Properties

Label 390.2.bh.c.11.4
Level $390$
Weight $2$
Character 390.11
Analytic conductor $3.114$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [390,2,Mod(11,390)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(390, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("390.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.bh (of order \(12\), 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: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 11.4
Character \(\chi\) \(=\) 390.11
Dual form 390.2.bh.c.71.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965926 - 0.258819i) q^{2} +(0.888751 - 1.48665i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.24324 + 1.20597i) q^{6} +(0.431103 + 1.60890i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.42024 - 2.64252i) q^{9} +O(q^{10})\) \(q+(-0.965926 - 0.258819i) q^{2} +(0.888751 - 1.48665i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.24324 + 1.20597i) q^{6} +(0.431103 + 1.60890i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.42024 - 2.64252i) q^{9} +(0.866025 - 0.500000i) q^{10} +(0.985615 - 3.67836i) q^{11} +(1.51301 - 0.843099i) q^{12} +(2.83555 - 2.22703i) q^{13} -1.66565i q^{14} +(0.422776 + 1.67966i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.660987 - 1.14486i) q^{17} +(0.687914 + 2.92006i) q^{18} +(5.54438 - 1.48561i) q^{19} +(-0.965926 + 0.258819i) q^{20} +(2.77501 + 0.789012i) q^{21} +(-1.90406 + 3.29793i) q^{22} +(-3.32990 - 5.76756i) q^{23} +(-1.67966 + 0.422776i) q^{24} -1.00000i q^{25} +(-3.31533 + 1.41726i) q^{26} +(-5.19074 - 0.237145i) q^{27} +(-0.431103 + 1.60890i) q^{28} +(-1.32839 + 0.766948i) q^{29} +(0.0263575 - 1.73185i) q^{30} +(5.84819 + 5.84819i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-4.59246 - 4.73441i) q^{33} +(-0.934777 + 0.934777i) q^{34} +(-1.44250 - 0.832827i) q^{35} +(0.0912946 - 2.99861i) q^{36} +(-9.72471 - 2.60573i) q^{37} -5.73996 q^{38} +(-0.790720 - 6.19474i) q^{39} +1.00000 q^{40} +(4.33407 + 1.16131i) q^{41} +(-2.47624 - 1.48035i) q^{42} +(-6.30456 - 3.63994i) q^{43} +(2.69275 - 2.69275i) q^{44} +(2.87281 + 0.864281i) q^{45} +(1.72368 + 6.43288i) q^{46} +(9.18700 + 9.18700i) q^{47} +(1.73185 + 0.0263575i) q^{48} +(3.65947 - 2.11280i) q^{49} +(-0.258819 + 0.965926i) q^{50} +(-1.11455 - 2.00015i) q^{51} +(3.56917 - 0.510896i) q^{52} -0.302458i q^{53} +(4.95249 + 1.57253i) q^{54} +(1.90406 + 3.29793i) q^{55} +(0.832827 - 1.44250i) q^{56} +(2.71899 - 9.56288i) q^{57} +(1.48163 - 0.397002i) q^{58} +(-3.71613 + 0.995733i) q^{59} +(-0.473695 + 1.66602i) q^{60} +(2.23843 - 3.87708i) q^{61} +(-4.13529 - 7.16254i) q^{62} +(3.63928 - 3.42422i) q^{63} +1.00000i q^{64} +(-0.430282 + 3.57978i) q^{65} +(3.21062 + 5.76171i) q^{66} +(-0.0586497 + 0.218884i) q^{67} +(1.14486 - 0.660987i) q^{68} +(-11.5338 - 0.175536i) q^{69} +(1.17780 + 1.17780i) q^{70} +(3.95652 + 14.7659i) q^{71} +(-0.864281 + 2.87281i) q^{72} +(-0.682227 + 0.682227i) q^{73} +(8.71894 + 5.03388i) q^{74} +(-1.48665 - 0.888751i) q^{75} +(5.54438 + 1.48561i) q^{76} +6.34302 q^{77} +(-0.839539 + 6.18831i) q^{78} -8.02282 q^{79} +(-0.965926 - 0.258819i) q^{80} +(-4.96583 + 7.50604i) q^{81} +(-3.88582 - 2.24348i) q^{82} +(-8.80953 + 8.80953i) q^{83} +(2.00872 + 2.07081i) q^{84} +(0.342152 + 1.27693i) q^{85} +(5.14765 + 5.14765i) q^{86} +(-0.0404297 + 2.65648i) q^{87} +(-3.29793 + 1.90406i) q^{88} +(2.31981 - 8.65764i) q^{89} +(-2.55123 - 1.57837i) q^{90} +(4.80548 + 3.60202i) q^{91} -6.65980i q^{92} +(13.8918 - 3.49661i) q^{93} +(-6.49619 - 11.2517i) q^{94} +(-2.86998 + 4.97095i) q^{95} +(-1.66602 - 0.473695i) q^{96} +(-1.63135 + 0.437120i) q^{97} +(-4.08161 + 1.09366i) q^{98} +(-11.1200 + 2.61966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 8 q^{6} - 8 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 8 q^{6} - 8 q^{7} + 8 q^{9} + 8 q^{13} + 4 q^{15} + 20 q^{16} - 8 q^{18} - 16 q^{19} + 4 q^{21} - 8 q^{22} + 8 q^{24} - 48 q^{27} + 8 q^{28} + 36 q^{31} + 12 q^{33} + 16 q^{34} - 12 q^{36} - 64 q^{37} - 60 q^{39} + 40 q^{40} - 12 q^{42} + 8 q^{45} - 32 q^{46} + 48 q^{49} + 24 q^{52} - 28 q^{54} + 8 q^{55} - 76 q^{57} - 28 q^{58} + 4 q^{60} - 40 q^{61} + 80 q^{63} + 40 q^{66} - 28 q^{67} - 36 q^{69} + 16 q^{70} + 16 q^{72} + 8 q^{73} - 16 q^{76} - 28 q^{78} + 40 q^{79} + 12 q^{81} + 20 q^{84} + 44 q^{85} + 40 q^{87} + 12 q^{88} + 120 q^{91} - 8 q^{93} - 16 q^{94} + 4 q^{96} - 160 q^{97} - 96 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 0.258819i −0.683013 0.183013i
\(3\) 0.888751 1.48665i 0.513121 0.858316i
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) −0.707107 + 0.707107i −0.316228 + 0.316228i
\(6\) −1.24324 + 1.20597i −0.507551 + 0.492333i
\(7\) 0.431103 + 1.60890i 0.162942 + 0.608106i 0.998294 + 0.0583912i \(0.0185971\pi\)
−0.835352 + 0.549715i \(0.814736\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −1.42024 2.64252i −0.473414 0.880840i
\(10\) 0.866025 0.500000i 0.273861 0.158114i
\(11\) 0.985615 3.67836i 0.297174 1.10907i −0.642301 0.766452i \(-0.722020\pi\)
0.939475 0.342616i \(-0.111313\pi\)
\(12\) 1.51301 0.843099i 0.436767 0.243382i
\(13\) 2.83555 2.22703i 0.786439 0.617668i
\(14\) 1.66565i 0.445165i
\(15\) 0.422776 + 1.67966i 0.109160 + 0.433687i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 0.660987 1.14486i 0.160313 0.277670i −0.774668 0.632368i \(-0.782083\pi\)
0.934981 + 0.354698i \(0.115416\pi\)
\(18\) 0.687914 + 2.92006i 0.162143 + 0.688266i
\(19\) 5.54438 1.48561i 1.27197 0.340823i 0.441183 0.897417i \(-0.354559\pi\)
0.830785 + 0.556594i \(0.187892\pi\)
\(20\) −0.965926 + 0.258819i −0.215988 + 0.0578737i
\(21\) 2.77501 + 0.789012i 0.605556 + 0.172177i
\(22\) −1.90406 + 3.29793i −0.405947 + 0.703121i
\(23\) −3.32990 5.76756i −0.694333 1.20262i −0.970405 0.241482i \(-0.922366\pi\)
0.276073 0.961137i \(-0.410967\pi\)
\(24\) −1.67966 + 0.422776i −0.342859 + 0.0862989i
\(25\) 1.00000i 0.200000i
\(26\) −3.31533 + 1.41726i −0.650189 + 0.277947i
\(27\) −5.19074 0.237145i −0.998958 0.0456385i
\(28\) −0.431103 + 1.60890i −0.0814708 + 0.304053i
\(29\) −1.32839 + 0.766948i −0.246677 + 0.142419i −0.618242 0.785988i \(-0.712155\pi\)
0.371565 + 0.928407i \(0.378821\pi\)
\(30\) 0.0263575 1.73185i 0.00481221 0.316191i
\(31\) 5.84819 + 5.84819i 1.05037 + 1.05037i 0.998662 + 0.0517031i \(0.0164650\pi\)
0.0517031 + 0.998662i \(0.483535\pi\)
\(32\) −0.258819 0.965926i −0.0457532 0.170753i
\(33\) −4.59246 4.73441i −0.799445 0.824155i
\(34\) −0.934777 + 0.934777i −0.160313 + 0.160313i
\(35\) −1.44250 0.832827i −0.243827 0.140773i
\(36\) 0.0912946 2.99861i 0.0152158 0.499768i
\(37\) −9.72471 2.60573i −1.59873 0.428379i −0.654073 0.756432i \(-0.726941\pi\)
−0.944659 + 0.328052i \(0.893608\pi\)
\(38\) −5.73996 −0.931145
\(39\) −0.790720 6.19474i −0.126617 0.991952i
\(40\) 1.00000 0.158114
\(41\) 4.33407 + 1.16131i 0.676868 + 0.181366i 0.580847 0.814013i \(-0.302722\pi\)
0.0960213 + 0.995379i \(0.469388\pi\)
\(42\) −2.47624 1.48035i −0.382092 0.228423i
\(43\) −6.30456 3.63994i −0.961436 0.555085i −0.0648212 0.997897i \(-0.520648\pi\)
−0.896615 + 0.442812i \(0.853981\pi\)
\(44\) 2.69275 2.69275i 0.405947 0.405947i
\(45\) 2.87281 + 0.864281i 0.428253 + 0.128839i
\(46\) 1.72368 + 6.43288i 0.254143 + 0.948476i
\(47\) 9.18700 + 9.18700i 1.34006 + 1.34006i 0.895992 + 0.444070i \(0.146466\pi\)
0.444070 + 0.895992i \(0.353534\pi\)
\(48\) 1.73185 + 0.0263575i 0.249971 + 0.00380438i
\(49\) 3.65947 2.11280i 0.522782 0.301828i
\(50\) −0.258819 + 0.965926i −0.0366025 + 0.136603i
\(51\) −1.11455 2.00015i −0.156069 0.280077i
\(52\) 3.56917 0.510896i 0.494955 0.0708485i
\(53\) 0.302458i 0.0415458i −0.999784 0.0207729i \(-0.993387\pi\)
0.999784 0.0207729i \(-0.00661269\pi\)
\(54\) 4.95249 + 1.57253i 0.673949 + 0.213994i
\(55\) 1.90406 + 3.29793i 0.256744 + 0.444693i
\(56\) 0.832827 1.44250i 0.111291 0.192762i
\(57\) 2.71899 9.56288i 0.360140 1.26663i
