Properties

Label 495.2.n.d.361.1
Level $495$
Weight $2$
Character 495.361
Analytic conductor $3.953$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.n (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.95259490005\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
Defining polynomial: \(x^{8} - 3 x^{7} + 5 x^{6} - 3 x^{5} + 4 x^{4} + 3 x^{3} + 5 x^{2} + 3 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 361.1
Root \(0.418926 - 1.28932i\) of defining polynomial
Character \(\chi\) \(=\) 495.361
Dual form 495.2.n.d.181.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.758911 + 2.33569i) q^{2} +(-3.26145 - 2.36959i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-2.65911 - 1.93196i) q^{7} +(4.03606 - 2.93237i) q^{8} +O(q^{10})\) \(q+(-0.758911 + 2.33569i) q^{2} +(-3.26145 - 2.36959i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-2.65911 - 1.93196i) q^{7} +(4.03606 - 2.93237i) q^{8} -2.45589 q^{10} +(-2.96813 + 1.47994i) q^{11} +(-0.0967635 + 0.297808i) q^{13} +(6.53048 - 4.74467i) q^{14} +(1.29455 + 3.98423i) q^{16} +(-1.54508 - 4.75528i) q^{17} +(6.03048 - 4.38140i) q^{19} +(1.24576 - 3.83407i) q^{20} +(-1.20413 - 8.05576i) q^{22} -1.07392 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-0.622150 - 0.452019i) q^{26} +(4.09463 + 12.6020i) q^{28} +(-4.07459 - 2.96036i) q^{29} +(1.06580 - 3.28018i) q^{31} -0.310680 q^{32} +12.2794 q^{34} +(1.01569 - 3.12597i) q^{35} +(-2.13118 - 1.54839i) q^{37} +(5.65698 + 17.4104i) q^{38} +(4.03606 + 2.93237i) q^{40} +(8.77557 - 6.37583i) q^{41} -5.51468 q^{43} +(13.1873 + 2.20648i) q^{44} +(0.815010 - 2.50834i) q^{46} +(-9.70674 + 7.05236i) q^{47} +(1.17529 + 3.61718i) q^{49} +(-0.758911 - 2.33569i) q^{50} +(1.02127 - 0.741996i) q^{52} +(-1.52513 + 4.69387i) q^{53} +(-2.32471 - 2.36553i) q^{55} -16.3975 q^{56} +(10.0067 - 7.27031i) q^{58} +(-7.41391 - 5.38652i) q^{59} +(2.83811 + 8.73480i) q^{61} +(6.85264 + 4.97873i) q^{62} +(-2.35333 + 7.24280i) q^{64} -0.313133 q^{65} -15.2739 q^{67} +(-6.22882 + 19.1704i) q^{68} +(6.53048 + 4.74467i) q^{70} +(-0.949335 - 2.92175i) q^{71} +(7.00018 + 5.08592i) q^{73} +(5.23394 - 3.80268i) q^{74} -30.0502 q^{76} +(10.7518 + 1.79898i) q^{77} +(1.67316 - 5.14946i) q^{79} +(-3.38919 + 2.46239i) q^{80} +(8.23206 + 25.3357i) q^{82} +(-5.02011 - 15.4503i) q^{83} +(4.04508 - 2.93893i) q^{85} +(4.18515 - 12.8806i) q^{86} +(-7.63981 + 14.6768i) q^{88} -1.62118 q^{89} +(0.832656 - 0.604960i) q^{91} +(3.50254 + 2.54475i) q^{92} +(-9.10556 - 28.0240i) q^{94} +(6.03048 + 4.38140i) q^{95} +(0.0692451 - 0.213115i) q^{97} -9.34054 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{4} - 2 q^{5} + q^{7} - 5 q^{8} + O(q^{10}) \) \( 8 q - 2 q^{4} - 2 q^{5} + q^{7} - 5 q^{8} - 10 q^{10} + 3 q^{11} + 6 q^{13} + 10 q^{14} - 20 q^{16} + 10 q^{17} + 6 q^{19} - 7 q^{20} - 25 q^{22} + 10 q^{23} - 2 q^{25} + 8 q^{26} + 31 q^{28} + 3 q^{31} - 60 q^{32} + 50 q^{34} + q^{35} - 19 q^{37} + 28 q^{38} - 5 q^{40} + 25 q^{41} - 4 q^{43} - 7 q^{44} - 6 q^{46} - 15 q^{47} + 21 q^{49} + 6 q^{52} - 7 q^{53} - 7 q^{55} - 20 q^{56} - 2 q^{58} - 35 q^{59} + 21 q^{61} + 19 q^{62} - 77 q^{64} + 6 q^{65} - 26 q^{67} + 35 q^{68} + 10 q^{70} - 25 q^{71} + q^{73} + 29 q^{74} - 14 q^{76} + 61 q^{77} + 30 q^{79} + 5 q^{80} + 57 q^{82} - 11 q^{83} + 10 q^{85} + 34 q^{86} - 85 q^{88} - 32 q^{89} + 37 q^{91} + 10 q^{92} - 39 q^{94} + 6 q^{95} + 5 q^{97} - 50 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.758911 + 2.33569i −0.536631 + 1.65158i 0.203468 + 0.979082i \(0.434779\pi\)
−0.740098 + 0.672499i \(0.765221\pi\)
\(3\) 0 0
\(4\) −3.26145 2.36959i −1.63073 1.18479i
\(5\) 0.309017 + 0.951057i 0.138197 + 0.425325i
\(6\) 0 0
\(7\) −2.65911 1.93196i −1.00505 0.730211i −0.0418845 0.999122i \(-0.513336\pi\)
−0.963165 + 0.268911i \(0.913336\pi\)
\(8\) 4.03606 2.93237i 1.42696 1.03675i
\(9\) 0 0
\(10\) −2.45589 −0.776620
\(11\) −2.96813 + 1.47994i −0.894924 + 0.446218i
\(12\) 0 0
\(13\) −0.0967635 + 0.297808i −0.0268374 + 0.0825970i −0.963578 0.267427i \(-0.913827\pi\)
0.936741 + 0.350024i \(0.113827\pi\)
\(14\) 6.53048 4.74467i 1.74534 1.26807i
\(15\) 0 0
\(16\) 1.29455 + 3.98423i 0.323638 + 0.996057i
\(17\) −1.54508 4.75528i −0.374738 1.15333i −0.943655 0.330930i \(-0.892637\pi\)
0.568917 0.822395i \(-0.307363\pi\)
\(18\) 0 0
\(19\) 6.03048 4.38140i 1.38349 1.00516i 0.386941 0.922104i \(-0.373532\pi\)
0.996545 0.0830568i \(-0.0264683\pi\)
\(20\) 1.24576 3.83407i 0.278561 0.857324i
\(21\) 0 0
\(22\) −1.20413 8.05576i −0.256721 1.71749i
\(23\) −1.07392 −0.223928 −0.111964 0.993712i \(-0.535714\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(24\) 0 0
\(25\) −0.809017 + 0.587785i −0.161803 + 0.117557i
\(26\) −0.622150 0.452019i −0.122014 0.0886482i
\(27\) 0 0
\(28\) 4.09463 + 12.6020i 0.773813 + 2.38155i
\(29\) −4.07459 2.96036i −0.756632 0.549725i 0.141243 0.989975i \(-0.454890\pi\)
−0.897875 + 0.440250i \(0.854890\pi\)
\(30\) 0 0
