Properties

Label 81.2.g.a.13.4
Level $81$
Weight $2$
Character 81.13
Analytic conductor $0.647$
Analytic rank $0$
Dimension $144$
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] = [81,2,Mod(4,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 81.g (of order \(27\), degree \(18\), 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: \(0.646788256372\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 13.4
Character \(\chi\) \(=\) 81.13
Dual form 81.2.g.a.25.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.698417 - 0.350758i) q^{2} +(0.295453 - 1.70667i) q^{3} +(-0.829563 - 1.11430i) q^{4} +(0.424677 + 1.41852i) q^{5} +(-0.804976 + 1.08833i) q^{6} +(-1.50560 - 3.49038i) q^{7} +(0.459961 + 2.60857i) q^{8} +(-2.82541 - 1.00848i) q^{9} +O(q^{10})\) \(q+(-0.698417 - 0.350758i) q^{2} +(0.295453 - 1.70667i) q^{3} +(-0.829563 - 1.11430i) q^{4} +(0.424677 + 1.41852i) q^{5} +(-0.804976 + 1.08833i) q^{6} +(-1.50560 - 3.49038i) q^{7} +(0.459961 + 2.60857i) q^{8} +(-2.82541 - 1.00848i) q^{9} +(0.200956 - 1.13968i) q^{10} +(4.91819 - 1.16563i) q^{11} +(-2.14683 + 1.08656i) q^{12} +(3.75323 + 2.46854i) q^{13} +(-0.172741 + 2.96584i) q^{14} +(2.54641 - 0.305675i) q^{15} +(-0.203113 + 0.678443i) q^{16} +(-4.30582 + 1.56719i) q^{17} +(1.61958 + 1.69538i) q^{18} +(4.19524 + 1.52694i) q^{19} +(1.22836 - 1.64997i) q^{20} +(-6.40175 + 1.53832i) q^{21} +(-3.84380 - 0.910998i) q^{22} +(-1.36843 + 3.17237i) q^{23} +(4.58785 - 0.0142893i) q^{24} +(2.34559 - 1.54272i) q^{25} +(-1.75546 - 3.04054i) q^{26} +(-2.55592 + 4.52408i) q^{27} +(-2.64032 + 4.57318i) q^{28} +(-0.0379650 - 0.651834i) q^{29} +(-1.88567 - 0.679686i) q^{30} +(-0.653701 + 0.0764066i) q^{31} +(4.01527 - 4.25594i) q^{32} +(-0.536249 - 8.73810i) q^{33} +(3.55696 + 0.415749i) q^{34} +(4.31178 - 3.61801i) q^{35} +(1.22011 + 3.98495i) q^{36} +(0.766165 + 0.642889i) q^{37} +(-2.39444 - 2.53796i) q^{38} +(5.32187 - 5.67616i) q^{39} +(-3.50497 + 1.76026i) q^{40} +(-0.610184 + 0.306446i) q^{41} +(5.01066 + 1.17108i) q^{42} +(-5.75968 - 6.10490i) q^{43} +(-5.37881 - 4.51336i) q^{44} +(0.230661 - 4.43619i) q^{45} +(2.06847 - 1.73565i) q^{46} +(-7.88112 - 0.921171i) q^{47} +(1.09787 + 0.547094i) q^{48} +(-5.11223 + 5.41864i) q^{49} +(-2.17932 + 0.254726i) q^{50} +(1.40250 + 7.81162i) q^{51} +(-0.362857 - 6.23001i) q^{52} +(-2.07469 + 3.59347i) q^{53} +(3.37195 - 2.26318i) q^{54} +(3.74212 + 6.48154i) q^{55} +(8.41238 - 5.53291i) q^{56} +(3.84548 - 6.70874i) q^{57} +(-0.202121 + 0.468568i) q^{58} +(5.12792 + 1.21534i) q^{59} +(-2.45302 - 2.58388i) q^{60} +(-4.05529 + 5.44719i) q^{61} +(0.483356 + 0.175927i) q^{62} +(0.733974 + 11.3801i) q^{63} +(-2.96617 + 1.07960i) q^{64} +(-1.90776 + 6.37236i) q^{65} +(-2.69043 + 6.29093i) q^{66} +(-0.308237 + 5.29223i) q^{67} +(5.31826 + 3.49787i) q^{68} +(5.00987 + 3.27274i) q^{69} +(-4.28047 + 1.01449i) q^{70} +(-1.06500 + 6.03991i) q^{71} +(1.33111 - 7.83415i) q^{72} +(-0.764322 - 4.33469i) q^{73} +(-0.309604 - 0.717743i) q^{74} +(-1.93989 - 4.45894i) q^{75} +(-1.77875 - 5.94144i) q^{76} +(-11.4734 - 15.4114i) q^{77} +(-5.70784 + 2.09764i) q^{78} +(10.0467 + 5.04564i) q^{79} -1.04864 q^{80} +(6.96594 + 5.69875i) q^{81} +0.533651 q^{82} +(1.44915 + 0.727793i) q^{83} +(7.02479 + 5.85731i) q^{84} +(-4.05167 - 5.44234i) q^{85} +(1.88131 + 6.28402i) q^{86} +(-1.12368 - 0.127793i) q^{87} +(5.30281 + 12.2933i) q^{88} +(-0.181087 - 1.02699i) q^{89} +(-1.71713 + 3.01740i) q^{90} +(2.96526 - 16.8168i) q^{91} +(4.67016 - 1.10685i) q^{92} +(-0.0627375 + 1.13822i) q^{93} +(5.18120 + 3.40773i) q^{94} +(-0.384377 + 6.59950i) q^{95} +(-6.07714 - 8.11016i) q^{96} +(-1.43062 + 4.77859i) q^{97} +(5.47110 - 1.99132i) q^{98} +(-15.0715 - 1.66650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/81\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{4}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.698417 0.350758i −0.493855 0.248023i 0.184398 0.982852i \(-0.440966\pi\)
−0.678253 + 0.734828i \(0.737263\pi\)
\(3\) 0.295453 1.70667i 0.170580 0.985344i
\(4\) −0.829563 1.11430i −0.414781 0.557148i
\(5\) 0.424677 + 1.41852i 0.189921 + 0.634382i 0.998915 + 0.0465645i \(0.0148273\pi\)
−0.808994 + 0.587817i \(0.799987\pi\)
\(6\) −0.804976 + 1.08833i −0.328630 + 0.444309i
\(7\) −1.50560 3.49038i −0.569065 1.31924i −0.923299 0.384083i \(-0.874518\pi\)
0.354234 0.935157i \(-0.384742\pi\)
\(8\) 0.459961 + 2.60857i 0.162621 + 0.922268i
\(9\) −2.82541 1.00848i −0.941805 0.336160i
\(10\) 0.200956 1.13968i 0.0635478 0.360398i
\(11\) 4.91819 1.16563i 1.48289 0.351452i 0.592100 0.805865i \(-0.298299\pi\)
0.890791 + 0.454413i \(0.150151\pi\)
\(12\) −2.14683 + 1.08656i −0.619736 + 0.313664i
\(13\) 3.75323 + 2.46854i 1.04096 + 0.684649i 0.950332 0.311237i \(-0.100743\pi\)
0.0906250 + 0.995885i \(0.471114\pi\)
\(14\) −0.172741 + 2.96584i −0.0461669 + 0.792655i
\(15\) 2.54641 0.305675i 0.657481 0.0789250i
\(16\) −0.203113 + 0.678443i −0.0507782 + 0.169611i
\(17\) −4.30582 + 1.56719i −1.04431 + 0.380099i −0.806514 0.591215i \(-0.798648\pi\)
−0.237800 + 0.971314i \(0.576426\pi\)
\(18\) 1.61958 + 1.69538i 0.381740 + 0.399604i
\(19\) 4.19524 + 1.52694i 0.962455 + 0.350305i 0.774995 0.631967i \(-0.217752\pi\)
0.187460 + 0.982272i \(0.439975\pi\)
\(20\) 1.22836 1.64997i 0.274669 0.368944i
\(21\) −6.40175 + 1.53832i −1.39698 + 0.335688i
\(22\) −3.84380 0.910998i −0.819502 0.194225i
\(23\) −1.36843 + 3.17237i −0.285337 + 0.661486i −0.999249 0.0387500i \(-0.987662\pi\)
0.713912 + 0.700235i \(0.246922\pi\)
\(24\) 4.58785 0.0142893i 0.936491 0.00291679i
\(25\) 2.34559 1.54272i 0.469118 0.308544i
\(26\) −1.75546 3.04054i −0.344273 0.596299i
\(27\) −2.55592 + 4.52408i −0.491886 + 0.870659i
\(28\) −2.64032 + 4.57318i −0.498974 + 0.864249i
\(29\) −0.0379650 0.651834i −0.00704993 0.121043i −0.999997 0.00248341i \(-0.999210\pi\)
0.992947 0.118559i \(-0.0378275\pi\)
\(30\) −1.88567 0.679686i −0.344276 0.124093i
\(31\) −0.653701 + 0.0764066i −0.117408 + 0.0137230i −0.174594 0.984641i \(-0.555861\pi\)
0.0571859 + 0.998364i \(0.481787\pi\)
\(32\) 4.01527 4.25594i 0.709807 0.752351i
\(33\) −0.536249 8.73810i −0.0933490 1.52111i
\(34\) 3.55696 + 0.415749i 0.610013 + 0.0713003i
\(35\) 4.31178 3.61801i 0.728824 0.611556i
\(36\) 1.22011 + 3.98495i 0.203352 + 0.664158i
\(37\) 0.766165 + 0.642889i 0.125957 + 0.105690i 0.703590 0.710606i \(-0.251579\pi\)
−0.577633 + 0.816296i \(0.696024\pi\)
\(38\) −2.39444 2.53796i −0.388429 0.411711i
\(39\) 5.32187 5.67616i 0.852181 0.908914i
\(40\) −3.50497 + 1.76026i −0.554185 + 0.278322i
\(41\) −0.610184 + 0.306446i −0.0952947 + 0.0478588i −0.495808 0.868432i \(-0.665128\pi\)
0.400513 + 0.916291i \(0.368832\pi\)
\(42\) 5.01066 + 1.17108i 0.773162 + 0.180701i
\(43\) −5.75968 6.10490i −0.878343 0.930989i 0.119745 0.992805i \(-0.461792\pi\)
−0.998088 + 0.0618156i \(0.980311\pi\)
\(44\) −5.37881 4.51336i −0.810886 0.680414i
\(45\) 0.230661 4.43619i 0.0343849 0.661308i
\(46\) 2.06847 1.73565i 0.304979 0.255908i
\(47\) −7.88112 0.921171i −1.14958 0.134367i −0.480111 0.877207i \(-0.659404\pi\)
−0.669468 + 0.742841i \(0.733478\pi\)
\(48\) 1.09787 + 0.547094i 0.158463 + 0.0789662i
\(49\) −5.11223 + 5.41864i −0.730318 + 0.774092i
\(50\) −2.17932 + 0.254726i −0.308202 + 0.0360237i
\(51\) 1.40250 + 7.81162i 0.196389 + 1.09385i
\(52\) −0.362857 6.23001i −0.0503192 0.863947i
\(53\) −2.07469 + 3.59347i −0.284981 + 0.493601i −0.972605 0.232466i \(-0.925321\pi\)
0.687624 + 0.726067i \(0.258654\pi\)
\(54\) 3.37195 2.26318i 0.458865 0.307980i
\(55\) 3.74212 + 6.48154i 0.504587 + 0.873971i
\(56\) 8.41238 5.53291i 1.12415 0.739366i
\(57\) 3.84548 6.70874i 0.509346 0.888594i
\(58\) −0.202121 + 0.468568i −0.0265397 + 0.0615261i
\(59\) 5.12792 + 1.21534i 0.667598 + 0.158224i 0.550421 0.834887i \(-0.314467\pi\)
0.117177 + 0.993111i \(0.462615\pi\)
\(60\) −2.45302 2.58388i −0.316684 0.333577i
\(61\) −4.05529 + 5.44719i −0.519226 + 0.697442i −0.981967 0.189052i \(-0.939459\pi\)
0.462741 + 0.886494i \(0.346866\pi\)
\(62\) 0.483356 + 0.175927i 0.0613862 + 0.0223428i
\(63\) 0.733974 + 11.3801i 0.0924720 + 1.43376i
