Properties

Label 546.2.p.c.281.4
Level $546$
Weight $2$
Character 546.281
Analytic conductor $4.360$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.p (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + 1065 x^{12} - 2080 x^{11} + 3712 x^{10} - 6240 x^{9} + 9585 x^{8} - 14364 x^{7} + 23328 x^{6} - 34020 x^{5} + 40824 x^{4} - 43740 x^{3} + 52488 x^{2} - 78732 x + 59049\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 281.4
Root \(1.72939 - 0.0958811i\) of defining polynomial
Character \(\chi\) \(=\) 546.281
Dual form 546.2.p.c.239.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.15507 - 1.29067i) q^{3} -1.00000i q^{4} +(0.616653 - 0.616653i) q^{5} +(0.0958811 + 1.72939i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.331633 - 2.98161i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.15507 - 1.29067i) q^{3} -1.00000i q^{4} +(0.616653 - 0.616653i) q^{5} +(0.0958811 + 1.72939i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.331633 - 2.98161i) q^{9} +0.872079i q^{10} +(-2.63014 - 2.63014i) q^{11} +(-1.29067 - 1.15507i) q^{12} +(1.08413 - 3.43870i) q^{13} +1.00000i q^{14} +(-0.0836158 - 1.50817i) q^{15} -1.00000 q^{16} -5.36595 q^{17} +(2.34282 + 1.87382i) q^{18} +(3.60391 + 3.60391i) q^{19} +(-0.616653 - 0.616653i) q^{20} +(-0.0958811 - 1.72939i) q^{21} +3.71958 q^{22} +2.67136 q^{23} +(1.72939 - 0.0958811i) q^{24} +4.23948i q^{25} +(1.66493 + 3.19813i) q^{26} +(-4.23132 - 3.01594i) q^{27} +(-0.707107 - 0.707107i) q^{28} +3.00014i q^{29} +(1.12556 + 1.00731i) q^{30} +(-6.60062 - 6.60062i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-6.43263 + 0.356638i) q^{33} +(3.79430 - 3.79430i) q^{34} -0.872079i q^{35} +(-2.98161 + 0.331633i) q^{36} +(4.44970 - 4.44970i) q^{37} -5.09669 q^{38} +(-3.18596 - 5.37119i) q^{39} +0.872079 q^{40} +(8.43789 - 8.43789i) q^{41} +(1.29067 + 1.15507i) q^{42} -0.610209i q^{43} +(-2.63014 + 2.63014i) q^{44} +(-2.04312 - 1.63412i) q^{45} +(-1.88894 + 1.88894i) q^{46} +(3.46010 + 3.46010i) q^{47} +(-1.15507 + 1.29067i) q^{48} -1.00000i q^{49} +(-2.99776 - 2.99776i) q^{50} +(-6.19805 + 6.92565i) q^{51} +(-3.43870 - 1.08413i) q^{52} +0.464507i q^{53} +(5.12459 - 0.859404i) q^{54} -3.24377 q^{55} +1.00000 q^{56} +(8.81419 - 0.488676i) q^{57} +(-2.12142 - 2.12142i) q^{58} +(8.93448 + 8.93448i) q^{59} +(-1.50817 + 0.0836158i) q^{60} -8.37831 q^{61} +9.33468 q^{62} +(-2.34282 - 1.87382i) q^{63} +1.00000i q^{64} +(-1.45195 - 2.78902i) q^{65} +(4.29637 - 4.80074i) q^{66} +(1.77932 + 1.77932i) q^{67} +5.36595i q^{68} +(3.08561 - 3.44784i) q^{69} +(0.616653 + 0.616653i) q^{70} +(-0.00980127 + 0.00980127i) q^{71} +(1.87382 - 2.34282i) q^{72} +(11.1380 - 11.1380i) q^{73} +6.29283i q^{74} +(5.47175 + 4.89689i) q^{75} +(3.60391 - 3.60391i) q^{76} -3.71958 q^{77} +(6.05082 + 1.54519i) q^{78} +6.11811 q^{79} +(-0.616653 + 0.616653i) q^{80} +(-8.78004 + 1.97760i) q^{81} +11.9330i q^{82} +(-3.29926 + 3.29926i) q^{83} +(-1.72939 + 0.0958811i) q^{84} +(-3.30893 + 3.30893i) q^{85} +(0.431483 + 0.431483i) q^{86} +(3.87217 + 3.46536i) q^{87} -3.71958i q^{88} +(8.90085 + 8.90085i) q^{89} +(2.60020 - 0.289210i) q^{90} +(-1.66493 - 3.19813i) q^{91} -2.67136i q^{92} +(-16.1433 + 0.895019i) q^{93} -4.89332 q^{94} +4.44472 q^{95} +(-0.0958811 - 1.72939i) q^{96} +(-5.41720 - 5.41720i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-6.96983 + 8.71431i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 4q^{5} - 4q^{6} - 8q^{9} + O(q^{10}) \) \( 20q - 4q^{5} - 4q^{6} - 8q^{9} - 16q^{11} - 8q^{12} + 4q^{13} - 4q^{15} - 20q^{16} + 12q^{17} - 8q^{18} + 12q^{19} + 4q^{20} + 4q^{21} - 12q^{22} - 4q^{23} + 4q^{24} + 24q^{27} + 12q^{30} - 8q^{31} - 48q^{33} - 4q^{34} + 32q^{37} - 4q^{38} - 16q^{39} - 4q^{40} + 8q^{41} + 8q^{42} - 16q^{44} + 16q^{45} - 8q^{46} + 32q^{50} - 8q^{51} - 8q^{52} + 28q^{54} + 28q^{55} + 20q^{56} + 36q^{57} - 4q^{58} + 20q^{59} - 4q^{60} - 4q^{61} + 48q^{62} + 8q^{63} + 52q^{65} - 36q^{67} + 68q^{69} - 4q^{70} - 28q^{71} - 16q^{72} - 24q^{73} - 76q^{75} + 12q^{76} + 12q^{77} + 40q^{78} - 64q^{79} + 4q^{80} + 32q^{81} - 24q^{83} - 4q^{84} + 24q^{85} + 4q^{86} + 4q^{87} - 4q^{89} - 8q^{90} - 32q^{93} - 40q^{94} - 76q^{95} + 4q^{96} + 32q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 1.15507 1.29067i 0.666879 0.745166i
\(4\) 1.00000i 0.500000i
\(5\) 0.616653 0.616653i 0.275775 0.275775i −0.555645 0.831420i \(-0.687528\pi\)
0.831420 + 0.555645i \(0.187528\pi\)
\(6\) 0.0958811 + 1.72939i 0.0391433 + 0.706023i
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −0.331633 2.98161i −0.110544 0.993871i
\(10\) 0.872079i 0.275775i
\(11\) −2.63014 2.63014i −0.793018 0.793018i 0.188966 0.981984i \(-0.439486\pi\)
−0.981984 + 0.188966i \(0.939486\pi\)
\(12\) −1.29067 1.15507i −0.372583 0.333440i
\(13\) 1.08413 3.43870i 0.300684 0.953724i
\(14\) 1.00000i 0.267261i
\(15\) −0.0836158 1.50817i −0.0215895 0.389407i
\(16\) −1.00000 −0.250000
\(17\) −5.36595 −1.30144 −0.650718 0.759320i \(-0.725532\pi\)
−0.650718 + 0.759320i \(0.725532\pi\)
\(18\) 2.34282 + 1.87382i 0.552208 + 0.441664i
\(19\) 3.60391 + 3.60391i 0.826793 + 0.826793i 0.987072 0.160279i \(-0.0512394\pi\)
−0.160279 + 0.987072i \(0.551239\pi\)
\(20\) −0.616653 0.616653i −0.137888 0.137888i
\(21\) −0.0958811 1.72939i −0.0209230 0.377385i
\(22\) 3.71958 0.793018
\(23\) 2.67136 0.557018 0.278509 0.960434i \(-0.410160\pi\)
0.278509 + 0.960434i \(0.410160\pi\)
\(24\) 1.72939 0.0958811i 0.353011 0.0195716i
\(25\) 4.23948i 0.847896i
\(26\) 1.66493 + 3.19813i 0.326520 + 0.627204i
\(27\) −4.23132 3.01594i −0.814318 0.580418i
\(28\) −0.707107 0.707107i −0.133631 0.133631i
\(29\) 3.00014i 0.557111i 0.960420 + 0.278556i \(0.0898556\pi\)
−0.960420 + 0.278556i \(0.910144\pi\)
\(30\) 1.12556 + 1.00731i 0.205498 + 0.183909i
