Properties

Label 441.2.h.e.373.3
Level $441$
Weight $2$
Character 441.373
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.3
Root \(-0.766044 + 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.e.214.3

$q$-expansion

\(f(q)\) \(=\) \(q+2.53209 q^{2} +(0.592396 - 1.62760i) q^{3} +4.41147 q^{4} +(-0.439693 - 0.761570i) q^{5} +(1.50000 - 4.12122i) q^{6} +6.10607 q^{8} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})\) \(q+2.53209 q^{2} +(0.592396 - 1.62760i) q^{3} +4.41147 q^{4} +(-0.439693 - 0.761570i) q^{5} +(1.50000 - 4.12122i) q^{6} +6.10607 q^{8} +(-2.29813 - 1.92836i) q^{9} +(-1.11334 - 1.92836i) q^{10} +(-1.93969 + 3.35965i) q^{11} +(2.61334 - 7.18009i) q^{12} +(-2.72668 + 4.72275i) q^{13} +(-1.50000 + 0.264490i) q^{15} +6.63816 q^{16} +(0.826352 + 1.43128i) q^{17} +(-5.81908 - 4.88279i) q^{18} +(1.20574 - 2.08840i) q^{19} +(-1.93969 - 3.35965i) q^{20} +(-4.91147 + 8.50692i) q^{22} +(-1.58125 - 2.73881i) q^{23} +(3.61721 - 9.93821i) q^{24} +(2.11334 - 3.66041i) q^{25} +(-6.90420 + 11.9584i) q^{26} +(-4.50000 + 2.59808i) q^{27} +(3.02481 + 5.23913i) q^{29} +(-3.79813 + 0.669713i) q^{30} +4.55438 q^{31} +4.59627 q^{32} +(4.31908 + 5.14728i) q^{33} +(2.09240 + 3.62414i) q^{34} +(-10.1382 - 8.50692i) q^{36} +(2.27719 - 3.94421i) q^{37} +(3.05303 - 5.28801i) q^{38} +(6.07145 + 7.23567i) q^{39} +(-2.68479 - 4.65020i) q^{40} +(-0.592396 + 1.02606i) q^{41} +(-0.0923963 - 0.160035i) q^{43} +(-8.55690 + 14.8210i) q^{44} +(-0.458111 + 2.59808i) q^{45} +(-4.00387 - 6.93491i) q^{46} +1.02229 q^{47} +(3.93242 - 10.8042i) q^{48} +(5.35117 - 9.26849i) q^{50} +(2.81908 - 0.497079i) q^{51} +(-12.0287 + 20.8343i) q^{52} +(-3.64543 - 6.31407i) q^{53} +(-11.3944 + 6.57856i) q^{54} +3.41147 q^{55} +(-2.68479 - 3.19961i) q^{57} +(7.65910 + 13.2660i) q^{58} -6.66044 q^{59} +(-6.61721 + 1.16679i) q^{60} +2.59627 q^{61} +11.5321 q^{62} -1.63816 q^{64} +4.79561 q^{65} +(10.9363 + 13.0334i) q^{66} -2.95811 q^{67} +(3.64543 + 6.31407i) q^{68} +(-5.39440 + 0.951178i) q^{69} -3.68004 q^{71} +(-14.0326 - 11.7747i) q^{72} +(-6.39053 - 11.0687i) q^{73} +(5.76604 - 9.98708i) q^{74} +(-4.70574 - 5.60808i) q^{75} +(5.31908 - 9.21291i) q^{76} +(15.3735 + 18.3214i) q^{78} -5.95811 q^{79} +(-2.91875 - 5.05542i) q^{80} +(1.56283 + 8.86327i) q^{81} +(-1.50000 + 2.59808i) q^{82} +(-0.109470 - 0.189608i) q^{83} +(0.726682 - 1.25865i) q^{85} +(-0.233956 - 0.405223i) q^{86} +(10.3191 - 1.81953i) q^{87} +(-11.8439 + 20.5142i) q^{88} +(5.51367 - 9.54996i) q^{89} +(-1.15998 + 6.57856i) q^{90} +(-6.97565 - 12.0822i) q^{92} +(2.69800 - 7.41268i) q^{93} +2.58853 q^{94} -2.12061 q^{95} +(2.72281 - 7.48086i) q^{96} +(6.25150 + 10.8279i) q^{97} +(10.9363 - 3.98048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{2} + 6q^{4} + 3q^{5} + 9q^{6} + 12q^{8} + O(q^{10}) \) \( 6q + 6q^{2} + 6q^{4} + 3q^{5} + 9q^{6} + 12q^{8} - 6q^{11} + 9q^{12} - 3q^{13} - 9q^{15} + 6q^{16} + 6q^{17} - 18q^{18} - 3q^{19} - 6q^{20} - 9q^{22} - 12q^{23} - 9q^{24} + 6q^{25} - 3q^{26} - 27q^{27} - 9q^{29} - 9q^{30} + 6q^{31} + 9q^{33} + 9q^{34} - 27q^{36} + 3q^{37} + 6q^{38} + 36q^{39} - 9q^{40} + 3q^{43} - 15q^{44} - 9q^{45} - 6q^{47} + 6q^{50} - 21q^{52} - 6q^{53} - 27q^{54} - 9q^{57} + 9q^{58} + 6q^{59} - 9q^{60} - 12q^{61} + 60q^{62} + 24q^{64} + 30q^{65} + 18q^{66} - 24q^{67} + 6q^{68} + 9q^{69} + 18q^{71} - 9q^{72} - 21q^{73} + 30q^{74} - 18q^{75} + 15q^{76} + 54q^{78} - 42q^{79} - 15q^{80} - 9q^{82} - 18q^{83} - 9q^{85} - 6q^{86} + 45q^{87} - 27q^{88} + 12q^{89} - 27q^{90} - 3q^{92} + 54q^{93} + 36q^{94} - 24q^{95} + 27q^{96} - 3q^{97} + 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.53209 1.79046 0.895229 0.445607i \(-0.147012\pi\)
0.895229 + 0.445607i \(0.147012\pi\)
\(3\) 0.592396 1.62760i 0.342020 0.939693i
\(4\) 4.41147 2.20574
\(5\) −0.439693 0.761570i −0.196637 0.340584i 0.750799 0.660530i \(-0.229669\pi\)
−0.947436 + 0.319946i \(0.896335\pi\)
\(6\) 1.50000 4.12122i 0.612372 1.68248i
\(7\) 0 0
\(8\) 6.10607 2.15882
\(9\) −2.29813 1.92836i −0.766044 0.642788i
\(10\) −1.11334 1.92836i −0.352069 0.609802i
\(11\) −1.93969 + 3.35965i −0.584839 + 1.01297i 0.410056 + 0.912060i \(0.365509\pi\)
−0.994895 + 0.100911i \(0.967824\pi\)
\(12\) 2.61334 7.18009i 0.754407 2.07271i
\(13\) −2.72668 + 4.72275i −0.756245 + 1.30986i 0.188507 + 0.982072i \(0.439635\pi\)
−0.944753 + 0.327784i \(0.893698\pi\)
\(14\) 0 0
\(15\) −1.50000 + 0.264490i −0.387298 + 0.0682911i
\(16\) 6.63816 1.65954
\(17\) 0.826352 + 1.43128i 0.200420 + 0.347137i 0.948664 0.316286i \(-0.102436\pi\)
−0.748244 + 0.663424i \(0.769103\pi\)
\(18\) −5.81908 4.88279i −1.37157 1.15088i
\(19\) 1.20574 2.08840i 0.276615 0.479111i −0.693926 0.720046i \(-0.744121\pi\)
0.970541 + 0.240935i \(0.0774540\pi\)
\(20\) −1.93969 3.35965i −0.433728 0.751240i
\(21\) 0 0
\(22\) −4.91147 + 8.50692i −1.04713 + 1.81368i
\(23\) −1.58125 2.73881i −0.329714 0.571081i 0.652741 0.757581i \(-0.273619\pi\)
−0.982455 + 0.186500i \(0.940286\pi\)
\(24\) 3.61721 9.93821i 0.738360 2.02863i
\(25\) 2.11334 3.66041i 0.422668 0.732083i
\(26\) −6.90420 + 11.9584i −1.35403 + 2.34524i
\(27\) −4.50000 + 2.59808i −0.866025 + 0.500000i
\(28\) 0 0
\(29\) 3.02481 + 5.23913i 0.561694 + 0.972883i 0.997349 + 0.0727688i \(0.0231835\pi\)
−0.435655 + 0.900114i \(0.643483\pi\)
\(30\) −3.79813 + 0.669713i −0.693441 + 0.122272i
\(31\) 4.55438 0.817990 0.408995 0.912537i \(-0.365879\pi\)
0.408995 + 0.912537i \(0.365879\pi\)
