Properties

Label 864.2.v.b.109.6
Level $864$
Weight $2$
Character 864.109
Analytic conductor $6.899$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.v (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 109.6
Character \(\chi\) \(=\) 864.109
Dual form 864.2.v.b.325.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.14607 - 0.828563i) q^{2} +(0.626968 + 1.89919i) q^{4} +(-2.89399 + 1.19873i) q^{5} +(-3.03933 + 3.03933i) q^{7} +(0.855044 - 2.69609i) q^{8} +O(q^{10})\) \(q+(-1.14607 - 0.828563i) q^{2} +(0.626968 + 1.89919i) q^{4} +(-2.89399 + 1.19873i) q^{5} +(-3.03933 + 3.03933i) q^{7} +(0.855044 - 2.69609i) q^{8} +(4.30995 + 1.02402i) q^{10} +(-2.07833 - 5.01753i) q^{11} +(0.154565 + 0.0640231i) q^{13} +(6.00158 - 0.965021i) q^{14} +(-3.21382 + 2.38146i) q^{16} +4.77723i q^{17} +(-3.30151 - 1.36753i) q^{19} +(-4.09106 - 4.74467i) q^{20} +(-1.77542 + 7.47248i) q^{22} +(1.87996 + 1.87996i) q^{23} +(3.40271 - 3.40271i) q^{25} +(-0.124096 - 0.201442i) q^{26} +(-7.67783 - 3.86670i) q^{28} +(1.81073 - 4.37148i) q^{29} +9.71647 q^{31} +(5.65646 - 0.0664742i) q^{32} +(3.95824 - 5.47506i) q^{34} +(5.15247 - 12.4392i) q^{35} +(8.56912 - 3.54945i) q^{37} +(2.65069 + 4.30280i) q^{38} +(0.757396 + 8.82744i) q^{40} +(-3.98159 - 3.98159i) q^{41} +(-0.172185 - 0.415692i) q^{43} +(8.22618 - 7.09296i) q^{44} +(-0.596908 - 3.71224i) q^{46} -6.11328i q^{47} -11.4751i q^{49} +(-6.71911 + 1.08040i) q^{50} +(-0.0246842 + 0.333689i) q^{52} +(2.21266 + 5.34183i) q^{53} +(12.0293 + 12.0293i) q^{55} +(5.59555 + 10.7931i) q^{56} +(-5.69727 + 3.50974i) q^{58} +(2.09529 - 0.867896i) q^{59} +(-3.46853 + 8.37378i) q^{61} +(-11.1358 - 8.05070i) q^{62} +(-6.53780 - 4.61055i) q^{64} -0.524058 q^{65} +(4.88800 - 11.8007i) q^{67} +(-9.07286 + 2.99517i) q^{68} +(-16.2117 + 9.98705i) q^{70} +(-8.20687 + 8.20687i) q^{71} +(-1.88142 - 1.88142i) q^{73} +(-12.7618 - 3.03213i) q^{74} +(0.527254 - 7.12759i) q^{76} +(21.5667 + 8.93321i) q^{77} -15.0641i q^{79} +(6.44605 - 10.7444i) q^{80} +(1.26420 + 7.86220i) q^{82} +(1.42473 + 0.590143i) q^{83} +(-5.72662 - 13.8253i) q^{85} +(-0.147090 + 0.619080i) q^{86} +(-15.3048 + 1.31315i) q^{88} +(-1.32189 + 1.32189i) q^{89} +(-0.664364 + 0.275188i) q^{91} +(-2.39172 + 4.74908i) q^{92} +(-5.06523 + 7.00626i) q^{94} +11.1939 q^{95} -1.06320 q^{97} +(-9.50784 + 13.1513i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.14607 0.828563i −0.810396 0.585882i
\(3\) 0 0
\(4\) 0.626968 + 1.89919i 0.313484 + 0.949593i
\(5\) −2.89399 + 1.19873i −1.29423 + 0.536089i −0.920244 0.391344i \(-0.872010\pi\)
−0.373989 + 0.927433i \(0.622010\pi\)
\(6\) 0 0
\(7\) −3.03933 + 3.03933i −1.14876 + 1.14876i −0.161964 + 0.986797i \(0.551783\pi\)
−0.986797 + 0.161964i \(0.948217\pi\)
\(8\) 0.855044 2.69609i 0.302304 0.953212i
\(9\) 0 0
\(10\) 4.30995 + 1.02402i 1.36293 + 0.323824i
\(11\) −2.07833 5.01753i −0.626639 1.51284i −0.843774 0.536699i \(-0.819671\pi\)
0.217134 0.976142i \(-0.430329\pi\)
\(12\) 0 0
\(13\) 0.154565 + 0.0640231i 0.0428687 + 0.0177568i 0.404015 0.914752i \(-0.367614\pi\)
−0.361146 + 0.932509i \(0.617614\pi\)
\(14\) 6.00158 0.965021i 1.60399 0.257913i
\(15\) 0 0
\(16\) −3.21382 + 2.38146i −0.803456 + 0.595365i
\(17\) 4.77723i 1.15865i 0.815097 + 0.579325i \(0.196684\pi\)
−0.815097 + 0.579325i \(0.803316\pi\)
\(18\) 0 0
\(19\) −3.30151 1.36753i −0.757419 0.313733i −0.0296543 0.999560i \(-0.509441\pi\)
−0.727765 + 0.685827i \(0.759441\pi\)
\(20\) −4.09106 4.74467i −0.914788 1.06094i
\(21\) 0 0
\(22\) −1.77542 + 7.47248i −0.378521 + 1.59314i
\(23\) 1.87996 + 1.87996i 0.391999 + 0.391999i 0.875399 0.483400i \(-0.160598\pi\)
−0.483400 + 0.875399i \(0.660598\pi\)
\(24\) 0 0
\(25\) 3.40271 3.40271i 0.680542 0.680542i
\(26\) −0.124096 0.201442i −0.0243373 0.0395061i
\(27\) 0 0
\(28\) −7.67783 3.86670i −1.45097 0.730737i
\(29\) 1.81073 4.37148i 0.336243 0.811763i −0.661826 0.749657i \(-0.730218\pi\)
0.998070 0.0621060i \(-0.0197817\pi\)
\(30\) 0 0
\(31\) 9.71647 1.74513 0.872565 0.488499i \(-0.162455\pi\)
0.872565 + 0.488499i \(0.162455\pi\)
\(32\) 5.65646 0.0664742i 0.999931 0.0117511i
\(33\) 0 0
\(34\) 3.95824 5.47506i 0.678832 0.938965i
\(35\) 5.15247 12.4392i 0.870926 2.10260i
\(36\) 0 0
\(37\) 8.56912 3.54945i 1.40876 0.583526i 0.456747 0.889597i \(-0.349015\pi\)
0.952009 + 0.306071i \(0.0990146\pi\)
\(38\) 2.65069 + 4.30280i 0.429999 + 0.698006i
\(39\) 0 0
\(40\) 0.757396 + 8.82744i 0.119755 + 1.39574i
\(41\) −3.98159 3.98159i −0.621821 0.621821i 0.324176 0.945997i \(-0.394913\pi\)
−0.945997 + 0.324176i \(0.894913\pi\)
\(42\) 0 0
\(43\) −0.172185 0.415692i −0.0262580 0.0633924i 0.910207 0.414154i \(-0.135923\pi\)
−0.936465 + 0.350762i \(0.885923\pi\)
\(44\) 8.22618 7.09296i 1.24014 1.06930i
\(45\) 0 0
\(46\) −0.596908 3.71224i −0.0880093 0.547340i
\(47\) 6.11328i 0.891713i −0.895104 0.445856i \(-0.852899\pi\)
0.895104 0.445856i \(-0.147101\pi\)
\(48\) 0 0
\(49\) 11.4751i 1.63930i
