{88} + 26q^{89} - 45q^{90} - 20q^{92} + 52q^{94} - 23q^{96} + 4q^{98} + 14q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.46260 1.03421 0.517107 0.855921i \(-0.327009\pi\)
0.517107 + 0.855921i \(0.327009\pi\)
\(3\) 1.16170 1.28470i 0.670709 0.741721i
\(4\) 0.139194 0.0695971
\(5\) 0.594299i 0.265779i 0.991131 + 0.132889i \(0.0424255\pi\)
−0.991131 + 0.132889i \(0.957575\pi\)
\(6\) 1.69910 1.87900i 0.693656 0.767097i
\(7\) 1.86081 0.703319 0.351659 0.936128i \(-0.385618\pi\)
0.351659 + 0.936128i \(0.385618\pi\)
\(8\) −2.72161 −0.962235
\(9\) −0.300896 2.98487i −0.100299 0.994957i
\(10\) 0.869221i 0.274872i
\(11\) −0.676596 −0.204001 −0.102001 0.994784i \(-0.532524\pi\)
−0.102001 + 0.994784i \(0.532524\pi\)
\(12\) 0.161702 0.178822i 0.0466794 0.0516216i
\(13\) 5.37545i 1.49088i 0.666573 + 0.745440i \(0.267761\pi\)
−0.666573 + 0.745440i \(0.732239\pi\)
\(14\) 2.72161 0.727381
\(15\) 0.763495 + 0.690399i 0.197133 + 0.178260i
\(16\) −4.25901 −1.06475
\(17\) 1.70017i 0.412353i −0.978515 0.206176i \(-0.933898\pi\)
0.978515 0.206176i \(-0.0661021\pi\)
\(18\) −0.440090 4.36567i −0.103730 1.02900i
\(19\) −2.25901 −0.518253 −0.259127 0.965843i \(-0.583435\pi\)
−0.259127 + 0.965843i \(0.583435\pi\)
\(20\) 0.0827230i 0.0184974i
\(21\) 2.16170 2.39057i 0.471722 0.521666i
\(22\) −0.989588 −0.210981
\(23\) −4.86081 −1.01355 −0.506774 0.862079i \(-0.669162\pi\)
−0.506774 + 0.862079i \(0.669162\pi\)
\(24\) −3.16170 + 3.49645i −0.645380 + 0.713710i
\(25\) 4.64681 0.929362
\(26\) 7.86212i 1.54189i
\(27\) −4.18421 3.08097i −0.805252 0.592933i
\(28\) 0.259013 0.0489489
\(29\) 6.24467i 1.15961i 0.814757 + 0.579803i \(0.196870\pi\)
−0.814757 + 0.579803i \(0.803130\pi\)
\(30\) 1.11669 + 1.00978i 0.203878 + 0.184359i
\(31\) 2.48667i 0.446620i 0.974748 + 0.223310i \(0.0716861\pi\)
−0.974748 + 0.223310i \(0.928314\pi\)
\(32\) −0.786003 −0.138947
\(33\) −0.786003 + 0.869221i −0.136826 + 0.151312i
\(34\) 2.48667i 0.426461i
\(35\) 1.10588i 0.186927i
\(36\) −0.0418830 0.415477i −0.00698050 0.0692461i
\(37\) 7.86212i 1.29252i −0.763116 0.646262i \(-0.776331\pi\)
0.763116 0.646262i \(-0.223669\pi\)
\(38\) −3.30403 −0.535984
\(39\) 6.90582 + 6.24467i 1.10582 + 0.999947i
\(40\) 1.61745i 0.255742i
\(41\) 2.29447i 0.358337i 0.983818 + 0.179168i \(0.0573407\pi\)
−0.983818 + 0.179168i \(0.942659\pi\)
\(42\) 3.16170 3.49645i 0.487861 0.539514i
\(43\) 7.11389i 1.08486i −0.840102 0.542429i \(-0.817505\pi\)
0.840102 0.542429i \(-0.182495\pi\)
\(44\) −0.0941782 −0.0141979
\(45\) 1.77391 0.178822i 0.264438 0.0266573i
\(46\) −7.10941 −1.04822
\(47\) 8.46260 1.23440 0.617198 0.786808i \(-0.288268\pi\)
0.617198 + 0.786808i \(0.288268\pi\)
\(48\) −4.94770 + 5.47154i −0.714140 + 0.789749i
\(49\) −3.53740 −0.505343
\(50\) 6.79641 0.961158
\(51\) −2.18421 1.97510i −0.305851 0.276569i
\(52\) 0.748230i 0.103761i
\(53\) 5.73309i 0.787500i 0.919217 + 0.393750i \(0.128823\pi\)
−0.919217 + 0.393750i \(0.871177\pi\)
\(54\) −6.11982 4.50622i −0.832802 0.613219i
\(55\) 0.402100i 0.0542192i
\(56\) −5.06439 −0.676758
\(57\) −2.62430 + 2.90215i −0.347597 + 0.384399i
\(58\) 9.13344i 1.19928i
\(59\) −1.93561 7.43326i −0.251995 0.967729i
\(60\) 0.106274 + 0.0960994i 0.0137199 + 0.0124064i
\(61\) 10.0027i 1.28071i −0.768079 0.640355i \(-0.778787\pi\)
0.768079 0.640355i \(-0.221213\pi\)
\(62\) 3.63700i 0.461900i
\(63\) −0.559910 5.55427i −0.0705420 0.699772i
\(64\) 7.36842 0.921053
\(65\) −3.19462 −0.396244
\(66\) −1.14961 + 1.27132i −0.141507 + 0.156489i
\(67\) 5.37545i 0.656715i −0.944553 0.328358i \(-0.893505\pi\)
0.944553 0.328358i \(-0.106495\pi\)
\(68\) 0.236654i 0.0286986i
\(69\) −5.64681 + 6.24467i −0.679796 + 0.751769i
\(70\) 1.61745i 0.193322i
\(71\) 5.92529i 0.703202i −0.936150 0.351601i \(-0.885637\pi\)
0.936150 0.351601i \(-0.114363\pi\)
\(72\) 0.818923 + 8.12366i 0.0965110 + 0.957383i
\(73\) 8.26422i 0.967254i 0.875274 + 0.483627i \(0.160681\pi\)
−0.875274 + 0.483627i \(0.839319\pi\)
\(74\) 11.4991i 1.33675i
\(75\) 5.39821 5.96974i 0.623331 0.689327i
\(76\) −0.314441 −0.0360689
\(77\) −1.25901 −0.143478
\(78\) 10.1004 + 9.13344i 1.14365 + 1.03416i
\(79\) 8.29362 0.933105 0.466552 0.884494i \(-0.345496\pi\)
0.466552 + 0.884494i \(0.345496\pi\)
\(80\) 2.53113i 0.282989i
\(81\) −8.81892 + 1.79627i −0.979880 + 0.199586i
\(82\) 3.35589i 0.370596i
\(83\) −0.0941782 −0.0103374 −0.00516870 0.999987i \(-0.501645\pi\)
−0.00516870 + 0.999987i \(0.501645\pi\)
\(84\) 0.300896 0.332754i 0.0328305 0.0363064i
\(85\) 1.01041 0.109595
\(86\) 10.4048i 1.12197i
\(87\) 8.02251 + 7.25444i 0.860103 + 0.777758i
\(88\) 1.84143 0.196297
