Properties

Label 1110.2.o.a.253.10
Level $1110$
Weight $2$
Character 1110.253
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.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 253.10
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.10

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(1.91070 + 1.16157i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.90687 - 2.90687i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(1.91070 + 1.16157i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.90687 - 2.90687i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-1.91070 - 1.16157i) q^{10} +2.74715i q^{11} +(0.707107 - 0.707107i) q^{12} +5.21529 q^{13} +(-2.90687 + 2.90687i) q^{14} +(2.17242 - 0.529716i) q^{15} +1.00000 q^{16} -4.16103i q^{17} +1.00000i q^{18} +(-1.87829 - 1.87829i) q^{19} +(1.91070 + 1.16157i) q^{20} -4.11094i q^{21} -2.74715i q^{22} -0.941868 q^{23} +(-0.707107 + 0.707107i) q^{24} +(2.30153 + 4.43880i) q^{25} -5.21529 q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.90687 - 2.90687i) q^{28} +(-4.28806 + 4.28806i) q^{29} +(-2.17242 + 0.529716i) q^{30} +(5.51242 + 5.51242i) q^{31} -1.00000 q^{32} +(1.94253 + 1.94253i) q^{33} +4.16103i q^{34} +(8.93067 - 2.17763i) q^{35} -1.00000i q^{36} +(-2.77109 - 5.41489i) q^{37} +(1.87829 + 1.87829i) q^{38} +(3.68777 - 3.68777i) q^{39} +(-1.91070 - 1.16157i) q^{40} -7.59421i q^{41} +4.11094i q^{42} -6.23482 q^{43} +2.74715i q^{44} +(1.16157 - 1.91070i) q^{45} +0.941868 q^{46} +(-6.04950 + 6.04950i) q^{47} +(0.707107 - 0.707107i) q^{48} -9.89979i q^{49} +(-2.30153 - 4.43880i) q^{50} +(-2.94229 - 2.94229i) q^{51} +5.21529 q^{52} +(8.31822 + 8.31822i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-3.19100 + 5.24898i) q^{55} +(-2.90687 + 2.90687i) q^{56} -2.65630 q^{57} +(4.28806 - 4.28806i) q^{58} +(1.92935 + 1.92935i) q^{59} +(2.17242 - 0.529716i) q^{60} +(-8.68618 - 8.68618i) q^{61} +(-5.51242 - 5.51242i) q^{62} +(-2.90687 - 2.90687i) q^{63} +1.00000 q^{64} +(9.96485 + 6.05791i) q^{65} +(-1.94253 - 1.94253i) q^{66} +(5.51165 + 5.51165i) q^{67} -4.16103i q^{68} +(-0.666001 + 0.666001i) q^{69} +(-8.93067 + 2.17763i) q^{70} -8.51973 q^{71} +1.00000i q^{72} +(-2.98121 + 2.98121i) q^{73} +(2.77109 + 5.41489i) q^{74} +(4.76613 + 1.51128i) q^{75} +(-1.87829 - 1.87829i) q^{76} +(7.98561 + 7.98561i) q^{77} +(-3.68777 + 3.68777i) q^{78} +(1.46581 + 1.46581i) q^{79} +(1.91070 + 1.16157i) q^{80} -1.00000 q^{81} +7.59421i q^{82} +(7.26193 + 7.26193i) q^{83} -4.11094i q^{84} +(4.83331 - 7.95047i) q^{85} +6.23482 q^{86} +6.06423i q^{87} -2.74715i q^{88} +(-1.62770 + 1.62770i) q^{89} +(-1.16157 + 1.91070i) q^{90} +(15.1602 - 15.1602i) q^{91} -0.941868 q^{92} +7.79574 q^{93} +(6.04950 - 6.04950i) q^{94} +(-1.40708 - 5.77059i) q^{95} +(-0.707107 + 0.707107i) q^{96} -10.0910i q^{97} +9.89979i q^{98} +2.74715 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
\(5\) 1.91070 + 1.16157i 0.854490 + 0.519468i
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) 2.90687 2.90687i 1.09869 1.09869i 0.104130 0.994564i \(-0.466794\pi\)
0.994564 0.104130i \(-0.0332058\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000i 0.333333i
\(10\) −1.91070 1.16157i −0.604216 0.367319i
\(11\) 2.74715i 0.828297i 0.910209 + 0.414149i \(0.135921\pi\)
−0.910209 + 0.414149i \(0.864079\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) 5.21529 1.44646 0.723231 0.690606i \(-0.242656\pi\)
0.723231 + 0.690606i \(0.242656\pi\)
\(14\) −2.90687 + 2.90687i −0.776894 + 0.776894i
\(15\) 2.17242 0.529716i 0.560916 0.136772i
\(16\) 1.00000 0.250000
\(17\) 4.16103i 1.00920i −0.863354 0.504599i \(-0.831640\pi\)
0.863354 0.504599i \(-0.168360\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.87829 1.87829i −0.430909 0.430909i 0.458029 0.888937i \(-0.348556\pi\)
−0.888937 + 0.458029i \(0.848556\pi\)
\(20\) 1.91070 + 1.16157i 0.427245 + 0.259734i
\(21\) 4.11094i 0.897080i
\(22\) 2.74715i 0.585695i
\(23\) −0.941868 −0.196393 −0.0981965 0.995167i \(-0.531307\pi\)
−0.0981965 + 0.995167i \(0.531307\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) 2.30153 + 4.43880i 0.460306 + 0.887760i
\(26\) −5.21529 −1.02280
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 2.90687 2.90687i 0.549347 0.549347i
\(29\) −4.28806 + 4.28806i −0.796273 + 0.796273i −0.982506 0.186233i \(-0.940372\pi\)
0.186233 + 0.982506i \(0.440372\pi\)
\(30\) −2.17242 + 0.529716i −0.396627 + 0.0967125i
\(31\) 5.51242 + 5.51242i 0.990060 + 0.990060i 0.999951 0.00989083i \(-0.00314840\pi\)
−0.00989083 + 0.999951i \(0.503148\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.94253 + 1.94253i 0.338151 + 0.338151i
\(34\) 4.16103i 0.713611i
\(35\) 8.93067 2.17763i 1.50956 0.368086i
\(36\) 1.00000i 0.166667i
\(37\) −2.77109 5.41489i −0.455565 0.890202i
\(38\) 1.87829 + 1.87829i 0.304699 + 0.304699i
\(39\) 3.68777 3.68777i 0.590516 0.590516i
\(40\) −1.91070 1.16157i −0.302108 0.183660i
\(41\) 7.59421i 1.18602i −0.805196 0.593008i \(-0.797940\pi\)
0.805196 0.593008i \(-0.202060\pi\)
\(42\) 4.11094i 0.634331i
\(43\) −6.23482 −0.950802 −0.475401 0.879769i \(-0.657697\pi\)
−0.475401 + 0.879769i \(0.657697\pi\)
\(44\) 2.74715i 0.414149i
\(45\) 1.16157 1.91070i 0.173156 0.284830i
\(46\) 0.941868 0.138871
\(47\) −6.04950 + 6.04950i −0.882410 + 0.882410i −0.993779 0.111369i \(-0.964477\pi\)
0.111369 + 0.993779i \(0.464477\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 9.89979i 1.41426i
