Properties

Label 1110.2.u.e.401.16
Level $1110$
Weight $2$
Character 1110.401
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 401.16
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.e.191.16

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.64725 - 0.535321i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.54331 + 0.786252i) q^{6} -2.53955 q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.42686 + 1.76361i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.64725 - 0.535321i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.54331 + 0.786252i) q^{6} -2.53955 q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.42686 + 1.76361i) q^{9} +1.00000 q^{10} +1.55248 q^{11} +(-0.535321 + 1.64725i) q^{12} +(-1.11554 + 1.11554i) q^{13} +(-1.79574 + 1.79574i) q^{14} +(-0.786252 - 1.54331i) q^{15} -1.00000 q^{16} +(4.84198 + 4.84198i) q^{17} +(2.96312 - 0.468987i) q^{18} +(-2.49053 + 2.49053i) q^{19} +(0.707107 - 0.707107i) q^{20} +(4.18328 + 1.35948i) q^{21} +(1.09777 - 1.09777i) q^{22} +(0.856269 + 0.856269i) q^{23} +(0.786252 + 1.54331i) q^{24} +1.00000i q^{25} +1.57762i q^{26} +(-3.05355 - 4.20426i) q^{27} +2.53955i q^{28} +(5.19422 - 5.19422i) q^{29} +(-1.64725 - 0.535321i) q^{30} +(1.70231 + 1.70231i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.55731 - 0.831073i) q^{33} +6.84760 q^{34} +(-1.79574 - 1.79574i) q^{35} +(1.76361 - 2.42686i) q^{36} +(3.85543 - 4.70486i) q^{37} +3.52214i q^{38} +(2.43475 - 1.24041i) q^{39} -1.00000i q^{40} +10.4791 q^{41} +(3.91932 - 1.99673i) q^{42} +(-2.78010 + 2.78010i) q^{43} -1.55248i q^{44} +(0.468987 + 2.96312i) q^{45} +1.21095 q^{46} +10.4277i q^{47} +(1.64725 + 0.535321i) q^{48} -0.550669 q^{49} +(0.707107 + 0.707107i) q^{50} +(-5.38394 - 10.5680i) q^{51} +(1.11554 + 1.11554i) q^{52} -5.16143i q^{53} +(-5.13205 - 0.813678i) q^{54} +(1.09777 + 1.09777i) q^{55} +(1.79574 + 1.79574i) q^{56} +(5.43576 - 2.76929i) q^{57} -7.34574i q^{58} +(8.36584 + 8.36584i) q^{59} +(-1.54331 + 0.786252i) q^{60} +(7.41355 + 7.41355i) q^{61} +2.40742 q^{62} +(-6.16315 - 4.47879i) q^{63} +1.00000i q^{64} -1.57762 q^{65} +(-2.39595 + 1.22064i) q^{66} -1.98974i q^{67} +(4.84198 - 4.84198i) q^{68} +(-0.952110 - 1.86887i) q^{69} -2.53955 q^{70} +3.37621i q^{71} +(-0.468987 - 2.96312i) q^{72} +0.480190i q^{73} +(-0.600636 - 6.05304i) q^{74} +(0.535321 - 1.64725i) q^{75} +(2.49053 + 2.49053i) q^{76} -3.94259 q^{77} +(0.844532 - 2.59873i) q^{78} +(6.52251 - 6.52251i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(2.77933 + 8.56010i) q^{81} +(7.40987 - 7.40987i) q^{82} -8.64749i q^{83} +(1.35948 - 4.18328i) q^{84} +6.84760i q^{85} +3.93165i q^{86} +(-11.3368 + 5.77560i) q^{87} +(-1.09777 - 1.09777i) q^{88} +(10.5685 - 10.5685i) q^{89} +(2.42686 + 1.76361i) q^{90} +(2.83298 - 2.83298i) q^{91} +(0.856269 - 0.856269i) q^{92} +(-1.89284 - 3.71540i) q^{93} +(7.37349 + 7.37349i) q^{94} -3.52214 q^{95} +(1.54331 - 0.786252i) q^{96} +(-5.01332 + 5.01332i) q^{97} +(-0.389382 + 0.389382i) q^{98} +(3.76765 + 2.73797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 24q^{7} - 8q^{9} + O(q^{10}) \) \( 40q - 24q^{7} - 8q^{9} + 40q^{10} - 8q^{12} - 16q^{13} - 40q^{16} + 8q^{18} + 16q^{19} - 24q^{31} + 24q^{33} - 8q^{34} + 16q^{39} - 20q^{42} - 32q^{43} - 8q^{45} + 72q^{46} + 96q^{49} + 20q^{51} + 16q^{52} + 24q^{54} - 16q^{57} + 40q^{61} - 24q^{63} - 44q^{66} - 24q^{70} + 8q^{72} + 8q^{75} - 16q^{76} + 48q^{79} + 24q^{81} - 56q^{82} - 8q^{84} + 12q^{87} - 8q^{90} - 64q^{91} + 12q^{93} + 24q^{94} + 8q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −1.64725 0.535321i −0.951040 0.309068i
\(4\) 1.00000i 0.500000i
\(5\) 0.707107 + 0.707107i 0.316228 + 0.316228i
\(6\) −1.54331 + 0.786252i −0.630054 + 0.320986i
\(7\) −2.53955 −0.959861 −0.479930 0.877307i \(-0.659338\pi\)
−0.479930 + 0.877307i \(0.659338\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 2.42686 + 1.76361i 0.808954 + 0.587872i
\(10\) 1.00000 0.316228
\(11\) 1.55248 0.468089 0.234045 0.972226i \(-0.424804\pi\)
0.234045 + 0.972226i \(0.424804\pi\)
\(12\) −0.535321 + 1.64725i −0.154534 + 0.475520i
\(13\) −1.11554 + 1.11554i −0.309396 + 0.309396i −0.844675 0.535279i \(-0.820206\pi\)
0.535279 + 0.844675i \(0.320206\pi\)
\(14\) −1.79574 + 1.79574i −0.479930 + 0.479930i
\(15\) −0.786252 1.54331i −0.203009 0.398481i
\(16\) −1.00000 −0.250000
\(17\) 4.84198 + 4.84198i 1.17435 + 1.17435i 0.981161 + 0.193193i \(0.0618843\pi\)
0.193193 + 0.981161i \(0.438116\pi\)
\(18\) 2.96312 0.468987i 0.698413 0.110541i
\(19\) −2.49053 + 2.49053i −0.571367 + 0.571367i −0.932510 0.361143i \(-0.882387\pi\)
0.361143 + 0.932510i \(0.382387\pi\)
\(20\) 0.707107 0.707107i 0.158114 0.158114i
\(21\) 4.18328 + 1.35948i 0.912866 + 0.296662i
\(22\) 1.09777 1.09777i 0.234045 0.234045i
\(23\) 0.856269 + 0.856269i 0.178544 + 0.178544i 0.790721 0.612177i \(-0.209706\pi\)
−0.612177 + 0.790721i \(0.709706\pi\)
\(24\) 0.786252 + 1.54331i 0.160493 + 0.315027i
\(25\) 1.00000i 0.200000i
\(26\) 1.57762i 0.309396i
\(27\) −3.05355 4.20426i −0.587656 0.809111i
\(28\) 2.53955i 0.479930i
\(29\) 5.19422 5.19422i 0.964543 0.964543i −0.0348499 0.999393i \(-0.511095\pi\)
0.999393 + 0.0348499i \(0.0110953\pi\)
\(30\) −1.64725 0.535321i −0.300745 0.0977358i
\(31\) 1.70231 + 1.70231i 0.305743 + 0.305743i 0.843256 0.537513i \(-0.180636\pi\)
−0.537513 + 0.843256i \(0.680636\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −2.55731 0.831073i −0.445171 0.144671i
\(34\) 6.84760 1.17435
\(35\) −1.79574 1.79574i −0.303535 0.303535i
\(36\) 1.76361 2.42686i 0.293936 0.404477i
\(37\) 3.85543 4.70486i 0.633829 0.773474i
\(38\) 3.52214i 0.571367i
\(39\) 2.43475 1.24041i 0.389873 0.198624i
