Properties

Label 570.2.k.b.77.6
Level $570$
Weight $2$
Character 570.77
Analytic conductor $4.551$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 77.6
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.b.533.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.577604 + 1.63290i) q^{3} -1.00000i q^{4} +(2.23603 - 0.0135681i) q^{5} +(-1.56306 - 0.746209i) q^{6} +(3.38538 + 3.38538i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.33275 + 1.88634i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.577604 + 1.63290i) q^{3} -1.00000i q^{4} +(2.23603 - 0.0135681i) q^{5} +(-1.56306 - 0.746209i) q^{6} +(3.38538 + 3.38538i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.33275 + 1.88634i) q^{9} +(-1.57152 + 1.59070i) q^{10} -1.22574i q^{11} +(1.63290 - 0.577604i) q^{12} +(3.51689 - 3.51689i) q^{13} -4.78765 q^{14} +(1.31369 + 3.64338i) q^{15} -1.00000 q^{16} +(0.826034 - 0.826034i) q^{17} +(0.315656 - 2.98335i) q^{18} -1.00000i q^{19} +(-0.0135681 - 2.23603i) q^{20} +(-3.57259 + 7.48341i) q^{21} +(0.866730 + 0.866730i) q^{22} +(-1.04719 - 1.04719i) q^{23} +(-0.746209 + 1.56306i) q^{24} +(4.99963 - 0.0606771i) q^{25} +4.97363i q^{26} +(-4.42762 - 2.71959i) q^{27} +(3.38538 - 3.38538i) q^{28} -8.14348 q^{29} +(-3.50518 - 1.64734i) q^{30} +7.41990 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.00152 - 0.707993i) q^{33} +1.16819i q^{34} +(7.61574 + 7.52387i) q^{35} +(1.88634 + 2.33275i) q^{36} +(-5.83375 - 5.83375i) q^{37} +(0.707107 + 0.707107i) q^{38} +(7.77411 + 3.71137i) q^{39} +(1.59070 + 1.57152i) q^{40} -3.53572i q^{41} +(-2.76537 - 7.81778i) q^{42} +(-2.68748 + 2.68748i) q^{43} -1.22574 q^{44} +(-5.19049 + 4.24956i) q^{45} +1.48094 q^{46} +(-6.84848 + 6.84848i) q^{47} +(-0.577604 - 1.63290i) q^{48} +15.9216i q^{49} +(-3.49237 + 3.57818i) q^{50} +(1.82595 + 0.871713i) q^{51} +(-3.51689 - 3.51689i) q^{52} +(-3.40629 - 3.40629i) q^{53} +(5.05384 - 1.20776i) q^{54} +(-0.0166309 - 2.74079i) q^{55} +4.78765i q^{56} +(1.63290 - 0.577604i) q^{57} +(5.75831 - 5.75831i) q^{58} -9.91906 q^{59} +(3.64338 - 1.31369i) q^{60} -10.5422 q^{61} +(-5.24666 + 5.24666i) q^{62} +(-14.2832 - 1.51125i) q^{63} +1.00000i q^{64} +(7.81614 - 7.91158i) q^{65} +(-0.914660 + 1.91591i) q^{66} +(6.00309 + 6.00309i) q^{67} +(-0.826034 - 0.826034i) q^{68} +(1.10509 - 2.31481i) q^{69} +(-10.7053 + 0.0649592i) q^{70} -8.35839i q^{71} +(-2.98335 - 0.315656i) q^{72} +(-3.99393 + 3.99393i) q^{73} +8.25017 q^{74} +(2.98689 + 8.12887i) q^{75} -1.00000 q^{76} +(4.14960 - 4.14960i) q^{77} +(-8.12146 + 2.87279i) q^{78} +6.75057i q^{79} +(-2.23603 + 0.0135681i) q^{80} +(1.88342 - 8.80072i) q^{81} +(2.50013 + 2.50013i) q^{82} +(0.717790 + 0.717790i) q^{83} +(7.48341 + 3.57259i) q^{84} +(1.83583 - 1.85824i) q^{85} -3.80067i q^{86} +(-4.70370 - 13.2975i) q^{87} +(0.866730 - 0.866730i) q^{88} -0.384471 q^{89} +(0.665336 - 6.67513i) q^{90} +23.8120 q^{91} +(-1.04719 + 1.04719i) q^{92} +(4.28576 + 12.1160i) q^{93} -9.68521i q^{94} +(-0.0135681 - 2.23603i) q^{95} +(1.56306 + 0.746209i) q^{96} +(-12.5444 - 12.5444i) q^{97} +(-11.2583 - 11.2583i) q^{98} +(2.31217 + 2.85934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 4q^{6} + 20q^{7} + O(q^{10}) \) \( 36q + 4q^{3} + 4q^{6} + 20q^{7} - 4q^{10} - 4q^{12} + 8q^{13} + 4q^{15} - 36q^{16} + 16q^{21} - 4q^{22} + 16q^{25} - 44q^{27} + 20q^{28} + 32q^{30} - 24q^{31} - 4q^{33} + 4q^{36} - 8q^{40} + 12q^{42} - 8q^{43} + 28q^{45} - 16q^{46} - 4q^{48} + 40q^{51} - 8q^{52} - 36q^{55} - 4q^{57} + 44q^{58} + 16q^{60} - 120q^{61} - 12q^{63} + 80q^{67} - 36q^{70} + 44q^{73} + 4q^{75} - 36q^{76} - 64q^{78} + 36q^{81} + 8q^{82} - 24q^{85} - 28q^{87} - 4q^{88} + 44q^{90} - 72q^{93} - 4q^{96} + 92q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 0.577604 + 1.63290i 0.333480 + 0.942757i
\(4\) 1.00000i 0.500000i
\(5\) 2.23603 0.0135681i 0.999982 0.00606782i
\(6\) −1.56306 0.746209i −0.638119 0.304639i
\(7\) 3.38538 + 3.38538i 1.27955 + 1.27955i 0.940917 + 0.338638i \(0.109966\pi\)
0.338638 + 0.940917i \(0.390034\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.33275 + 1.88634i −0.777582 + 0.628781i
\(10\) −1.57152 + 1.59070i −0.496957 + 0.503025i
\(11\) 1.22574i 0.369575i −0.982779 0.184787i \(-0.940840\pi\)
0.982779 0.184787i \(-0.0591597\pi\)
\(12\) 1.63290 0.577604i 0.471379 0.166740i
\(13\) 3.51689 3.51689i 0.975410 0.975410i −0.0242950 0.999705i \(-0.507734\pi\)
0.999705 + 0.0242950i \(0.00773410\pi\)
\(14\) −4.78765 −1.27955
\(15\) 1.31369 + 3.64338i 0.339194 + 0.940716i
\(16\) −1.00000 −0.250000
\(17\) 0.826034 0.826034i 0.200343 0.200343i −0.599804 0.800147i \(-0.704755\pi\)
0.800147 + 0.599804i \(0.204755\pi\)
\(18\) 0.315656 2.98335i 0.0744008 0.703182i
\(19\) 1.00000i 0.229416i
\(20\) −0.0135681 2.23603i −0.00303391 0.499991i
\(21\) −3.57259 + 7.48341i −0.779604 + 1.63301i
\(22\) 0.866730 + 0.866730i 0.184787 + 0.184787i
\(23\) −1.04719 1.04719i −0.218353 0.218353i 0.589451 0.807804i \(-0.299344\pi\)
−0.807804 + 0.589451i \(0.799344\pi\)
\(24\) −0.746209 + 1.56306i −0.152319 + 0.319059i
\(25\) 4.99963 0.0606771i 0.999926 0.0121354i
\(26\) 4.97363i 0.975410i
\(27\) −4.42762 2.71959i −0.852096 0.523386i
\(28\) 3.38538 3.38538i 0.639777 0.639777i
\(29\) −8.14348 −1.51221 −0.756103 0.654453i \(-0.772899\pi\)
−0.756103 + 0.654453i \(0.772899\pi\)
\(30\) −3.50518 1.64734i −0.639955 0.300761i
\(31\) 7.41990 1.33265 0.666327 0.745660i \(-0.267866\pi\)
0.666327 + 0.745660i \(0.267866\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 2.00152 0.707993i 0.348419 0.123246i
\(34\) 1.16819i 0.200343i
\(35\) 7.61574 + 7.52387i 1.28730 + 1.27177i
\(36\) 1.88634 + 2.33275i 0.314390 + 0.388791i
\(37\) −5.83375 5.83375i −0.959063 0.959063i 0.0401316 0.999194i \(-0.487222\pi\)
−0.999194 + 0.0401316i \(0.987222\pi\)
