Properties

Label 1110.2.o.a.487.11
Level $1110$
Weight $2$
Character 1110.487
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.o (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 487.11
Character \(\chi\) \(=\) 1110.487
Dual form 1110.2.o.a.253.11

$q$-expansion

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

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 1.00000 0.500000
\(5\) −0.891783 + 2.05054i −0.398817 + 0.917030i
\(6\) −0.707107 0.707107i −0.288675 0.288675i
\(7\) −1.56460 1.56460i −0.591365 0.591365i 0.346635 0.938000i \(-0.387324\pi\)
−0.938000 + 0.346635i \(0.887324\pi\)
\(8\) −1.00000 −0.353553
\(9\) 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
\(13\) −0.319413 −0.0885893 −0.0442946 0.999019i \(-0.514104\pi\)
−0.0442946 + 0.999019i \(0.514104\pi\)
\(14\) 1.56460 + 1.56460i 0.418158 + 0.418158i
\(15\) −2.08054 + 0.819367i −0.537193 + 0.211560i
\(16\) 1.00000 0.250000
\(17\) 1.25497i 0.304376i 0.988352 + 0.152188i \(0.0486319\pi\)
−0.988352 + 0.152188i \(0.951368\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 2.17875 2.17875i 0.499839 0.499839i −0.411549 0.911388i \(-0.635012\pi\)
0.911388 + 0.411549i \(0.135012\pi\)
\(20\) −0.891783 + 2.05054i −0.199409 + 0.458515i
\(21\) 2.21268i 0.482847i
\(22\) 3.92190i 0.836152i
\(23\) −1.15203 −0.240215 −0.120107 0.992761i \(-0.538324\pi\)
−0.120107 + 0.992761i \(0.538324\pi\)
\(24\) −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 0.584312 0.811529i \(-0.301365\pi\)
−0.811529 + 0.584312i \(0.801365\pi\)
\(30\) 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 \(0.919583\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.77320 + 2.77320i −0.482753 + 0.482753i
\(34\) 1.25497i 0.215226i
\(35\) 4.60357 1.81300i 0.778146 0.306453i
\(36\) 1.00000i 0.166667i
\(37\) −6.08275 + 0.0100817i −0.999999 + 0.00165742i
\(38\) −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 \(0.900763\pi\)
\(42\) 2.21268i 0.341425i
\(43\) −1.87330 −0.285675 −0.142838 0.989746i \(-0.545623\pi\)
−0.142838 + 0.989746i \(0.545623\pi\)
\(44\) 3.92190i 0.591249i
\(45\) −2.05054 0.891783i −0.305677 0.132939i
\(46\) 1.15203 0.169857
\(47\) −4.88442 4.88442i −0.712466 0.712466i 0.254585 0.967051i \(-0.418061\pi\)
−0.967051 + 0.254585i \(0.918061\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 2.10403i 0.300576i
\(50\) 3.40945 + 3.65728i 0.482169 + 0.517217i
\(51\) −0.887401 + 0.887401i −0.124261 + 0.124261i
\(52\) −0.319413 −0.0442946
\(53\) −3.03226 + 3.03226i −0.416513 + 0.416513i −0.884000 0.467487i \(-0.845160\pi\)
0.467487 + 0.884000i \(0.345160\pi\)
\(54\) 0.707107 0.707107i 0.0962250 0.0962250i
\(55\) −8.04202 3.49748i −1.08439 0.471601i
\(56\) 1.56460 + 1.56460i 0.209079 + 0.209079i
\(57\) 3.08122 0.408117
\(58\) 1.22361 + 1.22361i 0.160667 + 0.160667i
\(59\) 4.70399 4.70399i 0.612407 0.612407i −0.331165 0.943573i \(-0.607442\pi\)
0.943573 + 0.331165i \(0.107442\pi\)
\(60\) −2.08054 + 0.819367i −0.268596 + 0.105780i
\(61\) −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 \(-0.547279\pi\)
0.988989 + 0.147986i \(0.0472791\pi\)
\(68\) 1.25497i 0.152188i
\(69\) −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 \(0.562546\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −8.53399 8.53399i −0.998828 0.998828i 0.00117124 0.999999i \(-0.499627\pi\)
−0.999999 + 0.00117124i \(0.999627\pi\)
\(74\) 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 −0.879638 0.475645i \(-0.842215\pi\)
0.475645 + 0.879638i \(0.342215\pi\)
\(80\) −0.891783 + 2.05054i −0.0997044 + 0.229258i
\(81\) −1.00000 −0.111111
\(82\) 3.92813i 0.433789i
\(83\) −1.13008 + 1.13008i −0.124042 + 0.124042i −0.766403 0.642360i \(-0.777955\pi\)
0.642360 + 0.766403i \(0.277955\pi\)
\(84\) 2.21268i 0.241424i
\(85\) −2.57338 1.11916i −0.279122 0.121390i
\(86\) 1.87330 0.202003
\(87\) 1.73044i 0.185523i
