Properties

Label 825.2.n.b.751.1
Level $825$
Weight $2$
Character 825.751
Analytic conductor $6.588$
Analytic rank $0$
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: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 751.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 825.751
Dual form 825.2.n.b.301.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.363271i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(0.500000 + 0.363271i) q^{6} +(-0.236068 + 0.726543i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.363271i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(0.500000 + 0.363271i) q^{6} +(-0.236068 + 0.726543i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(3.23607 + 0.726543i) q^{11} +1.61803 q^{12} +(1.00000 - 0.726543i) q^{13} +(-0.145898 - 0.449028i) q^{14} +(-1.50000 - 1.08981i) q^{16} +(-1.61803 - 1.17557i) q^{17} +(0.190983 - 0.587785i) q^{18} +(1.54508 + 4.75528i) q^{19} +0.763932 q^{21} +(-1.88197 + 0.812299i) q^{22} +2.38197 q^{23} +(-1.80902 + 1.31433i) q^{24} +(-0.236068 + 0.726543i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.00000 - 0.726543i) q^{28} +(-1.80902 + 5.56758i) q^{29} +(-5.66312 + 4.11450i) q^{31} +5.61803 q^{32} +(-0.309017 - 3.30220i) q^{33} +1.23607 q^{34} +(-0.500000 - 1.53884i) q^{36} +(-2.30902 + 7.10642i) q^{37} +(-2.50000 - 1.81636i) q^{38} +(-1.00000 - 0.726543i) q^{39} +(0.781153 + 2.40414i) q^{41} +(-0.381966 + 0.277515i) q^{42} -2.09017 q^{43} +(-2.73607 + 4.61653i) q^{44} +(-1.19098 + 0.865300i) q^{46} +(1.57295 + 4.84104i) q^{47} +(-0.572949 + 1.76336i) q^{48} +(5.19098 + 3.77147i) q^{49} +(-0.618034 + 1.90211i) q^{51} +(0.618034 + 1.90211i) q^{52} +(6.16312 - 4.47777i) q^{53} -0.618034 q^{54} +1.70820 q^{56} +(4.04508 - 2.93893i) q^{57} +(-1.11803 - 3.44095i) q^{58} +(-2.07295 + 6.37988i) q^{59} +(-5.66312 - 4.11450i) q^{61} +(1.33688 - 4.11450i) q^{62} +(-0.236068 - 0.726543i) q^{63} +(0.190983 - 0.138757i) q^{64} +(1.35410 + 1.53884i) q^{66} -9.38197 q^{67} +(2.61803 - 1.90211i) q^{68} +(-0.736068 - 2.26538i) q^{69} +(6.47214 + 4.70228i) q^{71} +(1.80902 + 1.31433i) q^{72} +(-4.16312 + 12.8128i) q^{73} +(-1.42705 - 4.39201i) q^{74} -8.09017 q^{76} +(-1.29180 + 2.17963i) q^{77} +0.763932 q^{78} +(6.54508 - 4.75528i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-1.26393 - 0.918300i) q^{82} +(4.61803 + 3.35520i) q^{83} +(-0.381966 + 1.17557i) q^{84} +(1.04508 - 0.759299i) q^{86} +5.85410 q^{87} +(-0.690983 - 7.38394i) q^{88} +10.8541 q^{89} +(0.291796 + 0.898056i) q^{91} +(-1.19098 + 3.66547i) q^{92} +(5.66312 + 4.11450i) q^{93} +(-2.54508 - 1.84911i) q^{94} +(-1.73607 - 5.34307i) q^{96} +(-9.28115 + 6.74315i) q^{97} -3.96556 q^{98} +(-3.04508 + 1.31433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} - 5 q^{8} - q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} + q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} - 5 q^{8} - q^{9} + 4 q^{11} + 2 q^{12} + 4 q^{13} - 14 q^{14} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 5 q^{19} + 12 q^{21} - 12 q^{22} + 14 q^{23} - 5 q^{24} + 8 q^{26} + q^{27} - 4 q^{28} - 5 q^{29} - 7 q^{31} + 18 q^{32} + q^{33} - 4 q^{34} - 2 q^{36} - 7 q^{37} - 10 q^{38} - 4 q^{39} - 17 q^{41} - 6 q^{42} + 14 q^{43} - 2 q^{44} - 7 q^{46} + 13 q^{47} - 9 q^{48} + 23 q^{49} + 2 q^{51} - 2 q^{52} + 9 q^{53} + 2 q^{54} - 20 q^{56} + 5 q^{57} - 15 q^{59} - 7 q^{61} + 21 q^{62} + 8 q^{63} + 3 q^{64} - 8 q^{66} - 42 q^{67} + 6 q^{68} + 6 q^{69} + 8 q^{71} + 5 q^{72} - q^{73} + q^{74} - 10 q^{76} - 32 q^{77} + 12 q^{78} + 15 q^{79} - q^{81} - 14 q^{82} + 14 q^{83} - 6 q^{84} - 7 q^{86} + 10 q^{87} - 5 q^{88} + 30 q^{89} + 28 q^{91} - 7 q^{92} + 7 q^{93} + q^{94} + 2 q^{96} - 17 q^{97} - 74 q^{98} - q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.363271i −0.353553 + 0.256872i −0.750358 0.661031i \(-0.770119\pi\)
0.396805 + 0.917903i \(0.370119\pi\)
\(3\) −0.309017 0.951057i −0.178411 0.549093i
\(4\) −0.500000 + 1.53884i −0.250000 + 0.769421i
\(5\) 0 0
\(6\) 0.500000 + 0.363271i 0.204124 + 0.148305i
\(7\) −0.236068 + 0.726543i −0.0892253 + 0.274607i −0.985706 0.168476i \(-0.946115\pi\)
0.896480 + 0.443083i \(0.146115\pi\)
\(8\) −0.690983 2.12663i −0.244299 0.751876i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) 0 0
\(11\) 3.23607 + 0.726543i 0.975711 + 0.219061i
\(12\) 1.61803 0.467086
\(13\) 1.00000 0.726543i 0.277350 0.201507i −0.440411 0.897796i \(-0.645167\pi\)
0.717761 + 0.696290i \(0.245167\pi\)
\(14\) −0.145898 0.449028i −0.0389929 0.120008i
\(15\) 0 0
\(16\) −1.50000 1.08981i −0.375000 0.272453i
\(17\) −1.61803 1.17557i −0.392431 0.285118i 0.374020 0.927421i \(-0.377979\pi\)
−0.766451 + 0.642303i \(0.777979\pi\)
\(18\) 0.190983 0.587785i 0.0450151 0.138542i
\(19\) 1.54508 + 4.75528i 0.354467 + 1.09094i 0.956318 + 0.292328i \(0.0944300\pi\)
−0.601851 + 0.798608i \(0.705570\pi\)
\(20\) 0 0
\(21\) 0.763932 0.166704
\(22\) −1.88197 + 0.812299i −0.401237 + 0.173183i
\(23\) 2.38197 0.496674 0.248337 0.968674i \(-0.420116\pi\)
0.248337 + 0.968674i \(0.420116\pi\)
\(24\) −1.80902 + 1.31433i −0.369264 + 0.268286i
\(25\) 0 0
\(26\) −0.236068 + 0.726543i −0.0462967 + 0.142487i
\(27\) 0.809017 + 0.587785i 0.155695 + 0.113119i
\(28\) −1.00000 0.726543i −0.188982 0.137304i
\(29\) −1.80902 + 5.56758i −0.335926 + 1.03387i 0.630338 + 0.776321i \(0.282916\pi\)
−0.966264 + 0.257553i \(0.917084\pi\)
\(30\) 0 0
