Properties

Label 360.2.w.d.163.1
Level $360$
Weight $2$
Character 360.163
Analytic conductor $2.875$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.w (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 5 x^{12} + 28 x^{8} + 80 x^{4} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 163.1
Root \(-0.512386 + 1.31813i\) of defining polynomial
Character \(\chi\) \(=\) 360.163
Dual form 360.2.w.d.307.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.31813 - 0.512386i) q^{2} +(1.47492 + 1.35078i) q^{4} +(1.83051 + 1.28422i) q^{5} +(2.94984 + 2.94984i) q^{7} +(-1.25201 - 2.53623i) q^{8} +O(q^{10})\) \(q+(-1.31813 - 0.512386i) q^{2} +(1.47492 + 1.35078i) q^{4} +(1.83051 + 1.28422i) q^{5} +(2.94984 + 2.94984i) q^{7} +(-1.25201 - 2.53623i) q^{8} +(-1.75483 - 2.63069i) q^{10} -1.61148 q^{11} +(-2.50967 + 2.50967i) q^{13} +(-2.37681 - 5.39972i) q^{14} +(0.350781 + 3.98459i) q^{16} +(-4.59398 + 4.59398i) q^{17} -4.00000i q^{19} +(0.965164 + 4.36674i) q^{20} +(2.12414 + 0.825702i) q^{22} +(1.09259 - 1.09259i) q^{23} +(1.70156 + 4.70156i) q^{25} +(4.59398 - 2.02214i) q^{26} +(0.366192 + 8.33537i) q^{28} +4.75362 q^{29} -5.01934i q^{31} +(1.57927 - 5.43193i) q^{32} +(8.40935 - 3.70156i) q^{34} +(1.61148 + 9.18797i) q^{35} +(2.50967 + 2.50967i) q^{37} +(-2.04955 + 5.27251i) q^{38} +(0.965252 - 6.25046i) q^{40} +9.18797 q^{41} +(-7.40312 - 7.40312i) q^{43} +(-2.37681 - 2.17676i) q^{44} +(-2.00000 + 0.880344i) q^{46} +(7.32206 + 7.32206i) q^{47} +10.4031i q^{49} +(0.166140 - 7.06912i) q^{50} +(-7.09158 + 0.311549i) q^{52} +(-3.11473 + 3.11473i) q^{53} +(-2.94984 - 2.06950i) q^{55} +(3.78824 - 11.1747i) q^{56} +(-6.26587 - 2.43569i) q^{58} -1.61148i q^{59} -6.78003i q^{61} +(-2.57184 + 6.61613i) q^{62} +(-4.86493 + 6.35078i) q^{64} +(-7.81695 + 1.37102i) q^{65} +(7.40312 - 7.40312i) q^{67} +(-12.9812 + 0.570295i) q^{68} +(2.58365 - 12.9366i) q^{70} +(5.00000 + 5.00000i) q^{73} +(-2.02214 - 4.59398i) q^{74} +(5.40312 - 5.89968i) q^{76} +(-4.75362 - 4.75362i) q^{77} +5.01934 q^{79} +(-4.47498 + 7.74433i) q^{80} +(-12.1109 - 4.70779i) q^{82} +(-7.57648 - 7.57648i) q^{83} +(-14.3090 + 2.50967i) q^{85} +(5.96500 + 13.5515i) q^{86} +(2.01759 + 4.08709i) q^{88} -2.74204i q^{89} -14.8062 q^{91} +(3.08733 - 0.135633i) q^{92} +(-5.89968 - 13.4031i) q^{94} +(5.13688 - 7.32206i) q^{95} +(2.40312 - 2.40312i) q^{97} +(5.33042 - 13.7126i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + O(q^{10}) \) \( 16 q - 8 q^{10} - 20 q^{16} + 36 q^{22} - 24 q^{25} + 44 q^{28} + 32 q^{40} - 16 q^{43} - 32 q^{46} - 8 q^{52} - 44 q^{58} + 16 q^{67} - 44 q^{70} + 80 q^{73} - 16 q^{76} - 8 q^{82} - 28 q^{88} - 32 q^{91} - 64 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31813 0.512386i −0.932057 0.362312i
\(3\) 0 0
\(4\) 1.47492 + 1.35078i 0.737460 + 0.675391i
\(5\) 1.83051 + 1.28422i 0.818631 + 0.574320i
\(6\) 0 0
\(7\) 2.94984 + 2.94984i 1.11494 + 1.11494i 0.992473 + 0.122462i \(0.0390789\pi\)
0.122462 + 0.992473i \(0.460921\pi\)
\(8\) −1.25201 2.53623i −0.442653 0.896693i
\(9\) 0 0
\(10\) −1.75483 2.63069i −0.554927 0.831899i
\(11\) −1.61148 −0.485880 −0.242940 0.970041i \(-0.578112\pi\)
−0.242940 + 0.970041i \(0.578112\pi\)
\(12\) 0 0
\(13\) −2.50967 + 2.50967i −0.696057 + 0.696057i −0.963558 0.267501i \(-0.913802\pi\)
0.267501 + 0.963558i \(0.413802\pi\)
\(14\) −2.37681 5.39972i −0.635229 1.44314i
\(15\) 0 0
\(16\) 0.350781 + 3.98459i 0.0876953 + 0.996147i
\(17\) −4.59398 + 4.59398i −1.11420 + 1.11420i −0.121629 + 0.992576i \(0.538812\pi\)
−0.992576 + 0.121629i \(0.961188\pi\)
\(18\) 0 0
\(19\) 4.00000i 0.917663i −0.888523 0.458831i \(-0.848268\pi\)
0.888523 0.458831i \(-0.151732\pi\)
\(20\) 0.965164 + 4.36674i 0.215817 + 0.976434i
\(21\) 0 0
\(22\) 2.12414 + 0.825702i 0.452868 + 0.176040i
\(23\) 1.09259 1.09259i 0.227821 0.227821i −0.583961 0.811782i \(-0.698498\pi\)
0.811782 + 0.583961i \(0.198498\pi\)
\(24\) 0 0
\(25\) 1.70156 + 4.70156i 0.340312 + 0.940312i
\(26\) 4.59398 2.02214i 0.900954 0.396575i
\(27\) 0 0
\(28\) 0.366192 + 8.33537i 0.0692037 + 1.57524i
\(29\) 4.75362 0.882725 0.441362 0.897329i \(-0.354495\pi\)
0.441362 + 0.897329i \(0.354495\pi\)
\(30\) 0 0
\(31\) 5.01934i 0.901500i −0.892650 0.450750i \(-0.851157\pi\)
0.892650 0.450750i \(-0.148843\pi\)
\(32\) 1.57927 5.43193i 0.279179 0.960239i
\(33\) 0 0
\(34\) 8.40935 3.70156i 1.44219 0.634813i
\(35\) 1.61148 + 9.18797i 0.272390 + 1.55305i
\(36\) 0 0
\(37\) 2.50967 + 2.50967i 0.412587 + 0.412587i 0.882639 0.470052i \(-0.155765\pi\)
−0.470052 + 0.882639i \(0.655765\pi\)
\(38\) −2.04955 + 5.27251i −0.332480 + 0.855314i
\(39\) 0 0
\(40\) 0.965252 6.25046i 0.152620 0.988285i
\(41\) 9.18797 1.43492 0.717460 0.696600i \(-0.245305\pi\)
0.717460 + 0.696600i \(0.245305\pi\)
\(42\) 0 0
