Properties

Label 966.2.i.n.415.1
Level $966$
Weight $2$
Character 966.415
Analytic conductor $7.714$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.173309020416.2
Defining polynomial: \(x^{8} - 5 x^{6} - 28 x^{5} - 4 x^{4} + 70 x^{3} + 51 x^{2} + 406 x + 841\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 415.1
Root \(0.435461 + 1.77894i\) of defining polynomial
Character \(\chi\) \(=\) 966.415
Dual form 966.2.i.n.277.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.94864 + 3.37514i) q^{5} +1.00000 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.94864 + 3.37514i) q^{5} +1.00000 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.94864 + 3.37514i) q^{10} +(-2.01318 - 3.48693i) q^{11} +(0.500000 - 0.866025i) q^{12} -0.619394 q^{13} -2.64575 q^{14} -3.89728 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.625764 + 1.08385i) q^{17} +(0.500000 + 0.866025i) q^{18} +(4.20698 - 7.28670i) q^{19} +3.89728 q^{20} +(1.32288 - 2.29129i) q^{21} -4.02636 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-5.09439 - 8.82374i) q^{25} +(-0.309697 + 0.536411i) q^{26} -1.00000 q^{27} +(-1.32288 + 2.29129i) q^{28} -9.41395 q^{29} +(-1.94864 + 3.37514i) q^{30} +(-2.59439 - 4.49362i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.01318 - 3.48693i) q^{33} +1.25153 q^{34} +10.3112 q^{35} +1.00000 q^{36} +(-0.690303 + 1.19564i) q^{37} +(-4.20698 - 7.28670i) q^{38} +(-0.309697 - 0.536411i) q^{39} +(1.94864 - 3.37514i) q^{40} -4.41395 q^{41} +(-1.32288 - 2.29129i) q^{42} +2.00000 q^{43} +(-2.01318 + 3.48693i) q^{44} +(-1.94864 - 3.37514i) q^{45} +(0.500000 + 0.866025i) q^{46} +(3.06803 - 5.31399i) q^{47} -1.00000 q^{48} +(-3.50000 + 6.06218i) q^{49} -10.1888 q^{50} +(-0.625764 + 1.08385i) q^{51} +(0.309697 + 0.536411i) q^{52} +(0.948639 + 1.64309i) q^{53} +(-0.500000 + 0.866025i) q^{54} +15.6918 q^{55} +(1.32288 + 2.29129i) q^{56} +8.41395 q^{57} +(-4.70698 + 8.15272i) q^{58} +(-5.50986 - 9.54336i) q^{59} +(1.94864 + 3.37514i) q^{60} +(0.102721 - 0.177918i) q^{61} -5.18878 q^{62} +2.64575 q^{63} +1.00000 q^{64} +(1.20698 - 2.09054i) q^{65} +(-2.01318 - 3.48693i) q^{66} +(-6.02636 - 10.4380i) q^{67} +(0.625764 - 1.08385i) q^{68} -1.00000 q^{69} +(5.15562 - 8.92979i) q^{70} +0.483327 q^{71} +(0.500000 - 0.866025i) q^{72} +(-1.57772 - 2.73269i) q^{73} +(0.690303 + 1.19564i) q^{74} +(5.09439 - 8.82374i) q^{75} -8.41395 q^{76} +(-5.32637 + 9.22554i) q^{77} -0.619394 q^{78} +(-7.73683 + 13.4006i) q^{79} +(-1.94864 - 3.37514i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.20698 + 3.82259i) q^{82} +7.13607 q^{83} -2.64575 q^{84} -4.87755 q^{85} +(1.00000 - 1.73205i) q^{86} +(-4.70698 - 8.15272i) q^{87} +(2.01318 + 3.48693i) q^{88} +(-5.10425 + 8.84083i) q^{89} -3.89728 q^{90} +(0.819381 + 1.41921i) q^{91} +1.00000 q^{92} +(2.59439 - 4.49362i) q^{93} +(-3.06803 - 5.31399i) q^{94} +(16.3958 + 28.3983i) q^{95} +(-0.500000 + 0.866025i) q^{96} +12.0531 q^{97} +(3.50000 + 6.06218i) q^{98} +4.02636 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9} + O(q^{10}) \) \( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{13} - 4 q^{15} - 4 q^{16} + 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{24} - 6 q^{25} - 2 q^{26} - 8 q^{27} - 20 q^{29} - 2 q^{30} + 14 q^{31} + 4 q^{32} + 6 q^{33} + 4 q^{34} + 8 q^{36} - 6 q^{37} - 6 q^{38} - 2 q^{39} + 2 q^{40} + 20 q^{41} + 16 q^{43} - 6 q^{44} - 2 q^{45} + 4 q^{46} + 10 q^{47} - 8 q^{48} - 28 q^{49} - 12 q^{50} - 2 q^{51} + 2 q^{52} - 6 q^{53} - 4 q^{54} + 44 q^{55} + 12 q^{57} - 10 q^{58} - 24 q^{59} + 2 q^{60} + 28 q^{61} + 28 q^{62} + 8 q^{64} - 18 q^{65} - 6 q^{66} - 28 q^{67} + 2 q^{68} - 8 q^{69} + 32 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 6 q^{75} - 12 q^{76} - 14 q^{77} - 4 q^{78} + 4 q^{79} - 2 q^{80} - 4 q^{81} + 10 q^{82} + 28 q^{83} - 52 q^{85} + 8 q^{86} - 10 q^{87} + 6 q^{88} + 14 q^{89} - 4 q^{90} + 14 q^{91} + 8 q^{92} - 14 q^{93} - 10 q^{94} + 34 q^{95} - 4 q^{96} + 28 q^{98} + 12 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.94864 + 3.37514i −0.871458 + 1.50941i −0.0109694 + 0.999940i \(0.503492\pi\)
−0.860489 + 0.509470i \(0.829842\pi\)
\(6\) 1.00000 0.408248
\(7\) −1.32288 2.29129i −0.500000 0.866025i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.94864 + 3.37514i 0.616214 + 1.06731i
\(11\) −2.01318 3.48693i −0.606996 1.05135i −0.991733 0.128322i \(-0.959041\pi\)
0.384736 0.923026i \(-0.374292\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −0.619394 −0.171789 −0.0858945 0.996304i \(-0.527375\pi\)
−0.0858945 + 0.996304i \(0.527375\pi\)
\(14\) −2.64575 −0.707107
\(15\) −3.89728 −1.00627
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.625764 + 1.08385i 0.151770 + 0.262873i 0.931878 0.362771i \(-0.118169\pi\)
−0.780108 + 0.625645i \(0.784836\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 4.20698 7.28670i 0.965146 1.67168i 0.255925 0.966697i \(-0.417620\pi\)
0.709221 0.704986i \(-0.249047\pi\)
\(20\) 3.89728 0.871458
\(21\) 1.32288 2.29129i 0.288675 0.500000i
\(22\) −4.02636 −0.858422
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −5.09439 8.82374i −1.01888 1.76475i
\(26\) −0.309697 + 0.536411i −0.0607366 + 0.105199i
\(27\) −1.00000 −0.192450
\(28\) −1.32288 + 2.29129i −0.250000 + 0.433013i
\(29\) −9.41395 −1.74813 −0.874063 0.485812i \(-0.838524\pi\)
−0.874063 + 0.485812i \(0.838524\pi\)
\(30\) −1.94864 + 3.37514i −0.355771 + 0.616214i
\(31\) −2.59439 4.49362i −0.465966 0.807077i 0.533278 0.845940i \(-0.320960\pi\)
−0.999245 + 0.0388626i \(0.987627\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 2.01318 3.48693i 0.350449 0.606996i
\(34\) 1.25153 0.214635
