Properties

Label 864.2.v.b.109.12
Level $864$
Weight $2$
Character 864.109
Analytic conductor $6.899$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.v (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 109.12
Character \(\chi\) \(=\) 864.109
Dual form 864.2.v.b.325.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.479175 + 1.33056i) q^{2} +(-1.54078 - 1.27514i) q^{4} +(-0.855212 + 0.354240i) q^{5} +(-3.04155 + 3.04155i) q^{7} +(2.43496 - 1.43909i) q^{8} +O(q^{10})\) \(q+(-0.479175 + 1.33056i) q^{2} +(-1.54078 - 1.27514i) q^{4} +(-0.855212 + 0.354240i) q^{5} +(-3.04155 + 3.04155i) q^{7} +(2.43496 - 1.43909i) q^{8} +(-0.0615424 - 1.30765i) q^{10} +(1.47477 + 3.56040i) q^{11} +(-0.524396 - 0.217212i) q^{13} +(-2.58953 - 5.50440i) q^{14} +(0.748026 + 3.92943i) q^{16} -5.34789i q^{17} +(-4.09576 - 1.69652i) q^{19} +(1.76940 + 0.544709i) q^{20} +(-5.44400 + 0.256212i) q^{22} +(2.03658 + 2.03658i) q^{23} +(-2.92963 + 2.92963i) q^{25} +(0.540290 - 0.593658i) q^{26} +(8.56477 - 0.807961i) q^{28} +(3.31480 - 8.00262i) q^{29} +2.51477 q^{31} +(-5.58679 - 0.887591i) q^{32} +(7.11569 + 2.56257i) q^{34} +(1.52373 - 3.67861i) q^{35} +(-7.84910 + 3.25120i) q^{37} +(4.21990 - 4.63673i) q^{38} +(-1.57262 + 2.09329i) q^{40} +(-8.96180 - 8.96180i) q^{41} +(-4.72038 - 11.3960i) q^{43} +(2.26772 - 7.36634i) q^{44} +(-3.68566 + 1.73391i) q^{46} -3.46822i q^{47} -11.5020i q^{49} +(-2.49425 - 5.30186i) q^{50} +(0.531004 + 1.00335i) q^{52} +(3.31524 + 8.00369i) q^{53} +(-2.52248 - 2.52248i) q^{55} +(-3.02898 + 11.7831i) q^{56} +(9.05961 + 8.24519i) q^{58} +(0.0488541 - 0.0202360i) q^{59} +(-0.0218216 + 0.0526820i) q^{61} +(-1.20501 + 3.34605i) q^{62} +(3.85804 - 7.00825i) q^{64} +0.525415 q^{65} +(2.67338 - 6.45412i) q^{67} +(-6.81931 + 8.23993i) q^{68} +(4.16448 + 3.79011i) q^{70} +(-0.889622 + 0.889622i) q^{71} +(-4.73977 - 4.73977i) q^{73} +(-0.564834 - 12.0016i) q^{74} +(4.14737 + 7.83664i) q^{76} +(-15.3147 - 6.34356i) q^{77} +12.2691i q^{79} +(-2.03169 - 3.09552i) q^{80} +(16.2185 - 7.62995i) q^{82} +(2.42613 + 1.00493i) q^{83} +(1.89444 + 4.57358i) q^{85} +(17.4250 - 0.820074i) q^{86} +(8.71473 + 6.54710i) q^{88} +(-4.26786 + 4.26786i) q^{89} +(2.25563 - 0.934314i) q^{91} +(-0.540999 - 5.73485i) q^{92} +(4.61467 + 1.66188i) q^{94} +4.10372 q^{95} -6.74287 q^{97} +(15.3042 + 5.51149i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.479175 + 1.33056i −0.338828 + 0.940848i
\(3\) 0 0
\(4\) −1.54078 1.27514i −0.770392 0.637571i
\(5\) −0.855212 + 0.354240i −0.382462 + 0.158421i −0.565627 0.824661i \(-0.691366\pi\)
0.183165 + 0.983082i \(0.441366\pi\)
\(6\) 0 0
\(7\) −3.04155 + 3.04155i −1.14960 + 1.14960i −0.162966 + 0.986632i \(0.552106\pi\)
−0.986632 + 0.162966i \(0.947894\pi\)
\(8\) 2.43496 1.43909i 0.860888 0.508795i
\(9\) 0 0
\(10\) −0.0615424 1.30765i −0.0194614 0.413517i
\(11\) 1.47477 + 3.56040i 0.444659 + 1.07350i 0.974295 + 0.225276i \(0.0723284\pi\)
−0.529636 + 0.848225i \(0.677672\pi\)
\(12\) 0 0
\(13\) −0.524396 0.217212i −0.145441 0.0602437i 0.308776 0.951135i \(-0.400081\pi\)
−0.454217 + 0.890891i \(0.650081\pi\)
\(14\) −2.58953 5.50440i −0.692082 1.47111i
\(15\) 0 0
\(16\) 0.748026 + 3.92943i 0.187007 + 0.982359i
\(17\) 5.34789i 1.29705i −0.761192 0.648526i \(-0.775386\pi\)
0.761192 0.648526i \(-0.224614\pi\)
\(18\) 0 0
\(19\) −4.09576 1.69652i −0.939631 0.389208i −0.140307 0.990108i \(-0.544809\pi\)
−0.799324 + 0.600900i \(0.794809\pi\)
\(20\) 1.76940 + 0.544709i 0.395651 + 0.121801i
\(21\) 0 0
\(22\) −5.44400 + 0.256212i −1.16066 + 0.0546246i
\(23\) 2.03658 + 2.03658i 0.424656 + 0.424656i 0.886803 0.462148i \(-0.152921\pi\)
−0.462148 + 0.886803i \(0.652921\pi\)
\(24\) 0 0
\(25\) −2.92963 + 2.92963i −0.585927 + 0.585927i
\(26\) 0.540290 0.593658i 0.105960 0.116426i
\(27\) 0 0
\(28\) 8.56477 0.807961i 1.61859 0.152690i
\(29\) 3.31480 8.00262i 0.615542 1.48605i −0.241289 0.970453i \(-0.577570\pi\)
0.856831 0.515597i \(-0.172430\pi\)
\(30\) 0 0
\(31\) 2.51477 0.451665 0.225833 0.974166i \(-0.427490\pi\)
0.225833 + 0.974166i \(0.427490\pi\)
\(32\) −5.58679 0.887591i −0.987614 0.156905i
\(33\) 0 0
\(34\) 7.11569 + 2.56257i 1.22033 + 0.439477i
\(35\) 1.52373 3.67861i 0.257557 0.621798i
\(36\) 0 0
\(37\) −7.84910 + 3.25120i −1.29038 + 0.534495i −0.919100 0.394024i \(-0.871083\pi\)
−0.371285 + 0.928519i \(0.621083\pi\)
\(38\) 4.21990 4.63673i 0.684559 0.752176i
\(39\) 0 0
\(40\) −1.57262 + 2.09329i −0.248653 + 0.330978i
\(41\) −8.96180 8.96180i −1.39960 1.39960i −0.801196 0.598402i \(-0.795803\pi\)
−0.598402 0.801196i \(-0.704197\pi\)
\(42\) 0 0
\(43\) −4.72038 11.3960i −0.719851 1.73787i −0.673776 0.738936i \(-0.735329\pi\)
−0.0460752 0.998938i \(-0.514671\pi\)
\(44\) 2.26772 7.36634i 0.341872 1.11052i
\(45\) 0 0
\(46\) −3.68566 + 1.73391i −0.543422 + 0.255651i
\(47\) 3.46822i 0.505892i −0.967480 0.252946i \(-0.918601\pi\)
0.967480 0.252946i \(-0.0813994\pi\)
\(48\) 0 0
\(49\) 11.5020i 1.64315i
