Properties

Label 507.2.e.j.22.2
Level $507$
Weight $2$
Character 507.22
Analytic conductor $4.048$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.64827.1
Defining polynomial: \(x^{6} - x^{5} + 3 x^{4} + 5 x^{2} - 2 x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.2
Root \(0.222521 - 0.385418i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.j.484.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.222521 + 0.385418i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.900969 + 1.56052i) q^{4} -0.246980 q^{5} +(-0.222521 - 0.385418i) q^{6} +(-0.876510 - 1.51816i) q^{7} -1.69202 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.222521 + 0.385418i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.900969 + 1.56052i) q^{4} -0.246980 q^{5} +(-0.222521 - 0.385418i) q^{6} +(-0.876510 - 1.51816i) q^{7} -1.69202 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.0549581 - 0.0951903i) q^{10} +(-2.82640 + 4.89546i) q^{11} -1.80194 q^{12} +0.780167 q^{14} +(0.123490 - 0.213891i) q^{15} +(-1.42543 + 2.46891i) q^{16} +(1.90097 + 3.29257i) q^{17} +0.445042 q^{18} +(-2.79105 - 4.83424i) q^{19} +(-0.222521 - 0.385418i) q^{20} +1.75302 q^{21} +(-1.25786 - 2.17869i) q^{22} +(-4.17241 + 7.22682i) q^{23} +(0.846011 - 1.46533i) q^{24} -4.93900 q^{25} +1.00000 q^{27} +(1.57942 - 2.73563i) q^{28} +(2.96950 - 5.14333i) q^{29} +(0.0549581 + 0.0951903i) q^{30} +5.26875 q^{31} +(-2.32640 - 4.02944i) q^{32} +(-2.82640 - 4.89546i) q^{33} -1.69202 q^{34} +(0.216480 + 0.374955i) q^{35} +(0.900969 - 1.56052i) q^{36} +(-1.59903 + 2.76960i) q^{37} +2.48427 q^{38} +0.417895 q^{40} +(-0.222521 + 0.385418i) q^{41} +(-0.390084 + 0.675645i) q^{42} +(-0.856896 - 1.48419i) q^{43} -10.1860 q^{44} +(0.123490 + 0.213891i) q^{45} +(-1.85690 - 3.21624i) q^{46} -6.73556 q^{47} +(-1.42543 - 2.46891i) q^{48} +(1.96346 - 3.40081i) q^{49} +(1.09903 - 1.90358i) q^{50} -3.80194 q^{51} -1.06100 q^{53} +(-0.222521 + 0.385418i) q^{54} +(0.698062 - 1.20908i) q^{55} +(1.48307 + 2.56876i) q^{56} +5.58211 q^{57} +(1.32155 + 2.28900i) q^{58} +(6.85086 + 11.8660i) q^{59} +0.445042 q^{60} +(4.25786 + 7.37484i) q^{61} +(-1.17241 + 2.03067i) q^{62} +(-0.876510 + 1.51816i) q^{63} -3.63102 q^{64} +2.51573 q^{66} +(-2.98039 + 5.16218i) q^{67} +(-3.42543 + 5.93301i) q^{68} +(-4.17241 - 7.22682i) q^{69} -0.192685 q^{70} +(2.85958 + 4.95295i) q^{71} +(0.846011 + 1.46533i) q^{72} +7.35690 q^{73} +(-0.711636 - 1.23259i) q^{74} +(2.46950 - 4.27730i) q^{75} +(5.02930 - 8.71101i) q^{76} +9.90946 q^{77} +4.45473 q^{79} +(0.352052 - 0.609771i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.0990311 - 0.171527i) q^{82} -10.1860 q^{83} +(1.57942 + 2.73563i) q^{84} +(-0.469501 - 0.813199i) q^{85} +0.762709 q^{86} +(2.96950 + 5.14333i) q^{87} +(4.78232 - 8.28323i) q^{88} +(-0.0685317 + 0.118700i) q^{89} -0.109916 q^{90} -15.0368 q^{92} +(-2.63437 + 4.56287i) q^{93} +(1.49880 - 2.59600i) q^{94} +(0.689333 + 1.19396i) q^{95} +4.65279 q^{96} +(6.84481 + 11.8556i) q^{97} +(0.873822 + 1.51350i) q^{98} +5.65279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} - 3q^{3} + q^{4} + 8q^{5} - q^{6} - 10q^{7} - 3q^{9} + O(q^{10}) \) \( 6q - q^{2} - 3q^{3} + q^{4} + 8q^{5} - q^{6} - 10q^{7} - 3q^{9} + q^{10} + q^{11} - 2q^{12} + 2q^{14} - 4q^{15} + 5q^{16} + 7q^{17} + 2q^{18} - 11q^{19} - q^{20} + 20q^{21} + 5q^{22} - 2q^{23} - 10q^{25} + 6q^{27} + q^{28} + 8q^{29} + q^{30} + 16q^{31} + 4q^{32} + q^{33} - 18q^{35} + q^{36} - 14q^{37} + 40q^{38} + 14q^{40} - q^{41} - q^{42} + 3q^{43} - 32q^{44} - 4q^{45} - 3q^{46} - 18q^{47} + 5q^{48} - 17q^{49} + 11q^{50} - 14q^{51} - 26q^{53} - q^{54} + 13q^{55} - 7q^{56} + 22q^{57} + 12q^{58} + 14q^{59} + 2q^{60} + 13q^{61} + 16q^{62} - 10q^{63} + 8q^{64} - 10q^{66} - 5q^{67} - 7q^{68} - 2q^{69} - 16q^{70} + 6q^{71} + 36q^{73} - 7q^{74} + 5q^{75} - q^{76} - 30q^{77} - 18q^{79} + 16q^{80} - 3q^{81} - 5q^{82} - 32q^{83} + q^{84} + 7q^{85} - 30q^{86} + 8q^{87} + 7q^{88} + 5q^{89} - 2q^{90} - 34q^{92} - 8q^{93} - 32q^{94} - 3q^{95} - 8q^{96} - 5q^{97} + 13q^{98} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.222521 + 0.385418i −0.157346 + 0.272531i −0.933911 0.357506i \(-0.883627\pi\)
0.776565 + 0.630037i \(0.216960\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0.900969 + 1.56052i 0.450484 + 0.780262i
\(5\) −0.246980 −0.110453 −0.0552263 0.998474i \(-0.517588\pi\)
−0.0552263 + 0.998474i \(0.517588\pi\)
\(6\) −0.222521 0.385418i −0.0908438 0.157346i
\(7\) −0.876510 1.51816i −0.331290 0.573811i 0.651475 0.758670i \(-0.274150\pi\)
−0.982765 + 0.184859i \(0.940817\pi\)
\(8\) −1.69202 −0.598220
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.0549581 0.0951903i 0.0173793 0.0301018i
\(11\) −2.82640 + 4.89546i −0.852191 + 1.47604i 0.0270365 + 0.999634i \(0.491393\pi\)
−0.879227 + 0.476403i \(0.841940\pi\)
\(12\) −1.80194 −0.520175
\(13\) 0 0
\(14\) 0.780167 0.208509
\(15\) 0.123490 0.213891i 0.0318849 0.0552263i
\(16\) −1.42543 + 2.46891i −0.356357 + 0.617228i
\(17\) 1.90097 + 3.29257i 0.461053 + 0.798567i 0.999014 0.0444031i \(-0.0141386\pi\)
−0.537961 + 0.842970i \(0.680805\pi\)
\(18\) 0.445042 0.104897
\(19\) −2.79105 4.83424i −0.640311 1.10905i −0.985363 0.170468i \(-0.945472\pi\)
0.345052 0.938584i \(-0.387861\pi\)
\(20\) −0.222521 0.385418i −0.0497572 0.0861820i
\(21\) 1.75302 0.382540
\(22\) −1.25786 2.17869i −0.268178 0.464497i
\(23\) −4.17241 + 7.22682i −0.870007 + 1.50690i −0.00801894 + 0.999968i \(0.502553\pi\)
−0.861988 + 0.506929i \(0.830781\pi\)
\(24\) 0.846011 1.46533i 0.172691 0.299110i
\(25\) −4.93900 −0.987800
