Properties

Label 546.2.s.e.127.3
Level $546$
Weight $2$
Character 546.127
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.195105024.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 4 x^{5} - 20 x^{4} + 12 x^{3} + 45 x^{2} - 108 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 127.3
Root \(1.72124 - 0.193255i\) of defining polynomial
Character \(\chi\) \(=\) 546.127
Dual form 546.2.s.e.43.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.78801i q^{5} +(0.866025 + 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.78801i q^{5} +(0.866025 + 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.894007 - 1.54846i) q^{10} +(2.74922 - 1.58726i) q^{11} +1.00000 q^{12} +(1.47952 + 3.28801i) q^{13} +1.00000 q^{14} +(1.54846 - 0.894007i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.78052 - 4.81599i) q^{17} +1.00000i q^{18} +(-5.36028 - 3.09476i) q^{19} +(-1.54846 - 0.894007i) q^{20} +1.00000i q^{21} +(1.58726 - 2.74922i) q^{22} +(3.06678 + 5.31181i) q^{23} +(0.866025 - 0.500000i) q^{24} +1.80301 q^{25} +(2.92531 + 2.10774i) q^{26} -1.00000 q^{27} +(0.866025 - 0.500000i) q^{28} +(-1.03880 - 1.79925i) q^{29} +(0.894007 - 1.54846i) q^{30} -5.63862i q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.74922 + 1.58726i) q^{33} -5.56103i q^{34} +(0.894007 - 1.54846i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-2.68202 + 1.54846i) q^{37} -6.18952 q^{38} +(-2.10774 + 2.92531i) q^{39} -1.78801 q^{40} +(-1.29768 + 0.749217i) q^{41} +(0.500000 + 0.866025i) q^{42} +(-4.81931 + 8.34729i) q^{43} -3.17452i q^{44} +(1.54846 + 0.894007i) q^{45} +(5.31181 + 3.06678i) q^{46} +10.5086i q^{47} +(0.500000 - 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(1.56145 - 0.901504i) q^{50} +5.56103 q^{51} +(3.58726 + 0.362708i) q^{52} +3.60200 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-2.83804 - 4.91564i) q^{55} +(0.500000 - 0.866025i) q^{56} -6.18952i q^{57} +(-1.79925 - 1.03880i) q^{58} +(-2.40874 - 1.39069i) q^{59} -1.78801i q^{60} +(-0.844395 + 1.46254i) q^{61} +(-2.81931 - 4.88319i) q^{62} +(-0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(5.87901 - 2.64539i) q^{65} +3.17452 q^{66} +(-10.0064 + 5.77720i) q^{67} +(-2.78052 - 4.81599i) q^{68} +(-3.06678 + 5.31181i) q^{69} -1.78801i q^{70} +(-0.518313 - 0.299248i) q^{71} +(0.866025 + 0.500000i) q^{72} -0.423973i q^{73} +(-1.54846 + 2.68202i) q^{74} +(0.901504 + 1.56145i) q^{75} +(-5.36028 + 3.09476i) q^{76} +3.17452 q^{77} +(-0.362708 + 3.58726i) q^{78} +6.96254 q^{79} +(-1.54846 + 0.894007i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.749217 + 1.29768i) q^{82} +4.30228i q^{83} +(0.866025 + 0.500000i) q^{84} +(-8.61106 - 4.97160i) q^{85} +9.63862i q^{86} +(1.03880 - 1.79925i) q^{87} +(-1.58726 - 2.74922i) q^{88} +(-14.1102 + 8.14654i) q^{89} +1.78801 q^{90} +(-0.362708 + 3.58726i) q^{91} +6.13356 q^{92} +(4.88319 - 2.81931i) q^{93} +(5.25429 + 9.10069i) q^{94} +(-5.53347 + 9.58425i) q^{95} -1.00000i q^{96} +(-15.1461 - 8.74462i) q^{97} +(0.866025 + 0.500000i) q^{98} +3.17452i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} + 4q^{4} - 4q^{9} + O(q^{10}) \) \( 8q + 4q^{3} + 4q^{4} - 4q^{9} + 6q^{10} + 6q^{11} + 8q^{12} + 12q^{13} + 8q^{14} + 6q^{15} - 4q^{16} + 2q^{17} - 12q^{19} - 6q^{20} - 4q^{22} + 8q^{23} - 24q^{25} + 6q^{26} - 8q^{27} + 2q^{29} - 6q^{30} + 6q^{33} - 6q^{35} + 4q^{36} + 18q^{37} - 4q^{38} + 12q^{40} + 12q^{41} + 4q^{42} - 8q^{43} + 6q^{45} + 18q^{46} + 4q^{48} + 4q^{49} + 12q^{50} + 4q^{51} + 12q^{52} - 12q^{53} - 22q^{55} + 4q^{56} - 24q^{58} + 18q^{59} - 8q^{61} + 8q^{62} - 8q^{64} + 46q^{65} - 8q^{66} + 18q^{67} - 2q^{68} - 8q^{69} + 6q^{71} - 6q^{74} - 12q^{75} - 12q^{76} - 8q^{77} + 6q^{78} - 4q^{79} - 6q^{80} - 4q^{81} + 10q^{82} - 54q^{85} - 2q^{87} + 4q^{88} - 18q^{89} - 12q^{90} + 6q^{91} + 16q^{92} + 30q^{93} - 2q^{94} - 50q^{95} - 54q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.78801i 0.799624i −0.916597 0.399812i \(-0.869075\pi\)
0.916597 0.399812i \(-0.130925\pi\)
\(6\) 0.866025 + 0.500000i 0.353553 + 0.204124i
\(7\) 0.866025 + 0.500000i 0.327327 + 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.894007 1.54846i −0.282710 0.489668i
\(11\) 2.74922 1.58726i 0.828920 0.478577i −0.0245627 0.999698i \(-0.507819\pi\)
0.853483 + 0.521121i \(0.174486\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.47952 + 3.28801i 0.410344 + 0.911931i
\(14\) 1.00000 0.267261
\(15\) 1.54846 0.894007i 0.399812 0.230832i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.78052 4.81599i 0.674374 1.16805i −0.302277 0.953220i \(-0.597747\pi\)
0.976651 0.214830i \(-0.0689198\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −5.36028 3.09476i −1.22973 0.709986i −0.262758 0.964862i \(-0.584632\pi\)
−0.966974 + 0.254875i \(0.917966\pi\)
\(20\) −1.54846 0.894007i −0.346247 0.199906i
\(21\) 1.00000i 0.218218i
\(22\) 1.58726 2.74922i 0.338405 0.586135i
\(23\) 3.06678 + 5.31181i 0.639467 + 1.10759i 0.985550 + 0.169386i \(0.0541784\pi\)
−0.346083 + 0.938204i \(0.612488\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 1.80301 0.360602
\(26\) 2.92531 + 2.10774i 0.573700 + 0.413363i
\(27\) −1.00000 −0.192450
\(28\) 0.866025 0.500000i 0.163663 0.0944911i
\(29\) −1.03880 1.79925i −0.192900 0.334112i 0.753310 0.657665i \(-0.228456\pi\)
−0.946210 + 0.323553i \(0.895123\pi\)
\(30\) 0.894007 1.54846i 0.163223 0.282710i
\(31\) 5.63862i 1.01273i −0.862320 0.506363i \(-0.830989\pi\)
0.862320 0.506363i \(-0.169011\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 2.74922 + 1.58726i 0.478577 + 0.276307i
\(34\) 5.56103i 0.953709i
\(35\) 0.894007 1.54846i 0.151115 0.261738i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −2.68202 + 1.54846i −0.440921 + 0.254566i −0.703988 0.710211i \(-0.748599\pi\)