\(58\) 1.48163 0.397002i 0.194548 0.0521289i
\(59\) −3.71613 + 0.995733i −0.483798 + 0.129633i −0.492471 0.870329i \(-0.663906\pi\)
0.00867240 + 0.999962i \(0.497239\pi\)
\(60\) −0.473695 + 1.66602i −0.0611538 + 0.215082i
\(61\) 2.23843 3.87708i 0.286602 0.496409i −0.686394 0.727229i \(-0.740808\pi\)
0.972996 + 0.230820i \(0.0741409\pi\)
\(62\) −4.13529 7.16254i −0.525183 0.909643i
\(63\) 3.63928 3.42422i 0.458506 0.431412i
\(64\) 1.00000i 0.125000i
\(65\) −0.430282 + 3.57978i −0.0533699 + 0.444018i
\(66\) 3.21062 + 5.76171i 0.395200 + 0.709217i
\(67\) −0.0586497 + 0.218884i −0.00716520 + 0.0267409i −0.969416 0.245424i \(-0.921073\pi\)
0.962251 + 0.272165i \(0.0877396\pi\)
\(68\) 1.14486 0.660987i 0.138835 0.0801564i
\(69\) −11.5338 0.175536i −1.38850 0.0211321i
\(70\) 1.17780 + 1.17780i 0.140773 + 0.140773i
\(71\) 3.95652 + 14.7659i 0.469553 + 1.75240i 0.641335 + 0.767261i \(0.278381\pi\)
−0.171782 + 0.985135i \(0.554953\pi\)
\(72\) −0.864281 + 2.87281i −0.101857 + 0.338564i
\(73\) −0.682227 + 0.682227i −0.0798487 + 0.0798487i −0.745903 0.666054i \(-0.767982\pi\)
0.666054 + 0.745903i \(0.267982\pi\)
\(74\) 8.71894 + 5.03388i 1.01356 + 0.585177i
\(75\) −1.48665 0.888751i −0.171663 0.102624i
\(76\) 5.54438 + 1.48561i 0.635984 + 0.170411i
\(77\) 6.34302 0.722854
\(78\) −0.839539 + 6.18831i −0.0950590 + 0.700688i
\(79\) −8.02282 −0.902638 −0.451319 0.892363i \(-0.649046\pi\)
−0.451319 + 0.892363i \(0.649046\pi\)
\(80\) −0.965926 0.258819i −0.107994 0.0289368i
\(81\) −4.96583 + 7.50604i −0.551758 + 0.834004i
\(82\) −3.88582 2.24348i −0.429117 0.247751i
\(83\) −8.80953 + 8.80953i −0.966972 + 0.966972i −0.999472 0.0324997i \(-0.989653\pi\)
0.0324997 + 0.999472i \(0.489653\pi\)
\(84\) 2.00872 + 2.07081i 0.219169 + 0.225944i
\(85\) 0.342152 + 1.27693i 0.0371116 + 0.138502i
\(86\) 5.14765 + 5.14765i 0.555085 + 0.555085i
\(87\) −0.0404297 + 2.65648i −0.00433452 + 0.284805i
\(88\) −3.29793 + 1.90406i −0.351561 + 0.202974i
\(89\) 2.31981 8.65764i 0.245899 0.917708i −0.727030 0.686606i \(-0.759100\pi\)
0.972929 0.231103i \(-0.0742334\pi\)
\(90\) −2.55123 1.57837i −0.268923 0.166375i
\(91\) 4.80548 + 3.60202i 0.503752 + 0.377595i
\(92\) 6.65980i 0.694333i
\(93\) 13.8918 3.49661i 1.44051 0.362581i
\(94\) −6.49619 11.2517i −0.670031 1.16053i
\(95\) −2.86998 + 4.97095i −0.294454 + 0.510009i
\(96\) −1.66602 0.473695i −0.170037 0.0483463i
\(97\) −1.63135 + 0.437120i −0.165639 + 0.0443828i −0.340685 0.940177i \(-0.610659\pi\)
0.175046 + 0.984560i \(0.443992\pi\)
\(98\) −4.08161 + 1.09366i −0.412305 + 0.110477i
\(99\) −11.1200 + 2.61966i −1.11760 + 0.263286i
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 3.60713 + 6.24773i 0.358923 + 0.621672i 0.987781 0.155848i \(-0.0498109\pi\)
−0.628859 + 0.777520i \(0.716478\pi\)
\(102\) 0.558899 + 2.22047i 0.0553393 + 0.219859i
\(103\) 14.1200i 1.39129i 0.718387 + 0.695643i \(0.244881\pi\)
−0.718387 + 0.695643i \(0.755119\pi\)
\(104\) −3.57978 0.430282i −0.351027 0.0421926i
\(105\) −2.52014 + 1.40431i −0.245941 + 0.137047i
\(106\) −0.0782818 + 0.292152i −0.00760340 + 0.0283763i
\(107\) 5.10228 2.94580i 0.493256 0.284781i −0.232668 0.972556i \(-0.574746\pi\)
0.725924 + 0.687775i \(0.241412\pi\)
\(108\) −4.37674 2.80074i −0.421152 0.269502i
\(109\) 7.40188 + 7.40188i 0.708971 + 0.708971i 0.966319 0.257348i \(-0.0828485\pi\)
−0.257348 + 0.966319i \(0.582849\pi\)
\(110\) −0.985615 3.67836i −0.0939747 0.350718i
\(111\) −12.5166 + 12.1414i −1.18803 + 1.15241i
\(112\) −1.17780 + 1.17780i −0.111291 + 0.111291i
\(113\) 9.89888 + 5.71512i 0.931208 + 0.537633i 0.887194 0.461398i \(-0.152652\pi\)
0.0440148 + 0.999031i \(0.485985\pi\)
\(114\) −5.10140 + 8.53330i −0.477790 + 0.799217i
\(115\) 6.43288 + 1.72368i 0.599869 + 0.160734i
\(116\) −1.53390 −0.142419
\(117\) −9.91214 4.33006i −0.916378 0.400314i
\(118\) 3.84722 0.354165
\(119\) 2.12692 + 0.569907i 0.194975 + 0.0522433i
\(120\) 0.888751 1.48665i 0.0811315 0.135712i
\(121\) −3.03264 1.75090i −0.275695 0.159173i
\(122\) −3.16562 + 3.16562i −0.286602 + 0.286602i
\(123\) 5.57837 5.41112i 0.502985 0.487904i
\(124\) 2.14059 + 7.98877i 0.192230 + 0.717413i
\(125\) 0.707107 + 0.707107i 0.0632456 + 0.0632456i
\(126\) −4.40152 + 2.36563i −0.392119 + 0.210747i
\(127\) −3.58413 + 2.06930i −0.318040 + 0.183621i −0.650519 0.759490i \(-0.725448\pi\)
0.332478 + 0.943111i \(0.392115\pi\)
\(128\) 0.258819 0.965926i 0.0228766 0.0853766i
\(129\) −11.0145 + 6.13765i −0.969772 + 0.540390i
\(130\) 1.34214 3.34644i 0.117713 0.293502i
\(131\) 4.18756i 0.365869i −0.983125 0.182935i \(-0.941440\pi\)
0.983125 0.182935i \(-0.0585597\pi\)
\(132\) −1.60998 6.39635i −0.140131 0.556731i
\(133\) 4.78040 + 8.27989i 0.414513 + 0.717958i
\(134\) 0.113303 0.196246i 0.00978785 0.0169531i
\(135\) 3.83809 3.50272i 0.330330 0.301466i
\(136\) −1.27693 + 0.342152i −0.109496 + 0.0293393i
\(137\) −11.6063 + 3.10990i −0.991593 + 0.265697i −0.717920 0.696126i \(-0.754906\pi\)
−0.273674 + 0.961823i \(0.588239\pi\)
\(138\) 11.0953 + 3.15472i 0.944499 + 0.268547i
\(139\) −1.87876 + 3.25411i −0.159354 + 0.276010i −0.934636 0.355606i \(-0.884275\pi\)
0.775282 + 0.631616i \(0.217608\pi\)
\(140\) −0.832827 1.44250i −0.0703867 0.121913i
\(141\) 21.8228 5.49287i 1.83781 0.462583i
\(142\) 15.2868i 1.28284i
\(143\) −5.39709 12.6252i −0.451327 1.05577i
\(144\) 1.57837 2.55123i 0.131531 0.212602i
\(145\) 0.397002 1.48163i 0.0329692 0.123043i
\(146\) 0.835555 0.482408i 0.0691510 0.0399243i
\(147\) 0.111376 7.31810i 0.00918616 0.603587i
\(148\) −7.11898 7.11898i −0.585177 0.585177i
\(149\) −0.101260 0.377907i −0.00829554 0.0309594i 0.961654 0.274265i \(-0.0884347\pi\)
−0.969950 + 0.243306i \(0.921768\pi\)
\(150\) 1.20597 + 1.24324i 0.0984667 + 0.101510i
\(151\) −13.6378 + 13.6378i −1.10983 + 1.10983i −0.116655 + 0.993172i \(0.537217\pi\)
−0.993172 + 0.116655i \(0.962783\pi\)
\(152\) −4.97095 2.86998i −0.403198 0.232786i
\(153\) −3.96409 0.120689i −0.320477 0.00975714i
\(154\) −6.12688 1.64169i −0.493718 0.132291i
\(155\) −8.27059 −0.664310
\(156\) 2.41258 5.76016i 0.193161 0.461182i
\(157\) 15.9176 1.27036 0.635180 0.772364i \(-0.280926\pi\)
0.635180 + 0.772364i \(0.280926\pi\)
\(158\) 7.74945 + 2.07646i 0.616513 + 0.165194i
\(159\) −0.449648 0.268810i −0.0356594 0.0213180i
\(160\) 0.866025 + 0.500000i 0.0684653 + 0.0395285i
\(161\) 7.84389 7.84389i 0.618185 0.618185i
\(162\) 6.73932 5.96502i 0.529491 0.468656i
\(163\) −3.45420 12.8913i −0.270554 1.00972i −0.958762 0.284209i \(-0.908269\pi\)
0.688208 0.725513i \(-0.258397\pi\)
\(164\) 3.17276 + 3.17276i 0.247751 + 0.247751i
\(165\) 6.59510 + 0.100373i 0.513428 + 0.00781401i
\(166\) 10.7894 6.22928i 0.837422 0.483486i
\(167\) 2.70988 10.1134i 0.209697 0.782599i −0.778270 0.627930i \(-0.783902\pi\)
0.987966 0.154669i \(-0.0494310\pi\)
\(168\) −1.40431 2.52014i −0.108345 0.194433i
\(169\) 3.08064 12.6297i 0.236972 0.971516i
\(170\) 1.32197i 0.101391i
\(171\) −11.8001 12.5412i −0.902378 0.959050i
\(172\) −3.63994 6.30456i −0.277543 0.480718i
\(173\) −4.64852 + 8.05147i −0.353420 + 0.612142i −0.986846 0.161661i \(-0.948315\pi\)
0.633426 + 0.773803i \(0.281648\pi\)
\(174\) 0.726600 2.55550i 0.0550834 0.193732i
\(175\) 1.60890 0.431103i 0.121621 0.0325883i
\(176\) 3.67836 0.985615i 0.277267 0.0742935i
\(177\) −1.82241 + 6.40953i −0.136981 + 0.481770i
\(178\) −4.48153 + 7.76223i −0.335905 + 0.581804i
\(179\) 7.73613 + 13.3994i 0.578226 + 1.00152i 0.995683 + 0.0928197i \(0.0295880\pi\)
−0.417457 + 0.908697i \(0.637079\pi\)
\(180\) 2.05578 + 2.18489i 0.153229 + 0.162852i
\(181\) 22.8979i 1.70199i −0.525173 0.850995i \(-0.676000\pi\)
0.525173 0.850995i \(-0.324000\pi\)
\(182\) −3.70947 4.72304i −0.274964 0.350095i
\(183\) −3.77444 6.77352i −0.279015 0.500713i
\(184\) −1.72368 + 6.43288i −0.127072 + 0.474238i
\(185\) 8.71894 5.03388i 0.641029 0.370098i
\(186\) −14.3234 0.217992i −1.05024 0.0159840i