\(38\) 0.707107 + 0.707107i 0.114708 + 0.114708i
\(39\) 7.77411 + 3.71137i 1.24485 + 0.594295i
\(40\) 1.59070 + 1.57152i 0.251512 + 0.248478i
\(41\) 3.53572i 0.552187i −0.961131 0.276093i \(-0.910960\pi\)
0.961131 0.276093i \(-0.0890399\pi\)
\(42\) −2.76537 7.81778i −0.426706 1.20631i
\(43\) −2.68748 + 2.68748i −0.409836 + 0.409836i −0.881681 0.471845i \(-0.843588\pi\)
0.471845 + 0.881681i \(0.343588\pi\)
\(44\) −1.22574 −0.184787
\(45\) −5.19049 + 4.24956i −0.773753 + 0.633488i
\(46\) 1.48094 0.218353
\(47\) −6.84848 + 6.84848i −0.998953 + 0.998953i −0.999999 0.00104620i \(-0.999667\pi\)
0.00104620 + 0.999999i \(0.499667\pi\)
\(48\) −0.577604 1.63290i −0.0833699 0.235689i
\(49\) 15.9216i 2.27452i
\(50\) −3.49237 + 3.57818i −0.493895 + 0.506031i
\(51\) 1.82595 + 0.871713i 0.255685 + 0.122064i
\(52\) −3.51689 3.51689i −0.487705 0.487705i
\(53\) −3.40629 3.40629i −0.467890 0.467890i 0.433340 0.901230i \(-0.357335\pi\)
−0.901230 + 0.433340i \(0.857335\pi\)
\(54\) 5.05384 1.20776i 0.687741 0.164355i
\(55\) −0.0166309 2.74079i −0.00224251 0.369568i
\(56\) 4.78765i 0.639777i
\(57\) 1.63290 0.577604i 0.216283 0.0765055i
\(58\) 5.75831 5.75831i 0.756103 0.756103i
\(59\) −9.91906 −1.29135 −0.645676 0.763612i \(-0.723424\pi\)
−0.645676 + 0.763612i \(0.723424\pi\)
\(60\) 3.64338 1.31369i 0.470358 0.169597i
\(61\) −10.5422 −1.34979 −0.674894 0.737915i \(-0.735811\pi\)
−0.674894 + 0.737915i \(0.735811\pi\)
\(62\) −5.24666 + 5.24666i −0.666327 + 0.666327i
\(63\) −14.2832 1.51125i −1.79952 0.190400i
\(64\) 1.00000i 0.125000i
\(65\) 7.81614 7.91158i 0.969473 0.981310i
\(66\) −0.914660 + 1.91591i −0.112587 + 0.235833i
\(67\) 6.00309 + 6.00309i 0.733394 + 0.733394i 0.971291 0.237896i \(-0.0764579\pi\)
−0.237896 + 0.971291i \(0.576458\pi\)
\(68\) −0.826034 0.826034i −0.100171 0.100171i
\(69\) 1.10509 2.31481i 0.133038 0.278671i
\(70\) −10.7053 + 0.0649592i −1.27953 + 0.00776411i
\(71\) 8.35839i 0.991958i −0.868334 0.495979i \(-0.834809\pi\)
0.868334 0.495979i \(-0.165191\pi\)
\(72\) −2.98335 0.315656i −0.351591 0.0372004i
\(73\) −3.99393 + 3.99393i −0.467454 + 0.467454i −0.901089 0.433635i \(-0.857231\pi\)
0.433635 + 0.901089i \(0.357231\pi\)
\(74\) 8.25017 0.959063
\(75\) 2.98689 + 8.12887i 0.344896 + 0.938641i
\(76\) −1.00000 −0.114708
\(77\) 4.14960 4.14960i 0.472891 0.472891i
\(78\) −8.12146 + 2.87279i −0.919575 + 0.325279i
\(79\) 6.75057i 0.759498i 0.925090 + 0.379749i \(0.123990\pi\)
−0.925090 + 0.379749i \(0.876010\pi\)
\(80\) −2.23603 + 0.0135681i −0.249995 + 0.00151695i
\(81\) 1.88342 8.80072i 0.209269 0.977858i
\(82\) 2.50013 + 2.50013i 0.276093 + 0.276093i
\(83\) 0.717790 + 0.717790i 0.0787877 + 0.0787877i 0.745402 0.666615i \(-0.232257\pi\)
−0.666615 + 0.745402i \(0.732257\pi\)
\(84\) 7.48341 + 3.57259i 0.816507 + 0.389802i
\(85\) 1.83583 1.85824i 0.199123 0.201555i
\(86\) 3.80067i 0.409836i
\(87\) −4.70370 13.2975i −0.504290 1.42564i
\(88\) 0.866730 0.866730i 0.0923937 0.0923937i
\(89\) −0.384471 −0.0407539 −0.0203769 0.999792i \(-0.506487\pi\)
−0.0203769 + 0.999792i \(0.506487\pi\)
\(90\) 0.665336 6.67513i 0.0701326 0.703620i
\(91\) 23.8120 2.49618
\(92\) −1.04719 + 1.04719i −0.109177 + 0.109177i
\(93\) 4.28576 + 12.1160i 0.444413 + 1.25637i
\(94\) 9.68521i 0.998953i
\(95\) −0.0135681 2.23603i −0.00139205 0.229412i
\(96\) 1.56306 + 0.746209i 0.159530 + 0.0761597i
\(97\) −12.5444 12.5444i −1.27369 1.27369i −0.944137 0.329554i \(-0.893101\pi\)
−0.329554 0.944137i \(-0.606899\pi\)
\(98\) −11.2583 11.2583i −1.13726 1.13726i
\(99\) 2.31217 + 2.85934i 0.232382 + 0.287375i
\(100\) −0.0606771 4.99963i −0.00606771 0.499963i
\(101\) 1.19949i 0.119354i −0.998218 0.0596768i \(-0.980993\pi\)
0.998218 0.0596768i \(-0.0190070\pi\)
\(102\) −1.90754 + 0.674750i −0.188875 + 0.0668102i
\(103\) 13.1711 13.1711i 1.29778 1.29778i 0.367931 0.929853i \(-0.380066\pi\)
0.929853 0.367931i \(-0.119934\pi\)
\(104\) 4.97363 0.487705
\(105\) −7.88688 + 16.7816i −0.769681 + 1.63772i
\(106\) 4.81722 0.467890
\(107\) 9.98389 9.98389i 0.965179 0.965179i −0.0342348 0.999414i \(-0.510899\pi\)
0.999414 + 0.0342348i \(0.0108994\pi\)
\(108\) −2.71959 + 4.42762i −0.261693 + 0.426048i
\(109\) 8.95394i 0.857632i 0.903392 + 0.428816i \(0.141069\pi\)
−0.903392 + 0.428816i \(0.858931\pi\)
\(110\) 1.94979 + 1.92627i 0.185905 + 0.183663i
\(111\) 6.15635 12.8956i 0.584335 1.22399i
\(112\) −3.38538 3.38538i −0.319889 0.319889i
\(113\) 13.3747 + 13.3747i 1.25818 + 1.25818i 0.951959 + 0.306225i \(0.0990661\pi\)
0.306225 + 0.951959i \(0.400934\pi\)
\(114\) −0.746209 + 1.56306i −0.0698889 + 0.146394i
\(115\) −2.35574 2.32733i −0.219674 0.217024i
\(116\) 8.14348i 0.756103i
\(117\) −1.56996 + 14.8381i −0.145142 + 1.37178i
\(118\) 7.01383 7.01383i 0.645676 0.645676i
\(119\) 5.59288 0.512699
\(120\) −1.64734 + 3.50518i −0.150381 + 0.319978i
\(121\) 9.49756 0.863414
\(122\) 7.45445 7.45445i 0.674894 0.674894i
\(123\) 5.77349 2.04225i 0.520578 0.184143i
\(124\) 7.41990i 0.666327i
\(125\) 11.1785 0.203511i 0.999834 0.0182026i
\(126\) 11.1684 9.03116i 0.994959 0.804560i
\(127\) −6.46428 6.46428i −0.573612 0.573612i 0.359524 0.933136i \(-0.382939\pi\)
−0.933136 + 0.359524i \(0.882939\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −5.94069 2.83609i −0.523048 0.249704i
\(130\) 0.0674826 + 11.1212i 0.00591861 + 0.975392i
\(131\) 4.64733i 0.406039i 0.979175 + 0.203020i \(0.0650755\pi\)
−0.979175 + 0.203020i \(0.934924\pi\)
\(132\) −0.707993 2.00152i −0.0616229 0.174210i
\(133\) 3.38538 3.38538i 0.293550 0.293550i
\(134\) −8.48965 −0.733394
\(135\) −9.93718 6.02101i −0.855256 0.518206i
\(136\) 1.16819 0.100171
\(137\) −0.825480 + 0.825480i −0.0705255 + 0.0705255i −0.741490 0.670964i \(-0.765880\pi\)
0.670964 + 0.741490i \(0.265880\pi\)
\(138\) 0.855399 + 2.41824i 0.0728164 + 0.205854i
\(139\) 3.47441i 0.294695i −0.989085 0.147348i \(-0.952926\pi\)