\(31\) −6.60062 6.60062i −1.18551 1.18551i −0.978297 0.207209i \(-0.933562\pi\)
−0.207209 0.978297i \(-0.566438\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −6.43263 + 0.356638i −1.11978 + 0.0620827i
\(34\) 3.79430 3.79430i 0.650718 0.650718i
\(35\) 0.872079i 0.147408i
\(36\) −2.98161 + 0.331633i −0.496936 + 0.0552721i
\(37\) 4.44970 4.44970i 0.731527 0.731527i −0.239395 0.970922i \(-0.576949\pi\)
0.970922 + 0.239395i \(0.0769492\pi\)
\(38\) −5.09669 −0.826793
\(39\) −3.18596 5.37119i −0.510162 0.860078i
\(40\) 0.872079 0.137888
\(41\) 8.43789 8.43789i 1.31778 1.31778i 0.402245 0.915532i \(-0.368230\pi\)
0.915532 0.402245i \(-0.131770\pi\)
\(42\) 1.29067 + 1.15507i 0.199154 + 0.178231i
\(43\) 0.610209i 0.0930560i −0.998917 0.0465280i \(-0.985184\pi\)
0.998917 0.0465280i \(-0.0148157\pi\)
\(44\) −2.63014 + 2.63014i −0.396509 + 0.396509i
\(45\) −2.04312 1.63412i −0.304571 0.243600i
\(46\) −1.88894 + 1.88894i −0.278509 + 0.278509i
\(47\) 3.46010 + 3.46010i 0.504707 + 0.504707i 0.912897 0.408190i \(-0.133840\pi\)
−0.408190 + 0.912897i \(0.633840\pi\)
\(48\) −1.15507 + 1.29067i −0.166720 + 0.186291i
\(49\) 1.00000i 0.142857i
\(50\) −2.99776 2.99776i −0.423948 0.423948i
\(51\) −6.19805 + 6.92565i −0.867900 + 0.969785i
\(52\) −3.43870 1.08413i −0.476862 0.150342i
\(53\) 0.464507i 0.0638049i 0.999491 + 0.0319024i \(0.0101566\pi\)
−0.999491 + 0.0319024i \(0.989843\pi\)
\(54\) 5.12459 0.859404i 0.697368 0.116950i
\(55\) −3.24377 −0.437390
\(56\) 1.00000 0.133631
\(57\) 8.81419 0.488676i 1.16747 0.0647268i
\(58\) −2.12142 2.12142i −0.278556 0.278556i
\(59\) 8.93448 + 8.93448i 1.16317 + 1.16317i 0.983778 + 0.179393i \(0.0574133\pi\)
0.179393 + 0.983778i \(0.442587\pi\)
\(60\) −1.50817 + 0.0836158i −0.194704 + 0.0107948i
\(61\) −8.37831 −1.07273 −0.536367 0.843985i \(-0.680204\pi\)
−0.536367 + 0.843985i \(0.680204\pi\)
\(62\) 9.33468 1.18551
\(63\) −2.34282 1.87382i −0.295167 0.236079i
\(64\) 1.00000i 0.125000i
\(65\) −1.45195 2.78902i −0.180092 0.345935i
\(66\) 4.29637 4.80074i 0.528847 0.590930i
\(67\) 1.77932 + 1.77932i 0.217379 + 0.217379i 0.807393 0.590014i \(-0.200878\pi\)
−0.590014 + 0.807393i \(0.700878\pi\)
\(68\) 5.36595i 0.650718i
\(69\) 3.08561 3.44784i 0.371464 0.415071i
\(70\) 0.616653 + 0.616653i 0.0737041 + 0.0737041i
\(71\) −0.00980127 + 0.00980127i −0.00116320 + 0.00116320i −0.707688 0.706525i \(-0.750262\pi\)
0.706525 + 0.707688i \(0.250262\pi\)
\(72\) 1.87382 2.34282i 0.220832 0.276104i
\(73\) 11.1380 11.1380i 1.30360 1.30360i 0.377650 0.925948i \(-0.376732\pi\)
0.925948 0.377650i \(-0.123268\pi\)
\(74\) 6.29283i 0.731527i
\(75\) 5.47175 + 4.89689i 0.631823 + 0.565444i
\(76\) 3.60391 3.60391i 0.413396 0.413396i
\(77\) −3.71958 −0.423886
\(78\) 6.05082 + 1.54519i 0.685120 + 0.174958i
\(79\) 6.11811 0.688341 0.344170 0.938907i \(-0.388160\pi\)
0.344170 + 0.938907i \(0.388160\pi\)
\(80\) −0.616653 + 0.616653i −0.0689439 + 0.0689439i
\(81\) −8.78004 + 1.97760i −0.975560 + 0.219733i
\(82\) 11.9330i 1.31778i
\(83\) −3.29926 + 3.29926i −0.362141 + 0.362141i −0.864601 0.502460i \(-0.832428\pi\)
0.502460 + 0.864601i \(0.332428\pi\)
\(84\) −1.72939 + 0.0958811i −0.188692 + 0.0104615i
\(85\) −3.30893 + 3.30893i −0.358904 + 0.358904i
\(86\) 0.431483 + 0.431483i 0.0465280 + 0.0465280i
\(87\) 3.87217 + 3.46536i 0.415140 + 0.371526i
\(88\) 3.71958i 0.396509i
\(89\) 8.90085 + 8.90085i 0.943489 + 0.943489i 0.998486 0.0549979i \(-0.0175152\pi\)
−0.0549979 + 0.998486i \(0.517515\pi\)
\(90\) 2.60020 0.289210i 0.274085 0.0304854i
\(91\) −1.66493 3.19813i −0.174532 0.335255i
\(92\) 2.67136i 0.278509i
\(93\) −16.1433 + 0.895019i −1.67399 + 0.0928092i
\(94\) −4.89332 −0.504707
\(95\) 4.44472 0.456018
\(96\) −0.0958811 1.72939i −0.00978582 0.176506i
\(97\) −5.41720 5.41720i −0.550033 0.550033i 0.376417 0.926450i \(-0.377156\pi\)
−0.926450 + 0.376417i \(0.877156\pi\)
\(98\) 0.707107 + 0.707107i 0.0714286 + 0.0714286i
\(99\) −6.96983 + 8.71431i −0.700494 + 0.875821i
\(100\) 4.23948 0.423948
\(101\) 9.74113 0.969278 0.484639 0.874714i \(-0.338951\pi\)
0.484639 + 0.874714i \(0.338951\pi\)
\(102\) −0.514494 9.27985i −0.0509424 0.918842i
\(103\) 13.8659i 1.36625i 0.730302 + 0.683124i \(0.239379\pi\)
−0.730302 + 0.683124i \(0.760621\pi\)
\(104\) 3.19813 1.66493i 0.313602 0.163260i
\(105\) −1.12556 1.00731i −0.109844 0.0983035i
\(106\) −0.328456 0.328456i −0.0319024 0.0319024i
\(107\) 2.77130i 0.267911i −0.990987 0.133956i \(-0.957232\pi\)
0.990987 0.133956i \(-0.0427680\pi\)
\(108\) −3.01594 + 4.23132i −0.290209 + 0.407159i
\(109\) 2.22915 + 2.22915i 0.213513 + 0.213513i 0.805758 0.592245i \(-0.201758\pi\)
−0.592245 + 0.805758i \(0.701758\pi\)
\(110\) 2.29369 2.29369i 0.218695 0.218695i
\(111\) −0.603364 10.8828i −0.0572687 1.03295i
\(112\) −0.707107 + 0.707107i −0.0668153 + 0.0668153i
\(113\) 13.7999i 1.29818i 0.760710 + 0.649091i \(0.224851\pi\)
−0.760710 + 0.649091i \(0.775149\pi\)
\(114\) −5.88703 + 6.57812i −0.551371 + 0.616098i
\(115\) 1.64730 1.64730i 0.153612 0.153612i
\(116\) 3.00014 0.278556
\(117\) −10.6124 2.09208i −0.981117 0.193413i
\(118\) −12.6353 −1.16317
\(119\) −3.79430 + 3.79430i −0.347823 + 0.347823i
\(120\) 1.00731 1.12556i 0.0919545 0.102749i
\(121\) 2.83530i 0.257754i
\(122\) 5.92436 5.92436i 0.536367 0.536367i
\(123\) −1.14415 20.6368i −0.103164 1.86076i
\(124\) −6.60062 + 6.60062i −0.592753 + 0.592753i
\(125\) 5.69755 + 5.69755i 0.509604 + 0.509604i
\(126\) 2.98161 0.331633i 0.265623 0.0295442i
\(127\) 21.3350i 1.89317i 0.322453 + 0.946585i \(0.395492\pi\)
−0.322453 + 0.946585i \(0.604508\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −0.787575 0.704833i −0.0693421 0.0620571i
\(130\) 2.99882 + 0.945448i 0.263014 + 0.0829213i
\(131\) 8.16389i 0.713282i −0.934242 0.356641i \(-0.883922\pi\)
0.934242 0.356641i \(-0.116078\pi\)
