Properties

Label 1110.2.u.f.401.7
Level $1110$
Weight $2$
Character 1110.401
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 401.7
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.f.191.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.70946 - 0.278802i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.01163 + 1.40592i) q^{6} -0.348034 q^{7} +(0.707107 + 0.707107i) q^{8} +(2.84454 - 0.953204i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.70946 - 0.278802i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.01163 + 1.40592i) q^{6} -0.348034 q^{7} +(0.707107 + 0.707107i) q^{8} +(2.84454 - 0.953204i) q^{9} -1.00000 q^{10} -3.72020 q^{11} +(-0.278802 - 1.70946i) q^{12} +(0.586358 - 0.586358i) q^{13} +(0.246097 - 0.246097i) q^{14} +(1.40592 + 1.01163i) q^{15} -1.00000 q^{16} +(2.90814 + 2.90814i) q^{17} +(-1.33738 + 2.68541i) q^{18} +(3.00391 - 3.00391i) q^{19} +(0.707107 - 0.707107i) q^{20} +(-0.594951 + 0.0970324i) q^{21} +(2.63058 - 2.63058i) q^{22} +(6.48575 + 6.48575i) q^{23} +(1.40592 + 1.01163i) q^{24} +1.00000i q^{25} +0.829235i q^{26} +(4.59688 - 2.42253i) q^{27} +0.348034i q^{28} +(-0.289070 + 0.289070i) q^{29} +(-1.70946 + 0.278802i) q^{30} +(4.18795 + 4.18795i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.35955 + 1.03720i) q^{33} -4.11273 q^{34} +(-0.246097 - 0.246097i) q^{35} +(-0.953204 - 2.84454i) q^{36} +(2.18867 - 5.67536i) q^{37} +4.24816i q^{38} +(0.838880 - 1.16584i) q^{39} +1.00000i q^{40} +9.94709 q^{41} +(0.352082 - 0.489306i) q^{42} +(-4.12802 + 4.12802i) q^{43} +3.72020i q^{44} +(2.68541 + 1.33738i) q^{45} -9.17224 q^{46} -7.55524i q^{47} +(-1.70946 + 0.278802i) q^{48} -6.87887 q^{49} +(-0.707107 - 0.707107i) q^{50} +(5.78215 + 4.16056i) q^{51} +(-0.586358 - 0.586358i) q^{52} -0.164161i q^{53} +(-1.53750 + 4.96348i) q^{54} +(-2.63058 - 2.63058i) q^{55} +(-0.246097 - 0.246097i) q^{56} +(4.29758 - 5.97257i) q^{57} -0.408806i q^{58} +(6.51580 + 6.51580i) q^{59} +(1.01163 - 1.40592i) q^{60} +(-8.60550 - 8.60550i) q^{61} -5.92266 q^{62} +(-0.989995 + 0.331747i) q^{63} +1.00000i q^{64} +0.829235 q^{65} +(3.76347 - 5.23029i) q^{66} +14.1406i q^{67} +(2.90814 - 2.90814i) q^{68} +(12.8954 + 9.27892i) q^{69} +0.348034 q^{70} +0.738626i q^{71} +(2.68541 + 1.33738i) q^{72} -15.9210i q^{73} +(2.46547 + 5.56071i) q^{74} +(0.278802 + 1.70946i) q^{75} +(-3.00391 - 3.00391i) q^{76} +1.29475 q^{77} +(0.231192 + 1.41755i) q^{78} +(6.84427 - 6.84427i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(7.18281 - 5.42285i) q^{81} +(-7.03365 + 7.03365i) q^{82} +9.66311i q^{83} +(0.0970324 + 0.594951i) q^{84} +4.11273i q^{85} -5.83790i q^{86} +(-0.413561 + 0.574747i) q^{87} +(-2.63058 - 2.63058i) q^{88} +(-5.63114 + 5.63114i) q^{89} +(-2.84454 + 0.953204i) q^{90} +(-0.204072 + 0.204072i) q^{91} +(6.48575 - 6.48575i) q^{92} +(8.32676 + 5.99154i) q^{93} +(5.34236 + 5.34236i) q^{94} +4.24816 q^{95} +(1.01163 - 1.40592i) q^{96} +(11.0221 - 11.0221i) q^{97} +(4.86410 - 4.86410i) q^{98} +(-10.5823 + 3.54611i) 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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

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

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
\(3\) 1.70946 0.278802i 0.986960 0.160966i
\(4\) 1.00000i 0.500000i
\(5\) 0.707107 + 0.707107i 0.316228 + 0.316228i
\(6\) −1.01163 + 1.40592i −0.412997 + 0.573963i
\(7\) −0.348034 −0.131544 −0.0657722 0.997835i \(-0.520951\pi\)
−0.0657722 + 0.997835i \(0.520951\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 2.84454 0.953204i 0.948180 0.317735i
\(10\) −1.00000 −0.316228
\(11\) −3.72020 −1.12168 −0.560841 0.827923i \(-0.689522\pi\)
−0.560841 + 0.827923i \(0.689522\pi\)
\(12\) −0.278802 1.70946i −0.0804832 0.493480i
\(13\) 0.586358 0.586358i 0.162626 0.162626i −0.621103 0.783729i \(-0.713315\pi\)
0.783729 + 0.621103i \(0.213315\pi\)
\(14\) 0.246097 0.246097i 0.0657722 0.0657722i
\(15\) 1.40592 + 1.01163i 0.363006 + 0.261202i
\(16\) −1.00000 −0.250000
\(17\) 2.90814 + 2.90814i 0.705327 + 0.705327i 0.965549 0.260222i \(-0.0837957\pi\)
−0.260222 + 0.965549i \(0.583796\pi\)
\(18\) −1.33738 + 2.68541i −0.315223 + 0.632957i
\(19\) 3.00391 3.00391i 0.689143 0.689143i −0.272899 0.962043i \(-0.587983\pi\)
0.962043 + 0.272899i \(0.0879826\pi\)
\(20\) 0.707107 0.707107i 0.158114 0.158114i
\(21\) −0.594951 + 0.0970324i −0.129829 + 0.0211742i
\(22\) 2.63058 2.63058i 0.560841 0.560841i
\(23\) 6.48575 + 6.48575i 1.35237 + 1.35237i 0.883000 + 0.469372i \(0.155520\pi\)
0.469372 + 0.883000i \(0.344480\pi\)
\(24\) 1.40592 + 1.01163i 0.286982 + 0.206498i
\(25\) 1.00000i 0.200000i
\(26\) 0.829235i 0.162626i
\(27\) 4.59688 2.42253i 0.884671 0.466216i
\(28\) 0.348034i 0.0657722i
\(29\) −0.289070 + 0.289070i −0.0536789 + 0.0536789i −0.733437 0.679758i \(-0.762085\pi\)
0.679758 + 0.733437i \(0.262085\pi\)
\(30\) −1.70946 + 0.278802i −0.312104 + 0.0509020i
\(31\) 4.18795 + 4.18795i 0.752178 + 0.752178i 0.974885 0.222707i \(-0.0714894\pi\)
−0.222707 + 0.974885i \(0.571489\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −6.35955 + 1.03720i −1.10706 + 0.180553i
\(34\) −4.11273 −0.705327
\(35\) −0.246097 0.246097i −0.0415980 0.0415980i
\(36\) −0.953204 2.84454i −0.158867 0.474090i
\(37\) 2.18867 5.67536i 0.359815 0.933024i
\(38\) 4.24816i 0.689143i
\(39\) 0.838880 1.16584i 0.134328 0.186683i
\(40\) 1.00000i 0.158114i
\(41\) 9.94709 1.55347 0.776737 0.629825i \(-0.216873\pi\)
0.776737 + 0.629825i \(0.216873\pi\)
\(42\) 0.352082 0.489306i 0.0543274 0.0755016i
\(43\) −4.12802 + 4.12802i −0.629517 + 0.629517i −0.947946 0.318430i \(-0.896844\pi\)
0.318430 + 0.947946i \(0.396844\pi\)
