Properties

Label 585.2.j.i.451.5
Level $585$
Weight $2$
Character 585.451
Analytic conductor $4.671$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.j (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \( x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 50x^{6} - 42x^{5} + 124x^{4} - 12x^{3} + 96x^{2} - 36x + 36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.5
Root \(1.31604 + 2.27945i\) of defining polynomial
Character \(\chi\) \(=\) 585.451
Dual form 585.2.j.i.406.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.31604 - 2.27945i) q^{2} +(-2.46394 - 4.26767i) q^{4} -1.00000 q^{5} +(-0.544875 - 0.943751i) q^{7} -7.70645 q^{8} +O(q^{10})\) \(q+(1.31604 - 2.27945i) q^{2} +(-2.46394 - 4.26767i) q^{4} -1.00000 q^{5} +(-0.544875 - 0.943751i) q^{7} -7.70645 q^{8} +(-1.31604 + 2.27945i) q^{10} +(2.36092 - 4.08923i) q^{11} +(-3.42647 - 1.12219i) q^{13} -2.86832 q^{14} +(-5.21415 + 9.03117i) q^{16} +(2.61184 + 4.52384i) q^{17} +(-1.46394 - 2.53562i) q^{19} +(2.46394 + 4.26767i) q^{20} +(-6.21415 - 10.7632i) q^{22} +(-3.85323 + 6.67399i) q^{23} +1.00000 q^{25} +(-7.06737 + 6.33362i) q^{26} +(-2.68508 + 4.65070i) q^{28} +(0.655591 - 1.13552i) q^{29} -2.32091 q^{31} +(6.01764 + 10.4229i) q^{32} +13.7492 q^{34} +(0.544875 + 0.943751i) q^{35} +(5.21415 - 9.03117i) q^{37} -7.70645 q^{38} +7.70645 q^{40} +(2.49373 - 4.31926i) q^{41} +(-2.98419 - 5.16877i) q^{43} -23.2687 q^{44} +(10.1420 + 17.5665i) q^{46} +8.51804 q^{47} +(2.90622 - 5.03372i) q^{49} +(1.31604 - 2.27945i) q^{50} +(3.65346 + 17.3881i) q^{52} +9.67627 q^{53} +(-2.36092 + 4.08923i) q^{55} +(4.19906 + 7.27298i) q^{56} +(-1.72557 - 2.98878i) q^{58} +(-1.58348 - 2.74266i) q^{59} +(-3.16045 - 5.47406i) q^{61} +(-3.05441 + 5.29040i) q^{62} +10.8213 q^{64} +(3.42647 + 1.12219i) q^{65} +(0.787679 - 1.36430i) q^{67} +(12.8709 - 22.2930i) q^{68} +2.86832 q^{70} +(-3.00113 - 5.19810i) q^{71} +12.3098 q^{73} +(-13.7241 - 23.7708i) q^{74} +(-7.21415 + 12.4953i) q^{76} -5.14562 q^{77} -3.04333 q^{79} +(5.21415 - 9.03117i) q^{80} +(-6.56371 - 11.3687i) q^{82} +1.40782 q^{83} +(-2.61184 - 4.52384i) q^{85} -15.7093 q^{86} +(-18.1943 + 31.5135i) q^{88} +(-4.33742 + 7.51262i) q^{89} +(0.807924 + 3.84519i) q^{91} +37.9765 q^{92} +(11.2101 - 19.4165i) q^{94} +(1.46394 + 2.53562i) q^{95} +(5.51622 + 9.55437i) q^{97} +(-7.64943 - 13.2492i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 2 q^{2} - 6 q^{4} - 10 q^{5} - q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 2 q^{2} - 6 q^{4} - 10 q^{5} - q^{7} - 12 q^{8} - 2 q^{10} + 8 q^{11} + q^{13} + 8 q^{14} - 4 q^{16} + 4 q^{19} + 6 q^{20} - 14 q^{22} - 6 q^{23} + 10 q^{25} + 10 q^{26} + 2 q^{28} + 16 q^{29} + 18 q^{31} + 14 q^{32} + q^{35} + 4 q^{37} - 12 q^{38} + 12 q^{40} + 6 q^{41} - 15 q^{43} - 28 q^{44} + 16 q^{46} - 20 q^{47} - 10 q^{49} + 2 q^{50} - 22 q^{52} + 40 q^{53} - 8 q^{55} - 2 q^{56} + 4 q^{58} + 12 q^{59} - 11 q^{61} - 22 q^{62} + 8 q^{64} - q^{65} - 5 q^{67} + 50 q^{68} - 8 q^{70} + 10 q^{71} + 2 q^{73} - 26 q^{74} - 24 q^{76} - 84 q^{77} - 34 q^{79} + 4 q^{80} - 16 q^{82} - 32 q^{83} - 88 q^{86} - 20 q^{88} + 4 q^{89} - q^{91} + 68 q^{92} + 16 q^{94} - 4 q^{95} + 11 q^{97} + 30 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.31604 2.27945i 0.930584 1.61182i 0.148258 0.988949i \(-0.452634\pi\)
0.782326 0.622869i \(-0.214033\pi\)
\(3\) 0 0
\(4\) −2.46394 4.26767i −1.23197 2.13384i
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −0.544875 0.943751i −0.205943 0.356704i 0.744489 0.667634i \(-0.232693\pi\)
−0.950433 + 0.310930i \(0.899360\pi\)
\(8\) −7.70645 −2.72464
\(9\) 0 0
\(10\) −1.31604 + 2.27945i −0.416170 + 0.720827i
\(11\) 2.36092 4.08923i 0.711844 1.23295i −0.252320 0.967644i \(-0.581194\pi\)
0.964164 0.265306i \(-0.0854730\pi\)
\(12\) 0 0
\(13\) −3.42647 1.12219i −0.950331 0.311241i
\(14\) −2.86832 −0.766590
\(15\) 0 0
\(16\) −5.21415 + 9.03117i −1.30354 + 2.25779i
\(17\) 2.61184 + 4.52384i 0.633465 + 1.09719i 0.986838 + 0.161711i \(0.0517012\pi\)
−0.353373 + 0.935482i \(0.614965\pi\)
\(18\) 0 0
\(19\) −1.46394 2.53562i −0.335852 0.581712i 0.647796 0.761813i \(-0.275691\pi\)
−0.983648 + 0.180101i \(0.942357\pi\)
\(20\) 2.46394 + 4.26767i 0.550954 + 0.954281i
\(21\) 0 0
\(22\) −6.21415 10.7632i −1.32486 2.29473i
\(23\) −3.85323 + 6.67399i −0.803453 + 1.39162i 0.113877 + 0.993495i \(0.463673\pi\)
−0.917330 + 0.398127i \(0.869660\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −7.06737 + 6.33362i −1.38603 + 1.24213i
\(27\) 0 0
\(28\) −2.68508 + 4.65070i −0.507433 + 0.878900i
\(29\) 0.655591 1.13552i 0.121740 0.210860i −0.798714 0.601711i \(-0.794486\pi\)
0.920454 + 0.390851i \(0.127819\pi\)
\(30\) 0 0
\(31\) −2.32091 −0.416847 −0.208423 0.978039i \(-0.566833\pi\)