\(50\) −2.49425 5.30186i −0.352740 0.749796i
\(51\) 0 0
\(52\) 0.531004 + 1.00335i 0.0736370 + 0.139140i
\(53\) 3.31524 + 8.00369i 0.455383 + 1.09939i 0.970247 + 0.242119i \(0.0778425\pi\)
−0.514864 + 0.857272i \(0.672158\pi\)
\(54\) 0 0
\(55\) −2.52248 2.52248i −0.340131 0.340131i
\(56\) −3.02898 + 11.7831i −0.404765 + 1.57458i
\(57\) 0 0
\(58\) 9.05961 + 8.24519i 1.18959 + 1.08265i
\(59\) 0.0488541 0.0202360i 0.00636027 0.00263451i −0.379501 0.925191i \(-0.623904\pi\)
0.385861 + 0.922557i \(0.373904\pi\)
\(60\) 0 0
\(61\) −0.0218216 + 0.0526820i −0.00279397 + 0.00674523i −0.925270 0.379308i \(-0.876162\pi\)
0.922476 + 0.386053i \(0.126162\pi\)
\(62\) −1.20501 + 3.34605i −0.153037 + 0.424949i
\(63\) 0 0
\(64\) 3.85804 7.00825i 0.482255 0.876031i
\(65\) 0.525415 0.0651696
\(66\) 0 0
\(67\) 2.67338 6.45412i 0.326606 0.788496i −0.672234 0.740339i \(-0.734665\pi\)
0.998840 0.0481572i \(-0.0153348\pi\)
\(68\) −6.81931 + 8.23993i −0.826963 + 0.999239i
\(69\) 0 0
\(70\) 4.16448 + 3.79011i 0.497750 + 0.453005i
\(71\) −0.889622 + 0.889622i −0.105579 + 0.105579i −0.757923 0.652344i \(-0.773786\pi\)
0.652344 + 0.757923i \(0.273786\pi\)
\(72\) 0 0
\(73\) −4.73977 4.73977i −0.554748 0.554748i 0.373060 0.927807i \(-0.378309\pi\)
−0.927807 + 0.373060i \(0.878309\pi\)
\(74\) −0.564834 12.0016i −0.0656606 1.39516i
\(75\) 0 0
\(76\) 4.14737 + 7.83664i 0.475736 + 0.898924i
\(77\) −15.3147 6.34356i −1.74527 0.722916i
\(78\) 0 0
\(79\) 12.2691i 1.38038i 0.723630 + 0.690189i \(0.242472\pi\)
−0.723630 + 0.690189i \(0.757528\pi\)
\(80\) −2.03169 3.09552i −0.227149 0.346090i
\(81\) 0 0
\(82\) 16.2185 7.62995i 1.79103 0.842587i
\(83\) 2.42613 + 1.00493i 0.266302 + 0.110306i 0.511839 0.859081i \(-0.328964\pi\)
−0.245537 + 0.969387i \(0.578964\pi\)
\(84\) 0 0
\(85\) 1.89444 + 4.57358i 0.205481 + 0.496074i
\(86\) 17.4250 0.820074i 1.87898 0.0884309i
\(87\) 0 0
\(88\) 8.71473 + 6.54710i 0.928993 + 0.697924i
\(89\) −4.26786 + 4.26786i −0.452392 + 0.452392i −0.896148 0.443756i \(-0.853646\pi\)
0.443756 + 0.896148i \(0.353646\pi\)
\(90\) 0 0
\(91\) 2.25563 0.934314i 0.236455 0.0979428i
\(92\) −0.540999 5.73485i −0.0564030 0.597899i
\(93\) 0 0
\(94\) 4.61467 + 1.66188i 0.475967 + 0.171410i
\(95\) 4.10372 0.421032
\(96\) 0 0
\(97\) −6.74287 −0.684635 −0.342317 0.939584i \(-0.611212\pi\)
−0.342317 + 0.939584i \(0.611212\pi\)
\(98\) 15.3042 + 5.51149i 1.54595 + 0.556744i
\(99\) 0 0
\(100\) 8.24963 0.778232i 0.824963 0.0778232i
\(101\) −2.21585 + 0.917836i −0.220485 + 0.0913281i −0.490192 0.871615i \(-0.663073\pi\)
0.269706 + 0.962943i \(0.413073\pi\)
\(102\) 0 0
\(103\) −1.95787 + 1.95787i −0.192914 + 0.192914i −0.796954 0.604040i \(-0.793557\pi\)
0.604040 + 0.796954i \(0.293557\pi\)
\(104\) −1.58947 + 0.225751i −0.155860 + 0.0221367i
\(105\) 0 0
\(106\) −12.2380 + 0.575958i −1.18866 + 0.0559420i
\(107\) 2.70991 + 6.54229i 0.261977 + 0.632467i 0.999061 0.0433336i \(-0.0137978\pi\)
−0.737084 + 0.675801i \(0.763798\pi\)
\(108\) 0 0
\(109\) 1.40147 + 0.580509i 0.134237 + 0.0556027i 0.448791 0.893637i \(-0.351855\pi\)
−0.314554 + 0.949240i \(0.601855\pi\)
\(110\) 4.56501 2.14760i 0.435257 0.204766i
\(111\) 0 0
\(112\) −14.2267 9.67641i −1.34430 0.914335i
\(113\) 8.10234i 0.762204i 0.924533 + 0.381102i \(0.124455\pi\)
−0.924533 + 0.381102i \(0.875545\pi\)
\(114\) 0 0
\(115\) −2.46314 1.02027i −0.229689 0.0951404i
\(116\) −15.3119 + 8.10348i −1.42167 + 0.752389i
\(117\) 0 0
\(118\) 0.00351562 + 0.0747000i 0.000323639 + 0.00687669i
\(119\) 16.2659 + 16.2659i 1.49109 + 1.49109i
\(120\) 0 0
\(121\) −2.72334 + 2.72334i −0.247576 + 0.247576i
\(122\) −0.0596402 0.0542788i −0.00539957 0.00491417i
\(123\) 0 0
\(124\) −3.87471 3.20668i −0.347959 0.287969i
\(125\) 3.23886 7.81931i 0.289693 0.699380i
\(126\) 0 0
\(127\) −10.2316 −0.907909 −0.453955 0.891025i \(-0.649987\pi\)
−0.453955 + 0.891025i \(0.649987\pi\)
\(128\) 7.47622 + 8.49153i 0.660811 + 0.750552i
\(129\) 0 0
\(130\) −0.251765 + 0.699096i −0.0220813 + 0.0613148i
\(131\) 6.84888 16.5347i 0.598389 1.44464i −0.276833 0.960918i \(-0.589285\pi\)
0.875222 0.483721i \(-0.160715\pi\)
\(132\) 0 0
\(133\) 17.6175 7.29740i 1.52763 0.632765i
\(134\) 7.30658 + 6.64975i 0.631192 + 0.574451i
\(135\) 0 0
\(136\) −7.69609 13.0219i −0.659934 1.11662i
\(137\) 9.25015 + 9.25015i 0.790294 + 0.790294i 0.981542 0.191248i \(-0.0612535\pi\)
−0.191248 + 0.981542i \(0.561254\pi\)
\(138\) 0 0
\(139\) 0.239980 + 0.579363i 0.0203548 + 0.0491409i 0.933730 0.357978i \(-0.116534\pi\)
−0.913375 + 0.407119i \(0.866534\pi\)
\(140\) −7.03849 + 3.72497i −0.594861 + 0.314817i
\(141\) 0 0
\(142\) −0.757412 1.60998i −0.0635606 0.135107i
\(143\) 2.18739i 0.182919i
\(144\) 0 0
\(145\) 8.01818i 0.665873i
\(146\) 8.57772 4.03537i 0.709897 0.333970i
\(147\) 0 0
\(148\) 16.2395 + 4.99932i 1.33488 + 0.410941i
\(149\) −1.41140 3.40742i −0.115626 0.279146i 0.855463 0.517864i \(-0.173273\pi\)
−0.971089 + 0.238718i \(0.923273\pi\)
