Properties

Label 637.2.x.a.80.2
Level $637$
Weight $2$
Character 637.80
Analytic conductor $5.086$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(19,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.x (of order \(12\), degree \(4\), not 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: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 80.2
Character \(\chi\) \(=\) 637.80
Dual form 637.2.x.a.215.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.521585 - 1.94658i) q^{2} -1.44369i q^{3} +(-1.78508 + 1.03062i) q^{4} +(-0.849184 + 3.16920i) q^{5} +(-2.81025 + 0.753004i) q^{6} +(0.0872533 + 0.0872533i) q^{8} +0.915773 q^{9} +O(q^{10})\) \(q+(-0.521585 - 1.94658i) q^{2} -1.44369i q^{3} +(-1.78508 + 1.03062i) q^{4} +(-0.849184 + 3.16920i) q^{5} +(-2.81025 + 0.753004i) q^{6} +(0.0872533 + 0.0872533i) q^{8} +0.915773 q^{9} +6.61202 q^{10} +(4.20434 + 4.20434i) q^{11} +(1.48788 + 2.57709i) q^{12} +(2.81021 - 2.25892i) q^{13} +(4.57532 + 1.22595i) q^{15} +(-1.93689 + 3.35480i) q^{16} +(0.314289 + 0.544364i) q^{17} +(-0.477654 - 1.78263i) q^{18} +(-0.521911 - 0.521911i) q^{19} +(-1.75036 - 6.53244i) q^{20} +(5.99117 - 10.3770i) q^{22} +(3.93752 + 2.27333i) q^{23} +(0.125966 - 0.125966i) q^{24} +(-4.99256 - 2.88246i) q^{25} +(-5.86293 - 4.29209i) q^{26} -5.65314i q^{27} +(-1.33622 - 2.31439i) q^{29} -9.54568i q^{30} +(1.06713 - 0.285936i) q^{31} +(7.77903 + 2.08438i) q^{32} +(6.06974 - 6.06974i) q^{33} +(0.895721 - 0.895721i) q^{34} +(-1.63473 + 0.943810i) q^{36} +(-2.44528 + 0.655210i) q^{37} +(-0.743721 + 1.28816i) q^{38} +(-3.26116 - 4.05706i) q^{39} +(-0.350617 + 0.202429i) q^{40} +(-0.746755 + 2.78693i) q^{41} +(3.49297 + 2.01667i) q^{43} +(-11.8381 - 3.17202i) q^{44} +(-0.777660 + 2.90227i) q^{45} +(2.37147 - 8.85043i) q^{46} +(7.10802 + 1.90459i) q^{47} +(4.84328 + 2.79627i) q^{48} +(-3.00689 + 11.2219i) q^{50} +(0.785891 - 0.453734i) q^{51} +(-2.68838 + 6.92859i) q^{52} +(3.89042 - 6.73840i) q^{53} +(-11.0043 + 2.94859i) q^{54} +(-16.8946 + 9.75412i) q^{55} +(-0.753475 + 0.753475i) q^{57} +(-3.80821 + 3.80821i) q^{58} +(-0.919907 - 0.246488i) q^{59} +(-9.43079 + 2.52697i) q^{60} -1.08909i q^{61} +(-1.11320 - 1.92811i) q^{62} -8.48212i q^{64} +(4.77256 + 10.8244i) q^{65} +(-14.9811 - 8.64936i) q^{66} +(-3.81608 + 3.81608i) q^{67} +(-1.12206 - 0.647822i) q^{68} +(3.28197 - 5.68453i) q^{69} +(0.590023 + 2.20200i) q^{71} +(0.0799043 + 0.0799043i) q^{72} +(1.59300 + 5.94515i) q^{73} +(2.55084 + 4.41818i) q^{74} +(-4.16136 + 7.20769i) q^{75} +(1.46954 + 0.393762i) q^{76} +(-6.19643 + 8.46422i) q^{78} +(-6.08299 - 10.5361i) q^{79} +(-8.98724 - 8.98724i) q^{80} -5.41404 q^{81} +5.81448 q^{82} +(3.59152 + 3.59152i) q^{83} +(-1.99209 + 0.533778i) q^{85} +(2.10373 - 7.85121i) q^{86} +(-3.34126 + 1.92908i) q^{87} +0.733685i q^{88} +(-1.05715 - 3.94532i) q^{89} +6.05511 q^{90} -9.37170 q^{92} +(-0.412802 - 1.54060i) q^{93} -14.8297i q^{94} +(2.09724 - 1.21084i) q^{95} +(3.00919 - 11.2305i) q^{96} +(8.41780 - 2.25554i) q^{97} +(3.85022 + 3.85022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 2 q^{2} - 6 q^{4} + 6 q^{5} - 12 q^{6} - 4 q^{8} - 12 q^{9} + 12 q^{10} + 2 q^{11} - 8 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 8 q^{19} + 36 q^{20} - 8 q^{22} - 6 q^{23} - 12 q^{24} - 24 q^{26} - 8 q^{29} + 38 q^{31} - 20 q^{32} - 18 q^{33} - 12 q^{34} + 54 q^{36} - 16 q^{37} + 28 q^{39} - 48 q^{40} - 18 q^{41} + 48 q^{43} - 6 q^{44} - 12 q^{45} + 18 q^{46} + 42 q^{47} - 12 q^{48} + 10 q^{50} + 12 q^{51} + 28 q^{52} + 12 q^{53} + 30 q^{54} + 6 q^{55} + 12 q^{57} + 62 q^{58} + 6 q^{59} + 16 q^{60} + 36 q^{62} - 2 q^{65} - 66 q^{66} - 4 q^{67} - 30 q^{68} - 42 q^{69} - 42 q^{71} - 38 q^{72} - 14 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} + 4 q^{79} - 12 q^{80} + 12 q^{81} + 108 q^{82} + 66 q^{83} - 54 q^{85} - 30 q^{86} - 42 q^{87} + 30 q^{89} + 72 q^{90} - 156 q^{92} + 14 q^{93} - 6 q^{95} - 18 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.521585 1.94658i −0.368816 1.37644i −0.862173 0.506614i \(-0.830897\pi\)
0.493357 0.869827i \(-0.335770\pi\)
\(3\) 1.44369i 0.833512i −0.909018 0.416756i \(-0.863167\pi\)
0.909018 0.416756i \(-0.136833\pi\)
\(4\) −1.78508 + 1.03062i −0.892539 + 0.515308i
\(5\) −0.849184 + 3.16920i −0.379766 + 1.41731i 0.466487 + 0.884528i \(0.345519\pi\)
−0.846254 + 0.532780i \(0.821147\pi\)
\(6\) −2.81025 + 0.753004i −1.14728 + 0.307413i
\(7\) 0 0
\(8\) 0.0872533 + 0.0872533i 0.0308487 + 0.0308487i
\(9\) 0.915773 0.305258
\(10\) 6.61202 2.09090
\(11\) 4.20434 + 4.20434i 1.26766 + 1.26766i 0.947296 + 0.320360i \(0.103804\pi\)
0.320360 + 0.947296i \(0.396196\pi\)
\(12\) 1.48788 + 2.57709i 0.429515 + 0.743942i
\(13\) 2.81021 2.25892i 0.779413 0.626511i
\(14\) 0 0
\(15\) 4.57532 + 1.22595i 1.18134 + 0.316540i
\(16\) −1.93689 + 3.35480i −0.484224 + 0.838700i
\(17\) 0.314289 + 0.544364i 0.0762262 + 0.132028i 0.901619 0.432531i \(-0.142380\pi\)
−0.825393 + 0.564559i \(0.809046\pi\)
\(18\) −0.477654 1.78263i −0.112584 0.420169i
\(19\) −0.521911 0.521911i −0.119735 0.119735i 0.644701 0.764435i \(-0.276982\pi\)
−0.764435 + 0.644701i \(0.776982\pi\)
\(20\) −1.75036 6.53244i −0.391393 1.46070i
\(21\) 0 0
\(22\) 5.99117 10.3770i 1.27732 2.21239i
\(23\) 3.93752 + 2.27333i 0.821029 + 0.474021i 0.850771 0.525536i \(-0.176135\pi\)
−0.0297422 + 0.999558i \(0.509469\pi\)
\(24\) 0.125966 0.125966i 0.0257128 0.0257128i
\(25\) −4.99256 2.88246i −0.998513 0.576492i
\(26\) −5.86293 4.29209i −1.14982 0.841749i
\(27\) 5.65314i 1.08795i
\(28\) 0 0
\(29\) −1.33622 2.31439i −0.248129 0.429772i 0.714878 0.699250i \(-0.246482\pi\)
−0.963007 + 0.269477i \(0.913149\pi\)
\(30\) 9.54568i 1.74279i
\(31\) 1.06713 0.285936i 0.191662 0.0513556i −0.161711 0.986838i \(-0.551701\pi\)
0.353373 + 0.935482i \(0.385035\pi\)
\(32\) 7.77903 + 2.08438i 1.37515 + 0.368471i
\(33\) 6.06974 6.06974i 1.05661 1.05661i
\(34\) 0.895721 0.895721i 0.153615 0.153615i
\(35\) 0 0
\(36\) −1.63473 + 0.943810i −0.272454 + 0.157302i
\(37\) −2.44528 + 0.655210i −0.402001 + 0.107716i −0.454154 0.890923i \(-0.650058\pi\)
0.0521528 + 0.998639i \(0.483392\pi\)
\(38\) −0.743721 + 1.28816i −0.120648 + 0.208968i
\(39\) −3.26116 4.05706i −0.522204 0.649650i
\(40\) −0.350617 + 0.202429i −0.0554374 + 0.0320068i
\(41\) −0.746755 + 2.78693i −0.116624 + 0.435245i −0.999403 0.0345422i \(-0.989003\pi\)
0.882780 + 0.469787i \(0.155669\pi\)
\(42\) 0 0
\(43\) 3.49297 + 2.01667i 0.532673 + 0.307539i 0.742104 0.670285i \(-0.233828\pi\)
−0.209431 + 0.977823i \(0.567161\pi\)
\(44\) −11.8381 3.17202i −1.78467 0.478200i
\(45\) −0.777660 + 2.90227i −0.115927 + 0.432644i
\(46\) 2.37147 8.85043i 0.349654 1.30492i
\(47\) 7.10802 + 1.90459i 1.03681 + 0.277813i 0.736791 0.676120i \(-0.236340\pi\)
0.300020 + 0.953933i \(0.403007\pi\)
\(48\) 4.84328 + 2.79627i 0.699067 + 0.403606i
\(49\) 0 0
\(50\) −3.00689 + 11.2219i −0.425239 + 1.58701i
\(51\) 0.785891 0.453734i 0.110047 0.0635355i
\(52\) −2.68838 + 6.92859i −0.372811 + 0.960823i
\(53\) 3.89042 6.73840i 0.534390 0.925590i −0.464803 0.885414i \(-0.653875\pi\)
0.999193 0.0401759i \(-0.0127918\pi\)
\(54\) −11.0043 + 2.94859i −1.49750 + 0.401253i