\(64\) −2.96617 + 1.07960i −0.370771 + 0.134950i
\(65\) −1.90776 + 6.37236i −0.236628 + 0.790394i
\(66\) −2.69043 + 6.29093i −0.331170 + 0.774360i
\(67\) −0.308237 + 5.29223i −0.0376572 + 0.646549i 0.925689 + 0.378286i \(0.123487\pi\)
−0.963346 + 0.268263i \(0.913551\pi\)
\(68\) 5.31826 + 3.49787i 0.644933 + 0.424179i
\(69\) 5.00987 + 3.27274i 0.603118 + 0.393991i
\(70\) −4.28047 + 1.01449i −0.511614 + 0.121255i
\(71\) −1.06500 + 6.03991i −0.126392 + 0.716805i 0.854079 + 0.520143i \(0.174121\pi\)
−0.980471 + 0.196662i \(0.936990\pi\)
\(72\) 1.33111 7.83415i 0.156873 0.923263i
\(73\) −0.764322 4.33469i −0.0894571 0.507337i −0.996306 0.0858796i \(-0.972630\pi\)
0.906848 0.421457i \(-0.138481\pi\)
\(74\) −0.309604 0.717743i −0.0359907 0.0834359i
\(75\) −1.93989 4.45894i −0.223999 0.514874i
\(76\) −1.77875 5.94144i −0.204037 0.681530i
\(77\) −11.4734 15.4114i −1.30751 1.75629i
\(78\) −5.70784 + 2.09764i −0.646286 + 0.237511i
\(79\) 10.0467 + 5.04564i 1.13034 + 0.567679i 0.912814 0.408375i \(-0.133904\pi\)
0.217528 + 0.976054i \(0.430201\pi\)
\(80\) −1.04864 −0.117242
\(81\) 6.96594 + 5.69875i 0.773993 + 0.633194i
\(82\) 0.533651 0.0589319
\(83\) 1.44915 + 0.727793i 0.159065 + 0.0798857i 0.526551 0.850144i \(-0.323485\pi\)
−0.367486 + 0.930029i \(0.619781\pi\)
\(84\) 7.02479 + 5.85731i 0.766467 + 0.639085i
\(85\) −4.05167 5.44234i −0.439465 0.590305i
\(86\) 1.88131 + 6.28402i 0.202867 + 0.677623i
\(87\) −1.12368 0.127793i −0.120471 0.0137009i
\(88\) 5.30281 + 12.2933i 0.565281 + 1.31047i
\(89\) −0.181087 1.02699i −0.0191952 0.108861i 0.973705 0.227813i \(-0.0731576\pi\)
−0.992900 + 0.118952i \(0.962046\pi\)
\(90\) −1.71713 + 3.01740i −0.181001 + 0.318062i
\(91\) 2.96526 16.8168i 0.310844 1.76288i
\(92\) 4.67016 1.10685i 0.486898 0.115397i
\(93\) −0.0627375 + 1.13822i −0.00650557 + 0.118028i
\(94\) 5.18120 + 3.40773i 0.534400 + 0.351480i
\(95\) −0.384377 + 6.59950i −0.0394362 + 0.677094i
\(96\) −6.07714 8.11016i −0.620246 0.827740i
\(97\) −1.43062 + 4.77859i −0.145257 + 0.485192i −0.999392 0.0348588i \(-0.988902\pi\)
0.854135 + 0.520051i \(0.174087\pi\)
\(98\) 5.47110 1.99132i 0.552664 0.201153i
\(99\) −15.0715 1.66650i −1.51474 0.167490i
\(100\) −3.66486 1.33390i −0.366486 0.133390i
\(101\) −5.71510 + 7.67671i −0.568673 + 0.763861i −0.989695 0.143190i \(-0.954264\pi\)
0.421022 + 0.907050i \(0.361672\pi\)
\(102\) 1.76046 5.94770i 0.174311 0.588910i
\(103\) 3.16740 + 0.750687i 0.312093 + 0.0739673i 0.383677 0.923467i \(-0.374657\pi\)
−0.0715847 + 0.997435i \(0.522806\pi\)
\(104\) −4.71300 + 10.9260i −0.462148 + 1.07138i
\(105\) −4.90081 8.42772i −0.478270 0.822461i
\(106\) 2.70944 1.78203i 0.263164 0.173086i
\(107\) −8.40680 14.5610i −0.812716 1.40767i −0.910956 0.412503i \(-0.864655\pi\)
0.0982402 0.995163i \(-0.468679\pi\)
\(108\) 7.16145 0.904959i 0.689111 0.0870797i
\(109\) −3.81772 + 6.61249i −0.365671 + 0.633361i −0.988884 0.148691i \(-0.952494\pi\)
0.623212 + 0.782053i \(0.285827\pi\)
\(110\) −0.340106 5.83939i −0.0324278 0.556764i
\(111\) 1.32356 1.11764i 0.125627 0.106082i
\(112\) 2.67383 0.312526i 0.252653 0.0295310i
\(113\) 6.87571 7.28783i 0.646812 0.685581i −0.318129 0.948048i \(-0.603054\pi\)
0.964941 + 0.262466i \(0.0845359\pi\)
\(114\) −5.03889 + 3.33666i −0.471935 + 0.312507i
\(115\) −5.08122 0.593909i −0.473826 0.0553823i
\(116\) −0.694842 + 0.583042i −0.0645144 + 0.0541340i
\(117\) −8.11495 10.7597i −0.750227 0.994734i
\(118\) −3.15514 2.64747i −0.290454 0.243720i
\(119\) 11.9529 + 12.6694i 1.09572 + 1.16140i
\(120\) 1.96862 + 6.50189i 0.179710 + 0.593539i
\(121\) 13.0000 6.52883i 1.18182 0.593530i
\(122\) 4.74293 2.38199i 0.429404 0.215655i
\(123\) 0.342720 + 1.13192i 0.0309020 + 0.102062i
\(124\) 0.627425 + 0.665032i 0.0563444 + 0.0597216i
\(125\) 8.85601 + 7.43107i 0.792105 + 0.664655i
\(126\) 3.47906 8.20553i 0.309939 0.731007i
\(127\) 2.97665 2.49770i 0.264135 0.221635i −0.501096 0.865392i \(-0.667070\pi\)
0.765230 + 0.643757i \(0.222625\pi\)
\(128\) −9.17279 1.07215i −0.810768 0.0947651i
\(129\) −12.1207 + 8.02613i −1.06717 + 0.706662i
\(130\) 3.56757 3.78140i 0.312896 0.331651i
\(131\) 16.5366 1.93285i 1.44481 0.168874i 0.642732 0.766091i \(-0.277801\pi\)
0.802080 + 0.597217i \(0.203727\pi\)
\(132\) −9.29198 + 7.84634i −0.808763 + 0.682936i
\(133\) −0.986757 16.9420i −0.0855627 1.46905i
\(134\) 2.07157 3.58807i 0.178956 0.309962i
\(135\) −7.50294 1.70435i −0.645750 0.146687i
\(136\) −6.06863 10.5112i −0.520380 0.901325i
\(137\) −7.74989 + 5.09718i −0.662118 + 0.435482i −0.835587 0.549358i \(-0.814873\pi\)
0.173470 + 0.984839i \(0.444502\pi\)
\(138\) −2.35104 4.04299i −0.200134 0.344162i
\(139\) 6.30605 14.6191i 0.534872 1.23997i −0.409866 0.912146i \(-0.634424\pi\)
0.944738 0.327827i \(-0.106316\pi\)
\(140\) −7.60843 1.80323i −0.643030 0.152401i
\(141\) −3.90063 + 13.1783i −0.328493 + 1.10981i
\(142\) 2.86236 3.84482i 0.240204 0.322650i
\(143\) 21.3365 + 7.76585i 1.78425 + 0.649413i
\(144\) 1.25807 1.71205i 0.104839 0.142671i
\(145\) 0.908517 0.330673i 0.0754483 0.0274609i
\(146\) −0.986611 + 3.29551i −0.0816525 + 0.272738i
\(147\) 7.73739 + 10.3258i 0.638169 + 0.851659i
\(148\) 0.0807865 1.38705i 0.00664061 0.114015i
\(149\) −19.5018 12.8265i −1.59765 1.05079i −0.959823 0.280607i \(-0.909464\pi\)
−0.637824 0.770182i \(-0.720165\pi\)
\(150\) −0.209155 + 3.79463i −0.0170775 + 0.309830i
\(151\) −2.26923 + 0.537818i −0.184667 + 0.0437670i −0.321909 0.946771i \(-0.604324\pi\)
0.137242 + 0.990538i \(0.456176\pi\)
\(152\) −2.05349 + 11.6459i −0.166560 + 0.944608i
\(153\) 13.7462 0.0856284i 1.11131 0.00692265i
\(154\) 2.60751 + 14.7879i 0.210119 + 1.19165i
\(155\) −0.385996 0.894840i −0.0310040 0.0718752i
\(156\) −10.7397 1.22140i −0.859868 0.0977904i
\(157\) 5.64522 + 18.8563i 0.450538 + 1.50490i 0.818196 + 0.574939i \(0.194974\pi\)
−0.367658 + 0.929961i \(0.619840\pi\)
\(158\) −5.24698 7.04792i −0.417428 0.560702i
\(159\) 5.51988 + 4.60251i 0.437755 + 0.365003i
\(160\) 7.74233 + 3.88835i 0.612085 + 0.307401i
\(161\) 13.1331 1.03503
\(162\) −2.86624 6.42346i −0.225193 0.504675i
\(163\) −17.6622 −1.38341 −0.691707 0.722179i \(-0.743141\pi\)
−0.691707 + 0.722179i \(0.743141\pi\)
\(164\) 0.847657 + 0.425709i 0.0661909 + 0.0332423i
\(165\) 12.1674 4.47155i 0.947234 0.348110i
\(166\) −0.756835 1.01661i −0.0587418 0.0789039i
\(167\) −0.972303 3.24772i −0.0752391 0.251316i 0.912093 0.409983i \(-0.134465\pi\)
−0.987332 + 0.158667i \(0.949280\pi\)
\(168\) −6.95736 15.9918i −0.536772 1.23380i
\(169\) 2.84400 + 6.59313i 0.218769 + 0.507164i
\(170\) 0.920811 + 5.22218i 0.0706230 + 0.400523i
\(171\) −10.3134 8.54507i −0.788686 0.653458i
\(172\) −2.02465 + 11.4824i −0.154378 + 0.875524i
\(173\) −18.1755 + 4.30767i −1.38186 + 0.327506i −0.853313 0.521399i \(-0.825410\pi\)
−0.528545 + 0.848906i \(0.677262\pi\)
\(174\) 0.739972 + 0.483393i 0.0560972 + 0.0366459i
\(175\) −8.91620 5.86428i −0.674002 0.443298i
\(176\) −0.208131 + 3.57347i −0.0156885 + 0.269360i
\(177\) 3.58924 8.39257i 0.269784 0.630824i
\(178\) −0.233753 + 0.780788i −0.0175205 + 0.0585225i
\(179\) −11.1678 + 4.06476i −0.834723 + 0.303814i −0.723796 0.690014i \(-0.757604\pi\)
−0.110927 + 0.993829i \(0.535382\pi\)
\(180\) −5.13457 + 3.42307i −0.382708 + 0.255141i
\(181\) 14.8329 + 5.39873i 1.10252 + 0.401284i 0.828244 0.560367i \(-0.189340\pi\)
0.274275 + 0.961651i \(0.411562\pi\)
\(182\) −7.96962 + 10.7051i −0.590748 + 0.793512i
\(183\) 8.09839 + 8.53041i 0.598650 + 0.630586i
\(184\) −8.90477 2.11047i −0.656469 0.155586i
\(185\) −0.586578 + 1.35984i −0.0431261 + 0.0999775i
\(186\) 0.443058 0.772948i 0.0324866 0.0566753i
\(187\) −19.3501 + 12.7267i −1.41502 + 0.930672i
\(188\) 5.51142 + 9.54607i 0.401962 + 0.696219i
\(189\) 19.6390 + 2.10965i 1.42852 + 0.153455i
\(190\) 2.58328 4.47437i 0.187411 0.324605i
\(191\) −0.335299 5.75686i −0.0242614 0.416552i −0.988471 0.151410i \(-0.951618\pi\)
0.964210 0.265141i \(-0.0854185\pi\)
\(192\) 0.966146 + 5.38123i 0.0697256 + 0.388357i
\(193\) −0.174569 + 0.0204042i −0.0125657 + 0.00146872i −0.122373 0.992484i \(-0.539051\pi\)
0.109808 + 0.993953i \(0.464976\pi\)
\(194\) 2.67529 2.83565i 0.192075 0.203588i
