Properties

Label 1110.2.o.a.253.15
Level $1110$
Weight $2$
Character 1110.253
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 253.15
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.15

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(1.94044 - 1.11117i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.636201 - 0.636201i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(1.94044 - 1.11117i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.636201 - 0.636201i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-1.94044 + 1.11117i) q^{10} +2.26858i q^{11} +(0.707107 - 0.707107i) q^{12} +1.29147 q^{13} +(-0.636201 + 0.636201i) q^{14} +(0.586380 - 2.15781i) q^{15} +1.00000 q^{16} +5.74699i q^{17} +1.00000i q^{18} +(4.10165 + 4.10165i) q^{19} +(1.94044 - 1.11117i) q^{20} -0.899724i q^{21} -2.26858i q^{22} +8.53431 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} -1.00000 q^{32} +(1.60413 + 1.60413i) q^{33} -5.74699i q^{34} +(0.527580 - 1.94144i) q^{35} -1.00000i q^{36} +(3.16223 - 5.19618i) q^{37} +(-4.10165 - 4.10165i) q^{38} +(0.913209 - 0.913209i) q^{39} +(-1.94044 + 1.11117i) q^{40} +9.02011i q^{41} +0.899724i q^{42} +0.853087 q^{43} +2.26858i q^{44} +(-1.11117 - 1.94044i) q^{45} -8.53431 q^{46} +(-0.326713 + 0.326713i) q^{47} +(0.707107 - 0.707107i) q^{48} +6.19050i q^{49} +(-2.53060 + 4.31232i) q^{50} +(4.06374 + 4.06374i) q^{51} +1.29147 q^{52} +(-6.79864 - 6.79864i) q^{53} +(0.707107 + 0.707107i) q^{54} +(2.52078 + 4.40204i) q^{55} +(-0.636201 + 0.636201i) q^{56} +5.80061 q^{57} +(-1.70155 + 1.70155i) q^{58} +(-3.51171 - 3.51171i) q^{59} +(0.586380 - 2.15781i) 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} +5.74699i q^{68} +(6.03467 - 6.03467i) q^{69} +(-0.527580 + 1.94144i) q^{70} -15.2892 q^{71} +1.00000i 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} +(1.94044 - 1.11117i) q^{80} -1.00000 q^{81} -9.02011i q^{82} +(9.12362 + 9.12362i) q^{83} -0.899724i q^{84} +(6.38589 + 11.1517i) q^{85} -0.853087 q^{86} -2.40635i q^{87} -2.26858i q^{88} +(6.32382 - 6.32382i) q^{89} +(1.11117 + 1.94044i) q^{90} +(0.821636 - 0.821636i) q^{91} +8.53431 q^{92} -8.21877 q^{93} +(0.326713 - 0.326713i) q^{94} +(12.5166 + 3.40136i) q^{95} +(-0.707107 + 0.707107i) q^{96} -9.28197i q^{97} -6.19050i q^{98} +2.26858 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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.00000 0.500000
\(5\) 1.94044 1.11117i 0.867790 0.496931i
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) 0.636201 0.636201i 0.240461 0.240461i −0.576580 0.817041i \(-0.695613\pi\)
0.817041 + 0.576580i \(0.195613\pi\)
\(8\) −1.00000 −0.353553
\(9\) 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
\(13\) 1.29147 0.358190 0.179095 0.983832i \(-0.442683\pi\)
0.179095 + 0.983832i \(0.442683\pi\)
\(14\) −0.636201 + 0.636201i −0.170032 + 0.170032i
\(15\) 0.586380 2.15781i 0.151403 0.557145i
\(16\) 1.00000 0.250000
\(17\) 5.74699i 1.39385i 0.717144 + 0.696925i \(0.245449\pi\)
−0.717144 + 0.696925i \(0.754551\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 4.10165 + 4.10165i 0.940982 + 0.940982i 0.998353 0.0573705i \(-0.0182716\pi\)
−0.0573705 + 0.998353i \(0.518272\pi\)
\(20\) 1.94044 1.11117i 0.433895 0.248465i
\(21\) 0.899724i 0.196336i
\(22\) 2.26858i 0.483663i
\(23\) 8.53431 1.77953 0.889763 0.456423i \(-0.150869\pi\)
0.889763 + 0.456423i \(0.150869\pi\)
\(24\) −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 −0.531247 0.847217i \(-0.678277\pi\)
0.847217 + 0.531247i \(0.178277\pi\)
\(30\) −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 \(-0.514261\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.60413 + 1.60413i 0.279243 + 0.279243i
\(34\) 5.74699i 0.985601i
\(35\) 0.527580 1.94144i 0.0891773 0.328163i
\(36\) 1.00000i 0.166667i
\(37\) 3.16223 5.19618i 0.519868 0.854247i
\(38\) −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 \(0.751238\pi\)
\(42\) 0.899724i 0.138830i
\(43\) 0.853087 0.130094 0.0650472 0.997882i \(-0.479280\pi\)
0.0650472 + 0.997882i \(0.479280\pi\)
\(44\) 2.26858i 0.342002i
