Properties

Label 85.2.l.a.36.2
Level $85$
Weight $2$
Character 85.36
Analytic conductor $0.679$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [85,2,Mod(26,85)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(85, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("85.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 85 = 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 85.l (of order \(8\), degree \(4\), 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: \(0.678728417181\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 36.2
Character \(\chi\) \(=\) 85.36
Dual form 85.2.l.a.26.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.27691 - 1.27691i) q^{2} +(0.635552 - 0.263254i) q^{3} +1.26102i q^{4} +(-0.382683 - 0.923880i) q^{5} +(-1.14770 - 0.475393i) q^{6} +(1.66158 - 4.01142i) q^{7} +(-0.943613 + 0.943613i) q^{8} +(-1.78670 + 1.78670i) q^{9} +(-0.691061 + 1.66837i) q^{10} +(0.0485041 + 0.0200910i) q^{11} +(0.331970 + 0.801445i) q^{12} -3.02508i q^{13} +(-7.24394 + 3.00054i) q^{14} +(-0.486431 - 0.486431i) q^{15} +4.93187 q^{16} +(3.12202 + 2.69314i) q^{17} +4.56292 q^{18} +(5.52988 + 5.52988i) q^{19} +(1.16503 - 0.482572i) q^{20} -2.98689i q^{21} +(-0.0362810 - 0.0875901i) q^{22} +(0.962654 + 0.398744i) q^{23} +(-0.351305 + 0.848125i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(-3.86277 + 3.86277i) q^{26} +(-1.45495 + 3.51255i) q^{27} +(5.05848 + 2.09529i) q^{28} +(-0.161016 - 0.388726i) q^{29} +1.24226i q^{30} +(-1.27892 + 0.529745i) q^{31} +(-4.41035 - 4.41035i) q^{32} +0.0361159 q^{33} +(-0.547638 - 7.42546i) q^{34} -4.34193 q^{35} +(-2.25306 - 2.25306i) q^{36} +(0.311301 - 0.128945i) q^{37} -14.1224i q^{38} +(-0.796365 - 1.92260i) q^{39} +(1.23289 + 0.510679i) q^{40} +(2.52291 - 6.09084i) q^{41} +(-3.81400 + 3.81400i) q^{42} +(-7.06729 + 7.06729i) q^{43} +(-0.0253352 + 0.0611647i) q^{44} +(2.33443 + 0.966953i) q^{45} +(-0.720064 - 1.73839i) q^{46} +6.13168i q^{47} +(3.13446 - 1.29834i) q^{48} +(-8.38087 - 8.38087i) q^{49} +1.80583 q^{50} +(2.69319 + 0.889748i) q^{51} +3.81469 q^{52} +(-8.52974 - 8.52974i) q^{53} +(6.34307 - 2.62739i) q^{54} -0.0525004i q^{55} +(2.21733 + 5.35312i) q^{56} +(4.97030 + 2.05876i) q^{57} +(-0.290767 + 0.701974i) q^{58} +(3.60468 - 3.60468i) q^{59} +(0.613400 - 0.613400i) q^{60} +(-2.28486 + 5.51614i) q^{61} +(2.30951 + 0.956630i) q^{62} +(4.19844 + 10.1359i) q^{63} +1.39954i q^{64} +(-2.79481 + 1.15765i) q^{65} +(-0.0461170 - 0.0461170i) q^{66} +0.916040 q^{67} +(-3.39611 + 3.93693i) q^{68} +0.716788 q^{69} +(5.54427 + 5.54427i) q^{70} +(3.86169 - 1.59956i) q^{71} -3.37190i q^{72} +(2.06289 + 4.98025i) q^{73} +(-0.562156 - 0.232853i) q^{74} +(-0.263254 + 0.635552i) q^{75} +(-6.97330 + 6.97330i) q^{76} +(0.161187 - 0.161187i) q^{77} +(-1.43810 + 3.47188i) q^{78} +(9.22305 + 3.82031i) q^{79} +(-1.88734 - 4.55645i) q^{80} -4.96488i q^{81} +(-10.9990 + 4.55595i) q^{82} +(-4.61746 - 4.61746i) q^{83} +3.76653 q^{84} +(1.29339 - 3.91499i) q^{85} +18.0487 q^{86} +(-0.204668 - 0.204668i) q^{87} +(-0.0647272 + 0.0268109i) q^{88} +10.2159i q^{89} +(-1.74615 - 4.21559i) q^{90} +(-12.1349 - 5.02642i) q^{91} +(-0.502825 + 1.21393i) q^{92} +(-0.673362 + 0.673362i) q^{93} +(7.82963 - 7.82963i) q^{94} +(2.99275 - 7.22514i) q^{95} +(-3.96405 - 1.64196i) q^{96} +(-7.35663 - 17.7605i) q^{97} +21.4033i q^{98} +(-0.122559 + 0.0507655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/85\mathbb{Z}\right)^\times\).

\(n\) \(52\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.27691 1.27691i −0.902915 0.902915i 0.0927724 0.995687i \(-0.470427\pi\)
−0.995687 + 0.0927724i \(0.970427\pi\)
\(3\) 0.635552 0.263254i 0.366936 0.151990i −0.191594 0.981474i \(-0.561366\pi\)
0.558530 + 0.829484i \(0.311366\pi\)
\(4\) 1.26102i 0.630511i
\(5\) −0.382683 0.923880i −0.171141 0.413171i
\(6\) −1.14770 0.475393i −0.468546 0.194078i
\(7\) 1.66158 4.01142i 0.628020 1.51617i −0.214060 0.976821i \(-0.568669\pi\)
0.842080 0.539353i \(-0.181331\pi\)
\(8\) −0.943613 + 0.943613i −0.333617 + 0.333617i
\(9\) −1.78670 + 1.78670i −0.595565 + 0.595565i
\(10\) −0.691061 + 1.66837i −0.218533 + 0.527585i
\(11\) 0.0485041 + 0.0200910i 0.0146245 + 0.00605768i 0.389984 0.920822i \(-0.372481\pi\)
−0.375359 + 0.926879i \(0.622481\pi\)
\(12\) 0.331970 + 0.801445i 0.0958313 + 0.231357i
\(13\) 3.02508i 0.839006i −0.907754 0.419503i \(-0.862204\pi\)
0.907754 0.419503i \(-0.137796\pi\)
\(14\) −7.24394 + 3.00054i −1.93602 + 0.801928i
\(15\) −0.486431 0.486431i −0.125596 0.125596i
\(16\) 4.93187 1.23297
\(17\) 3.12202 + 2.69314i 0.757200 + 0.653183i
\(18\) 4.56292 1.07549
\(19\) 5.52988 + 5.52988i 1.26864 + 1.26864i 0.946790 + 0.321851i \(0.104305\pi\)
0.321851 + 0.946790i \(0.395695\pi\)
\(20\) 1.16503 0.482572i 0.260509 0.107906i
\(21\) 2.98689i 0.651792i
\(22\) −0.0362810 0.0875901i −0.00773514 0.0186743i
\(23\) 0.962654 + 0.398744i 0.200727 + 0.0831439i 0.480782 0.876840i \(-0.340353\pi\)
−0.280055 + 0.959984i \(0.590353\pi\)
\(24\) −0.351305 + 0.848125i −0.0717098 + 0.173123i
\(25\) −0.707107 + 0.707107i −0.141421 + 0.141421i
\(26\) −3.86277 + 3.86277i −0.757551 + 0.757551i
\(27\) −1.45495 + 3.51255i −0.280005 + 0.675991i
\(28\) 5.05848 + 2.09529i 0.955964 + 0.395973i
\(29\) −0.161016 0.388726i −0.0298999 0.0721847i 0.908224 0.418484i \(-0.137438\pi\)
−0.938124 + 0.346299i \(0.887438\pi\)
\(30\) 1.24226i 0.226805i
\(31\) −1.27892 + 0.529745i −0.229701 + 0.0951451i −0.494565 0.869141i \(-0.664673\pi\)
0.264865 + 0.964286i \(0.414673\pi\)
\(32\) −4.41035 4.41035i −0.779647 0.779647i
\(33\) 0.0361159 0.00628698
\(34\) −0.547638 7.42546i −0.0939192 1.27346i
\(35\) −4.34193 −0.733920
\(36\) −2.25306 2.25306i −0.375510 0.375510i
\(37\) 0.311301 0.128945i 0.0511775 0.0211984i −0.356948 0.934124i \(-0.616183\pi\)
0.408125 + 0.912926i \(0.366183\pi\)
\(38\) 14.1224i 2.29095i
\(39\) −0.796365 1.92260i −0.127520 0.307862i
\(40\) 1.23289 + 0.510679i 0.194937 + 0.0807455i
\(41\) 2.52291 6.09084i 0.394012 0.951230i −0.595044 0.803693i \(-0.702865\pi\)
0.989057 0.147537i \(-0.0471345\pi\)
\(42\) −3.81400 + 3.81400i −0.588513 + 0.588513i
\(43\) −7.06729 + 7.06729i −1.07775 + 1.07775i −0.0810414 + 0.996711i \(0.525825\pi\)
−0.996711 + 0.0810414i \(0.974175\pi\)
\(44\) −0.0253352 + 0.0611647i −0.00381943 + 0.00922092i
\(45\) 2.33443 + 0.966953i 0.347996 + 0.144145i
\(46\) −0.720064 1.73839i −0.106168 0.256311i
\(47\) 6.13168i 0.894398i 0.894435 + 0.447199i \(0.147578\pi\)
−0.894435 + 0.447199i \(0.852422\pi\)
\(48\) 3.13446 1.29834i 0.452420 0.187399i
\(49\) −8.38087 8.38087i −1.19727 1.19727i
\(50\) 1.80583 0.255383
\(51\) 2.69319 + 0.889748i 0.377122 + 0.124590i
\(52\) 3.81469 0.529002
\(53\) −8.52974 8.52974i −1.17165 1.17165i −0.981816 0.189834i \(-0.939205\pi\)
−0.189834 0.981816i \(-0.560795\pi\)
\(54\) 6.34307 2.62739i 0.863183 0.357542i
\(55\) 0.0525004i 0.00707916i
\(56\) 2.21733 + 5.35312i 0.296304 + 0.715340i
\(57\) 4.97030 + 2.05876i 0.658332 + 0.272690i
\(58\) −0.290767 + 0.701974i −0.0381796 + 0.0921737i
\(59\) 3.60468 3.60468i 0.469290 0.469290i −0.432395 0.901684i \(-0.642331\pi\)
0.901684 + 0.432395i \(0.142331\pi\)
\(60\) 0.613400 0.613400i 0.0791896 0.0791896i
\(61\) −2.28486 + 5.51614i −0.292547 + 0.706270i −1.00000 0.000490243i \(-0.999844\pi\)
0.707453 + 0.706760i \(0.249844\pi\)
\(62\) 2.30951 + 0.956630i 0.293308 + 0.121492i
\(63\) 4.19844 + 10.1359i 0.528954 + 1.27701i
\(64\) 1.39954i 0.174943i
\(65\) −2.79481 + 1.15765i −0.346653 + 0.143588i
\(66\) −0.0461170 0.0461170i −0.00567661 0.00567661i
