Properties

Label 1470.2.n.k.949.1
Level $1470$
Weight $2$
Character 1470.949
Analytic conductor $11.738$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(79,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
 
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("1470.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.n (of order \(6\), degree \(2\), 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: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 18x^{14} + 227x^{12} - 1394x^{10} + 6177x^{8} - 14768x^{6} + 24768x^{4} - 11264x^{2} + 4096 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 949.1
Root \(-1.87108 + 1.08027i\) of defining polynomial
Character \(\chi\) \(=\) 1470.949
Dual form 1470.2.n.k.79.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.97257 + 1.05307i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.97257 + 1.05307i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.18176 - 1.89827i) q^{10} +(1.52773 - 2.64610i) q^{11} +(-0.866025 + 0.500000i) q^{12} +1.64124i q^{13} +(2.23483 + 0.0743018i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.51741 - 1.45342i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(1.10508 + 1.91405i) q^{19} +(-0.0743018 + 2.23483i) q^{20} +3.05545i q^{22} +(1.55005 - 0.894921i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.78209 - 4.15451i) q^{25} +(-0.820620 - 1.42135i) q^{26} -1.00000i q^{27} -5.58667 q^{29} +(-1.97257 + 1.05307i) q^{30} +(-0.472274 + 0.818002i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.64610 + 1.52773i) q^{33} +2.90685 q^{34} +1.00000 q^{36} +(9.27713 - 5.35615i) q^{37} +(-1.91405 - 1.10508i) q^{38} +(0.820620 - 1.42135i) q^{39} +(-1.05307 - 1.97257i) q^{40} +6.67982 q^{41} +10.5021i q^{43} +(-1.52773 - 2.64610i) q^{44} +(-1.89827 - 1.18176i) q^{45} +(-0.894921 + 1.55005i) q^{46} +(-9.85235 + 5.68826i) q^{47} +1.00000i q^{48} +(-0.332104 + 4.98896i) q^{50} +(1.45342 + 2.51741i) q^{51} +(1.42135 + 0.820620i) q^{52} +(-5.01415 - 2.89492i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-0.227026 + 6.82843i) q^{55} -2.21016i q^{57} +(4.83820 - 2.79334i) q^{58} +(-2.98896 + 5.17703i) q^{59} +(1.18176 - 1.89827i) q^{60} +(-0.222905 - 0.386083i) q^{61} -0.944547i q^{62} -1.00000 q^{64} +(-1.72834 - 3.23746i) q^{65} +(1.52773 - 2.64610i) q^{66} +(1.09605 + 0.632805i) q^{67} +(-2.51741 + 1.45342i) q^{68} -1.78984 q^{69} -14.8523 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-6.85577 - 3.95818i) q^{73} +(-5.35615 + 9.27713i) q^{74} +(-4.48662 + 2.20687i) q^{75} +2.21016 q^{76} +1.64124i q^{78} +(7.14949 + 12.3833i) q^{79} +(1.89827 + 1.18176i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.78490 + 3.33991i) q^{82} +0.874366i q^{83} +(6.49632 + 0.215984i) q^{85} +(-5.25107 - 9.09513i) q^{86} +(4.83820 + 2.79334i) q^{87} +(2.64610 + 1.52773i) q^{88} +(8.75413 + 15.1626i) q^{89} +(2.23483 + 0.0743018i) q^{90} -1.78984i q^{92} +(0.818002 - 0.472274i) q^{93} +(5.68826 - 9.85235i) q^{94} +(-4.19548 - 2.61188i) q^{95} +(-0.500000 - 0.866025i) q^{96} +10.4476i q^{97} +3.05545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} - 4 q^{5} + 16 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 4 q^{5} + 16 q^{6} + 8 q^{9} - 8 q^{16} + 24 q^{19} - 8 q^{20} + 8 q^{24} - 4 q^{25} + 32 q^{29} - 4 q^{30} - 32 q^{31} - 16 q^{34} + 16 q^{36} + 48 q^{41} + 4 q^{45} - 8 q^{46} - 8 q^{50} - 8 q^{51} + 8 q^{54} + 40 q^{59} - 24 q^{61} - 16 q^{64} - 28 q^{65} - 16 q^{69} - 80 q^{71} - 16 q^{74} - 4 q^{75} + 48 q^{76} - 16 q^{79} - 4 q^{80} - 8 q^{81} + 56 q^{85} - 8 q^{86} + 88 q^{89} + 24 q^{94} - 24 q^{95} - 8 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −1.97257 + 1.05307i −0.882162 + 0.470947i
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 1.18176 1.89827i 0.373707 0.600286i
\(11\) 1.52773 2.64610i 0.460627 0.797829i −0.538365 0.842711i \(-0.680958\pi\)
0.998992 + 0.0448824i \(0.0142913\pi\)
\(12\) −0.866025 + 0.500000i −0.250000 + 0.144338i
\(13\) 1.64124i 0.455198i 0.973755 + 0.227599i \(0.0730875\pi\)
−0.973755 + 0.227599i \(0.926912\pi\)
\(14\) 0 0
\(15\) 2.23483 + 0.0743018i 0.577031 + 0.0191846i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.51741 1.45342i −0.610560 0.352507i 0.162624 0.986688i \(-0.448004\pi\)
−0.773185 + 0.634181i \(0.781337\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) 1.10508 + 1.91405i 0.253522 + 0.439114i 0.964493 0.264108i \(-0.0850775\pi\)
−0.710971 + 0.703222i \(0.751744\pi\)
\(20\) −0.0743018 + 2.23483i −0.0166144 + 0.499724i
\(21\) 0 0
\(22\) 3.05545i 0.651425i
\(23\) 1.55005 0.894921i 0.323208 0.186604i −0.329614 0.944116i \(-0.606919\pi\)
0.652821 + 0.757512i \(0.273585\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 2.78209 4.15451i 0.556418 0.830903i
\(26\) −0.820620 1.42135i −0.160937 0.278751i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −5.58667 −1.03742 −0.518710 0.854951i \(-0.673587\pi\)
−0.518710 + 0.854951i \(0.673587\pi\)
\(30\) −1.97257 + 1.05307i −0.360141 + 0.192263i
\(31\) −0.472274 + 0.818002i −0.0848228 + 0.146917i −0.905316 0.424739i \(-0.860366\pi\)
0.820493 + 0.571657i \(0.193699\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) −2.64610 + 1.52773i −0.460627 + 0.265943i
\(34\) 2.90685 0.498521
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 9.27713 5.35615i 1.52515 0.880546i 0.525595 0.850735i \(-0.323843\pi\)
0.999556 0.0298114i \(-0.00949068\pi\)
\(38\) −1.91405 1.10508i −0.310500 0.179267i
\(39\) 0.820620 1.42135i 0.131404 0.227599i
\(40\) −1.05307 1.97257i −0.166505 0.311891i
\(41\) 6.67982 1.04321 0.521607 0.853186i \(-0.325333\pi\)
0.521607 + 0.853186i \(0.325333\pi\)
\(42\) 0 0
\(43\) 10.5021i 1.60156i 0.598957 + 0.800781i \(0.295582\pi\)
−0.598957 + 0.800781i \(0.704418\pi\)
\(44\) −1.52773 2.64610i −0.230313 0.398915i
\(45\) −1.89827 1.18176i −0.282978 0.176167i
\(46\) −0.894921 + 1.55005i −0.131949 + 0.228542i
\(47\) −9.85235 + 5.68826i −1.43711 + 0.829718i −0.997648 0.0685421i \(-0.978165\pi\)
−0.439465 + 0.898260i \(0.644832\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) −0.332104 + 4.98896i −0.0469666 + 0.705545i
\(51\) 1.45342 + 2.51741i 0.203520 + 0.352507i
\(52\) 1.42135 + 0.820620i 0.197106 + 0.113799i
\(53\) −5.01415 2.89492i −0.688747 0.397648i 0.114396 0.993435i \(-0.463507\pi\)
−0.803142 + 0.595787i \(0.796840\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −0.227026 + 6.82843i −0.0306121 + 0.920745i
\(56\) 0 0
\(57\) 2.21016i 0.292742i
\(58\) 4.83820 2.79334i 0.635287 0.366783i
\(59\) −2.98896 + 5.17703i −0.389129 + 0.673992i −0.992333 0.123596i \(-0.960557\pi\)
0.603203 + 0.797587i \(0.293891\pi\)
\(60\) 1.18176 1.89827i 0.152565 0.245066i
\(61\) −0.222905 0.386083i −0.0285401 0.0494329i 0.851403 0.524513i \(-0.175752\pi\)
−0.879943 + 0.475080i \(0.842419\pi\)
\(62\) 0.944547i 0.119958i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −1.72834 3.23746i −0.214374 0.401558i
