Properties

Label 637.2.x.b.80.8
Level $637$
Weight $2$
Character 637.80
Analytic conductor $5.086$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 80.8
Character \(\chi\) \(=\) 637.80
Dual form 637.2.x.b.215.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.664504 + 2.47996i) q^{2} +2.69629i q^{3} +(-3.97660 + 2.29589i) q^{4} +(0.103104 - 0.384791i) q^{5} +(-6.68671 + 1.79170i) q^{6} +(-4.70528 - 4.70528i) q^{8} -4.27000 q^{9} +O(q^{10})\) \(q+(0.664504 + 2.47996i) q^{2} +2.69629i q^{3} +(-3.97660 + 2.29589i) q^{4} +(0.103104 - 0.384791i) q^{5} +(-6.68671 + 1.79170i) q^{6} +(-4.70528 - 4.70528i) q^{8} -4.27000 q^{9} +1.02278 q^{10} +(2.56721 + 2.56721i) q^{11} +(-6.19040 - 10.7221i) q^{12} +(-3.44571 - 1.06165i) q^{13} +(1.03751 + 0.278000i) q^{15} +(3.95046 - 6.84240i) q^{16} +(-2.04856 - 3.54822i) q^{17} +(-2.83743 - 10.5895i) q^{18} +(0.569532 + 0.569532i) q^{19} +(0.473433 + 1.76688i) q^{20} +(-4.66067 + 8.07252i) q^{22} +(4.41149 + 2.54698i) q^{23} +(12.6868 - 12.6868i) q^{24} +(4.19269 + 2.42065i) q^{25} +(0.343169 - 9.25070i) q^{26} -3.42430i q^{27} +(1.00735 + 1.74478i) q^{29} +2.75772i q^{30} +(-6.06756 + 1.62580i) q^{31} +(6.73893 + 1.80569i) q^{32} +(-6.92197 + 6.92197i) q^{33} +(7.43817 - 7.43817i) q^{34} +(16.9801 - 9.80347i) q^{36} +(-1.73100 + 0.463819i) q^{37} +(-1.03396 + 1.79088i) q^{38} +(2.86252 - 9.29064i) q^{39} +(-2.29568 + 1.32541i) q^{40} +(-0.578490 + 2.15895i) q^{41} +(-2.65096 - 1.53053i) q^{43} +(-16.1028 - 4.31474i) q^{44} +(-0.440256 + 1.64306i) q^{45} +(-3.38495 + 12.6328i) q^{46} +(8.19540 + 2.19595i) q^{47} +(18.4491 + 10.6516i) q^{48} +(-3.21707 + 12.0063i) q^{50} +(9.56703 - 5.52353i) q^{51} +(16.1396 - 3.68921i) q^{52} +(-4.54674 + 7.87518i) q^{53} +(8.49214 - 2.27546i) q^{54} +(1.25253 - 0.723149i) q^{55} +(-1.53563 + 1.53563i) q^{57} +(-3.65761 + 3.65761i) q^{58} +(7.17731 + 1.92316i) q^{59} +(-4.76402 + 1.27652i) q^{60} +2.77536i q^{61} +(-8.06384 - 13.9670i) q^{62} +2.11035i q^{64} +(-0.763781 + 1.21642i) q^{65} +(-21.7659 - 12.5665i) q^{66} +(3.55672 - 3.55672i) q^{67} +(16.2926 + 9.40656i) q^{68} +(-6.86740 + 11.8947i) q^{69} +(-0.582978 - 2.17570i) q^{71} +(20.0916 + 20.0916i) q^{72} +(1.28173 + 4.78349i) q^{73} +(-2.30051 - 3.98460i) q^{74} +(-6.52679 + 11.3047i) q^{75} +(-3.57239 - 0.957219i) q^{76} +(24.9426 + 0.925283i) q^{78} +(1.80984 + 3.13473i) q^{79} +(-2.22558 - 2.22558i) q^{80} -3.57709 q^{81} -5.73853 q^{82} +(-5.36774 - 5.36774i) q^{83} +(-1.57654 + 0.422432i) q^{85} +(2.03409 - 7.59132i) q^{86} +(-4.70444 + 2.71611i) q^{87} -24.1589i q^{88} +(-3.09280 - 11.5425i) q^{89} -4.36728 q^{90} -23.3903 q^{92} +(-4.38363 - 16.3599i) q^{93} +21.7835i q^{94} +(0.277872 - 0.160430i) q^{95} +(-4.86867 + 18.1701i) q^{96} +(7.71975 - 2.06850i) q^{97} +(-10.9620 - 10.9620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + O(q^{10}) \) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + 20q^{11} - 8q^{15} + 12q^{16} - 64q^{18} + 4q^{22} + 12q^{23} + 4q^{29} + 64q^{32} + 4q^{37} + 36q^{39} - 48q^{43} - 84q^{44} - 108q^{46} - 44q^{50} + 12q^{51} - 36q^{53} - 92q^{57} + 44q^{58} + 28q^{60} + 28q^{65} + 64q^{67} + 84q^{71} + 4q^{72} - 24q^{74} + 148q^{78} + 40q^{79} - 56q^{81} + 36q^{85} + 108q^{86} + 24q^{92} - 24q^{93} + 84q^{95} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.664504 + 2.47996i 0.469875 + 1.75360i 0.640197 + 0.768211i \(0.278853\pi\)
−0.170322 + 0.985388i \(0.554481\pi\)
\(3\) 2.69629i 1.55671i 0.627827 + 0.778353i \(0.283945\pi\)
−0.627827 + 0.778353i \(0.716055\pi\)
\(4\) −3.97660 + 2.29589i −1.98830 + 1.14795i
\(5\) 0.103104 0.384791i 0.0461097 0.172084i −0.939031 0.343832i \(-0.888275\pi\)
0.985141 + 0.171748i \(0.0549416\pi\)
\(6\) −6.68671 + 1.79170i −2.72984 + 0.731458i
\(7\) 0 0
\(8\) −4.70528 4.70528i −1.66357 1.66357i
\(9\) −4.27000 −1.42333
\(10\) 1.02278 0.323432
\(11\) 2.56721 + 2.56721i 0.774044 + 0.774044i 0.978811 0.204767i \(-0.0656435\pi\)
−0.204767 + 0.978811i \(0.565644\pi\)
\(12\) −6.19040 10.7221i −1.78702 3.09520i
\(13\) −3.44571 1.06165i −0.955667 0.294449i
\(14\) 0 0
\(15\) 1.03751 + 0.278000i 0.267884 + 0.0717792i
\(16\) 3.95046 6.84240i 0.987615 1.71060i
\(17\) −2.04856 3.54822i −0.496850 0.860569i 0.503144 0.864203i \(-0.332177\pi\)
−0.999993 + 0.00363405i \(0.998843\pi\)
\(18\) −2.83743 10.5895i −0.668790 2.49596i
\(19\) 0.569532 + 0.569532i 0.130660 + 0.130660i 0.769412 0.638753i \(-0.220549\pi\)
−0.638753 + 0.769412i \(0.720549\pi\)
\(20\) 0.473433 + 1.76688i 0.105863 + 0.395086i
\(21\) 0 0
\(22\) −4.66067 + 8.07252i −0.993659 + 1.72107i
\(23\) 4.41149 + 2.54698i 0.919860 + 0.531081i 0.883590 0.468261i \(-0.155119\pi\)
0.0362693 + 0.999342i \(0.488453\pi\)
\(24\) 12.6868 12.6868i 2.58969 2.58969i
\(25\) 4.19269 + 2.42065i 0.838539 + 0.484131i
\(26\) 0.343169 9.25070i 0.0673009 1.81421i
\(27\) 3.42430i 0.659007i
\(28\) 0 0
\(29\) 1.00735 + 1.74478i 0.187060 + 0.323998i 0.944269 0.329175i \(-0.106771\pi\)
−0.757209 + 0.653173i \(0.773437\pi\)
\(30\) 2.75772i 0.503488i
\(31\) −6.06756 + 1.62580i −1.08977 + 0.292002i −0.758591 0.651567i \(-0.774112\pi\)
−0.331176 + 0.943569i \(0.607445\pi\)
\(32\) 6.73893 + 1.80569i 1.19129 + 0.319204i
\(33\) −6.92197 + 6.92197i −1.20496 + 1.20496i
\(34\) 7.43817 7.43817i 1.27563 1.27563i
\(35\) 0 0
\(36\) 16.9801 9.80347i 2.83002 1.63391i
\(37\) −1.73100 + 0.463819i −0.284574 + 0.0762514i −0.398283 0.917263i \(-0.630394\pi\)
0.113708 + 0.993514i \(0.463727\pi\)
\(38\) −1.03396 + 1.79088i −0.167731 + 0.290519i
\(39\) 2.86252 9.29064i 0.458371 1.48769i
