Properties

Label 1110.2.l.a.43.8
Level $1110$
Weight $2$
Character 1110.43
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
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: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.8
Character \(\chi\) \(=\) 1110.43
Dual form 1110.2.l.a.697.8

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.05054 - 0.891783i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.56460 + 1.56460i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.05054 - 0.891783i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.56460 + 1.56460i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(0.891783 + 2.05054i) q^{10} +3.92190i q^{11} +(0.707107 - 0.707107i) q^{12} -0.319413i q^{13} +(-1.56460 - 1.56460i) q^{14} +(-0.819367 + 2.08054i) q^{15} +1.00000 q^{16} +1.25497 q^{17} +1.00000 q^{18} +(-2.17875 + 2.17875i) q^{19} +(-2.05054 + 0.891783i) q^{20} -2.21268i q^{21} -3.92190 q^{22} -1.15203i q^{23} +(0.707107 + 0.707107i) q^{24} +(3.40945 - 3.65728i) q^{25} +0.319413 q^{26} +(0.707107 + 0.707107i) q^{27} +(1.56460 - 1.56460i) q^{28} +(1.22361 + 1.22361i) q^{29} +(-2.08054 - 0.819367i) q^{30} +(-6.78274 + 6.78274i) q^{31} +1.00000i q^{32} +(-2.77320 - 2.77320i) q^{33} +1.25497i q^{34} +(-1.81300 + 4.60357i) q^{35} +1.00000i q^{36} +(0.0100817 + 6.08275i) q^{37} +(-2.17875 - 2.17875i) q^{38} +(0.225859 + 0.225859i) q^{39} +(-0.891783 - 2.05054i) q^{40} +3.92813i q^{41} +2.21268 q^{42} -1.87330i q^{43} -3.92190i q^{44} +(-0.891783 - 2.05054i) q^{45} +1.15203 q^{46} +(-4.88442 + 4.88442i) q^{47} +(-0.707107 + 0.707107i) q^{48} +2.10403i q^{49} +(3.65728 + 3.40945i) q^{50} +(-0.887401 + 0.887401i) q^{51} +0.319413i q^{52} +(-3.03226 - 3.03226i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(3.49748 + 8.04202i) q^{55} +(1.56460 + 1.56460i) q^{56} -3.08122i q^{57} +(-1.22361 + 1.22361i) q^{58} +(-4.70399 + 4.70399i) q^{59} +(0.819367 - 2.08054i) q^{60} +(-5.56135 + 5.56135i) q^{61} +(-6.78274 - 6.78274i) q^{62} +(1.56460 + 1.56460i) q^{63} -1.00000 q^{64} +(-0.284847 - 0.654970i) q^{65} +(2.77320 - 2.77320i) q^{66} +(-6.88391 - 6.88391i) q^{67} -1.25497 q^{68} +(0.814607 + 0.814607i) q^{69} +(-4.60357 - 1.81300i) q^{70} -3.29012 q^{71} -1.00000 q^{72} +(8.53399 - 8.53399i) q^{73} +(-6.08275 + 0.0100817i) q^{74} +(0.175243 + 4.99693i) q^{75} +(2.17875 - 2.17875i) q^{76} +(-6.13622 - 6.13622i) q^{77} +(-0.225859 + 0.225859i) q^{78} +(3.59077 - 3.59077i) q^{79} +(2.05054 - 0.891783i) q^{80} -1.00000 q^{81} -3.92813 q^{82} +(-1.13008 - 1.13008i) q^{83} +2.21268i q^{84} +(2.57338 - 1.11916i) q^{85} +1.87330 q^{86} -1.73044 q^{87} +3.92190 q^{88} +(-1.33809 - 1.33809i) q^{89} +(2.05054 - 0.891783i) q^{90} +(0.499755 + 0.499755i) q^{91} +1.15203i q^{92} -9.59224i q^{93} +(-4.88442 - 4.88442i) q^{94} +(-2.52465 + 6.41059i) q^{95} +(-0.707107 - 0.707107i) q^{96} +4.01884 q^{97} -2.10403 q^{98} +3.92190 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{4} + 4q^{7} + O(q^{10}) \) \( 36q - 36q^{4} + 4q^{7} - 4q^{10} + 4q^{14} + 36q^{16} - 32q^{17} + 36q^{18} + 4q^{19} + 8q^{22} - 4q^{25} + 8q^{26} - 4q^{28} + 36q^{29} - 4q^{31} + 4q^{33} - 12q^{35} - 4q^{37} + 4q^{38} + 4q^{39} + 4q^{40} - 16q^{42} + 4q^{45} + 16q^{47} - 16q^{50} - 8q^{53} + 16q^{55} - 4q^{56} - 36q^{58} - 4q^{59} - 4q^{61} - 4q^{62} - 4q^{63} - 36q^{64} + 52q^{65} - 4q^{66} + 16q^{67} + 32q^{68} - 8q^{69} - 28q^{70} - 8q^{71} - 36q^{72} - 4q^{73} + 28q^{74} + 16q^{75} - 4q^{76} + 8q^{77} - 4q^{78} - 12q^{79} - 36q^{81} - 8q^{82} + 8q^{83} + 8q^{85} + 32q^{86} - 8q^{87} - 8q^{88} - 24q^{89} + 56q^{91} + 16q^{94} - 20q^{95} + 40q^{97} - 12q^{98} - 8q^{99} + O(q^{100}) \)

Character values

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

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

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
\(5\) 2.05054 0.891783i 0.917030 0.398817i
\(6\) −0.707107 0.707107i −0.288675 0.288675i
\(7\) −1.56460 + 1.56460i −0.591365 + 0.591365i −0.938000 0.346635i \(-0.887324\pi\)
0.346635 + 0.938000i \(0.387324\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) 0.891783 + 2.05054i 0.282007 + 0.648438i
\(11\) 3.92190i 1.18250i 0.806489 + 0.591249i \(0.201365\pi\)
−0.806489 + 0.591249i \(0.798635\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) 0.319413i 0.0885893i −0.999019 0.0442946i \(-0.985896\pi\)
0.999019 0.0442946i \(-0.0141040\pi\)
\(14\) −1.56460 1.56460i −0.418158 0.418158i
\(15\) −0.819367 + 2.08054i −0.211560 + 0.537193i
\(16\) 1.00000 0.250000
\(17\) 1.25497 0.304376 0.152188 0.988352i \(-0.451368\pi\)
0.152188 + 0.988352i \(0.451368\pi\)
\(18\) 1.00000 0.235702
\(19\) −2.17875 + 2.17875i −0.499839 + 0.499839i −0.911388 0.411549i \(-0.864988\pi\)
0.411549 + 0.911388i \(0.364988\pi\)
\(20\) −2.05054 + 0.891783i −0.458515 + 0.199409i
\(21\) 2.21268i 0.482847i
\(22\) −3.92190 −0.836152
\(23\) 1.15203i 0.240215i −0.992761 0.120107i \(-0.961676\pi\)
0.992761 0.120107i \(-0.0383239\pi\)
\(24\) 0.707107 + 0.707107i 0.144338 + 0.144338i
\(25\) 3.40945 3.65728i 0.681889 0.731455i
\(26\) 0.319413 0.0626421
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 1.56460 1.56460i 0.295682 0.295682i
\(29\) 1.22361 + 1.22361i 0.227218 + 0.227218i 0.811529 0.584312i \(-0.198635\pi\)
−0.584312 + 0.811529i \(0.698635\pi\)
\(30\) −2.08054 0.819367i −0.379853 0.149595i
\(31\) −6.78274 + 6.78274i −1.21822 + 1.21822i −0.249959 + 0.968256i \(0.580417\pi\)
−0.968256 + 0.249959i \(0.919583\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −2.77320 2.77320i −0.482753 0.482753i
\(34\) 1.25497i 0.215226i