\(32\) 4.59627 0.812513
\(33\) 4.31908 + 5.14728i 0.751855 + 0.896026i
\(34\) 2.09240 + 3.62414i 0.358843 + 0.621534i
\(35\) 0 0
\(36\) −10.1382 8.50692i −1.68969 1.41782i
\(37\) 2.27719 3.94421i 0.374368 0.648424i −0.615865 0.787852i \(-0.711193\pi\)
0.990232 + 0.139428i \(0.0445265\pi\)
\(38\) 3.05303 5.28801i 0.495267 0.857828i
\(39\) 6.07145 + 7.23567i 0.972210 + 1.15864i
\(40\) −2.68479 4.65020i −0.424503 0.735261i
\(41\) −0.592396 + 1.02606i −0.0925168 + 0.160244i −0.908570 0.417734i \(-0.862825\pi\)
0.816053 + 0.577977i \(0.196158\pi\)
\(42\) 0 0
\(43\) −0.0923963 0.160035i −0.0140903 0.0244051i 0.858894 0.512153i \(-0.171152\pi\)
−0.872985 + 0.487748i \(0.837819\pi\)
\(44\) −8.55690 + 14.8210i −1.29000 + 2.23435i
\(45\) −0.458111 + 2.59808i −0.0682911 + 0.387298i
\(46\) −4.00387 6.93491i −0.590338 1.02250i
\(47\) 1.02229 0.149116 0.0745581 0.997217i \(-0.476245\pi\)
0.0745581 + 0.997217i \(0.476245\pi\)
\(48\) 3.93242 10.8042i 0.567596 1.55946i
\(49\) 0 0
\(50\) 5.35117 9.26849i 0.756769 1.31076i
\(51\) 2.81908 0.497079i 0.394750 0.0696051i
\(52\) −12.0287 + 20.8343i −1.66808 + 2.88920i
\(53\) −3.64543 6.31407i −0.500738 0.867304i −1.00000 0.000852699i \(-0.999729\pi\)
0.499261 0.866451i \(-0.333605\pi\)
\(54\) −11.3944 + 6.57856i −1.55058 + 0.895229i
\(55\) 3.41147 0.460003
\(56\) 0 0
\(57\) −2.68479 3.19961i −0.355609 0.423799i
\(58\) 7.65910 + 13.2660i 1.00569 + 1.74190i
\(59\) −6.66044 −0.867116 −0.433558 0.901126i \(-0.642742\pi\)
−0.433558 + 0.901126i \(0.642742\pi\)
\(60\) −6.61721 + 1.16679i −0.854278 + 0.150632i
\(61\) 2.59627 0.332418 0.166209 0.986091i \(-0.446847\pi\)
0.166209 + 0.986091i \(0.446847\pi\)
\(62\) 11.5321 1.46458
\(63\) 0 0
\(64\) −1.63816 −0.204769
\(65\) 4.79561 0.594822
\(66\) 10.9363 + 13.0334i 1.34616 + 1.60430i
\(67\) −2.95811 −0.361391 −0.180695 0.983539i \(-0.557835\pi\)
−0.180695 + 0.983539i \(0.557835\pi\)
\(68\) 3.64543 + 6.31407i 0.442073 + 0.765693i
\(69\) −5.39440 + 0.951178i −0.649409 + 0.114508i
\(70\) 0 0
\(71\) −3.68004 −0.436741 −0.218370 0.975866i \(-0.570074\pi\)
−0.218370 + 0.975866i \(0.570074\pi\)
\(72\) −14.0326 11.7747i −1.65375 1.38766i
\(73\) −6.39053 11.0687i −0.747955 1.29550i −0.948801 0.315873i \(-0.897703\pi\)
0.200847 0.979623i \(-0.435631\pi\)
\(74\) 5.76604 9.98708i 0.670289 1.16097i
\(75\) −4.70574 5.60808i −0.543372 0.647565i
\(76\) 5.31908 9.21291i 0.610140 1.05679i
\(77\) 0 0
\(78\) 15.3735 + 18.3214i 1.74070 + 2.07449i
\(79\) −5.95811 −0.670340 −0.335170 0.942158i \(-0.608794\pi\)
−0.335170 + 0.942158i \(0.608794\pi\)
\(80\) −2.91875 5.05542i −0.326326 0.565213i
\(81\) 1.56283 + 8.86327i 0.173648 + 0.984808i
\(82\) −1.50000 + 2.59808i −0.165647 + 0.286910i
\(83\) −0.109470 0.189608i −0.0120159 0.0208122i 0.859955 0.510370i \(-0.170492\pi\)
−0.871971 + 0.489558i \(0.837158\pi\)
\(84\) 0 0
\(85\) 0.726682 1.25865i 0.0788197 0.136520i
\(86\) −0.233956 0.405223i −0.0252281 0.0436963i
\(87\) 10.3191 1.81953i 1.10632 0.195074i
\(88\) −11.8439 + 20.5142i −1.26256 + 2.18682i
\(89\) 5.51367 9.54996i 0.584448 1.01229i −0.410496 0.911862i \(-0.634644\pi\)
0.994944 0.100431i \(-0.0320222\pi\)
\(90\) −1.15998 + 6.57856i −0.122272 + 0.693441i
\(91\) 0 0
\(92\) −6.97565 12.0822i −0.727262 1.25965i
\(93\) 2.69800 7.41268i 0.279769 0.768660i
\(94\) 2.58853 0.266986
\(95\) −2.12061 −0.217570
\(96\) 2.72281 7.48086i 0.277896 0.763512i
\(97\) 6.25150 + 10.8279i 0.634743 + 1.09941i 0.986569 + 0.163342i \(0.0522275\pi\)
−0.351826 + 0.936065i \(0.614439\pi\)
\(98\) 0 0
\(99\) 10.9363 3.98048i 1.09914 0.400054i
\(100\) 9.32295 16.1478i 0.932295 1.61478i
\(101\) −4.85844 + 8.41507i −0.483433 + 0.837330i −0.999819 0.0190255i \(-0.993944\pi\)
0.516386 + 0.856356i \(0.327277\pi\)
\(102\) 7.13816 1.25865i 0.706783 0.124625i
\(103\) 3.29813 + 5.71253i 0.324975 + 0.562873i 0.981507 0.191425i \(-0.0613109\pi\)
−0.656533 + 0.754298i \(0.727978\pi\)
\(104\) −16.6493 + 28.8374i −1.63260 + 2.82774i
\(105\) 0 0
\(106\) −9.23055 15.9878i −0.896550 1.55287i
\(107\) −1.19459 + 2.06910i −0.115486 + 0.200027i −0.917974 0.396641i \(-0.870176\pi\)
0.802488 + 0.596668i \(0.203509\pi\)
\(108\) −19.8516 + 11.4613i −1.91022 + 1.10287i
\(109\) −1.97906 3.42782i −0.189559 0.328326i 0.755544 0.655098i \(-0.227373\pi\)
−0.945103 + 0.326772i \(0.894039\pi\)
\(110\) 8.63816 0.823616
\(111\) −5.07057 6.04288i −0.481278 0.573564i
\(112\) 0 0
\(113\) −8.22668 + 14.2490i −0.773901 + 1.34044i 0.161509 + 0.986871i \(0.448364\pi\)
−0.935410 + 0.353565i \(0.884969\pi\)
\(114\) −6.79813 8.10170i −0.636704 0.758794i
\(115\) −1.39053 + 2.40847i −0.129668 + 0.224591i
\(116\) 13.3439 + 23.1123i 1.23895 + 2.14592i
\(117\) 15.3735 5.59548i 1.42128 0.517302i
\(118\) −16.8648 −1.55253
\(119\) 0 0
\(120\) −9.15910 + 1.61500i −0.836108 + 0.147428i
\(121\) −2.02481 3.50708i −0.184074 0.318826i
\(122\) 6.57398 0.595180
\(123\) 1.31908 + 1.57202i 0.118937 + 0.141744i
\(124\) 20.0915 1.80427
\(125\) −8.11381 −0.725721
\(126\) 0 0
\(127\) 17.6536 1.56651 0.783253 0.621702i \(-0.213559\pi\)
0.783253 + 0.621702i \(0.213559\pi\)
\(128\) −13.3405 −1.17914
\(129\) −0.315207 + 0.0555796i −0.0277525 + 0.00489351i
\(130\) 12.1429 1.06500
\(131\) −9.59879 16.6256i −0.838650 1.45259i −0.891023 0.453958i \(-0.850012\pi\)
0.0523729 0.998628i \(-0.483322\pi\)
\(132\) 19.0535 + 22.7071i 1.65839 + 1.97640i
\(133\) 0 0
\(134\) −7.49020 −0.647055
\(135\) 3.95723 + 2.28471i 0.340584 + 0.196637i