\(88\) 3.92190i 0.418076i
\(89\) 1.33809 + 1.33809i 0.141837 + 0.141837i 0.774460 0.632623i \(-0.218022\pi\)
−0.632623 + 0.774460i \(0.718022\pi\)
\(90\) 2.05054 + 0.891783i 0.216146 + 0.0940022i
\(91\) 0.499755 + 0.499755i 0.0523886 + 0.0523886i
\(92\) −1.15203 −0.120107
\(93\) −9.59224 −0.994669
\(94\) 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
\(97\) 4.01884i 0.408051i 0.978966 + 0.204025i \(0.0654025\pi\)
−0.978966 + 0.204025i \(0.934597\pi\)
\(98\) 2.10403i 0.212539i
\(99\) −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
\(103\) 13.8134i 1.36107i −0.732715 0.680536i \(-0.761747\pi\)
0.732715 0.680536i \(-0.238253\pi\)
\(104\) 0.319413 0.0313210
\(105\) 4.53720 + 1.97323i 0.442785 + 0.192568i
\(106\) 3.03226 3.03226i 0.294520 0.294520i
\(107\) 1.55870 + 1.55870i 0.150685 + 0.150685i 0.778424 0.627739i \(-0.216019\pi\)
−0.627739 + 0.778424i \(0.716019\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) −4.24101 + 4.24101i −0.406215 + 0.406215i −0.880416 0.474201i \(-0.842737\pi\)
0.474201 + 0.880416i \(0.342737\pi\)
\(110\) 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
\(113\) 16.5384i 1.55580i 0.628390 + 0.777899i \(0.283714\pi\)
−0.628390 + 0.777899i \(0.716286\pi\)
\(114\) −3.08122 −0.288582
\(115\) 1.02736 2.36228i 0.0958018 0.220284i
\(116\) −1.22361 1.22361i −0.113609 0.113609i
\(117\) 0.319413i 0.0295298i
\(118\) −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
\(125\) 10.5399 3.72972i 0.942716 0.333596i
\(126\) −1.56460 + 1.56460i −0.139386 + 0.139386i
\(127\) 7.06209 + 7.06209i 0.626659 + 0.626659i 0.947226 0.320567i \(-0.103873\pi\)
−0.320567 + 0.947226i \(0.603873\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.32462 1.32462i −0.116626 0.116626i
\(130\) −0.284847 + 0.654970i −0.0249828 + 0.0574447i
\(131\) −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
\(133\) −6.81776 −0.591174
\(134\) −6.88391 + 6.88391i −0.594679 + 0.594679i
\(135\) −0.819367 2.08054i −0.0705198 0.179064i
\(136\) 1.25497i 0.107613i
\(137\) −14.5752 14.5752i −1.24525 1.24525i −0.957796 0.287450i \(-0.907193\pi\)
−0.287450 0.957796i \(-0.592807\pi\)
\(138\) 0.814607 + 0.814607i 0.0693440 + 0.0693440i
\(139\) −1.20629 −0.102316 −0.0511582 0.998691i \(-0.516291\pi\)
−0.0511582 + 0.998691i \(0.516291\pi\)
\(140\) 4.60357 1.81300i 0.389073 0.153226i
\(141\) 6.90761i 0.581726i
\(142\) 3.29012 0.276101
\(143\) 1.25271i 0.104757i
\(144\) 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
\(148\) −6.08275 + 0.0100817i −0.499999 + 0.000828712i
\(149\) 0.425764i 0.0348800i −0.999848 0.0174400i \(-0.994448\pi\)
0.999848 0.0174400i \(-0.00555160\pi\)
\(150\) −0.175243 + 4.99693i −0.0143085 + 0.407997i
\(151\) 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
\(153\) −1.25497 −0.101459
\(154\) −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 0.910661 0.413154i \(-0.135573\pi\)
−0.413154 + 0.910661i \(0.635573\pi\)
\(158\) 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
\(162\) 1.00000 0.0785674
\(163\) 15.4091i 1.20693i −0.797389 0.603466i \(-0.793786\pi\)
0.797389 0.603466i \(-0.206214\pi\)
\(164\) 3.92813i 0.306735i
\(165\) −3.21347 8.15967i −0.250169 0.635229i
\(166\) 1.13008 1.13008i 0.0877111 0.0877111i
\(167\) 16.8371i 1.30289i 0.758694 + 0.651447i \(0.225838\pi\)
−0.758694 + 0.651447i \(0.774162\pi\)
\(168\) 2.21268i 0.170712i
\(169\) −12.8980 −0.992152
\(170\) 2.57338 + 1.11916i 0.197369 + 0.0858360i
\(171\) 2.17875 + 2.17875i 0.166613 + 0.166613i
\(172\) −1.87330 −0.142838
\(173\) −5.18404 5.18404i −0.394136 0.394136i 0.482023 0.876159i \(-0.339902\pi\)
−0.876159 + 0.482023i \(0.839902\pi\)
\(174\) 1.73044i 0.131184i
\(175\) −0.387756 + 11.0566i −0.0293116 + 0.835802i
\(176\) 3.92190i 0.295624i
\(177\) 6.65245 0.500029
\(178\) −1.33809 1.33809i −0.100294 0.100294i
