Properties

Label 120.2.m.b.59.4
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 59.4
Root \(0.724535i\) of defining polynomial
Character \(\chi\) \(=\) 120.59
Dual form 120.2.m.b.59.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.30656 + 0.541196i) q^{2} +(0.541196 + 1.64533i) q^{3} +(1.41421 - 1.41421i) q^{4} +(1.25928 - 1.84776i) q^{5} +(-1.59755 - 1.85683i) q^{6} +3.29066 q^{7} +(-1.08239 + 2.61313i) q^{8} +(-2.41421 + 1.78089i) q^{9} +O(q^{10})\) \(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} +(-1.59755 - 1.85683i) 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} +(3.09221 + 1.56148i) q^{12} -4.65369 q^{13} +(-4.29945 + 1.78089i) q^{14} +(3.72169 + 1.07193i) q^{15} -4.00000i q^{16} +3.69552 q^{17} +(2.19051 - 3.63341i) 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} +(-4.88524 - 0.366677i) 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} +(-5.44274 + 0.613620i) 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} +(-0.895653 + 5.93277i) 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} +(-5.25700 - 6.11020i) q^{42} +6.01673i q^{43} +(3.56178 + 3.56178i) q^{44} +(0.250486 + 6.70353i) 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} +(7.16365 + 1.63772i) 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} +(6.77920 - 3.74732i) 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} +(4.67654 - 4.02353i) 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} +(-2.04057 - 8.23627i) q^{72} +6.58132i q^{73} +(2.51856 - 1.04322i) q^{74} +(6.66732 - 5.52692i) q^{75} +(1.17157 - 1.17157i) q^{76} +8.28772i q^{77} +(7.43452 + 8.64113i) 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} +(10.1754 + 5.13829i) 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} +(-3.95520 - 8.62302i) 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} +(-7.42733 + 6.39021i) 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
\(6\) −1.59755 1.85683i −0.652198 0.758049i
\(7\) 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 \(0.876032\pi\)
\(12\) 3.09221 + 1.56148i 0.892645 + 0.450760i
\(13\) −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
\(15\) 3.72169 + 1.07193i 0.960936 + 0.276771i
\(16\) 4.00000i 1.00000i
\(17\) 3.69552 0.896295 0.448147 0.893960i \(-0.352084\pi\)
0.448147 + 0.893960i \(0.352084\pi\)
\(18\) 2.19051 3.63341i 0.516308 0.856403i
\(19\) 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 \(-0.0878297\pi\)
\(24\) −4.88524 0.366677i −0.997195 0.0748477i
\(25\) −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 \(-0.690949\pi\)
−0.564546 + 0.825402i \(0.690949\pi\)
\(30\) −5.44274 + 0.613620i −0.993705 + 0.112031i
\(31\) 1.17157i 0.210421i −0.994450 0.105210i \(-0.966448\pi\)
0.994450 0.105210i \(-0.0335516\pi\)
\(32\) 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
\(36\) −0.895653 + 5.93277i −0.149276 + 0.988796i
\(37\) −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 \(-0.234333\pi\)
\(42\) −5.25700 6.11020i −0.811172 0.942824i
\(43\) 6.01673i 0.917542i 0.888554 + 0.458771i \(0.151710\pi\)
−0.888554 + 0.458771i \(0.848290\pi\)
\(44\) 3.56178 + 3.56178i 0.536959 + 0.536959i
\(45\) 0.250486 + 6.70353i 0.0373403 + 0.999303i
\(46\) 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 \(-0.102137\pi\)
\(54\) 7.16365 + 1.63772i 0.974849 + 0.222866i
\(55\) 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 \(-0.0524217\pi\)
\(60\) 6.77920 3.74732i 0.875191 0.483778i
\(61\) 8.48528i 1.08643i −0.839594 0.543214i \(-0.817207\pi\)
0.839594 0.543214i \(-0.182793\pi\)
