Properties

Label 825.2.bx.c.499.1
Level $825$
Weight $2$
Character 825.499
Analytic conductor $6.588$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.bx (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
Defining polynomial: \(x^{8} - x^{6} + x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 499.1
Root \(0.951057 - 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 825.499
Dual form 825.2.bx.c.124.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.363271 + 0.500000i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.500000 + 1.53884i) q^{4} +(0.500000 - 0.363271i) q^{6} +(-0.726543 + 0.236068i) q^{7} +(-2.12663 - 0.690983i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.363271 + 0.500000i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.500000 + 1.53884i) q^{4} +(0.500000 - 0.363271i) q^{6} +(-0.726543 + 0.236068i) q^{7} +(-2.12663 - 0.690983i) q^{8} +(0.809017 + 0.587785i) q^{9} +(3.23607 - 0.726543i) q^{11} -1.61803i q^{12} +(-0.726543 + 1.00000i) q^{13} +(0.145898 - 0.449028i) q^{14} +(-1.50000 + 1.08981i) q^{16} +(1.17557 + 1.61803i) q^{17} +(-0.587785 + 0.190983i) q^{18} +(-1.54508 + 4.75528i) q^{19} +0.763932 q^{21} +(-0.812299 + 1.88197i) q^{22} +2.38197i q^{23} +(1.80902 + 1.31433i) q^{24} +(-0.236068 - 0.726543i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(-0.726543 - 1.00000i) q^{28} +(1.80902 + 5.56758i) q^{29} +(-5.66312 - 4.11450i) q^{31} -5.61803i q^{32} +(-3.30220 - 0.309017i) q^{33} -1.23607 q^{34} +(-0.500000 + 1.53884i) q^{36} +(-7.10642 + 2.30902i) q^{37} +(-1.81636 - 2.50000i) q^{38} +(1.00000 - 0.726543i) q^{39} +(0.781153 - 2.40414i) q^{41} +(-0.277515 + 0.381966i) q^{42} -2.09017i q^{43} +(2.73607 + 4.61653i) q^{44} +(-1.19098 - 0.865300i) q^{46} +(-4.84104 - 1.57295i) q^{47} +(1.76336 - 0.572949i) q^{48} +(-5.19098 + 3.77147i) q^{49} +(-0.618034 - 1.90211i) q^{51} +(-1.90211 - 0.618034i) q^{52} +(-4.47777 + 6.16312i) q^{53} +0.618034 q^{54} +1.70820 q^{56} +(2.93893 - 4.04508i) q^{57} +(-3.44095 - 1.11803i) q^{58} +(2.07295 + 6.37988i) q^{59} +(-5.66312 + 4.11450i) q^{61} +(4.11450 - 1.33688i) q^{62} +(-0.726543 - 0.236068i) q^{63} +(-0.190983 - 0.138757i) q^{64} +(1.35410 - 1.53884i) q^{66} +9.38197i q^{67} +(-1.90211 + 2.61803i) q^{68} +(0.736068 - 2.26538i) q^{69} +(6.47214 - 4.70228i) q^{71} +(-1.31433 - 1.80902i) q^{72} +(12.8128 - 4.16312i) q^{73} +(1.42705 - 4.39201i) q^{74} -8.09017 q^{76} +(-2.17963 + 1.29180i) q^{77} +0.763932i q^{78} +(-6.54508 - 4.75528i) q^{79} +(0.309017 + 0.951057i) q^{81} +(0.918300 + 1.26393i) q^{82} +(3.35520 + 4.61803i) q^{83} +(0.381966 + 1.17557i) q^{84} +(1.04508 + 0.759299i) q^{86} -5.85410i q^{87} +(-7.38394 - 0.690983i) q^{88} -10.8541 q^{89} +(0.291796 - 0.898056i) q^{91} +(-3.66547 + 1.19098i) q^{92} +(4.11450 + 5.66312i) q^{93} +(2.54508 - 1.84911i) q^{94} +(-1.73607 + 5.34307i) q^{96} +(-6.74315 + 9.28115i) q^{97} -3.96556i q^{98} +(3.04508 + 1.31433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + 4 q^{6} + 2 q^{9} + O(q^{10}) \) \( 8 q + 4 q^{4} + 4 q^{6} + 2 q^{9} + 8 q^{11} + 28 q^{14} - 12 q^{16} + 10 q^{19} + 24 q^{21} + 10 q^{24} + 16 q^{26} + 10 q^{29} - 14 q^{31} + 8 q^{34} - 4 q^{36} + 8 q^{39} - 34 q^{41} + 4 q^{44} - 14 q^{46} - 46 q^{49} + 4 q^{51} - 4 q^{54} - 40 q^{56} + 30 q^{59} - 14 q^{61} - 6 q^{64} - 16 q^{66} - 12 q^{69} + 16 q^{71} - 2 q^{74} - 20 q^{76} - 30 q^{79} - 2 q^{81} + 12 q^{84} - 14 q^{86} - 60 q^{89} + 56 q^{91} - 2 q^{94} + 4 q^{96} + 2 q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.363271 + 0.500000i −0.256872 + 0.353553i −0.917903 0.396805i \(-0.870119\pi\)
0.661031 + 0.750358i \(0.270119\pi\)
\(3\) −0.951057 0.309017i −0.549093 0.178411i
\(4\) 0.500000 + 1.53884i 0.250000 + 0.769421i
\(5\) 0 0
\(6\) 0.500000 0.363271i 0.204124 0.148305i
\(7\) −0.726543 + 0.236068i −0.274607 + 0.0892253i −0.443083 0.896480i \(-0.646115\pi\)
0.168476 + 0.985706i \(0.446115\pi\)
\(8\) −2.12663 0.690983i −0.751876 0.244299i
\(9\) 0.809017 + 0.587785i 0.269672 + 0.195928i
\(10\) 0 0
\(11\) 3.23607 0.726543i 0.975711 0.219061i
\(12\) 1.61803i 0.467086i
\(13\) −0.726543 + 1.00000i −0.201507 + 0.277350i −0.897796 0.440411i \(-0.854833\pi\)
0.696290 + 0.717761i \(0.254833\pi\)
\(14\) 0.145898 0.449028i 0.0389929 0.120008i
\(15\) 0 0
\(16\) −1.50000 + 1.08981i −0.375000 + 0.272453i
\(17\) 1.17557 + 1.61803i 0.285118 + 0.392431i 0.927421 0.374020i \(-0.122021\pi\)
−0.642303 + 0.766451i \(0.722021\pi\)
\(18\) −0.587785 + 0.190983i −0.138542 + 0.0450151i
\(19\) −1.54508 + 4.75528i −0.354467 + 1.09094i 0.601851 + 0.798608i \(0.294430\pi\)
−0.956318 + 0.292328i \(0.905570\pi\)
\(20\) 0 0
\(21\) 0.763932 0.166704
\(22\) −0.812299 + 1.88197i −0.173183 + 0.401237i
\(23\) 2.38197i 0.496674i 0.968674 + 0.248337i \(0.0798841\pi\)
−0.968674 + 0.248337i \(0.920116\pi\)
\(24\) 1.80902 + 1.31433i 0.369264 + 0.268286i
\(25\) 0 0
\(26\) −0.236068 0.726543i −0.0462967 0.142487i
\(27\) −0.587785 0.809017i −0.113119 0.155695i
\(28\) −0.726543 1.00000i −0.137304 0.188982i
\(29\) 1.80902 + 5.56758i 0.335926 + 1.03387i 0.966264 + 0.257553i \(0.0829163\pi\)
−0.630338 + 0.776321i \(0.717084\pi\)
\(30\) 0 0
\(31\) −5.66312 4.11450i −1.01713 0.738985i −0.0514344 0.998676i \(-0.516379\pi\)
−0.965692 + 0.259691i \(0.916379\pi\)
\(32\) 5.61803i 0.993137i
\(33\) −3.30220 0.309017i −0.574839 0.0537930i