\(67\) 0.916040 0.111912 0.0559561 0.998433i \(-0.482179\pi\)
0.0559561 + 0.998433i \(0.482179\pi\)
\(68\) −3.39611 + 3.93693i −0.411839 + 0.477423i
\(69\) 0.716788 0.0862912
\(70\) 5.54427 + 5.54427i 0.662667 + 0.662667i
\(71\) 3.86169 1.59956i 0.458298 0.189833i −0.141577 0.989927i \(-0.545217\pi\)
0.599875 + 0.800094i \(0.295217\pi\)
\(72\) 3.37190i 0.397382i
\(73\) 2.06289 + 4.98025i 0.241443 + 0.582895i 0.997427 0.0716959i \(-0.0228411\pi\)
−0.755984 + 0.654590i \(0.772841\pi\)
\(74\) −0.562156 0.232853i −0.0653493 0.0270686i
\(75\) −0.263254 + 0.635552i −0.0303980 + 0.0733873i
\(76\) −6.97330 + 6.97330i −0.799892 + 0.799892i
\(77\) 0.161187 0.161187i 0.0183690 0.0183690i
\(78\) −1.43810 + 3.47188i −0.162833 + 0.393113i
\(79\) 9.22305 + 3.82031i 1.03767 + 0.429819i 0.835477 0.549526i \(-0.185192\pi\)
0.202198 + 0.979345i \(0.435192\pi\)
\(80\) −1.88734 4.55645i −0.211011 0.509427i
\(81\) 4.96488i 0.551653i
\(82\) −10.9990 + 4.55595i −1.21464 + 0.503120i
\(83\) −4.61746 4.61746i −0.506833 0.506833i 0.406720 0.913553i \(-0.366672\pi\)
−0.913553 + 0.406720i \(0.866672\pi\)
\(84\) 3.76653 0.410962
\(85\) 1.29339 3.91499i 0.140288 0.424640i
\(86\) 18.0487 1.94624
\(87\) −0.204668 0.204668i −0.0219427 0.0219427i
\(88\) −0.0647272 + 0.0268109i −0.00689994 + 0.00285805i
\(89\) 10.2159i 1.08289i 0.840738 + 0.541443i \(0.182122\pi\)
−0.840738 + 0.541443i \(0.817878\pi\)
\(90\) −1.74615 4.21559i −0.184061 0.444362i
\(91\) −12.1349 5.02642i −1.27208 0.526912i
\(92\) −0.502825 + 1.21393i −0.0524231 + 0.126561i
\(93\) −0.673362 + 0.673362i −0.0698244 + 0.0698244i
\(94\) 7.82963 7.82963i 0.807565 0.807565i
\(95\) 2.99275 7.22514i 0.307050 0.741283i
\(96\) −3.96405 1.64196i −0.404579 0.167582i
\(97\) −7.35663 17.7605i −0.746952 1.80330i −0.574916 0.818212i \(-0.694965\pi\)
−0.172036 0.985091i \(-0.555035\pi\)
\(98\) 21.4033i 2.16206i
\(99\) −0.122559 + 0.0507655i −0.0123176 + 0.00510212i
\(100\) −0.891677 0.891677i −0.0891677 0.0891677i
\(101\) −13.2926 −1.32266 −0.661331 0.750094i \(-0.730008\pi\)
−0.661331 + 0.750094i \(0.730008\pi\)
\(102\) −2.30284 4.57510i −0.228015 0.453003i
\(103\) −6.91299 −0.681157 −0.340579 0.940216i \(-0.610623\pi\)
−0.340579 + 0.940216i \(0.610623\pi\)
\(104\) 2.85450 + 2.85450i 0.279907 + 0.279907i
\(105\) −2.75952 + 1.14303i −0.269302 + 0.111549i
\(106\) 21.7835i 2.11580i
\(107\) 5.64104 + 13.6187i 0.545339 + 1.31657i 0.920911 + 0.389773i \(0.127446\pi\)
−0.375572 + 0.926793i \(0.622554\pi\)
\(108\) −4.42940 1.83472i −0.426220 0.176546i
\(109\) −1.81709 + 4.38684i −0.174046 + 0.420183i −0.986698 0.162566i \(-0.948023\pi\)
0.812652 + 0.582749i \(0.198023\pi\)
\(110\) −0.0670386 + 0.0670386i −0.00639188 + 0.00639188i
\(111\) 0.163903 0.163903i 0.0155569 0.0155569i
\(112\) 8.19471 19.7838i 0.774328 1.86939i
\(113\) 2.78393 + 1.15314i 0.261890 + 0.108478i 0.509765 0.860314i \(-0.329732\pi\)
−0.247875 + 0.968792i \(0.579732\pi\)
\(114\) −3.71778 8.97551i −0.348202 0.840633i
\(115\) 1.04197i 0.0971641i
\(116\) 0.490192 0.203044i 0.0455132 0.0188522i
\(117\) 5.40490 + 5.40490i 0.499683 + 0.499683i
\(118\) −9.20574 −0.847457
\(119\) 15.9908 8.04884i 1.46588 0.737836i
\(120\) 0.918004 0.0838020
\(121\) −7.77623 7.77623i −0.706930 0.706930i
\(122\) 9.96122 4.12607i 0.901846 0.373557i
\(123\) 4.53522i 0.408927i
\(124\) −0.668020 1.61274i −0.0599900 0.144829i
\(125\) 0.923880 + 0.382683i 0.0826343 + 0.0342282i
\(126\) 7.58167 18.3038i 0.675429 1.63063i
\(127\) 0.00585984 0.00585984i 0.000519977 0.000519977i −0.706847 0.707367i \(-0.749883\pi\)
0.707367 + 0.706847i \(0.249883\pi\)
\(128\) −7.03360 + 7.03360i −0.621689 + 0.621689i
\(129\) −2.63114 + 6.35213i −0.231659 + 0.559274i
\(130\) 5.04695 + 2.09051i 0.442647 + 0.183350i
\(131\) 3.13210 + 7.56157i 0.273653 + 0.660657i 0.999634 0.0270577i \(-0.00861380\pi\)
−0.725981 + 0.687715i \(0.758614\pi\)
\(132\) 0.0455430i 0.00396401i
\(133\) 31.3710 12.9943i 2.72021 1.12675i
\(134\) −1.16971 1.16971i −0.101047 0.101047i
\(135\) 3.80196 0.327221
\(136\) −5.48726 + 0.404693i −0.470528 + 0.0347021i
\(137\) −2.23387 −0.190852 −0.0954260 0.995437i \(-0.530421\pi\)
−0.0954260 + 0.995437i \(0.530421\pi\)
\(138\) −0.915277 0.915277i −0.0779136 0.0779136i
\(139\) −18.2335 + 7.55257i −1.54655 + 0.640601i −0.982688 0.185270i \(-0.940684\pi\)
−0.563859 + 0.825871i \(0.690684\pi\)
\(140\) 5.47526i 0.462744i
\(141\) 1.61419 + 3.89701i 0.135940 + 0.328187i
\(142\) −6.97355 2.88854i −0.585207 0.242401i
\(143\) 0.0607770 0.146729i 0.00508243 0.0122701i
\(144\) −8.81175 + 8.81175i −0.734313 + 0.734313i
\(145\) −0.297518 + 0.297518i −0.0247076 + 0.0247076i
\(146\) 3.72523 8.99349i 0.308302 0.744306i
\(147\) −7.53279 3.12018i −0.621294 0.257348i
\(148\) 0.162602 + 0.392557i 0.0133658 + 0.0322680i
\(149\) 10.1835i 0.834263i −0.908846 0.417132i \(-0.863035\pi\)
0.908846 0.417132i \(-0.136965\pi\)
\(150\) 1.14770 0.475393i 0.0937093 0.0388157i
\(151\) 10.8529 + 10.8529i 0.883200 + 0.883200i 0.993858 0.110659i \(-0.0352961\pi\)
−0.110659 + 0.993858i \(0.535296\pi\)
\(152\) −10.4361 −0.846482
\(153\) −10.3899 + 0.766271i −0.839975 + 0.0619494i
\(154\) −0.411645 −0.0331713
\(155\) 0.978842 + 0.978842i 0.0786225 + 0.0786225i
\(156\) 2.42443 1.00423i 0.194110 0.0804030i
\(157\) 9.41222i 0.751177i 0.926787 + 0.375588i \(0.122559\pi\)
−0.926787 + 0.375588i \(0.877441\pi\)
\(158\) −6.89884 16.6553i −0.548842 1.32502i
\(159\) −7.66659 3.17561i −0.608000 0.251842i
\(160\) −2.38686 + 5.76240i −0.188698 + 0.455558i
\(161\) 3.19906 3.19906i 0.252121 0.252121i
\(162\) −6.33972 + 6.33972i −0.498096 + 0.498096i
\(163\) −4.76262 + 11.4980i −0.373037 + 0.900592i 0.620195 + 0.784448i \(0.287053\pi\)
−0.993232 + 0.116144i \(0.962947\pi\)
\(164\) 7.68068 + 3.18144i 0.599761 + 0.248429i
\(165\) −0.0138210 0.0333668i −0.00107596 0.00259760i
\(166\) 11.7922i 0.915253i
\(167\) 11.6432 4.82277i 0.900977 0.373197i 0.116382 0.993205i \(-0.462870\pi\)
0.784596 + 0.620008i \(0.212870\pi\)
\(168\) 2.81846 + 2.81846i 0.217449 + 0.217449i
\(169\) 3.84890 0.296069
\(170\) −6.65066 + 3.34755i −0.510082 + 0.256746i
\(171\) −19.7604 −1.51112
\(172\) −8.91201 8.91201i −0.679534 0.679534i
\(173\) 11.2681 4.66741i 0.856699 0.354856i 0.0892832 0.996006i \(-0.471542\pi\)
0.767416 + 0.641150i \(0.221542\pi\)
\(174\) 0.522687i 0.0396248i
\(175\) 1.66158 + 4.01142i 0.125604 + 0.303235i
\(176\) 0.239216 + 0.0990864i 0.0180316 + 0.00746892i
\(177\) 1.34202 3.23991i 0.100872 0.243527i
\(178\) 13.0449 13.0449i 0.977754 0.977754i
\(179\) 9.80106 9.80106i 0.732566 0.732566i −0.238562 0.971127i \(-0.576676\pi\)
0.971127 + 0.238562i \(0.0766759\pi\)
\(180\) −1.21935 + 2.94377i −0.0908849 + 0.219415i
\(181\) 1.88863 + 0.782297i 0.140381 + 0.0581476i 0.451768 0.892136i \(-0.350794\pi\)
−0.311387 + 0.950283i \(0.600794\pi\)
\(182\) 9.07686 + 21.9135i 0.672822 + 1.62434i
\(183\) 4.10730i 0.303620i
\(184\) −1.28463 + 0.532112i −0.0947043 + 0.0392278i
\(185\) −0.238259 0.238259i −0.0175172 0.0175172i
\(186\) 1.71965 0.126091
\(187\) 0.0973225 + 0.193353i 0.00711693 + 0.0141394i
\(188\) −7.73218 −0.563927
\(189\) 11.6728 + 11.6728i 0.849071 + 0.849071i
\(190\) −13.0474 + 5.40440i −0.946556 + 0.392076i
\(191\) 3.08056i 0.222902i −0.993770 0.111451i \(-0.964450\pi\)
0.993770 0.111451i \(-0.0355498\pi\)
\(192\) 0.368435 + 0.889482i 0.0265895 + 0.0641928i
\(193\) 19.0706 + 7.89931i 1.37273 + 0.568605i 0.942528 0.334126i \(-0.108441\pi\)
0.430205 + 0.902731i \(0.358441\pi\)
\(194\) −13.2848 + 32.0724i −0.953794 + 2.30266i
\(195\) −1.47149 + 1.47149i −0.105376 + 0.105376i
\(196\) 10.5685 10.5685i 0.754890 0.754890i
