Properties

Label 441.2.g.b.67.1
Level $441$
Weight $2$
Character 441.67
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.g (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 67.1
Root \(-0.766044 + 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.b.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.26604 + 2.19285i) q^{2} +(-1.70574 + 0.300767i) q^{3} +(-2.20574 - 3.82045i) q^{4} +0.879385 q^{5} +(1.50000 - 4.12122i) q^{6} +6.10607 q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})\) \(q+(-1.26604 + 2.19285i) q^{2} +(-1.70574 + 0.300767i) q^{3} +(-2.20574 - 3.82045i) q^{4} +0.879385 q^{5} +(1.50000 - 4.12122i) q^{6} +6.10607 q^{8} +(2.81908 - 1.02606i) q^{9} +(-1.11334 + 1.92836i) q^{10} +3.87939 q^{11} +(4.91147 + 5.85327i) q^{12} +(-2.72668 + 4.72275i) q^{13} +(-1.50000 + 0.264490i) q^{15} +(-3.31908 + 5.74881i) q^{16} +(0.826352 - 1.43128i) q^{17} +(-1.31908 + 7.48086i) q^{18} +(1.20574 + 2.08840i) q^{19} +(-1.93969 - 3.35965i) q^{20} +(-4.91147 + 8.50692i) q^{22} +3.16250 q^{23} +(-10.4153 + 1.83651i) q^{24} -4.22668 q^{25} +(-6.90420 - 11.9584i) q^{26} +(-4.50000 + 2.59808i) q^{27} +(3.02481 + 5.23913i) q^{29} +(1.31908 - 3.62414i) q^{30} +(-2.27719 - 3.94421i) q^{31} +(-2.29813 - 3.98048i) q^{32} +(-6.61721 + 1.16679i) q^{33} +(2.09240 + 3.62414i) q^{34} +(-10.1382 - 8.50692i) q^{36} +(2.27719 + 3.94421i) q^{37} -6.10607 q^{38} +(3.23055 - 8.87587i) q^{39} +5.36959 q^{40} +(-0.592396 + 1.02606i) q^{41} +(-0.0923963 - 0.160035i) q^{43} +(-8.55690 - 14.8210i) q^{44} +(2.47906 - 0.902302i) q^{45} +(-4.00387 + 6.93491i) q^{46} +(-0.511144 + 0.885328i) q^{47} +(3.93242 - 10.8042i) q^{48} +(5.35117 - 9.26849i) q^{50} +(-0.979055 + 2.68993i) q^{51} +24.0574 q^{52} +(-3.64543 + 6.31407i) q^{53} -13.1571i q^{54} +3.41147 q^{55} +(-2.68479 - 3.19961i) q^{57} -15.3182 q^{58} +(3.33022 + 5.76811i) q^{59} +(4.31908 + 5.14728i) q^{60} +(-1.29813 + 2.24843i) q^{61} +11.5321 q^{62} -1.63816 q^{64} +(-2.39780 + 4.15312i) q^{65} +(5.81908 - 15.9878i) q^{66} +(1.47906 + 2.56180i) q^{67} -7.29086 q^{68} +(-5.39440 + 0.951178i) q^{69} -3.68004 q^{71} +(17.2135 - 6.26519i) q^{72} +(-6.39053 + 11.0687i) q^{73} -11.5321 q^{74} +(7.20961 - 1.27125i) q^{75} +(5.31908 - 9.21291i) q^{76} +(15.3735 + 18.3214i) q^{78} +(2.97906 - 5.15988i) q^{79} +(-2.91875 + 5.05542i) q^{80} +(6.89440 - 5.78509i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(-0.109470 - 0.189608i) q^{83} +(0.726682 - 1.25865i) q^{85} +0.467911 q^{86} +(-6.73530 - 8.02682i) q^{87} +23.6878 q^{88} +(5.51367 + 9.54996i) q^{89} +(-1.15998 + 6.57856i) q^{90} +(-6.97565 - 12.0822i) q^{92} +(5.07057 + 6.04288i) q^{93} +(-1.29426 - 2.24173i) q^{94} +(1.06031 + 1.83651i) q^{95} +(5.11721 + 6.09845i) q^{96} +(6.25150 + 10.8279i) q^{97} +(10.9363 - 3.98048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} - 3q^{4} - 6q^{5} + 9q^{6} + 12q^{8} + O(q^{10}) \) \( 6q - 3q^{2} - 3q^{4} - 6q^{5} + 9q^{6} + 12q^{8} + 12q^{11} + 9q^{12} - 3q^{13} - 9q^{15} - 3q^{16} + 6q^{17} + 9q^{18} - 3q^{19} - 6q^{20} - 9q^{22} + 24q^{23} - 18q^{24} - 12q^{25} - 3q^{26} - 27q^{27} - 9q^{29} - 9q^{30} - 3q^{31} - 9q^{33} + 9q^{34} - 27q^{36} + 3q^{37} - 12q^{38} - 18q^{39} + 18q^{40} + 3q^{43} - 15q^{44} + 18q^{45} + 3q^{47} + 6q^{50} - 9q^{51} + 42q^{52} - 6q^{53} - 9q^{57} - 18q^{58} - 3q^{59} + 9q^{60} + 6q^{61} + 60q^{62} + 24q^{64} - 15q^{65} + 18q^{66} + 12q^{67} - 12q^{68} + 9q^{69} + 18q^{71} + 45q^{72} - 21q^{73} - 60q^{74} + 9q^{75} + 15q^{76} + 54q^{78} + 21q^{79} - 15q^{80} - 9q^{82} - 18q^{83} - 9q^{85} + 12q^{86} - 36q^{87} + 54q^{88} + 12q^{89} - 27q^{90} - 3q^{92} - 27q^{93} - 18q^{94} + 12q^{95} - 3q^{97} + 18q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26604 + 2.19285i −0.895229 + 1.55058i −0.0617072 + 0.998094i \(0.519654\pi\)
−0.833521 + 0.552487i \(0.813679\pi\)
\(3\) −1.70574 + 0.300767i −0.984808 + 0.173648i
\(4\) −2.20574 3.82045i −1.10287 1.91022i
\(5\) 0.879385 0.393273 0.196637 0.980476i \(-0.436998\pi\)
0.196637 + 0.980476i \(0.436998\pi\)
\(6\) 1.50000 4.12122i 0.612372 1.68248i
\(7\) 0 0
\(8\) 6.10607 2.15882
\(9\) 2.81908 1.02606i 0.939693 0.342020i
\(10\) −1.11334 + 1.92836i −0.352069 + 0.609802i
\(11\) 3.87939 1.16968 0.584839 0.811149i \(-0.301158\pi\)
0.584839 + 0.811149i \(0.301158\pi\)
\(12\) 4.91147 + 5.85327i 1.41782 + 1.68969i
\(13\) −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
\(16\) −3.31908 + 5.74881i −0.829769 + 1.43720i
\(17\) 0.826352 1.43128i 0.200420 0.347137i −0.748244 0.663424i \(-0.769103\pi\)
