Properties

Label 570.2.u.b.271.1
Level $570$
Weight $2$
Character 570.271
Analytic conductor $4.551$
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] = [570,2,Mod(61,570)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(570, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("570.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.u (of order \(9\), degree \(6\), 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: \(4.55147291521\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 271.1
Root \(-0.173648 + 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 570.271
Dual form 570.2.u.b.61.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.939693 - 0.342020i) q^{2} +(0.173648 - 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-2.11334 - 3.66041i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\) \(q+(0.939693 - 0.342020i) q^{2} +(0.173648 - 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(-2.11334 - 3.66041i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-0.939693 - 0.342020i) q^{10} +(1.06031 - 1.83651i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.868241 + 4.92404i) q^{13} +(-3.23783 - 2.71686i) q^{14} +(-0.766044 + 0.642788i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-3.10607 + 1.13052i) q^{17} -1.00000 q^{18} +(-3.93969 - 1.86516i) q^{19} -1.00000 q^{20} +(-3.97178 + 1.44561i) q^{21} +(0.368241 - 2.08840i) q^{22} +(3.08125 - 2.58548i) q^{23} +(-0.766044 - 0.642788i) q^{24} +(0.173648 + 0.984808i) q^{25} +(2.50000 + 4.33013i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(-3.97178 - 1.44561i) q^{28} +(2.53209 + 0.921605i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(-5.29086 - 9.16404i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-1.62449 - 1.36310i) q^{33} +(-2.53209 + 2.12467i) q^{34} +(-0.733956 + 4.16247i) q^{35} +(-0.939693 + 0.342020i) q^{36} +10.4757 q^{37} +(-4.34002 - 0.405223i) q^{38} +5.00000 q^{39} +(-0.939693 + 0.342020i) q^{40} +(1.69594 - 9.61814i) q^{41} +(-3.23783 + 2.71686i) q^{42} +(4.94356 + 4.14814i) q^{43} +(-0.368241 - 2.08840i) q^{44} +(0.500000 + 0.866025i) q^{45} +(2.01114 - 3.48340i) q^{46} +(8.35117 + 3.03958i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(-5.43242 + 9.40923i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.573978 + 3.25519i) q^{51} +(3.83022 + 3.21394i) q^{52} +(6.05303 - 5.07910i) q^{53} +(-0.173648 + 0.984808i) q^{54} +(-1.99273 + 0.725293i) q^{55} -4.22668 q^{56} +(-2.52094 + 3.55596i) q^{57} +2.69459 q^{58} +(8.92514 - 3.24849i) q^{59} +(-0.173648 + 0.984808i) q^{60} +(-9.88713 + 8.29628i) q^{61} +(-8.10607 - 6.80180i) q^{62} +(0.733956 + 4.16247i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.50000 - 4.33013i) q^{65} +(-1.99273 - 0.725293i) q^{66} +(2.57398 + 0.936851i) q^{67} +(-1.65270 + 2.86257i) q^{68} +(-2.01114 - 3.48340i) q^{69} +(0.733956 + 4.16247i) q^{70} +(-7.04189 - 5.90885i) q^{71} +(-0.766044 + 0.642788i) q^{72} +(0.0983261 - 0.557635i) q^{73} +(9.84389 - 3.58288i) q^{74} +1.00000 q^{75} +(-4.21688 + 1.10359i) q^{76} -8.96316 q^{77} +(4.69846 - 1.71010i) q^{78} +(-2.24123 + 12.7106i) q^{79} +(-0.766044 + 0.642788i) q^{80} +(0.766044 + 0.642788i) q^{81} +(-1.69594 - 9.61814i) q^{82} +(3.41147 + 5.90885i) q^{83} +(-2.11334 + 3.66041i) q^{84} +(3.10607 + 1.13052i) q^{85} +(6.06418 + 2.20718i) q^{86} +(1.34730 - 2.33359i) q^{87} +(-1.06031 - 1.83651i) q^{88} +(1.42215 + 8.06542i) q^{89} +(0.766044 + 0.642788i) q^{90} +(16.1891 - 13.5843i) q^{91} +(0.698463 - 3.96118i) q^{92} +(-9.94356 + 3.61916i) q^{93} +8.88713 q^{94} +(1.81908 + 3.96118i) q^{95} -1.00000 q^{96} +(7.83750 - 2.85262i) q^{97} +(-1.88666 + 10.6998i) q^{98} +(-1.62449 + 1.36310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{7} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{7} + 3 q^{8} + 12 q^{11} - 3 q^{12} + 6 q^{17} - 6 q^{18} - 18 q^{19} - 6 q^{20} - 9 q^{21} - 3 q^{22} + 21 q^{23} + 15 q^{26} - 3 q^{27} - 9 q^{28} + 6 q^{29} - 3 q^{30} + 3 q^{33} - 6 q^{34} - 9 q^{35} + 24 q^{37} - 6 q^{38} + 30 q^{39} - 3 q^{41} + 3 q^{44} + 3 q^{45} + 6 q^{46} + 24 q^{47} - 9 q^{49} + 3 q^{50} - 12 q^{51} + 24 q^{53} + 6 q^{55} - 12 q^{56} - 12 q^{57} + 12 q^{58} + 12 q^{59} - 24 q^{62} + 9 q^{63} - 3 q^{64} + 15 q^{65} + 6 q^{66} - 12 q^{68} - 6 q^{69} + 9 q^{70} - 36 q^{71} + 24 q^{73} + 15 q^{74} + 6 q^{75} - 9 q^{76} - 30 q^{77} - 36 q^{79} + 3 q^{82} - 6 q^{84} - 6 q^{85} + 18 q^{86} + 6 q^{87} - 12 q^{88} + 48 q^{89} - 24 q^{92} - 30 q^{93} - 6 q^{94} - 6 q^{95} - 6 q^{96} + 42 q^{97} - 18 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{8}{9}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.939693 0.342020i 0.664463 0.241845i
\(3\) 0.173648 0.984808i 0.100256 0.568579i
\(4\) 0.766044 0.642788i 0.383022 0.321394i
\(5\) −0.766044 0.642788i −0.342585 0.287463i
\(6\) −0.173648 0.984808i −0.0708916 0.402046i
\(7\) −2.11334 3.66041i −0.798768 1.38351i −0.920419 0.390933i \(-0.872152\pi\)
0.121651 0.992573i \(-0.461181\pi\)
\(8\) 0.500000 0.866025i 0.176777 0.306186i
\(9\) −0.939693 0.342020i −0.313231 0.114007i
\(10\) −0.939693 0.342020i −0.297157 0.108156i
\(11\) 1.06031 1.83651i 0.319695 0.553727i −0.660730 0.750624i \(-0.729753\pi\)
0.980424 + 0.196897i \(0.0630863\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) 0.868241 + 4.92404i 0.240807 + 1.36568i 0.830033 + 0.557714i \(0.188322\pi\)
−0.589226 + 0.807968i \(0.700567\pi\)
\(14\) −3.23783 2.71686i −0.865345 0.726111i
\(15\) −0.766044 + 0.642788i −0.197792 + 0.165967i
\(16\) 0.173648 0.984808i 0.0434120 0.246202i
\(17\) −3.10607 + 1.13052i −0.753332 + 0.274190i −0.690007 0.723803i \(-0.742393\pi\)
−0.0633248 + 0.997993i \(0.520170\pi\)
\(18\) −1.00000 −0.235702
\(19\) −3.93969 1.86516i −0.903827 0.427897i
\(20\) −1.00000 −0.223607
\(21\) −3.97178 + 1.44561i −0.866714 + 0.315458i
\(22\) 0.368241 2.08840i 0.0785092 0.445248i
\(23\) 3.08125 2.58548i 0.642485 0.539109i −0.262295 0.964988i \(-0.584479\pi\)
0.904780 + 0.425878i \(0.140035\pi\)
\(24\) −0.766044 0.642788i −0.156368 0.131208i
\(25\) 0.173648 + 0.984808i 0.0347296 + 0.196962i
\(26\) 2.50000 + 4.33013i 0.490290 + 0.849208i
\(27\) −0.500000 + 0.866025i −0.0962250 + 0.166667i
\(28\) −3.97178 1.44561i −0.750596 0.273195i
\(29\) 2.53209 + 0.921605i 0.470197 + 0.171138i 0.566242 0.824239i \(-0.308397\pi\)
−0.0960445 + 0.995377i \(0.530619\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) −5.29086 9.16404i −0.950266 1.64591i −0.744847 0.667236i \(-0.767477\pi\)
−0.205420 0.978674i \(-0.565856\pi\)
\(32\) −0.173648 0.984808i −0.0306970 0.174091i
\(33\) −1.62449 1.36310i −0.282787 0.237286i
\(34\) −2.53209 + 2.12467i −0.434250 + 0.364379i
\(35\) −0.733956 + 4.16247i −0.124061 + 0.703586i
\(36\) −0.939693 + 0.342020i −0.156615 + 0.0570034i
\(37\) 10.4757 1.72219 0.861093 0.508447i \(-0.169780\pi\)
0.861093 + 0.508447i \(0.169780\pi\)
\(38\) −4.34002 0.405223i −0.704045 0.0657358i
\(39\) 5.00000 0.800641
\(40\) −0.939693 + 0.342020i −0.148578 + 0.0540781i
\(41\) 1.69594 9.61814i 0.264861 1.50210i −0.504570 0.863371i \(-0.668349\pi\)
0.769431 0.638730i \(-0.220540\pi\)
\(42\) −3.23783 + 2.71686i −0.499607 + 0.419220i
\(43\) 4.94356 + 4.14814i 0.753886 + 0.632586i 0.936528 0.350594i \(-0.114020\pi\)
−0.182641 + 0.983180i \(0.558465\pi\)
\(44\) −0.368241 2.08840i −0.0555144 0.314838i
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) 2.01114 3.48340i 0.296527 0.513600i
\(47\) 8.35117 + 3.03958i 1.21814 + 0.443368i 0.869521 0.493896i \(-0.164428\pi\)
0.348622 + 0.937264i \(0.386650\pi\)
\(48\) −0.939693 0.342020i −0.135633 0.0493664i
\(49\) −5.43242 + 9.40923i −0.776060 + 1.34418i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) 0.573978 + 3.25519i 0.0803730 + 0.455818i
\(52\) 3.83022 + 3.21394i 0.531156 + 0.445693i
\(53\) 6.05303 5.07910i 0.831448 0.697668i −0.124175 0.992260i \(-0.539628\pi\)