−0.208423 + 0.978039i \(0.566833\pi\)
\(32\) 6.01764 + 10.4229i 1.06378 + 1.84252i
\(33\) 0 0
\(34\) 13.7492 2.35797
\(35\) 0.544875 + 0.943751i 0.0921007 + 0.159523i
\(36\) 0 0
\(37\) 5.21415 9.03117i 0.857200 1.48471i −0.0173882 0.999849i \(-0.505535\pi\)
0.874589 0.484866i \(-0.161132\pi\)
\(38\) −7.70645 −1.25015
\(39\) 0 0
\(40\) 7.70645 1.21850
\(41\) 2.49373 4.31926i 0.389455 0.674555i −0.602921 0.797801i \(-0.705997\pi\)
0.992376 + 0.123245i \(0.0393301\pi\)
\(42\) 0 0
\(43\) −2.98419 5.16877i −0.455084 0.788229i 0.543609 0.839339i \(-0.317058\pi\)
−0.998693 + 0.0511094i \(0.983724\pi\)
\(44\) −23.2687 −3.50789
\(45\) 0 0
\(46\) 10.1420 + 17.5665i 1.49536 + 2.59004i
\(47\) 8.51804 1.24248 0.621242 0.783619i \(-0.286628\pi\)
0.621242 + 0.783619i \(0.286628\pi\)
\(48\) 0 0
\(49\) 2.90622 5.03372i 0.415175 0.719104i
\(50\) 1.31604 2.27945i 0.186117 0.322364i
\(51\) 0 0
\(52\) 3.65346 + 17.3881i 0.506644 + 2.41129i
\(53\) 9.67627 1.32914 0.664569 0.747227i \(-0.268615\pi\)
0.664569 + 0.747227i \(0.268615\pi\)
\(54\) 0 0
\(55\) −2.36092 + 4.08923i −0.318346 + 0.551392i
\(56\) 4.19906 + 7.27298i 0.561122 + 0.971892i
\(57\) 0 0
\(58\) −1.72557 2.98878i −0.226579 0.392446i
\(59\) −1.58348 2.74266i −0.206151 0.357064i 0.744348 0.667792i \(-0.232761\pi\)
−0.950499 + 0.310728i \(0.899427\pi\)
\(60\) 0 0
\(61\) −3.16045 5.47406i −0.404655 0.700882i 0.589627 0.807676i \(-0.299275\pi\)
−0.994281 + 0.106794i \(0.965942\pi\)
\(62\) −3.05441 + 5.29040i −0.387911 + 0.671881i
\(63\) 0 0
\(64\) 10.8213 1.35266
\(65\) 3.42647 + 1.12219i 0.425001 + 0.139191i
\(66\) 0 0
\(67\) 0.787679 1.36430i 0.0962303 0.166676i −0.813891 0.581017i \(-0.802655\pi\)
0.910121 + 0.414342i \(0.135988\pi\)
\(68\) 12.8709 22.2930i 1.56082 2.70342i
\(69\) 0 0
\(70\) 2.86832 0.342830
\(71\) −3.00113 5.19810i −0.356168 0.616901i 0.631149 0.775662i \(-0.282584\pi\)
−0.987317 + 0.158760i \(0.949250\pi\)
\(72\) 0 0
\(73\) 12.3098 1.44075 0.720374 0.693586i \(-0.243970\pi\)
0.720374 + 0.693586i \(0.243970\pi\)
\(74\) −13.7241 23.7708i −1.59539 2.76330i
\(75\) 0 0
\(76\) −7.21415 + 12.4953i −0.827519 + 1.43331i
\(77\) −5.14562 −0.586398
\(78\) 0 0
\(79\) −3.04333 −0.342401 −0.171201 0.985236i \(-0.554765\pi\)
−0.171201 + 0.985236i \(0.554765\pi\)
\(80\) 5.21415 9.03117i 0.582959 1.00972i
\(81\) 0 0
\(82\) −6.56371 11.3687i −0.724840 1.25546i
\(83\) 1.40782 0.154528 0.0772640 0.997011i \(-0.475382\pi\)
0.0772640 + 0.997011i \(0.475382\pi\)
\(84\) 0 0
\(85\) −2.61184 4.52384i −0.283294 0.490680i
\(86\) −15.7093 −1.69398
\(87\) 0 0
\(88\) −18.1943 + 31.5135i −1.93952 + 3.35935i
\(89\) −4.33742 + 7.51262i −0.459765 + 0.796337i −0.998948 0.0458520i \(-0.985400\pi\)
0.539183 + 0.842189i \(0.318733\pi\)
\(90\) 0 0
\(91\) 0.807924 + 3.84519i 0.0846935 + 0.403085i
\(92\) 37.9765 3.95933
\(93\) 0 0
\(94\) 11.2101 19.4165i 1.15624 2.00266i
\(95\) 1.46394 + 2.53562i 0.150197 + 0.260150i
\(96\) 0 0
\(97\) 5.51622 + 9.55437i 0.560087 + 0.970099i 0.997488 + 0.0708327i \(0.0225657\pi\)
−0.437401 + 0.899266i \(0.644101\pi\)
\(98\) −7.64943 13.2492i −0.772709 1.33837i
\(99\) 0 0
\(100\) −2.46394 4.26767i −0.246394 0.426767i
\(101\) −4.60746 + 7.98035i −0.458459 + 0.794075i −0.998880 0.0473204i \(-0.984932\pi\)
0.540421 + 0.841395i \(0.318265\pi\)
\(102\) 0 0
\(103\) 14.8586 1.46406 0.732031 0.681271i \(-0.238572\pi\)
0.732031 + 0.681271i \(0.238572\pi\)
\(104\) 26.4059 + 8.64814i 2.58931 + 0.848020i
\(105\) 0 0
\(106\) 12.7344 22.0566i 1.23687 2.14233i
\(107\) 3.44743 5.97113i 0.333276 0.577251i −0.649876 0.760040i \(-0.725179\pi\)
0.983152 + 0.182789i \(0.0585126\pi\)
\(108\) 0 0
\(109\) −14.5790 −1.39642 −0.698208 0.715895i \(-0.746019\pi\)
−0.698208 + 0.715895i \(0.746019\pi\)
\(110\) 6.21415 + 10.7632i 0.592496 + 1.02623i
\(111\) 0 0
\(112\) 11.3642 1.07382
\(113\) 6.64689 + 11.5127i 0.625286 + 1.08303i 0.988485 + 0.151316i \(0.0483512\pi\)
−0.363199 + 0.931712i \(0.618315\pi\)
\(114\) 0 0
\(115\) 3.85323 6.67399i 0.359315 0.622352i
\(116\) −6.46136 −0.599922
\(117\) 0 0
\(118\) −8.33570 −0.767364
\(119\) 2.84626 4.92986i 0.260916 0.451920i
\(120\) 0 0
\(121\) −5.64788 9.78241i −0.513443 0.889310i
\(122\) −16.6372 −1.50626
\(123\) 0 0
\(124\) 5.71858 + 9.90487i 0.513544 + 0.889484i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −7.72740 + 13.3842i −0.685696 + 1.18766i 0.287522 + 0.957774i \(0.407169\pi\)
−0.973218 + 0.229886i \(0.926165\pi\)
\(128\) 2.20605 3.82099i 0.194989 0.337731i
\(129\) 0 0
\(130\) 7.06737 6.33362i 0.619850 0.555495i
\(131\) 8.48870 0.741661 0.370831 0.928701i \(-0.379073\pi\)
0.370831 + 0.928701i \(0.379073\pi\)
\(132\) 0 0
\(133\) −1.59533 + 2.76320i −0.138333 + 0.239600i
