Properties

Label 1110.2.u.e.401.20
Level $1110$
Weight $2$
Character 1110.401
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 401.20
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.e.191.20

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.878679 - 1.49262i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.67676 - 0.434124i) q^{6} +2.38487 q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.45585 + 2.62307i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.878679 - 1.49262i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.67676 - 0.434124i) q^{6} +2.38487 q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.45585 + 2.62307i) q^{9} +1.00000 q^{10} +5.76715 q^{11} +(-1.49262 + 0.878679i) q^{12} +(-1.58054 + 1.58054i) q^{13} +(1.68635 - 1.68635i) q^{14} +(0.434124 - 1.67676i) q^{15} -1.00000 q^{16} +(-0.766912 - 0.766912i) q^{17} +(0.825355 + 2.88423i) q^{18} +(4.27127 - 4.27127i) q^{19} +(0.707107 - 0.707107i) q^{20} +(-2.09553 - 3.55970i) q^{21} +(4.07799 - 4.07799i) q^{22} +(5.87049 + 5.87049i) q^{23} +(-0.434124 + 1.67676i) q^{24} +1.00000i q^{25} +2.23522i q^{26} +(5.19448 - 0.131812i) q^{27} -2.38487i q^{28} +(-0.666860 + 0.666860i) q^{29} +(-0.878679 - 1.49262i) q^{30} +(-4.93081 - 4.93081i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-5.06748 - 8.60819i) q^{33} -1.08458 q^{34} +(1.68635 + 1.68635i) q^{35} +(2.62307 + 1.45585i) q^{36} +(5.79440 - 1.85066i) q^{37} -6.04049i q^{38} +(3.74793 + 0.970360i) q^{39} -1.00000i q^{40} +2.85384 q^{41} +(-3.99886 - 1.03533i) q^{42} +(-6.47528 + 6.47528i) q^{43} -5.76715i q^{44} +(-2.88423 + 0.825355i) q^{45} +8.30212 q^{46} -8.44283i q^{47} +(0.878679 + 1.49262i) q^{48} -1.31242 q^{49} +(0.707107 + 0.707107i) q^{50} +(-0.470841 + 1.81858i) q^{51} +(1.58054 + 1.58054i) q^{52} +7.21707i q^{53} +(3.57985 - 3.76626i) q^{54} +(4.07799 + 4.07799i) q^{55} +(-1.68635 - 1.68635i) q^{56} +(-10.1285 - 2.62232i) q^{57} +0.943082i q^{58} +(-5.63841 - 5.63841i) q^{59} +(-1.67676 - 0.434124i) q^{60} +(-8.82247 - 8.82247i) q^{61} -6.97322 q^{62} +(-3.47200 + 6.25568i) q^{63} +1.00000i q^{64} -2.23522 q^{65} +(-9.67016 - 2.50366i) q^{66} -2.96422i q^{67} +(-0.766912 + 0.766912i) q^{68} +(3.60415 - 13.9207i) q^{69} +2.38487 q^{70} -10.2106i q^{71} +(2.88423 - 0.825355i) q^{72} -1.48258i q^{73} +(2.78864 - 5.40587i) q^{74} +(1.49262 - 0.878679i) q^{75} +(-4.27127 - 4.27127i) q^{76} +13.7539 q^{77} +(3.33634 - 1.96404i) q^{78} +(-3.85057 + 3.85057i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(-4.76103 - 7.63758i) q^{81} +(2.01797 - 2.01797i) q^{82} +16.2511i q^{83} +(-3.55970 + 2.09553i) q^{84} -1.08458i q^{85} +9.15744i q^{86} +(1.58133 + 0.409414i) q^{87} +(-4.07799 - 4.07799i) q^{88} +(-3.88764 + 3.88764i) q^{89} +(-1.45585 + 2.62307i) q^{90} +(-3.76937 + 3.76937i) q^{91} +(5.87049 - 5.87049i) q^{92} +(-3.02724 + 11.6924i) q^{93} +(-5.96998 - 5.96998i) q^{94} +6.04049 q^{95} +(1.67676 + 0.434124i) q^{96} +(11.4270 - 11.4270i) q^{97} +(-0.928018 + 0.928018i) q^{98} +(-8.39609 + 15.1277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 24q^{7} - 8q^{9} + O(q^{10}) \) \( 40q - 24q^{7} - 8q^{9} + 40q^{10} - 8q^{12} - 16q^{13} - 40q^{16} + 8q^{18} + 16q^{19} - 24q^{31} + 24q^{33} - 8q^{34} + 16q^{39} - 20q^{42} - 32q^{43} - 8q^{45} + 72q^{46} + 96q^{49} + 20q^{51} + 16q^{52} + 24q^{54} - 16q^{57} + 40q^{61} - 24q^{63} - 44q^{66} - 24q^{70} + 8q^{72} + 8q^{75} - 16q^{76} + 48q^{79} + 24q^{81} - 56q^{82} - 8q^{84} + 12q^{87} - 8q^{90} - 64q^{91} + 12q^{93} + 24q^{94} + 8q^{97} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −0.878679 1.49262i −0.507306 0.861766i
\(4\) 1.00000i 0.500000i
\(5\) 0.707107 + 0.707107i 0.316228 + 0.316228i
\(6\) −1.67676 0.434124i −0.684536 0.177230i
\(7\) 2.38487 0.901395 0.450697 0.892677i \(-0.351175\pi\)
0.450697 + 0.892677i \(0.351175\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −1.45585 + 2.62307i −0.485282 + 0.874358i
\(10\) 1.00000 0.316228
\(11\) 5.76715 1.73886 0.869431 0.494054i \(-0.164485\pi\)
0.869431 + 0.494054i \(0.164485\pi\)
\(12\) −1.49262 + 0.878679i −0.430883 + 0.253653i
\(13\) −1.58054 + 1.58054i −0.438362 + 0.438362i −0.891460 0.453098i \(-0.850319\pi\)
0.453098 + 0.891460i \(0.350319\pi\)
\(14\) 1.68635 1.68635i 0.450697 0.450697i
\(15\) 0.434124 1.67676i 0.112090 0.432939i
\(16\) −1.00000 −0.250000
\(17\) −0.766912 0.766912i −0.186003 0.186003i 0.607962 0.793966i \(-0.291987\pi\)
−0.793966 + 0.607962i \(0.791987\pi\)
\(18\) 0.825355 + 2.88423i 0.194538 + 0.679820i
\(19\) 4.27127 4.27127i 0.979898 0.979898i −0.0199043 0.999802i \(-0.506336\pi\)
0.999802 + 0.0199043i \(0.00633614\pi\)
\(20\) 0.707107 0.707107i 0.158114 0.158114i
\(21\) −2.09553 3.55970i −0.457283 0.776791i
\(22\) 4.07799 4.07799i 0.869431 0.869431i
\(23\) 5.87049 + 5.87049i 1.22408 + 1.22408i 0.966168 + 0.257913i \(0.0830347\pi\)
0.257913 + 0.966168i \(0.416965\pi\)
\(24\) −0.434124 + 1.67676i −0.0886151 + 0.342268i
\(25\) 1.00000i 0.200000i
\(26\) 2.23522i 0.438362i
\(27\) 5.19448 0.131812i 0.999678 0.0253671i
\(28\) 2.38487i 0.450697i
\(29\) −0.666860 + 0.666860i −0.123833 + 0.123833i −0.766307 0.642474i \(-0.777908\pi\)
0.642474 + 0.766307i \(0.277908\pi\)
\(30\) −0.878679 1.49262i −0.160424 0.272514i
\(31\) −4.93081 4.93081i −0.885599 0.885599i 0.108497 0.994097i \(-0.465396\pi\)
−0.994097 + 0.108497i \(0.965396\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −5.06748 8.60819i −0.882135 1.49849i
\(34\) −1.08458 −0.186003
\(35\) 1.68635 + 1.68635i 0.285046 + 0.285046i
\(36\) 2.62307 + 1.45585i 0.437179 + 0.242641i
\(37\) 5.79440 1.85066i 0.952593 0.304247i
\(38\) 6.04049i 0.979898i
