Properties

Label 1110.2.l.b.697.10
Level $1110$
Weight $2$
Character 1110.697
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 697.10
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.b.43.10

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.07345 - 0.837144i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.93723 - 2.93723i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.07345 - 0.837144i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.93723 - 2.93723i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(0.837144 - 2.07345i) q^{10} +1.12978i q^{11} +(0.707107 + 0.707107i) q^{12} +2.10223i q^{13} +(2.93723 - 2.93723i) q^{14} +(0.874200 + 2.05810i) q^{15} +1.00000 q^{16} -3.81919 q^{17} -1.00000 q^{18} +(-0.0424776 - 0.0424776i) q^{19} +(2.07345 + 0.837144i) q^{20} +4.15387i q^{21} -1.12978 q^{22} -7.44945i q^{23} +(-0.707107 + 0.707107i) q^{24} +(3.59838 + 3.47155i) q^{25} -2.10223 q^{26} +(0.707107 - 0.707107i) q^{27} +(2.93723 + 2.93723i) q^{28} +(1.00026 - 1.00026i) q^{29} +(-2.05810 + 0.874200i) q^{30} +(5.55293 + 5.55293i) q^{31} +1.00000i q^{32} +(0.798875 - 0.798875i) q^{33} -3.81919i q^{34} +(3.63131 + 8.54909i) q^{35} -1.00000i q^{36} +(5.91653 + 1.41231i) q^{37} +(0.0424776 - 0.0424776i) q^{38} +(1.48650 - 1.48650i) q^{39} +(-0.837144 + 2.07345i) q^{40} +7.31338i q^{41} -4.15387 q^{42} +6.59679i q^{43} -1.12978i q^{44} +(0.837144 - 2.07345i) q^{45} +7.44945 q^{46} +(3.52289 + 3.52289i) q^{47} +(-0.707107 - 0.707107i) q^{48} +10.2547i q^{49} +(-3.47155 + 3.59838i) q^{50} +(2.70058 + 2.70058i) q^{51} -2.10223i q^{52} +(-6.43055 + 6.43055i) q^{53} +(0.707107 + 0.707107i) q^{54} +(0.945788 - 2.34254i) q^{55} +(-2.93723 + 2.93723i) q^{56} +0.0600724i q^{57} +(1.00026 + 1.00026i) q^{58} +(1.53440 + 1.53440i) q^{59} +(-0.874200 - 2.05810i) q^{60} +(3.13059 + 3.13059i) q^{61} +(-5.55293 + 5.55293i) q^{62} +(2.93723 - 2.93723i) q^{63} -1.00000 q^{64} +(1.75987 - 4.35887i) q^{65} +(0.798875 + 0.798875i) q^{66} +(2.59186 - 2.59186i) q^{67} +3.81919 q^{68} +(-5.26755 + 5.26755i) q^{69} +(-8.54909 + 3.63131i) q^{70} +2.10896 q^{71} +1.00000 q^{72} +(-6.95418 - 6.95418i) q^{73} +(-1.41231 + 5.91653i) q^{74} +(-0.0896820 - 4.99920i) q^{75} +(0.0424776 + 0.0424776i) q^{76} +(3.31842 - 3.31842i) q^{77} +(1.48650 + 1.48650i) q^{78} +(-8.44853 - 8.44853i) q^{79} +(-2.07345 - 0.837144i) q^{80} -1.00000 q^{81} -7.31338 q^{82} +(-2.80605 + 2.80605i) q^{83} -4.15387i q^{84} +(7.91890 + 3.19722i) q^{85} -6.59679 q^{86} -1.41459 q^{87} +1.12978 q^{88} +(-8.09450 + 8.09450i) q^{89} +(2.07345 + 0.837144i) q^{90} +(6.17474 - 6.17474i) q^{91} +7.44945i q^{92} -7.85303i q^{93} +(-3.52289 + 3.52289i) q^{94} +(0.0525152 + 0.123635i) q^{95} +(0.707107 - 0.707107i) q^{96} +10.4722 q^{97} -10.2547 q^{98} -1.12978 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{4} - 4q^{7} + O(q^{10}) \) \( 40q - 40q^{4} - 4q^{7} + 4q^{14} + 40q^{16} + 24q^{17} - 40q^{18} + 4q^{19} + 8q^{22} + 8q^{25} + 8q^{26} + 4q^{28} + 28q^{31} - 4q^{33} + 20q^{35} + 20q^{37} - 4q^{38} + 4q^{39} + 16q^{42} - 16q^{47} + 16q^{51} + 20q^{53} + 16q^{55} - 4q^{56} - 4q^{59} - 8q^{61} - 28q^{62} + 4q^{63} - 40q^{64} - 4q^{65} - 4q^{66} + 16q^{67} - 24q^{68} - 8q^{69} + 12q^{70} + 40q^{71} + 40q^{72} + 8q^{73} - 8q^{74} + 16q^{75} - 4q^{76} - 24q^{77} + 4q^{78} - 12q^{79} - 40q^{81} - 24q^{82} - 8q^{83} - 8q^{85} + 8q^{87} - 8q^{88} + 12q^{89} - 24q^{91} + 16q^{94} - 28q^{95} + 40q^{97} - 56q^{98} + 8q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) −1.00000 −0.500000
\(5\) −2.07345 0.837144i −0.927274 0.374382i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) −2.93723 2.93723i −1.11017 1.11017i −0.993127 0.117042i \(-0.962659\pi\)
−0.117042 0.993127i \(-0.537341\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) 0.837144 2.07345i 0.264728 0.655682i
\(11\) 1.12978i 0.340641i 0.985389 + 0.170321i \(0.0544803\pi\)
−0.985389 + 0.170321i \(0.945520\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 2.10223i 0.583054i 0.956563 + 0.291527i \(0.0941633\pi\)
−0.956563 + 0.291527i \(0.905837\pi\)
\(14\) 2.93723 2.93723i 0.785008 0.785008i
\(15\) 0.874200 + 2.05810i 0.225717 + 0.531399i
\(16\) 1.00000 0.250000
\(17\) −3.81919 −0.926291 −0.463145 0.886282i \(-0.653279\pi\)
−0.463145 + 0.886282i \(0.653279\pi\)
\(18\) −1.00000 −0.235702
\(19\) −0.0424776 0.0424776i −0.00974502 0.00974502i 0.702217 0.711963i \(-0.252193\pi\)
−0.711963 + 0.702217i \(0.752193\pi\)
\(20\) 2.07345 + 0.837144i 0.463637 + 0.187191i
\(21\) 4.15387i 0.906450i
\(22\) −1.12978 −0.240870
\(23\) 7.44945i 1.55332i −0.629922 0.776659i \(-0.716913\pi\)
0.629922 0.776659i \(-0.283087\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) 3.59838 + 3.47155i 0.719676 + 0.694310i
\(26\) −2.10223 −0.412281
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 2.93723 + 2.93723i 0.555085 + 0.555085i
\(29\) 1.00026 1.00026i 0.185744 0.185744i −0.608109 0.793854i \(-0.708072\pi\)
0.793854 + 0.608109i \(0.208072\pi\)
\(30\) −2.05810 + 0.874200i −0.375756 + 0.159606i
\(31\) 5.55293 + 5.55293i 0.997336 + 0.997336i 0.999996 0.00266011i \(-0.000846741\pi\)
−0.00266011 + 0.999996i \(0.500847\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.798875 0.798875i 0.139066 0.139066i
\(34\) 3.81919i 0.654986i
\(35\) 3.63131 + 8.54909i 0.613804 + 1.44506i
\(36\) 1.00000i 0.166667i
\(37\) 5.91653 + 1.41231i 0.972672 + 0.232183i
\(38\) 0.0424776 0.0424776i 0.00689077 0.00689077i
\(39\) 1.48650 1.48650i 0.238031 0.238031i
\(40\) −0.837144 + 2.07345i −0.132364 + 0.327841i