\(34\) −1.23607 −0.211984
\(35\) 0 0
\(36\) −0.500000 + 1.53884i −0.0833333 + 0.256474i
\(37\) −7.10642 + 2.30902i −1.16829 + 0.379600i −0.828004 0.560722i \(-0.810524\pi\)
−0.340285 + 0.940322i \(0.610524\pi\)
\(38\) −1.81636 2.50000i −0.294652 0.405554i
\(39\) 1.00000 0.726543i 0.160128 0.116340i
\(40\) 0 0
\(41\) 0.781153 2.40414i 0.121996 0.375464i −0.871346 0.490669i \(-0.836752\pi\)
0.993342 + 0.115205i \(0.0367525\pi\)
\(42\) −0.277515 + 0.381966i −0.0428214 + 0.0589386i
\(43\) 2.09017i 0.318748i −0.987218 0.159374i \(-0.949052\pi\)
0.987218 0.159374i \(-0.0509476\pi\)
\(44\) 2.73607 + 4.61653i 0.412478 + 0.695967i
\(45\) 0 0
\(46\) −1.19098 0.865300i −0.175601 0.127581i
\(47\) −4.84104 1.57295i −0.706138 0.229438i −0.0661352 0.997811i \(-0.521067\pi\)
−0.640003 + 0.768372i \(0.721067\pi\)
\(48\) 1.76336 0.572949i 0.254518 0.0826981i
\(49\) −5.19098 + 3.77147i −0.741569 + 0.538781i
\(50\) 0 0
\(51\) −0.618034 1.90211i −0.0865421 0.266349i
\(52\) −1.90211 0.618034i −0.263776 0.0857059i
\(53\) −4.47777 + 6.16312i −0.615069 + 0.846569i −0.996982 0.0776285i \(-0.975265\pi\)
0.381914 + 0.924198i \(0.375265\pi\)
\(54\) 0.618034 0.0841038
\(55\) 0 0
\(56\) 1.70820 0.228268
\(57\) 2.93893 4.04508i 0.389270 0.535785i
\(58\) −3.44095 1.11803i −0.451820 0.146805i
\(59\) 2.07295 + 6.37988i 0.269875 + 0.830590i 0.990530 + 0.137296i \(0.0438412\pi\)
−0.720655 + 0.693294i \(0.756159\pi\)
\(60\) 0 0
\(61\) −5.66312 + 4.11450i −0.725088 + 0.526807i −0.888006 0.459832i \(-0.847910\pi\)
0.162918 + 0.986640i \(0.447910\pi\)
\(62\) 4.11450 1.33688i 0.522542 0.169784i
\(63\) −0.726543 0.236068i −0.0915358 0.0297418i
\(64\) −0.190983 0.138757i −0.0238729 0.0173447i
\(65\) 0 0
\(66\) 1.35410 1.53884i 0.166678 0.189418i
\(67\) 9.38197i 1.14619i 0.819489 + 0.573095i \(0.194257\pi\)
−0.819489 + 0.573095i \(0.805743\pi\)
\(68\) −1.90211 + 2.61803i −0.230665 + 0.317483i
\(69\) 0.736068 2.26538i 0.0886122 0.272720i
\(70\) 0 0
\(71\) 6.47214 4.70228i 0.768101 0.558058i −0.133283 0.991078i \(-0.542552\pi\)
0.901384 + 0.433020i \(0.142552\pi\)
\(72\) −1.31433 1.80902i −0.154895 0.213195i
\(73\) 12.8128 4.16312i 1.49962 0.487256i 0.559713 0.828686i \(-0.310911\pi\)
0.939907 + 0.341430i \(0.110911\pi\)
\(74\) 1.42705 4.39201i 0.165891 0.510561i
\(75\) 0 0
\(76\) −8.09017 −0.928006
\(77\) −2.17963 + 1.29180i −0.248392 + 0.147214i
\(78\) 0.763932i 0.0864983i
\(79\) −6.54508 4.75528i −0.736380 0.535011i 0.155196 0.987884i \(-0.450399\pi\)
−0.891575 + 0.452873i \(0.850399\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 0.918300 + 1.26393i 0.101409 + 0.139578i
\(83\) 3.35520 + 4.61803i 0.368281 + 0.506895i 0.952433 0.304749i \(-0.0985727\pi\)
−0.584152 + 0.811644i \(0.698573\pi\)
\(84\) 0.381966 + 1.17557i 0.0416759 + 0.128265i
\(85\) 0 0
\(86\) 1.04508 + 0.759299i 0.112694 + 0.0818773i
\(87\) 5.85410i 0.627626i
\(88\) −7.38394 0.690983i −0.787130 0.0736590i
\(89\) −10.8541 −1.15053 −0.575266 0.817966i \(-0.695102\pi\)
−0.575266 + 0.817966i \(0.695102\pi\)
\(90\) 0 0
\(91\) 0.291796 0.898056i 0.0305885 0.0941418i
\(92\) −3.66547 + 1.19098i −0.382152 + 0.124169i
\(93\) 4.11450 + 5.66312i 0.426653 + 0.587238i
\(94\) 2.54508 1.84911i 0.262505 0.190721i
\(95\) 0 0
\(96\) −1.73607 + 5.34307i −0.177187 + 0.545325i
\(97\) −6.74315 + 9.28115i −0.684663 + 0.942358i −0.999978 0.00662888i \(-0.997890\pi\)
0.315315 + 0.948987i \(0.397890\pi\)
\(98\) 3.96556i 0.400582i
\(99\) 3.04508 + 1.31433i 0.306043 + 0.132095i
\(100\) 0 0
\(101\) 0.454915 + 0.330515i 0.0452657 + 0.0328875i 0.610188 0.792257i \(-0.291094\pi\)
−0.564922 + 0.825144i \(0.691094\pi\)
\(102\) 1.17557 + 0.381966i 0.116399 + 0.0378203i
\(103\) −2.26538 + 0.736068i −0.223215 + 0.0725269i −0.418489 0.908222i \(-0.637440\pi\)
0.195274 + 0.980749i \(0.437440\pi\)
\(104\) 2.23607 1.62460i 0.219265 0.159305i
\(105\) 0 0
\(106\) −1.45492 4.47777i −0.141314 0.434919i
\(107\) −2.71441 0.881966i −0.262412 0.0852629i 0.174856 0.984594i \(-0.444054\pi\)
−0.437268 + 0.899331i \(0.644054\pi\)
\(108\) 0.951057 1.30902i 0.0915155 0.125960i
\(109\) −4.14590 −0.397105 −0.198553 0.980090i \(-0.563624\pi\)
−0.198553 + 0.980090i \(0.563624\pi\)
\(110\) 0 0
\(111\) 7.47214 0.709224
\(112\) 0.832544 1.14590i 0.0786680 0.108277i
\(113\) 5.20431 + 1.69098i 0.489580 + 0.159074i 0.543396 0.839477i \(-0.317138\pi\)
−0.0538155 + 0.998551i \(0.517138\pi\)
\(114\) 0.954915 + 2.93893i 0.0894360 + 0.275256i
\(115\) 0 0
\(116\) −7.66312 + 5.56758i −0.711503 + 0.516937i
\(117\) −1.17557 + 0.381966i −0.108682 + 0.0353128i
\(118\) −3.94298 1.28115i −0.362981 0.117940i
\(119\) −1.23607 0.898056i −0.113310 0.0823247i
\(120\) 0 0
\(121\) 9.94427 4.70228i 0.904025 0.427480i
\(122\) 4.32624i 0.391679i
\(123\) −1.48584 + 2.04508i −0.133974 + 0.184399i
\(124\) 3.50000 10.7719i 0.314309 0.967344i
\(125\) 0 0
\(126\) 0.381966 0.277515i 0.0340282 0.0247230i
\(127\) 9.37181 + 12.8992i 0.831613 + 1.14462i 0.987621 + 0.156862i \(0.0501377\pi\)
−0.156007 + 0.987756i \(0.549862\pi\)
\(128\) 10.8249 3.51722i 0.956794 0.310881i
\(129\) −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 \(0.304696\pi\)
\(132\) −1.17557 5.23607i −0.102320 0.455741i
\(133\) 3.81966i 0.331207i
\(134\) −4.69098 3.40820i −0.405239 0.294424i
\(135\) 0 0
\(136\) −1.38197 4.25325i −0.118503 0.364714i
\(137\) 10.9964 + 15.1353i 0.939486 + 1.29309i 0.956042 + 0.293229i \(0.0947299\pi\)