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 1.57942 2.73563i 0.298482 0.516986i
\(29\) 2.96950 5.14333i 0.551422 0.955092i −0.446750 0.894659i \(-0.647419\pi\)
0.998172 0.0604327i \(-0.0192481\pi\)
\(30\) 0.0549581 + 0.0951903i 0.0100339 + 0.0173793i
\(31\) 5.26875 0.946295 0.473148 0.880983i \(-0.343118\pi\)
0.473148 + 0.880983i \(0.343118\pi\)
\(32\) −2.32640 4.02944i −0.411253 0.712311i
\(33\) −2.82640 4.89546i −0.492012 0.852191i
\(34\) −1.69202 −0.290179
\(35\) 0.216480 + 0.374955i 0.0365918 + 0.0633789i
\(36\) 0.900969 1.56052i 0.150161 0.260087i
\(37\) −1.59903 + 2.76960i −0.262879 + 0.455320i −0.967006 0.254754i \(-0.918005\pi\)
0.704127 + 0.710074i \(0.251339\pi\)
\(38\) 2.48427 0.403002
\(39\) 0 0
\(40\) 0.417895 0.0660750
\(41\) −0.222521 + 0.385418i −0.0347519 + 0.0601921i −0.882878 0.469602i \(-0.844397\pi\)
0.848126 + 0.529794i \(0.177731\pi\)
\(42\) −0.390084 + 0.675645i −0.0601912 + 0.104254i
\(43\) −0.856896 1.48419i −0.130675 0.226336i 0.793262 0.608881i \(-0.208381\pi\)
−0.923937 + 0.382544i \(0.875048\pi\)
\(44\) −10.1860 −1.53559
\(45\) 0.123490 + 0.213891i 0.0184088 + 0.0318849i
\(46\) −1.85690 3.21624i −0.273784 0.474208i
\(47\) −6.73556 −0.982483 −0.491241 0.871024i \(-0.663457\pi\)
−0.491241 + 0.871024i \(0.663457\pi\)
\(48\) −1.42543 2.46891i −0.205743 0.356357i
\(49\) 1.96346 3.40081i 0.280494 0.485830i
\(50\) 1.09903 1.90358i 0.155426 0.269207i
\(51\) −3.80194 −0.532378
\(52\) 0 0
\(53\) −1.06100 −0.145739 −0.0728697 0.997341i \(-0.523216\pi\)
−0.0728697 + 0.997341i \(0.523216\pi\)
\(54\) −0.222521 + 0.385418i −0.0302813 + 0.0524487i
\(55\) 0.698062 1.20908i 0.0941267 0.163032i
\(56\) 1.48307 + 2.56876i 0.198184 + 0.343265i
\(57\) 5.58211 0.739368
\(58\) 1.32155 + 2.28900i 0.173528 + 0.300560i
\(59\) 6.85086 + 11.8660i 0.891905 + 1.54483i 0.837589 + 0.546302i \(0.183965\pi\)
0.0543169 + 0.998524i \(0.482702\pi\)
\(60\) 0.445042 0.0574547
\(61\) 4.25786 + 7.37484i 0.545164 + 0.944251i 0.998597 + 0.0529608i \(0.0168658\pi\)
−0.453433 + 0.891290i \(0.649801\pi\)
\(62\) −1.17241 + 2.03067i −0.148896 + 0.257895i
\(63\) −0.876510 + 1.51816i −0.110430 + 0.191270i
\(64\) −3.63102 −0.453878
\(65\) 0 0
\(66\) 2.51573 0.309665
\(67\) −2.98039 + 5.16218i −0.364112 + 0.630661i −0.988633 0.150347i \(-0.951961\pi\)
0.624521 + 0.781008i \(0.285294\pi\)
\(68\) −3.42543 + 5.93301i −0.415394 + 0.719484i
\(69\) −4.17241 7.22682i −0.502299 0.870007i
\(70\) −0.192685 −0.0230303
\(71\) 2.85958 + 4.95295i 0.339370 + 0.587806i 0.984314 0.176423i \(-0.0564527\pi\)
−0.644944 + 0.764230i \(0.723119\pi\)
\(72\) 0.846011 + 1.46533i 0.0997033 + 0.172691i
\(73\) 7.35690 0.861060 0.430530 0.902576i \(-0.358327\pi\)
0.430530 + 0.902576i \(0.358327\pi\)
\(74\) −0.711636 1.23259i −0.0827260 0.143286i
\(75\) 2.46950 4.27730i 0.285153 0.493900i
\(76\) 5.02930 8.71101i 0.576901 0.999221i
\(77\) 9.90946 1.12929
\(78\) 0 0
\(79\) 4.45473 0.501196 0.250598 0.968091i \(-0.419373\pi\)
0.250598 + 0.968091i \(0.419373\pi\)
\(80\) 0.352052 0.609771i 0.0393606 0.0681745i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −0.0990311 0.171527i −0.0109362 0.0189420i
\(83\) −10.1860 −1.11806 −0.559028 0.829149i \(-0.688826\pi\)
−0.559028 + 0.829149i \(0.688826\pi\)
\(84\) 1.57942 + 2.73563i 0.172329 + 0.298482i
\(85\) −0.469501 0.813199i −0.0509245 0.0882038i
\(86\) 0.762709 0.0822450
\(87\) 2.96950 + 5.14333i 0.318364 + 0.551422i
\(88\) 4.78232 8.28323i 0.509797 0.882995i
\(89\) −0.0685317 + 0.118700i −0.00726434 + 0.0125822i −0.869635 0.493696i \(-0.835646\pi\)
0.862370 + 0.506278i \(0.168979\pi\)
\(90\) −0.109916 −0.0115862
\(91\) 0 0
\(92\) −15.0368 −1.56770
\(93\) −2.63437 + 4.56287i −0.273172 + 0.473148i
\(94\) 1.49880 2.59600i 0.154590 0.267757i
\(95\) 0.689333 + 1.19396i 0.0707241 + 0.122498i
\(96\) 4.65279 0.474874
\(97\) 6.84481 + 11.8556i 0.694986 + 1.20375i 0.970186 + 0.242363i \(0.0779226\pi\)
−0.275200 + 0.961387i \(0.588744\pi\)
\(98\) 0.873822 + 1.51350i 0.0882693 + 0.152887i
\(99\) 5.65279 0.568127
\(100\) −4.44989 7.70743i −0.444989 0.770743i
\(101\) 2.70560 4.68623i 0.269217 0.466297i −0.699443 0.714688i \(-0.746569\pi\)
0.968660 + 0.248391i \(0.0799019\pi\)
\(102\) 0.846011 1.46533i 0.0837675 0.145090i
\(103\) 13.7560 1.35542 0.677710 0.735330i \(-0.262973\pi\)
0.677710 + 0.735330i \(0.262973\pi\)
\(104\) 0 0
\(105\) −0.432960 −0.0422526
\(106\) 0.236094 0.408928i 0.0229315 0.0397186i
\(107\) 6.40850 11.0999i 0.619533 1.07306i −0.370038 0.929017i \(-0.620655\pi\)
0.989571 0.144046i \(-0.0460114\pi\)
\(108\) 0.900969 + 1.56052i 0.0866958 + 0.150161i
\(109\) 12.1468 1.16345 0.581724 0.813386i \(-0.302378\pi\)
0.581724 + 0.813386i \(0.302378\pi\)
\(110\) 0.310667 + 0.538091i 0.0296209 + 0.0513050i
\(111\) −1.59903 2.76960i −0.151773 0.262879i
\(112\) 4.99761 0.472229
\(113\) 0.818864 + 1.41831i 0.0770322 + 0.133424i 0.901968 0.431802i \(-0.142122\pi\)
−0.824936 + 0.565226i \(0.808789\pi\)
\(114\) −1.24214 + 2.15144i −0.116337 + 0.201501i
\(115\) 1.03050 1.78488i 0.0960946 0.166441i
\(116\) 10.7017 0.993629
\(117\) 0 0
\(118\) −6.09783 −0.561351
\(119\) 3.33244 5.77195i 0.305484 0.529114i
\(120\) −0.208947 + 0.361908i −0.0190742 + 0.0330375i
\(121\) −10.4770 18.1468i −0.952458 1.64970i
\(122\) −3.78986 −0.343117
\(123\) −0.222521 0.385418i −0.0200640 0.0347519i
\(124\) 4.74698 + 8.22201i 0.426291 + 0.738358i
\(125\) 2.45473 0.219558
\(126\) −0.390084 0.675645i −0.0347514 0.0601912i
\(127\) −5.39977 + 9.35268i −0.479152 + 0.829916i −0.999714 0.0239078i \(-0.992389\pi\)
0.520562 + 0.853824i \(0.325723\pi\)
