Properties

Label 1110.2.l.a.697.4
Level $1110$
Weight $2$
Character 1110.697
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 697.4
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.a.43.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.11117 - 1.94044i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.636201 + 0.636201i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.11117 - 1.94044i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.636201 + 0.636201i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(-1.94044 - 1.11117i) q^{10} +2.26858i q^{11} +(0.707107 + 0.707107i) q^{12} -1.29147i q^{13} +(0.636201 - 0.636201i) q^{14} +(-2.15781 + 0.586380i) q^{15} +1.00000 q^{16} -5.74699 q^{17} +1.00000 q^{18} +(-4.10165 - 4.10165i) q^{19} +(-1.11117 + 1.94044i) q^{20} -0.899724i q^{21} +2.26858 q^{22} -8.53431i q^{23} +(0.707107 - 0.707107i) q^{24} +(-2.53060 - 4.31232i) q^{25} -1.29147 q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.636201 - 0.636201i) q^{28} +(-1.70155 + 1.70155i) q^{29} +(0.586380 + 2.15781i) q^{30} +(-5.81155 - 5.81155i) q^{31} -1.00000i q^{32} +(1.60413 - 1.60413i) q^{33} +5.74699i q^{34} +(1.94144 - 0.527580i) q^{35} -1.00000i q^{36} +(5.19618 + 3.16223i) q^{37} +(-4.10165 + 4.10165i) q^{38} +(-0.913209 + 0.913209i) q^{39} +(1.94044 + 1.11117i) q^{40} +9.02011i q^{41} -0.899724 q^{42} -0.853087i q^{43} -2.26858i q^{44} +(1.94044 + 1.11117i) q^{45} -8.53431 q^{46} +(-0.326713 - 0.326713i) q^{47} +(-0.707107 - 0.707107i) q^{48} -6.19050i q^{49} +(-4.31232 + 2.53060i) q^{50} +(4.06374 + 4.06374i) q^{51} +1.29147i q^{52} +(-6.79864 + 6.79864i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(4.40204 + 2.52078i) q^{55} +(-0.636201 + 0.636201i) q^{56} +5.80061i q^{57} +(1.70155 + 1.70155i) q^{58} +(3.51171 + 3.51171i) q^{59} +(2.15781 - 0.586380i) q^{60} +(-2.06460 - 2.06460i) q^{61} +(-5.81155 + 5.81155i) q^{62} +(-0.636201 + 0.636201i) q^{63} -1.00000 q^{64} +(-2.50602 - 1.43505i) q^{65} +(-1.60413 - 1.60413i) q^{66} +(3.98347 - 3.98347i) q^{67} +5.74699 q^{68} +(-6.03467 + 6.03467i) q^{69} +(-0.527580 - 1.94144i) q^{70} -15.2892 q^{71} -1.00000 q^{72} +(-11.8322 - 11.8322i) q^{73} +(3.16223 - 5.19618i) q^{74} +(-1.25987 + 4.83867i) q^{75} +(4.10165 + 4.10165i) q^{76} +(-1.44327 + 1.44327i) q^{77} +(0.913209 + 0.913209i) q^{78} +(9.04382 + 9.04382i) q^{79} +(1.11117 - 1.94044i) q^{80} -1.00000 q^{81} +9.02011 q^{82} +(9.12362 - 9.12362i) q^{83} +0.899724i q^{84} +(-6.38589 + 11.1517i) q^{85} -0.853087 q^{86} +2.40635 q^{87} -2.26858 q^{88} +(-6.32382 + 6.32382i) q^{89} +(1.11117 - 1.94044i) q^{90} +(0.821636 - 0.821636i) q^{91} +8.53431i q^{92} +8.21877i q^{93} +(-0.326713 + 0.326713i) q^{94} +(-12.5166 + 3.40136i) q^{95} +(-0.707107 + 0.707107i) q^{96} +9.28197 q^{97} -6.19050 q^{98} -2.26858 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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

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

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
\(5\) 1.11117 1.94044i 0.496931 0.867790i
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) 0.636201 + 0.636201i 0.240461 + 0.240461i 0.817041 0.576580i \(-0.195613\pi\)
−0.576580 + 0.817041i \(0.695613\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) −1.94044 1.11117i −0.613620 0.351383i
\(11\) 2.26858i 0.684003i 0.939699 + 0.342002i \(0.111105\pi\)
−0.939699 + 0.342002i \(0.888895\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 1.29147i 0.358190i −0.983832 0.179095i \(-0.942683\pi\)
0.983832 0.179095i \(-0.0573169\pi\)
\(14\) 0.636201 0.636201i 0.170032 0.170032i
\(15\) −2.15781 + 0.586380i −0.557145 + 0.151403i
\(16\) 1.00000 0.250000
\(17\) −5.74699 −1.39385 −0.696925 0.717144i \(-0.745449\pi\)
−0.696925 + 0.717144i \(0.745449\pi\)
\(18\) 1.00000 0.235702
\(19\) −4.10165 4.10165i −0.940982 0.940982i 0.0573705 0.998353i \(-0.481728\pi\)
−0.998353 + 0.0573705i \(0.981728\pi\)
\(20\) −1.11117 + 1.94044i −0.248465 + 0.433895i
\(21\) 0.899724i 0.196336i
\(22\) 2.26858 0.483663
\(23\) 8.53431i 1.77953i −0.456423 0.889763i \(-0.650869\pi\)
0.456423 0.889763i \(-0.349131\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) −2.53060 4.31232i −0.506119 0.862464i
\(26\) −1.29147 −0.253278
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −0.636201 0.636201i −0.120231 0.120231i
\(29\) −1.70155 + 1.70155i −0.315969 + 0.315969i −0.847217 0.531247i \(-0.821723\pi\)
0.531247 + 0.847217i \(0.321723\pi\)
\(30\) 0.586380 + 2.15781i 0.107058 + 0.393961i
\(31\) −5.81155 5.81155i −1.04379 1.04379i −0.998996 0.0447888i \(-0.985739\pi\)
−0.0447888 0.998996i \(-0.514261\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.60413 1.60413i 0.279243 0.279243i
\(34\) 5.74699i 0.985601i
\(35\) 1.94144 0.527580i 0.328163 0.0891773i
\(36\) 1.00000i 0.166667i
\(37\) 5.19618 + 3.16223i 0.854247 + 0.519868i
\(38\) −4.10165 + 4.10165i −0.665375 + 0.665375i
\(39\) −0.913209 + 0.913209i −0.146230 + 0.146230i
\(40\) 1.94044 + 1.11117i 0.306810 + 0.175692i
\(41\) 9.02011i 1.40870i 0.709851 + 0.704352i \(0.248762\pi\)
−0.709851 + 0.704352i \(0.751238\pi\)
\(42\) −0.899724 −0.138830
\(43\) 0.853087i 0.130094i −0.997882 0.0650472i \(-0.979280\pi\)
0.997882 0.0650472i \(-0.0207198\pi\)
\(44\) 2.26858i 0.342002i
\(45\) 1.94044 + 1.11117i 0.289263 + 0.165644i
\(46\) −8.53431 −1.25832
\(47\) −0.326713 0.326713i −0.0476560 0.0476560i 0.682877 0.730533i \(-0.260728\pi\)