\(50\) −6.71911 + 1.08040i −0.950226 + 0.152791i
\(51\) 0 0
\(52\) −0.0246842 + 0.333689i −0.00342309 + 0.0462743i
\(53\) 2.21266 + 5.34183i 0.303932 + 0.733757i 0.999877 + 0.0156620i \(0.00498558\pi\)
−0.695945 + 0.718095i \(0.745014\pi\)
\(54\) 0 0
\(55\) 12.0293 + 12.0293i 1.62204 + 1.62204i
\(56\) 5.59555 + 10.7931i 0.747737 + 1.44229i
\(57\) 0 0
\(58\) −5.69727 + 3.50974i −0.748088 + 0.460851i
\(59\) 2.09529 0.867896i 0.272783 0.112990i −0.242099 0.970252i \(-0.577836\pi\)
0.514882 + 0.857261i \(0.327836\pi\)
\(60\) 0 0
\(61\) −3.46853 + 8.37378i −0.444100 + 1.07215i 0.530396 + 0.847750i \(0.322043\pi\)
−0.974496 + 0.224403i \(0.927957\pi\)
\(62\) −11.1358 8.05070i −1.41425 1.02244i
\(63\) 0 0
\(64\) −6.53780 4.61055i −0.817225 0.576319i
\(65\) −0.524058 −0.0650014
\(66\) 0 0
\(67\) 4.88800 11.8007i 0.597164 1.44168i −0.279296 0.960205i \(-0.590101\pi\)
0.876459 0.481476i \(-0.159899\pi\)
\(68\) −9.07286 + 2.99517i −1.10025 + 0.363218i
\(69\) 0 0
\(70\) −16.2117 + 9.98705i −1.93767 + 1.19368i
\(71\) −8.20687 + 8.20687i −0.973976 + 0.973976i −0.999670 0.0256934i \(-0.991821\pi\)
0.0256934 + 0.999670i \(0.491821\pi\)
\(72\) 0 0
\(73\) −1.88142 1.88142i −0.220204 0.220204i 0.588380 0.808584i \(-0.299766\pi\)
−0.808584 + 0.588380i \(0.799766\pi\)
\(74\) −12.7618 3.03213i −1.48353 0.352478i
\(75\) 0 0
\(76\) 0.527254 7.12759i 0.0604802 0.817590i
\(77\) 21.5667 + 8.93321i 2.45775 + 1.01803i
\(78\) 0 0
\(79\) 15.0641i 1.69485i −0.530917 0.847424i \(-0.678152\pi\)
0.530917 0.847424i \(-0.321848\pi\)
\(80\) 6.44605 10.7444i 0.720690 1.20126i
\(81\) 0 0
\(82\) 1.26420 + 7.86220i 0.139607 + 0.868235i
\(83\) 1.42473 + 0.590143i 0.156385 + 0.0647766i 0.459503 0.888176i \(-0.348028\pi\)
−0.303118 + 0.952953i \(0.598028\pi\)
\(84\) 0 0
\(85\) −5.72662 13.8253i −0.621139 1.49956i
\(86\) −0.147090 + 0.619080i −0.0158611 + 0.0667571i
\(87\) 0 0
\(88\) −15.3048 + 1.31315i −1.63149 + 0.139983i
\(89\) −1.32189 + 1.32189i −0.140120 + 0.140120i −0.773687 0.633568i \(-0.781590\pi\)
0.633568 + 0.773687i \(0.281590\pi\)
\(90\) 0 0
\(91\) −0.664364 + 0.275188i −0.0696442 + 0.0288476i
\(92\) −2.39172 + 4.74908i −0.249354 + 0.495125i
\(93\) 0 0
\(94\) −5.06523 + 7.00626i −0.522439 + 0.722641i
\(95\) 11.1939 1.14847
\(96\) 0 0
\(97\) −1.06320 −0.107952 −0.0539759 0.998542i \(-0.517189\pi\)
−0.0539759 + 0.998542i \(0.517189\pi\)
\(98\) −9.50784 + 13.1513i −0.960437 + 1.32848i
\(99\) 0 0
\(100\) 8.59577 + 4.32899i 0.859577 + 0.432899i
\(101\) −5.27745 + 2.18599i −0.525125 + 0.217514i −0.629467 0.777027i \(-0.716727\pi\)
0.104341 + 0.994542i \(0.466727\pi\)
\(102\) 0 0
\(103\) −4.14160 + 4.14160i −0.408084 + 0.408084i −0.881070 0.472986i \(-0.843176\pi\)
0.472986 + 0.881070i \(0.343176\pi\)
\(104\) 0.304772 0.361980i 0.0298854 0.0354950i
\(105\) 0 0
\(106\) 1.89017 7.95545i 0.183590 0.772702i
\(107\) −4.42929 10.6932i −0.428195 1.03376i −0.979859 0.199689i \(-0.936007\pi\)
0.551664 0.834066i \(-0.313993\pi\)
\(108\) 0 0
\(109\) 12.2310 + 5.06625i 1.17152 + 0.485259i 0.881694 0.471821i \(-0.156403\pi\)
0.289824 + 0.957080i \(0.406403\pi\)
\(110\) −3.81944 23.7536i −0.364170 2.26481i
\(111\) 0 0
\(112\) 2.52983 17.0059i 0.239046 1.60691i
\(113\) 2.93674i 0.276265i −0.990414 0.138133i \(-0.955890\pi\)
0.990414 0.138133i \(-0.0441100\pi\)
\(114\) 0 0
\(115\) −7.69417 3.18703i −0.717485 0.297192i
\(116\) 9.43752 + 0.698129i 0.876252 + 0.0648197i
\(117\) 0 0
\(118\) −3.12046 0.741403i −0.287261 0.0682517i
\(119\) −14.5196 14.5196i −1.33101 1.33101i
\(120\) 0 0
\(121\) −13.0779 + 13.0779i −1.18890 + 1.18890i
\(122\) 10.9134 6.72307i 0.988052 0.608678i
\(123\) 0 0
\(124\) 6.09192 + 18.4534i 0.547070 + 1.65716i
\(125\) 0.225172 0.543613i 0.0201400 0.0486222i
\(126\) 0 0
\(127\) −1.29466 −0.114882 −0.0574412 0.998349i \(-0.518294\pi\)
−0.0574412 + 0.998349i \(0.518294\pi\)
\(128\) 3.67267 + 10.7010i 0.324621 + 0.945844i
\(129\) 0 0
\(130\) 0.600609 + 0.434215i 0.0526769 + 0.0380832i
\(131\) −0.734568 + 1.77340i −0.0641795 + 0.154943i −0.952715 0.303864i \(-0.901723\pi\)
0.888536 + 0.458807i \(0.151723\pi\)
\(132\) 0 0
\(133\) 14.1908 5.87801i 1.23050 0.509688i
\(134\) −15.3796 + 9.47442i −1.32859 + 0.818465i
\(135\) 0 0
\(136\) 12.8799 + 4.08474i 1.10444 + 0.350264i
\(137\) 7.45884 + 7.45884i 0.637252 + 0.637252i 0.949877 0.312625i \(-0.101208\pi\)
−0.312625 + 0.949877i \(0.601208\pi\)
\(138\) 0 0
\(139\) −4.48857 10.8364i −0.380716 0.919129i −0.991828 0.127585i \(-0.959278\pi\)
0.611112 0.791544i \(-0.290722\pi\)
\(140\) 26.8547 + 1.98654i 2.26964 + 0.167894i
\(141\) 0 0
\(142\) 16.2056 2.60577i 1.35994 0.218671i
\(143\) 0.908597i 0.0759807i
\(144\) 0 0
\(145\) 14.8216i 1.23087i
\(146\) 0.597372 + 3.71513i 0.0494389 + 0.307466i
\(147\) 0 0
\(148\) 12.1136 + 14.0490i 0.995734 + 1.15482i
\(149\) 1.02055 + 2.46383i 0.0836068 + 0.201845i 0.960154 0.279471i \(-0.0901591\pi\)
−0.876547 + 0.481316i \(0.840159\pi\)
