Properties

Label 378.2.u.a.85.1
Level $378$
Weight $2$
Character 378.85
Analytic conductor $3.018$
Analytic rank $0$
Dimension $6$
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] = [378,2,Mod(43,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.u (of order \(9\), 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: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 85.1
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 378.85
Dual form 378.2.u.a.169.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.939693 - 0.342020i) q^{2} +(0.592396 - 1.62760i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.152704 - 0.866025i) q^{5} +(-1.11334 + 1.32683i) q^{6} +(0.766044 - 0.642788i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})\) \(q+(-0.939693 - 0.342020i) q^{2} +(0.592396 - 1.62760i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.152704 - 0.866025i) q^{5} +(-1.11334 + 1.32683i) q^{6} +(0.766044 - 0.642788i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.29813 - 1.92836i) q^{9} +(-0.439693 + 0.761570i) q^{10} +(-0.358441 - 2.03282i) q^{11} +(1.50000 - 0.866025i) q^{12} +(-0.326352 + 0.118782i) q^{13} +(-0.939693 + 0.342020i) q^{14} +(-1.31908 - 0.761570i) q^{15} +(0.173648 + 0.984808i) q^{16} +(1.70574 - 2.95442i) q^{17} +(1.50000 + 2.59808i) q^{18} +(1.02094 + 1.76833i) q^{19} +(0.673648 - 0.565258i) q^{20} +(-0.592396 - 1.62760i) q^{21} +(-0.358441 + 2.03282i) q^{22} +(-4.36231 - 3.66041i) q^{23} +(-1.70574 + 0.300767i) q^{24} +(3.97178 + 1.44561i) q^{25} +0.347296 q^{26} +(-4.50000 + 2.59808i) q^{27} +1.00000 q^{28} +(-1.78699 - 0.650411i) q^{29} +(0.979055 + 1.16679i) q^{30} +(-2.03209 - 1.70513i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-3.52094 - 0.620838i) q^{33} +(-2.61334 + 2.19285i) q^{34} +(-0.439693 - 0.761570i) q^{35} +(-0.520945 - 2.95442i) q^{36} +(-0.226682 + 0.392624i) q^{37} +(-0.354570 - 2.01087i) q^{38} +0.601535i q^{39} +(-0.826352 + 0.300767i) q^{40} +(-5.06418 + 1.84321i) q^{41} +1.73205i q^{42} +(-0.336152 - 1.90641i) q^{43} +(1.03209 - 1.78763i) q^{44} +(-2.02094 + 1.69577i) q^{45} +(2.84730 + 4.93166i) q^{46} +(2.04916 - 1.71945i) q^{47} +(1.70574 + 0.300767i) q^{48} +(0.173648 - 0.984808i) q^{49} +(-3.23783 - 2.71686i) q^{50} +(-3.79813 - 4.52644i) q^{51} +(-0.326352 - 0.118782i) q^{52} +10.0915 q^{53} +(5.11721 - 0.902302i) q^{54} -1.81521 q^{55} +(-0.939693 - 0.342020i) q^{56} +(3.48293 - 0.614134i) q^{57} +(1.45677 + 1.22237i) q^{58} +(0.177519 - 1.00676i) q^{59} +(-0.520945 - 1.43128i) q^{60} +(-2.62449 + 2.20220i) q^{61} +(1.32635 + 2.29731i) q^{62} -3.00000 q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0530334 + 0.300767i) q^{65} +(3.09627 + 1.78763i) q^{66} +(10.0706 - 3.66539i) q^{67} +(3.20574 - 1.16679i) q^{68} +(-8.54189 + 4.93166i) q^{69} +(0.152704 + 0.866025i) q^{70} +(2.87211 - 4.97464i) q^{71} +(-0.520945 + 2.95442i) q^{72} +(6.20961 + 10.7554i) q^{73} +(0.347296 - 0.291416i) q^{74} +(4.70574 - 5.60808i) q^{75} +(-0.354570 + 2.01087i) q^{76} +(-1.58125 - 1.32683i) q^{77} +(0.205737 - 0.565258i) q^{78} +(6.33750 + 2.30666i) q^{79} +0.879385 q^{80} +(1.56283 + 8.86327i) q^{81} +5.38919 q^{82} +(3.41147 + 1.24168i) q^{83} +(0.592396 - 1.62760i) q^{84} +(-2.29813 - 1.92836i) q^{85} +(-0.336152 + 1.90641i) q^{86} +(-2.11721 + 2.52319i) q^{87} +(-1.58125 + 1.32683i) q^{88} +(9.38326 + 16.2523i) q^{89} +(2.47906 - 0.902302i) q^{90} +(-0.173648 + 0.300767i) q^{91} +(-0.988856 - 5.60808i) q^{92} +(-3.97906 + 2.29731i) q^{93} +(-2.51367 + 0.914901i) q^{94} +(1.68732 - 0.614134i) q^{95} +(-1.50000 - 0.866025i) q^{96} +(-1.24376 - 7.05369i) q^{97} +(-0.500000 + 0.866025i) q^{98} +(-3.09627 + 5.36289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{5} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{5} - 3 q^{8} + 3 q^{10} + 6 q^{11} + 9 q^{12} - 3 q^{13} + 9 q^{15} + 9 q^{18} + 3 q^{19} + 3 q^{20} + 6 q^{22} + 6 q^{23} + 9 q^{25} - 27 q^{27} + 6 q^{28} - 3 q^{29} + 9 q^{30} - 3 q^{31} - 18 q^{33} - 9 q^{34} + 3 q^{35} + 12 q^{37} - 18 q^{38} - 6 q^{40} - 12 q^{41} - 6 q^{43} - 3 q^{44} - 9 q^{45} + 15 q^{46} + 24 q^{47} - 9 q^{51} - 3 q^{52} - 18 q^{55} + 24 q^{58} - 24 q^{59} - 3 q^{61} + 9 q^{62} - 18 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 3 q^{67} + 9 q^{68} - 45 q^{69} + 3 q^{70} - 12 q^{71} + 3 q^{73} + 18 q^{75} - 18 q^{76} - 12 q^{77} - 9 q^{78} + 33 q^{79} - 6 q^{80} + 24 q^{82} - 6 q^{86} + 18 q^{87} - 12 q^{88} + 21 q^{89} + 18 q^{90} - 12 q^{92} - 27 q^{93} + 6 q^{94} - 12 q^{95} - 9 q^{96} - 15 q^{97} - 3 q^{98} + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.939693 0.342020i −0.664463 0.241845i
\(3\) 0.592396 1.62760i 0.342020 0.939693i
\(4\) 0.766044 + 0.642788i 0.383022 + 0.321394i
\(5\) 0.152704 0.866025i 0.0682911 0.387298i −0.931435 0.363907i \(-0.881443\pi\)
0.999726 0.0233912i \(-0.00744633\pi\)
\(6\) −1.11334 + 1.32683i −0.454519 + 0.541675i
\(7\) 0.766044 0.642788i 0.289538 0.242951i
\(8\) −0.500000 0.866025i −0.176777 0.306186i
\(9\) −2.29813 1.92836i −0.766044 0.642788i
\(10\) −0.439693 + 0.761570i −0.139043 + 0.240830i
\(11\) −0.358441 2.03282i −0.108074 0.612918i −0.989948 0.141433i \(-0.954829\pi\)
0.881874 0.471485i \(-0.156282\pi\)
\(12\) 1.50000 0.866025i 0.433013 0.250000i
\(13\) −0.326352 + 0.118782i −0.0905137 + 0.0329443i −0.386880 0.922130i \(-0.626447\pi\)
0.296366 + 0.955074i \(0.404225\pi\)
\(14\) −0.939693 + 0.342020i −0.251143 + 0.0914087i
\(15\) −1.31908 0.761570i −0.340584 0.196637i
\(16\) 0.173648 + 0.984808i 0.0434120 + 0.246202i
\(17\) 1.70574 2.95442i 0.413702 0.716553i −0.581589 0.813483i \(-0.697569\pi\)
0.995291 + 0.0969297i \(0.0309022\pi\)
\(18\) 1.50000 + 2.59808i 0.353553 + 0.612372i
\(19\) 1.02094 + 1.76833i 0.234221 + 0.405682i 0.959046 0.283251i \(-0.0914128\pi\)
−0.724825 + 0.688933i \(0.758079\pi\)
\(20\) 0.673648 0.565258i 0.150632 0.126396i
\(21\) −0.592396 1.62760i −0.129271 0.355170i
\(22\) −0.358441 + 2.03282i −0.0764198 + 0.433398i
\(23\) −4.36231 3.66041i −0.909605 0.763249i 0.0624390 0.998049i \(-0.480112\pi\)
−0.972044 + 0.234800i \(0.924557\pi\)
\(24\) −1.70574 + 0.300767i −0.348182 + 0.0613939i
\(25\) 3.97178 + 1.44561i 0.794356 + 0.289122i
\(26\) 0.347296 0.0681104
\(27\) −4.50000 + 2.59808i −0.866025 + 0.500000i
\(28\) 1.00000 0.188982
\(29\) −1.78699 0.650411i −0.331836 0.120778i 0.170729 0.985318i \(-0.445388\pi\)
−0.502564 + 0.864540i \(0.667610\pi\)
\(30\) 0.979055 + 1.16679i 0.178750 + 0.213026i
\(31\) −2.03209 1.70513i −0.364974 0.306249i 0.441796 0.897116i \(-0.354342\pi\)
−0.806770 + 0.590866i \(0.798786\pi\)
\(32\) 0.173648 0.984808i 0.0306970 0.174091i
\(33\) −3.52094 0.620838i −0.612918 0.108074i
\(34\) −2.61334 + 2.19285i −0.448184 + 0.376071i
\(35\) −0.439693 0.761570i −0.0743216 0.128729i
\(36\) −0.520945 2.95442i −0.0868241 0.492404i
\(37\) −0.226682 + 0.392624i −0.0372662 + 0.0645470i −0.884057 0.467379i \(-0.845198\pi\)
0.846791 + 0.531926i \(0.178532\pi\)
\(38\) −0.354570 2.01087i −0.0575189 0.326206i
\(39\) 0.601535i 0.0963227i
\(40\) −0.826352 + 0.300767i −0.130658 + 0.0475555i
\(41\) −5.06418 + 1.84321i −0.790892 + 0.287861i −0.705707 0.708504i \(-0.749370\pi\)
−0.0851850 + 0.996365i \(0.527148\pi\)
\(42\) 1.73205i 0.267261i
\(43\) −0.336152 1.90641i −0.0512627 0.290725i 0.948389 0.317109i \(-0.102712\pi\)
−0.999652 + 0.0263835i \(0.991601\pi\)
\(44\) 1.03209 1.78763i 0.155593 0.269495i
\(45\) −2.02094 + 1.69577i −0.301265 + 0.252791i
\(46\) 2.84730 + 4.93166i 0.419811 + 0.727134i
\(47\) 2.04916 1.71945i 0.298901 0.250808i −0.480986 0.876728i \(-0.659721\pi\)
0.779887 + 0.625921i \(0.215277\pi\)
\(48\) 1.70574 + 0.300767i 0.246202 + 0.0434120i
\(49\) 0.173648 0.984808i 0.0248069 0.140687i
\(50\) −3.23783 2.71686i −0.457898 0.384222i
\(51\) −3.79813 4.52644i −0.531845 0.633828i
\(52\) −0.326352 0.118782i −0.0452569 0.0164721i
\(53\) 10.0915 1.38618 0.693088 0.720853i \(-0.256250\pi\)