\(62\) 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
\(66\) 4.67654 4.02353i 0.575643 0.495263i
\(67\) 3.29066i 0.402018i −0.979589 0.201009i \(-0.935578\pi\)
0.979589 0.201009i \(-0.0644220\pi\)
\(68\) 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 \(-0.638920\pi\)
−0.422706 + 0.906267i \(0.638920\pi\)
\(72\) −2.04057 8.23627i −0.240483 0.970653i
\(73\) 6.58132i 0.770285i 0.922857 + 0.385142i \(0.125848\pi\)
−0.922857 + 0.385142i \(0.874152\pi\)
\(74\) 2.51856 1.04322i 0.292777 0.121272i
\(75\) 6.66732 5.52692i 0.769875 0.638194i
\(76\) 1.17157 1.17157i 0.134389 0.134389i
\(77\) 8.28772i 0.944473i
\(78\) 7.43452 + 8.64113i 0.841793 + 0.978415i
\(79\) 16.4853i 1.85474i 0.374147 + 0.927370i \(0.377936\pi\)
−0.374147 + 0.927370i \(0.622064\pi\)
\(80\) −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 \(-0.671930\pi\)
−0.514252 + 0.857639i \(0.671930\pi\)
\(84\) 10.1754 + 5.13829i 1.11023 + 0.560634i
\(85\) 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 \(0.913979\pi\)
\(90\) −3.95520 8.62302i −0.416914 0.908946i
\(91\) −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
\(96\) −7.42733 + 6.39021i −0.758049 + 0.652198i
\(97\) 2.72607i 0.276790i −0.990377 0.138395i \(-0.955806\pi\)
0.990377 0.138395i \(-0.0441944\pi\)
\(98\) −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 \(-0.271859\pi\)
0.656919 + 0.753961i \(0.271859\pi\)
\(102\) −5.90378 6.86196i −0.584562 0.679435i
\(103\) −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
\(105\) 12.2468 + 3.52735i 1.19517 + 0.344235i
\(106\) 2.48528 + 6.00000i 0.241392 + 0.582772i
\(107\) 8.47343 0.819157 0.409579 0.912275i \(-0.365676\pi\)
0.409579 + 0.912275i \(0.365676\pi\)
\(108\) −10.2461 + 1.73715i −0.985930 + 0.167157i
\(109\) 0.485281i 0.0464815i 0.999730 + 0.0232408i \(0.00739843\pi\)
−0.999730 + 0.0232408i \(0.992602\pi\)
\(110\) −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 \(-0.362155\pi\)
0.419645 + 0.907688i \(0.362155\pi\)
\(114\) −1.32346 1.53825i −0.123953 0.144070i
\(115\) −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
\(120\) −6.82941 + 8.56499i −0.623437 + 0.781873i
\(121\) 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
\(126\) 7.20822 11.9563i 0.642159 1.06515i
\(127\) −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 \(0.598544\pi\)
\(132\) −3.93268 + 7.78793i −0.342296 + 0.677852i
\(133\) 2.72607 0.236380
\(134\) 1.78089 + 4.29945i 0.153846 + 0.371416i
\(135\) −10.8939 + 4.04005i −0.937601 + 0.347713i
\(136\) −4.00000 + 9.65685i −0.342997 + 0.828068i
\(137\) −11.9832 −1.02380 −0.511899 0.859046i \(-0.671058\pi\)
−0.511899 + 0.859046i \(0.671058\pi\)
\(138\) −4.85214 + 4.17461i −0.413041 + 0.355366i
\(139\) 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 \(-0.294656\pi\)
0.601285 + 0.799034i \(0.294656\pi\)
\(150\) −5.72012 + 10.8296i −0.467046 + 0.884233i
\(151\) 2.82843i 0.230174i 0.993355 + 0.115087i \(0.0367147\pi\)
−0.993355 + 0.115087i \(0.963285\pi\)
\(152\) −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
\(156\) −14.3902 7.26665i −1.15214 0.581797i
\(157\) 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
\(162\) 1.18235 + 12.6729i 0.0928938 + 0.995676i
\(163\) 6.01673i 0.471266i −0.971842 0.235633i \(-0.924284\pi\)
0.971842 0.235633i \(-0.0757164\pi\)
\(164\) −12.1607 12.1607i −0.949590 0.949590i
\(165\) −2.69972 + 9.37330i −0.210173 + 0.729710i
\(166\) 12.2426 5.07107i 0.950213 0.393591i
\(167\) 17.3952i 1.34608i 0.739606 + 0.673040i \(0.235012\pi\)
−0.739606 + 0.673040i \(0.764988\pi\)
\(168\) −16.0756 1.20661i −1.24026 0.0930920i
