Properties

Label 120.2.m.b.59.15
Level $120$
Weight $2$
Character 120.59
Analytic conductor $0.958$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.m (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.958204824255\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 24x^{14} + 192x^{12} + 672x^{10} + 1092x^{8} + 880x^{6} + 352x^{4} + 64x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 59.15
Root \(2.13875i\) of defining polynomial
Character \(\chi\) \(=\) 120.59
Dual form 120.2.m.b.59.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.30656 + 0.541196i) q^{2} +(-0.541196 - 1.64533i) q^{3} +(1.41421 + 1.41421i) q^{4} +(-1.25928 - 1.84776i) q^{5} +(0.183339 - 2.44262i) q^{6} +3.29066 q^{7} +(1.08239 + 2.61313i) q^{8} +(-2.41421 + 1.78089i) q^{9} +O(q^{10})\) \(q+(1.30656 + 0.541196i) q^{2} +(-0.541196 - 1.64533i) q^{3} +(1.41421 + 1.41421i) q^{4} +(-1.25928 - 1.84776i) q^{5} +(0.183339 - 2.44262i) q^{6} +3.29066 q^{7} +(1.08239 + 2.61313i) q^{8} +(-2.41421 + 1.78089i) q^{9} +(-0.645329 - 3.09573i) q^{10} +2.51856i q^{11} +(1.56148 - 3.09221i) q^{12} -4.65369 q^{13} +(4.29945 + 1.78089i) q^{14} +(-2.35865 + 3.07193i) q^{15} +4.00000i q^{16} -3.69552 q^{17} +(-4.11813 + 1.02028i) q^{18} +0.828427 q^{19} +(0.832235 - 4.39402i) q^{20} +(-1.78089 - 5.41421i) q^{21} +(-1.36303 + 3.29066i) q^{22} -2.61313i q^{23} +(3.71366 - 3.19510i) q^{24} +(-1.82843 + 4.65369i) q^{25} +(-6.08034 - 2.51856i) q^{26} +(4.23671 + 3.00836i) q^{27} +(4.65369 + 4.65369i) q^{28} +6.08034 q^{29} +(-4.74425 + 2.73718i) q^{30} +1.17157i q^{31} +(-2.16478 + 5.22625i) q^{32} +(4.14386 - 1.36303i) q^{33} +(-4.82843 - 2.00000i) q^{34} +(-4.14386 - 6.08034i) q^{35} +(-5.93277 - 0.895653i) q^{36} -1.92762 q^{37} +(1.08239 + 0.448342i) q^{38} +(2.51856 + 7.65685i) q^{39} +(3.46539 - 5.29066i) q^{40} -8.59890i q^{41} +(0.603305 - 8.03782i) q^{42} -6.01673i q^{43} +(-3.56178 + 3.56178i) q^{44} +(6.33083 + 2.21824i) q^{45} +(1.41421 - 3.41421i) q^{46} +2.61313i q^{47} +(6.58132 - 2.16478i) q^{48} +3.82843 q^{49} +(-4.90752 + 5.09080i) q^{50} +(2.00000 + 6.08034i) q^{51} +(-6.58132 - 6.58132i) q^{52} -4.59220i q^{53} +(3.90742 + 6.22351i) q^{54} +(4.65369 - 3.17157i) q^{55} +(3.56178 + 8.59890i) q^{56} +(-0.448342 - 1.36303i) q^{57} +(7.94435 + 3.29066i) q^{58} -2.51856i q^{59} +(-7.68000 + 1.00872i) q^{60} +8.48528i q^{61} +(-0.634051 + 1.53073i) q^{62} +(-7.94435 + 5.86030i) q^{63} +(-5.65685 + 5.65685i) q^{64} +(5.86030 + 8.59890i) q^{65} +(6.15188 + 0.461750i) q^{66} +3.29066i q^{67} +(-5.22625 - 5.22625i) q^{68} +(-4.29945 + 1.41421i) q^{69} +(-2.12356 - 10.1870i) q^{70} +7.12356 q^{71} +(-7.26682 - 4.38102i) q^{72} -6.58132i q^{73} +(-2.51856 - 1.04322i) q^{74} +(8.64639 + 0.489804i) q^{75} +(1.17157 + 1.17157i) q^{76} +8.28772i q^{77} +(-0.853202 + 11.3672i) q^{78} -16.4853i q^{79} +(7.39104 - 5.03712i) q^{80} +(2.65685 - 8.59890i) q^{81} +(4.65369 - 11.2350i) q^{82} +9.37011 q^{83} +(5.13829 - 10.1754i) q^{84} +(4.65369 + 6.82843i) q^{85} +(3.25623 - 7.86123i) q^{86} +(-3.29066 - 10.0042i) q^{87} +(-6.58132 + 2.72607i) q^{88} +5.03712i q^{89} +(7.07112 + 6.32450i) q^{90} -15.3137 q^{91} +(3.69552 - 3.69552i) q^{92} +(1.92762 - 0.634051i) q^{93} +(-1.41421 + 3.41421i) q^{94} +(-1.04322 - 1.53073i) q^{95} +(9.77048 + 0.733355i) q^{96} +2.72607i q^{97} +(5.00208 + 2.07193i) q^{98} +(-4.48528 - 6.08034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{9} + 16 q^{10} - 32 q^{19} - 32 q^{24} + 16 q^{25} + 16 q^{30} - 32 q^{34} - 32 q^{36} + 32 q^{40} + 16 q^{49} + 32 q^{51} + 32 q^{54} + 64 q^{66} - 64 q^{70} + 32 q^{75} + 64 q^{76} - 48 q^{81} + 32 q^{84} - 16 q^{90} - 64 q^{91} + 64 q^{96} + 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30656 + 0.541196i 0.923880 + 0.382683i
\(3\) −0.541196 1.64533i −0.312460 0.949931i
\(4\) 1.41421 + 1.41421i 0.707107 + 0.707107i
\(5\) −1.25928 1.84776i −0.563167 0.826343i
\(6\) 0.183339 2.44262i 0.0748477 0.997195i
\(7\) 3.29066 1.24375 0.621876 0.783116i \(-0.286371\pi\)
0.621876 + 0.783116i \(0.286371\pi\)
\(8\) 1.08239 + 2.61313i 0.382683 + 0.923880i
\(9\) −2.41421 + 1.78089i −0.804738 + 0.593630i
\(10\) −0.645329 3.09573i −0.204071 0.978956i
\(11\) 2.51856i 0.759374i 0.925115 + 0.379687i \(0.123968\pi\)
−0.925115 + 0.379687i \(0.876032\pi\)
\(12\) 1.56148 3.09221i 0.450760 0.892645i
\(13\) −4.65369 −1.29070 −0.645351 0.763886i \(-0.723289\pi\)
−0.645351 + 0.763886i \(0.723289\pi\)
\(14\) 4.29945 + 1.78089i 1.14908 + 0.475963i
\(15\) −2.35865 + 3.07193i −0.609002 + 0.793169i
\(16\) 4.00000i 1.00000i
\(17\) −3.69552 −0.896295 −0.448147 0.893960i \(-0.647916\pi\)
−0.448147 + 0.893960i \(0.647916\pi\)
\(18\) −4.11813 + 1.02028i −0.970653 + 0.240483i
\(19\) 0.828427 0.190054 0.0950271 0.995475i \(-0.469706\pi\)
0.0950271 + 0.995475i \(0.469706\pi\)
\(20\) 0.832235 4.39402i 0.186093 0.982532i
\(21\) −1.78089 5.41421i −0.388622 1.18148i
\(22\) −1.36303 + 3.29066i −0.290600 + 0.701571i
\(23\) 2.61313i 0.544874i −0.962174 0.272437i \(-0.912170\pi\)
0.962174 0.272437i \(-0.0878297\pi\)
\(24\) 3.71366 3.19510i 0.758049 0.652198i
\(25\) −1.82843 + 4.65369i −0.365685 + 0.930739i
\(26\) −6.08034 2.51856i −1.19245 0.493930i
\(27\) 4.23671 + 3.00836i 0.815356 + 0.578960i
\(28\) 4.65369 + 4.65369i 0.879465 + 0.879465i
\(29\) 6.08034 1.12909 0.564546 0.825402i \(-0.309051\pi\)
0.564546 + 0.825402i \(0.309051\pi\)
\(30\) −4.74425 + 2.73718i −0.866177 + 0.499738i
\(31\) 1.17157i 0.210421i 0.994450 + 0.105210i \(0.0335516\pi\)
−0.994450 + 0.105210i \(0.966448\pi\)
\(32\) −2.16478 + 5.22625i −0.382683 + 0.923880i
\(33\) 4.14386 1.36303i 0.721353 0.237274i
\(34\) −4.82843 2.00000i −0.828068 0.342997i
\(35\) −4.14386 6.08034i −0.700440 1.02777i
