Properties

Label 507.2.e.j.484.2
Level $507$
Weight $2$
Character 507.484
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 484.2
Root \(0.222521 + 0.385418i\) of defining polynomial
Character \(\chi\) \(=\) 507.484
Dual form 507.2.e.j.22.2

$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

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

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 0.776565 0.630037i \(-0.216960\pi\)
−0.933911 + 0.357506i \(0.883627\pi\)
\(3\) −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 −0.982765 0.184859i \(-0.940817\pi\)
0.651475 + 0.758670i \(0.274150\pi\)
\(8\) −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 −0.879227 0.476403i \(-0.841940\pi\)
0.0270365 0.999634i \(-0.491393\pi\)
\(12\) −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 −0.537961 0.842970i \(-0.680805\pi\)
0.999014 + 0.0444031i \(0.0141386\pi\)
\(18\) 0.445042 0.104897
\(19\) −2.79105 + 4.83424i −0.640311 + 1.10905i 0.345052 + 0.938584i \(0.387861\pi\)
−0.985363 + 0.170468i \(0.945472\pi\)
\(20\) −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 −0.861988 0.506929i \(-0.830781\pi\)
−0.00801894 0.999968i \(-0.502553\pi\)
\(24\) 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 0.998172 + 0.0604327i \(0.0192481\pi\)
−0.446750 + 0.894659i \(0.647419\pi\)
\(30\) 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 0.704127 0.710074i \(-0.251339\pi\)
−0.967006 + 0.254754i \(0.918005\pi\)
\(38\) 2.48427 0.403002
\(39\) 0 0
\(40\) 0.417895 0.0660750
\(41\) −0.222521 0.385418i −0.0347519 0.0601921i 0.848126 0.529794i \(-0.177731\pi\)
−0.882878 + 0.469602i \(0.844397\pi\)
\(42\) −0.390084 0.675645i −0.0601912 0.104254i
\(43\) −0.856896 + 1.48419i −0.130675 + 0.226336i −0.923937 0.382544i \(-0.875048\pi\)
0.793262 + 0.608881i \(0.208381\pi\)
\(44\) −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 0.0543169 0.998524i \(-0.482702\pi\)
0.837589 0.546302i \(-0.183965\pi\)
\(60\) 0.445042 0.0574547
\(61\) 4.25786 7.37484i 0.545164 0.944251i −0.453433 0.891290i \(-0.649801\pi\)
0.998597 0.0529608i \(-0.0168658\pi\)
\(62\) −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 0.624521 0.781008i \(-0.285294\pi\)
−0.988633 + 0.150347i \(0.951961\pi\)
\(68\) −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 −0.644944 0.764230i \(-0.723119\pi\)
0.984314 + 0.176423i \(0.0564527\pi\)
\(72\) 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 0.862370 0.506278i \(-0.168979\pi\)
−0.869635 + 0.493696i \(0.835646\pi\)
\(90\) −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 −0.275200 0.961387i \(-0.588744\pi\)
0.970186 0.242363i \(-0.0779226\pi\)
\(98\) 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 0.968660 0.248391i \(-0.0799019\pi\)
−0.699443 + 0.714688i \(0.746569\pi\)
\(102\) 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 0.989571 + 0.144046i \(0.0460114\pi\)
−0.370038 + 0.929017i \(0.620655\pi\)
\(108\) 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 −0.824936 0.565226i \(-0.808789\pi\)
0.901968 + 0.431802i \(0.142122\pi\)
\(114\) −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 0.520562 0.853824i \(-0.325723\pi\)
−0.999714 + 0.0239078i \(0.992389\pi\)
\(128\) 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 −0.586771 0.809753i \(-0.699601\pi\)
0.994652 + 0.103282i \(0.0329344\pi\)
\(138\) 3.71379 0.316139
\(139\) 2.04623 3.54417i 0.173559 0.300613i −0.766103 0.642718i \(-0.777807\pi\)