\(31\) 1.06580 3.28018i 0.191423 0.589138i −0.808577 0.588390i \(-0.799762\pi\)
1.00000 0.000748050i \(-0.000238112\pi\)
\(32\) −0.310680 −0.0549210
\(33\) 0 0
\(34\) 12.2794 2.10591
\(35\) 1.01569 3.12597i 0.171683 0.528386i
\(36\) 0 0
\(37\) −2.13118 1.54839i −0.350364 0.254554i 0.398658 0.917100i \(-0.369476\pi\)
−0.749022 + 0.662546i \(0.769476\pi\)
\(38\) 5.65698 + 17.4104i 0.917683 + 2.82434i
\(39\) 0 0
\(40\) 4.03606 + 2.93237i 0.638156 + 0.463648i
\(41\) 8.77557 6.37583i 1.37051 0.995737i 0.372817 0.927905i \(-0.378392\pi\)
0.997697 0.0678321i \(-0.0216082\pi\)
\(42\) 0 0
\(43\) −5.51468 −0.840980 −0.420490 0.907297i \(-0.638142\pi\)
−0.420490 + 0.907297i \(0.638142\pi\)
\(44\) 13.1873 + 2.20648i 1.98805 + 0.332640i
\(45\) 0 0
\(46\) 0.815010 2.50834i 0.120167 0.369835i
\(47\) −9.70674 + 7.05236i −1.41587 + 1.02869i −0.423438 + 0.905925i \(0.639177\pi\)
−0.992435 + 0.122767i \(0.960823\pi\)
\(48\) 0 0
\(49\) 1.17529 + 3.61718i 0.167899 + 0.516740i
\(50\) −0.758911 2.33569i −0.107326 0.330316i
\(51\) 0 0
\(52\) 1.02127 0.741996i 0.141625 0.102896i
\(53\) −1.52513 + 4.69387i −0.209493 + 0.644753i 0.790006 + 0.613099i \(0.210077\pi\)
−0.999499 + 0.0316539i \(0.989923\pi\)
\(54\) 0 0
\(55\) −2.32471 2.36553i −0.313463 0.318968i
\(56\) −16.3975 −2.19121
\(57\) 0 0
\(58\) 10.0067 7.27031i 1.31395 0.954639i
\(59\) −7.41391 5.38652i −0.965208 0.701265i −0.0108537 0.999941i \(-0.503455\pi\)
−0.954354 + 0.298676i \(0.903455\pi\)
\(60\) 0 0
\(61\) 2.83811 + 8.73480i 0.363382 + 1.11838i 0.950988 + 0.309229i \(0.100071\pi\)
−0.587605 + 0.809148i \(0.699929\pi\)
\(62\) 6.85264 + 4.97873i 0.870286 + 0.632300i
\(63\) 0 0
\(64\) −2.35333 + 7.24280i −0.294166 + 0.905350i
\(65\) −0.313133 −0.0388394
\(66\) 0 0
\(67\) −15.2739 −1.86600 −0.933000 0.359876i \(-0.882819\pi\)
−0.933000 + 0.359876i \(0.882819\pi\)
\(68\) −6.22882 + 19.1704i −0.755356 + 2.32475i
\(69\) 0 0
\(70\) 6.53048 + 4.74467i 0.780541 + 0.567096i
\(71\) −0.949335 2.92175i −0.112665 0.346748i 0.878788 0.477213i \(-0.158353\pi\)
−0.991453 + 0.130465i \(0.958353\pi\)
\(72\) 0 0
\(73\) 7.00018 + 5.08592i 0.819309 + 0.595262i 0.916514 0.400002i \(-0.130991\pi\)
−0.0972058 + 0.995264i \(0.530991\pi\)
\(74\) 5.23394 3.80268i 0.608433 0.442052i
\(75\) 0 0
\(76\) −30.0502 −3.44700
\(77\) 10.7518 + 1.79898i 1.22528 + 0.205012i
\(78\) 0 0
\(79\) 1.67316 5.14946i 0.188245 0.579360i −0.811744 0.584014i \(-0.801481\pi\)
0.999989 + 0.00465401i \(0.00148142\pi\)
\(80\) −3.38919 + 2.46239i −0.378922 + 0.275303i
\(81\) 0 0
\(82\) 8.23206 + 25.3357i 0.909079 + 2.79786i
\(83\) −5.02011 15.4503i −0.551029 1.69589i −0.706207 0.708006i \(-0.749595\pi\)
0.155178 0.987887i \(-0.450405\pi\)
\(84\) 0 0
\(85\) 4.04508 2.93893i 0.438751 0.318771i
\(86\) 4.18515 12.8806i 0.451296 1.38895i
\(87\) 0 0
\(88\) −7.63981 + 14.6768i −0.814406 + 1.56455i
\(89\) −1.62118 −0.171845 −0.0859223 0.996302i \(-0.527384\pi\)
−0.0859223 + 0.996302i \(0.527384\pi\)
\(90\) 0 0
\(91\) 0.832656 0.604960i 0.0872861 0.0634171i
\(92\) 3.50254 + 2.54475i 0.365165 + 0.265308i
\(93\) 0 0
\(94\) −9.10556 28.0240i −0.939166 2.89046i
\(95\) 6.03048 + 4.38140i 0.618714 + 0.449522i
\(96\) 0 0
\(97\) 0.0692451 0.213115i 0.00703078 0.0216385i −0.947480 0.319816i \(-0.896379\pi\)
0.954510 + 0.298178i \(0.0963788\pi\)
\(98\) −9.34054 −0.943537
\(99\) 0 0
\(100\) 4.03138 0.403138
\(101\) 0.156154 0.480593i 0.0155379 0.0478208i −0.942987 0.332830i \(-0.891997\pi\)
0.958525 + 0.285009i \(0.0919966\pi\)
\(102\) 0 0
\(103\) 5.17930 + 3.76298i 0.510332 + 0.370778i 0.812949 0.582334i \(-0.197861\pi\)
−0.302618 + 0.953112i \(0.597861\pi\)
\(104\) 0.482738 + 1.48571i 0.0473363 + 0.145686i
\(105\) 0 0
\(106\) −9.80598 7.12446i −0.952441 0.691989i
\(107\) 1.69286 1.22993i 0.163655 0.118902i −0.502943 0.864319i \(-0.667750\pi\)
0.666598 + 0.745417i \(0.267750\pi\)
\(108\) 0 0
\(109\) −6.69278 −0.641052 −0.320526 0.947240i \(-0.603860\pi\)
−0.320526 + 0.947240i \(0.603860\pi\)
\(110\) 7.28939 3.63456i 0.695016 0.346542i
\(111\) 0 0
\(112\) 4.25499 13.0955i 0.402059 1.23741i
\(113\) −8.73262 + 6.34462i −0.821496 + 0.596852i −0.917141 0.398564i \(-0.869509\pi\)
0.0956448 + 0.995416i \(0.469509\pi\)
\(114\) 0 0
\(115\) −0.331860 1.02136i −0.0309461 0.0952423i
\(116\) 6.27426 + 19.3102i 0.582550 + 1.79290i
\(117\) 0 0
\(118\) 18.2077 13.2287i 1.67616 1.21780i
\(119\) −5.07845 + 15.6299i −0.465541 + 1.43279i
\(120\) 0 0
\(121\) 6.61956 8.78529i 0.601779 0.798663i
\(122\) −22.5556 −2.04209
\(123\) 0 0
\(124\) −11.2487 + 8.17267i −1.01017 + 0.733928i
\(125\) −0.809017 0.587785i −0.0723607 0.0525731i
\(126\) 0 0
\(127\) −5.25430 16.1711i −0.466244 1.43495i −0.857411 0.514632i \(-0.827929\pi\)
0.391167 0.920320i \(-0.372071\pi\)
\(128\) −15.6336 11.3585i −1.38183 1.00396i
\(129\) 0 0
\(130\) 0.237640 0.731382i 0.0208424 0.0641464i
\(131\) 0.0430508 0.00376136 0.00188068 0.999998i \(-0.499401\pi\)
0.00188068 + 0.999998i \(0.499401\pi\)
\(132\) 0 0
\(133\) −24.5004 −2.12445