\(195\) 10.3118 + 5.13864i 0.738445 + 0.367986i
\(196\) 10.2789 + 1.20143i 0.734206 + 0.0858164i
\(197\) 8.59155 7.20917i 0.612123 0.513632i −0.283194 0.959063i \(-0.591394\pi\)
0.895316 + 0.445431i \(0.146950\pi\)
\(198\) 9.94162 + 6.45035i 0.706520 + 0.458406i
\(199\) −15.6873 13.1632i −1.11204 0.933114i −0.113866 0.993496i \(-0.536324\pi\)
−0.998175 + 0.0603824i \(0.980768\pi\)
\(200\) 5.10316 + 5.40904i 0.360848 + 0.382477i
\(201\) 8.94100 + 2.08967i 0.630649 + 0.147394i
\(202\) 6.68418 3.35692i 0.470298 0.236192i
\(203\) −2.21799 + 1.11392i −0.155672 + 0.0781816i
\(204\) 7.54100 8.04303i 0.527975 0.563125i
\(205\) −0.693831 0.735418i −0.0484593 0.0513638i
\(206\) −1.94885 1.63528i −0.135783 0.113935i
\(207\) 7.06565 7.58324i 0.491097 0.527071i
\(208\) −2.43709 + 2.04496i −0.168982 + 0.141792i
\(209\) 22.4129 + 2.61969i 1.55033 + 0.181208i
\(210\) 0.466716 + 7.60506i 0.0322064 + 0.524799i
\(211\) −0.817579 + 0.866583i −0.0562844 + 0.0596580i −0.754904 0.655835i \(-0.772317\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(212\) 5.72528 0.669189i 0.393214 0.0459601i
\(213\) 9.99345 + 3.60211i 0.684740 + 0.246812i
\(214\) 0.764060 + 13.1184i 0.0522301 + 0.896756i
\(215\) 6.21393 10.7628i 0.423786 0.734019i
\(216\) −12.9770 4.58638i −0.882972 0.312064i
\(217\) 1.25090 + 2.16663i 0.0849168 + 0.147080i
\(218\) 4.98574 3.27918i 0.337677 0.222094i
\(219\) −7.62368 + 0.0237447i −0.515161 + 0.00160452i
\(220\) 4.11803 9.54667i 0.277638 0.643636i
\(221\) −20.0294 4.74705i −1.34732 0.319321i
\(222\) −1.31642 + 0.316331i −0.0883524 + 0.0212307i
\(223\) −8.89760 + 11.9515i −0.595827 + 0.800335i −0.993088 0.117371i \(-0.962553\pi\)
0.397261 + 0.917706i \(0.369961\pi\)
\(224\) −20.9003 7.60707i −1.39646 0.508269i
\(225\) −8.18306 + 1.99334i −0.545538 + 0.132889i
\(226\) −7.35838 + 2.67823i −0.489472 + 0.178153i
\(227\) 7.05501 23.5654i 0.468258 1.56409i −0.319179 0.947694i \(-0.603407\pi\)
0.787437 0.616395i \(-0.211408\pi\)
\(228\) −10.6656 + 1.28031i −0.706346 + 0.0847908i
\(229\) −0.0887860 + 1.52440i −0.00586714 + 0.100735i −0.999970 0.00770332i \(-0.997548\pi\)
0.994103 + 0.108438i \(0.0345850\pi\)
\(230\) 3.34049 + 2.19707i 0.220265 + 0.144871i
\(231\) −29.6919 + 15.0278i −1.95359 + 0.988759i
\(232\) 1.68289 0.398853i 0.110487 0.0261860i
\(233\) 2.44148 13.8463i 0.159946 0.907101i −0.794177 0.607687i \(-0.792098\pi\)
0.954123 0.299414i \(-0.0967912\pi\)
\(234\) 1.89357 + 10.3611i 0.123786 + 0.677328i
\(235\) −2.04023 11.5707i −0.133090 0.754791i
\(236\) −2.89968 6.72222i −0.188753 0.437579i
\(237\) 11.5796 15.6556i 0.752173 1.01694i
\(238\) −3.90425 13.0411i −0.253075 0.845329i
\(239\) −13.6853 18.3826i −0.885229 1.18907i −0.981066 0.193672i \(-0.937960\pi\)
0.0958376 0.995397i \(-0.469447\pi\)
\(240\) −0.309825 + 1.78968i −0.0199991 + 0.115524i
\(241\) −6.31686 3.17245i −0.406905 0.204355i 0.233561 0.972342i \(-0.424962\pi\)
−0.640465 + 0.767987i \(0.721259\pi\)
\(242\) −11.3694 −0.730855
\(243\) 11.7840 10.2048i 0.755942 0.654639i
\(244\) 9.43390 0.603943
\(245\) −9.85750 4.95062i −0.629773 0.316284i
\(246\) 0.157669 0.910764i 0.0100526 0.0580682i
\(247\) 11.9764 + 16.0871i 0.762039 + 1.02360i
\(248\) −0.499989 1.67008i −0.0317493 0.106050i
\(249\) 1.67026 2.25819i 0.105848 0.143107i
\(250\) −3.57867 8.29630i −0.226335 0.524704i
\(251\) 0.0115419 + 0.0654574i 0.000728518 + 0.00413163i 0.985170 0.171582i \(-0.0548878\pi\)
−0.984441 + 0.175714i \(0.943777\pi\)
\(252\) 12.0720 10.2584i 0.760463 0.646219i
\(253\) −3.03237 + 17.1974i −0.190644 + 1.08119i
\(254\) −2.95503 + 0.700355i −0.185415 + 0.0439442i
\(255\) −10.4853 + 5.30689i −0.656617 + 0.332330i
\(256\) 11.3048 + 7.43532i 0.706553 + 0.464707i
\(257\) −1.12474 + 19.3110i −0.0701591 + 1.20459i 0.761075 + 0.648663i \(0.224672\pi\)
−0.831235 + 0.555922i \(0.812365\pi\)
\(258\) 11.2806 1.35414i 0.702297 0.0843048i
\(259\) 1.09039 3.64214i 0.0677533 0.226312i
\(260\) 8.68330 3.16046i 0.538515 0.196003i
\(261\) −0.550095 + 1.87999i −0.0340500 + 0.116368i
\(262\) −12.2274 4.45042i −0.755413 0.274948i
\(263\) 8.99328 12.0801i 0.554549 0.744889i −0.433139 0.901327i \(-0.642594\pi\)
0.987688 + 0.156439i \(0.0500013\pi\)
\(264\) 22.5473 5.41803i 1.38769 0.333456i
\(265\) −5.97849 1.41693i −0.367256 0.0870412i
\(266\) −5.25336 + 12.1787i −0.322104 + 0.746722i
\(267\) −1.80624 + 0.00562570i −0.110540 + 0.000344287i
\(268\) 6.15281 4.04677i 0.375843 0.247196i
\(269\) 5.86823 + 10.1641i 0.357792 + 0.619715i 0.987592 0.157043i \(-0.0501962\pi\)
−0.629799 + 0.776758i \(0.716863\pi\)
\(270\) 4.64236 + 3.82206i 0.282525 + 0.232603i
\(271\) 1.44013 2.49438i 0.0874817 0.151523i −0.818964 0.573844i \(-0.805451\pi\)
0.906446 + 0.422322i \(0.138785\pi\)
\(272\) −0.188683 3.23957i −0.0114406 0.196428i
\(273\) −27.8246 10.0293i −1.68402 0.607000i
\(274\) 7.20053 0.841621i 0.435000 0.0508442i
\(275\) 9.73782 10.3215i 0.587213 0.622409i
\(276\) −0.509205 8.29742i −0.0306506 0.499446i
\(277\) 2.28547 + 0.267133i 0.137320 + 0.0160504i 0.184475 0.982837i \(-0.440941\pi\)
−0.0471550 + 0.998888i \(0.515015\pi\)
\(278\) −9.53200 + 7.99830i −0.571692 + 0.479706i
\(279\) 1.92403 + 0.443364i 0.115189 + 0.0265435i
\(280\) 11.4211 + 9.58343i 0.682540 + 0.572719i
\(281\) −4.35455 4.61556i −0.259771 0.275341i 0.584341 0.811508i \(-0.301353\pi\)
−0.844112 + 0.536167i \(0.819872\pi\)
\(282\) 7.34665 7.83575i 0.437487 0.466612i
\(283\) −13.1201 + 6.58917i −0.779910 + 0.391686i −0.793770 0.608218i \(-0.791885\pi\)
0.0138596 + 0.999904i \(0.495588\pi\)
\(284\) 7.61373 3.82376i 0.451792 0.226898i
\(285\) 11.1496 + 2.60585i 0.660443 + 0.154357i
\(286\) −12.1778 12.9077i −0.720090 0.763251i
\(287\) 1.98831 + 1.66839i 0.117366 + 0.0984819i
\(288\) −15.6368 + 7.97547i −0.921410 + 0.469959i
\(289\) 3.06122 2.56867i 0.180072 0.151098i
\(290\) −0.750510 0.0877220i −0.0440715 0.00515121i
\(291\) 7.73277 + 3.85343i 0.453303 + 0.225892i
\(292\) −4.19607 + 4.44757i −0.245556 + 0.260275i
\(293\) 25.1838 2.94357i 1.47125 0.171965i 0.657623 0.753347i \(-0.271562\pi\)
0.813631 + 0.581382i \(0.197488\pi\)
\(294\) −1.78206 9.92567i −0.103932 0.578877i
\(295\) 0.453727 + 7.79019i 0.0264170 + 0.453562i
\(296\) −1.32461 + 2.29430i −0.0769916 + 0.133353i
\(297\) −7.29707 + 25.2296i −0.423419 + 1.46397i
\(298\) 9.12136 + 15.7987i 0.528386 + 0.915191i
\(299\) −12.9671 + 8.52862i −0.749909 + 0.493223i
\(300\) −3.35931 + 5.86058i −0.193950 + 0.338361i
\(301\) −12.6366 + 29.2950i −0.728364 + 1.68854i
\(302\) 1.77351 + 0.420330i 0.102054 + 0.0241873i
\(303\) 11.4130 + 12.0219i 0.655661 + 0.690638i
\(304\) −1.88805 + 2.53609i −0.108287 + 0.145455i
\(305\) −9.44914 3.43921i −0.541056 0.196928i
\(306\) −9.63061 4.76179i −0.550545 0.272213i
\(307\) 11.4486 4.16694i 0.653405 0.237820i 0.00601852 0.999982i \(-0.498084\pi\)
0.647386 + 0.762162i \(0.275862\pi\)
\(308\) −7.65498 + 25.5694i −0.436183 + 1.45695i
\(309\) 2.21699 5.18389i 0.126120 0.294901i
\(310\) −0.0442860 + 0.760362i −0.00251528 + 0.0431857i
\(311\) 21.0005 + 13.8123i 1.19083 + 0.783221i 0.980903 0.194496i \(-0.0623070\pi\)
0.209927 + 0.977717i \(0.432677\pi\)
\(312\) 17.2545 + 11.2716i 0.976844 + 0.638131i
\(313\) 28.7660 6.81767i 1.62595 0.385358i 0.686254 0.727362i \(-0.259254\pi\)
0.939698 + 0.342005i \(0.111106\pi\)
\(314\) 2.67130 15.1497i 0.150750 0.854947i
\(315\) −15.8313 + 5.87404i −0.891991 + 0.330965i
\(316\) −2.71203 15.3807i −0.152563 0.865230i
\(317\) 1.69844 + 3.93743i 0.0953940 + 0.221148i 0.959231 0.282623i \(-0.0912046\pi\)
−0.863837 + 0.503771i \(0.831945\pi\)
\(318\) −2.24081 5.15061i −0.125658 0.288832i
\(319\) −0.946519 3.16159i −0.0529949 0.177015i
\(320\) −2.79109 3.74909i −0.156027 0.209580i
\(321\) −27.3346 + 10.0455i −1.52567 + 0.560685i
\(322\) −9.17238 4.60654i −0.511157 0.256712i
\(323\) −20.4570 −1.13826
\(324\) 0.571413 12.4896i 0.0317452 0.693866i
\(325\) 12.6118 0.699576
\(326\) 12.3356 + 6.19517i 0.683206 + 0.343119i
\(327\) 10.1573 + 8.46926i 0.561703 + 0.468351i
\(328\) −1.08005 1.45075i −0.0596355 0.0801044i
\(329\) 8.65060 + 28.8950i 0.476923 + 1.59303i
\(330\) −10.0664 1.14482i −0.554136 0.0630203i
