Properties

Label 210.2.m.b.97.1
Level $210$
Weight $2$
Character 210.97
Analytic conductor $1.677$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,2,Mod(13,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.m (of order \(4\), degree \(2\), 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: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.1698758656.6
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 97.1
Root \(2.16053i\) of defining polynomial
Character \(\chi\) \(=\) 210.97
Dual form 210.2.m.b.13.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-2.23483 + 0.0743018i) q^{5} -1.00000i q^{6} +(2.52773 + 0.781409i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-2.23483 + 0.0743018i) q^{5} -1.00000i q^{6} +(2.52773 + 0.781409i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(1.63280 + 1.52773i) q^{10} +4.90685 q^{11} +(-0.707107 + 0.707107i) q^{12} +(3.41421 + 3.41421i) q^{13} +(-1.23483 - 2.33991i) q^{14} +(-1.63280 - 1.52773i) q^{15} -1.00000 q^{16} +(-2.74632 + 2.74632i) q^{17} +(0.707107 - 0.707107i) q^{18} -1.26561 q^{19} +(-0.0743018 - 2.23483i) q^{20} +(1.23483 + 2.33991i) q^{21} +(-3.46967 - 3.46967i) q^{22} +(-1.05545 + 1.05545i) q^{23} +1.00000 q^{24} +(4.98896 - 0.332104i) q^{25} -4.82843i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.781409 + 2.52773i) q^{28} -4.76687i q^{29} +(0.0743018 + 2.23483i) q^{30} -7.05545i q^{31} +(0.707107 + 0.707107i) q^{32} +(3.46967 + 3.46967i) q^{33} +3.88388 q^{34} +(-5.70711 - 1.55850i) q^{35} -1.00000 q^{36} +(-4.74632 - 4.74632i) q^{37} +(0.894921 + 0.894921i) q^{38} +4.82843i q^{39} +(-1.52773 + 1.63280i) q^{40} -5.44670i q^{41} +(0.781409 - 2.52773i) q^{42} +(-7.58667 + 7.58667i) q^{43} +4.90685i q^{44} +(-0.0743018 - 2.23483i) q^{45} +1.49264 q^{46} +(-0.734390 + 0.734390i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(5.77880 + 3.95037i) q^{49} +(-3.76256 - 3.29289i) q^{50} -3.88388 q^{51} +(-3.41421 + 3.41421i) q^{52} +(1.26561 - 1.26561i) q^{53} +1.00000 q^{54} +(-10.9660 + 0.364588i) q^{55} +(2.33991 - 1.23483i) q^{56} +(-0.894921 - 0.894921i) q^{57} +(-3.37069 + 3.37069i) q^{58} -1.39735 q^{59} +(1.52773 - 1.63280i) q^{60} -2.29721i q^{61} +(-4.98896 + 4.98896i) q^{62} +(-0.781409 + 2.52773i) q^{63} -1.00000i q^{64} +(-7.88388 - 7.37652i) q^{65} -4.90685i q^{66} +(3.05545 + 3.05545i) q^{67} +(-2.74632 - 2.74632i) q^{68} -1.49264 q^{69} +(2.93351 + 5.13756i) q^{70} -13.0334 q^{71} +(0.707107 + 0.707107i) q^{72} +(-5.04441 - 5.04441i) q^{73} +6.71231i q^{74} +(3.76256 + 3.29289i) q^{75} -1.26561i q^{76} +(12.4032 + 3.83425i) q^{77} +(3.41421 - 3.41421i) q^{78} -14.8063i q^{79} +(2.23483 - 0.0743018i) q^{80} -1.00000 q^{81} +(-3.85140 + 3.85140i) q^{82} +(9.29809 + 9.29809i) q^{83} +(-2.33991 + 1.23483i) q^{84} +(5.93351 - 6.34162i) q^{85} +10.7292 q^{86} +(3.37069 - 3.37069i) q^{87} +(3.46967 - 3.46967i) q^{88} +15.3596 q^{89} +(-1.52773 + 1.63280i) q^{90} +(5.96230 + 11.2981i) q^{91} +(-1.05545 - 1.05545i) q^{92} +(4.98896 - 4.98896i) q^{93} +1.03858 q^{94} +(2.82843 - 0.0940371i) q^{95} +1.00000i q^{96} +(8.42614 - 8.42614i) q^{97} +(-1.29289 - 6.87957i) q^{98} +4.90685i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{7} + 4 q^{10} + 8 q^{11} + 16 q^{13} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 12 q^{17} + 8 q^{19} - 4 q^{20} - 8 q^{21} + 8 q^{22} + 16 q^{23} + 8 q^{24} - 4 q^{25} - 4 q^{28} + 4 q^{30} - 8 q^{33} - 16 q^{34} - 40 q^{35} - 8 q^{36} - 28 q^{37} + 4 q^{38} + 4 q^{42} - 4 q^{45} - 8 q^{46} - 24 q^{47} - 4 q^{49} + 16 q^{51} - 16 q^{52} - 8 q^{53} + 8 q^{54} - 28 q^{55} + 4 q^{56} - 4 q^{57} - 12 q^{58} - 8 q^{59} + 4 q^{62} - 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} + 4 q^{70} + 8 q^{71} + 28 q^{73} + 44 q^{77} + 16 q^{78} - 8 q^{81} - 24 q^{82} + 16 q^{83} - 4 q^{84} + 28 q^{85} + 8 q^{86} + 12 q^{87} - 8 q^{88} + 64 q^{89} - 8 q^{91} + 16 q^{92} - 4 q^{93} - 8 q^{94} + 28 q^{97} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) −2.23483 + 0.0743018i −0.999448 + 0.0332288i
\(6\) 1.00000i 0.408248i
\(7\) 2.52773 + 0.781409i 0.955391 + 0.295345i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 1.63280 + 1.52773i 0.516338 + 0.483109i
\(11\) 4.90685 1.47947 0.739735 0.672898i \(-0.234951\pi\)
0.739735 + 0.672898i \(0.234951\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) 3.41421 + 3.41421i 0.946932 + 0.946932i 0.998661 0.0517287i \(-0.0164731\pi\)
−0.0517287 + 0.998661i \(0.516473\pi\)
\(14\) −1.23483 2.33991i −0.330023 0.625368i
\(15\) −1.63280 1.52773i −0.421588 0.394457i
\(16\) −1.00000 −0.250000
\(17\) −2.74632 + 2.74632i −0.666080 + 0.666080i −0.956806 0.290726i \(-0.906103\pi\)
0.290726 + 0.956806i \(0.406103\pi\)
\(18\) 0.707107 0.707107i 0.166667 0.166667i
\(19\) −1.26561 −0.290351 −0.145175 0.989406i \(-0.546375\pi\)
−0.145175 + 0.989406i \(0.546375\pi\)
\(20\) −0.0743018 2.23483i −0.0166144 0.499724i
\(21\) 1.23483 + 2.33991i 0.269463 + 0.510611i
\(22\) −3.46967 3.46967i −0.739735 0.739735i
\(23\) −1.05545 + 1.05545i −0.220077 + 0.220077i −0.808531 0.588454i \(-0.799737\pi\)
0.588454 + 0.808531i \(0.299737\pi\)
\(24\) 1.00000 0.204124
\(25\) 4.98896 0.332104i 0.997792 0.0664208i
\(26\) 4.82843i 0.946932i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) −0.781409 + 2.52773i −0.147672 + 0.477695i
\(29\) 4.76687i 0.885186i −0.896723 0.442593i \(-0.854059\pi\)
0.896723 0.442593i \(-0.145941\pi\)
\(30\) 0.0743018 + 2.23483i 0.0135656 + 0.408023i
\(31\) 7.05545i 1.26720i −0.773662 0.633598i \(-0.781577\pi\)
0.773662 0.633598i \(-0.218423\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 3.46967 + 3.46967i 0.603991 + 0.603991i
\(34\) 3.88388 0.666080
\(35\) −5.70711 1.55850i −0.964677 0.263435i
\(36\) −1.00000 −0.166667
\(37\) −4.74632 4.74632i −0.780290 0.780290i 0.199590 0.979880i \(-0.436039\pi\)
−0.979880 + 0.199590i \(0.936039\pi\)
\(38\) 0.894921 + 0.894921i 0.145175 + 0.145175i
\(39\) 4.82843i 0.773167i
\(40\) −1.52773 + 1.63280i −0.241555 + 0.258169i
\(41\) 5.44670i 0.850631i −0.905045 0.425316i \(-0.860163\pi\)
0.905045 0.425316i \(-0.139837\pi\)
\(42\) 0.781409 2.52773i 0.120574 0.390037i
\(43\) −7.58667 + 7.58667i −1.15696 + 1.15696i −0.171830 + 0.985127i \(0.554968\pi\)
−0.985127 + 0.171830i \(0.945032\pi\)
\(44\) 4.90685i 0.739735i
\(45\) −0.0743018 2.23483i −0.0110763 0.333149i
\(46\) 1.49264 0.220077
\(47\) −0.734390 + 0.734390i −0.107122 + 0.107122i −0.758636 0.651514i \(-0.774134\pi\)
0.651514 + 0.758636i \(0.274134\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 5.77880 + 3.95037i 0.825543 + 0.564339i
\(50\) −3.76256 3.29289i −0.532106 0.465685i
\(51\) −3.88388 −0.543852
\(52\) −3.41421 + 3.41421i −0.473466 + 0.473466i
\(53\) 1.26561 1.26561i 0.173845 0.173845i −0.614821 0.788666i \(-0.710772\pi\)
0.788666 + 0.614821i \(0.210772\pi\)
\(54\) 1.00000 0.136083
\(55\) −10.9660 + 0.364588i −1.47865 + 0.0491610i
\(56\) 2.33991 1.23483i 0.312684 0.165012i
\(57\) −0.894921 0.894921i −0.118535 0.118535i
\(58\) −3.37069 + 3.37069i −0.442593 + 0.442593i
\(59\) −1.39735 −0.181919 −0.0909594 0.995855i \(-0.528993\pi\)
−0.0909594 + 0.995855i \(0.528993\pi\)
\(60\) 1.52773 1.63280i 0.197229 0.210794i
\(61\) 2.29721i 0.294127i −0.989127 0.147064i \(-0.953018\pi\)