\(187\) −3.55974 3.55974i −0.260314 0.260314i
\(188\) 3.36268 + 12.5497i 0.245248 + 0.915280i
\(189\) −1.85620 8.45360i −0.135019 0.614909i
\(190\) 4.05877 4.05877i 0.294454 0.294454i
\(191\) −6.68706 3.86078i −0.483859 0.279356i 0.238164 0.971225i \(-0.423454\pi\)
−0.722023 + 0.691869i \(0.756788\pi\)
\(192\) 1.48665 + 0.888751i 0.107290 + 0.0641401i
\(193\) −6.17479 1.65453i −0.444471 0.119096i 0.0296403 0.999561i \(-0.490564\pi\)
−0.474111 + 0.880465i \(0.657230\pi\)
\(194\) 1.68890 0.121256
\(195\) 4.93946 + 3.82122i 0.353722 + 0.273643i
\(196\) 4.22560 0.301828
\(197\) 14.1811 + 3.79982i 1.01036 + 0.270726i 0.725781 0.687925i \(-0.241478\pi\)
0.284582 + 0.958652i \(0.408145\pi\)
\(198\) 11.4191 + 0.347661i 0.811518 + 0.0247072i
\(199\) −2.52204 1.45610i −0.178782 0.103220i 0.407938 0.913010i \(-0.366248\pi\)
−0.586720 + 0.809790i \(0.699581\pi\)
\(200\) −0.707107 + 0.707107i −0.0500000 + 0.0500000i
\(201\) 0.273278 + 0.281725i 0.0192755 + 0.0198713i
\(202\) −1.86719 6.96843i −0.131375 0.490297i
\(203\) −1.80662 1.80662i −0.126800 0.126800i
\(204\) 0.0348440 2.28946i 0.00243957 0.160294i
\(205\) −3.88582 + 2.24348i −0.271397 + 0.156691i
\(206\) 3.65453 13.6389i 0.254623 0.950266i
\(207\) −10.5116 + 16.9907i −0.730609 + 1.18093i
\(208\) 3.34644 + 1.34214i 0.232034 + 0.0930605i
\(209\) 21.8585i 1.51198i
\(210\) 2.79773 0.704199i 0.193062 0.0485944i
\(211\) 3.43660 + 5.95236i 0.236585 + 0.409777i 0.959732 0.280917i \(-0.0906384\pi\)
−0.723147 + 0.690694i \(0.757305\pi\)
\(212\) 0.151229 0.261936i 0.0103864 0.0179898i
\(213\) 25.4681 + 7.24130i 1.74505 + 0.496166i
\(214\) −5.69085 + 1.52486i −0.389019 + 0.104237i
\(215\) 7.03182 1.88417i 0.479566 0.128499i
\(216\) 3.50272 + 3.83809i 0.238330 + 0.261149i
\(217\) −6.88797 + 11.9303i −0.467586 + 0.809882i
\(218\) −5.23392 9.06541i −0.354486 0.613987i
\(219\) 0.407901 + 1.62056i 0.0275634 + 0.109507i
\(220\) 3.80812i 0.256744i
\(221\) −0.675391 4.71835i −0.0454317 0.317391i
\(222\) 15.2326 8.48812i 1.02234 0.569685i
\(223\) 0.408906 1.52606i 0.0273824 0.102192i −0.950882 0.309553i \(-0.899821\pi\)
0.978265 + 0.207360i \(0.0664873\pi\)
\(224\) 1.44250 0.832827i 0.0963810 0.0556456i
\(225\) −2.64252 + 1.42024i −0.176168 + 0.0946828i
\(226\) −8.08240 8.08240i −0.537633 0.537633i
\(227\) 1.72914 + 6.45324i 0.114767 + 0.428317i 0.999269 0.0382192i \(-0.0121685\pi\)
−0.884502 + 0.466536i \(0.845502\pi\)
\(228\) 7.13616 6.92220i 0.472604 0.458434i
\(229\) 16.0756 16.0756i 1.06230 1.06230i 0.0643787 0.997926i \(-0.479493\pi\)
0.997926 0.0643787i \(-0.0205066\pi\)
\(230\) −5.76756 3.32990i −0.380302 0.219567i
\(231\) 5.63736 9.42983i 0.370911 0.620437i
\(232\) 1.48163 + 0.397002i 0.0972738 + 0.0260644i
\(233\) −20.9127 −1.37004 −0.685018 0.728526i \(-0.740206\pi\)
−0.685018 + 0.728526i \(0.740206\pi\)
\(234\) 8.45369 + 6.74797i 0.552635 + 0.441128i
\(235\) −12.9924 −0.847530
\(236\) −3.71613 0.995733i −0.241899 0.0648167i
\(237\) −7.13029 + 11.9271i −0.463162 + 0.774749i
\(238\) −1.90695 1.10098i −0.123609 0.0713657i
\(239\) 2.33729 2.33729i 0.151186 0.151186i −0.627461 0.778648i \(-0.715906\pi\)
0.778648 + 0.627461i \(0.215906\pi\)
\(240\) −1.24324 + 1.20597i −0.0802508 + 0.0778447i
\(241\) 2.66309 + 9.93879i 0.171545 + 0.640214i 0.997114 + 0.0759136i \(0.0241873\pi\)
−0.825570 + 0.564300i \(0.809146\pi\)
\(242\) 2.47614 + 2.47614i 0.159173 + 0.159173i
\(243\) 6.74544 + 14.0534i 0.432720 + 0.901528i
\(244\) 3.87708 2.23843i 0.248205 0.143301i
\(245\) −1.09366 + 4.08161i −0.0698717 + 0.260765i
\(246\) −6.78879 + 3.78295i −0.432837 + 0.241192i
\(247\) 12.4128 16.5600i 0.789810 1.05369i
\(248\) 8.27059i 0.525183i
\(249\) 5.26719 + 20.9262i 0.333794 + 1.32614i
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) −11.4780 + 19.8805i −0.724485 + 1.25485i 0.234700 + 0.972068i \(0.424589\pi\)
−0.959186 + 0.282777i \(0.908744\pi\)
\(252\) 4.86382 1.14583i 0.306392 0.0721803i
\(253\) −24.4972 + 6.56400i −1.54012 + 0.412675i
\(254\) 3.99758 1.07115i 0.250831 0.0672098i
\(255\) 2.20243 + 0.626213i 0.137922 + 0.0392150i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −2.27804 3.94568i −0.142100 0.246125i 0.786187 0.617989i \(-0.212052\pi\)
−0.928287 + 0.371864i \(0.878719\pi\)
\(258\) 12.2277 3.07776i 0.761265 0.191613i
\(259\) 16.7694i 1.04200i
\(260\) −2.16253 + 2.88504i −0.134114 + 0.178923i
\(261\) 3.91332 + 2.42106i 0.242228 + 0.149860i
\(262\) −1.08382 + 4.04488i −0.0669587 + 0.249893i
\(263\) −12.3668 + 7.13996i −0.762568 + 0.440269i −0.830217 0.557441i \(-0.811783\pi\)
0.0676492 + 0.997709i \(0.478450\pi\)
\(264\) −0.100373 + 6.59510i −0.00617751 + 0.405900i
\(265\) 0.213870 + 0.213870i 0.0131379 + 0.0131379i
\(266\) −2.47452 9.23502i −0.151722 0.566235i
\(267\) −10.8091 11.1432i −0.661508 0.681955i
\(268\) −0.160234 + 0.160234i −0.00978785 + 0.00978785i
\(269\) −15.2218 8.78829i −0.928087 0.535831i −0.0418811 0.999123i \(-0.513335\pi\)
−0.886206 + 0.463291i \(0.846668\pi\)
\(270\) −4.61388 + 2.39000i −0.280792 + 0.145451i
\(271\) −27.7623 7.43888i −1.68644 0.451879i −0.716971 0.697103i \(-0.754472\pi\)
−0.969467 + 0.245224i \(0.921139\pi\)
\(272\) 1.32197 0.0801564
\(273\) 9.62582 3.94276i 0.582581 0.238627i
\(274\) 12.0157 0.725897
\(275\) −3.67836 0.985615i −0.221814 0.0594348i
\(276\) −9.90078 5.91891i −0.595957 0.356277i
\(277\) 12.2976 + 7.10003i 0.738892 + 0.426600i 0.821666 0.569969i \(-0.193045\pi\)
−0.0827742 + 0.996568i \(0.526378\pi\)
\(278\) 2.65697 2.65697i 0.159354 0.159354i
\(279\) 7.14811 23.7598i 0.427946 1.42246i
\(280\) 0.431103 + 1.60890i 0.0257633 + 0.0961501i
\(281\) −4.41645 4.41645i −0.263463 0.263463i 0.562996 0.826460i \(-0.309649\pi\)
−0.826460 + 0.562996i \(0.809649\pi\)
\(282\) −22.5009 0.342447i −1.33991 0.0203924i
\(283\) 14.6603 8.46410i 0.871462 0.503139i 0.00362808 0.999993i \(-0.498845\pi\)
0.867834 + 0.496855i \(0.165512\pi\)
\(284\) −3.95652 + 14.7659i −0.234777 + 0.876198i
\(285\) 4.83936 + 8.68459i 0.286659 + 0.514431i
\(286\) 1.94555 + 13.5918i 0.115043 + 0.803702i
\(287\) 7.47372i 0.441160i
\(288\) −2.18489 + 2.05578i −0.128746 + 0.121138i
\(289\) 7.62619 + 13.2090i 0.448600 + 0.776997i
\(290\) −0.766948 + 1.32839i −0.0450368 + 0.0780060i
\(291\) −0.800025 + 2.81374i −0.0468983 + 0.164944i
\(292\) −0.931940 + 0.249713i −0.0545377 + 0.0146133i
\(293\) −10.8549 + 2.90856i −0.634149 + 0.169920i −0.561552 0.827442i \(-0.689795\pi\)
−0.0725974 + 0.997361i \(0.523129\pi\)
\(294\) −2.00164 + 7.03992i −0.116738 + 0.410576i
\(295\) 1.92361 3.33179i 0.111997 0.193984i
\(296\) 5.03388 + 8.71894i 0.292588 + 0.506778i
\(297\) −5.98837 + 18.8597i −0.347481 + 1.09435i
\(298\) 0.391239i 0.0226638i
\(299\) −22.2866 8.93837i −1.28887 0.516919i
\(300\) −0.843099 1.51301i −0.0486763 0.0873534i
\(301\) 3.13838 11.7126i 0.180893 0.675102i
\(302\) 16.7028 9.64337i 0.961139 0.554914i
\(303\) 12.4940 + 0.190150i 0.717762 + 0.0109238i
\(304\) 4.05877 + 4.05877i 0.232786 + 0.232786i
\(305\) 1.15870 + 4.32432i 0.0663469 + 0.247610i
\(306\) 3.79778 + 1.14256i 0.217104 + 0.0653157i
\(307\) −20.4845 + 20.4845i −1.16911 + 1.16911i −0.186694 + 0.982418i \(0.559777\pi\)
−0.982418 + 0.186694i \(0.940223\pi\)
\(308\) 5.49321 + 3.17151i 0.313005 + 0.180713i
\(309\) 20.9915 + 12.5492i 1.19416 + 0.713898i
\(310\) 7.98877 + 2.14059i 0.453732 + 0.121577i
\(311\) 8.83372 0.500914 0.250457 0.968128i \(-0.419419\pi\)
0.250457 + 0.968128i \(0.419419\pi\)
\(312\) −3.82122 + 4.93946i −0.216334 + 0.279642i
\(313\) −20.4565 −1.15627 −0.578135 0.815941i \(-0.696219\pi\)
−0.578135 + 0.815941i \(0.696219\pi\)
\(314\) −15.3752 4.11977i −0.867673 0.232492i
\(315\) −0.152065 + 4.99465i −0.00856791 + 0.281417i
\(316\) −6.94796 4.01141i −0.390854 0.225659i
\(317\) 14.7971 14.7971i 0.831089 0.831089i −0.156577 0.987666i \(-0.550046\pi\)
0.987666 + 0.156577i \(0.0500460\pi\)
\(318\) 0.364754 + 0.376028i 0.0204544 + 0.0210866i