0.955623 + 0.294593i \(0.0951839\pi\)
\(54\) −0.173648 + 0.984808i −0.0236305 + 0.134015i
\(55\) −1.99273 + 0.725293i −0.268699 + 0.0977985i
\(56\) −4.22668 −0.564814
\(57\) −2.52094 + 3.55596i −0.333907 + 0.470998i
\(58\) 2.69459 0.353817
\(59\) 8.92514 3.24849i 1.16195 0.422917i 0.312159 0.950030i \(-0.398948\pi\)
0.849795 + 0.527113i \(0.176725\pi\)
\(60\) −0.173648 + 0.984808i −0.0224179 + 0.127138i
\(61\) −9.88713 + 8.29628i −1.26592 + 1.06223i −0.270891 + 0.962610i \(0.587318\pi\)
−0.995026 + 0.0996203i \(0.968237\pi\)
\(62\) −8.10607 6.80180i −1.02947 0.863829i
\(63\) 0.733956 + 4.16247i 0.0924697 + 0.524422i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 2.50000 4.33013i 0.310087 0.537086i
\(66\) −1.99273 0.725293i −0.245288 0.0892774i
\(67\) 2.57398 + 0.936851i 0.314461 + 0.114455i 0.494429 0.869218i \(-0.335377\pi\)
−0.179968 + 0.983673i \(0.557599\pi\)
\(68\) −1.65270 + 2.86257i −0.200420 + 0.347137i
\(69\) −2.01114 3.48340i −0.242113 0.419353i
\(70\) 0.733956 + 4.16247i 0.0877245 + 0.497510i
\(71\) −7.04189 5.90885i −0.835718 0.701251i 0.120878 0.992667i \(-0.461429\pi\)
−0.956596 + 0.291416i \(0.905874\pi\)
\(72\) −0.766044 + 0.642788i −0.0902792 + 0.0757532i
\(73\) 0.0983261 0.557635i 0.0115082 0.0652662i −0.978513 0.206186i \(-0.933895\pi\)
0.990021 + 0.140920i \(0.0450059\pi\)
\(74\) 9.84389 3.58288i 1.14433 0.416502i
\(75\) 1.00000 0.115470
\(76\) −4.21688 + 1.10359i −0.483709 + 0.126590i
\(77\) −8.96316 −1.02145
\(78\) 4.69846 1.71010i 0.531996 0.193631i
\(79\) −2.24123 + 12.7106i −0.252158 + 1.43006i 0.551106 + 0.834436i \(0.314206\pi\)
−0.803264 + 0.595624i \(0.796905\pi\)
\(80\) −0.766044 + 0.642788i −0.0856464 + 0.0718658i
\(81\) 0.766044 + 0.642788i 0.0851160 + 0.0714208i
\(82\) −1.69594 9.61814i −0.187285 1.06215i
\(83\) 3.41147 + 5.90885i 0.374458 + 0.648580i 0.990246 0.139332i \(-0.0444955\pi\)
−0.615788 + 0.787912i \(0.711162\pi\)
\(84\) −2.11334 + 3.66041i −0.230584 + 0.399384i
\(85\) 3.10607 + 1.13052i 0.336900 + 0.122622i
\(86\) 6.06418 + 2.20718i 0.653917 + 0.238006i
\(87\) 1.34730 2.33359i 0.144445 0.250187i
\(88\) −1.06031 1.83651i −0.113029 0.195772i
\(89\) 1.42215 + 8.06542i 0.150748 + 0.854933i 0.962571 + 0.271030i \(0.0873642\pi\)
−0.811823 + 0.583903i \(0.801525\pi\)
\(90\) 0.766044 + 0.642788i 0.0807482 + 0.0677558i
\(91\) 16.1891 13.5843i 1.69708 1.42402i
\(92\) 0.698463 3.96118i 0.0728198 0.412982i
\(93\) −9.94356 + 3.61916i −1.03110 + 0.375290i
\(94\) 8.88713 0.916637
\(95\) 1.81908 + 3.96118i 0.186633 + 0.406409i
\(96\) −1.00000 −0.102062
\(97\) 7.83750 2.85262i 0.795777 0.289639i 0.0880417 0.996117i \(-0.471939\pi\)
0.707735 + 0.706478i \(0.249717\pi\)
\(98\) −1.88666 + 10.6998i −0.190581 + 1.08084i
\(99\) −1.62449 + 1.36310i −0.163267 + 0.136997i
\(100\) 0.766044 + 0.642788i 0.0766044 + 0.0642788i
\(101\) 0.0368366 + 0.208911i 0.00366538 + 0.0207874i 0.986586 0.163245i \(-0.0521960\pi\)
−0.982920 + 0.184032i \(0.941085\pi\)
\(102\) 1.65270 + 2.86257i 0.163642 + 0.283436i
\(103\) −4.80793 + 8.32759i −0.473740 + 0.820541i −0.999548 0.0300618i \(-0.990430\pi\)
0.525808 + 0.850603i \(0.323763\pi\)
\(104\) 4.69846 + 1.71010i 0.460722 + 0.167689i
\(105\) 3.97178 + 1.44561i 0.387606 + 0.141077i
\(106\) 3.95084 6.84305i 0.383739 0.664656i
\(107\) −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) 0.173648 + 0.984808i 0.0167093 + 0.0947632i
\(109\) −5.04189 4.23065i −0.482925 0.405223i 0.368557 0.929605i \(-0.379852\pi\)
−0.851483 + 0.524382i \(0.824296\pi\)
\(110\) −1.62449 + 1.36310i −0.154889 + 0.129967i
\(111\) 1.81908 10.3165i 0.172659 0.979199i
\(112\) −3.97178 + 1.44561i −0.375298 + 0.136597i
\(113\) 2.08378 0.196025 0.0980127 0.995185i \(-0.468751\pi\)
0.0980127 + 0.995185i \(0.468751\pi\)
\(114\) −1.15270 + 4.20372i −0.107961 + 0.393715i
\(115\) −4.02229 −0.375080
\(116\) 2.53209 0.921605i 0.235099 0.0855689i
\(117\) 0.868241 4.92404i 0.0802689 0.455228i
\(118\) 7.27584 6.10516i 0.669796 0.562025i
\(119\) 10.7023 + 8.98032i 0.981081 + 0.823225i
\(120\) 0.173648 + 0.984808i 0.0158518 + 0.0899002i
\(121\) 3.25150 + 5.63176i 0.295591 + 0.511978i
\(122\) −6.45336 + 11.1776i −0.584260 + 1.01197i
\(123\) −9.17752 3.34034i −0.827509 0.301189i
\(124\) −9.94356 3.61916i −0.892958 0.325010i
\(125\) 0.500000 0.866025i 0.0447214 0.0774597i
\(126\) 2.11334 + 3.66041i 0.188271 + 0.326096i
\(127\) 2.39306 + 13.5717i 0.212349 + 1.20429i 0.885447 + 0.464740i \(0.153852\pi\)
−0.673098 + 0.739553i \(0.735037\pi\)
\(128\) −0.766044 0.642788i −0.0677094 0.0568149i
\(129\) 4.94356 4.14814i 0.435256 0.365224i
\(130\) 0.868241 4.92404i 0.0761498 0.431867i
\(131\) 18.3614 6.68302i 1.60425 0.583898i 0.623956 0.781460i \(-0.285525\pi\)
0.980290 + 0.197562i \(0.0633024\pi\)
\(132\) −2.12061 −0.184576
\(133\) 1.49866 + 18.3626i 0.129950 + 1.59224i
\(134\) 2.73917 0.236628
\(135\) 0.939693 0.342020i 0.0808759 0.0294364i
\(136\) −0.573978 + 3.25519i −0.0492182 + 0.279130i
\(137\) 16.5594 13.8950i 1.41477 1.18713i 0.460694 0.887559i \(-0.347601\pi\)
0.954074 0.299572i \(-0.0968438\pi\)
\(138\) −3.08125 2.58548i −0.262294 0.220090i
\(139\) −1.57738 8.94578i −0.133792 0.758771i −0.975693 0.219140i \(-0.929675\pi\)
0.841902 0.539631i \(-0.181436\pi\)
\(140\) 2.11334 + 3.66041i 0.178610 + 0.309361i
\(141\) 4.44356 7.69648i 0.374216 0.648160i
\(142\) −8.63816 3.14403i −0.724898 0.263841i
\(143\) 9.96363 + 3.62646i 0.833201 + 0.303260i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −1.34730 2.33359i −0.111887 0.193794i
\(146\) −0.0983261 0.557635i −0.00813752 0.0461502i
\(147\) 8.32295 + 6.98378i 0.686465 + 0.576013i
\(148\) 8.02481 6.73362i 0.659636 0.553500i
\(149\) −2.80066 + 15.8833i −0.229439 + 1.30121i 0.624576 + 0.780964i \(0.285272\pi\)
−0.854015 + 0.520249i \(0.825839\pi\)
\(150\) 0.939693 0.342020i 0.0767256 0.0279258i
\(151\) −19.7297 −1.60558 −0.802789 0.596263i \(-0.796652\pi\)
−0.802789 + 0.596263i \(0.796652\pi\)
\(152\) −3.58512 + 2.47929i −0.290792 + 0.201097i
\(153\) 3.30541 0.267226
\(154\) −8.42262 + 3.06558i −0.678714 + 0.247032i
\(155\) −1.83750 + 10.4210i −0.147591 + 0.837032i
\(156\) 3.83022 3.21394i 0.306663 0.257321i
\(157\) −3.52687 2.95940i −0.281475 0.236186i 0.491109 0.871098i \(-0.336592\pi\)
−0.772584 + 0.634912i \(0.781036\pi\)
\(158\) 2.24123 + 12.7106i 0.178303 + 1.01120i
\(159\) −3.95084 6.84305i −0.313322 0.542689i
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) −15.9757 5.81466i −1.25906 0.458260i
\(162\) 0.939693 + 0.342020i 0.0738292 + 0.0268716i
\(163\) −3.06418 + 5.30731i −0.240005 + 0.415701i −0.960715 0.277535i \(-0.910482\pi\)
0.720710 + 0.693236i \(0.243816\pi\)
\(164\) −4.88326 8.45805i −0.381318 0.660462i
\(165\) 0.368241 + 2.08840i 0.0286675 + 0.162582i
\(166\) 5.22668 + 4.38571i 0.405669 + 0.340397i
\(167\) 4.87346 4.08931i 0.377119 0.316441i −0.434451 0.900695i \(-0.643058\pi\)
0.811570 + 0.584255i \(0.198613\pi\)
\(168\) −0.733956 + 4.16247i −0.0566259 + 0.321141i
\(169\) −11.2763 + 4.10424i −0.867409 + 0.315711i
\(170\) 3.30541 0.253513
\(171\) 3.06418 + 3.10013i 0.234324 + 0.237073i
\(172\) 6.45336 0.492064
\(173\) −14.2417 + 5.18355i −1.08278 + 0.394098i −0.820940 0.571014i \(-0.806550\pi\)
−0.261836 + 0.965112i \(0.584328\pi\)
\(174\) 0.467911 2.65366i 0.0354722 0.201173i
\(175\) 3.23783 2.71686i 0.244757 0.205375i
\(176\) −1.62449 1.36310i −0.122450 0.102748i
\(177\) −1.64930 9.35365i −0.123969 0.703063i
\(178\) 4.09492 + 7.09261i 0.306927 + 0.531614i
\(179\) 0.969255 1.67880i 0.0724455 0.125479i −0.827527 0.561426i \(-0.810253\pi\)
0.899973 + 0.435947i \(0.143586\pi\)
\(180\) 0.939693 + 0.342020i 0.0700406 + 0.0254927i
\(181\) −11.3969 4.14814i −0.847127 0.308329i −0.118259 0.992983i \(-0.537731\pi\)
−0.728868 + 0.684654i \(0.759953\pi\)
\(182\) 10.5667 18.3021i 0.783256 1.35664i
\(183\) 6.45336 + 11.1776i 0.477046 + 0.826268i
