Properties

Label 546.2.bk.b.415.6
Level $546$
Weight $2$
Character 546.415
Analytic conductor $4.360$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(25,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bk (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 415.6
Root \(0.385124 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 546.415
Dual form 546.2.bk.b.25.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.25312 + 1.30084i) q^{5} -1.00000i q^{6} +(-1.49160 - 2.18521i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.25312 + 1.30084i) q^{5} -1.00000i q^{6} +(-1.49160 - 2.18521i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.30084 + 2.25312i) q^{10} +(3.11915 - 1.80084i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.60168 - 0.167055i) q^{13} +(-0.199160 - 2.63824i) q^{14} -2.60168i q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.41647 + 2.45340i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-1.15537 - 0.667055i) q^{19} +2.60168i q^{20} +(-1.14664 + 2.38437i) q^{21} +3.60168 q^{22} +(-1.46789 + 2.54247i) q^{23} +(0.866025 - 0.500000i) q^{24} +(0.884367 + 1.53177i) q^{25} +(3.20267 + 1.65617i) q^{26} +1.00000 q^{27} +(1.14664 - 2.38437i) q^{28} +8.97209 q^{29} +(1.30084 - 2.25312i) q^{30} +(-3.46410 + 2.00000i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.11915 - 1.80084i) q^{33} +2.83294i q^{34} +(-0.518152 - 6.86387i) q^{35} -1.00000 q^{36} +(-0.144674 - 0.0835276i) q^{37} +(-0.667055 - 1.15537i) q^{38} +(-1.94551 - 3.03562i) q^{39} +(-1.30084 + 2.25312i) q^{40} -3.03630i q^{41} +(-2.18521 + 1.49160i) q^{42} +2.33411 q^{43} +(3.11915 + 1.80084i) q^{44} +(-2.25312 + 1.30084i) q^{45} +(-2.54247 + 1.46789i) q^{46} +(-8.43580 - 4.87041i) q^{47} +1.00000 q^{48} +(-2.55026 + 6.51891i) q^{49} +1.76873i q^{50} +(1.41647 - 2.45340i) q^{51} +(1.94551 + 3.03562i) q^{52} +(-1.50000 - 2.59808i) q^{53} +(0.866025 + 0.500000i) q^{54} +9.37041 q^{55} +(2.18521 - 1.49160i) q^{56} +1.33411i q^{57} +(7.77006 + 4.48605i) q^{58} +(-10.0232 + 5.78689i) q^{59} +(2.25312 - 1.30084i) q^{60} +(-2.01815 + 3.49554i) q^{61} -4.00000 q^{62} +(2.63824 - 0.199160i) q^{63} -1.00000 q^{64} +(8.33233 + 4.30881i) q^{65} +(-1.80084 - 3.11915i) q^{66} +(10.1679 - 5.87041i) q^{67} +(-1.41647 + 2.45340i) q^{68} +2.93579 q^{69} +(2.98320 - 6.20336i) q^{70} -5.76873i q^{71} +(-0.866025 - 0.500000i) q^{72} +(-9.93411 + 5.73546i) q^{73} +(-0.0835276 - 0.144674i) q^{74} +(0.884367 - 1.53177i) q^{75} -1.33411i q^{76} +(-8.58773 - 4.12985i) q^{77} +(-0.167055 - 3.60168i) q^{78} +(-3.37041 + 5.83773i) q^{79} +(-2.25312 + 1.30084i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.51815 - 2.62952i) q^{82} -8.10051i q^{83} +(-2.63824 + 0.199160i) q^{84} +7.37041i q^{85} +(2.02140 + 1.16706i) q^{86} +(-4.48605 - 7.77006i) q^{87} +(1.80084 + 3.11915i) q^{88} +(-7.07288 - 4.08353i) q^{89} -2.60168 q^{90} +(-5.73732 - 7.62123i) q^{91} -2.93579 q^{92} +(3.46410 + 2.00000i) q^{93} +(-4.87041 - 8.43580i) q^{94} +(-1.73546 - 3.00591i) q^{95} +(0.866025 + 0.500000i) q^{96} +0.139148i q^{97} +(-5.46804 + 4.37041i) q^{98} +3.60168i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9} + 6 q^{12} + 12 q^{13} - 18 q^{14} - 6 q^{16} + 18 q^{17} + 12 q^{22} - 6 q^{25} + 12 q^{27} + 12 q^{29} + 24 q^{35} - 12 q^{36} - 6 q^{38} - 6 q^{39} + 6 q^{42} + 24 q^{43} + 12 q^{48} - 18 q^{49} + 18 q^{51} + 6 q^{52} - 18 q^{53} + 48 q^{55} - 6 q^{56} + 6 q^{61} - 48 q^{62} - 12 q^{64} - 12 q^{65} - 6 q^{66} - 18 q^{68} - 6 q^{75} - 24 q^{77} + 24 q^{79} - 6 q^{81} - 12 q^{82} - 6 q^{87} + 6 q^{88} - 24 q^{91} + 6 q^{94} + 24 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 2.25312 + 1.30084i 1.00763 + 0.581753i 0.910496 0.413519i \(-0.135700\pi\)
0.0971303 + 0.995272i \(0.469034\pi\)
\(6\) 1.00000i 0.408248i
\(7\) −1.49160 2.18521i −0.563772 0.825931i
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.30084 + 2.25312i 0.411362 + 0.712499i
\(11\) 3.11915 1.80084i 0.940458 0.542974i 0.0503540 0.998731i \(-0.483965\pi\)
0.890104 + 0.455758i \(0.150632\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 3.60168 0.167055i 0.998926 0.0463328i
\(14\) −0.199160 2.63824i −0.0532279 0.705101i
\(15\) 2.60168i 0.671751i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.41647 + 2.45340i 0.343545 + 0.595037i 0.985088 0.172049i \(-0.0550389\pi\)
−0.641543 + 0.767087i \(0.721706\pi\)
\(18\) −0.866025 + 0.500000i −0.204124 + 0.117851i
\(19\) −1.15537 0.667055i −0.265061 0.153033i 0.361580 0.932341i \(-0.382237\pi\)
−0.626641 + 0.779308i \(0.715571\pi\)
\(20\) 2.60168i 0.581753i
\(21\) −1.14664 + 2.38437i −0.250218 + 0.520312i
\(22\) 3.60168 0.767881
\(23\) −1.46789 + 2.54247i −0.306077 + 0.530141i −0.977501 0.210933i \(-0.932350\pi\)
0.671423 + 0.741074i \(0.265683\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 0.884367 + 1.53177i 0.176873 + 0.306354i
\(26\) 3.20267 + 1.65617i 0.628096 + 0.324801i
\(27\) 1.00000 0.192450
\(28\) 1.14664 2.38437i 0.216695 0.450603i
\(29\) 8.97209 1.66608 0.833038 0.553216i \(-0.186600\pi\)
0.833038 + 0.553216i \(0.186600\pi\)
\(30\) 1.30084 2.25312i 0.237500 0.411362i
\(31\) −3.46410 + 2.00000i −0.622171 + 0.359211i −0.777714 0.628619i \(-0.783621\pi\)
0.155543 + 0.987829i \(0.450287\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −3.11915 1.80084i −0.542974 0.313486i
\(34\) 2.83294i 0.485846i
\(35\) −0.518152 6.86387i −0.0875836 1.16021i
\(36\) −1.00000 −0.166667
\(37\) −0.144674 0.0835276i −0.0237843 0.0137319i 0.488061 0.872810i \(-0.337704\pi\)
−0.511845 + 0.859078i \(0.671038\pi\)
\(38\) −0.667055 1.15537i −0.108211 0.187426i
\(39\) −1.94551 3.03562i −0.311531 0.486088i
\(40\) −1.30084 + 2.25312i −0.205681 + 0.356250i
\(41\) 3.03630i 0.474191i −0.971486 0.237095i \(-0.923805\pi\)
0.971486 0.237095i \(-0.0761954\pi\)
\(42\) −2.18521 + 1.49160i −0.337185 + 0.230159i
\(43\) 2.33411 0.355948 0.177974 0.984035i \(-0.443046\pi\)
0.177974 + 0.984035i \(0.443046\pi\)
\(44\) 3.11915 + 1.80084i 0.470229 + 0.271487i
\(45\) −2.25312 + 1.30084i −0.335875 + 0.193918i
\(46\) −2.54247 + 1.46789i −0.374866 + 0.216429i
\(47\) −8.43580 4.87041i −1.23049 0.710423i −0.263357 0.964699i \(-0.584830\pi\)
−0.967132 + 0.254276i \(0.918163\pi\)
\(48\) 1.00000 0.144338
\(49\) −2.55026 + 6.51891i −0.364322 + 0.931273i
\(50\) 1.76873i 0.250137i
\(51\) 1.41647 2.45340i 0.198346 0.343545i
\(52\) 1.94551 + 3.03562i 0.269794 + 0.420964i
\(53\) −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) 9.37041 1.26351
\(56\) 2.18521 1.49160i 0.292011 0.199323i
\(57\) 1.33411i 0.176707i
\(58\) 7.77006 + 4.48605i 1.02026 + 0.589047i
\(59\) −10.0232 + 5.78689i −1.30491 + 0.753388i −0.981241 0.192783i \(-0.938249\pi\)
−0.323666 + 0.946172i \(0.604915\pi\)
\(60\) 2.25312 1.30084i 0.290877 0.167938i
\(61\) −2.01815 + 3.49554i −0.258398 + 0.447558i −0.965813 0.259240i \(-0.916528\pi\)
0.707415 + 0.706798i \(0.249861\pi\)
\(62\) −4.00000 −0.508001
\(63\) 2.63824 0.199160i 0.332388 0.0250919i
\(64\) −1.00000 −0.125000
\(65\) 8.33233 + 4.30881i 1.03350 + 0.534442i
\(66\) −1.80084 3.11915i −0.221668 0.383940i
\(67\) 10.1679 5.87041i 1.24220 0.717185i 0.272659 0.962111i \(-0.412097\pi\)
0.969542 + 0.244926i \(0.0787635\pi\)
\(68\) −1.41647 + 2.45340i −0.171773 + 0.297519i
\(69\) 2.93579 0.353428
\(70\) 2.98320 6.20336i 0.356561 0.741443i
\(71\) 5.76873i 0.684623i −0.939587 0.342311i \(-0.888790\pi\)
