Properties

Label 120.2.m.b.59.13
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 59.13
Root \(-0.357857i\) of defining polynomial
Character \(\chi\) \(=\) 120.59
Dual form 120.2.m.b.59.16

$q$-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} +(2.64533 + 1.73270i) q^{10} +2.51856i q^{11} +(-3.09221 - 1.56148i) 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} +(-2.19051 + 3.63341i) q^{18} +0.828427 q^{19} +(4.39402 + 0.832235i) 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} +(1.41921 - 5.29016i) 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} +(6.19146 - 1.29066i) q^{40} -8.59890i q^{41} +(5.25700 + 6.11020i) 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} +(0.129605 + 7.06988i) 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} +(-1.00872 - 7.68000i) 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} +(-8.70487 - 5.70171i) q^{70} -7.12356 q^{71} +(2.04057 + 8.23627i) 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} +(-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} +(-9.47213 + 0.527944i) 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 \(-0.713629\pi\)
−0.621876 + 0.783116i \(0.713629\pi\)
\(8\) 1.08239 2.61313i 0.382683 0.923880i
\(9\) −2.41421 + 1.78089i −0.804738 + 0.593630i
\(10\) 2.64533 + 1.73270i 0.836526 + 0.547927i
\(11\) 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 \(-0.276711\pi\)
0.645351 + 0.763886i \(0.276711\pi\)
\(14\) −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 \(0.647916\pi\)
\(18\) −2.19051 + 3.63341i −0.516308 + 0.856403i
\(19\) 0.828427 0.190054 0.0950271 0.995475i \(-0.469706\pi\)
0.0950271 + 0.995475i \(0.469706\pi\)
\(20\) 4.39402 + 0.832235i 0.982532 + 0.186093i
\(21\) 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 \(0.0878297\pi\)
−0.962174 + 0.272437i \(0.912170\pi\)
\(24\) −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 \(0.690949\pi\)
\(30\) 1.41921 5.29016i 0.259112 0.965847i
\(31\) 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 \(-0.449350\pi\)
0.158450 + 0.987367i \(0.449350\pi\)
\(38\) 1.08239 0.448342i 0.175587 0.0727306i
\(39\) −2.51856 7.65685i −0.403292 1.22608i
\(40\) 6.19146 1.29066i 0.978956 0.204071i
\(41\) 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 \(-0.848290\pi\)
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 \(-0.938963\pi\)
0.981671 0.190582i \(-0.0610374\pi\)
\(48\) −6.58132 + 2.16478i −0.949931 + 0.312460i
\(49\) 3.82843 0.546918
\(50\) 0.129605 + 7.06988i 0.0183289 + 0.999832i
\(51\) 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 \(0.102137\pi\)
−0.948961 + 0.315394i \(0.897863\pi\)
\(54\) 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 \(-0.0524217\pi\)
\(60\) −1.00872 7.68000i −0.130226 0.991484i
\(61\) 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 \(0.0644220\pi\)
−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
\(70\) −8.70487 5.70171i −1.04043 0.681485i
\(71\) −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 \(-0.874152\pi\)
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
\(78\) −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 \(-0.328070\pi\)
0.514252 + 0.857639i \(0.328070\pi\)
\(84\) 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 \(0.913979\pi\)
\(90\) −9.47213 + 0.527944i −0.998450 + 0.0556502i
\(91\) −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 \(0.0441944\pi\)
−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
\(100\) 3.99553 + 9.16710i 0.399553 + 0.916710i
\(101\) 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 \(-0.404206\pi\)
0.296423 + 0.955057i \(0.404206\pi\)
\(104\) 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 \(0.634324\pi\)
\(108\) 10.2461 1.73715i 0.985930 0.167157i