\(197\) −6.97881 + 16.8483i −0.497219 + 1.20039i 0.453756 + 0.891126i \(0.350084\pi\)
−0.950975 + 0.309268i \(0.899916\pi\)
\(198\) 0.221320 + 0.0916738i 0.0157285 + 0.00651497i
\(199\) −10.2053 24.6377i −0.723432 1.74652i −0.663328 0.748328i \(-0.730857\pi\)
−0.0601040 0.998192i \(-0.519143\pi\)
\(200\) 1.33447i 0.0943613i
\(201\) 0.582192 0.241152i 0.0410646 0.0170095i
\(202\) 16.9735 + 16.9735i 1.19425 + 1.19425i
\(203\) −1.82689 −0.128222
\(204\) −1.12199 + 3.39617i −0.0785551 + 0.237779i
\(205\) −6.59268 −0.460453
\(206\) 8.82730 + 8.82730i 0.615027 + 0.615027i
\(207\) −2.43240 + 1.00754i −0.169064 + 0.0700285i
\(208\) 14.9193i 1.03447i
\(209\) 0.157121 + 0.379323i 0.0108683 + 0.0262383i
\(210\) 4.98323 + 2.06412i 0.343876 + 0.142438i
\(211\) 2.98710 7.21149i 0.205640 0.496460i −0.787087 0.616842i \(-0.788412\pi\)
0.992728 + 0.120382i \(0.0384119\pi\)
\(212\) 10.7562 10.7562i 0.738738 0.738738i
\(213\) 2.03321 2.03321i 0.139313 0.139313i
\(214\) 10.1868 24.5930i 0.696352 1.68114i
\(215\) 9.23386 + 3.82479i 0.629744 + 0.260849i
\(216\) −1.94158 4.68739i −0.132108 0.318937i
\(217\) 6.01049i 0.408019i
\(218\) 7.92189 3.28135i 0.536538 0.222241i
\(219\) 2.62215 + 2.62215i 0.177188 + 0.177188i
\(220\) 0.0662042 0.00446348
\(221\) 8.14696 9.44435i 0.548024 0.635295i
\(222\) −0.418579 −0.0280932
\(223\) 3.37213 + 3.37213i 0.225815 + 0.225815i 0.810942 0.585127i \(-0.198955\pi\)
−0.585127 + 0.810942i \(0.698955\pi\)
\(224\) −25.0199 + 10.3636i −1.67171 + 0.692447i
\(225\) 2.52677i 0.168451i
\(226\) −2.08238 5.02731i −0.138518 0.334411i
\(227\) −10.3577 4.29029i −0.687464 0.284757i 0.0114793 0.999934i \(-0.496346\pi\)
−0.698943 + 0.715177i \(0.746346\pi\)
\(228\) −2.59614 + 6.26765i −0.171934 + 0.415085i
\(229\) −14.6007 + 14.6007i −0.964838 + 0.964838i −0.999402 0.0345640i \(-0.988996\pi\)
0.0345640 + 0.999402i \(0.488996\pi\)
\(230\) −1.33051 + 1.33051i −0.0877309 + 0.0877309i
\(231\) 0.0600097 0.144876i 0.00394835 0.00953215i
\(232\) 0.518744 + 0.214871i 0.0340572 + 0.0141069i
\(233\) −1.17044 2.82569i −0.0766781 0.185117i 0.880892 0.473317i \(-0.156943\pi\)
−0.957570 + 0.288199i \(0.906943\pi\)
\(234\) 13.8032i 0.902342i
\(235\) 5.66494 2.34649i 0.369540 0.153068i
\(236\) 4.54558 + 4.54558i 0.295892 + 0.295892i
\(237\) 6.86745 0.446089
\(238\) −30.6966 10.1412i −1.98976 0.657358i
\(239\) 4.94072 0.319588 0.159794 0.987150i \(-0.448917\pi\)
0.159794 + 0.987150i \(0.448917\pi\)
\(240\) −2.39901 2.39901i −0.154856 0.154856i
\(241\) 1.53527 0.635928i 0.0988952 0.0409637i −0.332687 0.943037i \(-0.607955\pi\)
0.431583 + 0.902073i \(0.357955\pi\)
\(242\) 19.8592i 1.27659i
\(243\) −5.67187 13.6931i −0.363850 0.878413i
\(244\) −6.95597 2.88126i −0.445311 0.184454i
\(245\) −4.53570 + 10.9501i −0.289775 + 0.699579i
\(246\) −5.79109 + 5.79109i −0.369226 + 0.369226i
\(247\) 16.7283 16.7283i 1.06440 1.06440i
\(248\) 0.706929 1.70668i 0.0448900 0.108374i
\(249\) −4.15021 1.71907i −0.263009 0.108942i
\(250\) −0.691061 1.66837i −0.0437065 0.105517i
\(251\) 9.14240i 0.577063i −0.957470 0.288531i \(-0.906833\pi\)
0.957470 0.288531i \(-0.0931670\pi\)
\(252\) −12.7816 + 5.29432i −0.805167 + 0.333511i
\(253\) 0.0386814 + 0.0386814i 0.00243188 + 0.00243188i
\(254\) −0.0149650 −0.000938989
\(255\) −0.208619 2.82867i −0.0130642 0.177138i
\(256\) 20.7617 1.29761
\(257\) −11.7749 11.7749i −0.734498 0.734498i 0.237009 0.971507i \(-0.423833\pi\)
−0.971507 + 0.237009i \(0.923833\pi\)
\(258\) 11.4709 4.75139i 0.714145 0.295809i
\(259\) 1.46301i 0.0909070i
\(260\) −1.45982 3.52431i −0.0905341 0.218569i
\(261\) 0.982222 + 0.406850i 0.0607980 + 0.0251834i
\(262\) 5.65605 13.6549i 0.349432 0.843603i
\(263\) 15.3640 15.3640i 0.947387 0.947387i −0.0512969 0.998683i \(-0.516335\pi\)
0.998683 + 0.0512969i \(0.0163355\pi\)
\(264\) −0.0340795 + 0.0340795i −0.00209745 + 0.00209745i
\(265\) −4.61626 + 11.1446i −0.283575 + 0.684610i
\(266\) −56.6507 23.4655i −3.47348 1.43876i
\(267\) 2.68939 + 6.49276i 0.164588 + 0.397350i
\(268\) 1.15515i 0.0705618i
\(269\) −21.4082 + 8.86758i −1.30528 + 0.540666i −0.923504 0.383588i \(-0.874688\pi\)
−0.381779 + 0.924254i \(0.624688\pi\)
\(270\) −4.85478 4.85478i −0.295452 0.295452i
\(271\) −3.95595 −0.240307 −0.120153 0.992755i \(-0.538339\pi\)
−0.120153 + 0.992755i \(0.538339\pi\)
\(272\) 15.3974 + 13.2822i 0.933603 + 0.805353i
\(273\) −9.03556 −0.546857
\(274\) 2.85246 + 2.85246i 0.172323 + 0.172323i
\(275\) −0.0485041 + 0.0200910i −0.00292491 + 0.00121154i
\(276\) 0.903885i 0.0544075i
\(277\) −6.47115 15.6227i −0.388814 0.938679i −0.990192 0.139714i \(-0.955382\pi\)
0.601378 0.798964i \(-0.294618\pi\)
\(278\) 32.9266 + 13.6387i 1.97481 + 0.817992i
\(279\) 1.33854 3.23153i 0.0801366 0.193467i
\(280\) 4.09710 4.09710i 0.244848 0.244848i
\(281\) 3.30210 3.30210i 0.196987 0.196987i −0.601720 0.798707i \(-0.705518\pi\)
0.798707 + 0.601720i \(0.205518\pi\)
\(282\) 2.91496 7.03733i 0.173583 0.419067i
\(283\) −8.03809 3.32949i −0.477815 0.197917i 0.130760 0.991414i \(-0.458258\pi\)
−0.608575 + 0.793497i \(0.708258\pi\)
\(284\) 2.01708 + 4.86967i 0.119692 + 0.288962i
\(285\) 5.37981i 0.318672i
\(286\) −0.264967 + 0.109753i −0.0156678 + 0.00648982i
\(287\) −20.2409 20.2409i −1.19478 1.19478i
\(288\) 15.7599 0.928661
\(289\) 2.49398 + 16.8161i 0.146705 + 0.989180i
\(290\) 0.759811 0.0446176
\(291\) −9.35105 9.35105i −0.548168 0.548168i
\(292\) −6.28021 + 2.60135i −0.367521 + 0.152232i
\(293\) 0.739100i 0.0431787i 0.999767 + 0.0215893i \(0.00687263\pi\)
−0.999767 + 0.0215893i \(0.993127\pi\)
\(294\) 5.63452 + 13.6029i 0.328612 + 0.793339i
\(295\) −4.70974 1.95084i −0.274212 0.113582i
\(296\) −0.172073 + 0.415421i −0.0100015 + 0.0241459i
\(297\) −0.141142 + 0.141142i −0.00818987 + 0.00818987i
\(298\) −13.0034 + 13.0034i −0.753269 + 0.753269i
\(299\) 1.20623 2.91210i 0.0697582 0.168411i
\(300\) −0.801445 0.331970i −0.0462715 0.0191663i
\(301\) 16.6070 + 40.0928i 0.957210 + 2.31091i
\(302\) 27.7165i 1.59491i
\(303\) −8.44813 + 3.49933i −0.485333 + 0.201031i
\(304\) 27.2726 + 27.2726i 1.56419 + 1.56419i
\(305\) 5.97063 0.341877
\(306\) 14.2455 + 12.2886i 0.814361 + 0.702491i
\(307\) −2.86108 −0.163290 −0.0816451 0.996661i \(-0.526017\pi\)
−0.0816451 + 0.996661i \(0.526017\pi\)
\(308\) 0.203261 + 0.203261i 0.0115818 + 0.0115818i
\(309\) −4.39357 + 1.81988i −0.249941 + 0.103529i
\(310\) 2.49979i 0.141979i
\(311\) 7.84424 + 18.9377i 0.444806 + 1.07386i 0.974242 + 0.225507i \(0.0724038\pi\)
−0.529435 + 0.848350i \(0.677596\pi\)
\(312\) 2.56565 + 1.06273i 0.145251 + 0.0601650i
\(313\) 3.23958 7.82103i 0.183112 0.442071i −0.805493 0.592605i \(-0.798099\pi\)
0.988605 + 0.150534i \(0.0480994\pi\)
\(314\) 12.0186 12.0186i 0.678249 0.678249i
\(315\) 7.75771 7.75771i 0.437097 0.437097i
\(316\) −4.81750 + 11.6305i −0.271005 + 0.654265i
\(317\) −19.4863 8.07149i −1.09446 0.453340i −0.238900 0.971044i \(-0.576787\pi\)
−0.855560 + 0.517704i \(0.826787\pi\)
\(318\) 5.73460 + 13.8446i 0.321581 + 0.776364i
\(319\) 0.0220898i 0.00123679i
\(320\) 1.29301 0.535581i 0.0722813 0.0299399i
\(321\) 7.17035 + 7.17035i 0.400210 + 0.400210i
\(322\) −8.16985 −0.455288
\(323\) 2.37163 + 32.1571i 0.131961 + 1.78927i
\(324\) 6.26082 0.347823
\(325\) 2.13905 + 2.13905i 0.118653 + 0.118653i
\(326\) 20.7634 8.60048i 1.14998 0.476337i
\(327\) 3.26643i 0.180634i
\(328\) 3.36675 + 8.12805i 0.185897 + 0.448796i
\(329\) 24.5967 + 10.1883i 1.35606 + 0.561699i
\(330\) −0.0249583 + 0.0602547i −0.00137391 + 0.00331691i
\(331\) 10.7665 10.7665i 0.591780 0.591780i −0.346332 0.938112i \(-0.612573\pi\)