\(150\) 0 0
\(151\) −10.4711 10.4711i −0.852128 0.852128i 0.138267 0.990395i \(-0.455847\pi\)
−0.990395 + 0.138267i \(0.955847\pi\)
\(152\) −6.50992 + 7.73187i −0.528025 + 0.627138i
\(153\) 0 0
\(154\) −17.3153 28.1074i −1.39530 2.26496i
\(155\) −28.1194 + 11.6474i −2.25860 + 0.935545i
\(156\) 0 0
\(157\) 3.37313 8.14346i 0.269205 0.649919i −0.730241 0.683189i \(-0.760592\pi\)
0.999446 + 0.0332707i \(0.0105923\pi\)
\(158\) −12.4816 + 17.2646i −0.992981 + 1.37350i
\(159\) 0 0
\(160\) −16.2901 + 6.97296i −1.28784 + 0.551261i
\(161\) −11.4277 −0.900626
\(162\) 0 0
\(163\) 8.77772 21.1913i 0.687524 1.65983i −0.0621857 0.998065i \(-0.519807\pi\)
0.749710 0.661766i \(-0.230193\pi\)
\(164\) 5.06546 10.0581i 0.395546 0.785408i
\(165\) 0 0
\(166\) −1.14388 1.85683i −0.0887820 0.144118i
\(167\) 1.59009 1.59009i 0.123045 0.123045i −0.642903 0.765948i \(-0.722270\pi\)
0.765948 + 0.642903i \(0.222270\pi\)
\(168\) 0 0
\(169\) −9.17260 9.17260i −0.705584 0.705584i
\(170\) −4.89199 + 20.5897i −0.375198 + 1.57915i
\(171\) 0 0
\(172\) 0.681522 0.587637i 0.0519656 0.0448069i
\(173\) 4.55540 + 1.88691i 0.346341 + 0.143459i 0.549071 0.835776i \(-0.314982\pi\)
−0.202731 + 0.979235i \(0.564982\pi\)
\(174\) 0 0
\(175\) 20.6839i 1.56356i
\(176\) 18.6284 + 11.1760i 1.40417 + 0.842421i
\(177\) 0 0
\(178\) 2.61025 0.419714i 0.195646 0.0314589i
\(179\) 13.9431 + 5.77541i 1.04215 + 0.431674i 0.837085 0.547073i \(-0.184258\pi\)
0.205069 + 0.978747i \(0.434258\pi\)
\(180\) 0 0
\(181\) 3.42297 + 8.26378i 0.254427 + 0.614242i 0.998552 0.0537992i \(-0.0171331\pi\)
−0.744125 + 0.668041i \(0.767133\pi\)
\(182\) 0.989420 + 0.235081i 0.0733407 + 0.0174253i
\(183\) 0 0
\(184\) 6.67600 3.46110i 0.492161 0.255155i
\(185\) −20.5442 + 20.5442i −1.51044 + 1.51044i
\(186\) 0 0
\(187\) 23.9699 9.92866i 1.75285 0.726055i
\(188\) 11.6103 3.83283i 0.846765 0.279538i
\(189\) 0 0
\(190\) −12.8290 9.27481i −0.930712 0.672866i
\(191\) −0.522075 −0.0377760 −0.0188880 0.999822i \(-0.506013\pi\)
−0.0188880 + 0.999822i \(0.506013\pi\)
\(192\) 0 0
\(193\) 10.9570 0.788705 0.394353 0.918959i \(-0.370969\pi\)
0.394353 + 0.918959i \(0.370969\pi\)
\(194\) 1.21851 + 0.880930i 0.0874838 + 0.0632471i
\(195\) 0 0
\(196\) 21.7934 7.19453i 1.55667 0.513895i
\(197\) −20.1650 + 8.35262i −1.43670 + 0.595100i −0.958995 0.283422i \(-0.908530\pi\)
−0.477702 + 0.878522i \(0.658530\pi\)
\(198\) 0 0
\(199\) −4.19008 + 4.19008i −0.297027 + 0.297027i −0.839848 0.542821i \(-0.817356\pi\)
0.542821 + 0.839848i \(0.317356\pi\)
\(200\) −6.26454 12.0835i −0.442970 0.854431i
\(201\) 0 0
\(202\) 7.85957 + 1.86739i 0.552997 + 0.131389i
\(203\) 7.78299 + 18.7898i 0.546259 + 1.31878i
\(204\) 0 0
\(205\) 16.2956 + 6.74985i 1.13813 + 0.471430i
\(206\) 8.17815 1.31500i 0.569798 0.0916205i
\(207\) 0 0
\(208\) −0.649214 + 0.162332i −0.0450149 + 0.0112557i
\(209\) 19.4076i 1.34245i
\(210\) 0 0
\(211\) −5.32672 2.20640i −0.366707 0.151895i 0.191718 0.981450i \(-0.438594\pi\)
−0.558425 + 0.829555i \(0.688594\pi\)
\(212\) −8.75787 + 7.55141i −0.601493 + 0.518633i
\(213\) 0 0
\(214\) −3.78373 + 15.9252i −0.258651 + 1.08862i
\(215\) 0.996606 + 0.996606i 0.0679680 + 0.0679680i
\(216\) 0 0
\(217\) −29.5316 + 29.5316i −2.00474 + 2.00474i
\(218\) −9.81993 15.9405i −0.665090 1.07962i
\(219\) 0 0
\(220\) −15.3039 + 30.3880i −1.03179 + 2.04876i
\(221\) −0.305853 + 0.738395i −0.0205739 + 0.0496698i
\(222\) 0 0
\(223\) 15.9884 1.07066 0.535332 0.844642i \(-0.320187\pi\)
0.535332 + 0.844642i \(0.320187\pi\)
\(224\) −16.9898 + 17.3939i −1.13518 + 1.16218i
\(225\) 0 0
\(226\) −2.43327 + 3.36572i −0.161859 + 0.223884i
\(227\) 7.20470 17.3937i 0.478192 1.15446i −0.482263 0.876026i \(-0.660185\pi\)
0.960456 0.278432i \(-0.0898148\pi\)
\(228\) 0 0
\(229\) −0.156196 + 0.0646985i −0.0103217 + 0.00427540i −0.387838 0.921727i \(-0.626778\pi\)
0.377517 + 0.926003i \(0.376778\pi\)
\(230\) 6.17743 + 10.0277i 0.407328 + 0.661205i
\(231\) 0 0
\(232\) −10.2377 8.61969i −0.672135 0.565910i
\(233\) 20.4708 + 20.4708i 1.34108 + 1.34108i 0.894982 + 0.446102i \(0.147188\pi\)
0.446102 + 0.894982i \(0.352812\pi\)
\(234\) 0 0
\(235\) 7.32818 + 17.6918i 0.478038 + 1.15408i
\(236\) 2.96197 + 3.43520i 0.192808 + 0.223612i
\(237\) 0 0
\(238\) 4.61013 + 28.6709i 0.298830 + 1.85846i
\(239\) 29.7686i 1.92557i −0.270270 0.962785i \(-0.587113\pi\)
0.270270 0.962785i \(-0.412887\pi\)
\(240\) 0 0
\(241\) 18.8662i 1.21528i 0.794212 + 0.607640i \(0.207884\pi\)
−0.794212 + 0.607640i \(0.792116\pi\)
\(242\) 25.8242 4.15239i 1.66004 0.266926i
\(243\) 0 0
\(244\) −18.0780 1.33730i −1.15733 0.0856119i
\(245\) 13.7556 + 33.2089i 0.878811 + 2.12164i
\(246\) 0 0
\(247\) −0.422746 0.422746i −0.0268987 0.0268987i
\(248\) 8.30801 26.1965i 0.527559 1.66348i
\(249\) 0 0
\(250\) −0.708481 + 0.436451i −0.0448083 + 0.0276036i
\(251\) 7.20956 2.98630i 0.455063 0.188493i −0.143365 0.989670i \(-0.545792\pi\)
0.598428 + 0.801177i \(0.295792\pi\)