\(331\) −11.0234 25.5552i −0.605903 1.40464i −0.894447 0.447174i \(-0.852431\pi\)
0.288545 0.957466i \(-0.406829\pi\)
\(332\) −0.391188 2.21854i −0.0214692 0.121758i
\(333\) −1.51639 2.58909i −0.0830978 0.141881i
\(334\) −0.460091 + 2.60930i −0.0251750 + 0.142775i
\(335\) −7.63804 + 1.81025i −0.417311 + 0.0989044i
\(336\) 0.256615 4.65568i 0.0139995 0.253988i
\(337\) −22.4760 14.7827i −1.22435 0.805267i −0.238214 0.971213i \(-0.576562\pi\)
−0.986135 + 0.165946i \(0.946932\pi\)
\(338\) 0.326297 5.60231i 0.0177482 0.304725i
\(339\) −10.4064 13.8878i −0.565200 0.754279i
\(340\) −2.70326 + 9.02952i −0.146605 + 0.489695i
\(341\) −3.12596 + 1.13776i −0.169280 + 0.0616130i
\(342\) 4.20581 + 9.58553i 0.227424 + 0.518326i
\(343\) 1.60598 + 0.584529i 0.0867148 + 0.0315616i
\(344\) 13.2758 17.8325i 0.715785 0.961466i
\(345\) −2.51487 + 8.49646i −0.135396 + 0.457434i
\(346\) 14.2050 + 3.36665i 0.763667 + 0.180992i
\(347\) −12.0799 + 28.0044i −0.648485 + 1.50336i 0.203109 + 0.979156i \(0.434895\pi\)
−0.851594 + 0.524201i \(0.824364\pi\)
\(348\) 0.789764 + 1.35812i 0.0423358 + 0.0728031i
\(349\) 6.66329 4.38252i 0.356678 0.234591i −0.358506 0.933528i \(-0.616714\pi\)
0.715183 + 0.698937i \(0.246343\pi\)
\(350\) 4.17028 + 7.22314i 0.222911 + 0.386093i
\(351\) −20.7608 + 10.6705i −1.10813 + 0.569550i
\(352\) 14.7870 25.6119i 0.788151 1.36512i
\(353\) 1.26931 + 21.7932i 0.0675587 + 1.15994i 0.846340 + 0.532643i \(0.178801\pi\)
−0.778782 + 0.627295i \(0.784162\pi\)
\(354\) −5.45055 + 4.60256i −0.289693 + 0.244623i
\(355\) −9.02001 + 1.05429i −0.478733 + 0.0559558i
\(356\) −0.994153 + 1.05374i −0.0526900 + 0.0558481i
\(357\) 25.1539 16.6565i 1.33129 0.881553i
\(358\) 9.22555 + 1.07831i 0.487585 + 0.0569906i
\(359\) −13.2606 + 11.1269i −0.699866 + 0.587258i −0.921736 0.387819i \(-0.873229\pi\)
0.221869 + 0.975076i \(0.428784\pi\)
\(360\) 11.6782 1.43878i 0.615494 0.0758303i
\(361\) 0.713665 + 0.598836i 0.0375613 + 0.0315177i
\(362\) −8.46589 8.97332i −0.444957 0.471627i
\(363\) −7.30164 24.1156i −0.383237 1.26574i
\(364\) −21.1988 + 10.6464i −1.11112 + 0.558024i
\(365\) 5.82425 2.92505i 0.304855 0.153104i
\(366\) −2.66394 8.79836i −0.139246 0.459897i
\(367\) 16.4058 + 17.3891i 0.856376 + 0.907705i 0.996598 0.0824149i \(-0.0262633\pi\)
−0.140222 + 0.990120i \(0.544782\pi\)
\(368\) −1.87433 1.57275i −0.0977062 0.0819853i
\(369\) 2.03307 0.250478i 0.105837 0.0130394i
\(370\) 0.886651 0.743989i 0.0460948 0.0386781i
\(371\) 15.6663 + 1.83112i 0.813351 + 0.0950671i
\(372\) 1.32036 0.874319i 0.0684576 0.0453313i
\(373\) 7.91296 8.38725i 0.409718 0.434275i −0.489348 0.872088i \(-0.662765\pi\)
0.899066 + 0.437813i \(0.144247\pi\)
\(374\) 17.9784 2.10138i 0.929642 0.108660i
\(375\) 15.2989 12.9187i 0.790031 0.667119i
\(376\) −1.22207 20.9821i −0.0630235 1.08207i
\(377\) 1.46658 2.54020i 0.0755329 0.130827i
\(378\) −12.9762 8.36194i −0.667424 0.430092i
\(379\) −10.3656 17.9537i −0.532443 0.922218i −0.999282 0.0378763i \(-0.987941\pi\)
0.466839 0.884342i \(-0.345393\pi\)
\(380\) 7.67266 5.04638i 0.393599 0.258874i
\(381\) −3.38328 5.81810i −0.173331 0.298070i
\(382\) −1.78509 + 4.13829i −0.0913329 + 0.211734i
\(383\) −15.4278 3.65646i −0.788324 0.186836i −0.183314 0.983054i \(-0.558683\pi\)
−0.605010 + 0.796218i \(0.706831\pi\)
\(384\) −4.53992 + 15.3381i −0.231677 + 0.782720i
\(385\) 16.9889 22.8200i 0.865834 1.16302i
\(386\) 0.129079 + 0.0469808i 0.00656994 + 0.00239126i
\(387\) 10.1168 + 23.0574i 0.514266 + 1.17207i
\(388\) 6.51155 2.37001i 0.330574 0.120319i
\(389\) 8.17648 27.3114i 0.414564 1.38474i −0.454811 0.890588i \(-0.650293\pi\)
0.869375 0.494153i \(-0.164522\pi\)
\(390\) −5.39953 7.20587i −0.273416 0.364883i
\(391\) 0.920492 15.8042i 0.0465513 0.799255i
\(392\) −16.4863 10.8432i −0.832685 0.547665i
\(393\) 1.58707 28.7936i 0.0800569 1.45244i
\(394\) −8.52915 + 2.02145i −0.429693 + 0.101839i
\(395\) −2.89074 + 16.3942i −0.145449 + 0.824882i
\(396\) 10.6457 + 18.1765i 0.534968 + 0.913405i
\(397\) 5.49087 + 31.1403i 0.275579 + 1.56289i 0.737117 + 0.675765i \(0.236187\pi\)
−0.461538 + 0.887120i \(0.652702\pi\)
\(398\) 6.33916 + 14.6958i 0.317753 + 0.736635i
\(399\) −29.2058 3.32150i −1.46212 0.166283i
\(400\) 0.570228 + 1.90470i 0.0285114 + 0.0952348i
\(401\) 10.1802 + 13.6744i 0.508376 + 0.682867i 0.980015 0.198924i \(-0.0637449\pi\)
−0.471639 + 0.881792i \(0.656337\pi\)
\(402\) −5.51158 4.59558i −0.274892 0.229207i
\(403\) −2.64210 1.32691i −0.131612 0.0660982i
\(404\) 13.2952 0.661458
\(405\) −5.12552 + 12.3014i −0.254689 + 0.611264i
\(406\) 1.93980 0.0962705
\(407\) 4.51752 + 2.26878i 0.223925 + 0.112459i
\(408\) −19.7320 + 7.25155i −0.976882 + 0.359005i
\(409\) −14.2344 19.1202i −0.703848 0.945432i 0.296105 0.955155i \(-0.404312\pi\)
−0.999953 + 0.00972374i \(0.996905\pi\)
\(410\) 0.226629 + 0.756995i 0.0111924 + 0.0373853i
\(411\) 6.40945 + 14.7324i 0.316155 + 0.726698i
\(412\) −1.79107 4.15216i −0.0882395 0.204562i
\(413\) −3.47862 19.7282i −0.171172 0.970762i
\(414\) −7.59465 + 2.81792i −0.373257 + 0.138493i
\(415\) −0.416966 + 2.36473i −0.0204681 + 0.116080i
\(416\) 25.5762 6.06166i 1.25397 0.297197i
\(417\) −23.0867 15.0816i −1.13056 0.738548i
\(418\) −14.7346 9.69113i −0.720695 0.474009i
\(419\) 0.914980 15.7096i 0.0446997 0.767464i −0.899262 0.437410i \(-0.855896\pi\)
0.943962 0.330054i \(-0.107067\pi\)
\(420\) −5.32545 + 12.4523i −0.259855 + 0.607609i
\(421\) 6.75647 22.5682i 0.329290 1.09991i −0.619763 0.784789i \(-0.712771\pi\)
0.949053 0.315116i \(-0.102044\pi\)
\(422\) 0.874971 0.318464i 0.0425929 0.0155026i
\(423\) 21.3384 + 10.5506i 1.03751 + 0.512990i
\(424\) −10.3281 3.75912i −0.501577 0.182559i
\(425\) −7.68195 + 10.3186i −0.372629 + 0.500528i
\(426\) −5.71612 6.02105i −0.276947 0.291721i
\(427\) 25.1184 + 5.95318i 1.21557 + 0.288094i
\(428\) −9.25130 + 21.4469i −0.447179 + 1.03668i
\(429\) 19.5576 34.1198i 0.944252 1.64732i
\(430\) −8.11506 + 5.33736i −0.391343 + 0.257390i
\(431\) 0.705848 + 1.22256i 0.0339995 + 0.0588888i 0.882524 0.470267i \(-0.155842\pi\)
−0.848525 + 0.529155i \(0.822509\pi\)
\(432\) −2.55019 2.65294i −0.122696 0.127640i
\(433\) −6.50524 + 11.2674i −0.312622 + 0.541477i −0.978929 0.204200i \(-0.934541\pi\)
0.666307 + 0.745677i \(0.267874\pi\)
\(434\) −0.113689 1.95197i −0.00545727 0.0936977i
\(435\) −0.295924 1.64823i −0.0141885 0.0790268i
\(436\) 10.5353 1.23140i 0.504550 0.0589734i
\(437\) −10.5849 + 11.2194i −0.506346 + 0.536695i
\(438\) 5.33284 + 2.65748i 0.254813 + 0.126979i
\(439\) −20.5982 2.40758i −0.983097 0.114908i −0.390669 0.920531i \(-0.627756\pi\)
−0.592428 + 0.805624i \(0.701830\pi\)
\(440\) −15.1863 + 12.7428i −0.723979 + 0.607490i
\(441\) 19.9088 10.1543i 0.948036 0.483540i
\(442\) 12.3238 + 10.3409i 0.586182 + 0.491865i
\(443\) −23.3099 24.7070i −1.10749 1.17387i −0.983373 0.181599i \(-0.941873\pi\)
−0.124113 0.992268i \(-0.539609\pi\)
\(444\) −2.34336 0.547684i −0.111211 0.0259920i
\(445\) 1.37991 0.693016i 0.0654140 0.0328521i
\(446\) 10.4063 5.22626i 0.492754 0.247470i
\(447\) −27.6524 + 29.4934i −1.30791 + 1.39499i
\(448\) 8.23407 + 8.72761i 0.389023 + 0.412341i
\(449\) 0.919709 + 0.771727i 0.0434038 + 0.0364201i 0.664231 0.747527i \(-0.268759\pi\)
−0.620828 + 0.783947i \(0.713203\pi\)
\(450\) 6.41437 + 1.47809i 0.302376 + 0.0696780i
\(451\) −2.64380 + 2.21841i −0.124492 + 0.104461i
\(452\) −13.8246 1.61587i −0.650256 0.0760040i
\(453\) 0.247423 + 4.03172i 0.0116249 + 0.189427i
\(454\) −13.1931 + 13.9839i −0.619182 + 0.656295i
\(455\) 25.1143 2.93544i 1.17738 0.137615i
\(456\) 19.2690 + 6.94544i 0.902352 + 0.325250i
\(457\) 1.86373 + 31.9990i 0.0871815 + 1.49685i 0.704257 + 0.709945i \(0.251280\pi\)
−0.617076 + 0.786904i \(0.711683\pi\)
\(458\) 0.596704 1.03352i 0.0278821 0.0482933i
\(459\) 3.91522 23.4855i 0.182747 1.09621i
\(460\) 3.55340 + 6.15466i 0.165678 + 0.286963i
\(461\) −0.281296 + 0.185011i −0.0131013 + 0.00861684i −0.556043 0.831154i \(-0.687681\pi\)
0.542941 + 0.839771i \(0.317311\pi\)
\(462\) 26.0085 0.0810058i 1.21002 0.00376873i
\(463\) −1.16952 + 2.71124i −0.0543520 + 0.126002i −0.943228 0.332145i \(-0.892228\pi\)