\(134\) 11.5915 35.6750i 1.00135 3.08185i
\(135\) 0 0
\(136\) −20.1803 14.6618i −1.73044 1.25724i
\(137\) −2.27516 7.00222i −0.194380 0.598240i −0.999983 0.00578480i \(-0.998159\pi\)
0.805603 0.592455i \(-0.201841\pi\)
\(138\) 0 0
\(139\) −10.7109 7.78189i −0.908483 0.660052i 0.0321478 0.999483i \(-0.489765\pi\)
−0.940631 + 0.339432i \(0.889765\pi\)
\(140\) −10.7199 + 7.78845i −0.905996 + 0.658244i
\(141\) 0 0
\(142\) 7.54476 0.633142
\(143\) −0.153530 1.02713i −0.0128388 0.0858933i
\(144\) 0 0
\(145\) 1.55635 4.78997i 0.129248 0.397785i
\(146\) −17.1916 + 12.4905i −1.42279 + 1.03372i
\(147\) 0 0
\(148\) 3.28170 + 10.1000i 0.269754 + 0.830217i
\(149\) 1.81658 + 5.59087i 0.148820 + 0.458022i 0.997482 0.0709136i \(-0.0225915\pi\)
−0.848662 + 0.528935i \(0.822591\pi\)
\(150\) 0 0
\(151\) −6.17135 + 4.48375i −0.502217 + 0.364882i −0.809863 0.586619i \(-0.800459\pi\)
0.307646 + 0.951501i \(0.400459\pi\)
\(152\) 11.4915 35.3671i 0.932082 2.86865i
\(153\) 0 0
\(154\) −12.3615 + 23.7475i −0.996116 + 1.91363i
\(155\) 3.44899 0.277029
\(156\) 0 0
\(157\) 8.19795 5.95616i 0.654267 0.475353i −0.210455 0.977604i \(-0.567494\pi\)
0.864722 + 0.502250i \(0.167494\pi\)
\(158\) 10.7578 + 7.81596i 0.855841 + 0.621805i
\(159\) 0 0
\(160\) −0.0960054 0.295474i −0.00758989 0.0233593i
\(161\) 2.85567 + 2.07477i 0.225059 + 0.163515i
\(162\) 0 0
\(163\) −1.55407 + 4.78292i −0.121724 + 0.374627i −0.993290 0.115651i \(-0.963105\pi\)
0.871566 + 0.490278i \(0.163105\pi\)
\(164\) −43.7292 −3.41468
\(165\) 0 0
\(166\) 39.8969 3.09660
\(167\) −1.78953 + 5.50761i −0.138478 + 0.426192i −0.996115 0.0880642i \(-0.971932\pi\)
0.857637 + 0.514256i \(0.171932\pi\)
\(168\) 0 0
\(169\) 10.4379 + 7.58357i 0.802915 + 0.583352i
\(170\) 3.79455 + 11.6784i 0.291029 + 0.895695i
\(171\) 0 0
\(172\) 17.9859 + 13.0675i 1.37141 + 0.996387i
\(173\) 12.9970 9.44290i 0.988146 0.717930i 0.0286316 0.999590i \(-0.490885\pi\)
0.959514 + 0.281660i \(0.0908850\pi\)
\(174\) 0 0
\(175\) 3.28684 0.248462
\(176\) −9.73881 9.90983i −0.734090 0.746982i
\(177\) 0 0
\(178\) 1.23033 3.78657i 0.0922171 0.283815i
\(179\) −6.71734 + 4.88043i −0.502078 + 0.364781i −0.809810 0.586692i \(-0.800430\pi\)
0.307732 + 0.951473i \(0.400430\pi\)
\(180\) 0 0
\(181\) −1.99756 6.14787i −0.148478 0.456968i 0.848964 0.528451i \(-0.177227\pi\)
−0.997442 + 0.0714830i \(0.977227\pi\)
\(182\) 0.781086 + 2.40394i 0.0578980 + 0.178192i
\(183\) 0 0
\(184\) −4.33440 + 3.14913i −0.319536 + 0.232157i
\(185\) 0.814038 2.50535i 0.0598493 0.184197i
\(186\) 0 0
\(187\) 11.6235 + 11.8277i 0.849997 + 0.864924i
\(188\) 48.3693 3.52769
\(189\) 0 0
\(190\) −14.8102 + 10.7602i −1.07444 + 0.780628i
\(191\) 12.4340 + 9.03384i 0.899694 + 0.653666i 0.938387 0.345585i \(-0.112320\pi\)
−0.0386935 + 0.999251i \(0.512320\pi\)
\(192\) 0 0
\(193\) 4.86757 + 14.9808i 0.350375 + 1.07834i 0.958643 + 0.284612i \(0.0918648\pi\)
−0.608267 + 0.793732i \(0.708135\pi\)
\(194\) 0.445218 + 0.323470i 0.0319648 + 0.0232238i
\(195\) 0 0
\(196\) 4.73805 14.5822i 0.338432 1.04159i
\(197\) −16.3940 −1.16802 −0.584010 0.811746i \(-0.698517\pi\)
−0.584010 + 0.811746i \(0.698517\pi\)
\(198\) 0 0
\(199\) 6.96500 0.493736 0.246868 0.969049i \(-0.420599\pi\)
0.246868 + 0.969049i \(0.420599\pi\)
\(200\) −1.54164 + 4.74467i −0.109010 + 0.335499i
\(201\) 0 0
\(202\) 1.00401 + 0.729455i 0.0706418 + 0.0513242i
\(203\) 5.11549 + 15.7439i 0.359037 + 1.10500i
\(204\) 0 0
\(205\) 8.77557 + 6.37583i 0.612913 + 0.445307i
\(206\) −12.7198 + 9.24146i −0.886229 + 0.643883i
\(207\) 0 0
\(208\) −1.31180 −0.0909569
\(209\) −11.4150 + 21.9293i −0.789594 + 1.51688i
\(210\) 0 0
\(211\) −6.16585 + 18.9765i −0.424475 + 1.30640i 0.479022 + 0.877803i \(0.340992\pi\)
−0.903496 + 0.428596i \(0.859008\pi\)
\(212\) 16.0967 11.6949i 1.10552 0.803211i
\(213\) 0 0
\(214\) 1.58801 + 4.88740i 0.108554 + 0.334096i
\(215\) −1.70413 5.24477i −0.116221 0.357690i
\(216\) 0 0
\(217\) −9.17124 + 6.66330i −0.622585 + 0.452334i
\(218\) 5.07922 15.6322i 0.344008 1.05875i
\(219\) 0 0
\(220\) 1.97660 + 13.2237i 0.133262 + 0.891539i
\(221\) 1.56567 0.105318
\(222\) 0 0
\(223\) 16.2990 11.8419i 1.09146 0.792992i 0.111815 0.993729i \(-0.464334\pi\)
0.979645 + 0.200737i \(0.0643336\pi\)
\(224\) 0.826133 + 0.600220i 0.0551983 + 0.0401039i
\(225\) 0 0
\(226\) −8.19177 25.2117i −0.544908 1.67706i
\(227\) 0.431964 + 0.313840i 0.0286705 + 0.0208303i 0.602028 0.798475i \(-0.294359\pi\)
−0.573358 + 0.819305i \(0.694359\pi\)
\(228\) 0 0
\(229\) −6.85803 + 21.1068i −0.453191 + 1.39478i 0.420054 + 0.907499i \(0.362011\pi\)
−0.873245 + 0.487281i \(0.837989\pi\)
\(230\) 2.63743 0.173907
\(231\) 0 0
\(232\) −25.1261 −1.64961
\(233\) 1.41087 4.34221i 0.0924291 0.284467i −0.894146 0.447775i \(-0.852216\pi\)
0.986575 + 0.163308i \(0.0522164\pi\)
\(234\) 0 0
\(235\) −9.70674 7.05236i −0.633198 0.460045i
\(236\) 11.4163 + 35.1358i 0.743138 + 2.28714i
\(237\) 0 0
\(238\) −32.6524 23.7233i −2.11654 1.53776i