\(109\) 0.485281i 0.0464815i 0.999730 + 0.0232408i \(0.00739843\pi\)
−0.999730 + 0.0232408i \(0.992602\pi\)
\(110\) −4.36390 + 6.66242i −0.416081 + 0.635237i
\(111\) −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 \(0.637845\pi\)
\(114\) −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
\(120\) −5.47435 9.48849i −0.499738 0.866177i
\(121\) 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 \(-0.453360\pi\)
0.145999 + 0.989285i \(0.453360\pi\)
\(128\) −10.4525 4.32957i −0.923880 0.382683i
\(129\) −9.89949 + 3.25623i −0.871602 + 0.286695i
\(130\) 12.3105 + 8.06343i 1.07971 + 0.707210i
\(131\) 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
\(135\) −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 \(0.328942\pi\)
\(138\) 4.85214 4.17461i 0.413041 0.355366i
\(139\) 14.4853 1.22863 0.614313 0.789063i \(-0.289433\pi\)
0.614313 + 0.789063i \(0.289433\pi\)
\(140\) −14.4592 2.73860i −1.22203 0.231454i
\(141\) −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 \(0.294656\pi\)
\(150\) 11.5621 4.03943i 0.944044 0.329818i
\(151\) 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 \(-0.574122\pi\)
−0.230762 + 0.973010i \(0.574122\pi\)
\(158\) 8.92177 + 21.5391i 0.709778 + 1.71356i
\(159\) 7.55568 2.48528i 0.599204 0.197096i
\(160\) 6.93078 10.5813i 0.547927 0.836526i
\(161\) 8.59890i 0.677688i
\(162\) −1.18235 12.6729i −0.0928938 0.995676i
\(163\) 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 \(-0.764988\pi\)
0.739606 0.673040i \(-0.235012\pi\)
\(168\) 16.0756 + 1.20661i 1.24026 + 0.0930920i
\(169\) 8.65685 0.665912
\(170\) −9.77586 6.40321i −0.749774 0.491104i
\(171\) −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 \(-0.694644\pi\)
0.574090 0.818792i \(-0.305356\pi\)
\(174\) 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 \(-0.117340\pi\)
\(180\) −12.0902 + 5.81607i −0.901151 + 0.433504i
\(181\) 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
\(190\) 2.19146 + 1.43541i 0.158985 + 0.104136i
\(191\) −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 \(0.251576\pi\)
−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 \(0.140389\pi\)
−0.904306 + 0.426885i \(0.859611\pi\)
\(198\) −9.15096 5.51693i −0.650330 0.392071i
\(199\) 9.17157i 0.650156i −0.945687 0.325078i \(-0.894610\pi\)
0.945687 0.325078i \(-0.105390\pi\)
\(200\) 10.1816 + 9.81503i 0.719949 + 0.694027i
\(201\) 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
\(210\) −4.67014 + 17.4081i −0.322271 + 1.20127i
\(211\) 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
\(220\) −2.09603 + 11.0666i −0.141315 + 0.746110i
\(221\) −17.1978 −1.15685
\(222\) −3.07948 3.57927i −0.206681 0.240225i
\(223\) −21.9054 −1.46690 −0.733448 0.679746i \(-0.762090\pi\)
−0.733448 + 0.679746i \(0.762090\pi\)
\(224\) 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 \(0.543913\pi\)
\(228\) −2.56167 1.29357i −0.169651 0.0856689i
\(229\) 19.3137i 1.27629i 0.769918 + 0.638143i \(0.220297\pi\)
−0.769918 + 0.638143i \(0.779703\pi\)
\(230\) −4.52775 + 6.91258i −0.298551 + 0.455802i
\(231\) −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 \(0.674880\pi\)
\(234\) −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 \(0.755459\pi\)
\(240\) −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
\(246\) −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
\(250\) −12.9002 + 9.14244i −0.815882 + 0.578219i
\(251\) 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
\(255\) −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 \(0.330096\pi\)
\(258\) −11.1721 + 9.61204i −0.695542 + 0.598419i
\(259\) −6.34315 −0.394144
\(260\) 20.4484 + 3.87297i 1.26816 + 0.240191i
\(261\) 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 \(-0.759366\pi\)
0.727604 0.685998i \(-0.240634\pi\)