\(128\) 5.46077 9.45833i 0.482669 0.836006i
\(129\) 1.71379 0.150891
\(130\) 0 0
\(131\) 0.907542 0.0792923 0.0396462 0.999214i \(-0.487377\pi\)
0.0396462 + 0.999214i \(0.487377\pi\)
\(132\) 5.09299 8.82132i 0.443288 0.767797i
\(133\) −4.89277 + 8.47453i −0.424257 + 0.734835i
\(134\) −1.32640 2.29739i −0.114583 0.198464i
\(135\) −0.246980 −0.0212566
\(136\) −3.21648 5.57111i −0.275811 0.477718i
\(137\) 4.77413 + 8.26903i 0.407881 + 0.706471i 0.994652 0.103282i \(-0.0329344\pi\)
−0.586771 + 0.809753i \(0.699601\pi\)
\(138\) 3.71379 0.316139
\(139\) 2.04623 + 3.54417i 0.173559 + 0.300613i 0.939662 0.342105i \(-0.111140\pi\)
−0.766103 + 0.642718i \(0.777807\pi\)
\(140\) −0.390084 + 0.675645i −0.0329681 + 0.0571024i
\(141\) 3.36778 5.83317i 0.283618 0.491241i
\(142\) −2.54527 −0.213594
\(143\) 0 0
\(144\) 2.85086 0.237571
\(145\) −0.733406 + 1.27030i −0.0609061 + 0.105492i
\(146\) −1.63706 + 2.83548i −0.135484 + 0.234666i
\(147\) 1.96346 + 3.40081i 0.161943 + 0.280494i
\(148\) −5.76271 −0.473692
\(149\) 7.69418 + 13.3267i 0.630332 + 1.09177i 0.987484 + 0.157720i \(0.0504144\pi\)
−0.357152 + 0.934046i \(0.616252\pi\)
\(150\) 1.09903 + 1.90358i 0.0897355 + 0.155426i
\(151\) −3.67456 −0.299032 −0.149516 0.988759i \(-0.547772\pi\)
−0.149516 + 0.988759i \(0.547772\pi\)
\(152\) 4.72252 + 8.17965i 0.383047 + 0.663457i
\(153\) 1.90097 3.29257i 0.153684 0.266189i
\(154\) −2.20506 + 3.81928i −0.177689 + 0.307766i
\(155\) −1.30127 −0.104521
\(156\) 0 0
\(157\) −4.87800 −0.389307 −0.194653 0.980872i \(-0.562358\pi\)
−0.194653 + 0.980872i \(0.562358\pi\)
\(158\) −0.991271 + 1.71693i −0.0788613 + 0.136592i
\(159\) 0.530499 0.918852i 0.0420713 0.0728697i
\(160\) 0.574572 + 0.995189i 0.0454239 + 0.0786766i
\(161\) 14.6286 1.15290
\(162\) −0.222521 0.385418i −0.0174829 0.0302813i
\(163\) −4.31551 7.47468i −0.338017 0.585462i 0.646043 0.763301i \(-0.276423\pi\)
−0.984060 + 0.177839i \(0.943089\pi\)
\(164\) −0.801938 −0.0626208
\(165\) 0.698062 + 1.20908i 0.0543441 + 0.0941267i
\(166\) 2.26659 3.92586i 0.175922 0.304706i
\(167\) −4.73490 + 8.20108i −0.366397 + 0.634619i −0.988999 0.147920i \(-0.952742\pi\)
0.622602 + 0.782539i \(0.286076\pi\)
\(168\) −2.96615 −0.228843
\(169\) 0 0
\(170\) 0.417895 0.0320511
\(171\) −2.79105 + 4.83424i −0.213437 + 0.369684i
\(172\) 1.54407 2.67441i 0.117734 0.203922i
\(173\) −2.38740 4.13509i −0.181510 0.314385i 0.760885 0.648887i \(-0.224765\pi\)
−0.942395 + 0.334502i \(0.891432\pi\)
\(174\) −2.64310 −0.200373
\(175\) 4.32908 + 7.49819i 0.327248 + 0.566810i
\(176\) −8.05765 13.9563i −0.607368 1.05199i
\(177\) −13.7017 −1.02988
\(178\) −0.0304995 0.0528266i −0.00228603 0.00395952i
\(179\) −1.71768 + 2.97510i −0.128385 + 0.222370i −0.923051 0.384677i \(-0.874313\pi\)
0.794666 + 0.607047i \(0.207646\pi\)
\(180\) −0.222521 + 0.385418i −0.0165857 + 0.0287273i
\(181\) −13.4862 −1.00242 −0.501210 0.865326i \(-0.667112\pi\)
−0.501210 + 0.865326i \(0.667112\pi\)
\(182\) 0 0
\(183\) −8.51573 −0.629501
\(184\) 7.05980 12.2279i 0.520456 0.901455i
\(185\) 0.394928 0.684035i 0.0290357 0.0502913i
\(186\) −1.17241 2.03067i −0.0859651 0.148896i
\(187\) −21.4916 −1.57162
\(188\) −6.06853 10.5110i −0.442593 0.766594i
\(189\) −0.876510 1.51816i −0.0637567 0.110430i
\(190\) −0.613564 −0.0445126
\(191\) 0.650637 + 1.12694i 0.0470784 + 0.0815422i 0.888604 0.458674i \(-0.151676\pi\)
−0.841526 + 0.540217i \(0.818342\pi\)
\(192\) 1.81551 3.14456i 0.131023 0.226939i
\(193\) 4.59783 7.96368i 0.330959 0.573238i −0.651741 0.758442i \(-0.725961\pi\)
0.982700 + 0.185203i \(0.0592944\pi\)
\(194\) −6.09246 −0.437413
\(195\) 0 0
\(196\) 7.07606 0.505433
\(197\) −2.05615 + 3.56136i −0.146495 + 0.253737i −0.929930 0.367737i \(-0.880133\pi\)
0.783435 + 0.621474i \(0.213466\pi\)
\(198\) −1.25786 + 2.17869i −0.0893926 + 0.154832i
\(199\) 12.3862 + 21.4535i 0.878034 + 1.52080i 0.853495 + 0.521101i \(0.174479\pi\)
0.0245395 + 0.999699i \(0.492188\pi\)
\(200\) 8.35690 0.590922
\(201\) −2.98039 5.16218i −0.210220 0.364112i
\(202\) 1.20410 + 2.08557i 0.0847204 + 0.146740i
\(203\) −10.4112 −0.730722
\(204\) −3.42543 5.93301i −0.239828 0.415394i
\(205\) 0.0549581 0.0951903i 0.00383844 0.00664838i
\(206\) −3.06100 + 5.30181i −0.213270 + 0.369394i
\(207\) 8.34481 0.580005
\(208\) 0 0
\(209\) 31.5545 2.18267
\(210\) 0.0963427 0.166870i 0.00664828 0.0115152i
\(211\) 2.96950 5.14333i 0.204429 0.354081i −0.745522 0.666481i \(-0.767800\pi\)
0.949951 + 0.312400i \(0.101133\pi\)
\(212\) −0.955927 1.65571i −0.0656533 0.113715i
\(213\) −5.71917 −0.391871
\(214\) 2.85205 + 4.93990i 0.194962 + 0.337684i
\(215\) 0.211636 + 0.366564i 0.0144334 + 0.0249995i
\(216\) −1.69202 −0.115127
\(217\) −4.61811 7.99881i −0.313498 0.542994i
\(218\) −2.70291 + 4.68157i −0.183064 + 0.317076i
\(219\) −3.67845 + 6.37126i −0.248566 + 0.430530i
\(220\) 2.51573 0.169610
\(221\) 0 0
\(222\) 1.42327 0.0955237
\(223\) −7.10052 + 12.2985i −0.475486 + 0.823566i −0.999606 0.0280785i \(-0.991061\pi\)
0.524120 + 0.851645i \(0.324395\pi\)
\(224\) −4.07822 + 7.06368i −0.272488 + 0.471962i
\(225\) 2.46950 + 4.27730i 0.164633 + 0.285153i
\(226\) −0.728857 −0.0484829
\(227\) −8.00365 13.8627i −0.531221 0.920101i −0.999336 0.0364340i \(-0.988400\pi\)
0.468115 0.883667i \(-0.344933\pi\)
\(228\) 5.02930 + 8.71101i 0.333074 + 0.576901i
\(229\) 1.84117 0.121668 0.0608339 0.998148i \(-0.480624\pi\)
0.0608339 + 0.998148i \(0.480624\pi\)
\(230\) 0.458615 + 0.794345i 0.0302402 + 0.0523776i
\(231\) −4.95473 + 8.58185i −0.325997 + 0.564644i
\(232\) −5.02446 + 8.70262i −0.329872 + 0.571355i