0.938112 + 0.346332i \(0.112573\pi\)
\(332\) 5.82272 5.82272i 0.319563 0.319563i
\(333\) −0.325814 + 0.786585i −0.0178545 + 0.0431046i
\(334\) −21.0256 8.70910i −1.15047 0.476541i
\(335\) −0.350554 0.846311i −0.0191528 0.0462389i
\(336\) 14.7309i 0.803638i
\(337\) 10.6003 4.39079i 0.577435 0.239182i −0.0747994 0.997199i \(-0.523832\pi\)
0.652235 + 0.758017i \(0.273832\pi\)
\(338\) −4.91472 4.91472i −0.267326 0.267326i
\(339\) 2.07290 0.112585
\(340\) 4.93688 + 1.63100i 0.267740 + 0.0884532i
\(341\) −0.0726759 −0.00393562
\(342\) 25.2324 + 25.2324i 1.36441 + 1.36441i
\(343\) −19.4648 + 8.06258i −1.05100 + 0.435338i
\(344\) 13.3376i 0.719114i
\(345\) −0.274303 0.662226i −0.0147680 0.0356530i
\(346\) −20.3483 8.42854i −1.09393 0.453121i
\(347\) −5.73424 + 13.8437i −0.307830 + 0.743168i 0.691945 + 0.721950i \(0.256754\pi\)
−0.999775 + 0.0212172i \(0.993246\pi\)
\(348\) 0.258091 0.258091i 0.0138351 0.0138351i
\(349\) −3.20791 + 3.20791i −0.171715 + 0.171715i −0.787733 0.616017i \(-0.788745\pi\)
0.616017 + 0.787733i \(0.288745\pi\)
\(350\) 3.00054 7.24394i 0.160386 0.387205i
\(351\) 10.6257 + 4.40133i 0.567160 + 0.234925i
\(352\) −0.125311 0.302528i −0.00667912 0.0161248i
\(353\) 7.71469i 0.410612i 0.978698 + 0.205306i \(0.0658189\pi\)
−0.978698 + 0.205306i \(0.934181\pi\)
\(354\) −5.85073 + 2.42345i −0.310963 + 0.128805i
\(355\) −2.95561 2.95561i −0.156867 0.156867i
\(356\) −12.8825 −0.682771
\(357\) 8.04411 9.32511i 0.425739 0.493537i
\(358\) −25.0302 −1.32289
\(359\) −7.79826 7.79826i −0.411577 0.411577i 0.470711 0.882287i \(-0.343997\pi\)
−0.882287 + 0.470711i \(0.843997\pi\)
\(360\) −3.11523 + 1.29037i −0.164187 + 0.0680084i
\(361\) 42.1592i 2.21890i
\(362\) −1.41269 3.41055i −0.0742496 0.179254i
\(363\) −6.98933 2.89507i −0.366844 0.151952i
\(364\) 6.33843 15.3023i 0.332224 0.802059i
\(365\) 3.81172 3.81172i 0.199515 0.199515i
\(366\) 5.24467 5.24467i 0.274143 0.274143i
\(367\) −6.13386 + 14.8084i −0.320185 + 0.772995i 0.679058 + 0.734085i \(0.262389\pi\)
−0.999243 + 0.0389098i \(0.987611\pi\)
\(368\) 4.74768 + 1.96655i 0.247490 + 0.102514i
\(369\) 6.37481 + 15.3902i 0.331860 + 0.801180i
\(370\) 0.608473i 0.0316330i
\(371\) −48.3892 + 20.0435i −2.51224 + 1.04061i
\(372\) −0.849124 0.849124i −0.0440250 0.0440250i
\(373\) −10.2501 −0.530732 −0.265366 0.964148i \(-0.585493\pi\)
−0.265366 + 0.964148i \(0.585493\pi\)
\(374\) 0.122623 0.371168i 0.00634066 0.0191926i
\(375\) 0.687917 0.0355239
\(376\) −5.78593 5.78593i −0.298387 0.298387i
\(377\) −1.17593 + 0.487085i −0.0605634 + 0.0250862i
\(378\) 29.8103i 1.53328i
\(379\) −5.33919 12.8899i −0.274256 0.662112i 0.725401 0.688327i \(-0.241654\pi\)
−0.999656 + 0.0262152i \(0.991654\pi\)
\(380\) 9.11105 + 3.77392i 0.467387 + 0.193598i
\(381\) 0.00218161 0.00526686i 0.000111767 0.000269830i
\(382\) −3.93362 + 3.93362i −0.201261 + 0.201261i
\(383\) −3.97525 + 3.97525i −0.203126 + 0.203126i −0.801338 0.598212i \(-0.795878\pi\)
0.598212 + 0.801338i \(0.295878\pi\)
\(384\) −2.61860 + 6.32185i −0.133630 + 0.322611i
\(385\) −0.210601 0.0872339i −0.0107332 0.00444585i
\(386\) −14.2648 34.4383i −0.726060 1.75286i
\(387\) 25.2542i 1.28374i
\(388\) 22.3963 9.27687i 1.13700 0.470962i
\(389\) −25.3255 25.3255i −1.28406 1.28406i −0.938339 0.345717i \(-0.887636\pi\)
−0.345717 0.938339i \(-0.612364\pi\)
\(390\) 3.75794 0.190291
\(391\) 1.93155 + 3.83745i 0.0976825 + 0.194068i
\(392\) 15.8166 0.798858
\(393\) 3.98123 + 3.98123i 0.200827 + 0.200827i
\(394\) 30.4252 12.6025i 1.53280 0.634907i
\(395\) 9.98296i 0.502297i
\(396\) −0.0640163 0.154549i −0.00321694 0.00776638i
\(397\) 3.59405 + 1.48870i 0.180380 + 0.0747159i 0.471046 0.882109i \(-0.343877\pi\)
−0.290665 + 0.956825i \(0.593877\pi\)
\(398\) −18.4290 + 44.4915i −0.923761 + 2.23016i
\(399\) 16.5171 16.5171i 0.826891 0.826891i
\(400\) −3.48736 + 3.48736i −0.174368 + 0.174368i
\(401\) 14.0592 33.9420i 0.702085 1.69498i −0.0168056 0.999859i \(-0.505350\pi\)
0.718890 0.695124i \(-0.244650\pi\)
\(402\) −1.05134 0.435479i −0.0524360 0.0217197i
\(403\) 1.60252 + 3.86883i 0.0798273 + 0.192720i
\(404\) 16.7622i 0.833952i
\(405\) −4.58695 + 1.89998i −0.227927 + 0.0944106i
\(406\) 2.33278 + 2.33278i 0.115774 + 0.115774i
\(407\) 0.0176900 0.000876860
\(408\) −3.38090 + 1.70175i −0.167380 + 0.0842491i
\(409\) −22.3529 −1.10528 −0.552641 0.833419i \(-0.686380\pi\)
−0.552641 + 0.833419i \(0.686380\pi\)
\(410\) 8.41829 + 8.41829i 0.415750 + 0.415750i
\(411\) −1.41974 + 0.588075i −0.0700306 + 0.0290076i
\(412\) 8.71743i 0.429477i
\(413\) −8.47041 20.4494i −0.416802 1.00625i
\(414\) 4.39251 + 1.81944i 0.215880 + 0.0894204i
\(415\) −2.49895 + 6.03301i −0.122669 + 0.296149i
\(416\) −13.3416 + 13.3416i −0.654128 + 0.654128i
\(417\) −9.60011 + 9.60011i −0.470119 + 0.470119i
\(418\) 0.283733 0.684993i 0.0138778 0.0335041i
\(419\) 20.2014 + 8.36768i 0.986901 + 0.408788i 0.816978 0.576669i \(-0.195648\pi\)
0.169924 + 0.985457i \(0.445648\pi\)
\(420\) −1.44139 3.47982i −0.0703325 0.169798i
\(421\) 20.6111i 1.00453i −0.864715 0.502263i \(-0.832501\pi\)
0.864715 0.502263i \(-0.167499\pi\)
\(422\) −13.0227 + 5.39419i −0.633937 + 0.262585i
\(423\) −10.9555 10.9555i −0.532672 0.532672i
\(424\) 16.0975 0.781766
\(425\) −4.11194 + 0.303261i −0.199458 + 0.0147103i
\(426\) −5.19248 −0.251576
\(427\) 18.3311 + 18.3311i 0.887103 + 0.887103i
\(428\) −17.1734 + 7.11347i −0.830109 + 0.343842i
\(429\) 0.109254i 0.00527481i
\(430\) −6.90692 16.6748i −0.333081 0.804130i
\(431\) 20.6074 + 8.53585i 0.992621 + 0.411157i 0.819086 0.573670i \(-0.194481\pi\)
0.173535 + 0.984828i \(0.444481\pi\)
\(432\) −7.17561 + 17.3234i −0.345236 + 0.833475i
\(433\) −6.31536 + 6.31536i −0.303497 + 0.303497i −0.842380 0.538883i \(-0.818846\pi\)
0.538883 + 0.842380i \(0.318846\pi\)
\(434\) 7.67489 7.67489i 0.368406 0.368406i
\(435\) −0.110765 + 0.267412i −0.00531080 + 0.0128214i
\(436\) −5.53190 2.29139i −0.264930 0.109738i
\(437\) 3.11835 + 7.52837i 0.149171 + 0.360131i
\(438\) 6.69652i 0.319972i
\(439\) 20.5695 8.52016i 0.981728 0.406645i 0.166663 0.986014i \(-0.446701\pi\)
0.815066 + 0.579369i \(0.196701\pi\)
\(440\) 0.0495401 + 0.0495401i 0.00236173 + 0.00236173i
\(441\) 29.9481 1.42610
\(442\) −22.4626 + 1.65665i −1.06844 + 0.0787987i
\(443\) −6.17421 −0.293346 −0.146673 0.989185i \(-0.546856\pi\)
−0.146673 + 0.989185i \(0.546856\pi\)
\(444\) 0.206685 + 0.206685i 0.00980882 + 0.00980882i
\(445\) 9.43828 3.90946i 0.447418 0.185326i
\(446\) 8.61184i 0.407783i
\(447\) −2.68085 6.47214i −0.126800 0.306122i
\(448\) 5.61414 + 2.32545i 0.265243 + 0.109867i
\(449\) 11.5947 27.9922i 0.547189 1.32103i −0.372371 0.928084i \(-0.621455\pi\)
0.919561 0.392948i \(-0.128545\pi\)
\(450\) −3.22647 + 3.22647i −0.152097 + 0.152097i
\(451\) 0.244743 0.244743i 0.0115245 0.0115245i
\(452\) −1.45414 + 3.51060i −0.0683968 + 0.165125i
\(453\) 9.75470 + 4.04053i 0.458316 + 0.189841i
\(454\) 7.74754 + 18.7042i 0.363610 + 0.877833i
\(455\) 13.1347i 0.615763i
\(456\) −6.63271 + 2.74736i −0.310605 + 0.128657i
\(457\) 18.0847 + 18.0847i 0.845965 + 0.845965i 0.989627 0.143662i \(-0.0458877\pi\)
−0.143662 + 0.989627i \(0.545888\pi\)
\(458\) 37.2876 1.74233
\(459\) −14.0022 + 7.04787i −0.653565 + 0.328966i
\(460\) 1.31395 0.0612630
\(461\) −9.93945 9.93945i −0.462926 0.462926i 0.436687 0.899613i \(-0.356152\pi\)
−0.899613 + 0.436687i \(0.856152\pi\)
\(462\) −0.261622 + 0.108367i −0.0121717 + 0.00504170i
\(463\) 25.1233i 1.16758i −0.811905 0.583789i \(-0.801569\pi\)
0.811905 0.583789i \(-0.198431\pi\)
\(464\) −0.794108 1.91715i −0.0368656 0.0890013i