\(40\) −2.29568 + 1.32541i −0.362979 + 0.209566i
\(41\) −0.578490 + 2.15895i −0.0903449 + 0.337172i −0.996273 0.0862606i \(-0.972508\pi\)
0.905928 + 0.423432i \(0.139175\pi\)
\(42\) 0 0
\(43\) −2.65096 1.53053i −0.404267 0.233404i 0.284057 0.958808i \(-0.408320\pi\)
−0.688323 + 0.725404i \(0.741653\pi\)
\(44\) −16.1028 4.31474i −2.42759 0.650472i
\(45\) −0.440256 + 1.64306i −0.0656295 + 0.244933i
\(46\) −3.38495 + 12.6328i −0.499084 + 1.86261i
\(47\) 8.19540 + 2.19595i 1.19542 + 0.320312i 0.801027 0.598629i \(-0.204288\pi\)
0.394395 + 0.918941i \(0.370954\pi\)
\(48\) 18.4491 + 10.6516i 2.66290 + 1.53743i
\(49\) 0 0
\(50\) −3.21707 + 12.0063i −0.454962 + 1.69794i
\(51\) 9.56703 5.52353i 1.33965 0.773449i
\(52\) 16.1396 3.68921i 2.23817 0.511601i
\(53\) −4.54674 + 7.87518i −0.624542 + 1.08174i 0.364087 + 0.931365i \(0.381381\pi\)
−0.988629 + 0.150374i \(0.951952\pi\)
\(54\) 8.49214 2.27546i 1.15563 0.309651i
\(55\) 1.25253 0.723149i 0.168891 0.0975094i
\(56\) 0 0
\(57\) −1.53563 + 1.53563i −0.203399 + 0.203399i
\(58\) −3.65761 + 3.65761i −0.480267 + 0.480267i
\(59\) 7.17731 + 1.92316i 0.934407 + 0.250374i 0.693733 0.720232i \(-0.255965\pi\)
0.240674 + 0.970606i \(0.422632\pi\)
\(60\) −4.76402 + 1.27652i −0.615032 + 0.164797i
\(61\) 2.77536i 0.355349i 0.984089 + 0.177674i \(0.0568574\pi\)
−0.984089 + 0.177674i \(0.943143\pi\)
\(62\) −8.06384 13.9670i −1.02411 1.77381i
\(63\) 0 0
\(64\) 2.11035i 0.263794i
\(65\) −0.763781 + 1.21642i −0.0947354 + 0.150878i
\(66\) −21.7659 12.5665i −2.67920 1.54684i
\(67\) 3.55672 3.55672i 0.434523 0.434523i −0.455641 0.890164i \(-0.650590\pi\)
0.890164 + 0.455641i \(0.150590\pi\)
\(68\) 16.2926 + 9.40656i 1.97577 + 1.14071i
\(69\) −6.86740 + 11.8947i −0.826737 + 1.43195i
\(70\) 0 0
\(71\) −0.582978 2.17570i −0.0691867 0.258208i 0.922666 0.385601i \(-0.126006\pi\)
−0.991852 + 0.127393i \(0.959339\pi\)
\(72\) 20.0916 + 20.0916i 2.36781 + 2.36781i
\(73\) 1.28173 + 4.78349i 0.150016 + 0.559866i 0.999481 + 0.0322210i \(0.0102580\pi\)
−0.849465 + 0.527645i \(0.823075\pi\)
\(74\) −2.30051 3.98460i −0.267429 0.463200i
\(75\) −6.52679 + 11.3047i −0.753649 + 1.30536i
\(76\) −3.57239 0.957219i −0.409781 0.109801i
\(77\) 0 0
\(78\) 24.9426 + 0.925283i 2.82419 + 0.104768i
\(79\) 1.80984 + 3.13473i 0.203622 + 0.352684i 0.949693 0.313183i \(-0.101395\pi\)
−0.746071 + 0.665867i \(0.768062\pi\)
\(80\) −2.22558 2.22558i −0.248828 0.248828i
\(81\) −3.57709 −0.397454
\(82\) −5.73853 −0.633715
\(83\) −5.36774 5.36774i −0.589186 0.589186i 0.348225 0.937411i \(-0.386785\pi\)
−0.937411 + 0.348225i \(0.886785\pi\)
\(84\) 0 0
\(85\) −1.57654 + 0.422432i −0.170999 + 0.0458191i
\(86\) 2.03409 7.59132i 0.219341 0.818593i
\(87\) −4.70444 + 2.71611i −0.504369 + 0.291198i
\(88\) 24.1589i 2.57535i
\(89\) −3.09280 11.5425i −0.327836 1.22350i −0.911430 0.411454i \(-0.865021\pi\)
0.583595 0.812045i \(-0.301646\pi\)
\(90\) −4.36728 −0.460351
\(91\) 0 0
\(92\) −23.3903 −2.43861
\(93\) −4.38363 16.3599i −0.454561 1.69645i
\(94\) 21.7835i 2.24680i
\(95\) 0.277872 0.160430i 0.0285091 0.0164597i
\(96\) −4.86867 + 18.1701i −0.496907 + 1.85448i
\(97\) 7.71975 2.06850i 0.783822 0.210024i 0.155353 0.987859i \(-0.450349\pi\)
0.628469 + 0.777835i \(0.283682\pi\)
\(98\) 0 0
\(99\) −10.9620 10.9620i −1.10172 1.10172i
\(100\) −22.2302 −2.22302
\(101\) −4.50245 −0.448011 −0.224005 0.974588i \(-0.571913\pi\)
−0.224005 + 0.974588i \(0.571913\pi\)
\(102\) 20.0555 + 20.0555i 1.98579 + 1.98579i
\(103\) 8.05002 + 13.9430i 0.793192 + 1.37385i 0.923981 + 0.382439i \(0.124916\pi\)
−0.130788 + 0.991410i \(0.541751\pi\)
\(104\) 11.2177 + 21.2084i 1.09998 + 2.07965i
\(105\) 0 0
\(106\) −22.5515 6.04265i −2.19039 0.586914i
\(107\) 5.40840 9.36762i 0.522850 0.905602i −0.476797 0.879014i \(-0.658202\pi\)
0.999646 0.0265887i \(-0.00846443\pi\)
\(108\) 7.86183 + 13.6171i 0.756505 + 1.31030i
\(109\) 0.863031 + 3.22088i 0.0826634 + 0.308504i 0.994861 0.101246i \(-0.0322828\pi\)
−0.912198 + 0.409749i \(0.865616\pi\)
\(110\) 2.62570 + 2.62570i 0.250350 + 0.250350i
\(111\) −1.25059 4.66728i −0.118701 0.442998i
\(112\) 0 0
\(113\) 3.82032 6.61699i 0.359386 0.622474i −0.628473 0.777832i \(-0.716320\pi\)
0.987858 + 0.155357i \(0.0496529\pi\)
\(114\) −4.82873 2.78787i −0.452252 0.261108i
\(115\) 1.43490 1.43490i 0.133805 0.133805i
\(116\) −8.01166 4.62553i −0.743864 0.429470i
\(117\) 14.7132 + 4.53325i 1.36023 + 0.419099i
\(118\) 19.0774i 1.75622i
\(119\) 0 0
\(120\) −3.57371 6.18984i −0.326233 0.565052i
\(121\) 2.18118i 0.198289i
\(122\) −6.88279 + 1.84424i −0.623139 + 0.166970i
\(123\) −5.82117 1.55978i −0.524877 0.140640i
\(124\) 20.3956 20.3956i 1.83158 1.83158i
\(125\) 2.77216 2.77216i 0.247950 0.247950i
\(126\) 0 0
\(127\) 10.8931 6.28911i 0.966602 0.558068i 0.0684037 0.997658i \(-0.478209\pi\)
0.898199 + 0.439590i \(0.144876\pi\)
\(128\) 8.24427 2.20905i 0.728697 0.195254i
\(129\) 4.12676 7.14775i 0.363341 0.629325i
\(130\) −3.52420 1.08584i −0.309093 0.0952341i
\(131\) −10.1944 + 5.88576i −0.890691 + 0.514241i −0.874169 0.485623i \(-0.838593\pi\)
−0.0165228 + 0.999863i \(0.505260\pi\)
\(132\) 11.6338 43.4180i 1.01259 3.77905i
\(133\) 0 0
\(134\) 11.1840 + 6.45709i 0.966151 + 0.557808i
\(135\) −1.31764 0.353060i −0.113404 0.0303866i
\(136\) −7.05628 + 26.3344i −0.605071 + 2.25816i
\(137\) 3.37005 12.5772i 0.287923 1.07454i −0.658754 0.752358i \(-0.728916\pi\)
0.946677 0.322184i \(-0.104417\pi\)
\(138\) −34.0618 9.12683i −2.89953 0.776927i
\(139\) −7.49780 4.32886i −0.635955 0.367169i 0.147099 0.989122i \(-0.453006\pi\)