\(43\) −7.40312 7.40312i −1.12897 1.12897i −0.990346 0.138620i \(-0.955733\pi\)
−0.138620 0.990346i \(-0.544267\pi\)
\(44\) −2.37681 2.17676i −0.358317 0.328159i
\(45\) 0 0
\(46\) −2.00000 + 0.880344i −0.294884 + 0.129800i
\(47\) 7.32206 + 7.32206i 1.06803 + 1.06803i 0.997510 + 0.0705213i \(0.0224663\pi\)
0.0705213 + 0.997510i \(0.477534\pi\)
\(48\) 0 0
\(49\) 10.4031i 1.48616i
\(50\) 0.166140 7.06912i 0.0234958 0.999724i
\(51\) 0 0
\(52\) −7.09158 + 0.311549i −0.983425 + 0.0432041i
\(53\) −3.11473 + 3.11473i −0.427841 + 0.427841i −0.887892 0.460051i \(-0.847831\pi\)
0.460051 + 0.887892i \(0.347831\pi\)
\(54\) 0 0
\(55\) −2.94984 2.06950i −0.397756 0.279051i
\(56\) 3.78824 11.1747i 0.506225 1.49328i
\(57\) 0 0
\(58\) −6.26587 2.43569i −0.822750 0.319822i
\(59\) 1.61148i 0.209797i −0.994483 0.104899i \(-0.966548\pi\)
0.994483 0.104899i \(-0.0334518\pi\)
\(60\) 0 0
\(61\) 6.78003i 0.868093i −0.900890 0.434047i \(-0.857085\pi\)
0.900890 0.434047i \(-0.142915\pi\)
\(62\) −2.57184 + 6.61613i −0.326624 + 0.840249i
\(63\) 0 0
\(64\) −4.86493 + 6.35078i −0.608117 + 0.793848i
\(65\) −7.81695 + 1.37102i −0.969573 + 0.170054i
\(66\) 0 0
\(67\) 7.40312 7.40312i 0.904436 0.904436i −0.0913805 0.995816i \(-0.529128\pi\)
0.995816 + 0.0913805i \(0.0291279\pi\)
\(68\) −12.9812 + 0.570295i −1.57421 + 0.0691584i
\(69\) 0 0
\(70\) 2.58365 12.9366i 0.308805 1.54622i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 5.00000 + 5.00000i 0.585206 + 0.585206i 0.936329 0.351123i \(-0.114200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −2.02214 4.59398i −0.235069 0.534040i
\(75\) 0 0
\(76\) 5.40312 5.89968i 0.619781 0.676740i
\(77\) −4.75362 4.75362i −0.541725 0.541725i
\(78\) 0 0
\(79\) 5.01934 0.564720 0.282360 0.959309i \(-0.408883\pi\)
0.282360 + 0.959309i \(0.408883\pi\)
\(80\) −4.47498 + 7.74433i −0.500318 + 0.865842i
\(81\) 0 0
\(82\) −12.1109 4.70779i −1.33743 0.519888i
\(83\) −7.57648 7.57648i −0.831627 0.831627i 0.156112 0.987739i \(-0.450104\pi\)
−0.987739 + 0.156112i \(0.950104\pi\)
\(84\) 0 0
\(85\) −14.3090 + 2.50967i −1.55203 + 0.272212i
\(86\) 5.96500 + 13.5515i 0.643223 + 1.46130i
\(87\) 0 0
\(88\) 2.01759 + 4.08709i 0.215076 + 0.435685i
\(89\) 2.74204i 0.290655i −0.989384 0.145328i \(-0.953576\pi\)
0.989384 0.145328i \(-0.0464236\pi\)
\(90\) 0 0
\(91\) −14.8062 −1.55212
\(92\) 3.08733 0.135633i 0.321877 0.0141408i
\(93\) 0 0
\(94\) −5.89968 13.4031i −0.608506 1.38243i
\(95\) 5.13688 7.32206i 0.527032 0.751227i
\(96\) 0 0
\(97\) 2.40312 2.40312i 0.244000 0.244000i −0.574503 0.818503i \(-0.694804\pi\)
0.818503 + 0.574503i \(0.194804\pi\)
\(98\) 5.33042 13.7126i 0.538454 1.38519i
\(99\) 0 0
\(100\) −3.84111 + 9.23287i −0.384111 + 0.923287i
\(101\) 8.79790i 0.875424i −0.899115 0.437712i \(-0.855789\pi\)
0.899115 0.437712i \(-0.144211\pi\)
\(102\) 0 0
\(103\) 7.96918 7.96918i 0.785227 0.785227i −0.195481 0.980707i \(-0.562627\pi\)
0.980707 + 0.195481i \(0.0626268\pi\)
\(104\) 9.50723 + 3.22296i 0.932261 + 0.316038i
\(105\) 0 0
\(106\) 5.70156 2.50967i 0.553785 0.243761i
\(107\) −1.61148 + 1.61148i −0.155788 + 0.155788i −0.780697 0.624909i \(-0.785136\pi\)
0.624909 + 0.780697i \(0.285136\pi\)
\(108\) 0 0
\(109\) −11.7994 −1.13017 −0.565087 0.825031i \(-0.691157\pi\)
−0.565087 + 0.825031i \(0.691157\pi\)
\(110\) 2.82788 + 4.23932i 0.269628 + 0.404203i
\(111\) 0 0
\(112\) −10.7192 + 12.7887i −1.01287 + 1.20841i
\(113\) −4.59398 4.59398i −0.432166 0.432166i 0.457199 0.889364i \(-0.348853\pi\)
−0.889364 + 0.457199i \(0.848853\pi\)
\(114\) 0 0
\(115\) 3.40312 0.596876i 0.317343 0.0556590i
\(116\) 7.01121 + 6.42110i 0.650974 + 0.596184i
\(117\) 0 0
\(118\) −0.825702 + 2.12414i −0.0760120 + 0.195543i
\(119\) −27.1030 −2.48453
\(120\) 0 0
\(121\) −8.40312 −0.763920
\(122\) −3.47399 + 8.93694i −0.314521 + 0.809112i
\(123\) 0 0
\(124\) 6.78003 7.40312i 0.608864 0.664820i
\(125\) −2.92310 + 10.7915i −0.261450 + 0.965217i
\(126\) 0 0
\(127\) 3.83019 + 3.83019i 0.339874 + 0.339874i 0.856320 0.516446i \(-0.172745\pi\)
−0.516446 + 0.856320i \(0.672745\pi\)
\(128\) 9.66666 5.87841i 0.854420 0.519583i
\(129\) 0 0
\(130\) 11.0062 + 2.19812i 0.965310 + 0.192788i
\(131\) 13.5415 1.18313 0.591563 0.806259i \(-0.298511\pi\)
0.591563 + 0.806259i \(0.298511\pi\)
\(132\) 0 0
\(133\) 11.7994 11.7994i 1.02313 1.02313i
\(134\) −13.5515 + 5.96500i −1.17067 + 0.515298i
\(135\) 0 0
\(136\) 17.4031 + 5.89968i 1.49231 + 0.505894i
\(137\) 11.0399 11.0399i 0.943203 0.943203i −0.0552681 0.998472i \(-0.517601\pi\)
0.998472 + 0.0552681i \(0.0176013\pi\)
\(138\) 0 0
\(139\) 4.00000i 0.339276i 0.985506 + 0.169638i \(0.0542598\pi\)
−0.985506 + 0.169638i \(0.945740\pi\)
\(140\) −10.0341 + 15.7283i −0.848038 + 1.32928i
\(141\) 0 0
\(142\) 0 0
\(143\) 4.04429 4.04429i 0.338200 0.338200i