\(89\) 10.9806 1.16394 0.581972 0.813209i \(-0.302281\pi\)
0.581972 + 0.813209i \(0.302281\pi\)
\(90\) 2.59451 0.261545i 0.273486 0.0275693i
\(91\) 10.0027i 1.04856i
\(92\) −0.676596 −0.0705400
\(93\) 3.19462 + 2.88877i 0.331267 + 0.299552i
\(94\) 12.3774 1.27663
\(95\) 1.34253i 0.137741i
\(96\) −0.913101 + 1.00978i −0.0931930 + 0.103060i
\(97\) 17.8648i 1.81389i −0.421246 0.906947i \(-0.638407\pi\)
0.421246 0.906947i \(-0.361593\pi\)
\(98\) −5.17380 −0.522633
\(99\) 0.203585 + 2.01955i 0.0204611 + 0.202973i
\(100\) 0.646809 0.0646809
\(101\) −8.36842 −0.832689 −0.416344 0.909207i \(-0.636689\pi\)
−0.416344 + 0.909207i \(0.636689\pi\)
\(102\) −3.19462 2.88877i −0.316315 0.286031i
\(103\) 1.73844i 0.171294i 0.996326 + 0.0856469i \(0.0272957\pi\)
−0.996326 + 0.0856469i \(0.972704\pi\)
\(104\) 14.6299i 1.43458i
\(105\) 1.42072 + 1.28470i 0.138648 + 0.125374i
\(106\) 8.38521i 0.814443i
\(107\) 7.66992i 0.741479i 0.928737 + 0.370740i \(0.120896\pi\)
−0.928737 + 0.370740i \(0.879104\pi\)
\(108\) −0.582418 0.428853i −0.0560432 0.0412664i
\(109\) 15.3781i 1.47296i 0.676462 + 0.736478i \(0.263512\pi\)
−0.676462 + 0.736478i \(0.736488\pi\)
\(110\) 0.588111i 0.0560742i
\(111\) −10.1004 9.13344i −0.958692 0.866908i
\(112\) −7.92520 −0.748861
\(113\) 6.11982 0.575704 0.287852 0.957675i \(-0.407059\pi\)
0.287852 + 0.957675i \(0.407059\pi\)
\(114\) −3.83830 + 4.24468i −0.359490 + 0.397551i
\(115\) 2.88877i 0.269379i
\(116\) 0.869221i 0.0807051i
\(117\) 16.0450 1.61745i 1.48336 0.149533i
\(118\) −2.83102 10.8719i −0.260616 1.00084i
\(119\) 3.16369i 0.290015i
\(120\) −2.07794 1.87900i −0.189689 0.171528i
\(121\) −10.5422 −0.958383
\(122\) 14.6299i 1.32453i
\(123\) 2.94770 + 2.66549i 0.265786 + 0.240340i
\(124\) 0.346130i 0.0310834i
\(125\) 5.73309i 0.512783i
\(126\) −0.818923 8.12366i −0.0729554 0.723713i
\(127\) 6.20359 0.550479 0.275240 0.961376i \(-0.411243\pi\)
0.275240 + 0.961376i \(0.411243\pi\)
\(128\) 12.3490 1.09151
\(129\) −9.13919 8.26422i −0.804661 0.727624i
\(130\) −4.67245 −0.409801
\(131\) 16.5180 1.44319 0.721593 0.692317i \(-0.243410\pi\)
0.721593 + 0.692317i \(0.243410\pi\)
\(132\) −0.109407 + 0.120990i −0.00952265 + 0.0105309i
\(133\) −4.20359 −0.364497
\(134\) 7.86212i 0.679184i
\(135\) 1.83102 2.48667i 0.157589 0.214019i
\(136\) 4.62721i 0.396780i
\(137\) 17.5071i 1.49574i 0.663848 + 0.747868i \(0.268922\pi\)
−0.663848 + 0.747868i \(0.731078\pi\)
\(138\) −8.25901 + 9.13344i −0.703054 + 0.777490i
\(139\) 5.69182 0.482774 0.241387 0.970429i \(-0.422398\pi\)
0.241387 + 0.970429i \(0.422398\pi\)
\(140\) 0.153931i 0.0130096i
\(141\) 9.83102 10.8719i 0.827921 0.915578i
\(142\) 8.66632i 0.727261i
\(143\) 3.63700i 0.304141i
\(144\) 1.28152 + 12.7126i 0.106793 + 1.05938i
\(145\) −3.71120 −0.308198
\(146\) 12.0872i 1.00035i
\(147\) −4.10941 + 4.54449i −0.338938 + 0.374823i
\(148\) 1.09436i 0.0899559i
\(149\) −21.5976 −1.76935 −0.884674 0.466210i \(-0.845619\pi\)
−0.884674 + 0.466210i \(0.845619\pi\)
\(150\) 7.89541 8.73134i 0.644658 0.712911i
\(151\) 8.26422i 0.672533i 0.941767 + 0.336266i \(0.109164\pi\)
−0.941767 + 0.336266i \(0.890836\pi\)
\(152\) 6.14816 0.498681
\(153\) −5.07480 + 0.511576i −0.410274 + 0.0413585i
\(154\) −1.84143 −0.148387
\(155\) −1.47783 −0.118702
\(156\) 0.961250 + 0.869221i 0.0769616 + 0.0695934i
\(157\) 12.8914i 1.02885i 0.857536 + 0.514424i \(0.171994\pi\)
−0.857536 + 0.514424i \(0.828006\pi\)
\(158\) 12.1302 0.965029
\(159\) 7.36529 + 6.66014i 0.584105 + 0.528184i
\(160\) 0.467121i 0.0369291i
\(161\) −9.04502 −0.712847
\(162\) −12.8985 + 2.62723i −1.01341 + 0.206414i
\(163\) −15.7562 −1.23412 −0.617061 0.786915i \(-0.711677\pi\)
−0.617061 + 0.786915i \(0.711677\pi\)
\(164\) 0.319377i 0.0249392i
\(165\) −0.516577 0.467121i −0.0402155 0.0363653i
\(166\) −0.137745 −0.0106911
\(167\) 13.0454i 1.00948i −0.863271 0.504740i \(-0.831588\pi\)
0.863271 0.504740i \(-0.168412\pi\)
\(168\) −5.88331 + 6.50621i −0.453908 + 0.501965i
\(169\) −15.8954 −1.22272
\(170\) 1.47783 0.113344
\(171\) 0.679729 + 6.74287i 0.0519802 + 0.515640i
\(172\) 0.990211i 0.0755029i
\(173\) −9.40862 −0.715324 −0.357662 0.933851i \(-0.616426\pi\)
−0.357662 + 0.933851i \(0.616426\pi\)
\(174\) 11.7337 + 10.6103i 0.889530 + 0.804367i
\(175\) 8.64681 0.653637
\(176\) 2.88163 0.217211
\(177\) −11.7981 6.14857i −0.886799 0.462155i
\(178\) 16.0602 1.20377
\(179\) −23.0450 −1.72247 −0.861233 0.508211i \(-0.830307\pi\)
−0.861233 + 0.508211i \(0.830307\pi\)
\(180\) 0.246917 0.0248910i 0.0184041 0.00185527i
\(181\) −7.58242 −0.563597 −0.281798 0.959474i \(-0.590931\pi\)
−0.281798 + 0.959474i \(0.590931\pi\)
\(182\) 14.6299i 1.08444i