\(45\) −1.11117 1.94044i −0.165644 0.289263i
\(46\) −8.53431 −1.25832
\(47\) −0.326713 + 0.326713i −0.0476560 + 0.0476560i −0.730533 0.682877i \(-0.760728\pi\)
0.682877 + 0.730533i \(0.260728\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 6.19050i 0.884357i
\(50\) −2.53060 + 4.31232i −0.357880 + 0.609854i
\(51\) 4.06374 + 4.06374i 0.569037 + 0.569037i
\(52\) 1.29147 0.179095
\(53\) −6.79864 6.79864i −0.933866 0.933866i 0.0640792 0.997945i \(-0.479589\pi\)
−0.997945 + 0.0640792i \(0.979589\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) 2.52078 + 4.40204i 0.339902 + 0.593571i
\(56\) −0.636201 + 0.636201i −0.0850159 + 0.0850159i
\(57\) 5.80061 0.768309
\(58\) −1.70155 + 1.70155i −0.223424 + 0.223424i
\(59\) −3.51171 3.51171i −0.457186 0.457186i 0.440545 0.897731i \(-0.354785\pi\)
−0.897731 + 0.440545i \(0.854785\pi\)
\(60\) 0.586380 2.15781i 0.0757013 0.278573i
\(61\) −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 \(-0.361823\pi\)
−0.907250 + 0.420591i \(0.861823\pi\)
\(68\) 5.74699i 0.696925i
\(69\) 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 \(0.861821\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 11.8322 11.8322i 1.38486 1.38486i 0.549108 0.835751i \(-0.314968\pi\)
0.835751 0.549108i \(-0.185032\pi\)
\(74\) −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 \(-0.994377\pi\)
−0.0176652 0.999844i \(-0.505623\pi\)
\(80\) 1.94044 1.11117i 0.216948 0.124233i
\(81\) −1.00000 −0.111111
\(82\) 9.02011i 0.996104i
\(83\) 9.12362 + 9.12362i 1.00145 + 1.00145i 0.999999 + 0.00144791i \(0.000460883\pi\)
0.00144791 + 0.999999i \(0.499539\pi\)
\(84\) 0.899724i 0.0981680i
\(85\) 6.38589 + 11.1517i 0.692647 + 1.20957i
\(86\) −0.853087 −0.0919907
\(87\) 2.40635i 0.257988i
\(88\) 2.26858i 0.241832i
\(89\) 6.32382 6.32382i 0.670323 0.670323i −0.287467 0.957791i \(-0.592813\pi\)
0.957791 + 0.287467i \(0.0928132\pi\)
\(90\) 1.11117 + 1.94044i 0.117128 + 0.204540i
\(91\) 0.821636 0.821636i 0.0861308 0.0861308i
\(92\) 8.53431 0.889763
\(93\) −8.21877 −0.852247
\(94\) 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
\(97\) 9.28197i 0.942441i −0.882015 0.471220i \(-0.843814\pi\)
0.882015 0.471220i \(-0.156186\pi\)
\(98\) 6.19050i 0.625335i
\(99\) 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
\(103\) 1.02968i 0.101458i 0.998712 + 0.0507289i \(0.0161544\pi\)
−0.998712 + 0.0507289i \(0.983846\pi\)
\(104\) −1.29147 −0.126639
\(105\) −0.999748 1.74586i −0.0975654 0.170378i
\(106\) 6.79864 + 6.79864i 0.660343 + 0.660343i
\(107\) −13.8598 + 13.8598i −1.33988 + 1.33988i −0.443708 + 0.896171i \(0.646337\pi\)
−0.896171 + 0.443708i \(0.853663\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) −5.32683 5.32683i −0.510218 0.510218i 0.404375 0.914593i \(-0.367489\pi\)
−0.914593 + 0.404375i \(0.867489\pi\)
\(110\) −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
\(113\) 17.2755i 1.62515i 0.582859 + 0.812573i \(0.301934\pi\)
−0.582859 + 0.812573i \(0.698066\pi\)
\(114\) −5.80061 −0.543276
\(115\) 16.5603 9.48308i 1.54426 0.884302i
\(116\) 1.70155 1.70155i 0.157985 0.157985i
\(117\) 1.29147i 0.119397i
\(118\) 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
\(125\) 0.118740 11.1797i 0.0106204 0.999944i
\(126\) 0.636201 + 0.636201i 0.0566773 + 0.0566773i
\(127\) 0.916380 0.916380i 0.0813156 0.0813156i −0.665279 0.746595i \(-0.731687\pi\)
0.746595 + 0.665279i \(0.231687\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.603223 0.603223i 0.0531109 0.0531109i
\(130\) −2.50602 + 1.43505i −0.219793 + 0.125862i
\(131\) −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
\(133\) 5.21895 0.452540
\(134\) 3.98347 + 3.98347i 0.344120 + 0.344120i
\(135\) −2.15781 0.586380i −0.185715 0.0504675i
\(136\) 5.74699i 0.492800i
\(137\) 10.4523 10.4523i 0.893004 0.893004i −0.101801 0.994805i \(-0.532461\pi\)
0.994805 + 0.101801i \(0.0324605\pi\)
\(138\) −6.03467 + 6.03467i −0.513705 + 0.513705i
\(139\) 14.4443 1.22515 0.612574 0.790414i \(-0.290134\pi\)
0.612574 + 0.790414i \(0.290134\pi\)
\(140\) 0.527580 1.94144i 0.0445887 0.164081i
\(141\) 0.462042i 0.0389110i