\(134\) −2.07324 3.59096i −0.179101 0.310211i
\(135\) 0 0
\(136\) −20.1280 34.8628i −1.72597 2.98946i
\(137\) −2.86093 4.95527i −0.244426 0.423357i 0.717544 0.696513i \(-0.245266\pi\)
−0.961970 + 0.273155i \(0.911933\pi\)
\(138\) 0 0
\(139\) 9.19692 + 15.9295i 0.780072 + 1.35112i 0.931899 + 0.362718i \(0.118151\pi\)
−0.151827 + 0.988407i \(0.548516\pi\)
\(140\) 2.68508 4.65070i 0.226931 0.393056i
\(141\) 0 0
\(142\) −15.7985 −1.32578
\(143\) −12.6785 + 11.3622i −1.06023 + 0.950156i
\(144\) 0 0
\(145\) −0.655591 + 1.13552i −0.0544439 + 0.0942996i
\(146\) 16.2002 28.0595i 1.34074 2.32222i
\(147\) 0 0
\(148\) −51.3894 −4.22419
\(149\) 11.3302 + 19.6244i 0.928202 + 1.60769i 0.786328 + 0.617809i \(0.211979\pi\)
0.141874 + 0.989885i \(0.454687\pi\)
\(150\) 0 0
\(151\) −2.26871 −0.184625 −0.0923125 0.995730i \(-0.529426\pi\)
−0.0923125 + 0.995730i \(0.529426\pi\)
\(152\) 11.2818 + 19.5407i 0.915076 + 1.58496i
\(153\) 0 0
\(154\) −6.77187 + 11.7292i −0.545693 + 0.945167i
\(155\) 2.32091 0.186420
\(156\) 0 0
\(157\) −13.8934 −1.10882 −0.554409 0.832245i \(-0.687056\pi\)
−0.554409 + 0.832245i \(0.687056\pi\)
\(158\) −4.00515 + 6.93713i −0.318633 + 0.551888i
\(159\) 0 0
\(160\) −6.01764 10.4229i −0.475736 0.823999i
\(161\) 8.39811 0.661864
\(162\) 0 0
\(163\) −12.3109 21.3231i −0.964264 1.67015i −0.711580 0.702605i \(-0.752020\pi\)
−0.252684 0.967549i \(-0.581313\pi\)
\(164\) −24.5776 −1.91919
\(165\) 0 0
\(166\) 1.85275 3.20906i 0.143801 0.249071i
\(167\) 1.89994 3.29079i 0.147022 0.254649i −0.783104 0.621891i \(-0.786365\pi\)
0.930125 + 0.367242i \(0.119698\pi\)
\(168\) 0 0
\(169\) 10.4814 + 7.69033i 0.806258 + 0.591564i
\(170\) −13.7492 −1.05452
\(171\) 0 0
\(172\) −14.7057 + 25.4711i −1.12130 + 1.94215i
\(173\) 9.04014 + 15.6580i 0.687309 + 1.19045i 0.972705 + 0.232044i \(0.0745414\pi\)
−0.285396 + 0.958410i \(0.592125\pi\)
\(174\) 0 0
\(175\) −0.544875 0.943751i −0.0411887 0.0713409i
\(176\) 24.6204 + 42.6437i 1.85583 + 3.21439i
\(177\) 0 0
\(178\) 11.4165 + 19.7739i 0.855700 + 1.48212i
\(179\) 12.8224 22.2091i 0.958394 1.65999i 0.231991 0.972718i \(-0.425476\pi\)
0.726403 0.687269i \(-0.241191\pi\)
\(180\) 0 0
\(181\) −19.0957 −1.41937 −0.709686 0.704518i \(-0.751163\pi\)
−0.709686 + 0.704518i \(0.751163\pi\)
\(182\) 9.82820 + 3.21881i 0.728515 + 0.238594i
\(183\) 0 0
\(184\) 29.6947 51.4328i 2.18912 3.79167i
\(185\) −5.21415 + 9.03117i −0.383352 + 0.663985i
\(186\) 0 0
\(187\) 24.6654 1.80371
\(188\) −20.9880 36.3522i −1.53071 2.65126i
\(189\) 0 0
\(190\) 7.70645 0.559085
\(191\) −12.0769 20.9178i −0.873853 1.51356i −0.857979 0.513684i \(-0.828280\pi\)
−0.0158737 0.999874i \(-0.505053\pi\)
\(192\) 0 0
\(193\) −6.39781 + 11.0813i −0.460524 + 0.797652i −0.998987 0.0449976i \(-0.985672\pi\)
0.538463 + 0.842649i \(0.319005\pi\)
\(194\) 29.0383 2.08483
\(195\) 0 0
\(196\) −28.6431 −2.04593
\(197\) 0.326273 0.565122i 0.0232460 0.0402632i −0.854168 0.519997i \(-0.825933\pi\)
0.877414 + 0.479733i \(0.159267\pi\)
\(198\) 0 0
\(199\) 3.19389 + 5.53198i 0.226409 + 0.392152i 0.956741 0.290940i \(-0.0939681\pi\)
−0.730332 + 0.683092i \(0.760635\pi\)
\(200\) −7.70645 −0.544929
\(201\) 0 0
\(202\) 12.1272 + 21.0050i 0.853269 + 1.47791i
\(203\) −1.42886 −0.100286
\(204\) 0 0
\(205\) −2.49373 + 4.31926i −0.174169 + 0.301670i
\(206\) 19.5546 33.8695i 1.36243 2.35980i
\(207\) 0 0
\(208\) 28.0008 25.0937i 1.94151 1.73994i
\(209\) −13.8250 −0.956296
\(210\) 0 0
\(211\) 8.74879 15.1534i 0.602292 1.04320i −0.390182 0.920738i \(-0.627588\pi\)
0.992473 0.122462i \(-0.0390789\pi\)
\(212\) −23.8418 41.2952i −1.63746 2.83617i
\(213\) 0 0
\(214\) −9.07395 15.7165i −0.620282 1.07436i
\(215\) 2.98419 + 5.16877i 0.203520 + 0.352507i
\(216\) 0 0
\(217\) 1.26460 + 2.19036i 0.0858469 + 0.148691i
\(218\) −19.1866 + 33.2322i −1.29948 + 2.25077i
\(219\) 0 0
\(220\) 23.2687 1.56877
\(221\) −3.87276 18.4318i −0.260510 1.23986i
\(222\) 0 0
\(223\) 1.32675 2.29800i 0.0888458 0.153885i −0.818178 0.574965i \(-0.805016\pi\)
0.907024 + 0.421080i \(0.138349\pi\)
\(224\) 6.55772 11.3583i 0.438156 0.758909i
\(225\) 0 0
\(226\) 34.9904 2.32753
\(227\) −2.55482 4.42508i −0.169569 0.293703i 0.768699 0.639611i \(-0.220904\pi\)
−0.938269 + 0.345908i \(0.887571\pi\)
\(228\) 0 0
\(229\) 17.2929 1.14275 0.571375 0.820689i \(-0.306410\pi\)
0.571375 + 0.820689i \(0.306410\pi\)
\(230\) −10.1420 17.5665i −0.668746 1.15830i
\(231\) 0 0
\(232\) −5.05228 + 8.75081i −0.331699 + 0.574519i
\(233\) −2.40701 −0.157688 −0.0788441 0.996887i \(-0.525123\pi\)
−0.0788441 + 0.996887i \(0.525123\pi\)
\(234\) 0 0
\(235\) −8.51804 −0.555656
\(236\) −7.80320 + 13.5155i −0.507945 + 0.879786i
\(237\) 0 0
\(238\) −7.49160 12.9758i −0.485608 0.841098i
\(239\) −8.83530 −0.571508 −0.285754 0.958303i \(-0.592244\pi\)