\(41\) 7.31338i 1.14216i 0.820895 + 0.571079i \(0.193475\pi\)
−0.820895 + 0.571079i \(0.806525\pi\)
\(42\) −4.15387 −0.640957
\(43\) 6.59679i 1.00600i 0.864286 + 0.503001i \(0.167771\pi\)
−0.864286 + 0.503001i \(0.832229\pi\)
\(44\) 1.12978i 0.170321i
\(45\) 0.837144 2.07345i 0.124794 0.309091i
\(46\) 7.44945 1.09836
\(47\) 3.52289 + 3.52289i 0.513867 + 0.513867i 0.915709 0.401842i \(-0.131630\pi\)
−0.401842 + 0.915709i \(0.631630\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 10.2547i 1.46495i
\(50\) −3.47155 + 3.59838i −0.490951 + 0.508888i
\(51\) 2.70058 + 2.70058i 0.378157 + 0.378157i
\(52\) 2.10223i 0.291527i
\(53\) −6.43055 + 6.43055i −0.883304 + 0.883304i −0.993869 0.110565i \(-0.964734\pi\)
0.110565 + 0.993869i \(0.464734\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) 0.945788 2.34254i 0.127530 0.315868i
\(56\) −2.93723 + 2.93723i −0.392504 + 0.392504i
\(57\) 0.0600724i 0.00795678i
\(58\) 1.00026 + 1.00026i 0.131341 + 0.131341i
\(59\) 1.53440 + 1.53440i 0.199762 + 0.199762i 0.799898 0.600136i \(-0.204887\pi\)
−0.600136 + 0.799898i \(0.704887\pi\)
\(60\) −0.874200 2.05810i −0.112859 0.265700i
\(61\) 3.13059 + 3.13059i 0.400830 + 0.400830i 0.878526 0.477695i \(-0.158528\pi\)
−0.477695 + 0.878526i \(0.658528\pi\)
\(62\) −5.55293 + 5.55293i −0.705223 + 0.705223i
\(63\) 2.93723 2.93723i 0.370056 0.370056i
\(64\) −1.00000 −0.125000
\(65\) 1.75987 4.35887i 0.218285 0.540651i
\(66\) 0.798875 + 0.798875i 0.0983347 + 0.0983347i
\(67\) 2.59186 2.59186i 0.316646 0.316646i −0.530832 0.847477i \(-0.678120\pi\)
0.847477 + 0.530832i \(0.178120\pi\)
\(68\) 3.81919 0.463145
\(69\) −5.26755 + 5.26755i −0.634139 + 0.634139i
\(70\) −8.54909 + 3.63131i −1.02181 + 0.434025i
\(71\) 2.10896 0.250287 0.125144 0.992139i \(-0.460061\pi\)
0.125144 + 0.992139i \(0.460061\pi\)
\(72\) 1.00000 0.117851
\(73\) −6.95418 6.95418i −0.813925 0.813925i 0.171295 0.985220i \(-0.445205\pi\)
−0.985220 + 0.171295i \(0.945205\pi\)
\(74\) −1.41231 + 5.91653i −0.164178 + 0.687783i
\(75\) −0.0896820 4.99920i −0.0103556 0.577257i
\(76\) 0.0424776 + 0.0424776i 0.00487251 + 0.00487251i
\(77\) 3.31842 3.31842i 0.378170 0.378170i
\(78\) 1.48650 + 1.48650i 0.168313 + 0.168313i
\(79\) −8.44853 8.44853i −0.950534 0.950534i 0.0482988 0.998833i \(-0.484620\pi\)
−0.998833 + 0.0482988i \(0.984620\pi\)
\(80\) −2.07345 0.837144i −0.231819 0.0935955i
\(81\) −1.00000 −0.111111
\(82\) −7.31338 −0.807627
\(83\) −2.80605 + 2.80605i −0.308003 + 0.308003i −0.844135 0.536131i \(-0.819885\pi\)
0.536131 + 0.844135i \(0.319885\pi\)
\(84\) 4.15387i 0.453225i
\(85\) 7.91890 + 3.19722i 0.858926 + 0.346787i
\(86\) −6.59679 −0.711350
\(87\) −1.41459 −0.151660
\(88\) 1.12978 0.120435
\(89\) −8.09450 + 8.09450i −0.858015 + 0.858015i −0.991104 0.133089i \(-0.957511\pi\)
0.133089 + 0.991104i \(0.457511\pi\)
\(90\) 2.07345 + 0.837144i 0.218561 + 0.0882427i
\(91\) 6.17474 6.17474i 0.647289 0.647289i
\(92\) 7.44945i 0.776659i
\(93\) 7.85303i 0.814322i
\(94\) −3.52289 + 3.52289i −0.363359 + 0.363359i
\(95\) 0.0525152 + 0.123635i 0.00538795 + 0.0126847i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) 10.4722 1.06329 0.531646 0.846966i \(-0.321574\pi\)
0.531646 + 0.846966i \(0.321574\pi\)
\(98\) −10.2547 −1.03588
\(99\) −1.12978 −0.113547
\(100\) −3.59838 3.47155i −0.359838 0.347155i
\(101\) 6.85371i 0.681970i −0.940069 0.340985i \(-0.889240\pi\)
0.940069 0.340985i \(-0.110760\pi\)
\(102\) −2.70058 + 2.70058i −0.267397 + 0.267397i
\(103\) 11.0473 1.08852 0.544262 0.838915i \(-0.316810\pi\)
0.544262 + 0.838915i \(0.316810\pi\)
\(104\) 2.10223 0.206141
\(105\) 3.47739 8.61284i 0.339359 0.840528i
\(106\) −6.43055 6.43055i −0.624591 0.624591i
\(107\) 2.67190 + 2.67190i 0.258303 + 0.258303i 0.824363 0.566061i \(-0.191533\pi\)
−0.566061 + 0.824363i \(0.691533\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) −1.57675 1.57675i −0.151025 0.151025i 0.627551 0.778576i \(-0.284057\pi\)
−0.778576 + 0.627551i \(0.784057\pi\)
\(110\) 2.34254 + 0.945788i 0.223352 + 0.0901773i
\(111\) −3.18497 5.18228i −0.302304 0.491880i
\(112\) −2.93723 2.93723i −0.277542 0.277542i
\(113\) −13.9588 −1.31314 −0.656568 0.754267i \(-0.727992\pi\)
−0.656568 + 0.754267i \(0.727992\pi\)
\(114\) −0.0600724 −0.00562629
\(115\) −6.23626 + 15.4460i −0.581534 + 1.44035i
\(116\) −1.00026 + 1.00026i −0.0928722 + 0.0928722i
\(117\) −2.10223 −0.194351
\(118\) −1.53440 + 1.53440i −0.141253 + 0.141253i
\(119\) 11.2179 + 11.2179i 1.02834 + 1.02834i
\(120\) 2.05810 0.874200i 0.187878 0.0798031i
\(121\) 9.72360 0.883964
\(122\) −3.13059 + 3.13059i −0.283430 + 0.283430i
\(123\) 5.17134 5.17134i 0.466284 0.466284i
\(124\) −5.55293 5.55293i −0.498668 0.498668i
\(125\) −4.55487 10.2104i −0.407400 0.913250i
\(126\) 2.93723 + 2.93723i 0.261669 + 0.261669i
\(127\) 8.02624 + 8.02624i 0.712214 + 0.712214i 0.966998 0.254784i \(-0.0820044\pi\)
−0.254784 + 0.966998i \(0.582004\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 4.66464 4.66464i 0.410698 0.410698i
\(130\) 4.35887 + 1.75987i 0.382298 + 0.154351i
\(131\) 4.61659 + 4.61659i 0.403353 + 0.403353i 0.879413 0.476060i \(-0.157935\pi\)
−0.476060 + 0.879413i \(0.657935\pi\)
\(132\) −0.798875 + 0.798875i −0.0695331 + 0.0695331i
\(133\) 0.249533i 0.0216373i
\(134\) 2.59186 + 2.59186i 0.223902 + 0.223902i
\(135\) −2.05810 + 0.874200i −0.177133 + 0.0752391i
\(136\) 3.81919i 0.327493i
\(137\) −12.7568 12.7568i −1.08989 1.08989i −0.995539 0.0943459i \(-0.969924\pi\)
−0.0943459 0.995539i \(-0.530076\pi\)
\(138\) −5.26755 5.26755i −0.448404 0.448404i