\(142\) 15.2892 1.28304
\(143\) 2.92981i 0.245003i
\(144\) 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
\(148\) 3.16223 5.19618i 0.259934 0.427123i
\(149\) 19.0997i 1.56471i 0.622831 + 0.782356i \(0.285982\pi\)
−0.622831 + 0.782356i \(0.714018\pi\)
\(150\) 1.25987 + 4.83867i 0.102868 + 0.395076i
\(151\) 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
\(153\) 5.74699 0.464617
\(154\) −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 −0.0332164 0.999448i \(-0.510575\pi\)
0.999448 + 0.0332164i \(0.0105751\pi\)
\(158\) 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
\(162\) 1.00000 0.0785674
\(163\) 24.2268i 1.89759i 0.315894 + 0.948795i \(0.397696\pi\)
−0.315894 + 0.948795i \(0.602304\pi\)
\(164\) 9.02011i 0.704352i
\(165\) 4.89518 + 1.33025i 0.381089 + 0.103560i
\(166\) −9.12362 9.12362i −0.708130 0.708130i
\(167\) 9.66372i 0.747801i −0.927469 0.373900i \(-0.878020\pi\)
0.927469 0.373900i \(-0.121980\pi\)
\(168\) 0.899724i 0.0694152i
\(169\) −11.3321 −0.871700
\(170\) −6.38589 11.1517i −0.489776 0.855295i
\(171\) 4.10165 4.10165i 0.313661 0.313661i
\(172\) 0.853087 0.0650472
\(173\) 6.77556 6.77556i 0.515136 0.515136i −0.400959 0.916096i \(-0.631323\pi\)
0.916096 + 0.400959i \(0.131323\pi\)
\(174\) 2.40635i 0.182425i
\(175\) −1.13353 4.35347i −0.0856870 0.329091i
\(176\) 2.26858i 0.171001i
\(177\) −4.96631 −0.373290
\(178\) −6.32382 + 6.32382i −0.473990 + 0.473990i
\(179\) −7.36463 + 7.36463i −0.550458 + 0.550458i −0.926573 0.376115i \(-0.877260\pi\)
0.376115 + 0.926573i \(0.377260\pi\)
\(180\) −1.11117 1.94044i −0.0828218 0.144632i
\(181\) −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
\(183\) −2.91979 −0.215837
\(184\) −8.53431 −0.629158
\(185\) 0.362266 13.5966i 0.0266343 0.999645i
\(186\) 8.21877 0.602630
\(187\) −13.0375 −0.953398
\(188\) −0.326713 + 0.326713i −0.0238280 + 0.0238280i
\(189\) −0.899724 −0.0654453
\(190\) −12.5166 3.40136i −0.908051 0.246760i
\(191\) −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
\(193\) −2.80664 −0.202026 −0.101013 0.994885i \(-0.532208\pi\)
−0.101013 + 0.994885i \(0.532208\pi\)
\(194\) 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 −0.165557 0.986200i \(-0.552942\pi\)
0.986200 + 0.165557i \(0.0529422\pi\)
\(198\) −2.26858 −0.161221
\(199\) −10.3470 + 10.3470i −0.733481 + 0.733481i −0.971308 0.237827i \(-0.923565\pi\)
0.237827 + 0.971308i \(0.423565\pi\)
\(200\) −2.53060 + 4.31232i −0.178940 + 0.304927i
\(201\) −5.63348 −0.397355
\(202\) 1.47408i 0.103716i
\(203\) 2.16505i 0.151957i
\(204\) 4.06374 + 4.06374i 0.284518 + 0.284518i
\(205\) 10.0229 + 17.5030i 0.700029 + 1.22246i
\(206\) 1.02968i 0.0717414i
\(207\) 8.53431i 0.593175i
\(208\) 1.29147 0.0895475
\(209\) −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
\(217\) −7.39463 −0.501980
\(218\) 5.32683 + 5.32683i 0.360779 + 0.360779i
\(219\) 16.7333i 1.13073i
\(220\) 2.52078 + 4.40204i 0.169951 + 0.296786i
\(221\) 7.42208i 0.499263i
\(222\) 1.43822 + 5.91029i 0.0965269 + 0.396673i
\(223\) 16.8923 + 16.8923i 1.13119 + 1.13119i 0.989980 + 0.141210i \(0.0450992\pi\)
0.141210 + 0.989980i \(0.454901\pi\)
\(224\) −0.636201 + 0.636201i −0.0425080 + 0.0425080i
\(225\) −4.31232 2.53060i −0.287488 0.168706i
\(226\) 17.2755i 1.14915i
\(227\) 25.0030i 1.65950i 0.558132 + 0.829752i \(0.311518\pi\)
−0.558132 + 0.829752i \(0.688482\pi\)
\(228\) 5.80061 0.384154
\(229\) 11.3572i 0.750503i 0.926923 + 0.375252i \(0.122444\pi\)
−0.926923 + 0.375252i \(0.877556\pi\)
\(230\) −16.5603 + 9.48308i −1.09195 + 0.625296i
\(231\) 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 \(-0.820962\pi\)
0.533271 + 0.845944i \(0.320962\pi\)
\(234\) 1.29147i 0.0844262i
\(235\) −0.270932 + 0.997001i −0.0176737 + 0.0650371i
\(236\) −3.51171 3.51171i −0.228593 0.228593i
\(237\) −12.7899 −0.830793
\(238\) −3.65624 3.65624i −0.236999 0.236999i
\(239\) 2.96858 + 2.96858i 0.192022 + 0.192022i 0.796569 0.604547i \(-0.206646\pi\)
−0.604547 + 0.796569i \(0.706646\pi\)
\(240\) 0.586380 2.15781i 0.0378507 0.139286i
\(241\) −5.75647 + 5.75647i −0.370807 + 0.370807i −0.867771 0.496964i \(-0.834448\pi\)
