Properties

Label 931.2.v.b.606.1
Level $931$
Weight $2$
Character 931.606
Analytic conductor $7.434$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [931,2,Mod(177,931)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(931, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([6, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("931.177");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.v (of order \(9\), degree \(6\), 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: \(7.43407242818\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 19)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 606.1
Root \(-0.766044 - 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 931.606
Dual form 931.2.v.b.275.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.26604 - 0.460802i) q^{2} +(2.70574 - 0.984808i) q^{3} +(-0.141559 + 0.118782i) q^{4} +(0.673648 + 0.565258i) q^{5} +(2.97178 - 2.49362i) q^{6} +(-1.47178 + 2.54920i) q^{8} +(4.05303 - 3.40090i) q^{9} +O(q^{10})\) \(q+(1.26604 - 0.460802i) q^{2} +(2.70574 - 0.984808i) q^{3} +(-0.141559 + 0.118782i) q^{4} +(0.673648 + 0.565258i) q^{5} +(2.97178 - 2.49362i) q^{6} +(-1.47178 + 2.54920i) q^{8} +(4.05303 - 3.40090i) q^{9} +(1.11334 + 0.405223i) q^{10} +(1.11334 + 1.92836i) q^{11} +(-0.266044 + 0.460802i) q^{12} +(1.97178 - 1.65452i) q^{13} +(2.37939 + 0.866025i) q^{15} +(-0.624485 + 3.54163i) q^{16} +(0.358441 + 0.300767i) q^{17} +(3.56418 - 6.17334i) q^{18} +(2.77719 + 3.35965i) q^{19} -0.162504 q^{20} +(2.29813 + 1.92836i) q^{22} +(-0.467911 - 2.65366i) q^{23} +(-1.47178 + 8.34689i) q^{24} +(-0.733956 - 4.16247i) q^{25} +(1.73396 - 3.00330i) q^{26} +(3.29813 - 5.71253i) q^{27} +(-1.19459 - 6.77487i) q^{29} +3.41147 q^{30} -7.10607 q^{31} +(-0.180922 - 1.02606i) q^{32} +(4.91147 + 4.12122i) q^{33} +(0.592396 + 0.215615i) q^{34} +(-0.169778 + 0.962858i) q^{36} +(-2.47178 - 4.28125i) q^{37} +(5.06418 + 2.97373i) q^{38} +(3.70574 - 6.41852i) q^{39} +(-2.43242 + 0.885328i) q^{40} +(1.89646 + 1.59132i) q^{41} +(-3.66637 + 1.33445i) q^{43} +(-0.386659 - 0.140732i) q^{44} +4.65270 q^{45} +(-1.81521 - 3.14403i) q^{46} +(-5.58512 + 4.68647i) q^{47} +(1.79813 + 10.1977i) q^{48} +(-2.84730 - 4.93166i) q^{50} +(1.26604 + 0.460802i) q^{51} +(-0.0825961 + 0.468426i) q^{52} +(-2.17365 + 1.82391i) q^{53} +(1.54323 - 8.75211i) q^{54} +(-0.340022 + 1.92836i) q^{55} +(10.8229 + 6.35532i) q^{57} +(-4.63429 - 8.02682i) q^{58} +(-4.83022 - 4.05304i) q^{59} +(-0.439693 + 0.160035i) q^{60} +(1.58512 + 8.98968i) q^{61} +(-8.99660 + 3.27449i) q^{62} +(-4.29813 - 7.44459i) q^{64} +2.26352 q^{65} +(8.11721 + 2.95442i) q^{66} +(-7.21213 - 2.62500i) q^{67} -0.0864665 q^{68} +(-3.87939 - 6.71929i) q^{69} +(8.74422 - 3.18264i) q^{71} +(2.70439 + 15.3374i) q^{72} +(-1.30541 + 0.475129i) q^{73} +(-5.10220 - 4.28125i) q^{74} +(-6.08512 - 10.5397i) q^{75} +(-0.792204 - 0.145708i) q^{76} +(1.73396 - 9.83375i) q^{78} +(-2.05690 + 11.6653i) q^{79} +(-2.42262 + 2.03282i) q^{80} +(0.541889 - 3.07321i) q^{81} +(3.13429 + 1.14079i) q^{82} +(7.41534 + 12.8438i) q^{83} +(0.0714517 + 0.405223i) q^{85} +(-4.02687 + 3.37895i) q^{86} +(-9.90420 - 17.1546i) q^{87} -6.55438 q^{88} +(9.67024 + 3.51968i) q^{89} +(5.89053 - 2.14398i) q^{90} +(0.381445 + 0.320070i) q^{92} +(-19.2271 + 6.99811i) q^{93} +(-4.91147 + 8.50692i) q^{94} +(-0.0282185 + 3.83305i) q^{95} +(-1.50000 - 2.59808i) q^{96} +(1.64156 - 9.30975i) q^{97} +(11.0706 + 4.02936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} + 6 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} + 6 q^{3} - 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} + 12 q^{9} + 3 q^{12} - 3 q^{13} + 3 q^{15} + 9 q^{16} - 6 q^{17} + 3 q^{18} + 6 q^{19} - 6 q^{20} - 12 q^{23} + 6 q^{24} - 9 q^{25} + 15 q^{26} + 6 q^{27} - 3 q^{29} - 18 q^{31} - 18 q^{32} + 9 q^{33} - 24 q^{36} + 12 q^{38} + 12 q^{39} + 9 q^{40} + 21 q^{41} - 3 q^{43} - 9 q^{44} + 30 q^{45} - 18 q^{46} - 12 q^{47} - 3 q^{48} - 15 q^{50} + 3 q^{51} + 6 q^{52} - 12 q^{53} - 6 q^{54} + 18 q^{55} + 24 q^{57} - 18 q^{58} - 6 q^{59} + 3 q^{60} - 12 q^{61} - 12 q^{62} - 12 q^{64} + 24 q^{65} + 18 q^{66} + 6 q^{67} + 30 q^{68} - 12 q^{69} - 6 q^{71} + 15 q^{72} - 12 q^{73} - 30 q^{74} - 15 q^{75} + 36 q^{76} + 15 q^{78} + 24 q^{79} + 12 q^{80} - 3 q^{81} + 9 q^{82} - 48 q^{86} - 21 q^{87} - 18 q^{88} + 15 q^{89} + 18 q^{90} + 42 q^{92} - 36 q^{93} - 9 q^{94} - 15 q^{95} - 9 q^{96} + 18 q^{97} + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/931\mathbb{Z}\right)^\times\).

\(n\) \(248\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.26604 0.460802i 0.895229 0.325837i 0.146889 0.989153i \(-0.453074\pi\)
0.748339 + 0.663316i \(0.230852\pi\)
\(3\) 2.70574 0.984808i 1.56216 0.568579i 0.590928 0.806724i \(-0.298762\pi\)
0.971230 + 0.238145i \(0.0765393\pi\)
\(4\) −0.141559 + 0.118782i −0.0707796 + 0.0593912i
\(5\) 0.673648 + 0.565258i 0.301265 + 0.252791i 0.780870 0.624693i \(-0.214776\pi\)
−0.479606 + 0.877484i \(0.659220\pi\)
\(6\) 2.97178 2.49362i 1.21322 1.01802i
\(7\) 0 0
\(8\) −1.47178 + 2.54920i −0.520353 + 0.901278i
\(9\) 4.05303 3.40090i 1.35101 1.13363i
\(10\) 1.11334 + 0.405223i 0.352069 + 0.128143i
\(11\) 1.11334 + 1.92836i 0.335685 + 0.581423i 0.983616 0.180276i \(-0.0576989\pi\)
−0.647931 + 0.761699i \(0.724366\pi\)
\(12\) −0.266044 + 0.460802i −0.0768004 + 0.133022i
\(13\) 1.97178 1.65452i 0.546874 0.458882i −0.327007 0.945022i \(-0.606040\pi\)
0.873881 + 0.486140i \(0.161596\pi\)
\(14\) 0 0
\(15\) 2.37939 + 0.866025i 0.614355 + 0.223607i
\(16\) −0.624485 + 3.54163i −0.156121 + 0.885408i
\(17\) 0.358441 + 0.300767i 0.0869346 + 0.0729468i 0.685219 0.728337i \(-0.259706\pi\)
−0.598285 + 0.801284i \(0.704151\pi\)
\(18\) 3.56418 6.17334i 0.840085 1.45507i
\(19\) 2.77719 + 3.35965i 0.637131 + 0.770756i
\(20\) −0.162504 −0.0363370
\(21\) 0 0
\(22\) 2.29813 + 1.92836i 0.489964 + 0.411128i
\(23\) −0.467911 2.65366i −0.0975662 0.553325i −0.993931 0.110008i \(-0.964912\pi\)
0.896365 0.443318i \(-0.146199\pi\)
\(24\) −1.47178 + 8.34689i −0.300426 + 1.70380i
\(25\) −0.733956 4.16247i −0.146791 0.832494i
\(26\) 1.73396 3.00330i 0.340057 0.588995i
\(27\) 3.29813 5.71253i 0.634726 1.09938i
\(28\) 0 0
\(29\) −1.19459 6.77487i −0.221830 1.25806i −0.868653 0.495421i \(-0.835014\pi\)
0.646822 0.762641i \(-0.276097\pi\)
\(30\) 3.41147 0.622847
\(31\) −7.10607 −1.27629 −0.638144 0.769917i \(-0.720297\pi\)
−0.638144 + 0.769917i \(0.720297\pi\)
\(32\) −0.180922 1.02606i −0.0319828 0.181384i
\(33\) 4.91147 + 4.12122i 0.854978 + 0.717412i
\(34\) 0.592396 + 0.215615i 0.101595 + 0.0369776i
\(35\) 0 0
\(36\) −0.169778 + 0.962858i −0.0282963 + 0.160476i
\(37\) −2.47178 4.28125i −0.406358 0.703833i 0.588120 0.808774i \(-0.299868\pi\)
−0.994479 + 0.104940i \(0.966535\pi\)
\(38\) 5.06418 + 2.97373i 0.821518 + 0.482402i
\(39\) 3.70574 6.41852i 0.593393 1.02779i
\(40\) −2.43242 + 0.885328i −0.384599 + 0.139983i
\(41\) 1.89646 + 1.59132i 0.296177 + 0.248522i 0.778751 0.627333i \(-0.215854\pi\)
−0.482574 + 0.875855i \(0.660298\pi\)
\(42\) 0 0
\(43\) −3.66637 + 1.33445i −0.559117 + 0.203502i −0.606093 0.795394i \(-0.707264\pi\)
0.0469757 + 0.998896i \(0.485042\pi\)
\(44\) −0.386659 0.140732i −0.0582911 0.0212162i
\(45\) 4.65270 0.693584
\(46\) −1.81521 3.14403i −0.267638 0.463562i
\(47\) −5.58512 + 4.68647i −0.814674 + 0.683592i −0.951718 0.306972i \(-0.900684\pi\)
0.137045 + 0.990565i \(0.456240\pi\)
\(48\) 1.79813 + 10.1977i 0.259538 + 1.47191i
\(49\) 0 0
\(50\) −2.84730 4.93166i −0.402669 0.697442i
\(51\) 1.26604 + 0.460802i 0.177282 + 0.0645253i
