Properties

Label 507.2.j.h.316.3
Level $507$
Weight $2$
Character 507.316
Analytic conductor $4.048$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.17213603549184.1
Defining polynomial: \(x^{12} - 5 x^{10} + 19 x^{8} - 28 x^{6} + 31 x^{4} - 6 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 316.3
Root \(-0.385418 - 0.222521i\) of defining polynomial
Character \(\chi\) \(=\) 507.316
Dual form 507.2.j.h.361.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.385418 - 0.222521i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.900969 - 1.56052i) q^{4} -0.246980i q^{5} +(0.385418 - 0.222521i) q^{6} +(-1.51816 + 0.876510i) q^{7} +1.69202i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.385418 - 0.222521i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.900969 - 1.56052i) q^{4} -0.246980i q^{5} +(0.385418 - 0.222521i) q^{6} +(-1.51816 + 0.876510i) q^{7} +1.69202i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.0549581 + 0.0951903i) q^{10} +(4.89546 + 2.82640i) q^{11} +1.80194 q^{12} +0.780167 q^{14} +(0.213891 + 0.123490i) q^{15} +(-1.42543 + 2.46891i) q^{16} +(-1.90097 - 3.29257i) q^{17} +0.445042i q^{18} +(4.83424 - 2.79105i) q^{19} +(-0.385418 + 0.222521i) q^{20} -1.75302i q^{21} +(-1.25786 - 2.17869i) q^{22} +(4.17241 - 7.22682i) q^{23} +(-1.46533 - 0.846011i) q^{24} +4.93900 q^{25} +1.00000 q^{27} +(2.73563 + 1.57942i) q^{28} +(2.96950 - 5.14333i) q^{29} +(-0.0549581 - 0.0951903i) q^{30} +5.26875i q^{31} +(4.02944 - 2.32640i) q^{32} +(-4.89546 + 2.82640i) q^{33} +1.69202i q^{34} +(0.216480 + 0.374955i) q^{35} +(-0.900969 + 1.56052i) q^{36} +(2.76960 + 1.59903i) q^{37} -2.48427 q^{38} +0.417895 q^{40} +(-0.385418 - 0.222521i) q^{41} +(-0.390084 + 0.675645i) q^{42} +(0.856896 + 1.48419i) q^{43} -10.1860i q^{44} +(-0.213891 + 0.123490i) q^{45} +(-3.21624 + 1.85690i) q^{46} +6.73556i q^{47} +(-1.42543 - 2.46891i) q^{48} +(-1.96346 + 3.40081i) q^{49} +(-1.90358 - 1.09903i) q^{50} +3.80194 q^{51} -1.06100 q^{53} +(-0.385418 - 0.222521i) q^{54} +(0.698062 - 1.20908i) q^{55} +(-1.48307 - 2.56876i) q^{56} +5.58211i q^{57} +(-2.28900 + 1.32155i) q^{58} +(11.8660 - 6.85086i) q^{59} -0.445042i q^{60} +(4.25786 + 7.37484i) q^{61} +(1.17241 - 2.03067i) q^{62} +(1.51816 + 0.876510i) q^{63} +3.63102 q^{64} +2.51573 q^{66} +(-5.16218 - 2.98039i) q^{67} +(-3.42543 + 5.93301i) q^{68} +(4.17241 + 7.22682i) q^{69} -0.192685i q^{70} +(-4.95295 + 2.85958i) q^{71} +(1.46533 - 0.846011i) q^{72} -7.35690i q^{73} +(-0.711636 - 1.23259i) q^{74} +(-2.46950 + 4.27730i) q^{75} +(-8.71101 - 5.02930i) q^{76} -9.90946 q^{77} +4.45473 q^{79} +(0.609771 + 0.352052i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.0990311 + 0.171527i) q^{82} -10.1860i q^{83} +(-2.73563 + 1.57942i) q^{84} +(-0.813199 + 0.469501i) q^{85} -0.762709i q^{86} +(2.96950 + 5.14333i) q^{87} +(-4.78232 + 8.28323i) q^{88} +(0.118700 + 0.0685317i) q^{89} +0.109916 q^{90} -15.0368 q^{92} +(-4.56287 - 2.63437i) q^{93} +(1.49880 - 2.59600i) q^{94} +(-0.689333 - 1.19396i) q^{95} +4.65279i q^{96} +(-11.8556 + 6.84481i) q^{97} +(1.51350 - 0.873822i) q^{98} -5.65279i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 6q^{3} - 2q^{4} - 6q^{9} + O(q^{10}) \) \( 12q - 6q^{3} - 2q^{4} - 6q^{9} - 2q^{10} + 4q^{12} + 4q^{14} + 10q^{16} - 14q^{17} + 10q^{22} + 4q^{23} + 20q^{25} + 12q^{27} + 16q^{29} - 2q^{30} - 36q^{35} - 2q^{36} - 80q^{38} + 28q^{40} - 2q^{42} - 6q^{43} + 10q^{48} + 34q^{49} + 28q^{51} - 52q^{53} + 26q^{55} + 14q^{56} + 26q^{61} - 32q^{62} - 16q^{64} - 20q^{66} - 14q^{68} + 4q^{69} - 14q^{74} - 10q^{75} + 60q^{77} - 36q^{79} - 6q^{81} + 10q^{82} + 16q^{87} - 14q^{88} + 4q^{90} - 68q^{92} - 64q^{94} + 6q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.385418 0.222521i −0.272531 0.157346i 0.357506 0.933911i \(-0.383627\pi\)
−0.630037 + 0.776565i \(0.716960\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.900969 1.56052i −0.450484 0.780262i
\(5\) 0.246980i 0.110453i −0.998474 0.0552263i \(-0.982412\pi\)
0.998474 0.0552263i \(-0.0175880\pi\)
\(6\) 0.385418 0.222521i 0.157346 0.0908438i
\(7\) −1.51816 + 0.876510i −0.573811 + 0.331290i −0.758670 0.651475i \(-0.774150\pi\)
0.184859 + 0.982765i \(0.440817\pi\)
\(8\) 1.69202i 0.598220i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.0549581 + 0.0951903i −0.0173793 + 0.0301018i
\(11\) 4.89546 + 2.82640i 1.47604 + 0.852191i 0.999634 0.0270365i \(-0.00860703\pi\)
0.476403 + 0.879227i \(0.341940\pi\)
\(12\) 1.80194 0.520175
\(13\) 0 0
\(14\) 0.780167 0.208509
\(15\) 0.213891 + 0.123490i 0.0552263 + 0.0318849i
\(16\) −1.42543 + 2.46891i −0.356357 + 0.617228i
\(17\) −1.90097 3.29257i −0.461053 0.798567i 0.537961 0.842970i \(-0.319195\pi\)
−0.999014 + 0.0444031i \(0.985861\pi\)
\(18\) 0.445042i 0.104897i
\(19\) 4.83424 2.79105i 1.10905 0.640311i 0.170468 0.985363i \(-0.445472\pi\)
0.938584 + 0.345052i \(0.112139\pi\)
\(20\) −0.385418 + 0.222521i −0.0861820 + 0.0497572i
\(21\) 1.75302i 0.382540i
\(22\) −1.25786 2.17869i −0.268178 0.464497i
\(23\) 4.17241 7.22682i 0.870007 1.50690i 0.00801894 0.999968i \(-0.497447\pi\)
0.861988 0.506929i \(-0.169219\pi\)
\(24\) −1.46533 0.846011i −0.299110 0.172691i
\(25\) 4.93900 0.987800
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 2.73563 + 1.57942i 0.516986 + 0.298482i