0.989127 0.147064i \(-0.0469822\pi\)
\(62\) −4.98896 + 4.98896i −0.633598 + 0.633598i
\(63\) −0.781409 + 2.52773i −0.0984482 + 0.318464i
\(64\) 1.00000i 0.125000i
\(65\) −7.88388 7.37652i −0.977875 0.914944i
\(66\) 4.90685i 0.603991i
\(67\) 3.05545 + 3.05545i 0.373283 + 0.373283i 0.868672 0.495389i \(-0.164974\pi\)
−0.495389 + 0.868672i \(0.664974\pi\)
\(68\) −2.74632 2.74632i −0.333040 0.333040i
\(69\) −1.49264 −0.179692
\(70\) 2.93351 + 5.13756i 0.350621 + 0.614056i
\(71\) −13.0334 −1.54678 −0.773388 0.633933i \(-0.781440\pi\)
−0.773388 + 0.633933i \(0.781440\pi\)
\(72\) 0.707107 + 0.707107i 0.0833333 + 0.0833333i
\(73\) −5.04441 5.04441i −0.590404 0.590404i 0.347337 0.937740i \(-0.387086\pi\)
−0.937740 + 0.347337i \(0.887086\pi\)
\(74\) 6.71231i 0.780290i
\(75\) 3.76256 + 3.29289i 0.434463 + 0.380231i
\(76\) 1.26561i 0.145175i
\(77\) 12.4032 + 3.83425i 1.41347 + 0.436954i
\(78\) 3.41421 3.41421i 0.386584 0.386584i
\(79\) 14.8063i 1.66584i −0.553391 0.832922i \(-0.686666\pi\)
0.553391 0.832922i \(-0.313334\pi\)
\(80\) 2.23483 0.0743018i 0.249862 0.00830719i
\(81\) −1.00000 −0.111111
\(82\) −3.85140 + 3.85140i −0.425316 + 0.425316i
\(83\) 9.29809 + 9.29809i 1.02060 + 1.02060i 0.999783 + 0.0208150i \(0.00662610\pi\)
0.0208150 + 0.999783i \(0.493374\pi\)
\(84\) −2.33991 + 1.23483i −0.255305 + 0.134731i
\(85\) 5.93351 6.34162i 0.643579 0.687845i
\(86\) 10.7292 1.15696
\(87\) 3.37069 3.37069i 0.361376 0.361376i
\(88\) 3.46967 3.46967i 0.369868 0.369868i
\(89\) 15.3596 1.62812 0.814060 0.580781i \(-0.197253\pi\)
0.814060 + 0.580781i \(0.197253\pi\)
\(90\) −1.52773 + 1.63280i −0.161036 + 0.172113i
\(91\) 5.96230 + 11.2981i 0.625019 + 1.18436i
\(92\) −1.05545 1.05545i −0.110039 0.110039i
\(93\) 4.98896 4.98896i 0.517331 0.517331i
\(94\) 1.03858 0.107122
\(95\) 2.82843 0.0940371i 0.290191 0.00964800i
\(96\) 1.00000i 0.102062i
\(97\) 8.42614 8.42614i 0.855545 0.855545i −0.135264 0.990810i \(-0.543188\pi\)
0.990810 + 0.135264i \(0.0431884\pi\)
\(98\) −1.29289 6.87957i −0.130602 0.694941i
\(99\) 4.90685i 0.493157i
\(100\) 0.332104 + 4.98896i 0.0332104 + 0.498896i
\(101\) 18.1504i 1.80603i 0.429609 + 0.903015i \(0.358651\pi\)
−0.429609 + 0.903015i \(0.641349\pi\)
\(102\) 2.74632 + 2.74632i 0.271926 + 0.271926i
\(103\) −8.36459 8.36459i −0.824187 0.824187i 0.162518 0.986706i \(-0.448038\pi\)
−0.986706 + 0.162518i \(0.948038\pi\)
\(104\) 4.82843 0.473466
\(105\) −2.93351 5.13756i −0.286281 0.501375i
\(106\) −1.78984 −0.173845
\(107\) 3.77297 + 3.77297i 0.364747 + 0.364747i 0.865557 0.500810i \(-0.166964\pi\)
−0.500810 + 0.865557i \(0.666964\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) 0.0870500i 0.00833787i 0.999991 + 0.00416894i \(0.00132702\pi\)
−0.999991 + 0.00416894i \(0.998673\pi\)
\(110\) 8.01193 + 7.49632i 0.763907 + 0.714746i
\(111\) 6.71231i 0.637104i
\(112\) −2.52773 0.781409i −0.238848 0.0738362i
\(113\) 2.03248 2.03248i 0.191200 0.191200i −0.605014 0.796214i \(-0.706833\pi\)
0.796214 + 0.605014i \(0.206833\pi\)
\(114\) 1.26561i 0.118535i
\(115\) 2.28034 2.43718i 0.212643 0.227268i
\(116\) 4.76687 0.442593
\(117\) −3.41421 + 3.41421i −0.315644 + 0.315644i
\(118\) 0.988072 + 0.988072i 0.0909594 + 0.0909594i
\(119\) −9.08794 + 4.79594i −0.833090 + 0.439643i
\(120\) −2.23483 + 0.0743018i −0.204011 + 0.00678279i
\(121\) 13.0772 1.18883
\(122\) −1.62437 + 1.62437i −0.147064 + 0.147064i
\(123\) 3.85140 3.85140i 0.347269 0.347269i
\(124\) 7.05545 0.633598
\(125\) −11.1248 + 1.11289i −0.995034 + 0.0995396i
\(126\) 2.33991 1.23483i 0.208456 0.110008i
\(127\) −11.1761 11.1761i −0.991723 0.991723i 0.00824340 0.999966i \(-0.497376\pi\)
−0.999966 + 0.00824340i \(0.997376\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −10.7292 −0.944651
\(130\) 0.358761 + 10.7907i 0.0314654 + 0.946410i
\(131\) 12.8367i 1.12154i −0.827970 0.560772i \(-0.810504\pi\)
0.827970 0.560772i \(-0.189496\pi\)
\(132\) −3.46967 + 3.46967i −0.301996 + 0.301996i
\(133\) −3.19912 0.988958i −0.277399 0.0857536i
\(134\) 4.32106i 0.373283i
\(135\) 1.52773 1.63280i 0.131486 0.140529i
\(136\) 3.88388i 0.333040i
\(137\) −3.62437 3.62437i −0.309651 0.309651i 0.535123 0.844774i \(-0.320265\pi\)
−0.844774 + 0.535123i \(0.820265\pi\)
\(138\) 1.05545 + 1.05545i 0.0898461 + 0.0898461i
\(139\) −3.90596 −0.331299 −0.165650 0.986185i \(-0.552972\pi\)
−0.165650 + 0.986185i \(0.552972\pi\)
\(140\) 1.55850 5.70711i 0.131718 0.482339i
\(141\) −1.03858 −0.0874646
\(142\) 9.21598 + 9.21598i 0.773388 + 0.773388i
\(143\) 16.7530 + 16.7530i 1.40096 + 1.40096i
\(144\) 1.00000i 0.0833333i
\(145\) 0.354187 + 10.6532i 0.0294137 + 0.884697i
\(146\) 7.13387i 0.590404i
\(147\) 1.29289 + 6.87957i 0.106636 + 0.567417i
\(148\) 4.74632 4.74632i 0.390145 0.390145i
\(149\) 5.64124i 0.462148i −0.972936 0.231074i \(-0.925776\pi\)
0.972936 0.231074i \(-0.0742240\pi\)
\(150\) −0.332104 4.98896i −0.0271162 0.407347i
\(151\) −11.7678 −0.957647 −0.478823 0.877911i \(-0.658937\pi\)
−0.478823 + 0.877911i \(0.658937\pi\)
\(152\) −0.894921 + 0.894921i −0.0725877 + 0.0725877i
\(153\) −2.74632 2.74632i −0.222027 0.222027i
\(154\) −6.05914 11.4816i −0.488259 0.925213i
\(155\) 0.524233 + 15.7678i 0.0421074 + 1.26650i
\(156\) −4.82843 −0.386584
\(157\) 13.7132 13.7132i 1.09443 1.09443i 0.0993827 0.995049i \(-0.468313\pi\)
0.995049 0.0993827i \(-0.0316868\pi\)
\(158\) −10.4697 + 10.4697i −0.832922 + 0.832922i
\(159\) 1.78984 0.141944
\(160\) −1.63280 1.52773i −0.129085 0.120777i
\(161\) −3.49264 + 1.84316i −0.275258 + 0.145261i
\(162\) 0.707107 + 0.707107i 0.0555556 + 0.0555556i
\(163\) −7.21967 + 7.21967i −0.565488 + 0.565488i −0.930861 0.365373i \(-0.880941\pi\)
0.365373 + 0.930861i \(0.380941\pi\)
\(164\) 5.44670 0.425316
\(165\) −8.01193 7.49632i −0.623728 0.583588i
\(166\) 13.1495i 1.02060i
\(167\) 6.73439 6.73439i 0.521123 0.521123i −0.396788 0.917910i \(-0.629875\pi\)
0.917910 + 0.396788i \(0.129875\pi\)
\(168\) 2.52773 + 0.781409i 0.195018 + 0.0602870i
\(169\) 10.3137i 0.793362i
\(170\) −8.67982 + 0.288579i −0.665712 + 0.0221330i
\(171\) 1.26561i 0.0967836i
\(172\) −7.58667 7.58667i −0.578478 0.578478i
\(173\) −14.1605 14.1605i −1.07661 1.07661i −0.996811 0.0797939i \(-0.974574\pi\)
−0.0797939 0.996811i \(-0.525426\pi\)
\(174\) −4.76687 −0.361376
\(175\) 12.8702 + 3.05895i 0.972898 + 0.231235i
\(176\) −4.90685 −0.369868
\(177\) −0.988072 0.988072i −0.0742681 0.0742681i
\(178\) −10.8609 10.8609i −0.814060 0.814060i
\(179\) 3.28123i 0.245250i 0.992453 + 0.122625i \(0.0391313\pi\)
−0.992453 + 0.122625i \(0.960869\pi\)
\(180\) 2.23483 0.0743018i 0.166575 0.00553813i
\(181\) 19.3934i 1.44150i 0.693196 + 0.720749i \(0.256202\pi\)
−0.693196 + 0.720749i \(0.743798\pi\)
\(182\) 3.77297 12.2049i 0.279671 0.904691i
\(183\) 1.62437 1.62437i 0.120077 0.120077i
\(184\) 1.49264i 0.110039i
\(185\) 10.9599 + 10.2546i 0.805787 + 0.753931i
\(186\) −7.05545 −0.517331
\(187\) −13.4758 + 13.4758i −0.985446 + 0.985446i
\(188\) −0.734390 0.734390i −0.0535609 0.0535609i
\(189\) −2.33991 + 1.23483i −0.170204 + 0.0898209i
\(190\) −2.06649 1.93351i −0.149919 0.140271i
\(191\) −16.8453 −1.21888 −0.609441 0.792831i \(-0.708606\pi\)
−0.609441 + 0.792831i \(0.708606\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) −4.81370 + 4.81370i −0.346498 + 0.346498i −0.858803 0.512306i \(-0.828792\pi\)