\(184\) −0.698463 3.96118i −0.0514914 0.292022i
\(185\) −8.02481 6.73362i −0.589996 0.495066i
\(186\) −8.10607 + 6.80180i −0.594366 + 0.498732i
\(187\) −1.21719 + 6.90301i −0.0890095 + 0.504798i
\(188\) 8.35117 3.03958i 0.609071 0.221684i
\(189\) 4.22668 0.307446
\(190\) 3.06418 + 3.10013i 0.222299 + 0.224907i
\(191\) 6.53714 0.473011 0.236505 0.971630i \(-0.423998\pi\)
0.236505 + 0.971630i \(0.423998\pi\)
\(192\) −0.939693 + 0.342020i −0.0678165 + 0.0246832i
\(193\) 0.453363 2.57115i 0.0326338 0.185075i −0.964134 0.265418i \(-0.914490\pi\)
0.996767 + 0.0803421i \(0.0256013\pi\)
\(194\) 6.38919 5.36116i 0.458717 0.384909i
\(195\) −3.83022 3.21394i −0.274288 0.230155i
\(196\) 1.88666 + 10.6998i 0.134761 + 0.764270i
\(197\) 0.144086 + 0.249563i 0.0102657 + 0.0177807i 0.871113 0.491083i \(-0.163399\pi\)
−0.860847 + 0.508864i \(0.830066\pi\)
\(198\) −1.06031 + 1.83651i −0.0753528 + 0.130515i
\(199\) −8.79561 3.20134i −0.623504 0.226937i 0.0108975 0.999941i \(-0.496531\pi\)
−0.634402 + 0.773004i \(0.718753\pi\)
\(200\) 0.939693 + 0.342020i 0.0664463 + 0.0241845i
\(201\) 1.36959 2.37219i 0.0966031 0.167321i
\(202\) 0.106067 + 0.183713i 0.00746284 + 0.0129260i
\(203\) −1.97771 11.2162i −0.138808 0.787220i
\(204\) 2.53209 + 2.12467i 0.177282 + 0.148757i
\(205\) −7.48158 + 6.27779i −0.522536 + 0.438460i
\(206\) −1.66978 + 9.46978i −0.116339 + 0.659791i
\(207\) −3.77972 + 1.37570i −0.262708 + 0.0956180i
\(208\) 5.00000 0.346688
\(209\) −7.60266 + 5.25763i −0.525887 + 0.363678i
\(210\) 4.22668 0.291669
\(211\) 23.0646 8.39484i 1.58784 0.577925i 0.610947 0.791672i \(-0.290789\pi\)
0.976889 + 0.213747i \(0.0685668\pi\)
\(212\) 1.37211 7.78163i 0.0942370 0.534445i
\(213\) −7.04189 + 5.90885i −0.482502 + 0.404867i
\(214\) −9.19253 7.71345i −0.628389 0.527281i
\(215\) −1.12061 6.35532i −0.0764253 0.433429i
\(216\) 0.500000 + 0.866025i 0.0340207 + 0.0589256i
\(217\) −22.3628 + 38.7335i −1.51808 + 2.62940i
\(218\) −6.18479 2.25108i −0.418887 0.152462i
\(219\) −0.532089 0.193665i −0.0359552 0.0130866i
\(220\) −1.06031 + 1.83651i −0.0714859 + 0.123817i
\(221\) −8.26352 14.3128i −0.555864 0.962785i
\(222\) −1.81908 10.3165i −0.122089 0.692398i
\(223\) 6.78699 + 5.69496i 0.454490 + 0.381363i 0.841099 0.540881i \(-0.181909\pi\)
−0.386609 + 0.922244i \(0.626354\pi\)
\(224\) −3.23783 + 2.71686i −0.216336 + 0.181528i
\(225\) 0.173648 0.984808i 0.0115765 0.0656539i
\(226\) 1.95811 0.712694i 0.130252 0.0474077i
\(227\) −14.7939 −0.981902 −0.490951 0.871187i \(-0.663351\pi\)
−0.490951 + 0.871187i \(0.663351\pi\)
\(228\) 0.354570 + 4.34445i 0.0234820 + 0.287718i
\(229\) −0.0837781 −0.00553621 −0.00276811 0.999996i \(-0.500881\pi\)
−0.00276811 + 0.999996i \(0.500881\pi\)
\(230\) −3.77972 + 1.37570i −0.249227 + 0.0907112i
\(231\) −1.55644 + 8.82699i −0.102406 + 0.580773i
\(232\) 2.06418 1.73205i 0.135520 0.113715i
\(233\) 1.43376 + 1.20307i 0.0939289 + 0.0788157i 0.688543 0.725196i \(-0.258251\pi\)
−0.594614 + 0.804011i \(0.702695\pi\)
\(234\) −0.868241 4.92404i −0.0567587 0.321894i
\(235\) −4.44356 7.69648i −0.289866 0.502063i
\(236\) 4.74897 8.22546i 0.309132 0.535432i
\(237\) 12.1284 + 4.41436i 0.787821 + 0.286744i
\(238\) 13.1284 + 4.77833i 0.850985 + 0.309733i
\(239\) 12.7665 22.1122i 0.825797 1.43032i −0.0755117 0.997145i \(-0.524059\pi\)
0.901309 0.433177i \(-0.142608\pi\)
\(240\) 0.500000 + 0.866025i 0.0322749 + 0.0559017i
\(241\) −1.72028 9.75622i −0.110813 0.628453i −0.988738 0.149655i \(-0.952184\pi\)
0.877925 0.478798i \(-0.158927\pi\)
\(242\) 4.98158 + 4.18004i 0.320228 + 0.268703i
\(243\) 0.766044 0.642788i 0.0491418 0.0412348i
\(244\) −2.24123 + 12.7106i −0.143480 + 0.813716i
\(245\) 10.2096 3.71599i 0.652268 0.237406i
\(246\) −9.76651 −0.622690
\(247\) 5.76352 21.0186i 0.366724 1.33738i
\(248\) −10.5817 −0.671940
\(249\) 6.41147 2.33359i 0.406311 0.147885i
\(250\) 0.173648 0.984808i 0.0109825 0.0622847i
\(251\) −4.14337 + 3.47670i −0.261527 + 0.219447i −0.764117 0.645078i \(-0.776825\pi\)
0.502590 + 0.864525i \(0.332381\pi\)
\(252\) 3.23783 + 2.71686i 0.203964 + 0.171146i
\(253\) −1.48117 8.40014i −0.0931204 0.528112i
\(254\) 6.89053 + 11.9347i 0.432350 + 0.748853i
\(255\) 1.65270 2.86257i 0.103496 0.179261i
\(256\) −0.939693 0.342020i −0.0587308 0.0213763i
\(257\) 0.972659 + 0.354019i 0.0606728 + 0.0220831i 0.372178 0.928161i \(-0.378611\pi\)
−0.311505 + 0.950244i \(0.600833\pi\)
\(258\) 3.22668 5.58878i 0.200884 0.347942i
\(259\) −22.1386 38.3452i −1.37563 2.38266i
\(260\) −0.868241 4.92404i −0.0538460 0.305376i
\(261\) −2.06418 1.73205i −0.127769 0.107211i
\(262\) 14.9684 12.5600i 0.924749 0.775957i
\(263\) −2.94996 + 16.7301i −0.181902 + 1.03162i 0.747969 + 0.663734i \(0.231029\pi\)
−0.929871 + 0.367885i \(0.880082\pi\)
\(264\) −1.99273 + 0.725293i −0.122644 + 0.0446387i
\(265\) −7.90167 −0.485396
\(266\) 7.68866 + 16.7427i 0.471422 + 1.02656i
\(267\) 8.18984 0.501210
\(268\) 2.57398 0.936851i 0.157231 0.0572273i
\(269\) −0.179740 + 1.01936i −0.0109589 + 0.0621513i −0.989797 0.142486i \(-0.954490\pi\)
0.978838 + 0.204637i \(0.0656015\pi\)
\(270\) 0.766044 0.642788i 0.0466200 0.0391188i
\(271\) 13.1702 + 11.0511i 0.800035 + 0.671309i 0.948207 0.317652i \(-0.102894\pi\)
−0.148172 + 0.988962i \(0.547339\pi\)
\(272\) 0.573978 + 3.25519i 0.0348025 + 0.197375i
\(273\) −10.5667 18.3021i −0.639526 1.10769i
\(274\) 10.8084 18.7207i 0.652959 1.13096i
\(275\) 1.99273 + 0.725293i 0.120166 + 0.0437368i
\(276\) −3.77972 1.37570i −0.227512 0.0828076i
\(277\) −0.110815 + 0.191936i −0.00665820 + 0.0115323i −0.869335 0.494223i \(-0.835453\pi\)
0.862677 + 0.505755i \(0.168786\pi\)
\(278\) −4.54189 7.86678i −0.272404 0.471818i
\(279\) 1.83750 + 10.4210i 0.110008 + 0.623886i
\(280\) 3.23783 + 2.71686i 0.193497 + 0.162363i
\(281\) −1.92468 + 1.61500i −0.114817 + 0.0963426i −0.698388 0.715719i \(-0.746099\pi\)
0.583572 + 0.812062i \(0.301655\pi\)
\(282\) 1.54323 8.75211i 0.0918982 0.521181i
\(283\) −0.532089 + 0.193665i −0.0316294 + 0.0115122i −0.357786 0.933803i \(-0.616468\pi\)
0.326157 + 0.945316i \(0.394246\pi\)
\(284\) −9.19253 −0.545476
\(285\) 4.21688 1.10359i 0.249786 0.0653710i
\(286\) 10.6031 0.626973
\(287\) −38.7904 + 14.1186i −2.28973 + 0.833393i
\(288\) −0.173648 + 0.984808i −0.0102323 + 0.0580304i
\(289\) −4.65317 + 3.90447i −0.273716 + 0.229675i
\(290\) −2.06418 1.73205i −0.121213 0.101710i
\(291\) −1.44831 8.21378i −0.0849015 0.481500i
\(292\) −0.283119 0.490376i −0.0165683 0.0286971i
\(293\) −15.6951 + 27.1846i −0.916915 + 1.58814i −0.112842 + 0.993613i \(0.535995\pi\)
−0.804073 + 0.594531i \(0.797338\pi\)
\(294\) 10.2096 + 3.71599i 0.595436 + 0.216721i
\(295\) −8.92514 3.24849i −0.519642 0.189134i
\(296\) 5.23783 9.07218i 0.304442 0.527310i
\(297\) 1.06031 + 1.83651i 0.0615253 + 0.106565i
\(298\) 2.80066 + 15.8833i 0.162238 + 0.920097i
\(299\) 15.4063 + 12.9274i 0.890967 + 0.747610i
\(300\) 0.766044 0.642788i 0.0442276 0.0371114i
\(301\) 4.73648 26.8619i 0.273006 1.54830i
\(302\) −18.5398 + 6.74795i −1.06685 + 0.388301i
\(303\) 0.212134 0.0121868
\(304\) −2.52094 + 3.55596i −0.144586 + 0.203948i
\(305\) 12.9067 0.739037
\(306\) 3.10607 1.13052i 0.177562 0.0646273i
\(307\) −2.30810 + 13.0899i −0.131730 + 0.747078i 0.845351 + 0.534211i \(0.179391\pi\)
−0.977081 + 0.212867i \(0.931720\pi\)
\(308\) −6.86618 + 5.76141i −0.391237 + 0.328287i
\(309\) 7.36618 + 6.18096i 0.419047 + 0.351623i
\(310\) 1.83750 + 10.4210i 0.104363 + 0.591871i
\(311\) 2.83750 + 4.91469i 0.160900 + 0.278686i 0.935192 0.354142i \(-0.115227\pi\)
−0.774292 + 0.632829i \(0.781894\pi\)
\(312\) 2.50000 4.33013i 0.141535 0.245145i
\(313\) −12.0770 4.39566i −0.682631 0.248457i −0.0226541 0.999743i \(-0.507212\pi\)
−0.659977 + 0.751286i \(0.729434\pi\)
\(314\) −4.32635 1.57466i −0.244150 0.0888634i
\(315\) 2.11334 3.66041i 0.119073 0.206241i
\(316\) 6.45336 + 11.1776i 0.363030 + 0.628786i