0.989085 0.147348i \(-0.0470736\pi\)
\(140\) 7.52387 7.61574i 0.635883 0.643648i
\(141\) −15.1386 7.22720i −1.27490 0.608640i
\(142\) 5.91027 + 5.91027i 0.495979 + 0.495979i
\(143\) −4.31080 4.31080i −0.360487 0.360487i
\(144\) 2.33275 1.88634i 0.194396 0.157195i
\(145\) −18.2090 + 0.110491i −1.51218 + 0.00917579i
\(146\) 5.64827i 0.467454i
\(147\) −25.9985 + 9.19640i −2.14432 + 0.758506i
\(148\) −5.83375 + 5.83375i −0.479531 + 0.479531i
\(149\) −1.10597 −0.0906042 −0.0453021 0.998973i \(-0.514425\pi\)
−0.0453021 + 0.998973i \(0.514425\pi\)
\(150\) −7.86003 3.63593i −0.641768 0.296872i
\(151\) 3.28699 0.267491 0.133746 0.991016i \(-0.457299\pi\)
0.133746 + 0.991016i \(0.457299\pi\)
\(152\) 0.707107 0.707107i 0.0573539 0.0573539i
\(153\) −0.368745 + 3.48511i −0.0298113 + 0.281755i
\(154\) 5.86842i 0.472891i
\(155\) 16.5911 0.100674i 1.33263 0.00808630i
\(156\) 3.71137 7.77411i 0.297148 0.622427i
\(157\) −12.0134 12.0134i −0.958773 0.958773i 0.0404098 0.999183i \(-0.487134\pi\)
−0.999183 + 0.0404098i \(0.987134\pi\)
\(158\) −4.77337 4.77337i −0.379749 0.379749i
\(159\) 3.59466 7.52963i 0.285075 0.597138i
\(160\) 1.57152 1.59070i 0.124239 0.125756i
\(161\) 7.09025i 0.558790i
\(162\) 4.89127 + 7.55483i 0.384295 + 0.593564i
\(163\) 3.82552 3.82552i 0.299638 0.299638i −0.541234 0.840872i \(-0.682043\pi\)
0.840872 + 0.541234i \(0.182043\pi\)
\(164\) −3.53572 −0.276093
\(165\) 4.46584 1.61025i 0.347665 0.125358i
\(166\) −1.01511 −0.0787877
\(167\) 14.1056 14.1056i 1.09152 1.09152i 0.0961553 0.995366i \(-0.469345\pi\)
0.995366 0.0961553i \(-0.0306545\pi\)
\(168\) −7.81778 + 2.76537i −0.603155 + 0.213353i
\(169\) 11.7370i 0.902849i
\(170\) 0.0158500 + 2.61210i 0.00121564 + 0.200339i
\(171\) 1.88634 + 2.33275i 0.144252 + 0.178390i
\(172\) 2.68748 + 2.68748i 0.204918 + 0.204918i
\(173\) 6.57463 + 6.57463i 0.499860 + 0.499860i 0.911394 0.411535i \(-0.135007\pi\)
−0.411535 + 0.911394i \(0.635007\pi\)
\(174\) 12.7288 + 6.07674i 0.964966 + 0.460676i
\(175\) 17.1311 + 16.7203i 1.29499 + 1.26393i
\(176\) 1.22574i 0.0923937i
\(177\) −5.72929 16.1969i −0.430639 1.21743i
\(178\) 0.271862 0.271862i 0.0203769 0.0203769i
\(179\) −11.2885 −0.843741 −0.421870 0.906656i \(-0.638626\pi\)
−0.421870 + 0.906656i \(0.638626\pi\)
\(180\) 4.24956 + 5.19049i 0.316744 + 0.386876i
\(181\) −9.96083 −0.740383 −0.370191 0.928956i \(-0.620708\pi\)
−0.370191 + 0.928956i \(0.620708\pi\)
\(182\) −16.8377 + 16.8377i −1.24809 + 1.24809i
\(183\) −6.08920 17.2144i −0.450127 1.27252i
\(184\) 1.48094i 0.109177i
\(185\) −13.1236 12.9653i −0.964865 0.953226i
\(186\) −11.5978 5.53680i −0.850391 0.405978i
\(187\) −1.01250 1.01250i −0.0740416 0.0740416i
\(188\) 6.84848 + 6.84848i 0.499477 + 0.499477i
\(189\) −5.78233 24.1961i −0.420602 1.76000i
\(190\) 1.59070 + 1.57152i 0.115402 + 0.114010i
\(191\) 10.1454i 0.734095i 0.930202 + 0.367048i \(0.119631\pi\)
−0.930202 + 0.367048i \(0.880369\pi\)
\(192\) −1.63290 + 0.577604i −0.117845 + 0.0416850i
\(193\) 1.33016 1.33016i 0.0957468 0.0957468i −0.657611 0.753358i \(-0.728433\pi\)
0.753358 + 0.657611i \(0.228433\pi\)
\(194\) 17.7405 1.27369
\(195\) 17.4335 + 8.19325i 1.24844 + 0.586731i
\(196\) 15.9216 1.13726
\(197\) 3.67465 3.67465i 0.261808 0.261808i −0.563980 0.825788i \(-0.690731\pi\)
0.825788 + 0.563980i \(0.190731\pi\)
\(198\) −3.65681 0.386912i −0.259878 0.0274966i
\(199\) 0.894086i 0.0633801i −0.999498 0.0316900i \(-0.989911\pi\)
0.999498 0.0316900i \(-0.0100889\pi\)
\(200\) 3.57818 + 3.49237i 0.253015 + 0.246948i
\(201\) −6.33506 + 13.2699i −0.446841 + 0.935985i
\(202\) 0.848167 + 0.848167i 0.0596768 + 0.0596768i
\(203\) −27.5688 27.5688i −1.93495 1.93495i
\(204\) 0.871713 1.82595i 0.0610321 0.127842i
\(205\) −0.0479729 7.90597i −0.00335057 0.552177i
\(206\) 18.6267i 1.29778i
\(207\) 4.41817 + 0.467469i 0.307084 + 0.0324913i
\(208\) −3.51689 + 3.51689i −0.243852 + 0.243852i
\(209\) −1.22574 −0.0847863
\(210\) −6.28951 17.4432i −0.434017 1.20370i
\(211\) −0.656325 −0.0451833 −0.0225916 0.999745i \(-0.507192\pi\)
−0.0225916 + 0.999745i \(0.507192\pi\)
\(212\) −3.40629 + 3.40629i −0.233945 + 0.233945i
\(213\) 13.6484 4.82784i 0.935176 0.330798i
\(214\) 14.1194i 0.965179i
\(215\) −5.97281 + 6.04574i −0.407342 + 0.412316i
\(216\) −1.20776 5.05384i −0.0821775 0.343870i
\(217\) 25.1192 + 25.1192i 1.70520 + 1.70520i
\(218\) −6.33139 6.33139i −0.428816 0.428816i
\(219\) −8.82861 4.21479i −0.596582 0.284809i
\(220\) −2.74079 + 0.0166309i −0.184784 + 0.00112126i
\(221\) 5.81014i 0.390832i
\(222\) 4.76533 + 13.4717i 0.319828 + 0.904163i
\(223\) −5.81309 + 5.81309i −0.389273 + 0.389273i −0.874428 0.485155i \(-0.838763\pi\)
0.485155 + 0.874428i \(0.338763\pi\)
\(224\) 4.78765 0.319889
\(225\) −11.5484 + 9.57256i −0.769895 + 0.638171i
\(226\) −18.9147 −1.25818
\(227\) −11.1211 + 11.1211i −0.738133 + 0.738133i −0.972217 0.234083i \(-0.924791\pi\)
0.234083 + 0.972217i \(0.424791\pi\)
\(228\) −0.577604 1.63290i −0.0382528 0.108142i
\(229\) 15.9766i 1.05576i 0.849318 + 0.527881i \(0.177013\pi\)
−0.849318 + 0.527881i \(0.822987\pi\)
\(230\) 3.31143 0.0200935i 0.218349 0.00132493i
\(231\) 9.17273 + 4.37907i 0.603521 + 0.288122i
\(232\) −5.75831 5.75831i −0.378051 0.378051i
\(233\) 10.3048 + 10.3048i 0.675090 + 0.675090i 0.958885 0.283795i \(-0.0915935\pi\)
−0.283795 + 0.958885i \(0.591593\pi\)
\(234\) −9.38198 11.6022i −0.613319 0.758462i
\(235\) −15.2205 + 15.4063i −0.992873 + 1.00500i
\(236\) 9.91906i 0.645676i
\(237\) −11.0230 + 3.89915i −0.716022 + 0.253277i
\(238\) −3.95477 + 3.95477i −0.256349 + 0.256349i
\(239\) 16.1045 1.04172 0.520858 0.853644i \(-0.325612\pi\)
0.520858 + 0.853644i \(0.325612\pi\)
\(240\) −1.31369 3.64338i −0.0847985 0.235179i
\(241\) −19.9193 −1.28312 −0.641559 0.767074i \(-0.721712\pi\)
−0.641559 + 0.767074i \(0.721712\pi\)