\(35\) 10.3112 1.74292
\(36\) 1.00000 0.166667
\(37\) −0.690303 + 1.19564i −0.113485 + 0.196562i −0.917173 0.398489i \(-0.869535\pi\)
0.803688 + 0.595051i \(0.202868\pi\)
\(38\) −4.20698 7.28670i −0.682462 1.18206i
\(39\) −0.309697 0.536411i −0.0495912 0.0858945i
\(40\) 1.94864 3.37514i 0.308107 0.533657i
\(41\) −4.41395 −0.689343 −0.344672 0.938723i \(-0.612010\pi\)
−0.344672 + 0.938723i \(0.612010\pi\)
\(42\) −1.32288 2.29129i −0.204124 0.353553i
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −2.01318 + 3.48693i −0.303498 + 0.525674i
\(45\) −1.94864 3.37514i −0.290486 0.503137i
\(46\) 0.500000 + 0.866025i 0.0737210 + 0.127688i
\(47\) 3.06803 5.31399i 0.447519 0.775125i −0.550705 0.834700i \(-0.685641\pi\)
0.998224 + 0.0595747i \(0.0189745\pi\)
\(48\) −1.00000 −0.144338
\(49\) −3.50000 + 6.06218i −0.500000 + 0.866025i
\(50\) −10.1888 −1.44091
\(51\) −0.625764 + 1.08385i −0.0876244 + 0.151770i
\(52\) 0.309697 + 0.536411i 0.0429473 + 0.0743868i
\(53\) 0.948639 + 1.64309i 0.130306 + 0.225696i 0.923794 0.382889i \(-0.125071\pi\)
−0.793489 + 0.608585i \(0.791737\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 15.6918 2.11589
\(56\) 1.32288 + 2.29129i 0.176777 + 0.306186i
\(57\) 8.41395 1.11446
\(58\) −4.70698 + 8.15272i −0.618056 + 1.07050i
\(59\) −5.50986 9.54336i −0.717323 1.24244i −0.962057 0.272850i \(-0.912034\pi\)
0.244733 0.969590i \(-0.421300\pi\)
\(60\) 1.94864 + 3.37514i 0.251568 + 0.435729i
\(61\) 0.102721 0.177918i 0.0131521 0.0227801i −0.859374 0.511347i \(-0.829147\pi\)
0.872527 + 0.488567i \(0.162480\pi\)
\(62\) −5.18878 −0.658976
\(63\) 2.64575 0.333333
\(64\) 1.00000 0.125000
\(65\) 1.20698 2.09054i 0.149707 0.259300i
\(66\) −2.01318 3.48693i −0.247805 0.429211i
\(67\) −6.02636 10.4380i −0.736237 1.27520i −0.954179 0.299238i \(-0.903268\pi\)
0.217942 0.975962i \(-0.430066\pi\)
\(68\) 0.625764 1.08385i 0.0758850 0.131437i
\(69\) −1.00000 −0.120386
\(70\) 5.15562 8.92979i 0.616214 1.06731i
\(71\) 0.483327 0.0573604 0.0286802 0.999589i \(-0.490870\pi\)
0.0286802 + 0.999589i \(0.490870\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −1.57772 2.73269i −0.184658 0.319837i 0.758803 0.651320i \(-0.225784\pi\)
−0.943461 + 0.331483i \(0.892451\pi\)
\(74\) 0.690303 + 1.19564i 0.0802461 + 0.138990i
\(75\) 5.09439 8.82374i 0.588250 1.01888i
\(76\) −8.41395 −0.965146
\(77\) −5.32637 + 9.22554i −0.606996 + 1.05135i
\(78\) −0.619394 −0.0701326
\(79\) −7.73683 + 13.4006i −0.870461 + 1.50768i −0.00894055 + 0.999960i \(0.502846\pi\)
−0.861521 + 0.507723i \(0.830487\pi\)
\(80\) −1.94864 3.37514i −0.217865 0.377352i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.20698 + 3.82259i −0.243720 + 0.422135i
\(83\) 7.13607 0.783285 0.391643 0.920117i \(-0.371907\pi\)
0.391643 + 0.920117i \(0.371907\pi\)
\(84\) −2.64575 −0.288675
\(85\) −4.87755 −0.529045
\(86\) 1.00000 1.73205i 0.107833 0.186772i
\(87\) −4.70698 8.15272i −0.504641 0.874063i
\(88\) 2.01318 + 3.48693i 0.214606 + 0.371708i
\(89\) −5.10425 + 8.84083i −0.541050 + 0.937126i 0.457794 + 0.889058i \(0.348640\pi\)
−0.998844 + 0.0480677i \(0.984694\pi\)
\(90\) −3.89728 −0.410809
\(91\) 0.819381 + 1.41921i 0.0858945 + 0.148774i
\(92\) 1.00000 0.104257
\(93\) 2.59439 4.49362i 0.269026 0.465966i
\(94\) −3.06803 5.31399i −0.316443 0.548096i
\(95\) 16.3958 + 28.3983i 1.68217 + 2.91360i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 12.0531 1.22380 0.611902 0.790934i \(-0.290405\pi\)
0.611902 + 0.790934i \(0.290405\pi\)
\(98\) 3.50000 + 6.06218i 0.353553 + 0.612372i
\(99\) 4.02636 0.404664
\(100\) −5.09439 + 8.82374i −0.509439 + 0.882374i
\(101\) 5.09439 + 8.82374i 0.506911 + 0.877995i 0.999968 + 0.00799839i \(0.00254599\pi\)
−0.493057 + 0.869997i \(0.664121\pi\)
\(102\) 0.625764 + 1.08385i 0.0619598 + 0.107318i
\(103\) −3.47849 + 6.02492i −0.342746 + 0.593653i −0.984942 0.172887i \(-0.944690\pi\)
0.642196 + 0.766541i \(0.278024\pi\)
\(104\) 0.619394 0.0607366
\(105\) 5.15562 + 8.92979i 0.503137 + 0.871458i
\(106\) 1.89728 0.184280
\(107\) −5.56803 + 9.64412i −0.538282 + 0.932332i 0.460715 + 0.887548i \(0.347593\pi\)
−0.998997 + 0.0447836i \(0.985740\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −0.683933 1.18461i −0.0655089 0.113465i 0.831411 0.555658i \(-0.187534\pi\)
−0.896920 + 0.442194i \(0.854200\pi\)
\(110\) 7.84592 13.5895i 0.748079 1.29571i
\(111\) −1.38061 −0.131041
\(112\) 2.64575 0.250000
\(113\) 19.7582 1.85869 0.929346 0.369210i \(-0.120372\pi\)
0.929346 + 0.369210i \(0.120372\pi\)
\(114\) 4.20698 7.28670i 0.394019 0.682462i
\(115\) −1.94864 3.37514i −0.181712 0.314734i
\(116\) 4.70698 + 8.15272i 0.437032 + 0.756961i
\(117\) 0.309697 0.536411i 0.0286315 0.0495912i
\(118\) −11.0197 −1.01445
\(119\) 1.65562 2.86761i 0.151770 0.262873i
\(120\) 3.89728 0.355771
\(121\) −2.60578 + 4.51334i −0.236889 + 0.410303i
\(122\) −0.102721 0.177918i −0.00929995 0.0161080i
\(123\) −2.20698 3.82259i −0.198996 0.344672i
\(124\) −2.59439 + 4.49362i −0.232983 + 0.403539i
\(125\) 20.2221 1.80872
\(126\) 1.32288 2.29129i 0.117851 0.204124i
\(127\) −15.4337 −1.36952 −0.684759 0.728770i \(-0.740092\pi\)
−0.684759 + 0.728770i \(0.740092\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 1.00000 + 1.73205i 0.0880451 + 0.152499i
\(130\) −1.20698 2.09054i −0.105859 0.183353i
\(131\) −10.4471 + 18.0949i −0.912769 + 1.58096i −0.102634 + 0.994719i \(0.532727\pi\)
−0.810135 + 0.586243i \(0.800606\pi\)
\(132\) −4.02636 −0.350449
\(133\) −22.2612 −1.93029
\(134\) −12.0527 −1.04120
\(135\) 1.94864 3.37514i 0.167712 0.290486i
\(136\) −0.625764 1.08385i −0.0536588 0.0929398i
\(137\) −3.18699 5.52003i −0.272283 0.471608i 0.697163 0.716912i \(-0.254445\pi\)