\(183\) −12.8504 11.6201i −0.949928 0.858983i
\(184\) 13.2292 0.975271
\(185\) 4.67245 0.343525
\(186\) 4.67245 + 4.22511i 0.342601 + 0.309800i
\(187\) 1.15033i 0.0841205i
\(188\) 1.17794 0.0859104
\(189\) −7.78600 5.73309i −0.566348 0.417021i
\(190\) 1.96358i 0.142453i
\(191\) 6.11982 0.442815 0.221407 0.975181i \(-0.428935\pi\)
0.221407 + 0.975181i \(0.428935\pi\)
\(192\) 8.55991 9.46619i 0.617758 0.683164i
\(193\) −8.19462 −0.589862 −0.294931 0.955519i \(-0.595297\pi\)
−0.294931 + 0.955519i \(0.595297\pi\)
\(194\) 26.1290i 1.87595i
\(195\) −3.71120 + 4.10412i −0.265765 + 0.293902i
\(196\) −0.492386 −0.0351704
\(197\) 24.4288i 1.74048i 0.492627 + 0.870241i \(0.336037\pi\)
−0.492627 + 0.870241i \(0.663963\pi\)
\(198\) 0.297763 + 2.95379i 0.0211611 + 0.209917i
\(199\) 11.8608 0.840790 0.420395 0.907341i \(-0.361891\pi\)
0.420395 + 0.907341i \(0.361891\pi\)
\(200\) −12.6468 −0.894264
\(201\) −6.90582 6.24467i −0.487099 0.440465i
\(202\) −12.2396 −0.861178
\(203\) 11.6201i 0.815572i
\(204\) −0.304029 0.274922i −0.0212863 0.0192484i
\(205\) −1.36360 −0.0952382
\(206\) 2.54264i 0.177154i
\(207\) 1.46260 + 14.5089i 0.101658 + 1.00844i
\(208\) 22.8941i 1.58742i
\(209\) 1.52844 0.105724
\(210\) 2.07794 + 1.87900i 0.143391 + 0.129663i
\(211\) 17.1165i 1.17835i 0.808005 + 0.589176i \(0.200547\pi\)
−0.808005 + 0.589176i \(0.799453\pi\)
\(212\) 0.798013i 0.0548077i
\(213\) −7.61220 6.88342i −0.521580 0.471644i
\(214\) 11.2180i 0.766847i
\(215\) 4.22778 0.288332
\(216\) 11.3878 + 8.38521i 0.774841 + 0.570541i
\(217\) 4.62721i 0.314116i
\(218\) 22.4920i 1.52335i
\(219\) 10.6170 + 9.60056i 0.717432 + 0.648746i
\(220\) 0.0559700i 0.00377350i
\(221\) 9.13919 0.614769
\(222\) −14.7729 13.3586i −0.991492 0.896567i
\(223\) −7.31444 −0.489811 −0.244906 0.969547i \(-0.578757\pi\)
−0.244906 + 0.969547i \(0.578757\pi\)
\(224\) −1.46260 −0.0977240
\(225\) −1.39821 13.8701i −0.0932138 0.924675i
\(226\) 8.95084 0.595401
\(227\) 15.7473 1.04518 0.522591 0.852584i \(-0.324966\pi\)
0.522591 + 0.852584i \(0.324966\pi\)
\(228\) −0.365287 + 0.403962i −0.0241917 + 0.0267530i
\(229\) 26.5311i 1.75322i −0.481198 0.876612i \(-0.659798\pi\)
0.481198 0.876612i \(-0.340202\pi\)
\(230\) 4.22511i 0.278596i
\(231\) −1.46260 + 1.61745i −0.0962319 + 0.106420i
\(232\) 16.9956i 1.11581i
\(233\) −15.1648 −0.993481 −0.496741 0.867899i \(-0.665470\pi\)
−0.496741 + 0.867899i \(0.665470\pi\)
\(234\) 23.4674 2.36568i 1.53411 0.154649i
\(235\) 5.02931i 0.328076i
\(236\) −0.269425 1.03467i −0.0175381 0.0673511i
\(237\) 9.63471 10.6548i 0.625842 0.692103i
\(238\) 4.62721i 0.299938i
\(239\) 17.0338i 1.10183i −0.834563 0.550913i \(-0.814280\pi\)
0.834563 0.550913i \(-0.185720\pi\)
\(240\) −3.25173 2.94042i −0.209899 0.189803i
\(241\) −10.2847 −0.662493 −0.331246 0.943544i \(-0.607469\pi\)
−0.331246 + 0.943544i \(0.607469\pi\)
\(242\) −15.4190 −0.991173
\(243\) −7.93729 + 13.4164i −0.509178 + 0.860661i
\(244\) 1.39231i 0.0891336i
\(245\) 2.10227i 0.134309i
\(246\) 4.31131 + 3.89855i 0.274879 + 0.248562i
\(247\) 12.1432i 0.772653i
\(248\) 6.76776i 0.429753i
\(249\) −0.109407 + 0.120990i −0.00693339 + 0.00766746i
\(250\) 8.38521i 0.530327i
\(251\) 15.1299i 0.954993i 0.878634 + 0.477497i \(0.158456\pi\)
−0.878634 + 0.477497i \(0.841544\pi\)
\(252\) −0.0779361 0.773122i −0.00490952 0.0487021i
\(253\) 3.28880 0.206765
\(254\) 9.07335 0.569313
\(255\) 1.17380 1.29807i 0.0735061 0.0812886i
\(256\) 3.32485 0.207803
\(257\) 6.13519i 0.382703i 0.981522 + 0.191351i \(0.0612870\pi\)
−0.981522 + 0.191351i \(0.938713\pi\)
\(258\) −13.3670 12.0872i −0.832191 0.752518i
\(259\) 14.6299i 0.909056i
\(260\) −0.444673 −0.0275774
\(261\) 18.6395 1.87900i 1.15376 0.116307i
\(262\) 24.1592 1.49256
\(263\) 23.7073i 1.46186i −0.682454 0.730929i \(-0.739087\pi\)
0.682454 0.730929i \(-0.260913\pi\)
\(264\) 2.13919 2.36568i 0.131658 0.145598i
\(265\) −3.40717 −0.209301
\(266\) −6.14816 −0.376968
\(267\) 12.7562 14.1068i 0.780668 0.863321i
\(268\) 0.748230i 0.0457055i
\(269\) 26.1890 1.59677 0.798387 0.602145i \(-0.205687\pi\)
0.798387 + 0.602145i \(0.205687\pi\)
\(270\) 2.67805 3.63700i 0.162981 0.221341i
\(271\) 22.3144 1.35551 0.677753 0.735290i \(-0.262954\pi\)
0.677753 + 0.735290i \(0.262954\pi\)
\(272\) 7.24107i 0.439054i
\(273\) 12.8504 + 11.6201i 0.777741 + 0.703281i
\(274\) 25.6059i 1.54691i
\(275\) −3.14401 −0.189591
\(276\) −0.786003 + 0.869221i −0.0473118 + 0.0523210i
\(277\) 23.8269 1.43162 0.715809 0.698296i \(-0.246058\pi\)
0.715809 + 0.698296i \(0.246058\pi\)
\(278\) 8.32485 0.499292
\(279\) 7.42240 0.748230i 0.444367 0.0447954i
\(280\) 3.00976i 0.179868i