\(252\) 0 0
\(253\) 5.52558 13.3399i 0.347390 0.838675i
\(254\) 1.48377 + 1.07271i 0.0931003 + 0.0673076i
\(255\) 0 0
\(256\) 4.65730 15.3072i 0.291081 0.956698i
\(257\) 17.7208 1.10539 0.552696 0.833383i \(-0.313599\pi\)
0.552696 + 0.833383i \(0.313599\pi\)
\(258\) 0 0
\(259\) −15.2565 + 36.8324i −0.947991 + 2.28865i
\(260\) −0.328568 0.995284i −0.0203769 0.0617249i
\(261\) 0 0
\(262\) 2.31125 1.42382i 0.142789 0.0879636i
\(263\) 6.87392 6.87392i 0.423864 0.423864i −0.462668 0.886532i \(-0.653108\pi\)
0.886532 + 0.462668i \(0.153108\pi\)
\(264\) 0 0
\(265\) −12.8068 12.8068i −0.786718 0.786718i
\(266\) −21.1340 5.02132i −1.29581 0.307877i
\(267\) 0 0
\(268\) 25.4763 + 1.88458i 1.55621 + 0.115119i
\(269\) −23.8231 9.86787i −1.45252 0.601655i −0.489725 0.871877i \(-0.662903\pi\)
−0.962798 + 0.270223i \(0.912903\pi\)
\(270\) 0 0
\(271\) 18.6652i 1.13383i 0.823775 + 0.566916i \(0.191864\pi\)
−0.823775 + 0.566916i \(0.808136\pi\)
\(272\) −11.3768 15.3532i −0.689819 0.930923i
\(273\) 0 0
\(274\) −2.36826 14.7285i −0.143072 0.889781i
\(275\) −24.1451 10.0012i −1.45601 0.603097i
\(276\) 0 0
\(277\) −5.19701 12.5467i −0.312258 0.753858i −0.999621 0.0275432i \(-0.991232\pi\)
0.687363 0.726314i \(-0.258768\pi\)
\(278\) −3.83438 + 16.1383i −0.229971 + 0.967913i
\(279\) 0 0
\(280\) −29.1315 24.5275i −1.74094 1.46580i
\(281\) 16.4615 16.4615i 0.982008 0.982008i −0.0178325 0.999841i \(-0.505677\pi\)
0.999841 + 0.0178325i \(0.00567656\pi\)
\(282\) 0 0
\(283\) −1.69249 + 0.701052i −0.100608 + 0.0416732i −0.432420 0.901672i \(-0.642340\pi\)
0.331812 + 0.943346i \(0.392340\pi\)
\(284\) −20.7318 10.4409i −1.23021 0.619556i
\(285\) 0 0
\(286\) −0.752829 + 1.04132i −0.0445157 + 0.0615745i
\(287\) 24.2028 1.42865
\(288\) 0 0
\(289\) −5.82196 −0.342468
\(290\) 12.2806 16.9867i 0.721144 0.997491i
\(291\) 0 0
\(292\) 2.39358 4.75277i 0.140074 0.278135i
\(293\) −27.7774 + 11.5058i −1.62277 + 0.672174i −0.994394 0.105735i \(-0.966281\pi\)
−0.628377 + 0.777909i \(0.716281\pi\)
\(294\) 0 0
\(295\) −5.02337 + 5.02337i −0.292472 + 0.292472i
\(296\) −2.24265 26.1381i −0.130352 1.51924i
\(297\) 0 0
\(298\) 0.871809 3.66932i 0.0505026 0.212558i
\(299\) 0.170216 + 0.410938i 0.00984386 + 0.0237652i
\(300\) 0 0
\(301\) 1.78676 + 0.740098i 0.102987 + 0.0426586i
\(302\) 3.32469 + 20.6767i 0.191315 + 1.18981i
\(303\) 0 0
\(304\) 13.8672 3.46741i 0.795338 0.198870i
\(305\) 28.3915i 1.62569i
\(306\) 0 0
\(307\) −17.1668 7.11073i −0.979763 0.405831i −0.165425 0.986222i \(-0.552900\pi\)
−0.814338 + 0.580391i \(0.802900\pi\)
\(308\) −3.44422 + 46.5600i −0.196252 + 2.65300i
\(309\) 0 0
\(310\) 41.8775 + 9.94987i 2.37848 + 0.565114i
\(311\) −13.7172 13.7172i −0.777832 0.777832i 0.201630 0.979462i \(-0.435376\pi\)
−0.979462 + 0.201630i \(0.935376\pi\)
\(312\) 0 0
\(313\) 8.67327 8.67327i 0.490242 0.490242i −0.418140 0.908382i \(-0.637318\pi\)
0.908382 + 0.418140i \(0.137318\pi\)
\(314\) −10.6132 + 6.53815i −0.598939 + 0.368969i
\(315\) 0 0
\(316\) 28.6096 9.44473i 1.60942 0.531308i
\(317\) −0.485904 + 1.17307i −0.0272911 + 0.0658864i −0.936938 0.349497i \(-0.886353\pi\)
0.909646 + 0.415383i \(0.136353\pi\)
\(318\) 0 0
\(319\) −25.6973 −1.43877
\(320\) 24.4472 + 5.50584i 1.36664 + 0.307786i
\(321\) 0 0
\(322\) 13.0969 + 9.46854i 0.729864 + 0.527661i
\(323\) 6.53302 15.7721i 0.363507 0.877583i
\(324\) 0 0
\(325\) 0.743793 0.308089i 0.0412582 0.0170897i
\(326\) −27.6182 + 17.0139i −1.52963 + 0.942312i
\(327\) 0 0
\(328\) −14.1392 + 7.33030i −0.780705 + 0.404748i
\(329\) 18.5803 + 18.5803i 1.02436 + 1.02436i
\(330\) 0 0
\(331\) −3.36914 8.13382i −0.185185 0.447075i 0.803836 0.594850i \(-0.202789\pi\)
−0.989021 + 0.147775i \(0.952789\pi\)
\(332\) −0.227531 + 3.07583i −0.0124874 + 0.168808i
\(333\) 0 0
\(334\) −3.13985 + 0.504871i −0.171805 + 0.0276253i
\(335\) 40.0105i 2.18600i
\(336\) 0 0
\(337\) 6.76122i 0.368307i 0.982897 + 0.184154i \(0.0589544\pi\)
−0.982897 + 0.184154i \(0.941046\pi\)
\(338\) 2.91240 + 18.1125i 0.158414 + 0.985192i
\(339\) 0 0
\(340\) 22.6664 19.5439i 1.22926 1.05992i
\(341\) −20.1940 48.7526i −1.09357 2.64010i
\(342\) 0 0
\(343\) 13.6013 + 13.6013i 0.734403 + 0.734403i
\(344\) −1.26797 + 0.108792i −0.0683643 + 0.00586567i
\(345\) 0 0
\(346\) −3.65740 5.93697i −0.196623 0.319174i
\(347\) 17.8881 7.40950i 0.960285 0.397763i 0.153198 0.988196i \(-0.451043\pi\)
0.807087 + 0.590432i \(0.201043\pi\)
\(348\) 0 0
\(349\) 3.93563 9.50144i 0.210669 0.508601i −0.782857 0.622201i \(-0.786239\pi\)
0.993526 + 0.113601i \(0.0362385\pi\)
\(350\) 17.1379 23.7053i 0.916062 1.26710i
\(351\) 0 0
\(352\) −12.0895 28.2433i −0.644374 1.50537i
\(353\) −3.64417 −0.193960 −0.0969798 0.995286i \(-0.530918\pi\)
−0.0969798 + 0.995286i \(0.530918\pi\)
\(354\) 0 0
\(355\) 13.9128 33.5885i 0.738415 1.78269i
\(356\) −3.33929 1.68173i −0.176982 0.0891316i
\(357\) 0 0
\(358\) −11.1945 18.1717i −0.591647 0.960407i