−0.969446 + 0.245305i \(0.921112\pi\)
\(138\) −0.500000 + 0.866025i −0.0425628 + 0.0737210i
\(139\) −2.13607 −0.181179 −0.0905894 0.995888i \(-0.528875\pi\)
−0.0905894 + 0.995888i \(0.528875\pi\)
\(140\) −5.15562 8.92979i −0.435729 0.754705i
\(141\) 6.13607 0.516750
\(142\) 0.241664 0.418574i 0.0202800 0.0351259i
\(143\) 1.24695 + 2.15978i 0.104275 + 0.180610i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 18.3444 31.7734i 1.52342 2.63864i
\(146\) −3.15544 −0.261146
\(147\) −7.00000 −0.577350
\(148\) 1.38061 0.113485
\(149\) −5.91090 + 10.2380i −0.484240 + 0.838727i −0.999836 0.0181040i \(-0.994237\pi\)
0.515597 + 0.856831i \(0.327570\pi\)
\(150\) −5.09439 8.82374i −0.415955 0.720456i
\(151\) −4.71684 8.16981i −0.383851 0.664849i 0.607758 0.794122i \(-0.292069\pi\)
−0.991609 + 0.129273i \(0.958736\pi\)
\(152\) −4.20698 + 7.28670i −0.341231 + 0.591029i
\(153\) −1.25153 −0.101180
\(154\) 5.32637 + 9.22554i 0.429211 + 0.743415i
\(155\) 20.2221 1.62428
\(156\) −0.309697 + 0.536411i −0.0247956 + 0.0429473i
\(157\) −1.89091 3.27515i −0.150911 0.261385i 0.780652 0.624966i \(-0.214887\pi\)
−0.931563 + 0.363581i \(0.881554\pi\)
\(158\) 7.73683 + 13.4006i 0.615509 + 1.06609i
\(159\) −0.948639 + 1.64309i −0.0752320 + 0.130306i
\(160\) −3.89728 −0.308107
\(161\) 2.64575 0.208514
\(162\) −1.00000 −0.0785674
\(163\) −2.24166 + 3.88268i −0.175581 + 0.304115i −0.940362 0.340175i \(-0.889514\pi\)
0.764781 + 0.644290i \(0.222847\pi\)
\(164\) 2.20698 + 3.82259i 0.172336 + 0.298494i
\(165\) 7.84592 + 13.5895i 0.610804 + 1.05794i
\(166\) 3.56803 6.18002i 0.276933 0.479662i
\(167\) 17.1388 1.32624 0.663119 0.748514i \(-0.269232\pi\)
0.663119 + 0.748514i \(0.269232\pi\)
\(168\) −1.32288 + 2.29129i −0.102062 + 0.176777i
\(169\) −12.6164 −0.970489
\(170\) −2.43878 + 4.22408i −0.187046 + 0.323972i
\(171\) 4.20698 + 7.28670i 0.321715 + 0.557228i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 1.42228 2.46346i 0.108134 0.187294i −0.806880 0.590715i \(-0.798846\pi\)
0.915014 + 0.403421i \(0.132179\pi\)
\(174\) −9.41395 −0.713670
\(175\) −13.4785 + 23.3454i −1.01888 + 1.76475i
\(176\) 4.02636 0.303498
\(177\) 5.50986 9.54336i 0.414147 0.717323i
\(178\) 5.10425 + 8.84083i 0.382580 + 0.662648i
\(179\) −6.63912 11.4993i −0.496231 0.859498i 0.503759 0.863844i \(-0.331950\pi\)
−0.999991 + 0.00434631i \(0.998617\pi\)
\(180\) −1.94864 + 3.37514i −0.145243 + 0.251568i
\(181\) 14.5066 1.07827 0.539135 0.842219i \(-0.318751\pi\)
0.539135 + 0.842219i \(0.318751\pi\)
\(182\) 1.63876 0.121473
\(183\) 0.205443 0.0151868
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −2.69030 4.65974i −0.197795 0.342591i
\(186\) −2.59439 4.49362i −0.190230 0.329488i
\(187\) 2.51955 4.36399i 0.184248 0.319126i
\(188\) −6.13607 −0.447519
\(189\) 1.32288 + 2.29129i 0.0962250 + 0.166667i
\(190\) 32.7915 2.37895
\(191\) 7.62093 13.1998i 0.551431 0.955106i −0.446741 0.894663i \(-0.647415\pi\)
0.998172 0.0604429i \(-0.0192513\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −5.97500 10.3490i −0.430090 0.744937i 0.566791 0.823862i \(-0.308185\pi\)
−0.996881 + 0.0789245i \(0.974851\pi\)
\(194\) 6.02654 10.4383i 0.432680 0.749424i
\(195\) 2.41395 0.172867
\(196\) 7.00000 0.500000
\(197\) −18.5391 −1.32086 −0.660428 0.750889i \(-0.729625\pi\)
−0.660428 + 0.750889i \(0.729625\pi\)
\(198\) 2.01318 3.48693i 0.143070 0.247805i
\(199\) 4.45876 + 7.72280i 0.316073 + 0.547455i 0.979665 0.200640i \(-0.0643021\pi\)
−0.663592 + 0.748095i \(0.730969\pi\)
\(200\) 5.09439 + 8.82374i 0.360228 + 0.623933i
\(201\) 6.02636 10.4380i 0.425066 0.736237i
\(202\) 10.1888 0.716880
\(203\) 12.4535 + 21.5701i 0.874063 + 1.51392i
\(204\) 1.25153 0.0876244
\(205\) 8.60120 14.8977i 0.600734 1.04050i
\(206\) 3.47849 + 6.02492i 0.242358 + 0.419776i
\(207\) −0.500000 0.866025i −0.0347524 0.0601929i
\(208\) 0.309697 0.536411i 0.0214736 0.0371934i
\(209\) −33.8776 −2.34336
\(210\) 10.3112 0.711542
\(211\) 17.1694 1.18199 0.590996 0.806675i \(-0.298735\pi\)
0.590996 + 0.806675i \(0.298735\pi\)
\(212\) 0.948639 1.64309i 0.0651528 0.112848i
\(213\) 0.241664 + 0.418574i 0.0165585 + 0.0286802i
\(214\) 5.56803 + 9.64412i 0.380623 + 0.659258i
\(215\) −3.89728 + 6.75028i −0.265792 + 0.460366i
\(216\) 1.00000 0.0680414
\(217\) −6.86411 + 11.8890i −0.465966 + 0.807077i
\(218\) −1.36787 −0.0926436
\(219\) 1.57772 2.73269i 0.106612 0.184658i
\(220\) −7.84592 13.5895i −0.528972 0.916206i
\(221\) −0.387594 0.671333i −0.0260724 0.0451588i
\(222\) −0.690303 + 1.19564i −0.0463301 + 0.0802461i
\(223\) −9.39422 −0.629084 −0.314542 0.949244i \(-0.601851\pi\)
−0.314542 + 0.949244i \(0.601851\pi\)
\(224\) 1.32288 2.29129i 0.0883883 0.153093i
\(225\) 10.1888 0.679252
\(226\) 9.87908 17.1111i 0.657147 1.13821i
\(227\) −12.6589 21.9259i −0.840203 1.45527i −0.889723 0.456501i \(-0.849103\pi\)
0.0495204 0.998773i \(-0.484231\pi\)
\(228\) −4.20698 7.28670i −0.278614 0.482573i
\(229\) 5.98001 10.3577i 0.395170 0.684455i −0.597953 0.801531i \(-0.704019\pi\)
0.993123 + 0.117076i \(0.0373522\pi\)
\(230\) −3.89728 −0.256979
\(231\) −10.6527 −0.700899
\(232\) 9.41395 0.618056
\(233\) 4.43215 7.67670i 0.290360 0.502917i −0.683535 0.729918i \(-0.739558\pi\)
0.973895 + 0.227000i \(0.0728918\pi\)
\(234\) −0.309697 0.536411i −0.0202455 0.0350663i
\(235\) 11.9570 + 20.7101i 0.779987 + 1.35098i
\(236\) −5.50986 + 9.54336i −0.358662 + 0.621220i
\(237\) −15.4737 −1.00512
\(238\) −1.65562 2.86761i −0.107318 0.185880i
\(239\) 9.93062 0.642359 0.321179 0.947018i \(-0.395921\pi\)
0.321179 + 0.947018i \(0.395921\pi\)
\(240\) 1.94864 3.37514i 0.125784 0.217865i