0.939662 + 0.342105i \(0.111140\pi\)
\(140\) −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 −0.357152 0.934046i \(-0.616252\pi\)
0.987484 0.157720i \(-0.0504144\pi\)
\(150\) 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 −0.984060 0.177839i \(-0.943089\pi\)
0.646043 + 0.763301i \(0.276423\pi\)
\(164\) −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 0.622602 0.782539i \(-0.286076\pi\)
−0.988999 + 0.147920i \(0.952742\pi\)
\(168\) −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 −0.942395 0.334502i \(-0.891432\pi\)
0.760885 + 0.648887i \(0.224765\pi\)
\(174\) −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 0.794666 0.607047i \(-0.207646\pi\)
−0.923051 + 0.384677i \(0.874313\pi\)
\(180\) −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 −0.841526 0.540217i \(-0.818342\pi\)
0.888604 + 0.458674i \(0.151676\pi\)
\(192\) 1.81551 + 3.14456i 0.131023 + 0.226939i
\(193\) 4.59783 + 7.96368i 0.330959 + 0.573238i 0.982700 0.185203i \(-0.0592944\pi\)
−0.651741 + 0.758442i \(0.725961\pi\)
\(194\) −6.09246 −0.437413
\(195\) 0 0
\(196\) 7.07606 0.505433
\(197\) −2.05615 3.56136i −0.146495 0.253737i 0.783435 0.621474i \(-0.213466\pi\)
−0.929930 + 0.367737i \(0.880133\pi\)
\(198\) −1.25786 2.17869i −0.0893926 0.154832i
\(199\) 12.3862 21.4535i 0.878034 1.52080i 0.0245395 0.999699i \(-0.492188\pi\)
0.853495 0.521101i \(-0.174479\pi\)
\(200\) 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 0.949951 0.312400i \(-0.101133\pi\)
−0.745522 + 0.666481i \(0.767800\pi\)
\(212\) −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 0.524120 0.851645i \(-0.324395\pi\)
−0.999606 + 0.0280785i \(0.991061\pi\)
\(224\) −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 0.468115 + 0.883667i \(0.344933\pi\)
−0.999336 + 0.0364340i \(0.988400\pi\)
\(228\) 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 −0.970884 0.239549i \(-0.923000\pi\)
0.692898 + 0.721036i \(0.256334\pi\)
\(242\) 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 −0.799775 0.600300i \(-0.795048\pi\)
0.919763 + 0.392475i \(0.128381\pi\)
\(252\) −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 0.984901 + 0.173118i \(0.0553841\pi\)
−0.342526 + 0.939508i \(0.611283\pi\)
\(258\) −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 0.860851 0.508858i \(-0.169932\pi\)
−0.871109 + 0.491089i \(0.836599\pi\)
\(264\) 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 0.0638154 + 0.997962i \(0.479673\pi\)
−0.896168 + 0.443715i \(0.853660\pi\)
\(270\) 0.0549581 + 0.0951903i 0.00334465 + 0.00579310i
\(271\) −13.9928 24.2362i −0.850000 1.47224i −0.881207 0.472730i \(-0.843269\pi\)
0.0312076 0.999513i \(-0.490065\pi\)
\(272\) −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 −0.832703 0.553721i \(-0.813208\pi\)
0.895887 + 0.444281i \(0.146541\pi\)
\(278\) −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 0.776757 0.629801i \(-0.216863\pi\)
−0.933802 + 0.357791i \(0.883530\pi\)
\(284\) −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 −0.217625 + 0.976033i \(0.569831\pi\)
−0.736457 + 0.676485i \(0.763502\pi\)
\(294\) −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 −0.937283 0.348569i \(-0.886668\pi\)
0.770511 + 0.637426i \(0.220001\pi\)
\(332\) −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 0.367859 + 0.929882i \(0.380091\pi\)
−0.989231 + 0.146365i \(0.953242\pi\)
\(348\) −5.35086 9.26795i −0.286836 0.496814i
\(349\) 11.0978 + 19.2220i 0.594053 + 1.02893i 0.993680 + 0.112253i \(0.0358066\pi\)