\(150\) 0 0
\(151\) 9.73971 + 9.73971i 0.792606 + 0.792606i 0.981917 0.189311i \(-0.0606254\pi\)
−0.189311 + 0.981917i \(0.560625\pi\)
\(152\) −12.4144 + 1.76321i −1.00694 + 0.143015i
\(153\) 0 0
\(154\) 15.7789 17.3375i 1.27150 1.39709i
\(155\) −2.15066 + 0.890832i −0.172745 + 0.0715533i
\(156\) 0 0
\(157\) 3.33119 8.04219i 0.265858 0.641837i −0.733423 0.679773i \(-0.762078\pi\)
0.999280 + 0.0379360i \(0.0120783\pi\)
\(158\) −16.3247 5.87902i −1.29873 0.467710i
\(159\) 0 0
\(160\) 5.09231 1.21999i 0.402582 0.0964484i
\(161\) −12.3887 −0.976366
\(162\) 0 0
\(163\) −5.38043 + 12.9895i −0.421427 + 1.01742i 0.560499 + 0.828155i \(0.310609\pi\)
−0.981927 + 0.189261i \(0.939391\pi\)
\(164\) 2.38062 + 25.2358i 0.185896 + 1.97058i
\(165\) 0 0
\(166\) −2.49967 + 2.74657i −0.194012 + 0.213175i
\(167\) −10.7945 + 10.7945i −0.835305 + 0.835305i −0.988237 0.152931i \(-0.951129\pi\)
0.152931 + 0.988237i \(0.451129\pi\)
\(168\) 0 0
\(169\) −8.96458 8.96458i −0.689583 0.689583i
\(170\) −6.99319 + 0.329122i −0.536353 + 0.0252425i
\(171\) 0 0
\(172\) −7.25844 + 23.5779i −0.553451 + 1.79780i
\(173\) 1.23615 + 0.512030i 0.0939827 + 0.0389289i 0.429179 0.903219i \(-0.358803\pi\)
−0.335197 + 0.942148i \(0.608803\pi\)
\(174\) 0 0
\(175\) 17.8212i 1.34716i
\(176\) −12.8872 + 8.45827i −0.971409 + 0.637566i
\(177\) 0 0
\(178\) −3.63359 7.72369i −0.272349 0.578915i
\(179\) 6.04611 + 2.50438i 0.451908 + 0.187186i 0.597016 0.802230i \(-0.296353\pi\)
−0.145108 + 0.989416i \(0.546353\pi\)
\(180\) 0 0
\(181\) −0.246883 0.596027i −0.0183506 0.0443023i 0.914439 0.404725i \(-0.132633\pi\)
−0.932789 + 0.360422i \(0.882633\pi\)
\(182\) 0.162319 + 3.44896i 0.0120319 + 0.255654i
\(183\) 0 0
\(184\) 7.88979 + 2.02816i 0.581643 + 0.149518i
\(185\) 5.56094 5.56094i 0.408848 0.408848i
\(186\) 0 0
\(187\) 19.0406 7.88688i 1.39239 0.576746i
\(188\) −4.42247 + 5.34377i −0.322542 + 0.389735i
\(189\) 0 0
\(190\) −1.96640 + 5.46024i −0.142657 + 0.396128i
\(191\) −12.9033 −0.933653 −0.466827 0.884349i \(-0.654603\pi\)
−0.466827 + 0.884349i \(0.654603\pi\)
\(192\) 0 0
\(193\) −23.5010 −1.69164 −0.845820 0.533469i \(-0.820888\pi\)
−0.845820 + 0.533469i \(0.820888\pi\)
\(194\) 3.23101 8.97180i 0.231973 0.644138i
\(195\) 0 0
\(196\) −14.6667 + 17.7221i −1.04762 + 1.26587i
\(197\) −19.2884 + 7.98950i −1.37424 + 0.569229i −0.942935 0.332978i \(-0.891947\pi\)
−0.431305 + 0.902206i \(0.641947\pi\)
\(198\) 0 0
\(199\) −11.3518 + 11.3518i −0.804708 + 0.804708i −0.983827 0.179119i \(-0.942675\pi\)
0.179119 + 0.983827i \(0.442675\pi\)
\(200\) −2.91753 + 11.3495i −0.206300 + 0.802533i
\(201\) 0 0
\(202\) −0.159456 3.38813i −0.0112193 0.238388i
\(203\) 14.2583 + 34.4225i 1.00073 + 2.41598i
\(204\) 0 0
\(205\) 10.8389 + 4.48961i 0.757020 + 0.313568i
\(206\) −1.66690 3.54322i −0.116139 0.246868i
\(207\) 0 0
\(208\) 0.461258 2.22306i 0.0319825 0.154141i
\(209\) 17.0845i 1.18176i
\(210\) 0 0
\(211\) −2.32439 0.962795i −0.160018 0.0662816i 0.301237 0.953549i \(-0.402601\pi\)
−0.461255 + 0.887268i \(0.652601\pi\)
\(212\) 5.09778 16.5593i 0.350117 1.13730i
\(213\) 0 0
\(214\) −10.0034 + 0.470794i −0.683821 + 0.0321828i
\(215\) 8.07385 + 8.07385i 0.550632 + 0.550632i
\(216\) 0 0
\(217\) −7.64878 + 7.64878i −0.519233 + 0.519233i
\(218\) −1.44395 + 1.58658i −0.0977969 + 0.107457i
\(219\) 0 0
\(220\) 0.670074 + 7.10310i 0.0451764 + 0.478891i
\(221\) −1.16162 + 2.80441i −0.0781393 + 0.188645i
\(222\) 0 0
\(223\) −27.9863 −1.87410 −0.937051 0.349193i \(-0.886456\pi\)
−0.937051 + 0.349193i \(0.886456\pi\)
\(224\) 19.6921 14.2928i 1.31574 0.954980i
\(225\) 0 0
\(226\) −10.7807 3.88244i −0.717118 0.258256i
\(227\) −9.62412 + 23.2347i −0.638776 + 1.54214i 0.189537 + 0.981874i \(0.439301\pi\)
−0.828312 + 0.560267i \(0.810699\pi\)
\(228\) 0 0
\(229\) 13.3775 5.54114i 0.884010 0.366169i 0.105959 0.994370i \(-0.466209\pi\)
0.778051 + 0.628202i \(0.216209\pi\)
\(230\) 2.53780 2.78847i 0.167338 0.183867i
\(231\) 0 0
\(232\) −3.44511 24.2563i −0.226182 1.59251i
\(233\) −5.89713 5.89713i −0.386334 0.386334i 0.487044 0.873378i \(-0.338075\pi\)
−0.873378 + 0.487044i \(0.838075\pi\)
\(234\) 0 0
\(235\) 1.22858 + 2.96606i 0.0801439 + 0.193485i
\(236\) −0.101077 0.0311166i −0.00657958 0.00202552i
\(237\) 0 0
\(238\) −29.4369 + 13.8485i −1.90811 + 0.897666i
\(239\) 6.07025i 0.392652i −0.980539 0.196326i \(-0.937099\pi\)
0.980539 0.196326i \(-0.0629010\pi\)
\(240\) 0 0
\(241\) 1.35136i 0.0870490i 0.999052 + 0.0435245i \(0.0138587\pi\)
−0.999052 + 0.0435245i \(0.986141\pi\)
\(242\) −2.31861 4.92853i −0.149046 0.316818i
\(243\) 0 0
\(244\) 0.100799 0.0533459i 0.00645301 0.00341512i
\(245\) 4.07449 + 9.83668i 0.260309 + 0.628443i
\(246\) 0 0
\(247\) 1.77929 + 1.77929i 0.113214 + 0.113214i
\(248\) 6.12335 3.61897i 0.388833 0.229805i
\(249\) 0 0
\(250\) 8.85209 + 8.05632i 0.559855 + 0.509527i
\(251\) 23.1337 9.58228i 1.46018 0.604828i 0.495588 0.868558i \(-0.334953\pi\)
0.964597 + 0.263729i \(0.0849526\pi\)