\(39\) 3.74793 + 0.970360i 0.600149 + 0.155382i
\(40\) 1.00000i 0.158114i
\(41\) 2.85384 0.445695 0.222847 0.974853i \(-0.428465\pi\)
0.222847 + 0.974853i \(0.428465\pi\)
\(42\) −3.99886 1.03533i −0.617037 0.159754i
\(43\) −6.47528 + 6.47528i −0.987472 + 0.987472i −0.999922 0.0124508i \(-0.996037\pi\)
0.0124508 + 0.999922i \(0.496037\pi\)
\(44\) 5.76715i 0.869431i
\(45\) −2.88423 + 0.825355i −0.429956 + 0.123037i
\(46\) 8.30212 1.22408
\(47\) 8.44283i 1.23151i −0.787936 0.615757i \(-0.788850\pi\)
0.787936 0.615757i \(-0.211150\pi\)
\(48\) 0.878679 + 1.49262i 0.126826 + 0.215442i
\(49\) −1.31242 −0.187488
\(50\) 0.707107 + 0.707107i 0.100000 + 0.100000i
\(51\) −0.470841 + 1.81858i −0.0659309 + 0.254652i
\(52\) 1.58054 + 1.58054i 0.219181 + 0.219181i
\(53\) 7.21707i 0.991341i 0.868511 + 0.495670i \(0.165078\pi\)
−0.868511 + 0.495670i \(0.834922\pi\)
\(54\) 3.57985 3.76626i 0.487156 0.512523i
\(55\) 4.07799 + 4.07799i 0.549877 + 0.549877i
\(56\) −1.68635 1.68635i −0.225349 0.225349i
\(57\) −10.1285 2.62232i −1.34155 0.347335i
\(58\) 0.943082i 0.123833i
\(59\) −5.63841 5.63841i −0.734059 0.734059i 0.237362 0.971421i \(-0.423717\pi\)
−0.971421 + 0.237362i \(0.923717\pi\)
\(60\) −1.67676 0.434124i −0.216469 0.0560451i
\(61\) −8.82247 8.82247i −1.12960 1.12960i −0.990242 0.139360i \(-0.955496\pi\)
−0.139360 0.990242i \(-0.544504\pi\)
\(62\) −6.97322 −0.885599
\(63\) −3.47200 + 6.25568i −0.437430 + 0.788141i
\(64\) 1.00000i 0.125000i
\(65\) −2.23522 −0.277244
\(66\) −9.67016 2.50366i −1.19031 0.308179i
\(67\) 2.96422i 0.362137i −0.983471 0.181068i \(-0.942045\pi\)
0.983471 0.181068i \(-0.0579555\pi\)
\(68\) −0.766912 + 0.766912i −0.0930017 + 0.0930017i
\(69\) 3.60415 13.9207i 0.433888 1.67585i
\(70\) 2.38487 0.285046
\(71\) 10.2106i 1.21177i −0.795552 0.605886i \(-0.792819\pi\)
0.795552 0.605886i \(-0.207181\pi\)
\(72\) 2.88423 0.825355i 0.339910 0.0972690i
\(73\) 1.48258i 0.173523i −0.996229 0.0867615i \(-0.972348\pi\)
0.996229 0.0867615i \(-0.0276518\pi\)
\(74\) 2.78864 5.40587i 0.324173 0.628420i
\(75\) 1.49262 0.878679i 0.172353 0.101461i
\(76\) −4.27127 4.27127i −0.489949 0.489949i
\(77\) 13.7539 1.56740
\(78\) 3.33634 1.96404i 0.377766 0.222384i
\(79\) −3.85057 + 3.85057i −0.433223 + 0.433223i −0.889723 0.456500i \(-0.849103\pi\)
0.456500 + 0.889723i \(0.349103\pi\)
\(80\) −0.707107 0.707107i −0.0790569 0.0790569i
\(81\) −4.76103 7.63758i −0.529003 0.848620i
\(82\) 2.01797 2.01797i 0.222847 0.222847i
\(83\) 16.2511i 1.78378i 0.452248 + 0.891892i \(0.350622\pi\)
−0.452248 + 0.891892i \(0.649378\pi\)
\(84\) −3.55970 + 2.09553i −0.388396 + 0.228641i
\(85\) 1.08458i 0.117639i
\(86\) 9.15744i 0.987472i
\(87\) 1.58133 + 0.409414i 0.169536 + 0.0438938i
\(88\) −4.07799 4.07799i −0.434716 0.434716i
\(89\) −3.88764 + 3.88764i −0.412089 + 0.412089i −0.882466 0.470377i \(-0.844118\pi\)
0.470377 + 0.882466i \(0.344118\pi\)
\(90\) −1.45585 + 2.62307i −0.153460 + 0.276496i
\(91\) −3.76937 + 3.76937i −0.395137 + 0.395137i
\(92\) 5.87049 5.87049i 0.612040 0.612040i
\(93\) −3.02724 + 11.6924i −0.313910 + 1.21245i
\(94\) −5.96998 5.96998i −0.615757 0.615757i
\(95\) 6.04049 0.619742
\(96\) 1.67676 + 0.434124i 0.171134 + 0.0443076i
\(97\) 11.4270 11.4270i 1.16024 1.16024i 0.175815 0.984423i \(-0.443744\pi\)
0.984423 0.175815i \(-0.0562561\pi\)
\(98\) −0.928018 + 0.928018i −0.0937440 + 0.0937440i
\(99\) −8.39609 + 15.1277i −0.843838 + 1.52039i
\(100\) 1.00000 0.100000
\(101\) −2.32729 −0.231574 −0.115787 0.993274i \(-0.536939\pi\)
−0.115787 + 0.993274i \(0.536939\pi\)
\(102\) 0.952995 + 1.61886i 0.0943606 + 0.160291i
\(103\) 3.07081 + 3.07081i 0.302576 + 0.302576i 0.842021 0.539445i \(-0.181366\pi\)
−0.539445 + 0.842021i \(0.681366\pi\)
\(104\) 2.23522 0.219181
\(105\) 1.03533 3.99886i 0.101038 0.390248i
\(106\) 5.10324 + 5.10324i 0.495670 + 0.495670i
\(107\) 10.7333i 1.03762i 0.854888 + 0.518812i \(0.173625\pi\)
−0.854888 + 0.518812i \(0.826375\pi\)
\(108\) −0.131812 5.19448i −0.0126836 0.499839i
\(109\) −6.01820 + 6.01820i −0.576439 + 0.576439i −0.933920 0.357481i \(-0.883636\pi\)
0.357481 + 0.933920i \(0.383636\pi\)
\(110\) 5.76715 0.549877
\(111\) −7.85376 7.02271i −0.745446 0.666567i
\(112\) −2.38487 −0.225349
\(113\) 12.0416 12.0416i 1.13278 1.13278i 0.143069 0.989713i \(-0.454303\pi\)
0.989713 0.143069i \(-0.0456972\pi\)
\(114\) −9.01618 + 5.30766i −0.844443 + 0.497108i
\(115\) 8.30212i 0.774177i
\(116\) 0.666860 + 0.666860i 0.0619164 + 0.0619164i
\(117\) −1.84485 6.44688i −0.170556 0.596014i
\(118\) −7.97392 −0.734059
\(119\) −1.82898 1.82898i −0.167662 0.167662i
\(120\) −1.49262 + 0.878679i −0.136257 + 0.0802121i
\(121\) 22.2601 2.02364
\(122\) −12.4769 −1.12960
\(123\) −2.50761 4.25971i −0.226104 0.384085i
\(124\) −4.93081 + 4.93081i −0.442800 + 0.442800i
\(125\) −0.707107 + 0.707107i −0.0632456 + 0.0632456i
\(126\) 1.96836 + 6.87850i 0.175355 + 0.612786i
\(127\) −10.6143 −0.941868 −0.470934 0.882169i \(-0.656083\pi\)
−0.470934 + 0.882169i \(0.656083\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 15.3549 + 3.97546i 1.35192 + 0.350020i
\(130\) −1.58054 + 1.58054i −0.138622 + 0.138622i
\(131\) −4.84087 + 4.84087i −0.422949 + 0.422949i −0.886218 0.463269i \(-0.846676\pi\)
0.463269 + 0.886218i \(0.346676\pi\)
\(132\) −8.60819 + 5.06748i −0.749246 + 0.441067i
\(133\) 10.1864 10.1864i 0.883274 0.883274i
\(134\) −2.09602 2.09602i −0.181068 0.181068i
\(135\) 3.76626 + 3.57985i 0.324148 + 0.308104i
\(136\) 1.08458i 0.0930017i
\(137\) 22.0782i 1.88627i 0.332415 + 0.943133i \(0.392136\pi\)
−0.332415 + 0.943133i \(0.607864\pi\)
\(138\) −7.29490 12.3919i −0.620983 1.05487i
\(139\) 4.31292i 0.365817i −0.983130 0.182909i \(-0.941449\pi\)