\(241\) 6.14200 + 10.6383i 0.395641 + 0.685270i 0.993183 0.116568i \(-0.0371892\pi\)
−0.597542 + 0.801838i \(0.703856\pi\)
\(242\) 2.60578 + 4.51334i 0.167506 + 0.290128i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −0.205443 −0.0131521
\(245\) −13.6405 23.6260i −0.871458 1.50941i
\(246\) −4.41395 −0.281423
\(247\) −2.60578 + 4.51334i −0.165802 + 0.287177i
\(248\) 2.59439 + 4.49362i 0.164744 + 0.285345i
\(249\) 3.56803 + 6.18002i 0.226115 + 0.391643i
\(250\) 10.1111 17.5129i 0.639480 1.10761i
\(251\) 6.81481 0.430147 0.215073 0.976598i \(-0.431001\pi\)
0.215073 + 0.976598i \(0.431001\pi\)
\(252\) −1.32288 2.29129i −0.0833333 0.144338i
\(253\) 4.02636 0.253135
\(254\) −7.71684 + 13.3660i −0.484198 + 0.838655i
\(255\) −2.43878 4.22408i −0.152722 0.264522i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 11.7500 20.3516i 0.732945 1.26950i −0.222674 0.974893i \(-0.571478\pi\)
0.955619 0.294605i \(-0.0951882\pi\)
\(258\) 2.00000 0.124515
\(259\) 3.65274 0.226970
\(260\) −2.41395 −0.149707
\(261\) 4.70698 8.15272i 0.291354 0.504641i
\(262\) 10.4471 + 18.0949i 0.645425 + 1.11791i
\(263\) −9.42669 16.3275i −0.581275 1.00680i −0.995329 0.0965449i \(-0.969221\pi\)
0.414054 0.910252i \(-0.364112\pi\)
\(264\) −2.01318 + 3.48693i −0.123903 + 0.214606i
\(265\) −7.39422 −0.454224
\(266\) −11.1306 + 19.2788i −0.682462 + 1.18206i
\(267\) −10.2085 −0.624751
\(268\) −6.02636 + 10.4380i −0.368118 + 0.637600i
\(269\) 13.3988 + 23.2074i 0.816940 + 1.41498i 0.907926 + 0.419129i \(0.137665\pi\)
−0.0909865 + 0.995852i \(0.529002\pi\)
\(270\) −1.94864 3.37514i −0.118590 0.205405i
\(271\) 14.2401 24.6646i 0.865027 1.49827i −0.00199332 0.999998i \(-0.500634\pi\)
0.867020 0.498273i \(-0.166032\pi\)
\(272\) −1.25153 −0.0758850
\(273\) −0.819381 + 1.41921i −0.0495912 + 0.0858945i
\(274\) −6.37398 −0.385066
\(275\) −20.5118 + 35.5275i −1.23691 + 2.14239i
\(276\) 0.500000 + 0.866025i 0.0300965 + 0.0521286i
\(277\) −9.69847 16.7982i −0.582724 1.00931i −0.995155 0.0983191i \(-0.968653\pi\)
0.412431 0.910989i \(-0.364680\pi\)
\(278\) −1.06803 + 1.84989i −0.0640564 + 0.110949i
\(279\) 5.18878 0.310644
\(280\) −10.3112 −0.616214
\(281\) 22.3903 1.33569 0.667847 0.744299i \(-0.267216\pi\)
0.667847 + 0.744299i \(0.267216\pi\)
\(282\) 3.06803 5.31399i 0.182699 0.316443i
\(283\) 5.01973 + 8.69442i 0.298392 + 0.516830i 0.975768 0.218807i \(-0.0702165\pi\)
−0.677376 + 0.735637i \(0.736883\pi\)
\(284\) −0.241664 0.418574i −0.0143401 0.0248378i
\(285\) −16.3958 + 28.3983i −0.971201 + 1.68217i
\(286\) 2.49390 0.147468
\(287\) 5.83911 + 10.1136i 0.344672 + 0.596989i
\(288\) −1.00000 −0.0589256
\(289\) 7.71684 13.3660i 0.453932 0.786233i
\(290\) −18.3444 31.7734i −1.07722 1.86580i
\(291\) 6.02654 + 10.4383i 0.353282 + 0.611902i
\(292\) −1.57772 + 2.73269i −0.0923290 + 0.159918i
\(293\) −25.0228 −1.46185 −0.730924 0.682459i \(-0.760910\pi\)
−0.730924 + 0.682459i \(0.760910\pi\)
\(294\) −3.50000 + 6.06218i −0.204124 + 0.353553i
\(295\) 42.9469 2.50047
\(296\) 0.690303 1.19564i 0.0401230 0.0694951i
\(297\) 2.01318 + 3.48693i 0.116816 + 0.202332i
\(298\) 5.91090 + 10.2380i 0.342409 + 0.593070i
\(299\) 0.309697 0.536411i 0.0179102 0.0310215i
\(300\) −10.1888 −0.588250
\(301\) −2.64575 4.58258i −0.152499 0.264135i
\(302\) −9.43368 −0.542847
\(303\) −5.09439 + 8.82374i −0.292665 + 0.506911i
\(304\) 4.20698 + 7.28670i 0.241287 + 0.417921i
\(305\) 0.400334 + 0.693398i 0.0229230 + 0.0397039i
\(306\) −0.625764 + 1.08385i −0.0357725 + 0.0619598i
\(307\) −27.6221 −1.57648 −0.788238 0.615370i \(-0.789007\pi\)
−0.788238 + 0.615370i \(0.789007\pi\)
\(308\) 10.6527 0.606996
\(309\) −6.95698 −0.395769
\(310\) 10.1111 17.5129i 0.574270 0.994665i
\(311\) −6.41683 11.1143i −0.363865 0.630232i 0.624728 0.780842i \(-0.285210\pi\)
−0.988593 + 0.150610i \(0.951876\pi\)
\(312\) 0.309697 + 0.536411i 0.0175331 + 0.0303683i
\(313\) 5.66530 9.81259i 0.320222 0.554640i −0.660312 0.750991i \(-0.729576\pi\)
0.980534 + 0.196351i \(0.0629093\pi\)
\(314\) −3.78182 −0.213420
\(315\) −5.15562 + 8.92979i −0.290486 + 0.503137i
\(316\) 15.4737 0.870461
\(317\) −14.5099 + 25.1318i −0.814955 + 1.41154i 0.0944050 + 0.995534i \(0.469905\pi\)
−0.909360 + 0.416010i \(0.863428\pi\)
\(318\) 0.948639 + 1.64309i 0.0531971 + 0.0921400i
\(319\) 18.9520 + 32.8258i 1.06111 + 1.83789i
\(320\) −1.94864 + 3.37514i −0.108932 + 0.188676i
\(321\) −11.1361 −0.621555
\(322\) 1.32288 2.29129i 0.0737210 0.127688i
\(323\) 10.5303 0.585921
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 3.15544 + 5.46537i 0.175032 + 0.303164i
\(326\) 2.24166 + 3.88268i 0.124154 + 0.215041i
\(327\) 0.683933 1.18461i 0.0378216 0.0655089i
\(328\) 4.41395 0.243720
\(329\) −16.2345 −0.895037
\(330\) 15.6918 0.863807
\(331\) −14.5512 + 25.2034i −0.799806 + 1.38530i 0.119936 + 0.992782i \(0.461731\pi\)
−0.919742 + 0.392523i \(0.871602\pi\)
\(332\) −3.56803 6.18002i −0.195821 0.339172i
\(333\) −0.690303 1.19564i −0.0378284 0.0655207i
\(334\) 8.56939 14.8426i 0.468896 0.812152i
\(335\) 46.9728 2.56640
\(336\) 1.32288 + 2.29129i 0.0721688 + 0.125000i
\(337\) 2.54215 0.138480 0.0692399 0.997600i \(-0.477943\pi\)
0.0692399 + 0.997600i \(0.477943\pi\)
\(338\) −6.30818 + 10.9261i −0.343120 + 0.594300i
\(339\) 9.87908 + 17.1111i 0.536558 + 0.929346i
\(340\) 2.43878 + 4.22408i 0.132261 + 0.229083i
\(341\) −10.4459 + 18.0929i −0.565680 + 0.979786i
\(342\) 8.41395 0.454974
\(343\) 18.5203 1.00000
\(344\) −2.00000 −0.107833
\(345\) 1.94864 3.37514i 0.104911 0.181712i
\(346\) −1.42228 2.46346i −0.0764624 0.132437i
\(347\) −10.1888 17.6475i −0.546962 0.947367i −0.998481 0.0551048i \(-0.982451\pi\)
0.451518 0.892262i \(-0.350883\pi\)