\(29\) 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
\(31\) 5.26875i 0.946295i 0.880983 + 0.473148i \(0.156882\pi\)
−0.880983 + 0.473148i \(0.843118\pi\)
\(32\) 4.02944 2.32640i 0.712311 0.411253i
\(33\) −4.89546 + 2.82640i −0.852191 + 0.492012i
\(34\) 1.69202i 0.290179i
\(35\) 0.216480 + 0.374955i 0.0365918 + 0.0633789i
\(36\) −0.900969 + 1.56052i −0.150161 + 0.260087i
\(37\) 2.76960 + 1.59903i 0.455320 + 0.262879i 0.710074 0.704127i \(-0.248661\pi\)
−0.254754 + 0.967006i \(0.581995\pi\)
\(38\) −2.48427 −0.403002
\(39\) 0 0
\(40\) 0.417895 0.0660750
\(41\) −0.385418 0.222521i −0.0601921 0.0347519i 0.469602 0.882878i \(-0.344397\pi\)
−0.529794 + 0.848126i \(0.677731\pi\)
\(42\) −0.390084 + 0.675645i −0.0601912 + 0.104254i
\(43\) 0.856896 + 1.48419i 0.130675 + 0.226336i 0.923937 0.382544i \(-0.124952\pi\)
−0.793262 + 0.608881i \(0.791619\pi\)
\(44\) 10.1860i 1.53559i
\(45\) −0.213891 + 0.123490i −0.0318849 + 0.0184088i
\(46\) −3.21624 + 1.85690i −0.474208 + 0.273784i
\(47\) 6.73556i 0.982483i 0.871024 + 0.491241i \(0.163457\pi\)
−0.871024 + 0.491241i \(0.836543\pi\)
\(48\) −1.42543 2.46891i −0.205743 0.356357i
\(49\) −1.96346 + 3.40081i −0.280494 + 0.485830i
\(50\) −1.90358 1.09903i −0.269207 0.155426i
\(51\) 3.80194 0.532378
\(52\) 0 0
\(53\) −1.06100 −0.145739 −0.0728697 0.997341i \(-0.523216\pi\)
−0.0728697 + 0.997341i \(0.523216\pi\)
\(54\) −0.385418 0.222521i −0.0524487 0.0302813i
\(55\) 0.698062 1.20908i 0.0941267 0.163032i
\(56\) −1.48307 2.56876i −0.198184 0.343265i
\(57\) 5.58211i 0.739368i
\(58\) −2.28900 + 1.32155i −0.300560 + 0.173528i
\(59\) 11.8660 6.85086i 1.54483 0.891905i 0.546302 0.837589i \(-0.316035\pi\)
0.998524 0.0543169i \(-0.0172981\pi\)
\(60\) 0.445042i 0.0574547i
\(61\) 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
\(63\) 1.51816 + 0.876510i 0.191270 + 0.110430i
\(64\) 3.63102 0.453878
\(65\) 0 0
\(66\) 2.51573 0.309665
\(67\) −5.16218 2.98039i −0.630661 0.364112i 0.150347 0.988633i \(-0.451961\pi\)
−0.781008 + 0.624521i \(0.785294\pi\)
\(68\) −3.42543 + 5.93301i −0.415394 + 0.719484i
\(69\) 4.17241 + 7.22682i 0.502299 + 0.870007i
\(70\) 0.192685i 0.0230303i
\(71\) −4.95295 + 2.85958i −0.587806 + 0.339370i −0.764230 0.644944i \(-0.776881\pi\)
0.176423 + 0.984314i \(0.443547\pi\)
\(72\) 1.46533 0.846011i 0.172691 0.0997033i
\(73\) 7.35690i 0.861060i −0.902576 0.430530i \(-0.858327\pi\)
0.902576 0.430530i \(-0.141673\pi\)
\(74\) −0.711636 1.23259i −0.0827260 0.143286i
\(75\) −2.46950 + 4.27730i −0.285153 + 0.493900i
\(76\) −8.71101 5.02930i −0.999221 0.576901i
\(77\) −9.90946 −1.12929
\(78\) 0 0
\(79\) 4.45473 0.501196 0.250598 0.968091i \(-0.419373\pi\)
0.250598 + 0.968091i \(0.419373\pi\)
\(80\) 0.609771 + 0.352052i 0.0681745 + 0.0393606i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0.0990311 + 0.171527i 0.0109362 + 0.0189420i
\(83\) 10.1860i 1.11806i −0.829149 0.559028i \(-0.811174\pi\)
0.829149 0.559028i \(-0.188826\pi\)
\(84\) −2.73563 + 1.57942i −0.298482 + 0.172329i
\(85\) −0.813199 + 0.469501i −0.0882038 + 0.0509245i
\(86\) 0.762709i 0.0822450i
\(87\) 2.96950 + 5.14333i 0.318364 + 0.551422i
\(88\) −4.78232 + 8.28323i −0.509797 + 0.882995i
\(89\) 0.118700 + 0.0685317i 0.0125822 + 0.00726434i 0.506278 0.862370i \(-0.331021\pi\)
−0.493696 + 0.869635i \(0.664354\pi\)
\(90\) 0.109916 0.0115862
\(91\) 0 0
\(92\) −15.0368 −1.56770
\(93\) −4.56287 2.63437i −0.473148 0.273172i
\(94\) 1.49880 2.59600i 0.154590 0.267757i
\(95\) −0.689333 1.19396i −0.0707241 0.122498i
\(96\) 4.65279i 0.474874i
\(97\) −11.8556 + 6.84481i −1.20375 + 0.694986i −0.961387 0.275200i \(-0.911256\pi\)
−0.242363 + 0.970186i \(0.577923\pi\)
\(98\) 1.51350 0.873822i 0.152887 0.0882693i
\(99\) 5.65279i 0.568127i
\(100\) −4.44989 7.70743i −0.444989 0.770743i
\(101\) −2.70560 + 4.68623i −0.269217 + 0.466297i −0.968660 0.248391i \(-0.920098\pi\)
0.699443 + 0.714688i \(0.253431\pi\)
\(102\) −1.46533 0.846011i −0.145090 0.0837675i
\(103\) −13.7560 −1.35542 −0.677710 0.735330i \(-0.737027\pi\)
−0.677710 + 0.735330i \(0.737027\pi\)
\(104\) 0 0
\(105\) −0.432960 −0.0422526
\(106\) 0.408928 + 0.236094i 0.0397186 + 0.0229315i
\(107\) 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
\(109\) 12.1468i 1.16345i 0.813386 + 0.581724i \(0.197622\pi\)
−0.813386 + 0.581724i \(0.802378\pi\)
\(110\) −0.538091 + 0.310667i −0.0513050 + 0.0296209i
\(111\) −2.76960 + 1.59903i −0.262879 + 0.151773i
\(112\) 4.99761i 0.472229i
\(113\) 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
\(115\) −1.78488 1.03050i −0.166441 0.0960946i
\(116\) −10.7017 −0.993629
\(117\) 0 0
\(118\) −6.09783 −0.561351
\(119\) 5.77195 + 3.33244i 0.529114 + 0.305484i
\(120\) −0.208947 + 0.361908i −0.0190742 + 0.0330375i
\(121\) 10.4770 + 18.1468i 0.952458 + 1.64970i
\(122\) 3.78986i 0.343117i
\(123\) 0.385418 0.222521i 0.0347519 0.0200640i
\(124\) 8.22201 4.74698i 0.738358 0.426291i
\(125\) 2.45473i 0.219558i
\(126\) −0.390084 0.675645i −0.0347514 0.0601912i
\(127\) 5.39977 9.35268i 0.479152 0.829916i −0.520562 0.853824i \(-0.674277\pi\)
0.999714 + 0.0239078i \(0.00761081\pi\)
\(128\) −9.45833 5.46077i −0.836006 0.482669i
\(129\) −1.71379 −0.150891
\(130\) 0 0
\(131\) 0.907542 0.0792923 0.0396462 0.999214i \(-0.487377\pi\)
