Properties

Label 637.2.x.b.80.7
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 80.7
Character \(\chi\) \(=\) 637.80
Dual form 637.2.x.b.215.8

$q$-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 \(-0.716055\pi\)
0.627827 0.778353i \(-0.283945\pi\)
\(4\) −3.97660 + 2.29589i −1.98830 + 1.14795i
\(5\) −0.103104 + 0.384791i −0.0461097 + 0.172084i −0.985141 0.171748i \(-0.945058\pi\)
0.939031 + 0.343832i \(0.111725\pi\)
\(6\) 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 0.999993 0.00363405i \(-0.00115676\pi\)
−0.503144 + 0.864203i \(0.667823\pi\)
\(18\) −2.83743 10.5895i −0.668790 2.49596i
\(19\) −0.569532 0.569532i −0.130660 0.130660i 0.638753 0.769412i \(-0.279451\pi\)
−0.769412 + 0.638753i \(0.779451\pi\)
\(20\) −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 0.331176 0.943569i \(-0.392555\pi\)
0.758591 + 0.651567i \(0.225888\pi\)
\(32\) 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 −0.905928 0.423432i \(-0.860825\pi\)
0.996273 + 0.0862606i \(0.0274918\pi\)
\(42\) 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 −0.394395 0.918941i \(-0.629046\pi\)
−0.801027 + 0.598629i \(0.795712\pi\)
\(48\) −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 −0.240674 0.970606i \(-0.577368\pi\)
−0.693733 + 0.720232i \(0.744035\pi\)
\(60\) −4.76402 + 1.27652i −0.615032 + 0.164797i
\(61\) 2.77536i 0.355349i −0.984089 0.177674i \(-0.943143\pi\)
0.984089 0.177674i \(-0.0568574\pi\)
\(62\) 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 \(-0.989742\pi\)
0.849465 0.527645i \(-0.176925\pi\)
\(74\) −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 0.937411 0.348225i \(-0.113215\pi\)
−0.348225 + 0.937411i \(0.613215\pi\)
\(84\) 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 \(0.134979\pi\)
−0.583595 + 0.812045i \(0.698354\pi\)
\(90\) 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 −0.628469 0.777835i \(-0.716318\pi\)
−0.155353 + 0.987859i \(0.549651\pi\)
\(98\) 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 \(-0.428087\pi\)
0.224005 + 0.974588i \(0.428087\pi\)
\(102\) 20.0555 + 20.0555i 1.98579 + 1.98579i
\(103\) −8.05002 13.9430i −0.793192 1.37385i −0.923981 0.382439i \(-0.875084\pi\)
0.130788 0.991410i \(-0.458249\pi\)
\(104\) −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 0.0165228 0.999863i \(-0.494740\pi\)
0.874169 + 0.485623i \(0.161407\pi\)
\(132\) −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 0.783055 0.621953i \(-0.213660\pi\)
−0.147099 + 0.989122i \(0.546994\pi\)
\(140\) 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 −0.0696019 0.997575i \(-0.522173\pi\)
−0.898726 + 0.438510i \(0.855506\pi\)
\(158\) −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 −0.124453 0.992226i \(-0.539718\pi\)
−0.603892 + 0.797066i \(0.706384\pi\)
\(168\) 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 \(-0.276234\pi\)
0.646496 + 0.762918i \(0.276234\pi\)
\(174\) 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 \(-0.780728\pi\)
−0.771969 + 0.635661i \(0.780728\pi\)
\(182\) 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 0.918020 0.396534i \(-0.129787\pi\)
−0.802418 + 0.596762i \(0.796454\pi\)
\(200\) −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 −0.902627 0.430423i \(-0.858364\pi\)
0.996910 + 0.0785566i \(0.0250311\pi\)
\(224\) 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 −0.962884 0.269917i \(-0.913004\pi\)
0.968840 + 0.247687i \(0.0796705\pi\)
\(228\) 2.58094 9.63221i 0.170927 0.637909i
\(229\) −25.6082 6.86169i −1.69224 0.453433i −0.721270 0.692654i \(-0.756441\pi\)
−0.970965 + 0.239220i \(0.923108\pi\)
\(230\) −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 \(-0.992312\pi\)
−0.877849 0.478938i \(-0.841022\pi\)
\(242\) −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 \(-0.656880\pi\)
0.999527 0.0307412i \(-0.00978676\pi\)
\(252\) 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 −0.610323 0.792153i \(-0.708960\pi\)
0.991186 + 0.132479i \(0.0422937\pi\)
\(258\) −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 −0.625781 0.779999i \(-0.715219\pi\)
0.362609 + 0.931941i \(0.381886\pi\)
\(270\) 3.50231i 0.213144i
\(271\) −6.85721 25.5915i −0.416546 1.55457i −0.781719 0.623631i \(-0.785657\pi\)
0.365173 0.930940i \(-0.381010\pi\)
\(272\) 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 \(-0.232843\pi\)
0.744174 + 0.667986i \(0.232843\pi\)
\(284\) 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 \(-0.902090\pi\)
0.673996 0.738735i \(-0.264577\pi\)
\(294\) 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 −0.988495 0.151252i \(-0.951670\pi\)
0.151252 + 0.988495i \(0.451670\pi\)
\(308\) 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 −0.937076 0.349125i \(-0.886479\pi\)
