Properties

Label 1110.2.l.b.697.6
Level $1110$
Weight $2$
Character 1110.697
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.l (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 697.6
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.b.43.6

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(2.21384 + 0.314477i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.376687 - 0.376687i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(2.21384 + 0.314477i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.376687 - 0.376687i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-0.314477 + 2.21384i) q^{10} -1.28566i q^{11} +(0.707107 + 0.707107i) q^{12} -5.12767i q^{13} +(0.376687 - 0.376687i) q^{14} +(-1.34306 - 1.78779i) q^{15} +1.00000 q^{16} -2.31038 q^{17} -1.00000 q^{18} +(3.87466 + 3.87466i) q^{19} +(-2.21384 - 0.314477i) q^{20} +0.532716i q^{21} +1.28566 q^{22} -6.29757i q^{23} +(-0.707107 + 0.707107i) q^{24} +(4.80221 + 1.39241i) q^{25} +5.12767 q^{26} +(0.707107 - 0.707107i) q^{27} +(0.376687 + 0.376687i) q^{28} +(-1.15504 + 1.15504i) q^{29} +(1.78779 - 1.34306i) q^{30} +(-7.11133 - 7.11133i) q^{31} +1.00000i q^{32} +(-0.909099 + 0.909099i) q^{33} -2.31038i q^{34} +(-0.715467 - 0.952386i) q^{35} -1.00000i q^{36} +(5.17182 - 3.20192i) q^{37} +(-3.87466 + 3.87466i) q^{38} +(-3.62581 + 3.62581i) q^{39} +(0.314477 - 2.21384i) q^{40} +2.12896i q^{41} -0.532716 q^{42} -2.56124i q^{43} +1.28566i q^{44} +(-0.314477 + 2.21384i) q^{45} +6.29757 q^{46} +(2.64523 + 2.64523i) q^{47} +(-0.707107 - 0.707107i) q^{48} -6.71621i q^{49} +(-1.39241 + 4.80221i) q^{50} +(1.63368 + 1.63368i) q^{51} +5.12767i q^{52} +(0.572887 - 0.572887i) q^{53} +(0.707107 + 0.707107i) q^{54} +(0.404311 - 2.84625i) q^{55} +(-0.376687 + 0.376687i) q^{56} -5.47960i q^{57} +(-1.15504 - 1.15504i) q^{58} +(-1.04438 - 1.04438i) q^{59} +(1.34306 + 1.78779i) q^{60} +(3.44882 + 3.44882i) q^{61} +(7.11133 - 7.11133i) q^{62} +(0.376687 - 0.376687i) q^{63} -1.00000 q^{64} +(1.61253 - 11.3519i) q^{65} +(-0.909099 - 0.909099i) q^{66} +(5.32260 - 5.32260i) q^{67} +2.31038 q^{68} +(-4.45305 + 4.45305i) q^{69} +(0.952386 - 0.715467i) q^{70} +4.38568 q^{71} +1.00000 q^{72} +(9.81049 + 9.81049i) q^{73} +(3.20192 + 5.17182i) q^{74} +(-2.41109 - 4.38025i) q^{75} +(-3.87466 - 3.87466i) q^{76} +(-0.484292 + 0.484292i) q^{77} +(-3.62581 - 3.62581i) q^{78} +(-11.4000 - 11.4000i) q^{79} +(2.21384 + 0.314477i) q^{80} -1.00000 q^{81} -2.12896 q^{82} +(11.5202 - 11.5202i) q^{83} -0.532716i q^{84} +(-5.11482 - 0.726561i) q^{85} +2.56124 q^{86} +1.63348 q^{87} -1.28566 q^{88} +(8.09354 - 8.09354i) q^{89} +(-2.21384 - 0.314477i) q^{90} +(-1.93153 + 1.93153i) q^{91} +6.29757i q^{92} +10.0569i q^{93} +(-2.64523 + 2.64523i) q^{94} +(7.35940 + 9.79638i) q^{95} +(0.707107 - 0.707107i) q^{96} +8.07546 q^{97} +6.71621 q^{98} +1.28566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{4} - 4q^{7} + O(q^{10}) \) \( 40q - 40q^{4} - 4q^{7} + 4q^{14} + 40q^{16} + 24q^{17} - 40q^{18} + 4q^{19} + 8q^{22} + 8q^{25} + 8q^{26} + 4q^{28} + 28q^{31} - 4q^{33} + 20q^{35} + 20q^{37} - 4q^{38} + 4q^{39} + 16q^{42} - 16q^{47} + 16q^{51} + 20q^{53} + 16q^{55} - 4q^{56} - 4q^{59} - 8q^{61} - 28q^{62} + 4q^{63} - 40q^{64} - 4q^{65} - 4q^{66} + 16q^{67} - 24q^{68} - 8q^{69} + 12q^{70} + 40q^{71} + 40q^{72} + 8q^{73} - 8q^{74} + 16q^{75} - 4q^{76} - 24q^{77} + 4q^{78} - 12q^{79} - 40q^{81} - 24q^{82} - 8q^{83} - 8q^{85} + 8q^{87} - 8q^{88} + 12q^{89} - 24q^{91} + 16q^{94} - 28q^{95} + 40q^{97} - 56q^{98} + 8q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) −1.00000 −0.500000
\(5\) 2.21384 + 0.314477i 0.990061 + 0.140638i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) −0.376687 0.376687i −0.142374 0.142374i 0.632327 0.774702i \(-0.282100\pi\)
−0.774702 + 0.632327i \(0.782100\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) −0.314477 + 2.21384i −0.0994464 + 0.700079i
\(11\) 1.28566i 0.387641i −0.981037 0.193821i \(-0.937912\pi\)
0.981037 0.193821i \(-0.0620880\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 5.12767i 1.42216i −0.703112 0.711080i \(-0.748207\pi\)
0.703112 0.711080i \(-0.251793\pi\)
\(14\) 0.376687 0.376687i 0.100674 0.100674i
\(15\) −1.34306 1.78779i −0.346775 0.461606i
\(16\) 1.00000 0.250000
\(17\) −2.31038 −0.560349 −0.280175 0.959949i \(-0.590392\pi\)
−0.280175 + 0.959949i \(0.590392\pi\)
\(18\) −1.00000 −0.235702
\(19\) 3.87466 + 3.87466i 0.888908 + 0.888908i 0.994418 0.105510i \(-0.0336476\pi\)
−0.105510 + 0.994418i \(0.533648\pi\)
\(20\) −2.21384 0.314477i −0.495031 0.0703192i
\(21\) 0.532716i 0.116248i
\(22\) 1.28566 0.274104
\(23\) 6.29757i 1.31313i −0.754268 0.656567i \(-0.772008\pi\)
0.754268 0.656567i \(-0.227992\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) 4.80221 + 1.39241i 0.960442 + 0.278481i
\(26\) 5.12767 1.00562
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 0.376687 + 0.376687i 0.0711872 + 0.0711872i
\(29\) −1.15504 + 1.15504i −0.214486 + 0.214486i −0.806170 0.591684i \(-0.798463\pi\)
0.591684 + 0.806170i \(0.298463\pi\)
\(30\) 1.78779 1.34306i 0.326405 0.245207i
\(31\) −7.11133 7.11133i −1.27723 1.27723i −0.942210 0.335023i \(-0.891256\pi\)
−0.335023 0.942210i \(-0.608744\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −0.909099 + 0.909099i −0.158254 + 0.158254i
\(34\) 2.31038i 0.396227i
\(35\) −0.715467 0.952386i −0.120936 0.160983i
\(36\) 1.00000i 0.166667i
\(37\) 5.17182 3.20192i 0.850242 0.526392i
\(38\) −3.87466 + 3.87466i −0.628553 + 0.628553i
\(39\) −3.62581 + 3.62581i −0.580594 + 0.580594i