0.693088 + 0.720853i \(0.256250\pi\)
\(54\) 5.11721 0.902302i 0.696364 0.122788i
\(55\) −1.81521 −0.244763
\(56\) −0.939693 0.342020i −0.125572 0.0457044i
\(57\) 3.48293 0.614134i 0.461325 0.0813440i
\(58\) 1.45677 + 1.22237i 0.191283 + 0.160505i
\(59\) 0.177519 1.00676i 0.0231109 0.131069i −0.971069 0.238798i \(-0.923247\pi\)
0.994180 + 0.107729i \(0.0343579\pi\)
\(60\) −0.520945 1.43128i −0.0672537 0.184778i
\(61\) −2.62449 + 2.20220i −0.336031 + 0.281963i −0.795152 0.606410i \(-0.792609\pi\)
0.459121 + 0.888374i \(0.348164\pi\)
\(62\) 1.32635 + 2.29731i 0.168447 + 0.291759i
\(63\) −3.00000 −0.377964
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) 0.0530334 + 0.300767i 0.00657799 + 0.0373056i
\(66\) 3.09627 + 1.78763i 0.381124 + 0.220042i
\(67\) 10.0706 3.66539i 1.23032 0.447799i 0.356611 0.934253i \(-0.383932\pi\)
0.873706 + 0.486455i \(0.161710\pi\)
\(68\) 3.20574 1.16679i 0.388753 0.141494i
\(69\) −8.54189 + 4.93166i −1.02832 + 0.593702i
\(70\) 0.152704 + 0.866025i 0.0182516 + 0.103510i
\(71\) 2.87211 4.97464i 0.340857 0.590381i −0.643735 0.765248i \(-0.722616\pi\)
0.984592 + 0.174867i \(0.0559495\pi\)
\(72\) −0.520945 + 2.95442i −0.0613939 + 0.348182i
\(73\) 6.20961 + 10.7554i 0.726780 + 1.25882i 0.958237 + 0.285974i \(0.0923172\pi\)
−0.231458 + 0.972845i \(0.574350\pi\)
\(74\) 0.347296 0.291416i 0.0403724 0.0338765i
\(75\) 4.70574 5.60808i 0.543372 0.647565i
\(76\) −0.354570 + 2.01087i −0.0406720 + 0.230662i
\(77\) −1.58125 1.32683i −0.180200 0.151206i
\(78\) 0.205737 0.565258i 0.0232951 0.0640029i
\(79\) 6.33750 + 2.30666i 0.713024 + 0.259520i 0.672961 0.739678i \(-0.265022\pi\)
0.0400627 + 0.999197i \(0.487244\pi\)
\(80\) 0.879385 0.0983183
\(81\) 1.56283 + 8.86327i 0.173648 + 0.984808i
\(82\) 5.38919 0.595136
\(83\) 3.41147 + 1.24168i 0.374458 + 0.136292i 0.522392 0.852706i \(-0.325040\pi\)
−0.147934 + 0.988997i \(0.547262\pi\)
\(84\) 0.592396 1.62760i 0.0646357 0.177585i
\(85\) −2.29813 1.92836i −0.249268 0.209160i
\(86\) −0.336152 + 1.90641i −0.0362482 + 0.205574i
\(87\) −2.11721 + 2.52319i −0.226989 + 0.270515i
\(88\) −1.58125 + 1.32683i −0.168562 + 0.141440i
\(89\) 9.38326 + 16.2523i 0.994623 + 1.72274i 0.586998 + 0.809588i \(0.300310\pi\)
0.407625 + 0.913149i \(0.366357\pi\)
\(90\) 2.47906 0.902302i 0.261315 0.0951110i
\(91\) −0.173648 + 0.300767i −0.0182033 + 0.0315290i
\(92\) −0.988856 5.60808i −0.103095 0.584683i
\(93\) −3.97906 + 2.29731i −0.412609 + 0.238220i
\(94\) −2.51367 + 0.914901i −0.259265 + 0.0943649i
\(95\) 1.68732 0.614134i 0.173115 0.0630088i
\(96\) −1.50000 0.866025i −0.153093 0.0883883i
\(97\) −1.24376 7.05369i −0.126284 0.716194i −0.980537 0.196335i \(-0.937096\pi\)
0.854253 0.519858i \(-0.174015\pi\)
\(98\) −0.500000 + 0.866025i −0.0505076 + 0.0874818i
\(99\) −3.09627 + 5.36289i −0.311187 + 0.538991i
\(100\) 2.11334 + 3.66041i 0.211334 + 0.366041i
\(101\) −1.91147 + 1.60392i −0.190199 + 0.159596i −0.732915 0.680321i \(-0.761841\pi\)
0.542716 + 0.839916i \(0.317396\pi\)
\(102\) 2.02094 + 5.55250i 0.200103 + 0.549779i
\(103\) 0.176174 0.999135i 0.0173590 0.0984477i −0.974897 0.222655i \(-0.928528\pi\)
0.992256 + 0.124207i \(0.0396388\pi\)
\(104\) 0.266044 + 0.223238i 0.0260878 + 0.0218903i
\(105\) −1.50000 + 0.264490i −0.146385 + 0.0258116i
\(106\) −9.48293 3.45150i −0.921063 0.335240i
\(107\) 11.3131 1.09368 0.546842 0.837236i \(-0.315830\pi\)
0.546842 + 0.837236i \(0.315830\pi\)
\(108\) −5.11721 0.902302i −0.492404 0.0868241i
\(109\) 12.7588 1.22207 0.611034 0.791604i \(-0.290754\pi\)
0.611034 + 0.791604i \(0.290754\pi\)
\(110\) 1.70574 + 0.620838i 0.162636 + 0.0591945i
\(111\) 0.504748 + 0.601535i 0.0479085 + 0.0570952i
\(112\) 0.766044 + 0.642788i 0.0723844 + 0.0607377i
\(113\) −3.15910 + 17.9161i −0.297183 + 1.68541i 0.361011 + 0.932561i \(0.382432\pi\)
−0.658194 + 0.752848i \(0.728680\pi\)
\(114\) −3.48293 0.614134i −0.326206 0.0575189i
\(115\) −3.83615 + 3.21891i −0.357723 + 0.300165i
\(116\) −0.950837 1.64690i −0.0882830 0.152911i
\(117\) 0.979055 + 0.356347i 0.0905137 + 0.0329443i
\(118\) −0.511144 + 0.885328i −0.0470547 + 0.0815010i
\(119\) −0.592396 3.35965i −0.0543049 0.307978i
\(120\) 1.52314i 0.139043i
\(121\) 6.33275 2.30493i 0.575704 0.209539i
\(122\) 3.21941 1.17177i 0.291471 0.106087i
\(123\) 9.33434i 0.841649i
\(124\) −0.460637 2.61240i −0.0413664 0.234601i
\(125\) 4.05690 7.02676i 0.362861 0.628493i
\(126\) 2.81908 + 1.02606i 0.251143 + 0.0914087i
\(127\) 6.14156 + 10.6375i 0.544975 + 0.943925i 0.998608 + 0.0527364i \(0.0167943\pi\)
−0.453633 + 0.891188i \(0.649872\pi\)
\(128\) 0.766044 0.642788i 0.0677094 0.0568149i
\(129\) −3.30200 0.582232i −0.290725 0.0512627i
\(130\) 0.0530334 0.300767i 0.00465134 0.0263791i
\(131\) 1.70574 + 1.43128i 0.149031 + 0.125052i 0.714255 0.699886i \(-0.246766\pi\)
−0.565224 + 0.824938i \(0.691210\pi\)
\(132\) −2.29813 2.73881i −0.200027 0.238383i
\(133\) 1.91875 + 0.698367i 0.166377 + 0.0605561i
\(134\) −10.7169 −0.925798
\(135\) 1.56283 + 4.29385i 0.134507 + 0.369556i
\(136\) −3.41147 −0.292531
\(137\) 6.01842 + 2.19053i 0.514188 + 0.187149i 0.586065 0.810264i \(-0.300676\pi\)
−0.0718764 + 0.997414i \(0.522899\pi\)
\(138\) 9.71348 1.71275i 0.826866 0.145799i
\(139\) −16.7815 14.0814i −1.42339 1.19437i −0.949494 0.313786i \(-0.898403\pi\)
−0.473897 0.880580i \(-0.657153\pi\)
\(140\) 0.152704 0.866025i 0.0129058 0.0731925i
\(141\) −1.58466 4.35381i −0.133452 0.366657i
\(142\) −4.40033 + 3.69232i −0.369267 + 0.309852i
\(143\) 0.358441 + 0.620838i 0.0299743 + 0.0519170i
\(144\) 1.50000 2.59808i 0.125000 0.216506i
\(145\) −0.836152 + 1.44826i −0.0694386 + 0.120271i
\(146\) −2.15657 12.2305i −0.178479 1.01221i
\(147\) −1.50000 0.866025i −0.123718 0.0714286i
\(148\) −0.426022 + 0.155059i −0.0350188 + 0.0127458i
\(149\) −20.7528 + 7.55342i −1.70014 + 0.618800i −0.995841 0.0911048i \(-0.970960\pi\)
−0.704298 + 0.709905i \(0.748738\pi\)
\(150\) −6.34002 + 3.66041i −0.517661 + 0.298872i
\(151\) −3.12361 17.7149i −0.254196 1.44161i −0.798129 0.602487i \(-0.794177\pi\)
0.543933 0.839128i \(-0.316934\pi\)
\(152\) 1.02094 1.76833i 0.0828095 0.143430i
\(153\) −9.61721 + 3.50038i −0.777505 + 0.282989i
\(154\) 1.03209 + 1.78763i 0.0831681 + 0.144051i
\(155\) −1.78699 + 1.49946i −0.143534 + 0.120440i
\(156\) −0.386659 + 0.460802i −0.0309575 + 0.0368937i
\(157\) 3.40554 19.3138i 0.271792 1.54141i −0.477179 0.878806i \(-0.658341\pi\)
0.748971 0.662603i \(-0.230548\pi\)
\(158\) −5.16637 4.33510i −0.411015 0.344882i
\(159\) 5.97818 16.4249i 0.474100 1.30258i
\(160\) −0.826352 0.300767i −0.0653288 0.0237778i
\(161\) −5.69459 −0.448797
\(162\) 1.56283 8.86327i 0.122788 0.696364i
\(163\) 8.96585 0.702260 0.351130 0.936327i \(-0.385798\pi\)
0.351130 + 0.936327i \(0.385798\pi\)
\(164\) −5.06418 1.84321i −0.395446 0.143931i
\(165\) −1.07532 + 2.95442i −0.0837137 + 0.230002i
\(166\) −2.78106 2.33359i −0.215852 0.181121i
\(167\) −0.273785 + 1.55271i −0.0211861 + 0.120153i −0.993567 0.113248i \(-0.963874\pi\)
0.972381 + 0.233401i \(0.0749855\pi\)
\(168\) −1.11334 + 1.32683i −0.0858961 + 0.102367i
\(169\) −9.86618 + 8.27871i −0.758937 + 0.636824i
\(170\) 1.50000 + 2.59808i 0.115045 + 0.199263i
\(171\) 1.06371 6.03260i 0.0813440 0.461325i
\(172\) 0.967911 1.67647i 0.0738025 0.127830i
\(173\) 3.33363 + 18.9059i 0.253451 + 1.43739i 0.800018 + 0.599976i \(0.204823\pi\)
−0.546567 + 0.837415i \(0.684066\pi\)
\(174\) 2.85251 1.64690i 0.216248 0.124851i
\(175\) 3.97178 1.44561i 0.300238 0.109278i
\(176\) 1.93969 0.705990i 0.146210 0.0532160i
\(177\) −1.53343 0.885328i −0.115260 0.0665453i
\(178\) −3.25877 18.4814i −0.244255 1.38524i
\(179\) 8.03596 13.9187i 0.600636 1.04033i −0.392089 0.919927i \(-0.628248\pi\)
0.992725 0.120404i \(-0.0384191\pi\)
\(180\) −2.63816 −0.196637
\(181\) −11.1630 19.3348i −0.829737 1.43715i −0.898244 0.439496i \(-0.855157\pi\)
0.0685074 0.997651i \(-0.478176\pi\)