\(179\) 1.70251 + 1.70251i 0.127252 + 0.127252i 0.767864 0.640613i \(-0.221320\pi\)
−0.640613 + 0.767864i \(0.721320\pi\)
\(180\) −2.05054 0.891783i −0.152838 0.0664696i
\(181\) 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
\(183\) −7.86494 −0.581393
\(184\) 1.15203 0.0849287
\(185\) 5.40382 12.4819i 0.397297 0.917690i
\(186\) 9.59224 0.703337
\(187\) −4.92188 −0.359924
\(188\) −4.88442 4.88442i −0.356233 0.356233i
\(189\) 2.21268 0.160949
\(190\) −2.52465 6.41059i −0.183157 0.465073i
\(191\) 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
\(193\) −5.51547 −0.397012 −0.198506 0.980100i \(-0.563609\pi\)
−0.198506 + 0.980100i \(0.563609\pi\)
\(194\) 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 0.571971 0.820274i \(-0.306179\pi\)
−0.820274 + 0.571971i \(0.806179\pi\)
\(198\) 3.92190 0.278717
\(199\) 11.0862 + 11.0862i 0.785883 + 0.785883i 0.980817 0.194933i \(-0.0624490\pi\)
−0.194933 + 0.980817i \(0.562449\pi\)
\(200\) 3.40945 + 3.65728i 0.241084 + 0.258609i
\(201\) 9.73532 0.686676
\(202\) 11.0673i 0.778692i
\(203\) 3.82892i 0.268737i
\(204\) −0.887401 + 0.887401i −0.0621305 + 0.0621305i
\(205\) −8.05479 3.50304i −0.562571 0.244663i
\(206\) 13.8134i 0.962423i
\(207\) 1.15203i 0.0800715i
\(208\) −0.319413 −0.0221473
\(209\) 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
\(217\) 21.2246 1.44082
\(218\) 4.24101 4.24101i 0.287237 0.287237i
\(219\) 12.0689i 0.815540i
\(220\) −8.04202 3.49748i −0.542193 0.235800i
\(221\) 0.400855i 0.0269644i
\(222\) 4.30829 + 4.29403i 0.289153 + 0.288196i
\(223\) 11.1865 11.1865i 0.749103 0.749103i −0.225208 0.974311i \(-0.572306\pi\)
0.974311 + 0.225208i \(0.0723061\pi\)
\(224\) 1.56460 + 1.56460i 0.104539 + 0.104539i
\(225\) 3.65728 3.40945i 0.243818 0.227296i
\(226\) 16.5384i 1.10011i
\(227\) 1.74912i 0.116093i 0.998314 + 0.0580467i \(0.0184872\pi\)
−0.998314 + 0.0580467i \(0.981513\pi\)
\(228\) 3.08122 0.204058
\(229\) 8.51464i 0.562663i −0.959611 0.281332i \(-0.909224\pi\)
0.959611 0.281332i \(-0.0907761\pi\)
\(230\) −1.02736 + 2.36228i −0.0677421 + 0.155764i
\(231\) 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 \(-0.153798\pi\)
−0.464589 + 0.885526i \(0.653798\pi\)
\(234\) 0.319413i 0.0208807i
\(235\) 14.3716 5.65987i 0.937497 0.369209i
\(236\) 4.70399 4.70399i 0.306204 0.306204i
\(237\) −5.07811 −0.329859
\(238\) −1.96354 + 1.96354i −0.127277 + 0.127277i
\(239\) −10.4976 + 10.4976i −0.679036 + 0.679036i −0.959782 0.280746i \(-0.909418\pi\)
0.280746 + 0.959782i \(0.409418\pi\)
\(240\) −2.08054 + 0.819367i −0.134298 + 0.0528899i
\(241\) 6.66851 + 6.66851i 0.429556 + 0.429556i 0.888477 0.458921i \(-0.151764\pi\)
−0.458921 + 0.888477i \(0.651764\pi\)
\(242\) 4.38131 0.281641
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) −5.56135 + 5.56135i −0.356029 + 0.356029i
\(245\) 4.31440 + 1.87634i 0.275637 + 0.119875i
\(246\) 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
\(253\) 4.51814i 0.284053i
\(254\) −7.06209 7.06209i −0.443115 0.443115i
\(255\) −1.02828 2.61102i −0.0643936 0.163508i
\(256\) 1.00000 0.0625000
\(257\) 31.3639i 1.95642i 0.207609 + 0.978212i \(0.433432\pi\)
−0.207609 + 0.978212i \(0.566568\pi\)
\(258\) 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 \(-0.145374\pi\)
−0.440995 + 0.897509i \(0.645374\pi\)
\(264\) 2.77320 2.77320i 0.170679 0.170679i
\(265\) −3.51366 8.92191i −0.215843 0.548068i
\(266\) 6.81776 0.418023
\(267\) 1.89234i 0.115809i
\(268\) 6.88391 6.88391i 0.420502 0.420502i
\(269\) 3.41947i 0.208489i 0.994552 + 0.104244i \(0.0332424\pi\)
−0.994552 + 0.104244i \(0.966758\pi\)
\(270\) 0.819367 + 2.08054i 0.0498651 + 0.126618i
\(271\) 17.8704 1.08555 0.542775 0.839878i \(-0.317374\pi\)
0.542775 + 0.839878i \(0.317374\pi\)
\(272\) 1.25497i 0.0760940i
\(273\) 0.706760i 0.0427751i
\(274\) 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