\(239\) −4.74126 + 3.44473i −0.306687 + 0.222821i −0.730474 0.682941i \(-0.760701\pi\)
0.423787 + 0.905762i \(0.360701\pi\)
\(240\) 0 0
\(241\) 9.96074 0.641628 0.320814 0.947142i \(-0.396044\pi\)
0.320814 + 0.947142i \(0.396044\pi\)
\(242\) 15.4960 + 22.1285i 0.996123 + 1.42247i
\(243\) 0 0
\(244\) 11.4415 35.2133i 0.732466 2.25430i
\(245\) −3.07696 + 2.23554i −0.196580 + 0.142823i
\(246\) 0 0
\(247\) 0.721283 + 2.21988i 0.0458941 + 0.141248i
\(248\) −5.31709 16.3643i −0.337635 1.03913i
\(249\) 0 0
\(250\) 1.98685 1.44353i 0.125660 0.0912971i
\(251\) 5.21584 16.0527i 0.329221 1.01324i −0.640279 0.768143i \(-0.721181\pi\)
0.969499 0.245094i \(-0.0788189\pi\)
\(252\) 0 0
\(253\) 3.18753 1.58934i 0.200399 0.0999207i
\(254\) 41.7581 2.62014
\(255\) 0 0
\(256\) 26.0723 18.9426i 1.62952 1.18391i
\(257\) 9.01534 + 6.55003i 0.562362 + 0.408580i 0.832323 0.554292i \(-0.187011\pi\)
−0.269961 + 0.962871i \(0.587011\pi\)
\(258\) 0 0
\(259\) 2.67561 + 8.23470i 0.166255 + 0.511679i
\(260\) 1.02127 + 0.741996i 0.0633365 + 0.0460167i
\(261\) 0 0
\(262\) −0.0326717 + 0.100553i −0.00201846 + 0.00621220i
\(263\) 26.8726 1.65704 0.828519 0.559961i \(-0.189184\pi\)
0.828519 + 0.559961i \(0.189184\pi\)
\(264\) 0 0
\(265\) −4.93543 −0.303181
\(266\) 18.5936 57.2252i 1.14005 3.50870i
\(267\) 0 0
\(268\) 49.8150 + 36.1927i 3.04294 + 2.21082i
\(269\) 3.10961 + 9.57038i 0.189596 + 0.583516i 0.999997 0.00235886i \(-0.000750850\pi\)
−0.810401 + 0.585875i \(0.800751\pi\)
\(270\) 0 0
\(271\) −8.53037 6.19767i −0.518183 0.376482i 0.297736 0.954648i \(-0.403768\pi\)
−0.815919 + 0.578166i \(0.803768\pi\)
\(272\) 16.9459 12.3119i 1.02750 0.746521i
\(273\) 0 0
\(274\) 18.0816 1.09235
\(275\) 1.53138 2.94192i 0.0923457 0.177404i
\(276\) 0 0
\(277\) −5.54302 + 17.0597i −0.333048 + 1.02502i 0.634628 + 0.772818i \(0.281153\pi\)
−0.967676 + 0.252198i \(0.918847\pi\)
\(278\) 26.3047 19.1114i 1.57765 1.14623i
\(279\) 0 0
\(280\) −5.06711 15.5950i −0.302818 0.931978i
\(281\) −2.29013 7.04830i −0.136618 0.420467i 0.859220 0.511606i \(-0.170949\pi\)
−0.995838 + 0.0911392i \(0.970949\pi\)
\(282\) 0 0
\(283\) −4.35804 + 3.16630i −0.259059 + 0.188217i −0.709732 0.704472i \(-0.751184\pi\)
0.450673 + 0.892689i \(0.351184\pi\)
\(284\) −3.82713 + 11.7787i −0.227098 + 0.698937i
\(285\) 0 0
\(286\) 2.51558 + 0.420905i 0.148749 + 0.0248886i
\(287\) −35.6530 −2.10453
\(288\) 0 0
\(289\) −6.47214 + 4.70228i −0.380714 + 0.276605i
\(290\) 10.0067 + 7.27031i 0.587615 + 0.426927i
\(291\) 0 0
\(292\) −10.7792 33.1750i −0.630806 1.94142i
\(293\) −1.40774 1.02278i −0.0822409 0.0597515i 0.545905 0.837847i \(-0.316186\pi\)
−0.628146 + 0.778096i \(0.716186\pi\)
\(294\) 0 0
\(295\) 2.83186 8.71557i 0.164877 0.507440i
\(296\) −13.1420 −0.763864
\(297\) 0 0
\(298\) −14.4371 −0.836321
\(299\) 0.103916 0.319822i 0.00600964 0.0184958i
\(300\) 0 0
\(301\) 14.6641 + 10.6541i 0.845227 + 0.614093i
\(302\) −5.78913 17.8171i −0.333127 1.02526i
\(303\) 0 0
\(304\) 25.2633 + 18.3548i 1.44895 + 1.05272i
\(305\) −7.43026 + 5.39840i −0.425456 + 0.309112i
\(306\) 0 0
\(307\) 21.3566 1.21889 0.609444 0.792829i \(-0.291393\pi\)
0.609444 + 0.792829i \(0.291393\pi\)
\(308\) −30.8035 31.3445i −1.75519 1.78602i
\(309\) 0 0
\(310\) −2.61747 + 8.05576i −0.148663 + 0.457536i
\(311\) 26.5435 19.2850i 1.50514 1.09355i 0.536870 0.843665i \(-0.319607\pi\)
0.968275 0.249886i \(-0.0803933\pi\)
\(312\) 0 0
\(313\) −1.06874 3.28925i −0.0604089 0.185919i 0.916298 0.400497i \(-0.131163\pi\)
−0.976707 + 0.214578i \(0.931163\pi\)
\(314\) 7.69021 + 23.6680i 0.433984 + 1.33566i
\(315\) 0 0
\(316\) −17.6590 + 12.8300i −0.993398 + 0.721746i
\(317\) 0.888626 2.73491i 0.0499102 0.153608i −0.922995 0.384812i \(-0.874266\pi\)
0.972905 + 0.231204i \(0.0742664\pi\)
\(318\) 0 0
\(319\) 16.4751 + 2.75659i 0.922426 + 0.154340i
\(320\) −7.61553 −0.425721
\(321\) 0 0
\(322\) −7.01321 + 5.09540i −0.390831 + 0.283955i
\(323\) −30.1524 21.9070i −1.67772 1.21894i
\(324\) 0 0
\(325\) −0.0967635 0.297808i −0.00536748 0.0165194i
\(326\) −9.99201 7.25962i −0.553406 0.402073i
\(327\) 0 0
\(328\) 16.7224 51.4664i 0.923342 2.84176i
\(329\) 39.4362 2.17419
\(330\) 0 0
\(331\) −14.1221 −0.776219 −0.388109 0.921613i \(-0.626872\pi\)
−0.388109 + 0.921613i \(0.626872\pi\)
\(332\) −20.2380 + 62.2861i −1.11070 + 3.41839i
\(333\) 0 0
\(334\) −11.5060 8.35958i −0.629579 0.457416i
\(335\) −4.71989 14.5263i −0.257875 0.793657i
\(336\) 0 0
\(337\) −12.9030 9.37457i −0.702870 0.510665i 0.177995 0.984031i \(-0.443039\pi\)
−0.880866 + 0.473366i \(0.843039\pi\)
\(338\) −25.6343 + 18.6244i −1.39432 + 1.01303i
\(339\) 0 0
\(340\) −20.1569 −1.09316
\(341\) 1.69105 + 11.3133i 0.0915755 + 0.612650i
\(342\) 0 0
\(343\) −3.24683 + 9.99271i −0.175312 + 0.539555i
\(344\) −22.2575 + 16.1711i −1.20005 + 0.871885i
\(345\) 0 0
\(346\) 12.1921 + 37.5233i 0.655449 + 2.01727i
\(347\) −9.17166 28.2275i −0.492360 1.51533i −0.821030 0.570884i \(-0.806600\pi\)