\(281\) 2.40395i 0.143408i 0.997426 + 0.0717038i \(0.0228436\pi\)
−0.997426 + 0.0717038i \(0.977156\pi\)
\(282\) 14.3788 15.9012i 0.856247 0.946902i
\(283\) 10.4048i 0.618499i 0.950981 + 0.309249i \(0.100078\pi\)
−0.950981 + 0.309249i \(0.899922\pi\)
\(284\) 0.824766i 0.0489408i
\(285\) −1.72474 1.55962i −0.102165 0.0923839i
\(286\) 5.31948i 0.314547i
\(287\) 4.26957i 0.252025i
\(288\) 0.236505 + 2.34612i 0.0139362 + 0.138246i
\(289\) 14.1094 0.829965
\(290\) −5.42799 −0.318743
\(291\) −22.9508 20.7535i −1.34540 1.21659i
\(292\) 1.15033i 0.0673180i
\(293\) 26.3212i 1.53770i 0.639429 + 0.768850i \(0.279171\pi\)
−0.639429 + 0.768850i \(0.720829\pi\)
\(294\) −6.01041 + 6.64677i −0.350534 + 0.387647i
\(295\) 4.41758 1.15033i 0.257202 0.0669748i
\(296\) 21.3976i 1.24371i
\(297\) 2.83102 + 2.08457i 0.164272 + 0.120959i
\(298\) −31.5887 −1.82988
\(299\) 26.1290i 1.51108i
\(300\) 0.751399 0.830953i 0.0433820 0.0479751i
\(301\) 13.2376i 0.763000i
\(302\) 12.0872i 0.695542i
\(303\) −9.72161 + 10.7509i −0.558492 + 0.617623i
\(304\) 9.62117 0.551812
\(305\) 5.94457 0.340385
\(306\) −7.42240 + 0.748230i −0.424310 + 0.0427735i
\(307\) −7.89541 −0.450615 −0.225307 0.974288i \(-0.572339\pi\)
−0.225307 + 0.974288i \(0.572339\pi\)
\(308\) −0.175247 −0.00998564
\(309\) 2.23337 + 2.01955i 0.127052 + 0.114888i
\(310\) −2.16147 −0.122763
\(311\) 25.2980i 1.43452i −0.696805 0.717260i \(-0.745396\pi\)
0.696805 0.717260i \(-0.254604\pi\)
\(312\) −18.7950 16.9956i −1.06406 0.962184i
\(313\) 2.08457i 0.117827i 0.998263 + 0.0589135i \(0.0187636\pi\)
−0.998263 + 0.0589135i \(0.981236\pi\)
\(314\) 18.8550i 1.06405i
\(315\) 3.30090 0.332754i 0.185984 0.0187486i
\(316\) 1.15442 0.0649414
\(317\) 18.8879i 1.06085i −0.847731 0.530426i \(-0.822032\pi\)
0.847731 0.530426i \(-0.177968\pi\)
\(318\) 10.7725 + 9.74111i 0.604089 + 0.546255i
\(319\) 4.22511i 0.236561i
\(320\) 4.37905i 0.244796i
\(321\) 9.85353 + 8.91016i 0.549970 + 0.497317i
\(322\) −13.2292 −0.737236
\(323\) 3.84072i 0.213703i
\(324\) −1.22754 + 0.250031i −0.0681968 + 0.0138906i
\(325\) 24.9787i 1.38557i
\(326\) −23.0450 −1.27635
\(327\) 19.7562 + 17.8648i 1.09252 + 0.987924i
\(328\) 6.24467i 0.344804i
\(329\) 15.7473 0.868174
\(330\) −0.755545 0.683210i −0.0415914 0.0376095i
\(331\) 29.3595 1.61374 0.806871 0.590728i \(-0.201159\pi\)
0.806871 + 0.590728i \(0.201159\pi\)
\(332\) −0.0131090 −0.000719453
\(333\) −23.4674 + 2.36568i −1.28601 + 0.129639i
\(334\) 19.0801i 1.04402i
\(335\) 3.19462 0.174541
\(336\) −9.20672 + 10.1815i −0.502268 + 0.555445i
\(337\) 12.8355i 0.699192i 0.936901 + 0.349596i \(0.113681\pi\)
−0.936901 + 0.349596i \(0.886319\pi\)
\(338\) −23.2486 −1.26456
\(339\) 7.10941 7.86212i 0.386130 0.427012i
\(340\) 0.140643 0.00762746
\(341\) 1.68247i 0.0911110i
\(342\) 0.994170 + 9.86210i 0.0537586 + 0.533282i
\(343\) −19.6081 −1.05874
\(344\) 19.3612i 1.04389i
\(345\) −3.71120 3.35589i −0.199804 0.180675i
\(346\) −13.7610 −0.739798
\(347\) −27.7175 −1.48795 −0.743976 0.668207i \(-0.767062\pi\)
−0.743976 + 0.668207i \(0.767062\pi\)
\(348\) 1.11669 + 1.00978i 0.0598607 + 0.0541297i
\(349\) 7.11389i 0.380798i 0.981707 + 0.190399i \(0.0609781\pi\)
−0.981707 + 0.190399i \(0.939022\pi\)
\(350\) 12.6468 0.676000
\(351\) 16.5616 22.4920i 0.883992 1.20053i
\(352\) 0.531806 0.0283454
\(353\) −8.00482 −0.426053 −0.213027 0.977046i \(-0.568332\pi\)
−0.213027 + 0.977046i \(0.568332\pi\)
\(354\) −17.2559 8.99288i −0.917140 0.477966i
\(355\) 3.52139 0.186896
\(356\) 1.52844 0.0810071
\(357\) −4.06439 3.67527i −0.215110 0.194516i
\(358\) −33.7056 −1.78140
\(359\) 3.75799i 0.198339i −0.995071 0.0991697i \(-0.968381\pi\)
0.995071 0.0991697i \(-0.0316187\pi\)
\(360\) −4.82789 + 0.486685i −0.254452 + 0.0256506i
\(361\) −13.8969 −0.731414
\(362\) −11.0900 −0.582879
\(363\) −12.2469 + 13.5436i −0.642796 + 0.710853i
\(364\) 1.39231i 0.0729770i
\(365\) −4.91142 −0.257075
\(366\) −18.7950 16.9956i −0.982429 0.888372i
\(367\) 11.1530i 0.582181i 0.956695 + 0.291091i \(0.0940181\pi\)
−0.956695 + 0.291091i \(0.905982\pi\)
\(368\) 20.7022 1.07918
\(369\) 6.84871 0.690399i 0.356530 0.0359407i
\(370\) 6.83392 0.355278
\(371\) 10.6682i 0.553864i
\(372\) 0.444673 + 0.402100i 0.0230552 + 0.0208479i
\(373\) 12.7320 0.659239 0.329620 0.944114i \(-0.393080\pi\)
0.329620 + 0.944114i \(0.393080\pi\)
\(374\) 1.68247i 0.0869986i
\(375\) 7.36529 + 6.66014i 0.380342 + 0.343928i
\(376\) −23.0319 −1.18778
\(377\) −33.5679 −1.72883
\(378\) −11.3878 8.38521i −0.585725 0.431289i
\(379\) −21.8656 −1.12316 −0.561581 0.827422i \(-0.689807\pi\)
−0.561581 + 0.827422i \(0.689807\pi\)
\(380\) 0.186872i 0.00958634i
