Properties

Label 280.2.h.b.251.4
Level $280$
Weight $2$
Character 280.251
Analytic conductor $2.236$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - x^{15} - 2 x^{12} + 6 x^{11} - 12 x^{9} + 8 x^{8} - 24 x^{7} + 48 x^{5} - 32 x^{4} - 128 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.4
Root \(-1.24098 - 0.678208i\) of defining polynomial
Character \(\chi\) \(=\) 280.251
Dual form 280.2.h.b.251.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.24098 + 0.678208i) q^{2} -1.61069i q^{3} +(1.08007 - 1.68329i) q^{4} +1.00000 q^{5} +(1.09238 + 1.99883i) q^{6} +(2.13463 - 1.56312i) q^{7} +(-0.198727 + 2.82144i) q^{8} +0.405694 q^{9} +O(q^{10})\) \(q+(-1.24098 + 0.678208i) q^{2} -1.61069i q^{3} +(1.08007 - 1.68329i) q^{4} +1.00000 q^{5} +(1.09238 + 1.99883i) q^{6} +(2.13463 - 1.56312i) q^{7} +(-0.198727 + 2.82144i) q^{8} +0.405694 q^{9} +(-1.24098 + 0.678208i) q^{10} -6.01679 q^{11} +(-2.71124 - 1.73965i) q^{12} +4.25411 q^{13} +(-1.58892 + 3.38753i) q^{14} -1.61069i q^{15} +(-1.66690 - 3.63613i) q^{16} -5.42124i q^{17} +(-0.503458 + 0.275145i) q^{18} +4.53588i q^{19} +(1.08007 - 1.68329i) q^{20} +(-2.51769 - 3.43822i) q^{21} +(7.46673 - 4.08064i) q^{22} -5.19890i q^{23} +(4.54445 + 0.320086i) q^{24} +1.00000 q^{25} +(-5.27927 + 2.88517i) q^{26} -5.48550i q^{27} +(-0.325625 - 5.28147i) q^{28} -0.376818i q^{29} +(1.09238 + 1.99883i) q^{30} +2.93636 q^{31} +(4.53465 + 3.38186i) q^{32} +9.69116i q^{33} +(3.67672 + 6.72765i) q^{34} +(2.13463 - 1.56312i) q^{35} +(0.438177 - 0.682898i) q^{36} +0.372265i q^{37} +(-3.07627 - 5.62894i) q^{38} -6.85203i q^{39} +(-0.198727 + 2.82144i) q^{40} +5.75560i q^{41} +(5.45624 + 2.55925i) q^{42} -4.96515 q^{43} +(-6.49855 + 10.1280i) q^{44} +0.405694 q^{45} +(3.52593 + 6.45173i) q^{46} +3.86303 q^{47} +(-5.85666 + 2.68486i) q^{48} +(2.11332 - 6.67337i) q^{49} +(-1.24098 + 0.678208i) q^{50} -8.73190 q^{51} +(4.59473 - 7.16089i) q^{52} +10.2224i q^{53} +(3.72031 + 6.80740i) q^{54} -6.01679 q^{55} +(3.98603 + 6.33337i) q^{56} +7.30587 q^{57} +(0.255561 + 0.467624i) q^{58} -10.5835i q^{59} +(-2.71124 - 1.73965i) q^{60} -5.58001 q^{61} +(-3.64396 + 1.99146i) q^{62} +(0.866007 - 0.634147i) q^{63} +(-7.92102 - 1.12139i) q^{64} +4.25411 q^{65} +(-6.57262 - 12.0265i) q^{66} -0.782596 q^{67} +(-9.12549 - 5.85531i) q^{68} -8.37378 q^{69} +(-1.58892 + 3.38753i) q^{70} +15.3803i q^{71} +(-0.0806221 + 1.14464i) q^{72} +8.77164i q^{73} +(-0.252473 - 0.461974i) q^{74} -1.61069i q^{75} +(7.63518 + 4.89906i) q^{76} +(-12.8437 + 9.40496i) q^{77} +(4.64710 + 8.50324i) q^{78} +8.74609i q^{79} +(-1.66690 - 3.63613i) q^{80} -7.61833 q^{81} +(-3.90349 - 7.14259i) q^{82} +8.42742i q^{83} +(-8.50679 + 0.524480i) q^{84} -5.42124i q^{85} +(6.16165 - 3.36740i) q^{86} -0.606935 q^{87} +(1.19570 - 16.9760i) q^{88} +1.94765i q^{89} +(-0.503458 + 0.275145i) q^{90} +(9.08097 - 6.64968i) q^{91} +(-8.75123 - 5.61516i) q^{92} -4.72954i q^{93} +(-4.79395 + 2.61994i) q^{94} +4.53588i q^{95} +(5.44711 - 7.30389i) q^{96} +3.14377i q^{97} +(1.90334 + 9.71480i) q^{98} -2.44098 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + q^{2} + q^{4} + 16q^{5} + q^{8} - 16q^{9} + O(q^{10}) \) \( 16q + q^{2} + q^{4} + 16q^{5} + q^{8} - 16q^{9} + q^{10} - 4q^{11} + 14q^{12} - q^{14} + 9q^{16} - 15q^{18} + q^{20} - 4q^{21} + 6q^{22} + 22q^{24} + 16q^{25} - 20q^{26} + q^{28} - 16q^{31} - 19q^{32} - 14q^{34} + 15q^{36} - 30q^{38} + q^{40} + 44q^{42} - 4q^{43} - 20q^{44} - 16q^{45} + 6q^{46} - 34q^{48} - 8q^{49} + q^{50} - 40q^{51} - 38q^{52} + 26q^{54} - 4q^{55} + 33q^{56} - 16q^{57} + 18q^{58} + 14q^{60} - 8q^{61} + 28q^{62} + 28q^{63} - 23q^{64} + 46q^{66} + 20q^{67} + 12q^{68} - 40q^{69} - q^{70} - 13q^{72} - 28q^{74} + 34q^{76} - 4q^{77} - 6q^{78} + 9q^{80} + 24q^{81} - 16q^{82} - 42q^{84} - 24q^{86} + 72q^{87} - 44q^{88} - 15q^{90} - 32q^{91} - 30q^{92} - 58q^{94} - 30q^{96} + 5q^{98} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.24098 + 0.678208i −0.877506 + 0.479565i
\(3\) 1.61069i 0.929929i −0.885329 0.464965i \(-0.846067\pi\)
0.885329 0.464965i \(-0.153933\pi\)
\(4\) 1.08007 1.68329i 0.540034 0.841643i
\(5\) 1.00000 0.447214
\(6\) 1.09238 + 1.99883i 0.445962 + 0.816019i
\(7\) 2.13463 1.56312i 0.806816 0.590803i
\(8\) −0.198727 + 2.82144i −0.0702605 + 0.997529i
\(9\) 0.405694 0.135231
\(10\) −1.24098 + 0.678208i −0.392433 + 0.214468i
\(11\) −6.01679 −1.81413 −0.907066 0.420989i \(-0.861683\pi\)
−0.907066 + 0.420989i \(0.861683\pi\)
\(12\) −2.71124 1.73965i −0.782669 0.502194i
\(13\) 4.25411 1.17988 0.589939 0.807448i \(-0.299152\pi\)
0.589939 + 0.807448i \(0.299152\pi\)
\(14\) −1.58892 + 3.38753i −0.424657 + 0.905354i
\(15\) 1.61069i 0.415877i
\(16\) −1.66690 3.63613i −0.416726 0.909032i
\(17\) 5.42124i 1.31484i −0.753523 0.657421i \(-0.771647\pi\)
0.753523 0.657421i \(-0.228353\pi\)
\(18\) −0.503458 + 0.275145i −0.118666 + 0.0648522i
\(19\) 4.53588i 1.04060i 0.853983 + 0.520301i \(0.174180\pi\)
−0.853983 + 0.520301i \(0.825820\pi\)
\(20\) 1.08007 1.68329i 0.241511 0.376394i
\(21\) −2.51769 3.43822i −0.549405 0.750282i
\(22\) 7.46673 4.08064i 1.59191 0.869995i
\(23\) 5.19890i 1.08404i −0.840364 0.542022i \(-0.817659\pi\)
0.840364 0.542022i \(-0.182341\pi\)
\(24\) 4.54445 + 0.320086i 0.927631 + 0.0653373i
\(25\) 1.00000 0.200000
\(26\) −5.27927 + 2.88517i −1.03535 + 0.565829i
\(27\) 5.48550i 1.05568i
\(28\) −0.325625 5.28147i −0.0615374 0.998105i
\(29\) 0.376818i 0.0699733i −0.999388 0.0349866i \(-0.988861\pi\)
0.999388 0.0349866i \(-0.0111389\pi\)