\(44\) 3.72020i 0.560841i
\(45\) 2.68541 + 1.33738i 0.400317 + 0.199364i
\(46\) −9.17224 −1.35237
\(47\) 7.55524i 1.10205i −0.834490 0.551023i \(-0.814238\pi\)
0.834490 0.551023i \(-0.185762\pi\)
\(48\) −1.70946 + 0.278802i −0.246740 + 0.0402416i
\(49\) −6.87887 −0.982696
\(50\) −0.707107 0.707107i −0.100000 0.100000i
\(51\) 5.78215 + 4.16056i 0.809663 + 0.582596i
\(52\) −0.586358 0.586358i −0.0813132 0.0813132i
\(53\) 0.164161i 0.0225492i −0.999936 0.0112746i \(-0.996411\pi\)
0.999936 0.0112746i \(-0.00358889\pi\)
\(54\) −1.53750 + 4.96348i −0.209227 + 0.675444i
\(55\) −2.63058 2.63058i −0.354707 0.354707i
\(56\) −0.246097 0.246097i −0.0328861 0.0328861i
\(57\) 4.29758 5.97257i 0.569228 0.791086i
\(58\) 0.408806i 0.0536789i
\(59\) 6.51580 + 6.51580i 0.848285 + 0.848285i 0.989919 0.141634i \(-0.0452355\pi\)
−0.141634 + 0.989919i \(0.545236\pi\)
\(60\) 1.01163 1.40592i 0.130601 0.181503i
\(61\) −8.60550 8.60550i −1.10182 1.10182i −0.994191 0.107630i \(-0.965674\pi\)
−0.107630 0.994191i \(-0.534326\pi\)
\(62\) −5.92266 −0.752178
\(63\) −0.989995 + 0.331747i −0.124728 + 0.0417962i
\(64\) 1.00000i 0.125000i
\(65\) 0.829235 0.102854
\(66\) 3.76347 5.23029i 0.463251 0.643804i
\(67\) 14.1406i 1.72755i 0.503879 + 0.863774i \(0.331906\pi\)
−0.503879 + 0.863774i \(0.668094\pi\)
\(68\) 2.90814 2.90814i 0.352664 0.352664i
\(69\) 12.8954 + 9.27892i 1.55242 + 1.11705i
\(70\) 0.348034 0.0415980
\(71\) 0.738626i 0.0876587i 0.999039 + 0.0438294i \(0.0139558\pi\)
−0.999039 + 0.0438294i \(0.986044\pi\)
\(72\) 2.68541 + 1.33738i 0.316479 + 0.157611i
\(73\) 15.9210i 1.86341i −0.363210 0.931707i \(-0.618319\pi\)
0.363210 0.931707i \(-0.381681\pi\)
\(74\) 2.46547 + 5.56071i 0.286605 + 0.646419i
\(75\) 0.278802 + 1.70946i 0.0321933 + 0.197392i
\(76\) −3.00391 3.00391i −0.344572 0.344572i
\(77\) 1.29475 0.147551
\(78\) 0.231192 + 1.41755i 0.0261774 + 0.160506i
\(79\) 6.84427 6.84427i 0.770041 0.770041i −0.208073 0.978113i \(-0.566719\pi\)
0.978113 + 0.208073i \(0.0667191\pi\)
\(80\) −0.707107 0.707107i −0.0790569 0.0790569i
\(81\) 7.18281 5.42285i 0.798089 0.602539i
\(82\) −7.03365 + 7.03365i −0.776737 + 0.776737i
\(83\) 9.66311i 1.06066i 0.847790 + 0.530332i \(0.177933\pi\)
−0.847790 + 0.530332i \(0.822067\pi\)
\(84\) 0.0970324 + 0.594951i 0.0105871 + 0.0649145i
\(85\) 4.11273i 0.446088i
\(86\) 5.83790i 0.629517i
\(87\) −0.413561 + 0.574747i −0.0443384 + 0.0616194i
\(88\) −2.63058 2.63058i −0.280421 0.280421i
\(89\) −5.63114 + 5.63114i −0.596900 + 0.596900i −0.939486 0.342586i \(-0.888697\pi\)
0.342586 + 0.939486i \(0.388697\pi\)
\(90\) −2.84454 + 0.953204i −0.299841 + 0.100476i
\(91\) −0.204072 + 0.204072i −0.0213926 + 0.0213926i
\(92\) 6.48575 6.48575i 0.676186 0.676186i
\(93\) 8.32676 + 5.99154i 0.863445 + 0.621294i
\(94\) 5.34236 + 5.34236i 0.551023 + 0.551023i
\(95\) 4.24816 0.435852
\(96\) 1.01163 1.40592i 0.103249 0.143491i
\(97\) 11.0221 11.0221i 1.11913 1.11913i 0.127257 0.991870i \(-0.459383\pi\)
0.991870 0.127257i \(-0.0406171\pi\)
\(98\) 4.86410 4.86410i 0.491348 0.491348i
\(99\) −10.5823 + 3.54611i −1.06356 + 0.356397i
\(100\) 1.00000 0.100000
\(101\) −16.0733 −1.59936 −0.799678 0.600429i \(-0.794997\pi\)
−0.799678 + 0.600429i \(0.794997\pi\)
\(102\) −7.03056 + 1.14664i −0.696129 + 0.113534i
\(103\) −6.58533 6.58533i −0.648872 0.648872i 0.303848 0.952720i \(-0.401728\pi\)
−0.952720 + 0.303848i \(0.901728\pi\)
\(104\) 0.829235 0.0813132
\(105\) −0.489306 0.352082i −0.0477514 0.0343597i
\(106\) 0.116079 + 0.116079i 0.0112746 + 0.0112746i
\(107\) 9.53842i 0.922114i −0.887371 0.461057i \(-0.847470\pi\)
0.887371 0.461057i \(-0.152530\pi\)
\(108\) −2.42253 4.59688i −0.233108 0.442335i
\(109\) −9.32002 + 9.32002i −0.892696 + 0.892696i −0.994776 0.102080i \(-0.967450\pi\)
0.102080 + 0.994776i \(0.467450\pi\)
\(110\) 3.72020 0.354707
\(111\) 2.15915 10.3120i 0.204937 0.978775i
\(112\) 0.348034 0.0328861
\(113\) −5.27517 + 5.27517i −0.496247 + 0.496247i −0.910267 0.414021i \(-0.864124\pi\)
0.414021 + 0.910267i \(0.364124\pi\)
\(114\) 1.18440 + 7.26209i 0.110929 + 0.680157i
\(115\) 9.17224i 0.855316i
\(116\) 0.289070 + 0.289070i 0.0268394 + 0.0268394i
\(117\) 1.10900 2.22684i 0.102527 0.205871i
\(118\) −9.21474 −0.848285
\(119\) −1.01213 1.01213i −0.0927818 0.0927818i
\(120\) 0.278802 + 1.70946i 0.0254510 + 0.156052i
\(121\) 2.83989 0.258172
\(122\) 12.1700 1.10182
\(123\) 17.0042 2.77327i 1.53322 0.250057i
\(124\) 4.18795 4.18795i 0.376089 0.376089i
\(125\) −0.707107 + 0.707107i −0.0632456 + 0.0632456i
\(126\) 0.465452 0.934613i 0.0414657 0.0832619i
\(127\) 6.85581 0.608355 0.304178 0.952615i \(-0.401618\pi\)
0.304178 + 0.952615i \(0.401618\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −5.90580 + 8.20760i −0.519977 + 0.722639i
\(130\) −0.586358 + 0.586358i −0.0514270 + 0.0514270i
\(131\) −3.32864 + 3.32864i −0.290824 + 0.290824i −0.837406 0.546582i \(-0.815929\pi\)
0.546582 + 0.837406i \(0.315929\pi\)
\(132\) 1.03720 + 6.35955i 0.0902766 + 0.553528i
\(133\) −1.04546 + 1.04546i −0.0906529 + 0.0906529i
\(134\) −9.99891 9.99891i −0.863774 0.863774i
\(135\) 4.96348 + 1.53750i 0.427188 + 0.132327i
\(136\) 4.11273i 0.352664i
\(137\) 2.18171i 0.186396i 0.995648 + 0.0931980i \(0.0297089\pi\)
−0.995648 + 0.0931980i \(0.970291\pi\)
\(138\) −15.6796 + 2.55724i −1.33474 + 0.217686i
\(139\) 3.77025i 0.319788i 0.987134 + 0.159894i \(0.0511153\pi\)
−0.987134 + 0.159894i \(0.948885\pi\)
\(140\) −0.246097 + 0.246097i −0.0207990 + 0.0207990i
\(141\) −2.10642 12.9154i −0.177392 1.08767i
\(142\) −0.522287 0.522287i −0.0438294 0.0438294i
\(143\) −2.18137 + 2.18137i −0.182415 + 0.182415i
\(144\) −2.84454 + 0.953204i −0.237045 + 0.0794336i