\(55\) −16.8946 + 9.75412i −2.27807 + 1.31525i
\(56\) 0 0
\(57\) −0.753475 + 0.753475i −0.0998002 + 0.0998002i
\(58\) −3.80821 + 3.80821i −0.500042 + 0.500042i
\(59\) −0.919907 0.246488i −0.119762 0.0320901i 0.198440 0.980113i \(-0.436412\pi\)
−0.318202 + 0.948023i \(0.603079\pi\)
\(60\) −9.43079 + 2.52697i −1.21751 + 0.326231i
\(61\) 1.08909i 0.139443i −0.997566 0.0697217i \(-0.977789\pi\)
0.997566 0.0697217i \(-0.0222111\pi\)
\(62\) −1.11320 1.92811i −0.141376 0.244870i
\(63\) 0 0
\(64\) 8.48212i 1.06026i
\(65\) 4.77256 + 10.8244i 0.591963 + 1.34260i
\(66\) −14.9811 8.64936i −1.84405 1.06466i
\(67\) −3.81608 + 3.81608i −0.466208 + 0.466208i −0.900684 0.434476i \(-0.856934\pi\)
0.434476 + 0.900684i \(0.356934\pi\)
\(68\) −1.12206 0.647822i −0.136070 0.0785599i
\(69\) 3.28197 5.68453i 0.395102 0.684338i
\(70\) 0 0
\(71\) 0.590023 + 2.20200i 0.0700229 + 0.261329i 0.992059 0.125776i \(-0.0401419\pi\)
−0.922036 + 0.387105i \(0.873475\pi\)
\(72\) 0.0799043 + 0.0799043i 0.00941681 + 0.00941681i
\(73\) 1.59300 + 5.94515i 0.186446 + 0.695827i 0.994316 + 0.106466i \(0.0339537\pi\)
−0.807870 + 0.589361i \(0.799380\pi\)
\(74\) 2.55084 + 4.41818i 0.296529 + 0.513603i
\(75\) −4.16136 + 7.20769i −0.480513 + 0.832273i
\(76\) 1.46954 + 0.393762i 0.168568 + 0.0451677i
\(77\) 0 0
\(78\) −6.19643 + 8.46422i −0.701608 + 0.958385i
\(79\) −6.08299 10.5361i −0.684390 1.18540i −0.973628 0.228141i \(-0.926735\pi\)
0.289238 0.957257i \(-0.406598\pi\)
\(80\) −8.98724 8.98724i −1.00480 1.00480i
\(81\) −5.41404 −0.601560
\(82\) 5.81448 0.642102
\(83\) 3.59152 + 3.59152i 0.394220 + 0.394220i 0.876189 0.481968i \(-0.160078\pi\)
−0.481968 + 0.876189i \(0.660078\pi\)
\(84\) 0 0
\(85\) −1.99209 + 0.533778i −0.216072 + 0.0578963i
\(86\) 2.10373 7.85121i 0.226851 0.846618i
\(87\) −3.34126 + 1.92908i −0.358220 + 0.206819i
\(88\) 0.733685i 0.0782111i
\(89\) −1.05715 3.94532i −0.112057 0.418203i 0.886993 0.461783i \(-0.152790\pi\)
−0.999050 + 0.0435803i \(0.986124\pi\)
\(90\) 6.05511 0.638265
\(91\) 0 0
\(92\) −9.37170 −0.977067
\(93\) −0.412802 1.54060i −0.0428055 0.159752i
\(94\) 14.8297i 1.52957i
\(95\) 2.09724 1.21084i 0.215172 0.124230i
\(96\) 3.00919 11.2305i 0.307125 1.14620i
\(97\) 8.41780 2.25554i 0.854698 0.229016i 0.195239 0.980756i \(-0.437452\pi\)
0.659460 + 0.751740i \(0.270785\pi\)
\(98\) 0 0
\(99\) 3.85022 + 3.85022i 0.386962 + 0.386962i
\(100\) 11.8828 1.18828
\(101\) 17.1752 1.70899 0.854496 0.519458i \(-0.173866\pi\)
0.854496 + 0.519458i \(0.173866\pi\)
\(102\) −1.29314 1.29314i −0.128040 0.128040i
\(103\) −7.19481 12.4618i −0.708926 1.22790i −0.965256 0.261306i \(-0.915847\pi\)
0.256330 0.966589i \(-0.417487\pi\)
\(104\) 0.442298 + 0.0481025i 0.0433709 + 0.00471684i
\(105\) 0 0
\(106\) −15.1460 4.05836i −1.47111 0.394183i
\(107\) −1.56036 + 2.70262i −0.150846 + 0.261272i −0.931539 0.363643i \(-0.881533\pi\)
0.780693 + 0.624915i \(0.214866\pi\)
\(108\) 5.82622 + 10.0913i 0.560628 + 0.971036i
\(109\) 2.45900 + 9.17711i 0.235529 + 0.879008i 0.977909 + 0.209029i \(0.0670302\pi\)
−0.742380 + 0.669979i \(0.766303\pi\)
\(110\) 27.7992 + 27.7992i 2.65055 + 2.65055i
\(111\) 0.945917 + 3.53021i 0.0897825 + 0.335073i
\(112\) 0 0
\(113\) 1.34080 2.32234i 0.126132 0.218467i −0.796043 0.605240i \(-0.793077\pi\)
0.922175 + 0.386773i \(0.126410\pi\)
\(114\) 1.85970 + 1.07370i 0.174177 + 0.100561i
\(115\) −10.5483 + 10.5483i −0.983633 + 0.983633i
\(116\) 4.77050 + 2.75425i 0.442930 + 0.255726i
\(117\) 2.57352 2.06866i 0.237922 0.191247i
\(118\) 1.91924i 0.176680i
\(119\) 0 0
\(120\) 0.292243 + 0.506181i 0.0266781 + 0.0462077i
\(121\) 24.3529i 2.21390i
\(122\) −2.12000 + 0.568052i −0.191936 + 0.0514290i
\(123\) 4.02345 + 1.07808i 0.362782 + 0.0972071i
\(124\) −1.61022 + 1.61022i −0.144602 + 0.144602i
\(125\) 1.77462 1.77462i 0.158727 0.158727i
\(126\) 0 0
\(127\) −4.93218 + 2.84760i −0.437661 + 0.252683i −0.702605 0.711580i \(-0.747980\pi\)
0.264944 + 0.964264i \(0.414646\pi\)
\(128\) −0.953075 + 0.255376i −0.0842407 + 0.0225722i
\(129\) 2.91143 5.04275i 0.256337 0.443989i
\(130\) 18.5812 14.9360i 1.62968 1.30997i
\(131\) −15.1645 + 8.75520i −1.32492 + 0.764946i −0.984510 0.175329i \(-0.943901\pi\)
−0.340415 + 0.940275i \(0.610568\pi\)
\(132\) −4.57939 + 17.0905i −0.398585 + 1.48754i
\(133\) 0 0
\(134\) 9.41872 + 5.43790i 0.813653 + 0.469763i
\(135\) 17.9159 + 4.80056i 1.54196 + 0.413166i
\(136\) −0.0200748 + 0.0749203i −0.00172140 + 0.00642437i
\(137\) 3.79415 14.1600i 0.324156 1.20977i −0.591001 0.806671i \(-0.701267\pi\)
0.915157 0.403097i \(-0.132066\pi\)
\(138\) −12.7772 3.42365i −1.08767 0.291440i
\(139\) 3.10457 + 1.79243i 0.263327 + 0.152032i 0.625851 0.779943i \(-0.284752\pi\)
−0.362525 + 0.931974i \(0.618085\pi\)
\(140\) 0 0
\(141\) 2.74963 10.2617i 0.231560 0.864195i
\(142\) 3.97862 2.29706i 0.333878 0.192765i
\(143\) 21.3123 + 2.31784i 1.78223 + 0.193827i
\(144\) −1.77376 + 3.07224i −0.147813 + 0.256020i
\(145\) 8.46946 2.26939i 0.703351 0.188462i
\(146\) 10.7418 6.20180i 0.889001 0.513265i
\(147\) 0 0
\(148\) 3.68974 3.68974i 0.303295 0.303295i
\(149\) 10.1485 10.1485i 0.831400 0.831400i −0.156308 0.987708i \(-0.549959\pi\)
0.987708 + 0.156308i \(0.0499593\pi\)
\(150\) 16.2009 + 4.34101i 1.32279 + 0.354442i
\(151\) −22.9711 + 6.15509i −1.86936 + 0.500894i −0.869386 + 0.494134i \(0.835485\pi\)
−0.999977 + 0.00676075i \(0.997848\pi\)
\(152\) 0.0910769i 0.00738732i
\(153\) 0.287817 + 0.498514i 0.0232687 + 0.0403025i
\(154\) 0 0
\(155\) 3.62475i 0.291147i
\(156\) 10.0027 + 3.88117i 0.800857 + 0.310742i
\(157\) −6.58929 3.80433i −0.525882 0.303618i 0.213456 0.976953i \(-0.431528\pi\)
−0.739338 + 0.673334i \(0.764861\pi\)
\(158\) −17.3365 + 17.3365i −1.37922 + 1.37922i
\(159\) −9.72812 5.61653i −0.771490 0.445420i
\(160\) −13.2116 + 22.8832i −1.04447 + 1.80908i
\(161\) 0 0
\(162\) 2.82388 + 10.5389i 0.221865 + 0.828012i
\(163\) −1.81864 1.81864i −0.142447 0.142447i 0.632287 0.774734i \(-0.282116\pi\)
−0.774734 + 0.632287i \(0.782116\pi\)
\(164\) −1.53923 5.74450i −0.120194 0.448570i
\(165\) 14.0819 + 24.3905i 1.09627 + 1.89880i
\(166\) 5.11790 8.86446i 0.397226 0.688016i
\(167\) 3.28638 + 0.880582i 0.254308 + 0.0681415i 0.383720 0.923449i \(-0.374643\pi\)
−0.129413 + 0.991591i \(0.541309\pi\)
\(168\) 0 0
\(169\) 2.79460 12.6961i 0.214969 0.976621i
\(170\) 2.07808 + 3.59935i 0.159382 + 0.276057i
\(171\) −0.477952 0.477952i −0.0365499 0.0365499i
\(172\) −8.31363 −0.633908
\(173\) 14.0503 1.06823 0.534114 0.845412i \(-0.320645\pi\)
0.534114 + 0.845412i \(0.320645\pi\)
\(174\) 5.49785 + 5.49785i 0.416791 + 0.416791i
\(175\) 0 0
\(176\) −22.2481 + 5.96136i −1.67701 + 0.449354i
\(177\) −0.355852 + 1.32806i −0.0267474 + 0.0998228i
\(178\) −7.12850 + 4.11564i −0.534303 + 0.308480i
\(179\) 14.9624i 1.11834i 0.829053 + 0.559170i \(0.188880\pi\)
−0.829053 + 0.559170i \(0.811120\pi\)
\(180\) −1.60294 5.98224i −0.119476 0.445890i
\(181\) −15.4409 −1.14772 −0.573858 0.818955i \(-0.694554\pi\)
−0.573858 + 0.818955i \(0.694554\pi\)
\(182\) 0 0
\(183\) −1.57230 −0.116228
\(184\) 0.145206 + 0.541917i 0.0107047 + 0.0399506i
\(185\) 8.30596i 0.610666i
\(186\) −2.78359 + 1.60710i −0.204102 + 0.117839i
\(187\) −0.967315 + 3.61007i −0.0707371 + 0.263994i