\(40\) 1.00000i 0.158114i
\(41\) 10.4791 1.63657 0.818284 0.574815i \(-0.194926\pi\)
0.818284 + 0.574815i \(0.194926\pi\)
\(42\) 3.91932 1.99673i 0.604764 0.308102i
\(43\) −2.78010 + 2.78010i −0.423961 + 0.423961i −0.886565 0.462604i \(-0.846915\pi\)
0.462604 + 0.886565i \(0.346915\pi\)
\(44\) 1.55248i 0.234045i
\(45\) 0.468987 + 2.96312i 0.0699125 + 0.441715i
\(46\) 1.21095 0.178544
\(47\) 10.4277i 1.52104i 0.649317 + 0.760518i \(0.275055\pi\)
−0.649317 + 0.760518i \(0.724945\pi\)
\(48\) 1.64725 + 0.535321i 0.237760 + 0.0772669i
\(49\) −0.550669 −0.0786670
\(50\) 0.707107 + 0.707107i 0.100000 + 0.100000i
\(51\) −5.38394 10.5680i −0.753902 1.47981i
\(52\) 1.11554 + 1.11554i 0.154698 + 0.154698i
\(53\) 5.16143i 0.708978i −0.935060 0.354489i \(-0.884655\pi\)
0.935060 0.354489i \(-0.115345\pi\)
\(54\) −5.13205 0.813678i −0.698383 0.110728i
\(55\) 1.09777 + 1.09777i 0.148023 + 0.148023i
\(56\) 1.79574 + 1.79574i 0.239965 + 0.239965i
\(57\) 5.43576 2.76929i 0.719984 0.366802i
\(58\) 7.34574i 0.964543i
\(59\) 8.36584 + 8.36584i 1.08914 + 1.08914i 0.995617 + 0.0935229i \(0.0298128\pi\)
0.0935229 + 0.995617i \(0.470187\pi\)
\(60\) −1.54331 + 0.786252i −0.199241 + 0.101505i
\(61\) 7.41355 + 7.41355i 0.949208 + 0.949208i 0.998771 0.0495632i \(-0.0157829\pi\)
−0.0495632 + 0.998771i \(0.515783\pi\)
\(62\) 2.40742 0.305743
\(63\) −6.16315 4.47879i −0.776484 0.564275i
\(64\) 1.00000i 0.125000i
\(65\) −1.57762 −0.195679
\(66\) −2.39595 + 1.22064i −0.294921 + 0.150250i
\(67\) 1.98974i 0.243085i −0.992586 0.121543i \(-0.961216\pi\)
0.992586 0.121543i \(-0.0387841\pi\)
\(68\) 4.84198 4.84198i 0.587177 0.587177i
\(69\) −0.952110 1.86887i −0.114621 0.224985i
\(70\) −2.53955 −0.303535
\(71\) 3.37621i 0.400682i 0.979726 + 0.200341i \(0.0642050\pi\)
−0.979726 + 0.200341i \(0.935795\pi\)
\(72\) −0.468987 2.96312i −0.0552707 0.349206i
\(73\) 0.480190i 0.0562020i 0.999605 + 0.0281010i \(0.00894601\pi\)
−0.999605 + 0.0281010i \(0.991054\pi\)
\(74\) −0.600636 6.05304i −0.0698225 0.703651i
\(75\) 0.535321 1.64725i 0.0618135 0.190208i
\(76\) 2.49053 + 2.49053i 0.285684 + 0.285684i
\(77\) −3.94259 −0.449300
\(78\) 0.844532 2.59873i 0.0956244 0.294248i
\(79\) 6.52251 6.52251i 0.733840 0.733840i −0.237538 0.971378i \(-0.576341\pi\)
0.971378 + 0.237538i \(0.0763405\pi\)
\(80\) −0.707107 0.707107i −0.0790569 0.0790569i
\(81\) 2.77933 + 8.56010i 0.308814 + 0.951122i
\(82\) 7.40987 7.40987i 0.818284 0.818284i
\(83\) 8.64749i 0.949186i −0.880205 0.474593i \(-0.842595\pi\)
0.880205 0.474593i \(-0.157405\pi\)
\(84\) 1.35948 4.18328i 0.148331 0.456433i
\(85\) 6.84760i 0.742726i
\(86\) 3.93165i 0.423961i
\(87\) −11.3368 + 5.77560i −1.21543 + 0.619210i
\(88\) −1.09777 1.09777i −0.117022 0.117022i
\(89\) 10.5685 10.5685i 1.12026 1.12026i 0.128557 0.991702i \(-0.458965\pi\)
0.991702 0.128557i \(-0.0410345\pi\)
\(90\) 2.42686 + 1.76361i 0.255814 + 0.185901i
\(91\) 2.83298 2.83298i 0.296977 0.296977i
\(92\) 0.856269 0.856269i 0.0892722 0.0892722i
\(93\) −1.89284 3.71540i −0.196279 0.385269i
\(94\) 7.37349 + 7.37349i 0.760518 + 0.760518i
\(95\) −3.52214 −0.361364
\(96\) 1.54331 0.786252i 0.157513 0.0802465i
\(97\) −5.01332 + 5.01332i −0.509026 + 0.509026i −0.914227 0.405202i \(-0.867201\pi\)
0.405202 + 0.914227i \(0.367201\pi\)
\(98\) −0.389382 + 0.389382i −0.0393335 + 0.0393335i
\(99\) 3.76765 + 2.73797i 0.378663 + 0.275176i
\(100\) 1.00000 0.100000
\(101\) −3.12753 −0.311201 −0.155600 0.987820i \(-0.549731\pi\)
−0.155600 + 0.987820i \(0.549731\pi\)
\(102\) −11.2797 3.66566i −1.11686 0.362955i
\(103\) −9.44888 9.44888i −0.931026 0.931026i 0.0667446 0.997770i \(-0.478739\pi\)
−0.997770 + 0.0667446i \(0.978739\pi\)
\(104\) 1.57762 0.154698
\(105\) 1.99673 + 3.91932i 0.194861 + 0.382486i
\(106\) −3.64969 3.64969i −0.354489 0.354489i
\(107\) 1.92564i 0.186159i 0.995659 + 0.0930794i \(0.0296710\pi\)
−0.995659 + 0.0930794i \(0.970329\pi\)
\(108\) −4.20426 + 3.05355i −0.404556 + 0.293828i
\(109\) −1.77468 + 1.77468i −0.169983 + 0.169983i −0.786972 0.616989i \(-0.788352\pi\)
0.616989 + 0.786972i \(0.288352\pi\)
\(110\) 1.55248 0.148023
\(111\) −8.86946 + 5.68618i −0.841852 + 0.539708i
\(112\) 2.53955 0.239965
\(113\) −11.3932 + 11.3932i −1.07178 + 1.07178i −0.0745674 + 0.997216i \(0.523758\pi\)
−0.997216 + 0.0745674i \(0.976242\pi\)
\(114\) 1.88548 5.80185i 0.176591 0.543393i
\(115\) 1.21095i 0.112921i
\(116\) −5.19422 5.19422i −0.482271 0.482271i
\(117\) −4.67466 + 0.739883i −0.432173 + 0.0684022i
\(118\) 11.8311 1.08914
\(119\) −12.2965 12.2965i −1.12722 1.12722i
\(120\) −0.535321 + 1.64725i −0.0488679 + 0.150373i
\(121\) −8.58982 −0.780893
\(122\) 10.4843 0.949208
\(123\) −17.2618 5.60971i −1.55644 0.505810i
\(124\) 1.70231 1.70231i 0.152872 0.152872i
\(125\) −0.707107 + 0.707107i −0.0632456 + 0.0632456i
\(126\) −7.52499 + 1.19102i −0.670379 + 0.106104i
\(127\) 14.3170 1.27043 0.635215 0.772336i \(-0.280912\pi\)
0.635215 + 0.772336i \(0.280912\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 6.06776 3.09127i 0.534236 0.272171i
\(130\) −1.11554 + 1.11554i −0.0978397 + 0.0978397i
\(131\) 0.642612 0.642612i 0.0561453 0.0561453i −0.678477 0.734622i \(-0.737360\pi\)
0.734622 + 0.678477i \(0.237360\pi\)
\(132\) −0.831073 + 2.55731i −0.0723356 + 0.222586i
\(133\) 6.32484 6.32484i 0.548433 0.548433i
\(134\) −1.40696 1.40696i −0.121543 0.121543i
\(135\) 0.813678 5.13205i 0.0700303 0.441696i
\(136\) 6.84760i 0.587177i
\(137\) 22.7686i 1.94525i 0.232373 + 0.972627i \(0.425351\pi\)
−0.232373 + 0.972627i \(0.574649\pi\)
\(138\) −1.99473 0.648245i −0.169803 0.0551823i
\(139\) 6.95397i 0.589828i 0.955524 + 0.294914i \(0.0952910\pi\)
−0.955524 + 0.294914i \(0.904709\pi\)