0.939587 0.342311i \(-0.111210\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) −9.93411 + 5.73546i −1.16270 + 0.671285i −0.951950 0.306255i \(-0.900924\pi\)
−0.210751 + 0.977540i \(0.567591\pi\)
\(74\) −0.0835276 0.144674i −0.00970988 0.0168180i
\(75\) 0.884367 1.53177i 0.102118 0.176873i
\(76\) 1.33411i 0.153033i
\(77\) −8.58773 4.12985i −0.978662 0.470640i
\(78\) −0.167055 3.60168i −0.0189153 0.407810i
\(79\) −3.37041 + 5.83773i −0.379201 + 0.656796i −0.990946 0.134259i \(-0.957134\pi\)
0.611745 + 0.791055i \(0.290468\pi\)
\(80\) −2.25312 + 1.30084i −0.251906 + 0.145438i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.51815 2.62952i 0.167652 0.290381i
\(83\) 8.10051i 0.889147i −0.895742 0.444573i \(-0.853355\pi\)
0.895742 0.444573i \(-0.146645\pi\)
\(84\) −2.63824 + 0.199160i −0.287856 + 0.0217302i
\(85\) 7.37041i 0.799434i
\(86\) 2.02140 + 1.16706i 0.217973 + 0.125847i
\(87\) −4.48605 7.77006i −0.480955 0.833038i
\(88\) 1.80084 + 3.11915i 0.191970 + 0.332502i
\(89\) −7.07288 4.08353i −0.749723 0.432853i 0.0758705 0.997118i \(-0.475826\pi\)
−0.825594 + 0.564265i \(0.809160\pi\)
\(90\) −2.60168 −0.274241
\(91\) −5.73732 7.62123i −0.601434 0.798922i
\(92\) −2.93579 −0.306077
\(93\) 3.46410 + 2.00000i 0.359211 + 0.207390i
\(94\) −4.87041 8.43580i −0.502345 0.870087i
\(95\) −1.73546 3.00591i −0.178055 0.308400i
\(96\) 0.866025 + 0.500000i 0.0883883 + 0.0510310i
\(97\) 0.139148i 0.0141283i 0.999975 + 0.00706416i \(0.00224861\pi\)
−0.999975 + 0.00706416i \(0.997751\pi\)
\(98\) −5.46804 + 4.37041i −0.552356 + 0.441478i
\(99\) 3.60168i 0.361982i
\(100\) −0.884367 + 1.53177i −0.0884367 + 0.153177i
\(101\) −1.78269 3.08771i −0.177384 0.307238i 0.763600 0.645690i \(-0.223430\pi\)
−0.940984 + 0.338452i \(0.890097\pi\)
\(102\) 2.45340 1.41647i 0.242923 0.140252i
\(103\) −9.53747 + 16.5194i −0.939755 + 1.62770i −0.173827 + 0.984776i \(0.555613\pi\)
−0.765928 + 0.642927i \(0.777720\pi\)
\(104\) 0.167055 + 3.60168i 0.0163811 + 0.353174i
\(105\) −5.68521 + 3.88067i −0.554819 + 0.378714i
\(106\) 3.00000i 0.291386i
\(107\) 4.03630 6.99108i 0.390204 0.675853i −0.602272 0.798291i \(-0.705738\pi\)
0.992476 + 0.122437i \(0.0390711\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −11.1451 + 6.43462i −1.06751 + 0.616325i −0.927499 0.373825i \(-0.878046\pi\)
−0.140007 + 0.990150i \(0.544713\pi\)
\(110\) 8.11502 + 4.68521i 0.773736 + 0.446717i
\(111\) 0.167055i 0.0158562i
\(112\) 2.63824 0.199160i 0.249291 0.0188189i
\(113\) −19.8800 −1.87015 −0.935075 0.354449i \(-0.884668\pi\)
−0.935075 + 0.354449i \(0.884668\pi\)
\(114\) −0.667055 + 1.15537i −0.0624754 + 0.108211i
\(115\) −6.61469 + 3.81899i −0.616823 + 0.356123i
\(116\) 4.48605 + 7.77006i 0.416519 + 0.721432i
\(117\) −1.65617 + 3.20267i −0.153113 + 0.296087i
\(118\) −11.5738 −1.06545
\(119\) 3.24838 6.75478i 0.297779 0.619210i
\(120\) 2.60168 0.237500
\(121\) 0.986046 1.70788i 0.0896406 0.155262i
\(122\) −3.49554 + 2.01815i −0.316471 + 0.182715i
\(123\) −2.62952 + 1.51815i −0.237095 + 0.136887i
\(124\) −3.46410 2.00000i −0.311086 0.179605i
\(125\) 8.40672i 0.751920i
\(126\) 2.38437 + 1.14664i 0.212416 + 0.102151i
\(127\) −10.0386 −0.890785 −0.445392 0.895335i \(-0.646936\pi\)
−0.445392 + 0.895335i \(0.646936\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −1.16706 2.02140i −0.102753 0.177974i
\(130\) 5.06160 + 7.89770i 0.443932 + 0.692674i
\(131\) −4.05562 + 7.02454i −0.354341 + 0.613737i −0.987005 0.160690i \(-0.948628\pi\)
0.632664 + 0.774427i \(0.281962\pi\)
\(132\) 3.60168i 0.313486i
\(133\) 0.265702 + 3.51971i 0.0230393 + 0.305198i
\(134\) 11.7408 1.01425
\(135\) 2.25312 + 1.30084i 0.193918 + 0.111958i
\(136\) −2.45340 + 1.41647i −0.210378 + 0.121462i
\(137\) 4.00934 2.31479i 0.342541 0.197766i −0.318854 0.947804i \(-0.603298\pi\)
0.661395 + 0.750038i \(0.269965\pi\)
\(138\) 2.54247 + 1.46789i 0.216429 + 0.124955i
\(139\) −0.935789 −0.0793726 −0.0396863 0.999212i \(-0.512636\pi\)
−0.0396863 + 0.999212i \(0.512636\pi\)
\(140\) 5.68521 3.88067i 0.480488 0.327976i
\(141\) 9.74083i 0.820326i
\(142\) 2.88437 4.99587i 0.242051 0.419244i
\(143\) 10.9333 7.00712i 0.914290 0.585964i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 20.2152 + 11.6713i 1.67878 + 0.969245i
\(146\) −11.4709 −0.949341
\(147\) 6.92067 1.05087i 0.570807 0.0866741i
\(148\) 0.167055i 0.0137319i
\(149\) 7.04871 + 4.06957i 0.577453 + 0.333392i 0.760120 0.649782i \(-0.225140\pi\)
−0.182668 + 0.983175i \(0.558473\pi\)
\(150\) 1.53177 0.884367i 0.125068 0.0722083i
\(151\) 17.3278 10.0042i 1.41011 0.814130i 0.414716 0.909951i \(-0.363881\pi\)
0.995399 + 0.0958208i \(0.0305476\pi\)
\(152\) 0.667055 1.15537i 0.0541053 0.0937132i
\(153\) −2.83294 −0.229030
\(154\) −5.37227 7.87041i −0.432910 0.634216i
\(155\) −10.4067 −0.835888
\(156\) 1.65617 3.20267i 0.132599 0.256419i
\(157\) −10.6724 18.4852i −0.851752 1.47528i −0.879626 0.475666i \(-0.842207\pi\)
0.0278743 0.999611i \(-0.491126\pi\)
\(158\) −5.83773 + 3.37041i −0.464425 + 0.268136i
\(159\) −1.50000 + 2.59808i −0.118958 + 0.206041i
\(160\) −2.60168 −0.205681
\(161\) 7.74533 0.584693i 0.610418 0.0460803i
\(162\) 1.00000i 0.0785674i
\(163\) −0.890194 0.513954i −0.0697254 0.0402560i 0.464732 0.885451i \(-0.346151\pi\)
−0.534457 + 0.845195i \(0.679484\pi\)
\(164\) 2.62952 1.51815i 0.205331 0.118548i
\(165\) −4.68521 8.11502i −0.364743 0.631753i
\(166\) 4.05026 7.01525i 0.314361 0.544489i
\(167\) 5.96976i 0.461954i −0.972959 0.230977i \(-0.925808\pi\)
0.972959 0.230977i \(-0.0741922\pi\)
\(168\) −2.38437 1.14664i −0.183958 0.0884655i
\(169\) 12.9442 1.20336i 0.995707 0.0925660i
\(170\) −3.68521 + 6.38297i −0.282642 + 0.489551i
\(171\) 1.15537 0.667055i 0.0883536 0.0510110i
\(172\) 1.16706 + 2.02140i 0.0889871 + 0.154130i
\(173\) 8.29108 14.3606i 0.630359 1.09181i −0.357119 0.934059i \(-0.616241\pi\)
0.987478 0.157756i \(-0.0504258\pi\)
\(174\) 8.97209i 0.680173i
\(175\) 2.02811 4.21731i 0.153311 0.318799i
\(176\) 3.60168i 0.271487i
\(177\) 10.0232 + 5.78689i 0.753388 + 0.434969i
\(178\) −4.08353 7.07288i −0.306073 0.530135i
\(179\) 9.37041 + 16.2300i 0.700378 + 1.21309i 0.968334 + 0.249659i \(0.0803184\pi\)
−0.267956 + 0.963431i \(0.586348\pi\)
\(180\) −2.25312 1.30084i −0.167938 0.0969589i
\(181\) −0.426228 −0.0316813 −0.0158406 0.999875i \(-0.505042\pi\)
−0.0158406 + 0.999875i \(0.505042\pi\)
\(182\) −1.15804 9.46884i −0.0858400 0.701877i
\(183\) 4.03630 0.298372
\(184\) −2.54247 1.46789i −0.187433 0.108215i
\(185\) −0.217312 0.376395i −0.0159771 0.0276731i
\(186\) 2.00000 + 3.46410i 0.146647 + 0.254000i
\(187\) 8.83637 + 5.10168i 0.646179 + 0.373072i
\(188\) 9.74083i 0.710423i
\(189\) −1.49160 2.18521i −0.108498 0.158950i
\(190\) 3.47093i 0.251808i
\(191\) 4.43462 7.68099i 0.320878 0.555777i −0.659791 0.751449i \(-0.729355\pi\)
0.980669 + 0.195672i \(0.0626887\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −6.06945 + 3.50420i −0.436888 + 0.252238i −0.702277 0.711904i \(-0.747833\pi\)
0.265388 + 0.964142i \(0.414500\pi\)
\(194\) −0.0695739 + 0.120505i −0.00499511 + 0.00865179i
\(195\) −0.434624 9.37041i −0.0311241 0.671029i
\(196\) −6.92067 + 1.05087i −0.494334 + 0.0750620i
\(197\) 17.8050i 1.26856i 0.773105 + 0.634278i \(0.218703\pi\)
−0.773105 + 0.634278i \(0.781297\pi\)
\(198\) −1.80084 + 3.11915i −0.127980 + 0.221668i