\(169\) 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 \(0.694644\pi\)
\(174\) 9.71366 + 11.2902i 0.736391 + 0.855906i
\(175\) −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 \(-0.117340\pi\)
\(180\) 9.83446 + 9.12598i 0.733017 + 0.680210i
\(181\) 10.3431i 0.768800i 0.923167 + 0.384400i \(0.125592\pi\)
−0.923167 + 0.384400i \(0.874408\pi\)
\(182\) 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
\(186\) −2.17541 + 1.87165i −0.159509 + 0.137236i
\(187\) 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 \(-0.558334\pi\)
−0.182237 + 0.983255i \(0.558334\pi\)
\(192\) 6.24592 12.3689i 0.450760 0.892645i
\(193\) 19.7439i 1.42120i −0.703596 0.710600i \(-0.748424\pi\)
0.703596 0.710600i \(-0.251576\pi\)
\(194\) 1.47534 + 3.56178i 0.105923 + 0.255721i
\(195\) −17.3196 4.98843i −1.24028 0.357229i
\(196\) 5.41421 5.41421i 0.386730 0.386730i
\(197\) 11.9832i 0.853770i −0.904306 0.426885i \(-0.859611\pi\)
0.904306 0.426885i \(-0.140389\pi\)
\(198\) 9.15096 + 5.51693i 0.650330 + 0.392071i
\(199\) 9.17157i 0.650156i −0.945687 0.325078i \(-0.894610\pi\)
0.945687 0.325078i \(-0.105390\pi\)
\(200\) 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
\(204\) 11.4273 + 5.77048i 0.800073 + 0.404014i
\(205\) −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
\(210\) −17.9102 + 2.01921i −1.23592 + 0.139339i
\(211\) 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
\(216\) 12.4470 7.81484i 0.846912 0.531732i
\(217\) 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
\(222\) 3.07948 + 3.57927i 0.206681 + 0.240225i
\(223\) 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
\(225\) 12.7019 + 7.97878i 0.846796 + 0.531919i
\(226\) −11.6569 + 4.82843i −0.775402 + 0.321182i
\(227\) 4.14386 0.275038 0.137519 0.990499i \(-0.456087\pi\)
0.137519 + 0.990499i \(0.456087\pi\)
\(228\) 2.56167 + 1.29357i 0.169651 + 0.0856689i
\(229\) 19.3137i 1.27629i 0.769918 + 0.638143i \(0.220297\pi\)
−0.769918 + 0.638143i \(0.779703\pi\)
\(230\) 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 \(-0.325120\pi\)
0.522178 + 0.852837i \(0.325120\pi\)
\(234\) −10.1940 + 16.9088i −0.666400 + 1.10536i
\(235\) 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 \(-0.755459\pi\)
−0.719129 + 0.694877i \(0.755459\pi\)
\(240\) 4.28772 14.8868i 0.276771 0.960936i
\(241\) −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
\(246\) −15.9667 + 13.7372i −1.01800 + 0.875852i
\(247\) −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 \(-0.120694\pi\)
\(252\) −2.94729 + 19.5227i −0.185662 + 1.22982i
\(253\) 6.58132 0.413764
\(254\) 4.29945 1.78089i 0.269772 0.111743i
\(255\) 13.7536 + 3.96134i 0.861282 + 0.248068i
\(256\) −16.0000 −1.00000
\(257\) −16.3128 −1.01756 −0.508782 0.860895i \(-0.669904\pi\)
−0.508782 + 0.860895i \(0.669904\pi\)
\(258\) 11.1721 9.61204i 0.695542 0.598419i
\(259\) −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 \(0.759366\pi\)
\(264\) 0.923499 12.3038i 0.0568375 0.757244i
\(265\) −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 \(-0.594968\pi\)
−0.293945 + 0.955822i \(0.594968\pi\)
\(270\) 12.0472 11.1743i 0.733167 0.680049i
\(271\) 14.1421i 0.859074i −0.903049 0.429537i \(-0.858677\pi\)
0.903049 0.429537i \(-0.141323\pi\)
\(272\) 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
\(276\) 4.08034 8.08034i 0.245608 0.486379i
\(277\) −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 \(0.966119\pi\)
\(282\) 4.85214 4.17461i 0.288941 0.248594i
\(283\) 18.0502i 1.07297i −0.843909 0.536486i \(-0.819751\pi\)
0.843909 0.536486i \(-0.180249\pi\)