\(40\) 0.314477 2.21384i 0.0497232 0.350039i
\(41\) 2.12896i 0.332487i 0.986085 + 0.166244i \(0.0531638\pi\)
−0.986085 + 0.166244i \(0.946836\pi\)
\(42\) −0.532716 −0.0821999
\(43\) 2.56124i 0.390585i −0.980745 0.195292i \(-0.937434\pi\)
0.980745 0.195292i \(-0.0625656\pi\)
\(44\) 1.28566i 0.193821i
\(45\) −0.314477 + 2.21384i −0.0468795 + 0.330020i
\(46\) 6.29757 0.928526
\(47\) 2.64523 + 2.64523i 0.385847 + 0.385847i 0.873203 0.487356i \(-0.162039\pi\)
−0.487356 + 0.873203i \(0.662039\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 6.71621i 0.959459i
\(50\) −1.39241 + 4.80221i −0.196916 + 0.679135i
\(51\) 1.63368 + 1.63368i 0.228762 + 0.228762i
\(52\) 5.12767i 0.711080i
\(53\) 0.572887 0.572887i 0.0786920 0.0786920i −0.666665 0.745357i \(-0.732279\pi\)
0.745357 + 0.666665i \(0.232279\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) 0.404311 2.84625i 0.0545172 0.383788i
\(56\) −0.376687 + 0.376687i −0.0503369 + 0.0503369i
\(57\) 5.47960i 0.725790i
\(58\) −1.15504 1.15504i −0.151664 0.151664i
\(59\) −1.04438 1.04438i −0.135966 0.135966i 0.635848 0.771814i \(-0.280651\pi\)
−0.771814 + 0.635848i \(0.780651\pi\)
\(60\) 1.34306 + 1.78779i 0.173388 + 0.230803i
\(61\) 3.44882 + 3.44882i 0.441576 + 0.441576i 0.892542 0.450965i \(-0.148920\pi\)
−0.450965 + 0.892542i \(0.648920\pi\)
\(62\) 7.11133 7.11133i 0.903140 0.903140i
\(63\) 0.376687 0.376687i 0.0474581 0.0474581i
\(64\) −1.00000 −0.125000
\(65\) 1.61253 11.3519i 0.200010 1.40802i
\(66\) −0.909099 0.909099i −0.111902 0.111902i
\(67\) 5.32260 5.32260i 0.650259 0.650259i −0.302797 0.953055i \(-0.597920\pi\)
0.953055 + 0.302797i \(0.0979203\pi\)
\(68\) 2.31038 0.280175
\(69\) −4.45305 + 4.45305i −0.536085 + 0.536085i
\(70\) 0.952386 0.715467i 0.113832 0.0855147i
\(71\) 4.38568 0.520484 0.260242 0.965543i \(-0.416198\pi\)
0.260242 + 0.965543i \(0.416198\pi\)
\(72\) 1.00000 0.117851
\(73\) 9.81049 + 9.81049i 1.14823 + 1.14823i 0.986901 + 0.161330i \(0.0515783\pi\)
0.161330 + 0.986901i \(0.448422\pi\)
\(74\) 3.20192 + 5.17182i 0.372215 + 0.601212i
\(75\) −2.41109 4.38025i −0.278409 0.505788i
\(76\) −3.87466 3.87466i −0.444454 0.444454i
\(77\) −0.484292 + 0.484292i −0.0551902 + 0.0551902i
\(78\) −3.62581 3.62581i −0.410542 0.410542i
\(79\) −11.4000 11.4000i −1.28259 1.28259i −0.939186 0.343409i \(-0.888418\pi\)
−0.343409 0.939186i \(-0.611582\pi\)
\(80\) 2.21384 + 0.314477i 0.247515 + 0.0351596i
\(81\) −1.00000 −0.111111
\(82\) −2.12896 −0.235104
\(83\) 11.5202 11.5202i 1.26450 1.26450i 0.315617 0.948887i \(-0.397788\pi\)
0.948887 0.315617i \(-0.102212\pi\)
\(84\) 0.532716i 0.0581241i
\(85\) −5.11482 0.726561i −0.554780 0.0788066i
\(86\) 2.56124 0.276185
\(87\) 1.63348 0.175127
\(88\) −1.28566 −0.137052
\(89\) 8.09354 8.09354i 0.857914 0.857914i −0.133179 0.991092i \(-0.542518\pi\)
0.991092 + 0.133179i \(0.0425184\pi\)
\(90\) −2.21384 0.314477i −0.233360 0.0331488i
\(91\) −1.93153 + 1.93153i −0.202479 + 0.202479i
\(92\) 6.29757i 0.656567i
\(93\) 10.0569i 1.04286i
\(94\) −2.64523 + 2.64523i −0.272835 + 0.272835i
\(95\) 7.35940 + 9.79638i 0.755059 + 1.00509i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) 8.07546 0.819939 0.409969 0.912099i \(-0.365539\pi\)
0.409969 + 0.912099i \(0.365539\pi\)
\(98\) 6.71621 0.678440
\(99\) 1.28566 0.129214
\(100\) −4.80221 1.39241i −0.480221 0.139241i
\(101\) 15.8768i 1.57980i 0.613233 + 0.789902i \(0.289869\pi\)
−0.613233 + 0.789902i \(0.710131\pi\)
\(102\) −1.63368 + 1.63368i −0.161759 + 0.161759i
\(103\) −9.00947 −0.887729 −0.443865 0.896094i \(-0.646393\pi\)
−0.443865 + 0.896094i \(0.646393\pi\)
\(104\) −5.12767 −0.502809
\(105\) −0.167527 + 1.17935i −0.0163490 + 0.115093i
\(106\) 0.572887 + 0.572887i 0.0556437 + 0.0556437i
\(107\) 1.41163 + 1.41163i 0.136468 + 0.136468i 0.772041 0.635573i \(-0.219236\pi\)
−0.635573 + 0.772041i \(0.719236\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) −1.15892 1.15892i −0.111004 0.111004i 0.649423 0.760427i \(-0.275010\pi\)
−0.760427 + 0.649423i \(0.775010\pi\)
\(110\) 2.84625 + 0.404311i 0.271379 + 0.0385495i
\(111\) −5.92113 1.39293i −0.562009 0.132211i
\(112\) −0.376687 0.376687i −0.0355936 0.0355936i
\(113\) 2.77598 0.261142 0.130571 0.991439i \(-0.458319\pi\)
0.130571 + 0.991439i \(0.458319\pi\)
\(114\) 5.47960 0.513211
\(115\) 1.98044 13.9418i 0.184677 1.30008i
\(116\) 1.15504 1.15504i 0.107243 0.107243i
\(117\) 5.12767 0.474053
\(118\) 1.04438 1.04438i 0.0961427 0.0961427i
\(119\) 0.870290 + 0.870290i 0.0797794 + 0.0797794i
\(120\) −1.78779 + 1.34306i −0.163202 + 0.122604i
\(121\) 9.34708 0.849734
\(122\) −3.44882 + 3.44882i −0.312242 + 0.312242i
\(123\) 1.50540 1.50540i 0.135737 0.135737i
\(124\) 7.11133 + 7.11133i 0.638616 + 0.638616i
\(125\) 10.1935 + 4.59275i 0.911731 + 0.410788i
\(126\) 0.376687 + 0.376687i 0.0335580 + 0.0335580i
\(127\) −10.6282 10.6282i −0.943105 0.943105i 0.0553618 0.998466i \(-0.482369\pi\)
−0.998466 + 0.0553618i \(0.982369\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −1.81107 + 1.81107i −0.159456 + 0.159456i
\(130\) 11.3519 + 1.61253i 0.995623 + 0.141429i
\(131\) 10.6555 + 10.6555i 0.930972 + 0.930972i 0.997767 0.0667945i \(-0.0212772\pi\)
−0.0667945 + 0.997767i \(0.521277\pi\)
\(132\) 0.909099 0.909099i 0.0791269 0.0791269i
\(133\) 2.91907i 0.253115i
\(134\) 5.32260 + 5.32260i 0.459802 + 0.459802i
\(135\) 1.78779 1.34306i 0.153869 0.115592i
\(136\) 2.31038i 0.198113i
\(137\) 8.98795 + 8.98795i 0.767892 + 0.767892i 0.977735 0.209843i \(-0.0672953\pi\)
−0.209843 + 0.977735i \(0.567295\pi\)