\(30\) 1.09238 + 1.99883i 0.199440 + 0.364935i
\(31\) 2.93636 0.527385 0.263693 0.964607i \(-0.415060\pi\)
0.263693 + 0.964607i \(0.415060\pi\)
\(32\) 4.53465 + 3.38186i 0.801620 + 0.597834i
\(33\) 9.69116i 1.68701i
\(34\) 3.67672 + 6.72765i 0.630553 + 1.15378i
\(35\) 2.13463 1.56312i 0.360819 0.264215i
\(36\) 0.438177 0.682898i 0.0730295 0.113816i
\(37\) 0.372265i 0.0612000i 0.999532 + 0.0306000i \(0.00974181\pi\)
−0.999532 + 0.0306000i \(0.990258\pi\)
\(38\) −3.07627 5.62894i −0.499037 0.913135i
\(39\) 6.85203i 1.09720i
\(40\) −0.198727 + 2.82144i −0.0314214 + 0.446108i
\(41\) 5.75560i 0.898874i 0.893312 + 0.449437i \(0.148375\pi\)
−0.893312 + 0.449437i \(0.851625\pi\)
\(42\) 5.45624 + 2.55925i 0.841916 + 0.394901i
\(43\) −4.96515 −0.757178 −0.378589 0.925565i \(-0.623591\pi\)
−0.378589 + 0.925565i \(0.623591\pi\)
\(44\) −6.49855 + 10.1280i −0.979693 + 1.52685i
\(45\) 0.405694 0.0604772
\(46\) 3.52593 + 6.45173i 0.519870 + 0.951256i
\(47\) 3.86303 0.563481 0.281741 0.959491i \(-0.409088\pi\)
0.281741 + 0.959491i \(0.409088\pi\)
\(48\) −5.85666 + 2.68486i −0.845336 + 0.387526i
\(49\) 2.11332 6.67337i 0.301903 0.953339i
\(50\) −1.24098 + 0.678208i −0.175501 + 0.0959131i
\(51\) −8.73190 −1.22271
\(52\) 4.59473 7.16089i 0.637174 0.993036i
\(53\) 10.2224i 1.40416i 0.712099 + 0.702079i \(0.247745\pi\)
−0.712099 + 0.702079i \(0.752255\pi\)
\(54\) 3.72031 + 6.80740i 0.506270 + 0.926370i
\(55\) −6.01679 −0.811304
\(56\) 3.98603 + 6.33337i 0.532656 + 0.846332i
\(57\) 7.30587 0.967686
\(58\) 0.255561 + 0.467624i 0.0335568 + 0.0614020i
\(59\) 10.5835i 1.37786i −0.724828 0.688930i \(-0.758081\pi\)
0.724828 0.688930i \(-0.241919\pi\)
\(60\) −2.71124 1.73965i −0.350020 0.224588i
\(61\) −5.58001 −0.714447 −0.357223 0.934019i \(-0.616277\pi\)
−0.357223 + 0.934019i \(0.616277\pi\)
\(62\) −3.64396 + 1.99146i −0.462784 + 0.252916i
\(63\) 0.866007 0.634147i 0.109107 0.0798950i
\(64\) −7.92102 1.12139i −0.990127 0.140174i
\(65\) 4.25411 0.527657
\(66\) −6.57262 12.0265i −0.809034 1.48037i
\(67\) −0.782596 −0.0956093 −0.0478047 0.998857i \(-0.515223\pi\)
−0.0478047 + 0.998857i \(0.515223\pi\)
\(68\) −9.12549 5.85531i −1.10663 0.710060i
\(69\) −8.37378 −1.00809
\(70\) −1.58892 + 3.38753i −0.189912 + 0.404887i
\(71\) 15.3803i 1.82531i 0.408735 + 0.912653i \(0.365970\pi\)
−0.408735 + 0.912653i \(0.634030\pi\)
\(72\) −0.0806221 + 1.14464i −0.00950141 + 0.134897i
\(73\) 8.77164i 1.02664i 0.858196 + 0.513321i \(0.171585\pi\)
−0.858196 + 0.513321i \(0.828415\pi\)
\(74\) −0.252473 0.461974i −0.0293494 0.0537034i
\(75\) 1.61069i 0.185986i
\(76\) 7.63518 + 4.89906i 0.875816 + 0.561961i
\(77\) −12.8437 + 9.40496i −1.46367 + 1.07179i
\(78\) 4.64710 + 8.50324i 0.526181 + 0.962803i
\(79\) 8.74609i 0.984012i 0.870592 + 0.492006i \(0.163736\pi\)
−0.870592 + 0.492006i \(0.836264\pi\)
\(80\) −1.66690 3.63613i −0.186366 0.406531i
\(81\) −7.61833 −0.846481
\(82\) −3.90349 7.14259i −0.431069 0.788767i
\(83\) 8.42742i 0.925029i 0.886612 + 0.462515i \(0.153053\pi\)
−0.886612 + 0.462515i \(0.846947\pi\)
\(84\) −8.50679 + 0.524480i −0.928167 + 0.0572254i
\(85\) 5.42124i 0.588016i
\(86\) 6.16165 3.36740i 0.664428 0.363116i
\(87\) −0.606935 −0.0650702
\(88\) 1.19570 16.9760i 0.127462 1.80965i
\(89\) 1.94765i 0.206451i 0.994658 + 0.103225i \(0.0329163\pi\)
−0.994658 + 0.103225i \(0.967084\pi\)
\(90\) −0.503458 + 0.275145i −0.0530691 + 0.0290028i
\(91\) 9.08097 6.64968i 0.951944 0.697076i
\(92\) −8.75123 5.61516i −0.912379 0.585421i
\(93\) 4.72954i 0.490431i
\(94\) −4.79395 + 2.61994i −0.494458 + 0.270226i
\(95\) 4.53588i 0.465371i
\(96\) 5.44711 7.30389i 0.555943 0.745450i
\(97\) 3.14377i 0.319201i 0.987182 + 0.159601i \(0.0510206\pi\)
−0.987182 + 0.159601i \(0.948979\pi\)
\(98\) 1.90334 + 9.71480i 0.192266 + 0.981343i
\(99\) −2.44098 −0.245327
\(100\) 1.08007 1.68329i 0.108007 0.168329i
\(101\) 16.3016 1.62207 0.811037 0.584995i \(-0.198904\pi\)
0.811037 + 0.584995i \(0.198904\pi\)
\(102\) 10.8361 5.92205i 1.07294 0.586370i
\(103\) 11.8940 1.17195 0.585974 0.810330i \(-0.300712\pi\)
0.585974 + 0.810330i \(0.300712\pi\)
\(104\) −0.845405 + 12.0027i −0.0828988 + 1.17696i
\(105\) −2.51769 3.43822i −0.245702 0.335536i
\(106\) −6.93293 12.6858i −0.673385 1.23216i
\(107\) 10.4794 1.01308 0.506542 0.862215i \(-0.330923\pi\)
0.506542 + 0.862215i \(0.330923\pi\)
\(108\) −9.23367 5.92471i −0.888510 0.570106i
\(109\) 0.676794i 0.0648251i 0.999475 + 0.0324126i \(0.0103190\pi\)
−0.999475 + 0.0324126i \(0.989681\pi\)
\(110\) 7.46673 4.08064i 0.711925 0.389073i
\(111\) 0.599602 0.0569117
\(112\) −9.24193 5.15623i −0.873280 0.487218i
\(113\) −9.10537 −0.856562 −0.428281 0.903646i \(-0.640881\pi\)
−0.428281 + 0.903646i \(0.640881\pi\)
\(114\) −9.06645 + 4.95490i −0.849151 + 0.464069i
\(115\) 5.19890i 0.484800i
\(116\) −0.634292 0.406989i −0.0588925 0.0377880i
\(117\) 1.72587 0.159556
\(118\) 7.17784 + 13.1340i 0.660774 + 1.20908i
\(119\) −8.47403 11.5724i −0.776813 1.06084i
\(120\) 4.54445 + 0.320086i 0.414849 + 0.0292197i
\(121\) 25.2018 2.29107
\(122\) 6.92468 3.78440i 0.626931 0.342624i
\(123\) 9.27046 0.835889
\(124\) 3.17147 4.94273i 0.284806 0.443870i
\(125\) 1.00000 0.0894427
\(126\) −0.644615 + 1.37430i −0.0574269 + 0.122432i
\(127\) 3.74123i 0.331980i −0.986127 0.165990i \(-0.946918\pi\)
0.986127 0.165990i \(-0.0530820\pi\)
\(128\) 10.5904 3.98047i 0.936065 0.351827i
\(129\) 7.99729i 0.704122i
\(130\) −5.27927 + 2.88517i −0.463023 + 0.253046i
\(131\) 17.5774i 1.53575i 0.640601 + 0.767874i \(0.278685\pi\)
−0.640601 + 0.767874i \(0.721315\pi\)