\(284\) −10.0742 + 10.0742i −0.597796 + 0.597796i
\(285\) 3.08315 + 0.888016i 0.182630 + 0.0526015i
\(286\) 6.34315 + 15.3137i 0.375078 + 0.905519i
\(287\) 28.2960i 1.67026i
\(288\) −14.5336 8.76204i −0.856403 0.516308i
\(289\) −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 \(-0.0225889\pi\)
\(294\) −6.11611 7.10875i −0.356699 0.414591i
\(295\) −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
\(300\) 1.61276 17.2453i 0.0931127 0.995656i
\(301\) 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
\(306\) 8.09507 13.4273i 0.462764 0.767589i
\(307\) 7.14590i 0.407838i 0.978988 + 0.203919i \(0.0653680\pi\)
−0.978988 + 0.203919i \(0.934632\pi\)
\(308\) 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 \(-0.0710411\pi\)
0.975198 + 0.221334i \(0.0710411\pi\)
\(312\) 22.7344 + 1.70640i 1.28708 + 0.0966061i
\(313\) 17.0179i 0.961907i 0.876746 + 0.480954i \(0.159709\pi\)
−0.876746 + 0.480954i \(0.840291\pi\)
\(314\) −7.55568 + 3.12967i −0.426392 + 0.176617i
\(315\) 0.824265 + 22.0590i 0.0464421 + 1.24288i
\(316\) 23.3137 + 23.3137i 1.31150 + 1.31150i
\(317\) 13.2513i 0.744269i −0.928179 0.372135i \(-0.878626\pi\)
0.928179 0.372135i \(-0.121374\pi\)
\(318\) −8.52695 + 7.33628i −0.478168 + 0.411398i
\(319\) 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
\(324\) −8.40333 15.9180i −0.466851 0.884336i
\(325\) 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
\(330\) −1.54544 13.7079i −0.0850736 0.754594i
\(331\) −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 \(0.275050\pi\)
−0.649328 + 0.760508i \(0.724950\pi\)
\(338\) −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
\(342\) 1.81468 3.01001i 0.0981266 0.162763i
\(343\) −10.4366 −0.563521
\(344\) −15.7225 6.51246i −0.847699 0.351128i
\(345\) 2.80109 9.72524i 0.150805 0.523589i
\(346\) −11.6569 28.1421i −0.626676 1.51293i
\(347\) −0.185709 −0.00996939 −0.00498469 0.999988i \(-0.501587\pi\)
−0.00498469 + 0.999988i \(0.501587\pi\)
\(348\) −18.8017 9.49433i −1.00788 0.508949i
\(349\) 2.34315i 0.125426i 0.998032 + 0.0627129i \(0.0199752\pi\)
−0.998032 + 0.0627129i \(0.980025\pi\)
\(350\) 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 \(-0.169680\pi\)
0.861254 + 0.508175i \(0.169680\pi\)
\(354\) −4.67654 + 4.02353i −0.248556 + 0.213848i
\(355\) −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 \(-0.578146\pi\)
−0.243043 + 0.970016i \(0.578146\pi\)
\(360\) −17.7883 6.60129i −0.937525 0.347919i
\(361\) −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
\(366\) −15.7557 + 13.5557i −0.823566 + 0.708567i
\(367\) −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
\(372\) 1.82939 3.62275i 0.0948493 0.187831i
\(373\) 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
\(375\) −1.81640 19.2795i −0.0937987 0.995591i
\(376\) −6.82843 2.82843i −0.352149 0.145865i
\(377\) 28.2960 1.45732
\(378\) 23.5731 + 5.38919i 1.21247 + 0.277190i
\(379\) 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 \(-0.267014\pi\)
\(384\) −1.46671 + 19.5410i −0.0748477 + 0.997195i
\(385\) 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 \(-0.561350\pi\)
−0.191544 + 0.981484i \(0.561350\pi\)
\(390\) 25.3289 2.85560i 1.28258 0.144599i
\(391\) 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
\(396\) −14.9420 2.25576i −0.750866 0.113356i
\(397\) 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 \(0.876848\pi\)
\(402\) −6.11020 + 5.25700i −0.304749 + 0.262195i
\(403\) 5.45214i 0.271590i
\(404\) 18.6731 18.6731i 0.929024 0.929024i
\(405\) −12.5430 15.7377i −0.623266 0.782010i
\(406\) 26.1421 10.8284i 1.29741 0.537406i