−0.730533 + 0.682877i \(0.760728\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 6.19050i 0.884357i
\(50\) −4.31232 + 2.53060i −0.609854 + 0.357880i
\(51\) 4.06374 + 4.06374i 0.569037 + 0.569037i
\(52\) 1.29147i 0.179095i
\(53\) −6.79864 + 6.79864i −0.933866 + 0.933866i −0.997945 0.0640792i \(-0.979589\pi\)
0.0640792 + 0.997945i \(0.479589\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) 4.40204 + 2.52078i 0.593571 + 0.339902i
\(56\) −0.636201 + 0.636201i −0.0850159 + 0.0850159i
\(57\) 5.80061i 0.768309i
\(58\) 1.70155 + 1.70155i 0.223424 + 0.223424i
\(59\) 3.51171 + 3.51171i 0.457186 + 0.457186i 0.897731 0.440545i \(-0.145215\pi\)
−0.440545 + 0.897731i \(0.645215\pi\)
\(60\) 2.15781 0.586380i 0.278573 0.0757013i
\(61\) −2.06460 2.06460i −0.264345 0.264345i 0.562472 0.826817i \(-0.309851\pi\)
−0.826817 + 0.562472i \(0.809851\pi\)
\(62\) −5.81155 + 5.81155i −0.738068 + 0.738068i
\(63\) −0.636201 + 0.636201i −0.0801538 + 0.0801538i
\(64\) −1.00000 −0.125000
\(65\) −2.50602 1.43505i −0.310834 0.177996i
\(66\) −1.60413 1.60413i −0.197455 0.197455i
\(67\) 3.98347 3.98347i 0.486659 0.486659i −0.420591 0.907250i \(-0.638177\pi\)
0.907250 + 0.420591i \(0.138177\pi\)
\(68\) 5.74699 0.696925
\(69\) −6.03467 + 6.03467i −0.726489 + 0.726489i
\(70\) −0.527580 1.94144i −0.0630579 0.232046i
\(71\) −15.2892 −1.81450 −0.907248 0.420596i \(-0.861821\pi\)
−0.907248 + 0.420596i \(0.861821\pi\)
\(72\) −1.00000 −0.117851
\(73\) −11.8322 11.8322i −1.38486 1.38486i −0.835751 0.549108i \(-0.814968\pi\)
−0.549108 0.835751i \(-0.685032\pi\)
\(74\) 3.16223 5.19618i 0.367602 0.604044i
\(75\) −1.25987 + 4.83867i −0.145477 + 0.558722i
\(76\) 4.10165 + 4.10165i 0.470491 + 0.470491i
\(77\) −1.44327 + 1.44327i −0.164476 + 0.164476i
\(78\) 0.913209 + 0.913209i 0.103401 + 0.103401i
\(79\) 9.04382 + 9.04382i 1.01751 + 1.01751i 0.999844 + 0.0176652i \(0.00562329\pi\)
0.0176652 + 0.999844i \(0.494377\pi\)
\(80\) 1.11117 1.94044i 0.124233 0.216948i
\(81\) −1.00000 −0.111111
\(82\) 9.02011 0.996104
\(83\) 9.12362 9.12362i 1.00145 1.00145i 0.00144791 0.999999i \(-0.499539\pi\)
0.999999 0.00144791i \(-0.000460883\pi\)
\(84\) 0.899724i 0.0981680i
\(85\) −6.38589 + 11.1517i −0.692647 + 1.20957i
\(86\) −0.853087 −0.0919907
\(87\) 2.40635 0.257988
\(88\) −2.26858 −0.241832
\(89\) −6.32382 + 6.32382i −0.670323 + 0.670323i −0.957791 0.287467i \(-0.907187\pi\)
0.287467 + 0.957791i \(0.407187\pi\)
\(90\) 1.11117 1.94044i 0.117128 0.204540i
\(91\) 0.821636 0.821636i 0.0861308 0.0861308i
\(92\) 8.53431i 0.889763i
\(93\) 8.21877i 0.852247i
\(94\) −0.326713 + 0.326713i −0.0336979 + 0.0336979i
\(95\) −12.5166 + 3.40136i −1.28418 + 0.348972i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) 9.28197 0.942441 0.471220 0.882015i \(-0.343814\pi\)
0.471220 + 0.882015i \(0.343814\pi\)
\(98\) −6.19050 −0.625335
\(99\) −2.26858 −0.228001
\(100\) 2.53060 + 4.31232i 0.253060 + 0.431232i
\(101\) 1.47408i 0.146677i 0.997307 + 0.0733383i \(0.0233653\pi\)
−0.997307 + 0.0733383i \(0.976635\pi\)
\(102\) 4.06374 4.06374i 0.402370 0.402370i
\(103\) 1.02968 0.101458 0.0507289 0.998712i \(-0.483846\pi\)
0.0507289 + 0.998712i \(0.483846\pi\)
\(104\) 1.29147 0.126639
\(105\) −1.74586 0.999748i −0.170378 0.0975654i
\(106\) 6.79864 + 6.79864i 0.660343 + 0.660343i
\(107\) −13.8598 13.8598i −1.33988 1.33988i −0.896171 0.443708i \(-0.853663\pi\)
−0.443708 0.896171i \(-0.646337\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) 5.32683 + 5.32683i 0.510218 + 0.510218i 0.914593 0.404375i \(-0.132511\pi\)
−0.404375 + 0.914593i \(0.632511\pi\)
\(110\) 2.52078 4.40204i 0.240347 0.419718i
\(111\) −1.43822 5.91029i −0.136510 0.560980i
\(112\) 0.636201 + 0.636201i 0.0601153 + 0.0601153i
\(113\) 17.2755 1.62515 0.812573 0.582859i \(-0.198066\pi\)
0.812573 + 0.582859i \(0.198066\pi\)
\(114\) 5.80061 0.543276
\(115\) −16.5603 9.48308i −1.54426 0.884302i
\(116\) 1.70155 1.70155i 0.157985 0.157985i
\(117\) 1.29147 0.119397
\(118\) 3.51171 3.51171i 0.323279 0.323279i
\(119\) −3.65624 3.65624i −0.335167 0.335167i
\(120\) −0.586380 2.15781i −0.0535289 0.196981i
\(121\) 5.85354 0.532140
\(122\) −2.06460 + 2.06460i −0.186920 + 0.186920i
\(123\) 6.37818 6.37818i 0.575101 0.575101i
\(124\) 5.81155 + 5.81155i 0.521893 + 0.521893i
\(125\) −11.1797 + 0.118740i −0.999944 + 0.0106204i
\(126\) 0.636201 + 0.636201i 0.0566773 + 0.0566773i
\(127\) 0.916380 + 0.916380i 0.0813156 + 0.0813156i 0.746595 0.665279i \(-0.231687\pi\)
−0.665279 + 0.746595i \(0.731687\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −0.603223 + 0.603223i −0.0531109 + 0.0531109i
\(130\) −1.43505 + 2.50602i −0.125862 + 0.219793i
\(131\) −6.28943 6.28943i −0.549510 0.549510i 0.376789 0.926299i \(-0.377028\pi\)
−0.926299 + 0.376789i \(0.877028\pi\)
\(132\) −1.60413 + 1.60413i −0.139622 + 0.139622i
\(133\) 5.21895i 0.452540i
\(134\) −3.98347 3.98347i −0.344120 0.344120i
\(135\) −0.586380 2.15781i −0.0504675 0.185715i
\(136\) 5.74699i 0.492800i
\(137\) 10.4523 + 10.4523i 0.893004 + 0.893004i 0.994805 0.101801i \(-0.0324605\pi\)
−0.101801 + 0.994805i \(0.532461\pi\)
\(138\) 6.03467 + 6.03467i 0.513705 + 0.513705i
\(139\) −14.4443 −1.22515 −0.612574 0.790414i \(-0.709866\pi\)
−0.612574 + 0.790414i \(0.709866\pi\)
\(140\) −1.94144 + 0.527580i −0.164081 + 0.0445887i
\(141\) 0.462042i 0.0389110i
\(142\) 15.2892i 1.28304i
\(143\) 2.92981 0.245003
\(144\) 1.00000i 0.0833333i
\(145\) 1.41104 + 5.19246i 0.117180 + 0.431210i
\(146\) −11.8322 + 11.8322i −0.979243 + 0.979243i