\(50\) −2.30153 4.43880i −0.325485 0.627741i
\(51\) −2.94229 2.94229i −0.412004 0.412004i
\(52\) 5.21529 0.723231
\(53\) 8.31822 + 8.31822i 1.14259 + 1.14259i 0.987974 + 0.154621i \(0.0494156\pi\)
0.154621 + 0.987974i \(0.450584\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) −3.19100 + 5.24898i −0.430274 + 0.707772i
\(56\) −2.90687 + 2.90687i −0.388447 + 0.388447i
\(57\) −2.65630 −0.351836
\(58\) 4.28806 4.28806i 0.563050 0.563050i
\(59\) 1.92935 + 1.92935i 0.251180 + 0.251180i 0.821454 0.570274i \(-0.193163\pi\)
−0.570274 + 0.821454i \(0.693163\pi\)
\(60\) 2.17242 0.529716i 0.280458 0.0683860i
\(61\) −8.68618 8.68618i −1.11215 1.11215i −0.992859 0.119292i \(-0.961937\pi\)
−0.119292 0.992859i \(-0.538063\pi\)
\(62\) −5.51242 5.51242i −0.700078 0.700078i
\(63\) −2.90687 2.90687i −0.366231 0.366231i
\(64\) 1.00000 0.125000
\(65\) 9.96485 + 6.05791i 1.23599 + 0.751391i
\(66\) −1.94253 1.94253i −0.239109 0.239109i
\(67\) 5.51165 + 5.51165i 0.673355 + 0.673355i 0.958488 0.285133i \(-0.0920377\pi\)
−0.285133 + 0.958488i \(0.592038\pi\)
\(68\) 4.16103i 0.504599i
\(69\) −0.666001 + 0.666001i −0.0801771 + 0.0801771i
\(70\) −8.93067 + 2.17763i −1.06742 + 0.260276i
\(71\) −8.51973 −1.01111 −0.505553 0.862796i \(-0.668711\pi\)
−0.505553 + 0.862796i \(0.668711\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −2.98121 + 2.98121i −0.348924 + 0.348924i −0.859709 0.510785i \(-0.829355\pi\)
0.510785 + 0.859709i \(0.329355\pi\)
\(74\) 2.77109 + 5.41489i 0.322133 + 0.629468i
\(75\) 4.76613 + 1.51128i 0.550346 + 0.174508i
\(76\) −1.87829 1.87829i −0.215454 0.215454i
\(77\) 7.98561 + 7.98561i 0.910045 + 0.910045i
\(78\) −3.68777 + 3.68777i −0.417558 + 0.417558i
\(79\) 1.46581 + 1.46581i 0.164916 + 0.164916i 0.784741 0.619824i \(-0.212796\pi\)
−0.619824 + 0.784741i \(0.712796\pi\)
\(80\) 1.91070 + 1.16157i 0.213622 + 0.129867i
\(81\) −1.00000 −0.111111
\(82\) 7.59421i 0.838640i
\(83\) 7.26193 + 7.26193i 0.797101 + 0.797101i 0.982637 0.185536i \(-0.0594023\pi\)
−0.185536 + 0.982637i \(0.559402\pi\)
\(84\) 4.11094i 0.448540i
\(85\) 4.83331 7.95047i 0.524246 0.862350i
\(86\) 6.23482 0.672318
\(87\) 6.06423i 0.650154i
\(88\) 2.74715i 0.292847i
\(89\) −1.62770 + 1.62770i −0.172535 + 0.172535i −0.788092 0.615557i \(-0.788931\pi\)
0.615557 + 0.788092i \(0.288931\pi\)
\(90\) −1.16157 + 1.91070i −0.122440 + 0.201405i
\(91\) 15.1602 15.1602i 1.58922 1.58922i
\(92\) −0.941868 −0.0981965
\(93\) 7.79574 0.808381
\(94\) 6.04950 6.04950i 0.623958 0.623958i
\(95\) −1.40708 5.77059i −0.144364 0.592051i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) 10.0910i 1.02459i −0.858810 0.512294i \(-0.828796\pi\)
0.858810 0.512294i \(-0.171204\pi\)
\(98\) 9.89979i 1.00003i
\(99\) 2.74715 0.276099
\(100\) 2.30153 + 4.43880i 0.230153 + 0.443880i
\(101\) 9.40183i 0.935517i −0.883856 0.467759i \(-0.845062\pi\)
0.883856 0.467759i \(-0.154938\pi\)
\(102\) 2.94229 + 2.94229i 0.291330 + 0.291330i
\(103\) 7.77490i 0.766084i 0.923731 + 0.383042i \(0.125123\pi\)
−0.923731 + 0.383042i \(0.874877\pi\)
\(104\) −5.21529 −0.511402
\(105\) 4.77512 7.85475i 0.466004 0.766546i
\(106\) −8.31822 8.31822i −0.807937 0.807937i
\(107\) 5.67037 5.67037i 0.548176 0.548176i −0.377737 0.925913i \(-0.623298\pi\)
0.925913 + 0.377737i \(0.123298\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) −5.58777 5.58777i −0.535211 0.535211i 0.386908 0.922118i \(-0.373543\pi\)
−0.922118 + 0.386908i \(0.873543\pi\)
\(110\) 3.19100 5.24898i 0.304250 0.500470i
\(111\) −5.78837 1.86945i −0.549407 0.177440i
\(112\) 2.90687 2.90687i 0.274673 0.274673i
\(113\) 14.2804i 1.34339i −0.740829 0.671694i \(-0.765567\pi\)
0.740829 0.671694i \(-0.234433\pi\)
\(114\) 2.65630 0.248785
\(115\) −1.79963 1.09404i −0.167816 0.102020i
\(116\) −4.28806 + 4.28806i −0.398136 + 0.398136i
\(117\) 5.21529i 0.482154i
\(118\) −1.92935 1.92935i −0.177611 0.177611i
\(119\) −12.0956 12.0956i −1.10880 1.10880i
\(120\) −2.17242 + 0.529716i −0.198314 + 0.0483562i
\(121\) 3.45316 0.313923
\(122\) 8.68618 + 8.68618i 0.786410 + 0.786410i
\(123\) −5.36992 5.36992i −0.484189 0.484189i
\(124\) 5.51242 + 5.51242i 0.495030 + 0.495030i
\(125\) −0.758434 + 11.1546i −0.0678364 + 0.997696i
\(126\) 2.90687 + 2.90687i 0.258965 + 0.258965i
\(127\) 8.01885 8.01885i 0.711558 0.711558i −0.255303 0.966861i \(-0.582175\pi\)
0.966861 + 0.255303i \(0.0821752\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.40869 + 4.40869i −0.388163 + 0.388163i
\(130\) −9.96485 6.05791i −0.873975 0.531314i
\(131\) 6.63665 + 6.63665i 0.579847 + 0.579847i 0.934861 0.355014i \(-0.115524\pi\)
−0.355014 + 0.934861i \(0.615524\pi\)
\(132\) 1.94253 + 1.94253i 0.169075 + 0.169075i
\(133\) −10.9199 −0.946874
\(134\) −5.51165 5.51165i −0.476134 0.476134i
\(135\) −0.529716 2.17242i −0.0455907 0.186972i
\(136\) 4.16103i 0.356806i
\(137\) 7.91811 7.91811i 0.676490 0.676490i −0.282714 0.959204i \(-0.591235\pi\)
0.959204 + 0.282714i \(0.0912348\pi\)
\(138\) 0.666001 0.666001i 0.0566938 0.0566938i
\(139\) 13.0683 1.10844 0.554221 0.832369i \(-0.313016\pi\)
0.554221 + 0.832369i \(0.313016\pi\)
\(140\) 8.93067 2.17763i 0.754779 0.184043i
\(141\) 8.55529i 0.720485i
\(142\) 8.51973 0.714960
\(143\) 14.3272i 1.19810i
\(144\) 1.00000i 0.0833333i
\(145\) −13.1741 + 3.21232i −1.09405 + 0.266769i
\(146\) 2.98121 2.98121i 0.246727 0.246727i
\(147\) −7.00021 7.00021i −0.577368 0.577368i
\(148\) −2.77109 5.41489i −0.227783 0.445101i