\(252\) 0 0
\(253\) −4.24755 + 10.2545i −0.267041 + 0.644695i
\(254\) 4.90273 13.6138i 0.307625 0.854205i
\(255\) 0 0
\(256\) −14.8809 + 5.87864i −0.930057 + 0.367415i
\(257\) −22.9216 −1.42981 −0.714906 0.699220i \(-0.753531\pi\)
−0.714906 + 0.699220i \(0.753531\pi\)
\(258\) 0 0
\(259\) 13.9847 33.7621i 0.868969 2.09788i
\(260\) −0.809550 0.669978i −0.0502062 0.0415503i
\(261\) 0 0
\(262\) 18.7185 + 17.0358i 1.15644 + 1.05248i
\(263\) −10.9350 + 10.9350i −0.674278 + 0.674278i −0.958699 0.284421i \(-0.908199\pi\)
0.284421 + 0.958699i \(0.408199\pi\)
\(264\) 0 0
\(265\) −5.67046 5.67046i −0.348334 0.348334i
\(266\) 1.26778 + 26.9379i 0.0777328 + 1.65167i
\(267\) 0 0
\(268\) −12.3490 + 6.53545i −0.754336 + 0.399216i
\(269\) −23.8790 9.89099i −1.45593 0.603065i −0.492326 0.870411i \(-0.663853\pi\)
−0.963601 + 0.267346i \(0.913853\pi\)
\(270\) 0 0
\(271\) 17.4859i 1.06219i 0.847311 + 0.531096i \(0.178220\pi\)
−0.847311 + 0.531096i \(0.821780\pi\)
\(272\) 21.0142 4.00036i 1.27417 0.242557i
\(273\) 0 0
\(274\) −16.7403 + 7.87545i −1.01132 + 0.475773i
\(275\) −14.7512 6.11014i −0.889530 0.368455i
\(276\) 0 0
\(277\) −1.93766 4.67793i −0.116423 0.281069i 0.854917 0.518765i \(-0.173608\pi\)
−0.971340 + 0.237695i \(0.923608\pi\)
\(278\) −0.885870 + 0.0416919i −0.0531309 + 0.00250051i
\(279\) 0 0
\(280\) −1.58363 11.1500i −0.0946401 0.666342i
\(281\) 20.0932 20.0932i 1.19866 1.19866i 0.224094 0.974568i \(-0.428058\pi\)
0.974568 0.224094i \(-0.0719422\pi\)
\(282\) 0 0
\(283\) 1.09431 0.453279i 0.0650501 0.0269446i −0.349921 0.936779i \(-0.613792\pi\)
0.414971 + 0.909835i \(0.363792\pi\)
\(284\) 2.50511 0.236321i 0.148651 0.0140230i
\(285\) 0 0
\(286\) 2.91046 + 1.04814i 0.172099 + 0.0619781i
\(287\) 54.5155 3.21795
\(288\) 0 0
\(289\) −11.5999 −0.682346
\(290\) −10.6687 3.84211i −0.626486 0.225616i
\(291\) 0 0
\(292\) 1.25908 + 13.3468i 0.0736820 + 0.781064i
\(293\) 17.1536 7.10527i 1.00213 0.415094i 0.179550 0.983749i \(-0.442536\pi\)
0.822577 + 0.568654i \(0.192536\pi\)
\(294\) 0 0
\(295\) −0.0346122 + 0.0346122i −0.00201520 + 0.00201520i
\(296\) −14.4335 + 19.2121i −0.838928 + 1.11668i
\(297\) 0 0
\(298\) 5.21008 0.245203i 0.301812 0.0142042i
\(299\) −0.625603 1.51034i −0.0361796 0.0873452i
\(300\) 0 0
\(301\) 49.0188 + 20.3042i 2.82539 + 1.17032i
\(302\) −17.6263 + 8.29225i −1.01428 + 0.477166i
\(303\) 0 0
\(304\) 3.60262 17.3631i 0.206625 0.995839i
\(305\) 0.0527843i 0.00302242i
\(306\) 0 0
\(307\) 17.8200 + 7.38127i 1.01704 + 0.421271i 0.828018 0.560702i \(-0.189469\pi\)
0.189021 + 0.981973i \(0.439469\pi\)
\(308\) 15.5077 + 29.3025i 0.883633 + 1.66966i
\(309\) 0 0
\(310\) −0.154765 3.28844i −0.00879005 0.186771i
\(311\) −14.1128 14.1128i −0.800264 0.800264i 0.182873 0.983137i \(-0.441460\pi\)
−0.983137 + 0.182873i \(0.941460\pi\)
\(312\) 0 0
\(313\) −5.88822 + 5.88822i −0.332822 + 0.332822i −0.853657 0.520835i \(-0.825621\pi\)
0.520835 + 0.853657i \(0.325621\pi\)
\(314\) 9.10441 + 8.28596i 0.513791 + 0.467604i
\(315\) 0 0
\(316\) 15.6448 18.9040i 0.880088 1.06343i
\(317\) 12.9292 31.2138i 0.726175 1.75314i 0.0712382 0.997459i \(-0.477305\pi\)
0.654937 0.755683i \(-0.272695\pi\)
\(318\) 0 0
\(319\) 33.3811 1.86898
\(320\) −0.816838 + 7.36021i −0.0456627 + 0.411448i
\(321\) 0 0
\(322\) 5.93635 16.4839i 0.330820 0.918612i
\(323\) −9.07279 + 21.9036i −0.504823 + 1.21875i
\(324\) 0 0
\(325\) 2.17264 0.899936i 0.120516 0.0499194i
\(326\) −14.7051 13.3832i −0.814443 0.741228i
\(327\) 0 0
\(328\) −34.7184 8.92477i −1.91701 0.492788i
\(329\) 10.5488 + 10.5488i 0.581572 + 0.581572i
\(330\) 0 0
\(331\) 0.203102 + 0.490332i 0.0111635 + 0.0269511i 0.929363 0.369167i \(-0.120357\pi\)
−0.918199 + 0.396118i \(0.870357\pi\)
\(332\) −2.45670 4.64204i −0.134829 0.254765i
\(333\) 0 0
\(334\) −9.19031 19.5352i −0.502871 1.06892i
\(335\) 6.46666i 0.353311i
\(336\) 0 0
\(337\) 3.29629i 0.179560i −0.995962 0.0897801i \(-0.971384\pi\)
0.995962 0.0897801i \(-0.0286164\pi\)
\(338\) 16.2235 7.63232i 0.882443 0.415143i
\(339\) 0 0
\(340\) 2.91304 9.46257i 0.157982 0.513180i
\(341\) 3.70869 + 8.95357i 0.200837 + 0.484863i
\(342\) 0 0
\(343\) 13.6932 + 13.6932i 0.739362 + 0.739362i
\(344\) −27.8938 20.9557i −1.50393 1.12986i
\(345\) 0 0
\(346\) −1.27362 + 1.39942i −0.0684701 + 0.0752333i
\(347\) −8.71908 + 3.61156i −0.468065 + 0.193879i −0.604234 0.796807i \(-0.706521\pi\)
0.136169 + 0.990686i \(0.456521\pi\)
\(348\) 0 0
\(349\) 0.660845 1.59542i 0.0353742 0.0854009i −0.905205 0.424975i \(-0.860283\pi\)
0.940579 + 0.339574i \(0.110283\pi\)
\(350\) 23.7122 + 8.53949i 1.26747 + 0.456455i
\(351\) 0 0
\(352\) −5.07902 21.2002i −0.270713 1.12997i
\(353\) −21.0472 −1.12023 −0.560114 0.828415i \(-0.689243\pi\)
−0.560114 + 0.828415i \(0.689243\pi\)
\(354\) 0 0
\(355\) 0.445676 1.07596i 0.0236540 0.0571058i
\(356\) 12.0180 1.13372i 0.636951 0.0600870i
\(357\) 0 0
\(358\) −6.22937 + 6.84468i −0.329233 + 0.361753i