\(132\) 0.356638 + 6.43263i 0.0310413 + 0.559888i
\(133\) 5.09669 0.441939
\(134\) −2.51634 −0.217379
\(135\) −4.46905 + 0.749468i −0.384634 + 0.0645039i
\(136\) −3.79430 3.79430i −0.325359 0.325359i
\(137\) −9.21910 9.21910i −0.787641 0.787641i 0.193466 0.981107i \(-0.438027\pi\)
−0.981107 + 0.193466i \(0.938027\pi\)
\(138\) 0.256133 + 4.61984i 0.0218035 + 0.393267i
\(139\) −2.49440 −0.211572 −0.105786 0.994389i \(-0.533736\pi\)
−0.105786 + 0.994389i \(0.533736\pi\)
\(140\) −0.872079 −0.0737041
\(141\) 8.46248 0.469177i 0.712670 0.0395118i
\(142\) 0.0138611i 0.00116320i
\(143\) −11.8957 + 6.19285i −0.994768 + 0.517872i
\(144\) 0.331633 + 2.98161i 0.0276360 + 0.248468i
\(145\) 1.85004 + 1.85004i 0.153638 + 0.153638i
\(146\) 15.7514i 1.30360i
\(147\) −1.29067 1.15507i −0.106452 0.0952685i
\(148\) −4.44970 4.44970i −0.365763 0.365763i
\(149\) −12.3117 + 12.3117i −1.00862 + 1.00862i −0.00865511 + 0.999963i \(0.502755\pi\)
−0.999963 + 0.00865511i \(0.997245\pi\)
\(150\) −7.33173 + 0.406486i −0.598634 + 0.0331894i
\(151\) −3.48920 + 3.48920i −0.283947 + 0.283947i −0.834681 0.550734i \(-0.814348\pi\)
0.550734 + 0.834681i \(0.314348\pi\)
\(152\) 5.09669i 0.413396i
\(153\) 1.77952 + 15.9992i 0.143866 + 1.29346i
\(154\) 2.63014 2.63014i 0.211943 0.211943i
\(155\) −8.14057 −0.653867
\(156\) −5.37119 + 3.18596i −0.430039 + 0.255081i
\(157\) 0.911415 0.0727388 0.0363694 0.999338i \(-0.488421\pi\)
0.0363694 + 0.999338i \(0.488421\pi\)
\(158\) −4.32615 + 4.32615i −0.344170 + 0.344170i
\(159\) 0.599522 + 0.536537i 0.0475452 + 0.0425502i
\(160\) 0.872079i 0.0689439i
\(161\) 1.88894 1.88894i 0.148869 0.148869i
\(162\) 4.81005 7.60680i 0.377913 0.597647i
\(163\) −13.4803 + 13.4803i −1.05586 + 1.05586i −0.0575128 + 0.998345i \(0.518317\pi\)
−0.998345 + 0.0575128i \(0.981683\pi\)
\(164\) −8.43789 8.43789i −0.658888 0.658888i
\(165\) −3.74678 + 4.18662i −0.291686 + 0.325928i
\(166\) 4.66586i 0.362141i
\(167\) 4.56615 + 4.56615i 0.353339 + 0.353339i 0.861350 0.508011i \(-0.169619\pi\)
−0.508011 + 0.861350i \(0.669619\pi\)
\(168\) 1.15507 1.29067i 0.0891155 0.0995770i
\(169\) −10.6493 7.45601i −0.819178 0.573539i
\(170\) 4.67953i 0.358904i
\(171\) 9.55028 11.9406i 0.730328 0.913122i
\(172\) −0.610209 −0.0465280
\(173\) 20.5507 1.56244 0.781221 0.624255i \(-0.214597\pi\)
0.781221 + 0.624255i \(0.214597\pi\)
\(174\) −5.18842 + 0.287656i −0.393333 + 0.0218072i
\(175\) 2.99776 + 2.99776i 0.226610 + 0.226610i
\(176\) 2.63014 + 2.63014i 0.198254 + 0.198254i
\(177\) 21.8514 1.21148i 1.64245 0.0910606i
\(178\) −12.5877 −0.943489
\(179\) −12.5336 −0.936809 −0.468404 0.883514i \(-0.655171\pi\)
−0.468404 + 0.883514i \(0.655171\pi\)
\(180\) −1.63412 + 2.04312i −0.121800 + 0.152285i
\(181\) 13.2739i 0.986643i 0.869847 + 0.493321i \(0.164217\pi\)
−0.869847 + 0.493321i \(0.835783\pi\)
\(182\) 3.43870 + 1.08413i 0.254893 + 0.0803612i
\(183\) −9.67753 + 10.8136i −0.715383 + 0.799364i
\(184\) 1.88894 + 1.88894i 0.139254 + 0.139254i
\(185\) 5.48784i 0.403474i
\(186\) 10.7822 12.0479i 0.790589 0.883398i
\(187\) 14.1132 + 14.1132i 1.03206 + 1.03206i
\(188\) 3.46010 3.46010i 0.252354 0.252354i
\(189\) −5.12459 + 0.859404i −0.372759 + 0.0625124i
\(190\) −3.14289 + 3.14289i −0.228009 + 0.228009i
\(191\) 3.21043i 0.232299i −0.993232 0.116149i \(-0.962945\pi\)
0.993232 0.116149i \(-0.0370552\pi\)
\(192\) 1.29067 + 1.15507i 0.0931457 + 0.0833599i
\(193\) 16.2407 16.2407i 1.16903 1.16903i 0.186594 0.982437i \(-0.440255\pi\)
0.982437 0.186594i \(-0.0597450\pi\)
\(194\) 7.66107 0.550033
\(195\) −5.27679 1.34752i −0.377879 0.0964982i
\(196\) −1.00000 −0.0714286
\(197\) 14.8966 14.8966i 1.06134 1.06134i 0.0633475 0.997992i \(-0.479822\pi\)
0.997992 0.0633475i \(-0.0201777\pi\)
\(198\) −1.23353 11.0904i −0.0876635 0.788158i
\(199\) 15.1640i 1.07495i 0.843281 + 0.537473i \(0.180621\pi\)
−0.843281 + 0.537473i \(0.819379\pi\)
\(200\) −2.99776 + 2.99776i −0.211974 + 0.211974i
\(201\) 4.35175 0.241270i 0.306949 0.0170178i
\(202\) −6.88802 + 6.88802i −0.484639 + 0.484639i
\(203\) 2.12142 + 2.12142i 0.148894 + 0.148894i
\(204\) 6.92565 + 6.19805i 0.484892 + 0.433950i
\(205\) 10.4065i 0.726821i
\(206\) −9.80468 9.80468i −0.683124 0.683124i
\(207\) −0.885911 7.96498i −0.0615751 0.553604i
\(208\) −1.08413 + 3.43870i −0.0751710 + 0.238431i
\(209\) 18.9576i 1.31132i
\(210\) 1.50817 0.0836158i 0.104073 0.00577004i
\(211\) 2.49834 0.171993 0.0859965 0.996295i \(-0.472593\pi\)
0.0859965 + 0.996295i \(0.472593\pi\)
\(212\) 0.464507 0.0319024
\(213\) 0.00132902 + 0.0239713i 9.10627e−5 + 0.00164249i
\(214\) 1.95960 + 1.95960i 0.133956 + 0.133956i
\(215\) −0.376287 0.376287i −0.0256626 0.0256626i
\(216\) −0.859404 5.12459i −0.0584750 0.348684i
\(217\) −9.33468 −0.633679
\(218\) −3.15249 −0.213513
\(219\) −1.51027 27.2405i −0.102054 1.84074i
\(220\) 3.24377i 0.218695i
\(221\) −5.81740 + 18.4519i −0.391321 + 1.24121i
\(222\) 8.12194 + 7.26865i 0.545109 + 0.487840i
\(223\) 6.63646 + 6.63646i 0.444410 + 0.444410i 0.893491 0.449081i \(-0.148249\pi\)
−0.449081 + 0.893491i \(0.648249\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) 12.6405 1.40595i 0.842699 0.0937299i
\(226\) −9.75798 9.75798i −0.649091 0.649091i
\(227\) −8.75850 + 8.75850i −0.581322 + 0.581322i −0.935266 0.353944i \(-0.884840\pi\)
0.353944 + 0.935266i \(0.384840\pi\)
\(228\) −0.488676 8.81419i −0.0323634 0.583734i
\(229\) 4.24481 4.24481i 0.280505 0.280505i −0.552805 0.833310i \(-0.686443\pi\)
0.833310 + 0.552805i \(0.186443\pi\)
\(230\) 2.32964i 0.153612i
\(231\) −4.29637 + 4.80074i −0.282681 + 0.315865i
\(232\) −2.12142 + 2.12142i −0.139278 + 0.139278i
\(233\) 5.81776 0.381134 0.190567 0.981674i \(-0.438967\pi\)
0.190567 + 0.981674i \(0.438967\pi\)
\(234\) 8.98343 6.02478i 0.587265 0.393852i
\(235\) 4.26736 0.278372