−0.0165558 + 0.999863i \(0.505270\pi\)
\(138\) 0.865300 + 1.19098i 0.0736592 + 0.101383i
\(139\) −6.54508 20.1437i −0.555147 1.70857i −0.695555 0.718473i \(-0.744842\pi\)
0.140408 0.990094i \(-0.455158\pi\)
\(140\) 0 0
\(141\) 4.11803 + 2.99193i 0.346801 + 0.251966i
\(142\) 4.94427i 0.414914i
\(143\) −1.62460 + 3.76393i −0.135856 + 0.314756i
\(144\) −1.85410 −0.154508
\(145\) 0 0
\(146\) −2.57295 + 7.91872i −0.212939 + 0.655358i
\(147\) 6.10237 1.98278i 0.503315 0.163537i
\(148\) −7.10642 9.78115i −0.584144 0.804006i
\(149\) 16.2812 11.8290i 1.33380 0.969065i 0.334156 0.942518i \(-0.391549\pi\)
0.999648 0.0265477i \(-0.00845140\pi\)
\(150\) 0 0
\(151\) −3.32624 + 10.2371i −0.270685 + 0.833084i 0.719643 + 0.694344i \(0.244305\pi\)
−0.990329 + 0.138740i \(0.955695\pi\)
\(152\) 6.57164 9.04508i 0.533030 0.733653i
\(153\) 2.00000i 0.161690i
\(154\) 0.145898 1.55909i 0.0117568 0.125635i
\(155\) 0 0
\(156\) 1.61803 + 1.17557i 0.129546 + 0.0941210i
\(157\) 3.16344 + 1.02786i 0.252470 + 0.0820325i 0.432518 0.901625i \(-0.357625\pi\)
−0.180048 + 0.983658i \(0.557625\pi\)
\(158\) 4.75528 1.54508i 0.378310 0.122920i
\(159\) 6.16312 4.47777i 0.488767 0.355110i
\(160\) 0 0
\(161\) −0.562306 1.73060i −0.0443159 0.136390i
\(162\) −0.587785 0.190983i −0.0461808 0.0150050i
\(163\) 7.97172 10.9721i 0.624394 0.859404i −0.373270 0.927723i \(-0.621763\pi\)
0.997664 + 0.0683187i \(0.0217635\pi\)
\(164\) 4.09017 0.319389
\(165\) 0 0
\(166\) −3.52786 −0.273815
\(167\) 11.7759 16.2082i 0.911250 1.25423i −0.0554876 0.998459i \(-0.517671\pi\)
0.966738 0.255769i \(-0.0823287\pi\)
\(168\) −1.62460 0.527864i −0.125340 0.0407256i
\(169\) 3.54508 + 10.9106i 0.272699 + 0.839281i
\(170\) 0 0
\(171\) −4.04508 + 2.93893i −0.309335 + 0.224745i
\(172\) 3.21644 1.04508i 0.245251 0.0796870i
\(173\) 3.38795 + 1.10081i 0.257581 + 0.0836933i 0.434961 0.900449i \(-0.356762\pi\)
−0.177380 + 0.984142i \(0.556762\pi\)
\(174\) 2.92705 + 2.12663i 0.221899 + 0.161219i
\(175\) 0 0
\(176\) −4.06231 + 4.61653i −0.306208 + 0.347984i
\(177\) 6.70820i 0.504219i
\(178\) 3.94298 5.42705i 0.295539 0.406775i
\(179\) 6.01722 18.5191i 0.449748 1.38418i −0.427443 0.904042i \(-0.640586\pi\)
0.877192 0.480141i \(-0.159414\pi\)
\(180\) 0 0
\(181\) 4.23607 3.07768i 0.314864 0.228762i −0.419117 0.907932i \(-0.637660\pi\)
0.733981 + 0.679170i \(0.237660\pi\)
\(182\) 0.343027 + 0.472136i 0.0254268 + 0.0349970i
\(183\) 6.65740 2.16312i 0.492129 0.159902i
\(184\) 1.64590 5.06555i 0.121337 0.373438i
\(185\) 0 0
\(186\) −4.32624 −0.317215
\(187\) 4.97980 + 4.38197i 0.364159 + 0.320441i
\(188\) 8.23607i 0.600677i
\(189\) 0.618034 + 0.449028i 0.0449554 + 0.0326620i
\(190\) 0 0
\(191\) 3.21885 + 9.90659i 0.232908 + 0.716816i 0.997392 + 0.0721737i \(0.0229936\pi\)
−0.764484 + 0.644642i \(0.777006\pi\)
\(192\) 0.138757 + 0.190983i 0.0100139 + 0.0137830i
\(193\) 12.3637 + 17.0172i 0.889961 + 1.22493i 0.973561 + 0.228427i \(0.0733582\pi\)
−0.0836000 + 0.996499i \(0.526642\pi\)
\(194\) −2.19098 6.74315i −0.157303 0.484130i
\(195\) 0 0
\(196\) −8.39919 6.10237i −0.599942 0.435883i
\(197\) 14.2361i 1.01428i −0.861864 0.507139i \(-0.830703\pi\)
0.861864 0.507139i \(-0.169297\pi\)
\(198\) −1.76336 + 1.04508i −0.125316 + 0.0742710i
\(199\) −19.7984 −1.40347 −0.701735 0.712438i \(-0.747591\pi\)
−0.701735 + 0.712438i \(0.747591\pi\)
\(200\) 0 0
\(201\) 2.89919 8.92278i 0.204493 0.629364i
\(202\) −0.330515 + 0.107391i −0.0232550 + 0.00755600i
\(203\) −2.62866 3.61803i −0.184495 0.253936i
\(204\) 2.61803 1.90211i 0.183299 0.133175i
\(205\) 0 0
\(206\) 0.454915 1.40008i 0.0316954 0.0975485i
\(207\) −1.40008 + 1.92705i −0.0973126 + 0.133939i
\(208\) 2.29180i 0.158907i
\(209\) −1.54508 + 16.5110i −0.106876 + 1.14209i
\(210\) 0 0
\(211\) 3.11803 + 2.26538i 0.214654 + 0.155955i 0.689917 0.723888i \(-0.257647\pi\)
−0.475263 + 0.879844i \(0.657647\pi\)
\(212\) −11.7229 3.80902i −0.805135 0.261604i
\(213\) −7.60845 + 2.47214i −0.521323 + 0.169388i
\(214\) 1.42705 1.03681i 0.0975512 0.0708751i
\(215\) 0 0
\(216\) 0.690983 + 2.12663i 0.0470154 + 0.144699i
\(217\) 5.08580 + 1.65248i 0.345246 + 0.112177i
\(218\) 1.50609 2.07295i 0.102005 0.140398i
\(219\) −13.4721 −0.910363
\(220\) 0 0
\(221\) −2.47214 −0.166294
\(222\) −2.71441 + 3.73607i −0.182179 + 0.250748i
\(223\) 7.64121 + 2.48278i 0.511693 + 0.166259i 0.553472 0.832868i \(-0.313303\pi\)
−0.0417790 + 0.999127i \(0.513303\pi\)
\(224\) 1.32624 + 4.08174i 0.0886130 + 0.272723i
\(225\) 0 0
\(226\) −2.73607 + 1.98787i −0.182001 + 0.132231i
\(227\) 24.6745 8.01722i 1.63770 0.532122i 0.661679 0.749788i \(-0.269844\pi\)
0.976023 + 0.217666i \(0.0698443\pi\)
\(228\) 7.69421 + 2.50000i 0.509561 + 0.165567i
\(229\) 14.6353 + 10.6331i 0.967125 + 0.702657i 0.954795 0.297267i \(-0.0960750\pi\)
0.0123304 + 0.999924i \(0.496075\pi\)
\(230\) 0 0
\(231\) 2.47214 0.555029i 0.162655 0.0365182i
\(232\) 13.0902i 0.859412i
\(233\) −13.6781 + 18.8262i −0.896080 + 1.23335i 0.0756220 + 0.997137i \(0.475906\pi\)
−0.971702 + 0.236211i \(0.924094\pi\)
\(234\) 0.236068 0.726543i 0.0154322 0.0474956i
\(235\) 0 0
\(236\) −8.78115 + 6.37988i −0.571604 + 0.415295i
\(237\) 4.75528 + 6.54508i 0.308889 + 0.425149i
\(238\) 0.898056 0.291796i 0.0582123 0.0189143i
\(239\) 2.17376 6.69015i 0.140609 0.432750i −0.855811 0.517288i \(-0.826942\pi\)
0.996420 + 0.0845383i \(0.0269415\pi\)