\(359\) 3.16613 3.16613i 0.167102 0.167102i −0.618602 0.785704i \(-0.712301\pi\)
0.785704 + 0.618602i \(0.212301\pi\)
\(360\) 0 0
\(361\) 0.462029 + 0.462029i 0.0243173 + 0.0243173i
\(362\) 0.911350 0.0428911i 0.0478995 0.00225430i
\(363\) 0 0
\(364\) −4.66683 1.43668i −0.244608 0.0753024i
\(365\) 5.73252 + 2.37449i 0.300054 + 0.124286i
\(366\) 0 0
\(367\) 17.1425i 0.894833i 0.894326 + 0.447416i \(0.147656\pi\)
−0.894326 + 0.447416i \(0.852344\pi\)
\(368\) −6.47918 + 9.52601i −0.337751 + 0.496577i
\(369\) 0 0
\(370\) 4.73451 + 10.0638i 0.246135 + 0.523193i
\(371\) −34.4271 14.2602i −1.78736 0.740350i
\(372\) 0 0
\(373\) 7.52495 + 18.1668i 0.389627 + 0.940643i 0.990019 + 0.140937i \(0.0450114\pi\)
−0.600392 + 0.799706i \(0.704989\pi\)
\(374\) 1.37019 + 29.1139i 0.0708510 + 1.50544i
\(375\) 0 0
\(376\) −4.99108 8.44497i −0.257395 0.435516i
\(377\) −3.47653 + 3.47653i −0.179050 + 0.179050i
\(378\) 0 0
\(379\) −13.0553 + 5.40768i −0.670605 + 0.277774i −0.691893 0.722000i \(-0.743223\pi\)
0.0212882 + 0.999773i \(0.493223\pi\)
\(380\) −6.32294 5.23282i −0.324360 0.268438i
\(381\) 0 0
\(382\) 6.18295 17.1687i 0.316347 0.878426i
\(383\) 25.0479 1.27989 0.639943 0.768422i \(-0.278958\pi\)
0.639943 + 0.768422i \(0.278958\pi\)
\(384\) 0 0
\(385\) 15.3445 0.782026
\(386\) 11.2611 31.2695i 0.573174 1.59158i
\(387\) 0 0
\(388\) 10.3893 + 8.59812i 0.527437 + 0.436503i
\(389\) −10.3585 + 4.29064i −0.525198 + 0.217544i −0.629499 0.777002i \(-0.716740\pi\)
0.104300 + 0.994546i \(0.466740\pi\)
\(390\) 0 0
\(391\) 10.8914 10.8914i 0.550801 0.550801i
\(392\) −16.5525 28.0070i −0.836026 1.41457i
\(393\) 0 0
\(394\) −1.38802 29.4927i −0.0699275 1.48582i
\(395\) −4.34620 10.4926i −0.218681 0.527942i
\(396\) 0 0
\(397\) 14.2652 + 5.90883i 0.715948 + 0.296555i 0.710763 0.703431i \(-0.248350\pi\)
0.00518475 + 0.999987i \(0.498350\pi\)
\(398\) −9.66477 20.5438i −0.484451 1.02977i
\(399\) 0 0
\(400\) −13.7032 9.32036i −0.685162 0.466018i
\(401\) 30.5445i 1.52532i 0.646801 + 0.762659i \(0.276106\pi\)
−0.646801 + 0.762659i \(0.723894\pi\)
\(402\) 0 0
\(403\) −1.31873 0.546237i −0.0656907 0.0272100i
\(404\) 4.58452 + 1.41134i 0.228088 + 0.0702167i
\(405\) 0 0
\(406\) −52.6334 + 2.47710i −2.61215 + 0.122936i
\(407\) −23.1512 23.1512i −1.14756 1.14756i
\(408\) 0 0
\(409\) 23.0606 23.0606i 1.14027 1.14027i 0.151875 0.988400i \(-0.451469\pi\)
0.988400 0.151875i \(-0.0485312\pi\)
\(410\) −11.1674 + 12.2705i −0.551519 + 0.605995i
\(411\) 0 0
\(412\) 5.51321 0.520091i 0.271616 0.0256230i
\(413\) −0.0870433 + 0.210141i −0.00428312 + 0.0103404i
\(414\) 0 0
\(415\) −2.43084 −0.119325
\(416\) 2.73689 + 1.67896i 0.134187 + 0.0823180i
\(417\) 0 0
\(418\) 22.7320 + 8.18646i 1.11186 + 0.400413i
\(419\) 10.2186 24.6698i 0.499211 1.20520i −0.450699 0.892676i \(-0.648825\pi\)
0.949910 0.312525i \(-0.101175\pi\)
\(420\) 0 0
\(421\) −4.20371 + 1.74123i −0.204876 + 0.0848625i −0.482762 0.875752i \(-0.660366\pi\)
0.277886 + 0.960614i \(0.410366\pi\)
\(422\) 2.39485 2.63140i 0.116579 0.128095i
\(423\) 0 0
\(424\) 19.5905 + 14.7177i 0.951398 + 0.714756i
\(425\) 15.6673 + 15.6673i 0.759978 + 0.759978i
\(426\) 0 0
\(427\) −0.0938634 0.226606i −0.00454237 0.0109662i
\(428\) 4.16697 13.5358i 0.201418 0.654276i
\(429\) 0 0
\(430\) −14.6115 + 6.87396i −0.704630 + 0.331492i
\(431\) 28.7138i 1.38309i −0.722332 0.691547i \(-0.756930\pi\)
0.722332 0.691547i \(-0.243070\pi\)
\(432\) 0 0
\(433\) 6.26663i 0.301155i 0.988598 + 0.150578i \(0.0481133\pi\)
−0.988598 + 0.150578i \(0.951887\pi\)
\(434\) −6.51207 13.8423i −0.312589 0.664450i
\(435\) 0 0
\(436\) −1.41914 2.68152i −0.0679643 0.128421i
\(437\) −4.88623 11.7964i −0.233740 0.564299i
\(438\) 0 0
\(439\) −0.329078 0.329078i −0.0157060 0.0157060i 0.699210 0.714916i \(-0.253535\pi\)
−0.714916 + 0.699210i \(0.753535\pi\)
\(440\) −9.77219 2.51205i −0.465871 0.119757i
\(441\) 0 0
\(442\) −3.17481 2.88941i −0.151010 0.137435i
\(443\) 25.7914 10.6831i 1.22538 0.507571i 0.326267 0.945278i \(-0.394209\pi\)
0.899118 + 0.437707i \(0.144209\pi\)
\(444\) 0 0
\(445\) 2.13807 5.16177i 0.101354 0.244691i
\(446\) 13.4103 37.2375i 0.634998 1.76325i
\(447\) 0 0
\(448\) 9.58151 + 33.0503i 0.452684 + 1.56148i
\(449\) −25.7331 −1.21442 −0.607209 0.794542i \(-0.707711\pi\)
−0.607209 + 0.794542i \(0.707711\pi\)
\(450\) 0 0
\(451\) 18.6910 45.1242i 0.880127 2.12481i
\(452\) 10.3316 12.4839i 0.485959 0.587196i
\(453\) 0 0
\(454\) −26.3035 23.9390i −1.23449 1.12351i
\(455\) −1.59807 + 1.59807i −0.0749189 + 0.0749189i
\(456\) 0 0
\(457\) 29.5529 + 29.5529i 1.38243 + 1.38243i 0.840290 + 0.542138i \(0.182385\pi\)
0.542138 + 0.840290i \(0.317615\pi\)
\(458\) 0.962666 + 20.4547i 0.0449824 + 0.955788i
\(459\) 0 0
\(460\) 2.49418 + 4.71287i 0.116292 + 0.219739i
\(461\) 30.7137 + 12.7220i 1.43048 + 0.592525i 0.957470 0.288532i \(-0.0931670\pi\)
0.473011 + 0.881056i \(0.343167\pi\)
\(462\) 0 0
\(463\) 34.2809i 1.59317i 0.604529 + 0.796583i \(0.293361\pi\)