0.0396462 + 0.999214i \(0.487377\pi\)
\(132\) 8.82132 + 5.09299i 0.767797 + 0.443288i
\(133\) −4.89277 + 8.47453i −0.424257 + 0.734835i
\(134\) 1.32640 + 2.29739i 0.114583 + 0.198464i
\(135\) 0.246980i 0.0212566i
\(136\) 5.57111 3.21648i 0.477718 0.275811i
\(137\) 8.26903 4.77413i 0.706471 0.407881i −0.103282 0.994652i \(-0.532934\pi\)
0.809753 + 0.586771i \(0.199601\pi\)
\(138\) 3.71379i 0.316139i
\(139\) 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
\(141\) −5.83317 3.36778i −0.491241 0.283618i
\(142\) 2.54527 0.213594
\(143\) 0 0
\(144\) 2.85086 0.237571
\(145\) −1.27030 0.733406i −0.105492 0.0609061i
\(146\) −1.63706 + 2.83548i −0.135484 + 0.234666i
\(147\) −1.96346 3.40081i −0.161943 0.280494i
\(148\) 5.76271i 0.473692i
\(149\) −13.3267 + 7.69418i −1.09177 + 0.630332i −0.934046 0.357152i \(-0.883748\pi\)
−0.157720 + 0.987484i \(0.550414\pi\)
\(150\) 1.90358 1.09903i 0.155426 0.0897355i
\(151\) 3.67456i 0.299032i 0.988759 + 0.149516i \(0.0477715\pi\)
−0.988759 + 0.149516i \(0.952228\pi\)
\(152\) 4.72252 + 8.17965i 0.383047 + 0.663457i
\(153\) −1.90097 + 3.29257i −0.153684 + 0.266189i
\(154\) 3.81928 + 2.20506i 0.307766 + 0.177689i
\(155\) 1.30127 0.104521
\(156\) 0 0
\(157\) −4.87800 −0.389307 −0.194653 0.980872i \(-0.562358\pi\)
−0.194653 + 0.980872i \(0.562358\pi\)
\(158\) −1.71693 0.991271i −0.136592 0.0788613i
\(159\) 0.530499 0.918852i 0.0420713 0.0728697i
\(160\) −0.574572 0.995189i −0.0454239 0.0786766i
\(161\) 14.6286i 1.15290i
\(162\) 0.385418 0.222521i 0.0302813 0.0174829i
\(163\) −7.47468 + 4.31551i −0.585462 + 0.338017i −0.763301 0.646043i \(-0.776423\pi\)
0.177839 + 0.984060i \(0.443089\pi\)
\(164\) 0.801938i 0.0626208i
\(165\) 0.698062 + 1.20908i 0.0543441 + 0.0941267i
\(166\) −2.26659 + 3.92586i −0.175922 + 0.304706i
\(167\) 8.20108 + 4.73490i 0.634619 + 0.366397i 0.782539 0.622602i \(-0.213924\pi\)
−0.147920 + 0.988999i \(0.547258\pi\)
\(168\) 2.96615 0.228843
\(169\) 0 0
\(170\) 0.417895 0.0320511
\(171\) −4.83424 2.79105i −0.369684 0.213437i
\(172\) 1.54407 2.67441i 0.117734 0.203922i
\(173\) 2.38740 + 4.13509i 0.181510 + 0.314385i 0.942395 0.334502i \(-0.108568\pi\)
−0.760885 + 0.648887i \(0.775235\pi\)
\(174\) 2.64310i 0.200373i
\(175\) −7.49819 + 4.32908i −0.566810 + 0.327248i
\(176\) −13.9563 + 8.05765i −1.05199 + 0.607368i
\(177\) 13.7017i 1.02988i
\(178\) −0.0304995 0.0528266i −0.00228603 0.00395952i
\(179\) 1.71768 2.97510i 0.128385 0.222370i −0.794666 0.607047i \(-0.792354\pi\)
0.923051 + 0.384677i \(0.125687\pi\)
\(180\) 0.385418 + 0.222521i 0.0287273 + 0.0165857i
\(181\) 13.4862 1.00242 0.501210 0.865326i \(-0.332888\pi\)
0.501210 + 0.865326i \(0.332888\pi\)
\(182\) 0 0
\(183\) −8.51573 −0.629501
\(184\) 12.2279 + 7.05980i 0.901455 + 0.520456i
\(185\) 0.394928 0.684035i 0.0290357 0.0502913i
\(186\) 1.17241 + 2.03067i 0.0859651 + 0.148896i
\(187\) 21.4916i 1.57162i
\(188\) 10.5110 6.06853i 0.766594 0.442593i
\(189\) −1.51816 + 0.876510i −0.110430 + 0.0637567i
\(190\) 0.613564i 0.0445126i
\(191\) 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
\(193\) −7.96368 4.59783i −0.573238 0.330959i 0.185203 0.982700i \(-0.440706\pi\)
−0.758442 + 0.651741i \(0.774039\pi\)
\(194\) 6.09246 0.437413
\(195\) 0 0
\(196\) 7.07606 0.505433
\(197\) −3.56136 2.05615i −0.253737 0.146495i 0.367737 0.929930i \(-0.380133\pi\)
−0.621474 + 0.783435i \(0.713466\pi\)
\(198\) −1.25786 + 2.17869i −0.0893926 + 0.154832i
\(199\) −12.3862 21.4535i −0.878034 1.52080i −0.853495 0.521101i \(-0.825521\pi\)
−0.0245395 0.999699i \(-0.507812\pi\)
\(200\) 8.35690i 0.590922i
\(201\) 5.16218 2.98039i 0.364112 0.210220i
\(202\) 2.08557 1.20410i 0.146740 0.0847204i
\(203\) 10.4112i 0.730722i
\(204\) −3.42543 5.93301i −0.239828 0.415394i
\(205\) −0.0549581 + 0.0951903i −0.00383844 + 0.00664838i
\(206\) 5.30181 + 3.06100i 0.369394 + 0.213270i
\(207\) −8.34481 −0.580005
\(208\) 0 0
\(209\) 31.5545 2.18267
\(210\) 0.166870 + 0.0963427i 0.0115152 + 0.00664828i
\(211\) 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
\(213\) 5.71917i 0.391871i
\(214\) −4.93990 + 2.85205i −0.337684 + 0.194962i
\(215\) 0.366564 0.211636i 0.0249995 0.0144334i
\(216\) 1.69202i 0.115127i
\(217\) −4.61811 7.99881i −0.313498 0.542994i
\(218\) 2.70291 4.68157i 0.183064 0.317076i
\(219\) 6.37126 + 3.67845i 0.430530 + 0.248566i
\(220\) −2.51573 −0.169610
\(221\) 0 0
\(222\) 1.42327 0.0955237
\(223\) −12.2985 7.10052i −0.823566 0.475486i 0.0280785 0.999606i \(-0.491061\pi\)
−0.851645 + 0.524120i \(0.824395\pi\)
\(224\) −4.07822 + 7.06368i −0.272488 + 0.471962i
\(225\) −2.46950 4.27730i −0.164633 0.285153i
\(226\) 0.728857i 0.0484829i
\(227\) 13.8627 8.00365i 0.920101 0.531221i 0.0364340 0.999336i \(-0.488400\pi\)
0.883667 + 0.468115i \(0.155067\pi\)
\(228\) 8.71101 5.02930i 0.576901 0.333074i
\(229\) 1.84117i 0.121668i −0.998148 0.0608339i \(-0.980624\pi\)
0.998148 0.0608339i \(-0.0193760\pi\)
\(230\) 0.458615 + 0.794345i 0.0302402 + 0.0523776i
\(231\) 4.95473 8.58185i 0.325997 0.564644i
\(232\) 8.70262 + 5.02446i 0.571355 + 0.329872i
\(233\) 23.4252 1.53464 0.767318 0.641267i \(-0.221591\pi\)
0.767318 + 0.641267i \(0.221591\pi\)
\(234\) 0 0
\(235\) 1.66355 0.108518
\(236\) −21.3818 12.3448i −1.39184 0.803579i