\(319\) 1.51183 + 5.64223i 0.0846463 + 0.315904i
\(320\) −0.707107 0.707107i −0.0395285 0.0395285i
\(321\) 0.155288 10.2034i 0.00866734 0.569497i
\(322\) −9.60676 + 5.54646i −0.535364 + 0.309092i
\(323\) 1.96394 7.32953i 0.109277 0.407826i
\(324\) −8.05355 + 4.01750i −0.447419 + 0.223195i
\(325\) −2.22703 2.83555i −0.123534 0.157288i
\(326\) 13.3460i 0.739168i
\(327\) 17.5824 4.42555i 0.972310 0.244734i
\(328\) −2.24348 3.88582i −0.123875 0.214559i
\(329\) −10.8204 + 18.7415i −0.596549 + 1.03325i
\(330\) −6.34440 1.80389i −0.349248 0.0993009i
\(331\) −26.8683 + 7.19933i −1.47681 + 0.395711i −0.905261 0.424855i \(-0.860325\pi\)
−0.571551 + 0.820566i \(0.693658\pi\)
\(332\) −12.0340 + 3.22451i −0.660454 + 0.176968i
\(333\) 6.92575 + 29.3985i 0.379529 + 1.61103i
\(334\) −5.23508 + 9.06743i −0.286451 + 0.496148i
\(335\) −0.113303 0.196246i −0.00619038 0.0107221i
\(336\) 0.704199 + 2.79773i 0.0384172 + 0.152629i
\(337\) 5.59425i 0.304738i −0.988324 0.152369i \(-0.951310\pi\)
0.988324 0.152369i \(-0.0486903\pi\)
\(338\) −6.24448 + 11.4020i −0.339655 + 0.620189i
\(339\) 17.2940 9.63682i 0.939282 0.523400i
\(340\) −0.342152 + 1.27693i −0.0185558 + 0.0692512i
\(341\) 27.2758 15.7477i 1.47707 0.852786i
\(342\) 8.15214 + 15.1680i 0.440817 + 0.820190i
\(343\) 13.2215 + 13.2215i 0.713891 + 0.713891i
\(344\) 1.88417 + 7.03182i 0.101588 + 0.379130i
\(345\) 8.27974 8.03149i 0.445766 0.432401i
\(346\) 6.57400 6.57400i 0.353420 0.353420i
\(347\) 29.8164 + 17.2145i 1.60063 + 0.924122i 0.991362 + 0.131154i \(0.0418683\pi\)
0.609264 + 0.792967i \(0.291465\pi\)
\(348\) −1.36325 + 2.28036i −0.0730780 + 0.122240i
\(349\) −14.0346 3.76057i −0.751256 0.201298i −0.137181 0.990546i \(-0.543804\pi\)
−0.614075 + 0.789248i \(0.710471\pi\)
\(350\) −1.66565 −0.0890330
\(351\) −15.2467 + 10.8875i −0.813809 + 0.581133i
\(352\) −3.80812 −0.202974
\(353\) −9.59155 2.57005i −0.510507 0.136790i −0.00563473 0.999984i \(-0.501794\pi\)
−0.504872 + 0.863194i \(0.668460\pi\)
\(354\) 3.41922 5.71945i 0.181729 0.303986i
\(355\) −13.2388 7.64342i −0.702642 0.405670i
\(356\) 6.33783 6.33783i 0.335905 0.335905i
\(357\) 2.73756 2.65548i 0.144887 0.140543i
\(358\) −4.00452 14.9451i −0.211645 0.789871i
\(359\) 11.6427 + 11.6427i 0.614477 + 0.614477i 0.944109 0.329632i \(-0.106925\pi\)
−0.329632 + 0.944109i \(0.606925\pi\)
\(360\) −1.42024 2.64252i −0.0748533 0.139273i
\(361\) 12.0786 6.97359i 0.635717 0.367031i
\(362\) −5.92642 + 22.1177i −0.311486 + 1.16248i
\(363\) −5.29824 + 2.95236i −0.278085 + 0.154959i
\(364\) 2.36066 + 5.52219i 0.123732 + 0.289441i
\(365\) 0.964815i 0.0505007i
\(366\) 1.89271 + 7.51962i 0.0989337 + 0.393057i
\(367\) 2.43188 + 4.21213i 0.126943 + 0.219872i 0.922491 0.386019i \(-0.126150\pi\)
−0.795548 + 0.605891i \(0.792817\pi\)
\(368\) 3.32990 5.76756i 0.173583 0.300655i
\(369\) −3.08664 13.1022i −0.160684 0.682074i
\(370\) −9.72471 + 2.60573i −0.505564 + 0.135465i
\(371\) 0.486624 0.130390i 0.0252642 0.00676954i
\(372\) 13.7789 + 3.91774i 0.714405 + 0.203125i
\(373\) 18.2902 31.6796i 0.947031 1.64031i 0.195399 0.980724i \(-0.437400\pi\)
0.751632 0.659582i \(-0.229267\pi\)
\(374\) 2.51712 + 4.35978i 0.130157 + 0.225439i
\(375\) 1.67966 0.422776i 0.0867373 0.0218321i
\(376\) 12.9924i 0.670031i
\(377\) −2.05870 + 5.13310i −0.106028 + 0.264368i
\(378\) −0.395001 + 8.64597i −0.0203167 + 0.444701i
\(379\) −0.672900 + 2.51130i −0.0345646 + 0.128997i −0.981052 0.193743i \(-0.937937\pi\)
0.946488 + 0.322740i \(0.104604\pi\)
\(380\) −4.97095 + 2.86998i −0.255005 + 0.147227i
\(381\) −0.109083 + 7.16744i −0.00558851 + 0.367199i
\(382\) 5.45996 + 5.45996i 0.279356 + 0.279356i
\(383\) 1.94574 + 7.26162i 0.0994229 + 0.371051i 0.997653 0.0684745i \(-0.0218132\pi\)
−0.898230 + 0.439526i \(0.855147\pi\)
\(384\) −1.20597 1.24324i −0.0615417 0.0634439i
\(385\) −4.48519 + 4.48519i −0.228586 + 0.228586i
\(386\) 5.53616 + 3.19630i 0.281783 + 0.162688i
\(387\) −0.664613 + 21.8295i −0.0337842 + 1.10966i
\(388\) −1.63135 0.437120i −0.0828195 0.0221914i
\(389\) 3.37539 0.171139 0.0855694 0.996332i \(-0.472729\pi\)
0.0855694 + 0.996332i \(0.472729\pi\)
\(390\) −3.78215 4.96944i −0.191517 0.251637i
\(391\) −8.80409 −0.445242
\(392\) −4.08161 1.09366i −0.206153 0.0552384i
\(393\) −6.22543 3.72170i −0.314032 0.187735i
\(394\) −12.7145 7.34069i −0.640545 0.369819i
\(395\) 5.67299 5.67299i 0.285439 0.285439i
\(396\) −10.9400 3.29129i −0.549756 0.165394i
\(397\) 0.728848 + 2.72010i 0.0365798 + 0.136518i 0.981801 0.189913i \(-0.0608206\pi\)
−0.945221 + 0.326431i \(0.894154\pi\)
\(398\) 2.05923 + 2.05923i 0.103220 + 0.103220i
\(399\) 16.5579 + 0.251999i 0.828930 + 0.0126157i
\(400\) 0.866025 0.500000i 0.0433013 0.0250000i
\(401\) 8.32881 31.0836i 0.415921 1.55224i −0.367062 0.930196i \(-0.619636\pi\)
0.782984 0.622042i \(-0.213697\pi\)
\(402\) −0.191051 0.342855i −0.00952873 0.0171000i
\(403\) 29.6069 + 3.55869i 1.47483 + 0.177271i
\(404\) 7.21425i 0.358923i
\(405\) −1.79620 8.81894i −0.0892539 0.438217i
\(406\) 1.27747 + 2.21264i 0.0633998 + 0.109812i
\(407\) −19.1696 + 33.2028i −0.950203 + 1.64580i
\(408\) −0.626213 + 2.20243i −0.0310022 + 0.109037i
\(409\) −2.65386 + 0.711101i −0.131225 + 0.0351617i −0.323834 0.946114i \(-0.604972\pi\)
0.192609 + 0.981276i \(0.438305\pi\)
\(410\) 4.33407 1.16131i 0.214044 0.0573530i
\(411\) −5.69179 + 20.0184i −0.280755 + 0.987435i
\(412\) −7.06001 + 12.2283i −0.347822 + 0.602445i
\(413\) −3.20407 5.54960i −0.157662 0.273078i
\(414\) 14.5510 13.6911i 0.715141 0.672881i
\(415\) 12.4586i 0.611567i
\(416\) −2.88504 2.16253i −0.141451 0.106027i
\(417\) 3.16796 + 5.68515i 0.155136 + 0.278403i
\(418\) −5.65739 + 21.1137i −0.276712 + 1.03270i
\(419\) 12.3545 7.13285i 0.603555 0.348463i −0.166884 0.985977i \(-0.553371\pi\)
0.770439 + 0.637514i \(0.220037\pi\)
\(420\) −2.88466 0.0439025i −0.140757 0.00214222i
\(421\) −23.2751 23.2751i −1.13436 1.13436i −0.989444 0.144916i \(-0.953709\pi\)
−0.144916 0.989444i \(-0.546291\pi\)
\(422\) −1.77891 6.63900i −0.0865962 0.323181i
\(423\) 11.2291 37.3246i 0.545976 1.81478i
\(424\) −0.213870 + 0.213870i −0.0103864 + 0.0103864i
\(425\) −1.14486 0.660987i −0.0555340 0.0320626i
\(426\) −22.7261 13.5862i −1.10108 0.658253i
\(427\) 7.20282 + 1.92999i 0.348569 + 0.0933988i
\(428\) 5.89160 0.284781
\(429\) −23.5658 3.19707i −1.13777 0.154356i
\(430\) −7.27987 −0.351067
\(431\) 26.6309 + 7.13573i 1.28277 + 0.343716i 0.834909 0.550389i \(-0.185520\pi\)
0.447858 + 0.894105i \(0.352187\pi\)
\(432\) −2.39000 4.61388i −0.114989 0.221986i
\(433\) 7.32263 + 4.22772i 0.351903 + 0.203171i 0.665523 0.746377i \(-0.268208\pi\)
−0.313620 + 0.949549i \(0.601542\pi\)
\(434\) 9.74106 9.74106i 0.467586 0.467586i
\(435\) −1.84983 1.90700i −0.0886924 0.0914338i
\(436\) 2.70928 + 10.1112i 0.129751 + 0.484236i
\(437\) −27.0306 27.0306i −1.29305 1.29305i
\(438\) 0.0254302 1.67092i 0.00121510 0.0798394i
\(439\) 10.9300 6.31042i 0.521659 0.301180i −0.215954 0.976404i \(-0.569286\pi\)
0.737613 + 0.675224i \(0.235953\pi\)
\(440\) 0.985615 3.67836i 0.0469873 0.175359i
\(441\) −10.7804 6.66955i −0.513355 0.317598i
\(442\) −0.568822 + 4.73238i −0.0270561 + 0.225096i
\(443\) 28.5436i 1.35615i −0.734994 0.678074i \(-0.762815\pi\)
0.734994 0.678074i \(-0.237185\pi\)
\(444\) −16.9104 + 4.25641i −0.802533 + 0.202000i
\(445\) 4.48153 + 7.76223i 0.212445 + 0.367965i
\(446\) −0.789946 + 1.36823i −0.0374050 + 0.0647874i
\(447\) −0.651810 0.185328i −0.0308296 0.00876571i
\(448\) −1.60890 + 0.431103i −0.0760133 + 0.0203677i
\(449\) 28.8338 7.72600i 1.36075 0.364612i 0.496659 0.867946i \(-0.334560\pi\)
0.864092 + 0.503333i \(0.167893\pi\)
\(450\) 2.92006 0.687914i 0.137653 0.0324286i
\(451\) 8.54344 14.7977i 0.402295 0.696795i
\(452\) 5.71512 + 9.89888i 0.268817 + 0.465604i
\(453\) 8.15398 + 32.3952i 0.383107 + 1.52206i
\(454\) 6.68089i 0.313550i
\(455\) −5.94501 + 0.850975i −0.278706 + 0.0398943i