\(199\) 13.5545 + 23.4770i 0.960850 + 1.66424i 0.720374 + 0.693585i \(0.243970\pi\)
0.240475 + 0.970655i \(0.422697\pi\)
\(200\) −1.53177 + 0.884367i −0.108312 + 0.0625342i
\(201\) −10.1679 5.87041i −0.717185 0.414067i
\(202\) 3.56538i 0.250859i
\(203\) −13.3828 19.6059i −0.939287 1.37606i
\(204\) 2.83294 0.198346
\(205\) 3.94974 6.84116i 0.275862 0.477807i
\(206\) −16.5194 + 9.53747i −1.15096 + 0.664507i
\(207\) −1.46789 2.54247i −0.102026 0.176714i
\(208\) −1.65617 + 3.20267i −0.114834 + 0.222065i
\(209\) −4.80504 −0.332371
\(210\) −6.86387 + 0.518152i −0.473652 + 0.0357559i
\(211\) 22.6743 1.56096 0.780481 0.625179i \(-0.214974\pi\)
0.780481 + 0.625179i \(0.214974\pi\)
\(212\) 1.50000 2.59808i 0.103020 0.178437i
\(213\) −4.99587 + 2.88437i −0.342311 + 0.197634i
\(214\) 6.99108 4.03630i 0.477901 0.275916i
\(215\) 5.25903 + 3.03630i 0.358663 + 0.207074i
\(216\) 1.00000i 0.0680414i
\(217\) 9.53747 + 4.58658i 0.647446 + 0.311357i
\(218\) −12.8692 −0.871615
\(219\) 9.93411 + 5.73546i 0.671285 + 0.387567i
\(220\) 4.68521 + 8.11502i 0.315877 + 0.547114i
\(221\) 5.51153 + 8.59974i 0.370746 + 0.578481i
\(222\) −0.0835276 + 0.144674i −0.00560600 + 0.00970988i
\(223\) 9.19496i 0.615740i 0.951428 + 0.307870i \(0.0996162\pi\)
−0.951428 + 0.307870i \(0.900384\pi\)
\(224\) 2.38437 + 1.14664i 0.159312 + 0.0766134i
\(225\) −1.76873 −0.117916
\(226\) −17.2166 9.93999i −1.14523 0.661198i
\(227\) −11.7238 + 6.76873i −0.778135 + 0.449257i −0.835769 0.549081i \(-0.814978\pi\)
0.0576337 + 0.998338i \(0.481644\pi\)
\(228\) −1.15537 + 0.667055i −0.0765165 + 0.0441768i
\(229\) 15.9407 + 9.20336i 1.05339 + 0.608175i 0.923597 0.383366i \(-0.125235\pi\)
0.129794 + 0.991541i \(0.458569\pi\)
\(230\) −7.63798 −0.503634
\(231\) 0.717312 + 9.50211i 0.0471957 + 0.625193i
\(232\) 8.97209i 0.589047i
\(233\) 5.86505 10.1586i 0.384232 0.665510i −0.607430 0.794373i \(-0.707800\pi\)
0.991662 + 0.128863i \(0.0411329\pi\)
\(234\) −3.03562 + 1.94551i −0.198445 + 0.127182i
\(235\) −12.6713 21.9473i −0.826581 1.43168i
\(236\) −10.0232 5.78689i −0.652453 0.376694i
\(237\) 6.74083 0.437864
\(238\) 6.19057 4.22562i 0.401275 0.273906i
\(239\) 11.1731i 0.722729i 0.932425 + 0.361365i \(0.117689\pi\)
−0.932425 + 0.361365i \(0.882311\pi\)
\(240\) 2.25312 + 1.30084i 0.145438 + 0.0839688i
\(241\) −12.7659 + 7.37041i −0.822326 + 0.474770i −0.851218 0.524812i \(-0.824135\pi\)
0.0288920 + 0.999583i \(0.490802\pi\)
\(242\) 1.70788 0.986046i 0.109787 0.0633855i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −4.03630 −0.258398
\(245\) −14.2261 + 11.3704i −0.908872 + 0.726429i
\(246\) −3.03630 −0.193588
\(247\) −4.27272 2.20951i −0.271867 0.140588i
\(248\) −2.00000 3.46410i −0.127000 0.219971i
\(249\) −7.01525 + 4.05026i −0.444573 + 0.256675i
\(250\) 4.20336 7.28043i 0.265844 0.460455i
\(251\) 22.9465 1.44837 0.724186 0.689605i \(-0.242216\pi\)
0.724186 + 0.689605i \(0.242216\pi\)
\(252\) 1.49160 + 2.18521i 0.0939620 + 0.137655i
\(253\) 10.5738i 0.664767i
\(254\) −8.69371 5.01932i −0.545492 0.314940i
\(255\) 6.38297 3.68521i 0.399717 0.230777i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0.370413 0.641575i 0.0231058 0.0400203i −0.854241 0.519877i \(-0.825978\pi\)
0.877347 + 0.479856i \(0.159311\pi\)
\(258\) 2.33411i 0.145315i
\(259\) 0.0332708 + 0.440732i 0.00206735 + 0.0273858i
\(260\) 0.434624 + 9.37041i 0.0269542 + 0.581128i
\(261\) −4.48605 + 7.77006i −0.277679 + 0.480955i
\(262\) −7.02454 + 4.05562i −0.433978 + 0.250557i
\(263\) 10.5042 + 18.1938i 0.647717 + 1.12188i 0.983667 + 0.179998i \(0.0576092\pi\)
−0.335950 + 0.941880i \(0.609057\pi\)
\(264\) 1.80084 3.11915i 0.110834 0.191970i
\(265\) 7.80504i 0.479460i
\(266\) −1.52975 + 3.18101i −0.0937950 + 0.195040i
\(267\) 8.16706i 0.499816i
\(268\) 10.1679 + 5.87041i 0.621101 + 0.358593i
\(269\) 15.5587 + 26.9484i 0.948628 + 1.64307i 0.748319 + 0.663339i \(0.230861\pi\)
0.200308 + 0.979733i \(0.435806\pi\)
\(270\) 1.30084 + 2.25312i 0.0791666 + 0.137121i
\(271\) 1.73932 + 1.00420i 0.105656 + 0.0610007i 0.551897 0.833912i \(-0.313904\pi\)
−0.446241 + 0.894913i \(0.647237\pi\)
\(272\) −2.83294 −0.171773
\(273\) −3.73152 + 8.77928i −0.225842 + 0.531346i
\(274\) 4.62959 0.279684
\(275\) 5.51694 + 3.18521i 0.332684 + 0.192075i
\(276\) 1.46789 + 2.54247i 0.0883569 + 0.153039i
\(277\) −7.68404 13.3091i −0.461689 0.799669i 0.537356 0.843356i \(-0.319423\pi\)
−0.999045 + 0.0436862i \(0.986090\pi\)
\(278\) −0.810417 0.467895i −0.0486056 0.0280625i
\(279\) 4.00000i 0.239474i
\(280\) 6.86387 0.518152i 0.410194 0.0309655i
\(281\) 16.6682i 0.994343i −0.867652 0.497171i \(-0.834372\pi\)
0.867652 0.497171i \(-0.165628\pi\)
\(282\) −4.87041 + 8.43580i −0.290029 + 0.502345i
\(283\) −8.90252 15.4196i −0.529200 0.916601i −0.999420 0.0340519i \(-0.989159\pi\)
0.470220 0.882549i \(-0.344174\pi\)
\(284\) 4.99587 2.88437i 0.296450 0.171156i
\(285\) −1.73546 + 3.00591i −0.102800 + 0.178055i
\(286\) 12.9721 0.601679i 0.767056 0.0355780i
\(287\) −6.63495 + 4.52895i −0.391649 + 0.267336i
\(288\) 1.00000i 0.0589256i
\(289\) 4.48721 7.77208i 0.263954 0.457181i
\(290\) 11.6713 + 20.2152i 0.685360 + 1.18708i
\(291\) 0.120505 0.0695739i 0.00706416 0.00407849i
\(292\) −9.93411 5.73546i −0.581350 0.335643i
\(293\) 26.4733i 1.54658i −0.634050 0.773292i \(-0.718609\pi\)
0.634050 0.773292i \(-0.281391\pi\)
\(294\) 6.51891 + 2.55026i 0.380191 + 0.148734i
\(295\) −30.1112 −1.75314
\(296\) 0.0835276 0.144674i 0.00485494 0.00840901i
\(297\) 3.11915 1.80084i 0.180991 0.104495i
\(298\) 4.06957 + 7.04871i 0.235744 + 0.408321i
\(299\) −4.86215 + 9.40237i −0.281186 + 0.543753i
\(300\) 1.76873 0.102118
\(301\) −3.48156 5.10051i −0.200674 0.293989i
\(302\) 20.0084 1.15135
\(303\) −1.78269 + 3.08771i −0.102413 + 0.177384i
\(304\) 1.15537 0.667055i 0.0662652 0.0382582i
\(305\) −9.09428 + 5.25058i −0.520737 + 0.300647i
\(306\) −2.45340 1.41647i −0.140252 0.0809743i
\(307\) 23.2783i 1.32856i 0.747483 + 0.664281i \(0.231262\pi\)
−0.747483 + 0.664281i \(0.768738\pi\)
\(308\) −0.717312 9.50211i −0.0408726 0.541433i
\(309\) 19.0749 1.08514
\(310\) −9.01248 5.20336i −0.511875 0.295531i
\(311\) −8.27293 14.3291i −0.469115 0.812531i 0.530262 0.847834i \(-0.322094\pi\)
−0.999377 + 0.0353031i \(0.988760\pi\)
\(312\) 3.03562 1.94551i 0.171858 0.110143i
\(313\) 5.01395 8.68442i 0.283405 0.490873i −0.688816 0.724936i \(-0.741869\pi\)
0.972221 + 0.234064i \(0.0752025\pi\)
\(314\) 21.3448i 1.20456i
\(315\) 6.20336 + 2.98320i 0.349520 + 0.168084i
\(316\) −6.74083 −0.379201
\(317\) 18.5408 + 10.7045i 1.04135 + 0.601226i 0.920216 0.391410i \(-0.128012\pi\)
0.121137 + 0.992636i \(0.461346\pi\)
\(318\) −2.59808 + 1.50000i −0.145693 + 0.0841158i
\(319\) 27.9853 16.1573i 1.56687 0.904635i
\(320\) −2.25312 1.30084i −0.125953 0.0727191i
\(321\) −8.07261 −0.450569
\(322\) 7.00000 + 3.36631i 0.390095 + 0.187597i
\(323\) 3.77946i 0.210295i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) 3.44110 + 5.36920i 0.190878 + 0.297830i
\(326\) −0.513954 0.890194i −0.0284653 0.0493033i
\(327\) 11.1451 + 6.43462i 0.616325 + 0.355836i
\(328\) 3.03630 0.167652
\(329\) 1.93999 + 25.6987i 0.106955 + 1.41681i
\(330\) 9.37041i 0.515824i
\(331\) −31.0561 17.9302i −1.70700 0.985535i −0.938235 0.345998i \(-0.887540\pi\)
−0.768761 0.639536i \(-0.779126\pi\)
\(332\) 7.01525 4.05026i 0.385012 0.222287i
\(333\) 0.144674 0.0835276i 0.00792809 0.00457728i
\(334\) 2.98488 5.16997i 0.163325 0.282888i
