Properties

Label 1110.2.u.f.191.1
Level $1110$
Weight $2$
Character 1110.191
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 191.1
Character \(\chi\) \(=\) 1110.191
Dual form 1110.2.u.f.401.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.169604 - 1.72373i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.33879 + 1.09893i) q^{6} +1.82689 q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.94247 - 0.584702i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.169604 - 1.72373i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.33879 + 1.09893i) q^{6} +1.82689 q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.94247 - 0.584702i) q^{9} -1.00000 q^{10} +5.15936 q^{11} +(1.72373 + 0.169604i) q^{12} +(-3.16917 - 3.16917i) q^{13} +(-1.29181 - 1.29181i) q^{14} +(-1.09893 - 1.33879i) q^{15} -1.00000 q^{16} +(-2.98694 + 2.98694i) q^{17} +(1.66719 + 2.49409i) q^{18} +(-2.92931 - 2.92931i) q^{19} +(0.707107 + 0.707107i) q^{20} +(0.309848 - 3.14906i) q^{21} +(-3.64822 - 3.64822i) q^{22} +(3.68979 - 3.68979i) q^{23} +(-1.09893 - 1.33879i) q^{24} -1.00000i q^{25} +4.48188i q^{26} +(-1.50692 + 4.97285i) q^{27} +1.82689i q^{28} +(4.89488 + 4.89488i) q^{29} +(-0.169604 + 1.72373i) q^{30} +(6.21752 - 6.21752i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.875047 - 8.89332i) q^{33} +4.22417 q^{34} +(1.29181 - 1.29181i) q^{35} +(0.584702 - 2.94247i) q^{36} +(0.159948 - 6.08066i) q^{37} +4.14267i q^{38} +(-6.00028 + 4.92527i) q^{39} -1.00000i q^{40} -0.816209 q^{41} +(-2.44582 + 2.00763i) q^{42} +(-2.69720 - 2.69720i) q^{43} +5.15936i q^{44} +(-2.49409 + 1.66719i) q^{45} -5.21815 q^{46} -6.46196i q^{47} +(-0.169604 + 1.72373i) q^{48} -3.66246 q^{49} +(-0.707107 + 0.707107i) q^{50} +(4.64208 + 5.65527i) q^{51} +(3.16917 - 3.16917i) q^{52} -12.1785i q^{53} +(4.58189 - 2.45078i) q^{54} +(3.64822 - 3.64822i) q^{55} +(1.29181 - 1.29181i) q^{56} +(-5.54615 + 4.55251i) q^{57} -6.92241i q^{58} +(-0.207760 + 0.207760i) q^{59} +(1.33879 - 1.09893i) q^{60} +(-8.45738 + 8.45738i) q^{61} -8.79291 q^{62} +(-5.37558 - 1.06819i) q^{63} -1.00000i q^{64} -4.48188 q^{65} +(-6.90728 + 5.66978i) q^{66} -12.0378i q^{67} +(-2.98694 - 2.98694i) q^{68} +(-5.73439 - 6.98599i) q^{69} -1.82689 q^{70} +11.3303i q^{71} +(-2.49409 + 1.66719i) q^{72} +10.9001i q^{73} +(-4.41278 + 4.18658i) q^{74} +(-1.72373 - 0.169604i) q^{75} +(2.92931 - 2.92931i) q^{76} +9.42559 q^{77} +(7.72553 + 0.760144i) q^{78} +(5.32048 + 5.32048i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(8.31625 + 3.44093i) q^{81} +(0.577147 + 0.577147i) q^{82} +14.3723i q^{83} +(3.14906 + 0.309848i) q^{84} +4.22417i q^{85} +3.81442i q^{86} +(9.26763 - 7.60725i) q^{87} +(3.64822 - 3.64822i) q^{88} +(-6.37672 - 6.37672i) q^{89} +(2.94247 + 0.584702i) q^{90} +(-5.78973 - 5.78973i) q^{91} +(3.68979 + 3.68979i) q^{92} +(-9.66280 - 11.7718i) q^{93} +(-4.56930 + 4.56930i) q^{94} -4.14267 q^{95} +(1.33879 - 1.09893i) q^{96} +(-8.32365 - 8.32365i) q^{97} +(2.58975 + 2.58975i) q^{98} +(-15.1812 - 3.01668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 24q^{7} - 8q^{9} + O(q^{10}) \) \( 40q + 24q^{7} - 8q^{9} - 40q^{10} + 16q^{13} - 40q^{16} + 8q^{18} + 16q^{19} - 16q^{22} - 8q^{31} + 24q^{33} + 24q^{34} + 32q^{37} + 16q^{39} + 12q^{42} + 32q^{43} + 8q^{45} - 56q^{46} - 32q^{49} - 44q^{51} - 16q^{52} - 24q^{54} + 16q^{55} + 8q^{57} - 72q^{61} + 24q^{63} - 28q^{66} + 16q^{69} - 24q^{70} + 8q^{72} - 16q^{76} - 48q^{79} + 120q^{81} - 24q^{82} - 24q^{84} + 20q^{87} + 16q^{88} + 8q^{90} - 92q^{93} - 8q^{94} - 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) 0.169604 1.72373i 0.0979209 0.995194i
\(4\) 1.00000i 0.500000i
\(5\) 0.707107 0.707107i 0.316228 0.316228i
\(6\) −1.33879 + 1.09893i −0.546558 + 0.448637i
\(7\) 1.82689 0.690501 0.345250 0.938511i \(-0.387794\pi\)
0.345250 + 0.938511i \(0.387794\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −2.94247 0.584702i −0.980823 0.194901i
\(10\) −1.00000 −0.316228
\(11\) 5.15936 1.55560 0.777802 0.628509i \(-0.216335\pi\)
0.777802 + 0.628509i \(0.216335\pi\)
\(12\) 1.72373 + 0.169604i 0.497597 + 0.0489604i
\(13\) −3.16917 3.16917i −0.878968 0.878968i 0.114459 0.993428i \(-0.463486\pi\)
−0.993428 + 0.114459i \(0.963486\pi\)
\(14\) −1.29181 1.29181i −0.345250 0.345250i
\(15\) −1.09893 1.33879i −0.283743 0.345673i
\(16\) −1.00000 −0.250000
\(17\) −2.98694 + 2.98694i −0.724440 + 0.724440i −0.969506 0.245066i \(-0.921190\pi\)
0.245066 + 0.969506i \(0.421190\pi\)
\(18\) 1.66719 + 2.49409i 0.392961 + 0.587862i
\(19\) −2.92931 2.92931i −0.672030 0.672030i 0.286154 0.958184i \(-0.407623\pi\)
−0.958184 + 0.286154i \(0.907623\pi\)
\(20\) 0.707107 + 0.707107i 0.158114 + 0.158114i
\(21\) 0.309848 3.14906i 0.0676144 0.687182i
\(22\) −3.64822 3.64822i −0.777802 0.777802i
\(23\) 3.68979 3.68979i 0.769374 0.769374i −0.208622 0.977996i \(-0.566898\pi\)
0.977996 + 0.208622i \(0.0668979\pi\)
\(24\) −1.09893 1.33879i −0.224318 0.273279i
\(25\) 1.00000i 0.200000i
\(26\) 4.48188i 0.878968i
\(27\) −1.50692 + 4.97285i −0.290007 + 0.957025i
\(28\) 1.82689i 0.345250i
\(29\) 4.89488 + 4.89488i 0.908957 + 0.908957i 0.996188 0.0872311i \(-0.0278018\pi\)
−0.0872311 + 0.996188i \(0.527802\pi\)
\(30\) −0.169604 + 1.72373i −0.0309653 + 0.314708i
\(31\) 6.21752 6.21752i 1.11670 1.11670i 0.124478 0.992222i \(-0.460274\pi\)
0.992222 0.124478i \(-0.0397255\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 0.875047 8.89332i 0.152326 1.54813i
\(34\) 4.22417 0.724440
\(35\) 1.29181 1.29181i 0.218355 0.218355i
\(36\) 0.584702 2.94247i 0.0974503 0.490412i
\(37\) 0.159948 6.08066i 0.0262952 0.999654i
\(38\) 4.14267i 0.672030i
\(39\) −6.00028 + 4.92527i −0.960814 + 0.788675i