0.770889 + 0.636969i \(0.219812\pi\)
\(312\) −57.1840 + 30.2461i −3.23741 + 1.71235i
\(313\) −17.6735 + 10.2038i −0.998967 + 0.576754i −0.907942 0.419095i \(-0.862347\pi\)
−0.0910244 + 0.995849i \(0.529014\pi\)
\(314\) 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 0.363510 0.931590i \(-0.381578\pi\)
−0.150986 + 0.988536i \(0.548245\pi\)
\(350\) 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 0.471938 0.881632i \(-0.343555\pi\)
−0.881632 + 0.471938i \(0.843555\pi\)
\(354\) −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 \(0.225597\pi\)
−0.759187 + 0.650873i \(0.774403\pi\)
\(368\) 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 0.594408 0.804164i \(-0.297387\pi\)
−0.804164 + 0.594408i \(0.797387\pi\)
\(384\) −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 −0.703323 0.710870i \(-0.748301\pi\)
0.710870 + 0.703323i \(0.248301\pi\)
\(398\) −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 \(-0.831393\pi\)
0.999981 0.00609589i \(-0.00194039\pi\)
\(410\) −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 −0.521906 0.853003i \(-0.674779\pi\)
0.477769 + 0.878485i \(0.341445\pi\)
\(420\) 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 −0.999688 0.0249929i \(-0.992044\pi\)
0.521488 + 0.853258i \(0.325377\pi\)
\(434\) 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 −0.766219 0.642579i \(-0.777864\pi\)
0.939599 + 0.342276i \(0.111198\pi\)
\(440\) 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 0.601386 0.798959i \(-0.294615\pi\)
0.920295 + 0.391226i \(0.127949\pi\)
\(462\) 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 0.986353 0.164646i \(-0.0526481\pi\)
−0.635764 + 0.771884i \(0.719315\pi\)
\(468\) 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 −0.984966 0.172746i \(-0.944736\pi\)
0.172746 + 0.984966i \(0.444736\pi\)
\(480\) 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 0.920525 0.390685i \(-0.127762\pi\)
0.121920 + 0.992540i \(0.461095\pi\)
\(504\) 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 −0.149602 0.988746i \(-0.547799\pi\)
0.364814 + 0.931081i \(0.381133\pi\)
\(510\) −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 0.931953 0.362578i \(-0.118103\pi\)
0.151975 + 0.988384i \(0.451437\pi\)
\(522\) 15.6180 15.6180i 0.683581 0.683581i
\(523\) −15.9700 9.22026i −0.698318 0.403174i 0.108403 0.994107i \(-0.465426\pi\)
−0.806720 + 0.590933i \(0.798760\pi\)
\(524\) −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 0.906914 0.421316i \(-0.138432\pi\)
−0.818327 + 0.574752i \(0.805098\pi\)
\(564\) −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 −0.0828109 0.996565i \(-0.526390\pi\)
0.426566 + 0.904456i \(0.359723\pi\)
\(578\) 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 \(0.413141\pi\)
−0.714895 + 0.699231i \(0.753526\pi\)
\(588\) 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 0.436623 0.899645i \(-0.356175\pi\)
−0.0716962 + 0.997427i \(0.522841\pi\)
\(594\) −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 0.0398987 0.999204i \(-0.487296\pi\)
0.885285 + 0.465049i \(0.153963\pi\)
\(602\) 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 \(0.126924\pi\)
−0.921550 + 0.388260i \(0.873076\pi\)
\(608\) −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 \(-0.903921\pi\)
0.678234 0.734846i \(-0.262746\pi\)
\(620\) −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 −0.777136 0.629333i \(-0.783328\pi\)
−0.358353 + 0.933586i \(0.616662\pi\)
\(644\) 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 \(-0.412860\pi\)
0.270352 + 0.962761i \(0.412860\pi\)
\(648\) 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 −0.818023 0.575185i \(-0.804930\pi\)
0.575185 + 0.818023i \(0.304930\pi\)
\(662\) 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 −0.837185 0.546920i \(-0.815800\pi\)
0.0550539 + 0.998483i \(0.482467\pi\)
\(678\) 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 −0.975496 0.220019i \(-0.929388\pi\)
−0.734795 + 0.678290i \(0.762721\pi\)
\(692\) −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 \(-0.577710\pi\)
−0.241714 + 0.970347i \(0.577710\pi\)
\(720\) −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 \(-0.130856\pi\)
0.916684 + 0.399614i \(0.130856\pi\)
\(728\) 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 \(-0.698960\pi\)
0.912211 0.409720i \(-0.134374\pi\)
\(734\) −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 \(0.504757\pi\)
−0.999888 + 0.0149439i \(0.995243\pi\)
\(762\) 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 −0.938822 0.344404i \(-0.888081\pi\)
0.985245 + 0.171148i \(0.0547478\pi\)
\(770\) 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 \(0.286840\pi\)
−0.929576 + 0.368630i \(0.879827\pi\)
\(774\) −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