\(139\) −10.7050 −0.907987 −0.453993 0.891005i \(-0.650001\pi\)
−0.453993 + 0.891005i \(0.650001\pi\)
\(140\) −3.63131 8.54909i −0.306902 0.722530i
\(141\) 4.98212i 0.419570i
\(142\) 2.10896i 0.176980i
\(143\) −2.37506 −0.198612
\(144\) 1.00000i 0.0833333i
\(145\) −2.91136 + 1.23663i −0.241776 + 0.102697i
\(146\) 6.95418 6.95418i 0.575532 0.575532i
\(147\) 7.25114 7.25114i 0.598064 0.598064i
\(148\) −5.91653 1.41231i −0.486336 0.116091i
\(149\) 21.7914i 1.78522i 0.450832 + 0.892609i \(0.351127\pi\)
−0.450832 + 0.892609i \(0.648873\pi\)
\(150\) 4.99920 0.0896820i 0.408183 0.00732250i
\(151\) 1.57215i 0.127940i −0.997952 0.0639698i \(-0.979624\pi\)
0.997952 0.0639698i \(-0.0203761\pi\)
\(152\) −0.0424776 + 0.0424776i −0.00344539 + 0.00344539i
\(153\) 3.81919i 0.308764i
\(154\) 3.31842 + 3.31842i 0.267406 + 0.267406i
\(155\) −6.86512 16.1623i −0.551420 1.29819i
\(156\) −1.48650 + 1.48650i −0.119015 + 0.119015i
\(157\) 0.999991 + 0.999991i 0.0798079 + 0.0798079i 0.745884 0.666076i \(-0.232027\pi\)
−0.666076 + 0.745884i \(0.732027\pi\)
\(158\) 8.44853 8.44853i 0.672129 0.672129i
\(159\) 9.09418 0.721215
\(160\) 0.837144 2.07345i 0.0661820 0.163921i
\(161\) −21.8808 + 21.8808i −1.72445 + 1.72445i
\(162\) 1.00000i 0.0785674i
\(163\) 19.9337 1.56133 0.780664 0.624952i \(-0.214881\pi\)
0.780664 + 0.624952i \(0.214881\pi\)
\(164\) 7.31338i 0.571079i
\(165\) −2.32520 + 0.987653i −0.181016 + 0.0768887i
\(166\) −2.80605 2.80605i −0.217791 0.217791i
\(167\) −2.23975 −0.173317 −0.0866586 0.996238i \(-0.527619\pi\)
−0.0866586 + 0.996238i \(0.527619\pi\)
\(168\) 4.15387 0.320478
\(169\) 8.58063 0.660048
\(170\) −3.19722 + 7.91890i −0.245215 + 0.607352i
\(171\) 0.0424776 0.0424776i 0.00324834 0.00324834i
\(172\) 6.59679i 0.503001i
\(173\) 6.82631 + 6.82631i 0.518995 + 0.518995i 0.917267 0.398272i \(-0.130390\pi\)
−0.398272 + 0.917267i \(0.630390\pi\)
\(174\) 1.41459i 0.107240i
\(175\) −0.372528 20.7660i −0.0281604 1.56976i
\(176\) 1.12978i 0.0851603i
\(177\) 2.16997i 0.163105i
\(178\) −8.09450 8.09450i −0.606709 0.606709i
\(179\) 1.80725 1.80725i 0.135080 0.135080i −0.636334 0.771414i \(-0.719550\pi\)
0.771414 + 0.636334i \(0.219550\pi\)
\(180\) −0.837144 + 2.07345i −0.0623970 + 0.154546i
\(181\) 16.0321 1.19166 0.595828 0.803112i \(-0.296824\pi\)
0.595828 + 0.803112i \(0.296824\pi\)
\(182\) 6.17474 + 6.17474i 0.457702 + 0.457702i
\(183\) 4.42732i 0.327277i
\(184\) −7.44945 −0.549181
\(185\) −11.0853 7.88135i −0.815009 0.579448i
\(186\) 7.85303 0.575812
\(187\) 4.31485i 0.315533i
\(188\) −3.52289 3.52289i −0.256933 0.256933i
\(189\) −4.15387 −0.302150
\(190\) −0.123635 + 0.0525152i −0.00896942 + 0.00380985i
\(191\) 3.79156 3.79156i 0.274348 0.274348i −0.556500 0.830848i \(-0.687856\pi\)
0.830848 + 0.556500i \(0.187856\pi\)
\(192\) 0.707107 + 0.707107i 0.0510310 + 0.0510310i
\(193\) 6.10797i 0.439661i 0.975538 + 0.219831i \(0.0705504\pi\)
−0.975538 + 0.219831i \(0.929450\pi\)
\(194\) 10.4722i 0.751861i
\(195\) −4.32660 + 1.83777i −0.309834 + 0.131605i
\(196\) 10.2547i 0.732476i
\(197\) −16.3684 16.3684i −1.16620 1.16620i −0.983094 0.183104i \(-0.941385\pi\)
−0.183104 0.983094i \(-0.558615\pi\)
\(198\) 1.12978i 0.0802899i
\(199\) −14.9530 + 14.9530i −1.05999 + 1.05999i −0.0619052 + 0.998082i \(0.519718\pi\)
−0.998082 + 0.0619052i \(0.980282\pi\)
\(200\) 3.47155 3.59838i 0.245476 0.254444i
\(201\) −3.66544 −0.258540
\(202\) 6.85371 0.482225
\(203\) −5.87602 −0.412416
\(204\) −2.70058 2.70058i −0.189078 0.189078i
\(205\) 6.12235 15.1639i 0.427603 1.05909i
\(206\) 11.0473i 0.769702i
\(207\) 7.44945 0.517772
\(208\) 2.10223i 0.145763i
\(209\) 0.0479903 0.0479903i 0.00331956 0.00331956i
\(210\) 8.61284 + 3.47739i 0.594343 + 0.239963i
\(211\) −6.95993 −0.479142 −0.239571 0.970879i \(-0.577007\pi\)
−0.239571 + 0.970879i \(0.577007\pi\)
\(212\) 6.43055 6.43055i 0.441652 0.441652i
\(213\) −1.49126 1.49126i −0.102179 0.102179i
\(214\) −2.67190 + 2.67190i −0.182647 + 0.182647i
\(215\) 5.52247 13.6781i 0.376629 0.932839i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) 32.6205i 2.21442i
\(218\) 1.57675 1.57675i 0.106791 0.106791i
\(219\) 9.83469i 0.664567i
\(220\) −0.945788 + 2.34254i −0.0637650 + 0.157934i
\(221\) 8.02883i 0.540077i
\(222\) 5.18228 3.18497i 0.347812 0.213761i
\(223\) −1.57965 + 1.57965i −0.105781 + 0.105781i −0.758017 0.652235i \(-0.773831\pi\)
0.652235 + 0.758017i \(0.273831\pi\)
\(224\) 2.93723 2.93723i 0.196252 0.196252i
\(225\) −3.47155 + 3.59838i −0.231437 + 0.239892i
\(226\) 13.9588i 0.928527i
\(227\) −0.343113 −0.0227732 −0.0113866 0.999935i \(-0.503625\pi\)
−0.0113866 + 0.999935i \(0.503625\pi\)
\(228\) 0.0600724i 0.00397839i
\(229\) 29.6963i 1.96239i 0.193028 + 0.981193i \(0.438169\pi\)
−0.193028 + 0.981193i \(0.561831\pi\)
\(230\) −15.4460 6.23626i −1.01848 0.411207i
\(231\) −4.69296 −0.308774
\(232\) −1.00026 1.00026i −0.0656706 0.0656706i
\(233\) 4.57105 + 4.57105i 0.299459 + 0.299459i 0.840802 0.541343i \(-0.182084\pi\)
−0.541343 + 0.840802i \(0.682084\pi\)
\(234\) 2.10223i 0.137427i
\(235\) −4.35537 10.2537i −0.284113 0.668878i
\(236\) −1.53440 1.53440i −0.0998809 0.0998809i
\(237\) 11.9480i 0.776108i
\(238\) −11.2179 + 11.2179i −0.727146 + 0.727146i
\(239\) 12.3303 + 12.3303i 0.797581 + 0.797581i 0.982714 0.185133i \(-0.0592715\pi\)
−0.185133 + 0.982714i \(0.559272\pi\)
\(240\) 0.874200 + 2.05810i 0.0564293 + 0.132850i
\(241\) −19.4485 + 19.4485i −1.25279 + 1.25279i −0.298326 + 0.954464i \(0.596428\pi\)
−0.954464 + 0.298326i \(0.903572\pi\)