\(36\) −5.93277 0.895653i −0.988796 0.149276i
\(37\) −1.92762 −0.316899 −0.158450 0.987367i \(-0.550650\pi\)
−0.158450 + 0.987367i \(0.550650\pi\)
\(38\) 1.08239 + 0.448342i 0.175587 + 0.0727306i
\(39\) 2.51856 + 7.65685i 0.403292 + 1.22608i
\(40\) 3.46539 5.29066i 0.547927 0.836526i
\(41\) 8.59890i 1.34292i −0.741039 0.671461i \(-0.765667\pi\)
0.741039 0.671461i \(-0.234333\pi\)
\(42\) 0.603305 8.03782i 0.0930920 1.24026i
\(43\) 6.01673i 0.917542i −0.888554 0.458771i \(-0.848290\pi\)
0.888554 0.458771i \(-0.151710\pi\)
\(44\) −3.56178 + 3.56178i −0.536959 + 0.536959i
\(45\) 6.33083 + 2.21824i 0.943744 + 0.330676i
\(46\) 1.41421 3.41421i 0.208514 0.503398i
\(47\) 2.61313i 0.381164i 0.981671 + 0.190582i \(0.0610374\pi\)
−0.981671 + 0.190582i \(0.938963\pi\)
\(48\) 6.58132 2.16478i 0.949931 0.312460i
\(49\) 3.82843 0.546918
\(50\) −4.90752 + 5.09080i −0.694027 + 0.719949i
\(51\) 2.00000 + 6.08034i 0.280056 + 0.851418i
\(52\) −6.58132 6.58132i −0.912664 0.912664i
\(53\) 4.59220i 0.630787i −0.948961 0.315394i \(-0.897863\pi\)
0.948961 0.315394i \(-0.102137\pi\)
\(54\) 3.90742 + 6.22351i 0.531732 + 0.846912i
\(55\) 4.65369 3.17157i 0.627504 0.427655i
\(56\) 3.56178 + 8.59890i 0.475963 + 1.14908i
\(57\) −0.448342 1.36303i −0.0593843 0.180538i
\(58\) 7.94435 + 3.29066i 1.04314 + 0.432085i
\(59\) 2.51856i 0.327889i −0.986470 0.163944i \(-0.947578\pi\)
0.986470 0.163944i \(-0.0524217\pi\)
\(60\) −7.68000 + 1.00872i −0.991484 + 0.130226i
\(61\) 8.48528i 1.08643i 0.839594 + 0.543214i \(0.182793\pi\)
−0.839594 + 0.543214i \(0.817207\pi\)
\(62\) −0.634051 + 1.53073i −0.0805245 + 0.194403i
\(63\) −7.94435 + 5.86030i −1.00089 + 0.738329i
\(64\) −5.65685 + 5.65685i −0.707107 + 0.707107i
\(65\) 5.86030 + 8.59890i 0.726881 + 1.06656i
\(66\) 6.15188 + 0.461750i 0.757244 + 0.0568375i
\(67\) 3.29066i 0.402018i 0.979589 + 0.201009i \(0.0644220\pi\)
−0.979589 + 0.201009i \(0.935578\pi\)
\(68\) −5.22625 5.22625i −0.633776 0.633776i
\(69\) −4.29945 + 1.41421i −0.517593 + 0.170251i
\(70\) −2.12356 10.1870i −0.253813 1.21758i
\(71\) 7.12356 0.845412 0.422706 0.906267i \(-0.361080\pi\)
0.422706 + 0.906267i \(0.361080\pi\)
\(72\) −7.26682 4.38102i −0.856403 0.516308i
\(73\) 6.58132i 0.770285i −0.922857 0.385142i \(-0.874152\pi\)
0.922857 0.385142i \(-0.125848\pi\)
\(74\) −2.51856 1.04322i −0.292777 0.121272i
\(75\) 8.64639 + 0.489804i 0.998399 + 0.0565576i
\(76\) 1.17157 + 1.17157i 0.134389 + 0.134389i
\(77\) 8.28772i 0.944473i
\(78\) −0.853202 + 11.3672i −0.0966061 + 1.28708i
\(79\) 16.4853i 1.85474i −0.374147 0.927370i \(-0.622064\pi\)
0.374147 0.927370i \(-0.377936\pi\)
\(80\) 7.39104 5.03712i 0.826343 0.563167i
\(81\) 2.65685 8.59890i 0.295206 0.955434i
\(82\) 4.65369 11.2350i 0.513914 1.24070i
\(83\) 9.37011 1.02850 0.514252 0.857639i \(-0.328070\pi\)
0.514252 + 0.857639i \(0.328070\pi\)
\(84\) 5.13829 10.1754i 0.560634 1.11023i
\(85\) 4.65369 + 6.82843i 0.504764 + 0.740647i
\(86\) 3.25623 7.86123i 0.351128 0.847699i
\(87\) −3.29066 10.0042i −0.352796 1.07256i
\(88\) −6.58132 + 2.72607i −0.701571 + 0.290600i
\(89\) 5.03712i 0.533934i 0.963706 + 0.266967i \(0.0860214\pi\)
−0.963706 + 0.266967i \(0.913979\pi\)
\(90\) 7.07112 + 6.32450i 0.745362 + 0.666660i
\(91\) −15.3137 −1.60531
\(92\) 3.69552 3.69552i 0.385284 0.385284i
\(93\) 1.92762 0.634051i 0.199885 0.0657480i
\(94\) −1.41421 + 3.41421i −0.145865 + 0.352149i
\(95\) −1.04322 1.53073i −0.107032 0.157050i
\(96\) 9.77048 + 0.733355i 0.997195 + 0.0748477i
\(97\) 2.72607i 0.276790i 0.990377 + 0.138395i \(0.0441944\pi\)
−0.990377 + 0.138395i \(0.955806\pi\)
\(98\) 5.00208 + 2.07193i 0.505286 + 0.209297i
\(99\) −4.48528 6.08034i −0.450788 0.611097i
\(100\) −9.16710 + 3.99553i −0.916710 + 0.399553i
\(101\) −13.2039 −1.31384 −0.656919 0.753961i \(-0.728141\pi\)
−0.656919 + 0.753961i \(0.728141\pi\)
\(102\) −0.677532 + 9.02674i −0.0670856 + 0.893781i
\(103\) −6.01673 −0.592846 −0.296423 0.955057i \(-0.595794\pi\)
−0.296423 + 0.955057i \(0.595794\pi\)
\(104\) −5.03712 12.1607i −0.493930 1.19245i
\(105\) −7.76152 + 10.1087i −0.757447 + 0.986505i
\(106\) 2.48528 6.00000i 0.241392 0.582772i
\(107\) −8.47343 −0.819157 −0.409579 0.912275i \(-0.634324\pi\)
−0.409579 + 0.912275i \(0.634324\pi\)
\(108\) 1.73715 + 10.2461i 0.167157 + 0.985930i
\(109\) 0.485281i 0.0464815i −0.999730 0.0232408i \(-0.992602\pi\)
0.999730 0.0232408i \(-0.00739843\pi\)
\(110\) 7.79679 1.62530i 0.743394 0.154966i
\(111\) 1.04322 + 3.17157i 0.0990182 + 0.301032i
\(112\) 13.1626i 1.24375i
\(113\) −8.92177 −0.839290 −0.419645 0.907688i \(-0.637845\pi\)
−0.419645 + 0.907688i \(0.637845\pi\)
\(114\) 0.151883 2.02353i 0.0142251 0.189521i
\(115\) −4.82843 + 3.29066i −0.450253 + 0.306855i
\(116\) 8.59890 + 8.59890i 0.798388 + 0.798388i
\(117\) 11.2350 8.28772i 1.03868 0.766200i
\(118\) 1.36303 3.29066i 0.125478 0.302930i
\(119\) −12.1607 −1.11477
\(120\) −10.5803 2.83843i −0.965847 0.259112i
\(121\) 4.65685 0.423350
\(122\) −4.59220 + 11.0866i −0.415758 + 1.00373i
\(123\) −14.1480 + 4.65369i −1.27568 + 0.419609i
\(124\) −1.65685 + 1.65685i −0.148790 + 0.148790i
\(125\) 10.9014 2.48181i 0.975051 0.221980i
\(126\) −13.5514 + 3.35740i −1.20725 + 0.299101i
\(127\) −3.29066 −0.291999 −0.145999 0.989285i \(-0.546640\pi\)
−0.145999 + 0.989285i \(0.546640\pi\)
\(128\) −10.4525 + 4.32957i −0.923880 + 0.382683i
\(129\) −9.89949 + 3.25623i −0.871602 + 0.286695i
\(130\) 3.00316 + 14.4066i 0.263395 + 1.26354i
\(131\) 21.8028i 1.90492i 0.304663 + 0.952460i \(0.401456\pi\)
−0.304663 + 0.952460i \(0.598544\pi\)
\(132\) 7.78793 + 3.93268i 0.677852 + 0.342296i
\(133\) 2.72607 0.236380
\(134\) −1.78089 + 4.29945i −0.153846 + 0.371416i
\(135\) 0.223521 11.6168i 0.0192377 0.999815i
\(136\) −4.00000 9.65685i −0.342997 0.828068i