\(182\) 0.266044 0.223238i 0.0197205 0.0165475i
\(183\) 2.02956 + 5.57618i 0.150030 + 0.412203i
\(184\) −0.988856 + 5.60808i −0.0728994 + 0.413433i
\(185\) 0.305407 + 0.256267i 0.0224540 + 0.0188411i
\(186\) 4.52481 0.797847i 0.331776 0.0585010i
\(187\) −6.61721 2.40847i −0.483898 0.176125i
\(188\) 2.67499 0.195094
\(189\) −1.77719 + 4.88279i −0.129271 + 0.355170i
\(190\) −1.79561 −0.130267
\(191\) −13.3157 4.84651i −0.963488 0.350681i −0.188089 0.982152i \(-0.560229\pi\)
−0.775400 + 0.631471i \(0.782452\pi\)
\(192\) 1.11334 + 1.32683i 0.0803485 + 0.0957556i
\(193\) 7.43242 + 6.23654i 0.534997 + 0.448916i 0.869823 0.493364i \(-0.164233\pi\)
−0.334826 + 0.942280i \(0.608677\pi\)
\(194\) −1.24376 + 7.05369i −0.0892965 + 0.506425i
\(195\) 0.520945 + 0.0918566i 0.0373056 + 0.00657799i
\(196\) 0.766044 0.642788i 0.0547175 0.0459134i
\(197\) 2.96198 + 5.13030i 0.211032 + 0.365519i 0.952038 0.305980i \(-0.0989841\pi\)
−0.741005 + 0.671499i \(0.765651\pi\)
\(198\) 4.74376 3.98048i 0.337124 0.282881i
\(199\) −9.23308 + 15.9922i −0.654516 + 1.13365i 0.327499 + 0.944851i \(0.393794\pi\)
−0.982015 + 0.188803i \(0.939539\pi\)
\(200\) −0.733956 4.16247i −0.0518985 0.294331i
\(201\) 18.5622i 1.30928i
\(202\) 2.34477 0.853427i 0.164977 0.0600469i
\(203\) −1.78699 + 0.650411i −0.125422 + 0.0456499i
\(204\) 5.90885i 0.413702i
\(205\) 0.822948 + 4.66717i 0.0574772 + 0.325969i
\(206\) −0.507274 + 0.878624i −0.0353435 + 0.0612167i
\(207\) 2.96657 + 16.8242i 0.206191 + 1.16937i
\(208\) −0.173648 0.300767i −0.0120403 0.0208545i
\(209\) 3.22874 2.70924i 0.223337 0.187402i
\(210\) 1.50000 + 0.264490i 0.103510 + 0.0182516i
\(211\) 3.21823 18.2515i 0.221552 1.25648i −0.647617 0.761966i \(-0.724234\pi\)
0.869168 0.494516i \(-0.164655\pi\)
\(212\) 7.73055 + 6.48670i 0.530936 + 0.445509i
\(213\) −6.39528 7.62159i −0.438197 0.522223i
\(214\) −10.6309 3.86932i −0.726712 0.264502i
\(215\) −1.70233 −0.116098
\(216\) 4.50000 + 2.59808i 0.306186 + 0.176777i
\(217\) −2.65270 −0.180077
\(218\) −11.9893 4.36376i −0.812019 0.295551i
\(219\) 21.1839 3.73530i 1.43148 0.252408i
\(220\) −1.39053 1.16679i −0.0937495 0.0786652i
\(221\) −0.205737 + 1.16679i −0.0138394 + 0.0784870i
\(222\) −0.268571 0.737892i −0.0180253 0.0495241i
\(223\) −8.05169 + 6.75617i −0.539181 + 0.452427i −0.871258 0.490826i \(-0.836695\pi\)
0.332077 + 0.943252i \(0.392251\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) −6.34002 10.9812i −0.422668 0.732083i
\(226\) 9.09627 15.7552i 0.605075 1.04802i
\(227\) −2.22328 12.6088i −0.147564 0.836878i −0.965272 0.261245i \(-0.915867\pi\)
0.817708 0.575633i \(-0.195244\pi\)
\(228\) 3.06283 + 1.76833i 0.202841 + 0.117110i
\(229\) −9.75624 + 3.55098i −0.644711 + 0.234656i −0.643622 0.765344i \(-0.722569\pi\)
−0.00108918 + 0.999999i \(0.500347\pi\)
\(230\) 4.70574 1.71275i 0.310287 0.112935i
\(231\) −3.09627 + 1.78763i −0.203719 + 0.117617i
\(232\) 0.330222 + 1.87278i 0.0216802 + 0.122954i
\(233\) 2.00134 3.46643i 0.131112 0.227093i −0.792993 0.609230i \(-0.791478\pi\)
0.924106 + 0.382137i \(0.124812\pi\)
\(234\) −0.798133 0.669713i −0.0521756 0.0437805i
\(235\) −1.17617 2.03719i −0.0767252 0.132892i
\(236\) 0.783119 0.657115i 0.0509767 0.0427745i
\(237\) 7.50862 8.94842i 0.487737 0.581263i
\(238\) −0.592396 + 3.35965i −0.0383993 + 0.217774i
\(239\) 16.3537 + 13.7224i 1.05783 + 0.887627i 0.993895 0.110327i \(-0.0351898\pi\)
0.0639371 + 0.997954i \(0.479634\pi\)
\(240\) 0.520945 1.43128i 0.0336268 0.0923889i
\(241\) 5.34642 + 1.94594i 0.344393 + 0.125349i 0.508425 0.861106i \(-0.330228\pi\)
−0.164032 + 0.986455i \(0.552450\pi\)
\(242\) −6.73917 −0.433210
\(243\) 15.3516 + 2.70691i 0.984808 + 0.173648i
\(244\) −3.42602 −0.219329
\(245\) −0.826352 0.300767i −0.0527937 0.0192153i
\(246\) 3.19253 8.77141i 0.203548 0.559245i
\(247\) −0.543233 0.455827i −0.0345651 0.0290036i
\(248\) −0.460637 + 2.61240i −0.0292505 + 0.165888i
\(249\) 4.04189 4.81694i 0.256144 0.305261i
\(250\) −6.21554 + 5.21546i −0.393105 + 0.329854i
\(251\) 6.46451 + 11.1969i 0.408036 + 0.706739i 0.994670 0.103113i \(-0.0328804\pi\)
−0.586634 + 0.809853i \(0.699547\pi\)
\(252\) −2.29813 1.92836i −0.144769 0.121475i
\(253\) −5.87733 + 10.1798i −0.369504 + 0.640000i
\(254\) −2.13294 12.0965i −0.133833 0.759003i
\(255\) −4.50000 + 2.59808i −0.281801 + 0.162698i
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) −27.5107 + 10.0131i −1.71607 + 0.624599i −0.997488 0.0708401i \(-0.977432\pi\)
−0.718585 + 0.695439i \(0.755210\pi\)
\(258\) 2.90373 + 1.67647i 0.180779 + 0.104373i
\(259\) 0.0787257 + 0.446476i 0.00489178 + 0.0277426i
\(260\) −0.152704 + 0.264490i −0.00947028 + 0.0164030i
\(261\) 2.85251 + 4.94069i 0.176566 + 0.305821i
\(262\) −1.11334 1.92836i −0.0687824 0.119135i
\(263\) −5.35117 + 4.49016i −0.329967 + 0.276875i −0.792686 0.609630i \(-0.791318\pi\)
0.462719 + 0.886505i \(0.346874\pi\)
\(264\) 1.22281 + 3.35965i 0.0752588 + 0.206772i
\(265\) 1.54101 8.73951i 0.0946636 0.536864i
\(266\) −1.56418 1.31250i −0.0959059 0.0804746i
\(267\) 32.0107 5.64436i 1.95903 0.345429i
\(268\) 10.0706 + 3.66539i 0.615158 + 0.223899i
\(269\) −18.9786 −1.15715 −0.578574 0.815630i \(-0.696391\pi\)
−0.578574 + 0.815630i \(0.696391\pi\)
\(270\) 4.56942i 0.278086i
\(271\) −28.8033 −1.74968 −0.874839 0.484413i \(-0.839033\pi\)
−0.874839 + 0.484413i \(0.839033\pi\)
\(272\) 3.20574 + 1.16679i 0.194376 + 0.0707472i
\(273\) 0.386659 + 0.460802i 0.0234017 + 0.0278890i
\(274\) −4.90626 4.11684i −0.296398 0.248707i
\(275\) 1.51501 8.59208i 0.0913588 0.518122i
\(276\) −9.71348 1.71275i −0.584683 0.103095i
\(277\) −18.0326 + 15.1311i −1.08347 + 0.909140i −0.996204 0.0870446i \(-0.972258\pi\)
−0.0872669 + 0.996185i \(0.527813\pi\)
\(278\) 10.9534 + 18.9718i 0.656939 + 1.13785i
\(279\) 1.38191 + 7.83721i 0.0827329 + 0.469201i
\(280\) −0.439693 + 0.761570i −0.0262767 + 0.0455125i
\(281\) 3.93464 + 22.3145i 0.234721 + 1.33117i 0.843201 + 0.537599i \(0.180669\pi\)
−0.608480 + 0.793570i \(0.708220\pi\)
\(282\) 4.63322i 0.275904i
\(283\) 8.45811 3.07850i 0.502783 0.182998i −0.0781626 0.996941i \(-0.524905\pi\)
0.580945 + 0.813943i \(0.302683\pi\)
\(284\) 5.39780 1.96464i 0.320301 0.116580i
\(285\) 3.11008i 0.184225i
\(286\) −0.124485 0.705990i −0.00736096 0.0417461i
\(287\) −2.69459 + 4.66717i −0.159057 + 0.275494i
\(288\) −2.29813 + 1.92836i −0.135419 + 0.113630i
\(289\) 2.68092 + 4.64349i 0.157701 + 0.273147i
\(290\) 1.28106 1.07494i 0.0752264 0.0631224i
\(291\) −12.2173 2.15425i −0.716194 0.126284i
\(292\) −2.15657 + 12.2305i −0.126204 + 0.715738i
\(293\) 6.99067 + 5.86587i 0.408399 + 0.342688i 0.823729 0.566983i \(-0.191890\pi\)
−0.415330 + 0.909671i \(0.636334\pi\)
\(294\) 1.11334 + 1.32683i 0.0649314 + 0.0773822i
\(295\) −0.844770 0.307471i −0.0491844 0.0179017i
\(296\) 0.453363 0.0263512
\(297\) 6.89440 + 8.21643i 0.400054 + 0.476765i
\(298\) 22.0847 1.27933
\(299\) 1.85844 + 0.676417i 0.107476 + 0.0391182i
\(300\) 7.20961 1.27125i 0.416247 0.0733956i
\(301\) −1.48293 1.24432i −0.0854744 0.0717216i
\(302\) −3.12361 + 17.7149i −0.179743 + 1.01938i
\(303\) 1.47818 + 4.06126i 0.0849191 + 0.233313i
\(304\) −1.56418 + 1.31250i −0.0897117 + 0.0752771i
\(305\) 1.50640 + 2.60916i 0.0862560 + 0.149400i
\(306\) 10.2344 0.585063
\(307\) −5.69712 + 9.86770i −0.325152 + 0.563179i −0.981543 0.191241i \(-0.938749\pi\)
0.656391 + 0.754421i \(0.272082\pi\)
\(308\) −0.358441 2.03282i −0.0204241 0.115831i
\(309\) −1.52182 0.878624i −0.0865734 0.0499832i
\(310\) 2.19207 0.797847i 0.124501 0.0453147i
\(311\) −2.13903 + 0.778544i −0.121293 + 0.0441472i −0.401954 0.915660i \(-0.631669\pi\)
0.280660 + 0.959807i \(0.409447\pi\)
\(312\) 0.520945 0.300767i 0.0294927 0.0170276i
\(313\) −0.253718 1.43891i −0.0143410 0.0813318i 0.976797 0.214166i \(-0.0687033\pi\)
−0.991138 + 0.132834i \(0.957592\pi\)
\(314\) −9.80587 + 16.9843i −0.553377 + 0.958478i
\(315\) −0.458111 + 2.59808i −0.0258116 + 0.146385i