\(140\) −1.79574 + 1.79574i −0.151767 + 0.151767i
\(141\) 5.58216 17.1770i 0.470103 1.44657i
\(142\) 2.38734 + 2.38734i 0.200341 + 0.200341i
\(143\) −1.73185 + 1.73185i −0.144825 + 0.144825i
\(144\) −2.42686 1.76361i −0.202239 0.146968i
\(145\) 7.34574 0.610030
\(146\) 0.339546 + 0.339546i 0.0281010 + 0.0281010i
\(147\) 0.907089 + 0.294785i 0.0748154 + 0.0243134i
\(148\) −4.70486 3.85543i −0.386737 0.316914i
\(149\) 15.3710i 1.25924i 0.776904 + 0.629619i \(0.216789\pi\)
−0.776904 + 0.629619i \(0.783211\pi\)
\(150\) −0.786252 1.54331i −0.0641972 0.126011i
\(151\) 8.84452i 0.719756i −0.932999 0.359878i \(-0.882818\pi\)
0.932999 0.359878i \(-0.117182\pi\)
\(152\) 3.52214 0.285684
\(153\) 3.21144 + 20.2902i 0.259629 + 1.64037i
\(154\) −2.78784 + 2.78784i −0.224650 + 0.224650i
\(155\) 2.40742i 0.193369i
\(156\) −1.24041 2.43475i −0.0993119 0.194936i
\(157\) 4.17933 0.333547 0.166774 0.985995i \(-0.446665\pi\)
0.166774 + 0.985995i \(0.446665\pi\)
\(158\) 9.22422i 0.733840i
\(159\) −2.76302 + 8.50217i −0.219122 + 0.674266i
\(160\) −1.00000 −0.0790569
\(161\) −2.17454 2.17454i −0.171378 0.171378i
\(162\) 8.01819 + 4.08763i 0.629968 + 0.321154i
\(163\) 1.54752 + 1.54752i 0.121211 + 0.121211i 0.765110 0.643899i \(-0.222684\pi\)
−0.643899 + 0.765110i \(0.722684\pi\)
\(164\) 10.4791i 0.818284i
\(165\) −1.22064 2.39595i −0.0950265 0.186525i
\(166\) −6.11470 6.11470i −0.474593 0.474593i
\(167\) 13.7766 + 13.7766i 1.06607 + 1.06607i 0.997657 + 0.0684095i \(0.0217924\pi\)
0.0684095 + 0.997657i \(0.478208\pi\)
\(168\) −1.99673 3.91932i −0.154051 0.302382i
\(169\) 10.5111i 0.808548i
\(170\) 4.84198 + 4.84198i 0.371363 + 0.371363i
\(171\) −10.4365 + 1.65184i −0.798101 + 0.126319i
\(172\) 2.78010 + 2.78010i 0.211980 + 0.211980i
\(173\) −22.4262 −1.70503 −0.852517 0.522699i \(-0.824925\pi\)
−0.852517 + 0.522699i \(0.824925\pi\)
\(174\) −3.93233 + 12.1003i −0.298109 + 0.917319i
\(175\) 2.53955i 0.191972i
\(176\) −1.55248 −0.117022
\(177\) −9.30222 18.2590i −0.699198 1.37243i
\(178\) 14.9461i 1.12026i
\(179\) −5.77543 + 5.77543i −0.431676 + 0.431676i −0.889198 0.457522i \(-0.848737\pi\)
0.457522 + 0.889198i \(0.348737\pi\)
\(180\) 2.96312 0.468987i 0.220858 0.0349563i
\(181\) 13.1382 0.976553 0.488276 0.872689i \(-0.337626\pi\)
0.488276 + 0.872689i \(0.337626\pi\)
\(182\) 4.00644i 0.296977i
\(183\) −8.24334 16.1806i −0.609365 1.19610i
\(184\) 1.21095i 0.0892722i
\(185\) 6.05304 0.600636i 0.445028 0.0441596i
\(186\) −3.96563 1.28874i −0.290774 0.0944954i
\(187\) 7.51706 + 7.51706i 0.549702 + 0.549702i
\(188\) 10.4277 0.760518
\(189\) 7.75465 + 10.6770i 0.564068 + 0.776634i
\(190\) −2.49053 + 2.49053i −0.180682 + 0.180682i
\(191\) −6.53325 6.53325i −0.472729 0.472729i 0.430068 0.902797i \(-0.358490\pi\)
−0.902797 + 0.430068i \(0.858490\pi\)
\(192\) 0.535321 1.64725i 0.0386335 0.118880i
\(193\) 1.18075 1.18075i 0.0849921 0.0849921i −0.663333 0.748325i \(-0.730859\pi\)
0.748325 + 0.663333i \(0.230859\pi\)
\(194\) 7.08991i 0.509026i
\(195\) 2.59873 + 0.844532i 0.186099 + 0.0604782i
\(196\) 0.550669i 0.0393335i
\(197\) 3.07165i 0.218846i 0.993995 + 0.109423i \(0.0349003\pi\)
−0.993995 + 0.109423i \(0.965100\pi\)
\(198\) 4.60016 0.728091i 0.326919 0.0517432i
\(199\) −1.93640 1.93640i −0.137268 0.137268i 0.635134 0.772402i \(-0.280945\pi\)
−0.772402 + 0.635134i \(0.780945\pi\)
\(200\) 0.707107 0.707107i 0.0500000 0.0500000i
\(201\) −1.06515 + 3.27760i −0.0751298 + 0.231184i
\(202\) −2.21150 + 2.21150i −0.155600 + 0.155600i
\(203\) −13.1910 + 13.1910i −0.925827 + 0.925827i
\(204\) −10.5680 + 5.38394i −0.739906 + 0.376951i
\(205\) 7.40987 + 7.40987i 0.517528 + 0.517528i
\(206\) −13.3627 −0.931026
\(207\) 0.567919 + 3.58817i 0.0394731 + 0.249395i
\(208\) 1.11554 1.11554i 0.0773490 0.0773490i
\(209\) −3.86649 + 3.86649i −0.267451 + 0.267451i
\(210\) 4.18328 + 1.35948i 0.288674 + 0.0938128i
\(211\) −24.0332 −1.65451 −0.827257 0.561824i \(-0.810100\pi\)
−0.827257 + 0.561824i \(0.810100\pi\)
\(212\) −5.16143 −0.354489
\(213\) 1.80736 5.56146i 0.123838 0.381065i
\(214\) 1.36163 + 1.36163i 0.0930794 + 0.0930794i
\(215\) −3.93165 −0.268136
\(216\) −0.813678 + 5.13205i −0.0553638 + 0.349192i
\(217\) −4.32310 4.32310i −0.293471 0.293471i
\(218\) 2.50977i 0.169983i
\(219\) 0.257056 0.790993i 0.0173702 0.0534504i
\(220\) 1.09777 1.09777i 0.0740114 0.0740114i
\(221\) −10.8029 −0.726681
\(222\) −2.25092 + 10.2924i −0.151072 + 0.690780i
\(223\) −19.6653 −1.31688 −0.658442 0.752631i \(-0.728784\pi\)
−0.658442 + 0.752631i \(0.728784\pi\)
\(224\) 1.79574 1.79574i 0.119983 0.119983i
\(225\) −1.76361 + 2.42686i −0.117574 + 0.161791i
\(226\) 16.1124i 1.07178i
\(227\) 2.56107 + 2.56107i 0.169984 + 0.169984i 0.786972 0.616988i \(-0.211647\pi\)
−0.616988 + 0.786972i \(0.711647\pi\)
\(228\) −2.76929 5.43576i −0.183401 0.359992i
\(229\) 13.0356 0.861418 0.430709 0.902491i \(-0.358264\pi\)
0.430709 + 0.902491i \(0.358264\pi\)
\(230\) 0.856269 + 0.856269i 0.0564607 + 0.0564607i
\(231\) 6.49444 + 2.11055i 0.427303 + 0.138864i
\(232\) −7.34574 −0.482271
\(233\) −20.4916 −1.34245 −0.671223 0.741255i \(-0.734231\pi\)
−0.671223 + 0.741255i \(0.734231\pi\)
\(234\) −2.78231 + 3.82866i −0.181885 + 0.250287i
\(235\) −7.37349 + 7.37349i −0.480994 + 0.480994i
\(236\) 8.36584 8.36584i 0.544570 0.544570i
\(237\) −14.2358 + 7.25257i −0.924717 + 0.471105i
\(238\) −17.3898 −1.12722
\(239\) −16.0579 16.0579i −1.03870 1.03870i −0.999220 0.0394798i \(-0.987430\pi\)
−0.0394798 0.999220i \(-0.512570\pi\)
\(240\) 0.786252 + 1.54331i 0.0507524 + 0.0996203i
\(241\) −8.01194 + 8.01194i −0.516095 + 0.516095i −0.916387 0.400293i \(-0.868908\pi\)
0.400293 + 0.916387i \(0.368908\pi\)