\(66\) 1.52773 2.64610i 0.188050 0.325712i
\(67\) 1.09605 + 0.632805i 0.133904 + 0.0773094i 0.565456 0.824779i \(-0.308700\pi\)
−0.431552 + 0.902088i \(0.642034\pi\)
\(68\) −2.51741 + 1.45342i −0.305280 + 0.176254i
\(69\) −1.78984 −0.215472
\(70\) 0 0
\(71\) −14.8523 −1.76264 −0.881321 0.472518i \(-0.843345\pi\)
−0.881321 + 0.472518i \(0.843345\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) −6.85577 3.95818i −0.802407 0.463270i 0.0419049 0.999122i \(-0.486657\pi\)
−0.844312 + 0.535851i \(0.819991\pi\)
\(74\) −5.35615 + 9.27713i −0.622640 + 1.07844i
\(75\) −4.48662 + 2.20687i −0.518070 + 0.254827i
\(76\) 2.21016 0.253522
\(77\) 0 0
\(78\) 1.64124i 0.185834i
\(79\) 7.14949 + 12.3833i 0.804380 + 1.39323i 0.916709 + 0.399557i \(0.130836\pi\)
−0.112328 + 0.993671i \(0.535831\pi\)
\(80\) 1.89827 + 1.18176i 0.212233 + 0.132125i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −5.78490 + 3.33991i −0.638835 + 0.368832i
\(83\) 0.874366i 0.0959741i 0.998848 + 0.0479871i \(0.0152806\pi\)
−0.998848 + 0.0479871i \(0.984719\pi\)
\(84\) 0 0
\(85\) 6.49632 + 0.215984i 0.704625 + 0.0234268i
\(86\) −5.25107 9.09513i −0.566238 0.980753i
\(87\) 4.83820 + 2.79334i 0.518710 + 0.299477i
\(88\) 2.64610 + 1.52773i 0.282075 + 0.162856i
\(89\) 8.75413 + 15.1626i 0.927935 + 1.60723i 0.786771 + 0.617245i \(0.211751\pi\)
0.141165 + 0.989986i \(0.454915\pi\)
\(90\) 2.23483 + 0.0743018i 0.235572 + 0.00783210i
\(91\) 0 0
\(92\) 1.78984i 0.186604i
\(93\) 0.818002 0.472274i 0.0848228 0.0489725i
\(94\) 5.68826 9.85235i 0.586699 1.01619i
\(95\) −4.19548 2.61188i −0.430447 0.267974i
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) 10.4476i 1.06079i 0.847750 + 0.530396i \(0.177957\pi\)
−0.847750 + 0.530396i \(0.822043\pi\)
\(98\) 0 0
\(99\) 3.05545 0.307085
\(100\) −2.20687 4.48662i −0.220687 0.448662i
\(101\) −7.72747 + 13.3844i −0.768912 + 1.33179i 0.169242 + 0.985575i \(0.445868\pi\)
−0.938153 + 0.346220i \(0.887465\pi\)
\(102\) −2.51741 1.45342i −0.249260 0.143910i
\(103\) 2.70688 1.56282i 0.266717 0.153989i −0.360678 0.932690i \(-0.617455\pi\)
0.627395 + 0.778701i \(0.284121\pi\)
\(104\) −1.64124 −0.160937
\(105\) 0 0
\(106\) 5.78984 0.562359
\(107\) 4.14176 2.39124i 0.400399 0.231170i −0.286257 0.958153i \(-0.592411\pi\)
0.686656 + 0.726982i \(0.259078\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) −4.55178 + 7.88391i −0.435981 + 0.755141i −0.997375 0.0724073i \(-0.976932\pi\)
0.561394 + 0.827549i \(0.310265\pi\)
\(110\) −3.21760 6.02710i −0.306786 0.574662i
\(111\) −10.7123 −1.01677
\(112\) 0 0
\(113\) 14.3982i 1.35447i 0.735766 + 0.677236i \(0.236822\pi\)
−0.735766 + 0.677236i \(0.763178\pi\)
\(114\) 1.10508 + 1.91405i 0.103500 + 0.179267i
\(115\) −2.11517 + 3.39761i −0.197241 + 0.316829i
\(116\) −2.79334 + 4.83820i −0.259355 + 0.449216i
\(117\) −1.42135 + 0.820620i −0.131404 + 0.0758663i
\(118\) 5.97792i 0.550312i
\(119\) 0 0
\(120\) −0.0743018 + 2.23483i −0.00678279 + 0.204011i
\(121\) 0.832104 + 1.44125i 0.0756458 + 0.131022i
\(122\) 0.386083 + 0.222905i 0.0349544 + 0.0201809i
\(123\) −5.78490 3.33991i −0.521607 0.301150i
\(124\) 0.472274 + 0.818002i 0.0424114 + 0.0734587i
\(125\) −1.11289 + 11.1248i −0.0995396 + 0.995034i
\(126\) 0 0
\(127\) 8.45405i 0.750176i 0.926989 + 0.375088i \(0.122387\pi\)
−0.926989 + 0.375088i \(0.877613\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 5.25107 9.09513i 0.462331 0.800781i
\(130\) 3.11552 + 1.93956i 0.273249 + 0.170110i
\(131\) −4.16053 7.20625i −0.363507 0.629613i 0.625028 0.780602i \(-0.285087\pi\)
−0.988535 + 0.150989i \(0.951754\pi\)
\(132\) 3.05545i 0.265943i
\(133\) 0 0
\(134\) −1.26561 −0.109332
\(135\) 1.05307 + 1.97257i 0.0906338 + 0.169772i
\(136\) 1.45342 2.51741i 0.124630 0.215866i
\(137\) 8.54508 + 4.93351i 0.730056 + 0.421498i 0.818443 0.574588i \(-0.194838\pi\)
−0.0883869 + 0.996086i \(0.528171\pi\)
\(138\) 1.55005 0.894921i 0.131949 0.0761808i
\(139\) −16.9632 −1.43880 −0.719399 0.694597i \(-0.755583\pi\)
−0.719399 + 0.694597i \(0.755583\pi\)
\(140\) 0 0
\(141\) 11.3765 0.958075
\(142\) 12.8625 7.42614i 1.07939 0.623188i
\(143\) 4.34288 + 2.50736i 0.363170 + 0.209676i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 11.0201 5.88315i 0.915171 0.488569i
\(146\) 7.91636 0.655163
\(147\) 0 0
\(148\) 10.7123i 0.880546i
\(149\) 4.02405 + 6.96986i 0.329663 + 0.570993i 0.982445 0.186553i \(-0.0597316\pi\)
−0.652782 + 0.757546i \(0.726398\pi\)
\(150\) 2.78209 4.15451i 0.227157 0.339215i
\(151\) 4.98896 8.64113i 0.405996 0.703205i −0.588441 0.808540i \(-0.700258\pi\)
0.994437 + 0.105335i \(0.0335915\pi\)
\(152\) −1.91405 + 1.10508i −0.155250 + 0.0896337i
\(153\) 2.90685i 0.235005i
\(154\) 0 0
\(155\) 0.0701816 2.11091i 0.00563712 0.169552i
\(156\) −0.820620 1.42135i −0.0657022 0.113799i
\(157\) −10.9705 6.33381i −0.875540 0.505493i −0.00635459 0.999980i \(-0.502023\pi\)
−0.869185 + 0.494487i \(0.835356\pi\)
\(158\) −12.3833 7.14949i −0.985161 0.568783i
\(159\) 2.89492 + 5.01415i 0.229582 + 0.397648i
\(160\) −2.23483 0.0743018i −0.176679 0.00587407i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) −20.4075 + 11.7823i −1.59844 + 0.922861i −0.606654 + 0.794966i \(0.707488\pi\)
−0.991788 + 0.127894i \(0.959178\pi\)
\(164\) 3.33991 5.78490i 0.260803 0.451725i
\(165\) 3.61082 5.80008i 0.281102 0.451536i
\(166\) −0.437183 0.757223i −0.0339320 0.0587719i
\(167\) 18.0818i 1.39921i −0.714528 0.699607i \(-0.753358\pi\)
0.714528 0.699607i \(-0.246642\pi\)
\(168\) 0 0
\(169\) 10.3063 0.792795
\(170\) −5.73397 + 3.06111i −0.439776 + 0.234777i
\(171\) −1.10508 + 1.91405i −0.0845075 + 0.146371i
\(172\) 9.09513 + 5.25107i 0.693497 + 0.400391i
\(173\) −1.67874 + 0.969223i −0.127633 + 0.0736887i −0.562457 0.826827i \(-0.690144\pi\)
0.434824 + 0.900515i \(0.356810\pi\)
\(174\) −5.58667 −0.423525
\(175\) 0 0
\(176\) −3.05545 −0.230313
\(177\) 5.17703 2.98896i 0.389129 0.224664i
\(178\) −15.1626 8.75413i −1.13648 0.656149i
\(179\) −12.2232 + 21.1711i −0.913602 + 1.58241i −0.104667 + 0.994507i \(0.533378\pi\)
−0.808935 + 0.587898i \(0.799956\pi\)
\(180\) −1.97257 + 1.05307i −0.147027 + 0.0784912i
\(181\) −16.9788 −1.26202 −0.631012 0.775773i \(-0.717360\pi\)
−0.631012 + 0.775773i \(0.717360\pi\)
\(182\) 0 0
\(183\) 0.445811i 0.0329553i
\(184\) 0.894921 + 1.55005i 0.0659745 + 0.114271i
\(185\) −12.6594 + 20.3349i −0.930739 + 1.49505i
\(186\) −0.472274 + 0.818002i −0.0346288 + 0.0599788i
\(187\) −7.69181 + 4.44087i −0.562481 + 0.324749i
\(188\) 11.3765i 0.829718i
\(189\) 0 0
\(190\) 4.93933 + 0.164219i 0.358337 + 0.0119137i
\(191\) −0.370689 0.642051i −0.0268221 0.0464572i 0.852303 0.523049i \(-0.175205\pi\)
−0.879125 + 0.476592i \(0.841872\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) 5.29220 + 3.05545i 0.380941 + 0.219936i 0.678228 0.734852i \(-0.262748\pi\)
−0.297287 + 0.954788i \(0.596082\pi\)