\(240\) 0 0
\(241\) −1.61803 −0.104227 −0.0521134 0.998641i \(-0.516596\pi\)
−0.0521134 + 0.998641i \(0.516596\pi\)
\(242\) −1.26133 + 6.68034i −0.0810812 + 0.429429i
\(243\) 1.00000i 0.0641500i
\(244\) −9.16312 6.65740i −0.586609 0.426196i
\(245\) 0 0
\(246\) −0.482779 1.48584i −0.0307809 0.0947338i
\(247\) −3.63271 5.00000i −0.231144 0.318142i
\(248\) 9.20029 + 12.6631i 0.584219 + 0.804109i
\(249\) −1.76393 5.42882i −0.111785 0.344038i
\(250\) 0 0
\(251\) −6.09017 4.42477i −0.384408 0.279289i 0.378752 0.925498i \(-0.376353\pi\)
−0.763160 + 0.646209i \(0.776353\pi\)
\(252\) 1.23607i 0.0778650i
\(253\) 1.73060 + 7.70820i 0.108802 + 0.484611i
\(254\) −9.85410 −0.618301
\(255\) 0 0
\(256\) −2.02786 + 6.24112i −0.126742 + 0.390070i
\(257\) −10.0453 + 3.26393i −0.626612 + 0.203598i −0.605074 0.796170i \(-0.706856\pi\)
−0.0215381 + 0.999768i \(0.506856\pi\)
\(258\) −0.759299 1.04508i −0.0472719 0.0650641i
\(259\) 4.61803 3.35520i 0.286951 0.208482i
\(260\) 0 0
\(261\) −1.80902 + 5.56758i −0.111975 + 0.344625i
\(262\) −4.78804 + 6.59017i −0.295806 + 0.407142i
\(263\) 27.2148i 1.67814i −0.544027 0.839068i \(-0.683101\pi\)
0.544027 0.839068i \(-0.316899\pi\)
\(264\) 6.80902 + 2.93893i 0.419066 + 0.180878i
\(265\) 0 0
\(266\) 1.90983 + 1.38757i 0.117099 + 0.0850775i
\(267\) 10.3229 + 3.35410i 0.631749 + 0.205268i
\(268\) −14.4374 + 4.69098i −0.881902 + 0.286547i
\(269\) −4.73607 + 3.44095i −0.288763 + 0.209799i −0.722731 0.691130i \(-0.757113\pi\)
0.433967 + 0.900929i \(0.357113\pi\)
\(270\) 0 0
\(271\) 6.37132 + 19.6089i 0.387030 + 1.19116i 0.934997 + 0.354656i \(0.115402\pi\)
−0.547966 + 0.836500i \(0.684598\pi\)
\(272\) −3.52671 1.14590i −0.213838 0.0694803i
\(273\) −0.555029 + 0.763932i −0.0335919 + 0.0462353i
\(274\) −11.5623 −0.698504
\(275\) 0 0
\(276\) 3.85410 0.231990
\(277\) 5.08580 7.00000i 0.305576 0.420589i −0.628419 0.777875i \(-0.716298\pi\)
0.933995 + 0.357286i \(0.116298\pi\)
\(278\) 12.4495 + 4.04508i 0.746671 + 0.242608i
\(279\) −2.16312 6.65740i −0.129503 0.398568i
\(280\) 0 0
\(281\) −8.16312 + 5.93085i −0.486971 + 0.353805i −0.804018 0.594605i \(-0.797309\pi\)
0.317047 + 0.948410i \(0.397309\pi\)
\(282\) −2.99193 + 0.972136i −0.178167 + 0.0578899i
\(283\) 12.3965 + 4.02786i 0.736895 + 0.239432i 0.653333 0.757071i \(-0.273370\pi\)
0.0835622 + 0.996503i \(0.473370\pi\)
\(284\) 10.4721 + 7.60845i 0.621407 + 0.451479i
\(285\) 0 0
\(286\) −1.29180 2.17963i −0.0763855 0.128884i
\(287\) 1.93112i 0.113990i
\(288\) 3.30220 4.54508i 0.194584 0.267822i
\(289\) 4.01722 12.3637i 0.236307 0.727279i
\(290\) 0 0
\(291\) 9.28115 6.74315i 0.544071 0.395291i
\(292\) 12.8128 + 17.6353i 0.749810 + 1.03203i
\(293\) −15.7189 + 5.10739i −0.918310 + 0.298377i −0.729773 0.683689i \(-0.760374\pi\)
−0.188537 + 0.982066i \(0.560374\pi\)
\(294\) −1.22542 + 3.77147i −0.0714682 + 0.219957i
\(295\) 0 0
\(296\) 16.7082 0.971145
\(297\) −2.48990 2.19098i −0.144479 0.127134i
\(298\) 12.4377i 0.720496i
\(299\) −2.38197 1.73060i −0.137753 0.100083i
\(300\) 0 0
\(301\) 0.493422 + 1.51860i 0.0284404 + 0.0875305i
\(302\) −3.91023 5.38197i −0.225008 0.309697i
\(303\) −0.330515 0.454915i −0.0189876 0.0261342i
\(304\) −2.86475 8.81678i −0.164304 0.505677i
\(305\) 0 0
\(306\) −1.00000 0.726543i −0.0571662 0.0415337i
\(307\) 12.1246i 0.691988i −0.938237 0.345994i \(-0.887542\pi\)
0.938237 0.345994i \(-0.112458\pi\)
\(308\) −3.07768 2.70820i −0.175367 0.154314i
\(309\) 2.38197 0.135505
\(310\) 0 0
\(311\) 6.63525 20.4212i 0.376251 1.15798i −0.566380 0.824144i \(-0.691657\pi\)
0.942631 0.333837i \(-0.108343\pi\)
\(312\) −2.62866 + 0.854102i −0.148818 + 0.0483540i
\(313\) −0.277515 0.381966i −0.0156860 0.0215900i 0.801102 0.598528i \(-0.204247\pi\)
−0.816788 + 0.576938i \(0.804247\pi\)
\(314\) −1.66312 + 1.20833i −0.0938552 + 0.0681898i
\(315\) 0 0
\(316\) 4.04508 12.4495i 0.227554 0.700339i
\(317\) −17.8783 + 24.6074i −1.00415 + 1.38209i −0.0813997 + 0.996682i \(0.525939\pi\)
−0.922747 + 0.385407i \(0.874061\pi\)
\(318\) 4.70820i 0.264023i
\(319\) 9.89919 + 16.7027i 0.554248 + 0.935174i
\(320\) 0 0
\(321\) 2.30902 + 1.67760i 0.128877 + 0.0936344i
\(322\) 1.06957 + 0.347524i 0.0596048 + 0.0193668i
\(323\) −9.51057 + 3.09017i −0.529182 + 0.171942i
\(324\) −1.30902 + 0.951057i −0.0727232 + 0.0528365i
\(325\) 0 0
\(326\) 2.59017 + 7.97172i 0.143456 + 0.441513i
\(327\) 3.94298 + 1.28115i 0.218047 + 0.0708479i
\(328\) −3.32244 + 4.57295i −0.183451 + 0.252499i
\(329\) 3.88854 0.214382
\(330\) 0 0
\(331\) 21.5967 1.18706 0.593532 0.804810i \(-0.297733\pi\)
0.593532 + 0.804810i \(0.297733\pi\)
\(332\) −5.42882 + 7.47214i −0.297945 + 0.410087i
\(333\) −7.10642 2.30902i −0.389430 0.126533i
\(334\) 3.82624 + 11.7759i 0.209362 + 0.644351i
\(335\) 0 0
\(336\) −1.14590 + 0.832544i −0.0625139 + 0.0454190i
\(337\) −21.0620 + 6.84346i −1.14732 + 0.372787i −0.820133 0.572173i \(-0.806101\pi\)
−0.327187 + 0.944960i \(0.606101\pi\)
\(338\) −6.74315 2.19098i −0.366779 0.119174i
\(339\) −4.42705 3.21644i −0.240444 0.174693i
\(340\) 0 0
\(341\) −21.3156 9.20029i −1.15430 0.498224i
\(342\) 3.09017i 0.167097i
\(343\) 6.02434 8.29180i 0.325284 0.447715i
\(344\) −1.44427 + 4.44501i −0.0778699 + 0.239659i
\(345\) 0 0
\(346\) −1.78115 + 1.29408i −0.0957554 + 0.0695704i
\(347\) 3.42071 + 4.70820i 0.183633 + 0.252750i 0.890902 0.454195i \(-0.150073\pi\)
