Properties

Label 507.2.e.k.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.k.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 0.933911 0.357506i \(-0.116373\pi\)
−0.776565 + 0.630037i \(0.783040\pi\)
\(3\) −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 \(-0.482412\pi\)
0.0552263 + 0.998474i \(0.482412\pi\)
\(6\) 0.222521 0.385418i 0.0908438 0.157346i
\(7\) 0.876510 1.51816i 0.331290 0.573811i −0.651475 0.758670i \(-0.725850\pi\)
0.982765 + 0.184859i \(0.0591829\pi\)
\(8\) 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 \(0.158060\pi\)
−0.0270365 + 0.999634i \(0.508607\pi\)
\(12\) −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 \(-0.612139\pi\)
0.985363 0.170468i \(-0.0545280\pi\)
\(20\) 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 \(-0.656882\pi\)
−0.473148 + 0.880983i \(0.656882\pi\)
\(32\) 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 \(-0.0819946\pi\)
−0.704127 + 0.710074i \(0.748661\pi\)
\(38\) 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 \(-0.155603\pi\)
−0.848126 + 0.529794i \(0.822269\pi\)
\(42\) −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 \(-0.336543\pi\)
0.491241 + 0.871024i \(0.336543\pi\)
\(48\) −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 \(0.517298\pi\)
−0.837589 + 0.546302i \(0.816035\pi\)
\(60\) −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 0.988633 0.150347i \(-0.0480392\pi\)
−0.624521 + 0.781008i \(0.714706\pi\)
\(68\) −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 \(-0.943547\pi\)
0.644944 + 0.764230i \(0.276881\pi\)
\(72\) −0.846011 + 1.46533i −0.0997033 + 0.172691i
\(73\) −7.35690 −0.861060 −0.430530 0.902576i \(-0.641673\pi\)
−0.430530 + 0.902576i \(0.641673\pi\)
\(74\) −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 \(-0.311174\pi\)
0.559028 + 0.829149i \(0.311174\pi\)
\(84\) −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 \(-0.164354\pi\)
−0.862370 + 0.506278i \(0.831021\pi\)
\(90\) −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 \(0.411256\pi\)
−0.970186 + 0.242363i \(0.922077\pi\)
\(98\) −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 \(-0.697622\pi\)
−0.581724 + 0.813386i \(0.697622\pi\)
\(110\) −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 −0.994652 0.103282i \(-0.967066\pi\)
0.586771 + 0.809753i \(0.300399\pi\)
\(138\) −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 \(0.383748\pi\)
−0.987484 + 0.157720i \(0.949586\pi\)
\(150\) −1.09903 + 1.90358i −0.0897355 + 0.155426i
\(151\) 3.67456 0.299032 0.149516 0.988759i \(-0.452228\pi\)
0.149516 + 0.988759i \(0.452228\pi\)
\(152\) 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 \(-0.723577\pi\)
0.984060 + 0.177839i \(0.0569106\pi\)
\(164\) 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 \(-0.0472577\pi\)
−0.622602 + 0.782539i \(0.713924\pi\)
\(168\) −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 0.651741 0.758442i \(-0.274039\pi\)
−0.982700 + 0.185203i \(0.940706\pi\)
\(194\) −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 \(-0.119867\pi\)
−0.783435 + 0.621474i \(0.786534\pi\)
\(198\) −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 0.999606 0.0280785i \(-0.00893883\pi\)
−0.524120 + 0.851645i \(0.675605\pi\)
\(224\) −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 \(-0.655067\pi\)
0.999336 0.0364340i \(-0.0115999\pi\)
\(228\) −5.02930 + 8.71101i −0.333074 + 0.576901i
\(229\) −1.84117 −0.121668 −0.0608339 0.998148i \(-0.519376\pi\)
−0.0608339 + 0.998148i \(0.519376\pi\)
\(230\) 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 \(-0.656556\pi\)
−0.472246 + 0.881467i \(0.656556\pi\)
\(240\) −0.352052 + 0.609771i −0.0227248 + 0.0393606i
\(241\) 4.31551 7.47468i 0.277987 0.481487i −0.692898 0.721036i \(-0.743666\pi\)
0.970884 + 0.239549i \(0.0769996\pi\)
\(242\) −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 \(0.156731\pi\)
−0.0312076 + 0.999513i \(0.509935\pi\)
\(272\) −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 \(-0.801811\pi\)
−0.812349 + 0.583172i \(0.801811\pi\)
\(282\) 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 \(-0.430169\pi\)
0.736457 0.676485i \(-0.236498\pi\)
\(294\) 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 \(-0.298158\pi\)
0.592457 + 0.805602i \(0.298158\pi\)
\(308\) 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 \(-0.643129\pi\)
−0.434653 + 0.900598i \(0.643129\pi\)
\(318\) −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 \(-0.779999\pi\)
0.937283 + 0.348569i \(0.113332\pi\)
\(332\) 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 \(-0.964193\pi\)
0.399626 0.916678i \(-0.369140\pi\)