\(465\) 0.879790 + 0.364421i 0.0407993 + 0.0168996i
\(466\) −2.11362 + 5.10272i −0.0979114 + 0.236379i
\(467\) −15.7614 + 15.7614i −0.729352 + 0.729352i −0.970491 0.241139i \(-0.922479\pi\)
0.241139 + 0.970491i \(0.422479\pi\)
\(468\) −6.81569 + 6.81569i −0.315055 + 0.315055i
\(469\) 1.52208 3.67462i 0.0702830 0.169678i
\(470\) −10.2299 4.23737i −0.471871 0.195455i
\(471\) 2.47781 + 5.98196i 0.114171 + 0.275634i
\(472\) 6.80285i 0.313126i
\(473\) −0.484782 + 0.200803i −0.0222903 + 0.00923294i
\(474\) −8.76915 8.76915i −0.402780 0.402780i
\(475\) −7.82043 −0.358826
\(476\) 10.1498 + 20.1648i 0.465213 + 0.924250i
\(477\) 30.4801 1.39559
\(478\) −6.30887 6.30887i −0.288561 0.288561i
\(479\) 24.7134 10.2366i 1.12919 0.467724i 0.261681 0.965154i \(-0.415723\pi\)
0.867504 + 0.497430i \(0.165723\pi\)
\(480\) 4.29066i 0.195841i
\(481\) −0.390068 0.941709i −0.0177856 0.0429382i
\(482\) −2.77243 1.14838i −0.126281 0.0523072i
\(483\) 1.19100 2.87534i 0.0541926 0.130832i
\(484\) 9.80599 9.80599i 0.445727 0.445727i
\(485\) −13.5933 + 13.5933i −0.617239 + 0.617239i
\(486\) −10.2424 + 24.7274i −0.464606 + 1.12166i
\(487\) −21.3841 8.85760i −0.969008 0.401376i −0.158665 0.987332i \(-0.550719\pi\)
−0.810343 + 0.585956i \(0.800719\pi\)
\(488\) −3.04908 7.36113i −0.138025 0.333223i
\(489\) 8.56135i 0.387158i
\(490\) 19.7741 8.19069i 0.893302 0.370018i
\(491\) −5.50823 5.50823i −0.248583 0.248583i 0.571806 0.820389i \(-0.306243\pi\)
−0.820389 + 0.571806i \(0.806243\pi\)
\(492\) 5.71901 0.257833
\(493\) 0.544201 1.64725i 0.0245096 0.0741883i
\(494\) −42.7213 −1.92212
\(495\) 0.0938023 + 0.0938023i 0.00421610 + 0.00421610i
\(496\) −6.30746 + 2.61263i −0.283213 + 0.117311i
\(497\) 18.1487i 0.814079i
\(498\) 3.10435 + 7.49457i 0.139109 + 0.335840i
\(499\) −8.12796 3.36671i −0.363858 0.150715i 0.193262 0.981147i \(-0.438093\pi\)
−0.557119 + 0.830432i \(0.688093\pi\)
\(500\) −0.482572 + 1.16503i −0.0215813 + 0.0521018i
\(501\) 6.13025 6.13025i 0.273879 0.273879i
\(502\) −11.6741 + 11.6741i −0.521039 + 0.521039i
\(503\) −3.00003 + 7.24271i −0.133765 + 0.322937i −0.976542 0.215325i \(-0.930919\pi\)
0.842778 + 0.538262i \(0.180919\pi\)
\(504\) −13.5261 5.60269i −0.602500 0.249564i
\(505\) 5.08685 + 12.2807i 0.226362 + 0.546486i
\(506\) 0.0987858i 0.00439156i
\(507\) 2.44618 1.01324i 0.108639 0.0449996i
\(508\) 0.00738938 + 0.00738938i 0.000327851 + 0.000327851i
\(509\) 2.52868 0.112082 0.0560409 0.998428i \(-0.482152\pi\)
0.0560409 + 0.998428i \(0.482152\pi\)
\(510\) −3.34558 + 3.87836i −0.148145 + 0.171737i
\(511\) 23.4055 1.03540
\(512\) −12.4437 12.4437i −0.549940 0.549940i
\(513\) −27.4697 + 11.3783i −1.21282 + 0.502365i
\(514\) 30.0711i 1.32638i
\(515\) 2.64549 + 6.38677i 0.116574 + 0.281435i
\(516\) −8.01017 3.31792i −0.352628 0.146063i
\(517\) −0.123192 + 0.297412i −0.00541797 + 0.0130801i
\(518\) −1.86814 + 1.86814i −0.0820813 + 0.0820813i
\(519\) 5.93276 5.93276i 0.260419 0.260419i
\(520\) 1.54485 3.72959i 0.0677459 0.163553i
\(521\) 9.33885 + 3.86828i 0.409142 + 0.169472i 0.577755 0.816210i \(-0.303929\pi\)
−0.168613 + 0.985682i \(0.553929\pi\)
\(522\) −0.734701 1.77373i −0.0321570 0.0776339i
\(523\) 5.80494i 0.253833i 0.991913 + 0.126916i \(0.0405079\pi\)
−0.991913 + 0.126916i \(0.959492\pi\)
\(524\) −9.53530 + 3.94965i −0.416552 + 0.172541i
\(525\) 2.11205 + 2.11205i 0.0921773 + 0.0921773i
\(526\) −39.2371 −1.71082
\(527\) −5.41948 1.79043i −0.236076 0.0779925i
\(528\) 0.178119 0.00775164
\(529\) −15.4958 15.4958i −0.673728 0.673728i
\(530\) 20.1253 8.33618i 0.874188 0.362101i
\(531\) 12.8809i 0.558985i
\(532\) 16.3861 + 39.5595i 0.710427 + 1.71512i
\(533\) −18.4253 7.63200i −0.798087 0.330579i
\(534\) 4.85658 11.7248i 0.210165 0.507382i
\(535\) 10.4233 10.4233i 0.450637 0.450637i
\(536\) −0.864387 + 0.864387i −0.0373358 + 0.0373358i
\(537\) 3.64892 8.80926i 0.157462 0.380148i
\(538\) 38.6596 + 16.0133i 1.66674 + 0.690384i
\(539\) −0.238126 0.574887i −0.0102568 0.0247621i
\(540\) 4.79435i 0.206316i
\(541\) 39.1174 16.2030i 1.68179 0.696620i 0.682380 0.730998i \(-0.260945\pi\)
0.999409 + 0.0343783i \(0.0109451\pi\)
\(542\) 5.05141 + 5.05141i 0.216976 + 0.216976i
\(543\) 1.40627 0.0603487
\(544\) −1.89149 25.6469i −0.0810971 1.09960i
\(545\) 4.74828 0.203394
\(546\) 11.5376 + 11.5376i 0.493766 + 0.493766i
\(547\) 18.4832 7.65599i 0.790285 0.327347i 0.0492266 0.998788i \(-0.484324\pi\)
0.741058 + 0.671441i \(0.234324\pi\)
\(548\) 2.81695i 0.120334i
\(549\) −5.77332 13.9380i −0.246399 0.594860i
\(550\) 0.0875901 + 0.0362810i 0.00373485 + 0.00154703i
\(551\) 1.25921 3.04001i 0.0536443 0.129509i
\(552\) −0.676370 + 0.676370i −0.0287882 + 0.0287882i
\(553\) 30.6498 30.6498i 1.30336 1.30336i
\(554\) −11.6858 + 28.2120i −0.496482 + 1.19861i
\(555\) −0.214149 0.0887034i −0.00909012 0.00376525i
\(556\) −9.52395 22.9929i −0.403906 0.975114i
\(557\) 25.8965i 1.09727i 0.836062 + 0.548636i \(0.184853\pi\)
−0.836062 + 0.548636i \(0.815147\pi\)
\(558\) −5.83560 + 2.41718i −0.247041 + 0.102328i
\(559\) 21.3791 + 21.3791i 0.904240 + 0.904240i
\(560\) −21.4138 −0.904899
\(561\) 0.112755 + 0.0972653i 0.00476050 + 0.00410655i
\(562\) −8.43299 −0.355724
\(563\) 19.8208 + 19.8208i 0.835349 + 0.835349i 0.988243 0.152894i \(-0.0488593\pi\)
−0.152894 + 0.988243i \(0.548859\pi\)
\(564\) −4.91421 + 2.03553i −0.206925 + 0.0857113i
\(565\) 3.01331i 0.126771i
\(566\) 6.01248 + 14.5154i 0.252724 + 0.610129i
\(567\) −19.9162 8.24956i −0.836402 0.346449i
\(568\) −2.13457 + 5.15331i −0.0895645 + 0.216228i
\(569\) −27.7130 + 27.7130i −1.16179 + 1.16179i −0.177706 + 0.984084i \(0.556868\pi\)
−0.984084 + 0.177706i \(0.943132\pi\)
\(570\) −6.86956 + 6.86956i −0.287734 + 0.287734i
\(571\) 1.48008 3.57322i 0.0619392 0.149535i −0.889880 0.456196i \(-0.849212\pi\)
0.951819 + 0.306661i \(0.0992118\pi\)
\(572\) 0.185028 + 0.0766411i 0.00773641 + 0.00320452i
\(573\) −0.810972 1.95786i −0.0338788 0.0817908i
\(574\) 51.6918i 2.15757i
\(575\) −0.962654 + 0.398744i −0.0401454 + 0.0166288i
\(576\) −2.50055 2.50055i −0.104190 0.104190i
\(577\) 14.4808 0.602845 0.301423 0.953491i \(-0.402539\pi\)
0.301423 + 0.953491i \(0.402539\pi\)
\(578\) 18.2881 24.6573i 0.760684 1.02561i
\(579\) 14.1999 0.590128
\(580\) −0.375177 0.375177i −0.0155784 0.0155784i
\(581\) −26.1949 + 10.8503i −1.08675 + 0.450145i
\(582\) 23.8810i 0.989898i
\(583\) −0.242356 0.585099i −0.0100374 0.0242323i
\(584\) −6.64600 2.75286i −0.275013 0.113914i
\(585\) 2.92511 7.06184i 0.120938 0.291971i
\(586\) 0.943767 0.943767i 0.0389867 0.0389867i
\(587\) 22.0937 22.0937i 0.911905 0.911905i −0.0845171 0.996422i \(-0.526935\pi\)
0.996422 + 0.0845171i \(0.0269347\pi\)
\(588\) 3.93462 9.49900i 0.162261 0.391732i
\(589\) −10.0017 4.14284i −0.412113 0.170703i
\(590\) 3.52289 + 8.50500i 0.145035 + 0.350145i
\(591\) 12.5452i 0.516041i
\(592\) 1.53529 0.635939i 0.0631002 0.0261369i
\(593\) 1.41805 + 1.41805i 0.0582323 + 0.0582323i 0.735623 0.677391i \(-0.236889\pi\)
−0.677391 + 0.735623i \(0.736889\pi\)
\(594\) 0.360452 0.0147895
\(595\) −13.5556 11.6934i −0.555724 0.479384i
\(596\) 12.8416 0.526012
\(597\) −12.9720 12.9720i −0.530907 0.530907i
\(598\) −5.25876 + 2.17825i −0.215047 + 0.0890753i
\(599\) 36.0451i 1.47276i 0.676567 + 0.736381i \(0.263467\pi\)
−0.676567 + 0.736381i \(0.736533\pi\)
\(600\) −0.351305 0.848125i −0.0143420 0.0346246i
\(601\) −35.8417 14.8461i −1.46201 0.605586i −0.496993 0.867755i \(-0.665562\pi\)
−0.965022 + 0.262168i \(0.915562\pi\)
\(602\) 29.9894 72.4007i 1.22228 2.95083i
\(603\) −1.63669 + 1.63669i −0.0666510 + 0.0666510i