−0.783055 + 0.621953i \(0.786340\pi\)
\(140\) 0 0
\(141\) −5.92093 + 22.0972i −0.498632 + 1.86092i
\(142\) 5.00827 2.89153i 0.420285 0.242652i
\(143\) −6.12038 11.5714i −0.511812 0.967645i
\(144\) −16.8685 + 29.2171i −1.40571 + 2.43476i
\(145\) 0.775238 0.207724i 0.0643800 0.0172506i
\(146\) −11.0112 + 6.35730i −0.911291 + 0.526134i
\(147\) 0 0
\(148\) 5.81861 5.81861i 0.478287 0.478287i
\(149\) −13.2090 + 13.2090i −1.08212 + 1.08212i −0.0858119 + 0.996311i \(0.527348\pi\)
−0.996311 + 0.0858119i \(0.972652\pi\)
\(150\) −32.3724 8.67416i −2.64320 0.708242i
\(151\) −13.5918 + 3.64190i −1.10608 + 0.296374i −0.765238 0.643747i \(-0.777379\pi\)
−0.340842 + 0.940120i \(0.610712\pi\)
\(152\) 5.35962i 0.434723i
\(153\) 8.74737 + 15.1509i 0.707183 + 1.22488i
\(154\) 0 0
\(155\) 2.50237i 0.200995i
\(156\) 9.94720 + 43.5172i 0.796413 + 3.48417i
\(157\) 12.1331 + 7.00506i 0.968328 + 0.559064i 0.898726 0.438510i \(-0.144494\pi\)
0.0696019 + 0.997575i \(0.477827\pi\)
\(158\) −6.57136 + 6.57136i −0.522790 + 0.522790i
\(159\) −21.2338 12.2593i −1.68395 0.972229i
\(160\) 1.38963 2.40690i 0.109860 0.190282i
\(161\) 0 0
\(162\) −2.37699 8.87104i −0.186754 0.696975i
\(163\) 6.70194 + 6.70194i 0.524936 + 0.524936i 0.919058 0.394122i \(-0.128951\pi\)
−0.394122 + 0.919058i \(0.628951\pi\)
\(164\) −2.65630 9.91345i −0.207422 0.774110i
\(165\) 1.94982 + 3.37719i 0.151794 + 0.262914i
\(166\) 9.74492 16.8787i 0.756353 1.31004i
\(167\) 9.41229 + 2.52202i 0.728345 + 0.195159i 0.603892 0.797066i \(-0.293616\pi\)
0.124453 + 0.992226i \(0.460282\pi\)
\(168\) 0 0
\(169\) 10.7458 + 7.31628i 0.826600 + 0.562790i
\(170\) −2.09523 3.62905i −0.160697 0.278335i
\(171\) −2.43191 2.43191i −0.185972 0.185972i
\(172\) 14.0557 1.07174
\(173\) −17.0066 −1.29299 −0.646496 0.762918i \(-0.723766\pi\)
−0.646496 + 0.762918i \(0.723766\pi\)
\(174\) −9.86198 9.86198i −0.747635 0.747635i
\(175\) 0 0
\(176\) 27.7076 7.42423i 2.08854 0.559622i
\(177\) −5.18539 + 19.3522i −0.389758 + 1.45460i
\(178\) 26.5697 15.3400i 1.99149 1.14978i
\(179\) 10.8682i 0.812328i 0.913800 + 0.406164i \(0.133134\pi\)
−0.913800 + 0.406164i \(0.866866\pi\)
\(180\) −2.02156 7.54457i −0.150678 0.562339i
\(181\) 20.7716 1.54394 0.771969 0.635661i \(-0.219272\pi\)
0.771969 + 0.635661i \(0.219272\pi\)
\(182\) 0 0
\(183\) −7.48319 −0.553173
\(184\) −8.77307 32.7415i −0.646759 2.41374i
\(185\) 0.713894i 0.0524865i
\(186\) 37.6591 21.7425i 2.76130 1.59424i
\(187\) 3.84993 14.3681i 0.281535 1.05070i
\(188\) −37.6315 + 10.0833i −2.74456 + 0.735402i
\(189\) 0 0
\(190\) 0.582507 + 0.582507i 0.0422595 + 0.0422595i
\(191\) 1.48438 0.107406 0.0537031 0.998557i \(-0.482898\pi\)
0.0537031 + 0.998557i \(0.482898\pi\)
\(192\) −5.69013 −0.410649
\(193\) −5.19197 5.19197i −0.373726 0.373726i 0.495106 0.868833i \(-0.335129\pi\)
−0.868833 + 0.495106i \(0.835129\pi\)
\(194\) 10.2596 + 17.7702i 0.736597 + 1.27582i
\(195\) −3.27981 2.05938i −0.234872 0.147475i
\(196\) 0 0
\(197\) 17.4416 + 4.67347i 1.24266 + 0.332971i 0.819499 0.573081i \(-0.194252\pi\)
0.423166 + 0.906052i \(0.360919\pi\)
\(198\) 19.9011 34.4697i 1.41431 2.44965i
\(199\) −1.63076 2.82456i −0.115602 0.200228i 0.802418 0.596762i \(-0.203546\pi\)
−0.918020 + 0.396534i \(0.870213\pi\)
\(200\) −8.33795 31.1177i −0.589582 2.20035i
\(201\) 9.58998 + 9.58998i 0.676425 + 0.676425i
\(202\) −2.99190 11.1659i −0.210509 0.785631i
\(203\) 0 0
\(204\) −25.3629 + 43.9298i −1.77576 + 3.07570i
\(205\) 0.771100 + 0.445195i 0.0538560 + 0.0310938i
\(206\) −29.2290 + 29.2290i −2.03648 + 2.03648i
\(207\) −18.8371 10.8756i −1.30927 0.755906i
\(208\) −20.8764 + 19.3829i −1.44752 + 1.34396i
\(209\) 2.92422i 0.202273i
\(210\) 0 0
\(211\) 1.10904 + 1.92091i 0.0763492 + 0.132241i 0.901672 0.432420i \(-0.142340\pi\)
−0.825323 + 0.564661i \(0.809007\pi\)
\(212\) 41.7553i 2.86776i
\(213\) 5.86633 1.57188i 0.401955 0.107703i
\(214\) 26.8253 + 7.18781i 1.83374 + 0.491348i
\(215\) −0.862259 + 0.862259i −0.0588056 + 0.0588056i
\(216\) −16.1123 + 16.1123i −1.09630 + 1.09630i
\(217\) 0 0
\(218\) −7.41417 + 4.28057i −0.502151 + 0.289917i
\(219\) −12.8977 + 3.45593i −0.871546 + 0.233530i
\(220\) −3.32055 + 5.75136i −0.223871 + 0.387756i
\(221\) 3.29178 + 14.4010i 0.221429 + 0.968714i
\(222\) 10.7437 6.20285i 0.721067 0.416308i
\(223\) −1.40793 + 5.25448i −0.0942823 + 0.351866i −0.996910 0.0785566i \(-0.974969\pi\)
0.902627 + 0.430423i \(0.141636\pi\)
\(224\) 0 0
\(225\) −17.9028 10.3362i −1.19352 0.689080i
\(226\) 18.9485 + 5.07724i 1.26044 + 0.337733i
\(227\) −0.0897430 + 0.334926i −0.00595646 + 0.0222298i −0.968840 0.247687i \(-0.920330\pi\)
0.962884 + 0.269917i \(0.0869962\pi\)
\(228\) 2.58094 9.63221i 0.170927 0.637909i
\(229\) 25.6082 + 6.86169i 1.69224 + 0.453433i 0.970965 0.239220i \(-0.0768919\pi\)
0.721270 + 0.692654i \(0.243559\pi\)
\(230\) 4.51199 + 2.60500i 0.297512 + 0.171768i
\(231\) 0 0
\(232\) 3.46982 12.9496i 0.227805 0.850180i
\(233\) −18.9024 + 10.9133i −1.23833 + 0.714953i −0.968754 0.248025i \(-0.920218\pi\)
−0.269581 + 0.962978i \(0.586885\pi\)
\(234\) −1.46533 + 39.5005i −0.0957916 + 2.58223i
\(235\) 1.68996 2.92710i 0.110241 0.190943i
\(236\) −32.9567 + 8.83072i −2.14530 + 0.574831i
\(237\) −8.45215 + 4.87985i −0.549026 + 0.316980i
\(238\) 0 0
\(239\) 2.02192 2.02192i 0.130787 0.130787i −0.638683 0.769470i \(-0.720520\pi\)
0.769470 + 0.638683i \(0.220520\pi\)
\(240\) 6.00082 6.00082i 0.387352 0.387352i
\(241\) 29.1475 + 7.81005i 1.87756 + 0.503090i 0.999708 + 0.0241515i \(0.00768840\pi\)