\(242\) −6.71579 + 6.71579i −0.431707 + 0.431707i
\(243\) 15.4586 2.00789i 0.991670 0.128806i
\(244\) 10.5422i 0.674894i
\(245\) 0.216026 + 35.6012i 0.0138014 + 2.27448i
\(246\) −2.63839 + 5.52656i −0.168218 + 0.352361i
\(247\) −3.51689 3.51689i −0.223774 0.223774i
\(248\) 5.24666 + 5.24666i 0.333163 + 0.333163i
\(249\) −0.757484 + 1.58668i −0.0480036 + 0.100552i
\(250\) −7.76048 + 8.04829i −0.490816 + 0.509018i
\(251\) 17.8998i 1.12982i 0.825151 + 0.564912i \(0.191090\pi\)
−0.825151 + 0.564912i \(0.808910\pi\)
\(252\) −1.51125 + 14.2832i −0.0951998 + 0.899759i
\(253\) −1.28358 + 1.28358i −0.0806979 + 0.0806979i
\(254\) 9.14187 0.573612
\(255\) 4.09471 + 1.92440i 0.256421 + 0.120511i
\(256\) 1.00000 0.0625000
\(257\) 14.5464 14.5464i 0.907378 0.907378i −0.0886822 0.996060i \(-0.528266\pi\)
0.996060 + 0.0886822i \(0.0282655\pi\)
\(258\) 6.20612 2.19528i 0.386376 0.136672i
\(259\) 39.4990i 2.45435i
\(260\) −7.91158 7.81614i −0.490655 0.484737i
\(261\) 18.9967 15.3614i 1.17586 0.950846i
\(262\) −3.28616 3.28616i −0.203020 0.203020i
\(263\) −6.05674 6.05674i −0.373475 0.373475i 0.495266 0.868741i \(-0.335070\pi\)
−0.868741 + 0.495266i \(0.835070\pi\)
\(264\) 1.91591 + 0.914660i 0.117916 + 0.0562934i
\(265\) −7.66277 7.57034i −0.470720 0.465042i
\(266\) 4.78765i 0.293550i
\(267\) −0.222072 0.627804i −0.0135906 0.0384210i
\(268\) 6.00309 6.00309i 0.366697 0.366697i
\(269\) 9.51326 0.580034 0.290017 0.957022i \(-0.406339\pi\)
0.290017 + 0.957022i \(0.406339\pi\)
\(270\) 11.2841 2.76915i 0.686731 0.168525i
\(271\) 0.405502 0.0246325 0.0123162 0.999924i \(-0.496080\pi\)
0.0123162 + 0.999924i \(0.496080\pi\)
\(272\) −0.826034 + 0.826034i −0.0500857 + 0.0500857i
\(273\) 13.7539 + 38.8828i 0.832426 + 2.35329i
\(274\) 1.16740i 0.0705255i
\(275\) −0.0743744 6.12825i −0.00448494 0.369548i
\(276\) −2.31481 1.10509i −0.139335 0.0665189i
\(277\) 3.15621 + 3.15621i 0.189639 + 0.189639i 0.795540 0.605901i \(-0.207187\pi\)
−0.605901 + 0.795540i \(0.707187\pi\)
\(278\) 2.45678 + 2.45678i 0.147348 + 0.147348i
\(279\) −17.3088 + 13.9965i −1.03625 + 0.837947i
\(280\) 0.0649592 + 10.7053i 0.00388205 + 0.639765i
\(281\) 11.9223i 0.711227i 0.934633 + 0.355613i \(0.115728\pi\)
−0.934633 + 0.355613i \(0.884272\pi\)
\(282\) 15.8150 5.59422i 0.941770 0.333131i
\(283\) 11.1386 11.1386i 0.662120 0.662120i −0.293759 0.955879i \(-0.594906\pi\)
0.955879 + 0.293759i \(0.0949063\pi\)
\(284\) −8.35839 −0.495979
\(285\) 3.64338 1.31369i 0.215815 0.0778165i
\(286\) 6.09639 0.360487
\(287\) 11.9698 11.9698i 0.706553 0.706553i
\(288\) −0.315656 + 2.98335i −0.0186002 + 0.175795i
\(289\) 15.6353i 0.919726i
\(290\) 12.7976 12.9539i 0.751501 0.760677i
\(291\) 13.2381 27.7295i 0.776031 1.62553i
\(292\) 3.99393 + 3.99393i 0.233727 + 0.233727i
\(293\) −3.32969 3.32969i −0.194522 0.194522i 0.603125 0.797647i \(-0.293922\pi\)
−0.797647 + 0.603125i \(0.793922\pi\)
\(294\) 11.8809 24.8866i 0.692907 1.45141i
\(295\) −22.1793 + 0.134582i −1.29133 + 0.00783569i
\(296\) 8.25017i 0.479531i
\(297\) −3.33352 + 5.42712i −0.193430 + 0.314913i
\(298\) 0.782036 0.782036i 0.0453021 0.0453021i
\(299\) −7.36568 −0.425968
\(300\) 8.12887 2.98689i 0.469320 0.172448i
\(301\) −18.1963 −1.04882
\(302\) −2.32425 + 2.32425i −0.133746 + 0.133746i
\(303\) 1.95865 0.692830i 0.112522 0.0398020i
\(304\) 1.00000i 0.0573539i
\(305\) −23.5726 + 0.143037i −1.34976 + 0.00819027i
\(306\) −2.20360 2.72509i −0.125972 0.155783i
\(307\) −1.69015 1.69015i −0.0964621 0.0964621i 0.657229 0.753691i \(-0.271728\pi\)
−0.753691 + 0.657229i \(0.771728\pi\)
\(308\) −4.14960 4.14960i −0.236446 0.236446i
\(309\) 29.1147 + 13.8994i 1.65628 + 0.790711i
\(310\) −11.6605 + 11.8029i −0.662271 + 0.670358i
\(311\) 14.3337i 0.812790i 0.913697 + 0.406395i \(0.133214\pi\)
−0.913697 + 0.406395i \(0.866786\pi\)
\(312\) 2.87279 + 8.12146i 0.162640 + 0.459787i
\(313\) 1.56414 1.56414i 0.0884102 0.0884102i −0.661519 0.749929i \(-0.730088\pi\)
0.749929 + 0.661519i \(0.230088\pi\)
\(314\) 16.9895 0.958773
\(315\) −31.9582 3.18540i −1.80064 0.179477i
\(316\) 6.75057 0.379749
\(317\) −21.5987 + 21.5987i −1.21311 + 1.21311i −0.243107 + 0.969999i \(0.578167\pi\)
−0.969999 + 0.243107i \(0.921833\pi\)
\(318\) 2.78245 + 7.86606i 0.156032 + 0.441107i
\(319\) 9.98179i 0.558873i
\(320\) 0.0135681 + 2.23603i 0.000758477 + 0.124998i
\(321\) 22.0695 + 10.5360i 1.23180 + 0.588062i
\(322\) 5.01356 + 5.01356i 0.279395 + 0.279395i
\(323\) −0.826034 0.826034i −0.0459618 0.0459618i
\(324\) −8.80072 1.88342i −0.488929 0.104635i
\(325\) 17.3698 17.7966i 0.963501 0.987175i
\(326\) 5.41010i 0.299638i
\(327\) −14.6209 + 5.17183i −0.808538 + 0.286003i
\(328\) 2.50013 2.50013i 0.138047 0.138047i
\(329\) −46.3694 −2.55643
\(330\) −2.01921 + 4.29644i −0.111154 + 0.236511i
\(331\) −6.37126 −0.350196 −0.175098 0.984551i \(-0.556024\pi\)
−0.175098 + 0.984551i \(0.556024\pi\)
\(332\) 0.717790 0.717790i 0.0393939 0.0393939i
\(333\) 24.6131 + 2.60421i 1.34879 + 0.142710i
\(334\) 19.9483i 1.09152i
\(335\) 13.5045 + 13.3416i 0.737831 + 0.728931i
\(336\) 3.57259 7.48341i 0.194901 0.408254i
\(337\) 1.13280 + 1.13280i 0.0617073 + 0.0617073i 0.737287 0.675580i \(-0.236107\pi\)
−0.675580 + 0.737287i \(0.736107\pi\)
\(338\) 8.29934 + 8.29934i 0.451424 + 0.451424i
\(339\) −14.1143 + 29.5648i −0.766583 + 1.60574i
\(340\) −1.85824 1.83583i −0.100777 0.0995617i
\(341\) 9.09487i 0.492515i
\(342\) −2.98335 0.315656i −0.161321 0.0170687i
\(343\) −30.2032 + 30.2032i −1.63082 + 1.63082i
\(344\) −3.80067 −0.204918
\(345\) 2.43961 5.19098i 0.131344 0.279473i
\(346\) −9.29793 −0.499860
\(347\) 22.1434 22.1434i 1.18872 1.18872i 0.211296 0.977422i \(-0.432232\pi\)
0.977422 0.211296i \(-0.0677683\pi\)
\(348\) −13.2975 + 4.70370i −0.712821 + 0.252145i
\(349\) 19.6754i 1.05320i −0.850113 0.526600i \(-0.823467\pi\)