0.512306 + 0.858803i \(0.328792\pi\)
\(194\) −11.9164 −0.855545
\(195\) −0.358761 10.7907i −0.0256914 0.772740i
\(196\) −3.95037 + 5.77880i −0.282170 + 0.412772i
\(197\) 13.0334 + 13.0334i 0.928589 + 0.928589i 0.997615 0.0690257i \(-0.0219891\pi\)
−0.0690257 + 0.997615i \(0.521989\pi\)
\(198\) 3.46967 3.46967i 0.246578 0.246578i
\(199\) −11.7509 −0.832999 −0.416499 0.909136i \(-0.636743\pi\)
−0.416499 + 0.909136i \(0.636743\pi\)
\(200\) 3.29289 3.76256i 0.232843 0.266053i
\(201\) 4.32106i 0.304784i
\(202\) 12.8343 12.8343i 0.903015 0.903015i
\(203\) 3.72488 12.0494i 0.261435 0.845699i
\(204\) 3.88388i 0.271926i
\(205\) 0.404699 + 12.1725i 0.0282654 + 0.850161i
\(206\) 11.8293i 0.824187i
\(207\) −1.05545 1.05545i −0.0733590 0.0733590i
\(208\) −3.41421 3.41421i −0.236733 0.236733i
\(209\) −6.21016 −0.429566
\(210\) −1.55850 + 5.70711i −0.107547 + 0.393828i
\(211\) 16.5502 1.13937 0.569683 0.821864i \(-0.307066\pi\)
0.569683 + 0.821864i \(0.307066\pi\)
\(212\) 1.26561 + 1.26561i 0.0869224 + 0.0869224i
\(213\) −9.21598 9.21598i −0.631469 0.631469i
\(214\) 5.33579i 0.364747i
\(215\) 16.3912 17.5187i 1.11787 1.19476i
\(216\) 1.00000i 0.0680414i
\(217\) 5.51319 17.8343i 0.374260 1.21067i
\(218\) 0.0615536 0.0615536i 0.00416894 0.00416894i
\(219\) 7.13387i 0.482063i
\(220\) −0.364588 10.9660i −0.0245805 0.739327i
\(221\) −18.7530 −1.26147
\(222\) −4.74632 + 4.74632i −0.318552 + 0.318552i
\(223\) 8.26067 + 8.26067i 0.553175 + 0.553175i 0.927356 0.374181i \(-0.122076\pi\)
−0.374181 + 0.927356i \(0.622076\pi\)
\(224\) 1.23483 + 2.33991i 0.0825058 + 0.156342i
\(225\) 0.332104 + 4.98896i 0.0221403 + 0.332597i
\(226\) −2.87437 −0.191200
\(227\) −5.91295 + 5.91295i −0.392456 + 0.392456i −0.875562 0.483106i \(-0.839509\pi\)
0.483106 + 0.875562i \(0.339509\pi\)
\(228\) 0.894921 0.894921i 0.0592676 0.0592676i
\(229\) 9.31371 0.615467 0.307734 0.951473i \(-0.400429\pi\)
0.307734 + 0.951473i \(0.400429\pi\)
\(230\) −3.33579 + 0.110906i −0.219956 + 0.00731289i
\(231\) 6.05914 + 11.4816i 0.398662 + 0.755433i
\(232\) −3.37069 3.37069i −0.221297 0.221297i
\(233\) 16.0563 16.0563i 1.05189 1.05189i 0.0533076 0.998578i \(-0.483024\pi\)
0.998578 0.0533076i \(-0.0169764\pi\)
\(234\) 4.82843 0.315644
\(235\) 1.58667 1.69581i 0.103503 0.110622i
\(236\) 1.39735i 0.0909594i
\(237\) 10.4697 10.4697i 0.680078 0.680078i
\(238\) 9.81739 + 3.03490i 0.636367 + 0.196723i
\(239\) 1.68592i 0.109053i −0.998512 0.0545267i \(-0.982635\pi\)
0.998512 0.0545267i \(-0.0173650\pi\)
\(240\) 1.63280 + 1.52773i 0.105397 + 0.0986143i
\(241\) 3.61574i 0.232910i −0.993196 0.116455i \(-0.962847\pi\)
0.993196 0.116455i \(-0.0371532\pi\)
\(242\) −9.24695 9.24695i −0.594417 0.594417i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 2.29721 0.147064
\(245\) −13.2082 8.39905i −0.843839 0.536596i
\(246\) −5.44670 −0.347269
\(247\) −4.32106 4.32106i −0.274943 0.274943i
\(248\) −4.98896 4.98896i −0.316799 0.316799i
\(249\) 13.1495i 0.833315i
\(250\) 8.65336 + 7.07950i 0.547287 + 0.447747i
\(251\) 4.78896i 0.302276i 0.988513 + 0.151138i \(0.0482938\pi\)
−0.988513 + 0.151138i \(0.951706\pi\)
\(252\) −2.52773 0.781409i −0.159232 0.0492241i
\(253\) −5.17895 + 5.17895i −0.325598 + 0.325598i
\(254\) 15.8055i 0.991723i
\(255\) 8.67982 0.288579i 0.543552 0.0180715i
\(256\) 1.00000 0.0625000
\(257\) −20.8113 + 20.8113i −1.29817 + 1.29817i −0.368574 + 0.929599i \(0.620154\pi\)
−0.929599 + 0.368574i \(0.879846\pi\)
\(258\) 7.58667 + 7.58667i 0.472326 + 0.472326i
\(259\) −8.28858 15.7062i −0.515027 0.975936i
\(260\) 7.37652 7.88388i 0.457472 0.488937i
\(261\) 4.76687 0.295062
\(262\) −9.07689 + 9.07689i −0.560772 + 0.560772i
\(263\) 6.61827 6.61827i 0.408100 0.408100i −0.472976 0.881076i \(-0.656820\pi\)
0.881076 + 0.472976i \(0.156820\pi\)
\(264\) 4.90685 0.301996
\(265\) −2.73439 + 2.92246i −0.167972 + 0.179526i
\(266\) 1.56282 + 2.96142i 0.0958225 + 0.181576i
\(267\) 10.8609 + 10.8609i 0.664677 + 0.664677i
\(268\) −3.05545 + 3.05545i −0.186641 + 0.186641i
\(269\) −13.1192 −0.799890 −0.399945 0.916539i \(-0.630971\pi\)
−0.399945 + 0.916539i \(0.630971\pi\)
\(270\) −2.23483 + 0.0743018i −0.136008 + 0.00452186i
\(271\) 18.0836i 1.09850i 0.835658 + 0.549250i \(0.185087\pi\)
−0.835658 + 0.549250i \(0.814913\pi\)
\(272\) 2.74632 2.74632i 0.166520 0.166520i
\(273\) −3.77297 + 12.2049i −0.228351 + 0.738677i
\(274\) 5.12563i 0.309651i
\(275\) 24.4801 1.62959i 1.47620 0.0982677i
\(276\) 1.49264i 0.0898461i
\(277\) 2.63541 + 2.63541i 0.158347 + 0.158347i 0.781834 0.623487i \(-0.214285\pi\)
−0.623487 + 0.781834i \(0.714285\pi\)
\(278\) 2.76193 + 2.76193i 0.165650 + 0.165650i
\(279\) 7.05545 0.422399
\(280\) −5.13756 + 2.93351i −0.307028 + 0.175310i
\(281\) 20.4558 1.22029 0.610146 0.792289i \(-0.291111\pi\)
0.610146 + 0.792289i \(0.291111\pi\)
\(282\) 0.734390 + 0.734390i 0.0437323 + 0.0437323i
\(283\) −10.7751 10.7751i −0.640514 0.640514i 0.310168 0.950682i \(-0.399615\pi\)
−0.950682 + 0.310168i \(0.899615\pi\)
\(284\) 13.0334i 0.773388i
\(285\) 2.06649 + 1.93351i 0.122409 + 0.114531i
\(286\) 23.6924i 1.40096i
\(287\) 4.25610 13.7678i 0.251229 0.812685i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) 1.91548i 0.112675i
\(290\) 7.28248 7.78337i 0.427642 0.457056i
\(291\) 11.9164 0.698550
\(292\) 5.04441 5.04441i 0.295202 0.295202i
\(293\) 3.15965 + 3.15965i 0.184588 + 0.184588i 0.793352 0.608763i \(-0.208334\pi\)
−0.608763 + 0.793352i \(0.708334\pi\)
\(294\) 3.95037 5.77880i 0.230390 0.337027i
\(295\) 3.12283 0.103825i 0.181818 0.00604494i
\(296\) −6.71231 −0.390145
\(297\) −3.46967 + 3.46967i −0.201330 + 0.201330i
\(298\) −3.98896 + 3.98896i −0.231074 + 0.231074i
\(299\) −7.20708 −0.416796
\(300\) −3.29289 + 3.76256i −0.190115 + 0.217231i
\(301\) −25.1053 + 13.2487i −1.44705 + 0.763645i
\(302\) 8.32106 + 8.32106i 0.478823 + 0.478823i
\(303\) −12.8343 + 12.8343i −0.737309 + 0.737309i
\(304\) 1.26561 0.0725877
\(305\) 0.170687 + 5.13387i 0.00977349 + 0.293965i
\(306\) 3.88388i 0.222027i
\(307\) −20.8011 + 20.8011i −1.18718 + 1.18718i −0.209340 + 0.977843i \(0.567132\pi\)
−0.977843 + 0.209340i \(0.932868\pi\)
\(308\) −3.83425 + 12.4032i −0.218477 + 0.706736i
\(309\) 11.8293i 0.672946i
\(310\) 10.7788 11.5202i 0.612195 0.654302i
\(311\) 11.4706i 0.650435i −0.945639 0.325218i \(-0.894562\pi\)
0.945639 0.325218i \(-0.105438\pi\)
\(312\) 3.41421 + 3.41421i 0.193292 + 0.193292i
\(313\) −0.612443 0.612443i −0.0346173 0.0346173i 0.689586 0.724204i \(-0.257792\pi\)
−0.724204 + 0.689586i \(0.757792\pi\)
\(314\) −19.3934 −1.09443
\(315\) 1.55850 5.70711i 0.0878117 0.321559i
\(316\) 14.8063 0.832922
\(317\) 7.03984 + 7.03984i 0.395397 + 0.395397i 0.876606 0.481209i \(-0.159802\pi\)
−0.481209 + 0.876606i \(0.659802\pi\)
\(318\) −1.26561 1.26561i −0.0709719 0.0709719i
\(319\) 23.3903i 1.30961i
\(320\) 0.0743018 + 2.23483i 0.00415360 + 0.124931i
\(321\) 5.33579i 0.297815i
\(322\) 3.77297 + 1.16636i 0.210260 + 0.0649986i
\(323\) 3.47577 3.47577i 0.193397 0.193397i
\(324\) 1.00000i 0.0555556i
\(325\) 18.1672 + 15.8995i 1.00774 + 0.881945i
\(326\) 10.2102 0.565488
\(327\) −0.0615536 + 0.0615536i −0.00340392 + 0.00340392i