\(242\) −6.07392 + 6.07392i −0.390446 + 0.390446i
\(243\) 0.00415661 15.5885i 0.000266647 1.00000i
\(244\) 7.41355 7.41355i 0.474604 0.474604i
\(245\) −0.389382 0.389382i −0.0248767 0.0248767i
\(246\) −16.1726 + 8.23925i −1.03113 + 0.525315i
\(247\) 5.55660i 0.353558i
\(248\) 2.40742i 0.152872i
\(249\) −4.62918 + 14.2446i −0.293363 + 0.902714i
\(250\) 1.00000i 0.0632456i
\(251\) 5.39840 5.39840i 0.340744 0.340744i −0.515903 0.856647i \(-0.672543\pi\)
0.856647 + 0.515903i \(0.172543\pi\)
\(252\) −4.47879 + 6.16315i −0.282137 + 0.388242i
\(253\) 1.32934 + 1.32934i 0.0835747 + 0.0835747i
\(254\) 10.1237 10.1237i 0.635215 0.635215i
\(255\) 3.66566 11.2797i 0.229553 0.706363i
\(256\) 1.00000 0.0625000
\(257\) −12.9474 12.9474i −0.807636 0.807636i 0.176640 0.984276i \(-0.443477\pi\)
−0.984276 + 0.176640i \(0.943477\pi\)
\(258\) 2.10470 6.47641i 0.131033 0.403204i
\(259\) −9.79107 + 11.9482i −0.608387 + 0.742427i
\(260\) 1.57762i 0.0978397i
\(261\) 21.7663 3.44506i 1.34730 0.213244i
\(262\) 0.908791i 0.0561453i
\(263\) 7.40115 0.456375 0.228187 0.973617i \(-0.426720\pi\)
0.228187 + 0.973617i \(0.426720\pi\)
\(264\) 1.22064 + 2.39595i 0.0751250 + 0.147461i
\(265\) 3.64969 3.64969i 0.224198 0.224198i
\(266\) 8.94467i 0.548433i
\(267\) −23.0665 + 11.7514i −1.41165 + 0.719175i
\(268\) −1.98974 −0.121543
\(269\) 22.3915i 1.36523i −0.730776 0.682617i \(-0.760842\pi\)
0.730776 0.682617i \(-0.239158\pi\)
\(270\) −3.05355 4.20426i −0.185833 0.255863i
\(271\) 18.4875 1.12304 0.561518 0.827465i \(-0.310218\pi\)
0.561518 + 0.827465i \(0.310218\pi\)
\(272\) −4.84198 4.84198i −0.293588 0.293588i
\(273\) −6.18319 + 3.15008i −0.374223 + 0.190651i
\(274\) 16.0998 + 16.0998i 0.972627 + 0.972627i
\(275\) 1.55248i 0.0936178i
\(276\) −1.86887 + 0.952110i −0.112493 + 0.0573103i
\(277\) 7.72665 + 7.72665i 0.464249 + 0.464249i 0.900045 0.435796i \(-0.143533\pi\)
−0.435796 + 0.900045i \(0.643533\pi\)
\(278\) 4.91720 + 4.91720i 0.294914 + 0.294914i
\(279\) 1.12905 + 7.13348i 0.0675946 + 0.427070i
\(280\) 2.53955i 0.151767i
\(281\) −3.95236 3.95236i −0.235778 0.235778i 0.579321 0.815099i \(-0.303318\pi\)
−0.815099 + 0.579321i \(0.803318\pi\)
\(282\) −8.19880 16.0932i −0.488231 0.958334i
\(283\) 4.17375 + 4.17375i 0.248104 + 0.248104i 0.820192 0.572088i \(-0.193867\pi\)
−0.572088 + 0.820192i \(0.693867\pi\)
\(284\) 3.37621 0.200341
\(285\) 5.80185 + 1.88548i 0.343672 + 0.111686i
\(286\) 2.44921i 0.144825i
\(287\) −26.6123 −1.57088
\(288\) −2.96312 + 0.468987i −0.174603 + 0.0276353i
\(289\) 29.8896i 1.75821i
\(290\) 5.19422 5.19422i 0.305015 0.305015i
\(291\) 10.9419 5.57445i 0.641427 0.326780i
\(292\) 0.480190 0.0281010
\(293\) 15.2274i 0.889593i −0.895632 0.444796i \(-0.853276\pi\)
0.895632 0.444796i \(-0.146724\pi\)
\(294\) 0.849853 0.432965i 0.0495644 0.0252510i
\(295\) 11.8311i 0.688833i
\(296\) −6.05304 + 0.600636i −0.351826 + 0.0349113i
\(297\) −4.74056 6.52702i −0.275075 0.378736i
\(298\) 10.8689 + 10.8689i 0.629619 + 0.629619i
\(299\) −1.91041 −0.110482
\(300\) −1.64725 0.535321i −0.0951040 0.0309068i
\(301\) 7.06021 7.06021i 0.406944 0.406944i
\(302\) −6.25402 6.25402i −0.359878 0.359878i
\(303\) 5.15182 + 1.67423i 0.295964 + 0.0961821i
\(304\) 2.49053 2.49053i 0.142842 0.142842i
\(305\) 10.4843i 0.600332i
\(306\) 16.6182 + 12.0765i 0.949998 + 0.690369i
\(307\) 22.5433i 1.28661i −0.765609 0.643306i \(-0.777562\pi\)
0.765609 0.643306i \(-0.222438\pi\)
\(308\) 3.94259i 0.224650i
\(309\) 10.5065 + 20.6228i 0.597693 + 1.17319i
\(310\) 1.70231 + 1.70231i 0.0966845 + 0.0966845i
\(311\) 6.11792 6.11792i 0.346915 0.346915i −0.512044 0.858959i \(-0.671112\pi\)
0.858959 + 0.512044i \(0.171112\pi\)
\(312\) −2.59873 0.844532i −0.147124 0.0478122i
\(313\) 3.26673 3.26673i 0.184646 0.184646i −0.608731 0.793377i \(-0.708321\pi\)
0.793377 + 0.608731i \(0.208321\pi\)
\(314\) 2.95524 2.95524i 0.166774 0.166774i
\(315\) −1.19102 7.52499i −0.0671063 0.423985i
\(316\) −6.52251 6.52251i −0.366920 0.366920i
\(317\) 30.0184 1.68600 0.843001 0.537912i \(-0.180787\pi\)
0.843001 + 0.537912i \(0.180787\pi\)
\(318\) 4.05819 + 7.96570i 0.227572 + 0.446694i
\(319\) 8.06390 8.06390i 0.451492 0.451492i
\(320\) −0.707107 + 0.707107i −0.0395285 + 0.0395285i
\(321\) 1.03084 3.17201i 0.0575357 0.177044i
\(322\) −3.07526 −0.171378
\(323\) −24.1182 −1.34197
\(324\) 8.56010 2.77933i 0.475561 0.154407i
\(325\) −1.11554 1.11554i −0.0618792 0.0618792i
\(326\) 2.18852 0.121211
\(327\) 3.87336 1.97331i 0.214197 0.109124i
\(328\) −7.40987 7.40987i −0.409142 0.409142i
\(329\) 26.4817i 1.45998i
\(330\) −2.55731 0.831073i −0.140776 0.0457490i
\(331\) 9.21805 9.21805i 0.506670 0.506670i −0.406833 0.913503i \(-0.633367\pi\)
0.913503 + 0.406833i \(0.133367\pi\)
\(332\) −8.64749 −0.474593
\(333\) 17.6541 4.61855i 0.967441 0.253095i
\(334\) 19.4831 1.06607
\(335\) 1.40696 1.40696i 0.0768704 0.0768704i
\(336\) −4.18328 1.35948i −0.228217 0.0741655i
\(337\) 22.7367i 1.23855i −0.785175 0.619275i \(-0.787427\pi\)
0.785175 0.619275i \(-0.212573\pi\)
\(338\) 7.43249 + 7.43249i 0.404274 + 0.404274i
\(339\) 24.8665 12.6684i 1.35056 0.688055i
\(340\) 6.84760 0.371363
\(341\) 2.64279 + 2.64279i 0.143115 + 0.143115i
\(342\) −6.21171 + 8.54776i −0.335891 + 0.462210i
\(343\) 19.1753 1.03537
\(344\) 3.93165 0.211980
\(345\) 0.648245 1.99473i 0.0349003 0.107393i
\(346\) −15.8577 + 15.8577i −0.852517 + 0.852517i
\(347\) 12.8734 12.8734i 0.691078 0.691078i −0.271391 0.962469i \(-0.587484\pi\)
0.962469 + 0.271391i \(0.0874837\pi\)
\(348\) 5.77560 + 11.3368i 0.309605 + 0.607714i
\(349\) −17.1933 −0.920336 −0.460168 0.887832i \(-0.652211\pi\)
−0.460168 + 0.887832i \(0.652211\pi\)
\(350\) −1.79574 1.79574i −0.0959861 0.0959861i