0.328670 0.944445i \(-0.393400\pi\)
\(348\) 0 0
\(349\) −25.6408 + 18.6291i −1.37252 + 0.997194i −0.374984 + 0.927031i \(0.622352\pi\)
−0.997536 + 0.0701620i \(0.977648\pi\)
\(350\) −2.49442 + 7.67703i −0.133332 + 0.410355i
\(351\) 0 0
\(352\) 0.922138 0.459787i 0.0491501 0.0245067i
\(353\) −1.20189 −0.0639703 −0.0319852 0.999488i \(-0.510183\pi\)
−0.0319852 + 0.999488i \(0.510183\pi\)
\(354\) 0 0
\(355\) 2.48539 1.80574i 0.131911 0.0958388i
\(356\) 5.28740 + 3.84152i 0.280232 + 0.203600i
\(357\) 0 0
\(358\) −6.30130 19.3934i −0.333034 1.02497i
\(359\) −9.43239 6.85304i −0.497823 0.361689i 0.310362 0.950618i \(-0.399550\pi\)
−0.808185 + 0.588929i \(0.799550\pi\)
\(360\) 0 0
\(361\) 11.2987 34.7737i 0.594667 1.83020i
\(362\) 15.8755 0.834396
\(363\) 0 0
\(364\) −4.14918 −0.217476
\(365\) −2.67383 + 8.22920i −0.139955 + 0.430736i
\(366\) 0 0
\(367\) −12.9330 9.39636i −0.675096 0.490486i 0.196631 0.980478i \(-0.437000\pi\)
−0.871727 + 0.489991i \(0.837000\pi\)
\(368\) −1.39025 4.27874i −0.0724717 0.223045i
\(369\) 0 0
\(370\) 5.23394 + 3.80268i 0.272099 + 0.197692i
\(371\) 13.1239 9.53504i 0.681357 0.495035i
\(372\) 0 0
\(373\) 0.321975 0.0166712 0.00833561 0.999965i \(-0.497347\pi\)
0.00833561 + 0.999965i \(0.497347\pi\)
\(374\) −36.4469 + 18.1728i −1.88463 + 0.939693i
\(375\) 0 0
\(376\) −18.4968 + 56.9274i −0.953902 + 2.93581i
\(377\) 1.27589 0.926988i 0.0657117 0.0477423i
\(378\) 0 0
\(379\) 3.52819 + 10.8586i 0.181231 + 0.557771i 0.999863 0.0165471i \(-0.00526734\pi\)
−0.818632 + 0.574318i \(0.805267\pi\)
\(380\) −9.28603 28.5795i −0.476363 1.46610i
\(381\) 0 0
\(382\) −30.5365 + 22.1861i −1.56239 + 1.13514i
\(383\) −8.76597 + 26.9789i −0.447920 + 1.37856i 0.431329 + 0.902195i \(0.358045\pi\)
−0.879249 + 0.476362i \(0.841955\pi\)
\(384\) 0 0
\(385\) 1.61155 + 10.7814i 0.0821321 + 0.549473i
\(386\) −38.6846 −1.96899
\(387\) 0 0
\(388\) −0.730833 + 0.530981i −0.0371024 + 0.0269565i
\(389\) 12.2810 + 8.92269i 0.622673 + 0.452398i 0.853854 0.520513i \(-0.174259\pi\)
−0.231181 + 0.972911i \(0.574259\pi\)
\(390\) 0 0
\(391\) 1.65930 + 5.10680i 0.0839143 + 0.258262i
\(392\) 15.3504 + 11.1528i 0.775315 + 0.563299i
\(393\) 0 0
\(394\) 12.4415 38.2911i 0.626796 1.92908i
\(395\) 5.41446 0.272431
\(396\) 0 0
\(397\) 5.22461 0.262216 0.131108 0.991368i \(-0.458147\pi\)
0.131108 + 0.991368i \(0.458147\pi\)
\(398\) −5.28581 + 16.2681i −0.264954 + 0.815444i
\(399\) 0 0
\(400\) −3.38919 2.46239i −0.169459 0.123119i
\(401\) −4.32644 13.3154i −0.216052 0.664941i −0.999077 0.0429502i \(-0.986324\pi\)
0.783025 0.621990i \(-0.213676\pi\)
\(402\) 0 0
\(403\) 0.873733 + 0.634804i 0.0435238 + 0.0316219i
\(404\) −1.64810 + 1.19741i −0.0819959 + 0.0595735i
\(405\) 0 0
\(406\) −40.6549 −2.01767
\(407\) 8.61714 + 1.44181i 0.427136 + 0.0714680i
\(408\) 0 0
\(409\) 10.2937 31.6809i 0.508993 1.56652i −0.284960 0.958539i \(-0.591980\pi\)
0.793953 0.607979i \(-0.208020\pi\)
\(410\) −21.5518 + 15.6583i −1.06437 + 0.773309i
\(411\) 0 0
\(412\) −7.97535 24.5456i −0.392917 1.20927i
\(413\) 9.30787 + 28.6467i 0.458011 + 1.40961i
\(414\) 0 0
\(415\) 13.1428 9.54882i 0.645156 0.468733i
\(416\) 0.0300625 0.0925229i 0.00147394 0.00453631i
\(417\) 0 0
\(418\) −42.5569 43.3043i −2.08153 2.11808i
\(419\) 5.28460 0.258170 0.129085 0.991634i \(-0.458796\pi\)
0.129085 + 0.991634i \(0.458796\pi\)
\(420\) 0 0
\(421\) 24.9023 18.0926i 1.21367 0.881780i 0.218107 0.975925i \(-0.430012\pi\)
0.995558 + 0.0941452i \(0.0300118\pi\)
\(422\) −39.6439 28.8030i −1.92984 1.40211i
\(423\) 0 0
\(424\) 7.60864 + 23.4170i 0.369508 + 1.13723i
\(425\) 4.04508 + 2.93893i 0.196215 + 0.142559i
\(426\) 0 0
\(427\) 9.32841 28.7099i 0.451433 1.38937i
\(428\) −8.43562 −0.407751
\(429\) 0 0
\(430\) 13.5434 0.653122
\(431\) −3.81656 + 11.7462i −0.183837 + 0.565793i −0.999926 0.0121333i \(-0.996138\pi\)
0.816089 + 0.577926i \(0.196138\pi\)
\(432\) 0 0
\(433\) −1.14304 0.830465i −0.0549308 0.0399096i 0.559981 0.828505i \(-0.310808\pi\)
−0.614912 + 0.788596i \(0.710808\pi\)
\(434\) −8.60323 26.4780i −0.412968 1.27098i
\(435\) 0 0
\(436\) 21.8282 + 15.8591i 1.04538 + 0.759514i
\(437\) −6.47625 + 4.70527i −0.309801 + 0.225084i
\(438\) 0 0
\(439\) −7.58532 −0.362028 −0.181014 0.983481i \(-0.557938\pi\)
−0.181014 + 0.983481i \(0.557938\pi\)
\(440\) −16.3192 2.73052i −0.777990 0.130173i
\(441\) 0 0
\(442\) −1.18820 + 3.65691i −0.0565170 + 0.173941i
\(443\) 8.95274 6.50455i 0.425358 0.309040i −0.354432 0.935082i \(-0.615326\pi\)
0.779790 + 0.626041i \(0.215326\pi\)
\(444\) 0 0
\(445\) −0.500972 1.54183i −0.0237483 0.0730899i
\(446\) 15.2895 + 47.0562i 0.723979 + 2.22818i
\(447\) 0 0
\(448\) 20.2505 14.7129i 0.956748 0.695118i
\(449\) −1.95563 + 6.01882i −0.0922920 + 0.284045i −0.986538 0.163529i \(-0.947712\pi\)
0.894247 + 0.447575i \(0.147712\pi\)
\(450\) 0 0
\(451\) −16.6112 + 31.9116i −0.782190 + 1.50266i
\(452\) 43.5152 2.04678
\(453\) 0 0
\(454\) −1.06085 + 0.770756i −0.0497884 + 0.0361734i