\(40\) 1.00000i 0.158114i
\(41\) −0.816209 −0.127471 −0.0637353 0.997967i \(-0.520301\pi\)
−0.0637353 + 0.997967i \(0.520301\pi\)
\(42\) −2.44582 + 2.00763i −0.377398 + 0.309784i
\(43\) −2.69720 2.69720i −0.411319 0.411319i 0.470879 0.882198i \(-0.343937\pi\)
−0.882198 + 0.470879i \(0.843937\pi\)
\(44\) 5.15936i 0.777802i
\(45\) −2.49409 + 1.66719i −0.371796 + 0.248531i
\(46\) −5.21815 −0.769374
\(47\) 6.46196i 0.942574i −0.881980 0.471287i \(-0.843790\pi\)
0.881980 0.471287i \(-0.156210\pi\)
\(48\) −0.169604 + 1.72373i −0.0244802 + 0.248799i
\(49\) −3.66246 −0.523209
\(50\) −0.707107 + 0.707107i −0.100000 + 0.100000i
\(51\) 4.64208 + 5.65527i 0.650021 + 0.791896i
\(52\) 3.16917 3.16917i 0.439484 0.439484i
\(53\) 12.1785i 1.67285i −0.548079 0.836426i \(-0.684641\pi\)
0.548079 0.836426i \(-0.315359\pi\)
\(54\) 4.58189 2.45078i 0.623516 0.333509i
\(55\) 3.64822 3.64822i 0.491925 0.491925i
\(56\) 1.29181 1.29181i 0.172625 0.172625i
\(57\) −5.54615 + 4.55251i −0.734606 + 0.602994i
\(58\) 6.92241i 0.908957i
\(59\) −0.207760 + 0.207760i −0.0270481 + 0.0270481i −0.720501 0.693453i \(-0.756088\pi\)
0.693453 + 0.720501i \(0.256088\pi\)
\(60\) 1.33879 1.09893i 0.172837 0.141871i
\(61\) −8.45738 + 8.45738i −1.08286 + 1.08286i −0.0866145 + 0.996242i \(0.527605\pi\)
−0.996242 + 0.0866145i \(0.972395\pi\)
\(62\) −8.79291 −1.11670
\(63\) −5.37558 1.06819i −0.677259 0.134579i
\(64\) 1.00000i 0.125000i
\(65\) −4.48188 −0.555908
\(66\) −6.90728 + 5.66978i −0.850227 + 0.697901i
\(67\) 12.0378i 1.47065i −0.677716 0.735323i \(-0.737030\pi\)
0.677716 0.735323i \(-0.262970\pi\)
\(68\) −2.98694 2.98694i −0.362220 0.362220i
\(69\) −5.73439 6.98599i −0.690339 0.841015i
\(70\) −1.82689 −0.218355
\(71\) 11.3303i 1.34466i 0.740253 + 0.672329i \(0.234706\pi\)
−0.740253 + 0.672329i \(0.765294\pi\)
\(72\) −2.49409 + 1.66719i −0.293931 + 0.196481i
\(73\) 10.9001i 1.27576i 0.770138 + 0.637878i \(0.220187\pi\)
−0.770138 + 0.637878i \(0.779813\pi\)
\(74\) −4.41278 + 4.18658i −0.512975 + 0.486680i
\(75\) −1.72373 0.169604i −0.199039 0.0195842i
\(76\) 2.92931 2.92931i 0.336015 0.336015i
\(77\) 9.42559 1.07415
\(78\) 7.72553 + 0.760144i 0.874744 + 0.0860693i
\(79\) 5.32048 + 5.32048i 0.598601 + 0.598601i 0.939940 0.341339i \(-0.110881\pi\)
−0.341339 + 0.939940i \(0.610881\pi\)
\(80\) −0.707107 + 0.707107i −0.0790569 + 0.0790569i
\(81\) 8.31625 + 3.44093i 0.924028 + 0.382326i
\(82\) 0.577147 + 0.577147i 0.0637353 + 0.0637353i
\(83\) 14.3723i 1.57756i 0.614673 + 0.788782i \(0.289288\pi\)
−0.614673 + 0.788782i \(0.710712\pi\)
\(84\) 3.14906 + 0.309848i 0.343591 + 0.0338072i
\(85\) 4.22417i 0.458176i
\(86\) 3.81442i 0.411319i
\(87\) 9.26763 7.60725i 0.993595 0.815583i
\(88\) 3.64822 3.64822i 0.388901 0.388901i
\(89\) −6.37672 6.37672i −0.675931 0.675931i 0.283146 0.959077i \(-0.408622\pi\)
−0.959077 + 0.283146i \(0.908622\pi\)
\(90\) 2.94247 + 0.584702i 0.310163 + 0.0616330i
\(91\) −5.78973 5.78973i −0.606928 0.606928i
\(92\) 3.68979 + 3.68979i 0.384687 + 0.384687i
\(93\) −9.66280 11.7718i −1.00199 1.22068i
\(94\) −4.56930 + 4.56930i −0.471287 + 0.471287i
\(95\) −4.14267 −0.425029
\(96\) 1.33879 1.09893i 0.136639 0.112159i
\(97\) −8.32365 8.32365i −0.845139 0.845139i 0.144383 0.989522i \(-0.453880\pi\)
−0.989522 + 0.144383i \(0.953880\pi\)
\(98\) 2.58975 + 2.58975i 0.261604 + 0.261604i
\(99\) −15.1812 3.01668i −1.52577 0.303188i
\(100\) 1.00000 0.100000
\(101\) 8.26384 0.822283 0.411141 0.911572i \(-0.365130\pi\)
0.411141 + 0.911572i \(0.365130\pi\)
\(102\) 0.716437 7.28132i 0.0709378 0.720959i
\(103\) −8.51882 + 8.51882i −0.839384 + 0.839384i −0.988778 0.149394i \(-0.952268\pi\)
0.149394 + 0.988778i \(0.452268\pi\)
\(104\) −4.48188 −0.439484
\(105\) −2.00763 2.44582i −0.195925 0.238688i
\(106\) −8.61154 + 8.61154i −0.836426 + 0.836426i
\(107\) 7.75936i 0.750126i 0.926999 + 0.375063i \(0.122379\pi\)
−0.926999 + 0.375063i \(0.877621\pi\)
\(108\) −4.97285 1.50692i −0.478512 0.145003i
\(109\) 0.985941 + 0.985941i 0.0944360 + 0.0944360i 0.752747 0.658310i \(-0.228729\pi\)
−0.658310 + 0.752747i \(0.728729\pi\)
\(110\) −5.15936 −0.491925
\(111\) −10.4543 1.30701i −0.992275 0.124056i
\(112\) −1.82689 −0.172625
\(113\) 4.37433 + 4.37433i 0.411502 + 0.411502i 0.882262 0.470759i \(-0.156020\pi\)
−0.470759 + 0.882262i \(0.656020\pi\)
\(114\) 7.14083 + 0.702613i 0.668800 + 0.0658057i
\(115\) 5.21815i 0.486595i
\(116\) −4.89488 + 4.89488i −0.454479 + 0.454479i
\(117\) 7.47216 + 11.1782i 0.690801 + 1.03342i
\(118\) 0.293817 0.0270481
\(119\) −5.45682 + 5.45682i −0.500226 + 0.500226i
\(120\) −1.72373 0.169604i −0.157354 0.0154826i
\(121\) 15.6189 1.41990
\(122\) 11.9605 1.08286
\(123\) −0.138432 + 1.40692i −0.0124820 + 0.126858i
\(124\) 6.21752 + 6.21752i 0.558350 + 0.558350i
\(125\) −0.707107 0.707107i −0.0632456 0.0632456i
\(126\) 3.04578 + 4.55643i 0.271340 + 0.405919i
\(127\) 2.09841 0.186203 0.0931017 0.995657i \(-0.470322\pi\)
0.0931017 + 0.995657i \(0.470322\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −5.10669 + 4.19178i −0.449619 + 0.369066i
\(130\) 3.16917 + 3.16917i 0.277954 + 0.277954i
\(131\) −13.8897 13.8897i −1.21355 1.21355i −0.969851 0.243698i \(-0.921639\pi\)
−0.243698 0.969851i \(-0.578361\pi\)
\(132\) 8.89332 + 0.875047i 0.774064 + 0.0761630i
\(133\) −5.35154 5.35154i −0.464037 0.464037i
\(134\) −8.51198 + 8.51198i −0.735323 + 0.735323i
\(135\) 2.45078 + 4.58189i 0.210929 + 0.394346i
\(136\) 4.22417i 0.362220i
\(137\) 6.46639i 0.552461i −0.961091 0.276231i \(-0.910915\pi\)
0.961091 0.276231i \(-0.0890853\pi\)
\(138\) −0.885019 + 8.99467i −0.0753378 + 0.765677i
\(139\) 1.28795i 0.109243i −0.998507 0.0546213i \(-0.982605\pi\)