\(145\) −0.408806 −0.0339495
\(146\) 11.2579 + 11.2579i 0.931707 + 0.931707i
\(147\) −11.7592 + 1.91784i −0.969882 + 0.158181i
\(148\) −5.67536 2.18867i −0.466512 0.179907i
\(149\) 14.7936i 1.21194i 0.795489 + 0.605968i \(0.207214\pi\)
−0.795489 + 0.605968i \(0.792786\pi\)
\(150\) −1.40592 1.01163i −0.114793 0.0825994i
\(151\) 2.35718i 0.191825i 0.995390 + 0.0959124i \(0.0305769\pi\)
−0.995390 + 0.0959124i \(0.969423\pi\)
\(152\) 4.24816 0.344572
\(153\) 11.0444 + 5.50026i 0.892884 + 0.444670i
\(154\) −0.915530 + 0.915530i −0.0737755 + 0.0737755i
\(155\) 5.92266i 0.475719i
\(156\) −1.16584 0.838880i −0.0933415 0.0671642i
\(157\) −17.5824 −1.40323 −0.701616 0.712555i \(-0.747538\pi\)
−0.701616 + 0.712555i \(0.747538\pi\)
\(158\) 9.67926i 0.770041i
\(159\) −0.0457683 0.280627i −0.00362966 0.0222552i
\(160\) 1.00000 0.0790569
\(161\) −2.25726 2.25726i −0.177897 0.177897i
\(162\) −1.24448 + 8.91354i −0.0977753 + 0.700314i
\(163\) 2.83898 + 2.83898i 0.222366 + 0.222366i 0.809494 0.587128i \(-0.199742\pi\)
−0.587128 + 0.809494i \(0.699742\pi\)
\(164\) 9.94709i 0.776737i
\(165\) −5.23029 3.76347i −0.407178 0.292986i
\(166\) −6.83285 6.83285i −0.530332 0.530332i
\(167\) −8.73935 8.73935i −0.676272 0.676272i 0.282883 0.959154i \(-0.408709\pi\)
−0.959154 + 0.282883i \(0.908709\pi\)
\(168\) −0.489306 0.352082i −0.0377508 0.0271637i
\(169\) 12.3124i 0.947105i
\(170\) −2.90814 2.90814i −0.223044 0.223044i
\(171\) 5.68139 11.4081i 0.434467 0.872396i
\(172\) 4.12802 + 4.12802i 0.314758 + 0.314758i
\(173\) 19.5438 1.48588 0.742942 0.669356i \(-0.233430\pi\)
0.742942 + 0.669356i \(0.233430\pi\)
\(174\) −0.113976 0.698840i −0.00864049 0.0529789i
\(175\) 0.348034i 0.0263089i
\(176\) 3.72020 0.280421
\(177\) 12.9552 + 9.32192i 0.973769 + 0.700678i
\(178\) 7.96364i 0.596900i
\(179\) −4.09892 + 4.09892i −0.306368 + 0.306368i −0.843499 0.537131i \(-0.819508\pi\)
0.537131 + 0.843499i \(0.319508\pi\)
\(180\) 1.33738 2.68541i 0.0996821 0.200159i
\(181\) −10.8868 −0.809211 −0.404605 0.914491i \(-0.632591\pi\)
−0.404605 + 0.914491i \(0.632591\pi\)
\(182\) 0.288602i 0.0213926i
\(183\) −17.1100 12.3116i −1.26481 0.910097i
\(184\) 9.17224i 0.676186i
\(185\) 5.56071 2.46547i 0.408831 0.181265i
\(186\) −10.1246 + 1.65125i −0.742370 + 0.121075i
\(187\) −10.8189 10.8189i −0.791153 0.791153i
\(188\) −7.55524 −0.551023
\(189\) −1.59987 + 0.843122i −0.116373 + 0.0613281i
\(190\) −3.00391 + 3.00391i −0.217926 + 0.217926i
\(191\) −14.0022 14.0022i −1.01316 1.01316i −0.999912 0.0132497i \(-0.995782\pi\)
−0.0132497 0.999912i \(-0.504218\pi\)
\(192\) 0.278802 + 1.70946i 0.0201208 + 0.123370i
\(193\) 11.7248 11.7248i 0.843971 0.843971i −0.145401 0.989373i \(-0.546447\pi\)
0.989373 + 0.145401i \(0.0464473\pi\)
\(194\) 15.5876i 1.11913i
\(195\) 1.41755 0.231192i 0.101513 0.0165560i
\(196\) 6.87887i 0.491348i
\(197\) 1.38691i 0.0988132i −0.998779 0.0494066i \(-0.984267\pi\)
0.998779 0.0494066i \(-0.0157330\pi\)
\(198\) 4.97531 9.99026i 0.353580 0.709977i
\(199\) 12.9450 + 12.9450i 0.917647 + 0.917647i 0.996858 0.0792111i \(-0.0252401\pi\)
−0.0792111 + 0.996858i \(0.525240\pi\)
\(200\) −0.707107 + 0.707107i −0.0500000 + 0.0500000i
\(201\) 3.94242 + 24.1728i 0.278077 + 1.70502i
\(202\) 11.3656 11.3656i 0.799678 0.799678i
\(203\) 0.100606 0.100606i 0.00706115 0.00706115i
\(204\) 4.16056 5.78215i 0.291298 0.404832i
\(205\) 7.03365 + 7.03365i 0.491252 + 0.491252i
\(206\) 9.31307 0.648872
\(207\) 24.6312 + 12.2667i 1.71199 + 0.852597i
\(208\) −0.586358 + 0.586358i −0.0406566 + 0.0406566i
\(209\) −11.1751 + 11.1751i −0.773000 + 0.773000i
\(210\) 0.594951 0.0970324i 0.0410555 0.00669587i
\(211\) 16.2108 1.11600 0.557999 0.829841i \(-0.311569\pi\)
0.557999 + 0.829841i \(0.311569\pi\)
\(212\) −0.164161 −0.0112746
\(213\) 0.205930 + 1.26265i 0.0141101 + 0.0865157i
\(214\) 6.74468 + 6.74468i 0.461057 + 0.461057i
\(215\) −5.83790 −0.398141
\(216\) 4.96348 + 1.53750i 0.337722 + 0.104614i
\(217\) −1.45755 1.45755i −0.0989448 0.0989448i
\(218\) 13.1805i 0.892696i
\(219\) −4.43881 27.2164i −0.299947 1.83912i
\(220\) −2.63058 + 2.63058i −0.177354 + 0.177354i
\(221\) 3.41042 0.229410
\(222\) 5.76496 + 8.81846i 0.386919 + 0.591856i
\(223\) −5.18177 −0.346997 −0.173498 0.984834i \(-0.555507\pi\)
−0.173498 + 0.984834i \(0.555507\pi\)
\(224\) −0.246097 + 0.246097i −0.0164430 + 0.0164430i
\(225\) 0.953204 + 2.84454i 0.0635469 + 0.189636i
\(226\) 7.46022i 0.496247i
\(227\) −14.9028 14.9028i −0.989133 0.989133i 0.0108088 0.999942i \(-0.496559\pi\)
−0.999942 + 0.0108088i \(0.996559\pi\)
\(228\) −5.97257 4.29758i −0.395543 0.284614i
\(229\) −15.8227 −1.04559 −0.522796 0.852458i \(-0.675111\pi\)
−0.522796 + 0.852458i \(0.675111\pi\)
\(230\) −6.48575 6.48575i −0.427658 0.427658i
\(231\) 2.21334 0.360980i 0.145627 0.0237507i
\(232\) −0.408806 −0.0268394
\(233\) −17.2520 −1.13022 −0.565109 0.825016i \(-0.691166\pi\)
−0.565109 + 0.825016i \(0.691166\pi\)
\(234\) 0.790430 + 2.35879i 0.0516720 + 0.154199i
\(235\) 5.34236 5.34236i 0.348497 0.348497i
\(236\) 6.51580 6.51580i 0.424143 0.424143i
\(237\) 9.79184 13.6082i 0.636049 0.883950i
\(238\) 1.43137 0.0927818
\(239\) −8.68104 8.68104i −0.561530 0.561530i 0.368212 0.929742i \(-0.379970\pi\)
−0.929742 + 0.368212i \(0.879970\pi\)
\(240\) −1.40592 1.01163i −0.0907515 0.0653005i
\(241\) 11.6905 11.6905i 0.753050 0.753050i −0.221997 0.975047i \(-0.571258\pi\)
0.975047 + 0.221997i \(0.0712576\pi\)
\(242\) −2.00811 + 2.00811i −0.129086 + 0.129086i
\(243\) 10.7669 11.2728i 0.690694 0.723147i
\(244\) −8.60550 + 8.60550i −0.550911 + 0.550911i
\(245\) −4.86410 4.86410i −0.310756 0.310756i
\(246\) −10.0628 + 13.9848i −0.641580 + 0.891637i
\(247\) 3.52273i 0.224146i