\(316\) 3.37211 + 5.84067i 0.189696 + 0.328563i
\(317\) −0.320422 + 0.268866i −0.0179967 + 0.0151010i −0.651742 0.758441i \(-0.725961\pi\)
0.633745 + 0.773542i \(0.281517\pi\)
\(318\) −11.2353 + 13.3897i −0.630044 + 0.750858i
\(319\) −0.681637 + 3.86576i −0.0381644 + 0.216441i
\(320\) 0.673648 + 0.565258i 0.0376581 + 0.0315989i
\(321\) 6.70187 18.4132i 0.374062 1.02773i
\(322\) 5.35117 + 1.94767i 0.298209 + 0.108539i
\(323\) 6.96585 0.387590
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) −1.46791 −0.0814251
\(326\) −8.42514 3.06650i −0.466626 0.169838i
\(327\) 7.55825 20.7661i 0.417972 1.14837i
\(328\) 4.12836 + 3.46410i 0.227950 + 0.191273i
\(329\) 0.464508 2.63435i 0.0256091 0.145237i
\(330\) 2.02094 2.40847i 0.111249 0.132582i
\(331\) 8.74170 7.33515i 0.480487 0.403177i −0.370115 0.928986i \(-0.620682\pi\)
0.850603 + 0.525809i \(0.176237\pi\)
\(332\) 1.81521 + 3.14403i 0.0996225 + 0.172551i
\(333\) 1.27807 0.465178i 0.0700376 0.0254916i
\(334\) 0.788333 1.36543i 0.0431357 0.0747132i
\(335\) −1.63651 9.28109i −0.0894119 0.507080i
\(336\) 1.50000 0.866025i 0.0818317 0.0472456i
\(337\) 23.4047 8.51860i 1.27493 0.464038i 0.386180 0.922423i \(-0.373794\pi\)
0.888753 + 0.458386i \(0.151572\pi\)
\(338\) 12.1027 4.40501i 0.658298 0.239601i
\(339\) 27.2888 + 15.7552i 1.48212 + 0.855705i
\(340\) −0.520945 2.95442i −0.0282522 0.160226i
\(341\) −2.73783 + 4.74205i −0.148262 + 0.256797i
\(342\) −3.06283 + 5.30498i −0.165619 + 0.286861i
\(343\) −0.500000 0.866025i −0.0269975 0.0467610i
\(344\) −1.48293 + 1.24432i −0.0799540 + 0.0670894i
\(345\) 2.96657 + 8.15058i 0.159715 + 0.438812i
\(346\) 3.33363 18.9059i 0.179217 1.01639i
\(347\) −9.02481 7.57272i −0.484477 0.406525i 0.367565 0.929998i \(-0.380192\pi\)
−0.852042 + 0.523473i \(0.824636\pi\)
\(348\) −3.24376 + 0.571962i −0.173884 + 0.0306604i
\(349\) 21.8332 + 7.94664i 1.16871 + 0.425374i 0.852200 0.523217i \(-0.175268\pi\)
0.316506 + 0.948591i \(0.397490\pi\)
\(350\) −4.22668 −0.225926
\(351\) 1.15998 1.38241i 0.0619150 0.0737875i
\(352\) −2.06418 −0.110021
\(353\) −9.70486 3.53228i −0.516538 0.188004i 0.0705798 0.997506i \(-0.477515\pi\)
−0.587117 + 0.809502i \(0.699737\pi\)
\(354\) 1.13816 + 1.35640i 0.0604923 + 0.0720919i
\(355\) −3.86959 3.24697i −0.205376 0.172331i
\(356\) −3.25877 + 18.4814i −0.172714 + 0.979513i
\(357\) −5.81908 1.02606i −0.307978 0.0543049i
\(358\) −12.3118 + 10.3308i −0.650699 + 0.546001i
\(359\) −2.58512 4.47756i −0.136438 0.236317i 0.789708 0.613483i \(-0.210232\pi\)
−0.926146 + 0.377166i \(0.876899\pi\)
\(360\) 2.47906 + 0.902302i 0.130658 + 0.0475555i
\(361\) 7.41534 12.8438i 0.390281 0.675987i
\(362\) 3.87686 + 21.9868i 0.203763 + 1.15560i
\(363\) 11.6726i 0.612652i
\(364\) −0.326352 + 0.118782i −0.0171055 + 0.00622589i
\(365\) 10.2626 3.73530i 0.537171 0.195514i
\(366\) 5.93404i 0.310177i
\(367\) 2.55216 + 14.4740i 0.133221 + 0.755536i 0.976082 + 0.217404i \(0.0697589\pi\)
−0.842860 + 0.538133i \(0.819130\pi\)
\(368\) 2.84730 4.93166i 0.148426 0.257081i
\(369\) 15.1925 + 5.52963i 0.790892 + 0.287861i
\(370\) −0.199340 0.345268i −0.0103632 0.0179496i
\(371\) 7.73055 6.48670i 0.401350 0.336773i
\(372\) −4.52481 0.797847i −0.234601 0.0413664i
\(373\) −1.91740 + 10.8741i −0.0992794 + 0.563042i 0.894072 + 0.447923i \(0.147836\pi\)
−0.993352 + 0.115119i \(0.963275\pi\)
\(374\) 5.39440 + 4.52644i 0.278938 + 0.234057i
\(375\) −9.03343 10.7656i −0.466484 0.555935i
\(376\) −2.51367 0.914901i −0.129633 0.0471824i
\(377\) 0.660444 0.0340146
\(378\) 3.34002 3.98048i 0.171792 0.204734i
\(379\) −4.77332 −0.245189 −0.122594 0.992457i \(-0.539121\pi\)
−0.122594 + 0.992457i \(0.539121\pi\)
\(380\) 1.68732 + 0.614134i 0.0865576 + 0.0315044i
\(381\) 20.9518 3.69436i 1.07339 0.189268i
\(382\) 10.8550 + 9.10846i 0.555392 + 0.466029i
\(383\) 3.23355 18.3383i 0.165226 0.937046i −0.783604 0.621260i \(-0.786621\pi\)
0.948831 0.315785i \(-0.102268\pi\)
\(384\) −0.592396 1.62760i −0.0302306 0.0830579i
\(385\) −1.39053 + 1.16679i −0.0708680 + 0.0594653i
\(386\) −4.85117 8.40247i −0.246918 0.427674i
\(387\) −2.90373 + 5.02941i −0.147605 + 0.255659i
\(388\) 3.58125 6.20291i 0.181811 0.314905i
\(389\) 0.400492 + 2.27130i 0.0203057 + 0.115160i 0.993276 0.115771i \(-0.0369340\pi\)
−0.972970 + 0.230931i \(0.925823\pi\)
\(390\) −0.458111 0.264490i −0.0231973 0.0133930i
\(391\) −18.2554 + 6.64441i −0.923214 + 0.336022i
\(392\) −0.939693 + 0.342020i −0.0474616 + 0.0172746i
\(393\) 3.34002 1.92836i 0.168482 0.0972730i
\(394\) −1.02869 5.83396i −0.0518244 0.293911i
\(395\) 2.96538 5.13620i 0.149205 0.258430i
\(396\) −5.81908 + 2.11797i −0.292420 + 0.106432i
\(397\) −13.6224 23.5947i −0.683690 1.18419i −0.973847 0.227207i \(-0.927041\pi\)
0.290157 0.956979i \(-0.406293\pi\)
\(398\) 14.1459 11.8698i 0.709070 0.594980i
\(399\) 2.27332 2.70924i 0.113808 0.135631i
\(400\) −0.733956 + 4.16247i −0.0366978 + 0.208123i
\(401\) −22.0385 18.4925i −1.10055 0.923471i −0.103088 0.994672i \(-0.532872\pi\)
−0.997462 + 0.0712017i \(0.977317\pi\)
\(402\) −6.34864 + 17.4427i −0.316641 + 0.869965i
\(403\) 0.865715 + 0.315094i 0.0431243 + 0.0156960i
\(404\) −2.49525 −0.124143
\(405\) 7.91447 0.393273
\(406\) 1.90167 0.0943785
\(407\) 0.879385 + 0.320070i 0.0435895 + 0.0158653i
\(408\) −2.02094 + 5.55250i −0.100052 + 0.274890i
\(409\) 24.2160 + 20.3196i 1.19740 + 1.00474i 0.999700 + 0.0244798i \(0.00779293\pi\)
0.197704 + 0.980262i \(0.436652\pi\)
\(410\) 0.822948 4.66717i 0.0406425 0.230495i
\(411\) 7.13058 8.49789i 0.351725 0.419170i
\(412\) 0.777189 0.652139i 0.0382893 0.0321286i
\(413\) −0.511144 0.885328i −0.0251518 0.0435641i
\(414\) 2.96657 16.8242i 0.145799 0.826866i
\(415\) 1.59627 2.76481i 0.0783576 0.135719i
\(416\) 0.0603074 + 0.342020i 0.00295681 + 0.0167689i
\(417\) −32.8601 + 18.9718i −1.60917 + 0.929052i
\(418\) −3.96064 + 1.44155i −0.193721 + 0.0705087i
\(419\) −0.118089 + 0.0429807i −0.00576900 + 0.00209975i −0.344903 0.938638i \(-0.612088\pi\)
0.339134 + 0.940738i \(0.389866\pi\)
\(420\) −1.31908 0.761570i −0.0643644 0.0371608i
\(421\) −5.13176 29.1037i −0.250107 1.41843i −0.808328 0.588733i \(-0.799627\pi\)
0.558221 0.829692i \(-0.311484\pi\)
\(422\) −9.26651 + 16.0501i −0.451087 + 0.781305i
\(423\) −8.02498 −0.390188
\(424\) −5.04576 8.73951i −0.245044 0.424428i
\(425\) 11.0458 9.26849i 0.535798 0.449588i
\(426\) 3.40286 + 9.34927i 0.164869 + 0.452974i
\(427\) −0.594922 + 3.37397i −0.0287903 + 0.163278i
\(428\) 8.66637 + 7.27195i 0.418905 + 0.351503i
\(429\) 1.22281 0.215615i 0.0590379 0.0104100i
\(430\) 1.59967 + 0.582232i 0.0771429 + 0.0280777i
\(431\) −9.25578 −0.445835 −0.222918 0.974837i \(-0.571558\pi\)
−0.222918 + 0.974837i \(0.571558\pi\)
\(432\) −3.34002 3.98048i −0.160697 0.191511i
\(433\) −4.85978 −0.233546 −0.116773 0.993159i \(-0.537255\pi\)
−0.116773 + 0.993159i \(0.537255\pi\)
\(434\) 2.49273 + 0.907278i 0.119655 + 0.0435507i
\(435\) 1.86184 + 2.21886i 0.0892686 + 0.106386i
\(436\) 9.77379 + 8.20118i 0.468079 + 0.392765i
\(437\) 2.01913 11.4511i 0.0965883 0.547779i
\(438\) −21.1839 3.73530i −1.01221 0.178479i
\(439\) −22.7931 + 19.1257i −1.08786 + 0.912820i −0.996549 0.0830022i \(-0.973549\pi\)
−0.0913077 + 0.995823i \(0.529105\pi\)
\(440\) 0.907604 + 1.57202i 0.0432683 + 0.0749429i
\(441\) −2.29813 + 1.92836i −0.109435 + 0.0918268i
\(442\) 0.592396 1.02606i 0.0281774 0.0488047i
\(443\) −3.69547 20.9581i −0.175577 0.995747i −0.937476 0.348051i \(-0.886844\pi\)
0.761899 0.647696i \(-0.224267\pi\)
\(444\) 0.785248i 0.0372662i
\(445\) 15.5077 5.64436i 0.735137 0.267568i
\(446\) 9.87686 3.59488i 0.467683 0.170223i
\(447\) 38.2518i 1.80925i
\(448\) 0.173648 + 0.984808i 0.00820411 + 0.0465278i
\(449\) 5.89171 10.2047i 0.278047 0.481592i −0.692852 0.721080i \(-0.743646\pi\)
0.970899 + 0.239488i \(0.0769795\pi\)
\(450\) 2.20187 + 12.4874i 0.103797 + 0.588662i
\(451\) 5.56212 + 9.63387i 0.261910 + 0.453641i