0.998507 0.0546213i \(-0.0173952\pi\)
\(140\) 1.29181 + 1.29181i 0.109178 + 0.109178i
\(141\) −11.1387 1.09597i −0.938044 0.0922977i
\(142\) 8.01172 8.01172i 0.672329 0.672329i
\(143\) −16.3509 16.3509i −1.36733 1.36733i
\(144\) 2.94247 + 0.584702i 0.245206 + 0.0487251i
\(145\) 6.92241 0.574875
\(146\) 7.70750 7.70750i 0.637878 0.637878i
\(147\) −0.621168 + 6.31308i −0.0512331 + 0.520694i
\(148\) 6.08066 + 0.159948i 0.499827 + 0.0131476i
\(149\) 5.06286i 0.414766i −0.978260 0.207383i \(-0.933505\pi\)
0.978260 0.207383i \(-0.0664946\pi\)
\(150\) 1.09893 + 1.33879i 0.0897273 + 0.109312i
\(151\) 0.958969i 0.0780398i 0.999238 + 0.0390199i \(0.0124236\pi\)
−0.999238 + 0.0390199i \(0.987576\pi\)
\(152\) −4.14267 −0.336015
\(153\) 10.5355 7.04252i 0.851741 0.569354i
\(154\) −6.66490 6.66490i −0.537073 0.537073i
\(155\) 8.79291i 0.706263i
\(156\) −4.92527 6.00028i −0.394337 0.480407i
\(157\) 23.5311 1.87799 0.938995 0.343932i \(-0.111759\pi\)
0.938995 + 0.343932i \(0.111759\pi\)
\(158\) 7.52430i 0.598601i
\(159\) −20.9925 2.06553i −1.66481 0.163807i
\(160\) 1.00000 0.0790569
\(161\) 6.74085 6.74085i 0.531253 0.531253i
\(162\) −3.44737 8.31358i −0.270851 0.653177i
\(163\) 1.12493 1.12493i 0.0881116 0.0881116i −0.661677 0.749789i \(-0.730155\pi\)
0.749789 + 0.661677i \(0.230155\pi\)
\(164\) 0.816209i 0.0637353i
\(165\) −5.66978 6.90728i −0.441391 0.537731i
\(166\) 10.1627 10.1627i 0.788782 0.788782i
\(167\) −5.15136 + 5.15136i −0.398624 + 0.398624i −0.877748 0.479123i \(-0.840955\pi\)
0.479123 + 0.877748i \(0.340955\pi\)
\(168\) −2.00763 2.44582i −0.154892 0.188699i
\(169\) 7.08722i 0.545171i
\(170\) 2.98694 2.98694i 0.229088 0.229088i
\(171\) 6.90663 + 10.3322i 0.528163 + 0.790121i
\(172\) 2.69720 2.69720i 0.205660 0.205660i
\(173\) 10.8091 0.821800 0.410900 0.911680i \(-0.365215\pi\)
0.410900 + 0.911680i \(0.365215\pi\)
\(174\) −11.9323 1.17407i −0.904589 0.0890059i
\(175\) 1.82689i 0.138100i
\(176\) −5.15936 −0.388901
\(177\) 0.322885 + 0.393359i 0.0242695 + 0.0295667i
\(178\) 9.01804i 0.675931i
\(179\) 8.35712 + 8.35712i 0.624640 + 0.624640i 0.946714 0.322074i \(-0.104380\pi\)
−0.322074 + 0.946714i \(0.604380\pi\)
\(180\) −1.66719 2.49409i −0.124265 0.185898i
\(181\) 25.7306 1.91254 0.956270 0.292484i \(-0.0944819\pi\)
0.956270 + 0.292484i \(0.0944819\pi\)
\(182\) 8.18791i 0.606928i
\(183\) 13.1438 + 16.0126i 0.971618 + 1.18369i
\(184\) 5.21815i 0.384687i
\(185\) −4.18658 4.41278i −0.307803 0.324434i
\(186\) −1.49131 + 15.1566i −0.109348 + 1.11133i
\(187\) −15.4107 + 15.4107i −1.12694 + 1.12694i
\(188\) 6.46196 0.471287
\(189\) −2.75298 + 9.08486i −0.200250 + 0.660826i
\(190\) 2.92931 + 2.92931i 0.212514 + 0.212514i
\(191\) −7.19370 + 7.19370i −0.520518 + 0.520518i −0.917728 0.397210i \(-0.869978\pi\)
0.397210 + 0.917728i \(0.369978\pi\)
\(192\) −1.72373 0.169604i −0.124399 0.0122401i
\(193\) 2.35783 + 2.35783i 0.169720 + 0.169720i 0.786856 0.617136i \(-0.211707\pi\)
−0.617136 + 0.786856i \(0.711707\pi\)
\(194\) 11.7714i 0.845139i
\(195\) −0.760144 + 7.72553i −0.0544350 + 0.553237i
\(196\) 3.66246i 0.261604i
\(197\) 12.5331i 0.892949i −0.894796 0.446474i \(-0.852679\pi\)
0.894796 0.446474i \(-0.147321\pi\)
\(198\) 8.60164 + 12.8679i 0.611292 + 0.914480i
\(199\) 0.389611 0.389611i 0.0276188 0.0276188i −0.693163 0.720781i \(-0.743783\pi\)
0.720781 + 0.693163i \(0.243783\pi\)
\(200\) −0.707107 0.707107i −0.0500000 0.0500000i
\(201\) −20.7498 2.04165i −1.46358 0.144007i
\(202\) −5.84342 5.84342i −0.411141 0.411141i
\(203\) 8.94243 + 8.94243i 0.627635 + 0.627635i
\(204\) −5.65527 + 4.64208i −0.395948 + 0.325010i
\(205\) −0.577147 + 0.577147i −0.0403097 + 0.0403097i
\(206\) 12.0474 0.839384
\(207\) −13.0145 + 8.69967i −0.904571 + 0.604669i
\(208\) 3.16917 + 3.16917i 0.219742 + 0.219742i
\(209\) −15.1133 15.1133i −1.04541 1.04541i
\(210\) −0.309848 + 3.14906i −0.0213816 + 0.217306i
\(211\) 11.3256 0.779683 0.389842 0.920882i \(-0.372530\pi\)
0.389842 + 0.920882i \(0.372530\pi\)
\(212\) 12.1785 0.836426
\(213\) 19.5303 + 1.92166i 1.33820 + 0.131670i
\(214\) 5.48670 5.48670i 0.375063 0.375063i
\(215\) −3.81442 −0.260141
\(216\) 2.45078 + 4.58189i 0.166754 + 0.311758i
\(217\) 11.3587 11.3587i 0.771082 0.771082i
\(218\) 1.39433i 0.0944360i
\(219\) 18.7887 + 1.84869i 1.26962 + 0.124923i
\(220\) 3.64822 + 3.64822i 0.245963 + 0.245963i
\(221\) 18.9322 1.27352
\(222\) 6.46809 + 8.31648i 0.434110 + 0.558166i
\(223\) 5.35541 0.358625 0.179313 0.983792i \(-0.442613\pi\)
0.179313 + 0.983792i \(0.442613\pi\)
\(224\) 1.29181 + 1.29181i 0.0863126 + 0.0863126i
\(225\) −0.584702 + 2.94247i −0.0389801 + 0.196165i
\(226\) 6.18624i 0.411502i
\(227\) 11.4661 11.4661i 0.761032 0.761032i −0.215477 0.976509i \(-0.569130\pi\)
0.976509 + 0.215477i \(0.0691305\pi\)
\(228\) −4.55251 5.54615i −0.301497 0.367303i
\(229\) −20.8218 −1.37595 −0.687973 0.725737i \(-0.741499\pi\)
−0.687973 + 0.725737i \(0.741499\pi\)
\(230\) −3.68979 + 3.68979i −0.243298 + 0.243298i
\(231\) 1.59862 16.2471i 0.105181 1.06898i
\(232\) 6.92241 0.454479
\(233\) 30.2639 1.98265 0.991327 0.131420i \(-0.0419537\pi\)
0.991327 + 0.131420i \(0.0419537\pi\)
\(234\) 2.62056 13.1878i 0.171311 0.862112i
\(235\) −4.56930 4.56930i −0.298068 0.298068i
\(236\) −0.207760 0.207760i −0.0135240 0.0135240i
\(237\) 10.0734 8.26868i 0.654340 0.537109i
\(238\) 7.71712 0.500226
\(239\) −14.0684 + 14.0684i −0.910008 + 0.910008i −0.996272 0.0862646i \(-0.972507\pi\)
0.0862646 + 0.996272i \(0.472507\pi\)
\(240\) 1.09893 + 1.33879i 0.0709357 + 0.0864183i
\(241\) 0.972895 + 0.972895i 0.0626697 + 0.0626697i 0.737747 0.675077i \(-0.235890\pi\)
−0.675077 + 0.737747i \(0.735890\pi\)