\(144\) 0 0
\(145\) 8.70156 + 6.10469i 0.722625 + 0.506967i
\(146\) −4.02871 9.15257i −0.333418 0.757472i
\(147\) 0 0
\(148\) 0.311549 + 7.09158i 0.0256092 + 0.582924i
\(149\) 8.79790 0.720752 0.360376 0.932807i \(-0.382648\pi\)
0.360376 + 0.932807i \(0.382648\pi\)
\(150\) 0 0
\(151\) 0.880344i 0.0716414i −0.999358 0.0358207i \(-0.988595\pi\)
0.999358 0.0358207i \(-0.0114045\pi\)
\(152\) −10.1449 + 5.00805i −0.822862 + 0.406206i
\(153\) 0 0
\(154\) 3.83019 + 8.70156i 0.308645 + 0.701192i
\(155\) 6.44593 9.18797i 0.517750 0.737995i
\(156\) 0 0
\(157\) 9.28970 + 9.28970i 0.741398 + 0.741398i 0.972847 0.231449i \(-0.0743465\pi\)
−0.231449 + 0.972847i \(0.574347\pi\)
\(158\) −6.61613 2.57184i −0.526351 0.204605i
\(159\) 0 0
\(160\) 9.86668 7.91509i 0.780029 0.625743i
\(161\) 6.44593 0.508010
\(162\) 0 0
\(163\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) 13.5515 + 12.4109i 1.05820 + 0.969131i
\(165\) 0 0
\(166\) 6.10469 + 13.8689i 0.473816 + 1.07643i
\(167\) −7.32206 7.32206i −0.566598 0.566598i 0.364576 0.931174i \(-0.381214\pi\)
−0.931174 + 0.364576i \(0.881214\pi\)
\(168\) 0 0
\(169\) 0.403124i 0.0310096i
\(170\) 20.1471 + 4.02369i 1.54521 + 0.308603i
\(171\) 0 0
\(172\) −0.919020 20.9190i −0.0700746 1.59506i
\(173\) −7.86835 + 7.86835i −0.598220 + 0.598220i −0.939839 0.341619i \(-0.889025\pi\)
0.341619 + 0.939839i \(0.389025\pi\)
\(174\) 0 0
\(175\) −8.84952 + 18.8882i −0.668961 + 1.42781i
\(176\) −0.565278 6.42110i −0.0426094 0.484008i
\(177\) 0 0
\(178\) −1.40498 + 3.61436i −0.105308 + 0.270907i
\(179\) 26.4333i 1.97572i −0.155343 0.987861i \(-0.549648\pi\)
0.155343 0.987861i \(-0.450352\pi\)
\(180\) 0 0
\(181\) 11.7994i 0.877040i 0.898721 + 0.438520i \(0.144497\pi\)
−0.898721 + 0.438520i \(0.855503\pi\)
\(182\) 19.5165 + 7.58652i 1.44666 + 0.562350i
\(183\) 0 0
\(184\) −4.13899 1.40312i −0.305131 0.103440i
\(185\) 1.37102 + 7.81695i 0.100799 + 0.574713i
\(186\) 0 0
\(187\) 7.40312 7.40312i 0.541370 0.541370i
\(188\) 0.908956 + 20.6899i 0.0662924 + 1.50897i
\(189\) 0 0
\(190\) −10.5228 + 7.01934i −0.763403 + 0.509236i
\(191\) 19.0145i 1.37584i 0.725787 + 0.687919i \(0.241476\pi\)
−0.725787 + 0.687919i \(0.758524\pi\)
\(192\) 0 0
\(193\) −12.4031 12.4031i −0.892796 0.892796i 0.101989 0.994786i \(-0.467479\pi\)
−0.994786 + 0.101989i \(0.967479\pi\)
\(194\) −4.39895 + 1.93630i −0.315826 + 0.139018i
\(195\) 0 0
\(196\) −14.0523 + 15.3438i −1.00374 + 1.09598i
\(197\) −9.34420 9.34420i −0.665747 0.665747i 0.290982 0.956729i \(-0.406018\pi\)
−0.956729 + 0.290982i \(0.906018\pi\)
\(198\) 0 0
\(199\) −20.9577 −1.48565 −0.742826 0.669485i \(-0.766515\pi\)
−0.742826 + 0.669485i \(0.766515\pi\)
\(200\) 9.79387 10.2020i 0.692531 0.721388i
\(201\) 0 0
\(202\) −4.50793 + 11.5968i −0.317177 + 0.815945i
\(203\) 14.0224 + 14.0224i 0.984181 + 0.984181i
\(204\) 0 0
\(205\) 16.8187 + 11.7994i 1.17467 + 0.824103i
\(206\) −14.5877 + 6.42110i −1.01637 + 0.447379i
\(207\) 0 0
\(208\) −10.8803 9.11966i −0.754416 0.632334i
\(209\) 6.44593i 0.445874i
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) −8.80131 + 0.386661i −0.604476 + 0.0265560i
\(213\) 0 0
\(214\) 2.94984 1.29844i 0.201647 0.0887594i
\(215\) −4.04429 23.0588i −0.275818 1.57259i
\(216\) 0 0
\(217\) 14.8062 14.8062i 1.00511 1.00511i
\(218\) 15.5531 + 6.04583i 1.05339 + 0.409475i
\(219\) 0 0
\(220\) −1.55534 7.03693i −0.104861 0.474430i
\(221\) 23.0588i 1.55110i
\(222\) 0 0
\(223\) 3.83019 3.83019i 0.256488 0.256488i −0.567136 0.823624i \(-0.691949\pi\)
0.823624 + 0.567136i \(0.191949\pi\)
\(224\) 20.6819 11.3647i 1.38187 0.759338i
\(225\) 0 0
\(226\) 3.70156 + 8.40935i 0.246224 + 0.559382i
\(227\) −15.6339 + 15.6339i −1.03766 + 1.03766i −0.0383956 + 0.999263i \(0.512225\pi\)
−0.999263 + 0.0383956i \(0.987775\pi\)
\(228\) 0 0
\(229\) 6.78003 0.448037 0.224018 0.974585i \(-0.428082\pi\)
0.224018 + 0.974585i \(0.428082\pi\)
\(230\) −4.79158 0.956956i −0.315948 0.0630998i
\(231\) 0 0
\(232\) −5.95158 12.0563i −0.390741 0.791533i
\(233\) −11.0399 11.0399i −0.723249 0.723249i 0.246017 0.969266i \(-0.420878\pi\)
−0.969266 + 0.246017i \(0.920878\pi\)
\(234\) 0 0
\(235\) 4.00000 + 22.8062i 0.260931 + 1.48772i
\(236\) 2.17676 2.37681i 0.141695 0.154717i
\(237\) 0 0
\(238\) 35.7253 + 13.8872i 2.31573 + 0.900175i
\(239\) 8.08857 0.523206 0.261603 0.965176i \(-0.415749\pi\)
0.261603 + 0.965176i \(0.415749\pi\)
\(240\) 0 0
\(241\) −6.80625 −0.438429 −0.219215 0.975677i \(-0.570349\pi\)
−0.219215 + 0.975677i \(0.570349\pi\)
\(242\) 11.0764 + 4.30565i 0.712017 + 0.276777i
\(243\) 0 0
\(244\) 9.15833 10.0000i 0.586302 0.640184i
\(245\) −13.3599 + 19.0431i −0.853532 + 1.21662i
\(246\) 0 0
\(247\) 10.0387 + 10.0387i 0.638746 + 0.638746i
\(248\) −12.7302 + 6.28427i −0.808368 + 0.399051i