\(136\) 5.04576 + 8.73951i 0.432670 + 0.749407i
\(137\) −9.07785 + 15.7233i −0.775573 + 1.34333i 0.158899 + 0.987295i \(0.449206\pi\)
−0.934472 + 0.356037i \(0.884128\pi\)
\(138\) −13.6591 + 2.40847i −1.16274 + 0.205022i
\(139\) 11.0287 19.1022i 0.935441 1.62023i 0.161595 0.986857i \(-0.448336\pi\)
0.773846 0.633374i \(-0.218330\pi\)
\(140\) 0 0
\(141\) 0.605600 1.66387i 0.0510007 0.140123i
\(142\) −9.31820 −0.781966
\(143\) −10.5778 18.3214i −0.884564 1.53211i
\(144\) −15.2554 12.8008i −1.27128 1.06673i
\(145\) 2.65998 4.60722i 0.220899 0.382608i
\(146\) −16.1814 28.0270i −1.33918 2.31953i
\(147\) 0 0
\(148\) 10.0458 17.3998i 0.825756 1.43025i
\(149\) 7.57785 + 13.1252i 0.620802 + 1.07526i 0.989337 + 0.145646i \(0.0465261\pi\)
−0.368535 + 0.929614i \(0.620141\pi\)
\(150\) −11.9153 14.2002i −0.972884 1.15944i
\(151\) 9.47818 16.4167i 0.771323 1.33597i −0.165515 0.986207i \(-0.552929\pi\)
0.936838 0.349764i \(-0.113738\pi\)
\(152\) 7.36231 12.7519i 0.597162 1.03432i
\(153\) 0.860967 4.88279i 0.0696051 0.394750i
\(154\) 0 0
\(155\) −2.00253 3.46848i −0.160847 0.278595i
\(156\) 26.7841 + 31.9200i 2.14444 + 2.55564i
\(157\) 18.0574 1.44114 0.720568 0.693385i \(-0.243881\pi\)
0.720568 + 0.693385i \(0.243881\pi\)
\(158\) −15.0865 −1.20021
\(159\) −12.4363 + 2.19285i −0.986262 + 0.173905i
\(160\) −2.02094 3.50038i −0.159770 0.276729i
\(161\) 0 0
\(162\) 3.95723 + 22.4426i 0.310910 + 1.76326i
\(163\) −0.479055 + 0.829748i −0.0375225 + 0.0649909i −0.884177 0.467152i \(-0.845280\pi\)
0.846654 + 0.532143i \(0.178613\pi\)
\(164\) −2.61334 + 4.52644i −0.204068 + 0.353456i
\(165\) 2.02094 5.55250i 0.157330 0.432261i
\(166\) −0.277189 0.480105i −0.0215140 0.0372634i
\(167\) 9.91921 17.1806i 0.767572 1.32947i −0.171304 0.985218i \(-0.554798\pi\)
0.938876 0.344255i \(-0.111869\pi\)
\(168\) 0 0
\(169\) −8.36959 14.4965i −0.643814 1.11512i
\(170\) 1.84002 3.18701i 0.141123 0.244433i
\(171\) −6.79813 + 2.47432i −0.519866 + 0.189216i
\(172\) −0.407604 0.705990i −0.0310795 0.0538313i
\(173\) −22.6827 −1.72454 −0.862268 0.506452i \(-0.830957\pi\)
−0.862268 + 0.506452i \(0.830957\pi\)
\(174\) 26.1288 4.60722i 1.98082 0.349272i
\(175\) 0 0
\(176\) −12.8760 + 22.3019i −0.970564 + 1.68107i
\(177\) −3.94562 + 10.8405i −0.296571 + 0.814823i
\(178\) 13.9611 24.1813i 1.04643 1.81247i
\(179\) 3.67365 + 6.36295i 0.274581 + 0.475589i 0.970029 0.242988i \(-0.0781274\pi\)
−0.695448 + 0.718576i \(0.744794\pi\)
\(180\) −2.02094 + 11.4613i −0.150632 + 0.854278i
\(181\) 3.44562 0.256111 0.128056 0.991767i \(-0.459126\pi\)
0.128056 + 0.991767i \(0.459126\pi\)
\(182\) 0 0
\(183\) 1.53802 4.22567i 0.113694 0.312371i
\(184\) −9.65523 16.7233i −0.711793 1.23286i
\(185\) −4.00505 −0.294457
\(186\) 6.83157 18.7696i 0.500915 1.37625i
\(187\) −6.41147 −0.468853
\(188\) 4.50980 0.328911
\(189\) 0 0
\(190\) −5.36959 −0.389551
\(191\) 5.65776 0.409381 0.204690 0.978827i \(-0.434381\pi\)
0.204690 + 0.978827i \(0.434381\pi\)
\(192\) −0.970437 + 2.66625i −0.0700353 + 0.192420i
\(193\) 9.59627 0.690754 0.345377 0.938464i \(-0.387751\pi\)
0.345377 + 0.938464i \(0.387751\pi\)
\(194\) 15.8293 + 27.4172i 1.13648 + 1.96844i
\(195\) 2.84090 7.80531i 0.203441 0.558950i
\(196\) 0 0
\(197\) 8.31996 0.592772 0.296386 0.955068i \(-0.404218\pi\)
0.296386 + 0.955068i \(0.404218\pi\)
\(198\) 27.6917 10.0789i 1.96796 0.716279i
\(199\) 3.29813 + 5.71253i 0.233798 + 0.404951i 0.958923 0.283667i \(-0.0915511\pi\)
−0.725124 + 0.688618i \(0.758218\pi\)
\(200\) 12.9042 22.3507i 0.912465 1.58044i
\(201\) −1.75237 + 4.81461i −0.123603 + 0.339596i
\(202\) −12.3020 + 21.3077i −0.865566 + 1.49920i
\(203\) 0 0
\(204\) 12.4363 2.19285i 0.870714 0.153530i
\(205\) 1.04189 0.0727687
\(206\) 8.35117 + 14.4646i 0.581853 + 1.00780i
\(207\) −1.64749 + 9.34337i −0.114508 + 0.649409i
\(208\) −18.1001 + 31.3504i −1.25502 + 2.17376i
\(209\) 4.67752 + 8.10170i 0.323551 + 0.560406i
\(210\) 0 0
\(211\) 1.68479 2.91815i 0.115986 0.200893i −0.802188 0.597072i \(-0.796331\pi\)
0.918173 + 0.396179i \(0.129664\pi\)
\(212\) −16.0817 27.8544i −1.10450 1.91304i
\(213\) −2.18004 + 5.98962i −0.149374 + 0.410402i
\(214\) −3.02481 + 5.23913i −0.206772 + 0.358140i
\(215\) −0.0812519 + 0.140732i −0.00554133 + 0.00959787i
\(216\) −27.4773 + 15.8640i −1.86959 + 1.07941i
\(217\) 0 0
\(218\) −5.01114 8.67956i −0.339398 0.587854i
\(219\) −21.8011 + 3.84413i −1.47318 + 0.259762i
\(220\) 15.0496 1.01465
\(221\) −9.01279 −0.606266
\(222\) −12.8391 15.3011i −0.861707 1.02694i
\(223\) −3.13816 5.43545i −0.210146 0.363984i 0.741614 0.670827i \(-0.234061\pi\)
−0.951760 + 0.306843i \(0.900727\pi\)
\(224\) 0 0
\(225\) −11.9153 + 4.33683i −0.794356 + 0.289122i
\(226\) −20.8307 + 36.0798i −1.38564 + 2.39999i
\(227\) −3.08125 + 5.33688i −0.204510 + 0.354221i −0.949976 0.312322i \(-0.898893\pi\)
0.745467 + 0.666543i \(0.232227\pi\)
\(228\) −11.8439 14.1150i −0.784381 0.934789i
\(229\) 11.6925 + 20.2521i 0.772664 + 1.33829i 0.936098 + 0.351740i \(0.114410\pi\)
−0.163434 + 0.986554i \(0.552257\pi\)
\(230\) −3.52094 + 6.09845i −0.232164 + 0.402120i
\(231\) 0 0
\(232\) 18.4697 + 31.9905i 1.21260 + 2.10028i
\(233\) 4.26264 7.38311i 0.279255 0.483684i −0.691945 0.721950i \(-0.743246\pi\)
0.971200 + 0.238267i \(0.0765792\pi\)
\(234\) 38.9270 14.1683i 2.54473 0.926208i
\(235\) −0.449493 0.778544i −0.0293217 0.0507866i
\(236\) −29.3824 −1.91263
\(237\) −3.52956 + 9.69739i −0.229270 + 0.629913i