\(132\) 16.3130 + 10.4671i 1.41986 + 0.911045i
\(133\) 7.09012 + 9.68244i 0.614791 + 0.839574i
\(134\) 0.971187 0.530763i 0.0838978 0.0458509i
\(135\) 5.48550i 0.472117i
\(136\) 15.2957 + 1.07734i 1.31159 + 0.0923815i
\(137\) −0.767338 −0.0655581 −0.0327791 0.999463i \(-0.510436\pi\)
−0.0327791 + 0.999463i \(0.510436\pi\)
\(138\) 10.3917 5.67917i 0.884601 0.483443i
\(139\) 2.01854i 0.171210i −0.996329 0.0856052i \(-0.972718\pi\)
0.996329 0.0856052i \(-0.0272824\pi\)
\(140\) −0.325625 5.28147i −0.0275204 0.446366i
\(141\) 6.22213i 0.523998i
\(142\) −10.4310 19.0867i −0.875354 1.60172i
\(143\) −25.5961 −2.14045
\(144\) −0.676253 1.47515i −0.0563544 0.122930i
\(145\) 0.376818i 0.0312930i
\(146\) −5.94899 10.8854i −0.492342 0.900885i
\(147\) −10.7487 3.40390i −0.886538 0.280749i
\(148\) 0.626629 + 0.402072i 0.0515086 + 0.0330501i
\(149\) 4.23267i 0.346754i 0.984856 + 0.173377i \(0.0554679\pi\)
−0.984856 + 0.173377i \(0.944532\pi\)
\(150\) 1.09238 + 1.99883i 0.0891924 + 0.163204i
\(151\) 0.625768i 0.0509243i −0.999676 0.0254622i \(-0.991894\pi\)
0.999676 0.0254622i \(-0.00810573\pi\)
\(152\) −12.7977 0.901400i −1.03803 0.0731132i
\(153\) 2.19936i 0.177808i
\(154\) 9.56021 20.3820i 0.770384 1.64243i
\(155\) 2.93636 0.235854
\(156\) −11.5339 7.40066i −0.923454 0.592527i
\(157\) −2.91713 −0.232812 −0.116406 0.993202i \(-0.537137\pi\)
−0.116406 + 0.993202i \(0.537137\pi\)
\(158\) −5.93167 10.8537i −0.471898 0.863477i
\(159\) 16.4651 1.30577
\(160\) 4.53465 + 3.38186i 0.358495 + 0.267359i
\(161\) −8.12649 11.0977i −0.640457 0.874624i
\(162\) 9.45421 5.16681i 0.742793 0.405943i
\(163\) −7.14397 −0.559559 −0.279779 0.960064i \(-0.590261\pi\)
−0.279779 + 0.960064i \(0.590261\pi\)
\(164\) 9.68833 + 6.21644i 0.756531 + 0.485423i
\(165\) 9.69116i 0.754456i
\(166\) −5.71554 10.4583i −0.443612 0.811719i
\(167\) 6.26796 0.485029 0.242515 0.970148i \(-0.422028\pi\)
0.242515 + 0.970148i \(0.422028\pi\)
\(168\) 10.2011 6.42024i 0.787029 0.495332i
\(169\) 5.09746 0.392112
\(170\) 3.67672 + 6.72765i 0.281992 + 0.515987i
\(171\) 1.84018i 0.140722i
\(172\) −5.36270 + 8.35776i −0.408902 + 0.637274i
\(173\) 9.11366 0.692898 0.346449 0.938069i \(-0.387387\pi\)
0.346449 + 0.938069i \(0.387387\pi\)
\(174\) 0.753195 0.411628i 0.0570995 0.0312054i
\(175\) 2.13463 1.56312i 0.161363 0.118161i
\(176\) 10.0294 + 21.8778i 0.755996 + 1.64910i
\(177\) −17.0468 −1.28131
\(178\) −1.32091 2.41700i −0.0990067 0.181162i
\(179\) 10.9518 0.818579 0.409290 0.912405i \(-0.365777\pi\)
0.409290 + 0.912405i \(0.365777\pi\)
\(180\) 0.438177 0.682898i 0.0326598 0.0509002i
\(181\) −18.7975 −1.39721 −0.698603 0.715509i \(-0.746195\pi\)
−0.698603 + 0.715509i \(0.746195\pi\)
\(182\) −6.75945 + 14.4109i −0.501043 + 1.06821i
\(183\) 8.98763i 0.664385i
\(184\) 14.6684 + 1.03316i 1.08137 + 0.0761655i
\(185\) 0.372265i 0.0273695i
\(186\) 3.20761 + 5.86928i 0.235194 + 0.430356i
\(187\) 32.6185i 2.38530i
\(188\) 4.17234 6.50259i 0.304299 0.474250i
\(189\) −8.57449 11.7095i −0.623702 0.851743i
\(190\) −3.07627 5.62894i −0.223176 0.408366i
\(191\) 1.13019i 0.0817778i −0.999164 0.0408889i \(-0.986981\pi\)
0.999164 0.0408889i \(-0.0130190\pi\)
\(192\) −1.80621 + 12.7583i −0.130352 + 0.920748i
\(193\) −3.27357 −0.235636 −0.117818 0.993035i \(-0.537590\pi\)
−0.117818 + 0.993035i \(0.537590\pi\)
\(194\) −2.13213 3.90136i −0.153078 0.280101i
\(195\) 6.85203i 0.490684i
\(196\) −8.95066 10.7650i −0.639333 0.768930i
\(197\) 21.2252i 1.51223i −0.654437 0.756116i \(-0.727094\pi\)
0.654437 0.756116i \(-0.272906\pi\)
\(198\) 3.02920 1.65549i 0.215276 0.117650i
\(199\) −17.9614 −1.27325 −0.636626 0.771172i \(-0.719671\pi\)
−0.636626 + 0.771172i \(0.719671\pi\)
\(200\) −0.198727 + 2.82144i −0.0140521 + 0.199506i
\(201\) 1.26052i 0.0889099i
\(202\) −20.2300 + 11.0559i −1.42338 + 0.777890i
\(203\) −0.589011 0.804368i −0.0413404 0.0564556i
\(204\) −9.43105 + 14.6983i −0.660306 + 1.02909i
\(205\) 5.75560i 0.401989i
\(206\) −14.7602 + 8.06659i −1.02839 + 0.562026i
\(207\) 2.10916i 0.146597i
\(208\) −7.09120 15.4685i −0.491686 1.07255i
\(209\) 27.2915i 1.88779i
\(210\) 5.45624 + 2.55925i 0.376516 + 0.176605i
\(211\) −7.43642 −0.511944 −0.255972 0.966684i \(-0.582396\pi\)
−0.255972 + 0.966684i \(0.582396\pi\)
\(212\) 17.2073 + 11.0409i 1.18180 + 0.758293i
\(213\) 24.7728 1.69741
\(214\) −13.0048 + 7.10723i −0.888988 + 0.485840i
\(215\) −4.96515 −0.338620
\(216\) 15.4770 + 1.09011i 1.05308 + 0.0741729i
\(217\) 6.26804 4.58987i 0.425503 0.311581i
\(218\) −0.459007 0.839889i −0.0310879 0.0568845i
\(219\) 14.1283 0.954705
\(220\) −6.49855 + 10.1280i −0.438132 + 0.682829i
\(221\) 23.0625i 1.55135i
\(222\) −0.744095 + 0.406655i −0.0499404 + 0.0272929i
\(223\) −23.8641 −1.59806 −0.799029 0.601293i \(-0.794653\pi\)
−0.799029 + 0.601293i \(0.794653\pi\)
\(224\) 14.9661 + 0.130838i 0.999962 + 0.00874200i
\(225\) 0.405694 0.0270462
\(226\) 11.2996 6.17534i 0.751638 0.410777i
\(227\) 12.1282i 0.804974i 0.915426 + 0.402487i \(0.131854\pi\)
−0.915426 + 0.402487i \(0.868146\pi\)
\(228\) 7.89084 12.2979i 0.522584 0.814447i
\(229\) −16.4001 −1.08375 −0.541875 0.840459i \(-0.682285\pi\)
−0.541875 + 0.840459i \(0.682285\pi\)
\(230\) 3.52593 + 6.45173i 0.232493 + 0.425415i
\(231\) 15.1484 + 20.6871i 0.996694 + 1.36111i
\(232\) 1.06317 + 0.0748837i 0.0698004 + 0.00491636i
\(233\) −26.4108 −1.73023 −0.865114 0.501575i \(-0.832754\pi\)
−0.865114 + 0.501575i \(0.832754\pi\)
\(234\) −2.14177 + 1.17050i −0.140012 + 0.0765177i
\(235\) 3.86303 0.251997