0.850113 0.526600i \(-0.176533\pi\)
\(350\) −23.9365 + 0.290501i −1.27946 + 0.0155279i
\(351\) −25.1360 + 6.00695i −1.34166 + 0.320627i
\(352\) −0.866730 0.866730i −0.0461969 0.0461969i
\(353\) −24.9047 24.9047i −1.32554 1.32554i −0.909214 0.416330i \(-0.863316\pi\)
−0.416330 0.909214i \(-0.636684\pi\)
\(354\) 15.5041 + 7.40169i 0.824035 + 0.393396i
\(355\) −0.113407 18.6896i −0.00601902 0.991940i
\(356\) 0.384471i 0.0203769i
\(357\) 3.23047 + 9.13264i 0.170975 + 0.483350i
\(358\) 7.98216 7.98216i 0.421870 0.421870i
\(359\) 20.9304 1.10466 0.552331 0.833625i \(-0.313739\pi\)
0.552331 + 0.833625i \(0.313739\pi\)
\(360\) −6.67513 0.665336i −0.351810 0.0350663i
\(361\) −1.00000 −0.0526316
\(362\) 7.04337 7.04337i 0.370191 0.370191i
\(363\) 5.48583 + 15.5086i 0.287931 + 0.813990i
\(364\) 23.8120i 1.24809i
\(365\) −8.87634 + 8.98472i −0.464609 + 0.470282i
\(366\) 16.4781 + 7.86667i 0.861325 + 0.411198i
\(367\) 26.3718 + 26.3718i 1.37660 + 1.37660i 0.850298 + 0.526301i \(0.176422\pi\)
0.526301 + 0.850298i \(0.323578\pi\)
\(368\) 1.04719 + 1.04719i 0.0545883 + 0.0545883i
\(369\) 6.66958 + 8.24795i 0.347205 + 0.429371i
\(370\) 18.4476 0.111939i 0.959045 0.00581942i
\(371\) 23.0632i 1.19738i
\(372\) 12.1160 4.28576i 0.628184 0.222206i
\(373\) −6.66242 + 6.66242i −0.344967 + 0.344967i −0.858231 0.513264i \(-0.828436\pi\)
0.513264 + 0.858231i \(0.328436\pi\)
\(374\) 1.43190 0.0740416
\(375\) 6.78905 + 18.1358i 0.350585 + 0.936531i
\(376\) −9.68521 −0.499477
\(377\) −28.6397 + 28.6397i −1.47502 + 1.47502i
\(378\) 21.1979 + 13.0205i 1.09030 + 0.669701i
\(379\) 0.205871i 0.0105749i 0.999986 + 0.00528745i \(0.00168305\pi\)
−0.999986 + 0.00528745i \(0.998317\pi\)
\(380\) −2.23603 + 0.0135681i −0.114706 + 0.000696027i
\(381\) 6.82175 14.2893i 0.349489 0.732065i
\(382\) −7.17388 7.17388i −0.367048 0.367048i
\(383\) 8.26926 + 8.26926i 0.422539 + 0.422539i 0.886077 0.463538i \(-0.153420\pi\)
−0.463538 + 0.886077i \(0.653420\pi\)
\(384\) 0.746209 1.56306i 0.0380798 0.0797648i
\(385\) 9.22232 9.33493i 0.470013 0.475752i
\(386\) 1.88113i 0.0957468i
\(387\) 1.19970 11.3387i 0.0609843 0.576379i
\(388\) −12.5444 + 12.5444i −0.636846 + 0.636846i
\(389\) 25.3999 1.28782 0.643912 0.765099i \(-0.277310\pi\)
0.643912 + 0.765099i \(0.277310\pi\)
\(390\) −18.1208 + 6.53383i −0.917584 + 0.330853i
\(391\) −1.73002 −0.0874910
\(392\) −11.2583 + 11.2583i −0.568630 + 0.568630i
\(393\) −7.58865 + 2.68432i −0.382797 + 0.135406i
\(394\) 5.19674i 0.261808i
\(395\) 0.0915921 + 15.0944i 0.00460850 + 0.759484i
\(396\) 2.85934 2.31217i 0.143687 0.116191i
\(397\) 14.4297 + 14.4297i 0.724206 + 0.724206i 0.969459 0.245253i \(-0.0788711\pi\)
−0.245253 + 0.969459i \(0.578871\pi\)
\(398\) 0.632214 + 0.632214i 0.0316900 + 0.0316900i
\(399\) 7.48341 + 3.57259i 0.374639 + 0.178853i
\(400\) −4.99963 + 0.0606771i −0.249982 + 0.00303385i
\(401\) 8.03063i 0.401030i 0.979691 + 0.200515i \(0.0642616\pi\)
−0.979691 + 0.200515i \(0.935738\pi\)
\(402\) −4.90366 13.8628i −0.244572 0.691413i
\(403\) 26.0950 26.0950i 1.29988 1.29988i
\(404\) −1.19949 −0.0596768
\(405\) 4.09197 19.7042i 0.203332 0.979110i
\(406\) 38.9882 1.93495
\(407\) −7.15067 + 7.15067i −0.354445 + 0.354445i
\(408\) 0.674750 + 1.90754i 0.0334051 + 0.0944373i
\(409\) 13.8653i 0.685596i −0.939409 0.342798i \(-0.888625\pi\)
0.939409 0.342798i \(-0.111375\pi\)
\(410\) 5.62429 + 5.55644i 0.277764 + 0.274413i
\(411\) −1.82473 0.871129i −0.0900073 0.0429696i
\(412\) −13.1711 13.1711i −0.648892 0.648892i
\(413\) −33.5798 33.5798i −1.65235 1.65235i
\(414\) −3.45467 + 2.79357i −0.169788 + 0.137296i
\(415\) 1.61474 + 1.59526i 0.0792643 + 0.0783082i
\(416\) 4.97363i 0.243852i
\(417\) 5.67337 2.00683i 0.277826 0.0982749i
\(418\) 0.866730 0.866730i 0.0423931 0.0423931i
\(419\) −17.7272 −0.866028 −0.433014 0.901387i \(-0.642550\pi\)
−0.433014 + 0.901387i \(0.642550\pi\)
\(420\) 16.7816 + 7.88688i 0.818858 + 0.384840i
\(421\) 2.65269 0.129284 0.0646420 0.997909i \(-0.479409\pi\)
0.0646420 + 0.997909i \(0.479409\pi\)
\(422\) 0.464092 0.464092i 0.0225916 0.0225916i
\(423\) 3.05719 28.8943i 0.148646 1.40489i
\(424\) 4.81722i 0.233945i
\(425\) 4.07974 4.17999i 0.197897 0.202759i
\(426\) −6.23711 + 13.0647i −0.302189 + 0.632987i
\(427\) −35.6893 35.6893i −1.72713 1.72713i
\(428\) −9.98389 9.98389i −0.482590 0.482590i
\(429\) 4.54918 9.52905i 0.219637 0.460067i
\(430\) −0.0515677 8.49839i −0.00248681 0.409829i
\(431\) 17.0087i 0.819280i 0.912247 + 0.409640i \(0.134346\pi\)
−0.912247 + 0.409640i \(0.865654\pi\)
\(432\) 4.42762 + 2.71959i 0.213024 + 0.130846i
\(433\) 13.8732 13.8732i 0.666705 0.666705i −0.290247 0.956952i \(-0.593738\pi\)
0.956952 + 0.290247i \(0.0937375\pi\)
\(434\) −35.5239 −1.70520
\(435\) −10.6980 29.6698i −0.512931 1.42256i
\(436\) 8.95394 0.428816
\(437\) −1.04719 + 1.04719i −0.0500937 + 0.0500937i
\(438\) 9.22308 3.26246i 0.440696 0.155887i
\(439\) 7.44257i 0.355214i 0.984101 + 0.177607i \(0.0568357\pi\)
−0.984101 + 0.177607i \(0.943164\pi\)
\(440\) 1.92627 1.94979i 0.0918314 0.0929526i
\(441\) −30.0337 37.1412i −1.43017 1.76863i
\(442\) 4.10839 + 4.10839i 0.195416 + 0.195416i
\(443\) 14.0091 + 14.0091i 0.665593 + 0.665593i 0.956693 0.291100i \(-0.0940213\pi\)
−0.291100 + 0.956693i \(0.594021\pi\)
\(444\) −12.8956 6.15635i −0.611996 0.292168i
\(445\) −0.859688 + 0.00521653i −0.0407531 + 0.000247287i
\(446\) 8.22095i 0.389273i
\(447\) −0.638810 1.80593i −0.0302147 0.0854178i
\(448\) −3.38538 + 3.38538i −0.159944 + 0.159944i
\(449\) −17.0757 −0.805851 −0.402926 0.915233i \(-0.632007\pi\)
−0.402926 + 0.915233i \(0.632007\pi\)
\(450\) 1.39714 14.9348i 0.0658619 0.704033i
\(451\) −4.33388 −0.204074
\(452\) 13.3747 13.3747i 0.629092 0.629092i
\(453\) 1.89858 + 5.36734i 0.0892030 + 0.252179i
\(454\) 15.7276i 0.738133i
\(455\) 53.2444 0.323083i 2.49613 0.0151464i