\(52\) −0.0825961 + 0.468426i −0.0114540 + 0.0649590i
\(53\) −2.17365 + 1.82391i −0.298574 + 0.250533i −0.779750 0.626091i \(-0.784654\pi\)
0.481177 + 0.876624i \(0.340210\pi\)
\(54\) 1.54323 8.75211i 0.210007 1.19101i
\(55\) −0.340022 + 1.92836i −0.0458486 + 0.260020i
\(56\) 0 0
\(57\) 10.8229 + 6.35532i 1.43353 + 0.841783i
\(58\) −4.63429 8.02682i −0.608511 1.05397i
\(59\) −4.83022 4.05304i −0.628841 0.527661i 0.271727 0.962374i \(-0.412405\pi\)
−0.900569 + 0.434714i \(0.856850\pi\)
\(60\) −0.439693 + 0.160035i −0.0567641 + 0.0206604i
\(61\) 1.58512 + 8.98968i 0.202954 + 1.15101i 0.900627 + 0.434593i \(0.143108\pi\)
−0.697673 + 0.716417i \(0.745781\pi\)
\(62\) −8.99660 + 3.27449i −1.14257 + 0.415861i
\(63\) 0 0
\(64\) −4.29813 7.44459i −0.537267 0.930573i
\(65\) 2.26352 0.280755
\(66\) 8.11721 + 2.95442i 0.999160 + 0.363664i
\(67\) −7.21213 2.62500i −0.881102 0.320695i −0.138448 0.990370i \(-0.544211\pi\)
−0.742655 + 0.669675i \(0.766434\pi\)
\(68\) −0.0864665 −0.0104856
\(69\) −3.87939 6.71929i −0.467023 0.808908i
\(70\) 0 0
\(71\) 8.74422 3.18264i 1.03775 0.377709i 0.233722 0.972303i \(-0.424909\pi\)
0.804026 + 0.594594i \(0.202687\pi\)
\(72\) 2.70439 + 15.3374i 0.318716 + 1.80753i
\(73\) −1.30541 + 0.475129i −0.152786 + 0.0556097i −0.417281 0.908777i \(-0.637017\pi\)
0.264495 + 0.964387i \(0.414795\pi\)
\(74\) −5.10220 4.28125i −0.593118 0.497685i
\(75\) −6.08512 10.5397i −0.702649 1.21702i
\(76\) −0.792204 0.145708i −0.0908720 0.0167139i
\(77\) 0 0
\(78\) 1.73396 9.83375i 0.196332 1.11345i
\(79\) −2.05690 + 11.6653i −0.231420 + 1.31245i 0.618604 + 0.785703i \(0.287698\pi\)
−0.850024 + 0.526744i \(0.823413\pi\)
\(80\) −2.42262 + 2.03282i −0.270857 + 0.227276i
\(81\) 0.541889 3.07321i 0.0602099 0.341467i
\(82\) 3.13429 + 1.14079i 0.346124 + 0.125979i
\(83\) 7.41534 + 12.8438i 0.813940 + 1.40979i 0.910087 + 0.414418i \(0.136015\pi\)
−0.0961469 + 0.995367i \(0.530652\pi\)
\(84\) 0 0
\(85\) 0.0714517 + 0.405223i 0.00775003 + 0.0439526i
\(86\) −4.02687 + 3.37895i −0.434229 + 0.364361i
\(87\) −9.90420 17.1546i −1.06184 1.83916i
\(88\) −6.55438 −0.698699
\(89\) 9.67024 + 3.51968i 1.02504 + 0.373085i 0.799192 0.601076i \(-0.205261\pi\)
0.225852 + 0.974162i \(0.427483\pi\)
\(90\) 5.89053 2.14398i 0.620916 0.225995i
\(91\) 0 0
\(92\) 0.381445 + 0.320070i 0.0397684 + 0.0333696i
\(93\) −19.2271 + 6.99811i −1.99376 + 0.725670i
\(94\) −4.91147 + 8.50692i −0.506580 + 0.877422i
\(95\) −0.0282185 + 3.83305i −0.00289516 + 0.393262i
\(96\) −1.50000 2.59808i −0.153093 0.265165i
\(97\) 1.64156 9.30975i 0.166675 0.945261i −0.780645 0.624974i \(-0.785109\pi\)
0.947320 0.320287i \(-0.103779\pi\)
\(98\) 0 0
\(99\) 11.0706 + 4.02936i 1.11263 + 0.404966i
\(100\) 0.598326 + 0.502055i 0.0598326 + 0.0502055i
\(101\) −1.60607 9.10846i −0.159810 0.906325i −0.954256 0.298991i \(-0.903350\pi\)
0.794446 0.607334i \(-0.207761\pi\)
\(102\) 1.81521 0.179732
\(103\) −5.50980 −0.542897 −0.271448 0.962453i \(-0.587503\pi\)
−0.271448 + 0.962453i \(0.587503\pi\)
\(104\) 1.31567 + 7.46156i 0.129012 + 0.731666i
\(105\) 0 0
\(106\) −1.91147 + 3.31077i −0.185659 + 0.321570i
\(107\) −5.11721 + 8.86327i −0.494699 + 0.856845i −0.999981 0.00610974i \(-0.998055\pi\)
0.505282 + 0.862954i \(0.331389\pi\)
\(108\) 0.211667 + 1.20042i 0.0203677 + 0.115511i
\(109\) −0.316552 + 1.79525i −0.0303201 + 0.171954i −0.996208 0.0870081i \(-0.972269\pi\)
0.965887 + 0.258962i \(0.0833805\pi\)
\(110\) 0.458111 + 2.59808i 0.0436792 + 0.247717i
\(111\) −10.9042 9.14971i −1.03498 0.868452i
\(112\) 0 0
\(113\) −17.6878 −1.66393 −0.831963 0.554830i \(-0.812783\pi\)
−0.831963 + 0.554830i \(0.812783\pi\)
\(114\) 16.6309 + 3.05888i 1.55762 + 0.286490i
\(115\) 1.18479 2.05212i 0.110482 0.191361i
\(116\) 0.973841 + 0.817150i 0.0904189 + 0.0758704i
\(117\) 2.36484 13.4117i 0.218629 1.23991i
\(118\) −7.98293 2.90555i −0.734888 0.267477i
\(119\) 0 0
\(120\) −5.70961 + 4.79093i −0.521213 + 0.437350i
\(121\) 3.02094 5.23243i 0.274631 0.475675i
\(122\) 6.14930 + 10.6509i 0.556731 + 0.964287i
\(123\) 6.69846 + 2.43804i 0.603980 + 0.219831i
\(124\) 1.00593 0.844075i 0.0903352 0.0758002i
\(125\) 4.05690 7.02676i 0.362861 0.628493i
\(126\) 0 0
\(127\) 8.88919 7.45891i 0.788788 0.661871i −0.156657 0.987653i \(-0.550072\pi\)
0.945445 + 0.325782i \(0.105627\pi\)
\(128\) −7.27584 6.10516i −0.643100 0.539625i
\(129\) −8.60607 + 7.22135i −0.757722 + 0.635804i
\(130\) 2.86571 1.04303i 0.251340 0.0914802i
\(131\) −1.73396 + 0.631108i −0.151496 + 0.0551402i −0.416655 0.909065i \(-0.636798\pi\)
0.265159 + 0.964205i \(0.414576\pi\)
\(132\) −1.18479 −0.103123
\(133\) 0 0
\(134\) −10.3405 −0.893282
\(135\) 5.45084 1.98394i 0.469133 0.170751i
\(136\) −1.29426 + 0.471073i −0.110982 + 0.0403942i
\(137\) 0.195937 0.164411i 0.0167400 0.0140465i −0.634379 0.773022i \(-0.718744\pi\)
0.651119 + 0.758975i \(0.274300\pi\)
\(138\) −8.00774 6.71929i −0.681664 0.571984i
\(139\) 3.26604 2.74054i 0.277022 0.232449i −0.493682 0.869643i \(-0.664349\pi\)
0.770704 + 0.637193i \(0.219905\pi\)
\(140\) 0 0
\(141\) −10.4966 + 18.1806i −0.883973 + 1.53109i
\(142\) 9.60401 8.05872i 0.805950 0.676273i
\(143\) 5.38578 + 1.96026i 0.450382 + 0.163926i
\(144\) 9.51367 + 16.4782i 0.792806 + 1.37318i
\(145\) 3.02481 5.23913i 0.251197 0.435086i
\(146\) −1.43376 + 1.20307i −0.118659 + 0.0995668i
\(147\) 0 0
\(148\) 0.858441 + 0.312447i 0.0705634 + 0.0256830i
\(149\) 2.87551 16.3079i 0.235571 1.33599i −0.605836 0.795590i \(-0.707161\pi\)
0.841407 0.540402i \(-0.181728\pi\)
\(150\) −12.5608 10.5397i −1.02558 0.860566i
\(151\) 2.18092 3.77747i 0.177481 0.307406i −0.763536 0.645765i \(-0.776539\pi\)
0.941017 + 0.338359i \(0.109872\pi\)
\(152\) −12.6518 + 2.13495i −1.02620 + 0.173167i
\(153\) 2.47565 0.200145
\(154\) 0 0
\(155\) −4.78699 4.01676i −0.384500 0.322634i
\(156\) 0.237826 + 1.34878i 0.0190413 + 0.107989i
\(157\) −1.67024 + 9.47243i −0.133300 + 0.755982i 0.842728 + 0.538339i \(0.180948\pi\)
−0.976028 + 0.217643i \(0.930163\pi\)
\(158\) 2.77126 + 15.7166i 0.220470 + 1.25034i
\(159\) −4.08512 + 7.07564i −0.323971 + 0.561135i
\(160\) 0.458111 0.793471i 0.0362168 0.0627294i
\(161\) 0 0
\(162\) −0.730085 4.14052i −0.0573609 0.325310i
\(163\) 8.35504 0.654417 0.327209 0.944952i \(-0.393892\pi\)
0.327209 + 0.944952i \(0.393892\pi\)
\(164\) −0.457482 −0.0357233
\(165\) 0.979055 + 5.55250i 0.0762194 + 0.432261i
\(166\) 15.3066 + 12.8438i 1.18802 + 0.996869i
\(167\) −3.79174 1.38008i −0.293413 0.106794i 0.191120 0.981567i \(-0.438788\pi\)
−0.484533 + 0.874773i \(0.661010\pi\)
\(168\) 0 0
\(169\) −1.10694 + 6.27779i −0.0851496 + 0.482907i
\(170\) 0.277189 + 0.480105i 0.0212594 + 0.0368224i
\(171\) 22.6819 + 4.17182i 1.73452 + 0.319027i
\(172\) 0.360500 0.624404i 0.0274879 0.0476104i
\(173\) 18.9290 6.88960i 1.43915 0.523806i 0.499608 0.866251i \(-0.333477\pi\)
0.939538 + 0.342445i \(0.111255\pi\)
\(174\) −20.4440 17.1546i −1.54986 1.30049i
\(175\) 0 0
\(176\) −7.52481 + 2.73881i −0.567204 + 0.206445i
\(177\) −17.0608 6.20961i −1.28237 0.466743i
\(178\) 13.8648 1.03921
\(179\) 5.75624 + 9.97011i 0.430242 + 0.745201i 0.996894 0.0787564i \(-0.0250949\pi\)
−0.566652 + 0.823957i \(0.691762\pi\)
\(180\) −0.658633 + 0.552659i −0.0490916 + 0.0411928i
\(181\) 1.48246 + 8.40744i 0.110190 + 0.624920i 0.989020 + 0.147784i \(0.0472141\pi\)
−0.878829 + 0.477136i \(0.841675\pi\)
\(182\) 0 0
\(183\) 13.1420 + 22.7627i 0.971487 + 1.68266i
\(184\) 7.45336 + 2.71280i 0.549469 + 0.199990i
\(185\) 0.754900 4.28125i 0.0555014 0.314764i
\(186\) −21.1177 + 17.7198i −1.54842 + 1.29928i
\(187\) −0.180922 + 1.02606i −0.0132303 + 0.0750330i