0.263067 + 0.964778i \(0.415266\pi\)
\(38\) −6.18952 −1.00407
\(39\) −2.10774 + 2.92531i −0.337509 + 0.468424i
\(40\) −1.78801 −0.282710
\(41\) −1.29768 + 0.749217i −0.202664 + 0.117008i −0.597897 0.801573i \(-0.703997\pi\)
0.395234 + 0.918581i \(0.370664\pi\)
\(42\) 0.500000 + 0.866025i 0.0771517 + 0.133631i
\(43\) −4.81931 + 8.34729i −0.734938 + 1.27295i 0.219812 + 0.975542i \(0.429456\pi\)
−0.954750 + 0.297408i \(0.903878\pi\)
\(44\) 3.17452i 0.478577i
\(45\) 1.54846 + 0.894007i 0.230832 + 0.133271i
\(46\) 5.31181 + 3.06678i 0.783184 + 0.452172i
\(47\) 10.5086i 1.53283i 0.642344 + 0.766416i \(0.277962\pi\)
−0.642344 + 0.766416i \(0.722038\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) 1.56145 0.901504i 0.220823 0.127492i
\(51\) 5.56103 0.778700
\(52\) 3.58726 + 0.362708i 0.497464 + 0.0502985i
\(53\) 3.60200 0.494773 0.247386 0.968917i \(-0.420428\pi\)
0.247386 + 0.968917i \(0.420428\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) −2.83804 4.91564i −0.382682 0.662824i
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 6.18952i 0.819822i
\(58\) −1.79925 1.03880i −0.236253 0.136401i
\(59\) −2.40874 1.39069i −0.313592 0.181052i 0.334941 0.942239i \(-0.391284\pi\)
−0.648533 + 0.761187i \(0.724617\pi\)
\(60\) 1.78801i 0.230832i
\(61\) −0.844395 + 1.46254i −0.108114 + 0.187259i −0.915006 0.403440i \(-0.867814\pi\)
0.806892 + 0.590699i \(0.201148\pi\)
\(62\) −2.81931 4.88319i −0.358053 0.620166i
\(63\) −0.866025 + 0.500000i −0.109109 + 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) 5.87901 2.64539i 0.729202 0.328121i
\(66\) 3.17452 0.390757
\(67\) −10.0064 + 5.77720i −1.22248 + 0.705797i −0.965445 0.260606i \(-0.916078\pi\)
−0.257031 + 0.966403i \(0.582744\pi\)
\(68\) −2.78052 4.81599i −0.337187 0.584025i
\(69\) −3.06678 + 5.31181i −0.369197 + 0.639467i
\(70\) 1.78801i 0.213708i
\(71\) −0.518313 0.299248i −0.0615124 0.0355142i 0.468928 0.883236i \(-0.344640\pi\)
−0.530441 + 0.847722i \(0.677974\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 0.423973i 0.0496223i −0.999692 0.0248112i \(-0.992102\pi\)
0.999692 0.0248112i \(-0.00789845\pi\)
\(74\) −1.54846 + 2.68202i −0.180005 + 0.311778i
\(75\) 0.901504 + 1.56145i 0.104097 + 0.180301i
\(76\) −5.36028 + 3.09476i −0.614866 + 0.354993i
\(77\) 3.17452 0.361770
\(78\) −0.362708 + 3.58726i −0.0410686 + 0.406177i
\(79\) 6.96254 0.783346 0.391673 0.920104i \(-0.371896\pi\)
0.391673 + 0.920104i \(0.371896\pi\)
\(80\) −1.54846 + 0.894007i −0.173124 + 0.0999530i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −0.749217 + 1.29768i −0.0827372 + 0.143305i
\(83\) 4.30228i 0.472237i 0.971724 + 0.236118i \(0.0758753\pi\)
−0.971724 + 0.236118i \(0.924125\pi\)
\(84\) 0.866025 + 0.500000i 0.0944911 + 0.0545545i
\(85\) −8.61106 4.97160i −0.934001 0.539246i
\(86\) 9.63862i 1.03936i
\(87\) 1.03880 1.79925i 0.111371 0.192900i
\(88\) −1.58726 2.74922i −0.169203 0.293068i
\(89\) −14.1102 + 8.14654i −1.49568 + 0.863532i −0.999988 0.00496618i \(-0.998419\pi\)
−0.495693 + 0.868498i \(0.665086\pi\)
\(90\) 1.78801 0.188473
\(91\) −0.362708 + 3.58726i −0.0380221 + 0.376047i
\(92\) 6.13356 0.639467
\(93\) 4.88319 2.81931i 0.506363 0.292349i
\(94\) 5.25429 + 9.10069i 0.541938 + 0.938665i
\(95\) −5.53347 + 9.58425i −0.567722 + 0.983323i
\(96\) 1.00000i 0.102062i
\(97\) −15.1461 8.74462i −1.53786 0.887881i −0.998964 0.0455062i \(-0.985510\pi\)
−0.538892 0.842375i \(-0.681157\pi\)
\(98\) 0.866025 + 0.500000i 0.0874818 + 0.0505076i
\(99\) 3.17452i 0.319052i
\(100\) 0.901504 1.56145i 0.0901504 0.156145i
\(101\) −2.03433 3.52357i −0.202424 0.350608i 0.746885 0.664953i \(-0.231548\pi\)
−0.949309 + 0.314345i \(0.898215\pi\)
\(102\) 4.81599 2.78052i 0.476855 0.275312i
\(103\) −18.0768 −1.78116 −0.890578 0.454831i \(-0.849700\pi\)
−0.890578 + 0.454831i \(0.849700\pi\)
\(104\) 3.28801 1.47952i 0.322416 0.145079i
\(105\) 1.78801 0.174492
\(106\) 3.11942 1.80100i 0.302985 0.174929i
\(107\) 0.770847 + 1.33515i 0.0745206 + 0.129073i 0.900878 0.434073i \(-0.142924\pi\)
−0.826357 + 0.563146i \(0.809591\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 7.37731i 0.706618i −0.935507 0.353309i \(-0.885056\pi\)
0.935507 0.353309i \(-0.114944\pi\)
\(110\) −4.91564 2.83804i −0.468688 0.270597i
\(111\) −2.68202 1.54846i −0.254566 0.146974i
\(112\) 1.00000i 0.0944911i
\(113\) 4.95660 8.58509i 0.466278 0.807617i −0.532980 0.846128i \(-0.678928\pi\)
0.999258 + 0.0385104i \(0.0122613\pi\)
\(114\) −3.09476 5.36028i −0.289851 0.502036i
\(115\) 9.49759 5.48344i 0.885655 0.511333i
\(116\) −2.07759 −0.192900
\(117\) −3.58726 0.362708i −0.331642 0.0335324i
\(118\) −2.78138 −0.256047
\(119\) 4.81599 2.78052i 0.441481 0.254889i
\(120\) −0.894007 1.54846i −0.0816113 0.141355i
\(121\) −0.461204 + 0.798828i −0.0419276 + 0.0726208i
\(122\) 1.68879i 0.152896i
\(123\) −1.29768 0.749217i −0.117008 0.0675546i
\(124\) −4.88319 2.81931i −0.438524 0.253182i
\(125\) 12.1639i 1.08797i
\(126\) −0.500000 + 0.866025i −0.0445435 + 0.0771517i
\(127\) 9.17452 + 15.8907i 0.814107 + 1.41008i 0.909967 + 0.414680i \(0.136107\pi\)
−0.0958600 + 0.995395i \(0.530560\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −9.63862 −0.848634
\(130\) 3.76868 5.23048i 0.330535 0.458744i
\(131\) 5.91928 0.517170 0.258585 0.965989i \(-0.416744\pi\)
0.258585 + 0.965989i \(0.416744\pi\)
\(132\) 2.74922 1.58726i 0.239289 0.138153i
\(133\) −3.09476 5.36028i −0.268350 0.464795i
\(134\) −5.77720 + 10.0064i −0.499074 + 0.864421i
\(135\) 1.78801i 0.153888i
\(136\) −4.81599 2.78052i −0.412968 0.238427i
\(137\) 7.62363 + 4.40150i 0.651331 + 0.376046i 0.788966 0.614437i \(-0.210617\pi\)
−0.137635 + 0.990483i \(0.543950\pi\)
\(138\) 6.13356i 0.522123i