0.983130 0.182909i \(-0.0585512\pi\)
\(140\) 1.68635 1.68635i 0.142523 0.142523i
\(141\) −12.6020 + 7.41854i −1.06128 + 0.624754i
\(142\) −7.21996 7.21996i −0.605886 0.605886i
\(143\) −9.11520 + 9.11520i −0.762251 + 0.762251i
\(144\) 1.45585 2.62307i 0.121320 0.218589i
\(145\) −0.943082 −0.0783187
\(146\) −1.04834 1.04834i −0.0867615 0.0867615i
\(147\) 1.15319 + 1.95894i 0.0951137 + 0.161571i
\(148\) −1.85066 5.79440i −0.152123 0.476297i
\(149\) 19.4968i 1.59724i −0.601837 0.798619i \(-0.705564\pi\)
0.601837 0.798619i \(-0.294436\pi\)
\(150\) 0.434124 1.67676i 0.0354460 0.136907i
\(151\) 3.98542i 0.324329i −0.986764 0.162165i \(-0.948152\pi\)
0.986764 0.162165i \(-0.0518476\pi\)
\(152\) −6.04049 −0.489949
\(153\) 3.12817 0.895161i 0.252898 0.0723695i
\(154\) 9.72547 9.72547i 0.783701 0.783701i
\(155\) 6.97322i 0.560102i
\(156\) 0.970360 3.74793i 0.0776910 0.300075i
\(157\) 22.7620 1.81661 0.908305 0.418310i \(-0.137377\pi\)
0.908305 + 0.418310i \(0.137377\pi\)
\(158\) 5.44553i 0.433223i
\(159\) 10.7724 6.34149i 0.854304 0.502913i
\(160\) −1.00000 −0.0790569
\(161\) 14.0003 + 14.0003i 1.10338 + 1.10338i
\(162\) −8.76714 2.03403i −0.688811 0.159808i
\(163\) −7.51726 7.51726i −0.588798 0.588798i 0.348508 0.937306i \(-0.386688\pi\)
−0.937306 + 0.348508i \(0.886688\pi\)
\(164\) 2.85384i 0.222847i
\(165\) 2.50366 9.67016i 0.194910 0.752821i
\(166\) 11.4912 + 11.4912i 0.891892 + 0.891892i
\(167\) 12.5348 + 12.5348i 0.969973 + 0.969973i 0.999562 0.0295892i \(-0.00941992\pi\)
−0.0295892 + 0.999562i \(0.509420\pi\)
\(168\) −1.03533 + 3.99886i −0.0798772 + 0.308518i
\(169\) 8.00381i 0.615677i
\(170\) −0.766912 0.766912i −0.0588195 0.0588195i
\(171\) 4.98555 + 17.4222i 0.381255 + 1.33231i
\(172\) 6.47528 + 6.47528i 0.493736 + 0.493736i
\(173\) −15.9099 −1.20960 −0.604802 0.796376i \(-0.706748\pi\)
−0.604802 + 0.796376i \(0.706748\pi\)
\(174\) 1.40767 0.828666i 0.106715 0.0628210i
\(175\) 2.38487i 0.180279i
\(176\) −5.76715 −0.434716
\(177\) −3.46167 + 13.3704i −0.260195 + 1.00498i
\(178\) 5.49796i 0.412089i
\(179\) −9.10948 + 9.10948i −0.680875 + 0.680875i −0.960197 0.279322i \(-0.909890\pi\)
0.279322 + 0.960197i \(0.409890\pi\)
\(180\) 0.825355 + 2.88423i 0.0615183 + 0.214978i
\(181\) 4.67113 0.347202 0.173601 0.984816i \(-0.444460\pi\)
0.173601 + 0.984816i \(0.444460\pi\)
\(182\) 5.33069i 0.395137i
\(183\) −5.41650 + 20.9207i −0.400399 + 1.54651i
\(184\) 8.30212i 0.612040i
\(185\) 5.40587 + 2.78864i 0.397448 + 0.205025i
\(186\) 6.12722 + 10.4084i 0.449270 + 0.763180i
\(187\) −4.42290 4.42290i −0.323434 0.323434i
\(188\) −8.44283 −0.615757
\(189\) 12.3881 0.314353i 0.901104 0.0228658i
\(190\) 4.27127 4.27127i 0.309871 0.309871i
\(191\) −2.51857 2.51857i −0.182237 0.182237i 0.610093 0.792330i \(-0.291132\pi\)
−0.792330 + 0.610093i \(0.791132\pi\)
\(192\) 1.49262 0.878679i 0.107721 0.0634132i
\(193\) −4.71089 + 4.71089i −0.339098 + 0.339098i −0.856028 0.516930i \(-0.827075\pi\)
0.516930 + 0.856028i \(0.327075\pi\)
\(194\) 16.1603i 1.16024i
\(195\) 1.96404 + 3.33634i 0.140648 + 0.238920i
\(196\) 1.31242i 0.0937440i
\(197\) 10.7908i 0.768811i 0.923164 + 0.384406i \(0.125594\pi\)
−0.923164 + 0.384406i \(0.874406\pi\)
\(198\) 4.75995 + 16.6338i 0.338275 + 1.18211i
\(199\) 4.64611 + 4.64611i 0.329354 + 0.329354i 0.852341 0.522987i \(-0.175182\pi\)
−0.522987 + 0.852341i \(0.675182\pi\)
\(200\) 0.707107 0.707107i 0.0500000 0.0500000i
\(201\) −4.42446 + 2.60459i −0.312077 + 0.183714i
\(202\) −1.64564 + 1.64564i −0.115787 + 0.115787i
\(203\) −1.59037 + 1.59037i −0.111622 + 0.111622i
\(204\) 1.81858 + 0.470841i 0.127326 + 0.0329654i
\(205\) 2.01797 + 2.01797i 0.140941 + 0.140941i
\(206\) 4.34279 0.302576
\(207\) −23.9452 + 6.85219i −1.66431 + 0.476260i
\(208\) 1.58054 1.58054i 0.109591 0.109591i
\(209\) 24.6331 24.6331i 1.70391 1.70391i
\(210\) −2.09553 3.55970i −0.144605 0.245643i
\(211\) 3.92953 0.270520 0.135260 0.990810i \(-0.456813\pi\)
0.135260 + 0.990810i \(0.456813\pi\)
\(212\) 7.21707 0.495670
\(213\) −15.2405 + 8.97181i −1.04426 + 0.614738i
\(214\) 7.58956 + 7.58956i 0.518812 + 0.518812i
\(215\) −9.15744 −0.624532
\(216\) −3.76626 3.57985i −0.256261 0.243578i
\(217\) −11.7593 11.7593i −0.798275 0.798275i
\(218\) 8.51102i 0.576439i
\(219\) −2.21293 + 1.30271i −0.149536 + 0.0880292i
\(220\) 4.07799 4.07799i 0.274938 0.274938i
\(221\) 2.42426 0.163074
\(222\) −10.5193 + 0.587635i −0.706006 + 0.0394395i
\(223\) 15.8876 1.06391 0.531956 0.846772i \(-0.321457\pi\)
0.531956 + 0.846772i \(0.321457\pi\)
\(224\) −1.68635 + 1.68635i −0.112674 + 0.112674i
\(225\) −2.62307 1.45585i −0.174872 0.0970564i
\(226\) 17.0294i 1.13278i
\(227\) 2.98325 + 2.98325i 0.198005 + 0.198005i 0.799144 0.601139i \(-0.205286\pi\)
−0.601139 + 0.799144i \(0.705286\pi\)
\(228\) −2.62232 + 10.1285i −0.173667 + 0.670775i
\(229\) 23.9167 1.58046 0.790229 0.612812i \(-0.209962\pi\)
0.790229 + 0.612812i \(0.209962\pi\)
\(230\) 5.87049 + 5.87049i 0.387088 + 0.387088i
\(231\) −12.0853 20.5294i −0.795152 1.35073i
\(232\) 0.943082 0.0619164
\(233\) −25.6460 −1.68013 −0.840063 0.542489i \(-0.817482\pi\)
−0.840063 + 0.542489i \(0.817482\pi\)
\(234\) −5.86314 3.25413i −0.383285 0.212729i
\(235\) 5.96998 5.96998i 0.389439 0.389439i
\(236\) −5.63841 + 5.63841i −0.367029 + 0.367029i
\(237\) 9.13087 + 2.36403i 0.593114 + 0.153561i
\(238\) −2.58657 −0.167662
\(239\) 11.0015 + 11.0015i 0.711626 + 0.711626i 0.966875 0.255249i \(-0.0821574\pi\)
−0.255249 + 0.966875i \(0.582157\pi\)
\(240\) −0.434124 + 1.67676i −0.0280226 + 0.108235i
\(241\) −20.6461 + 20.6461i −1.32993 + 1.32993i −0.424503 + 0.905427i \(0.639551\pi\)
−0.905427 + 0.424503i \(0.860449\pi\)