\(248\) 5.92266i 0.376089i
\(249\) 2.69409 + 16.5187i 0.170731 + 1.04683i
\(250\) 1.00000i 0.0632456i
\(251\) −5.17135 + 5.17135i −0.326413 + 0.326413i −0.851221 0.524808i \(-0.824137\pi\)
0.524808 + 0.851221i \(0.324137\pi\)
\(252\) 0.331747 + 0.989995i 0.0208981 + 0.0623638i
\(253\) −24.1283 24.1283i −1.51693 1.51693i
\(254\) −4.84779 + 4.84779i −0.304178 + 0.304178i
\(255\) 1.14664 + 7.03056i 0.0718051 + 0.440271i
\(256\) 1.00000 0.0625000
\(257\) −20.9443 20.9443i −1.30647 1.30647i −0.923947 0.382520i \(-0.875056\pi\)
−0.382520 0.923947i \(-0.624944\pi\)
\(258\) −1.62762 9.97968i −0.101331 0.621308i
\(259\) −0.761730 + 1.97522i −0.0473316 + 0.122734i
\(260\) 0.829235i 0.0514270i
\(261\) −0.546728 + 1.09781i −0.0338416 + 0.0679529i
\(262\) 4.70740i 0.290824i
\(263\) −0.826816 −0.0509837 −0.0254918 0.999675i \(-0.508115\pi\)
−0.0254918 + 0.999675i \(0.508115\pi\)
\(264\) −5.23029 3.76347i −0.321902 0.231626i
\(265\) 0.116079 0.116079i 0.00713068 0.00713068i
\(266\) 1.47850i 0.0906529i
\(267\) −8.05627 + 11.1962i −0.493035 + 0.685197i
\(268\) 14.1406 0.863774
\(269\) 22.9891i 1.40167i −0.713323 0.700835i \(-0.752811\pi\)
0.713323 0.700835i \(-0.247189\pi\)
\(270\) −4.59688 + 2.42253i −0.279757 + 0.147431i
\(271\) −8.57848 −0.521105 −0.260553 0.965460i \(-0.583905\pi\)
−0.260553 + 0.965460i \(0.583905\pi\)
\(272\) −2.90814 2.90814i −0.176332 0.176332i
\(273\) −0.291959 + 0.405750i −0.0176701 + 0.0245571i
\(274\) −1.54270 1.54270i −0.0931980 0.0931980i
\(275\) 3.72020i 0.224337i
\(276\) 9.27892 12.8954i 0.558526 0.776212i
\(277\) −12.4445 12.4445i −0.747719 0.747719i 0.226332 0.974050i \(-0.427327\pi\)
−0.974050 + 0.226332i \(0.927327\pi\)
\(278\) −2.66597 2.66597i −0.159894 0.159894i
\(279\) 15.9048 + 7.92082i 0.952193 + 0.474207i
\(280\) 0.348034i 0.0207990i
\(281\) 0.971269 + 0.971269i 0.0579410 + 0.0579410i 0.735484 0.677543i \(-0.236955\pi\)
−0.677543 + 0.735484i \(0.736955\pi\)
\(282\) 10.6220 + 7.64312i 0.632533 + 0.455141i
\(283\) −1.46923 1.46923i −0.0873364 0.0873364i 0.662089 0.749425i \(-0.269670\pi\)
−0.749425 + 0.662089i \(0.769670\pi\)
\(284\) 0.738626 0.0438294
\(285\) 7.26209 1.18440i 0.430169 0.0701576i
\(286\) 3.08492i 0.182415i
\(287\) −3.46192 −0.204351
\(288\) 1.33738 2.68541i 0.0788056 0.158239i
\(289\) 0.0854698i 0.00502764i
\(290\) 0.289070 0.289070i 0.0169748 0.0169748i
\(291\) 15.7689 21.9149i 0.924391 1.28467i
\(292\) −15.9210 −0.931707
\(293\) 1.74107i 0.101715i 0.998706 + 0.0508573i \(0.0161954\pi\)
−0.998706 + 0.0508573i \(0.983805\pi\)
\(294\) 6.95888 9.67112i 0.405850 0.564031i
\(295\) 9.21474i 0.536503i
\(296\) 5.56071 2.46547i 0.323210 0.143302i
\(297\) −17.1013 + 9.01230i −0.992320 + 0.522947i
\(298\) −10.4606 10.4606i −0.605968 0.605968i
\(299\) 7.60594 0.439863
\(300\) 1.70946 0.278802i 0.0986960 0.0160966i
\(301\) 1.43669 1.43669i 0.0828093 0.0828093i
\(302\) −1.66678 1.66678i −0.0959124 0.0959124i
\(303\) −27.4768 + 4.48127i −1.57850 + 0.257442i
\(304\) −3.00391 + 3.00391i −0.172286 + 0.172286i
\(305\) 12.1700i 0.696853i
\(306\) −11.6988 + 3.92027i −0.668777 + 0.224107i
\(307\) 9.43400i 0.538427i −0.963081 0.269213i \(-0.913236\pi\)
0.963081 0.269213i \(-0.0867637\pi\)
\(308\) 1.29475i 0.0737755i
\(309\) −13.0934 9.42139i −0.744857 0.535964i
\(310\) −4.18795 4.18795i −0.237860 0.237860i
\(311\) −17.4484 + 17.4484i −0.989408 + 0.989408i −0.999944 0.0105370i \(-0.996646\pi\)
0.0105370 + 0.999944i \(0.496646\pi\)
\(312\) 1.41755 0.231192i 0.0802529 0.0130887i
\(313\) 7.61657 7.61657i 0.430514 0.430514i −0.458289 0.888803i \(-0.651538\pi\)
0.888803 + 0.458289i \(0.151538\pi\)
\(314\) 12.4327 12.4327i 0.701616 0.701616i
\(315\) −0.934613 0.465452i −0.0526595 0.0262252i
\(316\) −6.84427 6.84427i −0.385020 0.385020i
\(317\) −20.5090 −1.15190 −0.575951 0.817485i \(-0.695368\pi\)
−0.575951 + 0.817485i \(0.695368\pi\)
\(318\) 0.230796 + 0.166070i 0.0129424 + 0.00931275i
\(319\) 1.07540 1.07540i 0.0602107 0.0602107i
\(320\) −0.707107 + 0.707107i −0.0395285 + 0.0395285i
\(321\) −2.65933 16.3056i −0.148429 0.910089i
\(322\) 3.19225 0.177897
\(323\) 17.4715 0.972143
\(324\) −5.42285 7.18281i −0.301269 0.399045i
\(325\) 0.586358 + 0.586358i 0.0325253 + 0.0325253i
\(326\) −4.01492 −0.222366
\(327\) −13.3338 + 18.5307i −0.737362 + 1.02475i
\(328\) 7.03365 + 7.03365i 0.388369 + 0.388369i
\(329\) 2.62948i 0.144968i
\(330\) 6.35955 1.03720i 0.350082 0.0570959i
\(331\) −1.37048 + 1.37048i −0.0753283 + 0.0753283i −0.743767 0.668439i \(-0.766963\pi\)
0.668439 + 0.743767i \(0.266963\pi\)
\(332\) 9.66311 0.530332
\(333\) 0.815972 18.2300i 0.0447150 0.999000i
\(334\) 12.3593 0.676272
\(335\) −9.99891 + 9.99891i −0.546299 + 0.546299i
\(336\) 0.594951 0.0970324i 0.0324572 0.00529355i
\(337\) 33.5414i 1.82711i −0.406711 0.913557i \(-0.633324\pi\)
0.406711 0.913557i \(-0.366676\pi\)
\(338\) −8.70616 8.70616i −0.473553 0.473553i
\(339\) −7.54699 + 10.4884i −0.409896 + 0.569654i
\(340\) 4.11273 0.223044
\(341\) −15.5800 15.5800i −0.843705 0.843705i
\(342\) 4.04937 + 12.0841i 0.218965 + 0.653432i
\(343\) 4.83031 0.260812
\(344\) −5.83790 −0.314758
\(345\) 2.55724 + 15.6796i 0.137677 + 0.844162i
\(346\) −13.8195 + 13.8195i −0.742942 + 0.742942i
\(347\) 14.2780 14.2780i 0.766484 0.766484i −0.211002 0.977486i \(-0.567673\pi\)
0.977486 + 0.211002i \(0.0676727\pi\)
\(348\) 0.574747 + 0.413561i 0.0308097 + 0.0221692i
\(349\) 6.56028 0.351164 0.175582 0.984465i \(-0.443819\pi\)
0.175582 + 0.984465i \(0.443819\pi\)
\(350\) 0.246097 + 0.246097i 0.0131544 + 0.0131544i
\(351\) 1.27495 4.11589i 0.0680517 0.219690i
\(352\) −2.63058 + 2.63058i −0.140210 + 0.140210i