\(139\) −9.48720 + 16.4323i −0.804694 + 1.39377i 0.111804 + 0.993730i \(0.464337\pi\)
−0.916498 + 0.400040i \(0.868996\pi\)
\(140\) −0.894007 1.54846i −0.0755574 0.130869i
\(141\) −9.10069 + 5.25429i −0.766416 + 0.442491i
\(142\) −0.598496 −0.0502247
\(143\) 9.28645 + 6.69108i 0.776572 + 0.559537i
\(144\) 1.00000 0.0833333
\(145\) −3.21708 + 1.85738i −0.267164 + 0.154247i
\(146\) −0.211987 0.367172i −0.0175441 0.0303873i
\(147\) −0.500000 + 0.866025i −0.0412393 + 0.0714286i
\(148\) 3.09693i 0.254566i
\(149\) 12.0919 + 6.98127i 0.990608 + 0.571928i 0.905456 0.424440i \(-0.139529\pi\)
0.0851520 + 0.996368i \(0.472862\pi\)
\(150\) 1.56145 + 0.901504i 0.127492 + 0.0736075i
\(151\) 17.8426i 1.45201i −0.687688 0.726006i \(-0.741374\pi\)
0.687688 0.726006i \(-0.258626\pi\)
\(152\) −3.09476 + 5.36028i −0.251018 + 0.434776i
\(153\) 2.78052 + 4.81599i 0.224791 + 0.389350i
\(154\) 2.74922 1.58726i 0.221538 0.127905i
\(155\) −10.0819 −0.809800
\(156\) 1.47952 + 3.28801i 0.118456 + 0.263252i
\(157\) 4.57916 0.365457 0.182728 0.983163i \(-0.441507\pi\)
0.182728 + 0.983163i \(0.441507\pi\)
\(158\) 6.02973 3.48127i 0.479700 0.276955i
\(159\) 1.80100 + 3.11942i 0.142829 + 0.247386i
\(160\) −0.894007 + 1.54846i −0.0706774 + 0.122417i
\(161\) 6.13356i 0.483392i
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) 10.6267 + 6.13531i 0.832344 + 0.480554i 0.854655 0.519197i \(-0.173769\pi\)
−0.0223103 + 0.999751i \(0.507102\pi\)
\(164\) 1.49843i 0.117008i
\(165\) 2.83804 4.91564i 0.220941 0.382682i
\(166\) 2.15114 + 3.72589i 0.166961 + 0.289185i
\(167\) 14.4610 8.34904i 1.11902 0.646068i 0.177872 0.984054i \(-0.443079\pi\)
0.941151 + 0.337985i \(0.109745\pi\)
\(168\) 1.00000 0.0771517
\(169\) −8.62206 + 9.72934i −0.663236 + 0.748411i
\(170\) −9.94320 −0.762609
\(171\) 5.36028 3.09476i 0.409911 0.236662i
\(172\) 4.81931 + 8.34729i 0.367469 + 0.636475i
\(173\) 3.68865 6.38894i 0.280443 0.485742i −0.691051 0.722806i \(-0.742852\pi\)
0.971494 + 0.237064i \(0.0761852\pi\)
\(174\) 2.07759i 0.157502i
\(175\) 1.56145 + 0.901504i 0.118035 + 0.0681473i
\(176\) −2.74922 1.58726i −0.207230 0.119644i
\(177\) 2.78138i 0.209061i
\(178\) −8.14654 + 14.1102i −0.610609 + 1.05761i
\(179\) 9.91008 + 17.1648i 0.740714 + 1.28295i 0.952171 + 0.305567i \(0.0988459\pi\)
−0.211457 + 0.977387i \(0.567821\pi\)
\(180\) 1.54846 0.894007i 0.115416 0.0666353i
\(181\) −18.3266 −1.36220 −0.681102 0.732189i \(-0.738499\pi\)
−0.681102 + 0.732189i \(0.738499\pi\)
\(182\) 1.47952 + 3.28801i 0.109669 + 0.243724i
\(183\) −1.68879 −0.124839
\(184\) 5.31181 3.06678i 0.391592 0.226086i
\(185\) 2.76868 + 4.79549i 0.203557 + 0.352571i
\(186\) 2.81931 4.88319i 0.206722 0.358053i
\(187\) 17.6536i 1.29096i
\(188\) 9.10069 + 5.25429i 0.663736 + 0.383208i
\(189\) −0.866025 0.500000i −0.0629941 0.0363696i
\(190\) 11.0669i 0.802880i
\(191\) 7.51518 13.0167i 0.543779 0.941854i −0.454903 0.890541i \(-0.650326\pi\)
0.998683 0.0513127i \(-0.0163405\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −4.72408 + 2.72745i −0.340047 + 0.196326i −0.660293 0.751008i \(-0.729568\pi\)
0.320246 + 0.947334i \(0.396234\pi\)
\(194\) −17.4892 −1.25565
\(195\) 5.23048 + 3.76868i 0.374563 + 0.269880i
\(196\) 1.00000 0.0714286
\(197\) −6.60751 + 3.81485i −0.470766 + 0.271797i −0.716560 0.697525i \(-0.754284\pi\)
0.245795 + 0.969322i \(0.420951\pi\)
\(198\) 1.58726 + 2.74922i 0.112802 + 0.195378i
\(199\) 2.99512 5.18769i 0.212318 0.367746i −0.740121 0.672473i \(-0.765232\pi\)
0.952440 + 0.304727i \(0.0985653\pi\)
\(200\) 1.80301i 0.127492i
\(201\) −10.0064 5.77720i −0.705797 0.407492i
\(202\) −3.52357 2.03433i −0.247917 0.143135i
\(203\) 2.07759i 0.145818i
\(204\) 2.78052 4.81599i 0.194675 0.337187i
\(205\) 1.33961 + 2.32027i 0.0935624 + 0.162055i
\(206\) −15.6549 + 9.03838i −1.09073 + 0.629734i
\(207\) −6.13356 −0.426312
\(208\) 2.10774 2.92531i 0.146146 0.202833i
\(209\) −19.6488 −1.35913
\(210\) 1.54846 0.894007i 0.106854 0.0616923i
\(211\) 1.38651 + 2.40150i 0.0954512 + 0.165326i 0.909797 0.415054i \(-0.136237\pi\)
−0.814346 + 0.580380i \(0.802904\pi\)
\(212\) 1.80100 3.11942i 0.123693 0.214243i
\(213\) 0.598496i 0.0410083i
\(214\) 1.33515 + 0.770847i 0.0912687 + 0.0526940i
\(215\) 14.9251 + 8.61699i 1.01788 + 0.587674i
\(216\) 1.00000i 0.0680414i
\(217\) 2.81931 4.88319i 0.191387 0.331493i
\(218\) −3.68865 6.38894i −0.249827 0.432713i
\(219\) 0.367172 0.211987i 0.0248112 0.0143247i
\(220\) −5.67609 −0.382682
\(221\) 19.9489 + 2.01703i 1.34191 + 0.135680i
\(222\) −3.09693 −0.207852
\(223\) 19.5163 11.2677i 1.30691 0.754542i 0.325327 0.945602i \(-0.394526\pi\)
0.981578 + 0.191060i \(0.0611924\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) −0.901504 + 1.56145i −0.0601003 + 0.104097i
\(226\) 9.91321i 0.659417i
\(227\) −1.58616 0.915773i −0.105277 0.0607820i 0.446437 0.894815i \(-0.352693\pi\)
−0.551714 + 0.834033i \(0.686026\pi\)
\(228\) −5.36028 3.09476i −0.354993 0.204955i
\(229\) 22.6060i 1.49385i −0.664910 0.746924i \(-0.731530\pi\)
0.664910 0.746924i \(-0.268470\pi\)
\(230\) 5.48344 9.49759i 0.361567 0.626253i
\(231\) 1.58726 + 2.74922i 0.104434 + 0.180885i
\(232\) −1.79925 + 1.03880i −0.118126 + 0.0682003i
\(233\) −9.43897 −0.618367 −0.309184 0.951002i \(-0.600056\pi\)
−0.309184 + 0.951002i \(0.600056\pi\)
\(234\) −3.28801 + 1.47952i −0.214944 + 0.0967190i
\(235\) 18.7895 1.22569
\(236\) −2.40874 + 1.39069i −0.156796 + 0.0905262i
\(237\) 3.48127 + 6.02973i 0.226133 + 0.391673i
\(238\) 2.78052 4.81599i 0.180234 0.312175i
\(239\) 15.8757i 1.02692i −0.858115 0.513458i \(-0.828364\pi\)
0.858115 0.513458i \(-0.171636\pi\)
\(240\) −1.54846 0.894007i −0.0999530 0.0577079i
\(241\) 20.7197 + 11.9625i 1.33467 + 0.770575i 0.986012 0.166674i \(-0.0533027\pi\)
