Properties

Label 825.2.n.c.526.1
Level $825$
Weight $2$
Character 825.526
Analytic conductor $6.588$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.n (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 526.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 825.526
Dual form 825.2.n.c.676.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.809017 - 2.48990i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-3.92705 - 2.85317i) q^{4} +(0.809017 + 2.48990i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-6.04508 + 4.39201i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(0.809017 - 2.48990i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-3.92705 - 2.85317i) q^{4} +(0.809017 + 2.48990i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-6.04508 + 4.39201i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-3.30902 - 0.224514i) q^{11} +4.85410 q^{12} +(-0.0729490 + 0.224514i) q^{13} +(-2.11803 + 1.53884i) q^{14} +(3.04508 + 9.37181i) q^{16} +(0.354102 + 1.08981i) q^{17} +(-2.11803 - 1.53884i) q^{18} +(-4.73607 + 3.44095i) q^{19} +1.00000 q^{21} +(-3.23607 + 8.05748i) q^{22} -0.236068 q^{23} +(2.30902 - 7.10642i) q^{24} +(0.500000 + 0.363271i) q^{26} +(0.309017 + 0.951057i) q^{27} +(1.50000 + 4.61653i) q^{28} +(4.85410 + 3.52671i) q^{29} +(-1.88197 + 5.79210i) q^{31} +10.8541 q^{32} +(2.80902 - 1.76336i) q^{33} +3.00000 q^{34} +(-3.92705 + 2.85317i) q^{36} +(-5.04508 - 3.66547i) q^{37} +(4.73607 + 14.5761i) q^{38} +(-0.0729490 - 0.224514i) q^{39} +(-0.190983 + 0.138757i) q^{41} +(0.809017 - 2.48990i) q^{42} +6.70820 q^{43} +(12.3541 + 10.3229i) q^{44} +(-0.190983 + 0.587785i) q^{46} +(-8.16312 + 5.93085i) q^{47} +(-7.97214 - 5.79210i) q^{48} +(-1.85410 - 5.70634i) q^{49} +(-0.927051 - 0.673542i) q^{51} +(0.927051 - 0.673542i) q^{52} +(0.118034 - 0.363271i) q^{53} +2.61803 q^{54} +7.47214 q^{56} +(1.80902 - 5.56758i) q^{57} +(12.7082 - 9.23305i) q^{58} +(-5.97214 - 4.33901i) q^{59} +(-3.57295 - 10.9964i) q^{61} +(12.8992 + 9.37181i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(2.69098 - 8.28199i) q^{64} +(-2.11803 - 8.42075i) q^{66} -1.85410 q^{67} +(1.71885 - 5.29007i) q^{68} +(0.190983 - 0.138757i) q^{69} +(3.19098 + 9.82084i) q^{71} +(2.30902 + 7.10642i) q^{72} +(-4.61803 - 3.35520i) q^{73} +(-13.2082 + 9.59632i) q^{74} +28.4164 q^{76} +(2.54508 + 2.12663i) q^{77} -0.618034 q^{78} +(3.39919 - 10.4616i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(0.190983 + 0.587785i) q^{82} +(-0.454915 - 1.40008i) q^{83} +(-3.92705 - 2.85317i) q^{84} +(5.42705 - 16.7027i) q^{86} -6.00000 q^{87} +(20.9894 - 13.1760i) q^{88} -8.23607 q^{89} +(0.190983 - 0.138757i) q^{91} +(0.927051 + 0.673542i) q^{92} +(-1.88197 - 5.79210i) q^{93} +(8.16312 + 25.1235i) q^{94} +(-8.78115 + 6.37988i) q^{96} +(-2.42705 + 7.46969i) q^{97} -15.7082 q^{98} +(-1.23607 + 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} - q^{3} - 9 q^{4} + q^{6} - q^{7} - 13 q^{8} - q^{9} + O(q^{10}) \) \( 4 q + q^{2} - q^{3} - 9 q^{4} + q^{6} - q^{7} - 13 q^{8} - q^{9} - 11 q^{11} + 6 q^{12} - 7 q^{13} - 4 q^{14} + q^{16} - 12 q^{17} - 4 q^{18} - 10 q^{19} + 4 q^{21} - 4 q^{22} + 8 q^{23} + 7 q^{24} + 2 q^{26} - q^{27} + 6 q^{28} + 6 q^{29} - 12 q^{31} + 30 q^{32} + 9 q^{33} + 12 q^{34} - 9 q^{36} - 9 q^{37} + 10 q^{38} - 7 q^{39} - 3 q^{41} + q^{42} + 36 q^{44} - 3 q^{46} - 17 q^{47} - 14 q^{48} + 6 q^{49} + 3 q^{51} - 3 q^{52} - 4 q^{53} + 6 q^{54} + 12 q^{56} + 5 q^{57} + 24 q^{58} - 6 q^{59} - 21 q^{61} + 27 q^{62} - q^{63} + 13 q^{64} - 4 q^{66} + 6 q^{67} + 27 q^{68} + 3 q^{69} + 15 q^{71} + 7 q^{72} - 14 q^{73} - 26 q^{74} + 60 q^{76} - q^{77} + 2 q^{78} - 11 q^{79} - q^{81} + 3 q^{82} - 13 q^{83} - 9 q^{84} + 15 q^{86} - 24 q^{87} + 37 q^{88} - 24 q^{89} + 3 q^{91} - 3 q^{92} - 12 q^{93} + 17 q^{94} - 15 q^{96} - 3 q^{97} - 36 q^{98} + 4 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 2.48990i 0.572061 1.76062i −0.0739128 0.997265i \(-0.523549\pi\)
0.645974 0.763359i \(-0.276451\pi\)
\(3\) −0.809017 + 0.587785i −0.467086 + 0.339358i
\(4\) −3.92705 2.85317i −1.96353 1.42658i
\(5\) 0 0
\(6\) 0.809017 + 2.48990i 0.330280 + 1.01650i
\(7\) −0.809017 0.587785i −0.305780 0.222162i 0.424304 0.905520i \(-0.360519\pi\)
−0.730084 + 0.683358i \(0.760519\pi\)
\(8\) −6.04508 + 4.39201i −2.13726 + 1.55281i
\(9\) 0.309017 0.951057i 0.103006 0.317019i
\(10\) 0 0
\(11\) −3.30902 0.224514i −0.997706 0.0676935i
\(12\) 4.85410 1.40126
\(13\) −0.0729490 + 0.224514i −0.0202324 + 0.0622690i −0.960663 0.277717i \(-0.910422\pi\)
0.940431 + 0.339986i \(0.110422\pi\)
\(14\) −2.11803 + 1.53884i −0.566068 + 0.411273i
\(15\) 0 0
\(16\) 3.04508 + 9.37181i 0.761271 + 2.34295i
\(17\) 0.354102 + 1.08981i 0.0858823 + 0.264319i 0.984770 0.173860i \(-0.0556239\pi\)
−0.898888 + 0.438178i \(0.855624\pi\)
\(18\) −2.11803 1.53884i −0.499225 0.362708i
\(19\) −4.73607 + 3.44095i −1.08653 + 0.789409i −0.978810 0.204772i \(-0.934355\pi\)
−0.107719 + 0.994181i \(0.534355\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) −3.23607 + 8.05748i −0.689932 + 1.71786i
\(23\) −0.236068 −0.0492236 −0.0246118 0.999697i \(-0.507835\pi\)
−0.0246118 + 0.999697i \(0.507835\pi\)
\(24\) 2.30902 7.10642i 0.471326 1.45059i
\(25\) 0 0
\(26\) 0.500000 + 0.363271i 0.0980581 + 0.0712434i
\(27\) 0.309017 + 0.951057i 0.0594703 + 0.183031i
\(28\) 1.50000 + 4.61653i 0.283473 + 0.872441i