0.877849 + 0.478938i \(0.158978\pi\)
\(242\) −5.40925 + 1.44940i −0.347720 + 0.0931712i
\(243\) 19.9178i 1.27773i
\(244\) −6.37193 11.0365i −0.407921 0.706540i
\(245\) 0 0
\(246\) 15.4728i 0.986508i
\(247\) −1.35780 2.56709i −0.0863946 0.163340i
\(248\) 36.1994 + 20.8997i 2.29867 + 1.32714i
\(249\) 14.4730 14.4730i 0.917190 0.917190i
\(250\) 8.71697 + 5.03275i 0.551310 + 0.318299i
\(251\) −8.33953 + 14.4445i −0.526386 + 0.911728i 0.473141 + 0.880987i \(0.343120\pi\)
−0.999527 + 0.0307412i \(0.990213\pi\)
\(252\) 0 0
\(253\) 4.78661 + 17.8639i 0.300932 + 1.12309i
\(254\) 22.8352 + 22.8352i 1.43281 + 1.43281i
\(255\) −1.13900 4.25081i −0.0713269 0.266196i
\(256\) 13.0671 + 22.6328i 0.816691 + 1.41455i
\(257\) −6.10569 + 10.5754i −0.380863 + 0.659674i −0.991186 0.132479i \(-0.957706\pi\)
0.610323 + 0.792153i \(0.291040\pi\)
\(258\) 20.4684 + 5.48450i 1.27431 + 0.341450i
\(259\) 0 0
\(260\) 0.244494 6.59076i 0.0151629 0.408742i
\(261\) −4.30139 7.45022i −0.266249 0.461157i
\(262\) −21.3707 21.3707i −1.32029 1.32029i
\(263\) 14.6063 0.900662 0.450331 0.892862i \(-0.351306\pi\)
0.450331 + 0.892862i \(0.351306\pi\)
\(264\) 65.1396 4.00906
\(265\) 2.56151 + 2.56151i 0.157352 + 0.157352i
\(266\) 0 0
\(267\) 31.1219 8.33909i 1.90463 0.510344i
\(268\) −5.97782 + 22.3095i −0.365154 + 1.36277i
\(269\) 4.31634 2.49204i 0.263172 0.151942i −0.362609 0.931941i \(-0.618114\pi\)
0.625781 + 0.779999i \(0.284781\pi\)
\(270\) 3.50231i 0.213144i
\(271\) 6.85721 + 25.5915i 0.416546 + 1.55457i 0.781719 + 0.623631i \(0.214343\pi\)
−0.365173 + 0.930940i \(0.618990\pi\)
\(272\) −32.3711 −1.96278
\(273\) 0 0
\(274\) 33.4304 2.01960
\(275\) 4.54921 + 16.9779i 0.274328 + 1.02380i
\(276\) 63.0672i 3.79620i
\(277\) −17.6881 + 10.2122i −1.06277 + 0.613592i −0.926198 0.377038i \(-0.876943\pi\)
−0.136574 + 0.990630i \(0.543609\pi\)
\(278\) 5.75309 21.4708i 0.345047 1.28773i
\(279\) 25.9085 6.94216i 1.55110 0.415617i
\(280\) 0 0
\(281\) −3.86728 3.86728i −0.230703 0.230703i 0.582283 0.812986i \(-0.302159\pi\)
−0.812986 + 0.582283i \(0.802159\pi\)
\(282\) −58.7347 −3.49760
\(283\) −25.0379 −1.48835 −0.744174 0.667986i \(-0.767157\pi\)
−0.744174 + 0.667986i \(0.767157\pi\)
\(284\) 7.31345 + 7.31345i 0.433973 + 0.433973i
\(285\) 0.432565 + 0.749225i 0.0256230 + 0.0443803i
\(286\) 24.6295 22.8675i 1.45637 1.35219i
\(287\) 0 0
\(288\) −28.7753 7.71031i −1.69560 0.454334i
\(289\) 0.106779 0.184946i 0.00628111 0.0108792i
\(290\) 1.03030 + 1.78453i 0.0605012 + 0.104791i
\(291\) 5.57729 + 20.8147i 0.326946 + 1.22018i
\(292\) −16.0793 16.0793i −0.940972 0.940972i
\(293\) 4.77690 + 17.8276i 0.279069 + 1.04150i 0.953065 + 0.302766i \(0.0979100\pi\)
−0.673996 + 0.738735i \(0.735423\pi\)
\(294\) 0 0
\(295\) 1.48003 2.56348i 0.0861704 0.149251i
\(296\) 10.3272 + 5.96243i 0.600258 + 0.346559i
\(297\) 8.79091 8.79091i 0.510101 0.510101i
\(298\) −41.5353 23.9804i −2.40607 1.38915i
\(299\) −12.4967 13.4596i −0.722703 0.778389i
\(300\) 59.9393i 3.46059i
\(301\) 0 0
\(302\) −18.0636 31.2870i −1.03944 1.80036i
\(303\) 12.1399i 0.697421i
\(304\) 6.14688 1.64705i 0.352548 0.0944649i
\(305\) 1.06793 + 0.286152i 0.0611497 + 0.0163850i
\(306\) −31.7610 + 31.7610i −1.81565 + 1.81565i
\(307\) 14.6697 14.6697i 0.837243 0.837243i −0.151252 0.988495i \(-0.548330\pi\)
0.988495 + 0.151252i \(0.0483305\pi\)
\(308\) 0 0
\(309\) −37.5946 + 21.7052i −2.13868 + 1.23477i
\(310\) −6.20579 + 1.66284i −0.352465 + 0.0944427i
\(311\) 2.93074 5.07620i 0.166187 0.287845i −0.770889 0.636969i \(-0.780188\pi\)
0.937076 + 0.349125i \(0.113521\pi\)
\(312\) −57.1840 + 30.2461i −3.23741 + 1.71235i
\(313\) 17.6735 10.2038i 0.998967 0.576754i 0.0910244 0.995849i \(-0.470986\pi\)
0.907942 + 0.419095i \(0.137653\pi\)
\(314\) −9.30978 + 34.7446i −0.525381 + 1.96075i
\(315\) 0 0
\(316\) −14.3940 8.31037i −0.809725 0.467495i
\(317\) 7.40911 + 1.98526i 0.416137 + 0.111504i 0.460812 0.887498i \(-0.347558\pi\)
−0.0446745 + 0.999002i \(0.514225\pi\)
\(318\) 16.2928 60.8054i 0.913653 3.40980i
\(319\) −1.89314 + 7.06531i −0.105996 + 0.395582i
\(320\) 0.812043 + 0.217586i 0.0453946 + 0.0121634i
\(321\) 25.2579 + 14.5826i 1.40976 + 0.813923i
\(322\) 0 0
\(323\) 0.854101 3.18755i 0.0475234 0.177360i
\(324\) 14.2246 8.21260i 0.790258 0.456256i
\(325\) −11.8769 12.7920i −0.658812 0.709575i
\(326\) −12.1671 + 21.0740i −0.673873 + 1.16718i
\(327\) −8.68443 + 2.32699i −0.480250 + 0.128683i
\(328\) 12.8804 7.43652i 0.711203 0.410613i
\(329\) 0 0
\(330\) −7.07965 + 7.07965i −0.389722 + 0.389722i
\(331\) 17.8253 17.8253i 0.979770 0.979770i −0.0200296 0.999799i \(-0.506376\pi\)
0.999799 + 0.0200296i \(0.00637603\pi\)
\(332\) 33.6691 + 9.02162i 1.84783 + 0.495126i
\(333\) 7.39136 1.98051i 0.405044 0.108531i
\(334\) 25.0180i 1.36893i
\(335\) −1.00188 1.73531i −0.0547386 0.0948100i
\(336\) 0 0
\(337\) 30.1306i 1.64132i −0.571417 0.820660i \(-0.693606\pi\)
0.571417 0.820660i \(-0.306394\pi\)
\(338\) −11.0035 + 31.5109i −0.598510 + 1.71397i
\(339\) 17.8414 + 10.3007i 0.969010 + 0.559458i
\(340\) 5.29940 5.29940i 0.287400 0.287400i
\(341\) −19.7505 11.4030i −1.06955 0.617505i
\(342\) 4.41503 7.64705i 0.238737 0.413505i
\(343\) 0 0
\(344\) 5.27192 + 19.6751i 0.284243 + 1.06081i
\(345\) 3.86890 + 3.86890i 0.208295 + 0.208295i
\(346\) −11.3010 42.1759i −0.607545 2.26739i
\(347\) −17.2300 29.8433i −0.924957 1.60207i −0.791631 0.611000i \(-0.790768\pi\)
−0.133326 0.991072i \(-0.542566\pi\)
\(348\) 12.4718 21.6018i 0.668559 1.15798i
\(349\) −3.97028 1.06383i −0.212524 0.0569457i 0.150986 0.988536i \(-0.451755\pi\)