\(188\) −14.6513 + 3.92580i −1.06855 + 0.286318i
\(189\) 0 0
\(190\) −3.45089 3.45089i −0.250354 0.250354i
\(191\) −17.1549 −1.24129 −0.620643 0.784093i \(-0.713128\pi\)
−0.620643 + 0.784093i \(0.713128\pi\)
\(192\) −12.2455 −0.883743
\(193\) −4.33644 4.33644i −0.312144 0.312144i 0.533596 0.845740i \(-0.320840\pi\)
−0.845740 + 0.533596i \(0.820840\pi\)
\(194\) −8.78120 15.2095i −0.630453 1.09198i
\(195\) 15.6270 6.89008i 1.11907 0.493409i
\(196\) 0 0
\(197\) 24.7906 + 6.64263i 1.76626 + 0.473268i 0.987971 0.154640i \(-0.0494219\pi\)
0.778288 + 0.627908i \(0.216089\pi\)
\(198\) 5.48655 9.50299i 0.389912 0.675348i
\(199\) −4.36369 7.55813i −0.309334 0.535782i 0.668883 0.743368i \(-0.266773\pi\)
−0.978217 + 0.207586i \(0.933439\pi\)
\(200\) −0.184114 0.687122i −0.0130188 0.0485869i
\(201\) 5.50921 + 5.50921i 0.388590 + 0.388590i
\(202\) −8.95830 33.4328i −0.630304 2.35233i
\(203\) 0 0
\(204\) −0.935251 + 1.61990i −0.0654806 + 0.113416i
\(205\) −8.19819 4.73323i −0.572586 0.330583i
\(206\) −20.5052 + 20.5052i −1.42866 + 1.42866i
\(207\) 3.60587 + 2.08185i 0.250625 + 0.144699i
\(208\) 2.13513 + 13.8030i 0.148044 + 0.957065i
\(209\) 4.38858i 0.303565i
\(210\) 0 0
\(211\) −5.41370 9.37680i −0.372694 0.645525i 0.617285 0.786740i \(-0.288233\pi\)
−0.989979 + 0.141214i \(0.954899\pi\)
\(212\) 16.0381i 1.10150i
\(213\) 3.17899 0.851808i 0.217821 0.0583649i
\(214\) 6.07473 + 1.62772i 0.415260 + 0.111269i
\(215\) −9.35739 + 9.35739i −0.638168 + 0.638168i
\(216\) 0.493256 0.493256i 0.0335618 0.0335618i
\(217\) 0 0
\(218\) 16.5814 9.57329i 1.12304 0.648385i
\(219\) 8.58292 2.29979i 0.579980 0.155405i
\(220\) 20.1055 34.8237i 1.35551 2.34782i
\(221\) 2.11289 + 0.819827i 0.142128 + 0.0551476i
\(222\) 6.37847 3.68261i 0.428095 0.247161i
\(223\) 2.01754 7.52957i 0.135105 0.504217i −0.864893 0.501957i \(-0.832614\pi\)
0.999997 0.00226068i \(-0.000719598\pi\)
\(224\) 0 0
\(225\) −4.57206 2.63968i −0.304804 0.175979i
\(226\) −5.21997 1.39869i −0.347227 0.0930392i
\(227\) −3.68960 + 13.7698i −0.244888 + 0.913933i 0.728552 + 0.684990i \(0.240194\pi\)
−0.973440 + 0.228943i \(0.926473\pi\)
\(228\) 0.568469 2.12156i 0.0376478 0.140503i
\(229\) −11.0227 2.95351i −0.728398 0.195174i −0.124482 0.992222i \(-0.539727\pi\)
−0.603916 + 0.797048i \(0.706394\pi\)
\(230\) 26.0349 + 15.0313i 1.71669 + 0.991133i
\(231\) 0 0
\(232\) 0.0853493 0.318528i 0.00560346 0.0209124i
\(233\) −18.9544 + 10.9433i −1.24175 + 0.716922i −0.969450 0.245291i \(-0.921117\pi\)
−0.272297 + 0.962213i \(0.587783\pi\)
\(234\) −5.36911 3.93058i −0.350990 0.256950i
\(235\) −12.0720 + 20.9094i −0.787492 + 1.36398i
\(236\) 1.89614 0.508069i 0.123428 0.0330725i
\(237\) −15.2107 + 8.78193i −0.988044 + 0.570448i
\(238\) 0 0
\(239\) 3.79044 3.79044i 0.245183 0.245183i −0.573807 0.818990i \(-0.694534\pi\)
0.818990 + 0.573807i \(0.194534\pi\)
\(240\) −12.9747 + 12.9747i −0.837516 + 0.837516i
\(241\) 15.0798 + 4.04063i 0.971377 + 0.260280i 0.709409 0.704797i \(-0.248962\pi\)
0.261968 + 0.965077i \(0.415629\pi\)
\(242\) 47.4050 12.7021i 3.04731 0.816523i
\(243\) 9.14326i 0.586541i
\(244\) 1.12243 + 1.94411i 0.0718563 + 0.124459i
\(245\) 0 0
\(246\) 8.39427i 0.535199i
\(247\) −2.64563 0.287728i −0.168338 0.0183077i
\(248\) 0.118059 + 0.0681616i 0.00749677 + 0.00432826i
\(249\) 5.18502 5.18502i 0.328587 0.328587i
\(250\) −4.38005 2.52882i −0.277019 0.159937i
\(251\) −2.30694 + 3.99573i −0.145612 + 0.252208i −0.929601 0.368567i \(-0.879849\pi\)
0.783989 + 0.620775i \(0.213182\pi\)
\(252\) 0 0
\(253\) 6.99682 + 26.1125i 0.439886 + 1.64168i
\(254\) 8.11563 + 8.11563i 0.509220 + 0.509220i
\(255\) 0.770607 + 2.87595i 0.0482573 + 0.180099i
\(256\) −7.48790 12.9694i −0.467994 0.810589i
\(257\) −7.83278 + 13.5668i −0.488596 + 0.846273i −0.999914 0.0131189i \(-0.995824\pi\)
0.511318 + 0.859391i \(0.329157\pi\)
\(258\) −11.3347 3.03712i −0.705666 0.189083i
\(259\) 0 0
\(260\) −19.6751 14.4036i −1.22020 0.893276i
\(261\) −1.22367 2.11946i −0.0757434 0.131191i
\(262\) 24.9523 + 24.9523i 1.54156 + 1.54156i
\(263\) −23.9108 −1.47441 −0.737203 0.675671i \(-0.763854\pi\)
−0.737203 + 0.675671i \(0.763854\pi\)
\(264\) 1.05921 0.0651899
\(265\) 18.0516 + 18.0516i 1.10890 + 1.10890i
\(266\) 0 0
\(267\) −5.69580 + 1.52618i −0.348577 + 0.0934010i
\(268\) 2.87909 10.7449i 0.175868 0.656350i
\(269\) −11.7207 + 6.76695i −0.714624 + 0.412588i −0.812771 0.582584i \(-0.802042\pi\)
0.0981467 + 0.995172i \(0.468709\pi\)
\(270\) 37.3787i 2.27480i
\(271\) 5.60453 + 20.9164i 0.340451 + 1.27058i 0.897838 + 0.440327i \(0.145137\pi\)
−0.557387 + 0.830253i \(0.688196\pi\)
\(272\) −2.43498 −0.147642
\(273\) 0 0
\(274\) −29.5425 −1.78473
\(275\) −8.87160 33.1093i −0.534978 1.99656i
\(276\) 13.5298i 0.814397i
\(277\) 18.5473 10.7083i 1.11440 0.643399i 0.174434 0.984669i \(-0.444190\pi\)
0.939965 + 0.341270i \(0.110857\pi\)
\(278\) 1.86981 6.97821i 0.112143 0.418525i
\(279\) 0.977247 0.261853i 0.0585063 0.0156767i
\(280\) 0 0
\(281\) 0.874765 + 0.874765i 0.0521841 + 0.0521841i 0.732717 0.680533i \(-0.238252\pi\)
−0.680533 + 0.732717i \(0.738252\pi\)
\(282\) −21.4095 −1.27492
\(283\) −18.4612 −1.09741 −0.548703 0.836018i \(-0.684878\pi\)
−0.548703 + 0.836018i \(0.684878\pi\)
\(284\) −3.32265 3.32265i −0.197163 0.197163i
\(285\) −1.74807 3.02775i −0.103547 0.179348i
\(286\) −6.60433 42.6952i −0.390522 2.52462i
\(287\) 0 0
\(288\) 7.12383 + 1.90882i 0.419775 + 0.112479i
\(289\) 8.30245 14.3803i 0.488379 0.845897i
\(290\) −8.83509 15.3028i −0.518814 0.898613i
\(291\) −3.25629 12.1527i −0.190887 0.712401i
\(292\) −8.97079 8.97079i −0.524976 0.524976i
\(293\) −3.21602 12.0024i −0.187882 0.701186i −0.993995 0.109424i \(-0.965099\pi\)
0.806113 0.591762i \(-0.201567\pi\)
\(294\) 0 0
\(295\) 1.56234 2.70605i 0.0909629 0.157552i
\(296\) −0.270528 0.156189i −0.0157241 0.00907832i
\(297\) 23.7677 23.7677i 1.37914 1.37914i
\(298\) −25.0483 14.4616i −1.45101 0.837739i
\(299\) 16.2005 2.50599i 0.936900 0.144925i
\(300\) 17.1551i 0.990448i
\(301\) 0 0
\(302\) 23.9628 + 41.5048i 1.37890 + 2.38833i
\(303\) 24.7955i 1.42447i
\(304\) 2.76179 0.740021i 0.158400 0.0424431i
\(305\) 3.45154 + 0.924836i 0.197634 + 0.0529560i
\(306\) 0.820277 0.820277i 0.0468921 0.0468921i
\(307\) 3.51390 3.51390i 0.200549 0.200549i −0.599686 0.800235i \(-0.704708\pi\)
0.800235 + 0.599686i \(0.204708\pi\)
\(308\) 0 0
\(309\) −17.9909 + 10.3870i −1.02347 + 0.590898i
\(310\) 7.05587 1.89061i 0.400746 0.107380i
\(311\) −9.18303 + 15.9055i −0.520722 + 0.901916i 0.478988 + 0.877821i \(0.341004\pi\)
−0.999710 + 0.0240949i \(0.992330\pi\)
\(312\) 0.0694448 0.638540i 0.00393154 0.0361502i
\(313\) −7.78607 + 4.49529i −0.440095 + 0.254089i −0.703638 0.710559i \(-0.748442\pi\)
0.263543 + 0.964648i \(0.415109\pi\)
\(314\) −3.96856 + 14.8109i −0.223959 + 0.835825i
\(315\) 0 0
\(316\) 21.7172 + 12.5385i 1.22169 + 0.705343i
\(317\) −13.9161 3.72880i −0.781605 0.209430i −0.154113 0.988053i \(-0.549252\pi\)
−0.627492 + 0.778623i \(0.715919\pi\)
\(318\) −5.85900 + 21.8661i −0.328556 + 1.22619i
\(319\) 4.11259 15.3484i 0.230261 0.859346i
\(320\) 26.8815 + 7.20287i 1.50272 + 0.402653i
\(321\) 3.90173 + 2.25267i 0.217773 + 0.125732i