\(188\) 0.233956 1.32683i 0.0170630 0.0967689i
\(189\) 0 0
\(190\) 1.73055 + 4.86581i 0.125547 + 0.353003i
\(191\) −9.16772 15.8790i −0.663353 1.14896i −0.979729 0.200327i \(-0.935800\pi\)
0.316376 0.948634i \(-0.397534\pi\)
\(192\) −18.9611 15.9103i −1.36840 1.14822i
\(193\) −0.279715 + 0.101808i −0.0201343 + 0.00732830i −0.352068 0.935975i \(-0.614521\pi\)
0.331933 + 0.943303i \(0.392299\pi\)
\(194\) −2.21167 12.5430i −0.158788 0.900534i
\(195\) 6.12449 2.22913i 0.438583 0.159631i
\(196\) 0 0
\(197\) −6.57057 11.3806i −0.468134 0.810832i 0.531203 0.847245i \(-0.321740\pi\)
−0.999337 + 0.0364128i \(0.988407\pi\)
\(198\) 15.8726 1.12802
\(199\) 0.241230 + 0.0878004i 0.0171003 + 0.00622400i 0.350556 0.936542i \(-0.385993\pi\)
−0.333456 + 0.942766i \(0.608215\pi\)
\(200\) 11.6912 + 4.25524i 0.826692 + 0.300891i
\(201\) −22.0993 −1.55876
\(202\) −6.23055 10.7916i −0.438380 0.759297i
\(203\) 0 0
\(204\) −0.233956 + 0.0851529i −0.0163802 + 0.00596189i
\(205\) 0.378041 + 2.14398i 0.0264035 + 0.149742i
\(206\) −6.97565 + 2.53893i −0.486017 + 0.176896i
\(207\) −10.9213 9.16404i −0.759081 0.636945i
\(208\) 4.62836 + 8.01655i 0.320919 + 0.555848i
\(209\) −3.38666 + 9.09586i −0.234260 + 0.629174i
\(210\) 0 0
\(211\) 0.425145 2.41112i 0.0292682 0.165988i −0.966670 0.256024i \(-0.917587\pi\)
0.995938 + 0.0900364i \(0.0286983\pi\)
\(212\) 0.0910521 0.516382i 0.00625348 0.0354653i
\(213\) 20.5253 17.2228i 1.40637 1.18008i
\(214\) −2.39440 + 13.5793i −0.163678 + 0.928263i
\(215\) −3.22416 1.17350i −0.219886 0.0800318i
\(216\) 9.70826 + 16.8152i 0.660564 + 1.14413i
\(217\) 0 0
\(218\) 0.426489 + 2.41874i 0.0288855 + 0.163818i
\(219\) −3.06418 + 2.57115i −0.207058 + 0.173742i
\(220\) −0.180922 0.313366i −0.0121978 0.0211272i
\(221\) 1.20439 0.0810162
\(222\) −18.0214 6.55926i −1.20952 0.440229i
\(223\) 7.99660 2.91052i 0.535492 0.194903i −0.0600971 0.998193i \(-0.519141\pi\)
0.595589 + 0.803289i \(0.296919\pi\)
\(224\) 0 0
\(225\) −17.1309 14.3745i −1.14206 0.958301i
\(226\) −22.3935 + 8.15058i −1.48959 + 0.542168i
\(227\) 7.07532 12.2548i 0.469606 0.813381i −0.529790 0.848129i \(-0.677729\pi\)
0.999396 + 0.0347477i \(0.0110628\pi\)
\(228\) −2.28699 + 0.385920i −0.151460 + 0.0255582i
\(229\) 10.2665 + 17.7821i 0.678430 + 1.17508i 0.975454 + 0.220205i \(0.0706727\pi\)
−0.297023 + 0.954870i \(0.595994\pi\)
\(230\) 0.554378 3.14403i 0.0365546 0.207311i
\(231\) 0 0
\(232\) 19.0287 + 6.92588i 1.24929 + 0.454706i
\(233\) 13.5214 + 11.3458i 0.885817 + 0.743289i 0.967367 0.253380i \(-0.0815425\pi\)
−0.0815496 + 0.996669i \(0.525987\pi\)
\(234\) −3.18614 18.0695i −0.208284 1.18124i
\(235\) −6.41147 −0.418238
\(236\) 1.16519 0.0758475
\(237\) 5.92262 + 33.5888i 0.384715 + 2.18183i
\(238\) 0 0
\(239\) −1.17617 + 2.03719i −0.0760804 + 0.131775i −0.901556 0.432663i \(-0.857574\pi\)
0.825475 + 0.564438i \(0.190907\pi\)
\(240\) −4.55303 + 7.88609i −0.293897 + 0.509045i
\(241\) 2.39646 + 13.5910i 0.154370 + 0.875473i 0.959360 + 0.282185i \(0.0910593\pi\)
−0.804990 + 0.593288i \(0.797830\pi\)
\(242\) 1.41353 8.01655i 0.0908654 0.515323i
\(243\) 1.87598 + 10.6392i 0.120344 + 0.682506i
\(244\) −1.29220 1.08429i −0.0827249 0.0694144i
\(245\) 0 0
\(246\) 9.60401 0.612329
\(247\) 11.0346 + 2.02957i 0.702116 + 0.129138i
\(248\) 10.4586 18.1148i 0.664120 1.15029i
\(249\) 32.7126 + 27.4491i 2.07308 + 1.73952i
\(250\) 1.89827 10.7656i 0.120057 0.680878i
\(251\) 3.91400 + 1.42458i 0.247050 + 0.0899187i 0.462577 0.886579i \(-0.346925\pi\)
−0.215528 + 0.976498i \(0.569147\pi\)
\(252\) 0 0
\(253\) 4.59627 3.85673i 0.288965 0.242470i
\(254\) 7.81702 13.5395i 0.490483 0.849542i
\(255\) 0.592396 + 1.02606i 0.0370973 + 0.0642544i
\(256\) 4.13088 + 1.50352i 0.258180 + 0.0939699i
\(257\) 0.511144 0.428901i 0.0318843 0.0267541i −0.626706 0.779256i \(-0.715597\pi\)
0.658591 + 0.752501i \(0.271153\pi\)
\(258\) −7.56805 + 13.1082i −0.471166 + 0.816084i
\(259\) 0 0
\(260\) −0.320422 + 0.268866i −0.0198717 + 0.0166744i
\(261\) −27.8824 23.3961i −1.72588 1.44818i
\(262\) −1.90445 + 1.59802i −0.117657 + 0.0987261i
\(263\) −10.7121 + 3.89890i −0.660538 + 0.240416i −0.650469 0.759533i \(-0.725428\pi\)
−0.0100696 + 0.999949i \(0.503205\pi\)
\(264\) −17.7344 + 6.45480i −1.09148 + 0.397266i
\(265\) −2.49525 −0.153282
\(266\) 0 0
\(267\) 29.6313 1.81341
\(268\) 1.33275 0.485081i 0.0814106 0.0296310i
\(269\) −18.2208 + 6.63181i −1.11094 + 0.404349i −0.831338 0.555768i \(-0.812424\pi\)
−0.279601 + 0.960116i \(0.590202\pi\)
\(270\) 5.98680 5.02352i 0.364345 0.305722i
\(271\) −10.2606 8.60965i −0.623286 0.522999i 0.275549 0.961287i \(-0.411141\pi\)
−0.898835 + 0.438288i \(0.855585\pi\)
\(272\) −1.28905 + 1.08164i −0.0781600 + 0.0655841i
\(273\) 0 0
\(274\) 0.172304 0.298439i 0.0104093 0.0180294i
\(275\) 7.20961 6.04958i 0.434756 0.364803i
\(276\) 1.34730 + 0.490376i 0.0810977 + 0.0295172i
\(277\) −8.87346 15.3693i −0.533154 0.923450i −0.999250 0.0387161i \(-0.987673\pi\)
0.466096 0.884734i \(-0.345660\pi\)
\(278\) 2.87211 4.97464i 0.172258 0.298359i
\(279\) −28.8011 + 24.1670i −1.72428 + 1.44684i
\(280\) 0 0
\(281\) −17.1766 6.25179i −1.02467 0.372950i −0.225622 0.974215i \(-0.572442\pi\)
−0.799050 + 0.601265i \(0.794664\pi\)
\(282\) −4.91147 + 27.8544i −0.292474 + 1.65870i
\(283\) 5.88919 + 4.94161i 0.350076 + 0.293748i 0.800820 0.598904i \(-0.204397\pi\)
−0.450745 + 0.892653i \(0.648842\pi\)
\(284\) −0.859785 + 1.48919i −0.0510188 + 0.0883672i
\(285\) 3.69846 + 10.3990i 0.219078 + 0.615984i
\(286\) 7.72193 0.456608
\(287\) 0 0
\(288\) −4.22281 3.54336i −0.248832 0.208794i
\(289\) −2.91400 16.5261i −0.171412 0.972125i
\(290\) 1.41534 8.02682i 0.0831119 0.471351i
\(291\) −4.72668 26.8063i −0.277083 1.57142i
\(292\) 0.128356 0.222318i 0.00751144 0.0130102i
\(293\) 5.25150 9.09586i 0.306796 0.531386i −0.670864 0.741581i \(-0.734076\pi\)
0.977660 + 0.210195i \(0.0674098\pi\)
\(294\) 0 0
\(295\) −0.962859 5.46064i −0.0560598 0.317931i
\(296\) 14.5517 0.845800
\(297\) 14.6878 0.852272
\(298\) −3.87417 21.9715i −0.224425 1.27278i
\(299\) −5.31315 4.45826i −0.307267 0.257828i
\(300\) 2.11334 + 0.769193i 0.122014 + 0.0444094i
\(301\) 0 0
\(302\) 1.02048 5.78742i 0.0587219 0.333028i
\(303\) −13.3157 23.0634i −0.764966 1.32496i
\(304\) −13.6329 + 7.73773i −0.781903 + 0.443789i
\(305\) −4.01367 + 6.95188i −0.229822 + 0.398064i
\(306\) 3.13429 1.14079i 0.179175 0.0652144i
\(307\) −8.95929 7.51774i −0.511334 0.429060i 0.350264 0.936651i \(-0.386092\pi\)
−0.861598 + 0.507591i \(0.830536\pi\)
\(308\) 0 0
\(309\) −14.9081 + 5.42609i −0.848091 + 0.308680i
\(310\) −7.91147 2.87954i −0.449342 0.163547i
\(311\) 15.9659 0.905340 0.452670 0.891678i \(-0.350471\pi\)
0.452670 + 0.891678i \(0.350471\pi\)
\(312\) 10.9081 + 18.8933i 0.617548 + 1.06962i
\(313\) −20.3987 + 17.1166i −1.15300 + 0.967486i −0.999786 0.0207063i \(-0.993409\pi\)
−0.153219 + 0.988192i \(0.548964\pi\)
\(314\) 2.25031 + 12.7622i 0.126993 + 0.720211i
\(315\) 0 0
\(316\) −1.09446 1.89565i −0.0615679 0.106639i
\(317\) −27.7511 10.1006i −1.55866 0.567304i −0.588228 0.808695i \(-0.700174\pi\)
−0.970428 + 0.241390i \(0.922397\pi\)
\(318\) −1.91147 + 10.8405i −0.107190 + 0.607906i
\(319\) 11.7344 9.84635i 0.657002 0.551290i
\(320\) 1.31268 7.44459i 0.0733811 0.416165i
\(321\) −5.11721 + 29.0211i −0.285615 + 1.61980i
\(322\) 0 0
\(323\) −0.0150147 + 2.03952i −0.000835443 + 0.113482i
\(324\) 0.288333 + 0.499408i 0.0160185 + 0.0277449i
\(325\) −8.33409 6.99313i −0.462292 0.387909i
\(326\) 10.5778 3.85002i 0.585853 0.213233i
\(327\) 0.911474 + 5.16923i 0.0504046 + 0.285859i
\(328\) −6.84776 + 2.49238i −0.378104 + 0.137619i