0.888876 + 0.458147i \(0.151487\pi\)
\(464\) 0.449944 + 0.106639i 0.0208881 + 0.00495057i
\(465\) −1.64124 + 0.394383i −0.0761105 + 0.0182891i
\(466\) −6.56187 + 8.81412i −0.303973 + 0.408306i
\(467\) −3.55605 1.29430i −0.164554 0.0598929i 0.258429 0.966030i \(-0.416795\pi\)
−0.422984 + 0.906137i \(0.639017\pi\)
\(468\) −5.25762 + 17.9683i −0.243034 + 0.830584i
\(469\) 18.9360 6.89213i 0.874382 0.318249i
\(470\) −2.63359 + 8.79682i −0.121479 + 0.405767i
\(471\) 33.8494 4.06333i 1.55970 0.187228i
\(472\) −0.811652 + 13.9355i −0.0373593 + 0.641435i
\(473\) −35.4433 23.3114i −1.62968 1.07186i
\(474\) −13.5787 + 6.87251i −0.623690 + 0.315665i
\(475\) 12.1960 2.89050i 0.559589 0.132625i
\(476\) 4.20172 23.8292i 0.192586 1.09221i
\(477\) 9.48581 8.06076i 0.434326 0.369077i
\(478\) 3.11022 + 17.6389i 0.142258 + 0.806785i
\(479\) −1.25429 2.90777i −0.0573100 0.132859i 0.887155 0.461472i \(-0.152678\pi\)
−0.944465 + 0.328612i \(0.893419\pi\)
\(480\) 8.92360 12.0647i 0.407305 0.550678i
\(481\) 1.28860 + 4.30421i 0.0587549 + 0.196255i
\(482\) 3.29904 + 4.43138i 0.150267 + 0.201844i
\(483\) 3.88022 22.4138i 0.176556 1.01986i
\(484\) −18.0593 9.06974i −0.820879 0.412261i
\(485\) −7.38607 −0.335384
\(486\) −11.8095 + 2.99389i −0.535692 + 0.135805i
\(487\) 1.22501 0.0555106 0.0277553 0.999615i \(-0.491164\pi\)
0.0277553 + 0.999615i \(0.491164\pi\)
\(488\) −16.0746 8.07299i −0.727665 0.365447i
\(489\) −5.21837 + 30.1435i −0.235983 + 1.36314i
\(490\) 5.14817 + 6.91520i 0.232571 + 0.312397i
\(491\) 11.6292 + 38.8443i 0.524819 + 1.75302i 0.649032 + 0.760761i \(0.275174\pi\)
−0.124213 + 0.992256i \(0.539641\pi\)
\(492\) 0.976987 1.32089i 0.0440460 0.0595503i
\(493\) 1.18502 + 2.74718i 0.0533705 + 0.123727i
\(494\) −2.72183 15.4363i −0.122461 0.694512i
\(495\) −4.03653 22.0869i −0.181429 0.992732i
\(496\) 0.0809373 0.459018i 0.00363419 0.0206105i
\(497\) 22.6850 5.37646i 1.01756 0.241167i
\(498\) −1.95861 + 0.991304i −0.0877676 + 0.0444214i
\(499\) 34.3817 + 22.6132i 1.53914 + 1.01231i 0.983506 + 0.180876i \(0.0578934\pi\)
0.555630 + 0.831429i \(0.312477\pi\)
\(500\) 0.933801 16.0328i 0.0417609 0.717006i
\(501\) −5.83004 + 0.699847i −0.260467 + 0.0312669i
\(502\) 0.0148986 0.0497649i 0.000664959 0.00222112i
\(503\) 9.54144 3.47280i 0.425432 0.154845i −0.120426 0.992722i \(-0.538426\pi\)
0.545858 + 0.837878i \(0.316204\pi\)
\(504\) −29.3483 + 7.14904i −1.30728 + 0.318444i
\(505\) −13.3166 4.84686i −0.592582 0.215682i
\(506\) 8.15000 10.9473i 0.362311 0.486669i
\(507\) 12.0925 2.90579i 0.537048 0.129051i
\(508\) −5.25250 1.24486i −0.233042 0.0552319i
\(509\) 9.60383 22.2642i 0.425682 0.986842i −0.561534 0.827454i \(-0.689789\pi\)
0.987216 0.159388i \(-0.0509522\pi\)
\(510\) 9.18457 0.0286062i 0.406699 0.00126670i
\(511\) −13.9789 + 9.19409i −0.618392 + 0.406723i
\(512\) 3.94773 + 6.83768i 0.174467 + 0.302186i
\(513\) −17.6307 + 15.0769i −0.778415 + 0.665660i
\(514\) 7.55901 13.0926i 0.333414 0.577490i
\(515\) 0.280256 + 4.81181i 0.0123496 + 0.212034i
\(516\) 18.9984 + 6.84792i 0.836358 + 0.301463i
\(517\) −39.8346 + 4.65600i −1.75192 + 0.204771i
\(518\) −2.03905 + 2.16127i −0.0895909 + 0.0949608i
\(519\) 1.98174 + 32.2922i 0.0869889 + 1.41747i
\(520\) −17.5002 2.04548i −0.767435 0.0897003i
\(521\) −4.86477 + 4.08202i −0.213129 + 0.178837i −0.743102 0.669178i \(-0.766646\pi\)
0.529973 + 0.848014i \(0.322202\pi\)
\(522\) 1.04362 1.12007i 0.0456779 0.0490239i
\(523\) 21.5335 + 18.0688i 0.941595 + 0.790092i 0.977862 0.209250i \(-0.0671024\pi\)
−0.0362674 + 0.999342i \(0.511547\pi\)
\(524\) −15.8719 16.8233i −0.693369 0.734928i
\(525\) −12.6427 + 13.4844i −0.551772 + 0.588506i
\(526\) −10.5182 + 5.28246i −0.458617 + 0.230326i
\(527\) 2.69497 1.35347i 0.117395 0.0589579i
\(528\) 6.03723 + 1.41100i 0.262737 + 0.0614061i
\(529\) 7.59220 + 8.04726i 0.330096 + 0.349881i
\(530\) 3.67848 + 3.08661i 0.159783 + 0.134074i
\(531\) −13.2629 8.60524i −0.575559 0.373436i
\(532\) −18.0598 + 15.1540i −0.782991 + 0.657008i
\(533\) −3.04663 0.356100i −0.131964 0.0154244i
\(534\) 1.26348 + 0.629624i 0.0546762 + 0.0272465i
\(535\) 17.0849 18.1089i 0.738645 0.782918i
\(536\) −13.9469 + 1.63016i −0.602415 + 0.0704122i
\(537\) 3.63761 + 20.2607i 0.156974 + 0.874314i
\(538\) −0.533340 9.15709i −0.0229939 0.394790i
\(539\) −18.8268 + 32.6089i −0.810926 + 1.40457i
\(540\) 4.32501 + 9.77435i 0.186119 + 0.420621i
\(541\) −1.34390 2.32771i −0.0577788 0.100076i 0.835689 0.549203i \(-0.185068\pi\)
−0.893468 + 0.449127i \(0.851735\pi\)
\(542\) −1.88074 + 1.23698i −0.0807845 + 0.0531328i
\(543\) 13.5962 23.7197i 0.583471 1.01791i
\(544\) −10.6192 + 24.6180i −0.455293 + 1.05549i
\(545\) −11.0012 2.60734i −0.471242 0.111686i
\(546\) 15.9153 + 16.7643i 0.681112 + 0.717447i
\(547\) 19.5913 26.3156i 0.837662 1.12518i −0.152918 0.988239i \(-0.548867\pi\)
0.990580 0.136937i \(-0.0437257\pi\)
\(548\) 12.1088 + 4.40724i 0.517262 + 0.188268i
\(549\) 16.9513 11.3009i 0.723462 0.482311i
\(550\) −10.4214 + 3.79308i −0.444370 + 0.161737i
\(551\) 0.836042 2.79257i 0.0356166 0.118968i
\(552\) −6.23281 + 14.5739i −0.265286 + 0.620307i
\(553\) 2.48487 42.6635i 0.105667 1.81424i
\(554\) −1.50251 0.988215i −0.0638355 0.0419852i
\(555\) 2.14749 + 1.40286i 0.0911557 + 0.0595482i
\(556\) −21.5212 + 5.10062i −0.912703 + 0.216315i
\(557\) 1.71906 9.74928i 0.0728390 0.413090i −0.926485 0.376331i \(-0.877185\pi\)
0.999324 0.0367591i \(-0.0117034\pi\)
\(558\) −1.18826 0.984522i −0.0503031 0.0416781i
\(559\) −6.54721 37.1311i −0.276917 1.57048i
\(560\) 1.57884 + 3.66016i 0.0667182 + 0.154670i
\(561\) 16.0032 + 36.7843i 0.675658 + 1.55303i
\(562\) 1.42235 + 4.75098i 0.0599982 + 0.200408i
\(563\) −4.20131 5.64334i −0.177064 0.237838i 0.704727 0.709479i \(-0.251070\pi\)
−0.881791 + 0.471640i \(0.843662\pi\)
\(564\) 17.9203 6.58574i 0.754581 0.277310i
\(565\) 13.2579 + 6.65836i 0.557764 + 0.280119i
\(566\) 11.4745 0.482310
\(567\) 9.40287 32.8938i 0.394883 1.38141i
\(568\) −16.2454 −0.681640
\(569\) 3.51923 + 1.76742i 0.147534 + 0.0740943i 0.521034 0.853536i \(-0.325546\pi\)
−0.373501 + 0.927630i \(0.621843\pi\)
\(570\) −6.87302 5.73077i −0.287879 0.240035i
\(571\) 15.2678 + 20.5083i 0.638939 + 0.858244i 0.997154 0.0753955i \(-0.0240219\pi\)
−0.358215 + 0.933639i \(0.616615\pi\)
\(572\) −9.04650 30.2174i −0.378253 1.26345i
\(573\) −9.92409 1.12864i −0.414585 0.0471496i
\(574\) −0.803467 1.86265i −0.0335361 0.0777453i
\(575\) 1.68431 + 9.55219i 0.0702405 + 0.398354i
\(576\) 9.46940 0.0589873i 0.394559 0.00245780i
\(577\) 0.816045 4.62802i 0.0339724 0.192667i −0.963099 0.269149i \(-0.913258\pi\)
0.997071 + 0.0764818i \(0.0243687\pi\)
\(578\) −3.03899 + 0.720254i −0.126405 + 0.0299586i
\(579\) −0.0167539 + 0.303959i −0.000696267 + 0.0126321i
\(580\) −1.12214 0.738043i −0.0465943 0.0306456i
\(581\) 0.358422 6.15387i 0.0148699 0.255306i
\(582\) −4.04907 5.40363i −0.167840 0.223988i
\(583\) −6.01507 + 20.0917i −0.249119 + 0.832114i
\(584\) 10.9558 3.98757i 0.453353 0.165007i
\(585\) 11.8166 16.0806i 0.488556 0.664852i
\(586\) −18.6213 6.77759i −0.769238 0.279980i
\(587\) 16.5849 22.2775i 0.684534 0.919489i −0.315028 0.949082i \(-0.602014\pi\)
0.999562 + 0.0295936i \(0.00942131\pi\)
\(588\) 5.08737 17.1876i 0.209800 0.708807i
\(589\) −2.85910 0.677620i −0.117807 0.0279208i
\(590\) 2.41558 5.59994i 0.0994479 0.230546i
\(591\) −9.76523 16.7929i −0.401688 0.690766i
\(592\) −0.591781 + 0.389221i −0.0243221 + 0.0159969i
\(593\) 7.16631 + 12.4124i 0.294285 + 0.509717i 0.974818 0.223000i \(-0.0715851\pi\)
−0.680533 + 0.732717i \(0.738252\pi\)
\(594\) 13.9459 15.0612i 0.572206 0.617970i
\(595\) −12.8956 + 22.3359i −0.528669 + 0.915682i
\(596\) 1.88540 + 32.3711i 0.0772291 + 1.32597i
\(597\) −27.1000 + 22.8838i −1.10913 + 0.936573i
\(598\) 12.0479 1.40820i 0.492677 0.0575857i
\(599\) −18.8738 + 20.0050i −0.771161 + 0.817383i −0.987281 0.158983i \(-0.949178\pi\)
0.216120 + 0.976367i \(0.430660\pi\)
\(600\) 10.7392 7.11128i 0.438425 0.290317i
\(601\) −18.6234 2.17676i −0.759665 0.0887921i −0.272564 0.962138i \(-0.587872\pi\)
−0.487101 + 0.873346i \(0.661946\pi\)