\(322\) 0 0
\(323\) 0.120079 0.448141i 0.00668137 0.0249352i
\(324\) 9.66448 5.57979i 0.536916 0.309988i
\(325\) −20.5414 + 3.17746i −1.13943 + 0.176254i
\(326\) −2.59156 + 4.48871i −0.143533 + 0.248607i
\(327\) 13.2489 3.55002i 0.732663 0.196317i
\(328\) −0.308326 + 0.178012i −0.0170244 + 0.00982906i
\(329\) 0 0
\(330\) 40.1333 40.1333i 2.20926 2.20926i
\(331\) 5.78697 5.78697i 0.318081 0.318081i −0.529949 0.848030i \(-0.677789\pi\)
0.848030 + 0.529949i \(0.177789\pi\)
\(332\) −10.1126 2.70967i −0.555001 0.148712i
\(333\) −2.23932 + 0.600024i −0.122714 + 0.0328811i
\(334\) 6.85650i 0.375171i
\(335\) −8.85335 15.3345i −0.483710 0.837811i
\(336\) 0 0
\(337\) 1.63832i 0.0892447i −0.999004 0.0446224i \(-0.985792\pi\)
0.999004 0.0446224i \(-0.0142085\pi\)
\(338\) −26.1716 + 1.18217i −1.42355 + 0.0643017i
\(339\) −3.35273 1.93570i −0.182095 0.105133i
\(340\) 3.00591 3.00591i 0.163018 0.163018i
\(341\) 5.68874 + 3.28439i 0.308062 + 0.177860i
\(342\) −0.681080 + 1.17967i −0.0368286 + 0.0637890i
\(343\) 0 0
\(344\) 0.128812 + 0.480734i 0.00694510 + 0.0259194i
\(345\) 15.2284 + 15.2284i 0.819870 + 0.819870i
\(346\) −7.32845 27.3501i −0.393980 1.47035i
\(347\) 4.81567 + 8.34098i 0.258519 + 0.447768i 0.965845 0.259119i \(-0.0834323\pi\)
−0.707327 + 0.706887i \(0.750099\pi\)
\(348\) 3.97627 6.88710i 0.213150 0.369187i
\(349\) −28.4665 7.62758i −1.52378 0.408295i −0.602794 0.797897i \(-0.705946\pi\)
−0.920983 + 0.389602i \(0.872613\pi\)
\(350\) 0 0
\(351\) −12.7700 15.8865i −0.681611 0.847961i
\(352\) 23.9422 + 41.4691i 1.27612 + 2.21031i
\(353\) −11.3032 11.3032i −0.601610 0.601610i 0.339130 0.940740i \(-0.389867\pi\)
−0.940740 + 0.339130i \(0.889867\pi\)
\(354\) 2.77078 0.147265
\(355\) −7.47960 −0.396976
\(356\) 5.95319 + 5.95319i 0.315519 + 0.315519i
\(357\) 0 0
\(358\) 29.1255 7.80415i 1.53933 0.412462i
\(359\) −1.48737 + 5.55095i −0.0785005 + 0.292968i −0.994004 0.109342i \(-0.965126\pi\)
0.915504 + 0.402309i \(0.131792\pi\)
\(360\) −0.321086 + 0.185379i −0.0169227 + 0.00977033i
\(361\) 18.4552i 0.971327i
\(362\) 8.05376 + 30.0570i 0.423296 + 1.57976i
\(363\) 35.1580 1.84531
\(364\) 0 0
\(365\) −20.1941 −1.05701
\(366\) 0.820088 + 3.06061i 0.0428667 + 0.159981i
\(367\) 25.4610i 1.32905i −0.747264 0.664527i \(-0.768633\pi\)
0.747264 0.664527i \(-0.231367\pi\)
\(368\) −15.2531 + 8.80639i −0.795123 + 0.459065i
\(369\) −0.683858 + 2.55219i −0.0356002 + 0.132862i
\(370\) −16.1682 + 4.33226i −0.840546 + 0.225224i
\(371\) 0 0
\(372\) 2.32465 + 2.32465i 0.120527 + 0.120527i
\(373\) 18.7156 0.969055 0.484528 0.874776i \(-0.338991\pi\)
0.484528 + 0.874776i \(0.338991\pi\)
\(374\) 7.53183 0.389462
\(375\) −2.56199 2.56199i −0.132301 0.132301i
\(376\) 0.454017 + 0.786380i 0.0234141 + 0.0405545i
\(377\) −8.98308 3.48554i −0.462652 0.179515i
\(378\) 0 0
\(379\) −20.5112 5.49596i −1.05359 0.282309i −0.309856 0.950784i \(-0.600281\pi\)
−0.743735 + 0.668475i \(0.766947\pi\)
\(380\) −2.49582 + 4.32289i −0.128033 + 0.221760i
\(381\) 4.11103 + 7.12052i 0.210615 + 0.364795i
\(382\) 8.94774 + 33.3934i 0.457806 + 1.70856i
\(383\) −22.9487 22.9487i −1.17262 1.17262i −0.981582 0.191039i \(-0.938814\pi\)
−0.191039 0.981582i \(-0.561186\pi\)
\(384\) 0.368682 + 1.37594i 0.0188142 + 0.0702157i
\(385\) 0 0
\(386\) −6.17941 + 10.7031i −0.314524 + 0.544771i
\(387\) 3.19877 + 1.84681i 0.162603 + 0.0938786i
\(388\) −12.7018 + 12.7018i −0.644838 + 0.644838i
\(389\) −6.03084 3.48191i −0.305776 0.176540i 0.339259 0.940693i \(-0.389824\pi\)
−0.645035 + 0.764153i \(0.723157\pi\)
\(390\) −21.5629 26.8254i −1.09188 1.35836i
\(391\) 2.85792i 0.144531i
\(392\) 0 0
\(393\) 12.6398 + 21.8927i 0.637591 + 1.10434i
\(394\) 51.7217i 2.60570i
\(395\) 38.5564 10.3312i 1.93998 0.519817i
\(396\) −10.8410 2.90485i −0.544783 0.145974i
\(397\) 10.5642 10.5642i 0.530203 0.530203i −0.390430 0.920633i \(-0.627674\pi\)
0.920633 + 0.390430i \(0.127674\pi\)
\(398\) −12.4365 + 12.4365i −0.623384 + 0.623384i
\(399\) 0 0
\(400\) 19.3401 11.1660i 0.967007 0.558302i
\(401\) −23.3513 + 6.25695i −1.16611 + 0.312457i −0.789402 0.613877i \(-0.789609\pi\)
−0.376704 + 0.926334i \(0.622943\pi\)
\(402\) 7.85061 13.5977i 0.391553 0.678190i
\(403\) 2.35295 3.21409i 0.117209 0.160105i
\(404\) −30.6590 + 17.7010i −1.52534 + 0.880657i
\(405\) 4.59751 17.1582i 0.228452 0.852595i
\(406\) 0 0
\(407\) −13.0355 7.52605i −0.646146 0.373052i
\(408\) 0.108161 + 0.0289818i 0.00535479 + 0.00143481i
\(409\) −9.71416 + 36.2537i −0.480334 + 1.79263i 0.119875 + 0.992789i \(0.461751\pi\)
−0.600209 + 0.799843i \(0.704916\pi\)
\(410\) −4.93756 + 18.4272i −0.243849 + 0.910056i
\(411\) −20.4425 5.47756i −1.00836 0.270188i
\(412\) 25.6866 + 14.8302i 1.26549 + 0.730630i
\(413\) 0 0
\(414\) 2.17172 8.10499i 0.106734 0.398338i
\(415\) −14.4321 + 8.33236i −0.708443 + 0.409020i
\(416\) 26.5692 11.7146i 1.30266 0.574356i
\(417\) 2.58770 4.48203i 0.126720 0.219486i
\(418\) −8.54273 + 2.28902i −0.417839 + 0.111960i
\(419\) 7.05130 4.07107i 0.344478 0.198885i −0.317772 0.948167i \(-0.602935\pi\)
0.662251 + 0.749282i \(0.269601\pi\)
\(420\) 0 0
\(421\) 2.46118 2.46118i 0.119951 0.119951i −0.644583 0.764534i \(-0.722969\pi\)
0.764534 + 0.644583i \(0.222969\pi\)
\(422\) −15.4290 + 15.4290i −0.751072 + 0.751072i
\(423\) 6.50934 + 1.74417i 0.316495 + 0.0848045i
\(424\) 0.927399 0.248496i 0.0450385 0.0120680i
\(425\) 3.62370i 0.175775i
\(426\) −3.31623 5.74387i −0.160672 0.278292i
\(427\) 0 0
\(428\) 6.43252i 0.310927i
\(429\) 3.34623 30.7683i 0.161557 1.48551i
\(430\) 23.0956 + 13.3342i 1.11377 + 0.643034i
\(431\) −10.8313 + 10.8313i −0.521724 + 0.521724i −0.918092 0.396368i \(-0.870271\pi\)
0.396368 + 0.918092i \(0.370271\pi\)
\(432\) 18.9652 + 10.9495i 0.912462 + 0.526810i
\(433\) −6.16396 + 10.6763i −0.296221 + 0.513070i −0.975268 0.221025i \(-0.929060\pi\)
0.679047 + 0.734095i \(0.262393\pi\)
\(434\) 0 0
\(435\) −3.27628 12.2272i −0.157086 0.586251i
\(436\) −13.8476 13.8476i −0.663179 0.663179i
\(437\) −0.868559 3.24151i −0.0415488 0.155062i
\(438\) −8.95345 15.5078i −0.427812 0.740993i
\(439\) 3.88598 6.73072i 0.185468 0.321240i −0.758266 0.651945i \(-0.773953\pi\)
0.943734 + 0.330705i \(0.107287\pi\)
\(440\) −2.32519 0.623033i −0.110849 0.0297019i
\(441\) 0 0
\(442\) 0.493808 4.54053i 0.0234881 0.215971i
\(443\) −3.14950 5.45509i −0.149637 0.259179i 0.781456 0.623960i \(-0.214477\pi\)
−0.931093 + 0.364781i \(0.881144\pi\)
\(444\) −5.32682 5.32682i −0.252800 0.252800i
\(445\) 13.4012 0.635278
\(446\) −15.7092 −0.743854
\(447\) −14.6513 14.6513i −0.692982 0.692982i
\(448\) 0 0
\(449\) 14.6362 3.92175i 0.690723 0.185079i 0.103651 0.994614i \(-0.466947\pi\)
0.587072 + 0.809535i \(0.300281\pi\)
\(450\) −2.75363 + 10.2767i −0.129808 + 0.484448i
\(451\) −14.8568 + 8.57758i −0.699579 + 0.403902i
\(452\) 5.52741i 0.259987i
\(453\) 8.88602 + 33.1631i 0.417501 + 1.55814i
\(454\) 28.7285 1.34829
\(455\) 0 0
\(456\) −0.131486 −0.00615742
\(457\) 4.02470 + 15.0204i 0.188267 + 0.702623i 0.993907 + 0.110218i \(0.0351549\pi\)
−0.805640 + 0.592405i \(0.798178\pi\)
\(458\) 22.9970i 1.07458i
\(459\) 3.07737 1.77672i 0.143639 0.0829302i
\(460\) 7.95829 29.7008i 0.371057 1.38480i
