Properties

Label 29.2.e.a.6.1
Level $29$
Weight $2$
Character 29.6
Analytic conductor $0.232$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [29,2,Mod(4,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 29.e (of order \(14\), degree \(6\), 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: \(0.231566165862\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{14})\)
Coefficient field: 12.0.7877952219361.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3x^{11} + 13x^{9} - 18x^{8} - 14x^{7} + 57x^{6} - 28x^{5} - 72x^{4} + 104x^{3} - 96x + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 6.1
Root \(1.23295 - 0.692694i\) of defining polynomial
Character \(\chi\) \(=\) 29.6
Dual form 29.2.e.a.5.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.909335 - 0.725171i) q^{2} +(0.960118 + 0.219141i) q^{3} +(-0.144024 - 0.631009i) q^{4} +(-1.18424 + 1.48499i) q^{5} +(-0.714155 - 0.895521i) q^{6} +(-0.339509 + 1.48749i) q^{7} +(-1.33591 + 2.77404i) q^{8} +(-1.82910 - 0.880850i) q^{9} +O(q^{10})\) \(q+(-0.909335 - 0.725171i) q^{2} +(0.960118 + 0.219141i) q^{3} +(-0.144024 - 0.631009i) q^{4} +(-1.18424 + 1.48499i) q^{5} +(-0.714155 - 0.895521i) q^{6} +(-0.339509 + 1.48749i) q^{7} +(-1.33591 + 2.77404i) q^{8} +(-1.82910 - 0.880850i) q^{9} +(2.15374 - 0.491577i) q^{10} +(-0.344864 - 0.716117i) q^{11} -0.637405i q^{12} +(5.80531 - 2.79569i) q^{13} +(1.38741 - 1.10642i) q^{14} +(-1.46243 + 1.16625i) q^{15} +(2.06017 - 0.992123i) q^{16} -4.03114i q^{17} +(1.02450 + 2.12740i) q^{18} +(-5.82771 + 1.33014i) q^{19} +(1.10760 + 0.533392i) q^{20} +(-0.651938 + 1.35376i) q^{21} +(-0.205710 + 0.901276i) q^{22} +(3.63046 + 4.55245i) q^{23} +(-1.89054 + 2.37066i) q^{24} +(0.309837 + 1.35748i) q^{25} +(-7.30633 - 1.66762i) q^{26} +(-3.87299 - 3.08860i) q^{27} +0.987516 q^{28} +(0.825172 - 5.32157i) q^{29} +2.17557 q^{30} +(0.493395 + 0.393469i) q^{31} +(3.41068 + 0.778466i) q^{32} +(-0.174180 - 0.763131i) q^{33} +(-2.92326 + 3.66566i) q^{34} +(-1.80684 - 2.26571i) q^{35} +(-0.292390 + 1.28104i) q^{36} +(-1.09871 + 2.28149i) q^{37} +(6.26391 + 3.01654i) q^{38} +(6.18643 - 1.41201i) q^{39} +(-2.53739 - 5.26894i) q^{40} -2.49005i q^{41} +(1.57454 - 0.758258i) q^{42} +(-6.40848 + 5.11059i) q^{43} +(-0.402208 + 0.320750i) q^{44} +(3.47414 - 1.67306i) q^{45} -6.77241i q^{46} +(2.92968 + 6.08354i) q^{47} +(2.19542 - 0.501089i) q^{48} +(4.20943 + 2.02715i) q^{49} +(0.702662 - 1.45909i) q^{50} +(0.883386 - 3.87037i) q^{51} +(-2.60021 - 3.26056i) q^{52} +(-0.429869 + 0.539039i) q^{53} +(1.28208 + 5.61715i) q^{54} +(1.47183 + 0.335935i) q^{55} +(-3.67280 - 2.92896i) q^{56} -5.88677 q^{57} +(-4.60940 + 4.24070i) q^{58} +2.67206 q^{59} +(0.946537 + 0.754838i) q^{60} +(-7.97990 - 1.82136i) q^{61} +(-0.163329 - 0.715591i) q^{62} +(1.93125 - 2.42171i) q^{63} +(-5.38829 - 6.75670i) q^{64} +(-2.72330 + 11.9316i) q^{65} +(-0.395012 + 0.820252i) q^{66} +(3.56216 + 1.71545i) q^{67} +(-2.54369 + 0.580580i) q^{68} +(2.48804 + 5.16647i) q^{69} +3.37055i q^{70} +(-2.81822 + 1.35718i) q^{71} +(4.88703 - 3.89728i) q^{72} +(0.715546 - 0.570629i) q^{73} +(2.65356 - 1.27789i) q^{74} +1.37124i q^{75} +(1.67866 + 3.48576i) q^{76} +(1.18230 - 0.269852i) q^{77} +(-6.64949 - 3.20223i) q^{78} +(5.58981 - 11.6074i) q^{79} +(-0.966435 + 4.23423i) q^{80} +(0.755651 + 0.947556i) q^{81} +(-1.80571 + 2.26429i) q^{82} +(-2.80913 - 12.3076i) q^{83} +(0.948131 + 0.216405i) q^{84} +(5.98619 + 4.77383i) q^{85} +9.53350 q^{86} +(1.95843 - 4.92850i) q^{87} +2.44725 q^{88} +(-1.43840 - 1.14709i) q^{89} +(-4.37241 - 0.997975i) q^{90} +(2.18760 + 9.58449i) q^{91} +(2.34977 - 2.94651i) q^{92} +(0.387492 + 0.485900i) q^{93} +(1.74754 - 7.65649i) q^{94} +(4.92615 - 10.2293i) q^{95} +(3.10406 + 1.49484i) q^{96} +(-0.117603 + 0.0268422i) q^{97} +(-2.35775 - 4.89592i) q^{98} +1.61363i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 7 q^{2} - 7 q^{3} - q^{4} - q^{5} - 3 q^{6} - 11 q^{7} + 14 q^{8} - 3 q^{9} - 7 q^{10} + 7 q^{11} + 9 q^{13} - 7 q^{14} + 7 q^{15} + 9 q^{16} + 42 q^{18} - 7 q^{19} - 11 q^{20} - 7 q^{21} - 4 q^{22} - 5 q^{23} - 25 q^{24} + 13 q^{25} - 21 q^{26} - 7 q^{27} + 12 q^{28} - 15 q^{29} + 2 q^{30} - 21 q^{31} - 17 q^{33} - 13 q^{34} + 19 q^{35} - 40 q^{36} + 7 q^{37} + 28 q^{38} + 21 q^{39} + 35 q^{40} + 50 q^{42} + 7 q^{43} + 42 q^{44} + 16 q^{45} - 7 q^{47} - 14 q^{48} + 13 q^{49} - 28 q^{50} + 20 q^{51} - 6 q^{52} - 10 q^{53} - 38 q^{54} - 35 q^{55} - 21 q^{56} - 14 q^{57} - 57 q^{58} + 44 q^{59} - 28 q^{60} - 7 q^{61} + 37 q^{62} - 13 q^{63} - 26 q^{64} - 6 q^{65} + 21 q^{66} - 37 q^{67} + 14 q^{68} + 21 q^{69} - 21 q^{71} + 35 q^{72} + 14 q^{73} + 7 q^{76} - 7 q^{77} + 17 q^{78} + 49 q^{79} - 6 q^{80} + q^{81} + 22 q^{82} + 5 q^{83} + 21 q^{84} + 14 q^{85} - 44 q^{86} + 15 q^{87} - 66 q^{88} + 7 q^{89} + 28 q^{90} - 3 q^{91} - 6 q^{92} + 19 q^{93} + 66 q^{94} - 7 q^{95} + 30 q^{96} + 14 q^{97} - 42 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.909335 0.725171i −0.642997 0.512773i 0.246837 0.969057i \(-0.420609\pi\)
−0.889834 + 0.456284i \(0.849180\pi\)
\(3\) 0.960118 + 0.219141i 0.554324 + 0.126521i 0.490501 0.871440i \(-0.336814\pi\)
0.0638227 + 0.997961i \(0.479671\pi\)
\(4\) −0.144024 0.631009i −0.0720119 0.315505i
\(5\) −1.18424 + 1.48499i −0.529607 + 0.664106i −0.972618 0.232410i \(-0.925339\pi\)
0.443011 + 0.896516i \(0.353910\pi\)
\(6\) −0.714155 0.895521i −0.291552 0.365595i
\(7\) −0.339509 + 1.48749i −0.128322 + 0.562217i 0.869360 + 0.494179i \(0.164531\pi\)
−0.997683 + 0.0680385i \(0.978326\pi\)
\(8\) −1.33591 + 2.77404i −0.472315 + 0.980773i
\(9\) −1.82910 0.880850i −0.609701 0.293617i
\(10\) 2.15374 0.491577i 0.681072 0.155450i
\(11\) −0.344864 0.716117i −0.103980 0.215918i 0.842487 0.538716i \(-0.181091\pi\)
−0.946468 + 0.322799i \(0.895376\pi\)
\(12\) 0.637405i 0.184003i
\(13\) 5.80531 2.79569i 1.61010 0.775385i 0.610246 0.792212i \(-0.291071\pi\)
0.999858 + 0.0168268i \(0.00535640\pi\)
\(14\) 1.38741 1.10642i 0.370801 0.295704i
\(15\) −1.46243 + 1.16625i −0.377597 + 0.301124i
\(16\) 2.06017 0.992123i 0.515041 0.248031i
\(17\) 4.03114i 0.977695i −0.872369 0.488847i \(-0.837417\pi\)
0.872369 0.488847i \(-0.162583\pi\)
\(18\) 1.02450 + 2.12740i 0.241477 + 0.501433i
\(19\) −5.82771 + 1.33014i −1.33697 + 0.305154i −0.830458 0.557081i \(-0.811921\pi\)
−0.506509 + 0.862235i \(0.669064\pi\)
\(20\) 1.10760 + 0.533392i 0.247667 + 0.119270i
\(21\) −0.651938 + 1.35376i −0.142264 + 0.295415i
\(22\) −0.205710 + 0.901276i −0.0438576 + 0.192153i
\(23\) 3.63046 + 4.55245i 0.757003 + 0.949252i 0.999783 0.0208297i \(-0.00663078\pi\)
−0.242780 + 0.970081i \(0.578059\pi\)
\(24\) −1.89054 + 2.37066i −0.385904 + 0.483908i
\(25\) 0.309837 + 1.35748i 0.0619674 + 0.271497i
\(26\) −7.30633 1.66762i −1.43289 0.327048i
\(27\) −3.87299 3.08860i −0.745357 0.594402i
\(28\) 0.987516 0.186623
\(29\) 0.825172 5.32157i 0.153231 0.988190i
\(30\) 2.17557 0.397202
\(31\) 0.493395 + 0.393469i 0.0886164 + 0.0706692i 0.666796 0.745240i \(-0.267665\pi\)
−0.578180 + 0.815910i \(0.696237\pi\)
\(32\) 3.41068 + 0.778466i 0.602929 + 0.137615i
\(33\) −0.174180 0.763131i −0.0303208 0.132844i
\(34\) −2.92326 + 3.66566i −0.501336 + 0.628655i
\(35\) −1.80684 2.26571i −0.305412 0.382974i
\(36\) −0.292390 + 1.28104i −0.0487317 + 0.213507i
\(37\) −1.09871 + 2.28149i −0.180626 + 0.375075i −0.971548 0.236843i \(-0.923887\pi\)
0.790922 + 0.611918i \(0.209602\pi\)
\(38\) 6.26391 + 3.01654i 1.01614 + 0.489348i
\(39\) 6.18643 1.41201i 0.990622 0.226103i
\(40\) −2.53739 5.26894i −0.401196 0.833092i
\(41\) 2.49005i 0.388881i −0.980914 0.194441i \(-0.937711\pi\)
0.980914 0.194441i \(-0.0622892\pi\)
\(42\) 1.57454 0.758258i 0.242957 0.117002i
\(43\) −6.40848 + 5.11059i −0.977284 + 0.779358i −0.975355 0.220640i \(-0.929185\pi\)
−0.00192838 + 0.999998i \(0.500614\pi\)
\(44\) −0.402208 + 0.320750i −0.0606352 + 0.0483549i
\(45\) 3.47414 1.67306i 0.517895 0.249405i
\(46\) 6.77241i 0.998537i
\(47\) 2.92968 + 6.08354i 0.427338 + 0.887376i 0.997815 + 0.0660626i \(0.0210437\pi\)
−0.570478 + 0.821313i \(0.693242\pi\)
\(48\) 2.19542 0.501089i 0.316881 0.0723260i
\(49\) 4.20943 + 2.02715i 0.601347 + 0.289593i