\(242\) −11.0443 11.0443i −0.709952 0.709952i
\(243\) 7.34170 13.7513i 0.470970 0.882149i
\(244\) −8.45738 8.45738i −0.541428 0.541428i
\(245\) −2.58975 + 2.58975i −0.165453 + 0.165453i
\(246\) 1.09273 0.896958i 0.0696700 0.0571879i
\(247\) 18.5669i 1.18139i
\(248\) 8.79291i 0.558350i
\(249\) 24.7739 + 2.43760i 1.56998 + 0.154476i
\(250\) 1.00000i 0.0632456i
\(251\) 2.10725 + 2.10725i 0.133009 + 0.133009i 0.770477 0.637468i \(-0.220018\pi\)
−0.637468 + 0.770477i \(0.720018\pi\)
\(252\) 1.06819 5.37558i 0.0672895 0.338629i
\(253\) 19.0369 19.0369i 1.19684 1.19684i
\(254\) −1.48380 1.48380i −0.0931017 0.0931017i
\(255\) 7.28132 + 0.716437i 0.455974 + 0.0448650i
\(256\) 1.00000 0.0625000
\(257\) 0.195695 0.195695i 0.0122071 0.0122071i −0.700977 0.713184i \(-0.747252\pi\)
0.713184 + 0.700977i \(0.247252\pi\)
\(258\) 6.57501 + 0.646940i 0.409342 + 0.0402767i
\(259\) 0.292207 11.1087i 0.0181569 0.690262i
\(260\) 4.48188i 0.277954i
\(261\) −11.5410 17.2651i −0.714370 1.06868i
\(262\) 19.6430i 1.21355i
\(263\) −8.71623 −0.537466 −0.268733 0.963215i \(-0.586605\pi\)
−0.268733 + 0.963215i \(0.586605\pi\)
\(264\) −5.66978 6.90728i −0.348951 0.425114i
\(265\) −8.61154 8.61154i −0.529002 0.529002i
\(266\) 7.56821i 0.464037i
\(267\) −12.0732 + 9.91021i −0.738870 + 0.606495i
\(268\) 12.0378 0.735323
\(269\) 21.2276i 1.29427i 0.762376 + 0.647134i \(0.224033\pi\)
−0.762376 + 0.647134i \(0.775967\pi\)
\(270\) 1.50692 4.97285i 0.0917082 0.302638i
\(271\) 16.3350 0.992282 0.496141 0.868242i \(-0.334750\pi\)
0.496141 + 0.868242i \(0.334750\pi\)
\(272\) 2.98694 2.98694i 0.181110 0.181110i
\(273\) −10.9619 + 8.99795i −0.663442 + 0.544581i
\(274\) −4.57243 + 4.57243i −0.276231 + 0.276231i
\(275\) 5.15936i 0.311121i
\(276\) 6.98599 5.73439i 0.420507 0.345170i
\(277\) 14.7587 14.7587i 0.886767 0.886767i −0.107444 0.994211i \(-0.534267\pi\)
0.994211 + 0.107444i \(0.0342667\pi\)
\(278\) −0.910719 + 0.910719i −0.0546213 + 0.0546213i
\(279\) −21.9303 + 14.6595i −1.31293 + 0.877640i
\(280\) 1.82689i 0.109178i
\(281\) 2.73296 2.73296i 0.163035 0.163035i −0.620875 0.783910i \(-0.713223\pi\)
0.783910 + 0.620875i \(0.213223\pi\)
\(282\) 7.10125 + 8.65119i 0.422873 + 0.515171i
\(283\) 18.4473 18.4473i 1.09658 1.09658i 0.101772 0.994808i \(-0.467549\pi\)
0.994808 0.101772i \(-0.0324511\pi\)
\(284\) −11.3303 −0.672329
\(285\) −0.702613 + 7.14083i −0.0416192 + 0.422986i
\(286\) 23.1236i 1.36733i
\(287\) −1.49113 −0.0880185
\(288\) −1.66719 2.49409i −0.0982403 0.146965i
\(289\) 0.843654i 0.0496267i
\(290\) −4.89488 4.89488i −0.287437 0.287437i
\(291\) −15.7594 + 12.9360i −0.923834 + 0.758320i
\(292\) −10.9001 −0.637878
\(293\) 17.4763i 1.02098i 0.859884 + 0.510490i \(0.170536\pi\)
−0.859884 + 0.510490i \(0.829464\pi\)
\(294\) 4.90326 4.02479i 0.285964 0.234731i
\(295\) 0.293817i 0.0171067i
\(296\) −4.18658 4.41278i −0.243340 0.256487i
\(297\) −7.77474 + 25.6567i −0.451136 + 1.48875i
\(298\) −3.57999 + 3.57999i −0.207383 + 0.207383i
\(299\) −23.3871 −1.35251
\(300\) 0.169604 1.72373i 0.00979209 0.0995194i
\(301\) −4.92749 4.92749i −0.284016 0.284016i
\(302\) 0.678093 0.678093i 0.0390199 0.0390199i
\(303\) 1.40158 14.2446i 0.0805186 0.818331i
\(304\) 2.92931 + 2.92931i 0.168007 + 0.168007i
\(305\) 11.9605i 0.684859i
\(306\) −12.4295 2.46988i −0.710547 0.141194i
\(307\) 1.88574i 0.107625i 0.998551 + 0.0538125i \(0.0171373\pi\)
−0.998551 + 0.0538125i \(0.982863\pi\)
\(308\) 9.42559i 0.537073i
\(309\) 13.2393 + 16.1289i 0.753157 + 0.917543i
\(310\) −6.21752 + 6.21752i −0.353132 + 0.353132i
\(311\) 11.7011 + 11.7011i 0.663511 + 0.663511i 0.956206 0.292695i \(-0.0945521\pi\)
−0.292695 + 0.956206i \(0.594552\pi\)
\(312\) −0.760144 + 7.72553i −0.0430347 + 0.437372i
\(313\) −11.8759 11.8759i −0.671265 0.671265i 0.286743 0.958008i \(-0.407428\pi\)
−0.958008 + 0.286743i \(0.907428\pi\)
\(314\) −16.6390 16.6390i −0.938995 0.938995i
\(315\) −4.55643 + 3.04578i −0.256726 + 0.171610i
\(316\) −5.32048 + 5.32048i −0.299300 + 0.299300i
\(317\) 15.5170 0.871524 0.435762 0.900062i \(-0.356479\pi\)
0.435762 + 0.900062i \(0.356479\pi\)
\(318\) 13.3834 + 16.3045i 0.750503 + 0.914310i
\(319\) 25.2544 + 25.2544i 1.41398 + 1.41398i
\(320\) −0.707107 0.707107i −0.0395285 0.0395285i
\(321\) 13.3750 + 1.31602i 0.746521 + 0.0734530i
\(322\) −9.53300 −0.531253
\(323\) 17.4994 0.973690
\(324\) −3.44093 + 8.31625i −0.191163 + 0.462014i
\(325\) −3.16917 + 3.16917i −0.175794 + 0.175794i
\(326\) −1.59090 −0.0881116
\(327\) 1.86671 1.53227i 0.103229 0.0847349i
\(328\) −0.577147 + 0.577147i −0.0318676 + 0.0318676i
\(329\) 11.8053i 0.650848i
\(330\) −0.875047 + 8.89332i −0.0481697 + 0.489561i
\(331\) 14.6764 + 14.6764i 0.806690 + 0.806690i 0.984131 0.177441i \(-0.0567819\pi\)
−0.177441 + 0.984131i \(0.556782\pi\)
\(332\) −14.3723 −0.788782
\(333\) −4.02601 + 17.7986i −0.220624 + 0.975359i
\(334\) 7.28513 0.398624
\(335\) −8.51198 8.51198i −0.465059 0.465059i
\(336\) −0.309848 + 3.14906i −0.0169036 + 0.171796i
\(337\) 4.00664i 0.218255i 0.994028 + 0.109128i \(0.0348057\pi\)
−0.994028 + 0.109128i \(0.965194\pi\)
\(338\) 5.01142 5.01142i 0.272585 0.272585i
\(339\) 8.28206 6.79825i 0.449820 0.369230i
\(340\) −4.22417 −0.229088
\(341\) 32.0784 32.0784i 1.73714 1.73714i
\(342\) 2.42223 12.1897i 0.130979 0.659142i
\(343\) −19.4792 −1.05178
\(344\) −3.81442 −0.205660
\(345\) −8.99467 0.885019i −0.484257 0.0476478i
\(346\) −7.64318 7.64318i −0.410900 0.410900i
\(347\) 4.04747 + 4.04747i 0.217280 + 0.217280i 0.807351 0.590071i \(-0.200900\pi\)
−0.590071 + 0.807351i \(0.700900\pi\)
\(348\) 7.60725 + 9.26763i 0.407791 + 0.496797i
\(349\) −22.3766 −1.19779 −0.598897 0.800826i \(-0.704394\pi\)
−0.598897 + 0.800826i \(0.704394\pi\)