−0.604529 + 0.796583i \(0.706639\pi\)
\(464\) 33.9253 + 7.03910i 1.57494 + 0.326782i
\(465\) 0 0
\(466\) 10.6722 5.02073i 0.494382 0.232581i
\(467\) −21.7245 8.99857i −1.00529 0.416404i −0.181555 0.983381i \(-0.558113\pi\)
−0.823734 + 0.566976i \(0.808113\pi\)
\(468\) 0 0
\(469\) 11.4993 + 27.7617i 0.530988 + 1.28192i
\(470\) −4.53523 + 0.213443i −0.209195 + 0.00984537i
\(471\) 0 0
\(472\) 0.0898363 0.119579i 0.00413505 0.00550409i
\(473\) 33.6129 33.6129i 1.54552 1.54552i
\(474\) 0 0
\(475\) 16.9692 7.02889i 0.778602 0.322508i
\(476\) −4.32088 45.8034i −0.198047 2.09940i
\(477\) 0 0
\(478\) 8.07683 + 2.90871i 0.369426 + 0.133041i
\(479\) −16.1430 −0.737592 −0.368796 0.929510i \(-0.620230\pi\)
−0.368796 + 0.929510i \(0.620230\pi\)
\(480\) 0 0
\(481\) 4.82223 0.219875
\(482\) −1.79807 0.647540i −0.0819000 0.0294946i
\(483\) 0 0
\(484\) 7.66872 0.723432i 0.348578 0.0328833i
\(485\) 5.76658 2.38860i 0.261847 0.108461i
\(486\) 0 0
\(487\) −15.6630 + 15.6630i −0.709760 + 0.709760i −0.966485 0.256725i \(-0.917357\pi\)
0.256725 + 0.966485i \(0.417357\pi\)
\(488\) 0.0226794 + 0.159682i 0.00102665 + 0.00722845i
\(489\) 0 0
\(490\) −15.0407 + 0.707863i −0.679469 + 0.0319780i
\(491\) −1.83009 4.41824i −0.0825909 0.199392i 0.877189 0.480145i \(-0.159416\pi\)
−0.959780 + 0.280753i \(0.909416\pi\)
\(492\) 0 0
\(493\) −42.7971 17.7271i −1.92749 0.798391i
\(494\) −3.22005 + 1.51487i −0.144877 + 0.0681570i
\(495\) 0 0
\(496\) 1.88111 + 9.88161i 0.0844644 + 0.443697i
\(497\) 5.41166i 0.242746i
\(498\) 0 0
\(499\) 2.18878 + 0.906622i 0.0979832 + 0.0405860i 0.431137 0.902287i \(-0.358113\pi\)
−0.333153 + 0.942873i \(0.608113\pi\)
\(500\) −14.9611 + 7.91785i −0.669082 + 0.354097i
\(501\) 0 0
\(502\) 1.66474 + 35.3723i 0.0743008 + 1.57875i
\(503\) −17.6732 17.6732i −0.788011 0.788011i 0.193157 0.981168i \(-0.438127\pi\)
−0.981168 + 0.193157i \(0.938127\pi\)
\(504\) 0 0
\(505\) 1.56989 1.56989i 0.0698591 0.0698591i
\(506\) −11.6089 10.5653i −0.516079 0.469686i
\(507\) 0 0
\(508\) 15.7647 + 13.0468i 0.699446 + 0.578857i
\(509\) −10.2708 + 24.7960i −0.455247 + 1.09906i 0.515053 + 0.857158i \(0.327772\pi\)
−0.970300 + 0.241905i \(0.922228\pi\)
\(510\) 0 0
\(511\) 28.8325 1.27547
\(512\) −0.691331 22.6169i −0.0305528 0.999533i
\(513\) 0 0
\(514\) 10.9835 30.4986i 0.484460 1.34524i
\(515\) 0.980836 2.36795i 0.0432208 0.104344i
\(516\) 0 0
\(517\) 12.3482 5.11481i 0.543075 0.224949i
\(518\) 38.2214 + 34.7855i 1.67935 + 1.52839i
\(519\) 0 0
\(520\) 1.27936 0.756119i 0.0561037 0.0331580i
\(521\) 15.0583 + 15.0583i 0.659715 + 0.659715i 0.955312 0.295598i \(-0.0955188\pi\)
−0.295598 + 0.955312i \(0.595519\pi\)
\(522\) 0 0
\(523\) −16.4769 39.7788i −0.720486 1.73941i −0.671963 0.740584i \(-0.734549\pi\)
−0.0485224 0.998822i \(-0.515451\pi\)
\(524\) −31.6367 + 16.7430i −1.38205 + 0.731422i
\(525\) 0 0
\(526\) −9.30987 19.7894i −0.405930 0.862858i
\(527\) 13.4487i 0.585834i
\(528\) 0 0
\(529\) 14.7047i 0.639335i
\(530\) 10.2620 4.82775i 0.445754 0.209704i
\(531\) 0 0
\(532\) −36.4500 11.2211i −1.58031 0.486496i
\(533\) 2.75292 + 6.64614i 0.119242 + 0.287876i
\(534\) 0 0
\(535\) −4.63509 4.63509i −0.200392 0.200392i
\(536\) −2.77848 19.5627i −0.120012 0.844982i
\(537\) 0 0
\(538\) 24.6028 27.0329i 1.06070 1.16547i
\(539\) 40.9519 16.9628i 1.76392 0.730640i
\(540\) 0 0
\(541\) 2.79019 6.73611i 0.119959 0.289608i −0.852481 0.522758i \(-0.824903\pi\)
0.972441 + 0.233150i \(0.0749033\pi\)
\(542\) −23.2661 8.37880i −0.999362 0.359900i
\(543\) 0 0
\(544\) −4.74674 + 29.8775i −0.203515 + 1.28099i
\(545\) −1.40420 −0.0601492
\(546\) 0 0
\(547\) −5.23404 + 12.6361i −0.223792 + 0.540281i −0.995399 0.0958187i \(-0.969453\pi\)
0.771607 + 0.636099i \(0.219453\pi\)
\(548\) −2.45722 26.0477i −0.104967 1.11270i
\(549\) 0 0
\(550\) 15.1983 16.6995i 0.648058 0.712070i
\(551\) −27.1532 + 27.1532i −1.15677 + 1.15677i
\(552\) 0 0
\(553\) −37.3169 37.3169i −1.58688 1.58688i
\(554\) 7.15274 0.336631i 0.303891 0.0143021i
\(555\) 0 0
\(556\) 0.369013 1.19868i 0.0156496 0.0508354i
\(557\) −35.0039 14.4991i −1.48316 0.614346i −0.513346 0.858182i \(-0.671594\pi\)
−0.969816 + 0.243836i \(0.921594\pi\)
\(558\) 0 0
\(559\) 7.00133i 0.296125i
\(560\) 15.5946 + 3.23570i 0.658994 + 0.136733i
\(561\) 0 0
\(562\) 17.1071 + 36.3634i 0.721619 + 1.53390i
\(563\) −3.78277 1.56687i −0.159425 0.0660358i 0.301544 0.953452i \(-0.402498\pi\)
−0.460969 + 0.887416i \(0.652498\pi\)
\(564\) 0 0
\(565\) −2.87018 6.92922i −0.120749 0.291514i
\(566\) 0.0787485 + 1.67325i 0.00331005 + 0.0703319i
\(567\) 0 0
\(568\) −0.885947 + 3.44644i −0.0371735 + 0.144609i
\(569\) 17.9967 17.9967i 0.754460 0.754460i −0.220848 0.975308i \(-0.570883\pi\)
0.975308 + 0.220848i \(0.0708826\pi\)
\(570\) 0 0
\(571\) −6.70495 + 2.77728i −0.280593 + 0.116226i −0.518542 0.855052i \(-0.673525\pi\)
0.237949 + 0.971278i \(0.423525\pi\)
\(572\) −2.78924 + 3.37030i −0.116624 + 0.140919i
\(573\) 0 0