\(137\) 11.9832 1.02380 0.511899 0.859046i \(-0.328942\pi\)
0.511899 + 0.859046i \(0.328942\pi\)
\(138\) −6.38287 0.479087i −0.543346 0.0407826i
\(139\) 14.4853 1.22863 0.614313 0.789063i \(-0.289433\pi\)
0.614313 + 0.789063i \(0.289433\pi\)
\(140\) 2.73860 14.4592i 0.231454 1.22203i
\(141\) 4.29945 1.41421i 0.362079 0.119098i
\(142\) 9.30739 + 3.85525i 0.781058 + 0.323525i
\(143\) 11.7206i 0.980126i
\(144\) −7.12356 9.65685i −0.593630 0.804738i
\(145\) −7.65685 11.2350i −0.635867 0.933017i
\(146\) 3.56178 8.59890i 0.294775 0.711650i
\(147\) −2.07193 6.29902i −0.170890 0.519535i
\(148\) −2.72607 2.72607i −0.224082 0.224082i
\(149\) −14.6792 −1.20257 −0.601285 0.799034i \(-0.705344\pi\)
−0.601285 + 0.799034i \(0.705344\pi\)
\(150\) 11.0320 + 5.31935i 0.900757 + 0.434323i
\(151\) 2.82843i 0.230174i −0.993355 0.115087i \(-0.963285\pi\)
0.993355 0.115087i \(-0.0367147\pi\)
\(152\) 0.896683 + 2.16478i 0.0727306 + 0.175587i
\(153\) 8.92177 6.58132i 0.721282 0.532068i
\(154\) −4.48528 + 10.8284i −0.361434 + 0.872580i
\(155\) 2.16478 1.47534i 0.173880 0.118502i
\(156\) −7.26665 + 14.3902i −0.581797 + 1.15214i
\(157\) 5.78287 0.461523 0.230762 0.973010i \(-0.425878\pi\)
0.230762 + 0.973010i \(0.425878\pi\)
\(158\) 8.92177 21.5391i 0.709778 1.71356i
\(159\) −7.55568 + 2.48528i −0.599204 + 0.197096i
\(160\) 12.3829 2.58132i 0.978956 0.204071i
\(161\) 8.59890i 0.677688i
\(162\) 8.12504 9.79713i 0.638363 0.769735i
\(163\) 6.01673i 0.471266i 0.971842 + 0.235633i \(0.0757164\pi\)
−0.971842 + 0.235633i \(0.924284\pi\)
\(164\) 12.1607 12.1607i 0.949590 0.949590i
\(165\) −7.73684 5.94041i −0.602312 0.462460i
\(166\) 12.2426 + 5.07107i 0.950213 + 0.393591i
\(167\) 17.3952i 1.34608i 0.739606 + 0.673040i \(0.235012\pi\)
−0.739606 + 0.673040i \(0.764988\pi\)
\(168\) 12.2204 10.5140i 0.942824 0.811172i
\(169\) 8.65685 0.665912
\(170\) 2.38482 + 11.4403i 0.182908 + 0.877433i
\(171\) −2.00000 + 1.47534i −0.152944 + 0.112822i
\(172\) 8.50894 8.50894i 0.648800 0.648800i
\(173\) 21.5391i 1.63758i 0.574090 + 0.818792i \(0.305356\pi\)
−0.574090 + 0.818792i \(0.694644\pi\)
\(174\) 1.11476 14.8520i 0.0845099 1.12592i
\(175\) −6.01673 + 15.3137i −0.454822 + 1.15761i
\(176\) −10.0742 −0.759374
\(177\) −4.14386 + 1.36303i −0.311472 + 0.102452i
\(178\) −2.72607 + 6.58132i −0.204328 + 0.493290i
\(179\) 9.64212i 0.720686i −0.932820 0.360343i \(-0.882660\pi\)
0.932820 0.360343i \(-0.117340\pi\)
\(180\) 5.81607 + 12.0902i 0.433504 + 0.901151i
\(181\) 10.3431i 0.768800i −0.923167 0.384400i \(-0.874408\pi\)
0.923167 0.384400i \(-0.125592\pi\)
\(182\) −20.0083 8.28772i −1.48312 0.614327i
\(183\) 13.9611 4.59220i 1.03203 0.339465i
\(184\) 6.82843 2.82843i 0.503398 0.208514i
\(185\) 2.42742 + 3.56178i 0.178467 + 0.261867i
\(186\) 2.86171 + 0.214795i 0.209830 + 0.0157495i
\(187\) 9.30739i 0.680623i
\(188\) −3.69552 + 3.69552i −0.269523 + 0.269523i
\(189\) 13.9416 + 9.89949i 1.01410 + 0.720082i
\(190\) −0.534608 2.56459i −0.0387845 0.186055i
\(191\) 5.03712 0.364473 0.182237 0.983255i \(-0.441666\pi\)
0.182237 + 0.983255i \(0.441666\pi\)
\(192\) 12.3689 + 6.24592i 0.892645 + 0.450760i
\(193\) 19.7439i 1.42120i 0.703596 + 0.710600i \(0.251576\pi\)
−0.703596 + 0.710600i \(0.748424\pi\)
\(194\) −1.47534 + 3.56178i −0.105923 + 0.255721i
\(195\) 10.9764 14.2958i 0.786040 1.02374i
\(196\) 5.41421 + 5.41421i 0.386730 + 0.386730i
\(197\) 11.9832i 0.853770i −0.904306 0.426885i \(-0.859611\pi\)
0.904306 0.426885i \(-0.140389\pi\)
\(198\) −2.56964 10.3718i −0.182617 0.737089i
\(199\) 9.17157i 0.650156i 0.945687 + 0.325078i \(0.105390\pi\)
−0.945687 + 0.325078i \(0.894610\pi\)
\(200\) −14.1398 + 0.259210i −0.999832 + 0.0183289i
\(201\) 5.41421 1.78089i 0.381889 0.125614i
\(202\) −17.2517 7.14590i −1.21383 0.502784i
\(203\) 20.0083 1.40431
\(204\) −5.77048 + 11.4273i −0.404014 + 0.800073i
\(205\) −15.8887 + 10.8284i −1.10971 + 0.756290i
\(206\) −7.86123 3.25623i −0.547718 0.226872i
\(207\) 4.65369 + 6.30864i 0.323454 + 0.438481i
\(208\) 18.6148i 1.29070i
\(209\) 2.08644i 0.144322i
\(210\) −15.6117 + 9.00711i −1.07731 + 0.621549i
\(211\) 18.4853 1.27258 0.636290 0.771450i \(-0.280468\pi\)
0.636290 + 0.771450i \(0.280468\pi\)
\(212\) 6.49435 6.49435i 0.446034 0.446034i
\(213\) −3.85525 11.7206i −0.264157 0.803083i
\(214\) −11.0711 4.58579i −0.756803 0.313478i
\(215\) −11.1175 + 7.57675i −0.758205 + 0.516730i
\(216\) −3.27545 + 14.3273i −0.222866 + 0.974849i
\(217\) 3.85525i 0.261711i
\(218\) 0.262632 0.634051i 0.0177877 0.0429433i
\(219\) −10.8284 + 3.56178i −0.731717 + 0.240683i
\(220\) 11.0666 + 2.09603i 0.746110 + 0.141315i
\(221\) 17.1978 1.15685
\(222\) −0.353408 + 4.70845i −0.0237192 + 0.316010i
\(223\) 21.9054 1.46690 0.733448 0.679746i \(-0.237910\pi\)
0.733448 + 0.679746i \(0.237910\pi\)
\(224\) −7.12356 + 17.1978i −0.475963 + 1.14908i
\(225\) −3.87351 14.4912i −0.258234 0.966082i
\(226\) −11.6569 4.82843i −0.775402 0.321182i
\(227\) −4.14386 −0.275038 −0.137519 0.990499i \(-0.543913\pi\)
−0.137519 + 0.990499i \(0.543913\pi\)
\(228\) 1.29357 2.56167i 0.0856689 0.169651i
\(229\) 19.3137i 1.27629i −0.769918 0.638143i \(-0.779703\pi\)
0.769918 0.638143i \(-0.220297\pi\)
\(230\) −8.08954 + 1.68633i −0.533408 + 0.111193i
\(231\) 13.6360 4.48528i 0.897184 0.295110i
\(232\) 6.58132 + 15.8887i 0.432085 + 1.04314i
\(233\) −15.9414 −1.04436 −0.522178 0.852837i \(-0.674880\pi\)
−0.522178 + 0.852837i \(0.674880\pi\)
\(234\) 19.1645 4.74808i 1.25282 0.310392i
\(235\) 4.82843 3.29066i 0.314972 0.214659i
\(236\) 3.56178 3.56178i 0.231852 0.231852i
\(237\) −27.1237 + 8.92177i −1.76187 + 0.579531i
\(238\) −15.8887 6.58132i −1.02991 0.426603i
\(239\) 22.2349 1.43826 0.719129 0.694877i \(-0.244541\pi\)
0.719129 + 0.694877i \(0.244541\pi\)