\(147\) −4.37734 + 4.37734i −0.361037 + 0.361037i
\(148\) −5.19618 3.16223i −0.427123 0.259934i
\(149\) 19.0997i 1.56471i −0.622831 0.782356i \(-0.714018\pi\)
0.622831 0.782356i \(-0.285982\pi\)
\(150\) 4.83867 + 1.25987i 0.395076 + 0.102868i
\(151\) 3.42513i 0.278733i −0.990241 0.139367i \(-0.955493\pi\)
0.990241 0.139367i \(-0.0445067\pi\)
\(152\) 4.10165 4.10165i 0.332688 0.332688i
\(153\) 5.74699i 0.464617i
\(154\) 1.44327 + 1.44327i 0.116302 + 0.116302i
\(155\) −17.7346 + 4.81932i −1.42448 + 0.387097i
\(156\) 0.913209 0.913209i 0.0731152 0.0731152i
\(157\) 12.1068 + 12.1068i 0.966232 + 0.966232i 0.999448 0.0332164i \(-0.0105751\pi\)
−0.0332164 + 0.999448i \(0.510575\pi\)
\(158\) 9.04382 9.04382i 0.719488 0.719488i
\(159\) 9.61473 0.762498
\(160\) −1.94044 1.11117i −0.153405 0.0878458i
\(161\) 5.42954 5.42954i 0.427907 0.427907i
\(162\) 1.00000i 0.0785674i
\(163\) 24.2268 1.89759 0.948795 0.315894i \(-0.102304\pi\)
0.948795 + 0.315894i \(0.102304\pi\)
\(164\) 9.02011i 0.704352i
\(165\) −1.33025 4.89518i −0.103560 0.381089i
\(166\) −9.12362 9.12362i −0.708130 0.708130i
\(167\) 9.66372 0.747801 0.373900 0.927469i \(-0.378020\pi\)
0.373900 + 0.927469i \(0.378020\pi\)
\(168\) 0.899724 0.0694152
\(169\) 11.3321 0.871700
\(170\) 11.1517 + 6.38589i 0.855295 + 0.489776i
\(171\) 4.10165 4.10165i 0.313661 0.313661i
\(172\) 0.853087i 0.0650472i
\(173\) −6.77556 6.77556i −0.515136 0.515136i 0.400959 0.916096i \(-0.368677\pi\)
−0.916096 + 0.400959i \(0.868677\pi\)
\(174\) 2.40635i 0.182425i
\(175\) 1.13353 4.35347i 0.0856870 0.329091i
\(176\) 2.26858i 0.171001i
\(177\) 4.96631i 0.373290i
\(178\) 6.32382 + 6.32382i 0.473990 + 0.473990i
\(179\) 7.36463 7.36463i 0.550458 0.550458i −0.376115 0.926573i \(-0.622740\pi\)
0.926573 + 0.376115i \(0.122740\pi\)
\(180\) −1.94044 1.11117i −0.144632 0.0828218i
\(181\) −13.9651 −1.03802 −0.519008 0.854769i \(-0.673699\pi\)
−0.519008 + 0.854769i \(0.673699\pi\)
\(182\) −0.821636 0.821636i −0.0609037 0.0609037i
\(183\) 2.91979i 0.215837i
\(184\) 8.53431 0.629158
\(185\) 11.9100 6.56908i 0.875638 0.482969i
\(186\) 8.21877 0.602630
\(187\) 13.0375i 0.953398i
\(188\) 0.326713 + 0.326713i 0.0238280 + 0.0238280i
\(189\) 0.899724 0.0654453
\(190\) 3.40136 + 12.5166i 0.246760 + 0.908051i
\(191\) −11.6459 + 11.6459i −0.842665 + 0.842665i −0.989205 0.146540i \(-0.953186\pi\)
0.146540 + 0.989205i \(0.453186\pi\)
\(192\) 0.707107 + 0.707107i 0.0510310 + 0.0510310i
\(193\) 2.80664i 0.202026i 0.994885 + 0.101013i \(0.0322084\pi\)
−0.994885 + 0.101013i \(0.967792\pi\)
\(194\) 9.28197i 0.666406i
\(195\) 0.757293 + 2.78676i 0.0542309 + 0.199564i
\(196\) 6.19050i 0.442178i
\(197\) 11.5183 + 11.5183i 0.820643 + 0.820643i 0.986200 0.165557i \(-0.0529422\pi\)
−0.165557 + 0.986200i \(0.552942\pi\)
\(198\) 2.26858i 0.161221i
\(199\) 10.3470 10.3470i 0.733481 0.733481i −0.237827 0.971308i \(-0.576435\pi\)
0.971308 + 0.237827i \(0.0764350\pi\)
\(200\) 4.31232 2.53060i 0.304927 0.178940i
\(201\) −5.63348 −0.397355
\(202\) 1.47408 0.103716
\(203\) −2.16505 −0.151957
\(204\) −4.06374 4.06374i −0.284518 0.284518i
\(205\) 17.5030 + 10.0229i 1.22246 + 0.700029i
\(206\) 1.02968i 0.0717414i
\(207\) 8.53431 0.593175
\(208\) 1.29147i 0.0895475i
\(209\) 9.30492 9.30492i 0.643635 0.643635i
\(210\) −0.999748 + 1.74586i −0.0689892 + 0.120476i
\(211\) −3.80993 −0.262286 −0.131143 0.991363i \(-0.541865\pi\)
−0.131143 + 0.991363i \(0.541865\pi\)
\(212\) 6.79864 6.79864i 0.466933 0.466933i
\(213\) 10.8111 + 10.8111i 0.740765 + 0.740765i
\(214\) −13.8598 + 13.8598i −0.947438 + 0.947438i
\(215\) −1.65536 0.947925i −0.112895 0.0646480i
\(216\) 0.707107 + 0.707107i 0.0481125 + 0.0481125i
\(217\) 7.39463i 0.501980i
\(218\) 5.32683 5.32683i 0.360779 0.360779i
\(219\) 16.7333i 1.13073i
\(220\) −4.40204 2.52078i −0.296786 0.169951i
\(221\) 7.42208i 0.499263i
\(222\) −5.91029 + 1.43822i −0.396673 + 0.0965269i
\(223\) 16.8923 16.8923i 1.13119 1.13119i 0.141210 0.989980i \(-0.454901\pi\)
0.989980 0.141210i \(-0.0450992\pi\)
\(224\) 0.636201 0.636201i 0.0425080 0.0425080i
\(225\) 4.31232 2.53060i 0.287488 0.168706i
\(226\) 17.2755i 1.14915i
\(227\) −25.0030 −1.65950 −0.829752 0.558132i \(-0.811518\pi\)
−0.829752 + 0.558132i \(0.811518\pi\)
\(228\) 5.80061i 0.384154i
\(229\) 11.3572i 0.750503i −0.926923 0.375252i \(-0.877556\pi\)
0.926923 0.375252i \(-0.122444\pi\)
\(230\) −9.48308 + 16.5603i −0.625296 + 1.09195i
\(231\) 2.04110 0.134294
\(232\) −1.70155 1.70155i −0.111712 0.111712i
\(233\) 4.77274 + 4.77274i 0.312673 + 0.312673i 0.845944 0.533271i \(-0.179038\pi\)
−0.533271 + 0.845944i \(0.679038\pi\)
\(234\) 1.29147i 0.0844262i
\(235\) −0.997001 + 0.270932i −0.0650371 + 0.0176737i
\(236\) −3.51171 3.51171i −0.228593 0.228593i
\(237\) 12.7899i 0.830793i
\(238\) −3.65624 + 3.65624i −0.236999 + 0.236999i
\(239\) −2.96858 2.96858i −0.192022 0.192022i 0.604547 0.796569i \(-0.293354\pi\)
−0.796569 + 0.604547i \(0.793354\pi\)
\(240\) −2.15781 + 0.586380i −0.139286 + 0.0378507i
\(241\) −5.75647 + 5.75647i −0.370807 + 0.370807i −0.867771 0.496964i \(-0.834448\pi\)
0.496964 + 0.867771i \(0.334448\pi\)
\(242\) 5.85354i 0.376279i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 2.06460 + 2.06460i 0.132172 + 0.132172i
\(245\) −12.0123 6.87870i −0.767436 0.439464i
\(246\) −6.37818 6.37818i −0.406658 0.406658i
\(247\) −5.29716 + 5.29716i −0.337050 + 0.337050i
\(248\) 5.81155 5.81155i 0.369034 0.369034i
\(249\) −12.9027 −0.817678
\(250\) 0.118740 + 11.1797i 0.00750979 + 0.707067i