0.948664 + 0.316286i \(0.102436\pi\)
\(18\) −1.31908 + 7.48086i −0.310910 + 1.76326i
\(19\) 1.20574 + 2.08840i 0.276615 + 0.479111i 0.970541 0.240935i \(-0.0774540\pi\)
−0.693926 + 0.720046i \(0.744121\pi\)
\(20\) −1.93969 3.35965i −0.433728 0.751240i
\(21\) 0 0
\(22\) −4.91147 + 8.50692i −1.04713 + 1.81368i
\(23\) 3.16250 0.659428 0.329714 0.944081i \(-0.393048\pi\)
0.329714 + 0.944081i \(0.393048\pi\)
\(24\) −10.4153 + 1.83651i −2.12602 + 0.374875i
\(25\) −4.22668 −0.845336
\(26\) −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 \(0.643483\pi\)
\(30\) 1.31908 3.62414i 0.240830 0.661674i
\(31\) −2.27719 3.94421i −0.408995 0.708400i 0.585782 0.810468i \(-0.300787\pi\)
−0.994777 + 0.102068i \(0.967454\pi\)
\(32\) −2.29813 3.98048i −0.406256 0.703657i
\(33\) −6.61721 + 1.16679i −1.15191 + 0.203113i
\(34\) 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 0.990232 0.139428i \(-0.0445265\pi\)
−0.615865 + 0.787852i \(0.711193\pi\)
\(38\) −6.10607 −0.990535
\(39\) 3.23055 8.87587i 0.517302 1.42128i
\(40\) 5.36959 0.849006
\(41\) −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
\(45\) 2.47906 0.902302i 0.369556 0.134507i
\(46\) −4.00387 + 6.93491i −0.590338 + 1.02250i
\(47\) −0.511144 + 0.885328i −0.0745581 + 0.129138i −0.900894 0.434039i \(-0.857088\pi\)
0.826336 + 0.563178i \(0.190421\pi\)
\(48\) 3.93242 10.8042i 0.567596 1.55946i
\(49\) 0 0
\(50\) 5.35117 9.26849i 0.756769 1.31076i
\(51\) −0.979055 + 2.68993i −0.137095 + 0.376666i
\(52\) 24.0574 3.33616
\(53\) −3.64543 + 6.31407i −0.500738 + 0.867304i 0.499261 + 0.866451i \(0.333605\pi\)
−1.00000 0.000852699i \(0.999729\pi\)
\(54\) 13.1571i 1.79046i
\(55\) 3.41147 0.460003
\(56\) 0 0
\(57\) −2.68479 3.19961i −0.355609 0.423799i
\(58\) −15.3182 −2.01138
\(59\) 3.33022 + 5.76811i 0.433558 + 0.750944i 0.997177 0.0750906i \(-0.0239246\pi\)
−0.563619 + 0.826035i \(0.690591\pi\)
\(60\) 4.31908 + 5.14728i 0.557591 + 0.664511i
\(61\) −1.29813 + 2.24843i −0.166209 + 0.287882i −0.937084 0.349104i \(-0.886486\pi\)
0.770875 + 0.636986i \(0.219819\pi\)
\(62\) 11.5321 1.46458
\(63\) 0 0
\(64\) −1.63816 −0.204769
\(65\) −2.39780 + 4.15312i −0.297411 + 0.515131i
\(66\) 5.81908 15.9878i 0.716279 1.96796i
\(67\) 1.47906 + 2.56180i 0.180695 + 0.312974i 0.942118 0.335283i \(-0.108832\pi\)
−0.761422 + 0.648256i \(0.775499\pi\)
\(68\) −7.29086 −0.884147
\(69\) −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 \(0.570074\pi\)
\(72\) 17.2135 6.26519i 2.02863 0.738360i
\(73\) −6.39053 + 11.0687i −0.747955 + 1.29550i 0.200847 + 0.979623i \(0.435631\pi\)
−0.948801 + 0.315873i \(0.897703\pi\)
\(74\) −11.5321 −1.34058
\(75\) 7.20961 1.27125i 0.832494 0.146791i
\(76\) 5.31908 9.21291i 0.610140 1.05679i
\(77\) 0 0
\(78\) 15.3735 + 18.3214i 1.74070 + 2.07449i
\(79\) 2.97906 5.15988i 0.335170 0.580531i −0.648348 0.761345i \(-0.724540\pi\)
0.983517 + 0.180813i \(0.0578729\pi\)
\(80\) −2.91875 + 5.05542i −0.326326 + 0.565213i
\(81\) 6.89440 5.78509i 0.766044 0.642788i
\(82\) −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
\(86\) 0.467911 0.0504562
\(87\) −6.73530 8.02682i −0.722100 0.860565i
\(88\) 23.6878 2.52513
\(89\) 5.51367 + 9.54996i 0.584448 + 1.01229i 0.994944 + 0.100431i \(0.0320222\pi\)
−0.410496 + 0.911862i \(0.634644\pi\)
\(90\) −1.15998 + 6.57856i −0.122272 + 0.693441i
\(91\) 0 0
\(92\) −6.97565 12.0822i −0.727262 1.25965i
\(93\) 5.07057 + 6.04288i 0.525794 + 0.626617i
\(94\) −1.29426 2.24173i −0.133493 0.231217i
\(95\) 1.06031 + 1.83651i 0.108785 + 0.188422i
\(96\) 5.11721 + 6.09845i 0.522273 + 0.622421i
\(97\) 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
\(101\) 9.71688 0.966866 0.483433 0.875381i \(-0.339390\pi\)
0.483433 + 0.875381i \(0.339390\pi\)
\(102\) −4.65910 5.55250i −0.461320 0.549779i
\(103\) −6.59627 −0.649949 −0.324975 0.945723i \(-0.605356\pi\)
−0.324975 + 0.945723i \(0.605356\pi\)
\(104\) −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 0.802488 0.596668i \(-0.203509\pi\)
−0.917974 + 0.396641i \(0.870176\pi\)
\(108\) 19.8516 + 11.4613i 1.91022 + 1.10287i
\(109\) −1.97906 + 3.42782i −0.189559 + 0.328326i −0.945103 0.326772i \(-0.894039\pi\)
0.755544 + 0.655098i \(0.227373\pi\)
\(110\) −4.31908 + 7.48086i −0.411808 + 0.713272i
\(111\) −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 \(0.884969\pi\)
\(114\) 10.4153 1.83651i 0.975486 0.172005i
\(115\) 2.78106 0.259335
\(116\) 13.3439 23.1123i 1.23895 2.14592i
\(117\) −2.84090 + 16.1115i −0.262641 + 1.48951i
\(118\) −16.8648 −1.55253
\(119\) 0 0