\(249\) 0 0
\(250\) 9.38242 12.7268i 0.593396 0.804911i
\(251\) −19.9874 −1.26159 −0.630797 0.775948i \(-0.717272\pi\)
−0.630797 + 0.775948i \(0.717272\pi\)
\(252\) 0 0
\(253\) −1.76069 + 1.76069i −0.110694 + 0.110694i
\(254\) −3.08614 7.01121i −0.193642 0.439922i
\(255\) 0 0
\(256\) −15.7539 + 2.79544i −0.984619 + 0.174715i
\(257\) 13.7820 13.7820i 0.859694 0.859694i −0.131607 0.991302i \(-0.542014\pi\)
0.991302 + 0.131607i \(0.0420138\pi\)
\(258\) 0 0
\(259\) 14.8062i 0.920016i
\(260\) −13.3813 8.53684i −0.829874 0.529432i
\(261\) 0 0
\(262\) −17.8494 6.93847i −1.10274 0.428660i
\(263\) −2.95170 + 2.95170i −0.182009 + 0.182009i −0.792231 0.610221i \(-0.791080\pi\)
0.610221 + 0.792231i \(0.291080\pi\)
\(264\) 0 0
\(265\) −9.70156 + 1.70156i −0.595962 + 0.104526i
\(266\) −21.5989 + 9.50723i −1.32431 + 0.582926i
\(267\) 0 0
\(268\) 20.9190 0.919020i 1.27783 0.0561381i
\(269\) 18.3051 1.11608 0.558042 0.829813i \(-0.311553\pi\)
0.558042 + 0.829813i \(0.311553\pi\)
\(270\) 0 0
\(271\) 12.6797i 0.770237i −0.922867 0.385119i \(-0.874160\pi\)
0.922867 0.385119i \(-0.125840\pi\)
\(272\) −19.9166 16.6937i −1.20762 1.01220i
\(273\) 0 0
\(274\) −20.2087 + 8.89531i −1.22085 + 0.537386i
\(275\) −2.74204 7.57648i −0.165351 0.456879i
\(276\) 0 0
\(277\) −7.52901 7.52901i −0.452374 0.452374i 0.443768 0.896142i \(-0.353642\pi\)
−0.896142 + 0.443768i \(0.853642\pi\)
\(278\) 2.04955 5.27251i 0.122924 0.316224i
\(279\) 0 0
\(280\) 21.2852 15.5905i 1.27203 0.931713i
\(281\) −27.5639 −1.64432 −0.822162 0.569253i \(-0.807232\pi\)
−0.822162 + 0.569253i \(0.807232\pi\)
\(282\) 0 0
\(283\) 7.40312 + 7.40312i 0.440070 + 0.440070i 0.892035 0.451965i \(-0.149277\pi\)
−0.451965 + 0.892035i \(0.649277\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −7.40312 + 3.25865i −0.437756 + 0.192688i
\(287\) 27.1030 + 27.1030i 1.59984 + 1.59984i
\(288\) 0 0
\(289\) 25.2094i 1.48290i
\(290\) −8.34181 12.5053i −0.489848 0.734337i
\(291\) 0 0
\(292\) 0.620697 + 14.1285i 0.0363236 + 0.826808i
\(293\) 3.11473 3.11473i 0.181965 0.181965i −0.610247 0.792211i \(-0.708930\pi\)
0.792211 + 0.610247i \(0.208930\pi\)
\(294\) 0 0
\(295\) 2.06950 2.94984i 0.120491 0.171746i
\(296\) 3.22296 9.50723i 0.187331 0.552597i
\(297\) 0 0
\(298\) −11.5968 4.50793i −0.671782 0.261137i
\(299\) 5.48408i 0.317152i
\(300\) 0 0
\(301\) 43.6761i 2.51745i
\(302\) −0.451076 + 1.16041i −0.0259565 + 0.0667739i
\(303\) 0 0
\(304\) 15.9384 1.40312i 0.914128 0.0804747i
\(305\) 8.70704 12.4109i 0.498564 0.710648i
\(306\) 0 0
\(307\) −20.0000 + 20.0000i −1.14146 + 1.14146i −0.153277 + 0.988183i \(0.548983\pi\)
−0.988183 + 0.153277i \(0.951017\pi\)
\(308\) −0.590111 13.4323i −0.0336247 0.765377i
\(309\) 0 0
\(310\) −13.2043 + 8.80811i −0.749956 + 0.500267i
\(311\) 8.08857i 0.458661i 0.973349 + 0.229330i \(0.0736537\pi\)
−0.973349 + 0.229330i \(0.926346\pi\)
\(312\) 0 0
\(313\) −19.8062 19.8062i −1.11952 1.11952i −0.991812 0.127703i \(-0.959240\pi\)
−0.127703 0.991812i \(-0.540760\pi\)
\(314\) −7.48509 17.0049i −0.422408 0.959643i
\(315\) 0 0
\(316\) 7.40312 + 6.78003i 0.416458 + 0.381406i
\(317\) −4.59058 4.59058i −0.257833 0.257833i 0.566339 0.824172i \(-0.308359\pi\)
−0.824172 + 0.566339i \(0.808359\pi\)
\(318\) 0 0
\(319\) −7.66037 −0.428898
\(320\) −17.0611 + 5.37755i −0.953746 + 0.300614i
\(321\) 0 0
\(322\) −8.49656 3.30281i −0.473495 0.184058i
\(323\) 18.3759 + 18.3759i 1.02246 + 1.02246i
\(324\) 0 0
\(325\) −16.0697 7.52901i −0.891388 0.417634i
\(326\) 0 0
\(327\) 0 0
\(328\) −11.5034 23.3028i −0.635171 1.28668i
\(329\) 43.1978i 2.38157i
\(330\) 0 0
\(331\) 2.80625 0.154245 0.0771227 0.997022i \(-0.475427\pi\)
0.0771227 + 0.997022i \(0.475427\pi\)
\(332\) −0.940541 21.4089i −0.0516189 1.17497i
\(333\) 0 0
\(334\) 5.89968 + 13.4031i 0.322816 + 0.733386i
\(335\) 23.0588 4.04429i 1.25983 0.220963i
\(336\) 0 0
\(337\) −2.40312 + 2.40312i −0.130907 + 0.130907i −0.769524 0.638618i \(-0.779507\pi\)
0.638618 + 0.769524i \(0.279507\pi\)
\(338\) 0.206555 0.531369i 0.0112351 0.0289027i
\(339\) 0 0
\(340\) −24.4947 15.6268i −1.32841 0.847483i
\(341\) 8.08857i 0.438021i
\(342\) 0 0
\(343\) −10.0387 + 10.0387i −0.542038 + 0.542038i
\(344\) −9.50723 + 28.0448i −0.512596 + 1.51208i
\(345\) 0 0
\(346\) 14.4031 6.33985i 0.774317 0.340833i
\(347\) 2.74204 2.74204i 0.147200 0.147200i −0.629666 0.776866i \(-0.716808\pi\)
0.776866 + 0.629666i \(0.216808\pi\)
\(348\) 0 0
\(349\) −6.78003 −0.362926 −0.181463 0.983398i \(-0.558083\pi\)
−0.181463 + 0.983398i \(0.558083\pi\)
\(350\) 21.3429 20.3627i 1.14082 1.08843i
\(351\) 0 0
\(352\) −2.54497 + 8.75346i −0.135648 + 0.466561i
\(353\) 13.7820 + 13.7820i 0.733539 + 0.733539i 0.971319 0.237780i \(-0.0764197\pi\)