\(194\) −5.22379 9.04787i −0.375046 0.649599i
\(195\) −0.121947 + 3.66790i −0.00873281 + 0.262663i
\(196\) 0 0
\(197\) 20.6832i 1.47362i −0.676100 0.736810i \(-0.736331\pi\)
0.676100 0.736810i \(-0.263669\pi\)
\(198\) −2.64610 + 1.52773i −0.188050 + 0.108571i
\(199\) 6.03509 10.4531i 0.427816 0.740999i −0.568863 0.822433i \(-0.692616\pi\)
0.996679 + 0.0814331i \(0.0259497\pi\)
\(200\) 4.15451 + 2.78209i 0.293768 + 0.196723i
\(201\) −0.632805 1.09605i −0.0446346 0.0773094i
\(202\) 15.4549i 1.08741i
\(203\) 0 0
\(204\) 2.90685 0.203520
\(205\) −13.1764 + 7.03432i −0.920283 + 0.491298i
\(206\) −1.56282 + 2.70688i −0.108887 + 0.188597i
\(207\) 1.55005 + 0.894921i 0.107736 + 0.0622013i
\(208\) 1.42135 0.820620i 0.0985532 0.0568997i
\(209\) 6.75303 0.467117
\(210\) 0 0
\(211\) 2.95153 0.203192 0.101596 0.994826i \(-0.467605\pi\)
0.101596 + 0.994826i \(0.467605\pi\)
\(212\) −5.01415 + 2.89492i −0.344373 + 0.198824i
\(213\) 12.8625 + 7.42614i 0.881321 + 0.508831i
\(214\) −2.39124 + 4.14176i −0.163462 + 0.283125i
\(215\) −11.0595 20.7163i −0.754251 1.41284i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 9.10355i 0.616570i
\(219\) 3.95818 + 6.85577i 0.267469 + 0.463270i
\(220\) 5.80008 + 3.61082i 0.391041 + 0.243442i
\(221\) 2.38542 4.13166i 0.160461 0.277926i
\(222\) 9.27713 5.35615i 0.622640 0.359481i
\(223\) 11.7678i 0.788027i −0.919105 0.394014i \(-0.871086\pi\)
0.919105 0.394014i \(-0.128914\pi\)
\(224\) 0 0
\(225\) 4.98896 + 0.332104i 0.332597 + 0.0221403i
\(226\) −7.19912 12.4692i −0.478878 0.829441i
\(227\) 11.4632 + 6.61827i 0.760838 + 0.439270i 0.829597 0.558363i \(-0.188570\pi\)
−0.0687586 + 0.997633i \(0.521904\pi\)
\(228\) −1.91405 1.10508i −0.126761 0.0731856i
\(229\) 12.6224 + 21.8626i 0.834111 + 1.44472i 0.894752 + 0.446563i \(0.147352\pi\)
−0.0606412 + 0.998160i \(0.519315\pi\)
\(230\) 0.132989 4.00000i 0.00876900 0.263752i
\(231\) 0 0
\(232\) 5.58667i 0.366783i
\(233\) 2.88249 1.66421i 0.188838 0.109026i −0.402600 0.915376i \(-0.631894\pi\)
0.591439 + 0.806350i \(0.298560\pi\)
\(234\) 0.820620 1.42135i 0.0536456 0.0929169i
\(235\) 13.4444 21.5957i 0.877013 1.40875i
\(236\) 2.98896 + 5.17703i 0.194565 + 0.336996i
\(237\) 14.2990i 0.928819i
\(238\) 0 0
\(239\) −24.8713 −1.60879 −0.804396 0.594094i \(-0.797511\pi\)
−0.804396 + 0.594094i \(0.797511\pi\)
\(240\) −1.05307 1.97257i −0.0679753 0.127329i
\(241\) −5.17677 + 8.96643i −0.333465 + 0.577579i −0.983189 0.182592i \(-0.941551\pi\)
0.649724 + 0.760171i \(0.274885\pi\)
\(242\) −1.44125 0.832104i −0.0926469 0.0534897i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −0.445811 −0.0285401
\(245\) 0 0
\(246\) 6.67982 0.425890
\(247\) −3.14142 + 1.81370i −0.199884 + 0.115403i
\(248\) −0.818002 0.472274i −0.0519432 0.0299894i
\(249\) 0.437183 0.757223i 0.0277053 0.0479871i
\(250\) −4.59862 10.1908i −0.290842 0.644524i
\(251\) 16.5502 1.04464 0.522321 0.852749i \(-0.325066\pi\)
0.522321 + 0.852749i \(0.325066\pi\)
\(252\) 0 0
\(253\) 5.46878i 0.343819i
\(254\) −4.22703 7.32142i −0.265227 0.459387i
\(255\) −5.51799 3.43521i −0.345550 0.215121i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 21.1783 12.2273i 1.32106 0.762717i 0.337166 0.941445i \(-0.390532\pi\)
0.983899 + 0.178728i \(0.0571982\pi\)
\(258\) 10.5021i 0.653835i
\(259\) 0 0
\(260\) −3.66790 0.121947i −0.227473 0.00756283i
\(261\) −2.79334 4.83820i −0.172903 0.299477i
\(262\) 7.20625 + 4.16053i 0.445204 + 0.257038i
\(263\) 10.8332 + 6.25457i 0.668006 + 0.385673i 0.795321 0.606189i \(-0.207303\pi\)
−0.127315 + 0.991862i \(0.540636\pi\)
\(264\) −1.52773 2.64610i −0.0940251 0.162856i
\(265\) 12.9393 + 0.430196i 0.794857 + 0.0264267i
\(266\) 0 0
\(267\) 17.5083i 1.07149i
\(268\) 1.09605 0.632805i 0.0669519 0.0386547i
\(269\) −9.48330 + 16.4256i −0.578207 + 1.00148i 0.417478 + 0.908687i \(0.362914\pi\)
−0.995685 + 0.0927970i \(0.970419\pi\)
\(270\) −1.89827 1.18176i −0.115525 0.0719199i
\(271\) −9.83192 17.0294i −0.597247 1.03446i −0.993226 0.116202i \(-0.962928\pi\)
0.395979 0.918260i \(-0.370405\pi\)
\(272\) 2.90685i 0.176254i
\(273\) 0 0
\(274\) −9.86701 −0.596088
\(275\) −6.74298 13.7086i −0.406617 0.826662i
\(276\) −0.894921 + 1.55005i −0.0538679 + 0.0933020i
\(277\) −5.31737 3.06999i −0.319490 0.184458i 0.331675 0.943394i \(-0.392386\pi\)
−0.651165 + 0.758936i \(0.725720\pi\)
\(278\) 14.6906 8.48159i 0.881081 0.508692i
\(279\) −0.944547 −0.0565486
\(280\) 0 0
\(281\) −12.1330 −0.723793 −0.361897 0.932218i \(-0.617871\pi\)
−0.361897 + 0.932218i \(0.617871\pi\)
\(282\) −9.85235 + 5.68826i −0.586699 + 0.338731i
\(283\) 15.0838 + 8.70862i 0.896637 + 0.517674i 0.876108 0.482116i \(-0.160131\pi\)
0.0205295 + 0.999789i \(0.493465\pi\)
\(284\) −7.42614 + 12.8625i −0.440660 + 0.763246i
\(285\) 2.32745 + 4.35970i 0.137866 + 0.258246i
\(286\) −5.01473 −0.296527
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −4.27511 7.40471i −0.251477 0.435571i
\(290\) −6.60213 + 10.6050i −0.387690 + 0.622748i
\(291\) 5.22379 9.04787i 0.306224 0.530396i
\(292\) −6.85577 + 3.95818i −0.401204 + 0.231635i
\(293\) 23.7521i 1.38762i −0.720160 0.693808i \(-0.755932\pi\)
0.720160 0.693808i \(-0.244068\pi\)
\(294\) 0 0
\(295\) 0.444170 13.3596i 0.0258606 0.777829i
\(296\) 5.35615 + 9.27713i 0.311320 + 0.539222i
\(297\) −2.64610 1.52773i −0.153542 0.0886477i
\(298\) −6.96986 4.02405i −0.403753 0.233107i
\(299\) 1.46878 + 2.54400i 0.0849417 + 0.147123i
\(300\) −0.332104 + 4.98896i −0.0191740 + 0.288038i
\(301\) 0 0
\(302\) 9.97792i 0.574165i
\(303\) 13.3844 7.72747i 0.768912 0.443931i
\(304\) 1.10508 1.91405i 0.0633806 0.109778i
\(305\) 0.846270 + 0.526843i 0.0484573 + 0.0301669i
\(306\) 1.45342 + 2.51741i 0.0830868 + 0.143910i
\(307\) 7.90812i 0.451340i 0.974204 + 0.225670i \(0.0724572\pi\)
−0.974204 + 0.225670i \(0.927543\pi\)
\(308\) 0 0
\(309\) −3.12563 −0.177811
\(310\) 0.994674 + 1.86319i 0.0564937 + 0.105822i
\(311\) 5.03858 8.72708i 0.285712 0.494868i −0.687070 0.726592i \(-0.741103\pi\)
0.972782 + 0.231724i \(0.0744366\pi\)
\(312\) 1.42135 + 0.820620i 0.0804684 + 0.0464584i
\(313\) 17.6534 10.1922i 0.997829 0.576097i 0.0902238 0.995922i \(-0.471242\pi\)
0.907605 + 0.419825i \(0.137908\pi\)
\(314\) 12.6676 0.714875
\(315\) 0 0
\(316\) 14.2990 0.804380
\(317\) 0.278048 0.160531i 0.0156168 0.00901634i −0.492171 0.870498i \(-0.663797\pi\)
0.507788 + 0.861482i \(0.330463\pi\)
\(318\) −5.01415 2.89492i −0.281180 0.162339i
\(319\) −8.53491 + 14.7829i −0.477863 + 0.827683i
\(320\) 1.97257 1.05307i 0.110270 0.0588684i
\(321\) −4.78249 −0.266932
\(322\) 0 0
\(323\) 6.42459i 0.357474i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 6.81855 + 4.56608i 0.378225 + 0.253280i
\(326\) 11.7823 20.4075i 0.652561 1.13027i
\(327\) 7.88391 4.55178i 0.435981 0.251714i
\(328\) 6.67982i 0.368832i
\(329\) 0 0
\(330\) −0.227026 + 6.82843i −0.0124973 + 0.375893i