\(351\) 8.09641 + 1.28367i 0.432154 + 0.0685174i
\(352\) −1.09777 + 1.09777i −0.0585111 + 0.0585111i
\(353\) 13.6457 13.6457i 0.726286 0.726286i −0.243592 0.969878i \(-0.578326\pi\)
0.969878 + 0.243592i \(0.0783257\pi\)
\(354\) −19.4888 6.33343i −1.03582 0.336618i
\(355\) −2.38734 + 2.38734i −0.126707 + 0.126707i
\(356\) −10.5685 10.5685i −0.560130 0.560130i
\(357\) 13.6728 + 26.8379i 0.723642 + 1.42041i
\(358\) 8.16769i 0.431676i
\(359\) 32.6347i 1.72239i 0.508272 + 0.861197i \(0.330284\pi\)
−0.508272 + 0.861197i \(0.669716\pi\)
\(360\) 1.76361 2.42686i 0.0929507 0.127907i
\(361\) 6.59450i 0.347079i
\(362\) 9.29009 9.29009i 0.488276 0.488276i
\(363\) 14.1496 + 4.59831i 0.742660 + 0.241349i
\(364\) −2.83298 2.83298i −0.148489 0.148489i
\(365\) −0.339546 + 0.339546i −0.0177726 + 0.0177726i
\(366\) −17.2703 5.61249i −0.902735 0.293369i
\(367\) −12.0728 −0.630194 −0.315097 0.949060i \(-0.602037\pi\)
−0.315097 + 0.949060i \(0.602037\pi\)
\(368\) −0.856269 0.856269i −0.0446361 0.0446361i
\(369\) 25.4314 + 18.4812i 1.32391 + 0.962091i
\(370\) 3.85543 4.70486i 0.200434 0.244594i
\(371\) 13.1077i 0.680520i
\(372\) −3.71540 + 1.89284i −0.192635 + 0.0981393i
\(373\) 26.6336i 1.37904i −0.724268 0.689518i \(-0.757822\pi\)
0.724268 0.689518i \(-0.242178\pi\)
\(374\) 10.6307 0.549702
\(375\) 1.54331 0.786252i 0.0796962 0.0406019i
\(376\) 7.37349 7.37349i 0.380259 0.380259i
\(377\) 11.5888i 0.596852i
\(378\) 13.0331 + 2.06638i 0.670351 + 0.106283i
\(379\) 20.7514 1.06593 0.532963 0.846139i \(-0.321078\pi\)
0.532963 + 0.846139i \(0.321078\pi\)
\(380\) 3.52214i 0.180682i
\(381\) −23.5837 7.66420i −1.20823 0.392649i
\(382\) −9.23941 −0.472729
\(383\) 15.8691 + 15.8691i 0.810874 + 0.810874i 0.984765 0.173891i \(-0.0556340\pi\)
−0.173891 + 0.984765i \(0.555634\pi\)
\(384\) −0.786252 1.54331i −0.0401233 0.0787567i
\(385\) −2.78784 2.78784i −0.142081 0.142081i
\(386\) 1.66983i 0.0849921i
\(387\) −11.6499 + 1.84390i −0.592200 + 0.0937305i
\(388\) 5.01332 + 5.01332i 0.254513 + 0.254513i
\(389\) −8.71629 8.71629i −0.441934 0.441934i 0.450728 0.892661i \(-0.351164\pi\)
−0.892661 + 0.450728i \(0.851164\pi\)
\(390\) 2.43475 1.24041i 0.123289 0.0628104i
\(391\) 8.29208i 0.419348i
\(392\) 0.389382 + 0.389382i 0.0196667 + 0.0196667i
\(393\) −1.40255 + 0.714539i −0.0707491 + 0.0360437i
\(394\) 2.17198 + 2.17198i 0.109423 + 0.109423i
\(395\) 9.22422 0.464121
\(396\) 2.73797 3.76765i 0.137588 0.189331i
\(397\) 0.0949796i 0.00476689i 0.999997 + 0.00238345i \(0.000758675\pi\)
−0.999997 + 0.00238345i \(0.999241\pi\)
\(398\) −2.73848 −0.137268
\(399\) −13.8044 + 7.03277i −0.691085 + 0.352079i
\(400\) 1.00000i 0.0500000i
\(401\) 3.89325 3.89325i 0.194420 0.194420i −0.603183 0.797603i \(-0.706101\pi\)
0.797603 + 0.603183i \(0.206101\pi\)
\(402\) 1.56444 + 3.07079i 0.0780270 + 0.153157i
\(403\) −3.79799 −0.189192
\(404\) 3.12753i 0.155600i
\(405\) −4.08763 + 8.01819i −0.203116 + 0.398427i
\(406\) 18.6549i 0.925827i
\(407\) 5.98546 7.30417i 0.296688 0.362054i
\(408\) −3.66566 + 11.2797i −0.181477 + 0.558429i
\(409\) 22.8071 + 22.8071i 1.12774 + 1.12774i 0.990544 + 0.137192i \(0.0438078\pi\)
0.137192 + 0.990544i \(0.456192\pi\)
\(410\) 10.4791 0.517528
\(411\) 12.1885 37.5056i 0.601215 1.85001i
\(412\) −9.44888 + 9.44888i −0.465513 + 0.465513i
\(413\) −21.2455 21.2455i −1.04542 1.04542i
\(414\) 2.93880 + 2.13564i 0.144434 + 0.104961i
\(415\) 6.11470 6.11470i 0.300159 0.300159i
\(416\) 1.57762i 0.0773490i
\(417\) 3.72260 11.4549i 0.182297 0.560950i
\(418\) 5.46804i 0.267451i
\(419\) 19.4604i 0.950701i 0.879797 + 0.475350i \(0.157679\pi\)
−0.879797 + 0.475350i \(0.842321\pi\)
\(420\) 3.91932 1.99673i 0.191243 0.0974304i
\(421\) −14.1201 14.1201i −0.688171 0.688171i 0.273657 0.961827i \(-0.411767\pi\)
−0.961827 + 0.273657i \(0.911767\pi\)
\(422\) −16.9940 + 16.9940i −0.827257 + 0.827257i
\(423\) −18.3904 + 25.3066i −0.894174 + 1.23045i
\(424\) −3.64969 + 3.64969i −0.177244 + 0.177244i
\(425\) −4.84198 + 4.84198i −0.234871 + 0.234871i
\(426\) −2.65455 5.21054i −0.128613 0.252451i
\(427\) −18.8271 18.8271i −0.911107 0.911107i
\(428\) 1.92564 0.0930794
\(429\) 3.77989 1.92570i 0.182495 0.0929736i
\(430\) −2.78010 + 2.78010i −0.134068 + 0.134068i
\(431\) 23.2957 23.2957i 1.12211 1.12211i 0.130692 0.991423i \(-0.458280\pi\)
0.991423 0.130692i \(-0.0417198\pi\)
\(432\) 3.05355 + 4.20426i 0.146914 + 0.202278i
\(433\) −6.51982 −0.313323 −0.156661 0.987652i \(-0.550073\pi\)
−0.156661 + 0.987652i \(0.550073\pi\)
\(434\) −6.11378 −0.293471
\(435\) −12.1003 3.93233i −0.580163 0.188541i
\(436\) 1.77468 + 1.77468i 0.0849916 + 0.0849916i
\(437\) −4.26513 −0.204029
\(438\) −0.377551 0.741083i −0.0180401 0.0354103i
\(439\) −7.97830 7.97830i −0.380783 0.380783i 0.490601 0.871384i \(-0.336777\pi\)
−0.871384 + 0.490601i \(0.836777\pi\)
\(440\) 1.55248i 0.0740114i
\(441\) −1.33640 0.971168i −0.0636380 0.0462461i
\(442\) −7.63880 + 7.63880i −0.363341 + 0.363341i
\(443\) −0.170503 −0.00810085 −0.00405043 0.999992i \(-0.501289\pi\)
−0.00405043 + 0.999992i \(0.501289\pi\)
\(444\) 5.68618 + 8.86946i 0.269854 + 0.420926i
\(445\) 14.9461 0.708514
\(446\) −13.9055 + 13.9055i −0.658442 + 0.658442i
\(447\) 8.22839 25.3198i 0.389190 1.19759i
\(448\) 2.53955i 0.119983i
\(449\) −25.9266 25.9266i −1.22355 1.22355i −0.966361 0.257189i \(-0.917204\pi\)
−0.257189 0.966361i \(-0.582796\pi\)
\(450\) 0.468987 + 2.96312i 0.0221083 + 0.139683i
\(451\) 16.2686 0.766059
\(452\) 11.3932 + 11.3932i 0.535892 + 0.535892i
\(453\) −4.73465 + 14.5691i −0.222453 + 0.684517i
\(454\) 3.62190 0.169984
\(455\) 4.00644 0.187825
\(456\) −5.80185 1.88548i −0.271697 0.0882956i