\(236\) −17.8151 11.4310i −1.15967 0.744092i
\(237\) 14.0872 0.915062
\(238\) 18.3646 + 8.61392i 1.19040 + 0.558357i
\(239\) 1.68909i 0.109258i 0.998507 + 0.0546292i \(0.0173977\pi\)
−0.998507 + 0.0546292i \(0.982602\pi\)
\(240\) −5.85666 + 2.68486i −0.378046 + 0.173307i
\(241\) 5.25118i 0.338258i −0.985594 0.169129i \(-0.945905\pi\)
0.985594 0.169129i \(-0.0540955\pi\)
\(242\) −31.2750 + 17.0921i −2.01043 + 1.09872i
\(243\) 4.18577i 0.268517i
\(244\) −6.02679 + 9.39275i −0.385826 + 0.601309i
\(245\) 2.11332 6.67337i 0.135015 0.426346i
\(246\) −11.5045 + 6.28730i −0.733498 + 0.400864i
\(247\) 19.2961i 1.22778i
\(248\) −0.583532 + 8.28474i −0.0370543 + 0.526082i
\(249\) 13.5739 0.860212
\(250\) −1.24098 + 0.678208i −0.0784865 + 0.0428936i
\(251\) 13.9692i 0.881730i 0.897574 + 0.440865i \(0.145328\pi\)
−0.897574 + 0.440865i \(0.854672\pi\)
\(252\) −0.132104 2.14266i −0.00832178 0.134975i
\(253\) 31.2807i 1.96660i
\(254\) 2.53733 + 4.64280i 0.159206 + 0.291315i
\(255\) −8.73190 −0.546813
\(256\) −10.4429 + 12.1222i −0.652679 + 0.757635i
\(257\) 21.6938i 1.35322i −0.736341 0.676610i \(-0.763448\pi\)
0.736341 0.676610i \(-0.236552\pi\)
\(258\) −5.42382 9.92448i −0.337672 0.617871i
\(259\) 0.581895 + 0.794650i 0.0361572 + 0.0493771i
\(260\) 4.59473 7.16089i 0.284953 0.444099i
\(261\) 0.152873i 0.00946257i
\(262\) −11.9212 21.8133i −0.736492 1.34763i
\(263\) 5.88968i 0.363173i −0.983375 0.181587i \(-0.941877\pi\)
0.983375 0.181587i \(-0.0581232\pi\)
\(264\) −27.3430 1.92589i −1.68285 0.118530i
\(265\) 10.2224i 0.627958i
\(266\) −15.3654 7.20715i −0.942114 0.441899i
\(267\) 3.13706 0.191985
\(268\) −0.845257 + 1.31733i −0.0516323 + 0.0804689i
\(269\) 13.3475 0.813810 0.406905 0.913470i \(-0.366608\pi\)
0.406905 + 0.913470i \(0.366608\pi\)
\(270\) 3.72031 + 6.80740i 0.226411 + 0.414285i
\(271\) 24.7908 1.50593 0.752966 0.658059i \(-0.228622\pi\)
0.752966 + 0.658059i \(0.228622\pi\)
\(272\) −19.7123 + 9.03668i −1.19523 + 0.547929i
\(273\) −10.7105 14.6266i −0.648231 0.885241i
\(274\) 0.952252 0.520415i 0.0575277 0.0314394i
\(275\) −6.01679 −0.362826
\(276\) −9.04426 + 14.0955i −0.544400 + 0.848448i
\(277\) 2.09066i 0.125616i 0.998026 + 0.0628078i \(0.0200055\pi\)
−0.998026 + 0.0628078i \(0.979994\pi\)
\(278\) 1.36899 + 2.50497i 0.0821065 + 0.150238i
\(279\) 1.19126 0.0713189
\(280\) 3.98603 + 6.33337i 0.238211 + 0.378491i
\(281\) −4.09181 −0.244097 −0.122048 0.992524i \(-0.538946\pi\)
−0.122048 + 0.992524i \(0.538946\pi\)
\(282\) 4.21990 + 7.72155i 0.251291 + 0.459811i
\(283\) 5.92294i 0.352082i −0.984383 0.176041i \(-0.943671\pi\)
0.984383 0.176041i \(-0.0563291\pi\)
\(284\) 25.8895 + 16.6118i 1.53626 + 0.985728i
\(285\) 7.30587 0.432763
\(286\) 31.7643 17.3595i 1.87826 1.02649i
\(287\) 8.99669 + 12.2861i 0.531058 + 0.725226i
\(288\) 1.83968 + 1.37200i 0.108404 + 0.0808458i
\(289\) −12.3898 −0.728812
\(290\) 0.255561 + 0.467624i 0.0150070 + 0.0274598i
\(291\) 5.06362 0.296835
\(292\) 14.7652 + 9.47397i 0.864067 + 0.554422i
\(293\) 9.44316 0.551675 0.275838 0.961204i \(-0.411045\pi\)
0.275838 + 0.961204i \(0.411045\pi\)
\(294\) 15.6475 3.06568i 0.912580 0.178794i
\(295\) 10.5835i 0.616198i
\(296\) −1.05032 0.0739790i −0.0610488 0.00429994i
\(297\) 33.0051i 1.91515i
\(298\) −2.87063 5.25267i −0.166291 0.304279i
\(299\) 22.1167i 1.27904i
\(300\) −2.71124 1.73965i −0.156534 0.100439i
\(301\) −10.5988 + 7.76111i −0.610903 + 0.447343i
\(302\) 0.424401 + 0.776567i 0.0244215 + 0.0446864i
\(303\) 26.2568i 1.50841i
\(304\) 16.4930 7.56088i 0.945941 0.433646i
\(305\) −5.58001 −0.319510
\(306\) 1.49162 + 2.72937i 0.0852704 + 0.156027i
\(307\) 24.1204i 1.37663i −0.725414 0.688313i \(-0.758351\pi\)
0.725414 0.688313i \(-0.241649\pi\)
\(308\) 1.95922 + 31.7775i 0.111637 + 1.81069i
\(309\) 19.1574i 1.08983i
\(310\) −3.64396 + 1.99146i −0.206963 + 0.113107i
\(311\) 16.5947 0.941001 0.470500 0.882400i \(-0.344073\pi\)
0.470500 + 0.882400i \(0.344073\pi\)
\(312\) 19.3326 + 1.36168i 1.09449 + 0.0770900i
\(313\) 11.3871i 0.643637i 0.946801 + 0.321819i \(0.104294\pi\)
−0.946801 + 0.321819i \(0.895706\pi\)
\(314\) 3.62010 1.97842i 0.204294 0.111649i
\(315\) 0.866007 0.634147i 0.0487940 0.0357301i
\(316\) 14.7222 + 9.44638i 0.828187 + 0.531400i
\(317\) 26.7084i 1.50009i −0.661386 0.750046i \(-0.730031\pi\)
0.661386 0.750046i \(-0.269969\pi\)
\(318\) −20.4329 + 11.1668i −1.14582 + 0.626201i
\(319\) 2.26723i 0.126941i
\(320\) −7.92102 1.12139i −0.442798 0.0626876i
\(321\) 16.8791i 0.942097i
\(322\) 17.6114 + 8.26064i 0.981445 + 0.460347i
\(323\) 24.5901 1.36823
\(324\) −8.22832 + 12.8238i −0.457129 + 0.712435i
\(325\) 4.25411 0.235976
\(326\) 8.86553 4.84510i 0.491016 0.268345i
\(327\) 1.09010 0.0602828
\(328\) −16.2391 1.14379i −0.896653 0.0631553i
\(329\) 8.24616 6.03838i 0.454626 0.332907i
\(330\) −6.57262 12.0265i −0.361811 0.662040i
\(331\) −3.25364 −0.178836 −0.0894182 0.995994i \(-0.528501\pi\)
−0.0894182 + 0.995994i \(0.528501\pi\)
\(332\) 14.1858 + 9.10219i 0.778545 + 0.499547i
\(333\) 0.151026i 0.00827615i
\(334\) −7.77842 + 4.25098i −0.425616 + 0.232603i
\(335\) −0.782596 −0.0427578
\(336\) −8.30507 + 14.8858i −0.453079 + 0.812089i
\(337\) −12.0157 −0.654539 −0.327270 0.944931i \(-0.606129\pi\)
−0.327270 + 0.944931i \(0.606129\pi\)
\(338\) −6.32585 + 3.45714i −0.344081 + 0.188043i
\(339\) 14.6659i 0.796542i
\(340\) −9.12549 5.85531i −0.494899 0.317549i
\(341\) −17.6675 −0.956746
\(342\) −1.24802 2.28363i −0.0674853 0.123484i
\(343\) −5.92010 17.5486i −0.319655 0.947534i
\(344\) 0.986707 14.0089i 0.0531997 0.755307i