\(50\) 0.702662 1.45909i 0.0993714 0.206347i
\(51\) 0.883386 3.87037i 0.123699 0.541960i
\(52\) −2.60021 3.26056i −0.360584 0.452158i
\(53\) −0.429869 + 0.539039i −0.0590471 + 0.0740427i −0.810478 0.585769i \(-0.800793\pi\)
0.751431 + 0.659812i \(0.229364\pi\)
\(54\) 1.28208 + 5.61715i 0.174469 + 0.764398i
\(55\) 1.47183 + 0.335935i 0.198461 + 0.0452974i
\(56\) −3.67280 2.92896i −0.490799 0.391399i
\(57\) −5.88677 −0.779722
\(58\) −4.60940 + 4.24070i −0.605244 + 0.556831i
\(59\) 2.67206 0.347873 0.173936 0.984757i \(-0.444351\pi\)
0.173936 + 0.984757i \(0.444351\pi\)
\(60\) 0.946537 + 0.754838i 0.122197 + 0.0974492i
\(61\) −7.97990 1.82136i −1.02172 0.233201i −0.321336 0.946965i \(-0.604132\pi\)
−0.700386 + 0.713764i \(0.746989\pi\)
\(62\) −0.163329 0.715591i −0.0207428 0.0908802i
\(63\) 1.93125 2.42171i 0.243315 0.305107i
\(64\) −5.38829 6.75670i −0.673536 0.844588i
\(65\) −2.72330 + 11.9316i −0.337784 + 1.47993i
\(66\) −0.395012 + 0.820252i −0.0486227 + 0.100966i
\(67\) 3.56216 + 1.71545i 0.435187 + 0.209575i 0.638634 0.769511i \(-0.279500\pi\)
−0.203446 + 0.979086i \(0.565214\pi\)
\(68\) −2.54369 + 0.580580i −0.308467 + 0.0704056i
\(69\) 2.48804 + 5.16647i 0.299525 + 0.621970i
\(70\) 3.37055i 0.402858i
\(71\) −2.81822 + 1.35718i −0.334461 + 0.161068i −0.593575 0.804779i \(-0.702284\pi\)
0.259114 + 0.965847i \(0.416570\pi\)
\(72\) 4.88703 3.89728i 0.575942 0.459299i
\(73\) 0.715546 0.570629i 0.0837483 0.0667870i −0.580721 0.814103i \(-0.697229\pi\)
0.664469 + 0.747316i \(0.268658\pi\)
\(74\) 2.65356 1.27789i 0.308471 0.148552i
\(75\) 1.37124i 0.158337i
\(76\) 1.67866 + 3.48576i 0.192555 + 0.399845i
\(77\) 1.18230 0.269852i 0.134736 0.0307525i
\(78\) −6.64949 3.20223i −0.752907 0.362581i
\(79\) 5.58981 11.6074i 0.628903 1.30593i −0.306340 0.951922i \(-0.599104\pi\)
0.935242 0.354008i \(-0.115181\pi\)
\(80\) −0.966435 + 4.23423i −0.108051 + 0.473401i
\(81\) 0.755651 + 0.947556i 0.0839612 + 0.105284i
\(82\) −1.80571 + 2.26429i −0.199408 + 0.250050i
\(83\) −2.80913 12.3076i −0.308342 1.35094i −0.857184 0.515010i \(-0.827788\pi\)
0.548842 0.835926i \(-0.315069\pi\)
\(84\) 0.948131 + 0.216405i 0.103450 + 0.0236117i
\(85\) 5.98619 + 4.77383i 0.649293 + 0.517794i
\(86\) 9.53350 1.02802
\(87\) 1.95843 4.92850i 0.209966 0.528391i
\(88\) 2.44725 0.260878
\(89\) −1.43840 1.14709i −0.152470 0.121591i 0.544283 0.838901i \(-0.316802\pi\)
−0.696754 + 0.717310i \(0.745373\pi\)
\(90\) −4.37241 0.997975i −0.460893 0.105196i
\(91\) 2.18760 + 9.58449i 0.229323 + 1.00473i
\(92\) 2.34977 2.94651i 0.244980 0.307195i
\(93\) 0.387492 + 0.485900i 0.0401811 + 0.0503855i
\(94\) 1.74754 7.65649i 0.180246 0.789707i
\(95\) 4.92615 10.2293i 0.505413 1.04950i
\(96\) 3.10406 + 1.49484i 0.316807 + 0.152566i
\(97\) −0.117603 + 0.0268422i −0.0119408 + 0.00272541i −0.228487 0.973547i \(-0.573378\pi\)
0.216546 + 0.976272i \(0.430521\pi\)
\(98\) −2.35775 4.89592i −0.238169 0.494562i
\(99\) 1.61363i 0.162176i
\(100\) 0.811961 0.391020i 0.0811961 0.0391020i
\(101\) −6.93495 + 5.53044i −0.690053 + 0.550299i −0.904520 0.426432i \(-0.859770\pi\)
0.214466 + 0.976731i \(0.431199\pi\)
\(102\) −3.60997 + 2.87886i −0.357440 + 0.285049i
\(103\) −5.93320 + 2.85728i −0.584616 + 0.281536i −0.702722 0.711465i \(-0.748032\pi\)
0.118106 + 0.993001i \(0.462318\pi\)
\(104\) 19.8390i 1.94537i
\(105\) −1.23827 2.57130i −0.120843 0.250933i
\(106\) 0.781791 0.178439i 0.0759342 0.0173315i
\(107\) −8.78569 4.23096i −0.849344 0.409023i −0.0420102 0.999117i \(-0.513376\pi\)
−0.807334 + 0.590094i \(0.799090\pi\)
\(108\) −1.39114 + 2.88872i −0.133862 + 0.277968i
\(109\) −0.573290 + 2.51175i −0.0549112 + 0.240582i −0.994934 0.100530i \(-0.967946\pi\)
0.940023 + 0.341112i \(0.110803\pi\)
\(110\) −1.09477 1.37280i −0.104383 0.130892i
\(111\) −1.55486 + 1.94973i −0.147580 + 0.185060i
\(112\) 0.776326 + 3.40131i 0.0733559 + 0.321393i
\(113\) 5.17102 + 1.18025i 0.486449 + 0.111029i 0.458709 0.888586i \(-0.348312\pi\)
0.0277396 + 0.999615i \(0.491169\pi\)
\(114\) 5.35305 + 4.26891i 0.501359 + 0.399820i
\(115\) −11.0597 −1.03132
\(116\) −3.47680 + 0.245741i −0.322813 + 0.0228165i
\(117\) −13.0811 −1.20935
\(118\) −2.42980 1.93770i −0.223681 0.178380i
\(119\) 5.99627 + 1.36861i 0.549677 + 0.125460i
\(120\) −1.28155 5.61484i −0.116989 0.512563i
\(121\) 6.46449 8.10622i 0.587681 0.736929i
\(122\) 5.93561 + 7.44302i 0.537385 + 0.673859i
\(123\) 0.545672 2.39075i 0.0492016 0.215566i
\(124\) 0.177222 0.368006i 0.0159150 0.0330479i
\(125\) −10.9391 5.26801i −0.978426 0.471185i
\(126\) −3.51231 + 0.801662i −0.312901 + 0.0714177i
\(127\) 5.54746 + 11.5194i 0.492258 + 1.02218i 0.988106 + 0.153774i \(0.0491429\pi\)
−0.495848 + 0.868409i \(0.665143\pi\)
\(128\) 3.05475i 0.270004i
\(129\) −7.27283 + 3.50241i −0.640337 + 0.308370i
\(130\) 11.1288 8.87494i 0.976063 0.778384i
\(131\) 13.4626 10.7360i 1.17623 0.938013i 0.177296 0.984158i \(-0.443265\pi\)
0.998935 + 0.0461448i \(0.0146935\pi\)
\(132\) −0.456457 + 0.219818i −0.0397294 + 0.0191327i
\(133\) 9.12023i 0.790824i
\(134\) −1.99521 4.14309i −0.172360 0.357909i
\(135\) 9.17308 2.09369i 0.789493 0.180197i
\(136\) 11.1826 + 5.38524i 0.958897 + 0.461780i
\(137\) −1.16340 + 2.41582i −0.0993959 + 0.206398i −0.944737 0.327829i \(-0.893683\pi\)
0.845341 + 0.534227i \(0.179397\pi\)
\(138\) 1.48411 6.50231i 0.126336 0.553513i
\(139\) −8.56114 10.7353i −0.726147 0.910559i 0.272521 0.962150i \(-0.412142\pi\)
−0.998668 + 0.0515904i \(0.983571\pi\)
\(140\) −1.16945 + 1.46645i −0.0988368 + 0.123937i
\(141\) 1.47969 + 6.48293i 0.124612 + 0.545961i
\(142\) 3.54689 + 0.809555i 0.297649 + 0.0679364i
\(143\) −4.00409 3.19315i −0.334839 0.267025i
\(144\) −4.64217 −0.386847
\(145\) 6.92526 + 7.52737i 0.575112 + 0.625114i
\(146\) −1.06447 −0.0880965
\(147\) 3.59732 + 2.86876i 0.296702 + 0.236612i
\(148\) 1.59788 + 0.364706i 0.131345 + 0.0299786i
\(149\) 0.128371 + 0.562429i 0.0105165 + 0.0460759i 0.979914 0.199421i \(-0.0639061\pi\)
−0.969397 + 0.245497i \(0.921049\pi\)
\(150\) 0.994385 1.24692i 0.0811912 0.101811i
\(151\) 13.7896 + 17.2916i 1.12218 + 1.40717i 0.902012 + 0.431712i \(0.142090\pi\)
0.220172 + 0.975461i \(0.429338\pi\)
\(152\) 4.09543 17.9433i 0.332183 1.45539i
\(153\) −3.55083 + 7.37337i −0.287067 + 0.596102i
\(154\) −1.27080 0.611983i −0.102404 0.0493150i
\(155\) −1.16859 + 0.266724i −0.0938637 + 0.0214238i
\(156\) −1.78199 3.70033i −0.142673 0.296264i
\(157\) 1.53417i 0.122440i 0.998124 + 0.0612199i \(0.0194991\pi\)
−0.998124 + 0.0612199i \(0.980501\pi\)
\(158\) −13.5003 + 6.50142i −1.07403 + 0.517225i
\(159\) −0.530850 + 0.423339i −0.0420992 + 0.0335730i
\(160\) −5.19507 + 4.14293i −0.410707 + 0.327528i
\(161\) −8.00429 + 3.85466i −0.630826 + 0.303790i
\(162\) 1.40962i 0.110750i
\(163\) −6.69890 13.9104i −0.524698 1.08955i −0.979961 0.199190i \(-0.936169\pi\)
0.455263 0.890357i \(-0.349545\pi\)
\(164\) −1.57125 + 0.358627i −0.122694 + 0.0280041i
\(165\) 1.33951 + 0.645074i 0.104281 + 0.0502189i
\(166\) −6.37068 + 13.2289i −0.494461 + 1.02676i
\(167\) −2.00595 + 8.78865i −0.155225 + 0.680086i 0.836092 + 0.548590i \(0.184835\pi\)
−0.991317 + 0.131496i \(0.958022\pi\)
\(168\) −2.88447 3.61701i −0.222542 0.279058i
\(169\) 17.7804 22.2959i 1.36772 1.71507i
\(170\) −1.98161 8.68202i −0.151983 0.665880i
\(171\) 11.8311 + 2.70038i 0.904749 + 0.206503i
\(172\) 4.14780 + 3.30776i 0.316267 + 0.252214i
\(173\) 9.60089 0.729942 0.364971 0.931019i \(-0.381079\pi\)
0.364971 + 0.931019i \(0.381079\pi\)
\(174\) −5.35488 + 3.06146i −0.405952 + 0.232089i
\(175\) −2.12443 −0.160592
\(176\) −1.42095 1.13317i −0.107108 0.0854161i
\(177\) 2.56549 + 0.585557i 0.192834 + 0.0440132i
\(178\) 0.476156 + 2.08618i 0.0356894 + 0.156366i
\(179\) −15.2483 + 19.1207i −1.13971 + 1.42915i −0.252612 + 0.967568i \(0.581290\pi\)
−0.887097 + 0.461583i \(0.847282\pi\)
\(180\) −1.55608 1.95126i −0.115983 0.145438i
\(181\) 1.30341 5.71062i 0.0968818 0.424467i −0.903106 0.429418i \(-0.858719\pi\)
0.999988 + 0.00495101i \(0.00157596\pi\)
\(182\) 4.96113 10.3019i 0.367744 0.763628i
\(183\) −7.26251 3.49744i −0.536860 0.258538i
\(184\) −17.4787 + 3.98939i −1.28854 + 0.294102i