\(237\) −2.22737 + 3.85791i −0.144683 + 0.250598i
\(238\) −1.48307 2.56876i −0.0961334 0.166508i
\(239\) 14.6015i 0.944491i 0.881467 + 0.472246i \(0.156556\pi\)
−0.881467 + 0.472246i \(0.843444\pi\)
\(240\) −0.609771 + 0.352052i −0.0393606 + 0.0227248i
\(241\) −7.47468 + 4.31551i −0.481487 + 0.277987i −0.721036 0.692898i \(-0.756334\pi\)
0.239549 + 0.970884i \(0.423000\pi\)
\(242\) 9.32544i 0.599462i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 7.67241 13.2890i 0.491176 0.850741i
\(245\) 0.839931 + 0.484935i 0.0536612 + 0.0309813i
\(246\) −0.198062 −0.0126280
\(247\) 0 0
\(248\) −8.91484 −0.566093
\(249\) 8.82132 + 5.09299i 0.559028 + 0.322755i
\(250\) −0.546229 + 0.946096i −0.0345466 + 0.0598364i
\(251\) −1.90097 3.29257i −0.119988 0.207825i 0.799775 0.600300i \(-0.204952\pi\)
−0.919763 + 0.392475i \(0.871619\pi\)
\(252\) 3.15883i 0.198988i
\(253\) 40.8517 23.5858i 2.56833 1.48282i
\(254\) −4.16233 + 2.40312i −0.261168 + 0.150785i
\(255\) 0.939001i 0.0588025i
\(256\) −1.20075 2.07976i −0.0750469 0.129985i
\(257\) −10.2981 + 17.8368i −0.642375 + 1.11263i 0.342526 + 0.939508i \(0.388717\pi\)
−0.984901 + 0.173118i \(0.944616\pi\)
\(258\) 0.660525 + 0.381355i 0.0411225 + 0.0237421i
\(259\) −5.60627 −0.348357
\(260\) 0 0
\(261\) −5.93900 −0.367615
\(262\) −0.349783 0.201947i −0.0216096 0.0124763i
\(263\) −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
\(265\) 0.262045i 0.0160973i
\(266\) 3.77152 2.17749i 0.231247 0.133510i
\(267\) −0.118700 + 0.0685317i −0.00726434 + 0.00419407i
\(268\) 10.7409i 0.656107i
\(269\) −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
\(271\) 24.2362 + 13.9928i 1.47224 + 0.850000i 0.999513 0.0312076i \(-0.00993529\pi\)
0.472730 + 0.881207i \(0.343269\pi\)
\(272\) 10.8388 0.657197
\(273\) 0 0
\(274\) −4.24937 −0.256714
\(275\) 24.1787 + 13.9596i 1.45803 + 0.841794i
\(276\) 7.51842 13.0223i 0.452556 0.783849i
\(277\) −1.05161 1.82143i −0.0631849 0.109439i 0.832703 0.553721i \(-0.186792\pi\)
−0.895887 + 0.444281i \(0.853459\pi\)
\(278\) 1.82132i 0.109235i
\(279\) 4.56287 2.63437i 0.273172 0.157716i
\(280\) −0.634431 + 0.366289i −0.0379145 + 0.0218900i
\(281\) 27.2349i 1.62470i −0.583172 0.812349i \(-0.698189\pi\)
0.583172 0.812349i \(-0.301811\pi\)
\(282\) 1.49880 + 2.59600i 0.0892525 + 0.154590i
\(283\) 2.64191 4.57592i 0.157045 0.272010i −0.776757 0.629801i \(-0.783137\pi\)
0.933802 + 0.357791i \(0.116470\pi\)
\(284\) 8.92490 + 5.15279i 0.529595 + 0.305762i
\(285\) 1.37867 0.0816651
\(286\) 0 0
\(287\) 0.780167 0.0460518
\(288\) −4.02944 2.32640i −0.237437 0.137084i
\(289\) 1.27263 2.20427i 0.0748609 0.129663i
\(290\) 0.326396 + 0.565335i 0.0191667 + 0.0331976i
\(291\) 13.6896i 0.802500i
\(292\) −11.4806 + 6.62833i −0.671852 + 0.387894i
\(293\) −28.2865 + 16.3312i −1.65252 + 0.954081i −0.676485 + 0.736457i \(0.736498\pi\)
−0.976033 + 0.217625i \(0.930169\pi\)
\(294\) 1.74764i 0.101925i
\(295\) −1.69202 2.93067i −0.0985133 0.170630i
\(296\) −2.70560 + 4.68623i −0.157260 + 0.272381i
\(297\) 4.89546 + 2.82640i 0.284064 + 0.164004i
\(298\) 6.84846 0.396721
\(299\) 0 0
\(300\) 8.89977 0.513829
\(301\) −2.60181 1.50216i −0.149966 0.0865828i
\(302\) 0.817667 1.41624i 0.0470515 0.0814955i
\(303\) −2.70560 4.68623i −0.155432 0.269217i
\(304\) 15.9138i 0.912717i
\(305\) 1.82143 1.05161i 0.104295 0.0602148i
\(306\) 1.46533 0.846011i 0.0837675 0.0483632i
\(307\) 20.7614i 1.18491i 0.805602 + 0.592457i \(0.201842\pi\)
−0.805602 + 0.592457i \(0.798158\pi\)
\(308\) 8.92812 + 15.4640i 0.508727 + 0.881140i
\(309\) 6.87800 11.9130i 0.391276 0.677710i
\(310\) −0.501534 0.289561i −0.0284852 0.0164459i
\(311\) 11.3013 0.640836 0.320418 0.947276i \(-0.396177\pi\)
0.320418 + 0.947276i \(0.396177\pi\)
\(312\) 0 0
\(313\) −4.27173 −0.241453 −0.120726 0.992686i \(-0.538522\pi\)
−0.120726 + 0.992686i \(0.538522\pi\)
\(314\) 1.88007 + 1.08546i 0.106098 + 0.0612559i
\(315\) 0.216480 0.374955i 0.0121973 0.0211263i
\(316\) −4.01357 6.95171i −0.225781 0.391064i
\(317\) 15.4776i 0.869307i 0.900598 + 0.434653i \(0.143129\pi\)
−0.900598 + 0.434653i \(0.856871\pi\)
\(318\) −0.408928 + 0.236094i −0.0229315 + 0.0132395i
\(319\) 29.0742 16.7860i 1.62784 0.939834i
\(320\) 0.896789i 0.0501320i
\(321\) 6.40850 + 11.0999i 0.357688 + 0.619533i
\(322\) 3.25518 5.63813i 0.181404 0.314201i
\(323\) −18.3795 10.6114i −1.02266 0.590435i
\(324\) 1.80194 0.100108
\(325\) 0 0
\(326\) 3.84117 0.212743
\(327\) −10.5194 6.07338i −0.581724 0.335858i
\(328\) 0.376510 0.652135i 0.0207893 0.0360081i
\(329\) −5.90379 10.2257i −0.325486 0.563759i
\(330\) 0.621334i 0.0342033i
\(331\) 5.25530 3.03415i 0.288857 0.166772i −0.348569 0.937283i \(-0.613332\pi\)
0.637426 + 0.770511i \(0.279999\pi\)
\(332\) −15.8955 + 9.17725i −0.872377 + 0.503667i
\(333\) 3.19806i 0.175253i
\(334\) −2.10723 3.64983i −0.115302 0.199710i
\(335\) −0.736094 + 1.27495i −0.0402171 + 0.0696581i
\(336\) 4.32805 + 2.49880i 0.236115 + 0.136321i
\(337\) −12.1239 −0.660432 −0.330216 0.943905i \(-0.607122\pi\)
−0.330216 + 0.943905i \(0.607122\pi\)
\(338\) 0 0
\(339\) −1.63773 −0.0889491
\(340\) 1.46533 + 0.846011i 0.0794689 + 0.0458814i
\(341\) −14.8916 + 25.7930i −0.806424 + 1.39677i
\(342\) 1.24214 + 2.15144i 0.0671670 + 0.116337i
\(343\) 19.1551i 1.03428i
\(344\) −2.51128 + 1.44989i −0.135399 + 0.0781726i