\(359\) 8.66290 8.66290i 0.457210 0.457210i −0.440528 0.897739i \(-0.645209\pi\)
0.897739 + 0.440528i \(0.145209\pi\)
\(360\) 0 0
\(361\) −4.40519 4.40519i −0.231852 0.231852i
\(362\) 2.92408 12.3070i 0.153686 0.646844i
\(363\) 0 0
\(364\) −0.939169 1.08922i −0.0492258 0.0570904i
\(365\) 7.70015 + 3.18951i 0.403044 + 0.166946i
\(366\) 0 0
\(367\) 31.3403i 1.63595i 0.575252 + 0.817976i \(0.304904\pi\)
−0.575252 + 0.817976i \(0.695096\pi\)
\(368\) −10.5189 1.56481i −0.548337 0.0815714i
\(369\) 0 0
\(370\) 40.5672 6.52299i 2.10899 0.339114i
\(371\) −22.9606 9.51060i −1.19206 0.493766i
\(372\) 0 0
\(373\) 2.39894 + 5.79155i 0.124212 + 0.299875i 0.973738 0.227672i \(-0.0731116\pi\)
−0.849525 + 0.527548i \(0.823112\pi\)
\(374\) −35.6978 8.48159i −1.84589 0.438573i
\(375\) 0 0
\(376\) −16.4819 5.22712i −0.849991 0.269568i
\(377\) 0.559751 0.559751i 0.0288287 0.0288287i
\(378\) 0 0
\(379\) −20.9093 + 8.66092i −1.07404 + 0.444881i −0.848414 0.529333i \(-0.822442\pi\)
−0.225624 + 0.974214i \(0.572442\pi\)
\(380\) 7.01819 + 21.2592i 0.360026 + 1.09058i
\(381\) 0 0
\(382\) 0.598336 + 0.432572i 0.0306135 + 0.0221323i
\(383\) −0.320505 −0.0163771 −0.00818853 0.999966i \(-0.502607\pi\)
−0.00818853 + 0.999966i \(0.502607\pi\)
\(384\) 0 0
\(385\) −73.1223 −3.72666
\(386\) −12.5576 9.07860i −0.639164 0.462088i
\(387\) 0 0
\(388\) −0.666594 2.01922i −0.0338412 0.102510i
\(389\) 21.6672 8.97486i 1.09857 0.455043i 0.241584 0.970380i \(-0.422333\pi\)
0.856988 + 0.515337i \(0.172333\pi\)
\(390\) 0 0
\(391\) −8.98102 + 8.98102i −0.454190 + 0.454190i
\(392\) −30.9379 9.81172i −1.56260 0.495567i
\(393\) 0 0
\(394\) 30.0312 + 7.13526i 1.51295 + 0.359469i
\(395\) 18.0579 + 43.5955i 0.908589 + 2.19353i
\(396\) 0 0
\(397\) −14.0703 5.82810i −0.706167 0.292504i 0.000550210 1.00000i \(-0.499825\pi\)
−0.706718 + 0.707496i \(0.749825\pi\)
\(398\) 8.27389 1.33040i 0.414732 0.0666867i
\(399\) 0 0
\(400\) −2.83229 + 19.0391i −0.141614 + 0.951956i
\(401\) 35.8868i 1.79210i −0.443952 0.896051i \(-0.646424\pi\)
0.443952 0.896051i \(-0.353576\pi\)
\(402\) 0 0
\(403\) 1.50183 + 0.622078i 0.0748115 + 0.0309879i
\(404\) −7.46039 8.65231i −0.371168 0.430469i
\(405\) 0 0
\(406\) 6.64864 27.9832i 0.329967 1.38878i
\(407\) −35.6189 35.6189i −1.76556 1.76556i
\(408\) 0 0
\(409\) 14.6781 14.6781i 0.725787 0.725787i −0.243990 0.969778i \(-0.578457\pi\)
0.969778 + 0.243990i \(0.0784566\pi\)
\(410\) −13.0833 21.2377i −0.646136 1.04886i
\(411\) 0 0
\(412\) −10.4623 5.26902i −0.515441 0.259586i
\(413\) −3.73045 + 9.00610i −0.183563 + 0.443161i
\(414\) 0 0
\(415\) −4.83059 −0.237124
\(416\) 0.878550 + 0.351870i 0.0430744 + 0.0172518i
\(417\) 0 0
\(418\) 16.0804 22.2425i 0.786519 1.08792i
\(419\) −1.01746 + 2.45637i −0.0497063 + 0.120002i −0.946782 0.321875i \(-0.895687\pi\)
0.897076 + 0.441876i \(0.145687\pi\)
\(420\) 0 0
\(421\) 6.99423 2.89711i 0.340878 0.141196i −0.205676 0.978620i \(-0.565939\pi\)
0.546554 + 0.837424i \(0.315939\pi\)
\(422\) 4.27667 + 6.94222i 0.208185 + 0.337942i
\(423\) 0 0
\(424\) 16.2940 1.39803i 0.791305 0.0678942i
\(425\) 16.2555 + 16.2555i 0.788510 + 0.788510i
\(426\) 0 0
\(427\) −14.9087 35.9927i −0.721482 1.74181i
\(428\) 17.5314 15.1164i 0.847415 0.730677i
\(429\) 0 0
\(430\) −0.316433 1.96793i −0.0152598 0.0949022i
\(431\) 15.5614i 0.749567i 0.927112 + 0.374783i \(0.122283\pi\)
−0.927112 + 0.374783i \(0.877717\pi\)
\(432\) 0 0
\(433\) 17.1441i 0.823891i −0.911208 0.411946i \(-0.864849\pi\)
0.911208 0.411946i \(-0.135151\pi\)
\(434\) 58.3141 9.37660i 2.79917 0.450091i
\(435\) 0 0
\(436\) −1.95330 + 26.4054i −0.0935463 + 1.26459i
\(437\) −3.63581 8.77763i −0.173924 0.419891i
\(438\) 0 0
\(439\) 8.64120 + 8.64120i 0.412422 + 0.412422i 0.882582 0.470159i \(-0.155804\pi\)
−0.470159 + 0.882582i \(0.655804\pi\)
\(440\) 42.7178 22.1466i 2.03649 1.05580i
\(441\) 0 0
\(442\) 0.962337 0.592836i 0.0457737 0.0281984i
\(443\) 2.60225 1.07789i 0.123637 0.0512120i −0.320007 0.947415i \(-0.603685\pi\)
0.443644 + 0.896203i \(0.353685\pi\)
\(444\) 0 0
\(445\) 2.24095 5.41012i 0.106231 0.256465i
\(446\) −18.3239 13.2474i −0.867662 0.627283i
\(447\) 0 0
\(448\) 33.8836 5.85756i 1.60085 0.276744i
\(449\) −11.6595 −0.550248 −0.275124 0.961409i \(-0.588719\pi\)
−0.275124 + 0.961409i \(0.588719\pi\)
\(450\) 0 0
\(451\) −11.7027 + 28.2528i −0.551059 + 1.33037i
\(452\) 5.57742 1.84124i 0.262340 0.0866047i
\(453\) 0 0
\(454\) −22.6689 + 13.9649i −1.06390 + 0.655404i
\(455\) 1.59279 1.59279i 0.0746710 0.0746710i
\(456\) 0 0
\(457\) 0.916734 + 0.916734i 0.0428830 + 0.0428830i 0.728223 0.685340i \(-0.240346\pi\)
−0.685340 + 0.728223i \(0.740346\pi\)
\(458\) 0.232619 + 0.0552689i 0.0108696 + 0.00258255i
\(459\) 0 0
\(460\) 1.22877 16.6108i 0.0572915 0.774484i
\(461\) 19.2249 + 7.96323i 0.895395 + 0.370885i 0.782448 0.622716i \(-0.213971\pi\)
0.112947 + 0.993601i \(0.463971\pi\)
\(462\) 0 0
\(463\) 2.04111i 0.0948585i 0.998875 + 0.0474292i \(0.0151029\pi\)