0.348662 + 0.937248i \(0.386636\pi\)
\(242\) 0.922407i 0.0592946i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0.844395 + 1.46254i 0.0540569 + 0.0936293i
\(245\) 1.54846 0.894007i 0.0989278 0.0571160i
\(246\) −1.49843 −0.0955367
\(247\) 2.24499 22.2034i 0.142845 1.41277i
\(248\) −5.63862 −0.358053
\(249\) −3.72589 + 2.15114i −0.236118 + 0.136323i
\(250\) −6.08193 10.5342i −0.384655 0.666243i
\(251\) −10.2618 + 17.7739i −0.647718 + 1.12188i 0.335949 + 0.941880i \(0.390943\pi\)
−0.983667 + 0.180000i \(0.942390\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) 16.8625 + 9.73555i 1.06013 + 0.612069i
\(254\) 15.8907 + 9.17452i 0.997074 + 0.575661i
\(255\) 9.94320i 0.622667i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.413344 0.715933i −0.0257837 0.0446587i 0.852846 0.522163i \(-0.174875\pi\)
−0.878629 + 0.477504i \(0.841541\pi\)
\(258\) −8.34729 + 4.81931i −0.519680 + 0.300037i
\(259\) −3.09693 −0.192434
\(260\) 0.648527 6.41407i 0.0402199 0.397784i
\(261\) 2.07759 0.128600
\(262\) 5.12624 2.95964i 0.316700 0.182847i
\(263\) −10.1805 17.6331i −0.627754 1.08730i −0.988001 0.154445i \(-0.950641\pi\)
0.360248 0.932857i \(-0.382692\pi\)
\(264\) 1.58726 2.74922i 0.0976892 0.169203i
\(265\) 6.44042i 0.395632i
\(266\) −5.36028 3.09476i −0.328660 0.189752i
\(267\) −14.1102 8.14654i −0.863532 0.498560i
\(268\) 11.5544i 0.705797i
\(269\) 10.2587 17.7687i 0.625487 1.08338i −0.362959 0.931805i \(-0.618234\pi\)
0.988446 0.151570i \(-0.0484330\pi\)
\(270\) 0.894007 + 1.54846i 0.0544075 + 0.0942366i
\(271\) −10.5495 + 6.09076i −0.640837 + 0.369988i −0.784937 0.619576i \(-0.787305\pi\)
0.144100 + 0.989563i \(0.453971\pi\)
\(272\) −5.56103 −0.337187
\(273\) −3.28801 + 1.47952i −0.199000 + 0.0895444i
\(274\) 8.80301 0.531809
\(275\) 4.95686 2.86185i 0.298910 0.172576i
\(276\) 3.06678 + 5.31181i 0.184598 + 0.319734i
\(277\) 4.31242 7.46933i 0.259108 0.448789i −0.706895 0.707318i \(-0.749905\pi\)
0.966003 + 0.258530i \(0.0832380\pi\)
\(278\) 18.9744i 1.13801i
\(279\) 4.88319 + 2.81931i 0.292349 + 0.168788i
\(280\) −1.54846 0.894007i −0.0925385 0.0534271i
\(281\) 24.2922i 1.44915i −0.689194 0.724577i \(-0.742035\pi\)
0.689194 0.724577i \(-0.257965\pi\)
\(282\) −5.25429 + 9.10069i −0.312888 + 0.541938i
\(283\) 5.36054 + 9.28472i 0.318651 + 0.551919i 0.980207 0.197976i \(-0.0634369\pi\)
−0.661556 + 0.749896i \(0.730104\pi\)
\(284\) −0.518313 + 0.299248i −0.0307562 + 0.0177571i
\(285\) −11.0669 −0.655549
\(286\) 11.3878 + 1.15142i 0.673377 + 0.0680852i
\(287\) −1.49843 −0.0884498
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) −6.96254 12.0595i −0.409561 0.709380i
\(290\) −1.85738 + 3.21708i −0.109069 + 0.188913i
\(291\) 17.4892i 1.02524i
\(292\) −0.367172 0.211987i −0.0214871 0.0124056i
\(293\) −18.5571 10.7139i −1.08412 0.625914i −0.152112 0.988363i \(-0.548607\pi\)
−0.932004 + 0.362449i \(0.881941\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) −2.48657 + 4.30687i −0.144774 + 0.250755i
\(296\) 1.54846 + 2.68202i 0.0900027 + 0.155889i
\(297\) −2.74922 + 1.58726i −0.159526 + 0.0921022i
\(298\) 13.9625 0.808828
\(299\) −12.9280 + 17.9425i −0.747644 + 1.03764i
\(300\) 1.80301 0.104097
\(301\) −8.34729 + 4.81931i −0.481130 + 0.277781i
\(302\) −8.92131 15.4522i −0.513364 0.889172i
\(303\) 2.03433 3.52357i 0.116869 0.202424i
\(304\) 6.18952i 0.354993i
\(305\) 2.61503 + 1.50979i 0.149736 + 0.0864503i
\(306\) 4.81599 + 2.78052i 0.275312 + 0.158952i
\(307\) 7.59364i 0.433392i 0.976239 + 0.216696i \(0.0695280\pi\)
−0.976239 + 0.216696i \(0.930472\pi\)
\(308\) 1.58726 2.74922i 0.0904426 0.156651i
\(309\) −9.03838 15.6549i −0.514175 0.890578i
\(310\) −8.73121 + 5.04097i −0.495899 + 0.286308i
\(311\) 25.6355 1.45366 0.726828 0.686820i \(-0.240994\pi\)
0.726828 + 0.686820i \(0.240994\pi\)
\(312\) 2.92531 + 2.10774i 0.165613 + 0.119328i
\(313\) −1.71308 −0.0968293 −0.0484146 0.998827i \(-0.515417\pi\)
−0.0484146 + 0.998827i \(0.515417\pi\)
\(314\) 3.96567 2.28958i 0.223796 0.129208i
\(315\) 0.894007 + 1.54846i 0.0503716 + 0.0872461i
\(316\) 3.48127 6.02973i 0.195837 0.339199i
\(317\) 33.2098i 1.86525i −0.360850 0.932624i \(-0.617513\pi\)
0.360850 0.932624i \(-0.382487\pi\)
\(318\) 3.11942 + 1.80100i 0.174929 + 0.100995i
\(319\) −5.71175 3.29768i −0.319797 0.184635i
\(320\) 1.78801i 0.0999530i
\(321\) −0.770847 + 1.33515i −0.0430245 + 0.0745206i
\(322\) 3.06678 + 5.31181i 0.170905 + 0.296016i
\(323\) −29.8087 + 17.2101i −1.65860 + 0.957593i
\(324\) −1.00000 −0.0555556
\(325\) 2.66758 + 5.92832i 0.147971 + 0.328844i
\(326\) 12.2706 0.679606
\(327\) 6.38894 3.68865i 0.353309 0.203983i
\(328\) 0.749217 + 1.29768i 0.0413686 + 0.0716525i
\(329\) −5.25429 + 9.10069i −0.289678 + 0.501737i
\(330\) 5.67609i 0.312458i
\(331\) 4.29537 + 2.47994i 0.236095 + 0.136310i 0.613381 0.789787i \(-0.289809\pi\)
−0.377286 + 0.926097i \(0.623142\pi\)
\(332\) 3.72589 + 2.15114i 0.204485 + 0.118059i
\(333\) 3.09693i 0.169711i
\(334\) 8.34904 14.4610i 0.456839 0.791269i
\(335\) 10.3297 + 17.8916i 0.564372 + 0.977521i
\(336\) 0.866025 0.500000i 0.0472456 0.0272772i
\(337\) 23.6174 1.28652 0.643260 0.765648i \(-0.277581\pi\)
0.643260 + 0.765648i \(0.277581\pi\)
\(338\) −2.60226 + 12.7369i −0.141544 + 0.692795i
\(339\) 9.91321 0.538412
\(340\) −8.61106 + 4.97160i −0.467000 + 0.269623i
\(341\) −8.94997 15.5018i −0.484668 0.839470i
\(342\) 3.09476 5.36028i 0.167345 0.289851i
\(343\) 1.00000i 0.0539949i
\(344\) 8.34729 + 4.81931i 0.450056 + 0.259840i
\(345\) 9.49759 + 5.48344i 0.511333 + 0.295218i
\(346\) 7.37731i 0.396607i
\(347\) 3.58483 6.20911i 0.192444 0.333323i −0.753616 0.657315i \(-0.771692\pi\)
0.946060 + 0.323993i \(0.105025\pi\)
\(348\) −1.03880 1.79925i −0.0556853 0.0964498i