\(238\) 0 0
\(239\) −7.28106 + 12.6112i −0.470973 + 0.815748i −0.999449 0.0331997i \(-0.989430\pi\)
0.528476 + 0.848948i \(0.322764\pi\)
\(240\) −9.95723 + 1.75573i −0.642737 + 0.113332i
\(241\) −2.70187 + 4.67977i −0.174043 + 0.301451i −0.939830 0.341644i \(-0.889016\pi\)
0.765787 + 0.643094i \(0.222350\pi\)
\(242\) −5.12701 8.88024i −0.329577 0.570844i
\(243\) 15.3516 + 2.70691i 0.984808 + 0.173648i
\(244\) 11.4534 0.733226
\(245\) 0 0
\(246\) 3.34002 + 3.98048i 0.212952 + 0.253786i
\(247\) 6.57532 + 11.3888i 0.418378 + 0.724651i
\(248\) 27.8093 1.76589
\(249\) −0.373455 + 0.0658503i −0.0236668 + 0.00417309i
\(250\) −20.5449 −1.29937
\(251\) 12.0669 0.761654 0.380827 0.924646i \(-0.375639\pi\)
0.380827 + 0.924646i \(0.375639\pi\)
\(252\) 0 0
\(253\) 12.2686 0.771318
\(254\) 44.7006 2.80476
\(255\) −1.61809 1.92836i −0.101329 0.120759i
\(256\) −30.5030 −1.90644
\(257\) 5.28312 + 9.15063i 0.329552 + 0.570801i 0.982423 0.186668i \(-0.0597690\pi\)
−0.652871 + 0.757469i \(0.726436\pi\)
\(258\) −0.798133 + 0.140732i −0.0496896 + 0.00876162i
\(259\) 0 0
\(260\) 21.1557 1.31202
\(261\) 3.15152 17.8732i 0.195074 1.10632i
\(262\) −24.3050 42.0975i −1.50157 2.60079i
\(263\) 14.1766 24.5547i 0.874169 1.51411i 0.0165240 0.999863i \(-0.494740\pi\)
0.857645 0.514242i \(-0.171927\pi\)
\(264\) 26.3726 + 31.4296i 1.62312 + 1.93436i
\(265\) −3.20574 + 5.55250i −0.196927 + 0.341087i
\(266\) 0 0
\(267\) −12.2772 14.6314i −0.751352 0.895426i
\(268\) −13.0496 −0.797133
\(269\) 3.74170 + 6.48081i 0.228135 + 0.395142i 0.957255 0.289244i \(-0.0934038\pi\)
−0.729120 + 0.684386i \(0.760070\pi\)
\(270\) 10.0201 + 5.78509i 0.609802 + 0.352069i
\(271\) 6.81908 11.8110i 0.414229 0.717467i −0.581118 0.813819i \(-0.697384\pi\)
0.995347 + 0.0963530i \(0.0307178\pi\)
\(272\) 5.48545 + 9.50108i 0.332604 + 0.576088i
\(273\) 0 0
\(274\) −22.9859 + 39.8128i −1.38863 + 2.40518i
\(275\) 8.19846 + 14.2002i 0.494386 + 0.856302i
\(276\) −23.7973 + 4.19610i −1.43243 + 0.252575i
\(277\) 3.07532 5.32661i 0.184778 0.320045i −0.758724 0.651413i \(-0.774177\pi\)
0.943502 + 0.331368i \(0.107510\pi\)
\(278\) 27.9256 48.3686i 1.67487 2.90095i
\(279\) −10.4666 8.78249i −0.626617 0.525794i
\(280\) 0 0
\(281\) −1.65611 2.86846i −0.0987951 0.171118i 0.812391 0.583113i \(-0.198165\pi\)
−0.911186 + 0.411995i \(0.864832\pi\)
\(282\) 1.53343 4.21307i 0.0913146 0.250885i
\(283\) −29.0232 −1.72525 −0.862626 0.505843i \(-0.831182\pi\)
−0.862626 + 0.505843i \(0.831182\pi\)
\(284\) −16.2344 −0.963336
\(285\) −1.25624 + 3.45150i −0.0744135 + 0.204449i
\(286\) −26.7841 46.3913i −1.58377 2.74318i
\(287\) 0 0
\(288\) −10.5628 8.86327i −0.622421 0.522273i
\(289\) 7.13429 12.3569i 0.419664 0.726879i
\(290\) 6.73530 11.6659i 0.395510 0.685044i
\(291\) 21.3268 3.76049i 1.25020 0.220444i
\(292\) −28.1917 48.8294i −1.64979 2.85752i
\(293\) −4.20961 + 7.29125i −0.245928 + 0.425960i −0.962392 0.271664i \(-0.912426\pi\)
0.716464 + 0.697624i \(0.245759\pi\)
\(294\) 0 0
\(295\) 2.92855 + 5.07239i 0.170507 + 0.295326i
\(296\) 13.9047 24.0836i 0.808192 1.39983i
\(297\) 20.1579i 1.16968i
\(298\) 19.1878 + 33.2342i 1.11152 + 1.92521i
\(299\) 17.2463 0.997378
\(300\) −20.7592 24.7399i −1.19854 1.42836i
\(301\) 0 0
\(302\) 23.9996 41.5685i 1.38102 2.39200i
\(303\) 10.8182 + 12.8926i 0.621489 + 0.740662i
\(304\) 8.00387 13.8631i 0.459053 0.795104i
\(305\) −1.14156 1.97724i −0.0653655 0.113216i
\(306\) 2.18004 12.3636i 0.124625 0.706783i
\(307\) 12.6878 0.724130 0.362065 0.932153i \(-0.382072\pi\)
0.362065 + 0.932153i \(0.382072\pi\)
\(308\) 0 0
\(309\) 11.2515 1.98394i 0.640075 0.112863i
\(310\) −5.07057 8.78249i −0.287989 0.498812i
\(311\) 16.4902 0.935073 0.467537 0.883974i \(-0.345142\pi\)
0.467537 + 0.883974i \(0.345142\pi\)
\(312\) 37.0727 + 44.1815i 2.09883 + 2.50129i
\(313\) −28.5185 −1.61196 −0.805980 0.591943i \(-0.798361\pi\)
−0.805980 + 0.591943i \(0.798361\pi\)
\(314\) 45.7229 2.58029
\(315\) 0 0
\(316\) −26.2841 −1.47859
\(317\) −25.8949 −1.45440 −0.727200 0.686425i \(-0.759179\pi\)
−0.727200 + 0.686425i \(0.759179\pi\)
\(318\) −31.4898 + 5.55250i −1.76586 + 0.311369i
\(319\) −23.4688 −1.31400
\(320\) 0.720285 + 1.24757i 0.0402652 + 0.0697413i
\(321\) 2.65998 + 3.17004i 0.148465 + 0.176934i
\(322\) 0 0
\(323\) 3.98545 0.221756
\(324\) 6.89440 + 39.1001i 0.383022 + 2.17223i
\(325\) 11.5248 + 19.9616i 0.639282 + 1.10727i
\(326\) −1.21301 + 2.10100i −0.0671825 + 0.116363i
\(327\) −6.75150 + 1.19047i −0.373359 + 0.0658332i
\(328\) −3.61721 + 6.26519i −0.199727 + 0.345937i
\(329\) 0 0
\(330\) 5.11721 14.0594i 0.281693 0.773946i
\(331\) 8.21894 0.451754 0.225877 0.974156i \(-0.427475\pi\)
0.225877 + 0.974156i \(0.427475\pi\)
\(332\) −0.482926 0.836452i −0.0265040 0.0459063i
\(333\) −12.8391 + 4.67307i −0.703581 + 0.256082i
\(334\) 25.1163 43.5028i 1.37430 2.38037i
\(335\) 1.30066 + 2.25281i 0.0710626 + 0.123084i
\(336\) 0 0
\(337\) −2.28564 + 3.95885i −0.124507 + 0.215652i −0.921540 0.388283i \(-0.873068\pi\)
0.797033 + 0.603936i \(0.206402\pi\)
\(338\) −21.1925 36.7065i −1.15272 1.99657i
\(339\) 18.3182 + 21.8308i 0.994908 + 1.18569i
\(340\) 3.20574 5.55250i 0.173856 0.301127i
\(341\) −8.83409 + 15.3011i −0.478393 + 0.828601i
\(342\) −17.2135 + 6.26519i −0.930798 + 0.338783i
\(343\) 0 0
\(344\) −0.564178 0.977185i −0.0304184 0.0526863i
\(345\) 3.09627 + 3.68999i 0.166697 + 0.198662i
\(346\) −57.4347 −3.08771