\(348\) −4.70698 + 8.15272i −0.252320 + 0.437032i
\(349\) 5.63876 0.301836 0.150918 0.988546i \(-0.451777\pi\)
0.150918 + 0.988546i \(0.451777\pi\)
\(350\) 13.4785 + 23.3454i 0.720456 + 1.24787i
\(351\) 0.619394 0.0330608
\(352\) 2.01318 3.48693i 0.107303 0.185854i
\(353\) 2.34879 + 4.06823i 0.125014 + 0.216530i 0.921738 0.387813i \(-0.126769\pi\)
−0.796725 + 0.604343i \(0.793436\pi\)
\(354\) −5.50986 9.54336i −0.292846 0.507224i
\(355\) −0.941830 + 1.63130i −0.0499872 + 0.0865803i
\(356\) 10.2085 0.541050
\(357\) 3.31123 0.175249
\(358\) −13.2782 −0.701777
\(359\) 14.2151 24.6213i 0.750246 1.29946i −0.197457 0.980312i \(-0.563268\pi\)
0.947703 0.319153i \(-0.103398\pi\)
\(360\) 1.94864 + 3.37514i 0.102702 + 0.177886i
\(361\) −25.8973 44.8554i −1.36302 2.36081i
\(362\) 7.25332 12.5631i 0.381226 0.660303i
\(363\) −5.21155 −0.273536
\(364\) 0.819381 1.41921i 0.0429473 0.0743868i
\(365\) 12.2976 0.643686
\(366\) 0.102721 0.177918i 0.00536933 0.00929995i
\(367\) 3.13589 + 5.43152i 0.163692 + 0.283523i 0.936190 0.351494i \(-0.114326\pi\)
−0.772498 + 0.635017i \(0.780993\pi\)
\(368\) −0.500000 0.866025i −0.0260643 0.0451447i
\(369\) 2.20698 3.82259i 0.114891 0.198996i
\(370\) −5.38061 −0.279724
\(371\) 2.50986 4.34721i 0.130306 0.225696i
\(372\) −5.18878 −0.269026
\(373\) 3.13698 5.43341i 0.162427 0.281331i −0.773312 0.634026i \(-0.781401\pi\)
0.935738 + 0.352695i \(0.114735\pi\)
\(374\) −2.51955 4.36399i −0.130283 0.225656i
\(375\) 10.1111 + 17.5129i 0.522133 + 0.904361i
\(376\) −3.06803 + 5.31399i −0.158222 + 0.274048i
\(377\) 5.83095 0.300309
\(378\) 2.64575 0.136083
\(379\) −28.2248 −1.44981 −0.724906 0.688848i \(-0.758117\pi\)
−0.724906 + 0.688848i \(0.758117\pi\)
\(380\) 16.3958 28.3983i 0.841085 1.45680i
\(381\) −7.71684 13.3660i −0.395346 0.684759i
\(382\) −7.62093 13.1998i −0.389921 0.675362i
\(383\) −4.72329 + 8.18098i −0.241349 + 0.418028i −0.961099 0.276205i \(-0.910923\pi\)
0.719750 + 0.694233i \(0.244256\pi\)
\(384\) 1.00000 0.0510310
\(385\) −20.7583 35.9545i −1.05794 1.83241i
\(386\) −11.9500 −0.608239
\(387\) −1.00000 + 1.73205i −0.0508329 + 0.0880451i
\(388\) −6.02654 10.4383i −0.305951 0.529923i
\(389\) −2.82091 4.88597i −0.143026 0.247728i 0.785609 0.618724i \(-0.212350\pi\)
−0.928635 + 0.370995i \(0.879017\pi\)
\(390\) 1.20698 2.09054i 0.0611176 0.105859i
\(391\) −1.25153 −0.0632925
\(392\) 3.50000 6.06218i 0.176777 0.306186i
\(393\) −20.8942 −1.05397
\(394\) −9.26955 + 16.0553i −0.466993 + 0.808856i
\(395\) −30.1526 52.2258i −1.51714 2.62776i
\(396\) −2.01318 3.48693i −0.101166 0.175225i
\(397\) 16.3694 28.3526i 0.821557 1.42298i −0.0829661 0.996552i \(-0.526439\pi\)
0.904523 0.426425i \(-0.140227\pi\)
\(398\) 8.91753 0.446995
\(399\) −11.1306 19.2788i −0.557228 0.965146i
\(400\) 10.1888 0.509439
\(401\) 4.94245 8.56057i 0.246814 0.427495i −0.715826 0.698279i \(-0.753950\pi\)
0.962640 + 0.270784i \(0.0872830\pi\)
\(402\) −6.02636 10.4380i −0.300567 0.520598i
\(403\) 1.60695 + 2.78332i 0.0800479 + 0.138647i
\(404\) 5.09439 8.82374i 0.253455 0.438998i
\(405\) 3.89728 0.193657
\(406\) 24.9070 1.23611
\(407\) 5.55881 0.275540
\(408\) 0.625764 1.08385i 0.0309799 0.0536588i
\(409\) 12.5531 + 21.7426i 0.620710 + 1.07510i 0.989354 + 0.145530i \(0.0464887\pi\)
−0.368644 + 0.929571i \(0.620178\pi\)
\(410\) −8.60120 14.8977i −0.424783 0.735746i
\(411\) 3.18699 5.52003i 0.157203 0.272283i
\(412\) 6.95698 0.342746
\(413\) −14.5777 + 25.2494i −0.717323 + 1.24244i
\(414\) −1.00000 −0.0491473
\(415\) −13.9056 + 24.0852i −0.682600 + 1.18230i
\(416\) −0.309697 0.536411i −0.0151841 0.0262997i
\(417\) −1.06803 1.84989i −0.0523018 0.0905894i
\(418\) −16.9388 + 29.3388i −0.828503 + 1.43501i
\(419\) −1.66548 −0.0813640 −0.0406820 0.999172i \(-0.512953\pi\)
−0.0406820 + 0.999172i \(0.512953\pi\)
\(420\) 5.15562 8.92979i 0.251568 0.435729i
\(421\) 4.61887 0.225110 0.112555 0.993645i \(-0.464097\pi\)
0.112555 + 0.993645i \(0.464097\pi\)
\(422\) 8.58471 14.8691i 0.417897 0.723819i
\(423\) 3.06803 + 5.31399i 0.149173 + 0.258375i
\(424\) −0.948639 1.64309i −0.0460700 0.0797956i
\(425\) 6.37577 11.0432i 0.309270 0.535672i
\(426\) 0.483327 0.0234173
\(427\) −0.543550 −0.0263042
\(428\) 11.1361 0.538282
\(429\) −1.24695 + 2.15978i −0.0602034 + 0.104275i
\(430\) 3.89728 + 6.75028i 0.187943 + 0.325528i
\(431\) 16.4337 + 28.4640i 0.791582 + 1.37106i 0.924987 + 0.379999i \(0.124076\pi\)
−0.133404 + 0.991062i \(0.542591\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 21.0079 1.00957 0.504787 0.863244i \(-0.331571\pi\)
0.504787 + 0.863244i \(0.331571\pi\)
\(434\) 6.86411 + 11.8890i 0.329488 + 0.570690i
\(435\) 36.6888 1.75909
\(436\) −0.683933 + 1.18461i −0.0327545 + 0.0567324i
\(437\) 4.20698 + 7.28670i 0.201247 + 0.348570i
\(438\) −1.57772 2.73269i −0.0753863 0.130573i
\(439\) 3.93502 6.81566i 0.187808 0.325294i −0.756711 0.653750i \(-0.773195\pi\)
0.944519 + 0.328456i \(0.106528\pi\)
\(440\) −15.6918 −0.748079
\(441\) −3.50000 6.06218i −0.166667 0.288675i
\(442\) −0.775189 −0.0368720
\(443\) −8.27806 + 14.3380i −0.393303 + 0.681220i −0.992883 0.119094i \(-0.962001\pi\)
0.599580 + 0.800315i \(0.295334\pi\)
\(444\) 0.690303 + 1.19564i 0.0327603 + 0.0567426i
\(445\) −19.8927 34.4552i −0.943005 1.63333i
\(446\) −4.69711 + 8.13564i −0.222415 + 0.385234i
\(447\) −11.8218 −0.559152
\(448\) −1.32288 2.29129i −0.0625000 0.108253i
\(449\) −10.4272 −0.492090 −0.246045 0.969258i \(-0.579131\pi\)
−0.246045 + 0.969258i \(0.579131\pi\)
\(450\) 5.09439 8.82374i 0.240152 0.415955i
\(451\) 8.88607 + 15.3911i 0.418429 + 0.724740i
\(452\) −9.87908 17.1111i −0.464673 0.804837i
\(453\) 4.71684 8.16981i 0.221616 0.383851i