\(349\) 10.7155 6.18662i 0.573590 0.331162i −0.184992 0.982740i \(-0.559226\pi\)
0.758582 + 0.651578i \(0.225893\pi\)
\(350\) 1.80301 0.0963749
\(351\) −1.47952 3.28801i −0.0789707 0.175501i
\(352\) −3.17452 −0.169203
\(353\) 22.7018 13.1069i 1.20830 0.697610i 0.245909 0.969293i \(-0.420913\pi\)
0.962387 + 0.271683i \(0.0875801\pi\)
\(354\) −1.39069 2.40874i −0.0739143 0.128023i
\(355\) −0.535059 + 0.926750i −0.0283980 + 0.0491868i
\(356\) 16.2931i 0.863532i
\(357\) 4.81599 + 2.78052i 0.254889 + 0.147160i
\(358\) 17.1648 + 9.91008i 0.907186 + 0.523764i
\(359\) 3.61956i 0.191033i 0.995428 + 0.0955165i \(0.0304503\pi\)
−0.995428 + 0.0955165i \(0.969550\pi\)
\(360\) 0.894007 1.54846i 0.0471183 0.0816113i
\(361\) 9.65506 + 16.7231i 0.508161 + 0.880161i
\(362\) −15.8713 + 9.16329i −0.834176 + 0.481612i
\(363\) −0.922407 −0.0484138
\(364\) 2.92531 + 2.10774i 0.153328 + 0.110476i
\(365\) −0.758070 −0.0396792
\(366\) −1.46254 + 0.844395i −0.0764480 + 0.0441373i
\(367\) 4.03245 + 6.98440i 0.210492 + 0.364583i 0.951869 0.306506i \(-0.0991601\pi\)
−0.741377 + 0.671089i \(0.765827\pi\)
\(368\) 3.06678 5.31181i 0.159867 0.276897i
\(369\) 1.49843i 0.0780054i
\(370\) 4.79549 + 2.76868i 0.249306 + 0.143937i
\(371\) 3.11942 + 1.80100i 0.161952 + 0.0935032i
\(372\) 5.63862i 0.292349i
\(373\) −14.5851 + 25.2621i −0.755187 + 1.30802i 0.190094 + 0.981766i \(0.439121\pi\)
−0.945281 + 0.326257i \(0.894213\pi\)
\(374\) −8.82681 15.2885i −0.456423 0.790549i
\(375\) 10.5342 6.08193i 0.543985 0.314070i
\(376\) 10.5086 0.541938
\(377\) 4.37904 6.07759i 0.225532 0.313012i
\(378\) −1.00000 −0.0514344
\(379\) −23.3797 + 13.4983i −1.20094 + 0.693361i −0.960763 0.277369i \(-0.910538\pi\)
−0.240173 + 0.970730i \(0.577204\pi\)
\(380\) 5.53347 + 9.58425i 0.283861 + 0.491662i
\(381\) −9.17452 + 15.8907i −0.470025 + 0.814107i
\(382\) 15.0304i 0.769020i
\(383\) 22.6159 + 13.0573i 1.15562 + 0.667197i 0.950250 0.311488i \(-0.100827\pi\)
0.205368 + 0.978685i \(0.434161\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 5.67609i 0.289280i
\(386\) −2.72745 + 4.72408i −0.138824 + 0.240450i
\(387\) −4.81931 8.34729i −0.244979 0.424317i
\(388\) −15.1461 + 8.74462i −0.768928 + 0.443941i
\(389\) −32.7110 −1.65852 −0.829258 0.558866i \(-0.811236\pi\)
−0.829258 + 0.558866i \(0.811236\pi\)
\(390\) 6.41407 + 0.648527i 0.324789 + 0.0328394i
\(391\) 34.1089 1.72496
\(392\) 0.866025 0.500000i 0.0437409 0.0252538i
\(393\) 2.95964 + 5.12624i 0.149294 + 0.258585i
\(394\) −3.81485 + 6.60751i −0.192189 + 0.332882i
\(395\) 12.4491i 0.626383i
\(396\) 2.74922 + 1.58726i 0.138153 + 0.0797629i
\(397\) −0.524826 0.303008i −0.0263403 0.0152076i 0.486772 0.873529i \(-0.338174\pi\)
−0.513112 + 0.858321i \(0.671508\pi\)
\(398\) 5.99023i 0.300263i
\(399\) 3.09476 5.36028i 0.154932 0.268350i
\(400\) −0.901504 1.56145i −0.0450752 0.0780726i
\(401\) 8.83963 5.10356i 0.441430 0.254860i −0.262774 0.964857i \(-0.584637\pi\)
0.704204 + 0.709998i \(0.251304\pi\)
\(402\) −11.5544 −0.576281
\(403\) 18.5399 8.34244i 0.923537 0.415566i
\(404\) −4.06866 −0.202424
\(405\) −1.54846 + 0.894007i −0.0769438 + 0.0444235i
\(406\) −1.03880 1.79925i −0.0515546 0.0892952i
\(407\) −4.91564 + 8.51413i −0.243659 + 0.422030i
\(408\) 5.56103i 0.275312i
\(409\) 8.01863 + 4.62956i 0.396496 + 0.228917i 0.684971 0.728570i \(-0.259815\pi\)
−0.288475 + 0.957487i \(0.593148\pi\)
\(410\) 2.32027 + 1.33961i 0.114590 + 0.0661586i
\(411\) 8.80301i 0.434220i
\(412\) −9.03838 + 15.6549i −0.445289 + 0.771263i
\(413\) −1.39069 2.40874i −0.0684313 0.118527i
\(414\) −5.31181 + 3.06678i −0.261061 + 0.150724i
\(415\) 7.69254 0.377612
\(416\) 0.362708 3.58726i 0.0177832 0.175880i
\(417\) −18.9744 −0.929180
\(418\) −17.0163 + 9.82438i −0.832296 + 0.480526i
\(419\) −6.42444 11.1275i −0.313855 0.543612i 0.665339 0.746542i \(-0.268287\pi\)
−0.979193 + 0.202930i \(0.934954\pi\)
\(420\) 0.894007 1.54846i 0.0436231 0.0755574i
\(421\) 7.21371i 0.351575i 0.984428 + 0.175787i \(0.0562471\pi\)
−0.984428 + 0.175787i \(0.943753\pi\)
\(422\) 2.40150 + 1.38651i 0.116903 + 0.0674942i
\(423\) −9.10069 5.25429i −0.442491 0.255472i
\(424\) 3.60200i 0.174929i
\(425\) 5.01329 8.68328i 0.243180 0.421201i
\(426\) −0.299248 0.518313i −0.0144986 0.0251123i
\(427\) −1.46254 + 0.844395i −0.0707771 + 0.0408632i
\(428\) 1.54169 0.0745206
\(429\) −1.15142 + 11.3878i −0.0555913 + 0.549810i
\(430\) 17.2340 0.831097
\(431\) −5.17941 + 2.99033i −0.249483 + 0.144039i −0.619528 0.784975i \(-0.712676\pi\)
0.370044 + 0.929014i \(0.379342\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 6.30144 10.9144i 0.302828 0.524513i −0.673947 0.738779i \(-0.735403\pi\)
0.976775 + 0.214266i \(0.0687359\pi\)
\(434\) 5.63862i 0.270663i
\(435\) −3.21708 1.85738i −0.154247 0.0890546i
\(436\) −6.38894 3.68865i −0.305975 0.176655i
\(437\) 37.9637i 1.81605i
\(438\) 0.211987 0.367172i 0.0101291 0.0175441i
\(439\) 9.77965 + 16.9389i 0.466757 + 0.808447i 0.999279 0.0379690i \(-0.0120888\pi\)
−0.532522 + 0.846416i \(0.678755\pi\)
\(440\) −4.91564 + 2.83804i −0.234344 + 0.135298i
\(441\) −1.00000 −0.0476190
\(442\) 18.2847 8.22764i 0.869717 0.391349i
\(443\) −40.2601 −1.91281 −0.956407 0.292038i \(-0.905666\pi\)
−0.956407 + 0.292038i \(0.905666\pi\)
\(444\) −2.68202 + 1.54846i −0.127283 + 0.0734869i
\(445\) 14.5661 + 25.2293i 0.690500 + 1.19598i
\(446\) 11.2677 19.5163i 0.533542 0.924121i
\(447\) 13.9625i 0.660405i
\(448\) −0.866025 0.500000i −0.0409159 0.0236228i
\(449\) −24.7821 14.3079i −1.16954 0.675234i −0.215967 0.976401i \(-0.569290\pi\)
−0.953571 + 0.301167i \(0.902624\pi\)
\(450\) 1.80301i 0.0849946i
\(451\) −2.37841 + 4.11952i −0.111995 + 0.193981i
\(452\) −4.95660 8.58509i −0.233139 0.403809i
\(453\) 15.4522 8.92131i 0.726006 0.419160i