\(185\) −2.08685 4.33339i −0.153428 0.318597i
\(186\) 0.722844i 0.0530015i
\(187\) −2.88677 + 1.39019i −0.211101 + 0.101661i
\(188\) 3.41683 2.72483i 0.249198 0.198729i
\(189\) 5.90918 4.71241i 0.429829 0.342777i
\(190\) −11.8975 + 5.72953i −0.863135 + 0.415664i
\(191\) 18.9202i 1.36902i 0.729003 + 0.684511i \(0.239984\pi\)
−0.729003 + 0.684511i \(0.760016\pi\)
\(192\) −3.69273 7.66802i −0.266499 0.553392i
\(193\) −3.44402 + 0.786075i −0.247906 + 0.0565829i −0.344668 0.938725i \(-0.612009\pi\)
0.0967621 + 0.995308i \(0.469151\pi\)
\(194\) 0.126406 + 0.0608739i 0.00907541 + 0.00437049i
\(195\) −5.22939 + 10.8589i −0.374484 + 0.777624i
\(196\) 0.672895 2.94815i 0.0480640 0.210582i
\(197\) 13.7700 + 17.2670i 0.981073 + 1.23023i 0.973130 + 0.230258i \(0.0739569\pi\)
0.00794294 + 0.999968i \(0.497472\pi\)
\(198\) 1.17015 1.46733i 0.0831593 0.104278i
\(199\) −1.86576 8.17444i −0.132260 0.579471i −0.997010 0.0772681i \(-0.975380\pi\)
0.864750 0.502203i \(-0.167477\pi\)
\(200\) −4.17964 0.953975i −0.295545 0.0674562i
\(201\) 3.04417 + 2.42764i 0.214719 + 0.171233i
\(202\) 10.3167 0.725881
\(203\) 7.63561 + 3.03416i 0.535915 + 0.212956i
\(204\) −2.56947 −0.179899
\(205\) 3.69770 + 2.94882i 0.258259 + 0.205954i
\(206\) 7.46728 + 1.70436i 0.520270 + 0.118748i
\(207\) −2.63046 11.5248i −0.182830 0.801028i
\(208\) 9.18623 11.5192i 0.636951 0.798711i
\(209\) 2.96230 + 3.71461i 0.204907 + 0.256945i
\(210\) −0.738625 + 3.23613i −0.0509700 + 0.223314i
\(211\) 1.62014 3.36426i 0.111535 0.231605i −0.837728 0.546088i \(-0.816117\pi\)
0.949263 + 0.314482i \(0.101831\pi\)
\(212\) 0.402050 + 0.193617i 0.0276129 + 0.0132977i
\(213\) −3.00323 + 0.685469i −0.205778 + 0.0469675i
\(214\) 4.92096 + 10.2185i 0.336390 + 0.698521i
\(215\) 15.5687i 1.06177i
\(216\) 13.7419 6.61775i 0.935017 0.450281i
\(217\) −0.752793 + 0.600333i −0.0511029 + 0.0407532i
\(218\) 2.34276 1.86829i 0.158672 0.126536i
\(219\) 0.812056 0.391066i 0.0548737 0.0264258i
\(220\) 0.977118i 0.0658773i
\(221\) −11.2698 23.4020i −0.758090 1.57419i
\(222\) 2.82777 0.645420i 0.189788 0.0433178i
\(223\) −3.85387 1.85593i −0.258074 0.124282i 0.300374 0.953822i \(-0.402889\pi\)
−0.558448 + 0.829540i \(0.688603\pi\)
\(224\) −2.31592 + 4.80905i −0.154739 + 0.321318i
\(225\) 0.629016 2.75590i 0.0419344 0.183727i
\(226\) −3.84631 4.82312i −0.255853 0.320829i
\(227\) 2.67448 3.35370i 0.177512 0.222593i −0.685113 0.728436i \(-0.740247\pi\)
0.862625 + 0.505844i \(0.168819\pi\)
\(228\) 0.847835 + 3.71461i 0.0561492 + 0.246006i
\(229\) −7.21032 1.64571i −0.476471 0.108751i −0.0224606 0.999748i \(-0.507150\pi\)
−0.454011 + 0.890996i \(0.650007\pi\)
\(230\) 10.0569 + 8.02014i 0.663135 + 0.528832i
\(231\) 1.19428 0.0785781
\(232\) 13.6599 + 9.39820i 0.896817 + 0.617022i
\(233\) 11.6776 0.765023 0.382511 0.923951i \(-0.375059\pi\)
0.382511 + 0.923951i \(0.375059\pi\)
\(234\) 11.8951 + 9.48603i 0.777608 + 0.620121i
\(235\) −12.5034 2.85382i −0.815633 0.186163i
\(236\) −0.384840 1.68609i −0.0250510 0.109755i
\(237\) 7.91052 9.91948i 0.513843 0.644339i
\(238\) −4.46014 5.59284i −0.289108 0.362530i
\(239\) 0.588962 2.58041i 0.0380968 0.166913i −0.952301 0.305161i \(-0.901290\pi\)
0.990398 + 0.138248i \(0.0441470\pi\)
\(240\) −1.85578 + 3.85357i −0.119790 + 0.248747i
\(241\) −24.0935 11.6028i −1.55200 0.747402i −0.555538 0.831491i \(-0.687488\pi\)
−0.996458 + 0.0840891i \(0.973202\pi\)
\(242\) −11.7568 + 2.68341i −0.755755 + 0.172496i
\(243\) 6.96590 + 14.4648i 0.446863 + 0.927921i
\(244\) 5.29771i 0.339151i
\(245\) −7.99526 + 3.85032i −0.510799 + 0.245988i
\(246\) −2.22990 + 1.77828i −0.142173 + 0.113379i
\(247\) −30.1130 + 24.0143i −1.91604 + 1.52799i
\(248\) −1.75063 + 0.843060i −0.111165 + 0.0535344i
\(249\) 12.4324i 0.787869i
\(250\) 6.12713 + 12.7231i 0.387514 + 0.804681i
\(251\) 7.46950 1.70487i 0.471471 0.107610i 0.0198175 0.999804i \(-0.493691\pi\)
0.451653 + 0.892193i \(0.350834\pi\)
\(252\) −1.80627 0.869853i −0.113784 0.0547956i
\(253\) 2.00808 4.16981i 0.126247 0.262154i
\(254\) 3.30905 14.4979i 0.207628 0.909678i
\(255\) 4.70131 + 5.89525i 0.294407 + 0.369175i
\(256\) −8.56137 + 10.7356i −0.535085 + 0.670976i
\(257\) 2.64473 + 11.5873i 0.164974 + 0.722796i 0.987957 + 0.154731i \(0.0494509\pi\)
−0.822983 + 0.568066i \(0.807692\pi\)
\(258\) 9.15329 + 2.08918i 0.569859 + 0.130067i
\(259\) −3.02067 2.40890i −0.187695 0.149682i
\(260\) 7.92116 0.491249
\(261\) −6.19683 + 9.00685i −0.383574 + 0.557510i
\(262\) −20.0275 −1.23730
\(263\) −12.3913 9.88175i −0.764082 0.609335i 0.161942 0.986800i \(-0.448224\pi\)
−0.926024 + 0.377466i \(0.876796\pi\)
\(264\) 2.34965 + 0.536292i 0.144611 + 0.0330065i
\(265\) −0.291399 1.27670i −0.0179005 0.0784271i
\(266\) −6.61373 + 8.29335i −0.405514 + 0.508498i
\(267\) −1.12966 1.41655i −0.0691343 0.0866916i
\(268\) 0.569427 2.49482i 0.0347833 0.152395i
\(269\) −0.450662 + 0.935810i −0.0274774 + 0.0570573i −0.914256 0.405137i \(-0.867224\pi\)
0.886778 + 0.462195i \(0.152938\pi\)
\(270\) −9.85969 4.74818i −0.600042 0.288965i
\(271\) 12.0113 2.74151i 0.729636 0.166535i 0.158464 0.987365i \(-0.449346\pi\)
0.571172 + 0.820830i \(0.306489\pi\)
\(272\) −3.99939 8.30481i −0.242498 0.503553i
\(273\) 9.68163i 0.585959i
\(274\) 2.80980 1.35313i 0.169746 0.0817456i
\(275\) 0.865267 0.690027i 0.0521775 0.0416102i
\(276\) 2.90175 2.31407i 0.174665 0.139291i
\(277\) 11.0646 5.32845i 0.664809 0.320155i −0.0708698 0.997486i \(-0.522577\pi\)
0.735679 + 0.677330i \(0.236863\pi\)
\(278\) 15.9703i 0.957836i
\(279\) −0.555883 1.15430i −0.0332799 0.0691063i
\(280\) 8.69894 1.98548i 0.519861 0.118655i
\(281\) −0.591214 0.284714i −0.0352689 0.0169846i 0.416166 0.909289i \(-0.363373\pi\)
−0.451435 + 0.892304i \(0.649088\pi\)
\(282\) 3.35570 6.96818i 0.199829 0.414949i
\(283\) 0.673096 2.94902i 0.0400114 0.175301i −0.950974 0.309270i \(-0.899915\pi\)
0.990986 + 0.133969i \(0.0427723\pi\)
\(284\) 1.26228 + 1.58286i 0.0749028 + 0.0939252i
\(285\) 6.97133 8.74178i 0.412946 0.517818i
\(286\) 1.32548 + 5.80729i 0.0783771 + 0.343392i
\(287\) 3.70393 + 0.845397i 0.218636 + 0.0499022i
\(288\) −5.55278 4.42819i −0.327201 0.260934i
\(289\) 0.749913 0.0441125
\(290\) −0.838755 11.8669i −0.0492534 0.696848i
\(291\) −0.118795 −0.00696389
\(292\) −0.463128 0.369332i −0.0271025 0.0216135i
\(293\) 15.1894 + 3.46689i 0.887377 + 0.202538i 0.641830 0.766847i \(-0.278175\pi\)
0.245547 + 0.969385i \(0.421033\pi\)
\(294\) −1.19082 5.21734i −0.0694502 0.304281i
\(295\) −3.16435 + 3.96798i −0.184236 + 0.231024i
\(296\) −4.86118 6.09573i −0.282550 0.354307i
\(297\) −0.876150 + 3.83866i −0.0508394 + 0.222742i
\(298\) 0.291125 0.604527i 0.0168644 0.0350193i
\(299\) 33.8032 + 16.2788i 1.95489 + 0.941425i
\(300\) 0.865267 0.197491i 0.0499562 0.0114022i
\(301\) −5.42620 11.2676i −0.312761 0.649455i
\(302\) 25.7237i 1.48023i
\(303\) −7.87031 + 3.79014i −0.452138 + 0.217738i
\(304\) −10.6864 + 8.52210i −0.612906 + 0.488776i
\(305\) 12.1548 9.69313i 0.695982 0.555027i
\(306\) 8.57585 4.12991i 0.490248 0.236091i
\(307\) 12.6496i 0.721952i −0.932575 0.360976i \(-0.882444\pi\)
0.932575 0.360976i \(-0.117556\pi\)
\(308\) −0.340559 0.707177i −0.0194051 0.0402952i
\(309\) −6.32272 + 1.44312i −0.359687 + 0.0820962i
\(310\) 1.25606 + 0.604889i 0.0713397 + 0.0343554i
\(311\) 7.18576 14.9214i 0.407467 0.846114i −0.591733 0.806134i \(-0.701556\pi\)
0.999200 0.0399803i \(-0.0127295\pi\)
\(312\) −4.34753 + 19.0478i −0.246130 + 1.07837i
\(313\) −2.19894 2.75738i −0.124291 0.155857i 0.715792 0.698313i \(-0.246066\pi\)
−0.840084 + 0.542457i \(0.817494\pi\)
\(314\) 1.11253 1.39507i 0.0627838 0.0787284i
\(315\) 1.30915 + 5.73576i 0.0737623 + 0.323174i
\(316\) −8.12942 1.85549i −0.457315 0.104379i
\(317\) −4.16855 3.32431i −0.234129 0.186712i 0.499396 0.866374i \(-0.333555\pi\)
−0.733526 + 0.679662i \(0.762127\pi\)
\(318\) 0.789714 0.0442850
\(319\) −4.09544 + 1.24430i −0.229301 + 0.0696673i
\(320\) 16.4146 0.917606
\(321\) −7.50812 5.98752i −0.419062 0.334191i
\(322\) 10.0739 + 2.29930i 0.561395 + 0.128135i
\(323\) 5.36196 + 23.4923i 0.298348 + 1.30715i
\(324\) 0.489085 0.613293i 0.0271714 0.0340718i
\(325\) 5.59381 + 7.01441i 0.310289 + 0.389090i