\(454\) −25.3179 −1.18823
\(455\) −6.38672 −0.299414
\(456\) −8.41395 −0.394019
\(457\) −12.9041 + 22.3505i −0.603628 + 1.04551i 0.388639 + 0.921390i \(0.372945\pi\)
−0.992267 + 0.124124i \(0.960388\pi\)
\(458\) −5.98001 10.3577i −0.279428 0.483983i
\(459\) −0.625764 1.08385i −0.0292081 0.0505900i
\(460\) −1.94864 + 3.37514i −0.0908558 + 0.157367i
\(461\) −19.1660 −0.892650 −0.446325 0.894871i \(-0.647267\pi\)
−0.446325 + 0.894871i \(0.647267\pi\)
\(462\) −5.32637 + 9.22554i −0.247805 + 0.429211i
\(463\) 11.6891 0.543240 0.271620 0.962405i \(-0.412441\pi\)
0.271620 + 0.962405i \(0.412441\pi\)
\(464\) 4.70698 8.15272i 0.218516 0.378481i
\(465\) 10.1111 + 17.5129i 0.468889 + 0.812140i
\(466\) −4.43215 7.67670i −0.205315 0.355616i
\(467\) −0.418788 + 0.725362i −0.0193792 + 0.0335657i −0.875552 0.483123i \(-0.839502\pi\)
0.856173 + 0.516689i \(0.172836\pi\)
\(468\) −0.619394 −0.0286315
\(469\) −15.9442 + 27.6162i −0.736237 + 1.27520i
\(470\) 23.9140 1.10307
\(471\) 1.89091 3.27515i 0.0871285 0.150911i
\(472\) 5.50986 + 9.54336i 0.253612 + 0.439269i
\(473\) −4.02636 6.97386i −0.185132 0.320658i
\(474\) −7.73683 + 13.4006i −0.355364 + 0.615509i
\(475\) −85.7279 −3.93347
\(476\) −3.31123 −0.151770
\(477\) −1.89728 −0.0868704
\(478\) 4.96531 8.60017i 0.227108 0.393363i
\(479\) −1.79302 3.10561i −0.0819254 0.141899i 0.822152 0.569269i \(-0.192774\pi\)
−0.904077 + 0.427370i \(0.859440\pi\)
\(480\) −1.94864 3.37514i −0.0889428 0.154053i
\(481\) 0.427570 0.740572i 0.0194955 0.0337672i
\(482\) 12.2840 0.559521
\(483\) 1.32288 + 2.29129i 0.0601929 + 0.104257i
\(484\) 5.21155 0.236889
\(485\) −23.4871 + 40.6808i −1.06649 + 1.84722i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 7.51803 + 13.0216i 0.340674 + 0.590065i 0.984558 0.175058i \(-0.0560113\pi\)
−0.643884 + 0.765123i \(0.722678\pi\)
\(488\) −0.102721 + 0.177918i −0.00464997 + 0.00805399i
\(489\) −4.48333 −0.202743
\(490\) −27.2810 −1.23243
\(491\) −6.13302 −0.276779 −0.138390 0.990378i \(-0.544193\pi\)
−0.138390 + 0.990378i \(0.544193\pi\)
\(492\) −2.20698 + 3.82259i −0.0994982 + 0.172336i
\(493\) −5.89091 10.2034i −0.265313 0.459536i
\(494\) 2.60578 + 4.51334i 0.117239 + 0.203065i
\(495\) −7.84592 + 13.5895i −0.352648 + 0.610804i
\(496\) 5.18878 0.232983
\(497\) −0.639382 1.10744i −0.0286802 0.0496755i
\(498\) 7.13607 0.319775
\(499\) 10.7463 18.6131i 0.481068 0.833235i −0.518696 0.854959i \(-0.673582\pi\)
0.999764 + 0.0217242i \(0.00691557\pi\)
\(500\) −10.1111 17.5129i −0.452181 0.783200i
\(501\) 8.56939 + 14.8426i 0.382852 + 0.663119i
\(502\) 3.40740 5.90179i 0.152080 0.263410i
\(503\) −14.0922 −0.628339 −0.314169 0.949367i \(-0.601726\pi\)
−0.314169 + 0.949367i \(0.601726\pi\)
\(504\) −2.64575 −0.117851
\(505\) −39.7085 −1.76701
\(506\) 2.01318 3.48693i 0.0894967 0.155013i
\(507\) −6.30818 10.9261i −0.280156 0.485244i
\(508\) 7.71684 + 13.3660i 0.342379 + 0.593019i
\(509\) −5.97875 + 10.3555i −0.265003 + 0.458999i −0.967565 0.252624i \(-0.918706\pi\)
0.702561 + 0.711623i \(0.252040\pi\)
\(510\) −4.87755 −0.215982
\(511\) −4.17425 + 7.23001i −0.184658 + 0.319837i
\(512\) −1.00000 −0.0441942
\(513\) −4.20698 + 7.28670i −0.185743 + 0.321715i
\(514\) −11.7500 20.3516i −0.518271 0.897671i
\(515\) −13.5566 23.4808i −0.597377 1.03469i
\(516\) 1.00000 1.73205i 0.0440225 0.0762493i
\(517\) −24.7060 −1.08657
\(518\) 1.82637 3.16337i 0.0802461 0.138990i
\(519\) 2.84456 0.124863
\(520\) −1.20698 + 2.09054i −0.0529294 + 0.0916764i
\(521\) −11.1888 19.3795i −0.490189 0.849033i 0.509747 0.860324i \(-0.329739\pi\)
−0.999936 + 0.0112915i \(0.996406\pi\)
\(522\) −4.70698 8.15272i −0.206019 0.356835i
\(523\) −7.63301 + 13.2208i −0.333768 + 0.578104i −0.983247 0.182276i \(-0.941654\pi\)
0.649479 + 0.760379i \(0.274987\pi\)
\(524\) 20.8942 0.912769
\(525\) −26.9570 −1.17650
\(526\) −18.8534 −0.822046
\(527\) 3.24695 5.62388i 0.141439 0.244980i
\(528\) 2.01318 + 3.48693i 0.0876124 + 0.151749i
\(529\) −0.500000 0.866025i −0.0217391 0.0376533i
\(530\) −3.69711 + 6.40359i −0.160592 + 0.278154i
\(531\) 11.0197 0.478215
\(532\) 11.1306 + 19.2788i 0.482573 + 0.835841i
\(533\) 2.73398 0.118422
\(534\) −5.10425 + 8.84083i −0.220883 + 0.382580i
\(535\) −21.7002 37.5858i −0.938181 1.62498i
\(536\) 6.02636 + 10.4380i 0.260299 + 0.450851i
\(537\) 6.63912 11.4993i 0.286499 0.496231i
\(538\) 26.7976 1.15533
\(539\) 28.1845 1.21399
\(540\) −3.89728 −0.167712
\(541\) −2.39576 + 4.14957i −0.103002 + 0.178404i −0.912920 0.408139i \(-0.866178\pi\)
0.809918 + 0.586543i \(0.199511\pi\)
\(542\) −14.2401 24.6646i −0.611666 1.05944i
\(543\) 7.25332 + 12.5631i 0.311270 + 0.539135i
\(544\) −0.625764 + 1.08385i −0.0268294 + 0.0464699i
\(545\) 5.33096 0.228353
\(546\) 0.819381 + 1.41921i 0.0350663 + 0.0607366i
\(547\) 20.5888 0.880312 0.440156 0.897921i \(-0.354923\pi\)
0.440156 + 0.897921i \(0.354923\pi\)
\(548\) −3.18699 + 5.52003i −0.136141 + 0.235804i
\(549\) 0.102721 + 0.177918i 0.00438404 + 0.00759338i
\(550\) 20.5118 + 35.5275i 0.874628 + 1.51490i
\(551\) −39.6043 + 68.5966i −1.68720 + 2.92231i
\(552\) 1.00000 0.0425628
\(553\) 40.9394 1.74092
\(554\) −19.3969 −0.824097
\(555\) 2.69030 4.65974i 0.114197 0.197795i
\(556\) 1.06803 + 1.84989i 0.0452947 + 0.0784527i
\(557\) −13.3490 23.1211i −0.565614 0.979672i −0.996992 0.0775012i \(-0.975306\pi\)
0.431378 0.902171i \(-0.358027\pi\)
\(558\) 2.59439 4.49362i 0.109829 0.190230i
\(559\) −1.23879 −0.0523952
\(560\) −5.15562 + 8.92979i −0.217865 + 0.377352i
\(561\) 5.03910 0.212751
\(562\) 11.1952 19.3906i 0.472239 0.817942i
\(563\) −10.5035 18.1926i −0.442670 0.766726i 0.555217 0.831705i \(-0.312635\pi\)
−0.997887 + 0.0649794i \(0.979302\pi\)