\(233\) −23.4252 −1.53464 −0.767318 0.641267i \(-0.778409\pi\)
−0.767318 + 0.641267i \(0.778409\pi\)
\(234\) 0 0
\(235\) 1.66355 0.108518
\(236\) −12.3448 + 21.3818i −0.803579 + 1.39184i
\(237\) −2.22737 + 3.85791i −0.144683 + 0.250598i
\(238\) 1.48307 + 2.56876i 0.0961334 + 0.166508i
\(239\) 14.6015 0.944491 0.472246 0.881467i \(-0.343444\pi\)
0.472246 + 0.881467i \(0.343444\pi\)
\(240\) 0.352052 + 0.609771i 0.0227248 + 0.0393606i
\(241\) −4.31551 7.47468i −0.277987 0.481487i 0.692898 0.721036i \(-0.256334\pi\)
−0.970884 + 0.239549i \(0.923000\pi\)
\(242\) 9.32544 0.599462
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −7.67241 + 13.2890i −0.491176 + 0.850741i
\(245\) −0.484935 + 0.839931i −0.0309813 + 0.0536612i
\(246\) 0.198062 0.0126280
\(247\) 0 0
\(248\) −8.91484 −0.566093
\(249\) 5.09299 8.82132i 0.322755 0.559028i
\(250\) −0.546229 + 0.946096i −0.0345466 + 0.0598364i
\(251\) 1.90097 + 3.29257i 0.119988 + 0.207825i 0.919763 0.392475i \(-0.128381\pi\)
−0.799775 + 0.600300i \(0.795048\pi\)
\(252\) −3.15883 −0.198988
\(253\) −23.5858 40.8517i −1.48282 2.56833i
\(254\) −2.40312 4.16233i −0.150785 0.261168i
\(255\) 0.939001 0.0588025
\(256\) −1.20075 2.07976i −0.0750469 0.129985i
\(257\) 10.2981 17.8368i 0.642375 1.11263i −0.342526 0.939508i \(-0.611283\pi\)
0.984901 0.173118i \(-0.0553841\pi\)
\(258\) −0.381355 + 0.660525i −0.0237421 + 0.0411225i
\(259\) 5.60627 0.348357
\(260\) 0 0
\(261\) −5.93900 −0.367615
\(262\) −0.201947 + 0.349783i −0.0124763 + 0.0216096i
\(263\) −0.166366 + 0.288155i −0.0102586 + 0.0177684i −0.871109 0.491089i \(-0.836599\pi\)
0.860851 + 0.508858i \(0.169932\pi\)
\(264\) 4.78232 + 8.28323i 0.294332 + 0.509797i
\(265\) 0.262045 0.0160973
\(266\) −2.17749 3.77152i −0.133510 0.231247i
\(267\) −0.0685317 0.118700i −0.00419407 0.00726434i
\(268\) −10.7409 −0.656107
\(269\) −13.6516 23.6453i −0.832353 1.44168i −0.896168 0.443715i \(-0.853660\pi\)
0.0638154 0.997962i \(-0.479673\pi\)
\(270\) 0.0549581 0.0951903i 0.00334465 0.00579310i
\(271\) −13.9928 + 24.2362i −0.850000 + 1.47224i 0.0312076 + 0.999513i \(0.490065\pi\)
−0.881207 + 0.472730i \(0.843269\pi\)
\(272\) −10.8388 −0.657197
\(273\) 0 0
\(274\) −4.24937 −0.256714
\(275\) 13.9596 24.1787i 0.841794 1.45803i
\(276\) 7.51842 13.0223i 0.452556 0.783849i
\(277\) 1.05161 + 1.82143i 0.0631849 + 0.109439i 0.895887 0.444281i \(-0.146541\pi\)
−0.832703 + 0.553721i \(0.813208\pi\)
\(278\) −1.82132 −0.109235
\(279\) −2.63437 4.56287i −0.157716 0.273172i
\(280\) −0.366289 0.634431i −0.0218900 0.0379145i
\(281\) 27.2349 1.62470 0.812349 0.583172i \(-0.198189\pi\)
0.812349 + 0.583172i \(0.198189\pi\)
\(282\) 1.49880 + 2.59600i 0.0892525 + 0.154590i
\(283\) −2.64191 + 4.57592i −0.157045 + 0.272010i −0.933802 0.357791i \(-0.883530\pi\)
0.776757 + 0.629801i \(0.216863\pi\)
\(284\) −5.15279 + 8.92490i −0.305762 + 0.529595i
\(285\) −1.37867 −0.0816651
\(286\) 0 0
\(287\) 0.780167 0.0460518
\(288\) −2.32640 + 4.02944i −0.137084 + 0.237437i
\(289\) 1.27263 2.20427i 0.0748609 0.129663i
\(290\) −0.326396 0.565335i −0.0191667 0.0331976i
\(291\) −13.6896 −0.802500
\(292\) 6.62833 + 11.4806i 0.387894 + 0.671852i
\(293\) −16.3312 28.2865i −0.954081 1.65252i −0.736457 0.676485i \(-0.763502\pi\)
−0.217625 0.976033i \(-0.569831\pi\)
\(294\) −1.74764 −0.101925
\(295\) −1.69202 2.93067i −0.0985133 0.170630i
\(296\) 2.70560 4.68623i 0.157260 0.272381i
\(297\) −2.82640 + 4.89546i −0.164004 + 0.284064i
\(298\) −6.84846 −0.396721
\(299\) 0 0
\(300\) 8.89977 0.513829
\(301\) −1.50216 + 2.60181i −0.0865828 + 0.149966i
\(302\) 0.817667 1.41624i 0.0470515 0.0814955i
\(303\) 2.70560 + 4.68623i 0.155432 + 0.269217i
\(304\) 15.9138 0.912717
\(305\) −1.05161 1.82143i −0.0602148 0.104295i
\(306\) 0.846011 + 1.46533i 0.0483632 + 0.0837675i
\(307\) −20.7614 −1.18491 −0.592457 0.805602i \(-0.701842\pi\)
−0.592457 + 0.805602i \(0.701842\pi\)
\(308\) 8.92812 + 15.4640i 0.508727 + 0.881140i
\(309\) −6.87800 + 11.9130i −0.391276 + 0.677710i
\(310\) 0.289561 0.501534i 0.0164459 0.0284852i
\(311\) −11.3013 −0.640836 −0.320418 0.947276i \(-0.603823\pi\)
−0.320418 + 0.947276i \(0.603823\pi\)
\(312\) 0 0
\(313\) −4.27173 −0.241453 −0.120726 0.992686i \(-0.538522\pi\)
−0.120726 + 0.992686i \(0.538522\pi\)
\(314\) 1.08546 1.88007i 0.0612559 0.106098i
\(315\) 0.216480 0.374955i 0.0121973 0.0211263i
\(316\) 4.01357 + 6.95171i 0.225781 + 0.391064i
\(317\) 15.4776 0.869307 0.434653 0.900598i \(-0.356871\pi\)
0.434653 + 0.900598i \(0.356871\pi\)
\(318\) 0.236094 + 0.408928i 0.0132395 + 0.0229315i
\(319\) 16.7860 + 29.0742i 0.939834 + 1.62784i
\(320\) 0.896789 0.0501320
\(321\) 6.40850 + 11.0999i 0.357688 + 0.619533i
\(322\) −3.25518 + 5.63813i −0.181404 + 0.314201i
\(323\) 10.6114 18.3795i 0.590435 1.02266i
\(324\) −1.80194 −0.100108
\(325\) 0 0
\(326\) 3.84117 0.212743
\(327\) −6.07338 + 10.5194i −0.335858 + 0.581724i
\(328\) 0.376510 0.652135i 0.0207893 0.0360081i
\(329\) 5.90379 + 10.2257i 0.325486 + 0.563759i
\(330\) −0.621334 −0.0342033
\(331\) −3.03415 5.25530i −0.166772 0.288857i 0.770511 0.637426i \(-0.220001\pi\)
−0.937283 + 0.348569i \(0.886668\pi\)
\(332\) −9.17725 15.8955i −0.503667 0.872377i
\(333\) 3.19806 0.175253
\(334\) −2.10723 3.64983i −0.115302 0.199710i
\(335\) 0.736094 1.27495i 0.0402171 0.0696581i
\(336\) −2.49880 + 4.32805i −0.136321 + 0.236115i
\(337\) 12.1239 0.660432 0.330216 0.943905i \(-0.392878\pi\)
0.330216 + 0.943905i \(0.392878\pi\)
\(338\) 0 0
\(339\) −1.63773 −0.0889491
\(340\) 0.846011 1.46533i 0.0458814 0.0794689i
\(341\) −14.8916 + 25.7930i −0.806424 + 1.39677i