−0.285754 + 0.958303i \(0.592244\pi\)
\(240\) 0 0
\(241\) 4.27027 + 7.39633i 0.275072 + 0.476439i 0.970153 0.242492i \(-0.0779648\pi\)
−0.695081 + 0.718931i \(0.744632\pi\)
\(242\) −29.7314 −1.91121
\(243\) 0 0
\(244\) −15.5744 + 26.9756i −0.997046 + 1.72693i
\(245\) −2.90622 + 5.03372i −0.185672 + 0.321593i
\(246\) 0 0
\(247\) 2.17069 + 10.3311i 0.138118 + 0.657350i
\(248\) 17.8860 1.13576
\(249\) 0 0
\(250\) −1.31604 + 2.27945i −0.0832339 + 0.144165i
\(251\) 1.27257 + 2.20415i 0.0803237 + 0.139125i 0.903389 0.428822i \(-0.141071\pi\)
−0.823065 + 0.567947i \(0.807738\pi\)
\(252\) 0 0
\(253\) 18.1943 + 31.5135i 1.14387 + 1.98124i
\(254\) 20.3392 + 35.2285i 1.27619 + 2.21043i
\(255\) 0 0
\(256\) 5.01480 + 8.68589i 0.313425 + 0.542868i
\(257\) 6.02563 10.4367i 0.375868 0.651023i −0.614588 0.788848i \(-0.710678\pi\)
0.990457 + 0.137825i \(0.0440111\pi\)
\(258\) 0 0
\(259\) −11.3642 −0.706139
\(260\) −3.65346 17.3881i −0.226578 1.07836i
\(261\) 0 0
\(262\) 11.1715 19.3496i 0.690178 1.19542i
\(263\) −5.23646 + 9.06982i −0.322894 + 0.559269i −0.981084 0.193583i \(-0.937989\pi\)
0.658190 + 0.752852i \(0.271322\pi\)
\(264\) 0 0
\(265\) −9.67627 −0.594409
\(266\) 4.19906 + 7.27298i 0.257461 + 0.445935i
\(267\) 0 0
\(268\) −7.76318 −0.474212
\(269\) 4.46163 + 7.72777i 0.272030 + 0.471170i 0.969382 0.245559i \(-0.0789716\pi\)
−0.697351 + 0.716729i \(0.745638\pi\)
\(270\) 0 0
\(271\) −3.38740 + 5.86714i −0.205770 + 0.356403i −0.950378 0.311098i \(-0.899303\pi\)
0.744608 + 0.667502i \(0.232636\pi\)
\(272\) −54.4741 −3.30298
\(273\) 0 0
\(274\) −15.0604 −0.909834
\(275\) 2.36092 4.08923i 0.142369 0.246590i
\(276\) 0 0
\(277\) 2.81829 + 4.88142i 0.169335 + 0.293296i 0.938186 0.346131i \(-0.112505\pi\)
−0.768852 + 0.639427i \(0.779171\pi\)
\(278\) 48.4142 2.90369
\(279\) 0 0
\(280\) −4.19906 7.27298i −0.250942 0.434644i
\(281\) 12.5297 0.747456 0.373728 0.927538i \(-0.378079\pi\)
0.373728 + 0.927538i \(0.378079\pi\)
\(282\) 0 0
\(283\) −12.6721 + 21.9487i −0.753279 + 1.30472i 0.192947 + 0.981209i \(0.438196\pi\)
−0.946226 + 0.323508i \(0.895138\pi\)
\(284\) −14.7892 + 25.6157i −0.877578 + 1.52001i
\(285\) 0 0
\(286\) 9.21415 + 43.8533i 0.544844 + 2.59310i
\(287\) −5.43508 −0.320823
\(288\) 0 0
\(289\) −5.14344 + 8.90871i −0.302556 + 0.524042i
\(290\) 1.72557 + 2.98878i 0.101329 + 0.175507i
\(291\) 0 0
\(292\) −30.3305 52.5340i −1.77496 3.07432i
\(293\) 8.92273 + 15.4546i 0.521272 + 0.902869i 0.999694 + 0.0247390i \(0.00787548\pi\)
−0.478422 + 0.878130i \(0.658791\pi\)
\(294\) 0 0
\(295\) 1.58348 + 2.74266i 0.0921936 + 0.159684i
\(296\) −40.1826 + 69.5983i −2.33557 + 4.04532i
\(297\) 0 0
\(298\) 59.6439 3.45508
\(299\) 20.6925 18.5441i 1.19668 1.07243i
\(300\) 0 0
\(301\) −3.25202 + 5.63266i −0.187443 + 0.324661i
\(302\) −2.98572 + 5.17142i −0.171809 + 0.297582i
\(303\) 0 0
\(304\) 30.5329 1.75118
\(305\) 3.16045 + 5.47406i 0.180967 + 0.313444i
\(306\) 0 0
\(307\) 10.0377 0.572880 0.286440 0.958098i \(-0.407528\pi\)
0.286440 + 0.958098i \(0.407528\pi\)
\(308\) 12.6785 + 21.9599i 0.722426 + 1.25128i
\(309\) 0 0
\(310\) 3.05441 5.29040i 0.173479 0.300475i
\(311\) −8.76317 −0.496914 −0.248457 0.968643i \(-0.579923\pi\)
−0.248457 + 0.968643i \(0.579923\pi\)
\(312\) 0 0
\(313\) 4.37893 0.247512 0.123756 0.992313i \(-0.460506\pi\)
0.123756 + 0.992313i \(0.460506\pi\)
\(314\) −18.2844 + 31.6695i −1.03185 + 1.78721i
\(315\) 0 0
\(316\) 7.49859 + 12.9879i 0.421829 + 0.730629i
\(317\) −11.7036 −0.657338 −0.328669 0.944445i \(-0.606600\pi\)
−0.328669 + 0.944445i \(0.606600\pi\)
\(318\) 0 0
\(319\) −3.09559 5.36173i −0.173320 0.300199i
\(320\) −10.8213 −0.604930
\(321\) 0 0
\(322\) 11.0523 19.1431i 0.615920 1.06680i
\(323\) 7.64718 13.2453i 0.425500 0.736988i
\(324\) 0 0
\(325\) −3.42647 1.12219i −0.190066 0.0622482i
\(326\) −64.8067 −3.58931
\(327\) 0 0
\(328\) −19.2178 + 33.2862i −1.06113 + 1.83792i
\(329\) −4.64127 8.03891i −0.255881 0.443200i
\(330\) 0 0
\(331\) 6.36162 + 11.0186i 0.349666 + 0.605640i 0.986190 0.165617i \(-0.0529617\pi\)
−0.636524 + 0.771257i \(0.719628\pi\)
\(332\) −3.46878 6.00811i −0.190374 0.329738i
\(333\) 0 0
\(334\) −5.00081 8.66166i −0.273632 0.473945i
\(335\) −0.787679 + 1.36430i −0.0430355 + 0.0745397i
\(336\) 0 0
\(337\) −4.03730 −0.219926 −0.109963 0.993936i \(-0.535073\pi\)
−0.109963 + 0.993936i \(0.535073\pi\)
\(338\) 31.3237 13.7710i 1.70378 0.749042i
\(339\) 0 0
\(340\) −12.8709 + 22.2930i −0.698021 + 1.20901i
\(341\) −5.47947 + 9.49072i −0.296730 + 0.513951i
\(342\) 0 0
\(343\) −13.9624 −0.753897
\(344\) 22.9975 + 39.8329i 1.23994 + 2.14764i
\(345\) 0 0
\(346\) 47.5889 2.55839
\(347\) 0.172172 + 0.298211i 0.00924268 + 0.0160088i 0.870610 0.491974i \(-0.163725\pi\)