−0.363510 + 0.931590i \(0.618422\pi\)
\(350\) 0 0
\(351\) −3.63541 + 11.7991i −0.194044 + 0.629791i
\(352\) 12.6647 + 21.9359i 0.675030 + 1.16919i
\(353\) 7.69746 + 7.69746i 0.409694 + 0.409694i 0.881632 0.471938i \(-0.156445\pi\)
−0.471938 + 0.881632i \(0.656445\pi\)
\(354\) −51.4383 −2.73392
\(355\) −0.897298 −0.0476236
\(356\) 38.7991 + 38.7991i 2.05635 + 2.05635i
\(357\) 0 0
\(358\) −26.9528 + 7.22197i −1.42450 + 0.381693i
\(359\) 7.96687 29.7328i 0.420475 1.56923i −0.353135 0.935572i \(-0.614884\pi\)
0.773610 0.633662i \(-0.218449\pi\)
\(360\) 9.80258 5.65952i 0.516641 0.298283i
\(361\) 18.3513i 0.965856i
\(362\) 13.8028 + 51.5127i 0.725458 + 2.70745i
\(363\) −5.88111 −0.308678
\(364\) 0 0
\(365\) 1.97280 0.103261
\(366\) −4.97261 18.5580i −0.259923 0.970044i
\(367\) 24.9379i 1.30175i −0.759187 0.650873i \(-0.774403\pi\)
0.759187 0.650873i \(-0.225597\pi\)
\(368\) 34.8548 20.1235i 1.81693 1.04901i
\(369\) 2.47015 9.21873i 0.128591 0.479908i
\(370\) −1.77043 + 0.474385i −0.0920403 + 0.0246621i
\(371\) 0 0
\(372\) 54.9926 + 54.9926i 2.85123 + 2.85123i
\(373\) 18.1892 0.941803 0.470902 0.882186i \(-0.343929\pi\)
0.470902 + 0.882186i \(0.343929\pi\)
\(374\) 38.1907 1.97480
\(375\) 7.47456 + 7.47456i 0.385985 + 0.385985i
\(376\) −28.2291 48.8942i −1.45580 2.52153i
\(377\) −1.61868 7.08146i −0.0833665 0.364714i
\(378\) 0 0
\(379\) −0.810924 0.217286i −0.0416544 0.0111613i 0.237932 0.971282i \(-0.423531\pi\)
−0.279586 + 0.960121i \(0.590197\pi\)
\(380\) −0.736658 + 1.27593i −0.0377898 + 0.0654538i
\(381\) 16.9573 + 29.3709i 0.868748 + 1.50472i
\(382\) 0.986379 + 3.68122i 0.0504676 + 0.188347i
\(383\) 4.10501 + 4.10501i 0.209756 + 0.209756i 0.804164 0.594408i \(-0.202613\pi\)
−0.594408 + 0.804164i \(0.702613\pi\)
\(384\) 5.95624 + 22.2290i 0.303953 + 1.13437i
\(385\) 0 0
\(386\) 9.42582 16.3260i 0.479761 0.830971i
\(387\) 11.3196 + 6.53537i 0.575407 + 0.332211i
\(388\) −25.9493 + 25.9493i −1.31738 + 1.31738i
\(389\) 7.55715 + 4.36312i 0.383163 + 0.221219i 0.679193 0.733959i \(-0.262330\pi\)
−0.296031 + 0.955178i \(0.595663\pi\)
\(390\) 2.92773 9.50229i 0.148252 0.481167i
\(391\) 20.8706i 1.05547i
\(392\) 0 0
\(393\) −15.8697 27.4872i −0.800522 1.38654i
\(394\) 46.3601i 2.33559i
\(395\) 1.39282 0.373204i 0.0700802 0.0187779i
\(396\) 68.7592 + 18.4240i 3.45528 + 0.925839i
\(397\) −0.150383 + 0.150383i −0.00754752 + 0.00754752i −0.710870 0.703323i \(-0.751699\pi\)
0.703323 + 0.710870i \(0.251699\pi\)
\(398\) 5.92117 5.92117i 0.296801 0.296801i
\(399\) 0 0
\(400\) 33.1261 19.1254i 1.65631 0.956269i
\(401\) 6.77934 1.81652i 0.338544 0.0907126i −0.0855419 0.996335i \(-0.527262\pi\)
0.424086 + 0.905622i \(0.360595\pi\)
\(402\) −17.4102 + 30.1554i −0.868342 + 1.50401i
\(403\) 22.6331 + 0.839608i 1.12743 + 0.0418238i
\(404\) 17.9045 10.3371i 0.890781 0.514292i
\(405\) −0.368813 + 1.37643i −0.0183265 + 0.0683953i
\(406\) 0 0
\(407\) −5.63456 3.25312i −0.279295 0.161251i
\(408\) −71.0053 19.0258i −3.51529 0.941918i
\(409\) −2.77106 + 10.3417i −0.137020 + 0.511366i 0.862961 + 0.505270i \(0.168607\pi\)
−0.999981 + 0.00609589i \(0.998060\pi\)
\(410\) −0.591668 + 2.20813i −0.0292204 + 0.109052i
\(411\) 33.9118 + 9.08664i 1.67275 + 0.448211i
\(412\) −64.0235 36.9640i −3.15421 1.82108i
\(413\) 0 0
\(414\) 14.4538 53.9421i 0.710363 2.65111i
\(415\) −2.61890 + 1.51202i −0.128557 + 0.0742222i
\(416\) −21.3034 13.3763i −1.04448 0.655826i
\(417\) 11.6719 20.2163i 0.571574 0.989996i
\(418\) −7.25197 + 1.94316i −0.354705 + 0.0950430i
\(419\) 0.903448 0.521606i 0.0441363 0.0254821i −0.477769 0.878485i \(-0.658555\pi\)
0.521906 + 0.853003i \(0.325221\pi\)
\(420\) 0 0
\(421\) −22.9876 + 22.9876i −1.12035 + 1.12035i −0.128658 + 0.991689i \(0.541067\pi\)
−0.991689 + 0.128658i \(0.958933\pi\)
\(422\) −4.02682 + 4.02682i −0.196022 + 0.196022i
\(423\) −34.9944 9.37671i −1.70148 0.455911i
\(424\) 58.4486 15.6613i 2.83851 0.760578i
\(425\) 19.8354i 0.962160i
\(426\) 7.79641 + 13.5038i 0.377737 + 0.654260i
\(427\) 0 0
\(428\) 49.6684i 2.40081i
\(429\) 31.1998 16.5024i 1.50634 0.796741i
\(430\) −2.71134 1.56540i −0.130753 0.0754901i
\(431\) −5.78670 + 5.78670i −0.278735 + 0.278735i −0.832604 0.553869i \(-0.813151\pi\)
0.553869 + 0.832604i \(0.313151\pi\)
\(432\) −23.4304 13.5276i −1.12730 0.650845i
\(433\) 9.95068 17.2351i 0.478199 0.828266i −0.521488 0.853258i \(-0.674623\pi\)
0.999688 + 0.0249929i \(0.00795632\pi\)
\(434\) 0 0
\(435\) 0.560086 + 2.09027i 0.0268541 + 0.100221i
\(436\) −10.8267 10.8267i −0.518506 0.518506i
\(437\) 1.06190 + 3.96307i 0.0507977 + 0.189579i
\(438\) −17.1412 29.6894i −0.819036 1.41861i
\(439\) −3.63272 + 6.29205i −0.173380 + 0.300303i −0.939599 0.342276i \(-0.888802\pi\)
0.766219 + 0.642579i \(0.222136\pi\)
\(440\) −9.29613 2.49089i −0.443176 0.118749i
\(441\) 0 0
\(442\) −33.5265 + 17.7330i −1.59469 + 0.843473i
\(443\) −13.2808 23.0031i −0.630992 1.09291i −0.987349 0.158561i \(-0.949315\pi\)
0.356357 0.934350i \(-0.384019\pi\)
\(444\) 15.6887 + 15.6887i 0.744552 + 0.744552i
\(445\) −4.76032 −0.225661
\(446\) −13.9665 −0.661333
\(447\) −35.6153 35.6153i −1.68455 1.68455i
\(448\) 0 0
\(449\) 19.1518 5.13170i 0.903828 0.242180i 0.223168 0.974780i \(-0.428360\pi\)
0.680659 + 0.732600i \(0.261693\pi\)
\(450\) 13.7369 51.2668i 0.647563 2.41674i
\(451\) −7.02760 + 4.05739i −0.330917 + 0.191055i
\(452\) 35.0842i 1.65022i
\(453\) −9.81963 36.6474i −0.461366 1.72184i
\(454\) −0.890238 −0.0417809
\(455\) 0 0
\(456\) 14.4511 0.676735
\(457\) −6.49628 24.2444i −0.303883 1.13411i −0.933903 0.357528i \(-0.883620\pi\)