−0.707269 + 0.706945i \(0.750073\pi\)
\(348\) 9.00854 2.92705i 0.482908 0.156906i
\(349\) −8.57953 + 26.4051i −0.459252 + 1.41343i 0.406819 + 0.913509i \(0.366638\pi\)
−0.866070 + 0.499922i \(0.833362\pi\)
\(350\) 0 0
\(351\) 1.23607 0.0659764
\(352\) −4.08174 18.1803i −0.217558 0.969015i
\(353\) 35.8328i 1.90719i −0.301095 0.953594i \(-0.597352\pi\)
0.301095 0.953594i \(-0.402648\pi\)
\(354\) 3.35410 + 2.43690i 0.178269 + 0.129520i
\(355\) 0 0
\(356\) −5.42705 16.7027i −0.287633 0.885244i
\(357\) 0.898056 + 1.23607i 0.0475302 + 0.0654197i
\(358\) 7.07367 + 9.73607i 0.373855 + 0.514567i
\(359\) −5.16312 15.8904i −0.272499 0.838666i −0.989870 0.141975i \(-0.954655\pi\)
0.717371 0.696691i \(-0.245345\pi\)
\(360\) 0 0
\(361\) −4.85410 3.52671i −0.255479 0.185616i
\(362\) 3.23607i 0.170084i
\(363\) −10.9106 + 1.39919i −0.572661 + 0.0734383i
\(364\) 1.52786 0.0800818
\(365\) 0 0
\(366\) −1.33688 + 4.11450i −0.0698799 + 0.215068i
\(367\) −17.2375 + 5.60081i −0.899792 + 0.292360i −0.722151 0.691735i \(-0.756846\pi\)
−0.177641 + 0.984095i \(0.556846\pi\)
\(368\) −2.59590 3.57295i −0.135321 0.186253i
\(369\) 2.04508 1.48584i 0.106463 0.0773498i
\(370\) 0 0
\(371\) 1.79837 5.53483i 0.0933669 0.287354i
\(372\) −6.65740 + 9.16312i −0.345170 + 0.475086i
\(373\) 9.74265i 0.504455i 0.967668 + 0.252228i \(0.0811631\pi\)
−0.967668 + 0.252228i \(0.918837\pi\)
\(374\) −4.00000 + 0.898056i −0.206835 + 0.0464374i
\(375\) 0 0
\(376\) 9.20820 + 6.69015i 0.474877 + 0.345018i
\(377\) −6.88191 2.23607i −0.354436 0.115163i
\(378\) −0.449028 + 0.145898i −0.0230955 + 0.00750419i
\(379\) −4.04508 + 2.93893i −0.207782 + 0.150963i −0.686810 0.726837i \(-0.740989\pi\)
0.479028 + 0.877800i \(0.340989\pi\)
\(380\) 0 0
\(381\) −4.92705 15.1639i −0.252420 0.776870i
\(382\) −6.12261 1.98936i −0.313260 0.101784i
\(383\) −18.4333 + 25.3713i −0.941900 + 1.29641i 0.0131328 + 0.999914i \(0.495820\pi\)
−0.955033 + 0.296500i \(0.904180\pi\)
\(384\) −11.3820 −0.580834
\(385\) 0 0
\(386\) −13.0000 −0.661683
\(387\) 1.22857 1.69098i 0.0624518 0.0859575i
\(388\) −17.6538 5.73607i −0.896236 0.291205i
\(389\) 12.0344 + 37.0382i 0.610170 + 1.87791i 0.456316 + 0.889818i \(0.349169\pi\)
0.153855 + 0.988093i \(0.450831\pi\)
\(390\) 0 0
\(391\) −3.85410 + 2.80017i −0.194910 + 0.141611i
\(392\) 13.6453 4.43363i 0.689192 0.223932i
\(393\) −12.5352 4.07295i −0.632320 0.205453i
\(394\) 7.11803 + 5.17155i 0.358601 + 0.260539i
\(395\) 0 0
\(396\) −0.500000 + 5.34307i −0.0251259 + 0.268499i
\(397\) 36.2705i 1.82036i −0.414208 0.910182i \(-0.635941\pi\)
0.414208 0.910182i \(-0.364059\pi\)
\(398\) 7.19218 9.89919i 0.360511 0.496201i
\(399\) −1.18034 + 3.63271i −0.0590909 + 0.181863i
\(400\) 0 0
\(401\) −3.95492 + 2.87341i −0.197499 + 0.143491i −0.682140 0.731222i \(-0.738950\pi\)
0.484641 + 0.874713i \(0.338950\pi\)
\(402\) 3.40820 + 4.69098i 0.169985 + 0.233965i
\(403\) 8.22899 2.67376i 0.409915 0.133190i
\(404\) −0.281153 + 0.865300i −0.0139879 + 0.0430503i
\(405\) 0 0
\(406\) 2.76393 0.137172
\(407\) −21.3193 + 12.6353i −1.05676 + 0.626306i
\(408\) 4.47214i 0.221404i
\(409\) 29.3713 + 21.3395i 1.45232 + 1.05517i 0.985283 + 0.170933i \(0.0546781\pi\)
0.467036 + 0.884238i \(0.345322\pi\)
\(410\) 0 0
\(411\) −5.78115 17.7926i −0.285163 0.877642i
\(412\) −2.26538 3.11803i −0.111607 0.153615i
\(413\) −3.01217 4.14590i −0.148219 0.204006i
\(414\) −0.454915 1.40008i −0.0223579 0.0688104i
\(415\) 0 0
\(416\) 5.61803 + 4.08174i 0.275447 + 0.200124i
\(417\) 21.1803i 1.03721i
\(418\) −7.69421 6.77051i −0.376336 0.331156i
\(419\) −24.5967 −1.20163 −0.600815 0.799388i \(-0.705157\pi\)
−0.600815 + 0.799388i \(0.705157\pi\)
\(420\) 0 0
\(421\) 0.881966 2.71441i 0.0429844 0.132292i −0.927261 0.374415i \(-0.877844\pi\)
0.970246 + 0.242123i \(0.0778436\pi\)
\(422\) −2.26538 + 0.736068i −0.110277 + 0.0358312i
\(423\) −2.99193 4.11803i −0.145472 0.200226i
\(424\) 13.7812 10.0126i 0.669272 0.486255i
\(425\) 0 0
\(426\) 1.52786 4.70228i 0.0740253 0.227826i
\(427\) 3.14320 4.32624i 0.152110 0.209361i
\(428\) 4.61803i 0.223221i
\(429\) 2.70820 3.07768i 0.130753 0.148592i
\(430\) 0 0
\(431\) −16.0902 11.6902i −0.775036 0.563097i 0.128449 0.991716i \(-0.459000\pi\)
−0.903485 + 0.428619i \(0.859000\pi\)
\(432\) 1.76336 + 0.572949i 0.0848395 + 0.0275660i
\(433\) −26.6623 + 8.66312i −1.28131 + 0.416323i −0.869041 0.494739i \(-0.835264\pi\)
−0.412269 + 0.911062i \(0.635264\pi\)
\(434\) −2.67376 + 1.94260i −0.128345 + 0.0932479i
\(435\) 0 0
\(436\) −2.07295 6.37988i −0.0992763 0.305541i
\(437\) −11.3269 3.68034i −0.541840 0.176055i
\(438\) 4.89404 6.73607i 0.233846 0.321862i
\(439\) −9.67376 −0.461703 −0.230852 0.972989i \(-0.574151\pi\)
−0.230852 + 0.972989i \(0.574151\pi\)
\(440\) 0 0
\(441\) −6.41641 −0.305543
\(442\) 0.898056 1.23607i 0.0427162 0.0587938i
\(443\) 24.0337 + 7.80902i 1.14187 + 0.371018i 0.818077 0.575109i \(-0.195040\pi\)
0.323798 + 0.946126i \(0.395040\pi\)
\(444\) 3.73607 + 11.4984i 0.177306 + 0.545692i
\(445\) 0 0
\(446\) −4.01722 + 2.91868i −0.190221 + 0.138204i
\(447\) −19.1396 + 6.21885i −0.905274 + 0.294141i
\(448\) 0.171513 + 0.0557281i 0.00810325 + 0.00263290i
\(449\) −0.590170 0.428784i −0.0278518 0.0202355i 0.573772 0.819015i \(-0.305479\pi\)
−0.601624 + 0.798779i \(0.705479\pi\)
\(450\) 0 0
\(451\) 0.781153 8.34751i 0.0367831 0.393069i
\(452\) 8.85410i 0.416462i
\(453\) 6.32688 8.70820i 0.297263 0.409147i