\(240\) −12.2877 9.43461i −0.793169 0.609002i
\(241\) −6.48528 −0.417754 −0.208877 0.977942i \(-0.566981\pi\)
−0.208877 + 0.977942i \(0.566981\pi\)
\(242\) 6.08447 + 2.52027i 0.391125 + 0.162009i
\(243\) −15.5859 + 0.282294i −0.999836 + 0.0181092i
\(244\) −12.0000 + 12.0000i −0.768221 + 0.768221i
\(245\) −4.82106 7.07401i −0.308006 0.451942i
\(246\) −21.0038 1.57651i −1.33916 0.100515i
\(247\) −3.85525 −0.245303
\(248\) −3.06147 + 1.26810i −0.194403 + 0.0805245i
\(249\) −5.07107 15.4169i −0.321366 0.977007i
\(250\) 15.5865 + 2.65716i 0.985778 + 0.168053i
\(251\) 11.7286i 0.740301i −0.928972 0.370150i \(-0.879306\pi\)
0.928972 0.370150i \(-0.120694\pi\)
\(252\) −19.5227 2.94729i −1.22982 0.185662i
\(253\) 6.58132 0.413764
\(254\) −4.29945 1.78089i −0.269772 0.111743i
\(255\) 8.71645 11.3524i 0.545845 0.710913i
\(256\) −16.0000 −1.00000
\(257\) 16.3128 1.01756 0.508782 0.860895i \(-0.330096\pi\)
0.508782 + 0.860895i \(0.330096\pi\)
\(258\) −14.6966 1.10310i −0.914969 0.0686760i
\(259\) −6.34315 −0.394144
\(260\) −3.87297 + 20.4484i −0.240191 + 1.26816i
\(261\) −14.6792 + 10.8284i −0.908622 + 0.670263i
\(262\) −11.7996 + 28.4867i −0.728981 + 1.75992i
\(263\) 22.2500i 1.37200i 0.727604 + 0.685998i \(0.240634\pi\)
−0.727604 + 0.685998i \(0.759366\pi\)
\(264\) 8.04706 + 9.35309i 0.495263 + 0.575643i
\(265\) −8.48528 + 5.78287i −0.521247 + 0.355239i
\(266\) 3.56178 + 1.47534i 0.218387 + 0.0904588i
\(267\) 8.28772 2.72607i 0.507200 0.166833i
\(268\) −4.65369 + 4.65369i −0.284270 + 0.284270i
\(269\) 9.64212 0.587891 0.293945 0.955822i \(-0.405032\pi\)
0.293945 + 0.955822i \(0.405032\pi\)
\(270\) 6.57901 15.0571i 0.400386 0.916347i
\(271\) 14.1421i 0.859074i 0.903049 + 0.429537i \(0.141323\pi\)
−0.903049 + 0.429537i \(0.858677\pi\)
\(272\) 14.7821i 0.896295i
\(273\) 8.28772 + 25.1961i 0.501596 + 1.52494i
\(274\) 15.6569 + 6.48528i 0.945865 + 0.391790i
\(275\) −11.7206 4.60500i −0.706779 0.277692i
\(276\) −8.08034 4.08034i −0.486379 0.245608i
\(277\) −15.0903 −0.906685 −0.453343 0.891336i \(-0.649769\pi\)
−0.453343 + 0.891336i \(0.649769\pi\)
\(278\) 18.9259 + 7.83938i 1.13510 + 0.470175i
\(279\) −2.08644 2.82843i −0.124912 0.169334i
\(280\) 11.4034 17.4097i 0.681485 1.04043i
\(281\) 3.56178i 0.212478i 0.994341 + 0.106239i \(0.0338809\pi\)
−0.994341 + 0.106239i \(0.966119\pi\)
\(282\) 6.38287 + 0.479087i 0.380094 + 0.0285292i
\(283\) 18.0502i 1.07297i 0.843909 + 0.536486i \(0.180249\pi\)
−0.843909 + 0.536486i \(0.819751\pi\)
\(284\) 10.0742 + 10.0742i 0.597796 + 0.597796i
\(285\) −1.95397 + 2.54487i −0.115743 + 0.150745i
\(286\) 6.34315 15.3137i 0.375078 0.905519i
\(287\) 28.2960i 1.67026i
\(288\) −4.08113 16.4725i −0.240483 0.970653i
\(289\) −3.34315 −0.196656
\(290\) −3.92382 18.8231i −0.230415 1.10533i
\(291\) 4.48528 1.47534i 0.262932 0.0864859i
\(292\) 9.30739 9.30739i 0.544674 0.544674i
\(293\) 2.42742i 0.141811i −0.997483 0.0709056i \(-0.977411\pi\)
0.997483 0.0709056i \(-0.0225889\pi\)
\(294\) 0.701899 9.35139i 0.0409356 0.545384i
\(295\) −4.65369 + 3.17157i −0.270948 + 0.184656i
\(296\) −2.08644 5.03712i −0.121272 0.292777i
\(297\) −7.57675 + 10.6704i −0.439647 + 0.619161i
\(298\) −19.1794 7.94435i −1.11103 0.460204i
\(299\) 12.1607i 0.703271i
\(300\) 11.5352 + 12.9205i 0.665983 + 0.745967i
\(301\) 19.7990i 1.14119i
\(302\) 1.53073 3.69552i 0.0880838 0.212653i
\(303\) 7.14590 + 21.7248i 0.410521 + 1.24806i
\(304\) 3.31371i 0.190054i
\(305\) 15.6788 10.6853i 0.897763 0.611841i
\(306\) 15.2186 3.77048i 0.869992 0.215544i
\(307\) 7.14590i 0.407838i −0.978988 0.203919i \(-0.934632\pi\)
0.978988 0.203919i \(-0.0653680\pi\)
\(308\) −11.7206 + 11.7206i −0.667843 + 0.667843i
\(309\) 3.25623 + 9.89949i 0.185240 + 0.563163i
\(310\) 3.62687 0.756050i 0.205993 0.0429407i
\(311\) −34.3956 −1.95040 −0.975198 0.221334i \(-0.928959\pi\)
−0.975198 + 0.221334i \(0.928959\pi\)
\(312\) −17.2823 + 14.8690i −0.978415 + 0.841793i
\(313\) 17.0179i 0.961907i −0.876746 0.480954i \(-0.840291\pi\)
0.876746 0.480954i \(-0.159709\pi\)
\(314\) 7.55568 + 3.12967i 0.426392 + 0.176617i
\(315\) 20.8326 + 7.29948i 1.17378 + 0.411279i
\(316\) 23.3137 23.3137i 1.31150 1.31150i
\(317\) 13.2513i 0.744269i −0.928179 0.372135i \(-0.878626\pi\)
0.928179 0.372135i \(-0.121374\pi\)
\(318\) −11.2170 0.841928i −0.629018 0.0472130i
\(319\) 15.3137i 0.857403i
\(320\) 17.5761 + 3.32894i 0.982532 + 0.186093i
\(321\) 4.58579 + 13.9416i 0.255954 + 0.778143i
\(322\) 4.65369 11.2350i 0.259340 0.626102i
\(323\) −3.06147 −0.170345
\(324\) 15.9180 8.40333i 0.884336 0.466851i
\(325\) 8.50894 21.6569i 0.471991 1.20131i
\(326\) −3.25623 + 7.86123i −0.180346 + 0.435393i
\(327\) −0.798447 + 0.262632i −0.0441542 + 0.0145236i
\(328\) 22.4700 9.30739i 1.24070 0.513914i
\(329\) 8.59890i 0.474073i
\(330\) −6.89374 11.9487i −0.379488 0.657753i
\(331\) −18.4853 −1.01604 −0.508021 0.861344i \(-0.669623\pi\)
−0.508021 + 0.861344i \(0.669623\pi\)
\(332\) 13.2513 + 13.2513i 0.727262 + 0.727262i
\(333\) 4.65369 3.43289i 0.255021 0.188121i
\(334\) −9.41421 + 22.7279i −0.515123 + 1.24362i
\(335\) 6.08034 4.14386i 0.332205 0.226403i
\(336\) 21.6569 7.12356i 1.18148 0.388622i
\(337\) 27.9222i 1.52102i −0.649328 0.760508i \(-0.724950\pi\)
0.649328 0.760508i \(-0.275050\pi\)
\(338\) 11.3107 + 4.68506i 0.615222 + 0.254833i
\(339\) 4.82843 + 14.6792i 0.262244 + 0.797267i
\(340\) −3.07554 + 16.2382i −0.166795 + 0.880638i
\(341\) −2.95068 −0.159788
\(342\) −3.41157 + 0.845230i −0.184477 + 0.0457048i
\(343\) −10.4366 −0.563521
\(344\) 15.7225 6.51246i 0.847699 0.351128i
\(345\) 8.02734 + 6.16346i 0.432177 + 0.331829i
\(346\) −11.6569 + 28.1421i −0.626676 + 1.51293i
\(347\) 0.185709 0.00996939 0.00498469 0.999988i \(-0.498413\pi\)