\(329\) 0 0
\(330\) 3.79813 + 6.57856i 0.209080 + 0.362138i
\(331\) 27.6655 1.52063 0.760317 0.649553i \(-0.225044\pi\)
0.760317 + 0.649553i \(0.225044\pi\)
\(332\) −2.57532 0.937341i −0.141339 0.0514432i
\(333\) −24.5783 8.94578i −1.34688 0.490225i
\(334\) −5.43645 −0.297469
\(335\) −3.37464 5.84504i −0.184376 0.319349i
\(336\) 0 0
\(337\) −16.7827 + 6.10841i −0.914212 + 0.332746i −0.755934 0.654648i \(-0.772817\pi\)
−0.158279 + 0.987394i \(0.550594\pi\)
\(338\) 1.49138 + 8.45805i 0.0811205 + 0.460057i
\(339\) −47.8585 + 17.4191i −2.59932 + 0.946074i
\(340\) −0.0582480 0.0488759i −0.00315894 0.00265067i
\(341\) −7.91147 13.7031i −0.428430 0.742063i
\(342\) 30.6386 5.17015i 1.65675 0.279569i
\(343\) 0 0
\(344\) 1.99432 11.3103i 0.107526 0.609813i
\(345\) 1.18479 6.71929i 0.0637871 0.361755i
\(346\) 20.7902 17.4451i 1.11769 0.937853i
\(347\) −1.00727 + 5.71253i −0.0540733 + 0.306665i −0.999834 0.0181980i \(-0.994207\pi\)
0.945761 + 0.324863i \(0.105318\pi\)
\(348\) 3.43969 + 1.25195i 0.184387 + 0.0671113i
\(349\) −2.68614 4.65253i −0.143786 0.249044i 0.785134 0.619326i \(-0.212594\pi\)
−0.928919 + 0.370282i \(0.879261\pi\)
\(350\) 0 0
\(351\) −2.94831 16.7207i −0.157369 0.892485i
\(352\) 1.77719 1.49124i 0.0947245 0.0794833i
\(353\) 12.6172 + 21.8537i 0.671546 + 1.16315i 0.977466 + 0.211095i \(0.0677029\pi\)
−0.305919 + 0.952057i \(0.598964\pi\)
\(354\) −24.4611 −1.30009
\(355\) 7.68954 + 2.79876i 0.408118 + 0.148543i
\(356\) −1.78699 + 0.650411i −0.0947102 + 0.0344717i
\(357\) 0 0
\(358\) 11.8819 + 9.97011i 0.627979 + 0.526937i
\(359\) −6.28359 + 2.28704i −0.331635 + 0.120705i −0.502471 0.864594i \(-0.667575\pi\)
0.170836 + 0.985300i \(0.445353\pi\)
\(360\) −6.84776 + 11.8607i −0.360909 + 0.625112i
\(361\) −3.57444 + 18.6607i −0.188129 + 0.982144i
\(362\) 5.75103 + 9.96108i 0.302267 + 0.523543i
\(363\) 3.02094 17.1326i 0.158558 0.899230i
\(364\) 0 0
\(365\) −1.14796 0.417822i −0.0600868 0.0218698i
\(366\) 27.1275 + 22.7627i 1.41798 + 1.18982i
\(367\) 1.40983 + 7.99552i 0.0735923 + 0.417363i 0.999240 + 0.0389764i \(0.0124097\pi\)
−0.925648 + 0.378386i \(0.876479\pi\)
\(368\) 9.69047 0.505151
\(369\) 13.0983 0.681872
\(370\) −1.01707 5.76811i −0.0528752 0.299870i
\(371\) 0 0
\(372\) 1.89053 3.27449i 0.0980194 0.169775i
\(373\) −17.4488 + 30.2222i −0.903463 + 1.56484i −0.0804968 + 0.996755i \(0.525651\pi\)
−0.822967 + 0.568090i \(0.807683\pi\)
\(374\) 0.243756 + 1.38241i 0.0126043 + 0.0714826i
\(375\) 4.05690 23.0078i 0.209498 1.18812i
\(376\) −3.72668 21.1351i −0.192189 1.08996i
\(377\) −13.5646 11.3821i −0.698615 0.586207i
\(378\) 0 0
\(379\) 1.70140 0.0873950 0.0436975 0.999045i \(-0.486086\pi\)
0.0436975 + 0.999045i \(0.486086\pi\)
\(380\) −0.451304 0.545955i −0.0231514 0.0280069i
\(381\) 16.7062 28.9360i 0.855885 1.48244i
\(382\) −18.9238 15.8790i −0.968226 0.812438i
\(383\) 0.509962 2.89214i 0.0260579 0.147781i −0.969003 0.247049i \(-0.920539\pi\)
0.995061 + 0.0992680i \(0.0316501\pi\)
\(384\) −25.6989 9.35365i −1.31144 0.477326i
\(385\) 0 0
\(386\) −0.307218 + 0.257787i −0.0156370 + 0.0131210i
\(387\) −10.3216 + 17.8775i −0.524677 + 0.908767i
\(388\) 0.873455 + 1.51287i 0.0443430 + 0.0768043i
\(389\) 23.0856 + 8.40247i 1.17049 + 0.426022i 0.852832 0.522185i \(-0.174883\pi\)
0.317654 + 0.948207i \(0.397105\pi\)
\(390\) 6.72668 5.64436i 0.340619 0.285813i
\(391\) 0.630415 1.09191i 0.0318815 0.0552203i
\(392\) 0 0
\(393\) −4.07011 + 3.41523i −0.205310 + 0.172275i
\(394\) −13.5628 11.3806i −0.683286 0.573345i
\(395\) −7.97952 + 6.69561i −0.401493 + 0.336893i
\(396\) −2.04576 + 0.744596i −0.102803 + 0.0374173i
\(397\) 29.9158 10.8885i 1.50143 0.546476i 0.545001 0.838436i \(-0.316529\pi\)
0.956431 + 0.291959i \(0.0943071\pi\)
\(398\) 0.345866 0.0173367
\(399\) 0 0
\(400\) 15.2003 0.760014
\(401\) 0.0812519 0.0295733i 0.00405753 0.00147682i −0.339991 0.940429i \(-0.610424\pi\)
0.344048 + 0.938952i \(0.388202\pi\)
\(402\) −27.9786 + 10.1834i −1.39545 + 0.507902i
\(403\) −14.0116 + 11.7571i −0.697968 + 0.585665i
\(404\) 1.30928 + 1.09861i 0.0651390 + 0.0546581i
\(405\) 2.10220 1.76395i 0.104459 0.0876515i
\(406\) 0 0
\(407\) 5.50387 9.53298i 0.272817 0.472532i
\(408\) −3.03802 + 2.54920i −0.150404 + 0.126204i
\(409\) −18.7995 6.84245i −0.929574 0.338337i −0.167534 0.985866i \(-0.553580\pi\)
−0.762041 + 0.647529i \(0.775802\pi\)
\(410\) 1.46657 + 2.54017i 0.0724286 + 0.125450i
\(411\) 0.368241 0.637812i 0.0181640 0.0314609i
\(412\) 0.779963 0.654467i 0.0384260 0.0322433i
\(413\) 0 0
\(414\) −18.0496 6.56953i −0.887091 0.322875i
\(415\) −2.26470 + 12.8438i −0.111170 + 0.630475i
\(416\) −2.05438 1.72383i −0.100724 0.0845176i
\(417\) 6.13816 10.6316i 0.300587 0.520632i
\(418\) −0.0962667 + 13.0763i −0.00470856 + 0.639585i
\(419\) 25.4097 1.24135 0.620673 0.784070i \(-0.286859\pi\)
0.620673 + 0.784070i \(0.286859\pi\)
\(420\) 0 0
\(421\) 3.34730 + 2.80872i 0.163137 + 0.136888i 0.720702 0.693245i \(-0.243820\pi\)
−0.557565 + 0.830134i \(0.688264\pi\)
\(422\) −0.572796 3.24849i −0.0278833 0.158134i
\(423\) −6.69846 + 37.9889i −0.325690 + 1.84708i
\(424\) −1.45037 8.22546i −0.0704362 0.399464i
\(425\) 0.988856 1.71275i 0.0479665 0.0830805i
\(426\) 18.0496 31.2629i 0.874507 1.51469i
\(427\) 0 0
\(428\) −0.328411 1.86251i −0.0158744 0.0900279i
\(429\) 16.5030 0.796772
\(430\) −4.62267 −0.222925
\(431\) −6.65183 37.7244i −0.320407 1.81712i −0.540158 0.841564i \(-0.681636\pi\)
0.219751 0.975556i \(-0.429476\pi\)
\(432\) 18.1721 + 15.2482i 0.874303 + 0.733628i
\(433\) 17.0376 + 6.20118i 0.818775 + 0.298010i 0.717244 0.696823i \(-0.245403\pi\)
0.101532 + 0.994832i \(0.467626\pi\)
\(434\) 0 0
\(435\) 3.02481 17.1546i 0.145029 0.822499i
\(436\) −0.168434 0.291736i −0.00806651 0.0139716i
\(437\) 7.61587 8.94172i 0.364316 0.427740i
\(438\) −2.69459 + 4.66717i −0.128753 + 0.223006i
\(439\) 5.72328 2.08310i 0.273157 0.0994211i −0.201810 0.979425i \(-0.564682\pi\)
0.474967 + 0.880004i \(0.342460\pi\)
\(440\) −4.41534 3.70491i −0.210493 0.176625i
\(441\) 0 0
\(442\) 1.52481 0.554987i 0.0725280 0.0263981i
\(443\) 28.0903 + 10.2240i 1.33461 + 0.485759i 0.908112 0.418728i \(-0.137524\pi\)
0.426501 + 0.904487i \(0.359746\pi\)
\(444\) 2.63041 0.124834
\(445\) 4.52481 + 7.83721i 0.214497 + 0.371519i
\(446\) 8.78287 7.36970i 0.415881 0.348966i
\(447\) −8.27972 46.9566i −0.391617 2.22097i
\(448\) 0 0
\(449\) 5.62495 + 9.74270i 0.265458 + 0.459787i 0.967683 0.252168i \(-0.0811435\pi\)
−0.702226 + 0.711955i \(0.747810\pi\)
\(450\) −28.3123 10.3048i −1.33465 0.485774i
\(451\) −0.957234 + 5.42874i −0.0450744 + 0.255629i
\(452\) 2.50387 2.10100i 0.117772 0.0988226i
\(453\) 2.18092 12.3686i 0.102469 0.581129i
\(454\) 3.31062 18.7755i 0.155375 0.881176i
\(455\) 0 0
\(456\) −32.1300 + 18.2362i −1.50463 + 0.853989i
\(457\) 11.6951 + 20.2564i 0.547072 + 0.947556i 0.998473 + 0.0552352i \(0.0175909\pi\)
−0.451402 + 0.892321i \(0.649076\pi\)
\(458\) 21.1919 + 17.7821i 0.990233 + 0.830904i
\(459\) 2.90033 1.05563i 0.135376 0.0492728i
\(460\) 0.0760373 + 0.431229i 0.00354526 + 0.0201062i
\(461\) 34.4149 12.5260i 1.60286 0.583395i 0.622853 0.782339i \(-0.285974\pi\)
0.980011 + 0.198945i \(0.0637514\pi\)
\(462\) 0 0
\(463\) 21.4932 + 37.2273i 0.998873 + 1.73010i 0.540534 + 0.841322i \(0.318222\pi\)
0.458340 + 0.888777i \(0.348444\pi\)
\(464\) 24.7401 1.14853
\(465\) −16.9081 6.15403i −0.784093 0.285387i
\(466\) 22.3469 + 8.13360i 1.03520 + 0.376782i
\(467\) 25.5963 1.18445 0.592227 0.805771i \(-0.298249\pi\)
0.592227 + 0.805771i \(0.298249\pi\)
\(468\) 1.25830 + 2.17945i 0.0581651 + 0.100745i
\(469\) 0 0