\(345\) −8.37378 −0.450829
\(346\) −11.3099 + 6.18095i −0.608023 + 0.332290i
\(347\) −15.5740 −0.836057 −0.418028 0.908434i \(-0.637279\pi\)
−0.418028 + 0.908434i \(0.637279\pi\)
\(348\) −0.655531 + 1.02164i −0.0351401 + 0.0547659i
\(349\) 34.7705 1.86122 0.930610 0.366012i \(-0.119277\pi\)
0.930610 + 0.366012i \(0.119277\pi\)
\(350\) −1.58892 + 3.38753i −0.0849314 + 0.181071i
\(351\) 23.3359i 1.24558i
\(352\) −27.2840 20.3479i −1.45424 1.08455i
\(353\) 12.5154i 0.666126i 0.942905 + 0.333063i \(0.108082\pi\)
−0.942905 + 0.333063i \(0.891918\pi\)
\(354\) 21.1547 11.5612i 1.12436 0.614473i
\(355\) 15.3803i 0.816302i
\(356\) 3.27846 + 2.10360i 0.173758 + 0.111491i
\(357\) −18.6394 + 13.6490i −0.986502 + 0.722382i
\(358\) −13.5910 + 7.42763i −0.718308 + 0.392562i
\(359\) 31.0752i 1.64009i 0.572301 + 0.820044i \(0.306051\pi\)
−0.572301 + 0.820044i \(0.693949\pi\)
\(360\) −0.0806221 + 1.14464i −0.00424916 + 0.0603278i
\(361\) −1.57420 −0.0828526
\(362\) 23.3273 12.7486i 1.22606 0.670052i
\(363\) 40.5922i 2.13054i
\(364\) −1.38525 22.4680i −0.0726066 1.17764i
\(365\) 8.77164i 0.459129i
\(366\) −6.09548 11.1535i −0.318616 0.583002i
\(367\) −14.0542 −0.733624 −0.366812 0.930295i \(-0.619551\pi\)
−0.366812 + 0.930295i \(0.619551\pi\)
\(368\) −18.9039 + 8.66606i −0.985431 + 0.451750i
\(369\) 2.33501i 0.121556i
\(370\) −0.252473 0.461974i −0.0131255 0.0240169i
\(371\) 15.9789 + 21.8211i 0.829581 + 1.13290i
\(372\) −7.96118 5.10823i −0.412768 0.264849i
\(373\) 19.7598i 1.02312i −0.859247 0.511561i \(-0.829067\pi\)
0.859247 0.511561i \(-0.170933\pi\)
\(374\) −22.1221 40.4789i −1.14391 2.09311i
\(375\) 1.61069i 0.0831754i
\(376\) −0.767688 + 10.8993i −0.0395905 + 0.562089i
\(377\) 1.60302i 0.0825600i
\(378\) 18.5823 + 8.71603i 0.955769 + 0.448304i
\(379\) −0.483016 −0.0248108 −0.0124054 0.999923i \(-0.503949\pi\)
−0.0124054 + 0.999923i \(0.503949\pi\)
\(380\) 7.63518 + 4.89906i 0.391677 + 0.251316i
\(381\) −6.02594 −0.308718
\(382\) 0.766505 + 1.40255i 0.0392178 + 0.0717605i
\(383\) −1.09585 −0.0559953 −0.0279977 0.999608i \(-0.508913\pi\)
−0.0279977 + 0.999608i \(0.508913\pi\)
\(384\) −6.41129 17.0577i −0.327175 0.870474i
\(385\) −12.8437 + 9.40496i −0.654573 + 0.479321i
\(386\) 4.06243 2.22016i 0.206772 0.113003i
\(387\) −2.01433 −0.102394
\(388\) 5.29186 + 3.39548i 0.268654 + 0.172380i
\(389\) 18.3250i 0.929114i −0.885543 0.464557i \(-0.846214\pi\)
0.885543 0.464557i \(-0.153786\pi\)
\(390\) 4.64710 + 8.50324i 0.235315 + 0.430578i
\(391\) −28.1844 −1.42535
\(392\) 18.4085 + 7.28878i 0.929771 + 0.368139i
\(393\) 28.3117 1.42814
\(394\) 14.3951 + 26.3401i 0.725214 + 1.32699i
\(395\) 8.74609i 0.440064i
\(396\) −2.63642 + 4.10886i −0.132485 + 0.206478i
\(397\) 0.717950 0.0360329 0.0180164 0.999838i \(-0.494265\pi\)
0.0180164 + 0.999838i \(0.494265\pi\)
\(398\) 22.2898 12.1816i 1.11729 0.610608i
\(399\) 15.5954 11.4199i 0.780745 0.571712i
\(400\) −1.66690 3.63613i −0.0833452 0.181806i
\(401\) −21.1139 −1.05438 −0.527189 0.849748i \(-0.676754\pi\)
−0.527189 + 0.849748i \(0.676754\pi\)
\(402\) −0.854892 1.56428i −0.0426381 0.0780190i
\(403\) 12.4916 0.622250
\(404\) 17.6069 27.4403i 0.875975 1.36521i
\(405\) −7.61833 −0.378558
\(406\) 1.27648 + 0.598734i 0.0633506 + 0.0297147i
\(407\) 2.23984i 0.111025i
\(408\) 1.73526 24.6365i 0.0859083 1.21969i
\(409\) 1.08609i 0.0537038i −0.999639 0.0268519i \(-0.991452\pi\)
0.999639 0.0268519i \(-0.00854825\pi\)
\(410\) −3.90349 7.14259i −0.192780 0.352748i
\(411\) 1.23594i 0.0609644i
\(412\) 12.8463 20.0210i 0.632892 0.986362i
\(413\) −16.5433 22.5920i −0.814044 1.11168i
\(414\) 1.43045 + 2.61743i 0.0703027 + 0.128639i
\(415\) 8.42742i 0.413686i
\(416\) 19.2909 + 14.3868i 0.945814 + 0.705371i
\(417\) −3.25123 −0.159214
\(418\) 18.5093 + 33.8682i 0.905318 + 1.65655i
\(419\) 0.208107i 0.0101667i 0.999987 + 0.00508334i \(0.00161808\pi\)
−0.999987 + 0.00508334i \(0.998382\pi\)
\(420\) −8.50679 + 0.524480i −0.415089 + 0.0255920i
\(421\) 9.48511i 0.462276i 0.972921 + 0.231138i \(0.0742449\pi\)
−0.972921 + 0.231138i \(0.925755\pi\)
\(422\) 9.22846 5.04344i 0.449234 0.245511i
\(423\) 1.56721 0.0762003
\(424\) −28.8419 2.03147i −1.40069 0.0986568i
\(425\) 5.42124i 0.262969i
\(426\) −30.7426 + 16.8011i −1.48948 + 0.814017i
\(427\) −11.9113 + 8.72221i −0.576427 + 0.422097i
\(428\) 11.3185 17.6399i 0.547100 0.852656i
\(429\) 41.2273i 1.99047i
\(430\) 6.16165 3.36740i 0.297141 0.162391i
\(431\) 13.6900i 0.659423i −0.944082 0.329711i \(-0.893049\pi\)
0.944082 0.329711i \(-0.106951\pi\)
\(432\) −19.9460 + 9.14381i −0.959651 + 0.439932i
\(433\) 6.48406i 0.311604i 0.987788 + 0.155802i \(0.0497962\pi\)
−0.987788 + 0.155802i \(0.950204\pi\)
\(434\) −4.66564 + 9.94698i −0.223958 + 0.477470i
\(435\) −0.606935 −0.0291003
\(436\) 1.13924 + 0.730984i 0.0545596 + 0.0350078i
\(437\) 23.5816 1.12806
\(438\) −17.5330 + 9.58196i −0.837760 + 0.457844i
\(439\) 9.04411 0.431652 0.215826 0.976432i \(-0.430756\pi\)
0.215826 + 0.976432i \(0.430756\pi\)
\(440\) 1.19570 16.9760i 0.0570026 0.809299i
\(441\) 0.857361 2.70734i 0.0408267 0.128921i
\(442\) 15.6412 + 28.6202i 0.743976 + 1.36132i
\(443\) 8.66264 0.411574 0.205787 0.978597i \(-0.434025\pi\)
0.205787 + 0.978597i \(0.434025\pi\)
\(444\) 0.647611 1.00930i 0.0307343 0.0478993i
\(445\) 1.94765i 0.0923277i
\(446\) 29.6149 16.1848i 1.40231 0.766373i
\(447\) 6.81750 0.322457
\(448\) −18.6613 + 9.98773i −0.881665 + 0.471876i
\(449\) −26.5808 −1.25443 −0.627213 0.778848i \(-0.715804\pi\)
−0.627213 + 0.778848i \(0.715804\pi\)