\(35\) −1.81300 + 4.60357i −0.306453 + 0.778146i
\(36\) 1.00000i 0.166667i
\(37\) 0.0100817 + 6.08275i 0.00165742 + 0.999999i
\(38\) −2.17875 2.17875i −0.353440 0.353440i
\(39\) 0.225859 + 0.225859i 0.0361664 + 0.0361664i
\(40\) −0.891783 2.05054i −0.141003 0.324219i
\(41\) 3.92813i 0.613470i 0.951795 + 0.306735i \(0.0992366\pi\)
−0.951795 + 0.306735i \(0.900763\pi\)
\(42\) 2.21268 0.341425
\(43\) 1.87330i 0.285675i −0.989746 0.142838i \(-0.954377\pi\)
0.989746 0.142838i \(-0.0456227\pi\)
\(44\) 3.92190i 0.591249i
\(45\) −0.891783 2.05054i −0.132939 0.305677i
\(46\) 1.15203 0.169857
\(47\) −4.88442 + 4.88442i −0.712466 + 0.712466i −0.967051 0.254585i \(-0.918061\pi\)
0.254585 + 0.967051i \(0.418061\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 2.10403i 0.300576i
\(50\) 3.65728 + 3.40945i 0.517217 + 0.482169i
\(51\) −0.887401 + 0.887401i −0.124261 + 0.124261i
\(52\) 0.319413i 0.0442946i
\(53\) −3.03226 3.03226i −0.416513 0.416513i 0.467487 0.884000i \(-0.345160\pi\)
−0.884000 + 0.467487i \(0.845160\pi\)
\(54\) −0.707107 + 0.707107i −0.0962250 + 0.0962250i
\(55\) 3.49748 + 8.04202i 0.471601 + 1.08439i
\(56\) 1.56460 + 1.56460i 0.209079 + 0.209079i
\(57\) 3.08122i 0.408117i
\(58\) −1.22361 + 1.22361i −0.160667 + 0.160667i
\(59\) −4.70399 + 4.70399i −0.612407 + 0.612407i −0.943573 0.331165i \(-0.892558\pi\)
0.331165 + 0.943573i \(0.392558\pi\)
\(60\) 0.819367 2.08054i 0.105780 0.268596i
\(61\) −5.56135 + 5.56135i −0.712058 + 0.712058i −0.966965 0.254908i \(-0.917955\pi\)
0.254908 + 0.966965i \(0.417955\pi\)
\(62\) −6.78274 6.78274i −0.861408 0.861408i
\(63\) 1.56460 + 1.56460i 0.197122 + 0.197122i
\(64\) −1.00000 −0.125000
\(65\) −0.284847 0.654970i −0.0353309 0.0812390i
\(66\) 2.77320 2.77320i 0.341358 0.341358i
\(67\) −6.88391 6.88391i −0.841003 0.841003i 0.147986 0.988989i \(-0.452721\pi\)
−0.988989 + 0.147986i \(0.952721\pi\)
\(68\) −1.25497 −0.152188
\(69\) 0.814607 + 0.814607i 0.0980672 + 0.0980672i
\(70\) −4.60357 1.81300i −0.550232 0.216695i
\(71\) −3.29012 −0.390466 −0.195233 0.980757i \(-0.562546\pi\)
−0.195233 + 0.980757i \(0.562546\pi\)
\(72\) −1.00000 −0.117851
\(73\) 8.53399 8.53399i 0.998828 0.998828i −0.00117124 0.999999i \(-0.500373\pi\)
0.999999 + 0.00117124i \(0.000372817\pi\)
\(74\) −6.08275 + 0.0100817i −0.707106 + 0.00117198i
\(75\) 0.175243 + 4.99693i 0.0202353 + 0.576996i
\(76\) 2.17875 2.17875i 0.249920 0.249920i
\(77\) −6.13622 6.13622i −0.699287 0.699287i
\(78\) −0.225859 + 0.225859i −0.0255735 + 0.0255735i
\(79\) 3.59077 3.59077i 0.403993 0.403993i −0.475645 0.879638i \(-0.657785\pi\)
0.879638 + 0.475645i \(0.157785\pi\)
\(80\) 2.05054 0.891783i 0.229258 0.0997044i
\(81\) −1.00000 −0.111111
\(82\) −3.92813 −0.433789
\(83\) −1.13008 1.13008i −0.124042 0.124042i 0.642360 0.766403i \(-0.277955\pi\)
−0.766403 + 0.642360i \(0.777955\pi\)
\(84\) 2.21268i 0.241424i
\(85\) 2.57338 1.11916i 0.279122 0.121390i
\(86\) 1.87330 0.202003
\(87\) −1.73044 −0.185523
\(88\) 3.92190 0.418076
\(89\) −1.33809 1.33809i −0.141837 0.141837i 0.632623 0.774460i \(-0.281978\pi\)
−0.774460 + 0.632623i \(0.781978\pi\)
\(90\) 2.05054 0.891783i 0.216146 0.0940022i
\(91\) 0.499755 + 0.499755i 0.0523886 + 0.0523886i
\(92\) 1.15203i 0.120107i
\(93\) 9.59224i 0.994669i
\(94\) −4.88442 4.88442i −0.503790 0.503790i
\(95\) −2.52465 + 6.41059i −0.259023 + 0.657712i
\(96\) −0.707107 0.707107i −0.0721688 0.0721688i
\(97\) 4.01884 0.408051 0.204025 0.978966i \(-0.434597\pi\)
0.204025 + 0.978966i \(0.434597\pi\)
\(98\) −2.10403 −0.212539
\(99\) 3.92190 0.394166
\(100\) −3.40945 + 3.65728i −0.340945 + 0.365728i
\(101\) 11.0673i 1.10124i 0.834757 + 0.550618i \(0.185608\pi\)
−0.834757 + 0.550618i \(0.814392\pi\)
\(102\) −0.887401 0.887401i −0.0878658 0.0878658i
\(103\) 13.8134 1.36107 0.680536 0.732715i \(-0.261747\pi\)
0.680536 + 0.732715i \(0.261747\pi\)
\(104\) −0.319413 −0.0313210
\(105\) −1.97323 4.53720i −0.192568 0.442785i
\(106\) 3.03226 3.03226i 0.294520 0.294520i
\(107\) 1.55870 1.55870i 0.150685 0.150685i −0.627739 0.778424i \(-0.716019\pi\)
0.778424 + 0.627739i \(0.216019\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) 4.24101 4.24101i 0.406215 0.406215i −0.474201 0.880416i \(-0.657263\pi\)
0.880416 + 0.474201i \(0.157263\pi\)
\(110\) −8.04202 + 3.49748i −0.766777 + 0.333472i
\(111\) −4.30829 4.29403i −0.408924 0.407571i
\(112\) −1.56460 + 1.56460i −0.147841 + 0.147841i
\(113\) −16.5384 −1.55580 −0.777899 0.628390i \(-0.783714\pi\)
−0.777899 + 0.628390i \(0.783714\pi\)
\(114\) 3.08122 0.288582
\(115\) −1.02736 2.36228i −0.0958018 0.220284i
\(116\) −1.22361 1.22361i −0.113609 0.113609i
\(117\) −0.319413 −0.0295298
\(118\) −4.70399 4.70399i −0.433037 0.433037i
\(119\) −1.96354 + 1.96354i −0.179997 + 0.179997i
\(120\) 2.08054 + 0.819367i 0.189926 + 0.0747976i
\(121\) −4.38131 −0.398301
\(122\) −5.56135 5.56135i −0.503501 0.503501i
\(123\) −2.77761 2.77761i −0.250448 0.250448i
\(124\) 6.78274 6.78274i 0.609108 0.609108i
\(125\) 3.72972 10.5399i 0.333596 0.942716i
\(126\) −1.56460 + 1.56460i −0.139386 + 0.139386i
\(127\) 7.06209 7.06209i 0.626659 0.626659i −0.320567 0.947226i \(-0.603873\pi\)
0.947226 + 0.320567i \(0.103873\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 1.32462 + 1.32462i 0.116626 + 0.116626i
\(130\) 0.654970 0.284847i 0.0574447 0.0249828i
\(131\) −9.32171 + 9.32171i −0.814442 + 0.814442i −0.985296 0.170855i \(-0.945347\pi\)
0.170855 + 0.985296i \(0.445347\pi\)
\(132\) 2.77320 + 2.77320i 0.241376 + 0.241376i
\(133\) 6.81776i 0.591174i
\(134\) 6.88391 6.88391i 0.594679 0.594679i
\(135\) 2.08054 + 0.819367i 0.179064 + 0.0705198i