\(317\) 1.19800 + 6.79417i 0.0672862 + 0.381599i 0.999791 + 0.0204415i \(0.00650718\pi\)
−0.932505 + 0.361157i \(0.882382\pi\)
\(318\) −6.05303 5.07910i −0.339437 0.284822i
\(319\) 4.37733 3.67301i 0.245083 0.205649i
\(320\) −0.173648 + 0.984808i −0.00970723 + 0.0550524i
\(321\) −11.2763 + 4.10424i −0.629382 + 0.229076i
\(322\) −17.0009 −0.947425
\(323\) 14.3455 + 1.33943i 0.798207 + 0.0745277i
\(324\) 1.00000 0.0555556
\(325\) −4.69846 + 1.71010i −0.260624 + 0.0948593i
\(326\) −1.06418 + 6.03525i −0.0589394 + 0.334262i
\(327\) −5.04189 + 4.23065i −0.278817 + 0.233955i
\(328\) −7.48158 6.27779i −0.413101 0.346633i
\(329\) −6.52276 36.9924i −0.359611 2.03946i
\(330\) 1.06031 + 1.83651i 0.0583680 + 0.101096i
\(331\) 10.7096 18.5496i 0.588653 1.01958i −0.405756 0.913981i \(-0.632992\pi\)
0.994409 0.105596i \(-0.0336750\pi\)
\(332\) 6.41147 + 2.33359i 0.351875 + 0.128072i
\(333\) −9.84389 3.58288i −0.539442 0.196341i
\(334\) 3.18092 5.50952i 0.174052 0.301467i
\(335\) −1.36959 2.37219i −0.0748284 0.129607i
\(336\) 0.733956 + 4.16247i 0.0400406 + 0.227081i
\(337\) −13.7365 11.5263i −0.748274 0.627876i 0.186772 0.982403i \(-0.440197\pi\)
−0.935046 + 0.354527i \(0.884642\pi\)
\(338\) −9.19253 + 7.71345i −0.500008 + 0.419556i
\(339\) 0.361844 2.05212i 0.0196527 0.111456i
\(340\) 3.10607 1.13052i 0.168450 0.0613108i
\(341\) −22.4397 −1.21518
\(342\) 3.93969 + 1.86516i 0.213034 + 0.100856i
\(343\) 16.3354 0.882031
\(344\) 6.06418 2.20718i 0.326959 0.119003i
\(345\) −0.698463 + 3.96118i −0.0376040 + 0.213263i
\(346\) −11.6099 + 9.74189i −0.624154 + 0.523727i
\(347\) −9.03003 7.57709i −0.484757 0.406760i 0.367386 0.930069i \(-0.380253\pi\)
−0.852143 + 0.523309i \(0.824697\pi\)
\(348\) −0.467911 2.65366i −0.0250827 0.142251i
\(349\) −0.120615 0.208911i −0.00645636 0.0111827i 0.862779 0.505581i \(-0.168722\pi\)
−0.869236 + 0.494398i \(0.835388\pi\)
\(350\) 2.11334 3.66041i 0.112963 0.195657i
\(351\) −4.69846 1.71010i −0.250785 0.0912784i
\(352\) −1.99273 0.725293i −0.106213 0.0386582i
\(353\) 8.58172 14.8640i 0.456759 0.791129i −0.542029 0.840360i \(-0.682344\pi\)
0.998787 + 0.0492306i \(0.0156769\pi\)
\(354\) −4.74897 8.22546i −0.252405 0.437178i
\(355\) 1.59627 + 9.05288i 0.0847210 + 0.480477i
\(356\) 6.27379 + 5.26433i 0.332510 + 0.279009i
\(357\) 10.7023 8.98032i 0.566428 0.475289i
\(358\) 0.336619 1.90906i 0.0177909 0.100897i
\(359\) −25.6459 + 9.33434i −1.35354 + 0.492648i −0.914050 0.405601i \(-0.867062\pi\)
−0.439488 + 0.898248i \(0.644840\pi\)
\(360\) 1.00000 0.0527046
\(361\) 12.0424 + 14.6963i 0.633808 + 0.773490i
\(362\) −12.1284 −0.637452
\(363\) 6.11081 2.22415i 0.320735 0.116738i
\(364\) 3.66978 20.8123i 0.192349 1.09086i
\(365\) −0.433763 + 0.363970i −0.0227042 + 0.0190511i
\(366\) 9.88713 + 8.29628i 0.516808 + 0.433654i
\(367\) −0.143619 0.814502i −0.00749683 0.0425167i 0.980830 0.194866i \(-0.0624272\pi\)
−0.988327 + 0.152349i \(0.951316\pi\)
\(368\) −2.01114 3.48340i −0.104838 0.181585i
\(369\) −4.88326 + 8.45805i −0.254212 + 0.440308i
\(370\) −9.84389 3.58288i −0.511760 0.186265i
\(371\) −31.3837 11.4227i −1.62936 0.593039i
\(372\) −5.29086 + 9.16404i −0.274318 + 0.475133i
\(373\) −7.73190 13.3920i −0.400342 0.693413i 0.593425 0.804890i \(-0.297775\pi\)
−0.993767 + 0.111476i \(0.964442\pi\)
\(374\) 1.21719 + 6.90301i 0.0629392 + 0.356946i
\(375\) −0.766044 0.642788i −0.0395584 0.0331934i
\(376\) 6.80793 5.71253i 0.351092 0.294601i
\(377\) −2.33956 + 13.2683i −0.120493 + 0.683351i
\(378\) 3.97178 1.44561i 0.204286 0.0743542i
\(379\) 15.3013 0.785974 0.392987 0.919544i \(-0.371442\pi\)
0.392987 + 0.919544i \(0.371442\pi\)
\(380\) 3.93969 + 1.86516i 0.202102 + 0.0956807i
\(381\) 13.7811 0.706025
\(382\) 6.14290 2.23583i 0.314298 0.114395i
\(383\) −2.15405 + 12.2162i −0.110067 + 0.624219i 0.879008 + 0.476806i \(0.158206\pi\)
−0.989075 + 0.147413i \(0.952905\pi\)
\(384\) −0.766044 + 0.642788i −0.0390920 + 0.0328021i
\(385\) 6.86618 + 5.76141i 0.349933 + 0.293629i
\(386\) −0.453363 2.57115i −0.0230756 0.130868i
\(387\) −3.22668 5.58878i −0.164021 0.284093i
\(388\) 4.17024 7.22308i 0.211712 0.366696i
\(389\) 16.2344 + 5.90885i 0.823118 + 0.299590i 0.719031 0.694978i \(-0.244586\pi\)
0.104087 + 0.994568i \(0.466808\pi\)
\(390\) −4.69846 1.71010i −0.237916 0.0865943i
\(391\) −6.64765 + 11.5141i −0.336186 + 0.582292i
\(392\) 5.43242 + 9.40923i 0.274379 + 0.475238i
\(393\) −3.39306 19.2430i −0.171157 0.970680i
\(394\) 0.220752 + 0.185233i 0.0111213 + 0.00933189i
\(395\) 9.88713 8.29628i 0.497475 0.417431i
\(396\) −0.368241 + 2.08840i −0.0185048 + 0.104946i
\(397\) 1.76604 0.642788i 0.0886352 0.0322606i −0.297322 0.954777i \(-0.596093\pi\)
0.385957 + 0.922517i \(0.373871\pi\)
\(398\) −9.36009 −0.469179
\(399\) 18.3439 + 1.71275i 0.918343 + 0.0857447i
\(400\) 1.00000 0.0500000
\(401\) −27.0428 + 9.84278i −1.35045 + 0.491525i −0.913090 0.407759i \(-0.866310\pi\)
−0.437365 + 0.899284i \(0.644088\pi\)
\(402\) 0.475652 2.69756i 0.0237234 0.134542i
\(403\) 40.5303 34.0090i 2.01896 1.69411i
\(404\) 0.162504 + 0.136357i 0.00808487 + 0.00678401i
\(405\) −0.173648 0.984808i −0.00862865 0.0489355i
\(406\) −5.69459 9.86332i −0.282618 0.489509i
\(407\) 11.1074 19.2386i 0.550574 0.953622i
\(408\) 3.10607 + 1.13052i 0.153773 + 0.0559689i
\(409\) 29.7511 + 10.8285i 1.47110 + 0.535435i 0.948398 0.317082i \(-0.102703\pi\)
0.522698 + 0.852518i \(0.324925\pi\)
\(410\) −4.88326 + 8.45805i −0.241167 + 0.417713i
\(411\) −10.8084 18.7207i −0.533139 0.923424i
\(412\) 1.66978 + 9.46978i 0.0822640 + 0.466543i
\(413\) −30.7527 25.8046i −1.51324 1.26976i
\(414\) −3.08125 + 2.58548i −0.151435 + 0.127069i
\(415\) 1.18479 6.71929i 0.0581592 0.329837i
\(416\) 4.69846 1.71010i 0.230361 0.0838446i
\(417\) −9.08378 −0.444835
\(418\) −5.34595 + 7.54082i −0.261479 + 0.368833i
\(419\) 3.04963 0.148984 0.0744921 0.997222i \(-0.476266\pi\)
0.0744921 + 0.997222i \(0.476266\pi\)
\(420\) 3.97178 1.44561i 0.193803 0.0705386i
\(421\) −0.837496 + 4.74968i −0.0408171 + 0.231485i −0.998391 0.0567022i \(-0.981941\pi\)
0.957574 + 0.288187i \(0.0930526\pi\)
\(422\) 18.8025 15.7771i 0.915290 0.768019i
\(423\) −6.80793 5.71253i −0.331013 0.277753i
\(424\) −1.37211 7.78163i −0.0666356 0.377909i
\(425\) −1.65270 2.86257i −0.0801679 0.138855i
\(426\) −4.59627 + 7.96097i −0.222690 + 0.385710i
\(427\) 51.2627 + 18.6581i 2.48078 + 0.902929i
\(428\) −11.2763 4.10424i −0.545061 0.198386i
\(429\) 5.30154 9.18253i 0.255961 0.443337i
\(430\) −3.22668 5.58878i −0.155604 0.269515i
\(431\) 6.35504 + 36.0412i 0.306111 + 1.73604i 0.618227 + 0.786000i \(0.287851\pi\)
−0.312116 + 0.950044i \(0.601038\pi\)
\(432\) 0.766044 + 0.642788i 0.0368563 + 0.0309261i
\(433\) −12.4757 + 10.4683i −0.599542 + 0.503075i −0.891298 0.453417i \(-0.850205\pi\)
0.291757 + 0.956493i \(0.405760\pi\)
\(434\) −7.76651 + 44.0461i −0.372804 + 2.11428i
\(435\) −2.53209 + 0.921605i −0.121404 + 0.0441876i
\(436\) −6.58172 −0.315207
\(437\) −16.9615 + 4.43896i −0.811379 + 0.212344i
\(438\) −0.566237 −0.0270559
\(439\) −11.9709 + 4.35705i −0.571340 + 0.207951i −0.611503 0.791242i \(-0.709435\pi\)
0.0401626 + 0.999193i \(0.487212\pi\)
\(440\) −0.368241 + 2.08840i −0.0175552 + 0.0995605i
\(441\) 8.32295 6.98378i 0.396331 0.332561i
\(442\) −12.6604 10.6234i −0.602196 0.505302i
\(443\) −2.51249 14.2490i −0.119372 0.676992i −0.984492 0.175428i \(-0.943869\pi\)
0.865120 0.501564i \(-0.167242\pi\)
\(444\) −5.23783 9.07218i −0.248576 0.430547i
\(445\) 4.09492 7.09261i 0.194118 0.336222i
\(446\) 8.32547 + 3.03022i 0.394223 + 0.143485i
\(447\) 15.1557 + 5.51622i 0.716840 + 0.260908i
\(448\) −2.11334 + 3.66041i −0.0998460 + 0.172938i
\(449\) 7.57785 + 13.1252i 0.357621 + 0.619417i 0.987563 0.157225i \(-0.0502547\pi\)
−0.629942 + 0.776642i \(0.716921\pi\)
\(450\) −0.173648 0.984808i −0.00818585 0.0464243i
\(451\) −15.8656 13.3128i −0.747080 0.626874i