\(381\) 7.20672 7.96973i 0.369211 0.408302i
\(382\) 8.95084 0.457965
\(383\) 11.2295i 0.573802i −0.957960 0.286901i \(-0.907375\pi\)
0.957960 0.286901i \(-0.0926251\pi\)
\(384\) 14.3459 15.8648i 0.732087 0.809597i
\(385\) 0.748230i 0.0381334i
\(386\) −11.9854 −0.610043
\(387\) −21.2340 + 2.14054i −1.07939 + 0.108810i
\(388\) 2.48667i 0.126242i
\(389\) 27.3559i 1.38700i 0.720458 + 0.693499i \(0.243932\pi\)
−0.720458 + 0.693499i \(0.756068\pi\)
\(390\) −5.42799 + 6.00269i −0.274857 + 0.303958i
\(391\) 8.26422i 0.417939i
\(392\) 9.62743 0.486259
\(393\) 19.1890 21.2207i 0.967958 1.07044i
\(394\) 35.7296i 1.80003i
\(395\) 4.92889i 0.247999i
\(396\) 0.0283379 + 0.281110i 0.00142403 + 0.0141263i
\(397\) 10.3488i 0.519391i −0.965691 0.259695i \(-0.916378\pi\)
0.965691 0.259695i \(-0.0836222\pi\)
\(398\) 17.3476 0.869556
\(399\) −4.88331 + 5.40034i −0.244471 + 0.270355i
\(400\) −19.7908 −0.989541
\(401\) 22.4120 1.11920 0.559601 0.828762i \(-0.310955\pi\)
0.559601 + 0.828762i \(0.310955\pi\)
\(402\) −10.1004 9.13344i −0.503764 0.455535i
\(403\) −13.3670 −0.665856
\(404\) −1.16484 −0.0579527
\(405\) −1.06752 5.24108i −0.0530457 0.260431i
\(406\) 16.9956i 0.843475i
\(407\) 5.31948i 0.263677i
\(408\) 5.94457 + 5.37545i 0.294300 + 0.266124i
\(409\) 21.7438i 1.07516i −0.843213 0.537580i \(-0.819339\pi\)
0.843213 0.537580i \(-0.180661\pi\)
\(410\) −1.99440 −0.0984966
\(411\) 22.4914 + 20.3381i 1.10942 + 1.00320i
\(412\) 0.241981i 0.0119215i
\(413\) −3.60179 13.8319i −0.177233 0.680621i
\(414\) 2.13919 + 21.2207i 0.105136 + 1.04294i
\(415\) 0.0559700i 0.00274746i
\(416\) 4.22511i 0.207153i
\(417\) 6.61220 7.31227i 0.323801 0.358084i
\(418\) 2.23549 0.109341
\(419\) 37.9404 1.85351 0.926756 0.375665i \(-0.122586\pi\)
0.926756 + 0.375665i \(0.122586\pi\)
\(420\) 0.197755 + 0.178822i 0.00964947 + 0.00872564i
\(421\) 21.3417i 1.04013i 0.854127 + 0.520064i \(0.174092\pi\)
−0.854127 + 0.520064i \(0.825908\pi\)
\(422\) 25.0346i 1.21867i
\(423\) −2.54636 25.2598i −0.123808 1.22817i
\(424\) 15.6032i 0.757761i
\(425\) 7.90038i 0.383225i
\(426\) −11.1336 10.0677i −0.539425 0.487781i
\(427\) 18.6130i 0.900747i
\(428\) 1.06761i 0.0516048i
\(429\) −4.67245 4.22511i −0.225588 0.203990i
\(430\) 6.18354 0.298197
\(431\) 19.5679 0.942551 0.471275 0.881986i \(-0.343794\pi\)
0.471275 + 0.881986i \(0.343794\pi\)
\(432\) 17.8206 + 13.1219i 0.857394 + 0.631328i
\(433\) 15.0346 0.722517 0.361258 0.932466i \(-0.382347\pi\)
0.361258 + 0.932466i \(0.382347\pi\)
\(434\) 6.76776i 0.324863i
\(435\) −4.31131 + 4.76777i −0.206711 + 0.228597i
\(436\) 2.14054i 0.102513i
\(437\) 10.9806 0.525275
\(438\) 15.5284 + 14.0418i 0.741978 + 0.670941i
\(439\) 9.76518 0.466067 0.233033 0.972469i \(-0.425135\pi\)
0.233033 + 0.972469i \(0.425135\pi\)
\(440\) 1.09436i 0.0521716i
\(441\) 1.06439 + 10.5587i 0.0506853 + 0.502795i
\(442\) 13.3670 0.635802
\(443\) −0.0435667 −0.00206991 −0.00103496 0.999999i \(-0.500329\pi\)
−0.00103496 + 0.999999i \(0.500329\pi\)
\(444\) −1.40592 1.27132i −0.0667221 0.0603342i
\(445\) 6.52578i 0.309351i
\(446\) −10.6981 −0.506569
\(447\) −25.0900 + 27.7464i −1.18672 + 1.31236i
\(448\) 13.7112 0.647793
\(449\) 6.28293i 0.296510i −0.988949 0.148255i \(-0.952634\pi\)
0.988949 0.148255i \(-0.0473656\pi\)
\(450\) −2.04502 20.2864i −0.0964030 0.956311i
\(451\) 1.55243i 0.0731011i
\(452\) 0.851843 0.0400673
\(453\) 10.6170 + 9.60056i 0.498831 + 0.451074i
\(454\) 23.0319 1.08094
\(455\) −5.94457 −0.278686
\(456\) 7.14233 7.89852i 0.334470 0.369882i
\(457\) 1.55243i 0.0726197i 0.999341 + 0.0363098i \(0.0115603\pi\)
−0.999341 + 0.0363098i \(0.988440\pi\)
\(458\) 38.8043i 1.81321i
\(459\) −5.23819 + 7.11389i −0.244498 + 0.332048i
\(460\) 0.402100i 0.0187480i
\(461\) 41.3799i 1.92726i −0.267249 0.963628i \(-0.586115\pi\)
0.267249 0.963628i \(-0.413885\pi\)
\(462\) −2.13919 + 2.36568i −0.0995243 + 0.110061i
\(463\) 13.6397i 0.633889i −0.948444 0.316944i \(-0.897343\pi\)
0.948444 0.316944i \(-0.102657\pi\)
\(464\) 26.5961i 1.23469i
\(465\) −1.71680 + 1.89856i −0.0796145 + 0.0880437i
\(466\) −22.1801 −1.02747
\(467\) −7.01523 −0.324626 −0.162313 0.986739i \(-0.551895\pi\)
−0.162313 + 0.986739i \(0.551895\pi\)
\(468\) 2.23337 0.225140i 0.103238 0.0104071i
\(469\) 10.0027i 0.461880i
\(470\) 7.35587i 0.339301i
\(471\) 16.5616 + 14.9760i 0.763118 + 0.690058i
\(472\) 5.26798 + 20.2305i 0.242478 + 0.931182i
\(473\) 4.81323i 0.221312i
\(474\) 14.0917 15.5837i 0.647254 0.715782i
\(475\) −10.4972 −0.481645
\(476\) 0.440368i 0.0201842i
\(477\) 17.1125 1.72507i 0.783529 0.0789853i
\(478\) 24.9136i 1.13952i
\(479\) 9.76601i 0.446220i −0.974793 0.223110i \(-0.928379\pi\)