\(454\) −1.83155 −0.0859587
\(455\) 6.41407 + 0.648527i 0.300696 + 0.0304034i
\(456\) −6.18952 −0.289851
\(457\) 5.49961 3.17520i 0.257261 0.148530i −0.365824 0.930684i \(-0.619213\pi\)
0.623084 + 0.782155i \(0.285879\pi\)
\(458\) −11.3030 19.5774i −0.528155 0.914791i
\(459\) −2.78052 + 4.81599i −0.129783 + 0.224791i
\(460\) 10.9669i 0.511333i
\(461\) 20.9785 + 12.1119i 0.977065 + 0.564109i 0.901383 0.433023i \(-0.142553\pi\)
0.0756821 + 0.997132i \(0.475887\pi\)
\(462\) 2.74922 + 1.58726i 0.127905 + 0.0738461i
\(463\) 17.3851i 0.807954i 0.914769 + 0.403977i \(0.132372\pi\)
−0.914769 + 0.403977i \(0.867628\pi\)
\(464\) −1.03880 + 1.79925i −0.0482249 + 0.0835280i
\(465\) −5.04097 8.73121i −0.233769 0.404900i
\(466\) −8.17439 + 4.71948i −0.378671 + 0.218626i
\(467\) −14.8537 −0.687349 −0.343675 0.939089i \(-0.611672\pi\)
−0.343675 + 0.939089i \(0.611672\pi\)
\(468\) −2.10774 + 2.92531i −0.0974305 + 0.135222i
\(469\) −11.5544 −0.533532
\(470\) 16.2722 9.39473i 0.750579 0.433347i
\(471\) 2.28958 + 3.96567i 0.105498 + 0.182728i
\(472\) −1.39069 + 2.40874i −0.0640117 + 0.110871i
\(473\) 30.5980i 1.40690i
\(474\) 6.02973 + 3.48127i 0.276955 + 0.159900i
\(475\) −9.66463 5.57988i −0.443444 0.256022i
\(476\) 5.56103i 0.254889i
\(477\) −1.80100 + 3.11942i −0.0824621 + 0.142829i
\(478\) −7.93787 13.7488i −0.363070 0.628855i
\(479\) −33.5014 + 19.3420i −1.53072 + 0.883759i −0.531387 + 0.847129i \(0.678329\pi\)
−0.999329 + 0.0366302i \(0.988338\pi\)
\(480\) −1.78801 −0.0816113
\(481\) −9.05947 6.52754i −0.413076 0.297630i
\(482\) 23.9251 1.08976
\(483\) −5.31181 + 3.06678i −0.241696 + 0.139543i
\(484\) 0.461204 + 0.798828i 0.0209638 + 0.0363104i
\(485\) −15.6355 + 27.0815i −0.709971 + 1.22971i
\(486\) 1.00000i 0.0453609i
\(487\) 22.2780 + 12.8622i 1.00951 + 0.582843i 0.911049 0.412298i \(-0.135274\pi\)
0.0984640 + 0.995141i \(0.468607\pi\)
\(488\) 1.46254 + 0.844395i 0.0662059 + 0.0382240i
\(489\) 12.2706i 0.554896i
\(490\) 0.894007 1.54846i 0.0403871 0.0699525i
\(491\) −9.17452 15.8907i −0.414040 0.717139i 0.581287 0.813699i \(-0.302549\pi\)
−0.995327 + 0.0965597i \(0.969216\pi\)
\(492\) −1.29768 + 0.749217i −0.0585040 + 0.0337773i
\(493\) −11.5536 −0.520346
\(494\) −9.15749 20.3512i −0.412015 0.915644i
\(495\) 5.67609 0.255121
\(496\) −4.88319 + 2.81931i −0.219262 + 0.126591i
\(497\) −0.299248 0.518313i −0.0134231 0.0232495i
\(498\) −2.15114 + 3.72589i −0.0963949 + 0.166961i
\(499\) 17.8096i 0.797269i −0.917110 0.398635i \(-0.869484\pi\)
0.917110 0.398635i \(-0.130516\pi\)
\(500\) −10.5342 6.08193i −0.471105 0.271992i
\(501\) 14.4610 + 8.34904i 0.646068 + 0.373008i
\(502\) 20.5236i 0.916012i
\(503\) −15.4711 + 26.7967i −0.689823 + 1.19481i 0.282072 + 0.959393i \(0.408978\pi\)
−0.971895 + 0.235415i \(0.924355\pi\)
\(504\) 0.500000 + 0.866025i 0.0222718 + 0.0385758i
\(505\) −6.30019 + 3.63741i −0.280355 + 0.161863i
\(506\) 19.4711 0.865596
\(507\) −12.7369 2.60226i −0.565665 0.115570i
\(508\) 18.3490 0.814107
\(509\) 11.9583 6.90414i 0.530044 0.306021i −0.210991 0.977488i \(-0.567669\pi\)
0.741034 + 0.671467i \(0.234336\pi\)
\(510\) −4.97160 8.61106i −0.220146 0.381304i
\(511\) 0.211987 0.367172i 0.00937774 0.0162427i
\(512\) 1.00000i 0.0441942i
\(513\) 5.36028 + 3.09476i 0.236662 + 0.136637i
\(514\) −0.715933 0.413344i −0.0315784 0.0182318i
\(515\) 32.3215i 1.42425i
\(516\) −4.81931 + 8.34729i −0.212158 + 0.367469i
\(517\) 16.6798 + 28.8903i 0.733579 + 1.27060i
\(518\) −2.68202 + 1.54846i −0.117841 + 0.0680356i
\(519\) 7.37731 0.323828
\(520\) −2.64539 5.87901i −0.116008 0.257812i
\(521\) −11.4549 −0.501848 −0.250924 0.968007i \(-0.580734\pi\)
−0.250924 + 0.968007i \(0.580734\pi\)
\(522\) 1.79925 1.03880i 0.0787509 0.0454669i
\(523\) −0.465198 0.805747i −0.0203417 0.0352329i 0.855675 0.517513i \(-0.173142\pi\)
−0.876017 + 0.482280i \(0.839809\pi\)
\(524\) 2.95964 5.12624i 0.129292 0.223941i
\(525\) 1.80301i 0.0786897i
\(526\) −17.6331 10.1805i −0.768838 0.443889i
\(527\) −27.1556 15.6783i −1.18292 0.682957i
\(528\) 3.17452i 0.138153i
\(529\) −7.31025 + 12.6617i −0.317837 + 0.550510i
\(530\) −3.22021 5.57757i −0.139877 0.242274i
\(531\) 2.40874 1.39069i 0.104531 0.0603508i
\(532\) −6.18952 −0.268350
\(533\) −4.38338 3.15832i −0.189865 0.136802i
\(534\) −16.2931 −0.705071
\(535\) 2.38726 1.37828i 0.103210 0.0595884i
\(536\) 5.77720 + 10.0064i 0.249537 + 0.432211i
\(537\) −9.91008 + 17.1648i −0.427651 + 0.740714i
\(538\) 20.5175i 0.884572i
\(539\) 2.74922 + 1.58726i 0.118417 + 0.0683682i
\(540\) 1.54846 + 0.894007i 0.0666353 + 0.0384719i
\(541\) 22.7965i 0.980097i −0.871695 0.490048i \(-0.836979\pi\)
0.871695 0.490048i \(-0.163021\pi\)
\(542\) −6.09076 + 10.5495i −0.261621 + 0.453140i
\(543\) −9.16329 15.8713i −0.393234 0.681102i
\(544\) −4.81599 + 2.78052i −0.206484 + 0.119214i
\(545\) −13.1907 −0.565029
\(546\) −2.10774 + 2.92531i −0.0902032 + 0.125192i
\(547\) 31.6698 1.35410 0.677052 0.735935i \(-0.263257\pi\)
0.677052 + 0.735935i \(0.263257\pi\)
\(548\) 7.62363 4.40150i 0.325665 0.188023i
\(549\) −0.844395 1.46254i −0.0360379 0.0624195i
\(550\) 2.86185 4.95686i 0.122029 0.211361i
\(551\) 12.8593i 0.547824i
\(552\) 5.31181 + 3.06678i 0.226086 + 0.130531i
\(553\) 6.02973 + 3.48127i 0.256410 + 0.148039i
\(554\) 8.62484i 0.366434i
\(555\) −2.76868 + 4.79549i −0.117524 + 0.203557i
\(556\) 9.48720 + 16.4323i 0.402347 + 0.696885i
\(557\) −9.38623 + 5.41914i −0.397707 + 0.229616i −0.685494 0.728078i \(-0.740414\pi\)
0.287787 + 0.957694i \(0.407080\pi\)
\(558\) 5.63862 0.238702
\(559\) −34.5763 3.49601i −1.46242 0.147865i
\(560\) −1.78801 −0.0755574
\(561\) 15.2885 8.82681i 0.645480 0.372668i
\(562\) −12.1461 21.0377i −0.512353 0.887422i
\(563\) 7.73626 13.3996i 0.326044 0.564725i −0.655679 0.755040i \(-0.727617\pi\)