\(138\) −4.45305 4.45305i −0.379069 0.379069i
\(139\) −19.4517 −1.64987 −0.824937 0.565225i \(-0.808789\pi\)
−0.824937 + 0.565225i \(0.808789\pi\)
\(140\) 0.715467 + 0.952386i 0.0604680 + 0.0804913i
\(141\) 3.74092i 0.315042i
\(142\) 4.38568i 0.368038i
\(143\) −6.59244 −0.551287
\(144\) 1.00000i 0.0833333i
\(145\) −2.92032 + 2.19385i −0.242519 + 0.182189i
\(146\) −9.81049 + 9.81049i −0.811922 + 0.811922i
\(147\) −4.74908 + 4.74908i −0.391698 + 0.391698i
\(148\) −5.17182 + 3.20192i −0.425121 + 0.263196i
\(149\) 15.6534i 1.28238i 0.767382 + 0.641190i \(0.221559\pi\)
−0.767382 + 0.641190i \(0.778441\pi\)
\(150\) 4.38025 2.41109i 0.357646 0.196865i
\(151\) 3.10992i 0.253082i 0.991961 + 0.126541i \(0.0403875\pi\)
−0.991961 + 0.126541i \(0.959612\pi\)
\(152\) 3.87466 3.87466i 0.314276 0.314276i
\(153\) 2.31038i 0.186783i
\(154\) −0.484292 0.484292i −0.0390253 0.0390253i
\(155\) −13.5070 17.9797i −1.08491 1.44417i
\(156\) 3.62581 3.62581i 0.290297 0.290297i
\(157\) −12.5025 12.5025i −0.997805 0.997805i 0.00219308 0.999998i \(-0.499302\pi\)
−0.999998 + 0.00219308i \(0.999302\pi\)
\(158\) 11.4000 11.4000i 0.906931 0.906931i
\(159\) −0.810184 −0.0642518
\(160\) −0.314477 + 2.21384i −0.0248616 + 0.175020i
\(161\) −2.37221 + 2.37221i −0.186957 + 0.186957i
\(162\) 1.00000i 0.0785674i
\(163\) −8.61293 −0.674617 −0.337308 0.941394i \(-0.609517\pi\)
−0.337308 + 0.941394i \(0.609517\pi\)
\(164\) 2.12896i 0.166244i
\(165\) −2.29849 + 1.72671i −0.178938 + 0.134424i
\(166\) 11.5202 + 11.5202i 0.894139 + 0.894139i
\(167\) −21.8398 −1.69001 −0.845007 0.534755i \(-0.820404\pi\)
−0.845007 + 0.534755i \(0.820404\pi\)
\(168\) 0.532716 0.0410999
\(169\) −13.2930 −1.02254
\(170\) 0.726561 5.11482i 0.0557247 0.392289i
\(171\) −3.87466 + 3.87466i −0.296303 + 0.296303i
\(172\) 2.56124i 0.195292i
\(173\) 1.32378 + 1.32378i 0.100645 + 0.100645i 0.755636 0.654991i \(-0.227328\pi\)
−0.654991 + 0.755636i \(0.727328\pi\)
\(174\) 1.63348i 0.123833i
\(175\) −1.28443 2.33343i −0.0970937 0.176391i
\(176\) 1.28566i 0.0969103i
\(177\) 1.47697i 0.111016i
\(178\) 8.09354 + 8.09354i 0.606636 + 0.606636i
\(179\) −17.8003 + 17.8003i −1.33046 + 1.33046i −0.425501 + 0.904958i \(0.639902\pi\)
−0.904958 + 0.425501i \(0.860098\pi\)
\(180\) 0.314477 2.21384i 0.0234397 0.165010i
\(181\) −1.98719 −0.147707 −0.0738533 0.997269i \(-0.523530\pi\)
−0.0738533 + 0.997269i \(0.523530\pi\)
\(182\) −1.93153 1.93153i −0.143174 0.143174i
\(183\) 4.87737i 0.360546i
\(184\) −6.29757 −0.464263
\(185\) 12.4565 5.46213i 0.915822 0.401584i
\(186\) −10.0569 −0.737411
\(187\) 2.97036i 0.217214i
\(188\) −2.64523 2.64523i −0.192923 0.192923i
\(189\) −0.532716 −0.0387494
\(190\) −9.79638 + 7.35940i −0.710704 + 0.533907i
\(191\) −4.41456 + 4.41456i −0.319426 + 0.319426i −0.848547 0.529120i \(-0.822522\pi\)
0.529120 + 0.848547i \(0.322522\pi\)
\(192\) 0.707107 + 0.707107i 0.0510310 + 0.0510310i
\(193\) 2.09366i 0.150705i 0.997157 + 0.0753524i \(0.0240082\pi\)
−0.997157 + 0.0753524i \(0.975992\pi\)
\(194\) 8.07546i 0.579784i
\(195\) −9.16721 + 6.88674i −0.656477 + 0.493170i
\(196\) 6.71621i 0.479730i
\(197\) −4.75052 4.75052i −0.338460 0.338460i 0.517327 0.855788i \(-0.326927\pi\)
−0.855788 + 0.517327i \(0.826927\pi\)
\(198\) 1.28566i 0.0913679i
\(199\) 4.93690 4.93690i 0.349968 0.349968i −0.510130 0.860097i \(-0.670403\pi\)
0.860097 + 0.510130i \(0.170403\pi\)
\(200\) 1.39241 4.80221i 0.0984580 0.339567i
\(201\) −7.52729 −0.530934
\(202\) −15.8768 −1.11709
\(203\) 0.870179 0.0610746
\(204\) −1.63368 1.63368i −0.114381 0.114381i
\(205\) −0.669508 + 4.71318i −0.0467605 + 0.329183i
\(206\) 9.00947i 0.627719i
\(207\) 6.29757 0.437711
\(208\) 5.12767i 0.355540i
\(209\) 4.98150 4.98150i 0.344577 0.344577i
\(210\) −1.17935 0.167527i −0.0813829 0.0115605i
\(211\) −13.1658 −0.906374 −0.453187 0.891416i \(-0.649713\pi\)
−0.453187 + 0.891416i \(0.649713\pi\)
\(212\) −0.572887 + 0.572887i −0.0393460 + 0.0393460i
\(213\) −3.10114 3.10114i −0.212487 0.212487i
\(214\) −1.41163 + 1.41163i −0.0964974 + 0.0964974i
\(215\) 0.805450 5.67018i 0.0549312 0.386703i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) 5.35750i 0.363690i
\(218\) 1.15892 1.15892i 0.0784919 0.0784919i
\(219\) 13.8741i 0.937526i
\(220\) −0.404311 + 2.84625i −0.0272586 + 0.191894i
\(221\) 11.8469i 0.796906i
\(222\) 1.39293 5.92113i 0.0934874 0.397400i
\(223\) −13.0670 + 13.0670i −0.875031 + 0.875031i −0.993015 0.117984i \(-0.962357\pi\)
0.117984 + 0.993015i \(0.462357\pi\)
\(224\) 0.376687 0.376687i 0.0251685 0.0251685i
\(225\) −1.39241 + 4.80221i −0.0928271 + 0.320147i
\(226\) 2.77598i 0.184655i
\(227\) 16.0865 1.06770 0.533848 0.845580i \(-0.320745\pi\)
0.533848 + 0.845580i \(0.320745\pi\)
\(228\) 5.47960i 0.362895i
\(229\) 6.71533i 0.443762i 0.975074 + 0.221881i \(0.0712196\pi\)
−0.975074 + 0.221881i \(0.928780\pi\)
\(230\) 13.9418 + 1.98044i 0.919297 + 0.130586i
\(231\) 0.684892 0.0450626
\(232\) 1.15504 + 1.15504i 0.0758322 + 0.0758322i
\(233\) 4.61749 + 4.61749i 0.302502 + 0.302502i 0.841992 0.539490i \(-0.181383\pi\)
−0.539490 + 0.841992i \(0.681383\pi\)
\(234\) 5.12767i 0.335206i
\(235\) 5.02426 + 6.68799i 0.327747 + 0.436277i
\(236\) 1.04438 + 1.04438i 0.0679832 + 0.0679832i
\(237\) 16.1220i 1.04723i
\(238\) −0.870290 + 0.870290i −0.0564125 + 0.0564125i
\(239\) 13.1078 + 13.1078i 0.847873 + 0.847873i 0.989867 0.141995i \(-0.0453516\pi\)
−0.141995 + 0.989867i \(0.545352\pi\)
\(240\) −1.34306 1.78779i −0.0866938 0.115402i
\(241\) −12.6538 + 12.6538i −0.815103 + 0.815103i −0.985394 0.170291i \(-0.945529\pi\)
0.170291 + 0.985394i \(0.445529\pi\)