\(347\) 22.4662 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(348\) 45.5223 8.02682i 2.44025 0.430283i
\(349\) 13.0496 + 22.6026i 0.698531 + 1.20989i 0.968976 + 0.247155i \(0.0794958\pi\)
−0.270445 + 0.962735i \(0.587171\pi\)
\(350\) 0 0
\(351\) 28.3365i 1.51249i
\(352\) −8.91534 + 15.4418i −0.475189 + 0.823052i
\(353\) −0.177519 + 0.307471i −0.00944836 + 0.0163650i −0.870711 0.491795i \(-0.836341\pi\)
0.861263 + 0.508160i \(0.169674\pi\)
\(354\) −9.99067 + 27.4491i −0.530998 + 1.45890i
\(355\) 1.61809 + 2.80261i 0.0858792 + 0.148747i
\(356\) 24.3234 42.1294i 1.28914 2.23285i
\(357\) 0 0
\(358\) 9.30200 + 16.1115i 0.491626 + 0.851522i
\(359\) −2.72803 + 4.72508i −0.143980 + 0.249380i −0.928992 0.370100i \(-0.879323\pi\)
0.785012 + 0.619480i \(0.212657\pi\)
\(360\) −2.79726 + 15.8640i −0.147428 + 0.836108i
\(361\) 6.59240 + 11.4184i 0.346968 + 0.600967i
\(362\) 8.72462 0.458556
\(363\) −6.90760 + 1.21800i −0.362555 + 0.0639283i
\(364\) 0 0
\(365\) −5.61974 + 9.73367i −0.294150 + 0.509484i
\(366\) 3.89440 10.6998i 0.203564 0.559286i
\(367\) 5.46198 9.46043i 0.285113 0.493830i −0.687523 0.726162i \(-0.741302\pi\)
0.972637 + 0.232332i \(0.0746355\pi\)
\(368\) −10.4966 18.1806i −0.547173 0.947731i
\(369\) 3.34002 1.21567i 0.173875 0.0632852i
\(370\) −10.1411 −0.527213
\(371\) 0 0
\(372\) 11.9021 32.7009i 0.617097 1.69546i
\(373\) −0.865715 1.49946i −0.0448250 0.0776392i 0.842742 0.538317i \(-0.180940\pi\)
−0.887567 + 0.460678i \(0.847606\pi\)
\(374\) −16.2344 −0.839462
\(375\) −4.80659 + 13.2060i −0.248211 + 0.681955i
\(376\) 6.24216 0.321915
\(377\) −32.9908 −1.69911
\(378\) 0 0
\(379\) −12.1334 −0.623251 −0.311626 0.950205i \(-0.600873\pi\)
−0.311626 + 0.950205i \(0.600873\pi\)
\(380\) −9.35504 −0.479903
\(381\) 10.4579 28.7330i 0.535777 1.47204i
\(382\) 14.3259 0.732979
\(383\) −4.35591 7.54467i −0.222577 0.385514i 0.733013 0.680215i \(-0.238113\pi\)
−0.955590 + 0.294700i \(0.904780\pi\)
\(384\) −7.90286 + 21.7129i −0.403291 + 1.10803i
\(385\) 0 0
\(386\) 24.2986 1.23677
\(387\) −0.0962667 + 0.545955i −0.00489351 + 0.0277525i
\(388\) 27.5783 + 47.7670i 1.40008 + 2.42500i
\(389\) −1.82160 + 3.15511i −0.0923590 + 0.159970i −0.908503 0.417878i \(-0.862774\pi\)
0.816144 + 0.577848i \(0.196107\pi\)
\(390\) 7.19341 19.7637i 0.364253 1.00078i
\(391\) 2.61334 4.52644i 0.132162 0.228912i
\(392\) 0 0
\(393\) −32.7460 + 5.77401i −1.65182 + 0.291260i
\(394\) 21.0669 1.06133
\(395\) 2.61974 + 4.53752i 0.131813 + 0.228307i
\(396\) 48.2452 17.5598i 2.42441 0.882413i
\(397\) −7.72281 + 13.3763i −0.387597 + 0.671337i −0.992126 0.125246i \(-0.960028\pi\)
0.604529 + 0.796583i \(0.293361\pi\)
\(398\) 8.35117 + 14.4646i 0.418606 + 0.725047i
\(399\) 0 0
\(400\) 14.0287 24.2984i 0.701434 1.21492i
\(401\) −9.21095 15.9538i −0.459973 0.796697i 0.538986 0.842315i \(-0.318808\pi\)
−0.998959 + 0.0456182i \(0.985474\pi\)
\(402\) −4.43717 + 12.1910i −0.221306 + 0.608033i
\(403\) −12.4183 + 21.5092i −0.618601 + 1.07145i
\(404\) −21.4329 + 37.1228i −1.06633 + 1.84693i
\(405\) 6.06283 5.08732i 0.301265 0.252791i
\(406\) 0 0
\(407\) 8.83409 + 15.3011i 0.437890 + 0.758447i
\(408\) 17.2135 3.03520i 0.852194 0.150265i
\(409\) 28.6364 1.41598 0.707989 0.706223i \(-0.249602\pi\)
0.707989 + 0.706223i \(0.249602\pi\)
\(410\) 2.63816 0.130289
\(411\) 20.2135 + 24.0895i 0.997057 + 1.18825i
\(412\) 14.5496 + 25.2007i 0.716809 + 1.24155i
\(413\) 0 0
\(414\) −4.17159 + 23.6583i −0.205022 + 1.16274i
\(415\) −0.0962667 + 0.166739i −0.00472554 + 0.00818488i
\(416\) −12.5326 + 21.7070i −0.614459 + 1.06427i
\(417\) −24.5574 29.2663i −1.20258 1.43318i
\(418\) 11.8439 + 20.5142i 0.579304 + 1.00338i
\(419\) −17.3478 + 30.0472i −0.847494 + 1.46790i 0.0359442 + 0.999354i \(0.488556\pi\)
−0.883438 + 0.468548i \(0.844777\pi\)
\(420\) 0 0
\(421\) 13.7010 + 23.7308i 0.667745 + 1.15657i 0.978533 + 0.206090i \(0.0660738\pi\)
−0.310788 + 0.950479i \(0.600593\pi\)
\(422\) 4.26604 7.38901i 0.207668 0.359691i
\(423\) −2.34936 1.97134i −0.114230 0.0958500i
\(424\) −22.2592 38.5541i −1.08100 1.87235i
\(425\) 6.98545 0.338844
\(426\) −5.52007 + 15.1663i −0.267448 + 0.734808i
\(427\) 0 0
\(428\) −5.26991 + 9.12776i −0.254731 + 0.441207i
\(429\) −36.0861 + 6.36295i −1.74225 + 0.307206i
\(430\) −0.205737 + 0.356347i −0.00992152 + 0.0171846i
\(431\) −13.2961 23.0295i −0.640449 1.10929i −0.985333 0.170645i \(-0.945415\pi\)
0.344883 0.938646i \(-0.387919\pi\)
\(432\) −29.8717 + 17.2464i −1.43720 + 0.829769i
\(433\) −37.1830 −1.78690 −0.893451 0.449160i \(-0.851723\pi\)
−0.893451 + 0.449160i \(0.851723\pi\)
\(434\) 0 0
\(435\) −5.92292 7.05866i −0.283982 0.338437i
\(436\) −8.73055 15.1218i −0.418118 0.724201i
\(437\) −7.62630 −0.364815
\(438\) −55.2024 + 9.73367i −2.63767 + 0.465093i
\(439\) −25.0746 −1.19675 −0.598373 0.801218i \(-0.704186\pi\)
−0.598373 + 0.801218i \(0.704186\pi\)
\(440\) 20.8307 0.993064
\(441\) 0 0
\(442\) −22.8212 −1.08549
\(443\) 2.04458 0.0971408 0.0485704 0.998820i \(-0.484533\pi\)
0.0485704 + 0.998820i \(0.484533\pi\)
\(444\) −22.3687 26.6580i −1.06157 1.26513i
\(445\) −9.69728 −0.459695
\(446\) −7.94609 13.7630i −0.376258 0.651698i
\(447\) 25.8516 4.55834i 1.22274 0.215602i
\(448\) 0 0
\(449\) −10.2344 −0.482992 −0.241496 0.970402i \(-0.577638\pi\)
−0.241496 + 0.970402i \(0.577638\pi\)
\(450\) −30.1707 + 10.9812i −1.42226 + 0.517661i
\(451\) −2.29813 3.98048i −0.108215 0.187434i
\(452\) −36.2918 + 62.8592i −1.70702 + 2.95665i