\(450\) −0.503458 + 0.275145i −0.0237332 + 0.0129704i
\(451\) 34.6303i 1.63068i
\(452\) −9.83443 + 15.3270i −0.462573 + 0.720919i
\(453\) −1.00792 −0.0473560
\(454\) −8.22541 15.0508i −0.386037 0.706369i
\(455\) 9.08097 6.64968i 0.425722 0.311742i
\(456\) −1.45187 + 20.6131i −0.0679901 + 0.965295i
\(457\) 33.4034 1.56254 0.781272 0.624191i \(-0.214571\pi\)
0.781272 + 0.624191i \(0.214571\pi\)
\(458\) 20.3522 11.1227i 0.950998 0.519729i
\(459\) −29.7382 −1.38806
\(460\) −8.75123 5.61516i −0.408028 0.261808i
\(461\) −9.70385 −0.451954 −0.225977 0.974133i \(-0.572557\pi\)
−0.225977 + 0.974133i \(0.572557\pi\)
\(462\) −32.8291 15.3985i −1.52735 0.716403i
\(463\) 28.6011i 1.32921i 0.747196 + 0.664604i \(0.231400\pi\)
−0.747196 + 0.664604i \(0.768600\pi\)
\(464\) −1.37016 + 0.628119i −0.0636080 + 0.0291597i
\(465\) 4.72954i 0.219327i
\(466\) 32.7753 17.9120i 1.51829 0.829758i
\(467\) 8.61107i 0.398473i −0.979951 0.199236i \(-0.936154\pi\)
0.979951 0.199236i \(-0.0638462\pi\)
\(468\) 1.86405 2.90513i 0.0861659 0.134289i
\(469\) −1.67056 + 1.22329i −0.0771391 + 0.0564863i
\(470\) −4.79395 + 2.61994i −0.221129 + 0.120849i
\(471\) 4.69857i 0.216499i
\(472\) 29.8608 + 2.10323i 1.37445 + 0.0968091i
\(473\) 29.8743 1.37362
\(474\) −17.4819 + 9.55405i −0.802973 + 0.438832i
\(475\) 4.53588i 0.208120i
\(476\) −28.6321 + 1.76529i −1.31235 + 0.0809120i
\(477\) 4.14717i 0.189886i
\(478\) −1.14556 2.09613i −0.0523965 0.0958749i
\(479\) −6.75741 −0.308754 −0.154377 0.988012i \(-0.549337\pi\)
−0.154377 + 0.988012i \(0.549337\pi\)
\(480\) 5.44711 7.30389i 0.248625 0.333375i
\(481\) 1.58366i 0.0722086i
\(482\) 3.56139 + 6.51661i 0.162217 + 0.296824i
\(483\) −17.8750 + 13.0892i −0.813339 + 0.595580i
\(484\) 27.2197 42.4219i 1.23726 1.92827i
\(485\) 3.14377i 0.142751i
\(486\) 2.83882 + 5.19446i 0.128771 + 0.235625i
\(487\) 7.72534i 0.350069i 0.984562 + 0.175034i \(0.0560036\pi\)
−0.984562 + 0.175034i \(0.943996\pi\)
\(488\) 1.10890 15.7436i 0.0501974 0.712681i
\(489\) 11.5067i 0.520350i
\(490\) 1.90334 + 9.71480i 0.0859841 + 0.438870i
\(491\) −33.1648 −1.49671 −0.748354 0.663300i \(-0.769156\pi\)
−0.748354 + 0.663300i \(0.769156\pi\)
\(492\) 10.0127 15.6048i 0.451409 0.703521i
\(493\) −2.04282 −0.0920039
\(494\) −13.0868 23.9461i −0.588802 1.07739i
\(495\) −2.44098 −0.109714
\(496\) −4.89463 10.6770i −0.219775 0.479410i
\(497\) 24.0412 + 32.8313i 1.07840 + 1.47269i
\(498\) −16.8450 + 9.20594i −0.754841 + 0.412528i
\(499\) −9.13507 −0.408942 −0.204471 0.978873i \(-0.565547\pi\)
−0.204471 + 0.978873i \(0.565547\pi\)
\(500\) 1.08007 1.68329i 0.0483021 0.0752788i
\(501\) 10.0957i 0.451043i
\(502\) −9.47404 17.3355i −0.422847 0.773723i
\(503\) 13.9338 0.621277 0.310639 0.950528i \(-0.399457\pi\)
0.310639 + 0.950528i \(0.399457\pi\)
\(504\) 1.61711 + 2.56941i 0.0720317 + 0.114450i
\(505\) 16.3016 0.725413
\(506\) −21.2148 38.8187i −0.943113 1.72570i
\(507\) 8.21040i 0.364637i
\(508\) −6.29756 4.04078i −0.279409 0.179281i
\(509\) −11.4366 −0.506918 −0.253459 0.967346i \(-0.581568\pi\)
−0.253459 + 0.967346i \(0.581568\pi\)
\(510\) 10.8361 5.92205i 0.479832 0.262233i
\(511\) 13.7111 + 18.7242i 0.606544 + 0.828311i
\(512\) 4.73805 22.1258i 0.209394 0.977831i
\(513\) 24.8816 1.09855
\(514\) 14.7129 + 26.9216i 0.648958 + 1.18746i
\(515\) 11.8940 0.524111
\(516\) 13.4617 + 8.63762i 0.592619 + 0.380250i
\(517\) −23.2431 −1.02223
\(518\) −1.26106 0.591500i −0.0554077 0.0259890i
\(519\) 14.6792i 0.644347i
\(520\) −0.845405 + 12.0027i −0.0370735 + 0.526353i
\(521\) 13.5526i 0.593751i 0.954916 + 0.296875i \(0.0959446\pi\)
−0.954916 + 0.296875i \(0.904055\pi\)
\(522\) 0.103679 + 0.189712i 0.00453792 + 0.00830347i
\(523\) 16.3634i 0.715522i 0.933813 + 0.357761i \(0.116460\pi\)
−0.933813 + 0.357761i \(0.883540\pi\)
\(524\) 29.5879 + 18.9848i 1.29255 + 0.829357i
\(525\) −2.51769 3.43822i −0.109881 0.150056i
\(526\) 3.99443 + 7.30898i 0.174165 + 0.318687i
\(527\) 15.9187i 0.693429i
\(528\) 35.2383 16.1542i 1.53355 0.703023i
\(529\) −4.02852 −0.175153
\(530\) −6.93293 12.6858i −0.301147 0.551037i
\(531\) 4.29368i 0.186330i
\(532\) 23.9561 1.47700i 1.03863 0.0640359i
\(533\) 24.4850i 1.06056i
\(534\) −3.89303 + 2.12758i −0.168468 + 0.0920693i
\(535\) 10.4794 0.453065
\(536\) 0.155523 2.20805i 0.00671756 0.0953731i
\(537\) 17.6400i 0.761221i
\(538\) −16.5640 + 9.05236i −0.714123 + 0.390275i
\(539\) −12.7154 + 40.1523i −0.547692 + 1.72948i
\(540\) −9.23367 5.92471i −0.397354 0.254959i
\(541\) 23.4050i 1.00626i 0.864211 + 0.503129i \(0.167818\pi\)
−0.864211 + 0.503129i \(0.832182\pi\)
\(542\) −30.7649 + 16.8133i −1.32146 + 0.722193i
\(543\) 30.2768i 1.29930i
\(544\) 18.3339 24.5834i 0.786058 1.05400i
\(545\) 0.676794i 0.0289907i
\(546\) 23.2114 + 10.8873i 0.993358 + 0.465935i
\(547\) 21.2928 0.910416 0.455208 0.890385i \(-0.349565\pi\)
0.455208 + 0.890385i \(0.349565\pi\)
\(548\) −0.828778 + 1.29165i −0.0354036 + 0.0551765i
\(549\) −2.26377 −0.0966155
\(550\) 7.46673 4.08064i 0.318382 0.173999i
\(551\) 1.70920 0.0728144
\(552\) 1.66409 23.6261i 0.0708285 1.00559i
\(553\) 13.6712 + 18.6697i 0.581358 + 0.793917i
\(554\) −1.41790 2.59447i −0.0602409 0.110228i
\(555\) 0.599602 0.0254517
\(556\) −3.39778 2.18016i −0.144098 0.0924594i
\(557\) 2.06871i 0.0876541i 0.999039 + 0.0438270i \(0.0139551\pi\)
−0.999039 + 0.0438270i \(0.986045\pi\)
\(558\) −1.47833 + 0.807922i −0.0625828 + 0.0342021i
\(559\) −21.1223 −0.893378
\(560\) −9.24193 5.15623i −0.390543 0.217891i
\(561\) 52.5381 2.21816
\(562\) 5.07785 2.77509i 0.214196 0.117060i