0.981723 + 0.190315i \(0.0609508\pi\)
\(564\) 10.5086i 0.442491i
\(565\) −15.3503 8.86247i −0.645790 0.372847i
\(566\) 9.28472 + 5.36054i 0.390266 + 0.225320i
\(567\) 1.00000i 0.0419961i
\(568\) −0.299248 + 0.518313i −0.0125562 + 0.0217479i
\(569\) 16.8667 + 29.2139i 0.707088 + 1.22471i 0.965933 + 0.258793i \(0.0833249\pi\)
−0.258845 + 0.965919i \(0.583342\pi\)
\(570\) −9.58425 + 5.53347i −0.401440 + 0.231772i
\(571\) −43.6140 −1.82519 −0.912594 0.408868i \(-0.865924\pi\)
−0.912594 + 0.408868i \(0.865924\pi\)
\(572\) 10.4379 4.69676i 0.436429 0.196381i
\(573\) 15.0304 0.627902
\(574\) −1.29768 + 0.749217i −0.0541642 + 0.0312717i
\(575\) 5.52943 + 9.57725i 0.230593 + 0.399399i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 10.8368i 0.451143i 0.974227 + 0.225571i \(0.0724249\pi\)
−0.974227 + 0.225571i \(0.927575\pi\)
\(578\) −12.0595 6.96254i −0.501608 0.289603i
\(579\) −4.72408 2.72745i −0.196326 0.113349i
\(580\) 3.71476i 0.154247i
\(581\) −2.15114 + 3.72589i −0.0892444 + 0.154576i
\(582\) −8.74462 15.1461i −0.362476 0.627827i
\(583\) 9.90268 5.71731i 0.410127 0.236787i
\(584\) −0.423973 −0.0175441
\(585\) −0.648527 + 6.41407i −0.0268133 + 0.265189i
\(586\) −21.4278 −0.885176
\(587\) 22.5632 13.0269i 0.931284 0.537677i 0.0440666 0.999029i \(-0.485969\pi\)
0.887217 + 0.461352i \(0.152635\pi\)
\(588\) 0.500000 + 0.866025i 0.0206197 + 0.0357143i
\(589\) −17.4502 + 30.2246i −0.719022 + 1.24538i
\(590\) 4.97314i 0.204741i
\(591\) −6.60751 3.81485i −0.271797 0.156922i
\(592\) 2.68202 + 1.54846i 0.110230 + 0.0636415i
\(593\) 1.68393i 0.0691509i −0.999402 0.0345754i \(-0.988992\pi\)
0.999402 0.0345754i \(-0.0110079\pi\)
\(594\) −1.58726 + 2.74922i −0.0651261 + 0.112802i
\(595\) −4.97160 8.61106i −0.203816 0.353019i
\(596\) 12.0919 6.98127i 0.495304 0.285964i
\(597\) 5.99023 0.245164
\(598\) −2.22469 + 22.0027i −0.0909743 + 0.899756i
\(599\) −6.54081 −0.267250 −0.133625 0.991032i \(-0.542662\pi\)
−0.133625 + 0.991032i \(0.542662\pi\)
\(600\) 1.56145 0.901504i 0.0637460 0.0368038i
\(601\) −19.2387 33.3224i −0.784763 1.35925i −0.929140 0.369727i \(-0.879451\pi\)
0.144377 0.989523i \(-0.453882\pi\)
\(602\) −4.81931 + 8.34729i −0.196420 + 0.340210i
\(603\) 11.5544i 0.470531i
\(604\) −15.4522 8.92131i −0.628740 0.363003i
\(605\) 1.42832 + 0.824638i 0.0580693 + 0.0335263i
\(606\) 4.06866i 0.165278i
\(607\) 4.71797 8.17176i 0.191496 0.331682i −0.754250 0.656587i \(-0.771999\pi\)
0.945746 + 0.324906i \(0.105333\pi\)
\(608\) 3.09476 + 5.36028i 0.125509 + 0.217388i
\(609\) 1.79925 1.03880i 0.0729092 0.0420941i
\(610\) 3.01958 0.122259
\(611\) −34.5523 + 15.5476i −1.39784 + 0.628989i
\(612\) 5.56103 0.224791
\(613\) −22.0191 + 12.7127i −0.889342 + 0.513462i −0.873727 0.486416i \(-0.838304\pi\)
−0.0156146 + 0.999878i \(0.504970\pi\)
\(614\) 3.79682 + 6.57628i 0.153227 + 0.265397i
\(615\) −1.33961 + 2.32027i −0.0540183 + 0.0935624i
\(616\) 3.17452i 0.127905i
\(617\) 24.8545 + 14.3497i 1.00060 + 0.577699i 0.908427 0.418044i \(-0.137284\pi\)
0.0921772 + 0.995743i \(0.470617\pi\)
\(618\) −15.6549 9.03838i −0.629734 0.363577i
\(619\) 9.61494i 0.386457i −0.981154 0.193229i \(-0.938104\pi\)
0.981154 0.193229i \(-0.0618959\pi\)
\(620\) −5.04097 + 8.73121i −0.202450 + 0.350654i
\(621\) −3.06678 5.31181i −0.123066 0.213156i
\(622\) 22.2010 12.8177i 0.890178 0.513945i
\(623\) −16.2931 −0.652769
\(624\) 3.58726 + 0.362708i 0.143605 + 0.0145199i
\(625\) −12.7341 −0.509365
\(626\) −1.48357 + 0.856542i −0.0592956 + 0.0342343i
\(627\) −9.82438 17.0163i −0.392348 0.679567i
\(628\) 2.28958 3.96567i 0.0913642 0.158247i
\(629\) 17.2221i 0.686691i
\(630\) 1.54846 + 0.894007i 0.0616923 + 0.0356181i
\(631\) 29.9445 + 17.2885i 1.19207 + 0.688244i 0.958776 0.284162i \(-0.0917153\pi\)
0.233297 + 0.972406i \(0.425049\pi\)
\(632\) 6.96254i 0.276955i
\(633\) −1.38651 + 2.40150i −0.0551088 + 0.0954512i
\(634\) −16.6049 28.7605i −0.659465 1.14223i
\(635\) 28.4129 16.4042i 1.12753 0.650980i
\(636\) 3.60200 0.142829
\(637\) −2.10774 + 2.92531i −0.0835119 + 0.115905i
\(638\) −6.59536 −0.261113
\(639\) 0.518313 0.299248i 0.0205041 0.0118381i
\(640\) 0.894007 + 1.54846i 0.0353387 + 0.0612085i
\(641\) 3.25646 5.64035i 0.128622 0.222780i −0.794521 0.607237i \(-0.792278\pi\)
0.923143 + 0.384457i \(0.125611\pi\)
\(642\) 1.54169i 0.0608458i
\(643\) −21.8991 12.6435i −0.863617 0.498609i 0.00160504 0.999999i \(-0.499489\pi\)
−0.865222 + 0.501389i \(0.832822\pi\)
\(644\) 5.31181 + 3.06678i 0.209315 + 0.120848i
\(645\) 17.2340i 0.678588i
\(646\) −17.2101 + 29.8087i −0.677120 + 1.17281i
\(647\) 5.95794 + 10.3194i 0.234231 + 0.405699i 0.959049 0.283241i \(-0.0914096\pi\)
−0.724818 + 0.688940i \(0.758076\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) −8.82955 −0.346590
\(650\) 5.27435 + 3.80028i 0.206877 + 0.149059i
\(651\) 5.63862 0.220995
\(652\) 10.6267 6.13531i 0.416172 0.240277i
\(653\) −20.7508 35.9415i −0.812043 1.40650i −0.911432 0.411451i \(-0.865022\pi\)
0.0993891 0.995049i \(-0.468311\pi\)
\(654\) 3.68865 6.38894i 0.144238 0.249827i
\(655\) 10.5837i 0.413541i
\(656\) 1.29768 + 0.749217i 0.0506660 + 0.0292520i
\(657\) 0.367172 + 0.211987i 0.0143247 + 0.00827039i
\(658\) 10.5086i 0.409667i
\(659\) −7.86778 + 13.6274i −0.306485 + 0.530848i −0.977591 0.210514i \(-0.932486\pi\)
0.671106 + 0.741362i \(0.265820\pi\)
\(660\) −2.83804 4.91564i −0.110471 0.191341i
\(661\) −22.6071 + 13.0522i −0.879315 + 0.507673i −0.870432 0.492288i \(-0.836161\pi\)
−0.00888248 + 0.999961i \(0.502827\pi\)
\(662\) 4.95987 0.192771
\(663\) 8.22764 + 18.2847i 0.319535 + 0.710121i
\(664\) 4.30228 0.166961
\(665\) −9.58425 + 5.53347i −0.371661 + 0.214579i
\(666\) −1.54846 2.68202i −0.0600018 0.103926i