\(251\) −14.7749 14.7749i −0.932584 0.932584i 0.0652824 0.997867i \(-0.479205\pi\)
−0.997867 + 0.0652824i \(0.979205\pi\)
\(252\) 0.636201 0.636201i 0.0400769 0.0400769i
\(253\) 19.3608 1.21720
\(254\) 0.916380 0.916380i 0.0574988 0.0574988i
\(255\) 12.4009 3.36992i 0.776577 0.211033i
\(256\) 1.00000 0.0625000
\(257\) 1.80027 0.112298 0.0561488 0.998422i \(-0.482118\pi\)
0.0561488 + 0.998422i \(0.482118\pi\)
\(258\) 0.603223 + 0.603223i 0.0375550 + 0.0375550i
\(259\) 1.29400 + 5.31763i 0.0804053 + 0.330421i
\(260\) 2.50602 + 1.43505i 0.155417 + 0.0889978i
\(261\) −1.70155 1.70155i −0.105323 0.105323i
\(262\) −6.28943 + 6.28943i −0.388563 + 0.388563i
\(263\) −9.25899 9.25899i −0.570934 0.570934i 0.361456 0.932389i \(-0.382280\pi\)
−0.932389 + 0.361456i \(0.882280\pi\)
\(264\) 1.60413 + 1.60413i 0.0987274 + 0.0987274i
\(265\) 5.63789 + 20.7468i 0.346333 + 1.27447i
\(266\) −5.21895 −0.319994
\(267\) 8.94323 0.547317
\(268\) −3.98347 + 3.98347i −0.243329 + 0.243329i
\(269\) 0.689017i 0.0420101i 0.999779 + 0.0210051i \(0.00668661\pi\)
−0.999779 + 0.0210051i \(0.993313\pi\)
\(270\) −2.15781 + 0.586380i −0.131320 + 0.0356859i
\(271\) −14.7629 −0.896783 −0.448392 0.893837i \(-0.648003\pi\)
−0.448392 + 0.893837i \(0.648003\pi\)
\(272\) −5.74699 −0.348462
\(273\) −1.16197 −0.0703255
\(274\) 10.4523 10.4523i 0.631449 0.631449i
\(275\) 9.78285 5.74087i 0.589928 0.346187i
\(276\) 6.03467 6.03467i 0.363244 0.363244i
\(277\) 32.3771i 1.94535i −0.232172 0.972675i \(-0.574583\pi\)
0.232172 0.972675i \(-0.425417\pi\)
\(278\) 14.4443i 0.866310i
\(279\) 5.81155 5.81155i 0.347928 0.347928i
\(280\) 0.527580 + 1.94144i 0.0315289 + 0.116023i
\(281\) 5.74725 5.74725i 0.342852 0.342852i −0.514586 0.857439i \(-0.672054\pi\)
0.857439 + 0.514586i \(0.172054\pi\)
\(282\) 0.462042 0.0275142
\(283\) 6.56809 0.390433 0.195216 0.980760i \(-0.437459\pi\)
0.195216 + 0.980760i \(0.437459\pi\)
\(284\) 15.2892 0.907248
\(285\) 11.2557 + 6.44547i 0.666731 + 0.381797i
\(286\) 2.92981i 0.173243i
\(287\) −5.73860 + 5.73860i −0.338739 + 0.338739i
\(288\) 1.00000 0.0589256
\(289\) 16.0279 0.942818
\(290\) 5.19246 1.41104i 0.304912 0.0828589i
\(291\) −6.56334 6.56334i −0.384750 0.384750i
\(292\) 11.8322 + 11.8322i 0.692430 + 0.692430i
\(293\) −22.0187 + 22.0187i −1.28634 + 1.28634i −0.349353 + 0.936991i \(0.613599\pi\)
−0.936991 + 0.349353i \(0.886401\pi\)
\(294\) 4.37734 + 4.37734i 0.255292 + 0.255292i
\(295\) 10.7164 2.91214i 0.623931 0.169551i
\(296\) −3.16223 + 5.19618i −0.183801 + 0.302022i
\(297\) 1.60413 + 1.60413i 0.0930811 + 0.0930811i
\(298\) −19.0997 −1.10642
\(299\) −11.0218 −0.637408
\(300\) 1.25987 4.83867i 0.0727385 0.279361i
\(301\) 0.542735 0.542735i 0.0312827 0.0312827i
\(302\) −3.42513 −0.197094
\(303\) 1.04233 1.04233i 0.0598805 0.0598805i
\(304\) −4.10165 4.10165i −0.235246 0.235246i
\(305\) −6.30035 + 1.71210i −0.360757 + 0.0980347i
\(306\) −5.74699 −0.328534
\(307\) 5.03677 5.03677i 0.287464 0.287464i −0.548613 0.836077i \(-0.684844\pi\)
0.836077 + 0.548613i \(0.184844\pi\)
\(308\) 1.44327 1.44327i 0.0822382 0.0822382i
\(309\) −0.728096 0.728096i −0.0414199 0.0414199i
\(310\) 4.81932 + 17.7346i 0.273719 + 1.00726i
\(311\) 3.85553 + 3.85553i 0.218627 + 0.218627i 0.807920 0.589293i \(-0.200594\pi\)
−0.589293 + 0.807920i \(0.700594\pi\)
\(312\) −0.913209 0.913209i −0.0517003 0.0517003i
\(313\) 19.5460i 1.10481i −0.833577 0.552404i \(-0.813711\pi\)
0.833577 0.552404i \(-0.186289\pi\)
\(314\) 12.1068 12.1068i 0.683229 0.683229i
\(315\) 0.527580 + 1.94144i 0.0297258 + 0.109388i
\(316\) −9.04382 9.04382i −0.508755 0.508755i
\(317\) 5.03252 5.03252i 0.282655 0.282655i −0.551512 0.834167i \(-0.685949\pi\)
0.834167 + 0.551512i \(0.185949\pi\)
\(318\) 9.61473i 0.539168i
\(319\) −3.86010 3.86010i −0.216124 0.216124i
\(320\) −1.11117 + 1.94044i −0.0621164 + 0.108474i
\(321\) 19.6007i 1.09401i
\(322\) −5.42954 5.42954i −0.302576 0.302576i
\(323\) 23.5721 + 23.5721i 1.31159 + 1.31159i
\(324\) 1.00000 0.0555556
\(325\) −5.56924 + 3.26819i −0.308926 + 0.181287i
\(326\) 24.2268i 1.34180i
\(327\) 7.53328i 0.416591i
\(328\) −9.02011 −0.498052
\(329\) 0.415710i 0.0229189i
\(330\) −4.89518 + 1.33025i −0.269471 + 0.0732279i
\(331\) −3.25748 + 3.25748i −0.179048 + 0.179048i −0.790941 0.611893i \(-0.790408\pi\)
0.611893 + 0.790941i \(0.290408\pi\)
\(332\) −9.12362 + 9.12362i −0.500723 + 0.500723i
\(333\) −3.16223 + 5.19618i −0.173289 + 0.284749i
\(334\) 9.66372i 0.528775i
\(335\) −3.30336 12.1560i −0.180482 0.664154i
\(336\) 0.899724i 0.0490840i
\(337\) 15.5648 15.5648i 0.847866 0.847866i −0.142000 0.989867i \(-0.545353\pi\)
0.989867 + 0.142000i \(0.0453534\pi\)
\(338\) 11.3321i 0.616385i
\(339\) −12.2157 12.2157i −0.663463 0.663463i
\(340\) 6.38589 11.1517i 0.346324 0.604785i
\(341\) 13.1840 13.1840i 0.713953 0.713953i
\(342\) −4.10165 4.10165i −0.221792 0.221792i
\(343\) 8.39181 8.39181i 0.453115 0.453115i
\(344\) 0.853087 0.0459953
\(345\) 5.00435 + 18.4154i 0.269425 + 0.991454i
\(346\) −6.77556 + 6.77556i −0.364256 + 0.364256i
\(347\) 19.7799i 1.06184i −0.847422 0.530920i \(-0.821846\pi\)
0.847422 0.530920i \(-0.178154\pi\)
\(348\) −2.40635 −0.128994
\(349\) 5.47518i 0.293080i 0.989205 + 0.146540i \(0.0468137\pi\)
−0.989205 + 0.146540i \(0.953186\pi\)
\(350\) −4.35347 1.13353i −0.232703 0.0605899i
\(351\) −0.913209 0.913209i −0.0487435 0.0487435i
\(352\) 2.26858 0.120916
\(353\) 28.1816 1.49995 0.749976 0.661465i \(-0.230065\pi\)