\(563\) 25.5312i 1.07601i −0.842941 0.538006i \(-0.819178\pi\)
0.842941 0.538006i \(-0.180822\pi\)
\(564\) −10.4736 6.72033i −0.441019 0.282977i
\(565\) −9.10537 −0.383066
\(566\) 4.01698 + 7.35025i 0.168846 + 0.308954i
\(567\) −16.2623 + 11.9084i −0.682954 + 0.500104i
\(568\) −43.3946 3.05648i −1.82080 0.128247i
\(569\) 26.3859 1.10616 0.553078 0.833130i \(-0.313453\pi\)
0.553078 + 0.833130i \(0.313453\pi\)
\(570\) −9.06645 + 4.95490i −0.379752 + 0.207538i
\(571\) 17.6202 0.737384 0.368692 0.929552i \(-0.379806\pi\)
0.368692 + 0.929552i \(0.379806\pi\)
\(572\) −27.6455 + 43.0856i −1.15592 + 1.80150i
\(573\) −1.82038 −0.0760476
\(574\) −19.4972 9.14520i −0.813799 0.381713i
\(575\) 5.19890i 0.216809i
\(576\) −3.21351 0.454941i −0.133896 0.0189559i
\(577\) 29.5306i 1.22938i −0.788770 0.614688i \(-0.789282\pi\)
0.788770 0.614688i \(-0.210718\pi\)
\(578\) 15.3755 8.40286i 0.639537 0.349513i
\(579\) 5.27268i 0.219125i
\(580\) −0.634292 0.406989i −0.0263375 0.0168993i
\(581\) 13.1731 + 17.9895i 0.546510 + 0.746328i
\(582\) −6.28386 + 3.43419i −0.260474 + 0.142352i
\(583\) 61.5062i 2.54733i
\(584\) −24.7486 1.74316i −1.02411 0.0721324i
\(585\) 1.72587 0.0713558
\(586\) −11.7188 + 6.40442i −0.484098 + 0.264564i
\(587\) 5.32153i 0.219643i −0.993951 0.109822i \(-0.964972\pi\)
0.993951 0.109822i \(-0.0350279\pi\)
\(588\) −17.3391 + 14.4167i −0.715051 + 0.594534i
\(589\) 13.3190i 0.548798i
\(590\) 7.17784 + 13.1340i 0.295507 + 0.540717i
\(591\) −34.1871 −1.40627
\(592\) 1.35360 0.620531i 0.0556328 0.0255037i
\(593\) 45.6864i 1.87611i −0.346481 0.938057i \(-0.612623\pi\)
0.346481 0.938057i \(-0.387377\pi\)
\(594\) −22.3843 40.9587i −0.918440 1.68056i
\(595\) −8.47403 11.5724i −0.347401 0.474420i
\(596\) 7.12480 + 4.57158i 0.291843 + 0.187259i
\(597\) 28.9302i 1.18404i
\(598\) 14.9997 + 27.4464i 0.613384 + 1.12237i
\(599\) 22.5049i 0.919525i 0.888042 + 0.459762i \(0.152065\pi\)
−0.888042 + 0.459762i \(0.847935\pi\)
\(600\) 4.54445 + 0.320086i 0.185526 + 0.0130675i
\(601\) 4.49699i 0.183436i −0.995785 0.0917181i \(-0.970764\pi\)
0.995785 0.0917181i \(-0.0292359\pi\)
\(602\) 7.88923 16.8196i 0.321541 0.685514i
\(603\) −0.317494 −0.0129294
\(604\) −1.05335 0.675873i −0.0428601 0.0275009i
\(605\) 25.2018 1.02460
\(606\) 17.8076 + 32.5842i 0.723383 + 1.32364i
\(607\) 10.8910 0.442051 0.221025 0.975268i \(-0.429060\pi\)
0.221025 + 0.975268i \(0.429060\pi\)
\(608\) −15.3397 + 20.5686i −0.622107 + 0.834167i
\(609\) −1.29558 + 0.948711i −0.0524997 + 0.0384437i
\(610\) 6.92468 3.78440i 0.280372 0.153226i
\(611\) 16.4338 0.664839
\(612\) −3.70215 2.37546i −0.149651 0.0960223i
\(613\) 30.5045i 1.23206i 0.787721 + 0.616032i \(0.211261\pi\)
−0.787721 + 0.616032i \(0.788739\pi\)
\(614\) 16.3587 + 29.9330i 0.660182 + 1.20800i
\(615\) 9.27046 0.373821
\(616\) −23.9831 38.1066i −0.966308 1.53536i
\(617\) −39.6859 −1.59769 −0.798847 0.601534i \(-0.794557\pi\)
−0.798847 + 0.601534i \(0.794557\pi\)
\(618\) 12.9927 + 23.7740i 0.522644 + 0.956332i
\(619\) 13.7231i 0.551579i −0.961218 0.275789i \(-0.911061\pi\)
0.961218 0.275789i \(-0.0889392\pi\)
\(620\) 3.17147 4.94273i 0.127369 0.198505i
\(621\) −28.5185 −1.14441
\(622\) −20.5937 + 11.2547i −0.825734 + 0.451271i
\(623\) 3.04441 + 4.15753i 0.121972 + 0.166568i
\(624\) −24.9149 + 11.4217i −0.997393 + 0.457233i
\(625\) 1.00000 0.0400000
\(626\) −7.72283 14.1312i −0.308666 0.564796i
\(627\) −43.9579 −1.75551
\(628\) −3.15070 + 4.91036i −0.125726 + 0.195945i
\(629\) 2.01814 0.0804684
\(630\) −0.644615 + 1.37430i −0.0256821 + 0.0547533i
\(631\) 36.7721i 1.46387i −0.681373 0.731936i \(-0.738617\pi\)
0.681373 0.731936i \(-0.261383\pi\)
\(632\) −24.6766 1.73808i −0.981580 0.0691372i
\(633\) 11.9777i 0.476072i
\(634\) 18.1138 + 33.1446i 0.719392 + 1.31634i
\(635\) 3.74123i 0.148466i
\(636\) 17.7834 27.7155i 0.705159 1.09899i
\(637\) 8.99031 28.3893i 0.356209 1.12482i
\(638\) −1.53766 2.81360i −0.0608764 0.111391i
\(639\) 6.23969i 0.246838i
\(640\) 10.5904 3.98047i 0.418621 0.157342i
\(641\) −40.2483 −1.58971 −0.794855 0.606799i \(-0.792453\pi\)
−0.794855 + 0.606799i \(0.792453\pi\)
\(642\) 11.4475 + 20.9466i 0.451797 + 0.826696i
\(643\) 12.3361i 0.486487i 0.969965 + 0.243243i \(0.0782114\pi\)
−0.969965 + 0.243243i \(0.921789\pi\)
\(644\) −27.4578 + 1.69289i −1.08199 + 0.0667093i
\(645\) 7.99729i 0.314893i
\(646\) −30.5158 + 16.6772i −1.20063 + 0.656155i
\(647\) −47.9622 −1.88559 −0.942794 0.333376i \(-0.891812\pi\)
−0.942794 + 0.333376i \(0.891812\pi\)
\(648\) 1.51397 21.4946i 0.0594742 0.844389i
\(649\) 63.6790i 2.49962i
\(650\) −5.27927 + 2.88517i −0.207070 + 0.113166i
\(651\) −7.39284 10.0958i −0.289748 0.395687i
\(652\) −7.71598 + 12.0253i −0.302181 + 0.470949i
\(653\) 36.7504i 1.43815i −0.694930 0.719077i \(-0.744565\pi\)
0.694930 0.719077i \(-0.255435\pi\)
\(654\) −1.35280 + 0.739316i −0.0528985 + 0.0289095i
\(655\) 17.5774i 0.686808i
\(656\) 20.9281 9.59404i 0.817105 0.374584i
\(657\) 3.55860i 0.138834i
\(658\) −6.13806 + 13.0861i −0.239286 + 0.510150i
\(659\) 15.4039 0.600050 0.300025 0.953931i \(-0.403005\pi\)
0.300025 + 0.953931i \(0.403005\pi\)
\(660\) 16.3130 + 10.4671i 0.634983 + 0.407432i
\(661\) −6.20639 −0.241400 −0.120700 0.992689i \(-0.538514\pi\)
−0.120700 + 0.992689i \(0.538514\pi\)
\(662\) 4.03771 2.20665i 0.156930 0.0857638i
\(663\) −37.1465 −1.44265
\(664\) −23.7774 1.67475i −0.922743 0.0649930i
\(665\) 7.09012 + 9.68244i 0.274943 + 0.375469i
\(666\) −0.102427 0.187420i −0.00396896 0.00726238i
\(667\) −1.95904 −0.0758542