\(335\) 30.5459 1.66890
\(336\) −1.49160 2.18521i −0.0813735 0.119213i
\(337\) 6.73850 0.367069 0.183535 0.983013i \(-0.441246\pi\)
0.183535 + 0.983013i \(0.441246\pi\)
\(338\) 11.8117 + 5.42995i 0.642470 + 0.295351i
\(339\) 9.93999 + 17.2166i 0.539866 + 0.935075i
\(340\) −6.38297 + 3.68521i −0.346165 + 0.199858i
\(341\) −7.20336 + 12.4766i −0.390084 + 0.675645i
\(342\) 1.33411 0.0721404
\(343\) 18.0491 4.15077i 0.974561 0.224121i
\(344\) 2.33411i 0.125847i
\(345\) 6.61469 + 3.81899i 0.356123 + 0.205608i
\(346\) 14.3606 8.29108i 0.772029 0.445731i
\(347\) −17.2869 29.9418i −0.928009 1.60736i −0.786650 0.617400i \(-0.788186\pi\)
−0.141359 0.989958i \(-0.545147\pi\)
\(348\) 4.48605 7.77006i 0.240477 0.416519i
\(349\) 21.7771i 1.16570i 0.812579 + 0.582852i \(0.198063\pi\)
−0.812579 + 0.582852i \(0.801937\pi\)
\(350\) 3.86505 2.63824i 0.206596 0.141020i
\(351\) 3.60168 0.167055i 0.192243 0.00891675i
\(352\) −1.80084 + 3.11915i −0.0959851 + 0.166251i
\(353\) 17.6244 10.1755i 0.938052 0.541585i 0.0487029 0.998813i \(-0.484491\pi\)
0.889349 + 0.457229i \(0.151158\pi\)
\(354\) 5.78689 + 10.0232i 0.307570 + 0.532726i
\(355\) 7.50420 12.9977i 0.398281 0.689844i
\(356\) 8.16706i 0.432853i
\(357\) −7.47400 + 0.564211i −0.395566 + 0.0298612i
\(358\) 18.7408i 0.990483i
\(359\) 1.24040 + 0.716146i 0.0654659 + 0.0377968i 0.532376 0.846508i \(-0.321299\pi\)
−0.466910 + 0.884305i \(0.654633\pi\)
\(360\) −1.30084 2.25312i −0.0685603 0.118750i
\(361\) −8.61007 14.9131i −0.453162 0.784899i
\(362\) −0.369125 0.213114i −0.0194008 0.0112010i
\(363\) −1.97209 −0.103508
\(364\) 3.73152 8.77928i 0.195585 0.460159i
\(365\) −29.8437 −1.56209
\(366\) 3.49554 + 2.01815i 0.182715 + 0.105490i
\(367\) −12.1755 21.0885i −0.635553 1.10081i −0.986398 0.164377i \(-0.947439\pi\)
0.350844 0.936434i \(-0.385895\pi\)
\(368\) −1.46789 2.54247i −0.0765193 0.132535i
\(369\) 2.62952 + 1.51815i 0.136887 + 0.0790318i
\(370\) 0.434624i 0.0225950i
\(371\) −3.43993 + 7.15310i −0.178592 + 0.371371i
\(372\) 4.00000i 0.207390i
\(373\) −15.9763 + 27.6717i −0.827221 + 1.43279i 0.0729891 + 0.997333i \(0.476746\pi\)
−0.900210 + 0.435456i \(0.856587\pi\)
\(374\) 5.10168 + 8.83637i 0.263802 + 0.456918i
\(375\) −7.28043 + 4.20336i −0.375960 + 0.217060i
\(376\) 4.87041 8.43580i 0.251172 0.435043i
\(377\) 32.3146 1.49883i 1.66429 0.0771939i
\(378\) −0.199160 2.63824i −0.0102437 0.135697i
\(379\) 2.79664i 0.143654i −0.997417 0.0718269i \(-0.977117\pi\)
0.997417 0.0718269i \(-0.0228829\pi\)
\(380\) 1.73546 3.00591i 0.0890274 0.154200i
\(381\) 5.01932 + 8.69371i 0.257147 + 0.445392i
\(382\) 7.68099 4.43462i 0.392994 0.226895i
\(383\) 8.52487 + 4.92184i 0.435600 + 0.251494i 0.701730 0.712443i \(-0.252411\pi\)
−0.266129 + 0.963937i \(0.585745\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −13.9769 20.4763i −0.712329 1.04357i
\(386\) −7.00840 −0.356718
\(387\) −1.16706 + 2.02140i −0.0593247 + 0.102753i
\(388\) −0.120505 + 0.0695739i −0.00611774 + 0.00353208i
\(389\) −8.19057 14.1865i −0.415278 0.719283i 0.580179 0.814489i \(-0.302982\pi\)
−0.995458 + 0.0952056i \(0.969649\pi\)
\(390\) 4.30881 8.33233i 0.218185 0.421924i
\(391\) −8.31693 −0.420605
\(392\) −6.51891 2.55026i −0.329255 0.128807i
\(393\) 8.11124 0.409158
\(394\) −8.90252 + 15.4196i −0.448502 + 0.776829i
\(395\) −15.1879 + 8.76873i −0.764186 + 0.441203i
\(396\) −3.11915 + 1.80084i −0.156743 + 0.0904956i
\(397\) −4.71379 2.72151i −0.236579 0.136589i 0.377025 0.926203i \(-0.376947\pi\)
−0.613603 + 0.789615i \(0.710281\pi\)
\(398\) 27.1089i 1.35885i
\(399\) 2.91531 1.98996i 0.145948 0.0996226i
\(400\) −1.76873 −0.0884367
\(401\) 15.2214 + 8.78805i 0.760118 + 0.438854i 0.829338 0.558747i \(-0.188718\pi\)
−0.0692201 + 0.997601i \(0.522051\pi\)
\(402\) −5.87041 10.1679i −0.292790 0.507126i
\(403\) −12.1425 + 7.78205i −0.604860 + 0.387652i
\(404\) 1.78269 3.08771i 0.0886920 0.153619i
\(405\) 2.60168i 0.129278i
\(406\) −1.78689 23.6706i −0.0886817 1.17475i
\(407\) −0.601679 −0.0298241
\(408\) 2.45340 + 1.41647i 0.121462 + 0.0701258i
\(409\) −16.4618 + 9.50420i −0.813981 + 0.469952i −0.848337 0.529457i \(-0.822396\pi\)
0.0343552 + 0.999410i \(0.489062\pi\)
\(410\) 6.84116 3.94974i 0.337861 0.195064i
\(411\) −4.00934 2.31479i −0.197766 0.114180i
\(412\) −19.0749 −0.939755
\(413\) 27.5961 + 13.2710i 1.35792 + 0.653023i
\(414\) 2.93579i 0.144286i
\(415\) 10.5375 18.2514i 0.517264 0.895928i
\(416\) −3.03562 + 1.94551i −0.148833 + 0.0953867i
\(417\) 0.467895 + 0.810417i 0.0229129 + 0.0396863i
\(418\) −4.16128 2.40252i −0.203535 0.117511i
\(419\) 5.48165 0.267796 0.133898 0.990995i \(-0.457250\pi\)
0.133898 + 0.990995i \(0.457250\pi\)
\(420\) −6.20336 2.98320i −0.302693 0.145565i
\(421\) 3.16472i 0.154239i −0.997022 0.0771196i \(-0.975428\pi\)
0.997022 0.0771196i \(-0.0245723\pi\)
\(422\) 19.6365 + 11.3371i 0.955890 + 0.551883i
\(423\) 8.43580 4.87041i 0.410163 0.236808i
\(424\) 2.59808 1.50000i 0.126174 0.0728464i
\(425\) −2.50536 + 4.33942i −0.121528 + 0.210493i
\(426\) −5.76873 −0.279496
\(427\) 10.6488 0.803872i 0.515329 0.0389021i
\(428\) 8.07261 0.390204
\(429\) −11.5350 5.96498i −0.556915 0.287992i
\(430\) 3.03630 + 5.25903i 0.146424 + 0.253613i
\(431\) −13.3688 + 7.71848i −0.643952 + 0.371786i −0.786135 0.618054i \(-0.787921\pi\)
0.142183 + 0.989840i \(0.454588\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 13.9419 0.670003 0.335001 0.942218i \(-0.391263\pi\)
0.335001 + 0.942218i \(0.391263\pi\)
\(434\) 5.96640 + 8.74083i 0.286396 + 0.419573i
\(435\) 23.3425i 1.11919i
\(436\) −11.1451 6.43462i −0.533753 0.308163i
\(437\) 3.39193 1.95833i 0.162258 0.0936798i
\(438\) 5.73546 + 9.93411i 0.274051 + 0.474670i
\(439\) 13.6936 23.7180i 0.653560 1.13200i −0.328693 0.944437i \(-0.606608\pi\)
0.982253 0.187562i \(-0.0600586\pi\)
\(440\) 9.37041i 0.446717i
\(441\) −4.37041 5.46804i −0.208115 0.260383i
\(442\) 0.473258 + 10.2034i 0.0225106 + 0.485324i
\(443\) −12.0556 + 20.8809i −0.572780 + 0.992084i 0.423499 + 0.905896i \(0.360802\pi\)
−0.996279 + 0.0861872i \(0.972532\pi\)
\(444\) −0.144674 + 0.0835276i −0.00686593 + 0.00396404i
\(445\) −10.6240 18.4014i −0.503627 0.872308i
\(446\) −4.59748 + 7.96307i −0.217697 + 0.377062i
\(447\) 8.13915i 0.384968i
\(448\) 1.49160 + 2.18521i 0.0704715 + 0.103241i
\(449\) 2.59095i 0.122275i 0.998129 + 0.0611373i \(0.0194728\pi\)
−0.998129 + 0.0611373i \(0.980527\pi\)
\(450\) −1.53177 0.884367i −0.0722083 0.0416895i
\(451\) −5.46789 9.47067i −0.257473 0.445957i
\(452\) −9.93999 17.2166i −0.467538 0.809799i
\(453\) −17.3278 10.0042i −0.814130 0.470038i
\(454\) −13.5375 −0.635345
\(455\) −3.01286 24.6349i −0.141245 1.15490i
\(456\) −1.33411 −0.0624754
\(457\) −9.06607 5.23430i −0.424093 0.244850i 0.272734 0.962089i \(-0.412072\pi\)
−0.696827 + 0.717239i \(0.745405\pi\)
\(458\) 9.20336 + 15.9407i 0.430045 + 0.744859i
\(459\) 1.41647 + 2.45340i 0.0661153 + 0.114515i
\(460\) −6.61469 3.81899i −0.308411 0.178061i
\(461\) 30.0168i 1.39802i 0.715111 + 0.699011i \(0.246376\pi\)
−0.715111 + 0.699011i \(0.753624\pi\)
\(462\) −4.12985 + 8.58773i −0.192138 + 0.399537i
\(463\) 19.4649i 0.904609i −0.891864 0.452304i \(-0.850602\pi\)
0.891864 0.452304i \(-0.149398\pi\)
\(464\) −4.48605 + 7.77006i −0.208259 + 0.360716i
\(465\) 5.20336 + 9.01248i 0.241300 + 0.417944i
\(466\) 10.1586 5.86505i 0.470586 0.271693i