\(604\) −13.6858 + 13.6858i −0.556867 + 0.556867i
\(605\) −4.20846 + 10.1601i −0.171098 + 0.413068i
\(606\) 15.2559 + 6.31920i 0.619728 + 0.256700i
\(607\) −11.0800 26.7496i −0.449725 1.08573i −0.972425 0.233215i \(-0.925075\pi\)
0.522701 0.852516i \(-0.324925\pi\)
\(608\) 48.7774i 1.97818i
\(609\) −1.16108 + 0.480936i −0.0470494 + 0.0194885i
\(610\) −7.62399 7.62399i −0.308686 0.308686i
\(611\) 18.5488 0.750405
\(612\) −0.966284 13.1019i −0.0390597 0.529613i
\(613\) 9.10707 0.367831 0.183915 0.982942i \(-0.441123\pi\)
0.183915 + 0.982942i \(0.441123\pi\)
\(614\) 3.65335 + 3.65335i 0.147437 + 0.147437i
\(615\) −4.19000 + 1.73555i −0.168957 + 0.0699842i
\(616\) 0.304197i 0.0122564i
\(617\) −1.93466 4.67068i −0.0778864 0.188035i 0.880140 0.474714i \(-0.157449\pi\)
−0.958027 + 0.286680i \(0.907449\pi\)
\(618\) 7.93404 + 3.28639i 0.319154 + 0.132198i
\(619\) 6.45177 15.5760i 0.259319 0.626051i −0.739575 0.673074i \(-0.764974\pi\)
0.998894 + 0.0470233i \(0.0149735\pi\)
\(620\) −1.23434 + 1.23434i −0.0495723 + 0.0495723i
\(621\) −2.80122 + 2.80122i −0.112409 + 0.112409i
\(622\) 14.1654 34.1982i 0.567979 1.37122i
\(623\) 40.9803 + 16.9746i 1.64184 + 0.680074i
\(624\) −3.92757 9.48199i −0.157229 0.379583i
\(625\) 1.00000i 0.0400000i
\(626\) −14.1235 + 5.85013i −0.564487 + 0.233818i
\(627\) 0.199717 + 0.199717i 0.00797592 + 0.00797592i
\(628\) −11.8690 −0.473625
\(629\) 1.31915 + 0.435808i 0.0525981 + 0.0173768i
\(630\) −19.8119 −0.789323
\(631\) 1.91845 + 1.91845i 0.0763722 + 0.0763722i 0.744261 0.667889i \(-0.232802\pi\)
−0.667889 + 0.744261i \(0.732802\pi\)
\(632\) −12.3079 + 5.09809i −0.489581 + 0.202791i
\(633\) 5.36965i 0.213424i
\(634\) 14.5757 + 35.1889i 0.578876 + 1.39753i
\(635\) −0.00765625 0.00317132i −0.000303829 0.000125850i
\(636\) 4.00451 9.66773i 0.158789 0.383351i
\(637\) −25.3528 + 25.3528i −1.00451 + 1.00451i
\(638\) −0.0282068 + 0.0282068i −0.00111672 + 0.00111672i
\(639\) −4.04173 + 9.75760i −0.159888 + 0.386005i
\(640\) 9.18985 + 3.80656i 0.363261 + 0.150467i
\(641\) −8.72988 21.0758i −0.344809 0.832443i −0.997215 0.0745739i \(-0.976240\pi\)
0.652406 0.757870i \(-0.273760\pi\)
\(642\) 18.3118i 0.722711i
\(643\) −17.8097 + 7.37702i −0.702346 + 0.290921i −0.705133 0.709075i \(-0.749113\pi\)
0.00278691 + 0.999996i \(0.499113\pi\)
\(644\) 4.03408 + 4.03408i 0.158965 + 0.158965i
\(645\) 6.87550 0.270722
\(646\) 38.0335 44.0903i 1.49641 1.73471i
\(647\) 12.8098 0.503606 0.251803 0.967778i \(-0.418976\pi\)
0.251803 + 0.967778i \(0.418976\pi\)
\(648\) 4.68492 + 4.68492i 0.184041 + 0.184041i
\(649\) 0.247264 0.102420i 0.00970595 0.00402033i
\(650\) 5.46278i 0.214268i
\(651\) 1.58229 + 3.81998i 0.0620148 + 0.149717i
\(652\) −14.4992 6.00577i −0.567833 0.235204i
\(653\) −15.9656 + 38.5442i −0.624780 + 1.50835i 0.221249 + 0.975217i \(0.428987\pi\)
−0.846030 + 0.533136i \(0.821013\pi\)
\(654\) 4.17095 4.17095i 0.163097 0.163097i
\(655\) 5.78738 5.78738i 0.226131 0.226131i
\(656\) 12.4427 30.0392i 0.485804 1.17284i
\(657\) −12.5840 5.21244i −0.490947 0.203357i
\(658\) −18.3983 44.4175i −0.717242 1.73158i
\(659\) 34.3290i 1.33727i 0.743592 + 0.668633i \(0.233120\pi\)
−0.743592 + 0.668633i \(0.766880\pi\)
\(660\) 0.0420762 0.0174285i 0.00163781 0.000678405i
\(661\) −19.5875 19.5875i −0.761865 0.761865i 0.214794 0.976659i \(-0.431092\pi\)
−0.976659 + 0.214794i \(0.931092\pi\)
\(662\) −27.4958 −1.06865
\(663\) 2.69156 8.14710i 0.104531 0.316407i
\(664\) 8.71419 0.338176
\(665\) −24.0103 24.0103i −0.931081 0.931081i
\(666\) 1.42044 0.588365i 0.0550409 0.0227987i
\(667\) 0.438413i 0.0169754i
\(668\) 6.08161 + 14.6823i 0.235305 + 0.568076i
\(669\) 3.03089 + 1.25544i 0.117181 + 0.0485380i
\(670\) −0.633040 + 1.52829i −0.0244565 + 0.0590431i
\(671\) −0.221650 + 0.221650i −0.00855671 + 0.00855671i
\(672\) −13.1732 + 13.1732i −0.508168 + 0.508168i
\(673\) 13.8561 33.4517i 0.534115 1.28947i −0.394662 0.918826i \(-0.629138\pi\)
0.928777 0.370640i \(-0.120862\pi\)
\(674\) −19.1423 7.92902i −0.737336 0.305414i
\(675\) −1.45495 3.51255i −0.0560009 0.135198i
\(676\) 4.85355i 0.186675i
\(677\) 15.8129 6.54992i 0.607739 0.251734i −0.0575224 0.998344i \(-0.518320\pi\)
0.665262 + 0.746610i \(0.268320\pi\)
\(678\) −2.64692 2.64692i −0.101654 0.101654i
\(679\) −83.4684 −3.20322
\(680\) 2.47377 + 4.91469i 0.0948647 + 0.188470i
\(681\) −7.71229 −0.295536
\(682\) 0.0928009 + 0.0928009i 0.00355353 + 0.00355353i
\(683\) 8.17654 3.38683i 0.312866 0.129594i −0.220725 0.975336i \(-0.570842\pi\)
0.533591 + 0.845743i \(0.320842\pi\)
\(684\) 24.9183i 0.952776i
\(685\) 0.854864 + 2.06382i 0.0326627 + 0.0788546i
\(686\) 35.1501 + 14.5596i 1.34204 + 0.555890i
\(687\) −5.43580 + 13.1232i −0.207389 + 0.500680i
\(688\) −34.8550 + 34.8550i −1.32883 + 1.32883i
\(689\) −25.8031 + 25.8031i −0.983021 + 0.983021i
\(690\) −0.495344 + 1.19587i −0.0188574 + 0.0455259i
\(691\) 1.29190 + 0.535121i 0.0491461 + 0.0203570i 0.407121 0.913374i \(-0.366533\pi\)
−0.357975 + 0.933731i \(0.616533\pi\)
\(692\) 5.88570 + 14.2093i 0.223741 + 0.540158i
\(693\) 0.575985i 0.0218799i
\(694\) 24.9993 10.3551i 0.948962 0.393073i
\(695\) 13.9553 + 13.9553i 0.529356 + 0.529356i
\(696\) 0.386254 0.0146409
\(697\) 24.2801 12.2212i 0.919673 0.462910i
\(698\) 8.19245 0.310089
\(699\) −1.48775 1.48775i −0.0562720 0.0562720i
\(700\) −5.05848 + 2.09529i −0.191193 + 0.0791946i
\(701\) 2.36331i 0.0892608i 0.999004 + 0.0446304i \(0.0142110\pi\)
−0.999004 + 0.0446304i \(0.985789\pi\)
\(702\) −7.94805 19.1883i −0.299980 0.724215i
\(703\) 2.43451 + 1.00841i 0.0918191 + 0.0380327i
\(704\) −0.0281182 + 0.0678834i −0.00105975 + 0.00255845i
\(705\) 2.98264 2.98264i 0.112333 0.112333i
\(706\) 9.85100 9.85100i 0.370747 0.370747i
\(707\) −22.0867 + 53.3221i −0.830657 + 2.00538i
\(708\) 4.08560 + 1.69231i 0.153546 + 0.0636009i
\(709\) 12.4474 + 30.0507i 0.467472 + 1.12858i 0.965263 + 0.261280i \(0.0841447\pi\)
−0.497791 + 0.867297i \(0.665855\pi\)
\(710\) 7.54812i 0.283276i
\(711\) −23.3045 + 9.65306i −0.873988 + 0.362018i
\(712\) −9.63987 9.63987i −0.361270 0.361270i
\(713\) −1.44239 −0.0540179
\(714\) −22.1790 + 1.63573i −0.830028 + 0.0612158i
\(715\) −0.158818 −0.00593945
\(716\) 12.3594 + 12.3594i 0.461891 + 0.461891i
\(717\) 3.14009 1.30067i 0.117269 0.0485743i
\(718\) 19.9154i 0.743237i
\(719\) −6.28758 15.1796i −0.234487 0.566102i 0.762208 0.647332i \(-0.224115\pi\)
−0.996695 + 0.0812299i \(0.974115\pi\)
\(720\) 11.5131 + 4.76888i 0.429068 + 0.177726i
\(721\) −11.4865 + 27.7309i −0.427780 + 1.03275i
\(722\) 53.8336 53.8336i 2.00348 2.00348i
\(723\) 0.808332 0.808332i 0.0300622 0.0300622i
\(724\) −0.986493 + 2.38160i −0.0366627 + 0.0885116i
\(725\) 0.388726 + 0.161016i 0.0144369 + 0.00597997i
\(726\) 5.22801 + 12.6215i 0.194030 + 0.468429i
\(727\) 32.4709i 1.20428i 0.798391 + 0.602139i \(0.205685\pi\)
−0.798391 + 0.602139i \(0.794315\pi\)
\(728\) 16.1936 6.70761i 0.600175 0.248600i
\(729\) 3.32256 + 3.32256i 0.123058 + 0.123058i
\(730\) −9.73448 −0.360289
\(731\) −41.0974 + 3.03099i −1.52004 + 0.112105i
\(732\) −5.17939 −0.191436
\(733\) −6.10533 6.10533i −0.225506 0.225506i 0.585307 0.810812i \(-0.300974\pi\)
−0.810812 + 0.585307i \(0.800974\pi\)
\(734\) 26.7415 11.0767i 0.987048 0.408849i
\(735\) 8.15343i 0.300744i
\(736\) −2.48704 6.00424i −0.0916734 0.221319i
\(737\) 0.0444317 + 0.0184042i 0.00163666 + 0.000677928i
\(738\) 11.5118 27.7920i 0.423756 1.02304i
\(739\) −7.49715 + 7.49715i −0.275787 + 0.275787i −0.831425 0.555637i \(-0.812474\pi\)
0.555637 + 0.831425i \(0.312474\pi\)
\(740\) 0.300450 0.300450i 0.0110448 0.0110448i