\(350\) −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 \(-0.209752\pi\)
−0.925576 + 0.378563i \(0.876418\pi\)
\(354\) 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 \(-0.354970\pi\)
0.440025 + 0.897986i \(0.354970\pi\)
\(360\) −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 0.507787 0.861483i \(-0.330464\pi\)
−0.999959 + 0.00901515i \(0.997130\pi\)
\(380\) −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 \(-0.961949\pi\)
0.599710 + 0.800218i \(0.295283\pi\)
\(384\) −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 \(-0.566817\pi\)
0.951203 0.308567i \(-0.0998493\pi\)
\(398\) 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 \(-0.990013\pi\)
0.472586 0.881285i \(-0.343321\pi\)
\(402\) 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 \(0.516379\pi\)
−0.839163 + 0.543880i \(0.816955\pi\)
\(410\) −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 \(-0.483739\pi\)
0.0510628 + 0.998695i \(0.483739\pi\)
\(422\) −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 \(-0.188807\pi\)
−0.898682 + 0.438601i \(0.855474\pi\)
\(432\) −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 \(0.404708\pi\)
−0.974965 + 0.222357i \(0.928625\pi\)
\(450\) 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 \(-0.305569\pi\)
−0.996198 + 0.0871147i \(0.972235\pi\)
\(458\) −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 \(-0.889724\pi\)
0.764356 + 0.644794i \(0.223057\pi\)
\(462\) 2.20506 3.81928i 0.102589 0.177689i
\(463\) −35.3551 −1.64309 −0.821545 0.570143i \(-0.806888\pi\)
−0.821545 + 0.570143i \(0.806888\pi\)
\(464\) 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 \(-0.968480\pi\)
0.411934 0.911214i \(-0.364853\pi\)
\(480\) −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 \(-0.715195\pi\)
0.988401 + 0.151867i \(0.0485285\pi\)
\(488\) 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 \(-0.442203\pi\)
0.180580 + 0.983560i \(0.442203\pi\)
\(500\) −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 0.987236 0.159264i \(-0.0509122\pi\)
−0.631545 + 0.775339i \(0.717579\pi\)
\(510\) −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 \(-0.231656\pi\)
0.746660 + 0.665205i \(0.231656\pi\)
\(542\) −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 \(0.00921969\pi\)
−0.474710 + 0.880142i \(0.657447\pi\)
\(558\) 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 \(-0.523676\pi\)
−0.0743110 + 0.997235i \(0.523676\pi\)
\(578\) −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 \(-0.242685\pi\)
−0.959723 + 0.280947i \(0.909351\pi\)
\(588\) −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 \(-0.351882\pi\)
0.448715 + 0.893675i \(0.351882\pi\)
\(594\) −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 0.950667 0.310214i \(-0.100401\pi\)
−0.743987 + 0.668194i \(0.767067\pi\)
\(614\) 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 \(-0.655881\pi\)
0.999426 0.0338776i \(-0.0107856\pi\)
\(618\) 3.06100 5.30181i 0.123131 0.213270i
\(619\) −29.0834 −1.16896 −0.584479 0.811408i \(-0.698701\pi\)
−0.584479 + 0.811408i \(0.698701\pi\)
\(620\) −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 \(-0.664259\pi\)
0.999971 0.00756243i \(-0.00240722\pi\)
\(632\) 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 \(0.391870\pi\)
−0.983138 + 0.182865i \(0.941463\pi\)
\(644\) −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 0.740429 0.672135i \(-0.234622\pi\)
−0.952300 + 0.305163i \(0.901289\pi\)
\(662\) 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 −0.581462 0.813573i \(-0.697519\pi\)
0.995306 + 0.0967744i \(0.0308525\pi\)
\(684\) 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 \(-0.150737\pi\)
−0.839929 + 0.542696i \(0.817404\pi\)
\(692\) 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 \(-0.689789\pi\)
0.997363 + 0.0725761i \(0.0231220\pi\)
\(710\) −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 \(-0.613337\pi\)
−0.348582 + 0.937278i \(0.613337\pi\)
\(734\) −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 \(0.169485\pi\)
0.00885483 + 0.999961i \(0.497181\pi\)
\(740\) 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 \(-0.218793\pi\)
−0.935954 + 0.352124i \(0.885460\pi\)
\(744\) 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 −0.984844 0.173441i \(-0.944511\pi\)
0.642627 + 0.766180i \(0.277845\pi\)
\(762\) −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 \(-0.238646\pi\)
−0.956081 + 0.293102i \(0.905312\pi\)
\(770\) 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 \(-0.526527\pi\)
0.904640 0.426177i \(-0.140140\pi\)
\(774\) 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