−0.399626 + 0.916678i \(0.630860\pi\)
\(350\) −3.85325 −0.205965
\(351\) 0 0
\(352\) 26.3013 1.40186
\(353\) 2.53534 + 4.39134i 0.134943 + 0.233728i 0.925576 0.378563i \(-0.123582\pi\)
−0.790633 + 0.612291i \(0.790248\pi\)
\(354\) 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 0.881005 0.473108i \(-0.156868\pi\)
−0.850226 + 0.526418i \(0.823535\pi\)
\(368\) −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 −0.153417 0.988161i \(-0.549028\pi\)
0.932482 0.361217i \(-0.117639\pi\)
\(374\) 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 0.999959 0.00901515i \(-0.00286965\pi\)
−0.507787 + 0.861483i \(0.669536\pi\)
\(380\) −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 −0.599710 0.800218i \(-0.704717\pi\)
0.992864 + 0.119255i \(0.0380506\pi\)
\(384\) 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 0.208375 + 0.978049i \(0.433183\pi\)
−0.951203 + 0.308567i \(0.900151\pi\)
\(398\) −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 0.999508 + 0.0313711i \(0.00998736\pi\)
−0.472586 + 0.881285i \(0.656679\pi\)
\(402\) 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 0.0514328 0.998676i \(-0.483621\pi\)
0.839163 0.543880i \(-0.183045\pi\)
\(410\) 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 0.783877 0.620917i \(-0.213239\pi\)
−0.929668 + 0.368399i \(0.879906\pi\)
\(420\) −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 0.898682 0.438601i \(-0.144526\pi\)
−0.829181 + 0.558981i \(0.811193\pi\)
\(432\) −1.42543 2.46891i −0.0685809 0.118786i
\(433\) 6.32424 10.9539i 0.303924 0.526411i −0.673097 0.739554i \(-0.735037\pi\)
0.977021 + 0.213143i \(0.0683699\pi\)
\(434\) 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 0.966443 0.256880i \(-0.0826946\pi\)
−0.705687 + 0.708524i \(0.749361\pi\)
\(440\) −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 −0.294916 0.955523i \(-0.595292\pi\)
0.974965 0.222357i \(-0.0713751\pi\)
\(450\) −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 0.996198 0.0871147i \(-0.0277647\pi\)
−0.573543 + 0.819176i \(0.694431\pi\)
\(458\) −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 −0.764356 0.644794i \(-0.776943\pi\)
0.940586 + 0.339555i \(0.110276\pi\)
\(462\) −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 0.995101 + 0.0988618i \(0.0315202\pi\)
−0.411934 + 0.911214i \(0.635147\pi\)
\(480\) −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 −0.988401 0.151867i \(-0.951471\pi\)
0.625721 + 0.780047i \(0.284805\pi\)
\(488\) −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 0.531371 0.847139i \(-0.321677\pi\)
−0.999330 + 0.0366110i \(0.988344\pi\)
\(492\) 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 −0.302481 0.953155i \(-0.597815\pi\)
0.976697 0.214622i \(-0.0688518\pi\)
\(504\) 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 0.631545 0.775339i \(-0.282421\pi\)
−0.987236 + 0.159264i \(0.949088\pi\)
\(510\) −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 −0.935426 0.353522i \(-0.884984\pi\)
0.161554 0.986864i \(-0.448349\pi\)
\(524\) 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 −0.999581 0.0289605i \(-0.990780\pi\)
0.474710 0.880142i \(-0.342553\pi\)
\(558\) 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 −0.916118 0.400909i \(-0.868694\pi\)
0.805256 + 0.592927i \(0.202028\pi\)
\(564\) 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 0.965837 + 0.259151i \(0.0834427\pi\)
−0.258487 + 0.966015i \(0.583224\pi\)