\(29\) 4.85410 + 3.52671i 0.901384 + 0.654894i 0.938821 0.344405i \(-0.111919\pi\)
−0.0374370 + 0.999299i \(0.511919\pi\)
\(30\) 0 0
\(31\) −1.88197 + 5.79210i −0.338011 + 1.04029i 0.627209 + 0.778851i \(0.284197\pi\)
−0.965220 + 0.261440i \(0.915803\pi\)
\(32\) 10.8541 1.91875
\(33\) 2.80902 1.76336i 0.488987 0.306961i
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) −3.92705 + 2.85317i −0.654508 + 0.475528i
\(37\) −5.04508 3.66547i −0.829407 0.602599i 0.0899846 0.995943i \(-0.471318\pi\)
−0.919391 + 0.393344i \(0.871318\pi\)
\(38\) 4.73607 + 14.5761i 0.768292 + 2.36456i
\(39\) −0.0729490 0.224514i −0.0116812 0.0359510i
\(40\) 0 0
\(41\) −0.190983 + 0.138757i −0.0298265 + 0.0216702i −0.602599 0.798044i \(-0.705868\pi\)
0.572772 + 0.819715i \(0.305868\pi\)
\(42\) 0.809017 2.48990i 0.124834 0.384200i
\(43\) 6.70820 1.02299 0.511496 0.859286i \(-0.329092\pi\)
0.511496 + 0.859286i \(0.329092\pi\)
\(44\) 12.3541 + 10.3229i 1.86245 + 1.55623i
\(45\) 0 0
\(46\) −0.190983 + 0.587785i −0.0281589 + 0.0866642i
\(47\) −8.16312 + 5.93085i −1.19071 + 0.865104i −0.993339 0.115224i \(-0.963241\pi\)
−0.197374 + 0.980328i \(0.563241\pi\)
\(48\) −7.97214 5.79210i −1.15068 0.836017i
\(49\) −1.85410 5.70634i −0.264872 0.815191i
\(50\) 0 0
\(51\) −0.927051 0.673542i −0.129813 0.0943147i
\(52\) 0.927051 0.673542i 0.128559 0.0934035i
\(53\) 0.118034 0.363271i 0.0162132 0.0498991i −0.942623 0.333860i \(-0.891649\pi\)
0.958836 + 0.283961i \(0.0916486\pi\)
\(54\) 2.61803 0.356269
\(55\) 0 0
\(56\) 7.47214 0.998506
\(57\) 1.80902 5.56758i 0.239610 0.737444i
\(58\) 12.7082 9.23305i 1.66867 1.21236i
\(59\) −5.97214 4.33901i −0.777506 0.564891i 0.126724 0.991938i \(-0.459554\pi\)
−0.904229 + 0.427047i \(0.859554\pi\)
\(60\) 0 0
\(61\) −3.57295 10.9964i −0.457469 1.40795i −0.868212 0.496194i \(-0.834730\pi\)
0.410742 0.911751i \(-0.365270\pi\)
\(62\) 12.8992 + 9.37181i 1.63820 + 1.19022i
\(63\) −0.809017 + 0.587785i −0.101927 + 0.0740540i
\(64\) 2.69098 8.28199i 0.336373 1.03525i
\(65\) 0 0
\(66\) −2.11803 8.42075i −0.260712 1.03652i
\(67\) −1.85410 −0.226515 −0.113257 0.993566i \(-0.536128\pi\)
−0.113257 + 0.993566i \(0.536128\pi\)
\(68\) 1.71885 5.29007i 0.208441 0.641515i
\(69\) 0.190983 0.138757i 0.0229917 0.0167044i
\(70\) 0 0
\(71\) 3.19098 + 9.82084i 0.378700 + 1.16552i 0.940948 + 0.338550i \(0.109937\pi\)
−0.562248 + 0.826968i \(0.690063\pi\)
\(72\) 2.30902 + 7.10642i 0.272120 + 0.837500i
\(73\) −4.61803 3.35520i −0.540500 0.392696i 0.283771 0.958892i \(-0.408415\pi\)
−0.824271 + 0.566196i \(0.808415\pi\)
\(74\) −13.2082 + 9.59632i −1.53542 + 1.11555i
\(75\) 0 0
\(76\) 28.4164 3.25959
\(77\) 2.54508 + 2.12663i 0.290039 + 0.242352i
\(78\) −0.618034 −0.0699786
\(79\) 3.39919 10.4616i 0.382438 1.17702i −0.555883 0.831260i \(-0.687620\pi\)
0.938322 0.345764i \(-0.112380\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 0.190983 + 0.587785i 0.0210905 + 0.0649100i
\(83\) −0.454915 1.40008i −0.0499334 0.153679i 0.922981 0.384846i \(-0.125746\pi\)
−0.972914 + 0.231167i \(0.925746\pi\)
\(84\) −3.92705 2.85317i −0.428476 0.311306i
\(85\) 0 0
\(86\) 5.42705 16.7027i 0.585214 1.80110i
\(87\) −6.00000 −0.643268
\(88\) 20.9894 13.1760i 2.23747 1.40457i
\(89\) −8.23607 −0.873021 −0.436511 0.899699i \(-0.643786\pi\)
−0.436511 + 0.899699i \(0.643786\pi\)
\(90\) 0 0
\(91\) 0.190983 0.138757i 0.0200205 0.0145457i
\(92\) 0.927051 + 0.673542i 0.0966517 + 0.0702216i
\(93\) −1.88197 5.79210i −0.195151 0.600612i
\(94\) 8.16312 + 25.1235i 0.841961 + 2.59129i
\(95\) 0 0
\(96\) −8.78115 + 6.37988i −0.896223 + 0.651144i
\(97\) −2.42705 + 7.46969i −0.246430 + 0.758433i 0.748968 + 0.662606i \(0.230549\pi\)
−0.995398 + 0.0958268i \(0.969451\pi\)
\(98\) −15.7082 −1.58677
\(99\) −1.23607 + 3.07768i −0.124230 + 0.309319i
\(100\) 0 0
\(101\) −3.16312 + 9.73508i −0.314742 + 0.968677i 0.661118 + 0.750282i \(0.270082\pi\)
−0.975860 + 0.218395i \(0.929918\pi\)
\(102\) −2.42705 + 1.76336i −0.240314 + 0.174598i
\(103\) −8.85410 6.43288i −0.872421 0.633851i 0.0588148 0.998269i \(-0.481268\pi\)
−0.931235 + 0.364418i \(0.881268\pi\)
\(104\) −0.545085 1.67760i −0.0534500 0.164502i
\(105\) 0 0
\(106\) −0.809017 0.587785i −0.0785787 0.0570908i
\(107\) −9.28115 + 6.74315i −0.897243 + 0.651885i −0.937756 0.347294i \(-0.887101\pi\)
0.0405134 + 0.999179i \(0.487101\pi\)
\(108\) 1.50000 4.61653i 0.144338 0.444225i
\(109\) −12.0000 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) 0 0
\(111\) 6.23607 0.591901
\(112\) 3.04508 9.37181i 0.287733 0.885553i
\(113\) 10.8992 7.91872i 1.02531 0.744931i 0.0579448 0.998320i \(-0.481545\pi\)
0.967364 + 0.253389i \(0.0815453\pi\)
\(114\) −12.3992 9.00854i −1.16129 0.843727i
\(115\) 0 0
\(116\) −9.00000 27.6992i −0.835629 2.57180i
\(117\) 0.190983 + 0.138757i 0.0176564 + 0.0128281i
\(118\) −15.6353 + 11.3597i −1.43934 + 1.04574i
\(119\) 0.354102 1.08981i 0.0324605 0.0999031i
\(120\) 0 0
\(121\) 10.8992 + 1.48584i 0.990835 + 0.135076i
\(122\) −30.2705 −2.74056
\(123\) 0.0729490 0.224514i 0.00657759 0.0202437i
\(124\) 23.9164 17.3763i 2.14776 1.56044i
\(125\) 0 0
\(126\) 0.809017 + 2.48990i 0.0720730 + 0.221818i
\(127\) −2.38197 7.33094i −0.211365 0.650516i −0.999392 0.0348741i \(-0.988897\pi\)
0.788026 0.615641i \(-0.211103\pi\)
\(128\) −0.881966 0.640786i −0.0779555 0.0566380i
\(129\) −5.42705 + 3.94298i −0.477825 + 0.347160i
\(130\) 0 0
\(131\) −11.7984 −1.03083 −0.515414 0.856941i \(-0.672362\pi\)