−0.861367 + 0.507983i \(0.830391\pi\)
\(348\) 0 0
\(349\) 17.3201 29.9993i 0.927125 1.60583i 0.139017 0.990290i \(-0.455606\pi\)
0.788108 0.615537i \(-0.211061\pi\)
\(350\) −2.86832 −0.153318
\(351\) 0 0
\(352\) 56.8286 3.02898
\(353\) −8.92012 + 15.4501i −0.474770 + 0.822326i −0.999583 0.0288917i \(-0.990802\pi\)
0.524812 + 0.851218i \(0.324136\pi\)
\(354\) 0 0
\(355\) 3.00113 + 5.19810i 0.159283 + 0.275887i
\(356\) 42.7486 2.26567
\(357\) 0 0
\(358\) −33.7498 58.4563i −1.78373 3.08951i
\(359\) 7.22285 0.381207 0.190604 0.981667i \(-0.438955\pi\)
0.190604 + 0.981667i \(0.438955\pi\)
\(360\) 0 0
\(361\) 5.21374 9.03046i 0.274407 0.475288i
\(362\) −25.1308 + 43.5278i −1.32084 + 2.28777i
\(363\) 0 0
\(364\) 14.4193 12.9223i 0.755779 0.677312i
\(365\) −12.3098 −0.644322
\(366\) 0 0
\(367\) 14.8752 25.7647i 0.776481 1.34490i −0.157477 0.987523i \(-0.550336\pi\)
0.933958 0.357382i \(-0.116331\pi\)
\(368\) −40.1826 69.5983i −2.09466 3.62806i
\(369\) 0 0
\(370\) 13.7241 + 23.7708i 0.713482 + 1.23579i
\(371\) −5.27236 9.13200i −0.273727 0.474110i
\(372\) 0 0
\(373\) −1.92089 3.32707i −0.0994597 0.172269i 0.812001 0.583655i \(-0.198378\pi\)
−0.911461 + 0.411386i \(0.865045\pi\)
\(374\) 32.4607 56.2237i 1.67851 2.90726i
\(375\) 0 0
\(376\) −65.6439 −3.38533
\(377\) −3.52063 + 3.15511i −0.181322 + 0.162497i
\(378\) 0 0
\(379\) −15.5513 + 26.9356i −0.798816 + 1.38359i 0.121572 + 0.992583i \(0.461206\pi\)
−0.920388 + 0.391006i \(0.872127\pi\)
\(380\) 7.21415 12.4953i 0.370078 0.640994i
\(381\) 0 0
\(382\) −63.5749 −3.25277
\(383\) 6.48045 + 11.2245i 0.331136 + 0.573544i 0.982735 0.185020i \(-0.0592349\pi\)
−0.651599 + 0.758563i \(0.725902\pi\)
\(384\) 0 0
\(385\) 5.14562 0.262245
\(386\) 16.8396 + 29.1670i 0.857113 + 1.48456i
\(387\) 0 0
\(388\) 27.1833 47.0828i 1.38002 2.39027i
\(389\) −14.1302 −0.716432 −0.358216 0.933639i \(-0.616615\pi\)
−0.358216 + 0.933639i \(0.616615\pi\)
\(390\) 0 0
\(391\) −40.2561 −2.03584
\(392\) −22.3967 + 38.7922i −1.13120 + 1.95930i
\(393\) 0 0
\(394\) −0.858780 1.48745i −0.0432647 0.0749366i
\(395\) 3.04333 0.153126
\(396\) 0 0
\(397\) 14.1550 + 24.5172i 0.710419 + 1.23048i 0.964700 + 0.263352i \(0.0848281\pi\)
−0.254280 + 0.967131i \(0.581839\pi\)
\(398\) 16.8132 0.842770
\(399\) 0 0
\(400\) −5.21415 + 9.03117i −0.260707 + 0.451558i
\(401\) 2.21775 3.84126i 0.110749 0.191824i −0.805323 0.592836i \(-0.798008\pi\)
0.916073 + 0.401012i \(0.131342\pi\)
\(402\) 0 0
\(403\) 7.95251 + 2.60451i 0.396143 + 0.129740i
\(404\) 45.4101 2.25923
\(405\) 0 0
\(406\) −1.88044 + 3.25702i −0.0933249 + 0.161643i
\(407\) −24.6204 42.6437i −1.22039 2.11377i
\(408\) 0 0
\(409\) 4.48420 + 7.76686i 0.221729 + 0.384046i 0.955333 0.295531i \(-0.0954965\pi\)
−0.733604 + 0.679577i \(0.762163\pi\)
\(410\) 6.56371 + 11.3687i 0.324159 + 0.561459i
\(411\) 0 0
\(412\) −36.6108 63.4117i −1.80368 3.12407i
\(413\) −1.72560 + 2.98882i −0.0849110 + 0.147070i
\(414\) 0 0
\(415\) −1.40782 −0.0691071
\(416\) −8.92277 42.4665i −0.437475 2.08209i
\(417\) 0 0
\(418\) −18.1943 + 31.5135i −0.889913 + 1.54137i
\(419\) −17.1960 + 29.7844i −0.840081 + 1.45506i 0.0497447 + 0.998762i \(0.484159\pi\)
−0.889826 + 0.456301i \(0.849174\pi\)
\(420\) 0 0
\(421\) 20.1940 0.984198 0.492099 0.870539i \(-0.336230\pi\)
0.492099 + 0.870539i \(0.336230\pi\)
\(422\) −23.0276 39.8850i −1.12097 1.94157i
\(423\) 0 0
\(424\) −74.5698 −3.62143
\(425\) 2.61184 + 4.52384i 0.126693 + 0.219439i
\(426\) 0 0
\(427\) −3.44410 + 5.96536i −0.166672 + 0.288684i
\(428\) −33.9771 −1.64235
\(429\) 0 0
\(430\) 15.7093 0.757569
\(431\) 10.3846 17.9866i 0.500208 0.866385i −0.499792 0.866145i \(-0.666590\pi\)
1.00000 0.000240043i \(-7.64081e-5\pi\)
\(432\) 0 0
\(433\) −18.3462 31.7765i −0.881661 1.52708i −0.849494 0.527599i \(-0.823092\pi\)
−0.0321670 0.999483i \(-0.510241\pi\)
\(434\) 6.65710 0.319551
\(435\) 0 0
\(436\) 35.9218 + 62.2185i 1.72034 + 2.97972i
\(437\) 22.5636 1.07936
\(438\) 0 0
\(439\) 10.1493 17.5791i 0.484400 0.839005i −0.515440 0.856926i \(-0.672371\pi\)
0.999839 + 0.0179207i \(0.00570465\pi\)
\(440\) 18.1943 31.5135i 0.867380 1.50235i
\(441\) 0 0
\(442\) −47.1112 15.4293i −2.24085 0.733896i
\(443\) 10.0068 0.475439 0.237720 0.971334i \(-0.423600\pi\)
0.237720 + 0.971334i \(0.423600\pi\)
\(444\) 0 0
\(445\) 4.33742 7.51262i 0.205613 0.356133i
\(446\) −3.49212 6.04854i −0.165357 0.286406i
\(447\) 0 0
\(448\) −5.89626 10.2126i −0.278572 0.482501i
\(449\) −5.28181 9.14837i −0.249264 0.431738i 0.714058 0.700087i \(-0.246855\pi\)
−0.963322 + 0.268349i \(0.913522\pi\)
\(450\) 0 0
\(451\) −11.7750 20.3949i −0.554462 0.960356i
\(452\) 32.7551 56.7335i 1.54067 2.66852i
\(453\) 0 0
\(454\) −13.4490 −0.631194
\(455\) −0.807924 3.84519i −0.0378761 0.180265i