\(31\) −5.66312 + 4.11450i −1.01713 + 0.738985i −0.965692 0.259691i \(-0.916379\pi\)
−0.0514344 + 0.998676i \(0.516379\pi\)
\(32\) 5.61803 0.993137
\(33\) −0.309017 3.30220i −0.0537930 0.574839i
\(34\) 1.23607 0.211984
\(35\) 0 0
\(36\) −0.500000 1.53884i −0.0833333 0.256474i
\(37\) −2.30902 + 7.10642i −0.379600 + 1.16829i 0.560722 + 0.828004i \(0.310524\pi\)
−0.940322 + 0.340285i \(0.889476\pi\)
\(38\) −2.50000 1.81636i −0.405554 0.294652i
\(39\) −1.00000 0.726543i −0.160128 0.116340i
\(40\) 0 0
\(41\) 0.781153 + 2.40414i 0.121996 + 0.375464i 0.993342 0.115205i \(-0.0367525\pi\)
−0.871346 + 0.490669i \(0.836752\pi\)
\(42\) −0.381966 + 0.277515i −0.0589386 + 0.0428214i
\(43\) −2.09017 −0.318748 −0.159374 0.987218i \(-0.550948\pi\)
−0.159374 + 0.987218i \(0.550948\pi\)
\(44\) −2.73607 + 4.61653i −0.412478 + 0.695967i
\(45\) 0 0
\(46\) −1.19098 + 0.865300i −0.175601 + 0.127581i
\(47\) 1.57295 + 4.84104i 0.229438 + 0.706138i 0.997811 + 0.0661352i \(0.0210669\pi\)
−0.768372 + 0.640003i \(0.778933\pi\)
\(48\) −0.572949 + 1.76336i −0.0826981 + 0.254518i
\(49\) 5.19098 + 3.77147i 0.741569 + 0.538781i
\(50\) 0 0
\(51\) −0.618034 + 1.90211i −0.0865421 + 0.266349i
\(52\) 0.618034 + 1.90211i 0.0857059 + 0.263776i
\(53\) 6.16312 4.47777i 0.846569 0.615069i −0.0776285 0.996982i \(-0.524735\pi\)
0.924198 + 0.381914i \(0.124735\pi\)
\(54\) −0.618034 −0.0841038
\(55\) 0 0
\(56\) 1.70820 0.228268
\(57\) 4.04508 2.93893i 0.535785 0.389270i
\(58\) −1.11803 3.44095i −0.146805 0.451820i
\(59\) −2.07295 + 6.37988i −0.269875 + 0.830590i 0.720655 + 0.693294i \(0.243841\pi\)
−0.990530 + 0.137296i \(0.956159\pi\)
\(60\) 0 0
\(61\) −5.66312 4.11450i −0.725088 0.526807i 0.162918 0.986640i \(-0.447910\pi\)
−0.888006 + 0.459832i \(0.847910\pi\)
\(62\) 1.33688 4.11450i 0.169784 0.522542i
\(63\) −0.236068 0.726543i −0.0297418 0.0915358i
\(64\) 0.190983 0.138757i 0.0238729 0.0173447i
\(65\) 0 0
\(66\) 1.35410 + 1.53884i 0.166678 + 0.189418i
\(67\) −9.38197 −1.14619 −0.573095 0.819489i \(-0.694257\pi\)
−0.573095 + 0.819489i \(0.694257\pi\)
\(68\) 2.61803 1.90211i 0.317483 0.230665i
\(69\) −0.736068 2.26538i −0.0886122 0.272720i
\(70\) 0 0
\(71\) 6.47214 + 4.70228i 0.768101 + 0.558058i 0.901384 0.433020i \(-0.142552\pi\)
−0.133283 + 0.991078i \(0.542552\pi\)
\(72\) 1.80902 + 1.31433i 0.213195 + 0.154895i
\(73\) −4.16312 + 12.8128i −0.487256 + 1.49962i 0.341430 + 0.939907i \(0.389089\pi\)
−0.828686 + 0.559713i \(0.810911\pi\)
\(74\) −1.42705 4.39201i −0.165891 0.510561i
\(75\) 0 0
\(76\) −8.09017 −0.928006
\(77\) −1.29180 + 2.17963i −0.147214 + 0.248392i
\(78\) 0.763932 0.0864983
\(79\) 6.54508 4.75528i 0.736380 0.535011i −0.155196 0.987884i \(-0.549601\pi\)
0.891575 + 0.452873i \(0.149601\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) −1.26393 0.918300i −0.139578 0.101409i
\(83\) 4.61803 + 3.35520i 0.506895 + 0.368281i 0.811644 0.584152i \(-0.198573\pi\)
−0.304749 + 0.952433i \(0.598573\pi\)
\(84\) −0.381966 + 1.17557i −0.0416759 + 0.128265i
\(85\) 0 0
\(86\) 1.04508 0.759299i 0.112694 0.0818773i
\(87\) 5.85410 0.627626
\(88\) −0.690983 7.38394i −0.0736590 0.787130i
\(89\) 10.8541 1.15053 0.575266 0.817966i \(-0.304898\pi\)
0.575266 + 0.817966i \(0.304898\pi\)
\(90\) 0 0
\(91\) 0.291796 + 0.898056i 0.0305885 + 0.0941418i
\(92\) −1.19098 + 3.66547i −0.124169 + 0.382152i
\(93\) 5.66312 + 4.11450i 0.587238 + 0.426653i
\(94\) −2.54508 1.84911i −0.262505 0.190721i
\(95\) 0 0
\(96\) −1.73607 5.34307i −0.177187 0.545325i
\(97\) −9.28115 + 6.74315i −0.942358 + 0.684663i −0.948987 0.315315i \(-0.897890\pi\)
0.00662888 + 0.999978i \(0.497890\pi\)
\(98\) −3.96556 −0.400582
\(99\) −3.04508 + 1.31433i −0.306043 + 0.132095i
\(100\) 0 0
\(101\) 0.454915 0.330515i 0.0452657 0.0328875i −0.564922 0.825144i \(-0.691094\pi\)
0.610188 + 0.792257i \(0.291094\pi\)
\(102\) −0.381966 1.17557i −0.0378203 0.116399i
\(103\) 0.736068 2.26538i 0.0725269 0.223215i −0.908222 0.418489i \(-0.862560\pi\)
0.980749 + 0.195274i \(0.0625597\pi\)
\(104\) −2.23607 1.62460i −0.219265 0.159305i
\(105\) 0 0
\(106\) −1.45492 + 4.47777i −0.141314 + 0.434919i
\(107\) 0.881966 + 2.71441i 0.0852629 + 0.262412i 0.984594 0.174856i \(-0.0559460\pi\)
−0.899331 + 0.437268i \(0.855946\pi\)
\(108\) −1.30902 + 0.951057i −0.125960 + 0.0915155i
\(109\) 4.14590 0.397105 0.198553 0.980090i \(-0.436376\pi\)
0.198553 + 0.980090i \(0.436376\pi\)
\(110\) 0 0
\(111\) 7.47214 0.709224
\(112\) 1.14590 0.832544i 0.108277 0.0786680i
\(113\) 1.69098 + 5.20431i 0.159074 + 0.489580i 0.998551 0.0538155i \(-0.0171383\pi\)
−0.839477 + 0.543396i \(0.817138\pi\)
\(114\) −0.954915 + 2.93893i −0.0894360 + 0.275256i
\(115\) 0 0
\(116\) −7.66312 5.56758i −0.711503 0.516937i
\(117\) −0.381966 + 1.17557i −0.0353128 + 0.108682i
\(118\) −1.28115 3.94298i −0.117940 0.362981i
\(119\) 1.23607 0.898056i 0.113310 0.0823247i
\(120\) 0 0
\(121\) 9.94427 + 4.70228i 0.904025 + 0.427480i
\(122\) 4.32624 0.391679
\(123\) 2.04508 1.48584i 0.184399 0.133974i
\(124\) −3.50000 10.7719i −0.314309 0.967344i
\(125\) 0 0
\(126\) 0.381966 + 0.277515i 0.0340282 + 0.0247230i
\(127\) −12.8992 9.37181i −1.14462 0.831613i −0.156862 0.987621i \(-0.550138\pi\)
−0.987756 + 0.156007i \(0.950138\pi\)
\(128\) −3.51722 + 10.8249i −0.310881 + 0.956794i
\(129\) 0.645898 + 1.98787i 0.0568682 + 0.175022i
\(130\) 0 0
\(131\) 13.1803 1.15157 0.575786 0.817601i \(-0.304696\pi\)
0.575786 + 0.817601i \(0.304696\pi\)