\(136\) 1.25497i 0.107613i
\(137\) −14.5752 + 14.5752i −1.24525 + 1.24525i −0.287450 + 0.957796i \(0.592807\pi\)
−0.957796 + 0.287450i \(0.907193\pi\)
\(138\) −0.814607 + 0.814607i −0.0693440 + 0.0693440i
\(139\) 1.20629 0.102316 0.0511582 0.998691i \(-0.483709\pi\)
0.0511582 + 0.998691i \(0.483709\pi\)
\(140\) 1.81300 4.60357i 0.153226 0.389073i
\(141\) 6.90761i 0.581726i
\(142\) 3.29012i 0.276101i
\(143\) 1.25271 0.104757
\(144\) 1.00000i 0.0833333i
\(145\) 3.60025 + 1.41786i 0.298984 + 0.117747i
\(146\) 8.53399 + 8.53399i 0.706278 + 0.706278i
\(147\) −1.48777 1.48777i −0.122710 0.122710i
\(148\) −0.0100817 6.08275i −0.000828712 0.499999i
\(149\) 0.425764i 0.0348800i 0.999848 + 0.0174400i \(0.00555160\pi\)
−0.999848 + 0.0174400i \(0.994448\pi\)
\(150\) −4.99693 + 0.175243i −0.407997 + 0.0143085i
\(151\) 18.6559i 1.51820i 0.650976 + 0.759098i \(0.274360\pi\)
−0.650976 + 0.759098i \(0.725640\pi\)
\(152\) 2.17875 + 2.17875i 0.176720 + 0.176720i
\(153\) 1.25497i 0.101459i
\(154\) 6.13622 6.13622i 0.494471 0.494471i
\(155\) −7.85956 + 19.9570i −0.631295 + 1.60299i
\(156\) −0.225859 0.225859i −0.0180832 0.0180832i
\(157\) 6.23375 6.23375i 0.497507 0.497507i −0.413154 0.910661i \(-0.635573\pi\)
0.910661 + 0.413154i \(0.135573\pi\)
\(158\) 3.59077 + 3.59077i 0.285666 + 0.285666i
\(159\) 4.28827 0.340082
\(160\) 0.891783 + 2.05054i 0.0705016 + 0.162110i
\(161\) 1.80247 + 1.80247i 0.142054 + 0.142054i
\(162\) 1.00000i 0.0785674i
\(163\) 15.4091 1.20693 0.603466 0.797389i \(-0.293786\pi\)
0.603466 + 0.797389i \(0.293786\pi\)
\(164\) 3.92813i 0.306735i
\(165\) −8.15967 3.21347i −0.635229 0.250169i
\(166\) 1.13008 1.13008i 0.0877111 0.0877111i
\(167\) 16.8371 1.30289 0.651447 0.758694i \(-0.274162\pi\)
0.651447 + 0.758694i \(0.274162\pi\)
\(168\) −2.21268 −0.170712
\(169\) 12.8980 0.992152
\(170\) 1.11916 + 2.57338i 0.0858360 + 0.197369i
\(171\) 2.17875 + 2.17875i 0.166613 + 0.166613i
\(172\) 1.87330i 0.142838i
\(173\) 5.18404 5.18404i 0.394136 0.394136i −0.482023 0.876159i \(-0.660098\pi\)
0.876159 + 0.482023i \(0.160098\pi\)
\(174\) 1.73044i 0.131184i
\(175\) 0.387756 + 11.0566i 0.0293116 + 0.835802i
\(176\) 3.92190i 0.295624i
\(177\) 6.65245i 0.500029i
\(178\) 1.33809 1.33809i 0.100294 0.100294i
\(179\) −1.70251 1.70251i −0.127252 0.127252i 0.640613 0.767864i \(-0.278680\pi\)
−0.767864 + 0.640613i \(0.778680\pi\)
\(180\) 0.891783 + 2.05054i 0.0664696 + 0.152838i
\(181\) 8.75170 0.650509 0.325254 0.945627i \(-0.394550\pi\)
0.325254 + 0.945627i \(0.394550\pi\)
\(182\) −0.499755 + 0.499755i −0.0370443 + 0.0370443i
\(183\) 7.86494i 0.581393i
\(184\) −1.15203 −0.0849287
\(185\) 5.44517 + 12.4640i 0.400337 + 0.916368i
\(186\) 9.59224 0.703337
\(187\) 4.92188i 0.359924i
\(188\) 4.88442 4.88442i 0.356233 0.356233i
\(189\) −2.21268 −0.160949
\(190\) −6.41059 2.52465i −0.465073 0.183157i
\(191\) 4.56780 + 4.56780i 0.330514 + 0.330514i 0.852782 0.522268i \(-0.174914\pi\)
−0.522268 + 0.852782i \(0.674914\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) 5.51547i 0.397012i −0.980100 0.198506i \(-0.936391\pi\)
0.980100 0.198506i \(-0.0636090\pi\)
\(194\) 4.01884i 0.288536i
\(195\) 0.664551 + 0.261716i 0.0475895 + 0.0187419i
\(196\) 2.10403i 0.150288i
\(197\) −3.48510 + 3.48510i −0.248303 + 0.248303i −0.820274 0.571971i \(-0.806179\pi\)
0.571971 + 0.820274i \(0.306179\pi\)
\(198\) 3.92190i 0.278717i
\(199\) −11.0862 11.0862i −0.785883 0.785883i 0.194933 0.980817i \(-0.437551\pi\)
−0.980817 + 0.194933i \(0.937551\pi\)
\(200\) −3.65728 3.40945i −0.258609 0.241084i
\(201\) 9.73532 0.686676
\(202\) −11.0673 −0.778692
\(203\) −3.82892 −0.268737
\(204\) 0.887401 0.887401i 0.0621305 0.0621305i
\(205\) 3.50304 + 8.05479i 0.244663 + 0.562571i
\(206\) 13.8134i 0.962423i
\(207\) −1.15203 −0.0800715
\(208\) 0.319413i 0.0221473i
\(209\) −8.54484 8.54484i −0.591059 0.591059i
\(210\) 4.53720 1.97323i 0.313097 0.136166i
\(211\) 27.2170 1.87370 0.936848 0.349737i \(-0.113729\pi\)
0.936848 + 0.349737i \(0.113729\pi\)
\(212\) 3.03226 + 3.03226i 0.208257 + 0.208257i
\(213\) 2.32647 2.32647i 0.159407 0.159407i
\(214\) 1.55870 + 1.55870i 0.106551 + 0.106551i
\(215\) −1.67057 3.84128i −0.113932 0.261973i
\(216\) 0.707107 0.707107i 0.0481125 0.0481125i
\(217\) 21.2246i 1.44082i
\(218\) 4.24101 + 4.24101i 0.287237 + 0.287237i
\(219\) 12.0689i 0.815540i
\(220\) −3.49748 8.04202i −0.235800 0.542193i
\(221\) 0.400855i 0.0269644i
\(222\) 4.29403 4.30829i 0.288196 0.289153i
\(223\) 11.1865 + 11.1865i 0.749103 + 0.749103i 0.974311 0.225208i \(-0.0723061\pi\)
−0.225208 + 0.974311i \(0.572306\pi\)
\(224\) −1.56460 1.56460i −0.104539 0.104539i
\(225\) −3.65728 3.40945i −0.243818 0.227296i
\(226\) 16.5384i 1.10011i
\(227\) 1.74912 0.116093 0.0580467 0.998314i \(-0.481513\pi\)
0.0580467 + 0.998314i \(0.481513\pi\)
\(228\) 3.08122i 0.204058i
\(229\) 8.51464i 0.562663i 0.959611 + 0.281332i \(0.0907761\pi\)
−0.959611 + 0.281332i \(0.909224\pi\)
\(230\) 2.36228 1.02736i 0.155764 0.0677421i
\(231\) 8.67793 0.570966
\(232\) 1.22361 1.22361i 0.0803336 0.0803336i
\(233\) −6.42533 + 6.42533i −0.420938 + 0.420938i −0.885526 0.464589i \(-0.846202\pi\)
0.464589 + 0.885526i \(0.346202\pi\)
\(234\) 0.319413i 0.0208807i
\(235\) −5.65987 + 14.3716i −0.369209 + 0.937497i
\(236\) 4.70399 4.70399i 0.306204 0.306204i
\(237\) 5.07811i 0.329859i
\(238\) −1.96354 1.96354i −0.127277 0.127277i
\(239\) 10.4976 10.4976i 0.679036 0.679036i −0.280746 0.959782i \(-0.590582\pi\)
0.959782 + 0.280746i \(0.0905818\pi\)
\(240\) −0.819367 + 2.08054i −0.0528899 + 0.134298i
\(241\) 6.66851 + 6.66851i 0.429556 + 0.429556i 0.888477 0.458921i \(-0.151764\pi\)