\(342\) −1.24214 2.15144i −0.0671670 0.116337i
\(343\) −19.1551 −1.03428
\(344\) 1.44989 + 2.51128i 0.0781726 + 0.135399i
\(345\) 1.03050 + 1.78488i 0.0554802 + 0.0960946i
\(346\) 2.12498 0.114240
\(347\) −11.5749 20.0483i −0.621371 1.07625i −0.989231 0.146365i \(-0.953242\pi\)
0.367859 0.929882i \(-0.380091\pi\)
\(348\) −5.35086 + 9.26795i −0.286836 + 0.496814i
\(349\) 11.0978 19.2220i 0.594053 1.02893i −0.399626 0.916678i \(-0.630860\pi\)
0.993680 0.112253i \(-0.0358066\pi\)
\(350\) −3.85325 −0.205965
\(351\) 0 0
\(352\) 26.3013 1.40186
\(353\) 2.53534 4.39134i 0.134943 0.233728i −0.790633 0.612291i \(-0.790248\pi\)
0.925576 + 0.378563i \(0.123582\pi\)
\(354\) 3.04892 5.28088i 0.162048 0.280676i
\(355\) −0.706259 1.22328i −0.0374843 0.0649248i
\(356\) −0.246980 −0.0130899
\(357\) 3.33244 + 5.77195i 0.176371 + 0.305484i
\(358\) −0.764438 1.32405i −0.0404018 0.0699780i
\(359\) −16.6746 −0.880050 −0.440025 0.897986i \(-0.645030\pi\)
−0.440025 + 0.897986i \(0.645030\pi\)
\(360\) −0.208947 0.361908i −0.0110125 0.0190742i
\(361\) −6.07995 + 10.5308i −0.319997 + 0.554252i
\(362\) 3.00096 5.19781i 0.157727 0.273191i
\(363\) 20.9541 1.09980
\(364\) 0 0
\(365\) −1.81700 −0.0951063
\(366\) 1.89493 3.28211i 0.0990495 0.171559i
\(367\) 0.589638 1.02128i 0.0307789 0.0533105i −0.850226 0.526418i \(-0.823535\pi\)
0.881005 + 0.473108i \(0.156868\pi\)
\(368\) −11.8949 20.6026i −0.620066 1.07399i
\(369\) 0.445042 0.0231680
\(370\) 0.175760 + 0.304424i 0.00913730 + 0.0158263i
\(371\) 0.929976 + 1.61077i 0.0482820 + 0.0836268i
\(372\) −9.49396 −0.492239
\(373\) 15.0462 + 26.0608i 0.779064 + 1.34938i 0.932482 + 0.361217i \(0.117639\pi\)
−0.153417 + 0.988161i \(0.549028\pi\)
\(374\) 4.78232 8.28323i 0.247288 0.428315i
\(375\) −1.22737 + 2.12586i −0.0633809 + 0.109779i
\(376\) 11.3967 0.587741
\(377\) 0 0
\(378\) 0.780167 0.0401275
\(379\) 9.58157 16.5958i 0.492172 0.852467i −0.507787 0.861483i \(-0.669536\pi\)
0.999959 + 0.00901515i \(0.00286965\pi\)
\(380\) −1.24214 + 2.15144i −0.0637202 + 0.110367i
\(381\) −5.39977 9.35268i −0.276639 0.479152i
\(382\) −0.579121 −0.0296304
\(383\) 7.69418 + 13.3267i 0.393154 + 0.680963i 0.992864 0.119255i \(-0.0380506\pi\)
−0.599710 + 0.800218i \(0.704717\pi\)
\(384\) 5.46077 + 9.45833i 0.278669 + 0.482669i
\(385\) −2.44743 −0.124733
\(386\) 2.04623 + 3.54417i 0.104150 + 0.180394i
\(387\) −0.856896 + 1.48419i −0.0435585 + 0.0754455i
\(388\) −12.3339 + 21.3630i −0.626160 + 1.08454i
\(389\) −24.0315 −1.21844 −0.609222 0.793000i \(-0.708518\pi\)
−0.609222 + 0.793000i \(0.708518\pi\)
\(390\) 0 0
\(391\) −31.7265 −1.60448
\(392\) −3.32222 + 5.75425i −0.167797 + 0.290633i
\(393\) −0.453771 + 0.785955i −0.0228897 + 0.0396462i
\(394\) −0.915075 1.58496i −0.0461008 0.0798489i
\(395\) −1.10023 −0.0553585
\(396\) 5.09299 + 8.82132i 0.255932 + 0.443288i
\(397\) −14.8007 25.6356i −0.742828 1.28662i −0.951203 0.308567i \(-0.900151\pi\)
0.208375 0.978049i \(-0.433183\pi\)
\(398\) −11.0248 −0.552621
\(399\) −4.89277 8.47453i −0.244945 0.424257i
\(400\) 7.04019 12.1940i 0.352009 0.609698i
\(401\) 10.5516 18.2759i 0.526922 0.912656i −0.472586 0.881285i \(-0.656679\pi\)
0.999508 0.0313711i \(-0.00998736\pi\)
\(402\) 2.65279 0.132309
\(403\) 0 0
\(404\) 9.75063 0.485112
\(405\) 0.123490 0.213891i 0.00613626 0.0106283i
\(406\) 2.31671 4.01266i 0.114976 0.199145i
\(407\) −9.03899 15.6560i −0.448046 0.776039i
\(408\) 6.43296 0.318479
\(409\) 18.0112 + 31.1963i 0.890596 + 1.54256i 0.839163 + 0.543880i \(0.183045\pi\)
0.0514328 + 0.998676i \(0.483621\pi\)
\(410\) 0.0244587 + 0.0423637i 0.00120793 + 0.00209219i
\(411\) −9.54825 −0.470981
\(412\) 12.3937 + 21.4666i 0.610595 + 1.05758i
\(413\) 12.0097 20.8014i 0.590958 1.02357i
\(414\) −1.85690 + 3.21624i −0.0912615 + 0.158069i
\(415\) 2.51573 0.123492
\(416\) 0 0
\(417\) −4.09246 −0.200409
\(418\) −7.02153 + 12.1617i −0.343434 + 0.594846i
\(419\) −2.98427 + 5.16891i −0.145791 + 0.252518i −0.929668 0.368399i \(-0.879906\pi\)
0.783877 + 0.620917i \(0.213239\pi\)
\(420\) −0.390084 0.675645i −0.0190341 0.0329681i
\(421\) −2.09544 −0.102126 −0.0510628 0.998695i \(-0.516261\pi\)
−0.0510628 + 0.998695i \(0.516261\pi\)
\(422\) 1.32155 + 2.28900i 0.0643321 + 0.111427i
\(423\) 3.36778 + 5.83317i 0.163747 + 0.283618i
\(424\) 1.79523 0.0871842
\(425\) −9.38889 16.2620i −0.455428 0.788824i
\(426\) 1.27263 2.20427i 0.0616594 0.106797i
\(427\) 7.46412 12.9282i 0.361214 0.625641i
\(428\) 23.0954 1.11636
\(429\) 0 0
\(430\) −0.188374 −0.00908418
\(431\) 1.44289 2.49915i 0.0695014 0.120380i −0.829181 0.558981i \(-0.811193\pi\)
0.898682 + 0.438601i \(0.144526\pi\)
\(432\) −1.42543 + 2.46891i −0.0685809 + 0.118786i
\(433\) 6.32424 + 10.9539i 0.303924 + 0.526411i 0.977021 0.213143i \(-0.0683699\pi\)
−0.673097 + 0.739554i \(0.735037\pi\)
\(434\) 4.11051 0.197311
\(435\) −0.733406 1.27030i −0.0351641 0.0609061i
\(436\) 10.9438 + 18.9553i 0.524115 + 0.907794i
\(437\) 46.5816 2.22830
\(438\) −1.63706 2.83548i −0.0782219 0.135484i
\(439\) 5.46346 9.46299i 0.260757 0.451644i −0.705687 0.708524i \(-0.749361\pi\)
0.966443 + 0.256880i \(0.0826946\pi\)
\(440\) −1.18114 + 2.04579i −0.0563085 + 0.0975291i
\(441\) −3.92692 −0.186996
\(442\) 0 0
\(443\) −19.2403 −0.914133 −0.457067 0.889433i \(-0.651100\pi\)
−0.457067 + 0.889433i \(0.651100\pi\)
\(444\) 2.88135 4.99065i 0.136743 0.236846i
\(445\) 0.0169259 0.0293166i 0.000802366 0.00138974i
\(446\) −3.16003 5.47333i −0.149632 0.259170i
\(447\) −15.3884 −0.727844
\(448\) 3.18263 + 5.51247i 0.150365 + 0.260440i