0.496964 + 0.867771i \(0.334448\pi\)
\(242\) −5.85354 −0.376279
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) −2.06460 2.06460i −0.132172 0.132172i
\(245\) 6.87870 + 12.0123i 0.439464 + 0.767436i
\(246\) −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
\(253\) 19.3608i 1.21720i
\(254\) −0.916380 + 0.916380i −0.0574988 + 0.0574988i
\(255\) 12.4009 + 3.36992i 0.776577 + 0.211033i
\(256\) 1.00000 0.0625000
\(257\) 1.80027i 0.112298i −0.998422 0.0561488i \(-0.982118\pi\)
0.998422 0.0561488i \(-0.0178821\pi\)
\(258\) −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 \(-0.617720\pi\)
0.932389 + 0.361456i \(0.117720\pi\)
\(264\) −1.60413 1.60413i −0.0987274 0.0987274i
\(265\) −20.7468 5.63789i −1.27447 0.346333i
\(266\) −5.21895 −0.319994
\(267\) 8.94323i 0.547317i
\(268\) −3.98347 3.98347i −0.243329 0.243329i
\(269\) 0.689017i 0.0420101i −0.999779 0.0210051i \(-0.993313\pi\)
0.999779 0.0210051i \(-0.00668661\pi\)
\(270\) 2.15781 + 0.586380i 0.131320 + 0.0356859i
\(271\) −14.7629 −0.896783 −0.448392 0.893837i \(-0.648003\pi\)
−0.448392 + 0.893837i \(0.648003\pi\)
\(272\) 5.74699i 0.348462i
\(273\) 1.16197i 0.0703255i
\(274\) −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
\(277\) −32.3771 −1.94535 −0.972675 0.232172i \(-0.925417\pi\)
−0.972675 + 0.232172i \(0.925417\pi\)
\(278\) −14.4443 −0.866310
\(279\) −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 \(0.172054\pi\)
\(282\) 0.462042i 0.0275142i
\(283\) 6.56809i 0.390433i 0.980760 + 0.195216i \(0.0625409\pi\)
−0.980760 + 0.195216i \(0.937459\pi\)
\(284\) −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
\(288\) 1.00000i 0.0589256i
\(289\) −16.0279 −0.942818
\(290\) −1.41104 + 5.19246i −0.0828589 + 0.304912i
\(291\) −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 −0.936991 0.349353i \(-0.886401\pi\)
−0.349353 0.936991i \(-0.613599\pi\)
\(294\) −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
\(298\) 19.0997i 1.10642i
\(299\) 11.0218 0.637408
\(300\) −1.25987 4.83867i −0.0727385 0.279361i
\(301\) 0.542735 0.542735i 0.0312827 0.0312827i
\(302\) 3.42513i 0.197094i
\(303\) 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 \(-0.315156\pi\)
−0.836077 + 0.548613i \(0.815156\pi\)
\(308\) 1.44327 + 1.44327i 0.0822382 + 0.0822382i
\(309\) 0.728096 + 0.728096i 0.0414199 + 0.0414199i
\(310\) 17.7346 + 4.81932i 1.00726 + 0.273719i
\(311\) 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
\(313\) 19.5460 1.10481 0.552404 0.833577i \(-0.313711\pi\)
0.552404 + 0.833577i \(0.313711\pi\)
\(314\) −12.1068 + 12.1068i −0.683229 + 0.683229i
\(315\) −1.94144 0.527580i −0.109388 0.0297258i
\(316\) −9.04382 9.04382i −0.508755 0.508755i
\(317\) −5.03252 5.03252i −0.282655 0.282655i 0.551512 0.834167i \(-0.314051\pi\)
−0.834167 + 0.551512i \(0.814051\pi\)
\(318\) 9.61473 0.539168
\(319\) 3.86010 + 3.86010i 0.216124 + 0.216124i
\(320\) 1.94044 1.11117i 0.108474 0.0621164i
\(321\) 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
\(325\) 3.26819 5.56924i 0.181287 0.308926i
\(326\) 24.2268i 1.34180i
\(327\) −7.53328 −0.416591
\(328\) 9.02011i 0.498052i
\(329\) 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
\(333\) −5.19618 3.16223i −0.284749 0.173289i
\(334\) 9.66372i 0.528775i
\(335\) −12.1560 3.30336i −0.664154 0.180482i
\(336\) 0.899724i 0.0490840i
\(337\) −15.5648 15.5648i −0.847866 0.847866i 0.142000 0.989867i \(-0.454647\pi\)
−0.989867 + 0.142000i \(0.954647\pi\)
\(338\) 11.3321 0.616385
\(339\) 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
\(347\) −19.7799 −1.06184 −0.530920 0.847422i \(-0.678154\pi\)
−0.530920 + 0.847422i \(0.678154\pi\)
\(348\) 2.40635i 0.128994i
\(349\) 5.47518i 0.293080i −0.989205 0.146540i \(-0.953186\pi\)
0.989205 0.146540i \(-0.0468137\pi\)
\(350\) 1.13353 + 4.35347i 0.0605899 + 0.232703i
\(351\) −0.913209 0.913209i −0.0487435 0.0487435i
\(352\) 2.26858i 0.120916i
\(353\) 28.1816i 1.49995i 0.661465 + 0.749976i \(0.269935\pi\)
−0.661465 + 0.749976i \(0.730065\pi\)
\(354\) 4.96631 0.263956
\(355\) −29.6678 + 16.9889i −1.57460 + 0.901679i