\(236\) 8.93448 8.93448i 0.581585 0.581585i
\(237\) 7.06683 7.89643i 0.459040 0.512928i
\(238\) 5.36595i 0.347823i
\(239\) −6.19473 + 6.19473i −0.400704 + 0.400704i −0.878481 0.477777i \(-0.841443\pi\)
0.477777 + 0.878481i \(0.341443\pi\)
\(240\) 0.0836158 + 1.50817i 0.00539738 + 0.0973518i
\(241\) 19.2493 19.2493i 1.23996 1.23996i 0.279940 0.960018i \(-0.409686\pi\)
0.960018 0.279940i \(-0.0903144\pi\)
\(242\) −2.00486 2.00486i −0.128877 0.128877i
\(243\) −7.58913 + 13.6164i −0.486843 + 0.873490i
\(244\) 8.37831i 0.536367i
\(245\) −0.616653 0.616653i −0.0393965 0.0393965i
\(246\) 15.4015 + 13.7834i 0.981962 + 0.878798i
\(247\) 16.2999 8.48564i 1.03714 0.539928i
\(248\) 9.33468i 0.592753i
\(249\) 0.447367 + 8.06911i 0.0283508 + 0.511359i
\(250\) −8.05755 −0.509604
\(251\) −21.2530 −1.34148 −0.670738 0.741694i \(-0.734023\pi\)
−0.670738 + 0.741694i \(0.734023\pi\)
\(252\) −1.87382 + 2.34282i −0.118040 + 0.147584i
\(253\) −7.02607 7.02607i −0.441725 0.441725i
\(254\) −15.0861 15.0861i −0.946585 0.946585i
\(255\) 0.448679 + 8.09276i 0.0280974 + 0.506788i
\(256\) 1.00000 0.0625000
\(257\) 13.2098 0.824005 0.412002 0.911183i \(-0.364830\pi\)
0.412002 + 0.911183i \(0.364830\pi\)
\(258\) 1.05529 0.0585075i 0.0656996 0.00364252i
\(259\) 6.29283i 0.391018i
\(260\) −2.78902 + 1.45195i −0.172967 + 0.0900461i
\(261\) 8.94524 0.994943i 0.553697 0.0615854i
\(262\) 5.77274 + 5.77274i 0.356641 + 0.356641i
\(263\) 15.8036i 0.974493i −0.873264 0.487247i \(-0.838001\pi\)
0.873264 0.487247i \(-0.161999\pi\)
\(264\) −4.80074 4.29637i −0.295465 0.264424i
\(265\) 0.286439 + 0.286439i 0.0175958 + 0.0175958i
\(266\) −3.60391 + 3.60391i −0.220970 + 0.220970i
\(267\) 21.7691 1.20692i 1.33225 0.0738625i
\(268\) 1.77932 1.77932i 0.108689 0.108689i
\(269\) 7.86513i 0.479545i 0.970829 + 0.239773i \(0.0770729\pi\)
−0.970829 + 0.239773i \(0.922927\pi\)
\(270\) 2.63014 3.69005i 0.160065 0.224569i
\(271\) 7.27480 7.27480i 0.441913 0.441913i −0.450742 0.892654i \(-0.648840\pi\)
0.892654 + 0.450742i \(0.148840\pi\)
\(272\) 5.36595 0.325359
\(273\) −6.05082 1.54519i −0.366212 0.0935189i
\(274\) 13.0378 0.787641
\(275\) 11.1504 11.1504i 0.672396 0.672396i
\(276\) −3.44784 3.08561i −0.207535 0.185732i
\(277\) 15.2302i 0.915091i −0.889186 0.457546i \(-0.848729\pi\)
0.889186 0.457546i \(-0.151271\pi\)
\(278\) 1.76381 1.76381i 0.105786 0.105786i
\(279\) −17.4915 + 21.8695i −1.04719 + 1.30929i
\(280\) 0.616653 0.616653i 0.0368520 0.0368520i
\(281\) −19.8714 19.8714i −1.18543 1.18543i −0.978318 0.207110i \(-0.933594\pi\)
−0.207110 0.978318i \(-0.566406\pi\)
\(282\) −5.65212 + 6.31564i −0.336579 + 0.376091i
\(283\) 11.9364i 0.709548i −0.934952 0.354774i \(-0.884558\pi\)
0.934952 0.354774i \(-0.115442\pi\)
\(284\) 0.00980127 + 0.00980127i 0.000581598 + 0.000581598i
\(285\) 5.13395 5.73664i 0.304109 0.339809i
\(286\) 4.03252 12.7905i 0.238448 0.756320i
\(287\) 11.9330i 0.704381i
\(288\) −2.34282 1.87382i −0.138052 0.110416i
\(289\) 11.7935 0.693733
\(290\) −2.61635 −0.153638
\(291\) −13.2490 + 0.734552i −0.776672 + 0.0430602i
\(292\) −11.1380 11.1380i −0.651799 0.651799i
\(293\) 12.0322 + 12.0322i 0.702931 + 0.702931i 0.965039 0.262108i \(-0.0844175\pi\)
−0.262108 + 0.965039i \(0.584418\pi\)
\(294\) 1.72939 0.0958811i 0.100860 0.00559190i
\(295\) 11.0189 0.641548
\(296\) 6.29283 0.365763
\(297\) 3.19662 + 19.0613i 0.185487 + 1.10605i
\(298\) 17.4114i 1.00862i
\(299\) 2.89611 9.18602i 0.167486 0.531241i
\(300\) 4.89689 5.47175i 0.282722 0.315911i
\(301\) −0.431483 0.431483i −0.0248703 0.0248703i
\(302\) 4.93447i 0.283947i
\(303\) 11.2517 12.5725i 0.646392 0.722273i
\(304\) −3.60391 3.60391i −0.206698 0.206698i
\(305\) −5.16651 + 5.16651i −0.295833 + 0.295833i
\(306\) −12.5715 10.0548i −0.718662 0.574796i
\(307\) −8.97229 + 8.97229i −0.512076 + 0.512076i −0.915162 0.403086i \(-0.867937\pi\)
0.403086 + 0.915162i \(0.367937\pi\)
\(308\) 3.71958i 0.211943i
\(309\) 17.8962 + 16.0161i 1.01808 + 0.911123i
\(310\) 5.75626 5.75626i 0.326933 0.326933i
\(311\) −27.6299 −1.56675 −0.783373 0.621551i \(-0.786503\pi\)
−0.783373 + 0.621551i \(0.786503\pi\)
\(312\) 1.54519 6.05082i 0.0874790 0.342560i
\(313\) 14.2907 0.807757 0.403878 0.914813i \(-0.367662\pi\)
0.403878 + 0.914813i \(0.367662\pi\)
\(314\) −0.644468 + 0.644468i −0.0363694 + 0.0363694i
\(315\) −2.60020 + 0.289210i −0.146505 + 0.0162951i
\(316\) 6.11811i 0.344170i
\(317\) 2.71639 2.71639i 0.152568 0.152568i −0.626696 0.779264i \(-0.715593\pi\)
0.779264 + 0.626696i \(0.215593\pi\)
\(318\) −0.803315 + 0.0445374i −0.0450477 + 0.00249753i
\(319\) 7.89078 7.89078i 0.441799 0.441799i
\(320\) 0.616653 + 0.616653i 0.0344719 + 0.0344719i
\(321\) −3.57682 3.20104i −0.199638 0.178665i
\(322\) 2.67136i 0.148869i
\(323\) −19.3384 19.3384i −1.07602 1.07602i
\(324\) 1.97760 + 8.78004i 0.109867 + 0.487780i
\(325\) 14.5783 + 4.59616i 0.808658 + 0.254949i
\(326\) 19.0640i 1.05586i
\(327\) 5.45190 0.302264i 0.301491 0.0167152i
\(328\) 11.9330 0.658888
\(329\) 4.89332 0.269777
\(330\) −0.311016 5.60976i −0.0171209 0.308807i
\(331\) −10.6402 10.6402i −0.584837 0.584837i 0.351392 0.936229i \(-0.385709\pi\)
−0.936229 + 0.351392i \(0.885709\pi\)
\(332\) 3.29926 + 3.29926i 0.181070 + 0.181070i
\(333\) −14.7430 11.7916i −0.807910 0.646178i
\(334\) −6.45750 −0.353339
\(335\) 2.19445 0.119895
\(336\) 0.0958811 + 1.72939i 0.00523074 + 0.0943462i
\(337\) 26.4051i 1.43838i 0.694816 + 0.719188i \(0.255486\pi\)
−0.694816 + 0.719188i \(0.744514\pi\)
\(338\) 12.8024 2.25801i 0.696359 0.122819i
\(339\) 17.8110 + 15.9398i 0.967361 + 0.865731i
\(340\) 3.30893 + 3.30893i 0.179452 + 0.179452i
\(341\) 34.7211i 1.88025i
\(342\) 1.69023 + 15.1964i 0.0913971 + 0.821725i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 0.431483 0.431483i 0.0232640 0.0232640i
\(345\) −0.223368 4.02887i −0.0120257 0.216907i