\(149\) 6.80855i 0.557778i −0.960323 0.278889i \(-0.910034\pi\)
0.960323 0.278889i \(-0.0899661\pi\)
\(150\) −4.76613 1.51128i −0.389153 0.123395i
\(151\) 17.8917i 1.45600i −0.685575 0.728002i \(-0.740449\pi\)
0.685575 0.728002i \(-0.259551\pi\)
\(152\) 1.87829 + 1.87829i 0.152349 + 0.152349i
\(153\) −4.16103 −0.336399
\(154\) −7.98561 7.98561i −0.643499 0.643499i
\(155\) 4.12953 + 16.9356i 0.331692 + 1.36030i
\(156\) 3.68777 3.68777i 0.295258 0.295258i
\(157\) 3.05662 3.05662i 0.243945 0.243945i −0.574535 0.818480i \(-0.694817\pi\)
0.818480 + 0.574535i \(0.194817\pi\)
\(158\) −1.46581 1.46581i −0.116613 0.116613i
\(159\) 11.7637 0.932925
\(160\) −1.91070 1.16157i −0.151054 0.0918298i
\(161\) −2.73789 + 2.73789i −0.215776 + 0.215776i
\(162\) 1.00000 0.0785674
\(163\) 19.5350i 1.53010i 0.643971 + 0.765050i \(0.277286\pi\)
−0.643971 + 0.765050i \(0.722714\pi\)
\(164\) 7.59421i 0.593008i
\(165\) 1.45521 + 5.96796i 0.113288 + 0.464605i
\(166\) −7.26193 7.26193i −0.563635 0.563635i
\(167\) 7.60664i 0.588620i 0.955710 + 0.294310i \(0.0950898\pi\)
−0.955710 + 0.294310i \(0.904910\pi\)
\(168\) 4.11094i 0.317166i
\(169\) 14.1993 1.09225
\(170\) −4.83331 + 7.95047i −0.370698 + 0.609773i
\(171\) −1.87829 + 1.87829i −0.143636 + 0.143636i
\(172\) −6.23482 −0.475401
\(173\) −17.6561 + 17.6561i −1.34237 + 1.34237i −0.448675 + 0.893695i \(0.648104\pi\)
−0.893695 + 0.448675i \(0.851896\pi\)
\(174\) 6.06423i 0.459728i
\(175\) 19.5933 + 6.21277i 1.48111 + 0.469642i
\(176\) 2.74715i 0.207074i
\(177\) 2.72851 0.205087
\(178\) 1.62770 1.62770i 0.122001 0.122001i
\(179\) −5.23093 + 5.23093i −0.390978 + 0.390978i −0.875036 0.484058i \(-0.839162\pi\)
0.484058 + 0.875036i \(0.339162\pi\)
\(180\) 1.16157 1.91070i 0.0865780 0.142415i
\(181\) 6.81886 0.506842 0.253421 0.967356i \(-0.418444\pi\)
0.253421 + 0.967356i \(0.418444\pi\)
\(182\) −15.1602 + 15.1602i −1.12375 + 1.12375i
\(183\) −12.2841 −0.908068
\(184\) 0.941868 0.0694354
\(185\) 0.995030 13.5650i 0.0731560 0.997321i
\(186\) −7.79574 −0.571612
\(187\) 11.4310 0.835916
\(188\) −6.04950 + 6.04950i −0.441205 + 0.441205i
\(189\) −4.11094 −0.299027
\(190\) 1.40708 + 5.77059i 0.102081 + 0.418643i
\(191\) −7.19163 + 7.19163i −0.520368 + 0.520368i −0.917683 0.397315i \(-0.869942\pi\)
0.397315 + 0.917683i \(0.369942\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) −16.3418 −1.17631 −0.588154 0.808749i \(-0.700145\pi\)
−0.588154 + 0.808749i \(0.700145\pi\)
\(194\) 10.0910i 0.724493i
\(195\) 11.3298 2.76262i 0.811344 0.197836i
\(196\) 9.89979i 0.707128i
\(197\) −11.4834 + 11.4834i −0.818161 + 0.818161i −0.985841 0.167680i \(-0.946372\pi\)
0.167680 + 0.985841i \(0.446372\pi\)
\(198\) −2.74715 −0.195232
\(199\) −12.9349 + 12.9349i −0.916929 + 0.916929i −0.996805 0.0798762i \(-0.974548\pi\)
0.0798762 + 0.996805i \(0.474548\pi\)
\(200\) −2.30153 4.43880i −0.162743 0.313871i
\(201\) 7.79465 0.549792
\(202\) 9.40183i 0.661511i
\(203\) 24.9297i 1.74972i
\(204\) −2.94229 2.94229i −0.206002 0.206002i
\(205\) 8.82118 14.5102i 0.616098 1.01344i
\(206\) 7.77490i 0.541703i
\(207\) 0.941868i 0.0654644i
\(208\) 5.21529 0.361616
\(209\) 5.15994 5.15994i 0.356921 0.356921i
\(210\) −4.77512 + 7.85475i −0.329515 + 0.542030i
\(211\) −23.4609 −1.61512 −0.807558 0.589788i \(-0.799211\pi\)
−0.807558 + 0.589788i \(0.799211\pi\)
\(212\) 8.31822 + 8.31822i 0.571297 + 0.571297i
\(213\) −6.02436 + 6.02436i −0.412782 + 0.412782i
\(214\) −5.67037 + 5.67037i −0.387619 + 0.387619i
\(215\) −11.9129 7.24216i −0.812450 0.493911i
\(216\) 0.707107 + 0.707107i 0.0481125 + 0.0481125i
\(217\) 32.0478 2.17555
\(218\) 5.58777 + 5.58777i 0.378451 + 0.378451i
\(219\) 4.21607i 0.284895i
\(220\) −3.19100 + 5.24898i −0.215137 + 0.353886i
\(221\) 21.7010i 1.45977i
\(222\) 5.78837 + 1.86945i 0.388490 + 0.125469i
\(223\) −2.83314 2.83314i −0.189721 0.189721i 0.605854 0.795576i \(-0.292831\pi\)
−0.795576 + 0.605854i \(0.792831\pi\)
\(224\) −2.90687 + 2.90687i −0.194223 + 0.194223i
\(225\) 4.43880 2.30153i 0.295920 0.153435i
\(226\) 14.2804i 0.949919i
\(227\) 7.49379i 0.497380i −0.968583 0.248690i \(-0.920000\pi\)
0.968583 0.248690i \(-0.0800001\pi\)
\(228\) −2.65630 −0.175918
\(229\) 24.0930i 1.59211i 0.605224 + 0.796055i \(0.293083\pi\)
−0.605224 + 0.796055i \(0.706917\pi\)
\(230\) 1.79963 + 1.09404i 0.118664 + 0.0721390i
\(231\) 11.2934 0.743049
\(232\) 4.28806 4.28806i 0.281525 0.281525i
\(233\) 7.78522 7.78522i 0.510027 0.510027i −0.404508 0.914535i \(-0.632557\pi\)
0.914535 + 0.404508i \(0.132557\pi\)
\(234\) 5.21529i 0.340934i
\(235\) −18.5857 + 4.53187i −1.21239 + 0.295627i
\(236\) 1.92935 + 1.92935i 0.125590 + 0.125590i
\(237\) 2.07297 0.134654
\(238\) 12.0956 + 12.0956i 0.784040 + 0.784040i
\(239\) −1.88427 1.88427i −0.121884 0.121884i 0.643534 0.765418i \(-0.277468\pi\)
−0.765418 + 0.643534i \(0.777468\pi\)
\(240\) 2.17242 0.529716i 0.140229 0.0341930i
\(241\) −18.1268 + 18.1268i −1.16765 + 1.16765i −0.184888 + 0.982760i \(0.559192\pi\)
−0.982760 + 0.184888i \(0.940808\pi\)
\(242\) −3.45316 −0.221977
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) −8.68618 8.68618i −0.556076 0.556076i
\(245\) 11.4993 18.9155i 0.734661 1.20847i
\(246\) 5.36992 + 5.36992i 0.342373 + 0.342373i
\(247\) −9.79582 9.79582i −0.623293 0.623293i
\(248\) −5.51242 5.51242i −0.350039 0.350039i
\(249\) 10.2699 0.650830
\(250\) 0.758434 11.1546i 0.0479676 0.705478i