\(453\) −21.1049 25.1518i −0.991594 1.18174i
\(454\) −7.80200 + 13.5135i −0.366166 + 0.634218i
\(455\) 0 0
\(456\) −16.3935 19.5370i −0.767697 0.914906i
\(457\) −42.5945 −1.99249 −0.996244 0.0865948i \(-0.972401\pi\)
−0.996244 + 0.0865948i \(0.972401\pi\)
\(458\) 29.6065 + 51.2800i 1.38342 + 2.39616i
\(459\) −7.43717 4.29385i −0.347137 0.200420i
\(460\) −6.13429 + 10.6249i −0.286013 + 0.495388i
\(461\) 0.252374 + 0.437124i 0.0117542 + 0.0203589i 0.871843 0.489786i \(-0.162925\pi\)
−0.860088 + 0.510145i \(0.829592\pi\)
\(462\) 0 0
\(463\) −1.34002 + 2.32099i −0.0622761 + 0.107865i −0.895482 0.445097i \(-0.853169\pi\)
0.833206 + 0.552962i \(0.186503\pi\)
\(464\) 20.0792 + 34.7782i 0.932153 + 1.61454i
\(465\) −6.83157 + 1.20459i −0.316806 + 0.0558615i
\(466\) 10.7934 18.6947i 0.499994 0.866015i
\(467\) −15.7083 + 27.2075i −0.726892 + 1.25901i 0.231299 + 0.972883i \(0.425702\pi\)
−0.958191 + 0.286131i \(0.907631\pi\)
\(468\) 67.8196 24.6843i 3.13496 1.14103i
\(469\) 0 0
\(470\) −1.13816 1.97134i −0.0524992 0.0909313i
\(471\) 10.6971 29.3901i 0.492897 1.35422i
\(472\) −40.6691 −1.87195
\(473\) 0.716881 0.0329622
\(474\) −8.93717 + 24.5547i −0.410498 + 1.12783i
\(475\) −5.09627 8.82699i −0.233833 0.405010i
\(476\) 0 0
\(477\) −3.79813 + 21.5403i −0.173905 + 0.986262i
\(478\) −18.4363 + 31.9326i −0.843256 + 1.46056i
\(479\) −8.22028 + 14.2380i −0.375594 + 0.650549i −0.990416 0.138118i \(-0.955895\pi\)
0.614821 + 0.788666i \(0.289228\pi\)
\(480\) −6.89440 + 1.21567i −0.314685 + 0.0554874i
\(481\) 12.4183 + 21.5092i 0.566227 + 0.980735i
\(482\) −6.84137 + 11.8496i −0.311616 + 0.539734i
\(483\) 0 0
\(484\) −8.93242 15.4714i −0.406019 0.703246i
\(485\) 5.49747 9.52190i 0.249627 0.432367i
\(486\) 38.8717 + 6.85413i 1.76326 + 0.310910i
\(487\) 1.48767 + 2.57673i 0.0674129 + 0.116763i 0.897762 0.440481i \(-0.145192\pi\)
−0.830349 + 0.557244i \(0.811859\pi\)
\(488\) 15.8530 0.717631
\(489\) 1.06670 + 1.27125i 0.0482380 + 0.0574878i
\(490\) 0 0
\(491\) 13.2430 22.9376i 0.597650 1.03516i −0.395517 0.918459i \(-0.629435\pi\)
0.993167 0.116702i \(-0.0372321\pi\)
\(492\) 5.81908 + 6.93491i 0.262344 + 0.312650i
\(493\) −4.99912 + 8.65873i −0.225149 + 0.389970i
\(494\) 16.6493 + 28.8374i 0.749087 + 1.29746i
\(495\) −7.84002 6.57856i −0.352383 0.295684i
\(496\) 30.2327 1.35749
\(497\) 0 0
\(498\) −0.945622 + 0.166739i −0.0423744 + 0.00747174i
\(499\) 6.72193 + 11.6427i 0.300915 + 0.521200i 0.976343 0.216225i \(-0.0693746\pi\)
−0.675428 + 0.737426i \(0.736041\pi\)
\(500\) −35.7939 −1.60075
\(501\) −22.0869 26.3222i −0.986771 1.17599i
\(502\) 30.5544 1.36371
\(503\) 22.6631 1.01050 0.505250 0.862973i \(-0.331400\pi\)
0.505250 + 0.862973i \(0.331400\pi\)
\(504\) 0 0
\(505\) 8.54488 0.380242
\(506\) 31.0651 1.38101
\(507\) −28.5526 + 5.03460i −1.26807 + 0.223594i
\(508\) 77.8786 3.45530
\(509\) 4.77379 + 8.26844i 0.211594 + 0.366492i 0.952214 0.305433i \(-0.0988011\pi\)
−0.740619 + 0.671925i \(0.765468\pi\)
\(510\) −4.09714 4.88279i −0.181425 0.216213i
\(511\) 0 0
\(512\) −50.5553 −2.23425
\(513\) 12.5304i 0.553230i
\(514\) 13.3773 + 23.1702i 0.590049 + 1.02199i
\(515\) 2.90033 5.02352i 0.127804 0.221363i
\(516\) −1.39053 + 0.245188i −0.0612147 + 0.0107938i
\(517\) −1.98293 + 3.43453i −0.0872090 + 0.151050i
\(518\) 0 0
\(519\) −13.4372 + 36.9183i −0.589826 + 1.62053i
\(520\) 29.2823 1.28411
\(521\) −1.55644 2.69583i −0.0681887 0.118106i 0.829915 0.557889i \(-0.188389\pi\)
−0.898104 + 0.439783i \(0.855055\pi\)
\(522\) 7.97993 45.2564i 0.349272 1.98082i
\(523\) −8.07444 + 13.9853i −0.353071 + 0.611537i −0.986786 0.162030i \(-0.948196\pi\)
0.633715 + 0.773567i \(0.281529\pi\)
\(524\) −42.3448 73.3434i −1.84984 3.20402i
\(525\) 0 0
\(526\) 35.8965 62.1746i 1.56516 2.71094i
\(527\) 3.76352 + 6.51860i 0.163941 + 0.283955i
\(528\) 28.6707 + 34.1684i 1.24773 + 1.48699i
\(529\) 6.49928 11.2571i 0.282578 0.489439i
\(530\) −8.11721 + 14.0594i −0.352589 + 0.610702i
\(531\) 15.3066 + 12.8438i 0.664249 + 0.557371i
\(532\) 0 0
\(533\) −3.23055 5.59548i −0.139931 0.242367i
\(534\) −31.0869 37.0480i −1.34526 1.60322i
\(535\) 2.10101 0.0908348
\(536\) −18.0624 −0.780178
\(537\) 12.5326 2.20983i 0.540820 0.0953611i
\(538\) 9.47431 + 16.4100i 0.408466 + 0.707485i
\(539\) 0 0
\(540\) 17.4572 + 10.0789i 0.751240 + 0.433728i
\(541\) 2.50774 4.34353i 0.107816 0.186743i −0.807069 0.590457i \(-0.798948\pi\)
0.914885 + 0.403714i \(0.132281\pi\)
\(542\) 17.2665 29.9065i 0.741660 1.28459i
\(543\) 2.04117 5.60808i 0.0875952 0.240666i
\(544\) 3.79813 + 6.57856i 0.162844 + 0.282053i
\(545\) −1.74035 + 3.01438i −0.0745485 + 0.129122i
\(546\) 0 0
\(547\) −8.23901 14.2704i −0.352275 0.610157i 0.634373 0.773027i \(-0.281258\pi\)
−0.986648 + 0.162870i \(0.947925\pi\)
\(548\) −40.0467 + 69.3629i −1.71071 + 2.96304i
\(549\) −5.96657 5.00654i −0.254647 0.213674i
\(550\) 20.7592 + 35.9561i 0.885177 + 1.53317i
\(551\) 14.5885 0.621492
\(552\) −32.9386 + 5.80796i −1.40196 + 0.247203i
\(553\) 0 0
\(554\) 7.78699 13.4875i 0.330837 0.573027i
\(555\) −2.37258 + 6.51860i −0.100710 + 0.276699i
\(556\) 48.6528 84.2691i 2.06334 3.57380i
\(557\) 17.2815 + 29.9325i 0.732242 + 1.26828i 0.955923 + 0.293618i \(0.0948592\pi\)
−0.223681 + 0.974662i \(0.571807\pi\)
\(558\) −26.5023 22.2381i −1.12193 0.941412i
\(559\) 1.00774 0.0426229
\(560\) 0 0
\(561\) −3.79813 + 10.4353i −0.160357 + 0.440578i
\(562\) −4.19341 7.26320i −0.176888 0.306380i