\(326\) −3.99587 + 17.5071i −0.221311 + 0.969627i
\(327\) −1.10085 + 2.28594i −0.0608772 + 0.126413i
\(328\) 6.90752 + 3.32649i 0.381404 + 0.183675i
\(329\) −10.0438 + 2.29244i −0.553735 + 0.126386i
\(330\) −0.750275 1.55796i −0.0413013 0.0857629i
\(331\) 0.600782i 0.0330220i −0.999864 0.0165110i \(-0.994744\pi\)
0.999864 0.0165110i \(-0.00525585\pi\)
\(332\) −7.36164 + 3.54518i −0.404022 + 0.194567i
\(333\) 4.01930 3.20528i 0.220256 0.175649i
\(334\) 8.19735 6.53717i 0.448539 0.357698i
\(335\) −6.76586 + 3.25827i −0.369659 + 0.178018i
\(336\) 3.43578i 0.187437i
\(337\) 10.4761 + 21.7538i 0.570669 + 1.18501i 0.964072 + 0.265640i \(0.0855831\pi\)
−0.393404 + 0.919366i \(0.628703\pi\)
\(338\) −32.3367 + 7.38064i −1.75888 + 0.401454i
\(339\) 4.70615 + 2.26636i 0.255603 + 0.123092i
\(340\) 2.15018 4.46489i 0.116610 0.242142i
\(341\) 0.111616 0.489022i 0.00604435 0.0264820i
\(342\) −8.80023 11.0351i −0.475862 0.596712i
\(343\) −11.1035 + 13.9233i −0.599532 + 0.751790i
\(344\) −5.61586 24.6047i −0.302787 1.32660i
\(345\) −10.6186 2.42362i −0.571685 0.130483i
\(346\) −8.73042 6.96228i −0.469351 0.374295i
\(347\) −16.7193 −0.897540 −0.448770 0.893647i \(-0.648138\pi\)
−0.448770 + 0.893647i \(0.648138\pi\)
\(348\) −3.39199 0.525968i −0.181830 0.0281949i
\(349\) 10.7789 0.576983 0.288491 0.957482i \(-0.406846\pi\)
0.288491 + 0.957482i \(0.406846\pi\)
\(350\) 1.93182 + 1.54058i 0.103260 + 0.0823473i
\(351\) −31.1187 7.10264i −1.66099 0.379111i
\(352\) −0.618749 2.71091i −0.0329794 0.144492i
\(353\) −6.51106 + 8.16462i −0.346549 + 0.434559i −0.924307 0.381649i \(-0.875356\pi\)
0.577758 + 0.816208i \(0.303928\pi\)
\(354\) −1.90826 2.39289i −0.101423 0.127181i
\(355\) 1.32204 5.79224i 0.0701667 0.307420i
\(356\) −0.516659 + 1.07285i −0.0273829 + 0.0568611i
\(357\) 5.45721 + 2.62805i 0.288826 + 0.139091i
\(358\) 27.7316 6.32955i 1.46566 0.334527i
\(359\) −1.55629 3.23167i −0.0821379 0.170561i 0.855855 0.517216i \(-0.173032\pi\)
−0.937993 + 0.346655i \(0.887317\pi\)
\(360\) 11.8725i 0.625735i
\(361\) 15.0745 7.25949i 0.793394 0.382078i
\(362\) −5.32641 + 4.24767i −0.279950 + 0.223253i
\(363\) 7.98308 6.36629i 0.419003 0.334144i
\(364\) 5.73284 2.76079i 0.300482 0.144705i
\(365\) 1.73834i 0.0909887i
\(366\) 4.06782 + 8.44691i 0.212628 + 0.441527i
\(367\) 8.99463 2.05297i 0.469516 0.107164i 0.0187845 0.999824i \(-0.494020\pi\)
0.450731 + 0.892660i \(0.351163\pi\)
\(368\) 11.9959 + 5.77694i 0.625331 + 0.301144i
\(369\) −2.19336 + 4.55457i −0.114182 + 0.237101i
\(370\) −1.24480 + 5.45383i −0.0647142 + 0.283531i
\(371\) −0.655869 0.822434i −0.0340510 0.0426986i
\(372\) 0.250799 0.314492i 0.0130033 0.0163057i
\(373\) 4.78506 + 20.9647i 0.247761 + 1.08551i 0.933757 + 0.357908i \(0.116510\pi\)
−0.685996 + 0.727606i \(0.740633\pi\)
\(374\) 3.63317 + 0.829247i 0.187867 + 0.0428794i
\(375\) −9.34842 7.45512i −0.482750 0.384981i
\(376\) −20.7898 −1.07215
\(377\) −10.0871 33.2003i −0.519511 1.70990i
\(378\) −8.79073 −0.452146
\(379\) 14.8475 + 11.8405i 0.762666 + 0.608206i 0.925632 0.378426i \(-0.123534\pi\)
−0.162965 + 0.986632i \(0.552106\pi\)
\(380\) −7.16424 1.63519i −0.367518 0.0838836i
\(381\) 2.80184 + 12.2757i 0.143543 + 0.628902i
\(382\) 13.7204 17.2048i 0.701997 0.880277i
\(383\) −18.2471 22.8811i −0.932384 1.16917i −0.985345 0.170575i \(-0.945437\pi\)
0.0529611 0.998597i \(-0.483134\pi\)
\(384\) −0.669419 + 2.93292i −0.0341612 + 0.149670i
\(385\) −0.999397 + 2.07527i −0.0509340 + 0.105766i
\(386\) 3.70181 + 1.78270i 0.188417 + 0.0907369i
\(387\) 16.2234 3.70289i 0.824683 0.188229i
\(388\) 0.0338753 + 0.0703428i 0.00171976 + 0.00357111i
\(389\) 35.4572i 1.79775i 0.438203 + 0.898876i \(0.355615\pi\)
−0.438203 + 0.898876i \(0.644385\pi\)
\(390\) 12.6298 6.08221i 0.639537 0.307985i
\(391\) 18.3516 14.6349i 0.928079 0.740118i
\(392\) −11.2468 + 8.96905i −0.568051 + 0.453005i
\(393\) 15.2784 7.35767i 0.770691 0.371145i
\(394\) 25.6871i 1.29410i
\(395\) 10.6171 + 22.0467i 0.534205 + 1.10929i
\(396\) 1.01821 0.232400i 0.0511671 0.0116786i
\(397\) −14.5073 6.98633i −0.728099 0.350634i 0.0328373 0.999461i \(-0.489546\pi\)
−0.760936 + 0.648827i \(0.775260\pi\)
\(398\) −4.23126 + 8.78631i −0.212094 + 0.440418i
\(399\) 1.99861 8.75650i 0.100056 0.438373i
\(400\) 1.98511 + 2.48925i 0.0992554 + 0.124462i
\(401\) −15.0541 + 18.8772i −0.751764 + 0.942682i −0.999659 0.0261051i \(-0.991690\pi\)
0.247896 + 0.968787i \(0.420261\pi\)
\(402\) −1.00771 4.41509i −0.0502602 0.220204i
\(403\) 3.96433 + 0.904833i 0.197477 + 0.0450729i
\(404\) 4.48856 + 3.57950i 0.223314 + 0.178087i
\(405\) −2.30198 −0.114386
\(406\) −4.74305 8.29619i −0.235394 0.411733i
\(407\) 2.01272 0.0997668
\(408\) 9.55645 + 7.62102i 0.473115 + 0.377296i
\(409\) −16.0546 3.66436i −0.793848 0.181191i −0.193680 0.981065i \(-0.562042\pi\)
−0.600168 + 0.799874i \(0.704900\pi\)
\(410\) −1.22405 5.36293i −0.0604517 0.264856i
\(411\) −1.64640 + 2.06453i −0.0812112 + 0.101836i
\(412\) 2.65749 + 3.33239i 0.130925 + 0.164175i
\(413\) −0.907190 + 3.97466i −0.0446399 + 0.195580i
\(414\) −5.96547 + 12.3874i −0.293187 + 0.608809i
\(415\) 21.6033 + 10.4036i 1.06047 + 0.510694i
\(416\) 21.9764 5.01598i 1.07748 0.245929i
\(417\) −5.86716 12.1833i −0.287316 0.596618i
\(418\) 5.52599i 0.270285i
\(419\) 13.9754 6.73021i 0.682744 0.328792i −0.0601613 0.998189i \(-0.519162\pi\)
0.742905 + 0.669396i \(0.233447\pi\)
\(420\) −1.44417 + 1.15169i −0.0704683 + 0.0561966i
\(421\) 9.57860 7.63868i 0.466833 0.372287i −0.361639 0.932318i \(-0.617783\pi\)
0.828471 + 0.560032i \(0.189211\pi\)
\(422\) −3.91292 + 1.88436i −0.190478 + 0.0917293i
\(423\) 13.7080i 0.666507i
\(424\) −0.921052 1.91258i −0.0447302 0.0928833i
\(425\) 5.47221 1.24900i 0.265441 0.0605852i
\(426\) 3.22803 + 1.55454i 0.156399 + 0.0753176i
\(427\) 5.41850 11.2516i 0.262220 0.544505i
\(428\) −1.40443 + 6.15321i −0.0678857 + 0.297427i
\(429\) −3.14465 3.94326i −0.151825 0.190382i
\(430\) −11.2899 + 14.1571i −0.544449 + 0.682717i
\(431\) −4.74015 20.7680i −0.228325 1.00036i −0.951005 0.309175i \(-0.899947\pi\)
0.722680 0.691183i \(-0.242910\pi\)
\(432\) −11.0433 2.52055i −0.531320 0.121270i
\(433\) 18.5434 + 14.7879i 0.891141 + 0.710661i 0.957898 0.287108i \(-0.0926939\pi\)
−0.0667572 + 0.997769i \(0.521265\pi\)
\(434\) 1.11988 0.0537562
\(435\) 4.99951 + 8.74477i 0.239708 + 0.419280i
\(436\) 1.66750 0.0798589
\(437\) −27.2126 21.7013i −1.30176 1.03812i
\(438\) −1.02202 0.233269i −0.0488340 0.0111460i
\(439\) −4.49014 19.6726i −0.214302 0.938921i −0.961605 0.274437i \(-0.911509\pi\)
0.747303 0.664484i \(-0.231349\pi\)
\(440\) −2.89812 + 3.63413i −0.138163 + 0.173251i
\(441\) −5.91386 7.41575i −0.281613 0.353131i
\(442\) −6.72242 + 29.4528i −0.319753 + 1.40093i
\(443\) 7.84179 16.2836i 0.372574 0.773659i −0.627413 0.778687i \(-0.715886\pi\)
0.999987 + 0.00502788i \(0.00160043\pi\)
\(444\) 1.45423 + 0.700321i 0.0690148 + 0.0332358i
\(445\) 3.40682 0.777585i 0.161499 0.0368611i
\(446\) 2.15860 + 4.48238i 0.102213 + 0.212247i
\(447\) 0.568129i 0.0268716i
\(448\) 11.8799 5.72105i 0.561272 0.270294i
\(449\) −24.1685 + 19.2737i −1.14058 + 0.909583i −0.996793 0.0800259i \(-0.974500\pi\)
−0.143788 + 0.989609i \(0.545928\pi\)
\(450\) −2.57048 + 2.04989i −0.121174 + 0.0966328i
\(451\) −1.78317 + 0.858730i −0.0839663 + 0.0404360i
\(452\) 3.43295i 0.161472i
\(453\) 9.45036 + 19.6239i 0.444016 + 0.922010i
\(454\) −4.86400 + 1.11018i −0.228279 + 0.0521032i
\(455\) −16.8235 8.10176i −0.788697 0.379817i
\(456\) 7.86419 16.3302i 0.368275 0.764730i
\(457\) −5.57593 + 24.4298i −0.260831 + 1.14278i 0.659521 + 0.751686i \(0.270759\pi\)
−0.920353 + 0.391090i \(0.872098\pi\)
\(458\) 5.36318 + 6.72521i 0.250605 + 0.314249i
\(459\) −12.4506 + 15.6126i −0.581144 + 0.728732i
\(460\) 1.59285 + 6.97875i 0.0742672 + 0.325386i
\(461\) −34.0368 7.76868i −1.58525 0.361823i −0.663063 0.748563i \(-0.730744\pi\)
−0.922189 + 0.386740i \(0.873601\pi\)
\(462\) −1.08600 0.866059i −0.0505255 0.0402927i
\(463\) −13.9627 −0.648901 −0.324450 0.945903i \(-0.605179\pi\)
−0.324450 + 0.945903i \(0.605179\pi\)
\(464\) −3.57966 11.7820i −0.166182 0.546965i
\(465\) −1.18044 −0.0547415
\(466\) −10.6188 8.46823i −0.491908 0.392283i