\(264\) 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 \(0.594968\pi\)
\(270\) 5.99492 + 15.2990i 0.364839 + 0.931070i
\(271\) 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 \(-0.350231\pi\)
0.453343 + 0.891336i \(0.350231\pi\)
\(278\) 18.9259 7.83938i 1.13510 0.470175i
\(279\) 2.08644 + 2.82843i 0.124912 + 0.169334i
\(280\) −20.3740 + 4.24711i −1.21758 + 0.253813i
\(281\) 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 \(0.180249\pi\)
−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
\(288\) 14.5336 + 8.76204i 0.856403 + 0.516308i
\(289\) −3.34315 −0.196656
\(290\) −16.0845 10.5354i −0.944515 0.618659i
\(291\) 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 \(0.0225889\pi\)
−0.997483 + 0.0709056i \(0.977411\pi\)
\(294\) −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
\(300\) 12.9205 11.5352i 0.745967 0.665983i
\(301\) 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 \(-0.934632\pi\)
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
\(310\) 2.02998 3.09920i 0.115295 0.176022i
\(311\) 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 \(-0.840291\pi\)
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 \(0.121374\pi\)
−0.928179 + 0.372135i \(0.878626\pi\)
\(318\) 8.52695 7.33628i 0.478168 0.411398i
\(319\) 15.3137i 0.857403i
\(320\) 3.32894 17.5761i 0.186093 0.982532i
\(321\) 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
\(330\) 13.3236 + 3.57437i 0.733440 + 0.196763i
\(331\) −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
\(340\) −16.2382 3.07554i −0.880638 0.166795i
\(341\) 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
\(345\) 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 \(0.498413\pi\)
\(348\) 18.8017 + 9.49433i 1.00788 + 0.508949i
\(349\) 2.34315i 0.125426i 0.998032 + 0.0627129i \(0.0199752\pi\)
−0.998032 + 0.0627129i \(0.980025\pi\)
\(350\) −0.426486 23.2646i −0.0227966 1.24354i
\(351\) 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 \(0.830320\pi\)
\(354\) −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 \(0.578146\pi\)
\(360\) −12.6490 + 14.1422i −0.666660 + 0.745362i
\(361\) −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 \(-0.482033\pi\)
0.0564142 + 0.998407i \(0.482033\pi\)
\(368\) 10.4525 0.544874
\(369\) 15.3137 + 20.7596i 0.797200 + 1.08070i
\(370\) 5.09920 + 3.33998i 0.265095 + 0.173638i
\(371\) 15.1114i 0.784543i
\(372\) −1.82939 + 3.62275i −0.0948493 + 0.187831i
\(373\) −24.3976 −1.26326 −0.631631 0.775269i \(-0.717614\pi\)
−0.631631 + 0.775269i \(0.717614\pi\)
\(374\) −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
\(378\) −23.5731 5.38919i −1.21247 0.277190i
\(379\) 20.8284 1.06988 0.534942 0.844889i \(-0.320333\pi\)
0.534942 + 0.844889i \(0.320333\pi\)
\(380\) 3.64012 + 0.689446i 0.186734 + 0.0353678i
\(381\) −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 \(0.267014\pi\)
−0.668320 + 0.743874i \(0.732986\pi\)
\(384\) −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 \(0.561350\pi\)
\(390\) 6.60458 24.6188i 0.334436 1.24662i
\(391\) 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 \(-0.738303\pi\)
−0.680650 + 0.732609i \(0.738303\pi\)
\(398\) −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
\(405\) 19.2344 5.91920i 0.955766 0.294127i
\(406\) 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 \(0.602730\pi\)
\(410\) 14.8993 22.7469i 0.735823 1.12339i
\(411\) −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 \(0.980405\pi\)
\(420\) 3.31937 + 25.2723i 0.161969 + 1.23316i
\(421\) 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
\(430\) 10.4252 15.9162i 0.502746 0.767548i
\(431\) −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 \(0.191916\pi\)
−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
\(438\) −12.2204 + 10.5140i −0.583913 + 0.502378i