\(251\) −10.2960 10.2960i −0.649879 0.649879i 0.303085 0.952964i \(-0.401983\pi\)
−0.952964 + 0.303085i \(0.901983\pi\)
\(252\) −2.90687 2.90687i −0.183116 0.183116i
\(253\) 2.58745i 0.162672i
\(254\) −8.01885 + 8.01885i −0.503148 + 0.503148i
\(255\) −2.20417 9.03950i −0.138030 0.566076i
\(256\) 1.00000 0.0625000
\(257\) 2.69763i 0.168274i −0.996454 0.0841369i \(-0.973187\pi\)
0.996454 0.0841369i \(-0.0268133\pi\)
\(258\) 4.40869 4.40869i 0.274473 0.274473i
\(259\) −23.7956 7.68517i −1.47859 0.477533i
\(260\) 9.96485 + 6.05791i 0.617994 + 0.375695i
\(261\) 4.28806 + 4.28806i 0.265424 + 0.265424i
\(262\) −6.63665 6.63665i −0.410014 0.410014i
\(263\) −15.0006 + 15.0006i −0.924974 + 0.924974i −0.997376 0.0724014i \(-0.976934\pi\)
0.0724014 + 0.997376i \(0.476934\pi\)
\(264\) −1.94253 1.94253i −0.119554 0.119554i
\(265\) 6.23144 + 25.5557i 0.382794 + 1.56988i
\(266\) 10.9199 0.669541
\(267\) 2.30191i 0.140875i
\(268\) 5.51165 + 5.51165i 0.336678 + 0.336678i
\(269\) 3.86256i 0.235505i 0.993043 + 0.117752i \(0.0375689\pi\)
−0.993043 + 0.117752i \(0.962431\pi\)
\(270\) 0.529716 + 2.17242i 0.0322375 + 0.132209i
\(271\) −11.2551 −0.683697 −0.341848 0.939755i \(-0.611053\pi\)
−0.341848 + 0.939755i \(0.611053\pi\)
\(272\) 4.16103i 0.252300i
\(273\) 21.4397i 1.29759i
\(274\) −7.91811 + 7.91811i −0.478351 + 0.478351i
\(275\) −12.1941 + 6.32265i −0.735330 + 0.381270i
\(276\) −0.666001 + 0.666001i −0.0400886 + 0.0400886i
\(277\) 16.2009 0.973420 0.486710 0.873564i \(-0.338197\pi\)
0.486710 + 0.873564i \(0.338197\pi\)
\(278\) −13.0683 −0.783787
\(279\) 5.51242 5.51242i 0.330020 0.330020i
\(280\) −8.93067 + 2.17763i −0.533710 + 0.130138i
\(281\) −7.78699 + 7.78699i −0.464533 + 0.464533i −0.900138 0.435605i \(-0.856534\pi\)
0.435605 + 0.900138i \(0.356534\pi\)
\(282\) 8.55529i 0.509460i
\(283\) 21.1035i 1.25447i 0.778829 + 0.627237i \(0.215814\pi\)
−0.778829 + 0.627237i \(0.784186\pi\)
\(284\) −8.51973 −0.505553
\(285\) −5.07539 3.08547i −0.300640 0.182767i
\(286\) 14.3272i 0.847185i
\(287\) −22.0754 22.0754i −1.30307 1.30307i
\(288\) 1.00000i 0.0589256i
\(289\) −0.314185 −0.0184815
\(290\) 13.1741 3.21232i 0.773607 0.188634i
\(291\) −7.13543 7.13543i −0.418286 0.418286i
\(292\) −2.98121 + 2.98121i −0.174462 + 0.174462i
\(293\) −2.76877 2.76877i −0.161753 0.161753i 0.621590 0.783343i \(-0.286487\pi\)
−0.783343 + 0.621590i \(0.786487\pi\)
\(294\) 7.00021 + 7.00021i 0.408261 + 0.408261i
\(295\) 1.44534 + 5.92747i 0.0841507 + 0.345110i
\(296\) 2.77109 + 5.41489i 0.161067 + 0.314734i
\(297\) 1.94253 1.94253i 0.112717 0.112717i
\(298\) 6.80855i 0.394408i
\(299\) −4.91212 −0.284075
\(300\) 4.76613 + 1.51128i 0.275173 + 0.0872538i
\(301\) −18.1238 + 18.1238i −1.04464 + 1.04464i
\(302\) 17.8917i 1.02955i
\(303\) −6.64810 6.64810i −0.381923 0.381923i
\(304\) −1.87829 1.87829i −0.107727 0.107727i
\(305\) −6.50709 26.6862i −0.372595 1.52805i
\(306\) 4.16103 0.237870
\(307\) 6.12720 + 6.12720i 0.349698 + 0.349698i 0.859997 0.510299i \(-0.170465\pi\)
−0.510299 + 0.859997i \(0.670465\pi\)
\(308\) 7.98561 + 7.98561i 0.455023 + 0.455023i
\(309\) 5.49768 + 5.49768i 0.312752 + 0.312752i
\(310\) −4.12953 16.9356i −0.234542 0.961878i
\(311\) −1.06423 1.06423i −0.0603471 0.0603471i 0.676289 0.736636i \(-0.263587\pi\)
−0.736636 + 0.676289i \(0.763587\pi\)
\(312\) −3.68777 + 3.68777i −0.208779 + 0.208779i
\(313\) −7.63668 −0.431650 −0.215825 0.976432i \(-0.569244\pi\)
−0.215825 + 0.976432i \(0.569244\pi\)
\(314\) −3.05662 + 3.05662i −0.172495 + 0.172495i
\(315\) −2.17763 8.93067i −0.122695 0.503186i
\(316\) 1.46581 + 1.46581i 0.0824581 + 0.0824581i
\(317\) 19.5287 + 19.5287i 1.09684 + 1.09684i 0.994778 + 0.102064i \(0.0325445\pi\)
0.102064 + 0.994778i \(0.467455\pi\)
\(318\) −11.7637 −0.659677
\(319\) −11.7800 11.7800i −0.659551 0.659551i
\(320\) 1.91070 + 1.16157i 0.106811 + 0.0649335i
\(321\) 8.01912i 0.447584i
\(322\) 2.73789 2.73789i 0.152577 0.152577i
\(323\) −7.81562 + 7.81562i −0.434872 + 0.434872i
\(324\) −1.00000 −0.0555556
\(325\) 12.0032 + 23.1497i 0.665815 + 1.28411i
\(326\) 19.5350i 1.08194i
\(327\) −7.90229 −0.436998
\(328\) 7.59421i 0.419320i
\(329\) 35.1702i 1.93900i
\(330\) −1.45521 5.96796i −0.0801067 0.328526i
\(331\) −10.6002 + 10.6002i −0.582640 + 0.582640i −0.935628 0.352988i \(-0.885166\pi\)
0.352988 + 0.935628i \(0.385166\pi\)
\(332\) 7.26193 + 7.26193i 0.398550 + 0.398550i
\(333\) −5.41489 + 2.77109i −0.296734 + 0.151855i
\(334\) 7.60664i 0.416217i
\(335\) 4.12895 + 16.9332i 0.225589 + 0.925162i
\(336\) 4.11094i 0.224270i
\(337\) −14.7087 14.7087i −0.801235 0.801235i 0.182054 0.983289i \(-0.441725\pi\)
−0.983289 + 0.182054i \(0.941725\pi\)
\(338\) −14.1993 −0.772340
\(339\) −10.0978 10.0978i −0.548436 0.548436i
\(340\) 4.83331 7.95047i 0.262123 0.431175i
\(341\) −15.1435 + 15.1435i −0.820064 + 0.820064i
\(342\) 1.87829 1.87829i 0.101566 0.101566i
\(343\) −8.42932 8.42932i −0.455140 0.455140i
\(344\) 6.23482 0.336159
\(345\) −2.04613 + 0.498923i −0.110160 + 0.0268611i
\(346\) 17.6561 17.6561i 0.949199 0.949199i
\(347\) −5.20503 −0.279421 −0.139710 0.990192i \(-0.544617\pi\)
−0.139710 + 0.990192i \(0.544617\pi\)
\(348\) 6.06423i 0.325077i
\(349\) 8.31963i 0.445339i −0.974894 0.222670i \(-0.928523\pi\)
0.974894 0.222670i \(-0.0714771\pi\)
\(350\) −19.5933 6.21277i −1.04730 0.332087i
\(351\) −3.68777 3.68777i −0.196839 0.196839i
\(352\) 2.74715i 0.146424i
\(353\) 32.6034i 1.73530i −0.497173 0.867651i \(-0.665629\pi\)