\(242\) 9.34708i 0.600853i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) −3.44882 3.44882i −0.220788 0.220788i
\(245\) 2.11209 14.8686i 0.134937 0.949923i
\(246\) 1.50540 + 1.50540i 0.0959808 + 0.0959808i
\(247\) 19.8680 19.8680i 1.26417 1.26417i
\(248\) −7.11133 + 7.11133i −0.451570 + 0.451570i
\(249\) −16.2920 −1.03246
\(250\) −4.59275 + 10.1935i −0.290471 + 0.644691i
\(251\) −0.829972 0.829972i −0.0523874 0.0523874i 0.680428 0.732815i \(-0.261794\pi\)
−0.732815 + 0.680428i \(0.761794\pi\)
\(252\) −0.376687 + 0.376687i −0.0237291 + 0.0237291i
\(253\) −8.09653 −0.509025
\(254\) 10.6282 10.6282i 0.666876 0.666876i
\(255\) 3.10297 + 4.13048i 0.194315 + 0.258661i
\(256\) 1.00000 0.0625000
\(257\) −9.61238 −0.599604 −0.299802 0.954001i \(-0.596921\pi\)
−0.299802 + 0.954001i \(0.596921\pi\)
\(258\) −1.81107 1.81107i −0.112752 0.112752i
\(259\) −3.15428 0.742037i −0.195997 0.0461079i
\(260\) −1.61253 + 11.3519i −0.100005 + 0.704012i
\(261\) −1.15504 1.15504i −0.0714953 0.0714953i
\(262\) −10.6555 + 10.6555i −0.658297 + 0.658297i
\(263\) 11.2512 + 11.2512i 0.693779 + 0.693779i 0.963061 0.269283i \(-0.0867866\pi\)
−0.269283 + 0.963061i \(0.586787\pi\)
\(264\) 0.909099 + 0.909099i 0.0559512 + 0.0559512i
\(265\) 1.44844 1.08812i 0.0889770 0.0668428i
\(266\) 2.91907 0.178980
\(267\) −11.4460 −0.700483
\(268\) −5.32260 + 5.32260i −0.325129 + 0.325129i
\(269\) 23.2912i 1.42009i −0.704158 0.710043i \(-0.748675\pi\)
0.704158 0.710043i \(-0.251325\pi\)
\(270\) 1.34306 + 1.78779i 0.0817357 + 0.108802i
\(271\) 13.8775 0.842996 0.421498 0.906829i \(-0.361504\pi\)
0.421498 + 0.906829i \(0.361504\pi\)
\(272\) −2.31038 −0.140087
\(273\) 2.73159 0.165323
\(274\) −8.98795 + 8.98795i −0.542982 + 0.542982i
\(275\) 1.79016 6.17401i 0.107951 0.372307i
\(276\) 4.45305 4.45305i 0.268042 0.268042i
\(277\) 6.57502i 0.395055i −0.980297 0.197527i \(-0.936709\pi\)
0.980297 0.197527i \(-0.0632912\pi\)
\(278\) 19.4517i 1.16664i
\(279\) 7.11133 7.11133i 0.425744 0.425744i
\(280\) −0.952386 + 0.715467i −0.0569160 + 0.0427573i
\(281\) −13.5903 + 13.5903i −0.810729 + 0.810729i −0.984743 0.174015i \(-0.944326\pi\)
0.174015 + 0.984743i \(0.444326\pi\)
\(282\) 3.74092 0.222769
\(283\) 8.54984 0.508235 0.254118 0.967173i \(-0.418215\pi\)
0.254118 + 0.967173i \(0.418215\pi\)
\(284\) −4.38568 −0.260242
\(285\) 1.72321 12.1310i 0.102074 0.718577i
\(286\) 6.59244i 0.389819i
\(287\) 0.801951 0.801951i 0.0473377 0.0473377i
\(288\) −1.00000 −0.0589256
\(289\) −11.6621 −0.686009
\(290\) −2.19385 2.92032i −0.128827 0.171487i
\(291\) −5.71021 5.71021i −0.334739 0.334739i
\(292\) −9.81049 9.81049i −0.574115 0.574115i
\(293\) 7.61554 7.61554i 0.444905 0.444905i −0.448752 0.893656i \(-0.648131\pi\)
0.893656 + 0.448752i \(0.148131\pi\)
\(294\) −4.74908 4.74908i −0.276972 0.276972i
\(295\) −1.98366 2.64052i −0.115493 0.153737i
\(296\) −3.20192 5.17182i −0.186108 0.300606i
\(297\) −0.909099 0.909099i −0.0527513 0.0527513i
\(298\) −15.6534 −0.906779
\(299\) −32.2918 −1.86749
\(300\) 2.41109 + 4.38025i 0.139205 + 0.252894i
\(301\) −0.964785 + 0.964785i −0.0556093 + 0.0556093i
\(302\) −3.10992 −0.178956
\(303\) 11.2266 11.2266i 0.644952 0.644952i
\(304\) 3.87466 + 3.87466i 0.222227 + 0.222227i
\(305\) 6.55058 + 8.71973i 0.375085 + 0.499290i
\(306\) 2.31038 0.132076
\(307\) 19.6731 19.6731i 1.12280 1.12280i 0.131482 0.991319i \(-0.458026\pi\)
0.991319 0.131482i \(-0.0419736\pi\)
\(308\) 0.484292 0.484292i 0.0275951 0.0275951i
\(309\) 6.37065 + 6.37065i 0.362414 + 0.362414i
\(310\) 17.9797 13.5070i 1.02118 0.767147i
\(311\) −3.86047 3.86047i −0.218907 0.218907i 0.589131 0.808038i \(-0.299470\pi\)
−0.808038 + 0.589131i \(0.799470\pi\)
\(312\) 3.62581 + 3.62581i 0.205271 + 0.205271i
\(313\) 18.9968i 1.07376i −0.843659 0.536880i \(-0.819603\pi\)
0.843659 0.536880i \(-0.180397\pi\)
\(314\) 12.5025 12.5025i 0.705554 0.705554i
\(315\) 0.952386 0.715467i 0.0536609 0.0403120i
\(316\) 11.4000 + 11.4000i 0.641297 + 0.641297i
\(317\) −17.8153 + 17.8153i −1.00061 + 1.00061i −0.000608272 1.00000i \(0.500194\pi\)
−1.00000 0.000608272i \(0.999806\pi\)
\(318\) 0.810184i 0.0454329i
\(319\) 1.48499 + 1.48499i 0.0831435 + 0.0831435i
\(320\) −2.21384 0.314477i −0.123758 0.0175798i
\(321\) 1.99635i 0.111426i
\(322\) −2.37221 2.37221i −0.132198 0.132198i
\(323\) −8.95194 8.95194i −0.498099 0.498099i
\(324\) 1.00000 0.0555556
\(325\) 7.13980 24.6241i 0.396045 1.36590i
\(326\) 8.61293i 0.477026i
\(327\) 1.63896i 0.0906347i
\(328\) 2.12896 0.117552
\(329\) 1.99285i 0.109869i
\(330\) −1.72671 2.29849i −0.0950524 0.126528i
\(331\) −1.11563 + 1.11563i −0.0613208 + 0.0613208i −0.737102 0.675781i \(-0.763806\pi\)
0.675781 + 0.737102i \(0.263806\pi\)
\(332\) −11.5202 + 11.5202i −0.632252 + 0.632252i
\(333\) 3.20192 + 5.17182i 0.175464 + 0.283414i
\(334\) 21.8398i 1.19502i
\(335\) 13.4572 10.1096i 0.735247 0.552344i
\(336\) 0.532716i 0.0290621i
\(337\) 19.6821 19.6821i 1.07215 1.07215i 0.0749653 0.997186i \(-0.476115\pi\)
0.997186 0.0749653i \(-0.0238846\pi\)
\(338\) 13.2930i 0.723042i
\(339\) −1.96291 1.96291i −0.106611 0.106611i
\(340\) 5.11482 + 0.726561i 0.277390 + 0.0394033i
\(341\) −9.14275 + 9.14275i −0.495108 + 0.495108i
\(342\) −3.87466 3.87466i −0.209518 0.209518i
\(343\) −5.16672 + 5.16672i −0.278977 + 0.278977i
\(344\) −2.56124 −0.138093
\(345\) −11.2587 + 8.45798i −0.606151 + 0.455362i
\(346\) −1.32378 + 1.32378i −0.0711669 + 0.0711669i
\(347\) 3.98304i 0.213821i −0.994269 0.106910i \(-0.965904\pi\)
0.994269 0.106910i \(-0.0340958\pi\)
\(348\) −1.63348 −0.0875635