\(602\) 19.1011 16.0277i 0.778503 0.653242i
\(603\) 6.20801 14.6419i 0.252810 0.596264i
\(604\) 2.48176 + 2.08244i 0.100981 + 0.0847333i
\(605\) 14.7821 + 15.6681i 0.600976 + 0.636998i
\(606\) −3.75428 12.3995i −0.152507 0.503695i
\(607\) 23.5997 11.8522i 0.957881 0.481066i 0.100041 0.994983i \(-0.468103\pi\)
0.857840 + 0.513918i \(0.171806\pi\)
\(608\) 23.3436 11.7236i 0.946709 0.475455i
\(609\) 1.24577 + 4.11448i 0.0504811 + 0.166727i
\(610\) 5.39311 + 5.71636i 0.218361 + 0.231449i
\(611\) −27.3057 22.9122i −1.10467 0.926928i
\(612\) −11.4987 15.2463i −0.464809 0.616295i
\(613\) −26.7821 + 22.4728i −1.08172 + 0.907670i −0.996062 0.0886553i \(-0.971743\pi\)
−0.0856560 + 0.996325i \(0.527299\pi\)
\(614\) −9.45747 1.10542i −0.381672 0.0446111i
\(615\) −1.46011 + 0.966856i −0.0588772 + 0.0389874i
\(616\) 34.9243 37.0176i 1.40714 1.49148i
\(617\) 7.10306 0.830228i 0.285958 0.0334237i 0.0280954 0.999605i \(-0.491056\pi\)
0.257863 + 0.966182i \(0.416982\pi\)
\(618\) −3.36667 + 2.84289i −0.135427 + 0.114358i
\(619\) 1.09438 + 18.7898i 0.0439868 + 0.755224i 0.946130 + 0.323787i \(0.104956\pi\)
−0.902143 + 0.431437i \(0.858007\pi\)
\(620\) −0.676908 + 1.17244i −0.0271853 + 0.0470863i
\(621\) −10.8545 14.2992i −0.435575 0.573807i
\(622\) −9.82235 17.0128i −0.393841 0.682152i
\(623\) −3.31196 + 2.17831i −0.132691 + 0.0872721i
\(624\) 2.77002 + 4.76349i 0.110889 + 0.190692i
\(625\) −1.22031 + 2.82901i −0.0488126 + 0.113160i
\(626\) −22.4820 5.32834i −0.898562 0.212963i
\(627\) 11.0929 37.4773i 0.443007 1.49670i
\(628\) 16.3285 21.9330i 0.651578 0.875221i
\(629\) −4.30649 1.56744i −0.171711 0.0624978i
\(630\) 13.1172 + 1.45041i 0.522601 + 0.0577858i
\(631\) −22.0642 + 8.03070i −0.878361 + 0.319697i −0.741548 0.670900i \(-0.765908\pi\)
−0.136813 + 0.990597i \(0.543686\pi\)
\(632\) −8.54081 + 28.5283i −0.339735 + 1.13479i
\(633\) 1.23741 + 1.65137i 0.0491827 + 0.0656360i
\(634\) 0.194865 3.34571i 0.00773909 0.132875i
\(635\) 4.80716 + 3.16172i 0.190766 + 0.125469i
\(636\) 0.549471 9.96885i 0.0217879 0.395291i
\(637\) −32.5634 + 7.71768i −1.29021 + 0.305786i
\(638\) −0.447890 + 2.54011i −0.0177321 + 0.100564i
\(639\) 9.10019 15.9912i 0.359998 0.632603i
\(640\) −2.37461 13.4671i −0.0938648 0.532334i
\(641\) −1.72652 4.00251i −0.0681933 0.158090i 0.880711 0.473654i \(-0.157065\pi\)
−0.948904 + 0.315565i \(0.897806\pi\)
\(642\) 22.6145 + 2.57188i 0.892522 + 0.101504i
\(643\) −5.45270 18.2133i −0.215034 0.718262i −0.995643 0.0932433i \(-0.970277\pi\)
0.780610 0.625019i \(-0.214909\pi\)
\(644\) −10.8947 14.6342i −0.429312 0.576667i
\(645\) −16.5326 13.7850i −0.650972 0.542784i
\(646\) 14.2875 + 7.17544i 0.562133 + 0.282314i
\(647\) −20.6268 −0.810924 −0.405462 0.914112i \(-0.632889\pi\)
−0.405462 + 0.914112i \(0.632889\pi\)
\(648\) −11.6615 + 20.7923i −0.458108 + 0.816799i
\(649\) 26.6367 1.04558
\(650\) −8.80828 4.42368i −0.345489 0.173511i
\(651\) 4.06729 1.49473i 0.159410 0.0585833i
\(652\) 14.6519 + 19.6810i 0.573814 + 0.770766i
\(653\) −1.71817 5.73909i −0.0672372 0.224588i 0.917767 0.397120i \(-0.129990\pi\)
−0.985004 + 0.172532i \(0.944805\pi\)
\(654\) −4.12340 9.47784i −0.161238 0.370613i
\(655\) 9.76452 + 22.6367i 0.381531 + 0.884489i
\(656\) −0.0839701 0.476218i −0.00327848 0.0185932i
\(657\) −2.21192 + 13.0181i −0.0862951 + 0.507884i
\(658\) 4.09344 23.2150i 0.159579 0.905016i
\(659\) −37.7920 + 8.95688i −1.47217 + 0.348910i −0.886912 0.461938i \(-0.847154\pi\)
−0.585256 + 0.810848i \(0.699006\pi\)
\(660\) −15.0763 9.84870i −0.586844 0.383360i
\(661\) −25.8965 17.0324i −1.00726 0.662483i −0.0651777 0.997874i \(-0.520761\pi\)
−0.942079 + 0.335390i \(0.891132\pi\)
\(662\) −1.26474 + 21.7147i −0.0491555 + 0.843967i
\(663\) −14.0194 + 32.7809i −0.544467 + 1.27310i
\(664\) −1.23194 + 4.11497i −0.0478086 + 0.159692i
\(665\) 23.6135 8.59460i 0.915691 0.333284i
\(666\) 0.150930 + 2.34015i 0.00584843 + 0.0906790i
\(667\) 2.11981 + 0.771549i 0.0820795 + 0.0298745i
\(668\) −2.81233 + 3.77762i −0.108812 + 0.146160i
\(669\) 17.7685 + 18.7163i 0.686969 + 0.723616i
\(670\) 5.96949 + 1.41480i 0.230622 + 0.0546583i
\(671\) −13.5952 + 31.5173i −0.524839 + 1.21671i
\(672\) −19.1578 + 33.4222i −0.739027 + 1.28929i
\(673\) 32.2411 21.2053i 1.24280 0.817405i 0.254085 0.967182i \(-0.418226\pi\)
0.988720 + 0.149777i \(0.0478554\pi\)
\(674\) 10.5125 + 18.2082i 0.404926 + 0.701352i
\(675\) 0.984249 + 14.5547i 0.0378838 + 0.560210i
\(676\) 4.98742 8.63847i 0.191824 0.332249i
\(677\) −0.231922 3.98194i −0.00891348 0.153039i −0.999828 0.0185455i \(-0.994096\pi\)
0.990915 0.134493i \(-0.0429406\pi\)
\(678\) 2.39679 + 13.3496i 0.0920480 + 0.512687i
\(679\) 18.8330 2.20127i 0.722745 0.0844768i
\(680\) 12.3331 13.0723i 0.472953 0.501301i
\(681\) −38.1338 19.0030i −1.46129 0.728197i
\(682\) 2.58230 + 0.301828i 0.0988815 + 0.0115576i
\(683\) 32.2624 27.0713i 1.23449 1.03586i 0.236551 0.971619i \(-0.423983\pi\)
0.997935 0.0642370i \(-0.0204614\pi\)
\(684\) −0.966116 + 18.5809i −0.0369404 + 0.710457i
\(685\) −10.5217 8.82872i −0.402012 0.337328i
\(686\) −0.916615 0.971555i −0.0349965 0.0370941i
\(687\) 2.57540 + 0.601916i 0.0982577 + 0.0229645i
\(688\) 5.31170 2.66763i 0.202506 0.101703i
\(689\) −16.6574 + 8.36566i −0.634597 + 0.318706i
\(690\) 4.73663 5.05196i 0.180320 0.192325i
\(691\) 5.86779 + 6.21949i 0.223221 + 0.236601i 0.829300 0.558804i \(-0.188740\pi\)
−0.606078 + 0.795405i \(0.707258\pi\)
\(692\) 19.8777 + 16.6794i 0.755638 + 0.634056i
\(693\) 16.8749 + 55.1142i 0.641024 + 2.09362i
\(694\) 18.2596 15.3216i 0.693125 0.581601i
\(695\) 23.4155 + 2.73688i 0.888200 + 0.103816i
\(696\) −0.183492 2.98997i −0.00695525 0.113335i
\(697\) 2.14708 2.27577i 0.0813265 0.0862011i
\(698\) −6.19096 + 0.723619i −0.234331 + 0.0273894i
\(699\) −22.9097 8.25772i −0.866523 0.312336i
\(700\) 0.862006 + 14.8001i 0.0325808 + 0.559390i
\(701\) −0.440975 + 0.763791i −0.0166554 + 0.0288480i −0.874233 0.485507i \(-0.838635\pi\)
0.857578 + 0.514355i \(0.171968\pi\)
\(702\) 18.2424 0.170458i 0.688517 0.00643351i
\(703\) 2.23259 + 3.86697i 0.0842039 + 0.145845i
\(704\) −13.3298 + 8.76713i −0.502385 + 0.330424i
\(705\) −20.3502 + 0.0633825i −0.766431 + 0.00238712i
\(706\) 6.75765 15.6660i 0.254327 0.589597i
\(707\) 35.3993 + 8.38979i 1.33133 + 0.315530i
\(708\) −12.3293 + 2.96269i −0.463364 + 0.111345i
\(709\) −24.0259 + 32.2724i −0.902312 + 1.21202i 0.0743501 + 0.997232i \(0.476312\pi\)
−0.976662 + 0.214783i \(0.931096\pi\)
\(710\) 6.66953 + 2.42751i 0.250303 + 0.0911028i
\(711\) −23.2977 24.3879i −0.873730 0.914619i
\(712\) 2.59569 0.944754i 0.0972777 0.0354062i
\(713\) 0.652152 2.17834i 0.0244233 0.0815795i
\(714\) −23.4103 + 2.81021i −0.876109 + 0.105169i
\(715\) −1.95489 + 33.5642i −0.0731089 + 1.25523i
\(716\) 13.7938 + 9.07230i 0.515497 + 0.339048i
\(717\) −35.4162 + 17.9251i −1.32264 + 0.669423i
\(718\) 13.1643 3.11999i 0.491286 0.116437i
\(719\) −2.39151 + 13.5629i −0.0891883 + 0.505812i 0.907186 + 0.420730i \(0.138226\pi\)
−0.996374 + 0.0850815i \(0.972885\pi\)
\(720\) 2.96285 + 1.05754i 0.110419 + 0.0394120i
\(721\) −2.14866 12.1857i −0.0800203 0.453817i
\(722\) −0.288389 0.668561i −0.0107327 0.0248813i
\(723\) −7.28064 + 9.84345i −0.270770 + 0.366082i
\(724\) −6.28902 21.0068i −0.233730 0.780712i
\(725\) −1.09465 1.47037i −0.0406542 0.0546080i
\(726\) −3.35914 + 19.4038i −0.124669 + 0.720143i
\(727\) −11.1569 5.60321i −0.413787 0.207812i 0.229712 0.973259i \(-0.426222\pi\)
−0.643499 + 0.765447i \(0.722518\pi\)
\(728\) 45.2317 1.67640
\(729\) −13.9346 23.1263i −0.516096 0.856531i
\(730\) −5.09374 −0.188528
\(731\) 34.3677 + 17.2601i 1.27113 + 0.638388i
\(732\) 2.78728 16.1005i 0.103021 0.595092i
\(733\) −16.0474 21.5554i −0.592725 0.796168i 0.400007 0.916512i \(-0.369008\pi\)
−0.992732 + 0.120344i \(0.961600\pi\)
\(734\) −5.35871 17.8993i −0.197793 0.660676i
\(735\) −11.3615 + 15.3608i −0.419075 + 0.566591i
\(736\) 8.00682 + 18.5619i 0.295135 + 0.684200i
\(737\) 4.65283 + 26.3875i 0.171389 + 0.971996i
\(738\) −1.50779 0.538177i −0.0555024 0.0198106i
\(739\) −4.23374 + 24.0107i −0.155740 + 0.883248i 0.802365 + 0.596833i \(0.203575\pi\)