0.00498469 + 0.999988i \(0.498413\pi\)
\(348\) 9.49433 18.8017i 0.508949 1.00788i
\(349\) 2.34315i 0.125426i −0.998032 0.0627129i \(-0.980025\pi\)
0.998032 0.0627129i \(-0.0199752\pi\)
\(350\) −16.1490 + 16.7521i −0.863198 + 0.895437i
\(351\) −19.7164 14.0000i −1.05238 0.747265i
\(352\) −13.1626 5.45214i −0.701571 0.290600i
\(353\) −32.3630 −1.72251 −0.861254 0.508175i \(-0.830320\pi\)
−0.861254 + 0.508175i \(0.830320\pi\)
\(354\) −6.15188 0.461750i −0.326969 0.0245417i
\(355\) −8.97056 13.1626i −0.476108 0.698600i
\(356\) −7.12356 + 7.12356i −0.377548 + 0.377548i
\(357\) 6.58132 + 20.0083i 0.348320 + 1.05895i
\(358\) 5.21828 12.5980i 0.275795 0.665827i
\(359\) 9.21001 0.486086 0.243043 0.970016i \(-0.421854\pi\)
0.243043 + 0.970016i \(0.421854\pi\)
\(360\) 1.05589 + 18.9443i 0.0556502 + 0.998450i
\(361\) −18.3137 −0.963879
\(362\) 5.59767 13.5140i 0.294207 0.710279i
\(363\) −2.52027 7.66206i −0.132280 0.402154i
\(364\) −21.6569 21.6569i −1.13513 1.13513i
\(365\) −12.1607 + 8.28772i −0.636519 + 0.433799i
\(366\) 20.7263 + 1.55568i 1.08338 + 0.0813167i
\(367\) −2.16148 −0.112828 −0.0564142 0.998407i \(-0.517967\pi\)
−0.0564142 + 0.998407i \(0.517967\pi\)
\(368\) 10.4525 0.544874
\(369\) 15.3137 + 20.7596i 0.797200 + 1.08070i
\(370\) 1.24395 + 5.96740i 0.0646699 + 0.310230i
\(371\) 15.1114i 0.784543i
\(372\) 3.62275 + 1.82939i 0.187831 + 0.0948493i
\(373\) 24.3976 1.26326 0.631631 0.775269i \(-0.282386\pi\)
0.631631 + 0.775269i \(0.282386\pi\)
\(374\) 5.03712 12.1607i 0.260463 0.628814i
\(375\) −9.98319 16.5932i −0.515530 0.856872i
\(376\) −6.82843 + 2.82843i −0.352149 + 0.145865i
\(377\) −28.2960 −1.45732
\(378\) 12.8580 + 20.4794i 0.661343 + 1.05335i
\(379\) 20.8284 1.06988 0.534942 0.844889i \(-0.320333\pi\)
0.534942 + 0.844889i \(0.320333\pi\)
\(380\) 0.689446 3.64012i 0.0353678 0.186734i
\(381\) 1.78089 + 5.41421i 0.0912378 + 0.277379i
\(382\) 6.58132 + 2.72607i 0.336729 + 0.139478i
\(383\) 29.1158i 1.48775i −0.668320 0.743874i \(-0.732986\pi\)
0.668320 0.743874i \(-0.267014\pi\)
\(384\) 12.7804 + 14.8547i 0.652198 + 0.758049i
\(385\) 15.3137 10.4366i 0.780459 0.531896i
\(386\) −10.6853 + 25.7967i −0.543870 + 1.31302i
\(387\) 10.7151 + 14.5257i 0.544681 + 0.738381i
\(388\) −3.85525 + 3.85525i −0.195720 + 0.195720i
\(389\) 7.55568 0.383088 0.191544 0.981484i \(-0.438650\pi\)
0.191544 + 0.981484i \(0.438650\pi\)
\(390\) 22.0783 12.7380i 1.11798 0.645012i
\(391\) 9.65685i 0.488368i
\(392\) 4.14386 + 10.0042i 0.209297 + 0.505286i
\(393\) 35.8728 11.7996i 1.80954 0.595211i
\(394\) 6.48528 15.6569i 0.326724 0.788781i
\(395\) −30.4608 + 20.7596i −1.53265 + 1.04453i
\(396\) 2.25576 14.9420i 0.113356 0.750866i
\(397\) 27.1237 1.36130 0.680650 0.732609i \(-0.261697\pi\)
0.680650 + 0.732609i \(0.261697\pi\)
\(398\) −4.96362 + 11.9832i −0.248804 + 0.600665i
\(399\) −1.47534 4.48528i −0.0738593 0.224545i
\(400\) −18.6148 7.31371i −0.930739 0.365685i
\(401\) 15.1114i 0.754625i 0.926086 + 0.377313i \(0.123152\pi\)
−0.926086 + 0.377313i \(0.876848\pi\)
\(402\) 8.03782 + 0.603305i 0.400890 + 0.0300901i
\(403\) 5.45214i 0.271590i
\(404\) −18.6731 18.6731i −0.929024 0.929024i
\(405\) −19.2344 + 5.91920i −0.955766 + 0.294127i
\(406\) 26.1421 + 10.8284i 1.29741 + 0.537406i
\(407\) 4.85483i 0.240645i
\(408\) −13.7239 + 11.8076i −0.679435 + 0.584562i
\(409\) −12.8284 −0.634325 −0.317162 0.948371i \(-0.602730\pi\)
−0.317162 + 0.948371i \(0.602730\pi\)
\(410\) −26.6199 + 5.54912i −1.31466 + 0.274051i
\(411\) −6.48528 19.7164i −0.319895 0.972537i
\(412\) −8.50894 8.50894i −0.419205 0.419205i
\(413\) 8.28772i 0.407812i
\(414\) 2.66613 + 10.7612i 0.131033 + 0.528884i
\(415\) −11.7996 17.3137i −0.579219 0.849897i
\(416\) 10.0742 24.3214i 0.493930 1.19245i
\(417\) −7.83938 23.8331i −0.383896 1.16711i
\(418\) −1.12918 + 2.72607i −0.0552298 + 0.133336i
\(419\) 2.51856i 0.123040i 0.998106 + 0.0615199i \(0.0195948\pi\)
−0.998106 + 0.0615199i \(0.980405\pi\)
\(420\) −25.2723 + 3.31937i −1.23316 + 0.161969i
\(421\) 34.8284i 1.69743i 0.528848 + 0.848717i \(0.322624\pi\)
−0.528848 + 0.848717i \(0.677376\pi\)
\(422\) 24.1522 + 10.0042i 1.17571 + 0.486995i
\(423\) −4.65369 6.30864i −0.226270 0.306737i
\(424\) 12.0000 4.97056i 0.582772 0.241392i
\(425\) 6.75699 17.1978i 0.327762 0.834216i
\(426\) 1.30603 17.4002i 0.0632771 0.843040i
\(427\) 27.9222i 1.35125i
\(428\) −11.9832 11.9832i −0.579232 0.579232i
\(429\) −19.2842 + 6.34315i −0.931052 + 0.306250i
\(430\) −18.6262 + 3.88277i −0.898234 + 0.187244i
\(431\) 27.2720 1.31365 0.656824 0.754044i \(-0.271899\pi\)
0.656824 + 0.754044i \(0.271899\pi\)
\(432\) −12.0335 + 16.9469i −0.578960 + 0.815356i
\(433\) 23.5992i 1.13410i 0.823682 + 0.567052i \(0.191916\pi\)
−0.823682 + 0.567052i \(0.808084\pi\)
\(434\) −2.08644 + 5.03712i −0.100152 + 0.241790i
\(435\) −14.3414 + 18.6784i −0.687619 + 0.895560i
\(436\) 0.686292 0.686292i 0.0328674 0.0328674i
\(437\) 2.16478i 0.103556i
\(438\) −16.0756 1.20661i −0.768124 0.0576541i
\(439\) 28.4853i 1.35953i −0.733431 0.679764i \(-0.762082\pi\)
0.733431 0.679764i \(-0.237918\pi\)
\(440\) 13.3248 + 8.72780i 0.635237 + 0.416081i
\(441\) −9.24264 + 6.81801i −0.440126 + 0.324667i
\(442\) 22.4700 + 9.30739i 1.06879 + 0.442707i
\(443\) 1.60766 0.0763821 0.0381910 0.999270i \(-0.487840\pi\)
0.0381910 + 0.999270i \(0.487840\pi\)
\(444\) −3.00994 + 5.96062i −0.142846 + 0.282878i
\(445\) 9.30739 6.34315i 0.441212 0.300694i
\(446\) 28.6208 + 11.8551i 1.35524 + 0.561357i
\(447\) 7.94435 + 24.1522i 0.375755 + 1.14236i
\(448\) −18.6148 + 18.6148i −0.879465 + 0.879465i
\(449\) 35.0067i 1.65207i −0.563620 0.826035i \(-0.690592\pi\)
0.563620 0.826035i \(-0.309408\pi\)
\(450\) 2.78162 21.0300i 0.131127 0.991366i
\(451\) 21.6569 1.01978