\(470\) −8.11721 + 2.95442i −0.374419 + 0.136277i
\(471\) 4.80928 + 27.2748i 0.221600 + 1.25676i
\(472\) 17.4410 6.34802i 0.802789 0.292191i
\(473\) −6.65523 5.58440i −0.306008 0.256771i
\(474\) 22.9761 + 39.7958i 1.05533 + 1.82788i
\(475\) 11.9461 14.0258i 0.548124 0.643548i
\(476\) 0 0
\(477\) −2.60694 + 14.7847i −0.119364 + 0.676946i
\(478\) −0.550345 + 3.12116i −0.0251722 + 0.142759i
\(479\) 29.2447 24.5392i 1.33622 1.12123i 0.353645 0.935380i \(-0.384942\pi\)
0.982579 0.185845i \(-0.0595023\pi\)
\(480\) 0.458111 2.59808i 0.0209098 0.118585i
\(481\) −11.9572 4.35208i −0.545203 0.198438i
\(482\) 9.29679 + 16.1025i 0.423457 + 0.733449i
\(483\) 0 0
\(484\) 0.193877 + 1.09953i 0.00881261 + 0.0499788i
\(485\) 6.36824 5.34359i 0.289167 0.242640i
\(486\) 7.27766 + 12.6053i 0.330121 + 0.571787i
\(487\) 7.76382 0.351812 0.175906 0.984407i \(-0.443714\pi\)
0.175906 + 0.984407i \(0.443714\pi\)
\(488\) −25.2494 9.19004i −1.14299 0.416014i
\(489\) 22.6065 8.22811i 1.02230 0.372088i
\(490\) 0 0
\(491\) −28.1313 23.6050i −1.26955 1.06528i −0.994596 0.103822i \(-0.966893\pi\)
−0.274954 0.961457i \(-0.588663\pi\)
\(492\) −1.23783 + 0.450532i −0.0558055 + 0.0203115i
\(493\) 1.60947 2.78768i 0.0724869 0.125551i
\(494\) 14.9055 2.51525i 0.670632 0.113167i
\(495\) 5.18004 + 8.97210i 0.232826 + 0.403266i
\(496\) 4.43763 25.1671i 0.199256 1.13003i
\(497\) 0 0
\(498\) 54.0642 + 19.6778i 2.42268 + 0.881782i
\(499\) 3.77379 + 3.16658i 0.168938 + 0.141756i 0.723337 0.690495i \(-0.242607\pi\)
−0.554399 + 0.832251i \(0.687052\pi\)
\(500\) 0.260363 + 1.47659i 0.0116438 + 0.0660352i
\(501\) −11.6186 −0.519079
\(502\) 5.61175 0.250465
\(503\) 5.72163 + 32.4490i 0.255115 + 1.44683i 0.795778 + 0.605589i \(0.207062\pi\)
−0.540663 + 0.841239i \(0.681827\pi\)
\(504\) 0 0
\(505\) 4.06670 7.04374i 0.180966 0.313442i
\(506\) 4.04189 7.00076i 0.179684 0.311222i
\(507\) 3.18732 + 18.0762i 0.141554 + 0.802791i
\(508\) −0.372360 + 2.11176i −0.0165208 + 0.0936941i
\(509\) −6.41370 36.3739i −0.284282 1.61224i −0.707839 0.706374i \(-0.750330\pi\)
0.423557 0.905870i \(-0.360781\pi\)
\(510\) 1.22281 + 1.02606i 0.0541470 + 0.0454347i
\(511\) 0 0
\(512\) 24.9186 1.10126
\(513\) 28.3516 4.78423i 1.25176 0.211229i
\(514\) 0.449493 0.778544i 0.0198263 0.0343401i
\(515\) −3.71167 3.11446i −0.163556 0.137239i
\(516\) 0.360500 2.04450i 0.0158701 0.0900040i
\(517\) −15.2554 5.55250i −0.670930 0.244199i
\(518\) 0 0
\(519\) 44.4320 37.2829i 1.95035 1.63654i
\(520\) −3.33140 + 5.77016i −0.146092 + 0.253038i
\(521\) −4.64590 8.04693i −0.203540 0.352542i 0.746126 0.665804i \(-0.231912\pi\)
−0.949667 + 0.313262i \(0.898578\pi\)
\(522\) −46.0813 16.7722i −2.01692 0.734100i
\(523\) −21.7672 + 18.2649i −0.951814 + 0.798667i −0.979602 0.200947i \(-0.935598\pi\)
0.0277878 + 0.999614i \(0.491154\pi\)
\(524\) 0.170493 0.295303i 0.00744802 0.0129004i
\(525\) 0 0
\(526\) −11.7654 + 9.87236i −0.512996 + 0.430455i
\(527\) −2.54710 2.13727i −0.110954 0.0931011i
\(528\) −17.6630 + 14.8210i −0.768682 + 0.645001i
\(529\) 14.7900 5.38311i 0.643043 0.234048i
\(530\) −3.15910 + 1.14982i −0.137223 + 0.0499449i
\(531\) −33.3610 −1.44775
\(532\) 0 0
\(533\) 6.37227 0.276014
\(534\) 37.5146 13.6542i 1.62342 0.590875i
\(535\) −8.45723 + 3.07818i −0.365638 + 0.133081i
\(536\) 17.3063 14.5217i 0.747520 0.627244i
\(537\) 25.3935 + 21.3077i 1.09581 + 0.919495i
\(538\) −20.0123 + 16.7923i −0.862793 + 0.723969i
\(539\) 0 0
\(540\) −0.535959 + 0.928309i −0.0230640 + 0.0399480i
\(541\) 11.4795 9.63246i 0.493543 0.414132i −0.361751 0.932275i \(-0.617821\pi\)
0.855294 + 0.518143i \(0.173376\pi\)
\(542\) −16.9577 6.17210i −0.728396 0.265114i
\(543\) 12.2909 + 21.2884i 0.527451 + 0.913572i
\(544\) 0.243756 0.422197i 0.0104509 0.0181016i
\(545\) −1.22803 + 1.03044i −0.0526028 + 0.0441390i
\(546\) 0 0
\(547\) 3.65270 + 1.32948i 0.156178 + 0.0568443i 0.418926 0.908020i \(-0.362407\pi\)
−0.262748 + 0.964864i \(0.584629\pi\)
\(548\) −0.00820761 + 0.0465477i −0.000350612 + 0.00198842i
\(549\) 36.9975 + 31.0446i 1.57902 + 1.32495i
\(550\) 6.34002 10.9812i 0.270339 0.468242i
\(551\) 19.4436 22.8285i 0.828324 0.972527i
\(552\) 22.8384 0.972068
\(553\) 0 0
\(554\) −18.3164 15.3693i −0.778189 0.652978i
\(555\) −2.17365 12.3274i −0.0922662 0.523268i
\(556\) −0.136812 + 0.775897i −0.00580210 + 0.0329054i
\(557\) 2.29292 + 13.0038i 0.0971541 + 0.550988i 0.994066 + 0.108779i \(0.0346940\pi\)
−0.896912 + 0.442209i \(0.854195\pi\)
\(558\) −25.3273 + 43.8681i −1.07219 + 1.85709i
\(559\) −5.02141 + 8.69734i −0.212383 + 0.367858i
\(560\) 0 0
\(561\) 0.520945 + 2.95442i 0.0219943 + 0.124736i
\(562\) −24.6272 −1.03884
\(563\) 10.7128 0.451489 0.225745 0.974187i \(-0.427519\pi\)
0.225745 + 0.974187i \(0.427519\pi\)
\(564\) −0.673648 3.82045i −0.0283657 0.160870i
\(565\) −11.9153 9.99816i −0.501282 0.420626i
\(566\) 9.73308 + 3.54255i 0.409112 + 0.148905i
\(567\) 0 0
\(568\) −4.75641 + 26.9749i −0.199574 + 1.13184i
\(569\) 6.73530 + 11.6659i 0.282358 + 0.489059i 0.971965 0.235125i \(-0.0755499\pi\)
−0.689607 + 0.724184i \(0.742217\pi\)
\(570\) 9.47431 + 11.4613i 0.396835 + 0.480063i
\(571\) −6.33275 + 10.9686i −0.265017 + 0.459023i −0.967568 0.252610i \(-0.918711\pi\)
0.702551 + 0.711634i \(0.252044\pi\)
\(572\) −0.995252 + 0.362242i −0.0416136 + 0.0151461i
\(573\) −40.4432 33.9358i −1.68954 1.41769i
\(574\) 0 0
\(575\) −10.7023 + 3.89533i −0.446318 + 0.162447i
\(576\) −42.7388 15.5556i −1.78078 0.648152i
\(577\) −10.5544 −0.439384 −0.219692 0.975569i \(-0.570505\pi\)
−0.219692 + 0.975569i \(0.570505\pi\)
\(578\) −11.3045 19.5800i −0.470206 0.814421i
\(579\) −0.656574 + 0.550931i −0.0272863 + 0.0228959i
\(580\) 0.194126 + 1.10094i 0.00806064 + 0.0457142i
\(581\) 0 0
\(582\) −18.3366 31.7600i −0.760077 1.31649i
\(583\) −5.93717 2.16095i −0.245892 0.0894975i
\(584\) 0.710074 4.02703i 0.0293831 0.166640i
\(585\) 9.17412 7.69800i 0.379303 0.318273i
\(586\) 2.45723 13.9357i 0.101507 0.575677i
\(587\) −3.32619 + 18.8638i −0.137287 + 0.778591i 0.835954 + 0.548800i \(0.184915\pi\)
−0.973240 + 0.229791i \(0.926196\pi\)
\(588\) 0 0
\(589\) −19.7349 23.8739i −0.813162 0.983706i
\(590\) −3.73530 6.46973i −0.153780 0.266355i
\(591\) −28.9859 24.3221i −1.19232 1.00048i
\(592\) 16.7062 6.08056i 0.686621 0.249910i
\(593\) −1.50980 8.56250i −0.0620001 0.351620i −0.999988 0.00495124i \(-0.998424\pi\)
0.937988 0.346669i \(-0.112687\pi\)
\(594\) 18.5954 6.76817i 0.762978 0.277701i
\(595\) 0 0
\(596\) 1.53003 + 2.65009i 0.0626724 + 0.108552i
\(597\) 0.739170 0.0302522
\(598\) −8.78106 3.19604i −0.359084 0.130696i
\(599\) −18.6356 6.78281i −0.761431 0.277138i −0.0680235 0.997684i \(-0.521669\pi\)
−0.693408 + 0.720545i \(0.743891\pi\)
\(600\) 35.8239 1.46250
\(601\) 16.8807 + 29.2383i 0.688579 + 1.19265i 0.972298 + 0.233747i \(0.0750986\pi\)
−0.283718 + 0.958908i \(0.591568\pi\)
\(602\) 0 0
\(603\) −38.1584 + 13.8885i −1.55393 + 0.565584i
\(604\) 0.139967 + 0.793791i 0.00569517 + 0.0322989i
\(605\) 4.99273 1.81720i 0.202983 0.0738798i
\(606\) −27.4859 23.0634i −1.11654 0.936888i
\(607\) −17.6425 30.5577i −0.716087 1.24030i −0.962539 0.271144i \(-0.912598\pi\)
0.246452 0.969155i \(-0.420735\pi\)
\(608\) 2.94475 3.45740i 0.119425 0.140216i
\(609\) 0 0
\(610\) −1.87804 + 10.6509i −0.0760397 + 0.431242i
\(611\) −3.25877 + 18.4814i −0.131836 + 0.747678i
\(612\) −0.350452 + 0.294064i −0.0141662 + 0.0118868i
\(613\) 3.20439 18.1730i 0.129424 0.734001i −0.849157 0.528140i \(-0.822889\pi\)
0.978581 0.205861i \(-0.0659994\pi\)
\(614\) −14.8071 5.38933i −0.597564 0.217496i
\(615\) 3.13429 + 5.42874i 0.126387 + 0.218908i