\(120\) −9.15910 + 1.61500i −0.836108 + 0.147428i
\(121\) 4.04963 0.368148
\(122\) −3.28699 5.69323i −0.297590 0.515441i
\(123\) 0.701867 1.92836i 0.0632852 0.173875i
\(124\) −10.0458 + 17.3998i −0.902136 + 1.56255i
\(125\) −8.11381 −0.725721
\(126\) 0 0
\(127\) 17.6536 1.56651 0.783253 0.621702i \(-0.213559\pi\)
0.783253 + 0.621702i \(0.213559\pi\)
\(128\) 6.67024 11.5532i 0.589572 1.02117i
\(129\) 0.205737 + 0.245188i 0.0181141 + 0.0215876i
\(130\) −6.07145 10.5161i −0.532502 0.922320i
\(131\) 19.1976 1.67730 0.838650 0.544670i \(-0.183345\pi\)
0.838650 + 0.544670i \(0.183345\pi\)
\(132\) 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
\(137\) 18.1557 1.55115 0.775573 0.631258i \(-0.217461\pi\)
0.775573 + 0.631258i \(0.217461\pi\)
\(138\) 4.74376 13.0334i 0.403815 1.10947i
\(139\) 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
\(142\) 4.65910 8.06980i 0.390983 0.677202i
\(143\) −10.5778 + 18.3214i −0.884564 + 1.53211i
\(144\) −3.45811 + 19.6119i −0.288176 + 1.63433i
\(145\) 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
\(149\) −15.1557 −1.24160 −0.620802 0.783968i \(-0.713193\pi\)
−0.620802 + 0.783968i \(0.713193\pi\)
\(150\) −6.34002 + 17.4191i −0.517661 + 1.42226i
\(151\) −18.9564 −1.54265 −0.771323 0.636444i \(-0.780405\pi\)
−0.771323 + 0.636444i \(0.780405\pi\)
\(152\) 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
\(156\) −41.0355 + 7.23567i −3.28547 + 0.579318i
\(157\) −9.02869 15.6381i −0.720568 1.24806i −0.960773 0.277337i \(-0.910548\pi\)
0.240205 0.970722i \(-0.422785\pi\)
\(158\) 7.54323 + 13.0653i 0.600107 + 1.03942i
\(159\) 4.31908 11.8666i 0.342525 0.941080i
\(160\) −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 0.846654 0.532143i \(-0.178613\pi\)
−0.884177 + 0.467152i \(0.845280\pi\)
\(164\) 5.22668 0.408135
\(165\) −5.81908 + 1.02606i −0.453015 + 0.0798787i
\(166\) 0.554378 0.0430280
\(167\) 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
\(171\) 5.54189 + 4.65020i 0.423799 + 0.355609i
\(172\) −0.407604 + 0.705990i −0.0310795 + 0.0538313i
\(173\) 11.3414 19.6438i 0.862268 1.49349i −0.00746626 0.999972i \(-0.502377\pi\)
0.869734 0.493520i \(-0.164290\pi\)
\(174\) 26.1288 4.60722i 1.98082 0.349272i
\(175\) 0 0
\(176\) −12.8760 + 22.3019i −0.970564 + 1.68107i
\(177\) −7.41534 8.83726i −0.557371 0.664249i
\(178\) −27.9222 −2.09286
\(179\) 3.67365 6.36295i 0.274581 0.475589i −0.695448 0.718576i \(-0.744794\pi\)
0.970029 + 0.242988i \(0.0781274\pi\)
\(180\) −8.91534 7.48086i −0.664511 0.557591i
\(181\) 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
\(184\) 19.3105 1.42359
\(185\) 2.00253 + 3.46848i 0.147229 + 0.255008i
\(186\) −19.6707 + 3.46848i −1.44233 + 0.254321i
\(187\) 3.20574 5.55250i 0.234427 0.406039i
\(188\) 4.50980 0.328911
\(189\) 0 0
\(190\) −5.36959 −0.389551
\(191\) −2.82888 + 4.89976i −0.204690 + 0.354534i −0.950034 0.312146i \(-0.898952\pi\)
0.745344 + 0.666680i \(0.232285\pi\)
\(192\) 2.79426 0.492704i 0.201659 0.0355578i
\(193\) −4.79813 8.31061i −0.345377 0.598211i 0.640045 0.768337i \(-0.278916\pi\)
−0.985422 + 0.170127i \(0.945582\pi\)
\(194\) −31.6587 −2.27296
\(195\) 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 \(0.404218\pi\)
\(198\) −5.11721 + 29.0211i −0.363664 + 2.06244i
\(199\) 3.29813 5.71253i 0.233798 0.404951i −0.725124 0.688618i \(-0.758218\pi\)
0.958923 + 0.283667i \(0.0915511\pi\)
\(200\) −25.8084 −1.82493
\(201\) −3.29339 3.92490i −0.232298 0.276841i
\(202\) −12.3020 + 21.3077i −0.865566 + 1.49920i
\(203\) 0 0
\(204\) 12.4363 2.19285i 0.870714 0.153530i
\(205\) −0.520945 + 0.902302i −0.0363843 + 0.0630195i
\(206\) 8.35117 14.4646i 0.581853 1.00780i
\(207\) 8.91534 3.24492i 0.619659 0.225538i
\(208\) −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 \(0.129664\pi\)
\(212\) 32.1634 2.20899
\(213\) 6.27719 1.10684i 0.430106 0.0758393i
\(214\) 6.04963 0.413544
\(215\) −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
\(219\) 7.57145 20.8024i 0.511631 1.40570i
\(220\) −7.52481 13.0334i −0.507323 0.878709i
\(221\) 4.50640 + 7.80531i 0.303133 + 0.525042i
\(222\) 19.6707 3.46848i 1.32021 0.232789i
\(223\) −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
\(227\) 6.16250 0.409020 0.204510 0.978865i \(-0.434440\pi\)
0.204510 + 0.978865i \(0.434440\pi\)
\(228\) −6.30200 + 17.3146i −0.417360 + 1.14669i
\(229\) −23.3851 −1.54533 −0.772664 0.634815i \(-0.781076\pi\)
−0.772664 + 0.634815i \(0.781076\pi\)
\(230\) −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 0.971200 0.238267i \(-0.0765792\pi\)