\(449\) 14.4100 + 24.9588i 0.680050 + 1.17788i 0.974965 + 0.222357i \(0.0713751\pi\)
−0.294916 + 0.955523i \(0.595292\pi\)
\(450\) −2.19806 −0.103618
\(451\) −1.25786 2.17869i −0.0592305 0.102590i
\(452\) −1.47554 + 2.55571i −0.0694036 + 0.120211i
\(453\) 1.83728 3.18226i 0.0863230 0.149516i
\(454\) 7.12392 0.334342
\(455\) 0 0
\(456\) −9.44504 −0.442305
\(457\) 9.03534 15.6497i 0.422656 0.732061i −0.573543 0.819176i \(-0.694431\pi\)
0.996198 + 0.0871147i \(0.0277647\pi\)
\(458\) −0.409698 + 0.709618i −0.0191439 + 0.0331583i
\(459\) 1.90097 + 3.29257i 0.0887296 + 0.153684i
\(460\) 3.71379 0.173156
\(461\) 3.78382 + 6.55376i 0.176230 + 0.305239i 0.940586 0.339555i \(-0.110276\pi\)
−0.764356 + 0.644794i \(0.776943\pi\)
\(462\) −2.20506 3.81928i −0.102589 0.177689i
\(463\) 35.3551 1.64309 0.821545 0.570143i \(-0.193112\pi\)
0.821545 + 0.570143i \(0.193112\pi\)
\(464\) 8.46562 + 14.6629i 0.393006 + 0.680707i
\(465\) 0.650637 1.12694i 0.0301726 0.0522604i
\(466\) 5.21260 9.02848i 0.241469 0.418236i
\(467\) 13.0000 0.601568 0.300784 0.953692i \(-0.402752\pi\)
0.300784 + 0.953692i \(0.402752\pi\)
\(468\) 0 0
\(469\) 10.4494 0.482506
\(470\) −0.370174 + 0.641160i −0.0170748 + 0.0295745i
\(471\) 2.43900 4.22447i 0.112383 0.194653i
\(472\) −11.5918 20.0776i −0.533556 0.924145i
\(473\) 9.68771 0.445441
\(474\) −0.991271 1.71693i −0.0455306 0.0788613i
\(475\) 13.7850 + 23.8763i 0.632500 + 1.09552i
\(476\) 12.0097 0.550463
\(477\) 0.530499 + 0.918852i 0.0242899 + 0.0420713i
\(478\) −3.24914 + 5.62767i −0.148612 + 0.257404i
\(479\) 12.7632 22.1066i 0.583167 1.01008i −0.411934 0.911214i \(-0.635147\pi\)
0.995101 0.0988618i \(-0.0315202\pi\)
\(480\) −1.14914 −0.0524510
\(481\) 0 0
\(482\) 3.84117 0.174960
\(483\) −7.31431 + 12.6688i −0.332813 + 0.576449i
\(484\) 18.8790 32.6993i 0.858135 1.48633i
\(485\) −1.69053 2.92808i −0.0767630 0.132957i
\(486\) 0.445042 0.0201875
\(487\) −8.00365 13.8627i −0.362680 0.628180i 0.625721 0.780047i \(-0.284805\pi\)
−0.988401 + 0.151867i \(0.951471\pi\)
\(488\) −7.20440 12.4784i −0.326128 0.564870i
\(489\) 8.63102 0.390308
\(490\) −0.215816 0.373805i −0.00974958 0.0168868i
\(491\) −10.3693 + 17.9601i −0.467959 + 0.810528i −0.999330 0.0366110i \(-0.988344\pi\)
0.531371 + 0.847139i \(0.321677\pi\)
\(492\) 0.400969 0.694498i 0.0180771 0.0313104i
\(493\) 22.5797 1.01694
\(494\) 0 0
\(495\) −1.39612 −0.0627511
\(496\) −7.51022 + 13.0081i −0.337219 + 0.584080i
\(497\) 5.01291 8.68261i 0.224860 0.389468i
\(498\) 2.26659 + 3.92586i 0.101569 + 0.175922i
\(499\) −8.06770 −0.361160 −0.180580 0.983560i \(-0.557797\pi\)
−0.180580 + 0.983560i \(0.557797\pi\)
\(500\) 2.21164 + 3.83067i 0.0989074 + 0.171313i
\(501\) −4.73490 8.20108i −0.211540 0.366397i
\(502\) −1.69202 −0.0755186
\(503\) 15.1211 + 26.1905i 0.674216 + 1.16778i 0.976697 + 0.214622i \(0.0688518\pi\)
−0.302481 + 0.953155i \(0.597815\pi\)
\(504\) 1.48307 2.56876i 0.0660614 0.114422i
\(505\) −0.668227 + 1.15740i −0.0297357 + 0.0515037i
\(506\) 20.9933 0.933266
\(507\) 0 0
\(508\) −19.4601 −0.863403
\(509\) −8.02475 + 13.8993i −0.355691 + 0.616075i −0.987236 0.159264i \(-0.949088\pi\)
0.631545 + 0.775339i \(0.282421\pi\)
\(510\) −0.208947 + 0.361908i −0.00925235 + 0.0160255i
\(511\) −6.44839 11.1689i −0.285260 0.494085i
\(512\) 22.9119 1.01257
\(513\) −2.79105 4.83424i −0.123228 0.213437i
\(514\) 4.58306 + 7.93810i 0.202150 + 0.350135i
\(515\) −3.39745 −0.149710
\(516\) 1.54407 + 2.67441i 0.0679740 + 0.117734i
\(517\) 19.0374 32.9737i 0.837262 1.45018i
\(518\) −1.24751 + 2.16075i −0.0548125 + 0.0949381i
\(519\) 4.77479 0.209590
\(520\) 0 0
\(521\) −2.69309 −0.117986 −0.0589931 0.998258i \(-0.518789\pi\)
−0.0589931 + 0.998258i \(0.518789\pi\)
\(522\) 1.32155 2.28900i 0.0578428 0.100187i
\(523\) −17.6978 + 30.6535i −0.773872 + 1.34039i 0.161554 + 0.986864i \(0.448349\pi\)
−0.935426 + 0.353522i \(0.884984\pi\)
\(524\) 0.817667 + 1.41624i 0.0357200 + 0.0618688i
\(525\) −8.65817 −0.377874
\(526\) −0.0740400 0.128241i −0.00322830 0.00559157i
\(527\) 10.0157 + 17.3478i 0.436292 + 0.755680i
\(528\) 16.1153 0.701328
\(529\) −23.3180 40.3879i −1.01382 1.75600i
\(530\) −0.0583105 + 0.100997i −0.00253285 + 0.00438702i
\(531\) 6.85086 11.8660i 0.297302 0.514942i
\(532\) −17.6329 −0.764485
\(533\) 0 0
\(534\) 0.0609989 0.00263968
\(535\) −1.58277 + 2.74144i −0.0684291 + 0.118523i
\(536\) 5.04288 8.73452i 0.217819 0.377274i
\(537\) −1.71768 2.97510i −0.0741232 0.128385i
\(538\) 12.1511 0.523870
\(539\) 11.0990 + 19.2241i 0.478069 + 0.828040i
\(540\) −0.222521 0.385418i −0.00957578 0.0165857i
\(541\) −34.7338 −1.49332 −0.746660 0.665205i \(-0.768344\pi\)
−0.746660 + 0.665205i \(0.768344\pi\)
\(542\) −6.22737 10.7861i −0.267488 0.463303i
\(543\) 6.74309 11.6794i 0.289374 0.501210i
\(544\) 8.84481 15.3197i 0.379218 0.656825i
\(545\) −3.00000 −0.128506
\(546\) 0 0
\(547\) −26.1183 −1.11674 −0.558368 0.829593i \(-0.688572\pi\)
−0.558368 + 0.829593i \(0.688572\pi\)
\(548\) −8.60268 + 14.9003i −0.367488 + 0.636508i
\(549\) 4.25786 7.37484i 0.181721 0.314750i
\(550\) 6.21260 + 10.7605i 0.264906 + 0.458831i
\(551\) −33.1521 −1.41233
\(552\) 7.05980 + 12.2279i 0.300485 + 0.520456i
\(553\) −3.90462 6.76299i −0.166041 0.287592i
\(554\) −0.936017 −0.0397676
\(555\) 0.394928 + 0.684035i 0.0167638 + 0.0290357i
\(556\) −3.68718 + 6.38638i −0.156371 + 0.270843i
\(557\) −12.3874 + 21.4556i −0.524871 + 0.909103i 0.474710 + 0.880142i \(0.342553\pi\)
−0.999581 + 0.0289605i \(0.990780\pi\)
\(558\) 2.34481 0.0992639
\(559\) 0 0
\(560\) −1.23431 −0.0521590
\(561\) 10.7458 18.6122i 0.453687 0.785809i