\(452\) −13.9363 + 11.6939i −0.655508 + 0.550036i
\(453\) −30.6830 5.41025i −1.44161 0.254196i
\(454\) −2.22328 + 12.6088i −0.104344 + 0.591762i
\(455\) 0.233956 + 0.196312i 0.0109680 + 0.00920325i
\(456\) −2.27332 2.70924i −0.106458 0.126872i
\(457\) 36.1117 + 13.1436i 1.68924 + 0.614832i 0.994529 0.104461i \(-0.0333117\pi\)
0.694707 + 0.719293i \(0.255534\pi\)
\(458\) 10.3824 0.485137
\(459\) 17.7265i 0.827404i
\(460\) −5.00774 −0.233487
\(461\) 23.0736 + 8.39809i 1.07464 + 0.391138i 0.817911 0.575345i \(-0.195132\pi\)
0.256732 + 0.966483i \(0.417354\pi\)
\(462\) 3.52094 0.620838i 0.163809 0.0288840i
\(463\) −5.23964 4.39658i −0.243507 0.204326i 0.512864 0.858470i \(-0.328585\pi\)
−0.756370 + 0.654144i \(0.773029\pi\)
\(464\) 0.330222 1.87278i 0.0153302 0.0869418i
\(465\) 1.38191 + 3.79677i 0.0640846 + 0.176071i
\(466\) −3.06624 + 2.57288i −0.142041 + 0.119186i
\(467\) −0.979055 1.69577i −0.0453053 0.0784711i 0.842484 0.538722i \(-0.181093\pi\)
−0.887789 + 0.460251i \(0.847759\pi\)
\(468\) 0.520945 + 0.902302i 0.0240807 + 0.0417089i
\(469\) 5.35844 9.28109i 0.247430 0.428561i
\(470\) 0.408481 + 2.31661i 0.0188418 + 0.106857i
\(471\) −29.4176 16.9843i −1.35549 0.782594i
\(472\) −0.960637 + 0.349643i −0.0442169 + 0.0160936i
\(473\) −3.75490 + 1.36667i −0.172650 + 0.0628396i
\(474\) −10.1163 + 5.84067i −0.464659 + 0.268271i
\(475\) 1.49866 + 8.49930i 0.0687630 + 0.389975i
\(476\) 1.70574 2.95442i 0.0781823 0.135416i
\(477\) −23.1917 19.4601i −1.06187 0.891017i
\(478\) −10.6741 18.4881i −0.488223 0.845626i
\(479\) −12.6138 + 10.5842i −0.576340 + 0.483606i −0.883743 0.467973i \(-0.844984\pi\)
0.307403 + 0.951579i \(0.400540\pi\)
\(480\) −0.979055 + 1.16679i −0.0446876 + 0.0532566i
\(481\) 0.0273411 0.155059i 0.00124665 0.00707010i
\(482\) −4.35844 3.65717i −0.198522 0.166579i
\(483\) −3.37346 + 9.26849i −0.153498 + 0.421731i
\(484\) 6.33275 + 2.30493i 0.287852 + 0.104770i
\(485\) −6.29860 −0.286005
\(486\) −13.5000 7.79423i −0.612372 0.353553i
\(487\) −7.53714 −0.341540 −0.170770 0.985311i \(-0.554626\pi\)
−0.170770 + 0.985311i \(0.554626\pi\)
\(488\) 3.21941 + 1.17177i 0.145736 + 0.0530435i
\(489\) 5.31134 14.5928i 0.240187 0.659908i
\(490\) 0.673648 + 0.565258i 0.0304323 + 0.0255358i
\(491\) 1.03667 5.87927i 0.0467845 0.265328i −0.952439 0.304729i \(-0.901434\pi\)
0.999223 + 0.0394014i \(0.0125451\pi\)
\(492\) −6.00000 + 7.15052i −0.270501 + 0.322370i
\(493\) −4.96972 + 4.17009i −0.223825 + 0.187811i
\(494\) 0.354570 + 0.614134i 0.0159529 + 0.0276312i
\(495\) 4.17159 + 3.50038i 0.187499 + 0.157330i
\(496\) 1.32635 2.29731i 0.0595550 0.103152i
\(497\) −0.997474 5.65695i −0.0447428 0.253749i
\(498\) −5.44562 + 3.14403i −0.244024 + 0.140887i
\(499\) −35.9111 + 13.0706i −1.60760 + 0.585119i −0.980963 0.194193i \(-0.937791\pi\)
−0.626637 + 0.779312i \(0.715569\pi\)
\(500\) 7.62449 2.77509i 0.340977 0.124106i
\(501\) 2.36500 + 1.36543i 0.105660 + 0.0610031i
\(502\) −2.24510 12.7326i −0.100204 0.568283i
\(503\) −5.44222 + 9.42620i −0.242657 + 0.420293i −0.961470 0.274909i \(-0.911352\pi\)
0.718814 + 0.695203i \(0.244685\pi\)
\(504\) 1.50000 + 2.59808i 0.0668153 + 0.115728i
\(505\) 1.09714 + 1.90031i 0.0488223 + 0.0845626i
\(506\) 9.00459 7.55574i 0.400303 0.335894i
\(507\) 7.62970 + 20.9624i 0.338847 + 0.930974i
\(508\) −2.13294 + 12.0965i −0.0946340 + 0.536696i
\(509\) −1.55644 1.30601i −0.0689879 0.0578877i 0.607642 0.794211i \(-0.292116\pi\)
−0.676630 + 0.736324i \(0.736560\pi\)
\(510\) 5.11721 0.902302i 0.226594 0.0399546i
\(511\) 11.6702 + 4.24762i 0.516261 + 0.187904i
\(512\) 1.00000 0.0441942
\(513\) −9.18850 5.30498i −0.405682 0.234221i
\(514\) 29.2763 1.29132
\(515\) −0.838374 0.305143i −0.0369432 0.0134462i
\(516\) −2.15523 2.56850i −0.0948787 0.113072i
\(517\) −4.22984 3.54925i −0.186028 0.156096i
\(518\) 0.0787257 0.446476i 0.00345901 0.0196170i
\(519\) 32.7460 + 5.77401i 1.43739 + 0.253451i
\(520\) 0.233956 0.196312i 0.0102596 0.00860885i
\(521\) −17.9534 31.0961i −0.786551 1.36235i −0.928068 0.372411i \(-0.878531\pi\)
0.141517 0.989936i \(-0.454802\pi\)
\(522\) −0.990667 5.61835i −0.0433603 0.245908i
\(523\) 4.68139 8.10840i 0.204703 0.354556i −0.745335 0.666690i \(-0.767711\pi\)
0.950038 + 0.312134i \(0.101044\pi\)
\(524\) 0.386659 + 2.19285i 0.0168913 + 0.0957952i
\(525\) 7.32083i 0.319507i
\(526\) 6.56418 2.38917i 0.286212 0.104173i
\(527\) −8.50387 + 3.09516i −0.370434 + 0.134827i
\(528\) 3.57526i 0.155593i
\(529\) 1.63722 + 9.28515i 0.0711836 + 0.403702i
\(530\) −4.43717 + 7.68540i −0.192738 + 0.333832i
\(531\) −2.34936 + 1.97134i −0.101953 + 0.0855490i
\(532\) 1.02094 + 1.76833i 0.0442636 + 0.0766667i
\(533\) 1.43376 1.20307i 0.0621032 0.0521107i
\(534\) −32.0107 5.64436i −1.38524 0.244255i
\(535\) 1.72756 9.79747i 0.0746889 0.423582i
\(536\) −8.20961 6.88868i −0.354601 0.297546i
\(537\) −17.8935 21.3247i −0.772162 0.920227i
\(538\) 17.8341 + 6.49108i 0.768882 + 0.279850i
\(539\) −2.06418 −0.0889104
\(540\) −1.56283 + 4.29385i −0.0672537 + 0.184778i
\(541\) −2.66313 −0.114497 −0.0572485 0.998360i \(-0.518233\pi\)
−0.0572485 + 0.998360i \(0.518233\pi\)
\(542\) 27.0663 + 9.85133i 1.16260 + 0.423151i
\(543\) −38.0822 + 6.71492i −1.63426 + 0.288165i
\(544\) −2.61334 2.19285i −0.112046 0.0940178i
\(545\) 1.94831 11.0494i 0.0834565 0.473305i
\(546\) −0.205737 0.565258i −0.00880473 0.0241908i
\(547\) −11.3543 + 9.52741i −0.485476 + 0.407363i −0.852402 0.522888i \(-0.824855\pi\)
0.366926 + 0.930250i \(0.380410\pi\)
\(548\) 3.20233 + 5.54660i 0.136797 + 0.236939i
\(549\) 10.2781 0.438657
\(550\) −4.36231 + 7.55574i −0.186010 + 0.322178i
\(551\) −0.674277 3.82402i −0.0287252 0.162909i
\(552\) 8.54189 + 4.93166i 0.363567 + 0.209905i
\(553\) 6.33750 2.30666i 0.269498 0.0980892i
\(554\) 22.1202 8.05110i 0.939797 0.342058i
\(555\) 0.598021 0.345268i 0.0253846 0.0146558i
\(556\) −3.80406 21.5739i −0.161328 0.914938i
\(557\) 8.58512 14.8699i 0.363763 0.630057i −0.624814 0.780774i \(-0.714825\pi\)
0.988577 + 0.150717i \(0.0481584\pi\)
\(558\) 1.38191 7.83721i 0.0585010 0.331776i
\(559\) 0.336152 + 0.582232i 0.0142177 + 0.0246258i
\(560\) 0.673648 0.565258i 0.0284668 0.0238865i
\(561\) −7.84002 + 9.34337i −0.331006 + 0.394478i
\(562\) 3.93464 22.3145i 0.165973 0.941278i
\(563\) 18.5458 + 15.5617i 0.781611 + 0.655849i 0.943654 0.330935i \(-0.107364\pi\)
−0.162043 + 0.986784i \(0.551808\pi\)
\(564\) 1.58466 4.35381i 0.0667260 0.183328i
\(565\) 15.0334 + 5.47172i 0.632461 + 0.230197i
\(566\) −9.00093 −0.378337
\(567\) 6.89440 + 5.78509i 0.289538 + 0.242951i
\(568\) −5.74422 −0.241022
\(569\) 10.7674 + 3.91901i 0.451392 + 0.164293i 0.557705 0.830039i \(-0.311682\pi\)
−0.106312 + 0.994333i \(0.533904\pi\)
\(570\) −1.06371 + 2.92252i −0.0445539 + 0.122411i
\(571\) −8.05169 6.75617i −0.336953 0.282737i 0.458573 0.888657i \(-0.348361\pi\)
−0.795526 + 0.605920i \(0.792805\pi\)
\(572\) −0.124485 + 0.705990i −0.00520499 + 0.0295189i
\(573\) −15.7763 + 18.8015i −0.659065 + 0.785443i
\(574\) 4.12836 3.46410i 0.172314 0.144589i
\(575\) −12.0346 20.8446i −0.501878 0.869278i
\(576\) 2.81908 1.02606i 0.117462 0.0427525i
\(577\) −2.52822 + 4.37900i −0.105251 + 0.182300i −0.913841 0.406073i \(-0.866898\pi\)
0.808590 + 0.588373i \(0.200231\pi\)
\(578\) −0.931074 5.28039i −0.0387276 0.219635i
\(579\) 14.5535 8.40247i 0.604823 0.349195i
\(580\) −1.57145 + 0.571962i −0.0652510 + 0.0237494i
\(581\) 3.41147 1.24168i 0.141532 0.0515134i
\(582\) 10.7438 + 6.20291i 0.445343 + 0.257119i
\(583\) −3.61721 20.5142i −0.149810 0.849612i
\(584\) 6.20961 10.7554i 0.256955 0.445060i
\(585\) 0.458111 0.793471i 0.0189406 0.0328060i
\(586\) −4.56283 7.90306i −0.188489 0.326472i
\(587\) 13.4684 11.3013i 0.555899 0.466455i −0.321033 0.947068i \(-0.604030\pi\)
0.876933 + 0.480613i \(0.159586\pi\)
\(588\) −0.592396 1.62760i −0.0244300 0.0671209i
\(589\) 0.940570 5.33424i 0.0387555 0.219793i
\(590\) 0.688663 + 0.577857i 0.0283518 + 0.0237900i