\(328\) −3.85140 3.85140i −0.212658 0.212658i
\(329\) −2.43020 + 1.28248i −0.133981 + 0.0707053i
\(330\) 0.364588 + 10.9660i 0.0200699 + 0.603658i
\(331\) 10.1759 0.559317 0.279658 0.960100i \(-0.409779\pi\)
0.279658 + 0.960100i \(0.409779\pi\)
\(332\) −9.29809 + 9.29809i −0.510299 + 0.510299i
\(333\) 4.74632 4.74632i 0.260097 0.260097i
\(334\) −9.52387 −0.521123
\(335\) −7.05545 6.60140i −0.385481 0.360673i
\(336\) −1.23483 2.33991i −0.0673657 0.127653i
\(337\) 16.8137 + 16.8137i 0.915901 + 0.915901i 0.996728 0.0808276i \(-0.0257563\pi\)
−0.0808276 + 0.996728i \(0.525756\pi\)
\(338\) 7.29289 7.29289i 0.396681 0.396681i
\(339\) 2.87437 0.156114
\(340\) 6.34162 + 5.93351i 0.343923 + 0.321790i
\(341\) 34.6200i 1.87478i
\(342\) −0.894921 + 0.894921i −0.0483918 + 0.0483918i
\(343\) 11.5204 + 14.5011i 0.622042 + 0.782984i
\(344\) 10.7292i 0.578478i
\(345\) 3.33579 0.110906i 0.179593 0.00597095i
\(346\) 20.0260i 1.07661i
\(347\) −7.83919 7.83919i −0.420830 0.420830i 0.464659 0.885489i \(-0.346177\pi\)
−0.885489 + 0.464659i \(0.846177\pi\)
\(348\) 3.37069 + 3.37069i 0.180688 + 0.180688i
\(349\) 5.10838 0.273445 0.136723 0.990609i \(-0.456343\pi\)
0.136723 + 0.990609i \(0.456343\pi\)
\(350\) −6.93763 11.2636i −0.370832 0.602066i
\(351\) −4.82843 −0.257722
\(352\) 3.46967 + 3.46967i 0.184934 + 0.184934i
\(353\) −12.0821 12.0821i −0.643066 0.643066i 0.308242 0.951308i \(-0.400259\pi\)
−0.951308 + 0.308242i \(0.900259\pi\)
\(354\) 1.39735i 0.0742681i
\(355\) 29.1274 0.968403i 1.54592 0.0513975i
\(356\) 15.3596i 0.814060i
\(357\) −9.81739 3.03490i −0.519591 0.160624i
\(358\) 2.32018 2.32018i 0.122625 0.122625i
\(359\) 3.90596i 0.206149i 0.994674 + 0.103074i \(0.0328680\pi\)
−0.994674 + 0.103074i \(0.967132\pi\)
\(360\) −1.63280 1.52773i −0.0860564 0.0805182i
\(361\) −17.3982 −0.915696
\(362\) 13.7132 13.7132i 0.720749 0.720749i
\(363\) 9.24695 + 9.24695i 0.485339 + 0.485339i
\(364\) −11.2981 + 5.96230i −0.592181 + 0.312510i
\(365\) 11.6482 + 10.8986i 0.609696 + 0.570459i
\(366\) −2.29721 −0.120077
\(367\) 3.98072 3.98072i 0.207792 0.207792i −0.595536 0.803328i \(-0.703060\pi\)
0.803328 + 0.595536i \(0.203060\pi\)
\(368\) 1.05545 1.05545i 0.0550193 0.0550193i
\(369\) 5.44670 0.283544
\(370\) −0.498736 15.0009i −0.0259281 0.779859i
\(371\) 4.18807 2.21016i 0.217434 0.114746i
\(372\) 4.98896 + 4.98896i 0.258665 + 0.258665i
\(373\) −8.95648 + 8.95648i −0.463749 + 0.463749i −0.899882 0.436133i \(-0.856348\pi\)
0.436133 + 0.899882i \(0.356348\pi\)
\(374\) 19.0576 0.985446
\(375\) −8.65336 7.07950i −0.446858 0.365584i
\(376\) 1.03858i 0.0535609i
\(377\) 16.2751 16.2751i 0.838212 0.838212i
\(378\) 2.52773 + 0.781409i 0.130012 + 0.0401913i
\(379\) 14.0190i 0.720109i 0.932931 + 0.360055i \(0.117242\pi\)
−0.932931 + 0.360055i \(0.882758\pi\)
\(380\) 0.0940371 + 2.82843i 0.00482400 + 0.145095i
\(381\) 15.8055i 0.809738i
\(382\) 11.9114 + 11.9114i 0.609441 + 0.609441i
\(383\) −7.00951 7.00951i −0.358169 0.358169i 0.504968 0.863138i \(-0.331504\pi\)
−0.863138 + 0.504968i \(0.831504\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −28.0039 7.64734i −1.42721 0.389745i
\(386\) 6.80760 0.346498
\(387\) −7.58667 7.58667i −0.385652 0.385652i
\(388\) 8.42614 + 8.42614i 0.427773 + 0.427773i
\(389\) 18.6560i 0.945895i −0.881091 0.472948i \(-0.843190\pi\)
0.881091 0.472948i \(-0.156810\pi\)
\(390\) −7.37652 + 7.88388i −0.373524 + 0.399216i
\(391\) 5.79722i 0.293178i
\(392\) 6.87957 1.29289i 0.347471 0.0653010i
\(393\) 9.07689 9.07689i 0.457869 0.457869i
\(394\) 18.4320i 0.928589i
\(395\) 1.10014 + 33.0897i 0.0553539 + 1.66492i
\(396\) −4.90685 −0.246578
\(397\) −19.3683 + 19.3683i −0.972066 + 0.972066i −0.999620 0.0275544i \(-0.991228\pi\)
0.0275544 + 0.999620i \(0.491228\pi\)
\(398\) 8.30913 + 8.30913i 0.416499 + 0.416499i
\(399\) −1.56282 2.96142i −0.0782387 0.148256i
\(400\) −4.98896 + 0.332104i −0.249448 + 0.0166052i
\(401\) −27.9099 −1.39375 −0.696877 0.717191i \(-0.745428\pi\)
−0.696877 + 0.717191i \(0.745428\pi\)
\(402\) 3.05545 3.05545i 0.152392 0.152392i
\(403\) 24.0888 24.0888i 1.19995 1.19995i
\(404\) −18.1504 −0.903015
\(405\) 2.23483 0.0743018i 0.111050 0.00369209i
\(406\) −11.1541 + 5.88629i −0.553567 + 0.292132i
\(407\) −23.2895 23.2895i −1.15442 1.15442i
\(408\) −2.74632 + 2.74632i −0.135963 + 0.135963i
\(409\) 18.3211 0.905918 0.452959 0.891531i \(-0.350368\pi\)
0.452959 + 0.891531i \(0.350368\pi\)
\(410\) 8.32106 8.89339i 0.410948 0.439213i
\(411\) 5.12563i 0.252829i
\(412\) 8.36459 8.36459i 0.412094 0.412094i
\(413\) −3.53211 1.09190i −0.173804 0.0537288i
\(414\) 1.49264i 0.0733590i
\(415\) −21.4706 20.0888i −1.05395 0.986122i
\(416\) 4.82843i 0.236733i
\(417\) −2.76193 2.76193i −0.135252 0.135252i
\(418\) 4.39124 + 4.39124i 0.214783 + 0.214783i
\(419\) 5.49605 0.268500 0.134250 0.990948i \(-0.457138\pi\)
0.134250 + 0.990948i \(0.457138\pi\)
\(420\) 5.13756 2.93351i 0.250687 0.143140i
\(421\) 24.5863 1.19826 0.599132 0.800651i \(-0.295513\pi\)
0.599132 + 0.800651i \(0.295513\pi\)
\(422\) −11.7028 11.7028i −0.569683 0.569683i
\(423\) −0.734390 0.734390i −0.0357073 0.0357073i
\(424\) 1.78984i 0.0869224i
\(425\) −12.7892 + 14.6133i −0.620367 + 0.708851i
\(426\) 13.0334i 0.631469i
\(427\) 1.79506 5.80671i 0.0868689 0.281006i
\(428\) −3.77297 + 3.77297i −0.182374 + 0.182374i
\(429\) 23.6924i 1.14388i
\(430\) −23.9779 + 0.797197i −1.15632 + 0.0384443i
\(431\) 22.8133 1.09888 0.549440 0.835533i \(-0.314841\pi\)
0.549440 + 0.835533i \(0.314841\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) −17.1216 17.1216i −0.822811 0.822811i 0.163700 0.986510i \(-0.447657\pi\)
−0.986510 + 0.163700i \(0.947657\pi\)
\(434\) −16.5091 + 8.71231i −0.792464 + 0.418204i
\(435\) −7.28248 + 7.78337i −0.349168 + 0.373184i
\(436\) −0.0870500 −0.00416894
\(437\) 1.33579 1.33579i 0.0638996 0.0638996i
\(438\) −5.04441 + 5.04441i −0.241031 + 0.241031i
\(439\) 35.8323 1.71018 0.855092 0.518476i \(-0.173500\pi\)
0.855092 + 0.518476i \(0.173500\pi\)
\(440\) −7.49632 + 8.01193i −0.357373 + 0.381954i
\(441\) −3.95037 + 5.77880i −0.188113 + 0.275181i
\(442\) 13.2604 + 13.2604i 0.630733 + 0.630733i
\(443\) 2.93109 2.93109i 0.139260 0.139260i −0.634040 0.773300i \(-0.718605\pi\)
0.773300 + 0.634040i \(0.218605\pi\)
\(444\) 6.71231 0.318552
\(445\) −34.3262 + 1.14125i −1.62722 + 0.0541004i
\(446\) 11.6824i 0.553175i
\(447\) 3.98896 3.98896i 0.188671 0.188671i
\(448\) 0.781409 2.52773i 0.0369181 0.119424i
\(449\) 1.70279i 0.0803598i 0.999192 + 0.0401799i \(0.0127931\pi\)
−0.999192 + 0.0401799i \(0.987207\pi\)
\(450\) 3.29289 3.76256i 0.155228 0.177369i
\(451\) 26.7261i 1.25848i
\(452\) 2.03248 + 2.03248i 0.0956000 + 0.0956000i
\(453\) −8.32106 8.32106i −0.390958 0.390958i
\(454\) 8.36217 0.392456
\(455\) −14.1642 24.8063i −0.664029 1.16294i
\(456\) −1.26561 −0.0592676
\(457\) −5.34315 5.34315i −0.249942 0.249942i 0.571005 0.820947i \(-0.306554\pi\)
−0.820947 + 0.571005i \(0.806554\pi\)
\(458\) −6.58579 6.58579i −0.307734 0.307734i
\(459\) 3.88388i 0.181284i
\(460\) 2.43718 + 2.28034i 0.113634 + 0.106321i
\(461\) 0.858751i 0.0399960i −0.999800 0.0199980i \(-0.993634\pi\)
0.999800 0.0199980i \(-0.00636599\pi\)
\(462\) 3.83425 12.4032i 0.178386 0.577048i