\(562\) −6.06033 + 10.4968i −0.255640 + 0.442781i
\(563\) −2.63049 4.55614i −0.110862 0.192019i 0.805256 0.592927i \(-0.202028\pi\)
−0.916118 + 0.400909i \(0.868694\pi\)
\(564\) 12.1371 0.511063
\(565\) −0.202243 0.350294i −0.00850841 0.0147370i
\(566\) −1.17576 2.03648i −0.0494209 0.0855994i
\(567\) 1.75302 0.0736199
\(568\) −4.83848 8.38049i −0.203018 0.351638i
\(569\) 16.8729 29.2248i 0.707350 1.22517i −0.258487 0.966015i \(-0.583224\pi\)
0.965837 0.259151i \(-0.0834427\pi\)
\(570\) 0.306782 0.531362i 0.0128497 0.0222563i
\(571\) 23.0887 0.966234 0.483117 0.875556i \(-0.339505\pi\)
0.483117 + 0.875556i \(0.339505\pi\)
\(572\) 0 0
\(573\) −1.30127 −0.0543615
\(574\) −0.173604 + 0.300690i −0.00724607 + 0.0125506i
\(575\) 20.6075 35.6933i 0.859393 1.48851i
\(576\) 1.81551 + 3.14456i 0.0756463 + 0.131023i
\(577\) 3.57002 0.148622 0.0743110 0.997235i \(-0.476324\pi\)
0.0743110 + 0.997235i \(0.476324\pi\)
\(578\) 0.566376 + 0.980992i 0.0235581 + 0.0408039i
\(579\) 4.59783 + 7.96368i 0.191079 + 0.330959i
\(580\) −2.64310 −0.109749
\(581\) 8.92812 + 15.4640i 0.370401 + 0.641553i
\(582\) 3.04623 5.27622i 0.126270 0.218706i
\(583\) 2.99880 5.19408i 0.124198 0.215117i
\(584\) −12.4480 −0.515103
\(585\) 0 0
\(586\) 14.5362 0.600484
\(587\) 5.73125 9.92682i 0.236554 0.409724i −0.723169 0.690671i \(-0.757315\pi\)
0.959723 + 0.280947i \(0.0906486\pi\)
\(588\) −3.53803 + 6.12805i −0.145906 + 0.252717i
\(589\) −14.7054 25.4704i −0.605924 1.04949i
\(590\) 1.50604 0.0620027
\(591\) −2.05615 3.56136i −0.0845789 0.146495i
\(592\) −4.55861 7.89574i −0.187358 0.324513i
\(593\) −21.8538 −0.897430 −0.448715 0.893675i \(-0.648118\pi\)
−0.448715 + 0.893675i \(0.648118\pi\)
\(594\) −1.25786 2.17869i −0.0516108 0.0893926i
\(595\) −0.823044 + 1.42555i −0.0337415 + 0.0584420i
\(596\) −13.8644 + 24.0139i −0.567909 + 0.983647i
\(597\) −24.7724 −1.01387
\(598\) 0 0
\(599\) 27.0573 1.10553 0.552765 0.833337i \(-0.313573\pi\)
0.552765 + 0.833337i \(0.313573\pi\)
\(600\) −4.17845 + 7.23728i −0.170584 + 0.295461i
\(601\) −5.43900 + 9.42063i −0.221861 + 0.384275i −0.955373 0.295401i \(-0.904547\pi\)
0.733512 + 0.679677i \(0.237880\pi\)
\(602\) −0.668522 1.15791i −0.0272469 0.0471931i
\(603\) 5.96077 0.242741
\(604\) −3.31067 5.73424i −0.134709 0.233323i
\(605\) 2.58761 + 4.48188i 0.105201 + 0.182214i
\(606\) −2.40821 −0.0978267
\(607\) 14.8180 + 25.6655i 0.601443 + 1.04173i 0.992603 + 0.121407i \(0.0387405\pi\)
−0.391160 + 0.920323i \(0.627926\pi\)
\(608\) −12.9862 + 22.4927i −0.526660 + 0.912201i
\(609\) 5.20560 9.01636i 0.210941 0.365361i
\(610\) 0.936017 0.0378982
\(611\) 0 0
\(612\) 6.85086 0.276929
\(613\) −5.11715 + 8.86317i −0.206680 + 0.357980i −0.950667 0.310214i \(-0.899599\pi\)
0.743987 + 0.668194i \(0.232933\pi\)
\(614\) 4.61984 8.00180i 0.186442 0.322926i
\(615\) 0.0549581 + 0.0951903i 0.00221613 + 0.00383844i
\(616\) −16.7670 −0.675563
\(617\) −13.1414 22.7615i −0.529052 0.916345i −0.999426 0.0338776i \(-0.989214\pi\)
0.470374 0.882467i \(-0.344119\pi\)
\(618\) −3.06100 5.30181i −0.123131 0.213270i
\(619\) 29.0834 1.16896 0.584479 0.811408i \(-0.301299\pi\)
0.584479 + 0.811408i \(0.301299\pi\)
\(620\) −1.17241 2.03067i −0.0470850 0.0815536i
\(621\) −4.17241 + 7.22682i −0.167433 + 0.290002i
\(622\) 2.51477 4.35571i 0.100833 0.174648i
\(623\) 0.240275 0.00962641
\(624\) 0 0
\(625\) 24.0887 0.963549
\(626\) 0.950550 1.64640i 0.0379916 0.0658034i
\(627\) −15.7772 + 27.3270i −0.630082 + 1.09133i
\(628\) −4.39493 7.61224i −0.175377 0.303761i
\(629\) −12.1588 −0.484804
\(630\) 0.0963427 + 0.166870i 0.00383839 + 0.00664828i
\(631\) −12.7240 22.0386i −0.506535 0.877344i −0.999971 0.00756243i \(-0.997593\pi\)
0.493436 0.869782i \(-0.335741\pi\)
\(632\) −7.53750 −0.299826
\(633\) 2.96950 + 5.14333i 0.118027 + 0.204429i
\(634\) −3.44408 + 5.96533i −0.136782 + 0.236913i
\(635\) 1.33363 2.30992i 0.0529236 0.0916664i
\(636\) 1.91185 0.0758099
\(637\) 0 0
\(638\) −14.9409 −0.591517
\(639\) 2.85958 4.95295i 0.113123 0.195935i
\(640\) −1.34870 + 2.33602i −0.0533120 + 0.0923391i
\(641\) 13.3705 + 23.1583i 0.528102 + 0.914699i 0.999463 + 0.0327590i \(0.0104294\pi\)
−0.471361 + 0.881940i \(0.656237\pi\)
\(642\) −5.70410 −0.225123
\(643\) 16.4807 + 28.5454i 0.649935 + 1.12572i 0.983138 + 0.182865i \(0.0585371\pi\)
−0.333203 + 0.942855i \(0.608130\pi\)
\(644\) 13.1799 + 22.8283i 0.519362 + 0.899562i
\(645\) −0.423272 −0.0166663
\(646\) 4.72252 + 8.17965i 0.185805 + 0.321824i
\(647\) −17.2473 + 29.8732i −0.678060 + 1.17443i 0.297504 + 0.954721i \(0.403846\pi\)
−0.975564 + 0.219714i \(0.929487\pi\)
\(648\) 0.846011 1.46533i 0.0332344 0.0575637i
\(649\) −77.4529 −3.04029
\(650\) 0 0
\(651\) 9.23623 0.361996
\(652\) 7.77628 13.4689i 0.304543 0.527483i
\(653\) −18.0758 + 31.3083i −0.707362 + 1.22519i 0.258471 + 0.966019i \(0.416781\pi\)
−0.965832 + 0.259167i \(0.916552\pi\)
\(654\) −2.70291 4.68157i −0.105692 0.183064i
\(655\) −0.224144 −0.00875805
\(656\) −0.634375 1.09877i −0.0247682 0.0428997i
\(657\) −3.67845 6.37126i −0.143510 0.248566i
\(658\) −5.25487 −0.204856
\(659\) 3.40850 + 5.90370i 0.132776 + 0.229975i 0.924746 0.380585i \(-0.124277\pi\)
−0.791969 + 0.610561i \(0.790944\pi\)
\(660\) −1.25786 + 2.17869i −0.0489623 + 0.0848052i
\(661\) 5.44720 9.43482i 0.211871 0.366972i −0.740429 0.672135i \(-0.765378\pi\)
0.952300 + 0.305163i \(0.0987109\pi\)
\(662\) 2.70065 0.104964
\(663\) 0 0
\(664\) 17.2349 0.668844
\(665\) 1.20841 2.09304i 0.0468603 0.0811645i
\(666\) −0.711636 + 1.23259i −0.0275753 + 0.0477619i
\(667\) 24.7799 + 42.9201i 0.959483 + 1.66187i
\(668\) −17.0640 −0.660225