\(455\) 0.832656 + 0.604960i 0.0390355 + 0.0283610i
\(456\) 0 0
\(457\) −0.0585832 0.180300i −0.00274040 0.00843410i 0.949677 0.313231i \(-0.101411\pi\)
−0.952417 + 0.304797i \(0.901411\pi\)
\(458\) −44.0944 32.0364i −2.06039 1.49696i
\(459\) 0 0
\(460\) −1.33785 + 4.11749i −0.0623777 + 0.191979i
\(461\) 26.6198 1.23981 0.619904 0.784678i \(-0.287172\pi\)
0.619904 + 0.784678i \(0.287172\pi\)
\(462\) 0 0
\(463\) 20.9935 0.975652 0.487826 0.872941i \(-0.337790\pi\)
0.487826 + 0.872941i \(0.337790\pi\)
\(464\) 6.51998 20.0664i 0.302682 0.931561i
\(465\) 0 0
\(466\) 9.07131 + 6.59070i 0.420221 + 0.305308i
\(467\) −2.44120 7.51324i −0.112965 0.347671i 0.878552 0.477647i \(-0.158510\pi\)
−0.991517 + 0.129976i \(0.958510\pi\)
\(468\) 0 0
\(469\) 40.6149 + 29.5085i 1.87542 + 1.36257i
\(470\) 23.8387 17.3198i 1.09960 0.798903i
\(471\) 0 0
\(472\) −45.7182 −2.10435
\(473\) 16.3683 8.16138i 0.752614 0.375261i
\(474\) 0 0
\(475\) −2.30344 + 7.08925i −0.105689 + 0.325277i
\(476\) 53.5994 38.9423i 2.45673 1.78492i
\(477\) 0 0
\(478\) −4.44762 13.6884i −0.203429 0.626091i
\(479\) −12.3523 38.0164i −0.564389 1.73701i −0.669758 0.742579i \(-0.733602\pi\)
0.105369 0.994433i \(-0.466398\pi\)
\(480\) 0 0
\(481\) 0.667344 0.484854i 0.0304282 0.0221074i
\(482\) −7.55931 + 23.2652i −0.344317 + 1.05970i
\(483\) 0 0
\(484\) −42.4069 + 12.9672i −1.92759 + 0.589419i
\(485\) 0.224082 0.0101750
\(486\) 0 0
\(487\) 8.03804 5.83998i 0.364238 0.264635i −0.390579 0.920569i \(-0.627725\pi\)
0.754818 + 0.655935i \(0.227725\pi\)
\(488\) 37.0684 + 26.9318i 1.67801 + 1.21914i
\(489\) 0 0
\(490\) −2.88639 8.88338i −0.130394 0.401310i
\(491\) 4.02364 + 2.92335i 0.181584 + 0.131929i 0.674864 0.737942i \(-0.264202\pi\)
−0.493280 + 0.869871i \(0.664202\pi\)
\(492\) 0 0
\(493\) −7.78177 + 23.9498i −0.350473 + 1.07865i
\(494\) −5.73234 −0.257910
\(495\) 0 0
\(496\) 14.4487 0.648767
\(497\) −3.12031 + 9.60333i −0.139965 + 0.430768i
\(498\) 0 0
\(499\) −35.4153 25.7307i −1.58541 1.15186i −0.910149 0.414281i \(-0.864033\pi\)
−0.675256 0.737584i \(-0.735967\pi\)
\(500\) 1.24576 + 3.83407i 0.0557123 + 0.171465i
\(501\) 0 0
\(502\) 33.5357 + 24.3651i 1.49677 + 1.08747i
\(503\) 5.08254 3.69268i 0.226619 0.164648i −0.468682 0.883367i \(-0.655271\pi\)
0.695301 + 0.718718i \(0.255271\pi\)
\(504\) 0 0
\(505\) 0.505326 0.0224867
\(506\) 1.29314 + 8.65125i 0.0574870 + 0.384595i
\(507\) 0 0
\(508\) −21.1821 + 65.1918i −0.939803 + 2.89242i
\(509\) 20.0945 14.5995i 0.890671 0.647111i −0.0453816 0.998970i \(-0.514450\pi\)
0.936053 + 0.351859i \(0.114450\pi\)
\(510\) 0 0
\(511\) −8.78845 27.0481i −0.388778 1.19654i
\(512\) 12.5144 + 38.5155i 0.553066 + 1.70216i
\(513\) 0 0
\(514\) −22.1407 + 16.0861i −0.976583 + 0.709529i
\(515\) −1.97832 + 6.08863i −0.0871751 + 0.268297i
\(516\) 0 0
\(517\) 18.3738 35.2977i 0.808078 1.55239i
\(518\) −21.2642 −0.934296
\(519\) 0 0
\(520\) −1.26382 + 0.918222i −0.0554223 + 0.0402667i
\(521\) −5.62161 4.08434i −0.246287 0.178938i 0.457792 0.889059i \(-0.348640\pi\)
−0.704080 + 0.710121i \(0.748640\pi\)
\(522\) 0 0
\(523\) −8.26650 25.4417i −0.361469 1.11249i −0.952163 0.305591i \(-0.901146\pi\)
0.590694 0.806896i \(-0.298854\pi\)
\(524\) −0.140408 0.102013i −0.00613376 0.00445644i
\(525\) 0 0
\(526\) −20.3939 + 62.7661i −0.889218 + 2.73673i
\(527\) −17.2449 −0.751202
\(528\) 0 0
\(529\) −21.8467 −0.949856
\(530\) 3.74555 11.5276i 0.162696 0.500728i
\(531\) 0 0
\(532\) 79.9069 + 58.0557i 3.46440 + 2.51704i
\(533\) 1.04961 + 3.23038i 0.0454638 + 0.139923i
\(534\) 0 0
\(535\) 1.69286 + 1.22993i 0.0731887 + 0.0531747i
\(536\) −61.6462 + 44.7886i −2.66271 + 1.93457i
\(537\) 0 0
\(538\) −24.7133 −1.06547
\(539\) −8.84162 8.99689i −0.380836 0.387524i
\(540\) 0 0
\(541\) 4.48336 13.7984i 0.192755 0.593237i −0.807241 0.590222i \(-0.799040\pi\)
0.999995 0.00301536i \(-0.000959822\pi\)
\(542\) 20.9496 15.2208i 0.899863 0.653789i
\(543\) 0 0
\(544\) 0.480027 + 1.47737i 0.0205810 + 0.0633418i
\(545\) −2.06818 6.36521i −0.0885912 0.272656i
\(546\) 0 0
\(547\) 21.6287 15.7142i 0.924777 0.671890i −0.0199316 0.999801i \(-0.506345\pi\)
0.944708 + 0.327912i \(0.106345\pi\)
\(548\) −9.17203 + 28.2286i −0.391810 + 1.20587i
\(549\) 0 0
\(550\) 5.70922 + 5.80948i 0.243442 + 0.247717i
\(551\) −37.5422 −1.59935
\(552\) 0 0
\(553\) −14.3977 + 10.4605i −0.612251 + 0.444826i
\(554\) −35.6394 25.8935i −1.51417 1.10011i
\(555\) 0 0
\(556\) 16.4931 + 50.7606i 0.699464 + 2.15273i
\(557\) 13.9510 + 10.1360i 0.591125 + 0.429477i 0.842718 0.538356i \(-0.180954\pi\)
−0.251593 + 0.967833i \(0.580954\pi\)
\(558\) 0 0
\(559\) 0.533620 1.64231i 0.0225697 0.0694624i
\(560\) 13.7694 0.581865
\(561\) 0 0
\(562\) 18.2006 0.767748
\(563\) 0.257075 0.791197i 0.0108344 0.0333450i −0.945493 0.325642i \(-0.894420\pi\)
0.956328 + 0.292297i \(0.0944196\pi\)
\(564\) 0 0
\(565\) −8.73262 6.34462i −0.367384 0.266920i
\(566\) −4.08813 12.5820i −0.171837 0.528860i
\(567\) 0 0
\(568\) −12.3992 9.00855i −0.520259 0.377991i