\(132\) 5.23607 + 1.17557i 0.455741 + 0.102320i
\(133\) −3.81966 −0.331207
\(134\) 4.69098 3.40820i 0.405239 0.294424i
\(135\) 0 0
\(136\) −1.38197 + 4.25325i −0.118503 + 0.364714i
\(137\) −15.1353 10.9964i −1.29309 0.939486i −0.293229 0.956042i \(-0.594730\pi\)
−0.999863 + 0.0165558i \(0.994730\pi\)
\(138\) 1.19098 + 0.865300i 0.101383 + 0.0736592i
\(139\) 6.54508 20.1437i 0.555147 1.70857i −0.140408 0.990094i \(-0.544842\pi\)
0.695555 0.718473i \(-0.255158\pi\)
\(140\) 0 0
\(141\) 4.11803 2.99193i 0.346801 0.251966i
\(142\) −4.94427 −0.414914
\(143\) 3.76393 1.62460i 0.314756 0.135856i
\(144\) 1.85410 0.154508
\(145\) 0 0
\(146\) −2.57295 7.91872i −0.212939 0.655358i
\(147\) 1.98278 6.10237i 0.163537 0.503315i
\(148\) −9.78115 7.10642i −0.804006 0.584144i
\(149\) −16.2812 11.8290i −1.33380 0.969065i −0.999648 0.0265477i \(-0.991549\pi\)
−0.334156 0.942518i \(-0.608451\pi\)
\(150\) 0 0
\(151\) −3.32624 10.2371i −0.270685 0.833084i −0.990329 0.138740i \(-0.955695\pi\)
0.719643 0.694344i \(-0.244305\pi\)
\(152\) 9.04508 6.57164i 0.733653 0.533030i
\(153\) 2.00000 0.161690
\(154\) −0.145898 1.55909i −0.0117568 0.125635i
\(155\) 0 0
\(156\) 1.61803 1.17557i 0.129546 0.0941210i
\(157\) −1.02786 3.16344i −0.0820325 0.252470i 0.901625 0.432518i \(-0.142375\pi\)
−0.983658 + 0.180048i \(0.942375\pi\)
\(158\) −1.54508 + 4.75528i −0.122920 + 0.378310i
\(159\) −6.16312 4.47777i −0.488767 0.355110i
\(160\) 0 0
\(161\) −0.562306 + 1.73060i −0.0443159 + 0.136390i
\(162\) 0.190983 + 0.587785i 0.0150050 + 0.0461808i
\(163\) −10.9721 + 7.97172i −0.859404 + 0.624394i −0.927723 0.373270i \(-0.878237\pi\)
0.0683187 + 0.997664i \(0.478237\pi\)
\(164\) −4.09017 −0.319389
\(165\) 0 0
\(166\) −3.52786 −0.273815
\(167\) 16.2082 11.7759i 1.25423 0.911250i 0.255769 0.966738i \(-0.417671\pi\)
0.998459 + 0.0554876i \(0.0176713\pi\)
\(168\) −0.527864 1.62460i −0.0407256 0.125340i
\(169\) −3.54508 + 10.9106i −0.272699 + 0.839281i
\(170\) 0 0
\(171\) −4.04508 2.93893i −0.309335 0.224745i
\(172\) 1.04508 3.21644i 0.0796870 0.245251i
\(173\) 1.10081 + 3.38795i 0.0836933 + 0.257581i 0.984142 0.177380i \(-0.0567621\pi\)
−0.900449 + 0.434961i \(0.856762\pi\)
\(174\) −2.92705 + 2.12663i −0.221899 + 0.161219i
\(175\) 0 0
\(176\) −4.06231 4.61653i −0.306208 0.347984i
\(177\) 6.70820 0.504219
\(178\) −5.42705 + 3.94298i −0.406775 + 0.295539i
\(179\) −6.01722 18.5191i −0.449748 1.38418i −0.877192 0.480141i \(-0.840586\pi\)
0.427443 0.904042i \(-0.359414\pi\)
\(180\) 0 0
\(181\) 4.23607 + 3.07768i 0.314864 + 0.228762i 0.733981 0.679170i \(-0.237660\pi\)
−0.419117 + 0.907932i \(0.637660\pi\)
\(182\) −0.472136 0.343027i −0.0349970 0.0254268i
\(183\) −2.16312 + 6.65740i −0.159902 + 0.492129i
\(184\) −1.64590 5.06555i −0.121337 0.373438i
\(185\) 0 0
\(186\) −4.32624 −0.317215
\(187\) −4.38197 4.97980i −0.320441 0.364159i
\(188\) −8.23607 −0.600677
\(189\) −0.618034 + 0.449028i −0.0449554 + 0.0326620i
\(190\) 0 0
\(191\) 3.21885 9.90659i 0.232908 0.716816i −0.764484 0.644642i \(-0.777006\pi\)
0.997392 0.0721737i \(-0.0229936\pi\)
\(192\) −0.190983 0.138757i −0.0137830 0.0100139i
\(193\) 17.0172 + 12.3637i 1.22493 + 0.889961i 0.996499 0.0836000i \(-0.0266418\pi\)
0.228427 + 0.973561i \(0.426642\pi\)
\(194\) 2.19098 6.74315i 0.157303 0.484130i
\(195\) 0 0
\(196\) −8.39919 + 6.10237i −0.599942 + 0.435883i
\(197\) 14.2361 1.01428 0.507139 0.861864i \(-0.330703\pi\)
0.507139 + 0.861864i \(0.330703\pi\)
\(198\) 1.04508 1.76336i 0.0742710 0.125316i
\(199\) 19.7984 1.40347 0.701735 0.712438i \(-0.252409\pi\)
0.701735 + 0.712438i \(0.252409\pi\)
\(200\) 0 0
\(201\) 2.89919 + 8.92278i 0.204493 + 0.629364i
\(202\) −0.107391 + 0.330515i −0.00755600 + 0.0232550i
\(203\) −3.61803 2.62866i −0.253936 0.184495i
\(204\) −2.61803 1.90211i −0.183299 0.133175i
\(205\) 0 0
\(206\) 0.454915 + 1.40008i 0.0316954 + 0.0975485i
\(207\) −1.92705 + 1.40008i −0.133939 + 0.0973126i
\(208\) −2.29180 −0.158907
\(209\) 1.54508 + 16.5110i 0.106876 + 1.14209i
\(210\) 0 0
\(211\) 3.11803 2.26538i 0.214654 0.155955i −0.475263 0.879844i \(-0.657647\pi\)
0.689917 + 0.723888i \(0.257647\pi\)
\(212\) 3.80902 + 11.7229i 0.261604 + 0.805135i
\(213\) 2.47214 7.60845i 0.169388 0.521323i
\(214\) −1.42705 1.03681i −0.0975512 0.0708751i
\(215\) 0 0
\(216\) 0.690983 2.12663i 0.0470154 0.144699i
\(217\) −1.65248 5.08580i −0.112177 0.345246i
\(218\) −2.07295 + 1.50609i −0.140398 + 0.102005i
\(219\) 13.4721 0.910363
\(220\) 0 0
\(221\) −2.47214 −0.166294
\(222\) −3.73607 + 2.71441i −0.250748 + 0.182179i
\(223\) 2.48278 + 7.64121i 0.166259 + 0.511693i 0.999127 0.0417790i \(-0.0133025\pi\)
−0.832868 + 0.553472i \(0.813303\pi\)
\(224\) −1.32624 + 4.08174i −0.0886130 + 0.272723i
\(225\) 0 0
\(226\) −2.73607 1.98787i −0.182001 0.132231i
\(227\) 8.01722 24.6745i 0.532122 1.63770i −0.217666 0.976023i \(-0.569844\pi\)
0.749788 0.661679i \(-0.230156\pi\)
\(228\) 2.50000 + 7.69421i 0.165567 + 0.509561i
\(229\) −14.6353 + 10.6331i −0.967125 + 0.702657i −0.954795 0.297267i \(-0.903925\pi\)
−0.0123304 + 0.999924i \(0.503925\pi\)
\(230\) 0 0
\(231\) 2.47214 + 0.555029i 0.162655 + 0.0365182i
\(232\) 13.0902 0.859412
\(233\) 18.8262 13.6781i 1.23335 0.896080i 0.236211 0.971702i \(-0.424094\pi\)
0.997137 + 0.0756220i \(0.0240942\pi\)
\(234\) −0.236068 0.726543i −0.0154322 0.0474956i
\(235\) 0 0
\(236\) −8.78115 6.37988i −0.571604 0.415295i
\(237\) −6.54508 4.75528i −0.425149 0.308889i