\(242\) 9.72360i 0.625057i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) −3.13059 3.13059i −0.200415 0.200415i
\(245\) 8.58463 21.2625i 0.548452 1.35841i
\(246\) 5.17134 + 5.17134i 0.329712 + 0.329712i
\(247\) 0.0892976 0.0892976i 0.00568187 0.00568187i
\(248\) 5.55293 5.55293i 0.352612 0.352612i
\(249\) 3.96835 0.251484
\(250\) 10.2104 4.55487i 0.645765 0.288075i
\(251\) −5.33183 5.33183i −0.336542 0.336542i 0.518522 0.855064i \(-0.326482\pi\)
−0.855064 + 0.518522i \(0.826482\pi\)
\(252\) −2.93723 + 2.93723i −0.185028 + 0.185028i
\(253\) 8.41623 0.529124
\(254\) −8.02624 + 8.02624i −0.503611 + 0.503611i
\(255\) −3.33874 7.86028i −0.209080 0.492230i
\(256\) 1.00000 0.0625000
\(257\) −0.0742306 −0.00463038 −0.00231519 0.999997i \(-0.500737\pi\)
−0.00231519 + 0.999997i \(0.500737\pi\)
\(258\) 4.66464 + 4.66464i 0.290408 + 0.290408i
\(259\) −13.2299 21.5265i −0.822069 1.33759i
\(260\) −1.75987 + 4.35887i −0.109142 + 0.270325i
\(261\) 1.00026 + 1.00026i 0.0619148 + 0.0619148i
\(262\) −4.61659 + 4.61659i −0.285214 + 0.285214i
\(263\) −10.0575 10.0575i −0.620173 0.620173i 0.325402 0.945576i \(-0.394500\pi\)
−0.945576 + 0.325402i \(0.894500\pi\)
\(264\) −0.798875 0.798875i −0.0491673 0.0491673i
\(265\) 18.7167 7.95012i 1.14976 0.488372i
\(266\) −0.249533 −0.0152998
\(267\) 11.4474 0.700567
\(268\) −2.59186 + 2.59186i −0.158323 + 0.158323i
\(269\) 0.705488i 0.0430144i 0.999769 + 0.0215072i \(0.00684648\pi\)
−0.999769 + 0.0215072i \(0.993154\pi\)
\(270\) −0.874200 2.05810i −0.0532021 0.125252i
\(271\) 26.3349 1.59973 0.799865 0.600180i \(-0.204904\pi\)
0.799865 + 0.600180i \(0.204904\pi\)
\(272\) −3.81919 −0.231573
\(273\) −8.73240 −0.528509
\(274\) 12.7568 12.7568i 0.770665 0.770665i
\(275\) −3.92209 + 4.06538i −0.236511 + 0.245151i
\(276\) 5.26755 5.26755i 0.317070 0.317070i
\(277\) 8.82636i 0.530325i 0.964204 + 0.265162i \(0.0854256\pi\)
−0.964204 + 0.265162i \(0.914574\pi\)
\(278\) 10.7050i 0.642044i
\(279\) −5.55293 + 5.55293i −0.332445 + 0.332445i
\(280\) 8.54909 3.63131i 0.510906 0.217013i
\(281\) −11.2760 + 11.2760i −0.672668 + 0.672668i −0.958330 0.285662i \(-0.907787\pi\)
0.285662 + 0.958330i \(0.407787\pi\)
\(282\) 4.98212 0.296681
\(283\) 21.3959 1.27185 0.635927 0.771749i \(-0.280618\pi\)
0.635927 + 0.771749i \(0.280618\pi\)
\(284\) −2.10896 −0.125144
\(285\) 0.0502892 0.124557i 0.00297888 0.00737812i
\(286\) 2.37506i 0.140440i
\(287\) 21.4811 21.4811i 1.26799 1.26799i
\(288\) −1.00000 −0.0589256
\(289\) −2.41375 −0.141986
\(290\) −1.23663 2.91136i −0.0726175 0.170961i
\(291\) −7.40498 7.40498i −0.434087 0.434087i
\(292\) 6.95418 + 6.95418i 0.406962 + 0.406962i
\(293\) −10.0273 + 10.0273i −0.585801 + 0.585801i −0.936491 0.350690i \(-0.885947\pi\)
0.350690 + 0.936491i \(0.385947\pi\)
\(294\) 7.25114 + 7.25114i 0.422895 + 0.422895i
\(295\) −1.89699 4.46601i −0.110447 0.260021i
\(296\) 1.41231 5.91653i 0.0820890 0.343892i
\(297\) 0.798875 + 0.798875i 0.0463554 + 0.0463554i
\(298\) −21.7914 −1.26234
\(299\) 15.6605 0.905668
\(300\) 0.0896820 + 4.99920i 0.00517779 + 0.288629i
\(301\) 19.3763 19.3763i 1.11683 1.11683i
\(302\) 1.57215 0.0904669
\(303\) −4.84630 + 4.84630i −0.278413 + 0.278413i
\(304\) −0.0424776 0.0424776i −0.00243626 0.00243626i
\(305\) −3.87036 9.11186i −0.221616 0.521744i
\(306\) 3.81919 0.218329
\(307\) −15.3558 + 15.3558i −0.876403 + 0.876403i −0.993160 0.116758i \(-0.962750\pi\)
0.116758 + 0.993160i \(0.462750\pi\)
\(308\) −3.31842 + 3.31842i −0.189085 + 0.189085i
\(309\) −7.81163 7.81163i −0.444388 0.444388i
\(310\) 16.1623 6.86512i 0.917959 0.389913i
\(311\) 21.4671 + 21.4671i 1.21729 + 1.21729i 0.968578 + 0.248710i \(0.0800065\pi\)
0.248710 + 0.968578i \(0.419994\pi\)
\(312\) −1.48650 1.48650i −0.0841566 0.0841566i
\(313\) 11.8966i 0.672435i −0.941784 0.336217i \(-0.890852\pi\)
0.941784 0.336217i \(-0.109148\pi\)
\(314\) −0.999991 + 0.999991i −0.0564327 + 0.0564327i
\(315\) −8.54909 + 3.63131i −0.481686 + 0.204601i
\(316\) 8.44853 + 8.44853i 0.475267 + 0.475267i
\(317\) 21.4453 21.4453i 1.20449 1.20449i 0.231701 0.972787i \(-0.425571\pi\)
0.972787 0.231701i \(-0.0744292\pi\)
\(318\) 9.09418i 0.509976i
\(319\) 1.13008 + 1.13008i 0.0632722 + 0.0632722i
\(320\) 2.07345 + 0.837144i 0.115909 + 0.0467978i
\(321\) 3.77864i 0.210903i
\(322\) −21.8808 21.8808i −1.21937 1.21937i
\(323\) 0.162230 + 0.162230i 0.00902672 + 0.00902672i
\(324\) 1.00000 0.0555556
\(325\) −7.29800 + 7.56462i −0.404820 + 0.419610i
\(326\) 19.9337i 1.10402i
\(327\) 2.22985i 0.123311i
\(328\) 7.31338 0.403814
\(329\) 20.6951i 1.14096i
\(330\) −0.987653 2.32520i −0.0543685 0.127998i
\(331\) −1.31507 + 1.31507i −0.0722829 + 0.0722829i −0.742324 0.670041i \(-0.766276\pi\)
0.670041 + 0.742324i \(0.266276\pi\)
\(332\) 2.80605 2.80605i 0.154002 0.154002i
\(333\) −1.41231 + 5.91653i −0.0773942 + 0.324224i
\(334\) 2.23975i 0.122554i
\(335\) −7.54384 + 3.20433i −0.412164 + 0.175071i
\(336\) 4.15387i 0.226612i
\(337\) −14.7026 + 14.7026i −0.800900 + 0.800900i −0.983236 0.182336i \(-0.941634\pi\)
0.182336 + 0.983236i \(0.441634\pi\)
\(338\) 8.58063i 0.466725i
\(339\) 9.87038 + 9.87038i 0.536085 + 0.536085i
\(340\) −7.91890 3.19722i −0.429463 0.173393i
\(341\) −6.27359 + 6.27359i −0.339734 + 0.339734i
\(342\) 0.0424776 + 0.0424776i 0.00229692 + 0.00229692i
\(343\) 9.55971 9.55971i 0.516176 0.516176i
\(344\) 6.59679 0.355675
\(345\) 15.3317 6.51230i 0.825431 0.350611i
\(346\) −6.82631 + 6.82631i −0.366985 + 0.366985i
\(347\) 31.6430i 1.69868i 0.527843 + 0.849342i \(0.323001\pi\)
−0.527843 + 0.849342i \(0.676999\pi\)
\(348\) 1.41459 0.0758299