\(456\) 0 0
\(457\) 2.40645 4.16810i 0.112569 0.194975i −0.804236 0.594310i \(-0.797425\pi\)
0.916805 + 0.399334i \(0.130759\pi\)
\(458\) 22.7583 39.4185i 1.06342 1.84190i
\(459\) 0 0
\(460\) −37.9765 −1.77067
\(461\) −9.78195 16.9428i −0.455591 0.789106i 0.543131 0.839648i \(-0.317239\pi\)
−0.998722 + 0.0505415i \(0.983905\pi\)
\(462\) 0 0
\(463\) 1.03118 0.0479230 0.0239615 0.999713i \(-0.492372\pi\)
0.0239615 + 0.999713i \(0.492372\pi\)
\(464\) 6.83670 + 11.8415i 0.317386 + 0.549728i
\(465\) 0 0
\(466\) −3.16772 + 5.48666i −0.146742 + 0.254165i
\(467\) −12.4884 −0.577896 −0.288948 0.957345i \(-0.593306\pi\)
−0.288948 + 0.957345i \(0.593306\pi\)
\(468\) 0 0
\(469\) −1.71675 −0.0792720
\(470\) −11.2101 + 19.4165i −0.517084 + 0.895616i
\(471\) 0 0
\(472\) 12.2030 + 21.1362i 0.561689 + 0.972873i
\(473\) −28.1817 −1.29580
\(474\) 0 0
\(475\) −1.46394 2.53562i −0.0671703 0.116342i
\(476\) −28.0521 −1.28576
\(477\) 0 0
\(478\) −11.6276 + 20.1397i −0.531836 + 0.921167i
\(479\) 3.32202 5.75390i 0.151787 0.262902i −0.780098 0.625658i \(-0.784831\pi\)
0.931884 + 0.362755i \(0.118164\pi\)
\(480\) 0 0
\(481\) −28.0008 + 25.0937i −1.27673 + 1.14417i
\(482\) 22.4795 1.02391
\(483\) 0 0
\(484\) −27.8321 + 48.2066i −1.26510 + 2.19121i
\(485\) −5.51622 9.55437i −0.250479 0.433842i
\(486\) 0 0
\(487\) −0.413437 0.716093i −0.0187346 0.0324493i 0.856506 0.516137i \(-0.172630\pi\)
−0.875241 + 0.483688i \(0.839297\pi\)
\(488\) 24.3559 + 42.1856i 1.10254 + 1.90965i
\(489\) 0 0
\(490\) 7.64943 + 13.2492i 0.345566 + 0.598538i
\(491\) 6.40991 11.1023i 0.289275 0.501039i −0.684362 0.729143i \(-0.739919\pi\)
0.973637 + 0.228103i \(0.0732524\pi\)
\(492\) 0 0
\(493\) 6.84920 0.308473
\(494\) 26.4059 + 8.64814i 1.18806 + 0.389098i
\(495\) 0 0
\(496\) 12.1015 20.9605i 0.543375 0.941154i
\(497\) −3.27048 + 5.66463i −0.146701 + 0.254094i
\(498\) 0 0
\(499\) 19.8651 0.889283 0.444642 0.895709i \(-0.353331\pi\)
0.444642 + 0.895709i \(0.353331\pi\)
\(500\) 2.46394 + 4.26767i 0.110191 + 0.190856i
\(501\) 0 0
\(502\) 6.69901 0.298992
\(503\) 9.35451 + 16.2025i 0.417097 + 0.722433i 0.995646 0.0932144i \(-0.0297142\pi\)
−0.578549 + 0.815648i \(0.696381\pi\)
\(504\) 0 0
\(505\) 4.60746 7.98035i 0.205029 0.355121i
\(506\) 95.7781 4.25785
\(507\) 0 0
\(508\) 76.1595 3.37903
\(509\) −5.01811 + 8.69163i −0.222424 + 0.385250i −0.955543 0.294850i \(-0.904730\pi\)
0.733119 + 0.680100i \(0.238064\pi\)
\(510\) 0 0
\(511\) −6.70728 11.6174i −0.296713 0.513921i
\(512\) 35.2230 1.55665
\(513\) 0 0
\(514\) −15.8600 27.4703i −0.699554 1.21166i
\(515\) −14.8586 −0.654749
\(516\) 0 0
\(517\) 20.1104 34.8323i 0.884455 1.53192i
\(518\) −14.9558 + 25.9043i −0.657122 + 1.13817i
\(519\) 0 0
\(520\) −26.4059 8.64814i −1.15798 0.379246i
\(521\) 2.06270 0.0903687 0.0451844 0.998979i \(-0.485612\pi\)
0.0451844 + 0.998979i \(0.485612\pi\)
\(522\) 0 0
\(523\) 16.0184 27.7448i 0.700438 1.21319i −0.267875 0.963454i \(-0.586321\pi\)
0.968313 0.249740i \(-0.0803453\pi\)
\(524\) −20.9157 36.2270i −0.913706 1.58258i
\(525\) 0 0
\(526\) 13.7828 + 23.8726i 0.600960 + 1.04089i
\(527\) −6.06184 10.4994i −0.264058 0.457362i
\(528\) 0 0
\(529\) −18.1947 31.5142i −0.791075 1.37018i
\(530\) −12.7344 + 22.0566i −0.553147 + 0.958079i
\(531\) 0 0
\(532\) 15.7232 0.681689
\(533\) −13.3917 + 12.0014i −0.580060 + 0.519837i
\(534\) 0 0
\(535\) −3.44743 + 5.97113i −0.149046 + 0.258154i
\(536\) −6.07021 + 10.5139i −0.262193 + 0.454132i
\(537\) 0 0
\(538\) 23.4868 1.01259
\(539\) −13.7227 23.7684i −0.591079 1.02378i
\(540\) 0 0
\(541\) −11.1795 −0.480644 −0.240322 0.970693i \(-0.577253\pi\)
−0.240322 + 0.970693i \(0.577253\pi\)
\(542\) 8.91592 + 15.4428i 0.382972 + 0.663326i
\(543\) 0 0
\(544\) −31.4342 + 54.4457i −1.34773 + 2.33434i
\(545\) 14.5790 0.624496
\(546\) 0 0
\(547\) −0.0903080 −0.00386129 −0.00193064 0.999998i \(-0.500615\pi\)
−0.00193064 + 0.999998i \(0.500615\pi\)
\(548\) −14.0983 + 24.4190i −0.602251 + 1.04313i
\(549\) 0 0
\(550\) −6.21415 10.7632i −0.264972 0.458945i
\(551\) −3.83899 −0.163547
\(552\) 0 0
\(553\) 1.65823 + 2.87215i 0.0705153 + 0.122136i
\(554\) 14.8360 0.630320
\(555\) 0 0
\(556\) 45.3214 78.4989i 1.92205 3.32909i
\(557\) −14.0621 + 24.3562i −0.595829 + 1.03201i 0.397600 + 0.917559i \(0.369843\pi\)
−0.993429 + 0.114447i \(0.963490\pi\)
\(558\) 0 0
\(559\) 4.42486 + 21.0594i 0.187152 + 0.890720i
\(560\) −11.3642 −0.480227
\(561\) 0 0
\(562\) 16.4896 28.5608i 0.695571 1.20476i
\(563\) −11.8278 20.4864i −0.498484 0.863399i 0.501515 0.865149i \(-0.332776\pi\)
−0.999998 + 0.00175021i \(0.999443\pi\)
\(564\) 0 0
\(565\) −6.64689 11.5127i −0.279637 0.484345i
\(566\) 33.3541 + 57.7710i 1.40198 + 2.42830i
\(567\) 0 0