−0.691945 + 0.721950i \(0.743246\pi\)
\(234\) −31.7335 26.6276i −2.07449 1.74070i
\(235\) −0.449493 + 0.778544i −0.0293217 + 0.0507866i
\(236\) 14.6912 25.4459i 0.956315 1.65639i
\(237\) −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 \(0.322764\pi\)
\(240\) 3.45811 9.50108i 0.223220 0.613292i
\(241\) 5.40373 0.348085 0.174043 0.984738i \(-0.444317\pi\)
0.174043 + 0.984738i \(0.444317\pi\)
\(242\) −5.12701 + 8.88024i −0.329577 + 0.570844i
\(243\) −10.0201 + 11.9415i −0.642788 + 0.766044i
\(244\) 11.4534 0.733226
\(245\) 0 0
\(246\) 3.34002 + 3.98048i 0.212952 + 0.253786i
\(247\) −13.1506 −0.836755
\(248\) −13.9047 24.0836i −0.882947 1.52931i
\(249\) 0.243756 + 0.290497i 0.0154474 + 0.0184095i
\(250\) 10.2724 17.7924i 0.649686 1.12529i
\(251\) 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
\(254\) −22.3503 + 38.7118i −1.40238 + 2.42900i
\(255\) −0.860967 + 2.36549i −0.0539158 + 0.148133i
\(256\) 15.2515 + 26.4164i 0.953219 + 1.65102i
\(257\) −10.5662 −0.659104 −0.329552 0.944137i \(-0.606898\pi\)
−0.329552 + 0.944137i \(0.606898\pi\)
\(258\) −0.798133 + 0.140732i −0.0496896 + 0.00876162i
\(259\) 0 0
\(260\) 21.1557 1.31202
\(261\) 13.9029 + 11.6659i 0.860565 + 0.722100i
\(262\) −24.3050 + 42.0975i −1.50157 + 2.60079i
\(263\) −28.3533 −1.74834 −0.874169 0.485622i \(-0.838593\pi\)
−0.874169 + 0.485622i \(0.838593\pi\)
\(264\) −40.4051 + 7.12452i −2.48676 + 0.438484i
\(265\) −3.20574 + 5.55250i −0.196927 + 0.341087i
\(266\) 0 0
\(267\) −12.2772 14.6314i −0.751352 0.895426i
\(268\) 6.52481 11.3013i 0.398567 0.690337i
\(269\) 3.74170 6.48081i 0.228135 0.395142i −0.729120 0.684386i \(-0.760070\pi\)
0.957255 + 0.289244i \(0.0934038\pi\)
\(270\) 11.5702i 0.704139i
\(271\) 6.81908 + 11.8110i 0.414229 + 0.717467i 0.995347 0.0963530i \(-0.0307178\pi\)
−0.581118 + 0.813819i \(0.697384\pi\)
\(272\) 5.48545 + 9.50108i 0.332604 + 0.576088i
\(273\) 0 0
\(274\) −22.9859 + 39.8128i −1.38863 + 2.40518i
\(275\) −16.3969 −0.988772
\(276\) 15.5326 + 18.5110i 0.934950 + 1.11423i
\(277\) −6.15064 −0.369556 −0.184778 0.982780i \(-0.559157\pi\)
−0.184778 + 0.982780i \(0.559157\pi\)
\(278\) 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 \(0.864832\pi\)
\(282\) 2.88191 + 3.43453i 0.171615 + 0.204523i
\(283\) 14.5116 + 25.1348i 0.862626 + 1.49411i 0.869385 + 0.494134i \(0.164515\pi\)
−0.00675974 + 0.999977i \(0.502152\pi\)
\(284\) 8.11721 + 14.0594i 0.481668 + 0.834273i
\(285\) −2.36097 2.81369i −0.139852 0.166669i
\(286\) −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
\(290\) −13.4706 −0.791021
\(291\) −13.9201 16.5893i −0.816010 0.972483i
\(292\) 56.3833 3.29958
\(293\) −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
\(297\) −17.4572 + 10.0789i −1.01297 + 0.584839i
\(298\) 19.1878 33.2342i 1.11152 1.92521i
\(299\) −8.62314 + 14.9357i −0.498689 + 0.863755i
\(300\) −20.7592 24.7399i −1.19854 1.42836i
\(301\) 0 0
\(302\) 23.9996 41.5685i 1.38102 2.39200i
\(303\) −16.5744 + 2.92252i −0.952177 + 0.167894i
\(304\) −16.0077 −0.918107
\(305\) −1.14156 + 1.97724i −0.0653655 + 0.113216i
\(306\) 9.61721 + 8.06980i 0.549779 + 0.461320i
\(307\) 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
\(310\) 10.1411 0.575979
\(311\) −8.24510 14.2809i −0.467537 0.809797i 0.531775 0.846886i \(-0.321525\pi\)
−0.999312 + 0.0370881i \(0.988192\pi\)
\(312\) 19.7260 54.1966i 1.11676 3.06828i
\(313\) 14.2592 24.6977i 0.805980 1.39600i −0.109648 0.993970i \(-0.534972\pi\)
0.915628 0.402027i \(-0.131694\pi\)
\(314\) 45.7229 2.58029
\(315\) 0 0
\(316\) −26.2841 −1.47859
\(317\) 12.9474 22.4256i 0.727200 1.25955i −0.230862 0.972987i \(-0.574154\pi\)
0.958062 0.286561i \(-0.0925122\pi\)
\(318\) 20.5535 + 24.4947i 1.15258 + 1.37360i
\(319\) 11.7344 + 20.3246i 0.657002 + 1.13796i
\(320\) −1.44057 −0.0805303
\(321\) 2.65998 + 3.17004i 0.148465 + 0.176934i
\(322\) 0 0
\(323\) 3.98545 0.221756
\(324\) −37.3089 13.5793i −2.07271 0.754407i
\(325\) 11.5248 19.9616i 0.639282 1.10727i
\(326\) 2.42602 0.134365
\(327\) 2.34477 6.44220i 0.129666 0.356255i
\(328\) −3.61721 + 6.26519i −0.199727 + 0.345937i
\(329\) 0 0
\(330\) 5.11721 14.0594i 0.281693 0.773946i
\(331\) −4.10947 + 7.11781i −0.225877 + 0.391230i −0.956582 0.291463i \(-0.905858\pi\)
0.730705 + 0.682693i \(0.239191\pi\)
\(332\) −0.482926 + 0.836452i −0.0265040 + 0.0459063i
\(333\) 10.4666 + 8.78249i 0.573564 + 0.481278i
\(334\) 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 \(0.206402\pi\)
\(338\) 42.3851 2.30544
\(339\) 9.74691 26.7794i 0.529380 1.45446i
\(340\) −6.41147 −0.347711