−0.998875 + 0.0474292i \(0.984897\pi\)
\(464\) 4.59115 + 18.3613i 0.213139 + 0.852403i
\(465\) 0 0
\(466\) −6.49969 40.4223i −0.301092 1.87253i
\(467\) 20.2562 + 8.39040i 0.937346 + 0.388261i 0.798460 0.602047i \(-0.205648\pi\)
0.138885 + 0.990308i \(0.455648\pi\)
\(468\) 0 0
\(469\) 21.0099 + 50.7224i 0.970148 + 2.34214i
\(470\) 6.26012 26.3479i 0.288758 1.21534i
\(471\) 0 0
\(472\) −0.548364 6.39117i −0.0252405 0.294177i
\(473\) −1.72789 + 1.72789i −0.0794484 + 0.0794484i
\(474\) 0 0
\(475\) −15.8874 + 6.58078i −0.728964 + 0.301947i
\(476\) 18.4721 36.6788i 0.846668 1.68117i
\(477\) 0 0
\(478\) −24.6651 + 34.1170i −1.12816 + 1.56047i
\(479\) −0.106626 −0.00487185 −0.00243592 0.999997i \(-0.500775\pi\)
−0.00243592 + 0.999997i \(0.500775\pi\)
\(480\) 0 0
\(481\) 1.55174 0.0707531
\(482\) 15.6319 21.6221i 0.712011 0.984859i
\(483\) 0 0
\(484\) −33.0369 16.6380i −1.50168 0.756273i
\(485\) 3.07690 1.27449i 0.139715 0.0578718i
\(486\) 0 0
\(487\) −1.49752 + 1.49752i −0.0678589 + 0.0678589i −0.740222 0.672363i \(-0.765279\pi\)
0.672363 + 0.740222i \(0.265279\pi\)
\(488\) 19.6107 + 16.5114i 0.887735 + 0.747437i
\(489\) 0 0
\(490\) 11.7507 49.4572i 0.530845 2.23425i
\(491\) 4.50143 + 10.8674i 0.203147 + 0.490440i 0.992315 0.123737i \(-0.0394881\pi\)
−0.789168 + 0.614177i \(0.789488\pi\)
\(492\) 0 0
\(493\) 20.8836 + 8.65026i 0.940549 + 0.389588i
\(494\) 0.134226 + 0.834769i 0.00603913 + 0.0375581i
\(495\) 0 0
\(496\) −31.2270 + 23.1394i −1.40213 + 1.03899i
\(497\) 49.8869i 2.23773i
\(498\) 0 0
\(499\) −35.1359 14.5538i −1.57290 0.651516i −0.585629 0.810579i \(-0.699153\pi\)
−0.987268 + 0.159063i \(0.949153\pi\)
\(500\) 1.17360 + 0.0868155i 0.0524849 + 0.00388251i
\(501\) 0 0
\(502\) −10.7370 2.55105i −0.479216 0.113859i
\(503\) 7.22205 + 7.22205i 0.322015 + 0.322015i 0.849540 0.527525i \(-0.176880\pi\)
−0.527525 + 0.849540i \(0.676880\pi\)
\(504\) 0 0
\(505\) 12.6525 12.6525i 0.563028 0.563028i
\(506\) −17.3857 + 10.7103i −0.772889 + 0.476129i
\(507\) 0 0
\(508\) −0.811710 2.45880i −0.0360138 0.109092i
\(509\) 13.6482 32.9496i 0.604945 1.46047i −0.263490 0.964662i \(-0.584874\pi\)
0.868435 0.495803i \(-0.165126\pi\)
\(510\) 0 0
\(511\) 11.4366 0.505923
\(512\) −18.0206 + 13.6843i −0.796404 + 0.604765i
\(513\) 0 0
\(514\) −20.3093 14.6828i −0.895806 0.647630i
\(515\) 7.02109 16.9504i 0.309386 0.746925i
\(516\) 0 0
\(517\) −30.6735 + 12.7054i −1.34902 + 0.558782i
\(518\) 48.0030 29.5717i 2.10913 1.29930i
\(519\) 0 0
\(520\) −0.448092 + 1.41291i −0.0196502 + 0.0619601i
\(521\) 11.0804 + 11.0804i 0.485441 + 0.485441i 0.906864 0.421423i \(-0.138469\pi\)
−0.421423 + 0.906864i \(0.638469\pi\)
\(522\) 0 0
\(523\) −5.54859 13.3955i −0.242623 0.585743i 0.754919 0.655818i \(-0.227676\pi\)
−0.997542 + 0.0700750i \(0.977676\pi\)
\(524\) −3.82858 0.283214i −0.167252 0.0123723i
\(525\) 0 0
\(526\) −13.5735 + 2.18254i −0.591832 + 0.0951634i
\(527\) 46.4178i 2.02199i
\(528\) 0 0
\(529\) 15.9315i 0.692673i
\(530\) 4.06631 + 25.2888i 0.176629 + 1.09848i
\(531\) 0 0
\(532\) 20.0606 + 23.2656i 0.869738 + 1.00869i
\(533\) −0.360503 0.870331i −0.0156151 0.0376982i
\(534\) 0 0
\(535\) 25.6367 + 25.6367i 1.10837 + 1.10837i
\(536\) −27.6362 23.2686i −1.19370 1.00505i
\(537\) 0 0
\(538\) 19.1269 + 31.0483i 0.824620 + 1.33859i
\(539\) −57.5766 + 23.8490i −2.48000 + 1.02725i
\(540\) 0 0
\(541\) 0.609513 1.47149i 0.0262050 0.0632644i −0.910235 0.414091i \(-0.864099\pi\)
0.936440 + 0.350827i \(0.114099\pi\)
\(542\) 15.4653 21.3917i 0.664293 0.918854i
\(543\) 0 0
\(544\) 0.317563 + 27.0222i 0.0136154 + 1.15857i
\(545\) −41.4696 −1.77636
\(546\) 0 0
\(547\) 4.75146 11.4711i 0.203158 0.490467i −0.789159 0.614189i \(-0.789483\pi\)
0.992317 + 0.123722i \(0.0394832\pi\)
\(548\) −9.48927 + 18.8422i −0.405362 + 0.804898i
\(549\) 0 0
\(550\) 19.3854 + 31.4679i 0.826598 + 1.34180i
\(551\) −11.9563 + 11.9563i −0.509354 + 0.509354i
\(552\) 0 0
\(553\) 45.7850 + 45.7850i 1.94697 + 1.94697i
\(554\) −4.43956 + 18.6855i −0.188619 + 0.793870i
\(555\) 0 0
\(556\) 17.7661 15.3187i 0.753450 0.649657i
\(557\) −1.89110 0.783320i −0.0801286 0.0331903i 0.342259 0.939606i \(-0.388808\pi\)
−0.422388 + 0.906415i \(0.638808\pi\)
\(558\) 0 0
\(559\) 0.0752754i 0.00318381i
\(560\) 13.0642 + 52.2476i 0.552065 + 2.20787i
\(561\) 0 0
\(562\) −32.5054 + 5.22669i −1.37116 + 0.220475i
\(563\) −31.3299 12.9773i −1.32040 0.546927i −0.392497 0.919753i \(-0.628389\pi\)
−0.927901 + 0.372827i \(0.878389\pi\)
\(564\) 0 0
\(565\) 3.52036 + 8.49890i 0.148103 + 0.357552i
\(566\) 2.52058 + 0.598876i 0.105948 + 0.0251727i
\(567\) 0 0
\(568\) 15.1092 + 29.1437i 0.633969 + 1.22284i
\(569\) −8.76894 + 8.76894i −0.367613 + 0.367613i −0.866606 0.498993i \(-0.833703\pi\)
0.498993 + 0.866606i \(0.333703\pi\)
\(570\) 0 0
\(571\) −3.18862 + 1.32077i −0.133440 + 0.0552725i −0.448404 0.893831i \(-0.648007\pi\)
0.314964 + 0.949103i \(0.398007\pi\)