\(563\) 37.2104 1.56823 0.784115 0.620615i \(-0.213117\pi\)
0.784115 + 0.620615i \(0.213117\pi\)
\(564\) 2.67159 7.34013i 0.112494 0.309075i
\(565\) 14.4688 0.608709
\(566\) −73.4894 −3.08899
\(567\) 0 0
\(568\) −22.4706 −0.942845
\(569\) 0.404667 0.0169645 0.00848226 0.999964i \(-0.497300\pi\)
0.00848226 + 0.999964i \(0.497300\pi\)
\(570\) −3.18092 + 8.73951i −0.133234 + 0.366058i
\(571\) −37.7793 −1.58101 −0.790507 0.612453i \(-0.790183\pi\)
−0.790507 + 0.612453i \(0.790183\pi\)
\(572\) −46.6639 80.8243i −1.95112 3.37943i
\(573\) 3.35163 9.20854i 0.140017 0.384692i
\(574\) 0 0
\(575\) −13.3669 −0.557438
\(576\) 3.76470 + 3.15896i 0.156863 + 0.131623i
\(577\) −1.10560 1.91496i −0.0460267 0.0797206i 0.842094 0.539330i \(-0.181323\pi\)
−0.888121 + 0.459610i \(0.847989\pi\)
\(578\) 18.0646 31.2889i 0.751390 1.30145i
\(579\) 5.68479 15.6188i 0.236252 0.649097i
\(580\) 11.7344 20.3246i 0.487245 0.843934i
\(581\) 0 0
\(582\) 54.0014 9.52190i 2.23843 0.394696i
\(583\) 28.2841 1.17141
\(584\) −39.0210 67.5864i −1.61470 2.79674i
\(585\) −11.0209 9.24767i −0.455660 0.382344i
\(586\) −10.6591 + 18.4621i −0.440323 + 0.762662i
\(587\) 12.1049 + 20.9663i 0.499622 + 0.865371i 1.00000 0.000436347i \(-0.000138894\pi\)
−0.500378 + 0.865807i \(0.666806\pi\)
\(588\) 0 0
\(589\) 5.49138 9.51135i 0.226268 0.391908i
\(590\) 7.41534 + 12.8438i 0.305285 + 0.528769i
\(591\) 4.92871 13.5415i 0.202740 0.557024i
\(592\) 15.1163 26.1823i 0.621277 1.07608i
\(593\) 6.11927 10.5989i 0.251288 0.435244i −0.712592 0.701578i \(-0.752479\pi\)
0.963881 + 0.266334i \(0.0858124\pi\)
\(594\) 51.0415i 2.09426i
\(595\) 0 0
\(596\) 33.4295 + 57.9016i 1.36932 + 2.37174i
\(597\) 11.2515 1.98394i 0.460493 0.0811974i
\(598\) 43.6691 1.78576
\(599\) 39.6168 1.61870 0.809349 0.587328i \(-0.199820\pi\)
0.809349 + 0.587328i \(0.199820\pi\)
\(600\) −28.7335 34.2433i −1.17304 1.39798i
\(601\) −15.0039 25.9875i −0.612021 1.06005i −0.990899 0.134605i \(-0.957024\pi\)
0.378879 0.925446i \(-0.376310\pi\)
\(602\) 0 0
\(603\) 6.79813 + 5.70431i 0.276841 + 0.232298i
\(604\) 41.8127 72.4218i 1.70134 2.94680i
\(605\) −1.78059 + 3.08408i −0.0723914 + 0.125386i
\(606\) 27.3926 + 32.6453i 1.11275 + 1.32612i
\(607\) −9.74216 16.8739i −0.395422 0.684891i 0.597733 0.801695i \(-0.296068\pi\)
−0.993155 + 0.116804i \(0.962735\pi\)
\(608\) 5.54189 9.59883i 0.224753 0.389284i
\(609\) 0 0
\(610\) −2.89053 5.00654i −0.117034 0.202709i
\(611\) −2.78746 + 4.82802i −0.112768 + 0.195321i
\(612\) 3.79813 21.5403i 0.153530 0.870714i
\(613\) 9.26382 + 16.0454i 0.374162 + 0.648068i 0.990201 0.139648i \(-0.0445970\pi\)
−0.616039 + 0.787716i \(0.711264\pi\)
\(614\) 32.1266 1.29652
\(615\) 0.617211 1.69577i 0.0248884 0.0683802i
\(616\) 0 0
\(617\) −13.9201 + 24.1103i −0.560402 + 0.970644i 0.437059 + 0.899433i \(0.356020\pi\)
−0.997461 + 0.0712118i \(0.977313\pi\)
\(618\) 28.4898 5.02352i 1.14603 0.202076i
\(619\) −22.4907 + 38.9550i −0.903976 + 1.56573i −0.0816906 + 0.996658i \(0.526032\pi\)
−0.822286 + 0.569075i \(0.807301\pi\)
\(620\) −8.83409 15.3011i −0.354786 0.614507i
\(621\) 14.2313 + 8.21643i 0.571081 + 0.329714i
\(622\) 41.7547 1.67421
\(623\) 0 0
\(624\) 40.3032 + 48.0315i 1.61342 + 1.92280i
\(625\) −6.99912 12.1228i −0.279965 0.484913i
\(626\) −72.2113 −2.88614
\(627\) 15.9572 2.81369i 0.637271 0.112368i
\(628\) 79.6596 3.17877
\(629\) 7.52704 0.300123
\(630\) 0 0
\(631\) 9.43613 0.375646 0.187823 0.982203i \(-0.439857\pi\)
0.187823 + 0.982203i \(0.439857\pi\)
\(632\) −36.3806 −1.44714
\(633\) −3.75150 4.47086i −0.149109 0.177701i
\(634\) −65.5681 −2.60404
\(635\) −7.76217 13.4445i −0.308032 0.533528i
\(636\) −54.8624 + 9.67372i −2.17543 + 0.383588i
\(637\) 0 0
\(638\) −59.4252 −2.35267
\(639\) 8.45723 + 7.09646i 0.334563 + 0.280732i
\(640\) 5.86571 + 10.1597i 0.231863 + 0.401598i
\(641\) −18.6951 + 32.3808i −0.738410 + 1.27896i 0.214800 + 0.976658i \(0.431090\pi\)
−0.953211 + 0.302306i \(0.902243\pi\)
\(642\) 6.73530 + 8.02682i 0.265821 + 0.316793i
\(643\) 0.805874 1.39581i 0.0317806 0.0550456i −0.849698 0.527270i \(-0.823216\pi\)
0.881478 + 0.472225i \(0.156549\pi\)
\(644\) 0 0
\(645\) 0.180922 + 0.215615i 0.00712380 + 0.00848982i
\(646\) 10.0915 0.397046
\(647\) −20.5881 35.6597i −0.809402 1.40193i −0.913278 0.407336i \(-0.866458\pi\)
0.103876 0.994590i \(-0.466875\pi\)
\(648\) 9.54277 + 54.1197i 0.374875 + 2.12602i
\(649\) 12.9192 22.3767i 0.507124 0.878364i
\(650\) 29.1819 + 50.5445i 1.14461 + 1.98252i
\(651\) 0 0
\(652\) −2.11334 + 3.66041i −0.0827648 + 0.143353i
\(653\) −1.52600 2.64310i −0.0597169 0.103433i 0.834621 0.550824i \(-0.185686\pi\)
−0.894338 + 0.447391i \(0.852353\pi\)
\(654\) −17.0954 + 3.01438i −0.668483 + 0.117872i
\(655\) −8.44104 + 14.6203i −0.329819 + 0.571263i
\(656\) −3.93242 + 6.81115i −0.153535 + 0.265931i
\(657\) −6.65822 + 37.7607i −0.259762 + 1.47318i
\(658\) 0 0
\(659\) −20.8175 36.0569i −0.810934 1.40458i −0.912211 0.409721i \(-0.865626\pi\)
0.101277 0.994858i \(-0.467707\pi\)
\(660\) 8.91534 24.4947i 0.347029 0.953455i
\(661\) −20.3010 −0.789616 −0.394808 0.918764i \(-0.629189\pi\)
−0.394808 + 0.918764i \(0.629189\pi\)
\(662\) 20.8111 0.808846
\(663\) −5.33915 + 14.6692i −0.207355 + 0.569704i
\(664\) −0.668434 1.15776i −0.0259403 0.0449298i
\(665\) 0 0
\(666\) −32.5099 + 11.8326i −1.25973 + 0.458505i
\(667\) 9.56599 16.5688i 0.370397 0.641546i
\(668\) 43.7584 75.7917i 1.69306 2.93247i
\(669\) −10.7057 + 1.88771i −0.413908 + 0.0729831i