\(467\) 0.150069 0.259927i 0.00694437 0.0120280i −0.862532 0.506002i \(-0.831123\pi\)
0.869477 + 0.493974i \(0.164456\pi\)
\(468\) −3.60168 + 0.167055i −0.166488 + 0.00772213i
\(469\) −27.9944 13.4626i −1.29266 0.621643i
\(470\) 25.3425i 1.16896i
\(471\) −10.6724 + 18.4852i −0.491759 + 0.851752i
\(472\) −5.78689 10.0232i −0.266363 0.461354i
\(473\) 7.28043 4.20336i 0.334755 0.193271i
\(474\) 5.83773 + 3.37041i 0.268136 + 0.154808i
\(475\) 2.35969i 0.108270i
\(476\) 7.47400 0.564211i 0.342570 0.0258605i
\(477\) 3.00000 0.137361
\(478\) −5.58656 + 9.67621i −0.255523 + 0.442579i
\(479\) 20.4248 11.7922i 0.933232 0.538802i 0.0453996 0.998969i \(-0.485544\pi\)
0.887832 + 0.460167i \(0.152211\pi\)
\(480\) 1.30084 + 2.25312i 0.0593749 + 0.102840i
\(481\) −0.535023 0.276671i −0.0243950 0.0126151i
\(482\) −14.7408 −0.671426
\(483\) −4.37902 6.41531i −0.199253 0.291907i
\(484\) 1.97209 0.0896406
\(485\) −0.181009 + 0.313517i −0.00821919 + 0.0142361i
\(486\) −0.866025 + 0.500000i −0.0392837 + 0.0226805i
\(487\) 29.6544 17.1210i 1.34377 0.775826i 0.356412 0.934329i \(-0.384000\pi\)
0.987359 + 0.158502i \(0.0506666\pi\)
\(488\) −3.49554 2.01815i −0.158236 0.0913574i
\(489\) 1.02791i 0.0464836i
\(490\) −18.0054 + 2.73402i −0.813399 + 0.123510i
\(491\) −39.7553 −1.79413 −0.897065 0.441898i \(-0.854305\pi\)
−0.897065 + 0.441898i \(0.854305\pi\)
\(492\) −2.62952 1.51815i −0.118548 0.0684436i
\(493\) 12.7087 + 22.0122i 0.572372 + 0.991377i
\(494\) −2.59553 4.04985i −0.116778 0.182211i
\(495\) −4.68521 + 8.11502i −0.210584 + 0.364743i
\(496\) 4.00000i 0.179605i
\(497\) −12.6059 + 8.60465i −0.565451 + 0.385971i
\(498\) −8.10051 −0.362993
\(499\) 10.6091 + 6.12519i 0.474931 + 0.274201i 0.718301 0.695732i \(-0.244920\pi\)
−0.243371 + 0.969933i \(0.578253\pi\)
\(500\) 7.28043 4.20336i 0.325591 0.187980i
\(501\) −5.16997 + 2.98488i −0.230977 + 0.133355i
\(502\) 19.8723 + 11.4733i 0.886943 + 0.512077i
\(503\) 2.12842 0.0949016 0.0474508 0.998874i \(-0.484890\pi\)
0.0474508 + 0.998874i \(0.484890\pi\)
\(504\) 0.199160 + 2.63824i 0.00887131 + 0.117517i
\(505\) 9.27596i 0.412775i
\(506\) −5.28689 + 9.15715i −0.235031 + 0.407085i
\(507\) −7.51423 10.6083i −0.333719 0.471132i
\(508\) −5.01932 8.69371i −0.222696 0.385721i
\(509\) 29.1741 + 16.8437i 1.29312 + 0.746583i 0.979206 0.202869i \(-0.0650266\pi\)
0.313913 + 0.949452i \(0.398360\pi\)
\(510\) 7.37041 0.326367
\(511\) 27.3509 + 13.1531i 1.20993 + 0.581858i
\(512\) 1.00000i 0.0441942i
\(513\) −1.15537 0.667055i −0.0510110 0.0294512i
\(514\) 0.641575 0.370413i 0.0282987 0.0163382i
\(515\) −42.9781 + 24.8134i −1.89384 + 1.09341i
\(516\) 1.16706 2.02140i 0.0513767 0.0889871i
\(517\) −35.0833 −1.54296
\(518\) −0.191553 + 0.398321i −0.00841635 + 0.0175012i
\(519\) −16.5822 −0.727876
\(520\) −4.30881 + 8.33233i −0.188954 + 0.365397i
\(521\) 0.130752 + 0.226469i 0.00572835 + 0.00992180i 0.868875 0.495031i \(-0.164843\pi\)
−0.863147 + 0.504953i \(0.831510\pi\)
\(522\) −7.77006 + 4.48605i −0.340086 + 0.196349i
\(523\) −5.23966 + 9.07536i −0.229114 + 0.396838i −0.957546 0.288281i \(-0.906916\pi\)
0.728432 + 0.685119i \(0.240250\pi\)
\(524\) −8.11124 −0.354341
\(525\) −4.66635 + 0.352262i −0.203656 + 0.0153740i
\(526\) 21.0084i 0.916010i
\(527\) −9.81361 5.66589i −0.427488 0.246810i
\(528\) 3.11915 1.80084i 0.135743 0.0783715i
\(529\) 7.19057 + 12.4544i 0.312633 + 0.541497i
\(530\) 3.90252 6.75936i 0.169515 0.293608i
\(531\) 11.5738i 0.502259i
\(532\) −2.91531 + 1.98996i −0.126395 + 0.0862757i
\(533\) −0.507230 10.9358i −0.0219706 0.473682i
\(534\) −4.08353 + 7.07288i −0.176712 + 0.306073i
\(535\) 18.1886 10.5012i 0.786360 0.454005i
\(536\) 5.87041 + 10.1679i 0.253563 + 0.439184i
\(537\) 9.37041 16.2300i 0.404363 0.700378i
\(538\) 31.1173i 1.34156i
\(539\) 3.78489 + 24.9260i 0.163027 + 1.07364i
\(540\) 2.60168i 0.111958i
\(541\) −18.8112 10.8607i −0.808757 0.466936i 0.0377670 0.999287i \(-0.487976\pi\)
−0.846524 + 0.532350i \(0.821309\pi\)
\(542\) 1.00420 + 1.73932i 0.0431340 + 0.0747103i
\(543\) 0.213114 + 0.369125i 0.00914560 + 0.0158406i
\(544\) −2.45340 1.41647i −0.105189 0.0607308i
\(545\) −33.4817 −1.43420
\(546\) −7.62123 + 5.73732i −0.326159 + 0.245534i
\(547\) −33.3593 −1.42634 −0.713170 0.700991i \(-0.752741\pi\)
−0.713170 + 0.700991i \(0.752741\pi\)
\(548\) 4.00934 + 2.31479i 0.171270 + 0.0988831i
\(549\) −2.01815 3.49554i −0.0861326 0.149186i
\(550\) 3.18521 + 5.51694i 0.135818 + 0.235243i
\(551\) −10.3661 5.98488i −0.441611 0.254964i
\(552\) 2.93579i 0.124955i
\(553\) 17.7840 1.34251i 0.756251 0.0570892i
\(554\) 15.3681i 0.652927i
\(555\) −0.217312 + 0.376395i −0.00922438 + 0.0159771i
\(556\) −0.467895 0.810417i −0.0198432 0.0343694i
\(557\) 33.2612 19.2034i 1.40932 0.813672i 0.413999 0.910277i \(-0.364132\pi\)
0.995323 + 0.0966049i \(0.0307983\pi\)
\(558\) 2.00000 3.46410i 0.0846668 0.146647i
\(559\) 8.40672 0.389925i 0.355566 0.0164921i
\(560\) 6.20336 + 2.98320i 0.262140 + 0.126063i
\(561\) 10.2034i 0.430786i
\(562\) 8.33411 14.4351i 0.351553 0.608908i
\(563\) −1.93346 3.34885i −0.0814856 0.141137i 0.822403 0.568906i \(-0.192633\pi\)
−0.903888 + 0.427769i \(0.859300\pi\)
\(564\) −8.43580 + 4.87041i −0.355211 + 0.205081i
\(565\) −44.7920 25.8607i −1.88441 1.08797i
\(566\) 17.8050i 0.748402i
\(567\) −1.14664 + 2.38437i −0.0481545 + 0.100134i
\(568\) 5.76873 0.242051
\(569\) 13.8371 23.9666i 0.580083 1.00473i −0.415386 0.909645i \(-0.636353\pi\)
0.995469 0.0950882i \(-0.0303133\pi\)
\(570\) −3.00591 + 1.73546i −0.125904 + 0.0726906i
\(571\) 20.0470 + 34.7225i 0.838942 + 1.45309i 0.890780 + 0.454435i \(0.150159\pi\)
−0.0518379 + 0.998656i \(0.516508\pi\)
\(572\) 11.5350 + 5.96498i 0.482303 + 0.249408i
\(573\) −8.86925 −0.370518
\(574\) −8.01051 + 0.604711i −0.334352 + 0.0252402i
\(575\) −5.19263 −0.216548
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 0.352227 0.203358i 0.0146634 0.00846592i −0.492650 0.870227i \(-0.663972\pi\)
0.507314 + 0.861761i \(0.330639\pi\)
\(578\) 7.77208 4.48721i 0.323276 0.186643i
\(579\) 6.06945 + 3.50420i 0.252238 + 0.145629i
\(580\) 23.3425i 0.969245i
\(581\) −17.7013 + 12.0827i −0.734374 + 0.501276i
\(582\) 0.139148 0.00576786
\(583\) −9.35744 5.40252i −0.387545 0.223749i
\(584\) −5.73546 9.93411i −0.237335 0.411077i
\(585\) −7.89770 + 5.06160i −0.326530 + 0.209271i
\(586\) 13.2366 22.9265i 0.546800 0.947086i
\(587\) 22.0131i 0.908576i 0.890855 + 0.454288i \(0.150106\pi\)
−0.890855 + 0.454288i \(0.849894\pi\)
\(588\) 4.37041 + 5.46804i 0.180233 + 0.225498i
\(589\) 5.33644 0.219884
\(590\) −26.0771 15.0556i −1.07358 0.619830i
\(591\) 15.4196 8.90252i 0.634278 0.366201i
\(592\) 0.144674 0.0835276i 0.00594607 0.00343296i
\(593\) −27.0080 15.5931i −1.10909 0.640331i −0.170494 0.985359i \(-0.554536\pi\)
−0.938593 + 0.345027i \(0.887870\pi\)
\(594\) 3.60168 0.147779
\(595\) 16.1059 10.9937i 0.660277 0.450698i
\(596\) 8.13915i 0.333392i
\(597\) 13.5545 23.4770i 0.554747 0.960850i
\(598\) −8.91194 + 5.71162i −0.364436 + 0.233565i
\(599\) 3.17009 + 5.49075i 0.129526 + 0.224346i 0.923493 0.383615i \(-0.125321\pi\)
−0.793967 + 0.607961i \(0.791988\pi\)
\(600\) 1.53177 + 0.884367i 0.0625342 + 0.0361041i
\(601\) −23.5566 −0.960893 −0.480447 0.877024i \(-0.659525\pi\)
−0.480447 + 0.877024i \(0.659525\pi\)
\(602\) −0.464862 6.15795i −0.0189464 0.250979i
\(603\) 11.7408i 0.478123i
\(604\) 17.3278 + 10.0042i 0.705057 + 0.407065i