\(456\) −8.68459 + 4.83936i −0.406693 + 0.226624i
\(457\) −8.25749 + 30.8174i −0.386269 + 1.44158i 0.449887 + 0.893085i \(0.351464\pi\)
−0.836157 + 0.548491i \(0.815203\pi\)
\(458\) −19.6885 + 11.3672i −0.919982 + 0.531152i
\(459\) −3.70251 + 5.78593i −0.172818 + 0.270064i
\(460\) 4.70919 + 4.70919i 0.219567 + 0.219567i
\(461\) 2.90972 + 10.8592i 0.135519 + 0.505764i 0.999995 + 0.00309039i \(0.000983704\pi\)
−0.864476 + 0.502674i \(0.832350\pi\)
\(462\) −7.88589 + 7.64946i −0.366885 + 0.355885i
\(463\) 9.47819 9.47819i 0.440489 0.440489i −0.451687 0.892176i \(-0.649178\pi\)
0.892176 + 0.451687i \(0.149178\pi\)
\(464\) −1.32839 0.766948i −0.0616691 0.0356047i
\(465\) −7.35050 + 12.2954i −0.340871 + 0.570188i
\(466\) 20.2001 + 5.41260i 0.935752 + 0.250734i
\(467\) 13.7987 0.638528 0.319264 0.947666i \(-0.396564\pi\)
0.319264 + 0.947666i \(0.396564\pi\)
\(468\) −6.41914 8.70601i −0.296725 0.402436i
\(469\) −0.377446 −0.0174288
\(470\) 12.5497 + 3.36268i 0.578874 + 0.155109i
\(471\) 14.1468 23.6638i 0.651849 1.09037i
\(472\) 3.33179 + 1.92361i 0.153358 + 0.0885412i
\(473\) −19.6029 + 19.6029i −0.901341 + 0.901341i
\(474\) 9.97429 9.67524i 0.458134 0.444399i
\(475\) −1.48561 5.54438i −0.0681646 0.254394i
\(476\) 1.55701 + 1.55701i 0.0713657 + 0.0713657i
\(477\) −0.799251 + 0.429563i −0.0365952 + 0.0196683i
\(478\) −2.86258 + 1.65271i −0.130931 + 0.0755932i
\(479\) −8.00989 + 29.8933i −0.365981 + 1.36586i 0.500105 + 0.865965i \(0.333295\pi\)
−0.866086 + 0.499895i \(0.833372\pi\)
\(480\) 1.51301 0.843099i 0.0690589 0.0384820i
\(481\) −33.3779 + 14.2686i −1.52190 + 0.650592i
\(482\) 10.2894i 0.468669i
\(483\) −4.68983 18.6324i −0.213395 0.847802i
\(484\) −1.75090 3.03264i −0.0795863 0.137847i
\(485\) 0.844451 1.46263i 0.0383445 0.0664147i
\(486\) −2.87830 15.3204i −0.130562 0.694949i
\(487\) 27.8851 7.47178i 1.26359 0.338579i 0.436020 0.899937i \(-0.356388\pi\)
0.827573 + 0.561358i \(0.189721\pi\)
\(488\) −4.32432 + 1.15870i −0.195753 + 0.0524518i
\(489\) −22.2347 6.32194i −1.00549 0.285888i
\(490\) 2.11280 3.65947i 0.0954465 0.165318i
\(491\) −3.99952 6.92737i −0.180496 0.312628i 0.761554 0.648102i \(-0.224437\pi\)
−0.942049 + 0.335474i \(0.891104\pi\)
\(492\) 7.53657 1.89698i 0.339775 0.0855225i
\(493\) 2.02777i 0.0913263i
\(494\) −16.2759 + 12.7831i −0.732289 + 0.575139i
\(495\) 6.01062 9.71538i 0.270157 0.436674i
\(496\) −2.14059 + 7.98877i −0.0961151 + 0.358707i
\(497\) −22.0512 + 12.7313i −0.989133 + 0.571076i
\(498\) 0.328377 21.5764i 0.0147149 0.966860i
\(499\) 15.4167 + 15.4167i 0.690144 + 0.690144i 0.962264 0.272119i \(-0.0877246\pi\)
−0.272119 + 0.962264i \(0.587725\pi\)
\(500\) 0.258819 + 0.965926i 0.0115747 + 0.0431975i
\(501\) −12.6267 13.0169i −0.564118 0.581554i
\(502\) 16.2323 16.2323i 0.724485 0.724485i
\(503\) −21.5869 12.4632i −0.962513 0.555707i −0.0655671 0.997848i \(-0.520886\pi\)
−0.896945 + 0.442141i \(0.854219\pi\)
\(504\) −4.99465 0.152065i −0.222479 0.00677352i
\(505\) −6.96843 1.86719i −0.310091 0.0830887i
\(506\) 25.3613 1.12745
\(507\) −16.0380 15.8045i −0.712273 0.701902i
\(508\) −4.13860 −0.183621
\(509\) 5.42645 + 1.45401i 0.240523 + 0.0644479i 0.377067 0.926186i \(-0.376933\pi\)
−0.136544 + 0.990634i \(0.543599\pi\)
\(510\) −1.96531 1.17491i −0.0870254 0.0520257i
\(511\) −1.39174 0.803524i −0.0615672 0.0355458i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −29.1317 + 6.39660i −1.28620 + 0.282417i
\(514\) 1.17920 + 4.40083i 0.0520123 + 0.194112i
\(515\) −9.98436 9.98436i −0.439963 0.439963i
\(516\) −12.6077 0.191880i −0.555021 0.00844703i
\(517\) 42.8480 24.7383i 1.88445 1.08799i
\(518\) −4.34024 + 16.1980i −0.190699 + 0.711699i
\(519\) 7.83832 + 14.0665i 0.344064 + 0.617449i
\(520\) 2.83555 2.22703i 0.124347 0.0976619i
\(521\) 12.8570i 0.563275i −0.959521 0.281637i \(-0.909122\pi\)
0.959521 0.281637i \(-0.0908775\pi\)
\(522\) −3.15336 3.35140i −0.138019 0.146687i
\(523\) 7.21582 + 12.4982i 0.315526 + 0.546507i 0.979549 0.201205i \(-0.0644858\pi\)
−0.664023 + 0.747712i \(0.731152\pi\)
\(524\) 2.09378 3.62654i 0.0914673 0.158426i
\(525\) 0.789012 2.77501i 0.0344353 0.121111i
\(526\) 13.7933 3.69591i 0.601418 0.161150i
\(527\) 10.5610 2.82980i 0.460042 0.123268i
\(528\) 1.80389 6.34440i 0.0785042 0.276104i
\(529\) −10.6765 + 18.4922i −0.464195 + 0.804010i
\(530\) −0.151229 0.261936i −0.00656896 0.0113778i
\(531\) 7.90904 + 8.40575i 0.343223 + 0.364779i
\(532\) 9.56080i 0.414513i
\(533\) 14.8757 6.35917i 0.644339 0.275446i
\(534\) 7.55674 + 13.5611i 0.327012 + 0.586848i
\(535\) −1.52486 + 5.69085i −0.0659254 + 0.246037i
\(536\) 0.196246 0.113303i 0.00847653 0.00489393i
\(537\) 26.7956 + 0.407811i 1.15632 + 0.0175983i
\(538\) 12.4285 + 12.4285i 0.535831 + 0.535831i
\(539\) −4.16481 15.5433i −0.179391 0.669496i
\(540\) 5.07525 1.11440i 0.218404 0.0479560i
\(541\) −15.6462 + 15.6462i −0.672681 + 0.672681i −0.958333 0.285652i \(-0.907790\pi\)
0.285652 + 0.958333i \(0.407790\pi\)
\(542\) 24.8910 + 14.3708i 1.06916 + 0.617279i
\(543\) −34.0412 20.3506i −1.46085 0.873327i
\(544\) −1.27693 0.342152i −0.0547479 0.0146696i
\(545\) −10.4678 −0.448393
\(546\) −10.3183 + 1.31707i −0.441582 + 0.0563652i
\(547\) 39.1213 1.67271 0.836354 0.548190i \(-0.184683\pi\)
0.836354 + 0.548190i \(0.184683\pi\)
\(548\) −11.6063 3.10990i −0.495797 0.132848i
\(549\) −13.4244 0.408714i −0.572939 0.0174435i
\(550\) 3.29793 + 1.90406i 0.140624 + 0.0811894i
\(551\) −6.22573 + 6.22573i −0.265225 + 0.265225i
\(552\) 8.03149 + 8.27974i 0.341843 + 0.352409i
\(553\) −3.45866 12.9079i −0.147077 0.548900i
\(554\) −10.0410 10.0410i −0.426600 0.426600i
\(555\) 0.265361 17.4359i 0.0112640 0.740111i
\(556\) −3.25411 + 1.87876i −0.138005 + 0.0796772i
\(557\) 6.52205 24.3406i 0.276348 1.03135i −0.678584 0.734523i \(-0.737406\pi\)
0.954933 0.296823i \(-0.0959271\pi\)
\(558\) −13.0540 + 21.1001i −0.552621 + 0.893240i
\(559\) −25.9831 + 3.71926i −1.09897 + 0.157308i
\(560\) 1.66565i 0.0703867i
\(561\) −8.45581 + 2.12836i −0.357005 + 0.0898593i
\(562\) 3.12290 + 5.40903i 0.131732 + 0.228166i
\(563\) −3.12854 + 5.41879i −0.131852 + 0.228375i −0.924391 0.381447i \(-0.875426\pi\)
0.792538 + 0.609822i \(0.208759\pi\)
\(564\) 21.6455 + 6.15443i 0.911442 + 0.259148i
\(565\) −11.0408 + 2.95836i −0.464489 + 0.124459i
\(566\) −16.3514 + 4.38134i −0.687300 + 0.184162i
\(567\) −14.2172 4.75364i −0.597068 0.199634i
\(568\) 7.64342 13.2388i 0.320711 0.555487i
\(569\) −9.18102 15.9020i −0.384889 0.666647i 0.606865 0.794805i \(-0.292427\pi\)
−0.991754 + 0.128158i \(0.959093\pi\)
\(570\) −2.42672 9.64119i −0.101644 0.403825i
\(571\) 37.1767i 1.55580i −0.628391 0.777898i \(-0.716286\pi\)
0.628391 0.777898i \(-0.283714\pi\)
\(572\) 1.63857 13.6323i 0.0685120 0.569993i
\(573\) −11.6827 + 6.51003i −0.488054 + 0.271960i
\(574\) 1.93434 7.21906i 0.0807378 0.301318i
\(575\) −5.76756 + 3.32990i −0.240524 + 0.138867i
\(576\) 2.64252 1.42024i 0.110105 0.0591767i
\(577\) −2.97894 2.97894i −0.124015 0.124015i 0.642375 0.766390i \(-0.277949\pi\)
−0.766390 + 0.642375i \(0.777949\pi\)
\(578\) −3.94761 14.7327i −0.164199 0.612798i
\(579\) −7.94755 + 7.70927i −0.330289 + 0.320386i
\(580\) 1.08463 1.08463i 0.0450368 0.0450368i
\(581\) −17.9715 10.3758i −0.745582 0.430462i
\(582\) 1.50101 2.51080i 0.0622190 0.104076i
\(583\) −1.11255 0.298107i −0.0460771 0.0123463i
\(584\) 0.964815 0.0399243
\(585\) 10.0708 3.94713i 0.416375 0.163194i
\(586\) 11.2378 0.464229
\(587\) −6.45368 1.72926i −0.266372 0.0713741i 0.123161 0.992387i \(-0.460697\pi\)
−0.389533 + 0.921013i \(0.627363\pi\)
\(588\) 3.75550 6.28197i 0.154874 0.259064i
\(589\) 41.1127 + 23.7364i 1.69402 + 0.978043i
\(590\) −2.72039 + 2.72039i −0.111997 + 0.111997i
\(591\) 18.2525 17.7052i 0.750807 0.728296i
\(592\) −2.60573 9.72471i −0.107095 0.399683i
\(593\) 26.8093 + 26.8093i 1.10092 + 1.10092i 0.994299 + 0.106625i \(0.0340045\pi\)