\(564\) −3.06803 5.31399i −0.129188 0.223759i
\(565\) −38.5015 + 66.6866i −1.61977 + 2.80553i
\(566\) 10.0395 0.421990
\(567\) −1.32288 + 2.29129i −0.0555556 + 0.0962250i
\(568\) −0.483327 −0.0202800
\(569\) 8.16905 14.1492i 0.342465 0.593166i −0.642425 0.766348i \(-0.722072\pi\)
0.984890 + 0.173182i \(0.0554050\pi\)
\(570\) 16.3958 + 28.3983i 0.686743 + 1.18947i
\(571\) 1.52484 + 2.64109i 0.0638124 + 0.110526i 0.896167 0.443718i \(-0.146341\pi\)
−0.832354 + 0.554244i \(0.813007\pi\)
\(572\) 1.24695 2.15978i 0.0521376 0.0903050i
\(573\) 15.2419 0.636738
\(574\) 11.6782 0.487439
\(575\) 10.1888 0.424902
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −1.94694 3.37220i −0.0810521 0.140386i 0.822650 0.568548i \(-0.192495\pi\)
−0.903702 + 0.428162i \(0.859161\pi\)
\(578\) −7.71684 13.3660i −0.320978 0.555951i
\(579\) 5.97500 10.3490i 0.248312 0.430090i
\(580\) −36.6888 −1.52342
\(581\) −9.44013 16.3508i −0.391643 0.678345i
\(582\) 12.0531 0.499616
\(583\) 3.81956 6.61567i 0.158190 0.273993i
\(584\) 1.57772 + 2.73269i 0.0652864 + 0.113079i
\(585\) 1.20698 + 2.09054i 0.0499023 + 0.0864333i
\(586\) −12.5114 + 21.6704i −0.516841 + 0.895195i
\(587\) −36.4701 −1.50528 −0.752641 0.658431i \(-0.771220\pi\)
−0.752641 + 0.658431i \(0.771220\pi\)
\(588\) 3.50000 + 6.06218i 0.144338 + 0.250000i
\(589\) −43.6582 −1.79890
\(590\) 21.4735 37.1931i 0.884049 1.53122i
\(591\) −9.26955 16.0553i −0.381298 0.660428i
\(592\) −0.690303 1.19564i −0.0283713 0.0491405i
\(593\) 13.4733 23.3364i 0.553282 0.958312i −0.444753 0.895653i \(-0.646709\pi\)
0.998035 0.0626592i \(-0.0199581\pi\)
\(594\) 4.02636 0.165203
\(595\) 6.45239 + 11.1759i 0.264522 + 0.458166i
\(596\) 11.8218 0.484240
\(597\) −4.45876 + 7.72280i −0.182485 + 0.316073i
\(598\) −0.309697 0.536411i −0.0126645 0.0219355i
\(599\) 19.6253 + 33.9921i 0.801869 + 1.38888i 0.918384 + 0.395690i \(0.129494\pi\)
−0.116515 + 0.993189i \(0.537172\pi\)
\(600\) −5.09439 + 8.82374i −0.207978 + 0.360228i
\(601\) −7.94999 −0.324287 −0.162143 0.986767i \(-0.551841\pi\)
−0.162143 + 0.986767i \(0.551841\pi\)
\(602\) −5.29150 −0.215666
\(603\) 12.0527 0.490824
\(604\) −4.71684 + 8.16981i −0.191925 + 0.332425i
\(605\) −10.1554 17.5897i −0.412877 0.715124i
\(606\) 5.09439 + 8.82374i 0.206945 + 0.358440i
\(607\) −9.06106 + 15.6942i −0.367777 + 0.637008i −0.989218 0.146453i \(-0.953214\pi\)
0.621441 + 0.783461i \(0.286548\pi\)
\(608\) 8.41395 0.341231
\(609\) −12.4535 + 21.5701i −0.504641 + 0.874063i
\(610\) 0.800667 0.0324181
\(611\) −1.90032 + 3.29145i −0.0768788 + 0.133158i
\(612\) 0.625764 + 1.08385i 0.0252950 + 0.0438122i
\(613\) 19.3328 + 33.4853i 0.780842 + 1.35246i 0.931452 + 0.363865i \(0.118543\pi\)
−0.150609 + 0.988593i \(0.548123\pi\)
\(614\) −13.8111 + 23.9214i −0.557369 + 0.965391i
\(615\) 17.2024 0.693668
\(616\) 5.32637 9.22554i 0.214606 0.371708i
\(617\) 11.9509 0.481124 0.240562 0.970634i \(-0.422668\pi\)
0.240562 + 0.970634i \(0.422668\pi\)
\(618\) −3.47849 + 6.02492i −0.139925 + 0.242358i
\(619\) 7.46513 + 12.9300i 0.300049 + 0.519700i 0.976147 0.217112i \(-0.0696636\pi\)
−0.676098 + 0.736812i \(0.736330\pi\)
\(620\) −10.1111 17.5129i −0.406070 0.703334i
\(621\) 0.500000 0.866025i 0.0200643 0.0347524i
\(622\) −12.8337 −0.514583
\(623\) 27.0092 1.08210
\(624\) 0.619394 0.0247956
\(625\) −13.9337 + 24.1338i −0.557347 + 0.965354i
\(626\) −5.66530 9.81259i −0.226431 0.392190i
\(627\) −16.9388 29.3388i −0.676470 1.17168i
\(628\) −1.89091 + 3.27515i −0.0754555 + 0.130693i
\(629\) −1.72787 −0.0688945
\(630\) 5.15562 + 8.92979i 0.205405 + 0.355771i
\(631\) 27.8917 1.11035 0.555176 0.831733i \(-0.312651\pi\)
0.555176 + 0.831733i \(0.312651\pi\)
\(632\) 7.73683 13.4006i 0.307754 0.533046i
\(633\) 8.58471 + 14.8691i 0.341211 + 0.590996i
\(634\) 14.5099 + 25.1318i 0.576260 + 0.998112i
\(635\) 30.0747 52.0909i 1.19348 2.06716i
\(636\) 1.89728 0.0752320
\(637\) 2.16788 3.75488i 0.0858945 0.148774i
\(638\) 37.9039 1.50063
\(639\) −0.241664 + 0.418574i −0.00956006 + 0.0165585i
\(640\) 1.94864 + 3.37514i 0.0770267 + 0.133414i
\(641\) −12.9770 22.4768i −0.512559 0.887779i −0.999894 0.0145637i \(-0.995364\pi\)
0.487334 0.873215i \(-0.337969\pi\)
\(642\) −5.56803 + 9.64412i −0.219753 + 0.380623i
\(643\) 49.0759 1.93536 0.967682 0.252175i \(-0.0811459\pi\)
0.967682 + 0.252175i \(0.0811459\pi\)
\(644\) −1.32288 2.29129i −0.0521286 0.0902894i
\(645\) −7.79456 −0.306910
\(646\) 5.26515 9.11950i 0.207154 0.358802i
\(647\) −9.15714 15.8606i −0.360004 0.623546i 0.627957 0.778248i \(-0.283891\pi\)
−0.987961 + 0.154703i \(0.950558\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −22.1847 + 38.4250i −0.870825 + 1.50831i
\(650\) 6.31087 0.247533
\(651\) −13.7282 −0.538052
\(652\) 4.48333 0.175581
\(653\) 0.584527 1.01243i 0.0228743 0.0396195i −0.854362 0.519679i \(-0.826052\pi\)
0.877236 + 0.480059i \(0.159385\pi\)
\(654\) −0.683933 1.18461i −0.0267439 0.0463218i
\(655\) −40.7153 70.5210i −1.59088 2.75548i
\(656\) 2.20698 3.82259i 0.0861679 0.149247i
\(657\) 3.15544 0.123105
\(658\) −8.11725 + 14.0595i −0.316443 + 0.548096i
\(659\) −4.40121 −0.171447 −0.0857234 0.996319i \(-0.527320\pi\)
−0.0857234 + 0.996319i \(0.527320\pi\)
\(660\) 7.84592 13.5895i 0.305402 0.528972i
\(661\) −5.64091 9.77035i −0.219406 0.380023i 0.735220 0.677828i \(-0.237079\pi\)
−0.954627 + 0.297805i \(0.903745\pi\)
\(662\) 14.5512 + 25.2034i 0.565548 + 0.979558i
\(663\) 0.387594 0.671333i 0.0150529 0.0260724i
\(664\) −7.13607 −0.276933
\(665\) 43.3791 75.1348i 1.68217 2.91360i
\(666\) −1.38061 −0.0534974
\(667\) 4.70698 8.15272i 0.182255 0.315675i
\(668\) −8.56939 14.8426i −0.331560 0.574278i