0.974793 0.223110i \(-0.0716209\pi\)
\(480\) −0.600109 0.542655i −0.0273911 0.0247687i
\(481\) 42.2624 1.92700
\(482\) −15.0423 −0.685159
\(483\) −10.5076 + 11.6201i −0.478113 + 0.528733i
\(484\) −1.46742 −0.0667007
\(485\) 10.6170 0.482094
\(486\) −11.6091 + 19.6228i −0.526598 + 0.890108i
\(487\) −11.2922 −0.511697 −0.255848 0.966717i \(-0.582355\pi\)
−0.255848 + 0.966717i \(0.582355\pi\)
\(488\) 27.2234i 1.23234i
\(489\) −18.3040 + 20.2420i −0.827737 + 0.915374i
\(490\) 3.07478i 0.138905i
\(491\) 19.8461i 0.895640i −0.894124 0.447820i \(-0.852201\pi\)
0.894124 0.447820i \(-0.147799\pi\)
\(492\) 0.410303 + 0.371021i 0.0184979 + 0.0167269i
\(493\) 10.6170 0.478167
\(494\) 17.7606i 0.799088i
\(495\) −1.20022 + 0.120990i −0.0539458 + 0.00543812i
\(496\) 10.5908i 0.475540i
\(497\) 11.0258i 0.494575i
\(498\) −0.160018 + 0.176960i −0.00717060 + 0.00792979i
\(499\) −35.8864 −1.60650 −0.803249 0.595643i \(-0.796897\pi\)
−0.803249 + 0.595643i \(0.796897\pi\)
\(500\) 0.798013i 0.0356882i
\(501\) −16.7593 15.1548i −0.748752 0.677068i
\(502\) 22.1290i 0.987667i
\(503\) 4.72306 0.210591 0.105295 0.994441i \(-0.466421\pi\)
0.105295 + 0.994441i \(0.466421\pi\)
\(504\) 1.52386 + 15.1166i 0.0678780 + 0.673345i
\(505\) 4.97334i 0.221311i
\(506\) 4.81019 0.213839
\(507\) −18.4657 + 20.4208i −0.820092 + 0.906919i
\(508\) 0.863503 0.0383117
\(509\) −0.501348 −0.0222219 −0.0111109 0.999938i \(-0.503537\pi\)
−0.0111109 + 0.999938i \(0.503537\pi\)
\(510\) 1.71680 1.89856i 0.0760210 0.0840697i
\(511\) 15.3781i 0.680287i
\(512\) −19.8352 −0.876599
\(513\) 9.45219 + 6.95996i 0.417324 + 0.307290i
\(514\) 8.97332i 0.395796i
\(515\) −1.03315 −0.0455262
\(516\) −1.27212 1.15033i −0.0560021 0.0506405i
\(517\) −5.72576 −0.251819
\(518\) 21.3976i 0.940158i
\(519\) −10.9300 + 12.0872i −0.479774 + 0.530571i
\(520\) 8.69452 0.381280
\(521\) 34.5969i 1.51572i −0.652418 0.757859i \(-0.726245\pi\)
0.652418 0.757859i \(-0.273755\pi\)
\(522\) 27.2621 2.74822i 1.19323 0.120286i
\(523\) 8.38365 0.366591 0.183296 0.983058i \(-0.441323\pi\)
0.183296 + 0.983058i \(0.441323\pi\)
\(524\) 2.29921 0.100442
\(525\) 10.0450 11.1085i 0.438400 0.484816i
\(526\) 34.6743i 1.51187i
\(527\) 4.22778 0.184165
\(528\) 3.34760 3.70202i 0.145685 0.161110i
\(529\) 0.627434 0.0272797
\(530\) −4.98332 −0.216462
\(531\) −21.6049 + 8.01419i −0.937574 + 0.347786i
\(532\) −0.585114 −0.0253679
\(533\) −12.3338 −0.534237
\(534\) 18.6572 20.6326i 0.807377 0.892858i
\(535\) −4.55823 −0.197069
\(536\) 14.6299i 0.631914i
\(537\) −26.7714 + 29.6059i −1.15527 + 1.27759i
\(538\) 38.3040 1.65140
\(539\) 2.39339 0.103091
\(540\) 0.254867 0.346130i 0.0109677 0.0148951i
\(541\) 10.3488i 0.444929i 0.974941 + 0.222465i \(0.0714102\pi\)
−0.974941 + 0.222465i \(0.928590\pi\)
\(542\) 32.6371 1.40188
\(543\) −8.80851 + 9.74111i −0.378009 + 0.418031i
\(544\) 1.33634i 0.0572952i
\(545\) −9.13919 −0.391480
\(546\) 18.7950 + 16.9956i 0.804350 + 0.727343i
\(547\) −35.9661 −1.53780 −0.768899 0.639370i \(-0.779195\pi\)
−0.768899 + 0.639370i \(0.779195\pi\)
\(548\) 2.43689i 0.104099i
\(549\) −29.8567 + 3.00976i −1.27425 + 0.128454i
\(550\) −4.59843 −0.196078
\(551\) 14.1068i 0.600969i
\(552\) 15.3684 16.9956i 0.654123 0.723379i
\(553\) 15.4328 0.656270
\(554\) 34.8491 1.48060
\(555\) 5.42799 6.00269i 0.230406 0.254800i
\(556\) 0.792269 0.0335997
\(557\) 19.5588i 0.828731i 0.910110 + 0.414366i \(0.135997\pi\)
−0.910110 + 0.414366i \(0.864003\pi\)
\(558\) 10.8560 1.09436i 0.459571 0.0463280i
\(559\) 38.2403 1.61739
\(560\) 4.70994i 0.199031i
\(561\) 1.47783 + 1.33634i 0.0623939 + 0.0564204i
\(562\) 3.51601i 0.148314i
\(563\) −32.9854 −1.39017 −0.695085 0.718927i \(-0.744633\pi\)
−0.695085 + 0.718927i \(0.744633\pi\)
\(564\) 1.36842 1.51330i 0.0576209 0.0637215i
\(565\) 3.63700i 0.153010i
\(566\) 15.2180i 0.639660i
\(567\) −16.4103 + 3.34252i −0.689168 + 0.140373i
\(568\) 16.1263i 0.676646i
\(569\) 14.7202 0.617101 0.308551 0.951208i \(-0.400156\pi\)
0.308551 + 0.951208i \(0.400156\pi\)
\(570\) −2.52261 2.28110i −0.105660 0.0955446i
\(571\) 32.0926i 1.34303i −0.740990 0.671516i \(-0.765644\pi\)
0.740990 0.671516i \(-0.234356\pi\)
\(572\) 0.506250i 0.0211674i
\(573\) 7.10941 7.86212i 0.297000 0.328445i
\(574\) 6.24467i 0.260647i
\(575\) −22.5872 −0.941953
\(576\) −2.21713 21.9938i −0.0923804 0.916408i
\(577\) −7.00000 −0.291414 −0.145707 0.989328i \(-0.546546\pi\)
−0.145707 + 0.989328i \(0.546546\pi\)
\(578\) 20.6364 0.858361
\(579\) −9.51971 + 10.5276i −0.395626 + 0.437513i
\(580\) −0.516577 −0.0214497
\(581\) −0.175247 −0.00727048
\(582\) −33.5679 30.3541i −1.39143 1.25822i