\(349\) 7.69090i 0.411684i 0.978585 + 0.205842i \(0.0659934\pi\)
−0.978585 + 0.205842i \(0.934007\pi\)
\(350\) 2.33343 1.28443i 0.124727 0.0686556i
\(351\) −3.62581 3.62581i −0.193531 0.193531i
\(352\) 1.28566 0.0685259
\(353\) −21.0577 −1.12079 −0.560395 0.828226i \(-0.689351\pi\)
−0.560395 + 0.828226i \(0.689351\pi\)
\(354\) −1.47697 −0.0785002
\(355\) 9.70920 + 1.37919i 0.515311 + 0.0732000i
\(356\) −8.09354 + 8.09354i −0.428957 + 0.428957i
\(357\) 1.23078i 0.0651396i
\(358\) −17.8003 17.8003i −0.940777 0.940777i
\(359\) 19.0802i 1.00701i 0.863992 + 0.503506i \(0.167957\pi\)
−0.863992 + 0.503506i \(0.832043\pi\)
\(360\) 2.21384 + 0.314477i 0.116680 + 0.0165744i
\(361\) 11.0260i 0.580315i
\(362\) 1.98719i 0.104444i
\(363\) −6.60938 6.60938i −0.346903 0.346903i
\(364\) 1.93153 1.93153i 0.101240 0.101240i
\(365\) 18.6337 + 24.8041i 0.975333 + 1.29830i
\(366\) 4.87737 0.254944
\(367\) 13.0910 + 13.0910i 0.683346 + 0.683346i 0.960753 0.277407i \(-0.0894750\pi\)
−0.277407 + 0.960753i \(0.589475\pi\)
\(368\) 6.29757i 0.328283i
\(369\) −2.12896 −0.110829
\(370\) 5.46213 + 12.4565i 0.283963 + 0.647584i
\(371\) −0.431598 −0.0224075
\(372\) 10.0569i 0.521428i
\(373\) 17.5157 + 17.5157i 0.906927 + 0.906927i 0.996023 0.0890959i \(-0.0283978\pi\)
−0.0890959 + 0.996023i \(0.528398\pi\)
\(374\) −2.97036 −0.153594
\(375\) −3.96030 10.4554i −0.204509 0.539916i
\(376\) 2.64523 2.64523i 0.136417 0.136417i
\(377\) 5.92267 + 5.92267i 0.305033 + 0.305033i
\(378\) 0.532716i 0.0274000i
\(379\) 21.8739i 1.12358i 0.827278 + 0.561792i \(0.189888\pi\)
−0.827278 + 0.561792i \(0.810112\pi\)
\(380\) −7.35940 9.79638i −0.377529 0.502544i
\(381\) 15.0306i 0.770042i
\(382\) −4.41456 4.41456i −0.225868 0.225868i
\(383\) 5.61751i 0.287042i 0.989647 + 0.143521i \(0.0458424\pi\)
−0.989647 + 0.143521i \(0.954158\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) −1.22444 + 0.919848i −0.0624035 + 0.0468798i
\(386\) −2.09366 −0.106564
\(387\) 2.56124 0.130195
\(388\) −8.07546 −0.409969
\(389\) −5.37334 5.37334i −0.272439 0.272439i 0.557642 0.830081i \(-0.311706\pi\)
−0.830081 + 0.557642i \(0.811706\pi\)
\(390\) −6.88674 9.16721i −0.348724 0.464200i
\(391\) 14.5498i 0.735814i
\(392\) −6.71621 −0.339220
\(393\) 15.0691i 0.760136i
\(394\) 4.75052 4.75052i 0.239328 0.239328i
\(395\) −21.6527 28.8227i −1.08946 1.45023i
\(396\) −1.28566 −0.0646069
\(397\) −17.9874 + 17.9874i −0.902761 + 0.902761i −0.995674 0.0929128i \(-0.970382\pi\)
0.0929128 + 0.995674i \(0.470382\pi\)
\(398\) 4.93690 + 4.93690i 0.247465 + 0.247465i
\(399\) −2.06409 + 2.06409i −0.103334 + 0.103334i
\(400\) 4.80221 + 1.39241i 0.240110 + 0.0696203i
\(401\) 15.1996 + 15.1996i 0.759033 + 0.759033i 0.976146 0.217113i \(-0.0696641\pi\)
−0.217113 + 0.976146i \(0.569664\pi\)
\(402\) 7.52729i 0.375427i
\(403\) −36.4645 + 36.4645i −1.81643 + 1.81643i
\(404\) 15.8768i 0.789902i
\(405\) −2.21384 0.314477i −0.110007 0.0156265i
\(406\) 0.870179i 0.0431863i
\(407\) −4.11658 6.64920i −0.204051 0.329589i
\(408\) 1.63368 1.63368i 0.0808795 0.0808795i
\(409\) 27.1312 27.1312i 1.34155 1.34155i 0.447033 0.894517i \(-0.352481\pi\)
0.894517 0.447033i \(-0.147519\pi\)
\(410\) −4.71318 0.669508i −0.232767 0.0330646i
\(411\) 12.7109i 0.626981i
\(412\) 9.00947 0.443865
\(413\) 0.786807i 0.0387163i
\(414\) 6.29757i 0.309509i
\(415\) 29.1267 21.8810i 1.42977 1.07410i
\(416\) 5.12767 0.251405
\(417\) 13.7544 + 13.7544i 0.673558 + 0.673558i
\(418\) 4.98150 + 4.98150i 0.243653 + 0.243653i
\(419\) 7.19965i 0.351726i 0.984415 + 0.175863i \(0.0562716\pi\)
−0.984415 + 0.175863i \(0.943728\pi\)
\(420\) 0.167527 1.17935i 0.00817448 0.0575464i
\(421\) 6.17926 + 6.17926i 0.301159 + 0.301159i 0.841467 0.540308i \(-0.181692\pi\)
−0.540308 + 0.841467i \(0.681692\pi\)
\(422\) 13.1658i 0.640903i
\(423\) −2.64523 + 2.64523i −0.128616 + 0.128616i
\(424\) −0.572887 0.572887i −0.0278218 0.0278218i
\(425\) −11.0949 3.21699i −0.538183 0.156047i
\(426\) 3.10114 3.10114i 0.150251 0.150251i
\(427\) 2.59825i 0.125738i
\(428\) −1.41163 1.41163i −0.0682340 0.0682340i
\(429\) 4.66156 + 4.66156i 0.225062 + 0.225062i
\(430\) 5.67018 + 0.805450i 0.273440 + 0.0388423i
\(431\) 19.0871 + 19.0871i 0.919394 + 0.919394i 0.996985 0.0775910i \(-0.0247228\pi\)
−0.0775910 + 0.996985i \(0.524723\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) −27.0193 + 27.0193i −1.29847 + 1.29847i −0.369061 + 0.929405i \(0.620321\pi\)
−0.929405 + 0.369061i \(0.879679\pi\)
\(434\) −5.35750 −0.257168
\(435\) 3.61626 + 0.513691i 0.173386 + 0.0246296i
\(436\) 1.15892 + 1.15892i 0.0555022 + 0.0555022i
\(437\) 24.4009 24.4009i 1.16726 1.16726i
\(438\) 13.8741 0.662931
\(439\) 8.21948 8.21948i 0.392294 0.392294i −0.483210 0.875504i \(-0.660529\pi\)
0.875504 + 0.483210i \(0.160529\pi\)
\(440\) −2.84625 0.404311i −0.135690 0.0192748i
\(441\) 6.71621 0.319820
\(442\) −11.8469 −0.563497
\(443\) −7.35664 7.35664i −0.349525 0.349525i 0.510408 0.859932i \(-0.329494\pi\)
−0.859932 + 0.510408i \(0.829494\pi\)
\(444\) 5.92113 + 1.39293i 0.281004 + 0.0661055i
\(445\) 20.4631 15.3726i 0.970042 0.728731i
\(446\) −13.0670 13.0670i −0.618740 0.618740i
\(447\) 11.0687 11.0687i 0.523529 0.523529i
\(448\) 0.376687 + 0.376687i 0.0177968 + 0.0177968i
\(449\) 15.3192 + 15.3192i 0.722956 + 0.722956i 0.969206 0.246250i \(-0.0791986\pi\)
−0.246250 + 0.969206i \(0.579199\pi\)
\(450\) −4.80221 1.39241i −0.226378 0.0656387i
\(451\) 2.73711 0.128886
\(452\) −2.77598 −0.130571
\(453\) 2.19905 2.19905i 0.103320 0.103320i
\(454\) 16.0865i 0.754975i
\(455\) −4.88352 + 3.66868i −0.228943 + 0.171990i