\(669\) −4.69711 8.13564i −0.181601 0.314542i
\(670\) 23.4864 40.6796i 0.907359 1.57159i
\(671\) −0.827185 −0.0319331
\(672\) 2.64575 0.102062
\(673\) 6.54966 0.252471 0.126235 0.992000i \(-0.459711\pi\)
0.126235 + 0.992000i \(0.459711\pi\)
\(674\) 1.27108 2.20157i 0.0489600 0.0848012i
\(675\) 5.09439 + 8.82374i 0.196083 + 0.339626i
\(676\) 6.30818 + 10.9261i 0.242622 + 0.420234i
\(677\) −2.37533 + 4.11419i −0.0912913 + 0.158121i −0.908055 0.418851i \(-0.862433\pi\)
0.816763 + 0.576973i \(0.195766\pi\)
\(678\) 19.7582 0.758808
\(679\) −15.9447 27.6171i −0.611902 1.05985i
\(680\) 4.87755 0.187046
\(681\) 12.6589 21.9259i 0.485091 0.840203i
\(682\) 10.4459 + 18.0929i 0.399996 + 0.692813i
\(683\) −9.19471 15.9257i −0.351826 0.609380i 0.634744 0.772723i \(-0.281106\pi\)
−0.986569 + 0.163343i \(0.947772\pi\)
\(684\) 4.20698 7.28670i 0.160858 0.278614i
\(685\) 24.8412 0.949132
\(686\) 9.26013 16.0390i 0.353553 0.612372i
\(687\) 11.9600 0.456303
\(688\) −1.00000 + 1.73205i −0.0381246 + 0.0660338i
\(689\) −0.587582 1.01772i −0.0223851 0.0387721i
\(690\) −1.94864 3.37514i −0.0741834 0.128489i
\(691\) 16.2250 28.1025i 0.617228 1.06907i −0.372761 0.927927i \(-0.621589\pi\)
0.989989 0.141143i \(-0.0450778\pi\)
\(692\) −2.84456 −0.108134
\(693\) −5.32637 9.22554i −0.202332 0.350449i
\(694\) −20.3776 −0.773522
\(695\) 4.16242 7.20953i 0.157890 0.273473i
\(696\) 4.70698 + 8.15272i 0.178417 + 0.309028i
\(697\) −2.76209 4.78408i −0.104622 0.181210i
\(698\) 2.81938 4.88331i 0.106715 0.184836i
\(699\) 8.86429 0.335278
\(700\) 26.9570 1.01888
\(701\) −33.9894 −1.28376 −0.641882 0.766804i \(-0.721846\pi\)
−0.641882 + 0.766804i \(0.721846\pi\)
\(702\) 0.309697 0.536411i 0.0116888 0.0202455i
\(703\) 5.80818 + 10.0601i 0.219059 + 0.379422i
\(704\) −2.01318 3.48693i −0.0758745 0.131419i
\(705\) −11.9570 + 20.7101i −0.450326 + 0.779987i
\(706\) 4.69759 0.176796
\(707\) 13.4785 23.3454i 0.506911 0.877995i
\(708\) −11.0197 −0.414147
\(709\) 8.33122 14.4301i 0.312885 0.541934i −0.666100 0.745862i \(-0.732038\pi\)
0.978986 + 0.203929i \(0.0653711\pi\)
\(710\) 0.941830 + 1.63130i 0.0353463 + 0.0612215i
\(711\) −7.73683 13.4006i −0.290154 0.502561i
\(712\) 5.10425 8.84083i 0.191290 0.331324i
\(713\) 5.18878 0.194321
\(714\) 1.65562 2.86761i 0.0619598 0.107318i
\(715\) −9.71943 −0.363486
\(716\) −6.63912 + 11.4993i −0.248116 + 0.429749i
\(717\) 4.96531 + 8.60017i 0.185433 + 0.321179i
\(718\) −14.2151 24.6213i −0.530504 0.918860i
\(719\) 16.5966 28.7462i 0.618950 1.07205i −0.370728 0.928741i \(-0.620892\pi\)
0.989678 0.143311i \(-0.0457748\pi\)
\(720\) 3.89728 0.145243
\(721\) 18.4064 0.685492
\(722\) −51.7946 −1.92759
\(723\) −6.14200 + 10.6383i −0.228423 + 0.395641i
\(724\) −7.25332 12.5631i −0.269568 0.466905i
\(725\) 47.9583 + 83.0663i 1.78113 + 3.08500i
\(726\) −2.60578 + 4.51334i −0.0967094 + 0.167506i
\(727\) 27.3991 1.01618 0.508089 0.861305i \(-0.330352\pi\)
0.508089 + 0.861305i \(0.330352\pi\)
\(728\) −0.819381 1.41921i −0.0303683 0.0525994i
\(729\) 1.00000 0.0370370
\(730\) 6.14881 10.6500i 0.227578 0.394176i
\(731\) 1.25153 + 2.16771i 0.0462894 + 0.0801756i
\(732\) −0.102721 0.177918i −0.00379669 0.00657606i
\(733\) 0.549400 0.951588i 0.0202925 0.0351477i −0.855701 0.517471i \(-0.826874\pi\)
0.875993 + 0.482323i \(0.160207\pi\)
\(734\) 6.27177 0.231495
\(735\) 13.6405 23.6260i 0.503137 0.871458i
\(736\) −1.00000 −0.0368605
\(737\) −24.2643 + 42.0269i −0.893786 + 1.54808i
\(738\) −2.20698 3.82259i −0.0812399 0.140712i
\(739\) 24.7568 + 42.8801i 0.910695 + 1.57737i 0.813085 + 0.582144i \(0.197786\pi\)
0.0976092 + 0.995225i \(0.468880\pi\)
\(740\) −2.69030 + 4.65974i −0.0988975 + 0.171295i
\(741\) −5.21155 −0.191451
\(742\) −2.50986 4.34721i −0.0921400 0.159591i
\(743\) 10.6054 0.389075 0.194538 0.980895i \(-0.437679\pi\)
0.194538 + 0.980895i \(0.437679\pi\)
\(744\) −2.59439 + 4.49362i −0.0951150 + 0.164744i
\(745\) −23.0364 39.9002i −0.843989 1.46183i
\(746\) −3.13698 5.43341i −0.114853 0.198931i
\(747\) −3.56803 + 6.18002i −0.130548 + 0.226115i
\(748\) −5.03910 −0.184248
\(749\) 29.4633 1.07656
\(750\) 20.2221 0.738408
\(751\) 2.08928 3.61874i 0.0762390 0.132050i −0.825385 0.564570i \(-0.809042\pi\)
0.901624 + 0.432520i \(0.142375\pi\)
\(752\) 3.06803 + 5.31399i 0.111880 + 0.193781i
\(753\) 3.40740 + 5.90179i 0.124173 + 0.215073i
\(754\) 2.91547 5.04975i 0.106175 0.183901i
\(755\) 36.7657 1.33804
\(756\) 1.32288 2.29129i 0.0481125 0.0833333i
\(757\) −18.0758 −0.656978 −0.328489 0.944508i \(-0.606539\pi\)
−0.328489 + 0.944508i \(0.606539\pi\)
\(758\) −14.1124 + 24.4434i −0.512586 + 0.887825i
\(759\) 2.01318 + 3.48693i 0.0730738 + 0.126567i
\(760\) −16.3958 28.3983i −0.594737 1.03011i
\(761\) 1.90884 3.30621i 0.0691955 0.119850i −0.829352 0.558727i \(-0.811290\pi\)
0.898547 + 0.438876i \(0.144623\pi\)
\(762\) −15.4337 −0.559103
\(763\) −1.80952 + 3.13418i −0.0655089 + 0.113465i
\(764\) −15.2419 −0.551431
\(765\) 2.43878 4.22408i 0.0881741 0.152722i
\(766\) 4.72329 + 8.18098i 0.170659 + 0.295591i
\(767\) 3.41278 + 5.91110i 0.123228 + 0.213438i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) 11.4105 0.411475 0.205737 0.978607i \(-0.434041\pi\)
0.205737 + 0.978607i \(0.434041\pi\)
\(770\) −41.5167 −1.49616
\(771\) 23.5000 0.846332
\(772\) −5.97500 + 10.3490i −0.215045 + 0.372469i
\(773\) −12.8279 22.2186i −0.461388 0.799147i 0.537643 0.843173i \(-0.319315\pi\)
−0.999030 + 0.0440259i \(0.985982\pi\)
\(774\) 1.00000 + 1.73205i 0.0359443 + 0.0622573i
\(775\) −26.4337 + 45.7845i −0.949526 + 1.64463i
\(776\) −12.0531 −0.432680
\(777\) 1.82637 + 3.16337i 0.0655207 + 0.113485i
\(778\) −5.64183 −0.202269