\(456\) 1.56306 + 0.746209i 0.0731972 + 0.0349445i
\(457\) −4.57545 4.57545i −0.214030 0.214030i 0.591947 0.805977i \(-0.298360\pi\)
−0.805977 + 0.591947i \(0.798360\pi\)
\(458\) −11.2971 11.2971i −0.527881 0.527881i
\(459\) −5.90384 + 1.41089i −0.275568 + 0.0658547i
\(460\) −2.32733 + 2.35574i −0.108512 + 0.109837i
\(461\) 0.120191i 0.00559787i 0.999996 + 0.00279893i \(0.000890930\pi\)
−0.999996 + 0.00279893i \(0.999109\pi\)
\(462\) −9.58257 + 3.38963i −0.445822 + 0.157700i
\(463\) −5.82164 + 5.82164i −0.270555 + 0.270555i −0.829323 0.558769i \(-0.811274\pi\)
0.558769 + 0.829323i \(0.311274\pi\)
\(464\) 8.14348 0.378051
\(465\) 9.74747 + 27.0335i 0.452028 + 1.25365i
\(466\) −14.5732 −0.675090
\(467\) 1.26700 1.26700i 0.0586298 0.0586298i −0.677184 0.735814i \(-0.736800\pi\)
0.735814 + 0.677184i \(0.236800\pi\)
\(468\) 14.8381 + 1.56996i 0.685890 + 0.0725712i
\(469\) 40.6455i 1.87684i
\(470\) −0.131410 21.6564i −0.00606147 0.998935i
\(471\) 12.6777 26.5557i 0.584159 1.22362i
\(472\) −7.01383 7.01383i −0.322838 0.322838i
\(473\) 3.29415 + 3.29415i 0.151465 + 0.151465i
\(474\) 5.03734 10.5516i 0.231373 0.484650i
\(475\) −0.0606771 4.99963i −0.00278406 0.229399i
\(476\) 5.59288i 0.256349i
\(477\) 14.3714 + 1.52058i 0.658023 + 0.0696227i
\(478\) −11.3876 + 11.3876i −0.520858 + 0.520858i
\(479\) 4.76857 0.217881 0.108941 0.994048i \(-0.465254\pi\)
0.108941 + 0.994048i \(0.465254\pi\)
\(480\) 3.50518 + 1.64734i 0.159989 + 0.0751903i
\(481\) −41.0333 −1.87096
\(482\) 14.0851 14.0851i 0.641559 0.641559i
\(483\) 11.5777 4.09536i 0.526803 0.186345i
\(484\) 9.49756i 0.431707i
\(485\) −28.2198 27.8794i −1.28140 1.26594i
\(486\) −9.51109 + 12.3507i −0.431432 + 0.560238i
\(487\) 18.6777 + 18.6777i 0.846368 + 0.846368i 0.989678 0.143310i \(-0.0457747\pi\)
−0.143310 + 0.989678i \(0.545775\pi\)
\(488\) −7.45445 7.45445i −0.337447 0.337447i
\(489\) 8.45634 + 4.03707i 0.382409 + 0.182563i
\(490\) −25.3266 25.0211i −1.14414 1.13034i
\(491\) 42.9796i 1.93964i −0.243814 0.969822i \(-0.578399\pi\)
0.243814 0.969822i \(-0.421601\pi\)
\(492\) −2.04225 5.77349i −0.0920716 0.260289i
\(493\) −6.72679 + 6.72679i −0.302959 + 0.302959i
\(494\) 4.97363 0.223774
\(495\) 5.20886 + 6.36220i 0.234121 + 0.285960i
\(496\) −7.41990 −0.333163
\(497\) 28.2963 28.2963i 1.26926 1.26926i
\(498\) −0.586331 1.65757i −0.0262741 0.0742777i
\(499\) 20.8455i 0.933173i 0.884475 + 0.466587i \(0.154516\pi\)
−0.884475 + 0.466587i \(0.845484\pi\)
\(500\) −0.203511 11.1785i −0.00910128 0.499917i
\(501\) 31.1805 + 14.8856i 1.39304 + 0.665040i
\(502\) −12.6570 12.6570i −0.564912 0.564912i
\(503\) 15.7847 + 15.7847i 0.703804 + 0.703804i 0.965225 0.261421i \(-0.0841911\pi\)
−0.261421 + 0.965225i \(0.584191\pi\)
\(504\) −9.03116 11.1684i −0.402280 0.497480i
\(505\) −0.0162747 2.68209i −0.000724216 0.119351i
\(506\) 1.81525i 0.0806979i
\(507\) 19.1654 6.77936i 0.851167 0.301082i
\(508\) −6.46428 + 6.46428i −0.286806 + 0.286806i
\(509\) −4.31039 −0.191055 −0.0955274 0.995427i \(-0.530454\pi\)
−0.0955274 + 0.995427i \(0.530454\pi\)
\(510\) −4.25615 + 1.53464i −0.188466 + 0.0679551i
\(511\) −27.0420 −1.19627
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −2.71959 + 4.42762i −0.120073 + 0.195484i
\(514\) 20.5717i 0.907378i
\(515\) 29.2722 29.6296i 1.28989 1.30563i
\(516\) −2.83609 + 5.94069i −0.124852 + 0.261524i
\(517\) 8.39446 + 8.39446i 0.369188 + 0.369188i
\(518\) 27.9300 + 27.9300i 1.22717 + 1.22717i
\(519\) −6.93820 + 14.5333i −0.304553 + 0.637939i
\(520\) 11.1212 0.0674826i 0.487696 0.00295931i
\(521\) 11.7874i 0.516417i 0.966089 + 0.258208i \(0.0831321\pi\)
−0.966089 + 0.258208i \(0.916868\pi\)
\(522\) −2.57053 + 24.2948i −0.112509 + 1.06336i
\(523\) −9.59018 + 9.59018i −0.419349 + 0.419349i −0.884979 0.465630i \(-0.845828\pi\)
0.465630 + 0.884979i \(0.345828\pi\)
\(524\) 4.64733 0.203020
\(525\) −17.4076 + 37.6311i −0.759729 + 1.64236i
\(526\) 8.56553 0.373475
\(527\) 6.12909 6.12909i 0.266987 0.266987i
\(528\) −2.00152 + 0.707993i −0.0871048 + 0.0308114i
\(529\) 20.8068i 0.904644i
\(530\) 10.7714 0.0653603i 0.467881 0.00283907i
\(531\) 23.1387 18.7107i 1.00413 0.811977i
\(532\) −3.38538 3.38538i −0.146775 0.146775i
\(533\) −12.4347 12.4347i −0.538609 0.538609i
\(534\) 0.600953 + 0.286896i 0.0260058 + 0.0124152i
\(535\) 22.1888 22.4597i 0.959305 0.971018i
\(536\) 8.48965i 0.366697i
\(537\) −6.52027 18.4330i −0.281370 0.795443i
\(538\) −6.72689 + 6.72689i −0.290017 + 0.290017i
\(539\) 19.5158 0.840605
\(540\) −6.02101 + 9.93718i −0.259103 + 0.427628i
\(541\) −29.8151 −1.28185 −0.640925 0.767603i \(-0.721449\pi\)
−0.640925 + 0.767603i \(0.721449\pi\)
\(542\) −0.286733 + 0.286733i −0.0123162 + 0.0123162i
\(543\) −5.75341 16.2651i −0.246903 0.698001i
\(544\) 1.16819i 0.0500857i
\(545\) 0.121488 + 20.0212i 0.00520395 + 0.857616i
\(546\) −37.2198 17.7688i −1.59286 0.760433i
\(547\) −9.70052 9.70052i −0.414764 0.414764i 0.468630 0.883395i \(-0.344748\pi\)
−0.883395 + 0.468630i \(0.844748\pi\)
\(548\) 0.825480 + 0.825480i 0.0352628 + 0.0352628i
\(549\) 24.5922 19.8862i 1.04957 0.848721i
\(550\) 4.38592 + 4.28074i 0.187016 + 0.182531i
\(551\) 8.14348i 0.346924i
\(552\) 2.41824 0.855399i 0.102927 0.0364082i
\(553\) −22.8533 + 22.8533i −0.971819 + 0.971819i
\(554\) −4.46356 −0.189639
\(555\) 13.5908 28.9183i 0.576898 1.22751i
\(556\) −3.47441 −0.147348
\(557\) 19.7758 19.7758i 0.837928 0.837928i −0.150658 0.988586i \(-0.548139\pi\)
0.988586 + 0.150658i \(0.0481393\pi\)
\(558\) 2.34213 22.1361i 0.0991504 0.937097i
\(559\) 18.9031i 0.799517i
\(560\) −7.61574 7.52387i −0.321824 0.317942i
\(561\) 1.06849 2.23815i 0.0451119 0.0944946i
\(562\) −8.43036 8.43036i −0.355613 0.355613i
\(563\) 26.3822 + 26.3822i 1.11188 + 1.11188i 0.992896 + 0.118981i \(0.0379629\pi\)
0.118981 + 0.992896i \(0.462037\pi\)