\(277\) −14.8527 −0.892410 −0.446205 0.894931i \(-0.647225\pi\)
−0.446205 + 0.894931i \(0.647225\pi\)
\(278\) 1.20629 0.0723486
\(279\) −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 \(0.688362\pi\)
\(282\) 6.90761i 0.411342i
\(283\) 32.3891i 1.92533i 0.270692 + 0.962666i \(0.412748\pi\)
−0.270692 + 0.962666i \(0.587252\pi\)
\(284\) −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
\(288\) 1.00000i 0.0589256i
\(289\) 15.4250 0.907355
\(290\) −3.60025 + 1.41786i −0.211414 + 0.0832599i
\(291\) −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 −0.616262 0.787541i \(-0.711354\pi\)
0.787541 + 0.616262i \(0.211354\pi\)
\(294\) −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
\(298\) 0.425764i 0.0246639i
\(299\) 0.367973 0.0212804
\(300\) 0.175243 4.99693i 0.0101176 0.288498i
\(301\) 2.93097 + 2.93097i 0.168938 + 0.168938i
\(302\) 18.6559i 1.07353i
\(303\) −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 \(-0.747106\pi\)
0.713506 + 0.700649i \(0.247106\pi\)
\(308\) 6.13622 6.13622i 0.349644 0.349644i
\(309\) 9.76753 9.76753i 0.555655 0.555655i
\(310\) 7.85956 + 19.9570i 0.446393 + 1.13348i
\(311\) 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
\(313\) −12.1187 −0.684987 −0.342494 0.939520i \(-0.611271\pi\)
−0.342494 + 0.939520i \(0.611271\pi\)
\(314\) −6.23375 6.23375i −0.351791 0.351791i
\(315\) 1.81300 + 4.60357i 0.102151 + 0.259382i
\(316\) −3.59077 + 3.59077i −0.201996 + 0.201996i
\(317\) −5.46058 + 5.46058i −0.306697 + 0.306697i −0.843627 0.536930i \(-0.819584\pi\)
0.536930 + 0.843627i \(0.319584\pi\)
\(318\) 4.28827 0.240474
\(319\) 4.79886 4.79886i 0.268685 0.268685i
\(320\) −0.891783 + 2.05054i −0.0498522 + 0.114629i
\(321\) 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
\(325\) 1.08902 + 1.16818i 0.0604081 + 0.0647991i
\(326\) 15.4091i 0.853430i
\(327\) −5.99769 −0.331673
\(328\) 3.92813i 0.216895i
\(329\) 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
\(333\) −0.0100817 6.08275i −0.000552474 0.333333i
\(334\) 16.8371i 0.921285i
\(335\) 7.97679 + 20.2547i 0.435819 + 1.10663i
\(336\) 2.21268i 0.120712i
\(337\) 23.4318 23.4318i 1.27641 1.27641i 0.333746 0.942663i \(-0.391687\pi\)
0.942663 0.333746i \(-0.108313\pi\)
\(338\) 12.8980 0.701557
\(339\) −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
\(347\) 4.74393 0.254667 0.127334 0.991860i \(-0.459358\pi\)
0.127334 + 0.991860i \(0.459358\pi\)
\(348\) 1.73044i 0.0927613i
\(349\) 14.8248i 0.793556i −0.917915 0.396778i \(-0.870128\pi\)
0.917915 0.396778i \(-0.129872\pi\)
\(350\) 0.387756 11.0566i 0.0207264 0.591001i
\(351\) 0.225859 0.225859i 0.0120555 0.0120555i
\(352\) 3.92190i 0.209038i
\(353\) 23.4920i 1.25035i 0.780483 + 0.625177i \(0.214973\pi\)
−0.780483 + 0.625177i \(0.785027\pi\)
\(354\) −6.65245 −0.353574
\(355\) 2.93407 6.74653i 0.155725 0.358069i
\(356\) 1.33809 + 1.33809i 0.0709185 + 0.0709185i
\(357\) 2.77686 0.146967
\(358\) −1.70251 1.70251i −0.0899805 0.0899805i
\(359\) 3.71905i 0.196284i 0.995172 + 0.0981419i \(0.0312899\pi\)
−0.995172 + 0.0981419i \(0.968710\pi\)
\(360\) 2.05054 + 0.891783i 0.108073 + 0.0470011i
\(361\) 9.50611i 0.500322i
\(362\) −8.75170 −0.459979
\(363\) −3.09806 3.09806i −0.162606 0.162606i
\(364\) 0.499755 + 0.499755i 0.0261943 + 0.0261943i
\(365\) 25.1098 9.88884i 1.31431 0.517606i
\(366\) 7.86494 0.411107
\(367\) 20.2784 + 20.2784i 1.05852 + 1.05852i 0.998178 + 0.0603458i \(0.0192203\pi\)
0.0603458 + 0.998178i \(0.480780\pi\)
\(368\) −1.15203 −0.0600536
\(369\) −3.92813 −0.204490
\(370\) −5.40382 + 12.4819i −0.280931 + 0.648905i
\(371\) 9.48858 0.492623
\(372\) −9.59224 −0.497334
\(373\) −17.0249 17.0249i −0.881515 0.881515i 0.112174 0.993689i \(-0.464219\pi\)
−0.993689 + 0.112174i \(0.964219\pi\)
\(374\) 4.92188 0.254505
\(375\) 10.0901 + 4.81552i 0.521052 + 0.248672i
\(376\) 4.88442 + 4.88442i 0.251895 + 0.251895i