\(238\) −0.291796 + 0.898056i −0.0189143 + 0.0582123i
\(239\) −2.17376 6.69015i −0.140609 0.432750i 0.855811 0.517288i \(-0.173058\pi\)
−0.996420 + 0.0845383i \(0.973058\pi\)
\(240\) 0 0
\(241\) −1.61803 −0.104227 −0.0521134 0.998641i \(-0.516596\pi\)
−0.0521134 + 0.998641i \(0.516596\pi\)
\(242\) −6.68034 + 1.26133i −0.429429 + 0.0810812i
\(243\) −1.00000 −0.0641500
\(244\) 9.16312 6.65740i 0.586609 0.426196i
\(245\) 0 0
\(246\) −0.482779 + 1.48584i −0.0307809 + 0.0947338i
\(247\) 5.00000 + 3.63271i 0.318142 + 0.231144i
\(248\) 12.6631 + 9.20029i 0.804109 + 0.584219i
\(249\) 1.76393 5.42882i 0.111785 0.344038i
\(250\) 0 0
\(251\) −6.09017 + 4.42477i −0.384408 + 0.279289i −0.763160 0.646209i \(-0.776353\pi\)
0.378752 + 0.925498i \(0.376353\pi\)
\(252\) 1.23607 0.0778650
\(253\) 7.70820 + 1.73060i 0.484611 + 0.108802i
\(254\) 9.85410 0.618301
\(255\) 0 0
\(256\) −2.02786 6.24112i −0.126742 0.390070i
\(257\) −3.26393 + 10.0453i −0.203598 + 0.626612i 0.796170 + 0.605074i \(0.206856\pi\)
−0.999768 + 0.0215381i \(0.993144\pi\)
\(258\) −1.04508 0.759299i −0.0650641 0.0472719i
\(259\) −4.61803 3.35520i −0.286951 0.208482i
\(260\) 0 0
\(261\) −1.80902 5.56758i −0.111975 0.344625i
\(262\) −6.59017 + 4.78804i −0.407142 + 0.295806i
\(263\) −27.2148 −1.67814 −0.839068 0.544027i \(-0.816899\pi\)
−0.839068 + 0.544027i \(0.816899\pi\)
\(264\) −6.80902 + 2.93893i −0.419066 + 0.180878i
\(265\) 0 0
\(266\) 1.90983 1.38757i 0.117099 0.0850775i
\(267\) −3.35410 10.3229i −0.205268 0.631749i
\(268\) 4.69098 14.4374i 0.286547 0.881902i
\(269\) 4.73607 + 3.44095i 0.288763 + 0.209799i 0.722731 0.691130i \(-0.242887\pi\)
−0.433967 + 0.900929i \(0.642887\pi\)
\(270\) 0 0
\(271\) 6.37132 19.6089i 0.387030 1.19116i −0.547966 0.836500i \(-0.684598\pi\)
0.934997 0.354656i \(-0.115402\pi\)
\(272\) 1.14590 + 3.52671i 0.0694803 + 0.213838i
\(273\) 0.763932 0.555029i 0.0462353 0.0335919i
\(274\) 11.5623 0.698504
\(275\) 0 0
\(276\) 3.85410 0.231990
\(277\) 7.00000 5.08580i 0.420589 0.305576i −0.357286 0.933995i \(-0.616298\pi\)
0.777875 + 0.628419i \(0.216298\pi\)
\(278\) 4.04508 + 12.4495i 0.242608 + 0.746671i
\(279\) 2.16312 6.65740i 0.129503 0.398568i
\(280\) 0 0
\(281\) −8.16312 5.93085i −0.486971 0.353805i 0.317047 0.948410i \(-0.397309\pi\)
−0.804018 + 0.594605i \(0.797309\pi\)
\(282\) −0.972136 + 2.99193i −0.0578899 + 0.178167i
\(283\) 4.02786 + 12.3965i 0.239432 + 0.736895i 0.996503 + 0.0835622i \(0.0266297\pi\)
−0.757071 + 0.653333i \(0.773370\pi\)
\(284\) −10.4721 + 7.60845i −0.621407 + 0.451479i
\(285\) 0 0
\(286\) −1.29180 + 2.17963i −0.0763855 + 0.128884i
\(287\) −1.93112 −0.113990
\(288\) −4.54508 + 3.30220i −0.267822 + 0.194584i
\(289\) −4.01722 12.3637i −0.236307 0.727279i
\(290\) 0 0
\(291\) 9.28115 + 6.74315i 0.544071 + 0.395291i
\(292\) −17.6353 12.8128i −1.03203 0.749810i
\(293\) 5.10739 15.7189i 0.298377 0.918310i −0.683689 0.729773i \(-0.739626\pi\)
0.982066 0.188537i \(-0.0603744\pi\)
\(294\) 1.22542 + 3.77147i 0.0714682 + 0.219957i
\(295\) 0 0
\(296\) 16.7082 0.971145
\(297\) 2.19098 + 2.48990i 0.127134 + 0.144479i
\(298\) 12.4377 0.720496
\(299\) 2.38197 1.73060i 0.137753 0.100083i
\(300\) 0 0
\(301\) 0.493422 1.51860i 0.0284404 0.0875305i
\(302\) 5.38197 + 3.91023i 0.309697 + 0.225008i
\(303\) −0.454915 0.330515i −0.0261342 0.0189876i
\(304\) 2.86475 8.81678i 0.164304 0.505677i
\(305\) 0 0
\(306\) −1.00000 + 0.726543i −0.0571662 + 0.0415337i
\(307\) 12.1246 0.691988 0.345994 0.938237i \(-0.387542\pi\)
0.345994 + 0.938237i \(0.387542\pi\)
\(308\) −2.70820 3.07768i −0.154314 0.175367i
\(309\) −2.38197 −0.135505
\(310\) 0 0
\(311\) 6.63525 + 20.4212i 0.376251 + 1.15798i 0.942631 + 0.333837i \(0.108343\pi\)
−0.566380 + 0.824144i \(0.691657\pi\)
\(312\) −0.854102 + 2.62866i −0.0483540 + 0.148818i
\(313\) −0.381966 0.277515i −0.0215900 0.0156860i 0.576938 0.816788i \(-0.304247\pi\)
−0.598528 + 0.801102i \(0.704247\pi\)
\(314\) 1.66312 + 1.20833i 0.0938552 + 0.0681898i
\(315\) 0 0
\(316\) 4.04508 + 12.4495i 0.227554 + 0.700339i
\(317\) −24.6074 + 17.8783i −1.38209 + 1.00415i −0.385407 + 0.922747i \(0.625939\pi\)
−0.996682 + 0.0813997i \(0.974061\pi\)
\(318\) 4.70820 0.264023
\(319\) −9.89919 + 16.7027i −0.554248 + 0.935174i
\(320\) 0 0
\(321\) 2.30902 1.67760i 0.128877 0.0936344i
\(322\) −0.347524 1.06957i −0.0193668 0.0596048i
\(323\) 3.09017 9.51057i 0.171942 0.529182i
\(324\) 1.30902 + 0.951057i 0.0727232 + 0.0528365i
\(325\) 0 0
\(326\) 2.59017 7.97172i 0.143456 0.441513i
\(327\) −1.28115 3.94298i −0.0708479 0.218047i
\(328\) 4.57295 3.32244i 0.252499 0.183451i
\(329\) −3.88854 −0.214382
\(330\) 0 0
\(331\) 21.5967 1.18706 0.593532 0.804810i \(-0.297733\pi\)
0.593532 + 0.804810i \(0.297733\pi\)
\(332\) −7.47214 + 5.42882i −0.410087 + 0.297945i
\(333\) −2.30902 7.10642i −0.126533 0.389430i
\(334\) −3.82624 + 11.7759i −0.209362 + 0.644351i
\(335\) 0 0
\(336\) −1.14590 0.832544i −0.0625139 0.0454190i
\(337\) −6.84346 + 21.0620i −0.372787 + 1.14732i 0.572173 + 0.820133i \(0.306101\pi\)
−0.944960 + 0.327187i \(0.893899\pi\)
\(338\) −2.19098 6.74315i −0.119174 0.366779i
\(339\) 4.42705 3.21644i 0.240444 0.174693i
\(340\) 0 0
\(341\) −21.3156 + 9.20029i −1.15430 + 0.498224i
\(342\) 3.09017 0.167097
\(343\) −8.29180 + 6.02434i −0.447715 + 0.325284i
\(344\) 1.44427 + 4.44501i 0.0778699 + 0.239659i
\(345\) 0 0
\(346\) −1.78115 1.29408i −0.0957554 0.0695704i