\(461\) −29.6778 + 7.95214i −1.38223 + 0.370368i −0.871931 0.489628i \(-0.837133\pi\)
−0.510301 + 0.859996i \(0.670466\pi\)
\(462\) 0 0
\(463\) −4.11310 4.11310i −0.191152 0.191152i 0.605042 0.796194i \(-0.293156\pi\)
−0.796194 + 0.605042i \(0.793156\pi\)
\(464\) 10.3524 0.480600
\(465\) 5.23300 0.242674
\(466\) 31.1885 + 31.1885i 1.44478 + 1.44478i
\(467\) 4.08246 + 7.07102i 0.188913 + 0.327208i 0.944888 0.327393i \(-0.106170\pi\)
−0.755975 + 0.654601i \(0.772837\pi\)
\(468\) −2.46194 + 6.34502i −0.113803 + 0.293299i
\(469\) 0 0
\(470\) 46.9984 + 12.5932i 2.16787 + 0.580880i
\(471\) −5.49225 + 9.51285i −0.253069 + 0.438329i
\(472\) −0.0587580 0.101772i −0.00270456 0.00468443i
\(473\) 6.20688 + 23.1644i 0.285393 + 1.06510i
\(474\) 25.0284 + 25.0284i 1.14959 + 1.14959i
\(475\) 1.10129 + 4.11006i 0.0505305 + 0.188583i
\(476\) 0 0
\(477\) 3.56274 6.17084i 0.163127 0.282544i
\(478\) −9.35544 5.40136i −0.427908 0.247053i
\(479\) 25.8476 25.8476i 1.18101 1.18101i 0.201523 0.979484i \(-0.435411\pi\)
0.979484 0.201523i \(-0.0645890\pi\)
\(480\) 33.0362 + 19.0735i 1.50789 + 0.870580i
\(481\) −5.39169 + 7.36496i −0.245840 + 0.335813i
\(482\) 31.4616i 1.43304i
\(483\) 0 0
\(484\) −25.0985 43.4719i −1.14084 1.97599i
\(485\) 28.5930i 1.29834i
\(486\) −17.7981 + 4.76899i −0.807339 + 0.216326i
\(487\) −16.2718 4.36001i −0.737344 0.197571i −0.129447 0.991586i \(-0.541320\pi\)
−0.607897 + 0.794016i \(0.707987\pi\)
\(488\) 0.0950266 0.0950266i 0.00430165 0.00430165i
\(489\) −2.62555 + 2.62555i −0.118731 + 0.118731i
\(490\) 0 0
\(491\) 8.48030 4.89611i 0.382711 0.220958i −0.296286 0.955099i \(-0.595748\pi\)
0.678997 + 0.734141i \(0.262415\pi\)
\(492\) −8.29325 + 2.22217i −0.373889 + 0.100183i
\(493\) 0.839916 1.45478i 0.0378279 0.0655199i
\(494\) 0.819837 + 5.30002i 0.0368862 + 0.238459i
\(495\) −15.4717 + 8.93256i −0.695399 + 0.401489i
\(496\) −1.10766 + 4.13383i −0.0497352 + 0.185614i
\(497\) 0 0
\(498\) −12.7975 7.38863i −0.573469 0.331093i
\(499\) 2.84635 + 0.762677i 0.127420 + 0.0341421i 0.321966 0.946751i \(-0.395656\pi\)
−0.194545 + 0.980894i \(0.562323\pi\)
\(500\) −1.33888 + 4.99678i −0.0598767 + 0.223463i
\(501\) 1.27128 4.74449i 0.0567968 0.211968i
\(502\) 8.98127 + 2.40653i 0.400854 + 0.107408i
\(503\) −24.6898 14.2547i −1.10086 0.635584i −0.164416 0.986391i \(-0.552574\pi\)
−0.936448 + 0.350807i \(0.885907\pi\)
\(504\) 0 0
\(505\) −14.5849 + 54.4314i −0.649018 + 2.42217i
\(506\) 47.1807 27.2398i 2.09744 1.21096i
\(507\) −18.3291 4.03452i −0.814025 0.179179i
\(508\) 5.86956 10.1664i 0.260419 0.451060i
\(509\) 18.6168 4.98837i 0.825177 0.221106i 0.178569 0.983927i \(-0.442853\pi\)
0.646609 + 0.762822i \(0.276187\pi\)
\(510\) 5.19632 3.00010i 0.230097 0.132847i
\(511\) 0 0
\(512\) −22.7359 + 22.7359i −1.00479 + 1.00479i
\(513\) −2.95044 + 2.95044i −0.130265 + 0.130265i
\(514\) 30.4943 + 8.17093i 1.34505 + 0.360404i
\(515\) 45.6035 12.2194i 2.00953 0.538452i
\(516\) 12.0023i 0.528370i
\(517\) 21.8770 + 37.8921i 0.962149 + 1.66649i
\(518\) 0 0
\(519\) 20.2843i 0.890381i
\(520\) −0.528039 + 1.36088i −0.0231560 + 0.0596786i
\(521\) −9.05428 5.22749i −0.396675 0.229020i 0.288373 0.957518i \(-0.406886\pi\)
−0.685048 + 0.728498i \(0.740219\pi\)
\(522\) −3.48746 + 3.48746i −0.152642 + 0.152642i
\(523\) −15.9637 9.21666i −0.698045 0.403016i 0.108574 0.994088i \(-0.465372\pi\)
−0.806619 + 0.591072i \(0.798705\pi\)
\(524\) 18.0465 31.2574i 0.788365 1.36549i
\(525\) 0 0
\(526\) 12.4715 + 46.5444i 0.543785 + 2.02943i
\(527\) 0.491040 + 0.491040i 0.0213900 + 0.0213900i
\(528\) 8.60632 + 32.1192i 0.374542 + 1.39781i
\(529\) −1.16397 2.01606i −0.0506076 0.0876549i
\(530\) 25.7235 44.5544i 1.11736 1.93532i
\(531\) −0.842426 0.225727i −0.0365582 0.00979574i
\(532\) 0 0
\(533\) 4.19689 + 9.51872i 0.181788 + 0.412301i
\(534\) 5.94169 + 10.2913i 0.257122 + 0.445348i
\(535\) −7.24010 7.24010i −0.313017 0.313017i
\(536\) −0.665931 −0.0287638
\(537\) 21.6010 0.932151
\(538\) 19.2858 + 19.2858i 0.831469 + 0.831469i
\(539\) 0 0
\(540\) −36.9288 + 9.89505i −1.58916 + 0.425815i
\(541\) −10.8498 + 40.4921i −0.466470 + 1.74089i 0.185499 + 0.982644i \(0.440610\pi\)
−0.651969 + 0.758246i \(0.726057\pi\)
\(542\) 37.7922 21.8193i 1.62331 0.937221i
\(543\) 22.2919i 0.956635i
\(544\) 1.31020 + 4.88972i 0.0561743 + 0.209645i
\(545\) −31.1722 −1.33527
\(546\) 0 0
\(547\) 39.3151 1.68099 0.840496 0.541818i \(-0.182264\pi\)
0.840496 + 0.541818i \(0.182264\pi\)
\(548\) 7.82062 + 29.1870i 0.334080 + 1.24680i
\(549\) 0.997358i 0.0425662i
\(550\) −59.8226 + 34.5386i −2.55084 + 1.47273i
\(551\) −0.510522 + 1.90529i −0.0217490 + 0.0811683i
\(552\) 0.782357 0.209632i 0.0332993 0.00892253i
\(553\) 0 0
\(554\) −30.5185 30.5185i −1.29661 1.29661i
\(555\) −11.9912 −0.508998
\(556\) −7.38921 −0.313372
\(557\) −30.1372 30.1372i −1.27695 1.27695i −0.942365 0.334587i \(-0.891403\pi\)
−0.334587 0.942365i \(-0.608597\pi\)
\(558\) −1.01943 1.76571i −0.0431561 0.0747486i
\(559\) 14.3715 2.22306i 0.607848 0.0940255i
\(560\) 0 0
\(561\) 5.21180 + 1.39650i 0.220042 + 0.0589602i
\(562\) 1.24654 2.15907i 0.0525820 0.0910747i
\(563\) 18.6963 + 32.3829i 0.787955 + 1.36478i 0.927218 + 0.374523i \(0.122193\pi\)
−0.139263 + 0.990255i \(0.544473\pi\)
\(564\) 5.66761 + 21.1518i 0.238650 + 0.890652i
\(565\) 6.22136 + 6.22136i 0.261735 + 0.261735i
\(566\) 9.62909 + 35.9363i 0.404741 + 1.51051i
\(567\) 0 0
\(568\) −0.140650 + 0.243613i −0.00590155 + 0.0102218i
\(569\) 26.9875 + 15.5812i 1.13137 + 0.653199i 0.944280 0.329143i \(-0.106760\pi\)
0.187094 + 0.982342i \(0.440093\pi\)
\(570\) −4.98199 + 4.98199i −0.208673 + 0.208673i
\(571\) 16.5495 + 9.55483i 0.692573 + 0.399857i 0.804575 0.593851i \(-0.202393\pi\)
−0.112002 + 0.993708i \(0.535726\pi\)
\(572\) −40.4330 + 17.8273i −1.69059 + 0.745397i
\(573\) 24.7663i 1.03463i
\(574\) 0 0
\(575\) −13.1055 22.6995i −0.546539 0.946633i
\(576\) 7.76770i 0.323654i
\(577\) −19.2526 + 5.15872i −0.801497 + 0.214760i −0.636241 0.771490i \(-0.719512\pi\)
−0.165256 + 0.986251i \(0.552845\pi\)
\(578\) −32.3228 8.66086i −1.34445 0.360244i
\(579\) −6.26045 + 6.26045i −0.260176 + 0.260176i
\(580\) −12.7798 + 12.7798i −0.530652 + 0.530652i
\(581\) 0 0
\(582\) −21.9577 + 12.6773i −0.910176 + 0.525490i
\(583\) 44.6871 11.9739i 1.85075 0.495907i
\(584\) −0.379740 + 0.657728i −0.0157137 + 0.0272170i
\(585\) 4.37058 + 9.91265i 0.180701 + 0.409838i
\(586\) −21.6861 + 12.5205i −0.895847 + 0.517217i
\(587\) −10.4047 + 38.8308i −0.429447 + 1.60272i 0.324569 + 0.945862i \(0.394781\pi\)
−0.754016 + 0.656856i \(0.771886\pi\)
\(588\) 0 0
\(589\) −0.706179 0.407713i −0.0290976 0.0167995i
\(590\) −6.08244 1.62979i −0.250410 0.0670972i
\(591\) 9.58986 35.7898i 0.394474 1.47220i
\(592\) 2.53815 9.47249i 0.104317 0.389317i
\(593\) 6.94560 + 1.86107i 0.285222 + 0.0764249i 0.398594 0.917128i \(-0.369498\pi\)
−0.113372 + 0.993553i \(0.536165\pi\)
\(594\) −58.6627 33.8689i −2.40696 1.38966i
\(595\) 0 0
\(596\) −7.65669 + 28.5752i −0.313630 + 1.17048i
\(597\) −10.9116 + 6.29979i −0.446580 + 0.257833i
\(598\) −13.3281 30.2285i −0.545025 1.23614i
\(599\) 14.6877 25.4398i 0.600123 1.03944i −0.392679 0.919676i \(-0.628452\pi\)
0.992802 0.119768i \(-0.0382150\pi\)