\(346\) −14.5316 + 14.5316i −0.781221 + 0.781221i
\(347\) 10.1701i 0.545960i −0.962020 0.272980i \(-0.911991\pi\)
0.962020 0.272980i \(-0.0880092\pi\)
\(348\) 3.46536 3.87217i 0.185763 0.207570i
\(349\) 0.699211 0.699211i 0.0374279 0.0374279i −0.688145 0.725573i \(-0.741575\pi\)
0.725573 + 0.688145i \(0.241575\pi\)
\(350\) −4.23948 −0.226610
\(351\) −14.9582 + 11.2806i −0.798411 + 0.602112i
\(352\) −3.71958 −0.198254
\(353\) −1.42912 + 1.42912i −0.0760646 + 0.0760646i −0.744116 0.668051i \(-0.767129\pi\)
0.668051 + 0.744116i \(0.267129\pi\)
\(354\) −14.5946 + 16.3079i −0.775694 + 0.866755i
\(355\) 0.0120880i 0.000641562i
\(356\) 8.90085 8.90085i 0.471744 0.471744i
\(357\) 0.514494 + 9.27985i 0.0272299 + 0.491142i
\(358\) 8.86263 8.86263i 0.468404 0.468404i
\(359\) 9.15856 + 9.15856i 0.483370 + 0.483370i 0.906206 0.422836i \(-0.138965\pi\)
−0.422836 + 0.906206i \(0.638965\pi\)
\(360\) −0.289210 2.60020i −0.0152427 0.137043i
\(361\) 6.97627i 0.367172i
\(362\) −9.38608 9.38608i −0.493321 0.493321i
\(363\) 3.65942 + 3.27497i 0.192070 + 0.171891i
\(364\) −3.19813 + 1.66493i −0.167627 + 0.0872661i
\(365\) 13.7365i 0.719001i
\(366\) −0.803322 14.4894i −0.0419903 0.757374i
\(367\) 34.3663 1.79391 0.896953 0.442125i \(-0.145775\pi\)
0.896953 + 0.442125i \(0.145775\pi\)
\(368\) −2.67136 −0.139254
\(369\) −27.9568 22.3602i −1.45537 1.16403i
\(370\) 3.88049 + 3.88049i 0.201737 + 0.201737i
\(371\) 0.328456 + 0.328456i 0.0170526 + 0.0170526i
\(372\) 0.895019 + 16.1433i 0.0464046 + 0.836994i
\(373\) −27.8414 −1.44157 −0.720787 0.693157i \(-0.756219\pi\)
−0.720787 + 0.693157i \(0.756219\pi\)
\(374\) −19.9591 −1.03206
\(375\) 13.9347 0.772567i 0.719584 0.0398952i
\(376\) 4.89332i 0.252354i
\(377\) 10.3166 + 3.25254i 0.531330 + 0.167515i
\(378\) 3.01594 4.23132i 0.155123 0.217636i
\(379\) −0.998941 0.998941i −0.0513121 0.0513121i 0.680985 0.732297i \(-0.261552\pi\)
−0.732297 + 0.680985i \(0.761552\pi\)
\(380\) 4.44472i 0.228009i
\(381\) 27.5363 + 24.6433i 1.41073 + 1.26252i
\(382\) 2.27012 + 2.27012i 0.116149 + 0.116149i
\(383\) −10.4955 + 10.4955i −0.536296 + 0.536296i −0.922439 0.386143i \(-0.873807\pi\)
0.386143 + 0.922439i \(0.373807\pi\)
\(384\) −1.72939 + 0.0958811i −0.0882528 + 0.00489291i
\(385\) −2.29369 + 2.29369i −0.116897 + 0.116897i
\(386\) 22.9678i 1.16903i
\(387\) −1.81941 + 0.202365i −0.0924857 + 0.0102868i
\(388\) −5.41720 + 5.41720i −0.275017 + 0.275017i
\(389\) −24.1159 −1.22273 −0.611363 0.791350i \(-0.709379\pi\)
−0.611363 + 0.791350i \(0.709379\pi\)
\(390\) 4.68410 2.77841i 0.237188 0.140690i
\(391\) −14.3344 −0.724923
\(392\) 0.707107 0.707107i 0.0357143 0.0357143i
\(393\) −10.5368 9.42985i −0.531513 0.475673i
\(394\) 21.0670i 1.06134i
\(395\) 3.77275 3.77275i 0.189827 0.189827i
\(396\) 8.71431 + 6.96983i 0.437911 + 0.350247i
\(397\) 0.284448 0.284448i 0.0142760 0.0142760i −0.699933 0.714209i \(-0.746787\pi\)
0.714209 + 0.699933i \(0.246787\pi\)
\(398\) −10.7226 10.7226i −0.537473 0.537473i
\(399\) 5.88703 6.57812i 0.294720 0.329318i
\(400\) 4.23948i 0.211974i
\(401\) −4.67831 4.67831i −0.233623 0.233623i 0.580580 0.814203i \(-0.302826\pi\)
−0.814203 + 0.580580i \(0.802826\pi\)
\(402\) −2.90655 + 3.24775i −0.144965 + 0.161983i
\(403\) −29.8535 + 15.5416i −1.48711 + 0.774182i
\(404\) 9.74113i 0.484639i
\(405\) −4.19474 + 6.63373i −0.208438 + 0.329633i
\(406\) −3.00014 −0.148894
\(407\) −23.4067 −1.16023
\(408\) −9.27985 + 0.514494i −0.459421 + 0.0254712i
\(409\) −20.7469 20.7469i −1.02587 1.02587i −0.999656 0.0262127i \(-0.991655\pi\)
−0.0262127 0.999656i \(-0.508345\pi\)
\(410\) 7.35850 + 7.35850i 0.363411 + 0.363411i
\(411\) −22.5475 + 1.25008i −1.11218 + 0.0616617i
\(412\) 13.8659 0.683124
\(413\) 12.6353 0.621741
\(414\) 6.25852 + 5.00565i 0.307590 + 0.246014i
\(415\) 4.06899i 0.199739i
\(416\) −1.66493 3.19813i −0.0816299 0.156801i
\(417\) −2.88120 + 3.21943i −0.141093 + 0.157656i
\(418\) 13.4050 + 13.4050i 0.655661 + 0.655661i
\(419\) 19.4610i 0.950732i −0.879788 0.475366i \(-0.842316\pi\)
0.879788 0.475366i \(-0.157684\pi\)
\(420\) −1.00731 + 1.12556i −0.0491517 + 0.0549218i
\(421\) −12.3696 12.3696i −0.602858 0.602858i 0.338212 0.941070i \(-0.390178\pi\)
−0.941070 + 0.338212i \(0.890178\pi\)
\(422\) −1.76660 + 1.76660i −0.0859965 + 0.0859965i
\(423\) 9.16920 11.4642i 0.445822 0.557407i
\(424\) −0.328456 + 0.328456i −0.0159512 + 0.0159512i
\(425\) 22.7488i 1.10348i
\(426\) −0.0178900 0.0160105i −0.000866774 0.000775711i
\(427\) −5.92436 + 5.92436i −0.286700 + 0.286700i
\(428\) −2.77130 −0.133956
\(429\) −5.74745 + 22.5065i −0.277490 + 1.08663i
\(430\) 0.532150 0.0256626
\(431\) 8.30885 8.30885i 0.400223 0.400223i −0.478088 0.878312i \(-0.658670\pi\)
0.878312 + 0.478088i \(0.158670\pi\)
\(432\) 4.23132 + 3.01594i 0.203580 + 0.145105i
\(433\) 9.90076i 0.475800i −0.971290 0.237900i \(-0.923541\pi\)
0.971290 0.237900i \(-0.0764591\pi\)
\(434\) 6.60062 6.60062i 0.316840 0.316840i
\(435\) 4.52471 0.250859i 0.216943 0.0120278i
\(436\) 2.22915 2.22915i 0.106757 0.106757i
\(437\) 9.62734 + 9.62734i 0.460538 + 0.460538i
\(438\) 20.3298 + 18.1940i 0.971397 + 0.869343i
\(439\) 16.7403i 0.798972i 0.916739 + 0.399486i \(0.130811\pi\)
−0.916739 + 0.399486i \(0.869189\pi\)
\(440\) −2.29369 2.29369i −0.109347 0.109347i
\(441\) −2.98161 + 0.331633i −0.141982 + 0.0157920i
\(442\) −8.93394 17.1610i −0.424944 0.816265i
\(443\) 7.56632i 0.359487i 0.983714 + 0.179743i \(0.0575267\pi\)
−0.983714 + 0.179743i \(0.942473\pi\)
\(444\) −10.8828 + 0.603364i −0.516474 + 0.0286344i
\(445\) 10.9775 0.520382
\(446\) −9.38537 −0.444410
\(447\) 1.66943 + 30.1113i 0.0789612 + 1.42421i
\(448\) 0.707107 + 0.707107i 0.0334077 + 0.0334077i
\(449\) 12.1480 + 12.1480i 0.573301 + 0.573301i 0.933049 0.359748i \(-0.117137\pi\)