0.497173 0.867651i \(-0.334371\pi\)
\(354\) −2.72851 −0.145019
\(355\) −16.2786 9.89623i −0.863980 0.525237i
\(356\) −1.62770 + 1.62770i −0.0862677 + 0.0862677i
\(357\) −17.1057 −0.905331
\(358\) 5.23093 5.23093i 0.276463 0.276463i
\(359\) 17.3163i 0.913921i −0.889487 0.456960i \(-0.848938\pi\)
0.889487 0.456960i \(-0.151062\pi\)
\(360\) −1.16157 + 1.91070i −0.0612199 + 0.100703i
\(361\) 11.9441i 0.628635i
\(362\) −6.81886 −0.358391
\(363\) 2.44175 2.44175i 0.128159 0.128159i
\(364\) 15.1602 15.1602i 0.794610 0.794610i
\(365\) −9.15906 + 2.23332i −0.479407 + 0.116897i
\(366\) 12.2841 0.642101
\(367\) −19.8485 + 19.8485i −1.03608 + 1.03608i −0.0367606 + 0.999324i \(0.511704\pi\)
−0.999324 + 0.0367606i \(0.988296\pi\)
\(368\) −0.941868 −0.0490983
\(369\) −7.59421 −0.395339
\(370\) −0.995030 + 13.5650i −0.0517291 + 0.705212i
\(371\) 48.3600 2.51072
\(372\) 7.79574 0.404190
\(373\) 19.3419 19.3419i 1.00149 1.00149i 0.00148728 0.999999i \(-0.499527\pi\)
0.999999 0.00148728i \(-0.000473415\pi\)
\(374\) −11.4310 −0.591082
\(375\) 7.35119 + 8.42378i 0.379614 + 0.435002i
\(376\) 6.04950 6.04950i 0.311979 0.311979i
\(377\) −22.3635 + 22.3635i −1.15178 + 1.15178i
\(378\) 4.11094 0.211444
\(379\) 3.56273i 0.183005i 0.995805 + 0.0915027i \(0.0291670\pi\)
−0.995805 + 0.0915027i \(0.970833\pi\)
\(380\) −1.40708 5.77059i −0.0721819 0.296025i
\(381\) 11.3404i 0.580985i
\(382\) 7.19163 7.19163i 0.367956 0.367956i
\(383\) −17.5102 −0.894730 −0.447365 0.894351i \(-0.647638\pi\)
−0.447365 + 0.894351i \(0.647638\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) 5.98228 + 24.5339i 0.304885 + 1.25036i
\(386\) 16.3418 0.831776
\(387\) 6.23482i 0.316934i
\(388\) 10.0910i 0.512294i
\(389\) 5.52680 + 5.52680i 0.280220 + 0.280220i 0.833197 0.552977i \(-0.186508\pi\)
−0.552977 + 0.833197i \(0.686508\pi\)
\(390\) −11.3298 + 2.76262i −0.573707 + 0.139891i
\(391\) 3.91914i 0.198200i
\(392\) 9.89979i 0.500015i
\(393\) 9.38564 0.473443
\(394\) 11.4834 11.4834i 0.578527 0.578527i
\(395\) 1.09808 + 4.50335i 0.0552505 + 0.226588i
\(396\) 2.74715 0.138050
\(397\) 7.17123 + 7.17123i 0.359913 + 0.359913i 0.863781 0.503867i \(-0.168090\pi\)
−0.503867 + 0.863781i \(0.668090\pi\)
\(398\) 12.9349 12.9349i 0.648366 0.648366i
\(399\) −7.72152 + 7.72152i −0.386560 + 0.386560i
\(400\) 2.30153 + 4.43880i 0.115076 + 0.221940i
\(401\) 12.3057 + 12.3057i 0.614518 + 0.614518i 0.944120 0.329602i \(-0.106914\pi\)
−0.329602 + 0.944120i \(0.606914\pi\)
\(402\) −7.79465 −0.388762
\(403\) 28.7489 + 28.7489i 1.43208 + 1.43208i
\(404\) 9.40183i 0.467759i
\(405\) −1.91070 1.16157i −0.0949433 0.0577187i
\(406\) 24.9297i 1.23724i
\(407\) 14.8755 7.61262i 0.737352 0.377343i
\(408\) 2.94229 + 2.94229i 0.145665 + 0.145665i
\(409\) −20.8384 + 20.8384i −1.03039 + 1.03039i −0.0308695 + 0.999523i \(0.509828\pi\)
−0.999523 + 0.0308695i \(0.990172\pi\)
\(410\) −8.82118 + 14.5102i −0.435647 + 0.716610i
\(411\) 11.1979i 0.552352i
\(412\) 7.77490i 0.383042i
\(413\) 11.2167 0.551939
\(414\) 0.941868i 0.0462903i
\(415\) 5.44014 + 22.3106i 0.267046 + 1.09518i
\(416\) −5.21529 −0.255701
\(417\) 9.24072 9.24072i 0.452520 0.452520i
\(418\) −5.15994 + 5.15994i −0.252381 + 0.252381i
\(419\) 36.4587i 1.78113i −0.454860 0.890563i \(-0.650311\pi\)
0.454860 0.890563i \(-0.349689\pi\)
\(420\) 4.77512 7.85475i 0.233002 0.383273i
\(421\) 15.1883 + 15.1883i 0.740231 + 0.740231i 0.972622 0.232392i \(-0.0746551\pi\)
−0.232392 + 0.972622i \(0.574655\pi\)
\(422\) 23.4609 1.14206
\(423\) 6.04950 + 6.04950i 0.294137 + 0.294137i
\(424\) −8.31822 8.31822i −0.403968 0.403968i
\(425\) 18.4700 9.57674i 0.895926 0.464540i
\(426\) 6.02436 6.02436i 0.291881 0.291881i
\(427\) −50.4992 −2.44383
\(428\) 5.67037 5.67037i 0.274088 0.274088i
\(429\) 10.1309 + 10.1309i 0.489123 + 0.489123i
\(430\) 11.9129 + 7.24216i 0.574489 + 0.349248i
\(431\) −6.39166 6.39166i −0.307875 0.307875i 0.536210 0.844085i \(-0.319856\pi\)
−0.844085 + 0.536210i \(0.819856\pi\)
\(432\) −0.707107 0.707107i −0.0340207 0.0340207i
\(433\) 15.4619 + 15.4619i 0.743053 + 0.743053i 0.973164 0.230111i \(-0.0739089\pi\)
−0.230111 + 0.973164i \(0.573909\pi\)
\(434\) −32.0478 −1.53834
\(435\) −7.04401 + 11.5869i −0.337734 + 0.555550i
\(436\) −5.58777 5.58777i −0.267605 0.267605i
\(437\) 1.76910 + 1.76910i 0.0846275 + 0.0846275i
\(438\) 4.21607i 0.201451i
\(439\) 15.6685 15.6685i 0.747816 0.747816i −0.226253 0.974069i \(-0.572648\pi\)
0.974069 + 0.226253i \(0.0726476\pi\)
\(440\) 3.19100 5.24898i 0.152125 0.250235i
\(441\) −9.89979 −0.471419
\(442\) 21.7010i 1.03221i
\(443\) 27.2120 27.2120i 1.29288 1.29288i 0.359887 0.932996i \(-0.382815\pi\)
0.932996 0.359887i \(-0.117185\pi\)
\(444\) −5.78837 1.86945i −0.274704 0.0887200i
\(445\) −5.00071 + 1.21936i −0.237056 + 0.0578031i
\(446\) 2.83314 + 2.83314i 0.134153 + 0.134153i
\(447\) −4.81437 4.81437i −0.227712 0.227712i
\(448\) 2.90687 2.90687i 0.137337 0.137337i
\(449\) −18.9735 18.9735i −0.895416 0.895416i 0.0996105 0.995027i \(-0.468240\pi\)
−0.995027 + 0.0996105i \(0.968240\pi\)
\(450\) −4.43880 + 2.30153i −0.209247 + 0.108495i
\(451\) 20.8624 0.982374
\(452\) 14.2804i 0.671694i
\(453\) −12.6513 12.6513i −0.594411 0.594411i
\(454\) 7.49379i 0.351701i
\(455\) 46.5761 11.3570i 2.18352 0.532423i
\(456\) 2.65630 0.124393
\(457\) 9.71477i 0.454438i 0.973844 + 0.227219i \(0.0729632\pi\)
−0.973844 + 0.227219i \(0.927037\pi\)
\(458\) 24.0930i 1.12579i
\(459\) −2.94229 + 2.94229i −0.137335 + 0.137335i