\(583\) 3.87898i 0.160651i
\(584\) 22.4920i 0.930725i
\(585\) 0.961250 + 9.53554i 0.0397428 + 0.394246i
\(586\) 38.4973i 1.59031i
\(587\) −24.0782 −0.993812 −0.496906 0.867804i \(-0.665531\pi\)
−0.496906 + 0.867804i \(0.665531\pi\)
\(588\) −0.572005 + 0.632567i −0.0235891 + 0.0260866i
\(589\) 5.61743i 0.231462i
\(590\) 6.46115 1.68247i 0.266001 0.0692663i
\(591\) 31.3836 + 28.3790i 1.29095 + 1.16736i
\(592\) 33.4849i 1.37622i
\(593\) 35.9012i 1.47429i −0.675737 0.737143i \(-0.736175\pi\)
0.675737 0.737143i \(-0.263825\pi\)
\(594\) 4.14064 + 3.04889i 0.169893 + 0.125098i
\(595\) 1.88018 0.0770799
\(596\) −3.00627 −0.123141
\(597\) 13.7787 15.2375i 0.563926 0.623631i
\(598\) 38.2162i 1.56278i
\(599\) 1.85411i 0.0757567i 0.999282 + 0.0378784i \(0.0120599\pi\)
−0.999282 + 0.0378784i \(0.987940\pi\)
\(600\) −14.6918 + 16.2473i −0.599791 + 0.663294i
\(601\) 0.346130i 0.0141189i 0.999975 + 0.00705947i \(0.00224712\pi\)
−0.999975 + 0.00705947i \(0.997753\pi\)
\(602\) 19.3612i 0.789105i
\(603\) −16.0450 + 1.61745i −0.653404 + 0.0658677i
\(604\) 1.15033i 0.0468063i
\(605\) 6.26523i 0.254718i
\(606\) −14.2188 + 15.7242i −0.577600 + 0.638753i
\(607\) 6.59283 0.267595 0.133797 0.991009i \(-0.457283\pi\)
0.133797 + 0.991009i \(0.457283\pi\)
\(608\) 1.77559 0.0720097
\(609\) 14.9283 + 13.4991i 0.604926 + 0.547011i
\(610\) 8.69452 0.352031
\(611\) 45.4902i 1.84034i
\(612\) −0.706383 + 0.0712084i −0.0285538 + 0.00287843i
\(613\) 18.2669i 0.737792i −0.929471 0.368896i \(-0.879736\pi\)
0.929471 0.368896i \(-0.120264\pi\)
\(614\) −11.5478 −0.466032
\(615\) −1.58410 + 1.75182i −0.0638771 + 0.0706401i
\(616\) 3.42655 0.138059
\(617\) 25.2215i 1.01538i 0.861540 + 0.507690i \(0.169500\pi\)
−0.861540 + 0.507690i \(0.830500\pi\)
\(618\) 3.26653 + 2.95379i 0.131399 + 0.118819i
\(619\) −0.700787 −0.0281670 −0.0140835 0.999901i \(-0.504483\pi\)
−0.0140835 + 0.999901i \(0.504483\pi\)
\(620\) −0.205705 −0.00826131
\(621\) 20.3386 + 14.9760i 0.816161 + 0.600966i
\(622\) 37.0009i 1.48360i
\(623\) 20.4328 0.818623
\(624\) −29.4120 26.5961i −1.17742 1.06470i
\(625\) 19.8269 0.793075
\(626\) 3.04889i 0.121858i
\(627\) 1.77559 1.96358i 0.0709103 0.0784179i
\(628\) 1.79441i 0.0716048i
\(629\) −13.3670 −0.532976
\(630\) 4.82789 0.486685i 0.192348 0.0193900i
\(631\) −19.1559 −0.762583 −0.381292 0.924455i \(-0.624521\pi\)
−0.381292 + 0.924455i \(0.624521\pi\)
\(632\) −22.5720 −0.897866
\(633\) 21.9896 + 19.8843i 0.874008 + 0.790331i
\(634\) 27.6255i 1.09715i
\(635\) 3.68679i 0.146306i
\(636\) 1.02520 + 0.927053i 0.0406520 + 0.0367600i
\(637\) 19.0151i 0.753406i
\(638\) 6.17965i 0.244655i
\(639\) −17.6862 + 1.78290i −0.699656 + 0.0705303i
\(640\) 7.33903i 0.290101i
\(641\) 28.5391i 1.12723i −0.826038 0.563614i \(-0.809411\pi\)
0.826038 0.563614i \(-0.190589\pi\)
\(642\) 14.4118 + 13.0320i 0.568787 + 0.514332i
\(643\) −46.4183 −1.83056 −0.915279 0.402821i \(-0.868030\pi\)
−0.915279 + 0.402821i \(0.868030\pi\)
\(644\) −1.25901 −0.0496121
\(645\) 4.91142 5.43142i 0.193387 0.213862i
\(646\) 5.61743i 0.221015i
\(647\) 17.6014i 0.691981i 0.938238 + 0.345991i \(0.112457\pi\)
−0.938238 + 0.345991i \(0.887543\pi\)
\(648\) 24.0017 4.88876i 0.942875 0.192049i
\(649\) 1.30962 + 5.02931i 0.0514073 + 0.197418i
\(650\) 36.5338i 1.43297i
\(651\) 5.94457 + 5.37545i 0.232986 + 0.210680i
\(652\) −2.19317 −0.0858913
\(653\) 32.0275i 1.25333i 0.779287 + 0.626667i \(0.215581\pi\)
−0.779287 + 0.626667i \(0.784419\pi\)
\(654\) 28.8954 + 26.1290i 1.12990 + 1.02172i
\(655\) 9.81665i 0.383568i
\(656\) 9.77219i 0.381540i
\(657\) 24.6676 2.48667i 0.962376 0.0970143i
\(658\) 23.0319 0.897877
\(659\) 36.2236 1.41107 0.705536 0.708674i \(-0.250706\pi\)
0.705536 + 0.708674i \(0.250706\pi\)
\(660\) −0.0719045 0.0650205i −0.00279888 0.00253092i
\(661\) −10.8552 −0.422219 −0.211109 0.977462i \(-0.567708\pi\)
−0.211109 + 0.977462i \(0.567708\pi\)
\(662\) 42.9411 1.66895
\(663\) 10.6170 11.7411i 0.412331 0.455987i
\(664\) 0.256316 0.00994701
\(665\) 2.49819i 0.0968755i
\(666\) −34.3234 + 3.46004i −1.33000 + 0.134074i
\(667\) 30.3541i 1.17532i
\(668\) 1.81584i 0.0702569i
\(669\) −8.49720 + 9.39685i −0.328521 + 0.363303i
\(670\) 4.67245 0.180512
\(671\) 6.76776i 0.261266i
\(672\) −1.69910 + 1.87900i −0.0655443 + 0.0724839i
\(673\) 38.2722i 1.47528i 0.675192 + 0.737642i \(0.264061\pi\)
−0.675192 + 0.737642i \(0.735939\pi\)
\(674\) 18.7731i 0.723114i
\(675\) −19.4432 14.3167i −0.748370 0.551049i
\(676\) −2.21255 −0.0850980
\(677\) 24.6478i 0.947291i 0.880716 + 0.473645i \(0.157062\pi\)
−0.880716 + 0.473645i \(0.842938\pi\)
\(678\) 10.3982 11.4991i 0.399341 0.441621i
\(679\) 33.2429i 1.27574i