\(452\) 1.59627 1.33943i 0.0750821 0.0630013i
\(453\) −3.42602 + 19.4299i −0.160969 + 0.912898i
\(454\) −13.9017 + 5.05980i −0.652438 + 0.237468i
\(455\) −21.1334 −0.990749
\(456\) 1.81908 + 3.96118i 0.0851861 + 0.185499i
\(457\) 11.6304 0.544048 0.272024 0.962290i \(-0.412307\pi\)
0.272024 + 0.962290i \(0.412307\pi\)
\(458\) −0.0787257 + 0.0286538i −0.00367861 + 0.00133890i
\(459\) 0.573978 3.25519i 0.0267910 0.151939i
\(460\) −3.08125 + 2.58548i −0.143664 + 0.120549i
\(461\) −16.2645 13.6475i −0.757511 0.635627i 0.179967 0.983673i \(-0.442401\pi\)
−0.937478 + 0.348045i \(0.886845\pi\)
\(462\) 1.55644 + 8.82699i 0.0724120 + 0.410669i
\(463\) 15.8268 + 27.4129i 0.735535 + 1.27398i 0.954488 + 0.298248i \(0.0964023\pi\)
−0.218954 + 0.975735i \(0.570264\pi\)
\(464\) 1.34730 2.33359i 0.0625467 0.108334i
\(465\) 9.94356 + 3.61916i 0.461122 + 0.167835i
\(466\) 1.75877 + 0.640140i 0.0814735 + 0.0296539i
\(467\) −8.33275 + 14.4327i −0.385594 + 0.667868i −0.991851 0.127400i \(-0.959337\pi\)
0.606258 + 0.795268i \(0.292670\pi\)
\(468\) −2.50000 4.33013i −0.115563 0.200160i
\(469\) −2.01043 11.4017i −0.0928330 0.526482i
\(470\) −6.80793 5.71253i −0.314027 0.263500i
\(471\) −3.52687 + 2.95940i −0.162510 + 0.136362i
\(472\) 1.64930 9.35365i 0.0759152 0.430536i
\(473\) 12.8598 4.68058i 0.591294 0.215213i
\(474\) 12.9067 0.592826
\(475\) 1.15270 4.20372i 0.0528897 0.192880i
\(476\) 13.9709 0.640355
\(477\) −7.42514 + 2.70253i −0.339974 + 0.123740i
\(478\) 4.43376 25.1451i 0.202796 1.15011i
\(479\) −3.66044 + 3.07148i −0.167250 + 0.140339i −0.722571 0.691297i \(-0.757040\pi\)
0.555321 + 0.831636i \(0.312595\pi\)
\(480\) 0.766044 + 0.642788i 0.0349650 + 0.0293391i
\(481\) 9.09539 + 51.5825i 0.414714 + 2.35196i
\(482\) −4.95336 8.57948i −0.225620 0.390784i
\(483\) −8.50047 + 14.7232i −0.386785 + 0.669931i
\(484\) 6.11081 + 2.22415i 0.277764 + 0.101098i
\(485\) −7.83750 2.85262i −0.355882 0.129531i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −3.04916 5.28131i −0.138171 0.239319i 0.788633 0.614864i \(-0.210789\pi\)
−0.926804 + 0.375545i \(0.877456\pi\)
\(488\) 2.24123 + 12.7106i 0.101456 + 0.575384i
\(489\) 4.69459 + 3.93923i 0.212297 + 0.178138i
\(490\) 8.32295 6.98378i 0.375992 0.315495i
\(491\) −1.99613 + 11.3206i −0.0900841 + 0.510892i 0.906059 + 0.423151i \(0.139076\pi\)
−0.996143 + 0.0877413i \(0.972035\pi\)
\(492\) −9.17752 + 3.34034i −0.413754 + 0.150594i
\(493\) −8.90673 −0.401139
\(494\) −1.77285 21.7223i −0.0797644 0.977331i
\(495\) 2.12061 0.0953145
\(496\) −9.94356 + 3.61916i −0.446479 + 0.162505i
\(497\) −6.74691 + 38.2636i −0.302640 + 1.71636i
\(498\) 5.22668 4.38571i 0.234213 0.196528i
\(499\) −30.7108 25.7694i −1.37480 1.15360i −0.971090 0.238712i \(-0.923275\pi\)
−0.403713 0.914886i \(-0.632281\pi\)
\(500\) −0.173648 0.984808i −0.00776578 0.0440419i
\(501\) −3.18092 5.50952i −0.142113 0.246147i
\(502\) −2.70439 + 4.68415i −0.120703 + 0.209064i
\(503\) −6.91400 2.51649i −0.308280 0.112205i 0.183247 0.983067i \(-0.441339\pi\)
−0.491527 + 0.870862i \(0.663561\pi\)
\(504\) 3.97178 + 1.44561i 0.176917 + 0.0643926i
\(505\) 0.106067 0.183713i 0.00471991 0.00817513i
\(506\) −4.26486 7.38696i −0.189596 0.328390i
\(507\) 2.08378 + 11.8177i 0.0925438 + 0.524842i
\(508\) 10.5569 + 8.85829i 0.468387 + 0.393023i
\(509\) 32.0874 26.9245i 1.42225 1.19341i 0.472127 0.881531i \(-0.343486\pi\)
0.950122 0.311878i \(-0.100958\pi\)
\(510\) 0.573978 3.25519i 0.0254162 0.144142i
\(511\) −2.24897 + 0.818558i −0.0994886 + 0.0362109i
\(512\) −1.00000 −0.0441942
\(513\) 3.58512 2.47929i 0.158287 0.109463i
\(514\) 1.03508 0.0456555
\(515\) 9.03596 3.28882i 0.398172 0.144923i
\(516\) 1.12061 6.35532i 0.0493323 0.279777i
\(517\) 14.4370 12.1141i 0.634939 0.532777i
\(518\) −33.9183 28.4609i −1.49029 1.25050i
\(519\) 2.63176 + 14.9254i 0.115521 + 0.655154i
\(520\) −2.50000 4.33013i −0.109632 0.189889i
\(521\) −16.4338 + 28.4641i −0.719976 + 1.24704i 0.241032 + 0.970517i \(0.422514\pi\)
−0.961009 + 0.276518i \(0.910819\pi\)
\(522\) −2.53209 0.921605i −0.110827 0.0403376i
\(523\) 8.44831 + 3.07493i 0.369419 + 0.134457i 0.520057 0.854131i \(-0.325911\pi\)
−0.150638 + 0.988589i \(0.548133\pi\)
\(524\) 9.76991 16.9220i 0.426801 0.739241i
\(525\) −2.11334 3.66041i −0.0922338 0.159754i
\(526\) 2.94996 + 16.7301i 0.128624 + 0.729465i
\(527\) 26.7939 + 22.4827i 1.16716 + 0.979362i
\(528\) −1.62449 + 1.36310i −0.0706966 + 0.0593215i
\(529\) −1.18449 + 6.71756i −0.0514995 + 0.292068i
\(530\) −7.42514 + 2.70253i −0.322528 + 0.117390i
\(531\) −9.49794 −0.412176
\(532\) 12.9513 + 13.1033i 0.561510 + 0.568099i
\(533\) 48.8326 2.11517
\(534\) 7.69594 2.80109i 0.333036 0.121215i
\(535\) −2.08378 + 11.8177i −0.0900896 + 0.510923i
\(536\) 2.09833 1.76070i 0.0906339 0.0760509i
\(537\) −1.48499 1.24605i −0.0640818 0.0537711i
\(538\) 0.179740 + 1.01936i 0.00774915 + 0.0439476i
\(539\) 11.5201 + 19.9533i 0.496204 + 0.859451i
\(540\) 0.500000 0.866025i 0.0215166 0.0372678i
\(541\) 6.49020 + 2.36224i 0.279035 + 0.101561i 0.477747 0.878497i \(-0.341454\pi\)
−0.198712 + 0.980058i \(0.563676\pi\)
\(542\) 16.1557 + 5.88019i 0.693947 + 0.252576i
\(543\) −6.06418 + 10.5035i −0.260239 + 0.450747i
\(544\) 1.65270 + 2.86257i 0.0708591 + 0.122732i
\(545\) 1.14290 + 6.48173i 0.0489566 + 0.277647i
\(546\) −16.1891 13.5843i −0.692831 0.581354i
\(547\) 16.1898 13.5849i 0.692228 0.580848i −0.227323 0.973819i \(-0.572997\pi\)
0.919551 + 0.392971i \(0.128553\pi\)
\(548\) 3.75372 21.2884i 0.160351 0.909395i
\(549\) 12.1284 4.41436i 0.517626 0.188400i
\(550\) 2.12061 0.0904233
\(551\) −8.25671 8.35359i −0.351748 0.355875i
\(552\) −4.02229 −0.171200
\(553\) 51.2627 18.6581i 2.17991 0.793423i
\(554\) −0.0384855 + 0.218262i −0.00163509 + 0.00927307i
\(555\) −8.02481 + 6.73362i −0.340634 + 0.285826i
\(556\) −6.95858 5.83894i −0.295109 0.247626i
\(557\) −1.12078 6.35624i −0.0474888 0.269323i 0.951813 0.306678i \(-0.0992176\pi\)
−0.999302 + 0.0373558i \(0.988107\pi\)
\(558\) 5.29086 + 9.16404i 0.223980 + 0.387945i
\(559\) −16.1334 + 27.9439i −0.682370 + 1.18190i
\(560\) 3.97178 + 1.44561i 0.167838 + 0.0610882i
\(561\) 6.58677 + 2.39739i 0.278094 + 0.101218i
\(562\) −1.25624 + 2.17588i −0.0529915 + 0.0917839i
\(563\) 8.61856 + 14.9278i 0.363229 + 0.629131i 0.988490 0.151285i \(-0.0483410\pi\)
−0.625261 + 0.780415i \(0.715008\pi\)
\(564\) −1.54323 8.75211i −0.0649818 0.368530i
\(565\) −1.59627 1.33943i −0.0671554 0.0563501i
\(566\) −0.433763 + 0.363970i −0.0182324 + 0.0152988i
\(567\) 0.733956 4.16247i 0.0308232 0.174807i
\(568\) −8.63816 + 3.14403i −0.362449 + 0.131921i
\(569\) 27.2226 1.14123 0.570615 0.821218i \(-0.306705\pi\)
0.570615 + 0.821218i \(0.306705\pi\)
\(570\) 3.58512 2.47929i 0.150164 0.103846i
\(571\) 42.8972 1.79519 0.897597 0.440818i \(-0.145311\pi\)
0.897597 + 0.440818i \(0.145311\pi\)
\(572\) 9.96363 3.62646i 0.416600 0.151630i
\(573\) 1.13516 6.43783i 0.0474221 0.268944i
\(574\) −31.6223 + 26.5342i −1.31989 + 1.10752i
\(575\) 3.08125 + 2.58548i 0.128497 + 0.107822i
\(576\) 0.173648 + 0.984808i 0.00723534 + 0.0410337i
\(577\) −1.00000 1.73205i −0.0416305 0.0721062i 0.844459 0.535620i \(-0.179922\pi\)
−0.886090 + 0.463513i \(0.846589\pi\)
\(578\) −3.03714 + 5.26048i −0.126328 + 0.218807i
\(579\) −2.45336 0.892951i −0.101958 0.0371098i
\(580\) −2.53209 0.921605i −0.105139 0.0382676i
\(581\) 14.4192 24.9748i 0.598210 1.03613i
\(582\) −4.17024 7.22308i −0.172862 0.299406i
\(583\) −2.90972 16.5018i −0.120508 0.683436i
\(584\) −0.433763 0.363970i −0.0179492 0.0150612i
\(585\) −3.83022 + 3.21394i −0.158360 + 0.132880i
\(586\) −5.45084 + 30.9132i −0.225172 + 1.27701i
\(587\) −13.1652 + 4.79174i −0.543386 + 0.197776i −0.599105 0.800670i \(-0.704477\pi\)
0.0557196 + 0.998446i \(0.482255\pi\)
\(588\) 10.8648 0.448058
\(589\) 3.75196 + 45.9718i 0.154597 + 1.89423i
\(590\) −9.49794 −0.391024