−0.458921 + 0.888477i \(0.651764\pi\)
\(242\) 4.38131i 0.281641i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) 5.56135 5.56135i 0.356029 0.356029i
\(245\) 1.87634 + 4.31440i 0.119875 + 0.275637i
\(246\) 2.77761 2.77761i 0.177094 0.177094i
\(247\) 0.695921 + 0.695921i 0.0442804 + 0.0442804i
\(248\) 6.78274 + 6.78274i 0.430704 + 0.430704i
\(249\) 1.59817 0.101280
\(250\) 10.5399 + 3.72972i 0.666601 + 0.235888i
\(251\) 19.9946 19.9946i 1.26205 1.26205i 0.311948 0.950099i \(-0.399019\pi\)
0.950099 0.311948i \(-0.100981\pi\)
\(252\) −1.56460 1.56460i −0.0985608 0.0985608i
\(253\) 4.51814 0.284053
\(254\) 7.06209 + 7.06209i 0.443115 + 0.443115i
\(255\) −1.02828 + 2.61102i −0.0643936 + 0.163508i
\(256\) 1.00000 0.0625000
\(257\) 31.3639 1.95642 0.978212 0.207609i \(-0.0665682\pi\)
0.978212 + 0.207609i \(0.0665682\pi\)
\(258\) −1.32462 + 1.32462i −0.0824673 + 0.0824673i
\(259\) −9.53287 9.50133i −0.592344 0.590384i
\(260\) 0.284847 + 0.654970i 0.0176655 + 0.0406195i
\(261\) 1.22361 1.22361i 0.0757393 0.0757393i
\(262\) −9.32171 9.32171i −0.575897 0.575897i
\(263\) −7.40341 + 7.40341i −0.456514 + 0.456514i −0.897509 0.440995i \(-0.854626\pi\)
0.440995 + 0.897509i \(0.354626\pi\)
\(264\) −2.77320 + 2.77320i −0.170679 + 0.170679i
\(265\) −8.92191 3.51366i −0.548068 0.215843i
\(266\) 6.81776 0.418023
\(267\) 1.89234 0.115809
\(268\) 6.88391 + 6.88391i 0.420502 + 0.420502i
\(269\) 3.41947i 0.208489i −0.994552 0.104244i \(-0.966758\pi\)
0.994552 0.104244i \(-0.0332424\pi\)
\(270\) −0.819367 + 2.08054i −0.0498651 + 0.126618i
\(271\) 17.8704 1.08555 0.542775 0.839878i \(-0.317374\pi\)
0.542775 + 0.839878i \(0.317374\pi\)
\(272\) 1.25497 0.0760940
\(273\) −0.706760 −0.0427751
\(274\) −14.5752 14.5752i −0.880522 0.880522i
\(275\) 14.3435 + 13.3715i 0.864944 + 0.806333i
\(276\) −0.814607 0.814607i −0.0490336 0.0490336i
\(277\) 14.8527i 0.892410i 0.894931 + 0.446205i \(0.147225\pi\)
−0.894931 + 0.446205i \(0.852775\pi\)
\(278\) 1.20629i 0.0723486i
\(279\) 6.78274 + 6.78274i 0.406072 + 0.406072i
\(280\) 4.60357 + 1.81300i 0.275116 + 0.108347i
\(281\) 4.56193 + 4.56193i 0.272142 + 0.272142i 0.829962 0.557820i \(-0.188362\pi\)
−0.557820 + 0.829962i \(0.688362\pi\)
\(282\) 6.90761 0.411342
\(283\) −32.3891 −1.92533 −0.962666 0.270692i \(-0.912748\pi\)
−0.962666 + 0.270692i \(0.912748\pi\)
\(284\) 3.29012 0.195233
\(285\) −2.74778 6.31816i −0.162764 0.374256i
\(286\) 1.25271i 0.0740741i
\(287\) −6.14596 6.14596i −0.362785 0.362785i
\(288\) 1.00000 0.0589256
\(289\) −15.4250 −0.907355
\(290\) −1.41786 + 3.60025i −0.0832599 + 0.211414i
\(291\) −2.84175 + 2.84175i −0.166586 + 0.166586i
\(292\) −8.53399 + 8.53399i −0.499414 + 0.499414i
\(293\) 2.93182 + 2.93182i 0.171279 + 0.171279i 0.787541 0.616262i \(-0.211354\pi\)
−0.616262 + 0.787541i \(0.711354\pi\)
\(294\) 1.48777 1.48777i 0.0867688 0.0867688i
\(295\) −5.45079 + 13.8407i −0.317357 + 0.805835i
\(296\) 6.08275 0.0100817i 0.353553 0.000585988i
\(297\) −2.77320 + 2.77320i −0.160918 + 0.160918i
\(298\) −0.425764 −0.0246639
\(299\) −0.367973 −0.0212804
\(300\) −0.175243 4.99693i −0.0101176 0.288498i
\(301\) 2.93097 + 2.93097i 0.168938 + 0.168938i
\(302\) −18.6559 −1.07353
\(303\) −7.82575 7.82575i −0.449578 0.449578i
\(304\) −2.17875 + 2.17875i −0.124960 + 0.124960i
\(305\) −6.44427 + 16.3633i −0.368998 + 0.936960i
\(306\) 1.25497 0.0717421
\(307\) −0.225281 0.225281i −0.0128575 0.0128575i 0.700649 0.713506i \(-0.252894\pi\)
−0.713506 + 0.700649i \(0.752894\pi\)
\(308\) 6.13622 + 6.13622i 0.349644 + 0.349644i
\(309\) −9.76753 + 9.76753i −0.555655 + 0.555655i
\(310\) −19.9570 7.85956i −1.13348 0.446393i
\(311\) 8.19803 8.19803i 0.464868 0.464868i −0.435379 0.900247i \(-0.643386\pi\)
0.900247 + 0.435379i \(0.143386\pi\)
\(312\) 0.225859 0.225859i 0.0127868 0.0127868i
\(313\) 12.1187i 0.684987i −0.939520 0.342494i \(-0.888729\pi\)
0.939520 0.342494i \(-0.111271\pi\)
\(314\) 6.23375 + 6.23375i 0.351791 + 0.351791i
\(315\) 4.60357 + 1.81300i 0.259382 + 0.102151i
\(316\) −3.59077 + 3.59077i −0.201996 + 0.201996i
\(317\) 5.46058 + 5.46058i 0.306697 + 0.306697i 0.843627 0.536930i \(-0.180416\pi\)
−0.536930 + 0.843627i \(0.680416\pi\)
\(318\) 4.28827i 0.240474i
\(319\) −4.79886 + 4.79886i −0.268685 + 0.268685i
\(320\) −2.05054 + 0.891783i −0.114629 + 0.0498522i
\(321\) 2.20433i 0.123034i
\(322\) −1.80247 + 1.80247i −0.100448 + 0.100448i
\(323\) −2.73427 + 2.73427i −0.152139 + 0.152139i
\(324\) 1.00000 0.0555556
\(325\) −1.16818 1.08902i −0.0647991 0.0604081i
\(326\) 15.4091i 0.853430i
\(327\) 5.99769i 0.331673i
\(328\) 3.92813 0.216895
\(329\) 15.2844i 0.842654i
\(330\) 3.21347 8.15967i 0.176896 0.449175i
\(331\) 14.2462 + 14.2462i 0.783041 + 0.783041i 0.980343 0.197302i \(-0.0632180\pi\)
−0.197302 + 0.980343i \(0.563218\pi\)
\(332\) 1.13008 + 1.13008i 0.0620211 + 0.0620211i
\(333\) 6.08275 0.0100817i 0.333333 0.000552474i
\(334\) 16.8371i 0.921285i
\(335\) −20.2547 7.97679i −1.10663 0.435819i
\(336\) 2.21268i 0.120712i
\(337\) −23.4318 23.4318i −1.27641 1.27641i −0.942663 0.333746i \(-0.891687\pi\)
−0.333746 0.942663i \(-0.608313\pi\)
\(338\) 12.8980i 0.701557i
\(339\) 11.6944 11.6944i 0.635152 0.635152i
\(340\) −2.57338 + 1.11916i −0.139561 + 0.0606952i
\(341\) −26.6012 26.6012i −1.44054 1.44054i
\(342\) −2.17875 + 2.17875i −0.117813 + 0.117813i
\(343\) −14.2442 14.2442i −0.769115 0.769115i
\(344\) −1.87330 −0.101001
\(345\) 2.39684 + 0.943934i 0.129041 + 0.0508197i
\(346\) 5.18404 + 5.18404i 0.278696 + 0.278696i
\(347\) 4.74393i 0.254667i −0.991860 0.127334i \(-0.959358\pi\)