\(407\) 4.85483i 0.240645i
\(408\) −18.0535 1.35506i −0.893781 0.0670856i
\(409\) −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
\(414\) −9.49456 5.72408i −0.466632 0.281323i
\(415\) −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 \(0.980405\pi\)
\(420\) 22.3080 12.3312i 1.08852 0.601699i
\(421\) 34.8284i 1.69743i −0.528848 0.848717i \(-0.677376\pi\)
0.528848 0.848717i \(-0.322624\pi\)
\(422\) −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
\(426\) 11.3803 + 13.2273i 0.551376 + 0.640863i
\(427\) 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 \(-0.728101\pi\)
−0.656824 + 0.754044i \(0.728101\pi\)
\(432\) −12.0335 + 16.9469i −0.578960 + 0.815356i
\(433\) 23.5992i 1.13410i −0.823682 0.567052i \(-0.808084\pi\)
0.823682 0.567052i \(-0.191916\pi\)
\(434\) 2.08644 + 5.03712i 0.100152 + 0.241790i
\(435\) −22.6291 6.51770i −1.08498 0.312500i
\(436\) 0.686292 + 0.686292i 0.0328674 + 0.0328674i
\(437\) 2.16478i 0.103556i
\(438\) 12.2204 10.5140i 0.583913 0.502378i
\(439\) 28.4853i 1.35953i 0.733431 + 0.679764i \(0.237918\pi\)
−0.733431 + 0.679764i \(0.762082\pi\)
\(440\) −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 \(-0.512160\pi\)
−0.0381910 + 0.999270i \(0.512160\pi\)
\(444\) −5.96062 3.00994i −0.282878 0.142846i
\(445\) 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 \(-0.309408\pi\)
\(450\) −20.9140 3.55054i −0.985893 0.167374i
\(451\) 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
\(456\) −4.04706 0.303766i −0.189521 0.0142251i
\(457\) 18.6148i 0.870762i −0.900246 0.435381i \(-0.856614\pi\)
0.900246 0.435381i \(-0.143386\pi\)
\(458\) −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 \(-0.470352\pi\)
0.0930072 + 0.995665i \(0.470352\pi\)
\(462\) 15.3889 13.2401i 0.715957 0.615984i
\(463\) −25.7607 −1.19720 −0.598600 0.801048i \(-0.704276\pi\)
−0.598600 + 0.801048i \(0.704276\pi\)
\(464\) 24.3214i 1.12909i
\(465\) 1.25584 4.36023i 0.0582384 0.202201i
\(466\) −20.8284 + 8.62742i −0.964858 + 0.399657i
\(467\) −15.8645 −0.734120 −0.367060 0.930197i \(-0.619636\pi\)
−0.367060 + 0.930197i \(0.619636\pi\)
\(468\) 4.16810 27.6093i 0.192670 1.27624i
\(469\) 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
\(474\) 30.6104 26.3361i 1.40598 1.20966i
\(475\) −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 \(-0.354780\pi\)
0.440560 + 0.897723i \(0.354780\pi\)
\(480\) 2.45448 + 21.7710i 0.112031 + 0.993705i
\(481\) 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
\(486\) −20.2112 + 8.80386i −0.916798 + 0.399351i
\(487\) −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 \(-0.313354\pi\)
\(492\) 13.4270 26.5896i 0.605336 1.19875i
\(493\) −22.4700 −1.01200
\(494\) 5.03712 2.08644i 0.226631 0.0938735i
\(495\) −16.8832 + 0.630865i −0.758845 + 0.0283553i
\(496\) −4.68629 −0.210421
\(497\) −23.4412 −1.05148
\(498\) 14.9692 + 17.3987i 0.670788 + 0.779656i
\(499\) −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 \(-0.0688941\pi\)
\(504\) −6.71481 27.1027i −0.299101 1.20725i
\(505\) 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 \(-0.405471\pi\)
0.292626 + 0.956227i \(0.405471\pi\)
\(510\) −20.1138 + 2.26764i −0.890652 + 0.100413i
\(511\) 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
\(516\) −9.39500 + 18.6050i −0.413592 + 0.819040i
\(517\) −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 \(0.728388\pi\)
\(522\) −13.3191 + 22.0924i −0.582959 + 0.966957i
\(523\) 12.5980i 0.550874i 0.961319 + 0.275437i \(0.0888225\pi\)
−0.961319 + 0.275437i \(0.911177\pi\)