\(331\) 8.30419 + 14.3833i 0.456440 + 0.790577i 0.998770 0.0495887i \(-0.0157910\pi\)
−0.542330 + 0.840166i \(0.682458\pi\)
\(332\) 0.757223 + 0.437183i 0.0415580 + 0.0239935i
\(333\) 9.27713 + 5.35615i 0.508384 + 0.293515i
\(334\) 9.04092 + 15.6593i 0.494697 + 0.856840i
\(335\) −2.82843 0.0940371i −0.154533 0.00513780i
\(336\) 0 0
\(337\) 1.91118i 0.104108i 0.998644 + 0.0520542i \(0.0165769\pi\)
−0.998644 + 0.0520542i \(0.983423\pi\)
\(338\) −8.92555 + 5.15317i −0.485486 + 0.280295i
\(339\) 7.19912 12.4692i 0.391002 0.677236i
\(340\) 3.43521 5.51799i 0.186300 0.299255i
\(341\) 1.44301 + 2.49937i 0.0781434 + 0.135348i
\(342\) 2.21016i 0.119512i
\(343\) 0 0
\(344\) −10.5021 −0.566238
\(345\) 3.53060 1.88483i 0.190081 0.101476i
\(346\) 0.969223 1.67874i 0.0521058 0.0902498i
\(347\) −6.84864 3.95406i −0.367654 0.212265i 0.304779 0.952423i \(-0.401417\pi\)
−0.672433 + 0.740158i \(0.734751\pi\)
\(348\) 4.83820 2.79334i 0.259355 0.149739i
\(349\) 23.5273 1.25939 0.629693 0.776844i \(-0.283181\pi\)
0.629693 + 0.776844i \(0.283181\pi\)
\(350\) 0 0
\(351\) 1.64124 0.0876029
\(352\) 2.64610 1.52773i 0.141038 0.0814281i
\(353\) 19.8942 + 11.4859i 1.05886 + 0.611333i 0.925117 0.379683i \(-0.123967\pi\)
0.133743 + 0.991016i \(0.457300\pi\)
\(354\) −2.98896 + 5.17703i −0.158861 + 0.275156i
\(355\) 29.2972 15.6405i 1.55493 0.830111i
\(356\) 17.5083 0.927935
\(357\) 0 0
\(358\) 24.4463i 1.29203i
\(359\) 5.51319 + 9.54913i 0.290975 + 0.503984i 0.974041 0.226373i \(-0.0726870\pi\)
−0.683065 + 0.730357i \(0.739354\pi\)
\(360\) 1.18176 1.89827i 0.0622844 0.100048i
\(361\) 7.05760 12.2241i 0.371453 0.643375i
\(362\) 14.7041 8.48940i 0.772829 0.446193i
\(363\) 1.66421i 0.0873483i
\(364\) 0 0
\(365\) 17.6918 + 0.588200i 0.926029 + 0.0307878i
\(366\) −0.222905 0.386083i −0.0116515 0.0201809i
\(367\) 8.78552 + 5.07232i 0.458600 + 0.264773i 0.711456 0.702731i \(-0.248036\pi\)
−0.252855 + 0.967504i \(0.581370\pi\)
\(368\) −1.55005 0.894921i −0.0808019 0.0466510i
\(369\) 3.33991 + 5.78490i 0.173869 + 0.301150i
\(370\) 0.795944 23.9402i 0.0413791 1.24459i
\(371\) 0 0
\(372\) 0.944547i 0.0489725i
\(373\) −22.9515 + 13.2511i −1.18839 + 0.686115i −0.957939 0.286970i \(-0.907352\pi\)
−0.230446 + 0.973085i \(0.574019\pi\)
\(374\) 4.44087 7.69181i 0.229632 0.397734i
\(375\) 6.52619 9.07793i 0.337011 0.468782i
\(376\) −5.68826 9.85235i −0.293349 0.508096i
\(377\) 9.16907i 0.472231i
\(378\) 0 0
\(379\) −29.4142 −1.51091 −0.755453 0.655203i \(-0.772583\pi\)
−0.755453 + 0.655203i \(0.772583\pi\)
\(380\) −4.35970 + 2.32745i −0.223648 + 0.119396i
\(381\) 4.22703 7.32142i 0.216557 0.375088i
\(382\) 0.642051 + 0.370689i 0.0328502 + 0.0189661i
\(383\) 3.15449 1.82125i 0.161187 0.0930613i −0.417237 0.908798i \(-0.637001\pi\)
0.578424 + 0.815737i \(0.303668\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −6.11091 −0.311037
\(387\) −9.09513 + 5.25107i −0.462331 + 0.266927i
\(388\) 9.04787 + 5.22379i 0.459336 + 0.265198i
\(389\) −11.8969 + 20.6060i −0.603196 + 1.04477i 0.389138 + 0.921180i \(0.372773\pi\)
−0.992334 + 0.123587i \(0.960560\pi\)
\(390\) −1.72834 3.23746i −0.0875178 0.163935i
\(391\) −5.20280 −0.263117
\(392\) 0 0
\(393\) 8.32106i 0.419742i
\(394\) 10.3416 + 17.9122i 0.521003 + 0.902404i
\(395\) −27.1433 16.8980i −1.36573 0.850232i
\(396\) 1.52773 2.64610i 0.0767711 0.132972i
\(397\) −8.45353 + 4.88065i −0.424270 + 0.244953i −0.696903 0.717166i \(-0.745439\pi\)
0.272632 + 0.962118i \(0.412106\pi\)
\(398\) 12.0702i 0.605024i
\(399\) 0 0
\(400\) −4.98896 0.332104i −0.249448 0.0166052i
\(401\) −4.98896 8.64113i −0.249137 0.431517i 0.714150 0.699993i \(-0.246814\pi\)
−0.963287 + 0.268475i \(0.913480\pi\)
\(402\) 1.09605 + 0.632805i 0.0546660 + 0.0315614i
\(403\) −1.34254 0.775114i −0.0668765 0.0386112i
\(404\) 7.72747 + 13.3844i 0.384456 + 0.665897i
\(405\) 0.0743018 2.23483i 0.00369209 0.111050i
\(406\) 0 0
\(407\) 32.7309i 1.62241i
\(408\) −2.51741 + 1.45342i −0.124630 + 0.0719552i
\(409\) 17.5919 30.4700i 0.869862 1.50665i 0.00772514 0.999970i \(-0.497541\pi\)
0.862137 0.506675i \(-0.169126\pi\)
\(410\) 7.89397 12.6801i 0.389856 0.626226i
\(411\) −4.93351 8.54508i −0.243352 0.421498i
\(412\) 3.12563i 0.153989i
\(413\) 0 0
\(414\) −1.78984 −0.0879660
\(415\) −0.920768 1.72475i −0.0451987 0.0846647i
\(416\) −0.820620 + 1.42135i −0.0402342 + 0.0696877i
\(417\) 14.6906 + 8.48159i 0.719399 + 0.415345i
\(418\) −5.84830 + 3.37652i −0.286050 + 0.165151i
\(419\) −18.6274 −0.910009 −0.455004 0.890489i \(-0.650362\pi\)
−0.455004 + 0.890489i \(0.650362\pi\)
\(420\) 0 0
\(421\) 31.6464 1.54235 0.771176 0.636622i \(-0.219669\pi\)
0.771176 + 0.636622i \(0.219669\pi\)
\(422\) −2.55610 + 1.47577i −0.124429 + 0.0718392i
\(423\) −9.85235 5.68826i −0.479038 0.276573i
\(424\) 2.89492 5.01415i 0.140590 0.243509i
\(425\) −13.0419 + 6.41503i −0.632626 + 0.311175i
\(426\) −14.8523 −0.719595
\(427\) 0 0
\(428\) 4.78249i 0.231170i
\(429\) −2.50736 4.34288i −0.121057 0.209676i
\(430\) 19.9359 + 12.4111i 0.961396 + 0.598514i
\(431\) 7.40229 12.8211i 0.356556 0.617572i −0.630827 0.775923i \(-0.717284\pi\)
0.987383 + 0.158351i \(0.0506177\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) 4.24731i 0.204113i 0.994779 + 0.102056i \(0.0325422\pi\)
−0.994779 + 0.102056i \(0.967458\pi\)
\(434\) 0 0
\(435\) −12.4853 0.415100i −0.598623 0.0199025i
\(436\) 4.55178 + 7.88391i 0.217991 + 0.377571i
\(437\) 3.42585 + 1.97792i 0.163881 + 0.0946166i
\(438\) −6.85577 3.95818i −0.327581 0.189129i
\(439\) −1.11440 1.93020i −0.0531874 0.0921232i 0.838206 0.545354i \(-0.183605\pi\)
−0.891393 + 0.453231i \(0.850271\pi\)
\(440\) −6.82843 0.227026i −0.325532 0.0108230i
\(441\) 0 0
\(442\) 4.77083i 0.226925i
\(443\) −4.02020 + 2.32106i −0.191005 + 0.110277i −0.592453 0.805605i \(-0.701840\pi\)
0.401448 + 0.915882i \(0.368507\pi\)
\(444\) −5.35615 + 9.27713i −0.254192 + 0.440273i
\(445\) −33.2354 20.6906i −1.57551 0.980829i
\(446\) 5.88388 + 10.1912i 0.278610 + 0.482566i
\(447\) 8.04810i 0.380662i
\(448\) 0 0
\(449\) 3.69059 0.174170 0.0870849 0.996201i \(-0.472245\pi\)
0.0870849 + 0.996201i \(0.472245\pi\)
\(450\) −4.48662 + 2.20687i −0.211501 + 0.104033i
\(451\) 10.2049 17.6755i 0.480532 0.832306i
\(452\) 12.4692 + 7.19912i 0.586503 + 0.338618i
\(453\) −8.64113 + 4.98896i −0.405996 + 0.234402i
\(454\) −13.2365 −0.621222
\(455\) 0 0
\(456\) 2.21016 0.103500
\(457\) 2.36401 1.36486i 0.110584 0.0638455i −0.443688 0.896181i \(-0.646330\pi\)
0.554272 + 0.832336i \(0.312997\pi\)
\(458\) −21.8626 12.6224i −1.02157 0.589806i
\(459\) −1.45342 + 2.51741i −0.0678400 + 0.117502i
\(460\) 1.88483 + 3.53060i 0.0878806 + 0.164615i
\(461\) 11.8072 0.549918 0.274959 0.961456i \(-0.411336\pi\)
0.274959 + 0.961456i \(0.411336\pi\)
\(462\) 0 0
\(463\) 2.40561i 0.111798i 0.998436 + 0.0558990i \(0.0178025\pi\)
−0.998436 + 0.0558990i \(0.982198\pi\)
\(464\) 2.79334 + 4.83820i 0.129677 + 0.224608i