\(568\) 23.1280 + 40.0590i 0.970431 + 1.68084i
\(569\) −4.88343 + 8.45835i −0.204724 + 0.354593i −0.950045 0.312114i \(-0.898963\pi\)
0.745321 + 0.666706i \(0.232296\pi\)
\(570\) 0 0
\(571\) −20.9688 −0.877518 −0.438759 0.898605i \(-0.644582\pi\)
−0.438759 + 0.898605i \(0.644582\pi\)
\(572\) 79.7294 + 26.1120i 3.33365 + 1.09180i
\(573\) 0 0
\(574\) −7.15280 + 12.3890i −0.298552 + 0.517108i
\(575\) −3.85323 + 6.67399i −0.160691 + 0.278324i
\(576\) 0 0
\(577\) −7.22602 −0.300823 −0.150412 0.988623i \(-0.548060\pi\)
−0.150412 + 0.988623i \(0.548060\pi\)
\(578\) 13.5380 + 23.4485i 0.563106 + 0.975329i
\(579\) 0 0
\(580\) 6.46136 0.268293
\(581\) −0.767085 1.32863i −0.0318240 0.0551209i
\(582\) 0 0
\(583\) 22.8449 39.5685i 0.946139 1.63876i
\(584\) −94.8646 −3.92552
\(585\) 0 0
\(586\) 46.9708 1.94035
\(587\) 12.0952 20.9495i 0.499221 0.864677i −0.500778 0.865576i \(-0.666953\pi\)
1.00000 0.000898897i \(0.000286128\pi\)
\(588\) 0 0
\(589\) 3.39767 + 5.88494i 0.139999 + 0.242485i
\(590\) 8.33570 0.343176
\(591\) 0 0
\(592\) 54.3746 + 94.1796i 2.23478 + 3.87076i
\(593\) −10.5786 −0.434410 −0.217205 0.976126i \(-0.569694\pi\)
−0.217205 + 0.976126i \(0.569694\pi\)
\(594\) 0 0
\(595\) −2.84626 + 4.92986i −0.116685 + 0.202105i
\(596\) 55.8337 96.7068i 2.28704 3.96127i
\(597\) 0 0
\(598\) −15.0383 71.5724i −0.614962 2.92681i
\(599\) −25.8978 −1.05816 −0.529078 0.848573i \(-0.677462\pi\)
−0.529078 + 0.848573i \(0.677462\pi\)
\(600\) 0 0
\(601\) 7.65231 13.2542i 0.312144 0.540650i −0.666682 0.745342i \(-0.732286\pi\)
0.978826 + 0.204692i \(0.0656194\pi\)
\(602\) 8.55960 + 14.8257i 0.348863 + 0.604249i
\(603\) 0 0
\(604\) 5.58997 + 9.68211i 0.227453 + 0.393960i
\(605\) 5.64788 + 9.78241i 0.229619 + 0.397712i
\(606\) 0 0
\(607\) 19.4724 + 33.7272i 0.790360 + 1.36894i 0.925744 + 0.378151i \(0.123440\pi\)
−0.135384 + 0.990793i \(0.543227\pi\)
\(608\) 17.6190 30.5169i 0.714543 1.23762i
\(609\) 0 0
\(610\) 16.6372 0.673620
\(611\) −29.1868 9.55890i −1.18077 0.386712i
\(612\) 0 0
\(613\) −20.2800 + 35.1259i −0.819100 + 1.41872i 0.0872463 + 0.996187i \(0.472193\pi\)
−0.906346 + 0.422536i \(0.861140\pi\)
\(614\) 13.2100 22.8804i 0.533113 0.923378i
\(615\) 0 0
\(616\) 39.6545 1.59773
\(617\) 15.8304 + 27.4190i 0.637307 + 1.10385i 0.986021 + 0.166619i \(0.0532849\pi\)
−0.348715 + 0.937229i \(0.613382\pi\)
\(618\) 0 0
\(619\) 18.4523 0.741661 0.370831 0.928700i \(-0.379073\pi\)
0.370831 + 0.928700i \(0.379073\pi\)
\(620\) −5.71858 9.90487i −0.229664 0.397789i
\(621\) 0 0
\(622\) −11.5327 + 19.9752i −0.462420 + 0.800934i
\(623\) 9.45340 0.378742
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 5.76287 9.98158i 0.230331 0.398944i
\(627\) 0 0
\(628\) 34.2327 + 59.2927i 1.36603 + 2.36604i
\(629\) 54.4741 2.17203
\(630\) 0 0
\(631\) −16.7536 29.0181i −0.666952 1.15519i −0.978752 0.205046i \(-0.934265\pi\)
0.311801 0.950148i \(-0.399068\pi\)
\(632\) 23.4533 0.932921
\(633\) 0 0
\(634\) −15.4024 + 26.6778i −0.611708 + 1.05951i
\(635\) 7.72740 13.3842i 0.306652 0.531138i
\(636\) 0 0
\(637\) −15.6069 + 13.9865i −0.618368 + 0.554167i
\(638\) −16.2958 −0.645155
\(639\) 0 0
\(640\) −2.20605 + 3.82099i −0.0872017 + 0.151038i
\(641\) 7.97169 + 13.8074i 0.314863 + 0.545359i 0.979408 0.201889i \(-0.0647081\pi\)
−0.664545 + 0.747248i \(0.731375\pi\)
\(642\) 0 0
\(643\) 7.36007 + 12.7480i 0.290253 + 0.502733i 0.973869 0.227109i \(-0.0729272\pi\)
−0.683617 + 0.729841i \(0.739594\pi\)
\(644\) −20.6925 35.8404i −0.815397 1.41231i
\(645\) 0 0
\(646\) −20.1280 34.8628i −0.791927 1.37166i
\(647\) −18.5419 + 32.1155i −0.728957 + 1.26259i 0.228367 + 0.973575i \(0.426661\pi\)
−0.957324 + 0.289016i \(0.906672\pi\)
\(648\) 0 0
\(649\) −14.9538 −0.586990
\(650\) −7.06737 + 6.33362i −0.277205 + 0.248425i
\(651\) 0 0
\(652\) −60.6667 + 105.078i −2.37589 + 4.11517i
\(653\) −10.2853 + 17.8146i −0.402494 + 0.697140i −0.994026 0.109141i \(-0.965190\pi\)
0.591532 + 0.806281i \(0.298523\pi\)
\(654\) 0 0
\(655\) −8.48870 −0.331681
\(656\) 26.0053 + 45.0425i 1.01534 + 1.75862i
\(657\) 0 0
\(658\) −24.4325 −0.952476
\(659\) 14.8316 + 25.6891i 0.577758 + 1.00071i 0.995736 + 0.0922489i \(0.0294056\pi\)
−0.417978 + 0.908457i \(0.637261\pi\)
\(660\) 0 0
\(661\) 8.05269 13.9477i 0.313213 0.542501i −0.665843 0.746092i \(-0.731928\pi\)
0.979056 + 0.203591i \(0.0652612\pi\)
\(662\) 33.4887 1.30157
\(663\) 0 0
\(664\) −10.8493 −0.421034
\(665\) 1.59533 2.76320i 0.0618643 0.107152i
\(666\) 0 0
\(667\) 5.05228 + 8.75081i 0.195625 + 0.338833i
\(668\) −18.7254 −0.724507
\(669\) 0 0
\(670\) 2.07324 + 3.59096i 0.0800963 + 0.138731i
\(671\) −29.8463 −1.15220
\(672\) 0 0
\(673\) −3.53317 + 6.11963i −0.136194 + 0.235894i −0.926053 0.377394i \(-0.876820\pi\)
0.789859 + 0.613288i \(0.210154\pi\)