\(349\) 21.1235i 1.13072i −0.824846 0.565358i \(-0.808738\pi\)
0.824846 0.565358i \(-0.191262\pi\)
\(350\) 20.7660 0.372528i 1.10999 0.0199124i
\(351\) 1.48650 + 1.48650i 0.0793436 + 0.0793436i
\(352\) −1.12978 −0.0602174
\(353\) −34.4460 −1.83338 −0.916689 0.399602i \(-0.869148\pi\)
−0.916689 + 0.399602i \(0.869148\pi\)
\(354\) 2.16997 0.115333
\(355\) −4.37282 1.76550i −0.232085 0.0937032i
\(356\) 8.09450 8.09450i 0.429008 0.429008i
\(357\) 15.8645i 0.839636i
\(358\) 1.80725 + 1.80725i 0.0955161 + 0.0955161i
\(359\) 12.0502i 0.635987i −0.948093 0.317994i \(-0.896991\pi\)
0.948093 0.317994i \(-0.103009\pi\)
\(360\) −2.07345 0.837144i −0.109280 0.0441214i
\(361\) 18.9964i 0.999810i
\(362\) 16.0321i 0.842628i
\(363\) −6.87562 6.87562i −0.360877 0.360877i
\(364\) −6.17474 + 6.17474i −0.323644 + 0.323644i
\(365\) 8.59748 + 20.2408i 0.450013 + 1.05945i
\(366\) 4.42732 0.231420
\(367\) −10.7675 10.7675i −0.562060 0.562060i 0.367832 0.929892i \(-0.380100\pi\)
−0.929892 + 0.367832i \(0.880100\pi\)
\(368\) 7.44945i 0.388329i
\(369\) −7.31338 −0.380719
\(370\) 7.88135 11.0853i 0.409732 0.576298i
\(371\) 37.7761 1.96124
\(372\) 7.85303i 0.407161i
\(373\) −0.907328 0.907328i −0.0469797 0.0469797i 0.683227 0.730206i \(-0.260576\pi\)
−0.730206 + 0.683227i \(0.760576\pi\)
\(374\) 4.31485 0.223115
\(375\) −3.99910 + 10.4407i −0.206512 + 0.539153i
\(376\) 3.52289 3.52289i 0.181679 0.181679i
\(377\) 2.10279 + 2.10279i 0.108299 + 0.108299i
\(378\) 4.15387i 0.213652i
\(379\) 30.6276i 1.57323i −0.617442 0.786617i \(-0.711831\pi\)
0.617442 0.786617i \(-0.288169\pi\)
\(380\) −0.0525152 0.123635i −0.00269397 0.00634234i
\(381\) 11.3508i 0.581520i
\(382\) 3.79156 + 3.79156i 0.193993 + 0.193993i
\(383\) 36.9850i 1.88985i 0.327293 + 0.944923i \(0.393864\pi\)
−0.327293 + 0.944923i \(0.606136\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) −9.65858 + 4.10258i −0.492247 + 0.209087i
\(386\) −6.10797 −0.310887
\(387\) −6.59679 −0.335334
\(388\) −10.4722 −0.531646
\(389\) −2.10277 2.10277i −0.106615 0.106615i 0.651787 0.758402i \(-0.274020\pi\)
−0.758402 + 0.651787i \(0.774020\pi\)
\(390\) −1.83777 4.32660i −0.0930591 0.219086i
\(391\) 28.4509i 1.43882i
\(392\) 10.2547 0.517939
\(393\) 6.52884i 0.329336i
\(394\) 16.3684 16.3684i 0.824626 0.824626i
\(395\) 10.4450 + 24.5902i 0.525543 + 1.23727i
\(396\) 1.12978 0.0567736
\(397\) 5.65369 5.65369i 0.283750 0.283750i −0.550852 0.834603i \(-0.685697\pi\)
0.834603 + 0.550852i \(0.185697\pi\)
\(398\) −14.9530 14.9530i −0.749524 0.749524i
\(399\) 0.176446 0.176446i 0.00883337 0.00883337i
\(400\) 3.59838 + 3.47155i 0.179919 + 0.173578i
\(401\) 17.2850 + 17.2850i 0.863170 + 0.863170i 0.991705 0.128535i \(-0.0410274\pi\)
−0.128535 + 0.991705i \(0.541027\pi\)
\(402\) 3.66544i 0.182815i
\(403\) −11.6735 + 11.6735i −0.581501 + 0.581501i
\(404\) 6.85371i 0.340985i
\(405\) 2.07345 + 0.837144i 0.103030 + 0.0415980i
\(406\) 5.87602i 0.291622i
\(407\) −1.59560 + 6.68438i −0.0790910 + 0.331332i
\(408\) 2.70058 2.70058i 0.133699 0.133699i
\(409\) −17.8635 + 17.8635i −0.883295 + 0.883295i −0.993868 0.110573i \(-0.964731\pi\)
0.110573 + 0.993868i \(0.464731\pi\)
\(410\) 15.1639 + 6.12235i 0.748892 + 0.302361i
\(411\) 18.0408i 0.889888i
\(412\) −11.0473 −0.544262
\(413\) 9.01377i 0.443539i
\(414\) 7.44945i 0.366120i
\(415\) 8.16726 3.46913i 0.400915 0.170293i
\(416\) −2.10223 −0.103070
\(417\) 7.56958 + 7.56958i 0.370684 + 0.370684i
\(418\) 0.0479903 + 0.0479903i 0.00234728 + 0.00234728i
\(419\) 13.1163i 0.640772i −0.947287 0.320386i \(-0.896187\pi\)
0.947287 0.320386i \(-0.103813\pi\)
\(420\) −3.47739 + 8.61284i −0.169679 + 0.420264i
\(421\) 1.41752 + 1.41752i 0.0690858 + 0.0690858i 0.740805 0.671720i \(-0.234444\pi\)
−0.671720 + 0.740805i \(0.734444\pi\)
\(422\) 6.95993i 0.338804i
\(423\) −3.52289 + 3.52289i −0.171289 + 0.171289i
\(424\) 6.43055 + 6.43055i 0.312295 + 0.312295i
\(425\) −13.7429 13.2585i −0.666629 0.643133i
\(426\) 1.49126 1.49126i 0.0722518 0.0722518i
\(427\) 18.3905i 0.889979i
\(428\) −2.67190 2.67190i −0.129151 0.129151i
\(429\) 1.67942 + 1.67942i 0.0810831 + 0.0810831i
\(430\) 13.6781 + 5.52247i 0.659617 + 0.266317i
\(431\) −21.4522 21.4522i −1.03331 1.03331i −0.999426 0.0338889i \(-0.989211\pi\)
−0.0338889 0.999426i \(-0.510789\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) −26.2287 + 26.2287i −1.26047 + 1.26047i −0.309607 + 0.950865i \(0.600197\pi\)
−0.950865 + 0.309607i \(0.899803\pi\)
\(434\) 32.6205 1.56583
\(435\) 2.93308 + 1.18421i 0.140630 + 0.0567787i
\(436\) 1.57675 + 1.57675i 0.0755124 + 0.0755124i
\(437\) −0.316434 + 0.316434i −0.0151371 + 0.0151371i
\(438\) −9.83469 −0.469920
\(439\) −10.4737 + 10.4737i −0.499884 + 0.499884i −0.911402 0.411518i \(-0.864999\pi\)
0.411518 + 0.911402i \(0.364999\pi\)
\(440\) −2.34254 0.945788i −0.111676 0.0450887i
\(441\) −10.2547 −0.488317
\(442\) 8.02883 0.381892
\(443\) 5.10023 + 5.10023i 0.242319 + 0.242319i 0.817809 0.575490i \(-0.195189\pi\)
−0.575490 + 0.817809i \(0.695189\pi\)
\(444\) 3.18497 + 5.18228i 0.151152 + 0.245940i
\(445\) 23.5598 10.0073i 1.11684 0.474390i
\(446\) −1.57965 1.57965i −0.0747987 0.0747987i
\(447\) 15.4088 15.4088i 0.728812 0.728812i
\(448\) 2.93723 + 2.93723i 0.138771 + 0.138771i
\(449\) −1.76700 1.76700i −0.0833897 0.0833897i 0.664182 0.747571i \(-0.268780\pi\)
−0.747571 + 0.664182i \(0.768780\pi\)
\(450\) −3.59838 3.47155i −0.169629 0.163650i
\(451\) −8.26250 −0.389066
\(452\) 13.9588 0.656568
\(453\) −1.11168 + 1.11168i −0.0522311 + 0.0522311i
\(454\) 0.343113i 0.0161031i
\(455\) −17.9722 + 7.63386i −0.842547 + 0.357881i