\(345\) 1.78488 1.03050i 0.0960946 0.0554802i
\(346\) 2.12498i 0.114240i
\(347\) −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
\(349\) −19.2220 11.0978i −1.02893 0.594053i −0.112253 0.993680i \(-0.535807\pi\)
−0.916678 + 0.399626i \(0.869140\pi\)
\(350\) 3.85325 0.205965
\(351\) 0 0
\(352\) 26.3013 1.40186
\(353\) 4.39134 + 2.53534i 0.233728 + 0.134943i 0.612291 0.790633i \(-0.290248\pi\)
−0.378563 + 0.925576i \(0.623582\pi\)
\(354\) 3.04892 5.28088i 0.162048 0.280676i
\(355\) 0.706259 + 1.22328i 0.0374843 + 0.0649248i
\(356\) 0.246980i 0.0130899i
\(357\) −5.77195 + 3.33244i −0.305484 + 0.176371i
\(358\) −1.32405 + 0.764438i −0.0699780 + 0.0404018i
\(359\) 16.6746i 0.880050i 0.897986 + 0.440025i \(0.145030\pi\)
−0.897986 + 0.440025i \(0.854970\pi\)
\(360\) −0.208947 0.361908i −0.0110125 0.0190742i
\(361\) 6.07995 10.5308i 0.319997 0.554252i
\(362\) −5.19781 3.00096i −0.273191 0.157727i
\(363\) −20.9541 −1.09980
\(364\) 0 0
\(365\) −1.81700 −0.0951063
\(366\) 3.28211 + 1.89493i 0.171559 + 0.0990495i
\(367\) 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
\(369\) 0.445042i 0.0231680i
\(370\) −0.304424 + 0.175760i −0.0158263 + 0.00913730i
\(371\) 1.61077 0.929976i 0.0836268 0.0482820i
\(372\) 9.49396i 0.492239i
\(373\) 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
\(375\) 2.12586 + 1.22737i 0.109779 + 0.0633809i
\(376\) −11.3967 −0.587741
\(377\) 0 0
\(378\) 0.780167 0.0401275
\(379\) 16.5958 + 9.58157i 0.852467 + 0.492172i 0.861483 0.507787i \(-0.169536\pi\)
−0.00901515 + 0.999959i \(0.502870\pi\)
\(380\) −1.24214 + 2.15144i −0.0637202 + 0.110367i
\(381\) 5.39977 + 9.35268i 0.276639 + 0.479152i
\(382\) 0.579121i 0.0296304i
\(383\) −13.3267 + 7.69418i −0.680963 + 0.393154i −0.800218 0.599710i \(-0.795283\pi\)
0.119255 + 0.992864i \(0.461949\pi\)
\(384\) 9.45833 5.46077i 0.482669 0.278669i
\(385\) 2.44743i 0.124733i
\(386\) 2.04623 + 3.54417i 0.104150 + 0.180394i
\(387\) 0.856896 1.48419i 0.0435585 0.0754455i
\(388\) 21.3630 + 12.3339i 1.08454 + 0.626160i
\(389\) 24.0315 1.21844 0.609222 0.793000i \(-0.291482\pi\)
0.609222 + 0.793000i \(0.291482\pi\)
\(390\) 0 0
\(391\) −31.7265 −1.60448
\(392\) −5.75425 3.32222i −0.290633 0.167797i
\(393\) −0.453771 + 0.785955i −0.0228897 + 0.0396462i
\(394\) 0.915075 + 1.58496i 0.0461008 + 0.0798489i
\(395\) 1.10023i 0.0553585i
\(396\) −8.82132 + 5.09299i −0.443288 + 0.255932i
\(397\) −25.6356 + 14.8007i −1.28662 + 0.742828i −0.978049 0.208375i \(-0.933183\pi\)
−0.308567 + 0.951203i \(0.599849\pi\)
\(398\) 11.0248i 0.552621i
\(399\) −4.89277 8.47453i −0.244945 0.424257i
\(400\) −7.04019 + 12.1940i −0.352009 + 0.609698i
\(401\) −18.2759 10.5516i −0.912656 0.526922i −0.0313711 0.999508i \(-0.509987\pi\)
−0.881285 + 0.472586i \(0.843321\pi\)
\(402\) −2.65279 −0.132309
\(403\) 0 0
\(404\) 9.75063 0.485112
\(405\) 0.213891 + 0.123490i 0.0106283 + 0.00613626i
\(406\) 2.31671 4.01266i 0.114976 0.199145i
\(407\) 9.03899 + 15.6560i 0.448046 + 0.776039i
\(408\) 6.43296i 0.318479i
\(409\) −31.1963 + 18.0112i −1.54256 + 0.890596i −0.543880 + 0.839163i \(0.683045\pi\)
−0.998676 + 0.0514328i \(0.983621\pi\)
\(410\) 0.0423637 0.0244587i 0.00209219 0.00120793i
\(411\) 9.54825i 0.470981i
\(412\) 12.3937 + 21.4666i 0.610595 + 1.05758i
\(413\) −12.0097 + 20.8014i −0.590958 + 1.02357i
\(414\) 3.21624 + 1.85690i 0.158069 + 0.0912615i
\(415\) −2.51573 −0.123492
\(416\) 0 0
\(417\) −4.09246 −0.200409
\(418\) −12.1617 7.02153i −0.594846 0.343434i
\(419\) −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
\(421\) 2.09544i 0.102126i −0.998695 0.0510628i \(-0.983739\pi\)
0.998695 0.0510628i \(-0.0162609\pi\)
\(422\) −2.28900 + 1.32155i −0.111427 + 0.0643321i
\(423\) 5.83317 3.36778i 0.283618 0.163747i
\(424\) 1.79523i 0.0871842i
\(425\) −9.38889 16.2620i −0.455428 0.788824i
\(426\) −1.27263 + 2.20427i −0.0616594 + 0.106797i
\(427\) −12.9282 7.46412i −0.625641 0.361214i
\(428\) −23.0954 −1.11636
\(429\) 0 0
\(430\) −0.188374 −0.00908418
\(431\) 2.49915 + 1.44289i 0.120380 + 0.0695014i 0.558981 0.829181i \(-0.311193\pi\)
−0.438601 + 0.898682i \(0.644526\pi\)
\(432\) −1.42543 + 2.46891i −0.0685809 + 0.118786i
\(433\) −6.32424 10.9539i −0.303924 0.526411i 0.673097 0.739554i \(-0.264963\pi\)
−0.977021 + 0.213143i \(0.931630\pi\)
\(434\) 4.11051i 0.197311i
\(435\) 1.27030 0.733406i 0.0609061 0.0351641i
\(436\) 18.9553 10.9438i 0.907794 0.524115i
\(437\) 46.5816i 2.22830i
\(438\) −1.63706 2.83548i −0.0782219 0.135484i
\(439\) −5.46346 + 9.46299i −0.260757 + 0.451644i −0.966443 0.256880i \(-0.917305\pi\)
0.705687 + 0.708524i \(0.250639\pi\)
\(440\) 2.04579 + 1.18114i 0.0975291 + 0.0563085i
\(441\) 3.92692 0.186996
\(442\) 0 0
\(443\) −19.2403 −0.914133 −0.457067 0.889433i \(-0.651100\pi\)
−0.457067 + 0.889433i \(0.651100\pi\)
\(444\) 4.99065 + 2.88135i 0.236846 + 0.136743i
\(445\) 0.0169259 0.0293166i 0.000802366 0.00138974i
\(446\) 3.16003 + 5.47333i 0.149632 + 0.259170i
\(447\) 15.3884i 0.727844i
\(448\) −5.51247 + 3.18263i −0.260440 + 0.150365i
\(449\) 24.9588 14.4100i 1.17788 0.680050i 0.222357 0.974965i \(-0.428625\pi\)
0.955523 + 0.294916i \(0.0952915\pi\)
\(450\) 2.19806i 0.103618i
\(451\) −1.25786 2.17869i −0.0592305 0.102590i
\(452\) 1.47554 2.55571i 0.0694036 0.120211i