\(605\) 4.44336 2.56538i 0.180648 0.104297i
\(606\) −3.08771 + 1.78269i −0.125429 + 0.0724168i
\(607\) −8.01932 + 13.8899i −0.325494 + 0.563772i −0.981612 0.190886i \(-0.938864\pi\)
0.656118 + 0.754658i \(0.272197\pi\)
\(608\) 1.33411 0.0541053
\(609\) −10.2878 + 21.3928i −0.416883 + 0.866878i
\(610\) −10.5012 −0.425180
\(611\) −31.1967 16.1324i −1.26208 0.652648i
\(612\) −1.41647 2.45340i −0.0572575 0.0991729i
\(613\) −7.37710 + 4.25917i −0.297958 + 0.172026i −0.641525 0.767102i \(-0.721698\pi\)
0.343567 + 0.939128i \(0.388365\pi\)
\(614\) −11.6391 + 20.1596i −0.469718 + 0.813575i
\(615\) −7.89949 −0.318538
\(616\) 4.12985 8.58773i 0.166396 0.346009i
\(617\) 1.40905i 0.0567261i 0.999598 + 0.0283631i \(0.00902945\pi\)
−0.999598 + 0.0283631i \(0.990971\pi\)
\(618\) 16.5194 + 9.53747i 0.664507 + 0.383653i
\(619\) −39.3641 + 22.7269i −1.58218 + 0.913470i −0.587635 + 0.809126i \(0.699941\pi\)
−0.994541 + 0.104344i \(0.966726\pi\)
\(620\) −5.20336 9.01248i −0.208972 0.361950i
\(621\) −1.46789 + 2.54247i −0.0589046 + 0.102026i
\(622\) 16.5459i 0.663429i
\(623\) 1.62655 + 21.5467i 0.0651665 + 0.863250i
\(624\) 3.60168 0.167055i 0.144183 0.00668756i
\(625\) 15.3576 26.6002i 0.614305 1.06401i
\(626\) 8.68442 5.01395i 0.347099 0.200398i
\(627\) 2.40252 + 4.16128i 0.0959474 + 0.166186i
\(628\) 10.6724 18.4852i 0.425876 0.737639i
\(629\) 0.473258i 0.0188700i
\(630\) 3.88067 + 5.68521i 0.154609 + 0.226504i
\(631\) 35.2313i 1.40253i 0.712898 + 0.701267i \(0.247382\pi\)
−0.712898 + 0.701267i \(0.752618\pi\)
\(632\) −5.83773 3.37041i −0.232212 0.134068i
\(633\) −11.3371 19.6365i −0.450611 0.780481i
\(634\) 10.7045 + 18.5408i 0.425131 + 0.736348i
\(635\) −22.6182 13.0587i −0.897578 0.518217i
\(636\) −3.00000 −0.118958
\(637\) −8.09619 + 23.9051i −0.320783 + 0.947153i
\(638\) 32.3146 1.27935
\(639\) 4.99587 + 2.88437i 0.197634 + 0.114104i
\(640\) −1.30084 2.25312i −0.0514202 0.0890624i
\(641\) −11.1168 19.2549i −0.439087 0.760521i 0.558532 0.829483i \(-0.311365\pi\)
−0.997619 + 0.0689616i \(0.978031\pi\)
\(642\) −6.99108 4.03630i −0.275916 0.159300i
\(643\) 3.64031i 0.143560i −0.997420 0.0717800i \(-0.977132\pi\)
0.997420 0.0717800i \(-0.0228679\pi\)
\(644\) 4.37902 + 6.41531i 0.172558 + 0.252799i
\(645\) 6.07261i 0.239109i
\(646\) 1.88973 3.27311i 0.0743505 0.128779i
\(647\) −7.02791 12.1727i −0.276296 0.478558i 0.694166 0.719815i \(-0.255774\pi\)
−0.970461 + 0.241257i \(0.922440\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −20.8425 + 36.1003i −0.818140 + 1.41706i
\(650\) 0.295476 + 6.37041i 0.0115895 + 0.249868i
\(651\) −0.796642 10.5530i −0.0312229 0.413604i
\(652\) 1.02791i 0.0402560i
\(653\) 8.62403 14.9373i 0.337484 0.584540i −0.646475 0.762936i \(-0.723757\pi\)
0.983959 + 0.178396i \(0.0570907\pi\)
\(654\) 6.43462 + 11.1451i 0.251614 + 0.435808i
\(655\) −18.2756 + 10.5514i −0.714087 + 0.412278i
\(656\) 2.62952 + 1.51815i 0.102665 + 0.0592739i
\(657\) 11.4709i 0.447523i
\(658\) −11.1693 + 23.2257i −0.435423 + 0.905432i
\(659\) −21.6999 −0.845307 −0.422653 0.906291i \(-0.638901\pi\)
−0.422653 + 0.906291i \(0.638901\pi\)
\(660\) 4.68521 8.11502i 0.182371 0.315877i
\(661\) 20.0758 11.5908i 0.780857 0.450828i −0.0558767 0.998438i \(-0.517795\pi\)
0.836734 + 0.547609i \(0.184462\pi\)
\(662\) −17.9302 31.0561i −0.696878 1.20703i
\(663\) 4.69183 9.07300i 0.182215 0.352366i
\(664\) 8.10051 0.314361
\(665\) −3.97992 + 8.27596i −0.154335 + 0.320928i
\(666\) 0.167055 0.00647326
\(667\) −13.1701 + 22.8113i −0.509948 + 0.883256i
\(668\) 5.16997 2.98488i 0.200032 0.115489i
\(669\) 7.96307 4.59748i 0.307870 0.177749i
\(670\) 26.4535 + 15.2729i 1.02199 + 0.590045i
\(671\) 14.5375i 0.561213i
\(672\) −0.199160 2.63824i −0.00768278 0.101772i
\(673\) 7.56538 0.291624 0.145812 0.989312i \(-0.453421\pi\)
0.145812 + 0.989312i \(0.453421\pi\)
\(674\) 5.83571 + 3.36925i 0.224783 + 0.129779i
\(675\) 0.884367 + 1.53177i 0.0340393 + 0.0589578i
\(676\) 7.51423 + 10.6083i 0.289009 + 0.408012i
\(677\) 10.4581 18.1140i 0.401939 0.696179i −0.592021 0.805923i \(-0.701670\pi\)
0.993960 + 0.109744i \(0.0350031\pi\)
\(678\) 19.8800i 0.763486i
\(679\) 0.304067 0.207553i 0.0116690 0.00796515i
\(680\) −7.37041 −0.282642
\(681\) 11.7238 + 6.76873i 0.449257 + 0.259378i
\(682\) −12.4766 + 7.20336i −0.477753 + 0.275831i
\(683\) −17.0981 + 9.87158i −0.654240 + 0.377725i −0.790079 0.613005i \(-0.789960\pi\)
0.135839 + 0.990731i \(0.456627\pi\)
\(684\) 1.15537 + 0.667055i 0.0441768 + 0.0255055i
\(685\) 12.0447 0.460204
\(686\) 17.7064 + 5.42989i 0.676033 + 0.207314i
\(687\) 18.4067i 0.702260i
\(688\) −1.16706 + 2.02140i −0.0444936 + 0.0770651i
\(689\) −5.83654 9.10685i −0.222354 0.346944i
\(690\) 3.81899 + 6.61469i 0.145387 + 0.251817i
\(691\) −23.4013 13.5107i −0.890226 0.513972i −0.0162096 0.999869i \(-0.505160\pi\)
−0.874016 + 0.485896i \(0.838493\pi\)
\(692\) 16.5822 0.630359
\(693\) 7.87041 5.37227i 0.298972 0.204076i
\(694\) 34.5738i 1.31240i
\(695\) −2.10845 1.21731i −0.0799779 0.0461753i
\(696\) 7.77006 4.48605i 0.294523 0.170043i
\(697\) 7.44927 4.30084i 0.282161 0.162906i
\(698\) −10.8886 + 18.8595i −0.412138 + 0.713844i
\(699\) −11.7301 −0.443673
\(700\) 4.66635 0.352262i 0.176372 0.0133142i
\(701\) 46.3956 1.75234 0.876169 0.482004i \(-0.160091\pi\)
0.876169 + 0.482004i \(0.160091\pi\)
\(702\) 3.20267 + 1.65617i 0.120877 + 0.0625079i
\(703\) 0.111435 + 0.193011i 0.00420285 + 0.00727955i
\(704\) −3.11915 + 1.80084i −0.117557 + 0.0678717i
\(705\) −12.6713 + 21.9473i −0.477227 + 0.826581i
\(706\) 20.3509 0.765916
\(707\) −4.08822 + 8.50117i −0.153753 + 0.319719i
\(708\) 11.5738i 0.434969i
\(709\) −35.7795 20.6573i −1.34373 0.775801i −0.356375 0.934343i \(-0.615987\pi\)
−0.987352 + 0.158542i \(0.949321\pi\)
\(710\) 12.9977 7.50420i 0.487793 0.281628i
\(711\) −3.37041 5.83773i −0.126400 0.218932i
\(712\) 4.08353 7.07288i 0.153037 0.265067i
\(713\) 11.7432i 0.439785i
\(714\) −6.75478 3.24838i −0.252791 0.121568i
\(715\) 33.7492 1.56538i 1.26215 0.0585417i
\(716\) −9.37041 + 16.2300i −0.350189 + 0.606545i
\(717\) 9.67621 5.58656i 0.361365 0.208634i
\(718\) 0.716146 + 1.24040i 0.0267263 + 0.0462914i
\(719\) 14.9721 25.9324i 0.558365 0.967116i −0.439268 0.898356i \(-0.644762\pi\)
0.997633 0.0687604i \(-0.0219044\pi\)
\(720\) 2.60168i 0.0969589i
\(721\) 50.3244 3.79897i 1.87418 0.141481i
\(722\) 17.2201i 0.640868i
\(723\) 12.7659 + 7.37041i 0.474770 + 0.274109i
\(724\) −0.213114 0.369125i −0.00792032 0.0137184i
\(725\) 7.93462 + 13.7432i 0.294685 + 0.510409i
\(726\) −1.70788 0.986046i −0.0633855 0.0365956i
\(727\) 22.8860 0.848796 0.424398 0.905476i \(-0.360486\pi\)
0.424398 + 0.905476i \(0.360486\pi\)
\(728\) 7.62123 5.73732i 0.282462 0.212639i
\(729\) 1.00000 0.0370370
\(730\) −25.8454 14.9218i −0.956580 0.552282i
\(731\) 3.30620 + 5.72651i 0.122284 + 0.211803i
\(732\) 2.01815 + 3.49554i 0.0745930 + 0.129199i
\(733\) 33.8210 + 19.5265i 1.24921 + 0.721229i 0.970951 0.239278i \(-0.0769107\pi\)
0.278255 + 0.960507i \(0.410244\pi\)
\(734\) 24.3509i 0.898808i
\(735\) 16.9601 + 6.63495i 0.625583 + 0.244734i
\(736\) 2.93579i 0.108215i
\(737\) 21.1433 36.6213i 0.778825 1.34896i
\(738\) 1.51815 + 2.62952i 0.0558839 + 0.0967938i
\(739\) 42.8282 24.7269i 1.57546 0.909593i 0.579980 0.814631i \(-0.303060\pi\)
0.995481 0.0949620i \(-0.0302729\pi\)
\(740\) 0.217312 0.376395i 0.00798855 0.0138366i