0.749976 + 0.661465i \(0.230065\pi\)
\(354\) −4.96631 −0.263956
\(355\) −16.9889 + 29.6678i −0.901679 + 1.57460i
\(356\) 6.32382 6.32382i 0.335162 0.335162i
\(357\) 5.17071i 0.273663i
\(358\) −7.36463 7.36463i −0.389233 0.389233i
\(359\) 2.05043i 0.108218i 0.998535 + 0.0541089i \(0.0172318\pi\)
−0.998535 + 0.0541089i \(0.982768\pi\)
\(360\) −1.11117 + 1.94044i −0.0585639 + 0.102270i
\(361\) 14.6470i 0.770896i
\(362\) 13.9651i 0.733988i
\(363\) −4.13907 4.13907i −0.217245 0.217245i
\(364\) −0.821636 + 0.821636i −0.0430654 + 0.0430654i
\(365\) −36.1074 + 9.81208i −1.88995 + 0.513588i
\(366\) 2.91979 0.152620
\(367\) −8.13886 8.13886i −0.424845 0.424845i 0.462023 0.886868i \(-0.347124\pi\)
−0.886868 + 0.462023i \(0.847124\pi\)
\(368\) 8.53431i 0.444882i
\(369\) −9.02011 −0.469568
\(370\) −6.56908 11.9100i −0.341510 0.619169i
\(371\) −8.65061 −0.449117
\(372\) 8.21877i 0.426124i
\(373\) −9.78820 9.78820i −0.506814 0.506814i 0.406733 0.913547i \(-0.366668\pi\)
−0.913547 + 0.406733i \(0.866668\pi\)
\(374\) −13.0375 −0.674154
\(375\) 7.98921 + 7.82129i 0.412561 + 0.403889i
\(376\) 0.326713 0.326713i 0.0168489 0.0168489i
\(377\) 2.19750 + 2.19750i 0.113177 + 0.113177i
\(378\) 0.899724i 0.0462768i
\(379\) 22.6146i 1.16164i −0.814034 0.580818i \(-0.802733\pi\)
0.814034 0.580818i \(-0.197267\pi\)
\(380\) 12.5166 3.40136i 0.642089 0.174486i
\(381\) 1.29596i 0.0663939i
\(382\) 11.6459 + 11.6459i 0.595854 + 0.595854i
\(383\) 9.52538i 0.486724i 0.969936 + 0.243362i \(0.0782503\pi\)
−0.969936 + 0.243362i \(0.921750\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) 1.19686 + 4.40431i 0.0609976 + 0.224464i
\(386\) 2.80664 0.142854
\(387\) 0.853087 0.0433648
\(388\) −9.28197 −0.471220
\(389\) 7.75553 + 7.75553i 0.393221 + 0.393221i 0.875834 0.482613i \(-0.160312\pi\)
−0.482613 + 0.875834i \(0.660312\pi\)
\(390\) 2.78676 0.757293i 0.141113 0.0383470i
\(391\) 49.0466i 2.48039i
\(392\) 6.19050 0.312667
\(393\) 8.89460i 0.448673i
\(394\) 11.5183 11.5183i 0.580282 0.580282i
\(395\) 27.5982 7.49973i 1.38862 0.377353i
\(396\) 2.26858 0.114001
\(397\) −18.6690 + 18.6690i −0.936970 + 0.936970i −0.998128 0.0611581i \(-0.980521\pi\)
0.0611581 + 0.998128i \(0.480521\pi\)
\(398\) −10.3470 10.3470i −0.518649 0.518649i
\(399\) −3.69035 + 3.69035i −0.184749 + 0.184749i
\(400\) −2.53060 4.31232i −0.126530 0.215616i
\(401\) 13.9114 + 13.9114i 0.694702 + 0.694702i 0.963263 0.268561i \(-0.0865481\pi\)
−0.268561 + 0.963263i \(0.586548\pi\)
\(402\) 5.63348i 0.280973i
\(403\) −7.50545 + 7.50545i −0.373873 + 0.373873i
\(404\) 1.47408i 0.0733383i
\(405\) −1.11117 + 1.94044i −0.0552146 + 0.0964211i
\(406\) 2.16505i 0.107450i
\(407\) −7.17378 + 11.7880i −0.355591 + 0.584308i
\(408\) −4.06374 + 4.06374i −0.201185 + 0.201185i
\(409\) −7.16339 + 7.16339i −0.354207 + 0.354207i −0.861672 0.507465i \(-0.830582\pi\)
0.507465 + 0.861672i \(0.330582\pi\)
\(410\) 10.0229 17.5030i 0.494995 0.864409i
\(411\) 14.7818i 0.729134i
\(412\) −1.02968 −0.0507289
\(413\) 4.46831i 0.219871i
\(414\) 8.53431i 0.419438i
\(415\) −7.56591 27.8417i −0.371396 1.36670i
\(416\) −1.29147 −0.0633196
\(417\) 10.2136 + 10.2136i 0.500164 + 0.500164i
\(418\) −9.30492 9.30492i −0.455119 0.455119i
\(419\) 23.8546i 1.16537i 0.812698 + 0.582686i \(0.197998\pi\)
−0.812698 + 0.582686i \(0.802002\pi\)
\(420\) 1.74586 + 0.999748i 0.0851892 + 0.0487827i
\(421\) −12.3787 12.3787i −0.603301 0.603301i 0.337886 0.941187i \(-0.390288\pi\)
−0.941187 + 0.337886i \(0.890288\pi\)
\(422\) 3.80993i 0.185464i
\(423\) 0.326713 0.326713i 0.0158853 0.0158853i
\(424\) −6.79864 6.79864i −0.330171 0.330171i
\(425\) 14.5433 + 24.7828i 0.705454 + 1.20214i
\(426\) 10.8111 10.8111i 0.523800 0.523800i
\(427\) 2.62700i 0.127130i
\(428\) 13.8598 + 13.8598i 0.669940 + 0.669940i
\(429\) −2.07169 2.07169i −0.100022 0.100022i
\(430\) −0.947925 + 1.65536i −0.0457130 + 0.0798286i
\(431\) 5.50143 + 5.50143i 0.264995 + 0.264995i 0.827080 0.562085i \(-0.190001\pi\)
−0.562085 + 0.827080i \(0.690001\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) 4.53175 4.53175i 0.217782 0.217782i −0.589781 0.807563i \(-0.700786\pi\)
0.807563 + 0.589781i \(0.200786\pi\)
\(434\) −7.39463 −0.354954
\(435\) 2.67387 4.66938i 0.128202 0.223879i
\(436\) −5.32683 5.32683i −0.255109 0.255109i
\(437\) −35.0047 + 35.0047i −1.67450 + 1.67450i
\(438\) 16.7333 0.799549
\(439\) 22.7618 22.7618i 1.08636 1.08636i 0.0904591 0.995900i \(-0.471167\pi\)
0.995900 0.0904591i \(-0.0288334\pi\)
\(440\) −2.52078 + 4.40204i −0.120174 + 0.209859i
\(441\) 6.19050 0.294786
\(442\) 7.42208 0.353032
\(443\) −18.5368 18.5368i −0.880708 0.880708i 0.112899 0.993606i \(-0.463986\pi\)
−0.993606 + 0.112899i \(0.963986\pi\)
\(444\) 1.43822 + 5.91029i 0.0682549 + 0.280490i
\(445\) 5.24413 + 19.2978i 0.248596 + 0.914804i
\(446\) −16.8923 16.8923i −0.799872 0.799872i
\(447\) −13.5056 + 13.5056i −0.638791 + 0.638791i
\(448\) −0.636201 0.636201i −0.0300577 0.0300577i
\(449\) 9.96142 + 9.96142i 0.470109 + 0.470109i 0.901950 0.431841i \(-0.142136\pi\)
−0.431841 + 0.901950i \(0.642136\pi\)
\(450\) −2.53060 4.31232i −0.119293 0.203285i
\(451\) −20.4629 −0.963558
\(452\) −17.2755 −0.812573
\(453\) −2.42193 + 2.42193i −0.113792 + 0.113792i
\(454\) 25.0030i 1.17345i
\(455\) −0.681355 2.50731i −0.0319424 0.117545i
\(456\) −5.80061 −0.271638
\(457\) −6.81678 −0.318876 −0.159438 0.987208i \(-0.550968\pi\)
−0.159438 + 0.987208i \(0.550968\pi\)
\(458\) −11.3572 −0.530686
\(459\) −4.06374 + 4.06374i −0.189679 + 0.189679i