\(353\) 25.6324 25.6324i 1.36427 1.36427i 0.495889 0.868386i \(-0.334842\pi\)
0.868386 0.495889i \(-0.165158\pi\)
\(354\) −15.7523 + 2.56909i −0.837224 + 0.136545i
\(355\) −0.522287 + 0.522287i −0.0277201 + 0.0277201i
\(356\) 5.63114 + 5.63114i 0.298450 + 0.298450i
\(357\) −2.01238 1.44802i −0.106507 0.0766372i
\(358\) 5.79675i 0.306368i
\(359\) 18.5723i 0.980209i 0.871664 + 0.490104i \(0.163041\pi\)
−0.871664 + 0.490104i \(0.836959\pi\)
\(360\) 0.953204 + 2.84454i 0.0502382 + 0.149920i
\(361\) 0.953098i 0.0501631i
\(362\) 7.69814 7.69814i 0.404605 0.404605i
\(363\) 4.85470 0.791767i 0.254805 0.0415570i
\(364\) 0.204072 + 0.204072i 0.0106963 + 0.0106963i
\(365\) 11.2579 11.2579i 0.589263 0.589263i
\(366\) 20.8042 3.39302i 1.08745 0.177356i
\(367\) −10.8985 −0.568898 −0.284449 0.958691i \(-0.591811\pi\)
−0.284449 + 0.958691i \(0.591811\pi\)
\(368\) −6.48575 6.48575i −0.338093 0.338093i
\(369\) 28.2949 9.48160i 1.47297 0.493592i
\(370\) −2.18867 + 5.67536i −0.113783 + 0.295048i
\(371\) 0.0571334i 0.00296622i
\(372\) 5.99154 8.32676i 0.310647 0.431722i
\(373\) 27.5555i 1.42677i 0.700772 + 0.713385i \(0.252839\pi\)
−0.700772 + 0.713385i \(0.747161\pi\)
\(374\) 15.3002 0.791153
\(375\) −1.01163 + 1.40592i −0.0522404 + 0.0726012i
\(376\) 5.34236 5.34236i 0.275511 0.275511i
\(377\) 0.338996i 0.0174592i
\(378\) 0.535102 1.72746i 0.0275227 0.0888508i
\(379\) 5.24130 0.269228 0.134614 0.990898i \(-0.457021\pi\)
0.134614 + 0.990898i \(0.457021\pi\)
\(380\) 4.24816i 0.217926i
\(381\) 11.7198 1.91141i 0.600422 0.0979247i
\(382\) 19.8021 1.01316
\(383\) 20.0864 + 20.0864i 1.02637 + 1.02637i 0.999643 + 0.0267254i \(0.00850796\pi\)
0.0267254 + 0.999643i \(0.491492\pi\)
\(384\) −1.40592 1.01163i −0.0717454 0.0516246i
\(385\) 0.915530 + 0.915530i 0.0466597 + 0.0466597i
\(386\) 16.5814i 0.843971i
\(387\) −7.80746 + 15.6771i −0.396876 + 0.796914i
\(388\) −11.0221 11.0221i −0.559563 0.559563i
\(389\) 5.94620 + 5.94620i 0.301484 + 0.301484i 0.841594 0.540110i \(-0.181617\pi\)
−0.540110 + 0.841594i \(0.681617\pi\)
\(390\) −0.838880 + 1.16584i −0.0424784 + 0.0590344i
\(391\) 37.7229i 1.90773i
\(392\) −4.86410 4.86410i −0.245674 0.245674i
\(393\) −4.76216 + 6.61822i −0.240219 + 0.333845i
\(394\) 0.980693 + 0.980693i 0.0494066 + 0.0494066i
\(395\) 9.67926 0.487016
\(396\) 3.54611 + 10.5823i 0.178199 + 0.531778i
\(397\) 12.6809i 0.636435i 0.948018 + 0.318218i \(0.103084\pi\)
−0.948018 + 0.318218i \(0.896916\pi\)
\(398\) −18.3070 −0.917647
\(399\) −1.49570 + 2.07865i −0.0748787 + 0.104063i
\(400\) 1.00000i 0.0500000i
\(401\) −21.8657 + 21.8657i −1.09192 + 1.09192i −0.0965961 + 0.995324i \(0.530796\pi\)
−0.995324 + 0.0965961i \(0.969204\pi\)
\(402\) −19.8805 14.3051i −0.991549 0.713472i
\(403\) 4.91127 0.244648
\(404\) 16.0733i 0.799678i
\(405\) 8.91354 + 1.24448i 0.442918 + 0.0618385i
\(406\) 0.142278i 0.00706115i
\(407\) −8.14228 + 21.1135i −0.403598 + 1.04656i
\(408\) 1.14664 + 7.03056i 0.0567669 + 0.348065i
\(409\) −19.3828 19.3828i −0.958419 0.958419i 0.0407505 0.999169i \(-0.487025\pi\)
−0.999169 + 0.0407505i \(0.987025\pi\)
\(410\) −9.94709 −0.491252
\(411\) 0.608264 + 3.72955i 0.0300035 + 0.183965i
\(412\) −6.58533 + 6.58533i −0.324436 + 0.324436i
\(413\) −2.26772 2.26772i −0.111587 0.111587i
\(414\) −26.0908 + 8.74301i −1.28229 + 0.429696i
\(415\) −6.83285 + 6.83285i −0.335411 + 0.335411i
\(416\) 0.829235i 0.0406566i
\(417\) 1.05115 + 6.44510i 0.0514751 + 0.315618i
\(418\) 15.8040i 0.773000i
\(419\) 24.4184i 1.19292i 0.802643 + 0.596459i \(0.203426\pi\)
−0.802643 + 0.596459i \(0.796574\pi\)
\(420\) −0.352082 + 0.489306i −0.0171798 + 0.0238757i
\(421\) 1.06044 + 1.06044i 0.0516825 + 0.0516825i 0.732476 0.680793i \(-0.238365\pi\)
−0.680793 + 0.732476i \(0.738365\pi\)
\(422\) −11.4628 + 11.4628i −0.557999 + 0.557999i
\(423\) −7.20169 21.4912i −0.350158 1.04494i
\(424\) 0.116079 0.116079i 0.00563730 0.00563730i
\(425\) −2.90814 + 2.90814i −0.141065 + 0.141065i
\(426\) −1.03845 0.747217i −0.0503129 0.0362028i
\(427\) 2.99500 + 2.99500i 0.144938 + 0.144938i
\(428\) −9.53842 −0.461057
\(429\) −3.12080 + 4.33714i −0.150674 + 0.209399i
\(430\) 4.12802 4.12802i 0.199071 0.199071i
\(431\) 10.7838 10.7838i 0.519437 0.519437i −0.397964 0.917401i \(-0.630283\pi\)
0.917401 + 0.397964i \(0.130283\pi\)
\(432\) −4.59688 + 2.42253i −0.221168 + 0.116554i
\(433\) 15.8953 0.763879 0.381940 0.924187i \(-0.375256\pi\)
0.381940 + 0.924187i \(0.375256\pi\)
\(434\) 2.06128 0.0989448
\(435\) −0.698840 + 0.113976i −0.0335068 + 0.00546473i
\(436\) 9.32002 + 9.32002i 0.446348 + 0.446348i
\(437\) 38.9652 1.86396
\(438\) 22.3836 + 16.1062i 1.06953 + 0.769584i
\(439\) −9.33981 9.33981i −0.445765 0.445765i 0.448179 0.893944i \(-0.352073\pi\)
−0.893944 + 0.448179i \(0.852073\pi\)
\(440\) 3.72020i 0.177354i
\(441\) −19.5672 + 6.55697i −0.931772 + 0.312237i
\(442\) −2.41153 + 2.41153i −0.114705 + 0.114705i
\(443\) −9.89122 −0.469946 −0.234973 0.972002i \(-0.575500\pi\)
−0.234973 + 0.972002i \(0.575500\pi\)
\(444\) −10.3120 2.15915i −0.489388 0.102469i
\(445\) −7.96364 −0.377513
\(446\) 3.66406 3.66406i 0.173498 0.173498i
\(447\) 4.12447 + 25.2891i 0.195081 + 1.19613i
\(448\) 0.348034i 0.0164430i
\(449\) −6.81279 6.81279i −0.321516 0.321516i 0.527833 0.849348i \(-0.323005\pi\)
−0.849348 + 0.527833i \(0.823005\pi\)
\(450\) −2.68541 1.33738i −0.126591 0.0630445i
\(451\) −37.0052 −1.74251
\(452\) 5.27517 + 5.27517i 0.248123 + 0.248123i
\(453\) 0.657187 + 4.02952i 0.0308773 + 0.189323i
\(454\) 21.0757 0.989133
\(455\) −0.288602 −0.0135299
\(456\) 7.26209 1.18440i 0.340078 0.0554644i
\(457\) 17.0996 17.0996i 0.799888 0.799888i −0.183190 0.983078i \(-0.558642\pi\)
0.983078 + 0.183190i \(0.0586423\pi\)