\(377\) 0.390836 + 0.390836i 0.0201291 + 0.0201291i
\(378\) −2.21268 −0.113808
\(379\) 3.59500i 0.184663i 0.995728 + 0.0923313i \(0.0294319\pi\)
−0.995728 + 0.0923313i \(0.970568\pi\)
\(380\) 2.52465 + 6.41059i 0.129512 + 0.328856i
\(381\) 9.98731i 0.511665i
\(382\) −4.56780 4.56780i −0.233709 0.233709i
\(383\) −18.9973 −0.970715 −0.485358 0.874316i \(-0.661311\pi\)
−0.485358 + 0.874316i \(0.661311\pi\)
\(384\) −0.707107 0.707107i −0.0360844 0.0360844i
\(385\) 7.11040 + 18.0548i 0.362380 + 0.920156i
\(386\) 5.51547 0.280730
\(387\) 1.87330i 0.0952251i
\(388\) 4.01884i 0.204025i
\(389\) −9.52518 + 9.52518i −0.482946 + 0.482946i −0.906071 0.423125i \(-0.860933\pi\)
0.423125 + 0.906071i \(0.360933\pi\)
\(390\) −0.664551 + 0.261716i −0.0336509 + 0.0132525i
\(391\) 1.44577i 0.0731155i
\(392\) 2.10403i 0.106270i
\(393\) −13.1829 −0.664989
\(394\) 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 \(-0.824768\pi\)
0.523120 + 0.852259i \(0.324768\pi\)
\(398\) −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 \(0.286619\pi\)
\(402\) −9.73532 −0.485554
\(403\) 2.16650 2.16650i 0.107921 0.107921i
\(404\) 11.0673i 0.550618i
\(405\) 0.891783 2.05054i 0.0443130 0.101892i
\(406\) 3.82892i 0.190026i
\(407\) −0.0395395 23.8560i −0.00195990 1.18250i
\(408\) 0.887401 0.887401i 0.0439329 0.0439329i
\(409\) −13.3605 13.3605i −0.660637 0.660637i 0.294893 0.955530i \(-0.404716\pi\)
−0.955530 + 0.294893i \(0.904716\pi\)
\(410\) 8.05479 + 3.50304i 0.397798 + 0.173003i
\(411\) 20.6125i 1.01674i
\(412\) 13.8134i 0.680536i
\(413\) −14.7198 −0.724312
\(414\) 1.15203i 0.0566191i
\(415\) −1.30949 3.32506i −0.0642803 0.163221i
\(416\) 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 \(-0.849825\pi\)
0.890756 0.454481i \(-0.150175\pi\)
\(420\) 4.53720 + 1.97323i 0.221393 + 0.0962839i
\(421\) 4.15626 4.15626i 0.202564 0.202564i −0.598534 0.801098i \(-0.704250\pi\)
0.801098 + 0.598534i \(0.204250\pi\)
\(422\) −27.2170 −1.32490
\(423\) 4.88442 4.88442i 0.237489 0.237489i
\(424\) 3.03226 3.03226i 0.147260 0.147260i
\(425\) 4.58979 4.27877i 0.222637 0.207551i
\(426\) 2.32647 + 2.32647i 0.112718 + 0.112718i
\(427\) 17.4026 0.842172
\(428\) 1.55870 + 1.55870i 0.0753426 + 0.0753426i
\(429\) 0.885798 0.885798i 0.0427667 0.0427667i
\(430\) −1.67057 + 3.84128i −0.0805623 + 0.185243i
\(431\) −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 0.0531948 0.998584i \(-0.483060\pi\)
0.998584 0.0531948i \(-0.0169404\pi\)
\(434\) −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
\(438\) 12.0689i 0.576674i
\(439\) 19.4929 + 19.4929i 0.930345 + 0.930345i 0.997727 0.0673822i \(-0.0214647\pi\)
−0.0673822 + 0.997727i \(0.521465\pi\)
\(440\) 8.04202 + 3.49748i 0.383388 + 0.166736i
\(441\) 2.10403 0.100192
\(442\) 0.400855i 0.0190667i
\(443\) −1.25482 1.25482i −0.0596181 0.0596181i 0.676669 0.736287i \(-0.263423\pi\)
−0.736287 + 0.676669i \(0.763423\pi\)
\(444\) −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 −0.825252 0.564765i \(-0.808967\pi\)
0.564765 + 0.825252i \(0.308967\pi\)
\(450\) −3.65728 + 3.40945i −0.172406 + 0.160723i
\(451\) −15.4057 −0.725427
\(452\) 16.5384i 0.777899i
\(453\) −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
\(457\) 6.65948i 0.311517i −0.987795 0.155759i \(-0.950218\pi\)
0.987795 0.155759i \(-0.0497822\pi\)
\(458\) 8.51464i 0.397863i
\(459\) −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 \(-0.554454\pi\)
\(462\) −8.67793 −0.403734
\(463\) 0.607120 0.0282153 0.0141076 0.999900i \(-0.495509\pi\)
0.0141076 + 0.999900i \(0.495509\pi\)
\(464\) −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
\(467\) 14.2821i 0.660896i −0.943824 0.330448i \(-0.892800\pi\)
0.943824 0.330448i \(-0.107200\pi\)
\(468\) 0.319413i 0.0147649i
\(469\) −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
\(473\) 7.34689i 0.337810i