\(460\) 16.5603 + 9.48308i 0.772128 + 0.442151i
\(461\) 24.7125 24.7125i 1.15097 1.15097i 0.164617 0.986358i \(-0.447361\pi\)
0.986358 0.164617i \(-0.0526389\pi\)
\(462\) 2.04110i 0.0949605i
\(463\) 32.0736i 1.49059i 0.666737 + 0.745293i \(0.267690\pi\)
−0.666737 + 0.745293i \(0.732310\pi\)
\(464\) −1.70155 + 1.70155i −0.0789924 + 0.0789924i
\(465\) 15.9480 + 9.13247i 0.739572 + 0.423508i
\(466\) 4.77274 4.77274i 0.221093 0.221093i
\(467\) 13.7531 0.636416 0.318208 0.948021i \(-0.396919\pi\)
0.318208 + 0.948021i \(0.396919\pi\)
\(468\) −1.29147 −0.0596983
\(469\) 5.06858 0.234045
\(470\) 0.270932 + 0.997001i 0.0124972 + 0.0459882i
\(471\) 17.1217i 0.788925i
\(472\) −3.51171 + 3.51171i −0.161640 + 0.161640i
\(473\) 1.93530 0.0889851
\(474\) −12.7899 −0.587459
\(475\) −7.30799 + 28.0672i −0.335314 + 1.28781i
\(476\) 3.65624 + 3.65624i 0.167584 + 0.167584i
\(477\) −6.79864 6.79864i −0.311289 0.311289i
\(478\) −2.96858 + 2.96858i −0.135780 + 0.135780i
\(479\) 15.9554 + 15.9554i 0.729021 + 0.729021i 0.970425 0.241404i \(-0.0776079\pi\)
−0.241404 + 0.970425i \(0.577608\pi\)
\(480\) 0.586380 + 2.15781i 0.0267645 + 0.0984903i
\(481\) 4.08393 6.71072i 0.186211 0.305983i
\(482\) 5.75647 + 5.75647i 0.262200 + 0.262200i
\(483\) −7.67852 −0.349385
\(484\) −5.85354 −0.266070
\(485\) 10.3139 18.0111i 0.468328 0.817841i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) 22.5078 1.01992 0.509962 0.860197i \(-0.329659\pi\)
0.509962 + 0.860197i \(0.329659\pi\)
\(488\) 2.06460 2.06460i 0.0934600 0.0934600i
\(489\) −17.1309 17.1309i −0.774688 0.774688i
\(490\) −6.87870 + 12.0123i −0.310748 + 0.542659i
\(491\) 31.0223 1.40002 0.700008 0.714135i \(-0.253180\pi\)
0.700008 + 0.714135i \(0.253180\pi\)
\(492\) −6.37818 + 6.37818i −0.287550 + 0.287550i
\(493\) 9.77878 9.77878i 0.440414 0.440414i
\(494\) 5.29716 + 5.29716i 0.238331 + 0.238331i
\(495\) −2.52078 + 4.40204i −0.113301 + 0.197857i
\(496\) −5.81155 5.81155i −0.260946 0.260946i
\(497\) −9.72702 9.72702i −0.436316 0.436316i
\(498\) 12.9027i 0.578186i
\(499\) 5.68409 5.68409i 0.254455 0.254455i −0.568339 0.822794i \(-0.692414\pi\)
0.822794 + 0.568339i \(0.192414\pi\)
\(500\) 11.1797 0.118740i 0.499972 0.00531022i
\(501\) −6.83328 6.83328i −0.305288 0.305288i
\(502\) −14.7749 + 14.7749i −0.659437 + 0.659437i
\(503\) 3.69027i 0.164541i −0.996610 0.0822705i \(-0.973783\pi\)
0.996610 0.0822705i \(-0.0262171\pi\)
\(504\) −0.636201 0.636201i −0.0283386 0.0283386i
\(505\) 2.86036 + 1.63796i 0.127285 + 0.0728882i
\(506\) 19.3608i 0.860692i
\(507\) −8.01300 8.01300i −0.355870 0.355870i
\(508\) −0.916380 0.916380i −0.0406578 0.0406578i
\(509\) 5.91876 0.262345 0.131172 0.991360i \(-0.458126\pi\)
0.131172 + 0.991360i \(0.458126\pi\)
\(510\) −3.36992 12.4009i −0.149223 0.549123i
\(511\) 15.0554i 0.666010i
\(512\) 1.00000i 0.0441942i
\(513\) −5.80061 −0.256103
\(514\) 1.80027i 0.0794064i
\(515\) 1.14415 1.99804i 0.0504175 0.0880440i
\(516\) 0.603223 0.603223i 0.0265554 0.0265554i
\(517\) 0.741175 0.741175i 0.0325969 0.0325969i
\(518\) 5.31763 1.29400i 0.233643 0.0568551i
\(519\) 9.58209i 0.420607i
\(520\) 1.43505 2.50602i 0.0629310 0.109896i
\(521\) 21.8007i 0.955107i 0.878603 + 0.477554i \(0.158476\pi\)
−0.878603 + 0.477554i \(0.841524\pi\)
\(522\) −1.70155 + 1.70155i −0.0744747 + 0.0744747i
\(523\) 17.1466i 0.749767i 0.927072 + 0.374883i \(0.122317\pi\)
−0.927072 + 0.374883i \(0.877683\pi\)
\(524\) 6.28943 + 6.28943i 0.274755 + 0.274755i
\(525\) −3.87990 + 2.27684i −0.169333 + 0.0993694i
\(526\) −9.25899 + 9.25899i −0.403711 + 0.403711i
\(527\) 33.3989 + 33.3989i 1.45488 + 1.45488i
\(528\) 1.60413 1.60413i 0.0698108 0.0698108i
\(529\) −49.8344 −2.16671
\(530\) 20.7468 5.63789i 0.901184 0.244894i
\(531\) −3.51171 + 3.51171i −0.152395 + 0.152395i
\(532\) 5.21895i 0.226270i
\(533\) 11.6492 0.504583
\(534\) 8.94323i 0.387011i
\(535\) −42.2948 + 11.4935i −1.82856 + 0.496907i
\(536\) 3.98347 + 3.98347i 0.172060 + 0.172060i
\(537\) −10.4152 −0.449447
\(538\) 0.689017 0.0297056
\(539\) 14.0436 0.604903
\(540\) 0.586380 + 2.15781i 0.0252338 + 0.0928575i
\(541\) −11.6362 + 11.6362i −0.500279 + 0.500279i −0.911525 0.411245i \(-0.865094\pi\)
0.411245 + 0.911525i \(0.365094\pi\)
\(542\) 14.7629i 0.634122i
\(543\) 9.87480 + 9.87480i 0.423768 + 0.423768i
\(544\) 5.74699i 0.246400i
\(545\) 16.2554 4.41736i 0.696305 0.189219i
\(546\) 1.16197i 0.0497277i
\(547\) 37.0105i 1.58245i 0.611523 + 0.791226i \(0.290557\pi\)
−0.611523 + 0.791226i \(0.709443\pi\)
\(548\) −10.4523 10.4523i −0.446502 0.446502i
\(549\) 2.06460 2.06460i 0.0881150 0.0881150i
\(550\) −5.74087 9.78285i −0.244791 0.417142i
\(551\) 13.9583 0.594643
\(552\) −6.03467 6.03467i −0.256853 0.256853i
\(553\) 11.5074i 0.489343i
\(554\) −32.3771 −1.37557
\(555\) −13.0667 3.77657i −0.554649 0.160307i
\(556\) 14.4443 0.612574
\(557\) 5.02764i 0.213028i −0.994311 0.106514i \(-0.966031\pi\)
0.994311 0.106514i \(-0.0339689\pi\)
\(558\) −5.81155 5.81155i −0.246023 0.246023i
\(559\) −1.10174 −0.0465985
\(560\) 1.94144 0.527580i 0.0820407 0.0222943i
\(561\) −9.21892 + 9.21892i −0.389223 + 0.389223i
\(562\) −5.74725 5.74725i −0.242433 0.242433i
\(563\) 14.7235i 0.620522i 0.950651 + 0.310261i \(0.100416\pi\)
−0.950651 + 0.310261i \(0.899584\pi\)
\(564\) 0.462042i 0.0194555i
\(565\) 19.1961 33.5221i 0.807586 1.41029i
\(566\) 6.56809i 0.276078i
\(567\) −0.636201 0.636201i −0.0267179 0.0267179i
\(568\) 15.2892i 0.641521i