\(463\) −20.3594 + 20.3594i −0.946180 + 0.946180i −0.998624 0.0524436i \(-0.983299\pi\)
0.0524436 + 0.998624i \(0.483299\pi\)
\(464\) 4.76687i 0.221297i
\(465\) −10.7788 + 11.5202i −0.499855 + 0.534235i
\(466\) −22.7071 −1.05189
\(467\) −8.77908 + 8.77908i −0.406247 + 0.406247i −0.880428 0.474181i \(-0.842744\pi\)
0.474181 + 0.880428i \(0.342744\pi\)
\(468\) −3.41421 3.41421i −0.157822 0.157822i
\(469\) 5.33579 + 10.1109i 0.246384 + 0.466878i
\(470\) −2.32106 + 0.0771687i −0.107063 + 0.00355953i
\(471\) 19.3934 0.893600
\(472\) −0.988072 + 0.988072i −0.0454797 + 0.0454797i
\(473\) −37.2267 + 37.2267i −1.71168 + 1.71168i
\(474\) −14.8063 −0.680078
\(475\) −6.31408 + 0.420314i −0.289710 + 0.0192853i
\(476\) −4.79594 9.08794i −0.219822 0.416545i
\(477\) 1.26561 + 1.26561i 0.0579483 + 0.0579483i
\(478\) −1.19213 + 1.19213i −0.0545267 + 0.0545267i
\(479\) 1.17157 0.0535305 0.0267653 0.999642i \(-0.491479\pi\)
0.0267653 + 0.999642i \(0.491479\pi\)
\(480\) −0.0743018 2.23483i −0.00339140 0.102006i
\(481\) 32.4099i 1.47776i
\(482\) −2.55672 + 2.55672i −0.116455 + 0.116455i
\(483\) −3.77297 1.16636i −0.171676 0.0530711i
\(484\) 13.0772i 0.594417i
\(485\) −18.2049 + 19.4571i −0.826644 + 0.883501i
\(486\) 1.00000i 0.0453609i
\(487\) 9.70737 + 9.70737i 0.439883 + 0.439883i 0.891972 0.452090i \(-0.149321\pi\)
−0.452090 + 0.891972i \(0.649321\pi\)
\(488\) −1.62437 1.62437i −0.0735318 0.0735318i
\(489\) −10.2102 −0.461719
\(490\) 3.40056 + 15.2786i 0.153622 + 0.690218i
\(491\) −16.9381 −0.764405 −0.382202 0.924079i \(-0.624834\pi\)
−0.382202 + 0.924079i \(0.624834\pi\)
\(492\) 3.85140 + 3.85140i 0.173634 + 0.173634i
\(493\) 13.0913 + 13.0913i 0.589605 + 0.589605i
\(494\) 6.11091i 0.274943i
\(495\) −0.364588 10.9660i −0.0163870 0.492885i
\(496\) 7.05545i 0.316799i
\(497\) −32.9448 10.1844i −1.47778 0.456832i
\(498\) 9.29809 9.29809i 0.416658 0.416658i
\(499\) 30.4117i 1.36141i 0.732556 + 0.680706i \(0.238327\pi\)
−0.732556 + 0.680706i \(0.761673\pi\)
\(500\) −1.11289 11.1248i −0.0497698 0.497517i
\(501\) 9.52387 0.425495
\(502\) 3.38630 3.38630i 0.151138 0.151138i
\(503\) 4.75825 + 4.75825i 0.212160 + 0.212160i 0.805184 0.593025i \(-0.202066\pi\)
−0.593025 + 0.805184i \(0.702066\pi\)
\(504\) 1.23483 + 2.33991i 0.0550038 + 0.104228i
\(505\) −1.34861 40.5631i −0.0600122 1.80503i
\(506\) 7.32414 0.325598
\(507\) −7.29289 + 7.29289i −0.323889 + 0.323889i
\(508\) 11.1761 11.1761i 0.495861 0.495861i
\(509\) 40.3501 1.78849 0.894243 0.447581i \(-0.147714\pi\)
0.894243 + 0.447581i \(0.147714\pi\)
\(510\) −6.34162 5.93351i −0.280812 0.262740i
\(511\) −8.80915 16.6926i −0.389694 0.738439i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0.894921 0.894921i 0.0395117 0.0395117i
\(514\) 29.4316 1.29817
\(515\) 19.3150 + 18.0720i 0.851119 + 0.796345i
\(516\) 10.7292i 0.472326i
\(517\) −3.60354 + 3.60354i −0.158484 + 0.158484i
\(518\) −5.24505 + 16.9669i −0.230454 + 0.745482i
\(519\) 20.0260i 0.879045i
\(520\) −10.7907 + 0.358761i −0.473205 + 0.0157327i
\(521\) 8.96879i 0.392930i −0.980511 0.196465i \(-0.937054\pi\)
0.980511 0.196465i \(-0.0629462\pi\)
\(522\) −3.37069 3.37069i −0.147531 0.147531i
\(523\) 8.40290 + 8.40290i 0.367433 + 0.367433i 0.866540 0.499107i \(-0.166339\pi\)
−0.499107 + 0.866540i \(0.666339\pi\)
\(524\) 12.8367 0.560772
\(525\) 6.93763 + 11.2636i 0.302783 + 0.491585i
\(526\) −9.35965 −0.408100
\(527\) 19.3765 + 19.3765i 0.844054 + 0.844054i
\(528\) −3.46967 3.46967i −0.150998 0.150998i
\(529\) 20.7720i 0.903132i
\(530\) 4.00000 0.132989i 0.173749 0.00577665i
\(531\) 1.39735i 0.0606396i
\(532\) 0.988958 3.19912i 0.0428768 0.138699i
\(533\) 18.5962 18.5962i 0.805490 0.805490i
\(534\) 15.3596i 0.664677i
\(535\) −8.71231 8.15163i −0.376666 0.352426i
\(536\) 4.32106 0.186641
\(537\) −2.32018 + 2.32018i −0.100123 + 0.100123i
\(538\) 9.27665 + 9.27665i 0.399945 + 0.399945i
\(539\) 28.3557 + 19.3839i 1.22137 + 0.834923i
\(540\) 1.63280 + 1.52773i 0.0702647 + 0.0657429i
\(541\) 27.1611 1.16775 0.583874 0.811844i \(-0.301536\pi\)
0.583874 + 0.811844i \(0.301536\pi\)
\(542\) 12.7870 12.7870i 0.549250 0.549250i
\(543\) −13.7132 + 13.7132i −0.588489 + 0.588489i
\(544\) −3.88388 −0.166520
\(545\) −0.00646797 0.194542i −0.000277057 0.00833327i
\(546\) 11.2981 5.96230i 0.483514 0.255163i
\(547\) −16.8471 16.8471i −0.720329 0.720329i 0.248343 0.968672i \(-0.420114\pi\)
−0.968672 + 0.248343i \(0.920114\pi\)
\(548\) 3.62437 3.62437i 0.154825 0.154825i
\(549\) 2.29721 0.0980424
\(550\) −18.4623 16.1577i −0.787236 0.688968i
\(551\) 6.03300i 0.257015i
\(552\) −1.05545 + 1.05545i −0.0449231 + 0.0449231i
\(553\) 11.5698 37.4264i 0.491998 1.59153i
\(554\) 3.72704i 0.158347i
\(555\) 0.498736 + 15.0009i 0.0211702 + 0.636752i
\(556\) 3.90596i 0.165650i
\(557\) −0.0529257 0.0529257i −0.00224253 0.00224253i 0.705985 0.708227i \(-0.250505\pi\)
−0.708227 + 0.705985i \(0.750505\pi\)
\(558\) −4.98896 4.98896i −0.211199 0.211199i
\(559\) −51.8050 −2.19112
\(560\) 5.70711 + 1.55850i 0.241169 + 0.0658588i
\(561\) −19.0576 −0.804613
\(562\) −14.4645 14.4645i −0.610146 0.610146i
\(563\) 7.84316 + 7.84316i 0.330550 + 0.330550i 0.852795 0.522246i \(-0.174906\pi\)
−0.522246 + 0.852795i \(0.674906\pi\)
\(564\) 1.03858i 0.0437323i
\(565\) −4.39124 + 4.69328i −0.184741 + 0.197448i
\(566\) 15.2383i 0.640514i
\(567\) −2.52773 0.781409i −0.106155 0.0328161i
\(568\) −9.21598 + 9.21598i −0.386694 + 0.386694i
\(569\) 6.12311i 0.256694i 0.991729 + 0.128347i \(0.0409671\pi\)
−0.991729 + 0.128347i \(0.959033\pi\)
\(570\) −0.0940371 2.82843i −0.00393878 0.118470i
\(571\) 30.4896 1.27595 0.637974 0.770058i \(-0.279773\pi\)
0.637974 + 0.770058i \(0.279773\pi\)
\(572\) −16.7530 + 16.7530i −0.700479 + 0.700479i
\(573\) −11.9114 11.9114i −0.497607 0.497607i
\(574\) −12.7448 + 6.72576i −0.531957 + 0.280728i
\(575\) −4.91509 + 5.61613i −0.204973 + 0.234209i
\(576\) 1.00000 0.0416667
\(577\) 11.5444 11.5444i 0.480600 0.480600i −0.424723 0.905323i \(-0.639629\pi\)
0.905323 + 0.424723i \(0.139629\pi\)
\(578\) 1.35445 1.35445i 0.0563376 0.0563376i
\(579\) −6.80760 −0.282914
\(580\) −10.6532 + 0.354187i −0.442349 + 0.0147068i
\(581\) 16.2374 + 30.7686i 0.673642 + 1.27650i
\(582\) −8.42614 8.42614i −0.349275 0.349275i
\(583\) 6.21016 6.21016i 0.257198 0.257198i
\(584\) −7.13387 −0.295202
\(585\) 7.37652 7.88388i 0.304981 0.325958i
\(586\) 4.46841i 0.184588i
\(587\) 7.24478 7.24478i 0.299024 0.299024i −0.541607 0.840632i \(-0.682184\pi\)
0.840632 + 0.541607i \(0.182184\pi\)
\(588\) −6.87957 + 1.29289i −0.283709 + 0.0533180i
\(589\) 8.92945i 0.367932i
\(590\) −2.28159 2.13476i −0.0939317 0.0878867i
\(591\) 18.4320i 0.758190i
\(592\) 4.74632 + 4.74632i 0.195072 + 0.195072i
\(593\) 6.67652 + 6.67652i 0.274172 + 0.274172i 0.830777 0.556605i \(-0.187896\pi\)
−0.556605 + 0.830777i \(0.687896\pi\)
\(594\) 4.90685 0.201330
\(595\) 19.9537 11.3934i 0.818021 0.467083i
\(596\) 5.64124 0.231074
\(597\) −8.30913 8.30913i −0.340070 0.340070i
\(598\) 5.09618 + 5.09618i 0.208398 + 0.208398i
\(599\) 2.62526i 0.107265i −0.998561 0.0536325i \(-0.982920\pi\)
0.998561 0.0536325i \(-0.0170800\pi\)
\(600\) 4.98896 0.332104i 0.203673 0.0135581i
\(601\) 11.7003i 0.477265i 0.971110 + 0.238632i \(0.0766991\pi\)
−0.971110 + 0.238632i \(0.923301\pi\)