\(242\) 15.7402 15.7402i 1.01182 1.01182i
\(243\) −7.21661 + 13.8174i −0.462946 + 0.886387i
\(244\) −8.82247 + 8.82247i −0.564801 + 0.564801i
\(245\) −0.928018 0.928018i −0.0592889 0.0592889i
\(246\) −4.78521 1.23892i −0.305094 0.0789906i
\(247\) 13.5018i 0.859100i
\(248\) 6.97322i 0.442800i
\(249\) 24.2567 14.2795i 1.53721 0.904924i
\(250\) 1.00000i 0.0632456i
\(251\) −3.73539 + 3.73539i −0.235776 + 0.235776i −0.815098 0.579323i \(-0.803317\pi\)
0.579323 + 0.815098i \(0.303317\pi\)
\(252\) 6.25568 + 3.47200i 0.394071 + 0.218715i
\(253\) 33.8560 + 33.8560i 2.12851 + 2.12851i
\(254\) −7.50545 + 7.50545i −0.470934 + 0.470934i
\(255\) −1.61886 + 0.952995i −0.101377 + 0.0596789i
\(256\) 1.00000 0.0625000
\(257\) −9.24794 9.24794i −0.576870 0.576870i 0.357169 0.934040i \(-0.383742\pi\)
−0.934040 + 0.357169i \(0.883742\pi\)
\(258\) 13.6686 8.04645i 0.850970 0.500950i
\(259\) 13.8189 4.41358i 0.858662 0.274246i
\(260\) 2.23522i 0.138622i
\(261\) −0.778377 2.72007i −0.0481803 0.168368i
\(262\) 6.84602i 0.422949i
\(263\) −13.9407 −0.859620 −0.429810 0.902919i \(-0.641419\pi\)
−0.429810 + 0.902919i \(0.641419\pi\)
\(264\) −2.50366 + 9.67016i −0.154090 + 0.595157i
\(265\) −5.10324 + 5.10324i −0.313489 + 0.313489i
\(266\) 14.4058i 0.883274i
\(267\) 9.21878 + 2.38679i 0.564180 + 0.146069i
\(268\) −2.96422 −0.181068
\(269\) 10.1133i 0.616617i −0.951287 0.308308i \(-0.900237\pi\)
0.951287 0.308308i \(-0.0997628\pi\)
\(270\) 5.19448 0.131812i 0.316126 0.00802180i
\(271\) 29.2907 1.77928 0.889640 0.456662i \(-0.150955\pi\)
0.889640 + 0.456662i \(0.150955\pi\)
\(272\) 0.766912 + 0.766912i 0.0465009 + 0.0465009i
\(273\) 8.93831 + 2.31418i 0.540971 + 0.140060i
\(274\) 15.6116 + 15.6116i 0.943133 + 0.943133i
\(275\) 5.76715i 0.347773i
\(276\) −13.9207 3.60415i −0.837927 0.216944i
\(277\) −11.9085 11.9085i −0.715514 0.715514i 0.252169 0.967683i \(-0.418856\pi\)
−0.967683 + 0.252169i \(0.918856\pi\)
\(278\) −3.04969 3.04969i −0.182909 0.182909i
\(279\) 20.1124 5.75538i 1.20410 0.344565i
\(280\) 2.38487i 0.142523i
\(281\) −3.54960 3.54960i −0.211751 0.211751i 0.593260 0.805011i \(-0.297841\pi\)
−0.805011 + 0.593260i \(0.797841\pi\)
\(282\) −3.66523 + 14.1566i −0.218261 + 0.843015i
\(283\) −9.57331 9.57331i −0.569074 0.569074i 0.362795 0.931869i \(-0.381823\pi\)
−0.931869 + 0.362795i \(0.881823\pi\)
\(284\) −10.2106 −0.605886
\(285\) −5.30766 9.01618i −0.314398 0.534072i
\(286\) 12.8908i 0.762251i
\(287\) 6.80602 0.401747
\(288\) −0.825355 2.88423i −0.0486345 0.169955i
\(289\) 15.8237i 0.930805i
\(290\) −0.666860 + 0.666860i −0.0391593 + 0.0391593i
\(291\) −27.0969 7.01555i −1.58845 0.411259i
\(292\) −1.48258 −0.0867615
\(293\) 4.08873i 0.238866i −0.992842 0.119433i \(-0.961892\pi\)
0.992842 0.119433i \(-0.0381077\pi\)
\(294\) 2.20061 + 0.569751i 0.128342 + 0.0332285i
\(295\) 7.97392i 0.464259i
\(296\) −5.40587 2.78864i −0.314210 0.162087i
\(297\) 29.9574 0.760178i 1.73830 0.0441100i
\(298\) −13.7863 13.7863i −0.798619 0.798619i
\(299\) −18.5570 −1.07318
\(300\) −0.878679 1.49262i −0.0507306 0.0861766i
\(301\) −15.4427 + 15.4427i −0.890102 + 0.890102i
\(302\) −2.81812 2.81812i −0.162165 0.162165i
\(303\) 2.04494 + 3.47376i 0.117479 + 0.199563i
\(304\) −4.27127 + 4.27127i −0.244974 + 0.244974i
\(305\) 12.4769i 0.714423i
\(306\) 1.57898 2.84493i 0.0902641 0.162634i
\(307\) 2.82576i 0.161275i −0.996744 0.0806373i \(-0.974304\pi\)
0.996744 0.0806373i \(-0.0256956\pi\)
\(308\) 13.7539i 0.783701i
\(309\) 1.88531 7.28183i 0.107251 0.414249i
\(310\) −4.93081 4.93081i −0.280051 0.280051i
\(311\) −9.24050 + 9.24050i −0.523981 + 0.523981i −0.918771 0.394790i \(-0.870817\pi\)
0.394790 + 0.918771i \(0.370817\pi\)
\(312\) −1.96404 3.33634i −0.111192 0.188883i
\(313\) −3.34887 + 3.34887i −0.189290 + 0.189290i −0.795389 0.606099i \(-0.792733\pi\)
0.606099 + 0.795389i \(0.292733\pi\)
\(314\) 16.0952 16.0952i 0.908305 0.908305i
\(315\) −6.87850 + 1.96836i −0.387560 + 0.110905i
\(316\) 3.85057 + 3.85057i 0.216612 + 0.216612i
\(317\) −25.0019 −1.40425 −0.702123 0.712056i \(-0.747764\pi\)
−0.702123 + 0.712056i \(0.747764\pi\)
\(318\) 3.13310 12.1013i 0.175696 0.678608i
\(319\) −3.84588 + 3.84588i −0.215328 + 0.215328i
\(320\) −0.707107 + 0.707107i −0.0395285 + 0.0395285i
\(321\) 16.0207 9.43109i 0.894189 0.526392i
\(322\) 19.7994 1.10338
\(323\) −6.55138 −0.364529
\(324\) −7.63758 + 4.76103i −0.424310 + 0.264501i
\(325\) −1.58054 1.58054i −0.0876724 0.0876724i
\(326\) −10.6310 −0.588798
\(327\) 14.2710 + 3.69484i 0.789187 + 0.204325i
\(328\) −2.01797 2.01797i −0.111424 0.111424i
\(329\) 20.1350i 1.11008i
\(330\) −5.06748 8.60819i −0.278956 0.473865i
\(331\) −16.1922 + 16.1922i −0.890002 + 0.890002i −0.994523 0.104520i \(-0.966669\pi\)
0.104520 + 0.994523i \(0.466669\pi\)
\(332\) 16.2511 0.891892
\(333\) −3.58133 + 17.8934i −0.196256 + 0.980553i
\(334\) 17.7269 0.969973
\(335\) 2.09602 2.09602i 0.114518 0.114518i
\(336\) 2.09553 + 3.55970i 0.114321 + 0.194198i
\(337\) 11.4390i 0.623121i 0.950226 + 0.311560i \(0.100852\pi\)
−0.950226 + 0.311560i \(0.899148\pi\)
\(338\) 5.65955 + 5.65955i 0.307839 + 0.307839i
\(339\) −28.5544 7.39289i −1.55086 0.401526i
\(340\) −1.08458 −0.0588195
\(341\) −28.4367 28.4367i −1.53994 1.53994i
\(342\) 15.8447 + 8.79403i 0.856781 + 0.475527i
\(343\) −19.8240 −1.07040
\(344\) 9.15744 0.493736
\(345\) 12.3919 7.29490i 0.667159 0.392744i
\(346\) −11.2500 + 11.2500i −0.604802 + 0.604802i
\(347\) −5.80793 + 5.80793i −0.311786 + 0.311786i −0.845601 0.533815i \(-0.820758\pi\)
0.533815 + 0.845601i \(0.320758\pi\)
\(348\) 0.409414 1.58133i 0.0219469 0.0847679i
\(349\) 11.5690 0.619277 0.309638 0.950854i \(-0.399792\pi\)