−0.359748 + 0.933049i \(0.617137\pi\)
\(450\) −7.94402 + 9.93233i −0.374485 + 0.468215i
\(451\) −44.3857 −2.09004
\(452\) 13.7999 0.649091
\(453\) 0.473122 + 8.53365i 0.0222292 + 0.400946i
\(454\) 12.3864i 0.581322i
\(455\) −2.99882 0.945448i −0.140587 0.0443233i
\(456\) 6.57812 + 5.88703i 0.308049 + 0.275685i
\(457\) 17.0229 + 17.0229i 0.796296 + 0.796296i 0.982509 0.186213i \(-0.0596215\pi\)
−0.186213 + 0.982509i \(0.559621\pi\)
\(458\) 6.00307i 0.280505i
\(459\) 22.7051 + 16.1834i 1.05978 + 0.755377i
\(460\) −1.64730 1.64730i −0.0768059 0.0768059i
\(461\) −4.28202 + 4.28202i −0.199434 + 0.199434i −0.799757 0.600324i \(-0.795038\pi\)
0.600324 + 0.799757i \(0.295038\pi\)
\(462\) −0.356638 6.43263i −0.0165923 0.299273i
\(463\) −14.6083 + 14.6083i −0.678904 + 0.678904i −0.959752 0.280848i \(-0.909384\pi\)
0.280848 + 0.959752i \(0.409384\pi\)
\(464\) 3.00014i 0.139278i
\(465\) −9.40292 + 10.5068i −0.436050 + 0.487239i
\(466\) −4.11378 + 4.11378i −0.190567 + 0.190567i
\(467\) 31.2477 1.44597 0.722985 0.690864i \(-0.242770\pi\)
0.722985 + 0.690864i \(0.242770\pi\)
\(468\) −2.09208 + 10.6124i −0.0967064 + 0.490559i
\(469\) 2.51634 0.116194
\(470\) −3.01748 + 3.01748i −0.139186 + 0.139186i
\(471\) 1.05275 1.17633i 0.0485080 0.0542025i
\(472\) 12.6353i 0.581585i
\(473\) −1.60494 + 1.60494i −0.0737951 + 0.0737951i
\(474\) 0.586611 + 10.5806i 0.0269439 + 0.485984i
\(475\) −15.2787 + 15.2787i −0.701034 + 0.701034i
\(476\) 3.79430 + 3.79430i 0.173912 + 0.173912i
\(477\) 1.38498 0.154046i 0.0634138 0.00705326i
\(478\) 8.76067i 0.400704i
\(479\) −10.8416 10.8416i −0.495365 0.495365i 0.414627 0.909992i \(-0.363912\pi\)
−0.909992 + 0.414627i \(0.863912\pi\)
\(480\) −1.12556 1.00731i −0.0513746 0.0459772i
\(481\) −10.4771 20.1253i −0.477716 0.917633i
\(482\) 27.2226i 1.23996i
\(483\) −0.256133 4.61984i −0.0116545 0.210210i
\(484\) 2.83530 0.128877
\(485\) −6.68106 −0.303371
\(486\) −4.26189 14.9945i −0.193323 0.680166i
\(487\) 17.7146 + 17.7146i 0.802727 + 0.802727i 0.983521 0.180794i \(-0.0578669\pi\)
−0.180794 + 0.983521i \(0.557867\pi\)
\(488\) −5.92436 5.92436i −0.268183 0.268183i
\(489\) 1.82788 + 32.9692i 0.0826595 + 1.49092i
\(490\) 0.872079 0.0393965
\(491\) −8.91977 −0.402543 −0.201272 0.979535i \(-0.564507\pi\)
−0.201272 + 0.979535i \(0.564507\pi\)
\(492\) −20.6368 + 1.14415i −0.930380 + 0.0515821i
\(493\) 16.0986i 0.725044i
\(494\) −5.52549 + 17.5260i −0.248603 + 0.788532i
\(495\) 1.07574 + 9.67166i 0.0483509 + 0.434709i
\(496\) 6.60062 + 6.60062i 0.296376 + 0.296376i
\(497\) 0.0138611i 0.000621755i
\(498\) −6.02206 5.38938i −0.269855 0.241504i
\(499\) −20.1012 20.1012i −0.899854 0.899854i 0.0955687 0.995423i \(-0.469533\pi\)
−0.995423 + 0.0955687i \(0.969533\pi\)
\(500\) 5.69755 5.69755i 0.254802 0.254802i
\(501\) 11.1676 0.619153i 0.498930 0.0276617i
\(502\) 15.0281 15.0281i 0.670738 0.670738i
\(503\) 1.38296i 0.0616631i −0.999525 0.0308316i \(-0.990184\pi\)
0.999525 0.0308316i \(-0.00981554\pi\)
\(504\) −0.331633 2.98161i −0.0147721 0.132812i
\(505\) 6.00689 6.00689i 0.267303 0.267303i
\(506\) 9.93636 0.441725
\(507\) −21.9239 + 5.13249i −0.973675 + 0.227942i
\(508\) 21.3350 0.946585
\(509\) 15.7238 15.7238i 0.696947 0.696947i −0.266804 0.963751i \(-0.585968\pi\)
0.963751 + 0.266804i \(0.0859676\pi\)
\(510\) −6.03971 5.40518i −0.267443 0.239346i
\(511\) 15.7514i 0.696803i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −4.38012 26.1185i −0.193387 1.15316i
\(514\) −9.34074 + 9.34074i −0.412002 + 0.412002i
\(515\) 8.55045 + 8.55045i 0.376778 + 0.376778i
\(516\) −0.704833 + 0.787575i −0.0310286 + 0.0346711i
\(517\) 18.2011i 0.800484i
\(518\) 4.44970 + 4.44970i 0.195509 + 0.195509i
\(519\) 23.7375 26.5241i 1.04196 1.16428i
\(520\) 0.945448 2.99882i 0.0414607 0.131507i
\(521\) 24.0452i 1.05344i −0.850039 0.526720i \(-0.823422\pi\)
0.850039 0.526720i \(-0.176578\pi\)
\(522\) −5.62171 + 7.02877i −0.246056 + 0.307641i
\(523\) −11.7120 −0.512132 −0.256066 0.966659i \(-0.582426\pi\)
−0.256066 + 0.966659i \(0.582426\pi\)
\(524\) −8.16389 −0.356641
\(525\) 7.33173 0.406486i 0.319983 0.0177405i
\(526\) 11.1748 + 11.1748i 0.487247 + 0.487247i
\(527\) 35.4186 + 35.4186i 1.54286 + 1.54286i
\(528\) 6.43263 0.356638i 0.279944 0.0155207i
\(529\) −15.8638 −0.689731
\(530\) −0.405086 −0.0175958
\(531\) 23.6762 29.6021i 1.02746 1.28462i
\(532\) 5.09669i 0.220970i
\(533\) −19.8676 38.1632i −0.860561 1.65303i
\(534\) −14.5397 + 16.2465i −0.629193 + 0.703055i
\(535\) −1.70893 1.70893i −0.0738834 0.0738834i
\(536\) 2.51634i 0.108689i
\(537\) −14.4772 + 16.1767i −0.624738 + 0.698078i
\(538\) −5.56149 5.56149i −0.239773 0.239773i
\(539\) −2.63014 + 2.63014i −0.113288 + 0.113288i
\(540\) 0.749468 + 4.46905i 0.0322520 + 0.192317i
\(541\) 1.33026 1.33026i 0.0571925 0.0571925i −0.677932 0.735125i \(-0.737124\pi\)
0.735125 + 0.677932i \(0.237124\pi\)
\(542\) 10.2881i 0.441913i
\(543\) 17.1322 + 15.3323i 0.735213 + 0.657972i
\(544\) −3.79430 + 3.79430i −0.162679 + 0.162679i
\(545\) 2.74922 0.117764
\(546\) 5.37119 3.18596i 0.229866 0.136347i
\(547\) −13.7724 −0.588865 −0.294433 0.955672i \(-0.595131\pi\)
−0.294433 + 0.955672i \(0.595131\pi\)
\(548\) −9.21910 + 9.21910i −0.393821 + 0.393821i
\(549\) 2.77852 + 24.9809i 0.118584 + 1.06616i
\(550\) 15.7691i 0.672396i
\(551\) −10.8122 + 10.8122i −0.460615 + 0.460615i
\(552\) 4.61984 0.256133i 0.196634 0.0109018i
\(553\) 4.32615 4.32615i 0.183967 0.183967i
\(554\) 10.7693 + 10.7693i 0.457546 + 0.457546i
\(555\) −7.08297 6.33884i −0.300655 0.269069i
\(556\) 2.49440i 0.105786i
\(557\) −17.7921 17.7921i −0.753876 0.753876i 0.221324 0.975200i \(-0.428962\pi\)
−0.975200 + 0.221324i \(0.928962\pi\)
\(558\) −3.09568 27.8324i −0.131051 1.17824i
\(559\) −2.09833 0.661547i −0.0887497 0.0279805i
\(560\) 0.872079i 0.0368520i