\(456\) −5.47960 −0.256606
\(457\) 11.9041 0.556852 0.278426 0.960458i \(-0.410187\pi\)
0.278426 + 0.960458i \(0.410187\pi\)
\(458\) −6.71533 −0.313787
\(459\) −1.63368 + 1.63368i −0.0762539 + 0.0762539i
\(460\) −1.98044 + 13.9418i −0.0923385 + 0.650041i
\(461\) −21.6193 + 21.6193i −1.00691 + 1.00691i −0.00693591 + 0.999976i \(0.502208\pi\)
−0.999976 + 0.00693591i \(0.997792\pi\)
\(462\) 0.684892i 0.0318641i
\(463\) 7.74140i 0.359773i −0.983687 0.179887i \(-0.942427\pi\)
0.983687 0.179887i \(-0.0575731\pi\)
\(464\) −1.15504 + 1.15504i −0.0536215 + 0.0536215i
\(465\) −3.16268 + 22.2645i −0.146666 + 1.03249i
\(466\) −4.61749 + 4.61749i −0.213901 + 0.213901i
\(467\) 40.6171 1.87954 0.939768 0.341813i \(-0.111041\pi\)
0.939768 + 0.341813i \(0.111041\pi\)
\(468\) −5.12767 −0.237027
\(469\) −4.00991 −0.185160
\(470\) −6.68799 + 5.02426i −0.308494 + 0.231752i
\(471\) 17.6811i 0.814704i
\(472\) −1.04438 + 1.04438i −0.0480714 + 0.0480714i
\(473\) −3.29288 −0.151407
\(474\) −16.1220 −0.740506
\(475\) 13.2118 + 24.0020i 0.606200 + 1.10129i
\(476\) −0.870290 0.870290i −0.0398897 0.0398897i
\(477\) 0.572887 + 0.572887i 0.0262307 + 0.0262307i
\(478\) −13.1078 + 13.1078i −0.599537 + 0.599537i
\(479\) 4.76750 + 4.76750i 0.217833 + 0.217833i 0.807585 0.589752i \(-0.200774\pi\)
−0.589752 + 0.807585i \(0.700774\pi\)
\(480\) 1.78779 1.34306i 0.0816012 0.0613018i
\(481\) −16.4184 26.5194i −0.748613 1.20918i
\(482\) −12.6538 12.6538i −0.576365 0.576365i
\(483\) 3.35482 0.152649
\(484\) −9.34708 −0.424867
\(485\) 17.8778 + 2.53955i 0.811789 + 0.115315i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) −16.5284 −0.748971 −0.374486 0.927233i \(-0.622181\pi\)
−0.374486 + 0.927233i \(0.622181\pi\)
\(488\) 3.44882 3.44882i 0.156121 0.156121i
\(489\) 6.09026 + 6.09026i 0.275411 + 0.275411i
\(490\) 14.8686 + 2.11209i 0.671697 + 0.0954147i
\(491\) −11.4600 −0.517185 −0.258592 0.965987i \(-0.583259\pi\)
−0.258592 + 0.965987i \(0.583259\pi\)
\(492\) −1.50540 + 1.50540i −0.0678687 + 0.0678687i
\(493\) 2.66858 2.66858i 0.120187 0.120187i
\(494\) 19.8680 + 19.8680i 0.893902 + 0.893902i
\(495\) 2.84625 + 0.404311i 0.127929 + 0.0181724i
\(496\) −7.11133 7.11133i −0.319308 0.319308i
\(497\) −1.65203 1.65203i −0.0741036 0.0741036i
\(498\) 16.2920i 0.730062i
\(499\) 11.0278 11.0278i 0.493674 0.493674i −0.415788 0.909462i \(-0.636494\pi\)
0.909462 + 0.415788i \(0.136494\pi\)
\(500\) −10.1935 4.59275i −0.455865 0.205394i
\(501\) 15.4431 + 15.4431i 0.689946 + 0.689946i
\(502\) 0.829972 0.829972i 0.0370435 0.0370435i
\(503\) 17.9392i 0.799870i −0.916543 0.399935i \(-0.869033\pi\)
0.916543 0.399935i \(-0.130967\pi\)
\(504\) −0.376687 0.376687i −0.0167790 0.0167790i
\(505\) −4.99290 + 35.1488i −0.222181 + 1.56410i
\(506\) 8.09653i 0.359935i
\(507\) 9.39955 + 9.39955i 0.417449 + 0.417449i
\(508\) 10.6282 + 10.6282i 0.471552 + 0.471552i
\(509\) 10.1276 0.448897 0.224448 0.974486i \(-0.427942\pi\)
0.224448 + 0.974486i \(0.427942\pi\)
\(510\) −4.13048 + 3.10297i −0.182901 + 0.137402i
\(511\) 7.39097i 0.326957i
\(512\) 1.00000i 0.0441942i
\(513\) 5.47960 0.241930
\(514\) 9.61238i 0.423984i
\(515\) −19.9455 2.83327i −0.878906 0.124849i
\(516\) 1.81107 1.81107i 0.0797278 0.0797278i
\(517\) 3.40087 3.40087i 0.149570 0.149570i
\(518\) 0.742037 3.15428i 0.0326032 0.138591i
\(519\) 1.87211i 0.0821764i
\(520\) −11.3519 1.61253i −0.497812 0.0707143i
\(521\) 2.42962i 0.106444i −0.998583 0.0532219i \(-0.983051\pi\)
0.998583 0.0532219i \(-0.0169491\pi\)
\(522\) 1.15504 1.15504i 0.0505548 0.0505548i
\(523\) 27.3470i 1.19580i 0.801570 + 0.597901i \(0.203998\pi\)
−0.801570 + 0.597901i \(0.796002\pi\)
\(524\) −10.6555 10.6555i −0.465486 0.465486i
\(525\) −0.741757 + 2.55821i −0.0323729 + 0.111650i
\(526\) −11.2512 + 11.2512i −0.490576 + 0.490576i
\(527\) 16.4299 + 16.4299i 0.715696 + 0.715696i
\(528\) −0.909099 + 0.909099i −0.0395635 + 0.0395635i
\(529\) −16.6594 −0.724321
\(530\) 1.08812 + 1.44844i 0.0472650 + 0.0629163i
\(531\) 1.04438 1.04438i 0.0453221 0.0453221i
\(532\) 2.91907i 0.126558i
\(533\) 10.9166 0.472850
\(534\) 11.4460i 0.495317i
\(535\) 2.68121 + 3.56907i 0.115919 + 0.154304i
\(536\) −5.32260 5.32260i −0.229901 0.229901i
\(537\) 25.1735 1.08632
\(538\) 23.2912 1.00415
\(539\) −8.63477 −0.371926
\(540\) −1.78779 + 1.34306i −0.0769344 + 0.0577959i
\(541\) 24.0214 24.0214i 1.03276 1.03276i 0.0333158 0.999445i \(-0.489393\pi\)
0.999445 0.0333158i \(-0.0106067\pi\)
\(542\) 13.8775i 0.596088i
\(543\) 1.40516 + 1.40516i 0.0603010 + 0.0603010i
\(544\) 2.31038i 0.0990567i
\(545\) −2.20121 2.93012i −0.0942896 0.125513i
\(546\) 2.73159i 0.116901i
\(547\) 37.8077i 1.61654i 0.588810 + 0.808271i \(0.299596\pi\)
−0.588810 + 0.808271i \(0.700404\pi\)
\(548\) −8.98795 8.98795i −0.383946 0.383946i
\(549\) −3.44882 + 3.44882i −0.147192 + 0.147192i
\(550\) 6.17401 + 1.79016i 0.263261 + 0.0763327i
\(551\) −8.95079 −0.381316
\(552\) 4.45305 + 4.45305i 0.189535 + 0.189535i
\(553\) 8.58843i 0.365217i
\(554\) 6.57502 0.279346
\(555\) −12.6704 4.94579i −0.537829 0.209937i
\(556\) 19.4517 0.824937
\(557\) 18.1545i 0.769231i −0.923077 0.384615i \(-0.874334\pi\)
0.923077 0.384615i \(-0.125666\pi\)
\(558\) 7.11133 + 7.11133i 0.301047 + 0.301047i
\(559\) −13.1332 −0.555474
\(560\) −0.715467 0.952386i −0.0302340 0.0402457i
\(561\) 2.10036 2.10036i 0.0886774 0.0886774i
\(562\) −13.5903 13.5903i −0.573272 0.573272i
\(563\) 19.8695i 0.837398i −0.908125 0.418699i \(-0.862486\pi\)
0.908125 0.418699i \(-0.137514\pi\)
\(564\) 3.74092i 0.157521i