\(670\) 3.29339 + 5.70431i 0.127235 + 0.220377i
\(671\) −5.03596 + 8.72254i −0.194411 + 0.336730i
\(672\) 0 0
\(673\) 0.415345 + 0.719398i 0.0160104 + 0.0277307i 0.873920 0.486071i \(-0.161570\pi\)
−0.857909 + 0.513801i \(0.828237\pi\)
\(674\) −5.78746 + 10.0242i −0.222924 + 0.386117i
\(675\) 21.9625i 0.845336i
\(676\) −36.9222 63.9511i −1.42008 2.45966i
\(677\) −10.8672 −0.417660 −0.208830 0.977952i \(-0.566966\pi\)
−0.208830 + 0.977952i \(0.566966\pi\)
\(678\) 46.3833 + 55.2775i 1.78134 + 2.12292i
\(679\) 0 0
\(680\) 4.43717 7.68540i 0.170158 0.294722i
\(681\) 6.86097 + 8.17658i 0.262913 + 0.313327i
\(682\) −22.3687 + 38.7437i −0.856542 + 1.48357i
\(683\) −16.3473 28.3143i −0.625512 1.08342i −0.988442 0.151602i \(-0.951557\pi\)
0.362930 0.931817i \(-0.381777\pi\)
\(684\) −29.9898 + 10.9154i −1.14669 + 0.417360i
\(685\) 15.9659 0.610024
\(686\) 0 0
\(687\) 39.8888 7.03347i 1.52185 0.268344i
\(688\) −0.613341 1.06234i −0.0233834 0.0405012i
\(689\) 39.7597 1.51472
\(690\) 7.84002 + 9.34337i 0.298465 + 0.355696i
\(691\) −14.9982 −0.570560 −0.285280 0.958444i \(-0.592087\pi\)
−0.285280 + 0.958444i \(0.592087\pi\)
\(692\) −100.064 −3.80387
\(693\) 0 0
\(694\) 56.8863 2.15937
\(695\) −19.3969 −0.735767
\(696\) 63.0090 11.1102i 2.38835 0.421130i
\(697\) −1.95811 −0.0741687
\(698\) 33.0428 + 57.2318i 1.25069 + 2.16626i
\(699\) −9.49154 11.3116i −0.359003 0.427843i
\(700\) 0 0
\(701\) 26.4688 0.999714 0.499857 0.866108i \(-0.333386\pi\)
0.499857 + 0.866108i \(0.333386\pi\)
\(702\) 71.7506i 2.70805i
\(703\) −5.49138 9.51135i −0.207111 0.358727i
\(704\) 3.17752 5.50362i 0.119757 0.207426i
\(705\) −1.53343 + 0.270386i −0.0577524 + 0.0101833i
\(706\) −0.449493 + 0.778544i −0.0169169 + 0.0293009i
\(707\) 0 0
\(708\) −17.4060 + 47.8226i −0.654158 + 1.79728i
\(709\) 15.3601 0.576860 0.288430 0.957501i \(-0.406867\pi\)
0.288430 + 0.957501i \(0.406867\pi\)
\(710\) 4.09714 + 7.09646i 0.153763 + 0.266325i
\(711\) 13.6925 + 11.4894i 0.513510 + 0.430886i
\(712\) 33.6668 58.3127i 1.26172 2.18536i
\(713\) −7.20162 12.4736i −0.269703 0.467139i
\(714\) 0 0
\(715\) −9.30200 + 16.1115i −0.347875 + 0.602538i
\(716\) 16.2062 + 28.0700i 0.605654 + 1.04902i
\(717\) 16.2126 + 19.3214i 0.605471 + 0.721572i
\(718\) −6.90760 + 11.9643i −0.257789 + 0.446504i
\(719\) 13.3653 23.1494i 0.498442 0.863326i −0.501557 0.865125i \(-0.667239\pi\)
0.999998 + 0.00179839i \(0.000572447\pi\)
\(720\) −3.04101 + 17.2464i −0.113332 + 0.642737i
\(721\) 0 0
\(722\) 16.6925 + 28.9123i 0.621232 + 1.07600i
\(723\) 6.01620 + 7.16982i 0.223745 + 0.266649i
\(724\) 15.2003 0.564914
\(725\) 25.5699 0.949641
\(726\) −17.4907 + 3.08408i −0.649140 + 0.114461i
\(727\) −22.8221 39.5290i −0.846424 1.46605i −0.884379 0.466770i \(-0.845418\pi\)
0.0379552 0.999279i \(-0.487916\pi\)
\(728\) 0 0
\(729\) 13.5000 23.3827i 0.500000 0.866025i
\(730\) −14.2297 + 24.6465i −0.526664 + 0.912209i
\(731\) 0.152704 0.264490i 0.00564795 0.00978253i
\(732\) 6.78493 18.6414i 0.250778 0.689007i
\(733\) 2.98751 + 5.17452i 0.110346 + 0.191125i 0.915910 0.401384i \(-0.131471\pi\)
−0.805564 + 0.592509i \(0.798137\pi\)
\(734\) 13.8302 23.9546i 0.510483 0.884182i
\(735\) 0 0
\(736\) −7.26786 12.5883i −0.267897 0.464011i
\(737\) 5.73783 9.93821i 0.211356 0.366079i
\(738\) 8.45723 3.07818i 0.311315 0.113309i
\(739\) 17.7981 + 30.8273i 0.654715 + 1.13400i 0.981965 + 0.189062i \(0.0605447\pi\)
−0.327250 + 0.944938i \(0.606122\pi\)
\(740\) −17.6682 −0.649495
\(741\) 22.4315 3.95529i 0.824043 0.145301i
\(742\) 0 0
\(743\) 14.6544 25.3821i 0.537616 0.931178i −0.461416 0.887184i \(-0.652658\pi\)
0.999032 0.0439943i \(-0.0140083\pi\)
\(744\) 16.4741 45.2623i 0.603971 1.65940i
\(745\) 6.66385 11.5421i 0.244145 0.422871i
\(746\) −2.19207 3.79677i −0.0802573 0.139010i
\(747\) −0.114056 + 0.646844i −0.00417309 + 0.0236668i
\(748\) −28.2841 −1.03417
\(749\) 0 0
\(750\) −12.1707 + 33.4388i −0.444412 + 1.22101i
\(751\) 8.66684 + 15.0114i 0.316258 + 0.547774i 0.979704 0.200450i \(-0.0642403\pi\)
−0.663446 + 0.748224i \(0.730907\pi\)
\(752\) 6.78611 0.247464
\(753\) 7.14837 19.6400i 0.260501 0.715720i
\(754\) −83.5357 −3.04219
\(755\) −16.6699 −0.606681
\(756\) 0 0
\(757\) −2.77156 −0.100734 −0.0503671 0.998731i \(-0.516039\pi\)
−0.0503671 + 0.998731i \(0.516039\pi\)
\(758\) −30.7229 −1.11590
\(759\) 7.26786 19.9683i 0.263806 0.724802i
\(760\) −12.9486 −0.469696
\(761\) 3.75372 + 6.50163i 0.136072 + 0.235684i 0.926007 0.377508i \(-0.123219\pi\)
−0.789934 + 0.613191i \(0.789885\pi\)
\(762\) 26.4805 72.7545i 0.959286 2.63562i
\(763\) 0 0
\(764\) 24.9590 0.902987
\(765\) −4.09714 + 1.49124i −0.148133 + 0.0539158i
\(766\) −11.0296 19.1038i −0.398514 0.690247i
\(767\) 18.1609 31.4556i 0.655752 1.13580i
\(768\) −18.0699 + 49.6465i −0.652040 + 1.79146i
\(769\) 1.02182 1.76985i 0.0368478 0.0638223i −0.847013 0.531572i \(-0.821602\pi\)
0.883861 + 0.467749i \(0.154935\pi\)
\(770\) 0 0
\(771\) 18.0232 3.17798i 0.649090 0.114452i
\(772\) 42.3337 1.52362
\(773\) −12.4709 21.6002i −0.448547 0.776907i 0.549744 0.835333i \(-0.314725\pi\)
−0.998292 + 0.0584263i \(0.981392\pi\)
\(774\) −0.243756 + 1.38241i −0.00876162 + 0.0496896i
\(775\) 9.62495 16.6709i 0.345738 0.598837i
\(776\) 38.1721 + 66.1159i 1.37030 + 2.37342i
\(777\) 0 0
\(778\) −4.61246 + 7.98902i −0.165365 + 0.286420i
\(779\) 1.42855 + 2.47432i 0.0511831 + 0.0886516i
\(780\) 12.5326 34.4329i 0.448737 1.23290i
\(781\) 7.13816