−0.515414 + 0.856941i \(0.672362\pi\)
\(132\) −16.0623 1.08981i −1.39804 0.0948561i
\(133\) 5.85410 0.507615
\(134\) −1.50000 + 4.61653i −0.129580 + 0.398807i
\(135\) 0 0
\(136\) −6.92705 5.03280i −0.593990 0.431559i
\(137\) −3.01722 9.28605i −0.257779 0.793361i −0.993269 0.115826i \(-0.963048\pi\)
0.735491 0.677535i \(-0.236952\pi\)
\(138\) −0.190983 0.587785i −0.0162576 0.0500356i
\(139\) −11.7812 8.55951i −0.999264 0.726008i −0.0373340 0.999303i \(-0.511887\pi\)
−0.961930 + 0.273295i \(0.911887\pi\)
\(140\) 0 0
\(141\) 3.11803 9.59632i 0.262586 0.808156i
\(142\) 27.0344 2.26868
\(143\) 0.291796 0.726543i 0.0244012 0.0607565i
\(144\) 9.85410 0.821175
\(145\) 0 0
\(146\) −12.0902 + 8.78402i −1.00059 + 0.726971i
\(147\) 4.85410 + 3.52671i 0.400360 + 0.290878i
\(148\) 9.35410 + 28.7890i 0.768902 + 2.36644i
\(149\) −1.30902 4.02874i −0.107239 0.330047i 0.883011 0.469353i \(-0.155513\pi\)
−0.990249 + 0.139306i \(0.955513\pi\)
\(150\) 0 0
\(151\) −0.854102 + 0.620541i −0.0695058 + 0.0504989i −0.621996 0.783021i \(-0.713678\pi\)
0.552490 + 0.833520i \(0.313678\pi\)
\(152\) 13.5172 41.6017i 1.09639 3.37435i
\(153\) 1.14590 0.0926404
\(154\) 7.35410 4.61653i 0.592610 0.372010i
\(155\) 0 0
\(156\) −0.354102 + 1.08981i −0.0283508 + 0.0872549i
\(157\) 12.7082 9.23305i 1.01423 0.736878i 0.0491340 0.998792i \(-0.484354\pi\)
0.965091 + 0.261915i \(0.0843539\pi\)
\(158\) −23.2984 16.9273i −1.85352 1.34666i
\(159\) 0.118034 + 0.363271i 0.00936070 + 0.0288093i
\(160\) 0 0
\(161\) 0.190983 + 0.138757i 0.0150516 + 0.0109356i
\(162\) −2.11803 + 1.53884i −0.166408 + 0.120903i
\(163\) 1.59017 4.89404i 0.124552 0.383331i −0.869267 0.494342i \(-0.835409\pi\)
0.993819 + 0.111011i \(0.0354090\pi\)
\(164\) 1.14590 0.0894796
\(165\) 0 0
\(166\) −3.85410 −0.299136
\(167\) −3.71885 + 11.4454i −0.287773 + 0.885674i 0.697781 + 0.716311i \(0.254171\pi\)
−0.985554 + 0.169363i \(0.945829\pi\)
\(168\) −6.04508 + 4.39201i −0.466388 + 0.338851i
\(169\) 10.4721 + 7.60845i 0.805549 + 0.585266i
\(170\) 0 0
\(171\) 1.80902 + 5.56758i 0.138339 + 0.425764i
\(172\) −26.3435 19.1396i −2.00867 1.45938i
\(173\) −14.5902 + 10.6004i −1.10927 + 0.805932i −0.982549 0.186006i \(-0.940445\pi\)
−0.126722 + 0.991938i \(0.540445\pi\)
\(174\) −4.85410 + 14.9394i −0.367989 + 1.13255i
\(175\) 0 0
\(176\) −7.97214 31.6951i −0.600922 2.38911i
\(177\) 7.38197 0.554863
\(178\) −6.66312 + 20.5070i −0.499422 + 1.53706i
\(179\) 6.89919 5.01255i 0.515669 0.374656i −0.299301 0.954159i \(-0.596753\pi\)
0.814970 + 0.579503i \(0.196753\pi\)
\(180\) 0 0
\(181\) 0.781153 + 2.40414i 0.0580626 + 0.178698i 0.975881 0.218301i \(-0.0700515\pi\)
−0.917819 + 0.396999i \(0.870051\pi\)
\(182\) −0.190983 0.587785i −0.0141566 0.0435695i
\(183\) 9.35410 + 6.79615i 0.691475 + 0.502386i
\(184\) 1.42705 1.03681i 0.105204 0.0764349i
\(185\) 0 0
\(186\) −15.9443 −1.16909
\(187\) −0.927051 3.68571i −0.0677927 0.269526i
\(188\) 48.9787 3.57214
\(189\) 0.309017 0.951057i 0.0224777 0.0691792i
\(190\) 0 0
\(191\) 0.663119 + 0.481784i 0.0479816 + 0.0348607i 0.611518 0.791231i \(-0.290559\pi\)
−0.563536 + 0.826092i \(0.690559\pi\)
\(192\) 2.69098 + 8.28199i 0.194205 + 0.597701i
\(193\) 0.972136 + 2.99193i 0.0699759 + 0.215364i 0.979929 0.199348i \(-0.0638824\pi\)
−0.909953 + 0.414712i \(0.863882\pi\)
\(194\) 16.6353 + 12.0862i 1.19434 + 0.867740i
\(195\) 0 0
\(196\) −9.00000 + 27.6992i −0.642857 + 1.97851i
\(197\) −13.0344 −0.928666 −0.464333 0.885661i \(-0.653706\pi\)
−0.464333 + 0.885661i \(0.653706\pi\)
\(198\) 6.66312 + 5.56758i 0.473527 + 0.395671i
\(199\) 6.70820 0.475532 0.237766 0.971322i \(-0.423585\pi\)
0.237766 + 0.971322i \(0.423585\pi\)
\(200\) 0 0
\(201\) 1.50000 1.08981i 0.105802 0.0768695i
\(202\) 21.6803 + 15.7517i 1.52542 + 1.10828i
\(203\) −1.85410 5.70634i −0.130132 0.400506i
\(204\) 1.71885 + 5.29007i 0.120343 + 0.370379i
\(205\) 0 0
\(206\) −23.1803 + 16.8415i −1.61505 + 1.17340i
\(207\) −0.0729490 + 0.224514i −0.00507031 + 0.0156048i
\(208\) −2.32624 −0.161296
\(209\) 16.4443 10.3229i 1.13747 0.714047i
\(210\) 0 0
\(211\) 1.11803 3.44095i 0.0769686 0.236885i −0.905168 0.425054i \(-0.860255\pi\)
0.982137 + 0.188169i \(0.0602552\pi\)
\(212\) −1.50000 + 1.08981i −0.103020 + 0.0748487i
\(213\) −8.35410 6.06961i −0.572414 0.415883i
\(214\) 9.28115 + 28.5645i 0.634447 + 1.95263i
\(215\) 0 0
\(216\) −6.04508 4.39201i −0.411316 0.298839i
\(217\) 4.92705 3.57971i 0.334470 0.243007i
\(218\) −9.70820 + 29.8788i −0.657523 + 2.02365i
\(219\) 5.70820 0.385725
\(220\) 0 0
\(221\) −0.270510 −0.0181965
\(222\) 5.04508 15.5272i 0.338604 1.04212i
\(223\) 5.80902 4.22050i 0.389001 0.282625i −0.376045 0.926601i \(-0.622716\pi\)
0.765046 + 0.643976i \(0.222716\pi\)
\(224\) −8.78115 6.37988i −0.586715 0.426274i
\(225\) 0 0
\(226\) −10.8992 33.5442i −0.725003 2.23133i
\(227\) 10.6631 + 7.74721i 0.707736 + 0.514200i 0.882443 0.470420i \(-0.155898\pi\)
−0.174706 + 0.984621i \(0.555898\pi\)
\(228\) −22.9894 + 16.7027i −1.52251 + 1.10617i
\(229\) 0.145898 0.449028i 0.00964121 0.0296726i −0.946120 0.323816i \(-0.895034\pi\)
0.955761 + 0.294143i \(0.0950342\pi\)
\(230\) 0 0
\(231\) −3.30902 0.224514i −0.217717 0.0147719i
\(232\) −44.8328 −2.94342
\(233\) 1.28115 3.94298i 0.0839311 0.258313i −0.900280 0.435311i \(-0.856638\pi\)
0.984211 + 0.176997i \(0.0566384\pi\)
\(234\) 0.500000 0.363271i 0.0326860 0.0237478i
\(235\) 0 0