0.106625 + 0.994299i \(0.465996\pi\)
\(594\) 10.6656 16.6672i 0.437614 0.683862i
\(595\) −1.90695 + 1.10098i −0.0781772 + 0.0451356i
\(596\) 0.101260 0.377907i 0.00414777 0.0154797i
\(597\) −4.40617 + 2.45527i −0.180332 + 0.100487i
\(598\) 19.2138 + 14.4020i 0.785712 + 0.588942i
\(599\) 25.7236i 1.05104i 0.850781 + 0.525520i \(0.176129\pi\)
−0.850781 + 0.525520i \(0.823871\pi\)
\(600\) 0.422776 + 1.67966i 0.0172598 + 0.0685719i
\(601\) 4.01013 + 6.94574i 0.163577 + 0.283323i 0.936149 0.351604i \(-0.114364\pi\)
−0.772572 + 0.634927i \(0.781030\pi\)
\(602\) −6.06288 + 10.5012i −0.247104 + 0.427997i
\(603\) 0.661702 0.155885i 0.0269466 0.00634812i
\(604\) −18.6296 + 4.99178i −0.758026 + 0.203113i
\(605\) 3.38248 0.906332i 0.137517 0.0368476i
\(606\) −12.0191 3.41736i −0.488241 0.138821i
\(607\) −5.80367 + 10.0522i −0.235564 + 0.408008i −0.959436 0.281925i \(-0.909027\pi\)
0.723873 + 0.689933i \(0.242360\pi\)
\(608\) −2.86998 4.97095i −0.116393 0.201599i
\(609\) −4.29144 + 1.08017i −0.173898 + 0.0437707i
\(610\) 4.47687i 0.181263i
\(611\) 46.5099 + 5.59039i 1.88159 + 0.226163i
\(612\) −3.37265 2.08656i −0.136331 0.0843443i
\(613\) −9.32778 + 34.8117i −0.376745 + 1.40603i 0.474033 + 0.880507i \(0.342798\pi\)
−0.850778 + 0.525525i \(0.823869\pi\)
\(614\) 25.0883 14.4847i 1.01248 0.584556i
\(615\) −0.118265 + 7.77074i −0.00476891 + 0.313346i
\(616\) −4.48519 4.48519i −0.180713 0.180713i
\(617\) −6.01064 22.4320i −0.241979 0.903078i −0.974878 0.222740i \(-0.928500\pi\)
0.732899 0.680338i \(-0.238167\pi\)
\(618\) −17.0283 17.5546i −0.684977 0.706149i
\(619\) −2.30174 + 2.30174i −0.0925149 + 0.0925149i −0.751850 0.659335i \(-0.770838\pi\)
0.659335 + 0.751850i \(0.270838\pi\)
\(620\) −7.16254 4.13529i −0.287654 0.166077i
\(621\) 15.9169 + 30.7276i 0.638723 + 1.23305i
\(622\) −8.53272 2.28634i −0.342131 0.0916737i
\(623\) 14.9293 0.598132
\(624\) 4.96944 3.78215i 0.198937 0.151407i
\(625\) −1.00000 −0.0400000
\(626\) 19.7595 + 5.29453i 0.789747 + 0.211612i
\(627\) −32.4959 19.4268i −1.29776 0.775830i
\(628\) 13.7850 + 7.95879i 0.550082 + 0.317590i
\(629\) −9.41111 + 9.41111i −0.375245 + 0.375245i
\(630\) 1.43959 4.78510i 0.0573548 0.190643i
\(631\) 9.17574 + 34.2443i 0.365281 + 1.36325i 0.867040 + 0.498239i \(0.166020\pi\)
−0.501759 + 0.865007i \(0.667314\pi\)
\(632\) 5.67299 + 5.67299i 0.225659 + 0.225659i
\(633\) 11.9033 + 0.181160i 0.473115 + 0.00720048i
\(634\) −18.1227 + 10.4631i −0.719744 + 0.415544i
\(635\) 1.07115 3.99758i 0.0425072 0.158639i
\(636\) −0.255002 0.457620i −0.0101115 0.0181458i
\(637\) 5.67133 14.1407i 0.224706 0.560275i
\(638\) 5.84127i 0.231258i
\(639\) 33.4001 31.4264i 1.32129 1.24321i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) 14.2640 24.7060i 0.563394 0.975828i −0.433803 0.901008i \(-0.642829\pi\)
0.997197 0.0748198i \(-0.0238381\pi\)
\(642\) −2.79082 + 9.81551i −0.110145 + 0.387387i
\(643\) 37.0551 9.92889i 1.46131 0.391557i 0.561369 0.827566i \(-0.310275\pi\)
0.899943 + 0.436009i \(0.143608\pi\)
\(644\) 10.7149 2.87106i 0.422228 0.113136i
\(645\) 3.44844 12.1284i 0.135782 0.477555i
\(646\) −3.79404 + 6.57147i −0.149275 + 0.258551i
\(647\) −9.53414 16.5136i −0.374826 0.649217i 0.615475 0.788156i \(-0.288964\pi\)
−0.990301 + 0.138939i \(0.955631\pi\)
\(648\) 8.81894 1.79620i 0.346441 0.0705614i
\(649\) 14.6507i 0.575089i
\(650\) 1.41726 + 3.31533i 0.0555894 + 0.130038i
\(651\) 11.6145 + 20.8431i 0.455207 + 0.816904i
\(652\) 3.45420 12.8913i 0.135277 0.504861i
\(653\) −28.6102 + 16.5181i −1.11961 + 0.646404i −0.941300 0.337571i \(-0.890395\pi\)
−0.178305 + 0.983975i \(0.557061\pi\)
\(654\) −18.1287 0.275906i −0.708889 0.0107888i
\(655\) 2.96106 + 2.96106i 0.115698 + 0.115698i
\(656\) 1.16131 + 4.33407i 0.0453415 + 0.169217i
\(657\) 2.77173 + 0.833872i 0.108135 + 0.0325324i
\(658\) 15.3024 15.3024i 0.596549 0.596549i
\(659\) −16.8251 9.71399i −0.655414 0.378403i 0.135113 0.990830i \(-0.456860\pi\)
−0.790527 + 0.612427i \(0.790193\pi\)
\(660\) 5.66134 + 3.38447i 0.220367 + 0.131740i
\(661\) 23.4203 + 6.27544i 0.910942 + 0.244086i 0.683710 0.729754i \(-0.260365\pi\)
0.227233 + 0.973840i \(0.427032\pi\)
\(662\) 27.8161 1.08110
\(663\) −7.61478 3.18937i −0.295734 0.123865i
\(664\) 12.4586 0.483486
\(665\) −9.23502 2.47452i −0.358119 0.0959576i
\(666\) 0.919132 30.1893i 0.0356157 1.16981i
\(667\) 8.84684 + 5.10773i 0.342551 + 0.197772i
\(668\) 7.40353 7.40353i 0.286451 0.286451i
\(669\) −1.90530 1.96419i −0.0736630 0.0759398i
\(670\) 0.0586497 + 0.218884i 0.00226584 + 0.00845622i
\(671\) −12.0551 12.0551i −0.465381 0.465381i
\(672\) 0.0439025 2.88466i 0.00169358 0.111278i
\(673\) −9.78648 + 5.65023i −0.377241 + 0.217800i −0.676617 0.736335i \(-0.736555\pi\)
0.299376 + 0.954135i \(0.403221\pi\)
\(674\) −1.44790 + 5.40363i −0.0557710 + 0.208140i
\(675\) −0.237145 + 5.19074i −0.00912770 + 0.199792i
\(676\) 8.98277 9.39734i 0.345491 0.361436i
\(677\) 25.6880i 0.987270i 0.869669 + 0.493635i \(0.164332\pi\)
−0.869669 + 0.493635i \(0.835668\pi\)
\(678\) −19.1989 + 4.83244i −0.737330 + 0.185589i
\(679\) −1.40656 2.43624i −0.0539789 0.0934943i
\(680\) 0.660987 1.14486i 0.0253477 0.0439035i
\(681\) 11.1305 + 3.16470i 0.426521 + 0.121272i
\(682\) −30.4222 + 8.15161i −1.16493 + 0.312141i
\(683\) 46.1988 12.3789i 1.76775 0.473667i 0.779485 0.626421i \(-0.215481\pi\)
0.988264 + 0.152754i \(0.0488141\pi\)
\(684\) −3.94860 16.7611i −0.150978 0.640875i
\(685\) 6.00786 10.4059i 0.229549 0.397590i
\(686\) −9.34898 16.1929i −0.356946 0.618248i
\(687\) −9.61153 38.1859i −0.366703 1.45688i
\(688\) 7.27987i 0.277543i
\(689\) −0.673584 0.857633i −0.0256615 0.0326732i
\(690\) −10.0763 + 5.61487i −0.383599 + 0.213755i
\(691\) −3.41753 + 12.7544i −0.130009 + 0.485200i −0.999969 0.00792315i \(-0.997478\pi\)
0.869960 + 0.493123i \(0.164145\pi\)
\(692\) −8.05147 + 4.64852i −0.306071 + 0.176710i
\(693\) −9.00862 16.7615i −0.342209 0.636718i
\(694\) −24.3450 24.3450i −0.924122 0.924122i
\(695\) −0.972518 3.62949i −0.0368897 0.137674i
\(696\) 1.90700 1.84983i 0.0722848 0.0701175i
\(697\) 4.19430 4.19430i 0.158871 0.158871i
\(698\) 12.5831 + 7.26485i 0.476277 + 0.274979i
\(699\) −18.5862 + 31.0898i −0.702994 + 1.17592i
\(700\) 1.60890 + 0.431103i 0.0608106 + 0.0162942i
\(701\) −33.1881 −1.25350 −0.626748 0.779222i \(-0.715614\pi\)
−0.626748 + 0.779222i \(0.715614\pi\)
\(702\) 17.5451 6.57040i 0.662196 0.247984i
\(703\) −57.7886 −2.17954
\(704\) 3.67836 + 0.985615i 0.138634 + 0.0371467i
\(705\) −11.5470 + 19.3151i −0.434885 + 0.727449i
\(706\) 8.59955 + 4.96495i 0.323648 + 0.186858i
\(707\) −8.49692 + 8.49692i −0.319559 + 0.319559i
\(708\) −4.78302 + 4.63961i −0.179757 + 0.174367i
\(709\) 6.64653 + 24.8052i 0.249616 + 0.931578i 0.971007 + 0.239050i \(0.0768361\pi\)
−0.721392 + 0.692527i \(0.756497\pi\)
\(710\) 10.8094 + 10.8094i 0.405670 + 0.405670i
\(711\) 11.3943 + 21.2005i 0.427321 + 0.795079i
\(712\) −7.76223 + 4.48153i −0.290902 + 0.167952i
\(713\) 14.2559 53.2037i 0.533887 1.99249i
\(714\) −3.33156 + 1.85646i −0.124681 + 0.0694764i
\(715\) 12.7437 + 5.11102i 0.476586 + 0.191141i
\(716\) 15.4723i 0.578226i
\(717\) −1.39745 5.55198i −0.0521889 0.207343i
\(718\) −8.23262 14.2593i −0.307239 0.532153i
\(719\) −3.79520 + 6.57348i −0.141537 + 0.245150i −0.928076 0.372392i \(-0.878538\pi\)
0.786539 + 0.617541i \(0.211871\pi\)
\(720\) 0.687914 + 2.92006i 0.0256370 + 0.108824i
\(721\) −22.7177 + 6.08718i −0.846050 + 0.226699i
\(722\) −13.4719 + 3.60980i −0.501374 + 0.134343i
\(723\) 17.1423 + 4.87404i 0.637529 + 0.181267i
\(724\) 11.4490 19.8302i 0.425498 0.736984i
\(725\) 0.766948 + 1.32839i 0.0284838 + 0.0493353i
\(726\) 5.88183 1.48048i 0.218295 0.0549457i
\(727\) 51.1962i 1.89876i −0.314129 0.949380i \(-0.601712\pi\)
0.314129 0.949380i \(-0.398288\pi\)
\(728\) −0.850975 5.94501i −0.0315392 0.220337i
\(729\) 26.8875 + 2.46191i 0.995834 + 0.0911819i