\(600\) −0.991988 + 0.265802i −0.0404977 + 0.0108513i
\(601\) 40.3495 23.2958i 1.64589 0.950255i 0.667208 0.744871i \(-0.267489\pi\)
0.978682 0.205384i \(-0.0658442\pi\)
\(602\) 0 0
\(603\) −3.49466 + 3.49466i −0.142314 + 0.142314i
\(604\) 34.6617 34.6617i 1.41036 1.41036i
\(605\) −77.1792 20.6801i −3.13778 0.840766i
\(606\) −48.2665 + 12.9330i −1.96069 + 0.525366i
\(607\) 21.4872i 0.872140i −0.899913 0.436070i \(-0.856370\pi\)
0.899913 0.436070i \(-0.143630\pi\)
\(608\) −2.97210 5.14782i −0.120534 0.208772i
\(609\) 0 0
\(610\) 7.20107i 0.291563i
\(611\) 24.2774 10.7041i 0.982157 0.433043i
\(612\) −1.02755 0.593258i −0.0415364 0.0239810i
\(613\) 20.2128 20.2128i 0.816389 0.816389i −0.169194 0.985583i \(-0.554116\pi\)
0.985583 + 0.169194i \(0.0541165\pi\)
\(614\) −8.67288 5.00729i −0.350009 0.202078i
\(615\) −6.83329 + 11.8356i −0.275545 + 0.477257i
\(616\) 0 0
\(617\) −5.40928 20.1877i −0.217769 0.812726i −0.985173 0.171562i \(-0.945119\pi\)
0.767404 0.641164i \(-0.221548\pi\)
\(618\) 29.6030 + 29.6030i 1.19081 + 1.19081i
\(619\) 1.16061 + 4.33146i 0.0466489 + 0.174096i 0.985320 0.170718i \(-0.0546087\pi\)
−0.938671 + 0.344814i \(0.887942\pi\)
\(620\) −3.73572 6.47046i −0.150030 0.259860i
\(621\) 12.8514 22.2593i 0.515711 0.893237i
\(622\) 35.7510 + 9.57946i 1.43349 + 0.384101i
\(623\) 0 0
\(624\) 19.9272 3.08245i 0.797725 0.123397i
\(625\) −10.2952 17.8317i −0.411806 0.713269i
\(626\) 12.8115 + 12.8115i 0.512052 + 0.512052i
\(627\) −6.33573 −0.253025
\(628\) 15.6832 0.625827
\(629\) −1.12520 1.12520i −0.0448645 0.0448645i
\(630\) 0 0
\(631\) −9.89598 + 2.65162i −0.393953 + 0.105559i −0.450357 0.892849i \(-0.648703\pi\)
0.0564039 + 0.998408i \(0.482037\pi\)
\(632\) 0.388544 1.45007i 0.0154555 0.0576806i
\(633\) −13.5371 + 7.81567i −0.538053 + 0.310645i
\(634\) 29.0337i 1.15307i
\(635\) −4.83627 18.0492i −0.191921 0.716260i
\(636\) 23.1539 0.918114
\(637\) 0 0
\(638\) −32.0220 −1.26776
\(639\) 0.540328 + 2.01653i 0.0213750 + 0.0797727i
\(640\) 3.23734i 0.127967i
\(641\) 27.7522 16.0227i 1.09615 0.632860i 0.160940 0.986964i \(-0.448547\pi\)
0.935206 + 0.354104i \(0.115214\pi\)
\(642\) 2.34991 8.77000i 0.0927437 0.346124i
\(643\) 44.5502 11.9372i 1.75689 0.470757i 0.770815 0.637059i \(-0.219849\pi\)
0.986075 + 0.166302i \(0.0531826\pi\)
\(644\) 0 0
\(645\) 13.5091 + 13.5091i 0.531921 + 0.531921i
\(646\) −0.934973 −0.0367860
\(647\) −30.7013 −1.20699 −0.603496 0.797366i \(-0.706226\pi\)
−0.603496 + 0.797366i \(0.706226\pi\)
\(648\) −0.472393 0.472393i −0.0185573 0.0185573i
\(649\) −2.83128 4.90392i −0.111137 0.192496i
\(650\) 16.8993 + 38.3282i 0.662844 + 1.50336i
\(651\) 0 0
\(652\) 5.12074 + 1.37210i 0.200544 + 0.0537355i
\(653\) 7.67694 13.2969i 0.300422 0.520346i −0.675810 0.737076i \(-0.736206\pi\)
0.976232 + 0.216730i \(0.0695392\pi\)
\(654\) −13.8208 23.9383i −0.540436 0.936063i
\(655\) −14.8696 55.4939i −0.581001 2.16833i
\(656\) −7.90320 7.90320i −0.308568 0.308568i
\(657\) 1.45883 + 5.44441i 0.0569142 + 0.212407i
\(658\) 0 0
\(659\) 4.71985 8.17502i 0.183859 0.318454i −0.759332 0.650703i \(-0.774474\pi\)
0.943192 + 0.332250i \(0.107808\pi\)
\(660\) −50.2745 29.0260i −1.95693 1.12984i
\(661\) 5.84186 5.84186i 0.227222 0.227222i −0.584309 0.811531i \(-0.698634\pi\)
0.811531 + 0.584309i \(0.198634\pi\)
\(662\) −14.2832 8.24641i −0.555132 0.320506i
\(663\) 1.18357 3.05035i 0.0459662 0.118466i
\(664\) 0.626743i 0.0243224i
\(665\) 0 0
\(666\) 2.33599 + 4.04605i 0.0905178 + 0.156781i
\(667\) 12.1506i 0.470474i
\(668\) −6.77398 + 1.81508i −0.262093 + 0.0702277i
\(669\) −10.8703 2.91270i −0.420271 0.112611i
\(670\) −25.2320 + 25.2320i −0.974797 + 0.974797i
\(671\) 4.57890 4.57890i 0.176766 0.176766i
\(672\) 0 0
\(673\) −27.2566 + 15.7366i −1.05067 + 0.606602i −0.922836 0.385194i \(-0.874134\pi\)
−0.127830 + 0.991796i \(0.540801\pi\)
\(674\) −3.18911 + 0.854521i −0.122840 + 0.0329149i
\(675\) −16.2950 + 28.2237i −0.627193 + 1.08633i
\(676\) 8.09619 + 25.5436i 0.311392 + 0.982447i
\(677\) 40.8799 23.6020i 1.57114 0.907099i 0.575112 0.818074i \(-0.304958\pi\)
0.996029 0.0890246i \(-0.0283750\pi\)
\(678\) −2.01926 + 7.53599i −0.0775493 + 0.289418i
\(679\) 0 0
\(680\) −0.220390 0.127242i −0.00845157 0.00487952i
\(681\) 19.8792 + 5.32663i 0.761774 + 0.204117i
\(682\) 3.42618 12.7867i 0.131195 0.489627i
\(683\) −11.7625 + 43.8982i −0.450079 + 1.67972i 0.252087 + 0.967705i \(0.418883\pi\)
−0.702166 + 0.712013i \(0.747784\pi\)
\(684\) 1.34577 + 0.360597i 0.0514567 + 0.0137878i
\(685\) 41.6538 + 24.0488i 1.59151 + 0.918858i
\(686\) 0 0
\(687\) −4.26394 + 15.9132i −0.162680 + 0.607128i
\(688\) −13.5310 + 7.81214i −0.515866 + 0.297835i
\(689\) −4.28858 27.7245i −0.163382 1.05622i
\(690\) 21.7004 37.5863i 0.826121 1.43088i
\(691\) 18.2526 4.89077i 0.694361 0.186054i 0.105658 0.994403i \(-0.466305\pi\)
0.588703 + 0.808349i \(0.299639\pi\)
\(692\) −25.0810 + 14.4805i −0.953435 + 0.550466i
\(693\) 0 0
\(694\) 13.7246 13.7246i 0.520980 0.520980i
\(695\) −8.31690 + 8.31690i −0.315478 + 0.315478i
\(696\) −0.459854 0.123218i −0.0174307 0.00467055i
\(697\) −1.75180 + 0.469393i −0.0663542 + 0.0177795i
\(698\) 59.3908i 2.24798i
\(699\) 15.7987 + 27.3642i 0.597563 + 1.03501i
\(700\) 0 0
\(701\) 31.6032i 1.19364i −0.802377 0.596818i \(-0.796431\pi\)
0.802377 0.596818i \(-0.203569\pi\)
\(702\) −24.2638 + 33.1440i −0.915779 + 1.25094i
\(703\) 1.61818 + 0.934256i 0.0610308 + 0.0352361i
\(704\) 35.6617 35.6617i 1.34405 1.34405i
\(705\) 30.1865 + 17.4282i 1.13689 + 0.656384i
\(706\) −16.1071 + 27.8982i −0.606197 + 1.04996i
\(707\) 0 0
\(708\) −0.733492 2.73743i −0.0275663 0.102879i
\(709\) −13.7245 13.7245i −0.515433 0.515433i 0.400753 0.916186i \(-0.368748\pi\)
−0.916186 + 0.400753i \(0.868748\pi\)
\(710\) 3.90125 + 14.5597i 0.146411 + 0.546414i
\(711\) −5.57064 9.64864i −0.208915 0.361852i
\(712\) 0.252003 0.436482i 0.00944421 0.0163578i
\(713\) 4.85186 + 1.30005i 0.181704 + 0.0486873i
\(714\) 0 0
\(715\) −25.4438 + 65.5747i −0.951543 + 2.45236i
\(716\) −15.4205 26.7090i −0.576290 0.998163i
\(717\) −5.47220 5.47220i −0.204363 0.204363i
\(718\) 11.5812 0.432205
\(719\) −4.47081 −0.166733 −0.0833665 0.996519i \(-0.526567\pi\)
−0.0833665 + 0.996519i \(0.526567\pi\)
\(720\) −8.23028 8.23028i −0.306724 0.306724i
\(721\) 0 0
\(722\) −35.9246 + 9.62596i −1.33697 + 0.358241i
\(723\) 5.83339 21.7705i 0.216946 0.809654i
\(724\) 27.5633 15.9137i 1.02438 0.591427i
\(725\) 15.4064i 0.572178i
\(726\) −18.3379 68.4378i −0.680582 2.53997i
\(727\) −25.9080 −0.960874 −0.480437 0.877029i \(-0.659522\pi\)
−0.480437 + 0.877029i \(0.659522\pi\)
\(728\) 0 0
\(729\) −29.4421 −1.09045
\(730\) 10.5329 + 39.3095i 0.389841 + 1.45491i
\(731\) 2.53526i 0.0937701i
\(732\) 2.80668 1.62044i 0.103738 0.0598931i
\(733\) 12.4133 46.3272i 0.458497 1.71114i −0.219100 0.975703i \(-0.570312\pi\)
0.677597 0.735433i \(-0.263021\pi\)
\(734\) −49.5619 + 13.2801i −1.82936 + 0.490177i
\(735\) 0 0
\(736\) 25.8916 + 25.8916i 0.954376 + 0.954376i
\(737\) −32.0882 −1.18198
\(738\) 5.32474 0.196007
\(739\) −12.3488 12.3488i −0.454258 0.454258i 0.442507 0.896765i \(-0.354089\pi\)
−0.896765 + 0.442507i \(0.854089\pi\)
\(740\) 8.56025 + 14.8268i 0.314681 + 0.545043i