\(347\) −4.70820 3.42071i −0.252750 0.183633i 0.454195 0.890902i \(-0.349927\pi\)
−0.706945 + 0.707269i \(0.749927\pi\)
\(348\) −2.92705 + 9.00854i −0.156906 + 0.482908i
\(349\) 8.57953 + 26.4051i 0.459252 + 1.41343i 0.866070 + 0.499922i \(0.166638\pi\)
−0.406819 + 0.913509i \(0.633362\pi\)
\(350\) 0 0
\(351\) 1.23607 0.0659764
\(352\) 18.1803 + 4.08174i 0.969015 + 0.217558i
\(353\) −35.8328 −1.90719 −0.953594 0.301095i \(-0.902648\pi\)
−0.953594 + 0.301095i \(0.902648\pi\)
\(354\) −3.35410 + 2.43690i −0.178269 + 0.129520i
\(355\) 0 0
\(356\) −5.42705 + 16.7027i −0.287633 + 0.885244i
\(357\) −1.23607 0.898056i −0.0654197 0.0475302i
\(358\) 9.73607 + 7.07367i 0.514567 + 0.373855i
\(359\) 5.16312 15.8904i 0.272499 0.838666i −0.717371 0.696691i \(-0.754655\pi\)
0.989870 0.141975i \(-0.0453451\pi\)
\(360\) 0 0
\(361\) −4.85410 + 3.52671i −0.255479 + 0.185616i
\(362\) −3.23607 −0.170084
\(363\) 1.39919 10.9106i 0.0734383 0.572661i
\(364\) −1.52786 −0.0800818
\(365\) 0 0
\(366\) −1.33688 4.11450i −0.0698799 0.215068i
\(367\) −5.60081 + 17.2375i −0.292360 + 0.899792i 0.691735 + 0.722151i \(0.256846\pi\)
−0.984095 + 0.177641i \(0.943154\pi\)
\(368\) −3.57295 2.59590i −0.186253 0.135321i
\(369\) −2.04508 1.48584i −0.106463 0.0773498i
\(370\) 0 0
\(371\) 1.79837 + 5.53483i 0.0933669 + 0.287354i
\(372\) −9.16312 + 6.65740i −0.475086 + 0.345170i
\(373\) 9.74265 0.504455 0.252228 0.967668i \(-0.418837\pi\)
0.252228 + 0.967668i \(0.418837\pi\)
\(374\) 4.00000 + 0.898056i 0.206835 + 0.0464374i
\(375\) 0 0
\(376\) 9.20820 6.69015i 0.474877 0.345018i
\(377\) 2.23607 + 6.88191i 0.115163 + 0.354436i
\(378\) 0.145898 0.449028i 0.00750419 0.0230955i
\(379\) 4.04508 + 2.93893i 0.207782 + 0.150963i 0.686810 0.726837i \(-0.259011\pi\)
−0.479028 + 0.877800i \(0.659011\pi\)
\(380\) 0 0
\(381\) −4.92705 + 15.1639i −0.252420 + 0.776870i
\(382\) 1.98936 + 6.12261i 0.101784 + 0.313260i
\(383\) 25.3713 18.4333i 1.29641 0.941900i 0.296500 0.955033i \(-0.404180\pi\)
0.999914 + 0.0131328i \(0.00418043\pi\)
\(384\) 11.3820 0.580834
\(385\) 0 0
\(386\) −13.0000 −0.661683
\(387\) 1.69098 1.22857i 0.0859575 0.0624518i
\(388\) −5.73607 17.6538i −0.291205 0.896236i
\(389\) −12.0344 + 37.0382i −0.610170 + 1.87791i −0.153855 + 0.988093i \(0.549169\pi\)
−0.456316 + 0.889818i \(0.650831\pi\)
\(390\) 0 0
\(391\) −3.85410 2.80017i −0.194910 0.141611i
\(392\) 4.43363 13.6453i 0.223932 0.689192i
\(393\) −4.07295 12.5352i −0.205453 0.632320i
\(394\) −7.11803 + 5.17155i −0.358601 + 0.260539i
\(395\) 0 0
\(396\) −0.500000 5.34307i −0.0251259 0.268499i
\(397\) 36.2705 1.82036 0.910182 0.414208i \(-0.135941\pi\)
0.910182 + 0.414208i \(0.135941\pi\)
\(398\) −9.89919 + 7.19218i −0.496201 + 0.360511i
\(399\) 1.18034 + 3.63271i 0.0590909 + 0.181863i
\(400\) 0 0
\(401\) −3.95492 2.87341i −0.197499 0.143491i 0.484641 0.874713i \(-0.338950\pi\)
−0.682140 + 0.731222i \(0.738950\pi\)
\(402\) −4.69098 3.40820i −0.233965 0.169985i
\(403\) −2.67376 + 8.22899i −0.133190 + 0.409915i
\(404\) 0.281153 + 0.865300i 0.0139879 + 0.0430503i
\(405\) 0 0
\(406\) 2.76393 0.137172
\(407\) −12.6353 + 21.3193i −0.626306 + 1.05676i
\(408\) 4.47214 0.221404
\(409\) −29.3713 + 21.3395i −1.45232 + 1.05517i −0.467036 + 0.884238i \(0.654678\pi\)
−0.985283 + 0.170933i \(0.945322\pi\)
\(410\) 0 0
\(411\) −5.78115 + 17.7926i −0.285163 + 0.877642i
\(412\) 3.11803 + 2.26538i 0.153615 + 0.111607i
\(413\) −4.14590 3.01217i −0.204006 0.148219i
\(414\) 0.454915 1.40008i 0.0223579 0.0688104i
\(415\) 0 0
\(416\) 5.61803 4.08174i 0.275447 0.200124i
\(417\) −21.1803 −1.03721
\(418\) −6.77051 7.69421i −0.331156 0.376336i
\(419\) 24.5967 1.20163 0.600815 0.799388i \(-0.294843\pi\)
0.600815 + 0.799388i \(0.294843\pi\)
\(420\) 0 0
\(421\) 0.881966 + 2.71441i 0.0429844 + 0.132292i 0.970246 0.242123i \(-0.0778436\pi\)
−0.927261 + 0.374415i \(0.877844\pi\)
\(422\) −0.736068 + 2.26538i −0.0358312 + 0.110277i
\(423\) −4.11803 2.99193i −0.200226 0.145472i
\(424\) −13.7812 10.0126i −0.669272 0.486255i
\(425\) 0 0
\(426\) 1.52786 + 4.70228i 0.0740253 + 0.227826i
\(427\) 4.32624 3.14320i 0.209361 0.152110i
\(428\) −4.61803 −0.223221
\(429\) −2.70820 3.07768i −0.130753 0.148592i
\(430\) 0 0
\(431\) −16.0902 + 11.6902i −0.775036 + 0.563097i −0.903485 0.428619i \(-0.859000\pi\)
0.128449 + 0.991716i \(0.459000\pi\)
\(432\) −0.572949 1.76336i −0.0275660 0.0848395i
\(433\) 8.66312 26.6623i 0.416323 1.28131i −0.494739 0.869041i \(-0.664736\pi\)
0.911062 0.412269i \(-0.135264\pi\)
\(434\) 2.67376 + 1.94260i 0.128345 + 0.0932479i
\(435\) 0 0
\(436\) −2.07295 + 6.37988i −0.0992763 + 0.305541i
\(437\) 3.68034 + 11.3269i 0.176055 + 0.541840i
\(438\) −6.73607 + 4.89404i −0.321862 + 0.233846i
\(439\) 9.67376 0.461703 0.230852 0.972989i \(-0.425849\pi\)
0.230852 + 0.972989i \(0.425849\pi\)
\(440\) 0 0
\(441\) −6.41641 −0.305543
\(442\) 1.23607 0.898056i 0.0587938 0.0427162i
\(443\) 7.80902 + 24.0337i 0.371018 + 1.14187i 0.946126 + 0.323798i \(0.104960\pi\)
−0.575109 + 0.818077i \(0.695040\pi\)
\(444\) −3.73607 + 11.4984i −0.177306 + 0.545692i
\(445\) 0 0
\(446\) −4.01722 2.91868i −0.190221 0.138204i
\(447\) −6.21885 + 19.1396i −0.294141 + 0.905274i
\(448\) 0.0557281 + 0.171513i 0.00263290 + 0.00810325i
\(449\) 0.590170 0.428784i 0.0278518 0.0202355i −0.573772 0.819015i \(-0.694521\pi\)
0.601624 + 0.798779i \(0.294521\pi\)
\(450\) 0 0
\(451\) 0.781153 + 8.34751i 0.0367831 + 0.393069i