\(565\) 6.14558 + 0.872982i 0.258547 + 0.0367266i
\(566\) 8.54984i 0.359376i
\(567\) 0.376687 + 0.376687i 0.0158194 + 0.0158194i
\(568\) 4.38568i 0.184019i
\(569\) −6.05236 + 6.05236i −0.253728 + 0.253728i −0.822497 0.568769i \(-0.807420\pi\)
0.568769 + 0.822497i \(0.307420\pi\)
\(570\) 12.1310 + 1.72321i 0.508111 + 0.0721772i
\(571\) 12.1222 0.507297 0.253648 0.967296i \(-0.418369\pi\)
0.253648 + 0.967296i \(0.418369\pi\)
\(572\) 6.59244 0.275644
\(573\) 6.24313 0.260810
\(574\) 0.801951 + 0.801951i 0.0334728 + 0.0334728i
\(575\) 8.76877 30.2422i 0.365683 1.26119i
\(576\) 1.00000i 0.0416667i
\(577\) 36.8080 1.53234 0.766168 0.642641i \(-0.222161\pi\)
0.766168 + 0.642641i \(0.222161\pi\)
\(578\) 11.6621i 0.485081i
\(579\) 1.48044 1.48044i 0.0615249 0.0615249i
\(580\) 2.92032 2.19385i 0.121260 0.0910946i
\(581\) −8.67901 −0.360066
\(582\) 5.71021 5.71021i 0.236696 0.236696i
\(583\) −0.736538 0.736538i −0.0305043 0.0305043i
\(584\) 9.81049 9.81049i 0.405961 0.405961i
\(585\) 11.3519 + 1.61253i 0.469341 + 0.0666701i
\(586\) 7.61554 + 7.61554i 0.314595 + 0.314595i
\(587\) 14.5475i 0.600439i −0.953870 0.300220i \(-0.902940\pi\)
0.953870 0.300220i \(-0.0970600\pi\)
\(588\) 4.74908 4.74908i 0.195849 0.195849i
\(589\) 55.1080i 2.27068i
\(590\) 2.64052 1.98366i 0.108709 0.0816658i
\(591\) 6.71825i 0.276352i
\(592\) 5.17182 3.20192i 0.212560 0.131598i
\(593\) −16.6115 + 16.6115i −0.682153 + 0.682153i −0.960485 0.278332i \(-0.910219\pi\)
0.278332 + 0.960485i \(0.410219\pi\)
\(594\) 0.909099 0.909099i 0.0373008 0.0373008i
\(595\) 1.65300 + 2.20037i 0.0677664 + 0.0902065i
\(596\) 15.6534i 0.641190i
\(597\) −6.98183 −0.285747
\(598\) 32.2918i 1.32051i
\(599\) 13.5361i 0.553069i 0.961004 + 0.276535i \(0.0891861\pi\)
−0.961004 + 0.276535i \(0.910814\pi\)
\(600\) −4.38025 + 2.41109i −0.178823 + 0.0984325i
\(601\) 8.79388 0.358710 0.179355 0.983784i \(-0.442599\pi\)
0.179355 + 0.983784i \(0.442599\pi\)
\(602\) −0.964785 0.964785i −0.0393217 0.0393217i
\(603\) 5.32260 + 5.32260i 0.216753 + 0.216753i
\(604\) 3.10992i 0.126541i
\(605\) 20.6930 + 2.93944i 0.841289 + 0.119505i
\(606\) 11.2266 + 11.2266i 0.456050 + 0.456050i
\(607\) 1.05689i 0.0428979i −0.999770 0.0214489i \(-0.993172\pi\)
0.999770 0.0214489i \(-0.00682793\pi\)
\(608\) −3.87466 + 3.87466i −0.157138 + 0.157138i
\(609\) −0.615309 0.615309i −0.0249336 0.0249336i
\(610\) −8.71973 + 6.55058i −0.353051 + 0.265225i
\(611\) 13.5639 13.5639i 0.548735 0.548735i
\(612\) 2.31038i 0.0933915i
\(613\) −31.3429 31.3429i −1.26593 1.26593i −0.948174 0.317753i \(-0.897072\pi\)
−0.317753 0.948174i \(-0.602928\pi\)
\(614\) 19.6731 + 19.6731i 0.793940 + 0.793940i
\(615\) 3.80613 2.85931i 0.153478 0.115298i
\(616\) 0.484292 + 0.484292i 0.0195127 + 0.0195127i
\(617\) 18.9748 18.9748i 0.763896 0.763896i −0.213128 0.977024i \(-0.568365\pi\)
0.977024 + 0.213128i \(0.0683652\pi\)
\(618\) −6.37065 + 6.37065i −0.256265 + 0.256265i
\(619\) 14.1356 0.568157 0.284079 0.958801i \(-0.408312\pi\)
0.284079 + 0.958801i \(0.408312\pi\)
\(620\) 13.5070 + 17.9797i 0.542455 + 0.722083i
\(621\) −4.45305 4.45305i −0.178695 0.178695i
\(622\) 3.86047 3.86047i 0.154791 0.154791i
\(623\) −6.09747 −0.244290
\(624\) −3.62581 + 3.62581i −0.145149 + 0.145149i
\(625\) 21.1224 + 13.3732i 0.844896 + 0.534930i
\(626\) 18.9968 0.759263
\(627\) −7.04490 −0.281346
\(628\) 12.5025 + 12.5025i 0.498902 + 0.498902i
\(629\) −11.9489 + 7.39765i −0.476432 + 0.294963i
\(630\) 0.715467 + 0.952386i 0.0285049 + 0.0379440i
\(631\) −13.8331 13.8331i −0.550688 0.550688i 0.375951 0.926639i \(-0.377316\pi\)
−0.926639 + 0.375951i \(0.877316\pi\)
\(632\) −11.4000 + 11.4000i −0.453466 + 0.453466i
\(633\) 9.30966 + 9.30966i 0.370026 + 0.370026i
\(634\) −17.8153 17.8153i −0.707537 0.707537i
\(635\) −20.1869 26.8716i −0.801094 1.06637i
\(636\) 0.810184 0.0321259
\(637\) −34.4385 −1.36450
\(638\) −1.48499 + 1.48499i −0.0587914 + 0.0587914i
\(639\) 4.38568i 0.173495i
\(640\) 0.314477 2.21384i 0.0124308 0.0875099i
\(641\) 24.5047 0.967877 0.483938 0.875102i \(-0.339206\pi\)
0.483938 + 0.875102i \(0.339206\pi\)
\(642\) 1.99635 0.0787898
\(643\) −1.49125 −0.0588093 −0.0294046 0.999568i \(-0.509361\pi\)
−0.0294046 + 0.999568i \(0.509361\pi\)
\(644\) 2.37221 2.37221i 0.0934783 0.0934783i
\(645\) −4.57896 + 3.43988i −0.180296 + 0.135445i
\(646\) 8.95194 8.95194i 0.352209 0.352209i
\(647\) 32.4023i 1.27386i 0.770920 + 0.636932i \(0.219797\pi\)
−0.770920 + 0.636932i \(0.780203\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −1.34271 + 1.34271i −0.0527062 + 0.0527062i
\(650\) 24.6241 + 7.13980i 0.965838 + 0.280046i
\(651\) 3.78832 3.78832i 0.148476 0.148476i
\(652\) 8.61293 0.337308
\(653\) −49.0619 −1.91994 −0.959971 0.280099i \(-0.909633\pi\)
−0.959971 + 0.280099i \(0.909633\pi\)
\(654\) −1.63896 −0.0640884
\(655\) 20.2386 + 26.9404i 0.790789 + 1.05265i
\(656\) 2.12896i 0.0831218i
\(657\) −9.81049 + 9.81049i −0.382743 + 0.382743i
\(658\) 1.99285 0.0776894
\(659\) 11.1464 0.434200 0.217100 0.976149i \(-0.430340\pi\)
0.217100 + 0.976149i \(0.430340\pi\)
\(660\) 2.29849 1.72671i 0.0894688 0.0672122i
\(661\) 31.4369 + 31.4369i 1.22275 + 1.22275i 0.966649 + 0.256103i \(0.0824386\pi\)
0.256103 + 0.966649i \(0.417561\pi\)
\(662\) −1.11563 1.11563i −0.0433603 0.0433603i
\(663\) 8.37699 8.37699i 0.325335 0.325335i
\(664\) −11.5202 11.5202i −0.447070 0.447070i
\(665\) 0.917981 6.46237i 0.0355978 0.250600i
\(666\) −5.17182 + 3.20192i −0.200404 + 0.124072i
\(667\) 7.27396 + 7.27396i 0.281649 + 0.281649i
\(668\) 21.8398 0.845007
\(669\) 18.4795 0.714460