\(574\) −26.1224 + 72.5362i −1.09033 + 3.02760i
\(575\) −11.9328 −0.497634
\(576\) 0 0
\(577\) −16.6125 −0.691589 −0.345794 0.938310i \(-0.612391\pi\)
−0.345794 + 0.938310i \(0.612391\pi\)
\(578\) 5.55837 15.4344i 0.231198 0.641985i
\(579\) 0 0
\(580\) 10.2243 12.3543i 0.424541 0.512983i
\(581\) −10.4357 + 4.32263i −0.432948 + 0.179333i
\(582\) 0 0
\(583\) −23.6071 + 23.6071i −0.977708 + 0.977708i
\(584\) −18.3621 4.72018i −0.759828 0.195323i
\(585\) 0 0
\(586\) 1.23440 + 26.2286i 0.0509927 + 1.08349i
\(587\) 1.79864 + 4.34230i 0.0742378 + 0.179226i 0.956642 0.291266i \(-0.0940765\pi\)
−0.882404 + 0.470492i \(0.844076\pi\)
\(588\) 0 0
\(589\) −10.2999 4.26635i −0.424399 0.175792i
\(590\) −0.0294684 0.0626390i −0.00121319 0.00257880i
\(591\) 0 0
\(592\) −18.6467 28.4106i −0.766376 1.16767i
\(593\) 11.4622i 0.470697i 0.971911 + 0.235348i \(0.0756231\pi\)
−0.971911 + 0.235348i \(0.924377\pi\)
\(594\) 0 0
\(595\) −19.6728 8.14873i −0.806505 0.334065i
\(596\) −2.17028 + 7.04982i −0.0888982 + 0.288772i
\(597\) 0 0
\(598\) 2.30937 0.108686i 0.0944372 0.00444452i
\(599\) 26.2359 + 26.2359i 1.07197 + 1.07197i 0.997201 + 0.0747702i \(0.0238223\pi\)
0.0747702 + 0.997201i \(0.476178\pi\)
\(600\) 0 0
\(601\) 4.12728 4.12728i 0.168355 0.168355i −0.617901 0.786256i \(-0.712017\pi\)
0.786256 + 0.617901i \(0.212017\pi\)
\(602\) −50.5046 + 55.4932i −2.05841 + 2.26173i
\(603\) 0 0
\(604\) −2.58727 27.4263i −0.105275 1.11596i
\(605\) 1.36432 3.29375i 0.0554673 0.133910i
\(606\) 0 0
\(607\) −35.3912 −1.43649 −0.718243 0.695792i \(-0.755053\pi\)
−0.718243 + 0.695792i \(0.755053\pi\)
\(608\) 21.3763 + 13.1134i 0.866924 + 0.531820i
\(609\) 0 0
\(610\) 0.0702328 + 0.0252929i 0.00284364 + 0.00102408i
\(611\) −0.753338 + 1.81872i −0.0304768 + 0.0735775i
\(612\) 0 0
\(613\) 15.0061 6.21571i 0.606089 0.251050i −0.0584665 0.998289i \(-0.518621\pi\)
0.664555 + 0.747239i \(0.268621\pi\)
\(614\) −18.3601 + 20.1736i −0.740953 + 0.814141i
\(615\) 0 0
\(616\) −46.4196 + 6.59294i −1.87030 + 0.265637i
\(617\) 17.0036 + 17.0036i 0.684540 + 0.684540i 0.961020 0.276480i \(-0.0891678\pi\)
−0.276480 + 0.961020i \(0.589168\pi\)
\(618\) 0 0
\(619\) 2.17702 + 5.25579i 0.0875018 + 0.211248i 0.961573 0.274550i \(-0.0885290\pi\)
−0.874071 + 0.485798i \(0.838529\pi\)
\(620\) 4.44963 + 1.36982i 0.178702 + 0.0550131i
\(621\) 0 0
\(622\) 25.5404 12.0154i 1.02408 0.481775i
\(623\) 25.9618i 1.04014i
\(624\) 0 0
\(625\) 12.8811i 0.515245i
\(626\) −5.01315 10.6561i −0.200366 0.425904i
\(627\) 0 0
\(628\) −15.3876 + 8.14354i −0.614031 + 0.324963i
\(629\) 17.3871 + 41.9761i 0.693268 + 1.67370i
\(630\) 0 0
\(631\) 3.76171 + 3.76171i 0.149751 + 0.149751i 0.778007 0.628256i \(-0.216231\pi\)
−0.628256 + 0.778007i \(0.716231\pi\)
\(632\) 17.6563 + 29.8746i 0.702329 + 1.18835i
\(633\) 0 0
\(634\) 35.3365 + 32.1599i 1.40339 + 1.27723i
\(635\) 8.75020 3.62445i 0.347241 0.143832i
\(636\) 0 0
\(637\) −2.49838 + 6.03162i −0.0989893 + 0.238981i
\(638\) −15.9954 + 44.4156i −0.633263 + 1.75843i
\(639\) 0 0
\(640\) −9.40180 4.61368i −0.371639 0.182372i
\(641\) −10.7295 −0.423791 −0.211896 0.977292i \(-0.567964\pi\)
−0.211896 + 0.977292i \(0.567964\pi\)
\(642\) 0 0
\(643\) −11.2121 + 27.0684i −0.442162 + 1.06747i 0.533027 + 0.846099i \(0.321055\pi\)
−0.975189 + 0.221375i \(0.928945\pi\)
\(644\) 19.0883 + 15.7973i 0.752184 + 0.622502i
\(645\) 0 0
\(646\) −24.7967 22.5676i −0.975612 0.887909i
\(647\) −28.0825 + 28.0825i −1.10404 + 1.10404i −0.110119 + 0.993918i \(0.535123\pi\)
−0.993918 + 0.110119i \(0.964877\pi\)
\(648\) 0 0
\(649\) 0.144097 + 0.144097i 0.00565630 + 0.00565630i
\(650\) 0.156346 + 3.32205i 0.00613241 + 0.130302i
\(651\) 0 0
\(652\) 24.8535 13.1532i 0.973339 0.515119i
\(653\) 27.5948 + 11.4301i 1.07987 + 0.447296i 0.850463 0.526035i \(-0.176322\pi\)
0.229405 + 0.973331i \(0.426322\pi\)
\(654\) 0 0
\(655\) 16.5668i 0.647318i
\(656\) 28.5111 41.9185i 1.11317 1.63664i
\(657\) 0 0
\(658\) −19.0905 + 8.98106i −0.744223 + 0.350118i
\(659\) −21.3865 8.85859i −0.833101 0.345082i −0.0749715 0.997186i \(-0.523887\pi\)
−0.758130 + 0.652104i \(0.773887\pi\)
\(660\) 0 0
\(661\) 10.5821 + 25.5475i 0.411597 + 0.993683i 0.984709 + 0.174206i \(0.0557358\pi\)
−0.573112 + 0.819477i \(0.694264\pi\)
\(662\) −0.749738 + 0.0352851i −0.0291394 + 0.00137139i
\(663\) 0 0
\(664\) 7.35371 1.04444i 0.285379 0.0405322i
\(665\) −12.4817 + 12.4817i −0.484018 + 0.484018i
\(666\) 0 0
\(667\) 23.0488 9.54712i 0.892453 0.369666i
\(668\) 30.3966 2.86747i 1.17608 0.110946i
\(669\) 0 0
\(670\) −8.60428 3.09866i −0.332412 0.119712i
\(671\) −0.219751 −0.00848338
\(672\) 0 0
\(673\) 24.0201 0.925908 0.462954 0.886382i \(-0.346790\pi\)
0.462954 + 0.886382i \(0.346790\pi\)
\(674\) 4.38591 + 1.57950i 0.168939 + 0.0608400i
\(675\) 0 0
\(676\) 2.38136 + 25.2436i 0.0915909 + 0.970907i
\(677\) 31.7111 13.1352i 1.21876 0.504826i 0.321743 0.946827i \(-0.395731\pi\)
0.897015 + 0.442001i \(0.145731\pi\)
\(678\) 0 0