\(454\) −4.95492 + 15.2497i −0.232546 + 0.715702i
\(455\) 0 0
\(456\) −9.04508 + 6.57164i −0.423575 + 0.307745i
\(457\) 0.865300 + 1.19098i 0.0404770 + 0.0557118i 0.828776 0.559581i \(-0.189038\pi\)
−0.788299 + 0.615293i \(0.789038\pi\)
\(458\) −10.6331 + 3.45492i −0.496854 + 0.161438i
\(459\) 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 \(0.293504\pi\)
\(462\) −0.620541 + 1.43769i −0.0288702 + 0.0668876i
\(463\) 33.2705i 1.54621i −0.634277 0.773106i \(-0.718702\pi\)
0.634277 0.773106i \(-0.281298\pi\)
\(464\) −8.78115 6.37988i −0.407655 0.296179i
\(465\) 0 0
\(466\) −4.44427 13.6781i −0.205877 0.633624i
\(467\) 2.87341 + 3.95492i 0.132966 + 0.183012i 0.870308 0.492507i \(-0.163920\pi\)
−0.737342 + 0.675519i \(0.763920\pi\)
\(468\) −1.17557 1.61803i −0.0543408 0.0747936i
\(469\) −2.21478 6.81640i −0.102269 0.314752i
\(470\) 0 0
\(471\) −2.69098 1.95511i −0.123994 0.0900869i
\(472\) 15.0000i 0.690431i
\(473\) −1.51860 6.76393i −0.0698252 0.311006i
\(474\) −5.00000 −0.229658
\(475\) 0 0
\(476\) 0.763932 2.35114i 0.0350148 0.107764i
\(477\) −7.24518 + 2.35410i −0.331734 + 0.107787i
\(478\) 2.55541 + 3.51722i 0.116882 + 0.160874i
\(479\) 27.0344 19.6417i 1.23524 0.897451i 0.237964 0.971274i \(-0.423520\pi\)
0.997271 + 0.0738231i \(0.0235200\pi\)
\(480\) 0 0
\(481\) 2.85410 8.78402i 0.130136 0.400517i
\(482\) 0.587785 0.809017i 0.0267729 0.0368497i
\(483\) 1.81966i 0.0827974i
\(484\) 12.2082 + 12.9515i 0.554918 + 0.588705i
\(485\) 0 0
\(486\) 0.500000 + 0.363271i 0.0226805 + 0.0164783i
\(487\) 13.4863 + 4.38197i 0.611123 + 0.198566i 0.598195 0.801351i \(-0.295885\pi\)
0.0129278 + 0.999916i \(0.495885\pi\)
\(488\) 14.8864 4.83688i 0.673875 0.218955i
\(489\) −10.9721 + 7.97172i −0.496177 + 0.360494i
\(490\) 0 0
\(491\) 9.82624 + 30.2421i 0.443452 + 1.36480i 0.884173 + 0.467160i \(0.154723\pi\)
−0.440721 + 0.897644i \(0.645277\pi\)
\(492\) −3.88998 1.26393i −0.175374 0.0569825i
\(493\) −6.88191 + 9.47214i −0.309946 + 0.426604i
\(494\) 3.81966 0.171855
\(495\) 0 0
\(496\) 12.9787 0.582761
\(497\) −3.59222 + 4.94427i −0.161133 + 0.221781i
\(498\) 3.35520 + 1.09017i 0.150350 + 0.0488517i
\(499\) 3.45492 + 10.6331i 0.154663 + 0.476005i 0.998127 0.0611822i \(-0.0194871\pi\)
−0.843463 + 0.537187i \(0.819487\pi\)
\(500\) 0 0
\(501\) −16.2082 + 11.7759i −0.724129 + 0.526111i
\(502\) 4.42477 1.43769i 0.197487 0.0641674i
\(503\) −20.8172 6.76393i −0.928195 0.301589i −0.194371 0.980928i \(-0.562266\pi\)
−0.733824 + 0.679339i \(0.762266\pi\)
\(504\) 1.38197 + 1.00406i 0.0615577 + 0.0447243i
\(505\) 0 0
\(506\) −4.48278 1.93487i −0.199284 0.0860154i
\(507\) 11.4721i 0.509495i
\(508\) −15.1639 + 20.8713i −0.672789 + 0.926015i
\(509\) −0.163119 + 0.502029i −0.00723012 + 0.0222520i −0.954606 0.297870i \(-0.903724\pi\)
0.947376 + 0.320122i \(0.103724\pi\)
\(510\) 0 0
\(511\) −8.32624 + 6.04937i −0.368331 + 0.267608i
\(512\) 10.9964 + 15.1353i 0.485977 + 0.668890i
\(513\) 4.75528 1.54508i 0.209951 0.0682172i
\(514\) 2.01722 6.20837i 0.0889758 0.273839i
\(515\) 0 0
\(516\) −3.38197 −0.148883
\(517\) −16.8087 1.57295i −0.739248 0.0691782i
\(518\) 3.52786i 0.155005i
\(519\) −2.88197 2.09387i −0.126504 0.0919107i
\(520\) 0 0
\(521\) −4.74671 14.6089i −0.207957 0.640026i −0.999579 0.0290150i \(-0.990763\pi\)
0.791622 0.611011i \(-0.209237\pi\)
\(522\) −2.12663 2.92705i −0.0930799 0.128114i
\(523\) −4.84104 6.66312i −0.211684 0.291358i 0.689951 0.723856i \(-0.257632\pi\)
−0.901635 + 0.432498i \(0.857632\pi\)
\(524\) 6.59017 + 20.2825i 0.287893 + 0.886043i
\(525\) 0 0
\(526\) 13.6074 + 9.88635i 0.593310 + 0.431065i
\(527\) 14.0000i 0.609850i
\(528\) 5.29007 3.13525i 0.230221 0.136444i
\(529\) 17.3262 0.753315
\(530\) 0 0
\(531\) −2.07295 + 6.37988i −0.0899583 + 0.276863i
\(532\) 5.87785 1.90983i 0.254837 0.0828016i
\(533\) 1.83660 + 2.52786i 0.0795520 + 0.109494i
\(534\) −5.42705 + 3.94298i −0.234851 + 0.170630i
\(535\) 0 0
\(536\) 6.48278 19.9519i 0.280013 0.861793i
\(537\) −11.4454 + 15.7533i −0.493907 + 0.679805i
\(538\) 3.61803i 0.155985i
\(539\) −14.0582 + 15.9762i −0.605531 + 0.688144i
\(540\) 0 0
\(541\) −0.500000 0.363271i −0.0214967 0.0156183i 0.576985 0.816755i \(-0.304229\pi\)
−0.598482 + 0.801136i \(0.704229\pi\)
\(542\) −12.1190 3.93769i −0.520555 0.169138i
\(543\) −4.97980 + 1.61803i −0.213704 + 0.0694365i
\(544\) 9.09017 6.60440i 0.389738 0.283161i
\(545\) 0 0
\(546\) −0.180340 0.555029i −0.00771783 0.0237531i
\(547\) 24.1194 + 7.83688i 1.03127 + 0.335081i 0.775293 0.631601i \(-0.217602\pi\)
0.255979 + 0.966682i \(0.417602\pi\)
\(548\) −17.7926 + 24.4894i −0.760060 + 1.04613i
\(549\) −7.00000 −0.298753
\(550\) 0 0
\(551\) −29.2705 −1.24697
\(552\) −3.13068 + 4.30902i −0.133251 + 0.183404i
\(553\) 5.87785 + 1.90983i 0.249952 + 0.0812142i
\(554\) 1.65248 + 5.08580i 0.0702070 + 0.216075i
\(555\) 0 0
\(556\) 27.7254 20.1437i 1.17582 0.854283i
\(557\) 29.8585 9.70163i 1.26515 0.411071i 0.401821 0.915718i \(-0.368377\pi\)
0.863326 + 0.504647i \(0.168377\pi\)
\(558\) 4.11450 + 1.33688i 0.174181 + 0.0565947i
\(559\) 2.09017 + 1.51860i 0.0884048 + 0.0642298i
\(560\) 0 0
\(561\) −3.38197 5.70634i −0.142787 0.240922i
\(562\) 6.23607i 0.263053i
\(563\) 21.3520 29.3885i 0.899881 1.23858i −0.0706255 0.997503i \(-0.522500\pi\)
0.970506 0.241077i \(-0.0775005\pi\)
\(564\) −2.54508 + 7.83297i −0.107167 + 0.329827i