\(524\) 30.8338 + 30.8338i 1.34698 + 1.34698i
\(525\) 21.9399 18.1872i 0.957534 0.793755i
\(526\) −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
\(534\) 9.35309 8.04706i 0.404748 0.348230i
\(535\) 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
\(540\) −9.69286 + 21.1199i −0.417114 + 0.908854i
\(541\) 16.0000i 0.687894i −0.938989 0.343947i \(-0.888236\pi\)
0.938989 0.343947i \(-0.111764\pi\)
\(542\) 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
\(546\) 24.4645 + 28.4350i 1.04698 + 1.21691i
\(547\) 11.0011i 0.470375i −0.971950 0.235188i \(-0.924430\pi\)
0.971950 0.235188i \(-0.0755704\pi\)
\(548\) −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
\(552\) −0.958174 + 12.7657i −0.0407826 + 0.543346i
\(553\) 54.2474i 2.30683i
\(554\) 19.7164 8.16679i 0.837668 0.346973i
\(555\) −7.17401 2.06628i −0.304520 0.0877085i
\(556\) 20.4853 20.4853i 0.868769 0.868769i
\(557\) 4.96362i 0.210315i 0.994456 + 0.105158i \(0.0335347\pi\)
−0.994456 + 0.105158i \(0.966465\pi\)
\(558\) −4.25680 2.56634i −0.180205 0.108642i
\(559\) 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 \(-0.653345\pi\)
−0.463329 + 0.886186i \(0.653345\pi\)
\(564\) −4.08034 + 8.08034i −0.171813 + 0.340244i
\(565\) 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 \(-0.106900\pi\)
\(570\) −4.50892 + 0.508339i −0.188858 + 0.0212920i
\(571\) 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
\(576\) 23.7311 + 3.58261i 0.988796 + 0.149276i
\(577\) 3.85525i 0.160496i 0.996775 + 0.0802480i \(0.0255712\pi\)
−0.996775 + 0.0802480i \(0.974429\pi\)
\(578\) 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
\(582\) −5.06186 + 4.35504i −0.209821 + 0.180522i
\(583\) 11.5657 0.479004
\(584\) −17.1978 7.12356i −0.711650 0.294775i
\(585\) −1.16569 31.1961i −0.0481952 1.28980i
\(586\) 1.31371 + 3.17157i 0.0542688 + 0.131016i
\(587\) 7.20533 0.297396 0.148698 0.988883i \(-0.452492\pi\)
0.148698 + 0.988883i \(0.452492\pi\)
\(588\) 11.8383 + 5.97801i 0.488204 + 0.246529i
\(589\) 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 \(-0.493428\pi\)
0.0206448 + 0.999787i \(0.493428\pi\)
\(594\) −4.12471 + 18.0421i −0.169239 + 0.740276i
\(595\) 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 \(-0.270532\pi\)
0.660058 + 0.751214i \(0.270532\pi\)
\(600\) 7.22590 + 23.4048i 0.294996 + 0.955498i
\(601\) 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
\(606\) −21.0939 24.5174i −0.856882 0.995953i
\(607\) 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
\(612\) −3.30990 + 21.9247i −0.133795 + 0.886252i
\(613\) −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
\(615\) 9.21742 32.0024i 0.371682 1.29046i
\(616\) −21.6569 8.97056i −0.872580 0.361434i
\(617\) −8.55035 −0.344224 −0.172112 0.985077i \(-0.555059\pi\)
−0.172112 + 0.985077i \(0.555059\pi\)
\(618\) 9.61204 + 11.1721i 0.386653 + 0.449406i
\(619\) −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
\(630\) −13.0152 28.3754i −0.518538 1.13050i
\(631\) 2.14214i 0.0852771i −0.999091 0.0426385i \(-0.986424\pi\)
0.999091 0.0426385i \(-0.0135764\pi\)
\(632\) −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
\(636\) 7.17063 14.2001i 0.284334 0.563069i
\(637\) −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 \(0.757020\pi\)
\(642\) −13.5367 15.7337i −0.534253 0.620961i
\(643\) 35.0681i 1.38295i 0.722401 + 0.691475i \(0.243039\pi\)
−0.722401 + 0.691475i \(0.756961\pi\)
\(644\) −12.1607 12.1607i −0.479198 0.479198i
\(645\) −6.44951 + 22.3924i −0.253949 + 0.881699i
\(646\) −4.00000 + 1.65685i −0.157378 + 0.0651881i