\(458\) 11.1883 11.1883i 0.522796 0.522796i
\(459\) 20.4134 + 6.32332i 0.952817 + 0.295147i
\(460\) 9.17224 0.427658
\(461\) −0.729355 0.729355i −0.0339694 0.0339694i 0.689918 0.723887i \(-0.257647\pi\)
−0.723887 + 0.689918i \(0.757647\pi\)
\(462\) −1.30981 + 1.82032i −0.0609381 + 0.0846888i
\(463\) 6.28322 6.28322i 0.292006 0.292006i −0.545866 0.837872i \(-0.683799\pi\)
0.837872 + 0.545866i \(0.183799\pi\)
\(464\) 0.289070 0.289070i 0.0134197 0.0134197i
\(465\) 1.65125 + 10.1246i 0.0765748 + 0.469516i
\(466\) 12.1990 12.1990i 0.565109 0.565109i
\(467\) −8.64673 8.64673i −0.400123 0.400123i 0.478153 0.878276i \(-0.341306\pi\)
−0.878276 + 0.478153i \(0.841306\pi\)
\(468\) −2.22684 1.10900i −0.102936 0.0512635i
\(469\) 4.92140i 0.227249i
\(470\) 7.55524i 0.348497i
\(471\) −30.0566 + 4.90202i −1.38493 + 0.225873i
\(472\) 9.21474i 0.424143i
\(473\) 15.3570 15.3570i 0.706118 0.706118i
\(474\) 2.69860 + 16.5464i 0.123951 + 0.759999i
\(475\) 3.00391 + 3.00391i 0.137829 + 0.137829i
\(476\) −1.01213 + 1.01213i −0.0463909 + 0.0463909i
\(477\) −0.156479 0.466961i −0.00716466 0.0213807i
\(478\) 12.2768 0.561530
\(479\) −4.52948 4.52948i −0.206957 0.206957i 0.596016 0.802973i \(-0.296750\pi\)
−0.802973 + 0.596016i \(0.796750\pi\)
\(480\) 1.70946 0.278802i 0.0780260 0.0127255i
\(481\) −2.04445 4.61113i −0.0932189 0.210250i
\(482\) 16.5328i 0.753050i
\(483\) −4.48803 3.22938i −0.204213 0.146942i
\(484\) 2.83989i 0.129086i
\(485\) 15.5876 0.707798
\(486\) 0.357725 + 15.5844i 0.0162267 + 0.706921i
\(487\) 3.72320 3.72320i 0.168714 0.168714i −0.617700 0.786414i \(-0.711935\pi\)
0.786414 + 0.617700i \(0.211935\pi\)
\(488\) 12.1700i 0.550911i
\(489\) 5.64465 + 4.06162i 0.255260 + 0.183673i
\(490\) 6.87887 0.310756
\(491\) 4.21252i 0.190108i 0.995472 + 0.0950542i \(0.0303024\pi\)
−0.995472 + 0.0950542i \(0.969698\pi\)
\(492\) −2.77327 17.0042i −0.125028 0.766608i
\(493\) −1.68131 −0.0757223
\(494\) 2.49094 + 2.49094i 0.112073 + 0.112073i
\(495\) −9.99026 4.97531i −0.449029 0.223623i
\(496\) −4.18795 4.18795i −0.188045 0.188045i
\(497\) 0.257067i 0.0115310i
\(498\) −13.5855 9.77550i −0.608782 0.438051i
\(499\) 14.6597 + 14.6597i 0.656259 + 0.656259i 0.954493 0.298234i \(-0.0963975\pi\)
−0.298234 + 0.954493i \(0.596398\pi\)
\(500\) 0.707107 + 0.707107i 0.0316228 + 0.0316228i
\(501\) −17.3762 12.5031i −0.776310 0.558596i
\(502\) 7.31340i 0.326413i
\(503\) −17.8082 17.8082i −0.794028 0.794028i 0.188118 0.982146i \(-0.439761\pi\)
−0.982146 + 0.188118i \(0.939761\pi\)
\(504\) −0.934613 0.465452i −0.0416310 0.0207329i
\(505\) −11.3656 11.3656i −0.505761 0.505761i
\(506\) 34.1226 1.51693
\(507\) 3.43271 + 21.0476i 0.152452 + 0.934755i
\(508\) 6.85581i 0.304178i
\(509\) −29.2452 −1.29627 −0.648136 0.761525i \(-0.724451\pi\)
−0.648136 + 0.761525i \(0.724451\pi\)
\(510\) −5.78215 4.16056i −0.256038 0.184233i
\(511\) 5.54105i 0.245122i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 6.53155 21.0857i 0.288375 0.930955i
\(514\) 29.6197 1.30647
\(515\) 9.31307i 0.410383i
\(516\) 8.20760 + 5.90580i 0.361319 + 0.259988i
\(517\) 28.1070i 1.23615i
\(518\) −0.858065 1.93531i −0.0377012 0.0850328i
\(519\) 33.4094 5.44883i 1.46651 0.239177i
\(520\) 0.586358 + 0.586358i 0.0257135 + 0.0257135i
\(521\) 43.3318 1.89840 0.949201 0.314670i \(-0.101894\pi\)
0.949201 + 0.314670i \(0.101894\pi\)
\(522\) −0.389676 1.16287i −0.0170556 0.0508972i
\(523\) −28.8478 + 28.8478i −1.26143 + 1.26143i −0.311025 + 0.950402i \(0.600672\pi\)
−0.950402 + 0.311025i \(0.899328\pi\)
\(524\) 3.32864 + 3.32864i 0.145412 + 0.145412i
\(525\) −0.0970324 0.594951i −0.00423484 0.0259658i
\(526\) 0.584647 0.584647i 0.0254918 0.0254918i
\(527\) 24.3583i 1.06106i
\(528\) 6.35955 1.03720i 0.276764 0.0451383i
\(529\) 61.1299i 2.65782i
\(530\) 0.164161i 0.00713068i
\(531\) 24.7453 + 12.3236i 1.07386 + 0.534797i
\(532\) 1.04546 + 1.04546i 0.0453265 + 0.0453265i
\(533\) 5.83255 5.83255i 0.252636 0.252636i
\(534\) −2.22028 13.6136i −0.0960808 0.589116i
\(535\) 6.74468 6.74468i 0.291598 0.291598i
\(536\) −9.99891 + 9.99891i −0.431887 + 0.431887i
\(537\) −5.86418 + 8.14975i −0.253058 + 0.351688i
\(538\) 16.2557 + 16.2557i 0.700835 + 0.700835i
\(539\) 25.5908 1.10227
\(540\) 1.53750 4.96348i 0.0661635 0.213594i
\(541\) −8.31534 + 8.31534i −0.357504 + 0.357504i −0.862892 0.505388i \(-0.831349\pi\)
0.505388 + 0.862892i \(0.331349\pi\)
\(542\) 6.06590 6.06590i 0.260553 0.260553i
\(543\) −18.6106 + 3.03526i −0.798658 + 0.130256i
\(544\) 4.11273 0.176332
\(545\) −13.1805 −0.564591
\(546\) −0.0804627 0.493354i −0.00344348 0.0211136i
\(547\) 23.2358 + 23.2358i 0.993489 + 0.993489i 0.999979 0.00648976i \(-0.00206577\pi\)
−0.00648976 + 0.999979i \(0.502066\pi\)
\(548\) 2.18171 0.0931980
\(549\) −32.6815 16.2759i −1.39481 0.694638i
\(550\) 2.63058 + 2.63058i 0.112168 + 0.112168i
\(551\) 1.73668i 0.0739849i
\(552\) 2.55724 + 15.6796i 0.108843 + 0.667369i
\(553\) −2.38204 + 2.38204i −0.101294 + 0.101294i
\(554\) 17.5992 0.747719
\(555\) 8.81846 5.76496i 0.374323 0.244709i
\(556\) 3.77025 0.159894
\(557\) 12.9487 12.9487i 0.548653 0.548653i −0.377398 0.926051i \(-0.623181\pi\)
0.926051 + 0.377398i \(0.123181\pi\)
\(558\) −16.8472 + 5.64550i −0.713200 + 0.238993i
\(559\) 4.84099i 0.204752i
\(560\) 0.246097 + 0.246097i 0.0103995 + 0.0103995i
\(561\) −21.5108 15.4781i −0.908185 0.653487i
\(562\) −1.37358 −0.0579410
\(563\) −13.8676 13.8676i −0.584452 0.584452i 0.351672 0.936123i \(-0.385613\pi\)
−0.936123 + 0.351672i \(0.885613\pi\)
\(564\) −12.9154 + 2.10642i −0.543837 + 0.0886961i
\(565\) −7.46022 −0.313854
\(566\) 2.07780 0.0873364
\(567\) −2.49986 + 1.88733i −0.104984 + 0.0792606i