\(465\) −1.11623 + 1.79301i −0.0517640 + 0.0831487i
\(466\) −1.66421 + 2.88249i −0.0770930 + 0.133529i
\(467\) 12.6969 7.33058i 0.587544 0.339219i −0.176582 0.984286i \(-0.556504\pi\)
0.764126 + 0.645067i \(0.223171\pi\)
\(468\) 1.64124i 0.0758663i
\(469\) 0 0
\(470\) −0.845296 + 25.4246i −0.0389906 + 1.17275i
\(471\) 6.33381 + 10.9705i 0.291847 + 0.505493i
\(472\) −5.17703 2.98896i −0.238292 0.137578i
\(473\) 27.7897 + 16.0444i 1.27777 + 0.737723i
\(474\) 7.14949 + 12.3833i 0.328387 + 0.568783i
\(475\) 11.0264 + 0.734003i 0.505925 + 0.0336783i
\(476\) 0 0
\(477\) 5.78984i 0.265099i
\(478\) 21.5392 12.4357i 0.985179 0.568794i
\(479\) 5.94669 10.3000i 0.271711 0.470617i −0.697589 0.716498i \(-0.745744\pi\)
0.969300 + 0.245881i \(0.0790772\pi\)
\(480\) 1.89827 + 1.18176i 0.0866438 + 0.0539399i
\(481\) 8.79073 + 15.2260i 0.400823 + 0.694245i
\(482\) 10.3535i 0.471591i
\(483\) 0 0
\(484\) 1.66421 0.0756458
\(485\) −11.0020 20.6086i −0.499576 0.935789i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) −30.7454 17.7509i −1.39321 0.804370i −0.399540 0.916716i \(-0.630830\pi\)
−0.993669 + 0.112346i \(0.964163\pi\)
\(488\) 0.386083 0.222905i 0.0174772 0.0100905i
\(489\) 23.5646 1.06563
\(490\) 0 0
\(491\) −0.978284 −0.0441493 −0.0220747 0.999756i \(-0.507027\pi\)
−0.0220747 + 0.999756i \(0.507027\pi\)
\(492\) −5.78490 + 3.33991i −0.260803 + 0.150575i
\(493\) 14.0639 + 8.11981i 0.633407 + 0.365698i
\(494\) 1.81370 3.14142i 0.0816021 0.141339i
\(495\) −6.02710 + 3.21760i −0.270898 + 0.144621i
\(496\) 0.944547 0.0424114
\(497\) 0 0
\(498\) 0.874366i 0.0391813i
\(499\) 5.86701 + 10.1620i 0.262644 + 0.454912i 0.966944 0.254991i \(-0.0820724\pi\)
−0.704300 + 0.709902i \(0.748739\pi\)
\(500\) 9.07793 + 6.52619i 0.405977 + 0.291860i
\(501\) −9.04092 + 15.6593i −0.403918 + 0.699607i
\(502\) −14.3329 + 8.27512i −0.639710 + 0.369337i
\(503\) 17.3618i 0.774125i 0.922054 + 0.387062i \(0.126510\pi\)
−0.922054 + 0.387062i \(0.873490\pi\)
\(504\) 0 0
\(505\) 1.14833 34.5392i 0.0511000 1.53697i
\(506\) 2.73439 + 4.73610i 0.121558 + 0.210545i
\(507\) −8.92555 5.15317i −0.396397 0.228860i
\(508\) 7.32142 + 4.22703i 0.324836 + 0.187544i
\(509\) 12.9147 + 22.3688i 0.572432 + 0.991481i 0.996315 + 0.0857647i \(0.0273333\pi\)
−0.423883 + 0.905717i \(0.639333\pi\)
\(510\) 6.49632 + 0.215984i 0.287662 + 0.00956394i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 1.91405 1.10508i 0.0845075 0.0487904i
\(514\) −12.2273 + 21.1783i −0.539322 + 0.934134i
\(515\) −3.69376 + 5.93330i −0.162767 + 0.261453i
\(516\) −5.25107 9.09513i −0.231166 0.400391i
\(517\) 34.7604i 1.52876i
\(518\) 0 0
\(519\) 1.93845 0.0850884
\(520\) 3.23746 1.72834i 0.141972 0.0757927i
\(521\) 12.3733 21.4312i 0.542083 0.938916i −0.456701 0.889620i \(-0.650969\pi\)
0.998784 0.0492955i \(-0.0156976\pi\)
\(522\) 4.83820 + 2.79334i 0.211762 + 0.122261i
\(523\) −1.39927 + 0.807871i −0.0611860 + 0.0353258i −0.530281 0.847822i \(-0.677914\pi\)
0.469095 + 0.883148i \(0.344580\pi\)
\(524\) −8.32106 −0.363507
\(525\) 0 0
\(526\) −12.5091 −0.545424
\(527\) 2.37781 1.37283i 0.103579 0.0598013i
\(528\) 2.64610 + 1.52773i 0.115157 + 0.0664858i
\(529\) −9.89823 + 17.1442i −0.430358 + 0.745402i
\(530\) −11.4209 + 6.09711i −0.496092 + 0.264841i
\(531\) −5.97792 −0.259420
\(532\) 0 0
\(533\) 10.9632i 0.474868i
\(534\) 8.75413 + 15.1626i 0.378828 + 0.656149i
\(535\) −5.65177 + 9.07846i −0.244347 + 0.392496i
\(536\) −0.632805 + 1.09605i −0.0273330 + 0.0473422i
\(537\) 21.1711 12.2232i 0.913602 0.527469i
\(538\) 18.9666i 0.817708i
\(539\) 0 0
\(540\) 2.23483 + 0.0743018i 0.0961719 + 0.00319744i
\(541\) −12.3765 21.4368i −0.532108 0.921638i −0.999297 0.0374808i \(-0.988067\pi\)
0.467189 0.884157i \(-0.345267\pi\)
\(542\) 17.0294 + 9.83192i 0.731475 + 0.422317i
\(543\) 14.7041 + 8.48940i 0.631012 + 0.364315i
\(544\) −1.45342 2.51741i −0.0623151 0.107933i
\(545\) 0.676410 20.3449i 0.0289742 0.871481i
\(546\) 0 0
\(547\) 44.0524i 1.88354i 0.336253 + 0.941772i \(0.390840\pi\)
−0.336253 + 0.941772i \(0.609160\pi\)
\(548\) 8.54508 4.93351i 0.365028 0.210749i
\(549\) 0.222905 0.386083i 0.00951337 0.0164776i
\(550\) 12.6939 + 8.50054i 0.541270 + 0.362464i
\(551\) −6.17371 10.6932i −0.263009 0.455545i
\(552\) 1.78984i 0.0761808i
\(553\) 0 0
\(554\) 6.13998 0.260863
\(555\) 21.1308 11.2808i 0.896953 0.478843i
\(556\) −8.48159 + 14.6906i −0.359700 + 0.623018i
\(557\) −1.79249 1.03490i −0.0759504 0.0438500i 0.461544 0.887117i \(-0.347296\pi\)
−0.537494 + 0.843267i \(0.680629\pi\)
\(558\) 0.818002 0.472274i 0.0346288 0.0199929i
\(559\) −17.2365 −0.729028
\(560\) 0 0
\(561\) 8.88174 0.374987
\(562\) 10.5075 6.06649i 0.443231 0.255900i
\(563\) −8.52596 4.92246i −0.359326 0.207457i 0.309459 0.950913i \(-0.399852\pi\)
−0.668785 + 0.743456i \(0.733185\pi\)
\(564\) 5.68826 9.85235i 0.239519 0.414859i
\(565\) −15.1623 28.4016i −0.637884 1.19486i
\(566\) −17.4172 −0.732101
\(567\) 0 0
\(568\) 14.8523i 0.623188i
\(569\) 6.87805 + 11.9131i 0.288343 + 0.499425i 0.973414 0.229051i \(-0.0735623\pi\)
−0.685071 + 0.728476i \(0.740229\pi\)
\(570\) −4.19548 2.61188i −0.175729 0.109400i
\(571\) −9.60354 + 16.6338i −0.401896 + 0.696104i −0.993955 0.109791i \(-0.964982\pi\)
0.592059 + 0.805895i \(0.298315\pi\)
\(572\) 4.34288 2.50736i 0.181585 0.104838i
\(573\) 0.741377i 0.0309715i
\(574\) 0 0
\(575\) 0.594414 8.92945i 0.0247888 0.372384i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −32.3090 18.6536i −1.34504 0.776560i −0.357500 0.933913i \(-0.616371\pi\)
−0.987542 + 0.157353i \(0.949704\pi\)
\(578\) 7.40471 + 4.27511i 0.307996 + 0.177821i
\(579\) −3.05545 5.29220i −0.126980 0.219936i
\(580\) 0.415100 12.4853i 0.0172361 0.518423i
\(581\) 0 0
\(582\) 10.4476i 0.433066i
\(583\) −15.3205 + 8.84530i −0.634510 + 0.366335i
\(584\) 3.95818 6.85577i 0.163791 0.283694i
\(585\) 1.93956 3.11552i 0.0801908 0.128811i
\(586\) 11.8761 + 20.5700i 0.490596 + 0.849737i
\(587\) 19.5459i 0.806748i 0.915035 + 0.403374i \(0.132163\pi\)
−0.915035 + 0.403374i \(0.867837\pi\)
\(588\) 0 0
\(589\) −2.08760 −0.0860180
\(590\) 6.29516 + 11.7919i 0.259168 + 0.485464i
\(591\) −10.3416 + 17.9122i −0.425397 + 0.736810i
\(592\) −9.27713 5.35615i −0.381288 0.220137i
\(593\) −25.0648 + 14.4712i −1.02929 + 0.594260i −0.916781 0.399391i \(-0.869222\pi\)
−0.112508 + 0.993651i \(0.535888\pi\)
\(594\) 3.05545 0.125367
\(595\) 0 0
\(596\) 8.04810 0.329663
\(597\) −10.4531 + 6.03509i −0.427816 + 0.247000i
\(598\) −2.54400 1.46878i −0.104032 0.0600629i
\(599\) −4.86585 + 8.42790i −0.198813 + 0.344355i −0.948144 0.317841i \(-0.897042\pi\)
0.749331 + 0.662196i \(0.230375\pi\)
\(600\) −2.20687 4.48662i −0.0900950 0.183165i
\(601\) 33.4038 1.36257 0.681284 0.732019i \(-0.261422\pi\)
0.681284 + 0.732019i \(0.261422\pi\)
\(602\) 0 0
\(603\) 1.26561i 0.0515396i
\(604\) −4.98896 8.64113i −0.202998 0.351603i
\(605\) −3.15912 1.96670i −0.128436 0.0799578i