−0.237780 + 0.971319i \(0.576420\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 3.70389 4.04429i 0.196306 0.214347i
\(357\) 0 0
\(358\) −13.5441 + 34.8425i −0.715827 + 1.84148i
\(359\) −35.1916 −1.85734 −0.928671 0.370904i \(-0.879048\pi\)
−0.928671 + 0.370904i \(0.879048\pi\)
\(360\) 0 0
\(361\) 3.00000 0.157895
\(362\) 6.04583 15.5531i 0.317762 0.817451i
\(363\) 0 0
\(364\) −21.8380 20.0000i −1.14462 1.04828i
\(365\) 2.73147 + 15.5737i 0.142972 + 0.815163i
\(366\) 0 0
\(367\) −14.7492 14.7492i −0.769902 0.769902i 0.208187 0.978089i \(-0.433244\pi\)
−0.978089 + 0.208187i \(0.933244\pi\)
\(368\) 4.73678 + 3.97026i 0.246922 + 0.206964i
\(369\) 0 0
\(370\) 2.19812 11.0062i 0.114275 0.572186i
\(371\) −18.3759 −0.954031
\(372\) 0 0
\(373\) 14.3090 14.3090i 0.740894 0.740894i −0.231856 0.972750i \(-0.574480\pi\)
0.972750 + 0.231856i \(0.0744799\pi\)
\(374\) −13.5515 + 5.96500i −0.700733 + 0.308443i
\(375\) 0 0
\(376\) 9.40312 27.7377i 0.484929 1.43046i
\(377\) −11.9300 + 11.9300i −0.614427 + 0.614427i
\(378\) 0 0
\(379\) 18.8062i 0.966012i 0.875617 + 0.483006i \(0.160455\pi\)
−0.875617 + 0.483006i \(0.839545\pi\)
\(380\) 17.4670 3.86065i 0.896037 0.198047i
\(381\) 0 0
\(382\) 9.74275 25.0635i 0.498483 1.28236i
\(383\) 26.0105 26.0105i 1.32907 1.32907i 0.422892 0.906180i \(-0.361015\pi\)
0.906180 0.422892i \(-0.138985\pi\)
\(384\) 0 0
\(385\) −2.59688 14.8062i −0.132349 0.754596i
\(386\) 9.99371 + 22.7041i 0.508666 + 1.15561i
\(387\) 0 0
\(388\) 6.79051 0.298323i 0.344736 0.0151450i
\(389\) 37.3196 1.89218 0.946090 0.323905i \(-0.104996\pi\)
0.946090 + 0.323905i \(0.104996\pi\)
\(390\) 0 0
\(391\) 10.0387i 0.507678i
\(392\) 26.3847 13.0248i 1.33263 0.657853i
\(393\) 0 0
\(394\) 7.52901 + 17.1047i 0.379306 + 0.861722i
\(395\) 9.18797 + 6.44593i 0.462297 + 0.324330i
\(396\) 0 0
\(397\) 19.3284 + 19.3284i 0.970063 + 0.970063i 0.999565 0.0295016i \(-0.00939202\pi\)
−0.0295016 + 0.999565i \(0.509392\pi\)
\(398\) 27.6249 + 10.7384i 1.38471 + 0.538269i
\(399\) 0 0
\(400\) −18.1369 + 8.42925i −0.906846 + 0.421462i
\(401\) 12.8919 0.643789 0.321894 0.946776i \(-0.395680\pi\)
0.321894 + 0.946776i \(0.395680\pi\)
\(402\) 0 0
\(403\) 12.5969 + 12.5969i 0.627495 + 0.627495i
\(404\) 11.8840 12.9762i 0.591253 0.645591i
\(405\) 0 0
\(406\) −11.2984 25.6682i −0.560732 1.27389i
\(407\) −4.04429 4.04429i −0.200468 0.200468i
\(408\) 0 0
\(409\) 3.40312i 0.168274i −0.996454 0.0841368i \(-0.973187\pi\)
0.996454 0.0841368i \(-0.0268133\pi\)
\(410\) −16.1234 24.1707i −0.796276 1.19371i
\(411\) 0 0
\(412\) 22.5185 0.989290i 1.10941 0.0487388i
\(413\) 4.75362 4.75362i 0.233910 0.233910i
\(414\) 0 0
\(415\) −4.13899 23.5987i −0.203175 1.15842i
\(416\) 9.66889 + 17.5958i 0.474057 + 0.862706i
\(417\) 0 0
\(418\) 3.30281 8.49656i 0.161546 0.415580i
\(419\) 31.9174i 1.55927i 0.626235 + 0.779634i \(0.284595\pi\)
−0.626235 + 0.779634i \(0.715405\pi\)
\(420\) 0 0
\(421\) 30.3788i 1.48057i 0.672293 + 0.740285i \(0.265309\pi\)
−0.672293 + 0.740285i \(0.734691\pi\)
\(422\) −15.8175 6.14864i −0.769985 0.299311i
\(423\) 0 0
\(424\) 11.7994 + 4.00000i 0.573028 + 0.194257i
\(425\) −29.4158 13.7820i −1.42688 0.668523i
\(426\) 0 0
\(427\) 20.0000 20.0000i 0.967868 0.967868i
\(428\) −4.55357 + 0.200049i −0.220105 + 0.00966971i
\(429\) 0 0
\(430\) −6.48410 + 32.4666i −0.312691 + 1.56568i
\(431\) 27.1030i 1.30551i 0.757570 + 0.652754i \(0.226386\pi\)
−0.757570 + 0.652754i \(0.773614\pi\)
\(432\) 0 0
\(433\) 12.4031 + 12.4031i 0.596056 + 0.596056i 0.939261 0.343205i \(-0.111512\pi\)
−0.343205 + 0.939261i \(0.611512\pi\)
\(434\) −27.1030 + 11.9300i −1.30099 + 0.572659i
\(435\) 0 0
\(436\) −17.4031 15.9384i −0.833458 0.763309i
\(437\) −4.37036 4.37036i −0.209063 0.209063i
\(438\) 0 0
\(439\) 10.9190 0.521136 0.260568 0.965455i \(-0.416090\pi\)
0.260568 + 0.965455i \(0.416090\pi\)
\(440\) −1.55549 + 10.0725i −0.0741549 + 0.480188i
\(441\) 0 0
\(442\) −11.8150 + 30.3944i −0.561982 + 1.44571i
\(443\) −15.6339 15.6339i −0.742789 0.742789i 0.230325 0.973114i \(-0.426021\pi\)
−0.973114 + 0.230325i \(0.926021\pi\)
\(444\) 0 0
\(445\) 3.52138 5.01934i 0.166929 0.237939i
\(446\) −7.01121 + 3.08614i −0.331990 + 0.146133i
\(447\) 0 0
\(448\) −33.0846 + 4.38301i −1.56310 + 0.207078i
\(449\) 6.44593i 0.304202i 0.988365 + 0.152101i \(0.0486039\pi\)
−0.988365 + 0.152101i \(0.951396\pi\)
\(450\) 0 0
\(451\) −14.8062 −0.697199
\(452\) −0.570295 12.9812i −0.0268244 0.610586i
\(453\) 0 0
\(454\) 28.6181 12.5969i 1.34311 0.591201i
\(455\) −27.1030 19.0145i −1.27061 0.891412i
\(456\) 0 0
\(457\) −9.80625 + 9.80625i −0.458717 + 0.458717i −0.898234 0.439517i \(-0.855150\pi\)
0.439517 + 0.898234i \(0.355150\pi\)
\(458\) −8.93694 3.47399i −0.417596 0.162329i
\(459\) 0 0
\(460\) 5.82559 + 3.71653i 0.271619 + 0.173284i