\(452\) −12.6173 12.6173i −0.593467 0.593467i
\(453\) −4.65369 + 1.53073i −0.218650 + 0.0719201i
\(454\) −5.41421 2.24264i −0.254102 0.105252i
\(455\) 19.2842 + 28.2960i 0.904060 + 1.32654i
\(456\) 3.07650 2.64691i 0.144070 0.123953i
\(457\) 18.6148i 0.870762i 0.900246 + 0.435381i \(0.143386\pi\)
−0.900246 + 0.435381i \(0.856614\pi\)
\(458\) 10.4525 25.2346i 0.488413 1.17913i
\(459\) −15.6569 11.1175i −0.730799 0.518919i
\(460\) −11.4821 2.17473i −0.535357 0.101398i
\(461\) −3.99390 −0.186014 −0.0930072 0.995665i \(-0.529648\pi\)
−0.0930072 + 0.995665i \(0.529648\pi\)
\(462\) 20.2437 + 1.51946i 0.941824 + 0.0706917i
\(463\) −25.7607 −1.19720 −0.598600 0.801048i \(-0.704276\pi\)
−0.598600 + 0.801048i \(0.704276\pi\)
\(464\) 24.3214i 1.12909i
\(465\) −3.59899 2.76333i −0.166899 0.128147i
\(466\) −20.8284 8.62742i −0.964858 0.399657i
\(467\) 15.8645 0.734120 0.367060 0.930197i \(-0.380364\pi\)
0.367060 + 0.930197i \(0.380364\pi\)
\(468\) 27.6093 + 4.16810i 1.27624 + 0.192670i
\(469\) 10.8284i 0.500010i
\(470\) 8.08954 1.68633i 0.373142 0.0777844i
\(471\) −3.12967 9.51472i −0.144207 0.438415i
\(472\) 6.58132 2.72607i 0.302930 0.125478i
\(473\) 15.1535 0.696758
\(474\) −40.2673 3.02239i −1.84954 0.138823i
\(475\) −1.51472 + 3.85525i −0.0695001 + 0.176891i
\(476\) −17.1978 17.1978i −0.788260 0.788260i
\(477\) 8.17821 + 11.0866i 0.374455 + 0.507618i
\(478\) 29.0513 + 12.0335i 1.32878 + 0.550397i
\(479\) −19.2842 −0.881120 −0.440560 0.897723i \(-0.645220\pi\)
−0.440560 + 0.897723i \(0.645220\pi\)
\(480\) −10.9487 18.9770i −0.499738 0.866177i
\(481\) 8.97056 0.409022
\(482\) −8.47343 3.50981i −0.385954 0.159867i
\(483\) −14.1480 + 4.65369i −0.643757 + 0.211750i
\(484\) 6.58579 + 6.58579i 0.299354 + 0.299354i
\(485\) 5.03712 3.43289i 0.228724 0.155879i
\(486\) −20.5167 8.06619i −0.930658 0.365890i
\(487\) −8.74280 −0.396174 −0.198087 0.980184i \(-0.563473\pi\)
−0.198087 + 0.980184i \(0.563473\pi\)
\(488\) −22.1731 + 9.18440i −1.00373 + 0.415758i
\(489\) 9.89949 3.25623i 0.447671 0.147252i
\(490\) −2.47059 11.8518i −0.111610 0.535409i
\(491\) 36.9142i 1.66591i −0.553338 0.832957i \(-0.686646\pi\)
0.553338 0.832957i \(-0.313354\pi\)
\(492\) −26.5896 13.4270i −1.19875 0.605336i
\(493\) −22.4700 −1.01200
\(494\) −5.03712 2.08644i −0.226631 0.0938735i
\(495\) −5.58678 + 15.9446i −0.251107 + 0.716655i
\(496\) −4.68629 −0.210421
\(497\) 23.4412 1.05148
\(498\) 1.71790 22.8876i 0.0769811 1.02562i
\(499\) −37.1127 −1.66139 −0.830696 0.556726i \(-0.812057\pi\)
−0.830696 + 0.556726i \(0.812057\pi\)
\(500\) 18.9267 + 11.9071i 0.846429 + 0.532502i
\(501\) 28.6208 9.41421i 1.27868 0.420596i
\(502\) 6.34746 15.3241i 0.283301 0.683949i
\(503\) 9.63274i 0.429503i −0.976669 0.214751i \(-0.931106\pi\)
0.976669 0.214751i \(-0.0688941\pi\)
\(504\) −23.9126 14.4164i −1.06515 0.642159i
\(505\) 16.6274 + 24.3976i 0.739910 + 1.08568i
\(506\) 8.59890 + 3.56178i 0.382268 + 0.158341i
\(507\) −4.68506 14.2434i −0.208071 0.632570i
\(508\) −4.65369 4.65369i −0.206474 0.206474i
\(509\) −13.2039 −0.585253 −0.292626 0.956227i \(-0.594529\pi\)
−0.292626 + 0.956227i \(0.594529\pi\)
\(510\) 17.5324 10.1153i 0.776350 0.447912i
\(511\) 21.6569i 0.958043i
\(512\) −20.9050 8.65914i −0.923880 0.382683i
\(513\) 3.50981 + 2.49221i 0.154962 + 0.110034i
\(514\) 21.3137 + 8.82843i 0.940107 + 0.389405i
\(515\) 7.57675 + 11.1175i 0.333871 + 0.489894i
\(516\) −18.6050 9.39500i −0.819040 0.413592i
\(517\) −6.58132 −0.289446
\(518\) −8.28772 3.43289i −0.364141 0.150832i
\(519\) 35.4388 11.6569i 1.55559 0.511679i
\(520\) −16.1269 + 24.6211i −0.707210 + 1.07971i
\(521\) 34.3956i 1.50690i 0.657506 + 0.753450i \(0.271612\pi\)
−0.657506 + 0.753450i \(0.728388\pi\)
\(522\) −25.0397 + 6.20367i −1.09596 + 0.271527i
\(523\) 12.5980i 0.550874i −0.961319 0.275437i \(-0.911177\pi\)
0.961319 0.275437i \(-0.0888225\pi\)
\(524\) −30.8338 + 30.8338i −1.34698 + 1.34698i
\(525\) 28.4523 + 1.61178i 1.24176 + 0.0703437i
\(526\) −12.0416 + 29.0711i −0.525040 + 1.26756i
\(527\) 4.32957i 0.188599i
\(528\) 5.45214 + 16.5754i 0.237274 + 0.721353i
\(529\) 16.1716 0.703112
\(530\) −14.2162 + 2.96348i −0.617513 + 0.128725i
\(531\) 4.48528 + 6.08034i 0.194645 + 0.263864i
\(532\) 3.85525 + 3.85525i 0.167146 + 0.167146i
\(533\) 40.0166i 1.73331i
\(534\) 12.3038 + 0.923499i 0.532436 + 0.0399637i
\(535\) 10.6704 + 15.6569i 0.461322 + 0.676905i
\(536\) −8.59890 + 3.56178i −0.371416 + 0.153846i
\(537\) −15.8645 + 5.21828i −0.684602 + 0.225185i
\(538\) 12.5980 + 5.21828i 0.543140 + 0.224976i
\(539\) 9.64212i 0.415316i
\(540\) 16.7447 16.1125i 0.720579 0.693373i
\(541\) 16.0000i 0.687894i 0.938989 + 0.343947i \(0.111764\pi\)
−0.938989 + 0.343947i \(0.888236\pi\)
\(542\) −7.65367 + 18.4776i −0.328753 + 0.793680i
\(543\) −17.0179 + 5.59767i −0.730307 + 0.240219i
\(544\) 8.00000 19.3137i 0.342997 0.828068i
\(545\) −0.896683 + 0.611105i −0.0384097 + 0.0261769i
\(546\) −2.80760 + 37.4056i −0.120154 + 1.60081i
\(547\) 11.0011i 0.470375i 0.971950 + 0.235188i \(0.0755704\pi\)
−0.971950 + 0.235188i \(0.924430\pi\)
\(548\) 16.9469 + 16.9469i 0.723934 + 0.723934i
\(549\) −15.1114 20.4853i −0.644937 0.874291i
\(550\) −12.8215 12.3599i −0.546711 0.527027i
\(551\) 5.03712 0.214589
\(552\) −8.34921 9.70427i −0.355366 0.413041i
\(553\) 54.2474i 2.30683i
\(554\) −19.7164 8.16679i −0.837668 0.346973i
\(555\) 4.54659 5.92152i 0.192992 0.251355i
\(556\) 20.4853 + 20.4853i 0.868769 + 0.868769i
\(557\) 4.96362i 0.210315i 0.994456 + 0.105158i \(0.0335347\pi\)
−0.994456 + 0.105158i \(0.966465\pi\)
\(558\) −1.19534 4.82469i −0.0506026 0.204246i
\(559\) 28.0000i 1.18427i
\(560\) 24.3214 16.5754i 1.02777 0.700440i
\(561\) −15.3137 + 5.03712i −0.646545 + 0.212667i
\(562\) −1.92762 + 4.65369i −0.0813119 + 0.196304i