\(564\) −7.22720 + 15.1386i −0.304320 + 0.637451i
\(565\) 30.0876 + 29.7247i 1.26580 + 1.25053i
\(566\) 15.7523i 0.662120i
\(567\) 36.1699 23.4177i 1.51899 0.983452i
\(568\) 5.91027 5.91027i 0.247990 0.247990i
\(569\) −21.7175 −0.910445 −0.455222 0.890378i \(-0.650440\pi\)
−0.455222 + 0.890378i \(0.650440\pi\)
\(570\) −1.64734 + 3.50518i −0.0689993 + 0.146816i
\(571\) −15.2769 −0.639319 −0.319660 0.947532i \(-0.603569\pi\)
−0.319660 + 0.947532i \(0.603569\pi\)
\(572\) −4.31080 + 4.31080i −0.180243 + 0.180243i
\(573\) −16.5665 + 5.86002i −0.692073 + 0.244806i
\(574\) 16.9278i 0.706553i
\(575\) −5.29908 5.17200i −0.220987 0.215687i
\(576\) −1.88634 2.33275i −0.0785976 0.0971978i
\(577\) 7.00181 + 7.00181i 0.291489 + 0.291489i 0.837668 0.546179i \(-0.183918\pi\)
−0.546179 + 0.837668i \(0.683918\pi\)
\(578\) −11.0559 11.0559i −0.459863 0.459863i
\(579\) 2.94032 + 1.40371i 0.122196 + 0.0583364i
\(580\) 0.110491 + 18.2090i 0.00458790 + 0.756089i
\(581\) 4.85999i 0.201626i
\(582\) 10.2470 + 28.9685i 0.424750 + 1.20078i
\(583\) −4.17523 + 4.17523i −0.172920 + 0.172920i
\(584\) −5.64827 −0.233727
\(585\) −3.30914 + 33.1996i −0.136816 + 1.37264i
\(586\) 4.70889 0.194522
\(587\) −5.53868 + 5.53868i −0.228606 + 0.228606i −0.812110 0.583504i \(-0.801681\pi\)
0.583504 + 0.812110i \(0.301681\pi\)
\(588\) 9.19640 + 25.9985i 0.379253 + 1.07216i
\(589\) 7.41990i 0.305732i
\(590\) 15.5880 15.7783i 0.641746 0.649582i
\(591\) 8.12283 + 3.87785i 0.334129 + 0.159514i
\(592\) 5.83375 + 5.83375i 0.239766 + 0.239766i
\(593\) 31.4864 + 31.4864i 1.29299 + 1.29299i 0.932929 + 0.360061i \(0.117244\pi\)
0.360061 + 0.932929i \(0.382756\pi\)
\(594\) −1.48040 6.19470i −0.0607415 0.254172i
\(595\) 12.5058 0.0758846i 0.512689 0.00311096i
\(596\) 1.10597i 0.0453021i
\(597\) 1.45996 0.516428i 0.0597520 0.0211360i
\(598\) 5.20832 5.20832i 0.212984 0.212984i
\(599\) −31.3766 −1.28201 −0.641007 0.767535i \(-0.721483\pi\)
−0.641007 + 0.767535i \(0.721483\pi\)
\(600\) −3.63593 + 7.86003i −0.148436 + 0.320884i
\(601\) −36.3695 −1.48354 −0.741771 0.670654i \(-0.766014\pi\)
−0.741771 + 0.670654i \(0.766014\pi\)
\(602\) 12.8667 12.8667i 0.524408 0.524408i
\(603\) −25.3276 2.67981i −1.03142 0.109130i
\(604\) 3.28699i 0.133746i
\(605\) 21.2368 0.128863i 0.863399 0.00523904i
\(606\) −0.895070 + 1.87488i −0.0363597 + 0.0761618i
\(607\) 8.74748 + 8.74748i 0.355049 + 0.355049i 0.861984 0.506935i \(-0.169222\pi\)
−0.506935 + 0.861984i \(0.669222\pi\)
\(608\) −0.707107 0.707107i −0.0286770 0.0286770i
\(609\) 29.0933 60.9410i 1.17892 2.46945i
\(610\) 16.5672 16.7695i 0.670786 0.678977i
\(611\) 48.1707i 1.94878i
\(612\) 3.48511 + 0.368745i 0.140877 + 0.0149056i
\(613\) −1.37399 + 1.37399i −0.0554951 + 0.0554951i −0.734310 0.678815i \(-0.762494\pi\)
0.678815 + 0.734310i \(0.262494\pi\)
\(614\) 2.39024 0.0964621
\(615\) 12.8820 4.64485i 0.519451 0.187299i
\(616\) 5.86842 0.236446
\(617\) 11.8837 11.8837i 0.478419 0.478419i −0.426207 0.904626i \(-0.640150\pi\)
0.904626 + 0.426207i \(0.140150\pi\)
\(618\) −30.4156 + 10.7589i −1.22350 + 0.432785i
\(619\) 4.06759i 0.163490i 0.996653 + 0.0817450i \(0.0260493\pi\)
−0.996653 + 0.0817450i \(0.973951\pi\)
\(620\) −0.100674 16.5911i −0.00404315 0.666314i
\(621\) 1.78862 + 7.48446i 0.0717750 + 0.300341i
\(622\) −10.1355 10.1355i −0.406395 0.406395i
\(623\) −1.30158 1.30158i −0.0521468 0.0521468i
\(624\) −7.77411 3.71137i −0.311214 0.148574i
\(625\) 24.9926 0.606726i 0.999705 0.0242690i
\(626\) 2.21202i 0.0884102i
\(627\) −0.707993 2.00152i −0.0282745 0.0799329i
\(628\) −12.0134 + 12.0134i −0.479387 + 0.479387i
\(629\) −9.63775 −0.384282
\(630\) 24.8503 20.3454i 0.990059 0.810582i
\(631\) −5.67496 −0.225917 −0.112958 0.993600i \(-0.536033\pi\)
−0.112958 + 0.993600i \(0.536033\pi\)
\(632\) −4.77337 + 4.77337i −0.189875 + 0.189875i
\(633\) −0.379096 1.07172i −0.0150677 0.0425969i
\(634\) 30.5452i 1.21311i
\(635\) −14.5420 14.3666i −0.577082 0.570121i
\(636\) −7.52963 3.59466i −0.298569 0.142537i
\(637\) 55.9947 + 55.9947i 2.21859 + 2.21859i
\(638\) −7.05819 7.05819i −0.279437 0.279437i
\(639\) 15.7668 + 19.4980i 0.623724 + 0.771329i
\(640\) −1.59070 1.57152i −0.0628781 0.0621196i
\(641\) 1.58825i 0.0627323i 0.999508 + 0.0313661i \(0.00998579\pi\)
−0.999508 + 0.0313661i \(0.990014\pi\)
\(642\) −23.0555 + 8.15539i −0.909930 + 0.321868i
\(643\) −8.25666 + 8.25666i −0.325611 + 0.325611i −0.850915 0.525304i \(-0.823952\pi\)
0.525304 + 0.850915i \(0.323952\pi\)
\(644\) −7.09025 −0.279395
\(645\) −13.3220 6.26098i −0.524554 0.246526i
\(646\) 1.16819 0.0459618
\(647\) −12.9377 + 12.9377i −0.508635 + 0.508635i −0.914107 0.405472i \(-0.867107\pi\)
0.405472 + 0.914107i \(0.367107\pi\)
\(648\) 7.55483 4.89127i 0.296782 0.192147i
\(649\) 12.1582i 0.477251i
\(650\) 0.301786 + 24.8663i 0.0118370 + 0.975338i
\(651\) −26.5083 + 55.5262i −1.03894 + 2.17624i
\(652\) −3.82552 3.82552i −0.149819 0.149819i
\(653\) 16.2867 + 16.2867i 0.637350 + 0.637350i 0.949901 0.312551i \(-0.101184\pi\)
−0.312551 + 0.949901i \(0.601184\pi\)
\(654\) 6.68151 13.9956i 0.261268 0.547271i
\(655\) 0.0630553 + 10.3916i 0.00246377 + 0.406032i
\(656\) 3.53572i 0.138047i
\(657\) 1.78291 16.8508i 0.0695579 0.657410i
\(658\) 32.7882 32.7882i 1.27822 1.27822i
\(659\) −40.1270 −1.56313 −0.781563 0.623827i \(-0.785577\pi\)
−0.781563 + 0.623827i \(0.785577\pi\)
\(660\) −1.61025 4.46584i −0.0626788 0.173833i
\(661\) −17.8333 −0.693634 −0.346817 0.937933i \(-0.612737\pi\)
−0.346817 + 0.937933i \(0.612737\pi\)
\(662\) 4.50516 4.50516i 0.175098 0.175098i
\(663\) 9.48740 3.35596i 0.368460 0.130335i
\(664\) 1.01511i 0.0393939i
\(665\) 7.52387 7.61574i 0.291763 0.295326i
\(666\) −19.2456 + 15.5626i −0.745750 + 0.603040i
\(667\) 8.52773 + 8.52773i 0.330195 + 0.330195i
\(668\) −14.1056 14.1056i −0.545761 0.545761i