\(356\) 6.32382 6.32382i 0.335162 0.335162i
\(357\) 5.17071 0.273663
\(358\) 7.36463 7.36463i 0.389233 0.389233i
\(359\) 2.05043i 0.108218i −0.998535 0.0541089i \(-0.982768\pi\)
0.998535 0.0541089i \(-0.0172318\pi\)
\(360\) 1.11117 + 1.94044i 0.0585639 + 0.102270i
\(361\) 14.6470i 0.770896i
\(362\) 13.9651 0.733988
\(363\) 4.13907 4.13907i 0.217245 0.217245i
\(364\) 0.821636 0.821636i 0.0430654 0.0430654i
\(365\) 9.81208 36.1074i 0.513588 1.88995i
\(366\) 2.91979 0.152620
\(367\) −8.13886 + 8.13886i −0.424845 + 0.424845i −0.886868 0.462023i \(-0.847124\pi\)
0.462023 + 0.886868i \(0.347124\pi\)
\(368\) 8.53431 0.444882
\(369\) 9.02011 0.469568
\(370\) −0.362266 + 13.5966i −0.0188333 + 0.706856i
\(371\) −8.65061 −0.449117
\(372\) −8.21877 −0.426124
\(373\) 9.78820 9.78820i 0.506814 0.506814i −0.406733 0.913547i \(-0.633332\pi\)
0.913547 + 0.406733i \(0.133332\pi\)
\(374\) 13.0375 0.674154
\(375\) −7.82129 7.98921i −0.403889 0.412561i
\(376\) 0.326713 0.326713i 0.0168489 0.0168489i
\(377\) 2.19750 2.19750i 0.113177 0.113177i
\(378\) 0.899724 0.0462768
\(379\) 22.6146i 1.16164i 0.814034 + 0.580818i \(0.197267\pi\)
−0.814034 + 0.580818i \(0.802733\pi\)
\(380\) 12.5166 + 3.40136i 0.642089 + 0.174486i
\(381\) 1.29596i 0.0663939i
\(382\) 11.6459 11.6459i 0.595854 0.595854i
\(383\) −9.52538 −0.486724 −0.243362 0.969936i \(-0.578250\pi\)
−0.243362 + 0.969936i \(0.578250\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) 4.40431 + 1.19686i 0.224464 + 0.0609976i
\(386\) 2.80664 0.142854
\(387\) 0.853087i 0.0433648i
\(388\) 9.28197i 0.471220i
\(389\) −7.75553 7.75553i −0.393221 0.393221i 0.482613 0.875834i \(-0.339688\pi\)
−0.875834 + 0.482613i \(0.839688\pi\)
\(390\) −0.757293 + 2.78676i −0.0383470 + 0.141113i
\(391\) 49.0466i 2.48039i
\(392\) 6.19050i 0.312667i
\(393\) −8.89460 −0.448673
\(394\) −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 \(-0.0194794\pi\)
−0.0611581 + 0.998128i \(0.519479\pi\)
\(398\) 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 \(0.586548\pi\)
\(402\) 5.63348 0.280973
\(403\) −7.50545 7.50545i −0.373873 0.373873i
\(404\) 1.47408i 0.0733383i
\(405\) −1.94044 + 1.11117i −0.0964211 + 0.0552146i
\(406\) 2.16505i 0.107450i
\(407\) 11.7880 + 7.17378i 0.584308 + 0.355591i
\(408\) −4.06374 4.06374i −0.201185 0.201185i
\(409\) 7.16339 7.16339i 0.354207 0.354207i −0.507465 0.861672i \(-0.669418\pi\)
0.861672 + 0.507465i \(0.169418\pi\)
\(410\) −10.0229 17.5030i −0.494995 0.864409i
\(411\) 14.7818i 0.729134i
\(412\) 1.02968i 0.0507289i
\(413\) −4.46831 −0.219871
\(414\) 8.53431i 0.419438i
\(415\) 27.8417 + 7.56591i 1.36670 + 0.371396i
\(416\) −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 \(-0.802002\pi\)
0.812698 0.582686i \(-0.197998\pi\)
\(420\) −0.999748 1.74586i −0.0487827 0.0851892i
\(421\) −12.3787 12.3787i −0.603301 0.603301i 0.337886 0.941187i \(-0.390288\pi\)
−0.941187 + 0.337886i \(0.890288\pi\)
\(422\) 3.80993 0.185464
\(423\) 0.326713 + 0.326713i 0.0158853 + 0.0158853i
\(424\) 6.79864 + 6.79864i 0.330171 + 0.330171i
\(425\) 24.7828 + 14.5433i 1.20214 + 0.705454i
\(426\) 10.8111 10.8111i 0.523800 0.523800i
\(427\) −2.62700 −0.127130
\(428\) −13.8598 + 13.8598i −0.669940 + 0.669940i
\(429\) 2.07169 + 2.07169i 0.100022 + 0.100022i
\(430\) −1.65536 + 0.947925i −0.0798286 + 0.0457130i
\(431\) 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 0.807563 0.589781i \(-0.200786\pi\)
−0.589781 + 0.807563i \(0.700786\pi\)
\(434\) 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
\(438\) 16.7333i 0.799549i
\(439\) −22.7618 + 22.7618i −1.08636 + 1.08636i −0.0904591 + 0.995900i \(0.528833\pi\)
−0.995900 + 0.0904591i \(0.971167\pi\)
\(440\) −2.52078 4.40204i −0.120174 0.209859i
\(441\) 6.19050 0.294786
\(442\) 7.42208i 0.353032i
\(443\) 18.5368 18.5368i 0.880708 0.880708i −0.112899 0.993606i \(-0.536014\pi\)
0.993606 + 0.112899i \(0.0360136\pi\)
\(444\) −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 0.431841 0.901950i \(-0.357864\pi\)
−0.901950 + 0.431841i \(0.857864\pi\)
\(450\) 4.31232 + 2.53060i 0.203285 + 0.119293i