\(467\) 38.8128 + 8.85877i 1.79604 + 0.409935i 0.984646 0.174562i \(-0.0558511\pi\)
0.811396 + 0.584497i \(0.198708\pi\)
\(468\) 1.88399 + 8.25430i 0.0870874 + 0.381555i
\(469\) −3.76109 + 4.71626i −0.173671 + 0.217777i
\(470\) 9.30029 + 11.6622i 0.428990 + 0.537937i
\(471\) −0.336198 + 1.47298i −0.0154912 + 0.0678713i
\(472\) −3.56963 + 7.41242i −0.164306 + 0.341184i
\(473\) 5.86984 + 2.82676i 0.269895 + 0.129975i
\(474\) −14.3866 + 3.28365i −0.660800 + 0.150823i
\(475\) −3.61128 7.49889i −0.165697 0.344073i
\(476\) 3.98081i 0.182460i
\(477\) 1.26109 0.607308i 0.0577412 0.0278067i
\(478\) −2.40680 + 1.91936i −0.110085 + 0.0877895i
\(479\) −9.47774 + 7.55825i −0.433049 + 0.345345i −0.815627 0.578578i \(-0.803608\pi\)
0.382578 + 0.923923i \(0.375036\pi\)
\(480\) −5.89576 + 2.83925i −0.269104 + 0.129593i
\(481\) 16.3164i 0.743964i
\(482\) 13.4950 + 28.0227i 0.614682 + 1.27640i
\(483\) −8.52977 + 1.94686i −0.388118 + 0.0885854i
\(484\) −6.04614 2.91167i −0.274825 0.132349i
\(485\) 0.0994099 0.206427i 0.00451397 0.00937335i
\(486\) 4.15514 18.2049i 0.188481 0.825790i
\(487\) 7.99751 + 10.0286i 0.362402 + 0.454437i 0.929287 0.369360i \(-0.120423\pi\)
−0.566885 + 0.823797i \(0.691852\pi\)
\(488\) 15.7130 19.7034i 0.711292 0.891932i
\(489\) −3.38340 14.8236i −0.153002 0.670348i
\(490\) 10.0625 + 2.29670i 0.454578 + 0.103754i
\(491\) −18.8502 15.0325i −0.850697 0.678408i 0.0977958 0.995207i \(-0.468821\pi\)
−0.948493 + 0.316798i \(0.897392\pi\)
\(492\) −1.58717 −0.0715553
\(493\) −21.4520 3.32638i −0.966149 0.149813i
\(494\) 44.7973 2.01553
\(495\) −2.39621 1.91092i −0.107702 0.0858893i
\(496\) 1.40685 + 0.321103i 0.0631692 + 0.0144180i
\(497\) −1.06198 4.65284i −0.0476363 0.208708i
\(498\) −9.01558 + 11.3052i −0.403998 + 0.506597i
\(499\) −11.4800 14.3955i −0.513917 0.644432i 0.455388 0.890293i \(-0.349501\pi\)
−0.969305 + 0.245861i \(0.920929\pi\)
\(500\) −1.74867 + 7.66141i −0.0782028 + 0.342629i
\(501\) −3.85190 + 7.99855i −0.172090 + 0.357349i
\(502\) −8.02860 3.86637i −0.358334 0.172565i
\(503\) 10.6367 2.42776i 0.474267 0.108248i 0.0212951 0.999773i \(-0.493221\pi\)
0.452972 + 0.891525i \(0.350364\pi\)
\(504\) 4.13796 + 8.59256i 0.184319 + 0.382743i
\(505\) 16.8477i 0.749711i
\(506\) −4.84984 + 2.33556i −0.215602 + 0.103828i
\(507\) 21.9572 17.5103i 0.975154 0.777660i
\(508\) 6.46990 5.15957i 0.287055 0.228919i
\(509\) 21.8142 10.5052i 0.966898 0.465634i 0.117319 0.993094i \(-0.462570\pi\)
0.849579 + 0.527461i \(0.176856\pi\)
\(510\) 8.77001i 0.388343i
\(511\) 0.605869 + 1.25810i 0.0268020 + 0.0556550i
\(512\) 21.5266 4.91331i 0.951352 0.217140i
\(513\) 26.6789 + 12.8479i 1.17790 + 0.567248i
\(514\) 5.99783 12.4546i 0.264553 0.549350i
\(515\) 2.78330 12.1944i 0.122647 0.537351i
\(516\) 3.25751 + 4.08479i 0.143404 + 0.179823i
\(517\) 3.34619 4.19599i 0.147165 0.184539i
\(518\) 0.999934 + 4.38100i 0.0439346 + 0.192490i
\(519\) 9.21798 + 2.10394i 0.404624 + 0.0923529i
\(520\) −29.4606 23.4941i −1.29193 1.03028i
\(521\) 41.7398 1.82865 0.914327 0.404976i \(-0.132720\pi\)
0.914327 + 0.404976i \(0.132720\pi\)
\(522\) 12.1665 3.69649i 0.532513 0.161791i
\(523\) −18.9831 −0.830074 −0.415037 0.909804i \(-0.636231\pi\)
−0.415037 + 0.909804i \(0.636231\pi\)
\(524\) −8.71348 6.94876i −0.380650 0.303558i
\(525\) −2.03971 0.465550i −0.0890201 0.0203183i
\(526\) 4.10191 + 17.9716i 0.178852 + 0.783601i
\(527\) 1.58613 1.98894i 0.0690929 0.0866398i
\(528\) −1.11596 1.39937i −0.0485659 0.0608997i
\(529\) −2.42660 + 10.6316i −0.105504 + 0.462245i
\(530\) −0.660847 + 1.37226i −0.0287054 + 0.0596073i
\(531\) −4.88748 2.35368i −0.212098 0.102141i
\(532\) −5.75495 + 1.31353i −0.249509 + 0.0569487i
\(533\) −6.96143 14.4555i −0.301533 0.626139i
\(534\) 2.10732i 0.0911926i
\(535\) 16.6873 8.03616i 0.721454 0.347434i
\(536\) −9.51745 + 7.58991i −0.411091 + 0.327834i
\(537\) −18.8303 + 15.0166i −0.812586 + 0.648016i
\(538\) 1.08843 0.524158i 0.0469253 0.0225981i
\(539\) 3.71354i 0.159953i
\(540\) −2.64228 5.48675i −0.113706 0.236112i
\(541\) −3.27895 + 0.748398i −0.140973 + 0.0321762i −0.292425 0.956288i \(-0.594462\pi\)
0.151452 + 0.988465i \(0.451605\pi\)
\(542\) −12.9104 6.21731i −0.554549 0.267057i
\(543\) 2.50286 5.19723i 0.107408 0.223035i
\(544\) 3.13811 13.7489i 0.134545 0.589481i
\(545\) −3.05100 3.82583i −0.130691 0.163881i
\(546\) 7.02084 8.80385i 0.300464 0.376770i
\(547\) 3.79156 + 16.6119i 0.162115 + 0.710274i 0.989002 + 0.147905i \(0.0472529\pi\)
−0.826886 + 0.562369i \(0.809890\pi\)
\(548\) 1.69196 + 0.386180i 0.0722771 + 0.0164968i
\(549\) 12.9917 + 10.3606i 0.554473 + 0.442178i
\(550\) −1.28720 −0.0548866
\(551\) 2.26955 + 32.1101i 0.0966860 + 1.36794i
\(552\) −17.6558 −0.751481
\(553\) 15.3680 + 12.2556i 0.653514 + 0.521160i
\(554\) −13.9255 3.17840i −0.591637 0.135037i
\(555\) −1.05400 4.61788i −0.0447399 0.196018i
\(556\) −5.54109 + 6.94830i −0.234994 + 0.294674i
\(557\) 3.07422 + 3.85495i 0.130259 + 0.163340i 0.842684 0.538409i \(-0.180974\pi\)
−0.712425 + 0.701749i \(0.752403\pi\)
\(558\) −0.331583 + 1.45276i −0.0140370 + 0.0615002i
\(559\) −22.9156 + 47.5847i −0.969226 + 2.01262i
\(560\) −5.97025 2.87512i −0.252289 0.121496i
\(561\) −3.07629 + 0.702142i −0.129881 + 0.0296445i
\(562\) 0.331146 + 0.687631i 0.0139685 + 0.0290060i
\(563\) 0.638084i 0.0268920i 0.999910 + 0.0134460i \(0.00428013\pi\)
−0.999910 + 0.0134460i \(0.995720\pi\)
\(564\) 3.87768 1.86739i 0.163280 0.0786313i
\(565\) −7.87638 + 6.28120i −0.331362 + 0.264252i
\(566\) −2.75062 + 2.19354i −0.115617 + 0.0922015i
\(567\) −1.66603 + 0.802317i −0.0699666 + 0.0336941i
\(568\) 9.63094i 0.404105i
\(569\) −13.6785 28.4037i −0.573434 1.19075i −0.962938 0.269723i \(-0.913068\pi\)
0.389505 0.921025i \(-0.372646\pi\)
\(570\) −12.6786 + 2.89380i −0.531046 + 0.121208i
\(571\) 11.5145 + 5.54509i 0.481867 + 0.232055i 0.659016 0.752129i \(-0.270973\pi\)
−0.177149 + 0.984184i \(0.556687\pi\)
\(572\) −1.43823 + 2.98651i −0.0601352 + 0.124872i
\(573\) −4.14619 + 18.1657i −0.173210 + 0.758881i
\(574\) −2.75505 3.45473i −0.114994 0.144198i
\(575\) −5.05503 + 6.33881i −0.210809 + 0.264347i
\(576\) 3.90410 + 17.1050i 0.162671 + 0.712708i
\(577\) −12.0087 2.74091i −0.499929 0.114106i −0.0348820 0.999391i \(-0.511106\pi\)
−0.465047 + 0.885286i \(0.653963\pi\)
\(578\) −0.681923 0.543815i −0.0283642 0.0226197i
\(579\) −3.47893 −0.144579
\(580\) 3.75244 5.45402i 0.155812 0.226466i
\(581\) 19.2612 0.799087
\(582\) 0.108025 + 0.0861467i 0.00447776 + 0.00357090i
\(583\) 0.534262 + 0.121942i 0.0221269 + 0.00505031i
\(584\) 0.627045 + 2.74726i 0.0259473 + 0.113683i
\(585\) 15.4911 19.4253i 0.640480 0.803136i
\(586\) −11.2982 14.1675i −0.466725 0.585254i
\(587\) 6.14919 26.9414i 0.253804 1.11199i −0.673944 0.738783i \(-0.735401\pi\)
0.927748 0.373207i \(-0.121742\pi\)
\(588\) 1.29212 2.68311i 0.0532860 0.110650i
\(589\) −3.39873 1.63674i −0.140042 0.0674408i
\(590\) 5.75492 1.31352i 0.236926 0.0540769i
\(591\) 9.43692 + 19.5960i 0.388183 + 0.806070i
\(592\) 5.79030i 0.237980i
\(593\) 2.04723 0.985896i 0.0840698 0.0404859i −0.391376 0.920231i \(-0.628001\pi\)
0.475446 + 0.879745i \(0.342287\pi\)
\(594\) 3.58040 2.85527i 0.146906 0.117153i
\(595\) −9.13338 + 7.28362i −0.374432 + 0.298599i
\(596\) 0.336409 0.162006i 0.0137799 0.00663603i
\(597\) 8.25729i 0.337948i
\(598\) −18.9336 39.3159i −0.774251 1.60775i
\(599\) −35.2252 + 8.03993i −1.43926 + 0.328503i −0.869756 0.493482i \(-0.835724\pi\)
−0.569509 + 0.821985i \(0.692867\pi\)
\(600\) −3.80389 1.83186i −0.155293 0.0747852i
\(601\) −16.4028 + 34.0607i −0.669083 + 1.38937i 0.239184 + 0.970974i \(0.423120\pi\)
−0.908267 + 0.418391i \(0.862594\pi\)
\(602\) −3.23671 + 14.1810i −0.131919 + 0.577973i
\(603\) −5.00451 6.27546i −0.203799 0.255556i
\(604\) 8.92515 11.1918i 0.363159 0.455387i
\(605\) 4.38213 + 19.1994i 0.178159 + 0.780566i
\(606\) 9.90525 + 2.26081i 0.402373 + 0.0918391i
\(607\) 9.80934 + 7.82269i 0.398149 + 0.317513i 0.802014 0.597305i \(-0.203762\pi\)
−0.403865 + 0.914819i \(0.632333\pi\)
\(608\) −20.9119 −0.848091
\(609\) 6.66618 + 4.58642i 0.270127 + 0.185851i
\(610\) −18.0820 −0.732117
\(611\) 34.0154 + 27.1264i 1.37612 + 1.09742i