\(572\) 1.72560 0.569661i 0.0721508 0.0238187i
\(573\) 0 0
\(574\) −27.7382 20.0535i −1.15777 0.837018i
\(575\) 12.7939 0.533544
\(576\) 0 0
\(577\) 25.0765 1.04395 0.521974 0.852961i \(-0.325196\pi\)
0.521974 + 0.852961i \(0.325196\pi\)
\(578\) 6.67240 + 4.82386i 0.277535 + 0.200646i
\(579\) 0 0
\(580\) −28.1490 + 9.29268i −1.16882 + 0.385857i
\(581\) −6.12388 + 2.53659i −0.254061 + 0.105236i
\(582\) 0 0
\(583\) 22.2041 22.2041i 0.919602 0.919602i
\(584\) −6.68119 + 3.46379i −0.276470 + 0.143333i
\(585\) 0 0
\(586\) 41.3682 + 9.82884i 1.70890 + 0.406026i
\(587\) 7.42363 + 17.9222i 0.306406 + 0.739729i 0.999816 + 0.0191861i \(0.00610750\pi\)
−0.693410 + 0.720543i \(0.743892\pi\)
\(588\) 0 0
\(589\) −32.0790 13.2876i −1.32179 0.547505i
\(590\) 9.91933 1.59497i 0.408372 0.0656641i
\(591\) 0 0
\(592\) −19.0868 + 31.8143i −0.784462 + 1.30756i
\(593\) 29.1981i 1.19902i −0.800367 0.599510i \(-0.795362\pi\)
0.800367 0.599510i \(-0.204638\pi\)
\(594\) 0 0
\(595\) 59.4248 + 24.6146i 2.43618 + 1.00910i
\(596\) −4.03942 + 3.48296i −0.165461 + 0.142668i
\(597\) 0 0
\(598\) 0.145408 0.612000i 0.00594617 0.0250265i
\(599\) −12.1085 12.1085i −0.494741 0.494741i 0.415055 0.909796i \(-0.363762\pi\)
−0.909796 + 0.415055i \(0.863762\pi\)
\(600\) 0 0
\(601\) −29.2254 + 29.2254i −1.19213 + 1.19213i −0.215663 + 0.976468i \(0.569191\pi\)
−0.976468 + 0.215663i \(0.930809\pi\)
\(602\) −1.43453 2.32865i −0.0584673 0.0949085i
\(603\) 0 0
\(604\) 13.3216 26.4517i 0.542047 1.07630i
\(605\) 22.1706 53.5245i 0.901361 2.17608i
\(606\) 0 0
\(607\) 9.78275 0.397070 0.198535 0.980094i \(-0.436382\pi\)
0.198535 + 0.980094i \(0.436382\pi\)
\(608\) −18.7658 7.51592i −0.761053 0.304811i
\(609\) 0 0
\(610\) −23.5241 + 32.5387i −0.952465 + 1.31746i
\(611\) 0.391391 0.944901i 0.0158340 0.0382266i
\(612\) 0 0
\(613\) 15.8338 6.55859i 0.639522 0.264899i −0.0392705 0.999229i \(-0.512503\pi\)
0.678793 + 0.734330i \(0.262503\pi\)
\(614\) 13.7828 + 22.3732i 0.556227 + 0.902910i
\(615\) 0 0
\(616\) 42.5252 50.5074i 1.71339 2.03500i
\(617\) −29.1705 29.1705i −1.17436 1.17436i −0.981159 0.193200i \(-0.938113\pi\)
−0.193200 0.981159i \(-0.561887\pi\)
\(618\) 0 0
\(619\) −13.8703 33.4858i −0.557494 1.34591i −0.911744 0.410759i \(-0.865264\pi\)
0.354250 0.935151i \(-0.384736\pi\)
\(620\) −39.7506 46.1014i −1.59642 1.85148i
\(621\) 0 0
\(622\) 4.35536 + 27.0865i 0.174634 + 1.08607i
\(623\) 8.03532i 0.321928i
\(624\) 0 0
\(625\) 25.9039i 1.03616i
\(626\) −17.1265 + 2.75385i −0.684514 + 0.110066i
\(627\) 0 0
\(628\) 17.5808 + 1.30052i 0.701550 + 0.0518963i
\(629\) 16.9565 + 40.9367i 0.676101 + 1.63225i
\(630\) 0 0
\(631\) −6.70079 6.70079i −0.266754 0.266754i 0.561037 0.827791i \(-0.310403\pi\)
−0.827791 + 0.561037i \(0.810403\pi\)
\(632\) −40.6143 12.8805i −1.61555 0.512359i
\(633\) 0 0
\(634\) 1.52885 0.941828i 0.0607183 0.0374048i
\(635\) 3.74674 1.55195i 0.148685 0.0615872i
\(636\) 0 0
\(637\) 0.734672 1.77365i 0.0291088 0.0702748i
\(638\) 29.4510 + 21.2918i 1.16598 + 0.842951i
\(639\) 0 0
\(640\) −23.4563 26.5661i −0.927192 1.05012i
\(641\) 8.08573 0.319367 0.159684 0.987168i \(-0.448953\pi\)
0.159684 + 0.987168i \(0.448953\pi\)
\(642\) 0 0
\(643\) 5.26286 12.7057i 0.207547 0.501062i −0.785489 0.618876i \(-0.787588\pi\)
0.993036 + 0.117813i \(0.0375885\pi\)
\(644\) −7.16478 21.7033i −0.282332 0.855229i
\(645\) 0 0
\(646\) −20.5555 + 12.6630i −0.808745 + 0.498218i
\(647\) −1.82520 + 1.82520i −0.0717562 + 0.0717562i −0.742074 0.670318i \(-0.766158\pi\)
0.670318 + 0.742074i \(0.266158\pi\)
\(648\) 0 0
\(649\) −8.70938 8.70938i −0.341873 0.341873i
\(650\) −1.10771 0.263186i −0.0434481 0.0103230i
\(651\) 0 0
\(652\) 45.7496 + 3.38427i 1.79169 + 0.132538i
\(653\) −6.14025 2.54338i −0.240287 0.0995300i 0.259290 0.965799i \(-0.416511\pi\)
−0.499577 + 0.866269i \(0.666511\pi\)
\(654\) 0 0
\(655\) 6.01277i 0.234938i
\(656\) 22.2781 + 3.31413i 0.869815 + 0.129395i
\(657\) 0 0
\(658\) −5.89944 36.6893i −0.229984 1.43030i
\(659\) 19.1064 + 7.91412i 0.744278 + 0.308290i 0.722405 0.691471i \(-0.243037\pi\)
0.0218737 + 0.999761i \(0.493037\pi\)
\(660\) 0 0
\(661\) 3.64083 + 8.78973i 0.141612 + 0.341881i 0.978734 0.205135i \(-0.0657635\pi\)
−0.837122 + 0.547016i \(0.815763\pi\)
\(662\) −2.87810 + 12.1135i −0.111860 + 0.470804i
\(663\) 0 0
\(664\) 2.80929 3.33661i 0.109021 0.129485i
\(665\) −34.0219 + 34.0219i −1.31931 + 1.31931i
\(666\) 0 0
\(667\) 11.6223 4.81412i 0.450018 0.186403i
\(668\) 4.01682 + 2.02294i 0.155415 + 0.0782701i
\(669\) 0 0
\(670\) 33.1512 45.8549i 1.28074 1.77153i
\(671\) 49.2244 1.90029
\(672\) 0 0
\(673\) −40.0366 −1.54330 −0.771648 0.636050i \(-0.780567\pi\)
−0.771648 + 0.636050i \(0.780567\pi\)
\(674\) 5.60209 7.74885i 0.215785 0.298475i
\(675\) 0 0
\(676\) 11.6696 23.1714i 0.448829 0.891208i
\(677\) −19.7757 + 8.19136i −0.760041 + 0.314819i −0.728831 0.684693i \(-0.759936\pi\)
−0.0312100 + 0.999513i \(0.509936\pi\)
\(678\) 0 0