\(341\) −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
\(345\) −4.74376 + 0.836452i −0.255395 + 0.0450331i
\(346\) 28.7173 + 49.7399i 1.54385 + 2.67403i
\(347\) −11.2331 19.4563i −0.603023 1.04447i −0.992361 0.123372i \(-0.960629\pi\)
0.389337 0.921095i \(-0.372704\pi\)
\(348\) −15.8097 + 43.4369i −0.847491 + 2.32846i
\(349\) 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
\(353\) 0.355037 0.0188967 0.00944836 0.999955i \(-0.496992\pi\)
0.00944836 + 0.999955i \(0.496992\pi\)
\(354\) 28.7670 5.07239i 1.52895 0.269595i
\(355\) −3.23618 −0.171758
\(356\) 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 0.785012 0.619480i \(-0.212657\pi\)
−0.928992 + 0.370100i \(0.879323\pi\)
\(360\) 15.1373 5.50952i 0.797805 0.290377i
\(361\) 6.59240 11.4184i 0.346968 0.600967i
\(362\) −4.36231 + 7.55574i −0.229278 + 0.397121i
\(363\) −6.90760 + 1.21800i −0.362555 + 0.0639283i
\(364\) 0 0
\(365\) −5.61974 + 9.73367i −0.294150 + 0.509484i
\(366\) 7.31908 + 8.72254i 0.382574 + 0.455934i
\(367\) −10.9240 −0.570226 −0.285113 0.958494i \(-0.592031\pi\)
−0.285113 + 0.958494i \(0.592031\pi\)
\(368\) −10.4966 + 18.1806i −0.547173 + 0.947731i
\(369\) −0.617211 + 3.50038i −0.0321307 + 0.182222i
\(370\) −10.1411 −0.527213
\(371\) 0 0
\(372\) 11.9021 32.7009i 0.617097 1.69546i
\(373\) 1.73143 0.0896500 0.0448250 0.998995i \(-0.485727\pi\)
0.0448250 + 0.998995i \(0.485727\pi\)
\(374\) 8.11721 + 14.0594i 0.419731 + 0.726995i
\(375\) 13.8400 2.44037i 0.714696 0.126020i
\(376\) −3.12108 + 5.40587i −0.160957 + 0.278787i
\(377\) −32.9908 −1.69911
\(378\) 0 0
\(379\) −12.1334 −0.623251 −0.311626 0.950205i \(-0.600873\pi\)
−0.311626 + 0.950205i \(0.600873\pi\)
\(380\) 4.67752 8.10170i 0.239952 0.415608i
\(381\) −30.1125 + 5.30964i −1.54271 + 0.272021i
\(382\) −7.16297 12.4066i −0.366489 0.634778i
\(383\) 8.71183 0.445154 0.222577 0.974915i \(-0.428553\pi\)
0.222577 + 0.974915i \(0.428553\pi\)
\(384\) −7.90286 + 21.7129i −0.403291 + 1.10803i
\(385\) 0 0
\(386\) 24.2986 1.23677
\(387\) −0.424678 0.356347i −0.0215876 0.0181141i
\(388\) 27.5783 47.7670i 1.40008 2.42500i
\(389\) 3.64321 0.184718 0.0923590 0.995726i \(-0.470559\pi\)
0.0923590 + 0.995726i \(0.470559\pi\)
\(390\) 13.5192 + 16.1115i 0.684571 + 0.815840i
\(391\) 2.61334 4.52644i 0.132162 0.228912i
\(392\) 0 0
\(393\) −32.7460 + 5.77401i −1.65182 + 0.291260i
\(394\) −10.5334 + 18.2444i −0.530667 + 0.919142i
\(395\) 2.61974 4.53752i 0.131813 0.228307i
\(396\) −39.3298 33.0016i −1.97640 1.65839i
\(397\) −7.72281 13.3763i −0.387597 0.671337i 0.604529 0.796583i \(-0.293361\pi\)
−0.992126 + 0.125246i \(0.960028\pi\)
\(398\) 8.35117 + 14.4646i 0.418606 + 0.725047i
\(399\) 0 0
\(400\) 14.0287 24.2984i 0.701434 1.21492i
\(401\) 18.4219 0.919946 0.459973 0.887933i \(-0.347859\pi\)
0.459973 + 0.887933i \(0.347859\pi\)
\(402\) 12.7763 2.25281i 0.637224 0.112360i
\(403\) 24.8367 1.23720
\(404\) −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
\(408\) −5.97818 + 16.4249i −0.295964 + 0.813154i
\(409\) −14.3182 24.7999i −0.707989 1.22627i −0.965602 0.260025i \(-0.916269\pi\)
0.257612 0.966248i \(-0.417064\pi\)
\(410\) −1.31908 2.28471i −0.0651446 0.112834i
\(411\) −30.9688 + 5.46064i −1.52758 + 0.269354i
\(412\) 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
\(416\) 25.0651 1.22892
\(417\) −13.0667 + 35.9005i −0.639879 + 1.75805i
\(418\) −23.6878 −1.15861
\(419\) −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
\(423\) −0.532556 + 3.02027i −0.0258937 + 0.146851i
\(424\) −22.2592 + 38.5541i −1.08100 + 1.87235i
\(425\) −3.49273 + 6.04958i −0.169422 + 0.293448i
\(426\) −5.52007 + 15.1663i −0.267448 + 0.734808i
\(427\) 0 0
\(428\) −5.26991 + 9.12776i −0.254731 + 0.441207i
\(429\) 12.5326 34.4329i 0.605077 1.66244i
\(430\) 0.411474 0.0198430
\(431\) −13.2961 + 23.0295i −0.640449 + 1.10929i 0.344883 + 0.938646i \(0.387919\pi\)
−0.985333 + 0.170645i \(0.945415\pi\)
\(432\) 34.4929i 1.65954i
\(433\) −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
\(436\) 17.4611 0.836235
\(437\) 3.81315 + 6.60457i 0.182408 + 0.315939i
\(438\) 36.0308 + 42.9398i 1.72162 + 2.05174i
\(439\) 12.5373 21.7152i 0.598373 1.03641i −0.394689 0.918815i \(-0.629147\pi\)
0.993061 0.117597i \(-0.0375192\pi\)
\(440\) 20.8307 0.993064
\(441\) 0 0
\(442\) −22.8212 −1.08549
\(443\) −1.02229 + 1.77066i −0.0485704 + 0.0841264i −0.889288 0.457347i \(-0.848800\pi\)
0.840718 + 0.541473i \(0.182133\pi\)
\(444\) −11.9021 + 32.7009i −0.564851 + 1.55191i
\(445\) 4.84864 + 8.39809i 0.229848 + 0.398108i
\(446\) 15.8922 0.752516