0.630019 0.776579i \(-0.283047\pi\)
\(458\) 68.0670i 3.18056i
\(459\) −12.1502 + 7.01490i −0.567121 + 0.327427i
\(460\) −2.41165 + 9.00038i −0.112444 + 0.419645i
\(461\) −32.6719 + 8.75440i −1.52168 + 0.407733i −0.920295 0.391226i \(-0.872051\pi\)
−0.601386 + 0.798959i \(0.705385\pi\)
\(462\) 0 0
\(463\) 13.6651 + 13.6651i 0.635073 + 0.635073i 0.949336 0.314263i \(-0.101757\pi\)
−0.314263 + 0.949336i \(0.601757\pi\)
\(464\) 15.9180 0.738974
\(465\) −6.74712 −0.312890
\(466\) −39.6252 39.6252i −1.83560 1.83560i
\(467\) −7.57629 13.1225i −0.350589 0.607238i 0.635764 0.771884i \(-0.280685\pi\)
−0.986353 + 0.164646i \(0.947352\pi\)
\(468\) −68.9163 + 15.7529i −3.18566 + 0.728180i
\(469\) 0 0
\(470\) 8.38209 + 2.24597i 0.386637 + 0.103599i
\(471\) −18.8877 + 32.7145i −0.870299 + 1.50740i
\(472\) −24.7223 42.8203i −1.13794 1.97096i
\(473\) −2.87637 10.7348i −0.132256 0.493585i
\(474\) −17.7183 17.7183i −0.813830 0.813830i
\(475\) 1.00923 + 3.76652i 0.0463069 + 0.172820i
\(476\) 0 0
\(477\) 19.4146 33.6270i 0.888932 1.53968i
\(478\) 6.35787 + 3.67072i 0.290802 + 0.167895i
\(479\) 17.7763 17.7763i 0.812220 0.812220i −0.172746 0.984966i \(-0.555264\pi\)
0.984966 + 0.172746i \(0.0552641\pi\)
\(480\) 6.48972 + 3.74684i 0.296214 + 0.171019i
\(481\) 6.45692 + 0.239529i 0.294410 + 0.0109216i
\(482\) 77.4746i 3.52887i
\(483\) 0 0
\(484\) −5.00776 8.67369i −0.227625 0.394259i
\(485\) 3.18376i 0.144567i
\(486\) 49.3954 13.2354i 2.24062 0.600372i
\(487\) 24.9540 + 6.68642i 1.13078 + 0.302990i 0.775237 0.631671i \(-0.217631\pi\)
0.355539 + 0.934661i \(0.384297\pi\)
\(488\) 13.0589 13.0589i 0.591147 0.591147i
\(489\) −18.0704 + 18.0704i −0.817172 + 0.817172i
\(490\) 0 0
\(491\) −31.2520 + 18.0433i −1.41038 + 0.814284i −0.995424 0.0955563i \(-0.969537\pi\)
−0.414958 + 0.909841i \(0.636204\pi\)
\(492\) 26.7296 7.16217i 1.20506 0.322895i
\(493\) 4.12724 7.14859i 0.185882 0.321956i
\(494\) 5.46402 5.07313i 0.245838 0.228251i
\(495\) −5.34831 + 3.08785i −0.240389 + 0.138789i
\(496\) −12.8453 + 47.9393i −0.576771 + 2.15254i
\(497\) 0 0
\(498\) 45.5099 + 26.2752i 2.03935 + 1.17742i
\(499\) −27.2810 7.30993i −1.22127 0.327237i −0.410093 0.912044i \(-0.634504\pi\)
−0.811173 + 0.584806i \(0.801171\pi\)
\(500\) −4.65920 + 17.3884i −0.208366 + 0.777632i
\(501\) −6.80010 + 25.3783i −0.303806 + 1.13382i
\(502\) −41.3635 11.0833i −1.84614 0.494672i
\(503\) −23.3796 13.4982i −1.04244 0.601855i −0.121920 0.992540i \(-0.538905\pi\)
−0.920525 + 0.390685i \(0.872238\pi\)
\(504\) 0 0
\(505\) −0.464223 + 1.73250i −0.0206576 + 0.0770954i
\(506\) −41.1210 + 23.7412i −1.82805 + 1.05543i
\(507\) −19.7268 + 28.9738i −0.876099 + 1.28677i
\(508\) −28.8782 + 50.0186i −1.28126 + 2.21922i
\(509\) −4.85539 + 1.30100i −0.215212 + 0.0576658i −0.364814 0.931081i \(-0.618867\pi\)
0.149602 + 0.988746i \(0.452201\pi\)
\(510\) 9.78497 5.64936i 0.433286 0.250158i
\(511\) 0 0
\(512\) −35.3750 + 35.3750i −1.56337 + 1.56337i
\(513\) 1.95025 1.95025i 0.0861057 0.0861057i
\(514\) −30.2838 8.11452i −1.33576 0.357916i
\(515\) 6.19515 1.65999i 0.272991 0.0731477i
\(516\) 37.8984i 1.66838i
\(517\) 15.4019 + 26.6768i 0.677373 + 1.17325i
\(518\) 0 0
\(519\) 45.8549i 2.01281i
\(520\) 9.31738 2.12977i 0.408594 0.0933967i
\(521\) −24.7411 14.2843i −1.08393 0.625806i −0.151975 0.988384i \(-0.548563\pi\)
−0.931953 + 0.362578i \(0.881897\pi\)
\(522\) 15.6180 15.6180i 0.683581 0.683581i
\(523\) 15.9700 + 9.22026i 0.698318 + 0.403174i 0.806720 0.590933i \(-0.201240\pi\)
−0.108403 + 0.994107i \(0.534574\pi\)
\(524\) 27.0261 46.8106i 1.18064 2.04493i
\(525\) 0 0
\(526\) 9.70594 + 36.2230i 0.423199 + 1.57940i
\(527\) 18.1985 + 18.1985i 0.792738 + 0.792738i
\(528\) 20.0179 + 74.7078i 0.871167 + 3.25124i
\(529\) 1.47417 + 2.55334i 0.0640944 + 0.111015i
\(530\) −4.65031 + 8.05458i −0.201997 + 0.349868i
\(531\) −30.6472 8.21188i −1.32997 0.356365i
\(532\) 0 0
\(533\) 4.28536 6.82496i 0.185620 0.295622i
\(534\) 41.3613 + 71.6398i 1.78988 + 3.10016i
\(535\) −3.04695 3.04695i −0.131731 0.131731i
\(536\) −33.4708 −1.44572
\(537\) −29.3039 −1.26456
\(538\) 9.04840 + 9.04840i 0.390104 + 0.390104i
\(539\) 0 0
\(540\) 6.05032 1.62118i 0.260364 0.0697644i
\(541\) −1.71180 + 6.38853i −0.0735961 + 0.274665i −0.992911 0.118858i \(-0.962077\pi\)
0.919315 + 0.393522i \(0.128743\pi\)
\(542\) −58.9092 + 34.0113i −2.53037 + 1.46091i
\(543\) 56.0062i 2.40346i
\(544\) −7.39814 27.6103i −0.317193 1.18378i
\(545\) 1.32835 0.0569001
\(546\) 0 0
\(547\) 33.8006 1.44521 0.722605 0.691261i \(-0.242944\pi\)
0.722605 + 0.691261i \(0.242944\pi\)
\(548\) 15.4745 + 57.7518i 0.661040 + 2.46703i
\(549\) 11.8508i 0.505780i
\(550\) −39.0816 + 22.5637i −1.66644 + 0.962121i
\(551\) −0.419991 + 1.56743i −0.0178922 + 0.0667747i
\(552\) 88.2808 23.6548i 3.75748 1.00681i
\(553\) 0 0
\(554\) −37.0797 37.0797i −1.57536 1.57536i
\(555\) −1.92487 −0.0817061
\(556\) 39.7544 1.68596
\(557\) 17.5294 + 17.5294i 0.742746 + 0.742746i 0.973106 0.230359i \(-0.0739901\pi\)
−0.230359 + 0.973106i \(0.573990\pi\)
\(558\) 34.4326 + 59.6391i 1.45765 + 2.52472i
\(559\) 7.50953 + 8.08815i 0.317619 + 0.342092i
\(560\) 0 0
\(561\) 38.7407 + 10.3805i 1.63563 + 0.438267i
\(562\) 7.02090 12.1606i 0.296159 0.512962i
\(563\) −2.10194 3.64067i −0.0885863 0.153436i 0.818327 0.574752i \(-0.194902\pi\)
−0.906914 + 0.421316i \(0.861568\pi\)
\(564\) −27.1876 101.466i −1.14481 4.27247i
\(565\) −2.15227 2.15227i −0.0905465 0.0905465i
\(566\) −16.6378 62.0931i −0.699338 2.60997i
\(567\) 0 0