0.991860 0.127334i \(-0.0406419\pi\)
\(348\) 1.73044 0.0927613
\(349\) 14.8248i 0.793556i 0.917915 + 0.396778i \(0.129872\pi\)
−0.917915 + 0.396778i \(0.870128\pi\)
\(350\) −11.0566 + 0.387756i −0.591001 + 0.0207264i
\(351\) 0.225859 0.225859i 0.0120555 0.0120555i
\(352\) −3.92190 −0.209038
\(353\) −23.4920 −1.25035 −0.625177 0.780483i \(-0.714973\pi\)
−0.625177 + 0.780483i \(0.714973\pi\)
\(354\) 6.65245 0.353574
\(355\) −6.74653 + 2.93407i −0.358069 + 0.155725i
\(356\) 1.33809 + 1.33809i 0.0709185 + 0.0709185i
\(357\) 2.77686i 0.146967i
\(358\) 1.70251 1.70251i 0.0899805 0.0899805i
\(359\) 3.71905i 0.196284i −0.995172 0.0981419i \(-0.968710\pi\)
0.995172 0.0981419i \(-0.0312899\pi\)
\(360\) −2.05054 + 0.891783i −0.108073 + 0.0470011i
\(361\) 9.50611i 0.500322i
\(362\) 8.75170i 0.459979i
\(363\) 3.09806 3.09806i 0.162606 0.162606i
\(364\) −0.499755 0.499755i −0.0261943 0.0261943i
\(365\) 9.88884 25.1098i 0.517606 1.31431i
\(366\) 7.86494 0.411107
\(367\) 20.2784 20.2784i 1.05852 1.05852i 0.0603458 0.998178i \(-0.480780\pi\)
0.998178 0.0603458i \(-0.0192203\pi\)
\(368\) 1.15203i 0.0600536i
\(369\) 3.92813 0.204490
\(370\) −12.4640 + 5.44517i −0.647970 + 0.283081i
\(371\) 9.48858 0.492623
\(372\) 9.59224i 0.497334i
\(373\) 17.0249 17.0249i 0.881515 0.881515i −0.112174 0.993689i \(-0.535781\pi\)
0.993689 + 0.112174i \(0.0357814\pi\)
\(374\) −4.92188 −0.254505
\(375\) 4.81552 + 10.0901i 0.248672 + 0.521052i
\(376\) 4.88442 + 4.88442i 0.251895 + 0.251895i
\(377\) 0.390836 0.390836i 0.0201291 0.0201291i
\(378\) 2.21268i 0.113808i
\(379\) 3.59500i 0.184663i −0.995728 0.0923313i \(-0.970568\pi\)
0.995728 0.0923313i \(-0.0294319\pi\)
\(380\) 2.52465 6.41059i 0.129512 0.328856i
\(381\) 9.98731i 0.511665i
\(382\) −4.56780 + 4.56780i −0.233709 + 0.233709i
\(383\) 18.9973i 0.970715i −0.874316 0.485358i \(-0.838689\pi\)
0.874316 0.485358i \(-0.161311\pi\)
\(384\) 0.707107 + 0.707107i 0.0360844 + 0.0360844i
\(385\) −18.0548 7.11040i −0.920156 0.362380i
\(386\) 5.51547 0.280730
\(387\) −1.87330 −0.0952251
\(388\) −4.01884 −0.204025
\(389\) 9.52518 9.52518i 0.482946 0.482946i −0.423125 0.906071i \(-0.639067\pi\)
0.906071 + 0.423125i \(0.139067\pi\)
\(390\) −0.261716 + 0.664551i −0.0132525 + 0.0336509i
\(391\) 1.44577i 0.0731155i
\(392\) 2.10403 0.106270
\(393\) 13.1829i 0.664989i
\(394\) −3.48510 3.48510i −0.175577 0.175577i
\(395\) 4.16084 10.5652i 0.209354 0.531593i
\(396\) −3.92190 −0.197083
\(397\) 6.55806 + 6.55806i 0.329139 + 0.329139i 0.852259 0.523120i \(-0.175232\pi\)
−0.523120 + 0.852259i \(0.675232\pi\)
\(398\) 11.0862 11.0862i 0.555703 0.555703i
\(399\) 4.82088 + 4.82088i 0.241346 + 0.241346i
\(400\) 3.40945 3.65728i 0.170472 0.182864i
\(401\) −3.25081 + 3.25081i −0.162337 + 0.162337i −0.783601 0.621264i \(-0.786619\pi\)
0.621264 + 0.783601i \(0.286619\pi\)
\(402\) 9.73532i 0.485554i
\(403\) 2.16650 + 2.16650i 0.107921 + 0.107921i
\(404\) 11.0673i 0.550618i
\(405\) −2.05054 + 0.891783i −0.101892 + 0.0443130i
\(406\) 3.82892i 0.190026i
\(407\) −23.8560 + 0.0395395i −1.18250 + 0.00195990i
\(408\) 0.887401 + 0.887401i 0.0439329 + 0.0439329i
\(409\) 13.3605 + 13.3605i 0.660637 + 0.660637i 0.955530 0.294893i \(-0.0952842\pi\)
−0.294893 + 0.955530i \(0.595284\pi\)
\(410\) −8.05479 + 3.50304i −0.397798 + 0.173003i
\(411\) 20.6125i 1.01674i
\(412\) −13.8134 −0.680536
\(413\) 14.7198i 0.724312i
\(414\) 1.15203i 0.0566191i
\(415\) −3.32506 1.30949i −0.163221 0.0642803i
\(416\) 0.319413 0.0156605
\(417\) −0.852977 + 0.852977i −0.0417705 + 0.0417705i
\(418\) 8.54484 8.54484i 0.417942 0.417942i
\(419\) 18.6060i 0.908963i 0.890756 + 0.454481i \(0.150175\pi\)
−0.890756 + 0.454481i \(0.849825\pi\)
\(420\) 1.97323 + 4.53720i 0.0962839 + 0.221393i
\(421\) 4.15626 4.15626i 0.202564 0.202564i −0.598534 0.801098i \(-0.704250\pi\)
0.801098 + 0.598534i \(0.204250\pi\)
\(422\) 27.2170i 1.32490i
\(423\) 4.88442 + 4.88442i 0.237489 + 0.237489i
\(424\) −3.03226 + 3.03226i −0.147260 + 0.147260i
\(425\) 4.27877 4.58979i 0.207551 0.222637i
\(426\) 2.32647 + 2.32647i 0.112718 + 0.112718i
\(427\) 17.4026i 0.842172i
\(428\) −1.55870 + 1.55870i −0.0753426 + 0.0753426i
\(429\) −0.885798 + 0.885798i −0.0427667 + 0.0427667i
\(430\) 3.84128 1.67057i 0.185243 0.0805623i
\(431\) −7.99513 + 7.99513i −0.385112 + 0.385112i −0.872940 0.487828i \(-0.837789\pi\)
0.487828 + 0.872940i \(0.337789\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) 21.8861 + 21.8861i 1.05178 + 1.05178i 0.998584 + 0.0531948i \(0.0169404\pi\)
0.0531948 + 0.998584i \(0.483060\pi\)
\(434\) 21.2246 1.01881
\(435\) −3.54834 + 1.54318i −0.170130 + 0.0739897i
\(436\) −4.24101 + 4.24101i −0.203107 + 0.203107i
\(437\) 2.50998 + 2.50998i 0.120069 + 0.120069i
\(438\) −12.0689 −0.576674
\(439\) −19.4929 19.4929i −0.930345 0.930345i 0.0673822 0.997727i \(-0.478535\pi\)
−0.997727 + 0.0673822i \(0.978535\pi\)
\(440\) 8.04202 3.49748i 0.383388 0.166736i
\(441\) 2.10403 0.100192
\(442\) 0.400855 0.0190667
\(443\) 1.25482 1.25482i 0.0596181 0.0596181i −0.676669 0.736287i \(-0.736577\pi\)
0.736287 + 0.676669i \(0.236577\pi\)
\(444\) 4.30829 + 4.29403i 0.204462 + 0.203786i
\(445\) −3.93709 1.55052i −0.186636 0.0735018i
\(446\) −11.1865 + 11.1865i −0.529696 + 0.529696i
\(447\) −0.301061 0.301061i −0.0142397 0.0142397i
\(448\) 1.56460 1.56460i 0.0739206 0.0739206i
\(449\) 5.51963 5.51963i 0.260487 0.260487i −0.564765 0.825252i \(-0.691033\pi\)
0.825252 + 0.564765i \(0.191033\pi\)
\(450\) 3.40945 3.65728i 0.160723 0.172406i
\(451\) −15.4057 −0.725427
\(452\) 16.5384 0.777899
\(453\) −13.1917 13.1917i −0.619801 0.619801i