\(461\) 18.3051i 0.852555i 0.904592 + 0.426278i \(0.140175\pi\)
−0.904592 + 0.426278i \(0.859825\pi\)
\(462\) 0 0
\(463\) −14.7492 + 14.7492i −0.685454 + 0.685454i −0.961224 0.275770i \(-0.911067\pi\)
0.275770 + 0.961224i \(0.411067\pi\)
\(464\) 1.66748 + 18.9412i 0.0774108 + 0.879324i
\(465\) 0 0
\(466\) 8.89531 + 20.2087i 0.412067 + 0.936151i
\(467\) 10.7994 10.7994i 0.499739 0.499739i −0.411618 0.911357i \(-0.635036\pi\)
0.911357 + 0.411618i \(0.135036\pi\)
\(468\) 0 0
\(469\) 43.6761 2.01677
\(470\) 6.41310 32.1111i 0.295814 1.48117i
\(471\) 0 0
\(472\) −4.08709 + 2.01759i −0.188124 + 0.0928673i
\(473\) 11.9300 + 11.9300i 0.548542 + 0.548542i
\(474\) 0 0
\(475\) 18.8062 6.80625i 0.862890 0.312292i
\(476\) −39.9748 36.6103i −1.83224 1.67803i
\(477\) 0 0
\(478\) −10.6618 4.14448i −0.487658 0.189564i
\(479\) 8.08857 0.369576 0.184788 0.982778i \(-0.440840\pi\)
0.184788 + 0.982778i \(0.440840\pi\)
\(480\) 0 0
\(481\) −12.5969 −0.574368
\(482\) 8.97150 + 3.48743i 0.408641 + 0.158848i
\(483\) 0 0
\(484\) −12.3939 11.3508i −0.563361 0.515945i
\(485\) 7.48509 1.31281i 0.339880 0.0596118i
\(486\) 0 0
\(487\) −2.06950 2.06950i −0.0937778 0.0937778i 0.658662 0.752439i \(-0.271123\pi\)
−0.752439 + 0.658662i \(0.771123\pi\)
\(488\) −17.1957 + 8.48867i −0.778413 + 0.384264i
\(489\) 0 0
\(490\) 27.3674 18.2558i 1.23634 0.824711i
\(491\) −11.2804 −0.509076 −0.254538 0.967063i \(-0.581923\pi\)
−0.254538 + 0.967063i \(0.581923\pi\)
\(492\) 0 0
\(493\) −21.8380 + 21.8380i −0.983536 + 0.983536i
\(494\) −8.08857 18.3759i −0.363922 0.826772i
\(495\) 0 0
\(496\) 20.0000 1.76069i 0.898027 0.0790573i
\(497\) 0 0
\(498\) 0 0
\(499\) 18.8062i 0.841883i −0.907088 0.420942i \(-0.861700\pi\)
0.907088 0.420942i \(-0.138300\pi\)
\(500\) −18.8882 + 11.9681i −0.844708 + 0.535228i
\(501\) 0 0
\(502\) 26.3460 + 10.2413i 1.17588 + 0.457091i
\(503\) −5.13688 + 5.13688i −0.229042 + 0.229042i −0.812292 0.583250i \(-0.801781\pi\)
0.583250 + 0.812292i \(0.301781\pi\)
\(504\) 0 0
\(505\) 11.2984 16.1047i 0.502774 0.716649i
\(506\) 3.22296 1.41866i 0.143278 0.0630671i
\(507\) 0 0
\(508\) 0.475477 + 10.8230i 0.0210959 + 0.480191i
\(509\) 12.8422 0.569220 0.284610 0.958643i \(-0.408136\pi\)
0.284610 + 0.958643i \(0.408136\pi\)
\(510\) 0 0
\(511\) 29.4984i 1.30493i
\(512\) 22.1980 + 4.38734i 0.981022 + 0.193895i
\(513\) 0 0
\(514\) −25.2281 + 11.1047i −1.11276 + 0.489807i
\(515\) 24.8219 4.35352i 1.09378 0.191839i
\(516\) 0 0
\(517\) −11.7994 11.7994i −0.518935 0.518935i
\(518\) 7.58652 19.5165i 0.333333 0.857507i
\(519\) 0 0
\(520\) 13.2641 + 18.1091i 0.581671 + 0.794135i
\(521\) 6.44593 0.282401 0.141201 0.989981i \(-0.454904\pi\)
0.141201 + 0.989981i \(0.454904\pi\)
\(522\) 0 0
\(523\) −5.19375 5.19375i −0.227107 0.227107i 0.584376 0.811483i \(-0.301339\pi\)
−0.811483 + 0.584376i \(0.801339\pi\)
\(524\) 19.9726 + 18.2916i 0.872508 + 0.799072i
\(525\) 0 0
\(526\) 5.40312 2.37830i 0.235587 0.103699i
\(527\) 23.0588 + 23.0588i 1.00446 + 1.00446i
\(528\) 0 0
\(529\) 20.6125i 0.896196i
\(530\) 13.6598 + 2.72807i 0.593342 + 0.118500i
\(531\) 0 0
\(532\) 33.3415 1.46477i 1.44554 0.0635057i
\(533\) −23.0588 + 23.0588i −0.998786 + 0.998786i
\(534\) 0 0
\(535\) −5.01934 + 0.880344i −0.217005 + 0.0380606i
\(536\) −28.0448 9.50723i −1.21135 0.410650i
\(537\) 0 0
\(538\) −24.1285 9.37930i −1.04025 0.404370i
\(539\) 16.7645i 0.722096i
\(540\) 0 0
\(541\) 8.27799i 0.355898i 0.984040 + 0.177949i \(0.0569463\pi\)
−0.984040 + 0.177949i \(0.943054\pi\)
\(542\) −6.49691 + 16.7135i −0.279066 + 0.717905i
\(543\) 0 0
\(544\) 17.6990 + 32.2094i 0.758840 + 1.38097i
\(545\) −21.5989 15.1530i −0.925195 0.649082i
\(546\) 0 0
\(547\) −22.2094 + 22.2094i −0.949604 + 0.949604i −0.998790 0.0491855i \(-0.984337\pi\)
0.0491855 + 0.998790i \(0.484337\pi\)
\(548\) 31.1955 1.37049i 1.33261 0.0585444i
\(549\) 0 0
\(550\) −0.267732 + 11.3918i −0.0114161 + 0.485746i
\(551\) 19.0145i 0.810044i
\(552\) 0 0
\(553\) 14.8062 + 14.8062i 0.629626 + 0.629626i
\(554\) 6.06643 + 13.7820i 0.257738 + 0.585539i
\(555\) 0 0
\(556\) −5.40312 + 5.89968i −0.229144 + 0.250202i
\(557\) −13.7146 13.7146i −0.581104 0.581104i 0.354102 0.935207i \(-0.384786\pi\)
−0.935207 + 0.354102i \(0.884786\pi\)
\(558\) 0 0
\(559\) 37.1588 1.57165
\(560\) −36.0450 + 9.64406i −1.52318 + 0.407536i
\(561\) 0 0
\(562\) 36.3327 + 14.1234i 1.53260 + 0.595758i
\(563\) −2.74204 2.74204i −0.115563 0.115563i 0.646960 0.762524i \(-0.276040\pi\)
−0.762524 + 0.646960i \(0.776040\pi\)
\(564\) 0 0
\(565\) −2.50967 14.3090i −0.105583 0.601986i
\(566\) −5.96500 13.5515i −0.250728 0.569613i
\(567\) 0 0
\(568\) 0 0
\(569\) 36.7519i 1.54072i −0.637610 0.770359i \(-0.720077\pi\)
0.637610 0.770359i \(-0.279923\pi\)
\(570\) 0 0
\(571\) 17.6125 0.737060 0.368530 0.929616i \(-0.379861\pi\)