\(350\) −1.29181 + 1.29181i −0.0690501 + 0.0690501i
\(351\) 20.5355 10.9841i 1.09610 0.586287i
\(352\) 3.64822 + 3.64822i 0.194451 + 0.194451i
\(353\) 23.6622 + 23.6622i 1.25941 + 1.25941i 0.951374 + 0.308038i \(0.0996724\pi\)
0.308038 + 0.951374i \(0.400328\pi\)
\(354\) 0.0498326 0.506461i 0.00264857 0.0269181i
\(355\) 8.01172 + 8.01172i 0.425218 + 0.425218i
\(356\) 6.37672 6.37672i 0.337965 0.337965i
\(357\) 8.48058 + 10.3316i 0.448840 + 0.546805i
\(358\) 11.8187i 0.624640i
\(359\) 6.19534i 0.326977i 0.986545 + 0.163489i \(0.0522747\pi\)
−0.986545 + 0.163489i \(0.947725\pi\)
\(360\) −0.584702 + 2.94247i −0.0308165 + 0.155082i
\(361\) 1.83829i 0.0967521i
\(362\) −18.1943 18.1943i −0.956270 0.956270i
\(363\) 2.64903 26.9228i 0.139038 1.41308i
\(364\) 5.78973 5.78973i 0.303464 0.303464i
\(365\) 7.70750 + 7.70750i 0.403429 + 0.403429i
\(366\) 2.02855 20.6167i 0.106034 1.07765i
\(367\) −33.1126 −1.72846 −0.864231 0.503095i \(-0.832194\pi\)
−0.864231 + 0.503095i \(0.832194\pi\)
\(368\) −3.68979 + 3.68979i −0.192344 + 0.192344i
\(369\) 2.40167 + 0.477239i 0.125026 + 0.0248441i
\(370\) −0.159948 + 6.08066i −0.00831528 + 0.316118i
\(371\) 22.2489i 1.15511i
\(372\) 11.7718 9.66280i 0.610341 0.500993i
\(373\) 31.8445i 1.64884i 0.565976 + 0.824422i \(0.308499\pi\)
−0.565976 + 0.824422i \(0.691501\pi\)
\(374\) 21.7940 1.12694
\(375\) −1.33879 + 1.09893i −0.0691347 + 0.0567485i
\(376\) −4.56930 4.56930i −0.235644 0.235644i
\(377\) 31.0254i 1.59789i
\(378\) 8.37062 4.47731i 0.430538 0.230288i
\(379\) 18.1662 0.933133 0.466567 0.884486i \(-0.345491\pi\)
0.466567 + 0.884486i \(0.345491\pi\)
\(380\) 4.14267i 0.212514i
\(381\) 0.355898 3.61708i 0.0182332 0.185309i
\(382\) 10.1734 0.520518
\(383\) −18.6163 + 18.6163i −0.951247 + 0.951247i −0.998866 0.0476184i \(-0.984837\pi\)
0.0476184 + 0.998866i \(0.484837\pi\)
\(384\) 1.09893 + 1.33879i 0.0560796 + 0.0683197i
\(385\) 6.66490 6.66490i 0.339675 0.339675i
\(386\) 3.33448i 0.169720i
\(387\) 6.35937 + 9.51348i 0.323265 + 0.483598i
\(388\) 8.32365 8.32365i 0.422569 0.422569i
\(389\) 2.92340 2.92340i 0.148222 0.148222i −0.629101 0.777323i \(-0.716577\pi\)
0.777323 + 0.629101i \(0.216577\pi\)
\(390\) 6.00028 4.92527i 0.303836 0.249401i
\(391\) 22.0424i 1.11473i
\(392\) −2.58975 + 2.58975i −0.130802 + 0.130802i
\(393\) −26.2978 + 21.5863i −1.32655 + 1.08889i
\(394\) −8.86227 + 8.86227i −0.446474 + 0.446474i
\(395\) 7.52430 0.378588
\(396\) 3.01668 15.1812i 0.151594 0.762886i
\(397\) 30.6306i 1.53730i 0.639667 + 0.768652i \(0.279072\pi\)
−0.639667 + 0.768652i \(0.720928\pi\)
\(398\) −0.550993 −0.0276188
\(399\) −10.1322 + 8.31694i −0.507246 + 0.416368i
\(400\) 1.00000i 0.0500000i
\(401\) 0.362967 + 0.362967i 0.0181257 + 0.0181257i 0.716112 0.697986i \(-0.245920\pi\)
−0.697986 + 0.716112i \(0.745920\pi\)
\(402\) 13.2287 + 16.1160i 0.659786 + 0.803793i
\(403\) −39.4087 −1.96309
\(404\) 8.26384i 0.411141i
\(405\) 8.31358 3.44737i 0.413105 0.171301i
\(406\) 12.6465i 0.627635i
\(407\) 0.825226 31.3723i 0.0409050 1.55507i
\(408\) 7.28132 + 0.716437i 0.360479 + 0.0354689i
\(409\) 15.8169 15.8169i 0.782097 0.782097i −0.198087 0.980184i \(-0.563473\pi\)
0.980184 + 0.198087i \(0.0634729\pi\)
\(410\) 0.816209 0.0403097
\(411\) −11.1463 1.09673i −0.549806 0.0540975i
\(412\) −8.51882 8.51882i −0.419692 0.419692i
\(413\) −0.379556 + 0.379556i −0.0186767 + 0.0186767i
\(414\) 15.3542 + 3.05106i 0.754620 + 0.149951i
\(415\) 10.1627 + 10.1627i 0.498870 + 0.498870i
\(416\) 4.48188i 0.219742i
\(417\) −2.22008 0.218442i −0.108718 0.0106971i
\(418\) 21.3735i 1.04541i
\(419\) 31.1819i 1.52333i 0.647969 + 0.761667i \(0.275619\pi\)
−0.647969 + 0.761667i \(0.724381\pi\)
\(420\) 2.44582 2.00763i 0.119344 0.0979623i
\(421\) −6.58898 + 6.58898i −0.321127 + 0.321127i −0.849200 0.528072i \(-0.822915\pi\)
0.528072 + 0.849200i \(0.322915\pi\)
\(422\) −8.00838 8.00838i −0.389842 0.389842i
\(423\) −3.77832 + 19.0141i −0.183708 + 0.924499i
\(424\) −8.61154 8.61154i −0.418213 0.418213i
\(425\) 2.98694 + 2.98694i 0.144888 + 0.144888i
\(426\) −12.4512 15.1688i −0.603263 0.734933i
\(427\) −15.4507 + 15.4507i −0.747713 + 0.747713i
\(428\) −7.75936 −0.375063
\(429\) −30.9576 + 25.4112i −1.49465 + 1.22687i
\(430\) 2.69720 + 2.69720i 0.130071 + 0.130071i
\(431\) 14.4596 + 14.4596i 0.696496 + 0.696496i 0.963653 0.267157i \(-0.0860842\pi\)
−0.267157 + 0.963653i \(0.586084\pi\)
\(432\) 1.50692 4.97285i 0.0725017 0.239256i
\(433\) −15.9254 −0.765327 −0.382663 0.923888i \(-0.624993\pi\)
−0.382663 + 0.923888i \(0.624993\pi\)
\(434\) −16.0637 −0.771082
\(435\) 1.17407 11.9323i 0.0562922 0.572112i
\(436\) −0.985941 + 0.985941i −0.0472180 + 0.0472180i
\(437\) −21.6171 −1.03408
\(438\) −11.9784 14.5929i −0.572351 0.697274i
\(439\) 22.9843 22.9843i 1.09698 1.09698i 0.102218 0.994762i \(-0.467406\pi\)
0.994762 0.102218i \(-0.0325940\pi\)
\(440\) 5.15936i 0.245963i
\(441\) 10.7767 + 2.14145i 0.513175 + 0.101974i
\(442\) −13.3871 13.3871i −0.636760 0.636760i
\(443\) 32.8593 1.56119 0.780595 0.625037i \(-0.214916\pi\)
0.780595 + 0.625037i \(0.214916\pi\)
\(444\) 1.30701 10.4543i 0.0620279 0.496138i
\(445\) −9.01804 −0.427496
\(446\) −3.78685 3.78685i −0.179313 0.179313i
\(447\) −8.72699 0.858681i −0.412773 0.0406142i
\(448\) 1.82689i 0.0863126i
\(449\) 16.6345 16.6345i 0.785033 0.785033i −0.195643 0.980675i \(-0.562679\pi\)
0.980675 + 0.195643i \(0.0626793\pi\)
\(450\) 2.49409 1.66719i 0.117572 0.0785922i
\(451\) −4.21111 −0.198294
\(452\) −4.37433 + 4.37433i −0.205751 + 0.205751i
\(453\) 1.65300 + 0.162645i 0.0776647 + 0.00764172i
\(454\) −16.2155 −0.761032
\(455\) −8.18791 −0.383855
\(456\) −0.702613 + 7.14083i −0.0329029 + 0.334400i