\(730\) −0.249713 + 0.931940i −0.00924228 + 0.0344926i
\(731\) −8.33446 + 4.81190i −0.308261 + 0.177975i
\(732\) 0.117999 7.75326i 0.00436138 0.286569i
\(733\) −19.8432 19.8432i −0.732925 0.732925i 0.238273 0.971198i \(-0.423419\pi\)
−0.971198 + 0.238273i \(0.923419\pi\)
\(734\) −1.25883 4.69802i −0.0464643 0.173407i
\(735\) 5.09592 + 5.25343i 0.187966 + 0.193776i
\(736\) −4.70919 + 4.70919i −0.173583 + 0.173583i
\(737\) 0.747328 + 0.431470i 0.0275282 + 0.0158934i
\(738\) −0.409635 + 13.4546i −0.0150789 + 0.495272i
\(739\) −33.6777 9.02391i −1.23885 0.331950i −0.420832 0.907138i \(-0.638262\pi\)
−0.818021 + 0.575189i \(0.804929\pi\)
\(740\) 10.0678 0.370098
\(741\) −13.5870 33.1713i −0.499132 1.21858i
\(742\) −0.503790 −0.0184947
\(743\) −27.9882 7.49941i −1.02679 0.275127i −0.294159 0.955756i \(-0.595040\pi\)
−0.732627 + 0.680630i \(0.761706\pi\)
\(744\) −12.2954 7.35050i −0.450773 0.269482i
\(745\) 0.338823 + 0.195619i 0.0124135 + 0.00716694i
\(746\) −25.8663 + 25.8663i −0.947031 + 0.947031i
\(747\) 35.7910 + 10.7677i 1.30953 + 0.393970i
\(748\) −1.30296 4.86270i −0.0476408 0.177798i
\(749\) 6.93910 + 6.93910i 0.253549 + 0.253549i
\(750\) −1.73185 0.0263575i −0.0632382 0.000962441i
\(751\) 23.9936 13.8527i 0.875537 0.505492i 0.00635294 0.999980i \(-0.497978\pi\)
0.869184 + 0.494488i \(0.164644\pi\)
\(752\) −3.36268 + 12.5497i −0.122624 + 0.457640i
\(753\) 19.3542 + 34.7326i 0.705306 + 1.26572i
\(754\) 3.31709 4.42536i 0.120801 0.161162i
\(755\) 19.2867i 0.701917i
\(756\) 2.61928 8.24914i 0.0952625 0.300018i
\(757\) 15.6835 + 27.1647i 0.570027 + 0.987316i 0.996562 + 0.0828451i \(0.0264007\pi\)
−0.426535 + 0.904471i \(0.640266\pi\)
\(758\) 1.29994 2.25157i 0.0472161 0.0817806i
\(759\) −12.0136 + 42.2524i −0.436064 + 1.53367i
\(760\) 5.54438 1.48561i 0.201116 0.0538888i
\(761\) −33.5908 + 9.00062i −1.21766 + 0.326272i −0.809765 0.586755i \(-0.800405\pi\)
−0.407900 + 0.913027i \(0.633739\pi\)
\(762\) 1.96044 6.89498i 0.0710191 0.249779i
\(763\) −8.71790 + 15.0998i −0.315609 + 0.546651i
\(764\) −3.86078 6.68706i −0.139678 0.241929i
\(765\) 2.88837 2.71769i 0.104429 0.0982583i
\(766\) 7.51778i 0.271628i
\(767\) −8.31971 + 11.0994i −0.300407 + 0.400776i
\(768\) 0.843099 + 1.51301i 0.0304227 + 0.0545959i
\(769\) −3.20108 + 11.9466i −0.115434 + 0.430805i −0.999319 0.0368988i \(-0.988252\pi\)
0.883885 + 0.467704i \(0.154919\pi\)
\(770\) 5.49321 3.17151i 0.197962 0.114293i
\(771\) −7.89045 0.120087i −0.284167 0.00432483i
\(772\) −4.52026 4.52026i −0.162688 0.162688i
\(773\) 9.35460 + 34.9119i 0.336462 + 1.25569i 0.902276 + 0.431159i \(0.141895\pi\)
−0.565814 + 0.824533i \(0.691438\pi\)
\(774\) 6.29186 20.9137i 0.226156 0.751726i
\(775\) 5.84819 5.84819i 0.210073 0.210073i
\(776\) 1.46263 + 0.844451i 0.0525054 + 0.0303140i
\(777\) −24.9302 14.9038i −0.894366 0.534672i
\(778\) −3.26037 0.873614i −0.116890 0.0313206i
\(779\) 25.7550 0.922768
\(780\) 2.36709 + 5.77900i 0.0847555 + 0.206921i
\(781\) 58.2141 2.08307
\(782\) 8.50410 + 2.27867i 0.304106 + 0.0814849i
\(783\) 7.07722 3.66601i 0.252919 0.131012i
\(784\) 3.65947 + 2.11280i 0.130695 + 0.0754571i
\(785\) −11.2554 + 11.2554i −0.401723 + 0.401723i
\(786\) 5.05006 + 5.20615i 0.180130 + 0.185697i
\(787\) 9.31123 + 34.7500i 0.331910 + 1.23870i 0.907181 + 0.420741i \(0.138230\pi\)
−0.575271 + 0.817963i \(0.695104\pi\)
\(788\) 10.3813 + 10.3813i 0.369819 + 0.369819i
\(789\) −0.376383 + 24.7307i −0.0133996 + 0.880435i
\(790\) −6.94796 + 4.01141i −0.247197 + 0.142720i
\(791\) −4.92761 + 18.3901i −0.175206 + 0.653877i
\(792\) 9.71538 + 6.01062i 0.345221 + 0.213578i
\(793\) −2.28721 15.9787i −0.0812213 0.567420i
\(794\) 2.81605i 0.0999380i
\(795\) 0.508026 0.127872i 0.0180178 0.00453515i
\(796\) −1.45610 2.52204i −0.0516100 0.0893912i
\(797\) 16.8835 29.2431i 0.598045 1.03584i −0.395065 0.918653i \(-0.629278\pi\)
0.993109 0.117191i \(-0.0373888\pi\)
\(798\) −15.9284 4.52890i −0.563861 0.160321i
\(799\) 16.5904 4.44537i 0.586924 0.157266i
\(800\) −0.965926 + 0.258819i −0.0341506 + 0.00915064i
\(801\) −26.1727 + 6.16581i −0.924766 + 0.217858i
\(802\) −16.0900 + 27.8688i −0.568159 + 0.984080i
\(803\) 1.83707 + 3.18189i 0.0648287 + 0.112287i
\(804\) 0.0958033 + 0.380620i 0.00337872 + 0.0134234i
\(805\) 11.0929i 0.390974i
\(806\) −27.6770 11.1003i −0.974882 0.390990i
\(807\) −26.5934 + 14.8188i −0.936134 + 0.521646i
\(808\) 1.86719 6.96843i 0.0656874 0.245149i
\(809\) 7.07341 4.08384i 0.248688 0.143580i −0.370475 0.928842i \(-0.620805\pi\)
0.619163 + 0.785262i \(0.287472\pi\)
\(810\) −0.547514 + 8.98333i −0.0192377 + 0.315642i
\(811\) −18.2887 18.2887i −0.642205 0.642205i 0.308892 0.951097i \(-0.400042\pi\)
−0.951097 + 0.308892i \(0.900042\pi\)
\(812\) −0.661268 2.46788i −0.0232059 0.0866058i
\(813\) −35.7327 + 34.6614i −1.25320 + 1.21563i
\(814\) 27.1100 27.1100i 0.950203 0.950203i
\(815\) 11.5580 + 6.67301i 0.404859 + 0.233745i
\(816\) 1.17491 1.96531i 0.0411299 0.0687996i
\(817\) −40.3624 10.8151i −1.41210 0.378371i
\(818\) 2.74748 0.0960635
\(819\) 2.69347 17.8143i 0.0941174 0.622483i
\(820\) −4.48696 −0.156691
\(821\) −40.7978 10.9318i −1.42385 0.381521i −0.537005 0.843579i \(-0.680444\pi\)
−0.886850 + 0.462058i \(0.847111\pi\)
\(822\) 10.6790 17.8632i 0.372473 0.623049i
\(823\) 38.7259 + 22.3584i 1.34990 + 0.779365i 0.988235 0.152944i \(-0.0488753\pi\)
0.361664 + 0.932308i \(0.382209\pi\)
\(824\) 9.98436 9.98436i 0.347822 0.347822i
\(825\) −4.73441 + 4.59246i −0.164831 + 0.159889i
\(826\) 1.65855 + 6.18978i 0.0577082 + 0.215370i
\(827\) −35.9420 35.9420i −1.24982 1.24982i −0.955797 0.294028i \(-0.905004\pi\)
−0.294028 0.955797i \(-0.594996\pi\)
\(828\) −17.5987 + 9.45853i −0.611596 + 0.328707i
\(829\) −21.1423 + 12.2065i −0.734301 + 0.423949i −0.819994 0.572373i \(-0.806023\pi\)
0.0856926 + 0.996322i \(0.472690\pi\)
\(830\) −3.22451 + 12.0340i −0.111924 + 0.417708i
\(831\) 21.4848 11.9721i 0.745298 0.415306i
\(832\) 2.22703 + 2.83555i 0.0772085 + 0.0983048i
\(833\) 5.58613i 0.193548i
\(834\) −1.58859 6.31136i −0.0550084 0.218545i
\(835\) 5.23508 + 9.06743i 0.181168 + 0.313791i
\(836\) 10.9292 18.9300i 0.377996 0.654708i
\(837\) −28.9695 31.7433i −1.00133 1.09721i
\(838\) −13.7796 + 3.69224i −0.476009 + 0.127546i
\(839\) 30.3149 8.12286i 1.04659 0.280432i 0.305746 0.952113i \(-0.401094\pi\)
0.740841 + 0.671681i \(0.234427\pi\)
\(840\) 2.77501 + 0.789012i 0.0957469 + 0.0272235i
\(841\) −13.3236 + 23.0771i −0.459434 + 0.795763i
\(842\) 16.4580 + 28.5061i 0.567180 + 0.982385i
\(843\) −10.4908 + 2.64058i −0.361324 + 0.0909464i
\(844\) 6.87320i 0.236585i
\(845\) 6.75222 + 11.1089i 0.232283 + 0.382158i
\(846\) −20.5068 + 33.1465i −0.705038 + 1.13960i
\(847\) 1.50964 5.63404i 0.0518717 0.193588i
\(848\) 0.261936 0.151229i 0.00899492 0.00519322i
\(849\) 0.446186 29.3171i 0.0153131 1.00616i
\(850\) 0.934777 + 0.934777i 0.0320626 + 0.0320626i
\(851\) 17.3536 + 64.7647i 0.594875 + 2.22010i
\(852\) 18.4354 + 19.0052i 0.631586 + 0.651108i
\(853\) 30.7798 30.7798i 1.05388 1.05388i 0.0554178 0.998463i \(-0.482351\pi\)
0.998463 0.0554178i \(-0.0176491\pi\)
\(854\) −6.45787 3.72846i −0.220984 0.127585i
\(855\) 17.2119 + 0.524028i 0.588635 + 0.0179214i
\(856\) −5.69085 1.52486i −0.194509 0.0521186i
\(857\) −28.3530 −0.968520 −0.484260 0.874924i \(-0.660911\pi\)
−0.484260 + 0.874924i \(0.660911\pi\)
\(858\) 21.9354 + 9.18742i 0.748862 + 0.313653i
\(859\) −42.4132 −1.44712 −0.723559 0.690262i \(-0.757495\pi\)
−0.723559 + 0.690262i \(0.757495\pi\)
\(860\) 7.03182 + 1.88417i 0.239783 + 0.0642497i
\(861\) 11.1108 + 6.64228i 0.378655 + 0.226368i
\(862\) −23.8766 13.7852i −0.813241 0.469525i
\(863\) −16.5706 + 16.5706i −0.564068 + 0.564068i −0.930461 0.366392i \(-0.880593\pi\)
0.366392 + 0.930461i \(0.380593\pi\)
\(864\) 1.11440 + 5.07525i 0.0379126 + 0.172663i
\(865\) −2.40625 8.98025i −0.0818150 0.305338i
\(866\) −5.97890 5.97890i −0.203171 0.203171i