\(453\) −3.18226 1.83728i −0.149516 0.0863230i
\(454\) −7.12392 −0.334342
\(455\) 0 0
\(456\) −9.44504 −0.442305
\(457\) 15.6497 + 9.03534i 0.732061 + 0.422656i 0.819176 0.573543i \(-0.194431\pi\)
−0.0871147 + 0.996198i \(0.527765\pi\)
\(458\) −0.409698 + 0.709618i −0.0191439 + 0.0331583i
\(459\) −1.90097 3.29257i −0.0887296 0.153684i
\(460\) 3.71379i 0.173156i
\(461\) −6.55376 + 3.78382i −0.305239 + 0.176230i −0.644794 0.764356i \(-0.723057\pi\)
0.339555 + 0.940586i \(0.389724\pi\)
\(462\) −3.81928 + 2.20506i −0.177689 + 0.102589i
\(463\) 35.3551i 1.64309i −0.570143 0.821545i \(-0.693112\pi\)
0.570143 0.821545i \(-0.306888\pi\)
\(464\) 8.46562 + 14.6629i 0.393006 + 0.680707i
\(465\) −0.650637 + 1.12694i −0.0301726 + 0.0522604i
\(466\) −9.02848 5.21260i −0.418236 0.241469i
\(467\) −13.0000 −0.601568 −0.300784 0.953692i \(-0.597248\pi\)
−0.300784 + 0.953692i \(0.597248\pi\)
\(468\) 0 0
\(469\) 10.4494 0.482506
\(470\) −0.641160 0.370174i −0.0295745 0.0170748i
\(471\) 2.43900 4.22447i 0.112383 0.194653i
\(472\) 11.5918 + 20.0776i 0.533556 + 0.924145i
\(473\) 9.68771i 0.445441i
\(474\) 1.71693 0.991271i 0.0788613 0.0455306i
\(475\) 23.8763 13.7850i 1.09552 0.632500i
\(476\) 12.0097i 0.550463i
\(477\) 0.530499 + 0.918852i 0.0242899 + 0.0420713i
\(478\) 3.24914 5.62767i 0.148612 0.257404i
\(479\) −22.1066 12.7632i −1.01008 0.583167i −0.0988618 0.995101i \(-0.531520\pi\)
−0.911214 + 0.411934i \(0.864853\pi\)
\(480\) 1.14914 0.0524510
\(481\) 0 0
\(482\) 3.84117 0.174960
\(483\) −12.6688 7.31431i −0.576449 0.332813i
\(484\) 18.8790 32.6993i 0.858135 1.48633i
\(485\) 1.69053 + 2.92808i 0.0767630 + 0.132957i
\(486\) 0.445042i 0.0201875i
\(487\) 13.8627 8.00365i 0.628180 0.362680i −0.151867 0.988401i \(-0.548529\pi\)
0.780047 + 0.625721i \(0.215195\pi\)
\(488\) −12.4784 + 7.20440i −0.564870 + 0.326128i
\(489\) 8.63102i 0.390308i
\(490\) −0.215816 0.373805i −0.00974958 0.0168868i
\(491\) 10.3693 17.9601i 0.467959 0.810528i −0.531371 0.847139i \(-0.678323\pi\)
0.999330 + 0.0366110i \(0.0116562\pi\)
\(492\) −0.694498 0.400969i −0.0313104 0.0180771i
\(493\) −22.5797 −1.01694
\(494\) 0 0
\(495\) −1.39612 −0.0627511
\(496\) −13.0081 7.51022i −0.584080 0.337219i
\(497\) 5.01291 8.68261i 0.224860 0.389468i
\(498\) −2.26659 3.92586i −0.101569 0.175922i
\(499\) 8.06770i 0.361160i −0.983560 0.180580i \(-0.942203\pi\)
0.983560 0.180580i \(-0.0577975\pi\)
\(500\) −3.83067 + 2.21164i −0.171313 + 0.0989074i
\(501\) −8.20108 + 4.73490i −0.366397 + 0.211540i
\(502\) 1.69202i 0.0755186i
\(503\) 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
\(505\) 1.15740 + 0.668227i 0.0515037 + 0.0297357i
\(506\) −20.9933 −0.933266
\(507\) 0 0
\(508\) −19.4601 −0.863403
\(509\) −13.8993 8.02475i −0.616075 0.355691i 0.159264 0.987236i \(-0.449088\pi\)
−0.775339 + 0.631545i \(0.782421\pi\)
\(510\) −0.208947 + 0.361908i −0.00925235 + 0.0160255i
\(511\) 6.44839 + 11.1689i 0.285260 + 0.494085i
\(512\) 22.9119i 1.01257i
\(513\) 4.83424 2.79105i 0.213437 0.123228i
\(514\) 7.93810 4.58306i 0.350135 0.202150i
\(515\) 3.39745i 0.149710i
\(516\) 1.54407 + 2.67441i 0.0679740 + 0.117734i
\(517\) −19.0374 + 32.9737i −0.837262 + 1.45018i
\(518\) 2.16075 + 1.24751i 0.0949381 + 0.0548125i
\(519\) −4.77479 −0.209590
\(520\) 0 0
\(521\) −2.69309 −0.117986 −0.0589931 0.998258i \(-0.518789\pi\)
−0.0589931 + 0.998258i \(0.518789\pi\)
\(522\) 2.28900 + 1.32155i 0.100187 + 0.0578428i
\(523\) −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
\(525\) 8.65817i 0.377874i
\(526\) 0.128241 0.0740400i 0.00559157 0.00322830i
\(527\) 17.3478 10.0157i 0.755680 0.436292i
\(528\) 16.1153i 0.701328i
\(529\) −23.3180 40.3879i −1.01382 1.75600i
\(530\) 0.0583105 0.100997i 0.00253285 0.00438702i
\(531\) −11.8660 6.85086i −0.514942 0.297302i
\(532\) 17.6329 0.764485
\(533\) 0 0
\(534\) 0.0609989 0.00263968
\(535\) −2.74144 1.58277i −0.118523 0.0684291i
\(536\) 5.04288 8.73452i 0.217819 0.377274i
\(537\) 1.71768 + 2.97510i 0.0741232 + 0.128385i
\(538\) 12.1511i 0.523870i
\(539\) −19.2241 + 11.0990i −0.828040 + 0.478069i
\(540\) −0.385418 + 0.222521i −0.0165857 + 0.00957578i
\(541\) 34.7338i 1.49332i 0.665205 + 0.746660i \(0.268344\pi\)
−0.665205 + 0.746660i \(0.731656\pi\)
\(542\) −6.22737 10.7861i −0.267488 0.463303i
\(543\) −6.74309 + 11.6794i −0.289374 + 0.501210i
\(544\) −15.3197 8.84481i −0.656825 0.379218i
\(545\) 3.00000 0.128506
\(546\) 0 0
\(547\) −26.1183 −1.11674 −0.558368 0.829593i \(-0.688572\pi\)
−0.558368 + 0.829593i \(0.688572\pi\)
\(548\) −14.9003 8.60268i −0.636508 0.367488i
\(549\) 4.25786 7.37484i 0.181721 0.314750i
\(550\) −6.21260 10.7605i −0.264906 0.458831i
\(551\) 33.1521i 1.41233i
\(552\) −12.2279 + 7.05980i −0.520456 + 0.300485i
\(553\) −6.76299 + 3.90462i −0.287592 + 0.166041i
\(554\) 0.936017i 0.0397676i
\(555\) 0.394928 + 0.684035i 0.0167638 + 0.0290357i
\(556\) 3.68718 6.38638i 0.156371 0.270843i
\(557\) 21.4556 + 12.3874i 0.909103 + 0.524871i 0.880142 0.474710i \(-0.157447\pi\)
0.0289605 + 0.999581i \(0.490780\pi\)
\(558\) −2.34481 −0.0992639
\(559\) 0 0
\(560\) −1.23431 −0.0521590
\(561\) 18.6122 + 10.7458i 0.785809 + 0.453687i
\(562\) −6.06033 + 10.4968i −0.255640 + 0.442781i
\(563\) 2.63049 + 4.55614i 0.110862 + 0.192019i 0.916118 0.400909i \(-0.131306\pi\)