\(741\) 0.222870 + 4.80504i 0.00818734 + 0.176517i
\(742\) −6.55562 + 4.47480i −0.240664 + 0.164275i
\(743\) 0.203358i 0.00746049i 0.999993 + 0.00373025i \(0.00118738\pi\)
−0.999993 + 0.00373025i \(0.998813\pi\)
\(744\) −2.00000 + 3.46410i −0.0733236 + 0.127000i
\(745\) 10.5877 + 18.3385i 0.387904 + 0.671870i
\(746\) −27.6717 + 15.9763i −1.01313 + 0.584934i
\(747\) 7.01525 + 4.05026i 0.256675 + 0.148191i
\(748\) 10.2034i 0.373072i
\(749\) −21.2975 + 1.60774i −0.778194 + 0.0587457i
\(750\) −8.40672 −0.306970
\(751\) 21.4733 37.1928i 0.783570 1.35718i −0.146279 0.989243i \(-0.546730\pi\)
0.929849 0.367940i \(-0.119937\pi\)
\(752\) 8.43580 4.87041i 0.307622 0.177606i
\(753\) −11.4733 19.8723i −0.418109 0.724186i
\(754\) 28.7347 + 14.8593i 1.04646 + 0.541143i
\(755\) 52.0554 1.89449
\(756\) 1.14664 2.38437i 0.0417031 0.0867186i
\(757\) −19.5180 −0.709392 −0.354696 0.934982i \(-0.615416\pi\)
−0.354696 + 0.934982i \(0.615416\pi\)
\(758\) 1.39832 2.42196i 0.0507893 0.0879696i
\(759\) 9.15715 5.28689i 0.332384 0.191902i
\(760\) 3.00591 1.73546i 0.109036 0.0629519i
\(761\) −36.3876 21.0084i −1.31905 0.761554i −0.335474 0.942049i \(-0.608896\pi\)
−0.983576 + 0.180496i \(0.942230\pi\)
\(762\) 10.0386i 0.363661i
\(763\) 30.6850 + 14.7565i 1.11087 + 0.534219i
\(764\) 8.86925 0.320878
\(765\) −6.38297 3.68521i −0.230777 0.133239i
\(766\) 4.92184 + 8.52487i 0.177833 + 0.308016i
\(767\) −35.1336 + 22.5169i −1.26860 + 0.813039i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 51.9502i 1.87337i 0.350168 + 0.936687i \(0.386125\pi\)
−0.350168 + 0.936687i \(0.613875\pi\)
\(770\) −1.86622 24.7214i −0.0672537 0.890899i
\(771\) −0.740827 −0.0266802
\(772\) −6.06945 3.50420i −0.218444 0.126119i
\(773\) 36.4022 21.0168i 1.30929 0.755921i 0.327316 0.944915i \(-0.393856\pi\)
0.981978 + 0.188993i \(0.0605225\pi\)
\(774\) −2.02140 + 1.16706i −0.0726577 + 0.0419489i
\(775\) −6.12708 3.53747i −0.220091 0.127070i
\(776\) −0.139148 −0.00499511
\(777\) 0.365050 0.249180i 0.0130961 0.00893927i
\(778\) 16.3811i 0.587292i
\(779\) −2.02538 + 3.50806i −0.0725668 + 0.125689i
\(780\) 7.89770 5.06160i 0.282783 0.181234i
\(781\) −10.3886 17.9935i −0.371732 0.643859i
\(782\) −7.20267 4.15846i −0.257567 0.148706i
\(783\) 8.97209 0.320636
\(784\) −4.37041 5.46804i −0.156086 0.195287i
\(785\) 55.5324i 1.98204i
\(786\) 7.02454 + 4.05562i 0.250557 + 0.144659i
\(787\) −7.61610 + 4.39716i −0.271485 + 0.156742i −0.629562 0.776950i \(-0.716766\pi\)
0.358078 + 0.933692i \(0.383432\pi\)
\(788\) −15.4196 + 8.90252i −0.549301 + 0.317139i
\(789\) 10.5042 18.1938i 0.373959 0.647717i
\(790\) −17.5375 −0.623955
\(791\) 29.6530 + 43.4419i 1.05434 + 1.54461i
\(792\) −3.60168 −0.127980
\(793\) −6.68479 + 12.9270i −0.237384 + 0.459050i
\(794\) −2.72151 4.71379i −0.0965828 0.167286i
\(795\) −6.75936 + 3.90252i −0.239730 + 0.138408i
\(796\) −13.5545 + 23.4770i −0.480425 + 0.832120i
\(797\) −6.25039 −0.221400 −0.110700 0.993854i \(-0.535309\pi\)
−0.110700 + 0.993854i \(0.535309\pi\)
\(798\) 3.51971 0.265702i 0.124596 0.00940575i
\(799\) 27.5952i 0.976249i
\(800\) −1.53177 0.884367i −0.0541562 0.0312671i
\(801\) 7.07288 4.08353i 0.249908 0.144284i
\(802\) 8.78805 + 15.2214i 0.310317 + 0.537485i
\(803\) −20.6573 + 35.7795i −0.728980 + 1.26263i
\(804\) 11.7408i 0.414067i
\(805\) 18.2118 + 8.75805i 0.641880 + 0.308681i
\(806\) −14.4067 + 0.668221i −0.507455 + 0.0235371i
\(807\) 15.5587 26.9484i 0.547691 0.948628i
\(808\) 3.08771 1.78269i 0.108625 0.0627147i
\(809\) 22.9260 + 39.7091i 0.806036 + 1.39610i 0.915589 + 0.402115i \(0.131725\pi\)
−0.109553 + 0.993981i \(0.534942\pi\)
\(810\) 1.30084 2.25312i 0.0457068 0.0791666i
\(811\) 29.5096i 1.03622i 0.855314 + 0.518110i \(0.173364\pi\)
−0.855314 + 0.518110i \(0.826636\pi\)
\(812\) 10.2878 21.3928i 0.361031 0.750739i
\(813\) 2.00840i 0.0704375i
\(814\) −0.521069 0.300840i −0.0182635 0.0105444i
\(815\) −1.33714 2.31600i −0.0468381 0.0811259i
\(816\) 1.41647 + 2.45340i 0.0495865 + 0.0858863i
\(817\) −2.69677 1.55698i −0.0943480 0.0544718i
\(818\) −19.0084 −0.664613
\(819\) 9.46884 1.15804i 0.330868 0.0404653i
\(820\) 7.89949 0.275862
\(821\) 20.9197 + 12.0780i 0.730101 + 0.421524i 0.818459 0.574565i \(-0.194829\pi\)
−0.0883581 + 0.996089i \(0.528162\pi\)
\(822\) −2.31479 4.00934i −0.0807377 0.139842i
\(823\) 15.3511 + 26.5889i 0.535106 + 0.926830i 0.999158 + 0.0410224i \(0.0130615\pi\)
−0.464053 + 0.885808i \(0.653605\pi\)
\(824\) −16.5194 9.53747i −0.575480 0.332253i
\(825\) 6.37041i 0.221789i
\(826\) 17.2634 + 25.2911i 0.600672 + 0.879989i
\(827\) 3.32338i 0.115565i −0.998329 0.0577827i \(-0.981597\pi\)
0.998329 0.0577827i \(-0.0184031\pi\)
\(828\) 1.46789 2.54247i 0.0510129 0.0883569i
\(829\) 14.8232 + 25.6745i 0.514831 + 0.891713i 0.999852 + 0.0172105i \(0.00547853\pi\)
−0.485021 + 0.874502i \(0.661188\pi\)
\(830\) 18.2514 10.5375i 0.633516 0.365761i
\(831\) −7.68404 + 13.3091i −0.266556 + 0.461689i
\(832\) −3.60168 + 0.167055i −0.124866 + 0.00579160i
\(833\) −19.6059 + 2.97705i −0.679303 + 0.103149i
\(834\) 0.935789i 0.0324037i
\(835\) 7.76570 13.4506i 0.268743 0.465477i
\(836\) −2.40252 4.16128i −0.0830928 0.143921i
\(837\) −3.46410 + 2.00000i −0.119737 + 0.0691301i
\(838\) 4.74725 + 2.74083i 0.163991 + 0.0946803i
\(839\) 5.51189i 0.190292i 0.995463 + 0.0951458i \(0.0303317\pi\)
−0.995463 + 0.0951458i \(0.969668\pi\)
\(840\) −3.88067 5.68521i −0.133896 0.196158i
\(841\) 51.4984 1.77581
\(842\) 1.58236 2.74073i 0.0545318 0.0944518i
\(843\) −14.4351 + 8.33411i −0.497171 + 0.287042i
\(844\) 11.3371 + 19.6365i 0.390241 + 0.675916i
\(845\) 30.7302 + 14.1270i 1.05715 + 0.485983i
\(846\) 9.74083 0.334897
\(847\) −5.20286 + 0.392763i −0.178772 + 0.0134955i
\(848\) 3.00000 0.103020
\(849\) −8.90252 + 15.4196i −0.305534 + 0.529200i
\(850\) −4.33942 + 2.50536i −0.148841 + 0.0859333i
\(851\) 0.424732 0.245219i 0.0145596 0.00840601i
\(852\) −4.99587 2.88437i −0.171156 0.0988168i
\(853\) 34.2611i 1.17308i −0.809921 0.586539i \(-0.800490\pi\)
0.809921 0.586539i \(-0.199510\pi\)
\(854\) 9.62403 + 4.62820i 0.329327 + 0.158374i
\(855\) 3.47093 0.118703
\(856\) 6.99108 + 4.03630i 0.238950 + 0.137958i
\(857\) −18.2299 31.5751i −0.622722 1.07859i −0.988977 0.148071i \(-0.952694\pi\)
0.366255 0.930515i \(-0.380640\pi\)
\(858\) −7.00712 10.9333i −0.239219 0.373257i
\(859\) −21.6743 + 37.5410i −0.739517 + 1.28088i 0.213196 + 0.977009i \(0.431613\pi\)
−0.952713 + 0.303872i \(0.901721\pi\)
\(860\) 6.07261i 0.207074i
\(861\) 7.23966 + 3.48156i 0.246727 + 0.118651i
\(862\) −15.4370 −0.525785
\(863\) −11.7907 6.80737i −0.401360 0.231726i 0.285710 0.958316i \(-0.407770\pi\)
−0.687071 + 0.726590i \(0.741104\pi\)
\(864\) −0.866025 + 0.500000i −0.0294628 + 0.0170103i
\(865\) 37.3616 21.5707i 1.27033 0.733427i
\(866\) 12.0740 + 6.97093i 0.410291 + 0.236882i
\(867\) −8.97442 −0.304787
\(868\) 0.796642 + 10.5530i 0.0270398 + 0.358191i
\(869\) 24.2783i 0.823585i
\(870\) 11.6713 20.2152i 0.395693 0.685360i
\(871\) 35.6407 22.8419i 1.20764 0.773970i
\(872\) −6.43462 11.1451i −0.217904 0.377421i
\(873\) −0.120505 0.0695739i −0.00407849 0.00235472i
\(874\) 3.91667 0.132483
\(875\) −18.3704 + 12.5395i −0.621033 + 0.423911i
\(876\) 11.4709i 0.387567i
\(877\) −23.8292 13.7578i −0.804656 0.464568i 0.0404407 0.999182i \(-0.487124\pi\)
−0.845097 + 0.534614i \(0.820457\pi\)
\(878\) 23.7180 13.6936i 0.800444 0.462137i
\(879\) −22.9265 + 13.2366i −0.773292 + 0.446460i