\(447\) 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 \(0.577638\pi\)
\(450\) 5.57532 31.6192i 0.262823 1.49054i
\(451\) −2.29813 + 3.98048i −0.108215 + 0.187434i
\(452\) 72.5836 3.41404
\(453\) 32.3346 5.70146i 1.51921 0.267878i
\(454\) −7.80200 + 13.5135i −0.366166 + 0.634218i
\(455\) 0 0
\(456\) −16.3935 19.5370i −0.767697 0.914906i
\(457\) 21.2973 36.8879i 0.996244 1.72554i 0.423129 0.906070i \(-0.360932\pi\)
0.573115 0.819475i \(-0.305735\pi\)
\(458\) 29.6065 51.2800i 1.38342 2.39616i
\(459\) 8.58770i 0.400840i
\(460\) −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 \(0.186503\pi\)
\(464\) −40.1584 −1.86431
\(465\) 4.45899 + 5.31402i 0.206781 + 0.246432i
\(466\) −21.5868 −0.999988
\(467\) −15.7083 27.2075i −0.726892 1.25901i −0.958191 0.286131i \(-0.907631\pi\)
0.231299 0.972883i \(-0.425702\pi\)
\(468\) 67.8196 24.6843i 3.13496 1.14103i
\(469\) 0 0
\(470\) −1.13816 1.97134i −0.0524992 0.0909313i
\(471\) 20.1040 + 23.9590i 0.926344 + 1.10397i
\(472\) 20.3346 + 35.2205i 0.935974 + 1.62115i
\(473\) −0.358441 0.620838i −0.0164811 0.0285461i
\(474\) −16.7964 20.0171i −0.771483 0.919418i
\(475\) −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
\(479\) 16.4406 0.751189 0.375594 0.926784i \(-0.377439\pi\)
0.375594 + 0.926784i \(0.377439\pi\)
\(480\) 4.50000 + 5.36289i 0.205396 + 0.244781i
\(481\) −24.8367 −1.13245
\(482\) −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
\(486\) −13.5000 37.0909i −0.612372 1.68248i
\(487\) 1.48767 2.57673i 0.0674129 0.116763i −0.830349 0.557244i \(-0.811859\pi\)
0.897762 + 0.440481i \(0.145192\pi\)
\(488\) −7.92649 + 13.7291i −0.358815 + 0.621486i
\(489\) 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 \(-0.0372321\pi\)
\(492\) −8.91534 + 1.57202i −0.401935 + 0.0708719i
\(493\) 9.99825 0.450298
\(494\) 16.6493 28.8374i 0.749087 1.29746i
\(495\) 9.61721 3.50038i 0.432261 0.157330i
\(496\) 30.2327 1.35749
\(497\) 0 0
\(498\) −0.945622 + 0.166739i −0.0423744 + 0.00747174i
\(499\) −13.4439 −0.601830 −0.300915 0.953651i \(-0.597292\pi\)
−0.300915 + 0.953651i \(0.597292\pi\)
\(500\) 17.8969 + 30.9984i 0.800375 + 1.38629i
\(501\) −11.7522 + 32.2889i −0.525050 + 1.44256i
\(502\) −15.2772 + 26.4609i −0.681854 + 1.18101i
\(503\) 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
\(506\) −15.5326 + 26.9032i −0.690506 + 1.19599i
\(507\) 18.6364 + 22.2100i 0.827672 + 0.986381i
\(508\) −38.9393 67.4448i −1.72765 2.99238i
\(509\) −9.54757 −0.423189 −0.211594 0.977358i \(-0.567866\pi\)
−0.211594 + 0.977358i \(0.567866\pi\)
\(510\) −4.09714 4.88279i −0.181425 0.216213i
\(511\) 0 0
\(512\) −50.5553 −2.23425
\(513\) −10.8516 6.26519i −0.479111 0.276615i
\(514\) 13.3773 23.1702i 0.590049 1.02199i
\(515\) −5.80066 −0.255608
\(516\) 0.482926 1.32683i 0.0212596 0.0584103i
\(517\) −1.98293 + 3.43453i −0.0872090 + 0.151050i
\(518\) 0 0
\(519\) −13.4372 + 36.9183i −0.589826 + 1.62053i
\(520\) −14.6411 + 25.3592i −0.642057 + 1.11208i
\(521\) −1.55644 + 2.69583i −0.0681887 + 0.118106i −0.898104 0.439783i \(-0.855055\pi\)
0.829915 + 0.557889i \(0.188389\pi\)
\(522\) −43.1832 + 15.7174i −1.89008 + 0.687932i
\(523\) −8.07444 13.9853i −0.353071 0.611537i 0.633715 0.773567i \(-0.281529\pi\)
−0.986786 + 0.162030i \(0.948196\pi\)
\(524\) −42.3448 73.3434i −1.84984 3.20402i
\(525\) 0 0
\(526\) 35.8965 62.1746i 1.56516 2.71094i
\(527\) −7.52704 −0.327883
\(528\) 15.2554 41.9138i 0.663905 1.82406i
\(529\) −12.9986 −0.565155
\(530\) −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
\(534\) 47.6279 8.39809i 2.06106 0.363421i
\(535\) −1.05051 1.81953i −0.0454174 0.0786652i
\(536\) 9.03121 + 15.6425i 0.390089 + 0.675654i
\(537\) −4.35251 + 11.9584i −0.187825 + 0.516044i
\(538\) 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 0.914885 0.403714i \(-0.132281\pi\)
−0.807069 + 0.590457i \(0.798948\pi\)
\(542\) −34.5330 −1.48332
\(543\) −5.87733 + 1.03633i −0.252220 + 0.0444732i
\(544\) −7.59627 −0.325687
\(545\) −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
\(549\) −1.35251 + 7.67047i −0.0577238 + 0.327368i
\(550\) 20.7592 35.9561i 0.885177 1.53317i
\(551\) −7.29426 + 12.6340i −0.310746 + 0.538228i
\(552\) −32.9386 + 5.80796i −1.40196 + 0.247203i
\(553\) 0 0
\(554\) 7.78699 13.4875i 0.330837 0.573027i
\(555\) −4.45899 5.31402i −0.189274 0.225567i
\(556\) −97.3055 −4.12667
\(557\) 17.2815 29.9325i 0.732242 1.26828i −0.223681 0.974662i \(-0.571807\pi\)
0.955923 0.293618i \(-0.0948592\pi\)
\(558\) 32.5099 11.8326i 1.37625 0.500915i
\(559\) 1.00774 0.0426229