\(568\) −0.522287 + 0.522287i −0.0219147 + 0.0219147i
\(569\) −4.33445 + 4.33445i −0.181710 + 0.181710i −0.792100 0.610391i \(-0.791012\pi\)
0.610391 + 0.792100i \(0.291012\pi\)
\(570\) −4.29758 + 5.97257i −0.180006 + 0.250163i
\(571\) −2.93311 −0.122747 −0.0613734 0.998115i \(-0.519548\pi\)
−0.0613734 + 0.998115i \(0.519548\pi\)
\(572\) 2.18137 + 2.18137i 0.0912076 + 0.0912076i
\(573\) −27.8401 20.0324i −1.16304 0.836865i
\(574\) 2.44795 2.44795i 0.102175 0.102175i
\(575\) −6.48575 + 6.48575i −0.270475 + 0.270475i
\(576\) 0.953204 + 2.84454i 0.0397168 + 0.118522i
\(577\) 9.36579 9.36579i 0.389903 0.389903i −0.484750 0.874653i \(-0.661089\pi\)
0.874653 + 0.484750i \(0.161089\pi\)
\(578\) 0.0604363 + 0.0604363i 0.00251382 + 0.00251382i
\(579\) 16.7743 23.3121i 0.697115 0.968817i
\(580\) 0.408806i 0.0169748i
\(581\) 3.36309i 0.139524i
\(582\) 4.34586 + 26.6465i 0.180142 + 1.10453i
\(583\) 0.610710i 0.0252930i
\(584\) 11.2579 11.2579i 0.465854 0.465854i
\(585\) 2.35879 0.790430i 0.0975240 0.0326803i
\(586\) −1.23113 1.23113i −0.0508573 0.0508573i
\(587\) −18.1736 + 18.1736i −0.750105 + 0.750105i −0.974499 0.224394i \(-0.927960\pi\)
0.224394 + 0.974499i \(0.427960\pi\)
\(588\) 1.91784 + 11.7592i 0.0790905 + 0.484941i
\(589\) 25.1604 1.03672
\(590\) −6.51580 6.51580i −0.268251 0.268251i
\(591\) −0.386673 2.37087i −0.0159056 0.0975247i
\(592\) −2.18867 + 5.67536i −0.0899537 + 0.233256i
\(593\) 43.6579i 1.79282i 0.443229 + 0.896408i \(0.353833\pi\)
−0.443229 + 0.896408i \(0.646167\pi\)
\(594\) 5.71981 18.4651i 0.234687 0.757633i
\(595\) 1.43137i 0.0586803i
\(596\) 14.7936 0.605968
\(597\) 25.7381 + 18.5199i 1.05339 + 0.757970i
\(598\) −5.37821 + 5.37821i −0.219931 + 0.219931i
\(599\) 10.4813i 0.428254i 0.976806 + 0.214127i \(0.0686907\pi\)
−0.976806 + 0.214127i \(0.931309\pi\)
\(600\) −1.01163 + 1.40592i −0.0412997 + 0.0573963i
\(601\) 31.5992 1.28896 0.644480 0.764621i \(-0.277074\pi\)
0.644480 + 0.764621i \(0.277074\pi\)
\(602\) 2.03178i 0.0828093i
\(603\) 13.4789 + 40.2235i 0.548902 + 1.63803i
\(604\) 2.35718 0.0959124
\(605\) 2.00811 + 2.00811i 0.0816412 + 0.0816412i
\(606\) 16.2603 22.5978i 0.660529 0.917972i
\(607\) 14.2922 + 14.2922i 0.580101 + 0.580101i 0.934931 0.354830i \(-0.115461\pi\)
−0.354830 + 0.934931i \(0.615461\pi\)
\(608\) 4.24816i 0.172286i
\(609\) 0.143933 0.200031i 0.00583247 0.00810568i
\(610\) 8.60550 + 8.60550i 0.348426 + 0.348426i
\(611\) −4.43008 4.43008i −0.179222 0.179222i
\(612\) 5.50026 11.0444i 0.222335 0.446442i
\(613\) 0.137392i 0.00554922i −0.999996 0.00277461i \(-0.999117\pi\)
0.999996 0.00277461i \(-0.000883187\pi\)
\(614\) 6.67084 + 6.67084i 0.269213 + 0.269213i
\(615\) 13.9848 + 10.0628i 0.563921 + 0.405771i
\(616\) 0.915530 + 0.915530i 0.0368878 + 0.0368878i
\(617\) −28.1830 −1.13461 −0.567303 0.823509i \(-0.692013\pi\)
−0.567303 + 0.823509i \(0.692013\pi\)
\(618\) 15.9204 2.59650i 0.640411 0.104447i
\(619\) 19.2838i 0.775080i 0.921853 + 0.387540i \(0.126675\pi\)
−0.921853 + 0.387540i \(0.873325\pi\)
\(620\) 5.92266 0.237860
\(621\) 45.5262 + 14.1023i 1.82690 + 0.565906i
\(622\) 24.6758i 0.989408i
\(623\) 1.95983 1.95983i 0.0785188 0.0785188i
\(624\) −0.838880 + 1.16584i −0.0335821 + 0.0466708i
\(625\) −1.00000 −0.0400000
\(626\) 10.7714i 0.430514i
\(627\) −15.9878 + 22.2191i −0.638493 + 0.887347i
\(628\) 17.5824i 0.701616i
\(629\) 22.8697 10.1398i 0.911874 0.404300i
\(630\) 0.989995 0.331747i 0.0394424 0.0132171i
\(631\) −1.01625 1.01625i −0.0404564 0.0404564i 0.686589 0.727046i \(-0.259107\pi\)
−0.727046 + 0.686589i \(0.759107\pi\)
\(632\) 9.67926 0.385020
\(633\) 27.7118 4.51961i 1.10145 0.179638i
\(634\) 14.5021 14.5021i 0.575951 0.575951i
\(635\) 4.84779 + 4.84779i 0.192379 + 0.192379i
\(636\) −0.280627 + 0.0457683i −0.0111276 + 0.00181483i
\(637\) −4.03348 + 4.03348i −0.159812 + 0.159812i
\(638\) 1.52084i 0.0602107i
\(639\) 0.704061 + 2.10105i 0.0278522 + 0.0831162i
\(640\) 1.00000i 0.0395285i
\(641\) 15.8819i 0.627297i −0.949539 0.313648i \(-0.898449\pi\)
0.949539 0.313648i \(-0.101551\pi\)
\(642\) 13.4102 + 9.64937i 0.529259 + 0.380830i
\(643\) 29.9979 + 29.9979i 1.18300 + 1.18300i 0.978963 + 0.204037i \(0.0654064\pi\)
0.204037 + 0.978963i \(0.434594\pi\)
\(644\) −2.25726 + 2.25726i −0.0889485 + 0.0889485i
\(645\) −9.97968 + 1.62762i −0.392949 + 0.0640873i
\(646\) −12.3542 + 12.3542i −0.486071 + 0.486071i
\(647\) −2.08271 + 2.08271i −0.0818800 + 0.0818800i −0.746861 0.664981i \(-0.768440\pi\)
0.664981 + 0.746861i \(0.268440\pi\)
\(648\) 8.91354 + 1.24448i 0.350157 + 0.0488876i
\(649\) −24.2401 24.2401i −0.951507 0.951507i
\(650\) −0.829235 −0.0325253
\(651\) −2.89799 2.08526i −0.113581 0.0817277i
\(652\) 2.83898 2.83898i 0.111183 0.111183i
\(653\) 18.6146 18.6146i 0.728447 0.728447i −0.241863 0.970310i \(-0.577759\pi\)
0.970310 + 0.241863i \(0.0777586\pi\)
\(654\) −3.67475 22.5316i −0.143694 0.881056i
\(655\) −4.70740 −0.183933
\(656\) −9.94709 −0.388369
\(657\) −15.1760 45.2880i −0.592071 1.76685i
\(658\) −1.85932 1.85932i −0.0724839 0.0724839i
\(659\) 6.86347 0.267363 0.133681 0.991024i \(-0.457320\pi\)
0.133681 + 0.991024i \(0.457320\pi\)
\(660\) −3.76347 + 5.23029i −0.146493 + 0.203589i
\(661\) −20.0138 20.0138i −0.778446 0.778446i 0.201121 0.979566i \(-0.435542\pi\)
−0.979566 + 0.201121i \(0.935542\pi\)
\(662\) 1.93815i 0.0753283i
\(663\) 5.82999 0.950831i 0.226418 0.0369272i
\(664\) −6.83285 + 6.83285i −0.265166 + 0.265166i
\(665\) −1.47850 −0.0573339
\(666\) 12.3136 + 13.4676i 0.477142 + 0.521857i
\(667\) −3.74967 −0.145188
\(668\) −8.73935 + 8.73935i −0.338136 + 0.338136i
\(669\) −8.85804 + 1.44469i −0.342472 + 0.0558548i
\(670\) 14.1406i 0.546299i
\(671\) 32.0142 + 32.0142i 1.23589 + 1.23589i