\(236\) 11.0729 + 34.0790i 0.720788 + 2.21836i
\(237\) 3.39919 + 10.4616i 0.220801 + 0.679555i
\(238\) −2.42705 1.76336i −0.157322 0.114301i
\(239\) −0.309017 + 0.224514i −0.0199886 + 0.0145226i −0.597735 0.801694i \(-0.703932\pi\)
0.577746 + 0.816217i \(0.303932\pi\)
\(240\) 0 0
\(241\) 8.29180 0.534122 0.267061 0.963680i \(-0.413948\pi\)
0.267061 + 0.963680i \(0.413948\pi\)
\(242\) 12.5172 25.9358i 0.804637 1.66722i
\(243\) 1.00000 0.0641500
\(244\) −17.3435 + 53.3777i −1.11030 + 3.41716i
\(245\) 0 0
\(246\) −0.500000 0.363271i −0.0318788 0.0231613i
\(247\) −0.427051 1.31433i −0.0271726 0.0836287i
\(248\) −14.0623 43.2793i −0.892957 2.74824i
\(249\) 1.19098 + 0.865300i 0.0754755 + 0.0548361i
\(250\) 0 0
\(251\) −6.79180 + 20.9030i −0.428694 + 1.31939i 0.470718 + 0.882284i \(0.343995\pi\)
−0.899412 + 0.437102i \(0.856005\pi\)
\(252\) 4.85410 0.305780
\(253\) 0.781153 + 0.0530006i 0.0491107 + 0.00333212i
\(254\) −20.1803 −1.26623
\(255\) 0 0
\(256\) 11.7812 8.55951i 0.736322 0.534969i
\(257\) 24.0623 + 17.4823i 1.50097 + 1.09052i 0.969995 + 0.243125i \(0.0781725\pi\)
0.530970 + 0.847390i \(0.321828\pi\)
\(258\) 5.42705 + 16.7027i 0.337873 + 1.03987i
\(259\) 1.92705 + 5.93085i 0.119741 + 0.368525i
\(260\) 0 0
\(261\) 4.85410 3.52671i 0.300461 0.218298i
\(262\) −9.54508 + 29.3768i −0.589697 + 1.81490i
\(263\) 15.2705 0.941620 0.470810 0.882235i \(-0.343962\pi\)
0.470810 + 0.882235i \(0.343962\pi\)
\(264\) −9.23607 + 22.9969i −0.568441 + 1.41536i
\(265\) 0 0
\(266\) 4.73607 14.5761i 0.290387 0.893719i
\(267\) 6.66312 4.84104i 0.407776 0.296267i
\(268\) 7.28115 + 5.29007i 0.444767 + 0.323142i
\(269\) −7.85410 24.1724i −0.478873 1.47382i −0.840662 0.541560i \(-0.817834\pi\)
0.361789 0.932260i \(-0.382166\pi\)
\(270\) 0 0
\(271\) −15.0623 10.9434i −0.914970 0.664765i 0.0272970 0.999627i \(-0.491310\pi\)
−0.942267 + 0.334863i \(0.891310\pi\)
\(272\) −9.13525 + 6.63715i −0.553906 + 0.402436i
\(273\) −0.0729490 + 0.224514i −0.00441508 + 0.0135882i
\(274\) −25.5623 −1.54428
\(275\) 0 0
\(276\) −1.14590 −0.0689750
\(277\) 9.02786 27.7849i 0.542432 1.66943i −0.184587 0.982816i \(-0.559095\pi\)
0.727019 0.686617i \(-0.240905\pi\)
\(278\) −30.8435 + 22.4091i −1.84987 + 1.34401i
\(279\) 4.92705 + 3.57971i 0.294975 + 0.214312i
\(280\) 0 0
\(281\) 7.65248 + 23.5519i 0.456508 + 1.40499i 0.869355 + 0.494188i \(0.164535\pi\)
−0.412847 + 0.910801i \(0.635465\pi\)
\(282\) −21.3713 15.5272i −1.27264 0.924630i
\(283\) −4.61803 + 3.35520i −0.274514 + 0.199446i −0.716521 0.697566i \(-0.754267\pi\)
0.442007 + 0.897011i \(0.354267\pi\)
\(284\) 15.4894 47.6713i 0.919124 2.82877i
\(285\) 0 0
\(286\) −1.57295 1.31433i −0.0930104 0.0777178i
\(287\) 0.236068 0.0139347
\(288\) 3.35410 10.3229i 0.197642 0.608281i
\(289\) 12.6910 9.22054i 0.746528 0.542385i
\(290\) 0 0
\(291\) −2.42705 7.46969i −0.142276 0.437881i
\(292\) 8.56231 + 26.3521i 0.501071 + 1.54214i
\(293\) −17.5172 12.7270i −1.02337 0.743520i −0.0563966 0.998408i \(-0.517961\pi\)
−0.966970 + 0.254889i \(0.917961\pi\)
\(294\) 12.7082 9.23305i 0.741158 0.538482i
\(295\) 0 0
\(296\) 46.5967 2.70838
\(297\) −0.809017 3.21644i −0.0469439 0.186637i
\(298\) −11.0902 −0.642436
\(299\) 0.0172209 0.0530006i 0.000995912 0.00306510i
\(300\) 0 0
\(301\) −5.42705 3.94298i −0.312810 0.227270i
\(302\) 0.854102 + 2.62866i 0.0491480 + 0.151262i
\(303\) −3.16312 9.73508i −0.181716 0.559266i
\(304\) −46.6697 33.9075i −2.67669 1.94473i
\(305\) 0 0
\(306\) 0.927051 2.85317i 0.0529960 0.163105i
\(307\) −27.9787 −1.59683 −0.798415 0.602108i \(-0.794328\pi\)
−0.798415 + 0.602108i \(0.794328\pi\)
\(308\) −3.92705 15.6129i −0.223764 0.889629i
\(309\) 10.9443 0.622598
\(310\) 0 0
\(311\) −9.42705 + 6.84915i −0.534559 + 0.388380i −0.822060 0.569400i \(-0.807175\pi\)
0.287501 + 0.957780i \(0.407175\pi\)
\(312\) 1.42705 + 1.03681i 0.0807909 + 0.0586980i
\(313\) 0.781153 + 2.40414i 0.0441534 + 0.135890i 0.970703 0.240282i \(-0.0772400\pi\)
−0.926550 + 0.376172i \(0.877240\pi\)
\(314\) −12.7082 39.1118i −0.717165 2.20721i
\(315\) 0 0
\(316\) −43.1976 + 31.3849i −2.43005 + 1.76554i
\(317\) 2.10739 6.48588i 0.118363 0.364283i −0.874271 0.485439i \(-0.838660\pi\)
0.992634 + 0.121155i \(0.0386599\pi\)
\(318\) 1.00000 0.0560772
\(319\) −15.2705 12.7598i −0.854984 0.714410i
\(320\) 0 0
\(321\) 3.54508 10.9106i 0.197867 0.608973i
\(322\) 0.500000 0.363271i 0.0278639 0.0202443i
\(323\) −5.42705 3.94298i −0.301969 0.219393i
\(324\) 1.50000 + 4.61653i 0.0833333 + 0.256474i
\(325\) 0 0
\(326\) −10.8992 7.91872i −0.603650 0.438577i
\(327\) 9.70820 7.05342i 0.536865 0.390055i
\(328\) 0.545085 1.67760i 0.0300973 0.0926299i
\(329\) 10.0902 0.556289
\(330\) 0 0
\(331\) 16.7082 0.918366 0.459183 0.888342i \(-0.348142\pi\)
0.459183 + 0.888342i \(0.348142\pi\)
\(332\) −2.20820 + 6.79615i −0.121191 + 0.372987i
\(333\) −5.04508 + 3.66547i −0.276469 + 0.200866i
\(334\) 25.4894 + 18.5191i 1.39472 + 1.01332i
\(335\) 0 0
\(336\) 3.04508 + 9.37181i 0.166123 + 0.511274i
\(337\) −14.7082 10.6861i −0.801207 0.582111i 0.110061 0.993925i \(-0.464895\pi\)
−0.911268 + 0.411814i \(0.864895\pi\)
\(338\) 27.4164 19.9192i 1.49126 1.08346i
\(339\) −4.16312 + 12.8128i −0.226110 + 0.695894i
\(340\) 0 0
\(341\) 7.52786 18.7436i 0.407657 1.01502i
\(342\) 15.3262 0.828748
\(343\) −4.01722 + 12.3637i −0.216910 + 0.667579i
\(344\) −40.5517 + 29.4625i −2.18640 + 1.58851i
\(345\) 0 0