\(591\) 0.270792 0.0985603i 0.0111389 0.00405423i
\(592\) 1.81908 10.3165i 0.0747636 0.424006i
\(593\) 4.29086 3.60046i 0.176204 0.147853i −0.550420 0.834888i \(-0.685532\pi\)
0.726625 + 0.687035i \(0.241088\pi\)
\(594\) 1.62449 + 1.36310i 0.0666534 + 0.0559289i
\(595\) −2.42602 13.7587i −0.0994572 0.564050i
\(596\) 8.06418 + 13.9676i 0.330322 + 0.572134i
\(597\) −4.68004 + 8.10608i −0.191541 + 0.331760i
\(598\) 18.8986 + 6.87852i 0.772820 + 0.281284i
\(599\) −8.54488 3.11008i −0.349134 0.127075i 0.161499 0.986873i \(-0.448367\pi\)
−0.510634 + 0.859798i \(0.670589\pi\)
\(600\) 0.500000 0.866025i 0.0204124 0.0353553i
\(601\) 9.27244 + 16.0603i 0.378231 + 0.655115i 0.990805 0.135298i \(-0.0431993\pi\)
−0.612574 + 0.790413i \(0.709866\pi\)
\(602\) −4.73648 26.8619i −0.193045 1.09481i
\(603\) −2.09833 1.76070i −0.0854504 0.0717014i
\(604\) −15.1138 + 12.6820i −0.614972 + 0.516023i
\(605\) 1.12923 6.40420i 0.0459098 0.260368i
\(606\) 0.199340 0.0725540i 0.00809765 0.00294730i
\(607\) 17.8726 0.725426 0.362713 0.931901i \(-0.381851\pi\)
0.362713 + 0.931901i \(0.381851\pi\)
\(608\) −1.15270 + 4.20372i −0.0467483 + 0.170483i
\(609\) −11.3892 −0.461513
\(610\) 12.1284 4.41436i 0.491063 0.178732i
\(611\) −7.71617 + 43.7606i −0.312163 + 1.77036i
\(612\) 2.53209 2.12467i 0.102354 0.0858849i
\(613\) 16.0096 + 13.4336i 0.646620 + 0.542578i 0.906043 0.423185i \(-0.139088\pi\)
−0.259423 + 0.965764i \(0.583533\pi\)
\(614\) 2.30810 + 13.0899i 0.0931472 + 0.528264i
\(615\) 4.88326 + 8.45805i 0.196912 + 0.341061i
\(616\) −4.48158 + 7.76233i −0.180568 + 0.312753i
\(617\) 26.5621 + 9.66782i 1.06935 + 0.389212i 0.815934 0.578145i \(-0.196223\pi\)
0.253417 + 0.967357i \(0.418446\pi\)
\(618\) 9.03596 + 3.28882i 0.363480 + 0.132296i
\(619\) −23.4051 + 40.5389i −0.940732 + 1.62940i −0.176652 + 0.984273i \(0.556527\pi\)
−0.764080 + 0.645122i \(0.776807\pi\)
\(620\) 5.29086 + 9.16404i 0.212486 + 0.368037i
\(621\) 0.698463 + 3.96118i 0.0280284 + 0.158957i
\(622\) 4.34730 + 3.64781i 0.174311 + 0.146264i
\(623\) 26.5173 22.2507i 1.06239 0.891453i
\(624\) 0.868241 4.92404i 0.0347575 0.197119i
\(625\) −0.939693 + 0.342020i −0.0375877 + 0.0136808i
\(626\) −12.8520 −0.513671
\(627\) 3.85756 + 8.40014i 0.154056 + 0.335469i
\(628\) −4.60401 −0.183720
\(629\) −32.5381 + 11.8429i −1.29738 + 0.472207i
\(630\) 0.733956 4.16247i 0.0292415 0.165837i
\(631\) −7.57398 + 6.35532i −0.301515 + 0.253001i −0.780975 0.624563i \(-0.785277\pi\)
0.479459 + 0.877564i \(0.340833\pi\)
\(632\) 9.88713 + 8.29628i 0.393289 + 0.330008i
\(633\) −4.26217 24.1720i −0.169406 0.960750i
\(634\) 3.44949 + 5.97470i 0.136997 + 0.237286i
\(635\) 6.89053 11.9347i 0.273442 0.473616i
\(636\) −7.42514 2.70253i −0.294426 0.107162i
\(637\) −51.0480 18.5800i −2.02260 0.736165i
\(638\) 2.85710 4.94864i 0.113114 0.195918i
\(639\) 4.59627 + 7.96097i 0.181825 + 0.314931i
\(640\) 0.173648 + 0.984808i 0.00686405 + 0.0389279i
\(641\) 27.2572 + 22.8715i 1.07659 + 0.903369i 0.995634 0.0933479i \(-0.0297569\pi\)
0.0809602 + 0.996717i \(0.474201\pi\)
\(642\) −9.19253 + 7.71345i −0.362800 + 0.304426i
\(643\) 3.34049 18.9449i 0.131736 0.747112i −0.845341 0.534227i \(-0.820603\pi\)
0.977077 0.212885i \(-0.0682861\pi\)
\(644\) −15.9757 + 5.81466i −0.629529 + 0.229130i
\(645\) −6.45336 −0.254101
\(646\) 13.9385 3.64781i 0.548403 0.143521i
\(647\) 4.02229 0.158132 0.0790662 0.996869i \(-0.474806\pi\)
0.0790662 + 0.996869i \(0.474806\pi\)
\(648\) 0.939693 0.342020i 0.0369146 0.0134358i
\(649\) 3.49753 19.8355i 0.137290 0.778611i
\(650\) −3.83022 + 3.21394i −0.150234 + 0.126061i
\(651\) 34.2618 + 28.7490i 1.34282 + 1.12676i
\(652\) 1.06418 + 6.03525i 0.0416764 + 0.236359i
\(653\) 0.645430 + 1.11792i 0.0252576 + 0.0437475i 0.878378 0.477967i \(-0.158626\pi\)
−0.853120 + 0.521714i \(0.825293\pi\)
\(654\) −3.29086 + 5.69994i −0.128683 + 0.222885i
\(655\) −18.3614 6.68302i −0.717441 0.261127i
\(656\) −9.17752 3.34034i −0.358322 0.130419i
\(657\) −0.283119 + 0.490376i −0.0110455 + 0.0191314i
\(658\) −18.7815 32.5306i −0.732180 1.26817i
\(659\) −8.81150 49.9725i −0.343247 1.94665i −0.321566 0.946887i \(-0.604209\pi\)
−0.0216811 0.999765i \(-0.506902\pi\)
\(660\) 1.62449 + 1.36310i 0.0632330 + 0.0530588i
\(661\) 31.5149 26.4441i 1.22579 1.02856i 0.227284 0.973828i \(-0.427015\pi\)
0.998501 0.0547279i \(-0.0174291\pi\)
\(662\) 3.71941 21.0938i 0.144559 0.819834i
\(663\) −15.5303 + 5.65258i −0.603148 + 0.219528i
\(664\) 6.82295 0.264782
\(665\) 10.6552 15.0299i 0.413192 0.582835i
\(666\) −10.4757 −0.405923
\(667\) 10.1848 3.70696i 0.394357 0.143534i
\(668\) 1.10472 6.26519i 0.0427430 0.242408i
\(669\) 6.78699 5.69496i 0.262400 0.220180i
\(670\) −2.09833 1.76070i −0.0810654 0.0680220i
\(671\) 4.75278 + 26.9544i 0.183479 + 1.04056i
\(672\) 2.11334 + 3.66041i 0.0815239 + 0.141204i
\(673\) 4.20708 7.28688i 0.162171 0.280889i −0.773476 0.633826i \(-0.781484\pi\)
0.935647 + 0.352937i \(0.114817\pi\)
\(674\) −16.8503 6.13300i −0.649049 0.236234i
\(675\) −0.939693 0.342020i −0.0361688 0.0131644i
\(676\) −6.00000 + 10.3923i −0.230769 + 0.399704i
\(677\) 5.70843 + 9.88728i 0.219393 + 0.379999i 0.954622 0.297819i \(-0.0962591\pi\)
−0.735230 + 0.677818i \(0.762926\pi\)
\(678\) −0.361844 2.05212i −0.0138965 0.0788112i
\(679\) −27.0051 22.6599i −1.03636 0.869608i
\(680\) 2.53209 2.12467i 0.0971012 0.0814776i
\(681\) −2.56893 + 14.5691i −0.0984414 + 0.558289i
\(682\) −21.0865 + 7.67485i −0.807443 + 0.293885i
\(683\) 2.44326 0.0934887 0.0467443 0.998907i \(-0.485115\pi\)
0.0467443 + 0.998907i \(0.485115\pi\)
\(684\) 4.34002 + 0.405223i 0.165945 + 0.0154941i
\(685\) −21.6168 −0.825935
\(686\) 15.3503 5.58705i 0.586077 0.213315i
\(687\) −0.0145479 + 0.0825054i −0.000555038 + 0.00314778i
\(688\) 4.94356 4.14814i 0.188472 0.158146i
\(689\) 30.2652 + 25.3955i 1.15301 + 0.967491i
\(690\) 0.698463 + 3.96118i 0.0265900 + 0.150800i
\(691\) 12.5364 + 21.7137i 0.476908 + 0.826029i 0.999650 0.0264620i \(-0.00842411\pi\)
−0.522742 + 0.852491i \(0.675091\pi\)
\(692\) −7.57785 + 13.1252i −0.288067 + 0.498946i
\(693\) 8.42262 + 3.06558i 0.319949 + 0.116452i
\(694\) −11.0770 4.03169i −0.420476 0.153041i
\(695\) −4.54189 + 7.86678i −0.172284 + 0.298404i
\(696\) −1.34730 2.33359i −0.0510691 0.0884543i
\(697\) 5.60576 + 31.7919i 0.212333 + 1.20420i
\(698\) −0.184793 0.155059i −0.00699450 0.00586908i
\(699\) 1.43376 1.20307i 0.0542299 0.0455043i
\(700\) 0.733956 4.16247i 0.0277409 0.157327i
\(701\) 44.3063 16.1262i 1.67343 0.609078i 0.681041 0.732245i \(-0.261527\pi\)
0.992386 + 0.123167i \(0.0393051\pi\)
\(702\) −5.00000 −0.188713
\(703\) −41.2708 19.5388i −1.55656 0.736919i
\(704\) −2.12061 −0.0799237
\(705\) −8.35117 + 3.03958i −0.314523 + 0.114477i
\(706\) 2.98040 16.9027i 0.112169 0.636141i
\(707\) 0.686852 0.576337i 0.0258317 0.0216754i
\(708\) −7.27584 6.10516i −0.273443 0.229446i
\(709\) 2.36865 + 13.4333i 0.0889566 + 0.504498i 0.996432 + 0.0843937i \(0.0268953\pi\)
−0.907476 + 0.420104i \(0.861994\pi\)
\(710\) 4.59627 + 7.96097i 0.172495 + 0.298770i
\(711\) 6.45336 11.1776i 0.242020 0.419191i
\(712\) 7.69594 + 2.80109i 0.288417 + 0.104975i
\(713\) −39.9959 14.5573i −1.49786 0.545176i
\(714\) 6.98545 12.0992i 0.261424 0.452800i
\(715\) −5.30154 9.18253i −0.198266 0.343407i
\(716\) −0.336619 1.90906i −0.0125800 0.0713449i
\(717\) −19.5594 16.4123i −0.730460 0.612929i
\(718\) −20.9067 + 17.5428i −0.780232 + 0.654692i
\(719\) 6.47472 36.7200i 0.241466 1.36942i −0.587092 0.809520i \(-0.699727\pi\)
0.828558 0.559903i \(-0.189162\pi\)
\(720\) 0.939693 0.342020i 0.0350203 0.0127463i
\(721\) 40.6432 1.51363
\(722\) 16.3425 + 9.69129i 0.608207 + 0.360672i
\(723\) −9.90673 −0.368435
\(724\) −11.3969 + 4.14814i −0.423563 + 0.154164i
\(725\) −0.467911 + 2.65366i −0.0173778 + 0.0985543i
\(726\) 4.98158 4.18004i 0.184884 0.155136i
\(727\) −29.2080 24.5084i −1.08327 0.908968i −0.0870775 0.996202i \(-0.527753\pi\)