\(569\) 9.38141 6.81599i 0.393289 0.285741i −0.373513 0.927625i \(-0.621847\pi\)
0.766802 + 0.641884i \(0.221847\pi\)
\(570\) 0 0
\(571\) 21.8414 0.914034 0.457017 0.889458i \(-0.348918\pi\)
0.457017 + 0.889458i \(0.348918\pi\)
\(572\) −1.93315 + 3.71376i −0.0808292 + 0.155280i
\(573\) 0 0
\(574\) 27.0575 83.2744i 1.12936 3.47580i
\(575\) 0.868820 0.631235i 0.0362323 0.0263243i
\(576\) 0 0
\(577\) 3.01164 + 9.26888i 0.125376 + 0.385868i 0.993969 0.109657i \(-0.0349754\pi\)
−0.868593 + 0.495526i \(0.834975\pi\)
\(578\) −6.07129 18.6855i −0.252532 0.777214i
\(579\) 0 0
\(580\) −16.4262 + 11.9343i −0.682061 + 0.495547i
\(581\) −16.5003 + 50.7827i −0.684548 + 2.10682i
\(582\) 0 0
\(583\) −2.41986 16.1891i −0.100220 0.670485i
\(584\) 43.1669 1.78626
\(585\) 0 0
\(586\) 3.45724 2.51183i 0.142817 0.103763i
\(587\) 18.5622 + 13.4862i 0.766143 + 0.556635i 0.900788 0.434258i \(-0.142990\pi\)
−0.134645 + 0.990894i \(0.542990\pi\)
\(588\) 0 0
\(589\) −7.94453 24.4507i −0.327349 1.00748i
\(590\) 18.2077 + 13.2287i 0.749600 + 0.544616i
\(591\) 0 0
\(592\) 3.41022 10.4956i 0.140159 0.431366i
\(593\) −28.7819 −1.18193 −0.590965 0.806697i \(-0.701253\pi\)
−0.590965 + 0.806697i \(0.701253\pi\)
\(594\) 0 0
\(595\) −16.4342 −0.673737
\(596\) 7.32333 22.5389i 0.299975 0.923229i
\(597\) 0 0
\(598\) 0.668140 + 0.485432i 0.0273223 + 0.0198508i
\(599\) 9.02179 + 27.7662i 0.368620 + 1.13450i 0.947683 + 0.319214i \(0.103419\pi\)
−0.579062 + 0.815283i \(0.696581\pi\)
\(600\) 0 0
\(601\) 5.40494 + 3.92692i 0.220472 + 0.160182i 0.692539 0.721380i \(-0.256492\pi\)
−0.472067 + 0.881563i \(0.656492\pi\)
\(602\) −36.0135 + 26.1653i −1.46780 + 1.06642i
\(603\) 0 0
\(604\) 30.7522 1.25129
\(605\) 10.4009 + 3.58078i 0.422855 + 0.145579i
\(606\) 0 0
\(607\) −13.1674 + 40.5252i −0.534450 + 1.64487i 0.210384 + 0.977619i \(0.432529\pi\)
−0.744834 + 0.667250i \(0.767471\pi\)
\(608\) −1.87355 + 1.36121i −0.0759824 + 0.0552044i
\(609\) 0 0
\(610\) −6.97007 21.4517i −0.282210 0.868553i
\(611\) −1.16099 3.57315i −0.0469685 0.144554i
\(612\) 0 0
\(613\) 4.71783 3.42771i 0.190552 0.138444i −0.488419 0.872609i \(-0.662426\pi\)
0.678971 + 0.734165i \(0.262426\pi\)
\(614\) −16.2078 + 49.8824i −0.654093 + 2.01309i
\(615\) 0 0
\(616\) 48.6699 24.2673i 1.96097 0.977758i
\(617\) 33.6386 1.35424 0.677119 0.735874i \(-0.263228\pi\)
0.677119 + 0.735874i \(0.263228\pi\)
\(618\) 0 0
\(619\) −34.4331 + 25.0171i −1.38398 + 1.00552i −0.387488 + 0.921875i \(0.626657\pi\)
−0.996495 + 0.0836477i \(0.973343\pi\)
\(620\) −11.2487 8.17267i −0.451760 0.328223i
\(621\) 0 0
\(622\) 24.8996 + 76.6329i 0.998381 + 3.07270i
\(623\) 4.31089 + 3.13205i 0.172712 + 0.125483i
\(624\) 0 0
\(625\) 0.309017 0.951057i 0.0123607 0.0380423i
\(626\) 8.49374 0.339478
\(627\) 0 0
\(628\) −40.8509 −1.63013
\(629\) −4.07019 + 12.5268i −0.162289 + 0.499475i
\(630\) 0 0
\(631\) 7.20016 + 5.23122i 0.286634 + 0.208252i 0.721806 0.692096i \(-0.243312\pi\)
−0.435172 + 0.900347i \(0.643312\pi\)
\(632\) −8.34713 25.6898i −0.332031 1.02189i
\(633\) 0 0
\(634\) 5.71351 + 4.15111i 0.226912 + 0.164862i
\(635\) 13.7559 9.99428i 0.545888 0.396611i
\(636\) 0 0
\(637\) −1.19095 −0.0471871
\(638\) −18.9416 + 36.3886i −0.749906 + 1.44064i
\(639\) 0 0
\(640\) 5.97152 18.3785i 0.236045 0.726472i
\(641\) −4.99007 + 3.62549i −0.197096 + 0.143198i −0.681956 0.731393i \(-0.738870\pi\)
0.484860 + 0.874592i \(0.338870\pi\)
\(642\) 0 0
\(643\) 1.34526 + 4.14029i 0.0530519 + 0.163277i 0.974072 0.226238i \(-0.0726427\pi\)
−0.921020 + 0.389515i \(0.872643\pi\)
\(644\) −4.39731 13.5335i −0.173278 0.533296i
\(645\) 0 0
\(646\) 74.0508 53.8011i 2.91349 2.11677i
\(647\) −4.16967 + 12.8329i −0.163927 + 0.504514i −0.998956 0.0456916i \(-0.985451\pi\)
0.835029 + 0.550206i \(0.185451\pi\)
\(648\) 0 0
\(649\) 29.9771 + 5.01575i 1.17671 + 0.196885i
\(650\) 0.769020 0.0301635
\(651\) 0 0
\(652\) 16.4021 11.9168i 0.642354 0.466697i
\(653\) 22.2060 + 16.1336i 0.868988 + 0.631357i 0.930315 0.366761i \(-0.119533\pi\)
−0.0613270 + 0.998118i \(0.519533\pi\)
\(654\) 0 0
\(655\) 0.0133034 + 0.0409437i 0.000519808 + 0.00159980i
\(656\) 36.7632 + 26.7100i 1.43536 + 1.04285i
\(657\) 0 0
\(658\) −29.9285 + 92.1105i −1.16674 + 3.59084i
\(659\) 18.7768 0.731441 0.365721 0.930725i \(-0.380823\pi\)
0.365721 + 0.930725i \(0.380823\pi\)
\(660\) 0 0
\(661\) −21.6525 −0.842184 −0.421092 0.907018i \(-0.638353\pi\)
−0.421092 + 0.907018i \(0.638353\pi\)
\(662\) 10.7174 32.9847i 0.416543 1.28199i
\(663\) 0 0
\(664\) −65.5674 47.6375i −2.54451 1.84869i
\(665\) −7.57103 23.3012i −0.293592 0.903583i
\(666\) 0 0
\(667\) 4.37578 + 3.17919i 0.169431 + 0.123099i
\(668\) 18.8872 13.7224i 0.730769 0.530935i
\(669\) 0 0
\(670\) 37.5109 1.44917
\(671\) −21.3508 21.7258i −0.824240 0.838714i
\(672\) 0 0
\(673\) 7.20076 22.1617i 0.277569 0.854269i −0.710959 0.703233i \(-0.751739\pi\)
0.988528 0.151036i \(-0.0482609\pi\)
\(674\) 31.6883 23.0229i 1.22059 0.886808i