\(569\) −15.1302 + 15.1302i −0.634291 + 0.634291i −0.949141 0.314850i \(-0.898046\pi\)
0.314850 + 0.949141i \(0.398046\pi\)
\(570\) 6.44547 11.2557i 0.269971 0.471450i
\(571\) −0.732604 −0.0306585 −0.0153293 0.999882i \(-0.504880\pi\)
−0.0153293 + 0.999882i \(0.504880\pi\)
\(572\) −2.92981 −0.122502
\(573\) 16.4697 0.688033
\(574\) 5.73860 + 5.73860i 0.239525 + 0.239525i
\(575\) −36.8026 + 21.5969i −1.53478 + 0.900653i
\(576\) 1.00000i 0.0416667i
\(577\) 13.0938 0.545102 0.272551 0.962141i \(-0.412133\pi\)
0.272551 + 0.962141i \(0.412133\pi\)
\(578\) 16.0279i 0.666673i
\(579\) 1.98459 1.98459i 0.0824768 0.0824768i
\(580\) −1.41104 5.19246i −0.0585901 0.215605i
\(581\) 11.6089 0.481619
\(582\) −6.56334 + 6.56334i −0.272059 + 0.272059i
\(583\) −15.4233 15.4233i −0.638767 0.638767i
\(584\) 11.8322 11.8322i 0.489622 0.489622i
\(585\) 1.43505 2.50602i 0.0593319 0.103611i
\(586\) 22.0187 + 22.0187i 0.909583 + 0.909583i
\(587\) 25.6946i 1.06053i −0.847832 0.530265i \(-0.822092\pi\)
0.847832 0.530265i \(-0.177908\pi\)
\(588\) 4.37734 4.37734i 0.180519 0.180519i
\(589\) 47.6739i 1.96437i
\(590\) −2.91214 10.7164i −0.119891 0.441186i
\(591\) 16.2893i 0.670052i
\(592\) 5.19618 + 3.16223i 0.213562 + 0.129967i
\(593\) −32.7884 + 32.7884i −1.34646 + 1.34646i −0.456986 + 0.889474i \(0.651071\pi\)
−0.889474 + 0.456986i \(0.848929\pi\)
\(594\) 1.60413 1.60413i 0.0658182 0.0658182i
\(595\) −11.1574 + 3.03200i −0.457410 + 0.124300i
\(596\) 19.0997i 0.782356i
\(597\) −14.6329 −0.598885
\(598\) 11.0218i 0.450716i
\(599\) 32.7946i 1.33995i −0.742383 0.669975i \(-0.766305\pi\)
0.742383 0.669975i \(-0.233695\pi\)
\(600\) −4.83867 1.25987i −0.197538 0.0514339i
\(601\) 27.3053 1.11381 0.556904 0.830577i \(-0.311989\pi\)
0.556904 + 0.830577i \(0.311989\pi\)
\(602\) −0.542735 0.542735i −0.0221202 0.0221202i
\(603\) 3.98347 + 3.98347i 0.162220 + 0.162220i
\(604\) 3.42513i 0.139367i
\(605\) 6.50428 11.3584i 0.264437 0.461785i
\(606\) −1.04233 1.04233i −0.0423419 0.0423419i
\(607\) 26.7432i 1.08547i −0.839903 0.542737i \(-0.817388\pi\)
0.839903 0.542737i \(-0.182612\pi\)
\(608\) −4.10165 + 4.10165i −0.166344 + 0.166344i
\(609\) 1.53092 + 1.53092i 0.0620362 + 0.0620362i
\(610\) 1.71210 + 6.30035i 0.0693210 + 0.255094i
\(611\) −0.421941 + 0.421941i −0.0170699 + 0.0170699i
\(612\) 5.74699i 0.232308i
\(613\) −23.6704 23.6704i −0.956040 0.956040i 0.0430339 0.999074i \(-0.486298\pi\)
−0.999074 + 0.0430339i \(0.986298\pi\)
\(614\) −5.03677 5.03677i −0.203268 0.203268i
\(615\) −5.28921 19.4637i −0.213281 0.784852i
\(616\) −1.44327 1.44327i −0.0581512 0.0581512i
\(617\) 3.77510 3.77510i 0.151980 0.151980i −0.627022 0.779002i \(-0.715726\pi\)
0.779002 + 0.627022i \(0.215726\pi\)
\(618\) −0.728096 + 0.728096i −0.0292883 + 0.0292883i
\(619\) 9.65130 0.387918 0.193959 0.981010i \(-0.437867\pi\)
0.193959 + 0.981010i \(0.437867\pi\)
\(620\) 17.7346 4.81932i 0.712238 0.193549i
\(621\) −6.03467 6.03467i −0.242163 0.242163i
\(622\) 3.85553 3.85553i 0.154593 0.154593i
\(623\) −8.04644 −0.322374
\(624\) −0.913209 + 0.913209i −0.0365576 + 0.0365576i
\(625\) −12.1922 + 21.8255i −0.487687 + 0.873019i
\(626\) −19.5460 −0.781217
\(627\) −13.1592 −0.525526
\(628\) −12.1068 12.1068i −0.483116 0.483116i
\(629\) −29.8624 18.1733i −1.19069 0.724618i
\(630\) 1.94144 0.527580i 0.0773487 0.0210193i
\(631\) 9.32454 + 9.32454i 0.371204 + 0.371204i 0.867916 0.496712i \(-0.165459\pi\)
−0.496712 + 0.867916i \(0.665459\pi\)
\(632\) −9.04382 + 9.04382i −0.359744 + 0.359744i
\(633\) 2.69402 + 2.69402i 0.107078 + 0.107078i
\(634\) −5.03252 5.03252i −0.199867 0.199867i
\(635\) 2.79643 0.759923i 0.110973 0.0301566i
\(636\) −9.61473 −0.381249
\(637\) −7.99485 −0.316768
\(638\) −3.86010 + 3.86010i −0.152823 + 0.152823i
\(639\) 15.2892i 0.604832i
\(640\) 1.94044 + 1.11117i 0.0767025 + 0.0439229i
\(641\) −7.81012 −0.308481 −0.154241 0.988033i \(-0.549293\pi\)
−0.154241 + 0.988033i \(0.549293\pi\)
\(642\) 19.6007 0.773580
\(643\) −39.3070 −1.55012 −0.775058 0.631890i \(-0.782279\pi\)
−0.775058 + 0.631890i \(0.782279\pi\)
\(644\) −5.42954 + 5.42954i −0.213954 + 0.213954i
\(645\) 0.500233 + 1.84080i 0.0196966 + 0.0724815i
\(646\) 23.5721 23.5721i 0.927433 0.927433i
\(647\) 31.8619i 1.25262i −0.779573 0.626311i \(-0.784564\pi\)
0.779573 0.626311i \(-0.215436\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −7.96660 + 7.96660i −0.312716 + 0.312716i
\(650\) 3.26819 + 5.56924i 0.128189 + 0.218443i
\(651\) −5.22879 + 5.22879i −0.204933 + 0.204933i
\(652\) −24.2268 −0.948795
\(653\) 40.2027 1.57325 0.786626 0.617430i \(-0.211826\pi\)
0.786626 + 0.617430i \(0.211826\pi\)
\(654\) −7.53328 −0.294575
\(655\) −19.1929 + 5.21562i −0.749929 + 0.203791i
\(656\) 9.02011i 0.352176i
\(657\) 11.8322 11.8322i 0.461620 0.461620i
\(658\) −0.415710 −0.0162061
\(659\) −22.6033 −0.880499 −0.440250 0.897875i \(-0.645110\pi\)
−0.440250 + 0.897875i \(0.645110\pi\)
\(660\) 1.33025 + 4.89518i 0.0517799 + 0.190545i
\(661\) 20.1421 + 20.1421i 0.783436 + 0.783436i 0.980409 0.196973i \(-0.0631111\pi\)
−0.196973 + 0.980409i \(0.563111\pi\)
\(662\) 3.25748 + 3.25748i 0.126606 + 0.126606i
\(663\) 5.24820 5.24820i 0.203823 0.203823i
\(664\) 9.12362 + 9.12362i 0.354065 + 0.354065i
\(665\) −10.1270 5.79914i −0.392710 0.224881i
\(666\) 5.19618 + 3.16223i 0.201348 + 0.122534i
\(667\) 14.5215 + 14.5215i 0.562276 + 0.562276i
\(668\) −9.66372 −0.373900
\(669\) −23.8893 −0.923612
\(670\) −12.1560 + 3.30336i −0.469628 + 0.127620i
\(671\) 4.68371 4.68371i 0.180813 0.180813i