\(679\) 20.5088 20.5088i 0.787054 0.787054i
\(680\) 11.1947 + 8.41020i 0.429296 + 0.322516i
\(681\) 0 0
\(682\) −13.6904 + 0.644313i −0.524232 + 0.0246720i
\(683\) −4.66467 11.2615i −0.178489 0.430910i 0.809161 0.587587i \(-0.199922\pi\)
−0.987650 + 0.156677i \(0.949922\pi\)
\(684\) 0 0
\(685\) −11.1876 4.63406i −0.427457 0.177058i
\(686\) −24.7810 + 11.6582i −0.946144 + 0.445111i
\(687\) 0 0
\(688\) 41.2489 27.0729i 1.57260 1.03215i
\(689\) 4.91721i 0.187331i
\(690\) 0 0
\(691\) 21.3386 + 8.83876i 0.811760 + 0.336242i 0.749656 0.661828i \(-0.230219\pi\)
0.0621042 + 0.998070i \(0.480219\pi\)
\(692\) −1.25173 2.36519i −0.0475835 0.0899111i
\(693\) 0 0
\(694\) −0.627439 13.3318i −0.0238173 0.506070i
\(695\) −0.410468 0.410468i −0.0155699 0.0155699i
\(696\) 0 0
\(697\) −47.9267 + 47.9267i −1.81535 + 1.81535i
\(698\) 1.80614 + 1.64378i 0.0683636 + 0.0622180i
\(699\) 0 0
\(700\) −22.7246 + 27.4587i −0.858910 + 1.03784i
\(701\) 9.87590 23.8425i 0.373008 0.900520i −0.620230 0.784420i \(-0.712961\pi\)
0.993238 0.116100i \(-0.0370393\pi\)
\(702\) 0 0
\(703\) 37.6638 1.42052
\(704\) 30.6419 + 3.40064i 1.15486 + 0.128167i
\(705\) 0 0
\(706\) 10.0853 28.0045i 0.379564 1.05397i
\(707\) 3.94798 9.53126i 0.148479 0.358460i
\(708\) 0 0
\(709\) −35.5689 + 14.7331i −1.33582 + 0.553315i −0.932310 0.361661i \(-0.882210\pi\)
−0.403510 + 0.914975i \(0.632210\pi\)
\(710\) 1.21807 + 1.10857i 0.0457133 + 0.0416039i
\(711\) 0 0
\(712\) −4.25022 + 16.5339i −0.159284 + 0.619633i
\(713\) 5.12151 + 5.12151i 0.191802 + 0.191802i
\(714\) 0 0
\(715\) 0.774864 + 1.87069i 0.0289783 + 0.0699597i
\(716\) −6.12231 11.5684i −0.228801 0.432330i
\(717\) 0 0
\(718\) 2.69560 + 5.72986i 0.100599 + 0.213836i
\(719\) 12.5206i 0.466941i 0.972364 + 0.233471i \(0.0750083\pi\)
−0.972364 + 0.233471i \(0.924992\pi\)
\(720\) 0 0
\(721\) 11.9099i 0.443548i
\(722\) −0.836150 + 0.393365i −0.0311183 + 0.0146395i
\(723\) 0 0
\(724\) −0.379627 + 1.23316i −0.0141087 + 0.0458300i
\(725\) 13.7336 + 33.1559i 0.510054 + 1.23138i
\(726\) 0 0
\(727\) −19.8374 19.8374i −0.735729 0.735729i 0.236020 0.971748i \(-0.424157\pi\)
−0.971748 + 0.236020i \(0.924157\pi\)
\(728\) 4.14781 5.52108i 0.153728 0.204625i
\(729\) 0 0
\(730\) −5.90628 + 6.48967i −0.218601 + 0.240194i
\(731\) −60.9445 + 25.2440i −2.25411 + 0.933685i
\(732\) 0 0
\(733\) −15.9981 + 38.6228i −0.590903 + 1.42657i 0.291729 + 0.956501i \(0.405769\pi\)
−0.882632 + 0.470065i \(0.844231\pi\)
\(734\) −22.8092 8.21426i −0.841902 0.303194i
\(735\) 0 0
\(736\) −9.57027 13.1856i −0.352765 0.486026i
\(737\) 26.9219 0.991679
\(738\) 0 0
\(739\) −6.18168 + 14.9239i −0.227397 + 0.548984i −0.995859 0.0909109i \(-0.971022\pi\)
0.768462 + 0.639895i \(0.221022\pi\)
\(740\) −15.6592 + 1.47722i −0.575643 + 0.0543035i
\(741\) 0 0
\(742\) 35.4706 38.9742i 1.30217 1.43079i
\(743\) −3.18178 + 3.18178i −0.116728 + 0.116728i −0.763058 0.646330i \(-0.776303\pi\)
0.646330 + 0.763058i \(0.276303\pi\)
\(744\) 0 0
\(745\) 2.41409 + 2.41409i 0.0884454 + 0.0884454i
\(746\) −27.7778 + 1.30731i −1.01702 + 0.0478642i
\(747\) 0 0
\(748\) −39.3944 12.1275i −1.44040 0.443426i
\(749\) −28.1410 11.6564i −1.02825 0.425915i
\(750\) 0 0
\(751\) 41.5823i 1.51736i −0.651463 0.758681i \(-0.725844\pi\)
0.651463 0.758681i \(-0.274156\pi\)
\(752\) 13.6281 2.59432i 0.496967 0.0946051i
\(753\) 0 0
\(754\) −2.95987 6.29160i −0.107792 0.229126i
\(755\) −11.7797 4.87932i −0.428708 0.177577i
\(756\) 0 0
\(757\) −19.7593 47.7033i −0.718166 1.73381i −0.678509 0.734592i \(-0.737374\pi\)
−0.0396566 0.999213i \(-0.512626\pi\)
\(758\) −0.939480 19.9621i −0.0341234 0.725055i
\(759\) 0 0
\(760\) 9.99238 5.90562i 0.362462 0.214219i
\(761\) 5.44211 5.44211i 0.197276 0.197276i −0.601555 0.798831i \(-0.705452\pi\)
0.798831 + 0.601555i \(0.205452\pi\)
\(762\) 0 0
\(763\) −6.02830 + 2.49700i −0.218239 + 0.0903976i
\(764\) 19.8813 + 16.4536i 0.719279 + 0.595270i
\(765\) 0 0
\(766\) −12.0023 + 33.3277i −0.433661 + 1.20418i
\(767\) −0.0300144 −0.00108376
\(768\) 0 0
\(769\) −3.21709 −0.116011 −0.0580056 0.998316i \(-0.518474\pi\)
−0.0580056 + 0.998316i \(0.518474\pi\)
\(770\) −7.35268 + 20.4167i −0.264972 + 0.735768i
\(771\) 0 0
\(772\) 36.2100 + 29.9671i 1.30322 + 1.07854i
\(773\) 1.06853 0.442600i 0.0384324 0.0159192i −0.363384 0.931639i \(-0.618379\pi\)
0.401817 + 0.915720i \(0.368379\pi\)
\(774\) 0 0
\(775\) −7.36734 + 7.36734i −0.264643 + 0.264643i
\(776\) −16.4186 + 9.70360i −0.589394 + 0.348339i
\(777\) 0 0
\(778\) −0.745416 15.8386i −0.0267245 0.567842i
\(779\) 21.5015 + 51.9092i 0.770371 + 1.85984i
\(780\) 0 0
\(781\) −4.47940 1.85543i −0.160285 0.0663924i
\(782\) 9.27277 + 19.7105i 0.331593 + 0.704847i
\(783\) 0 0
\(784\) 45.1965 8.60383i 1.61416 0.307280i
\(785\) 8.05782i 0.287596i
\(786\) 0 0
\(787\) −37.7933 15.6545i −1.34719 0.558022i −0.411678 0.911329i \(-0.635057\pi\)
−0.935507 + 0.353307i \(0.885057\pi\)
\(788\) 39.9069 + 12.2853i 1.42163 + 0.437646i