−0.996188 + 0.0872340i \(0.972197\pi\)
\(728\) −3.66978 20.8123i −0.136011 0.771357i
\(729\) −0.500000 0.866025i −0.0185185 0.0320750i
\(730\) −0.283119 + 0.490376i −0.0104787 + 0.0181496i
\(731\) −20.0446 7.29563i −0.741375 0.269839i
\(732\) 12.1284 + 4.41436i 0.448277 + 0.163159i
\(733\) 15.5744 26.9757i 0.575255 0.996371i −0.420759 0.907173i \(-0.638236\pi\)
0.996014 0.0891987i \(-0.0284306\pi\)
\(734\) −0.413534 0.716261i −0.0152638 0.0264377i
\(735\) −1.88666 10.6998i −0.0695905 0.394667i
\(736\) −3.08125 2.58548i −0.113576 0.0953020i
\(737\) 4.44974 3.73378i 0.163908 0.137535i
\(738\) −1.69594 + 9.61814i −0.0624283 + 0.354048i
\(739\) 0.284463 0.103536i 0.0104641 0.00380863i −0.336783 0.941582i \(-0.609339\pi\)
0.347247 + 0.937774i \(0.387117\pi\)
\(740\) −10.4757 −0.385093
\(741\) −19.6985 9.32580i −0.723641 0.342592i
\(742\) −33.3979 −1.22607
\(743\) −40.4552 + 14.7245i −1.48416 + 0.540189i −0.951904 0.306397i \(-0.900877\pi\)
−0.532253 + 0.846586i \(0.678654\pi\)
\(744\) −1.83750 + 10.4210i −0.0673659 + 0.382051i
\(745\) 12.3550 10.3671i 0.452654 0.379821i
\(746\) −11.8460 9.93993i −0.433711 0.363927i
\(747\) −1.18479 6.71929i −0.0433493 0.245846i
\(748\) 3.50475 + 6.07040i 0.128146 + 0.221956i
\(749\) −25.3601 + 43.9250i −0.926638 + 1.60498i
\(750\) −0.939693 0.342020i −0.0343127 0.0124888i
\(751\) −40.2918 14.6650i −1.47027 0.535134i −0.522095 0.852887i \(-0.674849\pi\)
−0.948173 + 0.317753i \(0.897072\pi\)
\(752\) 4.44356 7.69648i 0.162040 0.280662i
\(753\) 2.70439 + 4.68415i 0.0985536 + 0.170700i
\(754\) 2.33956 + 13.2683i 0.0852016 + 0.483202i
\(755\) 15.1138 + 12.6820i 0.550048 + 0.461545i
\(756\) 3.23783 2.71686i 0.117759 0.0988112i
\(757\) −0.00134417 + 0.00762319i −4.88548e−5 + 0.000277069i −0.984832 0.173510i \(-0.944489\pi\)
0.984783 + 0.173787i \(0.0556003\pi\)
\(758\) 14.3785 5.23335i 0.522251 0.190084i
\(759\) −8.52972 −0.309609
\(760\) 4.34002 + 0.405223i 0.157429 + 0.0146990i
\(761\) −31.3233 −1.13547 −0.567734 0.823212i \(-0.692180\pi\)
−0.567734 + 0.823212i \(0.692180\pi\)
\(762\) 12.9500 4.71340i 0.469128 0.170748i
\(763\) −4.83069 + 27.3962i −0.174883 + 0.991809i
\(764\) 5.00774 4.20199i 0.181174 0.152023i
\(765\) −2.53209 2.12467i −0.0915479 0.0768178i
\(766\) 2.15405 + 12.2162i 0.0778289 + 0.441390i
\(767\) 23.7449 + 41.1273i 0.857377 + 1.48502i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 10.6694 + 3.88333i 0.384747 + 0.140037i 0.527150 0.849772i \(-0.323261\pi\)
−0.142403 + 0.989809i \(0.545483\pi\)
\(770\) 8.42262 + 3.06558i 0.303530 + 0.110476i
\(771\) 0.517541 0.896407i 0.0186388 0.0322833i
\(772\) −1.30541 2.26103i −0.0469826 0.0813763i
\(773\) −4.44175 25.1904i −0.159759 0.906037i −0.954305 0.298833i \(-0.903402\pi\)
0.794547 0.607203i \(-0.207709\pi\)
\(774\) −4.94356 4.14814i −0.177693 0.149102i
\(775\) 8.10607 6.80180i 0.291179 0.244328i
\(776\) 1.44831 8.21378i 0.0519913 0.294857i
\(777\) −41.6070 + 15.1437i −1.49264 + 0.543278i
\(778\) 17.2763 0.619386
\(779\) −24.6208 + 34.7293i −0.882133 + 1.24431i
\(780\) −5.00000 −0.179029
\(781\) −18.3182 + 6.66728i −0.655477 + 0.238574i
\(782\) −2.30871 + 13.0933i −0.0825591 + 0.468216i
\(783\) −2.06418 + 1.73205i −0.0737677 + 0.0618984i
\(784\) 8.32295 + 6.98378i 0.297248 + 0.249421i
\(785\) 0.799478 + 4.53406i 0.0285346 + 0.161828i
\(786\) −9.76991 16.9220i −0.348481 0.603587i
\(787\) 18.3105 31.7146i 0.652697 1.13051i −0.329768 0.944062i \(-0.606971\pi\)
0.982466 0.186443i \(-0.0596960\pi\)
\(788\) 0.270792 + 0.0985603i 0.00964657 + 0.00351107i
\(789\) 15.9636 + 5.81029i 0.568320 + 0.206852i
\(790\) 6.45336 11.1776i 0.229600 0.397679i
\(791\) −4.40373 7.62749i −0.156579 0.271202i
\(792\) 0.368241 + 2.08840i 0.0130849 + 0.0742080i
\(793\) −49.4356 41.4814i −1.75551 1.47305i
\(794\) 1.43969 1.20805i 0.0510928 0.0428719i
\(795\) −1.37211 + 7.78163i −0.0486638 + 0.275986i
\(796\) −8.79561 + 3.20134i −0.311752 + 0.113468i
\(797\) 35.9840 1.27462 0.637310 0.770608i \(-0.280047\pi\)
0.637310 + 0.770608i \(0.280047\pi\)
\(798\) 17.8234 4.66452i 0.630942 0.165122i
\(799\) −29.3756 −1.03923
\(800\) 0.939693 0.342020i 0.0332232 0.0120922i
\(801\) 1.42215 8.06542i 0.0502493 0.284978i
\(802\) −22.0455 + 18.4984i −0.778454 + 0.653201i
\(803\) −0.919844 0.771841i −0.0324606 0.0272377i
\(804\) −0.475652 2.69756i −0.0167749 0.0951355i
\(805\) 8.50047 + 14.7232i 0.299602 + 0.518926i
\(806\) 26.4543 45.8202i 0.931813 1.61395i
\(807\) 0.972659 + 0.354019i 0.0342392 + 0.0124621i
\(808\) 0.199340 + 0.0725540i 0.00701277 + 0.00255244i
\(809\) −1.05169 + 1.82158i −0.0369754 + 0.0640433i −0.883921 0.467636i \(-0.845106\pi\)
0.846945 + 0.531680i \(0.178439\pi\)
\(810\) −0.500000 0.866025i −0.0175682 0.0304290i
\(811\) −0.985614 5.58970i −0.0346096 0.196281i 0.962601 0.270924i \(-0.0873293\pi\)
−0.997210 + 0.0746434i \(0.976218\pi\)
\(812\) −8.72462 7.32083i −0.306174 0.256911i
\(813\) 13.1702 11.0511i 0.461901 0.387581i
\(814\) 3.85756 21.8773i 0.135208 0.766800i
\(815\) 5.75877 2.09602i 0.201721 0.0734204i
\(816\) 3.30541 0.115712
\(817\) −11.7392 25.5629i −0.410702 0.894334i
\(818\) 31.6604 1.10698
\(819\) −19.8589 + 7.22805i −0.693926 + 0.252569i
\(820\) −1.69594 + 9.61814i −0.0592247 + 0.335880i
\(821\) 14.4388 12.1156i 0.503918 0.422838i −0.355065 0.934842i \(-0.615541\pi\)
0.858983 + 0.512004i \(0.171097\pi\)
\(822\) −16.5594 13.8950i −0.577576 0.484644i
\(823\) 0.558248 + 3.16598i 0.0194593 + 0.110359i 0.992990 0.118196i \(-0.0377110\pi\)
−0.973531 + 0.228555i \(0.926600\pi\)
\(824\) 4.80793 + 8.32759i 0.167492 + 0.290105i
\(825\) 1.06031 1.83651i 0.0369152 0.0639389i
\(826\) −37.7237 13.7303i −1.31258 0.477739i
\(827\) −14.4064 5.24351i −0.500960 0.182335i 0.0791655 0.996861i \(-0.474774\pi\)
−0.580126 + 0.814527i \(0.696997\pi\)
\(828\) −2.01114 + 3.48340i −0.0698921 + 0.121057i
\(829\) −7.98545 13.8312i −0.277346 0.480378i 0.693378 0.720574i \(-0.256122\pi\)
−0.970724 + 0.240196i \(0.922788\pi\)
\(830\) −1.18479 6.71929i −0.0411247 0.233230i
\(831\) 0.169778 + 0.142460i 0.00588953 + 0.00494190i
\(832\) 3.83022 3.21394i 0.132789 0.111423i
\(833\) 6.23618 35.3671i 0.216071 1.22540i
\(834\) −8.53596 + 3.10684i −0.295576 + 0.107581i
\(835\) −6.36184 −0.220161
\(836\) −2.44444 + 8.91447i −0.0845427 + 0.308314i
\(837\) 10.5817 0.365758
\(838\) 2.86571 1.04303i 0.0989945 0.0360310i
\(839\) −0.294978 + 1.67290i −0.0101838 + 0.0577551i −0.989476 0.144696i \(-0.953780\pi\)
0.979292 + 0.202451i \(0.0648907\pi\)
\(840\) 3.23783 2.71686i 0.111716 0.0937405i
\(841\) −16.6532 13.9737i −0.574247 0.481851i
\(842\) 0.837496 + 4.74968i 0.0288620 + 0.163685i
\(843\) 1.25624 + 2.17588i 0.0432674 + 0.0749412i
\(844\) 12.2724 21.2565i 0.422435 0.731679i
\(845\) 11.2763 + 4.10424i 0.387917 + 0.141190i
\(846\) −8.35117 3.03958i −0.287119 0.104503i
\(847\) 13.7430 23.8036i 0.472216 0.817903i
\(848\) −3.95084 6.84305i −0.135672 0.234991i
\(849\) 0.0983261 + 0.557635i 0.00337454 + 0.0191380i
\(850\) −2.53209 2.12467i −0.0868499 0.0728757i
\(851\) 32.2781 27.0846i 1.10648 0.928447i
\(852\) −1.59627 + 9.05288i −0.0546872 + 0.310146i
\(853\) −33.8987 + 12.3381i −1.16067 + 0.422450i −0.849337 0.527851i \(-0.822998\pi\)
−0.311334 + 0.950301i \(0.600776\pi\)
\(854\) 54.5526 1.86675
\(855\) −0.354570 4.34445i −0.0121260 0.148577i
\(856\) −12.0000 −0.410152
\(857\) 18.8033 6.84386i 0.642310 0.233782i −0.000270354 1.00000i \(-0.500086\pi\)
0.642580 + 0.766218i \(0.277864\pi\)
\(858\) 1.84120 10.4420i 0.0628577 0.356484i
\(859\) 4.82366 4.04753i 0.164581 0.138100i −0.556777 0.830662i \(-0.687962\pi\)
0.721359 + 0.692562i \(0.243518\pi\)
\(860\) −4.94356 4.14814i −0.168574 0.141450i
\(861\) 7.16819 + 40.6528i 0.244291 + 1.38544i
\(862\) 18.2986 + 31.6941i 0.623253 + 1.07951i
\(863\) 0.0876485 0.151812i 0.00298359 0.00516773i −0.864530 0.502582i \(-0.832384\pi\)