0.309638 + 0.950854i \(0.399792\pi\)
\(350\) 1.68635 + 1.68635i 0.0901395 + 0.0901395i
\(351\) −8.00173 + 8.41840i −0.427101 + 0.449341i
\(352\) −4.07799 + 4.07799i −0.217358 + 0.217358i
\(353\) −8.48939 + 8.48939i −0.451845 + 0.451845i −0.895966 0.444122i \(-0.853516\pi\)
0.444122 + 0.895966i \(0.353516\pi\)
\(354\) 7.00652 + 11.9021i 0.372392 + 0.632587i
\(355\) 7.21996 7.21996i 0.383196 0.383196i
\(356\) 3.88764 + 3.88764i 0.206045 + 0.206045i
\(357\) −1.12289 + 4.33707i −0.0594297 + 0.229542i
\(358\) 12.8828i 0.680875i
\(359\) 22.1081i 1.16682i 0.812177 + 0.583411i \(0.198282\pi\)
−0.812177 + 0.583411i \(0.801718\pi\)
\(360\) 2.62307 + 1.45585i 0.138248 + 0.0767298i
\(361\) 17.4876i 0.920399i
\(362\) 3.30299 3.30299i 0.173601 0.173601i
\(363\) −19.5595 33.2259i −1.02661 1.74391i
\(364\) 3.76937 + 3.76937i 0.197569 + 0.197569i
\(365\) 1.04834 1.04834i 0.0548728 0.0548728i
\(366\) 10.9632 + 18.6232i 0.573053 + 0.973452i
\(367\) −21.8077 −1.13835 −0.569176 0.822216i \(-0.692738\pi\)
−0.569176 + 0.822216i \(0.692738\pi\)
\(368\) −5.87049 5.87049i −0.306020 0.306020i
\(369\) −4.15475 + 7.48583i −0.216288 + 0.389697i
\(370\) 5.79440 1.85066i 0.301236 0.0962113i
\(371\) 17.2117i 0.893589i
\(372\) 11.6924 + 3.02724i 0.606225 + 0.156955i
\(373\) 18.7132i 0.968931i −0.874810 0.484465i \(-0.839014\pi\)
0.874810 0.484465i \(-0.160986\pi\)
\(374\) −6.25492 −0.323434
\(375\) 1.67676 + 0.434124i 0.0865877 + 0.0224180i
\(376\) −5.96998 + 5.96998i −0.307878 + 0.307878i
\(377\) 2.10799i 0.108567i
\(378\) 8.53746 8.98202i 0.439119 0.461985i
\(379\) −5.00400 −0.257038 −0.128519 0.991707i \(-0.541022\pi\)
−0.128519 + 0.991707i \(0.541022\pi\)
\(380\) 6.04049i 0.309871i
\(381\) 9.32657 + 15.8432i 0.477815 + 0.811670i
\(382\) −3.56179 −0.182237
\(383\) 7.07401 + 7.07401i 0.361465 + 0.361465i 0.864352 0.502887i \(-0.167729\pi\)
−0.502887 + 0.864352i \(0.667729\pi\)
\(384\) 0.434124 1.67676i 0.0221538 0.0855670i
\(385\) 9.72547 + 9.72547i 0.495656 + 0.495656i
\(386\) 6.66221i 0.339098i
\(387\) −7.55813 26.4122i −0.384201 1.34261i
\(388\) −11.4270 11.4270i −0.580119 0.580119i
\(389\) −8.14631 8.14631i −0.413034 0.413034i 0.469760 0.882794i \(-0.344340\pi\)
−0.882794 + 0.469760i \(0.844340\pi\)
\(390\) 3.74793 + 0.970360i 0.189784 + 0.0491361i
\(391\) 9.00429i 0.455367i
\(392\) 0.928018 + 0.928018i 0.0468720 + 0.0468720i
\(393\) 11.4792 + 2.97202i 0.579047 + 0.149919i
\(394\) 7.63023 + 7.63023i 0.384406 + 0.384406i
\(395\) −5.44553 −0.273994
\(396\) 15.1277 + 8.39609i 0.760194 + 0.421919i
\(397\) 24.1303i 1.21106i 0.795821 + 0.605532i \(0.207040\pi\)
−0.795821 + 0.605532i \(0.792960\pi\)
\(398\) 6.57059 0.329354
\(399\) −24.1551 6.25389i −1.20927 0.313086i
\(400\) 1.00000i 0.0500000i
\(401\) −2.25525 + 2.25525i −0.112622 + 0.112622i −0.761172 0.648550i \(-0.775376\pi\)
0.648550 + 0.761172i \(0.275376\pi\)
\(402\) −1.28684 + 4.97029i −0.0641815 + 0.247895i
\(403\) 15.5867 0.776426
\(404\) 2.32729i 0.115787i
\(405\) 2.03403 8.76714i 0.101072 0.435643i
\(406\) 2.24912i 0.111622i
\(407\) 33.4172 10.6730i 1.65643 0.529043i
\(408\) 1.61886 0.952995i 0.0801457 0.0471803i
\(409\) 0.672279 + 0.672279i 0.0332420 + 0.0332420i 0.723532 0.690290i \(-0.242517\pi\)
−0.690290 + 0.723532i \(0.742517\pi\)
\(410\) 2.85384 0.140941
\(411\) 32.9544 19.3996i 1.62552 0.956914i
\(412\) 3.07081 3.07081i 0.151288 0.151288i
\(413\) −13.4469 13.4469i −0.661676 0.661676i
\(414\) −12.0866 + 21.7771i −0.594024 + 1.07028i
\(415\) −11.4912 + 11.4912i −0.564082 + 0.564082i
\(416\) 2.23522i 0.109591i
\(417\) −6.43756 + 3.78967i −0.315249 + 0.185581i
\(418\) 34.8365i 1.70391i
\(419\) 8.78968i 0.429404i 0.976680 + 0.214702i \(0.0688780\pi\)
−0.976680 + 0.214702i \(0.931122\pi\)
\(420\) −3.99886 1.03533i −0.195124 0.0505188i
\(421\) −22.8305 22.8305i −1.11269 1.11269i −0.992786 0.119903i \(-0.961742\pi\)
−0.119903 0.992786i \(-0.538258\pi\)
\(422\) 2.77860 2.77860i 0.135260 0.135260i
\(423\) 22.1462 + 12.2915i 1.07678 + 0.597631i
\(424\) 5.10324 5.10324i 0.247835 0.247835i
\(425\) 0.766912 0.766912i 0.0372007 0.0372007i
\(426\) −4.43265 + 17.1207i −0.214762 + 0.829501i
\(427\) −21.0404 21.0404i −1.01822 1.01822i
\(428\) 10.7333 0.518812
\(429\) 21.6149 + 5.59622i 1.04358 + 0.270188i
\(430\) −6.47528 + 6.47528i −0.312266 + 0.312266i
\(431\) 21.2557 21.2557i 1.02385 1.02385i 0.0241401 0.999709i \(-0.492315\pi\)
0.999709 0.0241401i \(-0.00768479\pi\)
\(432\) −5.19448 + 0.131812i −0.249920 + 0.00634179i
\(433\) −20.9909 −1.00876 −0.504379 0.863483i \(-0.668278\pi\)
−0.504379 + 0.863483i \(0.668278\pi\)
\(434\) −16.6302 −0.798275
\(435\) 0.828666 + 1.40767i 0.0397315 + 0.0674924i
\(436\) 6.01820 + 6.01820i 0.288220 + 0.288220i
\(437\) 50.1489 2.39895
\(438\) −0.643624 + 2.48594i −0.0307535 + 0.118783i
\(439\) −1.49381 1.49381i −0.0712955 0.0712955i 0.670560 0.741855i \(-0.266054\pi\)
−0.741855 + 0.670560i \(0.766054\pi\)
\(440\) 5.76715i 0.274938i
\(441\) 1.91067 3.44256i 0.0909845 0.163932i
\(442\) 1.71421 1.71421i 0.0815369 0.0815369i
\(443\) 5.07352 0.241050 0.120525 0.992710i \(-0.461542\pi\)
0.120525 + 0.992710i \(0.461542\pi\)
\(444\) −7.02271 + 7.85376i −0.333283 + 0.372723i
\(445\) −5.49796 −0.260628
\(446\) 11.2342 11.2342i 0.531956 0.531956i
\(447\) −29.1013 + 17.1314i −1.37645 + 0.810288i
\(448\) 2.38487i 0.112674i
\(449\) −3.64509 3.64509i −0.172022 0.172022i 0.615845 0.787867i \(-0.288815\pi\)
−0.787867 + 0.615845i \(0.788815\pi\)
\(450\) −2.88423 + 0.825355i −0.135964 + 0.0389076i
\(451\) 16.4585 0.775002
\(452\) −12.0416 12.0416i −0.566391 0.566391i
\(453\) −5.94873 + 3.50191i −0.279496 + 0.164534i
\(454\) 4.21895 0.198005
\(455\) −5.33069 −0.249907