−0.805256 + 0.592927i \(0.797972\pi\)
\(564\) 12.1371i 0.511063i
\(565\) 0.350294 0.202243i 0.0147370 0.00850841i
\(566\) −2.03648 + 1.17576i −0.0855994 + 0.0494209i
\(567\) 1.75302i 0.0736199i
\(568\) −4.83848 8.38049i −0.203018 0.351638i
\(569\) −16.8729 + 29.2248i −0.707350 + 1.22517i 0.258487 + 0.966015i \(0.416776\pi\)
−0.965837 + 0.259151i \(0.916557\pi\)
\(570\) −0.531362 0.306782i −0.0222563 0.0128497i
\(571\) −23.0887 −0.966234 −0.483117 0.875556i \(-0.660495\pi\)
−0.483117 + 0.875556i \(0.660495\pi\)
\(572\) 0 0
\(573\) −1.30127 −0.0543615
\(574\) −0.300690 0.173604i −0.0125506 0.00724607i
\(575\) 20.6075 35.6933i 0.859393 1.48851i
\(576\) −1.81551 3.14456i −0.0756463 0.131023i
\(577\) 3.57002i 0.148622i 0.997235 + 0.0743110i \(0.0236758\pi\)
−0.997235 + 0.0743110i \(0.976324\pi\)
\(578\) −0.980992 + 0.566376i −0.0408039 + 0.0235581i
\(579\) 7.96368 4.59783i 0.330959 0.191079i
\(580\) 2.64310i 0.109749i
\(581\) 8.92812 + 15.4640i 0.370401 + 0.641553i
\(582\) −3.04623 + 5.27622i −0.126270 + 0.218706i
\(583\) −5.19408 2.99880i −0.215117 0.124198i
\(584\) 12.4480 0.515103
\(585\) 0 0
\(586\) 14.5362 0.600484
\(587\) 9.92682 + 5.73125i 0.409724 + 0.236554i 0.690671 0.723169i \(-0.257315\pi\)
−0.280947 + 0.959723i \(0.590649\pi\)
\(588\) −3.53803 + 6.12805i −0.145906 + 0.252717i
\(589\) 14.7054 + 25.4704i 0.605924 + 1.04949i
\(590\) 1.50604i 0.0620027i
\(591\) 3.56136 2.05615i 0.146495 0.0845789i
\(592\) −7.89574 + 4.55861i −0.324513 + 0.187358i
\(593\) 21.8538i 0.897430i 0.893675 + 0.448715i \(0.148118\pi\)
−0.893675 + 0.448715i \(0.851882\pi\)
\(594\) −1.25786 2.17869i −0.0516108 0.0893926i
\(595\) 0.823044 1.42555i 0.0337415 0.0584420i
\(596\) 24.0139 + 13.8644i 0.983647 + 0.567909i
\(597\) 24.7724 1.01387
\(598\) 0 0
\(599\) 27.0573 1.10553 0.552765 0.833337i \(-0.313573\pi\)
0.552765 + 0.833337i \(0.313573\pi\)
\(600\) −7.23728 4.17845i −0.295461 0.170584i
\(601\) −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
\(603\) 5.96077i 0.242741i
\(604\) 5.73424 3.31067i 0.233323 0.134709i
\(605\) 4.48188 2.58761i 0.182214 0.105201i
\(606\) 2.40821i 0.0978267i
\(607\) 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
\(609\) −9.01636 5.20560i −0.365361 0.210941i
\(610\) −0.936017 −0.0378982
\(611\) 0 0
\(612\) 6.85086 0.276929
\(613\) −8.86317 5.11715i −0.357980 0.206680i 0.310214 0.950667i \(-0.399599\pi\)
−0.668194 + 0.743987i \(0.732933\pi\)
\(614\) 4.61984 8.00180i 0.186442 0.322926i
\(615\) −0.0549581 0.0951903i −0.00221613 0.00383844i
\(616\) 16.7670i 0.675563i
\(617\) 22.7615 13.1414i 0.916345 0.529052i 0.0338776 0.999426i \(-0.489214\pi\)
0.882467 + 0.470374i \(0.155881\pi\)
\(618\) −5.30181 + 3.06100i −0.213270 + 0.123131i
\(619\) 29.0834i 1.16896i −0.811408 0.584479i \(-0.801299\pi\)
0.811408 0.584479i \(-0.198701\pi\)
\(620\) −1.17241 2.03067i −0.0470850 0.0815536i
\(621\) 4.17241 7.22682i 0.167433 0.290002i
\(622\) −4.35571 2.51477i −0.174648 0.100833i
\(623\) −0.240275 −0.00962641
\(624\) 0 0
\(625\) 24.0887 0.963549
\(626\) 1.64640 + 0.950550i 0.0658034 + 0.0379916i
\(627\) −15.7772 + 27.3270i −0.630082 + 1.09133i
\(628\) 4.39493 + 7.61224i 0.175377 + 0.303761i
\(629\) 12.1588i 0.484804i
\(630\) −0.166870 + 0.0963427i −0.00664828 + 0.00383839i
\(631\) −22.0386 + 12.7240i −0.877344 + 0.506535i −0.869782 0.493436i \(-0.835741\pi\)
−0.00756243 + 0.999971i \(0.502407\pi\)
\(632\) 7.53750i 0.299826i
\(633\) 2.96950 + 5.14333i 0.118027 + 0.204429i
\(634\) 3.44408 5.96533i 0.136782 0.236913i
\(635\) −2.30992 1.33363i −0.0916664 0.0529236i
\(636\) −1.91185 −0.0758099
\(637\) 0 0
\(638\) −14.9409 −0.591517
\(639\) 4.95295 + 2.85958i 0.195935 + 0.113123i
\(640\) −1.34870 + 2.33602i −0.0533120 + 0.0923391i
\(641\) −13.3705 23.1583i −0.528102 0.914699i −0.999463 0.0327590i \(-0.989571\pi\)
0.471361 0.881940i \(-0.343763\pi\)
\(642\) 5.70410i 0.225123i
\(643\) −28.5454 + 16.4807i −1.12572 + 0.649935i −0.942855 0.333203i \(-0.891870\pi\)
−0.182865 + 0.983138i \(0.558537\pi\)
\(644\) 22.8283 13.1799i 0.899562 0.519362i
\(645\) 0.423272i 0.0166663i
\(646\) 4.72252 + 8.17965i 0.185805 + 0.321824i
\(647\) 17.2473 29.8732i 0.678060 1.17443i −0.297504 0.954721i \(-0.596154\pi\)
0.975564 0.219714i \(-0.0705125\pi\)
\(648\) −1.46533 0.846011i −0.0575637 0.0332344i
\(649\) 77.4529 3.04029
\(650\) 0 0
\(651\) 9.23623 0.361996
\(652\) 13.4689 + 7.77628i 0.527483 + 0.304543i
\(653\) −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
\(655\) 0.224144i 0.00875805i
\(656\) 1.09877 0.634375i 0.0428997 0.0247682i
\(657\) −6.37126 + 3.67845i −0.248566 + 0.143510i
\(658\) 5.25487i 0.204856i
\(659\) 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
\(661\) −9.43482 5.44720i −0.366972 0.211871i 0.305163 0.952300i \(-0.401289\pi\)
−0.672135 + 0.740429i \(0.734622\pi\)
\(662\) −2.70065 −0.104964
\(663\) 0 0
\(664\) 17.2349 0.668844
\(665\) 2.09304 + 1.20841i 0.0811645 + 0.0468603i
\(666\) −0.711636 + 1.23259i −0.0275753 + 0.0477619i
\(667\) −24.7799 42.9201i −0.959483 1.66187i
\(668\) 17.0640i 0.660225i
\(669\) 12.2985 7.10052i 0.475486 0.274522i
\(670\) 0.567407 0.327593i 0.0219209 0.0126560i
\(671\) 48.1377i 1.85833i
\(672\) −4.07822 7.06368i −0.157321 0.272488i