\(741\) 6.22792 15.0355i 0.228788 0.552344i
\(742\) 87.3827 + 36.1951i 3.20792 + 1.32876i
\(743\) −8.55008 20.6417i −0.313672 0.757272i −0.999563 0.0295670i \(-0.990587\pi\)
0.685891 0.727705i \(-0.259413\pi\)
\(744\) 1.27079i 0.0465893i
\(745\) −9.40831 + 3.89705i −0.344694 + 0.142777i
\(746\) 13.0886 + 13.0886i 0.479206 + 0.479206i
\(747\) 16.5000 0.603704
\(748\) −0.243822 + 0.122726i −0.00891502 + 0.00448730i
\(749\) 64.0032 2.33863
\(750\) −0.878411 0.878411i −0.0320750 0.0320750i
\(751\) 6.59640 2.73232i 0.240706 0.0997037i −0.259069 0.965859i \(-0.583416\pi\)
0.499775 + 0.866155i \(0.333416\pi\)
\(752\) 30.2406i 1.10276i
\(753\) −2.40678 5.81047i −0.0877078 0.211745i
\(754\) 2.12353 + 0.879593i 0.0773342 + 0.0320329i
\(755\) 5.87357 14.1800i 0.213761 0.516065i
\(756\) −14.7197 + 14.7197i −0.535349 + 0.535349i
\(757\) 12.7467 12.7467i 0.463287 0.463287i −0.436444 0.899731i \(-0.643762\pi\)
0.899731 + 0.436444i \(0.143762\pi\)
\(758\) −9.64166 + 23.2770i −0.350201 + 0.845460i
\(759\) 0.0347671 + 0.0144010i 0.00126197 + 0.000522724i
\(760\) 3.99373 + 9.64173i 0.144868 + 0.349742i
\(761\) 49.9437i 1.81046i 0.424923 + 0.905230i \(0.360301\pi\)
−0.424923 + 0.905230i \(0.639699\pi\)
\(762\) −0.00951106 + 0.00393961i −0.000344549 + 0.000142717i
\(763\) 14.5782 + 14.5782i 0.527767 + 0.527767i
\(764\) 3.88466 0.140542
\(765\) 4.68399 + 9.30580i 0.169350 + 0.336452i
\(766\) 10.1521 0.366811
\(767\) −10.9044 10.9044i −0.393737 0.393737i
\(768\) 13.1952 5.46561i 0.476139 0.197223i
\(769\) 43.9115i 1.58349i −0.610852 0.791745i \(-0.709173\pi\)
0.610852 0.791745i \(-0.290827\pi\)
\(770\) 0.157530 + 0.380310i 0.00567697 + 0.0137054i
\(771\) −10.5834 4.38377i −0.381151 0.157878i
\(772\) −9.96120 + 24.0485i −0.358511 + 0.865523i
\(773\) 6.84309 6.84309i 0.246129 0.246129i −0.573251 0.819380i \(-0.694318\pi\)
0.819380 + 0.573251i \(0.194318\pi\)
\(774\) −32.2475 + 32.2475i −1.15911 + 1.15911i
\(775\) 0.529745 1.27892i 0.0190290 0.0459401i
\(776\) 23.7008 + 9.81720i 0.850810 + 0.352417i
\(777\) −0.385144 0.929820i −0.0138170 0.0333571i
\(778\) 64.6771i 2.31879i
\(779\) 47.6330 19.7302i 1.70663 0.706909i
\(780\) −1.85558 1.85558i −0.0664405 0.0664405i
\(781\) 0.219445 0.00785234
\(782\) 2.43367 7.36651i 0.0870280 0.263426i
\(783\) 1.59969 0.0571683
\(784\) −41.3334 41.3334i −1.47619 1.47619i
\(785\) 8.69576 3.60190i 0.310365 0.128557i
\(786\) 10.1674i 0.362659i
\(787\) 7.59181 + 18.3283i 0.270619 + 0.653332i 0.999510 0.0312976i \(-0.00996398\pi\)
−0.728891 + 0.684630i \(0.759964\pi\)
\(788\) −21.2461 8.80043i −0.756861 0.313502i
\(789\) 5.72000 13.8093i 0.203637 0.491624i
\(790\) −12.7474 + 12.7474i −0.453532 + 0.453532i
\(791\) 9.25147 9.25147i 0.328944 0.328944i
\(792\) 0.0677450 0.163551i 0.00240721 0.00581152i
\(793\) 16.6868 + 6.91188i 0.592564 + 0.245448i
\(794\) −2.68835 6.49024i −0.0954059 0.230330i
\(795\) 8.29826i 0.294309i
\(796\) 31.0687 12.8691i 1.10120 0.456132i
\(797\) −3.93230 3.93230i −0.139289 0.139289i 0.634024 0.773313i \(-0.281402\pi\)
−0.773313 + 0.634024i \(0.781402\pi\)
\(798\) −42.1819 −1.49322
\(799\) −16.5135 + 19.1432i −0.584205 + 0.677238i
\(800\) 6.23717 0.220517
\(801\) −18.2528 18.2528i −0.644929 0.644929i
\(802\) −61.2935 + 25.3886i −2.16435 + 0.896502i
\(803\) 0.283008i 0.00998714i
\(804\) 0.304097 + 0.734156i 0.0107247 + 0.0258917i
\(805\) −4.17977 1.73132i −0.147318 0.0610210i
\(806\) 2.89388 6.98644i 0.101933 0.246087i
\(807\) −11.2716 + 11.2716i −0.396780 + 0.396780i
\(808\) 12.5430 12.5430i 0.441263 0.441263i
\(809\) 11.8801 28.6811i 0.417683 1.00838i −0.565335 0.824862i \(-0.691253\pi\)
0.983017 0.183513i \(-0.0587471\pi\)
\(810\) 8.28325 + 3.43103i 0.291044 + 0.120554i
\(811\) −17.9749 43.3953i −0.631185 1.52382i −0.838134 0.545464i \(-0.816353\pi\)
0.206949 0.978352i \(-0.433647\pi\)
\(812\) 2.30374i 0.0808455i
\(813\) −2.51421 + 1.04142i −0.0881773 + 0.0365242i
\(814\) −0.0225886 0.0225886i −0.000791730 0.000791730i
\(815\) 12.4453 0.435941
\(816\) 13.2824 + 4.38812i 0.464979 + 0.153615i
\(817\) −78.1626 −2.73456
\(818\) 28.5428 + 28.5428i 0.997976 + 0.997976i
\(819\) 30.6620 12.7006i 1.07142 0.443795i
\(820\) 8.31351i 0.290320i
\(821\) 6.40739 + 15.4688i 0.223619 + 0.539865i 0.995376 0.0960527i \(-0.0306217\pi\)
−0.771757 + 0.635918i \(0.780622\pi\)
\(822\) 2.56381 + 1.06196i 0.0894231 + 0.0370402i
\(823\) −10.1792 + 24.5749i −0.354826 + 0.856626i 0.641184 + 0.767387i \(0.278443\pi\)
−0.996010 + 0.0892387i \(0.971557\pi\)
\(824\) 6.52318 6.52318i 0.227246 0.227246i
\(825\) −0.0255378 + 0.0255378i −0.000889113 + 0.000889113i
\(826\) −15.2961 + 36.9281i −0.532220 + 1.28489i
\(827\) 31.8605 + 13.1970i 1.10790 + 0.458906i 0.860213 0.509934i \(-0.170330\pi\)
0.247684 + 0.968841i \(0.420330\pi\)
\(828\) −1.27052 3.06731i −0.0441537 0.106597i
\(829\) 7.29346i 0.253312i 0.991947 + 0.126656i \(0.0404245\pi\)
−0.991947 + 0.126656i \(0.959576\pi\)
\(830\) 10.8946 4.51269i 0.378157 0.156638i
\(831\) −8.22551 8.22551i −0.285340 0.285340i
\(832\) 4.23372 0.146778
\(833\) −3.59436 48.7361i −0.124537 1.68861i
\(834\) 24.5170 0.848956
\(835\) −8.91131 8.91131i −0.308389 0.308389i
\(836\) −0.478334 + 0.198133i −0.0165435 + 0.00685256i
\(837\) 5.26302i 0.181917i
\(838\) −15.1106 36.4802i −0.521987 1.26019i
\(839\) −32.8053 13.5884i −1.13257 0.469124i −0.263913 0.964546i \(-0.585013\pi\)
−0.868652 + 0.495422i \(0.835013\pi\)
\(840\) 1.52534 3.68250i 0.0526293 0.127058i
\(841\) 20.3809 20.3809i 0.702790 0.702790i
\(842\) −26.3187 + 26.3187i −0.907001 + 0.907001i
\(843\) 1.22936 2.96795i 0.0423415 0.102222i
\(844\) 9.09385 + 3.76680i 0.313023 + 0.129658i
\(845\) −1.47291 3.55592i −0.0506697 0.122327i
\(846\) 27.9784i 0.961916i
\(847\) −44.1146 + 18.2728i −1.51579 + 0.627862i
\(848\) −42.0676 42.0676i −1.44461 1.44461i
\(849\) −5.98513 −0.205409
\(850\) 5.63783 + 4.86335i 0.193376 + 0.166812i
\(851\) 0.351091 0.0120352
\(852\) 2.56393 + 2.56393i 0.0878386 + 0.0878386i
\(853\) 0.220643 0.0913933i 0.00755467 0.00312925i −0.378903 0.925436i \(-0.623699\pi\)
0.386458 + 0.922307i \(0.373699\pi\)
\(854\) 46.8144i 1.60196i
\(855\) 7.56199 + 18.2563i 0.258615 + 0.624351i
\(856\) −18.1737 7.52779i −0.621164 0.257295i
\(857\) −6.96291 + 16.8099i −0.237848 + 0.574217i −0.997060 0.0766273i \(-0.975585\pi\)
0.759211 + 0.650844i \(0.225585\pi\)
\(858\) −0.139507 + 0.139507i −0.00476271 + 0.00476271i
\(859\) −14.2525 + 14.2525i −0.486288 + 0.486288i −0.907133 0.420845i \(-0.861734\pi\)
0.420845 + 0.907133i \(0.361734\pi\)
\(860\) −4.82314 + 11.6441i −0.164468 + 0.397061i
\(861\) −18.1927 7.53565i −0.620004 0.256814i
\(862\) −15.4143 37.2134i −0.525013 1.26749i
\(863\) 14.7597i 0.502424i −0.967932 0.251212i \(-0.919171\pi\)
0.967932 0.251212i \(-0.0808292\pi\)
\(864\) 21.9084 9.07476i 0.745339 0.308730i
\(865\) −8.62424 8.62424i −0.293233 0.293233i
\(866\) 16.1284 0.548064
\(867\) 6.01196 + 10.0309i 0.204177 + 0.340669i
\(868\) −7.57936 −0.257260
\(869\) 0.370602 + 0.370602i 0.0125718 + 0.0125718i
\(870\) 0.482900 0.200024i 0.0163718 0.00678144i
\(871\) 2.77109i 0.0938949i
\(872\) −2.42485 5.85411i −0.0821158 0.198245i
\(873\) 44.8766 + 18.5885i 1.51884 + 0.629126i
\(874\) 5.63121 13.5950i 0.190479 0.459856i
\(875\) 3.07021 3.07021i 0.103792 0.103792i
\(876\) −3.30658 + 3.30658i −0.111719 + 0.111719i
\(877\) 16.3627 39.5030i 0.552528 1.33392i −0.363046 0.931771i \(-0.618263\pi\)
0.915574 0.402149i \(-0.131737\pi\)
\(878\) −37.1450 15.3860i −1.25358 0.519251i
\(879\) 0.194571 + 0.469737i 0.00656273 + 0.0158438i
\(880\) 0.258925i 0.00872837i