\(679\) 3.23143 3.23143i 0.124011 0.124011i
\(680\) −42.1707 + 3.61826i −1.61717 + 0.138754i
\(681\) 0 0
\(682\) −17.2508 + 72.6061i −0.660567 + 2.78023i
\(683\) −2.17719 5.25621i −0.0833080 0.201123i 0.876736 0.480971i \(-0.159716\pi\)
−0.960044 + 0.279848i \(0.909716\pi\)
\(684\) 0 0
\(685\) −30.5270 12.6447i −1.16638 0.483129i
\(686\) −4.31857 26.8577i −0.164884 1.02543i
\(687\) 0 0
\(688\) 1.54333 + 0.925908i 0.0588388 + 0.0352999i
\(689\) 0.967323i 0.0368521i
\(690\) 0 0
\(691\) 22.9683 + 9.51376i 0.873754 + 0.361921i 0.774071 0.633099i \(-0.218217\pi\)
0.0996825 + 0.995019i \(0.468217\pi\)
\(692\) −0.727502 + 9.83459i −0.0276555 + 0.373855i
\(693\) 0 0
\(694\) −26.6403 6.32960i −1.01125 0.240268i
\(695\) 25.9798 + 25.9798i 0.985470 + 0.985470i
\(696\) 0 0
\(697\) 19.0210 19.0210i 0.720472 0.720472i
\(698\) −12.3831 + 7.62844i −0.468706 + 0.288741i
\(699\) 0 0
\(700\) −39.2827 + 12.9682i −1.48475 + 0.490151i
\(701\) −3.00103 + 7.24514i −0.113348 + 0.273645i −0.970366 0.241641i \(-0.922314\pi\)
0.857018 + 0.515286i \(0.172314\pi\)
\(702\) 0 0
\(703\) −33.1450 −1.25009
\(704\) −9.54587 + 42.3858i −0.359773 + 1.59748i
\(705\) 0 0
\(706\) 4.17649 + 3.01942i 0.157184 + 0.113638i
\(707\) 9.39597 22.6839i 0.353372 0.853115i
\(708\) 0 0
\(709\) 15.4583 6.40306i 0.580550 0.240472i −0.0730290 0.997330i \(-0.523267\pi\)
0.653579 + 0.756858i \(0.273267\pi\)
\(710\) −43.7752 + 26.9672i −1.64286 + 1.01206i
\(711\) 0 0
\(712\) 2.43366 + 4.69420i 0.0912051 + 0.175923i
\(713\) 18.2666 + 18.2666i 0.684089 + 0.684089i
\(714\) 0 0
\(715\) 1.08916 + 2.62947i 0.0407324 + 0.0983368i
\(716\) −2.22672 + 30.1015i −0.0832165 + 1.12495i
\(717\) 0 0
\(718\) −17.1061 + 2.75056i −0.638393 + 0.102650i
\(719\) 34.6573i 1.29250i −0.763125 0.646250i \(-0.776336\pi\)
0.763125 0.646250i \(-0.223664\pi\)
\(720\) 0 0
\(721\) 25.1754i 0.937581i
\(722\) 1.39869 + 8.69864i 0.0520540 + 0.323730i
\(723\) 0 0
\(724\) −13.5484 + 11.6820i −0.503521 + 0.434157i
\(725\) −8.71350 21.0363i −0.323611 0.781267i
\(726\) 0 0
\(727\) −15.5200 15.5200i −0.575605 0.575605i 0.358084 0.933689i \(-0.383430\pi\)
−0.933689 + 0.358084i \(0.883430\pi\)
\(728\) 0.173873 + 2.02648i 0.00644415 + 0.0751064i
\(729\) 0 0
\(730\) −6.18223 10.0355i −0.228815 0.371429i
\(731\) 1.98586 0.822569i 0.0734496 0.0304238i
\(732\) 0 0
\(733\) −13.9034 + 33.5658i −0.513534 + 1.23978i 0.428279 + 0.903646i \(0.359120\pi\)
−0.941814 + 0.336135i \(0.890880\pi\)
\(734\) 25.9674 35.9183i 0.958475 1.32577i
\(735\) 0 0
\(736\) 10.7589 + 10.5090i 0.396579 + 0.387366i
\(737\) −69.3690 −2.55524
\(738\) 0 0
\(739\) 12.0261 29.0335i 0.442386 1.06801i −0.532724 0.846289i \(-0.678832\pi\)
0.975109 0.221724i \(-0.0711685\pi\)
\(740\) −51.8977 26.1367i −1.90780 0.960803i
\(741\) 0 0
\(742\) 18.4344 + 29.9242i 0.676749 + 1.09855i
\(743\) −25.4316 + 25.4316i −0.932995 + 0.932995i −0.997892 0.0648970i \(-0.979328\pi\)
0.0648970 + 0.997892i \(0.479328\pi\)
\(744\) 0 0
\(745\) −5.90693 5.90693i −0.216413 0.216413i
\(746\) 2.04930 8.62522i 0.0750303 0.315792i
\(747\) 0 0
\(748\) 33.8847 + 39.2984i 1.23895 + 1.43689i
\(749\) 45.9624 + 19.0383i 1.67943 + 0.695643i
\(750\) 0 0
\(751\) 36.6217i 1.33634i 0.744007 + 0.668172i \(0.232923\pi\)
−0.744007 + 0.668172i \(0.767077\pi\)
\(752\) 14.5585 + 19.6470i 0.530895 + 0.716452i
\(753\) 0 0
\(754\) −1.10530 + 0.177727i −0.0402528 + 0.00647244i
\(755\) 42.8554 + 17.7513i 1.55967 + 0.646036i
\(756\) 0 0
\(757\) −8.01093 19.3401i −0.291162 0.702928i 0.708835 0.705375i \(-0.249221\pi\)
−0.999997 + 0.00244664i \(0.999221\pi\)
\(758\) 31.1397 + 7.39862i 1.13104 + 0.268730i
\(759\) 0 0
\(760\) 9.57124 30.1796i 0.347185 1.09473i
\(761\) 16.1825 16.1825i 0.586617 0.586617i −0.350097 0.936714i \(-0.613851\pi\)
0.936714 + 0.350097i \(0.113851\pi\)
\(762\) 0 0
\(763\) −52.5722 + 21.7761i −1.90324 + 0.788348i
\(764\) −0.327324 0.991517i −0.0118422 0.0358718i
\(765\) 0 0
\(766\) 0.367323 + 0.265559i 0.0132719 + 0.00959503i
\(767\) 0.379424 0.0137002
\(768\) 0 0
\(769\) −10.8742 −0.392133 −0.196066 0.980591i \(-0.562817\pi\)
−0.196066 + 0.980591i \(0.562817\pi\)
\(770\) 83.8036 + 60.5864i 3.02007 + 2.18338i
\(771\) 0 0
\(772\) 6.86972 + 20.8095i 0.247247 + 0.748949i
\(773\) 39.3921 16.3167i 1.41683 0.586872i 0.462772 0.886478i \(-0.346855\pi\)
0.954063 + 0.299605i \(0.0968550\pi\)
\(774\) 0 0
\(775\) 33.0623 33.0623i 1.18763 1.18763i
\(776\) −0.909085 + 2.86649i −0.0326342 + 0.102901i
\(777\) 0 0
\(778\) −32.2685 7.66681i −1.15688 0.274868i
\(779\) 7.70033 + 18.5902i 0.275893 + 0.666064i
\(780\) 0 0
\(781\) 58.2348 + 24.1216i 2.08380 + 0.863140i
\(782\) 17.7342 2.85157i 0.634175 0.101972i
\(783\) 0 0
\(784\) 27.3275 + 36.8789i 0.975982 + 1.31711i
\(785\) 27.6106i 0.985464i
\(786\) 0 0
\(787\) 43.8276 + 18.1540i 1.56228 + 0.647119i 0.985484 0.169767i \(-0.0543014\pi\)
0.576799 + 0.816886i \(0.304301\pi\)
\(788\) −28.5060 33.0603i −1.01548 1.17772i
\(789\)