\(602\) 27.1204 + 8.38387i 1.10535 + 0.341701i
\(603\) −3.05545 + 3.05545i −0.124428 + 0.124428i
\(604\) 11.7678i 0.478823i
\(605\) −29.2253 + 0.971657i −1.18818 + 0.0395035i
\(606\) 18.1504 0.737309
\(607\) −23.2749 + 23.2749i −0.944697 + 0.944697i −0.998549 0.0538519i \(-0.982850\pi\)
0.0538519 + 0.998549i \(0.482850\pi\)
\(608\) −0.894921 0.894921i −0.0362939 0.0362939i
\(609\) 11.1541 5.88629i 0.451985 0.238525i
\(610\) 3.50950 3.75089i 0.142096 0.151869i
\(611\) −5.01473 −0.202874
\(612\) 2.74632 2.74632i 0.111013 0.111013i
\(613\) 18.1372 18.1372i 0.732554 0.732554i −0.238571 0.971125i \(-0.576679\pi\)
0.971125 + 0.238571i \(0.0766789\pi\)
\(614\) 29.4172 1.18718
\(615\) −8.32106 + 8.89339i −0.335538 + 0.358616i
\(616\) 11.4816 6.05914i 0.462607 0.244130i
\(617\) 1.59063 + 1.59063i 0.0640365 + 0.0640365i 0.738400 0.674363i \(-0.235582\pi\)
−0.674363 + 0.738400i \(0.735582\pi\)
\(618\) −8.36459 + 8.36459i −0.336473 + 0.336473i
\(619\) −39.2232 −1.57651 −0.788257 0.615346i \(-0.789016\pi\)
−0.788257 + 0.615346i \(0.789016\pi\)
\(620\) −15.7678 + 0.524233i −0.633248 + 0.0210537i
\(621\) 1.49264i 0.0598974i
\(622\) −8.11091 + 8.11091i −0.325218 + 0.325218i
\(623\) 38.8250 + 12.0022i 1.55549 + 0.480856i
\(624\) 4.82843i 0.193292i
\(625\) 24.7794 3.31371i 0.991177 0.132548i
\(626\) 0.866125i 0.0346173i
\(627\) −4.39124 4.39124i −0.175369 0.175369i
\(628\) 13.7132 + 13.7132i 0.547216 + 0.547216i
\(629\) 26.0698 1.03947
\(630\) −5.13756 + 2.93351i −0.204685 + 0.116874i
\(631\) −1.69542 −0.0674935 −0.0337468 0.999430i \(-0.510744\pi\)
−0.0337468 + 0.999430i \(0.510744\pi\)
\(632\) −10.4697 10.4697i −0.416461 0.416461i
\(633\) 11.7028 + 11.7028i 0.465144 + 0.465144i
\(634\) 9.95583i 0.395397i
\(635\) 25.8072 + 24.1464i 1.02413 + 0.958221i
\(636\) 1.78984i 0.0709719i
\(637\) 6.24264 + 33.2175i 0.247342 + 1.31612i
\(638\) −16.5395 + 16.5395i −0.654804 + 0.654804i
\(639\) 13.0334i 0.515592i
\(640\) 1.52773 1.63280i 0.0603887 0.0645423i
\(641\) 23.0043 0.908615 0.454308 0.890845i \(-0.349887\pi\)
0.454308 + 0.890845i \(0.349887\pi\)
\(642\) 3.77297 3.77297i 0.148907 0.148907i
\(643\) 13.9948 + 13.9948i 0.551900 + 0.551900i 0.926989 0.375089i \(-0.122388\pi\)
−0.375089 + 0.926989i \(0.622388\pi\)
\(644\) −1.84316 3.49264i −0.0726305 0.137629i
\(645\) 23.9779 0.797197i 0.944130 0.0313896i
\(646\) −4.91548 −0.193397
\(647\) −5.22955 + 5.22955i −0.205595 + 0.205595i −0.802392 0.596797i \(-0.796440\pi\)
0.596797 + 0.802392i \(0.296440\pi\)
\(648\) −0.707107 + 0.707107i −0.0277778 + 0.0277778i
\(649\) −6.85656 −0.269144
\(650\) −1.60354 24.0888i −0.0628961 0.944841i
\(651\) 16.5091 8.71231i 0.647044 0.341462i
\(652\) −7.21967 7.21967i −0.282744 0.282744i
\(653\) 1.74516 1.74516i 0.0682933 0.0682933i −0.672135 0.740428i \(-0.734623\pi\)
0.740428 + 0.672135i \(0.234623\pi\)
\(654\) 0.0870500 0.00340392
\(655\) 0.953787 + 28.6878i 0.0372676 + 1.12093i
\(656\) 5.44670i 0.212658i
\(657\) 5.04441 5.04441i 0.196801 0.196801i
\(658\) 2.62526 + 0.811559i 0.102343 + 0.0316379i
\(659\) 21.4234i 0.834536i −0.908784 0.417268i \(-0.862988\pi\)
0.908784 0.417268i \(-0.137012\pi\)
\(660\) 7.49632 8.01193i 0.291794 0.311864i
\(661\) 15.6881i 0.610196i −0.952321 0.305098i \(-0.901311\pi\)
0.952321 0.305098i \(-0.0986892\pi\)
\(662\) −7.19543 7.19543i −0.279658 0.279658i
\(663\) −13.2604 13.2604i −0.514991 0.514991i
\(664\) 13.1495 0.510299
\(665\) 7.22297 + 1.97246i 0.280095 + 0.0764886i
\(666\) −6.71231 −0.260097
\(667\) 5.03121 + 5.03121i 0.194809 + 0.194809i
\(668\) 6.73439 + 6.73439i 0.260561 + 0.260561i
\(669\) 11.6824i 0.451666i
\(670\) 0.321063 + 9.65685i 0.0124037 + 0.373077i
\(671\) 11.2720i 0.435153i
\(672\) −0.781409 + 2.52773i −0.0301435 + 0.0975092i
\(673\) 26.0502 26.0502i 1.00416 1.00416i 0.00417159 0.999991i \(-0.498672\pi\)
0.999991 0.00417159i \(-0.00132786\pi\)
\(674\) 23.7782i 0.915901i
\(675\) −3.29289 + 3.76256i −0.126744 + 0.144821i
\(676\) −10.3137 −0.396681
\(677\) 3.99149 3.99149i 0.153405 0.153405i −0.626232 0.779637i \(-0.715404\pi\)
0.779637 + 0.626232i \(0.215404\pi\)
\(678\) −2.03248 2.03248i −0.0780571 0.0780571i
\(679\) 27.8832 14.7147i 1.07006 0.564699i
\(680\) −0.288579 8.67982i −0.0110665 0.332856i
\(681\) −8.36217 −0.320439
\(682\) −24.4801 + 24.4801i −0.937390 + 0.937390i
\(683\) −28.2530 + 28.2530i −1.08107 + 1.08107i −0.0846629 + 0.996410i \(0.526981\pi\)
−0.996410 + 0.0846629i \(0.973019\pi\)
\(684\) 1.26561 0.0483918
\(685\) 8.36916 + 7.83057i 0.319769 + 0.299191i
\(686\) 2.10767 18.3999i 0.0804713 0.702513i
\(687\) 6.58579 + 6.58579i 0.251263 + 0.251263i
\(688\) 7.58667 7.58667i 0.289239 0.289239i
\(689\) 8.64213 0.329239
\(690\) −2.43718 2.28034i −0.0927820 0.0868110i
\(691\) 2.45366i 0.0933418i −0.998910 0.0466709i \(-0.985139\pi\)
0.998910 0.0466709i \(-0.0148612\pi\)
\(692\) 14.1605 14.1605i 0.538303 0.538303i
\(693\) −3.83425 + 12.4032i −0.145651 + 0.471158i
\(694\) 11.0863i 0.420830i
\(695\) 8.72918 0.290220i 0.331116 0.0110087i
\(696\) 4.76687i 0.180688i
\(697\) 14.9584 + 14.9584i 0.566588 + 0.566588i
\(698\) −3.61217 3.61217i −0.136723 0.136723i
\(699\) 22.7071 0.858861
\(700\) −3.05895 + 12.8702i −0.115617 + 0.486449i
\(701\) −6.34833 −0.239773 −0.119887 0.992788i \(-0.538253\pi\)
−0.119887 + 0.992788i \(0.538253\pi\)
\(702\) 3.41421 + 3.41421i 0.128861 + 0.128861i
\(703\) 6.00699 + 6.00699i 0.226558 + 0.226558i
\(704\) 4.90685i 0.184934i
\(705\) 2.32106 0.0771687i 0.0874163 0.00290634i
\(706\) 17.0867i 0.643066i
\(707\) −14.1829 + 45.8792i −0.533401 + 1.72546i
\(708\) 0.988072 0.988072i 0.0371340 0.0371340i
\(709\) 20.3645i 0.764805i 0.923996 + 0.382402i \(0.124903\pi\)
−0.923996 + 0.382402i \(0.875097\pi\)
\(710\) −21.2810 19.9114i −0.798660 0.747262i
\(711\) 14.8063 0.555281
\(712\) 10.8609 10.8609i 0.407030 0.407030i
\(713\) 7.44670 + 7.44670i 0.278881 + 0.278881i
\(714\) 4.79594 + 9.08794i 0.179484 + 0.340107i
\(715\) −38.6850 36.1954i −1.44674 1.35363i
\(716\) −3.28123 −0.122625
\(717\) 1.19213 1.19213i 0.0445209 0.0445209i
\(718\) 2.76193 2.76193i 0.103074 0.103074i
\(719\) −25.9031 −0.966021 −0.483011 0.875614i \(-0.660457\pi\)
−0.483011 + 0.875614i \(0.660457\pi\)
\(720\) 0.0743018 + 2.23483i 0.00276906 + 0.0832873i
\(721\) −14.6072 27.6795i −0.544002 1.03084i
\(722\) 12.3024 + 12.3024i 0.457848 + 0.457848i
\(723\) 2.55672 2.55672i 0.0950853 0.0950853i
\(724\) −19.3934 −0.720749
\(725\) −1.58310 23.7817i −0.0587948 0.883231i
\(726\) 13.0772i 0.485339i
\(727\) 36.3373 36.3373i 1.34768 1.34768i 0.459495 0.888180i \(-0.348030\pi\)
0.888180 0.459495i \(-0.151970\pi\)
\(728\) 12.2049 + 3.77297i 0.452345 + 0.139836i
\(729\) 1.00000i 0.0370370i
\(730\) −0.530060 15.9430i −0.0196184 0.590078i
\(731\) 41.6708i 1.54125i
\(732\) 1.62437 + 1.62437i 0.0600385 + 0.0600385i
\(733\) −18.3535 18.3535i −0.677904 0.677904i 0.281622 0.959525i \(-0.409128\pi\)
−0.959525 + 0.281622i \(0.909128\pi\)
\(734\) −5.62959 −0.207792
\(735\) −3.40056 15.2786i −0.125432 0.563560i
\(736\) −1.49264 −0.0550193
\(737\) 14.9926 + 14.9926i 0.552261 + 0.552261i
\(738\) −3.85140 3.85140i −0.141772 0.141772i
\(739\) 21.3934i 0.786968i 0.919331 + 0.393484i \(0.128730\pi\)
−0.919331 + 0.393484i \(0.871270\pi\)
\(740\) −10.2546 + 10.9599i −0.376965 + 0.402894i