\(460\) −1.79963 1.09404i −0.0839080 0.0510100i
\(461\) 17.2735 17.2735i 0.804507 0.804507i −0.179290 0.983796i \(-0.557380\pi\)
0.983796 + 0.179290i \(0.0573799\pi\)
\(462\) −11.2934 −0.525415
\(463\) 16.3891 0.761664 0.380832 0.924644i \(-0.375638\pi\)
0.380832 + 0.924644i \(0.375638\pi\)
\(464\) −4.28806 + 4.28806i −0.199068 + 0.199068i
\(465\) 14.8953 + 9.05527i 0.690753 + 0.419928i
\(466\) −7.78522 + 7.78522i −0.360643 + 0.360643i
\(467\) 1.29508i 0.0599293i −0.999551 0.0299647i \(-0.990461\pi\)
0.999551 0.0299647i \(-0.00953947\pi\)
\(468\) 5.21529i 0.241077i
\(469\) 32.0433 1.47962
\(470\) 18.5857 4.53187i 0.857293 0.209040i
\(471\) 4.32271i 0.199180i
\(472\) −1.92935 1.92935i −0.0888054 0.0888054i
\(473\) 17.1280i 0.787547i
\(474\) −2.07297 −0.0952144
\(475\) 4.01441 12.6603i 0.184194 0.580894i
\(476\) −12.0956 12.0956i −0.554400 0.554400i
\(477\) 8.31822 8.31822i 0.380865 0.380865i
\(478\) 1.88427 + 1.88427i 0.0861847 + 0.0861847i
\(479\) 27.0885 + 27.0885i 1.23770 + 1.23770i 0.960937 + 0.276766i \(0.0892628\pi\)
0.276766 + 0.960937i \(0.410737\pi\)
\(480\) −2.17242 + 0.529716i −0.0991569 + 0.0241781i
\(481\) −14.4521 28.2402i −0.658958 1.28764i
\(482\) 18.1268 18.1268i 0.825652 0.825652i
\(483\) 3.87196i 0.176180i
\(484\) 3.45316 0.156962
\(485\) 11.7214 19.2809i 0.532241 0.875500i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) 27.5508i 1.24844i 0.781247 + 0.624222i \(0.214584\pi\)
−0.781247 + 0.624222i \(0.785416\pi\)
\(488\) 8.68618 + 8.68618i 0.393205 + 0.393205i
\(489\) 13.8133 + 13.8133i 0.624661 + 0.624661i
\(490\) −11.4993 + 18.9155i −0.519484 + 0.854515i
\(491\) −24.9010 −1.12376 −0.561882 0.827217i \(-0.689923\pi\)
−0.561882 + 0.827217i \(0.689923\pi\)
\(492\) −5.36992 5.36992i −0.242095 0.242095i
\(493\) 17.8428 + 17.8428i 0.803597 + 0.803597i
\(494\) 9.79582 + 9.79582i 0.440735 + 0.440735i
\(495\) 5.24898 + 3.19100i 0.235924 + 0.143425i
\(496\) 5.51242 + 5.51242i 0.247515 + 0.247515i
\(497\) −24.7657 + 24.7657i −1.11090 + 1.11090i
\(498\) −10.2699 −0.460206
\(499\) −9.41283 + 9.41283i −0.421376 + 0.421376i −0.885677 0.464301i \(-0.846305\pi\)
0.464301 + 0.885677i \(0.346305\pi\)
\(500\) −0.758434 + 11.1546i −0.0339182 + 0.498848i
\(501\) 5.37871 + 5.37871i 0.240303 + 0.240303i
\(502\) 10.2960 + 10.2960i 0.459534 + 0.459534i
\(503\) −32.7145 −1.45867 −0.729334 0.684158i \(-0.760170\pi\)
−0.729334 + 0.684158i \(0.760170\pi\)
\(504\) 2.90687 + 2.90687i 0.129482 + 0.129482i
\(505\) 10.9208 17.9641i 0.485971 0.799390i
\(506\) 2.58745i 0.115026i
\(507\) 10.0404 10.0404i 0.445910 0.445910i
\(508\) 8.01885 8.01885i 0.355779 0.355779i
\(509\) 13.1690 0.583707 0.291854 0.956463i \(-0.405728\pi\)
0.291854 + 0.956463i \(0.405728\pi\)
\(510\) 2.20417 + 9.03950i 0.0976021 + 0.400276i
\(511\) 17.3320i 0.766722i
\(512\) −1.00000 −0.0441942
\(513\) 2.65630i 0.117279i
\(514\) 2.69763i 0.118988i
\(515\) −9.03106 + 14.8555i −0.397956 + 0.654611i
\(516\) −4.40869 + 4.40869i −0.194082 + 0.194082i
\(517\) −16.6189 16.6189i −0.730898 0.730898i
\(518\) 23.7956 + 7.68517i 1.04552 + 0.337667i
\(519\) 24.9695i 1.09604i
\(520\) −9.96485 6.05791i −0.436988 0.265657i
\(521\) 30.7232i 1.34601i 0.739639 + 0.673004i \(0.234996\pi\)
−0.739639 + 0.673004i \(0.765004\pi\)
\(522\) −4.28806 4.28806i −0.187683 0.187683i
\(523\) 17.6544 0.771972 0.385986 0.922505i \(-0.373861\pi\)
0.385986 + 0.922505i \(0.373861\pi\)
\(524\) 6.63665 + 6.63665i 0.289924 + 0.289924i
\(525\) 18.2476 9.46144i 0.796392 0.412931i
\(526\) 15.0006 15.0006i 0.654055 0.654055i
\(527\) 22.9374 22.9374i 0.999167 0.999167i
\(528\) 1.94253 + 1.94253i 0.0845377 + 0.0845377i
\(529\) −22.1129 −0.961430
\(530\) −6.23144 25.5557i −0.270676 1.11007i
\(531\) 1.92935 1.92935i 0.0837266 0.0837266i
\(532\) −10.9199 −0.473437
\(533\) 39.6060i 1.71553i
\(534\) 2.30191i 0.0996134i
\(535\) 17.4209 4.24786i 0.753170 0.183651i
\(536\) −5.51165 5.51165i −0.238067 0.238067i
\(537\) 7.39765i 0.319232i
\(538\) 3.86256i 0.166527i
\(539\) 27.1962 1.17142
\(540\) −0.529716 2.17242i −0.0227953 0.0934860i
\(541\) −24.2940 + 24.2940i −1.04448 + 1.04448i −0.0455156 + 0.998964i \(0.514493\pi\)
−0.998964 + 0.0455156i \(0.985507\pi\)
\(542\) 11.2551 0.483447
\(543\) 4.82166 4.82166i 0.206917 0.206917i
\(544\) 4.16103i 0.178403i
\(545\) −4.18597 17.1671i −0.179307 0.735357i
\(546\) 21.4397i 0.917536i
\(547\) −22.8223 −0.975811 −0.487906 0.872896i \(-0.662239\pi\)
−0.487906 + 0.872896i \(0.662239\pi\)
\(548\) 7.91811 7.91811i 0.338245 0.338245i
\(549\) −8.68618 + 8.68618i −0.370717 + 0.370717i
\(550\) 12.1941 6.32265i 0.519957 0.269599i
\(551\) 16.1084 0.686242
\(552\) 0.666001 0.666001i 0.0283469 0.0283469i
\(553\) 8.52183 0.362385
\(554\) −16.2009 −0.688312
\(555\) −8.88833 10.2955i −0.377289 0.437020i
\(556\) 13.0683 0.554221
\(557\) 22.2337 0.942073 0.471036 0.882114i \(-0.343880\pi\)
0.471036 + 0.882114i \(0.343880\pi\)
\(558\) −5.51242 + 5.51242i −0.233359 + 0.233359i
\(559\) −32.5164 −1.37530
\(560\) 8.93067 2.17763i 0.377390 0.0920216i
\(561\) 8.08293 8.08293i 0.341261 0.341261i
\(562\) 7.78699 7.78699i 0.328474 0.328474i
\(563\) −25.9596 −1.09407 −0.547034 0.837110i \(-0.684243\pi\)
−0.547034 + 0.837110i \(0.684243\pi\)
\(564\) 8.55529i 0.360243i
\(565\) 16.5876 27.2855i 0.697847 1.14791i
\(566\) 21.1035i 0.887046i
\(567\) −2.90687 + 2.90687i −0.122077 + 0.122077i
\(568\) 8.51973 0.357480