\(867\) 26.4148 + 0.402015i 0.897095 + 0.0136532i
\(868\) −11.9303 + 6.88797i −0.404941 + 0.233793i
\(869\) −7.90741 + 29.5108i −0.268240 + 1.00109i
\(870\) 1.29323 + 2.32079i 0.0438445 + 0.0786823i
\(871\) 0.321158 + 0.751270i 0.0108820 + 0.0254558i
\(872\) 10.4678i 0.354486i
\(873\) 3.47202 + 3.69007i 0.117510 + 0.124890i
\(874\) 19.1135 + 33.1056i 0.646524 + 1.11981i
\(875\) −0.832827 + 1.44250i −0.0281547 + 0.0487654i
\(876\) −0.457028 + 1.60740i −0.0154416 + 0.0543090i
\(877\) −22.4068 + 6.00390i −0.756625 + 0.202737i −0.616455 0.787390i \(-0.711432\pi\)
−0.140170 + 0.990127i \(0.544765\pi\)
\(878\) −12.1908 + 3.26651i −0.411419 + 0.110240i
\(879\) −5.32330 + 18.7224i −0.179550 + 0.631490i
\(880\) −1.90406 + 3.29793i −0.0641859 + 0.111173i
\(881\) 2.39325 + 4.14523i 0.0806306 + 0.139656i 0.903521 0.428544i \(-0.140973\pi\)
−0.822890 + 0.568200i \(0.807640\pi\)
\(882\) 8.68691 + 9.23248i 0.292503 + 0.310874i
\(883\) 10.5075i 0.353606i 0.984246 + 0.176803i \(0.0565756\pi\)
−0.984246 + 0.176803i \(0.943424\pi\)
\(884\) 1.77427 4.42391i 0.0596752 0.148792i
\(885\) −3.24358 5.82086i −0.109032 0.195666i
\(886\) −7.38763 + 27.5710i −0.248192 + 0.926266i
\(887\) −17.3077 + 9.99260i −0.581136 + 0.335519i −0.761585 0.648066i \(-0.775578\pi\)
0.180449 + 0.983584i \(0.442245\pi\)
\(888\) 17.4359 + 0.265361i 0.585109 + 0.00890494i
\(889\) −4.87442 4.87442i −0.163483 0.163483i
\(890\) −2.31981 8.65764i −0.0777602 0.290205i
\(891\) 22.7155 + 25.6642i 0.760999 + 0.859782i
\(892\) 1.11715 1.11715i 0.0374050 0.0374050i
\(893\) 64.5846 + 37.2879i 2.16124 + 1.24779i
\(894\) 0.581634 + 0.347714i 0.0194527 + 0.0116293i
\(895\) −14.9451 4.00452i −0.499558 0.133856i
\(896\) 1.66565 0.0556456
\(897\) −33.0955 + 25.1884i −1.10503 + 0.841016i
\(898\) −29.8510 −0.996139
\(899\) −12.2540 3.28344i −0.408692 0.109509i
\(900\) −2.99861 0.0912946i −0.0999537 0.00304315i
\(901\) −0.346273 0.199921i −0.0115360 0.00666032i
\(902\) −12.0823 + 12.0823i −0.402295 + 0.402295i
\(903\) −14.6232 15.0752i −0.486631 0.501672i
\(904\) −2.95836 11.0408i −0.0983937 0.367210i
\(905\) 16.1913 + 16.1913i 0.538217 + 0.538217i
\(906\) 0.508351 33.4018i 0.0168888 1.10970i
\(907\) −5.19882 + 3.00154i −0.172624 + 0.0996644i −0.583822 0.811881i \(-0.698444\pi\)
0.411199 + 0.911546i \(0.365110\pi\)
\(908\) −1.72914 + 6.45324i −0.0573835 + 0.214158i
\(909\) 11.3868 18.4052i 0.377675 0.610462i
\(910\) 5.96268 + 0.716701i 0.197661 + 0.0237584i
\(911\) 27.5510i 0.912806i 0.889773 + 0.456403i \(0.150862\pi\)
−0.889773 + 0.456403i \(0.849138\pi\)
\(912\) 9.64119 2.42672i 0.319252 0.0803568i
\(913\) 23.7219 + 41.0875i 0.785079 + 1.35980i
\(914\) 15.9522 27.6301i 0.527653 0.913923i
\(915\) 7.45854 + 2.12067i 0.246572 + 0.0701072i
\(916\) 21.9597 5.88407i 0.725567 0.194415i
\(917\) 6.73737 1.80527i 0.222487 0.0596153i
\(918\) 5.07386 4.63050i 0.167462 0.152829i
\(919\) 16.2627 28.1677i 0.536456 0.929168i −0.462636 0.886548i \(-0.653096\pi\)
0.999091 0.0426199i \(-0.0135704\pi\)
\(920\) −3.32990 5.76756i −0.109784 0.190151i
\(921\) 12.2476 + 48.6589i 0.403572 + 1.60336i
\(922\) 11.2423i 0.370245i
\(923\) 44.1032 + 33.0582i 1.45167 + 1.08812i
\(924\) 9.59701 5.34779i 0.315719 0.175929i
\(925\) −2.60573 + 9.72471i −0.0856758 + 0.319746i
\(926\) −11.6084 + 6.70209i −0.381475 + 0.220244i
\(927\) 37.3124 20.0538i 1.22550 0.658655i
\(928\) 1.08463 + 1.08463i 0.0356047 + 0.0356047i
\(929\) −6.22343 23.2262i −0.204184 0.762026i −0.989697 0.143180i \(-0.954267\pi\)
0.785512 0.618846i \(-0.212399\pi\)
\(930\) 10.2823 9.97404i 0.337171 0.327062i
\(931\) 17.1507 17.1507i 0.562092 0.562092i
\(932\) −18.1109 10.4563i −0.593243 0.342509i
\(933\) 7.85098 13.1326i 0.257030 0.429943i
\(934\) −13.3285 3.57137i −0.436123 0.116859i
\(935\) 5.03424 0.164637
\(936\) 3.94713 + 10.0708i 0.129016 + 0.329173i
\(937\) −4.78415 −0.156292 −0.0781458 0.996942i \(-0.524900\pi\)
−0.0781458 + 0.996942i \(0.524900\pi\)
\(938\) 0.364585 + 0.0976902i 0.0119041 + 0.00318970i
\(939\) −18.1808 + 30.4116i −0.593306 + 0.992446i
\(940\) −11.2517 6.49619i −0.366991 0.211882i
\(941\) −2.48077 + 2.48077i −0.0808706 + 0.0808706i −0.746385 0.665514i \(-0.768212\pi\)
0.665514 + 0.746385i \(0.268212\pi\)
\(942\) −19.7894 + 19.1960i −0.644773 + 0.625441i
\(943\) −7.73410 28.8640i −0.251857 0.939943i
\(944\) −2.72039 2.72039i −0.0885412 0.0885412i
\(945\) 7.29013 + 4.66507i 0.237148 + 0.151755i
\(946\) 24.0085 13.8613i 0.780584 0.450671i
\(947\) −3.58159 + 13.3667i −0.116386 + 0.434359i −0.999387 0.0350128i \(-0.988853\pi\)
0.883001 + 0.469371i \(0.155519\pi\)
\(948\) −12.1386 + 6.76403i −0.394242 + 0.219685i
\(949\) −0.415143 + 3.45383i −0.0134761 + 0.112116i
\(950\) 5.73996i 0.186229i
\(951\) −8.84714 35.1490i −0.286888 1.13979i
\(952\) −1.10098 1.90695i −0.0356828 0.0618045i
\(953\) 23.6090 40.8920i 0.764770 1.32462i −0.175598 0.984462i \(-0.556186\pi\)
0.940368 0.340159i \(-0.110481\pi\)
\(954\) 0.883196 0.208065i 0.0285945 0.00673635i
\(955\) 7.45845 1.99848i 0.241350 0.0646695i
\(956\) 3.19279 0.855506i 0.103262 0.0276690i
\(957\) 9.73165 + 2.76698i 0.314580 + 0.0894438i
\(958\) 15.4739 26.8016i 0.499940 0.865921i
\(959\) −10.0070 17.3327i −0.323144 0.559701i
\(960\) −1.67966 + 0.422776i −0.0542108 + 0.0136450i
\(961\) 37.4026i 1.20654i
\(962\) 35.9336 5.14357i 1.15854 0.165836i
\(963\) −15.0308 9.29912i −0.484361 0.299660i
\(964\) −2.66309 + 9.93879i −0.0857724 + 0.320107i
\(965\) 5.53616 3.19630i 0.178215 0.102893i
\(966\) −0.292382 + 19.2113i −0.00940725 + 0.618113i
\(967\) −12.9619 12.9619i −0.416828 0.416828i 0.467281 0.884109i \(-0.345234\pi\)
−0.884109 + 0.467281i \(0.845234\pi\)
\(968\) 0.906332 + 3.38248i 0.0291306 + 0.108717i
\(969\) −9.15097 9.43381i −0.293971 0.303058i
\(970\) −1.19423 + 1.19423i −0.0383445 + 0.0383445i
\(971\) −7.70575 4.44892i −0.247289 0.142773i 0.371233 0.928540i \(-0.378935\pi\)
−0.618522 + 0.785767i \(0.712268\pi\)
\(972\) −1.18499 + 15.5434i −0.0380086 + 0.498553i
\(973\) −6.04547 1.61988i −0.193809 0.0519309i
\(974\) −28.8687 −0.925014
\(975\) −6.19474 + 0.790720i −0.198390 + 0.0253233i
\(976\) 4.47687 0.143301
\(977\) −6.37132 1.70719i −0.203837 0.0546178i 0.155456 0.987843i \(-0.450315\pi\)
−0.359293 + 0.933225i \(0.616982\pi\)
\(978\) 19.8408 + 11.8613i 0.634440 + 0.379282i
\(979\) −29.5595 17.0662i −0.944726 0.545438i
\(980\) −2.98795 + 2.98795i −0.0954465 + 0.0954465i
\(981\) 9.04716 30.0721i 0.288853 0.960127i
\(982\) 2.07030 + 7.72647i 0.0660660 + 0.246562i
\(983\) −17.6609 17.6609i −0.563294 0.563294i 0.366947 0.930242i \(-0.380403\pi\)
−0.930242 + 0.366947i \(0.880403\pi\)
\(984\) −7.77074 0.118265i −0.247722 0.00377016i
\(985\) −12.7145 + 7.34069i −0.405116 + 0.233894i
\(986\) 0.524826 1.95868i 0.0167139 0.0623770i
\(987\) 18.2454 + 32.7427i 0.580756 + 1.04221i
\(988\) 19.0298 8.13500i 0.605420 0.258809i
\(989\) 48.4825i 1.54165i
\(990\) −8.32034 + 7.82867i −0.264438 + 0.248812i
\(991\) −8.86830 15.3603i −0.281711 0.487937i 0.690095 0.723718i \(-0.257569\pi\)
−0.971806 + 0.235781i \(0.924235\pi\)
\(992\) 4.13529 7.16254i 0.131296 0.227411i
\(993\) −13.1763 + 46.3420i −0.418138 + 1.47062i
\(994\) 24.5950 6.59020i 0.780105 0.209028i
\(995\) 2.81296 0.753732i 0.0891770 0.0238949i
\(996\) −5.90156 + 20.7562i −0.186998 + 0.657685i
\(997\) 20.3319 35.2159i 0.643918 1.11530i −0.340632 0.940197i \(-0.610641\pi\)
0.984550 0.175102i \(-0.0560257\pi\)
\(998\) −10.9012 18.8815i −0.345072 0.597682i
\(999\) 49.8605 + 15.8318i 1.57752 + 0.500896i
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 390.2.bh.c.11.4 40
3.2 odd 2 inner 390.2.bh.c.11.6 yes 40
13.6 odd 12 inner 390.2.bh.c.71.6 yes 40
39.32 even 12 inner 390.2.bh.c.71.4 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.bh.c.11.4 40 1.1 even 1 trivial
390.2.bh.c.11.6 yes 40 3.2 odd 2 inner
390.2.bh.c.71.4 yes 40 39.32 even 12 inner
390.2.bh.c.71.6 yes 40 13.6 odd 12 inner