\(591\) 10.1047 1.78174i 0.415653 0.0732908i
\(592\) −0.426022 0.155059i −0.0175094 0.00637290i
\(593\) 12.7041 0.521694 0.260847 0.965380i \(-0.415998\pi\)
0.260847 + 0.965380i \(0.415998\pi\)
\(594\) −3.66843 10.0789i −0.150518 0.413544i
\(595\) −3.00000 −0.122988
\(596\) −20.7528 7.55342i −0.850069 0.309400i
\(597\) 20.5591 + 24.5014i 0.841429 + 1.00278i
\(598\) −1.51501 1.27125i −0.0619536 0.0519852i
\(599\) 6.82594 38.7118i 0.278900 1.58172i −0.447393 0.894338i \(-0.647647\pi\)
0.726293 0.687385i \(-0.241242\pi\)
\(600\) −7.20961 1.27125i −0.294331 0.0518985i
\(601\) 25.5881 21.4710i 1.04376 0.875819i 0.0513372 0.998681i \(-0.483652\pi\)
0.992424 + 0.122862i \(0.0392072\pi\)
\(602\) 0.967911 + 1.67647i 0.0394491 + 0.0683279i
\(603\) −30.2117 10.9962i −1.23032 0.447799i
\(604\) 8.99407 15.5782i 0.365964 0.633867i
\(605\) −1.02910 5.83629i −0.0418387 0.237279i
\(606\) 4.32190i 0.175565i
\(607\) −38.8482 + 14.1396i −1.57680 + 0.573909i −0.974505 0.224364i \(-0.927969\pi\)
−0.602296 + 0.798273i \(0.705747\pi\)
\(608\) 1.91875 0.698367i 0.0778155 0.0283225i
\(609\) 3.29380i 0.133471i
\(610\) −0.523166 2.96702i −0.0211824 0.120131i
\(611\) −0.464508 + 0.804551i −0.0187920 + 0.0325486i
\(612\) −9.61721 3.50038i −0.388753 0.141494i
\(613\) −3.52528 6.10597i −0.142385 0.246618i 0.786009 0.618215i \(-0.212144\pi\)
−0.928394 + 0.371597i \(0.878810\pi\)
\(614\) 8.72849 7.32407i 0.352253 0.295576i
\(615\) 8.08378 + 1.42539i 0.325969 + 0.0574772i
\(616\) −0.358441 + 2.03282i −0.0144420 + 0.0819046i
\(617\) 33.8011 + 28.3625i 1.36078 + 1.14183i 0.975740 + 0.218933i \(0.0702575\pi\)
0.385042 + 0.922899i \(0.374187\pi\)
\(618\) 1.12954 + 1.34613i 0.0454367 + 0.0541493i
\(619\) 36.0621 + 13.1255i 1.44946 + 0.527560i 0.942440 0.334375i \(-0.108525\pi\)
0.507019 + 0.861935i \(0.330747\pi\)
\(620\) −2.33275 −0.0936854
\(621\) 29.1404 + 5.13824i 1.16937 + 0.206191i
\(622\) 2.27631 0.0912718
\(623\) 17.6348 + 6.41852i 0.706521 + 0.257153i
\(624\) −0.592396 + 0.104455i −0.0237148 + 0.00418156i
\(625\) 10.7233 + 8.99790i 0.428931 + 0.359916i
\(626\) −0.253718 + 1.43891i −0.0101406 + 0.0575103i
\(627\) −2.49684 6.86002i −0.0997144 0.273963i
\(628\) 15.0235 12.6062i 0.599502 0.503042i
\(629\) 0.773318 + 1.33943i 0.0308342 + 0.0534064i
\(630\) 1.31908 2.28471i 0.0525533 0.0910250i
\(631\) −16.6755 + 28.8827i −0.663840 + 1.14980i 0.315759 + 0.948839i \(0.397741\pi\)
−0.979599 + 0.200964i \(0.935592\pi\)
\(632\) −1.17112 6.64176i −0.0465847 0.264195i
\(633\) −27.7995 16.0501i −1.10493 0.637933i
\(634\) 0.393056 0.143061i 0.0156102 0.00568166i
\(635\) 10.1502 3.69436i 0.402798 0.146606i
\(636\) 15.1373 8.73951i 0.600232 0.346544i
\(637\) 0.0603074 + 0.342020i 0.00238947 + 0.0135513i
\(638\) 1.96270 3.39949i 0.0777039 0.134587i
\(639\) −16.1934 + 5.89392i −0.640601 + 0.233160i
\(640\) −0.439693 0.761570i −0.0173804 0.0301037i
\(641\) −31.3601 + 26.3142i −1.23865 + 1.03935i −0.241021 + 0.970520i \(0.577482\pi\)
−0.997628 + 0.0688300i \(0.978073\pi\)
\(642\) −12.5954 + 15.0106i −0.497100 + 0.592421i
\(643\) −6.21869 + 35.2680i −0.245241 + 1.39083i 0.574690 + 0.818371i \(0.305123\pi\)
−0.819932 + 0.572461i \(0.805989\pi\)
\(644\) −4.36231 3.66041i −0.171899 0.144241i
\(645\) −1.00846 + 2.77071i −0.0397079 + 0.109097i
\(646\) −6.54576 2.38246i −0.257539 0.0937367i
\(647\) −34.1388 −1.34213 −0.671067 0.741397i \(-0.734164\pi\)
−0.671067 + 0.741397i \(0.734164\pi\)
\(648\) 6.89440 5.78509i 0.270838 0.227260i
\(649\) −2.11019 −0.0828320
\(650\) 1.37939 + 0.502055i 0.0541039 + 0.0196922i
\(651\) −1.57145 + 4.31753i −0.0615900 + 0.169217i
\(652\) 6.86824 + 5.76314i 0.268981 + 0.225702i
\(653\) 6.90003 39.1320i 0.270019 1.53135i −0.484334 0.874883i \(-0.660938\pi\)
0.754352 0.656470i \(-0.227951\pi\)
\(654\) −14.2049 + 16.9287i −0.555454 + 0.661964i
\(655\) 1.50000 1.25865i 0.0586098 0.0491795i
\(656\) −2.69459 4.66717i −0.105206 0.182222i
\(657\) 6.46972 36.6916i 0.252408 1.43148i
\(658\) −1.33750 + 2.31661i −0.0521410 + 0.0903109i
\(659\) 2.76563 + 15.6847i 0.107734 + 0.610989i 0.990093 + 0.140412i \(0.0448428\pi\)
−0.882359 + 0.470576i \(0.844046\pi\)
\(660\) −2.72281 + 1.57202i −0.105985 + 0.0611906i
\(661\) 6.12836 2.23054i 0.238365 0.0867579i −0.220075 0.975483i \(-0.570630\pi\)
0.458441 + 0.888725i \(0.348408\pi\)
\(662\) −10.7233 + 3.90295i −0.416772 + 0.151693i
\(663\) 1.77719 + 1.02606i 0.0690203 + 0.0398489i
\(664\) −0.630415 3.57526i −0.0244648 0.138747i
\(665\) 0.897804 1.55504i 0.0348153 0.0603019i
\(666\) −1.36009 −0.0527024
\(667\) 5.41463 + 9.37841i 0.209655 + 0.363134i
\(668\) −1.20780 + 1.01346i −0.0467310 + 0.0392120i
\(669\) 6.22652 + 17.1072i 0.240731 + 0.661403i
\(670\) −1.63651 + 9.28109i −0.0632238 + 0.358560i
\(671\) 5.41740 + 4.54574i 0.209137 + 0.175486i
\(672\) −1.70574 + 0.300767i −0.0658002 + 0.0116024i
\(673\) −15.3500 5.58694i −0.591698 0.215361i 0.0287778 0.999586i \(-0.490838\pi\)
−0.620476 + 0.784225i \(0.713061\pi\)
\(674\) −24.9067 −0.959371
\(675\) −21.6288 + 3.81374i −0.832494 + 0.146791i
\(676\) −12.8794 −0.495361
\(677\) 1.68092 + 0.611806i 0.0646031 + 0.0235136i 0.374120 0.927380i \(-0.377945\pi\)
−0.309516 + 0.950894i \(0.600167\pi\)
\(678\) −20.2545 24.1384i −0.777869 0.927028i
\(679\) −5.48680 4.60397i −0.210564 0.176684i
\(680\) −0.520945 + 2.95442i −0.0199773 + 0.113297i
\(681\) −21.8391 3.85083i −0.836878 0.147564i
\(682\) 4.19459 3.51968i 0.160619 0.134776i
\(683\) −7.89306 13.6712i −0.302019 0.523113i 0.674574 0.738207i \(-0.264327\pi\)
−0.976593 + 0.215094i \(0.930994\pi\)
\(684\) 4.69253 3.93750i 0.179423 0.150554i
\(685\) 2.81608 4.87760i 0.107597 0.186364i
\(686\) 0.173648 + 0.984808i 0.00662992 + 0.0376001i
\(687\) 17.9828i 0.686087i
\(688\) 1.81908 0.662090i 0.0693517 0.0252420i
\(689\) −3.29339 + 1.19869i −0.125468 + 0.0456666i
\(690\) 8.67366i 0.330201i
\(691\) −2.74376 15.5606i −0.104377 0.591954i −0.991467 0.130357i \(-0.958388\pi\)
0.887090 0.461597i \(-0.152723\pi\)
\(692\) −9.59879 + 16.6256i −0.364891 + 0.632010i
\(693\) 1.07532 + 6.09845i 0.0408481 + 0.231661i
\(694\) 5.89053 + 10.2027i 0.223601 + 0.387289i
\(695\) −14.7574 + 12.3830i −0.559781 + 0.469712i
\(696\) 3.24376 + 0.571962i 0.122954 + 0.0216802i
\(697\) −3.19253 + 18.1058i −0.120926 + 0.685804i
\(698\) −17.7986 14.9348i −0.673687 0.565290i
\(699\) −4.45636 5.31088i −0.168555 0.200876i
\(700\) 3.97178 + 1.44561i 0.150119 + 0.0546389i
\(701\) 29.6705 1.12064 0.560321 0.828276i \(-0.310678\pi\)
0.560321 + 0.828276i \(0.310678\pi\)
\(702\) −1.56283 + 0.902302i −0.0589854 + 0.0340552i
\(703\) −0.925717 −0.0349141
\(704\) 1.93969 + 0.705990i 0.0731049 + 0.0266080i
\(705\) −4.01249 + 0.707510i −0.151119 + 0.0266464i
\(706\) 7.91147 + 6.63852i 0.297752 + 0.249844i
\(707\) −0.433296 + 2.45734i −0.0162958 + 0.0924179i
\(708\) −0.605600 1.66387i −0.0227598 0.0625322i
\(709\) −8.70574 + 7.30498i −0.326951 + 0.274344i −0.791456 0.611226i \(-0.790677\pi\)
0.464505 + 0.885570i \(0.346232\pi\)
\(710\) 2.52569 + 4.37463i 0.0947875 + 0.164177i
\(711\) −10.1163 17.5220i −0.379392 0.657126i
\(712\) 9.38326 16.2523i 0.351652 0.609080i
\(713\) 2.62314 + 14.8766i 0.0982374 + 0.557132i
\(714\) 5.11721 + 2.95442i 0.191507 + 0.110567i
\(715\) 0.592396 0.215615i 0.0221544 0.00806353i
\(716\) 15.1027 5.49692i 0.564413 0.205430i
\(717\) 32.0223 18.4881i 1.19590 0.690451i
\(718\) 0.897804 + 5.09170i 0.0335057 + 0.190020i
\(719\) −19.5940 + 33.9379i −0.730735 + 1.26567i 0.225835 + 0.974166i \(0.427489\pi\)
−0.956570 + 0.291504i \(0.905844\pi\)
\(720\) −2.02094 1.69577i −0.0753162 0.0631978i
\(721\) −0.507274 0.878624i −0.0188919 0.0327217i
\(722\) −11.3610 + 9.53298i −0.422811 + 0.354781i
\(723\) 6.33440 7.54904i 0.235579 0.280752i
\(724\) 3.87686 21.9868i 0.144082 0.817132i
\(725\) −6.15729 5.16658i −0.228676 0.191882i
\(726\) −3.99226 + 10.9686i −0.148167 + 0.407084i