\(741\) −0.415389 + 3.81946i −0.0152597 + 0.140311i
\(742\) 0 0
\(743\) −33.0523 8.85634i −1.21257 0.324908i −0.404801 0.914405i \(-0.632659\pi\)
−0.807770 + 0.589497i \(0.799326\pi\)
\(744\) 0.0984038 0.170440i 0.00360766 0.00624865i
\(745\) 23.5447 + 40.7807i 0.862612 + 1.49409i
\(746\) −9.76176 36.4314i −0.357403 1.33385i
\(747\) 3.28901 + 3.28901i 0.120339 + 0.120339i
\(748\) −1.99386 7.44118i −0.0729027 0.272077i
\(749\) 0 0
\(750\) −3.65083 + 6.32342i −0.133309 + 0.230899i
\(751\) 4.81931 + 2.78243i 0.175859 + 0.101532i 0.585346 0.810784i \(-0.300959\pi\)
−0.409487 + 0.912316i \(0.634292\pi\)
\(752\) −20.1570 + 20.1570i −0.735050 + 0.735050i
\(753\) 5.76857 + 3.33049i 0.210219 + 0.121370i
\(754\) −2.09945 + 19.3043i −0.0764576 + 0.703021i
\(755\) 78.0268i 2.83969i
\(756\) 0 0
\(757\) −9.89589 17.1402i −0.359672 0.622971i 0.628234 0.778025i \(-0.283778\pi\)
−0.987906 + 0.155054i \(0.950445\pi\)
\(758\) 42.7934i 1.55433i
\(759\) 37.6982 10.1012i 1.36836 0.366651i
\(760\) 0.288641 + 0.0773410i 0.0104701 + 0.00280545i
\(761\) −23.9987 + 23.9987i −0.869953 + 0.869953i −0.992467 0.122514i \(-0.960904\pi\)
0.122514 + 0.992467i \(0.460904\pi\)
\(762\) 11.7164 11.7164i 0.424441 0.424441i
\(763\) 0 0
\(764\) 30.6229 17.6801i 1.10790 0.639644i
\(765\) −1.82430 + 0.488820i −0.0659577 + 0.0176733i
\(766\) −32.7018 + 56.6411i −1.18156 + 2.04653i
\(767\) −3.14193 + 1.38531i −0.113449 + 0.0500206i
\(768\) −18.7238 + 10.8102i −0.675635 + 0.390078i
\(769\) 4.79803 17.9065i 0.173021 0.645725i −0.823859 0.566795i \(-0.808183\pi\)
0.996880 0.0789297i \(-0.0251503\pi\)
\(770\) 0 0
\(771\) 19.5862 + 11.3081i 0.705378 + 0.407250i
\(772\) 12.2101 + 3.27168i 0.439451 + 0.117750i
\(773\) 6.00148 22.3978i 0.215858 0.805594i −0.770005 0.638038i \(-0.779746\pi\)
0.985863 0.167555i \(-0.0535873\pi\)
\(774\) 1.92654 7.18993i 0.0692479 0.258437i
\(775\) −6.15190 1.64840i −0.220983 0.0592122i
\(776\) 0.931285 + 0.537678i 0.0334312 + 0.0193015i
\(777\) 0 0
\(778\) −3.63222 + 13.5556i −0.130221 + 0.485993i
\(779\) 1.84427 1.06479i 0.0660778 0.0381500i
\(780\) −20.7943 + 28.4047i −0.744556 + 1.01705i
\(781\) −6.77729 + 11.7386i −0.242510 + 0.420040i
\(782\) 5.56318 1.49065i 0.198939 0.0533055i
\(783\) −13.0836 + 7.55382i −0.467570 + 0.269952i
\(784\) 0 0
\(785\) 17.6522 17.6522i 0.630033 0.630033i
\(786\) 36.0232 36.0232i 1.28491 1.28491i
\(787\) −15.1886 4.06976i −0.541414 0.145071i −0.0222599 0.999752i \(-0.507086\pi\)
−0.519154 + 0.854681i \(0.673753\pi\)
\(788\) −51.0992 + 13.6920i −1.82033 + 0.487757i
\(789\) 34.5197i 1.22894i
\(790\) −40.2209 69.6646i −1.43099 2.47856i
\(791\) 0 0
\(792\) 0.671889i 0.0238745i
\(793\) −2.46016 3.06057i −0.0873628 0.108684i
\(794\) −26.0742 15.0540i −0.925340 0.534245i
\(795\) 26.0609 26.0609i 0.924284 0.924284i
\(796\) 15.5790 + 8.99457i 0.552185 + 0.318804i
\(797\) 10.8696 18.8267i 0.385021 0.666876i −0.606751 0.794892i \(-0.707527\pi\)
0.991772 + 0.128016i \(0.0408608\pi\)
\(798\) 0 0
\(799\) 1.19718 + 4.46794i 0.0423533 + 0.158064i
\(800\) −32.8292 32.8292i −1.16069 1.16069i
\(801\) −0.968105 3.61302i −0.0342063 0.127660i
\(802\) 24.3593 + 42.1916i 0.860158 + 1.48984i
\(803\) −18.2979 + 31.6929i −0.645720 + 1.11842i
\(804\) −15.5123 4.15650i −0.547075 0.146588i
\(805\) 0 0
\(806\) −7.48376 2.90379i −0.263604 0.102282i
\(807\) 9.76935 + 16.9210i 0.343897 + 0.595648i
\(808\) 1.49859 + 1.49859i 0.0527202 + 0.0527202i
\(809\) 35.6805 1.25446 0.627229 0.778835i \(-0.284189\pi\)
0.627229 + 0.778835i \(0.284189\pi\)
\(810\) −35.7977 −1.25780
\(811\) 0.747882 + 0.747882i 0.0262617 + 0.0262617i 0.720116 0.693854i \(-0.244089\pi\)
−0.693854 + 0.720116i \(0.744089\pi\)
\(812\) 0 0
\(813\) 30.1967 8.09117i 1.05904 0.283770i
\(814\) −7.85095 + 29.3001i −0.275176 + 1.02697i
\(815\) 7.30800 4.21928i 0.255988 0.147795i
\(816\) 3.51534i 0.123062i
\(817\) −0.770499 2.87554i −0.0269563 0.100602i
\(818\) 75.6376 2.64461
\(819\) 0 0
\(820\) 19.5125 0.681407
\(821\) 2.86268 + 10.6837i 0.0999084 + 0.372863i 0.997718 0.0675209i \(-0.0215089\pi\)
−0.897809 + 0.440384i \(0.854842\pi\)
\(822\) 42.6501i 1.48759i
\(823\) 20.4465 11.8048i 0.712719 0.411488i −0.0993482 0.995053i \(-0.531676\pi\)
0.812067 + 0.583564i \(0.198342\pi\)
\(824\) 0.459560 1.71510i 0.0160095 0.0597484i
\(825\) −47.7994 + 12.8078i −1.66416 + 0.445910i
\(826\) 0 0
\(827\) −1.09240 1.09240i −0.0379865 0.0379865i 0.687858 0.725845i \(-0.258551\pi\)
−0.725845 + 0.687858i \(0.758551\pi\)
\(828\) −8.58235 −0.298257
\(829\) 38.2127 1.32718 0.663591 0.748095i \(-0.269031\pi\)
0.663591 + 0.748095i \(0.269031\pi\)
\(830\) 23.7472 + 23.7472i 0.824277 + 0.824277i
\(831\) −15.4594 26.7765i −0.536280 0.928865i
\(832\) −19.1604 23.8366i −0.664267 0.826384i
\(833\) 0 0
\(834\) −10.0743 2.69941i −0.348846 0.0934729i
\(835\) −5.58148 + 9.66740i −0.193155 + 0.334554i
\(836\) 4.52294 + 7.83396i 0.156429 + 0.270943i
\(837\) −1.61644 6.03263i −0.0558722 0.208518i
\(838\) −11.6025 11.6025i −0.400802 0.400802i
\(839\) 10.2082 + 38.0974i 0.352425 + 1.31527i 0.883694 + 0.468066i \(0.155049\pi\)
−0.531268 + 0.847204i \(0.678284\pi\)
\(840\) 0 0
\(841\) 10.9291 18.9297i 0.376864 0.652747i
\(842\) −6.07460 3.50717i −0.209345 0.120865i
\(843\) 1.26288 1.26288i 0.0434961 0.0434961i
\(844\) 19.3277 + 11.1589i 0.665288 + 0.384104i
\(845\) 37.8632 + 19.6379i 1.30253 + 0.675565i
\(846\) 13.5807i 0.466914i
\(847\) 0 0
\(848\) 15.0707 + 26.1031i 0.517528 + 0.896385i
\(849\) 26.6522i 0.914700i
\(850\) −7.05382 + 1.89007i −0.241944 + 0.0648288i
\(851\) −11.1178 2.97901i −0.381114 0.102119i
\(852\) −4.79686 + 4.79686i −0.164338 + 0.164338i
\(853\) 2.18217 2.18217i 0.0747162 0.0747162i −0.668761 0.743477i \(-0.733175\pi\)
0.743477 + 0.668761i \(0.233175\pi\)
\(854\) 0 0
\(855\) 1.92059 1.10886i 0.0656829 0.0379220i
\(856\) −0.371959 + 0.0996661i −0.0127133 + 0.00340652i
\(857\) 14.7330 25.5183i 0.503270 0.871689i −0.496723 0.867909i \(-0.665464\pi\)
0.999993 0.00377978i \(-0.00120314\pi\)
\(858\) −61.6384 + 9.53458i −2.10430 + 0.325505i
\(859\) 44.5926 25.7455i 1.52148 0.878426i 0.521800 0.853068i \(-0.325261\pi\)
0.999678 0.0253585i \(-0.00807272\pi\)
\(860\) 7.05980 26.3475i 0.240737 0.898443i
\(861\) 0 0
\(862\) 26.7334 + 15.4345i 0.910543 + 0.525702i
\(863\) −31.1185 8.33816i −1.05928 0.283834i −0.313201 0.949687i \(-0.601401\pi\)
−0.746083 + 0.665852i \(0.768068\pi\)
\(864\) 11.7833 43.9760i 0.400877 1.49609i
\(865\) −11.9313 + 44.5283i −0.405677 + 1.51401i
\(866\) 23.9973 + 6.43005i 0.815461 + 0.218502i
\(867\) −20.7606 11.9861i −0.705066 0.407070i
\(868\) 0 0
\(869\) 18.7222 69.8721i 0.635106 2.37025i
\(870\) −22.0925 + 12.7551i −0.749005 + 0.432438i
\(871\) −2.10379 + 19.3442i −0.0712843 + 0.655453i
\(872\) −0.586177 + 1.01529i −0.0198505 + 0.0343820i
\(873\) 7.70880 2.06557i 0.260903 0.0699088i
\(874\) −5.85683 + 3.38144i −0.198110 + 0.114379i
\(875\) 0 0
\(876\) −12.9510 + 12.9510i −0.437574 + 0.437574i
\(877\) 17.5437 17.5437i 0.592409 0.592409i −0.345873 0.938281i \(-0.612417\pi\)
0.938281 + 0.345873i \(0.112417\pi\)
\(878\) −15.1288 4.05374i −0.510571 0.136807i
\(879\) −17.3276 + 4.64293i −0.584447 + 0.156602i