\(456\) 5.30766 + 9.01618i 0.248554 + 0.422221i
\(457\) −14.4628 + 14.4628i −0.676539 + 0.676539i −0.959215 0.282676i \(-0.908778\pi\)
0.282676 + 0.959215i \(0.408778\pi\)
\(458\) 16.9116 16.9116i 0.790229 0.790229i
\(459\) −4.08480 3.88262i −0.190662 0.181225i
\(460\) 8.30212 0.387088
\(461\) −3.48415 3.48415i −0.162273 0.162273i 0.621300 0.783573i \(-0.286605\pi\)
−0.783573 + 0.621300i \(0.786605\pi\)
\(462\) −23.0620 5.97089i −1.07294 0.277791i
\(463\) 13.8483 13.8483i 0.643586 0.643586i −0.307849 0.951435i \(-0.599609\pi\)
0.951435 + 0.307849i \(0.0996091\pi\)
\(464\) 0.666860 0.666860i 0.0309582 0.0309582i
\(465\) −10.4084 + 6.12722i −0.482677 + 0.284143i
\(466\) −18.1345 + 18.1345i −0.840063 + 0.840063i
\(467\) −4.04485 4.04485i −0.187173 0.187173i 0.607300 0.794473i \(-0.292253\pi\)
−0.794473 + 0.607300i \(0.792253\pi\)
\(468\) −6.44688 + 1.84485i −0.298007 + 0.0852780i
\(469\) 7.06926i 0.326428i
\(470\) 8.44283i 0.389439i
\(471\) −20.0005 33.9751i −0.921576 1.56549i
\(472\) 7.97392i 0.367029i
\(473\) −37.3440 + 37.3440i −1.71708 + 1.71708i
\(474\) 8.12813 4.78488i 0.373337 0.219777i
\(475\) 4.27127 + 4.27127i 0.195980 + 0.195980i
\(476\) −1.82898 + 1.82898i −0.0838312 + 0.0838312i
\(477\) −18.9309 10.5069i −0.866786 0.481080i
\(478\) 15.5584 0.711626
\(479\) −4.03608 4.03608i −0.184413 0.184413i 0.608862 0.793276i \(-0.291626\pi\)
−0.793276 + 0.608862i \(0.791626\pi\)
\(480\) 0.878679 + 1.49262i 0.0401060 + 0.0681286i
\(481\) −6.23322 + 12.0833i −0.284211 + 0.550951i
\(482\) 29.1979i 1.32993i
\(483\) 8.59541 33.1990i 0.391105 1.51061i
\(484\) 22.2601i 1.01182i
\(485\) 16.1603 0.733799
\(486\) 4.66746 + 14.8733i 0.211720 + 0.674666i
\(487\) 5.50666 5.50666i 0.249531 0.249531i −0.571247 0.820778i \(-0.693540\pi\)
0.820778 + 0.571247i \(0.193540\pi\)
\(488\) 12.4769i 0.564801i
\(489\) −4.61518 + 17.8257i −0.208705 + 0.806106i
\(490\) −1.31242 −0.0592889
\(491\) 14.6275i 0.660132i 0.943958 + 0.330066i \(0.107071\pi\)
−0.943958 + 0.330066i \(0.892929\pi\)
\(492\) −4.25971 + 2.50761i −0.192042 + 0.113052i
\(493\) 1.02285 0.0460666
\(494\) 9.54722 + 9.54722i 0.429550 + 0.429550i
\(495\) −16.6338 + 4.75995i −0.747634 + 0.213944i
\(496\) 4.93081 + 4.93081i 0.221400 + 0.221400i
\(497\) 24.3508i 1.09228i
\(498\) 7.05497 27.2492i 0.316141 1.22106i
\(499\) −3.49525 3.49525i −0.156469 0.156469i 0.624531 0.781000i \(-0.285290\pi\)
−0.781000 + 0.624531i \(0.785290\pi\)
\(500\) 0.707107 + 0.707107i 0.0316228 + 0.0316228i
\(501\) 7.69567 29.7238i 0.343817 1.32796i
\(502\) 5.28264i 0.235776i
\(503\) 22.0215 + 22.0215i 0.981892 + 0.981892i 0.999839 0.0179468i \(-0.00571296\pi\)
−0.0179468 + 0.999839i \(0.505713\pi\)
\(504\) 6.87850 1.96836i 0.306393 0.0876777i
\(505\) −1.64564 1.64564i −0.0732301 0.0732301i
\(506\) 47.8796 2.12851
\(507\) 11.9467 7.03278i 0.530570 0.312337i
\(508\) 10.6143i 0.470934i
\(509\) −31.9079 −1.41429 −0.707147 0.707067i \(-0.750018\pi\)
−0.707147 + 0.707067i \(0.750018\pi\)
\(510\) −0.470841 + 1.81858i −0.0208492 + 0.0805281i
\(511\) 3.53576i 0.156413i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 21.6240 22.7501i 0.954725 1.00444i
\(514\) −13.0786 −0.576870
\(515\) 4.34279i 0.191366i
\(516\) 3.97546 15.3549i 0.175010 0.675960i
\(517\) 48.6911i 2.14143i
\(518\) 6.65054 12.8923i 0.292208 0.566454i
\(519\) 13.9797 + 23.7474i 0.613639 + 1.04240i
\(520\) 1.58054 + 1.58054i 0.0693111 + 0.0693111i
\(521\) −9.90496 −0.433944 −0.216972 0.976178i \(-0.569618\pi\)
−0.216972 + 0.976178i \(0.569618\pi\)
\(522\) −2.47377 1.37298i −0.108274 0.0600938i
\(523\) 13.6371 13.6371i 0.596307 0.596307i −0.343021 0.939328i \(-0.611450\pi\)
0.939328 + 0.343021i \(0.111450\pi\)
\(524\) 4.84087 + 4.84087i 0.211474 + 0.211474i
\(525\) 3.55970 2.09553i 0.155358 0.0914565i
\(526\) −9.85756 + 9.85756i −0.429810 + 0.429810i
\(527\) 7.56299i 0.329449i
\(528\) 5.06748 + 8.60819i 0.220534 + 0.374623i
\(529\) 45.9252i 1.99675i
\(530\) 7.21707i 0.313489i
\(531\) 22.9986 6.58131i 0.998055 0.285605i
\(532\) −10.1864 10.1864i −0.441637 0.441637i
\(533\) −4.51060 + 4.51060i −0.195376 + 0.195376i
\(534\) 8.20638 4.83094i 0.355125 0.209055i
\(535\) −7.58956 + 7.58956i −0.328125 + 0.328125i
\(536\) −2.09602 + 2.09602i −0.0905341 + 0.0905341i
\(537\) 21.6013 + 5.59271i 0.932167 + 0.241343i
\(538\) −7.15116 7.15116i −0.308308 0.308308i
\(539\) −7.56890 −0.326016
\(540\) 3.57985 3.76626i 0.154052 0.162074i
\(541\) 19.1072 19.1072i 0.821484 0.821484i −0.164837 0.986321i \(-0.552710\pi\)
0.986321 + 0.164837i \(0.0527099\pi\)
\(542\) 20.7116 20.7116i 0.889640 0.889640i
\(543\) −4.10442 6.97223i −0.176138 0.299207i
\(544\) 1.08458 0.0465009
\(545\) −8.51102 −0.364572
\(546\) 7.95671 4.68397i 0.340516 0.200455i
\(547\) −27.2486 27.2486i −1.16507 1.16507i −0.983351 0.181714i \(-0.941836\pi\)
−0.181714 0.983351i \(-0.558164\pi\)
\(548\) 22.0782 0.943133
\(549\) 35.9861 10.2978i 1.53585 0.439501i
\(550\) 4.07799 + 4.07799i 0.173886 + 0.173886i
\(551\) 5.69668i 0.242687i
\(552\) −12.3919 + 7.29490i −0.527436 + 0.310492i
\(553\) −9.18310 + 9.18310i −0.390505 + 0.390505i
\(554\) −16.8412 −0.715514
\(555\) −0.587635 10.5193i −0.0249437 0.446517i
\(556\) −4.31292 −0.182909
\(557\) −2.90028 + 2.90028i −0.122889 + 0.122889i −0.765876 0.642988i \(-0.777695\pi\)
0.642988 + 0.765876i \(0.277695\pi\)
\(558\) 10.1519 18.2913i 0.429765 0.774331i
\(559\) 20.4689i 0.865740i
\(560\) −1.68635 1.68635i −0.0712615 0.0712615i
\(561\) −2.71541 + 10.4880i −0.114645 + 0.442805i
\(562\) −5.01989 −0.211751
\(563\) −2.02165 2.02165i −0.0852024 0.0852024i 0.663221 0.748424i \(-0.269189\pi\)
−0.748424 + 0.663221i \(0.769189\pi\)