\(452\) −8.85410 −0.416462
\(453\) −8.70820 + 6.32688i −0.409147 + 0.297263i
\(454\) 4.95492 + 15.2497i 0.232546 + 0.715702i
\(455\) 0 0
\(456\) −9.04508 6.57164i −0.423575 0.307745i
\(457\) −1.19098 0.865300i −0.0557118 0.0404770i 0.559581 0.828776i \(-0.310962\pi\)
−0.615293 + 0.788299i \(0.710962\pi\)
\(458\) 3.45492 10.6331i 0.161438 0.496854i
\(459\) −0.618034 1.90211i −0.0288474 0.0887830i
\(460\) 0 0
\(461\) 25.9443 1.20835 0.604173 0.796853i \(-0.293504\pi\)
0.604173 + 0.796853i \(0.293504\pi\)
\(462\) −1.43769 + 0.620541i −0.0668876 + 0.0288702i
\(463\) −33.2705 −1.54621 −0.773106 0.634277i \(-0.781298\pi\)
−0.773106 + 0.634277i \(0.781298\pi\)
\(464\) 8.78115 6.37988i 0.407655 0.296179i
\(465\) 0 0
\(466\) −4.44427 + 13.6781i −0.205877 + 0.633624i
\(467\) −3.95492 2.87341i −0.183012 0.132966i 0.492507 0.870308i \(-0.336080\pi\)
−0.675519 + 0.737342i \(0.736080\pi\)
\(468\) −1.61803 1.17557i −0.0747936 0.0543408i
\(469\) 2.21478 6.81640i 0.102269 0.314752i
\(470\) 0 0
\(471\) −2.69098 + 1.95511i −0.123994 + 0.0900869i
\(472\) 15.0000 0.690431
\(473\) −6.76393 1.51860i −0.311006 0.0698252i
\(474\) 5.00000 0.229658
\(475\) 0 0
\(476\) 0.763932 + 2.35114i 0.0350148 + 0.107764i
\(477\) −2.35410 + 7.24518i −0.107787 + 0.331734i
\(478\) 3.51722 + 2.55541i 0.160874 + 0.116882i
\(479\) −27.0344 19.6417i −1.23524 0.897451i −0.237964 0.971274i \(-0.576480\pi\)
−0.997271 + 0.0738231i \(0.976480\pi\)
\(480\) 0 0
\(481\) 2.85410 + 8.78402i 0.130136 + 0.400517i
\(482\) 0.809017 0.587785i 0.0368497 0.0267729i
\(483\) 1.81966 0.0827974
\(484\) −12.2082 + 12.9515i −0.554918 + 0.588705i
\(485\) 0 0
\(486\) 0.500000 0.363271i 0.0226805 0.0164783i
\(487\) −4.38197 13.4863i −0.198566 0.611123i −0.999916 0.0129278i \(-0.995885\pi\)
0.801351 0.598195i \(-0.204115\pi\)
\(488\) −4.83688 + 14.8864i −0.218955 + 0.673875i
\(489\) 10.9721 + 7.97172i 0.496177 + 0.360494i
\(490\) 0 0
\(491\) 9.82624 30.2421i 0.443452 1.36480i −0.440721 0.897644i \(-0.645277\pi\)
0.884173 0.467160i \(-0.154723\pi\)
\(492\) 1.26393 + 3.88998i 0.0569825 + 0.175374i
\(493\) 9.47214 6.88191i 0.426604 0.309946i
\(494\) −3.81966 −0.171855
\(495\) 0 0
\(496\) 12.9787 0.582761
\(497\) −4.94427 + 3.59222i −0.221781 + 0.161133i
\(498\) 1.09017 + 3.35520i 0.0488517 + 0.150350i
\(499\) −3.45492 + 10.6331i −0.154663 + 0.476005i −0.998127 0.0611822i \(-0.980513\pi\)
0.843463 + 0.537187i \(0.180513\pi\)
\(500\) 0 0
\(501\) −16.2082 11.7759i −0.724129 0.526111i
\(502\) 1.43769 4.42477i 0.0641674 0.197487i
\(503\) −6.76393 20.8172i −0.301589 0.928195i −0.980928 0.194371i \(-0.937734\pi\)
0.679339 0.733824i \(-0.262266\pi\)
\(504\) −1.38197 + 1.00406i −0.0615577 + 0.0447243i
\(505\) 0 0
\(506\) −4.48278 + 1.93487i −0.199284 + 0.0860154i
\(507\) 11.4721 0.509495
\(508\) 20.8713 15.1639i 0.926015 0.672789i
\(509\) 0.163119 + 0.502029i 0.00723012 + 0.0222520i 0.954606 0.297870i \(-0.0962761\pi\)
−0.947376 + 0.320122i \(0.896276\pi\)
\(510\) 0 0
\(511\) −8.32624 6.04937i −0.368331 0.267608i
\(512\) −15.1353 10.9964i −0.668890 0.485977i
\(513\) −1.54508 + 4.75528i −0.0682172 + 0.209951i
\(514\) −2.01722 6.20837i −0.0889758 0.273839i
\(515\) 0 0
\(516\) −3.38197 −0.148883
\(517\) 1.57295 + 16.8087i 0.0691782 + 0.739248i
\(518\) 3.52786 0.155005
\(519\) 2.88197 2.09387i 0.126504 0.0919107i
\(520\) 0 0
\(521\) −4.74671 + 14.6089i −0.207957 + 0.640026i 0.791622 + 0.611011i \(0.209237\pi\)
−0.999579 + 0.0290150i \(0.990763\pi\)
\(522\) 2.92705 + 2.12663i 0.128114 + 0.0930799i
\(523\) −6.66312 4.84104i −0.291358 0.211684i 0.432498 0.901635i \(-0.357632\pi\)
−0.723856 + 0.689951i \(0.757632\pi\)
\(524\) −6.59017 + 20.2825i −0.287893 + 0.886043i
\(525\) 0 0
\(526\) 13.6074 9.88635i 0.593310 0.431065i
\(527\) 14.0000 0.609850
\(528\) −3.13525 + 5.29007i −0.136444 + 0.230221i
\(529\) −17.3262 −0.753315
\(530\) 0 0
\(531\) −2.07295 6.37988i −0.0899583 0.276863i
\(532\) 1.90983 5.87785i 0.0828016 0.254837i
\(533\) 2.52786 + 1.83660i 0.109494 + 0.0795520i
\(534\) 5.42705 + 3.94298i 0.234851 + 0.170630i
\(535\) 0 0
\(536\) 6.48278 + 19.9519i 0.280013 + 0.861793i
\(537\) −15.7533 + 11.4454i −0.679805 + 0.493907i
\(538\) −3.61803 −0.155985
\(539\) 14.0582 + 15.9762i 0.605531 + 0.688144i
\(540\) 0 0
\(541\) −0.500000 + 0.363271i −0.0214967 + 0.0156183i −0.598482 0.801136i \(-0.704229\pi\)
0.576985 + 0.816755i \(0.304229\pi\)
\(542\) 3.93769 + 12.1190i 0.169138 + 0.520555i
\(543\) 1.61803 4.97980i 0.0694365 0.213704i
\(544\) −9.09017 6.60440i −0.389738 0.283161i
\(545\) 0 0
\(546\) −0.180340 + 0.555029i −0.00771783 + 0.0237531i
\(547\) −7.83688 24.1194i −0.335081 1.03127i −0.966682 0.255979i \(-0.917602\pi\)
0.631601 0.775293i \(-0.282398\pi\)
\(548\) 24.4894 17.7926i 1.04613 0.760060i
\(549\) 7.00000 0.298753
\(550\) 0 0
\(551\) −29.2705 −1.24697
\(552\) −4.30902 + 3.13068i −0.183404 + 0.133251i
\(553\) 1.90983 + 5.87785i 0.0812142 + 0.249952i
\(554\) −1.65248 + 5.08580i −0.0702070 + 0.216075i
\(555\) 0 0
\(556\) 27.7254 + 20.1437i 1.17582 + 0.854283i
\(557\) 9.70163 29.8585i 0.411071 1.26515i −0.504647 0.863326i \(-0.668377\pi\)
0.915718 0.401821i \(-0.131623\pi\)
\(558\) 1.33688 + 4.11450i 0.0565947 + 0.174181i
\(559\) −2.09017 + 1.51860i −0.0884048 + 0.0642298i
\(560\) 0 0
\(561\) −3.38197 + 5.70634i −0.142787 + 0.240922i
\(562\) 6.23607 0.263053
\(563\) −29.3885 + 21.3520i −1.23858 + 0.899881i −0.997503 0.0706255i \(-0.977500\pi\)