\(565\) 0 0
\(566\) −6.51722 + 4.73504i −0.273939 + 0.199028i
\(567\) −0.449028 0.618034i −0.0188574 0.0259550i
\(568\) −17.0130 + 5.52786i −0.713850 + 0.231944i
\(569\) 0.753289 2.31838i 0.0315795 0.0971917i −0.934024 0.357209i \(-0.883728\pi\)
0.965604 + 0.260017i \(0.0837283\pi\)
\(570\) 0 0
\(571\) 0.0901699 0.00377349 0.00188675 0.999998i \(-0.499399\pi\)
0.00188675 + 0.999998i \(0.499399\pi\)
\(572\) −6.60440 0.618034i −0.276144 0.0258413i
\(573\) 10.4164i 0.435152i
\(574\) −0.965558 0.701519i −0.0403016 0.0292808i
\(575\) 0 0
\(576\) −0.0729490 0.224514i −0.00303954 0.00935475i
\(577\) −27.0459 37.2254i −1.12593 1.54971i −0.795571 0.605861i \(-0.792829\pi\)
−0.330363 0.943854i \(-0.607171\pi\)
\(578\) 4.72253 + 6.50000i 0.196431 + 0.270364i
\(579\) −6.50000 20.0049i −0.270131 0.831377i
\(580\) 0 0
\(581\) −3.52786 2.56314i −0.146360 0.106337i
\(582\) 7.09017i 0.293897i
\(583\) −10.0126 + 23.1976i −0.414679 + 0.960745i
\(584\) −30.1246 −1.24657
\(585\) 0 0
\(586\) 3.15654 9.71483i 0.130396 0.401316i
\(587\) −18.4333 + 5.98936i −0.760826 + 0.247207i −0.663633 0.748058i \(-0.730986\pi\)
−0.0971926 + 0.995266i \(0.530986\pi\)
\(588\) 6.10237 + 8.39919i 0.251657 + 0.346377i
\(589\) 28.3156 20.5725i 1.16672 0.847674i
\(590\) 0 0
\(591\) −4.39919 + 13.5393i −0.180958 + 0.556933i
\(592\) 8.14324 11.2082i 0.334685 0.460654i
\(593\) 38.8885i 1.59696i 0.602021 + 0.798481i \(0.294362\pi\)
−0.602021 + 0.798481i \(0.705638\pi\)
\(594\) 2.00000 0.449028i 0.0820610 0.0184238i
\(595\) 0 0
\(596\) 26.3435 + 19.1396i 1.07907 + 0.783990i
\(597\) 18.8294 + 6.11803i 0.770635 + 0.250394i
\(598\) 1.73060 0.562306i 0.0707695 0.0229944i
\(599\) −17.9894 + 13.0700i −0.735025 + 0.534027i −0.891149 0.453710i \(-0.850100\pi\)
0.156124 + 0.987737i \(0.450100\pi\)
\(600\) 0 0
\(601\) 10.6180 + 32.6789i 0.433119 + 1.33300i 0.895002 + 0.446062i \(0.147174\pi\)
−0.461884 + 0.886941i \(0.652826\pi\)
\(602\) −0.938545 0.304952i −0.0382522 0.0124289i
\(603\) −5.51458 + 7.59017i −0.224571 + 0.309096i
\(604\) −17.4164 −0.708664
\(605\) 0 0
\(606\) 0.347524 0.0141172
\(607\) 19.3969 26.6976i 0.787296 1.08362i −0.207143 0.978311i \(-0.566417\pi\)
0.994439 0.105310i \(-0.0335835\pi\)
\(608\) 26.7153 + 8.68034i 1.08345 + 0.352034i
\(609\) 1.38197 + 4.25325i 0.0560001 + 0.172351i
\(610\) 0 0
\(611\) 5.09017 3.69822i 0.205926 0.149614i
\(612\) −3.07768 + 1.00000i −0.124408 + 0.0404226i
\(613\) 7.83297 + 2.54508i 0.316371 + 0.102795i 0.462898 0.886412i \(-0.346810\pi\)
−0.146527 + 0.989207i \(0.546810\pi\)
\(614\) 6.06231 + 4.40452i 0.244655 + 0.177752i
\(615\) 0 0
\(616\) 5.52786 1.24108i 0.222724 0.0500047i
\(617\) 38.2492i 1.53986i 0.638131 + 0.769928i \(0.279708\pi\)
−0.638131 + 0.769928i \(0.720292\pi\)
\(618\) −0.865300 + 1.19098i −0.0348075 + 0.0479084i
\(619\) −2.19756 + 6.76340i −0.0883274 + 0.271844i −0.985457 0.169923i \(-0.945648\pi\)
0.897130 + 0.441767i \(0.145648\pi\)
\(620\) 0 0
\(621\) 1.92705 1.40008i 0.0773299 0.0561835i
\(622\) 7.80021 + 10.7361i 0.312760 + 0.430477i
\(623\) 7.88597 2.56231i 0.315945 0.102657i
\(624\) −0.708204 + 2.17963i −0.0283508 + 0.0872549i
\(625\) 0 0
\(626\) 0.291796 0.0116625
\(627\) 6.57164 15.2254i 0.262446 0.608045i
\(628\) 5.38197i 0.214764i
\(629\) −12.0902 8.78402i −0.482067 0.350242i
\(630\) 0 0
\(631\) 11.9377 + 36.7404i 0.475232 + 1.46261i 0.845644 + 0.533747i \(0.179216\pi\)
−0.370412 + 0.928867i \(0.620784\pi\)
\(632\) 10.6331 + 14.6353i 0.422963 + 0.582159i
\(633\) −2.26538 3.11803i −0.0900409 0.123931i
\(634\) −5.80902 17.8783i −0.230706 0.710039i
\(635\) 0 0
\(636\) 9.97214 + 7.24518i 0.395421 + 0.287290i
\(637\) 7.93112i 0.314242i
\(638\) −11.9475 1.11803i −0.473005 0.0442634i
\(639\) 8.00000 0.316475
\(640\) 0 0
\(641\) −0.0729490 + 0.224514i −0.00288131 + 0.00886777i −0.952487 0.304580i \(-0.901484\pi\)
0.949606 + 0.313448i \(0.101484\pi\)
\(642\) −1.67760 + 0.545085i −0.0662096 + 0.0215128i
\(643\) 17.2375 + 23.7254i 0.679782 + 0.935639i 0.999931 0.0117276i \(-0.00373311\pi\)
−0.320149 + 0.947367i \(0.603733\pi\)
\(644\) 2.38197 1.73060i 0.0938626 0.0681952i
\(645\) 0 0
\(646\) 1.90983 5.87785i 0.0751413 0.231261i
\(647\) 10.3431 14.2361i 0.406630 0.559678i −0.555763 0.831341i \(-0.687574\pi\)
0.962392 + 0.271663i \(0.0875737\pi\)
\(648\) 2.23607i 0.0878410i
\(649\) 11.3435 + 19.1396i 0.445270 + 0.751297i
\(650\) 0 0
\(651\) −4.32624 3.14320i −0.169559 0.123192i
\(652\) 20.8702 + 6.78115i 0.817342 + 0.265570i
\(653\) −22.2906 + 7.24265i −0.872297 + 0.283427i −0.710755 0.703439i \(-0.751647\pi\)
−0.161542 + 0.986866i \(0.551647\pi\)
\(654\) −2.07295 + 1.50609i −0.0810587 + 0.0588926i
\(655\) 0 0
\(656\) 1.44834 + 4.45752i 0.0565481 + 0.174037i
\(657\) 12.8128 + 4.16312i 0.499873 + 0.162419i
\(658\) −1.41260 + 1.94427i −0.0550687 + 0.0757956i
\(659\) −12.9656 −0.505066 −0.252533 0.967588i \(-0.581264\pi\)
−0.252533 + 0.967588i \(0.581264\pi\)
\(660\) 0 0
\(661\) 3.90983 0.152075 0.0760374 0.997105i \(-0.475773\pi\)
0.0760374 + 0.997105i \(0.475773\pi\)
\(662\) −7.84548 + 10.7984i −0.304923 + 0.419691i
\(663\) 2.35114 + 0.763932i 0.0913108 + 0.0296687i
\(664\) −3.94427 12.1392i −0.153067 0.471093i
\(665\) 0 0
\(666\) 3.73607 2.71441i 0.144770 0.105181i
\(667\) −13.2618 + 4.30902i −0.513499 + 0.166846i
\(668\) 30.8298 + 10.0172i 1.19284 + 0.387578i
\(669\) −6.50000 4.72253i −0.251305 0.182583i