\(346\) 14.5902 + 44.9039i 0.784372 + 2.41405i
\(347\) 0.472136 + 1.45309i 0.0253456 + 0.0780057i 0.962929 0.269754i \(-0.0869424\pi\)
−0.937584 + 0.347760i \(0.886942\pi\)
\(348\) 23.5623 + 17.1190i 1.26307 + 0.917676i
\(349\) −10.2812 + 7.46969i −0.550337 + 0.399844i −0.827910 0.560861i \(-0.810470\pi\)
0.277572 + 0.960705i \(0.410470\pi\)
\(350\) 0 0
\(351\) −0.236068 −0.0126004
\(352\) −35.9164 2.43690i −1.91435 0.129887i
\(353\) 12.0000 0.638696 0.319348 0.947638i \(-0.396536\pi\)
0.319348 + 0.947638i \(0.396536\pi\)
\(354\) 5.97214 18.3803i 0.317415 0.976904i
\(355\) 0 0
\(356\) 32.3435 + 23.4989i 1.71420 + 1.24544i
\(357\) 0.354102 + 1.08981i 0.0187411 + 0.0576791i
\(358\) −6.89919 21.2335i −0.364633 1.12223i
\(359\) 7.85410 + 5.70634i 0.414524 + 0.301169i 0.775431 0.631433i \(-0.217533\pi\)
−0.360907 + 0.932602i \(0.617533\pi\)
\(360\) 0 0
\(361\) 4.71885 14.5231i 0.248360 0.764375i
\(362\) 6.61803 0.347836
\(363\) −9.69098 + 5.20431i −0.508645 + 0.273155i
\(364\) −1.14590 −0.0600614
\(365\) 0 0
\(366\) 24.4894 17.7926i 1.28008 0.930032i
\(367\) 17.9164 + 13.0170i 0.935229 + 0.679484i 0.947267 0.320444i \(-0.103832\pi\)
−0.0120386 + 0.999928i \(0.503832\pi\)
\(368\) −0.718847 2.21238i −0.0374725 0.115328i
\(369\) 0.0729490 + 0.224514i 0.00379757 + 0.0116877i
\(370\) 0 0
\(371\) −0.309017 + 0.224514i −0.0160434 + 0.0116562i
\(372\) −9.13525 + 28.1154i −0.473641 + 1.45772i
\(373\) −0.888544 −0.0460071 −0.0230035 0.999735i \(-0.507323\pi\)
−0.0230035 + 0.999735i \(0.507323\pi\)
\(374\) −9.92705 0.673542i −0.513316 0.0348280i
\(375\) 0 0
\(376\) 23.2984 71.7050i 1.20152 3.69790i
\(377\) −1.14590 + 0.832544i −0.0590168 + 0.0428782i
\(378\) −2.11803 1.53884i −0.108940 0.0791495i
\(379\) −7.69098 23.6704i −0.395059 1.21587i −0.928915 0.370292i \(-0.879258\pi\)
0.533856 0.845575i \(-0.320742\pi\)
\(380\) 0 0
\(381\) 6.23607 + 4.53077i 0.319483 + 0.232118i
\(382\) 1.73607 1.26133i 0.0888250 0.0645351i
\(383\) 3.92705 12.0862i 0.200663 0.617577i −0.799201 0.601064i \(-0.794744\pi\)
0.999864 0.0165128i \(-0.00525642\pi\)
\(384\) 1.09017 0.0556325
\(385\) 0 0
\(386\) 8.23607 0.419205
\(387\) 2.07295 6.37988i 0.105374 0.324308i
\(388\) 30.8435 22.4091i 1.56584 1.13765i
\(389\) 29.7254 + 21.5968i 1.50714 + 1.09500i 0.967427 + 0.253151i \(0.0814669\pi\)
0.539712 + 0.841850i \(0.318533\pi\)
\(390\) 0 0
\(391\) −0.0835921 0.257270i −0.00422744 0.0130107i
\(392\) 36.2705 + 26.3521i 1.83194 + 1.33098i
\(393\) 9.54508 6.93491i 0.481486 0.349820i
\(394\) −10.5451 + 32.4544i −0.531254 + 1.63503i
\(395\) 0 0
\(396\) 13.6353 8.55951i 0.685197 0.430131i
\(397\) 18.7082 0.938938 0.469469 0.882949i \(-0.344445\pi\)
0.469469 + 0.882949i \(0.344445\pi\)
\(398\) 5.42705 16.7027i 0.272033 0.837233i
\(399\) −4.73607 + 3.44095i −0.237100 + 0.172263i
\(400\) 0 0
\(401\) −9.79180 30.1360i −0.488979 1.50492i −0.826134 0.563473i \(-0.809465\pi\)
0.337155 0.941449i \(-0.390535\pi\)
\(402\) −1.50000 4.61653i −0.0748132 0.230251i
\(403\) −1.16312 0.845055i −0.0579391 0.0420952i
\(404\) 40.1976 29.2052i 1.99990 1.45301i
\(405\) 0 0
\(406\) −15.7082 −0.779585
\(407\) 15.8713 + 13.2618i 0.786712 + 0.657363i
\(408\) 8.56231 0.423897
\(409\) −2.00000 + 6.15537i −0.0988936 + 0.304363i −0.988249 0.152854i \(-0.951154\pi\)
0.889355 + 0.457217i \(0.151154\pi\)
\(410\) 0 0
\(411\) 7.89919 + 5.73910i 0.389638 + 0.283089i
\(412\) 16.4164 + 50.5245i 0.808778 + 2.48916i
\(413\) 2.28115 + 7.02067i 0.112248 + 0.345464i
\(414\) 0.500000 + 0.363271i 0.0245737 + 0.0178538i
\(415\) 0 0
\(416\) −0.791796 + 2.43690i −0.0388210 + 0.119479i
\(417\) 14.5623 0.713119
\(418\) −12.3992 49.2959i −0.606464 2.41114i
\(419\) 31.4508 1.53647 0.768237 0.640165i \(-0.221134\pi\)
0.768237 + 0.640165i \(0.221134\pi\)
\(420\) 0 0
\(421\) −8.50000 + 6.17561i −0.414265 + 0.300981i −0.775326 0.631561i \(-0.782414\pi\)
0.361061 + 0.932542i \(0.382414\pi\)
\(422\) −7.66312 5.56758i −0.373035 0.271026i
\(423\) 3.11803 + 9.59632i 0.151604 + 0.466589i
\(424\) 0.881966 + 2.71441i 0.0428321 + 0.131824i
\(425\) 0 0
\(426\) −21.8713 + 15.8904i −1.05967 + 0.769895i
\(427\) −3.57295 + 10.9964i −0.172907 + 0.532153i
\(428\) 55.6869 2.69173
\(429\) 0.190983 + 0.759299i 0.00922075 + 0.0366593i
\(430\) 0 0
\(431\) −1.82624 + 5.62058i −0.0879668 + 0.270734i −0.985357 0.170504i \(-0.945460\pi\)
0.897390 + 0.441238i \(0.145460\pi\)
\(432\) −7.97214 + 5.79210i −0.383560 + 0.278672i
\(433\) 28.5623 + 20.7517i 1.37262 + 0.997264i 0.997528 + 0.0702758i \(0.0223879\pi\)
0.375089 + 0.926989i \(0.377612\pi\)
\(434\) −4.92705 15.1639i −0.236506 0.727891i
\(435\) 0 0
\(436\) 47.1246 + 34.2380i 2.25686 + 1.63970i
\(437\) 1.11803 0.812299i 0.0534828 0.0388575i
\(438\) 4.61803 14.2128i 0.220658 0.679116i
\(439\) 23.2918 1.11166 0.555828 0.831297i \(-0.312401\pi\)
0.555828 + 0.831297i \(0.312401\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) −0.218847 + 0.673542i −0.0104095 + 0.0320371i
\(443\) −25.5623 + 18.5721i −1.21450 + 0.882387i −0.995632 0.0933668i \(-0.970237\pi\)
−0.218870 + 0.975754i \(0.570237\pi\)
\(444\) −24.4894 17.7926i −1.16221 0.844397i
\(445\) 0 0
\(446\) −5.80902 17.8783i −0.275065 0.846563i
\(447\) 3.42705 + 2.48990i 0.162094 + 0.117768i
\(448\) −7.04508 + 5.11855i −0.332849 + 0.241829i
\(449\) −2.79837 + 8.61251i −0.132063 + 0.406449i −0.995122 0.0986549i \(-0.968546\pi\)
0.863058 + 0.505104i \(0.168546\pi\)
\(450\) 0 0