\(880\) −4.68521 + 8.11502i −0.157938 + 0.273557i
\(881\) −22.3341 −0.752455 −0.376228 0.926527i \(-0.622779\pi\)
−0.376228 + 0.926527i \(0.622779\pi\)
\(882\) −1.05087 6.92067i −0.0353846 0.233031i
\(883\) 9.28669 0.312522 0.156261 0.987716i \(-0.450056\pi\)
0.156261 + 0.987716i \(0.450056\pi\)
\(884\) −4.69183 + 9.07300i −0.157803 + 0.305158i
\(885\) 15.0556 + 26.0771i 0.506089 + 0.876572i
\(886\) −20.8809 + 12.0556i −0.701509 + 0.405016i
\(887\) 6.97209 12.0760i 0.234100 0.405473i −0.724911 0.688843i \(-0.758119\pi\)
0.959011 + 0.283370i \(0.0914524\pi\)
\(888\) −0.167055 −0.00560600
\(889\) 14.9736 + 21.9365i 0.502199 + 0.735726i
\(890\) 21.2481i 0.712236i
\(891\) −3.11915 1.80084i −0.104495 0.0603304i
\(892\) −7.96307 + 4.59748i −0.266623 + 0.153935i
\(893\) 6.49767 + 11.2543i 0.217436 + 0.376611i
\(894\) 4.06957 7.04871i 0.136107 0.235744i
\(895\) 48.7576i 1.62979i
\(896\) 0.199160 + 2.63824i 0.00665348 + 0.0881376i
\(897\) 10.5738 0.490439i 0.353048 0.0163753i
\(898\) −1.29548 + 2.24383i −0.0432306 + 0.0748776i
\(899\) −31.0802 + 17.9442i −1.03658 + 0.598472i
\(900\) −0.884367 1.53177i −0.0294789 0.0510590i
\(901\) 4.24942 7.36021i 0.141569 0.245204i
\(902\) 10.9358i 0.364122i
\(903\) −2.67639 + 5.56538i −0.0890648 + 0.185204i
\(904\) 19.8800i 0.661198i
\(905\) −0.960344 0.554455i −0.0319229 0.0184307i
\(906\) −10.0042 17.3278i −0.332367 0.575677i
\(907\) −2.06957 3.58461i −0.0687191 0.119025i 0.829619 0.558330i \(-0.188558\pi\)
−0.898338 + 0.439306i \(0.855225\pi\)
\(908\) −11.7238 6.76873i −0.389068 0.224628i
\(909\) 3.56538 0.118256
\(910\) 9.70823 22.8409i 0.321825 0.757167i
\(911\) 18.5566 0.614807 0.307404 0.951579i \(-0.400540\pi\)
0.307404 + 0.951579i \(0.400540\pi\)
\(912\) −1.15537 0.667055i −0.0382582 0.0220884i
\(913\) −14.5877 25.2667i −0.482783 0.836205i
\(914\) −5.23430 9.06607i −0.173135 0.299879i
\(915\) 9.09428 + 5.25058i 0.300647 + 0.173579i
\(916\) 18.4067i 0.608175i
\(917\) 21.3994 1.61544i 0.706672 0.0533465i
\(918\) 2.83294i 0.0935011i
\(919\) −25.6743 + 44.4692i −0.846917 + 1.46690i 0.0370298 + 0.999314i \(0.488210\pi\)
−0.883946 + 0.467588i \(0.845123\pi\)
\(920\) −3.81899 6.61469i −0.125908 0.218080i
\(921\) 20.1596 11.6391i 0.664281 0.383523i
\(922\) −15.0084 + 25.9953i −0.494275 + 0.856110i
\(923\) −0.963697 20.7771i −0.0317205 0.683888i
\(924\) −7.87041 + 5.37227i −0.258918 + 0.176735i
\(925\) 0.295476i 0.00971520i
\(926\) 9.73243 16.8571i 0.319828 0.553958i
\(927\) −9.53747 16.5194i −0.313252 0.542568i
\(928\) −7.77006 + 4.48605i −0.255065 + 0.147262i
\(929\) 6.01182 + 3.47093i 0.197241 + 0.113877i 0.595368 0.803453i \(-0.297006\pi\)
−0.398127 + 0.917330i \(0.630340\pi\)
\(930\) 10.4067i 0.341250i
\(931\) 7.29497 5.83061i 0.239083 0.191091i
\(932\) 11.7301 0.384232
\(933\) −8.27293 + 14.3291i −0.270844 + 0.469115i
\(934\) 0.259927 0.150069i 0.00850508 0.00491041i
\(935\) 13.2729 + 22.9894i 0.434071 + 0.751834i
\(936\) −3.20267 1.65617i −0.104683 0.0541335i
\(937\) 37.1005 1.21202 0.606010 0.795457i \(-0.292769\pi\)
0.606010 + 0.795457i \(0.292769\pi\)
\(938\) −17.5126 25.6561i −0.571807 0.837702i
\(939\) −10.0279 −0.327248
\(940\) 12.6713 21.9473i 0.413291 0.715840i
\(941\) 7.28447 4.20569i 0.237467 0.137102i −0.376545 0.926398i \(-0.622888\pi\)
0.614012 + 0.789297i \(0.289555\pi\)
\(942\) −18.4852 + 10.6724i −0.602279 + 0.347726i
\(943\) 7.71970 + 4.45697i 0.251388 + 0.145139i
\(944\) 11.5738i 0.376694i
\(945\) −0.518152 6.86387i −0.0168555 0.223282i
\(946\) 8.40672 0.273326
\(947\) 21.7953 + 12.5835i 0.708252 + 0.408910i 0.810414 0.585858i \(-0.199242\pi\)
−0.102161 + 0.994768i \(0.532576\pi\)
\(948\) 3.37041 + 5.83773i 0.109466 + 0.189601i
\(949\) −34.8214 + 22.3168i −1.13035 + 0.724435i
\(950\) 1.17984 2.04355i 0.0382792 0.0663015i
\(951\) 21.4090i 0.694236i
\(952\) 6.75478 + 3.24838i 0.218924 + 0.105281i
\(953\) 35.3681 1.14568 0.572842 0.819666i \(-0.305841\pi\)
0.572842 + 0.819666i \(0.305841\pi\)
\(954\) 2.59808 + 1.50000i 0.0841158 + 0.0485643i
\(955\) 19.9835 11.5375i 0.646650 0.373344i
\(956\) −9.67621 + 5.58656i −0.312951 + 0.180682i
\(957\) −27.9853 16.1573i −0.904635 0.522291i
\(958\) 23.5845 0.761981
\(959\) −11.0386 5.30849i −0.356456 0.171420i
\(960\) 2.60168i 0.0839688i
\(961\) −7.50000 + 12.9904i −0.241935 + 0.419045i
\(962\) −0.325008 0.507116i −0.0104787 0.0163501i
\(963\) 4.03630 + 6.99108i 0.130068 + 0.225284i
\(964\) −12.7659 7.37041i −0.411163 0.237385i
\(965\) −18.2336 −0.586960
\(966\) −0.584693 7.74533i −0.0188122 0.249202i
\(967\) 17.3123i 0.556725i 0.960476 + 0.278362i \(0.0897917\pi\)
−0.960476 + 0.278362i \(0.910208\pi\)
\(968\) 1.70788 + 0.986046i 0.0548934 + 0.0316927i
\(969\) −3.27311 + 1.88973i −0.105147 + 0.0607069i
\(970\) −0.313517 + 0.181009i −0.0100664 + 0.00581185i
\(971\) 26.6959 46.2387i 0.856713 1.48387i −0.0183332 0.999832i \(-0.505836\pi\)
0.875046 0.484039i \(-0.160831\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 1.39582 + 2.04489i 0.0447481 + 0.0655563i
\(974\) 34.2420 1.09718
\(975\) 2.92932 5.66468i 0.0938132 0.181415i
\(976\) −2.01815 3.49554i −0.0645995 0.111890i
\(977\) −28.4656 + 16.4346i −0.910695 + 0.525790i −0.880655 0.473758i \(-0.842897\pi\)
−0.0300405 + 0.999549i \(0.509564\pi\)
\(978\) −0.513954 + 0.890194i −0.0164344 + 0.0284653i
\(979\) −29.4151 −0.940111
\(980\) −16.9601 6.63495i −0.541771 0.211946i
\(981\) 12.8692i 0.410883i
\(982\) −34.4291 19.8776i −1.09868 0.634321i
\(983\) 8.42126 4.86202i 0.268597 0.155074i −0.359653 0.933086i \(-0.617105\pi\)
0.628250 + 0.778012i \(0.283772\pi\)
\(984\) −1.51815 2.62952i −0.0483969 0.0838259i
\(985\) −23.1615 + 40.1169i −0.737987 + 1.27823i
\(986\) 25.4174i 0.809456i
\(987\) 21.2857 14.5294i 0.677532 0.462477i
\(988\) −0.222870 4.80504i −0.00709044 0.152869i
\(989\) −3.42623 + 5.93440i −0.108948 + 0.188703i
\(990\) −8.11502 + 4.68521i −0.257912 + 0.148906i
\(991\) −16.2057 28.0691i −0.514791 0.891644i −0.999853 0.0171639i \(-0.994536\pi\)
0.485062 0.874480i \(-0.338797\pi\)
\(992\) 2.00000 3.46410i 0.0635001 0.109985i
\(993\) 35.8605i 1.13800i
\(994\) −15.2193 + 1.14890i −0.482728 + 0.0364410i
\(995\) 70.5287i 2.23591i
\(996\) −7.01525 4.05026i −0.222287 0.128337i
\(997\) 22.8395 + 39.5591i 0.723333 + 1.25285i 0.959656 + 0.281176i \(0.0907243\pi\)
−0.236323 + 0.971675i \(0.575942\pi\)
\(998\) 6.12519 + 10.6091i 0.193890 + 0.335827i
\(999\) −0.144674 0.0835276i −0.00457728 0.00264270i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 546.2.bk.b.415.6 yes 12
3.2 odd 2 1638.2.dm.c.415.1 12
7.2 even 3 3822.2.c.k.883.1 6
7.4 even 3 inner 546.2.bk.b.25.1 12
7.5 odd 6 3822.2.c.j.883.3 6
13.12 even 2 inner 546.2.bk.b.415.1 yes 12
21.11 odd 6 1638.2.dm.c.1117.6 12
39.38 odd 2 1638.2.dm.c.415.6 12
91.12 odd 6 3822.2.c.j.883.4 6
91.25 even 6 inner 546.2.bk.b.25.6 yes 12
91.51 even 6 3822.2.c.k.883.6 6
273.116 odd 6 1638.2.dm.c.1117.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bk.b.25.1 12 7.4 even 3 inner
546.2.bk.b.25.6 yes 12 91.25 even 6 inner
546.2.bk.b.415.1 yes 12 13.12 even 2 inner
546.2.bk.b.415.6 yes 12 1.1 even 1 trivial
1638.2.dm.c.415.1 12 3.2 odd 2
1638.2.dm.c.415.6 12 39.38 odd 2
1638.2.dm.c.1117.1 12 273.116 odd 6
1638.2.dm.c.1117.6 12 21.11 odd 6
3822.2.c.j.883.3 6 7.5 odd 6
3822.2.c.j.883.4 6 91.12 odd 6
3822.2.c.k.883.1 6 7.2 even 3
3822.2.c.k.883.6 6 91.51 even 6