\(457\) −1.83261 + 1.83261i −0.0857259 + 0.0857259i −0.748669 0.662944i \(-0.769307\pi\)
0.662944 + 0.748669i \(0.269307\pi\)
\(458\) 9.21757 9.21757i 0.430709 0.430709i
\(459\) 5.57174 35.1422i 0.260067 1.64030i
\(460\) 1.21095 0.0564607
\(461\) 11.4366 + 11.4366i 0.532656 + 0.532656i 0.921362 0.388706i \(-0.127078\pi\)
−0.388706 + 0.921362i \(0.627078\pi\)
\(462\) 6.08465 3.09987i 0.283083 0.144219i
\(463\) −14.6615 + 14.6615i −0.681376 + 0.681376i −0.960310 0.278934i \(-0.910019\pi\)
0.278934 + 0.960310i \(0.410019\pi\)
\(464\) −5.19422 + 5.19422i −0.241136 + 0.241136i
\(465\) 1.28874 3.96563i 0.0597641 0.183902i
\(466\) −14.4897 + 14.4897i −0.671223 + 0.671223i
\(467\) 7.91991 + 7.91991i 0.366490 + 0.366490i 0.866195 0.499706i \(-0.166558\pi\)
−0.499706 + 0.866195i \(0.666558\pi\)
\(468\) 0.739883 + 4.67466i 0.0342011 + 0.216086i
\(469\) 5.05305i 0.233328i
\(470\) 10.4277i 0.480994i
\(471\) −6.88441 2.23729i −0.317217 0.103089i
\(472\) 11.8311i 0.544570i
\(473\) −4.31603 + 4.31603i −0.198451 + 0.198451i
\(474\) −4.93792 + 15.1946i −0.226806 + 0.697911i
\(475\) −2.49053 2.49053i −0.114273 0.114273i
\(476\) −12.2965 + 12.2965i −0.563608 + 0.563608i
\(477\) 9.10278 12.5261i 0.416788 0.573530i
\(478\) −22.7093 −1.03870
\(479\) −18.6437 18.6437i −0.851853 0.851853i 0.138509 0.990361i \(-0.455769\pi\)
−0.990361 + 0.138509i \(0.955769\pi\)
\(480\) 1.64725 + 0.535321i 0.0751863 + 0.0244339i
\(481\) 0.947574 + 9.54937i 0.0432057 + 0.435414i
\(482\) 11.3306i 0.516095i
\(483\) 2.41793 + 4.74609i 0.110020 + 0.215954i
\(484\) 8.58982i 0.390446i
\(485\) −7.08991 −0.321936
\(486\) −11.0198 11.0256i −0.499867 0.500133i
\(487\) 8.90792 8.90792i 0.403657 0.403657i −0.475863 0.879519i \(-0.657864\pi\)
0.879519 + 0.475863i \(0.157864\pi\)
\(488\) 10.4843i 0.474604i
\(489\) −1.72073 3.37757i −0.0778142 0.152739i
\(490\) −0.550669 −0.0248767
\(491\) 0.432806i 0.0195322i 0.999952 + 0.00976612i \(0.00310870\pi\)
−0.999952 + 0.00976612i \(0.996891\pi\)
\(492\) −5.60971 + 17.2618i −0.252905 + 0.778220i
\(493\) 50.3007 2.26543
\(494\) −3.92911 3.92911i −0.176779 0.176779i
\(495\) 0.728091 + 4.60016i 0.0327253 + 0.206762i
\(496\) −1.70231 1.70231i −0.0764358 0.0764358i
\(497\) 8.57406i 0.384599i
\(498\) 6.79911 + 13.3458i 0.304675 + 0.598038i
\(499\) −19.8374 19.8374i −0.888044 0.888044i 0.106291 0.994335i \(-0.466102\pi\)
−0.994335 + 0.106291i \(0.966102\pi\)
\(500\) 0.707107 + 0.707107i 0.0316228 + 0.0316228i
\(501\) −15.3186 30.0684i −0.684385 1.34336i
\(502\) 7.63449i 0.340744i
\(503\) 20.0416 + 20.0416i 0.893611 + 0.893611i 0.994861 0.101250i \(-0.0322841\pi\)
−0.101250 + 0.994861i \(0.532284\pi\)
\(504\) 1.19102 + 7.52499i 0.0530522 + 0.335190i
\(505\) −2.21150 2.21150i −0.0984104 0.0984104i
\(506\) 1.87997 0.0835747
\(507\) 5.62683 17.3144i 0.249896 0.768962i
\(508\) 14.3170i 0.635215i
\(509\) 3.66498 0.162447 0.0812237 0.996696i \(-0.474117\pi\)
0.0812237 + 0.996696i \(0.474117\pi\)
\(510\) −5.38394 10.5680i −0.238405 0.467958i
\(511\) 1.21947i 0.0539461i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 18.0758 + 2.86589i 0.798067 + 0.126532i
\(514\) −18.3104 −0.807636
\(515\) 13.3627i 0.588832i
\(516\) −3.09127 6.06776i −0.136086 0.267118i
\(517\) 16.1887i 0.711980i
\(518\) 1.52535 + 15.3720i 0.0670199 + 0.675407i
\(519\) 36.9416 + 12.0052i 1.62156 + 0.526971i
\(520\) 1.11554 + 1.11554i 0.0489198 + 0.0489198i
\(521\) 3.46852 0.151959 0.0759793 0.997109i \(-0.475792\pi\)
0.0759793 + 0.997109i \(0.475792\pi\)
\(522\) 12.9551 17.8271i 0.567027 0.780271i
\(523\) 13.9403 13.9403i 0.609567 0.609567i −0.333266 0.942833i \(-0.608151\pi\)
0.942833 + 0.333266i \(0.108151\pi\)
\(524\) −0.642612 0.642612i −0.0280726 0.0280726i
\(525\) −1.35948 + 4.18328i −0.0593324 + 0.182573i
\(526\) 5.23341 5.23341i 0.228187 0.228187i
\(527\) 16.4851i 0.718101i
\(528\) 2.55731 + 0.831073i 0.111293 + 0.0361678i
\(529\) 21.5336i 0.936244i
\(530\) 5.16143i 0.224198i
\(531\) 5.54863 + 35.0569i 0.240790 + 1.52134i
\(532\) −6.32484 6.32484i −0.274217 0.274217i
\(533\) −11.6899 + 11.6899i −0.506348 + 0.506348i
\(534\) −8.00097 + 24.6200i −0.346236 + 1.06541i
\(535\) −1.36163 + 1.36163i −0.0588686 + 0.0588686i
\(536\) −1.40696 + 1.40696i −0.0607713 + 0.0607713i
\(537\) 12.6053 6.42187i 0.543958 0.277124i
\(538\) −15.8332 15.8332i −0.682617 0.682617i
\(539\) −0.854900 −0.0368231
\(540\) −5.13205 0.813678i −0.220848 0.0350151i
\(541\) −5.11347 + 5.11347i −0.219845 + 0.219845i −0.808433 0.588588i \(-0.799684\pi\)
0.588588 + 0.808433i \(0.299684\pi\)
\(542\) 13.0726 13.0726i 0.561518 0.561518i
\(543\) −21.6419 7.03314i −0.928741 0.301821i
\(544\) −6.84760 −0.293588
\(545\) −2.50977 −0.107507
\(546\) −2.14473 + 6.59961i −0.0917861 + 0.282437i
\(547\) −17.1654 17.1654i −0.733939 0.733939i 0.237459 0.971398i \(-0.423686\pi\)
−0.971398 + 0.237459i \(0.923686\pi\)
\(548\) 22.7686 0.972627
\(549\) 4.91702 + 31.0663i 0.209853 + 1.32588i
\(550\) 1.09777 + 1.09777i 0.0468089 + 0.0468089i
\(551\) 25.8728i 1.10222i
\(552\) −0.648245 + 1.99473i −0.0275911 + 0.0849014i
\(553\) −16.5643 + 16.5643i −0.704384 + 0.704384i
\(554\) 10.9271 0.464249
\(555\) −10.2924 2.25092i −0.436888 0.0955462i
\(556\) 6.95397 0.294914
\(557\) 21.7065 21.7065i 0.919733 0.919733i −0.0772768 0.997010i \(-0.524623\pi\)
0.997010 + 0.0772768i \(0.0246225\pi\)
\(558\) 5.84249 + 4.24577i 0.247332 + 0.179738i
\(559\) 6.20264i 0.262344i
\(560\) 1.79574 + 1.79574i 0.0758837 + 0.0758837i
\(561\) −8.35844 16.4065i −0.352893 0.692684i
\(562\) −5.58948 −0.235778
\(563\) 17.3652 + 17.3652i 0.731858 + 0.731858i 0.970988 0.239130i \(-0.0768622\pi\)
−0.239130 + 0.970988i \(0.576862\pi\)
\(564\) −17.1770 5.58216i −0.723283 0.235052i