\(647\) 28.3730i 1.11546i 0.830024 + 0.557728i \(0.188327\pi\)
−0.830024 + 0.557728i \(0.811673\pi\)
\(648\) 19.5943 + 16.2501i 0.769735 + 0.638363i
\(649\) 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 \(-0.157219\pi\)
\(654\) 0.901086 0.775262i 0.0352353 0.0303152i
\(655\) 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 \(0.907704\pi\)
\(660\) 9.43786 + 17.0738i 0.367368 + 0.664598i
\(661\) 44.7696i 1.74133i 0.491873 + 0.870667i \(0.336312\pi\)
−0.491873 + 0.870667i \(0.663688\pi\)
\(662\) 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
\(666\) −4.22248 + 7.00384i −0.163618 + 0.271393i
\(667\) 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
\(672\) −24.4408 + 21.0280i −0.942824 + 0.811172i
\(673\) 47.6661i 1.83739i −0.394964 0.918697i \(-0.629243\pi\)
0.394964 0.918697i \(-0.370757\pi\)
\(674\) −15.1114 36.4821i −0.582068 1.40524i
\(675\) −6.25348 + 25.2169i −0.240696 + 0.970600i
\(676\) 12.2426 12.2426i 0.470871 0.470871i
\(677\) 1.00547i 0.0386433i −0.999813 0.0193217i \(-0.993849\pi\)
0.999813 0.0193217i \(-0.00615066\pi\)
\(678\) −14.2530 16.5662i −0.547383 0.636222i
\(679\) 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 \(-0.592446\pi\)
−0.286363 + 0.958121i \(0.592446\pi\)
\(684\) −0.741983 + 4.91487i −0.0283704 + 0.187925i
\(685\) −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
\(690\) 1.60347 + 14.2226i 0.0610429 + 0.541444i
\(691\) −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
\(696\) 29.7039 + 2.22952i 1.12592 + 0.0845099i
\(697\) 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 \(-0.330804\pi\)
0.506865 + 0.862025i \(0.330804\pi\)
\(702\) −33.3374 7.62146i −1.25824 0.287654i
\(703\) −1.59689 −0.0602280
\(704\) 14.2471 14.2471i 0.536959 0.536959i
\(705\) −2.80109 + 9.72524i −0.105495 + 0.366274i
\(706\) −42.2843 + 17.5147i −1.59139 + 0.659175i
\(707\) 43.4495 1.63409
\(708\) 3.93268 7.78793i 0.147799 0.292688i
\(709\) 36.2843i 1.36268i −0.731965 0.681342i \(-0.761397\pi\)
0.731965 0.681342i \(-0.238603\pi\)
\(710\) 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
\(714\) −19.4273 22.5804i −0.727050 0.845048i
\(715\) −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 \(-0.517523\pi\)
−0.0550208 + 0.998485i \(0.517523\pi\)
\(720\) 26.8141 1.00195i 0.999303 0.0373403i
\(721\) −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
\(726\) −7.43957 8.64700i −0.276108 0.320920i
\(727\) 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
\(732\) 13.2496 26.2383i 0.489719 0.969795i
\(733\) −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
\(735\) 14.2482 + 4.10381i 0.525553 + 0.151371i
\(736\) 13.6569 5.65685i 0.503398 0.208514i
\(737\) 8.28772 0.305282
\(738\) −31.2433 18.8360i −1.15008 0.693362i
\(739\) −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 \(0.909873\pi\)
\(744\) −0.429589 + 5.72341i −0.0157495 + 0.209830i
\(745\) 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
\(750\) 12.8073 + 24.2069i 0.467655 + 0.883911i
\(751\) 35.1127i 1.28128i 0.767841 + 0.640640i \(0.221331\pi\)
−0.767841 + 0.640640i \(0.778669\pi\)
\(752\) 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
\(756\) −33.7164 + 5.71637i −1.22625 + 0.207902i
\(757\) −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 \(-0.100902\pi\)
\(762\) 5.25700 + 6.11020i 0.190441 + 0.221349i
\(763\) 1.59689i 0.0578115i
\(764\) −7.12356 + 7.12356i −0.257722 + 0.257722i
\(765\) 0.925677 + 24.7730i 0.0334679 + 0.895670i
\(766\) 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 \(-0.110081\pi\)
\(774\) 21.8612 + 13.1797i 0.785786 + 0.473735i