\(568\) −7.49422 + 12.9804i −0.314450 + 0.544644i
\(569\) 0.733859 + 0.423694i 0.0307650 + 0.0177622i 0.515304 0.857008i \(-0.327679\pi\)
−0.484539 + 0.874770i \(0.661012\pi\)
\(570\) −1.57061 + 1.57061i −0.0657856 + 0.0657856i
\(571\) −15.4798 8.93729i −0.647811 0.374014i 0.139806 0.990179i \(-0.455352\pi\)
−0.787617 + 0.616165i \(0.788685\pi\)
\(572\) 50.9049 + 31.9629i 2.12844 + 1.33644i
\(573\) 4.00234i 0.167200i
\(574\) 0 0
\(575\) 12.3307 + 21.3574i 0.514225 + 0.890664i
\(576\) 9.01120i 0.375467i
\(577\) −8.25729 + 2.21253i −0.343755 + 0.0921090i −0.426566 0.904456i \(-0.640277\pi\)
0.0828109 + 0.996565i \(0.473610\pi\)
\(578\) 0.529615 + 0.141910i 0.0220291 + 0.00590268i
\(579\) 13.9991 13.9991i 0.581782 0.581782i
\(580\) −2.60590 + 2.60590i −0.108204 + 0.108204i
\(581\) 0 0
\(582\) −47.9136 + 27.6629i −1.98608 + 1.14667i
\(583\) −31.8897 + 8.54482i −1.32074 + 0.353890i
\(584\) 16.4768 28.5386i 0.681813 1.18094i
\(585\) 3.26135 5.19410i 0.134840 0.214749i
\(586\) −41.0376 + 23.6931i −1.69525 + 0.978751i
\(587\) 10.7910 40.2727i 0.445394 1.66223i −0.269502 0.963000i \(-0.586859\pi\)
0.714895 0.699231i \(-0.246474\pi\)
\(588\) 0 0
\(589\) −4.38162 2.52973i −0.180541 0.104236i
\(590\) 7.34082 + 1.96697i 0.302217 + 0.0809787i
\(591\) −12.6011 + 47.0278i −0.518338 + 1.93446i
\(592\) −3.66460 + 13.6765i −0.150614 + 0.562100i
\(593\) −8.88654 2.38114i −0.364926 0.0977817i 0.0716962 0.997427i \(-0.477159\pi\)
−0.436623 + 0.899645i \(0.643825\pi\)
\(594\) 27.6427 + 15.9595i 1.13420 + 0.654828i
\(595\) 0 0
\(596\) 22.2005 82.8534i 0.909368 3.39381i
\(597\) 7.61585 4.39702i 0.311696 0.179958i
\(598\) 25.0752 39.9353i 1.02540 1.63308i
\(599\) 20.7873 36.0046i 0.849345 1.47111i −0.0324484 0.999473i \(-0.510330\pi\)
0.881794 0.471636i \(-0.156336\pi\)
\(600\) 83.9023 22.4816i 3.42530 0.917806i
\(601\) −22.6812 + 13.0950i −0.925184 + 0.534155i −0.885285 0.465049i \(-0.846037\pi\)
−0.0398987 + 0.999204i \(0.512704\pi\)
\(602\) 0 0
\(603\) −15.1872 + 15.1872i −0.618472 + 0.618472i
\(604\) 45.6876 45.6876i 1.85900 1.85900i
\(605\) 0.839298 + 0.224889i 0.0341223 + 0.00914305i
\(606\) 30.1066 8.06704i 1.22300 0.327701i
\(607\) 19.1314i 0.776519i −0.921550 0.388260i \(-0.873076\pi\)
0.921550 0.388260i \(-0.126924\pi\)
\(608\) 2.80964 + 4.86644i 0.113946 + 0.197360i
\(609\) 0 0
\(610\) 2.83859i 0.114931i
\(611\) −25.9076 16.2673i −1.04811 0.658103i
\(612\) −69.5696 40.1660i −2.81219 1.62362i
\(613\) 7.89553 7.89553i 0.318897 0.318897i −0.529446 0.848344i \(-0.677600\pi\)
0.848344 + 0.529446i \(0.177600\pi\)
\(614\) 46.1284 + 26.6322i 1.86159 + 1.07479i
\(615\) −1.20038 + 2.07911i −0.0484039 + 0.0838379i
\(616\) 0 0
\(617\) −2.84075 10.6018i −0.114364 0.426814i 0.884874 0.465830i \(-0.154244\pi\)
−0.999239 + 0.0390163i \(0.987578\pi\)
\(618\) −78.8099 78.8099i −3.17020 3.17020i
\(619\) 6.88065 + 25.6790i 0.276557 + 1.03212i 0.954791 + 0.297278i \(0.0960789\pi\)
−0.678234 + 0.734846i \(0.737254\pi\)
\(620\) −5.74517 9.95093i −0.230732 0.399639i
\(621\) 8.72161 15.1063i 0.349986 0.606194i
\(622\) 14.5363 + 3.89498i 0.582851 + 0.156175i
\(623\) 0 0
\(624\) −52.2620 56.2888i −2.09215 2.25336i
\(625\) 11.3224 + 19.6109i 0.452895 + 0.784438i
\(626\) 37.0492 + 37.0492i 1.48078 + 1.48078i
\(627\) −7.88457 −0.314879
\(628\) −64.3314 −2.56710
\(629\) 5.19179 + 5.19179i 0.207010 + 0.207010i
\(630\) 0 0
\(631\) −34.9180 + 9.35626i −1.39007 + 0.372467i −0.874767 0.484544i \(-0.838986\pi\)
−0.515298 + 0.857011i \(0.672319\pi\)
\(632\) 6.23399 23.2656i 0.247975 0.925454i
\(633\) −5.17933 + 2.99029i −0.205860 + 0.118853i
\(634\) 19.6935i 0.782130i
\(635\) −1.29687 4.83998i −0.0514647 0.192069i
\(636\) 112.584 4.46427
\(637\) 0 0
\(638\) −18.7797 −0.743496
\(639\) 2.48932 + 9.29025i 0.0984758 + 0.367517i
\(640\) 3.40008i 0.134400i
\(641\) −21.5157 + 12.4221i −0.849819 + 0.490643i −0.860590 0.509299i \(-0.829905\pi\)
0.0107708 + 0.999942i \(0.496571\pi\)
\(642\) −19.3804 + 72.3288i −0.764885 + 2.85459i
\(643\) 28.7931 7.71509i 1.13549 0.304253i 0.358353 0.933586i \(-0.383338\pi\)
0.777136 + 0.629333i \(0.216672\pi\)
\(644\) 0 0
\(645\) −2.32490 2.32490i −0.0915430 0.0915430i
\(646\) 8.47255 0.333348
\(647\) −13.7535 −0.540705 −0.270352 0.962761i \(-0.587140\pi\)
−0.270352 + 0.962761i \(0.587140\pi\)
\(648\) 16.8312 + 16.8312i 0.661192 + 0.661192i
\(649\) 13.4886 + 23.3629i 0.529472 + 0.917072i
\(650\) 23.8315 37.9547i 0.934750 1.48870i
\(651\) 0 0
\(652\) −42.0379 11.2640i −1.64633 0.441133i
\(653\) −0.855193 + 1.48124i −0.0334663 + 0.0579653i −0.882273 0.470737i \(-0.843988\pi\)
0.848807 + 0.528703i \(0.177321\pi\)
\(654\) −11.5417 19.9908i −0.451315 0.781701i
\(655\) 1.21369 + 4.52957i 0.0474230 + 0.176985i
\(656\) 12.4871 + 12.4871i 0.487540 + 0.487540i
\(657\) −5.47300 20.4255i −0.213522 0.796876i
\(658\) 0 0
\(659\) −4.73353 + 8.19872i −0.184392 + 0.319377i −0.943372 0.331738i \(-0.892365\pi\)
0.758979 + 0.651115i \(0.225698\pi\)
\(660\) −15.5073 8.95317i −0.603623 0.348502i
\(661\) 6.24335 6.24335i 0.242838 0.242838i −0.575185 0.818023i \(-0.695070\pi\)
0.818023 + 0.575185i \(0.195070\pi\)
\(662\) 56.0512 + 32.3612i 2.17849 + 1.25775i
\(663\) −38.8293 + 8.87561i −1.50800 + 0.344700i
\(664\) 50.5135i 1.96030i
\(665\) 0 0
\(666\) 9.82318 + 17.0143i 0.380641 + 0.659289i
\(667\) 10.2628i 0.397377i
\(668\) −43.2192 + 11.5806i −1.67220 + 0.448065i
\(669\) −14.1676 3.79621i −0.547752 0.146770i
\(670\) 3.63775 3.63775i 0.140538 0.140538i
\(671\) −7.12495 + 7.12495i −0.275056 + 0.275056i
\(672\) 0 0