\(606\) −7.72747 + 13.3844i −0.313907 + 0.543703i
\(607\) −37.4433 + 21.6179i −1.51978 + 0.877444i −0.520049 + 0.854137i \(0.674086\pi\)
−0.999728 + 0.0233069i \(0.992581\pi\)
\(608\) 2.21016i 0.0896337i
\(609\) 0 0
\(610\) −0.996313 0.0331245i −0.0403395 0.00134117i
\(611\) −9.33579 16.1701i −0.377686 0.654171i
\(612\) −2.51741 1.45342i −0.101760 0.0587512i
\(613\) 1.55038 + 0.895115i 0.0626195 + 0.0361534i 0.530983 0.847383i \(-0.321823\pi\)
−0.468363 + 0.883536i \(0.655156\pi\)
\(614\) −3.95406 6.84864i −0.159573 0.276388i
\(615\) 14.9283 + 0.496323i 0.601967 + 0.0200137i
\(616\) 0 0
\(617\) 38.2665i 1.54055i 0.637712 + 0.770275i \(0.279881\pi\)
−0.637712 + 0.770275i \(0.720119\pi\)
\(618\) 2.70688 1.56282i 0.108887 0.0628657i
\(619\) 0.0664943 0.115171i 0.00267263 0.00462913i −0.864686 0.502313i \(-0.832483\pi\)
0.867359 + 0.497684i \(0.165816\pi\)
\(620\) −1.79301 1.11623i −0.0720089 0.0448289i
\(621\) −0.894921 1.55005i −0.0359120 0.0622013i
\(622\) 10.0772i 0.404058i
\(623\) 0 0
\(624\) −1.64124 −0.0657022
\(625\) −9.51995 23.1165i −0.380798 0.924658i
\(626\) −10.1922 + 17.6534i −0.407362 + 0.705572i
\(627\) −5.84830 3.37652i −0.233558 0.134845i
\(628\) −10.9705 + 6.33381i −0.437770 + 0.252747i
\(629\) −31.1391 −1.24160
\(630\) 0 0
\(631\) −25.1850 −1.00260 −0.501299 0.865274i \(-0.667145\pi\)
−0.501299 + 0.865274i \(0.667145\pi\)
\(632\) −12.3833 + 7.14949i −0.492580 + 0.284391i
\(633\) −2.55610 1.47577i −0.101596 0.0586565i
\(634\) −0.160531 + 0.278048i −0.00637551 + 0.0110427i
\(635\) −8.90270 16.6762i −0.353293 0.661776i
\(636\) 5.78984 0.229582
\(637\) 0 0
\(638\) 17.0698i 0.675800i
\(639\) −7.42614 12.8625i −0.293774 0.508831i
\(640\) −1.18176 + 1.89827i −0.0467133 + 0.0750358i
\(641\) 12.2953 21.2961i 0.485635 0.841144i −0.514229 0.857653i \(-0.671922\pi\)
0.999864 + 0.0165088i \(0.00525514\pi\)
\(642\) 4.14176 2.39124i 0.163462 0.0943749i
\(643\) 9.15126i 0.360891i 0.983585 + 0.180445i \(0.0577539\pi\)
−0.983585 + 0.180445i \(0.942246\pi\)
\(644\) 0 0
\(645\) −0.780329 + 23.4706i −0.0307254 + 0.924152i
\(646\) 3.21230 + 5.56386i 0.126386 + 0.218907i
\(647\) −27.6494 15.9634i −1.08701 0.627585i −0.154231 0.988035i \(-0.549290\pi\)
−0.932779 + 0.360450i \(0.882623\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) 9.13262 + 15.8182i 0.358487 + 0.620917i
\(650\) −8.18807 0.545062i −0.321163 0.0213791i
\(651\) 0 0
\(652\) 23.5646i 0.922861i
\(653\) 2.65215 1.53122i 0.103787 0.0599213i −0.447208 0.894430i \(-0.647582\pi\)
0.550995 + 0.834509i \(0.314248\pi\)
\(654\) −4.55178 + 7.88391i −0.177989 + 0.308285i
\(655\) 15.7956 + 9.83353i 0.617187 + 0.384228i
\(656\) −3.33991 5.78490i −0.130402 0.225862i
\(657\) 7.91636i 0.308847i
\(658\) 0 0
\(659\) 9.16636 0.357071 0.178535 0.983934i \(-0.442864\pi\)
0.178535 + 0.983934i \(0.442864\pi\)
\(660\) −3.21760 6.02710i −0.125245 0.234605i
\(661\) −15.7091 + 27.2089i −0.611012 + 1.05830i 0.380058 + 0.924963i \(0.375904\pi\)
−0.991070 + 0.133341i \(0.957429\pi\)
\(662\) −14.3833 8.30419i −0.559022 0.322752i
\(663\) −4.13166 + 2.38542i −0.160461 + 0.0926419i
\(664\) −0.874366 −0.0339320
\(665\) 0 0
\(666\) −10.7123 −0.415093
\(667\) −8.65962 + 4.99963i −0.335302 + 0.193587i
\(668\) −15.6593 9.04092i −0.605878 0.349804i
\(669\) −5.88388 + 10.1912i −0.227484 + 0.394014i
\(670\) 2.49651 1.33278i 0.0964485 0.0514896i
\(671\) −1.36215 −0.0525854
\(672\) 0 0
\(673\) 6.45100i 0.248668i 0.992240 + 0.124334i \(0.0396794\pi\)
−0.992240 + 0.124334i \(0.960321\pi\)
\(674\) −0.955589 1.65513i −0.0368079 0.0637532i
\(675\) −4.15451 2.78209i −0.159907 0.107083i
\(676\) 5.15317 8.92555i 0.198199 0.343290i
\(677\) 5.20814 3.00692i 0.200165 0.115565i −0.396567 0.918006i \(-0.629799\pi\)
0.596732 + 0.802440i \(0.296465\pi\)
\(678\) 14.3982i 0.552961i
\(679\) 0 0
\(680\) −0.215984 + 6.49632i −0.00828261 + 0.249123i
\(681\) −6.61827 11.4632i −0.253613 0.439270i
\(682\) −2.49937 1.44301i −0.0957057 0.0552557i
\(683\) −7.72675 4.46104i −0.295656 0.170697i 0.344834 0.938664i \(-0.387935\pi\)
−0.640490 + 0.767967i \(0.721269\pi\)
\(684\) 1.10508 + 1.91405i 0.0422537 + 0.0731856i
\(685\) −22.0511 0.733137i −0.842530 0.0280117i
\(686\) 0 0
\(687\) 25.2448i 0.963148i
\(688\) 9.09513 5.25107i 0.346749 0.200195i
\(689\) 4.75126 8.22942i 0.181009 0.313516i
\(690\) −2.11517 + 3.39761i −0.0805232 + 0.129345i
\(691\) −23.8290 41.2731i −0.906499 1.57010i −0.818892 0.573948i \(-0.805411\pi\)
−0.0876076 0.996155i \(-0.527922\pi\)
\(692\) 1.93845i 0.0736887i
\(693\) 0 0
\(694\) 7.90812 0.300188
\(695\) 33.4611 17.8634i 1.26925 0.677598i
\(696\) −2.79334 + 4.83820i −0.105881 + 0.183392i
\(697\) −16.8158 9.70862i −0.636945 0.367740i
\(698\) −20.3752 + 11.7636i −0.771214 + 0.445260i
\(699\) −3.32842 −0.125892
\(700\) 0 0
\(701\) 31.0788 1.17383 0.586914 0.809649i \(-0.300343\pi\)
0.586914 + 0.809649i \(0.300343\pi\)
\(702\) −1.42135 + 0.820620i −0.0536456 + 0.0309723i
\(703\) 20.5039 + 11.8379i 0.773320 + 0.446476i
\(704\) −1.52773 + 2.64610i −0.0575784 + 0.0997286i
\(705\) −22.4410 + 11.9803i −0.845177 + 0.451203i
\(706\) −22.9718 −0.864556
\(707\) 0 0
\(708\) 5.97792i 0.224664i
\(709\) −6.09074 10.5495i −0.228742 0.396194i 0.728693 0.684840i \(-0.240128\pi\)
−0.957436 + 0.288647i \(0.906795\pi\)
\(710\) −17.5519 + 28.1937i −0.658711 + 1.05809i
\(711\) −7.14949 + 12.3833i −0.268127 + 0.464409i
\(712\) −15.1626 + 8.75413i −0.568242 + 0.328075i
\(713\) 1.69059i 0.0633131i
\(714\) 0 0
\(715\) −11.2071 0.372603i −0.419121 0.0139346i
\(716\) 12.2232 + 21.1711i 0.456801 + 0.791203i
\(717\) 21.5392 + 12.4357i 0.804396 + 0.464418i
\(718\) −9.54913 5.51319i −0.356370 0.205750i
\(719\) −15.9948 27.7038i −0.596505 1.03318i −0.993333 0.115284i \(-0.963222\pi\)
0.396828 0.917893i \(-0.370111\pi\)
\(720\) −0.0743018 + 2.23483i −0.00276906 + 0.0832873i
\(721\) 0 0
\(722\) 14.1152i 0.525314i
\(723\) 8.96643 5.17677i 0.333465 0.192526i
\(724\) −8.48940 + 14.7041i −0.315506 + 0.546473i
\(725\) −15.5426 + 23.2099i −0.577239 + 0.861994i
\(726\) 0.832104 + 1.44125i 0.0308823 + 0.0534897i
\(727\) 22.9992i 0.852995i 0.904489 + 0.426497i \(0.140253\pi\)
−0.904489 + 0.426497i \(0.859747\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) −15.6156 + 8.33648i −0.577960 + 0.308547i
\(731\) 15.2641 26.4382i 0.564562 0.977851i
\(732\) 0.386083 + 0.222905i 0.0142701 + 0.00823882i
\(733\) −15.2422 + 8.80006i −0.562982 + 0.325038i −0.754341 0.656482i \(-0.772044\pi\)
0.191360 + 0.981520i \(0.438710\pi\)
\(734\) −10.1446 −0.374446
\(735\) 0 0
\(736\) 1.78984 0.0659745
\(737\) 3.34893 1.93351i 0.123359 0.0712216i
\(738\) −5.78490 3.33991i −0.212945 0.122944i
\(739\) −0.0870500 + 0.150775i −0.00320218 + 0.00554635i −0.867622 0.497224i \(-0.834353\pi\)
0.864420 + 0.502771i \(0.167686\pi\)
\(740\) 11.2808 + 21.1308i 0.414691 + 0.776784i
\(741\) 3.62740 0.133256
\(742\) 0 0