\(727\) 41.9752 + 15.2777i 1.55678 + 0.566620i 0.969995 0.243126i \(-0.0781728\pi\)
0.586781 + 0.809746i \(0.300395\pi\)
\(728\) 0.347296 0.0128717
\(729\) 13.5000 23.3827i 0.500000 0.866025i
\(730\) −10.9213 −0.404214
\(731\) −6.20574 2.25870i −0.229527 0.0835412i
\(732\) −2.02956 + 5.57618i −0.0750148 + 0.206101i
\(733\) 25.5633 + 21.4502i 0.944202 + 0.792280i 0.978312 0.207139i \(-0.0664151\pi\)
−0.0341096 + 0.999418i \(0.510860\pi\)
\(734\) 2.55216 14.4740i 0.0942018 0.534245i
\(735\) −0.979055 + 1.16679i −0.0361130 + 0.0430378i
\(736\) −4.36231 + 3.66041i −0.160797 + 0.134925i
\(737\) −11.0608 19.1578i −0.407429 0.705687i
\(738\) −12.3851 10.3923i −0.455901 0.382546i
\(739\) 3.22921 5.59315i 0.118788 0.205747i −0.800499 0.599334i \(-0.795432\pi\)
0.919288 + 0.393586i \(0.128766\pi\)
\(740\) 0.0692302 + 0.392624i 0.00254495 + 0.0144331i
\(741\) −1.06371 + 0.614134i −0.0390764 + 0.0225608i
\(742\) −9.48293 + 3.45150i −0.348129 + 0.126709i
\(743\) 16.5342 6.01796i 0.606581 0.220777i −0.0204255 0.999791i \(-0.506502\pi\)
0.627007 + 0.779014i \(0.284280\pi\)
\(744\) 3.97906 + 2.29731i 0.145879 + 0.0842234i
\(745\) 3.37242 + 19.1259i 0.123556 + 0.700720i
\(746\) 5.52094 9.56256i 0.202136 0.350110i
\(747\) −5.44562 9.43209i −0.199245 0.345102i
\(748\) −3.52094 6.09845i −0.128738 0.222982i
\(749\) 8.66637 7.27195i 0.316662 0.265711i
\(750\) 4.80659 + 13.2060i 0.175512 + 0.482215i
\(751\) −2.54024 + 14.4064i −0.0926947 + 0.525698i 0.902735 + 0.430198i \(0.141556\pi\)
−0.995429 + 0.0955001i \(0.969555\pi\)
\(752\) 2.04916 + 1.71945i 0.0747253 + 0.0627020i
\(753\) 22.0535 3.88863i 0.803674 0.141709i
\(754\) −0.620615 0.225885i −0.0226015 0.00822626i
\(755\) −15.8185 −0.575694
\(756\) −4.50000 + 2.59808i −0.163663 + 0.0944911i
\(757\) −14.7692 −0.536796 −0.268398 0.963308i \(-0.586494\pi\)
−0.268398 + 0.963308i \(0.586494\pi\)
\(758\) 4.48545 + 1.63257i 0.162919 + 0.0592977i
\(759\) 13.0869 + 15.5964i 0.475026 + 0.566113i
\(760\) −1.37551 1.15419i −0.0498952 0.0418670i
\(761\) −3.67768 + 20.8572i −0.133316 + 0.756072i 0.842702 + 0.538380i \(0.180964\pi\)
−0.976018 + 0.217691i \(0.930147\pi\)
\(762\) −20.9518 3.69436i −0.759003 0.133833i
\(763\) 9.77379 8.20118i 0.353835 0.296903i
\(764\) −7.08512 12.2718i −0.256331 0.443978i
\(765\) 1.56283 + 8.86327i 0.0565044 + 0.320452i
\(766\) −9.31062 + 16.1265i −0.336406 + 0.582673i
\(767\) 0.0616516 + 0.349643i 0.00222611 + 0.0126249i
\(768\) 1.73205i 0.0625000i
\(769\) −4.42127 + 1.60921i −0.159435 + 0.0580297i −0.420505 0.907290i \(-0.638147\pi\)
0.261070 + 0.965320i \(0.415925\pi\)
\(770\) 1.70574 0.620838i 0.0614705 0.0223734i
\(771\) 50.7081i 1.82621i
\(772\) 1.68479 + 9.55493i 0.0606370 + 0.343890i
\(773\) 15.3746 26.6297i 0.552987 0.957802i −0.445070 0.895496i \(-0.646821\pi\)
0.998057 0.0623062i \(-0.0198455\pi\)
\(774\) 4.44878 3.73297i 0.159908 0.134179i
\(775\) −5.60607 9.70999i −0.201376 0.348793i
\(776\) −5.48680 + 4.60397i −0.196965 + 0.165273i
\(777\) 0.773318 + 0.136357i 0.0277426 + 0.00489178i
\(778\) 0.400492 2.27130i 0.0143583 0.0814301i
\(779\) −8.42964 7.07331i −0.302023 0.253428i
\(780\) 0.340022 + 0.405223i 0.0121748 + 0.0145093i
\(781\) −11.1420 4.05537i −0.398693 0.145112i
\(782\) 19.4270 0.694707
\(783\) 9.73127 1.71588i 0.347767 0.0613207i
\(784\) 1.00000 0.0357143
\(785\) −16.2062 5.89858i −0.578424 0.210529i
\(786\) −3.79813 + 0.669713i −0.135475 + 0.0238879i
\(787\) 26.6208 + 22.3375i 0.948930 + 0.796247i 0.979117 0.203297i \(-0.0651658\pi\)
−0.0301868 + 0.999544i \(0.509610\pi\)
\(788\) −1.02869 + 5.83396i −0.0366454 + 0.207826i
\(789\) 4.13816 + 11.3695i 0.147322 + 0.404765i
\(790\) −4.54323 + 3.81223i −0.161641 + 0.135633i
\(791\) 9.09627 + 15.7552i 0.323426 + 0.560190i
\(792\) 6.19253 0.220042
\(793\) 0.594922 1.03044i 0.0211263 0.0365919i
\(794\) 4.73102 + 26.8309i 0.167898 + 0.952194i
\(795\) −13.3115 7.68540i −0.472110 0.272573i
\(796\) −17.3525 + 6.31580i −0.615043 + 0.223858i
\(797\) −17.9379 + 6.52888i −0.635394 + 0.231265i −0.639578 0.768727i \(-0.720891\pi\)
0.00418315 + 0.999991i \(0.498668\pi\)
\(798\) −3.06283 + 1.76833i −0.108423 + 0.0625981i
\(799\) −1.58466 8.98703i −0.0560611 0.317938i
\(800\) 2.11334 3.66041i 0.0747179 0.129415i
\(801\) 9.77631 55.4442i 0.345429 1.95903i
\(802\) 14.3846 + 24.9149i 0.507938 + 0.879774i
\(803\) 19.6379 16.4782i 0.693007 0.581502i
\(804\) 11.9315 14.2195i 0.420793 0.501482i
\(805\) −0.869585 + 4.93166i −0.0306488 + 0.173818i
\(806\) −0.705737 0.592184i −0.0248585 0.0208588i
\(807\) −11.2429 + 30.8896i −0.395768 + 1.08736i
\(808\) 2.34477 + 0.853427i 0.0824887 + 0.0300234i
\(809\) −7.30129 −0.256700 −0.128350 0.991729i \(-0.540968\pi\)
−0.128350 + 0.991729i \(0.540968\pi\)
\(810\) −7.43717 2.70691i −0.261315 0.0951110i
\(811\) 19.8307 0.696350 0.348175 0.937430i \(-0.386802\pi\)
0.348175 + 0.937430i \(0.386802\pi\)
\(812\) −1.78699 0.650411i −0.0627110 0.0228249i
\(813\) −17.0630 + 46.8802i −0.598425 + 1.64416i
\(814\) −0.716881 0.601535i −0.0251267 0.0210838i
\(815\) 1.36912 7.76466i 0.0479581 0.271984i
\(816\) 3.79813 4.52644i 0.132961 0.158457i
\(817\) 3.02797 2.54077i 0.105935 0.0888902i
\(818\) −15.8059 27.3766i −0.552639 0.957200i
\(819\) 0.979055 0.356347i 0.0342110 0.0124518i
\(820\) −2.36959 + 4.10424i −0.0827495 + 0.143326i
\(821\) 7.52899 + 42.6990i 0.262764 + 1.49021i 0.775329 + 0.631558i \(0.217584\pi\)
−0.512565 + 0.858648i \(0.671305\pi\)
\(822\) −9.60700 + 5.54660i −0.335083 + 0.193460i
\(823\) 15.8953 5.78541i 0.554075 0.201667i −0.0497814 0.998760i \(-0.515852\pi\)
0.603856 + 0.797094i \(0.293630\pi\)
\(824\) −0.953363 + 0.346996i −0.0332120 + 0.0120882i
\(825\) −13.0869 7.55574i −0.455629 0.263057i
\(826\) 0.177519 + 1.00676i 0.00617666 + 0.0350296i
\(827\) 6.75150 11.6939i 0.234773 0.406638i −0.724434 0.689344i \(-0.757899\pi\)
0.959207 + 0.282706i \(0.0912321\pi\)
\(828\) −8.54189 + 14.7950i −0.296851 + 0.514161i
\(829\) 0.689540 + 1.19432i 0.0239487 + 0.0414804i 0.877751 0.479116i \(-0.159043\pi\)
−0.853803 + 0.520597i \(0.825709\pi\)
\(830\) −2.44562 + 2.05212i −0.0848888 + 0.0712302i
\(831\) 13.9449 + 38.3133i 0.483743 + 1.32907i
\(832\) 0.0603074 0.342020i 0.00209078 0.0118574i
\(833\) −2.61334 2.19285i −0.0905469 0.0759779i
\(834\) 37.3671 6.58883i 1.29392 0.228153i
\(835\) 1.30288 + 0.474210i 0.0450881 + 0.0164107i
\(836\) 4.21482 0.145773
\(837\) 13.5744 + 2.39354i 0.469201 + 0.0827329i
\(838\) 0.125667 0.00434110
\(839\) −13.3969 4.87608i −0.462513 0.168341i 0.100245 0.994963i \(-0.468037\pi\)
−0.562758 + 0.826622i \(0.690260\pi\)
\(840\) 0.979055 + 1.16679i 0.0337806 + 0.0402582i
\(841\) −19.4450 16.3163i −0.670517 0.562631i
\(842\) −5.13176 + 29.1037i −0.176852 + 1.00298i
\(843\) 38.6498 + 6.81500i 1.33117 + 0.234721i
\(844\) 14.1971 11.9128i 0.488685 0.410055i
\(845\) 5.66297 + 9.80855i 0.194812 + 0.337424i
\(846\) 7.54101 + 2.74470i 0.259265 + 0.0943649i
\(847\) 3.36959 5.83629i 0.115780 0.200537i
\(848\) 1.75237 + 9.93821i 0.0601768 + 0.341279i
\(849\) 15.5901i 0.535050i
\(850\) −13.5496 + 4.93166i −0.464748 + 0.169155i
\(851\) 2.42602 0.883000i 0.0831630 0.0302688i
\(852\) 9.94929i 0.340857i
\(853\) 1.74804 + 9.91361i 0.0598516 + 0.339435i 0.999999 0.00133235i \(-0.000424100\pi\)
−0.940147 + 0.340768i \(0.889313\pi\)
\(854\) 1.71301 2.96702i 0.0586180 0.101529i
\(855\) −5.06196 1.84240i −0.173115 0.0630088i
\(856\) −5.65657 9.79747i −0.193338 0.334871i
\(857\) −9.00000 + 7.55190i −0.307434 + 0.257968i −0.783431 0.621479i \(-0.786532\pi\)
0.475996 + 0.879447i \(0.342088\pi\)
\(858\) −1.22281 0.215615i −0.0417461 0.00736096i
\(859\) −9.08037 + 51.4974i −0.309818 + 1.75707i 0.290091 + 0.956999i \(0.406315\pi\)
−0.599909 + 0.800068i \(0.704797\pi\)
\(860\) −1.30406 1.09424i −0.0444682 0.0373132i
\(861\) 6.00000 + 7.15052i 0.204479 + 0.243689i
\(862\) 8.69759 + 3.16566i 0.296241 + 0.107823i
\(863\) 39.1881 1.33398 0.666989 0.745068i \(-0.267583\pi\)