\(563\) 21.9874 0.926658 0.463329 0.886186i \(-0.346655\pi\)
0.463329 + 0.886186i \(0.346655\pi\)
\(564\) 8.08034 + 4.08034i 0.340244 + 0.171813i
\(565\) 11.2350 + 16.4853i 0.472660 + 0.693541i
\(566\) −9.76869 + 23.5837i −0.410609 + 0.991297i
\(567\) 8.74280 28.2960i 0.367163 1.18832i
\(568\) 7.71049 + 18.6148i 0.323525 + 0.781058i
\(569\) 15.7225i 0.659120i −0.944135 0.329560i \(-0.893100\pi\)
0.944135 0.329560i \(-0.106900\pi\)
\(570\) −3.93026 + 2.26755i −0.164621 + 0.0949772i
\(571\) 21.1127 0.883539 0.441769 0.897129i \(-0.354351\pi\)
0.441769 + 0.897129i \(0.354351\pi\)
\(572\) 16.5754 16.5754i 0.693054 0.693054i
\(573\) −2.72607 8.28772i −0.113883 0.346224i
\(574\) 15.3137 36.9706i 0.639182 1.54312i
\(575\) 12.1607 + 4.77791i 0.507136 + 0.199253i
\(576\) 3.58261 23.7311i 0.149276 0.988796i
\(577\) 3.85525i 0.160496i −0.996775 0.0802480i \(-0.974429\pi\)
0.996775 0.0802480i \(-0.0255712\pi\)
\(578\) −4.36803 1.80930i −0.181686 0.0752569i
\(579\) 32.4853 10.6853i 1.35004 0.444068i
\(580\) 5.06027 26.7171i 0.210116 1.10937i
\(581\) 30.8338 1.27920
\(582\) 6.65875 + 0.499794i 0.276014 + 0.0207171i
\(583\) 11.5657 0.479004
\(584\) 17.1978 7.12356i 0.711650 0.294775i
\(585\) −29.4617 10.3230i −1.21809 0.426805i
\(586\) 1.31371 3.17157i 0.0542688 0.131016i
\(587\) −7.20533 −0.297396 −0.148698 0.988883i \(-0.547508\pi\)
−0.148698 + 0.988883i \(0.547508\pi\)
\(588\) 5.97801 11.8383i 0.246529 0.488204i
\(589\) 0.970563i 0.0399913i
\(590\) −7.79679 + 1.62530i −0.320989 + 0.0669125i
\(591\) −19.7164 + 6.48528i −0.811023 + 0.266769i
\(592\) 7.71049i 0.316899i
\(593\) −1.00547 −0.0412897 −0.0206448 0.999787i \(-0.506572\pi\)
−0.0206448 + 0.999787i \(0.506572\pi\)
\(594\) −15.6743 + 9.84107i −0.643124 + 0.403784i
\(595\) 15.3137 + 22.4700i 0.627801 + 0.921181i
\(596\) −20.7596 20.7596i −0.850346 0.850346i
\(597\) 15.0903 4.96362i 0.617603 0.203147i
\(598\) −6.58132 + 15.8887i −0.269130 + 0.649737i
\(599\) −32.3092 −1.32012 −0.660058 0.751214i \(-0.729468\pi\)
−0.660058 + 0.751214i \(0.729468\pi\)
\(600\) 8.07887 + 23.1243i 0.329818 + 0.944044i
\(601\) 13.5147 0.551277 0.275638 0.961261i \(-0.411111\pi\)
0.275638 + 0.961261i \(0.411111\pi\)
\(602\) 10.7151 25.8686i 0.436716 1.05433i
\(603\) −5.86030 7.94435i −0.238650 0.323519i
\(604\) 4.00000 4.00000i 0.162758 0.162758i
\(605\) −5.86428 8.60474i −0.238417 0.349833i
\(606\) −2.42079 + 32.2521i −0.0983378 + 1.31015i
\(607\) 4.88755 0.198380 0.0991898 0.995069i \(-0.468375\pi\)
0.0991898 + 0.995069i \(0.468375\pi\)
\(608\) −1.79337 + 4.32957i −0.0727306 + 0.175587i
\(609\) −10.8284 32.9203i −0.438790 1.33400i
\(610\) 26.2681 5.47580i 1.06357 0.221709i
\(611\) 12.1607i 0.491969i
\(612\) 21.9247 + 3.30990i 0.886252 + 0.133795i
\(613\) −23.2685 −0.939804 −0.469902 0.882718i \(-0.655711\pi\)
−0.469902 + 0.882718i \(0.655711\pi\)
\(614\) 3.86733 9.33657i 0.156073 0.376793i
\(615\) 26.4152 + 20.2818i 1.06516 + 0.817842i
\(616\) −21.6569 + 8.97056i −0.872580 + 0.361434i
\(617\) 8.55035 0.344224 0.172112 0.985077i \(-0.444941\pi\)
0.172112 + 0.985077i \(0.444941\pi\)
\(618\) −1.10310 + 14.6966i −0.0443732 + 0.591183i
\(619\) −2.48528 −0.0998919 −0.0499459 0.998752i \(-0.515905\pi\)
−0.0499459 + 0.998752i \(0.515905\pi\)
\(620\) 5.14791 + 0.975024i 0.206745 + 0.0391579i
\(621\) 7.86123 11.0711i 0.315460 0.444267i
\(622\) −44.9400 18.6148i −1.80193 0.746384i
\(623\) 16.5754i 0.664081i
\(624\) −30.6274 + 10.0742i −1.22608 + 0.403292i
\(625\) −18.3137 17.0179i −0.732548 0.680715i
\(626\) 9.21001 22.2349i 0.368106 0.888686i
\(627\) 3.43289 1.12918i 0.137096 0.0450949i
\(628\) 8.17821 + 8.17821i 0.326346 + 0.326346i
\(629\) 7.12356 0.284035
\(630\) 23.2686 + 20.8117i 0.927045 + 0.829160i
\(631\) 2.14214i 0.0852771i 0.999091 + 0.0426385i \(0.0135764\pi\)
−0.999091 + 0.0426385i \(0.986424\pi\)
\(632\) 43.0781 17.8435i 1.71356 0.709778i
\(633\) −10.0042 30.4144i −0.397630 1.20886i
\(634\) 7.17157 17.3137i 0.284820 0.687615i
\(635\) 4.14386 + 6.08034i 0.164444 + 0.241291i
\(636\) −14.2001 7.17063i −0.563069 0.284334i
\(637\) −17.8163 −0.705908
\(638\) −8.28772 + 20.0083i −0.328114 + 0.792137i
\(639\) −17.1978 + 12.6863i −0.680335 + 0.501862i
\(640\) 21.1626 + 13.8616i 0.836526 + 0.547927i
\(641\) 35.0067i 1.38268i 0.722529 + 0.691341i \(0.242980\pi\)
−0.722529 + 0.691341i \(0.757020\pi\)
\(642\) −1.55351 + 20.6974i −0.0613121 + 0.816859i
\(643\) 35.0681i 1.38295i −0.722401 0.691475i \(-0.756961\pi\)
0.722401 0.691475i \(-0.243039\pi\)
\(644\) 12.1607 12.1607i 0.479198 0.479198i
\(645\) 18.4830 + 14.1914i 0.727766 + 0.558785i
\(646\) −4.00000 1.65685i −0.157378 0.0651881i
\(647\) 28.3730i 1.11546i 0.830024 + 0.557728i \(0.188327\pi\)
−0.830024 + 0.557728i \(0.811673\pi\)
\(648\) 25.3458 2.36469i 0.995676 0.0928938i
\(649\) 6.34315 0.248990
\(650\) 22.8381 23.6910i 0.895783 0.929239i
\(651\) 6.34315 2.08644i 0.248607 0.0817742i
\(652\) −8.50894 + 8.50894i −0.333236 + 0.333236i
\(653\) 24.2291i 0.948158i −0.880482 0.474079i \(-0.842781\pi\)
0.880482 0.474079i \(-0.157219\pi\)
\(654\) −1.18536 0.0889709i −0.0463511 0.00347904i
\(655\) 40.2863 27.4558i 1.57412 1.07279i
\(656\) 34.3956 1.34292
\(657\) 11.7206 + 15.8887i 0.457264 + 0.619877i
\(658\) −4.65369 + 11.2350i −0.181420 + 0.437986i
\(659\) 14.6792i 0.571822i 0.958256 + 0.285911i \(0.0922962\pi\)
−0.958256 + 0.285911i \(0.907704\pi\)
\(660\) −2.54053 19.3426i −0.0988902 0.752908i
\(661\) 44.7696i 1.74133i −0.491873 0.870667i \(-0.663688\pi\)
0.491873 0.870667i \(-0.336312\pi\)
\(662\) −24.1522 10.0042i −0.938701 0.388823i
\(663\) −9.30739 28.2960i −0.361469 1.09893i
\(664\) 10.1421 + 24.4853i 0.393591 + 0.950213i
\(665\) −3.43289 5.03712i −0.133122 0.195331i