\(675\) 0 0
\(676\) −16.0728 49.4670i −0.618184 1.90258i
\(677\) −10.2843 31.6519i −0.395259 1.21648i −0.928760 0.370683i \(-0.879124\pi\)
0.533501 0.845800i \(-0.320876\pi\)
\(678\) 0 0
\(679\) −0.595859 + 0.432917i −0.0228670 + 0.0166138i
\(680\) 7.70818 23.7233i 0.295595 0.909749i
\(681\) 0 0
\(682\) −27.7077 4.63603i −1.06098 0.177523i
\(683\) −16.9244 −0.647593 −0.323796 0.946127i \(-0.604959\pi\)
−0.323796 + 0.946127i \(0.604959\pi\)
\(684\) 0 0
\(685\) 5.95645 4.32761i 0.227584 0.165350i
\(686\) −20.8758 15.1671i −0.797041 0.579084i
\(687\) 0 0
\(688\) −7.13905 21.9717i −0.272174 0.837664i
\(689\) −1.25029 0.908392i −0.0476324 0.0346070i
\(690\) 0 0
\(691\) −14.9668 + 46.0630i −0.569363 + 1.75232i 0.0852532 + 0.996359i \(0.472830\pi\)
−0.654617 + 0.755961i \(0.727170\pi\)
\(692\) −64.7650 −2.46200
\(693\) 0 0
\(694\) 72.8910 2.76690
\(695\) 4.09118 12.5914i 0.155187 0.477618i
\(696\) 0 0
\(697\) −43.8779 31.8791i −1.66199 1.20751i
\(698\) −24.0527 74.0267i −0.910409 2.80195i
\(699\) 0 0
\(700\) −10.7199 7.78845i −0.405174 0.294376i
\(701\) −36.7424 + 26.6949i −1.38774 + 1.00825i −0.391634 + 0.920121i \(0.628090\pi\)
−0.996109 + 0.0881330i \(0.971910\pi\)
\(702\) 0 0
\(703\) −19.6361 −0.740591
\(704\) −3.73392 24.9803i −0.140727 0.941482i
\(705\) 0 0
\(706\) 0.912130 2.80725i 0.0343285 0.105652i
\(707\) −1.34372 + 0.976267i −0.0505357 + 0.0367163i
\(708\) 0 0
\(709\) −0.545405 1.67858i −0.0204831 0.0630406i 0.940292 0.340368i \(-0.110551\pi\)
−0.960776 + 0.277327i \(0.910551\pi\)
\(710\) 2.33146 + 7.17549i 0.0874981 + 0.269291i
\(711\) 0 0
\(712\) −6.54317 + 4.75389i −0.245216 + 0.178160i
\(713\) −1.14458 + 3.52266i −0.0428649 + 0.131925i
\(714\) 0 0
\(715\) 0.929420 0.463418i 0.0347583 0.0173309i
\(716\) 33.4729 1.25094
\(717\) 0 0
\(718\) 23.1649 16.8303i 0.864506 0.628100i
\(719\) −2.66974 1.93968i −0.0995645 0.0723379i 0.536889 0.843653i \(-0.319599\pi\)
−0.636454 + 0.771315i \(0.719599\pi\)
\(720\) 0 0
\(721\) −6.50241 20.0124i −0.242163 0.745300i
\(722\) 72.6459 + 52.7803i 2.70360 + 1.96428i
\(723\) 0 0
\(724\) −8.05294 + 24.7844i −0.299285 + 0.921105i
\(725\) 5.03647 0.187050
\(726\) 0 0
\(727\) 11.7838 0.437037 0.218519 0.975833i \(-0.429878\pi\)
0.218519 + 0.975833i \(0.429878\pi\)
\(728\) 1.58668 4.88331i 0.0588064 0.180987i
\(729\) 0 0
\(730\) −17.1916 12.4905i −0.636291 0.462293i
\(731\) 8.52064 + 26.2238i 0.315147 + 0.969924i
\(732\) 0 0
\(733\) −4.63654 3.36865i −0.171255 0.124424i 0.498856 0.866685i \(-0.333754\pi\)
−0.670111 + 0.742261i \(0.733754\pi\)
\(734\) 31.7619 23.0764i 1.17235 0.851765i
\(735\) 0 0
\(736\) 0.333646 0.0122983
\(737\) 45.3348 22.6044i 1.66993 0.832643i
\(738\) 0 0
\(739\) −6.50638 + 20.0246i −0.239341 + 0.736616i 0.757175 + 0.653212i \(0.226579\pi\)
−0.996516 + 0.0834038i \(0.973421\pi\)
\(740\) −8.59160 + 6.24216i −0.315833 + 0.229466i
\(741\) 0 0
\(742\) 12.3110 + 37.8895i 0.451952 + 1.39097i
\(743\) −4.05686 12.4857i −0.148832 0.458058i 0.848652 0.528952i \(-0.177415\pi\)
−0.997484 + 0.0708942i \(0.977415\pi\)
\(744\) 0 0
\(745\) −4.75587 + 3.45534i −0.174242 + 0.126594i
\(746\) −0.244350 + 0.752032i −0.00894629 + 0.0275339i
\(747\) 0 0
\(748\) −9.88299 66.1183i −0.361358 2.41753i
\(749\) −6.87768 −0.251305
\(750\) 0 0
\(751\) −20.7311 + 15.0621i −0.756490 + 0.549622i −0.897832 0.440339i \(-0.854858\pi\)
0.141342 + 0.989961i \(0.454858\pi\)
\(752\) −40.6641 29.5442i −1.48287 1.07737i
\(753\) 0 0
\(754\) 1.19687 + 3.68358i 0.0435874 + 0.134148i
\(755\) −6.17135 4.48375i −0.224598 0.163180i
\(756\) 0 0
\(757\) 9.64039 29.6701i 0.350386 1.07838i −0.608251 0.793745i \(-0.708129\pi\)
0.958637 0.284632i \(-0.0918715\pi\)
\(758\) −28.0400 −1.01846
\(759\) 0 0
\(760\) 37.1872 1.34892
\(761\) −3.51539 + 10.8193i −0.127433 + 0.392198i −0.994336 0.106278i \(-0.966107\pi\)
0.866904 + 0.498476i \(0.166107\pi\)
\(762\) 0 0
\(763\) 17.7968 + 12.9302i 0.644289 + 0.468103i
\(764\) −19.1465 58.9269i −0.692697 2.13190i
\(765\) 0 0
\(766\) −56.3617 40.9491i −2.03643 1.47955i
\(767\) 2.32154 1.68670i 0.0838260 0.0609032i
\(768\) 0 0
\(769\) 10.3938 0.374811 0.187405 0.982283i \(-0.439992\pi\)
0.187405 + 0.982283i \(0.439992\pi\)
\(770\) −26.4051 4.41808i −0.951574 0.159217i
\(771\) 0 0
\(772\) 19.6230 60.3935i 0.706248 2.17361i
\(773\) 11.3544 8.24944i 0.408389 0.296712i −0.364560 0.931180i \(-0.618781\pi\)
0.772949 + 0.634468i \(0.218781\pi\)
\(774\) 0 0
\(775\) 1.06580 + 3.28018i 0.0382845 + 0.117828i
\(776\) −0.345453 1.06319i −0.0124010 0.0381665i
\(777\) 0 0
\(778\) −30.1608 + 21.9131i −1.08132 + 0.785623i
\(779\) 24.9858 76.8985i 0.895211 2.75518i
\(780\) 0 0
\(781\) 7.14176 + 7.26717i 0.255552 + 0.260040i
\(782\) −13.1871 −0.471571
\(783\) 0 0
\(784\) −12.8902 + 9.36527i −0.460364 + 0.334474i
\(785\) 8.19795 + 5.95616i 0.292597 + 0.212584i
\(786\) 0 0
\(787\) −4.26988 13.1414i −0.152205 0.468439i 0.845662 0.533719i \(-0.179206\pi\)
−0.997867 + 0.0652802i \(0.979206\pi\)