\(673\) 15.2065 8.77951i 0.586169 0.338425i −0.177412 0.984137i \(-0.556773\pi\)
0.763581 + 0.645712i \(0.223439\pi\)
\(674\) 74.7228 20.0219i 2.87822 0.771216i
\(675\) 8.28904 14.3570i 0.319045 0.552603i
\(676\) −59.5291 4.42273i −2.28958 0.170105i
\(677\) 20.3504 11.7493i 0.782131 0.451564i −0.0550539 0.998483i \(-0.517533\pi\)
0.837185 + 0.546920i \(0.184200\pi\)
\(678\) −13.6897 + 51.0908i −0.525751 + 1.96213i
\(679\) 0 0
\(680\) 9.40571 + 5.43039i 0.360692 + 0.208246i
\(681\) −0.903058 0.241974i −0.0346053 0.00927245i
\(682\) 15.1546 56.5579i 0.580301 2.16571i
\(683\) 9.01937 33.6607i 0.345117 1.28799i −0.547359 0.836898i \(-0.684367\pi\)
0.892476 0.451095i \(-0.148966\pi\)
\(684\) 15.2541 + 4.08733i 0.583256 + 0.156283i
\(685\) −4.49212 2.59353i −0.171635 0.0990936i
\(686\) 0 0
\(687\) −18.5011 + 69.0472i −0.705862 + 2.63431i
\(688\) −20.9450 + 12.0926i −0.798520 + 0.461026i
\(689\) 24.0274 22.3085i 0.915371 0.849886i
\(690\) −7.02384 + 12.1656i −0.267393 + 0.463138i
\(691\) 44.9582 12.0465i 1.71029 0.458271i 0.734795 0.678290i \(-0.237279\pi\)
0.975496 + 0.220019i \(0.0706119\pi\)
\(692\) 67.6287 39.0454i 2.57086 1.48428i
\(693\) 0 0
\(694\) 62.5609 62.5609i 2.37478 2.37478i
\(695\) −2.43876 + 2.43876i −0.0925075 + 0.0925075i
\(696\) 34.9158 + 9.35566i 1.32348 + 0.354625i
\(697\) 8.84550 2.37014i 0.335047 0.0897756i
\(698\) 10.5531i 0.399440i
\(699\) −29.4254 50.9663i −1.11297 1.92772i
\(700\) 0 0
\(701\) 7.19399i 0.271713i 0.990729 + 0.135857i \(0.0433787\pi\)
−0.990729 + 0.135857i \(0.956621\pi\)
\(702\) −31.6772 1.17511i −1.19558 0.0443518i
\(703\) −1.25002 0.721699i −0.0471454 0.0272194i
\(704\) −5.41772 + 5.41772i −0.204188 + 0.204188i
\(705\) 7.89233 + 4.55664i 0.297242 + 0.171613i
\(706\) −13.9744 + 24.2044i −0.525934 + 0.910945i
\(707\) 0 0
\(708\) −23.8102 88.8609i −0.894843 3.33960i
\(709\) 0.110125 + 0.110125i 0.00413582 + 0.00413582i 0.709172 0.705036i \(-0.249069\pi\)
−0.705036 + 0.709172i \(0.749069\pi\)
\(710\) −0.596258 2.22527i −0.0223772 0.0835127i
\(711\) −7.72800 13.3853i −0.289823 0.501988i
\(712\) −39.7581 + 68.8630i −1.49000 + 2.58075i
\(713\) −30.9079 8.28174i −1.15751 0.310154i
\(714\) 0 0
\(715\) −5.08359 + 1.16201i −0.190115 + 0.0434567i
\(716\) −24.9522 43.2186i −0.932509 1.61515i
\(717\) 5.45170 + 5.45170i 0.203597 + 0.203597i
\(718\) 79.0302 2.94938
\(719\) 12.9627 0.483429 0.241714 0.970347i \(-0.422290\pi\)
0.241714 + 0.970347i \(0.422290\pi\)
\(720\) 9.50324 + 9.50324i 0.354165 + 0.354165i
\(721\) 0 0
\(722\) 45.5105 12.1945i 1.69372 0.453832i
\(723\) −21.0582 + 78.5903i −0.783163 + 2.92280i
\(724\) −82.6002 + 47.6893i −3.06981 + 1.77236i
\(725\) 9.75378i 0.362246i
\(726\) −3.90802 14.5849i −0.145040 0.541297i
\(727\) −49.4330 −1.83337 −0.916684 0.399614i \(-0.869144\pi\)
−0.916684 + 0.399614i \(0.869144\pi\)
\(728\) 0 0
\(729\) 42.9729 1.59159
\(730\) 1.31093 + 4.89246i 0.0485198 + 0.181078i
\(731\) 12.5415i 0.463866i
\(732\) 29.7577 17.1806i 1.09988 0.635013i
\(733\) −8.85517 + 33.0480i −0.327073 + 1.22065i 0.585138 + 0.810934i \(0.301040\pi\)
−0.912211 + 0.409720i \(0.865626\pi\)
\(734\) 61.8450 16.5713i 2.28274 0.611658i
\(735\) 0 0
\(736\) 25.1297 + 25.1297i 0.926292 + 0.926292i
\(737\) 18.2618 0.672680
\(738\) 24.5036 0.901988
\(739\) 3.02262 + 3.02262i 0.111189 + 0.111189i 0.760512 0.649323i \(-0.224948\pi\)
−0.649323 + 0.760512i \(0.724948\pi\)
\(740\) −1.63902 2.83887i −0.0602517 0.104359i
\(741\) 6.92162 3.66102i 0.254272 0.134491i
\(742\) 0 0
\(743\) 23.2815 + 6.23826i 0.854115 + 0.228859i 0.659206 0.751962i \(-0.270892\pi\)
0.194909 + 0.980821i \(0.437559\pi\)
\(744\) −56.3519 + 97.6043i −2.06596 + 3.57835i
\(745\) 3.72080 + 6.44461i 0.136319 + 0.236112i
\(746\) 12.0868 + 45.1087i 0.442530 + 1.65155i
\(747\) 22.9203 + 22.9203i 0.838609 + 0.838609i
\(748\) 17.6780 + 65.9754i 0.646373 + 2.41230i
\(749\) 0 0
\(750\) −13.5698 + 23.5035i −0.495498 + 0.858227i
\(751\) 11.3539 + 6.55518i 0.414310 + 0.239202i 0.692640 0.721283i \(-0.256447\pi\)
−0.278330 + 0.960486i \(0.589781\pi\)
\(752\) 47.4012 47.4012i 1.72854 1.72854i
\(753\) −38.9466 22.4858i −1.41929 0.819429i
\(754\) 16.4861 8.71994i 0.600390 0.317561i
\(755\) 5.60548i 0.204004i
\(756\) 0 0
\(757\) 7.95111 + 13.7717i 0.288988 + 0.500542i 0.973568 0.228395i \(-0.0733479\pi\)
−0.684580 + 0.728937i \(0.740015\pi\)
\(758\) 2.15545i 0.0782895i
\(759\) −48.1663 + 12.9061i −1.74832 + 0.468462i
\(760\) −2.06233 0.552600i −0.0748087 0.0200449i
\(761\) 27.9954 27.9954i 1.01483 1.01483i 0.0149439 0.999888i \(-0.495243\pi\)
0.999888 0.0149439i \(-0.00475696\pi\)
\(762\) −61.5705 + 61.5705i −2.23047 + 2.23047i
\(763\) 0 0
\(764\) −5.90280 + 3.40799i −0.213556 + 0.123297i
\(765\) 6.73181 1.80378i 0.243389 0.0652160i
\(766\) −7.45248 + 12.9081i −0.269269 + 0.466388i
\(767\) −22.6892 14.2464i −0.819260 0.514409i
\(768\) −61.0247 + 35.2326i −2.20204 + 1.27135i
\(769\) −1.28737 + 4.80452i −0.0464236 + 0.173255i −0.985245 0.171148i \(-0.945252\pi\)
0.938822 + 0.344404i \(0.111919\pi\)
\(770\) 0 0
\(771\) −28.5143 16.4627i −1.02692 0.592891i
\(772\) 32.5666 + 8.72620i 1.17210 + 0.314063i
\(773\) 8.58704 32.0473i 0.308855 1.15266i −0.620722 0.784031i \(-0.713160\pi\)
0.929576 0.368630i \(-0.120173\pi\)
\(774\) −8.68556 + 32.4149i −0.312196 + 1.16513i
\(775\) −29.3749 7.87099i −1.05518 0.282734i
\(776\) −46.0565 26.5907i −1.65333 0.954551i
\(777\) 0 0
\(778\) −5.79862 + 21.6408i −0.207891 + 0.775859i
\(779\) −1.55906 + 0.900125i −0.0558592 + 0.0322503i
\(780\) 17.7706 + 0.659228i 0.636291 + 0.0236041i
\(781\) 4.08887 7.08212i