\(880\) 75.5708i 2.54749i
\(881\) 8.18440 + 14.1758i 0.275740 + 0.477595i 0.970321 0.241819i \(-0.0777439\pi\)
−0.694582 + 0.719414i \(0.744411\pi\)
\(882\) 0 0
\(883\) 13.3555i 0.449449i 0.974422 + 0.224724i \(0.0721482\pi\)
−0.974422 + 0.224724i \(0.927852\pi\)
\(884\) −4.61660 + 0.714123i −0.155273 + 0.0240185i
\(885\) −3.90669 2.25553i −0.131322 0.0758187i
\(886\) −8.97605 + 8.97605i −0.301556 + 0.301556i
\(887\) −14.2827 8.24614i −0.479567 0.276878i 0.240669 0.970607i \(-0.422633\pi\)
−0.720236 + 0.693729i \(0.755967\pi\)
\(888\) −0.225488 + 0.390557i −0.00756689 + 0.0131062i
\(889\) 0 0
\(890\) −6.98987 26.0865i −0.234301 0.874423i
\(891\) −22.7625 22.7625i −0.762571 0.762571i
\(892\) 4.15862 + 15.5202i 0.139241 + 0.519654i
\(893\) −2.71573 4.70378i −0.0908784 0.157406i
\(894\) −20.8780 + 36.1618i −0.698266 + 1.20943i
\(895\) −47.4187 12.7058i −1.58503 0.424708i
\(896\) 0 0
\(897\) −3.61786 23.3884i −0.120797 0.780917i
\(898\) −15.2680 26.4450i −0.509500 0.882480i
\(899\) −2.08768 2.08768i −0.0696281 0.0696281i
\(900\) 10.8820 0.362732
\(901\) 4.89086 0.162938
\(902\) 24.4460 + 24.4460i 0.813964 + 0.813964i
\(903\) 0 0
\(904\) 0.319621 0.0856423i 0.0106304 0.00284842i
\(905\) 13.1122 48.9354i 0.435864 1.62667i
\(906\) 59.9198 34.5947i 1.99070 1.14933i
\(907\) 13.0225i 0.432404i −0.976349 0.216202i \(-0.930633\pi\)
0.976349 0.216202i \(-0.0693670\pi\)
\(908\) −7.60512 28.3827i −0.252385 0.941913i
\(909\) 15.7285 0.521683
\(910\) 0 0
\(911\) 29.0374 0.962053 0.481026 0.876706i \(-0.340264\pi\)
0.481026 + 0.876706i \(0.340264\pi\)
\(912\) −1.06836 3.98716i −0.0353768 0.132028i
\(913\) 30.1999i 0.999471i
\(914\) 27.1392 15.6688i 0.897683 0.518278i
\(915\) 1.33517 4.98293i 0.0441394 0.164731i
\(916\) 22.7202 6.08787i 0.750698 0.201149i
\(917\) 0 0
\(918\) −5.06364 5.06364i −0.167125 0.167125i
\(919\) −15.4786 −0.510591 −0.255296 0.966863i \(-0.582173\pi\)
−0.255296 + 0.966863i \(0.582173\pi\)
\(920\) −1.84075 −0.0606876
\(921\) −5.07296 5.07296i −0.167160 0.167160i
\(922\) 30.9590 + 53.6225i 1.01958 + 1.76596i
\(923\) 6.63222 + 4.85527i 0.218302 + 0.159813i
\(924\) 0 0
\(925\) 14.0968 + 3.77723i 0.463501 + 0.124195i
\(926\) −5.86115 + 10.1518i −0.192609 + 0.333609i
\(927\) −6.58882 11.4122i −0.216405 0.374825i
\(928\) −5.57038 20.7889i −0.182857 0.682430i
\(929\) −31.9786 31.9786i −1.04918 1.04918i −0.998726 0.0504568i \(-0.983932\pi\)
−0.0504568 0.998726i \(-0.516068\pi\)
\(930\) −2.72945 10.1865i −0.0895023 0.334027i
\(931\) 0 0
\(932\) 22.5568 39.0695i 0.738871 1.27976i
\(933\) 22.9625 + 13.2574i 0.751758 + 0.434028i
\(934\) 11.6350 11.6350i 0.380708 0.380708i
\(935\) −10.6196 6.13122i −0.347298 0.200512i
\(936\) 0.405045 + 0.0440510i 0.0132393 + 0.00143985i
\(937\) 26.8615i 0.877526i 0.898603 + 0.438763i \(0.144583\pi\)
−0.898603 + 0.438763i \(0.855417\pi\)
\(938\) 0 0
\(939\) 6.48978 + 11.2406i 0.211786 + 0.366824i
\(940\) 49.7665i 1.62320i
\(941\) −1.40463 + 0.376369i −0.0457896 + 0.0122693i −0.281641 0.959520i \(-0.590879\pi\)
0.235852 + 0.971789i \(0.424212\pi\)
\(942\) 21.3822 + 5.72935i 0.696670 + 0.186672i
\(943\) −9.27596 + 9.27596i −0.302067 + 0.302067i
\(944\) 2.60868 2.60868i 0.0849054 0.0849054i
\(945\) 0 0
\(946\) 41.8539 24.1644i 1.36079 0.785652i
\(947\) 37.4500 10.0347i 1.21696 0.326084i 0.407472 0.913218i \(-0.366410\pi\)
0.809490 + 0.587133i \(0.199744\pi\)
\(948\) 18.1016 31.3529i 0.587912 1.01829i
\(949\) 17.9063 + 13.1087i 0.581262 + 0.425526i
\(950\) 7.42616 4.28749i 0.240936 0.139105i
\(951\) −5.38322 + 20.0904i −0.174563 + 0.651477i
\(952\) 0 0
\(953\) 20.6259 + 11.9084i 0.668138 + 0.385750i 0.795371 0.606123i \(-0.207276\pi\)
−0.127233 + 0.991873i \(0.540609\pi\)
\(954\) −13.8703 3.71654i −0.449068 0.120327i
\(955\) 14.5677 54.3673i 0.471399 1.75928i
\(956\) −2.85975 + 10.6727i −0.0924908 + 0.345180i
\(957\) −22.1583 5.93729i −0.716275 0.191925i
\(958\) −63.7962 36.8327i −2.06116 1.19001i
\(959\) 0 0
\(960\) 10.3987 38.8084i 0.335616 1.25254i
\(961\) −25.7898 + 14.8897i −0.831929 + 0.480314i
\(962\) 17.1487 + 6.65391i 0.552897 + 0.214531i
\(963\) −1.42893 + 2.47499i −0.0460468 + 0.0797553i
\(964\) −31.0830 + 8.32866i −1.00112 + 0.268248i
\(965\) 17.4255 10.0606i 0.560946 0.323862i
\(966\) 0 0
\(967\) 5.04001 5.04001i 0.162076 0.162076i −0.621410 0.783486i \(-0.713440\pi\)
0.783486 + 0.621410i \(0.213440\pi\)
\(968\) −2.12487 + 2.12487i −0.0682960 + 0.0682960i
\(969\) −0.646974 0.173356i −0.0207838 0.00556900i
\(970\) 55.6587 14.9137i 1.78709 0.478850i
\(971\) 16.7115i 0.536296i 0.963378 + 0.268148i \(0.0864117\pi\)
−0.963378 + 0.268148i \(0.913588\pi\)
\(972\) 9.42319 + 16.3214i 0.302249 + 0.523510i
\(973\) 0 0
\(974\) 33.9484i 1.08778i
\(975\) 4.58726 + 29.6553i 0.146910 + 0.949730i
\(976\) 3.65367 + 2.10945i 0.116951 + 0.0675218i
\(977\) −34.8162 + 34.8162i −1.11387 + 1.11387i −0.121248 + 0.992622i \(0.538690\pi\)
−0.992622 + 0.121248i \(0.961310\pi\)
\(978\) 6.48029 + 3.74140i 0.207217 + 0.119637i
\(979\) 12.1429 21.0321i 0.388088 0.672188i
\(980\) 0 0
\(981\) 2.25189 + 8.40415i 0.0718972 + 0.268324i
\(982\) −13.9539 13.9539i −0.445286 0.445286i
\(983\) 9.14216 + 34.1190i 0.291590 + 1.08823i 0.943888 + 0.330265i \(0.107138\pi\)
−0.652298 + 0.757962i \(0.726195\pi\)
\(984\) 0.256993 + 0.445125i 0.00819264 + 0.0141901i
\(985\) −42.1036 + 72.9255i −1.34153 + 2.32360i
\(986\) −3.26993 0.876175i −0.104136 0.0279031i
\(987\) 0 0
\(988\) 5.01920 2.21301i 0.159682 0.0704054i
\(989\) 9.16909 + 15.8813i 0.291560 + 0.504997i
\(990\) 25.4577 + 25.4577i 0.809100 + 0.809100i
\(991\) 6.83828 0.217225 0.108613 0.994084i \(-0.465359\pi\)
0.108613 + 0.994084i \(0.465359\pi\)
\(992\) 8.89722 0.282487
\(993\) −8.35456 8.35456i −0.265124 0.265124i
\(994\) 0 0
\(995\) 27.6588 7.41114i 0.876842 0.234949i
\(996\) −3.91190 + 14.5994i −0.123953 + 0.462600i
\(997\) 42.8521 24.7407i 1.35714 0.783545i 0.367903 0.929864i \(-0.380076\pi\)
0.989237 + 0.146319i \(0.0467425\pi\)
\(998\) 5.93845i 0.187978i
\(999\) 3.70400 + 13.8235i 0.117189 + 0.437356i
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 637.2.x.a.80.2 28
7.2 even 3 91.2.ba.a.54.2 yes 28
7.3 odd 6 637.2.bd.a.587.6 28
7.4 even 3 637.2.bd.b.587.6 28
7.5 odd 6 637.2.bb.a.509.2 28
7.6 odd 2 91.2.w.a.80.2 yes 28
13.7 odd 12 637.2.bb.a.423.2 28
21.2 odd 6 819.2.et.b.145.6 28
21.20 even 2 819.2.gh.b.262.6 28
91.20 even 12 91.2.ba.a.59.2 yes 28
91.33 even 12 inner 637.2.x.a.215.2 28
91.46 odd 12 637.2.bd.a.293.6 28
91.59 even 12 637.2.bd.b.293.6 28
91.72 odd 12 91.2.w.a.33.2 28
273.20 odd 12 819.2.et.b.514.6 28
273.254 even 12 819.2.gh.b.397.6 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.w.a.33.2 28 91.72 odd 12
91.2.w.a.80.2 yes 28 7.6 odd 2
91.2.ba.a.54.2 yes 28 7.2 even 3
91.2.ba.a.59.2 yes 28 91.20 even 12
637.2.x.a.80.2 28 1.1 even 1 trivial
637.2.x.a.215.2 28 91.33 even 12 inner
637.2.bb.a.423.2 28 13.7 odd 12
637.2.bb.a.509.2 28 7.5 odd 6
637.2.bd.a.293.6 28 91.46 odd 12
637.2.bd.a.587.6 28 7.3 odd 6
637.2.bd.b.293.6 28 91.59 even 12
637.2.bd.b.587.6 28 7.4 even 3
819.2.et.b.145.6 28 21.2 odd 6
819.2.et.b.514.6 28 273.20 odd 12
819.2.gh.b.262.6 28 21.20 even 2
819.2.gh.b.397.6 28 273.254 even 12