\(560\) 0 0
\(561\) −3.79813 + 10.4353i −0.160357 + 0.440578i
\(562\) 8.38682 0.353777
\(563\) −18.6052 32.2251i −0.784115 1.35813i −0.929526 0.368756i \(-0.879784\pi\)
0.145411 0.989371i \(-0.453550\pi\)
\(564\) −7.69253 + 1.35640i −0.323914 + 0.0571148i
\(565\) −7.23442 + 12.5304i −0.304354 + 0.527157i
\(566\) −73.4894 −3.08899
\(567\) 0 0
\(568\) −22.4706 −0.942845
\(569\) −0.202333 + 0.350452i −0.00848226 + 0.0146917i −0.870235 0.492636i \(-0.836033\pi\)
0.861753 + 0.507328i \(0.169367\pi\)
\(570\) 9.15910 1.61500i 0.383632 0.0676448i
\(571\) 18.8897 + 32.7178i 0.790507 + 1.36920i 0.925653 + 0.378373i \(0.123516\pi\)
−0.135146 + 0.990826i \(0.543150\pi\)
\(572\) 93.3278 3.90223
\(573\) 3.35163 9.20854i 0.140017 0.384692i
\(574\) 0 0
\(575\) −13.3669 −0.557438
\(576\) −4.61809 + 1.68085i −0.192420 + 0.0700353i
\(577\) −1.10560 + 1.91496i −0.0460267 + 0.0797206i −0.888121 0.459610i \(-0.847989\pi\)
0.842094 + 0.539330i \(0.181323\pi\)
\(578\) −36.1293 −1.50278
\(579\) 10.6839 + 12.7326i 0.444008 + 0.529149i
\(580\) 11.7344 20.3246i 0.487245 0.843934i
\(581\) 0 0
\(582\) 54.0014 9.52190i 2.23843 0.394696i
\(583\) −14.1420 + 24.4947i −0.585703 + 1.01447i
\(584\) −39.0210 + 67.5864i −1.61470 + 2.79674i
\(585\) −2.49825 + 14.1683i −0.103290 + 0.585785i
\(586\) −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
\(590\) −14.8307 −0.610570
\(591\) −14.1917 + 2.50237i −0.583767 + 0.102934i
\(592\) −30.2327 −1.24255
\(593\) 6.11927 + 10.5989i 0.251288 + 0.435244i 0.963881 0.266334i \(-0.0858124\pi\)
−0.712592 + 0.701578i \(0.752479\pi\)
\(594\) 51.0415i 2.09426i
\(595\) 0 0
\(596\) 33.4295 + 57.9016i 1.36932 + 2.37174i
\(597\) −3.90760 + 10.7361i −0.159928 + 0.439397i
\(598\) −21.8346 37.8186i −0.892882 1.54652i
\(599\) −19.8084 34.3092i −0.809349 1.40183i −0.913315 0.407253i \(-0.866487\pi\)
0.103966 0.994581i \(-0.466847\pi\)
\(600\) 44.0223 7.76233i 1.79720 0.316896i
\(601\) −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
\(605\) 3.56118 0.144783
\(606\) 14.5753 40.0454i 0.592082 1.62673i
\(607\) 19.4843 0.790844 0.395422 0.918499i \(-0.370598\pi\)
0.395422 + 0.918499i \(0.370598\pi\)
\(608\) 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
\(612\) −20.5535 + 7.48086i −0.830826 + 0.302396i
\(613\) 9.26382 16.0454i 0.374162 0.648068i −0.616039 0.787716i \(-0.711264\pi\)
0.990201 + 0.139648i \(0.0445970\pi\)
\(614\) −16.0633 + 27.8225i −0.648262 + 1.12282i
\(615\) 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 \(0.977313\pi\)
\(618\) −9.89440 + 27.1846i −0.398011 + 1.09353i
\(619\) 44.9813 1.80795 0.903976 0.427583i \(-0.140635\pi\)
0.903976 + 0.427583i \(0.140635\pi\)
\(620\) −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
\(625\) 13.9982 0.559930
\(626\) 36.1057 + 62.5368i 1.44307 + 2.49947i
\(627\) −10.4153 12.4125i −0.415949 0.495708i
\(628\) −39.8298 + 68.9873i −1.58938 + 2.75289i
\(629\) 7.52704 0.300123
\(630\) 0 0
\(631\) 9.43613 0.375646 0.187823 0.982203i \(-0.439857\pi\)
0.187823 + 0.982203i \(0.439857\pi\)
\(632\) 18.1903 31.5065i 0.723572 1.25326i
\(633\) −1.99613 + 5.48432i −0.0793390 + 0.217982i
\(634\) 32.7841 + 56.7836i 1.30202 + 2.25517i
\(635\) 15.5243 0.616065
\(636\) −54.8624 + 9.67372i −2.17543 + 0.383588i
\(637\) 0 0
\(638\) −59.4252 −2.35267
\(639\) −10.3743 + 3.77595i −0.410402 + 0.149374i
\(640\) 5.86571 10.1597i 0.231863 0.401598i
\(641\) 37.3901 1.47682 0.738410 0.674352i \(-0.235577\pi\)
0.738410 + 0.674352i \(0.235577\pi\)
\(642\) −10.3191 + 1.81953i −0.407262 + 0.0718112i
\(643\) 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
\(646\) −5.04576 + 8.73951i −0.198523 + 0.343851i
\(647\) −20.5881 + 35.6597i −0.809402 + 1.40193i 0.103876 + 0.994590i \(0.466875\pi\)
−0.913278 + 0.407336i \(0.866458\pi\)
\(648\) 42.0977 35.3241i 1.65375 1.38766i
\(649\) 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
\(653\) 3.05199 0.119434 0.0597169 0.998215i \(-0.480980\pi\)
0.0597169 + 0.998215i \(0.480980\pi\)
\(654\) 11.1582 + 13.2979i 0.436321 + 0.519987i
\(655\) 16.8821 0.659637
\(656\) −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 \(-0.467707\pi\)
\(660\) 16.7554 + 19.9683i 0.652202 + 0.777264i
\(661\) 10.1505 + 17.5812i 0.394808 + 0.683828i 0.993077 0.117468i \(-0.0374778\pi\)
−0.598269 + 0.801296i \(0.704144\pi\)
\(662\) −10.4055 18.0229i −0.404423 0.700481i
\(663\) −10.0343 11.9584i −0.389700 0.464427i
\(664\) −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
\(668\) −87.5167 −3.38612
\(669\) 6.98767 + 8.32759i 0.270159 + 0.321963i