\(451\) 0.663119 0.416272i 0.0312251 0.0196015i
\(452\) −65.3951 −3.07593
\(453\) 0.326238 1.00406i 0.0153280 0.0471747i
\(454\) 27.9164 20.2825i 1.31018 0.951903i
\(455\) 0 0
\(456\) 13.5172 + 41.6017i 0.633002 + 1.94818i
\(457\) −7.40983 22.8051i −0.346617 1.06678i −0.960712 0.277546i \(-0.910479\pi\)
0.614095 0.789232i \(-0.289521\pi\)
\(458\) −1.00000 0.726543i −0.0467269 0.0339491i
\(459\) −0.927051 + 0.673542i −0.0432710 + 0.0314382i
\(460\) 0 0
\(461\) 9.27051 0.431771 0.215885 0.976419i \(-0.430736\pi\)
0.215885 + 0.976419i \(0.430736\pi\)
\(462\) −3.23607 + 8.05748i −0.150556 + 0.374868i
\(463\) −1.72949 −0.0803762 −0.0401881 0.999192i \(-0.512796\pi\)
−0.0401881 + 0.999192i \(0.512796\pi\)
\(464\) −18.2705 + 56.2308i −0.848187 + 2.61045i
\(465\) 0 0
\(466\) −8.78115 6.37988i −0.406779 0.295542i
\(467\) −6.45492 19.8662i −0.298698 0.919297i −0.981954 0.189119i \(-0.939437\pi\)
0.683256 0.730179i \(-0.260563\pi\)
\(468\) −0.354102 1.08981i −0.0163684 0.0503767i
\(469\) 1.50000 + 1.08981i 0.0692636 + 0.0503229i
\(470\) 0 0
\(471\) −4.85410 + 14.9394i −0.223665 + 0.688371i
\(472\) 55.1591 2.53890
\(473\) −22.1976 1.50609i −1.02064 0.0692499i
\(474\) 28.7984 1.32275
\(475\) 0 0
\(476\) −4.50000 + 3.26944i −0.206257 + 0.149855i
\(477\) −0.309017 0.224514i −0.0141489 0.0102798i
\(478\) 0.309017 + 0.951057i 0.0141341 + 0.0435003i
\(479\) −8.77051 26.9929i −0.400735 1.23333i −0.924405 0.381414i \(-0.875437\pi\)
0.523670 0.851921i \(-0.324563\pi\)
\(480\) 0 0
\(481\) 1.19098 0.865300i 0.0543042 0.0394543i
\(482\) 6.70820 20.6457i 0.305550 0.940387i
\(483\) −0.236068 −0.0107415
\(484\) −38.5623 36.9322i −1.75283 1.67874i
\(485\) 0 0
\(486\) 0.809017 2.48990i 0.0366978 0.112944i
\(487\) −10.2812 + 7.46969i −0.465884 + 0.338484i −0.795835 0.605514i \(-0.792968\pi\)
0.329951 + 0.943998i \(0.392968\pi\)
\(488\) 69.8951 + 50.7818i 3.16400 + 2.29878i
\(489\) 1.59017 + 4.89404i 0.0719100 + 0.221316i
\(490\) 0 0
\(491\) 14.4894 + 10.5271i 0.653896 + 0.475083i 0.864596 0.502468i \(-0.167574\pi\)
−0.210700 + 0.977551i \(0.567574\pi\)
\(492\) −0.927051 + 0.673542i −0.0417947 + 0.0303656i
\(493\) −2.12461 + 6.53888i −0.0956877 + 0.294496i
\(494\) −3.61803 −0.162783
\(495\) 0 0
\(496\) −60.0132 −2.69467
\(497\) 3.19098 9.82084i 0.143135 0.440525i
\(498\) 3.11803 2.26538i 0.139722 0.101514i
\(499\) 14.6803 + 10.6659i 0.657182 + 0.477471i 0.865710 0.500546i \(-0.166867\pi\)
−0.208528 + 0.978016i \(0.566867\pi\)
\(500\) 0 0
\(501\) −3.71885 11.4454i −0.166146 0.511344i
\(502\) 46.5517 + 33.8218i 2.07770 + 1.50954i
\(503\) 7.00000 5.08580i 0.312115 0.226765i −0.420689 0.907205i \(-0.638212\pi\)
0.732803 + 0.680441i \(0.238212\pi\)
\(504\) 2.30902 7.10642i 0.102852 0.316545i
\(505\) 0 0
\(506\) 0.763932 1.90211i 0.0339609 0.0845592i
\(507\) −12.9443 −0.574875
\(508\) −11.5623 + 35.5851i −0.512994 + 1.57883i
\(509\) −31.3435 + 22.7724i −1.38927 + 1.00937i −0.393330 + 0.919397i \(0.628677\pi\)
−0.995945 + 0.0899695i \(0.971323\pi\)
\(510\) 0 0
\(511\) 1.76393 + 5.42882i 0.0780318 + 0.240157i
\(512\) −12.4549 38.3323i −0.550435 1.69406i
\(513\) −4.73607 3.44095i −0.209103 0.151922i
\(514\) 62.9959 45.7692i 2.77863 2.01879i
\(515\) 0 0
\(516\) 32.5623 1.43348
\(517\) 28.3435 17.7926i 1.24654 0.782516i
\(518\) 16.3262 0.717334
\(519\) 5.57295 17.1518i 0.244625 0.752879i
\(520\) 0 0
\(521\) −7.23607 5.25731i −0.317018 0.230327i 0.417884 0.908500i \(-0.362772\pi\)
−0.734902 + 0.678173i \(0.762772\pi\)
\(522\) −4.85410 14.9394i −0.212458 0.653879i
\(523\) −5.64590 17.3763i −0.246878 0.759812i −0.995322 0.0966140i \(-0.969199\pi\)
0.748444 0.663198i \(-0.230801\pi\)
\(524\) 46.3328 + 33.6628i 2.02406 + 1.47056i
\(525\) 0 0
\(526\) 12.3541 38.0220i 0.538664 1.65784i
\(527\) −6.97871 −0.303998
\(528\) 25.0795 + 20.9560i 1.09145 + 0.911993i
\(529\) −22.9443 −0.997577
\(530\) 0 0
\(531\) −5.97214 + 4.33901i −0.259169 + 0.188297i
\(532\) −22.9894 16.7027i −0.996715 0.724156i
\(533\) −0.0172209 0.0530006i −0.000745921 0.00229571i
\(534\) −6.66312 20.5070i −0.288341 0.887423i
\(535\) 0 0
\(536\) 11.2082 8.14324i 0.484121 0.351734i
\(537\) −2.63525 + 8.11048i −0.113720 + 0.349993i
\(538\) −66.5410 −2.86879
\(539\) 4.85410 + 19.2986i 0.209081 + 0.831251i
\(540\) 0 0
\(541\) −2.31559 + 7.12667i −0.0995552 + 0.306399i −0.988414 0.151782i \(-0.951499\pi\)
0.888859 + 0.458181i \(0.151499\pi\)
\(542\) −39.4336 + 28.6502i −1.69382 + 1.23063i
\(543\) −2.04508 1.48584i −0.0877630 0.0637635i
\(544\) 3.84346 + 11.8290i 0.164787 + 0.507162i
\(545\) 0 0
\(546\) 0.500000 + 0.363271i 0.0213980 + 0.0155466i
\(547\) −24.8713 + 18.0701i −1.06342 + 0.772621i −0.974718 0.223438i \(-0.928272\pi\)
−0.0887027 + 0.996058i \(0.528272\pi\)
\(548\) −14.6459 + 45.0754i −0.625642 + 1.92553i
\(549\) −11.5623 −0.493467
\(550\) 0 0
\(551\) −35.1246 −1.49636
\(552\) −0.545085 + 1.67760i −0.0232004 + 0.0714034i
\(553\) −8.89919 + 6.46564i −0.378432 + 0.274947i
\(554\) −61.8779 44.9569i −2.62894 1.91004i
\(555\) 0 0
\(556\) 21.8435 + 67.2273i 0.926369 + 2.85107i
\(557\) 30.4443 + 22.1191i 1.28997 + 0.937215i 0.999805 0.0197634i \(-0.00629130\pi\)
0.290161 + 0.956978i \(0.406291\pi\)
\(558\) 12.8992 9.37181i 0.546066 0.396740i
\(559\) −0.489357 + 1.50609i −0.0206976 + 0.0637006i
\(560\) 0 0
\(561\) 2.91641 + 2.43690i 0.123131 + 0.102886i
\(562\) 64.8328 2.73481
\(563\) −12.5451 + 38.6098i −0.528712 + 1.62721i 0.228144 + 0.973627i \(0.426734\pi\)