\(454\) 1.74912i 0.0820905i
\(455\) 1.47044 + 0.579096i 0.0689354 + 0.0271484i
\(456\) −3.08122 −0.144291
\(457\) −6.65948 −0.311517 −0.155759 0.987795i \(-0.549782\pi\)
−0.155759 + 0.987795i \(0.549782\pi\)
\(458\) −8.51464 −0.397863
\(459\) 0.887401 + 0.887401i 0.0414203 + 0.0414203i
\(460\) 1.02736 + 2.36228i 0.0479009 + 0.110142i
\(461\) −24.8127 24.8127i −1.15564 1.15564i −0.985403 0.170240i \(-0.945546\pi\)
−0.170240 0.985403i \(-0.554454\pi\)
\(462\) 8.67793i 0.403734i
\(463\) 0.607120i 0.0282153i 0.999900 + 0.0141076i \(0.00449075\pi\)
−0.999900 + 0.0141076i \(0.995509\pi\)
\(464\) 1.22361 + 1.22361i 0.0568045 + 0.0568045i
\(465\) −8.55419 19.6693i −0.396691 0.912141i
\(466\) −6.42533 6.42533i −0.297648 0.297648i
\(467\) −14.2821 −0.660896 −0.330448 0.943824i \(-0.607200\pi\)
−0.330448 + 0.943824i \(0.607200\pi\)
\(468\) 0.319413 0.0147649
\(469\) 21.5412 0.994679
\(470\) −14.3716 5.65987i −0.662910 0.261070i
\(471\) 8.81585i 0.406213i
\(472\) 4.70399 + 4.70399i 0.216519 + 0.216519i
\(473\) 7.34689 0.337810
\(474\) −5.07811 −0.233245
\(475\) 0.539960 + 15.3966i 0.0247751 + 0.706445i
\(476\) 1.96354 1.96354i 0.0899986 0.0899986i
\(477\) −3.03226 + 3.03226i −0.138838 + 0.138838i
\(478\) 10.4976 + 10.4976i 0.480151 + 0.480151i
\(479\) 12.8987 12.8987i 0.589358 0.589358i −0.348100 0.937458i \(-0.613173\pi\)
0.937458 + 0.348100i \(0.113173\pi\)
\(480\) −2.08054 0.819367i −0.0949631 0.0373988i
\(481\) 1.94291 0.00322023i 0.0885891 0.000146830i
\(482\) −6.66851 + 6.66851i −0.303742 + 0.303742i
\(483\) −2.54907 −0.115987
\(484\) 4.38131 0.199151
\(485\) 8.24079 3.58393i 0.374195 0.162738i
\(486\) 0.707107 + 0.707107i 0.0320750 + 0.0320750i
\(487\) 0.169467 0.00767930 0.00383965 0.999993i \(-0.498778\pi\)
0.00383965 + 0.999993i \(0.498778\pi\)
\(488\) 5.56135 + 5.56135i 0.251750 + 0.251750i
\(489\) −10.8959 + 10.8959i −0.492728 + 0.492728i
\(490\) −4.31440 + 1.87634i −0.194905 + 0.0847644i
\(491\) 11.6118 0.524033 0.262016 0.965063i \(-0.415613\pi\)
0.262016 + 0.965063i \(0.415613\pi\)
\(492\) 2.77761 + 2.77761i 0.125224 + 0.125224i
\(493\) 1.53559 + 1.53559i 0.0691596 + 0.0691596i
\(494\) −0.695921 + 0.695921i −0.0313110 + 0.0313110i
\(495\) 8.04202 3.49748i 0.361462 0.157200i
\(496\) −6.78274 + 6.78274i −0.304554 + 0.304554i
\(497\) 5.14774 5.14774i 0.230908 0.230908i
\(498\) 1.59817i 0.0716158i
\(499\) −15.8556 15.8556i −0.709793 0.709793i 0.256698 0.966492i \(-0.417365\pi\)
−0.966492 + 0.256698i \(0.917365\pi\)
\(500\) −3.72972 + 10.5399i −0.166798 + 0.471358i
\(501\) −11.9056 + 11.9056i −0.531904 + 0.531904i
\(502\) 19.9946 + 19.9946i 0.892402 + 0.892402i
\(503\) 22.2525i 0.992190i 0.868268 + 0.496095i \(0.165233\pi\)
−0.868268 + 0.496095i \(0.834767\pi\)
\(504\) 1.56460 1.56460i 0.0696930 0.0696930i
\(505\) 9.86962 + 22.6939i 0.439192 + 1.00987i
\(506\) 4.51814i 0.200856i
\(507\) −9.12025 + 9.12025i −0.405044 + 0.405044i
\(508\) −7.06209 + 7.06209i −0.313330 + 0.313330i
\(509\) 23.6164 1.04678 0.523390 0.852093i \(-0.324667\pi\)
0.523390 + 0.852093i \(0.324667\pi\)
\(510\) −2.61102 1.02828i −0.115618 0.0455332i
\(511\) 26.7046i 1.18134i
\(512\) 1.00000i 0.0441942i
\(513\) −3.08122 −0.136039
\(514\) 31.3639i 1.38340i
\(515\) 28.3249 12.3185i 1.24814 0.542819i
\(516\) −1.32462 1.32462i −0.0583132 0.0583132i
\(517\) −19.1562 19.1562i −0.842489 0.842489i
\(518\) 9.50133 9.53287i 0.417464 0.418850i
\(519\) 7.33134i 0.321810i
\(520\) −0.654970 + 0.284847i −0.0287223 + 0.0124914i
\(521\) 17.0507i 0.747006i −0.927629 0.373503i \(-0.878157\pi\)
0.927629 0.373503i \(-0.121843\pi\)
\(522\) 1.22361 + 1.22361i 0.0535558 + 0.0535558i
\(523\) 23.5794i 1.03105i −0.856873 0.515527i \(-0.827596\pi\)
0.856873 0.515527i \(-0.172404\pi\)
\(524\) 9.32171 9.32171i 0.407221 0.407221i
\(525\) −8.09240 7.54403i −0.353181 0.329248i
\(526\) −7.40341 7.40341i −0.322804 0.322804i
\(527\) −8.51216 + 8.51216i −0.370795 + 0.370795i
\(528\) −2.77320 2.77320i −0.120688 0.120688i
\(529\) 21.6728 0.942297
\(530\) 3.51366 8.92191i 0.152624 0.387543i
\(531\) 4.70399 + 4.70399i 0.204136 + 0.204136i
\(532\) 6.81776i 0.295587i
\(533\) 1.25470 0.0543469
\(534\) 1.89234i 0.0818896i
\(535\) 1.80616 4.58620i 0.0780870 0.198279i
\(536\) −6.88391 + 6.88391i −0.297340 + 0.297340i
\(537\) 2.40771 0.103901
\(538\) 3.41947 0.147424
\(539\) −8.25180 −0.355430
\(540\) −2.08054 0.819367i −0.0895321 0.0352599i
\(541\) −10.2113 10.2113i −0.439020 0.439020i 0.452662 0.891682i \(-0.350474\pi\)
−0.891682 + 0.452662i \(0.850474\pi\)
\(542\) 17.8704i 0.767600i
\(543\) −6.18839 + 6.18839i −0.265569 + 0.265569i
\(544\) 1.25497i 0.0538066i
\(545\) 4.91431 12.4784i 0.210506 0.534517i
\(546\) 0.706760i 0.0302465i
\(547\) 26.3899i 1.12835i −0.825655 0.564176i \(-0.809194\pi\)
0.825655 0.564176i \(-0.190806\pi\)
\(548\) 14.5752 14.5752i 0.622623 0.622623i
\(549\) 5.56135 + 5.56135i 0.237353 + 0.237353i
\(550\) −13.3715 + 14.3435i −0.570163 + 0.611608i
\(551\) −5.33186 −0.227145
\(552\) 0.814607 0.814607i 0.0346720 0.0346720i
\(553\) 11.2363i 0.477814i
\(554\) −14.8527 −0.631029
\(555\) −12.6637 4.96303i −0.537543 0.210669i
\(556\) −1.20629 −0.0511582
\(557\) 33.0054i 1.39849i 0.714885 + 0.699243i \(0.246479\pi\)
−0.714885 + 0.699243i \(0.753521\pi\)
\(558\) −6.78274 + 6.78274i −0.287136 + 0.287136i
\(559\) −0.598356 −0.0253078
\(560\) −1.81300 + 4.60357i −0.0766132 + 0.194536i
\(561\) −3.48030 3.48030i −0.146938 0.146938i
\(562\) −4.56193 + 4.56193i −0.192434 + 0.192434i
\(563\) 2.41113i 0.101617i 0.998708 + 0.0508086i \(0.0161798\pi\)
−0.998708 + 0.0508086i \(0.983820\pi\)
\(564\) 6.90761i 0.290863i