\(439\) 28.4853i 1.35953i 0.733431 + 0.679764i \(0.237918\pi\)
−0.733431 + 0.679764i \(0.762082\pi\)
\(440\) 3.25060 + 15.5936i 0.154966 + 0.743394i
\(441\) −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 \(0.487840\pi\)
\(444\) −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 \(-0.309408\pi\)
\(450\) −12.9036 16.8374i −0.608281 0.793722i
\(451\) 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 \(0.143386\pi\)
−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
\(460\) −2.17473 + 11.4821i −0.101398 + 0.535357i
\(461\) 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 \(-0.295724\pi\)
0.598600 + 0.801048i \(0.295724\pi\)
\(464\) 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 \(0.380364\pi\)
\(468\) −4.16810 + 27.6093i −0.192670 + 1.27624i
\(469\) 10.8284i 0.500010i
\(470\) 4.52775 6.91258i 0.208850 0.318853i
\(471\) 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 \(0.354780\pi\)
\(480\) −21.1607 5.67685i −0.965847 0.259112i
\(481\) 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 \(-0.436527\pi\)
0.198087 + 0.980184i \(0.436527\pi\)
\(488\) −22.1731 9.18440i −1.00373 0.415758i
\(489\) 9.89949 3.25623i 0.447671 0.147252i
\(490\) 10.1274 + 6.63350i 0.457511 + 0.299671i
\(491\) 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
\(495\) 5.58678 15.9446i 0.251107 0.716655i
\(496\) −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 \(0.812057\pi\)
\(500\) −11.9071 + 18.9267i −0.532502 + 0.846429i
\(501\) −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 \(0.0688941\pi\)
−0.976669 + 0.214751i \(0.931106\pi\)
\(504\) −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 \(0.405471\pi\)
\(510\) −5.24473 + 19.5499i −0.232240 + 0.865684i
\(511\) 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
\(520\) 28.8132 6.00632i 1.26354 0.263395i
\(521\) 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 \(-0.911177\pi\)
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
\(530\) −7.95689 + 12.1479i −0.345625 + 0.527670i
\(531\) 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
\(540\) 16.1125 + 16.7447i 0.693373 + 0.720579i
\(541\) 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 \(0.0755704\pi\)
−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
\(550\) −17.8059 + 0.326418i −0.759247 + 0.0139185i
\(551\) −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
\(555\) 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 \(-0.966465\pi\)
0.994456 0.105158i \(-0.0335347\pi\)
\(558\) 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 \(-0.346655\pi\)
0.463329 + 0.886186i \(0.346655\pi\)
\(564\) −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 \(-0.106900\pi\)
\(570\) 1.17571 4.38252i 0.0492453 0.183563i
\(571\) 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 \(-0.974429\pi\)
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
\(580\) −26.7171 5.06027i −1.10937 0.210116i
\(581\) −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
\(585\) −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 \(0.547508\pi\)
\(588\) −11.8383 5.97801i −0.488204 0.246529i
\(589\) 0.970563i 0.0399913i
\(590\) 4.36390 6.66242i 0.179659 0.274287i
\(591\) 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 \(0.506572\pi\)
\(594\) −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 \(0.270532\pi\)
\(600\) 10.6387 22.0640i 0.434323 0.900757i
\(601\) 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 \(-0.531625\pi\)
−0.0991898 + 0.995069i \(0.531625\pi\)
\(608\) −1.79337 4.32957i −0.0727306 0.175587i
\(609\) −10.8284 32.9203i −0.438790 1.33400i
\(610\) 14.7024 22.4464i 0.595283 0.908827i
\(611\) 12.1607i 0.491969i
\(612\) 3.30990 21.9247i 0.133795 0.886252i
\(613\) 23.2685 0.939804 0.469902 0.882718i \(-0.344289\pi\)