\(670\) 0 0
\(671\) −15.3369 + 17.4293i −0.592074 + 0.672850i
\(672\) 4.29180i 0.165560i
\(673\) 16.0494 22.0902i 0.618661 0.851513i −0.378594 0.925563i \(-0.623592\pi\)
0.997255 + 0.0740494i \(0.0235923\pi\)
\(674\) 4.22949 13.0170i 0.162914 0.501397i
\(675\) 0 0
\(676\) −15.0172 + 10.9106i −0.577585 + 0.419640i
\(677\) −7.02067 9.66312i −0.269826 0.371384i 0.652505 0.757785i \(-0.273718\pi\)
−0.922331 + 0.386401i \(0.873718\pi\)
\(678\) 3.21644 1.04508i 0.123527 0.0401362i
\(679\) 2.70820 8.33499i 0.103931 0.319868i
\(680\) 0 0
\(681\) −25.9443 −0.994187
\(682\) 12.3435 7.31559i 0.472657 0.280129i
\(683\) 2.29180i 0.0876931i −0.999038 0.0438466i \(-0.986039\pi\)
0.999038 0.0438466i \(-0.0139613\pi\)
\(684\) −6.54508 4.75528i −0.250258 0.181823i
\(685\) 0 0
\(686\) 1.95743 + 6.02434i 0.0747349 + 0.230010i
\(687\) −10.6331 14.6353i −0.405679 0.558370i
\(688\) 2.27790 + 3.13525i 0.0868440 + 0.119530i
\(689\) −2.90983 8.95554i −0.110856 0.341179i
\(690\) 0 0
\(691\) −26.9443 19.5762i −1.02501 0.744712i −0.0577049 0.998334i \(-0.518378\pi\)
−0.967304 + 0.253621i \(0.918378\pi\)
\(692\) 5.76393i 0.219112i
\(693\) −2.52265 0.236068i −0.0958277 0.00896748i
\(694\) −3.59675 −0.136531
\(695\) 0 0
\(696\) −4.04508 + 12.4495i −0.153329 + 0.471897i
\(697\) 4.80828 1.56231i 0.182127 0.0591766i
\(698\) −10.0858 13.8820i −0.381755 0.525440i
\(699\) 18.8262 13.6781i 0.712074 0.517352i
\(700\) 0 0
\(701\) 4.19756 12.9188i 0.158540 0.487935i −0.839963 0.542644i \(-0.817423\pi\)
0.998502 + 0.0547093i \(0.0174232\pi\)
\(702\) −0.449028 + 0.618034i −0.0169475 + 0.0233262i
\(703\) 37.3607i 1.40908i
\(704\) −0.718847 0.310271i −0.0270926 0.0116938i
\(705\) 0 0
\(706\) 17.9164 + 13.0170i 0.674293 + 0.489902i
\(707\) −0.408539 0.132742i −0.0153647 0.00499229i
\(708\) 10.3229 3.35410i 0.387957 0.126055i
\(709\) 33.3156 24.2052i 1.25119 0.909045i 0.252903 0.967492i \(-0.418615\pi\)
0.998291 + 0.0584464i \(0.0186147\pi\)
\(710\) 0 0
\(711\) −2.50000 7.69421i −0.0937573 0.288555i
\(712\) 23.0826 + 7.50000i 0.865058 + 0.281074i
\(713\) 9.80059 13.4894i 0.367035 0.505180i
\(714\) −0.944272 −0.0353385
\(715\) 0 0
\(716\) 31.5066 1.17746
\(717\) −4.13474 + 5.69098i −0.154415 + 0.212534i
\(718\) 9.82084 + 3.19098i 0.366510 + 0.119086i
\(719\) −11.7705 36.2259i −0.438966 1.35100i −0.888967 0.457970i \(-0.848577\pi\)
0.450001 0.893028i \(-0.351423\pi\)
\(720\) 0 0
\(721\) 1.47214 1.06957i 0.0548252 0.0398328i
\(722\) 3.52671 1.14590i 0.131251 0.0426459i
\(723\) 1.53884 + 0.500000i 0.0572301 + 0.0185952i
\(724\) 6.85410 + 4.97980i 0.254731 + 0.185073i
\(725\) 0 0
\(726\) 3.26393 5.96361i 0.121136 0.221330i
\(727\) 37.3262i 1.38435i −0.721728 0.692177i \(-0.756652\pi\)
0.721728 0.692177i \(-0.243348\pi\)
\(728\) −1.24108 + 1.70820i −0.0459976 + 0.0633102i
\(729\) −0.309017 + 0.951057i −0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) 3.38197 2.45714i 0.125087 0.0908807i
\(732\) 6.65740 + 9.16312i 0.246064 + 0.338679i
\(733\) −1.76336 + 0.572949i −0.0651310 + 0.0211624i −0.341401 0.939918i \(-0.610902\pi\)
0.276270 + 0.961080i \(0.410902\pi\)
\(734\) 3.46149 10.6534i 0.127766 0.393223i
\(735\) 0 0
\(736\) 13.3820 0.493266
\(737\) 6.81640 + 30.3607i 0.251085 + 1.11835i
\(738\) 1.56231i 0.0575093i
\(739\) −16.1803 11.7557i −0.595203 0.432441i 0.248970 0.968511i \(-0.419908\pi\)
−0.844173 + 0.536071i \(0.819908\pi\)
\(740\) 0 0
\(741\) 1.90983 + 5.87785i 0.0701594 + 0.215928i
\(742\) 2.11412 + 2.90983i 0.0776116 + 0.106823i
\(743\) −0.204270 0.281153i −0.00749392 0.0103145i 0.805254 0.592931i \(-0.202029\pi\)
−0.812748 + 0.582616i \(0.802029\pi\)
\(744\) −4.83688 14.8864i −0.177329 0.545762i
\(745\) 0 0
\(746\) −4.87132 3.53922i −0.178352 0.129580i
\(747\) 5.70820i 0.208852i
\(748\) −4.25325 + 9.85410i −0.155514 + 0.360302i
\(749\) 2.18034 0.0796679
\(750\) 0 0
\(751\) −14.1803 + 43.6426i −0.517448 + 1.59254i 0.261335 + 0.965248i \(0.415837\pi\)
−0.778783 + 0.627293i \(0.784163\pi\)
\(752\) 8.97578 2.91641i 0.327313 0.106350i
\(753\) 4.42477 + 6.09017i 0.161247 + 0.221938i
\(754\) 3.61803 2.62866i 0.131761 0.0957300i
\(755\) 0 0
\(756\) −0.381966 + 1.17557i −0.0138920 + 0.0427551i
\(757\) 14.2128 19.5623i 0.516575 0.711004i −0.468436 0.883497i \(-0.655182\pi\)
0.985011 + 0.172493i \(0.0551823\pi\)
\(758\) 3.09017i 0.112240i
\(759\) 0.736068 7.86572i 0.0267176 0.285508i
\(760\) 0 0
\(761\) −31.5795 22.9439i −1.14476 0.831715i −0.156982 0.987601i \(-0.550176\pi\)
−0.987775 + 0.155887i \(0.950176\pi\)
\(762\) 9.37181 + 3.04508i 0.339505 + 0.110312i
\(763\) 3.01217 0.978714i 0.109048 0.0354318i
\(764\) −13.6353 + 9.90659i −0.493306 + 0.358408i
\(765\) 0 0
\(766\) −5.98936 18.4333i −0.216404 0.666024i
\(767\) −7.88597 2.56231i −0.284746 0.0925195i
\(768\) 3.85723 5.30902i 0.139186 0.191573i
\(769\) −12.7639 −0.460279 −0.230140 0.973158i \(-0.573918\pi\)
−0.230140 + 0.973158i \(0.573918\pi\)
\(770\) 0 0
\(771\) 10.5623 0.380392
\(772\) −20.0049 + 27.5344i −0.719994 + 0.990986i
\(773\) −9.99235 3.24671i −0.359400 0.116776i 0.123751 0.992313i \(-0.460508\pi\)
−0.483151 + 0.875537i \(0.660508\pi\)
\(774\) 0.399187 + 1.22857i 0.0143485 + 0.0441601i
\(775\) 0 0
\(776\) 20.7533 15.0781i 0.745000 0.541274i
\(777\) −5.42882 + 1.76393i −0.194758 + 0.0632807i
\(778\) −22.8909 7.43769i −0.820677 0.266654i
\(779\) 10.2254 + 7.42921i 0.366364 + 0.266179i
\(780\) 0 0