−0.958106 + 0.286415i \(0.907536\pi\)
\(740\) 2.00187 0.474451i 0.0735901 0.0174412i
\(741\) 30.9937 15.6867i 1.13858 0.576265i
\(742\) −10.2993 6.77395i −0.378099 0.248680i
\(743\) 2.09728 36.0090i 0.0769418 1.32104i −0.710082 0.704118i \(-0.751342\pi\)
0.787024 0.616922i \(-0.211621\pi\)
\(744\) −2.99799 + 0.359883i −0.109912 + 0.0131940i
\(745\) 9.91272 33.1108i 0.363174 1.21308i
\(746\) −8.46844 + 3.08226i −0.310052 + 0.112850i
\(747\) −3.36050 3.51776i −0.122954 0.128708i
\(748\) 30.2335 + 11.0041i 1.10544 + 0.402349i
\(749\) −38.1661 + 51.2660i −1.39456 + 1.87322i
\(750\) −15.2163 + 3.65643i −0.555622 + 0.133514i
\(751\) −2.27344 0.538814i −0.0829588 0.0196616i 0.188927 0.981991i \(-0.439499\pi\)
−0.271886 + 0.962330i \(0.587647\pi\)
\(752\) 2.22572 5.15979i 0.0811635 0.188158i
\(753\) 0.115124 0.000358564i 0.00419535 1.30668e-5i
\(754\) −1.91528 + 1.25970i −0.0697505 + 0.0458756i
\(755\) −1.72660 2.99055i −0.0628372 0.108837i
\(756\) −13.9410 23.6337i −0.507028 0.859549i
\(757\) 8.08646 14.0062i 0.293907 0.509063i −0.680823 0.732448i \(-0.738378\pi\)
0.974730 + 0.223386i \(0.0717109\pi\)
\(758\) 0.942084 + 16.1750i 0.0342180 + 0.587501i
\(759\) 28.4543 + 10.2563i 1.03283 + 0.372279i
\(760\) −17.3920 + 2.03284i −0.630875 + 0.0737387i
\(761\) 31.1257 32.9914i 1.12831 1.19594i 0.150020 0.988683i \(-0.452066\pi\)
0.978287 0.207253i \(-0.0664523\pi\)
\(762\) 0.322198 + 5.25017i 0.0116720 + 0.190194i
\(763\) 28.8281 + 3.36952i 1.04365 + 0.121985i
\(764\) −6.13669 + 5.14929i −0.222018 + 0.186295i
\(765\) 5.95916 + 19.4629i 0.215454 + 0.703682i
\(766\) 9.49250 + 7.96515i 0.342978 + 0.287793i
\(767\) 16.2461 + 17.2199i 0.586614 + 0.621774i
\(768\) 16.0297 17.0968i 0.578420 0.616928i
\(769\) 16.4123 8.24257i 0.591843 0.297235i −0.127557 0.991831i \(-0.540713\pi\)
0.719399 + 0.694597i \(0.244417\pi\)
\(770\) −19.8696 + 9.97891i −0.716052 + 0.359615i
\(771\) 32.6251 + 7.62504i 1.17496 + 0.274609i
\(772\) 0.167552 + 0.177595i 0.00603033 + 0.00639178i
\(773\) 22.5821 + 18.9486i 0.812222 + 0.681536i 0.951137 0.308769i \(-0.0999169\pi\)
−0.138915 + 0.990304i \(0.544361\pi\)
\(774\) 1.02182 19.6522i 0.0367287 0.706385i
\(775\) −1.41544 + 1.18769i −0.0508441 + 0.0426633i
\(776\) −13.1233 1.53389i −0.471099 0.0550636i
\(777\) −5.89376 2.93701i −0.211438 0.105365i
\(778\) −15.2903 + 16.2067i −0.548183 + 0.581040i
\(779\) −3.02780 + 0.353899i −0.108482 + 0.0126797i
\(780\) −2.82834 15.7533i −0.101271 0.564057i
\(781\) 1.80245 + 30.9468i 0.0644967 + 1.10736i
\(782\) −6.18635 + 10.7151i −0.221224 + 0.383170i
\(783\) 3.04599 + 1.49428i 0.108855 + 0.0534011i
\(784\) −2.63788 4.56895i −0.0942102 0.163177i
\(785\) −24.3507 + 16.0157i −0.869114 + 0.571626i
\(786\) −11.2080 + 19.5532i −0.399776 + 0.697441i
\(787\) 12.6971 29.4351i 0.452601 1.04925i −0.527284 0.849689i \(-0.676790\pi\)
0.979886 0.199559i \(-0.0639510\pi\)
\(788\) −15.1604 3.59307i −0.540066 0.127998i
\(789\) −17.9595 18.9176i −0.639376 0.673485i
\(790\) 7.76935 10.4360i 0.276421 0.371298i
\(791\) −35.7894 13.0263i −1.27252 0.463161i
\(792\) −2.58509 40.0814i −0.0918573 1.42423i
\(793\) −28.6670 + 10.4339i −1.01799 + 0.370520i
\(794\) 7.08779 23.6749i 0.251536 0.840189i
\(795\) −4.18459 + 9.78464i −0.148412 + 0.347026i
\(796\) −1.65411 + 28.4000i −0.0586283 + 1.00661i
\(797\) −9.84741 6.47674i −0.348813 0.229418i 0.362996 0.931791i \(-0.381754\pi\)
−0.711810 + 0.702373i \(0.752124\pi\)
\(798\) 19.2328 + 12.5640i 0.680833 + 0.444759i
\(799\) 35.3783 8.38481i 1.25159 0.296633i
\(800\) 2.85246 16.1771i 0.100850 0.571948i
\(801\) −0.524058 + 3.08431i −0.0185167 + 0.108979i
\(802\) −2.31363 13.1212i −0.0816970 0.463327i
\(803\) −8.81174 20.4279i −0.310960 0.720885i
\(804\) −5.08861 11.6964i −0.179461 0.412501i
\(805\) 5.57733 + 18.6296i 0.196575 + 0.656606i
\(806\) 1.37986 + 1.85347i 0.0486035 + 0.0652859i
\(807\) 19.0805 7.01210i 0.671664 0.246838i
\(808\) −22.6539 11.3772i −0.796962 0.400249i
\(809\) 21.4155 0.752929 0.376464 0.926431i \(-0.377140\pi\)
0.376464 + 0.926431i \(0.377140\pi\)
\(810\) 7.89458 6.79372i 0.277387 0.238707i
\(811\) 1.73790 0.0610258 0.0305129 0.999534i \(-0.490286\pi\)
0.0305129 + 0.999534i \(0.490286\pi\)
\(812\) 3.08119 + 1.54743i 0.108129 + 0.0543043i
\(813\) −3.83158 3.19480i −0.134379 0.112046i
\(814\) −2.35932 3.16911i −0.0826940 0.111077i
\(815\) −7.50075 25.0542i −0.262740 0.877612i
\(816\) −5.58461 0.635122i −0.195500 0.0222337i
\(817\) −14.8414 34.4063i −0.519235 1.20372i
\(818\) 3.23502 + 18.3467i 0.113110 + 0.641477i
\(819\) −25.3375 + 44.5241i −0.885365 + 1.55580i
\(820\) −0.243897 + 1.38321i −0.00851725 + 0.0483037i
\(821\) −8.67839 + 2.05682i −0.302878 + 0.0717834i −0.379245 0.925296i \(-0.623816\pi\)
0.0763667 + 0.997080i \(0.475668\pi\)
\(822\) 0.691055 12.5376i 0.0241033 0.437297i
\(823\) −1.54747 1.01779i −0.0539414 0.0354778i 0.522252 0.852791i \(-0.325092\pi\)
−0.576193 + 0.817313i \(0.695462\pi\)
\(824\) −0.501339 + 8.60765i −0.0174650 + 0.299862i
\(825\) −14.7383 19.6687i −0.513120 0.684777i
\(826\) −4.49031 + 14.9987i −0.156238 + 0.521870i
\(827\) −19.7686 + 7.19517i −0.687420 + 0.250200i −0.662030 0.749477i \(-0.730305\pi\)
−0.0253900 + 0.999678i \(0.508083\pi\)
\(828\) −14.3114 1.58246i −0.497354 0.0549942i
\(829\) −5.33030 1.94007i −0.185129 0.0673814i 0.247792 0.968813i \(-0.420295\pi\)
−0.432921 + 0.901432i \(0.642517\pi\)
\(830\) 1.12067 1.50531i 0.0388989 0.0522502i
\(831\) 1.13115 3.82160i 0.0392393 0.132570i
\(832\) −13.7977 3.27012i −0.478350 0.113371i
\(833\) 13.5203 31.3435i 0.468450 1.08599i
\(834\) 10.8342 + 18.6311i 0.375156 + 0.645141i
\(835\) 4.19404 2.75846i 0.145141 0.0954606i
\(836\) −15.6738 27.1478i −0.542089 0.938925i
\(837\) 1.32513 3.15268i 0.0458034 0.108973i
\(838\) −6.14931 + 10.6509i −0.212424 + 0.367930i
\(839\) −1.39131 23.8879i −0.0480334 0.824701i −0.933184 0.359398i \(-0.882982\pi\)
0.885151 0.465304i \(-0.154055\pi\)
\(840\) 19.7301 16.6605i 0.680753 0.574842i
\(841\) 28.3805 3.31720i 0.978637 0.114386i
\(842\) −12.6348 + 13.3921i −0.435424 + 0.461522i
\(843\) −9.16378 + 6.06809i −0.315617 + 0.208996i
\(844\) 1.64386 + 0.192140i 0.0565841 + 0.00661373i
\(845\) −8.14471 + 6.83422i −0.280186 + 0.235104i
\(846\) −11.2024 14.8534i −0.385147 0.510670i
\(847\) −42.3609 35.5450i −1.45554 1.22134i
\(848\) −2.01657 2.13744i −0.0692494 0.0734000i
\(849\) 7.36913 + 24.3384i 0.252908 + 0.835293i
\(850\) 8.98455 4.51221i 0.308168 0.154768i
\(851\) −3.08792 + 1.55081i −0.105853 + 0.0531612i
\(852\) −4.27637 14.1238i −0.146506 0.483874i
\(853\) −4.63443 4.91221i −0.158680 0.168191i 0.643156 0.765735i \(-0.277625\pi\)
−0.801836 + 0.597544i \(0.796143\pi\)
\(854\) −15.4550 12.9683i −0.528860 0.443766i
\(855\) 7.74148 18.2587i 0.264753 0.624434i
\(856\) 34.1166 28.6272i 1.16608 0.978457i
\(857\) 18.7289 + 2.18910i 0.639768 + 0.0747782i 0.429791 0.902928i \(-0.358587\pi\)
0.209977 + 0.977706i \(0.432661\pi\)
\(858\) −25.6272 + 16.9698i −0.874898 + 0.579341i
\(859\) −22.2456 + 23.5790i −0.759010 + 0.804503i −0.985530 0.169503i \(-0.945784\pi\)
0.226520 + 0.974007i \(0.427265\pi\)
\(860\) −17.1478 + 2.00429i −0.584736 + 0.0683458i
\(861\) 3.43483 2.90045i 0.117059 0.0988469i
\(862\) −0.0641516 1.10144i −0.00218501 0.0375152i
\(863\) 23.6121 40.8973i 0.803765 1.39216i −0.113357 0.993554i \(-0.536160\pi\)
0.917122 0.398607i \(-0.130506\pi\)
\(864\) 8.99151 + 29.0432i 0.305897 + 0.988071i
\(865\) −13.8292 23.9529i −0.470208 0.814424i
\(866\) 8.49550 5.58758i 0.288689 0.189874i
\(867\) −3.47941 5.98340i −0.118167 0.203207i
\(868\) 1.37656 3.19123i 0.0467235 0.108317i
\(869\) 55.2930 + 13.1047i 1.87569 + 0.444546i
\(870\) −0.371453 + 1.25495i −0.0125934 + 0.0425468i
\(871\) −14.2209 + 19.1020i −0.481858 + 0.647248i
\(872\) −19.0051 6.91730i −0.643595 0.234249i
\(873\) 8.86119 12.0587i 0.299906 0.408127i
\(874\) 11.3280 4.12304i 0.383174 0.139464i
\(875\) 12.6036 42.0991i 0.426081 1.42321i
\(876\) 6.35078 + 8.47534i 0.214573 + 0.286355i
\(877\) −0.327452 + 5.62213i −0.0110573 + 0.189846i 0.988256 + 0.152804i \(0.0488304\pi\)
−0.999314 + 0.0370415i \(0.988207\pi\)