\(474\) 5.07811 0.233245
\(475\) −15.3966 0.539960i −0.706445 0.0247751i
\(476\) 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 −0.937458 0.348100i \(-0.886827\pi\)
0.348100 + 0.937458i \(0.386827\pi\)
\(480\) 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
\(483\) 2.54907i 0.115987i
\(484\) −4.38131 −0.199151
\(485\) −8.24079 3.58393i −0.374195 0.162738i
\(486\) 0.707107 + 0.707107i 0.0320750 + 0.0320750i
\(487\) 0.169467i 0.00767930i 0.999993 + 0.00383965i \(0.00122220\pi\)
−0.999993 + 0.00383965i \(0.998778\pi\)
\(488\) 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
\(495\) 3.49748 8.04202i 0.157200 0.361462i
\(496\) −6.78274 + 6.78274i −0.304554 + 0.304554i
\(497\) 5.14774 + 5.14774i 0.230908 + 0.230908i
\(498\) 1.59817 0.0716158
\(499\) 15.8556 + 15.8556i 0.709793 + 0.709793i 0.966492 0.256698i \(-0.0826347\pi\)
−0.256698 + 0.966492i \(0.582635\pi\)
\(500\) 10.5399 3.72972i 0.471358 0.166798i
\(501\) −11.9056 + 11.9056i −0.531904 + 0.531904i
\(502\) −19.9946 + 19.9946i −0.892402 + 0.892402i
\(503\) 22.2525 0.992190 0.496095 0.868268i \(-0.334767\pi\)
0.496095 + 0.868268i \(0.334767\pi\)
\(504\) −1.56460 + 1.56460i −0.0696930 + 0.0696930i
\(505\) −22.6939 9.86962i −1.00987 0.439192i
\(506\) 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 \(-0.675333\pi\)
−0.523390 + 0.852093i \(0.675333\pi\)
\(510\) 1.02828 + 2.61102i 0.0455332 + 0.115618i
\(511\) 26.7046i 1.18134i
\(512\) −1.00000 −0.0441942
\(513\) 3.08122i 0.136039i
\(514\) 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
\(518\) −9.53287 9.50133i −0.418850 0.417464i
\(519\) 7.33134i 0.321810i
\(520\) −0.284847 + 0.654970i −0.0124914 + 0.0287223i
\(521\) 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
\(523\) −23.5794 −1.03105 −0.515527 0.856873i \(-0.672404\pi\)
−0.515527 + 0.856873i \(0.672404\pi\)
\(524\) −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
\(532\) −6.81776 −0.295587
\(533\) 1.25470i 0.0543469i
\(534\) 1.89234i 0.0818896i
\(535\) −4.58620 + 1.80616i −0.198279 + 0.0780870i
\(536\) −6.88391 + 6.88391i −0.297340 + 0.297340i
\(537\) 2.40771i 0.103901i
\(538\) 3.41947i 0.147424i
\(539\) 8.25180 0.355430
\(540\) −0.819367 2.08054i −0.0352599 0.0895321i
\(541\) −10.2113 10.2113i −0.439020 0.439020i 0.452662 0.891682i \(-0.350474\pi\)
−0.891682 + 0.452662i \(0.850474\pi\)
\(542\) −17.8704 −0.767600
\(543\) 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
\(547\) 26.3899 1.12835 0.564176 0.825655i \(-0.309194\pi\)
0.564176 + 0.825655i \(0.309194\pi\)
\(548\) −14.5752 14.5752i −0.622623 0.622623i
\(549\) −5.56135 5.56135i −0.237353 0.237353i
\(550\) −14.3435 + 13.3715i −0.611608 + 0.570163i
\(551\) −5.33186 −0.227145
\(552\) 0.814607 + 0.814607i 0.0346720 + 0.0346720i
\(553\) 11.2363 0.477814
\(554\) 14.8527 0.631029
\(555\) 12.6471 5.00498i 0.536841 0.212450i
\(556\) −1.20629 −0.0511582
\(557\) −33.0054 −1.39849 −0.699243 0.714885i \(-0.746479\pi\)
−0.699243 + 0.714885i \(0.746479\pi\)
\(558\) 6.78274 + 6.78274i 0.287136 + 0.287136i
\(559\) 0.598356 0.0253078
\(560\) 4.60357 1.81300i 0.194536 0.0766132i
\(561\) −3.48030 3.48030i −0.146938 0.146938i
\(562\) −4.56193 4.56193i −0.192434 0.192434i
\(563\) 2.41113 0.101617 0.0508086 0.998708i \(-0.483820\pi\)
0.0508086 + 0.998708i \(0.483820\pi\)
\(564\) 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
\(568\) 3.29012 0.138050
\(569\) 16.6810 + 16.6810i 0.699306 + 0.699306i 0.964261 0.264955i \(-0.0853571\pi\)
−0.264955 + 0.964261i \(0.585357\pi\)
\(570\) 2.74778 6.31816i 0.115092 0.264639i
\(571\) −34.7939 −1.45608 −0.728041 0.685534i \(-0.759569\pi\)
−0.728041 + 0.685534i \(0.759569\pi\)
\(572\) 1.25271i 0.0523783i
\(573\) 6.45984i 0.269864i
\(574\) −6.14596 + 6.14596i −0.256528 + 0.256528i
\(575\) 3.92778 + 4.21329i 0.163800 + 0.175706i
\(576\) 1.00000i 0.0416667i