\(669\) −7.10052 12.2985i −0.274522 0.475486i
\(670\) 0.327593 + 0.567407i 0.0126560 + 0.0219209i
\(671\) −48.1377 −1.85833
\(672\) −4.07822 7.06368i −0.157321 0.272488i
\(673\) −10.3693 + 17.9601i −0.399706 + 0.692311i −0.993689 0.112166i \(-0.964221\pi\)
0.593983 + 0.804477i \(0.297554\pi\)
\(674\) −2.69783 + 4.67277i −0.103916 + 0.179988i
\(675\) −4.93900 −0.190102
\(676\) 0 0
\(677\) −25.5786 −0.983067 −0.491534 0.870859i \(-0.663564\pi\)
−0.491534 + 0.870859i \(0.663564\pi\)
\(678\) 0.364429 0.631209i 0.0139958 0.0242414i
\(679\) 11.9991 20.7830i 0.460483 0.797580i
\(680\) 0.794405 + 1.37595i 0.0304640 + 0.0527653i
\(681\) 16.0073 0.613401
\(682\) −6.62737 11.4789i −0.253775 0.439552i
\(683\) −10.8155 18.7330i −0.413844 0.716799i 0.581462 0.813573i \(-0.302481\pi\)
−0.995306 + 0.0967744i \(0.969147\pi\)
\(684\) −10.0586 −0.384600
\(685\) −1.17911 2.04228i −0.0450516 0.0780316i
\(686\) 4.26241 7.38272i 0.162740 0.281873i
\(687\) −0.920583 + 1.59450i −0.0351224 + 0.0608339i
\(688\) 4.88577 0.186268
\(689\) 0 0
\(690\) −0.917231 −0.0349184
\(691\) −1.31498 + 2.27761i −0.0500242 + 0.0866444i −0.889953 0.456052i \(-0.849263\pi\)
0.839929 + 0.542696i \(0.182596\pi\)
\(692\) 4.30194 7.45117i 0.163535 0.283251i
\(693\) −4.95473 8.58185i −0.188215 0.325997i
\(694\) 10.3026 0.391081
\(695\) −0.505377 0.875338i −0.0191700 0.0332035i
\(696\) −5.02446 8.70262i −0.190452 0.329872i
\(697\) −1.69202 −0.0640899
\(698\) 4.93900 + 8.55460i 0.186944 + 0.323796i
\(699\) 11.7126 20.2868i 0.443011 0.767318i
\(700\) −7.80074 + 13.5113i −0.294840 + 0.510678i
\(701\) 40.0925 1.51427 0.757136 0.653258i \(-0.226598\pi\)
0.757136 + 0.653258i \(0.226598\pi\)
\(702\) 0 0
\(703\) 17.8519 0.673298
\(704\) 10.2627 17.7755i 0.386790 0.669941i
\(705\) −0.831773 + 1.44067i −0.0313264 + 0.0542589i
\(706\) 1.12833 + 1.95433i 0.0424654 + 0.0735523i
\(707\) −9.48593 −0.356755
\(708\) −12.3448 21.3818i −0.463947 0.803579i
\(709\) −11.6048 20.1002i −0.435829 0.754877i 0.561534 0.827454i \(-0.310211\pi\)
−0.997363 + 0.0725761i \(0.976878\pi\)
\(710\) 0.628630 0.0235921
\(711\) −2.22737 3.85791i −0.0835327 0.144683i
\(712\) 0.115957 0.200844i 0.00434567 0.00752693i
\(713\) −21.9834 + 38.0763i −0.823284 + 1.42597i
\(714\) −2.96615 −0.111005
\(715\) 0 0
\(716\) −6.19029 −0.231342
\(717\) −7.30074 + 12.6453i −0.272651 + 0.472246i
\(718\) 3.71044 6.42667i 0.138472 0.239841i
\(719\) 13.0073 + 22.5293i 0.485090 + 0.840201i 0.999853 0.0171315i \(-0.00545340\pi\)
−0.514763 + 0.857333i \(0.672120\pi\)
\(720\) −0.704103 −0.0262404
\(721\) −12.0573 20.8838i −0.449036 0.777754i
\(722\) −2.70583 4.68664i −0.100701 0.174419i
\(723\) 8.63102 0.320991
\(724\) −12.1506 21.0455i −0.451575 0.782151i
\(725\) −14.6664 + 25.4029i −0.544695 + 0.943440i
\(726\) −4.66272 + 8.07607i −0.173050 + 0.299731i
\(727\) −16.5472 −0.613701 −0.306851 0.951758i \(-0.599275\pi\)
−0.306851 + 0.951758i \(0.599275\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0.404321 0.700305i 0.0149646 0.0259194i
\(731\) 3.25786 5.64279i 0.120496 0.208706i
\(732\) −7.67241 13.2890i −0.283580 0.491176i
\(733\) 18.8750 0.697165 0.348582 0.937278i \(-0.386663\pi\)
0.348582 + 0.937278i \(0.386663\pi\)
\(734\) 0.262414 + 0.454514i 0.00968586 + 0.0167764i
\(735\) −0.484935 0.839931i −0.0178871 0.0309813i
\(736\) 38.8267 1.43117
\(737\) −16.8475 29.1807i −0.620586 1.07489i
\(738\) −0.0990311 + 0.171527i −0.00364539 + 0.00631399i
\(739\) −23.6619 + 40.9837i −0.870419 + 1.50761i −0.00885483 + 0.999961i \(0.502819\pi\)
−0.861564 + 0.507649i \(0.830515\pi\)
\(740\) 1.42327 0.0523205
\(741\) 0 0
\(742\) −0.827757 −0.0303879
\(743\) 4.44385 7.69697i 0.163029 0.282374i −0.772925 0.634498i \(-0.781207\pi\)
0.935954 + 0.352124i \(0.114540\pi\)
\(744\) 4.45742 7.72048i 0.163417 0.283046i
\(745\) −1.90030 3.29142i −0.0696218 0.120588i
\(746\) −13.3924 −0.490331
\(747\) 5.09299 + 8.82132i 0.186343 + 0.322755i
\(748\) −19.3632 33.5381i −0.707990 1.22627i
\(749\) −22.4685 −0.820980
\(750\) −0.546229 0.946096i −0.0199455 0.0345466i
\(751\) −0.355404 + 0.615578i −0.0129689 + 0.0224627i −0.872437 0.488727i \(-0.837462\pi\)
0.859468 + 0.511189i \(0.170795\pi\)
\(752\) 9.60106 16.6295i 0.350114 0.606416i
\(753\) −3.80194 −0.138550
\(754\) 0 0
\(755\) 0.907542 0.0330288
\(756\) 1.57942 2.73563i 0.0574428 0.0994939i
\(757\) −4.89277 + 8.47453i −0.177831 + 0.308012i −0.941137 0.338025i \(-0.890241\pi\)
0.763306 + 0.646037i \(0.223575\pi\)
\(758\) 4.26420 + 7.38581i 0.154883 + 0.268265i
\(759\) 47.1715 1.71222
\(760\) −1.16637 2.02021i −0.0423086 0.0732806i
\(761\) 9.44049 + 16.3514i 0.342218 + 0.592738i 0.984844 0.173441i \(-0.0554887\pi\)
−0.642627 + 0.766180i \(0.722155\pi\)
\(762\) 4.80625 0.174112
\(763\) −10.6468 18.4407i −0.385438 0.667599i
\(764\) −1.17241 + 2.03067i −0.0424162 + 0.0734670i
\(765\) −0.469501 + 0.813199i −0.0169748 + 0.0294013i
\(766\) −6.84846 −0.247445
\(767\) 0 0
\(768\) 2.40150 0.0866567
\(769\) 6.21744 10.7689i 0.224207 0.388337i −0.731875 0.681439i \(-0.761354\pi\)
0.956081 + 0.293102i \(0.0946876\pi\)
\(770\) 0.544605 0.943284i 0.0196262 0.0339936i
\(771\) 10.2981 + 17.8368i 0.370875 + 0.642375i
\(772\) 16.5700 0.596368
\(773\) −22.8373 39.5553i −0.821400 1.42271i −0.904640 0.426177i \(-0.859860\pi\)
0.0832399 0.996530i \(-0.473473\pi\)
\(774\) −0.381355 0.660525i −0.0137075 0.0237421i
\(775\) −26.0224 −0.934751
\(776\) −11.5816 20.0599i −0.415754 0.720107i
\(777\) −2.80313 + 4.85517i −0.100562 + 0.174178i
\(778\) 5.34750 9.26215i 0.191717 0.332064i
\(779\) 2.48427 0.0890082
\(780\) 0 0