\(612\) 5.16407 + 1.17866i 0.208745 + 0.0476447i
\(613\) −8.15457 35.7275i −0.329360 1.44302i −0.820353 0.571857i \(-0.806223\pi\)
0.490994 0.871163i \(-0.336634\pi\)
\(614\) −9.17314 + 11.5028i −0.370198 + 0.464213i
\(615\) 2.90402 + 3.64153i 0.117101 + 0.146841i
\(616\) −0.830864 + 3.64025i −0.0334765 + 0.146670i
\(617\) 17.4746 36.2863i 0.703500 1.46083i −0.175732 0.984438i \(-0.556229\pi\)
0.879232 0.476395i \(-0.158057\pi\)
\(618\) 6.79598 + 3.27277i 0.273374 + 0.131650i
\(619\) −4.44437 + 1.01440i −0.178635 + 0.0407722i −0.310902 0.950442i \(-0.600631\pi\)
0.132268 + 0.991214i \(0.457774\pi\)
\(620\) 0.336611 + 0.698979i 0.0135186 + 0.0280717i
\(621\) 28.8446i 1.15750i
\(622\) −17.3548 + 8.35764i −0.695865 + 0.335111i
\(623\) 2.19463 1.75016i 0.0879261 0.0701187i
\(624\) 11.3442 9.04668i 0.454131 0.362157i
\(625\) 14.5049 6.98521i 0.580197 0.279408i
\(626\) 4.10199i 0.163949i
\(627\) 2.03013 + 4.21562i 0.0810758 + 0.168356i
\(628\) 0.968072 0.220956i 0.0386303 0.00881711i
\(629\) 9.19701 + 4.42904i 0.366709 + 0.176598i
\(630\) 2.96895 6.16509i 0.118286 0.245623i
\(631\) 8.10660 35.5173i 0.322718 1.41392i −0.509976 0.860189i \(-0.670346\pi\)
0.832694 0.553733i \(-0.186797\pi\)
\(632\) 24.7319 + 31.0128i 0.983781 + 1.23362i
\(633\) 2.29277 2.87505i 0.0911296 0.114273i
\(634\) 1.37992 + 6.04582i 0.0548036 + 0.240110i
\(635\) −23.6757 5.40383i −0.939542 0.214444i
\(636\) 0.343586 + 0.274001i 0.0136241 + 0.0108648i
\(637\) 30.1044 1.19278
\(638\) 4.62646 + 1.83841i 0.183163 + 0.0727833i
\(639\) 6.35029 0.251213
\(640\) −4.53626 3.61755i −0.179312 0.142996i
\(641\) 8.49724 + 1.93944i 0.335621 + 0.0766032i 0.387010 0.922075i \(-0.373508\pi\)
−0.0513894 + 0.998679i \(0.516365\pi\)
\(642\) 2.48542 + 10.8893i 0.0980917 + 0.429768i
\(643\) −14.6964 + 18.4287i −0.579571 + 0.726759i −0.982040 0.188675i \(-0.939581\pi\)
0.402469 + 0.915434i \(0.368152\pi\)
\(644\) 3.58513 + 4.49562i 0.141274 + 0.177152i
\(645\) 3.41172 14.9477i 0.134337 0.588567i
\(646\) 12.1601 25.2507i 0.478433 0.993476i
\(647\) −15.0558 7.25047i −0.591903 0.285045i 0.113856 0.993497i \(-0.463680\pi\)
−0.705759 + 0.708452i \(0.749394\pi\)
\(648\) −3.63804 + 0.830360i −0.142916 + 0.0326196i
\(649\) −0.921498 1.91351i −0.0361719 0.0751118i
\(650\) 10.4349i 0.409291i
\(651\) −0.854327 + 0.411422i −0.0334837 + 0.0161249i
\(652\) −7.81280 + 6.23050i −0.305973 + 0.244005i
\(653\) 15.1539 12.0848i 0.593016 0.472914i −0.280404 0.959882i \(-0.590468\pi\)
0.873420 + 0.486968i \(0.161897\pi\)
\(654\) 2.65874 1.28038i 0.103965 0.0500669i
\(655\) 32.7058i 1.27792i
\(656\) −2.47044 5.12992i −0.0964545 0.200290i
\(657\) −1.81145 + 0.413451i −0.0706712 + 0.0161302i
\(658\) 10.7956 + 5.19890i 0.420858 + 0.202674i
\(659\) −17.9113 + 37.1932i −0.697726 + 1.44884i 0.186823 + 0.982394i \(0.440181\pi\)
−0.884548 + 0.466448i \(0.845533\pi\)
\(660\) 0.214126 0.938149i 0.00833486 0.0365174i
\(661\) 2.02284 + 2.53656i 0.0786795 + 0.0986609i 0.819613 0.572917i \(-0.194188\pi\)
−0.740934 + 0.671578i \(0.765617\pi\)
\(662\) −0.435670 + 0.546312i −0.0169328 + 0.0212330i
\(663\) −5.69202 24.9384i −0.221060 0.968526i
\(664\) 37.8946 + 8.64920i 1.47060 + 0.335654i
\(665\) 13.5434 + 10.8005i 0.525192 + 0.418826i
\(666\) −5.97927 −0.231692
\(667\) 27.2219 15.5632i 1.05404 0.602609i
\(668\) 5.83462 0.225748
\(669\) −3.29346 2.62645i −0.127333 0.101544i
\(670\) 8.51524 + 1.94355i 0.328972 + 0.0750858i
\(671\) 1.44767 + 6.34267i 0.0558868 + 0.244856i
\(672\) −3.27741 + 4.10974i −0.126429 + 0.158537i
\(673\) −16.0518 20.1283i −0.618751 0.775889i 0.369418 0.929264i \(-0.379557\pi\)
−0.988168 + 0.153375i \(0.950986\pi\)
\(674\) 6.24895 27.3785i 0.240701 1.05458i
\(675\) 2.99274 6.21448i 0.115191 0.239196i
\(676\) −16.6297 8.00846i −0.639605 0.308018i
\(677\) −40.4962 + 9.24300i −1.55640 + 0.355237i −0.912240 0.409657i \(-0.865648\pi\)
−0.644156 + 0.764894i \(0.722791\pi\)
\(678\) −2.63597 5.47364i −0.101234 0.210214i
\(679\) 0.184046i 0.00706305i
\(680\) −21.2398 + 10.2286i −0.814510 + 0.392247i
\(681\) 3.30275 2.63385i 0.126562 0.100930i
\(682\) −0.456121 + 0.363744i −0.0174658 + 0.0139285i
\(683\) −43.4451 + 20.9220i −1.66238 + 0.800559i −0.663764 + 0.747942i \(0.731042\pi\)
−0.998615 + 0.0526174i \(0.983244\pi\)
\(684\) 7.85447i 0.300323i
\(685\) −2.20972 4.58854i −0.0844292 0.175319i
\(686\) 20.1936 4.60906i 0.770995 0.175975i
\(687\) −6.56211 3.16015i −0.250360 0.120567i
\(688\) −8.13219 + 16.8867i −0.310037 + 0.643798i
\(689\) −0.988539 + 4.33107i −0.0376603 + 0.165001i
\(690\) 7.89830 + 9.90416i 0.300683 + 0.377045i
\(691\) −2.57637 + 3.23067i −0.0980099 + 0.122901i −0.828418 0.560111i \(-0.810759\pi\)
0.730408 + 0.683011i \(0.239330\pi\)
\(692\) −1.38276 6.05825i −0.0525645 0.230300i
\(693\) −2.40025 0.547841i −0.0911779 0.0208108i
\(694\) 15.2035 + 12.1244i 0.577116 + 0.460234i
\(695\) 26.0803 0.989281
\(696\) 11.0556 + 12.0168i 0.419061 + 0.455496i
\(697\) −10.0378 −0.380207
\(698\) −9.80166 7.81656i −0.370998 0.295861i
\(699\) 11.2118 + 2.55903i 0.424071 + 0.0967914i
\(700\) 0.305969 + 1.34054i 0.0115645 + 0.0506675i
\(701\) 9.58933 12.0246i 0.362184 0.454164i −0.567035 0.823694i \(-0.691910\pi\)
0.929219 + 0.369529i \(0.120481\pi\)
\(702\) 23.1467 + 29.0250i 0.873616 + 1.09548i
\(703\) 3.36825 14.7573i 0.127036 0.556582i
\(704\) −2.98037 + 6.18879i −0.112327 + 0.233249i
\(705\) −11.3794 5.48001i −0.428571 0.206389i
\(706\) 11.8415 2.70274i 0.445660 0.101719i
\(707\) −5.87198 12.1933i −0.220838 0.458576i
\(708\) 1.70318i 0.0640096i
\(709\) −37.5460 + 18.0812i −1.41007 + 0.679053i −0.975176 0.221430i \(-0.928928\pi\)
−0.434892 + 0.900483i \(0.643213\pi\)
\(710\) −5.40255 + 4.30839i −0.202754 + 0.161691i
\(711\) −20.4487 + 16.3073i −0.766886 + 0.611571i
\(712\) 5.10365 2.45779i 0.191267 0.0921096i
\(713\) 3.67463i 0.137616i
\(714\) −3.05664 6.34719i −0.114392 0.237538i
\(715\) 9.48358 2.16457i 0.354666 0.0809502i
\(716\) 14.2615 + 6.86796i 0.532976 + 0.256668i
\(717\) 1.13094 2.34843i 0.0422359 0.0877038i
\(718\) −0.928323 + 4.06725i −0.0346447 + 0.151788i
\(719\) −29.0529 36.4312i −1.08349 1.35866i −0.928753 0.370700i \(-0.879118\pi\)
−0.154738 0.987955i \(-0.549453\pi\)
\(720\) 5.49743 6.89356i 0.204877 0.256908i
\(721\) −2.23579 9.79564i −0.0832652 0.364809i
\(722\) −18.9721 4.33026i −0.706069 0.161156i
\(723\) −20.5899 16.4199i −0.765747 0.610663i
\(724\) −3.79117 −0.140898
\(725\) 7.47961 0.528660i 0.277786 0.0196340i
\(726\) −11.8759 −0.440758
\(727\) 4.56246 + 3.63844i 0.169212 + 0.134942i 0.704434 0.709769i \(-0.251201\pi\)
−0.535222 + 0.844711i \(0.679772\pi\)
\(728\) −29.5103 6.73552i −1.09372 0.249635i
\(729\) 2.70919 + 11.8697i 0.100340 + 0.439619i
\(730\) 1.26059 1.58073i 0.0466565 0.0585055i
\(731\) 20.6015 + 25.8335i 0.761974 + 0.955485i
\(732\) −1.16094 + 5.08643i −0.0429097 + 0.188000i
\(733\) −3.63882 + 7.55609i −0.134403 + 0.279090i −0.957298 0.289103i \(-0.906643\pi\)
0.822895 + 0.568193i \(0.192357\pi\)
\(734\) −9.66789 4.65581i −0.356848 0.171849i
\(735\) −8.52015 + 1.94467i −0.314271 + 0.0717302i
\(736\) 8.83841 + 18.3532i 0.325788 + 0.676506i
\(737\) 3.14252i 0.115756i
\(738\) 5.29734 2.55107i 0.194998 0.0939060i
\(739\) 31.0065 24.7268i 1.14059 0.909591i 0.143798 0.989607i \(-0.454068\pi\)
0.996794 + 0.0800156i \(0.0254970\pi\)
\(740\) −2.43386 + 1.94093i −0.0894703 + 0.0713502i
\(741\) −34.1745 + 16.4576i −1.25543 + 0.604585i
\(742\) 1.22349i 0.0449156i
\(743\) −8.29109 17.2166i −0.304171 0.631617i 0.691722 0.722164i \(-0.256853\pi\)
−0.995892 + 0.0905476i \(0.971138\pi\)
\(744\) −1.86556 + 0.425802i −0.0683948 + 0.0156107i
\(745\) −0.987220 0.475420i −0.0361690 0.0174181i
\(746\) 10.8518 22.5340i 0.397312 0.825027i
\(747\) −5.70297 + 24.9863i −0.208661 + 0.914202i
\(748\) 1.29299 + 1.62136i 0.0472764 + 0.0592827i
\(749\) 9.27633 11.6321i 0.338950 0.425029i
\(750\) 3.09462 + 13.5584i 0.112999 + 0.495083i
\(751\) 31.2741 + 7.13811i 1.14121 + 0.260473i 0.751031 0.660267i \(-0.229557\pi\)
0.390177 + 0.920740i \(0.372414\pi\)
\(752\) 12.0712 + 9.62650i 0.440193 + 0.351042i
\(753\) 7.54521 0.274963
\(754\) −14.9033 + 37.5051i −0.542748 + 1.36585i