\(668\) 6.76983 10.5508i 0.261932 0.408222i
\(669\) 38.4375i 1.48608i
\(670\) 0.971187 0.530763i 0.0375202 0.0205052i
\(671\) 33.5738 1.29610
\(672\) 0.210739 24.1056i 0.00812945 0.929894i
\(673\) −46.2742 −1.78374 −0.891870 0.452291i \(-0.850607\pi\)
−0.891870 + 0.452291i \(0.850607\pi\)
\(674\) 14.9113 8.14917i 0.574362 0.313894i
\(675\) 5.48550i 0.211137i
\(676\) 5.50560 8.58048i 0.211754 0.330019i
\(677\) −0.112071 −0.00430726 −0.00215363 0.999998i \(-0.500686\pi\)
−0.00215363 + 0.999998i \(0.500686\pi\)
\(678\) −9.94652 18.2001i −0.381994 0.698970i
\(679\) 4.91408 + 6.71079i 0.188585 + 0.257537i
\(680\) 15.2957 + 1.07734i 0.586562 + 0.0413143i
\(681\) 19.5346 0.748569
\(682\) 21.9250 11.9822i 0.839551 0.458822i
\(683\) 0.561153 0.0214719 0.0107360 0.999942i \(-0.496583\pi\)
0.0107360 + 0.999942i \(0.496583\pi\)
\(684\) 3.09754 + 1.98752i 0.118438 + 0.0759946i
\(685\) −0.767338 −0.0293185
\(686\) 19.2483 + 17.7624i 0.734904 + 0.678171i
\(687\) 26.4154i 1.00781i
\(688\) 8.27643 + 18.0539i 0.315536 + 0.688299i
\(689\) 43.4873i 1.65673i
\(690\) 10.3917 5.67917i 0.395606 0.216202i
\(691\) 39.1762i 1.49033i −0.666879 0.745166i \(-0.732370\pi\)
0.666879 0.745166i \(-0.267630\pi\)
\(692\) 9.84337 15.3409i 0.374189 0.583173i
\(693\) −5.21059 + 3.81553i −0.197934 + 0.144940i
\(694\) 19.3271 10.5624i 0.733645 0.400944i
\(695\) 2.01854i 0.0765676i
\(696\) 0.120614 1.71243i 0.00457187 0.0649094i
\(697\) 31.2025 1.18188
\(698\) −43.1495 + 23.5816i −1.63323 + 0.892577i
\(699\) 42.5395i 1.60899i
\(700\) −0.325625 5.28147i −0.0123075 0.199621i
\(701\) 49.6478i 1.87517i 0.347753 + 0.937586i \(0.386945\pi\)
−0.347753 + 0.937586i \(0.613055\pi\)
\(702\) 15.8266 + 28.9594i 0.597337 + 1.09300i
\(703\) −1.68855 −0.0636849
\(704\) 47.6591 + 6.74717i 1.79622 + 0.254294i
\(705\) 6.22213i 0.234339i
\(706\) −8.48803 15.5313i −0.319451 0.584530i
\(707\) 34.7980 25.4814i 1.30871 0.958326i
\(708\) −18.4117 + 28.6946i −0.691953 + 1.07841i
\(709\) 13.0064i 0.488465i −0.969717 0.244233i \(-0.921464\pi\)
0.969717 0.244233i \(-0.0785360\pi\)
\(710\) −10.4310 19.0867i −0.391470 0.716310i
\(711\) 3.54823i 0.133069i
\(712\) −5.49518 0.387051i −0.205941 0.0145053i
\(713\) 15.2658i 0.571709i
\(714\) 13.8743 29.5795i 0.519233 1.10699i
\(715\) −25.5961 −0.957240
\(716\) 11.8287 18.4351i 0.442061 0.688952i
\(717\) 2.72060 0.101603
\(718\) −21.0755 38.5638i −0.786529 1.43919i
\(719\) 12.4976 0.466081 0.233041 0.972467i \(-0.425132\pi\)
0.233041 + 0.972467i \(0.425132\pi\)
\(720\) −0.676253 1.47515i −0.0252024 0.0549757i
\(721\) 25.3893 18.5917i 0.945546 0.692391i
\(722\) 1.95355 1.06763i 0.0727037 0.0397332i
\(723\) −8.45800 −0.314556
\(724\) −20.3026 + 31.6415i −0.754539 + 1.17595i
\(725\) 0.376818i 0.0139947i
\(726\) 27.5299 + 50.3741i 1.02173 + 1.86956i
\(727\) 49.8167 1.84760 0.923800 0.382875i \(-0.125066\pi\)
0.923800 + 0.382875i \(0.125066\pi\)
\(728\) 16.9570 + 26.9428i 0.628469 + 0.998568i
\(729\) −29.5969 −1.09618
\(730\) −5.94899 10.8854i −0.220182 0.402888i
\(731\) 26.9172i 0.995570i
\(732\) 15.1288 + 9.70726i 0.559175 + 0.358791i
\(733\) −48.8875 −1.80570 −0.902850 0.429955i \(-0.858529\pi\)
−0.902850 + 0.429955i \(0.858529\pi\)
\(734\) 17.4410 9.53168i 0.643760 0.351821i
\(735\) −10.7487 3.40390i −0.396472 0.125555i
\(736\) 17.5819 23.5752i 0.648079 0.868992i
\(737\) 4.70872 0.173448
\(738\) −1.58362 2.89770i −0.0582940 0.106666i
\(739\) −39.3743 −1.44841 −0.724204 0.689585i \(-0.757793\pi\)
−0.724204 + 0.689585i \(0.757793\pi\)
\(740\) 0.626629 + 0.402072i 0.0230353 + 0.0147805i
\(741\) 31.0800 1.14175
\(742\) −34.6287 16.2426i −1.27126 0.596285i
\(743\) 35.6179i 1.30669i −0.757059 0.653346i \(-0.773365\pi\)
0.757059 0.653346i \(-0.226635\pi\)
\(744\) 13.3441 + 0.939887i 0.489219 + 0.0344579i
\(745\) 4.23267i 0.155073i
\(746\) 13.4012 + 24.5215i 0.490654 + 0.897797i
\(747\) 3.41895i 0.125093i
\(748\) 54.9062 + 35.2302i 2.00757 + 1.28814i
\(749\) 22.3697 16.3806i 0.817373 0.598534i
\(750\) 1.09238 + 1.99883i 0.0398880 + 0.0729869i
\(751\) 13.2839i 0.484738i 0.970184 + 0.242369i \(0.0779245\pi\)
−0.970184 + 0.242369i \(0.922076\pi\)
\(752\) −6.43931 14.0465i −0.234817 0.512223i
\(753\) 22.5000 0.819946
\(754\) 1.08718 + 1.98932i 0.0395929 + 0.0724469i
\(755\) 0.625768i 0.0227740i
\(756\) −28.9715 + 1.78622i −1.05368 + 0.0649641i
\(757\) 20.0483i 0.728666i −0.931269 0.364333i \(-0.881297\pi\)
0.931269 0.364333i \(-0.118703\pi\)
\(758\) 0.599413 0.327585i 0.0217717 0.0118984i
\(759\) 50.3833 1.82880
\(760\) −12.7977 0.901400i −0.464221 0.0326972i
\(761\) 28.5860i 1.03624i −0.855307 0.518121i \(-0.826632\pi\)
0.855307 0.518121i \(-0.173368\pi\)
\(762\) 7.47808 4.08684i 0.270902 0.148051i
\(763\) 1.05791 + 1.44471i 0.0382989 + 0.0523019i
\(764\) −1.90244 1.22068i −0.0688277 0.0441628i
\(765\) 2.19936i 0.0795181i
\(766\) 1.35993 0.743214i 0.0491363 0.0268534i
\(767\) 45.0236i 1.62571i
\(768\) 19.5250 + 16.8202i 0.704547 + 0.606945i
\(769\) 26.3204i 0.949137i 0.880219 + 0.474569i \(0.157396\pi\)
−0.880219 + 0.474569i \(0.842604\pi\)
\(770\) 9.56021 20.3820i 0.344526 0.734518i
\(771\) −34.9418 −1.25840
\(772\) −3.53568 + 5.51035i −0.127252 + 0.198322i
\(773\) 0.586223 0.0210850 0.0105425 0.999944i \(-0.496644\pi\)
0.0105425 + 0.999944i \(0.496644\pi\)
\(774\) 2.49974 1.36613i 0.0898514 0.0491046i
\(775\) 2.93636 0.105477
\(776\) −8.86994 0.624750i −0.318412 0.0224272i
\(777\) 1.27993 0.937249i 0.0459173 0.0336236i
\(778\) 12.4282 + 22.7410i 0.445571 + 0.815303i
\(779\) −26.1067 −0.935370