\(670\) −6.58677 −0.254469
\(671\) −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
\(675\) 19.0201 10.9812i 0.732083 0.422668i
\(676\) −36.9222 + 63.9511i −1.42008 + 2.45966i
\(677\) 5.43360 9.41127i 0.208830 0.361705i −0.742516 0.669828i \(-0.766368\pi\)
0.951346 + 0.308124i \(0.0997011\pi\)
\(678\) 46.3833 + 55.2775i 1.78134 + 2.12292i
\(679\) 0 0
\(680\) 4.43717 7.68540i 0.170158 0.294722i
\(681\) −10.5116 + 1.85348i −0.402806 + 0.0710255i
\(682\) 44.7374 1.71308
\(683\) −16.3473 + 28.3143i −0.625512 + 1.08342i 0.362930 + 0.931817i \(0.381777\pi\)
−0.988442 + 0.151602i \(0.951557\pi\)
\(684\) 5.54189 31.4296i 0.211899 1.20174i
\(685\) 15.9659 0.610024
\(686\) 0 0
\(687\) 39.8888 7.03347i 1.52185 0.268344i
\(688\) 1.22668 0.0467668
\(689\) −19.8799 34.4329i −0.757362 1.31179i
\(690\) 4.17159 11.4613i 0.158810 0.436326i
\(691\) 7.49912 12.9889i 0.285280 0.494120i −0.687397 0.726282i \(-0.741247\pi\)
0.972677 + 0.232162i \(0.0745801\pi\)
\(692\) −100.064 −3.80387
\(693\) 0 0
\(694\) 56.8863 2.15937
\(695\) 9.69846 16.7982i 0.367884 0.637193i
\(696\) −41.1262 49.0123i −1.55888 1.85781i
\(697\) 0.979055 + 1.69577i 0.0370844 + 0.0642320i
\(698\) −66.0856 −2.50138
\(699\) −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 \(0.333386\pi\)
\(702\) 62.1378 + 35.8753i 2.34524 + 1.35403i
\(703\) −5.49138 + 9.51135i −0.207111 + 0.358727i
\(704\) −6.35504 −0.239514
\(705\) 0.532556 1.46318i 0.0200572 0.0551067i
\(706\) −0.449493 + 0.778544i −0.0169169 + 0.0293009i
\(707\) 0 0
\(708\) −17.4060 + 47.8226i −0.654158 + 1.79728i
\(709\) −7.68004 + 13.3022i −0.288430 + 0.499576i −0.973435 0.228963i \(-0.926467\pi\)
0.685005 + 0.728538i \(0.259800\pi\)
\(710\) 4.09714 7.09646i 0.153763 0.266325i
\(711\) 3.10385 17.6028i 0.116403 0.660156i
\(712\) 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
\(716\) −32.4124 −1.21131
\(717\) 8.62654 23.7012i 0.322164 0.885139i
\(718\) 13.8152 0.515579
\(719\) 13.3653 + 23.1494i 0.498442 + 0.863326i 0.999998 0.00179839i \(-0.000572447\pi\)
−0.501557 + 0.865125i \(0.667239\pi\)
\(720\) −3.04101 + 17.2464i −0.113332 + 0.642737i
\(721\) 0 0
\(722\) 16.6925 + 28.9123i 0.621232 + 1.07600i
\(723\) −9.21735 + 1.62527i −0.342797 + 0.0604443i
\(724\) −7.60014 13.1638i −0.282457 0.489230i
\(725\) −12.7849 22.1441i −0.474820 0.822413i
\(726\) 6.07444 16.6894i 0.225444 0.619402i
\(727\) −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
\(731\) −0.305407 −0.0112959
\(732\) −19.5364 + 3.44480i −0.722087 + 0.127323i
\(733\) −5.97502 −0.220693 −0.110346 0.993893i \(-0.535196\pi\)
−0.110346 + 0.993893i \(0.535196\pi\)
\(734\) 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
\(738\) −6.89440 5.78509i −0.253786 0.212952i
\(739\) 17.7981 30.8273i 0.654715 1.13400i −0.327250 0.944938i \(-0.606122\pi\)
0.981965 0.189062i \(-0.0605447\pi\)
\(740\) 8.83409 15.3011i 0.324748 0.562480i
\(741\) 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 \(-0.0140083\pi\)
\(744\) 30.9613 + 36.8982i 1.13510 + 1.35275i
\(745\) −13.3277 −0.488289
\(746\) −2.19207 + 3.79677i −0.0802573 + 0.139010i
\(747\) −0.503155 0.422197i −0.0184095 0.0154474i
\(748\) −28.2841 −1.03417
\(749\) 0 0
\(750\) −12.1707 + 33.4388i −0.444412 + 1.22101i
\(751\) −17.3337 −0.632515 −0.316258 0.948673i \(-0.602426\pi\)
−0.316258 + 0.948673i \(0.602426\pi\)
\(752\) −3.39306 5.87695i −0.123732 0.214310i
\(753\) −20.5829 + 3.62932i −0.750083 + 0.132260i
\(754\) 41.7679 72.3440i 1.52110 2.63461i
\(755\) −16.6699 −0.606681
\(756\) 0 0
\(757\) −2.77156 −0.100734 −0.0503671 0.998731i \(-0.516039\pi\)
−0.0503671 + 0.998731i \(0.516039\pi\)
\(758\) 15.3614 26.6068i 0.557952 0.966402i
\(759\) −20.9270 + 3.68999i −0.759600 + 0.133938i
\(760\) 6.47431 + 11.2138i 0.234848 + 0.406768i
\(761\) −7.50744 −0.272144 −0.136072 0.990699i \(-0.543448\pi\)
−0.136072 + 0.990699i \(0.543448\pi\)
\(762\) 26.4805 72.7545i 0.959286 2.63562i
\(763\) 0 0
\(764\) 24.9590 0.902987
\(765\) 0.757122 4.29385i 0.0273738 0.155244i
\(766\) −11.0296 + 19.1038i −0.398514 + 0.690247i
\(767\) −36.3218 −1.31150
\(768\) −33.9602 40.4722i −1.22543 1.46042i
\(769\) 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
\(772\) −21.1668 + 36.6620i −0.761811 + 1.31950i
\(773\) −12.4709 + 21.6002i −0.448547 + 0.776907i −0.998292 0.0584263i \(-0.981392\pi\)
0.549744 + 0.835333i \(0.314725\pi\)
\(774\) 1.31908 0.480105i 0.0474133 0.0172570i
\(775\) 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
\(779\) −2.85710 −0.102366
\(780\) −36.0861 + 6.36295i −1.29209 + 0.227830i