\(457\) 5.71433 + 5.71433i 0.267305 + 0.267305i 0.828013 0.560708i \(-0.189471\pi\)
−0.560708 + 0.828013i \(0.689471\pi\)
\(458\) 14.7233 + 14.7233i 0.687973 + 0.687973i
\(459\) −10.3525 19.3547i −0.483214 0.903400i
\(460\) 5.21815 0.243298
\(461\) −14.0336 + 14.0336i −0.653612 + 0.653612i −0.953861 0.300249i \(-0.902930\pi\)
0.300249 + 0.953861i \(0.402930\pi\)
\(462\) −12.6189 + 10.3581i −0.587082 + 0.481901i
\(463\) −24.6253 24.6253i −1.14443 1.14443i −0.987630 0.156805i \(-0.949880\pi\)
−0.156805 0.987630i \(-0.550120\pi\)
\(464\) −4.89488 4.89488i −0.227239 0.227239i
\(465\) −15.1566 1.49131i −0.702869 0.0691579i
\(466\) −21.3998 21.3998i −0.991327 0.991327i
\(467\) 24.1276 24.1276i 1.11649 1.11649i 0.124239 0.992252i \(-0.460351\pi\)
0.992252 0.124239i \(-0.0396488\pi\)
\(468\) −11.1782 + 7.47216i −0.516712 + 0.345401i
\(469\) 21.9917i 1.01548i
\(470\) 6.46196i 0.298068i
\(471\) 3.99097 40.5613i 0.183894 1.86896i
\(472\) 0.293817i 0.0135240i
\(473\) −13.9158 13.9158i −0.639850 0.639850i
\(474\) −12.9698 1.27615i −0.595724 0.0586155i
\(475\) −2.92931 + 2.92931i −0.134406 + 0.134406i
\(476\) −5.45682 5.45682i −0.250113 0.250113i
\(477\) −7.12082 + 35.8350i −0.326040 + 1.64077i
\(478\) 19.8957 0.910008
\(479\) 9.10014 9.10014i 0.415796 0.415796i −0.467956 0.883752i \(-0.655009\pi\)
0.883752 + 0.467956i \(0.155009\pi\)
\(480\) 0.169604 1.72373i 0.00774132 0.0786770i
\(481\) −19.7775 + 18.7637i −0.901777 + 0.855552i
\(482\) 1.37588i 0.0626697i
\(483\) −10.4761 12.7627i −0.476680 0.580721i
\(484\) 15.6189i 0.709952i
\(485\) −11.7714 −0.534513
\(486\) −14.9150 + 4.53231i −0.676560 + 0.205590i
\(487\) −3.65154 3.65154i −0.165467 0.165467i 0.619517 0.784984i \(-0.287329\pi\)
−0.784984 + 0.619517i \(0.787329\pi\)
\(488\) 11.9605i 0.541428i
\(489\) −1.74829 2.12987i −0.0790602 0.0963162i
\(490\) 3.66246 0.165453
\(491\) 9.68790i 0.437209i −0.975814 0.218604i \(-0.929850\pi\)
0.975814 0.218604i \(-0.0701504\pi\)
\(492\) −1.40692 0.138432i −0.0634290 0.00624101i
\(493\) −29.2415 −1.31697
\(494\) 13.1288 13.1288i 0.590693 0.590693i
\(495\) −12.8679 + 8.60164i −0.578368 + 0.386615i
\(496\) −6.21752 + 6.21752i −0.279175 + 0.279175i
\(497\) 20.6992i 0.928487i
\(498\) −15.7942 19.2414i −0.707753 0.862230i
\(499\) 14.5609 14.5609i 0.651836 0.651836i −0.301599 0.953435i \(-0.597520\pi\)
0.953435 + 0.301599i \(0.0975203\pi\)
\(500\) 0.707107 0.707107i 0.0316228 0.0316228i
\(501\) 8.00585 + 9.75323i 0.357675 + 0.435742i
\(502\) 2.98011i 0.133009i
\(503\) −16.9725 + 16.9725i −0.756766 + 0.756766i −0.975732 0.218966i \(-0.929732\pi\)
0.218966 + 0.975732i \(0.429732\pi\)
\(504\) −4.55643 + 3.04578i −0.202959 + 0.135670i
\(505\) 5.84342 5.84342i 0.260029 0.260029i
\(506\) −26.9223 −1.19684
\(507\) 12.2164 + 1.20202i 0.542551 + 0.0533836i
\(508\) 2.09841i 0.0931017i
\(509\) −15.8798 −0.703858 −0.351929 0.936027i \(-0.614474\pi\)
−0.351929 + 0.936027i \(0.614474\pi\)
\(510\) −4.64208 5.65527i −0.205555 0.250420i
\(511\) 19.9132i 0.880910i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 18.9812 10.1528i 0.838042 0.448256i
\(514\) −0.276755 −0.0122071
\(515\) 12.0474i 0.530873i
\(516\) −4.19178 5.10669i −0.184533 0.224810i
\(517\) 33.3396i 1.46627i
\(518\) −8.06167 + 7.64843i −0.354209 + 0.336053i
\(519\) 1.83326 18.6319i 0.0804714 0.817851i
\(520\) −3.16917 + 3.16917i −0.138977 + 0.138977i
\(521\) −6.74121 −0.295338 −0.147669 0.989037i \(-0.547177\pi\)
−0.147669 + 0.989037i \(0.547177\pi\)
\(522\) −4.04754 + 20.3690i −0.177156 + 0.891526i
\(523\) 0.762505 + 0.762505i 0.0333420 + 0.0333420i 0.723581 0.690239i \(-0.242495\pi\)
−0.690239 + 0.723581i \(0.742495\pi\)
\(524\) 13.8897 13.8897i 0.606775 0.606775i
\(525\) −3.14906 0.309848i −0.137436 0.0135229i
\(526\) 6.16330 + 6.16330i 0.268733 + 0.268733i
\(527\) 37.1428i 1.61796i
\(528\) −0.875047 + 8.89332i −0.0380815 + 0.387032i
\(529\) 4.22909i 0.183874i
\(530\) 12.1785i 0.529002i
\(531\) 0.732806 0.489850i 0.0318011 0.0212577i
\(532\) 5.35154 5.35154i 0.232018 0.232018i
\(533\) 2.58670 + 2.58670i 0.112043 + 0.112043i
\(534\) 15.5446 + 1.52950i 0.672682 + 0.0661877i
\(535\) 5.48670 + 5.48670i 0.237211 + 0.237211i
\(536\) −8.51198 8.51198i −0.367662 0.367662i
\(537\) 15.8228 12.9880i 0.682804 0.560473i
\(538\) 15.0102 15.0102i 0.647134 0.647134i
\(539\) −18.8959 −0.813906
\(540\) −4.58189 + 2.45078i −0.197173 + 0.105465i
\(541\) −30.2618 30.2618i −1.30106 1.30106i −0.927679 0.373379i \(-0.878199\pi\)
−0.373379 0.927679i \(-0.621801\pi\)
\(542\) −11.5506 11.5506i −0.496141 0.496141i
\(543\) 4.36401 44.3525i 0.187278 1.90335i
\(544\) −4.22417 −0.181110
\(545\) 1.39433 0.0597266
\(546\) 14.1137 + 1.38870i 0.604011 + 0.0594309i
\(547\) −13.5953 + 13.5953i −0.581292 + 0.581292i −0.935258 0.353966i \(-0.884833\pi\)
0.353966 + 0.935258i \(0.384833\pi\)
\(548\) 6.46639 0.276231
\(549\) 29.8306 19.9405i 1.27314 0.851041i
\(550\) −3.64822 + 3.64822i −0.155560 + 0.155560i
\(551\) 28.6773i 1.22169i
\(552\) −8.99467 0.885019i −0.382838 0.0376689i
\(553\) 9.71995 + 9.71995i 0.413334 + 0.413334i
\(554\) −20.8720 −0.886767
\(555\) −8.31648 + 6.46809i −0.353015 + 0.274555i
\(556\) 1.28795 0.0546213
\(557\) −19.8919 19.8919i −0.842846 0.842846i 0.146382 0.989228i \(-0.453237\pi\)
−0.989228 + 0.146382i \(0.953237\pi\)
\(558\) 25.8729 + 5.14123i 1.09529 + 0.217645i
\(559\) 17.0957i 0.723073i
\(560\) −1.29181 + 1.29181i −0.0545889 + 0.0545889i
\(561\) 23.9501 + 29.1776i 1.01117 + 1.23188i
\(562\) −3.86499 −0.163035
\(563\) −0.570464 + 0.570464i −0.0240422 + 0.0240422i −0.719026 0.694983i \(-0.755412\pi\)
0.694983 + 0.719026i \(0.255412\pi\)
\(564\) 1.09597 11.1387i 0.0461488 0.469022i
\(565\) 6.18624 0.260257