0.666989 + 0.745068i \(0.267583\pi\)
\(864\) 1.77719 + 4.88279i 0.0604612 + 0.166116i
\(865\) 16.8821 0.574008
\(866\) 4.56670 + 1.66214i 0.155183 + 0.0564820i
\(867\) 9.14590 1.61267i 0.310611 0.0547691i
\(868\) −2.03209 1.70513i −0.0689736 0.0578757i
\(869\) 2.41740 13.7098i 0.0820048 0.465072i
\(870\) −0.990667 2.72183i −0.0335867 0.0922788i
\(871\) −2.85117 + 2.39241i −0.0966081 + 0.0810638i
\(872\) −6.37939 11.0494i −0.216033 0.374181i
\(873\) −10.7438 + 18.6087i −0.363621 + 0.629810i
\(874\) −5.81386 + 10.0699i −0.196657 + 0.340620i
\(875\) −1.40895 7.99054i −0.0476311 0.270130i
\(876\) 18.6288 + 10.7554i 0.629410 + 0.363390i
\(877\) −41.0587 + 14.9442i −1.38645 + 0.504628i −0.924128 0.382082i \(-0.875207\pi\)
−0.462326 + 0.886710i \(0.652985\pi\)
\(878\) 27.9599 10.1766i 0.943602 0.343443i
\(879\) 13.6885 7.90306i 0.461702 0.266564i
\(880\) −0.315207 1.78763i −0.0106256 0.0602610i
\(881\) −11.2267 + 19.4452i −0.378237 + 0.655125i −0.990806 0.135292i \(-0.956803\pi\)
0.612569 + 0.790417i \(0.290136\pi\)
\(882\) 2.81908 1.02606i 0.0949233 0.0345493i
\(883\) 24.9317 + 43.1830i 0.839019 + 1.45322i 0.890716 + 0.454560i \(0.150204\pi\)
−0.0516975 + 0.998663i \(0.516463\pi\)
\(884\) −0.907604 + 0.761570i −0.0305260 + 0.0256144i
\(885\) −1.00088 + 1.19280i −0.0336441 + 0.0400955i
\(886\) −3.69547 + 20.9581i −0.124152 + 0.704100i
\(887\) −14.5032 12.1697i −0.486971 0.408617i 0.365968 0.930627i \(-0.380738\pi\)
−0.852939 + 0.522010i \(0.825182\pi\)
\(888\) 0.268571 0.737892i 0.00901264 0.0247620i
\(889\) 11.5424 + 4.20107i 0.387118 + 0.140899i
\(890\) −16.5030 −0.553182
\(891\) 17.4572 6.35391i 0.584839 0.212864i
\(892\) −10.5107 −0.351925
\(893\) 5.13264 + 1.86813i 0.171757 + 0.0625145i
\(894\) 13.0829 35.9450i 0.437558 1.20218i
\(895\) −10.8268 9.08478i −0.361901 0.303671i
\(896\) 0.173648 0.984808i 0.00580118 0.0329001i
\(897\) 2.20187 2.62408i 0.0735182 0.0876156i
\(898\) −9.02663 + 7.57424i −0.301222 + 0.252756i
\(899\) 2.52229 + 4.36873i 0.0841230 + 0.145705i
\(900\) 2.20187 12.4874i 0.0733956 0.416247i
\(901\) 17.2135 29.8146i 0.573464 0.993269i
\(902\) −1.93170 10.9552i −0.0643187 0.364769i
\(903\) −2.90373 + 1.67647i −0.0966302 + 0.0557895i
\(904\) 17.0954 6.22221i 0.568584 0.206948i
\(905\) −18.4491 + 6.71492i −0.613268 + 0.223211i
\(906\) 26.9822 + 15.5782i 0.896424 + 0.517551i
\(907\) −8.01290 45.4434i −0.266064 1.50892i −0.765988 0.642855i \(-0.777750\pi\)
0.499924 0.866069i \(-0.333361\pi\)
\(908\) 6.40167 11.0880i 0.212447 0.367969i
\(909\) 7.48576 0.248287
\(910\) −0.152704 0.264490i −0.00506208 0.00876777i
\(911\) −33.6098 + 28.2019i −1.11354 + 0.934372i −0.998260 0.0589606i \(-0.981221\pi\)
−0.115281 + 0.993333i \(0.536777\pi\)
\(912\) 1.20961 + 3.32337i 0.0400541 + 0.110048i
\(913\) 1.30129 7.37997i 0.0430664 0.244241i
\(914\) −29.4386 24.7019i −0.973741 0.817066i
\(915\) 5.13903 0.906150i 0.169891 0.0299564i
\(916\) −9.75624 3.55098i −0.322355 0.117328i
\(917\) 2.22668 0.0735315
\(918\) 6.06283 16.6575i 0.200103 0.549779i
\(919\) −4.09327 −0.135025 −0.0675123 0.997718i \(-0.521506\pi\)
−0.0675123 + 0.997718i \(0.521506\pi\)
\(920\) 4.70574 + 1.71275i 0.155144 + 0.0564676i
\(921\) 12.6857 + 15.1182i 0.418007 + 0.498161i
\(922\) −18.8097 15.7832i −0.619466 0.519794i
\(923\) −0.346419 + 1.96464i −0.0114025 + 0.0646669i
\(924\) −3.52094 0.620838i −0.115831 0.0204241i
\(925\) −1.46791 + 1.23172i −0.0482646 + 0.0404988i
\(926\) 3.41993 + 5.92349i 0.112386 + 0.194658i
\(927\) −2.33157 + 1.95642i −0.0765787 + 0.0642571i
\(928\) −0.950837 + 1.64690i −0.0312128 + 0.0540621i
\(929\) 9.88057 + 56.0355i 0.324171 + 1.83846i 0.515438 + 0.856927i \(0.327629\pi\)
−0.191268 + 0.981538i \(0.561260\pi\)
\(930\) 4.04044i 0.132491i
\(931\) 1.91875 0.698367i 0.0628844 0.0228881i
\(932\) 3.76130 1.36900i 0.123205 0.0448431i
\(933\) 3.94269i 0.129078i
\(934\) 0.340022 + 1.92836i 0.0111259 + 0.0630980i
\(935\) −3.09627 + 5.36289i −0.101259 + 0.175385i
\(936\) −0.180922 1.02606i −0.00591363 0.0335378i
\(937\) −13.4363 23.2723i −0.438944 0.760274i 0.558664 0.829394i \(-0.311314\pi\)
−0.997608 + 0.0691201i \(0.977981\pi\)
\(938\) −8.20961 + 6.88868i −0.268053 + 0.224923i
\(939\) −2.49226 0.439453i −0.0813318 0.0143410i
\(940\) 0.408481 2.31661i 0.0133232 0.0755595i
\(941\) 28.3601 + 23.7969i 0.924512 + 0.775758i 0.974824 0.222975i \(-0.0715770\pi\)
−0.0503116 + 0.998734i \(0.516021\pi\)
\(942\) 21.8346 + 26.0214i 0.711408 + 0.847824i
\(943\) 28.8384 + 10.4963i 0.939108 + 0.341808i
\(944\) 1.02229 0.0332727
\(945\) 3.95723 + 2.28471i 0.128729 + 0.0743216i
\(946\) 3.99588 0.129917
\(947\) 56.0189 + 20.3892i 1.82037 + 0.662561i 0.995221 + 0.0976470i \(0.0311316\pi\)
0.825150 + 0.564914i \(0.191091\pi\)
\(948\) 11.5039 2.02844i 0.373628 0.0658808i
\(949\) −3.30406 2.77244i −0.107254 0.0899972i
\(950\) 1.49866 8.49930i 0.0486228 0.275754i
\(951\) 0.247788 + 0.680793i 0.00803508 + 0.0220762i
\(952\) −2.61334 + 2.19285i −0.0846989 + 0.0710708i
\(953\) −19.9017 34.4707i −0.644678 1.11662i −0.984376 0.176081i \(-0.943658\pi\)
0.339697 0.940535i \(-0.389675\pi\)
\(954\) 15.1373 + 26.2185i 0.490087 + 0.848856i
\(955\) −6.23055 + 10.7916i −0.201616 + 0.349209i
\(956\) 3.70708 + 21.0239i 0.119896 + 0.679962i
\(957\) 5.88809 + 3.39949i 0.190335 + 0.109890i
\(958\) 15.4731 5.63176i 0.499914 0.181954i
\(959\) 6.01842 2.19053i 0.194345 0.0707357i
\(960\) 1.31908 0.761570i 0.0425731 0.0245796i
\(961\) −4.16116 23.5991i −0.134231 0.761262i
\(962\) −0.0787257 + 0.136357i −0.00253822 + 0.00439632i
\(963\) −25.9991 21.8159i −0.837810 0.703006i
\(964\) 2.84477 + 4.92729i 0.0916239 + 0.158697i
\(965\) 6.53596 5.48432i 0.210400 0.176547i
\(966\) 6.34002 7.55574i 0.203987 0.243102i
\(967\) 7.00016 39.6999i 0.225110 1.27666i −0.637365 0.770562i \(-0.719975\pi\)
0.862475 0.506100i \(-0.168913\pi\)
\(968\) −5.16250 4.33186i −0.165929 0.139231i
\(969\) 4.12654 11.3376i 0.132564 0.364216i
\(970\) 5.91875 + 2.15425i 0.190040 + 0.0691687i
\(971\) −20.1739 −0.647410 −0.323705 0.946158i \(-0.604929\pi\)
−0.323705 + 0.946158i \(0.604929\pi\)
\(972\) 10.0201 + 11.9415i 0.321394 + 0.383022i
\(973\) −21.9067 −0.702297
\(974\) 7.08260 + 2.57785i 0.226941 + 0.0825998i
\(975\) −0.869585 + 2.38917i −0.0278490 + 0.0765145i
\(976\) −2.62449 2.20220i −0.0840077 0.0704908i
\(977\) −0.678234 + 3.84645i −0.0216986 + 0.123059i −0.993733 0.111779i \(-0.964345\pi\)
0.972034 + 0.234838i \(0.0754561\pi\)
\(978\) −9.98205 + 11.8961i −0.319191 + 0.380397i
\(979\) 29.6746 24.8999i 0.948404 0.795805i
\(980\) −0.439693 0.761570i −0.0140455 0.0243275i
\(981\) −29.3214 24.6035i −0.936159 0.785531i
\(982\) −2.98499 + 5.17015i −0.0952547 + 0.164986i
\(983\) −5.38877 30.5613i −0.171875 0.974753i −0.941689 0.336484i \(-0.890762\pi\)
0.769814 0.638268i \(-0.220349\pi\)
\(984\) 8.08378 4.66717i 0.257701 0.148784i
\(985\) 4.89528 1.78174i 0.155977 0.0567708i
\(986\) 6.09627 2.21886i 0.194145 0.0706629i
\(987\) −4.01249 2.31661i −0.127719 0.0737386i
\(988\) −0.123141 0.698367i −0.00391764 0.0222180i
\(989\) −5.51186 + 9.54682i −0.175267 + 0.303571i
\(990\) −2.72281 4.71605i −0.0865366 0.149886i
\(991\) −12.4561 21.5745i −0.395680 0.685337i 0.597508 0.801863i \(-0.296158\pi\)
−0.993188 + 0.116526i \(0.962824\pi\)
\(992\) −2.03209 + 1.70513i −0.0645189 + 0.0541378i
\(993\) −6.76011 18.5733i −0.214526 0.589405i
\(994\) −0.997474 + 5.65695i −0.0316379 + 0.179428i
\(995\) 12.4397 + 10.4381i 0.394365 + 0.330911i
\(996\) 6.19253 1.09191i 0.196218 0.0345985i
\(997\) −48.5283 17.6628i −1.53691 0.559388i −0.571605 0.820529i \(-0.693679\pi\)
−0.965301 + 0.261141i \(0.915901\pi\)
\(998\) 38.2158 1.20970
\(999\) 2.35574i 0.0745324i
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 378.2.u.a.85.1 6
27.7 even 9 inner 378.2.u.a.169.1 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.u.a.85.1 6 1.1 even 1 trivial
378.2.u.a.169.1 yes 6 27.7 even 9 inner