\(755\) −42.0080 −1.52883
\(756\) −3.82464 3.05005i −0.139101 0.110929i
\(757\) 11.1963 + 2.55549i 0.406937 + 0.0928807i 0.421089 0.907019i \(-0.361648\pi\)
−0.0141525 + 0.999900i \(0.504505\pi\)
\(758\) −4.91499 21.5340i −0.178520 0.782149i
\(759\) 2.84176 3.56346i 0.103149 0.129345i
\(760\) 21.7955 + 27.3307i 0.790607 + 0.991390i
\(761\) −6.58342 + 28.8438i −0.238649 + 1.04559i 0.703579 + 0.710617i \(0.251584\pi\)
−0.942228 + 0.334972i \(0.891273\pi\)
\(762\) 6.35415 13.1945i 0.230186 0.477987i
\(763\) −3.54156 1.70552i −0.128213 0.0617441i
\(764\) 11.9389 2.72496i 0.431932 0.0985858i
\(765\) −6.74434 14.0048i −0.243842 0.506343i
\(766\) 34.0389i 1.22988i
\(767\) 15.5121 7.47026i 0.560111 0.269735i
\(768\) −10.5725 + 8.43131i −0.381503 + 0.304239i
\(769\) 39.6381 31.6103i 1.42939 1.13990i 0.461913 0.886925i \(-0.347163\pi\)
0.967474 0.252972i \(-0.0814081\pi\)
\(770\) 2.41371 1.16238i 0.0869842 0.0418894i
\(771\) 11.7047i 0.421536i
\(772\) 0.992042 + 2.06000i 0.0357044 + 0.0741409i
\(773\) 34.1987 7.80562i 1.23004 0.280749i 0.442363 0.896836i \(-0.354140\pi\)
0.787678 + 0.616087i \(0.211283\pi\)
\(774\) −17.4378 8.39758i −0.626787 0.301845i
\(775\) −0.381257 + 0.791687i −0.0136951 + 0.0284383i
\(776\) 0.0826459 0.362095i 0.00296681 0.0129985i
\(777\) −2.37231 2.97478i −0.0851061 0.106720i
\(778\) 25.7125 32.2425i 0.921839 1.15595i
\(779\) 3.31211 + 14.5113i 0.118669 + 0.519922i
\(780\) 7.60524 + 1.73585i 0.272311 + 0.0621533i
\(781\) 1.94380 + 1.55013i 0.0695548 + 0.0554681i
\(782\) −27.3005 −0.976264
\(783\) −19.6321 + 18.0617i −0.701594 + 0.645474i
\(784\) 10.6833 0.381547
\(785\) −2.27822 1.81682i −0.0813130 0.0648450i
\(786\) −19.2287 4.38883i −0.685866 0.156544i
\(787\) −5.78714 25.3551i −0.206289 0.903813i −0.967011 0.254735i \(-0.918012\pi\)
0.760722 0.649078i \(-0.224845\pi\)
\(788\) 8.91246 11.1759i 0.317493 0.398124i
\(789\) −9.73163 12.2031i −0.346455 0.434441i
\(790\) 6.33308 27.7470i 0.225321 0.987195i
\(791\) −3.51122 + 7.29112i −0.124845 + 0.259243i
\(792\) −4.47627 2.15566i −0.159057 0.0765980i
\(793\) −51.4178 + 11.7358i −1.82590 + 0.416750i
\(794\) 8.12569 + 16.8732i 0.288370 + 0.598806i
\(795\) 1.28964i 0.0457388i
\(796\) −4.88943 + 2.35463i −0.173301 + 0.0834576i
\(797\) 28.6524 22.8495i 1.01492 0.809372i 0.0331511 0.999450i \(-0.489446\pi\)
0.981769 + 0.190079i \(0.0608743\pi\)
\(798\) −8.16736 + 6.51326i −0.289122 + 0.230567i
\(799\) 24.5236 11.8099i 0.867583 0.417806i
\(800\) 4.87115i 0.172221i
\(801\) 1.62058 + 3.36516i 0.0572602 + 0.118902i
\(802\) 27.3784 6.24893i 0.966764 0.220657i
\(803\) −0.655403 0.315625i −0.0231287 0.0111382i
\(804\) 1.09343 2.27054i 0.0385624 0.0800757i
\(805\) 3.75486 16.4511i 0.132341 0.579825i
\(806\) −2.94875 3.69761i −0.103865 0.130243i
\(807\) −0.637763 + 0.799729i −0.0224503 + 0.0281518i
\(808\) −6.07722 26.6260i −0.213796 0.936701i
\(809\) 48.3139 + 11.0273i 1.69863 + 0.387700i 0.958573 0.284848i \(-0.0919431\pi\)
0.740053 + 0.672548i \(0.234800\pi\)
\(810\) 2.09327 + 1.66933i 0.0735500 + 0.0586542i
\(811\) −23.2411 −0.816106 −0.408053 0.912958i \(-0.633792\pi\)
−0.408053 + 0.912958i \(0.633792\pi\)
\(812\) 0.814870 5.25513i 0.0285963 0.184419i
\(813\) 12.1331 0.425525
\(814\) −1.83024 1.45957i −0.0641498 0.0511577i
\(815\) 28.5899 + 6.52545i 1.00146 + 0.228577i
\(816\) −2.01996 8.85003i −0.0707128 0.309813i
\(817\) 30.5489 38.3072i 1.06877 1.34020i
\(818\) 11.9417 + 14.9744i 0.417533 + 0.523569i
\(819\) 4.44116 19.4580i 0.155187 0.679917i
\(820\) 1.32817 2.75798i 0.0463819 0.0963129i
\(821\) 7.98951 + 3.84755i 0.278836 + 0.134280i 0.568076 0.822976i \(-0.307688\pi\)
−0.289240 + 0.957257i \(0.593402\pi\)
\(822\) 2.99427 0.683422i 0.104437 0.0238371i
\(823\) 21.9421 + 45.5632i 0.764853 + 1.58823i 0.808012 + 0.589166i \(0.200544\pi\)
−0.0431587 + 0.999068i \(0.513742\pi\)
\(824\) 20.2760i 0.706349i
\(825\) 0.981971 0.472892i 0.0341878 0.0164640i
\(826\) 3.70724 2.95643i 0.128992 0.102867i
\(827\) −27.9605 + 22.2978i −0.972283 + 0.775370i −0.974445 0.224628i \(-0.927883\pi\)
0.00216160 + 0.999998i \(0.499312\pi\)
\(828\) −6.89340 + 3.31969i −0.239562 + 0.115367i
\(829\) 36.7260i 1.27555i 0.770224 + 0.637774i \(0.220145\pi\)
−0.770224 + 0.637774i \(0.779855\pi\)
\(830\) −12.1003 25.1265i −0.420007 0.872153i
\(831\) 11.7910 2.69122i 0.409026 0.0933575i
\(832\) −50.1704 24.1608i −1.73934 0.837624i
\(833\) 8.17174 16.9688i 0.283134 0.587934i
\(834\) −3.49974 + 15.3334i −0.121186 + 0.530951i
\(835\) −10.6755 13.3867i −0.369441 0.463264i
\(836\) 1.91731 2.40423i 0.0663115 0.0831520i
\(837\) −0.695642 3.04781i −0.0240449 0.105348i
\(838\) −17.5889 4.01455i −0.607598 0.138680i
\(839\) 15.6051 + 12.4446i 0.538746 + 0.429636i 0.854687 0.519143i \(-0.173749\pi\)
−0.315941 + 0.948779i \(0.602320\pi\)
\(840\) 8.78711 0.303184
\(841\) −27.6382 8.78242i −0.953041 0.302842i
\(842\) −14.2495 −0.491071
\(843\) −0.505243 0.402918i −0.0174015 0.0138772i
\(844\) −2.35622 0.537792i −0.0811044 0.0185115i
\(845\) 12.0529 + 52.8073i 0.414633 + 1.81663i
\(846\) −9.94066 + 12.4652i −0.341767 + 0.428562i
\(847\) 9.86315 + 12.3680i 0.338902 + 0.424969i
\(848\) −0.350809 + 1.53699i −0.0120468 + 0.0527805i
\(849\) 1.29250 2.68391i 0.0443586 0.0921115i
\(850\) −5.88181 2.83253i −0.201744 0.0971550i
\(851\) −14.3752 + 3.28104i −0.492775 + 0.112473i
\(852\) 0.865074 + 1.79635i 0.0296370 + 0.0615418i
\(853\) 48.9528i 1.67611i 0.545584 + 0.838056i \(0.316308\pi\)
−0.545584 + 0.838056i \(0.683692\pi\)
\(854\) −13.0866 + 6.30217i −0.447814 + 0.215656i
\(855\) −18.0209 + 14.3712i −0.616301 + 0.491484i
\(856\) 23.4738 18.7197i 0.802317 0.639826i
\(857\) −42.8039 + 20.6133i −1.46215 + 0.704137i −0.984658 0.174497i \(-0.944170\pi\)
−0.477497 + 0.878633i \(0.658456\pi\)
\(858\) 5.86615i 0.200267i
\(859\) −4.60217 9.55651i −0.157024 0.326064i 0.807584 0.589753i \(-0.200775\pi\)
−0.964608 + 0.263689i \(0.915061\pi\)
\(860\) −9.82397 + 2.24226i −0.334995 + 0.0764603i
\(861\) 3.37094 + 1.62336i 0.114881 + 0.0553240i
\(862\) −10.7499 + 22.3225i −0.366144 + 0.760306i
\(863\) 4.38167 19.1973i 0.149154 0.653485i −0.843968 0.536394i \(-0.819786\pi\)
0.993121 0.117091i \(-0.0373568\pi\)
\(864\) −10.8052 13.5492i −0.367599 0.460955i
\(865\) −11.3697 + 14.2572i −0.386582 + 0.484759i
\(866\) −6.13845 26.8943i −0.208593 0.913906i
\(867\) 0.720005 + 0.164336i 0.0244526 + 0.00558116i
\(868\) 0.487235 + 0.388557i 0.0165378 + 0.0131885i
\(869\) −10.2400 −0.347367
\(870\) 1.79522 11.5774i 0.0608635 0.392511i
\(871\) 25.4753 0.863198
\(872\) −6.20184 4.94580i −0.210021 0.167486i
\(873\) 0.238752 + 0.0544936i 0.00808054 + 0.00184433i
\(874\) 9.00822 + 39.4676i 0.304708 + 1.33501i
\(875\) 11.5500 14.4833i 0.390462 0.489624i
\(876\) −0.363721 0.456092i −0.0122890 0.0154099i
\(877\) −1.71129 + 7.49765i −0.0577861 + 0.253178i −0.995568 0.0940484i \(-0.970019\pi\)
0.937782 + 0.347226i \(0.112876\pi\)
\(878\) −10.1829 + 21.1451i −0.343657 + 0.713612i
\(879\) 13.8239 + 6.65725i 0.466269 + 0.224543i
\(880\) 3.36549 0.768152i 0.113451 0.0258944i
\(881\) −11.9696 24.8552i −0.403266 0.837391i −0.999404 0.0345094i \(-0.989013\pi\)
0.596138 0.802882i \(-0.296701\pi\)
\(882\) 11.0320i 0.371466i
\(883\) −25.6400 + 12.3476i −0.862854 + 0.415529i −0.812333 0.583194i \(-0.801803\pi\)
−0.0505214 + 0.998723i \(0.516088\pi\)
\(884\) −13.1438 + 10.4818i −0.442073 + 0.352541i
\(885\) −3.90770 + 3.11628i −0.131356 + 0.104753i
\(886\) −18.9392 + 9.12065i −0.636276 + 0.306414i
\(887\) 22.5316i 0.756536i 0.925696 + 0.378268i \(0.123480\pi\)
−0.925696 + 0.378268i \(0.876520\pi\)
\(888\) −3.33148 6.91790i −0.111797 0.232150i
\(889\) −19.0184 + 4.34083i −0.637857 + 0.145587i
\(890\) −3.66183 1.76344i −0.122745 0.0591107i
\(891\) 0.417965 0.867913i 0.0140023 0.0290762i
\(892\) −0.616058 + 2.69913i −0.0206271 + 0.0903734i
\(893\) −25.1652 31.5562i −0.842123 1.05599i
\(894\) 0.411990 0.516620i 0.0137790 0.0172783i
\(895\) −10.3365 45.2870i −0.345510 1.51378i
\(896\) −4.54390 1.03712i −0.151801 0.0346476i
\(897\) 28.8877 + 23.0372i 0.964532 + 0.769189i
\(898\) 35.9540 1.19980
\(899\) 2.50101 2.30096i 0.0834134 0.0767412i
\(900\) −1.82959 −0.0609864