\(743\) 53.6360i 1.96771i 0.178957 + 0.983857i \(0.442728\pi\)
−0.178957 + 0.983857i \(0.557272\pi\)
\(744\) 0.472274 + 0.818002i 0.0173144 + 0.0299894i
\(745\) −15.2775 9.51095i −0.559723 0.348454i
\(746\) 13.2511 22.9515i 0.485156 0.840315i
\(747\) −0.757223 + 0.437183i −0.0277053 + 0.0159957i
\(748\) 8.88174i 0.324749i
\(749\) 0 0
\(750\) −1.11289 + 11.1248i −0.0406369 + 0.406221i
\(751\) −14.5466 25.1954i −0.530812 0.919393i −0.999354 0.0359513i \(-0.988554\pi\)
0.468542 0.883441i \(-0.344779\pi\)
\(752\) 9.85235 + 5.68826i 0.359278 + 0.207429i
\(753\) −14.3329 8.27512i −0.522321 0.301562i
\(754\) 4.58453 + 7.94064i 0.166959 + 0.289181i
\(755\) −0.741377 + 22.2990i −0.0269815 + 0.811543i
\(756\) 0 0
\(757\) 34.0842i 1.23881i 0.785072 + 0.619405i \(0.212626\pi\)
−0.785072 + 0.619405i \(0.787374\pi\)
\(758\) 25.4734 14.7071i 0.925237 0.534186i
\(759\) −2.73439 + 4.73610i −0.0992521 + 0.171910i
\(760\) 2.61188 4.19548i 0.0947430 0.152186i
\(761\) 3.81479 + 6.60741i 0.138286 + 0.239519i 0.926848 0.375437i \(-0.122507\pi\)
−0.788562 + 0.614955i \(0.789174\pi\)
\(762\) 8.45405i 0.306258i
\(763\) 0 0
\(764\) −0.741377 −0.0268221
\(765\) 3.06111 + 5.73397i 0.110675 + 0.207312i
\(766\) −1.82125 + 3.15449i −0.0658043 + 0.113976i
\(767\) −8.49674 4.90560i −0.306800 0.177131i
\(768\) 0.866025 0.500000i 0.0312500 0.0180422i
\(769\) 37.8241 1.36397 0.681986 0.731365i \(-0.261117\pi\)
0.681986 + 0.731365i \(0.261117\pi\)
\(770\) 0 0
\(771\) −24.4546 −0.880710
\(772\) 5.29220 3.05545i 0.190470 0.109968i
\(773\) 21.8541 + 12.6174i 0.786036 + 0.453818i 0.838565 0.544801i \(-0.183395\pi\)
−0.0525292 + 0.998619i \(0.516728\pi\)
\(774\) 5.25107 9.09513i 0.188746 0.326918i
\(775\) 2.08449 + 4.23782i 0.0748771 + 0.152227i
\(776\) −10.4476 −0.375046
\(777\) 0 0
\(778\) 23.7938i 0.853048i
\(779\) 7.38173 + 12.7855i 0.264478 + 0.458089i
\(780\) 3.11552 + 1.93956i 0.111553 + 0.0694473i
\(781\) −22.6902 + 39.3006i −0.811920 + 1.40629i
\(782\) 4.50576 2.60140i 0.161126 0.0930259i
\(783\) 5.58667i 0.199651i
\(784\) 0 0
\(785\) 28.3100 + 0.941227i 1.01043 + 0.0335938i
\(786\) −4.16053 7.20625i −0.148401 0.257038i
\(787\) −19.6755 11.3596i −0.701355 0.404928i 0.106497 0.994313i \(-0.466037\pi\)
−0.807852 + 0.589385i \(0.799370\pi\)
\(788\) −17.9122 10.3416i −0.638096 0.368405i
\(789\) −6.25457 10.8332i −0.222669 0.385673i
\(790\) 31.9558 + 1.06244i 1.13694 + 0.0377999i
\(791\) 0 0
\(792\) 3.05545i 0.108571i
\(793\) 0.633655 0.365841i 0.0225018 0.0129914i
\(794\) 4.88065 8.45353i 0.173208 0.300004i
\(795\) −10.9907 6.84223i −0.389800 0.242669i
\(796\) −6.03509 10.4531i −0.213908 0.370500i
\(797\) 10.1057i 0.357963i 0.983852 + 0.178981i \(0.0572802\pi\)
−0.983852 + 0.178981i \(0.942720\pi\)
\(798\) 0 0
\(799\) 33.0698 1.16993
\(800\) 4.48662 2.20687i 0.158626 0.0780246i
\(801\) −8.75413 + 15.1626i −0.309312 + 0.535744i
\(802\) 8.64113 + 4.98896i 0.305129 + 0.176166i
\(803\) −20.9475 + 12.0940i −0.739221 + 0.426789i
\(804\) −1.26561 −0.0446346
\(805\) 0 0
\(806\) 1.55023 0.0546045
\(807\) 16.4256 9.48330i 0.578207 0.333828i
\(808\) −13.3844 7.72747i −0.470860 0.271851i
\(809\) 23.1590 40.1126i 0.814227 1.41028i −0.0956543 0.995415i \(-0.530494\pi\)
0.909881 0.414868i \(-0.136172\pi\)
\(810\) 1.05307 + 1.97257i 0.0370011 + 0.0693092i
\(811\) −42.0012 −1.47486 −0.737431 0.675422i \(-0.763961\pi\)
−0.737431 + 0.675422i \(0.763961\pi\)
\(812\) 0 0
\(813\) 19.6638i 0.689641i
\(814\) 16.3655 + 28.3458i 0.573610 + 0.993521i
\(815\) 27.8478 44.7320i 0.975465 1.56689i
\(816\) 1.45342 2.51741i 0.0508800 0.0881268i
\(817\) −20.1017 + 11.6057i −0.703268 + 0.406032i
\(818\) 35.1837i 1.23017i
\(819\) 0 0
\(820\) −0.496323 + 14.9283i −0.0173323 + 0.521319i
\(821\) −8.44903 14.6341i −0.294873 0.510735i 0.680082 0.733136i \(-0.261944\pi\)
−0.974955 + 0.222401i \(0.928611\pi\)
\(822\) 8.54508 + 4.93351i 0.298044 + 0.172076i
\(823\) 39.1791 + 22.6200i 1.36570 + 0.788485i 0.990375 0.138410i \(-0.0441991\pi\)
0.375321 + 0.926895i \(0.377532\pi\)
\(824\) 1.56282 + 2.70688i 0.0544433 + 0.0942986i
\(825\) −1.01473 + 15.2435i −0.0353283 + 0.530711i
\(826\) 0 0
\(827\) 34.5452i 1.20125i −0.799529 0.600627i \(-0.794918\pi\)
0.799529 0.600627i \(-0.205082\pi\)
\(828\) 1.55005 0.894921i 0.0538679 0.0311007i
\(829\) −4.99802 + 8.65682i −0.173588 + 0.300664i −0.939672 0.342077i \(-0.888870\pi\)
0.766083 + 0.642741i \(0.222203\pi\)
\(830\) 1.65978 + 1.03329i 0.0576119 + 0.0358661i
\(831\) 3.06999 + 5.31737i 0.106497 + 0.184458i
\(832\) 1.64124i 0.0568997i
\(833\) 0 0
\(834\) −16.9632 −0.587387
\(835\) 19.0414 + 35.6677i 0.658956 + 1.23433i
\(836\) 3.37652 5.84830i 0.116779 0.202268i
\(837\) 0.818002 + 0.472274i 0.0282743 + 0.0163242i
\(838\) 16.1318 9.31371i 0.557264 0.321737i
\(839\) −32.3180 −1.11574 −0.557871 0.829928i \(-0.688382\pi\)
−0.557871 + 0.829928i \(0.688382\pi\)
\(840\) 0 0
\(841\) 2.21091 0.0762383
\(842\) −27.4066 + 15.8232i −0.944494 + 0.545304i
\(843\) 10.5075 + 6.06649i 0.361897 + 0.208941i
\(844\) 1.47577 2.55610i 0.0507980 0.0879847i
\(845\) −20.3300 + 10.8533i −0.699373 + 0.373364i
\(846\) 11.3765 0.391133
\(847\) 0 0
\(848\) 5.78984i 0.198824i
\(849\) −8.70862 15.0838i −0.298879 0.517674i
\(850\) 8.08712 12.0765i 0.277386 0.414222i
\(851\) 9.58667 16.6046i 0.328627 0.569199i
\(852\) 12.8625 7.42614i 0.440660 0.254415i
\(853\) 13.7577i 0.471056i −0.971868 0.235528i \(-0.924318\pi\)
0.971868 0.235528i \(-0.0756820\pi\)
\(854\) 0 0
\(855\) 0.164219 4.93933i 0.00561616 0.168922i
\(856\) 2.39124 + 4.14176i 0.0817310 + 0.141562i
\(857\) 6.45804 + 3.72855i 0.220602 + 0.127365i 0.606229 0.795290i \(-0.292681\pi\)
−0.385627 + 0.922655i \(0.626015\pi\)
\(858\) 4.34288 + 2.50736i 0.148264 + 0.0856000i
\(859\) −16.9430 29.3462i −0.578088 1.00128i −0.995699 0.0926521i \(-0.970466\pi\)
0.417610 0.908626i \(-0.362868\pi\)
\(860\) −23.4706 0.780329i −0.800339 0.0266090i
\(861\) 0 0
\(862\) 14.8046i 0.504246i
\(863\) 35.7532 20.6421i 1.21705 0.702666i 0.252767 0.967527i \(-0.418659\pi\)
0.964287 + 0.264861i \(0.0853261\pi\)
\(864\) 0.500000 0.866025i 0.0170103 0.0294628i
\(865\) 2.29079 3.67970i 0.0778891 0.125113i
\(866\) −2.12365 3.67828i −0.0721647 0.124993i
\(867\) 8.55023i 0.290381i
\(868\) 0 0
\(869\) 43.6899 1.48208
\(870\) 11.0201 5.88315i 0.373617 0.199458i
\(871\) −1.03858 + 1.79888i −0.0351911 + 0.0609528i
\(872\) −7.88391 4.55178i −0.266983 0.154143i
\(873\) −9.04787 + 5.22379i −0.306224 + 0.176799i
\(874\) −3.95583 −0.133808
\(875\) 0 0
\(876\) 7.91636 0.267469
\(877\) 23.2041 13.3969i 0.783546 0.452380i −0.0541396 0.998533i \(-0.517242\pi\)
0.837685 + 0.546153i \(0.183908\pi\)
\(878\) 1.93020 + 1.11440i 0.0651410 + 0.0376091i
\(879\) −11.8761 + 20.5700i −0.400570 + 0.693808i
\(880\) 6.02710 3.21760i 0.203174 0.108465i
\(881\) 31.0247 1.04525 0.522625 0.852563i \(-0.324953\pi\)
0.522625 + 0.852563i \(0.324953\pi\)
\(882\) 0 0