−0.241077 + 0.970506i \(0.577500\pi\)
\(564\) 2.54508 + 7.83297i 0.107167 + 0.329827i
\(565\) 0 0
\(566\) −6.51722 4.73504i −0.273939 0.199028i
\(567\) 0.618034 + 0.449028i 0.0259550 + 0.0188574i
\(568\) 5.52786 17.0130i 0.231944 0.713850i
\(569\) −0.753289 2.31838i −0.0315795 0.0971917i 0.934024 0.357209i \(-0.116272\pi\)
−0.965604 + 0.260017i \(0.916272\pi\)
\(570\) 0 0
\(571\) 0.0901699 0.00377349 0.00188675 0.999998i \(-0.499399\pi\)
0.00188675 + 0.999998i \(0.499399\pi\)
\(572\) 0.618034 + 6.60440i 0.0258413 + 0.276144i
\(573\) −10.4164 −0.435152
\(574\) 0.965558 0.701519i 0.0403016 0.0292808i
\(575\) 0 0
\(576\) −0.0729490 + 0.224514i −0.00303954 + 0.00935475i
\(577\) 37.2254 + 27.0459i 1.54971 + 1.12593i 0.943854 + 0.330363i \(0.107171\pi\)
0.605861 + 0.795571i \(0.292829\pi\)
\(578\) 6.50000 + 4.72253i 0.270364 + 0.196431i
\(579\) 6.50000 20.0049i 0.270131 0.831377i
\(580\) 0 0
\(581\) −3.52786 + 2.56314i −0.146360 + 0.106337i
\(582\) −7.09017 −0.293897
\(583\) 23.1976 10.0126i 0.960745 0.414679i
\(584\) 30.1246 1.24657
\(585\) 0 0
\(586\) 3.15654 + 9.71483i 0.130396 + 0.401316i
\(587\) −5.98936 + 18.4333i −0.247207 + 0.760826i 0.748058 + 0.663633i \(0.230986\pi\)
−0.995266 + 0.0971926i \(0.969014\pi\)
\(588\) 8.39919 + 6.10237i 0.346377 + 0.251657i
\(589\) −28.3156 20.5725i −1.16672 0.847674i
\(590\) 0 0
\(591\) −4.39919 13.5393i −0.180958 0.556933i
\(592\) 11.2082 8.14324i 0.460654 0.334685i
\(593\) 38.8885 1.59696 0.798481 0.602021i \(-0.205638\pi\)
0.798481 + 0.602021i \(0.205638\pi\)
\(594\) −2.00000 0.449028i −0.0820610 0.0184238i
\(595\) 0 0
\(596\) 26.3435 19.1396i 1.07907 0.783990i
\(597\) −6.11803 18.8294i −0.250394 0.770635i
\(598\) −0.562306 + 1.73060i −0.0229944 + 0.0707695i
\(599\) 17.9894 + 13.0700i 0.735025 + 0.534027i 0.891149 0.453710i \(-0.149900\pi\)
−0.156124 + 0.987737i \(0.549900\pi\)
\(600\) 0 0
\(601\) 10.6180 32.6789i 0.433119 1.33300i −0.461884 0.886941i \(-0.652826\pi\)
0.895002 0.446062i \(-0.147174\pi\)
\(602\) 0.304952 + 0.938545i 0.0124289 + 0.0382522i
\(603\) 7.59017 5.51458i 0.309096 0.224571i
\(604\) 17.4164 0.708664
\(605\) 0 0
\(606\) 0.347524 0.0141172
\(607\) 26.6976 19.3969i 1.08362 0.787296i 0.105310 0.994439i \(-0.466417\pi\)
0.978311 + 0.207143i \(0.0664165\pi\)
\(608\) 8.68034 + 26.7153i 0.352034 + 1.08345i
\(609\) −1.38197 + 4.25325i −0.0560001 + 0.172351i
\(610\) 0 0
\(611\) 5.09017 + 3.69822i 0.205926 + 0.149614i
\(612\) −1.00000 + 3.07768i −0.0404226 + 0.124408i
\(613\) 2.54508 + 7.83297i 0.102795 + 0.316371i 0.989207 0.146527i \(-0.0468096\pi\)
−0.886412 + 0.462898i \(0.846810\pi\)
\(614\) −6.06231 + 4.40452i −0.244655 + 0.177752i
\(615\) 0 0
\(616\) 5.52786 + 1.24108i 0.222724 + 0.0500047i
\(617\) −38.2492 −1.53986 −0.769928 0.638131i \(-0.779708\pi\)
−0.769928 + 0.638131i \(0.779708\pi\)
\(618\) 1.19098 0.865300i 0.0479084 0.0348075i
\(619\) 2.19756 + 6.76340i 0.0883274 + 0.271844i 0.985457 0.169923i \(-0.0543519\pi\)
−0.897130 + 0.441767i \(0.854352\pi\)
\(620\) 0 0
\(621\) 1.92705 + 1.40008i 0.0773299 + 0.0561835i
\(622\) −10.7361 7.80021i −0.430477 0.312760i
\(623\) −2.56231 + 7.88597i −0.102657 + 0.315945i
\(624\) 0.708204 + 2.17963i 0.0283508 + 0.0872549i
\(625\) 0 0
\(626\) 0.291796 0.0116625
\(627\) 15.2254 6.57164i 0.608045 0.262446i
\(628\) 5.38197 0.214764
\(629\) 12.0902 8.78402i 0.482067 0.350242i
\(630\) 0 0
\(631\) 11.9377 36.7404i 0.475232 1.46261i −0.370412 0.928867i \(-0.620784\pi\)
0.845644 0.533747i \(-0.179216\pi\)
\(632\) −14.6353 10.6331i −0.582159 0.422963i
\(633\) −3.11803 2.26538i −0.123931 0.0900409i
\(634\) 5.80902 17.8783i 0.230706 0.710039i
\(635\) 0 0
\(636\) 9.97214 7.24518i 0.395421 0.287290i
\(637\) 7.93112 0.314242
\(638\) −1.11803 11.9475i −0.0442634 0.473005i
\(639\) −8.00000 −0.316475
\(640\) 0 0
\(641\) −0.0729490 0.224514i −0.00288131 0.00886777i 0.949606 0.313448i \(-0.101484\pi\)
−0.952487 + 0.304580i \(0.901484\pi\)
\(642\) −0.545085 + 1.67760i −0.0215128 + 0.0662096i
\(643\) 23.7254 + 17.2375i 0.935639 + 0.679782i 0.947367 0.320149i \(-0.103733\pi\)
−0.0117276 + 0.999931i \(0.503733\pi\)
\(644\) −2.38197 1.73060i −0.0938626 0.0681952i
\(645\) 0 0
\(646\) 1.90983 + 5.87785i 0.0751413 + 0.231261i
\(647\) 14.2361 10.3431i 0.559678 0.406630i −0.271663 0.962392i \(-0.587574\pi\)
0.831341 + 0.555763i \(0.187574\pi\)
\(648\) −2.23607 −0.0878410
\(649\) −11.3435 + 19.1396i −0.445270 + 0.751297i
\(650\) 0 0
\(651\) −4.32624 + 3.14320i −0.169559 + 0.123192i
\(652\) −6.78115 20.8702i −0.265570 0.817342i
\(653\) 7.24265 22.2906i 0.283427 0.872297i −0.703439 0.710755i \(-0.748353\pi\)
0.986866 0.161542i \(-0.0516467\pi\)
\(654\) 2.07295 + 1.50609i 0.0810587 + 0.0588926i
\(655\) 0 0
\(656\) 1.44834 4.45752i 0.0565481 0.174037i
\(657\) −4.16312 12.8128i −0.162419 0.499873i
\(658\) 1.94427 1.41260i 0.0757956 0.0550687i
\(659\) 12.9656 0.505066 0.252533 0.967588i \(-0.418736\pi\)
0.252533 + 0.967588i \(0.418736\pi\)
\(660\) 0 0
\(661\) 3.90983 0.152075 0.0760374 0.997105i \(-0.475773\pi\)
0.0760374 + 0.997105i \(0.475773\pi\)
\(662\) −10.7984 + 7.84548i −0.419691 + 0.304923i
\(663\) 0.763932 + 2.35114i 0.0296687 + 0.0913108i
\(664\) 3.94427 12.1392i 0.153067 0.471093i
\(665\) 0 0
\(666\) 3.73607 + 2.71441i 0.144770 + 0.105181i
\(667\) −4.30902 + 13.2618i −0.166846 + 0.513499i
\(668\) 10.0172 + 30.8298i 0.387578 + 1.19284i
\(669\) 6.50000 4.72253i 0.251305 0.182583i