−0.756856 + 0.653582i \(0.773266\pi\)
\(564\) −39.6246 + 28.7890i −1.66850 + 1.21223i
\(565\) 0 0
\(566\) 4.61803 + 14.2128i 0.194110 + 0.597411i
\(567\) 0.309017 + 0.951057i 0.0129775 + 0.0399406i
\(568\) −62.4230 45.3530i −2.61921 1.90297i
\(569\) −27.6525 + 20.0907i −1.15925 + 0.842246i −0.989683 0.143272i \(-0.954237\pi\)
−0.169569 + 0.985518i \(0.554237\pi\)
\(570\) 0 0
\(571\) −9.09017 −0.380412 −0.190206 0.981744i \(-0.560916\pi\)
−0.190206 + 0.981744i \(0.560916\pi\)
\(572\) −3.21885 + 2.02063i −0.134587 + 0.0844866i
\(573\) −0.819660 −0.0342418
\(574\) 0.190983 0.587785i 0.00797148 0.0245337i
\(575\) 0 0
\(576\) −7.04508 5.11855i −0.293545 0.213273i
\(577\) −9.79837 30.1563i −0.407912 1.25542i −0.918439 0.395562i \(-0.870550\pi\)
0.510528 0.859861i \(-0.329450\pi\)
\(578\) −12.6910 39.0588i −0.527875 1.62463i
\(579\) −2.54508 1.84911i −0.105770 0.0768465i
\(580\) 0 0
\(581\) −0.454915 + 1.40008i −0.0188731 + 0.0580853i
\(582\) −20.5623 −0.852335
\(583\) −0.472136 + 1.17557i −0.0195539 + 0.0486872i
\(584\) 42.6525 1.76497
\(585\) 0 0
\(586\) −45.8607 + 33.3197i −1.89449 + 1.37643i
\(587\) −1.71885 1.24882i −0.0709444 0.0515441i 0.551748 0.834011i \(-0.313961\pi\)
−0.622692 + 0.782467i \(0.713961\pi\)
\(588\) −9.00000 27.6992i −0.371154 1.14229i
\(589\) −11.0172 33.9075i −0.453957 1.39714i
\(590\) 0 0
\(591\) 10.5451 7.66145i 0.433767 0.315150i
\(592\) 18.9894 58.4432i 0.780458 2.40200i
\(593\) 14.0344 0.576325 0.288163 0.957581i \(-0.406956\pi\)
0.288163 + 0.957581i \(0.406956\pi\)
\(594\) −8.66312 0.587785i −0.355452 0.0241171i
\(595\) 0 0
\(596\) −6.35410 + 19.5559i −0.260274 + 0.801041i
\(597\) −5.42705 + 3.94298i −0.222114 + 0.161376i
\(598\) −0.118034 0.0857567i −0.00482677 0.00350685i
\(599\) 3.90983 + 12.0332i 0.159751 + 0.491664i 0.998611 0.0526833i \(-0.0167774\pi\)
−0.838860 + 0.544347i \(0.816777\pi\)
\(600\) 0 0
\(601\) 5.57295 + 4.04898i 0.227325 + 0.165162i 0.695618 0.718412i \(-0.255131\pi\)
−0.468293 + 0.883573i \(0.655131\pi\)
\(602\) −14.2082 + 10.3229i −0.579083 + 0.420729i
\(603\) −0.572949 + 1.76336i −0.0233323 + 0.0718094i
\(604\) 5.12461 0.208517
\(605\) 0 0
\(606\) −26.7984 −1.08861
\(607\) 5.11803 15.7517i 0.207735 0.639341i −0.791855 0.610709i \(-0.790885\pi\)
0.999590 0.0286327i \(-0.00911532\pi\)
\(608\) −51.4058 + 37.3485i −2.08478 + 1.51468i
\(609\) 4.85410 + 3.52671i 0.196698 + 0.142910i
\(610\) 0 0
\(611\) −0.736068 2.26538i −0.0297781 0.0916476i
\(612\) −4.50000 3.26944i −0.181902 0.132159i
\(613\) −11.5623 + 8.40051i −0.466997 + 0.339293i −0.796270 0.604942i \(-0.793196\pi\)
0.329273 + 0.944235i \(0.393196\pi\)
\(614\) −22.6353 + 69.6642i −0.913485 + 2.81142i
\(615\) 0 0
\(616\) −24.7254 1.67760i −0.996216 0.0675924i
\(617\) −11.1803 −0.450104 −0.225052 0.974347i \(-0.572255\pi\)
−0.225052 + 0.974347i \(0.572255\pi\)
\(618\) 8.85410 27.2501i 0.356164 1.09616i
\(619\) −19.5172 + 14.1801i −0.784463 + 0.569946i −0.906315 0.422602i \(-0.861117\pi\)
0.121852 + 0.992548i \(0.461117\pi\)
\(620\) 0 0
\(621\) −0.0729490 0.224514i −0.00292734 0.00900944i
\(622\) 9.42705 + 29.0135i 0.377990 + 1.16333i
\(623\) 6.66312 + 4.84104i 0.266952 + 0.193952i
\(624\) 1.88197 1.36733i 0.0753389 0.0547369i
\(625\) 0 0
\(626\) 6.61803 0.264510
\(627\) −7.23607 + 18.0171i −0.288981 + 0.719533i
\(628\) −76.2492 −3.04268
\(629\) 2.20820 6.79615i 0.0880469 0.270980i
\(630\) 0 0
\(631\) −15.5451 11.2942i −0.618840 0.449614i 0.233676 0.972314i \(-0.424924\pi\)
−0.852516 + 0.522701i \(0.824924\pi\)
\(632\) 25.3992 + 78.1707i 1.01033 + 3.10946i
\(633\) 1.11803 + 3.44095i 0.0444379 + 0.136766i
\(634\) −14.4443 10.4944i −0.573655 0.416785i
\(635\) 0 0
\(636\) 0.572949 1.76336i 0.0227189 0.0699216i
\(637\) 1.41641 0.0561201
\(638\) −44.1246 + 27.6992i −1.74691 + 1.09662i
\(639\) 10.3262 0.408500
\(640\) 0 0
\(641\) 20.2984 14.7476i 0.801738 0.582496i −0.109686 0.993966i \(-0.534984\pi\)
0.911423 + 0.411470i \(0.134984\pi\)
\(642\) −24.2984 17.6538i −0.958980 0.696740i
\(643\) −6.44427 19.8334i −0.254137 0.782154i −0.993998 0.109394i \(-0.965109\pi\)
0.739861 0.672760i \(-0.234891\pi\)
\(644\) −0.354102 1.08981i −0.0139536 0.0429447i
\(645\) 0 0
\(646\) −14.2082 + 10.3229i −0.559014 + 0.406148i
\(647\) −13.9164 + 42.8303i −0.547110 + 1.68383i 0.168808 + 0.985649i \(0.446008\pi\)
−0.715918 + 0.698184i \(0.753992\pi\)
\(648\) 7.47214 0.293533
\(649\) 18.7877 + 15.6987i 0.737483 + 0.616227i
\(650\) 0 0
\(651\) −1.88197 + 5.79210i −0.0737601 + 0.227010i
\(652\) −20.2082 + 14.6821i −0.791414 + 0.574996i
\(653\) −4.54508 3.30220i −0.177863 0.129225i 0.495292 0.868727i \(-0.335061\pi\)
−0.673155 + 0.739502i \(0.735061\pi\)
\(654\) −9.70820 29.8788i −0.379621 1.16835i
\(655\) 0 0
\(656\) −1.88197 1.36733i −0.0734784 0.0533852i
\(657\) −4.61803 + 3.35520i −0.180167 + 0.130899i
\(658\) 8.16312 25.1235i 0.318232 0.979416i
\(659\) −41.1246 −1.60199 −0.800994 0.598673i \(-0.795695\pi\)
−0.800994 + 0.598673i \(0.795695\pi\)
\(660\) 0 0
\(661\) 36.5623 1.42211 0.711054 0.703137i \(-0.248218\pi\)
0.711054 + 0.703137i \(0.248218\pi\)
\(662\) 13.5172 41.6017i 0.525362 1.61690i
\(663\) 0.218847 0.159002i 0.00849932 0.00617511i
\(664\) 8.89919 + 6.46564i 0.345355 + 0.250915i
\(665\) 0 0
\(666\) 5.04508 + 15.5272i 0.195493 + 0.601666i
\(667\) −1.14590 0.832544i −0.0443693 0.0322362i
\(668\) 47.2599 34.3363i 1.82854 1.32851i