\(565\) −16.1124 −0.677855
\(566\) 5.90258 0.248104
\(567\) −7.05825 21.7388i −0.296419 0.912945i
\(568\) 2.38734 2.38734i 0.100171 0.100171i
\(569\) −0.287563 + 0.287563i −0.0120553 + 0.0120553i −0.713109 0.701053i \(-0.752713\pi\)
0.701053 + 0.713109i \(0.252713\pi\)
\(570\) 5.43576 2.76929i 0.227679 0.115993i
\(571\) −27.3088 −1.14284 −0.571420 0.820658i \(-0.693607\pi\)
−0.571420 + 0.820658i \(0.693607\pi\)
\(572\) 1.73185 + 1.73185i 0.0724125 + 0.0724125i
\(573\) 7.26450 + 14.2593i 0.303479 + 0.595690i
\(574\) −18.8178 + 18.8178i −0.785438 + 0.785438i
\(575\) −0.856269 + 0.856269i −0.0357089 + 0.0357089i
\(576\) −1.76361 + 2.42686i −0.0734839 + 0.101119i
\(577\) −20.2984 + 20.2984i −0.845034 + 0.845034i −0.989509 0.144475i \(-0.953851\pi\)
0.144475 + 0.989509i \(0.453851\pi\)
\(578\) 21.1352 + 21.1352i 0.879106 + 0.879106i
\(579\) −2.57707 + 1.31291i −0.107099 + 0.0545626i
\(580\) 7.34574i 0.305015i
\(581\) 21.9608i 0.911086i
\(582\) 3.79538 11.6788i 0.157323 0.484104i
\(583\) 8.01300i 0.331865i
\(584\) 0.339546 0.339546i 0.0140505 0.0140505i
\(585\) −3.82866 2.78231i −0.158296 0.115034i
\(586\) −10.7674 10.7674i −0.444796 0.444796i
\(587\) 14.6086 14.6086i 0.602960 0.602960i −0.338137 0.941097i \(-0.609797\pi\)
0.941097 + 0.338137i \(0.109797\pi\)
\(588\) 0.294785 0.907089i 0.0121567 0.0374077i
\(589\) −8.47930 −0.349383
\(590\) 8.36584 + 8.36584i 0.344416 + 0.344416i
\(591\) 1.64432 5.05977i 0.0676382 0.208131i
\(592\) −3.85543 + 4.70486i −0.158457 + 0.193368i
\(593\) 30.9176i 1.26963i −0.772663 0.634817i \(-0.781076\pi\)
0.772663 0.634817i \(-0.218924\pi\)
\(594\) −7.96738 1.26322i −0.326906 0.0518304i
\(595\) 17.3898i 0.712914i
\(596\) 15.3710 0.629619
\(597\) 2.15314 + 4.22633i 0.0881221 + 0.172972i
\(598\) −1.35086 + 1.35086i −0.0552409 + 0.0552409i
\(599\) 13.3000i 0.543423i 0.962379 + 0.271712i \(0.0875897\pi\)
−0.962379 + 0.271712i \(0.912410\pi\)
\(600\) −1.54331 + 0.786252i −0.0630054 + 0.0320986i
\(601\) −13.2105 −0.538866 −0.269433 0.963019i \(-0.586836\pi\)
−0.269433 + 0.963019i \(0.586836\pi\)
\(602\) 9.98464i 0.406944i
\(603\) 3.50913 4.82883i 0.142903 0.196645i
\(604\) −8.84452 −0.359878
\(605\) −6.07392 6.07392i −0.246940 0.246940i
\(606\) 4.82675 2.45903i 0.196073 0.0998912i
\(607\) −1.58980 1.58980i −0.0645280 0.0645280i 0.674106 0.738634i \(-0.264529\pi\)
−0.738634 + 0.674106i \(0.764529\pi\)
\(608\) 3.52214i 0.142842i
\(609\) 28.7903 14.6675i 1.16664 0.594355i
\(610\) 7.41355 + 7.41355i 0.300166 + 0.300166i
\(611\) −11.6326 11.6326i −0.470603 0.470603i
\(612\) 20.2902 3.21144i 0.820184 0.129815i
\(613\) 35.8533i 1.44810i −0.689747 0.724051i \(-0.742278\pi\)
0.689747 0.724051i \(-0.257722\pi\)
\(614\) −15.9405 15.9405i −0.643306 0.643306i
\(615\) −8.23925 16.1726i −0.332239 0.652141i
\(616\) 2.78784 + 2.78784i 0.112325 + 0.112325i
\(617\) 22.8071 0.918178 0.459089 0.888390i \(-0.348176\pi\)
0.459089 + 0.888390i \(0.348176\pi\)
\(618\) 22.0118 + 7.15335i 0.885443 + 0.287750i
\(619\) 33.8714i 1.36141i −0.732559 0.680704i \(-0.761674\pi\)
0.732559 0.680704i \(-0.238326\pi\)
\(620\) 2.40742 0.0966845
\(621\) 0.985321 6.21464i 0.0395396 0.249385i
\(622\) 8.65204i 0.346915i
\(623\) −26.8393 + 26.8393i −1.07529 + 1.07529i
\(624\) −2.43475 + 1.24041i −0.0974681 + 0.0496559i
\(625\) −1.00000 −0.0400000
\(626\) 4.61985i 0.184646i
\(627\) 8.43889 4.29926i 0.337017 0.171696i
\(628\) 4.17933i 0.166774i
\(629\) 41.4488 4.11292i 1.65267 0.163993i
\(630\) −6.16315 4.47879i −0.245546 0.178439i
\(631\) −3.90804 3.90804i −0.155576 0.155576i 0.625027 0.780603i \(-0.285088\pi\)
−0.780603 + 0.625027i \(0.785088\pi\)
\(632\) −9.22422 −0.366920
\(633\) 39.5887 + 12.8655i 1.57351 + 0.511357i
\(634\) 21.2262 21.2262i 0.843001 0.843001i
\(635\) 10.1237 + 10.1237i 0.401745 + 0.401745i
\(636\) 8.50217 + 2.76302i 0.337133 + 0.109561i
\(637\) 0.614295 0.614295i 0.0243393 0.0243393i
\(638\) 11.4041i 0.451492i
\(639\) −5.95433 + 8.19360i −0.235550 + 0.324134i
\(640\) 1.00000i 0.0395285i
\(641\) 29.9478i 1.18287i 0.806353 + 0.591434i \(0.201438\pi\)
−0.806353 + 0.591434i \(0.798562\pi\)
\(642\) −1.51404 2.97186i −0.0597544 0.117290i
\(643\) −16.6932 16.6932i −0.658317 0.658317i 0.296664 0.954982i \(-0.404126\pi\)
−0.954982 + 0.296664i \(0.904126\pi\)
\(644\) −2.17454 + 2.17454i −0.0856889 + 0.0856889i
\(645\) 6.47641 + 2.10470i 0.255008 + 0.0828723i
\(646\) −17.0542 + 17.0542i −0.670987 + 0.670987i
\(647\) 1.28867 1.28867i 0.0506627 0.0506627i −0.681322 0.731984i \(-0.738594\pi\)
0.731984 + 0.681322i \(0.238594\pi\)
\(648\) 4.08763 8.01819i 0.160577 0.314984i
\(649\) 12.9878 + 12.9878i 0.509814 + 0.509814i
\(650\) −1.57762 −0.0618792
\(651\) 4.80698 + 9.43547i 0.188400 + 0.369805i
\(652\) 1.54752 1.54752i 0.0606056 0.0606056i
\(653\) 8.09056 8.09056i 0.316608 0.316608i −0.530855 0.847463i \(-0.678129\pi\)
0.847463 + 0.530855i \(0.178129\pi\)
\(654\) 1.34353 4.13422i 0.0525363 0.161661i
\(655\) 0.908791 0.0355094
\(656\) −10.4791 −0.409142
\(657\) −0.846870 + 1.16536i −0.0330396 + 0.0454649i
\(658\) −18.7254 18.7254i −0.729991 0.729991i
\(659\) 12.6087 0.491164 0.245582 0.969376i \(-0.421021\pi\)
0.245582 + 0.969376i \(0.421021\pi\)
\(660\) −2.39595 + 1.22064i −0.0932623 + 0.0475133i
\(661\) −2.03012 2.03012i −0.0789624 0.0789624i 0.666523 0.745485i \(-0.267782\pi\)
−0.745485 + 0.666523i \(0.767782\pi\)
\(662\) 13.0363i 0.506670i
\(663\) 17.7951 + 5.78301i 0.691103 + 0.224594i
\(664\) −6.11470 + 6.11470i −0.237296 + 0.237296i
\(665\) 8.94467 0.346860
\(666\) 9.21756 15.7492i 0.357173 0.610268i
\(667\) 8.89530 0.344427
\(668\) 13.7766 13.7766i 0.533033 0.533033i
\(669\) 32.3936 + 10.5272i 1.25241 + 0.407007i