\(566\) −26.0884 −1.09658
\(567\) 15.1929 + 6.28622i 0.638042 + 0.263996i
\(568\) 8.01172 + 8.01172i 0.336164 + 0.336164i
\(569\) 21.4414 + 21.4414i 0.898870 + 0.898870i 0.995336 0.0964667i \(-0.0307541\pi\)
−0.0964667 + 0.995336i \(0.530754\pi\)
\(570\) 5.54615 4.55251i 0.232303 0.190684i
\(571\) −23.9185 −1.00096 −0.500480 0.865748i \(-0.666843\pi\)
−0.500480 + 0.865748i \(0.666843\pi\)
\(572\) 16.3509 16.3509i 0.683663 0.683663i
\(573\) 11.1799 + 13.6201i 0.467047 + 0.568986i
\(574\) 1.05439 + 1.05439i 0.0440092 + 0.0440092i
\(575\) −3.68979 3.68979i −0.153875 0.153875i
\(576\) −0.584702 + 2.94247i −0.0243626 + 0.122603i
\(577\) −24.0238 24.0238i −1.00012 1.00012i −1.00000 0.000123162i \(-0.999961\pi\)
−0.000123162 1.00000i \(-0.500039\pi\)
\(578\) −0.596554 + 0.596554i −0.0248134 + 0.0248134i
\(579\) 4.46416 3.66436i 0.185524 0.152286i
\(580\) 6.92241i 0.287437i
\(581\) 26.2566i 1.08931i
\(582\) 20.2907 + 1.99648i 0.841077 + 0.0827567i
\(583\) 62.8335i 2.60230i
\(584\) 7.70750 + 7.70750i 0.318939 + 0.318939i
\(585\) 13.1878 + 2.62056i 0.545248 + 0.108347i
\(586\) 12.3576 12.3576i 0.510490 0.510490i
\(587\) 7.33897 + 7.33897i 0.302912 + 0.302912i 0.842152 0.539240i \(-0.181289\pi\)
−0.539240 + 0.842152i \(0.681289\pi\)
\(588\) −6.31308 0.621168i −0.260347 0.0256165i
\(589\) −36.4261 −1.50091
\(590\) 0.207760 0.207760i 0.00855335 0.00855335i
\(591\) −21.6037 2.12567i −0.888658 0.0874383i
\(592\) −0.159948 + 6.08066i −0.00657380 + 0.249914i
\(593\) 4.63342i 0.190272i −0.995464 0.0951358i \(-0.969671\pi\)
0.995464 0.0951358i \(-0.0303285\pi\)
\(594\) 23.6396 12.6444i 0.969944 0.518808i
\(595\) 7.71712i 0.316371i
\(596\) 5.06286 0.207383
\(597\) −0.605504 0.737663i −0.0247816 0.0301905i
\(598\) 16.5372 + 16.5372i 0.676256 + 0.676256i
\(599\) 3.41553i 0.139555i 0.997563 + 0.0697773i \(0.0222289\pi\)
−0.997563 + 0.0697773i \(0.977771\pi\)
\(600\) −1.33879 + 1.09893i −0.0546558 + 0.0448637i
\(601\) 39.9252 1.62858 0.814290 0.580458i \(-0.197126\pi\)
0.814290 + 0.580458i \(0.197126\pi\)
\(602\) 6.96853i 0.284016i
\(603\) −7.03850 + 35.4207i −0.286630 + 1.44244i
\(604\) −0.958969 −0.0390199
\(605\) 11.0443 11.0443i 0.449013 0.449013i
\(606\) −11.0635 + 9.08139i −0.449425 + 0.368906i
\(607\) −8.29532 + 8.29532i −0.336697 + 0.336697i −0.855123 0.518426i \(-0.826518\pi\)
0.518426 + 0.855123i \(0.326518\pi\)
\(608\) 4.14267i 0.168007i
\(609\) 16.9310 13.8976i 0.686078 0.563161i
\(610\) 8.45738 8.45738i 0.342429 0.342429i
\(611\) −20.4790 + 20.4790i −0.828493 + 0.828493i
\(612\) 7.04252 + 10.5355i 0.284677 + 0.425871i
\(613\) 2.23084i 0.0901029i −0.998985 0.0450515i \(-0.985655\pi\)
0.998985 0.0450515i \(-0.0143452\pi\)
\(614\) 1.33342 1.33342i 0.0538125 0.0538125i
\(615\) 0.896958 + 1.09273i 0.0361688 + 0.0440632i
\(616\) 6.66490 6.66490i 0.268536 0.268536i
\(617\) −18.5224 −0.745682 −0.372841 0.927895i \(-0.621616\pi\)
−0.372841 + 0.927895i \(0.621616\pi\)
\(618\) 2.04329 20.7665i 0.0821932 0.835350i
\(619\) 20.8999i 0.840038i 0.907515 + 0.420019i \(0.137977\pi\)
−0.907515 + 0.420019i \(0.862023\pi\)
\(620\) 8.79291 0.353132
\(621\) 12.7885 + 23.9090i 0.513186 + 0.959434i
\(622\) 16.5479i 0.663511i
\(623\) −11.6496 11.6496i −0.466731 0.466731i
\(624\) 6.00028 4.92527i 0.240203 0.197169i
\(625\) −1.00000 −0.0400000
\(626\) 16.7950i 0.671265i
\(627\) −28.6146 + 23.4880i −1.14276 + 0.938021i
\(628\) 23.5311i 0.938995i
\(629\) 17.6848 + 18.6403i 0.705140 + 0.743239i
\(630\) 5.37558 + 1.06819i 0.214168 + 0.0425576i
\(631\) 28.0515 28.0515i 1.11671 1.11671i 0.124492 0.992221i \(-0.460270\pi\)
0.992221 0.124492i \(-0.0397300\pi\)
\(632\) 7.52430 0.299300
\(633\) 1.92086 19.5222i 0.0763473 0.775936i
\(634\) −10.9722 10.9722i −0.435762 0.435762i
\(635\) 1.48380 1.48380i 0.0588827 0.0588827i
\(636\) 2.06553 20.9925i 0.0819036 0.832407i
\(637\) 11.6069 + 11.6069i 0.459884 + 0.459884i
\(638\) 35.7152i 1.41398i
\(639\) 6.62484 33.3390i 0.262075 1.31887i
\(640\) 1.00000i 0.0395285i
\(641\) 11.3698i 0.449079i 0.974465 + 0.224540i \(0.0720878\pi\)
−0.974465 + 0.224540i \(0.927912\pi\)
\(642\) −8.52700 10.3881i −0.336534 0.409987i
\(643\) 7.89477 7.89477i 0.311339 0.311339i −0.534089 0.845428i \(-0.679345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(644\) 6.74085 + 6.74085i 0.265627 + 0.265627i
\(645\) −0.646940 + 6.57501i −0.0254732 + 0.258891i
\(646\) −12.3739 12.3739i −0.486845 0.486845i
\(647\) −18.1698 18.1698i −0.714327 0.714327i 0.253110 0.967437i \(-0.418546\pi\)
−0.967437 + 0.253110i \(0.918546\pi\)
\(648\) 8.31358 3.44737i 0.326588 0.135425i
\(649\) −1.07191 + 1.07191i −0.0420761 + 0.0420761i
\(650\) 4.48188 0.175794
\(651\) −17.6529 21.5059i −0.691871 0.842881i
\(652\) 1.12493 + 1.12493i 0.0440558 + 0.0440558i
\(653\) −16.0946 16.0946i −0.629832 0.629832i 0.318194 0.948026i \(-0.396924\pi\)
−0.948026 + 0.318194i \(0.896924\pi\)
\(654\) −2.40345 0.236484i −0.0939822 0.00924726i
\(655\) −19.6430 −0.767516
\(656\) 0.816209 0.0318676
\(657\) 6.37328 32.0731i 0.248645 1.25129i
\(658\) −8.34762 + 8.34762i −0.325424 + 0.325424i
\(659\) 22.0332 0.858292 0.429146 0.903235i \(-0.358815\pi\)
0.429146 + 0.903235i \(0.358815\pi\)
\(660\) 6.90728 5.66978i 0.268865 0.220696i
\(661\) −2.53133 + 2.53133i −0.0984575 + 0.0984575i −0.754620 0.656162i \(-0.772179\pi\)
0.656162 + 0.754620i \(0.272179\pi\)
\(662\) 20.7556i 0.806690i
\(663\) 3.21098 32.6340i 0.124704 1.26740i
\(664\) 10.1627 + 10.1627i 0.394391 + 0.394391i
\(665\) −7.56821 −0.293483
\(666\) 15.4324 9.73871i 0.597992 0.377367i
\(667\) 36.1222 1.39866
\(668\) −5.15136 5.15136i −0.199312 0.199312i
\(669\) 0.908299 9.23127i 0.0351169 0.356902i
\(670\) 12.0378i 0.465059i