\(565\) −33.9126 + 14.7486i −1.42671 + 0.620479i
\(566\) 32.3891i 1.36142i
\(567\) 1.56460 1.56460i 0.0657072 0.0657072i
\(568\) 3.29012i 0.138050i
\(569\) −16.6810 16.6810i −0.699306 0.699306i 0.264955 0.964261i \(-0.414643\pi\)
−0.964261 + 0.264955i \(0.914643\pi\)
\(570\) 6.31816 2.74778i 0.264639 0.115092i
\(571\) −34.7939 −1.45608 −0.728041 0.685534i \(-0.759569\pi\)
−0.728041 + 0.685534i \(0.759569\pi\)
\(572\) −1.25271 −0.0523783
\(573\) −6.45984 −0.269864
\(574\) 6.14596 6.14596i 0.256528 0.256528i
\(575\) −4.21329 3.92778i −0.175706 0.163800i
\(576\) 1.00000i 0.0416667i
\(577\) 42.4452 1.76702 0.883509 0.468414i \(-0.155174\pi\)
0.883509 + 0.468414i \(0.155174\pi\)
\(578\) 15.4250i 0.641597i
\(579\) 3.90003 + 3.90003i 0.162080 + 0.162080i
\(580\) −3.60025 1.41786i −0.149492 0.0588736i
\(581\) 3.53625 0.146708
\(582\) −2.84175 2.84175i −0.117794 0.117794i
\(583\) 11.8922 11.8922i 0.492526 0.492526i
\(584\) −8.53399 8.53399i −0.353139 0.353139i
\(585\) −0.654970 + 0.284847i −0.0270797 + 0.0117770i
\(586\) −2.93182 + 2.93182i −0.121112 + 0.121112i
\(587\) 25.7512i 1.06287i 0.847100 + 0.531433i \(0.178346\pi\)
−0.847100 + 0.531433i \(0.821654\pi\)
\(588\) 1.48777 + 1.48777i 0.0613548 + 0.0613548i
\(589\) 29.5558i 1.21782i
\(590\) −13.8407 5.45079i −0.569811 0.224406i
\(591\) 4.92868i 0.202739i
\(592\) 0.0100817 + 6.08275i 0.000414356 + 0.250000i
\(593\) −17.7350 17.7350i −0.728289 0.728289i 0.241990 0.970279i \(-0.422200\pi\)
−0.970279 + 0.241990i \(0.922200\pi\)
\(594\) −2.77320 2.77320i −0.113786 0.113786i
\(595\) −2.27527 + 5.77736i −0.0932768 + 0.236849i
\(596\) 0.425764i 0.0174400i
\(597\) 15.6783 0.641671
\(598\) 0.367973i 0.0150475i
\(599\) 33.5799i 1.37204i 0.727583 + 0.686020i \(0.240644\pi\)
−0.727583 + 0.686020i \(0.759356\pi\)
\(600\) 4.99693 0.175243i 0.203999 0.00715425i
\(601\) −28.5324 −1.16386 −0.581930 0.813239i \(-0.697702\pi\)
−0.581930 + 0.813239i \(0.697702\pi\)
\(602\) −2.93097 + 2.93097i −0.119457 + 0.119457i
\(603\) −6.88391 + 6.88391i −0.280334 + 0.280334i
\(604\) 18.6559i 0.759098i
\(605\) −8.98406 + 3.90718i −0.365254 + 0.158849i
\(606\) 7.82575 7.82575i 0.317900 0.317900i
\(607\) 26.3325i 1.06880i −0.845231 0.534401i \(-0.820537\pi\)
0.845231 0.534401i \(-0.179463\pi\)
\(608\) −2.17875 2.17875i −0.0883599 0.0883599i
\(609\) 2.70745 2.70745i 0.109712 0.109712i
\(610\) −16.3633 6.44427i −0.662531 0.260921i
\(611\) 1.56015 + 1.56015i 0.0631168 + 0.0631168i
\(612\) 1.25497i 0.0507293i
\(613\) −18.6885 + 18.6885i −0.754820 + 0.754820i −0.975375 0.220555i \(-0.929213\pi\)
0.220555 + 0.975375i \(0.429213\pi\)
\(614\) 0.225281 0.225281i 0.00909162 0.00909162i
\(615\) −8.17262 3.21858i −0.329552 0.129786i
\(616\) −6.13622 + 6.13622i −0.247235 + 0.247235i
\(617\) −3.48887 3.48887i −0.140457 0.140457i 0.633382 0.773839i \(-0.281666\pi\)
−0.773839 + 0.633382i \(0.781666\pi\)
\(618\) −9.76753 9.76753i −0.392907 0.392907i
\(619\) 3.83734 0.154236 0.0771178 0.997022i \(-0.475428\pi\)
0.0771178 + 0.997022i \(0.475428\pi\)
\(620\) 7.85956 19.9570i 0.315647 0.801493i
\(621\) 0.814607 0.814607i 0.0326891 0.0326891i
\(622\) 8.19803 + 8.19803i 0.328711 + 0.328711i
\(623\) 4.18715 0.167755
\(624\) 0.225859 + 0.225859i 0.00904160 + 0.00904160i
\(625\) −1.75135 24.9386i −0.0700540 0.997543i
\(626\) 12.1187 0.484359
\(627\) 12.0842 0.482597
\(628\) −6.23375 + 6.23375i −0.248754 + 0.248754i
\(629\) 0.0126523 + 7.63370i 0.000504480 + 0.304376i
\(630\) −1.81300 + 4.60357i −0.0722316 + 0.183411i
\(631\) 15.4358 15.4358i 0.614490 0.614490i −0.329623 0.944113i \(-0.606922\pi\)
0.944113 + 0.329623i \(0.106922\pi\)
\(632\) −3.59077 3.59077i −0.142833 0.142833i
\(633\) −19.2453 + 19.2453i −0.764933 + 0.764933i
\(634\) −5.46058 + 5.46058i −0.216868 + 0.216868i
\(635\) 8.18326 20.7790i 0.324743 0.824588i
\(636\) −4.28827 −0.170041
\(637\) 0.672055 0.0266278
\(638\) −4.79886 4.79886i −0.189989 0.189989i
\(639\) 3.29012i 0.130155i
\(640\) −0.891783 2.05054i −0.0352508 0.0810548i
\(641\) −41.6890 −1.64662 −0.823309 0.567594i \(-0.807874\pi\)
−0.823309 + 0.567594i \(0.807874\pi\)
\(642\) −2.20433 −0.0869982
\(643\) −3.74780 −0.147799 −0.0738993 0.997266i \(-0.523544\pi\)
−0.0738993 + 0.997266i \(0.523544\pi\)
\(644\) −1.80247 1.80247i −0.0710272 0.0710272i
\(645\) 3.89747 + 1.53492i 0.153463 + 0.0604373i
\(646\) −2.73427 2.73427i −0.107579 0.107579i
\(647\) 3.49319i 0.137331i 0.997640 + 0.0686657i \(0.0218742\pi\)
−0.997640 + 0.0686657i \(0.978126\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −18.4486 18.4486i −0.724170 0.724170i
\(650\) 1.08902 1.16818i 0.0427150 0.0458199i
\(651\) 15.0080 + 15.0080i 0.588212 + 0.588212i
\(652\) −15.4091 −0.603466
\(653\) −32.5364 −1.27325 −0.636624 0.771175i \(-0.719670\pi\)
−0.636624 + 0.771175i \(0.719670\pi\)
\(654\) −5.99769 −0.234528
\(655\) −10.8016 + 27.4275i −0.422054 + 1.07168i
\(656\) 3.92813i 0.153368i
\(657\) −8.53399 8.53399i −0.332943 0.332943i
\(658\) 15.2844 0.595847
\(659\) 2.62449 0.102236 0.0511178 0.998693i \(-0.483722\pi\)
0.0511178 + 0.998693i \(0.483722\pi\)
\(660\) 8.15967 + 3.21347i 0.317615 + 0.125084i
\(661\) 0.358911 0.358911i 0.0139600 0.0139600i −0.700092 0.714052i \(-0.746858\pi\)
0.714052 + 0.700092i \(0.246858\pi\)
\(662\) −14.2462 + 14.2462i −0.553693 + 0.553693i
\(663\) 0.283447 + 0.283447i 0.0110082 + 0.0110082i
\(664\) −1.13008 + 1.13008i −0.0438556 + 0.0438556i
\(665\) −6.07996 13.9801i −0.235771 0.542125i
\(666\) 0.0100817 + 6.08275i 0.000390658 + 0.235702i
\(667\) 1.40963 1.40963i 0.0545810 0.0545810i
\(668\) −16.8371 −0.651447
\(669\) −15.8201 −0.611640