\(616\) 0 0
\(617\) −6.19671 35.1433i −0.249470 1.41482i −0.809878 0.586598i \(-0.800467\pi\)
0.560408 0.828217i \(-0.310644\pi\)
\(618\) −16.3739 + 13.7394i −0.658656 + 0.552678i
\(619\) −1.82976 3.16923i −0.0735441 0.127382i 0.826908 0.562337i \(-0.190098\pi\)
−0.900452 + 0.434955i \(0.856764\pi\)
\(620\) 1.15476 0.0463764
\(621\) −16.7023 6.07915i −0.670242 0.243948i
\(622\) 20.2135 7.35710i 0.810487 0.294993i
\(623\) 0 0
\(624\) 20.4179 + 17.1326i 0.817369 + 0.685854i
\(625\) −13.1540 + 4.78768i −0.526162 + 0.191507i
\(626\) −17.9383 + 31.0701i −0.716961 + 1.24181i
\(627\) −0.205737 + 27.9462i −0.00821635 + 1.11606i
\(628\) −0.888719 1.53931i −0.0354637 0.0614250i
\(629\) 0.401674 2.27801i 0.0160158 0.0908301i
\(630\) 0 0
\(631\) 0.745977 + 0.271514i 0.0296969 + 0.0108088i 0.356826 0.934171i \(-0.383859\pi\)
−0.327129 + 0.944980i \(0.606081\pi\)
\(632\) −26.7098 22.4122i −1.06246 0.891510i
\(633\) −1.22416 6.94253i −0.0486558 0.275941i
\(634\) −39.7885 −1.58020
\(635\) 10.2044 0.404949
\(636\) −0.262174 1.48686i −0.0103959 0.0589579i
\(637\) 0 0
\(638\) 10.3191 17.8732i 0.408536 0.707605i
\(639\) 24.6168 42.6375i 0.973826 1.68672i
\(640\) −1.45037 8.22546i −0.0573309 0.325140i
\(641\) 5.10220 28.9360i 0.201525 1.14290i −0.701291 0.712875i \(-0.747393\pi\)
0.902816 0.430028i \(-0.141496\pi\)
\(642\) 6.89440 + 39.1001i 0.272100 + 1.54316i
\(643\) 17.0168 + 14.2788i 0.671078 + 0.563101i 0.913384 0.407098i \(-0.133459\pi\)
−0.242306 + 0.970200i \(0.577904\pi\)
\(644\) 0 0
\(645\) −9.87939 −0.389000
\(646\) 0.920807 + 2.58904i 0.0362287 + 0.101865i
\(647\) −5.62954 + 9.75065i −0.221320 + 0.383337i −0.955209 0.295932i \(-0.904370\pi\)
0.733889 + 0.679269i \(0.237703\pi\)
\(648\) 7.03667 + 5.90447i 0.276427 + 0.231950i
\(649\) 2.43804 13.8268i 0.0957016 0.542751i
\(650\) −13.7738 5.01325i −0.540252 0.196636i
\(651\) 0 0
\(652\) −1.18273 + 0.992431i −0.0463194 + 0.0388666i
\(653\) −13.5000 + 23.3827i −0.528296 + 0.915035i 0.471160 + 0.882048i \(0.343835\pi\)
−0.999456 + 0.0329874i \(0.989498\pi\)
\(654\) 3.53596 + 6.12446i 0.138267 + 0.239485i
\(655\) −1.52481 0.554987i −0.0595794 0.0216851i
\(656\) −6.82017 + 5.72281i −0.266283 + 0.223438i
\(657\) −3.67499 + 6.36527i −0.143375 + 0.248333i
\(658\) 0 0
\(659\) 21.4691 18.0147i 0.836317 0.701753i −0.120415 0.992724i \(-0.538423\pi\)
0.956732 + 0.290970i \(0.0939781\pi\)
\(660\) −0.798133 0.669713i −0.0310673 0.0260686i
\(661\) 8.70826 7.30710i 0.338712 0.284213i −0.457526 0.889196i \(-0.651264\pi\)
0.796239 + 0.604983i \(0.206820\pi\)
\(662\) 35.0257 12.7483i 1.36131 0.495478i
\(663\) 3.25877 1.18610i 0.126560 0.0460641i
\(664\) −43.6551 −1.69415
\(665\) 0 0
\(666\) −35.2395 −1.36550
\(667\) −17.4192 + 6.34008i −0.674475 + 0.245489i
\(668\) 0.700685 0.255028i 0.0271103 0.00986734i
\(669\) 18.7704 15.7502i 0.725705 0.608939i
\(670\) −6.96585 5.84504i −0.269114 0.225814i
\(671\) −15.5706 + 13.0653i −0.601095 + 0.504379i
\(672\) 0 0
\(673\) 8.28359 14.3476i 0.319309 0.553059i −0.661035 0.750355i \(-0.729883\pi\)
0.980344 + 0.197296i \(0.0632160\pi\)
\(674\) −18.4329 + 15.4670i −0.710008 + 0.595768i
\(675\) −26.1989 9.53563i −1.00840 0.367027i
\(676\) −0.588993 1.02017i −0.0226536 0.0392371i
\(677\) 4.52481 7.83721i 0.173903 0.301208i −0.765878 0.642986i \(-0.777695\pi\)
0.939781 + 0.341777i \(0.111029\pi\)
\(678\) −52.5642 + 44.1066i −2.01872 + 1.69390i
\(679\) 0 0
\(680\) −1.13816 0.414255i −0.0436463 0.0158859i
\(681\) 7.07532 40.1261i 0.271127 1.53764i
\(682\) −16.3307 13.7031i −0.625334 0.524718i
\(683\) −4.36571 + 7.56164i −0.167049 + 0.289338i −0.937381 0.348305i \(-0.886757\pi\)
0.770332 + 0.637643i \(0.220091\pi\)
\(684\) −3.70637 + 2.10364i −0.141716 + 0.0804348i
\(685\) 0.224927 0.00859402
\(686\) 0 0
\(687\) 45.2904 + 38.0032i 1.72794 + 1.44991i
\(688\) −2.43654 13.8183i −0.0928921 0.526817i
\(689\) −1.26827 + 7.19269i −0.0483171 + 0.274020i
\(690\) −1.59627 9.05288i −0.0607688 0.344637i
\(691\) −17.3601 + 30.0686i −0.660409 + 1.14386i 0.320099 + 0.947384i \(0.396284\pi\)
−0.980508 + 0.196478i \(0.937050\pi\)
\(692\) −1.86122 + 3.22372i −0.0707528 + 0.122547i
\(693\) 0 0
\(694\) 1.35710 + 7.69648i 0.0515147 + 0.292154i
\(695\) 3.74928 0.142218
\(696\) 58.3073 2.21013
\(697\) 0.201151 + 1.14079i 0.00761915 + 0.0432104i
\(698\) −5.54466 4.65253i −0.209869 0.176101i
\(699\) 47.7588 + 17.3828i 1.80640 + 0.657478i
\(700\) 0 0
\(701\) 6.84436 38.8163i 0.258508 1.46607i −0.528397 0.848997i \(-0.677207\pi\)
0.786905 0.617074i \(-0.211682\pi\)
\(702\) −11.4376 19.8106i −0.431686 0.747701i
\(703\) 7.51889 20.1942i 0.283580 0.761637i
\(704\) 9.57057 16.5767i 0.360705 0.624759i
\(705\) −17.3478 + 6.31407i −0.653355 + 0.237802i
\(706\) 26.0442 + 21.8537i 0.980185 + 0.822473i
\(707\) 0 0
\(708\) 3.15270 1.14749i 0.118486 0.0431253i
\(709\) 38.6416 + 14.0644i 1.45122 + 0.528200i 0.942931 0.332989i \(-0.108057\pi\)
0.508286 + 0.861189i \(0.330279\pi\)
\(710\) 11.0250 0.413760
\(711\) 31.3357 + 54.2751i 1.17518 + 2.03548i
\(712\) −23.2049 + 19.4712i −0.869639 + 0.729714i
\(713\) 3.32501 + 18.8571i 0.124523 + 0.706202i
\(714\) 0 0
\(715\) 2.52007 + 4.36488i 0.0942452 + 0.163237i
\(716\) −1.99912 0.727621i −0.0747107 0.0271925i
\(717\) −1.17617 + 6.67042i −0.0439250 + 0.249111i
\(718\) −6.90143 + 5.79098i −0.257559 + 0.216118i
\(719\) −7.36190 + 41.7514i −0.274553 + 1.55706i 0.465827 + 0.884876i \(0.345757\pi\)
−0.740379 + 0.672189i \(0.765354\pi\)
\(720\) −2.90554 + 16.4782i −0.108283 + 0.614105i
\(721\) 0 0
\(722\) 4.07351 + 25.2724i 0.151600 + 0.940543i
\(723\) 19.8687 + 34.4136i 0.738925 + 1.27986i
\(724\) −1.20851 1.01406i −0.0449140 0.0376873i
\(725\) −27.3234 + 9.94491i −1.01477 + 0.369345i
\(726\) −4.07011 23.0827i −0.151056 0.856680i
\(727\) −48.5411 + 17.6675i −1.80029 + 0.655251i −0.801965 + 0.597371i \(0.796212\pi\)
−0.998324 + 0.0578805i \(0.981566\pi\)
\(728\) 0 0
\(729\) 20.2344 + 35.0470i 0.749423 + 1.29804i
\(730\) −1.64590 −0.0609174
\(731\) −1.71554 0.624404i −0.0634514 0.0230944i
\(732\) −4.56418 1.66122i −0.168697 0.0614006i
\(733\) −22.9162 −0.846430 −0.423215 0.906029i \(-0.639098\pi\)
−0.423215 + 0.906029i \(0.639098\pi\)
\(734\) 5.46926 + 9.47303i 0.201874 + 0.349656i
\(735\) 0 0
\(736\) −2.63816 + 0.960210i −0.0972437 + 0.0353938i
\(737\) −2.96761 16.8301i −0.109313 0.619946i
\(738\) 16.5831 6.03574i 0.610431 0.222179i
\(739\) 21.5462 + 18.0794i 0.792591 + 0.665063i 0.946385 0.323040i \(-0.104705\pi\)
−0.153794 + 0.988103i \(0.549149\pi\)
\(740\) 0.401674 + 0.695720i 0.0147658 + 0.0255752i
\(741\) 31.8555 5.37549i 1.17024 0.197474i
\(742\) 0 0
\(743\) 1.06489 6.03931i 0.0390671 0.221561i −0.959024 0.283326i \(-0.908562\pi\)
0.998091 + 0.0617657i \(0.0196731\pi\)
\(744\) 10.4586 59.3135i 0.383430 2.17454i
\(745\) 11.1552 9.36035i 0.408696 0.342937i
\(746\) −8.16448 + 46.3030i −0.298923 + 1.69528i
\(747\) 73.7349 + 26.8373i 2.69782 + 0.981926i
\(748\) −0.0962667 0.166739i −0.00351986 0.00609657i
\(749\) 0 0
\(750\) −5.46585 30.9984i −0.199585 1.13190i
\(751\) 4.32114 3.62586i 0.157681 0.132310i −0.560534 0.828131i \(-0.689404\pi\)
0.718215 + 0.695822i \(0.244960\pi\)
\(752\) −13.1099 22.7071i −0.478070 0.828042i
\(753\) 11.9932 0.437056
\(754\) −22.4183 8.15961i −0.816428 0.297155i
\(755\) 3.60442 1.31190i 0.131178 0.0477450i
\(756\) 0 0
\(757\) 12.0207 + 10.0866i 0.436900 + 0.366602i 0.834548 0.550936i \(-0.185729\pi\)
−0.397648 + 0.917538i \(0.630173\pi\)
\(758\) 2.15405 0.784009i 0.0782385 0.0284765i
\(759\) 8.63816 14.9617i 0.313545 0.543076i
\(760\) −9.72967 5.71334i −0.352932 0.207245i