\(569\) 4.18660 4.18660i 0.175512 0.175512i −0.613884 0.789396i \(-0.710394\pi\)
0.789396 + 0.613884i \(0.210394\pi\)
\(570\) 5.07539 + 3.08547i 0.212585 + 0.129236i
\(571\) −24.7600 −1.03617 −0.518087 0.855328i \(-0.673356\pi\)
−0.518087 + 0.855328i \(0.673356\pi\)
\(572\) 14.3272i 0.599050i
\(573\) 10.1705i 0.424879i
\(574\) 22.0754 + 22.0754i 0.921409 + 0.921409i
\(575\) −2.16774 4.18077i −0.0904009 0.174350i
\(576\) 1.00000i 0.0416667i
\(577\) 34.1071i 1.41990i −0.704254 0.709948i \(-0.748718\pi\)
0.704254 0.709948i \(-0.251282\pi\)
\(578\) 0.314185 0.0130684
\(579\) −11.5554 + 11.5554i −0.480226 + 0.480226i
\(580\) −13.1741 + 3.21232i −0.547023 + 0.133384i
\(581\) 42.2190 1.75154
\(582\) 7.13543 + 7.13543i 0.295773 + 0.295773i
\(583\) −22.8514 + 22.8514i −0.946408 + 0.946408i
\(584\) 2.98121 2.98121i 0.123363 0.123363i
\(585\) 6.05791 9.96485i 0.250464 0.411996i
\(586\) 2.76877 + 2.76877i 0.114377 + 0.114377i
\(587\) −46.3514 −1.91313 −0.956564 0.291522i \(-0.905838\pi\)
−0.956564 + 0.291522i \(0.905838\pi\)
\(588\) −7.00021 7.00021i −0.288684 0.288684i
\(589\) 20.7078i 0.853251i
\(590\) −1.44534 5.92747i −0.0595035 0.244030i
\(591\) 16.2400i 0.668026i
\(592\) −2.77109 5.41489i −0.113891 0.222551i
\(593\) −16.9988 16.9988i −0.698058 0.698058i 0.265934 0.963991i \(-0.414320\pi\)
−0.963991 + 0.265934i \(0.914320\pi\)
\(594\) −1.94253 + 1.94253i −0.0797030 + 0.0797030i
\(595\) −9.06118 37.1608i −0.371472 1.52344i
\(596\) 6.80855i 0.278889i
\(597\) 18.2927i 0.748669i
\(598\) 4.91212 0.200871
\(599\) 12.7894i 0.522561i −0.965263 0.261281i \(-0.915855\pi\)
0.965263 0.261281i \(-0.0841448\pi\)
\(600\) −4.76613 1.51128i −0.194577 0.0616977i
\(601\) 17.7183 0.722744 0.361372 0.932422i \(-0.382308\pi\)
0.361372 + 0.932422i \(0.382308\pi\)
\(602\) 18.1238 18.1238i 0.738672 0.738672i
\(603\) 5.51165 5.51165i 0.224452 0.224452i
\(604\) 17.8917i 0.728002i
\(605\) 6.59794 + 4.01107i 0.268244 + 0.163073i
\(606\) 6.64810 + 6.64810i 0.270061 + 0.270061i
\(607\) 33.5114 1.36018 0.680092 0.733127i \(-0.261940\pi\)
0.680092 + 0.733127i \(0.261940\pi\)
\(608\) 1.87829 + 1.87829i 0.0761746 + 0.0761746i
\(609\) 17.6279 + 17.6279i 0.714320 + 0.714320i
\(610\) 6.50709 + 26.6862i 0.263464 + 1.08049i
\(611\) −31.5499 + 31.5499i −1.27637 + 1.27637i
\(612\) −4.16103 −0.168200
\(613\) −1.15839 + 1.15839i −0.0467871 + 0.0467871i −0.730113 0.683326i \(-0.760533\pi\)
0.683326 + 0.730113i \(0.260533\pi\)
\(614\) −6.12720 6.12720i −0.247274 0.247274i
\(615\) −4.02278 16.4978i −0.162214 0.665256i
\(616\) −7.98561 7.98561i −0.321750 0.321750i
\(617\) 15.5057 + 15.5057i 0.624237 + 0.624237i 0.946612 0.322375i \(-0.104481\pi\)
−0.322375 + 0.946612i \(0.604481\pi\)
\(618\) −5.49768 5.49768i −0.221149 0.221149i
\(619\) 23.4133 0.941060 0.470530 0.882384i \(-0.344063\pi\)
0.470530 + 0.882384i \(0.344063\pi\)
\(620\) 4.12953 + 16.9356i 0.165846 + 0.680151i
\(621\) 0.666001 + 0.666001i 0.0267257 + 0.0267257i
\(622\) 1.06423 + 1.06423i 0.0426719 + 0.0426719i
\(623\) 9.46300i 0.379127i
\(624\) 3.68777 3.68777i 0.147629 0.147629i
\(625\) −14.4059 + 20.4321i −0.576237 + 0.817283i
\(626\) 7.63668 0.305223
\(627\) 7.29726i 0.291424i
\(628\) 3.05662 3.05662i 0.121972 0.121972i
\(629\) −22.5315 + 11.5306i −0.898391 + 0.459756i
\(630\) 2.17763 + 8.93067i 0.0867588 + 0.355806i
\(631\) −29.2036 29.2036i −1.16258 1.16258i −0.983910 0.178667i \(-0.942821\pi\)
−0.178667 0.983910i \(-0.557179\pi\)
\(632\) −1.46581 1.46581i −0.0583067 0.0583067i
\(633\) −16.5894 + 16.5894i −0.659368 + 0.659368i
\(634\) −19.5287 19.5287i −0.775584 0.775584i
\(635\) 24.6360 6.00718i 0.977651 0.238388i
\(636\) 11.7637 0.466462
\(637\) 51.6303i 2.04567i
\(638\) 11.7800 + 11.7800i 0.466373 + 0.466373i
\(639\) 8.51973i 0.337035i
\(640\) −1.91070 1.16157i −0.0755269 0.0459149i
\(641\) −27.5707 −1.08898 −0.544488 0.838769i \(-0.683276\pi\)
−0.544488 + 0.838769i \(0.683276\pi\)
\(642\) 8.01912i 0.316489i
\(643\) 18.0002i 0.709858i −0.934893 0.354929i \(-0.884505\pi\)
0.934893 0.354929i \(-0.115495\pi\)
\(644\) −2.73789 + 2.73789i −0.107888 + 0.107888i
\(645\) −13.5446 + 3.30269i −0.533320 + 0.130043i
\(646\) 7.81562 7.81562i 0.307501 0.307501i
\(647\) 26.1609 1.02849 0.514245 0.857643i \(-0.328072\pi\)
0.514245 + 0.857643i \(0.328072\pi\)
\(648\) 1.00000 0.0392837
\(649\) −5.30021 + 5.30021i −0.208052 + 0.208052i
\(650\) −12.0032 23.1497i −0.470802 0.908004i
\(651\) 22.6612 22.6612i 0.888163 0.888163i
\(652\) 19.5350i 0.765050i
\(653\) 27.1758i 1.06347i −0.846911 0.531735i \(-0.821540\pi\)
0.846911 0.531735i \(-0.178460\pi\)
\(654\) 7.90229 0.309004
\(655\) 4.97173 + 20.3895i 0.194261 + 0.796685i
\(656\) 7.59421i 0.296504i
\(657\) 2.98121 + 2.98121i 0.116308 + 0.116308i
\(658\) 35.1702i 1.37108i
\(659\) 11.2236 0.437210 0.218605 0.975813i \(-0.429849\pi\)
0.218605 + 0.975813i \(0.429849\pi\)
\(660\) 1.45521 + 5.96796i 0.0566440 + 0.232303i
\(661\) −1.74533 1.74533i −0.0678853 0.0678853i 0.672349 0.740234i \(-0.265285\pi\)
−0.740234 + 0.672349i \(0.765285\pi\)
\(662\) 10.6002 10.6002i 0.411988 0.411988i
\(663\) −15.3449 15.3449i −0.595948 0.595948i
\(664\) −7.26193 7.26193i −0.281818 0.281818i
\(665\) −20.8646 12.6842i −0.809094 0.491871i
\(666\) 5.41489 2.77109i 0.209823 0.107378i
\(667\) 4.03879 4.03879i 0.156382 0.156382i
\(668\) 7.60664i 0.294310i
\(669\) −4.00667 −0.154907
\(670\) −4.12895 16.9332i −0.159515 0.654188i
\(671\) 23.8623 23.8623i 0.921192 0.921192i
\(672\) 4.11094i 0.158583i