\(456\) 0.0600724 0.00281315
\(457\) −31.6204 −1.47914 −0.739570 0.673080i \(-0.764971\pi\)
−0.739570 + 0.673080i \(0.764971\pi\)
\(458\) −29.6963 −1.38762
\(459\) −2.70058 + 2.70058i −0.126052 + 0.126052i
\(460\) 6.23626 15.4460i 0.290767 0.720176i
\(461\) 8.01857 8.01857i 0.373462 0.373462i −0.495274 0.868737i \(-0.664932\pi\)
0.868737 + 0.495274i \(0.164932\pi\)
\(462\) 4.69296i 0.218336i
\(463\) 13.1675i 0.611945i −0.952040 0.305973i \(-0.901018\pi\)
0.952040 0.305973i \(-0.0989816\pi\)
\(464\) 1.00026 1.00026i 0.0464361 0.0464361i
\(465\) −6.57412 + 16.2829i −0.304868 + 0.755100i
\(466\) −4.57105 + 4.57105i −0.211750 + 0.211750i
\(467\) −2.65254 −0.122745 −0.0613725 0.998115i \(-0.519548\pi\)
−0.0613725 + 0.998115i \(0.519548\pi\)
\(468\) 2.10223 0.0971756
\(469\) −15.2258 −0.703061
\(470\) 10.2537 4.35537i 0.472968 0.200898i
\(471\) 1.41420i 0.0651629i
\(472\) 1.53440 1.53440i 0.0706264 0.0706264i
\(473\) −7.45292 −0.342686
\(474\) −11.9480 −0.548791
\(475\) −0.00538741 0.300313i −0.000247191 0.0137793i
\(476\) −11.2179 11.2179i −0.514170 0.514170i
\(477\) −6.43055 6.43055i −0.294435 0.294435i
\(478\) −12.3303 + 12.3303i −0.563975 + 0.563975i
\(479\) 5.91428 + 5.91428i 0.270230 + 0.270230i 0.829193 0.558963i \(-0.188800\pi\)
−0.558963 + 0.829193i \(0.688800\pi\)
\(480\) −2.05810 + 0.874200i −0.0939390 + 0.0399016i
\(481\) −2.96901 + 12.4379i −0.135375 + 0.567120i
\(482\) −19.4485 19.4485i −0.885856 0.885856i
\(483\) 30.9441 1.40800
\(484\) −9.72360 −0.441982
\(485\) −21.7136 8.76675i −0.985964 0.398078i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) 15.5782 0.705915 0.352957 0.935639i \(-0.385176\pi\)
0.352957 + 0.935639i \(0.385176\pi\)
\(488\) 3.13059 3.13059i 0.141715 0.141715i
\(489\) −14.0952 14.0952i −0.637409 0.637409i
\(490\) 21.2625 + 8.58463i 0.960543 + 0.387814i
\(491\) 19.8002 0.893571 0.446785 0.894641i \(-0.352569\pi\)
0.446785 + 0.894641i \(0.352569\pi\)
\(492\) −5.17134 + 5.17134i −0.233142 + 0.233142i
\(493\) −3.82020 + 3.82020i −0.172053 + 0.172053i
\(494\) 0.0892976 + 0.0892976i 0.00401769 + 0.00401769i
\(495\) 2.34254 + 0.945788i 0.105289 + 0.0425100i
\(496\) 5.55293 + 5.55293i 0.249334 + 0.249334i
\(497\) −6.19450 6.19450i −0.277861 0.277861i
\(498\) 3.96835i 0.177826i
\(499\) 6.66081 6.66081i 0.298179 0.298179i −0.542122 0.840300i \(-0.682379\pi\)
0.840300 + 0.542122i \(0.182379\pi\)
\(500\) 4.55487 + 10.2104i 0.203700 + 0.456625i
\(501\) 1.58374 + 1.58374i 0.0707564 + 0.0707564i
\(502\) 5.33183 5.33183i 0.237971 0.237971i
\(503\) 20.9403i 0.933681i −0.884341 0.466841i \(-0.845392\pi\)
0.884341 0.466841i \(-0.154608\pi\)
\(504\) −2.93723 2.93723i −0.130835 0.130835i
\(505\) −5.73754 + 14.2108i −0.255317 + 0.632373i
\(506\) 8.41623i 0.374147i
\(507\) −6.06742 6.06742i −0.269464 0.269464i
\(508\) −8.02624 8.02624i −0.356107 0.356107i
\(509\) 18.1652 0.805159 0.402580 0.915385i \(-0.368114\pi\)
0.402580 + 0.915385i \(0.368114\pi\)
\(510\) 7.86028 3.33874i 0.348059 0.147842i
\(511\) 40.8521i 1.80719i
\(512\) 1.00000i 0.0441942i
\(513\) −0.0600724 −0.00265226
\(514\) 0.0742306i 0.00327417i
\(515\) −22.9060 9.24819i −1.00936 0.407524i
\(516\) −4.66464 + 4.66464i −0.205349 + 0.205349i
\(517\) −3.98009 + 3.98009i −0.175044 + 0.175044i
\(518\) 21.5265 13.2299i 0.945821 0.581290i
\(519\) 9.65387i 0.423758i
\(520\) −4.35887 1.75987i −0.191149 0.0771754i
\(521\) 44.3755i 1.94413i 0.234718 + 0.972063i \(0.424583\pi\)
−0.234718 + 0.972063i \(0.575417\pi\)
\(522\) −1.00026 + 1.00026i −0.0437804 + 0.0437804i
\(523\) 32.3600i 1.41500i 0.706712 + 0.707502i \(0.250178\pi\)
−0.706712 + 0.707502i \(0.749822\pi\)
\(524\) −4.61659 4.61659i −0.201676 0.201676i
\(525\) −14.4204 + 14.9472i −0.629357 + 0.652350i
\(526\) 10.0575 10.0575i 0.438529 0.438529i
\(527\) −21.2077 21.2077i −0.923823 0.923823i
\(528\) 0.798875 0.798875i 0.0347666 0.0347666i
\(529\) −32.4943 −1.41279
\(530\) 7.95012 + 18.7167i 0.345331 + 0.813002i
\(531\) −1.53440 + 1.53440i −0.0665873 + 0.0665873i
\(532\) 0.249533i 0.0108186i
\(533\) −15.3744 −0.665939
\(534\) 11.4474i 0.495375i
\(535\) −3.30329 7.77682i −0.142813 0.336221i
\(536\) −2.59186 2.59186i −0.111951 0.111951i
\(537\) −2.55584 −0.110293
\(538\) −0.705488 −0.0304158
\(539\) −11.5855 −0.499023
\(540\) 2.05810 0.874200i 0.0885665 0.0376196i
\(541\) −26.5457 + 26.5457i −1.14129 + 1.14129i −0.153072 + 0.988215i \(0.548917\pi\)
−0.988215 + 0.153072i \(0.951083\pi\)
\(542\) 26.3349i 1.13118i
\(543\) −11.3364 11.3364i −0.486491 0.486491i
\(544\) 3.81919i 0.163747i
\(545\) 1.94934 + 4.58926i 0.0835004 + 0.196582i
\(546\) 8.73240i 0.373712i
\(547\) 15.8829i 0.679106i −0.940587 0.339553i \(-0.889724\pi\)
0.940587 0.339553i \(-0.110276\pi\)
\(548\) 12.7568 + 12.7568i 0.544943 + 0.544943i
\(549\) −3.13059 + 3.13059i −0.133610 + 0.133610i
\(550\) −4.06538 3.92209i −0.173348 0.167238i
\(551\) −0.0849776 −0.00362017
\(552\) 5.26755 + 5.26755i 0.224202 + 0.224202i
\(553\) 49.6306i 2.11051i
\(554\) −8.82636 −0.374996
\(555\) 2.26555 + 13.4115i 0.0961673 + 0.569285i
\(556\) 10.7050 0.453993
\(557\) 2.64519i 0.112080i −0.998429 0.0560402i \(-0.982152\pi\)
0.998429 0.0560402i \(-0.0178475\pi\)
\(558\) −5.55293 5.55293i −0.235074 0.235074i
\(559\) −13.8680 −0.586553
\(560\) 3.63131 + 8.54909i 0.153451 + 0.361265i
\(561\) −3.05106 + 3.05106i −0.128816 + 0.128816i
\(562\) −11.2760 11.2760i −0.475648 0.475648i
\(563\) 34.7341i 1.46387i 0.681377 + 0.731933i \(0.261382\pi\)
−0.681377 + 0.731933i \(0.738618\pi\)
\(564\) 4.98212i 0.209785i
\(565\) 28.9429 + 11.6855i 1.21764 + 0.491614i