\(670\) 1.98974i 0.0768704i
\(671\) 11.5094 + 11.5094i 0.444314 + 0.444314i
\(672\) −3.91932 + 1.99673i −0.151191 + 0.0770255i
\(673\) −40.7016 −1.56893 −0.784466 0.620172i \(-0.787063\pi\)
−0.784466 + 0.620172i \(0.787063\pi\)
\(674\) −16.0773 16.0773i −0.619275 0.619275i
\(675\) 4.20426 3.05355i 0.161822 0.117531i
\(676\) 10.5111 0.404274
\(677\) −33.5797 −1.29057 −0.645286 0.763941i \(-0.723262\pi\)
−0.645286 + 0.763941i \(0.723262\pi\)
\(678\) 8.62533 26.5412i 0.331254 1.01931i
\(679\) 12.7316 12.7316i 0.488594 0.488594i
\(680\) 4.84198 4.84198i 0.185682 0.185682i
\(681\) −2.84773 5.58972i −0.109125 0.214198i
\(682\) 3.73747 0.143115
\(683\) −18.5669 18.5669i −0.710442 0.710442i 0.256186 0.966628i \(-0.417534\pi\)
−0.966628 + 0.256186i \(0.917534\pi\)
\(684\) 1.65184 + 10.4365i 0.0631597 + 0.399050i
\(685\) −16.0998 + 16.0998i −0.615143 + 0.615143i
\(686\) 13.5590 13.5590i 0.517685 0.517685i
\(687\) −21.4729 6.97824i −0.819243 0.266236i
\(688\) 2.78010 2.78010i 0.105990 0.105990i
\(689\) 5.75781 + 5.75781i 0.219355 + 0.219355i
\(690\) −0.952110 1.86887i −0.0362462 0.0711465i
\(691\) 14.7237i 0.560118i 0.959983 + 0.280059i \(0.0903540\pi\)
−0.959983 + 0.280059i \(0.909646\pi\)
\(692\) 22.4262i 0.852517i
\(693\) −9.56814 6.95322i −0.363463 0.264131i
\(694\) 18.2057i 0.691078i
\(695\) −4.91720 + 4.91720i −0.186520 + 0.186520i
\(696\) 12.1003 + 3.93233i 0.458659 + 0.149054i
\(697\) 50.7398 + 50.7398i 1.92191 + 1.92191i
\(698\) −12.1575 + 12.1575i −0.460168 + 0.460168i
\(699\) 33.7547 + 10.9696i 1.27672 + 0.414907i
\(700\) −2.53955 −0.0959861
\(701\) −1.36351 1.36351i −0.0514990 0.0514990i 0.680888 0.732387i \(-0.261594\pi\)
−0.732387 + 0.680888i \(0.761594\pi\)
\(702\) 6.63272 4.81733i 0.250336 0.181818i
\(703\) 2.11553 + 21.3197i 0.0797886 + 0.804086i
\(704\) 1.55248i 0.0585111i
\(705\) 16.0932 8.19880i 0.606104 0.308785i
\(706\) 19.2979i 0.726286i
\(707\) 7.94253 0.298710
\(708\) −18.2590 + 9.30222i −0.686217 + 0.349599i
\(709\) 5.92223 5.92223i 0.222414 0.222414i −0.587100 0.809514i \(-0.699731\pi\)
0.809514 + 0.587100i \(0.199731\pi\)
\(710\) 3.37621i 0.126707i
\(711\) 27.3324 4.32604i 1.02505 0.162239i
\(712\) −14.9461 −0.560130
\(713\) 2.91526i 0.109177i
\(714\) 28.6454 + 9.30915i 1.07203 + 0.348386i
\(715\) −2.44921 −0.0915953
\(716\) 5.77543 + 5.77543i 0.215838 + 0.215838i
\(717\) 17.8553 + 35.0475i 0.666817 + 1.30887i
\(718\) 23.0762 + 23.0762i 0.861197 + 0.861197i
\(719\) 30.0602i 1.12106i 0.828135 + 0.560529i \(0.189402\pi\)
−0.828135 + 0.560529i \(0.810598\pi\)
\(720\) −0.468987 2.96312i −0.0174781 0.110429i
\(721\) 23.9959 + 23.9959i 0.893655 + 0.893655i
\(722\) 4.66301 + 4.66301i 0.173539 + 0.173539i
\(723\) 17.4866 8.90871i 0.650335 0.331318i
\(724\) 13.1382i 0.488276i
\(725\) 5.19422 + 5.19422i 0.192909 + 0.192909i
\(726\) 13.2568 6.75377i 0.492004 0.250656i
\(727\) −0.0366111 0.0366111i −0.00135783 0.00135783i 0.706428 0.707785i \(-0.250306\pi\)
−0.707785 + 0.706428i \(0.750306\pi\)
\(728\) −4.00644 −0.148489
\(729\) −8.35167 + 25.6759i −0.309321 + 0.950958i
\(730\) 0.480190i 0.0177726i
\(731\) −26.9224 −0.995760
\(732\) −16.1806 + 8.24334i −0.598052 + 0.304683i
\(733\) 23.8385i 0.880494i 0.897877 + 0.440247i \(0.145109\pi\)
−0.897877 + 0.440247i \(0.854891\pi\)
\(734\) −8.53674 + 8.53674i −0.315097 + 0.315097i
\(735\) 0.432965 + 0.849853i 0.0159701 + 0.0313473i
\(736\) −1.21095 −0.0446361
\(737\) 3.08902i 0.113786i
\(738\) 31.0509 4.91459i 1.14300 0.180908i
\(739\) 38.4233i 1.41343i −0.707501 0.706713i \(-0.750177\pi\)
0.707501 0.706713i \(-0.249823\pi\)
\(740\) −0.600636 6.05304i −0.0220798 0.222514i
\(741\) −2.97456 + 9.15310i −0.109273 + 0.336248i
\(742\) 9.26857 + 9.26857i 0.340260 + 0.340260i
\(743\) −22.9840 −0.843202 −0.421601 0.906782i \(-0.638532\pi\)
−0.421601 + 0.906782i \(0.638532\pi\)
\(744\) −1.28874 + 3.96563i −0.0472477 + 0.145387i
\(745\) −10.8689 + 10.8689i −0.398206 + 0.398206i
\(746\) −18.8328 18.8328i −0.689518 0.689518i
\(747\) 15.2508 20.9863i 0.557999 0.767848i
\(748\) 7.51706 7.51706i 0.274851 0.274851i
\(749\) 4.89027i 0.178687i
\(750\) 0.535321 1.64725i 0.0195472 0.0601491i
\(751\) 12.4662i 0.454898i 0.973790 + 0.227449i \(0.0730385\pi\)
−0.973790 + 0.227449i \(0.926962\pi\)
\(752\) 10.4277i 0.380259i
\(753\) −11.7824 + 6.00264i −0.429374 + 0.218748i
\(754\) 8.19449 + 8.19449i 0.298426 + 0.298426i
\(755\) 6.25402 6.25402i 0.227607 0.227607i
\(756\) 10.6770 7.75465i 0.388317 0.282034i
\(757\) 16.0789 16.0789i 0.584398 0.584398i −0.351710 0.936109i \(-0.614400\pi\)
0.936109 + 0.351710i \(0.114400\pi\)
\(758\) 14.6734 14.6734i 0.532963 0.532963i
\(759\) −1.47813 2.90137i −0.0536526 0.105313i
\(760\) 2.49053 + 2.49053i 0.0903411 + 0.0903411i
\(761\) −29.9383 −1.08526 −0.542632 0.839971i \(-0.682572\pi\)
−0.542632 + 0.839971i \(0.682572\pi\)
\(762\) −22.0956 + 11.2568i −0.800439 + 0.407790i
\(763\) 4.50688 4.50688i 0.163160 0.163160i
\(764\) −6.53325 + 6.53325i −0.236365 + 0.236365i
\(765\) −12.0765 + 16.6182i −0.436628 + 0.600832i
\(766\) 22.4423 0.810874
\(767\) −18.6649 −0.673952
\(768\) −1.64725 0.535321i −0.0594400 0.0193167i
\(769\) −27.9340 27.9340i −1.00733 1.00733i −0.999973 0.00735452i \(-0.997659\pi\)
−0.00735452 0.999973i \(-0.502341\pi\)
\(770\) −3.94259 −0.142081
\(771\) 14.3966 + 28.2586i 0.518480 + 1.01771i
\(772\) −1.18075 1.18075i −0.0424961 0.0424961i
\(773\) 1.29800i 0.0466858i 0.999728 + 0.0233429i \(0.00743094\pi\)
−0.999728 + 0.0233429i \(0.992569\pi\)
\(774\) −6.93392 + 9.54158i −0.249235 + 0.342965i
\(775\) −1.70231 + 1.70231i −0.0611486 + 0.0611486i
\(776\) 7.08991 0.254513
\(777\) 22.5245 14.4404i 0.808061 0.518045i
\(778\) −12.3267 −0.441934
\(779\)