\(561\) 34.5172 1.91370i 1.45732 0.0807965i
\(562\) 28.1024 1.18543
\(563\) 2.64079 0.111296 0.0556480 0.998450i \(-0.482278\pi\)
0.0556480 + 0.998450i \(0.482278\pi\)
\(564\) −0.469177 8.46248i −0.0197559 0.356335i
\(565\) 8.50973 + 8.50973i 0.358007 + 0.358007i
\(566\) 8.44034 + 8.44034i 0.354774 + 0.354774i
\(567\) −4.81005 + 7.60680i −0.202003 + 0.319456i
\(568\) −0.0138611 −0.000581598
\(569\) −1.57360 −0.0659689 −0.0329844 0.999456i \(-0.510501\pi\)
−0.0329844 + 0.999456i \(0.510501\pi\)
\(570\) 0.426164 + 7.68667i 0.0178501 + 0.321959i
\(571\) 13.0500i 0.546126i 0.961996 + 0.273063i \(0.0880367\pi\)
−0.961996 + 0.273063i \(0.911963\pi\)
\(572\) 6.19285 + 11.8957i 0.258936 + 0.497384i
\(573\) −4.14360 3.70827i −0.173101 0.154915i
\(574\) 8.43789 + 8.43789i 0.352191 + 0.352191i
\(575\) 11.3252i 0.472293i
\(576\) 2.98161 0.331633i 0.124234 0.0138180i
\(577\) 30.4816 + 30.4816i 1.26896 + 1.26896i 0.946624 + 0.322340i \(0.104469\pi\)
0.322340 + 0.946624i \(0.395531\pi\)
\(578\) −8.33924 + 8.33924i −0.346867 + 0.346867i
\(579\) −2.20218 39.7204i −0.0915195 1.65072i
\(580\) 1.85004 1.85004i 0.0768188 0.0768188i
\(581\) 4.66586i 0.193572i
\(582\) 8.84907 9.88788i 0.366806 0.409866i
\(583\) 1.22172 1.22172i 0.0505984 0.0505984i
\(584\) 15.7514 0.651799
\(585\) −7.83426 + 5.25408i −0.323907 + 0.217230i
\(586\) −17.0162 −0.702931
\(587\) 8.10578 8.10578i 0.334561 0.334561i −0.519754 0.854316i \(-0.673977\pi\)
0.854316 + 0.519754i \(0.173977\pi\)
\(588\) −1.15507 + 1.29067i −0.0476342 + 0.0532261i
\(589\) 47.5760i 1.96033i
\(590\) −7.79157 + 7.79157i −0.320774 + 0.320774i
\(591\) −2.01992 36.4331i −0.0830886 1.49866i
\(592\) −4.44970 + 4.44970i −0.182882 + 0.182882i
\(593\) 17.6343 + 17.6343i 0.724154 + 0.724154i 0.969449 0.245295i \(-0.0788847\pi\)
−0.245295 + 0.969449i \(0.578885\pi\)
\(594\) −15.7388 11.2180i −0.645769 0.460282i
\(595\) 4.67953i 0.191842i
\(596\) 12.3117 + 12.3117i 0.504309 + 0.504309i
\(597\) 19.5716 + 17.5154i 0.801013 + 0.716859i
\(598\) 4.44764 + 8.54336i 0.181877 + 0.349364i
\(599\) 22.8023i 0.931675i −0.884870 0.465838i \(-0.845753\pi\)
0.884870 0.465838i \(-0.154247\pi\)
\(600\) 0.406486 + 7.33173i 0.0165947 + 0.299317i
\(601\) 10.1241 0.412970 0.206485 0.978450i \(-0.433798\pi\)
0.206485 + 0.978450i \(0.433798\pi\)
\(602\) 0.610209 0.0248703
\(603\) 4.71517 5.89533i 0.192017 0.240076i
\(604\) 3.48920 + 3.48920i 0.141973 + 0.141973i
\(605\) 1.74839 + 1.74839i 0.0710824 + 0.0710824i
\(606\) 0.933990 + 16.8463i 0.0379407 + 0.684332i
\(607\) −30.2863 −1.22928 −0.614642 0.788806i \(-0.710699\pi\)
−0.614642 + 0.788806i \(0.710699\pi\)
\(608\) 5.09669 0.206698
\(609\) 5.18842 0.287656i 0.210245 0.0116564i
\(610\) 7.30655i 0.295833i
\(611\) 15.6494 8.14704i 0.633109 0.329594i
\(612\) 15.9992 1.77952i 0.646729 0.0719330i
\(613\) 15.8557 + 15.8557i 0.640406 + 0.640406i 0.950655 0.310249i \(-0.100412\pi\)
−0.310249 + 0.950655i \(0.600412\pi\)
\(614\) 12.6887i 0.512076i
\(615\) −13.4313 12.0202i −0.541602 0.484702i
\(616\) −2.63014 2.63014i −0.105971 0.105971i
\(617\) −9.52955 + 9.52955i −0.383645 + 0.383645i −0.872414 0.488768i \(-0.837446\pi\)
0.488768 + 0.872414i \(0.337446\pi\)
\(618\) −23.9796 + 1.32948i −0.964602 + 0.0534795i
\(619\) 8.43686 8.43686i 0.339106 0.339106i −0.516925 0.856031i \(-0.672923\pi\)
0.856031 + 0.516925i \(0.172923\pi\)
\(620\) 8.14057i 0.326933i
\(621\) −11.3034 8.05668i −0.453590 0.323303i
\(622\) 19.5373 19.5373i 0.783373 0.783373i
\(623\) 12.5877 0.504316
\(624\) 3.18596 + 5.37119i 0.127541 + 0.215020i
\(625\) −14.1706 −0.566823
\(626\) −10.1050 + 10.1050i −0.403878 + 0.403878i
\(627\) −24.4679 21.8973i −0.977153 0.874494i
\(628\) 0.911415i 0.0363694i
\(629\) −23.8769 + 23.8769i −0.952035 + 0.952035i
\(630\) 1.63412 2.04312i 0.0651048 0.0813999i
\(631\) 6.47280 6.47280i 0.257678 0.257678i −0.566431 0.824109i \(-0.691676\pi\)
0.824109 + 0.566431i \(0.191676\pi\)
\(632\) 4.32615 + 4.32615i 0.172085 + 0.172085i
\(633\) 2.88576 3.22452i 0.114699 0.128163i
\(634\) 3.84155i 0.152568i
\(635\) 13.1563 + 13.1563i 0.522090 + 0.522090i
\(636\) 0.536537 0.599522i 0.0212751 0.0237726i
\(637\) −3.43870 1.08413i −0.136246 0.0429549i
\(638\) 11.1593i 0.441799i
\(639\) 0.0324740 + 0.0259732i 0.00128465 + 0.00102748i
\(640\) −0.872079 −0.0344719
\(641\) −9.04638 −0.357311 −0.178655 0.983912i \(-0.557175\pi\)
−0.178655 + 0.983912i \(0.557175\pi\)
\(642\) 4.79267 0.265715i 0.189151 0.0104869i
\(643\) 21.3385 + 21.3385i 0.841508 + 0.841508i 0.989055 0.147547i \(-0.0471378\pi\)
−0.147547 + 0.989055i \(0.547138\pi\)
\(644\) −1.88894 1.88894i −0.0744347 0.0744347i
\(645\) −0.920298 + 0.0510231i −0.0362367 + 0.00200903i
\(646\) 27.3486 1.07602
\(647\) 23.9618 0.942037 0.471018 0.882123i \(-0.343887\pi\)
0.471018 + 0.882123i \(0.343887\pi\)
\(648\) −7.60680 4.81005i −0.298823 0.188957i
\(649\) 46.9979i 1.84483i
\(650\) −13.5584 + 7.05844i −0.531804 + 0.276855i
\(651\) −10.7822 + 12.0479i −0.422588 + 0.472196i
\(652\) 13.4803 + 13.4803i 0.527929 + 0.527929i
\(653\) 16.8655i 0.659997i 0.943981 + 0.329998i \(0.107048\pi\)
−0.943981 + 0.329998i \(0.892952\pi\)
\(654\) −3.64134 + 4.06881i −0.142388 + 0.159103i
\(655\) −5.03428 5.03428i −0.196706 0.196706i
\(656\) −8.43789 + 8.43789i −0.329444 + 0.329444i
\(657\) −36.9028 29.5154i −1.43971 1.15150i
\(658\) −3.46010 + 3.46010i −0.134889 + 0.134889i
\(659\) 23.3034i 0.907773i −0.891060 0.453886i \(-0.850037\pi\)
0.891060 0.453886i \(-0.149963\pi\)
\(660\) 4.18662 + 3.74678i 0.162964 + 0.145843i
\(661\) −33.0664 + 33.0664i −1.28613 + 1.28613i −0.349019 + 0.937116i \(0.613485\pi\)
−0.937116 + 0.349019i \(0.886515\pi\)
\(662\) 15.0475 0.584837
\(663\) 17.0957 + 28.8215i 0.663943 + 1.11934i
\(664\) −4.66586 −0.181070
\(665\) 3.14289 3.14289i 0.121876 0.121876i