\(570\) 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 0.959723 0.280947i \(-0.0906486\pi\)
−0.723169 + 0.690671i \(0.757315\pi\)
\(588\) −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 0.733512 0.679677i \(-0.237880\pi\)
−0.955373 + 0.295401i \(0.904547\pi\)
\(602\) −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 −0.391160 0.920323i \(-0.627926\pi\)
0.992603 0.121407i \(-0.0387405\pi\)
\(608\) −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 0.743987 0.668194i \(-0.232933\pi\)
−0.950667 + 0.310214i \(0.899599\pi\)
\(614\) 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 0.470374 + 0.882467i \(0.344119\pi\)
−0.999426 + 0.0338776i \(0.989214\pi\)
\(618\) −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 0.493436 + 0.869782i \(0.335741\pi\)
−0.999971 + 0.00756243i \(0.997593\pi\)
\(632\) −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 −0.471361 0.881940i \(-0.656237\pi\)
0.999463 0.0327590i \(-0.0104294\pi\)
\(642\) −5.70410 −0.225123
\(643\) 16.4807 28.5454i 0.649935 1.12572i −0.333203 0.942855i \(-0.608130\pi\)
0.983138 0.182865i \(-0.0585371\pi\)
\(644\) 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 −0.975564 0.219714i \(-0.929487\pi\)
0.297504 0.954721i \(-0.403846\pi\)
\(648\) 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 −0.965832 0.259167i \(-0.916552\pi\)
0.258471 0.966019i \(-0.416781\pi\)
\(654\) −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 −0.791969 0.610561i \(-0.790944\pi\)
0.924746 + 0.380585i \(0.124277\pi\)
\(660\) −1.25786 2.17869i −0.0489623 0.0848052i
\(661\) 5.44720 + 9.43482i 0.211871 + 0.366972i 0.952300 0.305163i \(-0.0987109\pi\)
−0.740429 + 0.672135i \(0.765378\pi\)
\(662\) 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 0.593983 0.804477i \(-0.297554\pi\)
−0.993689 + 0.112166i \(0.964221\pi\)
\(674\) −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 −0.995306 0.0967744i \(-0.969147\pi\)
0.581462 + 0.813573i \(0.302481\pi\)
\(684\) −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 0.839929 0.542696i \(-0.182596\pi\)
−0.889953 + 0.456052i \(0.849263\pi\)
\(692\) 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 −0.997363 0.0725761i \(-0.976878\pi\)
0.561534 + 0.827454i \(0.310211\pi\)
\(710\) 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 −0.514763 0.857333i \(-0.672120\pi\)
0.999853 + 0.0171315i \(0.00545340\pi\)
\(720\) −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 −0.861564 0.507649i \(-0.830515\pi\)
−0.00885483 0.999961i \(-0.502819\pi\)
\(740\) 1.42327 0.0523205
\(741\) 0 0
\(742\) −0.827757 −0.0303879
\(743\) 4.44385 + 7.69697i 0.163029 + 0.282374i 0.935954 0.352124i \(-0.114540\pi\)
−0.772925 + 0.634498i \(0.781207\pi\)
\(744\) 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 0.859468 0.511189i \(-0.170795\pi\)
−0.872437 + 0.488727i \(0.837462\pi\)
\(752\) 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 0.763306 0.646037i \(-0.223575\pi\)
−0.941137 + 0.338025i \(0.890241\pi\)
\(758\) 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 −0.642627 0.766180i \(-0.722155\pi\)
0.984844 + 0.173441i \(0.0554887\pi\)
\(762\) 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 0.956081 0.293102i \(-0.0946876\pi\)
−0.731875 + 0.681439i \(0.761354\pi\)
\(770\) 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 0.0832399 + 0.996530i \(0.473473\pi\)
−0.904640 + 0.426177i \(0.859860\pi\)
\(774\) −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