\(878\) 13.5416 + 8.90647i 0.457008 + 0.300579i
\(879\) 2.41696 43.8500i 0.0815220 1.47902i
\(880\) −5.15743 + 1.22233i −0.173857 + 0.0412048i
\(881\) −0.984686 + 5.58443i −0.0331749 + 0.188144i −0.996892 0.0787820i \(-0.974897\pi\)
0.963717 + 0.266926i \(0.0860080\pi\)
\(882\) −17.4663 + 0.108802i −0.588122 + 0.00366355i
\(883\) 5.95650 + 33.7810i 0.200452 + 1.13682i 0.904437 + 0.426606i \(0.140291\pi\)
−0.703985 + 0.710215i \(0.748598\pi\)
\(884\) 11.3260 + 26.2566i 0.380934 + 0.883105i
\(885\) 13.4293 + 1.52728i 0.451421 + 0.0513389i
\(886\) 7.61382 + 25.4319i 0.255791 + 0.854403i
\(887\) 16.0539 + 21.5641i 0.539037 + 0.724053i 0.985297 0.170851i \(-0.0546516\pi\)
−0.446260 + 0.894904i \(0.647244\pi\)
\(888\) 3.52424 + 2.93853i 0.118266 + 0.0986106i
\(889\) −13.1996 6.62908i −0.442700 0.222332i
\(890\) −1.20683 −0.0404531
\(891\) 40.9025 + 19.9078i 1.37028 + 0.666937i
\(892\) 20.6987 0.693043
\(893\) −31.6566 15.8986i −1.05935 0.532025i
\(894\) 29.6579 10.8993i 0.991910 0.364528i
\(895\) −10.5087 14.1156i −0.351266 0.471832i
\(896\) 10.0684 + 33.6307i 0.336361 + 1.12352i
\(897\) 10.7243 + 24.6504i 0.358075 + 0.823052i
\(898\) −0.371650 0.861583i −0.0124021 0.0287514i
\(899\) 0.0746222 + 0.423204i 0.00248879 + 0.0141146i
\(900\) 9.00953 + 7.46476i 0.300318 + 0.248825i
\(901\) 3.30159 18.7243i 0.109992 0.623796i
\(902\) 2.62460 0.622041i 0.0873896 0.0207117i
\(903\) 46.2633 + 30.2218i 1.53955 + 1.00572i
\(904\) 22.1733 + 14.5836i 0.737475 + 0.485045i
\(905\) −1.35902 + 23.3335i −0.0451753 + 0.775631i
\(906\) 1.24135 2.90260i 0.0412412 0.0964326i
\(907\) −8.72987 + 29.1598i −0.289871 + 0.968235i 0.681729 + 0.731605i \(0.261228\pi\)
−0.971600 + 0.236631i \(0.923957\pi\)
\(908\) −32.1114 + 11.6876i −1.06565 + 0.387866i
\(909\) 23.8893 15.9263i 0.792359 0.528243i
\(910\) −18.5699 6.75888i −0.615585 0.224055i
\(911\) 8.39961 11.2826i 0.278291 0.373810i −0.640898 0.767626i \(-0.721438\pi\)
0.919189 + 0.393816i \(0.128845\pi\)
\(912\) 3.77043 + 3.97157i 0.124851 + 0.131512i
\(913\) 7.97556 + 1.89024i 0.263953 + 0.0625579i
\(914\) 9.92224 23.0023i 0.328199 0.760850i
\(915\) −8.66136 + 15.1104i −0.286336 + 0.499534i
\(916\) 1.77228 1.16565i 0.0585578 0.0385141i
\(917\) −31.6440 54.8090i −1.04498 1.80995i
\(918\) −10.9722 + 15.0293i −0.362136 + 0.496042i
\(919\) −14.5007 + 25.1160i −0.478335 + 0.828501i −0.999691 0.0248384i \(-0.992093\pi\)
0.521356 + 0.853339i \(0.325426\pi\)
\(920\) −0.787909 13.5279i −0.0259766 0.446001i
\(921\) −3.72906 20.7700i −0.122877 0.684396i
\(922\) 0.261356 0.0305482i 0.00860731 0.00100605i
\(923\) −18.9069 + 20.0402i −0.622329 + 0.659630i
\(924\) 41.3768 + 20.6191i 1.36120 + 0.678317i
\(925\) 2.78891 + 0.325976i 0.0916986 + 0.0107180i
\(926\) 1.76780 1.48336i 0.0580935 0.0487462i
\(927\) −8.19215 5.31526i −0.269066 0.174576i
\(928\) −2.92661 2.45572i −0.0960706 0.0806128i
\(929\) 30.5782 + 32.4109i 1.00324 + 1.06337i 0.997989 + 0.0633825i \(0.0201888\pi\)
0.00524738 + 0.999986i \(0.498330\pi\)
\(930\) 1.28460 + 0.300233i 0.0421237 + 0.00984503i
\(931\) −29.7210 + 14.9264i −0.974066 + 0.489194i
\(932\) −17.4542 + 8.76584i −0.571732 + 0.287135i
\(933\) 29.7776 31.7600i 0.974874 1.03978i
\(934\) 2.02962 + 2.15127i 0.0664112 + 0.0703918i
\(935\) −26.2707 22.0437i −0.859143 0.720907i
\(936\) 24.3348 26.1174i 0.795408 0.853675i
\(937\) −15.7744 + 13.2363i −0.515326 + 0.432409i −0.862999 0.505206i \(-0.831416\pi\)
0.347673 + 0.937616i \(0.386972\pi\)
\(938\) −15.6427 1.82837i −0.510752 0.0596983i
\(939\) −3.13647 51.1083i −0.102355 1.66786i
\(940\) −11.2007 + 11.8721i −0.365327 + 0.387224i
\(941\) −56.3981 + 6.59199i −1.83852 + 0.214893i −0.963226 0.268691i \(-0.913409\pi\)
−0.875298 + 0.483584i \(0.839335\pi\)
\(942\) −25.0662 9.03504i −0.816702 0.294378i
\(943\) −0.137168 2.35508i −0.00446680 0.0766920i
\(944\) −1.86608 + 3.23215i −0.0607359 + 0.105198i
\(945\) 5.34763 + 28.7542i 0.173958 + 0.935374i
\(946\) 16.5775 + 28.7131i 0.538982 + 0.933544i
\(947\) 13.1803 8.66883i 0.428303 0.281699i −0.317000 0.948426i \(-0.602675\pi\)
0.745302 + 0.666727i \(0.232305\pi\)
\(948\) −27.0509 + 0.0842527i −0.878574 + 0.00273640i
\(949\) 7.83165 18.1558i 0.254226 0.589363i
\(950\) −9.53173 2.25906i −0.309250 0.0732936i
\(951\) 7.22169 1.73534i 0.234179 0.0562724i
\(952\) −27.5510 + 37.0075i −0.892934 + 1.19942i
\(953\) 47.3933 + 17.2497i 1.53522 + 0.558774i 0.964893 0.262645i \(-0.0845947\pi\)
0.570326 + 0.821418i \(0.306817\pi\)
\(954\) −9.45243 + 2.30255i −0.306034 + 0.0745477i
\(955\) 8.02382 2.92043i 0.259645 0.0945030i
\(956\) −9.13079 + 30.4990i −0.295311 + 0.986407i
\(957\) −5.67543 + 0.681288i −0.183461 + 0.0220229i
\(958\) −0.143907 + 2.47079i −0.00464942 + 0.0798275i
\(959\) 29.4594 + 19.3757i 0.951293 + 0.625675i
\(960\) −7.22308 + 3.65578i −0.233124 + 0.117990i
\(961\) −29.7429 + 7.04920i −0.959449 + 0.227393i
\(962\) 0.609760 3.45812i 0.0196594 0.111494i
\(963\) 9.06821 + 49.6190i 0.292219 + 1.59895i
\(964\) 1.70519 + 9.67059i 0.0549203 + 0.311469i
\(965\) −0.103079 0.238964i −0.00331824 0.00769253i
\(966\) −10.5718 + 14.2932i −0.340143 + 0.459875i
\(967\) −6.27933 20.9744i −0.201930 0.674492i −0.997630 0.0688018i \(-0.978082\pi\)
0.795701 0.605690i \(-0.207103\pi\)
\(968\) 23.0104 + 30.9083i 0.739581 + 0.993430i
\(969\) −6.04408 + 34.9132i −0.194164 + 1.12157i
\(970\) 5.15856 + 2.59072i 0.165631 + 0.0831832i
\(971\) −21.3313 −0.684555 −0.342277 0.939599i \(-0.611198\pi\)
−0.342277 + 0.939599i \(0.611198\pi\)
\(972\) −21.1467 4.66530i −0.678281 0.149640i
\(973\) −60.5205 −1.94020
\(974\) −0.855569 0.429683i −0.0274142 0.0137679i
\(975\) 3.72619 21.5241i 0.119334 0.689323i
\(976\) −2.87193 3.85768i −0.0919283 0.123481i
\(977\) −2.05675 6.87002i −0.0658012 0.219791i 0.918765 0.394806i \(-0.129188\pi\)
−0.984566 + 0.175014i \(0.944003\pi\)
\(978\) 14.2177 19.2224i 0.454631 0.614663i
\(979\) −2.08772 4.83988i −0.0667238 0.154683i
\(980\) 2.66095 + 15.0910i 0.0850011 + 0.482065i
\(981\) 17.4552 14.8329i 0.557302 0.473579i
\(982\) 5.50290 31.2085i 0.175605 0.995904i
\(983\) −40.2972 + 9.55061i −1.28528 + 0.304617i −0.815805 0.578328i \(-0.803705\pi\)
−0.469477 + 0.882945i \(0.655557\pi\)
\(984\) −2.79505 + 1.41465i −0.0891030 + 0.0450973i
\(985\) 13.8750 + 9.12572i 0.442094 + 0.290770i
\(986\) 0.135959 2.33433i 0.00432983 0.0743403i
\(987\) 51.8700 6.22655i 1.65104 0.198193i
\(988\) 7.99060 26.6905i 0.254215 0.849137i
\(989\) 27.2487 9.91773i 0.866460 0.315365i
\(990\) −4.92797 + 16.8417i −0.156621 + 0.535264i
\(991\) 51.2878 + 18.6672i 1.62921 + 0.592984i 0.985105 0.171953i \(-0.0550079\pi\)
0.644105 + 0.764937i \(0.277230\pi\)
\(992\) −2.29960 + 3.08890i −0.0730125 + 0.0980728i
\(993\) −46.8711 + 11.2629i −1.48741 + 0.357419i
\(994\) −17.7295 4.20196i −0.562344 0.133278i
\(995\) 12.0102 27.8428i 0.380750 0.882677i
\(996\) −3.90188 + 0.0121528i −0.123636 + 0.000385075i
\(997\) 22.1506 14.5687i 0.701516 0.461395i −0.147979 0.988990i \(-0.547277\pi\)
0.849495 + 0.527596i \(0.176906\pi\)
\(998\) −16.0810 27.8531i −0.509035 0.881674i
\(999\) −4.86673 + 1.82302i −0.153977 + 0.0576778i
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 81.2.g.a.13.4 144
3.2 odd 2 243.2.g.a.10.5 144
9.2 odd 6 729.2.g.a.514.4 144
9.4 even 3 729.2.g.c.28.5 144
9.5 odd 6 729.2.g.b.28.4 144
9.7 even 3 729.2.g.d.514.5 144
81.2 odd 54 729.2.g.b.703.4 144
81.5 odd 54 6561.2.a.d.1.43 72
81.25 even 27 inner 81.2.g.a.25.4 yes 144
81.29 odd 54 729.2.g.a.217.4 144
81.52 even 27 729.2.g.d.217.5 144
81.56 odd 54 243.2.g.a.73.5 144
81.76 even 27 6561.2.a.c.1.30 72
81.79 even 27 729.2.g.c.703.5 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.13.4 144 1.1 even 1 trivial
81.2.g.a.25.4 yes 144 81.25 even 27 inner
243.2.g.a.10.5 144 3.2 odd 2
243.2.g.a.73.5 144 81.56 odd 54
729.2.g.a.217.4 144 81.29 odd 54
729.2.g.a.514.4 144 9.2 odd 6
729.2.g.b.28.4 144 9.5 odd 6
729.2.g.b.703.4 144 81.2 odd 54
729.2.g.c.28.5 144 9.4 even 3
729.2.g.c.703.5 144 81.79 even 27
729.2.g.d.217.5 144 81.52 even 27
729.2.g.d.514.5 144 9.7 even 3
6561.2.a.c.1.30 72 81.76 even 27
6561.2.a.d.1.43 72 81.5 odd 54