\(667\) 6.37151 11.0358i 0.246706 0.427307i
\(668\) 16.6981i 0.646068i
\(669\) 19.5163 + 11.2677i 0.754542 + 0.435635i
\(670\) 17.8916 + 10.3297i 0.691212 + 0.399071i
\(671\) 5.36110i 0.206963i
\(672\) 0.500000 0.866025i 0.0192879 0.0334077i
\(673\) 0.620853 + 1.07535i 0.0239321 + 0.0414516i 0.877743 0.479131i \(-0.159048\pi\)
−0.853811 + 0.520583i \(0.825715\pi\)
\(674\) 20.4532 11.8087i 0.787829 0.454853i
\(675\) −1.80301 −0.0693978
\(676\) 4.11482 + 12.3316i 0.158262 + 0.474292i
\(677\) 29.2845 1.12550 0.562748 0.826629i \(-0.309744\pi\)
0.562748 + 0.826629i \(0.309744\pi\)
\(678\) 8.58509 4.95660i 0.329708 0.190357i
\(679\) −8.74462 15.1461i −0.335588 0.581255i
\(680\) −4.97160 + 8.61106i −0.190652 + 0.330219i
\(681\) 1.83155i 0.0701850i
\(682\) −15.5018 8.94997i −0.593595 0.342712i
\(683\) −37.0486 21.3900i −1.41762 0.818466i −0.421535 0.906812i \(-0.638509\pi\)
−0.996090 + 0.0883461i \(0.971842\pi\)
\(684\) 6.18952i 0.236662i
\(685\) 7.86995 13.6311i 0.300695 0.520819i
\(686\) 0.500000 + 0.866025i 0.0190901 + 0.0330650i
\(687\) 19.5774 11.3030i 0.746924 0.431237i
\(688\) 9.63862 0.367469
\(689\) 5.32922 + 11.8434i 0.203027 + 0.451198i
\(690\) 10.9669 0.417502
\(691\) −16.3649 + 9.44827i −0.622549 + 0.359429i −0.777861 0.628437i \(-0.783695\pi\)
0.155312 + 0.987866i \(0.450362\pi\)
\(692\) −3.68865 6.38894i −0.140222 0.242871i
\(693\) −1.58726 + 2.74922i −0.0602951 + 0.104434i
\(694\) 7.16967i 0.272157i
\(695\) 29.3812 + 16.9632i 1.11449 + 0.643452i
\(696\) −1.79925 1.03880i −0.0682003 0.0393755i
\(697\) 8.33284i 0.315629i
\(698\) 6.18662 10.7155i 0.234167 0.405589i
\(699\) −4.71948 8.17439i −0.178507 0.309184i
\(700\) 1.56145 0.901504i 0.0590173 0.0340737i
\(701\) −3.35161 −0.126589 −0.0632943 0.997995i \(-0.520161\pi\)
−0.0632943 + 0.997995i \(0.520161\pi\)
\(702\) −2.92531 2.10774i −0.110409 0.0795517i
\(703\) 19.1685 0.722954
\(704\) −2.74922 + 1.58726i −0.103615 + 0.0598222i
\(705\) 9.39473 + 16.2722i 0.353826 + 0.612845i
\(706\) 13.1069 22.7018i 0.493285 0.854395i
\(707\) 4.06866i 0.153018i
\(708\) −2.40874 1.39069i −0.0905262 0.0522653i
\(709\) 31.8468 + 18.3867i 1.19603 + 0.690529i 0.959668 0.281136i \(-0.0907113\pi\)
0.236363 + 0.971665i \(0.424045\pi\)
\(710\) 1.07012i 0.0401608i
\(711\) −3.48127 + 6.02973i −0.130558 + 0.226133i
\(712\) 8.14654 + 14.1102i 0.305305 + 0.528803i
\(713\) 29.9513 17.2924i 1.12169 0.647606i
\(714\) 5.56103 0.208116
\(715\) 11.9637 16.6043i 0.447419 0.620965i
\(716\) 19.8202 0.740714
\(717\) 13.7488 7.93787i 0.513458 0.296445i
\(718\) 1.80978 + 3.13463i 0.0675404 + 0.116983i
\(719\) 8.08486 14.0034i 0.301514 0.522238i −0.674965 0.737850i \(-0.735841\pi\)
0.976479 + 0.215612i \(0.0691746\pi\)
\(720\) 1.78801i 0.0666353i
\(721\) −15.6549 9.03838i −0.583020 0.336607i
\(722\) 16.7231 + 9.65506i 0.622368 + 0.359324i
\(723\) 23.9251i 0.889783i
\(724\) −9.16329 + 15.8713i −0.340551 + 0.589851i
\(725\) −1.87296 3.24406i −0.0695599 0.120481i
\(726\) −0.798828 + 0.461204i −0.0296473 + 0.0171169i
\(727\) 27.2522 1.01073 0.505363 0.862907i \(-0.331358\pi\)
0.505363 + 0.862907i \(0.331358\pi\)
\(728\) 3.58726 + 0.362708i 0.132953 + 0.0134429i
\(729\) 1.00000 0.0370370
\(730\) −0.656508 + 0.379035i −0.0242984 + 0.0140287i
\(731\) 26.8003 + 46.4196i 0.991247 + 1.71689i
\(732\) −0.844395 + 1.46254i −0.0312098 + 0.0540569i
\(733\) 39.6734i 1.46537i −0.680567 0.732686i \(-0.738267\pi\)
0.680567 0.732686i \(-0.261733\pi\)
\(734\) 6.98440 + 4.03245i 0.257799 + 0.148840i
\(735\) 1.54846 + 0.894007i 0.0571160 + 0.0329759i
\(736\) 6.13356i 0.226086i
\(737\) −18.3398 + 31.7655i −0.675557 + 1.17010i
\(738\) −0.749217 1.29768i −0.0275791 0.0477683i
\(739\) −22.0125 + 12.7089i −0.809742 + 0.467505i −0.846866 0.531806i \(-0.821514\pi\)
0.0371244 + 0.999311i \(0.488180\pi\)
\(740\) 5.53735 0.203557
\(741\) 20.3512 9.15749i 0.747621 0.336409i
\(742\) 3.60200 0.132234
\(743\) −21.5143 + 12.4213i −0.789285 + 0.455694i −0.839711 0.543034i \(-0.817275\pi\)
0.0504260 + 0.998728i \(0.483942\pi\)
\(744\) −2.81931 4.88319i −0.103361 0.179026i
\(745\) 12.4826 21.6205i 0.457327 0.792114i
\(746\) 29.1702i 1.06800i
\(747\) −3.72589 2.15114i −0.136323 0.0787061i
\(748\) −15.2885 8.82681i −0.559002 0.322740i
\(749\) 1.54169i 0.0563323i
\(750\) 6.08193 10.5342i 0.222081 0.384655i
\(751\) −22.7211 39.3540i −0.829103 1.43605i −0.898743 0.438476i \(-0.855518\pi\)
0.0696398 0.997572i \(-0.477815\pi\)
\(752\) 9.10069 5.25429i 0.331868 0.191604i
\(753\) −20.5236 −0.747920
\(754\) 0.753559 7.45287i 0.0274430 0.271417i
\(755\) −31.9028 −1.16106
\(756\) −0.866025 + 0.500000i −0.0314970 + 0.0181848i
\(757\) −3.20643 5.55369i −0.116540 0.201852i 0.801855 0.597519i \(-0.203847\pi\)
−0.918394 + 0.395667i \(0.870514\pi\)
\(758\) −13.4983 + 23.3797i −0.490280 + 0.849190i
\(759\) 19.4711i 0.706756i
\(760\) 9.58425 + 5.53347i 0.347657 + 0.200720i
\(761\) 27.8313 + 16.0684i 1.00888 + 0.582479i 0.910864 0.412706i \(-0.135416\pi\)
0.0980185 + 0.995185i \(0.468750\pi\)
\(762\) 18.3490i 0.664716i
\(763\) 3.68865 6.38894i 0.133538 0.231295i
\(764\) −7.51518 13.0167i −0.271890 0.470927i
\(765\) 8.61106 4.97160i 0.311334 0.179749i
\(766\) 26.1146 0.943558
\(767\) 1.00883 9.97753i 0.0364267 0.360268i
\(768\) −1.00000 −0.0360844
\(769\) −33.7551 + 19.4885i −1.21724 + 0.702774i −0.964327 0.264714i \(-0.914722\pi\)
−0.252914 + 0.967489i \(0.581389\pi\)
\(770\) −2.83804 4.91564i −0.102276 0.177147i
\(771\) 0.413344 0.715933i 0.0148862 0.0257837i
\(772\) 5.45490i 0.196326i
\(773\) 2.09922 + 1.21199i 0.0755038 + 0.0435921i 0.537277 0.843406i \(-0.319453\pi\)
−0.461773 + 0.886998i \(0.652786\pi\)
\(774\) −8.34729 4.81931i −0.300037 0.173227i
\(775\) 10.1665i 0.365191i
\(776\) −8.74462 + 15.1461i −0.313913 + 0.543714i