\(670\) 0 0
\(671\) −15.3369 17.4293i −0.592074 0.672850i
\(672\) 4.29180 0.165560
\(673\) −22.0902 + 16.0494i −0.851513 + 0.618661i −0.925563 0.378594i \(-0.876408\pi\)
0.0740494 + 0.997255i \(0.476408\pi\)
\(674\) −4.22949 13.0170i −0.162914 0.501397i
\(675\) 0 0
\(676\) −15.0172 10.9106i −0.577585 0.419640i
\(677\) 9.66312 + 7.02067i 0.371384 + 0.269826i 0.757785 0.652505i \(-0.226282\pi\)
−0.386401 + 0.922331i \(0.626282\pi\)
\(678\) −1.04508 + 3.21644i −0.0401362 + 0.123527i
\(679\) −2.70820 8.33499i −0.103931 0.319868i
\(680\) 0 0
\(681\) −25.9443 −0.994187
\(682\) 7.31559 12.3435i 0.280129 0.472657i
\(683\) −2.29180 −0.0876931 −0.0438466 0.999038i \(-0.513961\pi\)
−0.0438466 + 0.999038i \(0.513961\pi\)
\(684\) 6.54508 4.75528i 0.250258 0.181823i
\(685\) 0 0
\(686\) 1.95743 6.02434i 0.0747349 0.230010i
\(687\) 14.6353 + 10.6331i 0.558370 + 0.405679i
\(688\) 3.13525 + 2.27790i 0.119530 + 0.0868440i
\(689\) 2.90983 8.95554i 0.110856 0.341179i
\(690\) 0 0
\(691\) −26.9443 + 19.5762i −1.02501 + 0.744712i −0.967304 0.253621i \(-0.918378\pi\)
−0.0577049 + 0.998334i \(0.518378\pi\)
\(692\) −5.76393 −0.219112
\(693\) −0.236068 2.52265i −0.00896748 0.0958277i
\(694\) 3.59675 0.136531
\(695\) 0 0
\(696\) −4.04508 12.4495i −0.153329 0.471897i
\(697\) 1.56231 4.80828i 0.0591766 0.182127i
\(698\) −13.8820 10.0858i −0.525440 0.381755i
\(699\) −18.8262 13.6781i −0.712074 0.517352i
\(700\) 0 0
\(701\) 4.19756 + 12.9188i 0.158540 + 0.487935i 0.998502 0.0547093i \(-0.0174232\pi\)
−0.839963 + 0.542644i \(0.817423\pi\)
\(702\) −0.618034 + 0.449028i −0.0233262 + 0.0169475i
\(703\) −37.3607 −1.40908
\(704\) 0.718847 0.310271i 0.0270926 0.0116938i
\(705\) 0 0
\(706\) 17.9164 13.0170i 0.674293 0.489902i
\(707\) 0.132742 + 0.408539i 0.00499229 + 0.0153647i
\(708\) −3.35410 + 10.3229i −0.126055 + 0.387957i
\(709\) −33.3156 24.2052i −1.25119 0.909045i −0.252903 0.967492i \(-0.581385\pi\)
−0.998291 + 0.0584464i \(0.981385\pi\)
\(710\) 0 0
\(711\) −2.50000 + 7.69421i −0.0937573 + 0.288555i
\(712\) −7.50000 23.0826i −0.281074 0.865058i
\(713\) −13.4894 + 9.80059i −0.505180 + 0.367035i
\(714\) 0.944272 0.0353385
\(715\) 0 0
\(716\) 31.5066 1.17746
\(717\) −5.69098 + 4.13474i −0.212534 + 0.154415i
\(718\) 3.19098 + 9.82084i 0.119086 + 0.366510i
\(719\) 11.7705 36.2259i 0.438966 1.35100i −0.450001 0.893028i \(-0.648577\pi\)
0.888967 0.457970i \(-0.151423\pi\)
\(720\) 0 0
\(721\) 1.47214 + 1.06957i 0.0548252 + 0.0398328i
\(722\) 1.14590 3.52671i 0.0426459 0.131251i
\(723\) 0.500000 + 1.53884i 0.0185952 + 0.0572301i
\(724\) −6.85410 + 4.97980i −0.254731 + 0.185073i
\(725\) 0 0
\(726\) 3.26393 + 5.96361i 0.121136 + 0.221330i
\(727\) 37.3262 1.38435 0.692177 0.721728i \(-0.256652\pi\)
0.692177 + 0.721728i \(0.256652\pi\)
\(728\) 1.70820 1.24108i 0.0633102 0.0459976i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) 3.38197 + 2.45714i 0.125087 + 0.0908807i
\(732\) −9.16312 6.65740i −0.338679 0.246064i
\(733\) 0.572949 1.76336i 0.0211624 0.0651310i −0.939918 0.341401i \(-0.889098\pi\)
0.961080 + 0.276270i \(0.0890985\pi\)
\(734\) −3.46149 10.6534i −0.127766 0.393223i
\(735\) 0 0
\(736\) 13.3820 0.493266
\(737\) −30.3607 6.81640i −1.11835 0.251085i
\(738\) 1.56231 0.0575093
\(739\) 16.1803 11.7557i 0.595203 0.432441i −0.248970 0.968511i \(-0.580092\pi\)
0.844173 + 0.536071i \(0.180092\pi\)
\(740\) 0 0
\(741\) 1.90983 5.87785i 0.0701594 0.215928i
\(742\) −2.90983 2.11412i −0.106823 0.0776116i
\(743\) −0.281153 0.204270i −0.0103145 0.00749392i 0.582616 0.812748i \(-0.302029\pi\)
−0.592931 + 0.805254i \(0.702029\pi\)
\(744\) 4.83688 14.8864i 0.177329 0.545762i
\(745\) 0 0
\(746\) −4.87132 + 3.53922i −0.178352 + 0.129580i
\(747\) −5.70820 −0.208852
\(748\) 9.85410 4.25325i 0.360302 0.155514i
\(749\) −2.18034 −0.0796679
\(750\) 0 0
\(751\) −14.1803 43.6426i −0.517448 1.59254i −0.778783 0.627293i \(-0.784163\pi\)
0.261335 0.965248i \(-0.415837\pi\)
\(752\) 2.91641 8.97578i 0.106350 0.327313i
\(753\) 6.09017 + 4.42477i 0.221938 + 0.161247i
\(754\) −3.61803 2.62866i −0.131761 0.0957300i
\(755\) 0 0
\(756\) −0.381966 1.17557i −0.0138920 0.0427551i
\(757\) 19.5623 14.2128i 0.711004 0.516575i −0.172493 0.985011i \(-0.555182\pi\)
0.883497 + 0.468436i \(0.155182\pi\)
\(758\) −3.09017 −0.112240
\(759\) −0.736068 7.86572i −0.0267176 0.285508i
\(760\) 0 0
\(761\) −31.5795 + 22.9439i −1.14476 + 0.831715i −0.987775 0.155887i \(-0.950176\pi\)
−0.156982 + 0.987601i \(0.550176\pi\)
\(762\) −3.04508 9.37181i −0.110312 0.339505i
\(763\) −0.978714 + 3.01217i −0.0354318 + 0.109048i
\(764\) 13.6353 + 9.90659i 0.493306 + 0.358408i
\(765\) 0 0
\(766\) −5.98936 + 18.4333i −0.216404 + 0.666024i
\(767\) 2.56231 + 7.88597i 0.0925195 + 0.284746i
\(768\) −5.30902 + 3.85723i −0.191573 + 0.139186i
\(769\) 12.7639 0.460279 0.230140 0.973158i \(-0.426082\pi\)
0.230140 + 0.973158i \(0.426082\pi\)
\(770\) 0 0
\(771\) 10.5623 0.380392
\(772\) −27.5344 + 20.0049i −0.990986 + 0.719994i
\(773\) −3.24671 9.99235i −0.116776 0.359400i 0.875537 0.483151i \(-0.160508\pi\)
−0.992313 + 0.123751i \(0.960508\pi\)
\(774\) −0.399187 + 1.22857i −0.0143485 + 0.0441601i
\(775\) 0 0
\(776\) 20.7533 + 15.0781i 0.745000 + 0.541274i
\(777\) −1.76393 + 5.42882i −0.0632807 + 0.194758i
\(778\) −7.43769 22.8909i −0.266654 0.820677i
\(779\) −10.2254 + 7.42921i −0.366364 + 0.266179i
\(780\) 0 0
\(781\) 17.5279 + 19.9192i 0.627196 + 0.712765i