\(883\) 39.6123i 1.33306i 0.745478 + 0.666530i \(0.232221\pi\)
−0.745478 + 0.666530i \(0.767779\pi\)
\(884\) −2.38542 4.13166i −0.0802303 0.138963i
\(885\) −7.06449 + 11.3477i −0.237470 + 0.381449i
\(886\) 2.32106 4.02020i 0.0779776 0.135061i
\(887\) 10.2583 5.92266i 0.344441 0.198863i −0.317793 0.948160i \(-0.602942\pi\)
0.662234 + 0.749297i \(0.269608\pi\)
\(888\) 10.7123i 0.359481i
\(889\) 0 0
\(890\) 39.1280 + 1.30089i 1.31157 + 0.0436061i
\(891\) 1.52773 + 2.64610i 0.0511808 + 0.0886477i
\(892\) −10.1912 5.88388i −0.341226 0.197007i
\(893\) −21.7752 12.5719i −0.728681 0.420704i
\(894\) 4.02405 + 6.96986i 0.134584 + 0.233107i
\(895\) 1.81641 54.6335i 0.0607158 1.82620i
\(896\) 0 0
\(897\) 2.93756i 0.0980823i
\(898\) −3.19615 + 1.84530i −0.106657 + 0.0615783i
\(899\) 2.63844 4.56991i 0.0879968 0.152415i
\(900\) 2.78209 4.15451i 0.0927363 0.138484i
\(901\) 8.41510 + 14.5754i 0.280348 + 0.485576i
\(902\) 20.4099i 0.679575i
\(903\) 0 0
\(904\) −14.3982 −0.478878
\(905\) 33.4919 17.8799i 1.11331 0.594347i
\(906\) 4.98896 8.64113i 0.165747 0.287082i
\(907\) 14.7093 + 8.49244i 0.488416 + 0.281987i 0.723917 0.689887i \(-0.242340\pi\)
−0.235501 + 0.971874i \(0.575673\pi\)
\(908\) 11.4632 6.61827i 0.380419 0.219635i
\(909\) −15.4549 −0.512608
\(910\) 0 0
\(911\) 15.5723 0.515934 0.257967 0.966154i \(-0.416947\pi\)
0.257967 + 0.966154i \(0.416947\pi\)
\(912\) −1.91405 + 1.10508i −0.0633806 + 0.0365928i
\(913\) 2.31366 + 1.33579i 0.0765709 + 0.0442082i
\(914\) −1.36486 + 2.36401i −0.0451456 + 0.0781945i
\(915\) −0.469470 0.879394i −0.0155202 0.0290719i
\(916\) 25.2448 0.834111
\(917\) 0 0
\(918\) 2.90685i 0.0959403i
\(919\) −18.4816 32.0111i −0.609652 1.05595i −0.991298 0.131639i \(-0.957976\pi\)
0.381646 0.924308i \(-0.375357\pi\)
\(920\) −3.39761 2.11517i −0.112016 0.0697351i
\(921\) 3.95406 6.84864i 0.130291 0.225670i
\(922\) −10.2254 + 5.90362i −0.336754 + 0.194425i
\(923\) 24.3761i 0.802351i
\(924\) 0 0
\(925\) 3.55760 53.4433i 0.116973 1.75720i
\(926\) −1.20280 2.08332i −0.0395266 0.0684620i
\(927\) 2.70688 + 1.56282i 0.0889056 + 0.0513296i
\(928\) −4.83820 2.79334i −0.158822 0.0916958i
\(929\) 16.9916 + 29.4302i 0.557475 + 0.965575i 0.997706 + 0.0676903i \(0.0215630\pi\)
−0.440232 + 0.897884i \(0.645104\pi\)
\(930\) 0.0701816 2.11091i 0.00230134 0.0692193i
\(931\) 0 0
\(932\) 3.32842i 0.109026i
\(933\) −8.72708 + 5.03858i −0.285712 + 0.164956i
\(934\) −7.33058 + 12.6969i −0.239864 + 0.415456i
\(935\) 10.4961 16.8600i 0.343260 0.551379i
\(936\) −0.820620 1.42135i −0.0268228 0.0464584i
\(937\) 43.1719i 1.41037i 0.709026 + 0.705183i \(0.249135\pi\)
−0.709026 + 0.705183i \(0.750865\pi\)
\(938\) 0 0
\(939\) −20.3844 −0.665219
\(940\) −11.9803 22.4410i −0.390753 0.731945i
\(941\) 16.5593 28.6816i 0.539818 0.934992i −0.459095 0.888387i \(-0.651826\pi\)
0.998913 0.0466053i \(-0.0148403\pi\)
\(942\) −10.9705 6.33381i −0.357438 0.206367i
\(943\) 10.3541 5.97792i 0.337174 0.194668i
\(944\) 5.97792 0.194565
\(945\) 0 0
\(946\) −32.0888 −1.04330
\(947\) −36.5816 + 21.1204i −1.18874 + 0.686321i −0.958021 0.286698i \(-0.907442\pi\)
−0.230723 + 0.973020i \(0.574109\pi\)
\(948\) −12.3833 7.14949i −0.402190 0.232205i
\(949\) 6.49632 11.2520i 0.210880 0.365254i
\(950\) −9.91613 + 4.87753i −0.321722 + 0.158248i
\(951\) −0.321063 −0.0104112
\(952\) 0 0
\(953\) 16.2358i 0.525929i −0.964806 0.262964i \(-0.915300\pi\)
0.964806 0.262964i \(-0.0847002\pi\)
\(954\) 2.89492 + 5.01415i 0.0937265 + 0.162339i
\(955\) 1.40734 + 0.876133i 0.0455403 + 0.0283510i
\(956\) −12.4357 + 21.5392i −0.402198 + 0.696627i
\(957\) 14.7829 8.53491i 0.477863 0.275894i
\(958\) 11.8934i 0.384257i
\(959\) 0 0
\(960\) −2.23483 0.0743018i −0.0721289 0.00239808i
\(961\) 15.0539 + 26.0741i 0.485610 + 0.841101i
\(962\) −15.2260 8.79073i −0.490906 0.283424i
\(963\) 4.14176 + 2.39124i 0.133466 + 0.0770568i
\(964\) 5.17677 + 8.96643i 0.166733 + 0.288789i
\(965\) −13.6569 0.454051i −0.439630 0.0146164i
\(966\) 0 0
\(967\) 56.9706i 1.83205i 0.401121 + 0.916025i \(0.368621\pi\)
−0.401121 + 0.916025i \(0.631379\pi\)
\(968\) −1.44125 + 0.832104i −0.0463234 + 0.0267448i
\(969\) −3.21230 + 5.56386i −0.103194 + 0.178737i
\(970\) 19.8323 + 12.3466i 0.636778 + 0.396425i
\(971\) 24.1997 + 41.9152i 0.776606 + 1.34512i 0.933887 + 0.357568i \(0.116394\pi\)
−0.157281 + 0.987554i \(0.550273\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 0 0
\(974\) 35.5018 1.13755
\(975\) −3.62200 7.36361i −0.115997 0.235824i
\(976\) −0.222905 + 0.386083i −0.00713503 + 0.0123582i
\(977\) 33.9829 + 19.6200i 1.08721 + 0.627701i 0.932832 0.360311i \(-0.117329\pi\)
0.154377 + 0.988012i \(0.450663\pi\)
\(978\) −20.4075 + 11.7823i −0.652561 + 0.376756i
\(979\) 53.4956 1.70973
\(980\) 0 0
\(981\) −9.10355 −0.290654
\(982\) 0.847219 0.489142i 0.0270358 0.0156091i
\(983\) −10.2583 5.92266i −0.327190 0.188903i 0.327403 0.944885i \(-0.393827\pi\)
−0.654593 + 0.755981i \(0.727160\pi\)
\(984\) 3.33991 5.78490i 0.106472 0.184416i
\(985\) 21.7809 + 40.7992i 0.693997 + 1.29997i
\(986\) −16.2396 −0.517175
\(987\) 0 0
\(988\) 3.62740i 0.115403i
\(989\) 9.39860 + 16.2789i 0.298858 + 0.517637i
\(990\) 3.61082 5.80008i 0.114760 0.184339i
\(991\) −3.07601 + 5.32780i −0.0977126 + 0.169243i −0.910738 0.412986i \(-0.864486\pi\)
0.813025 + 0.582229i \(0.197819\pi\)
\(992\) −0.818002 + 0.472274i −0.0259716 + 0.0149947i
\(993\) 16.6084i 0.527051i
\(994\) 0 0
\(995\) −0.896836 + 26.9748i −0.0284316 + 0.855160i
\(996\) −0.437183 0.757223i −0.0138527 0.0239935i
\(997\) −43.0945 24.8806i −1.36482 0.787978i −0.374557 0.927204i \(-0.622205\pi\)
−0.990261 + 0.139226i \(0.955539\pi\)
\(998\) −10.1620 5.86701i −0.321671 0.185717i
\(999\) −5.35615 9.27713i −0.169461 0.293515i
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 1470.2.n.k.949.1 16
5.4 even 2 inner 1470.2.n.k.949.8 16
7.2 even 3 inner 1470.2.n.k.79.8 16
7.3 odd 6 1470.2.g.j.589.3 8
7.4 even 3 1470.2.g.k.589.2 yes 8
7.5 odd 6 1470.2.n.l.79.5 16
7.6 odd 2 1470.2.n.l.949.4 16
35.3 even 12 7350.2.a.ds.1.1 4
35.4 even 6 1470.2.g.k.589.6 yes 8
35.9 even 6 inner 1470.2.n.k.79.1 16
35.17 even 12 7350.2.a.dt.1.1 4
35.18 odd 12 7350.2.a.dr.1.1 4
35.19 odd 6 1470.2.n.l.79.4 16
35.24 odd 6 1470.2.g.j.589.7 yes 8
35.32 odd 12 7350.2.a.du.1.1 4
35.34 odd 2 1470.2.n.l.949.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1470.2.g.j.589.3 8 7.3 odd 6
1470.2.g.j.589.7 yes 8 35.24 odd 6
1470.2.g.k.589.2 yes 8 7.4 even 3
1470.2.g.k.589.6 yes 8 35.4 even 6
1470.2.n.k.79.1 16 35.9 even 6 inner
1470.2.n.k.79.8 16 7.2 even 3 inner
1470.2.n.k.949.1 16 1.1 even 1 trivial
1470.2.n.k.949.8 16 5.4 even 2 inner
1470.2.n.l.79.4 16 35.19 odd 6
1470.2.n.l.79.5 16 7.5 odd 6
1470.2.n.l.949.4 16 7.6 odd 2
1470.2.n.l.949.5 16 35.34 odd 2
7350.2.a.dr.1.1 4 35.18 odd 12
7350.2.a.ds.1.1 4 35.3 even 12
7350.2.a.dt.1.1 4 35.17 even 12
7350.2.a.du.1.1 4 35.32 odd 12