\(666\) 7.93821 1.96672i 0.307599 0.0762089i
\(667\) 15.8887i 0.615213i
\(668\) −24.6005 + 24.6005i −0.951823 + 0.951823i
\(669\) −11.8551 36.0416i −0.458346 1.39345i
\(670\) 10.1870 2.12356i 0.393558 0.0820401i
\(671\) −21.3707 −0.825006
\(672\) 32.1513 + 2.41322i 1.24026 + 0.0930920i
\(673\) 47.6661i 1.83739i 0.394964 + 0.918697i \(0.370757\pi\)
−0.394964 + 0.918697i \(0.629243\pi\)
\(674\) 15.1114 36.4821i 0.582068 1.40524i
\(675\) −21.7465 + 14.2158i −0.837024 + 0.547166i
\(676\) 12.2426 + 12.2426i 0.470871 + 0.470871i
\(677\) 1.00547i 0.0386433i −0.999813 0.0193217i \(-0.993849\pi\)
0.999813 0.0193217i \(-0.00615066\pi\)
\(678\) −1.63571 + 21.7925i −0.0628189 + 0.836935i
\(679\) 8.97056i 0.344259i
\(680\) −12.8064 + 19.5517i −0.491104 + 0.749774i
\(681\) 2.24264 + 6.81801i 0.0859382 + 0.261267i
\(682\) −3.85525 1.59689i −0.147625 0.0611483i
\(683\) 14.9678 0.572726 0.286363 0.958121i \(-0.407554\pi\)
0.286363 + 0.958121i \(0.407554\pi\)
\(684\) −4.91487 0.741983i −0.187925 0.0283704i
\(685\) −15.0903 22.1421i −0.576569 0.846008i
\(686\) −13.6360 5.64823i −0.520626 0.215650i
\(687\) −31.7774 + 10.4525i −1.21238 + 0.398788i
\(688\) 24.0669 0.917542
\(689\) 21.3707i 0.814159i
\(690\) 7.15258 + 12.3973i 0.272294 + 0.471958i
\(691\) −7.17157 −0.272819 −0.136410 0.990653i \(-0.543556\pi\)
−0.136410 + 0.990653i \(0.543556\pi\)
\(692\) −30.4608 + 30.4608i −1.15795 + 1.15795i
\(693\) −14.7595 20.0083i −0.560668 0.760053i
\(694\) 0.242641 + 0.100505i 0.00921051 + 0.00381512i
\(695\) −18.2410 26.7653i −0.691922 1.01527i
\(696\) 22.5804 19.4273i 0.855906 0.736391i
\(697\) 31.7774i 1.20365i
\(698\) 1.26810 3.06147i 0.0479983 0.115878i
\(699\) 8.62742 + 26.2288i 0.326319 + 0.992065i
\(700\) −30.1658 + 13.1479i −1.14016 + 0.496945i
\(701\) −26.8399 −1.01373 −0.506865 0.862025i \(-0.669196\pi\)
−0.506865 + 0.862025i \(0.669196\pi\)
\(702\) −18.1839 28.9623i −0.686308 1.09311i
\(703\) −1.59689 −0.0602280
\(704\) −14.2471 14.2471i −0.536959 0.536959i
\(705\) −8.02734 6.16346i −0.302327 0.232129i
\(706\) −42.2843 17.5147i −1.59139 0.659175i
\(707\) −43.4495 −1.63409
\(708\) −7.78793 3.93268i −0.292688 0.147799i
\(709\) 36.2843i 1.36268i 0.731965 + 0.681342i \(0.238603\pi\)
−0.731965 + 0.681342i \(0.761397\pi\)
\(710\) −4.59704 22.0526i −0.172524 0.827621i
\(711\) 29.3585 + 39.7990i 1.10103 + 1.49258i
\(712\) −13.1626 + 5.45214i −0.493290 + 0.204328i
\(713\) 3.06147 0.114653
\(714\) −2.22952 + 29.7039i −0.0834379 + 1.11164i
\(715\) −21.6569 + 14.7595i −0.809920 + 0.551975i
\(716\) 13.6360 13.6360i 0.509602 0.509602i
\(717\) −12.0335 36.5838i −0.449398 1.36625i
\(718\) 12.0335 + 4.98442i 0.449085 + 0.186017i
\(719\) 2.95068 0.110042 0.0550208 0.998485i \(-0.482477\pi\)
0.0550208 + 0.998485i \(0.482477\pi\)
\(720\) −8.87298 + 25.3233i −0.330676 + 0.943744i
\(721\) −19.7990 −0.737353
\(722\) −23.9280 9.91131i −0.890508 0.368861i
\(723\) 3.50981 + 10.6704i 0.130531 + 0.396837i
\(724\) 14.6274 14.6274i 0.543624 0.543624i
\(725\) −11.1175 + 28.2960i −0.412892 + 1.05089i
\(726\) 0.853782 11.3749i 0.0316868 0.422163i
\(727\) 47.1015 1.74690 0.873449 0.486915i \(-0.161878\pi\)
0.873449 + 0.486915i \(0.161878\pi\)
\(728\) −16.5754 40.0166i −0.614327 1.48312i
\(729\) 8.89949 + 25.4912i 0.329611 + 0.944117i
\(730\) −20.3740 + 4.24711i −0.754075 + 0.157193i
\(731\) 22.2349i 0.822388i
\(732\) 26.2383 + 13.2496i 0.969795 + 0.489719i
\(733\) −9.63811 −0.355992 −0.177996 0.984031i \(-0.556961\pi\)
−0.177996 + 0.984031i \(0.556961\pi\)
\(734\) −2.82411 1.16979i −0.104240 0.0431776i
\(735\) −9.02993 + 11.7607i −0.333074 + 0.433798i
\(736\) 13.6569 + 5.65685i 0.503398 + 0.208514i
\(737\) −8.28772 −0.305282
\(738\) 8.77332 + 35.4114i 0.322950 + 1.30351i
\(739\) −27.1716 −0.999522 −0.499761 0.866163i \(-0.666579\pi\)
−0.499761 + 0.866163i \(0.666579\pi\)
\(740\) −1.60423 + 8.47001i −0.0589728 + 0.311364i
\(741\) 2.08644 + 6.34315i 0.0766474 + 0.233021i
\(742\) 8.17821 19.7439i 0.300232 0.724823i
\(743\) 15.2304i 0.558750i 0.960182 + 0.279375i \(0.0901272\pi\)
−0.960182 + 0.279375i \(0.909873\pi\)
\(744\) 3.74330 + 4.35083i 0.137236 + 0.159509i
\(745\) 18.4853 + 27.1237i 0.677248 + 0.993736i
\(746\) 31.8771 + 13.2039i 1.16710 + 0.483429i
\(747\) −22.6215 + 16.6871i −0.827676 + 0.610551i
\(748\) 13.1626 13.1626i 0.481273 0.481273i
\(749\) −27.8832 −1.01883
\(750\) −4.06347 27.0830i −0.148377 0.988931i
\(751\) 35.1127i 1.28128i −0.767841 0.640640i \(-0.778669\pi\)
0.767841 0.640640i \(-0.221331\pi\)
\(752\) −10.4525 −0.381164
\(753\) −19.2974 + 6.34746i −0.703235 + 0.231314i
\(754\) −36.9706 15.3137i −1.34639 0.557692i
\(755\) −5.22625 + 3.56178i −0.190203 + 0.129627i
\(756\) 5.71637 + 33.7164i 0.207902 + 1.22625i
\(757\) −12.8319 −0.466383 −0.233192 0.972431i \(-0.574917\pi\)
−0.233192 + 0.972431i \(0.574917\pi\)
\(758\) 27.2137 + 11.2723i 0.988444 + 0.409427i
\(759\) −3.56178 10.8284i −0.129284 0.393047i
\(760\) 2.87082 4.38292i 0.104136 0.158985i
\(761\) 17.1978i 0.623420i −0.950177 0.311710i \(-0.899098\pi\)
0.950177 0.311710i \(-0.100902\pi\)
\(762\) −0.603305 + 8.03782i −0.0218554 + 0.291180i
\(763\) 1.59689i 0.0578115i
\(764\) 7.12356 + 7.12356i 0.257722 + 0.257722i
\(765\) −23.3957 8.19756i −0.845873 0.296383i
\(766\) 15.7574 38.0416i 0.569337 1.37450i
\(767\) 11.7206i 0.423207i
\(768\) 8.65914 + 26.3253i 0.312460 + 0.949931i
\(769\) −49.5980 −1.78855 −0.894274 0.447519i \(-0.852308\pi\)
−0.894274 + 0.447519i \(0.852308\pi\)
\(770\) 25.6566 5.34830i 0.924598 0.192739i
\(771\) −8.82843 26.8399i −0.317948 0.966616i
\(772\) −27.9222 + 27.9222i −1.00494 + 1.00494i
\(773\) 18.8490i 0.677952i −0.940795 0.338976i \(-0.889919\pi\)
0.940795 0.338976i \(-0.110081\pi\)
\(774\) 6.13877 + 24.7777i 0.220653 + 0.890616i