\(673\) 21.3478 + 21.3478i 0.822898 + 0.822898i 0.986523 0.163624i \(-0.0523185\pi\)
−0.163624 + 0.986523i \(0.552318\pi\)
\(674\) 14.7087 + 14.7087i 0.566558 + 0.566558i
\(675\) 1.51128 4.76613i 0.0581692 0.183449i
\(676\) 14.1993 0.546127
\(677\) −29.6755 29.6755i −1.14052 1.14052i −0.988355 0.152168i \(-0.951375\pi\)
−0.152168 0.988355i \(-0.548625\pi\)
\(678\) 10.0978 + 10.0978i 0.387803 + 0.387803i
\(679\) −29.3333 29.3333i −1.12571 1.12571i
\(680\) −4.83331 + 7.95047i −0.185349 + 0.304887i
\(681\) −5.29891 5.29891i −0.203055 0.203055i
\(682\) 15.1435 15.1435i 0.579873 0.579873i
\(683\) −3.99926 −0.153027 −0.0765137 0.997069i \(-0.524379\pi\)
−0.0765137 + 0.997069i \(0.524379\pi\)
\(684\) −1.87829 + 1.87829i −0.0718181 + 0.0718181i
\(685\) 24.3265 5.93171i 0.929469 0.226639i
\(686\) 8.42932 + 8.42932i 0.321833 + 0.321833i
\(687\) 17.0363 + 17.0363i 0.649976 + 0.649976i
\(688\) −6.23482 −0.237700
\(689\) 43.3819 + 43.3819i 1.65272 + 1.65272i
\(690\) 2.04613 0.498923i 0.0778949 0.0189937i
\(691\) 20.3772i 0.775184i 0.921831 + 0.387592i \(0.126693\pi\)
−0.921831 + 0.387592i \(0.873307\pi\)
\(692\) −17.6561 + 17.6561i −0.671185 + 0.671185i
\(693\) 7.98561 7.98561i 0.303348 0.303348i
\(694\) 5.20503 0.197580
\(695\) 24.9697 + 15.1797i 0.947153 + 0.575801i
\(696\) 6.06423i 0.229864i
\(697\) −31.5998 −1.19693
\(698\) 8.31963i 0.314902i
\(699\) 11.0100i 0.416435i
\(700\) 19.5933 + 6.21277i 0.740556 + 0.234821i
\(701\) −5.28962 + 5.28962i −0.199786 + 0.199786i −0.799908 0.600122i \(-0.795119\pi\)
0.600122 + 0.799908i \(0.295119\pi\)
\(702\) 3.68777 + 3.68777i 0.139186 + 0.139186i
\(703\) −4.96581 + 15.3756i −0.187289 + 0.579903i
\(704\) 2.74715i 0.103537i
\(705\) −9.93753 + 16.3466i −0.374269 + 0.615647i
\(706\) 32.6034i 1.22704i
\(707\) −27.3299 27.3299i −1.02785 1.02785i
\(708\) 2.72851 0.102544
\(709\) −17.3563 17.3563i −0.651828 0.651828i 0.301605 0.953433i \(-0.402478\pi\)
−0.953433 + 0.301605i \(0.902478\pi\)
\(710\) 16.2786 + 9.89623i 0.610926 + 0.371399i
\(711\) 1.46581 1.46581i 0.0549721 0.0549721i
\(712\) 1.62770 1.62770i 0.0610005 0.0610005i
\(713\) −5.19197 5.19197i −0.194441 0.194441i
\(714\) 17.1057 0.640166
\(715\) −16.6420 + 27.3750i −0.622375 + 1.02377i
\(716\) −5.23093 + 5.23093i −0.195489 + 0.195489i
\(717\) −2.66477 −0.0995175
\(718\) 17.3163i 0.646240i
\(719\) 10.6066i 0.395558i 0.980247 + 0.197779i \(0.0633729\pi\)
−0.980247 + 0.197779i \(0.936627\pi\)
\(720\) 1.16157 1.91070i 0.0432890 0.0712075i
\(721\) 22.6006 + 22.6006i 0.841691 + 0.841691i
\(722\) 11.9441i 0.444512i
\(723\) 25.6351i 0.953381i
\(724\) 6.81886 0.253421
\(725\) −28.9029 9.16475i −1.07343 0.340370i
\(726\) −2.44175 + 2.44175i −0.0906219 + 0.0906219i
\(727\) 41.4047 1.53561 0.767807 0.640681i \(-0.221348\pi\)
0.767807 + 0.640681i \(0.221348\pi\)
\(728\) −15.1602 + 15.1602i −0.561874 + 0.561874i
\(729\) 1.00000i 0.0370370i
\(730\) 9.15906 2.23332i 0.338992 0.0826588i
\(731\) 25.9433i 0.959548i
\(732\) −12.2841 −0.454034
\(733\) 33.6863 33.6863i 1.24423 1.24423i 0.286005 0.958228i \(-0.407673\pi\)
0.958228 0.286005i \(-0.0923272\pi\)
\(734\) 19.8485 19.8485i 0.732622 0.732622i
\(735\) −5.24408 21.5065i −0.193431 0.793279i
\(736\) 0.941868 0.0347177
\(737\) −15.1413 + 15.1413i −0.557738 + 0.557738i
\(738\) 7.59421 0.279547
\(739\) 30.7911 1.13267 0.566335 0.824175i \(-0.308361\pi\)
0.566335 + 0.824175i \(0.308361\pi\)
\(740\) 0.995030 13.5650i 0.0365780 0.498660i
\(741\) −13.8534 −0.508917
\(742\) −48.3600 −1.77535
\(743\) 21.8367 21.8367i 0.801110 0.801110i −0.182159 0.983269i \(-0.558309\pi\)
0.983269 + 0.182159i \(0.0583086\pi\)
\(744\) −7.79574 −0.285806
\(745\) 7.90857 13.0091i 0.289748 0.476615i
\(746\) −19.3419 + 19.3419i −0.708158 + 0.708158i
\(747\) 7.26193 7.26193i 0.265700 0.265700i
\(748\) 11.4310 0.417958
\(749\) 32.9661i 1.20455i
\(750\) −7.35119 8.42378i −0.268427 0.307593i
\(751\) 4.98993i 0.182085i −0.995847 0.0910426i \(-0.970980\pi\)
0.995847 0.0910426i \(-0.0290199\pi\)
\(752\) −6.04950 + 6.04950i −0.220603 + 0.220603i
\(753\) −14.5608 −0.530624
\(754\) 22.3635 22.3635i 0.814430 0.814430i
\(755\) 20.7824 34.1856i 0.756348 1.24414i
\(756\) −4.11094 −0.149513
\(757\) 5.34349i 0.194213i 0.995274 + 0.0971063i \(0.0309587\pi\)
−0.995274 + 0.0971063i \(0.969041\pi\)
\(758\) 3.56273i 0.129404i
\(759\) −1.82961 1.82961i −0.0664105 0.0664105i
\(760\) 1.40708 + 5.77059i 0.0510403 + 0.209321i
\(761\) 29.9342i 1.08511i 0.840019 + 0.542557i \(0.182544\pi\)
−0.840019 + 0.542557i \(0.817456\pi\)
\(762\) 11.3404i 0.410818i
\(763\) −32.4858 −1.17607
\(764\) −7.19163 + 7.19163i −0.260184 + 0.260184i
\(765\) −7.95047 4.83331i −0.287450 0.174749i
\(766\) 17.5102 0.632670
\(767\) 10.0621 + 10.0621i 0.363322 + 0.363322i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) 17.9570 17.9570i 0.647546 0.647546i −0.304853 0.952399i \(-0.598607\pi\)
0.952399 + 0.304853i \(0.0986074\pi\)
\(770\) −5.98228 24.5339i −0.215586 0.884141i
\(771\) −1.90752 1.90752i −0.0686975 0.0686975i
\(772\) −16.3418 −0.588154
\(773\) 20.5041 + 20.5041i 0.737483 + 0.737483i 0.972090 0.234607i \(-0.0753804\pi\)
−0.234607 + 0.972090i \(0.575380\pi\)
\(774\) 6.23482i 0.224106i
\(775\) −11.7815 + 37.1556i −0.423206 + 1.33467i
\(776\) 10.0910i 0.362247i
\(777\) −22.2603 + 11.3918i −0.798583 + 0.408678i
\(778\) −5.52680 5.52680i −0.198145 0.198145i
\(779\) −14.2641 + 14.2641i −0.511065 + 0.511065i
\(780\) 11.3298 2.76262i