\(674\) −5.31326 + 9.20284i −0.204659 + 0.354480i
\(675\) 0 0
\(676\) 6.99434 63.6796i 0.269013 2.44921i
\(677\) 23.6740 0.909866 0.454933 0.890526i \(-0.349663\pi\)
0.454933 + 0.890526i \(0.349663\pi\)
\(678\) 0 0
\(679\) 6.01130 10.4119i 0.230693 0.399571i
\(680\) 20.1280 + 34.8628i 0.771875 + 1.33693i
\(681\) 0 0
\(682\) 14.4224 + 24.9804i 0.552264 + 0.956549i
\(683\) −10.0997 17.4932i −0.386454 0.669359i 0.605515 0.795834i \(-0.292967\pi\)
−0.991970 + 0.126475i \(0.959634\pi\)
\(684\) 0 0
\(685\) 2.86093 + 4.95527i 0.109310 + 0.189331i
\(686\) −18.3751 + 31.8266i −0.701564 + 1.21514i
\(687\) 0 0
\(688\) 62.2400 2.37288
\(689\) −33.1554 10.8587i −1.26312 0.413682i
\(690\) 0 0
\(691\) 15.5689 26.9661i 0.592269 1.02584i −0.401657 0.915790i \(-0.631566\pi\)
0.993926 0.110050i \(-0.0351010\pi\)
\(692\) 44.5488 77.1607i 1.69349 2.93321i
\(693\) 0 0
\(694\) 0.906344 0.0344044
\(695\) −9.19692 15.9295i −0.348859 0.604241i
\(696\) 0 0
\(697\) 26.0529 0.986824
\(698\) −45.5881 78.9609i −1.72553 2.98871i
\(699\) 0 0
\(700\) −2.68508 + 4.65070i −0.101487 + 0.175780i
\(701\) −24.0928 −0.909974 −0.454987 0.890498i \(-0.650356\pi\)
−0.454987 + 0.890498i \(0.650356\pi\)
\(702\) 0 0
\(703\) −30.5329 −1.15157
\(704\) 25.5482 44.2509i 0.962886 1.66777i
\(705\) 0 0
\(706\) 23.4785 + 40.6660i 0.883627 + 1.53049i
\(707\) 10.0420 0.377667
\(708\) 0 0
\(709\) −2.39040 4.14030i −0.0897734 0.155492i 0.817642 0.575727i \(-0.195281\pi\)
−0.907415 + 0.420235i \(0.861948\pi\)
\(710\) 15.7985 0.592906
\(711\) 0 0
\(712\) 33.4261 57.8957i 1.25270 2.16973i
\(713\) 8.94298 15.4897i 0.334917 0.580094i
\(714\) 0 0
\(715\) 12.6785 11.3622i 0.474150 0.424923i
\(716\) −126.375 −4.72286
\(717\) 0 0
\(718\) 9.50558 16.4642i 0.354745 0.614437i
\(719\) −6.75421 11.6986i −0.251889 0.436285i 0.712157 0.702021i \(-0.247719\pi\)
−0.964046 + 0.265735i \(0.914385\pi\)
\(720\) 0 0
\(721\) −8.09609 14.0228i −0.301514 0.522238i
\(722\) −13.7230 23.7690i −0.510718 0.884590i
\(723\) 0 0
\(724\) 47.0507 + 81.4942i 1.74863 + 3.02871i
\(725\) 0.655591 1.13552i 0.0243480 0.0421720i
\(726\) 0 0
\(727\) −6.06108 −0.224793 −0.112397 0.993663i \(-0.535853\pi\)
−0.112397 + 0.993663i \(0.535853\pi\)
\(728\) −6.22623 29.6328i −0.230759 1.09826i
\(729\) 0 0
\(730\) −16.2002 + 28.0595i −0.599596 + 1.03853i
\(731\) 15.5885 27.0000i 0.576560 0.998631i
\(732\) 0 0
\(733\) 5.63897 0.208280 0.104140 0.994563i \(-0.466791\pi\)
0.104140 + 0.994563i \(0.466791\pi\)
\(734\) −39.1529 67.8149i −1.44516 2.50309i
\(735\) 0 0
\(736\) −92.7493 −3.41878
\(737\) −3.71929 6.44200i −0.137002 0.237294i
\(738\) 0 0
\(739\) 1.56358 2.70820i 0.0575173 0.0996229i −0.835833 0.548984i \(-0.815015\pi\)
0.893350 + 0.449361i \(0.148348\pi\)
\(740\) 51.3894 1.88911
\(741\) 0 0
\(742\) −27.7546 −1.01890
\(743\) 24.3946 42.2528i 0.894953 1.55010i 0.0610897 0.998132i \(-0.480542\pi\)
0.833863 0.551971i \(-0.186124\pi\)
\(744\) 0 0
\(745\) −11.3302 19.6244i −0.415105 0.718982i
\(746\) −10.1119 −0.370222
\(747\) 0 0
\(748\) −60.7741 105.264i −2.22212 3.84883i
\(749\) −7.51368 −0.274544
\(750\) 0 0
\(751\) 22.3404 38.6947i 0.815212 1.41199i −0.0939637 0.995576i \(-0.529954\pi\)
0.909176 0.416413i \(-0.136713\pi\)
\(752\) −44.4143 + 76.9279i −1.61962 + 2.80527i
\(753\) 0 0
\(754\) 2.55863 + 12.1774i 0.0931797 + 0.443474i
\(755\) 2.26871 0.0825668
\(756\) 0 0
\(757\) 4.54891 7.87894i 0.165333 0.286365i −0.771441 0.636301i \(-0.780463\pi\)
0.936773 + 0.349936i \(0.113797\pi\)
\(758\) 40.9323 + 70.8969i 1.48673 + 2.57509i
\(759\) 0 0
\(760\) −11.2818 19.5407i −0.409234 0.708815i
\(761\) 15.2874 + 26.4785i 0.554167 + 0.959846i 0.997968 + 0.0637201i \(0.0202965\pi\)
−0.443801 + 0.896126i \(0.646370\pi\)
\(762\) 0 0
\(763\) 7.94374 + 13.7590i 0.287583 + 0.498108i
\(764\) −59.5135 + 103.080i −2.15312 + 3.72932i
\(765\) 0 0
\(766\) 34.1142 1.23260
\(767\) 2.34793 + 11.1746i 0.0847789 + 0.403492i
\(768\) 0 0
\(769\) 13.6230 23.5957i 0.491257 0.850882i −0.508693 0.860948i \(-0.669871\pi\)
0.999949 + 0.0100665i \(0.00320432\pi\)
\(770\) 6.77187 11.7292i 0.244041 0.422692i
\(771\) 0 0
\(772\) 63.0554 2.26941
\(773\) −3.66765 6.35256i −0.131916 0.228486i 0.792499 0.609873i \(-0.208780\pi\)
−0.924415 + 0.381388i \(0.875446\pi\)
\(774\) 0 0
\(775\) −2.32091 −0.0833694
\(776\) −42.5105 73.6303i −1.52604 2.64317i
\(777\) 0 0
\(778\) −18.5960 + 32.2092i −0.666700 + 1.15476i
\(779\) −14.6027 −0.523196
\(780\) 0 0
\(781\) −28.3417 −1.01414
\(782\) −52.9788 + 91.7620i −1.89452 + 3.28140i
\(783\) 0 0
\(784\) 30.3069 + 52.4932i 1.08239 + 1.87476i
\(785\) 13.8934 0.495878
\(786\) 0 0
\(787\) −25.6877 44.4925i −0.915669 1.58599i −0.805919 0.592026i \(-0.798328\pi\)
−0.109750 0.993959i \(-0.535005\pi\)