\(566\) 21.3959i 0.899337i
\(567\) 2.93723 + 2.93723i 0.123352 + 0.123352i
\(568\) 2.10896i 0.0884900i
\(569\) −26.8268 + 26.8268i −1.12464 + 1.12464i −0.133603 + 0.991035i \(0.542655\pi\)
−0.991035 + 0.133603i \(0.957345\pi\)
\(570\) 0.124557 + 0.0502892i 0.00521712 + 0.00210638i
\(571\) 17.9771 0.752318 0.376159 0.926555i \(-0.377245\pi\)
0.376159 + 0.926555i \(0.377245\pi\)
\(572\) 2.37506 0.0993061
\(573\) −5.36208 −0.224004
\(574\) 21.4811 + 21.4811i 0.896603 + 0.896603i
\(575\) 25.8611 26.8059i 1.07848 1.11789i
\(576\) 1.00000i 0.0416667i
\(577\) −6.76864 −0.281782 −0.140891 0.990025i \(-0.544997\pi\)
−0.140891 + 0.990025i \(0.544997\pi\)
\(578\) 2.41375i 0.100399i
\(579\) 4.31898 4.31898i 0.179491 0.179491i
\(580\) 2.91136 1.23663i 0.120888 0.0513483i
\(581\) 16.4840 0.683872
\(582\) 7.40498 7.40498i 0.306946 0.306946i
\(583\) −7.26511 7.26511i −0.300890 0.300890i
\(584\) −6.95418 + 6.95418i −0.287766 + 0.287766i
\(585\) 4.35887 + 1.75987i 0.180217 + 0.0727617i
\(586\) −10.0273 10.0273i −0.414224 0.414224i
\(587\) 13.0624i 0.539143i −0.962980 0.269571i \(-0.913118\pi\)
0.962980 0.269571i \(-0.0868820\pi\)
\(588\) −7.25114 + 7.25114i −0.299032 + 0.299032i
\(589\) 0.471750i 0.0194381i
\(590\) 4.46601 1.89699i 0.183863 0.0780976i
\(591\) 23.1484i 0.952196i
\(592\) 5.91653 + 1.41231i 0.243168 + 0.0580457i
\(593\) 10.6406 10.6406i 0.436957 0.436957i −0.454030 0.890986i \(-0.650014\pi\)
0.890986 + 0.454030i \(0.150014\pi\)
\(594\) −0.798875 + 0.798875i −0.0327782 + 0.0327782i
\(595\) −13.8687 32.6506i −0.568561 1.33855i
\(596\) 21.7914i 0.892609i
\(597\) 21.1467 0.865476
\(598\) 15.6605i 0.640404i
\(599\) 23.4022i 0.956189i −0.878309 0.478094i \(-0.841328\pi\)
0.878309 0.478094i \(-0.158672\pi\)
\(600\) −4.99920 + 0.0896820i −0.204091 + 0.00366125i
\(601\) −22.5030 −0.917918 −0.458959 0.888457i \(-0.651778\pi\)
−0.458959 + 0.888457i \(0.651778\pi\)
\(602\) 19.3763 + 19.3763i 0.789719 + 0.789719i
\(603\) 2.59186 + 2.59186i 0.105549 + 0.105549i
\(604\) 1.57215i 0.0639698i
\(605\) −20.1614 8.14005i −0.819677 0.330940i
\(606\) −4.84630 4.84630i −0.196868 0.196868i
\(607\) 35.7595i 1.45143i 0.687993 + 0.725717i \(0.258492\pi\)
−0.687993 + 0.725717i \(0.741508\pi\)
\(608\) 0.0424776 0.0424776i 0.00172269 0.00172269i
\(609\) 4.15497 + 4.15497i 0.168368 + 0.168368i
\(610\) 9.11186 3.87036i 0.368928 0.156706i
\(611\) −7.40593 + 7.40593i −0.299612 + 0.299612i
\(612\) 3.81919i 0.154382i
\(613\) 7.70270 + 7.70270i 0.311109 + 0.311109i 0.845339 0.534230i \(-0.179398\pi\)
−0.534230 + 0.845339i \(0.679398\pi\)
\(614\) −15.3558 15.3558i −0.619710 0.619710i
\(615\) −15.0517 + 6.39335i −0.606941 + 0.257805i
\(616\) −3.31842 3.31842i −0.133703 0.133703i
\(617\) 14.9706 14.9706i 0.602695 0.602695i −0.338332 0.941027i \(-0.609863\pi\)
0.941027 + 0.338332i \(0.109863\pi\)
\(618\) 7.81163 7.81163i 0.314230 0.314230i
\(619\) 18.5620 0.746068 0.373034 0.927818i \(-0.378317\pi\)
0.373034 + 0.927818i \(0.378317\pi\)
\(620\) 6.86512 + 16.1623i 0.275710 + 0.649095i
\(621\) −5.26755 5.26755i −0.211380 0.211380i
\(622\) −21.4671 + 21.4671i −0.860752 + 0.860752i
\(623\) 47.5509 1.90509
\(624\) 1.48650 1.48650i 0.0595077 0.0595077i
\(625\) 0.896676 + 24.9839i 0.0358670 + 0.999357i
\(626\) 11.8966 0.475483
\(627\) −0.0678685 −0.00271041
\(628\) −0.999991 0.999991i −0.0399040 0.0399040i
\(629\) −22.5964 5.39390i −0.900977 0.215069i
\(630\) −3.63131 8.54909i −0.144675 0.340604i
\(631\) 10.3185 + 10.3185i 0.410774 + 0.410774i 0.882008 0.471234i \(-0.156191\pi\)
−0.471234 + 0.882008i \(0.656191\pi\)
\(632\) −8.44853 + 8.44853i −0.336065 + 0.336065i
\(633\) 4.92142 + 4.92142i 0.195609 + 0.195609i
\(634\) 21.4453 + 21.4453i 0.851702 + 0.851702i
\(635\) −9.92288 23.3611i −0.393778 0.927058i
\(636\) −9.09418 −0.360608
\(637\) −21.5577 −0.854146
\(638\) −1.13008 + 1.13008i −0.0447402 + 0.0447402i
\(639\) 2.10896i 0.0834291i
\(640\) −0.837144 + 2.07345i −0.0330910 + 0.0819603i
\(641\) 5.52209 0.218109 0.109055 0.994036i \(-0.465218\pi\)
0.109055 + 0.994036i \(0.465218\pi\)
\(642\) 3.77864 0.149131
\(643\) 23.5970 0.930576 0.465288 0.885159i \(-0.345951\pi\)
0.465288 + 0.885159i \(0.345951\pi\)
\(644\) 21.8808 21.8808i 0.862223 0.862223i
\(645\) −13.5769 + 5.76691i −0.534588 + 0.227072i
\(646\) −0.162230 + 0.162230i −0.00638286 + 0.00638286i
\(647\) 32.6973i 1.28547i 0.766090 + 0.642733i \(0.222199\pi\)
−0.766090 + 0.642733i \(0.777801\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −1.73353 + 1.73353i −0.0680471 + 0.0680471i
\(650\) −7.56462 7.29800i −0.296709 0.286251i
\(651\) −23.0662 + 23.0662i −0.904035 + 0.904035i
\(652\) −19.9337 −0.780664
\(653\) −16.1246 −0.631003 −0.315501 0.948925i \(-0.602173\pi\)
−0.315501 + 0.948925i \(0.602173\pi\)
\(654\) −2.22985 −0.0871942
\(655\) −5.70751 13.4370i −0.223011 0.525027i
\(656\) 7.31338i 0.285539i
\(657\) 6.95418 6.95418i 0.271308 0.271308i
\(658\) 20.6951 0.806779
\(659\) 13.1116 0.510755 0.255377 0.966841i \(-0.417800\pi\)
0.255377 + 0.966841i \(0.417800\pi\)
\(660\) 2.32520 0.987653i 0.0905082 0.0384443i
\(661\) −5.13385 5.13385i −0.199684 0.199684i 0.600181 0.799864i \(-0.295095\pi\)
−0.799864 + 0.600181i \(0.795095\pi\)
\(662\) −1.31507 1.31507i −0.0511117 0.0511117i
\(663\) −5.67724 + 5.67724i −0.220486 + 0.220486i
\(664\) 2.80605 + 2.80605i 0.108896 + 0.108896i
\(665\) 0.208895 0.517394i 0.00810060 0.0200637i
\(666\) −5.91653 1.41231i −0.229261 0.0547260i
\(667\) −7.45142 7.45142i −0.288520 0.288520i
\(668\) 2.23975 0.0866586
\(669\) 2.23397 0.0863701