\(564\) 7.41854 + 12.6020i 0.312377 + 0.530638i
\(565\) 17.0294 0.716434
\(566\) −13.5387 −0.569074
\(567\) −11.3544 18.2146i −0.476840 0.764941i
\(568\) −7.21996 + 7.21996i −0.302943 + 0.302943i
\(569\) −1.16582 + 1.16582i −0.0488736 + 0.0488736i −0.731121 0.682248i \(-0.761003\pi\)
0.682248 + 0.731121i \(0.261003\pi\)
\(570\) −10.1285 2.62232i −0.424235 0.109837i
\(571\) 2.10782 0.0882095 0.0441048 0.999027i \(-0.485956\pi\)
0.0441048 + 0.999027i \(0.485956\pi\)
\(572\) 9.11520 + 9.11520i 0.381126 + 0.381126i
\(573\) −1.54626 + 5.97228i −0.0645958 + 0.249496i
\(574\) 4.81259 4.81259i 0.200873 0.200873i
\(575\) −5.87049 + 5.87049i −0.244816 + 0.244816i
\(576\) −2.62307 1.45585i −0.109295 0.0606602i
\(577\) −10.2491 + 10.2491i −0.426674 + 0.426674i −0.887494 0.460820i \(-0.847555\pi\)
0.460820 + 0.887494i \(0.347555\pi\)
\(578\) −11.1890 11.1890i −0.465403 0.465403i
\(579\) 11.1710 + 2.89222i 0.464249 + 0.120197i
\(580\) 0.943082i 0.0391593i
\(581\) 38.7566i 1.60789i
\(582\) −24.1212 + 14.1997i −0.999854 + 0.588596i
\(583\) 41.6219i 1.72381i
\(584\) −1.04834 + 1.04834i −0.0433808 + 0.0433808i
\(585\) 3.25413 5.86314i 0.134542 0.242411i
\(586\) −2.89117 2.89117i −0.119433 0.119433i
\(587\) −19.4626 + 19.4626i −0.803309 + 0.803309i −0.983611 0.180303i \(-0.942292\pi\)
0.180303 + 0.983611i \(0.442292\pi\)
\(588\) 1.95894 1.15319i 0.0807854 0.0475568i
\(589\) −42.1217 −1.73559
\(590\) −5.63841 5.63841i −0.232130 0.232130i
\(591\) 16.1066 9.48163i 0.662535 0.390022i
\(592\) −5.79440 + 1.85066i −0.238148 + 0.0760617i
\(593\) 19.0894i 0.783909i 0.919985 + 0.391954i \(0.128201\pi\)
−0.919985 + 0.391954i \(0.871799\pi\)
\(594\) 20.6455 21.7206i 0.847097 0.891206i
\(595\) 2.58657i 0.106039i
\(596\) −19.4968 −0.798619
\(597\) 2.85245 11.0173i 0.116743 0.450909i
\(598\) −13.1218 + 13.1218i −0.536591 + 0.536591i
\(599\) 6.46972i 0.264346i −0.991227 0.132173i \(-0.957805\pi\)
0.991227 0.132173i \(-0.0421954\pi\)
\(600\) −1.67676 0.434124i −0.0684536 0.0177230i
\(601\) 7.19361 0.293433 0.146717 0.989179i \(-0.453129\pi\)
0.146717 + 0.989179i \(0.453129\pi\)
\(602\) 21.8393i 0.890102i
\(603\) 7.77535 + 4.31544i 0.316637 + 0.175738i
\(604\) −3.98542 −0.162165
\(605\) 15.7402 + 15.7402i 0.639932 + 0.639932i
\(606\) 3.90231 + 1.01033i 0.158521 + 0.0410419i
\(607\) 10.2240 + 10.2240i 0.414978 + 0.414978i 0.883468 0.468491i \(-0.155202\pi\)
−0.468491 + 0.883468i \(0.655202\pi\)
\(608\) 6.04049i 0.244974i
\(609\) 3.77125 + 0.976398i 0.152819 + 0.0395656i
\(610\) −8.82247 8.82247i −0.357211 0.357211i
\(611\) 13.3442 + 13.3442i 0.539849 + 0.539849i
\(612\) −0.895161 3.12817i −0.0361847 0.126449i
\(613\) 10.1511i 0.409999i −0.978762 0.205000i \(-0.934281\pi\)
0.978762 0.205000i \(-0.0657193\pi\)
\(614\) −1.99811 1.99811i −0.0806373 0.0806373i
\(615\) 1.23892 4.78521i 0.0499580 0.192958i
\(616\) −9.72547 9.72547i −0.391850 0.391850i
\(617\) 37.4403 1.50729 0.753646 0.657281i \(-0.228294\pi\)
0.753646 + 0.657281i \(0.228294\pi\)
\(618\) −3.81592 6.48214i −0.153499 0.260750i
\(619\) 9.57027i 0.384661i −0.981330 0.192331i \(-0.938395\pi\)
0.981330 0.192331i \(-0.0616046\pi\)
\(620\) −6.97322 −0.280051
\(621\) 31.2679 + 29.7203i 1.25474 + 1.19264i
\(622\) 13.0680i 0.523981i
\(623\) −9.27151 + 9.27151i −0.371455 + 0.371455i
\(624\) −3.74793 0.970360i −0.150037 0.0388455i
\(625\) −1.00000 −0.0400000
\(626\) 4.73602i 0.189290i
\(627\) −58.4125 15.1233i −2.33277 0.603968i
\(628\) 22.7620i 0.908305i
\(629\) −5.86309 3.02450i −0.233777 0.120595i
\(630\) −3.47200 + 6.25568i −0.138328 + 0.249232i
\(631\) 31.7177 + 31.7177i 1.26266 + 1.26266i 0.949799 + 0.312862i \(0.101288\pi\)
0.312862 + 0.949799i \(0.398712\pi\)
\(632\) 5.44553 0.216612
\(633\) −3.45280 5.86530i −0.137236 0.233125i
\(634\) −17.6790 + 17.6790i −0.702123 + 0.702123i
\(635\) −7.50545 7.50545i −0.297845 0.297845i
\(636\) −6.34149 10.7724i −0.251456 0.427152i
\(637\) 2.07432 2.07432i 0.0821876 0.0821876i
\(638\) 5.43890i 0.215328i
\(639\) 26.7831 + 14.8650i 1.05952 + 0.588051i
\(640\) 1.00000i 0.0395285i
\(641\) 5.24179i 0.207038i −0.994627 0.103519i \(-0.966990\pi\)
0.994627 0.103519i \(-0.0330103\pi\)
\(642\) 4.65956 17.9971i 0.183898 0.710291i
\(643\) −33.1809 33.1809i −1.30853 1.30853i −0.922478 0.386049i \(-0.873839\pi\)
−0.386049 0.922478i \(-0.626161\pi\)
\(644\) 14.0003 14.0003i 0.551690 0.551690i
\(645\) 8.04645 + 13.6686i 0.316829 + 0.538200i
\(646\) −4.63253 + 4.63253i −0.182264 + 0.182264i
\(647\) −4.39581 + 4.39581i −0.172817 + 0.172817i −0.788216 0.615399i \(-0.788995\pi\)
0.615399 + 0.788216i \(0.288995\pi\)
\(648\) −2.03403 + 8.76714i −0.0799042 + 0.344406i
\(649\) −32.5176 32.5176i −1.27643 1.27643i
\(650\) −2.23522 −0.0876724
\(651\) −7.21956 + 27.8849i −0.282957 + 1.09290i
\(652\) −7.51726 + 7.51726i −0.294399 + 0.294399i
\(653\) −13.7401 + 13.7401i −0.537690 + 0.537690i −0.922850 0.385160i \(-0.874146\pi\)
0.385160 + 0.922850i \(0.374146\pi\)
\(654\) 12.7037 7.47846i 0.496756 0.292431i
\(655\) −6.84602 −0.267496
\(656\) −2.85384 −0.111424
\(657\) 3.88892 + 2.15841i 0.151721 + 0.0842076i
\(658\) −14.2376 14.2376i −0.555040 0.555040i
\(659\) 6.94050 0.270364 0.135182 0.990821i \(-0.456838\pi\)
0.135182 + 0.990821i \(0.456838\pi\)
\(660\) −9.67016 2.50366i −0.376410 0.0974548i
\(661\) −7.92259 7.92259i −0.308153 0.308153i 0.536040 0.844193i \(-0.319920\pi\)
−0.844193 + 0.536040i \(0.819920\pi\)
\(662\) 22.8992i 0.890002i
\(663\) −2.13015 3.61851i −0.0827282 0.140531i
\(664\) 11.4912 11.4912i 0.445946 0.445946i
\(665\) 14.4058 0.558632
\(666\) 10.1202 + 15.1849i 0.392148 + 0.588404i
\(667\) −7.82958 −0.303163
\(668\) 12.5348 12.5348i 0.484986 0.484986i