\(672\) −0.352082 + 0.489306i −0.0135818 + 0.0188754i
\(673\) 37.7218 1.45407 0.727034 0.686601i \(-0.240898\pi\)
0.727034 + 0.686601i \(0.240898\pi\)
\(674\) 23.7173 + 23.7173i 0.913557 + 0.913557i
\(675\) 2.42253 + 4.59688i 0.0932433 + 0.176934i
\(676\) 12.3124 0.473553
\(677\) −26.3889 −1.01421 −0.507104 0.861885i \(-0.669284\pi\)
−0.507104 + 0.861885i \(0.669284\pi\)
\(678\) −2.07992 12.7530i −0.0798790 0.489775i
\(679\) −3.83607 + 3.83607i −0.147215 + 0.147215i
\(680\) −2.90814 + 2.90814i −0.111522 + 0.111522i
\(681\) −29.6307 21.3209i −1.13545 0.817017i
\(682\) 22.0335 0.843705
\(683\) 30.4848 + 30.4848i 1.16647 + 1.16647i 0.983032 + 0.183435i \(0.0587218\pi\)
0.183435 + 0.983032i \(0.441278\pi\)
\(684\) −11.4081 5.68139i −0.436198 0.217234i
\(685\) −1.54270 + 1.54270i −0.0589436 + 0.0589436i
\(686\) −3.41555 + 3.41555i −0.130406 + 0.130406i
\(687\) −27.0483 + 4.41140i −1.03196 + 0.168305i
\(688\) 4.12802 4.12802i 0.157379 0.157379i
\(689\) −0.0962569 0.0962569i −0.00366709 0.00366709i
\(690\) −12.8954 9.27892i −0.490920 0.353243i
\(691\) 14.1593i 0.538646i −0.963050 0.269323i \(-0.913200\pi\)
0.963050 0.269323i \(-0.0867998\pi\)
\(692\) 19.5438i 0.742942i
\(693\) 3.68298 1.23417i 0.139905 0.0468821i
\(694\) 20.1922i 0.766484i
\(695\) −2.66597 + 2.66597i −0.101126 + 0.101126i
\(696\) −0.698840 + 0.113976i −0.0264895 + 0.00432025i
\(697\) 28.9275 + 28.9275i 1.09571 + 1.09571i
\(698\) −4.63882 + 4.63882i −0.175582 + 0.175582i
\(699\) −29.4917 + 4.80990i −1.11548 + 0.181927i
\(700\) −0.348034 −0.0131544
\(701\) −18.6242 18.6242i −0.703428 0.703428i 0.261717 0.965145i \(-0.415711\pi\)
−0.965145 + 0.261717i \(0.915711\pi\)
\(702\) 2.00885 + 3.81190i 0.0758191 + 0.143871i
\(703\) −10.4737 23.6228i −0.395023 0.890951i
\(704\) 3.72020i 0.140210i
\(705\) 7.64312 10.6220i 0.287857 0.400049i
\(706\) 36.2497i 1.36427i
\(707\) 5.59406 0.210386
\(708\) 9.32192 12.9552i 0.350339 0.486885i
\(709\) 16.5635 16.5635i 0.622054 0.622054i −0.324002 0.946056i \(-0.605029\pi\)
0.946056 + 0.324002i \(0.105029\pi\)
\(710\) 0.738626i 0.0277201i
\(711\) 12.9448 25.9928i 0.485468 0.974805i
\(712\) −7.96364 −0.298450
\(713\) 54.3240i 2.03445i
\(714\) 2.44687 0.399068i 0.0915719 0.0149347i
\(715\) −3.08492 −0.115370
\(716\) 4.09892 + 4.09892i 0.153184 + 0.153184i
\(717\) −17.2602 12.4196i −0.644595 0.463820i
\(718\) −13.1326 13.1326i −0.490104 0.490104i
\(719\) 12.6073i 0.470174i −0.971974 0.235087i \(-0.924462\pi\)
0.971974 0.235087i \(-0.0755376\pi\)
\(720\) −2.68541 1.33738i −0.100079 0.0498411i
\(721\) 2.29192 + 2.29192i 0.0853555 + 0.0853555i
\(722\) −0.673942 0.673942i −0.0250815 0.0250815i
\(723\) 16.7251 23.2438i 0.622014 0.864446i
\(724\) 10.8868i 0.404605i
\(725\) −0.289070 0.289070i −0.0107358 0.0107358i
\(726\) −2.87292 + 3.99265i −0.106624 + 0.148181i
\(727\) −16.6603 16.6603i −0.617895 0.617895i 0.327096 0.944991i \(-0.393930\pi\)
−0.944991 + 0.327096i \(0.893930\pi\)
\(728\) −0.288602 −0.0106963
\(729\) 15.2627 22.2722i 0.565285 0.824896i
\(730\) 15.9210i 0.589263i
\(731\) −24.0097 −0.888030
\(732\) −12.3116 + 17.1100i −0.455049 + 0.632405i
\(733\) 19.0725i 0.704460i −0.935913 0.352230i \(-0.885423\pi\)
0.935913 0.352230i \(-0.114577\pi\)
\(734\) 7.70642 7.70642i 0.284449 0.284449i
\(735\) −9.67112 6.95888i −0.356725 0.256682i
\(736\) 9.17224 0.338093
\(737\) 52.6058i 1.93776i
\(738\) −13.3030 + 26.7120i −0.489690 + 0.983283i
\(739\) 39.6325i 1.45791i −0.684563 0.728953i \(-0.740007\pi\)
0.684563 0.728953i \(-0.259993\pi\)
\(740\) −2.46547 5.56071i −0.0906323 0.204416i
\(741\) −0.982143 6.02198i −0.0360799 0.221223i
\(742\) −0.0403994 0.0403994i −0.00148311 0.00148311i
\(743\) 4.80447 0.176259 0.0881295 0.996109i \(-0.471911\pi\)
0.0881295 + 0.996109i \(0.471911\pi\)
\(744\) 1.65125 + 10.1246i 0.0605377 + 0.371185i
\(745\) −10.4606 + 10.4606i −0.383248 + 0.383248i
\(746\) −19.4847 19.4847i −0.713385 0.713385i
\(747\) 9.21091 + 27.4871i 0.337010 + 1.00570i
\(748\) −10.8189 + 10.8189i −0.395577 + 0.395577i
\(749\) 3.31969i 0.121299i
\(750\) −0.278802 1.70946i −0.0101804 0.0624208i
\(751\) 4.63856i 0.169264i 0.996412 + 0.0846318i \(0.0269714\pi\)
−0.996412 + 0.0846318i \(0.973029\pi\)
\(752\) 7.55524i 0.275511i
\(753\) −7.39847 + 10.2820i −0.269615 + 0.374698i
\(754\) −0.239707 0.239707i −0.00872960 0.00872960i
\(755\) −1.66678 + 1.66678i −0.0606603 + 0.0606603i
\(756\) 0.843122 + 1.59987i 0.0306641 + 0.0581867i
\(757\) −24.2357 + 24.2357i −0.880861 + 0.880861i −0.993622 0.112761i \(-0.964030\pi\)
0.112761 + 0.993622i \(0.464030\pi\)
\(758\) −3.70616 + 3.70616i −0.134614 + 0.134614i
\(759\) −47.9735 34.5195i −1.74133 1.25298i
\(760\) 3.00391 + 3.00391i 0.108963 + 0.108963i
\(761\) 1.10162 0.0399339 0.0199669 0.999801i \(-0.493644\pi\)
0.0199669 + 0.999801i \(0.493644\pi\)
\(762\) −6.93556 + 9.63870i −0.251249 + 0.349173i
\(763\) 3.24368 3.24368i 0.117429 0.117429i
\(764\) −14.0022 + 14.0022i −0.506581 + 0.506581i
\(765\) 3.92027 + 11.6988i 0.141738 + 0.422972i
\(766\) −28.4065 −1.02637
\(767\) 7.64119 0.275907
\(768\) 1.70946 0.278802i 0.0616850 0.0100604i
\(769\) −4.38921 4.38921i −0.158279 0.158279i 0.623525 0.781804i \(-0.285700\pi\)
−0.781804 + 0.623525i \(0.785700\pi\)
\(770\) −1.29475 −0.0466597
\(771\) −41.6428 29.9642i −1.49973 1.07913i
\(772\) −11.7248 11.7248i −0.421986 0.421986i
\(773\) 36.7986i 1.32355i 0.749701 + 0.661777i \(0.230197\pi\)
−0.749701 + 0.661777i \(0.769803\pi\)
\(774\) −5.56470 16.6061i −0.200019 0.596895i
\(775\) −4.18795 + 4.18795i −0.150436 + 0.150436i
\(776\) 15.5876 0.559563
\(777\) −0.751456 + 3.58894i −0.0269583 + 0.128752i
\(778\) −8.40919 −0.301484
\(779\) 29.8801