\(673\) 10.3693 17.9601i 0.399706 0.692311i −0.593983 0.804477i \(-0.702446\pi\)
0.993689 + 0.112166i \(0.0357789\pi\)
\(674\) 4.67277 + 2.69783i 0.179988 + 0.103916i
\(675\) 4.93900 0.190102
\(676\) 0 0
\(677\) −25.5786 −0.983067 −0.491534 0.870859i \(-0.663564\pi\)
−0.491534 + 0.870859i \(0.663564\pi\)
\(678\) 0.631209 + 0.364429i 0.0242414 + 0.0139958i
\(679\) 11.9991 20.7830i 0.460483 0.797580i
\(680\) −0.794405 1.37595i −0.0304640 0.0527653i
\(681\) 16.0073i 0.613401i
\(682\) 11.4789 6.62737i 0.439552 0.253775i
\(683\) −18.7330 + 10.8155i −0.716799 + 0.413844i −0.813573 0.581462i \(-0.802481\pi\)
0.0967744 + 0.995306i \(0.469147\pi\)
\(684\) 10.0586i 0.384600i
\(685\) −1.17911 2.04228i −0.0450516 0.0780316i
\(686\) −4.26241 + 7.38272i −0.162740 + 0.281873i
\(687\) 1.59450 + 0.920583i 0.0608339 + 0.0351224i
\(688\) −4.88577 −0.186268
\(689\) 0 0
\(690\) −0.917231 −0.0349184
\(691\) −2.27761 1.31498i −0.0866444 0.0500242i 0.456052 0.889953i \(-0.349263\pi\)
−0.542696 + 0.839929i \(0.682596\pi\)
\(692\) 4.30194 7.45117i 0.163535 0.283251i
\(693\) 4.95473 + 8.58185i 0.188215 + 0.325997i
\(694\) 10.3026i 0.391081i
\(695\) 0.875338 0.505377i 0.0332035 0.0191700i
\(696\) −8.70262 + 5.02446i −0.329872 + 0.190452i
\(697\) 1.69202i 0.0640899i
\(698\) 4.93900 + 8.55460i 0.186944 + 0.323796i
\(699\) −11.7126 + 20.2868i −0.443011 + 0.767318i
\(700\) 13.5113 + 7.80074i 0.510678 + 0.294840i
\(701\) −40.0925 −1.51427 −0.757136 0.653258i \(-0.773402\pi\)
−0.757136 + 0.653258i \(0.773402\pi\)
\(702\) 0 0
\(703\) 17.8519 0.673298
\(704\) 17.7755 + 10.2627i 0.669941 + 0.386790i
\(705\) −0.831773 + 1.44067i −0.0313264 + 0.0542589i
\(706\) −1.12833 1.95433i −0.0424654 0.0735523i
\(707\) 9.48593i 0.356755i
\(708\) 21.3818 12.3448i 0.803579 0.463947i
\(709\) −20.1002 + 11.6048i −0.754877 + 0.435829i −0.827454 0.561534i \(-0.810211\pi\)
0.0725761 + 0.997363i \(0.476878\pi\)
\(710\) 0.628630i 0.0235921i
\(711\) −2.22737 3.85791i −0.0835327 0.144683i
\(712\) −0.115957 + 0.200844i −0.00434567 + 0.00752693i
\(713\) 38.0763 + 21.9834i 1.42597 + 0.823284i
\(714\) 2.96615 0.111005
\(715\) 0 0
\(716\) −6.19029 −0.231342
\(717\) −12.6453 7.30074i −0.472246 0.272651i
\(718\) 3.71044 6.42667i 0.138472 0.239841i
\(719\) −13.0073 22.5293i −0.485090 0.840201i 0.514763 0.857333i \(-0.327880\pi\)
−0.999853 + 0.0171315i \(0.994547\pi\)
\(720\) 0.704103i 0.0262404i
\(721\) 20.8838 12.0573i 0.777754 0.449036i
\(722\) −4.68664 + 2.70583i −0.174419 + 0.100701i
\(723\) 8.63102i 0.320991i
\(724\) −12.1506 21.0455i −0.451575 0.782151i
\(725\) 14.6664 25.4029i 0.544695 0.943440i
\(726\) 8.07607 + 4.66272i 0.299731 + 0.173050i
\(727\) 16.5472 0.613701 0.306851 0.951758i \(-0.400725\pi\)
0.306851 + 0.951758i \(0.400725\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0.700305 + 0.404321i 0.0259194 + 0.0149646i
\(731\) 3.25786 5.64279i 0.120496 0.208706i
\(732\) 7.67241 + 13.2890i 0.283580 + 0.491176i
\(733\) 18.8750i 0.697165i 0.937278 + 0.348582i \(0.113337\pi\)
−0.937278 + 0.348582i \(0.886663\pi\)
\(734\) −0.454514 + 0.262414i −0.0167764 + 0.00968586i
\(735\) −0.839931 + 0.484935i −0.0309813 + 0.0178871i
\(736\) 38.8267i 1.43117i
\(737\) −16.8475 29.1807i −0.620586 1.07489i
\(738\) 0.0990311 0.171527i 0.00364539 0.00631399i
\(739\) 40.9837 + 23.6619i 1.50761 + 0.870419i 0.999961 + 0.00885483i \(0.00281862\pi\)
0.507649 + 0.861564i \(0.330515\pi\)
\(740\) −1.42327 −0.0523205
\(741\) 0 0
\(742\) −0.827757 −0.0303879
\(743\) 7.69697 + 4.44385i 0.282374 + 0.163029i 0.634498 0.772925i \(-0.281207\pi\)
−0.352124 + 0.935954i \(0.614540\pi\)
\(744\) 4.45742 7.72048i 0.163417 0.283046i
\(745\) 1.90030 + 3.29142i 0.0696218 + 0.120588i
\(746\) 13.3924i 0.490331i
\(747\) −8.82132 + 5.09299i −0.322755 + 0.186343i
\(748\) −33.5381 + 19.3632i −1.22627 + 0.707990i
\(749\) 22.4685i 0.820980i
\(750\) −0.546229 0.946096i −0.0199455 0.0345466i
\(751\) 0.355404 0.615578i 0.0129689 0.0224627i −0.859468 0.511189i \(-0.829205\pi\)
0.872437 + 0.488727i \(0.162538\pi\)
\(752\) −16.6295 9.60106i −0.606416 0.350114i
\(753\) 3.80194 0.138550
\(754\) 0 0
\(755\) 0.907542 0.0330288
\(756\) 2.73563 + 1.57942i 0.0994939 + 0.0574428i
\(757\) −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
\(759\) 47.1715i 1.71222i
\(760\) 2.02021 1.16637i 0.0732806 0.0423086i
\(761\) 16.3514 9.44049i 0.592738 0.342218i −0.173441 0.984844i \(-0.555489\pi\)
0.766180 + 0.642627i \(0.222155\pi\)
\(762\) 4.80625i 0.174112i
\(763\) −10.6468 18.4407i −0.385438 0.667599i
\(764\) 1.17241 2.03067i 0.0424162 0.0734670i
\(765\) 0.813199 + 0.469501i 0.0294013 + 0.0169748i
\(766\) 6.84846 0.247445
\(767\) 0 0
\(768\) 2.40150 0.0866567
\(769\) 10.7689 + 6.21744i 0.388337 + 0.224207i 0.681439 0.731875i \(-0.261354\pi\)
−0.293102 + 0.956081i \(0.594688\pi\)
\(770\) 0.544605 0.943284i 0.0196262 0.0339936i
\(771\) −10.2981 17.8368i −0.370875 0.642375i
\(772\) 16.5700i 0.596368i
\(773\) 39.5553 22.8373i 1.42271 0.821400i 0.426177 0.904640i \(-0.359860\pi\)
0.996530 + 0.0832399i \(0.0265268\pi\)
\(774\) −0.660525 + 0.381355i −0.0237421 + 0.0137075i
\(775\) 26.0224i 0.934751i
\(776\) −11.5816 20.0599i −0.415754 0.720107i
\(777\) 2.80313 4.85517i 0.100562 0.174178i
\(778\) −9.26215 5.34750i −0.332064 0.191717i
\(779\) −2.48427 −0.0890082
\(780\)