\(451\) −20.4629 −0.963558
\(452\) 17.2755i 0.812573i
\(453\) −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
\(457\) 6.81678i 0.318876i 0.987208 + 0.159438i \(0.0509681\pi\)
−0.987208 + 0.159438i \(0.949032\pi\)
\(458\) 11.3572i 0.530686i
\(459\) 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 \(-0.0526389\pi\)
\(462\) −2.04110 −0.0949605
\(463\) −32.0736 −1.49059 −0.745293 0.666737i \(-0.767690\pi\)
−0.745293 + 0.666737i \(0.767690\pi\)
\(464\) 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
\(467\) 13.7531i 0.636416i −0.948021 0.318208i \(-0.896919\pi\)
0.948021 0.318208i \(-0.103081\pi\)
\(468\) 1.29147i 0.0596983i
\(469\) −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
\(473\) 1.93530i 0.0889851i
\(474\) 12.7899 0.587459
\(475\) 28.0672 7.30799i 1.28781 0.335314i
\(476\) 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 0.241404 0.970425i \(-0.422392\pi\)
−0.970425 + 0.241404i \(0.922392\pi\)
\(480\) −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
\(483\) 7.67852i 0.349385i
\(484\) 5.85354 0.266070
\(485\) −10.3139 18.0111i −0.468328 0.817841i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) 22.5078i 1.01992i −0.860197 0.509962i \(-0.829659\pi\)
0.860197 0.509962i \(-0.170341\pi\)
\(488\) 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
\(495\) 4.40204 2.52078i 0.197857 0.113301i
\(496\) −5.81155 5.81155i −0.260946 0.260946i
\(497\) −9.72702 + 9.72702i −0.436316 + 0.436316i
\(498\) −12.9027 −0.578186
\(499\) −5.68409 + 5.68409i −0.254455 + 0.254455i −0.822794 0.568339i \(-0.807586\pi\)
0.568339 + 0.822794i \(0.307586\pi\)
\(500\) 0.118740 11.1797i 0.00531022 0.499972i
\(501\) −6.83328 6.83328i −0.305288 0.305288i
\(502\) 14.7749 + 14.7749i 0.659437 + 0.659437i
\(503\) 3.69027 0.164541 0.0822705 0.996610i \(-0.473783\pi\)
0.0822705 + 0.996610i \(0.473783\pi\)
\(504\) 0.636201 + 0.636201i 0.0283386 + 0.0283386i
\(505\) 1.63796 + 2.86036i 0.0728882 + 0.127285i
\(506\) 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 \(-0.541874\pi\)
−0.131172 + 0.991360i \(0.541874\pi\)
\(510\) −12.4009 3.36992i −0.549123 0.149223i
\(511\) 15.0554i 0.666010i
\(512\) −1.00000 −0.0441942
\(513\) 5.80061i 0.256103i
\(514\) 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
\(518\) 1.29400 + 5.31763i 0.0568551 + 0.233643i
\(519\) 9.58209i 0.420607i
\(520\) −2.50602 + 1.43505i −0.109896 + 0.0629310i
\(521\) 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
\(523\) −17.1466 −0.749767 −0.374883 0.927072i \(-0.622317\pi\)
−0.374883 + 0.927072i \(0.622317\pi\)
\(524\) −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
\(532\) 5.21895 0.226270
\(533\) 11.6492i 0.504583i
\(534\) 8.94323i 0.387011i
\(535\) −11.4935 + 42.2948i −0.496907 + 1.82856i
\(536\) 3.98347 + 3.98347i 0.172060 + 0.172060i
\(537\) 10.4152i 0.449447i
\(538\) 0.689017i 0.0297056i
\(539\) −14.0436 −0.604903
\(540\) −2.15781 0.586380i −0.0928575 0.0252338i
\(541\) −11.6362 + 11.6362i −0.500279 + 0.500279i −0.911525 0.411245i \(-0.865094\pi\)
0.411245 + 0.911525i \(0.365094\pi\)
\(542\) 14.7629 0.634122
\(543\) −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
\(547\) 37.0105 1.58245 0.791226 0.611523i \(-0.209443\pi\)
0.791226 + 0.611523i \(0.209443\pi\)
\(548\) 10.4523 10.4523i 0.446502 0.446502i
\(549\) −2.06460 + 2.06460i −0.0881150 + 0.0881150i
\(550\) −9.78285 5.74087i −0.417142 0.244791i
\(551\) 13.9583 0.594643
\(552\) −6.03467 + 6.03467i −0.256853 + 0.256853i
\(553\) −11.5074 −0.489343
\(554\) 32.3771 1.37557
\(555\) −9.35812 9.87044i −0.397230 0.418977i
\(556\) 14.4443 0.612574
\(557\) −5.02764 −0.213028 −0.106514 0.994311i \(-0.533969\pi\)
−0.106514 + 0.994311i \(0.533969\pi\)
\(558\) 5.81155 5.81155i 0.246023 0.246023i
\(559\) 1.10174 0.0465985
\(560\) 0.527580 1.94144i 0.0222943 0.0820407i
\(561\) −9.21892 + 9.21892i −0.389223 + 0.389223i
\(562\) −5.74725 + 5.74725i −0.242433 + 0.242433i
\(563\) −14.7235 −0.620522 −0.310261 0.950651i \(-0.600416\pi\)
−0.310261 + 0.950651i \(0.600416\pi\)
\(564\) 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