\(741\) 6.11091i 0.224490i
\(742\) −4.52423 1.39860i −0.166090 0.0513442i
\(743\) −29.9264 + 29.9264i −1.09789 + 1.09789i −0.103235 + 0.994657i \(0.532919\pi\)
−0.994657 + 0.103235i \(0.967081\pi\)
\(744\) 7.05545i 0.258665i
\(745\) 0.419154 + 12.6072i 0.0153566 + 0.461893i
\(746\) 12.6664 0.463749
\(747\) −9.29809 + 9.29809i −0.340199 + 0.340199i
\(748\) −13.4758 13.4758i −0.492723 0.492723i
\(749\) 6.58881 + 12.4853i 0.240750 + 0.456202i
\(750\) 1.11289 + 11.1248i 0.0406369 + 0.406221i
\(751\) −19.3081 −0.704563 −0.352281 0.935894i \(-0.614594\pi\)
−0.352281 + 0.935894i \(0.614594\pi\)
\(752\) 0.734390 0.734390i 0.0267804 0.0267804i
\(753\) −3.38630 + 3.38630i −0.123404 + 0.123404i
\(754\) −23.0165 −0.838212
\(755\) 26.2990 0.874366i 0.957118 0.0318214i
\(756\) −1.23483 2.33991i −0.0449104 0.0851018i
\(757\) −30.9872 30.9872i −1.12625 1.12625i −0.990782 0.135465i \(-0.956747\pi\)
−0.135465 0.990782i \(-0.543253\pi\)
\(758\) 9.91295 9.91295i 0.360055 0.360055i
\(759\) −7.32414 −0.265849
\(760\) 1.93351 2.06649i 0.0701356 0.0749596i
\(761\) 47.3418i 1.71614i 0.513532 + 0.858070i \(0.328337\pi\)
−0.513532 + 0.858070i \(0.671663\pi\)
\(762\) −11.1761 + 11.1761i −0.404869 + 0.404869i
\(763\) −0.0680216 + 0.220039i −0.00246255 + 0.00796593i
\(764\) 16.8453i 0.609441i
\(765\) 6.34162 + 5.93351i 0.229282 + 0.214526i
\(766\) 9.91295i 0.358169i
\(767\) −4.77083 4.77083i −0.172265 0.172265i
\(768\) 0.707107 + 0.707107i 0.0255155 + 0.0255155i
\(769\) −44.0520 −1.58856 −0.794278 0.607554i \(-0.792151\pi\)
−0.794278 + 0.607554i \(0.792151\pi\)
\(770\) 14.3943 + 25.2092i 0.518733 + 0.908478i
\(771\) −29.4316 −1.05995
\(772\) −4.81370 4.81370i −0.173249 0.173249i
\(773\) −11.1336 11.1336i −0.400448 0.400448i 0.477943 0.878391i \(-0.341383\pi\)
−0.878391 + 0.477943i \(0.841383\pi\)
\(774\) 10.7292i 0.385652i
\(775\) −2.34315 35.1994i −0.0841683 1.26440i
\(776\) 11.9164i 0.427773i
\(777\) 5.24505 16.9669i 0.188165 0.608683i
\(778\) −13.1918 + 13.1918i −0.472948 + 0.472948i
\(779\) 6.89339i 0.246981i
\(780\) 10.7907 0.358761i 0.386370 0.0128457i
\(781\) −63.9528 −2.28841
\(782\) −4.09925 + 4.09925i −0.146589 + 0.146589i
\(783\) 3.37069 + 3.37069i 0.120459 + 0.120459i
\(784\) −5.77880 3.95037i −0.206386 0.141085i
\(785\) −29.6278 + 31.6656i −1.05746 + 1.13019i
\(786\) −12.8367 −0.457869
\(787\) −11.7098 + 11.7098i −0.417409 + 0.417409i −0.884310 0.466901i \(-0.845370\pi\)
0.466901 + 0.884310i \(0.345370\pi\)
\(788\) −13.0334 + 13.0334i −0.464295 + 0.464295i
\(789\) 9.35965 0.333212
\(790\) 22.6200 24.1759i 0.804785 0.860139i
\(791\) 6.72576 3.54936i 0.239141 0.126201i
\(792\) 3.46967 + 3.46967i 0.123289 + 0.123289i
\(793\) 7.84316 7.84316i 0.278519 0.278519i
\(794\) 27.3909 0.972066
\(795\) −4.00000 + 0.132989i −0.141865 + 0.00471662i
\(796\) 11.7509i 0.416499i
\(797\) −12.7255 + 12.7255i −0.450760 + 0.450760i −0.895607 0.444847i \(-0.853258\pi\)
0.444847 + 0.895607i \(0.353258\pi\)
\(798\) −0.988958 + 3.19912i −0.0350088 + 0.113247i
\(799\) 4.03374i 0.142703i
\(800\) 3.76256 + 3.29289i 0.133027 + 0.116421i
\(801\) 15.3596i 0.542706i
\(802\) 19.7353 + 19.7353i 0.696877 + 0.696877i
\(803\) −24.7522 24.7522i −0.873485 0.873485i
\(804\) −4.32106 −0.152392
\(805\) 7.66851 4.37866i 0.270279 0.154327i
\(806\) −34.0667 −1.19995
\(807\) −9.27665 9.27665i −0.326554 0.326554i
\(808\) 12.8343 + 12.8343i 0.451507 + 0.451507i
\(809\) 22.8744i 0.804220i −0.915591 0.402110i \(-0.868277\pi\)
0.915591 0.402110i \(-0.131723\pi\)
\(810\) −1.63280 1.52773i −0.0573709 0.0536788i
\(811\) 0.722188i 0.0253595i 0.999920 + 0.0126797i \(0.00403619\pi\)
−0.999920 + 0.0126797i \(0.995964\pi\)
\(812\) 12.0494 + 3.72488i 0.422849 + 0.130718i
\(813\) −12.7870 + 12.7870i −0.448461 + 0.448461i
\(814\) 32.9363i 1.15442i
\(815\) 15.5983 16.6712i 0.546386 0.583967i
\(816\) 3.88388 0.135963
\(817\) 9.60177 9.60177i 0.335923 0.335923i
\(818\) −12.9549 12.9549i −0.452959 0.452959i
\(819\) −11.2981 + 5.96230i −0.394787 + 0.208340i
\(820\) −12.1725 + 0.404699i −0.425081 + 0.0141327i
\(821\) 21.2417 0.741341 0.370671 0.928764i \(-0.379128\pi\)
0.370671 + 0.928764i \(0.379128\pi\)
\(822\) −3.62437 + 3.62437i −0.126414 + 0.126414i
\(823\) 10.3066 10.3066i 0.359266 0.359266i −0.504276 0.863542i \(-0.668241\pi\)
0.863542 + 0.504276i \(0.168241\pi\)
\(824\) −11.8293 −0.412094
\(825\) 18.4623 + 16.1577i 0.642775 + 0.562540i
\(826\) 1.72549 + 3.26966i 0.0600374 + 0.113766i
\(827\) −26.1746 26.1746i −0.910181 0.910181i 0.0861054 0.996286i \(-0.472558\pi\)
−0.996286 + 0.0861054i \(0.972558\pi\)
\(828\) 1.05545 1.05545i 0.0366795 0.0366795i
\(829\) 21.0061 0.729571 0.364786 0.931092i \(-0.381142\pi\)
0.364786 + 0.931092i \(0.381142\pi\)
\(830\) 0.977031 + 29.3869i 0.0339132 + 1.02003i
\(831\) 3.72704i 0.129289i
\(832\) 3.41421 3.41421i 0.118367 0.118367i
\(833\) −26.7194 + 5.02144i −0.925773 + 0.173983i
\(834\) 3.90596i 0.135252i
\(835\) −14.5499 + 15.5506i −0.503519 + 0.538151i
\(836\) 6.21016i 0.214783i
\(837\) 4.98896 + 4.98896i 0.172444 + 0.172444i
\(838\) −3.88629 3.88629i −0.134250 0.134250i
\(839\) −50.2886 −1.73615 −0.868077 0.496430i \(-0.834644\pi\)
−0.868077 + 0.496430i \(0.834644\pi\)
\(840\) −5.70711 1.55850i −0.196914 0.0537735i
\(841\) 6.27692 0.216445
\(842\) −17.3851 17.3851i −0.599132 0.599132i
\(843\) 14.4645 + 14.4645i 0.498182 + 0.498182i
\(844\) 16.5502i 0.569683i
\(845\) −0.766327 23.0494i −0.0263625 0.792924i
\(846\) 1.03858i 0.0357073i
\(847\) 33.0555 + 10.2186i 1.13580 + 0.351116i
\(848\) −1.26561 + 1.26561i −0.0434612 + 0.0434612i
\(849\) 15.2383i 0.522978i
\(850\) 19.3765 1.28985i 0.664609 0.0442416i
\(851\) 10.0190 0.343448
\(852\) 9.21598 9.21598i 0.315734 0.315734i
\(853\) 13.1647 + 13.1647i 0.450751 + 0.450751i 0.895604 0.444853i \(-0.146744\pi\)
−0.444853 + 0.895604i \(0.646744\pi\)
\(854\) −5.37526 + 2.83667i −0.183938 + 0.0970688i
\(855\) 0.0940371 + 2.82843i 0.00321600 + 0.0967302i
\(856\) 5.33579 0.182374
\(857\) 19.5839 19.5839i 0.668973 0.668973i −0.288505 0.957478i \(-0.593158\pi\)
0.957478 + 0.288505i \(0.0931583\pi\)
\(858\) 16.7530 16.7530i 0.571939 0.571939i
\(859\) −7.58185 −0.258689 −0.129345 0.991600i \(-0.541287\pi\)
−0.129345 + 0.991600i \(0.541287\pi\)
\(860\) 17.5187 + 16.3912i 0.597381 + 0.558937i
\(861\) 12.7448 6.72576i 0.434341 0.229213i
\(862\) −16.1315 16.1315i −0.549440 0.549440i
\(863\) −22.1829 + 22.1829i −0.755113 + 0.755113i −0.975429 0.220315i \(-0.929291\pi\)
0.220315 + 0.975429i \(0.429291\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 32.6986 + 30.5943i 1.11179 + 1.04024i
\(866\) 24.2136i 0.822811i
\(867\) −1.35445 + 1.35445i −0.0459994 + 0.0459994i
\(868\) 17.8343 + 5.51319i 0.605334 + 0.187130i
\(869\) 72.6525i 2.46457i
\(870\) 10.6532 0.354187i 0.361176 0.0120081i
\(871\) 20.8639i 0.706948i
\(872\) 0.0615536 + 0.0615536i 0.00208447 + 0.00208447i
\(873\) 8.42614 + 8.42614i 0.285182 + 0.285182i
\(874\) −1.88909 −0.0638996
\(875\) −28.9901 5.87995i −0.980044 0.198779i
\(876\) 7.13387 0.241031
\(877\) −5.71511 5.71511i −0.192985 0.192985i 0.603999 0.796985i \(-0.293573\pi\)
−0.796985 + 0.603999i \(0.793573\pi\)
\(878\) −25.3373 25.3373i −0.855092 0.855092i
\(879\) 4.46841i 0.150716i
\(880\) 10.9660 0.364588i 0.369663 0.0122902i