\(680\) −2.74995 −0.105456
\(681\) 18.2936 20.2305i 0.701013 0.775233i
\(682\) 2.46078i 0.0942282i
\(683\) 41.1350 1.57399 0.786994 0.616960i \(-0.211636\pi\)
0.786994 + 0.616960i \(0.211636\pi\)
\(684\) 0.0946143 + 0.938567i 0.00361767 + 0.0358870i
\(685\) −10.4045 −0.397534
\(686\) −28.6787 −1.09496
\(687\) −34.0844 30.8212i −1.30040 1.17590i
\(688\) 30.2981i 1.15511i
\(689\) −30.8179 −1.17407
\(690\) −5.42799 4.90832i −0.206640 0.186857i
\(691\) 48.2189i 1.83433i −0.398504 0.917166i \(-0.630471\pi\)
0.398504 0.917166i \(-0.369529\pi\)
\(692\) −1.30962 −0.0497845
\(693\) 0.378832 + 3.75799i 0.0143907 + 0.142754i
\(694\) −40.5395 −1.53886
\(695\) 3.38265i 0.128311i
\(696\) −21.8342 19.7438i −0.827621 0.748386i
\(697\) 3.90101 0.147761
\(698\) 10.4048i 0.393826i
\(699\) −17.6170 + 19.4822i −0.666337 + 0.736886i
\(700\) 1.20359 0.0454912
\(701\) 17.0498 0.643963 0.321982 0.946746i \(-0.395651\pi\)
0.321982 + 0.946746i \(0.395651\pi\)
\(702\) 24.2230 32.8968i 0.914237 1.24161i
\(703\) 17.7606i 0.669855i
\(704\) −4.98544 −0.187896
\(705\) 6.46115 + 5.84257i 0.243341 + 0.220044i
\(706\) −11.7078 −0.440630
\(707\) −15.5720 −0.585646
\(708\) −1.64223 0.855844i −0.0617186 0.0321646i
\(709\) −19.3178 −0.725496 −0.362748 0.931887i \(-0.618161\pi\)
−0.362748 + 0.931887i \(0.618161\pi\)
\(710\) 5.15039 0.193291
\(711\) −2.49552 24.7554i −0.0935893 0.928400i
\(712\) −29.8850 −1.11999
\(713\) 12.0872i 0.452670i
\(714\) −5.94457 5.37545i −0.222470 0.201171i
\(715\) 2.16147 0.0808343
\(716\) −3.20773 −0.119879
\(717\) −21.8833 19.7882i −0.817247 0.739005i
\(718\) 5.49644i 0.205125i
\(719\) −21.8165 −0.813617 −0.406808 0.913514i \(-0.633358\pi\)
−0.406808 + 0.913514i \(0.633358\pi\)
\(720\) −7.55509 + 0.761607i −0.281562 + 0.0283834i
\(721\) 3.23490i 0.120474i
\(722\) −20.3255 −0.756438
\(723\) −11.9477 + 13.2127i −0.444340 + 0.491385i
\(724\) −1.05543 −0.0392247
\(725\) 29.0178i 1.07769i
\(726\) −17.9123 + 19.8088i −0.664789 + 0.735173i
\(727\) −3.24523 −0.120359 −0.0601795 0.998188i \(-0.519167\pi\)
−0.0601795 + 0.998188i \(0.519167\pi\)
\(728\) 27.2234i 1.00896i
\(729\) 8.01523 + 25.7829i 0.296860 + 0.954921i
\(730\) −7.18343 −0.265871
\(731\) −12.0948 −0.447344
\(732\) −1.78870 1.61745i −0.0661122 0.0597827i
\(733\) 28.5754 1.05546 0.527728 0.849414i \(-0.323044\pi\)
0.527728 + 0.849414i \(0.323044\pi\)
\(734\) 16.3123i 0.602100i
\(735\) −2.70079 2.44222i −0.0996200 0.0900825i
\(736\) 3.82061 0.140829
\(737\) 3.63700i 0.133971i
\(738\) 10.0169 1.00978i 0.368728 0.0371704i
\(739\) 17.9207i 0.659225i 0.944116 + 0.329613i \(0.106918\pi\)
−0.944116 + 0.329613i \(0.893082\pi\)
\(740\) 0.650378 0.0239084
\(741\) −15.6003 14.1068i −0.573093 0.518226i
\(742\) 15.6032i 0.572813i
\(743\) 29.3639i 1.07726i 0.842543 + 0.538628i \(0.181057\pi\)
−0.842543 + 0.538628i \(0.818943\pi\)
\(744\) −8.69452 7.86212i −0.318757 0.288239i
\(745\) 12.8355i 0.470255i
\(746\) 18.6218 0.681794
\(747\) 0.0283379 + 0.281110i 0.00103683 + 0.0102853i
\(748\) 0.160119i 0.00585454i
\(749\) 14.2722i 0.521496i
\(750\) 10.7725 + 9.74111i 0.393355 + 0.355695i
\(751\) 29.2597i 1.06770i 0.845578 + 0.533852i \(0.179256\pi\)
−0.845578 + 0.533852i \(0.820744\pi\)
\(752\) −36.0423 −1.31433
\(753\) 19.4374 + 17.5765i 0.708338 + 0.640522i
\(754\) −49.0963 −1.78798
\(755\) −4.91142 −0.178745
\(756\) −1.08377 0.798013i −0.0394162 0.0290234i
\(757\) −13.6635 −0.496608 −0.248304 0.968682i \(-0.579873\pi\)
−0.248304 + 0.968682i \(0.579873\pi\)
\(758\) −31.9806 −1.16159
\(759\) 3.82061 4.22511i 0.138679 0.153362i
\(760\) 3.65384i 0.132539i
\(761\) 9.99115i 0.362179i −0.983467 0.181089i \(-0.942038\pi\)
0.983467 0.181089i \(-0.0579623\pi\)
\(762\) 10.5405 11.6565i 0.381843 0.422271i
\(763\) 28.6157i 1.03596i
\(764\) 0.851843 0.0308186
\(765\) −0.304029 3.01595i −0.0109922 0.109042i
\(766\) 16.4243i 0.593434i
\(767\) 39.9571 10.4048i 1.44277 0.375694i
\(768\) 3.86249 4.27143i 0.139376 0.154132i
\(769\) 11.3390i 0.408895i −0.978878 0.204447i \(-0.934460\pi\)
0.978878 0.204447i \(-0.0655397\pi\)
\(770\) 1.09436i 0.0394380i
\(771\) 7.88186 + 7.12726i 0.283858 + 0.256682i
\(772\) −1.14064 −0.0410527
\(773\) 47.4737 1.70751 0.853755 0.520675i \(-0.174320\pi\)
0.853755 + 0.520675i \(0.174320\pi\)
\(774\) −31.0569 + 3.13075i −1.11632 + 0.112533i
\(775\) 11.5551i 0.415071i
\(776\) 48.6210i 1.74539i
\(777\) −18.7950 16.9956i −0.674266 0.609712i
\(778\) 40.0106i 1.43445i
\(779\) 5.18325i 0.185709i
\(780\) −0.516577 + 0.571270i −0.0184964 + 0.0204547i
\(781\) 4.00903i 0.143454i
\(782\) 12.0872i 0.432239i
\(783\) 19.2396 26.1290i 0.687569 0.933774i
\(784\) 15.0658