\(670\) 7.97679 20.2547i 0.308170 0.782507i
\(671\) −21.8111 21.8111i −0.842007 0.842007i
\(672\) 2.21268 0.0853561
\(673\) −14.4928 14.4928i −0.558658 0.558658i 0.370267 0.928925i \(-0.379266\pi\)
−0.928925 + 0.370267i \(0.879266\pi\)
\(674\) 23.4318 23.4318i 0.902557 0.902557i
\(675\) 4.99693 0.175243i 0.192332 0.00674509i
\(676\) −12.8980 −0.496076
\(677\) 9.12580 + 9.12580i 0.350733 + 0.350733i 0.860382 0.509649i \(-0.170225\pi\)
−0.509649 + 0.860382i \(0.670225\pi\)
\(678\) 11.6944 + 11.6944i 0.449120 + 0.449120i
\(679\) −6.28788 + 6.28788i −0.241307 + 0.241307i
\(680\) −1.11916 2.57338i −0.0429180 0.0986845i
\(681\) −1.23682 + 1.23682i −0.0473949 + 0.0473949i
\(682\) 26.6012 26.6012i 1.01861 1.01861i
\(683\) 24.7098i 0.945493i 0.881199 + 0.472746i \(0.156737\pi\)
−0.881199 + 0.472746i \(0.843263\pi\)
\(684\) −2.17875 2.17875i −0.0833065 0.0833065i
\(685\) −16.8892 + 42.8850i −0.645302 + 1.63855i
\(686\) 14.2442 14.2442i 0.543846 0.543846i
\(687\) −6.02076 6.02076i −0.229706 0.229706i
\(688\) 1.87330i 0.0714188i
\(689\) −0.968545 + 0.968545i −0.0368986 + 0.0368986i
\(690\) −0.943934 + 2.39684i −0.0359349 + 0.0912461i
\(691\) 47.7183i 1.81529i 0.419739 + 0.907645i \(0.362121\pi\)
−0.419739 + 0.907645i \(0.637879\pi\)
\(692\) −5.18404 + 5.18404i −0.197068 + 0.197068i
\(693\) −6.13622 + 6.13622i −0.233096 + 0.233096i
\(694\) 4.74393 0.180077
\(695\) 2.47355 1.07575i 0.0938272 0.0408055i
\(696\) 1.73044i 0.0655921i
\(697\) 4.92970i 0.186726i
\(698\) −14.8248 −0.561128
\(699\) 9.08679i 0.343694i
\(700\) −0.387756 11.0566i −0.0146558 0.417901i
\(701\) −2.69605 2.69605i −0.101828 0.101828i 0.654357 0.756186i \(-0.272939\pi\)
−0.756186 + 0.654357i \(0.772939\pi\)
\(702\) 0.225859 + 0.225859i 0.00852451 + 0.00852451i
\(703\) −13.2748 13.2308i −0.500667 0.499010i
\(704\) 3.92190i 0.147812i
\(705\) −6.16009 14.1644i −0.232002 0.533460i
\(706\) 23.4920i 0.884134i
\(707\) −17.3159 17.3159i −0.651232 0.651232i
\(708\) 6.65245i 0.250014i
\(709\) 20.0239 20.0239i 0.752014 0.752014i −0.222841 0.974855i \(-0.571533\pi\)
0.974855 + 0.222841i \(0.0715331\pi\)
\(710\) −2.93407 6.74653i −0.110114 0.253193i
\(711\) −3.59077 3.59077i −0.134664 0.134664i
\(712\) −1.33809 + 1.33809i −0.0501470 + 0.0501470i
\(713\) 7.81391 + 7.81391i 0.292633 + 0.292633i
\(714\) 2.77686 0.103921
\(715\) 2.56873 1.11714i 0.0960650 0.0417788i
\(716\) 1.70251 + 1.70251i 0.0636258 + 0.0636258i
\(717\) 14.8459i 0.554431i
\(718\) 3.71905 0.138794
\(719\) 32.6337i 1.21703i 0.793541 + 0.608517i \(0.208235\pi\)
−0.793541 + 0.608517i \(0.791765\pi\)
\(720\) −0.891783 2.05054i −0.0332348 0.0764192i
\(721\) −21.6124 + 21.6124i −0.804889 + 0.804889i
\(722\) −9.50611 −0.353781
\(723\) −9.43070 −0.350731
\(724\) −8.75170 −0.325254
\(725\) 8.64688 0.303247i 0.321137 0.0112623i
\(726\) 3.09806 + 3.09806i 0.114980 + 0.114980i
\(727\) 21.1503i 0.784422i 0.919875 + 0.392211i \(0.128290\pi\)
−0.919875 + 0.392211i \(0.871710\pi\)
\(728\) 0.499755 0.499755i 0.0185222 0.0185222i
\(729\) 1.00000i 0.0370370i
\(730\) 25.1098 + 9.88884i 0.929354 + 0.366002i
\(731\) 2.35094i 0.0869527i
\(732\) 7.86494i 0.290696i
\(733\) −26.3403 + 26.3403i −0.972902 + 0.972902i −0.999642 0.0267403i \(-0.991487\pi\)
0.0267403 + 0.999642i \(0.491487\pi\)
\(734\) 20.2784 + 20.2784i 0.748489 + 0.748489i
\(735\) −4.37752 1.72397i −0.161467 0.0635897i
\(736\) 1.15203 0.0424643
\(737\) 26.9980 26.9980i 0.994485 0.994485i
\(738\) 3.92813i 0.144596i
\(739\) −27.2865 −1.00375 −0.501876 0.864940i \(-0.667357\pi\)
−0.501876 + 0.864940i \(0.667357\pi\)
\(740\) −5.44517 12.4640i −0.200168 0.458184i
\(741\) −0.984181 −0.0361548
\(742\) 9.48858i 0.348337i
\(743\) 18.6520 18.6520i 0.684276 0.684276i −0.276684 0.960961i \(-0.589236\pi\)
0.960961 + 0.276684i \(0.0892357\pi\)
\(744\) −9.59224 −0.351668
\(745\) 0.379689 + 0.873048i 0.0139107 + 0.0319860i
\(746\) 17.0249 + 17.0249i 0.623325 + 0.623325i
\(747\) −1.13008 + 1.13008i −0.0413474 + 0.0413474i
\(748\) 4.92188i 0.179962i
\(749\) 4.87750i 0.178220i
\(750\) −10.0901 + 4.81552i −0.368440 + 0.175838i
\(751\) 29.3632i 1.07148i −0.844384 0.535738i \(-0.820033\pi\)
0.844384 0.535738i \(-0.179967\pi\)
\(752\) −4.88442 + 4.88442i −0.178116 + 0.178116i
\(753\) 28.2766i 1.03046i
\(754\) 0.390836 + 0.390836i 0.0142334 + 0.0142334i
\(755\) 16.6370 + 38.2547i 0.605483 + 1.39223i
\(756\) 2.21268 0.0804745
\(757\) 36.6279 1.33126 0.665631 0.746281i \(-0.268162\pi\)
0.665631 + 0.746281i \(0.268162\pi\)
\(758\) 3.59500 0.130576
\(759\) −3.19481 + 3.19481i −0.115964 + 0.115964i
\(760\) 6.41059 + 2.52465i 0.232536 + 0.0915785i
\(761\) 13.4727i 0.488386i −0.969727 0.244193i \(-0.921477\pi\)
0.969727 0.244193i \(-0.0785230\pi\)
\(762\) −9.98731 −0.361802
\(763\) 13.2710i 0.480442i
\(764\) −4.56780 4.56780i −0.165257 0.165257i
\(765\) −1.11916 2.57338i −0.0404635 0.0930407i
\(766\) 18.9973 0.686399
\(767\) 1.50252 + 1.50252i 0.0542527 + 0.0542527i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 11.9916 + 11.9916i 0.432427 + 0.432427i 0.889453 0.457026i \(-0.151085\pi\)
−0.457026 + 0.889453i \(0.651085\pi\)
\(770\) 7.11040 18.0548i 0.256241 0.650648i
\(771\) −22.1776 + 22.1776i −0.798707 + 0.798707i
\(772\) 5.51547i 0.198506i
\(773\) 14.0271 + 14.0271i 0.504520 + 0.504520i 0.912839 0.408319i \(-0.133885\pi\)
−0.408319 + 0.912839i \(0.633885\pi\)
\(774\) 1.87330i 0.0673343i
\(775\) 1.68097 + 47.9317i 0.0603822 + 1.72176i
\(776\) 4.01884i 0.144268i
\(777\) 13.4592 0.0223076i 0.482846 0.000800282i
\(778\) 9.52518 + 9.52518i 0.341494 + 0.341494i
\(779\) −8.55840 8.55840i −0.306637 0.306637i
\(780\) −0.664551 0.261716i