\(577\) 42.4452i 1.76702i 0.468414 + 0.883509i \(0.344826\pi\)
−0.468414 + 0.883509i \(0.655174\pi\)
\(578\) −15.4250 −0.641597
\(579\) −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
\(587\) −25.7512 −1.06287 −0.531433 0.847100i \(-0.678346\pi\)
−0.531433 + 0.847100i \(0.678346\pi\)
\(588\) 1.48777 1.48777i 0.0613548 0.0613548i
\(589\) 29.5558i 1.21782i
\(590\) −5.45079 13.8407i −0.224406 0.569811i
\(591\) 4.92868i 0.202739i
\(592\) −6.08275 + 0.0100817i −0.250000 + 0.000414356i
\(593\) −17.7350 + 17.7350i −0.728289 + 0.728289i −0.970279 0.241990i \(-0.922200\pi\)
0.241990 + 0.970279i \(0.422200\pi\)
\(594\) 2.77320 + 2.77320i 0.113786 + 0.113786i
\(595\) 2.27527 + 5.77736i 0.0932768 + 0.236849i
\(596\) 0.425764i 0.0174400i
\(597\) 15.6783i 0.641671i
\(598\) −0.367973 −0.0150475
\(599\) 33.5799i 1.37204i −0.727583 0.686020i \(-0.759356\pi\)
0.727583 0.686020i \(-0.240644\pi\)
\(600\) −0.175243 + 4.99693i −0.00715425 + 0.203999i
\(601\) −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
\(605\) 3.90718 8.98406i 0.158849 0.365254i
\(606\) 7.82575 7.82575i 0.317900 0.317900i
\(607\) 26.3325 1.06880 0.534401 0.845231i \(-0.320537\pi\)
0.534401 + 0.845231i \(0.320537\pi\)
\(608\) −2.17875 + 2.17875i −0.0883599 + 0.0883599i
\(609\) −2.70745 + 2.70745i −0.109712 + 0.109712i
\(610\) 6.44427 + 16.3633i 0.260921 + 0.662531i
\(611\) 1.56015 + 1.56015i 0.0631168 + 0.0631168i
\(612\) −1.25497 −0.0507293
\(613\) 18.6885 + 18.6885i 0.754820 + 0.754820i 0.975375 0.220555i \(-0.0707868\pi\)
−0.220555 + 0.975375i \(0.570787\pi\)
\(614\) −0.225281 + 0.225281i −0.00909162 + 0.00909162i
\(615\) −3.21858 8.17262i −0.129786 0.329552i
\(616\) −6.13622 + 6.13622i −0.247235 + 0.247235i
\(617\) 3.48887 3.48887i 0.140457 0.140457i −0.633382 0.773839i \(-0.718334\pi\)
0.773839 + 0.633382i \(0.218334\pi\)
\(618\) −9.76753 + 9.76753i −0.392907 + 0.392907i
\(619\) −3.83734 −0.154236 −0.0771178 0.997022i \(-0.524572\pi\)
−0.0771178 + 0.997022i \(0.524572\pi\)
\(620\) −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
\(623\) 4.18715i 0.167755i
\(624\) −0.225859 0.225859i −0.00904160 0.00904160i
\(625\) −1.75135 + 24.9386i −0.0700540 + 0.997543i
\(626\) 12.1187 0.484359
\(627\) 12.0842i 0.482597i
\(628\) 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
\(635\) −20.7790 + 8.18326i −0.824588 + 0.324743i
\(636\) −4.28827 −0.170041
\(637\) 0.672055i 0.0266278i
\(638\) −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 \(0.807874\pi\)
\(642\) 2.20433i 0.0869982i
\(643\) 3.74780i 0.147799i 0.997266 + 0.0738993i \(0.0235443\pi\)
−0.997266 + 0.0738993i \(0.976456\pi\)
\(644\) 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
\(647\) −3.49319 −0.137331 −0.0686657 0.997640i \(-0.521874\pi\)
−0.0686657 + 0.997640i \(0.521874\pi\)
\(648\) 1.00000 0.0392837
\(649\) 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
\(652\) 15.4091i 0.603466i
\(653\) 32.5364i 1.27325i 0.771175 + 0.636624i \(0.219670\pi\)
−0.771175 + 0.636624i \(0.780330\pi\)
\(654\) 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
\(658\) 15.2844i 0.595847i
\(659\) −2.62449 −0.102236 −0.0511178 0.998693i \(-0.516278\pi\)
−0.0511178 + 0.998693i \(0.516278\pi\)
\(660\) −3.21347 8.15967i −0.125084 0.317615i
\(661\) 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
\(668\) 16.8371i 0.651447i
\(669\) 15.8201 0.611640
\(670\) −7.97679 20.2547i −0.308170 0.782507i
\(671\) −21.8111 21.8111i −0.842007 0.842007i
\(672\) 2.21268i 0.0853561i
\(673\) −14.4928 + 14.4928i −0.558658 + 0.558658i −0.928925 0.370267i \(-0.879266\pi\)
0.370267 + 0.928925i \(0.379266\pi\)
\(674\) −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 \(-0.829775\pi\)
0.509649 + 0.860382i \(0.329775\pi\)
\(678\) 11.6944 11.6944i 0.449120 0.449120i
\(679\) 6.28788 6.28788i 0.241307 0.241307i
\(680\) 2.57338 + 1.11916i 0.0986845 + 0.0429180i