0.368530 + 0.929616i \(0.379861\pi\)
\(572\) 11.4279 0.502056i 0.477827 0.0209920i
\(573\) 0 0
\(574\) −21.8380 49.6125i −0.911502 2.07079i
\(575\) 6.99599 + 3.27777i 0.291753 + 0.136692i
\(576\) 0 0
\(577\) 12.4031 12.4031i 0.516349 0.516349i −0.400116 0.916465i \(-0.631030\pi\)
0.916465 + 0.400116i \(0.131030\pi\)
\(578\) −12.9169 + 33.2292i −0.537274 + 1.38215i
\(579\) 0 0
\(580\) 4.58802 + 20.7578i 0.190507 + 0.861922i
\(581\) 44.6989i 1.85442i
\(582\) 0 0
\(583\) 5.01934 5.01934i 0.207880 0.207880i
\(584\) 6.42110 18.9412i 0.265707 0.783793i
\(585\) 0 0
\(586\) −5.70156 + 2.50967i −0.235529 + 0.103673i
\(587\) 1.61148 1.61148i 0.0665130 0.0665130i −0.673068 0.739581i \(-0.735024\pi\)
0.739581 + 0.673068i \(0.235024\pi\)
\(588\) 0 0
\(589\) −20.0774 −0.827273
\(590\) −4.23932 + 2.82788i −0.174530 + 0.116422i
\(591\) 0 0
\(592\) −9.11966 + 10.8803i −0.374816 + 0.447179i
\(593\) 4.59398 + 4.59398i 0.188652 + 0.188652i 0.795113 0.606461i \(-0.207411\pi\)
−0.606461 + 0.795113i \(0.707411\pi\)
\(594\) 0 0
\(595\) −49.6125 34.8062i −2.03391 1.42692i
\(596\) 12.9762 + 11.8840i 0.531526 + 0.486789i
\(597\) 0 0
\(598\) 2.80997 7.22871i 0.114908 0.295604i
\(599\) −27.1030 −1.10740 −0.553700 0.832716i \(-0.686785\pi\)
−0.553700 + 0.832716i \(0.686785\pi\)
\(600\) 0 0
\(601\) 20.2094 0.824358 0.412179 0.911103i \(-0.364768\pi\)
0.412179 + 0.911103i \(0.364768\pi\)
\(602\) −22.3790 + 57.5706i −0.912101 + 2.34640i
\(603\) 0 0
\(604\) 1.18915 1.29844i 0.0483859 0.0528327i
\(605\) −15.3820 10.7915i −0.625369 0.438735i
\(606\) 0 0
\(607\) 18.8882 + 18.8882i 0.766648 + 0.766648i 0.977515 0.210867i \(-0.0676285\pi\)
−0.210867 + 0.977515i \(0.567629\pi\)
\(608\) −21.7277 6.31710i −0.881176 0.256192i
\(609\) 0 0
\(610\) −17.8362 + 11.8978i −0.722166 + 0.481729i
\(611\) −36.7519 −1.48682
\(612\) 0 0
\(613\) −19.3284 + 19.3284i −0.780666 + 0.780666i −0.979943 0.199278i \(-0.936140\pi\)
0.199278 + 0.979943i \(0.436140\pi\)
\(614\) 36.6103 16.1148i 1.47747 0.650341i
\(615\) 0 0
\(616\) −6.10469 + 18.0079i −0.245965 + 0.725557i
\(617\) 7.33602 7.33602i 0.295337 0.295337i −0.543847 0.839184i \(-0.683033\pi\)
0.839184 + 0.543847i \(0.183033\pi\)
\(618\) 0 0
\(619\) 10.8062i 0.434340i −0.976134 0.217170i \(-0.930317\pi\)
0.976134 0.217170i \(-0.0696826\pi\)
\(620\) 21.9182 4.84448i 0.880255 0.194559i
\(621\) 0 0
\(622\) 4.14448 10.6618i 0.166178 0.427498i
\(623\) 8.08857 8.08857i 0.324062 0.324062i
\(624\) 0 0
\(625\) −19.2094 + 16.0000i −0.768375 + 0.640000i
\(626\) 15.9587 + 36.2556i 0.637838 + 1.44907i
\(627\) 0 0
\(628\) 1.15322 + 26.2499i 0.0460184 + 1.04749i
\(629\) −23.0588 −0.919413
\(630\) 0 0
\(631\) 25.0967i 0.999083i −0.866290 0.499542i \(-0.833502\pi\)
0.866290 0.499542i \(-0.166498\pi\)
\(632\) −6.28427 12.7302i −0.249975 0.506380i
\(633\) 0 0
\(634\) 3.69882 + 8.40312i 0.146899 + 0.333731i
\(635\) 2.09241 + 11.9300i 0.0830348 + 0.473428i
\(636\) 0 0
\(637\) −26.1084 26.1084i −1.03445 1.03445i
\(638\) 10.0973 + 3.92507i 0.399758 + 0.155395i
\(639\) 0 0
\(640\) 25.2441 + 1.65359i 0.997862 + 0.0653638i
\(641\) 2.74204 0.108304 0.0541520 0.998533i \(-0.482754\pi\)
0.0541520 + 0.998533i \(0.482754\pi\)
\(642\) 0 0
\(643\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(644\) 9.50723 + 8.70704i 0.374638 + 0.343105i
\(645\) 0 0
\(646\) −14.8062 33.6374i −0.582544 1.32345i
\(647\) −19.7810 19.7810i −0.777671 0.777671i 0.201763 0.979434i \(-0.435333\pi\)
−0.979434 + 0.201763i \(0.935333\pi\)
\(648\) 0 0
\(649\) 2.59688i 0.101936i
\(650\) 17.3242 + 18.1581i 0.679510 + 0.712219i
\(651\) 0 0
\(652\) 0 0
\(653\) −15.1904 + 15.1904i −0.594447 + 0.594447i −0.938829 0.344383i \(-0.888088\pi\)
0.344383 + 0.938829i \(0.388088\pi\)
\(654\) 0 0
\(655\) 24.7879 + 17.3902i 0.968543 + 0.679493i
\(656\) 3.22296 + 36.6103i 0.125836 + 1.42939i
\(657\) 0 0
\(658\) 22.1340 56.9402i 0.862872 2.21976i
\(659\) 4.83445i 0.188323i −0.995557 0.0941617i \(-0.969983\pi\)
0.995557 0.0941617i \(-0.0300171\pi\)
\(660\) 0 0
\(661\) 26.8574i 1.04463i 0.852752 + 0.522315i \(0.174932\pi\)
−0.852752 + 0.522315i \(0.825068\pi\)
\(662\) −3.69899 1.43788i −0.143765 0.0558849i
\(663\) 0 0
\(664\) −9.72987 + 28.7016i −0.377592 + 1.11384i
\(665\) 36.7519 6.44593i 1.42518 0.249962i
\(666\) 0 0
\(667\) 5.19375 5.19375i 0.201103 0.201103i
\(668\) −0.908956 20.6899i −0.0351686 0.800518i
\(669\) 0 0
\(670\) −32.4666 6.48410i −1.25429 0.250503i
\(671\) 10.9259i 0.421789i
\(672\) 0 0
\(673\) 15.0000 + 15.0000i 0.578208 + 0.578208i 0.934409 0.356202i \(-0.115928\pi\)
−0.356202 + 0.934409i \(0.615928\pi\)
\(674\) 4.39895 1.93630i 0.169441 0.0745833i
\(675\) 0 0
\(676\) −0.544533 + 0.594576i −0.0209436 + 0.0228683i
\(677\) −18.1421 18.1421i −0.697258 0.697258i 0.266560 0.963818i \(-0.414113\pi\)