\(669\) −13.9601 23.7142i −0.539729 0.916843i
\(670\) 2.96422i 0.114518i
\(671\) −50.8806 50.8806i −1.96422 1.96422i
\(672\) 3.99886 + 1.03533i 0.154259 + 0.0399386i
\(673\) 34.0773 1.31358 0.656791 0.754073i \(-0.271913\pi\)
0.656791 + 0.754073i \(0.271913\pi\)
\(674\) 8.08858 + 8.08858i 0.311560 + 0.311560i
\(675\) 0.131812 + 5.19448i 0.00507343 + 0.199936i
\(676\) 8.00381 0.307839
\(677\) 6.68405 0.256889 0.128444 0.991717i \(-0.459002\pi\)
0.128444 + 0.991717i \(0.459002\pi\)
\(678\) −25.4185 + 14.9634i −0.976193 + 0.574667i
\(679\) 27.2519 27.2519i 1.04583 1.04583i
\(680\) −0.766912 + 0.766912i −0.0294097 + 0.0294097i
\(681\) 1.83155 7.07419i 0.0701850 0.271083i
\(682\) −40.2156 −1.53994
\(683\) −20.8898 20.8898i −0.799324 0.799324i 0.183665 0.982989i \(-0.441204\pi\)
−0.982989 + 0.183665i \(0.941204\pi\)
\(684\) 17.4222 4.98555i 0.666154 0.190627i
\(685\) −15.6116 + 15.6116i −0.596490 + 0.596490i
\(686\) −14.0177 + 14.0177i −0.535198 + 0.535198i
\(687\) −21.0151 35.6985i −0.801775 1.36198i
\(688\) 6.47528 6.47528i 0.246868 0.246868i
\(689\) −11.4068 11.4068i −0.434566 0.434566i
\(690\) 3.60415 13.9207i 0.137208 0.529952i
\(691\) 24.1662i 0.919324i −0.888094 0.459662i \(-0.847971\pi\)
0.888094 0.459662i \(-0.152029\pi\)
\(692\) 15.9099i 0.604802i
\(693\) −20.0235 + 36.0775i −0.760631 + 1.37047i
\(694\) 8.21366i 0.311786i
\(695\) 3.04969 3.04969i 0.115682 0.115682i
\(696\) −0.828666 1.40767i −0.0314105 0.0533574i
\(697\) −2.18864 2.18864i −0.0829008 0.0829008i
\(698\) 8.18055 8.18055i 0.309638 0.309638i
\(699\) 22.5346 + 38.2798i 0.852338 + 1.44788i
\(700\) 2.38487 0.0901395
\(701\) 4.73203 + 4.73203i 0.178726 + 0.178726i 0.790800 0.612074i \(-0.209665\pi\)
−0.612074 + 0.790800i \(0.709665\pi\)
\(702\) 0.294627 + 11.6108i 0.0111200 + 0.438221i
\(703\) 16.8448 32.6541i 0.635313 1.23157i
\(704\) 5.76715i 0.217358i
\(705\) −14.1566 3.66523i −0.533170 0.138041i
\(706\) 12.0058i 0.451845i
\(707\) −5.55027 −0.208739
\(708\) 13.3704 + 3.46167i 0.502490 + 0.130097i
\(709\) −2.36375 + 2.36375i −0.0887727 + 0.0887727i −0.750099 0.661326i \(-0.769994\pi\)
0.661326 + 0.750099i \(0.269994\pi\)
\(710\) 10.2106i 0.383196i
\(711\) −4.49449 15.7062i −0.168557 0.589028i
\(712\) 5.49796 0.206045
\(713\) 57.8925i 2.16809i
\(714\) 2.27277 + 3.86077i 0.0850561 + 0.144486i
\(715\) −12.8908 −0.482090
\(716\) 9.10948 + 9.10948i 0.340437 + 0.340437i
\(717\) 6.75429 26.0878i 0.252243 0.974268i
\(718\) 15.6328 + 15.6328i 0.583411 + 0.583411i
\(719\) 20.6295i 0.769349i −0.923052 0.384675i \(-0.874314\pi\)
0.923052 0.384675i \(-0.125686\pi\)
\(720\) 2.88423 0.825355i 0.107489 0.0307591i
\(721\) 7.32348 + 7.32348i 0.272741 + 0.272741i
\(722\) −12.3656 12.3656i −0.460199 0.460199i
\(723\) 48.9580 + 12.6755i 1.82077 + 0.471407i
\(724\) 4.67113i 0.173601i
\(725\) −0.666860 0.666860i −0.0247665 0.0247665i
\(726\) −37.3249 9.66362i −1.38526 0.358651i
\(727\) 4.87778 + 4.87778i 0.180907 + 0.180907i 0.791751 0.610844i \(-0.209170\pi\)
−0.610844 + 0.791751i \(0.709170\pi\)
\(728\) 5.33069 0.197569
\(729\) 26.9653 1.36939i 0.998713 0.0507180i
\(730\) 1.48258i 0.0548728i
\(731\) 9.93195 0.367346
\(732\) 20.9207 + 5.41650i 0.773253 + 0.200200i
\(733\) 27.2107i 1.00505i 0.864563 + 0.502525i \(0.167595\pi\)
−0.864563 + 0.502525i \(0.832405\pi\)
\(734\) −15.4204 + 15.4204i −0.569176 + 0.569176i
\(735\) −0.569751 + 2.20061i −0.0210156 + 0.0811708i
\(736\) −8.30212 −0.306020
\(737\) 17.0951i 0.629706i
\(738\) 2.35543 + 8.23113i 0.0867045 + 0.302992i
\(739\) 21.1878i 0.779406i 0.920941 + 0.389703i \(0.127422\pi\)
−0.920941 + 0.389703i \(0.872578\pi\)
\(740\) 2.78864 5.40587i 0.102513 0.198724i
\(741\) 20.1531 11.8638i 0.740343 0.435826i
\(742\) 12.1705 + 12.1705i 0.446794 + 0.446794i
\(743\) 30.3326 1.11279 0.556397 0.830917i \(-0.312183\pi\)
0.556397 + 0.830917i \(0.312183\pi\)
\(744\) 10.4084 6.12722i 0.381590 0.224635i
\(745\) 13.7863 13.7863i 0.505091 0.505091i
\(746\) −13.2322 13.2322i −0.484465 0.484465i
\(747\) −42.6277 23.6590i −1.55967 0.865638i
\(748\) −4.42290 + 4.42290i −0.161717 + 0.161717i
\(749\) 25.5974i 0.935308i
\(750\) 1.49262 0.878679i 0.0545029 0.0320848i
\(751\) 14.3381i 0.523204i 0.965176 + 0.261602i \(0.0842508\pi\)
−0.965176 + 0.261602i \(0.915749\pi\)
\(752\) 8.44283i 0.307878i
\(753\) 8.85774 + 2.29332i 0.322794 + 0.0835732i
\(754\) −1.49058 1.49058i −0.0542836 0.0542836i
\(755\) 2.81812 2.81812i 0.102562 0.102562i
\(756\) −0.314353 12.3881i −0.0114329 0.450552i
\(757\) 23.3542 23.3542i 0.848822 0.848822i −0.141164 0.989986i \(-0.545084\pi\)
0.989986 + 0.141164i \(0.0450845\pi\)
\(758\) −3.53836 + 3.53836i −0.128519 + 0.128519i
\(759\) 20.7857 80.2828i 0.754472 2.91408i
\(760\) −4.27127 4.27127i −0.154935 0.154935i
\(761\) 41.2576 1.49559 0.747794 0.663931i \(-0.231113\pi\)
0.747794 + 0.663931i \(0.231113\pi\)
\(762\) 17.7977 + 4.60792i 0.644742 + 0.166927i
\(763\) −14.3526 + 14.3526i −0.519599 + 0.519599i
\(764\) −2.51857 + 2.51857i −0.0911185 + 0.0911185i
\(765\) 2.84493 + 1.57898i 0.102858 + 0.0570880i
\(766\) 10.0042 0.361465
\(767\) 17.8234 0.643567
\(768\) −0.878679 1.49262i −0.0317066 0.0538604i
\(769\) −6.65238 6.65238i −0.239891 0.239891i 0.576914 0.816805i \(-0.304257\pi\)
−0.816805 + 0.576914i \(0.804257\pi\)
\(770\) 13.7539 0.495656
\(771\) −5.67771 + 21.9297i −0.204478 + 0.789777i
\(772\) 4.71089 + 4.71089i 0.169549 + 0.169549i
\(773\) 24.0960i 0.866674i −0.901232 0.433337i \(-0.857336\pi\)
0.901232 0.433337i \(-0.142664\pi\)
\(774\) −24.0206 13.3318i −0.863404 0.479202i
\(775\) 4.93081 4.93081i 0.177120 0.177120i
\(776\) −16.1603 −0.580119
\(777\) −18.7302 16.7482i −0.671940 0.600839i
\(778\) −11.5206 −0.413034