\(761\) −2.43242 4.21307i −0.0881751 0.152724i 0.818565 0.574414i \(-0.194770\pi\)
−0.906740 + 0.421691i \(0.861437\pi\)
\(762\) 7.81702 44.3325i 0.283181 1.60600i
\(763\) 0 0
\(764\) 3.18392 + 1.15885i 0.115190 + 0.0419257i
\(765\) 1.66772 + 1.39938i 0.0602965 + 0.0505948i
\(766\) −0.687070 3.89657i −0.0248249 0.140789i
\(767\) −16.2300 −0.586031
\(768\) 12.6578 0.456747
\(769\) 3.91266 + 22.1898i 0.141094 + 0.800184i 0.970421 + 0.241420i \(0.0776131\pi\)
−0.829327 + 0.558764i \(0.811276\pi\)
\(770\) 0 0
\(771\) 0.960637 1.66387i 0.0345965 0.0599229i
\(772\) 0.0275033 0.0476371i 0.000989864 0.00171450i
\(773\) −4.58987 26.0304i −0.165086 0.936250i −0.948976 0.315350i \(-0.897878\pi\)
0.783889 0.620900i \(-0.213233\pi\)
\(774\) −4.82959 + 27.3900i −0.173596 + 0.984513i
\(775\) 5.21554 + 29.5788i 0.187348 + 1.06250i
\(776\) 21.3164 + 17.8866i 0.765214 + 0.642091i
\(777\) 0 0
\(778\) 33.0993 1.18667
\(779\) −0.0794409 + 10.7908i −0.00284627 + 0.386621i
\(780\) −0.602196 + 1.04303i −0.0215621 + 0.0373466i
\(781\) 15.8726 + 13.3187i 0.567965 + 0.476580i
\(782\) 0.294978 1.67290i 0.0105484 0.0598229i
\(783\) −42.6416 15.5203i −1.52389 0.554650i
\(784\) 0 0
\(785\) −6.47952 + 5.43696i −0.231264 + 0.194054i
\(786\) −3.57919 + 6.19934i −0.127666 + 0.221123i
\(787\) 7.77884 + 13.4733i 0.277286 + 0.480273i 0.970709 0.240257i \(-0.0772318\pi\)
−0.693424 + 0.720530i \(0.743899\pi\)
\(788\) 2.28194 + 0.830557i 0.0812906 + 0.0295874i
\(789\) −25.1446 + 21.0988i −0.895170 + 0.751137i
\(790\) −7.01707 + 12.1539i −0.249656 + 0.432417i
\(791\) 0 0
\(792\) −26.5651 + 22.2908i −0.943950 + 0.792068i
\(793\) 17.9991 + 15.1031i 0.639168 + 0.536325i
\(794\) 32.8573 27.5706i 1.16606 0.978443i
\(795\) −6.75150 + 2.45734i −0.239451 + 0.0871530i
\(796\) −0.0445774 + 0.0162249i −0.00158000 + 0.000575075i
\(797\) 33.4935 1.18640 0.593200 0.805055i \(-0.297864\pi\)
0.593200 + 0.805055i \(0.297864\pi\)
\(798\) 0 0
\(799\) −3.41147 −0.120689
\(800\) −4.13816 + 1.50617i −0.146306 + 0.0532510i
\(801\) 51.1639 18.6221i 1.80779 0.657981i
\(802\) 0.0892411 0.0748822i 0.00315121 0.00264418i
\(803\) −2.36959 1.98832i −0.0836208 0.0701662i
\(804\) 3.12836 2.62500i 0.110329 0.0925767i
\(805\) 0 0
\(806\) −12.3216 + 21.3416i −0.434010 + 0.751727i
\(807\) −42.7695 + 35.8879i −1.50556 + 1.26331i
\(808\) 25.5831 + 9.31147i 0.900009 + 0.327576i
\(809\) −20.5581 35.6076i −0.722784 1.25190i −0.959880 0.280412i \(-0.909529\pi\)
0.237096 0.971486i \(-0.423804\pi\)
\(810\) 1.84864 3.20194i 0.0649546 0.112505i
\(811\) 12.7836 10.7267i 0.448892 0.376665i −0.390132 0.920759i \(-0.627571\pi\)
0.839025 + 0.544093i \(0.183126\pi\)
\(812\) 0 0
\(813\) −36.2413 13.1907i −1.27104 0.462620i
\(814\) 2.57532 14.6054i 0.0902650 0.511918i
\(815\) 5.62836 + 4.72275i 0.197153 + 0.165431i
\(816\) −2.42262 + 4.19610i −0.0848086 + 0.146893i
\(817\) −14.6655 8.61170i −0.513081 0.301285i
\(818\) −26.9540 −0.942424
\(819\) 0 0
\(820\) −0.308182 0.258595i −0.0107622 0.00903054i
\(821\) −5.45084 30.9132i −0.190236 1.07888i −0.919042 0.394160i \(-0.871036\pi\)
0.728807 0.684720i \(-0.240075\pi\)
\(822\) 0.172304 0.977185i 0.00600979 0.0340832i
\(823\) 8.04442 + 45.6221i 0.280411 + 1.59029i 0.721232 + 0.692693i \(0.243576\pi\)
−0.440822 + 0.897595i \(0.645313\pi\)
\(824\) 8.10922 14.0456i 0.282498 0.489301i
\(825\) 13.5496 23.4686i 0.471738 0.817073i
\(826\) 0 0
\(827\) 7.07769 + 40.1396i 0.246115 + 1.39579i 0.817888 + 0.575377i \(0.195145\pi\)
−0.571773 + 0.820412i \(0.693744\pi\)
\(828\) 2.63453 0.0915564
\(829\) −35.4834 −1.23239 −0.616195 0.787594i \(-0.711327\pi\)
−0.616195 + 0.787594i \(0.711327\pi\)
\(830\) 3.05122 + 17.3043i 0.105909 + 0.600642i
\(831\) −39.1450 32.8466i −1.35793 1.13943i
\(832\) −20.7922 7.56774i −0.720840 0.262364i
\(833\) 0 0
\(834\) 2.87211 16.2886i 0.0994531 0.564026i
\(835\) −1.77420 3.07300i −0.0613986 0.106345i
\(836\) −0.601014 1.68988i −0.0207865 0.0584457i
\(837\) −23.4368 + 40.5937i −0.810093 + 1.40312i
\(838\) 32.1698 11.7089i 1.11129 0.404476i
\(839\) −29.2649 24.5562i −1.01034 0.847774i −0.0219545 0.999759i \(-0.506989\pi\)
−0.988383 + 0.151985i \(0.951433\pi\)
\(840\) 0 0
\(841\) −17.2208 + 6.26784i −0.593819 + 0.216132i
\(842\) 5.53209 + 2.01352i 0.190648 + 0.0693903i
\(843\) −52.6323 −1.81275
\(844\) 0.226215 + 0.391815i 0.00778663 + 0.0134868i
\(845\) −4.29426 + 3.60331i −0.147727 + 0.123958i
\(846\) 9.02481 + 51.1823i 0.310280 + 1.75968i
\(847\) 0 0
\(848\) −5.10220 8.83726i −0.175210 0.303473i
\(849\) 20.8011 + 7.57099i 0.713893 + 0.259836i
\(850\) 0.462697 2.62408i 0.0158704 0.0900053i
\(851\) −10.2044 + 8.56250i −0.349802 + 0.293519i
\(852\) −0.859785 + 4.87608i −0.0294557 + 0.167052i
\(853\) −4.44568 + 25.2127i −0.152217 + 0.863266i 0.809069 + 0.587714i \(0.199972\pi\)
−0.961286 + 0.275552i \(0.911139\pi\)
\(854\) 0 0
\(855\) 12.9214 + 15.6314i 0.441904 + 0.534584i
\(856\) −15.0628 26.0896i −0.514837 0.891724i
\(857\) −16.1532 13.5541i −0.551782 0.463000i 0.323762 0.946139i \(-0.395052\pi\)
−0.875544 + 0.483139i \(0.839497\pi\)
\(858\) 20.8935 7.60462i 0.713293 0.259617i
\(859\) −3.39780 19.2699i −0.115932 0.657481i −0.986285 0.165053i \(-0.947221\pi\)
0.870353 0.492428i \(-0.163890\pi\)
\(860\) 0.595800 0.216853i 0.0203166 0.00739464i
\(861\) 0 0
\(862\) −25.8050 44.6956i −0.878922 1.52234i
\(863\) 4.94894 0.168464 0.0842319 0.996446i \(-0.473156\pi\)
0.0842319 + 0.996446i \(0.473156\pi\)
\(864\) −6.45811 2.35056i −0.219709 0.0799677i
\(865\) 16.6459 + 6.05861i 0.565977 + 0.205999i
\(866\) 24.4279 0.830093
\(867\) −24.1596 41.8456i −0.820502 1.42115i
\(868\) 0 0
\(869\) −24.7849 + 9.02098i −0.840771 + 0.306016i
\(870\) −4.07532 23.1123i −0.138166 0.783580i
\(871\) −18.5639 + 6.75670i −0.629013 + 0.228942i
\(872\) −4.11057 3.44917i −0.139201 0.116804i
\(873\) −25.0082 43.3155i −0.846400 1.46601i
\(874\) 5.52166 14.8300i 0.186773 0.501633i
\(875\) 0 0
\(876\) 0.128356 0.727940i 0.00433673 0.0245948i
\(877\) 0.211829 1.20134i 0.00715296 0.0405664i −0.981022 0.193895i \(-0.937888\pi\)
0.988175 + 0.153328i \(0.0489991\pi\)
\(878\) 6.28603 5.27460i 0.212143 0.178009i
\(879\) 5.25150 29.7827i 0.177129 1.00455i
\(880\) −6.61721 2.40847i −0.223066 0.0811894i
\(881\) −23.2515 40.2728i −0.783363 1.35682i −0.929972 0.367630i \(-0.880169\pi\)
0.146609 0.989194i \(-0.453164\pi\)
\(882\) 0 0
\(883\) 2.24438 + 12.7285i 0.0755296 + 0.428349i 0.999001 + 0.0446828i \(0.0142277\pi\)
−0.923472 + 0.383667i \(0.874661\pi\)
\(884\) −0.170493 + 0.143061i −0.00573430 + 0.00481165i
\(885\) −7.98293 13.8268i −0.268343 0.464784i
\(886\) 40.2749 1.35306
\(887\) 21.8237 + 7.94318i 0.732769 + 0.266706i 0.681336 0.731970i \(-0.261399\pi\)
0.0514324 + 0.998676i \(0.483621\pi\)
\(888\) 39.3730 14.3306i 1.32127 0.480904i
\(889\) 0 0
\(890\) 9.34002 + 7.83721i 0.313078 + 0.262704i
\(891\) 6.52956 2.37657i 0.218749 0.0796180i
\(892\) −0.786274 + 1.36187i −0.0263264 + 0.0455986i
\(893\) −31.2558 5.74881i −1.04594 0.192377i
\(894\) −32.1202 55.6338i −1.07426 1.86067i
\(895\) −1.75800 + 9.97011i −0.0587634 + 0.333264i
\(896\) 0 0
\(897\) −18.7665 6.83045i −0.626596 0.228062i
\(898\) 11.6109 + 9.74270i 0.387461 + 0.325118i
\(899\) 8.48886 + 48.1427i 0.283119 + 1.60565i
\(900\) 4.13247 0.137749
\(901\) −1.32770 −0.0442320
\(902\) 1.28968 + 7.31412i 0.0429416 + 0.243534i
\(903\) 0 0
\(904\) 26.0326 45.0897i 0.865830 1.49966i
\(905\) −3.75372 + 6.50163i −0.124778 + 0.216122i
\(906\) −2.93835 16.6642i −0.0976201 0.553631i
\(907\) −6.94537 + 39.3892i −0.230617 + 1.30790i 0.621032 + 0.783785i \(0.286713\pi\)
−0.851650 + 0.524111i \(0.824398\pi\)