−0.963818 + 0.266560i \(0.914113\pi\)
\(678\) 0 0
\(679\) 14.1777 0.544089
\(680\) 24.2802 + 33.1489i 0.931102 + 1.27120i
\(681\) 0 0
\(682\) 4.14448 10.6618i 0.158700 0.408260i
\(683\) −1.13056 1.13056i −0.0432595 0.0432595i 0.685146 0.728406i \(-0.259738\pi\)
−0.728406 + 0.685146i \(0.759738\pi\)
\(684\) 0 0
\(685\) 34.3864 6.03105i 1.31384 0.230434i
\(686\) 18.3759 8.08857i 0.701596 0.308823i
\(687\) 0 0
\(688\) 26.9015 32.0953i 1.02561 1.22362i
\(689\) 15.6339i 0.595604i
\(690\) 0 0
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) −22.2336 + 0.976773i −0.845195 + 0.0371313i
\(693\) 0 0
\(694\) −5.01934 + 2.20937i −0.190531 + 0.0838666i
\(695\) −5.13688 + 7.32206i −0.194853 + 0.277741i
\(696\) 0 0
\(697\) −42.2094 + 42.2094i −1.59879 + 1.59879i
\(698\) 8.93694 + 3.47399i 0.338268 + 0.131493i
\(699\) 0 0
\(700\) −38.5662 + 15.9048i −1.45766 + 0.601146i
\(701\) 3.33496i 0.125960i −0.998015 0.0629798i \(-0.979940\pi\)
0.998015 0.0629798i \(-0.0200604\pi\)
\(702\) 0 0
\(703\) 10.0387 10.0387i 0.378616 0.378616i
\(704\) 7.83976 10.2342i 0.295472 0.385715i
\(705\) 0 0
\(706\) −11.1047 25.2281i −0.417930 0.949470i
\(707\) 25.9524 25.9524i 0.976041 0.976041i
\(708\) 0 0
\(709\) −26.8574 −1.00865 −0.504325 0.863514i \(-0.668259\pi\)
−0.504325 + 0.863514i \(0.668259\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −6.95444 + 3.43306i −0.260629 + 0.128659i
\(713\) −5.48408 5.48408i −0.205380 0.205380i
\(714\) 0 0
\(715\) 12.5969 2.20937i 0.471096 0.0826259i
\(716\) 35.7057 38.9871i 1.33438 1.45702i
\(717\) 0 0
\(718\) 46.3870 + 18.0317i 1.73115 + 0.672937i
\(719\) 8.08857 0.301653 0.150826 0.988560i \(-0.451807\pi\)
0.150826 + 0.988560i \(0.451807\pi\)
\(720\) 0 0
\(721\) 47.0156 1.75095
\(722\) −3.95438 1.53716i −0.147167 0.0572071i
\(723\) 0 0
\(724\) −15.9384 + 17.4031i −0.592344 + 0.646782i
\(725\) 8.08857 + 22.3494i 0.300402 + 0.830037i
\(726\) 0 0
\(727\) −35.7069 35.7069i −1.32430 1.32430i −0.910261 0.414034i \(-0.864119\pi\)
−0.414034 0.910261i \(-0.635881\pi\)
\(728\) 18.5376 + 37.5521i 0.687049 + 1.39177i
\(729\) 0 0
\(730\) 4.37930 21.9276i 0.162085 0.811579i
\(731\) 68.0197 2.51580
\(732\) 0 0
\(733\) −2.50967 + 2.50967i −0.0926967 + 0.0926967i −0.751935 0.659238i \(-0.770879\pi\)
0.659238 + 0.751935i \(0.270879\pi\)
\(734\) 11.8840 + 26.9986i 0.438648 + 0.996537i
\(735\) 0 0
\(736\) −4.20937 7.66037i −0.155160 0.282365i
\(737\) −11.9300 + 11.9300i −0.439447 + 0.439447i
\(738\) 0 0
\(739\) 48.4187i 1.78111i −0.454873 0.890556i \(-0.650315\pi\)
0.454873 0.890556i \(-0.349685\pi\)
\(740\) −8.53684 + 13.3813i −0.313821 + 0.491907i
\(741\) 0 0
\(742\) 24.2218 + 9.41558i 0.889211 + 0.345657i
\(743\) −9.18116 + 9.18116i −0.336824 + 0.336824i −0.855171 0.518346i \(-0.826548\pi\)
0.518346 + 0.855171i \(0.326548\pi\)
\(744\) 0 0
\(745\) 16.1047 + 11.2984i 0.590030 + 0.413943i
\(746\) −26.1929 + 11.5294i −0.958990 + 0.422121i
\(747\) 0 0
\(748\) 20.9190 0.919020i 0.764875 0.0336027i
\(749\) −9.50723 −0.347387
\(750\) 0 0
\(751\) 15.0580i 0.549475i −0.961519 0.274737i \(-0.911409\pi\)
0.961519 0.274737i \(-0.0885909\pi\)
\(752\) −26.6069 + 31.7438i −0.970256 + 1.15758i
\(753\) 0 0
\(754\) 21.8380 9.61250i 0.795294 0.350066i
\(755\) 1.13056 1.61148i 0.0411451 0.0586479i
\(756\) 0 0
\(757\) −11.0504 11.0504i −0.401633 0.401633i 0.477175 0.878808i \(-0.341661\pi\)
−0.878808 + 0.477175i \(0.841661\pi\)
\(758\) 9.63606 24.7890i 0.349998 0.900378i
\(759\) 0 0
\(760\) −25.0019 3.86101i −0.906913 0.140053i
\(761\) 43.1978 1.56592 0.782960 0.622073i \(-0.213709\pi\)
0.782960 + 0.622073i \(0.213709\pi\)
\(762\) 0 0
\(763\) −34.8062 34.8062i −1.26007 1.26007i
\(764\) −25.6844 + 28.0448i −0.929228 + 1.01463i
\(765\) 0 0
\(766\) −47.6125 + 20.9577i −1.72031 + 0.757232i
\(767\) 4.04429 + 4.04429i 0.146031 + 0.146031i
\(768\) 0 0
\(769\) 1.40312i 0.0505980i −0.999680 0.0252990i \(-0.991946\pi\)
0.999680 0.0252990i \(-0.00805377\pi\)
\(770\) −4.16351 + 20.8471i −0.150042 + 0.751278i
\(771\) 0 0
\(772\) −1.53972 35.0475i −0.0554156 1.26139i
\(773\) 25.4642 25.4642i 0.915882 0.915882i −0.0808446 0.996727i \(-0.525762\pi\)
0.996727 + 0.0808446i \(0.0257617\pi\)
\(774\) 0 0
\(775\) 23.5987 8.54071i 0.847691 0.306792i
\(776\) −9.10362 3.08614i −0.326801 0.110786i
\(777\) 0 0
\(778\) −49.1920 19.1221i −1.76362 0.685559i
\(779\) 36.7519i 1.31677i
\(780\) 0 0
\(781\) 0 0
\(782\) 5.14368 13.2323i 0.183938 0.473184i
\(783\) 0 0
\(784\) −41.4522 + 3.64922i −1.48043 + 0.130329i
\(785\) 5.07491 + 28.9349i 0.181131 + 1.03273i
\(786\) 0 0
\(787\) −20.0000 + 20.0000i −0.712923 + 0.712923i −0.967146 0.254223i \(-0.918180\pi\)
0.254223 + 0.967146i \(0.418180\pi\)
\(788\) −1.15998 26.4039i −0.0413227 0.940601i
\(789\) 0 0