\(881\) 31.8033i 1.07148i 0.844383 + 0.535740i \(0.179967\pi\)
−0.844383 + 0.535740i \(0.820033\pi\)
\(882\) 6.87957 1.29289i 0.231647 0.0435340i
\(883\) −16.9653 + 16.9653i −0.570929 + 0.570929i −0.932388 0.361459i \(-0.882279\pi\)
0.361459 + 0.932388i \(0.382279\pi\)
\(884\) 18.7530i 0.630733i
\(885\) 2.28159 + 2.13476i 0.0766949 + 0.0717592i
\(886\) −4.14519 −0.139260
\(887\) 7.70801 7.70801i 0.258810 0.258810i −0.565760 0.824570i \(-0.691417\pi\)
0.824570 + 0.565760i \(0.191417\pi\)
\(888\) −4.74632 4.74632i −0.159276 0.159276i
\(889\) −19.5171 36.9834i −0.654583 1.24038i
\(890\) 25.0793 + 23.4653i 0.840660 + 0.786560i
\(891\) −4.90685 −0.164386
\(892\) −8.26067 + 8.26067i −0.276588 + 0.276588i
\(893\) 0.929451 0.929451i 0.0311029 0.0311029i
\(894\) −5.64124 −0.188671
\(895\) −0.243801 7.33299i −0.00814937 0.245115i
\(896\) −2.33991 + 1.23483i −0.0781710 + 0.0412529i
\(897\) −5.09618 5.09618i −0.170156 0.170156i
\(898\) 1.20406 1.20406i 0.0401799 0.0401799i
\(899\) −33.6325 −1.12171
\(900\) −4.98896 + 0.332104i −0.166299 + 0.0110701i
\(901\) 6.95153i 0.231589i
\(902\) −18.8982 + 18.8982i −0.629242 + 0.629242i
\(903\) −27.1204 8.38387i −0.902511 0.278998i
\(904\) 2.87437i 0.0956000i
\(905\) −1.44096 43.3410i −0.0478992 1.44070i
\(906\) 11.7678i 0.390958i
\(907\) 0.997860 + 0.997860i 0.0331334 + 0.0331334i 0.723479 0.690346i \(-0.242542\pi\)
−0.690346 + 0.723479i \(0.742542\pi\)
\(908\) −5.91295 5.91295i −0.196228 0.196228i
\(909\) −18.1504 −0.602010
\(910\) −7.52512 + 27.5563i −0.249455 + 0.913484i
\(911\) −21.9623 −0.727643 −0.363821 0.931469i \(-0.618528\pi\)
−0.363821 + 0.931469i \(0.618528\pi\)
\(912\) 0.894921 + 0.894921i 0.0296338 + 0.0296338i
\(913\) 45.6243 + 45.6243i 1.50995 + 1.50995i
\(914\) 7.55635i 0.249942i
\(915\) −3.50950 + 3.75089i −0.116021 + 0.124001i
\(916\) 9.31371i 0.307734i
\(917\) 10.0307 32.4476i 0.331242 1.07151i
\(918\) −2.74632 + 2.74632i −0.0906420 + 0.0906420i
\(919\) 32.6954i 1.07852i 0.842138 + 0.539262i \(0.181297\pi\)
−0.842138 + 0.539262i \(0.818703\pi\)
\(920\) −0.110906 3.33579i −0.00365645 0.109978i
\(921\) −29.4172 −0.969331
\(922\) −0.607228 + 0.607228i −0.0199980 + 0.0199980i
\(923\) −44.4987 44.4987i −1.46469 1.46469i
\(924\) −11.4816 + 6.05914i −0.377717 + 0.199331i
\(925\) −25.2555 22.1029i −0.830394 0.726739i
\(926\) 28.7925 0.946180
\(927\) 8.36459 8.36459i 0.274729 0.274729i
\(928\) 3.37069 3.37069i 0.110648 0.110648i
\(929\) 10.8063 0.354545 0.177272 0.984162i \(-0.443273\pi\)
0.177272 + 0.984162i \(0.443273\pi\)
\(930\) 15.7678 0.524233i 0.517045 0.0171903i
\(931\) −7.31371 4.99963i −0.239697 0.163856i
\(932\) 16.0563 + 16.0563i 0.525943 + 0.525943i
\(933\) 8.11091 8.11091i 0.265539 0.265539i
\(934\) 12.4155 0.406247
\(935\) 29.1148 31.1174i 0.952156 1.01765i
\(936\) 4.82843i 0.157822i
\(937\) 3.51804 3.51804i 0.114929 0.114929i −0.647303 0.762233i \(-0.724103\pi\)
0.762233 + 0.647303i \(0.224103\pi\)
\(938\) 3.37652 10.9225i 0.110247 0.356631i
\(939\) 0.866125i 0.0282649i
\(940\) 1.69581 + 1.58667i 0.0553111 + 0.0517516i
\(941\) 54.9021i 1.78976i −0.446309 0.894879i \(-0.647262\pi\)
0.446309 0.894879i \(-0.352738\pi\)
\(942\) −13.7132 13.7132i −0.446800 0.446800i
\(943\) 5.74873 + 5.74873i 0.187204 + 0.187204i
\(944\) 1.39735 0.0454797
\(945\) 5.13756 2.93351i 0.167125 0.0954269i
\(946\) 52.6464 1.71168
\(947\) −30.4494 30.4494i −0.989471 0.989471i 0.0104740 0.999945i \(-0.496666\pi\)
−0.999945 + 0.0104740i \(0.996666\pi\)
\(948\) 10.4697 + 10.4697i 0.340039 + 0.340039i
\(949\) 34.4454i 1.11814i
\(950\) 4.76193 + 4.16752i 0.154498 + 0.135212i
\(951\) 9.95583i 0.322840i
\(952\) −3.03490 + 9.81739i −0.0983616 + 0.318183i
\(953\) 40.3553 40.3553i 1.30724 1.30724i 0.383836 0.923401i \(-0.374603\pi\)
0.923401 0.383836i \(-0.125397\pi\)
\(954\) 1.78984i 0.0579483i
\(955\) 37.6464 1.25164i 1.21821 0.0405020i
\(956\) 1.68592 0.0545267
\(957\) 16.5395 16.5395i 0.534645 0.534645i
\(958\) −0.828427 0.828427i −0.0267653 0.0267653i
\(959\) −6.32930 11.9935i −0.204384 0.387291i
\(960\) −1.52773 + 1.63280i −0.0493072 + 0.0526986i
\(961\) −18.7794 −0.605788
\(962\) −22.9172 + 22.9172i −0.738882 + 0.738882i
\(963\) −3.77297 + 3.77297i −0.121582 + 0.121582i
\(964\) 3.61574 0.116455
\(965\) 10.4001 11.1155i 0.334793 0.357820i
\(966\) 1.84316 + 3.49264i 0.0593026 + 0.112374i
\(967\) 30.6566 + 30.6566i 0.985849 + 0.985849i 0.999901 0.0140521i \(-0.00447307\pi\)
−0.0140521 + 0.999901i \(0.504473\pi\)
\(968\) 9.24695 9.24695i 0.297208 0.297208i
\(969\) 4.91548 0.157908
\(970\) 26.6311 0.885407i 0.855073 0.0284287i
\(971\) 46.5248i 1.49305i 0.665357 + 0.746525i \(0.268279\pi\)
−0.665357 + 0.746525i \(0.731721\pi\)
\(972\) 0.707107 0.707107i 0.0226805 0.0226805i
\(973\) −9.87321 3.05215i −0.316520 0.0978475i
\(974\) 13.7283i 0.439883i
\(975\) 1.60354 + 24.0888i 0.0513544 + 0.771460i
\(976\) 2.29721i 0.0735318i
\(977\) 42.6690 + 42.6690i 1.36510 + 1.36510i 0.867278 + 0.497825i \(0.165868\pi\)
0.497825 + 0.867278i \(0.334132\pi\)
\(978\) 7.21967 + 7.21967i 0.230860 + 0.230860i
\(979\) 75.3675 2.40875
\(980\) 8.39905 13.2082i 0.268298 0.421920i
\(981\) −0.0870500 −0.00277929
\(982\) 11.9770 + 11.9770i 0.382202 + 0.382202i
\(983\) −1.34529 1.34529i −0.0429079 0.0429079i 0.685327 0.728235i \(-0.259659\pi\)
−0.728235 + 0.685327i \(0.759659\pi\)
\(984\) 5.44670i 0.173634i
\(985\) −30.0958 28.1590i −0.958932 0.897220i
\(986\) 18.5140i 0.589605i
\(987\) −2.62526 0.811559i −0.0835629 0.0258322i
\(988\) 4.32106 4.32106i 0.137471 0.137471i
\(989\) 16.0147i 0.509239i
\(990\) −7.49632 + 8.01193i −0.238249 + 0.254636i
\(991\) 3.44975 0.109585 0.0547925 0.998498i \(-0.482550\pi\)
0.0547925 + 0.998498i \(0.482550\pi\)
\(992\) 4.98896 4.98896i 0.158400 0.158400i
\(993\) 7.19543 + 7.19543i 0.228340 + 0.228340i
\(994\) 16.0940 + 30.4969i 0.510472 + 0.967304i
\(995\) 26.2613 0.873112i 0.832539 0.0276795i
\(996\) −13.1495 −0.416658
\(997\) −31.5368 + 31.5368i −0.998780 + 0.998780i −0.999999 0.00121964i \(-0.999612\pi\)
0.00121964 + 0.999999i \(0.499612\pi\)
\(998\) 21.5043 21.5043i 0.680706 0.680706i
\(999\) 6.71231 0.212368
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 210.2.m.b.97.1 yes 8
3.2 odd 2 630.2.p.c.307.4 8
4.3 odd 2 1680.2.cz.a.97.1 8
5.2 odd 4 1050.2.m.b.643.4 8
5.3 odd 4 210.2.m.a.13.2 8
5.4 even 2 1050.2.m.a.307.3 8
7.6 odd 2 210.2.m.a.97.2 yes 8
15.8 even 4 630.2.p.b.433.3 8
20.3 even 4 1680.2.cz.b.433.4 8
21.20 even 2 630.2.p.b.307.3 8
28.27 even 2 1680.2.cz.b.97.4 8
35.13 even 4 inner 210.2.m.b.13.1 yes 8
35.27 even 4 1050.2.m.a.643.3 8
35.34 odd 2 1050.2.m.b.307.4 8
105.83 odd 4 630.2.p.c.433.4 8
140.83 odd 4 1680.2.cz.a.433.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.m.a.13.2 8 5.3 odd 4
210.2.m.a.97.2 yes 8 7.6 odd 2
210.2.m.b.13.1 yes 8 35.13 even 4 inner
210.2.m.b.97.1 yes 8 1.1 even 1 trivial
630.2.p.b.307.3 8 21.20 even 2
630.2.p.b.433.3 8 15.8 even 4
630.2.p.c.307.4 8 3.2 odd 2
630.2.p.c.433.4 8 105.83 odd 4
1050.2.m.a.307.3 8 5.4 even 2
1050.2.m.a.643.3 8 35.27 even 4
1050.2.m.b.307.4 8 35.34 odd 2
1050.2.m.b.643.4 8 5.2 odd 4
1680.2.cz.a.97.1 8 4.3 odd 2
1680.2.cz.a.433.1 8 140.83 odd 4
1680.2.cz.b.97.4 8 28.27 even 2
1680.2.cz.b.433.4 8 20.3 even 4