\(908\) 0.454078 + 2.57521i 0.0150691 + 0.0854612i
\(909\) −37.4864 31.4548i −1.24334 1.04329i
\(910\) 0 0
\(911\) −18.7997 −0.622863 −0.311431 0.950269i \(-0.600808\pi\)
−0.311431 + 0.950269i \(0.600808\pi\)
\(912\) −29.2670 + 34.3621i −0.969126 + 1.13784i
\(913\) −16.5116 + 28.5989i −0.546455 + 0.946487i
\(914\) 24.1407 + 20.2564i 0.798503 + 0.670023i
\(915\) −4.01367 + 22.7627i −0.132688 + 0.752510i
\(916\) −3.56552 1.29774i −0.117808 0.0428787i
\(917\) 0 0
\(918\) 3.18551 2.67296i 0.105137 0.0882208i
\(919\) −19.9158 + 34.4952i −0.656962 + 1.13789i 0.324436 + 0.945908i \(0.394825\pi\)
−0.981398 + 0.191984i \(0.938508\pi\)
\(920\) 3.48751 + 6.04055i 0.114980 + 0.199151i
\(921\) −31.6450 11.5178i −1.04274 0.379526i
\(922\) 37.7988 31.7170i 1.24484 1.04454i
\(923\) 11.9760 20.7430i 0.394193 0.682763i
\(924\) 0 0
\(925\) −16.0064 + 13.4310i −0.526287 + 0.441607i
\(926\) 44.3658 + 37.2273i 1.45795 + 1.22337i
\(927\) −22.3314 + 18.7383i −0.733460 + 0.615446i
\(928\) −6.73530 + 2.45145i −0.221097 + 0.0804727i
\(929\) −25.3285 + 9.21881i −0.831000 + 0.302459i −0.722269 0.691612i \(-0.756901\pi\)
−0.108731 + 0.994071i \(0.534679\pi\)
\(930\) −24.2422 −0.794932
\(931\) 0 0
\(932\) −3.26176 −0.106843
\(933\) 43.1994 15.7233i 1.41428 0.514758i
\(934\) 32.4060 11.7948i 1.06036 0.385938i
\(935\) −0.701867 + 0.588936i −0.0229535 + 0.0192603i
\(936\) 30.7085 + 25.7675i 1.00374 + 0.842236i
\(937\) 2.00980 1.68642i 0.0656573 0.0550930i −0.609368 0.792887i \(-0.708577\pi\)
0.675026 + 0.737794i \(0.264133\pi\)
\(938\) 0 0
\(939\) −38.3371 + 66.4018i −1.25108 + 2.16694i
\(940\) 0.907604 0.761570i 0.0296028 0.0248397i
\(941\) 17.5437 + 6.38538i 0.571908 + 0.208158i 0.611754 0.791048i \(-0.290464\pi\)
−0.0398455 + 0.999206i \(0.512687\pi\)
\(942\) 18.6570 + 32.3149i 0.607879 + 1.05288i
\(943\) 3.33544 5.77715i 0.108617 0.188130i
\(944\) 17.3708 14.5758i 0.565370 0.474402i
\(945\) 0 0
\(946\) −10.9991 4.00335i −0.357612 0.130160i
\(947\) 1.45858 8.27201i 0.0473974 0.268804i −0.951895 0.306425i \(-0.900867\pi\)
0.999292 + 0.0376214i \(0.0119781\pi\)
\(948\) −4.82816 4.05131i −0.156811 0.131580i
\(949\) −1.78787 + 3.09668i −0.0580366 + 0.100522i
\(950\) 8.66116 23.2621i 0.281005 0.754721i
\(951\) −85.0343 −2.75742
\(952\) 0 0
\(953\) 25.8102 + 21.6573i 0.836075 + 0.701550i 0.956677 0.291151i \(-0.0940382\pi\)
−0.120602 + 0.992701i \(0.538483\pi\)
\(954\) 3.51233 + 19.9194i 0.113716 + 0.644914i
\(955\) 2.79989 15.8790i 0.0906022 0.513831i
\(956\) −0.0754843 0.428092i −0.00244134 0.0138455i
\(957\) 22.0535 38.1978i 0.712888 1.23476i
\(958\) 25.7173 44.5438i 0.830890 1.43914i
\(959\) 0 0
\(960\) −3.77972 21.4358i −0.121990 0.691838i
\(961\) 19.4962 0.628909
\(962\) −17.1438 −0.552739
\(963\) 9.40286 + 53.3262i 0.303003 + 1.71841i
\(964\) −1.95361 1.63927i −0.0629216 0.0527975i
\(965\) −0.245977 0.0895284i −0.00791829 0.00288202i
\(966\) 0 0
\(967\) 2.03920 11.5649i 0.0655763 0.371902i −0.934305 0.356475i \(-0.883978\pi\)
0.999881 0.0154262i \(-0.00491051\pi\)
\(968\) 8.89234 + 15.4020i 0.285811 + 0.495039i
\(969\) 1.96791 + 5.53320i 0.0632184 + 0.177752i
\(970\) 5.60014 9.69972i 0.179810 0.311439i
\(971\) −12.0368 + 4.38105i −0.386280 + 0.140595i −0.527858 0.849333i \(-0.677005\pi\)
0.141578 + 0.989927i \(0.454783\pi\)
\(972\) −1.52931 1.28325i −0.0490528 0.0411602i
\(973\) 0 0
\(974\) 9.82934 3.57759i 0.314953 0.114633i
\(975\) −29.4368 10.7141i −0.942731 0.343126i
\(976\) −32.8280 −1.05080
\(977\) −7.26382 12.5813i −0.232390 0.402512i 0.726121 0.687567i \(-0.241321\pi\)
−0.958511 + 0.285055i \(0.907988\pi\)
\(978\) 24.8293 20.8343i 0.793955 0.666207i
\(979\) 3.97906 + 22.5663i 0.127171 + 0.721224i
\(980\) 0 0
\(981\) 4.82248 + 8.35278i 0.153970 + 0.266684i
\(982\) −46.4928 16.9220i −1.48364 0.540002i
\(983\) −6.43371 + 36.4874i −0.205203 + 1.16377i 0.691916 + 0.721978i \(0.256767\pi\)
−0.897119 + 0.441788i \(0.854344\pi\)
\(984\) −16.0737 + 13.4875i −0.512412 + 0.429965i
\(985\) 2.00670 11.3806i 0.0639388 0.362615i
\(986\) 0.753089 4.27098i 0.0239832 0.136016i
\(987\) 0 0
\(988\) −1.80313 + 1.02341i −0.0573652 + 0.0325591i
\(989\) 5.25671 + 9.10489i 0.167154 + 0.289519i
\(990\) 10.6925 + 8.97210i 0.339831 + 0.285152i
\(991\) −3.22446 + 1.17361i −0.102428 + 0.0372809i −0.392726 0.919656i \(-0.628468\pi\)
0.290298 + 0.956936i \(0.406246\pi\)
\(992\) 1.28564 + 7.29125i 0.0408193 + 0.231498i
\(993\) 74.8556 27.2452i 2.37547 0.864600i
\(994\) 0 0
\(995\) 0.112874 + 0.195503i 0.00357835 + 0.00619788i
\(996\) −7.89124 −0.250044
\(997\) −12.0055 4.36965i −0.380219 0.138388i 0.144838 0.989455i \(-0.453734\pi\)
−0.525057 + 0.851067i \(0.675956\pi\)
\(998\) 6.23695 + 2.27006i 0.197427 + 0.0718576i
\(999\) −32.6091 −1.03170
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 931.2.v.b.606.1 6
7.2 even 3 931.2.x.a.226.1 6
7.3 odd 6 931.2.w.a.834.1 6
7.4 even 3 19.2.e.a.17.1 yes 6
7.5 odd 6 931.2.x.b.226.1 6
7.6 odd 2 931.2.v.a.606.1 6
19.9 even 9 931.2.x.a.655.1 6
21.11 odd 6 171.2.u.c.55.1 6
28.11 odd 6 304.2.u.b.17.1 6
35.4 even 6 475.2.l.a.226.1 6
35.18 odd 12 475.2.u.a.74.2 12
35.32 odd 12 475.2.u.a.74.1 12
133.4 even 9 361.2.e.g.234.1 6
133.9 even 9 inner 931.2.v.b.275.1 6
133.11 even 3 361.2.e.f.62.1 6
133.18 odd 6 361.2.e.h.245.1 6
133.25 even 9 361.2.e.f.99.1 6
133.32 odd 18 361.2.e.b.99.1 6
133.46 odd 6 361.2.e.b.62.1 6
133.47 odd 18 931.2.v.a.275.1 6
133.53 odd 18 361.2.e.a.234.1 6
133.60 odd 18 361.2.a.h.1.2 3
133.66 odd 18 931.2.w.a.883.1 6
133.67 odd 18 361.2.e.h.28.1 6
133.74 even 9 361.2.c.i.68.2 6
133.81 even 9 361.2.c.i.292.2 6
133.88 odd 6 361.2.e.a.54.1 6
133.102 even 3 361.2.e.g.54.1 6
133.104 odd 18 931.2.x.b.655.1 6
133.109 odd 18 361.2.c.h.292.2 6
133.116 odd 18 361.2.c.h.68.2 6
133.123 even 9 19.2.e.a.9.1 6
133.130 even 9 361.2.a.g.1.2 3
399.263 odd 18 3249.2.a.z.1.2 3
399.326 even 18 3249.2.a.s.1.2 3
399.389 odd 18 171.2.u.c.28.1 6
532.123 odd 18 304.2.u.b.161.1 6
532.263 odd 18 5776.2.a.br.1.3 3
532.459 even 18 5776.2.a.bi.1.1 3
665.123 odd 36 475.2.u.a.199.1 12
665.389 even 18 475.2.l.a.351.1 6
665.459 odd 18 9025.2.a.x.1.2 3
665.522 odd 36 475.2.u.a.199.2 12
665.529 even 18 9025.2.a.bd.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.2.e.a.9.1 6 133.123 even 9
19.2.e.a.17.1 yes 6 7.4 even 3
171.2.u.c.28.1 6 399.389 odd 18
171.2.u.c.55.1 6 21.11 odd 6
304.2.u.b.17.1 6 28.11 odd 6
304.2.u.b.161.1 6 532.123 odd 18
361.2.a.g.1.2 3 133.130 even 9
361.2.a.h.1.2 3 133.60 odd 18
361.2.c.h.68.2 6 133.116 odd 18
361.2.c.h.292.2 6 133.109 odd 18
361.2.c.i.68.2 6 133.74 even 9
361.2.c.i.292.2 6 133.81 even 9
361.2.e.a.54.1 6 133.88 odd 6
361.2.e.a.234.1 6 133.53 odd 18
361.2.e.b.62.1 6 133.46 odd 6
361.2.e.b.99.1 6 133.32 odd 18
361.2.e.f.62.1 6 133.11 even 3
361.2.e.f.99.1 6 133.25 even 9
361.2.e.g.54.1 6 133.102 even 3
361.2.e.g.234.1 6 133.4 even 9
361.2.e.h.28.1 6 133.67 odd 18
361.2.e.h.245.1 6 133.18 odd 6
475.2.l.a.226.1 6 35.4 even 6
475.2.l.a.351.1 6 665.389 even 18
475.2.u.a.74.1 12 35.32 odd 12
475.2.u.a.74.2 12 35.18 odd 12
475.2.u.a.199.1 12 665.123 odd 36
475.2.u.a.199.2 12 665.522 odd 36
931.2.v.a.275.1 6 133.47 odd 18
931.2.v.a.606.1 6 7.6 odd 2
931.2.v.b.275.1 6 133.9 even 9 inner
931.2.v.b.606.1 6 1.1 even 1 trivial
931.2.w.a.834.1 6 7.3 odd 6
931.2.w.a.883.1 6 133.66 odd 18
931.2.x.a.226.1 6 7.2 even 3
931.2.x.a.655.1 6 19.9 even 9
931.2.x.b.226.1 6 7.5 odd 6
931.2.x.b.655.1 6 133.104 odd 18
3249.2.a.s.1.2 3 399.326 even 18
3249.2.a.z.1.2 3 399.263 odd 18
5776.2.a.bi.1.1 3 532.459 even 18
5776.2.a.br.1.3 3 532.263 odd 18
9025.2.a.x.1.2 3 665.459 odd 18
9025.2.a.bd.1.2 3 665.529 even 18