\(672\) −0.899724 −0.0347076
\(673\) 23.9631 23.9631i 0.923709 0.923709i −0.0735806 0.997289i \(-0.523443\pi\)
0.997289 + 0.0735806i \(0.0234426\pi\)
\(674\) −15.5648 15.5648i −0.599532 0.599532i
\(675\) −4.83867 1.25987i −0.186241 0.0484923i
\(676\) −11.3321 −0.435850
\(677\) −18.3439 + 18.3439i −0.705012 + 0.705012i −0.965482 0.260470i \(-0.916122\pi\)
0.260470 + 0.965482i \(0.416122\pi\)
\(678\) −12.2157 + 12.2157i −0.469139 + 0.469139i
\(679\) 5.90520 + 5.90520i 0.226621 + 0.226621i
\(680\) −11.1517 6.38589i −0.427647 0.244888i
\(681\) 17.6798 + 17.6798i 0.677490 + 0.677490i
\(682\) −13.1840 13.1840i −0.504841 0.504841i
\(683\) 2.79715i 0.107030i −0.998567 0.0535149i \(-0.982958\pi\)
0.998567 0.0535149i \(-0.0170425\pi\)
\(684\) −4.10165 + 4.10165i −0.156830 + 0.156830i
\(685\) 31.8965 8.66777i 1.21870 0.331179i
\(686\) −8.39181 8.39181i −0.320401 0.320401i
\(687\) −8.03073 + 8.03073i −0.306392 + 0.306392i
\(688\) 0.853087i 0.0325236i
\(689\) 8.78026 + 8.78026i 0.334501 + 0.334501i
\(690\) 18.4154 5.00435i 0.701064 0.190512i
\(691\) 7.07761i 0.269245i 0.990897 + 0.134623i \(0.0429822\pi\)
−0.990897 + 0.134623i \(0.957018\pi\)
\(692\) 6.77556 + 6.77556i 0.257568 + 0.257568i
\(693\) −1.44327 1.44327i −0.0548255 0.0548255i
\(694\) −19.7799 −0.750835
\(695\) −16.0501 + 28.0282i −0.608813 + 1.06317i
\(696\) 2.40635i 0.0912125i
\(697\) 51.8385i 1.96352i
\(698\) 5.47518 0.207239
\(699\) 6.74968i 0.255296i
\(700\) −1.13353 + 4.35347i −0.0428435 + 0.164546i
\(701\) −25.0871 + 25.0871i −0.947527 + 0.947527i −0.998690 0.0511635i \(-0.983707\pi\)
0.0511635 + 0.998690i \(0.483707\pi\)
\(702\) −0.913209 + 0.913209i −0.0344668 + 0.0344668i
\(703\) −8.34254 34.2833i −0.314645 1.29302i
\(704\) 2.26858i 0.0855004i
\(705\) 0.896564 + 0.513408i 0.0337665 + 0.0193361i
\(706\) 28.1816i 1.06063i
\(707\) −0.937812 + 0.937812i −0.0352701 + 0.0352701i
\(708\) 4.96631i 0.186645i
\(709\) −6.08101 6.08101i −0.228377 0.228377i 0.583637 0.812014i \(-0.301629\pi\)
−0.812014 + 0.583637i \(0.801629\pi\)
\(710\) 29.6678 + 16.9889i 1.11341 + 0.637584i
\(711\) −9.04382 + 9.04382i −0.339170 + 0.339170i
\(712\) −6.32382 6.32382i −0.236995 0.236995i
\(713\) −49.5976 + 49.5976i −1.85744 + 1.85744i
\(714\) 5.17071 0.193509
\(715\) 3.25552 5.68511i 0.121750 0.212611i
\(716\) −7.36463 + 7.36463i −0.275229 + 0.275229i
\(717\) 4.19821i 0.156785i
\(718\) 2.05043 0.0765215
\(719\) 37.1763i 1.38644i 0.720724 + 0.693222i \(0.243809\pi\)
−0.720724 + 0.693222i \(0.756191\pi\)
\(720\) 1.94044 + 1.11117i 0.0723158 + 0.0414109i
\(721\) 0.655086 + 0.655086i 0.0243967 + 0.0243967i
\(722\) 14.6470 0.545106
\(723\) 8.14088 0.302762
\(724\) 13.9651 0.519008
\(725\) 11.6435 + 3.03168i 0.432430 + 0.112594i
\(726\) −4.13907 + 4.13907i −0.153615 + 0.153615i
\(727\) 10.8041i 0.400701i −0.979724 0.200350i \(-0.935792\pi\)
0.979724 0.200350i \(-0.0642081\pi\)
\(728\) 0.821636 + 0.821636i 0.0304519 + 0.0304519i
\(729\) 1.00000i 0.0370370i
\(730\) 9.81208 + 36.1074i 0.363161 + 1.33639i
\(731\) 4.90268i 0.181332i
\(732\) 2.91979i 0.107918i
\(733\) −2.31409 2.31409i −0.0854728 0.0854728i 0.663078 0.748551i \(-0.269250\pi\)
−0.748551 + 0.663078i \(0.769250\pi\)
\(734\) −8.13886 + 8.13886i −0.300411 + 0.300411i
\(735\) 3.62998 + 13.3579i 0.133894 + 0.492715i
\(736\) −8.53431 −0.314579
\(737\) 9.03684 + 9.03684i 0.332876 + 0.332876i
\(738\) 9.02011i 0.332035i
\(739\) −3.59606 −0.132283 −0.0661416 0.997810i \(-0.521069\pi\)
−0.0661416 + 0.997810i \(0.521069\pi\)
\(740\) −11.9100 + 6.56908i −0.437819 + 0.241484i
\(741\) 7.49132 0.275201
\(742\) 8.65061i 0.317574i
\(743\) 7.78930 + 7.78930i 0.285762 + 0.285762i 0.835402 0.549640i \(-0.185235\pi\)
−0.549640 + 0.835402i \(0.685235\pi\)
\(744\) −8.21877 −0.301315
\(745\) −37.0619 21.2231i −1.35784 0.777554i
\(746\) −9.78820 + 9.78820i −0.358371 + 0.358371i
\(747\) 9.12362 + 9.12362i 0.333816 + 0.333816i
\(748\) 13.0375i 0.476699i
\(749\) 17.6353i 0.644379i
\(750\) 7.82129 7.98921i 0.285593 0.291725i
\(751\) 31.8319i 1.16156i 0.814059 + 0.580782i \(0.197253\pi\)
−0.814059 + 0.580782i \(0.802747\pi\)
\(752\) −0.326713 0.326713i −0.0119140 0.0119140i
\(753\) 20.8949i 0.761452i
\(754\) 2.19750 2.19750i 0.0800283 0.0800283i
\(755\) −6.64625 3.80591i −0.241882 0.138511i
\(756\) −0.899724 −0.0327227
\(757\) 2.85691 0.103836 0.0519182 0.998651i \(-0.483467\pi\)
0.0519182 + 0.998651i \(0.483467\pi\)
\(758\) −22.6146 −0.821400
\(759\) −13.6901 13.6901i −0.496921 0.496921i
\(760\) −3.40136 12.5166i −0.123380 0.454026i
\(761\) 3.11943i 0.113079i −0.998400 0.0565396i \(-0.981993\pi\)
0.998400 0.0565396i \(-0.0180067\pi\)
\(762\) −1.29596 −0.0469476
\(763\) 6.77787i 0.245376i
\(764\) 11.6459 11.6459i 0.421332 0.421332i
\(765\) −11.1517 6.38589i −0.403190 0.230882i
\(766\) 9.52538 0.344166
\(767\) 4.53527 4.53527i 0.163759 0.163759i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) 22.4056 22.4056i 0.807966 0.807966i −0.176360 0.984326i \(-0.556432\pi\)
0.984326 + 0.176360i \(0.0564322\pi\)
\(770\) 4.40431 1.19686i 0.158720 0.0431318i
\(771\) −1.27298 1.27298i −0.0458453 0.0458453i
\(772\) 2.80664i 0.101013i
\(773\) −1.90608 + 1.90608i −0.0685571 + 0.0685571i −0.740554 0.671997i \(-0.765437\pi\)
0.671997 + 0.740554i \(0.265437\pi\)
\(774\) 0.853087i 0.0306636i
\(775\) −10.3546 + 39.7679i −0.371947 + 1.42851i
\(776\) 9.28197i 0.333203i
\(777\) 2.84514 4.67513i 0.102069 0.167719i
\(778\) 7.75553 7.75553i 0.278049 0.278049i
\(779\) 36.9973 36.9973i 1.32557 1.32557i