\(670\) −3.20433 7.54384i −0.123794 0.291444i
\(671\) −3.53687 + 3.53687i −0.136539 + 0.136539i
\(672\) −4.15387 −0.160239
\(673\) −8.33275 + 8.33275i −0.321204 + 0.321204i −0.849229 0.528025i \(-0.822933\pi\)
0.528025 + 0.849229i \(0.322933\pi\)
\(674\) −14.7026 14.7026i −0.566322 0.566322i
\(675\) 4.99920 0.0896820i 0.192419 0.00345186i
\(676\) −8.58063 −0.330024
\(677\) 3.81491 3.81491i 0.146619 0.146619i −0.629987 0.776606i \(-0.716940\pi\)
0.776606 + 0.629987i \(0.216940\pi\)
\(678\) −9.87038 + 9.87038i −0.379069 + 0.379069i
\(679\) −30.7593 30.7593i −1.18043 1.18043i
\(680\) 3.19722 7.91890i 0.122608 0.303676i
\(681\) 0.242618 + 0.242618i 0.00929714 + 0.00929714i
\(682\) −6.27359 6.27359i −0.240228 0.240228i
\(683\) 40.4422i 1.54748i −0.633505 0.773739i \(-0.718384\pi\)
0.633505 0.773739i \(-0.281616\pi\)
\(684\) −0.0424776 + 0.0424776i −0.00162417 + 0.00162417i
\(685\) 15.7713 + 37.1298i 0.602589 + 1.41866i
\(686\) 9.55971 + 9.55971i 0.364991 + 0.364991i
\(687\) 20.9985 20.9985i 0.801141 0.801141i
\(688\) 6.59679i 0.251500i
\(689\) −13.5185 13.5185i −0.515014 0.515014i
\(690\) 6.51230 + 15.3317i 0.247919 + 0.583668i
\(691\) 18.2232i 0.693245i −0.938005 0.346622i \(-0.887329\pi\)
0.938005 0.346622i \(-0.112671\pi\)
\(692\) −6.82631 6.82631i −0.259498 0.259498i
\(693\) 3.31842 + 3.31842i 0.126057 + 0.126057i
\(694\) −31.6430 −1.20115
\(695\) 22.1963 + 8.96163i 0.841953 + 0.339934i
\(696\) 1.41459i 0.0536198i
\(697\) 27.9312i 1.05797i
\(698\) 21.1235 0.799537
\(699\) 6.46444i 0.244508i
\(700\) 0.372528 + 20.7660i 0.0140802 + 0.784882i
\(701\) 22.7697 22.7697i 0.859999 0.859999i −0.131339 0.991338i \(-0.541928\pi\)
0.991338 + 0.131339i \(0.0419276\pi\)
\(702\) −1.48650 + 1.48650i −0.0561044 + 0.0561044i
\(703\) −0.191328 0.311312i −0.00721609 0.0117413i
\(704\) 1.12978i 0.0425802i
\(705\) −4.17075 + 10.3302i −0.157080 + 0.389057i
\(706\) 34.4460i 1.29639i
\(707\) −20.1309 + 20.1309i −0.757102 + 0.757102i
\(708\) 2.16997i 0.0815524i
\(709\) 36.5765 + 36.5765i 1.37366 + 1.37366i 0.854953 + 0.518706i \(0.173586\pi\)
0.518706 + 0.854953i \(0.326414\pi\)
\(710\) 1.76550 4.37282i 0.0662581 0.164109i
\(711\) 8.44853 8.44853i 0.316845 0.316845i
\(712\) 8.09450 + 8.09450i 0.303354 + 0.303354i
\(713\) 41.3663 41.3663i 1.54918 1.54918i
\(714\) 15.8645 0.593712
\(715\) 4.92456 + 1.98826i 0.184168 + 0.0743569i
\(716\) −1.80725 + 1.80725i −0.0675401 + 0.0675401i
\(717\) 17.4377i 0.651222i
\(718\) 12.0502 0.449711
\(719\) 17.7477i 0.661876i 0.943652 + 0.330938i \(0.107365\pi\)
−0.943652 + 0.330938i \(0.892635\pi\)
\(720\) 0.837144 2.07345i 0.0311985 0.0772729i
\(721\) −32.4485 32.4485i −1.20845 1.20845i
\(722\) 18.9964 0.706972
\(723\) 27.5044 1.02290
\(724\) −16.0321 −0.595828
\(725\) 7.07180 0.126863i 0.262640 0.00471157i
\(726\) 6.87562 6.87562i 0.255178 0.255178i
\(727\) 42.7261i 1.58462i 0.610117 + 0.792311i \(0.291122\pi\)
−0.610117 + 0.792311i \(0.708878\pi\)
\(728\) −6.17474 6.17474i −0.228851 0.228851i
\(729\) 1.00000i 0.0370370i
\(730\) −20.2408 + 8.59748i −0.749145 + 0.318207i
\(731\) 25.1944i 0.931850i
\(732\) 4.42732i 0.163638i
\(733\) 14.8671 + 14.8671i 0.549131 + 0.549131i 0.926189 0.377059i \(-0.123065\pi\)
−0.377059 + 0.926189i \(0.623065\pi\)
\(734\) 10.7675 10.7675i 0.397437 0.397437i
\(735\) −21.1051 + 8.96462i −0.778474 + 0.330665i
\(736\) 7.44945 0.274590
\(737\) 2.92823 + 2.92823i 0.107863 + 0.107863i
\(738\) 7.31338i 0.269209i
\(739\) 9.68871 0.356405 0.178202 0.983994i \(-0.442972\pi\)
0.178202 + 0.983994i \(0.442972\pi\)
\(740\) 11.0853 + 7.88135i 0.407505 + 0.289724i
\(741\) −0.126286 −0.00463923
\(742\) 37.7761i 1.38680i
\(743\) 2.02271 + 2.02271i 0.0742059 + 0.0742059i 0.743236 0.669030i \(-0.233290\pi\)
−0.669030 + 0.743236i \(0.733290\pi\)
\(744\) −7.85303 −0.287906
\(745\) 18.2425 45.1833i 0.668354 1.65539i
\(746\) 0.907328 0.907328i 0.0332196 0.0332196i
\(747\) −2.80605 2.80605i −0.102668 0.102668i
\(748\) 4.31485i 0.157766i
\(749\) 15.6960i 0.573519i
\(750\) −10.4407 3.99910i −0.381239 0.146026i
\(751\) 22.8435i 0.833572i −0.909005 0.416786i \(-0.863156\pi\)
0.909005 0.416786i \(-0.136844\pi\)
\(752\) 3.52289 + 3.52289i 0.128467 + 0.128467i
\(753\) 7.54034i 0.274785i
\(754\) −2.10279 + 2.10279i −0.0765790 + 0.0765790i
\(755\) −1.31611 + 3.25977i −0.0478983 + 0.118635i
\(756\) 4.15387 0.151075
\(757\) −6.59491 −0.239696 −0.119848 0.992792i \(-0.538241\pi\)
−0.119848 + 0.992792i \(0.538241\pi\)
\(758\) 30.6276 1.11244
\(759\) −5.95118 5.95118i −0.216014 0.216014i
\(760\) 0.123635 0.0525152i 0.00448471 0.00190493i
\(761\) 38.8564i 1.40855i −0.709930 0.704273i \(-0.751273\pi\)
0.709930 0.704273i \(-0.248727\pi\)
\(762\) 11.3508 0.411197
\(763\) 9.26253i 0.335326i
\(764\) −3.79156 + 3.79156i −0.137174 + 0.137174i
\(765\) −3.19722 + 7.91890i −0.115596 + 0.286309i
\(766\) −36.9850 −1.33632
\(767\) −3.22566 + 3.22566i −0.116472 + 0.116472i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) −11.6459 + 11.6459i −0.419962 + 0.419962i −0.885191 0.465228i \(-0.845972\pi\)
0.465228 + 0.885191i \(0.345972\pi\)
\(770\) −4.10258 9.65858i −0.147847 0.348071i
\(771\) 0.0524889 + 0.0524889i 0.00189034 + 0.00189034i
\(772\) 6.10797i 0.219831i
\(773\) −2.91229 + 2.91229i −0.104748 + 0.104748i −0.757538 0.652791i \(-0.773598\pi\)
0.652791 + 0.757538i \(0.273598\pi\)
\(774\) 6.59679i 0.237117i
\(775\) 0.704276 + 39.2589i 0.0252983 + 1.41022i
\(776\) 10.4722i 0.375931i
\(777\) −5.86657 + 24.5765i −0.210462 + 0.881678i
\(778\) 2.10277 2.10277i 0.0753880 0.0753880i
\(779\) 0.310654 0.310654i 0.0111303 0.0111303i
\(780\)