\(881\) −40.3580 + 16.7168i −1.35970 + 0.563205i −0.938975 0.343985i \(-0.888223\pi\)
−0.420721 + 0.907190i \(0.638223\pi\)
\(882\) −38.2412 38.2412i −1.28765 1.28765i
\(883\) 41.4824 1.39599 0.697997 0.716101i \(-0.254075\pi\)
0.697997 + 0.716101i \(0.254075\pi\)
\(884\) 11.9095 + 10.2735i 0.400561 + 0.345535i
\(885\) −3.50686 −0.117882
\(886\) 7.88394 + 7.88394i 0.264866 + 0.264866i
\(887\) 30.3770 12.5826i 1.01996 0.422481i 0.190881 0.981613i \(-0.438866\pi\)
0.829078 + 0.559132i \(0.188866\pi\)
\(888\) 0.309321i 0.0103801i
\(889\) −0.0137697 0.0332429i −0.000461819 0.00111493i
\(890\) −17.0439 7.05983i −0.571314 0.236646i
\(891\) 0.0997496 0.240817i 0.00334174 0.00806767i
\(892\) −4.25233 + 4.25233i −0.142378 + 0.142378i
\(893\) −33.9075 + 33.9075i −1.13467 + 1.13467i
\(894\) −4.84115 + 11.6876i −0.161912 + 0.390891i
\(895\) −12.8057 5.30430i −0.428048 0.177303i
\(896\) 16.5278 + 39.9017i 0.552155 + 1.33302i
\(897\) 2.16834i 0.0723988i
\(898\) −50.5491 + 20.9381i −1.68685 + 0.698714i
\(899\) 0.411852 + 0.411852i 0.0137360 + 0.0137360i
\(900\) 3.18631 0.106210
\(901\) −3.65820 49.6018i −0.121872 1.65248i
\(902\) −0.625031 −0.0208113
\(903\) 21.1092 + 21.1092i 0.702470 + 0.702470i
\(904\) −3.71507 + 1.53883i −0.123561 + 0.0511808i
\(905\) 2.04424i 0.0679528i
\(906\) −7.29650 17.6153i −0.242410 0.585230i
\(907\) 33.6731 + 13.9479i 1.11810 + 0.463131i 0.863719 0.503973i \(-0.168129\pi\)
0.254379 + 0.967105i \(0.418129\pi\)
\(908\) 5.41015 13.0613i 0.179542 0.433453i
\(909\) 23.7498 23.7498i 0.787731 0.787731i
\(910\) 16.7719 16.7719i 0.555982 0.555982i
\(911\) −11.4322 + 27.5999i −0.378767 + 0.914425i 0.613430 + 0.789749i \(0.289789\pi\)
−0.992197 + 0.124676i \(0.960211\pi\)
\(912\) 24.5128 + 10.1535i 0.811701 + 0.336218i
\(913\) −0.131196 0.316736i −0.00434196 0.0104824i
\(914\) 46.1852i 1.52767i
\(915\) 3.79465 1.57180i 0.125447 0.0519619i
\(916\) −18.4117 18.4117i −0.608341 0.608341i
\(917\) 35.5369 1.17353
\(918\) 26.8791 + 8.88004i 0.887143 + 0.293085i
\(919\) 11.6218 0.383368 0.191684 0.981457i \(-0.438605\pi\)
0.191684 + 0.981457i \(0.438605\pi\)
\(920\) 0.983215 + 0.983215i 0.0324156 + 0.0324156i
\(921\) −1.81836 + 0.753191i −0.0599171 + 0.0248185i
\(922\) 25.3837i 0.835966i
\(923\) −4.83880 11.6819i −0.159271 0.384515i
\(924\) 0.182692 + 0.0756735i 0.00601012 + 0.00248947i
\(925\) −0.128945 + 0.311301i −0.00423968 + 0.0102355i
\(926\) −32.0803 + 32.0803i −1.05422 + 1.05422i
\(927\) 12.3514 12.3514i 0.405674 0.405674i
\(928\) −1.00428 + 2.42455i −0.0329672 + 0.0795899i
\(929\) −4.65849 1.92961i −0.152840 0.0633085i 0.304952 0.952368i \(-0.401360\pi\)
−0.457792 + 0.889059i \(0.651360\pi\)
\(930\) −0.658082 1.58875i −0.0215794 0.0520972i
\(931\) 92.6904i 3.03781i
\(932\) 3.56326 1.47595i 0.116718 0.0483464i
\(933\) 9.97085 + 9.97085i 0.326431 + 0.326431i
\(934\) 40.2520 1.31709
\(935\) 0.141391 0.163907i 0.00462398 0.00536034i
\(936\) −10.2003 −0.333406
\(937\) 24.6863 + 24.6863i 0.806465 + 0.806465i 0.984097 0.177632i \(-0.0568437\pi\)
−0.177632 + 0.984097i \(0.556844\pi\)
\(938\) −6.63574 + 2.74861i −0.216665 + 0.0897454i
\(939\) 5.82351i 0.190043i
\(940\) 2.95898 + 7.14360i 0.0965112 + 0.232999i
\(941\) 10.2169 + 4.23196i 0.333060 + 0.137958i 0.542945 0.839768i \(-0.317309\pi\)
−0.209885 + 0.977726i \(0.567309\pi\)
\(942\) 4.47450 10.8024i 0.145787 0.351961i
\(943\) 4.85738 4.85738i 0.158178 0.158178i
\(944\) 17.7778 17.7778i 0.578619 0.578619i
\(945\) 6.31728 15.2513i 0.205501 0.496123i
\(946\) 0.875434 + 0.362616i 0.0284628 + 0.0117897i
\(947\) 4.39774 + 10.6171i 0.142907 + 0.345008i 0.979086 0.203449i \(-0.0652152\pi\)
−0.836178 + 0.548458i \(0.815215\pi\)
\(948\) 8.66000i 0.281264i
\(949\) 15.0657 6.24040i 0.489052 0.202572i
\(950\) 9.98602 + 9.98602i 0.323989 + 0.323989i
\(951\) −14.5094 −0.470500
\(952\) −7.49414 + 22.6841i −0.242887 + 0.735196i
\(953\) −0.704896 −0.0228338 −0.0114169 0.999935i \(-0.503634\pi\)
−0.0114169 + 0.999935i \(0.503634\pi\)
\(954\) −38.9205 38.9205i −1.26010 1.26010i
\(955\) −2.84607 + 1.17888i −0.0920966 + 0.0381477i
\(956\) 6.23035i 0.201504i
\(957\) −0.00581524 0.0140392i −0.000187980 0.000453824i
\(958\) −44.6282 18.4856i −1.44187 0.597243i
\(959\) −3.71176 + 8.96097i −0.119859 + 0.289365i
\(960\) 0.680780 0.680780i 0.0219721 0.0219721i
\(961\) −20.5653 + 20.5653i −0.663397 + 0.663397i
\(962\) −0.704397 + 1.70057i −0.0227107 + 0.0548284i
\(963\) −34.4112 14.2536i −1.10889 0.459316i
\(964\) 0.801919 + 1.93600i 0.0258281 + 0.0623545i
\(965\) 20.6419i 0.664486i
\(966\) −5.19237 + 2.15075i −0.167062 + 0.0691993i
\(967\) 28.2521 + 28.2521i 0.908527 + 0.908527i 0.996153 0.0876267i \(-0.0279283\pi\)
−0.0876267 + 0.996153i \(0.527928\pi\)
\(968\) 14.6755 0.471688
\(969\) 9.97281 + 19.8132i 0.320373 + 0.636492i
\(970\) 34.7149 1.11463
\(971\) 30.5851 + 30.5851i 0.981521 + 0.981521i 0.999832 0.0183111i \(-0.00582892\pi\)
−0.0183111 + 0.999832i \(0.505829\pi\)
\(972\) 17.2673 7.15235i 0.553849 0.229412i
\(973\) 85.6915i 2.74714i
\(974\) 15.9953 + 38.6161i 0.512523 + 1.23734i
\(975\) 1.92260 + 0.796365i 0.0615723 + 0.0255041i
\(976\) −11.2686 + 27.2049i −0.360700 + 0.870807i
\(977\) −34.5543 + 34.5543i −1.10549 + 1.10549i −0.111753 + 0.993736i \(0.535647\pi\)
−0.993736 + 0.111753i \(0.964353\pi\)
\(978\) 10.9321 10.9321i 0.349571 0.349571i
\(979\) −0.205249 + 0.495514i −0.00655977 + 0.0158367i
\(980\) −13.8084 5.71961i −0.441092 0.182706i
\(981\) −4.59137 11.0845i −0.146591 0.353902i
\(982\) 14.0671i 0.448898i
\(983\) −45.1621 + 18.7068i −1.44045 + 0.596653i −0.959907 0.280318i \(-0.909560\pi\)
−0.480542 + 0.876972i \(0.659560\pi\)
\(984\) 4.27949 + 4.27949i 0.136425 + 0.136425i
\(985\) 18.2365 0.581063
\(986\) −2.79829 + 1.40850i −0.0891158 + 0.0448557i
\(987\) 18.3146 0.582961
\(988\) 21.0948 + 21.0948i 0.671114 + 0.671114i
\(989\) −9.62140 + 3.98531i −0.305943 + 0.126726i
\(990\) 0.239555i 0.00761356i
\(991\) 5.56191 + 13.4276i 0.176680 + 0.426543i 0.987266 0.159076i \(-0.0508515\pi\)
−0.810586 + 0.585619i \(0.800851\pi\)
\(992\) 7.97684 + 3.30411i 0.253265 + 0.104906i
\(993\) 4.00834 9.67699i 0.127201 0.307090i
\(994\) −23.1743 + 23.1743i −0.735044 + 0.735044i
\(995\) −18.8569 + 18.8569i −0.597803 + 0.597803i
\(996\) 2.16779 5.23350i 0.0686890 0.165830i
\(997\) −40.8392 16.9161i −1.29339 0.535740i −0.373396 0.927672i \(-0.621807\pi\)
−0.919994 + 0.391933i \(0.871807\pi\)
\(998\) 6.07971 + 14.6777i 0.192450 + 0.464615i
\(999\) 1.28107i 0.0405312i
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 85.2.l.a.36.2 yes 24
3.2 odd 2 765.2.be.b.631.5 24
5.2 odd 4 425.2.n.c.274.5 24
5.3 odd 4 425.2.n.f.274.2 24
5.4 even 2 425.2.m.b.376.5 24
17.3 odd 16 1445.2.a.p.1.3 12
17.5 odd 16 1445.2.d.j.866.19 24
17.9 even 8 inner 85.2.l.a.26.2 24
17.12 odd 16 1445.2.d.j.866.20 24
17.14 odd 16 1445.2.a.q.1.3 12
51.26 odd 8 765.2.be.b.451.5 24
85.9 even 8 425.2.m.b.26.5 24
85.14 odd 16 7225.2.a.bq.1.10 12
85.43 odd 8 425.2.n.c.349.5 24
85.54 odd 16 7225.2.a.bs.1.10 12
85.77 odd 8 425.2.n.f.349.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
85.2.l.a.26.2 24 17.9 even 8 inner
85.2.l.a.36.2 yes 24 1.1 even 1 trivial
425.2.m.b.26.5 24 85.9 even 8
425.2.m.b.376.5 24 5.4 even 2
425.2.n.c.274.5 24 5.2 odd 4
425.2.n.c.349.5 24 85.43 odd 8
425.2.n.f.274.2 24 5.3 odd 4
425.2.n.f.349.2 24 85.77 odd 8
765.2.be.b.451.5 24 51.26 odd 8
765.2.be.b.631.5 24 3.2 odd 2
1445.2.a.p.1.3 12 17.3 odd 16
1445.2.a.q.1.3 12 17.14 odd 16
1445.2.d.j.866.19 24 17.5 odd 16
1445.2.d.j.866.20 24 17.12 odd 16
7225.2.a.bq.1.10 12 85.14 odd 16
7225.2.a.bs.1.10 12 85.54 odd 16