0.867513 + 0.497414i \(0.165717\pi\)
\(864\) 0.939693 + 0.342020i 0.0319690 + 0.0116358i
\(865\) 14.2417 + 5.18355i 0.484232 + 0.176246i
\(866\) −8.14290 + 14.1039i −0.276707 + 0.479271i
\(867\) 3.03714 + 5.26048i 0.103147 + 0.178655i
\(868\) 7.76651 + 44.0461i 0.263613 + 1.49502i
\(869\) 20.9668 + 17.5932i 0.711249 + 0.596809i
\(870\) −2.06418 + 1.73205i −0.0699822 + 0.0587220i
\(871\) −2.37826 + 13.4878i −0.0805842 + 0.457016i
\(872\) −6.18479 + 2.25108i −0.209444 + 0.0762312i
\(873\) −8.34049 −0.282283
\(874\) −14.4204 + 9.97244i −0.487777 + 0.337323i
\(875\) −4.22668 −0.142888
\(876\) −0.532089 + 0.193665i −0.0179776 + 0.00654332i
\(877\) −7.82816 + 44.3957i −0.264338 + 1.49914i 0.506575 + 0.862196i \(0.330912\pi\)
−0.770913 + 0.636941i \(0.780200\pi\)
\(878\) −9.75877 + 8.18858i −0.329343 + 0.276351i
\(879\) 24.0462 + 20.1772i 0.811059 + 0.680559i
\(880\) 0.368241 + 2.08840i 0.0124134 + 0.0703999i
\(881\) −21.5822 37.3814i −0.727122 1.25941i −0.958094 0.286452i \(-0.907524\pi\)
0.230972 0.972960i \(-0.425809\pi\)
\(882\) 5.43242 9.40923i 0.182919 0.316825i
\(883\) −5.70233 2.07548i −0.191899 0.0698455i 0.244283 0.969704i \(-0.421447\pi\)
−0.436182 + 0.899858i \(0.643670\pi\)
\(884\) −15.5303 5.65258i −0.522342 0.190117i
\(885\) −4.74897 + 8.22546i −0.159635 + 0.276496i
\(886\) −7.23442 12.5304i −0.243045 0.420967i
\(887\) −3.87362 21.9684i −0.130063 0.737626i −0.978171 0.207802i \(-0.933369\pi\)
0.848108 0.529824i \(-0.177742\pi\)
\(888\) −8.02481 6.73362i −0.269295 0.225965i
\(889\) 44.6207 37.4412i 1.49653 1.25574i
\(890\) 1.42215 8.06542i 0.0476706 0.270354i
\(891\) 1.99273 0.725293i 0.0667588 0.0242982i
\(892\) 8.85978 0.296648
\(893\) −27.2317 27.5513i −0.911275 0.921968i
\(894\) 16.1284 0.539413
\(895\) −1.82160 + 0.663010i −0.0608895 + 0.0221620i
\(896\) −0.733956 + 4.16247i −0.0245197 + 0.139058i
\(897\) 15.4063 12.9274i 0.514400 0.431633i
\(898\) 11.6099 + 9.74189i 0.387429 + 0.325091i
\(899\) −4.95130 28.0802i −0.165135 0.936528i
\(900\) −0.500000 0.866025i −0.0166667 0.0288675i
\(901\) −13.0591 + 22.6191i −0.435063 + 0.753550i
\(902\) −19.4620 7.08358i −0.648013 0.235857i
\(903\) −25.6313 9.32905i −0.852958 0.310451i
\(904\) 1.04189 1.80460i 0.0346527 0.0600203i
\(905\) 6.06418 + 10.5035i 0.201580 + 0.349147i
\(906\) 3.42602 + 19.4299i 0.113822 + 0.645516i
\(907\) −10.6340 8.92302i −0.353097 0.296284i 0.448935 0.893564i \(-0.351803\pi\)
−0.802032 + 0.597281i \(0.796248\pi\)
\(908\) −11.3327 + 9.50931i −0.376090 + 0.315577i
\(909\) 0.0368366 0.208911i 0.00122179 0.00692914i
\(910\) −19.8589 + 7.22805i −0.658316 + 0.239608i
\(911\) −0.251334 −0.00832708 −0.00416354 0.999991i \(-0.501325\pi\)
−0.00416354 + 0.999991i \(0.501325\pi\)
\(912\) 3.06418 + 3.10013i 0.101465 + 0.102656i
\(913\) 14.4688 0.478849
\(914\) 10.9290 3.97784i 0.361500 0.131575i
\(915\) 2.24123 12.7106i 0.0740928 0.420201i
\(916\) −0.0641778 + 0.0538515i −0.00212049 + 0.00177931i
\(917\) −63.2666 53.0870i −2.08925 1.75309i
\(918\) −0.573978 3.25519i −0.0189441 0.107437i
\(919\) 3.63547 + 6.29681i 0.119923 + 0.207713i 0.919737 0.392535i \(-0.128402\pi\)
−0.799814 + 0.600248i \(0.795069\pi\)
\(920\) −2.01114 + 3.48340i −0.0663055 + 0.114844i
\(921\) 12.4902 + 4.54606i 0.411566 + 0.149798i
\(922\) −19.9513 7.26168i −0.657061 0.239151i
\(923\) 22.9813 39.8048i 0.756440 1.31019i
\(924\) 4.48158 + 7.76233i 0.147433 + 0.255362i
\(925\) 1.81908 + 10.3165i 0.0598109 + 0.339205i
\(926\) 24.2481 + 20.3466i 0.796842 + 0.668630i
\(927\) 7.36618 6.18096i 0.241937 0.203009i
\(928\) 0.467911 2.65366i 0.0153599 0.0871105i
\(929\) 20.0360 7.29249i 0.657359 0.239259i 0.00826301 0.999966i \(-0.497370\pi\)
0.649095 + 0.760707i \(0.275148\pi\)
\(930\) 10.5817 0.346988
\(931\) 38.9518 26.9371i 1.27659 0.882829i
\(932\) 1.87164 0.0613078
\(933\) 5.33275 1.94096i 0.174586 0.0635442i
\(934\) −2.89393 + 16.4123i −0.0946924 + 0.537027i
\(935\) 5.36959 4.50562i 0.175604 0.147349i
\(936\) −3.83022 3.21394i −0.125195 0.105051i
\(937\) −2.09234 11.8662i −0.0683538 0.387653i −0.999722 0.0235751i \(-0.992495\pi\)
0.931368 0.364078i \(-0.118616\pi\)
\(938\) −5.78880 10.0265i −0.189011 0.327377i
\(939\) −6.42602 + 11.1302i −0.209705 + 0.363220i
\(940\) −8.35117 3.03958i −0.272385 0.0991400i
\(941\) 18.3310 + 6.67194i 0.597573 + 0.217499i 0.623057 0.782176i \(-0.285890\pi\)
−0.0254838 + 0.999675i \(0.508113\pi\)
\(942\) −2.30200 + 3.98719i −0.0750033 + 0.129910i
\(943\) −19.6419 34.0207i −0.639627 1.10787i
\(944\) −1.64930 9.35365i −0.0536801 0.304435i
\(945\) −3.23783 2.71686i −0.105326 0.0883794i
\(946\) 10.4834 8.79661i 0.340844 0.286002i
\(947\) 4.50744 25.5629i 0.146472 0.830684i −0.819701 0.572791i \(-0.805861\pi\)
0.966173 0.257893i \(-0.0830282\pi\)
\(948\) 12.1284 4.41436i 0.393911 0.143372i
\(949\) 2.83119 0.0919042
\(950\) −0.354570 4.34445i −0.0115038 0.140953i
\(951\) 6.89899 0.223715
\(952\) 13.1284 4.77833i 0.425492 0.154867i
\(953\) 3.43107 19.4586i 0.111143 0.630326i −0.877444 0.479679i \(-0.840753\pi\)
0.988588 0.150647i \(-0.0481357\pi\)
\(954\) −6.05303 + 5.07910i −0.195974 + 0.164442i
\(955\) −5.00774 4.20199i −0.162047 0.135973i
\(956\) −4.43376 25.1451i −0.143398 0.813251i
\(957\) −2.85710 4.94864i −0.0923568 0.159967i
\(958\) −2.38919 + 4.13819i −0.0771911 + 0.133699i
\(959\) −85.8572 31.2495i −2.77247 1.00910i
\(960\) 0.939693 + 0.342020i 0.0303284 + 0.0110387i
\(961\) −40.4864 + 70.1245i −1.30601 + 2.26208i
\(962\) 26.1891 + 45.3609i 0.844371 + 1.46249i
\(963\) 2.08378 + 11.8177i 0.0671488 + 0.380820i
\(964\) −7.58899 6.36792i −0.244425 0.205097i
\(965\) −2.00000 + 1.67820i −0.0643823 + 0.0540231i
\(966\) −2.95218 + 16.7427i −0.0949849 + 0.538686i
\(967\) −4.39868 + 1.60099i −0.141452 + 0.0514843i −0.411776 0.911285i \(-0.635091\pi\)
0.270324 + 0.962769i \(0.412869\pi\)
\(968\) 6.50299 0.209014
\(969\) 3.81016 13.8950i 0.122400 0.446372i
\(970\) −8.34049 −0.267797
\(971\) −5.86871 + 2.13603i −0.188336 + 0.0685486i −0.434466 0.900688i \(-0.643063\pi\)
0.246131 + 0.969237i \(0.420841\pi\)
\(972\) 0.173648 0.984808i 0.00556977 0.0315877i
\(973\) −29.4117 + 24.6793i −0.942896 + 0.791183i
\(974\) −4.67159 3.91993i −0.149687 0.125603i
\(975\) 0.868241 + 4.92404i 0.0278060 + 0.157695i
\(976\) 6.45336 + 11.1776i 0.206567 + 0.357785i
\(977\) 5.12061 8.86916i 0.163823 0.283750i −0.772414 0.635120i \(-0.780951\pi\)
0.936237 + 0.351370i \(0.114284\pi\)
\(978\) 5.75877 + 2.09602i 0.184145 + 0.0670234i
\(979\) 16.3201 + 5.94004i 0.521593 + 0.189844i
\(980\) 5.43242 9.40923i 0.173532 0.300567i
\(981\) 3.29086 + 5.69994i 0.105069 + 0.181985i
\(982\) 1.99613 + 11.3206i 0.0636991 + 0.361255i
\(983\) 8.47044 + 7.10754i 0.270165 + 0.226695i 0.767797 0.640693i \(-0.221353\pi\)
−0.497632 + 0.867388i \(0.665797\pi\)
\(984\) −7.48158 + 6.27779i −0.238504 + 0.200129i
\(985\) 0.0500404 0.283793i 0.00159442 0.00904240i
\(986\) −8.36959 + 3.04628i −0.266542 + 0.0970133i
\(987\) −37.5631 −1.19565
\(988\) −9.09539 19.8059i −0.289363 0.630110i
\(989\) 25.9573 0.825394
\(990\) 1.99273 0.725293i 0.0633330 0.0230513i
\(991\) 5.84255 33.1347i 0.185595 1.05256i −0.739594 0.673053i \(-0.764983\pi\)
0.925189 0.379507i \(-0.123906\pi\)
\(992\) −8.10607 + 6.80180i −0.257368 + 0.215957i
\(993\) −16.4081 13.7680i −0.520694 0.436914i
\(994\) 6.74691 + 38.2636i 0.213999 + 1.21365i
\(995\) 4.68004 + 8.10608i 0.148367 + 0.256980i
\(996\) 3.41147 5.90885i 0.108097 0.187229i
\(997\) 24.1844 + 8.80240i 0.765927 + 0.278775i 0.695292 0.718728i \(-0.255275\pi\)
0.0706353 + 0.997502i \(0.477497\pi\)
\(998\) −37.6724 13.7116i −1.19250 0.434034i
\(999\) −5.23783 + 9.07218i −0.165717 + 0.287031i
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 570.2.u.b.271.1 yes 6
19.4 even 9 inner 570.2.u.b.61.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.u.b.61.1 6 19.4 even 9 inner
570.2.u.b.271.1 yes 6 1.1 even 1 trivial