\(681\) −1.23682 + 1.23682i −0.0473949 + 0.0473949i
\(682\) 26.6012 + 26.6012i 1.01861 + 1.01861i
\(683\) 24.7098 0.945493 0.472746 0.881199i \(-0.343263\pi\)
0.472746 + 0.881199i \(0.343263\pi\)
\(684\) 2.17875 + 2.17875i 0.0833065 + 0.0833065i
\(685\) 42.8850 16.8892i 1.63855 0.645302i
\(686\) 14.2442 14.2442i 0.543846 0.543846i
\(687\) 6.02076 6.02076i 0.229706 0.229706i
\(688\) −1.87330 −0.0714188
\(689\) 0.968545 0.968545i 0.0368986 0.0368986i
\(690\) −2.39684 + 0.943934i −0.0912461 + 0.0359349i
\(691\) 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
\(695\) 1.07575 2.47355i 0.0408055 0.0938272i
\(696\) 1.73044i 0.0655921i
\(697\) −4.92970 −0.186726
\(698\) 14.8248i 0.561128i
\(699\) 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
\(703\) −13.2308 + 13.2748i −0.499010 + 0.500667i
\(704\) 3.92190i 0.147812i
\(705\) 14.1644 + 6.16009i 0.533460 + 0.232002i
\(706\) 23.4920i 0.884134i
\(707\) 17.3159 17.3159i 0.651232 0.651232i
\(708\) 6.65245 0.250014
\(709\) −20.0239 + 20.0239i −0.752014 + 0.752014i −0.974855 0.222841i \(-0.928467\pi\)
0.222841 + 0.974855i \(0.428467\pi\)
\(710\) −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
\(717\) −14.8459 −0.554431
\(718\) 3.71905i 0.138794i
\(719\) 32.6337i 1.21703i −0.793541 0.608517i \(-0.791765\pi\)
0.793541 0.608517i \(-0.208235\pi\)
\(720\) −2.05054 0.891783i −0.0764192 0.0332348i
\(721\) −21.6124 + 21.6124i −0.804889 + 0.804889i
\(722\) 9.50611i 0.353781i
\(723\) 9.43070i 0.350731i
\(724\) 8.75170 0.325254
\(725\) −0.303247 + 8.64688i −0.0112623 + 0.321137i
\(726\) 3.09806 + 3.09806i 0.114980 + 0.114980i
\(727\) −21.1503 −0.784422 −0.392211 0.919875i \(-0.628290\pi\)
−0.392211 + 0.919875i \(0.628290\pi\)
\(728\) −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
\(732\) −7.86494 −0.290696
\(733\) 26.3403 + 26.3403i 0.972902 + 0.972902i 0.999642 0.0267403i \(-0.00851273\pi\)
−0.0267403 + 0.999642i \(0.508513\pi\)
\(734\) −20.2784 20.2784i −0.748489 0.748489i
\(735\) 1.72397 + 4.37752i 0.0635897 + 0.161467i
\(736\) 1.15203 0.0424643
\(737\) 26.9980 + 26.9980i 0.994485 + 0.994485i
\(738\) 3.92813 0.144596
\(739\) 27.2865 1.00375 0.501876 0.864940i \(-0.332643\pi\)
0.501876 + 0.864940i \(0.332643\pi\)
\(740\) 5.40382 12.4819i 0.198648 0.458845i
\(741\) −0.984181 −0.0361548
\(742\) −9.48858 −0.348337
\(743\) −18.6520 18.6520i −0.684276 0.684276i 0.276684 0.960961i \(-0.410764\pi\)
−0.960961 + 0.276684i \(0.910764\pi\)
\(744\) 9.59224 0.351668
\(745\) 0.873048 + 0.379689i 0.0319860 + 0.0139107i
\(746\) 17.0249 + 17.0249i 0.623325 + 0.623325i
\(747\) −1.13008 1.13008i −0.0413474 0.0413474i
\(748\) −4.92188 −0.179962
\(749\) 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
\(753\) 28.2766 1.03046
\(754\) −0.390836 0.390836i −0.0142334 0.0142334i
\(755\) −38.2547 16.6370i −1.39223 0.605483i
\(756\) 2.21268 0.0804745
\(757\) 36.6279i 1.33126i 0.746281 + 0.665631i \(0.231838\pi\)
−0.746281 + 0.665631i \(0.768162\pi\)
\(758\) 3.59500i 0.130576i
\(759\) 3.19481 3.19481i 0.115964 0.115964i
\(760\) −2.52465 6.41059i −0.0915785 0.232536i
\(761\) 13.4727i 0.488386i −0.969727 0.244193i \(-0.921477\pi\)
0.969727 0.244193i \(-0.0785230\pi\)
\(762\) 9.98731i 0.361802i
\(763\) 13.2710 0.480442
\(764\) 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 0.457026 0.889453i \(-0.348915\pi\)
−0.889453 + 0.457026i \(0.848915\pi\)
\(770\) −7.11040 18.0548i −0.256241 0.650648i
\(771\) −22.1776 + 22.1776i −0.798707 + 0.798707i
\(772\) −5.51547 −0.198506
\(773\) 14.0271 14.0271i 0.504520 0.504520i −0.408319 0.912839i \(-0.633885\pi\)
0.912839 + 0.408319i \(0.133885\pi\)
\(774\) 1.87330i 0.0673343i
\(775\) 47.9317 + 1.68097i 1.72176 + 0.0603822i
\(776\) 4.01884i 0.144268i
\(777\) 0.0223076 + 13.4592i 0.000800282 + 0.482846i
\(778\) 9.52518 9.52518i 0.341494 0.341494i
\(779\) 8.55840 + 8.55840i