\(671\) −43.6346 + 43.6346i −1.68450 + 1.68450i
\(672\) 2.44582 2.00763i 0.0943496 0.0774460i
\(673\) 25.6452 0.988550 0.494275 0.869306i \(-0.335434\pi\)
0.494275 + 0.869306i \(0.335434\pi\)
\(674\) 2.83312 2.83312i 0.109128 0.109128i
\(675\) 4.97285 + 1.50692i 0.191405 + 0.0580014i
\(676\) −7.08722 −0.272585
\(677\) 36.1424 1.38907 0.694533 0.719461i \(-0.255611\pi\)
0.694533 + 0.719461i \(0.255611\pi\)
\(678\) −10.6634 1.04921i −0.409525 0.0402947i
\(679\) −15.2064 15.2064i −0.583569 0.583569i
\(680\) 2.98694 + 2.98694i 0.114544 + 0.114544i
\(681\) −17.8197 21.7091i −0.682854 0.831896i
\(682\) −45.3657 −1.73714
\(683\) −13.8969 + 13.8969i −0.531749 + 0.531749i −0.921093 0.389344i \(-0.872702\pi\)
0.389344 + 0.921093i \(0.372702\pi\)
\(684\) −10.3322 + 6.90663i −0.395061 + 0.264082i
\(685\) −4.57243 4.57243i −0.174704 0.174704i
\(686\) 13.7739 + 13.7739i 0.525888 + 0.525888i
\(687\) −3.53146 + 35.8911i −0.134734 + 1.36933i
\(688\) 2.69720 + 2.69720i 0.102830 + 0.102830i
\(689\) −38.5958 + 38.5958i −1.47038 + 1.47038i
\(690\) 5.73439 + 6.98599i 0.218304 + 0.265952i
\(691\) 45.4792i 1.73011i 0.501678 + 0.865055i \(0.332716\pi\)
−0.501678 + 0.865055i \(0.667284\pi\)
\(692\) 10.8091i 0.410900i
\(693\) −27.7345 5.51116i −1.05355 0.209352i
\(694\) 5.72399i 0.217280i
\(695\) −0.910719 0.910719i −0.0345456 0.0345456i
\(696\) 1.17407 11.9323i 0.0445029 0.452294i
\(697\) 2.43797 2.43797i 0.0923447 0.0923447i
\(698\) 15.8227 + 15.8227i 0.598897 + 0.598897i
\(699\) 5.13287 52.1667i 0.194143 1.97313i
\(700\) 1.82689 0.0690501
\(701\) −15.8539 + 15.8539i −0.598793 + 0.598793i −0.939991 0.341199i \(-0.889167\pi\)
0.341199 + 0.939991i \(0.389167\pi\)
\(702\) −22.2877 6.75383i −0.841194 0.254907i
\(703\) −18.2807 + 17.3436i −0.689469 + 0.654126i
\(704\) 5.15936i 0.194451i
\(705\) −8.65119 + 7.10125i −0.325823 + 0.267449i
\(706\) 33.4634i 1.25941i
\(707\) 15.0972 0.567787
\(708\) −0.393359 + 0.322885i −0.0147833 + 0.0121348i
\(709\) −10.2894 10.2894i −0.386425 0.386425i 0.486985 0.873410i \(-0.338097\pi\)
−0.873410 + 0.486985i \(0.838097\pi\)
\(710\) 11.3303i 0.425218i
\(711\) −12.5445 18.7662i −0.470454 0.703789i
\(712\) −9.01804 −0.337965
\(713\) 45.8827i 1.71832i
\(714\) 1.30885 13.3022i 0.0489826 0.497822i
\(715\) −23.1236 −0.864773
\(716\) −8.35712 + 8.35712i −0.312320 + 0.312320i
\(717\) 21.8640 + 26.6361i 0.816526 + 0.994743i
\(718\) 4.38077 4.38077i 0.163489 0.163489i
\(719\) 29.1987i 1.08893i 0.838784 + 0.544464i \(0.183267\pi\)
−0.838784 + 0.544464i \(0.816733\pi\)
\(720\) 2.49409 1.66719i 0.0929491 0.0621326i
\(721\) −15.5630 + 15.5630i −0.579595 + 0.579595i
\(722\) −1.29987 + 1.29987i −0.0483761 + 0.0483761i
\(723\) 1.84201 1.51200i 0.0685052 0.0562318i
\(724\) 25.7306i 0.956270i
\(725\) 4.89488 4.89488i 0.181791 0.181791i
\(726\) −20.9104 + 17.1641i −0.776059 + 0.637021i
\(727\) −11.2358 + 11.2358i −0.416714 + 0.416714i −0.884070 0.467355i \(-0.845207\pi\)
0.467355 + 0.884070i \(0.345207\pi\)
\(728\) −8.18791 −0.303464
\(729\) −22.4584 14.9874i −0.831792 0.555087i
\(730\) 10.9001i 0.403429i
\(731\) 16.1128 0.595952
\(732\) −16.0126 + 13.1438i −0.591843 + 0.485809i
\(733\) 29.6661i 1.09574i 0.836562 + 0.547872i \(0.184562\pi\)
−0.836562 + 0.547872i \(0.815438\pi\)
\(734\) 23.4141 + 23.4141i 0.864231 + 0.864231i
\(735\) 4.02479 + 4.90326i 0.148457 + 0.180859i
\(736\) 5.21815 0.192344
\(737\) 62.1071i 2.28774i
\(738\) −1.36078 2.03570i −0.0500910 0.0749350i
\(739\) 29.5097i 1.08553i −0.839883 0.542767i \(-0.817377\pi\)
0.839883 0.542767i \(-0.182623\pi\)
\(740\) 4.41278 4.18658i 0.162217 0.153902i
\(741\) 32.0043 + 3.14902i 1.17571 + 0.115682i
\(742\) −15.7324 + 15.7324i −0.577553 + 0.577553i
\(743\) 21.3251 0.782344 0.391172 0.920318i \(-0.372070\pi\)
0.391172 + 0.920318i \(0.372070\pi\)
\(744\) −15.1566 1.49131i −0.555667 0.0546741i
\(745\) −3.57999 3.57999i −0.131161 0.131161i
\(746\) 22.5174 22.5174i 0.824422 0.824422i
\(747\) 8.40350 42.2900i 0.307468 1.54731i
\(748\) −15.4107 15.4107i −0.563471 0.563471i
\(749\) 14.1755i 0.517962i
\(750\) 1.72373 + 0.169604i 0.0629416 + 0.00619306i
\(751\) 6.67039i 0.243406i −0.992567 0.121703i \(-0.961164\pi\)
0.992567 0.121703i \(-0.0388355\pi\)
\(752\) 6.46196i 0.235644i
\(753\) 3.98973 3.27493i 0.145394 0.119345i
\(754\) −21.9383 + 21.9383i −0.798945 + 0.798945i
\(755\) 0.678093 + 0.678093i 0.0246783 + 0.0246783i
\(756\) −9.08486 2.75298i −0.330413 0.100125i
\(757\) −6.34809 6.34809i −0.230725 0.230725i 0.582270 0.812995i \(-0.302165\pi\)
−0.812995 + 0.582270i \(0.802165\pi\)
\(758\) −12.8454 12.8454i −0.466567 0.466567i
\(759\) −29.5857 36.0432i −1.07389 1.30829i
\(760\) −2.92931 + 2.92931i −0.106257 + 0.106257i
\(761\) 29.4703 1.06830 0.534148 0.845391i \(-0.320633\pi\)
0.534148 + 0.845391i \(0.320633\pi\)
\(762\) −2.80932 + 2.30600i −0.101771 + 0.0835377i
\(763\) 1.80121 + 1.80121i 0.0652081 + 0.0652081i
\(764\) −7.19370 7.19370i −0.260259 0.260259i
\(765\) 2.46988 12.4295i 0.0892988 0.449390i
\(766\) 26.3274 0.951247
\(767\) 1.31685 0.0475488
\(768\) 0.169604 1.72373i 0.00612005 0.0621996i
\(769\) −35.2222 + 35.2222i −1.27014 + 1.27014i −0.324133 + 0.946012i \(0.605072\pi\)
−0.946012 + 0.324133i \(0.894928\pi\)
\(770\) −9.42559 −0.339675
\(771\) −0.304135 0.370516i −0.0109531 0.0133438i
\(772\) −2.35783 + 2.35783i −0.0848602 + 0.0848602i
\(773\) 22.3562i 0.804095i 0.915619 + 0.402048i \(0.131701\pi\)
−0.915619 + 0.402048i \(0.868299\pi\)
\(774\) 2.23030 11.2238i 0.0801663 0.403431i
\(775\) −6.21752 6.21752i −0.223340 0.223340i
\(776\) −11.7714 −0.422569
\(777\) −19.0988 2.38777i −0.685167 0.0856606i
\(778\) −4.13431 −0.148222
\(779\) 2.39093 + 2.39093i 0.0856640 +