\(666\) 18.7628 2.08691i 0.727044 0.0808660i
\(667\) 8.01445i 0.310321i
\(668\) 4.56615 4.56615i 0.176669 0.176669i
\(669\) 16.2310 0.899879i 0.627527 0.0347913i
\(670\) −1.55171 + 1.55171i −0.0599477 + 0.0599477i
\(671\) 22.0362 + 22.0362i 0.850696 + 0.850696i
\(672\) −1.29067 1.15507i −0.0497885 0.0445577i
\(673\) 27.1641i 1.04710i −0.851996 0.523549i \(-0.824608\pi\)
0.851996 0.523549i \(-0.175392\pi\)
\(674\) −18.6712 18.6712i −0.719188 0.719188i
\(675\) 12.7860 17.9386i 0.492134 0.690457i
\(676\) −7.45601 + 10.6493i −0.286770 + 0.409589i
\(677\) 21.1789i 0.813969i −0.913435 0.406985i \(-0.866580\pi\)
0.913435 0.406985i \(-0.133420\pi\)
\(678\) −23.8654 + 1.32315i −0.916546 + 0.0508151i
\(679\) −7.66107 −0.294005
\(680\) −4.67953 −0.179452
\(681\) 1.18762 + 21.4210i 0.0455097 + 0.820853i
\(682\) −24.5515 24.5515i −0.940127 0.940127i
\(683\) 16.6542 + 16.6542i 0.637256 + 0.637256i 0.949878 0.312622i \(-0.101207\pi\)
−0.312622 + 0.949878i \(0.601207\pi\)
\(684\) −11.9406 9.55028i −0.456561 0.365164i
\(685\) −11.3700 −0.434424
\(686\) 1.00000 0.0381802
\(687\) −0.575581 10.3817i −0.0219598 0.396086i
\(688\) 0.610209i 0.0232640i
\(689\) 1.59730 + 0.503587i 0.0608522 + 0.0191851i
\(690\) 3.00678 + 2.69089i 0.114466 + 0.102441i
\(691\) −12.0327 12.0327i −0.457746 0.457746i 0.440169 0.897915i \(-0.354919\pi\)
−0.897915 + 0.440169i \(0.854919\pi\)
\(692\) 20.5507i 0.781221i
\(693\) 1.23353 + 11.0904i 0.0468581 + 0.421288i
\(694\) 7.19135 + 7.19135i 0.272980 + 0.272980i
\(695\) −1.53818 + 1.53818i −0.0583464 + 0.0583464i
\(696\) 0.287656 + 5.18842i 0.0109036 + 0.196667i
\(697\) −45.2773 + 45.2773i −1.71500 + 1.71500i
\(698\) 0.988833i 0.0374279i
\(699\) 6.71991 7.50878i 0.254170 0.284008i
\(700\) 2.99776 2.99776i 0.113305 0.113305i
\(701\) −46.7003 −1.76385 −0.881923 0.471393i \(-0.843751\pi\)
−0.881923 + 0.471393i \(0.843751\pi\)
\(702\) 2.60050 18.5536i 0.0981496 0.700262i
\(703\) 32.0726 1.20964
\(704\) 2.63014 2.63014i 0.0991272 0.0991272i
\(705\) 4.92909 5.50773i 0.185640 0.207433i
\(706\) 2.02109i 0.0760646i
\(707\) 6.88802 6.88802i 0.259051 0.259051i
\(708\) −1.21148 21.8514i −0.0455303 0.821224i
\(709\) −23.8602 + 23.8602i −0.896089 + 0.896089i −0.995088 0.0989984i \(-0.968436\pi\)
0.0989984 + 0.995088i \(0.468436\pi\)
\(710\) −0.00854747 0.00854747i −0.000320781 0.000320781i
\(711\) −2.02896 18.2418i −0.0760921 0.684122i
\(712\) 12.5877i 0.471744i
\(713\) −17.6326 17.6326i −0.660348 0.660348i
\(714\) −6.92565 6.19805i −0.259186 0.231956i
\(715\) −3.51667 + 11.1543i −0.131516 + 0.417149i
\(716\) 12.5336i 0.468404i
\(717\) 0.839982 + 15.1507i 0.0313697 + 0.565812i
\(718\) −12.9522 −0.483370
\(719\) −18.8987 −0.704802 −0.352401 0.935849i \(-0.614635\pi\)
−0.352401 + 0.935849i \(0.614635\pi\)
\(720\) 2.04312 + 1.63412i 0.0761427 + 0.0609000i
\(721\) 9.80468 + 9.80468i 0.365145 + 0.365145i
\(722\) −4.93297 4.93297i −0.183586 0.183586i
\(723\) −2.61014 47.0787i −0.0970720 1.75088i
\(724\) 13.2739 0.493321
\(725\) −12.7190 −0.472372
\(726\) −4.90335 + 0.271852i −0.181980 + 0.0100894i
\(727\) 9.73860i 0.361185i −0.983558 0.180592i \(-0.942199\pi\)
0.983558 0.180592i \(-0.0578015\pi\)
\(728\) 1.08413 3.43870i 0.0401806 0.127447i
\(729\) 8.80819 + 25.5228i 0.326229 + 0.945291i
\(730\) 9.71317 + 9.71317i 0.359500 + 0.359500i
\(731\) 3.27435i 0.121106i
\(732\) 10.8136 + 9.67753i 0.399682 + 0.357692i
\(733\) 2.79274 + 2.79274i 0.103152 + 0.103152i 0.756799 0.653647i \(-0.226762\pi\)
−0.653647 + 0.756799i \(0.726762\pi\)
\(734\) −24.3006 + 24.3006i −0.896953 + 0.896953i
\(735\) −1.50817 + 0.0836158i −0.0556296 + 0.00308422i
\(736\) 1.88894 1.88894i 0.0696272 0.0696272i
\(737\) 9.35974i 0.344770i
\(738\) 35.5795 3.95736i 1.30970 0.145673i
\(739\) −4.29662 + 4.29662i −0.158054 + 0.158054i −0.781704 0.623650i \(-0.785649\pi\)
0.623650 + 0.781704i \(0.285649\pi\)
\(740\) −5.48784 −0.201737
\(741\) 7.87534 30.8392i 0.289308 1.13290i
\(742\) −0.464507 −0.0170526
\(743\) −26.3150 + 26.3150i −0.965406 + 0.965406i −0.999421 0.0340158i \(-0.989170\pi\)
0.0340158 + 0.999421i \(0.489170\pi\)
\(744\) −12.0479 10.7822i −0.441699 0.395295i
\(745\) 15.1841i 0.556304i
\(746\) 19.6868 19.6868i 0.720787 0.720787i
\(747\) 10.9313 + 8.74297i 0.399954 + 0.319889i
\(748\) 14.1132 14.1132i 0.516031 0.516031i
\(749\) −1.95960 1.95960i −0.0716023 0.0716023i
\(750\) −9.30703 + 10.3996i −0.339845 + 0.379740i
\(751\) 39.0092i 1.42347i 0.702450 + 0.711733i \(0.252090\pi\)
−0.702450 + 0.711733i \(0.747910\pi\)
\(752\) −3.46010 3.46010i −0.126177 0.126177i
\(753\) −24.5487 + 27.4305i −0.894603 + 0.999623i
\(754\) −9.59481 + 4.99502i −0.349422 + 0.181908i
\(755\) 4.30325i 0.156611i
\(756\) 0.859404 + 5.12459i 0.0312562 + 0.186380i
\(757\) −25.7810 −0.937025 −0.468513 0.883457i \(-0.655210\pi\)
−0.468513 + 0.883457i \(0.655210\pi\)
\(758\) 1.41272 0.0513121
\(759\) −17.1839 + 0.952709i −0.623736 + 0.0345812i
\(760\) 3.14289 + 3.14289i 0.114005 + 0.114005i
\(761\) −16.8635 16.8635i −0.611300 0.611300i 0.331985 0.943285i \(-0.392282\pi\)
−0.943285 + 0.331985i \(0.892282\pi\)
\(762\) −36.8966 + 2.04562i −1.33662 + 0.0741049i
\(763\) 3.15249 0.114128
\(764\) −3.21043 −0.116149
\(765\) 10.9633 + 8.76860i 0.396379 + 0.317029i
\(766\) 14.8429i 0.536296i
\(767\) 40.4092 21.0368i 1.45909 0.759596i
\(768\) 1.15507 1.29067i 0.0416800 0.0465729i
\(769\) −29.5659 29.5659i −1.06617 1.06617i −0.997649 0.0685256i \(-0.978171\pi\)
−0.0685256 0.997649i \(-0.521829\pi\)
\(770\) 3.24377i 0.116897i
\(771\) 15.2582 17.0494i 0.549512 0.614020i
\(772\) −16.2407 16.2407i −0.584516 0.584516i
\(773\) 16.1450 16.1450i 0.580696 0.580696i −0.354398 0.935095i \(-0.615314\pi\)
0.935095 + 0.354398i \(0.115314\pi\)
\(774\) 1.14342 1.42961i 0.0410994 0.0513862i
\(775\) 27.9832 27.9832i 1.00519 1.00519i
\(776\) 7.66107i