\(568\) 15.2892 0.641521
\(569\) 15.1302 15.1302i 0.634291 0.634291i −0.314850 0.949141i \(-0.601954\pi\)
0.949141 + 0.314850i \(0.101954\pi\)
\(570\) −11.2557 + 6.44547i −0.471450 + 0.269971i
\(571\) −0.732604 −0.0306585 −0.0153293 0.999882i \(-0.504880\pi\)
−0.0153293 + 0.999882i \(0.504880\pi\)
\(572\) 2.92981i 0.122502i
\(573\) 16.4697i 0.688033i
\(574\) −5.73860 5.73860i −0.239525 0.239525i
\(575\) 21.5969 36.8026i 0.900653 1.53478i
\(576\) 1.00000i 0.0416667i
\(577\) 13.0938i 0.545102i −0.962141 0.272551i \(-0.912133\pi\)
0.962141 0.272551i \(-0.0878673\pi\)
\(578\) 16.0279 0.666673
\(579\) −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
\(587\) −25.6946 −1.06053 −0.530265 0.847832i \(-0.677908\pi\)
−0.530265 + 0.847832i \(0.677908\pi\)
\(588\) 4.37734 + 4.37734i 0.180519 + 0.180519i
\(589\) 47.6739i 1.96437i
\(590\) 10.7164 + 2.91214i 0.441186 + 0.119891i
\(591\) 16.2893i 0.670052i
\(592\) 3.16223 5.19618i 0.129967 0.213562i
\(593\) −32.7884 32.7884i −1.34646 1.34646i −0.889474 0.456986i \(-0.848929\pi\)
−0.456986 0.889474i \(-0.651071\pi\)
\(594\) −1.60413 + 1.60413i −0.0658182 + 0.0658182i
\(595\) 11.1574 + 3.03200i 0.457410 + 0.124300i
\(596\) 19.0997i 0.782356i
\(597\) 14.6329i 0.598885i
\(598\) −11.0218 −0.450716
\(599\) 32.7946i 1.33995i 0.742383 + 0.669975i \(0.233695\pi\)
−0.742383 + 0.669975i \(0.766305\pi\)
\(600\) 1.25987 + 4.83867i 0.0514339 + 0.197538i
\(601\) 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
\(605\) 11.3584 6.50428i 0.461785 0.264437i
\(606\) −1.04233 1.04233i −0.0423419 0.0423419i
\(607\) −26.7432 −1.08547 −0.542737 0.839903i \(-0.682612\pi\)
−0.542737 + 0.839903i \(0.682612\pi\)
\(608\) −4.10165 4.10165i −0.166344 0.166344i
\(609\) −1.53092 1.53092i −0.0620362 0.0620362i
\(610\) 6.30035 + 1.71210i 0.255094 + 0.0693210i
\(611\) −0.421941 + 0.421941i −0.0170699 + 0.0170699i
\(612\) 5.74699 0.232308
\(613\) 23.6704 23.6704i 0.956040 0.956040i −0.0430339 0.999074i \(-0.513702\pi\)
0.999074 + 0.0430339i \(0.0137024\pi\)
\(614\) 5.03677 + 5.03677i 0.203268 + 0.203268i
\(615\) 19.4637 + 5.28921i 0.784852 + 0.213281i
\(616\) −1.44327 1.44327i −0.0581512 0.0581512i
\(617\) −3.77510 3.77510i −0.151980 0.151980i 0.627022 0.779002i \(-0.284274\pi\)
−0.779002 + 0.627022i \(0.784274\pi\)
\(618\) −0.728096 0.728096i −0.0292883 0.0292883i
\(619\) −9.65130 −0.387918 −0.193959 0.981010i \(-0.562133\pi\)
−0.193959 + 0.981010i \(0.562133\pi\)
\(620\) −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
\(623\) 8.04644i 0.322374i
\(624\) 0.913209 0.913209i 0.0365576 0.0365576i
\(625\) −12.1922 21.8255i −0.487687 0.873019i
\(626\) −19.5460 −0.781217
\(627\) 13.1592i 0.525526i
\(628\) 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
\(635\) 0.759923 2.79643i 0.0301566 0.110973i
\(636\) −9.61473 −0.381249
\(637\) 7.99485i 0.316768i
\(638\) −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 \(0.549293\pi\)
\(642\) 19.6007i 0.773580i
\(643\) 39.3070i 1.55012i −0.631890 0.775058i \(-0.717721\pi\)
0.631890 0.775058i \(-0.282279\pi\)
\(644\) 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
\(647\) −31.8619 −1.25262 −0.626311 0.779573i \(-0.715436\pi\)
−0.626311 + 0.779573i \(0.715436\pi\)
\(648\) 1.00000 0.0392837
\(649\) 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
\(652\) 24.2268i 0.948795i
\(653\) 40.2027i 1.57325i 0.617430 + 0.786626i \(0.288174\pi\)
−0.617430 + 0.786626i \(0.711826\pi\)
\(654\) 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
\(658\) 0.415710i 0.0162061i
\(659\) 22.6033 0.880499 0.440250 0.897875i \(-0.354890\pi\)
0.440250 + 0.897875i \(0.354890\pi\)
\(660\) 4.89518 + 1.33025i 0.190545 + 0.0517799i
\(661\) 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
\(668\) 9.66372i 0.373900i
\(669\) 23.8893 0.923612
\(670\) 12.1560 + 3.30336i 0.469628 + 0.127620i
\(671\) 4.68371 4.68371i 0.180813 0.180813i
\(672\) 0.899724i 0.0347076i
\(673\) 23.9631 + 23.9631i 0.923709 + 0.923709i 0.997289 0.0735806i \(-0.0234426\pi\)
−0.0735806 + 0.997289i \(0.523443\pi\)
\(674\) 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 \(-0.0838776\pi\)