\(669\) −2.21885 + 6.82891i −0.0857856 + 0.264021i
\(670\) 0 0
\(671\) 9.35410 + 37.1895i 0.361111 + 1.43568i
\(672\) 10.8541 0.418706
\(673\) −11.0729 + 34.0790i −0.426831 + 1.31365i 0.474399 + 0.880310i \(0.342665\pi\)
−0.901230 + 0.433340i \(0.857335\pi\)
\(674\) −38.5066 + 27.9767i −1.48322 + 1.07762i
\(675\) 0 0
\(676\) −19.4164 59.7576i −0.746785 2.29837i
\(677\) −4.18034 12.8658i −0.160664 0.494471i 0.838027 0.545629i \(-0.183709\pi\)
−0.998691 + 0.0511572i \(0.983709\pi\)
\(678\) 28.5344 + 20.7315i 1.09586 + 0.796188i
\(679\) 6.35410 4.61653i 0.243848 0.177166i
\(680\) 0 0
\(681\) −13.1803 −0.505072
\(682\) −40.5795 33.9075i −1.55387 1.29839i
\(683\) −9.06888 −0.347011 −0.173506 0.984833i \(-0.555509\pi\)
−0.173506 + 0.984833i \(0.555509\pi\)
\(684\) 8.78115 27.0256i 0.335756 1.03335i
\(685\) 0 0
\(686\) 27.5344 + 20.0049i 1.05127 + 0.763792i
\(687\) 0.145898 + 0.449028i 0.00556636 + 0.0171315i
\(688\) 20.4271 + 62.8680i 0.778774 + 2.39682i
\(689\) 0.0729490 + 0.0530006i 0.00277914 + 0.00201916i
\(690\) 0 0
\(691\) 0.416408 1.28157i 0.0158409 0.0487533i −0.942824 0.333292i \(-0.891840\pi\)
0.958665 + 0.284539i \(0.0918405\pi\)
\(692\) 87.5410 3.32781
\(693\) 2.80902 1.76336i 0.106706 0.0669843i
\(694\) 4.00000 0.151838
\(695\) 0 0
\(696\) 36.2705 26.3521i 1.37483 0.998873i
\(697\) −0.218847 0.159002i −0.00828942 0.00602262i
\(698\) 10.2812 + 31.6421i 0.389147 + 1.19767i
\(699\) 1.28115 + 3.94298i 0.0484577 + 0.149137i
\(700\) 0 0
\(701\) 28.1525 20.4540i 1.06330 0.772536i 0.0886075 0.996067i \(-0.471758\pi\)
0.974697 + 0.223531i \(0.0717583\pi\)
\(702\) −0.190983 + 0.587785i −0.00720819 + 0.0221845i
\(703\) 36.5066 1.37687
\(704\) −10.7639 + 26.8011i −0.405681 + 1.01010i
\(705\) 0 0
\(706\) 9.70820 29.8788i 0.365373 1.12450i
\(707\) 8.28115 6.01661i 0.311445 0.226278i
\(708\) −28.9894 21.0620i −1.08949 0.791558i
\(709\) 3.46556 + 10.6659i 0.130152 + 0.400566i 0.994804 0.101804i \(-0.0324615\pi\)
−0.864653 + 0.502370i \(0.832462\pi\)
\(710\) 0 0
\(711\) −8.89919 6.46564i −0.333746 0.242480i
\(712\) 49.7877 36.1729i 1.86587 1.35564i
\(713\) 0.444272 1.36733i 0.0166381 0.0512068i
\(714\) 3.00000 0.112272
\(715\) 0 0
\(716\) −41.3951 −1.54701
\(717\) 0.118034 0.363271i 0.00440806 0.0135666i
\(718\) 20.5623 14.9394i 0.767378 0.557533i
\(719\) 31.1353 + 22.6211i 1.16115 + 0.843624i 0.989923 0.141608i \(-0.0452271\pi\)
0.171226 + 0.985232i \(0.445227\pi\)
\(720\) 0 0
\(721\) 3.38197 + 10.4086i 0.125951 + 0.387637i
\(722\) −32.3435 23.4989i −1.20370 0.874538i
\(723\) −6.70820 + 4.87380i −0.249481 + 0.181258i
\(724\) 3.79180 11.6699i 0.140921 0.433710i
\(725\) 0 0
\(726\) 5.11803 + 28.3399i 0.189948 + 1.05179i
\(727\) 9.14590 0.339203 0.169601 0.985513i \(-0.445752\pi\)
0.169601 + 0.985513i \(0.445752\pi\)
\(728\) −0.545085 + 1.67760i −0.0202022 + 0.0621760i
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) 0 0
\(731\) 2.37539 + 7.31069i 0.0878569 + 0.270396i
\(732\) −17.3435 53.3777i −0.641033 1.97290i
\(733\) −0.326238 0.237026i −0.0120499 0.00875474i 0.581744 0.813372i \(-0.302371\pi\)
−0.593794 + 0.804617i \(0.702371\pi\)
\(734\) 46.9058 34.0790i 1.73132 1.25788i
\(735\) 0 0
\(736\) −2.56231 −0.0944478
\(737\) 6.13525 + 0.416272i 0.225995 + 0.0153336i
\(738\) 0.618034 0.0227501
\(739\) 0.927051 2.85317i 0.0341021 0.104956i −0.932557 0.361024i \(-0.882427\pi\)
0.966659 + 0.256068i \(0.0824272\pi\)
\(740\) 0 0
\(741\) 1.11803 + 0.812299i 0.0410720 + 0.0298406i
\(742\) 0.309017 + 0.951057i 0.0113444 + 0.0349144i
\(743\) 13.2533 + 40.7894i 0.486216 + 1.49642i 0.830212 + 0.557448i \(0.188219\pi\)
−0.343996 + 0.938971i \(0.611781\pi\)
\(744\) 36.8156 + 26.7481i 1.34973 + 0.980633i
\(745\) 0 0
\(746\) −0.718847 + 2.21238i −0.0263189 + 0.0810011i
\(747\) −1.47214 −0.0538626
\(748\) −6.87539 + 17.1190i −0.251389 + 0.625933i
\(749\) 11.4721 0.419183
\(750\) 0 0
\(751\) −13.0623 + 9.49032i −0.476650 + 0.346307i −0.800027 0.599963i \(-0.795182\pi\)
0.323377 + 0.946270i \(0.395182\pi\)
\(752\) −80.4402 58.4432i −2.93335 2.13121i
\(753\) −6.79180 20.9030i −0.247507 0.761748i
\(754\) 1.14590 + 3.52671i 0.0417311 + 0.128435i
\(755\) 0 0
\(756\) −3.92705 + 2.85317i −0.142825 + 0.103769i
\(757\) −1.54508 + 4.75528i −0.0561571 + 0.172834i −0.975201 0.221322i \(-0.928963\pi\)
0.919044 + 0.394156i \(0.128963\pi\)
\(758\) −65.1591 −2.36668
\(759\) −0.663119 + 0.416272i −0.0240697 + 0.0151097i
\(760\) 0 0
\(761\) 9.05166 27.8582i 0.328123 1.00986i −0.641889 0.766798i \(-0.721849\pi\)
0.970011 0.243060i \(-0.0781511\pi\)
\(762\) 16.3262 11.8617i 0.591437 0.429704i
\(763\) 9.70820 + 7.05342i 0.351461 + 0.255351i
\(764\) −1.22949 3.78398i −0.0444814 0.136900i
\(765\) 0 0
\(766\) −26.9164 19.5559i −0.972529 0.706584i
\(767\) 1.40983 1.02430i 0.0509060 0.0369854i
\(768\) −4.50000 + 13.8496i −0.162380 + 0.499754i
\(769\) −34.5066 −1.24434 −0.622170 0.782883i \(-0.713749\pi\)
−0.622170 + 0.782883i \(0.713749\pi\)
\(770\) 0 0
\(771\) −29.7426 −1.07116
\(772\) 4.71885 14.5231i 0.169835 0.522698i
\(773\) 21.9894 15.9762i 0.790902 0.574624i −0.117329 0.993093i \(-0.537433\pi\)
0.908231 + 0.418469i \(0.137433\pi\)
\(774\) −14.2082 10.3229i −0.510703 0.371048i
\(775\) 0 0
\(776\) −18.1353 55.8146i −0.651018 2.00363i
\(777\) −5.04508 3.66547i −0.180991 0.131498i
\(778\) 77.8222 56.5411i 2.79006 2.02710i
\(779\) 0.427051 1.31433i 0.0153007 0.0470907i
\(780\) 0 0