\(901\) 2.17294 + 1.73286i 0.0723912 + 0.0577300i
\(902\) 2.24423 + 0.512230i 0.0747246 + 0.0170554i
\(903\) −2.74060 12.0073i −0.0912014 0.399579i
\(904\) −10.1821 + 12.7679i −0.338651 + 0.424655i
\(905\) 6.93664 + 8.69827i 0.230582 + 0.289140i
\(906\) 5.63711 24.6978i 0.187280 0.820529i
\(907\) 17.9411 37.2552i 0.595726 1.23704i −0.357255 0.934007i \(-0.616287\pi\)
0.952981 0.303030i \(-0.0979983\pi\)
\(908\) −2.50140 1.20461i −0.0830119 0.0399764i
\(909\) 17.5562 4.00709i 0.582303 0.132907i
\(910\) 9.42303 + 19.5671i 0.312370 + 0.648644i
\(911\) 8.27165i 0.274052i −0.990567 0.137026i \(-0.956246\pi\)
0.990567 0.137026i \(-0.0437544\pi\)
\(912\) −12.1277 + 5.84040i −0.401589 + 0.193395i
\(913\) −7.84493 + 6.25612i −0.259629 + 0.207047i
\(914\) 22.7861 18.1713i 0.753698 0.601054i
\(915\) 13.7942 6.64293i 0.456022 0.219609i
\(916\) 4.78680i 0.158160i
\(917\) 11.3991 + 23.6704i 0.376430 + 0.781666i
\(918\) 22.6435 5.16824i 0.747348 0.170577i
\(919\) 24.9821 + 12.0308i 0.824085 + 0.396858i 0.797893 0.602799i \(-0.205948\pi\)
0.0261913 + 0.999657i \(0.491662\pi\)
\(920\) 14.7747 30.6800i 0.487107 1.01149i
\(921\) 2.77205 12.1451i 0.0913420 0.400196i
\(922\) 25.3173 + 31.7468i 0.833779 + 1.04553i
\(923\) −12.5664 + 15.7577i −0.413627 + 0.518672i
\(924\) −0.172005 0.753604i −0.00565855 0.0247917i
\(925\) −3.43751 0.784589i −0.113025 0.0257971i
\(926\) 12.6968 + 10.1253i 0.417241 + 0.332739i
\(927\) 13.3693 0.439105
\(928\) 6.95706 17.5078i 0.228377 0.574722i
\(929\) −29.3190 −0.961924 −0.480962 0.876742i \(-0.659712\pi\)
−0.480962 + 0.876742i \(0.659712\pi\)
\(930\) 1.07341 + 0.856019i 0.0351986 + 0.0280700i
\(931\) −27.2277 6.21455i −0.892352 0.203674i
\(932\) −1.68185 7.36865i −0.0550907 0.241368i
\(933\) 10.1691 12.7516i 0.332920 0.417468i
\(934\) −28.8697 36.2015i −0.944646 1.18455i
\(935\) 1.35420 5.93314i 0.0442871 0.194034i
\(936\) 17.4752 36.2876i 0.571194 1.18610i
\(937\) 3.37115 + 1.62346i 0.110131 + 0.0530361i 0.488138 0.872767i \(-0.337676\pi\)
−0.378007 + 0.925803i \(0.623391\pi\)
\(938\) 6.84019 1.56123i 0.223340 0.0509759i
\(939\) −1.50699 3.12929i −0.0491786 0.102121i
\(940\) 8.30079i 0.270742i
\(941\) 1.20496 0.580278i 0.0392806 0.0189165i −0.414140 0.910213i \(-0.635918\pi\)
0.453421 + 0.891297i \(0.350203\pi\)
\(942\) 1.37388 1.09563i 0.0447634 0.0356976i
\(943\) 11.3359 9.04004i 0.369146 0.294384i
\(944\) 5.50489 2.65101i 0.179169 0.0862831i
\(945\) 14.3557i 0.466990i
\(946\) −3.28776 6.82711i −0.106894 0.221968i
\(947\) 5.74852 1.31206i 0.186802 0.0426363i −0.128096 0.991762i \(-0.540887\pi\)
0.314898 + 0.949125i \(0.398030\pi\)
\(948\) −7.39858 3.56297i −0.240295 0.115720i
\(949\) 2.55867 5.31312i 0.0830578 0.172471i
\(950\) −2.15412 + 9.43780i −0.0698888 + 0.306203i
\(951\) −3.27381 4.10523i −0.106161 0.133121i
\(952\) −11.8071 + 14.8056i −0.382669 + 0.479852i
\(953\) 2.83040 + 12.4008i 0.0916856 + 0.401701i 0.999857 0.0168972i \(-0.00537879\pi\)
−0.908172 + 0.418598i \(0.862522\pi\)
\(954\) −1.58715 0.362257i −0.0513860 0.0117285i
\(955\) −28.0963 22.4061i −0.909176 0.725043i
\(956\) −1.71309 −0.0554052
\(957\) −4.20478 + 0.297195i −0.135921 + 0.00960694i
\(958\) 14.0995 0.455533
\(959\) −3.19852 2.55074i −0.103286 0.0823676i
\(960\) 15.7600 + 3.59711i 0.508651 + 0.116096i
\(961\) −6.80953 29.8345i −0.219662 0.962403i
\(962\) 11.8322 14.8371i 0.381485 0.478367i
\(963\) 12.3431 + 15.4777i 0.397750 + 0.498763i
\(964\) −3.85144 + 16.8743i −0.124047 + 0.543484i
\(965\) 2.91123 6.04523i 0.0937157 0.194603i
\(966\) 9.16823 + 4.41519i 0.294983 + 0.142056i
\(967\) −6.76051 + 1.54304i −0.217403 + 0.0496209i −0.329835 0.944039i \(-0.606993\pi\)
0.112432 + 0.993659i \(0.464136\pi\)
\(968\) 13.8510 + 28.7620i 0.445189 + 0.924445i
\(969\) 23.7304i 0.762330i
\(970\) −0.240091 + 0.115622i −0.00770887 + 0.00371240i
\(971\) −3.78925 + 3.02183i −0.121603 + 0.0969751i −0.682403 0.730976i \(-0.739065\pi\)
0.560800 + 0.827951i \(0.310494\pi\)
\(972\) 8.12420 6.47883i 0.260584 0.207809i
\(973\) 18.8753 9.08985i 0.605113 0.291407i
\(974\) 14.9189i 0.478032i
\(975\) 3.83357 + 7.96049i 0.122773 + 0.254940i
\(976\) −18.2469 + 4.16474i −0.584070 + 0.133310i
\(977\) 2.84620 + 1.37066i 0.0910580 + 0.0438512i 0.478858 0.877892i \(-0.341051\pi\)
−0.387800 + 0.921743i \(0.626765\pi\)
\(978\) −7.67302 + 15.9332i −0.245356 + 0.509487i
\(979\) −0.325397 + 1.42566i −0.0103997 + 0.0455641i
\(980\) 3.58109 + 4.49055i 0.114394 + 0.143445i
\(981\) 3.26108 4.08926i 0.104118 0.130560i
\(982\) 6.24000 + 27.3392i 0.199126 + 0.872429i
\(983\) 39.5951 + 9.03732i 1.26289 + 0.288246i 0.800985 0.598685i \(-0.204310\pi\)
0.461903 + 0.886931i \(0.347167\pi\)
\(984\) 5.90307 + 4.70754i 0.188183 + 0.150071i
\(985\) −41.9483 −1.33658
\(986\) 17.0949 + 18.5811i 0.544411 + 0.591744i
\(987\) −10.1456 −0.322939
\(988\) 19.4902 + 15.5430i 0.620067 + 0.494487i
\(989\) −46.5314 10.6205i −1.47961 0.337712i
\(990\) 0.793221 + 3.47533i 0.0252102 + 0.110453i
\(991\) −14.7185 + 18.4565i −0.467550 + 0.586289i −0.958569 0.284860i \(-0.908053\pi\)
0.491020 + 0.871149i \(0.336624\pi\)
\(992\) 1.37651 + 1.72609i 0.0437043 + 0.0548034i
\(993\) 0.131656 0.576822i 0.00417797 0.0183049i
\(994\) −2.40841 + 5.00111i −0.0763900 + 0.158626i
\(995\) 14.3484 + 6.90985i 0.454876 + 0.219057i
\(996\) −7.84493 + 1.79055i −0.248576 + 0.0567359i
\(997\) −18.6759 38.7810i −0.591472 1.22821i −0.954996 0.296620i \(-0.904141\pi\)
0.363523 0.931585i \(-0.381574\pi\)
\(998\) 21.4153i 0.677891i
\(999\) 11.3019 5.44271i 0.357576 0.172200i
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 29.2.e.a.6.1 yes 12
3.2 odd 2 261.2.o.a.64.2 12
4.3 odd 2 464.2.y.d.209.1 12
5.2 odd 4 725.2.p.a.499.3 24
5.3 odd 4 725.2.p.a.499.2 24
5.4 even 2 725.2.q.a.151.2 12
29.2 odd 28 841.2.d.m.778.2 24
29.3 odd 28 841.2.d.l.605.3 24
29.4 even 14 841.2.e.e.270.1 12
29.5 even 14 inner 29.2.e.a.5.1 12
29.6 even 14 841.2.e.f.651.2 12
29.7 even 7 841.2.e.a.236.2 12
29.8 odd 28 841.2.d.l.645.2 24
29.9 even 14 841.2.e.a.196.2 12
29.10 odd 28 841.2.d.k.571.2 24
29.11 odd 28 841.2.a.k.1.4 12
29.12 odd 4 841.2.d.m.574.3 24
29.13 even 14 841.2.b.e.840.9 12
29.14 odd 28 841.2.d.k.190.3 24
29.15 odd 28 841.2.d.k.190.2 24
29.16 even 7 841.2.b.e.840.4 12
29.17 odd 4 841.2.d.m.574.2 24
29.18 odd 28 841.2.a.k.1.9 12
29.19 odd 28 841.2.d.k.571.3 24
29.20 even 7 841.2.e.h.196.1 12
29.21 odd 28 841.2.d.l.645.3 24
29.22 even 14 841.2.e.h.236.1 12
29.23 even 7 841.2.e.e.651.1 12
29.24 even 7 841.2.e.i.63.2 12
29.25 even 7 841.2.e.f.270.2 12
29.26 odd 28 841.2.d.l.605.2 24
29.27 odd 28 841.2.d.m.778.3 24
29.28 even 2 841.2.e.i.267.2 12
87.5 odd 14 261.2.o.a.208.2 12
87.11 even 28 7569.2.a.bp.1.9 12
87.47 even 28 7569.2.a.bp.1.4 12
116.63 odd 14 464.2.y.d.353.1 12
145.34 even 14 725.2.q.a.701.2 12
145.63 odd 28 725.2.p.a.324.3 24
145.92 odd 28 725.2.p.a.324.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.2.e.a.5.1 12 29.5 even 14 inner
29.2.e.a.6.1 yes 12 1.1 even 1 trivial
261.2.o.a.64.2 12 3.2 odd 2
261.2.o.a.208.2 12 87.5 odd 14
464.2.y.d.209.1 12 4.3 odd 2
464.2.y.d.353.1 12 116.63 odd 14
725.2.p.a.324.2 24 145.92 odd 28
725.2.p.a.324.3 24 145.63 odd 28
725.2.p.a.499.2 24 5.3 odd 4
725.2.p.a.499.3 24 5.2 odd 4
725.2.q.a.151.2 12 5.4 even 2
725.2.q.a.701.2 12 145.34 even 14
841.2.a.k.1.4 12 29.11 odd 28
841.2.a.k.1.9 12 29.18 odd 28
841.2.b.e.840.4 12 29.16 even 7
841.2.b.e.840.9 12 29.13 even 14
841.2.d.k.190.2 24 29.15 odd 28
841.2.d.k.190.3 24 29.14 odd 28
841.2.d.k.571.2 24 29.10 odd 28
841.2.d.k.571.3 24 29.19 odd 28
841.2.d.l.605.2 24 29.26 odd 28
841.2.d.l.605.3 24 29.3 odd 28
841.2.d.l.645.2 24 29.8 odd 28
841.2.d.l.645.3 24 29.21 odd 28
841.2.d.m.574.2 24 29.17 odd 4
841.2.d.m.574.3 24 29.12 odd 4
841.2.d.m.778.2 24 29.2 odd 28
841.2.d.m.778.3 24 29.27 odd 28
841.2.e.a.196.2 12 29.9 even 14
841.2.e.a.236.2 12 29.7 even 7
841.2.e.e.270.1 12 29.4 even 14
841.2.e.e.651.1 12 29.23 even 7
841.2.e.f.270.2 12 29.25 even 7
841.2.e.f.651.2 12 29.6 even 14
841.2.e.h.196.1 12 29.20 even 7
841.2.e.h.236.1 12 29.22 even 14
841.2.e.i.63.2 12 29.24 even 7
841.2.e.i.267.2 12 29.28 even 2
7569.2.a.bp.1.4 12 87.47 even 28
7569.2.a.bp.1.9 12 87.11 even 28