0.469902 + 0.882718i \(0.344289\pi\)
\(614\) −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 \(0.444941\pi\)
\(618\) −9.61204 11.1721i −0.386653 0.449406i
\(619\) −2.48528 −0.0998919 −0.0499459 0.998752i \(-0.515905\pi\)
−0.0499459 + 0.998752i \(0.515905\pi\)
\(620\) 0.975024 5.14791i 0.0391579 0.206745i
\(621\) −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
\(630\) 31.1695 1.73728i 1.24182 0.0692150i
\(631\) 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
\(640\) −5.16263 24.7658i −0.204071 0.978956i
\(641\) 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 \(-0.756961\pi\)
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 \(-0.811673\pi\)
0.830024 0.557728i \(-0.188327\pi\)
\(648\) −19.5943 16.2501i −0.769735 0.638363i
\(649\) 6.34315 0.248990
\(650\) 0.603142 + 32.9010i 0.0236572 + 1.29049i
\(651\) 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 \(0.157219\pi\)
−0.880482 + 0.474079i \(0.842781\pi\)
\(654\) 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 \(0.907704\pi\)
\(660\) 19.3426 2.54053i 0.752908 0.0988902i
\(661\) 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
\(670\) −5.70171 + 8.70487i −0.220276 + 0.336299i
\(671\) 21.3707 0.825006
\(672\) 24.4408 21.0280i 0.942824 0.811172i
\(673\) 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 \(0.00615066\pi\)
−0.999813 + 0.0193217i \(0.993849\pi\)
\(678\) 14.2530 + 16.5662i 0.547383 + 0.636222i
\(679\) 8.97056i 0.344259i
\(680\) −22.8807 + 4.76965i −0.877433 + 0.182908i
\(681\) 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 \(0.407554\pi\)
\(684\) −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
\(690\) 13.8239 + 3.70858i 0.526266 + 0.141183i
\(691\) −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
\(700\) −13.1479 30.1658i −0.496945 1.14016i
\(701\) 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
\(705\) −8.02734 6.16346i −0.302327 0.232129i
\(706\) −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 \(-0.238603\pi\)
\(710\) −18.8442 12.3430i −0.707209 0.463223i
\(711\) −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 \(0.517523\pi\)
\(720\) −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
\(726\) −7.43957 8.64700i −0.276108 0.320920i
\(727\) −47.1015 −1.74690 −0.873449 0.486915i \(-0.838122\pi\)
−0.873449 + 0.486915i \(0.838122\pi\)
\(728\) −16.5754 + 40.0166i −0.614327 + 1.48312i
\(729\) 8.89949 + 25.4912i 0.329611 + 0.944117i
\(730\) 11.4034 17.4097i 0.422059 0.644363i
\(731\) 22.2349i 0.822388i
\(732\) −13.2496 + 26.2383i −0.489719 + 0.969795i
\(733\) 9.63811 0.355992 0.177996 0.984031i \(-0.443039\pi\)
0.177996 + 0.984031i \(0.443039\pi\)
\(734\) 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
\(738\) 31.2433 + 18.8360i 1.15008 + 0.693362i
\(739\) −27.1716 −0.999522 −0.499761 0.866163i \(-0.666579\pi\)
−0.499761 + 0.866163i \(0.666579\pi\)
\(740\) 8.47001 + 1.60423i 0.311364 + 0.0589728i
\(741\) −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 \(-0.909873\pi\)
0.960182 0.279375i \(-0.0901272\pi\)
\(744\) −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
\(750\) 22.0239 + 16.2773i 0.804198 + 0.594362i
\(751\) 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 \(-0.425083\pi\)
0.233192 + 0.972431i \(0.425083\pi\)
\(758\) 27.2137 11.2723i 0.988444 0.409427i
\(759\) 3.56178 + 10.8284i 0.129284 + 0.393047i
\(760\) 5.12918 1.06922i 0.186055 0.0387845i
\(761\) 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
\(765\) 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 \(0.852308\pi\)
\(770\) 14.3601 21.9237i 0.517502 0.790077i
\(771\) −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 \(0.110081\pi\)
−0.940795 + 0.338976i \(0.889919\pi\)
\(774\) 21.8612 + 13.1797i 0.785786 + 0.473735i