−0.260470 + 0.965482i \(0.583878\pi\)
\(678\) −12.2157 12.2157i −0.469139 0.469139i
\(679\) −5.90520 5.90520i −0.226621 0.226621i
\(680\) −6.38589 11.1517i −0.244888 0.427647i
\(681\) 17.6798 + 17.6798i 0.677490 + 0.677490i
\(682\) −13.1840 + 13.1840i −0.504841 + 0.504841i
\(683\) 2.79715 0.107030 0.0535149 0.998567i \(-0.482958\pi\)
0.0535149 + 0.998567i \(0.482958\pi\)
\(684\) 4.10165 4.10165i 0.156830 0.156830i
\(685\) 8.66777 31.8965i 0.331179 1.21870i
\(686\) −8.39181 8.39181i −0.320401 0.320401i
\(687\) 8.03073 + 8.03073i 0.306392 + 0.306392i
\(688\) 0.853087 0.0325236
\(689\) −8.78026 8.78026i −0.334501 0.334501i
\(690\) −5.00435 + 18.4154i −0.190512 + 0.701064i
\(691\) 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
\(695\) 28.0282 16.0501i 1.06317 0.608813i
\(696\) 2.40635i 0.0912125i
\(697\) −51.8385 −1.96352
\(698\) 5.47518i 0.207239i
\(699\) 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
\(703\) 34.2833 8.34254i 1.29302 0.314645i
\(704\) 2.26858i 0.0855004i
\(705\) 0.513408 + 0.896564i 0.0193361 + 0.0337665i
\(706\) 28.1816i 1.06063i
\(707\) 0.937812 + 0.937812i 0.0352701 + 0.0352701i
\(708\) −4.96631 −0.186645
\(709\) 6.08101 + 6.08101i 0.228377 + 0.228377i 0.812014 0.583637i \(-0.198371\pi\)
−0.583637 + 0.812014i \(0.698371\pi\)
\(710\) 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
\(717\) 4.19821 0.156785
\(718\) 2.05043i 0.0765215i
\(719\) 37.1763i 1.38644i −0.720724 0.693222i \(-0.756191\pi\)
0.720724 0.693222i \(-0.243809\pi\)
\(720\) −1.11117 1.94044i −0.0414109 0.0723158i
\(721\) 0.655086 + 0.655086i 0.0243967 + 0.0243967i
\(722\) 14.6470i 0.545106i
\(723\) 8.14088i 0.302762i
\(724\) −13.9651 −0.519008
\(725\) −3.03168 11.6435i −0.112594 0.432430i
\(726\) −4.13907 + 4.13907i −0.153615 + 0.153615i
\(727\) −10.8041 −0.400701 −0.200350 0.979724i \(-0.564208\pi\)
−0.200350 + 0.979724i \(0.564208\pi\)
\(728\) −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
\(732\) −2.91979 −0.107918
\(733\) 2.31409 2.31409i 0.0854728 0.0854728i −0.663078 0.748551i \(-0.730750\pi\)
0.748551 + 0.663078i \(0.230750\pi\)
\(734\) 8.13886 8.13886i 0.300411 0.300411i
\(735\) 13.3579 + 3.62998i 0.492715 + 0.133894i
\(736\) −8.53431 −0.314579
\(737\) 9.03684 9.03684i 0.332876 0.332876i
\(738\) −9.02011 −0.332035
\(739\) 3.59606 0.132283 0.0661416 0.997810i \(-0.478931\pi\)
0.0661416 + 0.997810i \(0.478931\pi\)
\(740\) 0.362266 13.5966i 0.0133172 0.499823i
\(741\) 7.49132 0.275201
\(742\) 8.65061 0.317574
\(743\) −7.78930 + 7.78930i −0.285762 + 0.285762i −0.835402 0.549640i \(-0.814765\pi\)
0.549640 + 0.835402i \(0.314765\pi\)
\(744\) 8.21877 0.301315
\(745\) 21.2231 + 37.0619i 0.777554 + 1.35784i
\(746\) −9.78820 + 9.78820i −0.358371 + 0.358371i
\(747\) 9.12362 9.12362i 0.333816 0.333816i
\(748\) −13.0375 −0.476699
\(749\) 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
\(753\) −20.8949 −0.761452
\(754\) −2.19750 + 2.19750i −0.0800283 + 0.0800283i
\(755\) −3.80591 6.64625i −0.138511 0.241882i
\(756\) −0.899724 −0.0327227
\(757\) 2.85691i 0.103836i −0.998651 0.0519182i \(-0.983467\pi\)
0.998651 0.0519182i \(-0.0165335\pi\)
\(758\) 22.6146i 0.821400i
\(759\) 13.6901 + 13.6901i 0.496921 + 0.496921i
\(760\) −12.5166 3.40136i −0.454026 0.123380i
\(761\) 3.11943i 0.113079i −0.998400 0.0565396i \(-0.981993\pi\)
0.998400 0.0565396i \(-0.0180067\pi\)
\(762\) 1.29596i 0.0469476i
\(763\) −6.77787 −0.245376
\(764\) −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 −0.984326 0.176360i \(-0.943568\pi\)
0.176360 + 0.984326i \(0.443568\pi\)
\(770\) −4.40431 1.19686i −0.158720 0.0431318i
\(771\) −1.27298 1.27298i −0.0458453 0.0458453i
\(772\) −2.80664 −0.101013
\(773\) −1.90608 1.90608i −0.0685571 0.0685571i 0.671997 0.740554i \(-0.265437\pi\)
−0.740554 + 0.671997i \(0.765437\pi\)
\(774\) 0.853087i 0.0306636i
\(775\) −39.7679 + 10.3546i −1.42851 + 0.371947i
\(776\) 9.28197i 0.333203i
\(777\) −4.67513 2.84514i −0.167719 0.102069i
\(778\) 7.75553 + 7.75553i 0.278049 + 0.278049i
\(779\) −36.9973 + 36.9973i −1.32557 + 1.32557i
\