\(669\) −12.8499 6.13455i −0.496805 0.237176i
\(670\) −18.9831 + 0.115188i −0.733381 + 0.00445010i
\(671\) 12.9220i 0.498848i
\(672\) 2.76537 + 7.81778i 0.106676 + 0.301577i
\(673\) 15.7599 15.7599i 0.607498 0.607498i −0.334793 0.942292i \(-0.608667\pi\)
0.942292 + 0.334793i \(0.108667\pi\)
\(674\) −1.60201 −0.0617073
\(675\) −22.3015 13.3283i −0.858385 0.513007i
\(676\) −11.7370 −0.451424
\(677\) 28.0078 28.0078i 1.07643 1.07643i 0.0795985 0.996827i \(-0.474636\pi\)
0.996827 0.0795985i \(-0.0253638\pi\)
\(678\) −10.9252 30.8858i −0.419579 1.18616i
\(679\) 84.9352i 3.25951i
\(680\) 2.61210 0.0158500i 0.100169 0.000607822i
\(681\) −24.5833 11.7361i −0.942033 0.449728i
\(682\) 6.43105 + 6.43105i 0.246258 + 0.246258i
\(683\) −11.0403 11.0403i −0.422444 0.422444i 0.463600 0.886045i \(-0.346557\pi\)
−0.886045 + 0.463600i \(0.846557\pi\)
\(684\) 2.33275 1.88634i 0.0891948 0.0721261i
\(685\) −1.83459 + 1.85700i −0.0700963 + 0.0709521i
\(686\) 42.7137i 1.63082i
\(687\) −26.0882 + 9.22813i −0.995327 + 0.352075i
\(688\) 2.68748 2.68748i 0.102459 0.102459i
\(689\) −23.9591 −0.912769
\(690\) 1.94551 + 5.39564i 0.0740642 + 0.205409i
\(691\) −34.6717 −1.31897 −0.659486 0.751717i \(-0.729226\pi\)
−0.659486 + 0.751717i \(0.729226\pi\)
\(692\) 6.57463 6.57463i 0.249930 0.249930i
\(693\) −1.85240 + 17.5075i −0.0703669 + 0.665057i
\(694\) 31.3154i 1.18872i
\(695\) −0.0471409 7.76887i −0.00178816 0.294690i
\(696\) 6.07674 12.7288i 0.230338 0.482483i
\(697\) −2.92063 2.92063i −0.110627 0.110627i
\(698\) 13.9126 + 13.9126i 0.526600 + 0.526600i
\(699\) −10.8747 + 22.7788i −0.411317 + 0.861575i
\(700\) 16.7203 17.1311i 0.631966 0.647494i
\(701\) 2.11730i 0.0799692i −0.999200 0.0399846i \(-0.987269\pi\)
0.999200 0.0399846i \(-0.0127309\pi\)
\(702\) 13.5263 22.0214i 0.510516 0.831143i
\(703\) −5.83375 + 5.83375i −0.220024 + 0.220024i
\(704\) 1.22574 0.0461969
\(705\) −33.9484 15.9548i −1.27857 0.600893i
\(706\) 35.2206 1.32554
\(707\) 4.06073 4.06073i 0.152719 0.152719i
\(708\) −16.1969 + 5.72929i −0.608715 + 0.215320i
\(709\) 14.5305i 0.545705i −0.962056 0.272852i \(-0.912033\pi\)
0.962056 0.272852i \(-0.0879670\pi\)
\(710\) 13.2957 + 13.1353i 0.498979 + 0.492960i
\(711\) −12.7339 15.7474i −0.477558 0.590572i
\(712\) −0.271862 0.271862i −0.0101885 0.0101885i
\(713\) −7.77001 7.77001i −0.290989 0.290989i
\(714\) −8.74204 4.17346i −0.327163 0.156188i
\(715\) −9.69755 9.58057i −0.362668 0.358293i
\(716\) 11.2885i 0.421870i
\(717\) 9.30204 + 26.2971i 0.347391 + 0.982085i
\(718\) −14.8000 + 14.8000i −0.552331 + 0.552331i
\(719\) −2.51322 −0.0937272 −0.0468636 0.998901i \(-0.514923\pi\)
−0.0468636 + 0.998901i \(0.514923\pi\)
\(720\) 5.19049 4.24956i 0.193438 0.158372i
\(721\) 89.1782 3.32117
\(722\) 0.707107 0.707107i 0.0263158 0.0263158i
\(723\) −11.5055 32.5264i −0.427894 1.20967i
\(724\) 9.96083i 0.370191i
\(725\) −40.7144 + 0.494122i −1.51209 + 0.0183512i
\(726\) −14.8453 7.08717i −0.550961 0.263029i
\(727\) −7.64794 7.64794i −0.283646 0.283646i 0.550915 0.834561i \(-0.314279\pi\)
−0.834561 + 0.550915i \(0.814279\pi\)
\(728\) 16.8377 + 16.8377i 0.624045 + 0.624045i
\(729\) 12.2076 + 24.0826i 0.452135 + 0.891950i
\(730\) −0.0766361 12.6297i −0.00283643 0.467446i
\(731\) 4.43990i 0.164215i
\(732\) −17.2144 + 6.08920i −0.636261 + 0.225063i
\(733\) 24.3729 24.3729i 0.900235 0.900235i −0.0952214 0.995456i \(-0.530356\pi\)
0.995456 + 0.0952214i \(0.0303559\pi\)
\(734\) −37.2954 −1.37660
\(735\) −58.0086 + 20.9161i −2.13968 + 0.771504i
\(736\) −1.48094 −0.0545883
\(737\) 7.35823 7.35823i 0.271044 0.271044i
\(738\) −10.5483 1.11607i −0.388288 0.0410831i
\(739\) 30.8274i 1.13401i −0.823716 0.567003i \(-0.808103\pi\)
0.823716 0.567003i \(-0.191897\pi\)
\(740\) −12.9653 + 13.1236i −0.476613 + 0.482432i
\(741\) 3.71137 7.77411i 0.136341 0.285589i
\(742\) 16.3081 + 16.3081i 0.598691 + 0.598691i
\(743\) −23.0214 23.0214i −0.844574 0.844574i 0.144876 0.989450i \(-0.453722\pi\)
−0.989450 + 0.144876i \(0.953722\pi\)
\(744\) −5.53680 + 11.5978i −0.202989 + 0.425195i
\(745\) −2.47297 + 0.0150058i −0.0906026 + 0.000549770i
\(746\) 9.42209i 0.344967i
\(747\) −3.02842 0.320425i −0.110804 0.0117237i
\(748\) −1.01250 + 1.01250i −0.0370208 + 0.0370208i
\(749\) 67.5986 2.47000
\(750\) −17.6246 8.02339i −0.643558 0.292973i
\(751\) 43.6630 1.59329 0.796643 0.604450i \(-0.206607\pi\)
0.796643 + 0.604450i \(0.206607\pi\)
\(752\) 6.84848 6.84848i 0.249738 0.249738i
\(753\) −29.2286 + 10.3390i −1.06515 + 0.376773i
\(754\) 40.5027i 1.47502i
\(755\) 7.34980 0.0445981i 0.267486 0.00162309i
\(756\) −24.1961 + 5.78233i −0.880002 + 0.210301i
\(757\) −8.25576 8.25576i −0.300061 0.300061i 0.540977 0.841038i \(-0.318055\pi\)
−0.841038 + 0.540977i \(0.818055\pi\)
\(758\) −0.145573 0.145573i −0.00528745 0.00528745i
\(759\) −2.83736 1.35456i −0.102990 0.0491674i
\(760\) 1.57152 1.59070i 0.0570049 0.0577009i
\(761\) 45.4398i 1.64719i 0.567176 + 0.823596i \(0.308036\pi\)
−0.567176 + 0.823596i \(0.691964\pi\)
\(762\) 5.28038 + 14.9278i 0.191288 + 0.540777i
\(763\) −30.3125 + 30.3125i −1.09739 + 1.09739i
\(764\) 10.1454 0.367048
\(765\) −0.777238 + 7.79781i −0.0281011 + 0.281930i
\(766\) −11.6945 −0.422539
\(767\) −34.8842 + 34.8842i −1.25960 + 1.25960i
\(768\) 0.577604 + 1.63290i 0.0208425 + 0.0589223i
\(769\) 14.3253i 0.516582i −0.966067 0.258291i \(-0.916841\pi\)
0.966067 0.258291i \(-0.0831593\pi\)
\(770\) 0.0796231 + 13.1220i 0.00286942 + 0.472882i
\(771\) 32.1549 + 15.3508i 1.15803 + 0.552845i
\(772\) −1.33016 1.33016i −0.0478734 0.0478734i
\(773\) −30.7793 30.7793i −1.10706 1.10706i −0.993536 0.113520i \(-0.963788\pi\)
−0.113520 0.993536i \(-0.536212\pi\)
\(774\) 7.16936 + 8.86600i 0.257697 + 0.318682i
\(775\) 37.0968 0.450218i 1.33256 0.0161723i
\(776\) 17.7405i 0.636846i
\(777\) 64.4980 22.8148i 2.31385 0.818475i