\(670\) 10.1096 + 13.4572i 0.390566 + 0.519898i
\(671\) 4.43401 4.43401i 0.171173 0.171173i
\(672\) −0.532716 −0.0205500
\(673\) −1.81889 + 1.81889i −0.0701132 + 0.0701132i −0.741294 0.671181i \(-0.765787\pi\)
0.671181 + 0.741294i \(0.265787\pi\)
\(674\) 19.6821 + 19.6821i 0.758126 + 0.758126i
\(675\) 4.38025 2.41109i 0.168596 0.0928031i
\(676\) 13.2930 0.511268
\(677\) 9.38604 9.38604i 0.360735 0.360735i −0.503349 0.864083i \(-0.667899\pi\)
0.864083 + 0.503349i \(0.167899\pi\)
\(678\) 1.96291 1.96291i 0.0753853 0.0753853i
\(679\) −3.04192 3.04192i −0.116738 0.116738i
\(680\) −0.726561 + 5.11482i −0.0278624 + 0.196144i
\(681\) −11.3749 11.3749i −0.435885 0.435885i
\(682\) −9.14275 9.14275i −0.350094 0.350094i
\(683\) 0.539905i 0.0206589i 0.999947 + 0.0103295i \(0.00328802\pi\)
−0.999947 + 0.0103295i \(0.996712\pi\)
\(684\) 3.87466 3.87466i 0.148151 0.148151i
\(685\) 17.0714 + 22.7244i 0.652265 + 0.868255i
\(686\) −5.16672 5.16672i −0.197266 0.197266i
\(687\) 4.74846 4.74846i 0.181165 0.181165i
\(688\) 2.56124i 0.0976462i
\(689\) −2.93757 2.93757i −0.111913 0.111913i
\(690\) −8.45798 11.2587i −0.321990 0.428613i
\(691\) 40.4342i 1.53819i −0.639135 0.769094i \(-0.720708\pi\)
0.639135 0.769094i \(-0.279292\pi\)
\(692\) −1.32378 1.32378i −0.0503226 0.0503226i
\(693\) −0.484292 0.484292i −0.0183967 0.0183967i
\(694\) 3.98304 0.151194
\(695\) −43.0631 6.11712i −1.63348 0.232036i
\(696\) 1.63348i 0.0619167i
\(697\) 4.91870i 0.186309i
\(698\) −7.69090 −0.291105
\(699\) 6.53012i 0.246992i
\(700\) 1.28443 + 2.33343i 0.0485469 + 0.0881954i
\(701\) 23.7123 23.7123i 0.895601 0.895601i −0.0994419 0.995043i \(-0.531706\pi\)
0.995043 + 0.0994419i \(0.0317057\pi\)
\(702\) 3.62581 3.62581i 0.136847 0.136847i
\(703\) 32.4454 + 7.63270i 1.22370 + 0.287873i
\(704\) 1.28566i 0.0484551i
\(705\) 1.17643 8.28182i 0.0443071 0.311911i
\(706\) 21.0577i 0.792518i
\(707\) 5.98060 5.98060i 0.224924 0.224924i
\(708\) 1.47697i 0.0555080i
\(709\) −16.8933 16.8933i −0.634441 0.634441i 0.314738 0.949179i \(-0.398083\pi\)
−0.949179 + 0.314738i \(0.898083\pi\)
\(710\) −1.37919 + 9.70920i −0.0517602 + 0.364380i
\(711\) 11.4000 11.4000i 0.427532 0.427532i
\(712\) −8.09354 8.09354i −0.303318 0.303318i
\(713\) −44.7841 + 44.7841i −1.67718 + 1.67718i
\(714\) 1.23078 0.0460607
\(715\) −14.5946 2.07317i −0.545808 0.0775322i
\(716\) 17.8003 17.8003i 0.665230 0.665230i
\(717\) 18.5372i 0.692285i
\(718\) −19.0802 −0.712065
\(719\) 13.6649i 0.509614i −0.966992 0.254807i \(-0.917988\pi\)
0.966992 0.254807i \(-0.0820120\pi\)
\(720\) −0.314477 + 2.21384i −0.0117199 + 0.0825051i
\(721\) 3.39375 + 3.39375i 0.126390 + 0.126390i
\(722\) −11.0260 −0.410345
\(723\) 17.8952 0.665529
\(724\) 1.98719 0.0738533
\(725\) −7.15504 + 3.93846i −0.265731 + 0.146271i
\(726\) 6.60938 6.60938i 0.245297 0.245297i
\(727\) 6.24565i 0.231638i −0.993270 0.115819i \(-0.963051\pi\)
0.993270 0.115819i \(-0.0369493\pi\)
\(728\) 1.93153 + 1.93153i 0.0715871 + 0.0715871i
\(729\) 1.00000i 0.0370370i
\(730\) −24.8041 + 18.6337i −0.918039 + 0.689665i
\(731\) 5.91743i 0.218864i
\(732\) 4.87737i 0.180273i
\(733\) 11.6047 + 11.6047i 0.428628 + 0.428628i 0.888161 0.459533i \(-0.151983\pi\)
−0.459533 + 0.888161i \(0.651983\pi\)
\(734\) −13.0910 + 13.0910i −0.483198 + 0.483198i
\(735\) −12.0072 + 9.02024i −0.442892 + 0.332717i
\(736\) 6.29757 0.232131
\(737\) −6.84305 6.84305i −0.252067 0.252067i
\(738\) 2.12896i 0.0783680i
\(739\) 26.9960 0.993065 0.496533 0.868018i \(-0.334606\pi\)
0.496533 + 0.868018i \(0.334606\pi\)
\(740\) −12.4565 + 5.46213i −0.457911 + 0.200792i
\(741\) −28.0976 −1.03219
\(742\) 0.431598i 0.0158445i
\(743\) −2.59470 2.59470i −0.0951901 0.0951901i 0.657908 0.753098i \(-0.271442\pi\)
−0.753098 + 0.657908i \(0.771442\pi\)
\(744\) 10.0569 0.368705
\(745\) −4.92265 + 34.6543i −0.180352 + 1.26963i
\(746\) −17.5157 + 17.5157i −0.641294 + 0.641294i
\(747\) 11.5202 + 11.5202i 0.421501 + 0.421501i
\(748\) 2.97036i 0.108607i
\(749\) 1.06349i 0.0388591i
\(750\) 10.4554 3.96030i 0.381778 0.144610i
\(751\) 37.6977i 1.37561i −0.725897 0.687803i \(-0.758575\pi\)
0.725897 0.687803i \(-0.241425\pi\)
\(752\) 2.64523 + 2.64523i 0.0964617 + 0.0964617i
\(753\) 1.17376i 0.0427741i
\(754\) −5.92267 + 5.92267i −0.215691 + 0.215691i
\(755\) −0.977999 + 6.88488i −0.0355930 + 0.250566i
\(756\) 0.532716 0.0193747
\(757\) −27.3872 −0.995406 −0.497703 0.867347i \(-0.665823\pi\)
−0.497703 + 0.867347i \(0.665823\pi\)
\(758\) −21.8739 −0.794494
\(759\) 5.72511 + 5.72511i 0.207808 + 0.207808i
\(760\) 9.79638 7.35940i 0.355352 0.266954i
\(761\) 41.7778i 1.51444i 0.653157 + 0.757222i \(0.273444\pi\)
−0.653157 + 0.757222i \(0.726556\pi\)
\(762\) −15.0306 −0.544502
\(763\) 0.873100i 0.0316083i
\(764\) 4.41456 4.41456i 0.159713 0.159713i
\(765\) 0.726561 5.11482i 0.0262689 0.184927i
\(766\) −5.61751 −0.202969
\(767\) −5.35522 + 5.35522i −0.193366 + 0.193366i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) 27.6843 27.6843i 0.998322 0.998322i −0.00167616 0.999999i \(-0.500534\pi\)
0.999999 + 0.00167616i \(0.000533537\pi\)
\(770\) −0.919848 1.22444i −0.0331490 0.0441259i
\(771\) 6.79698 + 6.79698i 0.244787 + 0.244787i
\(772\) 2.09366i 0.0753524i
\(773\) 19.1232 19.1232i 0.687812 0.687812i −0.273936 0.961748i \(-0.588326\pi\)
0.961748 + 0.273936i \(0.0883256\pi\)
\(774\) 2.56124i 0.0920618i
\(775\) −24.2482 44.0520i −0.871022 1.58239i
\(776\) 8.07546i 0.289892i
\(777\) 1.70571 + 2.75511i 0.0611921 + 0.0988391i
\(778\) 5.37334 5.37334i 0.192644 0.192644i
\(779\) −8.24898 + 8.24898i −0.295551 + 0.295551i
\(780\) 9.16721